LMFDB - Embedded newform 2009.2.a.r.1.15

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			1.15
Root			$2.52950$ of defining polynomial
Character	$\chi$	$=$	2009.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.52950 q^{2} +2.69617 q^{3} +4.39838 q^{4} -0.644502 q^{5} +6.81996 q^{6} +6.06670 q^{8} +4.26931 q^{9} +O(q^{10})$	\(q+2.52950 q^{2} +2.69617 q^{3} +4.39838 q^{4} -0.644502 q^{5} +6.81996 q^{6} +6.06670 q^{8} +4.26931 q^{9} -1.63027 q^{10} +2.63211 q^{11} +11.8588 q^{12} +0.526918 q^{13} -1.73769 q^{15} +6.54898 q^{16} -0.858264 q^{17} +10.7992 q^{18} -7.96606 q^{19} -2.83477 q^{20} +6.65793 q^{22} -8.34576 q^{23} +16.3568 q^{24} -4.58462 q^{25} +1.33284 q^{26} +3.42227 q^{27} +5.08349 q^{29} -4.39548 q^{30} -1.52987 q^{31} +4.43225 q^{32} +7.09661 q^{33} -2.17098 q^{34} +18.7780 q^{36} +7.48651 q^{37} -20.1502 q^{38} +1.42066 q^{39} -3.91001 q^{40} -1.00000 q^{41} +8.58561 q^{43} +11.5770 q^{44} -2.75158 q^{45} -21.1106 q^{46} -3.00495 q^{47} +17.6571 q^{48} -11.5968 q^{50} -2.31402 q^{51} +2.31759 q^{52} -6.09756 q^{53} +8.65663 q^{54} -1.69640 q^{55} -21.4778 q^{57} +12.8587 q^{58} -5.75277 q^{59} -7.64300 q^{60} -7.77404 q^{61} -3.86981 q^{62} -1.88658 q^{64} -0.339600 q^{65} +17.9509 q^{66} +12.1466 q^{67} -3.77497 q^{68} -22.5016 q^{69} +10.4340 q^{71} +25.9006 q^{72} +7.04404 q^{73} +18.9371 q^{74} -12.3609 q^{75} -35.0378 q^{76} +3.59356 q^{78} +3.37977 q^{79} -4.22083 q^{80} -3.58093 q^{81} -2.52950 q^{82} +15.4449 q^{83} +0.553153 q^{85} +21.7173 q^{86} +13.7059 q^{87} +15.9682 q^{88} -5.74732 q^{89} -6.96013 q^{90} -36.7078 q^{92} -4.12478 q^{93} -7.60104 q^{94} +5.13414 q^{95} +11.9501 q^{96} -6.76346 q^{97} +11.2373 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.52950	1.78863	0.894314	−	0.447440i	$-0.147664\pi$
$2$	2.52950	1.78863	0.894314	+	0.447440i	$0.147664\pi$
$3$	2.69617	1.55663	0.778316	−	0.627873i	$-0.216074\pi$
$3$	2.69617	1.55663	0.778316	+	0.627873i	$0.216074\pi$
$4$	4.39838	2.19919
$5$	−0.644502	−0.288230	−0.144115	−	0.989561i	$-0.546034\pi$
$5$	−0.644502	−0.288230	−0.144115	+	0.989561i	$0.546034\pi$
$6$	6.81996	2.78424
$7$	0	0
$7$	0	0
$8$	6.06670	2.14490
$9$	4.26931	1.42310
$10$	−1.63027	−0.515537
$11$	2.63211	0.793611	0.396806	−	0.917903i	$-0.370119\pi$
$11$	2.63211	0.793611	0.396806	+	0.917903i	$0.370119\pi$
$12$	11.8588	3.42333
$13$	0.526918	0.146141	0.0730704	−	0.997327i	$-0.476720\pi$
$13$	0.526918	0.146141	0.0730704	+	0.997327i	$0.476720\pi$
$14$	0	0
$15$	−1.73769	−0.448668
$16$	6.54898	1.63725
$17$	−0.858264	−0.208160	−0.104080	−	0.994569i	$-0.533190\pi$
$17$	−0.858264	−0.208160	−0.104080	+	0.994569i	$0.533190\pi$
$18$	10.7992	2.54540
$19$	−7.96606	−1.82754	−0.913770	−	0.406232i	$-0.866842\pi$
$19$	−7.96606	−1.82754	−0.913770	+	0.406232i	$0.866842\pi$
$20$	−2.83477	−0.633873
$21$	0	0
$22$	6.65793	1.41948
$23$	−8.34576	−1.74021	−0.870106	−	0.492865i	$-0.835950\pi$
$23$	−8.34576	−1.74021	−0.870106	+	0.492865i	$0.835950\pi$
$24$	16.3568	3.33883
$25$	−4.58462	−0.916923
$26$	1.33284	0.261392
$27$	3.42227	0.658616
$28$	0	0
$29$	5.08349	0.943980	0.471990	−	0.881604i	$-0.343536\pi$
$29$	5.08349	0.943980	0.471990	+	0.881604i	$0.343536\pi$
$30$	−4.39548	−0.802501
$31$	−1.52987	−0.274773	−0.137386	−	0.990518i	$-0.543870\pi$
$31$	−1.52987	−0.274773	−0.137386	+	0.990518i	$0.543870\pi$
$32$	4.43225	0.783519
$33$	7.09661	1.23536
$34$	−2.17098	−0.372320
$35$	0	0
$36$	18.7780	3.12967
$37$	7.48651	1.23077	0.615387	−	0.788225i	$-0.289000\pi$
$37$	7.48651	1.23077	0.615387	+	0.788225i	$0.289000\pi$
$38$	−20.1502	−3.26879
$39$	1.42066	0.227488
$40$	−3.91001	−0.618226
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	8.58561	1.30929	0.654647	−	0.755935i	$-0.272817\pi$
$43$	8.58561	1.30929	0.654647	+	0.755935i	$0.272817\pi$
$44$	11.5770	1.74530
$45$	−2.75158	−0.410181
$46$	−21.1106	−3.11259
$47$	−3.00495	−0.438318	−0.219159	−	0.975689i	$-0.570331\pi$
$47$	−3.00495	−0.438318	−0.219159	+	0.975689i	$0.570331\pi$
$48$	17.6571	2.54859
$49$	0	0
$50$	−11.5968	−1.64003
$51$	−2.31402	−0.324028
$52$	2.31759	0.321392
$53$	−6.09756	−0.837564	−0.418782	−	0.908087i	$-0.637543\pi$
$53$	−6.09756	−0.837564	−0.418782	+	0.908087i	$0.637543\pi$
$54$	8.65663	1.17802
$55$	−1.69640	−0.228743
$56$	0	0
$57$	−21.4778	−2.84481
$58$	12.8587	1.68843
$59$	−5.75277	−0.748947	−0.374473	−	0.927238i	$-0.622176\pi$
$59$	−5.75277	−0.748947	−0.374473	+	0.927238i	$0.622176\pi$
$60$	−7.64300	−0.986707
$61$	−7.77404	−0.995364	−0.497682	−	0.867360i	$-0.665815\pi$
$61$	−7.77404	−0.995364	−0.497682	+	0.867360i	$0.665815\pi$
$62$	−3.86981	−0.491466
$63$	0	0
$64$	−1.88658	−0.235822
$65$	−0.339600	−0.0421222
$66$	17.9509	2.20960
$67$	12.1466	1.48394	0.741970	−	0.670433i	$-0.233892\pi$
$67$	12.1466	1.48394	0.741970	+	0.670433i	$0.233892\pi$
$68$	−3.77497	−0.457783
$69$	−22.5016	−2.70887
$70$	0	0
$71$	10.4340	1.23829	0.619146	−	0.785276i	$-0.287479\pi$
$71$	10.4340	1.23829	0.619146	+	0.785276i	$0.287479\pi$
$72$	25.9006	3.05242
$73$	7.04404	0.824442	0.412221	−	0.911084i	$-0.364753\pi$
$73$	7.04404	0.824442	0.412221	+	0.911084i	$0.364753\pi$
$74$	18.9371	2.20140
$75$	−12.3609	−1.42731
$76$	−35.0378	−4.01911
$77$	0	0
$78$	3.59356	0.406891
$79$	3.37977	0.380254	0.190127	−	0.981760i	$-0.439110\pi$
$79$	3.37977	0.380254	0.190127	+	0.981760i	$0.439110\pi$
$80$	−4.22083	−0.471904
$81$	−3.58093	−0.397881
$82$	−2.52950	−0.279337
$83$	15.4449	1.69529	0.847647	−	0.530561i	$-0.178019\pi$
$83$	15.4449	1.69529	0.847647	+	0.530561i	$0.178019\pi$
$84$	0	0
$85$	0.553153	0.0599979
$86$	21.7173	2.34184
$87$	13.7059	1.46943
$88$	15.9682	1.70222
$89$	−5.74732	−0.609215	−0.304607	−	0.952478i	$-0.598525\pi$
$89$	−5.74732	−0.609215	−0.304607	+	0.952478i	$0.598525\pi$
$90$	−6.96013	−0.733662
$91$	0	0
$92$	−36.7078	−3.82705
$93$	−4.12478	−0.427720
$94$	−7.60104	−0.783987
$95$	5.13414	0.526752
$96$	11.9501	1.21965
$97$	−6.76346	−0.686725	−0.343362	−	0.939203i	$-0.611566\pi$
$97$	−6.76346	−0.686725	−0.343362	+	0.939203i	$0.611566\pi$
$98$	0	0
$99$	11.2373	1.12939
$100$	−20.1649	−2.01649
$101$	14.6024	1.45299	0.726497	−	0.687169i	$-0.241147\pi$
$101$	14.6024	1.45299	0.726497	+	0.687169i	$0.241147\pi$
$102$	−5.85333	−0.579566
$103$	15.0197	1.47993	0.739966	−	0.672645i	$-0.234842\pi$
$103$	15.0197	1.47993	0.739966	+	0.672645i	$0.234842\pi$
$104$	3.19666	0.313458
$105$	0	0
$106$	−15.4238	−1.49809
$107$	3.20982	0.310305	0.155153	−	0.987890i	$-0.450413\pi$
$107$	3.20982	0.310305	0.155153	+	0.987890i	$0.450413\pi$
$108$	15.0524	1.44842
$109$	6.15129	0.589187	0.294594	−	0.955623i	$-0.404816\pi$
$109$	6.15129	0.589187	0.294594	+	0.955623i	$0.404816\pi$
$110$	−4.29105	−0.409136
$111$	20.1849	1.91586
$112$	0	0
$113$	−1.20385	−0.113248	−0.0566241	−	0.998396i	$-0.518034\pi$
$113$	−1.20385	−0.113248	−0.0566241	+	0.998396i	$0.518034\pi$
$114$	−54.3282	−5.08830
$115$	5.37886	0.501581
$116$	22.3591	2.07599
$117$	2.24958	0.207974
$118$	−14.5516	−1.33959
$119$	0	0
$120$	−10.5420	−0.962350
$121$	−4.07199	−0.370181
$122$	−19.6645	−1.78034
$123$	−2.69617	−0.243105
$124$	−6.72894	−0.604277
$125$	6.17731	0.552515
$126$	0	0
$127$	1.15394	0.102396	0.0511980	−	0.998689i	$-0.483696\pi$
$127$	1.15394	0.102396	0.0511980	+	0.998689i	$0.483696\pi$
$128$	−13.6366	−1.20532
$129$	23.1482	2.03809
$130$	−0.859019	−0.0753410
$131$	−0.551102	−0.0481500	−0.0240750	−	0.999710i	$-0.507664\pi$
$131$	−0.551102	−0.0481500	−0.0240750	+	0.999710i	$0.507664\pi$
$132$	31.2136	2.71679
$133$	0	0
$134$	30.7248	2.65422
$135$	−2.20566	−0.189833
$136$	−5.20684	−0.446483
$137$	−3.48759	−0.297965	−0.148983	−	0.988840i	$-0.547600\pi$
$137$	−3.48759	−0.297965	−0.148983	+	0.988840i	$0.547600\pi$
$138$	−56.9177	−4.84516
$139$	−20.2092	−1.71412	−0.857060	−	0.515216i	$-0.827712\pi$
$139$	−20.2092	−1.71412	−0.857060	+	0.515216i	$0.827712\pi$
$140$	0	0
$141$	−8.10185	−0.682299
$142$	26.3929	2.21484
$143$	1.38691	0.115979
$144$	27.9596	2.32997
$145$	−3.27632	−0.272084
$146$	17.8179	1.47462
$147$	0	0
$148$	32.9285	2.70671
$149$	−19.9173	−1.63169	−0.815846	−	0.578269i	$-0.803728\pi$
$149$	−19.9173	−1.63169	−0.815846	+	0.578269i	$0.803728\pi$
$150$	−31.2669	−2.55293
$151$	−2.41695	−0.196689	−0.0983443	−	0.995152i	$-0.531355\pi$
$151$	−2.41695	−0.196689	−0.0983443	+	0.995152i	$0.531355\pi$
$152$	−48.3277	−3.91990
$153$	−3.66420	−0.296233
$154$	0	0
$155$	0.986004	0.0791977
$156$	6.24860	0.500288
$157$	13.3187	1.06295	0.531474	−	0.847074i	$-0.321638\pi$
$157$	13.3187	1.06295	0.531474	+	0.847074i	$0.321638\pi$
$158$	8.54913	0.680132
$159$	−16.4400	−1.30378
$160$	−2.85660	−0.225834
$161$	0	0
$162$	−9.05797	−0.711661
$163$	−18.7780	−1.47081	−0.735405	−	0.677628i	$-0.763008\pi$
$163$	−18.7780	−1.47081	−0.735405	+	0.677628i	$0.763008\pi$
$164$	−4.39838	−0.343456
$165$	−4.57378	−0.356068
$166$	39.0678	3.03225
$167$	−15.6037	−1.20745	−0.603724	−	0.797193i	$-0.706317\pi$
$167$	−15.6037	−1.20745	−0.603724	+	0.797193i	$0.706317\pi$
$168$	0	0
$169$	−12.7224	−0.978643
$170$	1.39920	0.107314
$171$	−34.0096	−2.60078
$172$	37.7628	2.87938
$173$	19.4963	1.48228	0.741140	−	0.671351i	$-0.234286\pi$
$173$	19.4963	1.48228	0.741140	+	0.671351i	$0.234286\pi$
$174$	34.6692	2.62826
$175$	0	0
$176$	17.2376	1.29934
$177$	−15.5104	−1.16583
$178$	−14.5379	−1.08966
$179$	11.7748	0.880086	0.440043	−	0.897977i	$-0.354963\pi$
$179$	11.7748	0.880086	0.440043	+	0.897977i	$0.354963\pi$
$180$	−12.1025	−0.902066
$181$	−2.16473	−0.160903	−0.0804516	−	0.996759i	$-0.525636\pi$
$181$	−2.16473	−0.160903	−0.0804516	+	0.996759i	$0.525636\pi$
$182$	0	0
$183$	−20.9601	−1.54942
$184$	−50.6313	−3.73259
$185$	−4.82507	−0.354746
$186$	−10.4336	−0.765031
$187$	−2.25905	−0.165198
$188$	−13.2169	−0.963944
$189$	0	0
$190$	12.9868	0.942164
$191$	0.507036	0.0366878	0.0183439	−	0.999832i	$-0.494161\pi$
$191$	0.507036	0.0366878	0.0183439	+	0.999832i	$0.494161\pi$
$192$	−5.08652	−0.367088
$193$	−9.86220	−0.709896	−0.354948	−	0.934886i	$-0.615502\pi$
$193$	−9.86220	−0.709896	−0.354948	+	0.934886i	$0.615502\pi$
$194$	−17.1082	−1.22830
$195$	−0.915618	−0.0655688
$196$	0	0
$197$	24.6866	1.75885	0.879424	−	0.476040i	$-0.157928\pi$
$197$	24.6866	1.75885	0.879424	+	0.476040i	$0.157928\pi$
$198$	28.4248	2.02006
$199$	15.0362	1.06589	0.532943	−	0.846151i	$-0.321086\pi$
$199$	15.0362	1.06589	0.532943	+	0.846151i	$0.321086\pi$
$200$	−27.8135	−1.96671
$201$	32.7492	2.30995
$202$	36.9368	2.59887
$203$	0	0
$204$	−10.1780	−0.712599
$205$	0.644502	0.0450140
$206$	37.9923	2.64705
$207$	−35.6306	−2.47650
$208$	3.45078	0.239268
$209$	−20.9676	−1.45036
$210$	0	0
$211$	−20.8674	−1.43657	−0.718287	−	0.695747i	$-0.755073\pi$
$211$	−20.8674	−1.43657	−0.718287	+	0.695747i	$0.755073\pi$
$212$	−26.8194	−1.84196
$213$	28.1319	1.92756
$214$	8.11926	0.555021
$215$	−5.53345	−0.377378
$216$	20.7619	1.41267
$217$	0	0
$218$	15.5597	1.05384
$219$	18.9919	1.28335
$220$	−7.46142	−0.503049
$221$	−0.452235	−0.0304206
$222$	51.0576	3.42676
$223$	−14.3661	−0.962024	−0.481012	−	0.876714i	$-0.659731\pi$
$223$	−14.3661	−0.962024	−0.481012	+	0.876714i	$0.659731\pi$
$224$	0	0
$225$	−19.5731	−1.30488
$226$	−3.04513	−0.202559
$227$	5.90944	0.392223	0.196112	−	0.980582i	$-0.437169\pi$
$227$	5.90944	0.392223	0.196112	+	0.980582i	$0.437169\pi$
$228$	−94.4676	−6.25627
$229$	4.19563	0.277255	0.138627	−	0.990345i	$-0.455731\pi$
$229$	4.19563	0.277255	0.138627	+	0.990345i	$0.455731\pi$
$230$	13.6058	0.897143
$231$	0	0
$232$	30.8400	2.02475
$233$	−10.8817	−0.712881	−0.356440	−	0.934318i	$-0.616010\pi$
$233$	−10.8817	−0.712881	−0.356440	+	0.934318i	$0.616010\pi$
$234$	5.69031	0.371987
$235$	1.93670	0.126336
$236$	−25.3029	−1.64708
$237$	9.11242	0.591915
$238$	0	0
$239$	−7.77413	−0.502867	−0.251433	−	0.967875i	$-0.580902\pi$
$239$	−7.77413	−0.502867	−0.251433	+	0.967875i	$0.580902\pi$
$240$	−11.3801	−0.734580
$241$	−9.52120	−0.613315	−0.306657	−	0.951820i	$-0.599211\pi$
$241$	−9.52120	−0.613315	−0.306657	+	0.951820i	$0.599211\pi$
$242$	−10.3001	−0.662116
$243$	−19.9216	−1.27797
$244$	−34.1932	−2.18899
$245$	0	0
$246$	−6.81996	−0.434824
$247$	−4.19746	−0.267078
$248$	−9.28126	−0.589361
$249$	41.6419	2.63895
$250$	15.6255	0.988244
$251$	20.4261	1.28928	0.644641	−	0.764485i	$-0.277007\pi$
$251$	20.4261	1.28928	0.644641	+	0.764485i	$0.277007\pi$
$252$	0	0
$253$	−21.9670	−1.38105
$254$	2.91891	0.183148
$255$	1.49139	0.0933947
$256$	−30.7207	−1.92004
$257$	9.52461	0.594129	0.297064	−	0.954857i	$-0.403992\pi$
$257$	9.52461	0.594129	0.297064	+	0.954857i	$0.403992\pi$
$258$	58.5535	3.64538
$259$	0	0
$260$	−1.49369	−0.0926347
$261$	21.7030	1.34338
$262$	−1.39401	−0.0861224
$263$	13.2599	0.817638	0.408819	−	0.912616i	$-0.365941\pi$
$263$	13.2599	0.817638	0.408819	+	0.912616i	$0.365941\pi$
$264$	43.0530	2.64973
$265$	3.92989	0.241411
$266$	0	0
$267$	−15.4957	−0.948323
$268$	53.4253	3.26347
$269$	−0.743264	−0.0453176	−0.0226588	−	0.999743i	$-0.507213\pi$
$269$	−0.743264	−0.0453176	−0.0226588	+	0.999743i	$0.507213\pi$
$270$	−5.57922	−0.339540
$271$	7.73276	0.469732	0.234866	−	0.972028i	$-0.424535\pi$
$271$	7.73276	0.469732	0.234866	+	0.972028i	$0.424535\pi$
$272$	−5.62076	−0.340809
$273$	0	0
$274$	−8.82187	−0.532949
$275$	−12.0672	−0.727681
$276$	−98.9704	−5.95732
$277$	−3.53511	−0.212404	−0.106202	−	0.994345i	$-0.533869\pi$
$277$	−3.53511	−0.212404	−0.106202	+	0.994345i	$0.533869\pi$
$278$	−51.1192	−3.06592
$279$	−6.53148	−0.391030
$280$	0	0
$281$	−15.0521	−0.897935	−0.448967	−	0.893548i	$-0.648208\pi$
$281$	−15.0521	−0.897935	−0.448967	+	0.893548i	$0.648208\pi$
$282$	−20.4937	−1.22038
$283$	10.7193	0.637197	0.318599	−	0.947890i	$-0.396788\pi$
$283$	10.7193	0.637197	0.318599	+	0.947890i	$0.396788\pi$
$284$	45.8928	2.72324
$285$	13.8425	0.819959
$286$	3.50819	0.207443
$287$	0	0
$288$	18.9226	1.11503
$289$	−16.2634	−0.956670
$290$	−8.28746	−0.486656
$291$	−18.2354	−1.06898
$292$	30.9824	1.81311
$293$	14.3727	0.839661	0.419831	−	0.907602i	$-0.362089\pi$
$293$	14.3727	0.839661	0.419831	+	0.907602i	$0.362089\pi$
$294$	0	0
$295$	3.70767	0.215869
$296$	45.4184	2.63989
$297$	9.00778	0.522685
$298$	−50.3810	−2.91849
$299$	−4.39754	−0.254316
$300$	−54.3679	−3.13893
$301$	0	0
$302$	−6.11368	−0.351803
$303$	39.3705	2.26178
$304$	−52.1696	−2.99213
$305$	5.01039	0.286894
$306$	−9.26859	−0.529850
$307$	27.4735	1.56800	0.783998	−	0.620764i	$-0.213177\pi$
$307$	27.4735	1.56800	0.783998	+	0.620764i	$0.213177\pi$
$308$	0	0
$309$	40.4955	2.30371
$310$	2.49410	0.141655
$311$	−18.3655	−1.04141	−0.520706	−	0.853736i	$-0.674331\pi$
$311$	−18.3655	−1.04141	−0.520706	+	0.853736i	$0.674331\pi$
$312$	8.61872	0.487939
$313$	6.78194	0.383338	0.191669	−	0.981460i	$-0.438610\pi$
$313$	6.78194	0.383338	0.191669	+	0.981460i	$0.438610\pi$
$314$	33.6897	1.90122
$315$	0	0
$316$	14.8655	0.836250
$317$	4.55467	0.255816	0.127908	−	0.991786i	$-0.459174\pi$
$317$	4.55467	0.255816	0.127908	+	0.991786i	$0.459174\pi$
$318$	−41.5851	−2.33197
$319$	13.3803	0.749153
$320$	1.21590	0.0679711
$321$	8.65422	0.483031
$322$	0	0
$323$	6.83699	0.380420
$324$	−15.7503	−0.875016
$325$	−2.41572	−0.134000
$326$	−47.4991	−2.63073
$327$	16.5849	0.917148
$328$	−6.06670	−0.334978
$329$	0	0
$330$	−11.5694	−0.636874
$331$	16.9899	0.933850	0.466925	−	0.884297i	$-0.345362\pi$
$331$	16.9899	0.933850	0.466925	+	0.884297i	$0.345362\pi$
$332$	67.9324	3.72827
$333$	31.9622	1.75152
$334$	−39.4695	−2.15967
$335$	−7.82850	−0.427717
$336$	0	0
$337$	7.10162	0.386850	0.193425	−	0.981115i	$-0.438040\pi$
$337$	7.10162	0.386850	0.193425	+	0.981115i	$0.438040\pi$
$338$	−32.1812	−1.75043
$339$	−3.24577	−0.176286
$340$	2.43298	0.131947
$341$	−4.02678	−0.218063
$342$	−86.0273	−4.65182
$343$	0	0
$344$	52.0864	2.80831
$345$	14.5023	0.780778
$346$	49.3160	2.65125
$347$	−8.01396	−0.430212	−0.215106	−	0.976591i	$-0.569010\pi$
$347$	−8.01396	−0.430212	−0.215106	+	0.976591i	$0.569010\pi$
$348$	60.2839	3.23156
$349$	−26.3690	−1.41150	−0.705751	−	0.708460i	$-0.749390\pi$
$349$	−26.3690	−1.41150	−0.705751	+	0.708460i	$0.749390\pi$
$350$	0	0
$351$	1.80326	0.0962507
$352$	11.6662	0.621809
$353$	−28.9335	−1.53998	−0.769988	−	0.638058i	$-0.779738\pi$
$353$	−28.9335	−1.53998	−0.769988	+	0.638058i	$0.779738\pi$
$354$	−39.2336	−2.08524
$355$	−6.72476	−0.356913
$356$	−25.2789	−1.33978
$357$	0	0
$358$	29.7843	1.57415
$359$	−2.77359	−0.146385	−0.0731923	−	0.997318i	$-0.523319\pi$
$359$	−2.77359	−0.146385	−0.0731923	+	0.997318i	$0.523319\pi$
$360$	−16.6930	−0.879799
$361$	44.4581	2.33990
$362$	−5.47569	−0.287796
$363$	−10.9788	−0.576236
$364$	0	0
$365$	−4.53990	−0.237629
$366$	−53.0186	−2.77133
$367$	−12.0923	−0.631214	−0.315607	−	0.948890i	$-0.602208\pi$
$367$	−12.0923	−0.631214	−0.315607	+	0.948890i	$0.602208\pi$
$368$	−54.6562	−2.84915
$369$	−4.26931	−0.222251
$370$	−12.2050	−0.634509
$371$	0	0
$372$	−18.1423	−0.940637
$373$	25.6166	1.32638	0.663190	−	0.748451i	$-0.269202\pi$
$373$	25.6166	1.32638	0.663190	+	0.748451i	$0.269202\pi$
$374$	−5.71426	−0.295478
$375$	16.6550	0.860063
$376$	−18.2302	−0.940149
$377$	2.67858	0.137954
$378$	0	0
$379$	9.08206	0.466514	0.233257	−	0.972415i	$-0.425062\pi$
$379$	9.08206	0.466514	0.233257	+	0.972415i	$0.425062\pi$
$380$	22.5819	1.15843
$381$	3.11123	0.159393
$382$	1.28255	0.0656208
$383$	−0.793644	−0.0405533	−0.0202767	−	0.999794i	$-0.506455\pi$
$383$	−0.793644	−0.0405533	−0.0202767	+	0.999794i	$0.506455\pi$
$384$	−36.7665	−1.87623
$385$	0	0
$386$	−24.9464	−1.26974
$387$	36.6546	1.86326
$388$	−29.7482	−1.51024
$389$	−9.18762	−0.465831	−0.232915	−	0.972497i	$-0.574826\pi$
$389$	−9.18762	−0.465831	−0.232915	+	0.972497i	$0.574826\pi$
$390$	−2.31606	−0.117278
$391$	7.16287	0.362242
$392$	0	0
$393$	−1.48586	−0.0749518
$394$	62.4448	3.14592
$395$	−2.17827	−0.109601
$396$	49.4259	2.48374
$397$	17.9868	0.902732	0.451366	−	0.892339i	$-0.350937\pi$
$397$	17.9868	0.902732	0.451366	+	0.892339i	$0.350937\pi$
$398$	38.0340	1.90647
$399$	0	0
$400$	−30.0246	−1.50123
$401$	−31.7289	−1.58446	−0.792232	−	0.610220i	$-0.791081\pi$
$401$	−31.7289	−1.58446	−0.792232	+	0.610220i	$0.791081\pi$
$402$	82.8391	4.13164
$403$	−0.806116	−0.0401555
$404$	64.2270	3.19541
$405$	2.30792	0.114681
$406$	0	0
$407$	19.7053	0.976756
$408$	−14.0385	−0.695009
$409$	29.9448	1.48068	0.740338	−	0.672234i	$-0.234665\pi$
$409$	29.9448	1.48068	0.740338	+	0.672234i	$0.234665\pi$
$410$	1.63027	0.0805133
$411$	−9.40312	−0.463822
$412$	66.0622	3.25465
$413$	0	0
$414$	−90.1277	−4.42954
$415$	−9.95425	−0.488635
$416$	2.33543	0.114504
$417$	−54.4873	−2.66825
$418$	−53.0375	−2.59415
$419$	21.7453	1.06233	0.531164	−	0.847269i	$-0.321755\pi$
$419$	21.7453	1.06233	0.531164	+	0.847269i	$0.321755\pi$
$420$	0	0
$421$	8.84059	0.430864	0.215432	−	0.976519i	$-0.430884\pi$
$421$	8.84059	0.430864	0.215432	+	0.976519i	$0.430884\pi$
$422$	−52.7842	−2.56949
$423$	−12.8291	−0.623771
$424$	−36.9921	−1.79649
$425$	3.93481	0.190867
$426$	71.1596	3.44769
$427$	0	0
$428$	14.1180	0.682421
$429$	3.73933	0.180537
$430$	−13.9969	−0.674988
$431$	29.9146	1.44094	0.720468	−	0.693488i	$-0.243927\pi$
$431$	29.9146	1.44094	0.720468	+	0.693488i	$0.243927\pi$
$432$	22.4124	1.07832
$433$	22.5127	1.08189	0.540946	−	0.841058i	$-0.318066\pi$
$433$	22.5127	1.08189	0.540946	+	0.841058i	$0.318066\pi$
$434$	0	0
$435$	−8.83350	−0.423534
$436$	27.0557	1.29573
$437$	66.4828	3.18030
$438$	48.0400	2.29544
$439$	−5.94025	−0.283512	−0.141756	−	0.989902i	$-0.545275\pi$
$439$	−5.94025	−0.283512	−0.141756	+	0.989902i	$0.545275\pi$
$440$	−10.2916	−0.490631
$441$	0	0
$442$	−1.14393	−0.0544112
$443$	−12.8904	−0.612441	−0.306221	−	0.951961i	$-0.599064\pi$
$443$	−12.8904	−0.612441	−0.306221	+	0.951961i	$0.599064\pi$
$444$	88.7807	4.21334
$445$	3.70416	0.175594
$446$	−36.3390	−1.72070
$447$	−53.7005	−2.53994
$448$	0	0
$449$	−24.0063	−1.13293	−0.566463	−	0.824087i	$-0.691689\pi$
$449$	−24.0063	−1.13293	−0.566463	+	0.824087i	$0.691689\pi$
$450$	−49.5103	−2.33394
$451$	−2.63211	−0.123941
$452$	−5.29497	−0.249054
$453$	−6.51650	−0.306172
$454$	14.9479	0.701541
$455$	0	0
$456$	−130.300	−6.10184
$457$	−8.32502	−0.389428	−0.194714	−	0.980860i	$-0.562378\pi$
$457$	−8.32502	−0.389428	−0.194714	+	0.980860i	$0.562378\pi$
$458$	10.6128	0.495906
$459$	−2.93721	−0.137097
$460$	23.6583	1.10307
$461$	3.47889	0.162028	0.0810139	−	0.996713i	$-0.474184\pi$
$461$	3.47889	0.162028	0.0810139	+	0.996713i	$0.474184\pi$
$462$	0	0
$463$	0.917022	0.0426176	0.0213088	−	0.999773i	$-0.493217\pi$
$463$	0.917022	0.0426176	0.0213088	+	0.999773i	$0.493217\pi$
$464$	33.2917	1.54553
$465$	2.65843	0.123282
$466$	−27.5252	−1.27508
$467$	5.44862	0.252132	0.126066	−	0.992022i	$-0.459765\pi$
$467$	5.44862	0.252132	0.126066	+	0.992022i	$0.459765\pi$
$468$	9.89450	0.457373
$469$	0	0
$470$	4.89889	0.225969
$471$	35.9094	1.65462
$472$	−34.9003	−1.60642
$473$	22.5983	1.03907
$474$	23.0499	1.05872
$475$	36.5213	1.67571
$476$	0	0
$477$	−26.0324	−1.19194
$478$	−19.6647	−0.899442
$479$	−0.0579629	−0.00264839	−0.00132420	−	0.999999i	$-0.500422\pi$
$479$	−0.0579629	−0.00264839	−0.00132420	+	0.999999i	$0.500422\pi$
$480$	−7.70186	−0.351540
$481$	3.94478	0.179866
$482$	−24.0839	−1.09699
$483$	0	0
$484$	−17.9102	−0.814099
$485$	4.35906	0.197935
$486$	−50.3917	−2.28581
$487$	1.87686	0.0850488	0.0425244	−	0.999095i	$-0.486460\pi$
$487$	1.87686	0.0850488	0.0425244	+	0.999095i	$0.486460\pi$
$488$	−47.1628	−2.13496
$489$	−50.6287	−2.28951
$490$	0	0
$491$	−16.1249	−0.727706	−0.363853	−	0.931456i	$-0.618539\pi$
$491$	−16.1249	−0.727706	−0.363853	+	0.931456i	$0.618539\pi$
$492$	−11.8588	−0.534634
$493$	−4.36298	−0.196499
$494$	−10.6175	−0.477704
$495$	−7.24246	−0.325524
$496$	−10.0191	−0.449870
$497$	0	0
$498$	105.333	4.72010
$499$	33.7331	1.51010	0.755052	−	0.655665i	$-0.227612\pi$
$499$	33.7331	1.51010	0.755052	+	0.655665i	$0.227612\pi$
$500$	27.1701	1.21509
$501$	−42.0701	−1.87955
$502$	51.6678	2.30605
$503$	−41.3274	−1.84270	−0.921349	−	0.388736i	$-0.872912\pi$
$503$	−41.3274	−1.84270	−0.921349	+	0.388736i	$0.872912\pi$
$504$	0	0
$505$	−9.41129	−0.418797
$506$	−55.5655	−2.47019
$507$	−34.3016	−1.52339
$508$	5.07549	0.225188
$509$	−14.8829	−0.659674	−0.329837	−	0.944038i	$-0.606994\pi$
$509$	−14.8829	−0.659674	−0.329837	+	0.944038i	$0.606994\pi$
$510$	3.77248	0.167048
$511$	0	0
$512$	−50.4347	−2.22892
$513$	−27.2620	−1.20365
$514$	24.0925	1.06268
$515$	−9.68021	−0.426561
$516$	101.815	4.48214
$517$	−7.90937	−0.347854
$518$	0	0
$519$	52.5654	2.30736
$520$	−2.06025	−0.0903481
$521$	36.1532	1.58390	0.791950	−	0.610585i	$-0.209066\pi$
$521$	36.1532	1.58390	0.791950	+	0.610585i	$0.209066\pi$
$522$	54.8977	2.40281
$523$	31.0927	1.35959	0.679794	−	0.733404i	$-0.262069\pi$
$523$	31.0927	1.35959	0.679794	+	0.733404i	$0.262069\pi$
$524$	−2.42395	−0.105891
$525$	0	0
$526$	33.5408	1.46245
$527$	1.31303	0.0571966
$528$	46.4755	2.02259
$529$	46.6517	2.02834
$530$	9.94066	0.431795
$531$	−24.5603	−1.06583
$532$	0	0
$533$	−0.526918	−0.0228234
$534$	−39.1965	−1.69620
$535$	−2.06874	−0.0894394
$536$	73.6897	3.18291
$537$	31.7467	1.36997
$538$	−1.88009	−0.0810563
$539$	0	0
$540$	−9.70132	−0.417479
$541$	31.0556	1.33518	0.667592	−	0.744527i	$-0.267325\pi$
$541$	31.0556	1.33518	0.667592	+	0.744527i	$0.267325\pi$
$542$	19.5600	0.840176
$543$	−5.83648	−0.250467
$544$	−3.80404	−0.163097
$545$	−3.96452	−0.169822
$546$	0	0
$547$	2.42712	0.103776	0.0518882	−	0.998653i	$-0.483476\pi$
$547$	2.42712	0.103776	0.0518882	+	0.998653i	$0.483476\pi$
$548$	−15.3398	−0.655282
$549$	−33.1898	−1.41651
$550$	−30.5241	−1.30155
$551$	−40.4954	−1.72516
$552$	−136.510	−5.81026
$553$	0	0
$554$	−8.94206	−0.379912
$555$	−13.0092	−0.552209
$556$	−88.8877	−3.76968
$557$	−11.1384	−0.471948	−0.235974	−	0.971759i	$-0.575828\pi$
$557$	−11.1384	−0.471948	−0.235974	+	0.971759i	$0.575828\pi$
$558$	−16.5214	−0.699406
$559$	4.52392	0.191341
$560$	0	0
$561$	−6.09077	−0.257152
$562$	−38.0744	−1.60607
$563$	−10.8677	−0.458021	−0.229010	−	0.973424i	$-0.573549\pi$
$563$	−10.8677	−0.458021	−0.229010	+	0.973424i	$0.573549\pi$
$564$	−35.6350	−1.50051
$565$	0.775881	0.0326416
$566$	27.1145	1.13971
$567$	0	0
$568$	63.3002	2.65602
$569$	10.5249	0.441229	0.220614	−	0.975361i	$-0.429194\pi$
$569$	10.5249	0.441229	0.220614	+	0.975361i	$0.429194\pi$
$570$	35.0146	1.46660
$571$	−26.3934	−1.10453	−0.552264	−	0.833669i	$-0.686236\pi$
$571$	−26.3934	−1.10453	−0.552264	+	0.833669i	$0.686236\pi$
$572$	6.10015	0.255060
$573$	1.36705	0.0571094
$574$	0	0
$575$	38.2621	1.59564
$576$	−8.05438	−0.335599
$577$	−9.51352	−0.396053	−0.198027	−	0.980197i	$-0.563453\pi$
$577$	−9.51352	−0.396053	−0.198027	+	0.980197i	$0.563453\pi$
$578$	−41.1383	−1.71113
$579$	−26.5901	−1.10505
$580$	−14.4105	−0.598364
$581$	0	0
$582$	−46.1265	−1.91200
$583$	−16.0494	−0.664700
$584$	42.7341	1.76835
$585$	−1.44986	−0.0599443
$586$	36.3557	1.50184
$587$	−12.9433	−0.534229	−0.267114	−	0.963665i	$-0.586070\pi$
$587$	−12.9433	−0.534229	−0.267114	+	0.963665i	$0.586070\pi$
$588$	0	0
$589$	12.1870	0.502158
$590$	9.37856	0.386109
$591$	66.5592	2.73788
$592$	49.0290	2.01508
$593$	−11.8167	−0.485253	−0.242627	−	0.970120i	$-0.578009\pi$
$593$	−11.8167	−0.485253	−0.242627	+	0.970120i	$0.578009\pi$
$594$	22.7852	0.934888
$595$	0	0
$596$	−87.6040	−3.58840
$597$	40.5400	1.65919
$598$	−11.1236	−0.454877
$599$	1.56685	0.0640199	0.0320099	−	0.999488i	$-0.489809\pi$
$599$	1.56685	0.0640199	0.0320099	+	0.999488i	$0.489809\pi$
$600$	−74.9898	−3.06145
$601$	−2.85578	−0.116490	−0.0582448	−	0.998302i	$-0.518550\pi$
$601$	−2.85578	−0.116490	−0.0582448	+	0.998302i	$0.518550\pi$
$602$	0	0
$603$	51.8575	2.11180
$604$	−10.6307	−0.432555
$605$	2.62441	0.106697
$606$	99.5878	4.04548
$607$	2.47089	0.100290	0.0501452	−	0.998742i	$-0.484032\pi$
$607$	2.47089	0.100290	0.0501452	+	0.998742i	$0.484032\pi$
$608$	−35.3076	−1.43191
$609$	0	0
$610$	12.6738	0.513147
$611$	−1.58337	−0.0640561
$612$	−16.1165	−0.651472
$613$	−35.9960	−1.45387	−0.726933	−	0.686708i	$-0.759055\pi$
$613$	−35.9960	−1.45387	−0.726933	+	0.686708i	$0.759055\pi$
$614$	69.4942	2.80456
$615$	1.73769	0.0700702
$616$	0	0
$617$	−23.5111	−0.946522	−0.473261	−	0.880922i	$-0.656923\pi$
$617$	−23.5111	−0.946522	−0.473261	+	0.880922i	$0.656923\pi$
$618$	102.433	4.12048
$619$	−19.6382	−0.789324	−0.394662	−	0.918826i	$-0.629138\pi$
$619$	−19.6382	−0.789324	−0.394662	+	0.918826i	$0.629138\pi$
$620$	4.33682	0.174171
$621$	−28.5614	−1.14613
$622$	−46.4556	−1.86270
$623$	0	0
$624$	9.30387	0.372453
$625$	18.9418	0.757672
$626$	17.1549	0.685648
$627$	−56.5320	−2.25767
$628$	58.5807	2.33763
$629$	−6.42540	−0.256198
$630$	0	0
$631$	41.0008	1.63222	0.816108	−	0.577900i	$-0.196128\pi$
$631$	41.0008	1.63222	0.816108	+	0.577900i	$0.196128\pi$
$632$	20.5041	0.815608
$633$	−56.2620	−2.23622
$634$	11.5210	0.457559
$635$	−0.743720	−0.0295136
$636$	−72.3094	−2.86726
$637$	0	0
$638$	33.8455	1.33996
$639$	44.5461	1.76222
$640$	8.78882	0.347409
$641$	22.1531	0.874996	0.437498	−	0.899219i	$-0.355865\pi$
$641$	22.1531	0.874996	0.437498	+	0.899219i	$0.355865\pi$
$642$	21.8909	0.863963
$643$	−7.61120	−0.300156	−0.150078	−	0.988674i	$-0.547953\pi$
$643$	−7.61120	−0.300156	−0.150078	+	0.988674i	$0.547953\pi$
$644$	0	0
$645$	−14.9191	−0.587438
$646$	17.2942	0.680430
$647$	−24.5598	−0.965546	−0.482773	−	0.875746i	$-0.660370\pi$
$647$	−24.5598	−0.965546	−0.482773	+	0.875746i	$0.660370\pi$
$648$	−21.7244	−0.853416
$649$	−15.1419	−0.594372
$650$	−6.11057	−0.239676
$651$	0	0
$652$	−82.5929	−3.23459
$653$	−33.8526	−1.32475	−0.662377	−	0.749171i	$-0.730452\pi$
$653$	−33.8526	−1.32475	−0.662377	+	0.749171i	$0.730452\pi$
$654$	41.9516	1.64044
$655$	0.355186	0.0138783
$656$	−6.54898	−0.255695
$657$	30.0732	1.17327
$658$	0	0
$659$	−27.0597	−1.05410	−0.527048	−	0.849836i	$-0.676701\pi$
$659$	−27.0597	−1.05410	−0.527048	+	0.849836i	$0.676701\pi$
$660$	−20.1172	−0.783062
$661$	11.4853	0.446728	0.223364	−	0.974735i	$-0.428296\pi$
$661$	11.4853	0.446728	0.223364	+	0.974735i	$0.428296\pi$
$662$	42.9760	1.67031
$663$	−1.21930	−0.0473537
$664$	93.6994	3.63624
$665$	0	0
$666$	80.8485	3.13281
$667$	−42.4256	−1.64273
$668$	−68.6308	−2.65541
$669$	−38.7333	−1.49752
$670$	−19.8022	−0.765026
$671$	−20.4621	−0.789932
$672$	0	0
$673$	13.7271	0.529142	0.264571	−	0.964366i	$-0.414770\pi$
$673$	13.7271	0.529142	0.264571	+	0.964366i	$0.414770\pi$
$674$	17.9636	0.691930
$675$	−15.6898	−0.603900
$676$	−55.9577	−2.15222
$677$	−4.50457	−0.173125	−0.0865623	−	0.996246i	$-0.527588\pi$
$677$	−4.50457	−0.173125	−0.0865623	+	0.996246i	$0.527588\pi$
$678$	−8.21017	−0.315310
$679$	0	0
$680$	3.35582	0.128690
$681$	15.9328	0.610547
$682$	−10.1858	−0.390033
$683$	0.557725	0.0213407	0.0106704	−	0.999943i	$-0.496603\pi$
$683$	0.557725	0.0213407	0.0106704	+	0.999943i	$0.496603\pi$
$684$	−149.587	−5.71960
$685$	2.24776	0.0858825
$686$	0	0
$687$	11.3121	0.431584
$688$	56.2270	2.14363
$689$	−3.21292	−0.122402
$690$	36.6836	1.39652
$691$	−7.64470	−0.290818	−0.145409	−	0.989372i	$-0.546450\pi$
$691$	−7.64470	−0.290818	−0.145409	+	0.989372i	$0.546450\pi$
$692$	85.7523	3.25981
$693$	0	0
$694$	−20.2713	−0.769489
$695$	13.0249	0.494061
$696$	83.1498	3.15179
$697$	0.858264	0.0325091
$698$	−66.7005	−2.52465
$699$	−29.3387	−1.10969
$700$	0	0
$701$	17.9965	0.679720	0.339860	−	0.940476i	$-0.389620\pi$
$701$	17.9965	0.679720	0.339860	+	0.940476i	$0.389620\pi$
$702$	4.56134	0.172157
$703$	−59.6380	−2.24929
$704$	−4.96568	−0.187151
$705$	5.22166	0.196659
$706$	−73.1874	−2.75444
$707$	0	0
$708$	−68.2207	−2.56389
$709$	−1.85510	−0.0696698	−0.0348349	−	0.999393i	$-0.511091\pi$
$709$	−1.85510	−0.0696698	−0.0348349	+	0.999393i	$0.511091\pi$
$710$	−17.0103	−0.638384
$711$	14.4293	0.541140
$712$	−34.8673	−1.30671
$713$	12.7679	0.478162
$714$	0	0
$715$	−0.893865	−0.0334287
$716$	51.7898	1.93548
$717$	−20.9604	−0.782779
$718$	−7.01581	−0.261828
$719$	13.2350	0.493582	0.246791	−	0.969069i	$-0.420624\pi$
$719$	13.2350	0.493582	0.246791	+	0.969069i	$0.420624\pi$
$720$	−18.0200	−0.671567
$721$	0	0
$722$	112.457	4.18521
$723$	−25.6707	−0.954705
$724$	−9.52131	−0.353857
$725$	−23.3059	−0.865558
$726$	−27.7708	−1.03067
$727$	13.8387	0.513248	0.256624	−	0.966511i	$-0.417390\pi$
$727$	13.8387	0.513248	0.256624	+	0.966511i	$0.417390\pi$
$728$	0	0
$729$	−42.9691	−1.59145
$730$	−11.4837	−0.425030
$731$	−7.36872	−0.272542
$732$	−92.1905	−3.40746
$733$	−31.4247	−1.16070	−0.580348	−	0.814368i	$-0.697084\pi$
$733$	−31.4247	−1.16070	−0.580348	+	0.814368i	$0.697084\pi$
$734$	−30.5876	−1.12901
$735$	0	0
$736$	−36.9905	−1.36349
$737$	31.9711	1.17767
$738$	−10.7992	−0.397525
$739$	40.8761	1.50365	0.751826	−	0.659362i	$-0.229173\pi$
$739$	40.8761	1.50365	0.751826	+	0.659362i	$0.229173\pi$
$740$	−21.2225	−0.780154
$741$	−11.3171	−0.415743
$742$	0	0
$743$	−2.43108	−0.0891876	−0.0445938	−	0.999005i	$-0.514199\pi$
$743$	−2.43108	−0.0891876	−0.0445938	+	0.999005i	$0.514199\pi$
$744$	−25.0238	−0.917418
$745$	12.8368	0.470303
$746$	64.7974	2.37240
$747$	65.9389	2.41258
$748$	−9.93615	−0.363301
$749$	0	0
$750$	42.1290	1.53833
$751$	2.76278	0.100815	0.0504076	−	0.998729i	$-0.483948\pi$
$751$	2.76278	0.100815	0.0504076	+	0.998729i	$0.483948\pi$
$752$	−19.6794	−0.717633
$753$	55.0721	2.00694
$754$	6.77549	0.246749
$755$	1.55773	0.0566916
$756$	0	0
$757$	0.390290	0.0141853	0.00709267	−	0.999975i	$-0.497742\pi$
$757$	0.390290	0.0141853	0.00709267	+	0.999975i	$0.497742\pi$
$758$	22.9731	0.834420
$759$	−59.2266	−2.14979
$760$	31.1473	1.12983
$761$	−2.01865	−0.0731761	−0.0365880	−	0.999330i	$-0.511649\pi$
$761$	−2.01865	−0.0731761	−0.0365880	+	0.999330i	$0.511649\pi$
$762$	7.86985	0.285095
$763$	0	0
$764$	2.23013	0.0806834
$765$	2.36158	0.0853832
$766$	−2.00752	−0.0725348
$767$	−3.03124	−0.109452
$768$	−82.8280	−2.98880
$769$	−5.65663	−0.203983	−0.101992	−	0.994785i	$-0.532521\pi$
$769$	−5.65663	−0.203983	−0.101992	+	0.994785i	$0.532521\pi$
$770$	0	0
$771$	25.6799	0.924840
$772$	−43.3777	−1.56120
$773$	−22.1785	−0.797704	−0.398852	−	0.917015i	$-0.630591\pi$
$773$	−22.1785	−0.797704	−0.398852	+	0.917015i	$0.630591\pi$
$774$	92.7179	3.33268
$775$	7.01386	0.251945
$776$	−41.0319	−1.47296
$777$	0	0
$778$	−23.2401	−0.833198
$779$	7.96606	0.285414
$780$	−4.02724	−0.144198
$781$	27.4635	0.982722
$782$	18.1185	0.647916
$783$	17.3971	0.621720
$784$	0	0
$785$	−8.58394	−0.306374
$786$	−3.75849	−0.134061
$787$	−20.0009	−0.712957	−0.356478	−	0.934304i	$-0.616023\pi$
$787$	−20.0009	−0.712957	−0.356478	+	0.934304i	$0.616023\pi$
$788$	108.581	3.86804
$789$	35.7508	1.27276
$790$	−5.50994	−0.196035
$791$	0	0
$792$	68.1733	2.42243
$793$	−4.09629	−0.145463
$794$	45.4977	1.61465
$795$	10.5956	0.375788
$796$	66.1348	2.34409
$797$	39.5775	1.40191	0.700953	−	0.713207i	$-0.252758\pi$
$797$	39.5775	1.40191	0.700953	+	0.713207i	$0.252758\pi$
$798$	0	0
$799$	2.57905	0.0912401
$800$	−20.3202	−0.718426
$801$	−24.5371	−0.866975
$802$	−80.2582	−2.83402
$803$	18.5407	0.654287
$804$	144.043	5.08002
$805$	0	0
$806$	−2.03907	−0.0718232
$807$	−2.00396	−0.0705428
$808$	88.5885	3.11653
$809$	−42.8950	−1.50811	−0.754054	−	0.656812i	$-0.771904\pi$
$809$	−42.8950	−1.50811	−0.754054	+	0.656812i	$0.771904\pi$
$810$	5.83788	0.205122
$811$	40.4952	1.42198	0.710990	−	0.703202i	$-0.248247\pi$
$811$	40.4952	1.42198	0.710990	+	0.703202i	$0.248247\pi$
$812$	0	0
$813$	20.8488	0.731200
$814$	49.8446	1.74705
$815$	12.1025	0.423932
$816$	−15.1545	−0.530513
$817$	−68.3935	−2.39278
$818$	75.7455	2.64838
$819$	0	0
$820$	2.83477	0.0989943
$821$	40.3368	1.40777	0.703883	−	0.710316i	$-0.251448\pi$
$821$	40.3368	1.40777	0.703883	+	0.710316i	$0.251448\pi$
$822$	−23.7852	−0.829605
$823$	9.67479	0.337242	0.168621	−	0.985681i	$-0.446069\pi$
$823$	9.67479	0.337242	0.168621	+	0.985681i	$0.446069\pi$
$824$	91.1198	3.17431
$825$	−32.5352	−1.13273
$826$	0	0
$827$	36.4876	1.26880	0.634399	−	0.773005i	$-0.281247\pi$
$827$	36.4876	1.26880	0.634399	+	0.773005i	$0.281247\pi$
$828$	−156.717	−5.44629
$829$	7.45853	0.259046	0.129523	−	0.991576i	$-0.458655\pi$
$829$	7.45853	0.259046	0.129523	+	0.991576i	$0.458655\pi$
$830$	−25.1793	−0.873986
$831$	−9.53124	−0.330635
$832$	−0.994072	−0.0344633
$833$	0	0
$834$	−137.826	−4.77252
$835$	10.0566	0.348023
$836$	−92.2232	−3.18961
$837$	−5.23562	−0.180969
$838$	55.0048	1.90011
$839$	5.51812	0.190507	0.0952534	−	0.995453i	$-0.469634\pi$
$839$	5.51812	0.190507	0.0952534	+	0.995453i	$0.469634\pi$
$840$	0	0
$841$	−3.15813	−0.108901
$842$	22.3623	0.770656
$843$	−40.5830	−1.39775
$844$	−91.7829	−3.15930
$845$	8.19959	0.282074
$846$	−32.4512	−1.11569
$847$	0	0
$848$	−39.9328	−1.37130
$849$	28.9011	0.991882
$850$	9.95312	0.341389
$851$	−62.4806	−2.14181
$852$	123.735	4.23908
$853$	28.9568	0.991461	0.495730	−	0.868476i	$-0.334900\pi$
$853$	28.9568	0.991461	0.495730	+	0.868476i	$0.334900\pi$
$854$	0	0
$855$	21.9192	0.749622
$856$	19.4731	0.665575
$857$	−13.6210	−0.465284	−0.232642	−	0.972562i	$-0.574737\pi$
$857$	−13.6210	−0.465284	−0.232642	+	0.972562i	$0.574737\pi$
$858$	9.45865	0.322913
$859$	4.73950	0.161710	0.0808549	−	0.996726i	$-0.474235\pi$
$859$	4.73950	0.161710	0.0808549	+	0.996726i	$0.474235\pi$
$860$	−24.3382	−0.829925
$861$	0	0
$862$	75.6690	2.57730
$863$	49.1363	1.67262	0.836309	−	0.548259i	$-0.184709\pi$
$863$	49.1363	1.67262	0.836309	+	0.548259i	$0.184709\pi$
$864$	15.1683	0.516038
$865$	−12.5654	−0.427238
$866$	56.9459	1.93510
$867$	−43.8488	−1.48918
$868$	0	0
$869$	8.89593	0.301774
$870$	−22.3444	−0.757545
$871$	6.40026	0.216864
$872$	37.3181	1.26375
$873$	−28.8753	−0.977280
$874$	168.168	5.68838
$875$	0	0
$876$	83.5336	2.82234
$877$	54.1123	1.82724	0.913621	−	0.406566i	$-0.133274\pi$
$877$	54.1123	1.82724	0.913621	+	0.406566i	$0.133274\pi$
$878$	−15.0259	−0.507098
$879$	38.7511	1.30704
$880$	−11.1097	−0.374508
$881$	−18.9504	−0.638454	−0.319227	−	0.947678i	$-0.603423\pi$
$881$	−18.9504	−0.638454	−0.319227	+	0.947678i	$0.603423\pi$
$882$	0	0
$883$	−4.18661	−0.140891	−0.0704453	−	0.997516i	$-0.522442\pi$
$883$	−4.18661	−0.140891	−0.0704453	+	0.997516i	$0.522442\pi$
$884$	−1.98910	−0.0669008
$885$	9.99650	0.336029
$886$	−32.6063	−1.09543
$887$	−18.6458	−0.626063	−0.313032	−	0.949743i	$-0.601345\pi$
$887$	−18.6458	−0.626063	−0.313032	+	0.949743i	$0.601345\pi$
$888$	122.456	4.10934
$889$	0	0
$890$	9.36968	0.314072
$891$	−9.42540	−0.315763
$892$	−63.1874	−2.11567
$893$	23.9376	0.801043
$894$	−135.835	−4.54302
$895$	−7.58886	−0.253667
$896$	0	0
$897$	−11.8565	−0.395876
$898$	−60.7239	−2.02638
$899$	−7.77707	−0.259380
$900$	−86.0901	−2.86967
$901$	5.23332	0.174347
$902$	−6.65793	−0.221685
$903$	0	0
$904$	−7.30338	−0.242907
$905$	1.39518	0.0463772
$906$	−16.4835	−0.547627
$907$	−4.48838	−0.149034	−0.0745172	−	0.997220i	$-0.523742\pi$
$907$	−4.48838	−0.149034	−0.0745172	+	0.997220i	$0.523742\pi$
$908$	25.9919	0.862573
$909$	62.3422	2.06776
$910$	0	0
$911$	−25.8175	−0.855372	−0.427686	−	0.903927i	$-0.640671\pi$
$911$	−25.8175	−0.855372	−0.427686	+	0.903927i	$0.640671\pi$
$912$	−140.658	−4.65765
$913$	40.6526	1.34540
$914$	−21.0581	−0.696542
$915$	13.5088	0.446588
$916$	18.4540	0.609736
$917$	0	0
$918$	−7.42968	−0.245216
$919$	−31.4503	−1.03745	−0.518725	−	0.854941i	$-0.673593\pi$
$919$	−31.4503	−1.03745	−0.518725	+	0.854941i	$0.673593\pi$
$920$	32.6320	1.07584
$921$	74.0731	2.44079
$922$	8.79985	0.289808
$923$	5.49788	0.180965
$924$	0	0
$925$	−34.3228	−1.12853
$926$	2.31961	0.0762271
$927$	64.1236	2.10609
$928$	22.5313	0.739626
$929$	17.3736	0.570010	0.285005	−	0.958526i	$-0.408005\pi$
$929$	17.3736	0.570010	0.285005	+	0.958526i	$0.408005\pi$
$930$	6.72450	0.220505
$931$	0	0
$932$	−47.8616	−1.56776
$933$	−49.5165	−1.62110
$934$	13.7823	0.450970
$935$	1.45596	0.0476150
$936$	13.6475	0.446083
$937$	−1.64679	−0.0537983	−0.0268992	−	0.999638i	$-0.508563\pi$
$937$	−1.64679	−0.0537983	−0.0268992	+	0.999638i	$0.508563\pi$
$938$	0	0
$939$	18.2852	0.596716
$940$	8.51834	0.277838
$941$	0.0468988	0.00152886	0.000764428	−	1.00000i	$-0.499757\pi$
$941$	0.0468988	0.00152886	0.000764428		1.00000i	$0.499757\pi$
$942$	90.8330	2.95950
$943$	8.34576	0.271775
$944$	−37.6748	−1.22621
$945$	0	0
$946$	57.1624	1.85851
$947$	−41.2388	−1.34008	−0.670041	−	0.742324i	$-0.733723\pi$
$947$	−41.2388	−1.34008	−0.670041	+	0.742324i	$0.733723\pi$
$948$	40.0799	1.30173
$949$	3.71163	0.120485
$950$	92.3808	2.99723
$951$	12.2801	0.398211
$952$	0	0
$953$	−17.5348	−0.568009	−0.284005	−	0.958823i	$-0.591663\pi$
$953$	−17.5348	−0.568009	−0.284005	+	0.958823i	$0.591663\pi$
$954$	−65.8489	−2.13194
$955$	−0.326786	−0.0105745
$956$	−34.1936	−1.10590
$957$	36.0755	1.16616
$958$	−0.146617	−0.00473699
$959$	0	0
$960$	3.27828	0.105806
$961$	−28.6595	−0.924500
$962$	9.97833	0.321714
$963$	13.7037	0.441597
$964$	−41.8779	−1.34880
$965$	6.35621	0.204614
$966$	0	0
$967$	3.69356	0.118777	0.0593884	−	0.998235i	$-0.481085\pi$
$967$	3.69356	0.118777	0.0593884	+	0.998235i	$0.481085\pi$
$968$	−24.7036	−0.794003
$969$	18.4336	0.592174
$970$	11.0263	0.354032
$971$	−54.6550	−1.75396	−0.876981	−	0.480524i	$-0.840446\pi$
$971$	−54.6550	−1.75396	−0.876981	+	0.480524i	$0.840446\pi$
$972$	−87.6226	−2.81050
$973$	0	0
$974$	4.74753	0.152121
$975$	−6.51318	−0.208589
$976$	−50.9120	−1.62965
$977$	−24.9332	−0.797685	−0.398842	−	0.917019i	$-0.630588\pi$
$977$	−24.9332	−0.797685	−0.398842	+	0.917019i	$0.630588\pi$
$978$	−128.065	−4.09508
$979$	−15.1276	−0.483480
$980$	0	0
$981$	26.2618	0.838474
$982$	−40.7879	−1.30160
$983$	−16.8168	−0.536374	−0.268187	−	0.963367i	$-0.586425\pi$
$983$	−16.8168	−0.536374	−0.268187	+	0.963367i	$0.586425\pi$
$984$	−16.3568	−0.521437
$985$	−15.9106	−0.506953
$986$	−11.0362	−0.351463
$987$	0	0
$988$	−18.4620	−0.587356
$989$	−71.6534	−2.27845
$990$	−18.3198	−0.582242
$991$	54.0682	1.71753	0.858766	−	0.512367i	$-0.171231\pi$
$991$	54.0682	1.71753	0.858766	+	0.512367i	$0.171231\pi$
$992$	−6.78076	−0.215289
$993$	45.8076	1.45366
$994$	0	0
$995$	−9.69085	−0.307221
$996$	183.157	5.80355
$997$	−30.9682	−0.980773	−0.490387	−	0.871505i	$-0.663144\pi$
$997$	−30.9682	−0.980773	−0.490387	+	0.871505i	$0.663144\pi$
$998$	85.3281	2.70101
$999$	25.6208	0.810607

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2009.2.a.r.1.15		17
7.3	odd	6		287.2.e.d.247.3	yes	34
7.5	odd	6		287.2.e.d.165.3	✓	34
7.6	odd	2		2009.2.a.s.1.15		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.e.d.165.3	✓	34	7.5	odd	6
287.2.e.d.247.3	yes	34	7.3	odd	6
2009.2.a.r.1.15		17	1.1	even	1	trivial
2009.2.a.s.1.15		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)

\(f(q)\)	\(=\)	\(q+2.52950 q^{2} +2.69617 q^{3} +4.39838 q^{4} -0.644502 q^{5} +6.81996 q^{6} +6.06670 q^{8} +4.26931 q^{9} +O(q^{10})\)	\(q+2.52950 q^{2} +2.69617 q^{3} +4.39838 q^{4} -0.644502 q^{5} +6.81996 q^{6} +6.06670 q^{8} +4.26931 q^{9} -1.63027 q^{10} +2.63211 q^{11} +11.8588 q^{12} +0.526918 q^{13} -1.73769 q^{15} +6.54898 q^{16} -0.858264 q^{17} +10.7992 q^{18} -7.96606 q^{19} -2.83477 q^{20} +6.65793 q^{22} -8.34576 q^{23} +16.3568 q^{24} -4.58462 q^{25} +1.33284 q^{26} +3.42227 q^{27} +5.08349 q^{29} -4.39548 q^{30} -1.52987 q^{31} +4.43225 q^{32} +7.09661 q^{33} -2.17098 q^{34} +18.7780 q^{36} +7.48651 q^{37} -20.1502 q^{38} +1.42066 q^{39} -3.91001 q^{40} -1.00000 q^{41} +8.58561 q^{43} +11.5770 q^{44} -2.75158 q^{45} -21.1106 q^{46} -3.00495 q^{47} +17.6571 q^{48} -11.5968 q^{50} -2.31402 q^{51} +2.31759 q^{52} -6.09756 q^{53} +8.65663 q^{54} -1.69640 q^{55} -21.4778 q^{57} +12.8587 q^{58} -5.75277 q^{59} -7.64300 q^{60} -7.77404 q^{61} -3.86981 q^{62} -1.88658 q^{64} -0.339600 q^{65} +17.9509 q^{66} +12.1466 q^{67} -3.77497 q^{68} -22.5016 q^{69} +10.4340 q^{71} +25.9006 q^{72} +7.04404 q^{73} +18.9371 q^{74} -12.3609 q^{75} -35.0378 q^{76} +3.59356 q^{78} +3.37977 q^{79} -4.22083 q^{80} -3.58093 q^{81} -2.52950 q^{82} +15.4449 q^{83} +0.553153 q^{85} +21.7173 q^{86} +13.7059 q^{87} +15.9682 q^{88} -5.74732 q^{89} -6.96013 q^{90} -36.7078 q^{92} -4.12478 q^{93} -7.60104 q^{94} +5.13414 q^{95} +11.9501 q^{96} -6.76346 q^{97} +11.2373 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 3 q^{2} - q^{3} + 25 q^{4} + q^{5} - 2 q^{6} + 9 q^{8} + 26 q^{9}+O(q^{10}) \) 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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