LMFDB - Embedded newform 2009.2.a.r.1.10

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			1.10
Root			$1.11543$ 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)

$f(q)$	$=$	$q+1.11543 q^{2} +2.75409 q^{3} -0.755825 q^{4} +1.34462 q^{5} +3.07199 q^{6} -3.07392 q^{8} +4.58503 q^{9} +O(q^{10})$	\(q+1.11543 q^{2} +2.75409 q^{3} -0.755825 q^{4} +1.34462 q^{5} +3.07199 q^{6} -3.07392 q^{8} +4.58503 q^{9} +1.49982 q^{10} -1.07728 q^{11} -2.08161 q^{12} +0.966204 q^{13} +3.70320 q^{15} -1.91708 q^{16} +6.52880 q^{17} +5.11426 q^{18} +7.07942 q^{19} -1.01630 q^{20} -1.20163 q^{22} +0.898247 q^{23} -8.46586 q^{24} -3.19200 q^{25} +1.07773 q^{26} +4.36532 q^{27} +2.82453 q^{29} +4.13065 q^{30} +1.38928 q^{31} +4.00948 q^{32} -2.96693 q^{33} +7.28240 q^{34} -3.46548 q^{36} -7.12505 q^{37} +7.89657 q^{38} +2.66102 q^{39} -4.13324 q^{40} -1.00000 q^{41} +1.23495 q^{43} +0.814235 q^{44} +6.16511 q^{45} +1.00193 q^{46} -7.85310 q^{47} -5.27981 q^{48} -3.56044 q^{50} +17.9809 q^{51} -0.730281 q^{52} +6.58939 q^{53} +4.86919 q^{54} -1.44853 q^{55} +19.4974 q^{57} +3.15055 q^{58} -2.72107 q^{59} -2.79897 q^{60} +11.0489 q^{61} +1.54964 q^{62} +8.30643 q^{64} +1.29917 q^{65} -3.30939 q^{66} +2.45673 q^{67} -4.93463 q^{68} +2.47385 q^{69} +2.40706 q^{71} -14.0940 q^{72} -8.12078 q^{73} -7.94747 q^{74} -8.79108 q^{75} -5.35081 q^{76} +2.96816 q^{78} -1.96133 q^{79} -2.57774 q^{80} -1.73260 q^{81} -1.11543 q^{82} +9.30225 q^{83} +8.77874 q^{85} +1.37750 q^{86} +7.77902 q^{87} +3.31147 q^{88} -12.7953 q^{89} +6.87672 q^{90} -0.678918 q^{92} +3.82622 q^{93} -8.75955 q^{94} +9.51912 q^{95} +11.0425 q^{96} -18.4064 q^{97} -4.93936 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.11543	0.788725	0.394363	−	0.918955i	$-0.370965\pi$
$2$	1.11543	0.788725	0.394363	+	0.918955i	$0.370965\pi$
$3$	2.75409	1.59008	0.795038	−	0.606559i	$-0.207451\pi$
$3$	2.75409	1.59008	0.795038	+	0.606559i	$0.207451\pi$
$4$	−0.755825	−0.377913
$5$	1.34462	0.601331	0.300666	−	0.953730i	$-0.402791\pi$
$5$	1.34462	0.601331	0.300666	+	0.953730i	$0.402791\pi$
$6$	3.07199	1.25413
$7$	0	0
$7$	0	0
$8$	−3.07392	−1.08679
$9$	4.58503	1.52834
$10$	1.49982	0.474285
$11$	−1.07728	−0.324812	−0.162406	−	0.986724i	$-0.551925\pi$
$11$	−1.07728	−0.324812	−0.162406	+	0.986724i	$0.551925\pi$
$12$	−2.08161	−0.600910
$13$	0.966204	0.267977	0.133988	−	0.990983i	$-0.457222\pi$
$13$	0.966204	0.267977	0.133988	+	0.990983i	$0.457222\pi$
$14$	0	0
$15$	3.70320	0.956163
$16$	−1.91708	−0.479269
$17$	6.52880	1.58347	0.791734	−	0.610866i	$-0.209179\pi$
$17$	6.52880	1.58347	0.791734	+	0.610866i	$0.209179\pi$
$18$	5.11426	1.20544
$19$	7.07942	1.62413	0.812065	−	0.583566i	$-0.198343\pi$
$19$	7.07942	1.62413	0.812065	+	0.583566i	$0.198343\pi$
$20$	−1.01630	−0.227251
$21$	0	0
$22$	−1.20163	−0.256187
$23$	0.898247	0.187297	0.0936487	−	0.995605i	$-0.470147\pi$
$23$	0.898247	0.187297	0.0936487	+	0.995605i	$0.470147\pi$
$24$	−8.46586	−1.72809
$25$	−3.19200	−0.638401
$26$	1.07773	0.211360
$27$	4.36532	0.840106
$28$	0	0
$29$	2.82453	0.524502	0.262251	−	0.965000i	$-0.415535\pi$
$29$	2.82453	0.524502	0.262251	+	0.965000i	$0.415535\pi$
$30$	4.13065	0.754149
$31$	1.38928	0.249523	0.124761	−	0.992187i	$-0.460183\pi$
$31$	1.38928	0.249523	0.124761	+	0.992187i	$0.460183\pi$
$32$	4.00948	0.708783
$33$	−2.96693	−0.516476
$34$	7.28240	1.24892
$35$	0	0
$36$	−3.46548	−0.577580
$37$	−7.12505	−1.17135	−0.585676	−	0.810545i	$-0.699171\pi$
$37$	−7.12505	−1.17135	−0.585676	+	0.810545i	$0.699171\pi$
$38$	7.89657	1.28099
$39$	2.66102	0.426103
$40$	−4.13324	−0.653523
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	1.23495	0.188328	0.0941642	−	0.995557i	$-0.469982\pi$
$43$	1.23495	0.188328	0.0941642	+	0.995557i	$0.469982\pi$
$44$	0.814235	0.122751
$45$	6.16511	0.919040
$46$	1.00193	0.147726
$47$	−7.85310	−1.14549	−0.572746	−	0.819733i	$-0.694122\pi$
$47$	−7.85310	−1.14549	−0.572746	+	0.819733i	$0.694122\pi$
$48$	−5.27981	−0.762075
$49$	0	0
$50$	−3.56044	−0.503523
$51$	17.9809	2.51783
$52$	−0.730281	−0.101272
$53$	6.58939	0.905122	0.452561	−	0.891733i	$-0.350510\pi$
$53$	6.58939	0.905122	0.452561	+	0.891733i	$0.350510\pi$
$54$	4.86919	0.662613
$55$	−1.44853	−0.195320
$56$	0	0
$57$	19.4974	2.58249
$58$	3.15055	0.413688
$59$	−2.72107	−0.354253	−0.177126	−	0.984188i	$-0.556680\pi$
$59$	−2.72107	−0.354253	−0.177126	+	0.984188i	$0.556680\pi$
$60$	−2.79897	−0.361346
$61$	11.0489	1.41467	0.707334	−	0.706880i	$-0.249898\pi$
$61$	11.0489	1.41467	0.707334	+	0.706880i	$0.249898\pi$
$62$	1.54964	0.196805
$63$	0	0
$64$	8.30643	1.03830
$65$	1.29917	0.161143
$66$	−3.30939	−0.407357
$67$	2.45673	0.300138	0.150069	−	0.988676i	$-0.452050\pi$
$67$	2.45673	0.300138	0.150069	+	0.988676i	$0.452050\pi$
$68$	−4.93463	−0.598412
$69$	2.47385	0.297817
$70$	0	0
$71$	2.40706	0.285666	0.142833	−	0.989747i	$-0.454379\pi$
$71$	2.40706	0.285666	0.142833	+	0.989747i	$0.454379\pi$
$72$	−14.0940	−1.66099
$73$	−8.12078	−0.950465	−0.475232	−	0.879860i	$-0.657636\pi$
$73$	−8.12078	−0.950465	−0.475232	+	0.879860i	$0.657636\pi$
$74$	−7.94747	−0.923875
$75$	−8.79108	−1.01511
$76$	−5.35081	−0.613780
$77$	0	0
$78$	2.96816	0.336078
$79$	−1.96133	−0.220666	−0.110333	−	0.993895i	$-0.535192\pi$
$79$	−1.96133	−0.220666	−0.110333	+	0.993895i	$0.535192\pi$
$80$	−2.57774	−0.288200
$81$	−1.73260	−0.192511
$82$	−1.11543	−0.123178
$83$	9.30225	1.02105	0.510527	−	0.859862i	$-0.329450\pi$
$83$	9.30225	1.02105	0.510527	+	0.859862i	$0.329450\pi$
$84$	0	0
$85$	8.77874	0.952188
$86$	1.37750	0.148539
$87$	7.77902	0.833999
$88$	3.31147	0.353004
$89$	−12.7953	−1.35629	−0.678147	−	0.734926i	$-0.737217\pi$
$89$	−12.7953	−1.35629	−0.678147	+	0.734926i	$0.737217\pi$
$90$	6.87672	0.724870
$91$	0	0
$92$	−0.678918	−0.0707820
$93$	3.82622	0.396760
$94$	−8.75955	−0.903478
$95$	9.51912	0.976641
$96$	11.0425	1.12702
$97$	−18.4064	−1.86888	−0.934442	−	0.356117i	$-0.884101\pi$
$97$	−18.4064	−1.86888	−0.934442	+	0.356117i	$0.884101\pi$
$98$	0	0
$99$	−4.93936	−0.496424
$100$	2.41260	0.241260
$101$	7.26316	0.722711	0.361356	−	0.932428i	$-0.382314\pi$
$101$	7.26316	0.722711	0.361356	+	0.932428i	$0.382314\pi$
$102$	20.0564	1.98588
$103$	−19.0867	−1.88066	−0.940332	−	0.340257i	$-0.889486\pi$
$103$	−19.0867	−1.88066	−0.940332	+	0.340257i	$0.889486\pi$
$104$	−2.97003	−0.291236
$105$	0	0
$106$	7.34997	0.713892
$107$	−11.6695	−1.12813	−0.564065	−	0.825730i	$-0.690763\pi$
$107$	−11.6695	−1.12813	−0.564065	+	0.825730i	$0.690763\pi$
$108$	−3.29942	−0.317487
$109$	17.0444	1.63256	0.816281	−	0.577656i	$-0.196032\pi$
$109$	17.0444	1.63256	0.816281	+	0.577656i	$0.196032\pi$
$110$	−1.61573	−0.154053
$111$	−19.6231	−1.86254
$112$	0	0
$113$	−4.74418	−0.446295	−0.223147	−	0.974785i	$-0.571633\pi$
$113$	−4.74418	−0.446295	−0.223147	+	0.974785i	$0.571633\pi$
$114$	21.7479	2.03688
$115$	1.20780	0.112628
$116$	−2.13485	−0.198216
$117$	4.43007	0.409560
$118$	−3.03515	−0.279408
$119$	0	0
$120$	−11.3833	−1.03915
$121$	−9.83947	−0.894497
$122$	12.3242	1.11578
$123$	−2.75409	−0.248328
$124$	−1.05006	−0.0942978
$125$	−11.0151	−0.985222
$126$	0	0
$127$	−9.95232	−0.883126	−0.441563	−	0.897230i	$-0.645576\pi$
$127$	−9.95232	−0.883126	−0.441563	+	0.897230i	$0.645576\pi$
$128$	1.24625	0.110154
$129$	3.40117	0.299457
$130$	1.44913	0.127097
$131$	−21.0937	−1.84297	−0.921484	−	0.388416i	$-0.873022\pi$
$131$	−21.0937	−1.84297	−0.921484	+	0.388416i	$0.873022\pi$
$132$	2.24248	0.195183
$133$	0	0
$134$	2.74030	0.236726
$135$	5.86968	0.505182
$136$	−20.0690	−1.72090
$137$	−8.00151	−0.683616	−0.341808	−	0.939770i	$-0.611039\pi$
$137$	−8.00151	−0.683616	−0.341808	+	0.939770i	$0.611039\pi$
$138$	2.75940	0.234896
$139$	7.13603	0.605270	0.302635	−	0.953107i	$-0.402134\pi$
$139$	7.13603	0.605270	0.302635	+	0.953107i	$0.402134\pi$
$140$	0	0
$141$	−21.6282	−1.82142
$142$	2.68490	0.225312
$143$	−1.04087	−0.0870420
$144$	−8.78986	−0.732488
$145$	3.79791	0.315400
$146$	−9.05812	−0.749656
$147$	0	0
$148$	5.38530	0.442669
$149$	−10.9781	−0.899361	−0.449680	−	0.893190i	$-0.648462\pi$
$149$	−10.9781	−0.899361	−0.449680	+	0.893190i	$0.648462\pi$
$150$	−9.80579	−0.800640
$151$	19.8359	1.61422	0.807112	−	0.590399i	$-0.201029\pi$
$151$	19.8359	1.61422	0.807112	+	0.590399i	$0.201029\pi$
$152$	−21.7616	−1.76510
$153$	29.9348	2.42008
$154$	0	0
$155$	1.86806	0.150046
$156$	−2.01126	−0.161030
$157$	9.62144	0.767875	0.383937	−	0.923359i	$-0.374568\pi$
$157$	9.62144	0.767875	0.383937	+	0.923359i	$0.374568\pi$
$158$	−2.18771	−0.174045
$159$	18.1478	1.43921
$160$	5.39122	0.426213
$161$	0	0
$162$	−1.93258	−0.151838
$163$	0.333705	0.0261378	0.0130689	−	0.999915i	$-0.495840\pi$
$163$	0.333705	0.0261378	0.0130689	+	0.999915i	$0.495840\pi$
$164$	0.755825	0.0590200
$165$	−3.98938	−0.310573
$166$	10.3760	0.805332
$167$	16.6780	1.29058	0.645290	−	0.763938i	$-0.276737\pi$
$167$	16.6780	1.29058	0.645290	+	0.763938i	$0.276737\pi$
$168$	0	0
$169$	−12.0665	−0.928188
$170$	9.79204	0.751015
$171$	32.4594	2.48223
$172$	−0.933408	−0.0711717
$173$	12.9458	0.984250	0.492125	−	0.870524i	$-0.336220\pi$
$173$	12.9458	0.984250	0.492125	+	0.870524i	$0.336220\pi$
$174$	8.67692	0.657796
$175$	0	0
$176$	2.06523	0.155672
$177$	−7.49408	−0.563289
$178$	−14.2722	−1.06974
$179$	17.0658	1.27556	0.637779	−	0.770219i	$-0.279853\pi$
$179$	17.0658	1.27556	0.637779	+	0.770219i	$0.279853\pi$
$180$	−4.65975	−0.347317
$181$	0.402992	0.0299541	0.0149771	−	0.999888i	$-0.495232\pi$
$181$	0.402992	0.0299541	0.0149771	+	0.999888i	$0.495232\pi$
$182$	0	0
$183$	30.4297	2.24943
$184$	−2.76114	−0.203554
$185$	−9.58047	−0.704370
$186$	4.26786	0.312935
$187$	−7.03334	−0.514329
$188$	5.93557	0.432896
$189$	0	0
$190$	10.6179	0.770301
$191$	−13.6069	−0.984559	−0.492280	−	0.870437i	$-0.663836\pi$
$191$	−13.6069	−0.984559	−0.492280	+	0.870437i	$0.663836\pi$
$192$	22.8767	1.65098
$193$	−6.39685	−0.460456	−0.230228	−	0.973137i	$-0.573947\pi$
$193$	−6.39685	−0.460456	−0.230228	+	0.973137i	$0.573947\pi$
$194$	−20.5309	−1.47404
$195$	3.57805	0.256229
$196$	0	0
$197$	−21.8587	−1.55737	−0.778684	−	0.627416i	$-0.784113\pi$
$197$	−21.8587	−1.55737	−0.778684	+	0.627416i	$0.784113\pi$
$198$	−5.50949	−0.391542
$199$	−22.1759	−1.57201	−0.786005	−	0.618220i	$-0.787854\pi$
$199$	−22.1759	−1.57201	−0.786005	+	0.618220i	$0.787854\pi$
$200$	9.81196	0.693810
$201$	6.76607	0.477242
$202$	8.10151	0.570020
$203$	0	0
$204$	−13.5904	−0.951521
$205$	−1.34462	−0.0939122
$206$	−21.2898	−1.48333
$207$	4.11849	0.286255
$208$	−1.85229	−0.128433
$209$	−7.62652	−0.527537
$210$	0	0
$211$	16.8283	1.15851	0.579254	−	0.815147i	$-0.303344\pi$
$211$	16.8283	1.15851	0.579254	+	0.815147i	$0.303344\pi$
$212$	−4.98043	−0.342057
$213$	6.62927	0.454230
$214$	−13.0164	−0.889785
$215$	1.66054	0.113248
$216$	−13.4186	−0.913022
$217$	0	0
$218$	19.0118	1.28764
$219$	−22.3654	−1.51131
$220$	1.09483	0.0738137
$221$	6.30815	0.424332
$222$	−21.8881	−1.46903
$223$	−3.85768	−0.258329	−0.129165	−	0.991623i	$-0.541230\pi$
$223$	−3.85768	−0.258329	−0.129165	+	0.991623i	$0.541230\pi$
$224$	0	0
$225$	−14.6354	−0.975695
$226$	−5.29178	−0.352004
$227$	28.1917	1.87115	0.935576	−	0.353126i	$-0.114881\pi$
$227$	28.1917	1.87115	0.935576	+	0.353126i	$0.114881\pi$
$228$	−14.7366	−0.975956
$229$	15.2236	1.00601	0.503003	−	0.864285i	$-0.332228\pi$
$229$	15.2236	1.00601	0.503003	+	0.864285i	$0.332228\pi$
$230$	1.34721	0.0888323
$231$	0	0
$232$	−8.68238	−0.570026
$233$	−29.0175	−1.90100	−0.950501	−	0.310722i	$-0.899429\pi$
$233$	−29.0175	−1.90100	−0.950501	+	0.310722i	$0.899429\pi$
$234$	4.94142	0.323031
$235$	−10.5594	−0.688820
$236$	2.05665	0.133877
$237$	−5.40168	−0.350877
$238$	0	0
$239$	25.0381	1.61958	0.809792	−	0.586718i	$-0.199580\pi$
$239$	25.0381	1.61958	0.809792	+	0.586718i	$0.199580\pi$
$240$	−7.09932	−0.458259
$241$	1.11382	0.0717474	0.0358737	−	0.999356i	$-0.488579\pi$
$241$	1.11382	0.0717474	0.0358737	+	0.999356i	$0.488579\pi$
$242$	−10.9752	−0.705512
$243$	−17.8677	−1.14621
$244$	−8.35104	−0.534621
$245$	0	0
$246$	−3.07199	−0.195863
$247$	6.84016	0.435229
$248$	−4.27054	−0.271180
$249$	25.6193	1.62356
$250$	−12.2865	−0.777069
$251$	−7.27825	−0.459399	−0.229700	−	0.973262i	$-0.573774\pi$
$251$	−7.27825	−0.459399	−0.229700	+	0.973262i	$0.573774\pi$
$252$	0	0
$253$	−0.967663	−0.0608364
$254$	−11.1011	−0.696544
$255$	24.1775	1.51405
$256$	−15.2228	−0.951423
$257$	8.89942	0.555130	0.277565	−	0.960707i	$-0.410473\pi$
$257$	8.89942	0.555130	0.277565	+	0.960707i	$0.410473\pi$
$258$	3.79376	0.236189
$259$	0	0
$260$	−0.981949	−0.0608979
$261$	12.9506	0.801619
$262$	−23.5285	−1.45360
$263$	−5.89870	−0.363729	−0.181865	−	0.983324i	$-0.558213\pi$
$263$	−5.89870	−0.363729	−0.181865	+	0.983324i	$0.558213\pi$
$264$	9.12009	0.561303
$265$	8.86021	0.544278
$266$	0	0
$267$	−35.2393	−2.15661
$268$	−1.85686	−0.113426
$269$	−4.18733	−0.255306	−0.127653	−	0.991819i	$-0.540744\pi$
$269$	−4.18733	−0.255306	−0.127653	+	0.991819i	$0.540744\pi$
$270$	6.54719	0.398450
$271$	−10.0501	−0.610499	−0.305250	−	0.952272i	$-0.598740\pi$
$271$	−10.0501	−0.610499	−0.305250	+	0.952272i	$0.598740\pi$
$272$	−12.5162	−0.758907
$273$	0	0
$274$	−8.92510	−0.539185
$275$	3.43868	0.207360
$276$	−1.86980	−0.112549
$277$	−6.16607	−0.370483	−0.185242	−	0.982693i	$-0.559307\pi$
$277$	−6.16607	−0.370483	−0.185242	+	0.982693i	$0.559307\pi$
$278$	7.95971	0.477392
$279$	6.36991	0.381356
$280$	0	0
$281$	−6.64050	−0.396139	−0.198069	−	0.980188i	$-0.563467\pi$
$281$	−6.64050	−0.396139	−0.198069	+	0.980188i	$0.563467\pi$
$282$	−24.1246	−1.43660
$283$	−32.4418	−1.92846	−0.964232	−	0.265061i	$-0.914608\pi$
$283$	−32.4418	−1.92846	−0.964232	+	0.265061i	$0.914608\pi$
$284$	−1.81932	−0.107957
$285$	26.2165	1.55293
$286$	−1.16101	−0.0686522
$287$	0	0
$288$	18.3836	1.08326
$289$	25.6253	1.50737
$290$	4.23629	0.248764
$291$	−50.6928	−2.97167
$292$	6.13789	0.359193
$293$	−3.63051	−0.212097	−0.106048	−	0.994361i	$-0.533820\pi$
$293$	−3.63051	−0.212097	−0.106048	+	0.994361i	$0.533820\pi$
$294$	0	0
$295$	−3.65880	−0.213023
$296$	21.9018	1.27302
$297$	−4.70267	−0.272876
$298$	−12.2453	−0.709349
$299$	0.867889	0.0501913
$300$	6.64452	0.383621
$301$	0	0
$302$	22.1255	1.27318
$303$	20.0034	1.14917
$304$	−13.5718	−0.778396
$305$	14.8566	0.850684
$306$	33.3900	1.90878
$307$	0.641523	0.0366136	0.0183068	−	0.999832i	$-0.494172\pi$
$307$	0.641523	0.0366136	0.0183068	+	0.999832i	$0.494172\pi$
$308$	0	0
$309$	−52.5664	−2.99040
$310$	2.08368	0.118345
$311$	11.8418	0.671485	0.335743	−	0.941954i	$-0.391013\pi$
$311$	11.8418	0.671485	0.335743	+	0.941954i	$0.391013\pi$
$312$	−8.17974	−0.463087
$313$	−19.7303	−1.11522	−0.557612	−	0.830102i	$-0.688282\pi$
$313$	−19.7303	−1.11522	−0.557612	+	0.830102i	$0.688282\pi$
$314$	10.7320	0.605642
$315$	0	0
$316$	1.48242	0.0833926
$317$	24.5065	1.37642	0.688211	−	0.725510i	$-0.258396\pi$
$317$	24.5065	1.37642	0.688211	+	0.725510i	$0.258396\pi$
$318$	20.2425	1.13514
$319$	−3.04281	−0.170365
$320$	11.1690	0.624365
$321$	−32.1388	−1.79381
$322$	0	0
$323$	46.2202	2.57176
$324$	1.30954	0.0727522
$325$	−3.08413	−0.171077
$326$	0.372223	0.0206155
$327$	46.9420	2.59590
$328$	3.07392	0.169729
$329$	0	0
$330$	−4.44986	−0.244957
$331$	27.8301	1.52968	0.764841	−	0.644219i	$-0.222817\pi$
$331$	27.8301	1.52968	0.764841	+	0.644219i	$0.222817\pi$
$332$	−7.03088	−0.385869
$333$	−32.6686	−1.79023
$334$	18.6030	1.01791
$335$	3.30337	0.180482
$336$	0	0
$337$	0.235392	0.0128226	0.00641130	−	0.999979i	$-0.497959\pi$
$337$	0.235392	0.0128226	0.00641130	+	0.999979i	$0.497959\pi$
$338$	−13.4592	−0.732086
$339$	−13.0659	−0.709643
$340$	−6.63520	−0.359844
$341$	−1.49665	−0.0810480
$342$	36.2060	1.95780
$343$	0	0
$344$	−3.79614	−0.204674
$345$	3.32639	0.179087
$346$	14.4401	0.776303
$347$	−0.509008	−0.0273250	−0.0136625	−	0.999907i	$-0.504349\pi$
$347$	−0.509008	−0.0273250	−0.0136625	+	0.999907i	$0.504349\pi$
$348$	−5.87958	−0.315179
$349$	23.8662	1.27753	0.638764	−	0.769403i	$-0.279446\pi$
$349$	23.8662	1.27753	0.638764	+	0.769403i	$0.279446\pi$
$350$	0	0
$351$	4.21779	0.225129
$352$	−4.31933	−0.230221
$353$	−13.6030	−0.724016	−0.362008	−	0.932175i	$-0.617909\pi$
$353$	−13.6030	−0.724016	−0.362008	+	0.932175i	$0.617909\pi$
$354$	−8.35909	−0.444280
$355$	3.23658	0.171780
$356$	9.67098	0.512561
$357$	0	0
$358$	19.0356	1.00607
$359$	−4.84897	−0.255919	−0.127959	−	0.991779i	$-0.540843\pi$
$359$	−4.84897	−0.255919	−0.127959	+	0.991779i	$0.540843\pi$
$360$	−18.9510	−0.998808
$361$	31.1182	1.63780
$362$	0.449507	0.0236256
$363$	−27.0988	−1.42232
$364$	0	0
$365$	−10.9193	−0.571544
$366$	33.9421	1.77418
$367$	20.2354	1.05628	0.528139	−	0.849158i	$-0.322890\pi$
$367$	20.2354	1.05628	0.528139	+	0.849158i	$0.322890\pi$
$368$	−1.72201	−0.0897659
$369$	−4.58503	−0.238687
$370$	−10.6863	−0.555555
$371$	0	0
$372$	−2.89195	−0.149941
$373$	−14.0870	−0.729399	−0.364700	−	0.931125i	$-0.618828\pi$
$373$	−14.0870	−0.729399	−0.364700	+	0.931125i	$0.618828\pi$
$374$	−7.84517	−0.405664
$375$	−30.3366	−1.56658
$376$	24.1398	1.24491
$377$	2.72907	0.140554
$378$	0	0
$379$	−2.35252	−0.120841	−0.0604205	−	0.998173i	$-0.519244\pi$
$379$	−2.35252	−0.120841	−0.0604205	+	0.998173i	$0.519244\pi$
$380$	−7.19479	−0.369085
$381$	−27.4096	−1.40424
$382$	−15.1775	−0.776547
$383$	11.8503	0.605524	0.302762	−	0.953066i	$-0.402091\pi$
$383$	11.8503	0.605524	0.302762	+	0.953066i	$0.402091\pi$
$384$	3.43229	0.175153
$385$	0	0
$386$	−7.13522	−0.363173
$387$	5.66229	0.287830
$388$	13.9120	0.706275
$389$	−8.23104	−0.417330	−0.208665	−	0.977987i	$-0.566912\pi$
$389$	−8.23104	−0.417330	−0.208665	+	0.977987i	$0.566912\pi$
$390$	3.99105	0.202094
$391$	5.86448	0.296579
$392$	0	0
$393$	−58.0941	−2.93046
$394$	−24.3818	−1.22834
$395$	−2.63723	−0.132694
$396$	3.73329	0.187605
$397$	7.05555	0.354108	0.177054	−	0.984201i	$-0.443343\pi$
$397$	7.05555	0.354108	0.177054	+	0.984201i	$0.443343\pi$
$398$	−24.7356	−1.23988
$399$	0	0
$400$	6.11932	0.305966
$401$	32.5397	1.62495	0.812477	−	0.582993i	$-0.198118\pi$
$401$	32.5397	1.62495	0.812477	+	0.582993i	$0.198118\pi$
$402$	7.54705	0.376413
$403$	1.34233	0.0668663
$404$	−5.48968	−0.273122
$405$	−2.32968	−0.115763
$406$	0	0
$407$	7.67567	0.380469
$408$	−55.2719	−2.73637
$409$	4.62355	0.228620	0.114310	−	0.993445i	$-0.463534\pi$
$409$	4.62355	0.228620	0.114310	+	0.993445i	$0.463534\pi$
$410$	−1.49982	−0.0740709
$411$	−22.0369	−1.08700
$412$	14.4262	0.710727
$413$	0	0
$414$	4.59387	0.225776
$415$	12.5080	0.613992
$416$	3.87397	0.189937
$417$	19.6533	0.962426
$418$	−8.50681	−0.416082
$419$	13.1741	0.643598	0.321799	−	0.946808i	$-0.395712\pi$
$419$	13.1741	0.643598	0.321799	+	0.946808i	$0.395712\pi$
$420$	0	0
$421$	30.1903	1.47139	0.735693	−	0.677316i	$-0.236857\pi$
$421$	30.1903	1.47139	0.735693	+	0.677316i	$0.236857\pi$
$422$	18.7707	0.913745
$423$	−36.0067	−1.75070
$424$	−20.2552	−0.983681
$425$	−20.8400	−1.01089
$426$	7.39446	0.358263
$427$	0	0
$428$	8.82008	0.426335
$429$	−2.86666	−0.138403
$430$	1.85221	0.0893214
$431$	−5.94948	−0.286576	−0.143288	−	0.989681i	$-0.545768\pi$
$431$	−5.94948	−0.286576	−0.143288	+	0.989681i	$0.545768\pi$
$432$	−8.36865	−0.402637
$433$	−27.8876	−1.34019	−0.670096	−	0.742274i	$-0.733747\pi$
$433$	−27.8876	−1.34019	−0.670096	+	0.742274i	$0.733747\pi$
$434$	0	0
$435$	10.4598	0.501509
$436$	−12.8826	−0.616966
$437$	6.35907	0.304195
$438$	−24.9469	−1.19201
$439$	−25.4479	−1.21456	−0.607281	−	0.794487i	$-0.707740\pi$
$439$	−25.4479	−1.21456	−0.607281	+	0.794487i	$0.707740\pi$
$440$	4.45266	0.212272
$441$	0	0
$442$	7.03628	0.334682
$443$	9.42035	0.447575	0.223787	−	0.974638i	$-0.428158\pi$
$443$	9.42035	0.447575	0.223787	+	0.974638i	$0.428158\pi$
$444$	14.8316	0.703877
$445$	−17.2047	−0.815582
$446$	−4.30295	−0.203751
$447$	−30.2347	−1.43005
$448$	0	0
$449$	−23.2678	−1.09808	−0.549038	−	0.835798i	$-0.685006\pi$
$449$	−23.2678	−1.09808	−0.549038	+	0.835798i	$0.685006\pi$
$450$	−16.3247	−0.769555
$451$	1.07728	0.0507271
$452$	3.58577	0.168660
$453$	54.6300	2.56674
$454$	31.4458	1.47582
$455$	0	0
$456$	−59.9334	−2.80664
$457$	4.86796	0.227713	0.113857	−	0.993497i	$-0.463680\pi$
$457$	4.86796	0.227713	0.113857	+	0.993497i	$0.463680\pi$
$458$	16.9808	0.793462
$459$	28.5003	1.33028
$460$	−0.912884	−0.0425635
$461$	−16.1888	−0.753987	−0.376993	−	0.926216i	$-0.623042\pi$
$461$	−16.1888	−0.753987	−0.376993	+	0.926216i	$0.623042\pi$
$462$	0	0
$463$	−12.0971	−0.562200	−0.281100	−	0.959679i	$-0.590699\pi$
$463$	−12.0971	−0.562200	−0.281100	+	0.959679i	$0.590699\pi$
$464$	−5.41484	−0.251378
$465$	5.14480	0.238584
$466$	−32.3669	−1.49937
$467$	−3.23514	−0.149704	−0.0748521	−	0.997195i	$-0.523848\pi$
$467$	−3.23514	−0.149704	−0.0748521	+	0.997195i	$0.523848\pi$
$468$	−3.34836	−0.154778
$469$	0	0
$470$	−11.7782	−0.543290
$471$	26.4983	1.22098
$472$	8.36434	0.385000
$473$	−1.33039	−0.0611713
$474$	−6.02517	−0.276745
$475$	−22.5975	−1.03685
$476$	0	0
$477$	30.2125	1.38334
$478$	27.9282	1.27741
$479$	12.2257	0.558605	0.279303	−	0.960203i	$-0.409897\pi$
$479$	12.2257	0.558605	0.279303	+	0.960203i	$0.409897\pi$
$480$	14.8479	0.677711
$481$	−6.88425	−0.313895
$482$	1.24238	0.0565890
$483$	0	0
$484$	7.43692	0.338042
$485$	−24.7495	−1.12382
$486$	−19.9301	−0.904047
$487$	3.36737	0.152590	0.0762951	−	0.997085i	$-0.475691\pi$
$487$	3.36737	0.152590	0.0762951	+	0.997085i	$0.475691\pi$
$488$	−33.9634	−1.53745
$489$	0.919055	0.0415611
$490$	0	0
$491$	−1.58497	−0.0715286	−0.0357643	−	0.999360i	$-0.511387\pi$
$491$	−1.58497	−0.0715286	−0.0357643	+	0.999360i	$0.511387\pi$
$492$	2.08161	0.0938464
$493$	18.4408	0.830532
$494$	7.62970	0.343276
$495$	−6.64155	−0.298515
$496$	−2.66336	−0.119589
$497$	0	0
$498$	28.5764	1.28054
$499$	−27.5970	−1.23541	−0.617706	−	0.786409i	$-0.711938\pi$
$499$	−27.5970	−1.23541	−0.617706	+	0.786409i	$0.711938\pi$
$500$	8.32550	0.372328
$501$	45.9326	2.05212
$502$	−8.11835	−0.362340
$503$	0.387957	0.0172982	0.00864908	−	0.999963i	$-0.497247\pi$
$503$	0.387957	0.0172982	0.00864908	+	0.999963i	$0.497247\pi$
$504$	0	0
$505$	9.76617	0.434589
$506$	−1.07936	−0.0479832
$507$	−33.2321	−1.47589
$508$	7.52222	0.333744
$509$	38.7667	1.71830	0.859151	−	0.511722i	$-0.170992\pi$
$509$	38.7667	1.71830	0.859151	+	0.511722i	$0.170992\pi$
$510$	26.9682	1.19417
$511$	0	0
$512$	−19.4724	−0.860565
$513$	30.9039	1.36444
$514$	9.92664	0.437845
$515$	−25.6643	−1.13090
$516$	−2.57069	−0.113168
$517$	8.45998	0.372069
$518$	0	0
$519$	35.6539	1.56503
$520$	−3.99356	−0.175129
$521$	0.619049	0.0271210	0.0135605	−	0.999908i	$-0.495683\pi$
$521$	0.619049	0.0271210	0.0135605	+	0.999908i	$0.495683\pi$
$522$	14.4454	0.632257
$523$	1.03218	0.0451341	0.0225670	−	0.999745i	$-0.492816\pi$
$523$	1.03218	0.0451341	0.0225670	+	0.999745i	$0.492816\pi$
$524$	15.9432	0.696481
$525$	0	0
$526$	−6.57956	−0.286883
$527$	9.07036	0.395111
$528$	5.68783	0.247531
$529$	−22.1932	−0.964920
$530$	9.88290	0.429286
$531$	−12.4762	−0.541420
$532$	0	0
$533$	−0.966204	−0.0418509
$534$	−39.3069	−1.70097
$535$	−15.6910	−0.678380
$536$	−7.55180	−0.326188
$537$	47.0008	2.02824
$538$	−4.67065	−0.201366
$539$	0	0
$540$	−4.43645	−0.190915
$541$	38.3318	1.64801	0.824007	−	0.566580i	$-0.191734\pi$
$541$	38.3318	1.64801	0.824007	+	0.566580i	$0.191734\pi$
$542$	−11.2101	−0.481516
$543$	1.10988	0.0476294
$544$	26.1771	1.12233
$545$	22.9183	0.981710
$546$	0	0
$547$	1.37593	0.0588306	0.0294153	−	0.999567i	$-0.490635\pi$
$547$	1.37593	0.0588306	0.0294153	+	0.999567i	$0.490635\pi$
$548$	6.04775	0.258347
$549$	50.6596	2.16210
$550$	3.83559	0.163550
$551$	19.9960	0.851860
$552$	−7.60443	−0.323666
$553$	0	0
$554$	−6.87780	−0.292210
$555$	−26.3855	−1.12000
$556$	−5.39359	−0.228739
$557$	−14.8018	−0.627174	−0.313587	−	0.949560i	$-0.601531\pi$
$557$	−14.8018	−0.627174	−0.313587	+	0.949560i	$0.601531\pi$
$558$	7.10516	0.300785
$559$	1.19322	0.0504676
$560$	0	0
$561$	−19.3705	−0.817823
$562$	−7.40698	−0.312445
$563$	−32.7991	−1.38232	−0.691158	−	0.722704i	$-0.742899\pi$
$563$	−32.7991	−1.38232	−0.691158	+	0.722704i	$0.742899\pi$
$564$	16.3471	0.688337
$565$	−6.37910	−0.268371
$566$	−36.1864	−1.52103
$567$	0	0
$568$	−7.39911	−0.310460
$569$	12.7274	0.533562	0.266781	−	0.963757i	$-0.414040\pi$
$569$	12.7274	0.533562	0.266781	+	0.963757i	$0.414040\pi$
$570$	29.2426	1.22484
$571$	25.8904	1.08348	0.541740	−	0.840546i	$-0.317766\pi$
$571$	25.8904	1.08348	0.541740	+	0.840546i	$0.317766\pi$
$572$	0.786717	0.0328943
$573$	−37.4746	−1.56552
$574$	0	0
$575$	−2.86721	−0.119571
$576$	38.0852	1.58688
$577$	15.7044	0.653784	0.326892	−	0.945062i	$-0.393999\pi$
$577$	15.7044	0.653784	0.326892	+	0.945062i	$0.393999\pi$
$578$	28.5831	1.18890
$579$	−17.6175	−0.732160
$580$	−2.87056	−0.119193
$581$	0	0
$582$	−56.5441	−2.34383
$583$	−7.09861	−0.293994
$584$	24.9626	1.03296
$585$	5.95675	0.246281
$586$	−4.04957	−0.167286
$587$	11.2577	0.464653	0.232327	−	0.972638i	$-0.425366\pi$
$587$	11.2577	0.464653	0.232327	+	0.972638i	$0.425366\pi$
$588$	0	0
$589$	9.83533	0.405258
$590$	−4.08112	−0.168017
$591$	−60.2009	−2.47634
$592$	13.6593	0.561393
$593$	3.77210	0.154902	0.0774508	−	0.996996i	$-0.475322\pi$
$593$	3.77210	0.154902	0.0774508	+	0.996996i	$0.475322\pi$
$594$	−5.24548	−0.215224
$595$	0	0
$596$	8.29752	0.339880
$597$	−61.0746	−2.49962
$598$	0.968066	0.0395872
$599$	22.1317	0.904278	0.452139	−	0.891947i	$-0.350661\pi$
$599$	22.1317	0.904278	0.452139	+	0.891947i	$0.350661\pi$
$600$	27.0231	1.10321
$601$	−16.4817	−0.672301	−0.336151	−	0.941808i	$-0.609125\pi$
$601$	−16.4817	−0.672301	−0.336151	+	0.941808i	$0.609125\pi$
$602$	0	0
$603$	11.2642	0.458713
$604$	−14.9925	−0.610036
$605$	−13.2303	−0.537889
$606$	22.3123	0.906376
$607$	−14.0566	−0.570539	−0.285270	−	0.958447i	$-0.592083\pi$
$607$	−14.0566	−0.570539	−0.285270	+	0.958447i	$0.592083\pi$
$608$	28.3848	1.15116
$609$	0	0
$610$	16.5714	0.670956
$611$	−7.58769	−0.306965
$612$	−22.6254	−0.914579
$613$	−36.8757	−1.48939	−0.744697	−	0.667403i	$-0.767406\pi$
$613$	−36.8757	−1.48939	−0.744697	+	0.667403i	$0.767406\pi$
$614$	0.715571	0.0288781
$615$	−3.70320	−0.149328
$616$	0	0
$617$	7.53517	0.303354	0.151677	−	0.988430i	$-0.451533\pi$
$617$	7.53517	0.303354	0.151677	+	0.988430i	$0.451533\pi$
$618$	−58.6340	−2.35860
$619$	−22.5002	−0.904358	−0.452179	−	0.891927i	$-0.649353\pi$
$619$	−22.5002	−0.904358	−0.452179	+	0.891927i	$0.649353\pi$
$620$	−1.41192	−0.0567042
$621$	3.92113	0.157350
$622$	13.2086	0.529617
$623$	0	0
$624$	−5.10137	−0.204218
$625$	1.14891	0.0459564
$626$	−22.0077	−0.879606
$627$	−21.0041	−0.838824
$628$	−7.27213	−0.290190
$629$	−46.5181	−1.85480
$630$	0	0
$631$	25.4663	1.01380	0.506899	−	0.862005i	$-0.330792\pi$
$631$	25.4663	1.01380	0.506899	+	0.862005i	$0.330792\pi$
$632$	6.02896	0.239819
$633$	46.3467	1.84212
$634$	27.3352	1.08562
$635$	−13.3821	−0.531051
$636$	−13.7166	−0.543897
$637$	0	0
$638$	−3.39403	−0.134371
$639$	11.0365	0.436595
$640$	1.67573	0.0662390
$641$	45.2070	1.78557	0.892785	−	0.450483i	$-0.148748\pi$
$641$	45.2070	1.78557	0.892785	+	0.450483i	$0.148748\pi$
$642$	−35.8485	−1.41483
$643$	−7.05984	−0.278413	−0.139206	−	0.990263i	$-0.544455\pi$
$643$	−7.05984	−0.278413	−0.139206	+	0.990263i	$0.544455\pi$
$644$	0	0
$645$	4.57328	0.180073
$646$	51.5552	2.02841
$647$	0.683172	0.0268583	0.0134291	−	0.999910i	$-0.495725\pi$
$647$	0.683172	0.0268583	0.0134291	+	0.999910i	$0.495725\pi$
$648$	5.32586	0.209220
$649$	2.93135	0.115066
$650$	−3.44011	−0.134932
$651$	0	0
$652$	−0.252223	−0.00987780
$653$	−17.1829	−0.672419	−0.336210	−	0.941787i	$-0.609145\pi$
$653$	−17.1829	−0.672419	−0.336210	+	0.941787i	$0.609145\pi$
$654$	52.3603	2.04745
$655$	−28.3630	−1.10823
$656$	1.91708	0.0748493
$657$	−37.2340	−1.45264
$658$	0	0
$659$	−7.11888	−0.277312	−0.138656	−	0.990341i	$-0.544278\pi$
$659$	−7.11888	−0.277312	−0.138656	+	0.990341i	$0.544278\pi$
$660$	3.01528	0.117369
$661$	24.3519	0.947180	0.473590	−	0.880745i	$-0.342958\pi$
$661$	24.3519	0.947180	0.473590	+	0.880745i	$0.342958\pi$
$662$	31.0424	1.20650
$663$	17.3732	0.674721
$664$	−28.5944	−1.10968
$665$	0	0
$666$	−36.4394	−1.41200
$667$	2.53713	0.0982379
$668$	−12.6056	−0.487726
$669$	−10.6244	−0.410763
$670$	3.68466	0.142351
$671$	−11.9028	−0.459501
$672$	0	0
$673$	45.7116	1.76205	0.881027	−	0.473066i	$-0.156853\pi$
$673$	45.7116	1.76205	0.881027	+	0.473066i	$0.156853\pi$
$674$	0.262562	0.0101135
$675$	−13.9341	−0.536324
$676$	9.12013	0.350774
$677$	−22.1983	−0.853151	−0.426576	−	0.904452i	$-0.640280\pi$
$677$	−22.1983	−0.853151	−0.426576	+	0.904452i	$0.640280\pi$
$678$	−14.5740	−0.559713
$679$	0	0
$680$	−26.9851	−1.03483
$681$	77.6427	2.97527
$682$	−1.66940	−0.0639246
$683$	11.3820	0.435522	0.217761	−	0.976002i	$-0.430125\pi$
$683$	11.3820	0.435522	0.217761	+	0.976002i	$0.430125\pi$
$684$	−24.5336	−0.938066
$685$	−10.7590	−0.411079
$686$	0	0
$687$	41.9273	1.59963
$688$	−2.36750	−0.0902601
$689$	6.36669	0.242552
$690$	3.71034	0.141250
$691$	38.3097	1.45737	0.728685	−	0.684849i	$-0.240132\pi$
$691$	38.3097	1.45737	0.728685	+	0.684849i	$0.240132\pi$
$692$	−9.78476	−0.371961
$693$	0	0
$694$	−0.567761	−0.0215519
$695$	9.59523	0.363968
$696$	−23.9121	−0.906385
$697$	−6.52880	−0.247296
$698$	26.6210	1.00762
$699$	−79.9170	−3.02274
$700$	0	0
$701$	−31.1871	−1.17792	−0.588961	−	0.808162i	$-0.700463\pi$
$701$	−31.1871	−1.17792	−0.588961	+	0.808162i	$0.700463\pi$
$702$	4.70463	0.177565
$703$	−50.4413	−1.90243
$704$	−8.94835	−0.337254
$705$	−29.0816	−1.09528
$706$	−15.1732	−0.571050
$707$	0	0
$708$	5.66421	0.212874
$709$	24.9158	0.935733	0.467867	−	0.883799i	$-0.345023\pi$
$709$	24.9158	0.935733	0.467867	+	0.883799i	$0.345023\pi$
$710$	3.61016	0.135487
$711$	−8.99274	−0.337254
$712$	39.3316	1.47401
$713$	1.24792	0.0467349
$714$	0	0
$715$	−1.39957	−0.0523411
$716$	−12.8988	−0.482050
$717$	68.9574	2.57526
$718$	−5.40867	−0.201850
$719$	−41.1707	−1.53541	−0.767704	−	0.640804i	$-0.778601\pi$
$719$	−41.1707	−1.53541	−0.767704	+	0.640804i	$0.778601\pi$
$720$	−11.8190	−0.440468
$721$	0	0
$722$	34.7101	1.29178
$723$	3.06756	0.114084
$724$	−0.304591	−0.0113200
$725$	−9.01591	−0.334843
$726$	−30.2267	−1.12182
$727$	2.84985	0.105695	0.0528475	−	0.998603i	$-0.483170\pi$
$727$	2.84985	0.105695	0.0528475	+	0.998603i	$0.483170\pi$
$728$	0	0
$729$	−44.0115	−1.63005
$730$	−12.1797	−0.450791
$731$	8.06276	0.298212
$732$	−22.9996	−0.850088
$733$	−36.0067	−1.32994	−0.664968	−	0.746872i	$-0.731555\pi$
$733$	−36.0067	−1.32994	−0.664968	+	0.746872i	$0.731555\pi$
$734$	22.5711	0.833113
$735$	0	0
$736$	3.60150	0.132753
$737$	−2.64659	−0.0974883
$738$	−5.11426	−0.188258
$739$	−5.90631	−0.217267	−0.108634	−	0.994082i	$-0.534648\pi$
$739$	−5.90631	−0.217267	−0.108634	+	0.994082i	$0.534648\pi$
$740$	7.24116	0.266190
$741$	18.8385	0.692048
$742$	0	0
$743$	−47.1256	−1.72887	−0.864436	−	0.502744i	$-0.832324\pi$
$743$	−47.1256	−1.72887	−0.864436	+	0.502744i	$0.832324\pi$
$744$	−11.7615	−0.431197
$745$	−14.7613	−0.540814
$746$	−15.7130	−0.575295
$747$	42.6511	1.56052
$748$	5.31598	0.194371
$749$	0	0
$750$	−33.8383	−1.23560
$751$	−3.99429	−0.145754	−0.0728768	−	0.997341i	$-0.523218\pi$
$751$	−3.99429	−0.145754	−0.0728768	+	0.997341i	$0.523218\pi$
$752$	15.0550	0.548999
$753$	−20.0450	−0.730480
$754$	3.04408	0.110859
$755$	26.6717	0.970683
$756$	0	0
$757$	0.0523804	0.00190380	0.000951899	−	1.00000i	$-0.499697\pi$
$757$	0.0523804	0.00190380	0.000951899		1.00000i	$0.499697\pi$
$758$	−2.62407	−0.0953104
$759$	−2.66503	−0.0967346
$760$	−29.2610	−1.06141
$761$	−47.4215	−1.71903	−0.859515	−	0.511111i	$-0.829234\pi$
$761$	−47.4215	−1.71903	−0.859515	+	0.511111i	$0.829234\pi$
$762$	−30.5734	−1.10756
$763$	0	0
$764$	10.2844	0.372077
$765$	40.2508	1.45527
$766$	13.2182	0.477592
$767$	−2.62911	−0.0949315
$768$	−41.9249	−1.51283
$769$	24.0845	0.868508	0.434254	−	0.900790i	$-0.357012\pi$
$769$	24.0845	0.868508	0.434254	+	0.900790i	$0.357012\pi$
$770$	0	0
$771$	24.5098	0.882700
$772$	4.83490	0.174012
$773$	−25.7537	−0.926297	−0.463148	−	0.886281i	$-0.653280\pi$
$773$	−25.7537	−0.926297	−0.463148	+	0.886281i	$0.653280\pi$
$774$	6.31587	0.227019
$775$	−4.43460	−0.159295
$776$	56.5797	2.03109
$777$	0	0
$778$	−9.18111	−0.329159
$779$	−7.07942	−0.253647
$780$	−2.70438	−0.0968323
$781$	−2.59308	−0.0927877
$782$	6.54139	0.233920
$783$	12.3300	0.440637
$784$	0	0
$785$	12.9372	0.461747
$786$	−64.7997	−2.31133
$787$	30.9026	1.10156	0.550780	−	0.834651i	$-0.314330\pi$
$787$	30.9026	1.10156	0.550780	+	0.834651i	$0.314330\pi$
$788$	16.5214	0.588549
$789$	−16.2456	−0.578358
$790$	−2.94164	−0.104659
$791$	0	0
$792$	15.1832	0.539511
$793$	10.6755	0.379098
$794$	7.86994	0.279294
$795$	24.4018	0.865444
$796$	16.7611	0.594083
$797$	39.1277	1.38598	0.692988	−	0.720949i	$-0.256294\pi$
$797$	39.1277	1.38598	0.692988	+	0.720949i	$0.256294\pi$
$798$	0	0
$799$	−51.2713	−1.81385
$800$	−12.7983	−0.452487
$801$	−58.6666	−2.07288
$802$	36.2956	1.28164
$803$	8.74834	0.308722
$804$	−5.11397	−0.180356
$805$	0	0
$806$	1.49727	0.0527391
$807$	−11.5323	−0.405956
$808$	−22.3264	−0.785438
$809$	15.7632	0.554205	0.277102	−	0.960840i	$-0.410626\pi$
$809$	15.7632	0.554205	0.277102	+	0.960840i	$0.410626\pi$
$810$	−2.59858	−0.0913049
$811$	32.9193	1.15595	0.577976	−	0.816054i	$-0.303843\pi$
$811$	32.9193	1.15595	0.577976	+	0.816054i	$0.303843\pi$
$812$	0	0
$813$	−27.6789	−0.970740
$814$	8.56164	0.300085
$815$	0.448706	0.0157175
$816$	−34.4708	−1.20672
$817$	8.74275	0.305870
$818$	5.15722	0.180318
$819$	0	0
$820$	1.01630	0.0354906
$821$	−41.7837	−1.45826	−0.729131	−	0.684375i	$-0.760075\pi$
$821$	−41.7837	−1.45826	−0.729131	+	0.684375i	$0.760075\pi$
$822$	−24.5805	−0.857345
$823$	35.0046	1.22018	0.610091	−	0.792331i	$-0.291133\pi$
$823$	35.0046	1.22018	0.610091	+	0.792331i	$0.291133\pi$
$824$	58.6708	2.04390
$825$	9.47044	0.329719
$826$	0	0
$827$	16.3017	0.566866	0.283433	−	0.958992i	$-0.408527\pi$
$827$	16.3017	0.566866	0.283433	+	0.958992i	$0.408527\pi$
$828$	−3.11286	−0.108179
$829$	−21.1961	−0.736171	−0.368085	−	0.929792i	$-0.619987\pi$
$829$	−21.1961	−0.736171	−0.368085	+	0.929792i	$0.619987\pi$
$830$	13.9517	0.484271
$831$	−16.9819	−0.589097
$832$	8.02571	0.278241
$833$	0	0
$834$	21.9218	0.759089
$835$	22.4255	0.776065
$836$	5.76431	0.199363
$837$	6.06466	0.209625
$838$	14.6948	0.507622
$839$	−33.6120	−1.16042	−0.580208	−	0.814468i	$-0.697029\pi$
$839$	−33.6120	−1.16042	−0.580208	+	0.814468i	$0.697029\pi$
$840$	0	0
$841$	−21.0220	−0.724897
$842$	33.6750	1.16052
$843$	−18.2885	−0.629891
$844$	−12.7193	−0.437815
$845$	−16.2248	−0.558149
$846$	−40.1628	−1.38082
$847$	0	0
$848$	−12.6324	−0.433797
$849$	−89.3477	−3.06640
$850$	−23.2454	−0.797312
$851$	−6.40006	−0.219391
$852$	−5.01057	−0.171659
$853$	49.5839	1.69772	0.848860	−	0.528618i	$-0.177289\pi$
$853$	49.5839	1.69772	0.848860	+	0.528618i	$0.177289\pi$
$854$	0	0
$855$	43.6454	1.49264
$856$	35.8710	1.22605
$857$	40.8291	1.39470	0.697348	−	0.716732i	$-0.254363\pi$
$857$	40.8291	1.39470	0.697348	+	0.716732i	$0.254363\pi$
$858$	−3.19754	−0.109162
$859$	5.75495	0.196356	0.0981782	−	0.995169i	$-0.468698\pi$
$859$	5.75495	0.196356	0.0981782	+	0.995169i	$0.468698\pi$
$860$	−1.25508	−0.0427978
$861$	0	0
$862$	−6.63621	−0.226030
$863$	−5.44313	−0.185286	−0.0926432	−	0.995699i	$-0.529532\pi$
$863$	−5.44313	−0.185286	−0.0926432	+	0.995699i	$0.529532\pi$
$864$	17.5027	0.595452
$865$	17.4071	0.591860
$866$	−31.1066	−1.05704
$867$	70.5744	2.39683
$868$	0	0
$869$	2.11290	0.0716751
$870$	11.6671	0.395553
$871$	2.37370	0.0804299
$872$	−52.3932	−1.77426
$873$	−84.3937	−2.85629
$874$	7.09307	0.239927
$875$	0	0
$876$	16.9043	0.571144
$877$	−0.0377361	−0.00127426	−0.000637128	−	1.00000i	$-0.500203\pi$
$877$	−0.0377361	−0.00127426	−0.000637128		1.00000i	$0.500203\pi$
$878$	−28.3852	−0.957956
$879$	−9.99877	−0.337250
$880$	2.77694	0.0936107
$881$	−43.4095	−1.46250	−0.731252	−	0.682108i	$-0.761064\pi$
$881$	−43.4095	−1.46250	−0.731252	+	0.682108i	$0.761064\pi$
$882$	0	0
$883$	29.9703	1.00858	0.504291	−	0.863534i	$-0.331754\pi$
$883$	29.9703	1.00858	0.504291	+	0.863534i	$0.331754\pi$
$884$	−4.76786	−0.160361
$885$	−10.0767	−0.338723
$886$	10.5077	0.353013
$887$	19.5093	0.655059	0.327529	−	0.944841i	$-0.393784\pi$
$887$	19.5093	0.655059	0.327529	+	0.944841i	$0.393784\pi$
$888$	60.3197	2.02420
$889$	0	0
$890$	−19.1906	−0.643270
$891$	1.86649	0.0625298
$892$	2.91573	0.0976259
$893$	−55.5954	−1.86043
$894$	−33.7246	−1.12792
$895$	22.9470	0.767033
$896$	0	0
$897$	2.39025	0.0798081
$898$	−25.9535	−0.866080
$899$	3.92407	0.130875
$900$	11.0618	0.368728
$901$	43.0208	1.43323
$902$	1.20163	0.0400097
$903$	0	0
$904$	14.5832	0.485031
$905$	0.541870	0.0180124
$906$	60.9357	2.02445
$907$	35.2788	1.17141	0.585707	−	0.810523i	$-0.300817\pi$
$907$	35.2788	1.17141	0.585707	+	0.810523i	$0.300817\pi$
$908$	−21.3080	−0.707132
$909$	33.3018	1.10455
$910$	0	0
$911$	15.2689	0.505882	0.252941	−	0.967482i	$-0.418602\pi$
$911$	15.2689	0.505882	0.252941	+	0.967482i	$0.418602\pi$
$912$	−37.3780	−1.23771
$913$	−10.0211	−0.331651
$914$	5.42984	0.179603
$915$	40.9163	1.35265
$916$	−11.5064	−0.380182
$917$	0	0
$918$	31.7900	1.04923
$919$	52.3612	1.72724	0.863619	−	0.504145i	$-0.168192\pi$
$919$	52.3612	1.72724	0.863619	+	0.504145i	$0.168192\pi$
$920$	−3.71267	−0.122403
$921$	1.76681	0.0582185
$922$	−18.0574	−0.594688
$923$	2.32571	0.0765518
$924$	0	0
$925$	22.7432	0.747792
$926$	−13.4934	−0.443421
$927$	−87.5129	−2.87430
$928$	11.3249	0.371758
$929$	−46.0886	−1.51212	−0.756060	−	0.654503i	$-0.772878\pi$
$929$	−46.0886	−1.51212	−0.756060	+	0.654503i	$0.772878\pi$
$930$	5.73864	0.188177
$931$	0	0
$932$	21.9322	0.718413
$933$	32.6133	1.06771
$934$	−3.60856	−0.118076
$935$	−9.45716	−0.309282
$936$	−13.6177	−0.445108
$937$	33.6725	1.10003	0.550016	−	0.835154i	$-0.314622\pi$
$937$	33.6725	1.10003	0.550016	+	0.835154i	$0.314622\pi$
$938$	0	0
$939$	−54.3392	−1.77329
$940$	7.98107	0.260314
$941$	9.44269	0.307823	0.153911	−	0.988085i	$-0.450813\pi$
$941$	9.44269	0.307823	0.153911	+	0.988085i	$0.450813\pi$
$942$	29.5569	0.963017
$943$	−0.898247	−0.0292509
$944$	5.21650	0.169783
$945$	0	0
$946$	−1.48395	−0.0482474
$947$	−30.4919	−0.990853	−0.495427	−	0.868650i	$-0.664988\pi$
$947$	−30.4919	−0.990853	−0.495427	+	0.868650i	$0.664988\pi$
$948$	4.08272	0.132601
$949$	−7.84632	−0.254702
$950$	−25.2059	−0.817787
$951$	67.4932	2.18862
$952$	0	0
$953$	−60.9536	−1.97448	−0.987241	−	0.159235i	$-0.949097\pi$
$953$	−60.9536	−1.97448	−0.987241	+	0.159235i	$0.949097\pi$
$954$	33.6998	1.09107
$955$	−18.2961	−0.592046
$956$	−18.9245	−0.612061
$957$	−8.38018	−0.270893
$958$	13.6368	0.440586
$959$	0	0
$960$	30.7604	0.992787
$961$	−29.0699	−0.937738
$962$	−7.67887	−0.247577
$963$	−53.5049	−1.72417
$964$	−0.841853	−0.0271143
$965$	−8.60132	−0.276886
$966$	0	0
$967$	13.3405	0.429001	0.214501	−	0.976724i	$-0.431188\pi$
$967$	13.3405	0.429001	0.214501	+	0.976724i	$0.431188\pi$
$968$	30.2457	0.972135
$969$	127.295	4.08929
$970$	−27.6063	−0.886383
$971$	−14.3391	−0.460163	−0.230081	−	0.973171i	$-0.573899\pi$
$971$	−14.3391	−0.460163	−0.230081	+	0.973171i	$0.573899\pi$
$972$	13.5048	0.433168
$973$	0	0
$974$	3.75605	0.120352
$975$	−8.49397	−0.272025
$976$	−21.1816	−0.678007
$977$	46.5148	1.48814	0.744069	−	0.668102i	$-0.232893\pi$
$977$	46.5148	1.48814	0.744069	+	0.668102i	$0.232893\pi$
$978$	1.02514	0.0327803
$979$	13.7841	0.440541
$980$	0	0
$981$	78.1493	2.49511
$982$	−1.76791	−0.0564164
$983$	43.7876	1.39661	0.698303	−	0.715802i	$-0.253939\pi$
$983$	43.7876	1.39661	0.698303	+	0.715802i	$0.253939\pi$
$984$	8.46586	0.269882
$985$	−29.3916	−0.936494
$986$	20.5693	0.655062
$987$	0	0
$988$	−5.16997	−0.164479
$989$	1.10929	0.0352734
$990$	−7.40815	−0.235447
$991$	−8.16795	−0.259463	−0.129732	−	0.991549i	$-0.541412\pi$
$991$	−8.16795	−0.259463	−0.129732	+	0.991549i	$0.541412\pi$
$992$	5.57030	0.176857
$993$	76.6468	2.43231
$994$	0	0
$995$	−29.8182	−0.945299
$996$	−19.3637	−0.613562
$997$	44.3813	1.40557	0.702786	−	0.711402i	$-0.251939\pi$
$997$	44.3813	1.40557	0.702786	+	0.711402i	$0.251939\pi$
$998$	−30.7824	−0.974401
$999$	−31.1031	−0.984059

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2009.2.a.r.1.10		17
7.3	odd	6		287.2.e.d.247.8	yes	34
7.5	odd	6		287.2.e.d.165.8	✓	34
7.6	odd	2		2009.2.a.s.1.10		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.e.d.165.8	✓	34	7.5	odd	6
287.2.e.d.247.8	yes	34	7.3	odd	6
2009.2.a.r.1.10		17	1.1	even	1	trivial
2009.2.a.s.1.10		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)

\(f(q)\)	\(=\)	\(q+1.11543 q^{2} +2.75409 q^{3} -0.755825 q^{4} +1.34462 q^{5} +3.07199 q^{6} -3.07392 q^{8} +4.58503 q^{9} +O(q^{10})\)	\(q+1.11543 q^{2} +2.75409 q^{3} -0.755825 q^{4} +1.34462 q^{5} +3.07199 q^{6} -3.07392 q^{8} +4.58503 q^{9} +1.49982 q^{10} -1.07728 q^{11} -2.08161 q^{12} +0.966204 q^{13} +3.70320 q^{15} -1.91708 q^{16} +6.52880 q^{17} +5.11426 q^{18} +7.07942 q^{19} -1.01630 q^{20} -1.20163 q^{22} +0.898247 q^{23} -8.46586 q^{24} -3.19200 q^{25} +1.07773 q^{26} +4.36532 q^{27} +2.82453 q^{29} +4.13065 q^{30} +1.38928 q^{31} +4.00948 q^{32} -2.96693 q^{33} +7.28240 q^{34} -3.46548 q^{36} -7.12505 q^{37} +7.89657 q^{38} +2.66102 q^{39} -4.13324 q^{40} -1.00000 q^{41} +1.23495 q^{43} +0.814235 q^{44} +6.16511 q^{45} +1.00193 q^{46} -7.85310 q^{47} -5.27981 q^{48} -3.56044 q^{50} +17.9809 q^{51} -0.730281 q^{52} +6.58939 q^{53} +4.86919 q^{54} -1.44853 q^{55} +19.4974 q^{57} +3.15055 q^{58} -2.72107 q^{59} -2.79897 q^{60} +11.0489 q^{61} +1.54964 q^{62} +8.30643 q^{64} +1.29917 q^{65} -3.30939 q^{66} +2.45673 q^{67} -4.93463 q^{68} +2.47385 q^{69} +2.40706 q^{71} -14.0940 q^{72} -8.12078 q^{73} -7.94747 q^{74} -8.79108 q^{75} -5.35081 q^{76} +2.96816 q^{78} -1.96133 q^{79} -2.57774 q^{80} -1.73260 q^{81} -1.11543 q^{82} +9.30225 q^{83} +8.77874 q^{85} +1.37750 q^{86} +7.77902 q^{87} +3.31147 q^{88} -12.7953 q^{89} +6.87672 q^{90} -0.678918 q^{92} +3.82622 q^{93} -8.75955 q^{94} +9.51912 q^{95} +11.0425 q^{96} -18.4064 q^{97} -4.93936 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 3 q^{2} - q^{3} + 25 q^{4} + q^{5} - 2 q^{6} + 9 q^{8} + 26 q^{9}+O(q^{10}) \) 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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