LMFDB - Embedded newform 2009.2.a.s.1.4

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			1.4
Root			$-1.77896$ 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)

$f(q)$	$=$	$q-1.77896 q^{2} +1.20779 q^{3} +1.16468 q^{4} -2.53283 q^{5} -2.14861 q^{6} +1.48599 q^{8} -1.54123 q^{9} +O(q^{10})$	\(q-1.77896 q^{2} +1.20779 q^{3} +1.16468 q^{4} -2.53283 q^{5} -2.14861 q^{6} +1.48599 q^{8} -1.54123 q^{9} +4.50580 q^{10} +4.69442 q^{11} +1.40670 q^{12} -2.97799 q^{13} -3.05914 q^{15} -4.97288 q^{16} -7.01187 q^{17} +2.74178 q^{18} +2.78486 q^{19} -2.94995 q^{20} -8.35117 q^{22} +4.04356 q^{23} +1.79477 q^{24} +1.41524 q^{25} +5.29771 q^{26} -5.48488 q^{27} +7.66082 q^{29} +5.44208 q^{30} +1.24213 q^{31} +5.87455 q^{32} +5.66990 q^{33} +12.4738 q^{34} -1.79505 q^{36} -5.48369 q^{37} -4.95414 q^{38} -3.59680 q^{39} -3.76377 q^{40} +1.00000 q^{41} +9.18117 q^{43} +5.46752 q^{44} +3.90368 q^{45} -7.19331 q^{46} -7.77039 q^{47} -6.00622 q^{48} -2.51765 q^{50} -8.46890 q^{51} -3.46842 q^{52} -9.44258 q^{53} +9.75735 q^{54} -11.8902 q^{55} +3.36354 q^{57} -13.6283 q^{58} +1.63269 q^{59} -3.56293 q^{60} +13.9531 q^{61} -2.20969 q^{62} -0.504809 q^{64} +7.54275 q^{65} -10.0865 q^{66} -3.75824 q^{67} -8.16662 q^{68} +4.88379 q^{69} -6.77038 q^{71} -2.29026 q^{72} +2.70572 q^{73} +9.75525 q^{74} +1.70932 q^{75} +3.24348 q^{76} +6.39855 q^{78} +12.4767 q^{79} +12.5955 q^{80} -2.00090 q^{81} -1.77896 q^{82} -0.292604 q^{83} +17.7599 q^{85} -16.3329 q^{86} +9.25269 q^{87} +6.97587 q^{88} +2.99498 q^{89} -6.94448 q^{90} +4.70947 q^{92} +1.50023 q^{93} +13.8232 q^{94} -7.05359 q^{95} +7.09525 q^{96} +11.1466 q^{97} -7.23520 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.77896	−1.25791	−0.628956	−	0.777441i	$-0.716517\pi$
$2$	−1.77896	−1.25791	−0.628956	+	0.777441i	$0.716517\pi$
$3$	1.20779	0.697320	0.348660	−	0.937249i	$-0.386637\pi$
$3$	1.20779	0.697320	0.348660	+	0.937249i	$0.386637\pi$
$4$	1.16468	0.582342
$5$	−2.53283	−1.13272	−0.566359	−	0.824159i	$-0.691648\pi$
$5$	−2.53283	−1.13272	−0.566359	+	0.824159i	$0.691648\pi$
$6$	−2.14861	−0.877168
$7$	0	0
$7$	0	0
$8$	1.48599	0.525377
$9$	−1.54123	−0.513744
$10$	4.50580	1.42486
$11$	4.69442	1.41542	0.707711	−	0.706502i	$-0.249728\pi$
$11$	4.69442	1.41542	0.707711	+	0.706502i	$0.249728\pi$
$12$	1.40670	0.406079
$13$	−2.97799	−0.825946	−0.412973	−	0.910743i	$-0.635510\pi$
$13$	−2.97799	−0.825946	−0.412973	+	0.910743i	$0.635510\pi$
$14$	0	0
$15$	−3.05914	−0.789867
$16$	−4.97288	−1.24322
$17$	−7.01187	−1.70063	−0.850315	−	0.526275i	$-0.823588\pi$
$17$	−7.01187	−1.70063	−0.850315	+	0.526275i	$0.823588\pi$
$18$	2.74178	0.646245
$19$	2.78486	0.638891	0.319445	−	0.947605i	$-0.396503\pi$
$19$	2.78486	0.638891	0.319445	+	0.947605i	$0.396503\pi$
$20$	−2.94995	−0.659629
$21$	0	0
$22$	−8.35117	−1.78048
$23$	4.04356	0.843140	0.421570	−	0.906796i	$-0.361479\pi$
$23$	4.04356	0.843140	0.421570	+	0.906796i	$0.361479\pi$
$24$	1.79477	0.366356
$25$	1.41524	0.283048
$26$	5.29771	1.03897
$27$	−5.48488	−1.05556
$28$	0	0
$29$	7.66082	1.42258	0.711289	−	0.702900i	$-0.248112\pi$
$29$	7.66082	1.42258	0.711289	+	0.702900i	$0.248112\pi$
$30$	5.44208	0.993583
$31$	1.24213	0.223092	0.111546	−	0.993759i	$-0.464420\pi$
$31$	1.24213	0.223092	0.111546	+	0.993759i	$0.464420\pi$
$32$	5.87455	1.03848
$33$	5.66990	0.987003
$34$	12.4738	2.13924
$35$	0	0
$36$	−1.79505	−0.299175
$37$	−5.48369	−0.901514	−0.450757	−	0.892647i	$-0.648846\pi$
$37$	−5.48369	−0.901514	−0.450757	+	0.892647i	$0.648846\pi$
$38$	−4.95414	−0.803668
$39$	−3.59680	−0.575949
$40$	−3.76377	−0.595104
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	9.18117	1.40012	0.700058	−	0.714086i	$-0.253157\pi$
$43$	9.18117	1.40012	0.700058	+	0.714086i	$0.253157\pi$
$44$	5.46752	0.824260
$45$	3.90368	0.581927
$46$	−7.19331	−1.06060
$47$	−7.77039	−1.13343	−0.566714	−	0.823915i	$-0.691786\pi$
$47$	−7.77039	−1.13343	−0.566714	+	0.823915i	$0.691786\pi$
$48$	−6.00622	−0.866923
$49$	0	0
$50$	−2.51765	−0.356050
$51$	−8.46890	−1.18588
$52$	−3.46842	−0.480983
$53$	−9.44258	−1.29704	−0.648519	−	0.761198i	$-0.724611\pi$
$53$	−9.44258	−1.29704	−0.648519	+	0.761198i	$0.724611\pi$
$54$	9.75735	1.32781
$55$	−11.8902	−1.60327
$56$	0	0
$57$	3.36354	0.445512
$58$	−13.6283	−1.78948
$59$	1.63269	0.212559	0.106279	−	0.994336i	$-0.466106\pi$
$59$	1.63269	0.212559	0.106279	+	0.994336i	$0.466106\pi$
$60$	−3.56293	−0.459973
$61$	13.9531	1.78651	0.893256	−	0.449548i	$-0.148415\pi$
$61$	13.9531	1.78651	0.893256	+	0.449548i	$0.148415\pi$
$62$	−2.20969	−0.280631
$63$	0	0
$64$	−0.504809	−0.0631012
$65$	7.54275	0.935563
$66$	−10.0865	−1.24156
$67$	−3.75824	−0.459142	−0.229571	−	0.973292i	$-0.573732\pi$
$67$	−3.75824	−0.459142	−0.229571	+	0.973292i	$0.573732\pi$
$68$	−8.16662	−0.990348
$69$	4.88379	0.587939
$70$	0	0
$71$	−6.77038	−0.803497	−0.401748	−	0.915750i	$-0.631597\pi$
$71$	−6.77038	−0.803497	−0.401748	+	0.915750i	$0.631597\pi$
$72$	−2.29026	−0.269909
$73$	2.70572	0.316681	0.158340	−	0.987385i	$-0.449386\pi$
$73$	2.70572	0.316681	0.158340	+	0.987385i	$0.449386\pi$
$74$	9.75525	1.13402
$75$	1.70932	0.197375
$76$	3.24348	0.372053
$77$	0	0
$78$	6.39855	0.724493
$79$	12.4767	1.40374	0.701870	−	0.712306i	$-0.252349\pi$
$79$	12.4767	1.40374	0.701870	+	0.712306i	$0.252349\pi$
$80$	12.5955	1.40822
$81$	−2.00090	−0.222323
$82$	−1.77896	−0.196453
$83$	−0.292604	−0.0321175	−0.0160587	−	0.999871i	$-0.505112\pi$
$83$	−0.292604	−0.0321175	−0.0160587	+	0.999871i	$0.505112\pi$
$84$	0	0
$85$	17.7599	1.92633
$86$	−16.3329	−1.76122
$87$	9.25269	0.991993
$88$	6.97587	0.743630
$89$	2.99498	0.317467	0.158733	−	0.987321i	$-0.449259\pi$
$89$	2.99498	0.317467	0.158733	+	0.987321i	$0.449259\pi$
$90$	−6.94448	−0.732013
$91$	0	0
$92$	4.70947	0.490996
$93$	1.50023	0.155567
$94$	13.8232	1.42575
$95$	−7.05359	−0.723683
$96$	7.09525	0.724156
$97$	11.1466	1.13176	0.565882	−	0.824486i	$-0.308536\pi$
$97$	11.1466	1.13176	0.565882	+	0.824486i	$0.308536\pi$
$98$	0	0
$99$	−7.23520	−0.727165
$100$	1.64831	0.164831
$101$	−1.72165	−0.171311	−0.0856553	−	0.996325i	$-0.527298\pi$
$101$	−1.72165	−0.171311	−0.0856553	+	0.996325i	$0.527298\pi$
$102$	15.0658	1.49174
$103$	15.0433	1.48226	0.741128	−	0.671364i	$-0.234291\pi$
$103$	15.0433	1.48226	0.741128	+	0.671364i	$0.234291\pi$
$104$	−4.42526	−0.433933
$105$	0	0
$106$	16.7979	1.63156
$107$	1.73679	0.167902	0.0839510	−	0.996470i	$-0.473246\pi$
$107$	1.73679	0.167902	0.0839510	+	0.996470i	$0.473246\pi$
$108$	−6.38815	−0.614700
$109$	18.1048	1.73413	0.867064	−	0.498196i	$-0.166004\pi$
$109$	18.1048	1.73413	0.867064	+	0.498196i	$0.166004\pi$
$110$	21.1521	2.01678
$111$	−6.62317	−0.628644
$112$	0	0
$113$	−15.2644	−1.43595	−0.717976	−	0.696068i	$-0.754931\pi$
$113$	−15.2644	−1.43595	−0.717976	+	0.696068i	$0.754931\pi$
$114$	−5.98359	−0.560414
$115$	−10.2417	−0.955039
$116$	8.92243	0.828427
$117$	4.58977	0.424325
$118$	−2.90449	−0.267380
$119$	0	0
$120$	−4.54585	−0.414978
$121$	11.0376	1.00342
$122$	−24.8220	−2.24727
$123$	1.20779	0.108903
$124$	1.44668	0.129916
$125$	9.07960	0.812104
$126$	0	0
$127$	5.98507	0.531090	0.265545	−	0.964099i	$-0.414448\pi$
$127$	5.98507	0.531090	0.265545	+	0.964099i	$0.414448\pi$
$128$	−10.8511	−0.959108
$129$	11.0890	0.976329
$130$	−13.4182	−1.17686
$131$	−6.99392	−0.611061	−0.305531	−	0.952182i	$-0.598834\pi$
$131$	−6.99392	−0.611061	−0.305531	+	0.952182i	$0.598834\pi$
$132$	6.60364	0.574773
$133$	0	0
$134$	6.68574	0.577560
$135$	13.8923	1.19566
$136$	−10.4196	−0.893471
$137$	8.30976	0.709951	0.354975	−	0.934876i	$-0.384489\pi$
$137$	8.30976	0.709951	0.354975	+	0.934876i	$0.384489\pi$
$138$	−8.68804	−0.739575
$139$	−5.14052	−0.436013	−0.218007	−	0.975947i	$-0.569955\pi$
$139$	−5.14052	−0.436013	−0.218007	+	0.975947i	$0.569955\pi$
$140$	0	0
$141$	−9.38504	−0.790363
$142$	12.0442	1.01073
$143$	−13.9799	−1.16906
$144$	7.66436	0.638697
$145$	−19.4036	−1.61138
$146$	−4.81336	−0.398356
$147$	0	0
$148$	−6.38677	−0.524989
$149$	15.0317	1.23144	0.615721	−	0.787964i	$-0.288865\pi$
$149$	15.0317	1.23144	0.615721	+	0.787964i	$0.288865\pi$
$150$	−3.04080	−0.248281
$151$	5.46293	0.444567	0.222284	−	0.974982i	$-0.428649\pi$
$151$	5.46293	0.444567	0.222284	+	0.974982i	$0.428649\pi$
$152$	4.13828	0.335659
$153$	10.8069	0.873688
$154$	0	0
$155$	−3.14610	−0.252701
$156$	−4.18913	−0.335399
$157$	21.9068	1.74835	0.874177	−	0.485607i	$-0.161401\pi$
$157$	21.9068	1.74835	0.874177	+	0.485607i	$0.161401\pi$
$158$	−22.1955	−1.76578
$159$	−11.4047	−0.904451
$160$	−14.8793	−1.17631
$161$	0	0
$162$	3.55952	0.279662
$163$	4.43254	0.347183	0.173592	−	0.984818i	$-0.444463\pi$
$163$	4.43254	0.347183	0.173592	+	0.984818i	$0.444463\pi$
$164$	1.16468	0.0909465
$165$	−14.3609	−1.11800
$166$	0.520530	0.0404009
$167$	−18.3642	−1.42107	−0.710534	−	0.703663i	$-0.751547\pi$
$167$	−18.3642	−1.42107	−0.710534	+	0.703663i	$0.751547\pi$
$168$	0	0
$169$	−4.13158	−0.317814
$170$	−31.5941	−2.42316
$171$	−4.29212	−0.328226
$172$	10.6932	0.815346
$173$	15.0583	1.14486	0.572430	−	0.819954i	$-0.306001\pi$
$173$	15.0583	1.14486	0.572430	+	0.819954i	$0.306001\pi$
$174$	−16.4601	−1.24784
$175$	0	0
$176$	−23.3448	−1.75968
$177$	1.97196	0.148221
$178$	−5.32793	−0.399345
$179$	16.1292	1.20556	0.602778	−	0.797909i	$-0.294060\pi$
$179$	16.1292	1.20556	0.602778	+	0.797909i	$0.294060\pi$
$180$	4.54656	0.338880
$181$	−2.53296	−0.188273	−0.0941366	−	0.995559i	$-0.530009\pi$
$181$	−2.53296	−0.188273	−0.0941366	+	0.995559i	$0.530009\pi$
$182$	0	0
$183$	16.8525	1.24577
$184$	6.00869	0.442966
$185$	13.8893	1.02116
$186$	−2.66885	−0.195690
$187$	−32.9167	−2.40711
$188$	−9.05005	−0.660043
$189$	0	0
$190$	12.5480	0.910329
$191$	20.0577	1.45132	0.725660	−	0.688053i	$-0.241534\pi$
$191$	20.0577	1.45132	0.725660	+	0.688053i	$0.241534\pi$
$192$	−0.609706	−0.0440017
$193$	9.96154	0.717047	0.358524	−	0.933521i	$-0.383280\pi$
$193$	9.96154	0.717047	0.358524	+	0.933521i	$0.383280\pi$
$194$	−19.8293	−1.42366
$195$	9.11009	0.652387
$196$	0	0
$197$	22.6858	1.61630	0.808150	−	0.588977i	$-0.200469\pi$
$197$	22.6858	1.61630	0.808150	+	0.588977i	$0.200469\pi$
$198$	12.8711	0.914709
$199$	−3.20741	−0.227367	−0.113684	−	0.993517i	$-0.536265\pi$
$199$	−3.20741	−0.227367	−0.113684	+	0.993517i	$0.536265\pi$
$200$	2.10303	0.148707
$201$	−4.53918	−0.320169
$202$	3.06274	0.215493
$203$	0	0
$204$	−9.86359	−0.690590
$205$	−2.53283	−0.176901
$206$	−26.7613	−1.86455
$207$	−6.23206	−0.433158
$208$	14.8092	1.02683
$209$	13.0733	0.904300
$210$	0	0
$211$	9.40518	0.647479	0.323740	−	0.946146i	$-0.395060\pi$
$211$	9.40518	0.647479	0.323740	+	0.946146i	$0.395060\pi$
$212$	−10.9976	−0.755320
$213$	−8.17723	−0.560295
$214$	−3.08968	−0.211206
$215$	−23.2544	−1.58594
$216$	−8.15047	−0.554569
$217$	0	0
$218$	−32.2077	−2.18138
$219$	3.26796	0.220828
$220$	−13.8483	−0.933653
$221$	20.8813	1.40463
$222$	11.7823	0.790778
$223$	3.72574	0.249494	0.124747	−	0.992189i	$-0.460188\pi$
$223$	3.72574	0.249494	0.124747	+	0.992189i	$0.460188\pi$
$224$	0	0
$225$	−2.18121	−0.145414
$226$	27.1547	1.80630
$227$	−0.832706	−0.0552687	−0.0276343	−	0.999618i	$-0.508797\pi$
$227$	−0.832706	−0.0552687	−0.0276343	+	0.999618i	$0.508797\pi$
$228$	3.91746	0.259440
$229$	−20.3333	−1.34366	−0.671831	−	0.740704i	$-0.734492\pi$
$229$	−20.3333	−1.34366	−0.671831	+	0.740704i	$0.734492\pi$
$230$	18.2195	1.20136
$231$	0	0
$232$	11.3839	0.747390
$233$	−3.59592	−0.235576	−0.117788	−	0.993039i	$-0.537580\pi$
$233$	−3.59592	−0.235576	−0.117788	+	0.993039i	$0.537580\pi$
$234$	−8.16501	−0.533763
$235$	19.6811	1.28385
$236$	1.90157	0.123782
$237$	15.0693	0.978856
$238$	0	0
$239$	7.82576	0.506206	0.253103	−	0.967439i	$-0.418549\pi$
$239$	7.82576	0.506206	0.253103	+	0.967439i	$0.418549\pi$
$240$	15.2127	0.981978
$241$	−13.0500	−0.840623	−0.420311	−	0.907380i	$-0.638079\pi$
$241$	−13.0500	−0.840623	−0.420311	+	0.907380i	$0.638079\pi$
$242$	−19.6354	−1.26221
$243$	14.0379	0.900535
$244$	16.2510	1.04036
$245$	0	0
$246$	−2.14861	−0.136991
$247$	−8.29329	−0.527689
$248$	1.84579	0.117208
$249$	−0.353406	−0.0223962
$250$	−16.1522	−1.02155
$251$	−2.49236	−0.157316	−0.0786582	−	0.996902i	$-0.525064\pi$
$251$	−2.49236	−0.157316	−0.0786582	+	0.996902i	$0.525064\pi$
$252$	0	0
$253$	18.9822	1.19340
$254$	−10.6472	−0.668064
$255$	21.4503	1.34327
$256$	20.3132	1.26957
$257$	−20.3331	−1.26834	−0.634171	−	0.773193i	$-0.718658\pi$
$257$	−20.3331	−1.26834	−0.634171	+	0.773193i	$0.718658\pi$
$258$	−19.7268	−1.22814
$259$	0	0
$260$	8.78492	0.544817
$261$	−11.8071	−0.730841
$262$	12.4419	0.768661
$263$	−23.6495	−1.45829	−0.729144	−	0.684360i	$-0.760082\pi$
$263$	−23.6495	−1.45829	−0.729144	+	0.684360i	$0.760082\pi$
$264$	8.42542	0.518549
$265$	23.9165	1.46918
$266$	0	0
$267$	3.61732	0.221376
$268$	−4.37716	−0.267378
$269$	4.03278	0.245883	0.122941	−	0.992414i	$-0.460767\pi$
$269$	4.03278	0.245883	0.122941	+	0.992414i	$0.460767\pi$
$270$	−24.7137	−1.50403
$271$	17.7083	1.07570	0.537852	−	0.843039i	$-0.319236\pi$
$271$	17.7083	1.07570	0.537852	+	0.843039i	$0.319236\pi$
$272$	34.8692	2.11426
$273$	0	0
$274$	−14.7827	−0.893055
$275$	6.64374	0.400633
$276$	5.68807	0.342381
$277$	17.5596	1.05506	0.527528	−	0.849538i	$-0.323119\pi$
$277$	17.5596	1.05506	0.527528	+	0.849538i	$0.323119\pi$
$278$	9.14476	0.548466
$279$	−1.91441	−0.114612
$280$	0	0
$281$	−13.2569	−0.790843	−0.395421	−	0.918500i	$-0.629401\pi$
$281$	−13.2569	−0.790843	−0.395421	+	0.918500i	$0.629401\pi$
$282$	16.6956	0.994206
$283$	9.58330	0.569668	0.284834	−	0.958577i	$-0.408061\pi$
$283$	9.58330	0.569668	0.284834	+	0.958577i	$0.408061\pi$
$284$	−7.88536	−0.467910
$285$	−8.51928	−0.504639
$286$	24.8697	1.47058
$287$	0	0
$288$	−9.05405	−0.533515
$289$	32.1664	1.89214
$290$	34.5181	2.02697
$291$	13.4628	0.789202
$292$	3.15131	0.184417
$293$	19.5179	1.14025	0.570125	−	0.821558i	$-0.306895\pi$
$293$	19.5179	1.14025	0.570125	+	0.821558i	$0.306895\pi$
$294$	0	0
$295$	−4.13534	−0.240769
$296$	−8.14872	−0.473634
$297$	−25.7483	−1.49407
$298$	−26.7407	−1.54904
$299$	−12.0417	−0.696388
$300$	1.99082	0.114940
$301$	0	0
$302$	−9.71831	−0.559226
$303$	−2.07940	−0.119458
$304$	−13.8488	−0.794282
$305$	−35.3409	−2.02361
$306$	−19.2250	−1.09902
$307$	11.4155	0.651519	0.325759	−	0.945453i	$-0.394380\pi$
$307$	11.4155	0.651519	0.325759	+	0.945453i	$0.394380\pi$
$308$	0	0
$309$	18.1692	1.03361
$310$	5.59677	0.317875
$311$	24.5477	1.39197	0.695985	−	0.718056i	$-0.254968\pi$
$311$	24.5477	1.39197	0.695985	+	0.718056i	$0.254968\pi$
$312$	−5.34481	−0.302590
$313$	12.7014	0.717926	0.358963	−	0.933352i	$-0.383130\pi$
$313$	12.7014	0.717926	0.358963	+	0.933352i	$0.383130\pi$
$314$	−38.9713	−2.19928
$315$	0	0
$316$	14.5314	0.817456
$317$	26.6083	1.49447	0.747237	−	0.664558i	$-0.231380\pi$
$317$	26.6083	1.49447	0.747237	+	0.664558i	$0.231380\pi$
$318$	20.2885	1.13772
$319$	35.9631	2.01355
$320$	1.27860	0.0714758
$321$	2.09769	0.117082
$322$	0	0
$323$	−19.5271	−1.08652
$324$	−2.33042	−0.129468
$325$	−4.21457	−0.233782
$326$	−7.88529	−0.436726
$327$	21.8669	1.20924
$328$	1.48599	0.0820501
$329$	0	0
$330$	25.5474	1.40634
$331$	−13.3106	−0.731617	−0.365809	−	0.930690i	$-0.619207\pi$
$331$	−13.3106	−0.731617	−0.365809	+	0.930690i	$0.619207\pi$
$332$	−0.340791	−0.0187033
$333$	8.45165	0.463147
$334$	32.6692	1.78758
$335$	9.51899	0.520078
$336$	0	0
$337$	−6.90555	−0.376169	−0.188085	−	0.982153i	$-0.560228\pi$
$337$	−6.90555	−0.376169	−0.188085	+	0.982153i	$0.560228\pi$
$338$	7.34990	0.399782
$339$	−18.4362	−1.00132
$340$	20.6847	1.12178
$341$	5.83107	0.315770
$342$	7.63549	0.412880
$343$	0	0
$344$	13.6431	0.735589
$345$	−12.3698	−0.665968
$346$	−26.7880	−1.44013
$347$	0.0561815	0.00301598	0.00150799	−	0.999999i	$-0.499520\pi$
$347$	0.0561815	0.00301598	0.00150799	+	0.999999i	$0.499520\pi$
$348$	10.7765	0.577679
$349$	−6.22816	−0.333386	−0.166693	−	0.986009i	$-0.553309\pi$
$349$	−6.22816	−0.333386	−0.166693	+	0.986009i	$0.553309\pi$
$350$	0	0
$351$	16.3339	0.871839
$352$	27.5776	1.46989
$353$	−1.81469	−0.0965863	−0.0482932	−	0.998833i	$-0.515378\pi$
$353$	−1.81469	−0.0965863	−0.0482932	+	0.998833i	$0.515378\pi$
$354$	−3.50803	−0.186450
$355$	17.1482	0.910134
$356$	3.48820	0.184874
$357$	0	0
$358$	−28.6932	−1.51648
$359$	−22.3519	−1.17969	−0.589845	−	0.807517i	$-0.700811\pi$
$359$	−22.3519	−1.17969	−0.589845	+	0.807517i	$0.700811\pi$
$360$	5.80084	0.305731
$361$	−11.2445	−0.591818
$362$	4.50602	0.236831
$363$	13.3312	0.699705
$364$	0	0
$365$	−6.85314	−0.358710
$366$	−29.9798	−1.56707
$367$	2.28250	0.119145	0.0595727	−	0.998224i	$-0.481026\pi$
$367$	2.28250	0.119145	0.0595727	+	0.998224i	$0.481026\pi$
$368$	−20.1081	−1.04821
$369$	−1.54123	−0.0802334
$370$	−24.7084	−1.28453
$371$	0	0
$372$	1.74730	0.0905932
$373$	−3.52330	−0.182429	−0.0912147	−	0.995831i	$-0.529075\pi$
$373$	−3.52330	−0.182429	−0.0912147	+	0.995831i	$0.529075\pi$
$374$	58.5574	3.02793
$375$	10.9663	0.566297
$376$	−11.5467	−0.595477
$377$	−22.8138	−1.17497
$378$	0	0
$379$	−15.2688	−0.784306	−0.392153	−	0.919900i	$-0.628270\pi$
$379$	−15.2688	−0.784306	−0.392153	+	0.919900i	$0.628270\pi$
$380$	−8.21520	−0.421431
$381$	7.22874	0.370340
$382$	−35.6817	−1.82563
$383$	−11.1027	−0.567323	−0.283661	−	0.958924i	$-0.591549\pi$
$383$	−11.1027	−0.567323	−0.283661	+	0.958924i	$0.591549\pi$
$384$	−13.1059	−0.668806
$385$	0	0
$386$	−17.7211	−0.901982
$387$	−14.1503	−0.719301
$388$	12.9822	0.659074
$389$	−16.4667	−0.834892	−0.417446	−	0.908702i	$-0.637075\pi$
$389$	−16.4667	−0.834892	−0.417446	+	0.908702i	$0.637075\pi$
$390$	−16.2064	−0.820645
$391$	−28.3529	−1.43387
$392$	0	0
$393$	−8.44722	−0.426106
$394$	−40.3571	−2.03316
$395$	−31.6014	−1.59004
$396$	−8.42672	−0.423459
$397$	−20.1657	−1.01209	−0.506043	−	0.862509i	$-0.668892\pi$
$397$	−20.1657	−1.01209	−0.506043	+	0.862509i	$0.668892\pi$
$398$	5.70584	0.286008
$399$	0	0
$400$	−7.03782	−0.351891
$401$	−18.7090	−0.934285	−0.467143	−	0.884182i	$-0.654717\pi$
$401$	−18.7090	−0.934285	−0.467143	+	0.884182i	$0.654717\pi$
$402$	8.07500	0.402744
$403$	−3.69904	−0.184262
$404$	−2.00518	−0.0997613
$405$	5.06796	0.251829
$406$	0	0
$407$	−25.7428	−1.27602
$408$	−12.5847	−0.623036
$409$	5.36315	0.265191	0.132595	−	0.991170i	$-0.457669\pi$
$409$	5.36315	0.265191	0.132595	+	0.991170i	$0.457669\pi$
$410$	4.50580	0.222525
$411$	10.0365	0.495063
$412$	17.5206	0.863180
$413$	0	0
$414$	11.0866	0.544875
$415$	0.741117	0.0363800
$416$	−17.4944	−0.857731
$417$	−6.20870	−0.304041
$418$	−23.2569	−1.13753
$419$	2.79177	0.136387	0.0681934	−	0.997672i	$-0.478277\pi$
$419$	2.79177	0.136387	0.0681934	+	0.997672i	$0.478277\pi$
$420$	0	0
$421$	−21.6956	−1.05738	−0.528689	−	0.848815i	$-0.677316\pi$
$421$	−21.6956	−1.05738	−0.528689	+	0.848815i	$0.677316\pi$
$422$	−16.7314	−0.814472
$423$	11.9760	0.582292
$424$	−14.0316	−0.681434
$425$	−9.92349	−0.481360
$426$	14.5469	0.704801
$427$	0	0
$428$	2.02281	0.0977764
$429$	−16.8849	−0.815211
$430$	41.3685	1.99497
$431$	4.61698	0.222392	0.111196	−	0.993798i	$-0.464532\pi$
$431$	4.61698	0.222392	0.111196	+	0.993798i	$0.464532\pi$
$432$	27.2756	1.31230
$433$	−5.83701	−0.280509	−0.140254	−	0.990115i	$-0.544792\pi$
$433$	−5.83701	−0.280509	−0.140254	+	0.990115i	$0.544792\pi$
$434$	0	0
$435$	−23.4355	−1.12365
$436$	21.0864	1.00986
$437$	11.2607	0.538675
$438$	−5.81355	−0.277782
$439$	−20.1437	−0.961407	−0.480703	−	0.876883i	$-0.659619\pi$
$439$	−20.1437	−0.961407	−0.480703	+	0.876883i	$0.659619\pi$
$440$	−17.6687	−0.842323
$441$	0	0
$442$	−37.1469	−1.76690
$443$	5.14409	0.244403	0.122202	−	0.992505i	$-0.461005\pi$
$443$	5.14409	0.244403	0.122202	+	0.992505i	$0.461005\pi$
$444$	−7.71390	−0.366086
$445$	−7.58577	−0.359600
$446$	−6.62792	−0.313841
$447$	18.1552	0.858709
$448$	0	0
$449$	6.86081	0.323782	0.161891	−	0.986809i	$-0.448241\pi$
$449$	6.86081	0.323782	0.161891	+	0.986809i	$0.448241\pi$
$450$	3.88029	0.182918
$451$	4.69442	0.221052
$452$	−17.7782	−0.836215
$453$	6.59810	0.310006
$454$	1.48135	0.0695231
$455$	0	0
$456$	4.99819	0.234062
$457$	7.22547	0.337993	0.168997	−	0.985617i	$-0.445947\pi$
$457$	7.22547	0.337993	0.168997	+	0.985617i	$0.445947\pi$
$458$	36.1721	1.69021
$459$	38.4593	1.79512
$460$	−11.9283	−0.556159
$461$	8.14091	0.379160	0.189580	−	0.981865i	$-0.439287\pi$
$461$	8.14091	0.379160	0.189580	+	0.981865i	$0.439287\pi$
$462$	0	0
$463$	18.0745	0.839993	0.419996	−	0.907526i	$-0.362031\pi$
$463$	18.0745	0.839993	0.419996	+	0.907526i	$0.362031\pi$
$464$	−38.0963	−1.76858
$465$	−3.79984	−0.176213
$466$	6.39698	0.296334
$467$	−34.4162	−1.59259	−0.796296	−	0.604907i	$-0.793210\pi$
$467$	−34.4162	−1.59259	−0.796296	+	0.604907i	$0.793210\pi$
$468$	5.34564	0.247102
$469$	0	0
$470$	−35.0118	−1.61497
$471$	26.4589	1.21916
$472$	2.42617	0.111673
$473$	43.1003	1.98176
$474$	−26.8076	−1.23131
$475$	3.94125	0.180837
$476$	0	0
$477$	14.5532	0.666346
$478$	−13.9217	−0.636763
$479$	−21.2341	−0.970211	−0.485105	−	0.874456i	$-0.661219\pi$
$479$	−21.2341	−0.970211	−0.485105	+	0.874456i	$0.661219\pi$
$480$	−17.9711	−0.820264
$481$	16.3304	0.744601
$482$	23.2153	1.05743
$483$	0	0
$484$	12.8553	0.584334
$485$	−28.2324	−1.28197
$486$	−24.9729	−1.13279
$487$	−24.8051	−1.12403	−0.562014	−	0.827128i	$-0.689973\pi$
$487$	−24.8051	−1.12403	−0.562014	+	0.827128i	$0.689973\pi$
$488$	20.7342	0.938592
$489$	5.35360	0.242098
$490$	0	0
$491$	37.9360	1.71203	0.856014	−	0.516953i	$-0.172934\pi$
$491$	37.9360	1.71203	0.856014	+	0.516953i	$0.172934\pi$
$492$	1.40670	0.0634189
$493$	−53.7167	−2.41928
$494$	14.7534	0.663786
$495$	18.3256	0.823672
$496$	−6.17694	−0.277353
$497$	0	0
$498$	0.628693	0.0281724
$499$	24.0701	1.07752	0.538762	−	0.842458i	$-0.318892\pi$
$499$	24.0701	1.07752	0.538762	+	0.842458i	$0.318892\pi$
$500$	10.5749	0.472922
$501$	−22.1802	−0.990940
$502$	4.43380	0.197890
$503$	3.13580	0.139819	0.0699093	−	0.997553i	$-0.477729\pi$
$503$	3.13580	0.139819	0.0699093	+	0.997553i	$0.477729\pi$
$504$	0	0
$505$	4.36065	0.194046
$506$	−33.7685	−1.50119
$507$	−4.99010	−0.221618
$508$	6.97072	0.309276
$509$	20.6034	0.913231	0.456616	−	0.889664i	$-0.349061\pi$
$509$	20.6034	0.913231	0.456616	+	0.889664i	$0.349061\pi$
$510$	−38.1592	−1.68972
$511$	0	0
$512$	−14.4341	−0.637905
$513$	−15.2746	−0.674391
$514$	36.1716	1.59546
$515$	−38.1021	−1.67898
$516$	12.9151	0.568558
$517$	−36.4775	−1.60428
$518$	0	0
$519$	18.1873	0.798334
$520$	11.2085	0.491523
$521$	−1.77725	−0.0778629	−0.0389314	−	0.999242i	$-0.512395\pi$
$521$	−1.77725	−0.0778629	−0.0389314	+	0.999242i	$0.512395\pi$
$522$	21.0043	0.919334
$523$	−23.3930	−1.02290	−0.511452	−	0.859312i	$-0.670892\pi$
$523$	−23.3930	−1.02290	−0.511452	+	0.859312i	$0.670892\pi$
$524$	−8.14570	−0.355847
$525$	0	0
$526$	42.0713	1.83440
$527$	−8.70963	−0.379398
$528$	−28.1957	−1.22706
$529$	−6.64964	−0.289115
$530$	−42.5464	−1.84810
$531$	−2.51636	−0.109201
$532$	0	0
$533$	−2.97799	−0.128991
$534$	−6.43504	−0.278472
$535$	−4.39900	−0.190185
$536$	−5.58471	−0.241223
$537$	19.4808	0.840659
$538$	−7.17414	−0.309299
$539$	0	0
$540$	16.1801	0.696281
$541$	26.9238	1.15754	0.578772	−	0.815489i	$-0.303532\pi$
$541$	26.9238	1.15754	0.578772	+	0.815489i	$0.303532\pi$
$542$	−31.5023	−1.35314
$543$	−3.05929	−0.131287
$544$	−41.1916	−1.76608
$545$	−45.8565	−1.96428
$546$	0	0
$547$	−24.3464	−1.04098	−0.520489	−	0.853869i	$-0.674250\pi$
$547$	−24.3464	−1.04098	−0.520489	+	0.853869i	$0.674250\pi$
$548$	9.67824	0.413434
$549$	−21.5050	−0.917810
$550$	−11.8189	−0.503960
$551$	21.3343	0.908872
$552$	7.25726	0.308890
$553$	0	0
$554$	−31.2378	−1.32717
$555$	16.7754	0.712076
$556$	−5.98708	−0.253909
$557$	−39.4429	−1.67125	−0.835625	−	0.549301i	$-0.814894\pi$
$557$	−39.4429	−1.67125	−0.835625	+	0.549301i	$0.814894\pi$
$558$	3.40564	0.144172
$559$	−27.3414	−1.15642
$560$	0	0
$561$	−39.7566	−1.67853
$562$	23.5835	0.994811
$563$	−4.52248	−0.190600	−0.0952998	−	0.995449i	$-0.530381\pi$
$563$	−4.52248	−0.190600	−0.0952998	+	0.995449i	$0.530381\pi$
$564$	−10.9306	−0.460261
$565$	38.6621	1.62653
$566$	−17.0483	−0.716592
$567$	0	0
$568$	−10.0607	−0.422139
$569$	−9.79397	−0.410584	−0.205292	−	0.978701i	$-0.565814\pi$
$569$	−9.79397	−0.410584	−0.205292	+	0.978701i	$0.565814\pi$
$570$	15.1554	0.634791
$571$	29.0757	1.21678	0.608390	−	0.793639i	$-0.291816\pi$
$571$	29.0757	1.21678	0.608390	+	0.793639i	$0.291816\pi$
$572$	−16.2822	−0.680794
$573$	24.2255	1.01204
$574$	0	0
$575$	5.72261	0.238649
$576$	0.778029	0.0324179
$577$	43.5350	1.81239	0.906193	−	0.422865i	$-0.138976\pi$
$577$	43.5350	1.81239	0.906193	+	0.422865i	$0.138976\pi$
$578$	−57.2225	−2.38014
$579$	12.0315	0.500012
$580$	−22.5990	−0.938373
$581$	0	0
$582$	−23.9497	−0.992747
$583$	−44.3275	−1.83586
$584$	4.02068	0.166377
$585$	−11.6251	−0.480640
$586$	−34.7215	−1.43433
$587$	22.0541	0.910271	0.455135	−	0.890422i	$-0.349591\pi$
$587$	22.0541	0.910271	0.455135	+	0.890422i	$0.349591\pi$
$588$	0	0
$589$	3.45915	0.142532
$590$	7.35659	0.302866
$591$	27.3998	1.12708
$592$	27.2697	1.12078
$593$	34.7750	1.42804	0.714019	−	0.700126i	$-0.246873\pi$
$593$	34.7750	1.42804	0.714019	+	0.700126i	$0.246873\pi$
$594$	45.8051	1.87941
$595$	0	0
$596$	17.5071	0.717120
$597$	−3.87389	−0.158548
$598$	21.4216	0.875994
$599$	−27.8457	−1.13775	−0.568873	−	0.822425i	$-0.692620\pi$
$599$	−27.8457	−1.13775	−0.568873	+	0.822425i	$0.692620\pi$
$600$	2.54003	0.103696
$601$	−6.64710	−0.271141	−0.135570	−	0.990768i	$-0.543287\pi$
$601$	−6.64710	−0.271141	−0.135570	+	0.990768i	$0.543287\pi$
$602$	0	0
$603$	5.79232	0.235881
$604$	6.36259	0.258890
$605$	−27.9564	−1.13659
$606$	3.69916	0.150268
$607$	−11.9432	−0.484760	−0.242380	−	0.970181i	$-0.577928\pi$
$607$	−11.9432	−0.484760	−0.242380	+	0.970181i	$0.577928\pi$
$608$	16.3598	0.663478
$609$	0	0
$610$	62.8699	2.54553
$611$	23.1401	0.936150
$612$	12.5867	0.508785
$613$	−10.1793	−0.411139	−0.205570	−	0.978642i	$-0.565905\pi$
$613$	−10.1793	−0.411139	−0.205570	+	0.978642i	$0.565905\pi$
$614$	−20.3077	−0.819553
$615$	−3.05914	−0.123356
$616$	0	0
$617$	−28.4430	−1.14507	−0.572536	−	0.819880i	$-0.694040\pi$
$617$	−28.4430	−1.14507	−0.572536	+	0.819880i	$0.694040\pi$
$618$	−32.3221	−1.30019
$619$	40.0289	1.60890	0.804448	−	0.594023i	$-0.202461\pi$
$619$	40.0289	1.60890	0.804448	+	0.594023i	$0.202461\pi$
$620$	−3.66421	−0.147158
$621$	−22.1784	−0.889989
$622$	−43.6692	−1.75098
$623$	0	0
$624$	17.8864	0.716031
$625$	−30.0733	−1.20293
$626$	−22.5952	−0.903087
$627$	15.7899	0.630587
$628$	25.5145	1.01814
$629$	38.4510	1.53314
$630$	0	0
$631$	−13.5759	−0.540446	−0.270223	−	0.962798i	$-0.587097\pi$
$631$	−13.5759	−0.540446	−0.270223	+	0.962798i	$0.587097\pi$
$632$	18.5403	0.737492
$633$	11.3595	0.451501
$634$	−47.3351	−1.87992
$635$	−15.1592	−0.601574
$636$	−13.2829	−0.526700
$637$	0	0
$638$	−63.9768	−2.53287
$639$	10.4347	0.412792
$640$	27.4839	1.08640
$641$	−5.11483	−0.202024	−0.101012	−	0.994885i	$-0.532208\pi$
$641$	−5.11483	−0.202024	−0.101012	+	0.994885i	$0.532208\pi$
$642$	−3.73169	−0.147278
$643$	−24.0339	−0.947804	−0.473902	−	0.880578i	$-0.657155\pi$
$643$	−24.0339	−0.947804	−0.473902	+	0.880578i	$0.657155\pi$
$644$	0	0
$645$	−28.0865	−1.10591
$646$	34.7378	1.36674
$647$	−28.0872	−1.10422	−0.552111	−	0.833771i	$-0.686178\pi$
$647$	−28.0872	−1.10422	−0.552111	+	0.833771i	$0.686178\pi$
$648$	−2.97332	−0.116803
$649$	7.66456	0.300860
$650$	7.49754	0.294078
$651$	0	0
$652$	5.16251	0.202179
$653$	29.8731	1.16903	0.584513	−	0.811385i	$-0.301286\pi$
$653$	29.8731	1.16903	0.584513	+	0.811385i	$0.301286\pi$
$654$	−38.9003	−1.52112
$655$	17.7144	0.692160
$656$	−4.97288	−0.194158
$657$	−4.17015	−0.162693
$658$	0	0
$659$	25.6367	0.998664	0.499332	−	0.866411i	$-0.333579\pi$
$659$	25.6367	0.998664	0.499332	+	0.866411i	$0.333579\pi$
$660$	−16.7259	−0.651055
$661$	15.0334	0.584733	0.292367	−	0.956306i	$-0.405557\pi$
$661$	15.0334	0.584733	0.292367	+	0.956306i	$0.405557\pi$
$662$	23.6790	0.920310
$663$	25.2203	0.979475
$664$	−0.434807	−0.0168738
$665$	0	0
$666$	−15.0351	−0.582598
$667$	30.9770	1.19943
$668$	−21.3885	−0.827547
$669$	4.49992	0.173977
$670$	−16.9339	−0.654212
$671$	65.5018	2.52867
$672$	0	0
$673$	−18.1067	−0.697961	−0.348981	−	0.937130i	$-0.613472\pi$
$673$	−18.1067	−0.697961	−0.348981	+	0.937130i	$0.613472\pi$
$674$	12.2847	0.473188
$675$	−7.76242	−0.298776
$676$	−4.81198	−0.185076
$677$	−31.1567	−1.19745	−0.598725	−	0.800954i	$-0.704326\pi$
$677$	−31.1567	−1.19745	−0.598725	+	0.800954i	$0.704326\pi$
$678$	32.7972	1.25957
$679$	0	0
$680$	26.3910	1.01205
$681$	−1.00574	−0.0385400
$682$	−10.3732	−0.397211
$683$	−32.3923	−1.23946	−0.619728	−	0.784817i	$-0.712757\pi$
$683$	−32.3923	−1.23946	−0.619728	+	0.784817i	$0.712757\pi$
$684$	−4.99896	−0.191140
$685$	−21.0472	−0.804173
$686$	0	0
$687$	−24.5585	−0.936964
$688$	−45.6569	−1.74065
$689$	28.1199	1.07128
$690$	22.0054	0.837729
$691$	−39.3721	−1.49778	−0.748892	−	0.662692i	$-0.769414\pi$
$691$	−39.3721	−1.49778	−0.748892	+	0.662692i	$0.769414\pi$
$692$	17.5381	0.666700
$693$	0	0
$694$	−0.0999444	−0.00379384
$695$	13.0201	0.493880
$696$	13.7494	0.521170
$697$	−7.01187	−0.265594
$698$	11.0796	0.419370
$699$	−4.34313	−0.164272
$700$	0	0
$701$	−25.4429	−0.960966	−0.480483	−	0.877004i	$-0.659539\pi$
$701$	−25.4429	−0.960966	−0.480483	+	0.877004i	$0.659539\pi$
$702$	−29.0573	−1.09670
$703$	−15.2713	−0.575969
$704$	−2.36979	−0.0893148
$705$	23.7707	0.895257
$706$	3.22826	0.121497
$707$	0	0
$708$	2.29671	0.0863156
$709$	−23.9649	−0.900022	−0.450011	−	0.893023i	$-0.648580\pi$
$709$	−23.9649	−0.900022	−0.450011	+	0.893023i	$0.648580\pi$
$710$	−30.5060	−1.14487
$711$	−19.2295	−0.721163
$712$	4.45051	0.166790
$713$	5.02261	0.188098
$714$	0	0
$715$	35.4089	1.32422
$716$	18.7855	0.702046
$717$	9.45191	0.352988
$718$	39.7631	1.48394
$719$	−28.2304	−1.05282	−0.526409	−	0.850232i	$-0.676462\pi$
$719$	−28.2304	−1.05282	−0.526409	+	0.850232i	$0.676462\pi$
$720$	−19.4125	−0.723463
$721$	0	0
$722$	20.0036	0.744455
$723$	−15.7617	−0.586183
$724$	−2.95009	−0.109639
$725$	10.8419	0.402658
$726$	−23.7156	−0.880168
$727$	17.4611	0.647595	0.323798	−	0.946126i	$-0.395040\pi$
$727$	17.4611	0.647595	0.323798	+	0.946126i	$0.395040\pi$
$728$	0	0
$729$	22.9577	0.850284
$730$	12.1914	0.451225
$731$	−64.3772	−2.38108
$732$	19.6278	0.725465
$733$	14.2857	0.527656	0.263828	−	0.964570i	$-0.415015\pi$
$733$	14.2857	0.527656	0.263828	+	0.964570i	$0.415015\pi$
$734$	−4.06046	−0.149874
$735$	0	0
$736$	23.7541	0.875587
$737$	−17.6428	−0.649880
$738$	2.74178	0.100926
$739$	12.0944	0.444898	0.222449	−	0.974944i	$-0.428595\pi$
$739$	12.0944	0.444898	0.222449	+	0.974944i	$0.428595\pi$
$740$	16.1766	0.594664
$741$	−10.0166	−0.367968
$742$	0	0
$743$	9.11337	0.334337	0.167168	−	0.985928i	$-0.446538\pi$
$743$	9.11337	0.334337	0.167168	+	0.985928i	$0.446538\pi$
$744$	2.22933	0.0817313
$745$	−38.0727	−1.39487
$746$	6.26779	0.229480
$747$	0.450971	0.0165002
$748$	−38.3376	−1.40176
$749$	0	0
$750$	−19.5085	−0.712351
$751$	−8.65418	−0.315796	−0.157898	−	0.987455i	$-0.550472\pi$
$751$	−8.65418	−0.315796	−0.157898	+	0.987455i	$0.550472\pi$
$752$	38.6412	1.40910
$753$	−3.01026	−0.109700
$754$	40.5848	1.47801
$755$	−13.8367	−0.503569
$756$	0	0
$757$	23.7596	0.863556	0.431778	−	0.901980i	$-0.357886\pi$
$757$	23.7596	0.863556	0.431778	+	0.901980i	$0.357886\pi$
$758$	27.1625	0.986588
$759$	22.9266	0.832182
$760$	−10.4816	−0.380206
$761$	−47.8706	−1.73531	−0.867655	−	0.497167i	$-0.834373\pi$
$761$	−47.8706	−1.73531	−0.867655	+	0.497167i	$0.834373\pi$
$762$	−12.8596	−0.465854
$763$	0	0
$764$	23.3608	0.845165
$765$	−27.3721	−0.989642
$766$	19.7513	0.713642
$767$	−4.86214	−0.175562
$768$	24.5342	0.885300
$769$	−37.0906	−1.33752	−0.668761	−	0.743478i	$-0.733175\pi$
$769$	−37.0906	−1.33752	−0.668761	+	0.743478i	$0.733175\pi$
$770$	0	0
$771$	−24.5582	−0.884440
$772$	11.6020	0.417567
$773$	−15.0756	−0.542231	−0.271115	−	0.962547i	$-0.587393\pi$
$773$	−15.0756	−0.542231	−0.271115	+	0.962547i	$0.587393\pi$
$774$	25.1728	0.904818
$775$	1.75791	0.0631459
$776$	16.5637	0.594603
$777$	0	0
$778$	29.2934	1.05022
$779$	2.78486	0.0997780
$780$	10.6104	0.379912
$781$	−31.7830	−1.13729
$782$	50.4386	1.80368
$783$	−42.0186	−1.50162
$784$	0	0
$785$	−55.4863	−1.98039
$786$	15.0272	0.536003
$787$	44.0273	1.56940	0.784702	−	0.619874i	$-0.212816\pi$
$787$	44.0273	1.56940	0.784702	+	0.619874i	$0.212816\pi$
$788$	26.4218	0.941239
$789$	−28.5637	−1.01689
$790$	56.2175	2.00013
$791$	0	0
$792$	−10.7514	−0.382036
$793$	−41.5522	−1.47556
$794$	35.8738	1.27311
$795$	28.8862	1.02449
$796$	−3.73562	−0.132406
$797$	12.7891	0.453015	0.226507	−	0.974009i	$-0.427269\pi$
$797$	12.7891	0.453015	0.226507	+	0.974009i	$0.427269\pi$
$798$	0	0
$799$	54.4850	1.92754
$800$	8.31390	0.293941
$801$	−4.61595	−0.163097
$802$	33.2826	1.17525
$803$	12.7018	0.448237
$804$	−5.28671	−0.186448
$805$	0	0
$806$	6.58043	0.231786
$807$	4.87077	0.171459
$808$	−2.55835	−0.0900026
$809$	28.6918	1.00875	0.504375	−	0.863485i	$-0.331723\pi$
$809$	28.6918	1.00875	0.504375	+	0.863485i	$0.331723\pi$
$810$	−9.01567	−0.316778
$811$	−19.8602	−0.697385	−0.348693	−	0.937237i	$-0.613374\pi$
$811$	−19.8602	−0.697385	−0.348693	+	0.937237i	$0.613374\pi$
$812$	0	0
$813$	21.3880	0.750111
$814$	45.7953	1.60512
$815$	−11.2269	−0.393261
$816$	42.1148	1.47431
$817$	25.5683	0.894521
$818$	−9.54080	−0.333586
$819$	0	0
$820$	−2.94995	−0.103017
$821$	−0.296096	−0.0103338	−0.00516690	−	0.999987i	$-0.501645\pi$
$821$	−0.296096	−0.0103338	−0.00516690	+	0.999987i	$0.501645\pi$
$822$	−17.8545	−0.622746
$823$	3.66971	0.127918	0.0639590	−	0.997953i	$-0.479627\pi$
$823$	3.66971	0.127918	0.0639590	+	0.997953i	$0.479627\pi$
$824$	22.3541	0.778743
$825$	8.02427	0.279369
$826$	0	0
$827$	−3.96494	−0.137875	−0.0689373	−	0.997621i	$-0.521961\pi$
$827$	−3.96494	−0.137875	−0.0689373	+	0.997621i	$0.521961\pi$
$828$	−7.25838	−0.252246
$829$	4.95467	0.172083	0.0860413	−	0.996292i	$-0.472578\pi$
$829$	4.95467	0.172083	0.0860413	+	0.996292i	$0.472578\pi$
$830$	−1.31841	−0.0457628
$831$	21.2084	0.735712
$832$	1.50332	0.0521181
$833$	0	0
$834$	11.0450	0.382457
$835$	46.5136	1.60967
$836$	15.2263	0.526612
$837$	−6.81291	−0.235489
$838$	−4.96643	−0.171563
$839$	45.6338	1.57545	0.787726	−	0.616025i	$-0.211258\pi$
$839$	45.6338	1.57545	0.787726	+	0.616025i	$0.211258\pi$
$840$	0	0
$841$	29.6881	1.02373
$842$	38.5955	1.33009
$843$	−16.0117	−0.551471
$844$	10.9541	0.377054
$845$	10.4646	0.359993
$846$	−21.3047	−0.732472
$847$	0	0
$848$	46.9568	1.61250
$849$	11.5747	0.397241
$850$	17.6534	0.605508
$851$	−22.1736	−0.760102
$852$	−9.52389	−0.326283
$853$	13.8659	0.474759	0.237379	−	0.971417i	$-0.423712\pi$
$853$	13.8659	0.474759	0.237379	+	0.971417i	$0.423712\pi$
$854$	0	0
$855$	10.8712	0.371788
$856$	2.58086	0.0882119
$857$	27.4574	0.937926	0.468963	−	0.883218i	$-0.344628\pi$
$857$	27.4574	0.937926	0.468963	+	0.883218i	$0.344628\pi$
$858$	30.0375	1.02546
$859$	12.6561	0.431819	0.215910	−	0.976413i	$-0.430728\pi$
$859$	12.6561	0.431819	0.215910	+	0.976413i	$0.430728\pi$
$860$	−27.0840	−0.923557
$861$	0	0
$862$	−8.21341	−0.279750
$863$	43.2918	1.47367	0.736834	−	0.676073i	$-0.236320\pi$
$863$	43.2918	1.47367	0.736834	+	0.676073i	$0.236320\pi$
$864$	−32.2212	−1.09619
$865$	−38.1401	−1.29680
$866$	10.3838	0.352855
$867$	38.8504	1.31943
$868$	0	0
$869$	58.5710	1.98688
$870$	41.6908	1.41345
$871$	11.1920	0.379226
$872$	26.9036	0.911071
$873$	−17.1795	−0.581437
$874$	−20.0324	−0.677605
$875$	0	0
$876$	3.80614	0.128597
$877$	50.3867	1.70144	0.850718	−	0.525622i	$-0.176167\pi$
$877$	50.3867	1.70144	0.850718	+	0.525622i	$0.176167\pi$
$878$	35.8348	1.20936
$879$	23.5736	0.795119
$880$	59.1285	1.99322
$881$	−4.56171	−0.153688	−0.0768440	−	0.997043i	$-0.524484\pi$
$881$	−4.56171	−0.153688	−0.0768440	+	0.997043i	$0.524484\pi$
$882$	0	0
$883$	9.01017	0.303216	0.151608	−	0.988441i	$-0.451555\pi$
$883$	9.01017	0.303216	0.151608	+	0.988441i	$0.451555\pi$
$884$	24.3201	0.817973
$885$	−4.99464	−0.167893
$886$	−9.15111	−0.307438
$887$	14.2743	0.479285	0.239642	−	0.970861i	$-0.422970\pi$
$887$	14.2743	0.479285	0.239642	+	0.970861i	$0.422970\pi$
$888$	−9.84197	−0.330275
$889$	0	0
$890$	13.4948	0.452345
$891$	−9.39309	−0.314680
$892$	4.33930	0.145291
$893$	−21.6395	−0.724137
$894$	−32.2972	−1.08018
$895$	−40.8527	−1.36555
$896$	0	0
$897$	−14.5439	−0.485606
$898$	−12.2051	−0.407289
$899$	9.51570	0.317366
$900$	−2.54043	−0.0846809
$901$	66.2102	2.20578
$902$	−8.35117	−0.278064
$903$	0	0
$904$	−22.6827	−0.754416
$905$	6.41556	0.213260
$906$	−11.7377	−0.389960
$907$	−40.2553	−1.33665	−0.668327	−	0.743867i	$-0.732990\pi$
$907$	−40.2553	−1.33665	−0.668327	+	0.743867i	$0.732990\pi$
$908$	−0.969840	−0.0321853
$909$	2.65346	0.0880098
$910$	0	0
$911$	−7.43178	−0.246226	−0.123113	−	0.992393i	$-0.539288\pi$
$911$	−7.43178	−0.246226	−0.123113	+	0.992393i	$0.539288\pi$
$912$	−16.7265	−0.553869
$913$	−1.37361	−0.0454598
$914$	−12.8538	−0.425165
$915$	−42.6845	−1.41111
$916$	−23.6819	−0.782471
$917$	0	0
$918$	−68.4173	−2.25811
$919$	2.77258	0.0914589	0.0457294	−	0.998954i	$-0.485439\pi$
$919$	2.77258	0.0914589	0.0457294	+	0.998954i	$0.485439\pi$
$920$	−15.2190	−0.501756
$921$	13.7876	0.454317
$922$	−14.4823	−0.476950
$923$	20.1621	0.663644
$924$	0	0
$925$	−7.76074	−0.255172
$926$	−32.1537	−1.05664
$927$	−23.1852	−0.761501
$928$	45.0039	1.47732
$929$	−17.1310	−0.562051	−0.281025	−	0.959700i	$-0.590675\pi$
$929$	−17.1310	−0.562051	−0.281025	+	0.959700i	$0.590675\pi$
$930$	6.75975	0.221661
$931$	0	0
$932$	−4.18811	−0.137186
$933$	29.6485	0.970649
$934$	61.2249	2.00334
$935$	83.3725	2.72657
$936$	6.82036	0.222930
$937$	20.2782	0.662461	0.331231	−	0.943550i	$-0.392536\pi$
$937$	20.2782	0.662461	0.331231	+	0.943550i	$0.392536\pi$
$938$	0	0
$939$	15.3407	0.500624
$940$	22.9223	0.747642
$941$	−9.63228	−0.314003	−0.157002	−	0.987598i	$-0.550183\pi$
$941$	−9.63228	−0.314003	−0.157002	+	0.987598i	$0.550183\pi$
$942$	−47.0693	−1.53360
$943$	4.04356	0.131676
$944$	−8.11919	−0.264257
$945$	0	0
$946$	−76.6736	−2.49287
$947$	−35.3846	−1.14984	−0.574922	−	0.818208i	$-0.694968\pi$
$947$	−35.3846	−1.14984	−0.574922	+	0.818208i	$0.694968\pi$
$948$	17.5510	0.570029
$949$	−8.05761	−0.261561
$950$	−7.01131	−0.227477
$951$	32.1374	1.04213
$952$	0	0
$953$	−24.5962	−0.796749	−0.398374	−	0.917223i	$-0.630426\pi$
$953$	−24.5962	−0.796749	−0.398374	+	0.917223i	$0.630426\pi$
$954$	−25.8895	−0.838204
$955$	−50.8027	−1.64394
$956$	9.11454	0.294785
$957$	43.4361	1.40409
$958$	37.7745	1.22044
$959$	0	0
$960$	1.54428	0.0498415
$961$	−29.4571	−0.950230
$962$	−29.0510	−0.936643
$963$	−2.67680	−0.0862587
$964$	−15.1991	−0.489530
$965$	−25.2309	−0.812212
$966$	0	0
$967$	32.7607	1.05351	0.526757	−	0.850016i	$-0.323408\pi$
$967$	32.7607	1.05351	0.526757	+	0.850016i	$0.323408\pi$
$968$	16.4018	0.527174
$969$	−23.5847	−0.757650
$970$	50.2242	1.61260
$971$	−46.1107	−1.47976	−0.739881	−	0.672738i	$-0.765118\pi$
$971$	−46.1107	−1.47976	−0.739881	+	0.672738i	$0.765118\pi$
$972$	16.3498	0.524419
$973$	0	0
$974$	44.1272	1.41393
$975$	−5.09034	−0.163021
$976$	−69.3871	−2.22103
$977$	58.7400	1.87926	0.939629	−	0.342194i	$-0.111170\pi$
$977$	58.7400	1.87926	0.939629	+	0.342194i	$0.111170\pi$
$978$	−9.52382	−0.304538
$979$	14.0597	0.449350
$980$	0	0
$981$	−27.9038	−0.890899
$982$	−67.4864	−2.15358
$983$	25.4675	0.812286	0.406143	−	0.913810i	$-0.366874\pi$
$983$	25.4675	0.812286	0.406143	+	0.913810i	$0.366874\pi$
$984$	1.79477	0.0572152
$985$	−57.4595	−1.83081
$986$	95.5596	3.04324
$987$	0	0
$988$	−9.65906	−0.307296
$989$	37.1246	1.18049
$990$	−32.6003	−1.03611
$991$	16.5141	0.524588	0.262294	−	0.964988i	$-0.415521\pi$
$991$	16.5141	0.524588	0.262294	+	0.964988i	$0.415521\pi$
$992$	7.29694	0.231678
$993$	−16.0765	−0.510171
$994$	0	0
$995$	8.12383	0.257543
$996$	−0.411606	−0.0130422
$997$	−6.12265	−0.193906	−0.0969532	−	0.995289i	$-0.530910\pi$
$997$	−6.12265	−0.193906	−0.0969532	+	0.995289i	$0.530910\pi$
$998$	−42.8196	−1.35543
$999$	30.0774	0.951606

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2009.2.a.s.1.4		17
7.2	even	3		287.2.e.d.165.14	✓	34
7.4	even	3		287.2.e.d.247.14	yes	34
7.6	odd	2		2009.2.a.r.1.4		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.e.d.165.14	✓	34	7.2	even	3
287.2.e.d.247.14	yes	34	7.4	even	3
2009.2.a.r.1.4		17	7.6	odd	2
2009.2.a.s.1.4		17	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q-1.77896 q^{2} +1.20779 q^{3} +1.16468 q^{4} -2.53283 q^{5} -2.14861 q^{6} +1.48599 q^{8} -1.54123 q^{9} +O(q^{10})\)	\(q-1.77896 q^{2} +1.20779 q^{3} +1.16468 q^{4} -2.53283 q^{5} -2.14861 q^{6} +1.48599 q^{8} -1.54123 q^{9} +4.50580 q^{10} +4.69442 q^{11} +1.40670 q^{12} -2.97799 q^{13} -3.05914 q^{15} -4.97288 q^{16} -7.01187 q^{17} +2.74178 q^{18} +2.78486 q^{19} -2.94995 q^{20} -8.35117 q^{22} +4.04356 q^{23} +1.79477 q^{24} +1.41524 q^{25} +5.29771 q^{26} -5.48488 q^{27} +7.66082 q^{29} +5.44208 q^{30} +1.24213 q^{31} +5.87455 q^{32} +5.66990 q^{33} +12.4738 q^{34} -1.79505 q^{36} -5.48369 q^{37} -4.95414 q^{38} -3.59680 q^{39} -3.76377 q^{40} +1.00000 q^{41} +9.18117 q^{43} +5.46752 q^{44} +3.90368 q^{45} -7.19331 q^{46} -7.77039 q^{47} -6.00622 q^{48} -2.51765 q^{50} -8.46890 q^{51} -3.46842 q^{52} -9.44258 q^{53} +9.75735 q^{54} -11.8902 q^{55} +3.36354 q^{57} -13.6283 q^{58} +1.63269 q^{59} -3.56293 q^{60} +13.9531 q^{61} -2.20969 q^{62} -0.504809 q^{64} +7.54275 q^{65} -10.0865 q^{66} -3.75824 q^{67} -8.16662 q^{68} +4.88379 q^{69} -6.77038 q^{71} -2.29026 q^{72} +2.70572 q^{73} +9.75525 q^{74} +1.70932 q^{75} +3.24348 q^{76} +6.39855 q^{78} +12.4767 q^{79} +12.5955 q^{80} -2.00090 q^{81} -1.77896 q^{82} -0.292604 q^{83} +17.7599 q^{85} -16.3329 q^{86} +9.25269 q^{87} +6.97587 q^{88} +2.99498 q^{89} -6.94448 q^{90} +4.70947 q^{92} +1.50023 q^{93} +13.8232 q^{94} -7.05359 q^{95} +7.09525 q^{96} +11.1466 q^{97} -7.23520 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 3 q^{2} + q^{3} + 25 q^{4} - q^{5} + 2 q^{6} + 9 q^{8} + 26 q^{9}+O(q^{10}) \) 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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