LMFDB - Embedded newform 2009.2.a.n.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2009,2,Mod(1,2009)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2009, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2009.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2009 = 7^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2009.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$16.0419457661$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.633117.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 6x^{3} + 4x^{2} + 6x - 3 $ x^5 - x^4 - 6x^3 + 4x^2 + 6*x - 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 287)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.20098$ 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)

$f(q)$	$=$	$q-1.20098 q^{2} +0.200978 q^{3} -0.557652 q^{4} +3.21704 q^{5} -0.241370 q^{6} +3.07168 q^{8} -2.95961 q^{9} +O(q^{10})$	\(q-1.20098 q^{2} +0.200978 q^{3} -0.557652 q^{4} +3.21704 q^{5} -0.241370 q^{6} +3.07168 q^{8} -2.95961 q^{9} -3.86360 q^{10} +4.57695 q^{11} -0.112076 q^{12} -0.703013 q^{13} +0.646554 q^{15} -2.57372 q^{16} -4.25337 q^{17} +3.55442 q^{18} -8.04736 q^{19} -1.79399 q^{20} -5.49681 q^{22} -5.34842 q^{23} +0.617340 q^{24} +5.34937 q^{25} +0.844303 q^{26} -1.19775 q^{27} -5.39204 q^{29} -0.776497 q^{30} -7.61900 q^{31} -3.05239 q^{32} +0.919865 q^{33} +5.10820 q^{34} +1.65043 q^{36} +5.19272 q^{37} +9.66470 q^{38} -0.141290 q^{39} +9.88174 q^{40} +1.00000 q^{41} +10.3241 q^{43} -2.55235 q^{44} -9.52119 q^{45} +6.42333 q^{46} -12.1160 q^{47} -0.517260 q^{48} -6.42448 q^{50} -0.854832 q^{51} +0.392037 q^{52} -12.2837 q^{53} +1.43847 q^{54} +14.7242 q^{55} -1.61734 q^{57} +6.47572 q^{58} +7.73023 q^{59} -0.360553 q^{60} +2.48971 q^{61} +9.15025 q^{62} +8.81329 q^{64} -2.26162 q^{65} -1.10474 q^{66} -3.09767 q^{67} +2.37190 q^{68} -1.07491 q^{69} +5.11581 q^{71} -9.09098 q^{72} -4.13640 q^{73} -6.23634 q^{74} +1.07511 q^{75} +4.48763 q^{76} +0.169686 q^{78} -13.7414 q^{79} -8.27977 q^{80} +8.63810 q^{81} -1.20098 q^{82} -4.90626 q^{83} -13.6833 q^{85} -12.3990 q^{86} -1.08368 q^{87} +14.0589 q^{88} -5.97567 q^{89} +11.4347 q^{90} +2.98256 q^{92} -1.53125 q^{93} +14.5511 q^{94} -25.8887 q^{95} -0.613462 q^{96} -1.45550 q^{97} -13.5460 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - q^{2} - 4 q^{3} + 3 q^{4} + 5 q^{5} - 12 q^{6} - 3 q^{8} + q^{9}+O(q^{10}) $ 5 * q - q^2 - 4 * q^3 + 3 * q^4 + 5 * q^5 - 12 * q^6 - 3 * q^8 + q^9	$ 5 q - q^{2} - 4 q^{3} + 3 q^{4} + 5 q^{5} - 12 q^{6} - 3 q^{8} + q^{9} + 2 q^{11} + 2 q^{12} - 5 q^{13} - 5 q^{15} - q^{16} - 13 q^{17} + 21 q^{18} + 23 q^{20} + q^{22} + 2 q^{23} - 2 q^{24} + 22 q^{25} - 10 q^{27} - 5 q^{29} - 33 q^{30} - 17 q^{31} - 12 q^{32} - 3 q^{33} + 8 q^{34} + 15 q^{36} - 7 q^{37} + 3 q^{38} + 5 q^{39} - 7 q^{40} + 5 q^{41} + q^{43} - 47 q^{44} + 23 q^{45} - 24 q^{46} - 9 q^{47} + 19 q^{48} + 2 q^{50} + 5 q^{51} - 20 q^{52} + 5 q^{53} - 2 q^{54} - 33 q^{55} - 3 q^{57} - 27 q^{58} - 7 q^{59} - 16 q^{60} - 22 q^{61} + 28 q^{62} - 3 q^{64} - 31 q^{65} + 42 q^{66} - 3 q^{67} - 17 q^{68} + 22 q^{69} - 24 q^{71} - 12 q^{72} - 40 q^{73} - 5 q^{74} - 24 q^{75} + 19 q^{76} + 30 q^{78} - 42 q^{79} - 24 q^{80} + 9 q^{81} - q^{82} + 12 q^{83} - 23 q^{85} + 16 q^{86} + 32 q^{87} + 26 q^{88} - 8 q^{89} + 59 q^{90} + 12 q^{92} - 11 q^{93} + 23 q^{94} - 17 q^{95} + 17 q^{96} - 16 q^{97} - 45 q^{99}+O(q^{100}) $ 5 * q - q^2 - 4 * q^3 + 3 * q^4 + 5 * q^5 - 12 * q^6 - 3 * q^8 + q^9 + 2 * q^11 + 2 * q^12 - 5 * q^13 - 5 * q^15 - q^16 - 13 * q^17 + 21 * q^18 + 23 * q^20 + q^22 + 2 * q^23 - 2 * q^24 + 22 * q^25 - 10 * q^27 - 5 * q^29 - 33 * q^30 - 17 * q^31 - 12 * q^32 - 3 * q^33 + 8 * q^34 + 15 * q^36 - 7 * q^37 + 3 * q^38 + 5 * q^39 - 7 * q^40 + 5 * q^41 + q^43 - 47 * q^44 + 23 * q^45 - 24 * q^46 - 9 * q^47 + 19 * q^48 + 2 * q^50 + 5 * q^51 - 20 * q^52 + 5 * q^53 - 2 * q^54 - 33 * q^55 - 3 * q^57 - 27 * q^58 - 7 * q^59 - 16 * q^60 - 22 * q^61 + 28 * q^62 - 3 * q^64 - 31 * q^65 + 42 * q^66 - 3 * q^67 - 17 * q^68 + 22 * q^69 - 24 * q^71 - 12 * q^72 - 40 * q^73 - 5 * q^74 - 24 * q^75 + 19 * q^76 + 30 * q^78 - 42 * q^79 - 24 * q^80 + 9 * q^81 - q^82 + 12 * q^83 - 23 * q^85 + 16 * q^86 + 32 * q^87 + 26 * q^88 - 8 * q^89 + 59 * q^90 + 12 * q^92 - 11 * q^93 + 23 * q^94 - 17 * q^95 + 17 * q^96 - 16 * q^97 - 45 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.20098	−0.849220	−0.424610	−	0.905376i	$-0.639589\pi$
$2$	−1.20098	−0.849220	−0.424610	+	0.905376i	$0.639589\pi$
$3$	0.200978	0.116035	0.0580173	−	0.998316i	$-0.481522\pi$
$3$	0.200978	0.116035	0.0580173	+	0.998316i	$0.481522\pi$
$4$	−0.557652	−0.278826
$5$	3.21704	1.43871	0.719353	−	0.694645i	$-0.244438\pi$
$5$	3.21704	1.43871	0.719353	+	0.694645i	$0.244438\pi$
$6$	−0.241370	−0.0985388
$7$	0	0
$7$	0	0
$8$	3.07168	1.08600
$9$	−2.95961	−0.986536
$10$	−3.86360	−1.22178
$11$	4.57695	1.38000	0.690001	−	0.723809i	$-0.257610\pi$
$11$	4.57695	1.38000	0.690001	+	0.723809i	$0.257610\pi$
$12$	−0.112076	−0.0323535
$13$	−0.703013	−0.194981	−0.0974904	−	0.995236i	$-0.531082\pi$
$13$	−0.703013	−0.194981	−0.0974904	+	0.995236i	$0.531082\pi$
$14$	0	0
$15$	0.646554	0.166940
$16$	−2.57372	−0.643430
$17$	−4.25337	−1.03159	−0.515796	−	0.856711i	$-0.672504\pi$
$17$	−4.25337	−1.03159	−0.515796	+	0.856711i	$0.672504\pi$
$18$	3.55442	0.837786
$19$	−8.04736	−1.84619	−0.923095	−	0.384571i	$-0.874349\pi$
$19$	−8.04736	−1.84619	−0.923095	+	0.384571i	$0.874349\pi$
$20$	−1.79399	−0.401149
$21$	0	0
$22$	−5.49681	−1.17192
$23$	−5.34842	−1.11522	−0.557611	−	0.830102i	$-0.688282\pi$
$23$	−5.34842	−1.11522	−0.557611	+	0.830102i	$0.688282\pi$
$24$	0.617340	0.126014
$25$	5.34937	1.06987
$26$	0.844303	0.165581
$27$	−1.19775	−0.230507
$28$	0	0
$29$	−5.39204	−1.00128	−0.500638	−	0.865657i	$-0.666901\pi$
$29$	−5.39204	−1.00128	−0.500638	+	0.865657i	$0.666901\pi$
$30$	−0.776497	−0.141768
$31$	−7.61900	−1.36841	−0.684206	−	0.729288i	$-0.739851\pi$
$31$	−7.61900	−1.36841	−0.684206	+	0.729288i	$0.739851\pi$
$32$	−3.05239	−0.539591
$33$	0.919865	0.160128
$34$	5.10820	0.876049
$35$	0	0
$36$	1.65043	0.275072
$37$	5.19272	0.853678	0.426839	−	0.904328i	$-0.359627\pi$
$37$	5.19272	0.853678	0.426839	+	0.904328i	$0.359627\pi$
$38$	9.66470	1.56782
$39$	−0.141290	−0.0226245
$40$	9.88174	1.56244
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	10.3241	1.57441	0.787205	−	0.616692i	$-0.211528\pi$
$43$	10.3241	1.57441	0.787205	+	0.616692i	$0.211528\pi$
$44$	−2.55235	−0.384781
$45$	−9.52119	−1.41934
$46$	6.42333	0.947068
$47$	−12.1160	−1.76730	−0.883651	−	0.468147i	$-0.844922\pi$
$47$	−12.1160	−1.76730	−0.883651	+	0.468147i	$0.844922\pi$
$48$	−0.517260	−0.0746601
$49$	0	0
$50$	−6.42448	−0.908559
$51$	−0.854832	−0.119700
$52$	0.392037	0.0543657
$53$	−12.2837	−1.68730	−0.843648	−	0.536897i	$-0.819596\pi$
$53$	−12.2837	−1.68730	−0.843648	+	0.536897i	$0.819596\pi$
$54$	1.43847	0.195751
$55$	14.7242	1.98542
$56$	0	0
$57$	−1.61734	−0.214222
$58$	6.47572	0.850303
$59$	7.73023	1.00639	0.503195	−	0.864173i	$-0.332158\pi$
$59$	7.73023	1.00639	0.503195	+	0.864173i	$0.332158\pi$
$60$	−0.360553	−0.0465471
$61$	2.48971	0.318774	0.159387	−	0.987216i	$-0.449048\pi$
$61$	2.48971	0.318774	0.159387	+	0.987216i	$0.449048\pi$
$62$	9.15025	1.16208
$63$	0	0
$64$	8.81329	1.10166
$65$	−2.26162	−0.280520
$66$	−1.10474	−0.135984
$67$	−3.09767	−0.378440	−0.189220	−	0.981935i	$-0.560596\pi$
$67$	−3.09767	−0.378440	−0.189220	+	0.981935i	$0.560596\pi$
$68$	2.37190	0.287635
$69$	−1.07491	−0.129404
$70$	0	0
$71$	5.11581	0.607135	0.303568	−	0.952810i	$-0.401822\pi$
$71$	5.11581	0.607135	0.303568	+	0.952810i	$0.401822\pi$
$72$	−9.09098	−1.07138
$73$	−4.13640	−0.484129	−0.242065	−	0.970260i	$-0.577825\pi$
$73$	−4.13640	−0.484129	−0.242065	+	0.970260i	$0.577825\pi$
$74$	−6.23634	−0.724960
$75$	1.07511	0.124142
$76$	4.48763	0.514766
$77$	0	0
$78$	0.169686	0.0192132
$79$	−13.7414	−1.54603	−0.773015	−	0.634388i	$-0.781252\pi$
$79$	−13.7414	−1.54603	−0.773015	+	0.634388i	$0.781252\pi$
$80$	−8.27977	−0.925706
$81$	8.63810	0.959789
$82$	−1.20098	−0.132626
$83$	−4.90626	−0.538532	−0.269266	−	0.963066i	$-0.586781\pi$
$83$	−4.90626	−0.538532	−0.269266	+	0.963066i	$0.586781\pi$
$84$	0	0
$85$	−13.6833	−1.48416
$86$	−12.3990	−1.33702
$87$	−1.08368	−0.116183
$88$	14.0589	1.49869
$89$	−5.97567	−0.633420	−0.316710	−	0.948522i	$-0.602578\pi$
$89$	−5.97567	−0.633420	−0.316710	+	0.948522i	$0.602578\pi$
$90$	11.4347	1.20533
$91$	0	0
$92$	2.98256	0.310953
$93$	−1.53125	−0.158783
$94$	14.5511	1.50083
$95$	−25.8887	−2.65613
$96$	−0.613462	−0.0626112
$97$	−1.45550	−0.147783	−0.0738916	−	0.997266i	$-0.523542\pi$
$97$	−1.45550	−0.147783	−0.0738916	+	0.997266i	$0.523542\pi$
$98$	0	0
$99$	−13.5460	−1.36142
$100$	−2.98309	−0.298309
$101$	−1.92425	−0.191470	−0.0957348	−	0.995407i	$-0.530520\pi$
$101$	−1.92425	−0.191470	−0.0957348	+	0.995407i	$0.530520\pi$
$102$	1.02663	0.101652
$103$	5.35990	0.528127	0.264063	−	0.964505i	$-0.414937\pi$
$103$	5.35990	0.528127	0.264063	+	0.964505i	$0.414937\pi$
$104$	−2.15943	−0.211750
$105$	0	0
$106$	14.7524	1.43288
$107$	2.83031	0.273617	0.136808	−	0.990598i	$-0.456316\pi$
$107$	2.83031	0.273617	0.136808	+	0.990598i	$0.456316\pi$
$108$	0.667927	0.0642713
$109$	11.3960	1.09154	0.545768	−	0.837936i	$-0.316238\pi$
$109$	11.3960	1.09154	0.545768	+	0.837936i	$0.316238\pi$
$110$	−17.6835	−1.68605
$111$	1.04362	0.0990561
$112$	0	0
$113$	18.4852	1.73894	0.869470	−	0.493986i	$-0.164461\pi$
$113$	18.4852	1.73894	0.869470	+	0.493986i	$0.164461\pi$
$114$	1.94239	0.181921
$115$	−17.2061	−1.60448
$116$	3.00688	0.279182
$117$	2.08064	0.192356
$118$	−9.28384	−0.854647
$119$	0	0
$120$	1.98601	0.181297
$121$	9.94845	0.904405
$122$	−2.99008	−0.270709
$123$	0.200978	0.0181216
$124$	4.24875	0.381549
$125$	1.12395	0.100530
$126$	0	0
$127$	9.98152	0.885717	0.442858	−	0.896592i	$-0.353964\pi$
$127$	9.98152	0.885717	0.442858	+	0.896592i	$0.353964\pi$
$128$	−4.47979	−0.395961
$129$	2.07491	0.182686
$130$	2.71616	0.238223
$131$	11.2796	0.985506	0.492753	−	0.870169i	$-0.335991\pi$
$131$	11.2796	0.985506	0.492753	+	0.870169i	$0.335991\pi$
$132$	−0.512965	−0.0446479
$133$	0	0
$134$	3.72023	0.321379
$135$	−3.85321	−0.331632
$136$	−13.0650	−1.12031
$137$	9.73838	0.832006	0.416003	−	0.909363i	$-0.363431\pi$
$137$	9.73838	0.832006	0.416003	+	0.909363i	$0.363431\pi$
$138$	1.29095	0.109893
$139$	4.85307	0.411632	0.205816	−	0.978591i	$-0.434015\pi$
$139$	4.85307	0.411632	0.205816	+	0.978591i	$0.434015\pi$
$140$	0	0
$141$	−2.43505	−0.205068
$142$	−6.14398	−0.515591
$143$	−3.21765	−0.269074
$144$	7.61720	0.634767
$145$	−17.3464	−1.44054
$146$	4.96773	0.411132
$147$	0	0
$148$	−2.89573	−0.238028
$149$	−6.47268	−0.530263	−0.265131	−	0.964212i	$-0.585415\pi$
$149$	−6.47268	−0.530263	−0.265131	+	0.964212i	$0.585415\pi$
$150$	−1.29118	−0.105424
$151$	−16.6124	−1.35190	−0.675949	−	0.736948i	$-0.736266\pi$
$151$	−16.6124	−1.35190	−0.675949	+	0.736948i	$0.736266\pi$
$152$	−24.7189	−2.00497
$153$	12.5883	1.01770
$154$	0	0
$155$	−24.5107	−1.96874
$156$	0.0787907	0.00630831
$157$	−21.5294	−1.71824	−0.859119	−	0.511777i	$-0.828988\pi$
$157$	−21.5294	−1.71824	−0.859119	+	0.511777i	$0.828988\pi$
$158$	16.5031	1.31292
$159$	−2.46875	−0.195785
$160$	−9.81967	−0.776313
$161$	0	0
$162$	−10.3742	−0.815072
$163$	−0.00553783	−0.000433757 0	−0.000216878	−	1.00000i	$-0.500069\pi$
$163$	−0.00553783	−0.000433757 0	−0.000216878		1.00000i	$0.500069\pi$
$164$	−0.557652	−0.0435453
$165$	2.95925	0.230377
$166$	5.89231	0.457332
$167$	−22.4914	−1.74044	−0.870220	−	0.492663i	$-0.836024\pi$
$167$	−22.4914	−1.74044	−0.870220	+	0.492663i	$0.836024\pi$
$168$	0	0
$169$	−12.5058	−0.961983
$170$	16.4333	1.26038
$171$	23.8170	1.82133
$172$	−5.75725	−0.438986
$173$	−6.07961	−0.462224	−0.231112	−	0.972927i	$-0.574236\pi$
$173$	−6.07961	−0.462224	−0.231112	+	0.972927i	$0.574236\pi$
$174$	1.30148	0.0986646
$175$	0	0
$176$	−11.7798	−0.887934
$177$	1.55361	0.116776
$178$	7.17665	0.537913
$179$	−7.91618	−0.591683	−0.295842	−	0.955237i	$-0.595600\pi$
$179$	−7.91618	−0.591683	−0.295842	+	0.955237i	$0.595600\pi$
$180$	5.30951	0.395748
$181$	2.20401	0.163823	0.0819115	−	0.996640i	$-0.473898\pi$
$181$	2.20401	0.163823	0.0819115	+	0.996640i	$0.473898\pi$
$182$	0	0
$183$	0.500376	0.0369888
$184$	−16.4286	−1.21114
$185$	16.7052	1.22819
$186$	1.83900	0.134842
$187$	−19.4674	−1.42360
$188$	6.75652	0.492770
$189$	0	0
$190$	31.0918	2.25563
$191$	−1.75601	−0.127061	−0.0635303	−	0.997980i	$-0.520236\pi$
$191$	−1.75601	−0.127061	−0.0635303	+	0.997980i	$0.520236\pi$
$192$	1.77128	0.127831
$193$	2.06376	0.148553	0.0742763	−	0.997238i	$-0.476335\pi$
$193$	2.06376	0.148553	0.0742763	+	0.997238i	$0.476335\pi$
$194$	1.74802	0.125500
$195$	−0.454536	−0.0325500
$196$	0	0
$197$	−21.2674	−1.51524	−0.757621	−	0.652695i	$-0.773638\pi$
$197$	−21.2674	−1.51524	−0.757621	+	0.652695i	$0.773638\pi$
$198$	16.2684	1.15615
$199$	6.50285	0.460975	0.230488	−	0.973075i	$-0.425968\pi$
$199$	6.50285	0.460975	0.230488	+	0.973075i	$0.425968\pi$
$200$	16.4316	1.16189
$201$	−0.622563	−0.0439122
$202$	2.31098	0.162600
$203$	0	0
$204$	0.476699	0.0333756
$205$	3.21704	0.224688
$206$	−6.43713	−0.448496
$207$	15.8292	1.10021
$208$	1.80936	0.125456
$209$	−36.8323	−2.54775
$210$	0	0
$211$	−10.4931	−0.722377	−0.361188	−	0.932493i	$-0.617629\pi$
$211$	−10.4931	−0.722377	−0.361188	+	0.932493i	$0.617629\pi$
$212$	6.85003	0.470462
$213$	1.02816	0.0704487
$214$	−3.39914	−0.232361
$215$	33.2131	2.26511
$216$	−3.67911	−0.250331
$217$	0	0
$218$	−13.6863	−0.926953
$219$	−0.831325	−0.0561757
$220$	−8.21101	−0.553586
$221$	2.99017	0.201141
$222$	−1.25337	−0.0841204
$223$	−14.4757	−0.969366	−0.484683	−	0.874690i	$-0.661065\pi$
$223$	−14.4757	−0.969366	−0.484683	+	0.874690i	$0.661065\pi$
$224$	0	0
$225$	−15.8321	−1.05547
$226$	−22.2003	−1.47674
$227$	17.5499	1.16483	0.582414	−	0.812892i	$-0.302108\pi$
$227$	17.5499	1.16483	0.582414	+	0.812892i	$0.302108\pi$
$228$	0.901914	0.0597307
$229$	0.189800	0.0125423	0.00627117	−	0.999980i	$-0.498004\pi$
$229$	0.189800	0.0125423	0.00627117	+	0.999980i	$0.498004\pi$
$230$	20.6641	1.36255
$231$	0	0
$232$	−16.5626	−1.08739
$233$	2.03466	0.133295	0.0666476	−	0.997777i	$-0.478770\pi$
$233$	2.03466	0.133295	0.0666476	+	0.997777i	$0.478770\pi$
$234$	−2.49881	−0.163352
$235$	−38.9777	−2.54263
$236$	−4.31078	−0.280608
$237$	−2.76172	−0.179393
$238$	0	0
$239$	11.6053	0.750684	0.375342	−	0.926886i	$-0.377525\pi$
$239$	11.6053	0.750684	0.375342	+	0.926886i	$0.377525\pi$
$240$	−1.66405	−0.107414
$241$	4.33539	0.279267	0.139633	−	0.990203i	$-0.455408\pi$
$241$	4.33539	0.279267	0.139633	+	0.990203i	$0.455408\pi$
$242$	−11.9479	−0.768038
$243$	5.32931	0.341876
$244$	−1.38839	−0.0888826
$245$	0	0
$246$	−0.241370	−0.0153892
$247$	5.65740	0.359972
$248$	−23.4032	−1.48610
$249$	−0.986049	−0.0624883
$250$	−1.34984	−0.0853716
$251$	−23.3501	−1.47385	−0.736923	−	0.675976i	$-0.763722\pi$
$251$	−23.3501	−1.47385	−0.736923	+	0.675976i	$0.763722\pi$
$252$	0	0
$253$	−24.4794	−1.53901
$254$	−11.9876	−0.752168
$255$	−2.75003	−0.172214
$256$	−12.2465	−0.765403
$257$	19.7199	1.23009	0.615046	−	0.788491i	$-0.289138\pi$
$257$	19.7199	1.23009	0.615046	+	0.788491i	$0.289138\pi$
$258$	−2.49192	−0.155140
$259$	0	0
$260$	1.26120	0.0782163
$261$	15.9583	0.987795
$262$	−13.5466	−0.836911
$263$	1.67120	0.103050	0.0515252	−	0.998672i	$-0.483592\pi$
$263$	1.67120	0.103050	0.0515252	+	0.998672i	$0.483592\pi$
$264$	2.82553	0.173900
$265$	−39.5172	−2.42752
$266$	0	0
$267$	−1.20098	−0.0734986
$268$	1.72742	0.105519
$269$	24.4059	1.48805	0.744027	−	0.668150i	$-0.232914\pi$
$269$	24.4059	1.48805	0.744027	+	0.668150i	$0.232914\pi$
$270$	4.62762	0.281628
$271$	−7.83315	−0.475830	−0.237915	−	0.971286i	$-0.576464\pi$
$271$	−7.83315	−0.475830	−0.237915	+	0.971286i	$0.576464\pi$
$272$	10.9470	0.663757
$273$	0	0
$274$	−11.6956	−0.706555
$275$	24.4838	1.47643
$276$	0.599428	0.0360813
$277$	−6.53052	−0.392381	−0.196190	−	0.980566i	$-0.562857\pi$
$277$	−6.53052	−0.392381	−0.196190	+	0.980566i	$0.562857\pi$
$278$	−5.82843	−0.349566
$279$	22.5493	1.34999
$280$	0	0
$281$	−2.23112	−0.133097	−0.0665487	−	0.997783i	$-0.521199\pi$
$281$	−2.23112	−0.133097	−0.0665487	+	0.997783i	$0.521199\pi$
$282$	2.92444	0.174148
$283$	18.2949	1.08752	0.543759	−	0.839242i	$-0.317001\pi$
$283$	18.2949	1.08752	0.543759	+	0.839242i	$0.317001\pi$
$284$	−2.85285	−0.169285
$285$	−5.20306	−0.308202
$286$	3.86433	0.228503
$287$	0	0
$288$	9.03387	0.532326
$289$	1.09112	0.0641835
$290$	20.8327	1.22334
$291$	−0.292522	−0.0171480
$292$	2.30667	0.134988
$293$	7.37440	0.430817	0.215409	−	0.976524i	$-0.430892\pi$
$293$	7.37440	0.430817	0.215409	+	0.976524i	$0.430892\pi$
$294$	0	0
$295$	24.8685	1.44790
$296$	15.9504	0.927098
$297$	−5.48203	−0.318100
$298$	7.77355	0.450309
$299$	3.76001	0.217447
$300$	−0.599535	−0.0346142
$301$	0	0
$302$	19.9511	1.14806
$303$	−0.386731	−0.0222171
$304$	20.7116	1.18789
$305$	8.00949	0.458622
$306$	−15.1183	−0.864254
$307$	11.6587	0.665398	0.332699	−	0.943033i	$-0.392041\pi$
$307$	11.6587	0.665398	0.332699	+	0.943033i	$0.392041\pi$
$308$	0	0
$309$	1.07722	0.0612810
$310$	29.4368	1.67190
$311$	19.2508	1.09161	0.545806	−	0.837911i	$-0.316223\pi$
$311$	19.2508	1.09161	0.545806	+	0.837911i	$0.316223\pi$
$312$	−0.433998	−0.0245703
$313$	3.73012	0.210839	0.105419	−	0.994428i	$-0.466382\pi$
$313$	3.73012	0.210839	0.105419	+	0.994428i	$0.466382\pi$
$314$	25.8564	1.45916
$315$	0	0
$316$	7.66293	0.431074
$317$	−19.6027	−1.10100	−0.550499	−	0.834836i	$-0.685562\pi$
$317$	−19.6027	−1.10100	−0.550499	+	0.834836i	$0.685562\pi$
$318$	2.96491	0.166264
$319$	−24.6791	−1.38176
$320$	28.3527	1.58497
$321$	0.568830	0.0317490
$322$	0	0
$323$	34.2284	1.90452
$324$	−4.81706	−0.267614
$325$	−3.76068	−0.208605
$326$	0.00665081	0.000368355 0
$327$	2.29034	0.126656
$328$	3.07168	0.169605
$329$	0	0
$330$	−3.55399	−0.195641
$331$	−23.4828	−1.29073	−0.645366	−	0.763873i	$-0.723295\pi$
$331$	−23.4828	−1.29073	−0.645366	+	0.763873i	$0.723295\pi$
$332$	2.73599	0.150157
$333$	−15.3684	−0.842184
$334$	27.0117	1.47802
$335$	−9.96534	−0.544465
$336$	0	0
$337$	1.20201	0.0654778	0.0327389	−	0.999464i	$-0.489577\pi$
$337$	1.20201	0.0654778	0.0327389	+	0.999464i	$0.489577\pi$
$338$	15.0192	0.816934
$339$	3.71511	0.201777
$340$	7.63051	0.413822
$341$	−34.8718	−1.88841
$342$	−28.6037	−1.54671
$343$	0	0
$344$	31.7123	1.70981
$345$	−3.45804	−0.186175
$346$	7.30148	0.392530
$347$	−3.01800	−0.162015	−0.0810074	−	0.996713i	$-0.525814\pi$
$347$	−3.01800	−0.162015	−0.0810074	+	0.996713i	$0.525814\pi$
$348$	0.604317	0.0323948
$349$	30.2795	1.62082	0.810412	−	0.585861i	$-0.199243\pi$
$349$	30.2795	1.62082	0.810412	+	0.585861i	$0.199243\pi$
$350$	0	0
$351$	0.842033	0.0449444
$352$	−13.9706	−0.744637
$353$	−4.59065	−0.244336	−0.122168	−	0.992509i	$-0.538985\pi$
$353$	−4.59065	−0.244336	−0.122168	+	0.992509i	$0.538985\pi$
$354$	−1.86585	−0.0991686
$355$	16.4578	0.873489
$356$	3.33235	0.176614
$357$	0	0
$358$	9.50716	0.502469
$359$	18.4050	0.971381	0.485691	−	0.874131i	$-0.338568\pi$
$359$	18.4050	0.971381	0.485691	+	0.874131i	$0.338568\pi$
$360$	−29.2461	−1.54140
$361$	45.7600	2.40842
$362$	−2.64697	−0.139122
$363$	1.99942	0.104942
$364$	0	0
$365$	−13.3070	−0.696519
$366$	−0.600940	−0.0314116
$367$	−17.0270	−0.888802	−0.444401	−	0.895828i	$-0.646583\pi$
$367$	−17.0270	−0.888802	−0.444401	+	0.895828i	$0.646583\pi$
$368$	13.7653	0.717567
$369$	−2.95961	−0.154071
$370$	−20.0626	−1.04300
$371$	0	0
$372$	0.853905	0.0442729
$373$	26.3381	1.36373	0.681867	−	0.731476i	$-0.261168\pi$
$373$	26.3381	1.36373	0.681867	+	0.731476i	$0.261168\pi$
$374$	23.3800	1.20895
$375$	0.225890	0.0116649
$376$	−37.2165	−1.91930
$377$	3.79067	0.195230
$378$	0	0
$379$	−25.4631	−1.30795	−0.653975	−	0.756516i	$-0.726900\pi$
$379$	−25.4631	−1.30795	−0.653975	+	0.756516i	$0.726900\pi$
$380$	14.4369	0.740597
$381$	2.00606	0.102774
$382$	2.10893	0.107902
$383$	−26.6465	−1.36157	−0.680786	−	0.732483i	$-0.738361\pi$
$383$	−26.6465	−1.36157	−0.680786	+	0.732483i	$0.738361\pi$
$384$	−0.900338	−0.0459452
$385$	0	0
$386$	−2.47853	−0.126154
$387$	−30.5553	−1.55321
$388$	0.811660	0.0412058
$389$	−33.7017	−1.70874	−0.854372	−	0.519662i	$-0.826058\pi$
$389$	−33.7017	−1.70874	−0.854372	+	0.519662i	$0.826058\pi$
$390$	0.545888	0.0276421
$391$	22.7488	1.15045
$392$	0	0
$393$	2.26695	0.114353
$394$	25.5417	1.28677
$395$	−44.2067	−2.22428
$396$	7.55394	0.379600
$397$	24.7242	1.24087	0.620437	−	0.784256i	$-0.286955\pi$
$397$	24.7242	1.24087	0.620437	+	0.784256i	$0.286955\pi$
$398$	−7.80978	−0.391469
$399$	0	0
$400$	−13.7678	−0.688389
$401$	14.7100	0.734581	0.367291	−	0.930106i	$-0.380285\pi$
$401$	14.7100	0.734581	0.367291	+	0.930106i	$0.380285\pi$
$402$	0.747684	0.0372911
$403$	5.35626	0.266814
$404$	1.07306	0.0533867
$405$	27.7892	1.38085
$406$	0	0
$407$	23.7668	1.17808
$408$	−2.62577	−0.129995
$409$	−18.8735	−0.933233	−0.466616	−	0.884460i	$-0.654527\pi$
$409$	−18.8735	−0.933233	−0.466616	+	0.884460i	$0.654527\pi$
$410$	−3.86360	−0.190810
$411$	1.95720	0.0965414
$412$	−2.98896	−0.147256
$413$	0	0
$414$	−19.0105	−0.934317
$415$	−15.7837	−0.774789
$416$	2.14587	0.105210
$417$	0.975359	0.0477635
$418$	44.2348	2.16360
$419$	−28.7795	−1.40597	−0.702985	−	0.711205i	$-0.748150\pi$
$419$	−28.7795	−1.40597	−0.702985	+	0.711205i	$0.748150\pi$
$420$	0	0
$421$	36.0120	1.75512	0.877559	−	0.479468i	$-0.159171\pi$
$421$	36.0120	1.75512	0.877559	+	0.479468i	$0.159171\pi$
$422$	12.6020	0.613456
$423$	35.8586	1.74351
$424$	−37.7316	−1.83241
$425$	−22.7528	−1.10368
$426$	−1.23480	−0.0598264
$427$	0	0
$428$	−1.57833	−0.0762915
$429$	−0.646677	−0.0312219
$430$	−39.8881	−1.92358
$431$	9.23519	0.444843	0.222422	−	0.974951i	$-0.428604\pi$
$431$	9.23519	0.444843	0.222422	+	0.974951i	$0.428604\pi$
$432$	3.08267	0.148315
$433$	18.1355	0.871537	0.435768	−	0.900059i	$-0.356477\pi$
$433$	18.1355	0.871537	0.435768	+	0.900059i	$0.356477\pi$
$434$	0	0
$435$	−3.48625	−0.167153
$436$	−6.35499	−0.304349
$437$	43.0406	2.05891
$438$	0.998402	0.0477055
$439$	6.79012	0.324075	0.162037	−	0.986785i	$-0.448193\pi$
$439$	6.79012	0.324075	0.162037	+	0.986785i	$0.448193\pi$
$440$	45.2282	2.15617
$441$	0	0
$442$	−3.59113	−0.170813
$443$	34.2284	1.62624	0.813119	−	0.582097i	$-0.197768\pi$
$443$	34.2284	1.62624	0.813119	+	0.582097i	$0.197768\pi$
$444$	−0.581978	−0.0276194
$445$	−19.2240	−0.911306
$446$	17.3850	0.823204
$447$	−1.30086	−0.0615288
$448$	0	0
$449$	−2.19148	−0.103422	−0.0517112	−	0.998662i	$-0.516468\pi$
$449$	−2.19148	−0.103422	−0.0517112	+	0.998662i	$0.516468\pi$
$450$	19.0139	0.896326
$451$	4.57695	0.215520
$452$	−10.3083	−0.484862
$453$	−3.33872	−0.156867
$454$	−21.0770	−0.989195
$455$	0	0
$456$	−4.96796	−0.232646
$457$	15.2932	0.715387	0.357694	−	0.933839i	$-0.383563\pi$
$457$	15.2932	0.715387	0.357694	+	0.933839i	$0.383563\pi$
$458$	−0.227946	−0.0106512
$459$	5.09446	0.237789
$460$	9.59502	0.447370
$461$	7.37440	0.343460	0.171730	−	0.985144i	$-0.445064\pi$
$461$	7.37440	0.343460	0.171730	+	0.985144i	$0.445064\pi$
$462$	0	0
$463$	−25.3329	−1.17732	−0.588661	−	0.808380i	$-0.700345\pi$
$463$	−25.3329	−1.17732	−0.588661	+	0.808380i	$0.700345\pi$
$464$	13.8776	0.644251
$465$	−4.92610	−0.228442
$466$	−2.44358	−0.113197
$467$	−9.05902	−0.419201	−0.209601	−	0.977787i	$-0.567216\pi$
$467$	−9.05902	−0.419201	−0.209601	+	0.977787i	$0.567216\pi$
$468$	−1.16028	−0.0536338
$469$	0	0
$470$	46.8114	2.15925
$471$	−4.32694	−0.199375
$472$	23.7448	1.09294
$473$	47.2528	2.17269
$474$	3.31676	0.152344
$475$	−43.0483	−1.97519
$476$	0	0
$477$	36.3549	1.66458
$478$	−13.9377	−0.637496
$479$	−15.7297	−0.718708	−0.359354	−	0.933201i	$-0.617003\pi$
$479$	−15.7297	−0.718708	−0.359354	+	0.933201i	$0.617003\pi$
$480$	−1.97353	−0.0900791
$481$	−3.65055	−0.166451
$482$	−5.20670	−0.237159
$483$	0	0
$484$	−5.54778	−0.252172
$485$	−4.68239	−0.212617
$486$	−6.40039	−0.290327
$487$	−11.5758	−0.524549	−0.262275	−	0.964993i	$-0.584473\pi$
$487$	−11.5758	−0.524549	−0.262275	+	0.964993i	$0.584473\pi$
$488$	7.64759	0.346190
$489$	−0.00111298	−5.03308e−5 0
$490$	0	0
$491$	−15.2590	−0.688628	−0.344314	−	0.938855i	$-0.611889\pi$
$491$	−15.2590	−0.688628	−0.344314	+	0.938855i	$0.611889\pi$
$492$	−0.112076	−0.00505276
$493$	22.9343	1.03291
$494$	−6.79441	−0.305695
$495$	−43.5780	−1.95869
$496$	19.6092	0.880478
$497$	0	0
$498$	1.18422	0.0530663
$499$	8.35644	0.374086	0.187043	−	0.982352i	$-0.440110\pi$
$499$	8.35644	0.374086	0.187043	+	0.982352i	$0.440110\pi$
$500$	−0.626776	−0.0280303
$501$	−4.52028	−0.201951
$502$	28.0430	1.25162
$503$	−2.53984	−0.113246	−0.0566230	−	0.998396i	$-0.518033\pi$
$503$	−2.53984	−0.113246	−0.0566230	+	0.998396i	$0.518033\pi$
$504$	0	0
$505$	−6.19038	−0.275468
$506$	29.3992	1.30696
$507$	−2.51338	−0.111623
$508$	−5.56622	−0.246961
$509$	6.48190	0.287305	0.143653	−	0.989628i	$-0.454115\pi$
$509$	6.48190	0.287305	0.143653	+	0.989628i	$0.454115\pi$
$510$	3.30273	0.146247
$511$	0	0
$512$	23.6673	1.04596
$513$	9.63871	0.425560
$514$	−23.6831	−1.04462
$515$	17.2430	0.759819
$516$	−1.15708	−0.0509376
$517$	−55.4543	−2.43888
$518$	0	0
$519$	−1.22187	−0.0536340
$520$	−6.94700	−0.304646
$521$	1.36749	0.0599107	0.0299553	−	0.999551i	$-0.490463\pi$
$521$	1.36749	0.0599107	0.0299553	+	0.999551i	$0.490463\pi$
$522$	−19.1656	−0.838855
$523$	−12.9198	−0.564944	−0.282472	−	0.959276i	$-0.591154\pi$
$523$	−12.9198	−0.564944	−0.282472	+	0.959276i	$0.591154\pi$
$524$	−6.29011	−0.274785
$525$	0	0
$526$	−2.00707	−0.0875123
$527$	32.4064	1.41164
$528$	−2.36747	−0.103031
$529$	5.60555	0.243720
$530$	47.4593	2.06150
$531$	−22.8785	−0.992841
$532$	0	0
$533$	−0.703013	−0.0304509
$534$	1.44235	0.0624165
$535$	9.10525	0.393654
$536$	−9.51506	−0.410988
$537$	−1.59098	−0.0686557
$538$	−29.3109	−1.26368
$539$	0	0
$540$	2.14875	0.0924676
$541$	−4.47397	−0.192351	−0.0961756	−	0.995364i	$-0.530661\pi$
$541$	−4.47397	−0.192351	−0.0961756	+	0.995364i	$0.530661\pi$
$542$	9.40744	0.404084
$543$	0.442958	0.0190091
$544$	12.9829	0.556638
$545$	36.6613	1.57040
$546$	0	0
$547$	−22.3133	−0.954048	−0.477024	−	0.878890i	$-0.658285\pi$
$547$	−22.3133	−0.954048	−0.477024	+	0.878890i	$0.658285\pi$
$548$	−5.43063	−0.231985
$549$	−7.36855	−0.314482
$550$	−29.4045	−1.25381
$551$	43.3917	1.84855
$552$	−3.30179	−0.140534
$553$	0	0
$554$	7.84300	0.333217
$555$	3.35738	0.142513
$556$	−2.70633	−0.114774
$557$	15.3755	0.651482	0.325741	−	0.945459i	$-0.394386\pi$
$557$	15.3755	0.651482	0.325741	+	0.945459i	$0.394386\pi$
$558$	−27.0812	−1.14644
$559$	−7.25797	−0.306979
$560$	0	0
$561$	−3.91252	−0.165187
$562$	2.67952	0.113029
$563$	4.13910	0.174442	0.0872212	−	0.996189i	$-0.472201\pi$
$563$	4.13910	0.174442	0.0872212	+	0.996189i	$0.472201\pi$
$564$	1.35791	0.0571783
$565$	59.4677	2.50182
$566$	−21.9717	−0.923541
$567$	0	0
$568$	15.7142	0.659351
$569$	20.9479	0.878182	0.439091	−	0.898443i	$-0.355301\pi$
$569$	20.9479	0.878182	0.439091	+	0.898443i	$0.355301\pi$
$570$	6.24875	0.261731
$571$	−20.5728	−0.860947	−0.430473	−	0.902603i	$-0.641653\pi$
$571$	−20.5728	−0.860947	−0.430473	+	0.902603i	$0.641653\pi$
$572$	1.79433	0.0750248
$573$	−0.352919	−0.0147434
$574$	0	0
$575$	−28.6107	−1.19315
$576$	−26.0839	−1.08683
$577$	26.3061	1.09514	0.547568	−	0.836761i	$-0.315554\pi$
$577$	26.3061	1.09514	0.547568	+	0.836761i	$0.315554\pi$
$578$	−1.31041	−0.0545059
$579$	0.414770	0.0172372
$580$	9.67327	0.401661
$581$	0	0
$582$	0.351313	0.0145624
$583$	−56.2218	−2.32847
$584$	−12.7057	−0.525766
$585$	6.69352	0.276743
$586$	−8.85649	−0.365858
$587$	0.835878	0.0345004	0.0172502	−	0.999851i	$-0.494509\pi$
$587$	0.835878	0.0345004	0.0172502	+	0.999851i	$0.494509\pi$
$588$	0	0
$589$	61.3128	2.52635
$590$	−29.8665	−1.22959
$591$	−4.27428	−0.175820
$592$	−13.3646	−0.549282
$593$	5.90293	0.242404	0.121202	−	0.992628i	$-0.461325\pi$
$593$	5.90293	0.242404	0.121202	+	0.992628i	$0.461325\pi$
$594$	6.58380	0.270137
$595$	0	0
$596$	3.60951	0.147851
$597$	1.30693	0.0534890
$598$	−4.51568	−0.184660
$599$	−20.7273	−0.846896	−0.423448	−	0.905920i	$-0.639180\pi$
$599$	−20.7273	−0.846896	−0.423448	+	0.905920i	$0.639180\pi$
$600$	3.30238	0.134819
$601$	−4.69241	−0.191407	−0.0957037	−	0.995410i	$-0.530510\pi$
$601$	−4.69241	−0.191407	−0.0957037	+	0.995410i	$0.530510\pi$
$602$	0	0
$603$	9.16789	0.373345
$604$	9.26395	0.376945
$605$	32.0046	1.30117
$606$	0.464455	0.0188672
$607$	−27.8857	−1.13184	−0.565922	−	0.824459i	$-0.691480\pi$
$607$	−27.8857	−1.13184	−0.565922	+	0.824459i	$0.691480\pi$
$608$	24.5637	0.996188
$609$	0	0
$610$	−9.61922	−0.389471
$611$	8.51771	0.344590
$612$	−7.01989	−0.283762
$613$	−15.6076	−0.630383	−0.315192	−	0.949028i	$-0.602069\pi$
$613$	−15.6076	−0.630383	−0.315192	+	0.949028i	$0.602069\pi$
$614$	−14.0019	−0.565069
$615$	0.646554	0.0260716
$616$	0	0
$617$	12.2414	0.492820	0.246410	−	0.969166i	$-0.420749\pi$
$617$	12.2414	0.492820	0.246410	+	0.969166i	$0.420749\pi$
$618$	−1.29372	−0.0520410
$619$	−23.4809	−0.943778	−0.471889	−	0.881658i	$-0.656428\pi$
$619$	−23.4809	−0.943778	−0.471889	+	0.881658i	$0.656428\pi$
$620$	13.6684	0.548937
$621$	6.40606	0.257066
$622$	−23.1198	−0.927019
$623$	0	0
$624$	0.363641	0.0145573
$625$	−23.1311	−0.925243
$626$	−4.47979	−0.179048
$627$	−7.40248	−0.295627
$628$	12.0059	0.479090
$629$	−22.0865	−0.880648
$630$	0	0
$631$	−0.0226990	−0.000903631 0	−0.000451816	−	1.00000i	$-0.500144\pi$
$631$	−0.0226990	−0.000903631 0	−0.000451816		1.00000i	$0.500144\pi$
$632$	−42.2093	−1.67899
$633$	−2.10889	−0.0838207
$634$	23.5424	0.934989
$635$	32.1110	1.27429
$636$	1.37670	0.0545899
$637$	0	0
$638$	29.6390	1.17342
$639$	−15.1408	−0.598961
$640$	−14.4117	−0.569671
$641$	38.0777	1.50398	0.751989	−	0.659175i	$-0.229095\pi$
$641$	38.0777	1.50398	0.751989	+	0.659175i	$0.229095\pi$
$642$	−0.683152	−0.0269619
$643$	−24.2224	−0.955239	−0.477619	−	0.878567i	$-0.658500\pi$
$643$	−24.2224	−0.955239	−0.477619	+	0.878567i	$0.658500\pi$
$644$	0	0
$645$	6.67509	0.262831
$646$	−41.1075	−1.61735
$647$	44.1321	1.73501	0.867507	−	0.497426i	$-0.165721\pi$
$647$	44.1321	1.73501	0.867507	+	0.497426i	$0.165721\pi$
$648$	26.5335	1.04234
$649$	35.3809	1.38882
$650$	4.51649	0.177151
$651$	0	0
$652$	0.00308819	0.000120943 0
$653$	−3.76579	−0.147367	−0.0736833	−	0.997282i	$-0.523475\pi$
$653$	−3.76579	−0.147367	−0.0736833	+	0.997282i	$0.523475\pi$
$654$	−2.75064	−0.107559
$655$	36.2871	1.41785
$656$	−2.57372	−0.100487
$657$	12.2421	0.477611
$658$	0	0
$659$	−21.1980	−0.825757	−0.412878	−	0.910786i	$-0.635477\pi$
$659$	−21.1980	−0.825757	−0.412878	+	0.910786i	$0.635477\pi$
$660$	−1.65023	−0.0642351
$661$	11.3027	0.439624	0.219812	−	0.975542i	$-0.429456\pi$
$661$	11.3027	0.439624	0.219812	+	0.975542i	$0.429456\pi$
$662$	28.2023	1.09612
$663$	0.600958	0.0233393
$664$	−15.0705	−0.584848
$665$	0	0
$666$	18.4571	0.715199
$667$	28.8389	1.11664
$668$	12.5424	0.485280
$669$	−2.90930	−0.112480
$670$	11.9682	0.462370
$671$	11.3953	0.439909
$672$	0	0
$673$	18.3138	0.705946	0.352973	−	0.935634i	$-0.385171\pi$
$673$	18.3138	0.705946	0.352973	+	0.935634i	$0.385171\pi$
$674$	−1.44359	−0.0556050
$675$	−6.40721	−0.246614
$676$	6.97387	0.268226
$677$	15.9963	0.614788	0.307394	−	0.951582i	$-0.400543\pi$
$677$	15.9963	0.614788	0.307394	+	0.951582i	$0.400543\pi$
$678$	−4.46177	−0.171353
$679$	0	0
$680$	−42.0307	−1.61180
$681$	3.52714	0.135160
$682$	41.8802	1.60368
$683$	6.75437	0.258449	0.129224	−	0.991615i	$-0.458751\pi$
$683$	6.75437	0.258449	0.129224	+	0.991615i	$0.458751\pi$
$684$	−13.2816	−0.507835
$685$	31.3288	1.19701
$686$	0	0
$687$	0.0381456	0.00145534
$688$	−26.5713	−1.01302
$689$	8.63560	0.328990
$690$	4.15303	0.158103
$691$	−8.11399	−0.308671	−0.154335	−	0.988019i	$-0.549324\pi$
$691$	−8.11399	−0.308671	−0.154335	+	0.988019i	$0.549324\pi$
$692$	3.39031	0.128880
$693$	0	0
$694$	3.62455	0.137586
$695$	15.6125	0.592217
$696$	−3.32872	−0.126175
$697$	−4.25337	−0.161108
$698$	−36.3650	−1.37644
$699$	0.408922	0.0154668
$700$	0	0
$701$	−49.0400	−1.85221	−0.926107	−	0.377260i	$-0.876866\pi$
$701$	−49.0400	−1.85221	−0.926107	+	0.377260i	$0.876866\pi$
$702$	−1.01126	−0.0381677
$703$	−41.7877	−1.57605
$704$	40.3380	1.52029
$705$	−7.83366	−0.295033
$706$	5.51327	0.207495
$707$	0	0
$708$	−0.866372	−0.0325602
$709$	10.8982	0.409292	0.204646	−	0.978836i	$-0.434396\pi$
$709$	10.8982	0.409292	0.204646	+	0.978836i	$0.434396\pi$
$710$	−19.7654	−0.741784
$711$	40.6692	1.52521
$712$	−18.3554	−0.687897
$713$	40.7496	1.52608
$714$	0	0
$715$	−10.3513	−0.387118
$716$	4.41448	0.164977
$717$	2.33241	0.0871053
$718$	−22.1040	−0.824916
$719$	−0.0450043	−0.00167838	−0.000839188	−	1.00000i	$-0.500267\pi$
$719$	−0.0450043	−0.00167838	−0.000839188		1.00000i	$0.500267\pi$
$720$	24.5049	0.913243
$721$	0	0
$722$	−54.9567	−2.04528
$723$	0.871316	0.0324046
$724$	−1.22907	−0.0456782
$725$	−28.8440	−1.07124
$726$	−2.40126	−0.0891190
$727$	29.3527	1.08863	0.544315	−	0.838881i	$-0.316790\pi$
$727$	29.3527	1.08863	0.544315	+	0.838881i	$0.316790\pi$
$728$	0	0
$729$	−24.8432	−0.920120
$730$	15.9814	0.591498
$731$	−43.9121	−1.62415
$732$	−0.279036	−0.0103135
$733$	−19.0948	−0.705281	−0.352640	−	0.935759i	$-0.614716\pi$
$733$	−19.0948	−0.705281	−0.352640	+	0.935759i	$0.614716\pi$
$734$	20.4490	0.754788
$735$	0	0
$736$	16.3254	0.601764
$737$	−14.1779	−0.522249
$738$	3.55442	0.130840
$739$	−29.0981	−1.07039	−0.535196	−	0.844728i	$-0.679762\pi$
$739$	−29.0981	−1.07039	−0.535196	+	0.844728i	$0.679762\pi$
$740$	−9.31570	−0.342452
$741$	1.13701	0.0417692
$742$	0	0
$743$	−10.9674	−0.402354	−0.201177	−	0.979555i	$-0.564477\pi$
$743$	−10.9674	−0.402354	−0.201177	+	0.979555i	$0.564477\pi$
$744$	−4.70351	−0.172439
$745$	−20.8229	−0.762892
$746$	−31.6314	−1.15811
$747$	14.5206	0.531281
$748$	10.8561	0.396937
$749$	0	0
$750$	−0.271289	−0.00990606
$751$	33.9703	1.23959	0.619797	−	0.784762i	$-0.287215\pi$
$751$	33.9703	1.23959	0.619797	+	0.784762i	$0.287215\pi$
$752$	31.1832	1.13713
$753$	−4.69286	−0.171017
$754$	−4.55251	−0.165793
$755$	−53.4428	−1.94498
$756$	0	0
$757$	7.52333	0.273440	0.136720	−	0.990610i	$-0.456344\pi$
$757$	7.52333	0.273440	0.136720	+	0.990610i	$0.456344\pi$
$758$	30.5806	1.11074
$759$	−4.91982	−0.178578
$760$	−79.5219	−2.88456
$761$	23.8739	0.865428	0.432714	−	0.901531i	$-0.357556\pi$
$761$	23.8739	0.865428	0.432714	+	0.901531i	$0.357556\pi$
$762$	−2.40924	−0.0872775
$763$	0	0
$764$	0.979244	0.0354278
$765$	40.4971	1.46418
$766$	32.0018	1.15627
$767$	−5.43446	−0.196227
$768$	−2.46126	−0.0888132
$769$	−2.21793	−0.0799805	−0.0399903	−	0.999200i	$-0.512733\pi$
$769$	−2.21793	−0.0799805	−0.0399903	+	0.999200i	$0.512733\pi$
$770$	0	0
$771$	3.96325	0.142733
$772$	−1.15086	−0.0414204
$773$	−18.4207	−0.662547	−0.331274	−	0.943535i	$-0.607478\pi$
$773$	−18.4207	−0.662547	−0.331274	+	0.943535i	$0.607478\pi$
$774$	36.6962	1.31902
$775$	−40.7569	−1.46403
$776$	−4.47082	−0.160493
$777$	0	0
$778$	40.4750	1.45110
$779$	−8.04736	−0.288327
$780$	0.253473	0.00907580
$781$	23.4148	0.837848
$782$	−27.3208	−0.976989
$783$	6.45831	0.230801
$784$	0	0
$785$	−69.2612	−2.47204
$786$	−2.72256	−0.0971106
$787$	−18.9009	−0.673745	−0.336873	−	0.941550i	$-0.609369\pi$
$787$	−18.9009	−0.673745	−0.336873	+	0.941550i	$0.609369\pi$
$788$	11.8598	0.422489
$789$	0.335873	0.0119574
$790$	53.0913	1.88890
$791$	0	0
$792$	−41.6089	−1.47851
$793$	−1.75030	−0.0621548
$794$	−29.6933	−1.05377
$795$	−7.94208	−0.281677
$796$	−3.62633	−0.128532
$797$	1.21120	0.0429028	0.0214514	−	0.999770i	$-0.493171\pi$
$797$	1.21120	0.0429028	0.0214514	+	0.999770i	$0.493171\pi$
$798$	0	0
$799$	51.5338	1.82313
$800$	−16.3284	−0.577295
$801$	17.6857	0.624892
$802$	−17.6664	−0.623821
$803$	−18.9321	−0.668099
$804$	0.347174	0.0122439
$805$	0	0
$806$	−6.43275	−0.226584
$807$	4.90504	0.172666
$808$	−5.91067	−0.207937
$809$	−1.52068	−0.0534643	−0.0267322	−	0.999643i	$-0.508510\pi$
$809$	−1.52068	−0.0534643	−0.0267322	+	0.999643i	$0.508510\pi$
$810$	−33.3742	−1.17265
$811$	27.6060	0.969379	0.484689	−	0.874686i	$-0.338933\pi$
$811$	27.6060	0.969379	0.484689	+	0.874686i	$0.338933\pi$
$812$	0	0
$813$	−1.57429	−0.0552127
$814$	−28.5434	−1.00045
$815$	−0.0178155	−0.000624048 0
$816$	2.20010	0.0770188
$817$	−83.0817	−2.90666
$818$	22.6666	0.792519
$819$	0	0
$820$	−1.79399	−0.0626489
$821$	50.0892	1.74813	0.874063	−	0.485813i	$-0.161476\pi$
$821$	50.0892	1.74813	0.874063	+	0.485813i	$0.161476\pi$
$822$	−2.35055	−0.0819849
$823$	−10.0645	−0.350826	−0.175413	−	0.984495i	$-0.556126\pi$
$823$	−10.0645	−0.350826	−0.175413	+	0.984495i	$0.556126\pi$
$824$	16.4639	0.573548
$825$	4.92070	0.171317
$826$	0	0
$827$	−7.95416	−0.276593	−0.138297	−	0.990391i	$-0.544163\pi$
$827$	−7.95416	−0.276593	−0.138297	+	0.990391i	$0.544163\pi$
$828$	−8.82720	−0.306766
$829$	−50.9978	−1.77123	−0.885614	−	0.464422i	$-0.846262\pi$
$829$	−50.9978	−1.77123	−0.885614	+	0.464422i	$0.846262\pi$
$830$	18.9558	0.657966
$831$	−1.31249	−0.0455297
$832$	−6.19586	−0.214803
$833$	0	0
$834$	−1.17138	−0.0405617
$835$	−72.3560	−2.50398
$836$	20.5396	0.710378
$837$	9.12565	0.315429
$838$	34.5635	1.19398
$839$	10.8839	0.375753	0.187877	−	0.982193i	$-0.439839\pi$
$839$	10.8839	0.375753	0.187877	+	0.982193i	$0.439839\pi$
$840$	0	0
$841$	0.0740626	0.00255388
$842$	−43.2496	−1.49048
$843$	−0.448405	−0.0154439
$844$	5.85152	0.201418
$845$	−40.2316	−1.38401
$846$	−43.0654	−1.48062
$847$	0	0
$848$	31.6148	1.08566
$849$	3.67686	0.126190
$850$	27.3257	0.937263
$851$	−27.7728	−0.952040
$852$	−0.573358	−0.0196429
$853$	13.4544	0.460670	0.230335	−	0.973111i	$-0.426018\pi$
$853$	13.4544	0.460670	0.230335	+	0.973111i	$0.426018\pi$
$854$	0	0
$855$	76.6204	2.62036
$856$	8.69383	0.297149
$857$	−39.6908	−1.35581	−0.677906	−	0.735149i	$-0.737112\pi$
$857$	−39.6908	−1.35581	−0.677906	+	0.735149i	$0.737112\pi$
$858$	0.776645	0.0265142
$859$	−23.5262	−0.802705	−0.401352	−	0.915924i	$-0.631460\pi$
$859$	−23.5262	−0.802705	−0.401352	+	0.915924i	$0.631460\pi$
$860$	−18.5213	−0.631572
$861$	0	0
$862$	−11.0913	−0.377770
$863$	−39.1998	−1.33438	−0.667189	−	0.744888i	$-0.732503\pi$
$863$	−39.1998	−1.33438	−0.667189	+	0.744888i	$0.732503\pi$
$864$	3.65599	0.124379
$865$	−19.5584	−0.665005
$866$	−21.7803	−0.740126
$867$	0.219291	0.00744751
$868$	0	0
$869$	−62.8937	−2.13352
$870$	4.18690	0.141949
$871$	2.17770	0.0737886
$872$	35.0048	1.18541
$873$	4.30770	0.145793
$874$	−51.6908	−1.74847
$875$	0	0
$876$	0.463590	0.0156633
$877$	24.7835	0.836879	0.418439	−	0.908245i	$-0.362577\pi$
$877$	24.7835	0.836879	0.418439	+	0.908245i	$0.362577\pi$
$878$	−8.15478	−0.275211
$879$	1.48209	0.0499897
$880$	−37.8961	−1.27748
$881$	−33.8534	−1.14055	−0.570275	−	0.821454i	$-0.693163\pi$
$881$	−33.8534	−1.14055	−0.570275	+	0.821454i	$0.693163\pi$
$882$	0	0
$883$	−9.96707	−0.335419	−0.167709	−	0.985837i	$-0.553637\pi$
$883$	−9.96707	−0.335419	−0.167709	+	0.985837i	$0.553637\pi$
$884$	−1.66748	−0.0560833
$885$	4.99802	0.168007
$886$	−41.1075	−1.38103
$887$	26.9208	0.903910	0.451955	−	0.892041i	$-0.350727\pi$
$887$	26.9208	0.903910	0.451955	+	0.892041i	$0.350727\pi$
$888$	3.20567	0.107575
$889$	0	0
$890$	23.0876	0.773898
$891$	39.5361	1.32451
$892$	8.07242	0.270285
$893$	97.5018	3.26277
$894$	1.56231	0.0522515
$895$	−25.4667	−0.851258
$896$	0	0
$897$	0.755678	0.0252313
$898$	2.63192	0.0878284
$899$	41.0819	1.37016
$900$	8.82878	0.294293
$901$	52.2471	1.74060
$902$	−5.49681	−0.183024
$903$	0	0
$904$	56.7806	1.88850
$905$	7.09041	0.235693
$906$	4.00973	0.133214
$907$	−26.0776	−0.865894	−0.432947	−	0.901419i	$-0.642526\pi$
$907$	−26.0776	−0.865894	−0.432947	+	0.901419i	$0.642526\pi$
$908$	−9.78674	−0.324785
$909$	5.69501	0.188892
$910$	0	0
$911$	−34.1407	−1.13113	−0.565566	−	0.824703i	$-0.691342\pi$
$911$	−34.1407	−1.13113	−0.565566	+	0.824703i	$0.691342\pi$
$912$	4.16258	0.137837
$913$	−22.4557	−0.743175
$914$	−18.3668	−0.607521
$915$	1.60973	0.0532160
$916$	−0.105842	−0.00349713
$917$	0	0
$918$	−6.11834	−0.201935
$919$	11.7633	0.388034	0.194017	−	0.980998i	$-0.437848\pi$
$919$	11.7633	0.388034	0.194017	+	0.980998i	$0.437848\pi$
$920$	−52.8517	−1.74247
$921$	2.34314	0.0772091
$922$	−8.85649	−0.291673
$923$	−3.59648	−0.118380
$924$	0	0
$925$	27.7778	0.913328
$926$	30.4243	0.999805
$927$	−15.8632	−0.521016
$928$	16.4586	0.540280
$929$	21.9176	0.719093	0.359547	−	0.933127i	$-0.382931\pi$
$929$	21.9176	0.719093	0.359547	+	0.933127i	$0.382931\pi$
$930$	5.91613	0.193998
$931$	0	0
$932$	−1.13463	−0.0371662
$933$	3.86898	0.126665
$934$	10.8797	0.355994
$935$	−62.6276	−2.04814
$936$	6.39108	0.208899
$937$	17.5365	0.572892	0.286446	−	0.958096i	$-0.407526\pi$
$937$	17.5365	0.572892	0.286446	+	0.958096i	$0.407526\pi$
$938$	0	0
$939$	0.749671	0.0244646
$940$	21.7360	0.708951
$941$	47.1279	1.53633	0.768163	−	0.640255i	$-0.221171\pi$
$941$	47.1279	1.53633	0.768163	+	0.640255i	$0.221171\pi$
$942$	5.19656	0.169313
$943$	−5.34842	−0.174168
$944$	−19.8955	−0.647542
$945$	0	0
$946$	−56.7496	−1.84509
$947$	15.4167	0.500976	0.250488	−	0.968120i	$-0.419409\pi$
$947$	15.4167	0.500976	0.250488	+	0.968120i	$0.419409\pi$
$948$	1.54008	0.0500194
$949$	2.90794	0.0943959
$950$	51.7001	1.67737
$951$	−3.93971	−0.127754
$952$	0	0
$953$	24.6552	0.798660	0.399330	−	0.916807i	$-0.369243\pi$
$953$	24.6552	0.798660	0.399330	+	0.916807i	$0.369243\pi$
$954$	−43.6615	−1.41359
$955$	−5.64917	−0.182803
$956$	−6.47172	−0.209310
$957$	−4.95995	−0.160332
$958$	18.8910	0.610341
$959$	0	0
$960$	5.69827	0.183911
$961$	27.0492	0.872554
$962$	4.38423	0.141353
$963$	−8.37662	−0.269933
$964$	−2.41764	−0.0778669
$965$	6.63920	0.213723
$966$	0	0
$967$	−28.2925	−0.909826	−0.454913	−	0.890536i	$-0.650330\pi$
$967$	−28.2925	−0.909826	−0.454913	+	0.890536i	$0.650330\pi$
$968$	30.5585	0.982187
$969$	6.87914	0.220990
$970$	5.62345	0.180558
$971$	−48.5600	−1.55837	−0.779183	−	0.626797i	$-0.784366\pi$
$971$	−48.5600	−1.55837	−0.779183	+	0.626797i	$0.784366\pi$
$972$	−2.97190	−0.0953239
$973$	0	0
$974$	13.9023	0.445458
$975$	−0.755813	−0.0242054
$976$	−6.40780	−0.205109
$977$	45.7403	1.46336	0.731682	−	0.681647i	$-0.238736\pi$
$977$	45.7403	1.46336	0.731682	+	0.681647i	$0.238736\pi$
$978$	0.00133667	4.27419e−5 0
$979$	−27.3504	−0.874121
$980$	0	0
$981$	−33.7276	−1.07684
$982$	18.3257	0.584797
$983$	−15.9534	−0.508834	−0.254417	−	0.967095i	$-0.581884\pi$
$983$	−15.9534	−0.508834	−0.254417	+	0.967095i	$0.581884\pi$
$984$	0.617340	0.0196801
$985$	−68.4183	−2.17999
$986$	−27.5436	−0.877167
$987$	0	0
$988$	−3.15486	−0.100370
$989$	−55.2175	−1.75582
$990$	52.3362	1.66335
$991$	−40.8830	−1.29869	−0.649346	−	0.760493i	$-0.724957\pi$
$991$	−40.8830	−1.29869	−0.649346	+	0.760493i	$0.724957\pi$
$992$	23.2561	0.738383
$993$	−4.71953	−0.149770
$994$	0	0
$995$	20.9200	0.663208
$996$	0.549873	0.0174234
$997$	−4.18063	−0.132402	−0.0662010	−	0.997806i	$-0.521088\pi$
$997$	−4.18063	−0.132402	−0.0662010	+	0.997806i	$0.521088\pi$
$998$	−10.0359	−0.317681
$999$	−6.21957	−0.196779

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2009.2.a.n.1.2		5
7.6	odd	2		287.2.a.e.1.2	✓	5
21.20	even	2		2583.2.a.r.1.4		5
28.27	even	2		4592.2.a.bb.1.4		5
35.34	odd	2		7175.2.a.n.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.a.e.1.2	✓	5	7.6	odd	2
2009.2.a.n.1.2		5	1.1	even	1	trivial
2583.2.a.r.1.4		5	21.20	even	2
4592.2.a.bb.1.4		5	28.27	even	2
7175.2.a.n.1.4		5	35.34	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2009 = 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2009.a (trivial)

\(f(q)\)	\(=\)	\(q-1.20098 q^{2} +0.200978 q^{3} -0.557652 q^{4} +3.21704 q^{5} -0.241370 q^{6} +3.07168 q^{8} -2.95961 q^{9} +O(q^{10})\)	\(q-1.20098 q^{2} +0.200978 q^{3} -0.557652 q^{4} +3.21704 q^{5} -0.241370 q^{6} +3.07168 q^{8} -2.95961 q^{9} -3.86360 q^{10} +4.57695 q^{11} -0.112076 q^{12} -0.703013 q^{13} +0.646554 q^{15} -2.57372 q^{16} -4.25337 q^{17} +3.55442 q^{18} -8.04736 q^{19} -1.79399 q^{20} -5.49681 q^{22} -5.34842 q^{23} +0.617340 q^{24} +5.34937 q^{25} +0.844303 q^{26} -1.19775 q^{27} -5.39204 q^{29} -0.776497 q^{30} -7.61900 q^{31} -3.05239 q^{32} +0.919865 q^{33} +5.10820 q^{34} +1.65043 q^{36} +5.19272 q^{37} +9.66470 q^{38} -0.141290 q^{39} +9.88174 q^{40} +1.00000 q^{41} +10.3241 q^{43} -2.55235 q^{44} -9.52119 q^{45} +6.42333 q^{46} -12.1160 q^{47} -0.517260 q^{48} -6.42448 q^{50} -0.854832 q^{51} +0.392037 q^{52} -12.2837 q^{53} +1.43847 q^{54} +14.7242 q^{55} -1.61734 q^{57} +6.47572 q^{58} +7.73023 q^{59} -0.360553 q^{60} +2.48971 q^{61} +9.15025 q^{62} +8.81329 q^{64} -2.26162 q^{65} -1.10474 q^{66} -3.09767 q^{67} +2.37190 q^{68} -1.07491 q^{69} +5.11581 q^{71} -9.09098 q^{72} -4.13640 q^{73} -6.23634 q^{74} +1.07511 q^{75} +4.48763 q^{76} +0.169686 q^{78} -13.7414 q^{79} -8.27977 q^{80} +8.63810 q^{81} -1.20098 q^{82} -4.90626 q^{83} -13.6833 q^{85} -12.3990 q^{86} -1.08368 q^{87} +14.0589 q^{88} -5.97567 q^{89} +11.4347 q^{90} +2.98256 q^{92} -1.53125 q^{93} +14.5511 q^{94} -25.8887 q^{95} -0.613462 q^{96} -1.45550 q^{97} -13.5460 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - q^{2} - 4 q^{3} + 3 q^{4} + 5 q^{5} - 12 q^{6} - 3 q^{8} + q^{9}+O(q^{10}) \) 5 * q - q^2 - 4 * q^3 + 3 * q^4 + 5 * q^5 - 12 * q^6 - 3 * q^8 + q^9	\( 5 q - q^{2} - 4 q^{3} + 3 q^{4} + 5 q^{5} - 12 q^{6} - 3 q^{8} + q^{9} + 2 q^{11} + 2 q^{12} - 5 q^{13} - 5 q^{15} - q^{16} - 13 q^{17} + 21 q^{18} + 23 q^{20} + q^{22} + 2 q^{23} - 2 q^{24} + 22 q^{25} - 10 q^{27} - 5 q^{29} - 33 q^{30} - 17 q^{31} - 12 q^{32} - 3 q^{33} + 8 q^{34} + 15 q^{36} - 7 q^{37} + 3 q^{38} + 5 q^{39} - 7 q^{40} + 5 q^{41} + q^{43} - 47 q^{44} + 23 q^{45} - 24 q^{46} - 9 q^{47} + 19 q^{48} + 2 q^{50} + 5 q^{51} - 20 q^{52} + 5 q^{53} - 2 q^{54} - 33 q^{55} - 3 q^{57} - 27 q^{58} - 7 q^{59} - 16 q^{60} - 22 q^{61} + 28 q^{62} - 3 q^{64} - 31 q^{65} + 42 q^{66} - 3 q^{67} - 17 q^{68} + 22 q^{69} - 24 q^{71} - 12 q^{72} - 40 q^{73} - 5 q^{74} - 24 q^{75} + 19 q^{76} + 30 q^{78} - 42 q^{79} - 24 q^{80} + 9 q^{81} - q^{82} + 12 q^{83} - 23 q^{85} + 16 q^{86} + 32 q^{87} + 26 q^{88} - 8 q^{89} + 59 q^{90} + 12 q^{92} - 11 q^{93} + 23 q^{94} - 17 q^{95} + 17 q^{96} - 16 q^{97} - 45 q^{99}+O(q^{100}) \) 5 * q - q^2 - 4 * q^3 + 3 * q^4 + 5 * q^5 - 12 * q^6 - 3 * q^8 + q^9 + 2 * q^11 + 2 * q^12 - 5 * q^13 - 5 * q^15 - q^16 - 13 * q^17 + 21 * q^18 + 23 * q^20 + q^22 + 2 * q^23 - 2 * q^24 + 22 * q^25 - 10 * q^27 - 5 * q^29 - 33 * q^30 - 17 * q^31 - 12 * q^32 - 3 * q^33 + 8 * q^34 + 15 * q^36 - 7 * q^37 + 3 * q^38 + 5 * q^39 - 7 * q^40 + 5 * q^41 + q^43 - 47 * q^44 + 23 * q^45 - 24 * q^46 - 9 * q^47 + 19 * q^48 + 2 * q^50 + 5 * q^51 - 20 * q^52 + 5 * q^53 - 2 * q^54 - 33 * q^55 - 3 * q^57 - 27 * q^58 - 7 * q^59 - 16 * q^60 - 22 * q^61 + 28 * q^62 - 3 * q^64 - 31 * q^65 + 42 * q^66 - 3 * q^67 - 17 * q^68 + 22 * q^69 - 24 * q^71 - 12 * q^72 - 40 * q^73 - 5 * q^74 - 24 * q^75 + 19 * q^76 + 30 * q^78 - 42 * q^79 - 24 * q^80 + 9 * q^81 - q^82 + 12 * q^83 - 23 * q^85 + 16 * q^86 + 32 * q^87 + 26 * q^88 - 8 * q^89 + 59 * q^90 + 12 * q^92 - 11 * q^93 + 23 * q^94 - 17 * q^95 + 17 * q^96 - 16 * q^97 - 45 * q^99

Introduction

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