LMFDB - Embedded newform 2009.2.a.s.1.16

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			1.16
Root			$2.57424$ of defining polynomial
Character	$\chi$	$=$	2009.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.57424 q^{2} +0.468252 q^{3} +4.62673 q^{4} +2.24224 q^{5} +1.20539 q^{6} +6.76185 q^{8} -2.78074 q^{9} +O(q^{10})$	\(q+2.57424 q^{2} +0.468252 q^{3} +4.62673 q^{4} +2.24224 q^{5} +1.20539 q^{6} +6.76185 q^{8} -2.78074 q^{9} +5.77207 q^{10} +5.76768 q^{11} +2.16648 q^{12} -0.0725380 q^{13} +1.04993 q^{15} +8.15319 q^{16} -5.01002 q^{17} -7.15830 q^{18} -5.06540 q^{19} +10.3742 q^{20} +14.8474 q^{22} +1.90926 q^{23} +3.16625 q^{24} +0.0276364 q^{25} -0.186731 q^{26} -2.70684 q^{27} +6.90161 q^{29} +2.70278 q^{30} +4.57558 q^{31} +7.46459 q^{32} +2.70073 q^{33} -12.8970 q^{34} -12.8657 q^{36} -4.99460 q^{37} -13.0396 q^{38} -0.0339661 q^{39} +15.1617 q^{40} +1.00000 q^{41} -6.83836 q^{43} +26.6855 q^{44} -6.23508 q^{45} +4.91490 q^{46} -9.65313 q^{47} +3.81774 q^{48} +0.0711428 q^{50} -2.34595 q^{51} -0.335614 q^{52} +12.2714 q^{53} -6.96807 q^{54} +12.9325 q^{55} -2.37188 q^{57} +17.7664 q^{58} -2.22331 q^{59} +4.85776 q^{60} -2.59124 q^{61} +11.7787 q^{62} +2.90930 q^{64} -0.162648 q^{65} +6.95233 q^{66} -1.01182 q^{67} -23.1800 q^{68} +0.894015 q^{69} -3.95904 q^{71} -18.8029 q^{72} -15.3317 q^{73} -12.8573 q^{74} +0.0129408 q^{75} -23.4362 q^{76} -0.0874370 q^{78} -5.48336 q^{79} +18.2814 q^{80} +7.07474 q^{81} +2.57424 q^{82} +4.84224 q^{83} -11.2337 q^{85} -17.6036 q^{86} +3.23169 q^{87} +39.0002 q^{88} +12.5800 q^{89} -16.0506 q^{90} +8.83364 q^{92} +2.14252 q^{93} -24.8495 q^{94} -11.3578 q^{95} +3.49531 q^{96} +18.1362 q^{97} -16.0384 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q + 3 q^{2} + q^{3} + 25 q^{4} - q^{5} + 2 q^{6} + 9 q^{8} + 26 q^{9}+O(q^{10}) $ 17 * q + 3 * q^2 + q^3 + 25 * q^4 - q^5 + 2 * q^6 + 9 * q^8 + 26 * q^9	$ 17 q + 3 q^{2} + q^{3} + 25 q^{4} - q^{5} + 2 q^{6} + 9 q^{8} + 26 q^{9} - 2 q^{10} + 15 q^{11} + 4 q^{12} - 5 q^{13} + 24 q^{15} + 33 q^{16} + 4 q^{17} + 10 q^{18} + 5 q^{19} - 26 q^{20} + 16 q^{22} + 12 q^{23} + 16 q^{24} + 24 q^{25} + 31 q^{26} - 11 q^{27} + 14 q^{29} - 33 q^{30} - 3 q^{31} + 16 q^{32} + 4 q^{33} - 24 q^{34} + 57 q^{36} + 24 q^{37} + 45 q^{39} + 36 q^{40} + 17 q^{41} + 14 q^{43} - 9 q^{44} - 21 q^{45} + 44 q^{46} + 19 q^{47} - 60 q^{48} - 4 q^{50} + 2 q^{51} - 25 q^{52} + 4 q^{53} + 68 q^{54} + 9 q^{55} - 12 q^{57} - q^{58} - 27 q^{59} + 66 q^{60} - q^{61} - 23 q^{62} + 75 q^{64} + 22 q^{65} - 16 q^{66} + 49 q^{67} + 45 q^{68} + 12 q^{69} + 40 q^{71} - 23 q^{72} - 14 q^{73} + 33 q^{74} + 27 q^{75} - 9 q^{76} - 12 q^{78} + 61 q^{79} - 82 q^{80} + 53 q^{81} + 3 q^{82} - 18 q^{83} - 13 q^{85} - 4 q^{86} - 17 q^{87} + 74 q^{88} + 18 q^{89} - 20 q^{90} + 28 q^{92} - 36 q^{93} - 5 q^{94} + 20 q^{95} + 148 q^{96} + 26 q^{97} + 38 q^{99}+O(q^{100}) $ 17 * q + 3 * q^2 + q^3 + 25 * q^4 - q^5 + 2 * q^6 + 9 * q^8 + 26 * q^9 - 2 * q^10 + 15 * q^11 + 4 * q^12 - 5 * q^13 + 24 * q^15 + 33 * q^16 + 4 * q^17 + 10 * q^18 + 5 * q^19 - 26 * q^20 + 16 * q^22 + 12 * q^23 + 16 * q^24 + 24 * q^25 + 31 * q^26 - 11 * q^27 + 14 * q^29 - 33 * q^30 - 3 * q^31 + 16 * q^32 + 4 * q^33 - 24 * q^34 + 57 * q^36 + 24 * q^37 + 45 * q^39 + 36 * q^40 + 17 * q^41 + 14 * q^43 - 9 * q^44 - 21 * q^45 + 44 * q^46 + 19 * q^47 - 60 * q^48 - 4 * q^50 + 2 * q^51 - 25 * q^52 + 4 * q^53 + 68 * q^54 + 9 * q^55 - 12 * q^57 - q^58 - 27 * q^59 + 66 * q^60 - q^61 - 23 * q^62 + 75 * q^64 + 22 * q^65 - 16 * q^66 + 49 * q^67 + 45 * q^68 + 12 * q^69 + 40 * q^71 - 23 * q^72 - 14 * q^73 + 33 * q^74 + 27 * q^75 - 9 * q^76 - 12 * q^78 + 61 * q^79 - 82 * q^80 + 53 * q^81 + 3 * q^82 - 18 * q^83 - 13 * q^85 - 4 * q^86 - 17 * q^87 + 74 * q^88 + 18 * q^89 - 20 * q^90 + 28 * q^92 - 36 * q^93 - 5 * q^94 + 20 * q^95 + 148 * q^96 + 26 * q^97 + 38 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.57424	1.82027	0.910133	−	0.414317i	$-0.135979\pi$
$2$	2.57424	1.82027	0.910133	+	0.414317i	$0.135979\pi$
$3$	0.468252	0.270345	0.135173	−	0.990822i	$-0.456841\pi$
$3$	0.468252	0.270345	0.135173	+	0.990822i	$0.456841\pi$
$4$	4.62673	2.31337
$5$	2.24224	1.00276	0.501380	−	0.865227i	$-0.332826\pi$
$5$	2.24224	1.00276	0.501380	+	0.865227i	$0.332826\pi$
$6$	1.20539	0.492100
$7$	0	0
$7$	0	0
$8$	6.76185	2.39067
$9$	−2.78074	−0.926913
$10$	5.77207	1.82529
$11$	5.76768	1.73902	0.869511	−	0.493914i	$-0.164434\pi$
$11$	5.76768	1.73902	0.869511	+	0.493914i	$0.164434\pi$
$12$	2.16648	0.625408
$13$	−0.0725380	−0.0201184	−0.0100592	−	0.999949i	$-0.503202\pi$
$13$	−0.0725380	−0.0201184	−0.0100592	+	0.999949i	$0.503202\pi$
$14$	0	0
$15$	1.04993	0.271091
$16$	8.15319	2.03830
$17$	−5.01002	−1.21511	−0.607554	−	0.794279i	$-0.707849\pi$
$17$	−5.01002	−1.21511	−0.607554	+	0.794279i	$0.707849\pi$
$18$	−7.15830	−1.68723
$19$	−5.06540	−1.16208	−0.581041	−	0.813874i	$-0.697354\pi$
$19$	−5.06540	−1.16208	−0.581041	+	0.813874i	$0.697354\pi$
$20$	10.3742	2.31975
$21$	0	0
$22$	14.8474	3.16548
$23$	1.90926	0.398108	0.199054	−	0.979988i	$-0.436213\pi$
$23$	1.90926	0.398108	0.199054	+	0.979988i	$0.436213\pi$
$24$	3.16625	0.646308
$25$	0.0276364	0.00552728
$26$	−0.186731	−0.0366209
$27$	−2.70684	−0.520932
$28$	0	0
$29$	6.90161	1.28160	0.640798	−	0.767709i	$-0.278603\pi$
$29$	6.90161	1.28160	0.640798	+	0.767709i	$0.278603\pi$
$30$	2.70278	0.493458
$31$	4.57558	0.821799	0.410899	−	0.911681i	$-0.365215\pi$
$31$	4.57558	0.821799	0.410899	+	0.911681i	$0.365215\pi$
$32$	7.46459	1.31957
$33$	2.70073	0.470136
$34$	−12.8970	−2.21182
$35$	0	0
$36$	−12.8657	−2.14429
$37$	−4.99460	−0.821107	−0.410554	−	0.911836i	$-0.634665\pi$
$37$	−4.99460	−0.821107	−0.410554	+	0.911836i	$0.634665\pi$
$38$	−13.0396	−2.11530
$39$	−0.0339661	−0.00543893
$40$	15.1617	2.39727
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	−6.83836	−1.04284	−0.521420	−	0.853300i	$-0.674597\pi$
$43$	−6.83836	−1.04284	−0.521420	+	0.853300i	$0.674597\pi$
$44$	26.6855	4.02299
$45$	−6.23508	−0.929472
$46$	4.91490	0.724663
$47$	−9.65313	−1.40805	−0.704027	−	0.710173i	$-0.748617\pi$
$47$	−9.65313	−1.40805	−0.704027	+	0.710173i	$0.748617\pi$
$48$	3.81774	0.551044
$49$	0	0
$50$	0.0711428	0.0100611
$51$	−2.34595	−0.328499
$52$	−0.335614	−0.0465413
$53$	12.2714	1.68560	0.842802	−	0.538224i	$-0.180905\pi$
$53$	12.2714	1.68560	0.842802	+	0.538224i	$0.180905\pi$
$54$	−6.96807	−0.948235
$55$	12.9325	1.74382
$56$	0	0
$57$	−2.37188	−0.314163
$58$	17.7664	2.33285
$59$	−2.22331	−0.289451	−0.144725	−	0.989472i	$-0.546230\pi$
$59$	−2.22331	−0.289451	−0.144725	+	0.989472i	$0.546230\pi$
$60$	4.85776	0.627134
$61$	−2.59124	−0.331774	−0.165887	−	0.986145i	$-0.553049\pi$
$61$	−2.59124	−0.331774	−0.165887	+	0.986145i	$0.553049\pi$
$62$	11.7787	1.49589
$63$	0	0
$64$	2.90930	0.363663
$65$	−0.162648	−0.0201740
$66$	6.95233	0.855773
$67$	−1.01182	−0.123613	−0.0618065	−	0.998088i	$-0.519686\pi$
$67$	−1.01182	−0.123613	−0.0618065	+	0.998088i	$0.519686\pi$
$68$	−23.1800	−2.81099
$69$	0.894015	0.107627
$70$	0	0
$71$	−3.95904	−0.469851	−0.234926	−	0.972013i	$-0.575485\pi$
$71$	−3.95904	−0.469851	−0.234926	+	0.972013i	$0.575485\pi$
$72$	−18.8029	−2.21595
$73$	−15.3317	−1.79444	−0.897220	−	0.441584i	$-0.854417\pi$
$73$	−15.3317	−1.79444	−0.897220	+	0.441584i	$0.854417\pi$
$74$	−12.8573	−1.49463
$75$	0.0129408	0.00149427
$76$	−23.4362	−2.68832
$77$	0	0
$78$	−0.0874370	−0.00990029
$79$	−5.48336	−0.616927	−0.308463	−	0.951236i	$-0.599815\pi$
$79$	−5.48336	−0.616927	−0.308463	+	0.951236i	$0.599815\pi$
$80$	18.2814	2.04392
$81$	7.07474	0.786082
$82$	2.57424	0.284278
$83$	4.84224	0.531505	0.265752	−	0.964041i	$-0.414380\pi$
$83$	4.84224	0.531505	0.265752	+	0.964041i	$0.414380\pi$
$84$	0	0
$85$	−11.2337	−1.21846
$86$	−17.6036	−1.89824
$87$	3.23169	0.346474
$88$	39.0002	4.15743
$89$	12.5800	1.33348	0.666739	−	0.745291i	$-0.267690\pi$
$89$	12.5800	1.33348	0.666739	+	0.745291i	$0.267690\pi$
$90$	−16.0506	−1.69188
$91$	0	0
$92$	8.83364	0.920970
$93$	2.14252	0.222169
$94$	−24.8495	−2.56303
$95$	−11.3578	−1.16529
$96$	3.49531	0.356738
$97$	18.1362	1.84145	0.920724	−	0.390216i	$-0.127600\pi$
$97$	18.1362	1.84145	0.920724	+	0.390216i	$0.127600\pi$
$98$	0	0
$99$	−16.0384	−1.61192
$100$	0.127866	0.0127866
$101$	10.1764	1.01259	0.506295	−	0.862361i	$-0.331015\pi$
$101$	10.1764	1.01259	0.506295	+	0.862361i	$0.331015\pi$
$102$	−6.03905	−0.597955
$103$	−0.543194	−0.0535225	−0.0267613	−	0.999642i	$-0.508519\pi$
$103$	−0.543194	−0.0535225	−0.0267613	+	0.999642i	$0.508519\pi$
$104$	−0.490491	−0.0480966
$105$	0	0
$106$	31.5895	3.06825
$107$	−0.396784	−0.0383585	−0.0191793	−	0.999816i	$-0.506105\pi$
$107$	−0.396784	−0.0383585	−0.0191793	+	0.999816i	$0.506105\pi$
$108$	−12.5238	−1.20511
$109$	−6.33114	−0.606413	−0.303206	−	0.952925i	$-0.598057\pi$
$109$	−6.33114	−0.606413	−0.303206	+	0.952925i	$0.598057\pi$
$110$	33.2915	3.17422
$111$	−2.33873	−0.221983
$112$	0	0
$113$	−4.39846	−0.413773	−0.206886	−	0.978365i	$-0.566333\pi$
$113$	−4.39846	−0.413773	−0.206886	+	0.978365i	$0.566333\pi$
$114$	−6.10580	−0.571861
$115$	4.28102	0.399207
$116$	31.9319	2.96480
$117$	0.201709	0.0186480
$118$	−5.72335	−0.526877
$119$	0	0
$120$	7.09949	0.648091
$121$	22.2662	2.02420
$122$	−6.67049	−0.603918
$123$	0.468252	0.0422208
$124$	21.1700	1.90112
$125$	−11.1492	−0.997217
$126$	0	0
$127$	−11.7138	−1.03943	−0.519715	−	0.854340i	$-0.673962\pi$
$127$	−11.7138	−1.03943	−0.519715	+	0.854340i	$0.673962\pi$
$128$	−7.43992	−0.657602
$129$	−3.20207	−0.281927
$130$	−0.418695	−0.0367220
$131$	22.2136	1.94081	0.970404	−	0.241486i	$-0.0776347\pi$
$131$	22.2136	1.94081	0.970404	+	0.241486i	$0.0776347\pi$
$132$	12.4955	1.08760
$133$	0	0
$134$	−2.60466	−0.225009
$135$	−6.06939	−0.522370
$136$	−33.8770	−2.90493
$137$	−5.95204	−0.508517	−0.254259	−	0.967136i	$-0.581831\pi$
$137$	−5.95204	−0.508517	−0.254259	+	0.967136i	$0.581831\pi$
$138$	2.30141	0.195909
$139$	8.89834	0.754747	0.377374	−	0.926061i	$-0.376827\pi$
$139$	8.89834	0.754747	0.377374	+	0.926061i	$0.376827\pi$
$140$	0	0
$141$	−4.52010	−0.380661
$142$	−10.1915	−0.855254
$143$	−0.418376	−0.0349864
$144$	−22.6719	−1.88932
$145$	15.4751	1.28513
$146$	−39.4675	−3.26636
$147$	0	0
$148$	−23.1087	−1.89952
$149$	8.15378	0.667983	0.333992	−	0.942576i	$-0.391604\pi$
$149$	8.15378	0.667983	0.333992	+	0.942576i	$0.391604\pi$
$150$	0.0333127	0.00271997
$151$	−8.19460	−0.666867	−0.333433	−	0.942774i	$-0.608207\pi$
$151$	−8.19460	−0.666867	−0.333433	+	0.942774i	$0.608207\pi$
$152$	−34.2515	−2.77816
$153$	13.9316	1.12630
$154$	0	0
$155$	10.2596	0.824067
$156$	−0.157152	−0.0125822
$157$	−7.64841	−0.610410	−0.305205	−	0.952287i	$-0.598725\pi$
$157$	−7.64841	−0.610410	−0.305205	+	0.952287i	$0.598725\pi$
$158$	−14.1155	−1.12297
$159$	5.74609	0.455695
$160$	16.7374	1.32321
$161$	0	0
$162$	18.2121	1.43088
$163$	−0.821579	−0.0643510	−0.0321755	−	0.999482i	$-0.510244\pi$
$163$	−0.821579	−0.0643510	−0.0321755	+	0.999482i	$0.510244\pi$
$164$	4.62673	0.361287
$165$	6.05568	0.471434
$166$	12.4651	0.967480
$167$	7.82917	0.605840	0.302920	−	0.953016i	$-0.402039\pi$
$167$	7.82917	0.605840	0.302920	+	0.953016i	$0.402039\pi$
$168$	0	0
$169$	−12.9947	−0.999595
$170$	−28.9182	−2.21792
$171$	14.0856	1.07715
$172$	−31.6392	−2.41247
$173$	−13.3628	−1.01596	−0.507978	−	0.861370i	$-0.669607\pi$
$173$	−13.3628	−1.01596	−0.507978	+	0.861370i	$0.669607\pi$
$174$	8.31916	0.630674
$175$	0	0
$176$	47.0250	3.54464
$177$	−1.04107	−0.0782516
$178$	32.3840	2.42728
$179$	8.21937	0.614345	0.307172	−	0.951654i	$-0.400617\pi$
$179$	8.21937	0.614345	0.307172	+	0.951654i	$0.400617\pi$
$180$	−28.8481	−2.15021
$181$	−13.3667	−0.993542	−0.496771	−	0.867882i	$-0.665481\pi$
$181$	−13.3667	−0.993542	−0.496771	+	0.867882i	$0.665481\pi$
$182$	0	0
$183$	−1.21335	−0.0896937
$184$	12.9101	0.951747
$185$	−11.1991	−0.823374
$186$	5.51538	0.404407
$187$	−28.8962	−2.11310
$188$	−44.6625	−3.25734
$189$	0	0
$190$	−29.2378	−2.12114
$191$	−2.34794	−0.169891	−0.0849457	−	0.996386i	$-0.527072\pi$
$191$	−2.34794	−0.169891	−0.0849457	+	0.996386i	$0.527072\pi$
$192$	1.36229	0.0983146
$193$	−4.71054	−0.339072	−0.169536	−	0.985524i	$-0.554227\pi$
$193$	−4.71054	−0.339072	−0.169536	+	0.985524i	$0.554227\pi$
$194$	46.6869	3.35192
$195$	−0.0761601	−0.00545394
$196$	0	0
$197$	−6.92302	−0.493245	−0.246622	−	0.969112i	$-0.579321\pi$
$197$	−6.92302	−0.493245	−0.246622	+	0.969112i	$0.579321\pi$
$198$	−41.2868	−2.93413
$199$	−23.7088	−1.68068	−0.840338	−	0.542063i	$-0.817643\pi$
$199$	−23.7088	−1.68068	−0.840338	+	0.542063i	$0.817643\pi$
$200$	0.186873	0.0132139
$201$	−0.473785	−0.0334182
$202$	26.1965	1.84318
$203$	0	0
$204$	−10.8541	−0.759938
$205$	2.24224	0.156605
$206$	−1.39831	−0.0974252
$207$	−5.30916	−0.369012
$208$	−0.591416	−0.0410073
$209$	−29.2156	−2.02089
$210$	0	0
$211$	7.20963	0.496331	0.248166	−	0.968718i	$-0.420172\pi$
$211$	7.20963	0.496331	0.248166	+	0.968718i	$0.420172\pi$
$212$	56.7764	3.89942
$213$	−1.85383	−0.127022
$214$	−1.02142	−0.0698227
$215$	−15.3332	−1.04572
$216$	−18.3033	−1.24538
$217$	0	0
$218$	−16.2979	−1.10383
$219$	−7.17910	−0.485118
$220$	59.8353	4.03410
$221$	0.363417	0.0244461
$222$	−6.02046	−0.404067
$223$	1.24287	0.0832285	0.0416142	−	0.999134i	$-0.486750\pi$
$223$	1.24287	0.0832285	0.0416142	+	0.999134i	$0.486750\pi$
$224$	0	0
$225$	−0.0768496	−0.00512331
$226$	−11.3227	−0.753176
$227$	15.5050	1.02911	0.514553	−	0.857459i	$-0.327958\pi$
$227$	15.5050	1.02911	0.514553	+	0.857459i	$0.327958\pi$
$228$	−10.9741	−0.726775
$229$	−3.24527	−0.214454	−0.107227	−	0.994235i	$-0.534197\pi$
$229$	−3.24527	−0.214454	−0.107227	+	0.994235i	$0.534197\pi$
$230$	11.0204	0.726663
$231$	0	0
$232$	46.6676	3.06388
$233$	−0.148664	−0.00973932	−0.00486966	−	0.999988i	$-0.501550\pi$
$233$	−0.148664	−0.00973932	−0.00486966	+	0.999988i	$0.501550\pi$
$234$	0.519249	0.0339444
$235$	−21.6446	−1.41194
$236$	−10.2867	−0.669605
$237$	−2.56759	−0.166783
$238$	0	0
$239$	15.7243	1.01712	0.508561	−	0.861026i	$-0.330178\pi$
$239$	15.7243	1.01712	0.508561	+	0.861026i	$0.330178\pi$
$240$	8.56029	0.552565
$241$	14.5039	0.934275	0.467138	−	0.884185i	$-0.345285\pi$
$241$	14.5039	0.934275	0.467138	+	0.884185i	$0.345285\pi$
$242$	57.3185	3.68457
$243$	11.4333	0.733446
$244$	−11.9890	−0.767516
$245$	0	0
$246$	1.20539	0.0768531
$247$	0.367434	0.0233793
$248$	30.9394	1.96465
$249$	2.26739	0.143690
$250$	−28.7008	−1.81520
$251$	17.6114	1.11162	0.555812	−	0.831308i	$-0.312407\pi$
$251$	17.6114	1.11162	0.555812	+	0.831308i	$0.312407\pi$
$252$	0	0
$253$	11.0120	0.692319
$254$	−30.1541	−1.89204
$255$	−5.26018	−0.329405
$256$	−24.9708	−1.56067
$257$	29.9238	1.86660	0.933298	−	0.359103i	$-0.116917\pi$
$257$	29.9238	1.86660	0.933298	+	0.359103i	$0.116917\pi$
$258$	−8.24292	−0.513182
$259$	0	0
$260$	−0.752527	−0.0466698
$261$	−19.1916	−1.18793
$262$	57.1832	3.53279
$263$	−30.0029	−1.85006	−0.925030	−	0.379894i	$-0.875960\pi$
$263$	−30.0029	−1.85006	−0.925030	+	0.379894i	$0.875960\pi$
$264$	18.2619	1.12394
$265$	27.5154	1.69026
$266$	0	0
$267$	5.89061	0.360499
$268$	−4.68140	−0.285962
$269$	4.67405	0.284982	0.142491	−	0.989796i	$-0.454489\pi$
$269$	4.67405	0.284982	0.142491	+	0.989796i	$0.454489\pi$
$270$	−15.6241	−0.950852
$271$	−8.70676	−0.528898	−0.264449	−	0.964400i	$-0.585190\pi$
$271$	−8.70676	−0.528898	−0.264449	+	0.964400i	$0.585190\pi$
$272$	−40.8476	−2.47675
$273$	0	0
$274$	−15.3220	−0.925636
$275$	0.159398	0.00961205
$276$	4.13637	0.248980
$277$	6.53178	0.392457	0.196228	−	0.980558i	$-0.437131\pi$
$277$	6.53178	0.392457	0.196228	+	0.980558i	$0.437131\pi$
$278$	22.9065	1.37384
$279$	−12.7235	−0.761736
$280$	0	0
$281$	22.9384	1.36839	0.684195	−	0.729299i	$-0.260154\pi$
$281$	22.9384	1.36839	0.684195	+	0.729299i	$0.260154\pi$
$282$	−11.6358	−0.692904
$283$	−17.9116	−1.06474	−0.532369	−	0.846513i	$-0.678698\pi$
$283$	−17.9116	−1.06474	−0.532369	+	0.846513i	$0.678698\pi$
$284$	−18.3174	−1.08694
$285$	−5.31833	−0.315030
$286$	−1.07700	−0.0636845
$287$	0	0
$288$	−20.7571	−1.22312
$289$	8.10027	0.476486
$290$	39.8366	2.33928
$291$	8.49229	0.497827
$292$	−70.9357	−4.15120
$293$	0.775720	0.0453181	0.0226590	−	0.999743i	$-0.492787\pi$
$293$	0.775720	0.0453181	0.0226590	+	0.999743i	$0.492787\pi$
$294$	0	0
$295$	−4.98520	−0.290249
$296$	−33.7727	−1.96300
$297$	−15.6122	−0.905912
$298$	20.9898	1.21591
$299$	−0.138494	−0.00800932
$300$	0.0598736	0.00345680
$301$	0	0
$302$	−21.0949	−1.21387
$303$	4.76512	0.273749
$304$	−41.2991	−2.36867
$305$	−5.81018	−0.332690
$306$	35.8632	2.05016
$307$	−2.48064	−0.141577	−0.0707887	−	0.997491i	$-0.522552\pi$
$307$	−2.48064	−0.141577	−0.0707887	+	0.997491i	$0.522552\pi$
$308$	0	0
$309$	−0.254352	−0.0144696
$310$	26.4106	1.50002
$311$	1.49389	0.0847108	0.0423554	−	0.999103i	$-0.486514\pi$
$311$	1.49389	0.0847108	0.0423554	+	0.999103i	$0.486514\pi$
$312$	−0.229673	−0.0130027
$313$	−14.7941	−0.836210	−0.418105	−	0.908399i	$-0.637306\pi$
$313$	−14.7941	−0.836210	−0.418105	+	0.908399i	$0.637306\pi$
$314$	−19.6889	−1.11111
$315$	0	0
$316$	−25.3701	−1.42718
$317$	15.2392	0.855919	0.427960	−	0.903798i	$-0.359233\pi$
$317$	15.2392	0.855919	0.427960	+	0.903798i	$0.359233\pi$
$318$	14.7918	0.829486
$319$	39.8063	2.22872
$320$	6.52336	0.364667
$321$	−0.185795	−0.0103700
$322$	0	0
$323$	25.3777	1.41205
$324$	32.7329	1.81850
$325$	−0.00200469	−0.000111200 0
$326$	−2.11495	−0.117136
$327$	−2.96457	−0.163941
$328$	6.76185	0.373361
$329$	0	0
$330$	15.5888	0.858135
$331$	21.2847	1.16991	0.584957	−	0.811064i	$-0.301111\pi$
$331$	21.2847	1.16991	0.584957	+	0.811064i	$0.301111\pi$
$332$	22.4037	1.22957
$333$	13.8887	0.761095
$334$	20.1542	1.10279
$335$	−2.26873	−0.123954
$336$	0	0
$337$	−19.3612	−1.05467	−0.527336	−	0.849657i	$-0.676809\pi$
$337$	−19.3612	−1.05467	−0.527336	+	0.849657i	$0.676809\pi$
$338$	−33.4516	−1.81953
$339$	−2.05959	−0.111861
$340$	−51.9751	−2.81875
$341$	26.3905	1.42913
$342$	36.2597	1.96070
$343$	0	0
$344$	−46.2399	−2.49309
$345$	2.00459	0.107924
$346$	−34.3992	−1.84931
$347$	9.20075	0.493922	0.246961	−	0.969025i	$-0.420568\pi$
$347$	9.20075	0.493922	0.246961	+	0.969025i	$0.420568\pi$
$348$	14.9522	0.801520
$349$	5.22287	0.279574	0.139787	−	0.990182i	$-0.455358\pi$
$349$	5.22287	0.279574	0.139787	+	0.990182i	$0.455358\pi$
$350$	0	0
$351$	0.196349	0.0104803
$352$	43.0534	2.29475
$353$	−32.9848	−1.75561	−0.877803	−	0.479022i	$-0.840992\pi$
$353$	−32.9848	−1.75561	−0.877803	+	0.479022i	$0.840992\pi$
$354$	−2.67997	−0.142439
$355$	−8.87710	−0.471148
$356$	58.2043	3.08482
$357$	0	0
$358$	21.1587	1.11827
$359$	10.6166	0.560322	0.280161	−	0.959953i	$-0.409612\pi$
$359$	10.6166	0.560322	0.280161	+	0.959953i	$0.409612\pi$
$360$	−42.1607	−2.22206
$361$	6.65826	0.350435
$362$	−34.4092	−1.80851
$363$	10.4262	0.547232
$364$	0	0
$365$	−34.3773	−1.79939
$366$	−3.12347	−0.163266
$367$	−1.48836	−0.0776916	−0.0388458	−	0.999245i	$-0.512368\pi$
$367$	−1.48836	−0.0776916	−0.0388458	+	0.999245i	$0.512368\pi$
$368$	15.5666	0.811463
$369$	−2.78074	−0.144760
$370$	−28.8292	−1.49876
$371$	0	0
$372$	9.91289	0.513959
$373$	−3.30390	−0.171070	−0.0855348	−	0.996335i	$-0.527260\pi$
$373$	−3.30390	−0.171070	−0.0855348	+	0.996335i	$0.527260\pi$
$374$	−74.3858	−3.84640
$375$	−5.22065	−0.269593
$376$	−65.2730	−3.36620
$377$	−0.500629	−0.0257837
$378$	0	0
$379$	18.2983	0.939922	0.469961	−	0.882687i	$-0.344268\pi$
$379$	18.2983	0.939922	0.469961	+	0.882687i	$0.344268\pi$
$380$	−52.5497	−2.69574
$381$	−5.48500	−0.281005
$382$	−6.04418	−0.309247
$383$	37.2631	1.90405	0.952027	−	0.306014i	$-0.0989956\pi$
$383$	37.2631	1.90405	0.952027	+	0.306014i	$0.0989956\pi$
$384$	−3.48376	−0.177780
$385$	0	0
$386$	−12.1261	−0.617201
$387$	19.0157	0.966622
$388$	83.9111	4.25994
$389$	−3.72353	−0.188790	−0.0943952	−	0.995535i	$-0.530092\pi$
$389$	−3.72353	−0.188790	−0.0943952	+	0.995535i	$0.530092\pi$
$390$	−0.196055	−0.00992761
$391$	−9.56543	−0.483744
$392$	0	0
$393$	10.4015	0.524689
$394$	−17.8215	−0.897836
$395$	−12.2950	−0.618629
$396$	−74.2055	−3.72897
$397$	−10.1751	−0.510672	−0.255336	−	0.966852i	$-0.582186\pi$
$397$	−10.1751	−0.510672	−0.255336	+	0.966852i	$0.582186\pi$
$398$	−61.0323	−3.05928
$399$	0	0
$400$	0.225325	0.0112662
$401$	−35.0565	−1.75064	−0.875319	−	0.483546i	$-0.839348\pi$
$401$	−35.0565	−1.75064	−0.875319	+	0.483546i	$0.839348\pi$
$402$	−1.21964	−0.0608300
$403$	−0.331904	−0.0165333
$404$	47.0835	2.34249
$405$	15.8633	0.788251
$406$	0	0
$407$	−28.8073	−1.42792
$408$	−15.8630	−0.785333
$409$	−16.5748	−0.819573	−0.409787	−	0.912181i	$-0.634397\pi$
$409$	−16.5748	−0.819573	−0.409787	+	0.912181i	$0.634397\pi$
$410$	5.77207	0.285062
$411$	−2.78705	−0.137475
$412$	−2.51321	−0.123817
$413$	0	0
$414$	−13.6671	−0.671700
$415$	10.8575	0.532972
$416$	−0.541467	−0.0265476
$417$	4.16666	0.204042
$418$	−75.2081	−3.67855
$419$	8.81409	0.430597	0.215298	−	0.976548i	$-0.430928\pi$
$419$	8.81409	0.430597	0.215298	+	0.976548i	$0.430928\pi$
$420$	0	0
$421$	31.9405	1.55668	0.778342	−	0.627841i	$-0.216061\pi$
$421$	31.9405	1.55668	0.778342	+	0.627841i	$0.216061\pi$
$422$	18.5593	0.903455
$423$	26.8429	1.30514
$424$	82.9772	4.02973
$425$	−0.138459	−0.00671624
$426$	−4.77220	−0.231214
$427$	0	0
$428$	−1.83581	−0.0887373
$429$	−0.195906	−0.00945841
$430$	−39.4715	−1.90348
$431$	30.4762	1.46799	0.733994	−	0.679156i	$-0.237654\pi$
$431$	30.4762	1.46799	0.733994	+	0.679156i	$0.237654\pi$
$432$	−22.0694	−1.06181
$433$	26.5128	1.27412	0.637062	−	0.770813i	$-0.280150\pi$
$433$	26.5128	1.27412	0.637062	+	0.770813i	$0.280150\pi$
$434$	0	0
$435$	7.24622	0.347430
$436$	−29.2925	−1.40286
$437$	−9.67116	−0.462634
$438$	−18.4807	−0.883044
$439$	−16.6922	−0.796675	−0.398338	−	0.917239i	$-0.630413\pi$
$439$	−16.6922	−0.796675	−0.398338	+	0.917239i	$0.630413\pi$
$440$	87.4478	4.16891
$441$	0	0
$442$	0.935524	0.0444983
$443$	3.07898	0.146287	0.0731434	−	0.997321i	$-0.476697\pi$
$443$	3.07898	0.146287	0.0731434	+	0.997321i	$0.476697\pi$
$444$	−10.8207	−0.513527
$445$	28.2074	1.33716
$446$	3.19944	0.151498
$447$	3.81802	0.180586
$448$	0	0
$449$	−22.4476	−1.05937	−0.529683	−	0.848196i	$-0.677689\pi$
$449$	−22.4476	−1.05937	−0.529683	+	0.848196i	$0.677689\pi$
$450$	−0.197830	−0.00932578
$451$	5.76768	0.271590
$452$	−20.3505	−0.957207
$453$	−3.83713	−0.180284
$454$	39.9137	1.87324
$455$	0	0
$456$	−16.0383	−0.751063
$457$	−38.6363	−1.80733	−0.903666	−	0.428239i	$-0.859134\pi$
$457$	−38.6363	−1.80733	−0.903666	+	0.428239i	$0.859134\pi$
$458$	−8.35412	−0.390362
$459$	13.5613	0.632988
$460$	19.8071	0.923512
$461$	−12.2417	−0.570155	−0.285077	−	0.958504i	$-0.592019\pi$
$461$	−12.2417	−0.570155	−0.285077	+	0.958504i	$0.592019\pi$
$462$	0	0
$463$	32.9753	1.53249	0.766246	−	0.642547i	$-0.222122\pi$
$463$	32.9753	1.53249	0.766246	+	0.642547i	$0.222122\pi$
$464$	56.2701	2.61227
$465$	4.80405	0.222783
$466$	−0.382698	−0.0177281
$467$	6.01914	0.278533	0.139266	−	0.990255i	$-0.455526\pi$
$467$	6.01914	0.278533	0.139266	+	0.990255i	$0.455526\pi$
$468$	0.933256	0.0431398
$469$	0	0
$470$	−55.7186	−2.57011
$471$	−3.58138	−0.165021
$472$	−15.0337	−0.691982
$473$	−39.4415	−1.81352
$474$	−6.60962	−0.303590
$475$	−0.139989	−0.00642315
$476$	0	0
$477$	−34.1235	−1.56241
$478$	40.4783	1.85143
$479$	20.5836	0.940489	0.470245	−	0.882536i	$-0.344166\pi$
$479$	20.5836	0.940489	0.470245	+	0.882536i	$0.344166\pi$
$480$	7.83732	0.357723
$481$	0.362299	0.0165194
$482$	37.3365	1.70063
$483$	0	0
$484$	103.020	4.68271
$485$	40.6656	1.84653
$486$	29.4321	1.33507
$487$	−3.46374	−0.156957	−0.0784785	−	0.996916i	$-0.525006\pi$
$487$	−3.46374	−0.156957	−0.0784785	+	0.996916i	$0.525006\pi$
$488$	−17.5216	−0.793165
$489$	−0.384706	−0.0173970
$490$	0	0
$491$	−8.93553	−0.403255	−0.201627	−	0.979462i	$-0.564623\pi$
$491$	−8.93553	−0.403255	−0.201627	+	0.979462i	$0.564623\pi$
$492$	2.16648	0.0976723
$493$	−34.5772	−1.55728
$494$	0.945865	0.0425565
$495$	−35.9620	−1.61637
$496$	37.3056	1.67507
$497$	0	0
$498$	5.83681	0.261554
$499$	6.58943	0.294984	0.147492	−	0.989063i	$-0.452880\pi$
$499$	6.58943	0.294984	0.147492	+	0.989063i	$0.452880\pi$
$500$	−51.5845	−2.30693
$501$	3.66602	0.163786
$502$	45.3362	2.02345
$503$	−21.0935	−0.940511	−0.470255	−	0.882530i	$-0.655838\pi$
$503$	−21.0935	−0.940511	−0.470255	+	0.882530i	$0.655838\pi$
$504$	0	0
$505$	22.8179	1.01538
$506$	28.3476	1.26020
$507$	−6.08481	−0.270236
$508$	−54.1965	−2.40458
$509$	−0.213577	−0.00946663	−0.00473332	−	0.999989i	$-0.501507\pi$
$509$	−0.213577	−0.00946663	−0.00473332	+	0.999989i	$0.501507\pi$
$510$	−13.5410	−0.599605
$511$	0	0
$512$	−49.4010	−2.18324
$513$	13.7112	0.605366
$514$	77.0312	3.39770
$515$	−1.21797	−0.0536702
$516$	−14.8151	−0.652200
$517$	−55.6762	−2.44864
$518$	0	0
$519$	−6.25717	−0.274659
$520$	−1.09980	−0.0482294
$521$	−14.1315	−0.619113	−0.309556	−	0.950881i	$-0.600181\pi$
$521$	−14.1315	−0.619113	−0.309556	+	0.950881i	$0.600181\pi$
$522$	−49.4038	−2.16235
$523$	38.4886	1.68299	0.841495	−	0.540265i	$-0.181676\pi$
$523$	38.4886	1.68299	0.841495	+	0.540265i	$0.181676\pi$
$524$	102.776	4.48980
$525$	0	0
$526$	−77.2349	−3.36760
$527$	−22.9237	−0.998574
$528$	22.0195	0.958277
$529$	−19.3547	−0.841510
$530$	70.8313	3.07671
$531$	6.18245	0.268296
$532$	0	0
$533$	−0.0725380	−0.00314197
$534$	15.1639	0.656205
$535$	−0.889684	−0.0384644
$536$	−6.84175	−0.295519
$537$	3.84874	0.166085
$538$	12.0321	0.518743
$539$	0	0
$540$	−28.0814	−1.20843
$541$	−9.77310	−0.420179	−0.210089	−	0.977682i	$-0.567375\pi$
$541$	−9.77310	−0.420179	−0.210089	+	0.977682i	$0.567375\pi$
$542$	−22.4133	−0.962735
$543$	−6.25900	−0.268599
$544$	−37.3977	−1.60341
$545$	−14.1959	−0.608087
$546$	0	0
$547$	−32.3733	−1.38418	−0.692092	−	0.721810i	$-0.743311\pi$
$547$	−32.3733	−1.38418	−0.692092	+	0.721810i	$0.743311\pi$
$548$	−27.5385	−1.17639
$549$	7.20557	0.307526
$550$	0.410329	0.0174965
$551$	−34.9594	−1.48932
$552$	6.04519	0.257300
$553$	0	0
$554$	16.8144	0.714375
$555$	−5.24399	−0.222595
$556$	41.1702	1.74601
$557$	−31.9026	−1.35176	−0.675879	−	0.737012i	$-0.736236\pi$
$557$	−31.9026	−1.35176	−0.675879	+	0.737012i	$0.736236\pi$
$558$	−32.7534	−1.38656
$559$	0.496041	0.0209803
$560$	0	0
$561$	−13.5307	−0.571266
$562$	59.0491	2.49083
$563$	32.5073	1.37002	0.685009	−	0.728535i	$-0.259798\pi$
$563$	32.5073	1.37002	0.685009	+	0.728535i	$0.259798\pi$
$564$	−20.9133	−0.880608
$565$	−9.86240	−0.414914
$566$	−46.1090	−1.93810
$567$	0	0
$568$	−26.7704	−1.12326
$569$	−35.5560	−1.49059	−0.745293	−	0.666737i	$-0.767691\pi$
$569$	−35.5560	−1.49059	−0.745293	+	0.666737i	$0.767691\pi$
$570$	−13.6907	−0.573439
$571$	5.13907	0.215063	0.107532	−	0.994202i	$-0.465705\pi$
$571$	5.13907	0.215063	0.107532	+	0.994202i	$0.465705\pi$
$572$	−1.93572	−0.0809363
$573$	−1.09943	−0.0459293
$574$	0	0
$575$	0.0527651	0.00220045
$576$	−8.09002	−0.337084
$577$	−23.4023	−0.974250	−0.487125	−	0.873332i	$-0.661954\pi$
$577$	−23.4023	−0.974250	−0.487125	+	0.873332i	$0.661954\pi$
$578$	20.8521	0.867332
$579$	−2.20572	−0.0916666
$580$	71.5989	2.97298
$581$	0	0
$582$	21.8612	0.906177
$583$	70.7774	2.93130
$584$	−103.671	−4.28992
$585$	0.452281	0.0186995
$586$	1.99689	0.0824909
$587$	21.6605	0.894023	0.447011	−	0.894528i	$-0.352488\pi$
$587$	21.6605	0.894023	0.447011	+	0.894528i	$0.352488\pi$
$588$	0	0
$589$	−23.1771	−0.954998
$590$	−12.8331	−0.528331
$591$	−3.24172	−0.133346
$592$	−40.7219	−1.67366
$593$	0.975484	0.0400583	0.0200292	−	0.999799i	$-0.493624\pi$
$593$	0.975484	0.0400583	0.0200292	+	0.999799i	$0.493624\pi$
$594$	−40.1896	−1.64900
$595$	0	0
$596$	37.7253	1.54529
$597$	−11.1017	−0.454363
$598$	−0.356517	−0.0145791
$599$	4.84115	0.197804	0.0989021	−	0.995097i	$-0.468467\pi$
$599$	4.84115	0.197804	0.0989021	+	0.995097i	$0.468467\pi$
$600$	0.0875037	0.00357232
$601$	−19.3928	−0.791048	−0.395524	−	0.918456i	$-0.629437\pi$
$601$	−19.3928	−0.791048	−0.395524	+	0.918456i	$0.629437\pi$
$602$	0	0
$603$	2.81360	0.114579
$604$	−37.9142	−1.54271
$605$	49.9260	2.02978
$606$	12.2666	0.498295
$607$	−5.15332	−0.209167	−0.104583	−	0.994516i	$-0.533351\pi$
$607$	−5.15332	−0.209167	−0.104583	+	0.994516i	$0.533351\pi$
$608$	−37.8111	−1.53344
$609$	0	0
$610$	−14.9568	−0.605584
$611$	0.700219	0.0283278
$612$	64.4576	2.60554
$613$	21.1298	0.853426	0.426713	−	0.904387i	$-0.359672\pi$
$613$	21.1298	0.853426	0.426713	+	0.904387i	$0.359672\pi$
$614$	−6.38576	−0.257708
$615$	1.04993	0.0423374
$616$	0	0
$617$	10.2828	0.413969	0.206985	−	0.978344i	$-0.433635\pi$
$617$	10.2828	0.413969	0.206985	+	0.978344i	$0.433635\pi$
$618$	−0.654763	−0.0263384
$619$	−30.7100	−1.23434	−0.617170	−	0.786830i	$-0.711721\pi$
$619$	−30.7100	−1.23434	−0.617170	+	0.786830i	$0.711721\pi$
$620$	47.4682	1.90637
$621$	−5.16807	−0.207387
$622$	3.84564	0.154196
$623$	0	0
$624$	−0.276932	−0.0110861
$625$	−25.1374	−1.00550
$626$	−38.0835	−1.52212
$627$	−13.6803	−0.546337
$628$	−35.3871	−1.41210
$629$	25.0230	0.997734
$630$	0	0
$631$	33.2191	1.32243	0.661216	−	0.750195i	$-0.270041\pi$
$631$	33.2191	1.32243	0.661216	+	0.750195i	$0.270041\pi$
$632$	−37.0777	−1.47487
$633$	3.37592	0.134181
$634$	39.2295	1.55800
$635$	−26.2651	−1.04230
$636$	26.5856	1.05419
$637$	0	0
$638$	102.471	4.05687
$639$	11.0090	0.435511
$640$	−16.6821	−0.659417
$641$	2.37937	0.0939794	0.0469897	−	0.998895i	$-0.485037\pi$
$641$	2.37937	0.0939794	0.0469897	+	0.998895i	$0.485037\pi$
$642$	−0.478281	−0.0188762
$643$	21.1865	0.835515	0.417757	−	0.908559i	$-0.362816\pi$
$643$	21.1865	0.835515	0.417757	+	0.908559i	$0.362816\pi$
$644$	0	0
$645$	−7.17981	−0.282705
$646$	65.3285	2.57031
$647$	−3.29111	−0.129387	−0.0646935	−	0.997905i	$-0.520607\pi$
$647$	−3.29111	−0.129387	−0.0646935	+	0.997905i	$0.520607\pi$
$648$	47.8383	1.87927
$649$	−12.8234	−0.503361
$650$	−0.00516056	−0.000202414 0
$651$	0	0
$652$	−3.80123	−0.148868
$653$	33.1264	1.29634	0.648168	−	0.761497i	$-0.275535\pi$
$653$	33.1264	1.29634	0.648168	+	0.761497i	$0.275535\pi$
$654$	−7.63152	−0.298416
$655$	49.8081	1.94617
$656$	8.15319	0.318328
$657$	42.6335	1.66329
$658$	0	0
$659$	15.3837	0.599266	0.299633	−	0.954055i	$-0.403136\pi$
$659$	15.3837	0.599266	0.299633	+	0.954055i	$0.403136\pi$
$660$	28.0180	1.09060
$661$	48.9638	1.90447	0.952236	−	0.305364i	$-0.0987781\pi$
$661$	48.9638	1.90447	0.952236	+	0.305364i	$0.0987781\pi$
$662$	54.7921	2.12955
$663$	0.170171	0.00660888
$664$	32.7425	1.27066
$665$	0	0
$666$	35.7529	1.38540
$667$	13.1770	0.510214
$668$	36.2235	1.40153
$669$	0.581975	0.0225004
$670$	−5.84028	−0.225630
$671$	−14.9455	−0.576963
$672$	0	0
$673$	18.9400	0.730082	0.365041	−	0.930992i	$-0.381055\pi$
$673$	18.9400	0.730082	0.365041	+	0.930992i	$0.381055\pi$
$674$	−49.8405	−1.91978
$675$	−0.0748073	−0.00287934
$676$	−60.1232	−2.31243
$677$	26.8445	1.03172	0.515859	−	0.856674i	$-0.327473\pi$
$677$	26.8445	1.03172	0.515859	+	0.856674i	$0.327473\pi$
$678$	−5.30188	−0.203618
$679$	0	0
$680$	−75.9603	−2.91294
$681$	7.26026	0.278214
$682$	67.9356	2.60139
$683$	45.1368	1.72711	0.863556	−	0.504252i	$-0.168232\pi$
$683$	45.1368	1.72711	0.863556	+	0.504252i	$0.168232\pi$
$684$	65.1701	2.49184
$685$	−13.3459	−0.509920
$686$	0	0
$687$	−1.51960	−0.0579765
$688$	−55.7544	−2.12562
$689$	−0.890142	−0.0339117
$690$	5.16032	0.196450
$691$	27.1345	1.03225	0.516123	−	0.856515i	$-0.327375\pi$
$691$	27.1345	1.03225	0.516123	+	0.856515i	$0.327375\pi$
$692$	−61.8262	−2.35028
$693$	0	0
$694$	23.6850	0.899070
$695$	19.9522	0.756830
$696$	21.8522	0.828306
$697$	−5.01002	−0.189768
$698$	13.4449	0.508899
$699$	−0.0696123	−0.00263298
$700$	0	0
$701$	48.7878	1.84269	0.921344	−	0.388748i	$-0.127092\pi$
$701$	48.7878	1.84269	0.921344	+	0.388748i	$0.127092\pi$
$702$	0.505450	0.0190770
$703$	25.2996	0.954194
$704$	16.7799	0.632418
$705$	−10.1351	−0.381711
$706$	−84.9110	−3.19567
$707$	0	0
$708$	−4.81675	−0.181025
$709$	12.1945	0.457975	0.228987	−	0.973429i	$-0.426459\pi$
$709$	12.1945	0.457975	0.228987	+	0.973429i	$0.426459\pi$
$710$	−22.8518	−0.857614
$711$	15.2478	0.571837
$712$	85.0641	3.18791
$713$	8.73598	0.327165
$714$	0	0
$715$	−0.938100	−0.0350829
$716$	38.0288	1.42120
$717$	7.36295	0.274974
$718$	27.3297	1.01993
$719$	10.3736	0.386869	0.193434	−	0.981113i	$-0.438037\pi$
$719$	10.3736	0.386869	0.193434	+	0.981113i	$0.438037\pi$
$720$	−50.8358	−1.89454
$721$	0	0
$722$	17.1400	0.637884
$723$	6.79146	0.252577
$724$	−61.8443	−2.29843
$725$	0.190736	0.00708374
$726$	26.8395	0.996107
$727$	−34.5870	−1.28276	−0.641380	−	0.767224i	$-0.721638\pi$
$727$	−34.5870	−1.28276	−0.641380	+	0.767224i	$0.721638\pi$
$728$	0	0
$729$	−15.8706	−0.587798
$730$	−88.4956	−3.27537
$731$	34.2603	1.26716
$732$	−5.61386	−0.207494
$733$	27.3160	1.00894	0.504470	−	0.863429i	$-0.331688\pi$
$733$	27.3160	1.00894	0.504470	+	0.863429i	$0.331688\pi$
$734$	−3.83140	−0.141419
$735$	0	0
$736$	14.2518	0.525330
$737$	−5.83583	−0.214966
$738$	−7.15830	−0.263501
$739$	−32.9855	−1.21339	−0.606695	−	0.794935i	$-0.707505\pi$
$739$	−32.9855	−1.21339	−0.606695	+	0.794935i	$0.707505\pi$
$740$	−51.8152	−1.90476
$741$	0.172052	0.00632048
$742$	0	0
$743$	33.5846	1.23210	0.616049	−	0.787708i	$-0.288732\pi$
$743$	33.5846	1.23210	0.616049	+	0.787708i	$0.288732\pi$
$744$	14.4874	0.531135
$745$	18.2827	0.669827
$746$	−8.50505	−0.311392
$747$	−13.4650	−0.492659
$748$	−133.695	−4.88837
$749$	0	0
$750$	−13.4392	−0.490731
$751$	6.22654	0.227210	0.113605	−	0.993526i	$-0.463760\pi$
$751$	6.22654	0.227210	0.113605	+	0.993526i	$0.463760\pi$
$752$	−78.7038	−2.87003
$753$	8.24659	0.300523
$754$	−1.28874	−0.0469332
$755$	−18.3742	−0.668707
$756$	0	0
$757$	−5.40058	−0.196288	−0.0981438	−	0.995172i	$-0.531291\pi$
$757$	−5.40058	−0.196288	−0.0981438	+	0.995172i	$0.531291\pi$
$758$	47.1044	1.71091
$759$	5.15639	0.187165
$760$	−76.8000	−2.78583
$761$	−15.6306	−0.566610	−0.283305	−	0.959030i	$-0.591431\pi$
$761$	−15.6306	−0.566610	−0.283305	+	0.959030i	$0.591431\pi$
$762$	−14.1197	−0.511504
$763$	0	0
$764$	−10.8633	−0.393021
$765$	31.2379	1.12941
$766$	95.9242	3.46588
$767$	0.161275	0.00582329
$768$	−11.6926	−0.421921
$769$	−3.23902	−0.116802	−0.0584009	−	0.998293i	$-0.518600\pi$
$769$	−3.23902	−0.116802	−0.0584009	+	0.998293i	$0.518600\pi$
$770$	0	0
$771$	14.0119	0.504625
$772$	−21.7944	−0.784398
$773$	8.42218	0.302925	0.151462	−	0.988463i	$-0.451602\pi$
$773$	8.42218	0.302925	0.151462	+	0.988463i	$0.451602\pi$
$774$	48.9510	1.75951
$775$	0.126453	0.00454231
$776$	122.634	4.40230
$777$	0	0
$778$	−9.58527	−0.343649
$779$	−5.06540	−0.181487
$780$	−0.352372	−0.0126169
$781$	−22.8345	−0.817081
$782$	−24.6237	−0.880543
$783$	−18.6816	−0.667625
$784$	0	0
$785$	−17.1496	−0.612094
$786$	26.7761	0.955072
$787$	−19.1587	−0.682933	−0.341467	−	0.939894i	$-0.610924\pi$
$787$	−19.1587	−0.682933	−0.341467	+	0.939894i	$0.610924\pi$
$788$	−32.0310	−1.14106
$789$	−14.0489	−0.500155
$790$	−31.6504	−1.12607
$791$	0	0
$792$	−108.449	−3.85358
$793$	0.187964	0.00667478
$794$	−26.1931	−0.929558
$795$	12.8841	0.456953
$796$	−109.694	−3.88802
$797$	49.1450	1.74080	0.870402	−	0.492342i	$-0.163859\pi$
$797$	49.1450	1.74080	0.870402	+	0.492342i	$0.163859\pi$
$798$	0	0
$799$	48.3624	1.71094
$800$	0.206294	0.00729360
$801$	−34.9817	−1.23602
$802$	−90.2440	−3.18662
$803$	−88.4284	−3.12057
$804$	−2.19208	−0.0773086
$805$	0	0
$806$	−0.854401	−0.0300950
$807$	2.18863	0.0770435
$808$	68.8113	2.42077
$809$	43.9060	1.54365	0.771826	−	0.635834i	$-0.219344\pi$
$809$	43.9060	1.54365	0.771826	+	0.635834i	$0.219344\pi$
$810$	40.8359	1.43483
$811$	21.3942	0.751252	0.375626	−	0.926771i	$-0.377428\pi$
$811$	21.3942	0.751252	0.375626	+	0.926771i	$0.377428\pi$
$812$	0	0
$813$	−4.07696	−0.142985
$814$	−74.1569	−2.59920
$815$	−1.84218	−0.0645286
$816$	−19.1270	−0.669578
$817$	34.6390	1.21187
$818$	−42.6677	−1.49184
$819$	0	0
$820$	10.3742	0.362284
$821$	−51.5951	−1.80068	−0.900340	−	0.435187i	$-0.856682\pi$
$821$	−51.5951	−1.80068	−0.900340	+	0.435187i	$0.856682\pi$
$822$	−7.17456	−0.250241
$823$	32.4684	1.13178	0.565889	−	0.824482i	$-0.308533\pi$
$823$	32.4684	1.13178	0.565889	+	0.824482i	$0.308533\pi$
$824$	−3.67300	−0.127955
$825$	0.0746383	0.00259857
$826$	0	0
$827$	19.7906	0.688187	0.344094	−	0.938935i	$-0.388186\pi$
$827$	19.7906	0.688187	0.344094	+	0.938935i	$0.388186\pi$
$828$	−24.5640	−0.853660
$829$	3.18668	0.110678	0.0553389	−	0.998468i	$-0.482376\pi$
$829$	3.18668	0.110678	0.0553389	+	0.998468i	$0.482376\pi$
$830$	27.9498	0.970150
$831$	3.05852	0.106099
$832$	−0.211035	−0.00731633
$833$	0	0
$834$	10.7260	0.371411
$835$	17.5549	0.607512
$836$	−135.173	−4.67505
$837$	−12.3854	−0.428101
$838$	22.6896	0.783800
$839$	−0.366627	−0.0126574	−0.00632868	−	0.999980i	$-0.502014\pi$
$839$	−0.366627	−0.0126574	−0.00632868	+	0.999980i	$0.502014\pi$
$840$	0	0
$841$	18.6322	0.642490
$842$	82.2226	2.83358
$843$	10.7410	0.369938
$844$	33.3570	1.14820
$845$	−29.1373	−1.00235
$846$	69.1000	2.37571
$847$	0	0
$848$	100.051	3.43576
$849$	−8.38716	−0.287847
$850$	−0.356427	−0.0122253
$851$	−9.53599	−0.326890
$852$	−8.57715	−0.293848
$853$	26.5967	0.910654	0.455327	−	0.890324i	$-0.349522\pi$
$853$	26.5967	0.910654	0.455327	+	0.890324i	$0.349522\pi$
$854$	0	0
$855$	31.5832	1.08012
$856$	−2.68299	−0.0917028
$857$	25.9523	0.886514	0.443257	−	0.896395i	$-0.353823\pi$
$857$	25.9523	0.886514	0.443257	+	0.896395i	$0.353823\pi$
$858$	−0.504309	−0.0172168
$859$	57.0932	1.94800	0.973998	−	0.226555i	$-0.0727465\pi$
$859$	57.0932	1.94800	0.973998	+	0.226555i	$0.0727465\pi$
$860$	−70.9428	−2.41913
$861$	0	0
$862$	78.4532	2.67213
$863$	−30.9029	−1.05195	−0.525974	−	0.850501i	$-0.676299\pi$
$863$	−30.9029	−1.05195	−0.525974	+	0.850501i	$0.676299\pi$
$864$	−20.2055	−0.687404
$865$	−29.9627	−1.01876
$866$	68.2504	2.31924
$867$	3.79297	0.128816
$868$	0	0
$869$	−31.6263	−1.07285
$870$	18.6535	0.632415
$871$	0.0733952	0.00248690
$872$	−42.8102	−1.44974
$873$	−50.4319	−1.70686
$874$	−24.8959	−0.842118
$875$	0	0
$876$	−33.2158	−1.12226
$877$	−9.96410	−0.336464	−0.168232	−	0.985747i	$-0.553806\pi$
$877$	−9.96410	−0.336464	−0.168232	+	0.985747i	$0.553806\pi$
$878$	−42.9698	−1.45016
$879$	0.363232	0.0122515
$880$	105.441	3.55442
$881$	−2.35418	−0.0793143	−0.0396572	−	0.999213i	$-0.512627\pi$
$881$	−2.35418	−0.0793143	−0.0396572	+	0.999213i	$0.512627\pi$
$882$	0	0
$883$	27.5946	0.928631	0.464315	−	0.885670i	$-0.346300\pi$
$883$	27.5946	0.928631	0.464315	+	0.885670i	$0.346300\pi$
$884$	1.68143	0.0565527
$885$	−2.33433	−0.0784676
$886$	7.92605	0.266281
$887$	−19.7827	−0.664239	−0.332119	−	0.943237i	$-0.607764\pi$
$887$	−19.7827	−0.664239	−0.332119	+	0.943237i	$0.607764\pi$
$888$	−15.8141	−0.530688
$889$	0	0
$890$	72.6127	2.43398
$891$	40.8048	1.36701
$892$	5.75041	0.192538
$893$	48.8970	1.63627
$894$	9.82852	0.328715
$895$	18.4298	0.616040
$896$	0	0
$897$	−0.0648501	−0.00216528
$898$	−57.7855	−1.92833
$899$	31.5789	1.05321
$900$	−0.355563	−0.0118521
$901$	−61.4798	−2.04819
$902$	14.8474	0.494365
$903$	0	0
$904$	−29.7417	−0.989196
$905$	−29.9714	−0.996284
$906$	−9.87772	−0.328165
$907$	−2.52400	−0.0838082	−0.0419041	−	0.999122i	$-0.513342\pi$
$907$	−2.52400	−0.0838082	−0.0419041	+	0.999122i	$0.513342\pi$
$908$	71.7376	2.38070
$909$	−28.2979	−0.938583
$910$	0	0
$911$	−44.3294	−1.46870	−0.734350	−	0.678771i	$-0.762513\pi$
$911$	−44.3294	−1.46870	−0.734350	+	0.678771i	$0.762513\pi$
$912$	−19.3384	−0.640358
$913$	27.9285	0.924298
$914$	−99.4593	−3.28982
$915$	−2.72063	−0.0899412
$916$	−15.0150	−0.496110
$917$	0	0
$918$	34.9102	1.15221
$919$	49.1888	1.62259	0.811294	−	0.584638i	$-0.198764\pi$
$919$	49.1888	1.62259	0.811294	+	0.584638i	$0.198764\pi$
$920$	28.9476	0.954374
$921$	−1.16156	−0.0382748
$922$	−31.5132	−1.03783
$923$	0.287181	0.00945267
$924$	0	0
$925$	−0.138033	−0.00453849
$926$	84.8865	2.78954
$927$	1.51048	0.0496107
$928$	51.5177	1.69115
$929$	7.57846	0.248641	0.124321	−	0.992242i	$-0.460325\pi$
$929$	7.57846	0.248641	0.124321	+	0.992242i	$0.460325\pi$
$930$	12.3668	0.405524
$931$	0	0
$932$	−0.687830	−0.0225306
$933$	0.699517	0.0229012
$934$	15.4947	0.507003
$935$	−64.7922	−2.11893
$936$	1.36393	0.0445814
$937$	−15.1160	−0.493817	−0.246909	−	0.969039i	$-0.579415\pi$
$937$	−15.1160	−0.493817	−0.246909	+	0.969039i	$0.579415\pi$
$938$	0	0
$939$	−6.92735	−0.226065
$940$	−100.144	−3.26633
$941$	28.8060	0.939050	0.469525	−	0.882919i	$-0.344425\pi$
$941$	28.8060	0.939050	0.469525	+	0.882919i	$0.344425\pi$
$942$	−9.21935	−0.300383
$943$	1.90926	0.0621741
$944$	−18.1271	−0.589986
$945$	0	0
$946$	−101.532	−3.30109
$947$	40.6344	1.32044	0.660221	−	0.751072i	$-0.270463\pi$
$947$	40.6344	1.32044	0.660221	+	0.751072i	$0.270463\pi$
$948$	−11.8796	−0.385831
$949$	1.11213	0.0361013
$950$	−0.360367	−0.0116918
$951$	7.13579	0.231394
$952$	0	0
$953$	37.5104	1.21508	0.607541	−	0.794289i	$-0.292156\pi$
$953$	37.5104	1.21508	0.607541	+	0.794289i	$0.292156\pi$
$954$	−87.8422	−2.84400
$955$	−5.26465	−0.170360
$956$	72.7523	2.35298
$957$	18.6394	0.602525
$958$	52.9872	1.71194
$959$	0	0
$960$	3.05457	0.0985859
$961$	−10.0640	−0.324647
$962$	0.932645	0.0300697
$963$	1.10335	0.0355550
$964$	67.1054	2.16132
$965$	−10.5622	−0.340008
$966$	0	0
$967$	−35.6540	−1.14655	−0.573277	−	0.819361i	$-0.694328\pi$
$967$	−35.6540	−1.14655	−0.573277	+	0.819361i	$0.694328\pi$
$968$	150.560	4.83919
$969$	11.8832	0.381742
$970$	104.683	3.36117
$971$	17.5452	0.563052	0.281526	−	0.959554i	$-0.409159\pi$
$971$	17.5452	0.563052	0.281526	+	0.959554i	$0.409159\pi$
$972$	52.8987	1.69673
$973$	0	0
$974$	−8.91651	−0.285703
$975$	−0.000938700 0	−3.00624e−5 0
$976$	−21.1269	−0.676255
$977$	−49.9851	−1.59917	−0.799583	−	0.600555i	$-0.794946\pi$
$977$	−49.9851	−1.59917	−0.799583	+	0.600555i	$0.794946\pi$
$978$	−0.990327	−0.0316672
$979$	72.5575	2.31895
$980$	0	0
$981$	17.6052	0.562092
$982$	−23.0022	−0.734031
$983$	−53.5608	−1.70833	−0.854163	−	0.520006i	$-0.825930\pi$
$983$	−53.5608	−1.70833	−0.854163	+	0.520006i	$0.825930\pi$
$984$	3.16625	0.100936
$985$	−15.5231	−0.494606
$986$	−89.0101	−2.83466
$987$	0	0
$988$	1.70002	0.0540848
$989$	−13.0562	−0.415163
$990$	−92.5749	−2.94222
$991$	9.93145	0.315483	0.157741	−	0.987480i	$-0.449579\pi$
$991$	9.93145	0.315483	0.157741	+	0.987480i	$0.449579\pi$
$992$	34.1548	1.08442
$993$	9.96661	0.316281
$994$	0	0
$995$	−53.1609	−1.68531
$996$	10.4906	0.332407
$997$	−17.2765	−0.547153	−0.273577	−	0.961850i	$-0.588207\pi$
$997$	−17.2765	−0.547153	−0.273577	+	0.961850i	$0.588207\pi$
$998$	16.9628	0.536948
$999$	13.5196	0.427741

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2009.2.a.s.1.16		17
7.2	even	3		287.2.e.d.165.2	✓	34
7.4	even	3		287.2.e.d.247.2	yes	34
7.6	odd	2		2009.2.a.r.1.16		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.e.d.165.2	✓	34	7.2	even	3
287.2.e.d.247.2	yes	34	7.4	even	3
2009.2.a.r.1.16		17	7.6	odd	2
2009.2.a.s.1.16		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)

\(f(q)\)	\(=\)	\(q+2.57424 q^{2} +0.468252 q^{3} +4.62673 q^{4} +2.24224 q^{5} +1.20539 q^{6} +6.76185 q^{8} -2.78074 q^{9} +O(q^{10})\)	\(q+2.57424 q^{2} +0.468252 q^{3} +4.62673 q^{4} +2.24224 q^{5} +1.20539 q^{6} +6.76185 q^{8} -2.78074 q^{9} +5.77207 q^{10} +5.76768 q^{11} +2.16648 q^{12} -0.0725380 q^{13} +1.04993 q^{15} +8.15319 q^{16} -5.01002 q^{17} -7.15830 q^{18} -5.06540 q^{19} +10.3742 q^{20} +14.8474 q^{22} +1.90926 q^{23} +3.16625 q^{24} +0.0276364 q^{25} -0.186731 q^{26} -2.70684 q^{27} +6.90161 q^{29} +2.70278 q^{30} +4.57558 q^{31} +7.46459 q^{32} +2.70073 q^{33} -12.8970 q^{34} -12.8657 q^{36} -4.99460 q^{37} -13.0396 q^{38} -0.0339661 q^{39} +15.1617 q^{40} +1.00000 q^{41} -6.83836 q^{43} +26.6855 q^{44} -6.23508 q^{45} +4.91490 q^{46} -9.65313 q^{47} +3.81774 q^{48} +0.0711428 q^{50} -2.34595 q^{51} -0.335614 q^{52} +12.2714 q^{53} -6.96807 q^{54} +12.9325 q^{55} -2.37188 q^{57} +17.7664 q^{58} -2.22331 q^{59} +4.85776 q^{60} -2.59124 q^{61} +11.7787 q^{62} +2.90930 q^{64} -0.162648 q^{65} +6.95233 q^{66} -1.01182 q^{67} -23.1800 q^{68} +0.894015 q^{69} -3.95904 q^{71} -18.8029 q^{72} -15.3317 q^{73} -12.8573 q^{74} +0.0129408 q^{75} -23.4362 q^{76} -0.0874370 q^{78} -5.48336 q^{79} +18.2814 q^{80} +7.07474 q^{81} +2.57424 q^{82} +4.84224 q^{83} -11.2337 q^{85} -17.6036 q^{86} +3.23169 q^{87} +39.0002 q^{88} +12.5800 q^{89} -16.0506 q^{90} +8.83364 q^{92} +2.14252 q^{93} -24.8495 q^{94} -11.3578 q^{95} +3.49531 q^{96} +18.1362 q^{97} -16.0384 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 3 q^{2} + q^{3} + 25 q^{4} - q^{5} + 2 q^{6} + 9 q^{8} + 26 q^{9}+O(q^{10}) \) 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

Introduction

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