LMFDB - Embedded newform 2009.2.a.r.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	$-0.543159\pi$
$3$	−0.468252	−0.270345	−0.135173	+	0.990822i	$0.543159\pi$
$4$	4.62673	2.31337
$5$	−2.24224	−1.00276	−0.501380	−	0.865227i	$-0.667174\pi$
$5$	−2.24224	−1.00276	−0.501380	+	0.865227i	$0.667174\pi$
$6$	−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	$-0.496798\pi$
$13$	0.0725380	0.0201184	0.0100592	+	0.999949i	$0.496798\pi$
$14$	0	0
$15$	1.04993	0.271091
$16$	8.15319	2.03830
$17$	5.01002	1.21511	0.607554	−	0.794279i	$-0.292151\pi$
$17$	5.01002	1.21511	0.607554	+	0.794279i	$0.292151\pi$
$18$	−7.15830	−1.68723
$19$	5.06540	1.16208	0.581041	−	0.813874i	$-0.302646\pi$
$19$	5.06540	1.16208	0.581041	+	0.813874i	$0.302646\pi$
$20$	−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	$-0.634785\pi$
$31$	−4.57558	−0.821799	−0.410899	+	0.911681i	$0.634785\pi$
$32$	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	$-0.251383\pi$
$47$	9.65313	1.40805	0.704027	+	0.710173i	$0.251383\pi$
$48$	−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	$-0.453770\pi$
$59$	2.22331	0.289451	0.144725	+	0.989472i	$0.453770\pi$
$60$	4.85776	0.627134
$61$	2.59124	0.331774	0.165887	−	0.986145i	$-0.446951\pi$
$61$	2.59124	0.331774	0.165887	+	0.986145i	$0.446951\pi$
$62$	−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	$-0.145583\pi$
$73$	15.3317	1.79444	0.897220	+	0.441584i	$0.145583\pi$
$74$	−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	$-0.585620\pi$
$83$	−4.84224	−0.531505	−0.265752	+	0.964041i	$0.585620\pi$
$84$	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	$-0.732310\pi$
$89$	−12.5800	−1.33348	−0.666739	+	0.745291i	$0.732310\pi$
$90$	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	$-0.872400\pi$
$97$	−18.1362	−1.84145	−0.920724	+	0.390216i	$0.872400\pi$
$98$	0	0
$99$	−16.0384	−1.61192
$100$	0.127866	0.0127866
$101$	−10.1764	−1.01259	−0.506295	−	0.862361i	$-0.668985\pi$
$101$	−10.1764	−1.01259	−0.506295	+	0.862361i	$0.668985\pi$
$102$	−6.03905	−0.597955
$103$	0.543194	0.0535225	0.0267613	−	0.999642i	$-0.491481\pi$
$103$	0.543194	0.0535225	0.0267613	+	0.999642i	$0.491481\pi$
$104$	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	$-0.922365\pi$
$131$	−22.2136	−1.94081	−0.970404	+	0.241486i	$0.922365\pi$
$132$	−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	$-0.623173\pi$
$139$	−8.89834	−0.754747	−0.377374	+	0.926061i	$0.623173\pi$
$140$	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	$-0.401275\pi$
$157$	7.64841	0.610410	0.305205	+	0.952287i	$0.401275\pi$
$158$	−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	$-0.597961\pi$
$167$	−7.82917	−0.605840	−0.302920	+	0.953016i	$0.597961\pi$
$168$	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	$-0.330393\pi$
$173$	13.3628	1.01596	0.507978	+	0.861370i	$0.330393\pi$
$174$	−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	$-0.334519\pi$
$181$	13.3667	0.993542	0.496771	+	0.867882i	$0.334519\pi$
$182$	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	$-0.182357\pi$
$199$	23.7088	1.68068	0.840338	+	0.542063i	$0.182357\pi$
$200$	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	$-0.513250\pi$
$223$	−1.24287	−0.0832285	−0.0416142	+	0.999134i	$0.513250\pi$
$224$	0	0
$225$	−0.0768496	−0.00512331
$226$	−11.3227	−0.753176
$227$	−15.5050	−1.02911	−0.514553	−	0.857459i	$-0.672042\pi$
$227$	−15.5050	−1.02911	−0.514553	+	0.857459i	$0.672042\pi$
$228$	−10.9741	−0.726775
$229$	3.24527	0.214454	0.107227	−	0.994235i	$-0.465803\pi$
$229$	3.24527	0.214454	0.107227	+	0.994235i	$0.465803\pi$
$230$	−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	$-0.654715\pi$
$241$	−14.5039	−0.934275	−0.467138	+	0.884185i	$0.654715\pi$
$242$	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	$-0.687593\pi$
$251$	−17.6114	−1.11162	−0.555812	+	0.831308i	$0.687593\pi$
$252$	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	$-0.883083\pi$
$257$	−29.9238	−1.86660	−0.933298	+	0.359103i	$0.883083\pi$
$258$	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	$-0.545511\pi$
$269$	−4.67405	−0.284982	−0.142491	+	0.989796i	$0.545511\pi$
$270$	−15.6241	−0.950852
$271$	8.70676	0.528898	0.264449	−	0.964400i	$-0.414810\pi$
$271$	8.70676	0.528898	0.264449	+	0.964400i	$0.414810\pi$
$272$	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	$-0.321302\pi$
$283$	17.9116	1.06474	0.532369	+	0.846513i	$0.321302\pi$
$284$	−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	$-0.507213\pi$
$293$	−0.775720	−0.0453181	−0.0226590	+	0.999743i	$0.507213\pi$
$294$	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	$-0.477448\pi$
$307$	2.48064	0.141577	0.0707887	+	0.997491i	$0.477448\pi$
$308$	0	0
$309$	−0.254352	−0.0144696
$310$	26.4106	1.50002
$311$	−1.49389	−0.0847108	−0.0423554	−	0.999103i	$-0.513486\pi$
$311$	−1.49389	−0.0847108	−0.0423554	+	0.999103i	$0.513486\pi$
$312$	−0.229673	−0.0130027
$313$	14.7941	0.836210	0.418105	−	0.908399i	$-0.362694\pi$
$313$	14.7941	0.836210	0.418105	+	0.908399i	$0.362694\pi$
$314$	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	$-0.544642\pi$
$349$	−5.22287	−0.279574	−0.139787	+	0.990182i	$0.544642\pi$
$350$	0	0
$351$	0.196349	0.0104803
$352$	43.0534	2.29475
$353$	32.9848	1.75561	0.877803	−	0.479022i	$-0.159008\pi$
$353$	32.9848	1.75561	0.877803	+	0.479022i	$0.159008\pi$
$354$	−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	$-0.487632\pi$
$367$	1.48836	0.0776916	0.0388458	+	0.999245i	$0.487632\pi$
$368$	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	$-0.901004\pi$
$383$	−37.2631	−1.90405	−0.952027	+	0.306014i	$0.901004\pi$
$384$	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	$-0.417814\pi$
$397$	10.1751	0.510672	0.255336	+	0.966852i	$0.417814\pi$
$398$	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	$-0.365603\pi$
$409$	16.5748	0.819573	0.409787	+	0.912181i	$0.365603\pi$
$410$	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	$-0.569072\pi$
$419$	−8.81409	−0.430597	−0.215298	+	0.976548i	$0.569072\pi$
$420$	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	$-0.719850\pi$
$433$	−26.5128	−1.27412	−0.637062	+	0.770813i	$0.719850\pi$
$434$	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	$-0.369587\pi$
$439$	16.6922	0.796675	0.398338	+	0.917239i	$0.369587\pi$
$440$	−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	$-0.407981\pi$
$461$	12.2417	0.570155	0.285077	+	0.958504i	$0.407981\pi$
$462$	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	$-0.544474\pi$
$467$	−6.01914	−0.278533	−0.139266	+	0.990255i	$0.544474\pi$
$468$	−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	$-0.655834\pi$
$479$	−20.5836	−0.940489	−0.470245	+	0.882536i	$0.655834\pi$
$480$	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	$-0.344162\pi$
$503$	21.0935	0.940511	0.470255	+	0.882530i	$0.344162\pi$
$504$	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	$-0.498493\pi$
$509$	0.213577	0.00946663	0.00473332	+	0.999989i	$0.498493\pi$
$510$	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	$-0.399819\pi$
$521$	14.1315	0.619113	0.309556	+	0.950881i	$0.399819\pi$
$522$	−49.4038	−2.16235
$523$	−38.4886	−1.68299	−0.841495	−	0.540265i	$-0.818324\pi$
$523$	−38.4886	−1.68299	−0.841495	+	0.540265i	$0.818324\pi$
$524$	−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	$-0.740202\pi$
$563$	−32.5073	−1.37002	−0.685009	+	0.728535i	$0.740202\pi$
$564$	−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	$-0.338046\pi$
$577$	23.4023	0.974250	0.487125	+	0.873332i	$0.338046\pi$
$578$	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	$-0.647512\pi$
$587$	−21.6605	−0.894023	−0.447011	+	0.894528i	$0.647512\pi$
$588$	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	$-0.506376\pi$
$593$	−0.975484	−0.0400583	−0.0200292	+	0.999799i	$0.506376\pi$
$594$	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	$-0.370563\pi$
$601$	19.3928	0.791048	0.395524	+	0.918456i	$0.370563\pi$
$602$	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	$-0.466649\pi$
$607$	5.15332	0.209167	0.104583	+	0.994516i	$0.466649\pi$
$608$	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	$-0.288279\pi$
$619$	30.7100	1.23434	0.617170	+	0.786830i	$0.288279\pi$
$620$	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	$-0.637184\pi$
$643$	−21.1865	−0.835515	−0.417757	+	0.908559i	$0.637184\pi$
$644$	0	0
$645$	−7.17981	−0.282705
$646$	65.3285	2.57031
$647$	3.29111	0.129387	0.0646935	−	0.997905i	$-0.479393\pi$
$647$	3.29111	0.129387	0.0646935	+	0.997905i	$0.479393\pi$
$648$	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	$-0.901222\pi$
$661$	−48.9638	−1.90447	−0.952236	+	0.305364i	$0.901222\pi$
$662$	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	$-0.672527\pi$
$677$	−26.8445	−1.03172	−0.515859	+	0.856674i	$0.672527\pi$
$678$	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	$-0.672625\pi$
$691$	−27.1345	−1.03225	−0.516123	+	0.856515i	$0.672625\pi$
$692$	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	$-0.561963\pi$
$719$	−10.3736	−0.386869	−0.193434	+	0.981113i	$0.561963\pi$
$720$	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	$-0.278362\pi$
$727$	34.5870	1.28276	0.641380	+	0.767224i	$0.278362\pi$
$728$	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	$-0.668312\pi$
$733$	−27.3160	−1.00894	−0.504470	+	0.863429i	$0.668312\pi$
$734$	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	$-0.408569\pi$
$761$	15.6306	0.566610	0.283305	+	0.959030i	$0.408569\pi$
$762$	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	$-0.481400\pi$
$769$	3.23902	0.116802	0.0584009	+	0.998293i	$0.481400\pi$
$770$	0	0
$771$	14.0119	0.504625
$772$	−21.7944	−0.784398
$773$	−8.42218	−0.302925	−0.151462	−	0.988463i	$-0.548398\pi$
$773$	−8.42218	−0.302925	−0.151462	+	0.988463i	$0.548398\pi$
$774$	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	$-0.389076\pi$
$787$	19.1587	0.682933	0.341467	+	0.939894i	$0.389076\pi$
$788$	−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	$-0.836141\pi$
$797$	−49.1450	−1.74080	−0.870402	+	0.492342i	$0.836141\pi$
$798$	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	$-0.622572\pi$
$811$	−21.3942	−0.751252	−0.375626	+	0.926771i	$0.622572\pi$
$812$	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	$-0.517624\pi$
$829$	−3.18668	−0.110678	−0.0553389	+	0.998468i	$0.517624\pi$
$830$	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	$-0.497986\pi$
$839$	0.366627	0.0126574	0.00632868	+	0.999980i	$0.497986\pi$
$840$	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	$-0.650478\pi$
$853$	−26.5967	−0.910654	−0.455327	+	0.890324i	$0.650478\pi$
$854$	0	0
$855$	31.5832	1.08012
$856$	−2.68299	−0.0917028
$857$	−25.9523	−0.886514	−0.443257	−	0.896395i	$-0.646177\pi$
$857$	−25.9523	−0.886514	−0.443257	+	0.896395i	$0.646177\pi$
$858$	−0.504309	−0.0172168
$859$	−57.0932	−1.94800	−0.973998	−	0.226555i	$-0.927254\pi$
$859$	−57.0932	−1.94800	−0.973998	+	0.226555i	$0.927254\pi$
$860$	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	$-0.487373\pi$
$881$	2.35418	0.0793143	0.0396572	+	0.999213i	$0.487373\pi$
$882$	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	$-0.392236\pi$
$887$	19.7827	0.664239	0.332119	+	0.943237i	$0.392236\pi$
$888$	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	$-0.539675\pi$
$929$	−7.57846	−0.248641	−0.124321	+	0.992242i	$0.539675\pi$
$930$	−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	$-0.420585\pi$
$937$	15.1160	0.493817	0.246909	+	0.969039i	$0.420585\pi$
$938$	0	0
$939$	−6.92735	−0.226065
$940$	−100.144	−3.26633
$941$	−28.8060	−0.939050	−0.469525	−	0.882919i	$-0.655575\pi$
$941$	−28.8060	−0.939050	−0.469525	+	0.882919i	$0.655575\pi$
$942$	−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	$-0.590841\pi$
$971$	−17.5452	−0.563052	−0.281526	+	0.959554i	$0.590841\pi$
$972$	−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	$-0.174070\pi$
$983$	53.5608	1.70833	0.854163	+	0.520006i	$0.174070\pi$
$984$	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	$-0.411793\pi$
$997$	17.2765	0.547153	0.273577	+	0.961850i	$0.411793\pi$
$998$	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.r.1.16		17
7.3	odd	6		287.2.e.d.247.2	yes	34
7.5	odd	6		287.2.e.d.165.2	✓	34
7.6	odd	2		2009.2.a.s.1.16		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.e.d.165.2	✓	34	7.5	odd	6
287.2.e.d.247.2	yes	34	7.3	odd	6
2009.2.a.r.1.16		17	1.1	even	1	trivial
2009.2.a.s.1.16		17	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

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

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