LMFDB - Embedded newform 2009.2.a.j.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("2009.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$16.0419457661$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.257.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 4x + 3 $ x^3 - x^2 - 4*x + 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 287)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$0.713538$ 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)

$f(q)$	$=$	$q+0.713538 q^{2} +3.20440 q^{3} -1.49086 q^{4} -2.00000 q^{5} +2.28646 q^{6} -2.49086 q^{8} +7.26819 q^{9} +O(q^{10})$	\(q+0.713538 q^{2} +3.20440 q^{3} -1.49086 q^{4} -2.00000 q^{5} +2.28646 q^{6} -2.49086 q^{8} +7.26819 q^{9} -1.42708 q^{10} -2.00000 q^{11} -4.77733 q^{12} -5.49086 q^{13} -6.40880 q^{15} +1.20440 q^{16} -5.69527 q^{17} +5.18613 q^{18} -4.71354 q^{19} +2.98173 q^{20} -1.42708 q^{22} -0.795598 q^{23} -7.98173 q^{24} -1.00000 q^{25} -3.91794 q^{26} +13.6770 q^{27} +2.57292 q^{29} -4.57292 q^{30} +1.42708 q^{31} +5.84111 q^{32} -6.40880 q^{33} -4.06379 q^{34} -10.8359 q^{36} -11.4543 q^{37} -3.36329 q^{38} -17.5949 q^{39} +4.98173 q^{40} +1.00000 q^{41} +11.8228 q^{43} +2.98173 q^{44} -14.5364 q^{45} -0.567690 q^{46} -5.89967 q^{47} +3.85939 q^{48} -0.713538 q^{50} -18.2499 q^{51} +8.18613 q^{52} -3.55465 q^{53} +9.75905 q^{54} +4.00000 q^{55} -15.1041 q^{57} +1.83588 q^{58} +4.00000 q^{59} +9.55465 q^{60} +5.55465 q^{61} +1.01827 q^{62} +1.75905 q^{64} +10.9817 q^{65} -4.57292 q^{66} +7.55465 q^{67} +8.49086 q^{68} -2.54942 q^{69} +1.83588 q^{71} -18.1041 q^{72} -9.39053 q^{73} -8.17309 q^{74} -3.20440 q^{75} +7.02724 q^{76} -12.5547 q^{78} +10.4088 q^{79} -2.40880 q^{80} +22.0220 q^{81} +0.713538 q^{82} -0.854152 q^{83} +11.3905 q^{85} +8.43605 q^{86} +8.24468 q^{87} +4.98173 q^{88} -7.19917 q^{89} -10.3723 q^{90} +1.18613 q^{92} +4.57292 q^{93} -4.20964 q^{94} +9.42708 q^{95} +18.7173 q^{96} -5.36852 q^{97} -14.5364 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + q^{2} + q^{3} + 3 q^{4} - 6 q^{5} + 8 q^{6} + 8 q^{9}+O(q^{10}) $ 3 * q + q^2 + q^3 + 3 * q^4 - 6 * q^5 + 8 * q^6 + 8 * q^9	$ 3 q + q^{2} + q^{3} + 3 q^{4} - 6 q^{5} + 8 q^{6} + 8 q^{9} - 2 q^{10} - 6 q^{11} - 8 q^{12} - 9 q^{13} - 2 q^{15} - 5 q^{16} - q^{17} - 8 q^{18} - 13 q^{19} - 6 q^{20} - 2 q^{22} - 11 q^{23} - 9 q^{24} - 3 q^{25} - 2 q^{26} + 10 q^{27} + 10 q^{29} - 16 q^{30} + 2 q^{31} + 6 q^{32} - 2 q^{33} - 7 q^{34} - 13 q^{36} + 3 q^{37} - 13 q^{38} - 12 q^{39} + 3 q^{41} + 9 q^{43} - 6 q^{44} - 16 q^{45} + 4 q^{46} + 7 q^{47} + 15 q^{48} - q^{50} - 26 q^{51} + q^{52} + 2 q^{53} + 8 q^{54} + 12 q^{55} - 12 q^{57} - 14 q^{58} + 12 q^{59} + 16 q^{60} + 4 q^{61} + 18 q^{62} - 16 q^{64} + 18 q^{65} - 16 q^{66} + 10 q^{67} + 18 q^{68} + 13 q^{69} - 14 q^{71} - 21 q^{72} + 4 q^{73} + 6 q^{74} - q^{75} - 14 q^{76} - 25 q^{78} + 14 q^{79} + 10 q^{80} + 23 q^{81} + q^{82} + 2 q^{83} + 2 q^{85} - 27 q^{86} - 12 q^{87} - 5 q^{89} + 16 q^{90} - 20 q^{92} + 16 q^{93} - 12 q^{94} + 26 q^{95} - 3 q^{96} - 27 q^{97} - 16 q^{99}+O(q^{100}) $ 3 * q + q^2 + q^3 + 3 * q^4 - 6 * q^5 + 8 * q^6 + 8 * q^9 - 2 * q^10 - 6 * q^11 - 8 * q^12 - 9 * q^13 - 2 * q^15 - 5 * q^16 - q^17 - 8 * q^18 - 13 * q^19 - 6 * q^20 - 2 * q^22 - 11 * q^23 - 9 * q^24 - 3 * q^25 - 2 * q^26 + 10 * q^27 + 10 * q^29 - 16 * q^30 + 2 * q^31 + 6 * q^32 - 2 * q^33 - 7 * q^34 - 13 * q^36 + 3 * q^37 - 13 * q^38 - 12 * q^39 + 3 * q^41 + 9 * q^43 - 6 * q^44 - 16 * q^45 + 4 * q^46 + 7 * q^47 + 15 * q^48 - q^50 - 26 * q^51 + q^52 + 2 * q^53 + 8 * q^54 + 12 * q^55 - 12 * q^57 - 14 * q^58 + 12 * q^59 + 16 * q^60 + 4 * q^61 + 18 * q^62 - 16 * q^64 + 18 * q^65 - 16 * q^66 + 10 * q^67 + 18 * q^68 + 13 * q^69 - 14 * q^71 - 21 * q^72 + 4 * q^73 + 6 * q^74 - q^75 - 14 * q^76 - 25 * q^78 + 14 * q^79 + 10 * q^80 + 23 * q^81 + q^82 + 2 * q^83 + 2 * q^85 - 27 * q^86 - 12 * q^87 - 5 * q^89 + 16 * q^90 - 20 * q^92 + 16 * q^93 - 12 * q^94 + 26 * q^95 - 3 * q^96 - 27 * q^97 - 16 * 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 $

$2$	0.713538	0.504548	0.252274	−	0.967656i	$-0.418822\pi$
$2$	0.713538	0.504548	0.252274	+	0.967656i	$0.418822\pi$
$3$	3.20440	1.85006	0.925031	−	0.379892i	$-0.124039\pi$
$3$	3.20440	1.85006	0.925031	+	0.379892i	$0.124039\pi$
$4$	−1.49086	−0.745432
$5$	−2.00000	−0.894427	−0.447214	−	0.894427i	$-0.647584\pi$
$5$	−2.00000	−0.894427	−0.447214	+	0.894427i	$0.647584\pi$
$6$	2.28646	0.933444
$7$	0	0
$7$	0	0
$8$	−2.49086	−0.880653
$9$	7.26819	2.42273
$10$	−1.42708	−0.451281
$11$	−2.00000	−0.603023	−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000	−0.603023	−0.301511	+	0.953463i	$0.597491\pi$
$12$	−4.77733	−1.37910
$13$	−5.49086	−1.52289	−0.761446	−	0.648229i	$-0.775510\pi$
$13$	−5.49086	−1.52289	−0.761446	+	0.648229i	$0.775510\pi$
$14$	0	0
$15$	−6.40880	−1.65475
$16$	1.20440	0.301100
$17$	−5.69527	−1.38130	−0.690652	−	0.723187i	$-0.742677\pi$
$17$	−5.69527	−1.38130	−0.690652	+	0.723187i	$0.742677\pi$
$18$	5.18613	1.22238
$19$	−4.71354	−1.08136	−0.540680	−	0.841228i	$-0.681833\pi$
$19$	−4.71354	−1.08136	−0.540680	+	0.841228i	$0.681833\pi$
$20$	2.98173	0.666734
$21$	0	0
$22$	−1.42708	−0.304254
$23$	−0.795598	−0.165894	−0.0829469	−	0.996554i	$-0.526433\pi$
$23$	−0.795598	−0.165894	−0.0829469	+	0.996554i	$0.526433\pi$
$24$	−7.98173	−1.62926
$25$	−1.00000	−0.200000
$26$	−3.91794	−0.768371
$27$	13.6770	2.63214
$28$	0	0
$29$	2.57292	0.477780	0.238890	−	0.971047i	$-0.423216\pi$
$29$	2.57292	0.477780	0.238890	+	0.971047i	$0.423216\pi$
$30$	−4.57292	−0.834898
$31$	1.42708	0.256310	0.128155	−	0.991754i	$-0.459094\pi$
$31$	1.42708	0.256310	0.128155	+	0.991754i	$0.459094\pi$
$32$	5.84111	1.03257
$33$	−6.40880	−1.11563
$34$	−4.06379	−0.696934
$35$	0	0
$36$	−10.8359	−1.80598
$37$	−11.4543	−1.88308	−0.941539	−	0.336904i	$-0.890620\pi$
$37$	−11.4543	−1.88308	−0.941539	+	0.336904i	$0.890620\pi$
$38$	−3.36329	−0.545597
$39$	−17.5949	−2.81744
$40$	4.98173	0.787680
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	11.8228	1.80297	0.901483	−	0.432814i	$-0.142479\pi$
$43$	11.8228	1.80297	0.901483	+	0.432814i	$0.142479\pi$
$44$	2.98173	0.449512
$45$	−14.5364	−2.16696
$46$	−0.567690	−0.0837013
$47$	−5.89967	−0.860555	−0.430277	−	0.902697i	$-0.641584\pi$
$47$	−5.89967	−0.860555	−0.430277	+	0.902697i	$0.641584\pi$
$48$	3.85939	0.557054
$49$	0	0
$50$	−0.713538	−0.100910
$51$	−18.2499	−2.55550
$52$	8.18613	1.13521
$53$	−3.55465	−0.488269	−0.244134	−	0.969741i	$-0.578504\pi$
$53$	−3.55465	−0.488269	−0.244134	+	0.969741i	$0.578504\pi$
$54$	9.75905	1.32804
$55$	4.00000	0.539360
$56$	0	0
$57$	−15.1041	−2.00058
$58$	1.83588	0.241063
$59$	4.00000	0.520756	0.260378	−	0.965507i	$-0.416153\pi$
$59$	4.00000	0.520756	0.260378	+	0.965507i	$0.416153\pi$
$60$	9.55465	1.23350
$61$	5.55465	0.711200	0.355600	−	0.934638i	$-0.384277\pi$
$61$	5.55465	0.711200	0.355600	+	0.934638i	$0.384277\pi$
$62$	1.01827	0.129321
$63$	0	0
$64$	1.75905	0.219882
$65$	10.9817	1.36212
$66$	−4.57292	−0.562888
$67$	7.55465	0.922948	0.461474	−	0.887154i	$-0.347321\pi$
$67$	7.55465	0.922948	0.461474	+	0.887154i	$0.347321\pi$
$68$	8.49086	1.02967
$69$	−2.54942	−0.306914
$70$	0	0
$71$	1.83588	0.217879	0.108939	−	0.994048i	$-0.465255\pi$
$71$	1.83588	0.217879	0.108939	+	0.994048i	$0.465255\pi$
$72$	−18.1041	−2.13358
$73$	−9.39053	−1.09908	−0.549539	−	0.835468i	$-0.685197\pi$
$73$	−9.39053	−1.09908	−0.549539	+	0.835468i	$0.685197\pi$
$74$	−8.17309	−0.950102
$75$	−3.20440	−0.370012
$76$	7.02724	0.806080
$77$	0	0
$78$	−12.5547	−1.42153
$79$	10.4088	1.17108	0.585541	−	0.810643i	$-0.300882\pi$
$79$	10.4088	1.17108	0.585541	+	0.810643i	$0.300882\pi$
$80$	−2.40880	−0.269312
$81$	22.0220	2.44689
$82$	0.713538	0.0787971
$83$	−0.854152	−0.0937553	−0.0468777	−	0.998901i	$-0.514927\pi$
$83$	−0.854152	−0.0937553	−0.0468777	+	0.998901i	$0.514927\pi$
$84$	0	0
$85$	11.3905	1.23548
$86$	8.43605	0.909682
$87$	8.24468	0.883923
$88$	4.98173	0.531054
$89$	−7.19917	−0.763110	−0.381555	−	0.924346i	$-0.624611\pi$
$89$	−7.19917	−0.763110	−0.381555	+	0.924346i	$0.624611\pi$
$90$	−10.3723	−1.09333
$91$	0	0
$92$	1.18613	0.123662
$93$	4.57292	0.474190
$94$	−4.20964	−0.434191
$95$	9.42708	0.967198
$96$	18.7173	1.91032
$97$	−5.36852	−0.545091	−0.272545	−	0.962143i	$-0.587866\pi$
$97$	−5.36852	−0.545091	−0.272545	+	0.962143i	$0.587866\pi$
$98$	0	0
$99$	−14.5364	−1.46096
$100$	1.49086	0.149086
$101$	9.74078	0.969244	0.484622	−	0.874724i	$-0.338957\pi$
$101$	9.74078	0.969244	0.484622	+	0.874724i	$0.338957\pi$
$102$	−13.0220	−1.28937
$103$	−12.8542	−1.26656	−0.633279	−	0.773924i	$-0.718291\pi$
$103$	−12.8542	−1.26656	−0.633279	+	0.773924i	$0.718291\pi$
$104$	13.6770	1.34114
$105$	0	0
$106$	−2.53638	−0.246355
$107$	−14.9582	−1.44607	−0.723033	−	0.690814i	$-0.757252\pi$
$107$	−14.9582	−1.44607	−0.723033	+	0.690814i	$0.757252\pi$
$108$	−20.3905	−1.96208
$109$	−14.0910	−1.34968	−0.674838	−	0.737966i	$-0.735786\pi$
$109$	−14.0910	−1.34968	−0.674838	+	0.737966i	$0.735786\pi$
$110$	2.85415	0.272133
$111$	−36.7042	−3.48381
$112$	0	0
$113$	−5.04028	−0.474150	−0.237075	−	0.971491i	$-0.576189\pi$
$113$	−5.04028	−0.474150	−0.237075	+	0.971491i	$0.576189\pi$
$114$	−10.7773	−1.00939
$115$	1.59120	0.148380
$116$	−3.83588	−0.356152
$117$	−39.9086	−3.68955
$118$	2.85415	0.262746
$119$	0	0
$120$	15.9635	1.45726
$121$	−7.00000	−0.636364
$122$	3.96345	0.358834
$123$	3.20440	0.288931
$124$	−2.12758	−0.191062
$125$	12.0000	1.07331
$126$	0	0
$127$	4.75382	0.421833	0.210917	−	0.977504i	$-0.432355\pi$
$127$	4.75382	0.421833	0.210917	+	0.977504i	$0.432355\pi$
$128$	−10.4271	−0.921632
$129$	37.8851	3.33560
$130$	7.83588	0.687252
$131$	15.8359	1.38359	0.691794	−	0.722095i	$-0.256821\pi$
$131$	15.8359	1.38359	0.691794	+	0.722095i	$0.256821\pi$
$132$	9.55465	0.831626
$133$	0	0
$134$	5.39053	0.465671
$135$	−27.3540	−2.35426
$136$	14.1861	1.21645
$137$	15.9635	1.36385	0.681925	−	0.731422i	$-0.261143\pi$
$137$	15.9635	1.36385	0.681925	+	0.731422i	$0.261143\pi$
$138$	−1.81911	−0.154853
$139$	7.26295	0.616036	0.308018	−	0.951381i	$-0.400334\pi$
$139$	7.26295	0.616036	0.308018	+	0.951381i	$0.400334\pi$
$140$	0	0
$141$	−18.9049	−1.59208
$142$	1.30997	0.109930
$143$	10.9817	0.918338
$144$	8.75382	0.729485
$145$	−5.14585	−0.427339
$146$	−6.70050	−0.554537
$147$	0	0
$148$	17.0768	1.40371
$149$	−22.3723	−1.83281	−0.916403	−	0.400256i	$-0.868921\pi$
$149$	−22.3723	−1.83281	−0.916403	+	0.400256i	$0.868921\pi$
$150$	−2.28646	−0.186689
$151$	−19.3905	−1.57798	−0.788989	−	0.614407i	$-0.789395\pi$
$151$	−19.3905	−1.57798	−0.788989	+	0.614407i	$0.789395\pi$
$152$	11.7408	0.952303
$153$	−41.3943	−3.34653
$154$	0	0
$155$	−2.85415	−0.229251
$156$	26.2316	2.10021
$157$	−7.65872	−0.611232	−0.305616	−	0.952155i	$-0.598862\pi$
$157$	−7.65872	−0.611232	−0.305616	+	0.952155i	$0.598862\pi$
$158$	7.42708	0.590866
$159$	−11.3905	−0.903328
$160$	−11.6822	−0.923561
$161$	0	0
$162$	15.7135	1.23457
$163$	1.35805	0.106371	0.0531855	−	0.998585i	$-0.483063\pi$
$163$	1.35805	0.106371	0.0531855	+	0.998585i	$0.483063\pi$
$164$	−1.49086	−0.116417
$165$	12.8176	0.997849
$166$	−0.609470	−0.0473040
$167$	13.5311	1.04707	0.523536	−	0.852004i	$-0.324613\pi$
$167$	13.5311	1.04707	0.523536	+	0.852004i	$0.324613\pi$
$168$	0	0
$169$	17.1496	1.31920
$170$	8.12758	0.623357
$171$	−34.2589	−2.61984
$172$	−17.6262	−1.34399
$173$	−3.01827	−0.229475	−0.114738	−	0.993396i	$-0.536603\pi$
$173$	−3.01827	−0.229475	−0.114738	+	0.993396i	$0.536603\pi$
$174$	5.88289	0.445981
$175$	0	0
$176$	−2.40880	−0.181570
$177$	12.8176	0.963430
$178$	−5.13688	−0.385025
$179$	−10.8176	−0.808546	−0.404273	−	0.914638i	$-0.632475\pi$
$179$	−10.8176	−0.808546	−0.404273	+	0.914638i	$0.632475\pi$
$180$	21.6718	1.61532
$181$	−15.3320	−1.13962	−0.569808	−	0.821778i	$-0.692983\pi$
$181$	−15.3320	−1.13962	−0.569808	+	0.821778i	$0.692983\pi$
$182$	0	0
$183$	17.7993	1.31576
$184$	1.98173	0.146095
$185$	22.9086	1.68428
$186$	3.26295	0.239251
$187$	11.3905	0.832958
$188$	8.79560	0.641485
$189$	0	0
$190$	6.72658	0.487997
$191$	−3.01827	−0.218395	−0.109197	−	0.994020i	$-0.534828\pi$
$191$	−3.01827	−0.218395	−0.109197	+	0.994020i	$0.534828\pi$
$192$	5.63671	0.406795
$193$	1.01827	0.0732969	0.0366484	−	0.999328i	$-0.488332\pi$
$193$	1.01827	0.0732969	0.0366484	+	0.999328i	$0.488332\pi$
$194$	−3.83064	−0.275024
$195$	35.1899	2.52000
$196$	0	0
$197$	14.8411	1.05739	0.528693	−	0.848813i	$-0.322682\pi$
$197$	14.8411	1.05739	0.528693	+	0.848813i	$0.322682\pi$
$198$	−10.3723	−0.737124
$199$	−9.77209	−0.692725	−0.346363	−	0.938101i	$-0.612583\pi$
$199$	−9.77209	−0.692725	−0.346363	+	0.938101i	$0.612583\pi$
$200$	2.49086	0.176131
$201$	24.2081	1.70751
$202$	6.95042	0.489030
$203$	0	0
$204$	27.2081	1.90495
$205$	−2.00000	−0.139686
$206$	−9.17192	−0.639038
$207$	−5.78256	−0.401916
$208$	−6.61320	−0.458543
$209$	9.42708	0.652084
$210$	0	0
$211$	10.6640	0.734137	0.367068	−	0.930194i	$-0.380361\pi$
$211$	10.6640	0.734137	0.367068	+	0.930194i	$0.380361\pi$
$212$	5.29950	0.363971
$213$	5.88289	0.403089
$214$	−10.6733	−0.729609
$215$	−23.6457	−1.61262
$216$	−34.0675	−2.31800
$217$	0	0
$218$	−10.0545	−0.680976
$219$	−30.0910	−2.03336
$220$	−5.96345	−0.402056
$221$	31.2719	2.10358
$222$	−26.1899	−1.75775
$223$	24.4998	1.64063	0.820315	−	0.571912i	$-0.193798\pi$
$223$	24.4998	1.64063	0.820315	+	0.571912i	$0.193798\pi$
$224$	0	0
$225$	−7.26819	−0.484546
$226$	−3.59643	−0.239231
$227$	10.8542	0.720415	0.360208	−	0.932872i	$-0.382706\pi$
$227$	10.8542	0.720415	0.360208	+	0.932872i	$0.382706\pi$
$228$	22.5181	1.49130
$229$	−3.07683	−0.203322	−0.101661	−	0.994819i	$-0.532416\pi$
$229$	−3.07683	−0.203322	−0.101661	+	0.994819i	$0.532416\pi$
$230$	1.13538	0.0748647
$231$	0	0
$232$	−6.40880	−0.420759
$233$	16.3827	1.07327	0.536634	−	0.843815i	$-0.319696\pi$
$233$	16.3827	1.07327	0.536634	+	0.843815i	$0.319696\pi$
$234$	−28.4763	−1.86156
$235$	11.7993	0.769704
$236$	−5.96345	−0.388188
$237$	33.3540	2.16657
$238$	0	0
$239$	−14.8281	−0.959148	−0.479574	−	0.877501i	$-0.659209\pi$
$239$	−14.8281	−0.959148	−0.479574	+	0.877501i	$0.659209\pi$
$240$	−7.71877	−0.498245
$241$	14.7811	0.952132	0.476066	−	0.879410i	$-0.342062\pi$
$241$	14.7811	0.952132	0.476066	+	0.879410i	$0.342062\pi$
$242$	−4.99477	−0.321076
$243$	29.5364	1.89476
$244$	−8.28123	−0.530151
$245$	0	0
$246$	2.28646	0.145779
$247$	25.8814	1.64679
$248$	−3.55465	−0.225721
$249$	−2.73705	−0.173453
$250$	8.56246	0.541537
$251$	10.2812	0.648945	0.324473	−	0.945895i	$-0.394813\pi$
$251$	10.2812	0.648945	0.324473	+	0.945895i	$0.394813\pi$
$252$	0	0
$253$	1.59120	0.100038
$254$	3.39203	0.212835
$255$	36.4998	2.28571
$256$	−10.9582	−0.684889
$257$	1.48563	0.0926710	0.0463355	−	0.998926i	$-0.485246\pi$
$257$	1.48563	0.0926710	0.0463355	+	0.998926i	$0.485246\pi$
$258$	27.0325	1.68297
$259$	0	0
$260$	−16.3723	−1.01536
$261$	18.7005	1.15753
$262$	11.2995	0.698085
$263$	28.3357	1.74725	0.873627	−	0.486595i	$-0.161761\pi$
$263$	28.3357	1.74725	0.873627	+	0.486595i	$0.161761\pi$
$264$	15.9635	0.982483
$265$	7.10930	0.436721
$266$	0	0
$267$	−23.0690	−1.41180
$268$	−11.2630	−0.687994
$269$	−15.8098	−0.963941	−0.481970	−	0.876188i	$-0.660079\pi$
$269$	−15.8098	−0.963941	−0.481970	+	0.876188i	$0.660079\pi$
$270$	−19.5181	−1.18783
$271$	−16.3357	−0.992324	−0.496162	−	0.868230i	$-0.665258\pi$
$271$	−16.3357	−0.992324	−0.496162	+	0.868230i	$0.665258\pi$
$272$	−6.85939	−0.415911
$273$	0	0
$274$	11.3905	0.688127
$275$	2.00000	0.120605
$276$	3.80083	0.228783
$277$	−1.93098	−0.116021	−0.0580106	−	0.998316i	$-0.518476\pi$
$277$	−1.93098	−0.116021	−0.0580106	+	0.998316i	$0.518476\pi$
$278$	5.18239	0.310819
$279$	10.3723	0.620971
$280$	0	0
$281$	−29.5181	−1.76090	−0.880451	−	0.474137i	$-0.842760\pi$
$281$	−29.5181	−1.76090	−0.880451	+	0.474137i	$0.842760\pi$
$282$	−13.4894	−0.803280
$283$	−8.03655	−0.477723	−0.238862	−	0.971054i	$-0.576774\pi$
$283$	−8.03655	−0.477723	−0.238862	+	0.971054i	$0.576774\pi$
$284$	−2.73705	−0.162414
$285$	30.2081	1.78938
$286$	7.83588	0.463345
$287$	0	0
$288$	42.4543	2.50164
$289$	15.4360	0.908003
$290$	−3.67176	−0.215613
$291$	−17.2029	−1.00845
$292$	14.0000	0.819288
$293$	6.56246	0.383383	0.191691	−	0.981455i	$-0.438603\pi$
$293$	6.56246	0.383383	0.191691	+	0.981455i	$0.438603\pi$
$294$	0	0
$295$	−8.00000	−0.465778
$296$	28.5311	1.65834
$297$	−27.3540	−1.58724
$298$	−15.9635	−0.924738
$299$	4.36852	0.252638
$300$	4.77733	0.275819
$301$	0	0
$302$	−13.8359	−0.796165
$303$	31.2134	1.79316
$304$	−5.67699	−0.325598
$305$	−11.1093	−0.636117
$306$	−29.5364	−1.68848
$307$	19.6457	1.12124	0.560619	−	0.828074i	$-0.310563\pi$
$307$	19.6457	1.12124	0.560619	+	0.828074i	$0.310563\pi$
$308$	0	0
$309$	−41.1899	−2.34321
$310$	−2.03655	−0.115668
$311$	1.32301	0.0750209	0.0375104	−	0.999296i	$-0.488057\pi$
$311$	1.32301	0.0750209	0.0375104	+	0.999296i	$0.488057\pi$
$312$	43.8266	2.48119
$313$	17.6222	0.996064	0.498032	−	0.867159i	$-0.334056\pi$
$313$	17.6222	0.996064	0.498032	+	0.867159i	$0.334056\pi$
$314$	−5.46479	−0.308396
$315$	0	0
$316$	−15.5181	−0.872962
$317$	−22.7811	−1.27951	−0.639756	−	0.768578i	$-0.720965\pi$
$317$	−22.7811	−1.27951	−0.639756	+	0.768578i	$0.720965\pi$
$318$	−8.12758	−0.455772
$319$	−5.14585	−0.288112
$320$	−3.51811	−0.196668
$321$	−47.9321	−2.67531
$322$	0	0
$323$	26.8448	1.49369
$324$	−32.8318	−1.82399
$325$	5.49086	0.304578
$326$	0.969023	0.0536692
$327$	−45.1533	−2.49698
$328$	−2.49086	−0.137535
$329$	0	0
$330$	9.14585	0.503462
$331$	22.0000	1.20923	0.604615	−	0.796518i	$-0.293327\pi$
$331$	22.0000	1.20923	0.604615	+	0.796518i	$0.293327\pi$
$332$	1.27342	0.0698882
$333$	−83.2522	−4.56219
$334$	9.65498	0.528297
$335$	−15.1093	−0.825509
$336$	0	0
$337$	6.63148	0.361240	0.180620	−	0.983553i	$-0.442190\pi$
$337$	6.63148	0.361240	0.180620	+	0.983553i	$0.442190\pi$
$338$	12.2369	0.665598
$339$	−16.1511	−0.877206
$340$	−16.9817	−0.920963
$341$	−2.85415	−0.154561
$342$	−24.4450	−1.32184
$343$	0	0
$344$	−29.4491	−1.58779
$345$	5.09883	0.274512
$346$	−2.15365	−0.115781
$347$	−18.0000	−0.966291	−0.483145	−	0.875540i	$-0.660506\pi$
$347$	−18.0000	−0.966291	−0.483145	+	0.875540i	$0.660506\pi$
$348$	−12.2917	−0.658904
$349$	−34.6274	−1.85356	−0.926781	−	0.375601i	$-0.877436\pi$
$349$	−34.6274	−1.85356	−0.926781	+	0.375601i	$0.877436\pi$
$350$	0	0
$351$	−75.0985	−4.00846
$352$	−11.6822	−0.622665
$353$	27.9635	1.48834	0.744172	−	0.667988i	$-0.232844\pi$
$353$	27.9635	1.48834	0.744172	+	0.667988i	$0.232844\pi$
$354$	9.14585	0.486096
$355$	−3.67176	−0.194877
$356$	10.7330	0.568847
$357$	0	0
$358$	−7.71877	−0.407950
$359$	11.9907	0.632845	0.316422	−	0.948618i	$-0.397518\pi$
$359$	11.9907	0.632845	0.316422	+	0.948618i	$0.397518\pi$
$360$	36.2081	1.90834
$361$	3.21744	0.169339
$362$	−10.9399	−0.574991
$363$	−22.4308	−1.17731
$364$	0	0
$365$	18.7811	0.983046
$366$	12.7005	0.663866
$367$	−28.4998	−1.48768	−0.743840	−	0.668358i	$-0.766997\pi$
$367$	−28.4998	−1.48768	−0.743840	+	0.668358i	$0.766997\pi$
$368$	−0.958220	−0.0499507
$369$	7.26819	0.378367
$370$	16.3462	0.849797
$371$	0	0
$372$	−6.81761	−0.353476
$373$	−14.8411	−0.768444	−0.384222	−	0.923241i	$-0.625530\pi$
$373$	−14.8411	−0.768444	−0.384222	+	0.923241i	$0.625530\pi$
$374$	8.12758	0.420267
$375$	38.4528	1.98570
$376$	14.6953	0.757850
$377$	−14.1276	−0.727607
$378$	0	0
$379$	7.20440	0.370065	0.185033	−	0.982732i	$-0.440761\pi$
$379$	7.20440	0.370065	0.185033	+	0.982732i	$0.440761\pi$
$380$	−14.0545	−0.720980
$381$	15.2331	0.780418
$382$	−2.15365	−0.110190
$383$	5.16786	0.264065	0.132033	−	0.991245i	$-0.457850\pi$
$383$	5.16786	0.264065	0.132033	+	0.991245i	$0.457850\pi$
$384$	−33.4125	−1.70508
$385$	0	0
$386$	0.726576	0.0369818
$387$	85.9306	4.36810
$388$	8.00373	0.406328
$389$	−4.34502	−0.220301	−0.110151	−	0.993915i	$-0.535133\pi$
$389$	−4.34502	−0.220301	−0.110151	+	0.993915i	$0.535133\pi$
$390$	25.1093	1.27146
$391$	4.53114	0.229150
$392$	0	0
$393$	50.7445	2.55972
$394$	10.5897	0.533501
$395$	−20.8176	−1.04745
$396$	21.6718	1.08905
$397$	−19.7083	−0.989131	−0.494566	−	0.869140i	$-0.664673\pi$
$397$	−19.7083	−0.989131	−0.494566	+	0.869140i	$0.664673\pi$
$398$	−6.97276	−0.349513
$399$	0	0
$400$	−1.20440	−0.0602201
$401$	−28.3995	−1.41820	−0.709102	−	0.705106i	$-0.750899\pi$
$401$	−28.3995	−1.41820	−0.709102	+	0.705106i	$0.750899\pi$
$402$	17.2734	0.861520
$403$	−7.83588	−0.390333
$404$	−14.5222	−0.722505
$405$	−44.0440	−2.18856
$406$	0	0
$407$	22.9086	1.13554
$408$	45.4581	2.25051
$409$	−19.2734	−0.953009	−0.476505	−	0.879172i	$-0.658096\pi$
$409$	−19.2734	−0.953009	−0.476505	+	0.879172i	$0.658096\pi$
$410$	−1.42708	−0.0704783
$411$	51.1533	2.52321
$412$	19.1638	0.944132
$413$	0	0
$414$	−4.12608	−0.202786
$415$	1.70830	0.0838573
$416$	−32.0728	−1.57250
$417$	23.2734	1.13970
$418$	6.72658	0.329008
$419$	15.9530	0.779354	0.389677	−	0.920952i	$-0.372587\pi$
$419$	15.9530	0.779354	0.389677	+	0.920952i	$0.372587\pi$
$420$	0	0
$421$	−38.0806	−1.85593	−0.927966	−	0.372664i	$-0.878445\pi$
$421$	−38.0806	−1.85593	−0.927966	+	0.372664i	$0.878445\pi$
$422$	7.60914	0.370407
$423$	−42.8799	−2.08489
$424$	8.85415	0.429996
$425$	5.69527	0.276261
$426$	4.19767	0.203378
$427$	0	0
$428$	22.3007	1.07794
$429$	35.1899	1.69898
$430$	−16.8721	−0.813644
$431$	−10.2917	−0.495734	−0.247867	−	0.968794i	$-0.579730\pi$
$431$	−10.2917	−0.495734	−0.247867	+	0.968794i	$0.579730\pi$
$432$	16.4726	0.792538
$433$	−9.98953	−0.480066	−0.240033	−	0.970765i	$-0.577158\pi$
$433$	−9.98953	−0.480066	−0.240033	+	0.970765i	$0.577158\pi$
$434$	0	0
$435$	−16.4894	−0.790604
$436$	21.0078	1.00609
$437$	3.75008	0.179391
$438$	−21.4711	−1.02593
$439$	−1.61320	−0.0769941	−0.0384970	−	0.999259i	$-0.512257\pi$
$439$	−1.61320	−0.0769941	−0.0384970	+	0.999259i	$0.512257\pi$
$440$	−9.96345	−0.474989
$441$	0	0
$442$	22.3137	1.06135
$443$	21.2096	1.00770	0.503850	−	0.863791i	$-0.331916\pi$
$443$	21.2096	1.00770	0.503850	+	0.863791i	$0.331916\pi$
$444$	54.7210	2.59694
$445$	14.3983	0.682546
$446$	17.4816	0.827776
$447$	−71.6897	−3.39081
$448$	0	0
$449$	12.0325	0.567848	0.283924	−	0.958847i	$-0.408364\pi$
$449$	12.0325	0.567848	0.283924	+	0.958847i	$0.408364\pi$
$450$	−5.18613	−0.244476
$451$	−2.00000	−0.0941763
$452$	7.51437	0.353446
$453$	−62.1350	−2.91936
$454$	7.74485	0.363484
$455$	0	0
$456$	37.6222	1.76182
$457$	−0.908636	−0.0425042	−0.0212521	−	0.999774i	$-0.506765\pi$
$457$	−0.908636	−0.0425042	−0.0212521	+	0.999774i	$0.506765\pi$
$458$	−2.19543	−0.102586
$459$	−77.8941	−3.63579
$460$	−2.37226	−0.110607
$461$	13.4010	0.624147	0.312073	−	0.950058i	$-0.398977\pi$
$461$	13.4010	0.624147	0.312073	+	0.950058i	$0.398977\pi$
$462$	0	0
$463$	−7.29950	−0.339237	−0.169618	−	0.985510i	$-0.554253\pi$
$463$	−7.29950	−0.339237	−0.169618	+	0.985510i	$0.554253\pi$
$464$	3.09883	0.143860
$465$	−9.14585	−0.424129
$466$	11.6897	0.541515
$467$	4.54685	0.210403	0.105202	−	0.994451i	$-0.466451\pi$
$467$	4.54685	0.210403	0.105202	+	0.994451i	$0.466451\pi$
$468$	59.4983	2.75031
$469$	0	0
$470$	8.41927	0.388352
$471$	−24.5416	−1.13082
$472$	−9.96345	−0.458605
$473$	−23.6457	−1.08723
$474$	23.7993	1.09314
$475$	4.71354	0.216272
$476$	0	0
$477$	−25.8359	−1.18294
$478$	−10.5804	−0.483936
$479$	−13.3581	−0.610345	−0.305173	−	0.952297i	$-0.598714\pi$
$479$	−13.3581	−0.610345	−0.305173	+	0.952297i	$0.598714\pi$
$480$	−37.4345	−1.70865
$481$	62.8941	2.86772
$482$	10.5468	0.480396
$483$	0	0
$484$	10.4360	0.474366
$485$	10.7370	0.487544
$486$	21.0753	0.955996
$487$	2.11454	0.0958188	0.0479094	−	0.998852i	$-0.484744\pi$
$487$	2.11454	0.0958188	0.0479094	+	0.998852i	$0.484744\pi$
$488$	−13.8359	−0.626321
$489$	4.35175	0.196793
$490$	0	0
$491$	−15.5767	−0.702965	−0.351482	−	0.936194i	$-0.614322\pi$
$491$	−15.5767	−0.702965	−0.351482	+	0.936194i	$0.614322\pi$
$492$	−4.77733	−0.215378
$493$	−14.6535	−0.659960
$494$	18.4674	0.830886
$495$	29.0728	1.30672
$496$	1.71877	0.0771752
$497$	0	0
$498$	−1.95299	−0.0875154
$499$	−12.5729	−0.562841	−0.281421	−	0.959584i	$-0.590806\pi$
$499$	−12.5729	−0.562841	−0.281421	+	0.959584i	$0.590806\pi$
$500$	−17.8904	−0.800081
$501$	43.3592	1.93715
$502$	7.33605	0.327424
$503$	34.4308	1.53519	0.767597	−	0.640933i	$-0.221452\pi$
$503$	34.4308	1.53519	0.767597	+	0.640933i	$0.221452\pi$
$504$	0	0
$505$	−19.4816	−0.866918
$506$	1.13538	0.0504738
$507$	54.9542	2.44060
$508$	−7.08729	−0.314448
$509$	−25.6184	−1.13552	−0.567759	−	0.823195i	$-0.692189\pi$
$509$	−25.6184	−1.13552	−0.567759	+	0.823195i	$0.692189\pi$
$510$	26.0440	1.15325
$511$	0	0
$512$	13.0350	0.576073
$513$	−64.4670	−2.84629
$514$	1.06005	0.0467569
$515$	25.7083	1.13284
$516$	−56.4816	−2.48646
$517$	11.7993	0.518934
$518$	0	0
$519$	−9.67176	−0.424543
$520$	−27.3540	−1.19955
$521$	−28.1988	−1.23541	−0.617707	−	0.786409i	$-0.711938\pi$
$521$	−28.1988	−1.23541	−0.617707	+	0.786409i	$0.711938\pi$
$522$	13.3435	0.584030
$523$	5.54418	0.242430	0.121215	−	0.992626i	$-0.461321\pi$
$523$	5.54418	0.242430	0.121215	+	0.992626i	$0.461321\pi$
$524$	−23.6091	−1.03137
$525$	0	0
$526$	20.2186	0.881573
$527$	−8.12758	−0.354043
$528$	−7.71877	−0.335916
$529$	−22.3670	−0.972479
$530$	5.07276	0.220346
$531$	29.0728	1.26165
$532$	0	0
$533$	−5.49086	−0.237836
$534$	−16.4606	−0.712321
$535$	29.9164	1.29340
$536$	−18.8176	−0.812797
$537$	−34.6640	−1.49586
$538$	−11.2809	−0.486354
$539$	0	0
$540$	40.7811	1.75494
$541$	−7.40357	−0.318304	−0.159152	−	0.987254i	$-0.550876\pi$
$541$	−7.40357	−0.318304	−0.159152	+	0.987254i	$0.550876\pi$
$542$	−11.6562	−0.500675
$543$	−49.1298	−2.10836
$544$	−33.2667	−1.42630
$545$	28.1821	1.20719
$546$	0	0
$547$	36.4633	1.55906	0.779529	−	0.626366i	$-0.215459\pi$
$547$	36.4633	1.55906	0.779529	+	0.626366i	$0.215459\pi$
$548$	−23.7993	−1.01666
$549$	40.3723	1.72305
$550$	1.42708	0.0608507
$551$	−12.1276	−0.516652
$552$	6.35025	0.270285
$553$	0	0
$554$	−1.37783	−0.0585382
$555$	73.4085	3.11602
$556$	−10.8281	−0.459213
$557$	−22.0545	−0.934478	−0.467239	−	0.884131i	$-0.654751\pi$
$557$	−22.0545	−0.934478	−0.467239	+	0.884131i	$0.654751\pi$
$558$	7.40100	0.313309
$559$	−64.9176	−2.74572
$560$	0	0
$561$	36.4998	1.54102
$562$	−21.0623	−0.888459
$563$	40.7538	1.71757	0.858784	−	0.512337i	$-0.171220\pi$
$563$	40.7538	1.71757	0.858784	+	0.512337i	$0.171220\pi$
$564$	28.1846	1.18679
$565$	10.0806	0.424092
$566$	−5.73438	−0.241034
$567$	0	0
$568$	−4.57292	−0.191876
$569$	30.5860	1.28223	0.641115	−	0.767445i	$-0.278472\pi$
$569$	30.5860	1.28223	0.641115	+	0.767445i	$0.278472\pi$
$570$	21.5547	0.902825
$571$	−14.2007	−0.594279	−0.297140	−	0.954834i	$-0.596033\pi$
$571$	−14.2007	−0.594279	−0.297140	+	0.954834i	$0.596033\pi$
$572$	−16.3723	−0.684558
$573$	−9.67176	−0.404043
$574$	0	0
$575$	0.795598	0.0331787
$576$	12.7851	0.532714
$577$	−14.5144	−0.604241	−0.302121	−	0.953270i	$-0.597695\pi$
$577$	−14.5144	−0.604241	−0.302121	+	0.953270i	$0.597695\pi$
$578$	11.0142	0.458130
$579$	3.26295	0.135604
$580$	7.67176	0.318552
$581$	0	0
$582$	−12.2749	−0.508812
$583$	7.10930	0.294437
$584$	23.3905	0.967907
$585$	79.8173	3.30004
$586$	4.68256	0.193435
$587$	−30.3958	−1.25457	−0.627284	−	0.778791i	$-0.715833\pi$
$587$	−30.3958	−1.25457	−0.627284	+	0.778791i	$0.715833\pi$
$588$	0	0
$589$	−6.72658	−0.277164
$590$	−5.70830	−0.235007
$591$	47.5569	1.95623
$592$	−13.7956	−0.566996
$593$	−4.54568	−0.186669	−0.0933344	−	0.995635i	$-0.529753\pi$
$593$	−4.54568	−0.186669	−0.0933344	+	0.995635i	$0.529753\pi$
$594$	−19.5181	−0.800838
$595$	0	0
$596$	33.3540	1.36623
$597$	−31.3137	−1.28158
$598$	3.11711	0.127468
$599$	−29.9542	−1.22389	−0.611947	−	0.790899i	$-0.709613\pi$
$599$	−29.9542	−1.22389	−0.611947	+	0.790899i	$0.709613\pi$
$600$	7.98173	0.325853
$601$	−19.9399	−0.813367	−0.406684	−	0.913569i	$-0.633315\pi$
$601$	−19.9399	−0.813367	−0.406684	+	0.913569i	$0.633315\pi$
$602$	0	0
$603$	54.9086	2.23605
$604$	28.9086	1.17628
$605$	14.0000	0.569181
$606$	22.2719	0.904735
$607$	31.0623	1.26078	0.630390	−	0.776279i	$-0.282895\pi$
$607$	31.0623	1.26078	0.630390	+	0.776279i	$0.282895\pi$
$608$	−27.5323	−1.11658
$609$	0	0
$610$	−7.92691	−0.320951
$611$	32.3943	1.31053
$612$	61.7132	2.49461
$613$	3.77733	0.152565	0.0762824	−	0.997086i	$-0.475695\pi$
$613$	3.77733	0.152565	0.0762824	+	0.997086i	$0.475695\pi$
$614$	14.0179	0.565718
$615$	−6.40880	−0.258428
$616$	0	0
$617$	−24.8046	−0.998594	−0.499297	−	0.866431i	$-0.666408\pi$
$617$	−24.8046	−0.998594	−0.499297	+	0.866431i	$0.666408\pi$
$618$	−29.3905	−1.18226
$619$	1.54418	0.0620659	0.0310330	−	0.999518i	$-0.490120\pi$
$619$	1.54418	0.0620659	0.0310330	+	0.999518i	$0.490120\pi$
$620$	4.25515	0.170891
$621$	−10.8814	−0.436655
$622$	0.944016	0.0378516
$623$	0	0
$624$	−21.1914	−0.848333
$625$	−19.0000	−0.760000
$626$	12.5741	0.502562
$627$	30.2081	1.20640
$628$	11.4181	0.455632
$629$	65.2354	2.60110
$630$	0	0
$631$	13.4438	0.535191	0.267596	−	0.963531i	$-0.413771\pi$
$631$	13.4438	0.535191	0.267596	+	0.963531i	$0.413771\pi$
$632$	−25.9269	−1.03132
$633$	34.1716	1.35820
$634$	−16.2552	−0.645575
$635$	−9.50764	−0.377299
$636$	16.9817	0.673369
$637$	0	0
$638$	−3.67176	−0.145366
$639$	13.3435	0.527861
$640$	20.8542	0.824333
$641$	−6.31777	−0.249537	−0.124769	−	0.992186i	$-0.539819\pi$
$641$	−6.31777	−0.249537	−0.124769	+	0.992186i	$0.539819\pi$
$642$	−34.2014	−1.34982
$643$	−39.1522	−1.54401	−0.772005	−	0.635616i	$-0.780746\pi$
$643$	−39.1522	−1.54401	−0.772005	+	0.635616i	$0.780746\pi$
$644$	0	0
$645$	−75.7703	−2.98345
$646$	19.1548	0.753636
$647$	29.6897	1.16722	0.583611	−	0.812033i	$-0.301639\pi$
$647$	29.6897	1.16722	0.583611	+	0.812033i	$0.301639\pi$
$648$	−54.8538	−2.15486
$649$	−8.00000	−0.314027
$650$	3.91794	0.153674
$651$	0	0
$652$	−2.02467	−0.0792923
$653$	−4.39833	−0.172120	−0.0860601	−	0.996290i	$-0.527428\pi$
$653$	−4.39833	−0.172120	−0.0860601	+	0.996290i	$0.527428\pi$
$654$	−32.2186	−1.25985
$655$	−31.6718	−1.23752
$656$	1.20440	0.0470240
$657$	−68.2522	−2.66277
$658$	0	0
$659$	14.3178	0.557741	0.278871	−	0.960329i	$-0.410040\pi$
$659$	14.3178	0.557741	0.278871	+	0.960329i	$0.410040\pi$
$660$	−19.1093	−0.743829
$661$	−1.26295	−0.0491232	−0.0245616	−	0.999698i	$-0.507819\pi$
$661$	−1.26295	−0.0491232	−0.0245616	+	0.999698i	$0.507819\pi$
$662$	15.6978	0.610114
$663$	100.208	3.89175
$664$	2.12758	0.0825659
$665$	0	0
$666$	−59.4036	−2.30184
$667$	−2.04701	−0.0792607
$668$	−20.1731	−0.780520
$669$	78.5073	3.03527
$670$	−10.7811	−0.416509
$671$	−11.1093	−0.428870
$672$	0	0
$673$	−30.7080	−1.18371	−0.591853	−	0.806046i	$-0.701603\pi$
$673$	−30.7080	−1.18371	−0.591853	+	0.806046i	$0.701603\pi$
$674$	4.73181	0.182263
$675$	−13.6770	−0.526428
$676$	−25.5677	−0.983373
$677$	−13.8098	−0.530754	−0.265377	−	0.964145i	$-0.585496\pi$
$677$	−13.8098	−0.530754	−0.265377	+	0.964145i	$0.585496\pi$
$678$	−11.5244	−0.442592
$679$	0	0
$680$	−28.3723	−1.08803
$681$	34.7811	1.33281
$682$	−2.03655	−0.0779834
$683$	40.5073	1.54997	0.774984	−	0.631980i	$-0.217758\pi$
$683$	40.5073	1.54997	0.774984	+	0.631980i	$0.217758\pi$
$684$	51.0753	1.95291
$685$	−31.9269	−1.21986
$686$	0	0
$687$	−9.85939	−0.376159
$688$	14.2394	0.542874
$689$	19.5181	0.743581
$690$	3.63821	0.138504
$691$	−17.2096	−0.654685	−0.327343	−	0.944906i	$-0.606153\pi$
$691$	−17.2096	−0.654685	−0.327343	+	0.944906i	$0.606153\pi$
$692$	4.49983	0.171058
$693$	0	0
$694$	−12.8437	−0.487540
$695$	−14.5259	−0.550999
$696$	−20.5364	−0.778429
$697$	−5.69527	−0.215724
$698$	−24.7080	−0.935210
$699$	52.4968	1.98561
$700$	0	0
$701$	24.9620	0.942800	0.471400	−	0.881920i	$-0.343749\pi$
$701$	24.9620	0.942800	0.471400	+	0.881920i	$0.343749\pi$
$702$	−53.5856	−2.02246
$703$	53.9904	2.03629
$704$	−3.51811	−0.132594
$705$	37.8098	1.42400
$706$	19.9530	0.750941
$707$	0	0
$708$	−19.1093	−0.718172
$709$	5.89036	0.221217	0.110609	−	0.993864i	$-0.464720\pi$
$709$	5.89036	0.221217	0.110609	+	0.993864i	$0.464720\pi$
$710$	−2.61994	−0.0983245
$711$	75.6532	2.83721
$712$	17.9321	0.672035
$713$	−1.13538	−0.0425203
$714$	0	0
$715$	−21.9635	−0.821387
$716$	16.1276	0.602716
$717$	−47.5151	−1.77448
$718$	8.55582	0.319300
$719$	−22.2917	−0.831340	−0.415670	−	0.909516i	$-0.636453\pi$
$719$	−22.2917	−0.831340	−0.415670	+	0.909516i	$0.636453\pi$
$720$	−17.5076	−0.652471
$721$	0	0
$722$	2.29577	0.0854395
$723$	47.3645	1.76150
$724$	22.8579	0.849507
$725$	−2.57292	−0.0955560
$726$	−16.0052	−0.594010
$727$	21.1768	0.785405	0.392702	−	0.919666i	$-0.371540\pi$
$727$	21.1768	0.785405	0.392702	+	0.919666i	$0.371540\pi$
$728$	0	0
$729$	28.5804	1.05853
$730$	13.4010	0.495993
$731$	−67.3342	−2.49045
$732$	−26.5364	−0.980813
$733$	30.6900	1.13356	0.566781	−	0.823868i	$-0.308189\pi$
$733$	30.6900	1.13356	0.566781	+	0.823868i	$0.308189\pi$
$734$	−20.3357	−0.750605
$735$	0	0
$736$	−4.64718	−0.171297
$737$	−15.1093	−0.556558
$738$	5.18613	0.190904
$739$	−39.9176	−1.46839	−0.734196	−	0.678937i	$-0.762441\pi$
$739$	−39.9176	−1.46839	−0.734196	+	0.678937i	$0.762441\pi$
$740$	−34.1537	−1.25551
$741$	82.9344	3.04667
$742$	0	0
$743$	24.9478	0.915244	0.457622	−	0.889147i	$-0.348701\pi$
$743$	24.9478	0.915244	0.457622	+	0.889147i	$0.348701\pi$
$744$	−11.3905	−0.417597
$745$	44.7445	1.63931
$746$	−10.5897	−0.387716
$747$	−6.20814	−0.227144
$748$	−16.9817	−0.620913
$749$	0	0
$750$	27.4375	1.00188
$751$	−35.1899	−1.28410	−0.642048	−	0.766664i	$-0.721915\pi$
$751$	−35.1899	−1.28410	−0.642048	+	0.766664i	$0.721915\pi$
$752$	−7.10557	−0.259113
$753$	32.9452	1.20059
$754$	−10.0806	−0.367112
$755$	38.7811	1.41139
$756$	0	0
$757$	12.8542	0.467192	0.233596	−	0.972334i	$-0.424951\pi$
$757$	12.8542	0.467192	0.233596	+	0.972334i	$0.424951\pi$
$758$	5.14061	0.186716
$759$	5.09883	0.185076
$760$	−23.4816	−0.851766
$761$	−29.3645	−1.06446	−0.532230	−	0.846600i	$-0.678646\pi$
$761$	−29.3645	−1.06446	−0.532230	+	0.846600i	$0.678646\pi$
$762$	10.8694	0.393758
$763$	0	0
$764$	4.49983	0.162798
$765$	82.7885	2.99323
$766$	3.68746	0.133233
$767$	−21.9635	−0.793054
$768$	−35.1145	−1.26709
$769$	2.00000	0.0721218	0.0360609	−	0.999350i	$-0.488519\pi$
$769$	2.00000	0.0721218	0.0360609	+	0.999350i	$0.488519\pi$
$770$	0	0
$771$	4.76055	0.171447
$772$	−1.51811	−0.0546378
$773$	28.1220	1.01148	0.505739	−	0.862686i	$-0.331220\pi$
$773$	28.1220	1.01148	0.505739	+	0.862686i	$0.331220\pi$
$774$	61.3148	2.20391
$775$	−1.42708	−0.0512621
$776$	13.3723	0.480036
$777$	0	0
$778$	−3.10033	−0.111152
$779$	−4.71354	−0.168880
$780$	−52.4633	−1.87849
$781$	−3.67176	−0.131386
$782$	3.23314	0.115617
$783$	35.1899	1.25758
$784$	0	0
$785$	15.3174	0.546703
$786$	36.2081	1.29150
$787$	5.51811	0.196699	0.0983496	−	0.995152i	$-0.468644\pi$
$787$	5.51811	0.196699	0.0983496	+	0.995152i	$0.468644\pi$
$788$	−22.1261	−0.788209
$789$	90.7990	3.23253
$790$	−14.8542	−0.528487
$791$	0	0
$792$	36.2081	1.28660
$793$	−30.4998	−1.08308
$794$	−14.0626	−0.499064
$795$	22.7811	0.807961
$796$	14.5689	0.516379
$797$	−37.5256	−1.32922	−0.664612	−	0.747189i	$-0.731403\pi$
$797$	−37.5256	−1.32922	−0.664612	+	0.747189i	$0.731403\pi$
$798$	0	0
$799$	33.6002	1.18869
$800$	−5.84111	−0.206515
$801$	−52.3249	−1.84881
$802$	−20.2641	−0.715551
$803$	18.7811	0.662769
$804$	−36.0910	−1.27283
$805$	0	0
$806$	−5.59120	−0.196942
$807$	−50.6610	−1.78335
$808$	−24.2630	−0.853568
$809$	14.8281	0.521327	0.260664	−	0.965430i	$-0.416059\pi$
$809$	14.8281	0.521327	0.260664	+	0.965430i	$0.416059\pi$
$810$	−31.4271	−1.10423
$811$	19.4271	0.682177	0.341088	−	0.940031i	$-0.389204\pi$
$811$	19.4271	0.682177	0.341088	+	0.940031i	$0.389204\pi$
$812$	0	0
$813$	−52.3462	−1.83586
$814$	16.3462	0.572933
$815$	−2.71611	−0.0951411
$816$	−21.9802	−0.769462
$817$	−55.7274	−1.94966
$818$	−13.7523	−0.480839
$819$	0	0
$820$	2.98173	0.104126
$821$	−16.0130	−0.558859	−0.279429	−	0.960166i	$-0.590145\pi$
$821$	−16.0130	−0.558859	−0.279429	+	0.960166i	$0.590145\pi$
$822$	36.4998	1.27308
$823$	18.9086	0.659114	0.329557	−	0.944136i	$-0.393101\pi$
$823$	18.9086	0.659114	0.329557	+	0.944136i	$0.393101\pi$
$824$	32.0179	1.11540
$825$	6.40880	0.223126
$826$	0	0
$827$	−16.6640	−0.579462	−0.289731	−	0.957108i	$-0.593566\pi$
$827$	−16.6640	−0.579462	−0.289731	+	0.957108i	$0.593566\pi$
$828$	8.62101	0.299601
$829$	−5.06229	−0.175821	−0.0879103	−	0.996128i	$-0.528019\pi$
$829$	−5.06229	−0.175821	−0.0879103	+	0.996128i	$0.528019\pi$
$830$	1.21894	0.0423100
$831$	−6.18763	−0.214646
$832$	−9.65872	−0.334856
$833$	0	0
$834$	16.6065	0.575035
$835$	−27.0623	−0.936529
$836$	−14.0545	−0.486085
$837$	19.5181	0.674644
$838$	11.3831	0.393221
$839$	−8.86869	−0.306181	−0.153091	−	0.988212i	$-0.548923\pi$
$839$	−8.86869	−0.306181	−0.153091	+	0.988212i	$0.548923\pi$
$840$	0	0
$841$	−22.3801	−0.771726
$842$	−27.1719	−0.936406
$843$	−94.5879	−3.25778
$844$	−15.8985	−0.547249
$845$	−34.2992	−1.17993
$846$	−30.5964	−1.05193
$847$	0	0
$848$	−4.28123	−0.147018
$849$	−25.7523	−0.883817
$850$	4.06379	0.139387
$851$	9.11304	0.312391
$852$	−8.77059	−0.300476
$853$	22.5729	0.772882	0.386441	−	0.922314i	$-0.373704\pi$
$853$	22.5729	0.772882	0.386441	+	0.922314i	$0.373704\pi$
$854$	0	0
$855$	68.5178	2.34326
$856$	37.2589	1.27348
$857$	−44.7811	−1.52969	−0.764846	−	0.644213i	$-0.777185\pi$
$857$	−44.7811	−1.52969	−0.764846	+	0.644213i	$0.777185\pi$
$858$	25.1093	0.857217
$859$	39.6352	1.35234	0.676168	−	0.736747i	$-0.263639\pi$
$859$	39.6352	1.35234	0.676168	+	0.736747i	$0.263639\pi$
$860$	35.2525	1.20210
$861$	0	0
$862$	−7.34352	−0.250121
$863$	6.21861	0.211684	0.105842	−	0.994383i	$-0.466246\pi$
$863$	6.21861	0.211684	0.105842	+	0.994383i	$0.466246\pi$
$864$	79.8889	2.71787
$865$	6.03655	0.205249
$866$	−7.12791	−0.242216
$867$	49.4633	1.67986
$868$	0	0
$869$	−20.8176	−0.706189
$870$	−11.7658	−0.398898
$871$	−41.4816	−1.40555
$872$	35.0988	1.18860
$873$	−39.0194	−1.32061
$874$	2.67583	0.0905112
$875$	0	0
$876$	44.8616	1.51573
$877$	4.08463	0.137928	0.0689641	−	0.997619i	$-0.478031\pi$
$877$	4.08463	0.137928	0.0689641	+	0.997619i	$0.478031\pi$
$878$	−1.15108	−0.0388472
$879$	21.0287	0.709282
$880$	4.81761	0.162401
$881$	−58.3537	−1.96598	−0.982992	−	0.183647i	$-0.941210\pi$
$881$	−58.3537	−1.96598	−0.982992	+	0.183647i	$0.941210\pi$
$882$	0	0
$883$	31.8724	1.07259	0.536296	−	0.844030i	$-0.319823\pi$
$883$	31.8724	1.07259	0.536296	+	0.844030i	$0.319823\pi$
$884$	−46.6222	−1.56807
$885$	−25.6352	−0.861718
$886$	15.1339	0.508433
$887$	−13.0821	−0.439253	−0.219626	−	0.975584i	$-0.570484\pi$
$887$	−13.0821	−0.439253	−0.219626	+	0.975584i	$0.570484\pi$
$888$	91.4252	3.06803
$889$	0	0
$890$	10.2738	0.344377
$891$	−44.0440	−1.47553
$892$	−36.5259	−1.22298
$893$	27.8083	0.930569
$894$	−51.1533	−1.71082
$895$	21.6352	0.723185
$896$	0	0
$897$	13.9985	0.467396
$898$	8.58563	0.286506
$899$	3.67176	0.122460
$900$	10.8359	0.361196
$901$	20.2447	0.674448
$902$	−1.42708	−0.0475164
$903$	0	0
$904$	12.5547	0.417561
$905$	30.6640	1.01930
$906$	−44.3357	−1.47296
$907$	−44.4256	−1.47513	−0.737564	−	0.675278i	$-0.764024\pi$
$907$	−44.4256	−1.47513	−0.737564	+	0.675278i	$0.764024\pi$
$908$	−16.1821	−0.537021
$909$	70.7978	2.34822
$910$	0	0
$911$	−24.0310	−0.796182	−0.398091	−	0.917346i	$-0.630327\pi$
$911$	−24.0310	−0.796182	−0.398091	+	0.917346i	$0.630327\pi$
$912$	−18.1914	−0.602376
$913$	1.70830	0.0565366
$914$	−0.648346	−0.0214454
$915$	−35.5987	−1.17686
$916$	4.58713	0.151563
$917$	0	0
$918$	−55.5804	−1.83443
$919$	−26.4453	−0.872352	−0.436176	−	0.899861i	$-0.643667\pi$
$919$	−26.4453	−0.872352	−0.436176	+	0.899861i	$0.643667\pi$
$920$	−3.96345	−0.130671
$921$	62.9527	2.07436
$922$	9.56212	0.314912
$923$	−10.0806	−0.331806
$924$	0	0
$925$	11.4543	0.376616
$926$	−5.20847	−0.171161
$927$	−93.4264	−3.06853
$928$	15.0287	0.493343
$929$	34.3032	1.12545	0.562726	−	0.826643i	$-0.309752\pi$
$929$	34.3032	1.12545	0.562726	+	0.826643i	$0.309752\pi$
$930$	−6.52591	−0.213993
$931$	0	0
$932$	−24.4244	−0.800048
$933$	4.23945	0.138793
$934$	3.24435	0.106158
$935$	−22.7811	−0.745020
$936$	99.4070	3.24922
$937$	−58.5427	−1.91251	−0.956253	−	0.292541i	$-0.905499\pi$
$937$	−58.5427	−1.91251	−0.956253	+	0.292541i	$0.905499\pi$
$938$	0	0
$939$	56.4685	1.84278
$940$	−17.5912	−0.573762
$941$	0.382726	0.0124765	0.00623826	−	0.999981i	$-0.498014\pi$
$941$	0.382726	0.0124765	0.00623826	+	0.999981i	$0.498014\pi$
$942$	−17.5114	−0.570551
$943$	−0.795598	−0.0259083
$944$	4.81761	0.156800
$945$	0	0
$946$	−16.8721	−0.548559
$947$	−28.5323	−0.927175	−0.463588	−	0.886051i	$-0.653438\pi$
$947$	−28.5323	−0.927175	−0.463588	+	0.886051i	$0.653438\pi$
$948$	−49.7262	−1.61503
$949$	51.5621	1.67378
$950$	3.36329	0.109119
$951$	−72.9997	−2.36718
$952$	0	0
$953$	18.9440	0.613657	0.306828	−	0.951765i	$-0.400732\pi$
$953$	18.9440	0.613657	0.306828	+	0.951765i	$0.400732\pi$
$954$	−18.4349	−0.596851
$955$	6.03655	0.195338
$956$	22.1066	0.714980
$957$	−16.4894	−0.533025
$958$	−9.53148	−0.307948
$959$	0	0
$960$	−11.2734	−0.363848
$961$	−28.9635	−0.934305
$962$	44.8773	1.44690
$963$	−108.719	−3.50343
$964$	−22.0365	−0.709749
$965$	−2.03655	−0.0655587
$966$	0	0
$967$	−5.93738	−0.190933	−0.0954666	−	0.995433i	$-0.530434\pi$
$967$	−5.93738	−0.190933	−0.0954666	+	0.995433i	$0.530434\pi$
$968$	17.4360	0.560416
$969$	86.0217	2.76341
$970$	7.66129	0.245989
$971$	43.7288	1.40332	0.701662	−	0.712510i	$-0.252442\pi$
$971$	43.7288	1.40332	0.701662	+	0.712510i	$0.252442\pi$
$972$	−44.0347	−1.41241
$973$	0	0
$974$	1.50880	0.0483452
$975$	17.5949	0.563489
$976$	6.69003	0.214143
$977$	−43.4920	−1.39143	−0.695717	−	0.718316i	$-0.744913\pi$
$977$	−43.4920	−1.39143	−0.695717	+	0.718316i	$0.744913\pi$
$978$	3.10514	0.0992914
$979$	14.3983	0.460173
$980$	0	0
$981$	−102.416	−3.26990
$982$	−11.1145	−0.354679
$983$	40.6640	1.29698	0.648489	−	0.761224i	$-0.275401\pi$
$983$	40.6640	1.29698	0.648489	+	0.761224i	$0.275401\pi$
$984$	−7.98173	−0.254448
$985$	−29.6822	−0.945754
$986$	−10.4558	−0.332981
$987$	0	0
$988$	−38.5856	−1.22757
$989$	−9.40623	−0.299101
$990$	20.7445	0.659304
$991$	−49.9164	−1.58565	−0.792824	−	0.609451i	$-0.791390\pi$
$991$	−49.9164	−1.58565	−0.792824	+	0.609451i	$0.791390\pi$
$992$	8.33571	0.264659
$993$	70.4968	2.23715
$994$	0	0
$995$	19.5442	0.619592
$996$	4.08056	0.129298
$997$	−1.06122	−0.0336091	−0.0168046	−	0.999859i	$-0.505349\pi$
$997$	−1.06122	−0.0336091	−0.0168046	+	0.999859i	$0.505349\pi$
$998$	−8.97126	−0.283980
$999$	−156.661	−4.95652

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2009.2.a.j.1.2		3
7.6	odd	2		287.2.a.c.1.2	✓	3
21.20	even	2		2583.2.a.m.1.2		3
28.27	even	2		4592.2.a.t.1.3		3
35.34	odd	2		7175.2.a.k.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.a.c.1.2	✓	3	7.6	odd	2
2009.2.a.j.1.2		3	1.1	even	1	trivial
2583.2.a.m.1.2		3	21.20	even	2
4592.2.a.t.1.3		3	28.27	even	2
7175.2.a.k.1.2		3	35.34	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+0.713538 q^{2} +3.20440 q^{3} -1.49086 q^{4} -2.00000 q^{5} +2.28646 q^{6} -2.49086 q^{8} +7.26819 q^{9} +O(q^{10})\)	\(q+0.713538 q^{2} +3.20440 q^{3} -1.49086 q^{4} -2.00000 q^{5} +2.28646 q^{6} -2.49086 q^{8} +7.26819 q^{9} -1.42708 q^{10} -2.00000 q^{11} -4.77733 q^{12} -5.49086 q^{13} -6.40880 q^{15} +1.20440 q^{16} -5.69527 q^{17} +5.18613 q^{18} -4.71354 q^{19} +2.98173 q^{20} -1.42708 q^{22} -0.795598 q^{23} -7.98173 q^{24} -1.00000 q^{25} -3.91794 q^{26} +13.6770 q^{27} +2.57292 q^{29} -4.57292 q^{30} +1.42708 q^{31} +5.84111 q^{32} -6.40880 q^{33} -4.06379 q^{34} -10.8359 q^{36} -11.4543 q^{37} -3.36329 q^{38} -17.5949 q^{39} +4.98173 q^{40} +1.00000 q^{41} +11.8228 q^{43} +2.98173 q^{44} -14.5364 q^{45} -0.567690 q^{46} -5.89967 q^{47} +3.85939 q^{48} -0.713538 q^{50} -18.2499 q^{51} +8.18613 q^{52} -3.55465 q^{53} +9.75905 q^{54} +4.00000 q^{55} -15.1041 q^{57} +1.83588 q^{58} +4.00000 q^{59} +9.55465 q^{60} +5.55465 q^{61} +1.01827 q^{62} +1.75905 q^{64} +10.9817 q^{65} -4.57292 q^{66} +7.55465 q^{67} +8.49086 q^{68} -2.54942 q^{69} +1.83588 q^{71} -18.1041 q^{72} -9.39053 q^{73} -8.17309 q^{74} -3.20440 q^{75} +7.02724 q^{76} -12.5547 q^{78} +10.4088 q^{79} -2.40880 q^{80} +22.0220 q^{81} +0.713538 q^{82} -0.854152 q^{83} +11.3905 q^{85} +8.43605 q^{86} +8.24468 q^{87} +4.98173 q^{88} -7.19917 q^{89} -10.3723 q^{90} +1.18613 q^{92} +4.57292 q^{93} -4.20964 q^{94} +9.42708 q^{95} +18.7173 q^{96} -5.36852 q^{97} -14.5364 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + q^{2} + q^{3} + 3 q^{4} - 6 q^{5} + 8 q^{6} + 8 q^{9}+O(q^{10}) \) 3 * q + q^2 + q^3 + 3 * q^4 - 6 * q^5 + 8 * q^6 + 8 * q^9	\( 3 q + q^{2} + q^{3} + 3 q^{4} - 6 q^{5} + 8 q^{6} + 8 q^{9} - 2 q^{10} - 6 q^{11} - 8 q^{12} - 9 q^{13} - 2 q^{15} - 5 q^{16} - q^{17} - 8 q^{18} - 13 q^{19} - 6 q^{20} - 2 q^{22} - 11 q^{23} - 9 q^{24} - 3 q^{25} - 2 q^{26} + 10 q^{27} + 10 q^{29} - 16 q^{30} + 2 q^{31} + 6 q^{32} - 2 q^{33} - 7 q^{34} - 13 q^{36} + 3 q^{37} - 13 q^{38} - 12 q^{39} + 3 q^{41} + 9 q^{43} - 6 q^{44} - 16 q^{45} + 4 q^{46} + 7 q^{47} + 15 q^{48} - q^{50} - 26 q^{51} + q^{52} + 2 q^{53} + 8 q^{54} + 12 q^{55} - 12 q^{57} - 14 q^{58} + 12 q^{59} + 16 q^{60} + 4 q^{61} + 18 q^{62} - 16 q^{64} + 18 q^{65} - 16 q^{66} + 10 q^{67} + 18 q^{68} + 13 q^{69} - 14 q^{71} - 21 q^{72} + 4 q^{73} + 6 q^{74} - q^{75} - 14 q^{76} - 25 q^{78} + 14 q^{79} + 10 q^{80} + 23 q^{81} + q^{82} + 2 q^{83} + 2 q^{85} - 27 q^{86} - 12 q^{87} - 5 q^{89} + 16 q^{90} - 20 q^{92} + 16 q^{93} - 12 q^{94} + 26 q^{95} - 3 q^{96} - 27 q^{97} - 16 q^{99}+O(q^{100}) \) 3 * q + q^2 + q^3 + 3 * q^4 - 6 * q^5 + 8 * q^6 + 8 * q^9 - 2 * q^10 - 6 * q^11 - 8 * q^12 - 9 * q^13 - 2 * q^15 - 5 * q^16 - q^17 - 8 * q^18 - 13 * q^19 - 6 * q^20 - 2 * q^22 - 11 * q^23 - 9 * q^24 - 3 * q^25 - 2 * q^26 + 10 * q^27 + 10 * q^29 - 16 * q^30 + 2 * q^31 + 6 * q^32 - 2 * q^33 - 7 * q^34 - 13 * q^36 + 3 * q^37 - 13 * q^38 - 12 * q^39 + 3 * q^41 + 9 * q^43 - 6 * q^44 - 16 * q^45 + 4 * q^46 + 7 * q^47 + 15 * q^48 - q^50 - 26 * q^51 + q^52 + 2 * q^53 + 8 * q^54 + 12 * q^55 - 12 * q^57 - 14 * q^58 + 12 * q^59 + 16 * q^60 + 4 * q^61 + 18 * q^62 - 16 * q^64 + 18 * q^65 - 16 * q^66 + 10 * q^67 + 18 * q^68 + 13 * q^69 - 14 * q^71 - 21 * q^72 + 4 * q^73 + 6 * q^74 - q^75 - 14 * q^76 - 25 * q^78 + 14 * q^79 + 10 * q^80 + 23 * q^81 + q^82 + 2 * q^83 + 2 * q^85 - 27 * q^86 - 12 * q^87 - 5 * q^89 + 16 * q^90 - 20 * q^92 + 16 * q^93 - 12 * q^94 + 26 * q^95 - 3 * q^96 - 27 * q^97 - 16 * q^99

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