LMFDB - Embedded newform 2009.2.a.o.1.1

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:	$6$
Coefficient field:	6.6.185257757.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 10x^{4} + 10x^{3} + 23x^{2} - 24x + 5 $ x^6 - x^5 - 10x^4 + 10x^3 + 23x^2 - 24x + 5
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			1.1
Root			$2.47904$ 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)

$f(q)$	$=$	$q-2.47904 q^{2} -2.84004 q^{3} +4.14562 q^{4} +3.76023 q^{5} +7.04056 q^{6} -5.31907 q^{8} +5.06582 q^{9} +O(q^{10})$	\(q-2.47904 q^{2} -2.84004 q^{3} +4.14562 q^{4} +3.76023 q^{5} +7.04056 q^{6} -5.31907 q^{8} +5.06582 q^{9} -9.32175 q^{10} +3.19012 q^{11} -11.7737 q^{12} -6.78719 q^{13} -10.6792 q^{15} +4.89494 q^{16} -0.305584 q^{17} -12.5583 q^{18} -2.42414 q^{19} +15.5885 q^{20} -7.90843 q^{22} +6.84004 q^{23} +15.1064 q^{24} +9.13935 q^{25} +16.8257 q^{26} -5.86700 q^{27} -1.18128 q^{29} +26.4741 q^{30} +6.37140 q^{31} -1.49658 q^{32} -9.06007 q^{33} +0.757553 q^{34} +21.0010 q^{36} -3.49263 q^{37} +6.00953 q^{38} +19.2759 q^{39} -20.0010 q^{40} -1.00000 q^{41} +2.03618 q^{43} +13.2250 q^{44} +19.0487 q^{45} -16.9567 q^{46} -0.930242 q^{47} -13.9018 q^{48} -22.6568 q^{50} +0.867869 q^{51} -28.1371 q^{52} -5.48908 q^{53} +14.5445 q^{54} +11.9956 q^{55} +6.88465 q^{57} +2.92843 q^{58} +1.01743 q^{59} -44.2719 q^{60} +12.0438 q^{61} -15.7949 q^{62} -6.07981 q^{64} -25.5214 q^{65} +22.4602 q^{66} +7.91984 q^{67} -1.26683 q^{68} -19.4260 q^{69} -1.64168 q^{71} -26.9455 q^{72} -6.23205 q^{73} +8.65837 q^{74} -25.9561 q^{75} -10.0496 q^{76} -47.7856 q^{78} +6.61631 q^{79} +18.4061 q^{80} +1.46505 q^{81} +2.47904 q^{82} -7.93292 q^{83} -1.14907 q^{85} -5.04776 q^{86} +3.35488 q^{87} -16.9685 q^{88} +14.9057 q^{89} -47.2223 q^{90} +28.3562 q^{92} -18.0950 q^{93} +2.30610 q^{94} -9.11532 q^{95} +4.25033 q^{96} +9.52696 q^{97} +16.1606 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{2} + 4 q^{3} + 9 q^{4} + q^{5} + 4 q^{6} + 3 q^{8} + 14 q^{9}+O(q^{10}) $ 6 * q - q^2 + 4 * q^3 + 9 * q^4 + q^5 + 4 * q^6 + 3 * q^8 + 14 * q^9	$ 6 q - q^{2} + 4 q^{3} + 9 q^{4} + q^{5} + 4 q^{6} + 3 q^{8} + 14 q^{9} - 10 q^{10} + 6 q^{11} - 9 q^{12} - 7 q^{13} - 13 q^{15} + 7 q^{16} - 7 q^{17} - 5 q^{18} - 2 q^{19} - 11 q^{20} + 15 q^{22} + 20 q^{23} + 36 q^{24} + 29 q^{25} + 43 q^{26} - 2 q^{27} - 9 q^{29} + 13 q^{30} + 27 q^{31} - 10 q^{32} - 17 q^{33} - 6 q^{34} + 29 q^{36} + 19 q^{37} + 23 q^{38} + q^{39} - 23 q^{40} - 6 q^{41} + 19 q^{43} + 21 q^{44} + 35 q^{45} - 8 q^{46} + 19 q^{47} + 9 q^{48} - 58 q^{50} - 19 q^{51} + 5 q^{53} + 37 q^{54} - 3 q^{55} + 37 q^{57} + 13 q^{58} + 7 q^{59} - 110 q^{60} + 12 q^{61} - 37 q^{64} - 13 q^{65} + 54 q^{66} + 27 q^{67} - 31 q^{68} - 16 q^{69} - 6 q^{71} + 5 q^{72} - 52 q^{73} - 14 q^{74} + 46 q^{75} - 13 q^{76} - 45 q^{78} + 26 q^{80} - 22 q^{81} + q^{82} - 12 q^{83} + 25 q^{85} - 10 q^{86} - 42 q^{87} - 2 q^{88} + 38 q^{89} - 93 q^{90} + 45 q^{92} + 33 q^{93} + 8 q^{94} + q^{95} + 12 q^{96} - 8 q^{97} + q^{99}+O(q^{100}) $ 6 * q - q^2 + 4 * q^3 + 9 * q^4 + q^5 + 4 * q^6 + 3 * q^8 + 14 * q^9 - 10 * q^10 + 6 * q^11 - 9 * q^12 - 7 * q^13 - 13 * q^15 + 7 * q^16 - 7 * q^17 - 5 * q^18 - 2 * q^19 - 11 * q^20 + 15 * q^22 + 20 * q^23 + 36 * q^24 + 29 * q^25 + 43 * q^26 - 2 * q^27 - 9 * q^29 + 13 * q^30 + 27 * q^31 - 10 * q^32 - 17 * q^33 - 6 * q^34 + 29 * q^36 + 19 * q^37 + 23 * q^38 + q^39 - 23 * q^40 - 6 * q^41 + 19 * q^43 + 21 * q^44 + 35 * q^45 - 8 * q^46 + 19 * q^47 + 9 * q^48 - 58 * q^50 - 19 * q^51 + 5 * q^53 + 37 * q^54 - 3 * q^55 + 37 * q^57 + 13 * q^58 + 7 * q^59 - 110 * q^60 + 12 * q^61 - 37 * q^64 - 13 * q^65 + 54 * q^66 + 27 * q^67 - 31 * q^68 - 16 * q^69 - 6 * q^71 + 5 * q^72 - 52 * q^73 - 14 * q^74 + 46 * q^75 - 13 * q^76 - 45 * q^78 + 26 * q^80 - 22 * q^81 + q^82 - 12 * q^83 + 25 * q^85 - 10 * q^86 - 42 * q^87 - 2 * q^88 + 38 * q^89 - 93 * q^90 + 45 * q^92 + 33 * q^93 + 8 * q^94 + q^95 + 12 * q^96 - 8 * q^97 + 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 $

$2$	−2.47904	−1.75294	−0.876472	−	0.481453i	$-0.840109\pi$
$2$	−2.47904	−1.75294	−0.876472	+	0.481453i	$0.840109\pi$
$3$	−2.84004	−1.63970	−0.819848	−	0.572581i	$-0.805942\pi$
$3$	−2.84004	−1.63970	−0.819848	+	0.572581i	$0.805942\pi$
$4$	4.14562	2.07281
$5$	3.76023	1.68163	0.840814	−	0.541325i	$-0.182077\pi$
$5$	3.76023	1.68163	0.840814	+	0.541325i	$0.182077\pi$
$6$	7.04056	2.87430
$7$	0	0
$7$	0	0
$8$	−5.31907	−1.88058
$9$	5.06582	1.68861
$10$	−9.32175	−2.94780
$11$	3.19012	0.961858	0.480929	−	0.876760i	$-0.340300\pi$
$11$	3.19012	0.961858	0.480929	+	0.876760i	$0.340300\pi$
$12$	−11.7737	−3.39878
$13$	−6.78719	−1.88243	−0.941214	−	0.337810i	$-0.890314\pi$
$13$	−6.78719	−1.88243	−0.941214	+	0.337810i	$0.890314\pi$
$14$	0	0
$15$	−10.6792	−2.75736
$16$	4.89494	1.22373
$17$	−0.305584	−0.0741149	−0.0370575	−	0.999313i	$-0.511798\pi$
$17$	−0.305584	−0.0741149	−0.0370575	+	0.999313i	$0.511798\pi$
$18$	−12.5583	−2.96003
$19$	−2.42414	−0.556135	−0.278068	−	0.960561i	$-0.589694\pi$
$19$	−2.42414	−0.556135	−0.278068	+	0.960561i	$0.589694\pi$
$20$	15.5885	3.48570
$21$	0	0
$22$	−7.90843	−1.68608
$23$	6.84004	1.42625	0.713123	−	0.701039i	$-0.247280\pi$
$23$	6.84004	1.42625	0.713123	+	0.701039i	$0.247280\pi$
$24$	15.1064	3.08358
$25$	9.13935	1.82787
$26$	16.8257	3.29979
$27$	−5.86700	−1.12910
$28$	0	0
$29$	−1.18128	−0.219358	−0.109679	−	0.993967i	$-0.534982\pi$
$29$	−1.18128	−0.219358	−0.109679	+	0.993967i	$0.534982\pi$
$30$	26.4741	4.83349
$31$	6.37140	1.14434	0.572169	−	0.820136i	$-0.306102\pi$
$31$	6.37140	1.14434	0.572169	+	0.820136i	$0.306102\pi$
$32$	−1.49658	−0.264560
$33$	−9.06007	−1.57716
$34$	0.757553	0.129919
$35$	0	0
$36$	21.0010	3.50016
$37$	−3.49263	−0.574186	−0.287093	−	0.957903i	$-0.592689\pi$
$37$	−3.49263	−0.574186	−0.287093	+	0.957903i	$0.592689\pi$
$38$	6.00953	0.974874
$39$	19.2759	3.08661
$40$	−20.0010	−3.16243
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	2.03618	0.310514	0.155257	−	0.987874i	$-0.450379\pi$
$43$	2.03618	0.310514	0.155257	+	0.987874i	$0.450379\pi$
$44$	13.2250	1.99375
$45$	19.0487	2.83961
$46$	−16.9567	−2.50013
$47$	−0.930242	−0.135690	−0.0678449	−	0.997696i	$-0.521612\pi$
$47$	−0.930242	−0.135690	−0.0678449	+	0.997696i	$0.521612\pi$
$48$	−13.9018	−2.00655
$49$	0	0
$50$	−22.6568	−3.20415
$51$	0.867869	0.121526
$52$	−28.1371	−3.90192
$53$	−5.48908	−0.753984	−0.376992	−	0.926217i	$-0.623042\pi$
$53$	−5.48908	−0.753984	−0.376992	+	0.926217i	$0.623042\pi$
$54$	14.5445	1.97926
$55$	11.9956	1.61749
$56$	0	0
$57$	6.88465	0.911894
$58$	2.92843	0.384522
$59$	1.01743	0.132458	0.0662292	−	0.997804i	$-0.478903\pi$
$59$	1.01743	0.132458	0.0662292	+	0.997804i	$0.478903\pi$
$60$	−44.2719	−5.71548
$61$	12.0438	1.54205	0.771023	−	0.636808i	$-0.219746\pi$
$61$	12.0438	1.54205	0.771023	+	0.636808i	$0.219746\pi$
$62$	−15.7949	−2.00596
$63$	0	0
$64$	−6.07981	−0.759976
$65$	−25.5214	−3.16554
$66$	22.4602	2.76466
$67$	7.91984	0.967563	0.483781	−	0.875189i	$-0.339263\pi$
$67$	7.91984	0.967563	0.483781	+	0.875189i	$0.339263\pi$
$68$	−1.26683	−0.153626
$69$	−19.4260	−2.33861
$70$	0	0
$71$	−1.64168	−0.194831	−0.0974157	−	0.995244i	$-0.531058\pi$
$71$	−1.64168	−0.194831	−0.0974157	+	0.995244i	$0.531058\pi$
$72$	−26.9455	−3.17555
$73$	−6.23205	−0.729406	−0.364703	−	0.931124i	$-0.618829\pi$
$73$	−6.23205	−0.729406	−0.364703	+	0.931124i	$0.618829\pi$
$74$	8.65837	1.00651
$75$	−25.9561	−2.99715
$76$	−10.0496	−1.15276
$77$	0	0
$78$	−47.7856	−5.41066
$79$	6.61631	0.744393	0.372197	−	0.928154i	$-0.378605\pi$
$79$	6.61631	0.744393	0.372197	+	0.928154i	$0.378605\pi$
$80$	18.4061	2.05786
$81$	1.46505	0.162783
$82$	2.47904	0.273764
$83$	−7.93292	−0.870751	−0.435376	−	0.900249i	$-0.643384\pi$
$83$	−7.93292	−0.870751	−0.435376	+	0.900249i	$0.643384\pi$
$84$	0	0
$85$	−1.14907	−0.124634
$86$	−5.04776	−0.544314
$87$	3.35488	0.359681
$88$	−16.9685	−1.80885
$89$	14.9057	1.58001	0.790003	−	0.613103i	$-0.210079\pi$
$89$	14.9057	1.58001	0.790003	+	0.613103i	$0.210079\pi$
$90$	−47.2223	−4.97767
$91$	0	0
$92$	28.3562	2.95634
$93$	−18.0950	−1.87637
$94$	2.30610	0.237856
$95$	−9.11532	−0.935213
$96$	4.25033	0.433798
$97$	9.52696	0.967316	0.483658	−	0.875257i	$-0.339308\pi$
$97$	9.52696	0.967316	0.483658	+	0.875257i	$0.339308\pi$
$98$	0	0
$99$	16.1606	1.62420
$100$	37.8883	3.78883
$101$	−15.1110	−1.50360	−0.751801	−	0.659390i	$-0.770815\pi$
$101$	−15.1110	−1.50360	−0.751801	+	0.659390i	$0.770815\pi$
$102$	−2.15148	−0.213028
$103$	15.1526	1.49303	0.746515	−	0.665369i	$-0.231726\pi$
$103$	15.1526	1.49303	0.746515	+	0.665369i	$0.231726\pi$
$104$	36.1016	3.54005
$105$	0	0
$106$	13.6076	1.32169
$107$	5.71634	0.552619	0.276310	−	0.961069i	$-0.410888\pi$
$107$	5.71634	0.552619	0.276310	+	0.961069i	$0.410888\pi$
$108$	−24.3224	−2.34042
$109$	−5.75069	−0.550816	−0.275408	−	0.961327i	$-0.588813\pi$
$109$	−5.75069	−0.550816	−0.275408	+	0.961327i	$0.588813\pi$
$110$	−29.7375	−2.83536
$111$	9.91922	0.941490
$112$	0	0
$113$	−7.81119	−0.734815	−0.367407	−	0.930060i	$-0.619755\pi$
$113$	−7.81119	−0.734815	−0.367407	+	0.930060i	$0.619755\pi$
$114$	−17.0673	−1.59850
$115$	25.7201	2.39842
$116$	−4.89714	−0.454688
$117$	−34.3827	−3.17868
$118$	−2.52225	−0.232192
$119$	0	0
$120$	56.8035	5.18543
$121$	−0.823125	−0.0748296
$122$	−29.8569	−2.70312
$123$	2.84004	0.256078
$124$	26.4134	2.37199
$125$	15.5649	1.39217
$126$	0	0
$127$	−1.88478	−0.167247	−0.0836237	−	0.996497i	$-0.526649\pi$
$127$	−1.88478	−0.167247	−0.0836237	+	0.996497i	$0.526649\pi$
$128$	18.0652	1.59675
$129$	−5.78282	−0.509149
$130$	63.2685	5.54902
$131$	8.98771	0.785260	0.392630	−	0.919696i	$-0.371565\pi$
$131$	8.98771	0.785260	0.392630	+	0.919696i	$0.371565\pi$
$132$	−37.5596	−3.26914
$133$	0	0
$134$	−19.6336	−1.69608
$135$	−22.0613	−1.89873
$136$	1.62542	0.139379
$137$	4.29905	0.367292	0.183646	−	0.982992i	$-0.441210\pi$
$137$	4.29905	0.367292	0.183646	+	0.982992i	$0.441210\pi$
$138$	48.1577	4.09945
$139$	−2.48995	−0.211195	−0.105598	−	0.994409i	$-0.533676\pi$
$139$	−2.48995	−0.211195	−0.105598	+	0.994409i	$0.533676\pi$
$140$	0	0
$141$	2.64192	0.222490
$142$	4.06978	0.341528
$143$	−21.6520	−1.81063
$144$	24.7968	2.06640
$145$	−4.44188	−0.368878
$146$	15.4495	1.27861
$147$	0	0
$148$	−14.4791	−1.19018
$149$	−6.61806	−0.542172	−0.271086	−	0.962555i	$-0.587383\pi$
$149$	−6.61806	−0.542172	−0.271086	+	0.962555i	$0.587383\pi$
$150$	64.3461	5.25384
$151$	−7.75251	−0.630891	−0.315445	−	0.948944i	$-0.602154\pi$
$151$	−7.75251	−0.630891	−0.315445	+	0.948944i	$0.602154\pi$
$152$	12.8942	1.04586
$153$	−1.54803	−0.125151
$154$	0	0
$155$	23.9579	1.92435
$156$	79.9105	6.39796
$157$	2.45378	0.195833	0.0979164	−	0.995195i	$-0.468782\pi$
$157$	2.45378	0.195833	0.0979164	+	0.995195i	$0.468782\pi$
$158$	−16.4021	−1.30488
$159$	15.5892	1.23630
$160$	−5.62748	−0.444891
$161$	0	0
$162$	−3.63191	−0.285350
$163$	−5.13908	−0.402524	−0.201262	−	0.979537i	$-0.564504\pi$
$163$	−5.13908	−0.402524	−0.201262	+	0.979537i	$0.564504\pi$
$164$	−4.14562	−0.323719
$165$	−34.0680	−2.65219
$166$	19.6660	1.52638
$167$	5.48429	0.424387	0.212194	−	0.977228i	$-0.431939\pi$
$167$	5.48429	0.424387	0.212194	+	0.977228i	$0.431939\pi$
$168$	0	0
$169$	33.0660	2.54354
$170$	2.84858	0.218476
$171$	−12.2802	−0.939093
$172$	8.44122	0.643637
$173$	−5.48311	−0.416873	−0.208436	−	0.978036i	$-0.566837\pi$
$173$	−5.48311	−0.416873	−0.208436	+	0.978036i	$0.566837\pi$
$174$	−8.31686	−0.630500
$175$	0	0
$176$	15.6154	1.17706
$177$	−2.88955	−0.217192
$178$	−36.9519	−2.76966
$179$	−21.1692	−1.58226	−0.791129	−	0.611650i	$-0.790506\pi$
$179$	−21.1692	−1.58226	−0.791129	+	0.611650i	$0.790506\pi$
$180$	78.9685	5.88596
$181$	−9.05287	−0.672894	−0.336447	−	0.941702i	$-0.609225\pi$
$181$	−9.05287	−0.672894	−0.336447	+	0.941702i	$0.609225\pi$
$182$	0	0
$183$	−34.2047	−2.52849
$184$	−36.3827	−2.68217
$185$	−13.1331	−0.965566
$186$	44.8582	3.28916
$187$	−0.974849	−0.0712880
$188$	−3.85643	−0.281259
$189$	0	0
$190$	22.5972	1.63937
$191$	17.0951	1.23696	0.618478	−	0.785802i	$-0.287750\pi$
$191$	17.0951	1.23696	0.618478	+	0.785802i	$0.287750\pi$
$192$	17.2669	1.24613
$193$	21.6348	1.55731	0.778655	−	0.627453i	$-0.215902\pi$
$193$	21.6348	1.55731	0.778655	+	0.627453i	$0.215902\pi$
$194$	−23.6177	−1.69565
$195$	72.4818	5.19053
$196$	0	0
$197$	4.22945	0.301336	0.150668	−	0.988584i	$-0.451858\pi$
$197$	4.22945	0.301336	0.150668	+	0.988584i	$0.451858\pi$
$198$	−40.0626	−2.84713
$199$	22.8647	1.62084	0.810418	−	0.585853i	$-0.199240\pi$
$199$	22.8647	1.62084	0.810418	+	0.585853i	$0.199240\pi$
$200$	−48.6129	−3.43745
$201$	−22.4927	−1.58651
$202$	37.4608	2.63573
$203$	0	0
$204$	3.59786	0.251900
$205$	−3.76023	−0.262626
$206$	−37.5638	−2.61720
$207$	34.6504	2.40837
$208$	−33.2229	−2.30359
$209$	−7.73330	−0.534923
$210$	0	0
$211$	6.67920	0.459815	0.229908	−	0.973212i	$-0.426158\pi$
$211$	6.67920	0.459815	0.229908	+	0.973212i	$0.426158\pi$
$212$	−22.7557	−1.56287
$213$	4.66243	0.319464
$214$	−14.1710	−0.968710
$215$	7.65650	0.522169
$216$	31.2070	2.12337
$217$	0	0
$218$	14.2562	0.965549
$219$	17.6993	1.19600
$220$	49.7292	3.35274
$221$	2.07406	0.139516
$222$	−24.5901	−1.65038
$223$	−12.0348	−0.805909	−0.402954	−	0.915220i	$-0.632017\pi$
$223$	−12.0348	−0.805909	−0.402954	+	0.915220i	$0.632017\pi$
$224$	0	0
$225$	46.2983	3.08655
$226$	19.3642	1.28809
$227$	18.0864	1.20044	0.600218	−	0.799836i	$-0.295080\pi$
$227$	18.0864	1.20044	0.600218	+	0.799836i	$0.295080\pi$
$228$	28.5411	1.89018
$229$	−19.0283	−1.25742	−0.628712	−	0.777638i	$-0.716418\pi$
$229$	−19.0283	−1.25742	−0.628712	+	0.777638i	$0.716418\pi$
$230$	−63.7612	−4.20429
$231$	0	0
$232$	6.28331	0.412520
$233$	4.43234	0.290372	0.145186	−	0.989404i	$-0.453622\pi$
$233$	4.43234	0.290372	0.145186	+	0.989404i	$0.453622\pi$
$234$	85.2359	5.57205
$235$	−3.49793	−0.228180
$236$	4.21789	0.274561
$237$	−18.7906	−1.22058
$238$	0	0
$239$	−7.32594	−0.473876	−0.236938	−	0.971525i	$-0.576144\pi$
$239$	−7.32594	−0.473876	−0.236938	+	0.971525i	$0.576144\pi$
$240$	−52.2740	−3.37427
$241$	30.1620	1.94291	0.971453	−	0.237231i	$-0.0762400\pi$
$241$	30.1620	1.94291	0.971453	+	0.237231i	$0.0762400\pi$
$242$	2.04056	0.131172
$243$	13.4402	0.862189
$244$	49.9289	3.19637
$245$	0	0
$246$	−7.04056	−0.448890
$247$	16.4531	1.04689
$248$	−33.8900	−2.15201
$249$	22.5298	1.42777
$250$	−38.5860	−2.44039
$251$	28.8842	1.82315	0.911576	−	0.411132i	$-0.134867\pi$
$251$	28.8842	1.82315	0.911576	+	0.411132i	$0.134867\pi$
$252$	0	0
$253$	21.8206	1.37185
$254$	4.67244	0.293175
$255$	3.26339	0.204361
$256$	−32.6247	−2.03904
$257$	−23.2471	−1.45011	−0.725057	−	0.688689i	$-0.758187\pi$
$257$	−23.2471	−1.45011	−0.725057	+	0.688689i	$0.758187\pi$
$258$	14.3358	0.892509
$259$	0	0
$260$	−105.802	−6.56157
$261$	−5.98414	−0.370409
$262$	−22.2809	−1.37652
$263$	20.9449	1.29152	0.645759	−	0.763541i	$-0.276541\pi$
$263$	20.9449	1.29152	0.645759	+	0.763541i	$0.276541\pi$
$264$	48.1912	2.96596
$265$	−20.6402	−1.26792
$266$	0	0
$267$	−42.3329	−2.59073
$268$	32.8327	2.00557
$269$	23.3453	1.42339	0.711695	−	0.702489i	$-0.247928\pi$
$269$	23.3453	1.42339	0.711695	+	0.702489i	$0.247928\pi$
$270$	54.6907	3.32837
$271$	15.9266	0.967470	0.483735	−	0.875215i	$-0.339280\pi$
$271$	15.9266	0.967470	0.483735	+	0.875215i	$0.339280\pi$
$272$	−1.49581	−0.0906970
$273$	0	0
$274$	−10.6575	−0.643843
$275$	29.1556	1.75815
$276$	−80.5327	−4.84750
$277$	−11.6509	−0.700033	−0.350017	−	0.936743i	$-0.613824\pi$
$277$	−11.6509	−0.700033	−0.350017	+	0.936743i	$0.613824\pi$
$278$	6.17269	0.370213
$279$	32.2763	1.93233
$280$	0	0
$281$	8.56467	0.510925	0.255463	−	0.966819i	$-0.417772\pi$
$281$	8.56467	0.510925	0.255463	+	0.966819i	$0.417772\pi$
$282$	−6.54942	−0.390012
$283$	−5.46995	−0.325155	−0.162577	−	0.986696i	$-0.551981\pi$
$283$	−5.46995	−0.325155	−0.162577	+	0.986696i	$0.551981\pi$
$284$	−6.80578	−0.403849
$285$	25.8879	1.53347
$286$	53.6760	3.17393
$287$	0	0
$288$	−7.58138	−0.446737
$289$	−16.9066	−0.994507
$290$	11.0116	0.646623
$291$	−27.0569	−1.58611
$292$	−25.8357	−1.51192
$293$	10.0930	0.589641	0.294820	−	0.955553i	$-0.404740\pi$
$293$	10.0930	0.589641	0.294820	+	0.955553i	$0.404740\pi$
$294$	0	0
$295$	3.82578	0.222746
$296$	18.5776	1.07980
$297$	−18.7164	−1.08604
$298$	16.4064	0.950397
$299$	−46.4247	−2.68481
$300$	−107.604	−6.21253
$301$	0	0
$302$	19.2188	1.10592
$303$	42.9159	2.46545
$304$	−11.8660	−0.680562
$305$	45.2873	2.59315
$306$	3.83762	0.219382
$307$	−21.6658	−1.23653	−0.618266	−	0.785969i	$-0.712165\pi$
$307$	−21.6658	−1.23653	−0.618266	+	0.785969i	$0.712165\pi$
$308$	0	0
$309$	−43.0340	−2.44812
$310$	−59.3926	−3.37327
$311$	−28.9827	−1.64346	−0.821728	−	0.569880i	$-0.806990\pi$
$311$	−28.9827	−1.64346	−0.821728	+	0.569880i	$0.806990\pi$
$312$	−102.530	−5.80461
$313$	−7.31243	−0.413323	−0.206662	−	0.978412i	$-0.566260\pi$
$313$	−7.31243	−0.413323	−0.206662	+	0.978412i	$0.566260\pi$
$314$	−6.08301	−0.343284
$315$	0	0
$316$	27.4287	1.54299
$317$	16.0271	0.900170	0.450085	−	0.892986i	$-0.351394\pi$
$317$	16.0271	0.900170	0.450085	+	0.892986i	$0.351394\pi$
$318$	−38.6462	−2.16717
$319$	−3.76842	−0.210991
$320$	−22.8615	−1.27800
$321$	−16.2346	−0.906128
$322$	0	0
$323$	0.740777	0.0412179
$324$	6.07353	0.337419
$325$	−62.0305	−3.44084
$326$	12.7400	0.705602
$327$	16.3322	0.903171
$328$	5.31907	0.293697
$329$	0	0
$330$	84.4557	4.64913
$331$	15.8171	0.869385	0.434692	−	0.900579i	$-0.356857\pi$
$331$	15.8171	0.869385	0.434692	+	0.900579i	$0.356857\pi$
$332$	−32.8869	−1.80490
$333$	−17.6930	−0.969573
$334$	−13.5958	−0.743926
$335$	29.7805	1.62708
$336$	0	0
$337$	2.91505	0.158793	0.0793964	−	0.996843i	$-0.474701\pi$
$337$	2.91505	0.158793	0.0793964	+	0.996843i	$0.474701\pi$
$338$	−81.9718	−4.45868
$339$	22.1841	1.20487
$340$	−4.76359	−0.258342
$341$	20.3255	1.10069
$342$	30.4432	1.64618
$343$	0	0
$344$	−10.8306	−0.583946
$345$	−73.0462	−3.93267
$346$	13.5928	0.730755
$347$	−0.749981	−0.0402611	−0.0201305	−	0.999797i	$-0.506408\pi$
$347$	−0.749981	−0.0402611	−0.0201305	+	0.999797i	$0.506408\pi$
$348$	13.9081	0.745550
$349$	14.7027	0.787018	0.393509	−	0.919321i	$-0.371261\pi$
$349$	14.7027	0.787018	0.393509	+	0.919321i	$0.371261\pi$
$350$	0	0
$351$	39.8204	2.12546
$352$	−4.77426	−0.254469
$353$	−4.99726	−0.265977	−0.132989	−	0.991118i	$-0.542457\pi$
$353$	−4.99726	−0.265977	−0.132989	+	0.991118i	$0.542457\pi$
$354$	7.16329	0.380725
$355$	−6.17309	−0.327634
$356$	61.7936	3.27505
$357$	0	0
$358$	52.4791	2.77361
$359$	−18.9459	−0.999926	−0.499963	−	0.866047i	$-0.666653\pi$
$359$	−18.9459	−0.999926	−0.499963	+	0.866047i	$0.666653\pi$
$360$	−101.321	−5.34010
$361$	−13.1236	−0.690713
$362$	22.4424	1.17955
$363$	2.33771	0.122698
$364$	0	0
$365$	−23.4340	−1.22659
$366$	84.7948	4.43229
$367$	31.9626	1.66843	0.834217	−	0.551436i	$-0.185920\pi$
$367$	31.9626	1.66843	0.834217	+	0.551436i	$0.185920\pi$
$368$	33.4816	1.74535
$369$	−5.06582	−0.263716
$370$	32.5575	1.69258
$371$	0	0
$372$	−75.0151	−3.88935
$373$	12.5901	0.651893	0.325947	−	0.945388i	$-0.394317\pi$
$373$	12.5901	0.651893	0.325947	+	0.945388i	$0.394317\pi$
$374$	2.41669	0.124964
$375$	−44.2050	−2.28274
$376$	4.94803	0.255175
$377$	8.01757	0.412926
$378$	0	0
$379$	−9.15556	−0.470290	−0.235145	−	0.971960i	$-0.575556\pi$
$379$	−9.15556	−0.470290	−0.235145	+	0.971960i	$0.575556\pi$
$380$	−37.7887	−1.93852
$381$	5.35285	0.274235
$382$	−42.3793	−2.16831
$383$	1.25598	0.0641774	0.0320887	−	0.999485i	$-0.489784\pi$
$383$	1.25598	0.0641774	0.0320887	+	0.999485i	$0.489784\pi$
$384$	−51.3059	−2.61819
$385$	0	0
$386$	−53.6335	−2.72988
$387$	10.3149	0.524336
$388$	39.4952	2.00506
$389$	12.0051	0.608684	0.304342	−	0.952563i	$-0.401563\pi$
$389$	12.0051	0.608684	0.304342	+	0.952563i	$0.401563\pi$
$390$	−179.685	−9.09871
$391$	−2.09020	−0.105706
$392$	0	0
$393$	−25.5254	−1.28759
$394$	−10.4850	−0.528224
$395$	24.8789	1.25179
$396$	66.9956	3.36666
$397$	31.4812	1.58000	0.789998	−	0.613109i	$-0.210081\pi$
$397$	31.4812	1.58000	0.789998	+	0.613109i	$0.210081\pi$
$398$	−56.6824	−2.84123
$399$	0	0
$400$	44.7365	2.23683
$401$	−23.3806	−1.16757	−0.583785	−	0.811908i	$-0.698429\pi$
$401$	−23.3806	−1.16757	−0.583785	+	0.811908i	$0.698429\pi$
$402$	55.7601	2.78106
$403$	−43.2439	−2.15413
$404$	−62.6446	−3.11668
$405$	5.50892	0.273740
$406$	0	0
$407$	−11.1419	−0.552285
$408$	−4.61626	−0.228539
$409$	−24.9739	−1.23488	−0.617441	−	0.786617i	$-0.711830\pi$
$409$	−24.9739	−1.23488	−0.617441	+	0.786617i	$0.711830\pi$
$410$	9.32175	0.460369
$411$	−12.2095	−0.602248
$412$	62.8169	3.09477
$413$	0	0
$414$	−85.8996	−4.22173
$415$	−29.8296	−1.46428
$416$	10.1576	0.498015
$417$	7.07157	0.346296
$418$	19.1711	0.937690
$419$	4.36180	0.213088	0.106544	−	0.994308i	$-0.466021\pi$
$419$	4.36180	0.213088	0.106544	+	0.994308i	$0.466021\pi$
$420$	0	0
$421$	28.7783	1.40257	0.701285	−	0.712881i	$-0.252610\pi$
$421$	28.7783	1.40257	0.701285	+	0.712881i	$0.252610\pi$
$422$	−16.5580	−0.806030
$423$	−4.71243	−0.229126
$424$	29.1968	1.41792
$425$	−2.79284	−0.135472
$426$	−11.5583	−0.560003
$427$	0	0
$428$	23.6978	1.14548
$429$	61.4924	2.96888
$430$	−18.9807	−0.915333
$431$	13.4374	0.647257	0.323628	−	0.946184i	$-0.395097\pi$
$431$	13.4374	0.647257	0.323628	+	0.946184i	$0.395097\pi$
$432$	−28.7186	−1.38172
$433$	14.3802	0.691067	0.345533	−	0.938407i	$-0.387698\pi$
$433$	14.3802	0.691067	0.345533	+	0.938407i	$0.387698\pi$
$434$	0	0
$435$	12.6151	0.604849
$436$	−23.8402	−1.14174
$437$	−16.5812	−0.793186
$438$	−43.8771	−2.09653
$439$	3.83813	0.183184	0.0915919	−	0.995797i	$-0.470804\pi$
$439$	3.83813	0.183184	0.0915919	+	0.995797i	$0.470804\pi$
$440$	−63.8055	−3.04181
$441$	0	0
$442$	−5.14166	−0.244564
$443$	−38.7709	−1.84206	−0.921030	−	0.389491i	$-0.872651\pi$
$443$	−38.7709	−1.84206	−0.921030	+	0.389491i	$0.872651\pi$
$444$	41.1213	1.95153
$445$	56.0491	2.65698
$446$	29.8347	1.41271
$447$	18.7955	0.888998
$448$	0	0
$449$	2.37624	0.112142	0.0560708	−	0.998427i	$-0.482143\pi$
$449$	2.37624	0.112142	0.0560708	+	0.998427i	$0.482143\pi$
$450$	−114.775	−5.41055
$451$	−3.19012	−0.150217
$452$	−32.3822	−1.52313
$453$	22.0174	1.03447
$454$	−44.8368	−2.10430
$455$	0	0
$456$	−36.6199	−1.71489
$457$	15.2107	0.711527	0.355763	−	0.934576i	$-0.384221\pi$
$457$	15.2107	0.711527	0.355763	+	0.934576i	$0.384221\pi$
$458$	47.1718	2.20419
$459$	1.79286	0.0836835
$460$	106.626	4.97146
$461$	28.6688	1.33524	0.667620	−	0.744502i	$-0.267313\pi$
$461$	28.6688	1.33524	0.667620	+	0.744502i	$0.267313\pi$
$462$	0	0
$463$	7.30345	0.339420	0.169710	−	0.985494i	$-0.445717\pi$
$463$	7.30345	0.339420	0.169710	+	0.985494i	$0.445717\pi$
$464$	−5.78228	−0.268436
$465$	−68.0415	−3.15535
$466$	−10.9879	−0.509006
$467$	28.0775	1.29927	0.649635	−	0.760246i	$-0.274922\pi$
$467$	28.0775	1.29927	0.649635	+	0.760246i	$0.274922\pi$
$468$	−142.538	−6.58880
$469$	0	0
$470$	8.67149	0.399986
$471$	−6.96882	−0.321106
$472$	−5.41180	−0.249098
$473$	6.49565	0.298670
$474$	46.5825	2.13961
$475$	−22.1551	−1.01654
$476$	0	0
$477$	−27.8067	−1.27318
$478$	18.1613	0.830677
$479$	−21.1717	−0.967361	−0.483680	−	0.875245i	$-0.660700\pi$
$479$	−21.1717	−0.967361	−0.483680	+	0.875245i	$0.660700\pi$
$480$	15.9822	0.729486
$481$	23.7052	1.08086
$482$	−74.7727	−3.40581
$483$	0	0
$484$	−3.41237	−0.155108
$485$	35.8236	1.62667
$486$	−33.3188	−1.51137
$487$	34.7065	1.57270	0.786352	−	0.617779i	$-0.211967\pi$
$487$	34.7065	1.57270	0.786352	+	0.617779i	$0.211967\pi$
$488$	−64.0616	−2.89993
$489$	14.5952	0.660018
$490$	0	0
$491$	5.88898	0.265766	0.132883	−	0.991132i	$-0.457577\pi$
$491$	5.88898	0.265766	0.132883	+	0.991132i	$0.457577\pi$
$492$	11.7737	0.530800
$493$	0.360979	0.0162577
$494$	−40.7878	−1.83513
$495$	60.7675	2.73130
$496$	31.1876	1.40036
$497$	0	0
$498$	−55.8522	−2.50280
$499$	22.7572	1.01875	0.509377	−	0.860543i	$-0.329876\pi$
$499$	22.7572	1.01875	0.509377	+	0.860543i	$0.329876\pi$
$500$	64.5263	2.88570
$501$	−15.5756	−0.695866
$502$	−71.6049	−3.19588
$503$	−9.33021	−0.416013	−0.208007	−	0.978127i	$-0.566698\pi$
$503$	−9.33021	−0.416013	−0.208007	+	0.978127i	$0.566698\pi$
$504$	0	0
$505$	−56.8210	−2.52850
$506$	−54.0939	−2.40477
$507$	−93.9087	−4.17063
$508$	−7.81359	−0.346672
$509$	−5.49076	−0.243374	−0.121687	−	0.992569i	$-0.538830\pi$
$509$	−5.49076	−0.243374	−0.121687	+	0.992569i	$0.538830\pi$
$510$	−8.09006	−0.358234
$511$	0	0
$512$	44.7474	1.97758
$513$	14.2224	0.627935
$514$	57.6304	2.54197
$515$	56.9773	2.51072
$516$	−23.9734	−1.05537
$517$	−2.96758	−0.130514
$518$	0	0
$519$	15.5722	0.683545
$520$	135.750	5.95305
$521$	−8.05796	−0.353026	−0.176513	−	0.984298i	$-0.556482\pi$
$521$	−8.05796	−0.353026	−0.176513	+	0.984298i	$0.556482\pi$
$522$	14.8349	0.649306
$523$	35.1810	1.53836	0.769179	−	0.639033i	$-0.220665\pi$
$523$	35.1810	1.53836	0.769179	+	0.639033i	$0.220665\pi$
$524$	37.2597	1.62770
$525$	0	0
$526$	−51.9232	−2.26396
$527$	−1.94700	−0.0848125
$528$	−44.3484	−1.93002
$529$	23.7861	1.03418
$530$	51.1679	2.22259
$531$	5.15413	0.223670
$532$	0	0
$533$	6.78719	0.293986
$534$	104.945	4.54140
$535$	21.4948	0.929300
$536$	−42.1262	−1.81958
$537$	60.1212	2.59442
$538$	−57.8739	−2.49512
$539$	0	0
$540$	−91.4577	−3.93571
$541$	4.47632	0.192452	0.0962259	−	0.995360i	$-0.469323\pi$
$541$	4.47632	0.192452	0.0962259	+	0.995360i	$0.469323\pi$
$542$	−39.4825	−1.69592
$543$	25.7105	1.10334
$544$	0.457329	0.0196078
$545$	−21.6239	−0.926267
$546$	0	0
$547$	−26.3522	−1.12674	−0.563369	−	0.826205i	$-0.690495\pi$
$547$	−26.3522	−1.12674	−0.563369	+	0.826205i	$0.690495\pi$
$548$	17.8222	0.761328
$549$	61.0115	2.60391
$550$	−72.2779	−3.08194
$551$	2.86358	0.121993
$552$	103.328	4.39794
$553$	0	0
$554$	28.8829	1.22712
$555$	37.2986	1.58324
$556$	−10.3224	−0.437768
$557$	15.9827	0.677207	0.338603	−	0.940929i	$-0.390045\pi$
$557$	15.9827	0.677207	0.338603	+	0.940929i	$0.390045\pi$
$558$	−80.0142	−3.38727
$559$	−13.8199	−0.584521
$560$	0	0
$561$	2.76861	0.116891
$562$	−21.2321	−0.895623
$563$	43.6094	1.83792	0.918959	−	0.394354i	$-0.129031\pi$
$563$	43.6094	1.83792	0.918959	+	0.394354i	$0.129031\pi$
$564$	10.9524	0.461180
$565$	−29.3719	−1.23568
$566$	13.5602	0.569978
$567$	0	0
$568$	8.73221	0.366395
$569$	44.5802	1.86890	0.934450	−	0.356094i	$-0.115892\pi$
$569$	44.5802	1.86890	0.934450	+	0.356094i	$0.115892\pi$
$570$	−64.1770	−2.68808
$571$	−1.27082	−0.0531820	−0.0265910	−	0.999646i	$-0.508465\pi$
$571$	−1.27082	−0.0531820	−0.0265910	+	0.999646i	$0.508465\pi$
$572$	−89.7609	−3.75309
$573$	−48.5506	−2.02823
$574$	0	0
$575$	62.5135	2.60699
$576$	−30.7992	−1.28330
$577$	40.5925	1.68989	0.844944	−	0.534854i	$-0.179634\pi$
$577$	40.5925	1.68989	0.844944	+	0.534854i	$0.179634\pi$
$578$	41.9121	1.74331
$579$	−61.4438	−2.55352
$580$	−18.4144	−0.764615
$581$	0	0
$582$	67.0751	2.78035
$583$	−17.5108	−0.725225
$584$	33.1487	1.37170
$585$	−129.287	−5.34535
$586$	−25.0210	−1.03361
$587$	−5.02174	−0.207269	−0.103635	−	0.994615i	$-0.533047\pi$
$587$	−5.02174	−0.207269	−0.103635	+	0.994615i	$0.533047\pi$
$588$	0	0
$589$	−15.4452	−0.636407
$590$	−9.48426	−0.390461
$591$	−12.0118	−0.494099
$592$	−17.0962	−0.702651
$593$	−19.0462	−0.782135	−0.391067	−	0.920362i	$-0.627894\pi$
$593$	−19.0462	−0.782135	−0.391067	+	0.920362i	$0.627894\pi$
$594$	46.3987	1.90376
$595$	0	0
$596$	−27.4360	−1.12382
$597$	−64.9366	−2.65768
$598$	115.088	4.70632
$599$	−0.832693	−0.0340229	−0.0170115	−	0.999855i	$-0.505415\pi$
$599$	−0.832693	−0.0340229	−0.0170115	+	0.999855i	$0.505415\pi$
$600$	138.062	5.63638
$601$	−32.2165	−1.31414	−0.657070	−	0.753829i	$-0.728205\pi$
$601$	−32.2165	−1.31414	−0.657070	+	0.753829i	$0.728205\pi$
$602$	0	0
$603$	40.1205	1.63383
$604$	−32.1390	−1.30772
$605$	−3.09514	−0.125835
$606$	−106.390	−4.32180
$607$	14.1151	0.572913	0.286457	−	0.958093i	$-0.407523\pi$
$607$	14.1151	0.572913	0.286457	+	0.958093i	$0.407523\pi$
$608$	3.62791	0.147131
$609$	0	0
$610$	−112.269	−4.54564
$611$	6.31373	0.255426
$612$	−6.41755	−0.259414
$613$	−30.1771	−1.21884	−0.609421	−	0.792847i	$-0.708598\pi$
$613$	−30.1771	−1.21884	−0.609421	+	0.792847i	$0.708598\pi$
$614$	53.7103	2.16757
$615$	10.6792	0.430627
$616$	0	0
$617$	20.0146	0.805757	0.402879	−	0.915253i	$-0.368010\pi$
$617$	20.0146	0.805757	0.402879	+	0.915253i	$0.368010\pi$
$618$	106.683	4.29141
$619$	11.1529	0.448273	0.224136	−	0.974558i	$-0.428044\pi$
$619$	11.1529	0.448273	0.224136	+	0.974558i	$0.428044\pi$
$620$	99.3206	3.98881
$621$	−40.1305	−1.61038
$622$	71.8491	2.88089
$623$	0	0
$624$	94.3542	3.77719
$625$	12.8310	0.513240
$626$	18.1278	0.724532
$627$	21.9629	0.877112
$628$	10.1724	0.405924
$629$	1.06729	0.0425557
$630$	0	0
$631$	42.3540	1.68608	0.843042	−	0.537848i	$-0.180762\pi$
$631$	42.3540	1.68608	0.843042	+	0.537848i	$0.180762\pi$
$632$	−35.1927	−1.39989
$633$	−18.9692	−0.753958
$634$	−39.7317	−1.57795
$635$	−7.08722	−0.281248
$636$	64.6270	2.56263
$637$	0	0
$638$	9.34206	0.369856
$639$	−8.31644	−0.328993
$640$	67.9294	2.68515
$641$	−16.1410	−0.637532	−0.318766	−	0.947833i	$-0.603268\pi$
$641$	−16.1410	−0.637532	−0.318766	+	0.947833i	$0.603268\pi$
$642$	40.2462	1.58839
$643$	17.9294	0.707065	0.353533	−	0.935422i	$-0.384980\pi$
$643$	17.9294	0.707065	0.353533	+	0.935422i	$0.384980\pi$
$644$	0	0
$645$	−21.7448	−0.856199
$646$	−1.83641	−0.0722527
$647$	26.7348	1.05105	0.525527	−	0.850777i	$-0.323868\pi$
$647$	26.7348	1.05105	0.525527	+	0.850777i	$0.323868\pi$
$648$	−7.79270	−0.306126
$649$	3.24573	0.127406
$650$	153.776	6.03159
$651$	0	0
$652$	−21.3047	−0.834356
$653$	11.4776	0.449153	0.224576	−	0.974457i	$-0.427900\pi$
$653$	11.4776	0.449153	0.224576	+	0.974457i	$0.427900\pi$
$654$	−40.4880	−1.58321
$655$	33.7959	1.32051
$656$	−4.89494	−0.191115
$657$	−31.5704	−1.23168
$658$	0	0
$659$	0.958982	0.0373566	0.0186783	−	0.999826i	$-0.494054\pi$
$659$	0.958982	0.0373566	0.0186783	+	0.999826i	$0.494054\pi$
$660$	−141.233	−5.49748
$661$	3.11324	0.121091	0.0605455	−	0.998165i	$-0.480716\pi$
$661$	3.11324	0.121091	0.0605455	+	0.998165i	$0.480716\pi$
$662$	−39.2111	−1.52398
$663$	−5.89040	−0.228764
$664$	42.1958	1.63751
$665$	0	0
$666$	43.8617	1.69961
$667$	−8.07999	−0.312859
$668$	22.7358	0.879674
$669$	34.1792	1.32145
$670$	−73.8268	−2.85218
$671$	38.4210	1.48323
$672$	0	0
$673$	14.8974	0.574252	0.287126	−	0.957893i	$-0.407300\pi$
$673$	14.8974	0.574252	0.287126	+	0.957893i	$0.407300\pi$
$674$	−7.22651	−0.278355
$675$	−53.6206	−2.06386
$676$	137.079	5.27227
$677$	36.5891	1.40623	0.703116	−	0.711075i	$-0.251791\pi$
$677$	36.5891	1.40623	0.703116	+	0.711075i	$0.251791\pi$
$678$	−54.9951	−2.11208
$679$	0	0
$680$	6.11197	0.234383
$681$	−51.3660	−1.96835
$682$	−50.3878	−1.92945
$683$	−11.8363	−0.452904	−0.226452	−	0.974022i	$-0.572713\pi$
$683$	−11.8363	−0.452904	−0.226452	+	0.974022i	$0.572713\pi$
$684$	−50.9092	−1.94656
$685$	16.1654	0.617649
$686$	0	0
$687$	54.0411	2.06180
$688$	9.96696	0.379987
$689$	37.2555	1.41932
$690$	181.084	6.89375
$691$	−12.8197	−0.487685	−0.243843	−	0.969815i	$-0.578408\pi$
$691$	−12.8197	−0.487685	−0.243843	+	0.969815i	$0.578408\pi$
$692$	−22.7309	−0.864099
$693$	0	0
$694$	1.85923	0.0705754
$695$	−9.36281	−0.355152
$696$	−17.8448	−0.676407
$697$	0.305584	0.0115748
$698$	−36.4485	−1.37960
$699$	−12.5880	−0.476122
$700$	0	0
$701$	−27.1462	−1.02530	−0.512649	−	0.858599i	$-0.671336\pi$
$701$	−27.1462	−1.02530	−0.512649	+	0.858599i	$0.671336\pi$
$702$	−98.7163	−3.72581
$703$	8.46663	0.319325
$704$	−19.3953	−0.730988
$705$	9.93424	0.374145
$706$	12.3884	0.466243
$707$	0	0
$708$	−11.9790	−0.450197
$709$	33.0846	1.24252	0.621258	−	0.783606i	$-0.286622\pi$
$709$	33.0846	1.24252	0.621258	+	0.783606i	$0.286622\pi$
$710$	15.3033	0.574323
$711$	33.5170	1.25699
$712$	−79.2848	−2.97132
$713$	43.5806	1.63211
$714$	0	0
$715$	−81.4164	−3.04480
$716$	−87.7593	−3.27972
$717$	20.8059	0.777012
$718$	46.9676	1.75281
$719$	−13.0958	−0.488390	−0.244195	−	0.969726i	$-0.578524\pi$
$719$	−13.0958	−0.488390	−0.244195	+	0.969726i	$0.578524\pi$
$720$	93.2419	3.47492
$721$	0	0
$722$	32.5338	1.21078
$723$	−85.6613	−3.18578
$724$	−37.5298	−1.39478
$725$	−10.7961	−0.400958
$726$	−5.79526	−0.215082
$727$	−38.7636	−1.43766	−0.718831	−	0.695185i	$-0.755322\pi$
$727$	−38.7636	−1.43766	−0.718831	+	0.695185i	$0.755322\pi$
$728$	0	0
$729$	−42.5658	−1.57651
$730$	58.0936	2.15014
$731$	−0.622222	−0.0230137
$732$	−141.800	−5.24107
$733$	−9.82849	−0.363023	−0.181512	−	0.983389i	$-0.558099\pi$
$733$	−9.82849	−0.363023	−0.181512	+	0.983389i	$0.558099\pi$
$734$	−79.2365	−2.92467
$735$	0	0
$736$	−10.2366	−0.377328
$737$	25.2653	0.930658
$738$	12.5583	0.462279
$739$	−13.9988	−0.514953	−0.257477	−	0.966285i	$-0.582891\pi$
$739$	−13.9988	−0.514953	−0.257477	+	0.966285i	$0.582891\pi$
$740$	−54.4450	−2.00144
$741$	−46.7274	−1.71657
$742$	0	0
$743$	−40.7133	−1.49363	−0.746813	−	0.665034i	$-0.768417\pi$
$743$	−40.7133	−1.49363	−0.746813	+	0.665034i	$0.768417\pi$
$744$	96.2488	3.52865
$745$	−24.8854	−0.911732
$746$	−31.2114	−1.14273
$747$	−40.1867	−1.47036
$748$	−4.04135	−0.147767
$749$	0	0
$750$	109.586	4.00151
$751$	12.1534	0.443483	0.221742	−	0.975105i	$-0.428826\pi$
$751$	12.1534	0.443483	0.221742	+	0.975105i	$0.428826\pi$
$752$	−4.55347	−0.166048
$753$	−82.0321	−2.98942
$754$	−19.8758	−0.723835
$755$	−29.1513	−1.06092
$756$	0	0
$757$	36.8139	1.33803	0.669013	−	0.743251i	$-0.266717\pi$
$757$	36.8139	1.33803	0.669013	+	0.743251i	$0.266717\pi$
$758$	22.6970	0.824391
$759$	−61.9712	−2.24941
$760$	48.4851	1.75874
$761$	22.7603	0.825061	0.412530	−	0.910944i	$-0.364645\pi$
$761$	22.7603	0.825061	0.412530	+	0.910944i	$0.364645\pi$
$762$	−13.2699	−0.480718
$763$	0	0
$764$	70.8697	2.56397
$765$	−5.82096	−0.210457
$766$	−3.11361	−0.112499
$767$	−6.90551	−0.249344
$768$	92.6554	3.34341
$769$	−20.7728	−0.749086	−0.374543	−	0.927210i	$-0.622200\pi$
$769$	−20.7728	−0.749086	−0.374543	+	0.927210i	$0.622200\pi$
$770$	0	0
$771$	66.0226	2.37775
$772$	89.6898	3.22801
$773$	−29.0604	−1.04523	−0.522615	−	0.852569i	$-0.675044\pi$
$773$	−29.0604	−1.04523	−0.522615	+	0.852569i	$0.675044\pi$
$774$	−25.5710	−0.919131
$775$	58.2305	2.09170
$776$	−50.6746	−1.81911
$777$	0	0
$778$	−29.7611	−1.06699
$779$	2.42414	0.0868538
$780$	300.482	10.7590
$781$	−5.23715	−0.187400
$782$	5.18169	0.185297
$783$	6.93056	0.247678
$784$	0	0
$785$	9.22678	0.329318
$786$	63.2785	2.25707
$787$	33.2253	1.18435	0.592177	−	0.805808i	$-0.298269\pi$
$787$	33.2253	1.18435	0.592177	+	0.805808i	$0.298269\pi$
$788$	17.5337	0.624612
$789$	−59.4844	−2.11770
$790$	−61.6756	−2.19432
$791$	0	0
$792$	−85.9593	−3.05443
$793$	−81.7433	−2.90279
$794$	−78.0430	−2.76964
$795$	58.6190	2.07900
$796$	94.7884	3.35968
$797$	−22.1771	−0.785551	−0.392776	−	0.919634i	$-0.628485\pi$
$797$	−22.1771	−0.785551	−0.392776	+	0.919634i	$0.628485\pi$
$798$	0	0
$799$	0.284267	0.0100566
$800$	−13.6777	−0.483581
$801$	75.5098	2.66801
$802$	57.9613	2.04669
$803$	−19.8810	−0.701585
$804$	−93.2460	−3.28853
$805$	0	0
$806$	107.203	3.77607
$807$	−66.3016	−2.33393
$808$	80.3767	2.82764
$809$	−18.0630	−0.635062	−0.317531	−	0.948248i	$-0.602854\pi$
$809$	−18.0630	−0.635062	−0.317531	+	0.948248i	$0.602854\pi$
$810$	−13.6568	−0.479852
$811$	−7.88978	−0.277048	−0.138524	−	0.990359i	$-0.544236\pi$
$811$	−7.88978	−0.277048	−0.138524	+	0.990359i	$0.544236\pi$
$812$	0	0
$813$	−45.2321	−1.58636
$814$	27.6212	0.968124
$815$	−19.3242	−0.676896
$816$	4.24816	0.148715
$817$	−4.93597	−0.172688
$818$	61.9113	2.16468
$819$	0	0
$820$	−15.5885	−0.544374
$821$	−44.2252	−1.54347	−0.771735	−	0.635944i	$-0.780611\pi$
$821$	−44.2252	−1.54347	−0.771735	+	0.635944i	$0.780611\pi$
$822$	30.2677	1.05571
$823$	10.8297	0.377500	0.188750	−	0.982025i	$-0.439556\pi$
$823$	10.8297	0.377500	0.188750	+	0.982025i	$0.439556\pi$
$824$	−80.5978	−2.80776
$825$	−82.8031	−2.88284
$826$	0	0
$827$	−49.7680	−1.73060	−0.865301	−	0.501252i	$-0.832873\pi$
$827$	−49.7680	−1.73060	−0.865301	+	0.501252i	$0.832873\pi$
$828$	143.647	4.99209
$829$	−28.7741	−0.999366	−0.499683	−	0.866208i	$-0.666550\pi$
$829$	−28.7741	−0.999366	−0.499683	+	0.866208i	$0.666550\pi$
$830$	73.9488	2.56680
$831$	33.0889	1.14784
$832$	41.2648	1.43060
$833$	0	0
$834$	−17.5307	−0.607038
$835$	20.6222	0.713661
$836$	−32.0593	−1.10879
$837$	−37.3810	−1.29208
$838$	−10.8131	−0.373531
$839$	46.2897	1.59810	0.799048	−	0.601267i	$-0.205337\pi$
$839$	46.2897	1.59810	0.799048	+	0.601267i	$0.205337\pi$
$840$	0	0
$841$	−27.6046	−0.951882
$842$	−71.3425	−2.45863
$843$	−24.3240	−0.837763
$844$	27.6895	0.953110
$845$	124.336	4.27728
$846$	11.6823	0.401646
$847$	0	0
$848$	−26.8687	−0.922675
$849$	15.5349	0.533155
$850$	6.92354	0.237476
$851$	−23.8898	−0.818930
$852$	19.3287	0.662189
$853$	−41.9319	−1.43572	−0.717860	−	0.696188i	$-0.754878\pi$
$853$	−41.9319	−1.43572	−0.717860	+	0.696188i	$0.754878\pi$
$854$	0	0
$855$	−46.1766	−1.57921
$856$	−30.4056	−1.03924
$857$	12.3276	0.421104	0.210552	−	0.977583i	$-0.432474\pi$
$857$	12.3276	0.421104	0.210552	+	0.977583i	$0.432474\pi$
$858$	−152.442	−5.20428
$859$	9.76045	0.333022	0.166511	−	0.986040i	$-0.446750\pi$
$859$	9.76045	0.333022	0.166511	+	0.986040i	$0.446750\pi$
$860$	31.7410	1.08236
$861$	0	0
$862$	−33.3118	−1.13460
$863$	−52.8763	−1.79993	−0.899965	−	0.435963i	$-0.856408\pi$
$863$	−52.8763	−1.79993	−0.899965	+	0.435963i	$0.856408\pi$
$864$	8.78041	0.298716
$865$	−20.6178	−0.701025
$866$	−35.6489	−1.21140
$867$	48.0154	1.63069
$868$	0	0
$869$	21.1068	0.716000
$870$	−31.2733	−1.06027
$871$	−53.7535	−1.82137
$872$	30.5883	1.03585
$873$	48.2618	1.63342
$874$	41.1054	1.39041
$875$	0	0
$876$	73.3744	2.47909
$877$	26.2640	0.886873	0.443437	−	0.896306i	$-0.353759\pi$
$877$	26.2640	0.886873	0.443437	+	0.896306i	$0.353759\pi$
$878$	−9.51486	−0.321111
$879$	−28.6646	−0.966832
$880$	58.7177	1.97937
$881$	−56.0153	−1.88720	−0.943601	−	0.331084i	$-0.892586\pi$
$881$	−56.0153	−1.88720	−0.943601	+	0.331084i	$0.892586\pi$
$882$	0	0
$883$	47.5144	1.59899	0.799493	−	0.600676i	$-0.205102\pi$
$883$	47.5144	1.59899	0.799493	+	0.600676i	$0.205102\pi$
$884$	8.59825	0.289190
$885$	−10.8654	−0.365235
$886$	96.1144	3.22903
$887$	−21.0769	−0.707692	−0.353846	−	0.935304i	$-0.615126\pi$
$887$	−21.0769	−0.707692	−0.353846	+	0.935304i	$0.615126\pi$
$888$	−52.7611	−1.77054
$889$	0	0
$890$	−138.948	−4.65754
$891$	4.67368	0.156574
$892$	−49.8917	−1.67050
$893$	2.25503	0.0754619
$894$	−46.5948	−1.55836
$895$	−79.6010	−2.66077
$896$	0	0
$897$	131.848	4.40227
$898$	−5.89078	−0.196578
$899$	−7.52640	−0.251019
$900$	191.935	6.39784
$901$	1.67737	0.0558814
$902$	7.90843	0.263322
$903$	0	0
$904$	41.5483	1.38188
$905$	−34.0409	−1.13156
$906$	−54.5820	−1.81337
$907$	−15.1726	−0.503797	−0.251899	−	0.967754i	$-0.581055\pi$
$907$	−15.1726	−0.503797	−0.251899	+	0.967754i	$0.581055\pi$
$908$	74.9793	2.48828
$909$	−76.5497	−2.53899
$910$	0	0
$911$	3.99346	0.132309	0.0661546	−	0.997809i	$-0.478927\pi$
$911$	3.99346	0.132309	0.0661546	+	0.997809i	$0.478927\pi$
$912$	33.6999	1.11592
$913$	−25.3070	−0.837539
$914$	−37.7079	−1.24727
$915$	−128.618	−4.25197
$916$	−78.8841	−2.60640
$917$	0	0
$918$	−4.44456	−0.146692
$919$	−14.9056	−0.491692	−0.245846	−	0.969309i	$-0.579066\pi$
$919$	−14.9056	−0.491692	−0.245846	+	0.969309i	$0.579066\pi$
$920$	−136.807	−4.51040
$921$	61.5317	2.02754
$922$	−71.0711	−2.34060
$923$	11.1424	0.366756
$924$	0	0
$925$	−31.9204	−1.04954
$926$	−18.1055	−0.594984
$927$	76.7603	2.52114
$928$	1.76787	0.0580333
$929$	−20.0118	−0.656566	−0.328283	−	0.944579i	$-0.606470\pi$
$929$	−20.0118	−0.656566	−0.328283	+	0.944579i	$0.606470\pi$
$930$	168.677	5.53115
$931$	0	0
$932$	18.3748	0.601886
$933$	82.3119	2.69477
$934$	−69.6051	−2.27755
$935$	−3.66566	−0.119880
$936$	182.884	5.97775
$937$	−8.76669	−0.286395	−0.143198	−	0.989694i	$-0.545738\pi$
$937$	−8.76669	−0.286395	−0.143198	+	0.989694i	$0.545738\pi$
$938$	0	0
$939$	20.7676	0.677724
$940$	−14.5011	−0.472973
$941$	−28.0446	−0.914227	−0.457114	−	0.889408i	$-0.651117\pi$
$941$	−28.0446	−0.914227	−0.457114	+	0.889408i	$0.651117\pi$
$942$	17.2760	0.562881
$943$	−6.84004	−0.222742
$944$	4.98027	0.162094
$945$	0	0
$946$	−16.1030	−0.523552
$947$	−21.4566	−0.697246	−0.348623	−	0.937263i	$-0.613351\pi$
$947$	−21.4566	−0.697246	−0.348623	+	0.937263i	$0.613351\pi$
$948$	−77.8986	−2.53003
$949$	42.2981	1.37305
$950$	54.9232	1.78194
$951$	−45.5175	−1.47601
$952$	0	0
$953$	52.5017	1.70070	0.850349	−	0.526219i	$-0.176391\pi$
$953$	52.5017	1.70070	0.850349	+	0.526219i	$0.176391\pi$
$954$	68.9338	2.23181
$955$	64.2814	2.08010
$956$	−30.3706	−0.982255
$957$	10.7025	0.345962
$958$	52.4855	1.69573
$959$	0	0
$960$	64.9275	2.09553
$961$	9.59474	0.309508
$962$	−58.7660	−1.89469
$963$	28.9579	0.933156
$964$	125.040	4.02728
$965$	81.3520	2.61881
$966$	0	0
$967$	−17.9210	−0.576301	−0.288151	−	0.957585i	$-0.593040\pi$
$967$	−17.9210	−0.576301	−0.288151	+	0.957585i	$0.593040\pi$
$968$	4.37827	0.140723
$969$	−2.10383	−0.0675849
$970$	−88.8080	−2.85145
$971$	36.6069	1.17477	0.587386	−	0.809307i	$-0.300157\pi$
$971$	36.6069	1.17477	0.587386	+	0.809307i	$0.300157\pi$
$972$	55.7180	1.78716
$973$	0	0
$974$	−86.0388	−2.75686
$975$	176.169	5.64193
$976$	58.9534	1.88705
$977$	−38.5076	−1.23197	−0.615983	−	0.787759i	$-0.711241\pi$
$977$	−38.5076	−1.23197	−0.615983	+	0.787759i	$0.711241\pi$
$978$	−36.1820	−1.15697
$979$	47.5511	1.51974
$980$	0	0
$981$	−29.1319	−0.930111
$982$	−14.5990	−0.465873
$983$	−10.2856	−0.328061	−0.164030	−	0.986455i	$-0.552450\pi$
$983$	−10.2856	−0.328061	−0.164030	+	0.986455i	$0.552450\pi$
$984$	−15.1064	−0.481574
$985$	15.9037	0.506734
$986$	−0.894881	−0.0284988
$987$	0	0
$988$	68.2083	2.17000
$989$	13.9275	0.442870
$990$	−150.645	−4.78781
$991$	45.2544	1.43755	0.718777	−	0.695241i	$-0.244702\pi$
$991$	45.2544	1.43755	0.718777	+	0.695241i	$0.244702\pi$
$992$	−9.53529	−0.302746
$993$	−44.9211	−1.42553
$994$	0	0
$995$	85.9766	2.72564
$996$	93.4000	2.95949
$997$	−13.4537	−0.426084	−0.213042	−	0.977043i	$-0.568337\pi$
$997$	−13.4537	−0.426084	−0.213042	+	0.977043i	$0.568337\pi$
$998$	−56.4160	−1.78582
$999$	20.4913	0.648315

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2009.2.a.o.1.1		6
7.6	odd	2		287.2.a.f.1.1	✓	6
21.20	even	2		2583.2.a.t.1.6		6
28.27	even	2		4592.2.a.bg.1.1		6
35.34	odd	2		7175.2.a.p.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.a.f.1.1	✓	6	7.6	odd	2
2009.2.a.o.1.1		6	1.1	even	1	trivial
2583.2.a.t.1.6		6	21.20	even	2
4592.2.a.bg.1.1		6	28.27	even	2
7175.2.a.p.1.6		6	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)

\(f(q)\)	\(=\)	\(q-2.47904 q^{2} -2.84004 q^{3} +4.14562 q^{4} +3.76023 q^{5} +7.04056 q^{6} -5.31907 q^{8} +5.06582 q^{9} +O(q^{10})\)	\(q-2.47904 q^{2} -2.84004 q^{3} +4.14562 q^{4} +3.76023 q^{5} +7.04056 q^{6} -5.31907 q^{8} +5.06582 q^{9} -9.32175 q^{10} +3.19012 q^{11} -11.7737 q^{12} -6.78719 q^{13} -10.6792 q^{15} +4.89494 q^{16} -0.305584 q^{17} -12.5583 q^{18} -2.42414 q^{19} +15.5885 q^{20} -7.90843 q^{22} +6.84004 q^{23} +15.1064 q^{24} +9.13935 q^{25} +16.8257 q^{26} -5.86700 q^{27} -1.18128 q^{29} +26.4741 q^{30} +6.37140 q^{31} -1.49658 q^{32} -9.06007 q^{33} +0.757553 q^{34} +21.0010 q^{36} -3.49263 q^{37} +6.00953 q^{38} +19.2759 q^{39} -20.0010 q^{40} -1.00000 q^{41} +2.03618 q^{43} +13.2250 q^{44} +19.0487 q^{45} -16.9567 q^{46} -0.930242 q^{47} -13.9018 q^{48} -22.6568 q^{50} +0.867869 q^{51} -28.1371 q^{52} -5.48908 q^{53} +14.5445 q^{54} +11.9956 q^{55} +6.88465 q^{57} +2.92843 q^{58} +1.01743 q^{59} -44.2719 q^{60} +12.0438 q^{61} -15.7949 q^{62} -6.07981 q^{64} -25.5214 q^{65} +22.4602 q^{66} +7.91984 q^{67} -1.26683 q^{68} -19.4260 q^{69} -1.64168 q^{71} -26.9455 q^{72} -6.23205 q^{73} +8.65837 q^{74} -25.9561 q^{75} -10.0496 q^{76} -47.7856 q^{78} +6.61631 q^{79} +18.4061 q^{80} +1.46505 q^{81} +2.47904 q^{82} -7.93292 q^{83} -1.14907 q^{85} -5.04776 q^{86} +3.35488 q^{87} -16.9685 q^{88} +14.9057 q^{89} -47.2223 q^{90} +28.3562 q^{92} -18.0950 q^{93} +2.30610 q^{94} -9.11532 q^{95} +4.25033 q^{96} +9.52696 q^{97} +16.1606 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{2} + 4 q^{3} + 9 q^{4} + q^{5} + 4 q^{6} + 3 q^{8} + 14 q^{9}+O(q^{10}) \) 6 * q - q^2 + 4 * q^3 + 9 * q^4 + q^5 + 4 * q^6 + 3 * q^8 + 14 * q^9	\( 6 q - q^{2} + 4 q^{3} + 9 q^{4} + q^{5} + 4 q^{6} + 3 q^{8} + 14 q^{9} - 10 q^{10} + 6 q^{11} - 9 q^{12} - 7 q^{13} - 13 q^{15} + 7 q^{16} - 7 q^{17} - 5 q^{18} - 2 q^{19} - 11 q^{20} + 15 q^{22} + 20 q^{23} + 36 q^{24} + 29 q^{25} + 43 q^{26} - 2 q^{27} - 9 q^{29} + 13 q^{30} + 27 q^{31} - 10 q^{32} - 17 q^{33} - 6 q^{34} + 29 q^{36} + 19 q^{37} + 23 q^{38} + q^{39} - 23 q^{40} - 6 q^{41} + 19 q^{43} + 21 q^{44} + 35 q^{45} - 8 q^{46} + 19 q^{47} + 9 q^{48} - 58 q^{50} - 19 q^{51} + 5 q^{53} + 37 q^{54} - 3 q^{55} + 37 q^{57} + 13 q^{58} + 7 q^{59} - 110 q^{60} + 12 q^{61} - 37 q^{64} - 13 q^{65} + 54 q^{66} + 27 q^{67} - 31 q^{68} - 16 q^{69} - 6 q^{71} + 5 q^{72} - 52 q^{73} - 14 q^{74} + 46 q^{75} - 13 q^{76} - 45 q^{78} + 26 q^{80} - 22 q^{81} + q^{82} - 12 q^{83} + 25 q^{85} - 10 q^{86} - 42 q^{87} - 2 q^{88} + 38 q^{89} - 93 q^{90} + 45 q^{92} + 33 q^{93} + 8 q^{94} + q^{95} + 12 q^{96} - 8 q^{97} + q^{99}+O(q^{100}) \) 6 * q - q^2 + 4 * q^3 + 9 * q^4 + q^5 + 4 * q^6 + 3 * q^8 + 14 * q^9 - 10 * q^10 + 6 * q^11 - 9 * q^12 - 7 * q^13 - 13 * q^15 + 7 * q^16 - 7 * q^17 - 5 * q^18 - 2 * q^19 - 11 * q^20 + 15 * q^22 + 20 * q^23 + 36 * q^24 + 29 * q^25 + 43 * q^26 - 2 * q^27 - 9 * q^29 + 13 * q^30 + 27 * q^31 - 10 * q^32 - 17 * q^33 - 6 * q^34 + 29 * q^36 + 19 * q^37 + 23 * q^38 + q^39 - 23 * q^40 - 6 * q^41 + 19 * q^43 + 21 * q^44 + 35 * q^45 - 8 * q^46 + 19 * q^47 + 9 * q^48 - 58 * q^50 - 19 * q^51 + 5 * q^53 + 37 * q^54 - 3 * q^55 + 37 * q^57 + 13 * q^58 + 7 * q^59 - 110 * q^60 + 12 * q^61 - 37 * q^64 - 13 * q^65 + 54 * q^66 + 27 * q^67 - 31 * q^68 - 16 * q^69 - 6 * q^71 + 5 * q^72 - 52 * q^73 - 14 * q^74 + 46 * q^75 - 13 * q^76 - 45 * q^78 + 26 * q^80 - 22 * q^81 + q^82 - 12 * q^83 + 25 * q^85 - 10 * q^86 - 42 * q^87 - 2 * q^88 + 38 * q^89 - 93 * q^90 + 45 * q^92 + 33 * q^93 + 8 * q^94 + q^95 + 12 * q^96 - 8 * q^97 + q^99

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