LMFDB - Embedded newform 2009.2.a.m.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("2009.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$16.0419457661$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.233489.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 6x^{3} + x^{2} + 5x - 1 $ x^5 - x^4 - 6x^3 + x^2 + 5x - 1
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			1.3
Root			$-1.72658$ of defining polynomial
Character	$\chi$	$=$	2009.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.12846 q^{2} -2.92944 q^{3} -0.726576 q^{4} +2.92944 q^{5} +3.30576 q^{6} +3.07683 q^{8} +5.58161 q^{9} +O(q^{10})$	\(q-1.12846 q^{2} -2.92944 q^{3} -0.726576 q^{4} +2.92944 q^{5} +3.30576 q^{6} +3.07683 q^{8} +5.58161 q^{9} -3.30576 q^{10} -3.80098 q^{11} +2.12846 q^{12} +2.92944 q^{13} -8.58161 q^{15} -2.01893 q^{16} -2.23136 q^{17} -6.29863 q^{18} -6.13230 q^{19} -2.12846 q^{20} +4.28925 q^{22} +1.05547 q^{23} -9.01340 q^{24} +3.58161 q^{25} -3.30576 q^{26} -7.56268 q^{27} +3.63708 q^{29} +9.68401 q^{30} +6.54374 q^{31} -3.87538 q^{32} +11.1347 q^{33} +2.51800 q^{34} -4.05547 q^{36} -9.35410 q^{37} +6.92006 q^{38} -8.58161 q^{39} +9.01340 q^{40} +1.00000 q^{41} -5.51434 q^{43} +2.76170 q^{44} +16.3510 q^{45} -1.19105 q^{46} -1.77249 q^{47} +5.91435 q^{48} -4.04171 q^{50} +6.53662 q^{51} -2.12846 q^{52} -0.934132 q^{53} +8.53419 q^{54} -11.1347 q^{55} +17.9642 q^{57} -4.10430 q^{58} +13.3106 q^{59} +6.23520 q^{60} +14.3579 q^{61} -7.38436 q^{62} +8.41108 q^{64} +8.58161 q^{65} -12.5651 q^{66} +10.4770 q^{67} +1.62125 q^{68} -3.09193 q^{69} -9.53905 q^{71} +17.1737 q^{72} +11.7652 q^{73} +10.5557 q^{74} -10.4921 q^{75} +4.45558 q^{76} +9.68401 q^{78} -15.0689 q^{79} -5.91435 q^{80} +5.40957 q^{81} -1.12846 q^{82} +1.86216 q^{83} -6.53662 q^{85} +6.22271 q^{86} -10.6546 q^{87} -11.6950 q^{88} -16.2206 q^{89} -18.4515 q^{90} -0.766878 q^{92} -19.1695 q^{93} +2.00018 q^{94} -17.9642 q^{95} +11.3527 q^{96} +7.70326 q^{97} -21.2156 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 2 q^{2} + 2 q^{3} + 6 q^{4} - 2 q^{5} - q^{6} - 3 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q - 2 * q^2 + 2 * q^3 + 6 * q^4 - 2 * q^5 - q^6 - 3 * q^8 + 5 * q^9	$ 5 q - 2 q^{2} + 2 q^{3} + 6 q^{4} - 2 q^{5} - q^{6} - 3 q^{8} + 5 q^{9} + q^{10} - 6 q^{11} + 7 q^{12} - 2 q^{13} - 20 q^{15} - 12 q^{16} + 3 q^{17} - 8 q^{18} - 7 q^{19} - 7 q^{20} - 13 q^{22} - 16 q^{24} - 5 q^{25} + q^{26} - 13 q^{27} - 10 q^{29} + 14 q^{30} + 6 q^{31} - 3 q^{32} + 17 q^{33} - q^{34} - 15 q^{36} - 18 q^{37} + 7 q^{38} - 20 q^{39} + 16 q^{40} + 5 q^{41} - 14 q^{43} + 2 q^{44} + 7 q^{45} - 3 q^{46} - 3 q^{47} - 9 q^{48} - 4 q^{50} - 7 q^{52} - 9 q^{53} + 25 q^{54} - 17 q^{55} + 31 q^{57} - 5 q^{58} + 19 q^{59} - 3 q^{60} + 23 q^{61} - 36 q^{62} - q^{64} + 20 q^{65} - 23 q^{66} - 11 q^{67} + 24 q^{68} - 19 q^{69} + 25 q^{72} - 13 q^{73} + 2 q^{74} - 11 q^{75} - 12 q^{76} + 14 q^{78} - 41 q^{79} + 9 q^{80} - 7 q^{81} - 2 q^{82} + 2 q^{83} + 20 q^{86} - 32 q^{87} - 10 q^{88} - 14 q^{89} - 22 q^{90} + 17 q^{92} - 15 q^{93} - 10 q^{94} - 31 q^{95} + 33 q^{96} + 27 q^{97} - 9 q^{99}+O(q^{100}) $ 5 * q - 2 * q^2 + 2 * q^3 + 6 * q^4 - 2 * q^5 - q^6 - 3 * q^8 + 5 * q^9 + q^10 - 6 * q^11 + 7 * q^12 - 2 * q^13 - 20 * q^15 - 12 * q^16 + 3 * q^17 - 8 * q^18 - 7 * q^19 - 7 * q^20 - 13 * q^22 - 16 * q^24 - 5 * q^25 + q^26 - 13 * q^27 - 10 * q^29 + 14 * q^30 + 6 * q^31 - 3 * q^32 + 17 * q^33 - q^34 - 15 * q^36 - 18 * q^37 + 7 * q^38 - 20 * q^39 + 16 * q^40 + 5 * q^41 - 14 * q^43 + 2 * q^44 + 7 * q^45 - 3 * q^46 - 3 * q^47 - 9 * q^48 - 4 * q^50 - 7 * q^52 - 9 * q^53 + 25 * q^54 - 17 * q^55 + 31 * q^57 - 5 * q^58 + 19 * q^59 - 3 * q^60 + 23 * q^61 - 36 * q^62 - q^64 + 20 * q^65 - 23 * q^66 - 11 * q^67 + 24 * q^68 - 19 * q^69 + 25 * q^72 - 13 * q^73 + 2 * q^74 - 11 * q^75 - 12 * q^76 + 14 * q^78 - 41 * q^79 + 9 * q^80 - 7 * q^81 - 2 * q^82 + 2 * q^83 + 20 * q^86 - 32 * q^87 - 10 * q^88 - 14 * q^89 - 22 * q^90 + 17 * q^92 - 15 * q^93 - 10 * q^94 - 31 * q^95 + 33 * q^96 + 27 * q^97 - 9 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.12846	−0.797942	−0.398971	−	0.916963i	$-0.630633\pi$
$2$	−1.12846	−0.797942	−0.398971	+	0.916963i	$0.630633\pi$
$3$	−2.92944	−1.69131	−0.845656	−	0.533728i	$-0.820791\pi$
$3$	−2.92944	−1.69131	−0.845656	+	0.533728i	$0.820791\pi$
$4$	−0.726576	−0.363288
$5$	2.92944	1.31008	0.655042	−	0.755592i	$-0.272651\pi$
$5$	2.92944	1.31008	0.655042	+	0.755592i	$0.272651\pi$
$6$	3.30576	1.34957
$7$	0	0
$7$	0	0
$8$	3.07683	1.08783
$9$	5.58161	1.86054
$10$	−3.30576	−1.04537
$11$	−3.80098	−1.14604	−0.573019	−	0.819542i	$-0.694228\pi$
$11$	−3.80098	−1.14604	−0.573019	+	0.819542i	$0.694228\pi$
$12$	2.12846	0.614434
$13$	2.92944	0.812480	0.406240	−	0.913766i	$-0.366840\pi$
$13$	2.92944	0.812480	0.406240	+	0.913766i	$0.366840\pi$
$14$	0	0
$15$	−8.58161	−2.21576
$16$	−2.01893	−0.504734
$17$	−2.23136	−0.541183	−0.270592	−	0.962694i	$-0.587219\pi$
$17$	−2.23136	−0.541183	−0.270592	+	0.962694i	$0.587219\pi$
$18$	−6.29863	−1.48460
$19$	−6.13230	−1.40685	−0.703423	−	0.710771i	$-0.748346\pi$
$19$	−6.13230	−1.40685	−0.703423	+	0.710771i	$0.748346\pi$
$20$	−2.12846	−0.475938
$21$	0	0
$22$	4.28925	0.914472
$23$	1.05547	0.220080	0.110040	−	0.993927i	$-0.464902\pi$
$23$	1.05547	0.220080	0.110040	+	0.993927i	$0.464902\pi$
$24$	−9.01340	−1.83985
$25$	3.58161	0.716323
$26$	−3.30576	−0.648312
$27$	−7.56268	−1.45544
$28$	0	0
$29$	3.63708	0.675389	0.337694	−	0.941256i	$-0.390353\pi$
$29$	3.63708	0.675389	0.337694	+	0.941256i	$0.390353\pi$
$30$	9.68401	1.76805
$31$	6.54374	1.17529	0.587646	−	0.809118i	$-0.300055\pi$
$31$	6.54374	1.17529	0.587646	+	0.809118i	$0.300055\pi$
$32$	−3.87538	−0.685077
$33$	11.1347	1.93831
$34$	2.51800	0.431833
$35$	0	0
$36$	−4.05547	−0.675911
$37$	−9.35410	−1.53780	−0.768902	−	0.639366i	$-0.779197\pi$
$37$	−9.35410	−1.53780	−0.768902	+	0.639366i	$0.779197\pi$
$38$	6.92006	1.12258
$39$	−8.58161	−1.37416
$40$	9.01340	1.42514
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	−5.51434	−0.840928	−0.420464	−	0.907309i	$-0.638133\pi$
$43$	−5.51434	−0.840928	−0.420464	+	0.907309i	$0.638133\pi$
$44$	2.76170	0.416342
$45$	16.3510	2.43746
$46$	−1.19105	−0.175611
$47$	−1.77249	−0.258544	−0.129272	−	0.991609i	$-0.541264\pi$
$47$	−1.77249	−0.258544	−0.129272	+	0.991609i	$0.541264\pi$
$48$	5.91435	0.853662
$49$	0	0
$50$	−4.04171	−0.571584
$51$	6.53662	0.915310
$52$	−2.12846	−0.295164
$53$	−0.934132	−0.128313	−0.0641565	−	0.997940i	$-0.520436\pi$
$53$	−0.934132	−0.128313	−0.0641565	+	0.997940i	$0.520436\pi$
$54$	8.53419	1.16136
$55$	−11.1347	−1.50141
$56$	0	0
$57$	17.9642	2.37942
$58$	−4.10430	−0.538921
$59$	13.3106	1.73290	0.866448	−	0.499268i	$-0.166398\pi$
$59$	13.3106	1.73290	0.866448	+	0.499268i	$0.166398\pi$
$60$	6.23520	0.804960
$61$	14.3579	1.83835	0.919173	−	0.393854i	$-0.128859\pi$
$61$	14.3579	1.83835	0.919173	+	0.393854i	$0.128859\pi$
$62$	−7.38436	−0.937815
$63$	0	0
$64$	8.41108	1.05139
$65$	8.58161	1.06442
$66$	−12.5651	−1.54666
$67$	10.4770	1.27997	0.639986	−	0.768386i	$-0.278940\pi$
$67$	10.4770	1.27997	0.639986	+	0.768386i	$0.278940\pi$
$68$	1.62125	0.196605
$69$	−3.09193	−0.372224
$70$	0	0
$71$	−9.53905	−1.13208	−0.566039	−	0.824379i	$-0.691525\pi$
$71$	−9.53905	−1.13208	−0.566039	+	0.824379i	$0.691525\pi$
$72$	17.1737	2.02394
$73$	11.7652	1.37701	0.688505	−	0.725231i	$-0.258267\pi$
$73$	11.7652	1.37701	0.688505	+	0.725231i	$0.258267\pi$
$74$	10.5557	1.22708
$75$	−10.4921	−1.21153
$76$	4.45558	0.511091
$77$	0	0
$78$	9.68401	1.09650
$79$	−15.0689	−1.69538	−0.847690	−	0.530492i	$-0.822007\pi$
$79$	−15.0689	−1.69538	−0.847690	+	0.530492i	$0.822007\pi$
$80$	−5.91435	−0.661244
$81$	5.40957	0.601063
$82$	−1.12846	−0.124618
$83$	1.86216	0.204399	0.102199	−	0.994764i	$-0.467412\pi$
$83$	1.86216	0.204399	0.102199	+	0.994764i	$0.467412\pi$
$84$	0	0
$85$	−6.53662	−0.708996
$86$	6.22271	0.671012
$87$	−10.6546	−1.14229
$88$	−11.6950	−1.24669
$89$	−16.2206	−1.71938	−0.859692	−	0.510813i	$-0.829344\pi$
$89$	−16.2206	−1.71938	−0.859692	+	0.510813i	$0.829344\pi$
$90$	−18.4515	−1.94495
$91$	0	0
$92$	−0.766878	−0.0799525
$93$	−19.1695	−1.98778
$94$	2.00018	0.206303
$95$	−17.9642	−1.84309
$96$	11.3527	1.15868
$97$	7.70326	0.782148	0.391074	−	0.920359i	$-0.372104\pi$
$97$	7.70326	0.782148	0.391074	+	0.920359i	$0.372104\pi$
$98$	0	0
$99$	−21.2156	−2.13225
$100$	−2.60232	−0.260232
$101$	−10.4815	−1.04294	−0.521472	−	0.853268i	$-0.674617\pi$
$101$	−10.4815	−1.04294	−0.521472	+	0.853268i	$0.674617\pi$
$102$	−7.37632	−0.730364
$103$	−6.04937	−0.596062	−0.298031	−	0.954556i	$-0.596330\pi$
$103$	−6.04937	−0.596062	−0.298031	+	0.954556i	$0.596330\pi$
$104$	9.01340	0.883836
$105$	0	0
$106$	1.05413	0.102386
$107$	−0.840786	−0.0812819	−0.0406409	−	0.999174i	$-0.512940\pi$
$107$	−0.840786	−0.0812819	−0.0406409	+	0.999174i	$0.512940\pi$
$108$	5.49486	0.528743
$109$	−1.42604	−0.136590	−0.0682950	−	0.997665i	$-0.521756\pi$
$109$	−1.42604	−0.136590	−0.0682950	+	0.997665i	$0.521756\pi$
$110$	12.5651	1.19804
$111$	27.4023	2.60091
$112$	0	0
$113$	−5.76585	−0.542406	−0.271203	−	0.962522i	$-0.587421\pi$
$113$	−5.76585	−0.542406	−0.271203	+	0.962522i	$0.587421\pi$
$114$	−20.2719	−1.89864
$115$	3.09193	0.288324
$116$	−2.64262	−0.245361
$117$	16.3510	1.51165
$118$	−15.0205	−1.38275
$119$	0	0
$120$	−26.4042	−2.41036
$121$	3.44744	0.313403
$122$	−16.2024	−1.46689
$123$	−2.92944	−0.264139
$124$	−4.75453	−0.426969
$125$	−4.15508	−0.371641
$126$	0	0
$127$	−13.7471	−1.21986	−0.609929	−	0.792456i	$-0.708802\pi$
$127$	−13.7471	−1.21986	−0.609929	+	0.792456i	$0.708802\pi$
$128$	−1.74082	−0.153868
$129$	16.1539	1.42227
$130$	−9.68401	−0.849344
$131$	1.97528	0.172581	0.0862903	−	0.996270i	$-0.472499\pi$
$131$	1.97528	0.172581	0.0862903	+	0.996270i	$0.472499\pi$
$132$	−8.09023	−0.704164
$133$	0	0
$134$	−11.8229	−1.02134
$135$	−22.1544	−1.90675
$136$	−6.86551	−0.588713
$137$	0.207905	0.0177625	0.00888126	−	0.999961i	$-0.497173\pi$
$137$	0.207905	0.0177625	0.00888126	+	0.999961i	$0.497173\pi$
$138$	3.48912	0.297014
$139$	−6.86618	−0.582381	−0.291191	−	0.956665i	$-0.594051\pi$
$139$	−6.86618	−0.582381	−0.291191	+	0.956665i	$0.594051\pi$
$140$	0	0
$141$	5.19239	0.437278
$142$	10.7644	0.903332
$143$	−11.1347	−0.931133
$144$	−11.2689	−0.939076
$145$	10.6546	0.884817
$146$	−13.2765	−1.09877
$147$	0	0
$148$	6.79647	0.558666
$149$	−3.98921	−0.326809	−0.163405	−	0.986559i	$-0.552248\pi$
$149$	−3.98921	−0.326809	−0.163405	+	0.986559i	$0.552248\pi$
$150$	11.8399	0.966727
$151$	−15.1185	−1.23033	−0.615165	−	0.788399i	$-0.710911\pi$
$151$	−15.1185	−1.23033	−0.615165	+	0.788399i	$0.710911\pi$
$152$	−18.8681	−1.53040
$153$	−12.4546	−1.00689
$154$	0	0
$155$	19.1695	1.53973
$156$	6.23520	0.499215
$157$	−7.04743	−0.562446	−0.281223	−	0.959642i	$-0.590740\pi$
$157$	−7.04743	−0.562446	−0.281223	+	0.959642i	$0.590740\pi$
$158$	17.0046	1.35282
$159$	2.73648	0.217017
$160$	−11.3527	−0.897509
$161$	0	0
$162$	−6.10448	−0.479614
$163$	16.1738	1.26683	0.633416	−	0.773811i	$-0.281652\pi$
$163$	16.1738	1.26683	0.633416	+	0.773811i	$0.281652\pi$
$164$	−0.726576	−0.0567361
$165$	32.6185	2.53935
$166$	−2.10138	−0.163099
$167$	5.14849	0.398402	0.199201	−	0.979959i	$-0.436165\pi$
$167$	5.14849	0.398402	0.199201	+	0.979959i	$0.436165\pi$
$168$	0	0
$169$	−4.41839	−0.339876
$170$	7.37632	0.565738
$171$	−34.2281	−2.61749
$172$	4.00659	0.305499
$173$	−8.74855	−0.665140	−0.332570	−	0.943079i	$-0.607916\pi$
$173$	−8.74855	−0.665140	−0.332570	+	0.943079i	$0.607916\pi$
$174$	12.0233	0.911484
$175$	0	0
$176$	7.67393	0.578444
$177$	−38.9927	−2.93087
$178$	18.3043	1.37197
$179$	−7.38369	−0.551883	−0.275941	−	0.961174i	$-0.588990\pi$
$179$	−7.38369	−0.551883	−0.275941	+	0.961174i	$0.588990\pi$
$180$	−11.8802	−0.885501
$181$	−9.92440	−0.737675	−0.368837	−	0.929494i	$-0.620244\pi$
$181$	−9.92440	−0.737675	−0.368837	+	0.929494i	$0.620244\pi$
$182$	0	0
$183$	−42.0607	−3.10922
$184$	3.24750	0.239409
$185$	−27.4023	−2.01465
$186$	21.6320	1.58614
$187$	8.48133	0.620216
$188$	1.28785	0.0939258
$189$	0	0
$190$	20.2719	1.47068
$191$	−1.62076	−0.117274	−0.0586369	−	0.998279i	$-0.518675\pi$
$191$	−1.62076	−0.117274	−0.0586369	+	0.998279i	$0.518675\pi$
$192$	−24.6398	−1.77822
$193$	3.55100	0.255607	0.127803	−	0.991800i	$-0.459207\pi$
$193$	3.55100	0.255607	0.127803	+	0.991800i	$0.459207\pi$
$194$	−8.69283	−0.624109
$195$	−25.1393	−1.80026
$196$	0	0
$197$	6.37250	0.454022	0.227011	−	0.973892i	$-0.427105\pi$
$197$	6.37250	0.454022	0.227011	+	0.973892i	$0.427105\pi$
$198$	23.9410	1.70141
$199$	−9.77316	−0.692801	−0.346400	−	0.938087i	$-0.612596\pi$
$199$	−9.77316	−0.692801	−0.346400	+	0.938087i	$0.612596\pi$
$200$	11.0200	0.779234
$201$	−30.6918	−2.16483
$202$	11.8279	0.832210
$203$	0	0
$204$	−4.74935	−0.332521
$205$	2.92944	0.204601
$206$	6.82647	0.475623
$207$	5.89121	0.409468
$208$	−5.91435	−0.410086
$209$	23.3087	1.61230
$210$	0	0
$211$	−4.31500	−0.297057	−0.148528	−	0.988908i	$-0.547454\pi$
$211$	−4.31500	−0.297057	−0.148528	+	0.988908i	$0.547454\pi$
$212$	0.678718	0.0466146
$213$	27.9441	1.91470
$214$	0.948794	0.0648582
$215$	−16.1539	−1.10169
$216$	−23.2691	−1.58326
$217$	0	0
$218$	1.60923	0.108991
$219$	−34.4654	−2.32896
$220$	8.09023	0.545443
$221$	−6.53662	−0.439701
$222$	−30.9224	−2.07537
$223$	11.7245	0.785130	0.392565	−	0.919724i	$-0.371588\pi$
$223$	11.7245	0.785130	0.392565	+	0.919724i	$0.371588\pi$
$224$	0	0
$225$	19.9912	1.33275
$226$	6.50654	0.432809
$227$	20.1471	1.33721	0.668604	−	0.743618i	$-0.266892\pi$
$227$	20.1471	1.33721	0.668604	+	0.743618i	$0.266892\pi$
$228$	−13.0524	−0.864414
$229$	22.7410	1.50277	0.751385	−	0.659864i	$-0.229386\pi$
$229$	22.7410	1.50277	0.751385	+	0.659864i	$0.229386\pi$
$230$	−3.48912	−0.230066
$231$	0	0
$232$	11.1907	0.734705
$233$	12.6339	0.827675	0.413837	−	0.910351i	$-0.364188\pi$
$233$	12.6339	0.827675	0.413837	+	0.910351i	$0.364188\pi$
$234$	−18.4515	−1.20621
$235$	−5.19239	−0.338714
$236$	−9.67118	−0.629540
$237$	44.1433	2.86742
$238$	0	0
$239$	20.8294	1.34734	0.673670	−	0.739033i	$-0.264717\pi$
$239$	20.8294	1.34734	0.673670	+	0.739033i	$0.264717\pi$
$240$	17.3257	1.11837
$241$	−7.60493	−0.489877	−0.244938	−	0.969539i	$-0.578768\pi$
$241$	−7.60493	−0.489877	−0.244938	+	0.969539i	$0.578768\pi$
$242$	−3.89030	−0.250078
$243$	6.84104	0.438853
$244$	−10.4321	−0.667849
$245$	0	0
$246$	3.30576	0.210767
$247$	−17.9642	−1.14303
$248$	20.1340	1.27851
$249$	−5.45509	−0.345702
$250$	4.68884	0.296548
$251$	−30.2279	−1.90797	−0.953984	−	0.299858i	$-0.903061\pi$
$251$	−30.2279	−1.90797	−0.953984	+	0.299858i	$0.903061\pi$
$252$	0	0
$253$	−4.01181	−0.252220
$254$	15.5131	0.973376
$255$	19.1486	1.19913
$256$	−14.8577	−0.928608
$257$	−9.87397	−0.615921	−0.307961	−	0.951399i	$-0.599647\pi$
$257$	−9.87397	−0.615921	−0.307961	+	0.951399i	$0.599647\pi$
$258$	−18.2291	−1.13489
$259$	0	0
$260$	−6.23520	−0.386690
$261$	20.3008	1.25659
$262$	−2.22902	−0.137709
$263$	−28.2264	−1.74051	−0.870256	−	0.492599i	$-0.836047\pi$
$263$	−28.2264	−1.74051	−0.870256	+	0.492599i	$0.836047\pi$
$264$	34.2597	2.10854
$265$	−2.73648	−0.168101
$266$	0	0
$267$	47.5174	2.90801
$268$	−7.61236	−0.464999
$269$	−19.7684	−1.20530	−0.602651	−	0.798005i	$-0.705889\pi$
$269$	−19.7684	−1.20530	−0.602651	+	0.798005i	$0.705889\pi$
$270$	25.0004	1.52147
$271$	−21.4838	−1.30505	−0.652524	−	0.757768i	$-0.726290\pi$
$271$	−21.4838	−1.30505	−0.652524	+	0.757768i	$0.726290\pi$
$272$	4.50496	0.273153
$273$	0	0
$274$	−0.234613	−0.0141735
$275$	−13.6136	−0.820933
$276$	2.24652	0.135225
$277$	−14.1780	−0.851876	−0.425938	−	0.904752i	$-0.640056\pi$
$277$	−14.1780	−0.851876	−0.425938	+	0.904752i	$0.640056\pi$
$278$	7.74821	0.464707
$279$	36.5246	2.18667
$280$	0	0
$281$	−8.15392	−0.486422	−0.243211	−	0.969973i	$-0.578201\pi$
$281$	−8.15392	−0.486422	−0.243211	+	0.969973i	$0.578201\pi$
$282$	−5.85941	−0.348923
$283$	−19.3217	−1.14855	−0.574276	−	0.818661i	$-0.694717\pi$
$283$	−19.3217	−1.14855	−0.574276	+	0.818661i	$0.694717\pi$
$284$	6.93085	0.411270
$285$	52.6250	3.11724
$286$	12.5651	0.742991
$287$	0	0
$288$	−21.6309	−1.27461
$289$	−12.0211	−0.707121
$290$	−12.0233	−0.706033
$291$	−22.5662	−1.32286
$292$	−8.54830	−0.500252
$293$	27.5658	1.61041	0.805206	−	0.592996i	$-0.202055\pi$
$293$	27.5658	1.61041	0.805206	+	0.592996i	$0.202055\pi$
$294$	0	0
$295$	38.9927	2.27024
$296$	−28.7810	−1.67286
$297$	28.7456	1.66799
$298$	4.50167	0.260775
$299$	3.09193	0.178811
$300$	7.62332	0.440133
$301$	0	0
$302$	17.0607	0.981732
$303$	30.7048	1.76395
$304$	12.3807	0.710083
$305$	42.0607	2.40839
$306$	14.0545	0.803441
$307$	−4.66137	−0.266039	−0.133019	−	0.991113i	$-0.542467\pi$
$307$	−4.66137	−0.266039	−0.133019	+	0.991113i	$0.542467\pi$
$308$	0	0
$309$	17.7212	1.00813
$310$	−21.6320	−1.22862
$311$	−1.98114	−0.112340	−0.0561700	−	0.998421i	$-0.517889\pi$
$311$	−1.98114	−0.112340	−0.0561700	+	0.998421i	$0.517889\pi$
$312$	−26.4042	−1.49484
$313$	−18.0432	−1.01986	−0.509932	−	0.860215i	$-0.670329\pi$
$313$	−18.0432	−1.01986	−0.509932	+	0.860215i	$0.670329\pi$
$314$	7.95274	0.448799
$315$	0	0
$316$	10.9487	0.615911
$317$	1.86215	0.104589	0.0522945	−	0.998632i	$-0.483347\pi$
$317$	1.86215	0.104589	0.0522945	+	0.998632i	$0.483347\pi$
$318$	−3.08801	−0.173167
$319$	−13.8245	−0.774021
$320$	24.6398	1.37740
$321$	2.46303	0.137473
$322$	0	0
$323$	13.6833	0.761362
$324$	−3.93046	−0.218359
$325$	10.4921	0.581998
$326$	−18.2515	−1.01086
$327$	4.17750	0.231016
$328$	3.07683	0.169890
$329$	0	0
$330$	−36.8087	−2.02625
$331$	8.07648	0.443923	0.221962	−	0.975055i	$-0.428754\pi$
$331$	8.07648	0.443923	0.221962	+	0.975055i	$0.428754\pi$
$332$	−1.35300	−0.0742557
$333$	−52.2110	−2.86114
$334$	−5.80987	−0.317902
$335$	30.6918	1.67687
$336$	0	0
$337$	−28.8996	−1.57426	−0.787130	−	0.616788i	$-0.788434\pi$
$337$	−28.8996	−1.57426	−0.787130	+	0.616788i	$0.788434\pi$
$338$	4.98598	0.271201
$339$	16.8907	0.917378
$340$	4.74935	0.257570
$341$	−24.8726	−1.34693
$342$	38.6251	2.08861
$343$	0	0
$344$	−16.9667	−0.914783
$345$	−9.05761	−0.487646
$346$	9.87239	0.530743
$347$	10.5621	0.567004	0.283502	−	0.958972i	$-0.408504\pi$
$347$	10.5621	0.567004	0.283502	+	0.958972i	$0.408504\pi$
$348$	7.74138	0.414982
$349$	−10.3215	−0.552498	−0.276249	−	0.961086i	$-0.589092\pi$
$349$	−10.3215	−0.552498	−0.276249	+	0.961086i	$0.589092\pi$
$350$	0	0
$351$	−22.1544	−1.18251
$352$	14.7302	0.785124
$353$	20.0946	1.06953	0.534765	−	0.845001i	$-0.320400\pi$
$353$	20.0946	1.06953	0.534765	+	0.845001i	$0.320400\pi$
$354$	44.0017	2.33866
$355$	−27.9441	−1.48312
$356$	11.7855	0.624632
$357$	0	0
$358$	8.33220	0.440371
$359$	2.68189	0.141545	0.0707725	−	0.997492i	$-0.477454\pi$
$359$	2.68189	0.141545	0.0707725	+	0.997492i	$0.477454\pi$
$360$	50.3093	2.65153
$361$	18.6051	0.979217
$362$	11.1993	0.588622
$363$	−10.0991	−0.530063
$364$	0	0
$365$	34.4654	1.80400
$366$	47.4639	2.48098
$367$	−27.4864	−1.43478	−0.717389	−	0.696673i	$-0.754663\pi$
$367$	−27.4864	−1.43478	−0.717389	+	0.696673i	$0.754663\pi$
$368$	−2.13092	−0.111082
$369$	5.58161	0.290567
$370$	30.9224	1.60758
$371$	0	0
$372$	13.9281	0.722139
$373$	−6.73944	−0.348955	−0.174477	−	0.984661i	$-0.555824\pi$
$373$	−6.73944	−0.348955	−0.174477	+	0.984661i	$0.555824\pi$
$374$	−9.57085	−0.494897
$375$	12.1720	0.628562
$376$	−5.45365	−0.281250
$377$	10.6546	0.548740
$378$	0	0
$379$	−34.3338	−1.76361	−0.881803	−	0.471617i	$-0.843670\pi$
$379$	−34.3338	−1.76361	−0.881803	+	0.471617i	$0.843670\pi$
$380$	13.0524	0.669572
$381$	40.2713	2.06316
$382$	1.82896	0.0935777
$383$	1.31545	0.0672163	0.0336082	−	0.999435i	$-0.489300\pi$
$383$	1.31545	0.0672163	0.0336082	+	0.999435i	$0.489300\pi$
$384$	5.09962	0.260239
$385$	0	0
$386$	−4.00717	−0.203960
$387$	−30.7789	−1.56458
$388$	−5.59701	−0.284145
$389$	15.3776	0.779676	0.389838	−	0.920883i	$-0.372531\pi$
$389$	15.3776	0.779676	0.389838	+	0.920883i	$0.372531\pi$
$390$	28.3687	1.43651
$391$	−2.35512	−0.119104
$392$	0	0
$393$	−5.78645	−0.291888
$394$	−7.19112	−0.362283
$395$	−44.1433	−2.22109
$396$	15.4147	0.774620
$397$	17.5242	0.879513	0.439757	−	0.898117i	$-0.355065\pi$
$397$	17.5242	0.879513	0.439757	+	0.898117i	$0.355065\pi$
$398$	11.0286	0.552815
$399$	0	0
$400$	−7.23104	−0.361552
$401$	−15.1234	−0.755227	−0.377614	−	0.925963i	$-0.623255\pi$
$401$	−15.1234	−0.755227	−0.377614	+	0.925963i	$0.623255\pi$
$402$	34.6345	1.72741
$403$	19.1695	0.954901
$404$	7.61558	0.378889
$405$	15.8470	0.787444
$406$	0	0
$407$	35.5547	1.76238
$408$	20.1121	0.995697
$409$	7.42945	0.367363	0.183681	−	0.982986i	$-0.441199\pi$
$409$	7.42945	0.367363	0.183681	+	0.982986i	$0.441199\pi$
$410$	−3.30576	−0.163260
$411$	−0.609045	−0.0300420
$412$	4.39533	0.216542
$413$	0	0
$414$	−6.64800	−0.326731
$415$	5.45509	0.267780
$416$	−11.3527	−0.556611
$417$	20.1140	0.984989
$418$	−26.3030	−1.28652
$419$	11.2835	0.551234	0.275617	−	0.961268i	$-0.411118\pi$
$419$	11.2835	0.551234	0.275617	+	0.961268i	$0.411118\pi$
$420$	0	0
$421$	−21.1179	−1.02922	−0.514611	−	0.857424i	$-0.672064\pi$
$421$	−21.1179	−1.02922	−0.514611	+	0.857424i	$0.672064\pi$
$422$	4.86931	0.237034
$423$	−9.89333	−0.481030
$424$	−2.87417	−0.139582
$425$	−7.99185	−0.387662
$426$	−31.5338	−1.52782
$427$	0	0
$428$	0.610895	0.0295287
$429$	32.6185	1.57484
$430$	18.2291	0.879083
$431$	17.5935	0.847451	0.423725	−	0.905791i	$-0.360722\pi$
$431$	17.5935	0.847451	0.423725	+	0.905791i	$0.360722\pi$
$432$	15.2686	0.734609
$433$	−9.24372	−0.444225	−0.222113	−	0.975021i	$-0.571295\pi$
$433$	−9.24372	−0.444225	−0.222113	+	0.975021i	$0.571295\pi$
$434$	0	0
$435$	−31.2120	−1.49650
$436$	1.03613	0.0496216
$437$	−6.47245	−0.309619
$438$	38.8928	1.85837
$439$	−24.9363	−1.19015	−0.595073	−	0.803671i	$-0.702877\pi$
$439$	−24.9363	−1.19015	−0.595073	+	0.803671i	$0.702877\pi$
$440$	−34.2597	−1.63327
$441$	0	0
$442$	7.37632	0.350856
$443$	30.9844	1.47211	0.736057	−	0.676920i	$-0.236686\pi$
$443$	30.9844	1.47211	0.736057	+	0.676920i	$0.236686\pi$
$444$	−19.9098	−0.944879
$445$	−47.5174	−2.25254
$446$	−13.2306	−0.626489
$447$	11.6862	0.552736
$448$	0	0
$449$	−9.24437	−0.436269	−0.218134	−	0.975919i	$-0.569997\pi$
$449$	−9.24437	−0.436269	−0.218134	+	0.975919i	$0.569997\pi$
$450$	−22.5593	−1.06345
$451$	−3.80098	−0.178981
$452$	4.18933	0.197050
$453$	44.2889	2.08087
$454$	−22.7352	−1.06702
$455$	0	0
$456$	55.2729	2.58839
$457$	−22.0735	−1.03256	−0.516278	−	0.856421i	$-0.672683\pi$
$457$	−22.0735	−1.03256	−0.516278	+	0.856421i	$0.672683\pi$
$458$	−25.6624	−1.19912
$459$	16.8750	0.787659
$460$	−2.24652	−0.104745
$461$	−42.2569	−1.96810	−0.984051	−	0.177886i	$-0.943074\pi$
$461$	−42.2569	−1.96810	−0.984051	+	0.177886i	$0.943074\pi$
$462$	0	0
$463$	−36.1774	−1.68131	−0.840654	−	0.541573i	$-0.817829\pi$
$463$	−36.1774	−1.68131	−0.840654	+	0.541573i	$0.817829\pi$
$464$	−7.34303	−0.340892
$465$	−56.1559	−2.60417
$466$	−14.2569	−0.660437
$467$	−12.9119	−0.597492	−0.298746	−	0.954333i	$-0.596568\pi$
$467$	−12.9119	−0.597492	−0.298746	+	0.954333i	$0.596568\pi$
$468$	−11.8802	−0.549165
$469$	0	0
$470$	5.85941	0.270274
$471$	20.6450	0.951272
$472$	40.9546	1.88509
$473$	20.9599	0.963736
$474$	−49.8140	−2.28803
$475$	−21.9635	−1.00776
$476$	0	0
$477$	−5.21396	−0.238731
$478$	−23.5051	−1.07510
$479$	8.56375	0.391288	0.195644	−	0.980675i	$-0.437320\pi$
$479$	8.56375	0.391288	0.195644	+	0.980675i	$0.437320\pi$
$480$	33.2570	1.51797
$481$	−27.4023	−1.24944
$482$	8.58186	0.390893
$483$	0	0
$484$	−2.50482	−0.113856
$485$	22.5662	1.02468
$486$	−7.71985	−0.350179
$487$	5.10652	0.231398	0.115699	−	0.993284i	$-0.463089\pi$
$487$	5.10652	0.231398	0.115699	+	0.993284i	$0.463089\pi$
$488$	44.1770	1.99980
$489$	−47.3803	−2.14261
$490$	0	0
$491$	1.80345	0.0813884	0.0406942	−	0.999172i	$-0.487043\pi$
$491$	1.80345	0.0813884	0.0406942	+	0.999172i	$0.487043\pi$
$492$	2.12846	0.0959584
$493$	−8.11562	−0.365509
$494$	20.2719	0.912076
$495$	−62.1498	−2.79342
$496$	−13.2114	−0.593209
$497$	0	0
$498$	6.15586	0.275851
$499$	−19.6827	−0.881118	−0.440559	−	0.897724i	$-0.645220\pi$
$499$	−19.6827	−0.881118	−0.440559	+	0.897724i	$0.645220\pi$
$500$	3.01898	0.135013
$501$	−15.0822	−0.673823
$502$	34.1110	1.52245
$503$	−3.71758	−0.165759	−0.0828795	−	0.996560i	$-0.526412\pi$
$503$	−3.71758	−0.165759	−0.0828795	+	0.996560i	$0.526412\pi$
$504$	0	0
$505$	−30.7048	−1.36635
$506$	4.52717	0.201257
$507$	12.9434	0.574836
$508$	9.98832	0.443160
$509$	−0.432846	−0.0191856	−0.00959278	−	0.999954i	$-0.503054\pi$
$509$	−0.432846	−0.0191856	−0.00959278	+	0.999954i	$0.503054\pi$
$510$	−21.6085	−0.956839
$511$	0	0
$512$	20.2480	0.894843
$513$	46.3766	2.04758
$514$	11.1424	0.491470
$515$	−17.7212	−0.780891
$516$	−11.7370	−0.516695
$517$	6.73718	0.296301
$518$	0	0
$519$	25.6283	1.12496
$520$	26.4042	1.15790
$521$	−23.5720	−1.03271	−0.516353	−	0.856376i	$-0.672711\pi$
$521$	−23.5720	−1.03271	−0.516353	+	0.856376i	$0.672711\pi$
$522$	−22.9086	−1.00268
$523$	23.6663	1.03485	0.517427	−	0.855727i	$-0.326890\pi$
$523$	23.6663	1.03485	0.517427	+	0.855727i	$0.326890\pi$
$524$	−1.43519	−0.0626965
$525$	0	0
$526$	31.8524	1.38883
$527$	−14.6014	−0.636048
$528$	−22.4803	−0.978329
$529$	−21.8860	−0.951565
$530$	3.08801	0.134135
$531$	74.2947	3.22412
$532$	0	0
$533$	2.92944	0.126888
$534$	−53.6215	−2.32043
$535$	−2.46303	−0.106486
$536$	32.2361	1.39239
$537$	21.6301	0.933406
$538$	22.3079	0.961761
$539$	0	0
$540$	16.0969	0.692699
$541$	16.8911	0.726207	0.363103	−	0.931749i	$-0.381717\pi$
$541$	16.8911	0.726207	0.363103	+	0.931749i	$0.381717\pi$
$542$	24.2436	1.04135
$543$	29.0729	1.24764
$544$	8.64735	0.370752
$545$	−4.17750	−0.178945
$546$	0	0
$547$	33.0460	1.41295	0.706473	−	0.707740i	$-0.250285\pi$
$547$	33.0460	1.41295	0.706473	+	0.707740i	$0.250285\pi$
$548$	−0.151059	−0.00645292
$549$	80.1405	3.42031
$550$	15.3625	0.655057
$551$	−22.3037	−0.950169
$552$	−9.51335	−0.404915
$553$	0	0
$554$	15.9994	0.679747
$555$	80.2733	3.40741
$556$	4.98880	0.211572
$557$	−38.9239	−1.64926	−0.824629	−	0.565674i	$-0.808616\pi$
$557$	−38.9239	−1.64926	−0.824629	+	0.565674i	$0.808616\pi$
$558$	−41.2166	−1.74484
$559$	−16.1539	−0.683238
$560$	0	0
$561$	−24.8455	−1.04898
$562$	9.20138	0.388137
$563$	−20.3367	−0.857089	−0.428544	−	0.903521i	$-0.640973\pi$
$563$	−20.3367	−0.857089	−0.428544	+	0.903521i	$0.640973\pi$
$564$	−3.77267	−0.158858
$565$	−16.8907	−0.710598
$566$	21.8037	0.916479
$567$	0	0
$568$	−29.3501	−1.23150
$569$	19.4159	0.813959	0.406979	−	0.913437i	$-0.366582\pi$
$569$	19.4159	0.813959	0.406979	+	0.913437i	$0.366582\pi$
$570$	−59.3853	−2.48738
$571$	3.64559	0.152563	0.0762816	−	0.997086i	$-0.475695\pi$
$571$	3.64559	0.152563	0.0762816	+	0.997086i	$0.475695\pi$
$572$	8.09023	0.338270
$573$	4.74791	0.198347
$574$	0	0
$575$	3.78028	0.157648
$576$	46.9474	1.95614
$577$	8.63811	0.359609	0.179805	−	0.983702i	$-0.442453\pi$
$577$	8.63811	0.359609	0.179805	+	0.983702i	$0.442453\pi$
$578$	13.5653	0.564242
$579$	−10.4025	−0.432311
$580$	−7.74138	−0.321443
$581$	0	0
$582$	25.4651	1.05556
$583$	3.55062	0.147051
$584$	36.1995	1.49795
$585$	47.8992	1.98039
$586$	−31.1069	−1.28502
$587$	−29.1822	−1.20448	−0.602238	−	0.798316i	$-0.705724\pi$
$587$	−29.1822	−1.20448	−0.602238	+	0.798316i	$0.705724\pi$
$588$	0	0
$589$	−40.1282	−1.65345
$590$	−44.0017	−1.81152
$591$	−18.6679	−0.767893
$592$	18.8853	0.776182
$593$	12.1891	0.500545	0.250273	−	0.968175i	$-0.419480\pi$
$593$	12.1891	0.500545	0.250273	+	0.968175i	$0.419480\pi$
$594$	−32.4383	−1.33096
$595$	0	0
$596$	2.89847	0.118726
$597$	28.6299	1.17174
$598$	−3.48912	−0.142681
$599$	37.4431	1.52988	0.764942	−	0.644099i	$-0.222767\pi$
$599$	37.4431	1.52988	0.764942	+	0.644099i	$0.222767\pi$
$600$	−32.2825	−1.31793
$601$	−32.4249	−1.32264	−0.661320	−	0.750104i	$-0.730003\pi$
$601$	−32.4249	−1.32264	−0.661320	+	0.750104i	$0.730003\pi$
$602$	0	0
$603$	58.4787	2.38144
$604$	10.9848	0.446964
$605$	10.0991	0.410585
$606$	−34.6492	−1.40753
$607$	19.7805	0.802866	0.401433	−	0.915888i	$-0.368512\pi$
$607$	19.7805	0.802866	0.401433	+	0.915888i	$0.368512\pi$
$608$	23.7650	0.963798
$609$	0	0
$610$	−47.4639	−1.92176
$611$	−5.19239	−0.210062
$612$	9.04919	0.365792
$613$	41.1308	1.66126	0.830628	−	0.556828i	$-0.187982\pi$
$613$	41.1308	1.66126	0.830628	+	0.556828i	$0.187982\pi$
$614$	5.26018	0.212283
$615$	−8.58161	−0.346044
$616$	0	0
$617$	2.77289	0.111633	0.0558163	−	0.998441i	$-0.482224\pi$
$617$	2.77289	0.111633	0.0558163	+	0.998441i	$0.482224\pi$
$618$	−19.9977	−0.804427
$619$	−9.47350	−0.380772	−0.190386	−	0.981709i	$-0.560974\pi$
$619$	−9.47350	−0.380772	−0.190386	+	0.981709i	$0.560974\pi$
$620$	−13.9281	−0.559366
$621$	−7.98216	−0.320313
$622$	2.23564	0.0896409
$623$	0	0
$624$	17.3257	0.693584
$625$	−30.0801	−1.20320
$626$	20.3611	0.813792
$627$	−68.2816	−2.72690
$628$	5.12049	0.204330
$629$	20.8723	0.832234
$630$	0	0
$631$	−18.4744	−0.735455	−0.367727	−	0.929934i	$-0.619864\pi$
$631$	−18.4744	−0.735455	−0.367727	+	0.929934i	$0.619864\pi$
$632$	−46.3644	−1.84428
$633$	12.6405	0.502416
$634$	−2.10137	−0.0834559
$635$	−40.2713	−1.59812
$636$	−1.98826	−0.0788398
$637$	0	0
$638$	15.6004	0.617624
$639$	−53.2433	−2.10627
$640$	−5.09962	−0.201580
$641$	−23.4848	−0.927594	−0.463797	−	0.885941i	$-0.653513\pi$
$641$	−23.4848	−0.927594	−0.463797	+	0.885941i	$0.653513\pi$
$642$	−2.77944	−0.109696
$643$	5.24905	0.207002	0.103501	−	0.994629i	$-0.466995\pi$
$643$	5.24905	0.207002	0.103501	+	0.994629i	$0.466995\pi$
$644$	0	0
$645$	47.3219	1.86330
$646$	−15.4411	−0.607523
$647$	10.9051	0.428725	0.214363	−	0.976754i	$-0.431233\pi$
$647$	10.9051	0.428725	0.214363	+	0.976754i	$0.431233\pi$
$648$	16.6443	0.653851
$649$	−50.5934	−1.98596
$650$	−11.8399	−0.464401
$651$	0	0
$652$	−11.7515	−0.460225
$653$	−13.0540	−0.510844	−0.255422	−	0.966830i	$-0.582214\pi$
$653$	−13.0540	−0.510844	−0.255422	+	0.966830i	$0.582214\pi$
$654$	−4.71415	−0.184338
$655$	5.78645	0.226095
$656$	−2.01893	−0.0788261
$657$	65.6687	2.56198
$658$	0	0
$659$	10.2628	0.399784	0.199892	−	0.979818i	$-0.435941\pi$
$659$	10.2628	0.399784	0.199892	+	0.979818i	$0.435941\pi$
$660$	−23.6998	−0.922515
$661$	−26.5579	−1.03298	−0.516492	−	0.856292i	$-0.672762\pi$
$661$	−26.5579	−1.03298	−0.516492	+	0.856292i	$0.672762\pi$
$662$	−9.11399	−0.354225
$663$	19.1486	0.743671
$664$	5.72957	0.222350
$665$	0	0
$666$	58.9180	2.28303
$667$	3.83882	0.148640
$668$	−3.74077	−0.144735
$669$	−34.3462	−1.32790
$670$	−34.6345	−1.33805
$671$	−54.5742	−2.10681
$672$	0	0
$673$	35.7468	1.37794	0.688969	−	0.724790i	$-0.258063\pi$
$673$	35.7468	1.37794	0.688969	+	0.724790i	$0.258063\pi$
$674$	32.6120	1.25617
$675$	−27.0866	−1.04256
$676$	3.21029	0.123473
$677$	−7.02385	−0.269949	−0.134974	−	0.990849i	$-0.543095\pi$
$677$	−7.02385	−0.269949	−0.134974	+	0.990849i	$0.543095\pi$
$678$	−19.0605	−0.732015
$679$	0	0
$680$	−20.1121	−0.771264
$681$	−59.0197	−2.26164
$682$	28.0678	1.07477
$683$	29.5719	1.13154	0.565768	−	0.824564i	$-0.308580\pi$
$683$	29.5719	1.13154	0.565768	+	0.824564i	$0.308580\pi$
$684$	24.8694	0.950903
$685$	0.609045	0.0232704
$686$	0	0
$687$	−66.6184	−2.54165
$688$	11.1331	0.424445
$689$	−2.73648	−0.104252
$690$	10.2212	0.389113
$691$	9.39444	0.357381	0.178691	−	0.983905i	$-0.442814\pi$
$691$	9.39444	0.357381	0.178691	+	0.983905i	$0.442814\pi$
$692$	6.35649	0.241637
$693$	0	0
$694$	−11.9189	−0.452437
$695$	−20.1140	−0.762969
$696$	−32.7825	−1.24262
$697$	−2.23136	−0.0845186
$698$	11.6474	0.440862
$699$	−37.0103	−1.39986
$700$	0	0
$701$	20.0205	0.756162	0.378081	−	0.925773i	$-0.376584\pi$
$701$	20.0205	0.756162	0.378081	+	0.925773i	$0.376584\pi$
$702$	25.0004	0.943579
$703$	57.3622	2.16345
$704$	−31.9703	−1.20493
$705$	15.2108	0.572871
$706$	−22.6760	−0.853423
$707$	0	0
$708$	28.3311	1.06475
$709$	−9.34140	−0.350824	−0.175412	−	0.984495i	$-0.556126\pi$
$709$	−9.34140	−0.350824	−0.175412	+	0.984495i	$0.556126\pi$
$710$	31.5338	1.18344
$711$	−84.1086	−3.15432
$712$	−49.9082	−1.87039
$713$	6.90671	0.258658
$714$	0	0
$715$	−32.6185	−1.21986
$716$	5.36481	0.200492
$717$	−61.0183	−2.27877
$718$	−3.02641	−0.112945
$719$	16.1023	0.600514	0.300257	−	0.953858i	$-0.402928\pi$
$719$	16.1023	0.600514	0.300257	+	0.953858i	$0.402928\pi$
$720$	−33.0116	−1.23027
$721$	0	0
$722$	−20.9952	−0.781359
$723$	22.2782	0.828534
$724$	7.21083	0.267988
$725$	13.0266	0.483796
$726$	11.3964	0.422960
$727$	−2.78212	−0.103183	−0.0515915	−	0.998668i	$-0.516429\pi$
$727$	−2.78212	−0.103183	−0.0515915	+	0.998668i	$0.516429\pi$
$728$	0	0
$729$	−36.2691	−1.34330
$730$	−38.8928	−1.43949
$731$	12.3044	0.455096
$732$	30.5603	1.12954
$733$	−17.3777	−0.641861	−0.320930	−	0.947103i	$-0.603996\pi$
$733$	−17.3777	−0.641861	−0.320930	+	0.947103i	$0.603996\pi$
$734$	31.0173	1.14487
$735$	0	0
$736$	−4.09034	−0.150772
$737$	−39.8229	−1.46690
$738$	−6.29863	−0.231856
$739$	28.8537	1.06140	0.530700	−	0.847560i	$-0.321929\pi$
$739$	28.8537	1.06140	0.530700	+	0.847560i	$0.321929\pi$
$740$	19.9098	0.731900
$741$	52.6250	1.93323
$742$	0	0
$743$	−2.11198	−0.0774811	−0.0387405	−	0.999249i	$-0.512335\pi$
$743$	−2.11198	−0.0774811	−0.0387405	+	0.999249i	$0.512335\pi$
$744$	−58.9814	−2.16236
$745$	−11.6862	−0.428148
$746$	7.60519	0.278446
$747$	10.3939	0.380292
$748$	−6.16233	−0.225317
$749$	0	0
$750$	−13.7357	−0.501556
$751$	−17.0564	−0.622399	−0.311199	−	0.950345i	$-0.600731\pi$
$751$	−17.0564	−0.622399	−0.311199	+	0.950345i	$0.600731\pi$
$752$	3.57853	0.130496
$753$	88.5508	3.22697
$754$	−12.0233	−0.437863
$755$	−44.2889	−1.61184
$756$	0	0
$757$	−49.7155	−1.80694	−0.903470	−	0.428652i	$-0.858989\pi$
$757$	−49.7155	−1.80694	−0.903470	+	0.428652i	$0.858989\pi$
$758$	38.7443	1.40726
$759$	11.7524	0.426583
$760$	−55.2729	−2.00496
$761$	48.7138	1.76587	0.882937	−	0.469491i	$-0.155563\pi$
$761$	48.7138	1.76587	0.882937	+	0.469491i	$0.155563\pi$
$762$	−45.4446	−1.64628
$763$	0	0
$764$	1.17760	0.0426042
$765$	−36.4849	−1.31911
$766$	−1.48443	−0.0536348
$767$	38.9927	1.40794
$768$	43.5248	1.57057
$769$	1.23591	0.0445680	0.0222840	−	0.999752i	$-0.492906\pi$
$769$	1.23591	0.0445680	0.0222840	+	0.999752i	$0.492906\pi$
$770$	0	0
$771$	28.9252	1.04172
$772$	−2.58008	−0.0928589
$773$	35.6833	1.28344	0.641720	−	0.766939i	$-0.278221\pi$
$773$	35.6833	1.28344	0.641720	+	0.766939i	$0.278221\pi$
$774$	34.7328	1.24844
$775$	23.4372	0.841888
$776$	23.7017	0.850840
$777$	0	0
$778$	−17.3530	−0.622136
$779$	−6.13230	−0.219713
$780$	18.2656	0.654014
$781$	36.2577	1.29740
$782$	2.65766	0.0950379
$783$	−27.5061	−0.982987
$784$	0	0
$785$	−20.6450	−0.736852
$786$	6.52978	0.232910
$787$	−19.3439	−0.689537	−0.344769	−	0.938688i	$-0.612043\pi$
$787$	−19.3439	−0.689537	−0.344769	+	0.938688i	$0.612043\pi$
$788$	−4.63011	−0.164941
$789$	82.6874	2.94375
$790$	49.8140	1.77230
$791$	0	0
$792$	−65.2769	−2.31951
$793$	42.0607	1.49362
$794$	−19.7753	−0.701801
$795$	8.01636	0.284311
$796$	7.10095	0.251686
$797$	−38.0350	−1.34727	−0.673635	−	0.739065i	$-0.735268\pi$
$797$	−38.0350	−1.34727	−0.673635	+	0.739065i	$0.735268\pi$
$798$	0	0
$799$	3.95505	0.139919
$800$	−13.8801	−0.490736
$801$	−90.5373	−3.19898
$802$	17.0662	0.602628
$803$	−44.7192	−1.57811
$804$	22.2999	0.786458
$805$	0	0
$806$	−21.6320	−0.761956
$807$	57.9104	2.03854
$808$	−32.2497	−1.13454
$809$	−38.6600	−1.35921	−0.679607	−	0.733576i	$-0.737850\pi$
$809$	−38.6600	−1.35921	−0.679607	+	0.733576i	$0.737850\pi$
$810$	−17.8827	−0.628335
$811$	−25.3938	−0.891696	−0.445848	−	0.895109i	$-0.647098\pi$
$811$	−25.3938	−0.891696	−0.445848	+	0.895109i	$0.647098\pi$
$812$	0	0
$813$	62.9355	2.20724
$814$	−40.1221	−1.40628
$815$	47.3803	1.65966
$816$	−13.1970	−0.461988
$817$	33.8156	1.18306
$818$	−8.38385	−0.293134
$819$	0	0
$820$	−2.12846	−0.0743291
$821$	23.8800	0.833416	0.416708	−	0.909040i	$-0.363184\pi$
$821$	23.8800	0.833416	0.416708	+	0.909040i	$0.363184\pi$
$822$	0.687284	0.0239718
$823$	−27.8693	−0.971462	−0.485731	−	0.874108i	$-0.661447\pi$
$823$	−27.8693	−0.971462	−0.485731	+	0.874108i	$0.661447\pi$
$824$	−18.6129	−0.648411
$825$	39.8803	1.38845
$826$	0	0
$827$	29.0555	1.01036	0.505179	−	0.863014i	$-0.331426\pi$
$827$	29.0555	1.01036	0.505179	+	0.863014i	$0.331426\pi$
$828$	−4.28041	−0.148755
$829$	−1.97233	−0.0685018	−0.0342509	−	0.999413i	$-0.510905\pi$
$829$	−1.97233	−0.0685018	−0.0342509	+	0.999413i	$0.510905\pi$
$830$	−6.15586	−0.213673
$831$	41.5337	1.44079
$832$	24.6398	0.854230
$833$	0	0
$834$	−22.6979	−0.785964
$835$	15.0822	0.521941
$836$	−16.9356	−0.585729
$837$	−49.4882	−1.71056
$838$	−12.7330	−0.439853
$839$	22.2354	0.767653	0.383826	−	0.923405i	$-0.374606\pi$
$839$	22.2354	0.767653	0.383826	+	0.923405i	$0.374606\pi$
$840$	0	0
$841$	−15.7716	−0.543850
$842$	23.8307	0.821260
$843$	23.8864	0.822692
$844$	3.13518	0.107917
$845$	−12.9434	−0.445266
$846$	11.1642	0.383834
$847$	0	0
$848$	1.88595	0.0647638
$849$	56.6016	1.94256
$850$	9.01849	0.309332
$851$	−9.87295	−0.338440
$852$	−20.3035	−0.695586
$853$	7.48352	0.256231	0.128115	−	0.991759i	$-0.459107\pi$
$853$	7.48352	0.256231	0.128115	+	0.991759i	$0.459107\pi$
$854$	0	0
$855$	−100.269	−3.42914
$856$	−2.58696	−0.0884205
$857$	11.3441	0.387508	0.193754	−	0.981050i	$-0.437934\pi$
$857$	11.3441	0.387508	0.193754	+	0.981050i	$0.437934\pi$
$858$	−36.8087	−1.25663
$859$	−4.75336	−0.162183	−0.0810913	−	0.996707i	$-0.525841\pi$
$859$	−4.75336	−0.162183	−0.0810913	+	0.996707i	$0.525841\pi$
$860$	11.7370	0.400230
$861$	0	0
$862$	−19.8536	−0.676217
$863$	41.6504	1.41779	0.708897	−	0.705312i	$-0.249193\pi$
$863$	41.6504	1.41779	0.708897	+	0.705312i	$0.249193\pi$
$864$	29.3083	0.997087
$865$	−25.6283	−0.871389
$866$	10.4312	0.354466
$867$	35.2149	1.19596
$868$	0	0
$869$	57.2764	1.94297
$870$	35.2215	1.19412
$871$	30.6918	1.03995
$872$	−4.38770	−0.148586
$873$	42.9966	1.45522
$874$	7.30390	0.247058
$875$	0	0
$876$	25.0417	0.846082
$877$	27.3478	0.923470	0.461735	−	0.887018i	$-0.347227\pi$
$877$	27.3478	0.923470	0.461735	+	0.887018i	$0.347227\pi$
$878$	28.1397	0.949668
$879$	−80.7523	−2.72371
$880$	22.4803	0.757811
$881$	32.2910	1.08791	0.543956	−	0.839114i	$-0.316926\pi$
$881$	32.2910	1.08791	0.543956	+	0.839114i	$0.316926\pi$
$882$	0	0
$883$	29.5079	0.993020	0.496510	−	0.868031i	$-0.334615\pi$
$883$	29.5079	0.993020	0.496510	+	0.868031i	$0.334615\pi$
$884$	4.74935	0.159738
$885$	−114.227	−3.83969
$886$	−34.9647	−1.17466
$887$	36.0201	1.20943	0.604717	−	0.796440i	$-0.293286\pi$
$887$	36.0201	1.20943	0.604717	+	0.796440i	$0.293286\pi$
$888$	84.3122	2.82933
$889$	0	0
$890$	53.6215	1.79740
$891$	−20.5616	−0.688841
$892$	−8.51874	−0.285229
$893$	10.8694	0.363731
$894$	−13.1874	−0.441052
$895$	−21.6301	−0.723013
$896$	0	0
$897$	−9.05761	−0.302425
$898$	10.4319	0.348117
$899$	23.8001	0.793779
$900$	−14.5251	−0.484171
$901$	2.08438	0.0694408
$902$	4.28925	0.142817
$903$	0	0
$904$	−17.7406	−0.590043
$905$	−29.0729	−0.966416
$906$	−49.9782	−1.66042
$907$	29.3360	0.974085	0.487042	−	0.873378i	$-0.338076\pi$
$907$	29.3360	0.974085	0.487042	+	0.873378i	$0.338076\pi$
$908$	−14.6384	−0.485792
$909$	−58.5035	−1.94044
$910$	0	0
$911$	27.7708	0.920086	0.460043	−	0.887897i	$-0.347834\pi$
$911$	27.7708	0.920086	0.460043	+	0.887897i	$0.347834\pi$
$912$	−36.2686	−1.20097
$913$	−7.07804	−0.234249
$914$	24.9091	0.823921
$915$	−123.214	−4.07334
$916$	−16.5231	−0.545938
$917$	0	0
$918$	−19.0428	−0.628506
$919$	−11.1099	−0.366482	−0.183241	−	0.983068i	$-0.558659\pi$
$919$	−11.1099	−0.366482	−0.183241	+	0.983068i	$0.558659\pi$
$920$	9.51335	0.313646
$921$	13.6552	0.449954
$922$	47.6853	1.57043
$923$	−27.9441	−0.919790
$924$	0	0
$925$	−33.5028	−1.10156
$926$	40.8248	1.34159
$927$	−33.7652	−1.10900
$928$	−14.0951	−0.462693
$929$	−25.9660	−0.851918	−0.425959	−	0.904743i	$-0.640063\pi$
$929$	−25.9660	−0.851918	−0.425959	+	0.904743i	$0.640063\pi$
$930$	63.3697	2.07797
$931$	0	0
$932$	−9.17949	−0.300684
$933$	5.80362	0.190002
$934$	14.5706	0.476764
$935$	24.8455	0.812536
$936$	50.3093	1.64441
$937$	−30.0886	−0.982953	−0.491476	−	0.870891i	$-0.663543\pi$
$937$	−30.0886	−0.982953	−0.491476	+	0.870891i	$0.663543\pi$
$938$	0	0
$939$	52.8565	1.72491
$940$	3.77267	0.123051
$941$	−37.1676	−1.21163	−0.605814	−	0.795606i	$-0.707152\pi$
$941$	−37.1676	−1.21163	−0.605814	+	0.795606i	$0.707152\pi$
$942$	−23.2971	−0.759060
$943$	1.05547	0.0343708
$944$	−26.8733	−0.874651
$945$	0	0
$946$	−23.6524	−0.769006
$947$	−17.3132	−0.562605	−0.281302	−	0.959619i	$-0.590766\pi$
$947$	−17.3132	−0.562605	−0.281302	+	0.959619i	$0.590766\pi$
$948$	−32.0735	−1.04170
$949$	34.4654	1.11879
$950$	24.7850	0.804131
$951$	−5.45506	−0.176893
$952$	0	0
$953$	18.4287	0.596965	0.298482	−	0.954415i	$-0.403520\pi$
$953$	18.4287	0.596965	0.298482	+	0.954415i	$0.403520\pi$
$954$	5.88375	0.190494
$955$	−4.74791	−0.153639
$956$	−15.1341	−0.489472
$957$	40.4979	1.30911
$958$	−9.66385	−0.312225
$959$	0	0
$960$	−72.1807	−2.32962
$961$	11.8206	0.381309
$962$	30.9224	0.996978
$963$	−4.69294	−0.151228
$964$	5.52556	0.177966
$965$	10.4025	0.334867
$966$	0	0
$967$	−0.639722	−0.0205721	−0.0102860	−	0.999947i	$-0.503274\pi$
$967$	−0.639722	−0.0205721	−0.0102860	+	0.999947i	$0.503274\pi$
$968$	10.6072	0.340928
$969$	−40.0845	−1.28770
$970$	−25.4651	−0.817635
$971$	6.39191	0.205126	0.102563	−	0.994727i	$-0.467296\pi$
$971$	6.39191	0.205126	0.102563	+	0.994727i	$0.467296\pi$
$972$	−4.97054	−0.159430
$973$	0	0
$974$	−5.76251	−0.184643
$975$	−30.7360	−0.984340
$976$	−28.9877	−0.927875
$977$	32.4435	1.03796	0.518980	−	0.854786i	$-0.326312\pi$
$977$	32.4435	1.03796	0.518980	+	0.854786i	$0.326312\pi$
$978$	53.4668	1.70968
$979$	61.6543	1.97048
$980$	0	0
$981$	−7.95962	−0.254131
$982$	−2.03512	−0.0649433
$983$	46.7849	1.49221	0.746104	−	0.665829i	$-0.231922\pi$
$983$	46.7849	1.49221	0.746104	+	0.665829i	$0.231922\pi$
$984$	−9.01340	−0.287337
$985$	18.6679	0.594808
$986$	9.15816	0.291655
$987$	0	0
$988$	13.0524	0.415251
$989$	−5.82020	−0.185072
$990$	70.1336	2.22899
$991$	5.23977	0.166447	0.0832234	−	0.996531i	$-0.473478\pi$
$991$	5.23977	0.166447	0.0832234	+	0.996531i	$0.473478\pi$
$992$	−25.3595	−0.805165
$993$	−23.6595	−0.750813
$994$	0	0
$995$	−28.6299	−0.907628
$996$	3.96354	0.125590
$997$	−9.18301	−0.290829	−0.145414	−	0.989371i	$-0.546452\pi$
$997$	−9.18301	−0.290829	−0.145414	+	0.989371i	$0.546452\pi$
$998$	22.2111	0.703081
$999$	70.7420	2.23818

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2009.2.a.m.1.3		5
7.3	odd	6		287.2.e.c.247.3	yes	10
7.5	odd	6		287.2.e.c.165.3	✓	10
7.6	odd	2		2009.2.a.l.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.e.c.165.3	✓	10	7.5	odd	6
287.2.e.c.247.3	yes	10	7.3	odd	6
2009.2.a.l.1.3		5	7.6	odd	2
2009.2.a.m.1.3		5	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.12846 q^{2} -2.92944 q^{3} -0.726576 q^{4} +2.92944 q^{5} +3.30576 q^{6} +3.07683 q^{8} +5.58161 q^{9} +O(q^{10})\)	\(q-1.12846 q^{2} -2.92944 q^{3} -0.726576 q^{4} +2.92944 q^{5} +3.30576 q^{6} +3.07683 q^{8} +5.58161 q^{9} -3.30576 q^{10} -3.80098 q^{11} +2.12846 q^{12} +2.92944 q^{13} -8.58161 q^{15} -2.01893 q^{16} -2.23136 q^{17} -6.29863 q^{18} -6.13230 q^{19} -2.12846 q^{20} +4.28925 q^{22} +1.05547 q^{23} -9.01340 q^{24} +3.58161 q^{25} -3.30576 q^{26} -7.56268 q^{27} +3.63708 q^{29} +9.68401 q^{30} +6.54374 q^{31} -3.87538 q^{32} +11.1347 q^{33} +2.51800 q^{34} -4.05547 q^{36} -9.35410 q^{37} +6.92006 q^{38} -8.58161 q^{39} +9.01340 q^{40} +1.00000 q^{41} -5.51434 q^{43} +2.76170 q^{44} +16.3510 q^{45} -1.19105 q^{46} -1.77249 q^{47} +5.91435 q^{48} -4.04171 q^{50} +6.53662 q^{51} -2.12846 q^{52} -0.934132 q^{53} +8.53419 q^{54} -11.1347 q^{55} +17.9642 q^{57} -4.10430 q^{58} +13.3106 q^{59} +6.23520 q^{60} +14.3579 q^{61} -7.38436 q^{62} +8.41108 q^{64} +8.58161 q^{65} -12.5651 q^{66} +10.4770 q^{67} +1.62125 q^{68} -3.09193 q^{69} -9.53905 q^{71} +17.1737 q^{72} +11.7652 q^{73} +10.5557 q^{74} -10.4921 q^{75} +4.45558 q^{76} +9.68401 q^{78} -15.0689 q^{79} -5.91435 q^{80} +5.40957 q^{81} -1.12846 q^{82} +1.86216 q^{83} -6.53662 q^{85} +6.22271 q^{86} -10.6546 q^{87} -11.6950 q^{88} -16.2206 q^{89} -18.4515 q^{90} -0.766878 q^{92} -19.1695 q^{93} +2.00018 q^{94} -17.9642 q^{95} +11.3527 q^{96} +7.70326 q^{97} -21.2156 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 2 q^{2} + 2 q^{3} + 6 q^{4} - 2 q^{5} - q^{6} - 3 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q - 2 * q^2 + 2 * q^3 + 6 * q^4 - 2 * q^5 - q^6 - 3 * q^8 + 5 * q^9	\( 5 q - 2 q^{2} + 2 q^{3} + 6 q^{4} - 2 q^{5} - q^{6} - 3 q^{8} + 5 q^{9} + q^{10} - 6 q^{11} + 7 q^{12} - 2 q^{13} - 20 q^{15} - 12 q^{16} + 3 q^{17} - 8 q^{18} - 7 q^{19} - 7 q^{20} - 13 q^{22} - 16 q^{24} - 5 q^{25} + q^{26} - 13 q^{27} - 10 q^{29} + 14 q^{30} + 6 q^{31} - 3 q^{32} + 17 q^{33} - q^{34} - 15 q^{36} - 18 q^{37} + 7 q^{38} - 20 q^{39} + 16 q^{40} + 5 q^{41} - 14 q^{43} + 2 q^{44} + 7 q^{45} - 3 q^{46} - 3 q^{47} - 9 q^{48} - 4 q^{50} - 7 q^{52} - 9 q^{53} + 25 q^{54} - 17 q^{55} + 31 q^{57} - 5 q^{58} + 19 q^{59} - 3 q^{60} + 23 q^{61} - 36 q^{62} - q^{64} + 20 q^{65} - 23 q^{66} - 11 q^{67} + 24 q^{68} - 19 q^{69} + 25 q^{72} - 13 q^{73} + 2 q^{74} - 11 q^{75} - 12 q^{76} + 14 q^{78} - 41 q^{79} + 9 q^{80} - 7 q^{81} - 2 q^{82} + 2 q^{83} + 20 q^{86} - 32 q^{87} - 10 q^{88} - 14 q^{89} - 22 q^{90} + 17 q^{92} - 15 q^{93} - 10 q^{94} - 31 q^{95} + 33 q^{96} + 27 q^{97} - 9 q^{99}+O(q^{100}) \) 5 * q - 2 * q^2 + 2 * q^3 + 6 * q^4 - 2 * q^5 - q^6 - 3 * q^8 + 5 * q^9 + q^10 - 6 * q^11 + 7 * q^12 - 2 * q^13 - 20 * q^15 - 12 * q^16 + 3 * q^17 - 8 * q^18 - 7 * q^19 - 7 * q^20 - 13 * q^22 - 16 * q^24 - 5 * q^25 + q^26 - 13 * q^27 - 10 * q^29 + 14 * q^30 + 6 * q^31 - 3 * q^32 + 17 * q^33 - q^34 - 15 * q^36 - 18 * q^37 + 7 * q^38 - 20 * q^39 + 16 * q^40 + 5 * q^41 - 14 * q^43 + 2 * q^44 + 7 * q^45 - 3 * q^46 - 3 * q^47 - 9 * q^48 - 4 * q^50 - 7 * q^52 - 9 * q^53 + 25 * q^54 - 17 * q^55 + 31 * q^57 - 5 * q^58 + 19 * q^59 - 3 * q^60 + 23 * q^61 - 36 * q^62 - q^64 + 20 * q^65 - 23 * q^66 - 11 * q^67 + 24 * q^68 - 19 * q^69 + 25 * q^72 - 13 * q^73 + 2 * q^74 - 11 * q^75 - 12 * q^76 + 14 * q^78 - 41 * q^79 + 9 * q^80 - 7 * q^81 - 2 * q^82 + 2 * q^83 + 20 * q^86 - 32 * q^87 - 10 * q^88 - 14 * q^89 - 22 * q^90 + 17 * q^92 - 15 * q^93 - 10 * q^94 - 31 * q^95 + 33 * q^96 + 27 * q^97 - 9 * q^99

Introduction

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