LMFDB - Embedded newform 2009.2.a.l.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:	$1$
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			1.1
Root			$2.80262$ 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)

$f(q)$	$=$	$q-2.40886 q^{2} -0.896451 q^{3} +3.80262 q^{4} +0.896451 q^{5} +2.15943 q^{6} -4.34226 q^{8} -2.19638 q^{9} +O(q^{10})$	\(q-2.40886 q^{2} -0.896451 q^{3} +3.80262 q^{4} +0.896451 q^{5} +2.15943 q^{6} -4.34226 q^{8} -2.19638 q^{9} -2.15943 q^{10} +1.30531 q^{11} -3.40886 q^{12} +0.896451 q^{13} -0.803625 q^{15} +2.85467 q^{16} -2.65673 q^{17} +5.29077 q^{18} +3.00972 q^{19} +3.40886 q^{20} -3.14432 q^{22} +5.35198 q^{23} +3.89263 q^{24} -4.19638 q^{25} -2.15943 q^{26} +4.65830 q^{27} +0.155602 q^{29} +1.93582 q^{30} -8.51297 q^{31} +1.80801 q^{32} -1.17015 q^{33} +6.39970 q^{34} -8.35198 q^{36} -2.06121 q^{37} -7.24999 q^{38} -0.803625 q^{39} -3.89263 q^{40} -1.00000 q^{41} -4.43766 q^{43} +4.96361 q^{44} -1.96894 q^{45} -12.8922 q^{46} +2.25759 q^{47} -2.55907 q^{48} +10.1085 q^{50} +2.38163 q^{51} +3.40886 q^{52} -10.0745 q^{53} -11.2212 q^{54} +1.17015 q^{55} -2.69806 q^{57} -0.374824 q^{58} +5.83856 q^{59} -3.05588 q^{60} -2.66207 q^{61} +20.5066 q^{62} -10.0646 q^{64} +0.803625 q^{65} +2.81873 q^{66} +4.21737 q^{67} -10.1025 q^{68} -4.79779 q^{69} +1.45793 q^{71} +9.53723 q^{72} +14.0034 q^{73} +4.96518 q^{74} +3.76185 q^{75} +11.4448 q^{76} +1.93582 q^{78} -14.2446 q^{79} +2.55907 q^{80} +2.41319 q^{81} +2.40886 q^{82} -4.73758 q^{83} -2.38163 q^{85} +10.6897 q^{86} -0.139490 q^{87} -5.66801 q^{88} +4.31745 q^{89} +4.74291 q^{90} +20.3515 q^{92} +7.63146 q^{93} -5.43822 q^{94} +2.69806 q^{95} -1.62079 q^{96} +14.5549 q^{97} -2.86696 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.40886	−1.70332	−0.851662	−	0.524092i	$-0.824405\pi$
$2$	−2.40886	−1.70332	−0.851662	+	0.524092i	$0.824405\pi$
$3$	−0.896451	−0.517566	−0.258783	−	0.965935i	$-0.583322\pi$
$3$	−0.896451	−0.517566	−0.258783	+	0.965935i	$0.583322\pi$
$4$	3.80262	1.90131
$5$	0.896451	0.400905	0.200453	−	0.979703i	$-0.435759\pi$
$5$	0.896451	0.400905	0.200453	+	0.979703i	$0.435759\pi$
$6$	2.15943	0.881583
$7$	0	0
$7$	0	0
$8$	−4.34226	−1.53522
$9$	−2.19638	−0.732125
$10$	−2.15943	−0.682871
$11$	1.30531	0.393567	0.196783	−	0.980447i	$-0.436950\pi$
$11$	1.30531	0.393567	0.196783	+	0.980447i	$0.436950\pi$
$12$	−3.40886	−0.984054
$13$	0.896451	0.248631	0.124315	−	0.992243i	$-0.460327\pi$
$13$	0.896451	0.248631	0.124315	+	0.992243i	$0.460327\pi$
$14$	0	0
$15$	−0.803625	−0.207495
$16$	2.85467	0.713668
$17$	−2.65673	−0.644352	−0.322176	−	0.946680i	$-0.604414\pi$
$17$	−2.65673	−0.644352	−0.322176	+	0.946680i	$0.604414\pi$
$18$	5.29077	1.24705
$19$	3.00972	0.690476	0.345238	−	0.938515i	$-0.387798\pi$
$19$	3.00972	0.690476	0.345238	+	0.938515i	$0.387798\pi$
$20$	3.40886	0.762245
$21$	0	0
$22$	−3.14432	−0.670372
$23$	5.35198	1.11596	0.557982	−	0.829853i	$-0.311576\pi$
$23$	5.35198	1.11596	0.557982	+	0.829853i	$0.311576\pi$
$24$	3.89263	0.794579
$25$	−4.19638	−0.839275
$26$	−2.15943	−0.423499
$27$	4.65830	0.896490
$28$	0	0
$29$	0.155602	0.0288946	0.0144473	−	0.999896i	$-0.495401\pi$
$29$	0.155602	0.0288946	0.0144473	+	0.999896i	$0.495401\pi$
$30$	1.93582	0.353431
$31$	−8.51297	−1.52897	−0.764487	−	0.644639i	$-0.777008\pi$
$31$	−8.51297	−1.52897	−0.764487	+	0.644639i	$0.777008\pi$
$32$	1.80801	0.319614
$33$	−1.17015	−0.203697
$34$	6.39970	1.09754
$35$	0	0
$36$	−8.35198	−1.39200
$37$	−2.06121	−0.338861	−0.169431	−	0.985542i	$-0.554193\pi$
$37$	−2.06121	−0.338861	−0.169431	+	0.985542i	$0.554193\pi$
$38$	−7.24999	−1.17610
$39$	−0.803625	−0.128683
$40$	−3.89263	−0.615478
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	−4.43766	−0.676736	−0.338368	−	0.941014i	$-0.609875\pi$
$43$	−4.43766	−0.676736	−0.338368	+	0.941014i	$0.609875\pi$
$44$	4.96361	0.748293
$45$	−1.96894	−0.293513
$46$	−12.8922	−1.90085
$47$	2.25759	0.329303	0.164651	−	0.986352i	$-0.447350\pi$
$47$	2.25759	0.329303	0.164651	+	0.986352i	$0.447350\pi$
$48$	−2.55907	−0.369371
$49$	0	0
$50$	10.1085	1.42956
$51$	2.38163	0.333495
$52$	3.40886	0.472724
$53$	−10.0745	−1.38383	−0.691916	−	0.721978i	$-0.743233\pi$
$53$	−10.0745	−1.38383	−0.691916	+	0.721978i	$0.743233\pi$
$54$	−11.2212	−1.52701
$55$	1.17015	0.157783
$56$	0	0
$57$	−2.69806	−0.357367
$58$	−0.374824	−0.0492168
$59$	5.83856	0.760116	0.380058	−	0.924963i	$-0.375904\pi$
$59$	5.83856	0.760116	0.380058	+	0.924963i	$0.375904\pi$
$60$	−3.05588	−0.394512
$61$	−2.66207	−0.340843	−0.170421	−	0.985371i	$-0.554513\pi$
$61$	−2.66207	−0.340843	−0.170421	+	0.985371i	$0.554513\pi$
$62$	20.5066	2.60434
$63$	0	0
$64$	−10.0646	−1.25807
$65$	0.803625	0.0996774
$66$	2.81873	0.346962
$67$	4.21737	0.515234	0.257617	−	0.966247i	$-0.417063\pi$
$67$	4.21737	0.515234	0.257617	+	0.966247i	$0.417063\pi$
$68$	−10.1025	−1.22511
$69$	−4.79779	−0.577586
$70$	0	0
$71$	1.45793	0.173025	0.0865125	−	0.996251i	$-0.472428\pi$
$71$	1.45793	0.173025	0.0865125	+	0.996251i	$0.472428\pi$
$72$	9.53723	1.12397
$73$	14.0034	1.63897	0.819486	−	0.573100i	$-0.194259\pi$
$73$	14.0034	1.63897	0.819486	+	0.573100i	$0.194259\pi$
$74$	4.96518	0.577190
$75$	3.76185	0.434381
$76$	11.4448	1.31281
$77$	0	0
$78$	1.93582	0.219189
$79$	−14.2446	−1.60264	−0.801322	−	0.598234i	$-0.795869\pi$
$79$	−14.2446	−1.60264	−0.801322	+	0.598234i	$0.795869\pi$
$80$	2.55907	0.286113
$81$	2.41319	0.268132
$82$	2.40886	0.266014
$83$	−4.73758	−0.520017	−0.260009	−	0.965606i	$-0.583725\pi$
$83$	−4.73758	−0.520017	−0.260009	+	0.965606i	$0.583725\pi$
$84$	0	0
$85$	−2.38163	−0.258324
$86$	10.6897	1.15270
$87$	−0.139490	−0.0149549
$88$	−5.66801	−0.604212
$89$	4.31745	0.457649	0.228825	−	0.973468i	$-0.426512\pi$
$89$	4.31745	0.457649	0.228825	+	0.973468i	$0.426512\pi$
$90$	4.74291	0.499947
$91$	0	0
$92$	20.3515	2.12179
$93$	7.63146	0.791346
$94$	−5.43822	−0.560909
$95$	2.69806	0.276816
$96$	−1.62079	−0.165421
$97$	14.5549	1.47782	0.738911	−	0.673803i	$-0.235340\pi$
$97$	14.5549	1.47782	0.738911	+	0.673803i	$0.235340\pi$
$98$	0	0
$99$	−2.86696	−0.288140
$100$	−15.9572	−1.59572
$101$	−7.60635	−0.756861	−0.378430	−	0.925630i	$-0.623536\pi$
$101$	−7.60635	−0.756861	−0.378430	+	0.925630i	$0.623536\pi$
$102$	−5.73702	−0.568050
$103$	−5.05935	−0.498512	−0.249256	−	0.968438i	$-0.580186\pi$
$103$	−5.05935	−0.498512	−0.249256	+	0.968438i	$0.580186\pi$
$104$	−3.89263	−0.381703
$105$	0	0
$106$	24.2680	2.35711
$107$	14.6564	1.41689	0.708445	−	0.705766i	$-0.249397\pi$
$107$	14.6564	1.41689	0.708445	+	0.705766i	$0.249397\pi$
$108$	17.7137	1.70450
$109$	−12.2455	−1.17291	−0.586454	−	0.809983i	$-0.699477\pi$
$109$	−12.2455	−1.17291	−0.586454	+	0.809983i	$0.699477\pi$
$110$	−2.81873	−0.268755
$111$	1.84778	0.175383
$112$	0	0
$113$	6.07154	0.571163	0.285581	−	0.958354i	$-0.407813\pi$
$113$	6.07154	0.571163	0.285581	+	0.958354i	$0.407813\pi$
$114$	6.49927	0.608712
$115$	4.79779	0.447396
$116$	0.591696	0.0549376
$117$	−1.96894	−0.182029
$118$	−14.0643	−1.29472
$119$	0	0
$120$	3.48955	0.318551
$121$	−9.29616	−0.845105
$122$	6.41255	0.580565
$123$	0.896451	0.0808303
$124$	−32.3716	−2.90705
$125$	−8.24410	−0.737375
$126$	0	0
$127$	−10.2213	−0.906998	−0.453499	−	0.891257i	$-0.649824\pi$
$127$	−10.2213	−0.906998	−0.453499	+	0.891257i	$0.649824\pi$
$128$	20.6282	1.82329
$129$	3.97814	0.350256
$130$	−1.93582	−0.169783
$131$	18.1927	1.58950	0.794750	−	0.606937i	$-0.207602\pi$
$131$	18.1927	1.58950	0.794750	+	0.606937i	$0.207602\pi$
$132$	−4.44964	−0.387291
$133$	0	0
$134$	−10.1591	−0.877610
$135$	4.17594	0.359407
$136$	11.5362	0.989223
$137$	7.35666	0.628522	0.314261	−	0.949337i	$-0.398243\pi$
$137$	7.35666	0.628522	0.314261	+	0.949337i	$0.398243\pi$
$138$	11.5572	0.983815
$139$	−21.3116	−1.80763	−0.903813	−	0.427927i	$-0.859244\pi$
$139$	−21.3116	−1.80763	−0.903813	+	0.427927i	$0.859244\pi$
$140$	0	0
$141$	−2.02382	−0.170436
$142$	−3.51196	−0.294717
$143$	1.17015	0.0978529
$144$	−6.26993	−0.522494
$145$	0.139490	0.0115840
$146$	−33.7322	−2.79170
$147$	0	0
$148$	−7.83800	−0.644280
$149$	−5.70602	−0.467456	−0.233728	−	0.972302i	$-0.575092\pi$
$149$	−5.70602	−0.467456	−0.233728	+	0.972302i	$0.575092\pi$
$150$	−9.06177	−0.739890
$151$	6.45075	0.524955	0.262477	−	0.964938i	$-0.415460\pi$
$151$	6.45075	0.524955	0.262477	+	0.964938i	$0.415460\pi$
$152$	−13.0690	−1.06003
$153$	5.83518	0.471747
$154$	0	0
$155$	−7.63146	−0.612974
$156$	−3.05588	−0.244666
$157$	−3.41757	−0.272752	−0.136376	−	0.990657i	$-0.543546\pi$
$157$	−3.41757	−0.272752	−0.136376	+	0.990657i	$0.543546\pi$
$158$	34.3133	2.72982
$159$	9.03126	0.716225
$160$	1.62079	0.128135
$161$	0	0
$162$	−5.81304	−0.456716
$163$	−21.2284	−1.66274	−0.831368	−	0.555722i	$-0.812442\pi$
$163$	−21.2284	−1.66274	−0.831368	+	0.555722i	$0.812442\pi$
$164$	−3.80262	−0.296935
$165$	−1.04898	−0.0816632
$166$	11.4122	0.885757
$167$	−13.6306	−1.05477	−0.527384	−	0.849627i	$-0.676827\pi$
$167$	−13.6306	−1.05477	−0.527384	+	0.849627i	$0.676827\pi$
$168$	0	0
$169$	−12.1964	−0.938183
$170$	5.73702	0.440010
$171$	−6.61047	−0.505515
$172$	−16.8747	−1.28669
$173$	10.7774	0.819388	0.409694	−	0.912223i	$-0.365636\pi$
$173$	10.7774	0.819388	0.409694	+	0.912223i	$0.365636\pi$
$174$	0.336012	0.0254730
$175$	0	0
$176$	3.72624	0.280876
$177$	−5.23398	−0.393410
$178$	−10.4002	−0.779524
$179$	−6.57474	−0.491419	−0.245710	−	0.969344i	$-0.579021\pi$
$179$	−6.57474	−0.491419	−0.245710	+	0.969344i	$0.579021\pi$
$180$	−7.48714	−0.558059
$181$	−0.346946	−0.0257883	−0.0128942	−	0.999917i	$-0.504104\pi$
$181$	−0.346946	−0.0257883	−0.0128942	+	0.999917i	$0.504104\pi$
$182$	0	0
$183$	2.38641	0.176409
$184$	−23.2397	−1.71325
$185$	−1.84778	−0.135851
$186$	−18.3831	−1.34792
$187$	−3.46787	−0.253596
$188$	8.58474	0.626107
$189$	0	0
$190$	−6.49927	−0.471506
$191$	−16.3003	−1.17945	−0.589725	−	0.807604i	$-0.700764\pi$
$191$	−16.3003	−1.17945	−0.589725	+	0.807604i	$0.700764\pi$
$192$	9.02241	0.651137
$193$	−18.1213	−1.30440	−0.652201	−	0.758046i	$-0.726154\pi$
$193$	−18.1213	−1.30440	−0.652201	+	0.758046i	$0.726154\pi$
$194$	−35.0607	−2.51721
$195$	−0.720411	−0.0515897
$196$	0	0
$197$	−2.71127	−0.193170	−0.0965849	−	0.995325i	$-0.530792\pi$
$197$	−2.71127	−0.193170	−0.0965849	+	0.995325i	$0.530792\pi$
$198$	6.90611	0.490796
$199$	7.49801	0.531520	0.265760	−	0.964039i	$-0.414377\pi$
$199$	7.49801	0.531520	0.265760	+	0.964039i	$0.414377\pi$
$200$	18.2218	1.28847
$201$	−3.78067	−0.266668
$202$	18.3227	1.28918
$203$	0	0
$204$	9.05644	0.634077
$205$	−0.896451	−0.0626109
$206$	12.1873	0.849127
$207$	−11.7549	−0.817025
$208$	2.55907	0.177440
$209$	3.92862	0.271749
$210$	0	0
$211$	−24.4598	−1.68388	−0.841940	−	0.539572i	$-0.818586\pi$
$211$	−24.4598	−1.68388	−0.841940	+	0.539572i	$0.818586\pi$
$212$	−38.3093	−2.63109
$213$	−1.30697	−0.0895519
$214$	−35.3053	−2.41342
$215$	−3.97814	−0.271307
$216$	−20.2275	−1.37631
$217$	0	0
$218$	29.4978	1.99784
$219$	−12.5533	−0.848277
$220$	4.44964	0.299994
$221$	−2.38163	−0.160206
$222$	−4.45104	−0.298734
$223$	9.17487	0.614395	0.307197	−	0.951646i	$-0.400609\pi$
$223$	9.17487	0.614395	0.307197	+	0.951646i	$0.400609\pi$
$224$	0	0
$225$	9.21681	0.614454
$226$	−14.6255	−0.972875
$227$	−26.1902	−1.73830	−0.869152	−	0.494545i	$-0.835335\pi$
$227$	−26.1902	−1.73830	−0.869152	+	0.494545i	$0.835335\pi$
$228$	−10.2597	−0.679466
$229$	8.03742	0.531127	0.265564	−	0.964093i	$-0.414442\pi$
$229$	8.03742	0.531127	0.265564	+	0.964093i	$0.414442\pi$
$230$	−11.5572	−0.762060
$231$	0	0
$232$	−0.675665	−0.0443596
$233$	−19.2931	−1.26393	−0.631966	−	0.774996i	$-0.717752\pi$
$233$	−19.2931	−1.26393	−0.631966	+	0.774996i	$0.717752\pi$
$234$	4.74291	0.310054
$235$	2.02382	0.132019
$236$	22.2018	1.44522
$237$	12.7696	0.829474
$238$	0	0
$239$	−18.7297	−1.21152	−0.605761	−	0.795647i	$-0.707131\pi$
$239$	−18.7297	−1.21152	−0.605761	+	0.795647i	$0.707131\pi$
$240$	−2.29409	−0.148083
$241$	17.5559	1.13087	0.565436	−	0.824792i	$-0.308708\pi$
$241$	17.5559	1.13087	0.565436	+	0.824792i	$0.308708\pi$
$242$	22.3932	1.43949
$243$	−16.1382	−1.03527
$244$	−10.1228	−0.648047
$245$	0	0
$246$	−2.15943	−0.137680
$247$	2.69806	0.171674
$248$	36.9655	2.34731
$249$	4.24701	0.269143
$250$	19.8589	1.25599
$251$	−5.31684	−0.335596	−0.167798	−	0.985821i	$-0.553666\pi$
$251$	−5.31684	−0.335596	−0.167798	+	0.985821i	$0.553666\pi$
$252$	0	0
$253$	6.98601	0.439207
$254$	24.6218	1.54491
$255$	2.13502	0.133700
$256$	−29.5613	−1.84758
$257$	1.75157	0.109260	0.0546300	−	0.998507i	$-0.482602\pi$
$257$	1.75157	0.109260	0.0546300	+	0.998507i	$0.482602\pi$
$258$	−9.58280	−0.596599
$259$	0	0
$260$	3.05588	0.189518
$261$	−0.341761	−0.0211545
$262$	−43.8236	−2.70743
$263$	−8.16093	−0.503225	−0.251612	−	0.967828i	$-0.580961\pi$
$263$	−8.16093	−0.503225	−0.251612	+	0.967828i	$0.580961\pi$
$264$	5.08110	0.312720
$265$	−9.03126	−0.554786
$266$	0	0
$267$	−3.87039	−0.236864
$268$	16.0371	0.979619
$269$	−28.6767	−1.74845	−0.874226	−	0.485519i	$-0.838631\pi$
$269$	−28.6767	−1.74845	−0.874226	+	0.485519i	$0.838631\pi$
$270$	−10.0593	−0.612187
$271$	−2.21913	−0.134803	−0.0674014	−	0.997726i	$-0.521471\pi$
$271$	−2.21913	−0.134803	−0.0674014	+	0.997726i	$0.521471\pi$
$272$	−7.58410	−0.459854
$273$	0	0
$274$	−17.7212	−1.07058
$275$	−5.47759	−0.330311
$276$	−18.2442	−1.09817
$277$	4.05971	0.243924	0.121962	−	0.992535i	$-0.461081\pi$
$277$	4.05971	0.243924	0.121962	+	0.992535i	$0.461081\pi$
$278$	51.3367	3.07897
$279$	18.6977	1.11940
$280$	0	0
$281$	−18.1101	−1.08036	−0.540179	−	0.841550i	$-0.681644\pi$
$281$	−18.1101	−1.08036	−0.540179	+	0.841550i	$0.681644\pi$
$282$	4.87510	0.290308
$283$	−6.83821	−0.406489	−0.203245	−	0.979128i	$-0.565149\pi$
$283$	−6.83821	−0.406489	−0.203245	+	0.979128i	$0.565149\pi$
$284$	5.54397	0.328974
$285$	−2.41868	−0.143270
$286$	−2.81873	−0.166675
$287$	0	0
$288$	−3.97107	−0.233997
$289$	−9.94177	−0.584810
$290$	−0.336012	−0.0197313
$291$	−13.0477	−0.764871
$292$	53.2495	3.11619
$293$	26.8765	1.57014	0.785072	−	0.619405i	$-0.212626\pi$
$293$	26.8765	1.57014	0.785072	+	0.619405i	$0.212626\pi$
$294$	0	0
$295$	5.23398	0.304734
$296$	8.95032	0.520227
$297$	6.08054	0.352829
$298$	13.7450	0.796228
$299$	4.79779	0.277463
$300$	14.3049	0.825892
$301$	0	0
$302$	−15.5390	−0.894167
$303$	6.81873	0.391726
$304$	8.59175	0.492771
$305$	−2.38641	−0.136646
$306$	−14.0562	−0.803537
$307$	−23.5760	−1.34555	−0.672777	−	0.739846i	$-0.734898\pi$
$307$	−23.5760	−1.34555	−0.672777	+	0.739846i	$0.734898\pi$
$308$	0	0
$309$	4.53546	0.258013
$310$	18.3831	1.04409
$311$	28.2111	1.59970	0.799852	−	0.600197i	$-0.204911\pi$
$311$	28.2111	1.59970	0.799852	+	0.600197i	$0.204911\pi$
$312$	3.48955	0.197557
$313$	−11.5863	−0.654895	−0.327447	−	0.944869i	$-0.606188\pi$
$313$	−11.5863	−0.654895	−0.327447	+	0.944869i	$0.606188\pi$
$314$	8.23246	0.464585
$315$	0	0
$316$	−54.1668	−3.04712
$317$	−25.3507	−1.42384	−0.711918	−	0.702263i	$-0.752173\pi$
$317$	−25.3507	−1.42384	−0.711918	+	0.702263i	$0.752173\pi$
$318$	−21.7551	−1.21996
$319$	0.203110	0.0113720
$320$	−9.02241	−0.504368
$321$	−13.1388	−0.733335
$322$	0	0
$323$	−7.99601	−0.444910
$324$	9.17644	0.509802
$325$	−3.76185	−0.208670
$326$	51.1363	2.83218
$327$	10.9775	0.607058
$328$	4.34226	0.239761
$329$	0	0
$330$	2.52686	0.139099
$331$	−22.9101	−1.25925	−0.629627	−	0.776898i	$-0.716792\pi$
$331$	−22.9101	−1.25925	−0.629627	+	0.776898i	$0.716792\pi$
$332$	−18.0152	−0.988713
$333$	4.52719	0.248089
$334$	32.8343	1.79661
$335$	3.78067	0.206560
$336$	0	0
$337$	30.4011	1.65605	0.828026	−	0.560690i	$-0.189464\pi$
$337$	30.4011	1.65605	0.828026	+	0.560690i	$0.189464\pi$
$338$	29.3794	1.59803
$339$	−5.44284	−0.295615
$340$	−9.05644	−0.491154
$341$	−11.1121	−0.601754
$342$	15.9237	0.861055
$343$	0	0
$344$	19.2695	1.03894
$345$	−4.30098	−0.231557
$346$	−25.9612	−1.39568
$347$	22.5879	1.21258	0.606292	−	0.795242i	$-0.292656\pi$
$347$	22.5879	1.21258	0.606292	+	0.795242i	$0.292656\pi$
$348$	−0.530426	−0.0284338
$349$	18.3169	0.980480	0.490240	−	0.871587i	$-0.336909\pi$
$349$	18.3169	0.980480	0.490240	+	0.871587i	$0.336909\pi$
$350$	0	0
$351$	4.17594	0.222895
$352$	2.36002	0.125789
$353$	11.7784	0.626902	0.313451	−	0.949604i	$-0.398515\pi$
$353$	11.7784	0.626902	0.313451	+	0.949604i	$0.398515\pi$
$354$	12.6079	0.670105
$355$	1.30697	0.0693666
$356$	16.4176	0.870133
$357$	0	0
$358$	15.8376	0.837045
$359$	−7.86062	−0.414868	−0.207434	−	0.978249i	$-0.566511\pi$
$359$	−7.86062	−0.414868	−0.207434	+	0.978249i	$0.566511\pi$
$360$	8.54967	0.450607
$361$	−9.94161	−0.523243
$362$	0.835746	0.0439258
$363$	8.33355	0.437398
$364$	0	0
$365$	12.5533	0.657072
$366$	−5.74854	−0.300481
$367$	−29.7087	−1.55078	−0.775392	−	0.631481i	$-0.782448\pi$
$367$	−29.7087	−1.55078	−0.775392	+	0.631481i	$0.782448\pi$
$368$	15.2781	0.796428
$369$	2.19638	0.114339
$370$	4.45104	0.231398
$371$	0	0
$372$	29.0195	1.50459
$373$	29.9161	1.54899	0.774497	−	0.632577i	$-0.218003\pi$
$373$	29.9161	1.54899	0.774497	+	0.632577i	$0.218003\pi$
$374$	8.35362	0.431956
$375$	7.39044	0.381640
$376$	−9.80303	−0.505553
$377$	0.139490	0.00718409
$378$	0	0
$379$	−12.7841	−0.656673	−0.328336	−	0.944561i	$-0.606488\pi$
$379$	−12.7841	−0.656673	−0.328336	+	0.944561i	$0.606488\pi$
$380$	10.2597	0.526312
$381$	9.16294	0.469432
$382$	39.2653	2.00899
$383$	34.6333	1.76968	0.884839	−	0.465896i	$-0.154268\pi$
$383$	34.6333	1.76968	0.884839	+	0.465896i	$0.154268\pi$
$384$	−18.4922	−0.943675
$385$	0	0
$386$	43.6518	2.22182
$387$	9.74676	0.495456
$388$	55.3466	2.80980
$389$	−12.6840	−0.643105	−0.321553	−	0.946892i	$-0.604205\pi$
$389$	−12.6840	−0.643105	−0.321553	+	0.946892i	$0.604205\pi$
$390$	1.73537	0.0878739
$391$	−14.2188	−0.719074
$392$	0	0
$393$	−16.3088	−0.822672
$394$	6.53107	0.329031
$395$	−12.7696	−0.642508
$396$	−10.9020	−0.547844
$397$	−13.5514	−0.680126	−0.340063	−	0.940403i	$-0.610448\pi$
$397$	−13.5514	−0.680126	−0.340063	+	0.940403i	$0.610448\pi$
$398$	−18.0617	−0.905350
$399$	0	0
$400$	−11.9793	−0.598964
$401$	−9.95837	−0.497297	−0.248649	−	0.968594i	$-0.579986\pi$
$401$	−9.95837	−0.497297	−0.248649	+	0.968594i	$0.579986\pi$
$402$	9.10711	0.454221
$403$	−7.63146	−0.380150
$404$	−28.9241	−1.43903
$405$	2.16331	0.107496
$406$	0	0
$407$	−2.69053	−0.133365
$408$	−10.3417	−0.511989
$409$	31.0779	1.53670	0.768351	−	0.640028i	$-0.221077\pi$
$409$	31.0779	1.53670	0.768351	+	0.640028i	$0.221077\pi$
$410$	2.15943	0.106647
$411$	−6.59489	−0.325302
$412$	−19.2388	−0.947826
$413$	0	0
$414$	28.3161	1.39166
$415$	−4.24701	−0.208478
$416$	1.62079	0.0794659
$417$	19.1048	0.935567
$418$	−9.46352	−0.462876
$419$	−8.89660	−0.434627	−0.217314	−	0.976102i	$-0.569729\pi$
$419$	−8.89660	−0.434627	−0.217314	+	0.976102i	$0.569729\pi$
$420$	0	0
$421$	14.3826	0.700964	0.350482	−	0.936569i	$-0.386018\pi$
$421$	14.3826	0.700964	0.350482	+	0.936569i	$0.386018\pi$
$422$	58.9202	2.86819
$423$	−4.95851	−0.241091
$424$	43.7459	2.12449
$425$	11.1486	0.540789
$426$	3.14830	0.152536
$427$	0	0
$428$	55.7328	2.69395
$429$	−1.04898	−0.0506454
$430$	9.58280	0.462124
$431$	23.2896	1.12182	0.560911	−	0.827876i	$-0.310451\pi$
$431$	23.2896	1.12182	0.560911	+	0.827876i	$0.310451\pi$
$432$	13.2979	0.639796
$433$	−38.2638	−1.83884	−0.919420	−	0.393277i	$-0.871341\pi$
$433$	−38.2638	−1.83884	−0.919420	+	0.393277i	$0.871341\pi$
$434$	0	0
$435$	−0.125046	−0.00599548
$436$	−46.5650	−2.23006
$437$	16.1079	0.770547
$438$	30.2393	1.44489
$439$	−26.0986	−1.24562	−0.622809	−	0.782374i	$-0.714009\pi$
$439$	−26.0986	−1.24562	−0.622809	+	0.782374i	$0.714009\pi$
$440$	−5.08110	−0.242232
$441$	0	0
$442$	5.73702	0.272882
$443$	20.9619	0.995930	0.497965	−	0.867197i	$-0.334081\pi$
$443$	20.9619	0.995930	0.497965	+	0.867197i	$0.334081\pi$
$444$	7.02639	0.333458
$445$	3.87039	0.183474
$446$	−22.1010	−1.04651
$447$	5.11517	0.241939
$448$	0	0
$449$	12.4845	0.589181	0.294590	−	0.955624i	$-0.404817\pi$
$449$	12.4845	0.589181	0.294590	+	0.955624i	$0.404817\pi$
$450$	−22.2020	−1.04661
$451$	−1.30531	−0.0614648
$452$	23.0878	1.08596
$453$	−5.78278	−0.271699
$454$	63.0886	2.96089
$455$	0	0
$456$	11.7157	0.548638
$457$	25.9610	1.21440	0.607202	−	0.794547i	$-0.292292\pi$
$457$	25.9610	1.21440	0.607202	+	0.794547i	$0.292292\pi$
$458$	−19.3610	−0.904682
$459$	−12.3759	−0.577655
$460$	18.2442	0.850638
$461$	−30.5008	−1.42056	−0.710282	−	0.703918i	$-0.751432\pi$
$461$	−30.5008	−1.42056	−0.710282	+	0.703918i	$0.751432\pi$
$462$	0	0
$463$	4.72338	0.219514	0.109757	−	0.993958i	$-0.464993\pi$
$463$	4.72338	0.219514	0.109757	+	0.993958i	$0.464993\pi$
$464$	0.444193	0.0206211
$465$	6.84123	0.317255
$466$	46.4744	2.15288
$467$	−0.292770	−0.0135478	−0.00677390	−	0.999977i	$-0.502156\pi$
$467$	−0.292770	−0.0135478	−0.00677390	+	0.999977i	$0.502156\pi$
$468$	−7.48714	−0.346093
$469$	0	0
$470$	−4.87510	−0.224871
$471$	3.06369	0.141167
$472$	−25.3526	−1.16695
$473$	−5.79254	−0.266341
$474$	−30.7602	−1.41286
$475$	−12.6299	−0.579499
$476$	0	0
$477$	22.1273	1.01314
$478$	45.1172	2.06361
$479$	−29.5822	−1.35164	−0.675822	−	0.737065i	$-0.736211\pi$
$479$	−29.5822	−1.35164	−0.675822	+	0.737065i	$0.736211\pi$
$480$	−1.45296	−0.0663183
$481$	−1.84778	−0.0842513
$482$	−42.2897	−1.92624
$483$	0	0
$484$	−35.3497	−1.60681
$485$	13.0477	0.592467
$486$	38.8747	1.76339
$487$	−12.0186	−0.544613	−0.272306	−	0.962211i	$-0.587786\pi$
$487$	−12.0186	−0.544613	−0.272306	+	0.962211i	$0.587786\pi$
$488$	11.5594	0.523269
$489$	19.0302	0.860577
$490$	0	0
$491$	−7.02928	−0.317227	−0.158613	−	0.987341i	$-0.550702\pi$
$491$	−7.02928	−0.317227	−0.158613	+	0.987341i	$0.550702\pi$
$492$	3.40886	0.153683
$493$	−0.413393	−0.0186183
$494$	−6.49927	−0.292416
$495$	−2.57009	−0.115517
$496$	−24.3017	−1.09118
$497$	0	0
$498$	−10.2305	−0.458438
$499$	−30.8518	−1.38112	−0.690558	−	0.723277i	$-0.742635\pi$
$499$	−30.8518	−1.38112	−0.690558	+	0.723277i	$0.742635\pi$
$500$	−31.3492	−1.40198
$501$	12.2192	0.545913
$502$	12.8075	0.571629
$503$	15.0642	0.671681	0.335840	−	0.941919i	$-0.390980\pi$
$503$	15.0642	0.671681	0.335840	+	0.941919i	$0.390980\pi$
$504$	0	0
$505$	−6.81873	−0.303429
$506$	−16.8283	−0.748111
$507$	10.9335	0.485572
$508$	−38.8679	−1.72448
$509$	−3.07539	−0.136314	−0.0681570	−	0.997675i	$-0.521712\pi$
$509$	−3.07539	−0.136314	−0.0681570	+	0.997675i	$0.521712\pi$
$510$	−5.14296	−0.227734
$511$	0	0
$512$	29.9527	1.32374
$513$	14.0202	0.619005
$514$	−4.21930	−0.186105
$515$	−4.53546	−0.199856
$516$	15.1274	0.665945
$517$	2.94686	0.129603
$518$	0	0
$519$	−9.66138	−0.424088
$520$	−3.48955	−0.153027
$521$	17.7386	0.777144	0.388572	−	0.921418i	$-0.372968\pi$
$521$	17.7386	0.777144	0.388572	+	0.921418i	$0.372968\pi$
$522$	0.823254	0.0360329
$523$	−14.9487	−0.653662	−0.326831	−	0.945083i	$-0.605981\pi$
$523$	−14.9487	−0.653662	−0.326831	+	0.945083i	$0.605981\pi$
$524$	69.1797	3.02213
$525$	0	0
$526$	19.6586	0.857154
$527$	22.6167	0.985198
$528$	−3.34040	−0.145372
$529$	5.64366	0.245377
$530$	21.7551	0.944979
$531$	−12.8237	−0.556500
$532$	0	0
$533$	−0.896451	−0.0388296
$534$	9.32323	0.403456
$535$	13.1388	0.568039
$536$	−18.3129	−0.790998
$537$	5.89393	0.254342
$538$	69.0783	2.97818
$539$	0	0
$540$	15.8795	0.683345
$541$	3.58744	0.154236	0.0771180	−	0.997022i	$-0.475428\pi$
$541$	3.58744	0.154236	0.0771180	+	0.997022i	$0.475428\pi$
$542$	5.34559	0.229613
$543$	0.311020	0.0133472
$544$	−4.80340	−0.205944
$545$	−10.9775	−0.470225
$546$	0	0
$547$	15.7526	0.673531	0.336765	−	0.941589i	$-0.390667\pi$
$547$	15.7526	0.673531	0.336765	+	0.941589i	$0.390667\pi$
$548$	27.9746	1.19501
$549$	5.84689	0.249539
$550$	13.1948	0.562626
$551$	0.468318	0.0199510
$552$	20.8332	0.886722
$553$	0	0
$554$	−9.77927	−0.415481
$555$	1.65644	0.0703120
$556$	−81.0399	−3.43686
$557$	11.9288	0.505440	0.252720	−	0.967539i	$-0.418675\pi$
$557$	11.9288	0.505440	0.252720	+	0.967539i	$0.418675\pi$
$558$	−45.0401	−1.90670
$559$	−3.97814	−0.168258
$560$	0	0
$561$	3.10878	0.131253
$562$	43.6248	1.84020
$563$	−27.6501	−1.16531	−0.582657	−	0.812718i	$-0.697987\pi$
$563$	−27.6501	−1.16531	−0.582657	+	0.812718i	$0.697987\pi$
$564$	−7.69580	−0.324052
$565$	5.44284	0.228982
$566$	16.4723	0.692382
$567$	0	0
$568$	−6.33073	−0.265632
$569$	−12.7437	−0.534245	−0.267122	−	0.963663i	$-0.586073\pi$
$569$	−12.7437	−0.534245	−0.267122	+	0.963663i	$0.586073\pi$
$570$	5.82627	0.244036
$571$	20.5748	0.861028	0.430514	−	0.902584i	$-0.358332\pi$
$571$	20.5748	0.861028	0.430514	+	0.902584i	$0.358332\pi$
$572$	4.44964	0.186049
$573$	14.6125	0.610444
$574$	0	0
$575$	−22.4589	−0.936601
$576$	22.1056	0.921067
$577$	−25.9639	−1.08089	−0.540445	−	0.841379i	$-0.681744\pi$
$577$	−25.9639	−1.08089	−0.540445	+	0.841379i	$0.681744\pi$
$578$	23.9484	0.996120
$579$	16.2449	0.675115
$580$	0.530426	0.0220248
$581$	0	0
$582$	31.4302	1.30282
$583$	−13.1503	−0.544631
$584$	−60.8063	−2.51618
$585$	−1.76506	−0.0729763
$586$	−64.7419	−2.67446
$587$	−38.0271	−1.56955	−0.784773	−	0.619783i	$-0.787220\pi$
$587$	−38.0271	−1.56955	−0.784773	+	0.619783i	$0.787220\pi$
$588$	0	0
$589$	−25.6216	−1.05572
$590$	−12.6079	−0.519061
$591$	2.43052	0.0999782
$592$	−5.88408	−0.241834
$593$	40.4865	1.66258	0.831291	−	0.555837i	$-0.187602\pi$
$593$	40.4865	1.66258	0.831291	+	0.555837i	$0.187602\pi$
$594$	−14.6472	−0.600981
$595$	0	0
$596$	−21.6978	−0.888778
$597$	−6.72160	−0.275097
$598$	−11.5572	−0.472609
$599$	−40.0177	−1.63508	−0.817540	−	0.575872i	$-0.804663\pi$
$599$	−40.0177	−1.63508	−0.817540	+	0.575872i	$0.804663\pi$
$600$	−16.3349	−0.666870
$601$	−18.2716	−0.745316	−0.372658	−	0.927969i	$-0.621554\pi$
$601$	−18.2716	−0.745316	−0.372658	+	0.927969i	$0.621554\pi$
$602$	0	0
$603$	−9.26293	−0.377216
$604$	24.5298	0.998101
$605$	−8.33355	−0.338807
$606$	−16.4254	−0.667235
$607$	−30.1832	−1.22510	−0.612548	−	0.790433i	$-0.709856\pi$
$607$	−30.1832	−1.22510	−0.612548	+	0.790433i	$0.709856\pi$
$608$	5.44159	0.220686
$609$	0	0
$610$	5.74854	0.232751
$611$	2.02382	0.0818748
$612$	22.1890	0.896936
$613$	−40.0718	−1.61849	−0.809243	−	0.587474i	$-0.800122\pi$
$613$	−40.0718	−1.61849	−0.809243	+	0.587474i	$0.800122\pi$
$614$	56.7913	2.29191
$615$	0.803625	0.0324053
$616$	0	0
$617$	43.3379	1.74472	0.872358	−	0.488867i	$-0.162590\pi$
$617$	43.3379	1.74472	0.872358	+	0.488867i	$0.162590\pi$
$618$	−10.9253	−0.439480
$619$	23.6793	0.951752	0.475876	−	0.879512i	$-0.342131\pi$
$619$	23.6793	0.951752	0.475876	+	0.879512i	$0.342131\pi$
$620$	−29.0195	−1.16545
$621$	24.9311	1.00045
$622$	−67.9566	−2.72481
$623$	0	0
$624$	−2.29409	−0.0918369
$625$	13.5914	0.543658
$626$	27.9097	1.11550
$627$	−3.52182	−0.140648
$628$	−12.9957	−0.518586
$629$	5.47609	0.218346
$630$	0	0
$631$	−15.6187	−0.621772	−0.310886	−	0.950447i	$-0.600626\pi$
$631$	−15.6187	−0.621772	−0.310886	+	0.950447i	$0.600626\pi$
$632$	61.8538	2.46041
$633$	21.9270	0.871519
$634$	61.0663	2.42525
$635$	−9.16294	−0.363620
$636$	34.3424	1.36177
$637$	0	0
$638$	−0.489263	−0.0193701
$639$	−3.20217	−0.126676
$640$	18.4922	0.730967
$641$	9.49912	0.375193	0.187596	−	0.982246i	$-0.439930\pi$
$641$	9.49912	0.375193	0.187596	+	0.982246i	$0.439930\pi$
$642$	31.6495	1.24911
$643$	33.6019	1.32513	0.662564	−	0.749005i	$-0.269468\pi$
$643$	33.6019	1.32513	0.662564	+	0.749005i	$0.269468\pi$
$644$	0	0
$645$	3.56621	0.140419
$646$	19.2613	0.757825
$647$	14.9445	0.587530	0.293765	−	0.955878i	$-0.405092\pi$
$647$	14.9445	0.587530	0.293765	+	0.955878i	$0.405092\pi$
$648$	−10.4787	−0.411642
$649$	7.62115	0.299156
$650$	9.06177	0.355432
$651$	0	0
$652$	−80.7235	−3.16138
$653$	15.1767	0.593910	0.296955	−	0.954891i	$-0.404029\pi$
$653$	15.1767	0.593910	0.296955	+	0.954891i	$0.404029\pi$
$654$	−26.4433	−1.03402
$655$	16.3088	0.637239
$656$	−2.85467	−0.111456
$657$	−30.7567	−1.19993
$658$	0	0
$659$	8.09942	0.315509	0.157754	−	0.987478i	$-0.449575\pi$
$659$	8.09942	0.315509	0.157754	+	0.987478i	$0.449575\pi$
$660$	−3.98888	−0.155267
$661$	15.0298	0.584591	0.292295	−	0.956328i	$-0.405581\pi$
$661$	15.0298	0.584591	0.292295	+	0.956328i	$0.405581\pi$
$662$	55.1873	2.14491
$663$	2.13502	0.0829172
$664$	20.5718	0.798341
$665$	0	0
$666$	−10.9054	−0.422575
$667$	0.832779	0.0322453
$668$	−51.8320	−2.00544
$669$	−8.22483	−0.317990
$670$	−9.10711	−0.351838
$671$	−3.47483	−0.134144
$672$	0	0
$673$	44.9730	1.73358	0.866790	−	0.498673i	$-0.166179\pi$
$673$	44.9730	1.73358	0.866790	+	0.498673i	$0.166179\pi$
$674$	−73.2320	−2.82079
$675$	−19.5480	−0.752401
$676$	−46.3782	−1.78378
$677$	51.7583	1.98923	0.994616	−	0.103624i	$-0.0330440\pi$
$677$	51.7583	1.98923	0.994616	+	0.103624i	$0.0330440\pi$
$678$	13.1111	0.503527
$679$	0	0
$680$	10.3417	0.396585
$681$	23.4782	0.899688
$682$	26.7675	1.02498
$683$	−14.3092	−0.547526	−0.273763	−	0.961797i	$-0.588268\pi$
$683$	−14.3092	−0.547526	−0.273763	+	0.961797i	$0.588268\pi$
$684$	−25.1371	−0.961140
$685$	6.59489	0.251978
$686$	0	0
$687$	−7.20515	−0.274894
$688$	−12.6681	−0.482965
$689$	−9.03126	−0.344063
$690$	10.3605	0.394417
$691$	28.0635	1.06759	0.533793	−	0.845615i	$-0.320766\pi$
$691$	28.0635	1.06759	0.533793	+	0.845615i	$0.320766\pi$
$692$	40.9822	1.55791
$693$	0	0
$694$	−54.4112	−2.06542
$695$	−19.1048	−0.724687
$696$	0.605701	0.0229590
$697$	2.65673	0.100631
$698$	−44.1228	−1.67007
$699$	17.2953	0.654169
$700$	0	0
$701$	42.0578	1.58850	0.794250	−	0.607591i	$-0.207864\pi$
$701$	42.0578	1.58850	0.794250	+	0.607591i	$0.207864\pi$
$702$	−10.0593	−0.379662
$703$	−6.20366	−0.233976
$704$	−13.1374	−0.495136
$705$	−1.81425	−0.0683287
$706$	−28.3726	−1.06782
$707$	0	0
$708$	−19.9028	−0.747995
$709$	7.43843	0.279356	0.139678	−	0.990197i	$-0.455393\pi$
$709$	7.43843	0.279356	0.139678	+	0.990197i	$0.455393\pi$
$710$	−3.14830	−0.118154
$711$	31.2865	1.17334
$712$	−18.7475	−0.702593
$713$	−45.5612	−1.70628
$714$	0	0
$715$	1.04898	0.0392297
$716$	−25.0012	−0.934340
$717$	16.7902	0.627043
$718$	18.9352	0.706654
$719$	−34.0504	−1.26987	−0.634933	−	0.772567i	$-0.718972\pi$
$719$	−34.0504	−1.26987	−0.634933	+	0.772567i	$0.718972\pi$
$720$	−5.62069	−0.209471
$721$	0	0
$722$	23.9480	0.891251
$723$	−15.7380	−0.585302
$724$	−1.31930	−0.0490315
$725$	−0.652965	−0.0242505
$726$	−20.0744	−0.745030
$727$	23.9058	0.886616	0.443308	−	0.896369i	$-0.353805\pi$
$727$	23.9058	0.886616	0.443308	+	0.896369i	$0.353805\pi$
$728$	0	0
$729$	7.22754	0.267687
$730$	−30.2393	−1.11921
$731$	11.7897	0.436057
$732$	9.07461	0.335407
$733$	−28.6022	−1.05645	−0.528224	−	0.849105i	$-0.677142\pi$
$733$	−28.6022	−1.05645	−0.528224	+	0.849105i	$0.677142\pi$
$734$	71.5643	2.64148
$735$	0	0
$736$	9.67642	0.356678
$737$	5.50499	0.202779
$738$	−5.29077	−0.194756
$739$	27.8308	1.02377	0.511887	−	0.859053i	$-0.328947\pi$
$739$	27.8308	1.02377	0.511887	+	0.859053i	$0.328947\pi$
$740$	−7.02639	−0.258295
$741$	−2.41868	−0.0888525
$742$	0	0
$743$	36.1223	1.32520	0.662599	−	0.748975i	$-0.269453\pi$
$743$	36.1223	1.32520	0.662599	+	0.748975i	$0.269453\pi$
$744$	−33.1378	−1.21489
$745$	−5.11517	−0.187405
$746$	−72.0637	−2.63844
$747$	10.4055	0.380718
$748$	−13.1870	−0.482164
$749$	0	0
$750$	−17.8025	−0.650057
$751$	21.1319	0.771112	0.385556	−	0.922684i	$-0.374010\pi$
$751$	21.1319	0.771112	0.385556	+	0.922684i	$0.374010\pi$
$752$	6.44467	0.235013
$753$	4.76629	0.173693
$754$	−0.336012	−0.0122368
$755$	5.78278	0.210457
$756$	0	0
$757$	−37.1869	−1.35158	−0.675791	−	0.737093i	$-0.736198\pi$
$757$	−37.1869	−1.35158	−0.675791	+	0.737093i	$0.736198\pi$
$758$	30.7950	1.11853
$759$	−6.26262	−0.227319
$760$	−11.7157	−0.424973
$761$	−39.0401	−1.41520	−0.707602	−	0.706611i	$-0.750223\pi$
$761$	−39.0401	−1.41520	−0.707602	+	0.706611i	$0.750223\pi$
$762$	−22.0723	−0.799593
$763$	0	0
$764$	−61.9840	−2.24250
$765$	5.23096	0.189126
$766$	−83.4268	−3.01433
$767$	5.23398	0.188988
$768$	26.5003	0.956246
$769$	7.69986	0.277664	0.138832	−	0.990316i	$-0.455665\pi$
$769$	7.69986	0.277664	0.138832	+	0.990316i	$0.455665\pi$
$770$	0	0
$771$	−1.57020	−0.0565493
$772$	−68.9085	−2.48007
$773$	−6.49894	−0.233751	−0.116875	−	0.993147i	$-0.537288\pi$
$773$	−6.49894	−0.233751	−0.116875	+	0.993147i	$0.537288\pi$
$774$	−23.4786	−0.843921
$775$	35.7236	1.28323
$776$	−63.2010	−2.26878
$777$	0	0
$778$	30.5541	1.09542
$779$	−3.00972	−0.107834
$780$	−2.73945	−0.0980879
$781$	1.90306	0.0680969
$782$	34.2511	1.22482
$783$	0.724841	0.0259037
$784$	0	0
$785$	−3.06369	−0.109348
$786$	39.2857	1.40128
$787$	20.1940	0.719839	0.359920	−	0.932983i	$-0.382804\pi$
$787$	20.1940	0.719839	0.359920	+	0.932983i	$0.382804\pi$
$788$	−10.3099	−0.367276
$789$	7.31588	0.260452
$790$	30.7602	1.09440
$791$	0	0
$792$	12.4491	0.442359
$793$	−2.38641	−0.0847440
$794$	32.6435	1.15847
$795$	8.09608	0.287138
$796$	28.5121	1.01058
$797$	−0.786646	−0.0278644	−0.0139322	−	0.999903i	$-0.504435\pi$
$797$	−0.786646	−0.0278644	−0.0139322	+	0.999903i	$0.504435\pi$
$798$	0	0
$799$	−5.99780	−0.212187
$800$	−7.58708	−0.268244
$801$	−9.48275	−0.335056
$802$	23.9883	0.847058
$803$	18.2788	0.645045
$804$	−14.3764	−0.507018
$805$	0	0
$806$	18.3831	0.647519
$807$	25.7073	0.904940
$808$	33.0288	1.16195
$809$	0.748252	0.0263071	0.0131536	−	0.999913i	$-0.495813\pi$
$809$	0.748252	0.0263071	0.0131536	+	0.999913i	$0.495813\pi$
$810$	−5.21111	−0.183100
$811$	37.4757	1.31595	0.657975	−	0.753039i	$-0.271413\pi$
$811$	37.4757	1.31595	0.657975	+	0.753039i	$0.271413\pi$
$812$	0	0
$813$	1.98934	0.0697694
$814$	6.48111	0.227163
$815$	−19.0302	−0.666600
$816$	6.79878	0.238005
$817$	−13.3561	−0.467270
$818$	−74.8623	−2.61750
$819$	0	0
$820$	−3.40886	−0.119043
$821$	2.30143	0.0803205	0.0401602	−	0.999193i	$-0.487213\pi$
$821$	2.30143	0.0803205	0.0401602	+	0.999193i	$0.487213\pi$
$822$	15.8862	0.554094
$823$	−32.4795	−1.13216	−0.566082	−	0.824349i	$-0.691541\pi$
$823$	−32.4795	−1.13216	−0.566082	+	0.824349i	$0.691541\pi$
$824$	21.9690	0.765326
$825$	4.91039	0.170958
$826$	0	0
$827$	19.7762	0.687685	0.343842	−	0.939027i	$-0.388271\pi$
$827$	19.7762	0.687685	0.343842	+	0.939027i	$0.388271\pi$
$828$	−44.6996	−1.55342
$829$	−9.99927	−0.347289	−0.173645	−	0.984808i	$-0.555554\pi$
$829$	−9.99927	−0.347289	−0.173645	+	0.984808i	$0.555554\pi$
$830$	10.2305	0.355105
$831$	−3.63933	−0.126247
$832$	−9.02241	−0.312796
$833$	0	0
$834$	−46.0209	−1.59357
$835$	−12.2192	−0.422862
$836$	14.9391	0.516678
$837$	−39.6559	−1.37071
$838$	21.4307	0.740311
$839$	9.04091	0.312127	0.156063	−	0.987747i	$-0.450120\pi$
$839$	9.04091	0.312127	0.156063	+	0.987747i	$0.450120\pi$
$840$	0	0
$841$	−28.9758	−0.999165
$842$	−34.6457	−1.19397
$843$	16.2348	0.559157
$844$	−93.0112	−3.20158
$845$	−10.9335	−0.376122
$846$	11.9444	0.410656
$847$	0	0
$848$	−28.7593	−0.987597
$849$	6.13012	0.210385
$850$	−26.8556	−0.921138
$851$	−11.0316	−0.378157
$852$	−4.96990	−0.170266
$853$	−43.3121	−1.48298	−0.741490	−	0.670964i	$-0.765880\pi$
$853$	−43.3121	−1.48298	−0.741490	+	0.670964i	$0.765880\pi$
$854$	0	0
$855$	−5.92596	−0.202664
$856$	−63.6421	−2.17524
$857$	52.0023	1.77636	0.888182	−	0.459493i	$-0.151969\pi$
$857$	52.0023	1.77636	0.888182	+	0.459493i	$0.151969\pi$
$858$	2.52686	0.0862654
$859$	−23.4142	−0.798882	−0.399441	−	0.916759i	$-0.630796\pi$
$859$	−23.4142	−0.798882	−0.399441	+	0.916759i	$0.630796\pi$
$860$	−15.1274	−0.515839
$861$	0	0
$862$	−56.1015	−1.91083
$863$	−21.5120	−0.732278	−0.366139	−	0.930560i	$-0.619321\pi$
$863$	−21.5120	−0.732278	−0.366139	+	0.930560i	$0.619321\pi$
$864$	8.42224	0.286531
$865$	9.66138	0.328497
$866$	92.1722	3.13214
$867$	8.91231	0.302678
$868$	0	0
$869$	−18.5937	−0.630747
$870$	0.301218	0.0102122
$871$	3.78067	0.128103
$872$	53.1732	1.80067
$873$	−31.9679	−1.08195
$874$	−38.8018	−1.31249
$875$	0	0
$876$	−47.7356	−1.61284
$877$	−15.4797	−0.522714	−0.261357	−	0.965242i	$-0.584170\pi$
$877$	−15.4797	−0.522714	−0.261357	+	0.965242i	$0.584170\pi$
$878$	62.8679	2.12169
$879$	−24.0935	−0.812654
$880$	3.34040	0.112605
$881$	−20.7757	−0.699951	−0.349975	−	0.936759i	$-0.613810\pi$
$881$	−20.7757	−0.699951	−0.349975	+	0.936759i	$0.613810\pi$
$882$	0	0
$883$	20.0013	0.673096	0.336548	−	0.941666i	$-0.390741\pi$
$883$	20.0013	0.673096	0.336548	+	0.941666i	$0.390741\pi$
$884$	−9.05644	−0.304601
$885$	−4.69201	−0.157720
$886$	−50.4944	−1.69639
$887$	15.4053	0.517261	0.258630	−	0.965976i	$-0.416729\pi$
$887$	15.4053	0.517261	0.258630	+	0.965976i	$0.416729\pi$
$888$	−8.02352	−0.269252
$889$	0	0
$890$	−9.32323	−0.312515
$891$	3.14997	0.105528
$892$	34.8885	1.16815
$893$	6.79470	0.227376
$894$	−12.3217	−0.412101
$895$	−5.89393	−0.197012
$896$	0	0
$897$	−4.30098	−0.143606
$898$	−30.0735	−1.00356
$899$	−1.32464	−0.0441791
$900$	35.0480	1.16827
$901$	26.7651	0.891676
$902$	3.14432	0.104694
$903$	0	0
$904$	−26.3642	−0.876861
$905$	−0.311020	−0.0103387
$906$	13.9299	0.462791
$907$	−19.0062	−0.631089	−0.315545	−	0.948911i	$-0.602187\pi$
$907$	−19.0062	−0.631089	−0.315545	+	0.948911i	$0.602187\pi$
$908$	−99.5913	−3.30505
$909$	16.7064	0.554117
$910$	0	0
$911$	5.36492	0.177748	0.0888739	−	0.996043i	$-0.471673\pi$
$911$	5.36492	0.177748	0.0888739	+	0.996043i	$0.471673\pi$
$912$	−7.70209	−0.255042
$913$	−6.18403	−0.204662
$914$	−62.5365	−2.06852
$915$	2.13930	0.0707231
$916$	30.5632	1.00984
$917$	0	0
$918$	29.8117	0.983934
$919$	2.83269	0.0934417	0.0467208	−	0.998908i	$-0.485123\pi$
$919$	2.83269	0.0934417	0.0467208	+	0.998908i	$0.485123\pi$
$920$	−20.8332	−0.686852
$921$	21.1347	0.696413
$922$	73.4722	2.41968
$923$	1.30697	0.0430193
$924$	0	0
$925$	8.64962	0.284398
$926$	−11.3780	−0.373903
$927$	11.1122	0.364973
$928$	0.281330	0.00923511
$929$	−49.9001	−1.63717	−0.818585	−	0.574386i	$-0.805241\pi$
$929$	−49.9001	−1.63717	−0.818585	+	0.574386i	$0.805241\pi$
$930$	−16.4796	−0.540387
$931$	0	0
$932$	−73.3642	−2.40313
$933$	−25.2899	−0.827953
$934$	0.705244	0.0230763
$935$	−3.10878	−0.101668
$936$	8.54967	0.279455
$937$	−7.68076	−0.250919	−0.125460	−	0.992099i	$-0.540041\pi$
$937$	−7.68076	−0.250919	−0.125460	+	0.992099i	$0.540041\pi$
$938$	0	0
$939$	10.3865	0.338951
$940$	7.69580	0.251009
$941$	36.7091	1.19668	0.598341	−	0.801241i	$-0.295827\pi$
$941$	36.7091	1.19668	0.598341	+	0.801241i	$0.295827\pi$
$942$	−7.38000	−0.240453
$943$	−5.35198	−0.174284
$944$	16.6672	0.542470
$945$	0	0
$946$	13.9534	0.453665
$947$	−37.1503	−1.20722	−0.603611	−	0.797279i	$-0.706272\pi$
$947$	−37.1503	−1.20722	−0.603611	+	0.797279i	$0.706272\pi$
$948$	48.5579	1.57709
$949$	12.5533	0.407499
$950$	30.4237	0.987075
$951$	22.7256	0.736929
$952$	0	0
$953$	−25.2779	−0.818831	−0.409415	−	0.912348i	$-0.634267\pi$
$953$	−25.2779	−0.818831	−0.409415	+	0.912348i	$0.634267\pi$
$954$	−53.3016	−1.72570
$955$	−14.6125	−0.472848
$956$	−71.2218	−2.30348
$957$	−0.182078	−0.00588574
$958$	71.2594	2.30229
$959$	0	0
$960$	8.08815	0.261044
$961$	41.4706	1.33776
$962$	4.45104	0.143507
$963$	−32.1910	−1.03734
$964$	66.7583	2.15014
$965$	−16.2449	−0.522941
$966$	0	0
$967$	−2.98768	−0.0960772	−0.0480386	−	0.998845i	$-0.515297\pi$
$967$	−2.98768	−0.0960772	−0.0480386	+	0.998845i	$0.515297\pi$
$968$	40.3663	1.29742
$969$	7.16804	0.230270
$970$	−31.4302	−1.00916
$971$	−23.7825	−0.763217	−0.381608	−	0.924324i	$-0.624630\pi$
$971$	−23.7825	−0.763217	−0.381608	+	0.924324i	$0.624630\pi$
$972$	−61.3674	−1.96836
$973$	0	0
$974$	28.9511	0.927652
$975$	3.37231	0.108000
$976$	−7.59932	−0.243248
$977$	−16.6059	−0.531270	−0.265635	−	0.964074i	$-0.585582\pi$
$977$	−16.6059	−0.531270	−0.265635	+	0.964074i	$0.585582\pi$
$978$	−45.8412	−1.46584
$979$	5.63563	0.180116
$980$	0	0
$981$	26.8958	0.858715
$982$	16.9326	0.540340
$983$	15.9287	0.508048	0.254024	−	0.967198i	$-0.418246\pi$
$983$	15.9287	0.508048	0.254024	+	0.967198i	$0.418246\pi$
$984$	−3.89263	−0.124092
$985$	−2.43052	−0.0774428
$986$	0.995808	0.0317130
$987$	0	0
$988$	10.2597	0.326405
$989$	−23.7502	−0.755214
$990$	6.19099	0.196763
$991$	−3.25503	−0.103399	−0.0516997	−	0.998663i	$-0.516464\pi$
$991$	−3.25503	−0.103399	−0.0516997	+	0.998663i	$0.516464\pi$
$992$	−15.3915	−0.488681
$993$	20.5378	0.651747
$994$	0	0
$995$	6.72160	0.213089
$996$	16.1498	0.511725
$997$	6.12263	0.193906	0.0969528	−	0.995289i	$-0.469090\pi$
$997$	6.12263	0.193906	0.0969528	+	0.995289i	$0.469090\pi$
$998$	74.3178	2.35249
$999$	−9.60174	−0.303785

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2009.2.a.l.1.1		5
7.2	even	3		287.2.e.c.165.5	✓	10
7.4	even	3		287.2.e.c.247.5	yes	10
7.6	odd	2		2009.2.a.m.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.e.c.165.5	✓	10	7.2	even	3
287.2.e.c.247.5	yes	10	7.4	even	3
2009.2.a.l.1.1		5	1.1	even	1	trivial
2009.2.a.m.1.1		5	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-2.40886 q^{2} -0.896451 q^{3} +3.80262 q^{4} +0.896451 q^{5} +2.15943 q^{6} -4.34226 q^{8} -2.19638 q^{9} +O(q^{10})\)	\(q-2.40886 q^{2} -0.896451 q^{3} +3.80262 q^{4} +0.896451 q^{5} +2.15943 q^{6} -4.34226 q^{8} -2.19638 q^{9} -2.15943 q^{10} +1.30531 q^{11} -3.40886 q^{12} +0.896451 q^{13} -0.803625 q^{15} +2.85467 q^{16} -2.65673 q^{17} +5.29077 q^{18} +3.00972 q^{19} +3.40886 q^{20} -3.14432 q^{22} +5.35198 q^{23} +3.89263 q^{24} -4.19638 q^{25} -2.15943 q^{26} +4.65830 q^{27} +0.155602 q^{29} +1.93582 q^{30} -8.51297 q^{31} +1.80801 q^{32} -1.17015 q^{33} +6.39970 q^{34} -8.35198 q^{36} -2.06121 q^{37} -7.24999 q^{38} -0.803625 q^{39} -3.89263 q^{40} -1.00000 q^{41} -4.43766 q^{43} +4.96361 q^{44} -1.96894 q^{45} -12.8922 q^{46} +2.25759 q^{47} -2.55907 q^{48} +10.1085 q^{50} +2.38163 q^{51} +3.40886 q^{52} -10.0745 q^{53} -11.2212 q^{54} +1.17015 q^{55} -2.69806 q^{57} -0.374824 q^{58} +5.83856 q^{59} -3.05588 q^{60} -2.66207 q^{61} +20.5066 q^{62} -10.0646 q^{64} +0.803625 q^{65} +2.81873 q^{66} +4.21737 q^{67} -10.1025 q^{68} -4.79779 q^{69} +1.45793 q^{71} +9.53723 q^{72} +14.0034 q^{73} +4.96518 q^{74} +3.76185 q^{75} +11.4448 q^{76} +1.93582 q^{78} -14.2446 q^{79} +2.55907 q^{80} +2.41319 q^{81} +2.40886 q^{82} -4.73758 q^{83} -2.38163 q^{85} +10.6897 q^{86} -0.139490 q^{87} -5.66801 q^{88} +4.31745 q^{89} +4.74291 q^{90} +20.3515 q^{92} +7.63146 q^{93} -5.43822 q^{94} +2.69806 q^{95} -1.62079 q^{96} +14.5549 q^{97} -2.86696 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 2 q^{2} - 2 q^{3} + 6 q^{4} + 2 q^{5} + q^{6} - 3 q^{8} + 5 q^{9}+O(q^{10}) \) 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

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