LMFDB - Embedded newform 1003.2.a.i.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1003,2,Mod(1,1003)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1003, 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("1003.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1003 = 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1003.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:	$8.00899532273$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 5 x^{17} - 16 x^{16} + 112 x^{15} + 52 x^{14} - 984 x^{13} + 431 x^{12} + 4304 x^{11} + \cdots + 28 $ x^18 - 5x^17 - 16x^16 + 112x^15 + 52x^14 - 984x^13 + 431x^12 + 4304x^11 - 3825x^10 - 9826x^9 + 11533x^8 + 11182x^7 - 15697x^6 - 5604x^5 + 9201x^4 + 1189x^3 - 1952x^2 - 100*x + 28
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-0.714378$ of defining polynomial
Character	$\chi$	$=$	1003.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.714378 q^{2} -2.62504 q^{3} -1.48966 q^{4} +0.882657 q^{5} +1.87527 q^{6} -0.838797 q^{7} +2.49294 q^{8} +3.89086 q^{9} +O(q^{10})$	\(q-0.714378 q^{2} -2.62504 q^{3} -1.48966 q^{4} +0.882657 q^{5} +1.87527 q^{6} -0.838797 q^{7} +2.49294 q^{8} +3.89086 q^{9} -0.630551 q^{10} -4.52472 q^{11} +3.91043 q^{12} -2.33914 q^{13} +0.599219 q^{14} -2.31701 q^{15} +1.19843 q^{16} +1.00000 q^{17} -2.77955 q^{18} -3.04868 q^{19} -1.31486 q^{20} +2.20188 q^{21} +3.23236 q^{22} -7.90876 q^{23} -6.54408 q^{24} -4.22092 q^{25} +1.67103 q^{26} -2.33855 q^{27} +1.24953 q^{28} -0.818311 q^{29} +1.65522 q^{30} -2.29104 q^{31} -5.84201 q^{32} +11.8776 q^{33} -0.714378 q^{34} -0.740370 q^{35} -5.79607 q^{36} +8.58988 q^{37} +2.17791 q^{38} +6.14035 q^{39} +2.20041 q^{40} +10.6404 q^{41} -1.57298 q^{42} -0.979313 q^{43} +6.74031 q^{44} +3.43429 q^{45} +5.64984 q^{46} -4.83264 q^{47} -3.14592 q^{48} -6.29642 q^{49} +3.01533 q^{50} -2.62504 q^{51} +3.48453 q^{52} +5.63575 q^{53} +1.67061 q^{54} -3.99377 q^{55} -2.09107 q^{56} +8.00293 q^{57} +0.584584 q^{58} -1.00000 q^{59} +3.45157 q^{60} +2.11105 q^{61} +1.63667 q^{62} -3.26364 q^{63} +1.77655 q^{64} -2.06466 q^{65} -8.48509 q^{66} +11.2466 q^{67} -1.48966 q^{68} +20.7608 q^{69} +0.528904 q^{70} +5.19582 q^{71} +9.69968 q^{72} +6.63693 q^{73} -6.13642 q^{74} +11.0801 q^{75} +4.54151 q^{76} +3.79532 q^{77} -4.38653 q^{78} +14.7194 q^{79} +1.05780 q^{80} -5.53378 q^{81} -7.60128 q^{82} +6.61943 q^{83} -3.28006 q^{84} +0.882657 q^{85} +0.699600 q^{86} +2.14810 q^{87} -11.2799 q^{88} -3.38821 q^{89} -2.45339 q^{90} +1.96207 q^{91} +11.7814 q^{92} +6.01408 q^{93} +3.45233 q^{94} -2.69094 q^{95} +15.3355 q^{96} -4.45791 q^{97} +4.49802 q^{98} -17.6051 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 5 q^{2} + q^{3} + 21 q^{4} + 21 q^{5} + 5 q^{6} - q^{7} + 9 q^{8} + 17 q^{9}+O(q^{10}) $ 18 * q + 5 * q^2 + q^3 + 21 * q^4 + 21 * q^5 + 5 * q^6 - q^7 + 9 * q^8 + 17 * q^9	\( 18 q + 5 q^{2} + q^{3} + 21 q^{4} + 21 q^{5} + 5 q^{6} - q^{7} + 9 q^{8} + 17 q^{9} + 10 q^{10} + 6 q^{11} + 20 q^{12} + 12 q^{13} + 9 q^{14} - q^{15} + 19 q^{16} + 18 q^{17} + 10 q^{18} - 14 q^{19} + 17 q^{20} - 14 q^{21} - 4 q^{22} + 7 q^{23} - 3 q^{24} + 35 q^{25} + 3 q^{26} + 13 q^{27} + q^{28} + 23 q^{29} + 17 q^{30} - q^{31} + 13 q^{32} + 7 q^{33} + 5 q^{34} + 5 q^{35} - 16 q^{36} + 36 q^{37} - 19 q^{38} + 8 q^{39} - 4 q^{40} + 37 q^{41} + 9 q^{42} - 15 q^{43} - 9 q^{44} + 17 q^{45} + q^{46} + 23 q^{47} + 17 q^{48} + 15 q^{49} + 32 q^{50} + q^{51} - 11 q^{52} + 35 q^{53} - 17 q^{54} - 6 q^{55} + 37 q^{56} - 16 q^{57} + 2 q^{58} - 18 q^{59} - 6 q^{60} + 39 q^{61} - q^{62} + 15 q^{63} + 5 q^{64} + 15 q^{65} - 36 q^{66} + 14 q^{67} + 21 q^{68} + 16 q^{69} - 45 q^{70} + 3 q^{71} - 71 q^{72} + 56 q^{73} - 27 q^{74} + 16 q^{75} - q^{76} + 39 q^{77} - 71 q^{78} - 22 q^{79} + 45 q^{80} - 18 q^{81} + 5 q^{82} + 12 q^{83} + 2 q^{84} + 21 q^{85} + 4 q^{86} + 8 q^{87} - 18 q^{88} + 34 q^{89} + 48 q^{90} + 3 q^{91} + 67 q^{92} - 19 q^{93} - 38 q^{94} - 72 q^{95} + 6 q^{96} + 31 q^{97} + 19 q^{98} + 44 q^{99}+O(q^{100}) \) 18 * q + 5 * q^2 + q^3 + 21 * q^4 + 21 * q^5 + 5 * q^6 - q^7 + 9 * q^8 + 17 * q^9 + 10 * q^10 + 6 * q^11 + 20 * q^12 + 12 * q^13 + 9 * q^14 - q^15 + 19 * q^16 + 18 * q^17 + 10 * q^18 - 14 * q^19 + 17 * q^20 - 14 * q^21 - 4 * q^22 + 7 * q^23 - 3 * q^24 + 35 * q^25 + 3 * q^26 + 13 * q^27 + q^28 + 23 * q^29 + 17 * q^30 - q^31 + 13 * q^32 + 7 * q^33 + 5 * q^34 + 5 * q^35 - 16 * q^36 + 36 * q^37 - 19 * q^38 + 8 * q^39 - 4 * q^40 + 37 * q^41 + 9 * q^42 - 15 * q^43 - 9 * q^44 + 17 * q^45 + q^46 + 23 * q^47 + 17 * q^48 + 15 * q^49 + 32 * q^50 + q^51 - 11 * q^52 + 35 * q^53 - 17 * q^54 - 6 * q^55 + 37 * q^56 - 16 * q^57 + 2 * q^58 - 18 * q^59 - 6 * q^60 + 39 * q^61 - q^62 + 15 * q^63 + 5 * q^64 + 15 * q^65 - 36 * q^66 + 14 * q^67 + 21 * q^68 + 16 * q^69 - 45 * q^70 + 3 * q^71 - 71 * q^72 + 56 * q^73 - 27 * q^74 + 16 * q^75 - q^76 + 39 * q^77 - 71 * q^78 - 22 * q^79 + 45 * q^80 - 18 * q^81 + 5 * q^82 + 12 * q^83 + 2 * q^84 + 21 * q^85 + 4 * q^86 + 8 * q^87 - 18 * q^88 + 34 * q^89 + 48 * q^90 + 3 * q^91 + 67 * q^92 - 19 * q^93 - 38 * q^94 - 72 * q^95 + 6 * q^96 + 31 * q^97 + 19 * q^98 + 44 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.714378	−0.505142	−0.252571	−	0.967578i	$-0.581276\pi$
$2$	−0.714378	−0.505142	−0.252571	+	0.967578i	$0.581276\pi$
$3$	−2.62504	−1.51557	−0.757785	−	0.652504i	$-0.773719\pi$
$3$	−2.62504	−1.51557	−0.757785	+	0.652504i	$0.773719\pi$
$4$	−1.48966	−0.744832
$5$	0.882657	0.394736	0.197368	−	0.980329i	$-0.436761\pi$
$5$	0.882657	0.394736	0.197368	+	0.980329i	$0.436761\pi$
$6$	1.87527	0.765578
$7$	−0.838797	−0.317036	−0.158518	−	0.987356i	$-0.550672\pi$
$7$	−0.838797	−0.317036	−0.158518	+	0.987356i	$0.550672\pi$
$8$	2.49294	0.881387
$9$	3.89086	1.29695
$10$	−0.630551	−0.199398
$11$	−4.52472	−1.36425	−0.682127	−	0.731234i	$-0.738945\pi$
$11$	−4.52472	−1.36425	−0.682127	+	0.731234i	$0.738945\pi$
$12$	3.91043	1.12885
$13$	−2.33914	−0.648761	−0.324381	−	0.945927i	$-0.605156\pi$
$13$	−2.33914	−0.648761	−0.324381	+	0.945927i	$0.605156\pi$
$14$	0.599219	0.160148
$15$	−2.31701	−0.598250
$16$	1.19843	0.299607
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−2.77955	−0.655145
$19$	−3.04868	−0.699416	−0.349708	−	0.936859i	$-0.613719\pi$
$19$	−3.04868	−0.699416	−0.349708	+	0.936859i	$0.613719\pi$
$20$	−1.31486	−0.294012
$21$	2.20188	0.480490
$22$	3.23236	0.689142
$23$	−7.90876	−1.64909	−0.824545	−	0.565797i	$-0.808569\pi$
$23$	−7.90876	−1.64909	−0.824545	+	0.565797i	$0.808569\pi$
$24$	−6.54408	−1.33580
$25$	−4.22092	−0.844183
$26$	1.67103	0.327716
$27$	−2.33855	−0.450054
$28$	1.24953	0.236138
$29$	−0.818311	−0.151957	−0.0759783	−	0.997109i	$-0.524208\pi$
$29$	−0.818311	−0.151957	−0.0759783	+	0.997109i	$0.524208\pi$
$30$	1.65522	0.302201
$31$	−2.29104	−0.411483	−0.205741	−	0.978606i	$-0.565961\pi$
$31$	−2.29104	−0.411483	−0.205741	+	0.978606i	$0.565961\pi$
$32$	−5.84201	−1.03273
$33$	11.8776	2.06762
$34$	−0.714378	−0.122515
$35$	−0.740370	−0.125145
$36$	−5.79607	−0.966012
$37$	8.58988	1.41217	0.706084	−	0.708128i	$-0.250460\pi$
$37$	8.58988	1.41217	0.706084	+	0.708128i	$0.250460\pi$
$38$	2.17791	0.353304
$39$	6.14035	0.983243
$40$	2.20041	0.347915
$41$	10.6404	1.66175	0.830876	−	0.556457i	$-0.187840\pi$
$41$	10.6404	1.66175	0.830876	+	0.556457i	$0.187840\pi$
$42$	−1.57298	−0.242715
$43$	−0.979313	−0.149344	−0.0746719	−	0.997208i	$-0.523791\pi$
$43$	−0.979313	−0.149344	−0.0746719	+	0.997208i	$0.523791\pi$
$44$	6.74031	1.01614
$45$	3.43429	0.511954
$46$	5.64984	0.833024
$47$	−4.83264	−0.704913	−0.352456	−	0.935828i	$-0.614654\pi$
$47$	−4.83264	−0.704913	−0.352456	+	0.935828i	$0.614654\pi$
$48$	−3.14592	−0.454075
$49$	−6.29642	−0.899488
$50$	3.01533	0.426432
$51$	−2.62504	−0.367580
$52$	3.48453	0.483218
$53$	5.63575	0.774129	0.387065	−	0.922053i	$-0.373489\pi$
$53$	5.63575	0.774129	0.387065	+	0.922053i	$0.373489\pi$
$54$	1.67061	0.227341
$55$	−3.99377	−0.538520
$56$	−2.09107	−0.279431
$57$	8.00293	1.06001
$58$	0.584584	0.0767596
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	3.45157	0.445596
$61$	2.11105	0.270292	0.135146	−	0.990826i	$-0.456850\pi$
$61$	2.11105	0.270292	0.135146	+	0.990826i	$0.456850\pi$
$62$	1.63667	0.207857
$63$	−3.26364	−0.411180
$64$	1.77655	0.222069
$65$	−2.06466	−0.256089
$66$	−8.48509	−1.04444
$67$	11.2466	1.37399	0.686995	−	0.726662i	$-0.258929\pi$
$67$	11.2466	1.37399	0.686995	+	0.726662i	$0.258929\pi$
$68$	−1.48966	−0.180648
$69$	20.7608	2.49931
$70$	0.528904	0.0632162
$71$	5.19582	0.616630	0.308315	−	0.951284i	$-0.400235\pi$
$71$	5.19582	0.616630	0.308315	+	0.951284i	$0.400235\pi$
$72$	9.69968	1.14312
$73$	6.63693	0.776794	0.388397	−	0.921492i	$-0.373029\pi$
$73$	6.63693	0.776794	0.388397	+	0.921492i	$0.373029\pi$
$74$	−6.13642	−0.713345
$75$	11.0801	1.27942
$76$	4.54151	0.520947
$77$	3.79532	0.432517
$78$	−4.38653	−0.496677
$79$	14.7194	1.65606	0.828030	−	0.560684i	$-0.189462\pi$
$79$	14.7194	1.65606	0.828030	+	0.560684i	$0.189462\pi$
$80$	1.05780	0.118266
$81$	−5.53378	−0.614865
$82$	−7.60128	−0.839420
$83$	6.61943	0.726577	0.363288	−	0.931677i	$-0.381654\pi$
$83$	6.61943	0.726577	0.363288	+	0.931677i	$0.381654\pi$
$84$	−3.28006	−0.357884
$85$	0.882657	0.0957376
$86$	0.699600	0.0754398
$87$	2.14810	0.230301
$88$	−11.2799	−1.20244
$89$	−3.38821	−0.359149	−0.179575	−	0.983744i	$-0.557472\pi$
$89$	−3.38821	−0.359149	−0.179575	+	0.983744i	$0.557472\pi$
$90$	−2.45339	−0.258610
$91$	1.96207	0.205680
$92$	11.7814	1.22829
$93$	6.01408	0.623631
$94$	3.45233	0.356081
$95$	−2.69094	−0.276085
$96$	15.3355	1.56518
$97$	−4.45791	−0.452632	−0.226316	−	0.974054i	$-0.572668\pi$
$97$	−4.45791	−0.452632	−0.226316	+	0.974054i	$0.572668\pi$
$98$	4.49802	0.454369
$99$	−17.6051	−1.76937
$100$	6.28775	0.628775
$101$	−18.0999	−1.80101	−0.900506	−	0.434844i	$-0.856803\pi$
$101$	−18.0999	−1.80101	−0.900506	+	0.434844i	$0.856803\pi$
$102$	1.87527	0.185680
$103$	1.84909	0.182197	0.0910983	−	0.995842i	$-0.470962\pi$
$103$	1.84909	0.182197	0.0910983	+	0.995842i	$0.470962\pi$
$104$	−5.83134	−0.571810
$105$	1.94351	0.189667
$106$	−4.02605	−0.391045
$107$	19.0744	1.84399	0.921996	−	0.387200i	$-0.126558\pi$
$107$	19.0744	1.84399	0.921996	+	0.387200i	$0.126558\pi$
$108$	3.48365	0.335215
$109$	7.58241	0.726264	0.363132	−	0.931738i	$-0.381707\pi$
$109$	7.58241	0.726264	0.363132	+	0.931738i	$0.381707\pi$
$110$	2.85307	0.272029
$111$	−22.5488	−2.14024
$112$	−1.00524	−0.0949859
$113$	0.301840	0.0283948	0.0141974	−	0.999899i	$-0.495481\pi$
$113$	0.301840	0.0283948	0.0141974	+	0.999899i	$0.495481\pi$
$114$	−5.71712	−0.535457
$115$	−6.98072	−0.650955
$116$	1.21901	0.113182
$117$	−9.10128	−0.841413
$118$	0.714378	0.0657638
$119$	−0.838797	−0.0768924
$120$	−5.77618	−0.527290
$121$	9.47309	0.861190
$122$	−1.50809	−0.136536
$123$	−27.9316	−2.51850
$124$	3.41288	0.306485
$125$	−8.13891	−0.727966
$126$	2.33148	0.207704
$127$	2.33289	0.207010	0.103505	−	0.994629i	$-0.466994\pi$
$127$	2.33289	0.207010	0.103505	+	0.994629i	$0.466994\pi$
$128$	10.4149	0.920555
$129$	2.57074	0.226341
$130$	1.47495	0.129361
$131$	12.0300	1.05107	0.525533	−	0.850773i	$-0.323866\pi$
$131$	12.0300	1.05107	0.525533	+	0.850773i	$0.323866\pi$
$132$	−17.6936	−1.54003
$133$	2.55723	0.221740
$134$	−8.03432	−0.694060
$135$	−2.06414	−0.177653
$136$	2.49294	0.213768
$137$	−13.3649	−1.14184	−0.570919	−	0.821006i	$-0.693413\pi$
$137$	−13.3649	−1.14184	−0.570919	+	0.821006i	$0.693413\pi$
$138$	−14.8311	−1.26251
$139$	−13.8079	−1.17117	−0.585584	−	0.810612i	$-0.699135\pi$
$139$	−13.8079	−1.17117	−0.585584	+	0.810612i	$0.699135\pi$
$140$	1.10290	0.0932123
$141$	12.6859	1.06835
$142$	−3.71178	−0.311485
$143$	10.5840	0.885075
$144$	4.66291	0.388576
$145$	−0.722288	−0.0599827
$146$	−4.74128	−0.392391
$147$	16.5284	1.36324
$148$	−12.7960	−1.05183
$149$	4.95855	0.406220	0.203110	−	0.979156i	$-0.434895\pi$
$149$	4.95855	0.406220	0.203110	+	0.979156i	$0.434895\pi$
$150$	−7.91538	−0.646288
$151$	−6.55646	−0.533557	−0.266778	−	0.963758i	$-0.585959\pi$
$151$	−6.55646	−0.533557	−0.266778	+	0.963758i	$0.585959\pi$
$152$	−7.60018	−0.616456
$153$	3.89086	0.314557
$154$	−2.71130	−0.218482
$155$	−2.02220	−0.162427
$156$	−9.14706	−0.732351
$157$	13.4358	1.07229	0.536146	−	0.844125i	$-0.319880\pi$
$157$	13.4358	1.07229	0.536146	+	0.844125i	$0.319880\pi$
$158$	−10.5152	−0.836545
$159$	−14.7941	−1.17325
$160$	−5.15649	−0.407656
$161$	6.63384	0.522820
$162$	3.95321	0.310594
$163$	−19.4506	−1.52348	−0.761742	−	0.647880i	$-0.775656\pi$
$163$	−19.4506	−1.52348	−0.761742	+	0.647880i	$0.775656\pi$
$164$	−15.8506	−1.23773
$165$	10.4838	0.816166
$166$	−4.72878	−0.367024
$167$	2.79086	0.215964	0.107982	−	0.994153i	$-0.465561\pi$
$167$	2.79086	0.215964	0.107982	+	0.994153i	$0.465561\pi$
$168$	5.48916	0.423498
$169$	−7.52842	−0.579109
$170$	−0.630551	−0.0483610
$171$	−11.8620	−0.907110
$172$	1.45885	0.111236
$173$	16.9445	1.28826	0.644132	−	0.764914i	$-0.277219\pi$
$173$	16.9445	1.28826	0.644132	+	0.764914i	$0.277219\pi$
$174$	−1.53456	−0.116335
$175$	3.54049	0.267636
$176$	−5.42254	−0.408739
$177$	2.62504	0.197310
$178$	2.42046	0.181421
$179$	12.8688	0.961862	0.480931	−	0.876759i	$-0.340299\pi$
$179$	12.8688	0.961862	0.480931	+	0.876759i	$0.340299\pi$
$180$	−5.11594	−0.381320
$181$	0.504317	0.0374856	0.0187428	−	0.999824i	$-0.494034\pi$
$181$	0.504317	0.0374856	0.0187428	+	0.999824i	$0.494034\pi$
$182$	−1.40166	−0.103898
$183$	−5.54159	−0.409646
$184$	−19.7161	−1.45349
$185$	7.58192	0.557434
$186$	−4.29633	−0.315022
$187$	−4.52472	−0.330880
$188$	7.19901	0.525042
$189$	1.96157	0.142683
$190$	1.92235	0.139462
$191$	17.1675	1.24219	0.621097	−	0.783734i	$-0.286687\pi$
$191$	17.1675	1.24219	0.621097	+	0.783734i	$0.286687\pi$
$192$	−4.66353	−0.336561
$193$	−10.3949	−0.748244	−0.374122	−	0.927379i	$-0.622056\pi$
$193$	−10.3949	−0.748244	−0.374122	+	0.927379i	$0.622056\pi$
$194$	3.18464	0.228643
$195$	5.41982	0.388122
$196$	9.37955	0.669968
$197$	10.8722	0.774614	0.387307	−	0.921951i	$-0.373405\pi$
$197$	10.8722	0.774614	0.387307	+	0.921951i	$0.373405\pi$
$198$	12.5767	0.893785
$199$	−26.0198	−1.84449	−0.922247	−	0.386600i	$-0.873649\pi$
$199$	−26.0198	−1.84449	−0.922247	+	0.386600i	$0.873649\pi$
$200$	−10.5225	−0.744052
$201$	−29.5228	−2.08238
$202$	12.9302	0.909766
$203$	0.686397	0.0481756
$204$	3.91043	0.273785
$205$	9.39183	0.655954
$206$	−1.32095	−0.0920351
$207$	−30.7719	−2.13879
$208$	−2.80329	−0.194373
$209$	13.7944	0.954181
$210$	−1.38840	−0.0958085
$211$	−8.70923	−0.599568	−0.299784	−	0.954007i	$-0.596915\pi$
$211$	−8.70923	−0.599568	−0.299784	+	0.954007i	$0.596915\pi$
$212$	−8.39537	−0.576596
$213$	−13.6392	−0.934546
$214$	−13.6263	−0.931477
$215$	−0.864397	−0.0589514
$216$	−5.82986	−0.396672
$217$	1.92172	0.130455
$218$	−5.41671	−0.366866
$219$	−17.4223	−1.17729
$220$	5.94938	0.401107
$221$	−2.33914	−0.157348
$222$	16.1084	1.08112
$223$	−8.80838	−0.589853	−0.294926	−	0.955520i	$-0.595295\pi$
$223$	−8.80838	−0.589853	−0.294926	+	0.955520i	$0.595295\pi$
$224$	4.90026	0.327412
$225$	−16.4230	−1.09487
$226$	−0.215628	−0.0143434
$227$	17.5218	1.16296	0.581482	−	0.813560i	$-0.302473\pi$
$227$	17.5218	1.16296	0.581482	+	0.813560i	$0.302473\pi$
$228$	−11.9217	−0.789532
$229$	12.6999	0.839233	0.419616	−	0.907702i	$-0.362165\pi$
$229$	12.6999	0.839233	0.419616	+	0.907702i	$0.362165\pi$
$230$	4.98687	0.328825
$231$	−9.96289	−0.655510
$232$	−2.04000	−0.133933
$233$	23.1323	1.51545	0.757723	−	0.652577i	$-0.226312\pi$
$233$	23.1323	1.51545	0.757723	+	0.652577i	$0.226312\pi$
$234$	6.50175	0.425033
$235$	−4.26556	−0.278255
$236$	1.48966	0.0969689
$237$	−38.6390	−2.50988
$238$	0.599219	0.0388416
$239$	1.70962	0.110586	0.0552930	−	0.998470i	$-0.482391\pi$
$239$	1.70962	0.110586	0.0552930	+	0.998470i	$0.482391\pi$
$240$	−2.77677	−0.179240
$241$	9.88163	0.636532	0.318266	−	0.948002i	$-0.396900\pi$
$241$	9.88163	0.636532	0.318266	+	0.948002i	$0.396900\pi$
$242$	−6.76737	−0.435023
$243$	21.5421	1.38193
$244$	−3.14475	−0.201322
$245$	−5.55758	−0.355061
$246$	19.9537	1.27220
$247$	7.13130	0.453754
$248$	−5.71142	−0.362676
$249$	−17.3763	−1.10118
$250$	5.81426	0.367726
$251$	6.32394	0.399164	0.199582	−	0.979881i	$-0.436042\pi$
$251$	6.32394	0.399164	0.199582	+	0.979881i	$0.436042\pi$
$252$	4.86173	0.306260
$253$	35.7849	2.24978
$254$	−1.66656	−0.104569
$255$	−2.31701	−0.145097
$256$	−10.9933	−0.687079
$257$	24.6158	1.53549	0.767745	−	0.640755i	$-0.221379\pi$
$257$	24.6158	1.53549	0.767745	+	0.640755i	$0.221379\pi$
$258$	−1.83648	−0.114334
$259$	−7.20517	−0.447708
$260$	3.07565	0.190744
$261$	−3.18393	−0.197081
$262$	−8.59397	−0.530937
$263$	−23.8364	−1.46981	−0.734907	−	0.678168i	$-0.762774\pi$
$263$	−23.8364	−1.46981	−0.734907	+	0.678168i	$0.762774\pi$
$264$	29.6101	1.82238
$265$	4.97443	0.305577
$266$	−1.82683	−0.112010
$267$	8.89420	0.544316
$268$	−16.7536	−1.02339
$269$	−2.18787	−0.133397	−0.0666985	−	0.997773i	$-0.521247\pi$
$269$	−2.18787	−0.133397	−0.0666985	+	0.997773i	$0.521247\pi$
$270$	1.47457	0.0897397
$271$	−21.9539	−1.33360	−0.666802	−	0.745235i	$-0.732337\pi$
$271$	−21.9539	−1.33360	−0.666802	+	0.745235i	$0.732337\pi$
$272$	1.19843	0.0726653
$273$	−5.15051	−0.311723
$274$	9.54757	0.576790
$275$	19.0985	1.15168
$276$	−30.9267	−1.86157
$277$	7.49102	0.450092	0.225046	−	0.974348i	$-0.427747\pi$
$277$	7.49102	0.450092	0.225046	+	0.974348i	$0.427747\pi$
$278$	9.86404	0.591606
$279$	−8.91411	−0.533674
$280$	−1.84570	−0.110302
$281$	−23.5976	−1.40771	−0.703857	−	0.710341i	$-0.748541\pi$
$281$	−23.5976	−1.40771	−0.703857	+	0.710341i	$0.748541\pi$
$282$	−9.06253	−0.539666
$283$	8.60964	0.511790	0.255895	−	0.966705i	$-0.417630\pi$
$283$	8.60964	0.511790	0.255895	+	0.966705i	$0.417630\pi$
$284$	−7.74002	−0.459286
$285$	7.06384	0.418426
$286$	−7.56095	−0.447088
$287$	−8.92515	−0.526835
$288$	−22.7304	−1.33940
$289$	1.00000	0.0588235
$290$	0.515987	0.0302998
$291$	11.7022	0.685996
$292$	−9.88680	−0.578581
$293$	−2.53872	−0.148314	−0.0741569	−	0.997247i	$-0.523627\pi$
$293$	−2.53872	−0.148314	−0.0741569	+	0.997247i	$0.523627\pi$
$294$	−11.8075	−0.688628
$295$	−0.882657	−0.0513903
$296$	21.4141	1.24467
$297$	10.5813	0.613988
$298$	−3.54228	−0.205199
$299$	18.4997	1.06987
$300$	−16.5056	−0.952952
$301$	0.821445	0.0473473
$302$	4.68379	0.269522
$303$	47.5132	2.72956
$304$	−3.65362	−0.209550
$305$	1.86333	0.106694
$306$	−2.77955	−0.158896
$307$	25.1659	1.43629	0.718147	−	0.695891i	$-0.244990\pi$
$307$	25.1659	1.43629	0.718147	+	0.695891i	$0.244990\pi$
$308$	−5.65376	−0.322153
$309$	−4.85395	−0.276132
$310$	1.44462	0.0820487
$311$	0.674004	0.0382193	0.0191096	−	0.999817i	$-0.493917\pi$
$311$	0.674004	0.0382193	0.0191096	+	0.999817i	$0.493917\pi$
$312$	15.3075	0.866618
$313$	10.3721	0.586267	0.293133	−	0.956072i	$-0.405302\pi$
$313$	10.3721	0.586267	0.293133	+	0.956072i	$0.405302\pi$
$314$	−9.59823	−0.541659
$315$	−2.88068	−0.162308
$316$	−21.9269	−1.23349
$317$	14.4801	0.813286	0.406643	−	0.913587i	$-0.366699\pi$
$317$	14.4801	0.813286	0.406643	+	0.913587i	$0.366699\pi$
$318$	10.5686	0.592656
$319$	3.70263	0.207307
$320$	1.56809	0.0876586
$321$	−50.0712	−2.79470
$322$	−4.73907	−0.264098
$323$	−3.04868	−0.169633
$324$	8.24348	0.457971
$325$	9.87332	0.547673
$326$	13.8950	0.769576
$327$	−19.9042	−1.10070
$328$	26.5259	1.46465
$329$	4.05361	0.223482
$330$	−7.48943	−0.412279
$331$	−30.0526	−1.65184	−0.825920	−	0.563787i	$-0.809344\pi$
$331$	−30.0526	−1.65184	−0.825920	+	0.563787i	$0.809344\pi$
$332$	−9.86073	−0.541178
$333$	33.4220	1.83152
$334$	−1.99373	−0.109092
$335$	9.92688	0.542364
$336$	2.63879	0.143958
$337$	−4.01072	−0.218478	−0.109239	−	0.994016i	$-0.534841\pi$
$337$	−4.01072	−0.218478	−0.109239	+	0.994016i	$0.534841\pi$
$338$	5.37814	0.292532
$339$	−0.792345	−0.0430342
$340$	−1.31486	−0.0713084
$341$	10.3663	0.561367
$342$	8.47396	0.458219
$343$	11.1530	0.602205
$344$	−2.44137	−0.131630
$345$	18.3247	0.986568
$346$	−12.1048	−0.650756
$347$	−12.2976	−0.660171	−0.330085	−	0.943951i	$-0.607078\pi$
$347$	−12.2976	−0.660171	−0.330085	+	0.943951i	$0.607078\pi$
$348$	−3.19995	−0.171535
$349$	25.5188	1.36599	0.682995	−	0.730423i	$-0.260677\pi$
$349$	25.5188	1.36599	0.682995	+	0.730423i	$0.260677\pi$
$350$	−2.52925	−0.135194
$351$	5.47020	0.291978
$352$	26.4335	1.40891
$353$	19.3711	1.03102	0.515511	−	0.856883i	$-0.327602\pi$
$353$	19.3711	1.03102	0.515511	+	0.856883i	$0.327602\pi$
$354$	−1.87527	−0.0996697
$355$	4.58612	0.243406
$356$	5.04729	0.267506
$357$	2.20188	0.116536
$358$	−9.19321	−0.485876
$359$	27.1142	1.43103	0.715516	−	0.698596i	$-0.246192\pi$
$359$	27.1142	1.43103	0.715516	+	0.698596i	$0.246192\pi$
$360$	8.56149	0.451230
$361$	−9.70553	−0.510817
$362$	−0.360273	−0.0189355
$363$	−24.8673	−1.30519
$364$	−2.92282	−0.153197
$365$	5.85814	0.306629
$366$	3.95879	0.206929
$367$	−10.3149	−0.538433	−0.269216	−	0.963080i	$-0.586765\pi$
$367$	−10.3149	−0.538433	−0.269216	+	0.963080i	$0.586765\pi$
$368$	−9.47806	−0.494078
$369$	41.4003	2.15522
$370$	−5.41636	−0.281583
$371$	−4.72725	−0.245427
$372$	−8.95896	−0.464500
$373$	−23.7655	−1.23053	−0.615264	−	0.788321i	$-0.710951\pi$
$373$	−23.7655	−1.23053	−0.615264	+	0.788321i	$0.710951\pi$
$374$	3.23236	0.167141
$375$	21.3650	1.10328
$376$	−12.0475	−0.621301
$377$	1.91415	0.0985835
$378$	−1.40130	−0.0720752
$379$	−5.44212	−0.279543	−0.139772	−	0.990184i	$-0.544637\pi$
$379$	−5.44212	−0.279543	−0.139772	+	0.990184i	$0.544637\pi$
$380$	4.00860	0.205637
$381$	−6.12393	−0.313738
$382$	−12.2641	−0.627484
$383$	27.7514	1.41803	0.709016	−	0.705192i	$-0.249139\pi$
$383$	27.7514	1.41803	0.709016	+	0.705192i	$0.249139\pi$
$384$	−27.3395	−1.39517
$385$	3.34997	0.170730
$386$	7.42592	0.377969
$387$	−3.81037	−0.193692
$388$	6.64079	0.337135
$389$	28.5347	1.44677	0.723384	−	0.690446i	$-0.242586\pi$
$389$	28.5347	1.44677	0.723384	+	0.690446i	$0.242586\pi$
$390$	−3.87180	−0.196056
$391$	−7.90876	−0.399963
$392$	−15.6966	−0.792798
$393$	−31.5793	−1.59297
$394$	−7.76688	−0.391290
$395$	12.9922	0.653707
$396$	26.2256	1.31789
$397$	−31.0714	−1.55943	−0.779714	−	0.626136i	$-0.784635\pi$
$397$	−31.0714	−1.55943	−0.779714	+	0.626136i	$0.784635\pi$
$398$	18.5880	0.931731
$399$	−6.71284	−0.336062
$400$	−5.05846	−0.252923
$401$	−30.2549	−1.51086	−0.755428	−	0.655232i	$-0.772571\pi$
$401$	−30.2549	−1.51086	−0.755428	+	0.655232i	$0.772571\pi$
$402$	21.0905	1.05190
$403$	5.35906	0.266954
$404$	26.9628	1.34145
$405$	−4.88443	−0.242709
$406$	−0.490347	−0.0243355
$407$	−38.8668	−1.92656
$408$	−6.54408	−0.323980
$409$	−12.7852	−0.632186	−0.316093	−	0.948728i	$-0.602371\pi$
$409$	−12.7852	−0.632186	−0.316093	+	0.948728i	$0.602371\pi$
$410$	−6.70932	−0.331350
$411$	35.0834	1.73054
$412$	−2.75453	−0.135706
$413$	0.838797	0.0412745
$414$	21.9827	1.08039
$415$	5.84269	0.286806
$416$	13.6653	0.669996
$417$	36.2463	1.77499
$418$	−9.85445	−0.481997
$419$	−7.61338	−0.371938	−0.185969	−	0.982556i	$-0.559542\pi$
$419$	−7.61338	−0.371938	−0.185969	+	0.982556i	$0.559542\pi$
$420$	−2.89517	−0.141270
$421$	−6.00936	−0.292878	−0.146439	−	0.989220i	$-0.546781\pi$
$421$	−6.00936	−0.292878	−0.146439	+	0.989220i	$0.546781\pi$
$422$	6.22168	0.302867
$423$	−18.8031	−0.914239
$424$	14.0496	0.682308
$425$	−4.22092	−0.204745
$426$	9.74358	0.472078
$427$	−1.77074	−0.0856921
$428$	−28.4144	−1.37346
$429$	−27.7834	−1.34139
$430$	0.617506	0.0297788
$431$	−13.3475	−0.642929	−0.321464	−	0.946922i	$-0.604175\pi$
$431$	−13.3475	−0.642929	−0.321464	+	0.946922i	$0.604175\pi$
$432$	−2.80258	−0.134839
$433$	−13.6036	−0.653747	−0.326874	−	0.945068i	$-0.605995\pi$
$433$	−13.6036	−0.653747	−0.326874	+	0.945068i	$0.605995\pi$
$434$	−1.37283	−0.0658981
$435$	1.89604	0.0909081
$436$	−11.2952	−0.540944
$437$	24.1113	1.15340
$438$	12.4461	0.594696
$439$	−29.0332	−1.38568	−0.692839	−	0.721092i	$-0.743641\pi$
$439$	−29.0332	−1.38568	−0.692839	+	0.721092i	$0.743641\pi$
$440$	−9.95624	−0.474645
$441$	−24.4985	−1.16659
$442$	1.67103	0.0794829
$443$	−27.2732	−1.29579	−0.647895	−	0.761730i	$-0.724350\pi$
$443$	−27.2732	−1.29579	−0.647895	+	0.761730i	$0.724350\pi$
$444$	33.5902	1.59412
$445$	−2.99062	−0.141769
$446$	6.29251	0.297959
$447$	−13.0164	−0.615655
$448$	−1.49017	−0.0704038
$449$	−9.99606	−0.471743	−0.235872	−	0.971784i	$-0.575794\pi$
$449$	−9.99606	−0.471743	−0.235872	+	0.971784i	$0.575794\pi$
$450$	11.7322	0.553063
$451$	−48.1449	−2.26705
$452$	−0.449641	−0.0211493
$453$	17.2110	0.808643
$454$	−12.5172	−0.587461
$455$	1.73183	0.0811895
$456$	19.9508	0.934283
$457$	22.3669	1.04628	0.523140	−	0.852247i	$-0.324761\pi$
$457$	22.3669	1.04628	0.523140	+	0.852247i	$0.324761\pi$
$458$	−9.07253	−0.423931
$459$	−2.33855	−0.109154
$460$	10.3989	0.484852
$461$	9.97255	0.464468	0.232234	−	0.972660i	$-0.425396\pi$
$461$	9.97255	0.464468	0.232234	+	0.972660i	$0.425396\pi$
$462$	7.11727	0.331126
$463$	−4.83371	−0.224642	−0.112321	−	0.993672i	$-0.535828\pi$
$463$	−4.83371	−0.224642	−0.112321	+	0.993672i	$0.535828\pi$
$464$	−0.980685	−0.0455272
$465$	5.30837	0.246170
$466$	−16.5252	−0.765515
$467$	19.2938	0.892813	0.446406	−	0.894830i	$-0.352704\pi$
$467$	19.2938	0.892813	0.446406	+	0.894830i	$0.352704\pi$
$468$	13.5578	0.626711
$469$	−9.43361	−0.435604
$470$	3.04722	0.140558
$471$	−35.2695	−1.62513
$472$	−2.49294	−0.114747
$473$	4.43112	0.203743
$474$	27.6029	1.26784
$475$	12.8682	0.590435
$476$	1.24953	0.0572719
$477$	21.9279	1.00401
$478$	−1.22131	−0.0558616
$479$	6.81394	0.311337	0.155668	−	0.987809i	$-0.450247\pi$
$479$	6.81394	0.311337	0.155668	+	0.987809i	$0.450247\pi$
$480$	13.5360	0.617832
$481$	−20.0930	−0.916160
$482$	−7.05922	−0.321539
$483$	−17.4141	−0.792371
$484$	−14.1117	−0.641442
$485$	−3.93481	−0.178670
$486$	−15.3892	−0.698068
$487$	37.9599	1.72013	0.860063	−	0.510189i	$-0.170424\pi$
$487$	37.9599	1.72013	0.860063	+	0.510189i	$0.170424\pi$
$488$	5.26271	0.238232
$489$	51.0586	2.30895
$490$	3.97021	0.179356
$491$	−27.8710	−1.25780	−0.628901	−	0.777486i	$-0.716495\pi$
$491$	−27.8710	−1.25780	−0.628901	+	0.777486i	$0.716495\pi$
$492$	41.6086	1.87586
$493$	−0.818311	−0.0368549
$494$	−5.09445	−0.229210
$495$	−15.5392	−0.698436
$496$	−2.74564	−0.123283
$497$	−4.35824	−0.195494
$498$	12.4133	0.556251
$499$	30.5466	1.36745	0.683727	−	0.729738i	$-0.260358\pi$
$499$	30.5466	1.36745	0.683727	+	0.729738i	$0.260358\pi$
$500$	12.1242	0.542212
$501$	−7.32614	−0.327308
$502$	−4.51769	−0.201634
$503$	38.8286	1.73128	0.865641	−	0.500665i	$-0.166911\pi$
$503$	38.8286	1.73128	0.865641	+	0.500665i	$0.166911\pi$
$504$	−8.13607	−0.362409
$505$	−15.9760	−0.710924
$506$	−25.5640	−1.13646
$507$	19.7624	0.877680
$508$	−3.47522	−0.154188
$509$	−22.9682	−1.01805	−0.509024	−	0.860752i	$-0.669994\pi$
$509$	−22.9682	−1.01805	−0.509024	+	0.860752i	$0.669994\pi$
$510$	1.65522	0.0732946
$511$	−5.56704	−0.246271
$512$	−12.9764	−0.573482
$513$	7.12950	0.314775
$514$	−17.5850	−0.775640
$515$	1.63212	0.0719196
$516$	−3.82954	−0.168586
$517$	21.8663	0.961681
$518$	5.14722	0.226156
$519$	−44.4800	−1.95245
$520$	−5.14707	−0.225714
$521$	42.9008	1.87952	0.939759	−	0.341837i	$-0.111049\pi$
$521$	42.9008	1.87952	0.939759	+	0.341837i	$0.111049\pi$
$522$	2.27453	0.0995536
$523$	17.7812	0.777517	0.388759	−	0.921340i	$-0.372904\pi$
$523$	17.7812	0.777517	0.388759	+	0.921340i	$0.372904\pi$
$524$	−17.9207	−0.782868
$525$	−9.29396	−0.405621
$526$	17.0282	0.742464
$527$	−2.29104	−0.0997992
$528$	14.2344	0.619473
$529$	39.5484	1.71950
$530$	−3.55362	−0.154360
$531$	−3.89086	−0.168849
$532$	−3.80941	−0.165159
$533$	−24.8894	−1.07808
$534$	−6.35382	−0.274957
$535$	16.8361	0.727890
$536$	28.0371	1.21102
$537$	−33.7813	−1.45777
$538$	1.56297	0.0673844
$539$	28.4895	1.22713
$540$	3.07487	0.132321
$541$	−6.81320	−0.292922	−0.146461	−	0.989216i	$-0.546788\pi$
$541$	−6.81320	−0.292922	−0.146461	+	0.989216i	$0.546788\pi$
$542$	15.6834	0.673659
$543$	−1.32385	−0.0568120
$544$	−5.84201	−0.250474
$545$	6.69267	0.286682
$546$	3.67941	0.157464
$547$	19.3250	0.826278	0.413139	−	0.910668i	$-0.364432\pi$
$547$	19.3250	0.826278	0.413139	+	0.910668i	$0.364432\pi$
$548$	19.9092	0.850478
$549$	8.21379	0.350556
$550$	−13.6435	−0.581762
$551$	2.49477	0.106281
$552$	51.7555	2.20286
$553$	−12.3466	−0.525030
$554$	−5.35142	−0.227360
$555$	−19.9029	−0.844830
$556$	20.5691	0.872323
$557$	−34.9155	−1.47942	−0.739708	−	0.672928i	$-0.765036\pi$
$557$	−34.9155	−1.47942	−0.739708	+	0.672928i	$0.765036\pi$
$558$	6.36805	0.269581
$559$	2.29075	0.0968885
$560$	−0.887279	−0.0374944
$561$	11.8776	0.501472
$562$	16.8576	0.711095
$563$	14.0489	0.592092	0.296046	−	0.955174i	$-0.404332\pi$
$563$	14.0489	0.592092	0.296046	+	0.955174i	$0.404332\pi$
$564$	−18.8977	−0.795738
$565$	0.266421	0.0112084
$566$	−6.15054	−0.258526
$567$	4.64172	0.194934
$568$	12.9529	0.543490
$569$	28.3817	1.18982	0.594911	−	0.803791i	$-0.297187\pi$
$569$	28.3817	1.18982	0.594911	+	0.803791i	$0.297187\pi$
$570$	−5.04625	−0.211364
$571$	−16.5283	−0.691686	−0.345843	−	0.938292i	$-0.612407\pi$
$571$	−16.5283	−0.691686	−0.345843	+	0.938292i	$0.612407\pi$
$572$	−15.7665	−0.659232
$573$	−45.0653	−1.88263
$574$	6.37593	0.266126
$575$	33.3822	1.39213
$576$	6.91231	0.288013
$577$	−5.31847	−0.221411	−0.110705	−	0.993853i	$-0.535311\pi$
$577$	−5.31847	−0.221411	−0.110705	+	0.993853i	$0.535311\pi$
$578$	−0.714378	−0.0297142
$579$	27.2872	1.13402
$580$	1.07597	0.0446771
$581$	−5.55236	−0.230351
$582$	−8.35981	−0.346525
$583$	−25.5002	−1.05611
$584$	16.5455	0.684657
$585$	−8.03330	−0.332136
$586$	1.81361	0.0749194
$587$	43.5141	1.79602	0.898009	−	0.439976i	$-0.145013\pi$
$587$	43.5141	1.79602	0.898009	+	0.439976i	$0.145013\pi$
$588$	−24.6217	−1.01538
$589$	6.98465	0.287798
$590$	0.630551	0.0259594
$591$	−28.5401	−1.17398
$592$	10.2943	0.423095
$593$	−30.9368	−1.27042	−0.635212	−	0.772338i	$-0.719087\pi$
$593$	−30.9368	−1.27042	−0.635212	+	0.772338i	$0.719087\pi$
$594$	−7.55904	−0.310151
$595$	−0.740370	−0.0303522
$596$	−7.38657	−0.302566
$597$	68.3031	2.79546
$598$	−13.2158	−0.540434
$599$	−33.0969	−1.35230	−0.676151	−	0.736763i	$-0.736353\pi$
$599$	−33.0969	−1.35230	−0.676151	+	0.736763i	$0.736353\pi$
$600$	27.6220	1.12766
$601$	−19.8676	−0.810418	−0.405209	−	0.914224i	$-0.632801\pi$
$601$	−19.8676	−0.810418	−0.405209	+	0.914224i	$0.632801\pi$
$602$	−0.586822	−0.0239171
$603$	43.7589	1.78200
$604$	9.76692	0.397410
$605$	8.36149	0.339943
$606$	−33.9424	−1.37881
$607$	27.8404	1.13001	0.565003	−	0.825089i	$-0.308875\pi$
$607$	27.8404	1.13001	0.565003	+	0.825089i	$0.308875\pi$
$608$	17.8104	0.722309
$609$	−1.80182	−0.0730136
$610$	−1.33112	−0.0538956
$611$	11.3042	0.457320
$612$	−5.79607	−0.234292
$613$	−26.0521	−1.05223	−0.526117	−	0.850412i	$-0.676352\pi$
$613$	−26.0521	−1.05223	−0.526117	+	0.850412i	$0.676352\pi$
$614$	−17.9780	−0.725532
$615$	−24.6540	−0.994144
$616$	9.46151	0.381215
$617$	24.3811	0.981547	0.490773	−	0.871287i	$-0.336714\pi$
$617$	24.3811	0.981547	0.490773	+	0.871287i	$0.336714\pi$
$618$	3.46756	0.139486
$619$	−16.2165	−0.651796	−0.325898	−	0.945405i	$-0.605667\pi$
$619$	−16.2165	−0.651796	−0.325898	+	0.945405i	$0.605667\pi$
$620$	3.01240	0.120981
$621$	18.4950	0.742179
$622$	−0.481494	−0.0193061
$623$	2.84202	0.113863
$624$	7.35876	0.294586
$625$	13.9207	0.556829
$626$	−7.40962	−0.296148
$627$	−36.2110	−1.44613
$628$	−20.0148	−0.798678
$629$	8.58988	0.342501
$630$	2.05789	0.0819884
$631$	−17.9845	−0.715953	−0.357977	−	0.933731i	$-0.616533\pi$
$631$	−17.9845	−0.715953	−0.357977	+	0.933731i	$0.616533\pi$
$632$	36.6945	1.45963
$633$	22.8621	0.908687
$634$	−10.3443	−0.410825
$635$	2.05914	0.0817144
$636$	22.0382	0.873872
$637$	14.7282	0.583553
$638$	−2.64508	−0.104720
$639$	20.2162	0.799740
$640$	9.19277	0.363376
$641$	8.31518	0.328430	0.164215	−	0.986425i	$-0.447491\pi$
$641$	8.31518	0.328430	0.164215	+	0.986425i	$0.447491\pi$
$642$	35.7697	1.41172
$643$	35.8652	1.41439	0.707194	−	0.707020i	$-0.249961\pi$
$643$	35.8652	1.41439	0.707194	+	0.707020i	$0.249961\pi$
$644$	−9.88220	−0.389413
$645$	2.26908	0.0893450
$646$	2.17791	0.0856888
$647$	−38.4831	−1.51293	−0.756464	−	0.654036i	$-0.773075\pi$
$647$	−38.4831	−1.51293	−0.756464	+	0.654036i	$0.773075\pi$
$648$	−13.7954	−0.541934
$649$	4.52472	0.177611
$650$	−7.05329	−0.276653
$651$	−5.04459	−0.197713
$652$	28.9748	1.13474
$653$	3.62611	0.141901	0.0709504	−	0.997480i	$-0.477397\pi$
$653$	3.62611	0.141901	0.0709504	+	0.997480i	$0.477397\pi$
$654$	14.2191	0.556011
$655$	10.6184	0.414894
$656$	12.7517	0.497872
$657$	25.8234	1.00747
$658$	−2.89581	−0.112890
$659$	−12.0527	−0.469506	−0.234753	−	0.972055i	$-0.575428\pi$
$659$	−12.0527	−0.469506	−0.234753	+	0.972055i	$0.575428\pi$
$660$	−15.6174	−0.607906
$661$	−11.1096	−0.432114	−0.216057	−	0.976381i	$-0.569320\pi$
$661$	−11.1096	−0.432114	−0.216057	+	0.976381i	$0.569320\pi$
$662$	21.4689	0.834413
$663$	6.14035	0.238472
$664$	16.5018	0.640396
$665$	2.25715	0.0875287
$666$	−23.8760	−0.925175
$667$	6.47182	0.250590
$668$	−4.15745	−0.160857
$669$	23.1224	0.893963
$670$	−7.09155	−0.273970
$671$	−9.55190	−0.368747
$672$	−12.8634	−0.496217
$673$	−34.6325	−1.33499	−0.667493	−	0.744616i	$-0.732632\pi$
$673$	−34.6325	−1.33499	−0.667493	+	0.744616i	$0.732632\pi$
$674$	2.86517	0.110362
$675$	9.87082	0.379928
$676$	11.2148	0.431339
$677$	−11.9001	−0.457360	−0.228680	−	0.973502i	$-0.573441\pi$
$677$	−11.9001	−0.457360	−0.228680	+	0.973502i	$0.573441\pi$
$678$	0.566034	0.0217384
$679$	3.73928	0.143501
$680$	2.20041	0.0843819
$681$	−45.9955	−1.76255
$682$	−7.40546	−0.283570
$683$	−23.8482	−0.912526	−0.456263	−	0.889845i	$-0.650812\pi$
$683$	−23.8482	−0.912526	−0.456263	+	0.889845i	$0.650812\pi$
$684$	17.6704	0.675645
$685$	−11.7966	−0.450725
$686$	−7.96746	−0.304199
$687$	−33.3378	−1.27192
$688$	−1.17363	−0.0447444
$689$	−13.1828	−0.502225
$690$	−13.0908	−0.498357
$691$	−35.9907	−1.36915	−0.684576	−	0.728942i	$-0.740012\pi$
$691$	−35.9907	−1.36915	−0.684576	+	0.728942i	$0.740012\pi$
$692$	−25.2416	−0.959540
$693$	14.7671	0.560955
$694$	8.78515	0.333480
$695$	−12.1876	−0.462302
$696$	5.35509	0.202984
$697$	10.6404	0.403034
$698$	−18.2301	−0.690019
$699$	−60.7233	−2.29676
$700$	−5.27415	−0.199344
$701$	41.5917	1.57090	0.785449	−	0.618927i	$-0.212432\pi$
$701$	41.5917	1.57090	0.785449	+	0.618927i	$0.212432\pi$
$702$	−3.90779	−0.147490
$703$	−26.1878	−0.987693
$704$	−8.03840	−0.302958
$705$	11.1973	0.421714
$706$	−13.8383	−0.520812
$707$	15.1822	0.570985
$708$	−3.91043	−0.146963
$709$	−0.0873362	−0.00327998	−0.00163999	−	0.999999i	$-0.500522\pi$
$709$	−0.0873362	−0.00327998	−0.00163999	+	0.999999i	$0.500522\pi$
$710$	−3.27623	−0.122955
$711$	57.2711	2.14783
$712$	−8.44660	−0.316550
$713$	18.1193	0.678572
$714$	−1.57298	−0.0588671
$715$	9.34201	0.349371
$716$	−19.1702	−0.716425
$717$	−4.48783	−0.167601
$718$	−19.3698	−0.722874
$719$	29.5136	1.10067	0.550336	−	0.834943i	$-0.314500\pi$
$719$	29.5136	1.10067	0.550336	+	0.834943i	$0.314500\pi$
$720$	4.11575	0.153385
$721$	−1.55102	−0.0577628
$722$	6.93342	0.258035
$723$	−25.9397	−0.964708
$724$	−0.751262	−0.0279204
$725$	3.45402	0.128279
$726$	17.7646	0.659308
$727$	13.1663	0.488313	0.244156	−	0.969736i	$-0.421489\pi$
$727$	13.1663	0.488313	0.244156	+	0.969736i	$0.421489\pi$
$728$	4.89131	0.181284
$729$	−39.9476	−1.47954
$730$	−4.18492	−0.154891
$731$	−0.979313	−0.0362212
$732$	8.25511	0.305118
$733$	−51.6208	−1.90666	−0.953328	−	0.301937i	$-0.902367\pi$
$733$	−51.6208	−1.90666	−0.953328	+	0.301937i	$0.902367\pi$
$734$	7.36873	0.271985
$735$	14.5889	0.538119
$736$	46.2030	1.70307
$737$	−50.8877	−1.87447
$738$	−29.5755	−1.08869
$739$	23.4289	0.861846	0.430923	−	0.902389i	$-0.358188\pi$
$739$	23.4289	0.861846	0.430923	+	0.902389i	$0.358188\pi$
$740$	−11.2945	−0.415194
$741$	−18.7200	−0.687696
$742$	3.37704	0.123975
$743$	−47.1262	−1.72889	−0.864446	−	0.502726i	$-0.832331\pi$
$743$	−47.1262	−1.72889	−0.864446	+	0.502726i	$0.832331\pi$
$744$	14.9927	0.549660
$745$	4.37670	0.160350
$746$	16.9775	0.621591
$747$	25.7553	0.942337
$748$	6.74031	0.246450
$749$	−15.9996	−0.584611
$750$	−15.2627	−0.557314
$751$	−4.29145	−0.156597	−0.0782987	−	0.996930i	$-0.524949\pi$
$751$	−4.29145	−0.156597	−0.0782987	+	0.996930i	$0.524949\pi$
$752$	−5.79156	−0.211196
$753$	−16.6006	−0.604961
$754$	−1.36742	−0.0497986
$755$	−5.78710	−0.210614
$756$	−2.92208	−0.106275
$757$	−6.77723	−0.246323	−0.123161	−	0.992387i	$-0.539303\pi$
$757$	−6.77723	−0.246323	−0.123161	+	0.992387i	$0.539303\pi$
$758$	3.88773	0.141209
$759$	−93.9370	−3.40970
$760$	−6.70835	−0.243338
$761$	−11.3430	−0.411182	−0.205591	−	0.978638i	$-0.565912\pi$
$761$	−11.3430	−0.411182	−0.205591	+	0.978638i	$0.565912\pi$
$762$	4.37480	0.158482
$763$	−6.36011	−0.230251
$764$	−25.5737	−0.925225
$765$	3.43429	0.124167
$766$	−19.8250	−0.716307
$767$	2.33914	0.0844615
$768$	28.8578	1.04132
$769$	28.1862	1.01642	0.508210	−	0.861233i	$-0.330307\pi$
$769$	28.1862	1.01642	0.508210	+	0.861233i	$0.330307\pi$
$770$	−2.39314	−0.0862429
$771$	−64.6175	−2.32714
$772$	15.4850	0.557316
$773$	16.1578	0.581157	0.290579	−	0.956851i	$-0.406152\pi$
$773$	16.1578	0.581157	0.290579	+	0.956851i	$0.406152\pi$
$774$	2.72205	0.0978419
$775$	9.67028	0.347367
$776$	−11.1133	−0.398944
$777$	18.9139	0.678532
$778$	−20.3846	−0.730823
$779$	−32.4392	−1.16226
$780$	−8.07372	−0.289085
$781$	−23.5096	−0.841240
$782$	5.64984	0.202038
$783$	1.91366	0.0683887
$784$	−7.54579	−0.269493
$785$	11.8592	0.423273
$786$	22.5596	0.804673
$787$	40.5163	1.44425	0.722125	−	0.691763i	$-0.243166\pi$
$787$	40.5163	1.44425	0.722125	+	0.691763i	$0.243166\pi$
$788$	−16.1960	−0.576957
$789$	62.5715	2.22761
$790$	−9.28132	−0.330214
$791$	−0.253183	−0.00900215
$792$	−43.8883	−1.55950
$793$	−4.93804	−0.175355
$794$	22.1967	0.787732
$795$	−13.0581	−0.463123
$796$	38.7608	1.37384
$797$	15.7839	0.559094	0.279547	−	0.960132i	$-0.409816\pi$
$797$	15.7839	0.559094	0.279547	+	0.960132i	$0.409816\pi$
$798$	4.79550	0.169759
$799$	−4.83264	−0.170966
$800$	24.6586	0.871814
$801$	−13.1830	−0.465800
$802$	21.6134	0.763196
$803$	−30.0303	−1.05975
$804$	43.9791	1.55102
$805$	5.85541	0.206376
$806$	−3.82840	−0.134850
$807$	5.74327	0.202173
$808$	−45.1221	−1.58739
$809$	8.78358	0.308814	0.154407	−	0.988007i	$-0.450653\pi$
$809$	8.78358	0.308814	0.154407	+	0.988007i	$0.450653\pi$
$810$	3.48933	0.122603
$811$	−7.67382	−0.269464	−0.134732	−	0.990882i	$-0.543017\pi$
$811$	−7.67382	−0.269464	−0.134732	+	0.990882i	$0.543017\pi$
$812$	−1.02250	−0.0358828
$813$	57.6299	2.02117
$814$	27.7656	0.973184
$815$	−17.1682	−0.601374
$816$	−3.14592	−0.110129
$817$	2.98562	0.104453
$818$	9.13345	0.319344
$819$	7.63413	0.266758
$820$	−13.9907	−0.488575
$821$	19.7579	0.689554	0.344777	−	0.938685i	$-0.387955\pi$
$821$	19.7579	0.689554	0.344777	+	0.938685i	$0.387955\pi$
$822$	−25.0628	−0.874166
$823$	16.8609	0.587735	0.293867	−	0.955846i	$-0.405058\pi$
$823$	16.8609	0.587735	0.293867	+	0.955846i	$0.405058\pi$
$824$	4.60968	0.160586
$825$	−50.1343	−1.74545
$826$	−0.599219	−0.0208495
$827$	45.8911	1.59579	0.797896	−	0.602796i	$-0.205947\pi$
$827$	45.8911	1.59579	0.797896	+	0.602796i	$0.205947\pi$
$828$	45.8397	1.59304
$829$	35.6224	1.23722	0.618608	−	0.785700i	$-0.287697\pi$
$829$	35.6224	1.23722	0.618608	+	0.785700i	$0.287697\pi$
$830$	−4.17389	−0.144878
$831$	−19.6643	−0.682145
$832$	−4.15561	−0.144070
$833$	−6.29642	−0.218158
$834$	−25.8935	−0.896620
$835$	2.46338	0.0852486
$836$	−20.5491	−0.710705
$837$	5.35771	0.185189
$838$	5.43883	0.187881
$839$	27.4317	0.947048	0.473524	−	0.880781i	$-0.342982\pi$
$839$	27.4317	0.947048	0.473524	+	0.880781i	$0.342982\pi$
$840$	4.84504	0.167170
$841$	−28.3304	−0.976909
$842$	4.29296	0.147945
$843$	61.9447	2.13349
$844$	12.9738	0.446577
$845$	−6.64501	−0.228595
$846$	13.4325	0.461820
$847$	−7.94600	−0.273028
$848$	6.75403	0.231934
$849$	−22.6007	−0.775653
$850$	3.01533	0.103425
$851$	−67.9353	−2.32879
$852$	20.3179	0.696080
$853$	20.0770	0.687424	0.343712	−	0.939075i	$-0.388316\pi$
$853$	20.0770	0.687424	0.343712	+	0.939075i	$0.388316\pi$
$854$	1.26498	0.0432867
$855$	−10.4701	−0.358069
$856$	47.5513	1.62527
$857$	5.21123	0.178012	0.0890061	−	0.996031i	$-0.471631\pi$
$857$	5.21123	0.178012	0.0890061	+	0.996031i	$0.471631\pi$
$858$	19.8478	0.677594
$859$	11.9051	0.406195	0.203098	−	0.979158i	$-0.434899\pi$
$859$	11.9051	0.406195	0.203098	+	0.979158i	$0.434899\pi$
$860$	1.28766	0.0439089
$861$	23.4289	0.798455
$862$	9.53520	0.324770
$863$	5.76280	0.196168	0.0980840	−	0.995178i	$-0.468729\pi$
$863$	5.76280	0.196168	0.0980840	+	0.995178i	$0.468729\pi$
$864$	13.6618	0.464785
$865$	14.9561	0.508524
$866$	9.71811	0.330235
$867$	−2.62504	−0.0891512
$868$	−2.86271	−0.0971668
$869$	−66.6011	−2.25929
$870$	−1.35449	−0.0459214
$871$	−26.3074	−0.891392
$872$	18.9025	0.640119
$873$	−17.3451	−0.587043
$874$	−17.2246	−0.582630
$875$	6.82689	0.230791
$876$	25.9533	0.876881
$877$	37.2045	1.25631	0.628153	−	0.778090i	$-0.283811\pi$
$877$	37.2045	1.25631	0.628153	+	0.778090i	$0.283811\pi$
$878$	20.7407	0.699964
$879$	6.66426	0.224780
$880$	−4.78624	−0.161344
$881$	−10.0115	−0.337296	−0.168648	−	0.985676i	$-0.553940\pi$
$881$	−10.0115	−0.337296	−0.168648	+	0.985676i	$0.553940\pi$
$882$	17.5012	0.589296
$883$	31.6712	1.06582	0.532910	−	0.846172i	$-0.321098\pi$
$883$	31.6712	1.06582	0.532910	+	0.846172i	$0.321098\pi$
$884$	3.48453	0.117198
$885$	2.31701	0.0778856
$886$	19.4834	0.654558
$887$	−19.9943	−0.671343	−0.335671	−	0.941979i	$-0.608963\pi$
$887$	−19.9943	−0.671343	−0.335671	+	0.941979i	$0.608963\pi$
$888$	−56.2129	−1.88638
$889$	−1.95682	−0.0656296
$890$	2.13644	0.0716135
$891$	25.0388	0.838832
$892$	13.1215	0.439341
$893$	14.7332	0.493027
$894$	9.29864	0.310993
$895$	11.3588	0.379682
$896$	−8.73598	−0.291849
$897$	−48.5625	−1.62146
$898$	7.14097	0.238297
$899$	1.87478	0.0625275
$900$	24.4647	0.815492
$901$	5.63575	0.187754
$902$	34.3936	1.14518
$903$	−2.15633	−0.0717582
$904$	0.752470	0.0250268
$905$	0.445139	0.0147969
$906$	−12.2952	−0.408479
$907$	−22.4710	−0.746137	−0.373069	−	0.927804i	$-0.621694\pi$
$907$	−22.4710	−0.746137	−0.373069	+	0.927804i	$0.621694\pi$
$908$	−26.1016	−0.866212
$909$	−70.4243	−2.33583
$910$	−1.23718	−0.0410122
$911$	−0.809822	−0.0268306	−0.0134153	−	0.999910i	$-0.504270\pi$
$911$	−0.809822	−0.0268306	−0.0134153	+	0.999910i	$0.504270\pi$
$912$	9.59092	0.317587
$913$	−29.9511	−0.991236
$914$	−15.9784	−0.528519
$915$	−4.89132	−0.161702
$916$	−18.9186	−0.625087
$917$	−10.0907	−0.333226
$918$	1.67061	0.0551383
$919$	−29.2285	−0.964159	−0.482080	−	0.876127i	$-0.660118\pi$
$919$	−29.2285	−0.964159	−0.482080	+	0.876127i	$0.660118\pi$
$920$	−17.4025	−0.573744
$921$	−66.0617	−2.17681
$922$	−7.12417	−0.234622
$923$	−12.1537	−0.400046
$924$	14.8414	0.488245
$925$	−36.2572	−1.19213
$926$	3.45310	0.113476
$927$	7.19457	0.236301
$928$	4.78058	0.156930
$929$	−49.4295	−1.62173	−0.810864	−	0.585234i	$-0.801003\pi$
$929$	−49.4295	−1.62173	−0.810864	+	0.585234i	$0.801003\pi$
$930$	−3.79218	−0.124351
$931$	19.1958	0.629117
$932$	−34.4593	−1.12875
$933$	−1.76929	−0.0579240
$934$	−13.7831	−0.450997
$935$	−3.99377	−0.130610
$936$	−22.6889	−0.741611
$937$	3.49257	0.114097	0.0570487	−	0.998371i	$-0.481831\pi$
$937$	3.49257	0.114097	0.0570487	+	0.998371i	$0.481831\pi$
$938$	6.73917	0.220042
$939$	−27.2273	−0.888529
$940$	6.35425	0.207253
$941$	−46.8179	−1.52622	−0.763109	−	0.646269i	$-0.776328\pi$
$941$	−46.8179	−1.52622	−0.763109	+	0.646269i	$0.776328\pi$
$942$	25.1958	0.820923
$943$	−84.1524	−2.74038
$944$	−1.19843	−0.0390054
$945$	1.73139	0.0563222
$946$	−3.16549	−0.102919
$947$	−36.6893	−1.19224	−0.596122	−	0.802894i	$-0.703292\pi$
$947$	−36.6893	−1.19224	−0.596122	+	0.802894i	$0.703292\pi$
$948$	57.5592	1.86944
$949$	−15.5247	−0.503954
$950$	−9.19279	−0.298253
$951$	−38.0110	−1.23259
$952$	−2.09107	−0.0677720
$953$	−19.6932	−0.637924	−0.318962	−	0.947768i	$-0.603334\pi$
$953$	−19.6932	−0.637924	−0.318962	+	0.947768i	$0.603334\pi$
$954$	−15.6648	−0.507167
$955$	15.1530	0.490339
$956$	−2.54676	−0.0823680
$957$	−9.71957	−0.314189
$958$	−4.86773	−0.157269
$959$	11.2104	0.362003
$960$	−4.11629	−0.132853
$961$	−25.7511	−0.830682
$962$	14.3540	0.462790
$963$	74.2158	2.39157
$964$	−14.7203	−0.474109
$965$	−9.17517	−0.295359
$966$	12.4403	0.400259
$967$	−45.6975	−1.46953	−0.734766	−	0.678320i	$-0.762708\pi$
$967$	−45.6975	−1.46953	−0.734766	+	0.678320i	$0.762708\pi$
$968$	23.6158	0.759042
$969$	8.00293	0.257091
$970$	2.81094	0.0902538
$971$	19.8877	0.638226	0.319113	−	0.947717i	$-0.396615\pi$
$971$	19.8877	0.638226	0.319113	+	0.947717i	$0.396615\pi$
$972$	−32.0905	−1.02930
$973$	11.5820	0.371302
$974$	−27.1177	−0.868907
$975$	−25.9179	−0.830038
$976$	2.52993	0.0809812
$977$	48.9502	1.56606	0.783028	−	0.621987i	$-0.213674\pi$
$977$	48.9502	1.56606	0.783028	+	0.621987i	$0.213674\pi$
$978$	−36.4751	−1.16635
$979$	15.3307	0.489971
$980$	8.27892	0.264460
$981$	29.5021	0.941930
$982$	19.9104	0.635368
$983$	47.7180	1.52197	0.760985	−	0.648770i	$-0.224716\pi$
$983$	47.7180	1.52197	0.760985	+	0.648770i	$0.224716\pi$
$984$	−69.6317	−2.21978
$985$	9.59644	0.305768
$986$	0.584584	0.0186169
$987$	−10.6409	−0.338703
$988$	−10.6232	−0.337970
$989$	7.74515	0.246281
$990$	11.1009	0.352809
$991$	53.7671	1.70797	0.853984	−	0.520299i	$-0.174180\pi$
$991$	53.7671	1.70797	0.853984	+	0.520299i	$0.174180\pi$
$992$	13.3843	0.424951
$993$	78.8894	2.50348
$994$	3.11343	0.0987520
$995$	−22.9666	−0.728089
$996$	25.8848	0.820193
$997$	1.68378	0.0533258	0.0266629	−	0.999644i	$-0.491512\pi$
$997$	1.68378	0.0533258	0.0266629	+	0.999644i	$0.491512\pi$
$998$	−21.8218	−0.690758
$999$	−20.0879	−0.635552

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1003.2.a.i.1.6	✓	18
3.2	odd	2		9027.2.a.q.1.13		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1003.2.a.i.1.6	✓	18	1.1	even	1	trivial
9027.2.a.q.1.13		18	3.2	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:	\( N \)	\(=\)	\( 1003 = 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1003.a (trivial)

\(f(q)\)	\(=\)	\(q-0.714378 q^{2} -2.62504 q^{3} -1.48966 q^{4} +0.882657 q^{5} +1.87527 q^{6} -0.838797 q^{7} +2.49294 q^{8} +3.89086 q^{9} +O(q^{10})\)	\(q-0.714378 q^{2} -2.62504 q^{3} -1.48966 q^{4} +0.882657 q^{5} +1.87527 q^{6} -0.838797 q^{7} +2.49294 q^{8} +3.89086 q^{9} -0.630551 q^{10} -4.52472 q^{11} +3.91043 q^{12} -2.33914 q^{13} +0.599219 q^{14} -2.31701 q^{15} +1.19843 q^{16} +1.00000 q^{17} -2.77955 q^{18} -3.04868 q^{19} -1.31486 q^{20} +2.20188 q^{21} +3.23236 q^{22} -7.90876 q^{23} -6.54408 q^{24} -4.22092 q^{25} +1.67103 q^{26} -2.33855 q^{27} +1.24953 q^{28} -0.818311 q^{29} +1.65522 q^{30} -2.29104 q^{31} -5.84201 q^{32} +11.8776 q^{33} -0.714378 q^{34} -0.740370 q^{35} -5.79607 q^{36} +8.58988 q^{37} +2.17791 q^{38} +6.14035 q^{39} +2.20041 q^{40} +10.6404 q^{41} -1.57298 q^{42} -0.979313 q^{43} +6.74031 q^{44} +3.43429 q^{45} +5.64984 q^{46} -4.83264 q^{47} -3.14592 q^{48} -6.29642 q^{49} +3.01533 q^{50} -2.62504 q^{51} +3.48453 q^{52} +5.63575 q^{53} +1.67061 q^{54} -3.99377 q^{55} -2.09107 q^{56} +8.00293 q^{57} +0.584584 q^{58} -1.00000 q^{59} +3.45157 q^{60} +2.11105 q^{61} +1.63667 q^{62} -3.26364 q^{63} +1.77655 q^{64} -2.06466 q^{65} -8.48509 q^{66} +11.2466 q^{67} -1.48966 q^{68} +20.7608 q^{69} +0.528904 q^{70} +5.19582 q^{71} +9.69968 q^{72} +6.63693 q^{73} -6.13642 q^{74} +11.0801 q^{75} +4.54151 q^{76} +3.79532 q^{77} -4.38653 q^{78} +14.7194 q^{79} +1.05780 q^{80} -5.53378 q^{81} -7.60128 q^{82} +6.61943 q^{83} -3.28006 q^{84} +0.882657 q^{85} +0.699600 q^{86} +2.14810 q^{87} -11.2799 q^{88} -3.38821 q^{89} -2.45339 q^{90} +1.96207 q^{91} +11.7814 q^{92} +6.01408 q^{93} +3.45233 q^{94} -2.69094 q^{95} +15.3355 q^{96} -4.45791 q^{97} +4.49802 q^{98} -17.6051 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 5 q^{2} + q^{3} + 21 q^{4} + 21 q^{5} + 5 q^{6} - q^{7} + 9 q^{8} + 17 q^{9}+O(q^{10}) \) 18 * q + 5 * q^2 + q^3 + 21 * q^4 + 21 * q^5 + 5 * q^6 - q^7 + 9 * q^8 + 17 * q^9	\( 18 q + 5 q^{2} + q^{3} + 21 q^{4} + 21 q^{5} + 5 q^{6} - q^{7} + 9 q^{8} + 17 q^{9} + 10 q^{10} + 6 q^{11} + 20 q^{12} + 12 q^{13} + 9 q^{14} - q^{15} + 19 q^{16} + 18 q^{17} + 10 q^{18} - 14 q^{19} + 17 q^{20} - 14 q^{21} - 4 q^{22} + 7 q^{23} - 3 q^{24} + 35 q^{25} + 3 q^{26} + 13 q^{27} + q^{28} + 23 q^{29} + 17 q^{30} - q^{31} + 13 q^{32} + 7 q^{33} + 5 q^{34} + 5 q^{35} - 16 q^{36} + 36 q^{37} - 19 q^{38} + 8 q^{39} - 4 q^{40} + 37 q^{41} + 9 q^{42} - 15 q^{43} - 9 q^{44} + 17 q^{45} + q^{46} + 23 q^{47} + 17 q^{48} + 15 q^{49} + 32 q^{50} + q^{51} - 11 q^{52} + 35 q^{53} - 17 q^{54} - 6 q^{55} + 37 q^{56} - 16 q^{57} + 2 q^{58} - 18 q^{59} - 6 q^{60} + 39 q^{61} - q^{62} + 15 q^{63} + 5 q^{64} + 15 q^{65} - 36 q^{66} + 14 q^{67} + 21 q^{68} + 16 q^{69} - 45 q^{70} + 3 q^{71} - 71 q^{72} + 56 q^{73} - 27 q^{74} + 16 q^{75} - q^{76} + 39 q^{77} - 71 q^{78} - 22 q^{79} + 45 q^{80} - 18 q^{81} + 5 q^{82} + 12 q^{83} + 2 q^{84} + 21 q^{85} + 4 q^{86} + 8 q^{87} - 18 q^{88} + 34 q^{89} + 48 q^{90} + 3 q^{91} + 67 q^{92} - 19 q^{93} - 38 q^{94} - 72 q^{95} + 6 q^{96} + 31 q^{97} + 19 q^{98} + 44 q^{99}+O(q^{100}) \) 18 * q + 5 * q^2 + q^3 + 21 * q^4 + 21 * q^5 + 5 * q^6 - q^7 + 9 * q^8 + 17 * q^9 + 10 * q^10 + 6 * q^11 + 20 * q^12 + 12 * q^13 + 9 * q^14 - q^15 + 19 * q^16 + 18 * q^17 + 10 * q^18 - 14 * q^19 + 17 * q^20 - 14 * q^21 - 4 * q^22 + 7 * q^23 - 3 * q^24 + 35 * q^25 + 3 * q^26 + 13 * q^27 + q^28 + 23 * q^29 + 17 * q^30 - q^31 + 13 * q^32 + 7 * q^33 + 5 * q^34 + 5 * q^35 - 16 * q^36 + 36 * q^37 - 19 * q^38 + 8 * q^39 - 4 * q^40 + 37 * q^41 + 9 * q^42 - 15 * q^43 - 9 * q^44 + 17 * q^45 + q^46 + 23 * q^47 + 17 * q^48 + 15 * q^49 + 32 * q^50 + q^51 - 11 * q^52 + 35 * q^53 - 17 * q^54 - 6 * q^55 + 37 * q^56 - 16 * q^57 + 2 * q^58 - 18 * q^59 - 6 * q^60 + 39 * q^61 - q^62 + 15 * q^63 + 5 * q^64 + 15 * q^65 - 36 * q^66 + 14 * q^67 + 21 * q^68 + 16 * q^69 - 45 * q^70 + 3 * q^71 - 71 * q^72 + 56 * q^73 - 27 * q^74 + 16 * q^75 - q^76 + 39 * q^77 - 71 * q^78 - 22 * q^79 + 45 * q^80 - 18 * q^81 + 5 * q^82 + 12 * q^83 + 2 * q^84 + 21 * q^85 + 4 * q^86 + 8 * q^87 - 18 * q^88 + 34 * q^89 + 48 * q^90 + 3 * q^91 + 67 * q^92 - 19 * q^93 - 38 * q^94 - 72 * q^95 + 6 * q^96 + 31 * q^97 + 19 * q^98 + 44 * q^99

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