LMFDB - Embedded newform 1003.2.a.g.1.1

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:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 3x^{9} - 10x^{8} + 34x^{7} + 28x^{6} - 129x^{5} - 3x^{4} + 178x^{3} - 56x^{2} - 56x + 15 $ x^10 - 3x^9 - 10x^8 + 34x^7 + 28x^6 - 129x^5 - 3x^4 + 178x^3 - 56x^2 - 56*x + 15
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.99318$ 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)

$f(q)$	$=$	$q-2.65122 q^{2} -2.99318 q^{3} +5.02897 q^{4} -3.73588 q^{5} +7.93559 q^{6} +2.50921 q^{7} -8.03048 q^{8} +5.95914 q^{9} +O(q^{10})$	\(q-2.65122 q^{2} -2.99318 q^{3} +5.02897 q^{4} -3.73588 q^{5} +7.93559 q^{6} +2.50921 q^{7} -8.03048 q^{8} +5.95914 q^{9} +9.90463 q^{10} -3.72828 q^{11} -15.0526 q^{12} -5.25900 q^{13} -6.65248 q^{14} +11.1822 q^{15} +11.2326 q^{16} -1.00000 q^{17} -15.7990 q^{18} -0.828462 q^{19} -18.7876 q^{20} -7.51053 q^{21} +9.88451 q^{22} +5.33910 q^{23} +24.0367 q^{24} +8.95677 q^{25} +13.9428 q^{26} -8.85725 q^{27} +12.6188 q^{28} +9.11822 q^{29} -29.6464 q^{30} +4.22220 q^{31} -13.7192 q^{32} +11.1594 q^{33} +2.65122 q^{34} -9.37411 q^{35} +29.9684 q^{36} +2.72490 q^{37} +2.19644 q^{38} +15.7411 q^{39} +30.0009 q^{40} +3.48787 q^{41} +19.9121 q^{42} -6.71625 q^{43} -18.7494 q^{44} -22.2626 q^{45} -14.1551 q^{46} -7.41241 q^{47} -33.6213 q^{48} -0.703850 q^{49} -23.7464 q^{50} +2.99318 q^{51} -26.4474 q^{52} +10.6012 q^{53} +23.4825 q^{54} +13.9284 q^{55} -20.1502 q^{56} +2.47974 q^{57} -24.1744 q^{58} -1.00000 q^{59} +56.2348 q^{60} +12.8953 q^{61} -11.1940 q^{62} +14.9528 q^{63} +13.9075 q^{64} +19.6470 q^{65} -29.5861 q^{66} +5.88788 q^{67} -5.02897 q^{68} -15.9809 q^{69} +24.8528 q^{70} +3.45664 q^{71} -47.8548 q^{72} -15.0105 q^{73} -7.22432 q^{74} -26.8093 q^{75} -4.16631 q^{76} -9.35506 q^{77} -41.7332 q^{78} +7.61134 q^{79} -41.9637 q^{80} +8.63394 q^{81} -9.24710 q^{82} +5.81532 q^{83} -37.7703 q^{84} +3.73588 q^{85} +17.8063 q^{86} -27.2925 q^{87} +29.9399 q^{88} -5.73720 q^{89} +59.0231 q^{90} -13.1959 q^{91} +26.8502 q^{92} -12.6378 q^{93} +19.6519 q^{94} +3.09503 q^{95} +41.0642 q^{96} -16.4754 q^{97} +1.86606 q^{98} -22.2174 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - q^{2} - 7 q^{3} + 15 q^{4} - 12 q^{5} + 5 q^{6} - 9 q^{7} - 12 q^{8} + 3 q^{9}+O(q^{10}) $ 10 * q - q^2 - 7 * q^3 + 15 * q^4 - 12 * q^5 + 5 * q^6 - 9 * q^7 - 12 * q^8 + 3 * q^9	\( 10 q - q^{2} - 7 q^{3} + 15 q^{4} - 12 q^{5} + 5 q^{6} - 9 q^{7} - 12 q^{8} + 3 q^{9} + 4 q^{10} + 12 q^{11} - 24 q^{12} - 11 q^{13} - 12 q^{14} + 9 q^{15} - 3 q^{16} - 10 q^{17} - 22 q^{18} - 5 q^{19} - 36 q^{20} - 10 q^{21} + 6 q^{22} - 7 q^{23} + 35 q^{24} + 2 q^{25} + q^{26} - 31 q^{27} - 4 q^{28} + 10 q^{29} - 9 q^{30} + 13 q^{31} - 15 q^{32} - 9 q^{33} + q^{34} - 8 q^{35} + 40 q^{36} + 12 q^{37} - 50 q^{38} + 24 q^{39} + 5 q^{40} - 29 q^{41} - 17 q^{42} - 18 q^{43} - 6 q^{44} - 14 q^{45} + 11 q^{46} - 18 q^{47} - 43 q^{48} - 9 q^{49} - 31 q^{50} + 7 q^{51} - 68 q^{52} + 19 q^{54} - 27 q^{55} - 7 q^{56} + 20 q^{57} + 23 q^{58} - 10 q^{59} + 38 q^{60} + 8 q^{61} - 46 q^{62} + 39 q^{63} - 20 q^{64} + 58 q^{65} - 34 q^{66} - 6 q^{67} - 15 q^{68} + 6 q^{69} + 73 q^{70} + 8 q^{71} - 70 q^{72} - 41 q^{73} - 10 q^{74} + 10 q^{75} + 12 q^{76} - 22 q^{77} - 43 q^{78} + 3 q^{79} - 15 q^{80} + 26 q^{81} + 8 q^{82} - 22 q^{84} + 12 q^{85} - 29 q^{86} - 28 q^{87} + 33 q^{88} - 45 q^{89} + 56 q^{90} - 14 q^{91} + 36 q^{92} - 19 q^{93} + 15 q^{94} - 17 q^{95} + 90 q^{96} - 5 q^{97} + 30 q^{98} + 14 q^{99}+O(q^{100}) \) 10 * q - q^2 - 7 * q^3 + 15 * q^4 - 12 * q^5 + 5 * q^6 - 9 * q^7 - 12 * q^8 + 3 * q^9 + 4 * q^10 + 12 * q^11 - 24 * q^12 - 11 * q^13 - 12 * q^14 + 9 * q^15 - 3 * q^16 - 10 * q^17 - 22 * q^18 - 5 * q^19 - 36 * q^20 - 10 * q^21 + 6 * q^22 - 7 * q^23 + 35 * q^24 + 2 * q^25 + q^26 - 31 * q^27 - 4 * q^28 + 10 * q^29 - 9 * q^30 + 13 * q^31 - 15 * q^32 - 9 * q^33 + q^34 - 8 * q^35 + 40 * q^36 + 12 * q^37 - 50 * q^38 + 24 * q^39 + 5 * q^40 - 29 * q^41 - 17 * q^42 - 18 * q^43 - 6 * q^44 - 14 * q^45 + 11 * q^46 - 18 * q^47 - 43 * q^48 - 9 * q^49 - 31 * q^50 + 7 * q^51 - 68 * q^52 + 19 * q^54 - 27 * q^55 - 7 * q^56 + 20 * q^57 + 23 * q^58 - 10 * q^59 + 38 * q^60 + 8 * q^61 - 46 * q^62 + 39 * q^63 - 20 * q^64 + 58 * q^65 - 34 * q^66 - 6 * q^67 - 15 * q^68 + 6 * q^69 + 73 * q^70 + 8 * q^71 - 70 * q^72 - 41 * q^73 - 10 * q^74 + 10 * q^75 + 12 * q^76 - 22 * q^77 - 43 * q^78 + 3 * q^79 - 15 * q^80 + 26 * q^81 + 8 * q^82 - 22 * q^84 + 12 * q^85 - 29 * q^86 - 28 * q^87 + 33 * q^88 - 45 * q^89 + 56 * q^90 - 14 * q^91 + 36 * q^92 - 19 * q^93 + 15 * q^94 - 17 * q^95 + 90 * q^96 - 5 * q^97 + 30 * q^98 + 14 * 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 $

$2$	−2.65122	−1.87470	−0.937348	−	0.348394i	$-0.886727\pi$
$2$	−2.65122	−1.87470	−0.937348	+	0.348394i	$0.886727\pi$
$3$	−2.99318	−1.72811	−0.864057	−	0.503393i	$-0.832085\pi$
$3$	−2.99318	−1.72811	−0.864057	+	0.503393i	$0.832085\pi$
$4$	5.02897	2.51449
$5$	−3.73588	−1.67073	−0.835367	−	0.549692i	$-0.814745\pi$
$5$	−3.73588	−1.67073	−0.835367	+	0.549692i	$0.814745\pi$
$6$	7.93559	3.23969
$7$	2.50921	0.948393	0.474197	−	0.880419i	$-0.342739\pi$
$7$	2.50921	0.948393	0.474197	+	0.880419i	$0.342739\pi$
$8$	−8.03048	−2.83920
$9$	5.95914	1.98638
$10$	9.90463	3.13212
$11$	−3.72828	−1.12412	−0.562060	−	0.827096i	$-0.689991\pi$
$11$	−3.72828	−1.12412	−0.562060	+	0.827096i	$0.689991\pi$
$12$	−15.0526	−4.34532
$13$	−5.25900	−1.45858	−0.729291	−	0.684203i	$-0.760150\pi$
$13$	−5.25900	−1.45858	−0.729291	+	0.684203i	$0.760150\pi$
$14$	−6.65248	−1.77795
$15$	11.1822	2.88722
$16$	11.2326	2.80816
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−15.7990	−3.72386
$19$	−0.828462	−0.190062	−0.0950311	−	0.995474i	$-0.530295\pi$
$19$	−0.828462	−0.190062	−0.0950311	+	0.995474i	$0.530295\pi$
$20$	−18.7876	−4.20104
$21$	−7.51053	−1.63893
$22$	9.88451	2.10738
$23$	5.33910	1.11328	0.556639	−	0.830754i	$-0.312090\pi$
$23$	5.33910	1.11328	0.556639	+	0.830754i	$0.312090\pi$
$24$	24.0367	4.90647
$25$	8.95677	1.79135
$26$	13.9428	2.73440
$27$	−8.85725	−1.70458
$28$	12.6188	2.38472
$29$	9.11822	1.69321	0.846605	−	0.532221i	$-0.178643\pi$
$29$	9.11822	1.69321	0.846605	+	0.532221i	$0.178643\pi$
$30$	−29.6464	−5.41266
$31$	4.22220	0.758330	0.379165	−	0.925329i	$-0.376211\pi$
$31$	4.22220	0.758330	0.379165	+	0.925329i	$0.376211\pi$
$32$	−13.7192	−2.42524
$33$	11.1594	1.94261
$34$	2.65122	0.454681
$35$	−9.37411	−1.58451
$36$	29.9684	4.99473
$37$	2.72490	0.447971	0.223986	−	0.974592i	$-0.428093\pi$
$37$	2.72490	0.447971	0.223986	+	0.974592i	$0.428093\pi$
$38$	2.19644	0.356309
$39$	15.7411	2.52060
$40$	30.0009	4.74356
$41$	3.48787	0.544713	0.272357	−	0.962196i	$-0.412197\pi$
$41$	3.48787	0.544713	0.272357	+	0.962196i	$0.412197\pi$
$42$	19.9121	3.07250
$43$	−6.71625	−1.02422	−0.512109	−	0.858920i	$-0.671136\pi$
$43$	−6.71625	−1.02422	−0.512109	+	0.858920i	$0.671136\pi$
$44$	−18.7494	−2.82659
$45$	−22.2626	−3.31871
$46$	−14.1551	−2.08706
$47$	−7.41241	−1.08121	−0.540605	−	0.841276i	$-0.681805\pi$
$47$	−7.41241	−1.08121	−0.540605	+	0.841276i	$0.681805\pi$
$48$	−33.6213	−4.85282
$49$	−0.703850	−0.100550
$50$	−23.7464	−3.35825
$51$	2.99318	0.419129
$52$	−26.4474	−3.66759
$53$	10.6012	1.45618	0.728092	−	0.685479i	$-0.240407\pi$
$53$	10.6012	1.45618	0.728092	+	0.685479i	$0.240407\pi$
$54$	23.4825	3.19557
$55$	13.9284	1.87811
$56$	−20.1502	−2.69268
$57$	2.47974	0.328449
$58$	−24.1744	−3.17426
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	56.2348	7.25988
$61$	12.8953	1.65107	0.825534	−	0.564352i	$-0.190874\pi$
$61$	12.8953	1.65107	0.825534	+	0.564352i	$0.190874\pi$
$62$	−11.1940	−1.42164
$63$	14.9528	1.88387
$64$	13.9075	1.73843
$65$	19.6470	2.43690
$66$	−29.5861	−3.64180
$67$	5.88788	0.719319	0.359660	−	0.933084i	$-0.382893\pi$
$67$	5.88788	0.719319	0.359660	+	0.933084i	$0.382893\pi$
$68$	−5.02897	−0.609853
$69$	−15.9809	−1.92387
$70$	24.8528	2.97048
$71$	3.45664	0.410228	0.205114	−	0.978738i	$-0.434243\pi$
$71$	3.45664	0.410228	0.205114	+	0.978738i	$0.434243\pi$
$72$	−47.8548	−5.63974
$73$	−15.0105	−1.75684	−0.878421	−	0.477888i	$-0.841403\pi$
$73$	−15.0105	−1.75684	−0.878421	+	0.477888i	$0.841403\pi$
$74$	−7.22432	−0.839810
$75$	−26.8093	−3.09567
$76$	−4.16631	−0.477909
$77$	−9.35506	−1.06611
$78$	−41.7332	−4.72536
$79$	7.61134	0.856342	0.428171	−	0.903698i	$-0.359158\pi$
$79$	7.61134	0.856342	0.428171	+	0.903698i	$0.359158\pi$
$80$	−41.9637	−4.69169
$81$	8.63394	0.959327
$82$	−9.24710	−1.02117
$83$	5.81532	0.638314	0.319157	−	0.947702i	$-0.396600\pi$
$83$	5.81532	0.638314	0.319157	+	0.947702i	$0.396600\pi$
$84$	−37.7703	−4.12107
$85$	3.73588	0.405213
$86$	17.8063	1.92010
$87$	−27.2925	−2.92606
$88$	29.9399	3.19161
$89$	−5.73720	−0.608142	−0.304071	−	0.952649i	$-0.598346\pi$
$89$	−5.73720	−0.608142	−0.304071	+	0.952649i	$0.598346\pi$
$90$	59.0231	6.22158
$91$	−13.1959	−1.38331
$92$	26.8502	2.79933
$93$	−12.6378	−1.31048
$94$	19.6519	2.02694
$95$	3.09503	0.317544
$96$	41.0642	4.19109
$97$	−16.4754	−1.67282	−0.836410	−	0.548104i	$-0.815350\pi$
$97$	−16.4754	−1.67282	−0.836410	+	0.548104i	$0.815350\pi$
$98$	1.86606	0.188501
$99$	−22.2174	−2.23293
$100$	45.0434	4.50434
$101$	−8.09827	−0.805808	−0.402904	−	0.915242i	$-0.631999\pi$
$101$	−8.09827	−0.805808	−0.402904	+	0.915242i	$0.631999\pi$
$102$	−7.93559	−0.785740
$103$	8.36480	0.824208	0.412104	−	0.911137i	$-0.364794\pi$
$103$	8.36480	0.824208	0.412104	+	0.911137i	$0.364794\pi$
$104$	42.2323	4.14121
$105$	28.0584	2.73822
$106$	−28.1061	−2.72990
$107$	−4.69326	−0.453715	−0.226857	−	0.973928i	$-0.572845\pi$
$107$	−4.69326	−0.453715	−0.226857	+	0.973928i	$0.572845\pi$
$108$	−44.5429	−4.28614
$109$	−5.37795	−0.515115	−0.257557	−	0.966263i	$-0.582918\pi$
$109$	−5.37795	−0.515115	−0.257557	+	0.966263i	$0.582918\pi$
$110$	−36.9273	−3.52088
$111$	−8.15613	−0.774146
$112$	28.1851	2.66324
$113$	−3.25798	−0.306485	−0.153242	−	0.988189i	$-0.548972\pi$
$113$	−3.25798	−0.306485	−0.153242	+	0.988189i	$0.548972\pi$
$114$	−6.57433	−0.615743
$115$	−19.9462	−1.85999
$116$	45.8553	4.25756
$117$	−31.3391	−2.89730
$118$	2.65122	0.244065
$119$	−2.50921	−0.230019
$120$	−89.7981	−8.19741
$121$	2.90011	0.263646
$122$	−34.1882	−3.09525
$123$	−10.4398	−0.941327
$124$	21.2334	1.90681
$125$	−14.7820	−1.32214
$126$	−39.6431	−3.53168
$127$	3.36825	0.298884	0.149442	−	0.988771i	$-0.452252\pi$
$127$	3.36825	0.298884	0.149442	+	0.988771i	$0.452252\pi$
$128$	−9.43329	−0.833793
$129$	20.1030	1.76997
$130$	−52.0884	−4.56846
$131$	8.64538	0.755350	0.377675	−	0.925938i	$-0.376724\pi$
$131$	8.64538	0.755350	0.377675	+	0.925938i	$0.376724\pi$
$132$	56.1205	4.88466
$133$	−2.07879	−0.180254
$134$	−15.6101	−1.34851
$135$	33.0896	2.84790
$136$	8.03048	0.688608
$137$	−14.6481	−1.25148	−0.625738	−	0.780034i	$-0.715202\pi$
$137$	−14.6481	−1.25148	−0.625738	+	0.780034i	$0.715202\pi$
$138$	42.3689	3.60668
$139$	1.07892	0.0915131	0.0457565	−	0.998953i	$-0.485430\pi$
$139$	1.07892	0.0915131	0.0457565	+	0.998953i	$0.485430\pi$
$140$	−47.1422	−3.98424
$141$	22.1867	1.86846
$142$	−9.16433	−0.769053
$143$	19.6070	1.63962
$144$	66.9369	5.57807
$145$	−34.0645	−2.82891
$146$	39.7961	3.29354
$147$	2.10675	0.173762
$148$	13.7035	1.12642
$149$	2.08447	0.170767	0.0853833	−	0.996348i	$-0.472789\pi$
$149$	2.08447	0.170767	0.0853833	+	0.996348i	$0.472789\pi$
$150$	71.0773	5.80343
$151$	−6.43379	−0.523574	−0.261787	−	0.965126i	$-0.584312\pi$
$151$	−6.43379	−0.523574	−0.261787	+	0.965126i	$0.584312\pi$
$152$	6.65295	0.539625
$153$	−5.95914	−0.481768
$154$	24.8023	1.99863
$155$	−15.7736	−1.26697
$156$	79.1617	6.33801
$157$	−12.4263	−0.991729	−0.495864	−	0.868400i	$-0.665149\pi$
$157$	−12.4263	−0.991729	−0.495864	+	0.868400i	$0.665149\pi$
$158$	−20.1793	−1.60538
$159$	−31.7313	−2.51645
$160$	51.2534	4.05193
$161$	13.3969	1.05583
$162$	−22.8905	−1.79845
$163$	9.89295	0.774876	0.387438	−	0.921896i	$-0.373360\pi$
$163$	9.89295	0.774876	0.387438	+	0.921896i	$0.373360\pi$
$164$	17.5404	1.36967
$165$	−41.6903	−3.24558
$166$	−15.4177	−1.19665
$167$	5.93312	0.459118	0.229559	−	0.973295i	$-0.426272\pi$
$167$	5.93312	0.459118	0.229559	+	0.973295i	$0.426272\pi$
$168$	60.3132	4.65326
$169$	14.6570	1.12746
$170$	−9.90463	−0.759651
$171$	−4.93692	−0.377536
$172$	−33.7759	−2.57538
$173$	22.3121	1.69636	0.848179	−	0.529710i	$-0.177699\pi$
$173$	22.3121	1.69636	0.848179	+	0.529710i	$0.177699\pi$
$174$	72.3584	5.48548
$175$	22.4744	1.69891
$176$	−41.8785	−3.15671
$177$	2.99318	0.224981
$178$	15.2106	1.14008
$179$	−23.9387	−1.78926	−0.894632	−	0.446803i	$-0.852562\pi$
$179$	−23.9387	−1.78926	−0.894632	+	0.446803i	$0.852562\pi$
$180$	−111.958	−8.34487
$181$	1.01759	0.0756371	0.0378185	−	0.999285i	$-0.487959\pi$
$181$	1.01759	0.0756371	0.0378185	+	0.999285i	$0.487959\pi$
$182$	34.9854	2.59329
$183$	−38.5979	−2.85324
$184$	−42.8755	−3.16083
$185$	−10.1799	−0.748441
$186$	33.5057	2.45676
$187$	3.72828	0.272639
$188$	−37.2768	−2.71869
$189$	−22.2247	−1.61661
$190$	−8.20561	−0.595298
$191$	−5.21443	−0.377303	−0.188651	−	0.982044i	$-0.560412\pi$
$191$	−5.21443	−0.377303	−0.188651	+	0.982044i	$0.560412\pi$
$192$	−41.6276	−3.00421
$193$	6.43244	0.463017	0.231509	−	0.972833i	$-0.425634\pi$
$193$	6.43244	0.463017	0.231509	+	0.972833i	$0.425634\pi$
$194$	43.6798	3.13603
$195$	−58.8069	−4.21125
$196$	−3.53964	−0.252832
$197$	−11.7248	−0.835360	−0.417680	−	0.908594i	$-0.637157\pi$
$197$	−11.7248	−0.835360	−0.417680	+	0.908594i	$0.637157\pi$
$198$	58.9032	4.18607
$199$	−16.2721	−1.15350	−0.576749	−	0.816921i	$-0.695679\pi$
$199$	−16.2721	−1.15350	−0.576749	+	0.816921i	$0.695679\pi$
$200$	−71.9272	−5.08602
$201$	−17.6235	−1.24307
$202$	21.4703	1.51065
$203$	22.8795	1.60583
$204$	15.0526	1.05390
$205$	−13.0302	−0.910071
$206$	−22.1769	−1.54514
$207$	31.8164	2.21140
$208$	−59.0724	−4.09593
$209$	3.08874	0.213653
$210$	−74.3891	−5.13333
$211$	−12.0330	−0.828383	−0.414192	−	0.910190i	$-0.635936\pi$
$211$	−12.0330	−0.828383	−0.414192	+	0.910190i	$0.635936\pi$
$212$	53.3131	3.66156
$213$	−10.3464	−0.708921
$214$	12.4429	0.850577
$215$	25.0911	1.71120
$216$	71.1280	4.83965
$217$	10.5944	0.719195
$218$	14.2581	0.965683
$219$	44.9291	3.03602
$220$	70.0456	4.72247
$221$	5.25900	0.353758
$222$	21.6237	1.45129
$223$	14.4540	0.967913	0.483957	−	0.875092i	$-0.339199\pi$
$223$	14.4540	0.967913	0.483957	+	0.875092i	$0.339199\pi$
$224$	−34.4245	−2.30008
$225$	53.3747	3.55831
$226$	8.63762	0.574566
$227$	20.5312	1.36270	0.681350	−	0.731958i	$-0.261393\pi$
$227$	20.5312	1.36270	0.681350	+	0.731958i	$0.261393\pi$
$228$	12.4705	0.825882
$229$	−21.4475	−1.41729	−0.708646	−	0.705564i	$-0.750694\pi$
$229$	−21.4475	−1.41729	−0.708646	+	0.705564i	$0.750694\pi$
$230$	52.8818	3.48692
$231$	28.0014	1.84236
$232$	−73.2237	−4.80737
$233$	−25.0315	−1.63987	−0.819935	−	0.572457i	$-0.805990\pi$
$233$	−25.0315	−1.63987	−0.819935	+	0.572457i	$0.805990\pi$
$234$	83.0869	5.43156
$235$	27.6918	1.80642
$236$	−5.02897	−0.327358
$237$	−22.7821	−1.47986
$238$	6.65248	0.431216
$239$	16.3150	1.05533	0.527663	−	0.849454i	$-0.323068\pi$
$239$	16.3150	1.05533	0.527663	+	0.849454i	$0.323068\pi$
$240$	125.605	8.10777
$241$	−24.9322	−1.60602	−0.803011	−	0.595964i	$-0.796770\pi$
$241$	−24.9322	−1.60602	−0.803011	+	0.595964i	$0.796770\pi$
$242$	−7.68882	−0.494256
$243$	0.728785	0.0467516
$244$	64.8499	4.15159
$245$	2.62950	0.167992
$246$	27.6783	1.76470
$247$	4.35688	0.277221
$248$	−33.9063	−2.15305
$249$	−17.4063	−1.10308
$250$	39.1904	2.47862
$251$	−2.19066	−0.138274	−0.0691368	−	0.997607i	$-0.522024\pi$
$251$	−2.19066	−0.138274	−0.0691368	+	0.997607i	$0.522024\pi$
$252$	75.1970	4.73697
$253$	−19.9057	−1.25146
$254$	−8.92997	−0.560316
$255$	−11.1822	−0.700254
$256$	−2.80519	−0.175325
$257$	−4.22215	−0.263371	−0.131685	−	0.991292i	$-0.542039\pi$
$257$	−4.22215	−0.263371	−0.131685	+	0.991292i	$0.542039\pi$
$258$	−53.2974	−3.31815
$259$	6.83736	0.424853
$260$	98.8040	6.12757
$261$	54.3367	3.36336
$262$	−22.9208	−1.41605
$263$	18.6417	1.14950	0.574748	−	0.818331i	$-0.305100\pi$
$263$	18.6417	1.14950	0.574748	+	0.818331i	$0.305100\pi$
$264$	−89.6156	−5.51546
$265$	−39.6047	−2.43290
$266$	5.51133	0.337921
$267$	17.1725	1.05094
$268$	29.6100	1.80872
$269$	−5.67229	−0.345846	−0.172923	−	0.984935i	$-0.555321\pi$
$269$	−5.67229	−0.345846	−0.172923	+	0.984935i	$0.555321\pi$
$270$	−87.7278	−5.33895
$271$	14.1674	0.860607	0.430304	−	0.902684i	$-0.358406\pi$
$271$	14.1674	0.860607	0.430304	+	0.902684i	$0.358406\pi$
$272$	−11.2326	−0.681078
$273$	39.4979	2.39052
$274$	38.8355	2.34614
$275$	−33.3934	−2.01370
$276$	−80.3675	−4.83756
$277$	−21.2770	−1.27841	−0.639205	−	0.769036i	$-0.720736\pi$
$277$	−21.2770	−1.27841	−0.639205	+	0.769036i	$0.720736\pi$
$278$	−2.86046	−0.171559
$279$	25.1607	1.50633
$280$	75.2786	4.49876
$281$	8.37638	0.499693	0.249847	−	0.968285i	$-0.419620\pi$
$281$	8.37638	0.499693	0.249847	+	0.968285i	$0.419620\pi$
$282$	−58.8218	−3.50279
$283$	17.2649	1.02629	0.513146	−	0.858301i	$-0.328480\pi$
$283$	17.2649	1.02629	0.513146	+	0.858301i	$0.328480\pi$
$284$	17.3834	1.03151
$285$	−9.26399	−0.548752
$286$	−51.9826	−3.07379
$287$	8.75180	0.516602
$288$	−81.7549	−4.81745
$289$	1.00000	0.0588235
$290$	90.3126	5.30334
$291$	49.3138	2.89082
$292$	−75.4872	−4.41756
$293$	−17.6805	−1.03291	−0.516453	−	0.856316i	$-0.672748\pi$
$293$	−17.6805	−1.03291	−0.516453	+	0.856316i	$0.672748\pi$
$294$	−5.58546	−0.325751
$295$	3.73588	0.217511
$296$	−21.8823	−1.27188
$297$	33.0224	1.91615
$298$	−5.52640	−0.320136
$299$	−28.0783	−1.62381
$300$	−134.823	−7.78401
$301$	−16.8525	−0.971362
$302$	17.0574	0.981543
$303$	24.2396	1.39253
$304$	−9.30581	−0.533725
$305$	−48.1751	−2.75850
$306$	15.7990	0.903169
$307$	15.7715	0.900129	0.450064	−	0.892996i	$-0.351401\pi$
$307$	15.7715	0.900129	0.450064	+	0.892996i	$0.351401\pi$
$308$	−47.0464	−2.68072
$309$	−25.0374	−1.42433
$310$	41.8194	2.37518
$311$	1.68249	0.0954054	0.0477027	−	0.998862i	$-0.484810\pi$
$311$	1.68249	0.0954054	0.0477027	+	0.998862i	$0.484810\pi$
$312$	−126.409	−7.15649
$313$	31.8087	1.79793	0.898966	−	0.438018i	$-0.144319\pi$
$313$	31.8087	1.79793	0.898966	+	0.438018i	$0.144319\pi$
$314$	32.9449	1.85919
$315$	−55.8616	−3.14745
$316$	38.2772	2.15326
$317$	−8.69140	−0.488158	−0.244079	−	0.969755i	$-0.578486\pi$
$317$	−8.69140	−0.488158	−0.244079	+	0.969755i	$0.578486\pi$
$318$	84.1266	4.71759
$319$	−33.9953	−1.90337
$320$	−51.9566	−2.90446
$321$	14.0478	0.784071
$322$	−35.5182	−1.97935
$323$	0.828462	0.0460969
$324$	43.4199	2.41222
$325$	−47.1036	−2.61284
$326$	−26.2284	−1.45266
$327$	16.0972	0.890177
$328$	−28.0092	−1.54655
$329$	−18.5993	−1.02541
$330$	110.530	6.08448
$331$	−17.1068	−0.940277	−0.470139	−	0.882593i	$-0.655796\pi$
$331$	−17.1068	−0.940277	−0.470139	+	0.882593i	$0.655796\pi$
$332$	29.2451	1.60503
$333$	16.2381	0.889841
$334$	−15.7300	−0.860708
$335$	−21.9964	−1.20179
$336$	−84.3631	−4.60238
$337$	6.14398	0.334684	0.167342	−	0.985899i	$-0.446482\pi$
$337$	6.14398	0.334684	0.167342	+	0.985899i	$0.446482\pi$
$338$	−38.8590	−2.11365
$339$	9.75173	0.529641
$340$	18.7876	1.01890
$341$	−15.7416	−0.852454
$342$	13.0889	0.707765
$343$	−19.3306	−1.04375
$344$	53.9347	2.90797
$345$	59.7026	3.21428
$346$	−59.1543	−3.18016
$347$	−26.7511	−1.43608	−0.718038	−	0.696004i	$-0.754960\pi$
$347$	−26.7511	−1.43608	−0.718038	+	0.696004i	$0.754960\pi$
$348$	−137.253	−7.35754
$349$	−15.7992	−0.845711	−0.422855	−	0.906197i	$-0.638972\pi$
$349$	−15.7992	−0.845711	−0.422855	+	0.906197i	$0.638972\pi$
$350$	−59.5847	−3.18494
$351$	46.5802	2.48627
$352$	51.1492	2.72626
$353$	−10.9820	−0.584511	−0.292255	−	0.956340i	$-0.594406\pi$
$353$	−10.9820	−0.584511	−0.292255	+	0.956340i	$0.594406\pi$
$354$	−7.93559	−0.421772
$355$	−12.9136	−0.685383
$356$	−28.8522	−1.52917
$357$	7.51053	0.397500
$358$	63.4669	3.35433
$359$	−27.7839	−1.46638	−0.733190	−	0.680024i	$-0.761970\pi$
$359$	−27.7839	−1.46638	−0.733190	+	0.680024i	$0.761970\pi$
$360$	178.780	9.42251
$361$	−18.3137	−0.963876
$362$	−2.69786	−0.141797
$363$	−8.68055	−0.455611
$364$	−66.3620	−3.47832
$365$	56.0772	2.93522
$366$	102.331	5.34895
$367$	2.71917	0.141939	0.0709697	−	0.997478i	$-0.477391\pi$
$367$	2.71917	0.141939	0.0709697	+	0.997478i	$0.477391\pi$
$368$	59.9721	3.12626
$369$	20.7847	1.08201
$370$	26.9892	1.40310
$371$	26.6006	1.38104
$372$	−63.5553	−3.29519
$373$	17.4303	0.902505	0.451252	−	0.892396i	$-0.350977\pi$
$373$	17.4303	0.902505	0.451252	+	0.892396i	$0.350977\pi$
$374$	−9.88451	−0.511116
$375$	44.2453	2.28482
$376$	59.5252	3.06978
$377$	−47.9527	−2.46969
$378$	58.9227	3.03066
$379$	15.2113	0.781352	0.390676	−	0.920528i	$-0.372241\pi$
$379$	15.2113	0.781352	0.390676	+	0.920528i	$0.372241\pi$
$380$	15.5648	0.798459
$381$	−10.0818	−0.516505
$382$	13.8246	0.707328
$383$	−12.9138	−0.659866	−0.329933	−	0.944004i	$-0.607026\pi$
$383$	−12.9138	−0.659866	−0.329933	+	0.944004i	$0.607026\pi$
$384$	28.2355	1.44089
$385$	34.9493	1.78118
$386$	−17.0538	−0.868017
$387$	−40.0231	−2.03449
$388$	−82.8542	−4.20628
$389$	−25.0470	−1.26994	−0.634968	−	0.772539i	$-0.718987\pi$
$389$	−25.0470	−1.26994	−0.634968	+	0.772539i	$0.718987\pi$
$390$	155.910	7.89482
$391$	−5.33910	−0.270010
$392$	5.65225	0.285482
$393$	−25.8772	−1.30533
$394$	31.0851	1.56605
$395$	−28.4350	−1.43072
$396$	−111.731	−5.61467
$397$	38.3017	1.92231	0.961153	−	0.276015i	$-0.0890138\pi$
$397$	38.3017	1.92231	0.961153	+	0.276015i	$0.0890138\pi$
$398$	43.1409	2.16246
$399$	6.22219	0.311499
$400$	100.608	5.03041
$401$	39.2630	1.96070	0.980350	−	0.197266i	$-0.0632061\pi$
$401$	39.2630	1.96070	0.980350	+	0.197266i	$0.0632061\pi$
$402$	46.7238	2.33037
$403$	−22.2046	−1.10609
$404$	−40.7260	−2.02619
$405$	−32.2553	−1.60278
$406$	−60.6587	−3.01044
$407$	−10.1592	−0.503574
$408$	−24.0367	−1.18999
$409$	7.98530	0.394848	0.197424	−	0.980318i	$-0.436742\pi$
$409$	7.98530	0.394848	0.197424	+	0.980318i	$0.436742\pi$
$410$	34.5460	1.70611
$411$	43.8446	2.16269
$412$	42.0664	2.07246
$413$	−2.50921	−0.123470
$414$	−84.3524	−4.14570
$415$	−21.7253	−1.06645
$416$	72.1494	3.53741
$417$	−3.22941	−0.158145
$418$	−8.18894	−0.400534
$419$	−0.660055	−0.0322458	−0.0161229	−	0.999870i	$-0.505132\pi$
$419$	−0.660055	−0.0322458	−0.0161229	+	0.999870i	$0.505132\pi$
$420$	141.105	6.88522
$421$	−2.77871	−0.135426	−0.0677130	−	0.997705i	$-0.521570\pi$
$421$	−2.77871	−0.135426	−0.0677130	+	0.997705i	$0.521570\pi$
$422$	31.9020	1.55297
$423$	−44.1716	−2.14770
$424$	−85.1326	−4.13440
$425$	−8.95677	−0.434467
$426$	27.4305	1.32901
$427$	32.3570	1.56586
$428$	−23.6023	−1.14086
$429$	−58.6874	−2.83346
$430$	−66.5220	−3.20798
$431$	4.62680	0.222865	0.111433	−	0.993772i	$-0.464456\pi$
$431$	4.62680	0.222865	0.111433	+	0.993772i	$0.464456\pi$
$432$	−99.4903	−4.78673
$433$	−5.60302	−0.269264	−0.134632	−	0.990896i	$-0.542985\pi$
$433$	−5.60302	−0.269264	−0.134632	+	0.990896i	$0.542985\pi$
$434$	−28.0881	−1.34827
$435$	101.961	4.88867
$436$	−27.0456	−1.29525
$437$	−4.42324	−0.211592
$438$	−119.117	−5.69162
$439$	−6.06991	−0.289701	−0.144851	−	0.989454i	$-0.546270\pi$
$439$	−6.06991	−0.289701	−0.144851	+	0.989454i	$0.546270\pi$
$440$	−111.852	−5.33233
$441$	−4.19434	−0.199731
$442$	−13.9428	−0.663189
$443$	3.75037	0.178186	0.0890928	−	0.996023i	$-0.471603\pi$
$443$	3.75037	0.178186	0.0890928	+	0.996023i	$0.471603\pi$
$444$	−41.0170	−1.94658
$445$	21.4335	1.01604
$446$	−38.3208	−1.81454
$447$	−6.23921	−0.295104
$448$	34.8968	1.64872
$449$	11.4755	0.541562	0.270781	−	0.962641i	$-0.412718\pi$
$449$	11.4755	0.541562	0.270781	+	0.962641i	$0.412718\pi$
$450$	−141.508	−6.67075
$451$	−13.0038	−0.612323
$452$	−16.3843	−0.770652
$453$	19.2575	0.904797
$454$	−54.4326	−2.55465
$455$	49.2984	2.31114
$456$	−19.9135	−0.932534
$457$	−8.67590	−0.405841	−0.202921	−	0.979195i	$-0.565043\pi$
$457$	−8.67590	−0.405841	−0.202921	+	0.979195i	$0.565043\pi$
$458$	56.8621	2.65699
$459$	8.85725	0.413421
$460$	−100.309	−4.67693
$461$	−0.852734	−0.0397158	−0.0198579	−	0.999803i	$-0.506321\pi$
$461$	−0.852734	−0.0397158	−0.0198579	+	0.999803i	$0.506321\pi$
$462$	−74.2379	−3.45386
$463$	−11.3859	−0.529147	−0.264574	−	0.964365i	$-0.585231\pi$
$463$	−11.3859	−0.529147	−0.264574	+	0.964365i	$0.585231\pi$
$464$	102.422	4.75480
$465$	47.2134	2.18947
$466$	66.3641	3.07426
$467$	32.2977	1.49456	0.747279	−	0.664510i	$-0.231360\pi$
$467$	32.2977	1.49456	0.747279	+	0.664510i	$0.231360\pi$
$468$	−157.604	−7.28522
$469$	14.7739	0.682198
$470$	−73.4172	−3.38648
$471$	37.1943	1.71382
$472$	8.03048	0.369633
$473$	25.0401	1.15134
$474$	60.4004	2.77428
$475$	−7.42034	−0.340469
$476$	−12.6188	−0.578380
$477$	63.1739	2.89254
$478$	−43.2546	−1.97842
$479$	−21.3060	−0.973494	−0.486747	−	0.873543i	$-0.661817\pi$
$479$	−21.3060	−0.973494	−0.486747	+	0.873543i	$0.661817\pi$
$480$	−153.411	−7.00221
$481$	−14.3303	−0.653403
$482$	66.1007	3.01080
$483$	−40.0995	−1.82459
$484$	14.5846	0.662935
$485$	61.5499	2.79484
$486$	−1.93217	−0.0876450
$487$	11.7339	0.531712	0.265856	−	0.964013i	$-0.414345\pi$
$487$	11.7339	0.531712	0.265856	+	0.964013i	$0.414345\pi$
$488$	−103.555	−4.68772
$489$	−29.6114	−1.33907
$490$	−6.97138	−0.314935
$491$	27.9394	1.26089	0.630444	−	0.776234i	$-0.282873\pi$
$491$	27.9394	1.26089	0.630444	+	0.776234i	$0.282873\pi$
$492$	−52.5016	−2.36695
$493$	−9.11822	−0.410664
$494$	−11.5510	−0.519706
$495$	83.0014	3.73063
$496$	47.4265	2.12951
$497$	8.67346	0.389058
$498$	46.1480	2.06794
$499$	−8.79343	−0.393648	−0.196824	−	0.980439i	$-0.563063\pi$
$499$	−8.79343	−0.393648	−0.196824	+	0.980439i	$0.563063\pi$
$500$	−74.3384	−3.32451
$501$	−17.7589	−0.793409
$502$	5.80794	0.259221
$503$	−21.7234	−0.968598	−0.484299	−	0.874903i	$-0.660925\pi$
$503$	−21.7234	−0.968598	−0.484299	+	0.874903i	$0.660925\pi$
$504$	−120.078	−5.34869
$505$	30.2541	1.34629
$506$	52.7744	2.34611
$507$	−43.8712	−1.94839
$508$	16.9388	0.751539
$509$	−18.5372	−0.821646	−0.410823	−	0.911715i	$-0.634759\pi$
$509$	−18.5372	−0.821646	−0.410823	+	0.911715i	$0.634759\pi$
$510$	29.6464	1.31276
$511$	−37.6644	−1.66618
$512$	26.3038	1.16247
$513$	7.33790	0.323976
$514$	11.1939	0.493740
$515$	−31.2499	−1.37703
$516$	101.097	4.45056
$517$	27.6356	1.21541
$518$	−18.1274	−0.796470
$519$	−66.7842	−2.93150
$520$	−157.775	−6.91887
$521$	−42.0497	−1.84223	−0.921115	−	0.389291i	$-0.872720\pi$
$521$	−42.0497	−1.84223	−0.921115	+	0.389291i	$0.872720\pi$
$522$	−144.059	−6.30528
$523$	11.4918	0.502502	0.251251	−	0.967922i	$-0.419158\pi$
$523$	11.4918	0.502502	0.251251	+	0.967922i	$0.419158\pi$
$524$	43.4774	1.89932
$525$	−67.2701	−2.93591
$526$	−49.4232	−2.15495
$527$	−4.22220	−0.183922
$528$	125.350	5.45515
$529$	5.50597	0.239390
$530$	105.001	4.56094
$531$	−5.95914	−0.258605
$532$	−10.4542	−0.453246
$533$	−18.3427	−0.794509
$534$	−45.5281	−1.97019
$535$	17.5334	0.758037
$536$	−47.2825	−2.04229
$537$	71.6530	3.09205
$538$	15.0385	0.648356
$539$	2.62415	0.113030
$540$	166.407	7.16100
$541$	14.2187	0.611310	0.305655	−	0.952142i	$-0.401125\pi$
$541$	14.2187	0.611310	0.305655	+	0.952142i	$0.401125\pi$
$542$	−37.5609	−1.61338
$543$	−3.04584	−0.130710
$544$	13.7192	0.588207
$545$	20.0914	0.860620
$546$	−104.718	−4.48150
$547$	−14.7492	−0.630630	−0.315315	−	0.948987i	$-0.602110\pi$
$547$	−14.7492	−0.630630	−0.315315	+	0.948987i	$0.602110\pi$
$548$	−73.6651	−3.14682
$549$	76.8447	3.27965
$550$	88.5333	3.77507
$551$	−7.55410	−0.321815
$552$	128.334	5.46227
$553$	19.0985	0.812149
$554$	56.4100	2.39663
$555$	30.4703	1.29339
$556$	5.42588	0.230108
$557$	−23.0684	−0.977440	−0.488720	−	0.872441i	$-0.662536\pi$
$557$	−23.0684	−0.977440	−0.488720	+	0.872441i	$0.662536\pi$
$558$	−66.7066	−2.82392
$559$	35.3207	1.49391
$560$	−105.296	−4.44957
$561$	−11.1594	−0.471152
$562$	−22.2076	−0.936773
$563$	3.17497	0.133809	0.0669044	−	0.997759i	$-0.478688\pi$
$563$	3.17497	0.133809	0.0669044	+	0.997759i	$0.478688\pi$
$564$	111.576	4.69821
$565$	12.1714	0.512055
$566$	−45.7731	−1.92399
$567$	21.6644	0.909819
$568$	−27.7585	−1.16472
$569$	27.3331	1.14586	0.572932	−	0.819603i	$-0.305806\pi$
$569$	27.3331	1.14586	0.572932	+	0.819603i	$0.305806\pi$
$570$	24.5609	1.02874
$571$	21.9179	0.917234	0.458617	−	0.888634i	$-0.348345\pi$
$571$	21.9179	0.917234	0.458617	+	0.888634i	$0.348345\pi$
$572$	98.6033	4.12281
$573$	15.6077	0.652022
$574$	−23.2030	−0.968473
$575$	47.8211	1.99428
$576$	82.8765	3.45319
$577$	34.8819	1.45215	0.726076	−	0.687615i	$-0.241342\pi$
$577$	34.8819	1.45215	0.726076	+	0.687615i	$0.241342\pi$
$578$	−2.65122	−0.110276
$579$	−19.2535	−0.800147
$580$	−171.310	−7.11325
$581$	14.5919	0.605373
$582$	−130.742	−5.41942
$583$	−39.5242	−1.63693
$584$	120.541	4.98803
$585$	117.079	4.84062
$586$	46.8749	1.93639
$587$	−36.9690	−1.52588	−0.762938	−	0.646472i	$-0.776244\pi$
$587$	−36.9690	−1.52588	−0.762938	+	0.646472i	$0.776244\pi$
$588$	10.5948	0.436922
$589$	−3.49794	−0.144130
$590$	−9.90463	−0.407767
$591$	35.0946	1.44360
$592$	30.6078	1.25797
$593$	−34.3018	−1.40861	−0.704304	−	0.709899i	$-0.748741\pi$
$593$	−34.3018	−1.40861	−0.704304	+	0.709899i	$0.748741\pi$
$594$	−87.5496	−3.59220
$595$	9.37411	0.384301
$596$	10.4828	0.429390
$597$	48.7053	1.99338
$598$	74.4418	3.04415
$599$	0.307672	0.0125711	0.00628557	−	0.999980i	$-0.497999\pi$
$599$	0.307672	0.0125711	0.00628557	+	0.999980i	$0.497999\pi$
$600$	215.291	8.78923
$601$	−22.9566	−0.936421	−0.468210	−	0.883617i	$-0.655101\pi$
$601$	−22.9566	−0.936421	−0.468210	+	0.883617i	$0.655101\pi$
$602$	44.6797	1.82101
$603$	35.0867	1.42884
$604$	−32.3554	−1.31652
$605$	−10.8344	−0.440483
$606$	−64.2646	−2.61057
$607$	12.3482	0.501199	0.250600	−	0.968091i	$-0.419372\pi$
$607$	12.3482	0.501199	0.250600	+	0.968091i	$0.419372\pi$
$608$	11.3659	0.460947
$609$	−68.4827	−2.77506
$610$	127.723	5.17135
$611$	38.9818	1.57704
$612$	−29.9684	−1.21140
$613$	−27.2235	−1.09955	−0.549774	−	0.835313i	$-0.685286\pi$
$613$	−27.2235	−1.09955	−0.549774	+	0.835313i	$0.685286\pi$
$614$	−41.8138	−1.68747
$615$	39.0019	1.57271
$616$	75.1256	3.02690
$617$	23.9601	0.964596	0.482298	−	0.876007i	$-0.339802\pi$
$617$	23.9601	0.964596	0.482298	+	0.876007i	$0.339802\pi$
$618$	66.3796	2.67018
$619$	22.8735	0.919364	0.459682	−	0.888084i	$-0.347963\pi$
$619$	22.8735	0.919364	0.459682	+	0.888084i	$0.347963\pi$
$620$	−79.3252	−3.18578
$621$	−47.2897	−1.89767
$622$	−4.46066	−0.178856
$623$	−14.3959	−0.576758
$624$	176.814	7.07824
$625$	10.4399	0.417596
$626$	−84.3318	−3.37058
$627$	−9.24517	−0.369216
$628$	−62.4917	−2.49369
$629$	−2.72490	−0.108649
$630$	148.102	5.90051
$631$	−35.6116	−1.41767	−0.708837	−	0.705372i	$-0.750780\pi$
$631$	−35.6116	−1.41767	−0.708837	+	0.705372i	$0.750780\pi$
$632$	−61.1227	−2.43133
$633$	36.0168	1.43154
$634$	23.0428	0.915148
$635$	−12.5834	−0.499355
$636$	−159.576	−6.32759
$637$	3.70154	0.146661
$638$	90.1291	3.56824
$639$	20.5986	0.814869
$640$	35.2416	1.39305
$641$	−36.5743	−1.44460	−0.722299	−	0.691581i	$-0.756914\pi$
$641$	−36.5743	−1.44460	−0.722299	+	0.691581i	$0.756914\pi$
$642$	−37.2438	−1.46989
$643$	31.6747	1.24913	0.624564	−	0.780974i	$-0.285277\pi$
$643$	31.6747	1.24913	0.624564	+	0.780974i	$0.285277\pi$
$644$	67.3728	2.65486
$645$	−75.1022	−2.95715
$646$	−2.19644	−0.0864176
$647$	29.0906	1.14367	0.571836	−	0.820368i	$-0.306231\pi$
$647$	29.0906	1.14367	0.571836	+	0.820368i	$0.306231\pi$
$648$	−69.3347	−2.72372
$649$	3.72828	0.146348
$650$	124.882	4.89828
$651$	−31.7110	−1.24285
$652$	49.7514	1.94842
$653$	−2.55243	−0.0998845	−0.0499422	−	0.998752i	$-0.515904\pi$
$653$	−2.55243	−0.0998845	−0.0499422	+	0.998752i	$0.515904\pi$
$654$	−42.6772	−1.66881
$655$	−32.2981	−1.26199
$656$	39.1779	1.52964
$657$	−89.4495	−3.48976
$658$	49.3109	1.92234
$659$	4.19485	0.163408	0.0817040	−	0.996657i	$-0.473964\pi$
$659$	4.19485	0.163408	0.0817040	+	0.996657i	$0.473964\pi$
$660$	−209.659	−8.16098
$661$	39.6586	1.54254	0.771271	−	0.636507i	$-0.219621\pi$
$661$	39.6586	1.54254	0.771271	+	0.636507i	$0.219621\pi$
$662$	45.3540	1.76273
$663$	−15.7411	−0.611335
$664$	−46.6998	−1.81230
$665$	7.76609	0.301156
$666$	−43.0507	−1.66818
$667$	48.6831	1.88502
$668$	29.8375	1.15445
$669$	−43.2635	−1.67267
$670$	58.3173	2.25299
$671$	−48.0772	−1.85600
$672$	103.039	3.97481
$673$	12.6630	0.488125	0.244062	−	0.969760i	$-0.421520\pi$
$673$	12.6630	0.488125	0.244062	+	0.969760i	$0.421520\pi$
$674$	−16.2891	−0.627431
$675$	−79.3324	−3.05350
$676$	73.7098	2.83499
$677$	−16.8952	−0.649335	−0.324667	−	0.945828i	$-0.605252\pi$
$677$	−16.8952	−0.649335	−0.324667	+	0.945828i	$0.605252\pi$
$678$	−25.8540	−0.992916
$679$	−41.3402	−1.58649
$680$	−30.0009	−1.15048
$681$	−61.4535	−2.35490
$682$	41.7344	1.59809
$683$	−27.5039	−1.05241	−0.526203	−	0.850359i	$-0.676385\pi$
$683$	−27.5039	−1.05241	−0.526203	+	0.850359i	$0.676385\pi$
$684$	−24.8277	−0.949309
$685$	54.7237	2.09088
$686$	51.2497	1.95672
$687$	64.1963	2.44924
$688$	−75.4412	−2.87617
$689$	−55.7516	−2.12396
$690$	−158.285	−6.02580
$691$	−42.1032	−1.60168	−0.800840	−	0.598878i	$-0.795613\pi$
$691$	−42.1032	−1.60168	−0.800840	+	0.598878i	$0.795613\pi$
$692$	112.207	4.26547
$693$	−55.7481	−2.11770
$694$	70.9232	2.69221
$695$	−4.03072	−0.152894
$696$	219.172	8.30769
$697$	−3.48787	−0.132112
$698$	41.8871	1.58545
$699$	74.9239	2.83388
$700$	113.023	4.27188
$701$	−6.55446	−0.247559	−0.123779	−	0.992310i	$-0.539502\pi$
$701$	−6.55446	−0.247559	−0.123779	+	0.992310i	$0.539502\pi$
$702$	−123.495	−4.66100
$703$	−2.25748	−0.0851424
$704$	−51.8510	−1.95421
$705$	−82.8867	−3.12170
$706$	29.1156	1.09578
$707$	−20.3203	−0.764223
$708$	15.0526	0.565713
$709$	21.0302	0.789805	0.394902	−	0.918723i	$-0.370778\pi$
$709$	21.0302	0.789805	0.394902	+	0.918723i	$0.370778\pi$
$710$	34.2368	1.28488
$711$	45.3570	1.70102
$712$	46.0725	1.72664
$713$	22.5428	0.844233
$714$	−19.9121	−0.745191
$715$	−73.2494	−2.73937
$716$	−120.387	−4.49908
$717$	−48.8336	−1.82373
$718$	73.6614	2.74902
$719$	28.8370	1.07544	0.537719	−	0.843124i	$-0.319286\pi$
$719$	28.8370	1.07544	0.537719	+	0.843124i	$0.319286\pi$
$720$	−250.068	−9.31948
$721$	20.9891	0.781673
$722$	48.5535	1.80698
$723$	74.6265	2.77539
$724$	5.11745	0.190188
$725$	81.6698	3.03314
$726$	23.0141	0.854132
$727$	−15.3191	−0.568153	−0.284076	−	0.958802i	$-0.591687\pi$
$727$	−15.3191	−0.568153	−0.284076	+	0.958802i	$0.591687\pi$
$728$	105.970	3.92750
$729$	−28.0832	−1.04012
$730$	−148.673	−5.50264
$731$	6.71625	0.248410
$732$	−194.108	−7.17443
$733$	−12.0991	−0.446891	−0.223446	−	0.974716i	$-0.571731\pi$
$733$	−12.0991	−0.446891	−0.223446	+	0.974716i	$0.571731\pi$
$734$	−7.20912	−0.266093
$735$	−7.87056	−0.290310
$736$	−73.2483	−2.69997
$737$	−21.9517	−0.808601
$738$	−55.1048	−2.02844
$739$	−33.6201	−1.23674	−0.618368	−	0.785889i	$-0.712206\pi$
$739$	−33.6201	−1.23674	−0.618368	+	0.785889i	$0.712206\pi$
$740$	−51.1945	−1.88195
$741$	−13.0409	−0.479070
$742$	−70.5241	−2.58902
$743$	−20.6858	−0.758890	−0.379445	−	0.925214i	$-0.623885\pi$
$743$	−20.6858	−0.758890	−0.379445	+	0.925214i	$0.623885\pi$
$744$	101.488	3.72072
$745$	−7.78733	−0.285306
$746$	−46.2115	−1.69192
$747$	34.6543	1.26793
$748$	18.7494	0.685548
$749$	−11.7764	−0.430300
$750$	−117.304	−4.28334
$751$	21.7786	0.794713	0.397357	−	0.917664i	$-0.369928\pi$
$751$	21.7786	0.794713	0.397357	+	0.917664i	$0.369928\pi$
$752$	−83.2609	−3.03621
$753$	6.55706	0.238953
$754$	127.133	4.62991
$755$	24.0358	0.874754
$756$	−111.768	−4.06495
$757$	−9.59096	−0.348589	−0.174295	−	0.984694i	$-0.555765\pi$
$757$	−9.59096	−0.348589	−0.174295	+	0.984694i	$0.555765\pi$
$758$	−40.3285	−1.46480
$759$	59.5813	2.16267
$760$	−24.8546	−0.901571
$761$	8.39476	0.304310	0.152155	−	0.988357i	$-0.451379\pi$
$761$	8.39476	0.304310	0.152155	+	0.988357i	$0.451379\pi$
$762$	26.7290	0.968291
$763$	−13.4944	−0.488531
$764$	−26.2232	−0.948723
$765$	22.2626	0.804907
$766$	34.2375	1.23705
$767$	5.25900	0.189891
$768$	8.39645	0.302981
$769$	29.6560	1.06942	0.534711	−	0.845035i	$-0.320420\pi$
$769$	29.6560	1.06942	0.534711	+	0.845035i	$0.320420\pi$
$770$	−92.6585	−3.33918
$771$	12.6377	0.455135
$772$	32.3486	1.16425
$773$	−5.94370	−0.213780	−0.106890	−	0.994271i	$-0.534089\pi$
$773$	−5.94370	−0.213780	−0.106890	+	0.994271i	$0.534089\pi$
$774$	106.110	3.81405
$775$	37.8173	1.35844
$776$	132.305	4.74948
$777$	−20.4655	−0.734195
$778$	66.4053	2.38074
$779$	−2.88956	−0.103529
$780$	−295.739	−10.5891
$781$	−12.8874	−0.461146
$782$	14.1551	0.506186
$783$	−80.7623	−2.88621
$784$	−7.90609	−0.282360
$785$	46.4232	1.65692
$786$	68.6061	2.44710
$787$	19.8863	0.708869	0.354435	−	0.935081i	$-0.384673\pi$
$787$	19.8863	0.708869	0.354435	+	0.935081i	$0.384673\pi$
$788$	−58.9639	−2.10050
$789$	−55.7980	−1.98646
$790$	75.3875	2.68217
$791$	−8.17496	−0.290668
$792$	178.416	6.33974
$793$	−67.8161	−2.40822
$794$	−101.546	−3.60374
$795$	118.544	4.20433
$796$	−81.8319	−2.90046
$797$	5.46259	0.193495	0.0967474	−	0.995309i	$-0.469156\pi$
$797$	5.46259	0.193495	0.0967474	+	0.995309i	$0.469156\pi$
$798$	−16.4964	−0.583966
$799$	7.41241	0.262232
$800$	−122.880	−4.34447
$801$	−34.1888	−1.20800
$802$	−104.095	−3.67572
$803$	55.9633	1.97490
$804$	−88.6281	−3.12567
$805$	−50.0493	−1.76401
$806$	58.8692	2.07358
$807$	16.9782	0.597661
$808$	65.0330	2.28785
$809$	6.05030	0.212717	0.106359	−	0.994328i	$-0.466081\pi$
$809$	6.05030	0.212717	0.106359	+	0.994328i	$0.466081\pi$
$810$	85.5161	3.00473
$811$	−2.08638	−0.0732628	−0.0366314	−	0.999329i	$-0.511663\pi$
$811$	−2.08638	−0.0732628	−0.0366314	+	0.999329i	$0.511663\pi$
$812$	115.061	4.03784
$813$	−42.4056	−1.48723
$814$	26.9343	0.944048
$815$	−36.9588	−1.29461
$816$	33.6213	1.17698
$817$	5.56416	0.194665
$818$	−21.1708	−0.740220
$819$	−78.6365	−2.74778
$820$	−65.5287	−2.28836
$821$	1.17044	0.0408487	0.0204244	−	0.999791i	$-0.493498\pi$
$821$	1.17044	0.0408487	0.0204244	+	0.999791i	$0.493498\pi$
$822$	−116.242	−4.05439
$823$	−21.5509	−0.751217	−0.375609	−	0.926778i	$-0.622566\pi$
$823$	−21.5509	−0.751217	−0.375609	+	0.926778i	$0.622566\pi$
$824$	−67.1734	−2.34009
$825$	99.9525	3.47990
$826$	6.65248	0.231469
$827$	−12.0562	−0.419235	−0.209618	−	0.977783i	$-0.567222\pi$
$827$	−12.0562	−0.419235	−0.209618	+	0.977783i	$0.567222\pi$
$828$	160.004	5.56053
$829$	−24.1779	−0.839735	−0.419867	−	0.907585i	$-0.637923\pi$
$829$	−24.1779	−0.839735	−0.419867	+	0.907585i	$0.637923\pi$
$830$	57.5986	1.99928
$831$	63.6859	2.20924
$832$	−73.1393	−2.53565
$833$	0.703850	0.0243870
$834$	8.56189	0.296474
$835$	−22.1654	−0.767065
$836$	15.5332	0.537227
$837$	−37.3971	−1.29263
$838$	1.74995	0.0604511
$839$	−35.2035	−1.21536	−0.607680	−	0.794182i	$-0.707900\pi$
$839$	−35.2035	−1.21536	−0.607680	+	0.794182i	$0.707900\pi$
$840$	−225.323	−7.77437
$841$	54.1419	1.86696
$842$	7.36697	0.253883
$843$	−25.0720	−0.863527
$844$	−60.5134	−2.08296
$845$	−54.7568	−1.88369
$846$	117.109	4.02628
$847$	7.27699	0.250040
$848$	119.079	4.08920
$849$	−51.6770	−1.77355
$850$	23.7464	0.814494
$851$	14.5485	0.498717
$852$	−52.0316	−1.78257
$853$	−2.81631	−0.0964285	−0.0482142	−	0.998837i	$-0.515353\pi$
$853$	−2.81631	−0.0964285	−0.0482142	+	0.998837i	$0.515353\pi$
$854$	−85.7854	−2.93552
$855$	18.4437	0.630762
$856$	37.6891	1.28819
$857$	38.7835	1.32482	0.662409	−	0.749142i	$-0.269534\pi$
$857$	38.7835	1.32482	0.662409	+	0.749142i	$0.269534\pi$
$858$	155.593	5.31187
$859$	16.8239	0.574023	0.287012	−	0.957927i	$-0.407338\pi$
$859$	16.8239	0.574023	0.287012	+	0.957927i	$0.407338\pi$
$860$	126.182	4.30279
$861$	−26.1957	−0.892748
$862$	−12.2667	−0.417804
$863$	50.0609	1.70409	0.852046	−	0.523466i	$-0.175361\pi$
$863$	50.0609	1.70409	0.852046	+	0.523466i	$0.175361\pi$
$864$	121.515	4.13401
$865$	−83.3553	−2.83416
$866$	14.8548	0.504788
$867$	−2.99318	−0.101654
$868$	53.2790	1.80841
$869$	−28.3772	−0.962631
$870$	−270.322	−9.16478
$871$	−30.9643	−1.04919
$872$	43.1876	1.46252
$873$	−98.1790	−3.32286
$874$	11.7270	0.396671
$875$	−37.0912	−1.25391
$876$	225.947	7.63404
$877$	6.65400	0.224690	0.112345	−	0.993669i	$-0.464164\pi$
$877$	6.65400	0.224690	0.112345	+	0.993669i	$0.464164\pi$
$878$	16.0927	0.543102
$879$	52.9210	1.78498
$880$	156.453	5.27402
$881$	0.228731	0.00770615	0.00385307	−	0.999993i	$-0.498774\pi$
$881$	0.228731	0.00770615	0.00385307	+	0.999993i	$0.498774\pi$
$882$	11.1201	0.374434
$883$	21.3448	0.718311	0.359155	−	0.933278i	$-0.383065\pi$
$883$	21.3448	0.718311	0.359155	+	0.933278i	$0.383065\pi$
$884$	26.4474	0.889521
$885$	−11.1822	−0.375884
$886$	−9.94307	−0.334044
$887$	0.968136	0.0325068	0.0162534	−	0.999868i	$-0.494826\pi$
$887$	0.968136	0.0325068	0.0162534	+	0.999868i	$0.494826\pi$
$888$	65.4977	2.19796
$889$	8.45165	0.283459
$890$	−56.8249	−1.90477
$891$	−32.1898	−1.07840
$892$	72.6889	2.43381
$893$	6.14090	0.205497
$894$	16.5415	0.553231
$895$	89.4321	2.98939
$896$	−23.6701	−0.790763
$897$	84.0435	2.80613
$898$	−30.4241	−1.01526
$899$	38.4990	1.28401
$900$	268.420	8.94733
$901$	−10.6012	−0.353176
$902$	34.4758	1.14792
$903$	50.4426	1.67863
$904$	26.1631	0.870173
$905$	−3.80160	−0.126369
$906$	−51.0559	−1.69622
$907$	−55.4464	−1.84107	−0.920533	−	0.390665i	$-0.872245\pi$
$907$	−55.4464	−1.84107	−0.920533	+	0.390665i	$0.872245\pi$
$908$	103.251	3.42649
$909$	−48.2588	−1.60064
$910$	−130.701	−4.33269
$911$	1.62858	0.0539571	0.0269786	−	0.999636i	$-0.491411\pi$
$911$	1.62858	0.0539571	0.0269786	+	0.999636i	$0.491411\pi$
$912$	27.8540	0.922338
$913$	−21.6812	−0.717542
$914$	23.0017	0.760830
$915$	144.197	4.76700
$916$	−107.859	−3.56376
$917$	21.6931	0.716369
$918$	−23.4825	−0.775039
$919$	−37.5993	−1.24028	−0.620142	−	0.784489i	$-0.712925\pi$
$919$	−37.5993	−1.24028	−0.620142	+	0.784489i	$0.712925\pi$
$920$	160.178	5.28090
$921$	−47.2071	−1.55553
$922$	2.26079	0.0744550
$923$	−18.1785	−0.598352
$924$	140.818	4.63258
$925$	24.4063	0.802475
$926$	30.1865	0.991991
$927$	49.8470	1.63719
$928$	−125.095	−4.10644
$929$	−35.9469	−1.17938	−0.589690	−	0.807630i	$-0.700750\pi$
$929$	−35.9469	−1.17938	−0.589690	+	0.807630i	$0.700750\pi$
$930$	−125.173	−4.10459
$931$	0.583113	0.0191108
$932$	−125.883	−4.12343
$933$	−5.03601	−0.164871
$934$	−85.6283	−2.80184
$935$	−13.9284	−0.455508
$936$	251.668	8.22603
$937$	25.3403	0.827831	0.413916	−	0.910315i	$-0.364161\pi$
$937$	25.3403	0.827831	0.413916	+	0.910315i	$0.364161\pi$
$938$	−39.1690	−1.27891
$939$	−95.2092	−3.10703
$940$	139.262	4.54221
$941$	−9.38530	−0.305952	−0.152976	−	0.988230i	$-0.548886\pi$
$941$	−9.38530	−0.305952	−0.152976	+	0.988230i	$0.548886\pi$
$942$	−98.6102	−3.21289
$943$	18.6221	0.606418
$944$	−11.2326	−0.365591
$945$	83.0288	2.70093
$946$	−66.3868	−2.15842
$947$	18.5494	0.602775	0.301387	−	0.953502i	$-0.402550\pi$
$947$	18.5494	0.602775	0.301387	+	0.953502i	$0.402550\pi$
$948$	−114.571	−3.72108
$949$	78.9399	2.56250
$950$	19.6730	0.638276
$951$	26.0149	0.843592
$952$	20.1502	0.653071
$953$	−16.1855	−0.524299	−0.262149	−	0.965027i	$-0.584431\pi$
$953$	−16.1855	−0.524299	−0.262149	+	0.965027i	$0.584431\pi$
$954$	−167.488	−5.42263
$955$	19.4805	0.630373
$956$	82.0475	2.65361
$957$	101.754	3.28925
$958$	56.4868	1.82501
$959$	−36.7553	−1.18689
$960$	155.515	5.01924
$961$	−13.1730	−0.424935
$962$	37.9927	1.22493
$963$	−27.9678	−0.901250
$964$	−125.383	−4.03832
$965$	−24.0308	−0.773579
$966$	106.313	3.42055
$967$	−7.53199	−0.242212	−0.121106	−	0.992640i	$-0.538644\pi$
$967$	−7.53199	−0.242212	−0.121106	+	0.992640i	$0.538644\pi$
$968$	−23.2893	−0.748545
$969$	−2.47974	−0.0796607
$970$	−163.182	−5.23947
$971$	−28.5218	−0.915308	−0.457654	−	0.889130i	$-0.651310\pi$
$971$	−28.5218	−0.915308	−0.457654	+	0.889130i	$0.651310\pi$
$972$	3.66504	0.117556
$973$	2.70725	0.0867904
$974$	−31.1090	−0.996798
$975$	140.990	4.51529
$976$	144.848	4.63646
$977$	16.4619	0.526662	0.263331	−	0.964706i	$-0.415179\pi$
$977$	16.4619	0.526662	0.263331	+	0.964706i	$0.415179\pi$
$978$	78.5064	2.51036
$979$	21.3899	0.683625
$980$	13.2237	0.422415
$981$	−32.0480	−1.02321
$982$	−74.0736	−2.36378
$983$	−25.4109	−0.810482	−0.405241	−	0.914210i	$-0.632812\pi$
$983$	−25.4109	−0.810482	−0.405241	+	0.914210i	$0.632812\pi$
$984$	83.8368	2.67262
$985$	43.8025	1.39567
$986$	24.1744	0.769870
$987$	55.6711	1.77203
$988$	21.9106	0.697070
$989$	−35.8587	−1.14024
$990$	−220.055	−6.99381
$991$	−50.7797	−1.61307	−0.806536	−	0.591185i	$-0.798660\pi$
$991$	−50.7797	−1.61307	−0.806536	+	0.591185i	$0.798660\pi$
$992$	−57.9254	−1.83913
$993$	51.2039	1.62491
$994$	−22.9953	−0.729365
$995$	60.7905	1.92719
$996$	−87.5359	−2.77368
$997$	−42.6628	−1.35114	−0.675571	−	0.737295i	$-0.736103\pi$
$997$	−42.6628	−1.35114	−0.675571	+	0.737295i	$0.736103\pi$
$998$	23.3133	0.737971
$999$	−24.1351	−0.763602

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1003.2.a.g.1.1	✓	10
3.2	odd	2		9027.2.a.j.1.10		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1003.2.a.g.1.1	✓	10	1.1	even	1	trivial
9027.2.a.j.1.10		10	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)

\(f(q)\)	\(=\)	\(q-2.65122 q^{2} -2.99318 q^{3} +5.02897 q^{4} -3.73588 q^{5} +7.93559 q^{6} +2.50921 q^{7} -8.03048 q^{8} +5.95914 q^{9} +O(q^{10})\)	\(q-2.65122 q^{2} -2.99318 q^{3} +5.02897 q^{4} -3.73588 q^{5} +7.93559 q^{6} +2.50921 q^{7} -8.03048 q^{8} +5.95914 q^{9} +9.90463 q^{10} -3.72828 q^{11} -15.0526 q^{12} -5.25900 q^{13} -6.65248 q^{14} +11.1822 q^{15} +11.2326 q^{16} -1.00000 q^{17} -15.7990 q^{18} -0.828462 q^{19} -18.7876 q^{20} -7.51053 q^{21} +9.88451 q^{22} +5.33910 q^{23} +24.0367 q^{24} +8.95677 q^{25} +13.9428 q^{26} -8.85725 q^{27} +12.6188 q^{28} +9.11822 q^{29} -29.6464 q^{30} +4.22220 q^{31} -13.7192 q^{32} +11.1594 q^{33} +2.65122 q^{34} -9.37411 q^{35} +29.9684 q^{36} +2.72490 q^{37} +2.19644 q^{38} +15.7411 q^{39} +30.0009 q^{40} +3.48787 q^{41} +19.9121 q^{42} -6.71625 q^{43} -18.7494 q^{44} -22.2626 q^{45} -14.1551 q^{46} -7.41241 q^{47} -33.6213 q^{48} -0.703850 q^{49} -23.7464 q^{50} +2.99318 q^{51} -26.4474 q^{52} +10.6012 q^{53} +23.4825 q^{54} +13.9284 q^{55} -20.1502 q^{56} +2.47974 q^{57} -24.1744 q^{58} -1.00000 q^{59} +56.2348 q^{60} +12.8953 q^{61} -11.1940 q^{62} +14.9528 q^{63} +13.9075 q^{64} +19.6470 q^{65} -29.5861 q^{66} +5.88788 q^{67} -5.02897 q^{68} -15.9809 q^{69} +24.8528 q^{70} +3.45664 q^{71} -47.8548 q^{72} -15.0105 q^{73} -7.22432 q^{74} -26.8093 q^{75} -4.16631 q^{76} -9.35506 q^{77} -41.7332 q^{78} +7.61134 q^{79} -41.9637 q^{80} +8.63394 q^{81} -9.24710 q^{82} +5.81532 q^{83} -37.7703 q^{84} +3.73588 q^{85} +17.8063 q^{86} -27.2925 q^{87} +29.9399 q^{88} -5.73720 q^{89} +59.0231 q^{90} -13.1959 q^{91} +26.8502 q^{92} -12.6378 q^{93} +19.6519 q^{94} +3.09503 q^{95} +41.0642 q^{96} -16.4754 q^{97} +1.86606 q^{98} -22.2174 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{2} - 7 q^{3} + 15 q^{4} - 12 q^{5} + 5 q^{6} - 9 q^{7} - 12 q^{8} + 3 q^{9}+O(q^{10}) \) 10 * q - q^2 - 7 * q^3 + 15 * q^4 - 12 * q^5 + 5 * q^6 - 9 * q^7 - 12 * q^8 + 3 * q^9	\( 10 q - q^{2} - 7 q^{3} + 15 q^{4} - 12 q^{5} + 5 q^{6} - 9 q^{7} - 12 q^{8} + 3 q^{9} + 4 q^{10} + 12 q^{11} - 24 q^{12} - 11 q^{13} - 12 q^{14} + 9 q^{15} - 3 q^{16} - 10 q^{17} - 22 q^{18} - 5 q^{19} - 36 q^{20} - 10 q^{21} + 6 q^{22} - 7 q^{23} + 35 q^{24} + 2 q^{25} + q^{26} - 31 q^{27} - 4 q^{28} + 10 q^{29} - 9 q^{30} + 13 q^{31} - 15 q^{32} - 9 q^{33} + q^{34} - 8 q^{35} + 40 q^{36} + 12 q^{37} - 50 q^{38} + 24 q^{39} + 5 q^{40} - 29 q^{41} - 17 q^{42} - 18 q^{43} - 6 q^{44} - 14 q^{45} + 11 q^{46} - 18 q^{47} - 43 q^{48} - 9 q^{49} - 31 q^{50} + 7 q^{51} - 68 q^{52} + 19 q^{54} - 27 q^{55} - 7 q^{56} + 20 q^{57} + 23 q^{58} - 10 q^{59} + 38 q^{60} + 8 q^{61} - 46 q^{62} + 39 q^{63} - 20 q^{64} + 58 q^{65} - 34 q^{66} - 6 q^{67} - 15 q^{68} + 6 q^{69} + 73 q^{70} + 8 q^{71} - 70 q^{72} - 41 q^{73} - 10 q^{74} + 10 q^{75} + 12 q^{76} - 22 q^{77} - 43 q^{78} + 3 q^{79} - 15 q^{80} + 26 q^{81} + 8 q^{82} - 22 q^{84} + 12 q^{85} - 29 q^{86} - 28 q^{87} + 33 q^{88} - 45 q^{89} + 56 q^{90} - 14 q^{91} + 36 q^{92} - 19 q^{93} + 15 q^{94} - 17 q^{95} + 90 q^{96} - 5 q^{97} + 30 q^{98} + 14 q^{99}+O(q^{100}) \) 10 * q - q^2 - 7 * q^3 + 15 * q^4 - 12 * q^5 + 5 * q^6 - 9 * q^7 - 12 * q^8 + 3 * q^9 + 4 * q^10 + 12 * q^11 - 24 * q^12 - 11 * q^13 - 12 * q^14 + 9 * q^15 - 3 * q^16 - 10 * q^17 - 22 * q^18 - 5 * q^19 - 36 * q^20 - 10 * q^21 + 6 * q^22 - 7 * q^23 + 35 * q^24 + 2 * q^25 + q^26 - 31 * q^27 - 4 * q^28 + 10 * q^29 - 9 * q^30 + 13 * q^31 - 15 * q^32 - 9 * q^33 + q^34 - 8 * q^35 + 40 * q^36 + 12 * q^37 - 50 * q^38 + 24 * q^39 + 5 * q^40 - 29 * q^41 - 17 * q^42 - 18 * q^43 - 6 * q^44 - 14 * q^45 + 11 * q^46 - 18 * q^47 - 43 * q^48 - 9 * q^49 - 31 * q^50 + 7 * q^51 - 68 * q^52 + 19 * q^54 - 27 * q^55 - 7 * q^56 + 20 * q^57 + 23 * q^58 - 10 * q^59 + 38 * q^60 + 8 * q^61 - 46 * q^62 + 39 * q^63 - 20 * q^64 + 58 * q^65 - 34 * q^66 - 6 * q^67 - 15 * q^68 + 6 * q^69 + 73 * q^70 + 8 * q^71 - 70 * q^72 - 41 * q^73 - 10 * q^74 + 10 * q^75 + 12 * q^76 - 22 * q^77 - 43 * q^78 + 3 * q^79 - 15 * q^80 + 26 * q^81 + 8 * q^82 - 22 * q^84 + 12 * q^85 - 29 * q^86 - 28 * q^87 + 33 * q^88 - 45 * q^89 + 56 * q^90 - 14 * q^91 + 36 * q^92 - 19 * q^93 + 15 * q^94 - 17 * q^95 + 90 * q^96 - 5 * q^97 + 30 * q^98 + 14 * q^99

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