LMFDB - Embedded newform 1003.2.a.g.1.10

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			1.10
Root			$1.29864$ 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)

$f(q)$	$=$	$q+2.30116 q^{2} +0.298636 q^{3} +3.29536 q^{4} -3.47217 q^{5} +0.687210 q^{6} -4.18349 q^{7} +2.98084 q^{8} -2.91082 q^{9} +O(q^{10})$	\(q+2.30116 q^{2} +0.298636 q^{3} +3.29536 q^{4} -3.47217 q^{5} +0.687210 q^{6} -4.18349 q^{7} +2.98084 q^{8} -2.91082 q^{9} -7.99004 q^{10} +4.06787 q^{11} +0.984112 q^{12} -5.70624 q^{13} -9.62691 q^{14} -1.03692 q^{15} +0.268676 q^{16} -1.00000 q^{17} -6.69827 q^{18} -3.10136 q^{19} -11.4421 q^{20} -1.24934 q^{21} +9.36084 q^{22} +8.75315 q^{23} +0.890184 q^{24} +7.05599 q^{25} -13.1310 q^{26} -1.76518 q^{27} -13.7861 q^{28} +6.12987 q^{29} -2.38611 q^{30} -4.64038 q^{31} -5.34340 q^{32} +1.21481 q^{33} -2.30116 q^{34} +14.5258 q^{35} -9.59219 q^{36} +6.05454 q^{37} -7.13675 q^{38} -1.70409 q^{39} -10.3500 q^{40} +1.84074 q^{41} -2.87494 q^{42} -1.61572 q^{43} +13.4051 q^{44} +10.1069 q^{45} +20.1424 q^{46} -6.94838 q^{47} +0.0802362 q^{48} +10.5016 q^{49} +16.2370 q^{50} -0.298636 q^{51} -18.8041 q^{52} -4.66552 q^{53} -4.06197 q^{54} -14.1244 q^{55} -12.4703 q^{56} -0.926178 q^{57} +14.1058 q^{58} -1.00000 q^{59} -3.41701 q^{60} -6.68012 q^{61} -10.6783 q^{62} +12.1774 q^{63} -12.8334 q^{64} +19.8131 q^{65} +2.79548 q^{66} -11.3061 q^{67} -3.29536 q^{68} +2.61400 q^{69} +33.4263 q^{70} -14.7785 q^{71} -8.67667 q^{72} +3.82954 q^{73} +13.9325 q^{74} +2.10717 q^{75} -10.2201 q^{76} -17.0179 q^{77} -3.92139 q^{78} -12.8244 q^{79} -0.932889 q^{80} +8.20530 q^{81} +4.23585 q^{82} +10.1911 q^{83} -4.11703 q^{84} +3.47217 q^{85} -3.71805 q^{86} +1.83060 q^{87} +12.1257 q^{88} +10.9421 q^{89} +23.2576 q^{90} +23.8720 q^{91} +28.8448 q^{92} -1.38578 q^{93} -15.9894 q^{94} +10.7685 q^{95} -1.59573 q^{96} -10.5548 q^{97} +24.1659 q^{98} -11.8408 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.30116	1.62717	0.813585	−	0.581447i	$-0.197513\pi$
$2$	2.30116	1.62717	0.813585	+	0.581447i	$0.197513\pi$
$3$	0.298636	0.172417	0.0862087	−	0.996277i	$-0.472525\pi$
$3$	0.298636	0.172417	0.0862087	+	0.996277i	$0.472525\pi$
$4$	3.29536	1.64768
$5$	−3.47217	−1.55280	−0.776402	−	0.630239i	$-0.782957\pi$
$5$	−3.47217	−1.55280	−0.776402	+	0.630239i	$0.782957\pi$
$6$	0.687210	0.280552
$7$	−4.18349	−1.58121	−0.790606	−	0.612326i	$-0.790234\pi$
$7$	−4.18349	−1.58121	−0.790606	+	0.612326i	$0.790234\pi$
$8$	2.98084	1.05388
$9$	−2.91082	−0.970272
$10$	−7.99004	−2.52667
$11$	4.06787	1.22651	0.613255	−	0.789885i	$-0.289860\pi$
$11$	4.06787	1.22651	0.613255	+	0.789885i	$0.289860\pi$
$12$	0.984112	0.284089
$13$	−5.70624	−1.58263	−0.791313	−	0.611411i	$-0.790602\pi$
$13$	−5.70624	−1.58263	−0.791313	+	0.611411i	$0.790602\pi$
$14$	−9.62691	−2.57290
$15$	−1.03692	−0.267730
$16$	0.268676	0.0671690
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−6.69827	−1.57880
$19$	−3.10136	−0.711502	−0.355751	−	0.934581i	$-0.615775\pi$
$19$	−3.10136	−0.711502	−0.355751	+	0.934581i	$0.615775\pi$
$20$	−11.4421	−2.55852
$21$	−1.24934	−0.272628
$22$	9.36084	1.99574
$23$	8.75315	1.82516	0.912579	−	0.408901i	$-0.134088\pi$
$23$	8.75315	1.82516	0.912579	+	0.408901i	$0.134088\pi$
$24$	0.890184	0.181708
$25$	7.05599	1.41120
$26$	−13.1310	−2.57520
$27$	−1.76518	−0.339709
$28$	−13.7861	−2.60533
$29$	6.12987	1.13829	0.569144	−	0.822238i	$-0.307275\pi$
$29$	6.12987	1.13829	0.569144	+	0.822238i	$0.307275\pi$
$30$	−2.38611	−0.435643
$31$	−4.64038	−0.833436	−0.416718	−	0.909036i	$-0.636820\pi$
$31$	−4.64038	−0.833436	−0.416718	+	0.909036i	$0.636820\pi$
$32$	−5.34340	−0.944589
$33$	1.21481	0.211472
$34$	−2.30116	−0.394647
$35$	14.5258	2.45531
$36$	−9.59219	−1.59870
$37$	6.05454	0.995361	0.497680	−	0.867360i	$-0.334185\pi$
$37$	6.05454	0.995361	0.497680	+	0.867360i	$0.334185\pi$
$38$	−7.13675	−1.15773
$39$	−1.70409	−0.272872
$40$	−10.3500	−1.63648
$41$	1.84074	0.287476	0.143738	−	0.989616i	$-0.454088\pi$
$41$	1.84074	0.287476	0.143738	+	0.989616i	$0.454088\pi$
$42$	−2.87494	−0.443613
$43$	−1.61572	−0.246395	−0.123198	−	0.992382i	$-0.539315\pi$
$43$	−1.61572	−0.246395	−0.123198	+	0.992382i	$0.539315\pi$
$44$	13.4051	2.02089
$45$	10.1069	1.50664
$46$	20.1424	2.96984
$47$	−6.94838	−1.01353	−0.506763	−	0.862086i	$-0.669158\pi$
$47$	−6.94838	−1.01353	−0.506763	+	0.862086i	$0.669158\pi$
$48$	0.0802362	0.0115811
$49$	10.5016	1.50023
$50$	16.2370	2.29626
$51$	−0.298636	−0.0418174
$52$	−18.8041	−2.60766
$53$	−4.66552	−0.640858	−0.320429	−	0.947273i	$-0.603827\pi$
$53$	−4.66552	−0.640858	−0.320429	+	0.947273i	$0.603827\pi$
$54$	−4.06197	−0.552764
$55$	−14.1244	−1.90453
$56$	−12.4703	−1.66641
$57$	−0.926178	−0.122675
$58$	14.1058	1.85219
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	−3.41701	−0.441134
$61$	−6.68012	−0.855302	−0.427651	−	0.903944i	$-0.640659\pi$
$61$	−6.68012	−0.855302	−0.427651	+	0.903944i	$0.640659\pi$
$62$	−10.6783	−1.35614
$63$	12.1774	1.53421
$64$	−12.8334	−1.60418
$65$	19.8131	2.45751
$66$	2.79548	0.344100
$67$	−11.3061	−1.38126	−0.690632	−	0.723206i	$-0.742668\pi$
$67$	−11.3061	−1.38126	−0.690632	+	0.723206i	$0.742668\pi$
$68$	−3.29536	−0.399621
$69$	2.61400	0.314689
$70$	33.4263	3.99521
$71$	−14.7785	−1.75389	−0.876943	−	0.480594i	$-0.840421\pi$
$71$	−14.7785	−1.75389	−0.876943	+	0.480594i	$0.840421\pi$
$72$	−8.67667	−1.02256
$73$	3.82954	0.448214	0.224107	−	0.974565i	$-0.428053\pi$
$73$	3.82954	0.448214	0.224107	+	0.974565i	$0.428053\pi$
$74$	13.9325	1.61962
$75$	2.10717	0.243315
$76$	−10.2201	−1.17233
$77$	−17.0179	−1.93937
$78$	−3.92139	−0.444010
$79$	−12.8244	−1.44286	−0.721430	−	0.692487i	$-0.756515\pi$
$79$	−12.8244	−1.44286	−0.721430	+	0.692487i	$0.756515\pi$
$80$	−0.932889	−0.104300
$81$	8.20530	0.911700
$82$	4.23585	0.467771
$83$	10.1911	1.11862	0.559311	−	0.828958i	$-0.311066\pi$
$83$	10.1911	1.11862	0.559311	+	0.828958i	$0.311066\pi$
$84$	−4.11703	−0.449204
$85$	3.47217	0.376610
$86$	−3.71805	−0.400927
$87$	1.83060	0.196261
$88$	12.1257	1.29260
$89$	10.9421	1.15986	0.579929	−	0.814667i	$-0.303080\pi$
$89$	10.9421	1.15986	0.579929	+	0.814667i	$0.303080\pi$
$90$	23.2576	2.45156
$91$	23.8720	2.50247
$92$	28.8448	3.00728
$93$	−1.38578	−0.143699
$94$	−15.9894	−1.64918
$95$	10.7685	1.10482
$96$	−1.59573	−0.162864
$97$	−10.5548	−1.07167	−0.535837	−	0.844321i	$-0.680004\pi$
$97$	−10.5548	−1.07167	−0.535837	+	0.844321i	$0.680004\pi$
$98$	24.1659	2.44113
$99$	−11.8408	−1.19005
$100$	23.2520	2.32520
$101$	−3.56767	−0.354996	−0.177498	−	0.984121i	$-0.556800\pi$
$101$	−3.56767	−0.354996	−0.177498	+	0.984121i	$0.556800\pi$
$102$	−0.687210	−0.0680439
$103$	−2.81818	−0.277684	−0.138842	−	0.990315i	$-0.544338\pi$
$103$	−2.81818	−0.277684	−0.138842	+	0.990315i	$0.544338\pi$
$104$	−17.0094	−1.66791
$105$	4.33793	0.423338
$106$	−10.7361	−1.04278
$107$	−3.48707	−0.337108	−0.168554	−	0.985692i	$-0.553910\pi$
$107$	−3.48707	−0.337108	−0.168554	+	0.985692i	$0.553910\pi$
$108$	−5.81691	−0.559732
$109$	−6.99253	−0.669763	−0.334882	−	0.942260i	$-0.608696\pi$
$109$	−6.99253	−0.669763	−0.334882	+	0.942260i	$0.608696\pi$
$110$	−32.5025	−3.09899
$111$	1.80810	0.171618
$112$	−1.12400	−0.106208
$113$	8.63790	0.812585	0.406292	−	0.913743i	$-0.366821\pi$
$113$	8.63790	0.812585	0.406292	+	0.913743i	$0.366821\pi$
$114$	−2.13129	−0.199613
$115$	−30.3924	−2.83411
$116$	20.2001	1.87553
$117$	16.6098	1.53558
$118$	−2.30116	−0.211839
$119$	4.18349	0.383500
$120$	−3.09087	−0.282157
$121$	5.54757	0.504324
$122$	−15.3721	−1.39172
$123$	0.549711	0.0495658
$124$	−15.2917	−1.37324
$125$	−7.13875	−0.638509
$126$	28.0222	2.49641
$127$	14.7398	1.30794	0.653971	−	0.756519i	$-0.273102\pi$
$127$	14.7398	1.30794	0.653971	+	0.756519i	$0.273102\pi$
$128$	−18.8450	−1.66568
$129$	−0.482513	−0.0424829
$130$	45.5931	3.99878
$131$	4.11403	0.359444	0.179722	−	0.983717i	$-0.442480\pi$
$131$	4.11403	0.359444	0.179722	+	0.983717i	$0.442480\pi$
$132$	4.00324	0.348437
$133$	12.9745	1.12503
$134$	−26.0173	−2.24755
$135$	6.12901	0.527502
$136$	−2.98084	−0.255605
$137$	−12.9688	−1.10800	−0.554001	−	0.832516i	$-0.686900\pi$
$137$	−12.9688	−1.10800	−0.554001	+	0.832516i	$0.686900\pi$
$138$	6.01525	0.512052
$139$	−3.92356	−0.332792	−0.166396	−	0.986059i	$-0.553213\pi$
$139$	−3.92356	−0.332792	−0.166396	+	0.986059i	$0.553213\pi$
$140$	47.8678	4.04556
$141$	−2.07503	−0.174749
$142$	−34.0078	−2.85387
$143$	−23.2123	−1.94111
$144$	−0.782066	−0.0651722
$145$	−21.2840	−1.76754
$146$	8.81241	0.729320
$147$	3.13616	0.258666
$148$	19.9519	1.64004
$149$	−1.27962	−0.104831	−0.0524154	−	0.998625i	$-0.516692\pi$
$149$	−1.27962	−0.104831	−0.0524154	+	0.998625i	$0.516692\pi$
$150$	4.84895	0.395915
$151$	−14.4990	−1.17991	−0.589957	−	0.807434i	$-0.700855\pi$
$151$	−14.4990	−1.17991	−0.589957	+	0.807434i	$0.700855\pi$
$152$	−9.24466	−0.749841
$153$	2.91082	0.235326
$154$	−39.1610	−3.15568
$155$	16.1122	1.29416
$156$	−5.61558	−0.449606
$157$	−10.4972	−0.837765	−0.418883	−	0.908040i	$-0.637578\pi$
$157$	−10.4972	−0.837765	−0.418883	+	0.908040i	$0.637578\pi$
$158$	−29.5111	−2.34778
$159$	−1.39329	−0.110495
$160$	18.5532	1.46676
$161$	−36.6187	−2.88596
$162$	18.8818	1.48349
$163$	15.8133	1.23859	0.619295	−	0.785159i	$-0.287419\pi$
$163$	15.8133	1.23859	0.619295	+	0.785159i	$0.287419\pi$
$164$	6.06591	0.473668
$165$	−4.21804	−0.328374
$166$	23.4515	1.82019
$167$	19.7785	1.53050	0.765252	−	0.643731i	$-0.222614\pi$
$167$	19.7785	1.53050	0.765252	+	0.643731i	$0.222614\pi$
$168$	−3.72408	−0.287319
$169$	19.5612	1.50471
$170$	7.99004	0.612808
$171$	9.02750	0.690350
$172$	−5.32439	−0.405981
$173$	−6.29093	−0.478291	−0.239145	−	0.970984i	$-0.576867\pi$
$173$	−6.29093	−0.478291	−0.239145	+	0.970984i	$0.576867\pi$
$174$	4.21251	0.319349
$175$	−29.5187	−2.23140
$176$	1.09294	0.0823833
$177$	−0.298636	−0.0224468
$178$	25.1795	1.88729
$179$	−0.972826	−0.0727124	−0.0363562	−	0.999339i	$-0.511575\pi$
$179$	−0.972826	−0.0727124	−0.0363562	+	0.999339i	$0.511575\pi$
$180$	33.3057	2.48246
$181$	0.385212	0.0286326	0.0143163	−	0.999898i	$-0.495443\pi$
$181$	0.385212	0.0286326	0.0143163	+	0.999898i	$0.495443\pi$
$182$	54.9335	4.07194
$183$	−1.99492	−0.147469
$184$	26.0917	1.92351
$185$	−21.0224	−1.54560
$186$	−3.18891	−0.233822
$187$	−4.06787	−0.297472
$188$	−22.8974	−1.66996
$189$	7.38462	0.537152
$190$	24.7800	1.79773
$191$	−14.2799	−1.03326	−0.516630	−	0.856209i	$-0.672814\pi$
$191$	−14.2799	−1.03326	−0.516630	+	0.856209i	$0.672814\pi$
$192$	−3.83251	−0.276588
$193$	−16.8770	−1.21483	−0.607415	−	0.794385i	$-0.707793\pi$
$193$	−16.8770	−1.21483	−0.607415	+	0.794385i	$0.707793\pi$
$194$	−24.2883	−1.74379
$195$	5.91689	0.423717
$196$	34.6066	2.47190
$197$	−10.0792	−0.718113	−0.359056	−	0.933316i	$-0.616901\pi$
$197$	−10.0792	−0.718113	−0.359056	+	0.933316i	$0.616901\pi$
$198$	−27.2477	−1.93641
$199$	22.5751	1.60031	0.800153	−	0.599796i	$-0.204752\pi$
$199$	22.5751	1.60031	0.800153	+	0.599796i	$0.204752\pi$
$200$	21.0327	1.48724
$201$	−3.37642	−0.238154
$202$	−8.20980	−0.577639
$203$	−25.6443	−1.79987
$204$	−0.984112	−0.0689016
$205$	−6.39138	−0.446393
$206$	−6.48510	−0.451838
$207$	−25.4788	−1.77090
$208$	−1.53313	−0.106303
$209$	−12.6159	−0.872663
$210$	9.98228	0.688843
$211$	14.1335	0.972992	0.486496	−	0.873683i	$-0.338275\pi$
$211$	14.1335	0.972992	0.486496	+	0.873683i	$0.338275\pi$
$212$	−15.3746	−1.05593
$213$	−4.41339	−0.302401
$214$	−8.02433	−0.548532
$215$	5.61007	0.382604
$216$	−5.26172	−0.358014
$217$	19.4130	1.31784
$218$	−16.0910	−1.08982
$219$	1.14364	0.0772799
$220$	−46.5448	−3.13805
$221$	5.70624	0.383843
$222$	4.16074	0.279251
$223$	−8.40747	−0.563006	−0.281503	−	0.959560i	$-0.590833\pi$
$223$	−8.40747	−0.563006	−0.281503	+	0.959560i	$0.590833\pi$
$224$	22.3541	1.49360
$225$	−20.5387	−1.36925
$226$	19.8772	1.32221
$227$	−9.38192	−0.622700	−0.311350	−	0.950295i	$-0.600781\pi$
$227$	−9.38192	−0.622700	−0.311350	+	0.950295i	$0.600781\pi$
$228$	−3.05209	−0.202130
$229$	17.2170	1.13773	0.568864	−	0.822431i	$-0.307383\pi$
$229$	17.2170	1.13773	0.568864	+	0.822431i	$0.307383\pi$
$230$	−69.9380	−4.61158
$231$	−5.08215	−0.334381
$232$	18.2721	1.19962
$233$	−25.8747	−1.69511	−0.847555	−	0.530707i	$-0.821927\pi$
$233$	−25.8747	−1.69511	−0.847555	+	0.530707i	$0.821927\pi$
$234$	38.2219	2.49865
$235$	24.1260	1.57381
$236$	−3.29536	−0.214510
$237$	−3.82983	−0.248774
$238$	9.62691	0.624020
$239$	7.15946	0.463107	0.231554	−	0.972822i	$-0.425619\pi$
$239$	7.15946	0.463107	0.231554	+	0.972822i	$0.425619\pi$
$240$	−0.278594	−0.0179832
$241$	23.7761	1.53155	0.765775	−	0.643108i	$-0.222355\pi$
$241$	23.7761	1.53155	0.765775	+	0.643108i	$0.222355\pi$
$242$	12.7659	0.820621
$243$	7.74594	0.496902
$244$	−22.0134	−1.40926
$245$	−36.4634	−2.32956
$246$	1.26498	0.0806519
$247$	17.6971	1.12604
$248$	−13.8322	−0.878346
$249$	3.04344	0.192870
$250$	−16.4274	−1.03896
$251$	22.0061	1.38901	0.694506	−	0.719487i	$-0.255623\pi$
$251$	22.0061	1.38901	0.694506	+	0.719487i	$0.255623\pi$
$252$	40.1288	2.52788
$253$	35.6067	2.23857
$254$	33.9186	2.12824
$255$	1.03692	0.0649341
$256$	−17.6986	−1.10616
$257$	−16.5714	−1.03369	−0.516847	−	0.856077i	$-0.672895\pi$
$257$	−16.5714	−1.03369	−0.516847	+	0.856077i	$0.672895\pi$
$258$	−1.11034	−0.0691268
$259$	−25.3291	−1.57388
$260$	65.2912	4.04919
$261$	−17.8429	−1.10445
$262$	9.46706	0.584877
$263$	8.71962	0.537675	0.268837	−	0.963186i	$-0.413361\pi$
$263$	8.71962	0.537675	0.268837	+	0.963186i	$0.413361\pi$
$264$	3.62115	0.222867
$265$	16.1995	0.995126
$266$	29.8565	1.83062
$267$	3.26770	0.199980
$268$	−37.2578	−2.27588
$269$	23.4767	1.43140	0.715700	−	0.698407i	$-0.246108\pi$
$269$	23.4767	1.43140	0.715700	+	0.698407i	$0.246108\pi$
$270$	14.1039	0.858334
$271$	11.4057	0.692846	0.346423	−	0.938078i	$-0.387396\pi$
$271$	11.4057	0.692846	0.346423	+	0.938078i	$0.387396\pi$
$272$	−0.268676	−0.0162909
$273$	7.12904	0.431469
$274$	−29.8434	−1.80291
$275$	28.7028	1.73085
$276$	8.61408	0.518507
$277$	−13.8073	−0.829599	−0.414799	−	0.909913i	$-0.636148\pi$
$277$	−13.8073	−0.829599	−0.414799	+	0.909913i	$0.636148\pi$
$278$	−9.02875	−0.541509
$279$	13.5073	0.808660
$280$	43.2991	2.58761
$281$	25.2632	1.50708	0.753539	−	0.657403i	$-0.228345\pi$
$281$	25.2632	1.50708	0.753539	+	0.657403i	$0.228345\pi$
$282$	−4.77500	−0.284347
$283$	3.50702	0.208470	0.104235	−	0.994553i	$-0.466761\pi$
$283$	3.50702	0.208470	0.104235	+	0.994553i	$0.466761\pi$
$284$	−48.7005	−2.88984
$285$	3.21585	0.190491
$286$	−53.4152	−3.15851
$287$	−7.70073	−0.454560
$288$	15.5537	0.916509
$289$	1.00000	0.0588235
$290$	−48.9779	−2.87608
$291$	−3.15203	−0.184775
$292$	12.6197	0.738513
$293$	−11.7776	−0.688055	−0.344028	−	0.938960i	$-0.611791\pi$
$293$	−11.7776	−0.688055	−0.344028	+	0.938960i	$0.611791\pi$
$294$	7.21681	0.420893
$295$	3.47217	0.202158
$296$	18.0476	1.04900
$297$	−7.18053	−0.416656
$298$	−2.94462	−0.170577
$299$	−49.9476	−2.88854
$300$	6.94388	0.400905
$301$	6.75937	0.389603
$302$	−33.3647	−1.91992
$303$	−1.06543	−0.0612076
$304$	−0.833262	−0.0477908
$305$	23.1945	1.32812
$306$	6.69827	0.382915
$307$	−2.58094	−0.147302	−0.0736510	−	0.997284i	$-0.523465\pi$
$307$	−2.58094	−0.147302	−0.0736510	+	0.997284i	$0.523465\pi$
$308$	−56.0801	−3.19546
$309$	−0.841610	−0.0478775
$310$	37.0768	2.10582
$311$	−10.0915	−0.572234	−0.286117	−	0.958195i	$-0.592365\pi$
$311$	−10.0915	−0.572234	−0.286117	+	0.958195i	$0.592365\pi$
$312$	−5.07961	−0.287576
$313$	17.1017	0.966643	0.483321	−	0.875443i	$-0.339430\pi$
$313$	17.1017	0.966643	0.483321	+	0.875443i	$0.339430\pi$
$314$	−24.1557	−1.36319
$315$	−42.2820	−2.38232
$316$	−42.2611	−2.37737
$317$	−29.5072	−1.65729	−0.828644	−	0.559776i	$-0.810887\pi$
$317$	−29.5072	−1.65729	−0.828644	+	0.559776i	$0.810887\pi$
$318$	−3.20619	−0.179794
$319$	24.9355	1.39612
$320$	44.5598	2.49097
$321$	−1.04136	−0.0581233
$322$	−84.2657	−4.69595
$323$	3.10136	0.172565
$324$	27.0394	1.50219
$325$	−40.2632	−2.23340
$326$	36.3889	2.01539
$327$	−2.08822	−0.115479
$328$	5.48695	0.302966
$329$	29.0685	1.60260
$330$	−9.70640	−0.534320
$331$	−34.8196	−1.91386	−0.956930	−	0.290318i	$-0.906239\pi$
$331$	−34.8196	−1.91386	−0.956930	+	0.290318i	$0.906239\pi$
$332$	33.5835	1.84313
$333$	−17.6237	−0.965771
$334$	45.5135	2.49039
$335$	39.2569	2.14483
$336$	−0.335668	−0.0183122
$337$	15.3850	0.838074	0.419037	−	0.907969i	$-0.362368\pi$
$337$	15.3850	0.838074	0.419037	+	0.907969i	$0.362368\pi$
$338$	45.0136	2.44841
$339$	2.57958	0.140104
$340$	11.4421	0.620533
$341$	−18.8764	−1.02222
$342$	20.7738	1.12332
$343$	−14.6489	−0.790969
$344$	−4.81621	−0.259672
$345$	−9.07627	−0.488650
$346$	−14.4765	−0.778260
$347$	−11.1353	−0.597776	−0.298888	−	0.954288i	$-0.596616\pi$
$347$	−11.1353	−0.597776	−0.298888	+	0.954288i	$0.596616\pi$
$348$	6.03248	0.323375
$349$	4.02420	0.215410	0.107705	−	0.994183i	$-0.465650\pi$
$349$	4.02420	0.215410	0.107705	+	0.994183i	$0.465650\pi$
$350$	−67.9273	−3.63087
$351$	10.0726	0.537633
$352$	−21.7363	−1.15855
$353$	−8.40883	−0.447557	−0.223778	−	0.974640i	$-0.571839\pi$
$353$	−8.40883	−0.447557	−0.223778	+	0.974640i	$0.571839\pi$
$354$	−0.687210	−0.0365248
$355$	51.3135	2.72344
$356$	36.0581	1.91108
$357$	1.24934	0.0661221
$358$	−2.23863	−0.118315
$359$	34.6336	1.82789	0.913946	−	0.405836i	$-0.133020\pi$
$359$	34.6336	1.82789	0.913946	+	0.405836i	$0.133020\pi$
$360$	30.1269	1.58783
$361$	−9.38154	−0.493765
$362$	0.886437	0.0465901
$363$	1.65670	0.0869543
$364$	78.6669	4.12327
$365$	−13.2968	−0.695988
$366$	−4.59065	−0.239957
$367$	−9.44022	−0.492775	−0.246388	−	0.969171i	$-0.579244\pi$
$367$	−9.44022	−0.492775	−0.246388	+	0.969171i	$0.579244\pi$
$368$	2.35176	0.122594
$369$	−5.35806	−0.278930
$370$	−48.3761	−2.51495
$371$	19.5182	1.01333
$372$	−4.56665	−0.236770
$373$	−23.3772	−1.21042	−0.605212	−	0.796064i	$-0.706912\pi$
$373$	−23.3772	−1.21042	−0.605212	+	0.796064i	$0.706912\pi$
$374$	−9.36084	−0.484038
$375$	−2.13189	−0.110090
$376$	−20.7120	−1.06814
$377$	−34.9785	−1.80149
$378$	16.9932	0.874037
$379$	−3.92745	−0.201739	−0.100870	−	0.994900i	$-0.532163\pi$
$379$	−3.92745	−0.201739	−0.100870	+	0.994900i	$0.532163\pi$
$380$	35.4860	1.82039
$381$	4.40182	0.225512
$382$	−32.8605	−1.68129
$383$	−26.1226	−1.33480	−0.667400	−	0.744699i	$-0.732593\pi$
$383$	−26.1226	−1.33480	−0.667400	+	0.744699i	$0.732593\pi$
$384$	−5.62778	−0.287192
$385$	59.0891	3.01146
$386$	−38.8367	−1.97673
$387$	4.70307	0.239071
$388$	−34.7817	−1.76578
$389$	8.16600	0.414032	0.207016	−	0.978338i	$-0.433625\pi$
$389$	8.16600	0.414032	0.207016	+	0.978338i	$0.433625\pi$
$390$	13.6157	0.689460
$391$	−8.75315	−0.442666
$392$	31.3036	1.58107
$393$	1.22860	0.0619745
$394$	−23.1939	−1.16849
$395$	44.5286	2.24048
$396$	−39.0198	−1.96082
$397$	2.11025	0.105911	0.0529553	−	0.998597i	$-0.483136\pi$
$397$	2.11025	0.105911	0.0529553	+	0.998597i	$0.483136\pi$
$398$	51.9490	2.60397
$399$	3.87466	0.193976
$400$	1.89577	0.0947887
$401$	−21.7642	−1.08685	−0.543425	−	0.839457i	$-0.682873\pi$
$401$	−21.7642	−1.08685	−0.543425	+	0.839457i	$0.682873\pi$
$402$	−7.76969	−0.387517
$403$	26.4791	1.31902
$404$	−11.7568	−0.584920
$405$	−28.4902	−1.41569
$406$	−59.0117	−2.92870
$407$	24.6291	1.22082
$408$	−0.890184	−0.0440707
$409$	12.7924	0.632543	0.316271	−	0.948669i	$-0.397569\pi$
$409$	12.7924	0.632543	0.316271	+	0.948669i	$0.397569\pi$
$410$	−14.7076	−0.726357
$411$	−3.87296	−0.191039
$412$	−9.28692	−0.457534
$413$	4.18349	0.205856
$414$	−58.6309	−2.88155
$415$	−35.3854	−1.73700
$416$	30.4908	1.49493
$417$	−1.17171	−0.0573791
$418$	−29.0314	−1.41997
$419$	24.6775	1.20558	0.602788	−	0.797902i	$-0.294057\pi$
$419$	24.6775	1.20558	0.602788	+	0.797902i	$0.294057\pi$
$420$	14.2950	0.697526
$421$	5.59187	0.272531	0.136265	−	0.990672i	$-0.456490\pi$
$421$	5.59187	0.272531	0.136265	+	0.990672i	$0.456490\pi$
$422$	32.5236	1.58322
$423$	20.2255	0.983395
$424$	−13.9071	−0.675390
$425$	−7.05599	−0.342266
$426$	−10.1559	−0.492057
$427$	27.9462	1.35241
$428$	−11.4912	−0.555446
$429$	−6.93201	−0.334681
$430$	12.9097	0.622561
$431$	16.7214	0.805440	0.402720	−	0.915323i	$-0.368065\pi$
$431$	16.7214	0.805440	0.402720	+	0.915323i	$0.368065\pi$
$432$	−0.474261	−0.0228179
$433$	18.7247	0.899852	0.449926	−	0.893066i	$-0.351450\pi$
$433$	18.7247	0.899852	0.449926	+	0.893066i	$0.351450\pi$
$434$	44.6725	2.14435
$435$	−6.35616	−0.304754
$436$	−23.0429	−1.10356
$437$	−27.1467	−1.29860
$438$	2.63170	0.125748
$439$	−31.7185	−1.51384	−0.756921	−	0.653506i	$-0.773297\pi$
$439$	−31.7185	−1.51384	−0.756921	+	0.653506i	$0.773297\pi$
$440$	−42.1024	−2.00715
$441$	−30.5683	−1.45563
$442$	13.1310	0.624578
$443$	1.37046	0.0651123	0.0325561	−	0.999470i	$-0.489635\pi$
$443$	1.37046	0.0651123	0.0325561	+	0.999470i	$0.489635\pi$
$444$	5.95835	0.282771
$445$	−37.9928	−1.80103
$446$	−19.3470	−0.916106
$447$	−0.382141	−0.0180747
$448$	53.6885	2.53654
$449$	11.8441	0.558957	0.279478	−	0.960152i	$-0.409838\pi$
$449$	11.8441	0.558957	0.279478	+	0.960152i	$0.409838\pi$
$450$	−47.2629	−2.22799
$451$	7.48790	0.352591
$452$	28.4650	1.33888
$453$	−4.32993	−0.203438
$454$	−21.5893	−1.01324
$455$	−82.8878	−3.88584
$456$	−2.76079	−0.129286
$457$	−24.1253	−1.12853	−0.564266	−	0.825593i	$-0.690841\pi$
$457$	−24.1253	−1.12853	−0.564266	+	0.825593i	$0.690841\pi$
$458$	39.6191	1.85128
$459$	1.76518	0.0823916
$460$	−100.154	−4.66971
$461$	−29.4518	−1.37171	−0.685853	−	0.727740i	$-0.740571\pi$
$461$	−29.4518	−1.37171	−0.685853	+	0.727740i	$0.740571\pi$
$462$	−11.6949	−0.544095
$463$	−12.0139	−0.558333	−0.279167	−	0.960243i	$-0.590058\pi$
$463$	−12.0139	−0.558333	−0.279167	+	0.960243i	$0.590058\pi$
$464$	1.64695	0.0764576
$465$	4.81168	0.223136
$466$	−59.5421	−2.75823
$467$	18.6281	0.862006	0.431003	−	0.902351i	$-0.358160\pi$
$467$	18.6281	0.862006	0.431003	+	0.902351i	$0.358160\pi$
$468$	54.7354	2.53014
$469$	47.2991	2.18407
$470$	55.5178	2.56085
$471$	−3.13483	−0.144445
$472$	−2.98084	−0.137204
$473$	−6.57255	−0.302206
$474$	−8.81307	−0.404798
$475$	−21.8832	−1.00407
$476$	13.7861	0.631885
$477$	13.5805	0.621807
$478$	16.4751	0.753554
$479$	−6.56916	−0.300152	−0.150076	−	0.988674i	$-0.547952\pi$
$479$	−6.56916	−0.300152	−0.150076	+	0.988674i	$0.547952\pi$
$480$	5.54066	0.252895
$481$	−34.5487	−1.57529
$482$	54.7126	2.49209
$483$	−10.9357	−0.497590
$484$	18.2812	0.830965
$485$	36.6480	1.66410
$486$	17.8247	0.808544
$487$	−41.7930	−1.89382	−0.946912	−	0.321494i	$-0.895815\pi$
$487$	−41.7930	−1.89382	−0.946912	+	0.321494i	$0.895815\pi$
$488$	−19.9123	−0.901389
$489$	4.72240	0.213554
$490$	−83.9083	−3.79059
$491$	−17.0743	−0.770554	−0.385277	−	0.922801i	$-0.625894\pi$
$491$	−17.0743	−0.770554	−0.385277	+	0.922801i	$0.625894\pi$
$492$	1.81150	0.0816686
$493$	−6.12987	−0.276075
$494$	40.7240	1.83226
$495$	41.1134	1.84791
$496$	−1.24676	−0.0559810
$497$	61.8258	2.77326
$498$	7.00345	0.313832
$499$	8.61403	0.385617	0.192808	−	0.981236i	$-0.438240\pi$
$499$	8.61403	0.385617	0.192808	+	0.981236i	$0.438240\pi$
$500$	−23.5247	−1.05206
$501$	5.90656	0.263886
$502$	50.6397	2.26016
$503$	−10.5155	−0.468863	−0.234432	−	0.972133i	$-0.575323\pi$
$503$	−10.5155	−0.468863	−0.234432	+	0.972133i	$0.575323\pi$
$504$	36.2988	1.61688
$505$	12.3876	0.551239
$506$	81.9368	3.64254
$507$	5.84168	0.259438
$508$	48.5728	2.15507
$509$	−7.88027	−0.349287	−0.174644	−	0.984632i	$-0.555877\pi$
$509$	−7.88027	−0.349287	−0.174644	+	0.984632i	$0.555877\pi$
$510$	2.38611	0.105659
$511$	−16.0209	−0.708721
$512$	−3.03740	−0.134235
$513$	5.47447	0.241704
$514$	−38.1335	−1.68200
$515$	9.78521	0.431188
$516$	−1.59005	−0.0699982
$517$	−28.2651	−1.24310
$518$	−58.2865	−2.56096
$519$	−1.87870	−0.0824656
$520$	59.0595	2.58993
$521$	−26.5223	−1.16196	−0.580981	−	0.813917i	$-0.697331\pi$
$521$	−26.5223	−1.16196	−0.580981	+	0.813917i	$0.697331\pi$
$522$	−41.0595	−1.79713
$523$	6.69008	0.292537	0.146268	−	0.989245i	$-0.453274\pi$
$523$	6.69008	0.292537	0.146268	+	0.989245i	$0.453274\pi$
$524$	13.5572	0.592249
$525$	−8.81533	−0.384733
$526$	20.0653	0.874888
$527$	4.64038	0.202138
$528$	0.326390	0.0142043
$529$	53.6176	2.33120
$530$	37.2777	1.61924
$531$	2.91082	0.126319
$532$	42.7558	1.85370
$533$	−10.5037	−0.454967
$534$	7.51951	0.325401
$535$	12.1077	0.523462
$536$	−33.7017	−1.45569
$537$	−0.290521	−0.0125369
$538$	54.0238	2.32913
$539$	42.7192	1.84005
$540$	20.1973	0.869154
$541$	22.3989	0.963006	0.481503	−	0.876444i	$-0.340091\pi$
$541$	22.3989	0.963006	0.481503	+	0.876444i	$0.340091\pi$
$542$	26.2463	1.12738
$543$	0.115038	0.00493676
$544$	5.34340	0.229097
$545$	24.2793	1.04001
$546$	16.4051	0.702073
$547$	33.3198	1.42465	0.712326	−	0.701849i	$-0.247642\pi$
$547$	33.3198	1.42465	0.712326	+	0.701849i	$0.247642\pi$
$548$	−42.7370	−1.82563
$549$	19.4446	0.829876
$550$	66.0500	2.81638
$551$	−19.0110	−0.809894
$552$	7.79191	0.331646
$553$	53.6509	2.28147
$554$	−31.7728	−1.34990
$555$	−6.27805	−0.266488
$556$	−12.9295	−0.548334
$557$	−31.2917	−1.32587	−0.662936	−	0.748676i	$-0.730690\pi$
$557$	−31.2917	−1.32587	−0.662936	+	0.748676i	$0.730690\pi$
$558$	31.0825	1.31583
$559$	9.21971	0.389952
$560$	3.90273	0.164921
$561$	−1.21481	−0.0512894
$562$	58.1349	2.45227
$563$	−10.6948	−0.450731	−0.225365	−	0.974274i	$-0.572358\pi$
$563$	−10.6948	−0.450731	−0.225365	+	0.974274i	$0.572358\pi$
$564$	−6.83798	−0.287931
$565$	−29.9923	−1.26178
$566$	8.07022	0.339217
$567$	−34.3268	−1.44159
$568$	−44.0523	−1.84839
$569$	22.1716	0.929483	0.464741	−	0.885447i	$-0.346147\pi$
$569$	22.1716	0.929483	0.464741	+	0.885447i	$0.346147\pi$
$570$	7.40020	0.309960
$571$	−5.37105	−0.224771	−0.112386	−	0.993665i	$-0.535849\pi$
$571$	−5.37105	−0.224771	−0.112386	+	0.993665i	$0.535849\pi$
$572$	−76.4927	−3.19832
$573$	−4.26450	−0.178152
$574$	−17.7206	−0.739646
$575$	61.7621	2.57566
$576$	37.3557	1.55649
$577$	−25.4470	−1.05937	−0.529687	−	0.848193i	$-0.677691\pi$
$577$	−25.4470	−1.05937	−0.529687	+	0.848193i	$0.677691\pi$
$578$	2.30116	0.0957158
$579$	−5.04006	−0.209458
$580$	−70.1383	−2.91234
$581$	−42.6346	−1.76878
$582$	−7.25334	−0.300661
$583$	−18.9787	−0.786018
$584$	11.4152	0.472366
$585$	−57.6722	−2.38445
$586$	−27.1022	−1.11958
$587$	5.81318	0.239936	0.119968	−	0.992778i	$-0.461721\pi$
$587$	5.81318	0.239936	0.119968	+	0.992778i	$0.461721\pi$
$588$	10.3348	0.426198
$589$	14.3915	0.592991
$590$	7.99004	0.328945
$591$	−3.01001	−0.123815
$592$	1.62671	0.0668574
$593$	23.3620	0.959360	0.479680	−	0.877443i	$-0.340753\pi$
$593$	23.3620	0.959360	0.479680	+	0.877443i	$0.340753\pi$
$594$	−16.5236	−0.677971
$595$	−14.5258	−0.595500
$596$	−4.21682	−0.172728
$597$	6.74173	0.275921
$598$	−114.938	−4.70015
$599$	−23.7322	−0.969671	−0.484835	−	0.874605i	$-0.661120\pi$
$599$	−23.7322	−0.969671	−0.484835	+	0.874605i	$0.661120\pi$
$600$	6.28113	0.256426
$601$	36.1017	1.47262	0.736310	−	0.676644i	$-0.236567\pi$
$601$	36.1017	1.47262	0.736310	+	0.676644i	$0.236567\pi$
$602$	15.5544	0.633951
$603$	32.9101	1.34020
$604$	−47.7795	−1.94412
$605$	−19.2621	−0.783117
$606$	−2.45174	−0.0995951
$607$	24.6193	0.999265	0.499632	−	0.866238i	$-0.333468\pi$
$607$	24.6193	0.999265	0.499632	+	0.866238i	$0.333468\pi$
$608$	16.5718	0.672077
$609$	−7.65829	−0.310330
$610$	53.3745	2.16107
$611$	39.6491	1.60403
$612$	9.59219	0.387741
$613$	39.5013	1.59544	0.797722	−	0.603025i	$-0.206038\pi$
$613$	39.5013	1.59544	0.797722	+	0.603025i	$0.206038\pi$
$614$	−5.93917	−0.239685
$615$	−1.90869	−0.0769659
$616$	−50.7276	−2.04387
$617$	−27.2311	−1.09628	−0.548142	−	0.836385i	$-0.684665\pi$
$617$	−27.2311	−1.09628	−0.548142	+	0.836385i	$0.684665\pi$
$618$	−1.93668	−0.0779048
$619$	−21.7180	−0.872920	−0.436460	−	0.899724i	$-0.643768\pi$
$619$	−21.7180	−0.872920	−0.436460	+	0.899724i	$0.643768\pi$
$620$	53.0955	2.13237
$621$	−15.4509	−0.620023
$622$	−23.2221	−0.931121
$623$	−45.7761	−1.83398
$624$	−0.457847	−0.0183286
$625$	−10.4930	−0.419719
$626$	39.3537	1.57289
$627$	−3.76757	−0.150462
$628$	−34.5919	−1.38037
$629$	−6.05454	−0.241410
$630$	−97.2978	−3.87644
$631$	−32.1299	−1.27907	−0.639535	−	0.768762i	$-0.720873\pi$
$631$	−32.1299	−1.27907	−0.639535	+	0.768762i	$0.720873\pi$
$632$	−38.2275	−1.52061
$633$	4.22077	0.167761
$634$	−67.9009	−2.69669
$635$	−51.1790	−2.03098
$636$	−4.59139	−0.182061
$637$	−59.9247	−2.37430
$638$	57.3807	2.27173
$639$	43.0175	1.70175
$640$	65.4330	2.58647
$641$	17.2007	0.679385	0.339692	−	0.940537i	$-0.389677\pi$
$641$	17.2007	0.679385	0.339692	+	0.940537i	$0.389677\pi$
$642$	−2.39635	−0.0945764
$643$	−22.4037	−0.883515	−0.441757	−	0.897135i	$-0.645645\pi$
$643$	−22.4037	−0.883515	−0.441757	+	0.897135i	$0.645645\pi$
$644$	−120.672	−4.75514
$645$	1.67537	0.0659675
$646$	7.13675	0.280792
$647$	−25.7698	−1.01311	−0.506557	−	0.862207i	$-0.669082\pi$
$647$	−25.7698	−1.01311	−0.506557	+	0.862207i	$0.669082\pi$
$648$	24.4587	0.960827
$649$	−4.06787	−0.159678
$650$	−92.6522	−3.63412
$651$	5.79741	0.227218
$652$	52.1104	2.04080
$653$	10.8406	0.424227	0.212114	−	0.977245i	$-0.431965\pi$
$653$	10.8406	0.424227	0.212114	+	0.977245i	$0.431965\pi$
$654$	−4.80534	−0.187904
$655$	−14.2846	−0.558147
$656$	0.494563	0.0193094
$657$	−11.1471	−0.434890
$658$	66.8914	2.60770
$659$	−5.10874	−0.199008	−0.0995040	−	0.995037i	$-0.531726\pi$
$659$	−5.10874	−0.199008	−0.0995040	+	0.995037i	$0.531726\pi$
$660$	−13.8999	−0.541055
$661$	−36.6823	−1.42677	−0.713387	−	0.700770i	$-0.752840\pi$
$661$	−36.6823	−1.42677	−0.713387	+	0.700770i	$0.752840\pi$
$662$	−80.1257	−3.11418
$663$	1.70409	0.0661813
$664$	30.3781	1.17890
$665$	−45.0498	−1.74696
$666$	−40.5550	−1.57147
$667$	53.6557	2.07756
$668$	65.1772	2.52178
$669$	−2.51077	−0.0970720
$670$	90.3365	3.49000
$671$	−27.1739	−1.04904
$672$	6.67573	0.257522
$673$	−28.9311	−1.11521	−0.557605	−	0.830106i	$-0.688280\pi$
$673$	−28.9311	−1.11521	−0.557605	+	0.830106i	$0.688280\pi$
$674$	35.4034	1.36369
$675$	−12.4551	−0.479397
$676$	64.4612	2.47928
$677$	−41.7557	−1.60480	−0.802402	−	0.596785i	$-0.796445\pi$
$677$	−41.7557	−1.60480	−0.802402	+	0.596785i	$0.796445\pi$
$678$	5.93605	0.227973
$679$	44.1558	1.69454
$680$	10.3500	0.396904
$681$	−2.80178	−0.107364
$682$	−43.4378	−1.66332
$683$	−42.8387	−1.63918	−0.819589	−	0.572952i	$-0.805798\pi$
$683$	−42.8387	−1.63918	−0.819589	+	0.572952i	$0.805798\pi$
$684$	29.7489	1.13748
$685$	45.0301	1.72051
$686$	−33.7096	−1.28704
$687$	5.14160	0.196164
$688$	−0.434106	−0.0165501
$689$	26.6226	1.01424
$690$	−20.8860	−0.795116
$691$	−8.52873	−0.324448	−0.162224	−	0.986754i	$-0.551867\pi$
$691$	−8.52873	−0.324448	−0.162224	+	0.986754i	$0.551867\pi$
$692$	−20.7309	−0.788070
$693$	49.5360	1.88172
$694$	−25.6242	−0.972683
$695$	13.6233	0.516760
$696$	5.45671	0.206836
$697$	−1.84074	−0.0697231
$698$	9.26035	0.350509
$699$	−7.72712	−0.292267
$700$	−97.2746	−3.67664
$701$	34.6599	1.30909	0.654543	−	0.756025i	$-0.272861\pi$
$701$	34.6599	1.30909	0.654543	+	0.756025i	$0.272861\pi$
$702$	23.1786	0.874820
$703$	−18.7773	−0.708201
$704$	−52.2046	−1.96754
$705$	7.20488	0.271351
$706$	−19.3501	−0.728251
$707$	14.9253	0.561324
$708$	−0.984112	−0.0369852
$709$	35.2878	1.32526	0.662631	−	0.748946i	$-0.269440\pi$
$709$	35.2878	1.32526	0.662631	+	0.748946i	$0.269440\pi$
$710$	118.081	4.43150
$711$	37.3295	1.39997
$712$	32.6166	1.22236
$713$	−40.6179	−1.52115
$714$	2.87494	0.107592
$715$	80.5970	3.01416
$716$	−3.20581	−0.119807
$717$	2.13807	0.0798477
$718$	79.6976	2.97429
$719$	−11.3081	−0.421721	−0.210861	−	0.977516i	$-0.567627\pi$
$719$	−11.3081	−0.421721	−0.210861	+	0.977516i	$0.567627\pi$
$720$	2.71547	0.101200
$721$	11.7898	0.439077
$722$	−21.5885	−0.803440
$723$	7.10038	0.264066
$724$	1.26941	0.0471774
$725$	43.2523	1.60635
$726$	3.81234	0.141489
$727$	−0.589209	−0.0218525	−0.0109263	−	0.999940i	$-0.503478\pi$
$727$	−0.589209	−0.0218525	−0.0109263	+	0.999940i	$0.503478\pi$
$728$	71.1586	2.63731
$729$	−22.3027	−0.826026
$730$	−30.5982	−1.13249
$731$	1.61572	0.0597597
$732$	−6.57399	−0.242982
$733$	−28.4915	−1.05236	−0.526179	−	0.850374i	$-0.676376\pi$
$733$	−28.4915	−1.05236	−0.526179	+	0.850374i	$0.676376\pi$
$734$	−21.7235	−0.801829
$735$	−10.8893	−0.401657
$736$	−46.7716	−1.72402
$737$	−45.9919	−1.69413
$738$	−12.3298	−0.453866
$739$	−13.4640	−0.495281	−0.247640	−	0.968852i	$-0.579655\pi$
$739$	−13.4640	−0.495281	−0.247640	+	0.968852i	$0.579655\pi$
$740$	−69.2765	−2.54665
$741$	5.28500	0.194149
$742$	44.9145	1.64886
$743$	−4.64110	−0.170266	−0.0851328	−	0.996370i	$-0.527131\pi$
$743$	−4.64110	−0.170266	−0.0851328	+	0.996370i	$0.527131\pi$
$744$	−4.13079	−0.151442
$745$	4.44307	0.162782
$746$	−53.7947	−1.96957
$747$	−29.6645	−1.08537
$748$	−13.4051	−0.490139
$749$	14.5881	0.533039
$750$	−4.90582	−0.179135
$751$	35.8943	1.30980	0.654901	−	0.755715i	$-0.272710\pi$
$751$	35.8943	1.30980	0.654901	+	0.755715i	$0.272710\pi$
$752$	−1.86686	−0.0680774
$753$	6.57181	0.239490
$754$	−80.4914	−2.93132
$755$	50.3432	1.83218
$756$	24.3350	0.885055
$757$	−30.6069	−1.11243	−0.556214	−	0.831039i	$-0.687747\pi$
$757$	−30.6069	−1.11243	−0.556214	+	0.831039i	$0.687747\pi$
$758$	−9.03771	−0.328264
$759$	10.6334	0.385969
$760$	32.0991	1.16436
$761$	26.9720	0.977734	0.488867	−	0.872358i	$-0.337410\pi$
$761$	26.9720	0.977734	0.488867	+	0.872358i	$0.337410\pi$
$762$	10.1293	0.366946
$763$	29.2532	1.05904
$764$	−47.0575	−1.70248
$765$	−10.1069	−0.365414
$766$	−60.1123	−2.17195
$767$	5.70624	0.206040
$768$	−5.28543	−0.190721
$769$	−50.8231	−1.83273	−0.916364	−	0.400346i	$-0.868890\pi$
$769$	−50.8231	−1.83273	−0.916364	+	0.400346i	$0.868890\pi$
$770$	135.974	4.90016
$771$	−4.94881	−0.178227
$772$	−55.6156	−2.00165
$773$	−13.7049	−0.492930	−0.246465	−	0.969152i	$-0.579269\pi$
$773$	−13.7049	−0.492930	−0.246465	+	0.969152i	$0.579269\pi$
$774$	10.8225	0.389008
$775$	−32.7424	−1.17614
$776$	−31.4620	−1.12942
$777$	−7.56419	−0.271364
$778$	18.7913	0.673701
$779$	−5.70881	−0.204539
$780$	19.4983	0.698150
$781$	−60.1170	−2.15116
$782$	−20.1424	−0.720292
$783$	−10.8203	−0.386687
$784$	2.82153	0.100769
$785$	36.4480	1.30088
$786$	2.82720	0.100843
$787$	41.1585	1.46714	0.733570	−	0.679613i	$-0.237852\pi$
$787$	41.1585	1.46714	0.733570	+	0.679613i	$0.237852\pi$
$788$	−33.2146	−1.18322
$789$	2.60399	0.0927045
$790$	102.468	3.64564
$791$	−36.1366	−1.28487
$792$	−35.2956	−1.25417
$793$	38.1184	1.35362
$794$	4.85604	0.172334
$795$	4.83774	0.171577
$796$	74.3930	2.63679
$797$	−8.55069	−0.302881	−0.151441	−	0.988466i	$-0.548391\pi$
$797$	−8.55069	−0.302881	−0.151441	+	0.988466i	$0.548391\pi$
$798$	8.91623	0.315631
$799$	6.94838	0.245816
$800$	−37.7030	−1.33300
$801$	−31.8504	−1.12538
$802$	−50.0829	−1.76849
$803$	15.5781	0.549739
$804$	−11.1265	−0.392402
$805$	127.147	4.48133
$806$	60.9328	2.14627
$807$	7.01099	0.246798
$808$	−10.6346	−0.374125
$809$	20.0484	0.704863	0.352431	−	0.935838i	$-0.385355\pi$
$809$	20.0484	0.704863	0.352431	+	0.935838i	$0.385355\pi$
$810$	−65.5607	−2.30357
$811$	−5.74520	−0.201741	−0.100871	−	0.994900i	$-0.532163\pi$
$811$	−5.74520	−0.201741	−0.100871	+	0.994900i	$0.532163\pi$
$812$	−84.5071	−2.96562
$813$	3.40614	0.119459
$814$	56.6756	1.98648
$815$	−54.9064	−1.92329
$816$	−0.0802362	−0.00280883
$817$	5.01095	0.175311
$818$	29.4374	1.02925
$819$	−69.4871	−2.42808
$820$	−21.0619	−0.735513
$821$	30.3031	1.05758	0.528792	−	0.848751i	$-0.322645\pi$
$821$	30.3031	1.05758	0.528792	+	0.848751i	$0.322645\pi$
$822$	−8.91232	−0.310853
$823$	−1.24233	−0.0433047	−0.0216524	−	0.999766i	$-0.506893\pi$
$823$	−1.24233	−0.0433047	−0.0216524	+	0.999766i	$0.506893\pi$
$824$	−8.40054	−0.292647
$825$	8.57170	0.298428
$826$	9.62691	0.334963
$827$	−27.7354	−0.964453	−0.482227	−	0.876046i	$-0.660172\pi$
$827$	−27.7354	−0.964453	−0.482227	+	0.876046i	$0.660172\pi$
$828$	−83.9618	−2.91788
$829$	−8.42897	−0.292750	−0.146375	−	0.989229i	$-0.546761\pi$
$829$	−8.42897	−0.292750	−0.146375	+	0.989229i	$0.546761\pi$
$830$	−81.4277	−2.82640
$831$	−4.12335	−0.143037
$832$	73.2305	2.53881
$833$	−10.5016	−0.363859
$834$	−2.69631	−0.0933655
$835$	−68.6743	−2.37657
$836$	−41.5741	−1.43787
$837$	8.19110	0.283126
$838$	56.7870	1.96167
$839$	48.1959	1.66391	0.831954	−	0.554845i	$-0.187222\pi$
$839$	48.1959	1.66391	0.831954	+	0.554845i	$0.187222\pi$
$840$	12.9306	0.446150
$841$	8.57531	0.295700
$842$	12.8678	0.443454
$843$	7.54450	0.259847
$844$	46.5750	1.60318
$845$	−67.9199	−2.33652
$846$	46.5421	1.60015
$847$	−23.2082	−0.797443
$848$	−1.25351	−0.0430458
$849$	1.04732	0.0359439
$850$	−16.2370	−0.556924
$851$	52.9963	1.81669
$852$	−14.5437	−0.498259
$853$	15.5785	0.533397	0.266698	−	0.963780i	$-0.414067\pi$
$853$	15.5785	0.533397	0.266698	+	0.963780i	$0.414067\pi$
$854$	64.3089	2.20060
$855$	−31.3451	−1.07198
$856$	−10.3944	−0.355273
$857$	−16.9119	−0.577701	−0.288850	−	0.957374i	$-0.593273\pi$
$857$	−16.9119	−0.577701	−0.288850	+	0.957374i	$0.593273\pi$
$858$	−15.9517	−0.544582
$859$	−46.2092	−1.57664	−0.788319	−	0.615267i	$-0.789048\pi$
$859$	−46.2092	−1.57664	−0.788319	+	0.615267i	$0.789048\pi$
$860$	18.4872	0.630408
$861$	−2.29971	−0.0783740
$862$	38.4786	1.31059
$863$	28.6087	0.973853	0.486927	−	0.873443i	$-0.338118\pi$
$863$	28.6087	0.973853	0.486927	+	0.873443i	$0.338118\pi$
$864$	9.43208	0.320886
$865$	21.8432	0.742691
$866$	43.0886	1.46421
$867$	0.298636	0.0101422
$868$	63.9727	2.17138
$869$	−52.1681	−1.76968
$870$	−14.6266	−0.495887
$871$	64.5156	2.18603
$872$	−20.8436	−0.705853
$873$	30.7230	1.03982
$874$	−62.4690	−2.11305
$875$	29.8649	1.00962
$876$	3.76870	0.127333
$877$	4.93074	0.166499	0.0832496	−	0.996529i	$-0.473470\pi$
$877$	4.93074	0.166499	0.0832496	+	0.996529i	$0.473470\pi$
$878$	−72.9896	−2.46328
$879$	−3.51722	−0.118633
$880$	−3.79487	−0.127925
$881$	19.2113	0.647245	0.323622	−	0.946186i	$-0.395099\pi$
$881$	19.2113	0.647245	0.323622	+	0.946186i	$0.395099\pi$
$882$	−70.3426	−2.36856
$883$	16.7196	0.562659	0.281330	−	0.959611i	$-0.409225\pi$
$883$	16.7196	0.562659	0.281330	+	0.959611i	$0.409225\pi$
$884$	18.8041	0.632451
$885$	1.03692	0.0348555
$886$	3.15364	0.105949
$887$	12.0050	0.403088	0.201544	−	0.979479i	$-0.435404\pi$
$887$	12.0050	0.403088	0.201544	+	0.979479i	$0.435404\pi$
$888$	5.38966	0.180865
$889$	−61.6637	−2.06813
$890$	−87.4278	−2.93058
$891$	33.3781	1.11821
$892$	−27.7056	−0.927653
$893$	21.5495	0.721125
$894$	−0.879370	−0.0294105
$895$	3.37782	0.112908
$896$	78.8378	2.63379
$897$	−14.9161	−0.498035
$898$	27.2552	0.909517
$899$	−28.4449	−0.948691
$900$	−67.6824	−2.25608
$901$	4.66552	0.155431
$902$	17.2309	0.573726
$903$	2.01859	0.0671744
$904$	25.7481	0.856371
$905$	−1.33752	−0.0444608
$906$	−9.96388	−0.331028
$907$	23.0165	0.764252	0.382126	−	0.924110i	$-0.375192\pi$
$907$	23.0165	0.764252	0.382126	+	0.924110i	$0.375192\pi$
$908$	−30.9168	−1.02601
$909$	10.3848	0.344443
$910$	−190.738	−6.32292
$911$	32.8945	1.08984	0.544921	−	0.838487i	$-0.316560\pi$
$911$	32.8945	1.08984	0.544921	+	0.838487i	$0.316560\pi$
$912$	−0.248842	−0.00823997
$913$	41.4562	1.37200
$914$	−55.5162	−1.83631
$915$	6.92672	0.228990
$916$	56.7361	1.87461
$917$	−17.2110	−0.568358
$918$	4.06197	0.134065
$919$	12.6766	0.418164	0.209082	−	0.977898i	$-0.432952\pi$
$919$	12.6766	0.418164	0.209082	+	0.977898i	$0.432952\pi$
$920$	−90.5949	−2.98683
$921$	−0.770761	−0.0253974
$922$	−67.7734	−2.23200
$923$	84.3297	2.77575
$924$	−16.7475	−0.550953
$925$	42.7208	1.40465
$926$	−27.6460	−0.908503
$927$	8.20321	0.269429
$928$	−32.7544	−1.07522
$929$	−8.37685	−0.274836	−0.137418	−	0.990513i	$-0.543880\pi$
$929$	−8.37685	−0.274836	−0.137418	+	0.990513i	$0.543880\pi$
$930$	11.0725	0.363080
$931$	−32.5693	−1.06742
$932$	−85.2666	−2.79300
$933$	−3.01367	−0.0986631
$934$	42.8663	1.40263
$935$	14.1244	0.461916
$936$	49.5112	1.61832
$937$	13.7631	0.449622	0.224811	−	0.974402i	$-0.427823\pi$
$937$	13.7631	0.449622	0.224811	+	0.974402i	$0.427823\pi$
$938$	108.843	3.55385
$939$	5.10716	0.166666
$940$	79.5038	2.59313
$941$	41.1055	1.34000	0.670001	−	0.742360i	$-0.266294\pi$
$941$	41.1055	1.34000	0.670001	+	0.742360i	$0.266294\pi$
$942$	−7.21376	−0.235037
$943$	16.1123	0.524688
$944$	−0.268676	−0.00874465
$945$	−25.6407	−0.834092
$946$	−15.1245	−0.491741
$947$	−47.7325	−1.55110	−0.775549	−	0.631287i	$-0.782527\pi$
$947$	−47.7325	−1.55110	−0.775549	+	0.631287i	$0.782527\pi$
$948$	−12.6207	−0.409900
$949$	−21.8523	−0.709356
$950$	−50.3568	−1.63379
$951$	−8.81190	−0.285745
$952$	12.4703	0.404165
$953$	−28.3156	−0.917232	−0.458616	−	0.888634i	$-0.651655\pi$
$953$	−28.3156	−0.917232	−0.458616	+	0.888634i	$0.651655\pi$
$954$	31.2509	1.01178
$955$	49.5824	1.60445
$956$	23.5930	0.763052
$957$	7.44664	0.240716
$958$	−15.1167	−0.488399
$959$	54.2550	1.75199
$960$	13.3072	0.429487
$961$	−9.46691	−0.305384
$962$	−79.5023	−2.56326
$963$	10.1502	0.327086
$964$	78.3507	2.52351
$965$	58.5997	1.88639
$966$	−25.1648	−0.809663
$967$	16.9831	0.546140	0.273070	−	0.961994i	$-0.411961\pi$
$967$	16.9831	0.546140	0.273070	+	0.961994i	$0.411961\pi$
$968$	16.5364	0.531500
$969$	0.926178	0.0297531
$970$	84.3330	2.70777
$971$	28.2297	0.905935	0.452968	−	0.891527i	$-0.350365\pi$
$971$	28.2297	0.905935	0.452968	+	0.891527i	$0.350365\pi$
$972$	25.5257	0.818736
$973$	16.4142	0.526214
$974$	−96.1727	−3.08157
$975$	−12.0240	−0.385077
$976$	−1.79479	−0.0574497
$977$	13.9651	0.446783	0.223392	−	0.974729i	$-0.428287\pi$
$977$	13.9651	0.446783	0.223392	+	0.974729i	$0.428287\pi$
$978$	10.8670	0.347489
$979$	44.5110	1.42258
$980$	−120.160	−3.83837
$981$	20.3540	0.649853
$982$	−39.2909	−1.25382
$983$	37.0742	1.18248	0.591242	−	0.806494i	$-0.298638\pi$
$983$	37.0742	1.18248	0.591242	+	0.806494i	$0.298638\pi$
$984$	1.63860	0.0522366
$985$	34.9967	1.11509
$986$	−14.1058	−0.449222
$987$	8.68089	0.276316
$988$	58.3184	1.85536
$989$	−14.1427	−0.449711
$990$	94.6087	3.00686
$991$	58.2444	1.85020	0.925098	−	0.379729i	$-0.123983\pi$
$991$	58.2444	1.85020	0.925098	+	0.379729i	$0.123983\pi$
$992$	24.7954	0.787255
$993$	−10.3984	−0.329983
$994$	142.271	4.51257
$995$	−78.3846	−2.48496
$996$	10.0292	0.317788
$997$	−30.6867	−0.971857	−0.485929	−	0.873999i	$-0.661518\pi$
$997$	−30.6867	−0.971857	−0.485929	+	0.873999i	$0.661518\pi$
$998$	19.8223	0.627464
$999$	−10.6874	−0.338133

Twists

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

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

\(f(q)\)	\(=\)	\(q+2.30116 q^{2} +0.298636 q^{3} +3.29536 q^{4} -3.47217 q^{5} +0.687210 q^{6} -4.18349 q^{7} +2.98084 q^{8} -2.91082 q^{9} +O(q^{10})\)	\(q+2.30116 q^{2} +0.298636 q^{3} +3.29536 q^{4} -3.47217 q^{5} +0.687210 q^{6} -4.18349 q^{7} +2.98084 q^{8} -2.91082 q^{9} -7.99004 q^{10} +4.06787 q^{11} +0.984112 q^{12} -5.70624 q^{13} -9.62691 q^{14} -1.03692 q^{15} +0.268676 q^{16} -1.00000 q^{17} -6.69827 q^{18} -3.10136 q^{19} -11.4421 q^{20} -1.24934 q^{21} +9.36084 q^{22} +8.75315 q^{23} +0.890184 q^{24} +7.05599 q^{25} -13.1310 q^{26} -1.76518 q^{27} -13.7861 q^{28} +6.12987 q^{29} -2.38611 q^{30} -4.64038 q^{31} -5.34340 q^{32} +1.21481 q^{33} -2.30116 q^{34} +14.5258 q^{35} -9.59219 q^{36} +6.05454 q^{37} -7.13675 q^{38} -1.70409 q^{39} -10.3500 q^{40} +1.84074 q^{41} -2.87494 q^{42} -1.61572 q^{43} +13.4051 q^{44} +10.1069 q^{45} +20.1424 q^{46} -6.94838 q^{47} +0.0802362 q^{48} +10.5016 q^{49} +16.2370 q^{50} -0.298636 q^{51} -18.8041 q^{52} -4.66552 q^{53} -4.06197 q^{54} -14.1244 q^{55} -12.4703 q^{56} -0.926178 q^{57} +14.1058 q^{58} -1.00000 q^{59} -3.41701 q^{60} -6.68012 q^{61} -10.6783 q^{62} +12.1774 q^{63} -12.8334 q^{64} +19.8131 q^{65} +2.79548 q^{66} -11.3061 q^{67} -3.29536 q^{68} +2.61400 q^{69} +33.4263 q^{70} -14.7785 q^{71} -8.67667 q^{72} +3.82954 q^{73} +13.9325 q^{74} +2.10717 q^{75} -10.2201 q^{76} -17.0179 q^{77} -3.92139 q^{78} -12.8244 q^{79} -0.932889 q^{80} +8.20530 q^{81} +4.23585 q^{82} +10.1911 q^{83} -4.11703 q^{84} +3.47217 q^{85} -3.71805 q^{86} +1.83060 q^{87} +12.1257 q^{88} +10.9421 q^{89} +23.2576 q^{90} +23.8720 q^{91} +28.8448 q^{92} -1.38578 q^{93} -15.9894 q^{94} +10.7685 q^{95} -1.59573 q^{96} -10.5548 q^{97} +24.1659 q^{98} -11.8408 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{2} - 7 q^{3} + 15 q^{4} - 12 q^{5} + 5 q^{6} - 9 q^{7} - 12 q^{8} + 3 q^{9}+O(q^{10}) \) 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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