LMFDB - Embedded newform 6017.2.a.f.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6017,2,Mod(1,6017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6017, 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("6017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6017 = 11 \cdot 547 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6017.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:	$48.0459868962$
Analytic rank:	$0$
Dimension:	$121$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	6017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.25579 q^{2} -2.77556 q^{3} +3.08857 q^{4} +0.288075 q^{5} +6.26106 q^{6} +1.78637 q^{7} -2.45557 q^{8} +4.70373 q^{9} +O(q^{10})$	\(q-2.25579 q^{2} -2.77556 q^{3} +3.08857 q^{4} +0.288075 q^{5} +6.26106 q^{6} +1.78637 q^{7} -2.45557 q^{8} +4.70373 q^{9} -0.649836 q^{10} -1.00000 q^{11} -8.57250 q^{12} +5.07395 q^{13} -4.02967 q^{14} -0.799570 q^{15} -0.637886 q^{16} -2.51700 q^{17} -10.6106 q^{18} -2.44919 q^{19} +0.889740 q^{20} -4.95818 q^{21} +2.25579 q^{22} -7.23846 q^{23} +6.81559 q^{24} -4.91701 q^{25} -11.4457 q^{26} -4.72879 q^{27} +5.51733 q^{28} -7.48543 q^{29} +1.80366 q^{30} -3.19569 q^{31} +6.35008 q^{32} +2.77556 q^{33} +5.67780 q^{34} +0.514610 q^{35} +14.5278 q^{36} -11.0014 q^{37} +5.52485 q^{38} -14.0830 q^{39} -0.707390 q^{40} +9.46750 q^{41} +11.1846 q^{42} +7.61735 q^{43} -3.08857 q^{44} +1.35503 q^{45} +16.3284 q^{46} -9.12690 q^{47} +1.77049 q^{48} -3.80887 q^{49} +11.0917 q^{50} +6.98607 q^{51} +15.6712 q^{52} -8.32897 q^{53} +10.6671 q^{54} -0.288075 q^{55} -4.38657 q^{56} +6.79787 q^{57} +16.8855 q^{58} +3.22138 q^{59} -2.46953 q^{60} +10.1317 q^{61} +7.20878 q^{62} +8.40261 q^{63} -13.0487 q^{64} +1.46168 q^{65} -6.26106 q^{66} +15.3378 q^{67} -7.77391 q^{68} +20.0908 q^{69} -1.16085 q^{70} -4.64867 q^{71} -11.5504 q^{72} -11.1549 q^{73} +24.8168 q^{74} +13.6475 q^{75} -7.56449 q^{76} -1.78637 q^{77} +31.7683 q^{78} -0.0153161 q^{79} -0.183759 q^{80} -0.986136 q^{81} -21.3566 q^{82} +1.08217 q^{83} -15.3137 q^{84} -0.725085 q^{85} -17.1831 q^{86} +20.7763 q^{87} +2.45557 q^{88} -14.0979 q^{89} -3.05665 q^{90} +9.06396 q^{91} -22.3565 q^{92} +8.86982 q^{93} +20.5883 q^{94} -0.705551 q^{95} -17.6250 q^{96} -8.81029 q^{97} +8.59200 q^{98} -4.70373 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 121 q + 2 q^{2} + 18 q^{3} + 138 q^{4} + 13 q^{5} + 10 q^{6} + 56 q^{7} + 12 q^{8} + 143 q^{9}+O(q^{10}) $ 121 * q + 2 * q^2 + 18 * q^3 + 138 * q^4 + 13 * q^5 + 10 * q^6 + 56 * q^7 + 12 * q^8 + 143 * q^9	\( 121 q + 2 q^{2} + 18 q^{3} + 138 q^{4} + 13 q^{5} + 10 q^{6} + 56 q^{7} + 12 q^{8} + 143 q^{9} + 20 q^{10} - 121 q^{11} + 40 q^{12} + 31 q^{13} + 7 q^{14} + 53 q^{15} + 164 q^{16} - 23 q^{17} + 14 q^{18} + 62 q^{19} + 53 q^{20} + 19 q^{21} - 2 q^{22} + 34 q^{23} + 34 q^{24} + 172 q^{25} + 34 q^{26} + 87 q^{27} + 91 q^{28} - 30 q^{29} + 2 q^{30} + 102 q^{31} + 31 q^{32} - 18 q^{33} + 30 q^{34} + 20 q^{35} + 164 q^{36} + 58 q^{37} + 35 q^{38} + 42 q^{39} + 52 q^{40} - 12 q^{41} + 56 q^{42} + 96 q^{43} - 138 q^{44} + 72 q^{45} + 48 q^{46} + 136 q^{47} + 99 q^{48} + 199 q^{49} - 7 q^{50} + 22 q^{51} + 81 q^{52} + 24 q^{53} + 37 q^{54} - 13 q^{55} + 28 q^{56} + 25 q^{57} + 76 q^{58} + 58 q^{59} + 81 q^{60} + 14 q^{61} - 2 q^{62} + 152 q^{63} + 236 q^{64} - 29 q^{65} - 10 q^{66} + 112 q^{67} - 61 q^{68} + 41 q^{69} + 105 q^{70} + 56 q^{71} + 71 q^{72} + 113 q^{73} - 23 q^{74} + 111 q^{75} + 144 q^{76} - 56 q^{77} + 59 q^{78} + 80 q^{79} + 100 q^{80} + 177 q^{81} + 123 q^{82} + 6 q^{83} + 79 q^{84} + 26 q^{85} + 14 q^{86} + 180 q^{87} - 12 q^{88} + 26 q^{89} + 75 q^{90} + 72 q^{91} + 58 q^{92} + 139 q^{93} + 37 q^{94} + 39 q^{95} + 66 q^{96} + 136 q^{97} + 7 q^{98} - 143 q^{99}+O(q^{100}) \) 121 * q + 2 * q^2 + 18 * q^3 + 138 * q^4 + 13 * q^5 + 10 * q^6 + 56 * q^7 + 12 * q^8 + 143 * q^9 + 20 * q^10 - 121 * q^11 + 40 * q^12 + 31 * q^13 + 7 * q^14 + 53 * q^15 + 164 * q^16 - 23 * q^17 + 14 * q^18 + 62 * q^19 + 53 * q^20 + 19 * q^21 - 2 * q^22 + 34 * q^23 + 34 * q^24 + 172 * q^25 + 34 * q^26 + 87 * q^27 + 91 * q^28 - 30 * q^29 + 2 * q^30 + 102 * q^31 + 31 * q^32 - 18 * q^33 + 30 * q^34 + 20 * q^35 + 164 * q^36 + 58 * q^37 + 35 * q^38 + 42 * q^39 + 52 * q^40 - 12 * q^41 + 56 * q^42 + 96 * q^43 - 138 * q^44 + 72 * q^45 + 48 * q^46 + 136 * q^47 + 99 * q^48 + 199 * q^49 - 7 * q^50 + 22 * q^51 + 81 * q^52 + 24 * q^53 + 37 * q^54 - 13 * q^55 + 28 * q^56 + 25 * q^57 + 76 * q^58 + 58 * q^59 + 81 * q^60 + 14 * q^61 - 2 * q^62 + 152 * q^63 + 236 * q^64 - 29 * q^65 - 10 * q^66 + 112 * q^67 - 61 * q^68 + 41 * q^69 + 105 * q^70 + 56 * q^71 + 71 * q^72 + 113 * q^73 - 23 * q^74 + 111 * q^75 + 144 * q^76 - 56 * q^77 + 59 * q^78 + 80 * q^79 + 100 * q^80 + 177 * q^81 + 123 * q^82 + 6 * q^83 + 79 * q^84 + 26 * q^85 + 14 * q^86 + 180 * q^87 - 12 * q^88 + 26 * q^89 + 75 * q^90 + 72 * q^91 + 58 * q^92 + 139 * q^93 + 37 * q^94 + 39 * q^95 + 66 * q^96 + 136 * q^97 + 7 * q^98 - 143 * 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 $

$2$	−2.25579	−1.59508	−0.797541	−	0.603265i	$-0.793866\pi$
$2$	−2.25579	−1.59508	−0.797541	+	0.603265i	$0.793866\pi$
$3$	−2.77556	−1.60247	−0.801235	−	0.598350i	$-0.795823\pi$
$3$	−2.77556	−1.60247	−0.801235	+	0.598350i	$0.795823\pi$
$4$	3.08857	1.54428
$5$	0.288075	0.128831	0.0644156	−	0.997923i	$-0.479482\pi$
$5$	0.288075	0.128831	0.0644156	+	0.997923i	$0.479482\pi$
$6$	6.26106	2.55607
$7$	1.78637	0.675185	0.337593	−	0.941292i	$-0.390387\pi$
$7$	1.78637	0.675185	0.337593	+	0.941292i	$0.390387\pi$
$8$	−2.45557	−0.868177
$9$	4.70373	1.56791
$10$	−0.649836	−0.205496
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−8.57250	−2.47467
$13$	5.07395	1.40726	0.703630	−	0.710567i	$-0.251561\pi$
$13$	5.07395	1.40726	0.703630	+	0.710567i	$0.251561\pi$
$14$	−4.02967	−1.07698
$15$	−0.799570	−0.206448
$16$	−0.637886	−0.159471
$17$	−2.51700	−0.610461	−0.305231	−	0.952278i	$-0.598734\pi$
$17$	−2.51700	−0.610461	−0.305231	+	0.952278i	$0.598734\pi$
$18$	−10.6106	−2.50094
$19$	−2.44919	−0.561883	−0.280941	−	0.959725i	$-0.590647\pi$
$19$	−2.44919	−0.561883	−0.280941	+	0.959725i	$0.590647\pi$
$20$	0.889740	0.198952
$21$	−4.95818	−1.08196
$22$	2.25579	0.480935
$23$	−7.23846	−1.50932	−0.754661	−	0.656114i	$-0.772199\pi$
$23$	−7.23846	−1.50932	−0.754661	+	0.656114i	$0.772199\pi$
$24$	6.81559	1.39123
$25$	−4.91701	−0.983403
$26$	−11.4457	−2.24469
$27$	−4.72879	−0.910057
$28$	5.51733	1.04268
$29$	−7.48543	−1.39001	−0.695005	−	0.719005i	$-0.744598\pi$
$29$	−7.48543	−1.39001	−0.695005	+	0.719005i	$0.744598\pi$
$30$	1.80366	0.329301
$31$	−3.19569	−0.573962	−0.286981	−	0.957936i	$-0.592652\pi$
$31$	−3.19569	−0.573962	−0.286981	+	0.957936i	$0.592652\pi$
$32$	6.35008	1.12255
$33$	2.77556	0.483163
$34$	5.67780	0.973735
$35$	0.514610	0.0869849
$36$	14.5278	2.42130
$37$	−11.0014	−1.80862	−0.904309	−	0.426879i	$-0.859613\pi$
$37$	−11.0014	−1.80862	−0.904309	+	0.426879i	$0.859613\pi$
$38$	5.52485	0.896249
$39$	−14.0830	−2.25509
$40$	−0.707390	−0.111848
$41$	9.46750	1.47857	0.739287	−	0.673390i	$-0.235163\pi$
$41$	9.46750	1.47857	0.739287	+	0.673390i	$0.235163\pi$
$42$	11.1846	1.72582
$43$	7.61735	1.16164	0.580818	−	0.814034i	$-0.302733\pi$
$43$	7.61735	1.16164	0.580818	+	0.814034i	$0.302733\pi$
$44$	−3.08857	−0.465619
$45$	1.35503	0.201996
$46$	16.3284	2.40749
$47$	−9.12690	−1.33130	−0.665648	−	0.746266i	$-0.731845\pi$
$47$	−9.12690	−1.33130	−0.665648	+	0.746266i	$0.731845\pi$
$48$	1.77049	0.255548
$49$	−3.80887	−0.544125
$50$	11.0917	1.56861
$51$	6.98607	0.978246
$52$	15.6712	2.17321
$53$	−8.32897	−1.14407	−0.572036	−	0.820228i	$-0.693846\pi$
$53$	−8.32897	−1.14407	−0.572036	+	0.820228i	$0.693846\pi$
$54$	10.6671	1.45161
$55$	−0.288075	−0.0388441
$56$	−4.38657	−0.586180
$57$	6.79787	0.900400
$58$	16.8855	2.21718
$59$	3.22138	0.419388	0.209694	−	0.977767i	$-0.432753\pi$
$59$	3.22138	0.419388	0.209694	+	0.977767i	$0.432753\pi$
$60$	−2.46953	−0.318814
$61$	10.1317	1.29724	0.648618	−	0.761114i	$-0.275347\pi$
$61$	10.1317	1.29724	0.648618	+	0.761114i	$0.275347\pi$
$62$	7.20878	0.915516
$63$	8.40261	1.05863
$64$	−13.0487	−1.63108
$65$	1.46168	0.181299
$66$	−6.26106	−0.770684
$67$	15.3378	1.87381	0.936905	−	0.349583i	$-0.113677\pi$
$67$	15.3378	1.87381	0.936905	+	0.349583i	$0.113677\pi$
$68$	−7.77391	−0.942726
$69$	20.0908	2.41864
$70$	−1.16085	−0.138748
$71$	−4.64867	−0.551696	−0.275848	−	0.961201i	$-0.588959\pi$
$71$	−4.64867	−0.551696	−0.275848	+	0.961201i	$0.588959\pi$
$72$	−11.5504	−1.36122
$73$	−11.1549	−1.30558	−0.652789	−	0.757540i	$-0.726401\pi$
$73$	−11.1549	−1.30558	−0.652789	+	0.757540i	$0.726401\pi$
$74$	24.8168	2.88489
$75$	13.6475	1.57587
$76$	−7.56449	−0.867707
$77$	−1.78637	−0.203576
$78$	31.7683	3.59705
$79$	−0.0153161	−0.00172320	−0.000861599	−	1.00000i	$-0.500274\pi$
$79$	−0.0153161	−0.00172320	−0.000861599		1.00000i	$0.500274\pi$
$80$	−0.183759	−0.0205449
$81$	−0.986136	−0.109571
$82$	−21.3566	−2.35845
$83$	1.08217	0.118784	0.0593918	−	0.998235i	$-0.481084\pi$
$83$	1.08217	0.118784	0.0593918	+	0.998235i	$0.481084\pi$
$84$	−15.3137	−1.67086
$85$	−0.725085	−0.0786465
$86$	−17.1831	−1.85290
$87$	20.7763	2.22745
$88$	2.45557	0.261765
$89$	−14.0979	−1.49438	−0.747188	−	0.664612i	$-0.768597\pi$
$89$	−14.0979	−1.49438	−0.747188	+	0.664612i	$0.768597\pi$
$90$	−3.05665	−0.322199
$91$	9.06396	0.950161
$92$	−22.3565	−2.33082
$93$	8.86982	0.919757
$94$	20.5883	2.12352
$95$	−0.705551	−0.0723880
$96$	−17.6250	−1.79885
$97$	−8.81029	−0.894549	−0.447275	−	0.894397i	$-0.647605\pi$
$97$	−8.81029	−0.894549	−0.447275	+	0.894397i	$0.647605\pi$
$98$	8.59200	0.867923
$99$	−4.70373	−0.472742
$100$	−15.1865	−1.51865
$101$	−3.04863	−0.303350	−0.151675	−	0.988430i	$-0.548467\pi$
$101$	−3.04863	−0.303350	−0.151675	+	0.988430i	$0.548467\pi$
$102$	−15.7591	−1.56038
$103$	2.82491	0.278347	0.139173	−	0.990268i	$-0.455555\pi$
$103$	2.82491	0.278347	0.139173	+	0.990268i	$0.455555\pi$
$104$	−12.4595	−1.22175
$105$	−1.42833	−0.139391
$106$	18.7884	1.82489
$107$	3.00220	0.290234	0.145117	−	0.989415i	$-0.453644\pi$
$107$	3.00220	0.290234	0.145117	+	0.989415i	$0.453644\pi$
$108$	−14.6052	−1.40539
$109$	9.08395	0.870085	0.435043	−	0.900410i	$-0.356733\pi$
$109$	9.08395	0.870085	0.435043	+	0.900410i	$0.356733\pi$
$110$	0.649836	0.0619594
$111$	30.5350	2.89825
$112$	−1.13950	−0.107673
$113$	10.0100	0.941665	0.470832	−	0.882223i	$-0.343954\pi$
$113$	10.0100	0.941665	0.470832	+	0.882223i	$0.343954\pi$
$114$	−15.3345	−1.43621
$115$	−2.08522	−0.194448
$116$	−23.1193	−2.14657
$117$	23.8665	2.20645
$118$	−7.26675	−0.668958
$119$	−4.49629	−0.412175
$120$	1.96340	0.179233
$121$	1.00000	0.0909091
$122$	−22.8550	−2.06920
$123$	−26.2776	−2.36937
$124$	−9.87009	−0.886361
$125$	−2.85685	−0.255524
$126$	−18.9545	−1.68860
$127$	20.5104	1.82001	0.910004	−	0.414600i	$-0.136078\pi$
$127$	20.5104	1.82001	0.910004	+	0.414600i	$0.136078\pi$
$128$	16.7348	1.47916
$129$	−21.1424	−1.86149
$130$	−3.29723	−0.289186
$131$	11.4704	1.00217	0.501087	−	0.865397i	$-0.332934\pi$
$131$	11.4704	1.00217	0.501087	+	0.865397i	$0.332934\pi$
$132$	8.57250	0.746140
$133$	−4.37517	−0.379375
$134$	−34.5988	−2.98888
$135$	−1.36225	−0.117244
$136$	6.18067	0.529988
$137$	17.2674	1.47525	0.737625	−	0.675211i	$-0.235947\pi$
$137$	17.2674	1.47525	0.737625	+	0.675211i	$0.235947\pi$
$138$	−45.3205	−3.85793
$139$	1.71425	0.145401	0.0727005	−	0.997354i	$-0.476838\pi$
$139$	1.71425	0.145401	0.0727005	+	0.997354i	$0.476838\pi$
$140$	1.58941	0.134329
$141$	25.3322	2.13336
$142$	10.4864	0.879999
$143$	−5.07395	−0.424305
$144$	−3.00044	−0.250037
$145$	−2.15637	−0.179077
$146$	25.1630	2.08250
$147$	10.5718	0.871943
$148$	−33.9785	−2.79302
$149$	−7.57899	−0.620895	−0.310448	−	0.950591i	$-0.600479\pi$
$149$	−7.57899	−0.620895	−0.310448	+	0.950591i	$0.600479\pi$
$150$	−30.7857	−2.51364
$151$	−6.95030	−0.565607	−0.282804	−	0.959178i	$-0.591264\pi$
$151$	−6.95030	−0.565607	−0.282804	+	0.959178i	$0.591264\pi$
$152$	6.01417	0.487814
$153$	−11.8393	−0.957148
$154$	4.02967	0.324720
$155$	−0.920598	−0.0739442
$156$	−43.4964	−3.48250
$157$	11.9607	0.954570	0.477285	−	0.878748i	$-0.341621\pi$
$157$	11.9607	0.954570	0.477285	+	0.878748i	$0.341621\pi$
$158$	0.0345499	0.00274864
$159$	23.1176	1.83334
$160$	1.82930	0.144619
$161$	−12.9306	−1.01907
$162$	2.22451	0.174774
$163$	6.51570	0.510349	0.255175	−	0.966895i	$-0.417867\pi$
$163$	6.51570	0.510349	0.255175	+	0.966895i	$0.417867\pi$
$164$	29.2410	2.28334
$165$	0.799570	0.0622464
$166$	−2.44114	−0.189470
$167$	−7.28437	−0.563682	−0.281841	−	0.959461i	$-0.590945\pi$
$167$	−7.28437	−0.563682	−0.281841	+	0.959461i	$0.590945\pi$
$168$	12.1752	0.939336
$169$	12.7449	0.980379
$170$	1.63564	0.125447
$171$	−11.5203	−0.880981
$172$	23.5267	1.79390
$173$	−26.2169	−1.99324	−0.996618	−	0.0821761i	$-0.973813\pi$
$173$	−26.2169	−1.99324	−0.996618	+	0.0821761i	$0.973813\pi$
$174$	−46.8668	−3.55296
$175$	−8.78362	−0.663979
$176$	0.637886	0.0480824
$177$	−8.94114	−0.672057
$178$	31.8019	2.38365
$179$	−3.05232	−0.228141	−0.114071	−	0.993473i	$-0.536389\pi$
$179$	−3.05232	−0.228141	−0.114071	+	0.993473i	$0.536389\pi$
$180$	4.18509	0.311938
$181$	−14.3626	−1.06756	−0.533781	−	0.845623i	$-0.679229\pi$
$181$	−14.3626	−1.06756	−0.533781	+	0.845623i	$0.679229\pi$
$182$	−20.4463	−1.51558
$183$	−28.1212	−2.07878
$184$	17.7746	1.31036
$185$	−3.16923	−0.233006
$186$	−20.0084	−1.46709
$187$	2.51700	0.184061
$188$	−28.1890	−2.05590
$189$	−8.44739	−0.614457
$190$	1.59157	0.115465
$191$	6.83561	0.494608	0.247304	−	0.968938i	$-0.420455\pi$
$191$	6.83561	0.494608	0.247304	+	0.968938i	$0.420455\pi$
$192$	36.2173	2.61376
$193$	23.1093	1.66345	0.831723	−	0.555191i	$-0.187355\pi$
$193$	23.1093	1.66345	0.831723	+	0.555191i	$0.187355\pi$
$194$	19.8741	1.42688
$195$	−4.05697	−0.290526
$196$	−11.7640	−0.840283
$197$	3.43700	0.244876	0.122438	−	0.992476i	$-0.460929\pi$
$197$	3.43700	0.244876	0.122438	+	0.992476i	$0.460929\pi$
$198$	10.6106	0.754062
$199$	−9.64110	−0.683439	−0.341720	−	0.939802i	$-0.611009\pi$
$199$	−9.64110	−0.683439	−0.341720	+	0.939802i	$0.611009\pi$
$200$	12.0741	0.853767
$201$	−42.5710	−3.00272
$202$	6.87704	0.483867
$203$	−13.3718	−0.938515
$204$	21.5770	1.51069
$205$	2.72735	0.190486
$206$	−6.37239	−0.443986
$207$	−34.0477	−2.36648
$208$	−3.23660	−0.224418
$209$	2.44919	0.169414
$210$	3.22201	0.222339
$211$	−0.611647	−0.0421075	−0.0210537	−	0.999778i	$-0.506702\pi$
$211$	−0.611647	−0.0421075	−0.0210537	+	0.999778i	$0.506702\pi$
$212$	−25.7246	−1.76677
$213$	12.9027	0.884076
$214$	−6.77232	−0.462947
$215$	2.19437	0.149655
$216$	11.6119	0.790090
$217$	−5.70869	−0.387531
$218$	−20.4915	−1.38786
$219$	30.9610	2.09215
$220$	−0.889740	−0.0599863
$221$	−12.7711	−0.859078
$222$	−68.8804	−4.62295
$223$	28.3451	1.89813	0.949064	−	0.315083i	$-0.102032\pi$
$223$	28.3451	1.89813	0.949064	+	0.315083i	$0.102032\pi$
$224$	11.3436	0.757927
$225$	−23.1283	−1.54189
$226$	−22.5805	−1.50203
$227$	12.0971	0.802914	0.401457	−	0.915878i	$-0.368504\pi$
$227$	12.0971	0.802914	0.401457	+	0.915878i	$0.368504\pi$
$228$	20.9957	1.39047
$229$	−9.03285	−0.596908	−0.298454	−	0.954424i	$-0.596471\pi$
$229$	−9.03285	−0.596908	−0.298454	+	0.954424i	$0.596471\pi$
$230$	4.70381	0.310160
$231$	4.95818	0.326224
$232$	18.3810	1.20677
$233$	−8.87297	−0.581288	−0.290644	−	0.956831i	$-0.593869\pi$
$233$	−8.87297	−0.581288	−0.290644	+	0.956831i	$0.593869\pi$
$234$	−53.8376	−3.51947
$235$	−2.62923	−0.171512
$236$	9.94946	0.647655
$237$	0.0425108	0.00276137
$238$	10.1427	0.657452
$239$	1.01325	0.0655414	0.0327707	−	0.999463i	$-0.489567\pi$
$239$	1.01325	0.0655414	0.0327707	+	0.999463i	$0.489567\pi$
$240$	0.510034	0.0329226
$241$	10.8492	0.698860	0.349430	−	0.936962i	$-0.386375\pi$
$241$	10.8492	0.698860	0.349430	+	0.936962i	$0.386375\pi$
$242$	−2.25579	−0.145007
$243$	16.9235	1.08564
$244$	31.2925	2.00330
$245$	−1.09724	−0.0701002
$246$	59.2766	3.77934
$247$	−12.4271	−0.790715
$248$	7.84725	0.498301
$249$	−3.00363	−0.190347
$250$	6.44443	0.407582
$251$	−19.2506	−1.21509	−0.607544	−	0.794286i	$-0.707845\pi$
$251$	−19.2506	−1.21509	−0.607544	+	0.794286i	$0.707845\pi$
$252$	25.9520	1.63482
$253$	7.23846	0.455078
$254$	−46.2672	−2.90306
$255$	2.01251	0.126029
$256$	−11.6528	−0.728300
$257$	−7.91006	−0.493416	−0.246708	−	0.969090i	$-0.579349\pi$
$257$	−7.91006	−0.493416	−0.246708	+	0.969090i	$0.579349\pi$
$258$	47.6927	2.96922
$259$	−19.6526	−1.22115
$260$	4.51449	0.279977
$261$	−35.2094	−2.17941
$262$	−25.8748	−1.59855
$263$	11.4691	0.707212	0.353606	−	0.935394i	$-0.384955\pi$
$263$	11.4691	0.707212	0.353606	+	0.935394i	$0.384955\pi$
$264$	−6.81559	−0.419471
$265$	−2.39937	−0.147392
$266$	9.86944	0.605134
$267$	39.1296	2.39469
$268$	47.3718	2.89370
$269$	−12.8929	−0.786092	−0.393046	−	0.919519i	$-0.628579\pi$
$269$	−12.8929	−0.786092	−0.393046	+	0.919519i	$0.628579\pi$
$270$	3.07294	0.187013
$271$	−12.8690	−0.781736	−0.390868	−	0.920447i	$-0.627825\pi$
$271$	−12.8690	−0.781736	−0.390868	+	0.920447i	$0.627825\pi$
$272$	1.60556	0.0973511
$273$	−25.1575	−1.52260
$274$	−38.9514	−2.35314
$275$	4.91701	0.296507
$276$	62.0517	3.73507
$277$	−22.1645	−1.33174	−0.665869	−	0.746069i	$-0.731939\pi$
$277$	−22.1645	−1.33174	−0.665869	+	0.746069i	$0.731939\pi$
$278$	−3.86699	−0.231926
$279$	−15.0316	−0.899920
$280$	−1.26366	−0.0755183
$281$	7.94582	0.474008	0.237004	−	0.971509i	$-0.423835\pi$
$281$	7.94582	0.474008	0.237004	+	0.971509i	$0.423835\pi$
$282$	−57.1441	−3.40288
$283$	10.1913	0.605810	0.302905	−	0.953021i	$-0.402043\pi$
$283$	10.1913	0.605810	0.302905	+	0.953021i	$0.402043\pi$
$284$	−14.3577	−0.851975
$285$	1.95830	0.116000
$286$	11.4457	0.676800
$287$	16.9125	0.998312
$288$	29.8691	1.76005
$289$	−10.6647	−0.627337
$290$	4.86430	0.285642
$291$	24.4535	1.43349
$292$	−34.4525	−2.01618
$293$	2.36782	0.138329	0.0691647	−	0.997605i	$-0.477967\pi$
$293$	2.36782	0.138329	0.0691647	+	0.997605i	$0.477967\pi$
$294$	−23.8476	−1.39082
$295$	0.928001	0.0540303
$296$	27.0147	1.57020
$297$	4.72879	0.274392
$298$	17.0966	0.990378
$299$	−36.7275	−2.12401
$300$	42.1511	2.43359
$301$	13.6074	0.784319
$302$	15.6784	0.902189
$303$	8.46164	0.486108
$304$	1.56230	0.0896042
$305$	2.91870	0.167124
$306$	26.7068	1.52673
$307$	19.9300	1.13747	0.568734	−	0.822522i	$-0.307433\pi$
$307$	19.9300	1.13747	0.568734	+	0.822522i	$0.307433\pi$
$308$	−5.51733	−0.314379
$309$	−7.84070	−0.446042
$310$	2.07667	0.117947
$311$	27.0353	1.53303	0.766515	−	0.642227i	$-0.221989\pi$
$311$	27.0353	1.53303	0.766515	+	0.642227i	$0.221989\pi$
$312$	34.5819	1.95782
$313$	−3.88262	−0.219459	−0.109729	−	0.993961i	$-0.534998\pi$
$313$	−3.88262	−0.219459	−0.109729	+	0.993961i	$0.534998\pi$
$314$	−26.9808	−1.52262
$315$	2.42058	0.136384
$316$	−0.0473049	−0.00266111
$317$	15.5513	0.873449	0.436724	−	0.899595i	$-0.356139\pi$
$317$	15.5513	0.873449	0.436724	+	0.899595i	$0.356139\pi$
$318$	−52.1482	−2.92433
$319$	7.48543	0.419104
$320$	−3.75899	−0.210134
$321$	−8.33279	−0.465091
$322$	29.1686	1.62550
$323$	6.16460	0.343008
$324$	−3.04575	−0.169208
$325$	−24.9487	−1.38390
$326$	−14.6980	−0.814048
$327$	−25.2131	−1.39428
$328$	−23.2481	−1.28366
$329$	−16.3040	−0.898871
$330$	−1.80366	−0.0992881
$331$	−33.7134	−1.85305	−0.926527	−	0.376228i	$-0.877221\pi$
$331$	−33.7134	−1.85305	−0.926527	+	0.376228i	$0.877221\pi$
$332$	3.34236	0.183436
$333$	−51.7475	−2.83575
$334$	16.4320	0.899118
$335$	4.41844	0.241405
$336$	3.16275	0.172542
$337$	9.27816	0.505414	0.252707	−	0.967543i	$-0.418679\pi$
$337$	9.27816	0.505414	0.252707	+	0.967543i	$0.418679\pi$
$338$	−28.7498	−1.56378
$339$	−27.7834	−1.50899
$340$	−2.23947	−0.121452
$341$	3.19569	0.173056
$342$	25.9874	1.40524
$343$	−19.3087	−1.04257
$344$	−18.7050	−1.00851
$345$	5.78765	0.311597
$346$	59.1397	3.17937
$347$	22.4488	1.20512	0.602558	−	0.798075i	$-0.294148\pi$
$347$	22.4488	1.20512	0.602558	+	0.798075i	$0.294148\pi$
$348$	64.1689	3.43981
$349$	24.4644	1.30955	0.654773	−	0.755825i	$-0.272764\pi$
$349$	24.4644	1.30955	0.654773	+	0.755825i	$0.272764\pi$
$350$	19.8140	1.05910
$351$	−23.9936	−1.28069
$352$	−6.35008	−0.338461
$353$	−19.1090	−1.01707	−0.508534	−	0.861042i	$-0.669812\pi$
$353$	−19.1090	−1.01707	−0.508534	+	0.861042i	$0.669812\pi$
$354$	20.1693	1.07199
$355$	−1.33917	−0.0710756
$356$	−43.5424	−2.30774
$357$	12.4797	0.660497
$358$	6.88539	0.363904
$359$	21.1199	1.11467	0.557333	−	0.830289i	$-0.311825\pi$
$359$	21.1199	1.11467	0.557333	+	0.830289i	$0.311825\pi$
$360$	−3.32737	−0.175368
$361$	−13.0015	−0.684288
$362$	32.3989	1.70285
$363$	−2.77556	−0.145679
$364$	27.9946	1.46732
$365$	−3.21344	−0.168199
$366$	63.4354	3.31582
$367$	10.5128	0.548764	0.274382	−	0.961621i	$-0.411527\pi$
$367$	10.5128	0.548764	0.274382	+	0.961621i	$0.411527\pi$
$368$	4.61731	0.240694
$369$	44.5325	2.31827
$370$	7.14910	0.371664
$371$	−14.8787	−0.772461
$372$	27.3950	1.42037
$373$	18.8868	0.977922	0.488961	−	0.872306i	$-0.337376\pi$
$373$	18.8868	0.977922	0.488961	+	0.872306i	$0.337376\pi$
$374$	−5.67780	−0.293592
$375$	7.92934	0.409470
$376$	22.4118	1.15580
$377$	−37.9807	−1.95610
$378$	19.0555	0.980109
$379$	3.07004	0.157698	0.0788488	−	0.996887i	$-0.474876\pi$
$379$	3.07004	0.157698	0.0788488	+	0.996887i	$0.474876\pi$
$380$	−2.17914	−0.111788
$381$	−56.9279	−2.91651
$382$	−15.4197	−0.788939
$383$	−5.52189	−0.282155	−0.141078	−	0.989999i	$-0.545057\pi$
$383$	−5.52189	−0.282155	−0.141078	+	0.989999i	$0.545057\pi$
$384$	−46.4484	−2.37031
$385$	−0.514610	−0.0262269
$386$	−52.1297	−2.65333
$387$	35.8300	1.82134
$388$	−27.2112	−1.38144
$389$	−24.8161	−1.25823	−0.629113	−	0.777314i	$-0.716582\pi$
$389$	−24.8161	−1.25823	−0.629113	+	0.777314i	$0.716582\pi$
$390$	9.15166	0.463412
$391$	18.2192	0.921383
$392$	9.35297	0.472396
$393$	−31.8368	−1.60595
$394$	−7.75314	−0.390598
$395$	−0.00441220	−0.000222002 0
$396$	−14.5278	−0.730048
$397$	3.47733	0.174522	0.0872611	−	0.996185i	$-0.472189\pi$
$397$	3.47733	0.174522	0.0872611	+	0.996185i	$0.472189\pi$
$398$	21.7482	1.09014
$399$	12.1435	0.607937
$400$	3.13649	0.156825
$401$	24.6427	1.23060	0.615300	−	0.788293i	$-0.289035\pi$
$401$	24.6427	1.23060	0.615300	+	0.788293i	$0.289035\pi$
$402$	96.0310	4.78959
$403$	−16.2147	−0.807714
$404$	−9.41588	−0.468458
$405$	−0.284082	−0.0141161
$406$	30.1639	1.49701
$407$	11.0014	0.545319
$408$	−17.1548	−0.849290
$409$	0.657742	0.0325233	0.0162616	−	0.999868i	$-0.494824\pi$
$409$	0.657742	0.0325233	0.0162616	+	0.999868i	$0.494824\pi$
$410$	−6.15232	−0.303841
$411$	−47.9265	−2.36404
$412$	8.72493	0.429846
$413$	5.75459	0.283165
$414$	76.8044	3.77473
$415$	0.311747	0.0153030
$416$	32.2200	1.57971
$417$	−4.75801	−0.233001
$418$	−5.52485	−0.270229
$419$	−13.2258	−0.646120	−0.323060	−	0.946378i	$-0.604712\pi$
$419$	−13.2258	−0.646120	−0.323060	+	0.946378i	$0.604712\pi$
$420$	−4.41149	−0.215259
$421$	13.4481	0.655419	0.327709	−	0.944779i	$-0.393723\pi$
$421$	13.4481	0.655419	0.327709	+	0.944779i	$0.393723\pi$
$422$	1.37974	0.0671649
$423$	−42.9304	−2.08735
$424$	20.4524	0.993257
$425$	12.3761	0.600329
$426$	−29.1056	−1.41017
$427$	18.0990	0.875874
$428$	9.27250	0.448203
$429$	14.0830	0.679935
$430$	−4.95003	−0.238712
$431$	−1.75557	−0.0845629	−0.0422815	−	0.999106i	$-0.513463\pi$
$431$	−1.75557	−0.0845629	−0.0422815	+	0.999106i	$0.513463\pi$
$432$	3.01643	0.145128
$433$	13.8354	0.664885	0.332443	−	0.943123i	$-0.392127\pi$
$433$	13.8354	0.664885	0.332443	+	0.943123i	$0.392127\pi$
$434$	12.8776	0.618143
$435$	5.98513	0.286965
$436$	28.0564	1.34366
$437$	17.7284	0.848063
$438$	−69.8413	−3.33715
$439$	22.1007	1.05481	0.527404	−	0.849615i	$-0.323165\pi$
$439$	22.1007	1.05481	0.527404	+	0.849615i	$0.323165\pi$
$440$	0.707390	0.0337235
$441$	−17.9159	−0.853138
$442$	28.8089	1.37030
$443$	33.1485	1.57493	0.787467	−	0.616357i	$-0.211392\pi$
$443$	33.1485	1.57493	0.787467	+	0.616357i	$0.211392\pi$
$444$	94.3094	4.47573
$445$	−4.06126	−0.192522
$446$	−63.9405	−3.02767
$447$	21.0359	0.994966
$448$	−23.3098	−1.10128
$449$	−9.06740	−0.427917	−0.213959	−	0.976843i	$-0.568636\pi$
$449$	−9.06740	−0.427917	−0.213959	+	0.976843i	$0.568636\pi$
$450$	52.1724	2.45943
$451$	−9.46750	−0.445807
$452$	30.9167	1.45420
$453$	19.2910	0.906368
$454$	−27.2885	−1.28071
$455$	2.61110	0.122410
$456$	−16.6927	−0.781706
$457$	4.27152	0.199813	0.0999067	−	0.994997i	$-0.468146\pi$
$457$	4.27152	0.199813	0.0999067	+	0.994997i	$0.468146\pi$
$458$	20.3762	0.952116
$459$	11.9024	0.555554
$460$	−6.44034	−0.300283
$461$	8.05656	0.375231	0.187616	−	0.982243i	$-0.439924\pi$
$461$	8.05656	0.375231	0.187616	+	0.982243i	$0.439924\pi$
$462$	−11.1846	−0.520354
$463$	27.1442	1.26150	0.630748	−	0.775988i	$-0.282748\pi$
$463$	27.1442	1.26150	0.630748	+	0.775988i	$0.282748\pi$
$464$	4.77485	0.221667
$465$	2.55517	0.118493
$466$	20.0155	0.927201
$467$	−4.10416	−0.189918	−0.0949589	−	0.995481i	$-0.530272\pi$
$467$	−4.10416	−0.189918	−0.0949589	+	0.995481i	$0.530272\pi$
$468$	73.7132	3.40739
$469$	27.3990	1.26517
$470$	5.93099	0.273576
$471$	−33.1977	−1.52967
$472$	−7.91035	−0.364103
$473$	−7.61735	−0.350246
$474$	−0.0958952	−0.00440461
$475$	12.0427	0.552557
$476$	−13.8871	−0.636515
$477$	−39.1772	−1.79380
$478$	−2.28566	−0.104544
$479$	27.6482	1.26328	0.631638	−	0.775263i	$-0.282383\pi$
$479$	27.6482	1.26328	0.631638	+	0.775263i	$0.282383\pi$
$480$	−5.07733	−0.231748
$481$	−55.8205	−2.54519
$482$	−24.4735	−1.11474
$483$	35.8896	1.63303
$484$	3.08857	0.140389
$485$	−2.53803	−0.115246
$486$	−38.1757	−1.73168
$487$	9.87200	0.447343	0.223671	−	0.974665i	$-0.428196\pi$
$487$	9.87200	0.447343	0.223671	+	0.974665i	$0.428196\pi$
$488$	−24.8792	−1.12623
$489$	−18.0847	−0.817819
$490$	2.47514	0.111816
$491$	−15.5527	−0.701884	−0.350942	−	0.936397i	$-0.614139\pi$
$491$	−15.5527	−0.701884	−0.350942	+	0.936397i	$0.614139\pi$
$492$	−81.1601	−3.65898
$493$	18.8408	0.848548
$494$	28.0328	1.26125
$495$	−1.35503	−0.0609039
$496$	2.03848	0.0915306
$497$	−8.30426	−0.372497
$498$	6.77554	0.303619
$499$	2.85994	0.128029	0.0640143	−	0.997949i	$-0.479610\pi$
$499$	2.85994	0.128029	0.0640143	+	0.997949i	$0.479610\pi$
$500$	−8.82356	−0.394602
$501$	20.2182	0.903283
$502$	43.4252	1.93816
$503$	12.6095	0.562230	0.281115	−	0.959674i	$-0.409296\pi$
$503$	12.6095	0.562230	0.281115	+	0.959674i	$0.409296\pi$
$504$	−20.6332	−0.919077
$505$	−0.878233	−0.0390809
$506$	−16.3284	−0.725886
$507$	−35.3743	−1.57103
$508$	63.3479	2.81061
$509$	−35.0444	−1.55331	−0.776657	−	0.629924i	$-0.783086\pi$
$509$	−35.0444	−1.55331	−0.776657	+	0.629924i	$0.783086\pi$
$510$	−4.53980	−0.201026
$511$	−19.9267	−0.881507
$512$	−7.18338	−0.317463
$513$	11.5817	0.511345
$514$	17.8434	0.787039
$515$	0.813787	0.0358597
$516$	−65.2998	−2.87466
$517$	9.12690	0.401401
$518$	44.3320	1.94784
$519$	72.7666	3.19410
$520$	−3.58926	−0.157399
$521$	21.9940	0.963576	0.481788	−	0.876288i	$-0.339987\pi$
$521$	21.9940	0.963576	0.481788	+	0.876288i	$0.339987\pi$
$522$	79.4249	3.47633
$523$	−7.76336	−0.339468	−0.169734	−	0.985490i	$-0.554291\pi$
$523$	−7.76336	−0.339468	−0.169734	+	0.985490i	$0.554291\pi$
$524$	35.4271	1.54764
$525$	24.3794	1.06401
$526$	−25.8717	−1.12806
$527$	8.04353	0.350382
$528$	−1.77049	−0.0770506
$529$	29.3953	1.27806
$530$	5.41247	0.235103
$531$	15.1525	0.657563
$532$	−13.5130	−0.585863
$533$	48.0376	2.08074
$534$	−88.2680	−3.81973
$535$	0.864860	0.0373912
$536$	−37.6631	−1.62680
$537$	8.47190	0.365590
$538$	29.0836	1.25388
$539$	3.80887	0.164060
$540$	−4.20740	−0.181057
$541$	3.16004	0.135861	0.0679303	−	0.997690i	$-0.478360\pi$
$541$	3.16004	0.135861	0.0679303	+	0.997690i	$0.478360\pi$
$542$	29.0297	1.24693
$543$	39.8642	1.71074
$544$	−15.9831	−0.685271
$545$	2.61686	0.112094
$546$	56.7500	2.42868
$547$	1.00000	0.0427569
$547$	1.00000	0.0427569
$548$	53.3314	2.27820
$549$	47.6569	2.03395
$550$	−11.0917	−0.472953
$551$	18.3333	0.781023
$552$	−49.3344	−2.09981
$553$	−0.0273603	−0.00116348
$554$	49.9984	2.12423
$555$	8.79638	0.373385
$556$	5.29459	0.224540
$557$	−9.88589	−0.418879	−0.209439	−	0.977822i	$-0.567164\pi$
$557$	−9.88589	−0.418879	−0.209439	+	0.977822i	$0.567164\pi$
$558$	33.9081	1.43545
$559$	38.6500	1.63472
$560$	−0.328262	−0.0138716
$561$	−6.98607	−0.294952
$562$	−17.9241	−0.756081
$563$	32.8492	1.38443	0.692214	−	0.721692i	$-0.256635\pi$
$563$	32.8492	1.38443	0.692214	+	0.721692i	$0.256635\pi$
$564$	78.2404	3.29451
$565$	2.88364	0.121316
$566$	−22.9894	−0.966316
$567$	−1.76161	−0.0739805
$568$	11.4152	0.478969
$569$	−11.0057	−0.461384	−0.230692	−	0.973027i	$-0.574099\pi$
$569$	−11.0057	−0.461384	−0.230692	+	0.973027i	$0.574099\pi$
$570$	−4.41750	−0.185029
$571$	−17.5138	−0.732930	−0.366465	−	0.930432i	$-0.619432\pi$
$571$	−17.5138	−0.732930	−0.366465	+	0.930432i	$0.619432\pi$
$572$	−15.6712	−0.655247
$573$	−18.9726	−0.792594
$574$	−38.1509	−1.59239
$575$	35.5916	1.48427
$576$	−61.3773	−2.55739
$577$	47.2193	1.96576	0.982882	−	0.184236i	$-0.0589812\pi$
$577$	47.2193	1.96576	0.982882	+	0.184236i	$0.0589812\pi$
$578$	24.0573	1.00065
$579$	−64.1413	−2.66562
$580$	−6.66009	−0.276545
$581$	1.93316	0.0802010
$582$	−55.1618	−2.28653
$583$	8.32897	0.344951
$584$	27.3916	1.13347
$585$	6.87534	0.284260
$586$	−5.34129	−0.220647
$587$	−28.5617	−1.17887	−0.589433	−	0.807817i	$-0.700649\pi$
$587$	−28.5617	−1.17887	−0.589433	+	0.807817i	$0.700649\pi$
$588$	32.6516	1.34653
$589$	7.82684	0.322500
$590$	−2.09337	−0.0861827
$591$	−9.53960	−0.392407
$592$	7.01763	0.288423
$593$	35.0155	1.43791	0.718957	−	0.695054i	$-0.244620\pi$
$593$	35.0155	1.43791	0.718957	+	0.695054i	$0.244620\pi$
$594$	−10.6671	−0.437678
$595$	−1.29527	−0.0531009
$596$	−23.4082	−0.958838
$597$	26.7594	1.09519
$598$	82.8495	3.38797
$599$	−17.4246	−0.711950	−0.355975	−	0.934495i	$-0.615851\pi$
$599$	−17.4246	−0.711950	−0.355975	+	0.934495i	$0.615851\pi$
$600$	−33.5124	−1.36814
$601$	33.5374	1.36802	0.684010	−	0.729472i	$-0.260234\pi$
$601$	33.5374	1.36802	0.684010	+	0.729472i	$0.260234\pi$
$602$	−30.6954	−1.25105
$603$	72.1448	2.93796
$604$	−21.4665	−0.873458
$605$	0.288075	0.0117119
$606$	−19.0876	−0.775382
$607$	−4.68848	−0.190300	−0.0951498	−	0.995463i	$-0.530333\pi$
$607$	−4.68848	−0.190300	−0.0951498	+	0.995463i	$0.530333\pi$
$608$	−15.5526	−0.630740
$609$	37.1141	1.50394
$610$	−6.58396	−0.266577
$611$	−46.3094	−1.87348
$612$	−36.5664	−1.47811
$613$	19.2799	0.778708	0.389354	−	0.921088i	$-0.372698\pi$
$613$	19.2799	0.778708	0.389354	+	0.921088i	$0.372698\pi$
$614$	−44.9579	−1.81435
$615$	−7.56992	−0.305249
$616$	4.38657	0.176740
$617$	5.77895	0.232652	0.116326	−	0.993211i	$-0.462888\pi$
$617$	5.77895	0.232652	0.116326	+	0.993211i	$0.462888\pi$
$618$	17.6869	0.711473
$619$	−36.3348	−1.46042	−0.730209	−	0.683224i	$-0.760577\pi$
$619$	−36.3348	−1.46042	−0.730209	+	0.683224i	$0.760577\pi$
$620$	−2.84333	−0.114191
$621$	34.2292	1.37357
$622$	−60.9858	−2.44531
$623$	−25.1841	−1.00898
$624$	8.98337	0.359622
$625$	23.7621	0.950483
$626$	8.75836	0.350055
$627$	−6.79787	−0.271481
$628$	36.9415	1.47413
$629$	27.6905	1.10409
$630$	−5.46032	−0.217544
$631$	−22.0364	−0.877254	−0.438627	−	0.898669i	$-0.644535\pi$
$631$	−22.0364	−0.877254	−0.438627	+	0.898669i	$0.644535\pi$
$632$	0.0376099	0.00149604
$633$	1.69766	0.0674760
$634$	−35.0804	−1.39322
$635$	5.90855	0.234474
$636$	71.4001	2.83120
$637$	−19.3260	−0.765725
$638$	−16.8855	−0.668505
$639$	−21.8661	−0.865009
$640$	4.82088	0.190562
$641$	−23.7688	−0.938812	−0.469406	−	0.882982i	$-0.655532\pi$
$641$	−23.7688	−0.938812	−0.469406	+	0.882982i	$0.655532\pi$
$642$	18.7970	0.741858
$643$	−33.5561	−1.32332	−0.661662	−	0.749802i	$-0.730149\pi$
$643$	−33.5561	−1.32332	−0.661662	+	0.749802i	$0.730149\pi$
$644$	−39.9370	−1.57374
$645$	−6.09061	−0.239817
$646$	−13.9060	−0.547125
$647$	25.8699	1.01705	0.508525	−	0.861047i	$-0.330191\pi$
$647$	25.8699	1.01705	0.508525	+	0.861047i	$0.330191\pi$
$648$	2.42153	0.0951268
$649$	−3.22138	−0.126450
$650$	56.2788	2.20744
$651$	15.8448	0.621006
$652$	20.1242	0.788124
$653$	10.4800	0.410115	0.205057	−	0.978750i	$-0.434262\pi$
$653$	10.4800	0.410115	0.205057	+	0.978750i	$0.434262\pi$
$654$	56.8752	2.22400
$655$	3.30434	0.129111
$656$	−6.03918	−0.235790
$657$	−52.4694	−2.04703
$658$	36.7784	1.43377
$659$	5.39149	0.210023	0.105011	−	0.994471i	$-0.466512\pi$
$659$	5.39149	0.210023	0.105011	+	0.994471i	$0.466512\pi$
$660$	2.46953	0.0961261
$661$	37.8691	1.47294	0.736469	−	0.676471i	$-0.236492\pi$
$661$	37.8691	1.47294	0.736469	+	0.676471i	$0.236492\pi$
$662$	76.0501	2.95577
$663$	35.4470	1.37665
$664$	−2.65735	−0.103125
$665$	−1.26038	−0.0488753
$666$	116.731	4.52325
$667$	54.1830	2.09797
$668$	−22.4983	−0.870485
$669$	−78.6735	−3.04169
$670$	−9.96706	−0.385061
$671$	−10.1317	−0.391131
$672$	−31.4849	−1.21456
$673$	−35.0557	−1.35130	−0.675649	−	0.737223i	$-0.736137\pi$
$673$	−35.0557	−1.35130	−0.675649	+	0.737223i	$0.736137\pi$
$674$	−20.9295	−0.806176
$675$	23.2515	0.894952
$676$	39.3636	1.51398
$677$	−18.4429	−0.708818	−0.354409	−	0.935090i	$-0.615318\pi$
$677$	−18.4429	−0.708818	−0.354409	+	0.935090i	$0.615318\pi$
$678$	62.6735	2.40696
$679$	−15.7385	−0.603987
$680$	1.78050	0.0682790
$681$	−33.5763	−1.28665
$682$	−7.20878	−0.276039
$683$	−43.2287	−1.65410	−0.827051	−	0.562127i	$-0.809983\pi$
$683$	−43.2287	−1.65410	−0.827051	+	0.562127i	$0.809983\pi$
$684$	−35.5813	−1.36048
$685$	4.97430	0.190058
$686$	43.5562	1.66298
$687$	25.0712	0.956527
$688$	−4.85900	−0.185248
$689$	−42.2608	−1.61001
$690$	−13.0557	−0.497022
$691$	−43.9096	−1.67040	−0.835201	−	0.549945i	$-0.814649\pi$
$691$	−43.9096	−1.67040	−0.835201	+	0.549945i	$0.814649\pi$
$692$	−80.9727	−3.07812
$693$	−8.40261	−0.319189
$694$	−50.6397	−1.92226
$695$	0.493834	0.0187322
$696$	−51.0177	−1.93382
$697$	−23.8297	−0.902613
$698$	−55.1863	−2.08883
$699$	24.6275	0.931496
$700$	−27.1288	−1.02537
$701$	0.275808	0.0104171	0.00520856	−	0.999986i	$-0.498342\pi$
$701$	0.275808	0.0104171	0.00520856	+	0.999986i	$0.498342\pi$
$702$	54.1245	2.04280
$703$	26.9445	1.01623
$704$	13.0487	0.491790
$705$	7.29759	0.274843
$706$	43.1058	1.62231
$707$	−5.44598	−0.204817
$708$	−27.6153	−1.03785
$709$	42.0342	1.57863	0.789313	−	0.613991i	$-0.210437\pi$
$709$	42.0342	1.57863	0.789313	+	0.613991i	$0.210437\pi$
$710$	3.02087	0.113371
$711$	−0.0720428	−0.00270182
$712$	34.6185	1.29738
$713$	23.1318	0.866294
$714$	−28.1516	−1.05355
$715$	−1.46168	−0.0546637
$716$	−9.42731	−0.352315
$717$	−2.81232	−0.105028
$718$	−47.6420	−1.77798
$719$	40.3075	1.50321	0.751607	−	0.659611i	$-0.229279\pi$
$719$	40.3075	1.50321	0.751607	+	0.659611i	$0.229279\pi$
$720$	−0.864352	−0.0322125
$721$	5.04634	0.187936
$722$	29.3285	1.09149
$723$	−30.1127	−1.11990
$724$	−44.3598	−1.64862
$725$	36.8060	1.36694
$726$	6.26106	0.232370
$727$	10.3962	0.385575	0.192788	−	0.981240i	$-0.438247\pi$
$727$	10.3962	0.385575	0.192788	+	0.981240i	$0.438247\pi$
$728$	−22.2572	−0.824908
$729$	−44.0136	−1.63014
$730$	7.24883	0.268291
$731$	−19.1729	−0.709134
$732$	−86.8543	−3.21023
$733$	−35.4616	−1.30980	−0.654901	−	0.755715i	$-0.727290\pi$
$733$	−35.4616	−1.30980	−0.654901	+	0.755715i	$0.727290\pi$
$734$	−23.7146	−0.875323
$735$	3.04546	0.112333
$736$	−45.9648	−1.69429
$737$	−15.3378	−0.564975
$738$	−100.456	−3.69783
$739$	41.3307	1.52037	0.760186	−	0.649705i	$-0.225108\pi$
$739$	41.3307	1.52037	0.760186	+	0.649705i	$0.225108\pi$
$740$	−9.78837	−0.359828
$741$	34.4920	1.26710
$742$	33.5630	1.23214
$743$	33.3636	1.22399	0.611996	−	0.790861i	$-0.290367\pi$
$743$	33.3636	1.22399	0.611996	+	0.790861i	$0.290367\pi$
$744$	−21.7805	−0.798512
$745$	−2.18332	−0.0799906
$746$	−42.6046	−1.55986
$747$	5.09023	0.186242
$748$	7.77391	0.284242
$749$	5.36305	0.195962
$750$	−17.8869	−0.653137
$751$	20.1232	0.734308	0.367154	−	0.930160i	$-0.380332\pi$
$751$	20.1232	0.734308	0.367154	+	0.930160i	$0.380332\pi$
$752$	5.82192	0.212303
$753$	53.4312	1.94714
$754$	85.6763	3.12015
$755$	−2.00221	−0.0728678
$756$	−26.0903	−0.948896
$757$	12.8664	0.467636	0.233818	−	0.972280i	$-0.424878\pi$
$757$	12.8664	0.467636	0.233818	+	0.972280i	$0.424878\pi$
$758$	−6.92536	−0.251540
$759$	−20.0908	−0.729249
$760$	1.73253	0.0628456
$761$	−53.4169	−1.93636	−0.968181	−	0.250252i	$-0.919487\pi$
$761$	−53.4169	−1.93636	−0.968181	+	0.250252i	$0.919487\pi$
$762$	128.417	4.65206
$763$	16.2273	0.587469
$764$	21.1123	0.763815
$765$	−3.41060	−0.123310
$766$	12.4562	0.450061
$767$	16.3451	0.590188
$768$	32.3430	1.16708
$769$	9.15986	0.330313	0.165157	−	0.986267i	$-0.447187\pi$
$769$	9.15986	0.330313	0.165157	+	0.986267i	$0.447187\pi$
$770$	1.16085	0.0418341
$771$	21.9548	0.790684
$772$	71.3747	2.56883
$773$	−12.3881	−0.445569	−0.222784	−	0.974868i	$-0.571515\pi$
$773$	−12.3881	−0.445569	−0.222784	+	0.974868i	$0.571515\pi$
$774$	−80.8247	−2.90518
$775$	15.7132	0.564436
$776$	21.6343	0.776627
$777$	54.5469	1.95686
$778$	55.9797	2.00697
$779$	−23.1877	−0.830786
$780$	−12.5302	−0.448655
$781$	4.64867	0.166343
$782$	−41.0985	−1.46968
$783$	35.3971	1.26499
$784$	2.42963	0.0867723
$785$	3.44559	0.122978
$786$	71.8169	2.56163
$787$	5.70568	0.203385	0.101693	−	0.994816i	$-0.467574\pi$
$787$	5.70568	0.203385	0.101693	+	0.994816i	$0.467574\pi$
$788$	10.6154	0.378159
$789$	−31.8330	−1.13329
$790$	0.00995297	0.000354111 0
$791$	17.8816	0.635798
$792$	11.5504	0.410424
$793$	51.4079	1.82555
$794$	−7.84411	−0.278377
$795$	6.65960	0.236192
$796$	−29.7772	−1.05542
$797$	7.58111	0.268537	0.134268	−	0.990945i	$-0.457132\pi$
$797$	7.58111	0.268537	0.134268	+	0.990945i	$0.457132\pi$
$798$	−27.3932	−0.969709
$799$	22.9724	0.812704
$800$	−31.2234	−1.10392
$801$	−66.3128	−2.34305
$802$	−55.5887	−1.96291
$803$	11.1549	0.393646
$804$	−131.483	−4.63706
$805$	−3.72498	−0.131288
$806$	36.5770	1.28837
$807$	35.7849	1.25969
$808$	7.48613	0.263361
$809$	−3.58109	−0.125904	−0.0629522	−	0.998017i	$-0.520052\pi$
$809$	−3.58109	−0.125904	−0.0629522	+	0.998017i	$0.520052\pi$
$810$	0.640827	0.0225164
$811$	−24.6170	−0.864419	−0.432210	−	0.901773i	$-0.642266\pi$
$811$	−24.6170	−0.864419	−0.432210	+	0.901773i	$0.642266\pi$
$812$	−41.2996	−1.44933
$813$	35.7187	1.25271
$814$	−24.8168	−0.869827
$815$	1.87701	0.0657489
$816$	−4.45632	−0.156002
$817$	−18.6564	−0.652703
$818$	−1.48373	−0.0518772
$819$	42.6344	1.48977
$820$	8.42361	0.294165
$821$	10.3674	0.361826	0.180913	−	0.983499i	$-0.442095\pi$
$821$	10.3674	0.361826	0.180913	+	0.983499i	$0.442095\pi$
$822$	108.112	3.77084
$823$	−14.7998	−0.515890	−0.257945	−	0.966160i	$-0.583045\pi$
$823$	−14.7998	−0.515890	−0.257945	+	0.966160i	$0.583045\pi$
$824$	−6.93678	−0.241654
$825$	−13.6475	−0.475143
$826$	−12.9811	−0.451671
$827$	−52.8232	−1.83684	−0.918421	−	0.395606i	$-0.870535\pi$
$827$	−52.8232	−1.83684	−0.918421	+	0.395606i	$0.870535\pi$
$828$	−105.159	−3.65452
$829$	−13.7974	−0.479202	−0.239601	−	0.970871i	$-0.577017\pi$
$829$	−13.7974	−0.479202	−0.239601	+	0.970871i	$0.577017\pi$
$830$	−0.703233	−0.0244096
$831$	61.5190	2.13407
$832$	−66.2082	−2.29535
$833$	9.58692	0.332167
$834$	10.7330	0.371655
$835$	−2.09845	−0.0726198
$836$	7.56449	0.261623
$837$	15.1117	0.522338
$838$	29.8345	1.03061
$839$	−29.6222	−1.02267	−0.511336	−	0.859381i	$-0.670849\pi$
$839$	−29.6222	−1.02267	−0.511336	+	0.859381i	$0.670849\pi$
$840$	3.50737	0.121016
$841$	27.0317	0.932128
$842$	−30.3360	−1.04545
$843$	−22.0541	−0.759583
$844$	−1.88911	−0.0650259
$845$	3.67150	0.126303
$846$	96.8419	3.32949
$847$	1.78637	0.0613805
$848$	5.31293	0.182447
$849$	−28.2866	−0.970792
$850$	−27.9178	−0.957574
$851$	79.6331	2.72979
$852$	39.8507	1.36526
$853$	−41.9044	−1.43478	−0.717390	−	0.696671i	$-0.754664\pi$
$853$	−41.9044	−1.43478	−0.717390	+	0.696671i	$0.754664\pi$
$854$	−40.8276	−1.39709
$855$	−3.31872	−0.113498
$856$	−7.37213	−0.251974
$857$	−32.4509	−1.10850	−0.554252	−	0.832349i	$-0.686995\pi$
$857$	−32.4509	−1.10850	−0.554252	+	0.832349i	$0.686995\pi$
$858$	−31.7683	−1.08455
$859$	19.4611	0.664005	0.332003	−	0.943278i	$-0.392276\pi$
$859$	19.4611	0.664005	0.332003	+	0.943278i	$0.392276\pi$
$860$	6.77746	0.231110
$861$	−46.9416	−1.59976
$862$	3.96019	0.134885
$863$	25.8898	0.881300	0.440650	−	0.897679i	$-0.354748\pi$
$863$	25.8898	0.881300	0.440650	+	0.897679i	$0.354748\pi$
$864$	−30.0282	−1.02158
$865$	−7.55245	−0.256791
$866$	−31.2096	−1.06055
$867$	29.6006	1.00529
$868$	−17.6317	−0.598458
$869$	0.0153161	0.000519564 0
$870$	−13.5012	−0.457732
$871$	77.8232	2.63694
$872$	−22.3063	−0.755388
$873$	−41.4412	−1.40257
$874$	−39.9914	−1.35273
$875$	−5.10339	−0.172526
$876$	95.6250	3.23087
$877$	34.2959	1.15809	0.579046	−	0.815295i	$-0.303425\pi$
$877$	34.2959	1.15809	0.579046	+	0.815295i	$0.303425\pi$
$878$	−49.8544	−1.68250
$879$	−6.57202	−0.221669
$880$	0.183759	0.00619452
$881$	44.9275	1.51365	0.756823	−	0.653620i	$-0.226750\pi$
$881$	44.9275	1.51365	0.756823	+	0.653620i	$0.226750\pi$
$882$	40.4144	1.36082
$883$	−46.1259	−1.55226	−0.776130	−	0.630573i	$-0.782820\pi$
$883$	−46.1259	−1.55226	−0.776130	+	0.630573i	$0.782820\pi$
$884$	−39.4444	−1.32666
$885$	−2.57572	−0.0865819
$886$	−74.7759	−2.51215
$887$	21.6909	0.728308	0.364154	−	0.931339i	$-0.381358\pi$
$887$	21.6909	0.728308	0.364154	+	0.931339i	$0.381358\pi$
$888$	−74.9810	−2.51620
$889$	36.6393	1.22884
$890$	9.16133	0.307089
$891$	0.986136	0.0330368
$892$	87.5457	2.93125
$893$	22.3535	0.748032
$894$	−47.4526	−1.58705
$895$	−0.879299	−0.0293917
$896$	29.8946	0.998708
$897$	101.939	3.40366
$898$	20.4541	0.682562
$899$	23.9211	0.797813
$900$	−71.4333	−2.38111
$901$	20.9640	0.698412
$902$	21.3566	0.711098
$903$	−37.7682	−1.25685
$904$	−24.5804	−0.817531
$905$	−4.13751	−0.137535
$906$	−43.5163	−1.44573
$907$	−30.5769	−1.01529	−0.507645	−	0.861566i	$-0.669484\pi$
$907$	−30.5769	−1.01529	−0.507645	+	0.861566i	$0.669484\pi$
$908$	37.3628	1.23993
$909$	−14.3399	−0.475624
$910$	−5.89009	−0.195254
$911$	11.6300	0.385320	0.192660	−	0.981266i	$-0.438289\pi$
$911$	11.6300	0.385320	0.192660	+	0.981266i	$0.438289\pi$
$912$	−4.33626	−0.143588
$913$	−1.08217	−0.0358146
$914$	−9.63564	−0.318719
$915$	−8.10103	−0.267812
$916$	−27.8986	−0.921795
$917$	20.4904	0.676653
$918$	−26.8492	−0.886154
$919$	−1.71864	−0.0566926	−0.0283463	−	0.999598i	$-0.509024\pi$
$919$	−1.71864	−0.0566926	−0.0283463	+	0.999598i	$0.509024\pi$
$920$	5.12042	0.168815
$921$	−55.3170	−1.82276
$922$	−18.1739	−0.598525
$923$	−23.5871	−0.776379
$924$	15.3137	0.503783
$925$	54.0940	1.77860
$926$	−61.2314	−2.01219
$927$	13.2876	0.436422
$928$	−47.5331	−1.56035
$929$	−17.5276	−0.575063	−0.287531	−	0.957771i	$-0.592835\pi$
$929$	−17.5276	−0.575063	−0.287531	+	0.957771i	$0.592835\pi$
$930$	−5.76392	−0.189007
$931$	9.32866	0.305734
$932$	−27.4048	−0.897673
$933$	−75.0380	−2.45663
$934$	9.25810	0.302934
$935$	0.725085	0.0237128
$936$	−58.6059	−1.91559
$937$	−2.75255	−0.0899220	−0.0449610	−	0.998989i	$-0.514316\pi$
$937$	−2.75255	−0.0899220	−0.0449610	+	0.998989i	$0.514316\pi$
$938$	−61.8063	−2.01805
$939$	10.7764	0.351676
$940$	−8.12057	−0.264864
$941$	−18.0014	−0.586828	−0.293414	−	0.955985i	$-0.594791\pi$
$941$	−18.0014	−0.586828	−0.293414	+	0.955985i	$0.594791\pi$
$942$	74.8869	2.43995
$943$	−68.5301	−2.23165
$944$	−2.05487	−0.0668804
$945$	−2.43348	−0.0791612
$946$	17.1831	0.558671
$947$	41.8284	1.35924	0.679620	−	0.733564i	$-0.262145\pi$
$947$	41.8284	1.35924	0.679620	+	0.733564i	$0.262145\pi$
$948$	0.131297	0.00426434
$949$	−56.5991	−1.83729
$950$	−27.1657	−0.881373
$951$	−43.1636	−1.39967
$952$	11.0410	0.357840
$953$	−14.2687	−0.462208	−0.231104	−	0.972929i	$-0.574234\pi$
$953$	−14.2687	−0.462208	−0.231104	+	0.972929i	$0.574234\pi$
$954$	88.3754	2.86126
$955$	1.96917	0.0637209
$956$	3.12948	0.101215
$957$	−20.7763	−0.671601
$958$	−62.3683	−2.01503
$959$	30.8459	0.996067
$960$	10.4333	0.336734
$961$	−20.7876	−0.670567
$962$	125.919	4.05979
$963$	14.1215	0.455060
$964$	33.5086	1.07924
$965$	6.65722	0.214304
$966$	−80.9592	−2.60482
$967$	−40.8331	−1.31310	−0.656552	−	0.754281i	$-0.727986\pi$
$967$	−40.8331	−1.31310	−0.656552	+	0.754281i	$0.727986\pi$
$968$	−2.45557	−0.0789252
$969$	−17.1102	−0.549660
$970$	5.72524	0.183826
$971$	−40.6696	−1.30515	−0.652575	−	0.757724i	$-0.726311\pi$
$971$	−40.6696	−1.30515	−0.652575	+	0.757724i	$0.726311\pi$
$972$	52.2692	1.67654
$973$	3.06229	0.0981726
$974$	−22.2691	−0.713548
$975$	69.2465	2.21766
$976$	−6.46288	−0.206872
$977$	−10.5141	−0.336376	−0.168188	−	0.985755i	$-0.553792\pi$
$977$	−10.5141	−0.336376	−0.168188	+	0.985755i	$0.553792\pi$
$978$	40.7952	1.30449
$979$	14.0979	0.450571
$980$	−3.38891	−0.108255
$981$	42.7284	1.36421
$982$	35.0836	1.11956
$983$	21.6369	0.690111	0.345056	−	0.938582i	$-0.387860\pi$
$983$	21.6369	0.690111	0.345056	+	0.938582i	$0.387860\pi$
$984$	64.5266	2.05703
$985$	0.990115	0.0315477
$986$	−42.5008	−1.35350
$987$	45.2528	1.44041
$988$	−38.3818	−1.22109
$989$	−55.1379	−1.75328
$990$	3.05665	0.0971467
$991$	−35.8843	−1.13990	−0.569951	−	0.821679i	$-0.693038\pi$
$991$	−35.8843	−1.13990	−0.569951	+	0.821679i	$0.693038\pi$
$992$	−20.2929	−0.644299
$993$	93.5734	2.96946
$994$	18.7326	0.594163
$995$	−2.77736	−0.0880483
$996$	−9.27691	−0.293950
$997$	15.6274	0.494925	0.247463	−	0.968897i	$-0.420403\pi$
$997$	15.6274	0.494925	0.247463	+	0.968897i	$0.420403\pi$
$998$	−6.45141	−0.204216
$999$	52.0233	1.64594

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6017.2.a.f.1.18	✓	121

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6017.2.a.f.1.18	✓	121	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6017 = 11 \cdot 547 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6017.a (trivial)

\(f(q)\)	\(=\)	\(q-2.25579 q^{2} -2.77556 q^{3} +3.08857 q^{4} +0.288075 q^{5} +6.26106 q^{6} +1.78637 q^{7} -2.45557 q^{8} +4.70373 q^{9} +O(q^{10})\)	\(q-2.25579 q^{2} -2.77556 q^{3} +3.08857 q^{4} +0.288075 q^{5} +6.26106 q^{6} +1.78637 q^{7} -2.45557 q^{8} +4.70373 q^{9} -0.649836 q^{10} -1.00000 q^{11} -8.57250 q^{12} +5.07395 q^{13} -4.02967 q^{14} -0.799570 q^{15} -0.637886 q^{16} -2.51700 q^{17} -10.6106 q^{18} -2.44919 q^{19} +0.889740 q^{20} -4.95818 q^{21} +2.25579 q^{22} -7.23846 q^{23} +6.81559 q^{24} -4.91701 q^{25} -11.4457 q^{26} -4.72879 q^{27} +5.51733 q^{28} -7.48543 q^{29} +1.80366 q^{30} -3.19569 q^{31} +6.35008 q^{32} +2.77556 q^{33} +5.67780 q^{34} +0.514610 q^{35} +14.5278 q^{36} -11.0014 q^{37} +5.52485 q^{38} -14.0830 q^{39} -0.707390 q^{40} +9.46750 q^{41} +11.1846 q^{42} +7.61735 q^{43} -3.08857 q^{44} +1.35503 q^{45} +16.3284 q^{46} -9.12690 q^{47} +1.77049 q^{48} -3.80887 q^{49} +11.0917 q^{50} +6.98607 q^{51} +15.6712 q^{52} -8.32897 q^{53} +10.6671 q^{54} -0.288075 q^{55} -4.38657 q^{56} +6.79787 q^{57} +16.8855 q^{58} +3.22138 q^{59} -2.46953 q^{60} +10.1317 q^{61} +7.20878 q^{62} +8.40261 q^{63} -13.0487 q^{64} +1.46168 q^{65} -6.26106 q^{66} +15.3378 q^{67} -7.77391 q^{68} +20.0908 q^{69} -1.16085 q^{70} -4.64867 q^{71} -11.5504 q^{72} -11.1549 q^{73} +24.8168 q^{74} +13.6475 q^{75} -7.56449 q^{76} -1.78637 q^{77} +31.7683 q^{78} -0.0153161 q^{79} -0.183759 q^{80} -0.986136 q^{81} -21.3566 q^{82} +1.08217 q^{83} -15.3137 q^{84} -0.725085 q^{85} -17.1831 q^{86} +20.7763 q^{87} +2.45557 q^{88} -14.0979 q^{89} -3.05665 q^{90} +9.06396 q^{91} -22.3565 q^{92} +8.86982 q^{93} +20.5883 q^{94} -0.705551 q^{95} -17.6250 q^{96} -8.81029 q^{97} +8.59200 q^{98} -4.70373 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 121 q + 2 q^{2} + 18 q^{3} + 138 q^{4} + 13 q^{5} + 10 q^{6} + 56 q^{7} + 12 q^{8} + 143 q^{9}+O(q^{10}) \) 121 * q + 2 * q^2 + 18 * q^3 + 138 * q^4 + 13 * q^5 + 10 * q^6 + 56 * q^7 + 12 * q^8 + 143 * q^9	\( 121 q + 2 q^{2} + 18 q^{3} + 138 q^{4} + 13 q^{5} + 10 q^{6} + 56 q^{7} + 12 q^{8} + 143 q^{9} + 20 q^{10} - 121 q^{11} + 40 q^{12} + 31 q^{13} + 7 q^{14} + 53 q^{15} + 164 q^{16} - 23 q^{17} + 14 q^{18} + 62 q^{19} + 53 q^{20} + 19 q^{21} - 2 q^{22} + 34 q^{23} + 34 q^{24} + 172 q^{25} + 34 q^{26} + 87 q^{27} + 91 q^{28} - 30 q^{29} + 2 q^{30} + 102 q^{31} + 31 q^{32} - 18 q^{33} + 30 q^{34} + 20 q^{35} + 164 q^{36} + 58 q^{37} + 35 q^{38} + 42 q^{39} + 52 q^{40} - 12 q^{41} + 56 q^{42} + 96 q^{43} - 138 q^{44} + 72 q^{45} + 48 q^{46} + 136 q^{47} + 99 q^{48} + 199 q^{49} - 7 q^{50} + 22 q^{51} + 81 q^{52} + 24 q^{53} + 37 q^{54} - 13 q^{55} + 28 q^{56} + 25 q^{57} + 76 q^{58} + 58 q^{59} + 81 q^{60} + 14 q^{61} - 2 q^{62} + 152 q^{63} + 236 q^{64} - 29 q^{65} - 10 q^{66} + 112 q^{67} - 61 q^{68} + 41 q^{69} + 105 q^{70} + 56 q^{71} + 71 q^{72} + 113 q^{73} - 23 q^{74} + 111 q^{75} + 144 q^{76} - 56 q^{77} + 59 q^{78} + 80 q^{79} + 100 q^{80} + 177 q^{81} + 123 q^{82} + 6 q^{83} + 79 q^{84} + 26 q^{85} + 14 q^{86} + 180 q^{87} - 12 q^{88} + 26 q^{89} + 75 q^{90} + 72 q^{91} + 58 q^{92} + 139 q^{93} + 37 q^{94} + 39 q^{95} + 66 q^{96} + 136 q^{97} + 7 q^{98} - 143 q^{99}+O(q^{100}) \) 121 * q + 2 * q^2 + 18 * q^3 + 138 * q^4 + 13 * q^5 + 10 * q^6 + 56 * q^7 + 12 * q^8 + 143 * q^9 + 20 * q^10 - 121 * q^11 + 40 * q^12 + 31 * q^13 + 7 * q^14 + 53 * q^15 + 164 * q^16 - 23 * q^17 + 14 * q^18 + 62 * q^19 + 53 * q^20 + 19 * q^21 - 2 * q^22 + 34 * q^23 + 34 * q^24 + 172 * q^25 + 34 * q^26 + 87 * q^27 + 91 * q^28 - 30 * q^29 + 2 * q^30 + 102 * q^31 + 31 * q^32 - 18 * q^33 + 30 * q^34 + 20 * q^35 + 164 * q^36 + 58 * q^37 + 35 * q^38 + 42 * q^39 + 52 * q^40 - 12 * q^41 + 56 * q^42 + 96 * q^43 - 138 * q^44 + 72 * q^45 + 48 * q^46 + 136 * q^47 + 99 * q^48 + 199 * q^49 - 7 * q^50 + 22 * q^51 + 81 * q^52 + 24 * q^53 + 37 * q^54 - 13 * q^55 + 28 * q^56 + 25 * q^57 + 76 * q^58 + 58 * q^59 + 81 * q^60 + 14 * q^61 - 2 * q^62 + 152 * q^63 + 236 * q^64 - 29 * q^65 - 10 * q^66 + 112 * q^67 - 61 * q^68 + 41 * q^69 + 105 * q^70 + 56 * q^71 + 71 * q^72 + 113 * q^73 - 23 * q^74 + 111 * q^75 + 144 * q^76 - 56 * q^77 + 59 * q^78 + 80 * q^79 + 100 * q^80 + 177 * q^81 + 123 * q^82 + 6 * q^83 + 79 * q^84 + 26 * q^85 + 14 * q^86 + 180 * q^87 - 12 * q^88 + 26 * q^89 + 75 * q^90 + 72 * q^91 + 58 * q^92 + 139 * q^93 + 37 * q^94 + 39 * q^95 + 66 * q^96 + 136 * q^97 + 7 * q^98 - 143 * q^99

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