LMFDB - Embedded newform 4019.2.a.a.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4019,2,Mod(1,4019)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4019, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4019.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4019 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4019.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:	$32.0918765724$
Analytic rank:	$1$
Dimension:	$149$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	4019.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.59547 q^{2} +1.08147 q^{3} +4.73647 q^{4} +0.749609 q^{5} -2.80691 q^{6} +2.15869 q^{7} -7.10242 q^{8} -1.83043 q^{9} +O(q^{10})$	\(q-2.59547 q^{2} +1.08147 q^{3} +4.73647 q^{4} +0.749609 q^{5} -2.80691 q^{6} +2.15869 q^{7} -7.10242 q^{8} -1.83043 q^{9} -1.94559 q^{10} -1.33194 q^{11} +5.12233 q^{12} -5.40153 q^{13} -5.60282 q^{14} +0.810677 q^{15} +8.96118 q^{16} +3.71006 q^{17} +4.75083 q^{18} +2.62958 q^{19} +3.55050 q^{20} +2.33455 q^{21} +3.45702 q^{22} -7.16420 q^{23} -7.68102 q^{24} -4.43809 q^{25} +14.0195 q^{26} -5.22395 q^{27} +10.2246 q^{28} +5.37172 q^{29} -2.10409 q^{30} -3.73250 q^{31} -9.05364 q^{32} -1.44045 q^{33} -9.62934 q^{34} +1.61818 q^{35} -8.66978 q^{36} -3.43149 q^{37} -6.82501 q^{38} -5.84157 q^{39} -5.32404 q^{40} +12.3564 q^{41} -6.05926 q^{42} +10.6649 q^{43} -6.30870 q^{44} -1.37211 q^{45} +18.5945 q^{46} +8.96610 q^{47} +9.69121 q^{48} -2.34005 q^{49} +11.5189 q^{50} +4.01230 q^{51} -25.5842 q^{52} +11.8726 q^{53} +13.5586 q^{54} -0.998437 q^{55} -15.3319 q^{56} +2.84381 q^{57} -13.9421 q^{58} -6.05553 q^{59} +3.83974 q^{60} -8.63196 q^{61} +9.68759 q^{62} -3.95134 q^{63} +5.57610 q^{64} -4.04904 q^{65} +3.73865 q^{66} +12.7955 q^{67} +17.5726 q^{68} -7.74784 q^{69} -4.19993 q^{70} -4.82490 q^{71} +13.0005 q^{72} -10.6019 q^{73} +8.90634 q^{74} -4.79964 q^{75} +12.4549 q^{76} -2.87526 q^{77} +15.1616 q^{78} -12.7865 q^{79} +6.71739 q^{80} -0.158221 q^{81} -32.0705 q^{82} +1.39946 q^{83} +11.0575 q^{84} +2.78109 q^{85} -27.6805 q^{86} +5.80933 q^{87} +9.46002 q^{88} -5.24730 q^{89} +3.56127 q^{90} -11.6603 q^{91} -33.9330 q^{92} -4.03657 q^{93} -23.2712 q^{94} +1.97116 q^{95} -9.79120 q^{96} -11.5726 q^{97} +6.07352 q^{98} +2.43803 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 149 q - 8 q^{2} - 12 q^{3} + 124 q^{4} - 36 q^{5} - 45 q^{6} - 32 q^{7} - 21 q^{8} + 115 q^{9}+O(q^{10}) $ 149 * q - 8 * q^2 - 12 * q^3 + 124 * q^4 - 36 * q^5 - 45 * q^6 - 32 * q^7 - 21 * q^8 + 115 * q^9	\( 149 q - 8 q^{2} - 12 q^{3} + 124 q^{4} - 36 q^{5} - 45 q^{6} - 32 q^{7} - 21 q^{8} + 115 q^{9} - 58 q^{10} - 33 q^{11} - 33 q^{12} - 107 q^{13} - 28 q^{14} - 24 q^{15} + 74 q^{16} - 39 q^{17} - 33 q^{18} - 93 q^{19} - 63 q^{20} - 113 q^{21} - 38 q^{22} - 11 q^{23} - 130 q^{24} + 85 q^{25} - 33 q^{26} - 30 q^{27} - 94 q^{28} - 85 q^{29} - 16 q^{30} - 129 q^{31} - 35 q^{32} - 64 q^{33} - 78 q^{34} - 27 q^{35} + 79 q^{36} - 135 q^{37} - 11 q^{38} - 73 q^{39} - 146 q^{40} - 101 q^{41} + 4 q^{42} - 55 q^{43} - 82 q^{44} - 168 q^{45} - 113 q^{46} - 40 q^{47} - 65 q^{48} + 27 q^{49} - 5 q^{50} - 49 q^{51} - 177 q^{52} - 32 q^{53} - 155 q^{54} - 128 q^{55} - 44 q^{56} - 47 q^{57} - 46 q^{58} - 53 q^{59} - 11 q^{60} - 347 q^{61} - 11 q^{62} - 73 q^{63} + q^{64} - 31 q^{65} - 37 q^{66} - 40 q^{67} - 80 q^{68} - 175 q^{69} - 61 q^{70} - 31 q^{71} - 68 q^{72} - 193 q^{73} - 33 q^{74} - 56 q^{75} - 248 q^{76} - 84 q^{77} + 40 q^{78} - 111 q^{79} - 54 q^{80} + 49 q^{81} - 74 q^{82} - 24 q^{83} - 159 q^{84} - 258 q^{85} - q^{86} - 66 q^{87} - 97 q^{88} - 76 q^{89} - 75 q^{90} - 134 q^{91} + 31 q^{92} - 97 q^{93} - 111 q^{94} - 14 q^{95} - 216 q^{96} - 140 q^{97} - 13 q^{98} - 116 q^{99}+O(q^{100}) \) 149 * q - 8 * q^2 - 12 * q^3 + 124 * q^4 - 36 * q^5 - 45 * q^6 - 32 * q^7 - 21 * q^8 + 115 * q^9 - 58 * q^10 - 33 * q^11 - 33 * q^12 - 107 * q^13 - 28 * q^14 - 24 * q^15 + 74 * q^16 - 39 * q^17 - 33 * q^18 - 93 * q^19 - 63 * q^20 - 113 * q^21 - 38 * q^22 - 11 * q^23 - 130 * q^24 + 85 * q^25 - 33 * q^26 - 30 * q^27 - 94 * q^28 - 85 * q^29 - 16 * q^30 - 129 * q^31 - 35 * q^32 - 64 * q^33 - 78 * q^34 - 27 * q^35 + 79 * q^36 - 135 * q^37 - 11 * q^38 - 73 * q^39 - 146 * q^40 - 101 * q^41 + 4 * q^42 - 55 * q^43 - 82 * q^44 - 168 * q^45 - 113 * q^46 - 40 * q^47 - 65 * q^48 + 27 * q^49 - 5 * q^50 - 49 * q^51 - 177 * q^52 - 32 * q^53 - 155 * q^54 - 128 * q^55 - 44 * q^56 - 47 * q^57 - 46 * q^58 - 53 * q^59 - 11 * q^60 - 347 * q^61 - 11 * q^62 - 73 * q^63 + q^64 - 31 * q^65 - 37 * q^66 - 40 * q^67 - 80 * q^68 - 175 * q^69 - 61 * q^70 - 31 * q^71 - 68 * q^72 - 193 * q^73 - 33 * q^74 - 56 * q^75 - 248 * q^76 - 84 * q^77 + 40 * q^78 - 111 * q^79 - 54 * q^80 + 49 * q^81 - 74 * q^82 - 24 * q^83 - 159 * q^84 - 258 * q^85 - q^86 - 66 * q^87 - 97 * q^88 - 76 * q^89 - 75 * q^90 - 134 * q^91 + 31 * q^92 - 97 * q^93 - 111 * q^94 - 14 * q^95 - 216 * q^96 - 140 * q^97 - 13 * q^98 - 116 * 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 $

$2$	−2.59547	−1.83527	−0.917637	−	0.397419i	$-0.869906\pi$
$2$	−2.59547	−1.83527	−0.917637	+	0.397419i	$0.869906\pi$
$3$	1.08147	0.624384	0.312192	−	0.950019i	$-0.398937\pi$
$3$	1.08147	0.624384	0.312192	+	0.950019i	$0.398937\pi$
$4$	4.73647	2.36823
$5$	0.749609	0.335236	0.167618	−	0.985852i	$-0.446393\pi$
$5$	0.749609	0.335236	0.167618	+	0.985852i	$0.446393\pi$
$6$	−2.80691	−1.14592
$7$	2.15869	0.815909	0.407954	−	0.913002i	$-0.366242\pi$
$7$	2.15869	0.815909	0.407954	+	0.913002i	$0.366242\pi$
$8$	−7.10242	−2.51108
$9$	−1.83043	−0.610144
$10$	−1.94559	−0.615249
$11$	−1.33194	−0.401596	−0.200798	−	0.979633i	$-0.564353\pi$
$11$	−1.33194	−0.401596	−0.200798	+	0.979633i	$0.564353\pi$
$12$	5.12233	1.47869
$13$	−5.40153	−1.49812	−0.749058	−	0.662504i	$-0.769494\pi$
$13$	−5.40153	−1.49812	−0.749058	+	0.662504i	$0.769494\pi$
$14$	−5.60282	−1.49742
$15$	0.810677	0.209316
$16$	8.96118	2.24030
$17$	3.71006	0.899821	0.449910	−	0.893074i	$-0.351456\pi$
$17$	3.71006	0.899821	0.449910	+	0.893074i	$0.351456\pi$
$18$	4.75083	1.11978
$19$	2.62958	0.603268	0.301634	−	0.953424i	$-0.402468\pi$
$19$	2.62958	0.603268	0.301634	+	0.953424i	$0.402468\pi$
$20$	3.55050	0.793916
$21$	2.33455	0.509441
$22$	3.45702	0.737039
$23$	−7.16420	−1.49384	−0.746920	−	0.664914i	$-0.768468\pi$
$23$	−7.16420	−1.49384	−0.746920	+	0.664914i	$0.768468\pi$
$24$	−7.68102	−1.56788
$25$	−4.43809	−0.887617
$26$	14.0195	2.74945
$27$	−5.22395	−1.00535
$28$	10.2246	1.93226
$29$	5.37172	0.997503	0.498751	−	0.866745i	$-0.333792\pi$
$29$	5.37172	0.997503	0.498751	+	0.866745i	$0.333792\pi$
$30$	−2.10409	−0.384152
$31$	−3.73250	−0.670377	−0.335188	−	0.942151i	$-0.608800\pi$
$31$	−3.73250	−0.670377	−0.335188	+	0.942151i	$0.608800\pi$
$32$	−9.05364	−1.60047
$33$	−1.44045	−0.250750
$34$	−9.62934	−1.65142
$35$	1.61818	0.273522
$36$	−8.66978	−1.44496
$37$	−3.43149	−0.564134	−0.282067	−	0.959395i	$-0.591020\pi$
$37$	−3.43149	−0.564134	−0.282067	+	0.959395i	$0.591020\pi$
$38$	−6.82501	−1.10716
$39$	−5.84157	−0.935400
$40$	−5.32404	−0.841805
$41$	12.3564	1.92974	0.964869	−	0.262732i	$-0.0846235\pi$
$41$	12.3564	1.92974	0.964869	+	0.262732i	$0.0846235\pi$
$42$	−6.05926	−0.934964
$43$	10.6649	1.62638	0.813192	−	0.581995i	$-0.197728\pi$
$43$	10.6649	1.62638	0.813192	+	0.581995i	$0.197728\pi$
$44$	−6.30870	−0.951073
$45$	−1.37211	−0.204542
$46$	18.5945	2.74161
$47$	8.96610	1.30784	0.653920	−	0.756564i	$-0.273123\pi$
$47$	8.96610	1.30784	0.653920	+	0.756564i	$0.273123\pi$
$48$	9.69121	1.39881
$49$	−2.34005	−0.334293
$50$	11.5189	1.62902
$51$	4.01230	0.561834
$52$	−25.5842	−3.54789
$53$	11.8726	1.63082	0.815412	−	0.578882i	$-0.196511\pi$
$53$	11.8726	1.63082	0.815412	+	0.578882i	$0.196511\pi$
$54$	13.5586	1.84509
$55$	−0.998437	−0.134629
$56$	−15.3319	−2.04882
$57$	2.84381	0.376671
$58$	−13.9421	−1.83069
$59$	−6.05553	−0.788363	−0.394181	−	0.919033i	$-0.628972\pi$
$59$	−6.05553	−0.788363	−0.394181	+	0.919033i	$0.628972\pi$
$60$	3.83974	0.495709
$61$	−8.63196	−1.10521	−0.552605	−	0.833444i	$-0.686366\pi$
$61$	−8.63196	−1.10521	−0.552605	+	0.833444i	$0.686366\pi$
$62$	9.68759	1.23033
$63$	−3.95134	−0.497822
$64$	5.57610	0.697013
$65$	−4.04904	−0.502222
$66$	3.73865	0.460196
$67$	12.7955	1.56322	0.781610	−	0.623768i	$-0.214399\pi$
$67$	12.7955	1.56322	0.781610	+	0.623768i	$0.214399\pi$
$68$	17.5726	2.13098
$69$	−7.74784	−0.932730
$70$	−4.19993	−0.501987
$71$	−4.82490	−0.572610	−0.286305	−	0.958139i	$-0.592427\pi$
$71$	−4.82490	−0.572610	−0.286305	+	0.958139i	$0.592427\pi$
$72$	13.0005	1.53212
$73$	−10.6019	−1.24085	−0.620427	−	0.784264i	$-0.713041\pi$
$73$	−10.6019	−1.24085	−0.620427	+	0.784264i	$0.713041\pi$
$74$	8.90634	1.03534
$75$	−4.79964	−0.554214
$76$	12.4549	1.42868
$77$	−2.87526	−0.327666
$78$	15.1616	1.71672
$79$	−12.7865	−1.43859	−0.719296	−	0.694704i	$-0.755535\pi$
$79$	−12.7865	−1.43859	−0.719296	+	0.694704i	$0.755535\pi$
$80$	6.71739	0.751027
$81$	−0.158221	−0.0175802
$82$	−32.0705	−3.54160
$83$	1.39946	0.153611	0.0768055	−	0.997046i	$-0.475528\pi$
$83$	1.39946	0.153611	0.0768055	+	0.997046i	$0.475528\pi$
$84$	11.0575	1.20647
$85$	2.78109	0.301652
$86$	−27.6805	−2.98486
$87$	5.80933	0.622825
$88$	9.46002	1.00844
$89$	−5.24730	−0.556213	−0.278106	−	0.960550i	$-0.589707\pi$
$89$	−5.24730	−0.556213	−0.278106	+	0.960550i	$0.589707\pi$
$90$	3.56127	0.375391
$91$	−11.6603	−1.22233
$92$	−33.9330	−3.53776
$93$	−4.03657	−0.418573
$94$	−23.2712	−2.40025
$95$	1.97116	0.202237
$96$	−9.79120	−0.999311
$97$	−11.5726	−1.17502	−0.587512	−	0.809216i	$-0.699892\pi$
$97$	−11.5726	−1.17502	−0.587512	+	0.809216i	$0.699892\pi$
$98$	6.07352	0.613519
$99$	2.43803	0.245031
$100$	−21.0208	−2.10208
$101$	−3.13754	−0.312197	−0.156099	−	0.987741i	$-0.549892\pi$
$101$	−3.13754	−0.312197	−0.156099	+	0.987741i	$0.549892\pi$
$102$	−10.4138	−1.03112
$103$	−4.19793	−0.413634	−0.206817	−	0.978380i	$-0.566310\pi$
$103$	−4.19793	−0.413634	−0.206817	+	0.978380i	$0.566310\pi$
$104$	38.3640	3.76190
$105$	1.75000	0.170783
$106$	−30.8149	−2.99301
$107$	−15.9586	−1.54277	−0.771387	−	0.636366i	$-0.780437\pi$
$107$	−15.9586	−1.54277	−0.771387	+	0.636366i	$0.780437\pi$
$108$	−24.7430	−2.38090
$109$	−5.39902	−0.517133	−0.258566	−	0.965993i	$-0.583250\pi$
$109$	−5.39902	−0.517133	−0.258566	+	0.965993i	$0.583250\pi$
$110$	2.59141	0.247082
$111$	−3.71104	−0.352236
$112$	19.3444	1.82788
$113$	−3.83969	−0.361208	−0.180604	−	0.983556i	$-0.557805\pi$
$113$	−3.83969	−0.361208	−0.180604	+	0.983556i	$0.557805\pi$
$114$	−7.38101	−0.691295
$115$	−5.37035	−0.500788
$116$	25.4430	2.36232
$117$	9.88714	0.914067
$118$	15.7169	1.44686
$119$	8.00887	0.734172
$120$	−5.75777	−0.525610
$121$	−9.22593	−0.838721
$122$	22.4040	2.02836
$123$	13.3630	1.20490
$124$	−17.6789	−1.58761
$125$	−7.07488	−0.632796
$126$	10.2556	0.913640
$127$	−21.1225	−1.87432	−0.937158	−	0.348906i	$-0.886553\pi$
$127$	−21.1225	−1.87432	−0.937158	+	0.348906i	$0.886553\pi$
$128$	3.63468	0.321263
$129$	11.5337	1.01549
$130$	10.5092	0.921715
$131$	12.0525	1.05303	0.526517	−	0.850165i	$-0.323498\pi$
$131$	12.0525	1.05303	0.526517	+	0.850165i	$0.323498\pi$
$132$	−6.82265	−0.593835
$133$	5.67646	0.492212
$134$	−33.2103	−2.86894
$135$	−3.91592	−0.337029
$136$	−26.3504	−2.25952
$137$	−13.0392	−1.11402	−0.557008	−	0.830507i	$-0.688051\pi$
$137$	−13.0392	−1.11402	−0.557008	+	0.830507i	$0.688051\pi$
$138$	20.1093	1.71182
$139$	4.84423	0.410883	0.205441	−	0.978669i	$-0.434137\pi$
$139$	4.84423	0.410883	0.205441	+	0.978669i	$0.434137\pi$
$140$	7.66444	0.647763
$141$	9.69653	0.816595
$142$	12.5229	1.05090
$143$	7.19454	0.601637
$144$	−16.4028	−1.36690
$145$	4.02669	0.334398
$146$	27.5168	2.27731
$147$	−2.53068	−0.208727
$148$	−16.2531	−1.33600
$149$	−9.61685	−0.787843	−0.393922	−	0.919144i	$-0.628882\pi$
$149$	−9.61685	−0.787843	−0.393922	+	0.919144i	$0.628882\pi$
$150$	12.4573	1.01714
$151$	−15.7152	−1.27889	−0.639443	−	0.768839i	$-0.720835\pi$
$151$	−15.7152	−1.27889	−0.639443	+	0.768839i	$0.720835\pi$
$152$	−18.6764	−1.51486
$153$	−6.79100	−0.549020
$154$	7.46264	0.601357
$155$	−2.79792	−0.224734
$156$	−27.6684	−2.21525
$157$	−9.29888	−0.742131	−0.371066	−	0.928607i	$-0.621008\pi$
$157$	−9.29888	−0.742131	−0.371066	+	0.928607i	$0.621008\pi$
$158$	33.1869	2.64021
$159$	12.8398	1.01826
$160$	−6.78670	−0.536536
$161$	−15.4653	−1.21884
$162$	0.410659	0.0322644
$163$	7.28826	0.570861	0.285430	−	0.958399i	$-0.407863\pi$
$163$	7.28826	0.570861	0.285430	+	0.958399i	$0.407863\pi$
$164$	58.5254	4.57007
$165$	−1.07978	−0.0840604
$166$	−3.63227	−0.281919
$167$	2.88520	0.223264	0.111632	−	0.993750i	$-0.464392\pi$
$167$	2.88520	0.223264	0.111632	+	0.993750i	$0.464392\pi$
$168$	−16.5810	−1.27925
$169$	16.1766	1.24435
$170$	−7.21824	−0.553614
$171$	−4.81328	−0.368080
$172$	50.5140	3.85166
$173$	3.41730	0.259813	0.129906	−	0.991526i	$-0.458532\pi$
$173$	3.41730	0.259813	0.129906	+	0.991526i	$0.458532\pi$
$174$	−15.0779	−1.14306
$175$	−9.58046	−0.724215
$176$	−11.9358	−0.899693
$177$	−6.54885	−0.492241
$178$	13.6192	1.02080
$179$	−18.6142	−1.39129	−0.695647	−	0.718384i	$-0.744882\pi$
$179$	−18.6142	−1.39129	−0.695647	+	0.718384i	$0.744882\pi$
$180$	−6.49895	−0.484403
$181$	2.06144	0.153226	0.0766130	−	0.997061i	$-0.475589\pi$
$181$	2.06144	0.153226	0.0766130	+	0.997061i	$0.475589\pi$
$182$	30.2638	2.24330
$183$	−9.33517	−0.690076
$184$	50.8831	3.75116
$185$	−2.57228	−0.189118
$186$	10.4768	0.768196
$187$	−4.94158	−0.361364
$188$	42.4676	3.09727
$189$	−11.2769	−0.820273
$190$	−5.11609	−0.371160
$191$	−6.83372	−0.494470	−0.247235	−	0.968955i	$-0.579522\pi$
$191$	−6.83372	−0.494470	−0.247235	+	0.968955i	$0.579522\pi$
$192$	6.03036	0.435204
$193$	−2.43136	−0.175013	−0.0875065	−	0.996164i	$-0.527890\pi$
$193$	−2.43136	−0.175013	−0.0875065	+	0.996164i	$0.527890\pi$
$194$	30.0364	2.15649
$195$	−4.37890	−0.313579
$196$	−11.0836	−0.791683
$197$	−14.9327	−1.06391	−0.531956	−	0.846772i	$-0.678543\pi$
$197$	−14.9327	−1.06391	−0.531956	+	0.846772i	$0.678543\pi$
$198$	−6.32784	−0.449700
$199$	4.27744	0.303220	0.151610	−	0.988440i	$-0.451554\pi$
$199$	4.27744	0.303220	0.151610	+	0.988440i	$0.451554\pi$
$200$	31.5211	2.22888
$201$	13.8379	0.976050
$202$	8.14340	0.572968
$203$	11.5959	0.813872
$204$	19.0041	1.33055
$205$	9.26244	0.646917
$206$	10.8956	0.759132
$207$	13.1136	0.911457
$208$	−48.4041	−3.35622
$209$	−3.50246	−0.242270
$210$	−4.54208	−0.313433
$211$	18.5182	1.27484	0.637422	−	0.770515i	$-0.280001\pi$
$211$	18.5182	1.27484	0.637422	+	0.770515i	$0.280001\pi$
$212$	56.2340	3.86217
$213$	−5.21796	−0.357529
$214$	41.4200	2.83141
$215$	7.99452	0.545222
$216$	37.1026	2.52452
$217$	−8.05732	−0.546966
$218$	14.0130	0.949081
$219$	−11.4656	−0.774771
$220$	−4.72906	−0.318833
$221$	−20.0400	−1.34804
$222$	9.63189	0.646450
$223$	1.97514	0.132265	0.0661327	−	0.997811i	$-0.478934\pi$
$223$	1.97514	0.132265	0.0661327	+	0.997811i	$0.478934\pi$
$224$	−19.5440	−1.30584
$225$	8.12361	0.541574
$226$	9.96581	0.662916
$227$	−18.2875	−1.21378	−0.606891	−	0.794785i	$-0.707583\pi$
$227$	−18.2875	−1.21378	−0.606891	+	0.794785i	$0.707583\pi$
$228$	13.4696	0.892045
$229$	14.9969	0.991021	0.495511	−	0.868602i	$-0.334981\pi$
$229$	14.9969	0.991021	0.495511	+	0.868602i	$0.334981\pi$
$230$	13.9386	0.919084
$231$	−3.10949	−0.204589
$232$	−38.1522	−2.50481
$233$	24.4970	1.60485	0.802425	−	0.596753i	$-0.203543\pi$
$233$	24.4970	1.60485	0.802425	+	0.596753i	$0.203543\pi$
$234$	−25.6618	−1.67756
$235$	6.72107	0.438434
$236$	−28.6818	−1.86703
$237$	−13.8281	−0.898234
$238$	−20.7868	−1.34741
$239$	−22.4858	−1.45449	−0.727243	−	0.686380i	$-0.759199\pi$
$239$	−22.4858	−1.45449	−0.727243	+	0.686380i	$0.759199\pi$
$240$	7.26462	0.468929
$241$	0.140757	0.00906697	0.00453349	−	0.999990i	$-0.498557\pi$
$241$	0.140757	0.00906697	0.00453349	+	0.999990i	$0.498557\pi$
$242$	23.9456	1.53928
$243$	15.5007	0.994372
$244$	−40.8850	−2.61739
$245$	−1.75412	−0.112067
$246$	−34.6832	−2.21132
$247$	−14.2038	−0.903766
$248$	26.5098	1.68337
$249$	1.51347	0.0959124
$250$	18.3626	1.16136
$251$	−6.62277	−0.418025	−0.209013	−	0.977913i	$-0.567025\pi$
$251$	−6.62277	−0.418025	−0.209013	+	0.977913i	$0.567025\pi$
$252$	−18.7154	−1.17896
$253$	9.54231	0.599920
$254$	54.8227	3.43988
$255$	3.00766	0.188347
$256$	−20.5859	−1.28662
$257$	4.52070	0.281994	0.140997	−	0.990010i	$-0.454969\pi$
$257$	4.52070	0.281994	0.140997	+	0.990010i	$0.454969\pi$
$258$	−29.9355	−1.86370
$259$	−7.40753	−0.460282
$260$	−19.1782	−1.18938
$261$	−9.83256	−0.608620
$262$	−31.2820	−1.93261
$263$	−27.7649	−1.71206	−0.856030	−	0.516926i	$-0.827076\pi$
$263$	−27.7649	−1.71206	−0.856030	+	0.516926i	$0.827076\pi$
$264$	10.2307	0.629655
$265$	8.89979	0.546710
$266$	−14.7331	−0.903344
$267$	−5.67477	−0.347291
$268$	60.6055	3.70207
$269$	−28.7275	−1.75155	−0.875773	−	0.482723i	$-0.839648\pi$
$269$	−28.7275	−1.75155	−0.875773	+	0.482723i	$0.839648\pi$
$270$	10.1637	0.618540
$271$	−17.5028	−1.06322	−0.531610	−	0.846989i	$-0.678413\pi$
$271$	−17.5028	−1.06322	−0.531610	+	0.846989i	$0.678413\pi$
$272$	33.2465	2.01586
$273$	−12.6102	−0.763202
$274$	33.8429	2.04452
$275$	5.91128	0.356463
$276$	−36.6974	−2.20892
$277$	−14.9934	−0.900867	−0.450434	−	0.892810i	$-0.648731\pi$
$277$	−14.9934	−0.900867	−0.450434	+	0.892810i	$0.648731\pi$
$278$	−12.5731	−0.754082
$279$	6.83209	0.409026
$280$	−11.4930	−0.686836
$281$	2.16270	0.129016	0.0645080	−	0.997917i	$-0.479452\pi$
$281$	2.16270	0.129016	0.0645080	+	0.997917i	$0.479452\pi$
$282$	−25.1670	−1.49868
$283$	−24.8361	−1.47635	−0.738176	−	0.674608i	$-0.764313\pi$
$283$	−24.8361	−1.47635	−0.738176	+	0.674608i	$0.764313\pi$
$284$	−22.8530	−1.35607
$285$	2.13174	0.126274
$286$	−18.6732	−1.10417
$287$	26.6736	1.57449
$288$	16.5721	0.976519
$289$	−3.23549	−0.190323
$290$	−10.4512	−0.613713
$291$	−12.5154	−0.733666
$292$	−50.2154	−2.93863
$293$	25.3608	1.48159	0.740797	−	0.671729i	$-0.234448\pi$
$293$	25.3608	1.48159	0.740797	+	0.671729i	$0.234448\pi$
$294$	6.56831	0.383071
$295$	−4.53928	−0.264287
$296$	24.3719	1.41659
$297$	6.95800	0.403744
$298$	24.9603	1.44591
$299$	38.6977	2.23794
$300$	−22.7333	−1.31251
$301$	23.0223	1.32698
$302$	40.7883	2.34711
$303$	−3.39315	−0.194931
$304$	23.5642	1.35150
$305$	−6.47060	−0.370505
$306$	17.6259	1.00760
$307$	13.4808	0.769390	0.384695	−	0.923044i	$-0.374307\pi$
$307$	13.4808	0.769390	0.384695	+	0.923044i	$0.374307\pi$
$308$	−13.6185	−0.775989
$309$	−4.53991	−0.258267
$310$	7.26191	0.412449
$311$	8.30967	0.471198	0.235599	−	0.971850i	$-0.424295\pi$
$311$	8.30967	0.471198	0.235599	+	0.971850i	$0.424295\pi$
$312$	41.4893	2.34887
$313$	0.412906	0.0233389	0.0116694	−	0.999932i	$-0.496285\pi$
$313$	0.412906	0.0233389	0.0116694	+	0.999932i	$0.496285\pi$
$314$	24.1350	1.36201
$315$	−2.96196	−0.166888
$316$	−60.5627	−3.40692
$317$	29.6928	1.66771	0.833857	−	0.551981i	$-0.186128\pi$
$317$	29.6928	1.66771	0.833857	+	0.551981i	$0.186128\pi$
$318$	−33.3253	−1.86879
$319$	−7.15482	−0.400593
$320$	4.17990	0.233663
$321$	−17.2587	−0.963284
$322$	40.1397	2.23690
$323$	9.75590	0.542833
$324$	−0.749410	−0.0416339
$325$	23.9725	1.32975
$326$	−18.9165	−1.04769
$327$	−5.83886	−0.322890
$328$	−87.7600	−4.84573
$329$	19.3550	1.06708
$330$	2.80253	0.154274
$331$	31.3408	1.72265	0.861324	−	0.508056i	$-0.169636\pi$
$331$	31.3408	1.72265	0.861324	+	0.508056i	$0.169636\pi$
$332$	6.62851	0.363787
$333$	6.28111	0.344203
$334$	−7.48846	−0.409750
$335$	9.59163	0.524047
$336$	20.9203	1.14130
$337$	13.5332	0.737202	0.368601	−	0.929588i	$-0.379837\pi$
$337$	13.5332	0.737202	0.368601	+	0.929588i	$0.379837\pi$
$338$	−41.9858	−2.28373
$339$	−4.15249	−0.225533
$340$	13.1726	0.714382
$341$	4.97148	0.269221
$342$	12.4927	0.675529
$343$	−20.1623	−1.08866
$344$	−75.7467	−4.08399
$345$	−5.80785	−0.312684
$346$	−8.86950	−0.476827
$347$	−17.5662	−0.943002	−0.471501	−	0.881866i	$-0.656288\pi$
$347$	−17.5662	−0.943002	−0.471501	+	0.881866i	$0.656288\pi$
$348$	27.5157	1.47500
$349$	−21.7759	−1.16564	−0.582819	−	0.812602i	$-0.698050\pi$
$349$	−21.7759	−1.16564	−0.582819	+	0.812602i	$0.698050\pi$
$350$	24.8658	1.32913
$351$	28.2173	1.50613
$352$	12.0589	0.642744
$353$	−6.02429	−0.320641	−0.160320	−	0.987065i	$-0.551253\pi$
$353$	−6.02429	−0.320641	−0.160320	+	0.987065i	$0.551253\pi$
$354$	16.9973	0.903398
$355$	−3.61679	−0.191959
$356$	−24.8537	−1.31724
$357$	8.66131	0.458405
$358$	48.3127	2.55341
$359$	23.6251	1.24688	0.623442	−	0.781869i	$-0.285734\pi$
$359$	23.6251	1.24688	0.623442	+	0.781869i	$0.285734\pi$
$360$	9.74529	0.513622
$361$	−12.0853	−0.636068
$362$	−5.35042	−0.281212
$363$	−9.97752	−0.523684
$364$	−55.2284	−2.89475
$365$	−7.94726	−0.415979
$366$	24.2292	1.26648
$367$	−36.7540	−1.91854	−0.959270	−	0.282489i	$-0.908840\pi$
$367$	−36.7540	−1.91854	−0.959270	+	0.282489i	$0.908840\pi$
$368$	−64.1997	−3.34664
$369$	−22.6175	−1.17742
$370$	6.67627	0.347083
$371$	25.6292	1.33060
$372$	−19.1191	−0.991278
$373$	32.6611	1.69113	0.845565	−	0.533873i	$-0.179264\pi$
$373$	32.6611	1.69113	0.845565	+	0.533873i	$0.179264\pi$
$374$	12.8257	0.663203
$375$	−7.65124	−0.395108
$376$	−63.6810	−3.28409
$377$	−29.0155	−1.49438
$378$	29.2688	1.50543
$379$	−23.2203	−1.19275	−0.596374	−	0.802707i	$-0.703392\pi$
$379$	−23.2203	−1.19275	−0.596374	+	0.802707i	$0.703392\pi$
$380$	9.33634	0.478944
$381$	−22.8432	−1.17029
$382$	17.7367	0.907489
$383$	18.6203	0.951454	0.475727	−	0.879593i	$-0.342185\pi$
$383$	18.6203	0.951454	0.475727	+	0.879593i	$0.342185\pi$
$384$	3.93078	0.200592
$385$	−2.15532	−0.109845
$386$	6.31052	0.321197
$387$	−19.5214	−0.992329
$388$	−54.8134	−2.78273
$389$	31.8936	1.61707	0.808536	−	0.588447i	$-0.200260\pi$
$389$	31.8936	1.61707	0.808536	+	0.588447i	$0.200260\pi$
$390$	11.3653	0.575505
$391$	−26.5796	−1.34419
$392$	16.6200	0.839437
$393$	13.0344	0.657498
$394$	38.7574	1.95257
$395$	−9.58487	−0.482267
$396$	11.5477	0.580291
$397$	26.2713	1.31852	0.659259	−	0.751916i	$-0.270870\pi$
$397$	26.2713	1.31852	0.659259	+	0.751916i	$0.270870\pi$
$398$	−11.1020	−0.556492
$399$	6.13890	0.307329
$400$	−39.7705	−1.98852
$401$	0.642227	0.0320713	0.0160356	−	0.999871i	$-0.494895\pi$
$401$	0.642227	0.0320713	0.0160356	+	0.999871i	$0.494895\pi$
$402$	−35.9158	−1.79132
$403$	20.1612	1.00430
$404$	−14.8609	−0.739356
$405$	−0.118604	−0.00589349
$406$	−30.0968	−1.49368
$407$	4.57055	0.226554
$408$	−28.4970	−1.41081
$409$	−18.2308	−0.901453	−0.450727	−	0.892662i	$-0.648835\pi$
$409$	−18.2308	−0.901453	−0.450727	+	0.892662i	$0.648835\pi$
$410$	−24.0404	−1.18727
$411$	−14.1015	−0.695574
$412$	−19.8833	−0.979581
$413$	−13.0720	−0.643232
$414$	−34.0359	−1.67277
$415$	1.04905	0.0514959
$416$	48.9036	2.39769
$417$	5.23887	0.256549
$418$	9.09052	0.444632
$419$	−5.47470	−0.267457	−0.133728	−	0.991018i	$-0.542695\pi$
$419$	−5.47470	−0.267457	−0.133728	+	0.991018i	$0.542695\pi$
$420$	8.28882	0.404453
$421$	0.933704	0.0455059	0.0227530	−	0.999741i	$-0.492757\pi$
$421$	0.933704	0.0455059	0.0227530	+	0.999741i	$0.492757\pi$
$422$	−48.0634	−2.33969
$423$	−16.4118	−0.797971
$424$	−84.3240	−4.09513
$425$	−16.4655	−0.798696
$426$	13.5431	0.656163
$427$	−18.6337	−0.901750
$428$	−75.5873	−3.65365
$429$	7.78064	0.375653
$430$	−20.7495	−1.00063
$431$	−7.54339	−0.363352	−0.181676	−	0.983358i	$-0.558152\pi$
$431$	−7.54339	−0.363352	−0.181676	+	0.983358i	$0.558152\pi$
$432$	−46.8127	−2.25228
$433$	38.5703	1.85357	0.926786	−	0.375591i	$-0.122560\pi$
$433$	38.5703	1.85357	0.926786	+	0.375591i	$0.122560\pi$
$434$	20.9125	1.00383
$435$	4.35473	0.208793
$436$	−25.5723	−1.22469
$437$	−18.8389	−0.901186
$438$	29.7585	1.42192
$439$	−1.05300	−0.0502570	−0.0251285	−	0.999684i	$-0.507999\pi$
$439$	−1.05300	−0.0502570	−0.0251285	+	0.999684i	$0.507999\pi$
$440$	7.09132	0.338065
$441$	4.28330	0.203967
$442$	52.0132	2.47402
$443$	27.9719	1.32899	0.664494	−	0.747294i	$-0.268647\pi$
$443$	27.9719	1.32899	0.664494	+	0.747294i	$0.268647\pi$
$444$	−17.5772	−0.834178
$445$	−3.93343	−0.186462
$446$	−5.12642	−0.242743
$447$	−10.4003	−0.491917
$448$	12.0371	0.568699
$449$	−8.61434	−0.406536	−0.203268	−	0.979123i	$-0.565156\pi$
$449$	−8.61434	−0.406536	−0.203268	+	0.979123i	$0.565156\pi$
$450$	−21.0846	−0.993938
$451$	−16.4580	−0.774975
$452$	−18.1866	−0.855424
$453$	−16.9955	−0.798516
$454$	47.4646	2.22762
$455$	−8.74064	−0.409767
$456$	−20.1979	−0.945853
$457$	25.3138	1.18413	0.592065	−	0.805890i	$-0.298313\pi$
$457$	25.3138	1.18413	0.592065	+	0.805890i	$0.298313\pi$
$458$	−38.9239	−1.81880
$459$	−19.3811	−0.904634
$460$	−25.4365	−1.18598
$461$	−29.2124	−1.36056	−0.680279	−	0.732953i	$-0.738142\pi$
$461$	−29.2124	−1.36056	−0.680279	+	0.732953i	$0.738142\pi$
$462$	8.07059	0.375478
$463$	−17.7406	−0.824476	−0.412238	−	0.911076i	$-0.635253\pi$
$463$	−17.7406	−0.824476	−0.412238	+	0.911076i	$0.635253\pi$
$464$	48.1369	2.23470
$465$	−3.02585	−0.140321
$466$	−63.5812	−2.94534
$467$	−16.7075	−0.773132	−0.386566	−	0.922262i	$-0.626339\pi$
$467$	−16.7075	−0.773132	−0.386566	+	0.922262i	$0.626339\pi$
$468$	46.8301	2.16472
$469$	27.6216	1.27544
$470$	−17.4443	−0.804648
$471$	−10.0564	−0.463375
$472$	43.0089	1.97964
$473$	−14.2051	−0.653149
$474$	35.8905	1.64851
$475$	−11.6703	−0.535471
$476$	37.9337	1.73869
$477$	−21.7319	−0.995037
$478$	58.3613	2.66938
$479$	19.7734	0.903472	0.451736	−	0.892152i	$-0.350805\pi$
$479$	19.7734	0.903472	0.451736	+	0.892152i	$0.350805\pi$
$480$	−7.33958	−0.335004
$481$	18.5353	0.845138
$482$	−0.365331	−0.0166404
$483$	−16.7252	−0.761023
$484$	−43.6983	−1.98629
$485$	−8.67496	−0.393910
$486$	−40.2317	−1.82495
$487$	−27.1381	−1.22975	−0.614873	−	0.788626i	$-0.710793\pi$
$487$	−27.1381	−1.22975	−0.614873	+	0.788626i	$0.710793\pi$
$488$	61.3078	2.77527
$489$	7.88201	0.356437
$490$	4.55277	0.205673
$491$	0.393664	0.0177658	0.00888291	−	0.999961i	$-0.497172\pi$
$491$	0.393664	0.0177658	0.00888291	+	0.999961i	$0.497172\pi$
$492$	63.2932	2.85348
$493$	19.9294	0.897574
$494$	36.8655	1.65866
$495$	1.82757	0.0821432
$496$	−33.4476	−1.50184
$497$	−10.4155	−0.467197
$498$	−3.92817	−0.176026
$499$	−20.5938	−0.921906	−0.460953	−	0.887425i	$-0.652492\pi$
$499$	−20.5938	−0.921906	−0.460953	+	0.887425i	$0.652492\pi$
$500$	−33.5099	−1.49861
$501$	3.12025	0.139402
$502$	17.1892	0.767192
$503$	−6.70011	−0.298743	−0.149372	−	0.988781i	$-0.547725\pi$
$503$	−6.70011	−0.298743	−0.149372	+	0.988781i	$0.547725\pi$
$504$	28.0641	1.25007
$505$	−2.35193	−0.104660
$506$	−24.7668	−1.10102
$507$	17.4944	0.776954
$508$	−100.046	−4.43882
$509$	−31.4472	−1.39387	−0.696937	−	0.717133i	$-0.745454\pi$
$509$	−31.4472	−1.39387	−0.696937	+	0.717133i	$0.745454\pi$
$510$	−7.80628	−0.345668
$511$	−22.8862	−1.01242
$512$	46.1607	2.04004
$513$	−13.7368	−0.606495
$514$	−11.7334	−0.517536
$515$	−3.14680	−0.138665
$516$	54.6292	2.40491
$517$	−11.9423	−0.525223
$518$	19.2260	0.844744
$519$	3.69569	0.162223
$520$	28.7580	1.26112
$521$	28.1904	1.23504	0.617522	−	0.786553i	$-0.288136\pi$
$521$	28.1904	1.23504	0.617522	+	0.786553i	$0.288136\pi$
$522$	25.5201	1.11699
$523$	−7.57788	−0.331358	−0.165679	−	0.986180i	$-0.552982\pi$
$523$	−7.57788	−0.331358	−0.165679	+	0.986180i	$0.552982\pi$
$524$	57.0864	2.49383
$525$	−10.3609	−0.452188
$526$	72.0631	3.14210
$527$	−13.8478	−0.603219
$528$	−12.9081	−0.561755
$529$	28.3258	1.23156
$530$	−23.0991	−1.00336
$531$	11.0842	0.481015
$532$	26.8864	1.16567
$533$	−66.7433	−2.89097
$534$	14.7287	0.637374
$535$	−11.9627	−0.517193
$536$	−90.8790	−3.92537
$537$	−20.1307	−0.868702
$538$	74.5613	3.21457
$539$	3.11681	0.134251
$540$	−18.5476	−0.798163
$541$	−22.3027	−0.958868	−0.479434	−	0.877578i	$-0.659158\pi$
$541$	−22.3027	−0.958868	−0.479434	+	0.877578i	$0.659158\pi$
$542$	45.4280	1.95130
$543$	2.22938	0.0956719
$544$	−33.5895	−1.44014
$545$	−4.04716	−0.173361
$546$	32.7293	1.40068
$547$	43.3587	1.85389	0.926943	−	0.375202i	$-0.122427\pi$
$547$	43.3587	1.85389	0.926943	+	0.375202i	$0.122427\pi$
$548$	−61.7598	−2.63825
$549$	15.8002	0.674337
$550$	−15.3425	−0.654208
$551$	14.1254	0.601762
$552$	55.0284	2.34216
$553$	−27.6021	−1.17376
$554$	38.9150	1.65334
$555$	−2.78183	−0.118082
$556$	22.9446	0.973066
$557$	15.4095	0.652921	0.326461	−	0.945211i	$-0.394144\pi$
$557$	15.4095	0.652921	0.326461	+	0.945211i	$0.394144\pi$
$558$	−17.7325	−0.750676
$559$	−57.6069	−2.43651
$560$	14.5008	0.612769
$561$	−5.34415	−0.225630
$562$	−5.61323	−0.236780
$563$	3.19261	0.134552	0.0672762	−	0.997734i	$-0.478569\pi$
$563$	3.19261	0.134552	0.0672762	+	0.997734i	$0.478569\pi$
$564$	45.9273	1.93389
$565$	−2.87827	−0.121090
$566$	64.4614	2.70951
$567$	−0.341551	−0.0143438
$568$	34.2684	1.43787
$569$	23.8055	0.997978	0.498989	−	0.866608i	$-0.333705\pi$
$569$	23.8055	0.997978	0.498989	+	0.866608i	$0.333705\pi$
$570$	−5.53288	−0.231747
$571$	25.8856	1.08328	0.541640	−	0.840610i	$-0.317804\pi$
$571$	25.8856	1.08328	0.541640	+	0.840610i	$0.317804\pi$
$572$	34.0767	1.42482
$573$	−7.39043	−0.308740
$574$	−69.2304	−2.88962
$575$	31.7953	1.32596
$576$	−10.2067	−0.425278
$577$	9.64042	0.401336	0.200668	−	0.979659i	$-0.435689\pi$
$577$	9.64042	0.401336	0.200668	+	0.979659i	$0.435689\pi$
$578$	8.39762	0.349295
$579$	−2.62943	−0.109275
$580$	19.0723	0.791933
$581$	3.02101	0.125333
$582$	32.4834	1.34648
$583$	−15.8136	−0.654932
$584$	75.2989	3.11589
$585$	7.41150	0.306428
$586$	−65.8232	−2.71913
$587$	−45.4139	−1.87443	−0.937215	−	0.348751i	$-0.886606\pi$
$587$	−45.4139	−1.87443	−0.937215	+	0.348751i	$0.886606\pi$
$588$	−11.9865	−0.494314
$589$	−9.81493	−0.404417
$590$	11.7816	0.485040
$591$	−16.1492	−0.664290
$592$	−30.7502	−1.26383
$593$	−20.8883	−0.857780	−0.428890	−	0.903357i	$-0.641095\pi$
$593$	−20.8883	−0.857780	−0.428890	+	0.903357i	$0.641095\pi$
$594$	−18.0593	−0.740981
$595$	6.00352	0.246120
$596$	−45.5499	−1.86580
$597$	4.62591	0.189326
$598$	−100.439	−4.10724
$599$	−44.2388	−1.80755	−0.903775	−	0.428009i	$-0.859215\pi$
$599$	−44.2388	−1.80755	−0.903775	+	0.428009i	$0.859215\pi$
$600$	34.0890	1.39168
$601$	12.4682	0.508588	0.254294	−	0.967127i	$-0.418157\pi$
$601$	12.4682	0.508588	0.254294	+	0.967127i	$0.418157\pi$
$602$	−59.7536	−2.43538
$603$	−23.4213	−0.953789
$604$	−74.4345	−3.02870
$605$	−6.91584	−0.281169
$606$	8.80681	0.357752
$607$	24.1111	0.978640	0.489320	−	0.872104i	$-0.337245\pi$
$607$	24.1111	0.978640	0.489320	+	0.872104i	$0.337245\pi$
$608$	−23.8073	−0.965514
$609$	12.5405	0.508169
$610$	16.7942	0.679979
$611$	−48.4307	−1.95930
$612$	−32.1654	−1.30021
$613$	−10.2287	−0.413133	−0.206567	−	0.978433i	$-0.566229\pi$
$613$	−10.2287	−0.413133	−0.206567	+	0.978433i	$0.566229\pi$
$614$	−34.9890	−1.41204
$615$	10.0170	0.403925
$616$	20.4213	0.822796
$617$	36.1857	1.45678	0.728391	−	0.685162i	$-0.240269\pi$
$617$	36.1857	1.45678	0.728391	+	0.685162i	$0.240269\pi$
$618$	11.7832	0.473990
$619$	8.38766	0.337129	0.168564	−	0.985691i	$-0.446087\pi$
$619$	8.38766	0.337129	0.168564	+	0.985691i	$0.446087\pi$
$620$	−13.2522	−0.532223
$621$	37.4254	1.50183
$622$	−21.5675	−0.864778
$623$	−11.3273	−0.453819
$624$	−52.3474	−2.09557
$625$	16.8870	0.675481
$626$	−1.07169	−0.0428332
$627$	−3.78779	−0.151270
$628$	−44.0438	−1.75754
$629$	−12.7310	−0.507619
$630$	7.68768	0.306285
$631$	19.0495	0.758347	0.379174	−	0.925326i	$-0.376208\pi$
$631$	19.0495	0.758347	0.379174	+	0.925326i	$0.376208\pi$
$632$	90.8149	3.61242
$633$	20.0268	0.795993
$634$	−77.0668	−3.06071
$635$	−15.8336	−0.628337
$636$	60.8152	2.41148
$637$	12.6399	0.500809
$638$	18.5701	0.735198
$639$	8.83164	0.349374
$640$	2.72459	0.107699
$641$	−17.5625	−0.693678	−0.346839	−	0.937925i	$-0.612745\pi$
$641$	−17.5625	−0.693678	−0.346839	+	0.937925i	$0.612745\pi$
$642$	44.7943	1.76789
$643$	−36.5435	−1.44114	−0.720568	−	0.693385i	$-0.756119\pi$
$643$	−36.5435	−1.44114	−0.720568	+	0.693385i	$0.756119\pi$
$644$	−73.2509	−2.88649
$645$	8.64580	0.340428
$646$	−25.3212	−0.996248
$647$	−2.38601	−0.0938037	−0.0469018	−	0.998900i	$-0.514935\pi$
$647$	−2.38601	−0.0938037	−0.0469018	+	0.998900i	$0.514935\pi$
$648$	1.12375	0.0441452
$649$	8.06562	0.316603
$650$	−62.2198	−2.44046
$651$	−8.71371	−0.341517
$652$	34.5206	1.35193
$653$	39.0295	1.52734	0.763671	−	0.645605i	$-0.223395\pi$
$653$	39.0295	1.52734	0.763671	+	0.645605i	$0.223395\pi$
$654$	15.1546	0.592591
$655$	9.03469	0.353015
$656$	110.727	4.32318
$657$	19.4060	0.757100
$658$	−50.2354	−1.95838
$659$	3.26390	0.127143	0.0635717	−	0.997977i	$-0.479751\pi$
$659$	3.26390	0.127143	0.0635717	+	0.997977i	$0.479751\pi$
$660$	−5.11432	−0.199075
$661$	−36.2972	−1.41180	−0.705899	−	0.708313i	$-0.749457\pi$
$661$	−36.2972	−1.41180	−0.705899	+	0.708313i	$0.749457\pi$
$662$	−81.3442	−3.16153
$663$	−21.6726	−0.841693
$664$	−9.93957	−0.385730
$665$	4.25513	0.165007
$666$	−16.3024	−0.631707
$667$	−38.4841	−1.49011
$668$	13.6657	0.528740
$669$	2.13605	0.0825844
$670$	−24.8948	−0.961770
$671$	11.4973	0.443848
$672$	−21.1362	−0.815346
$673$	−30.4877	−1.17522	−0.587608	−	0.809146i	$-0.699930\pi$
$673$	−30.4877	−1.17522	−0.587608	+	0.809146i	$0.699930\pi$
$674$	−35.1251	−1.35297
$675$	23.1843	0.892365
$676$	76.6198	2.94692
$677$	1.19767	0.0460301	0.0230151	−	0.999735i	$-0.492673\pi$
$677$	1.19767	0.0460301	0.0230151	+	0.999735i	$0.492673\pi$
$678$	10.7777	0.413914
$679$	−24.9818	−0.958712
$680$	−19.7525	−0.757473
$681$	−19.7773	−0.757866
$682$	−12.9033	−0.494094
$683$	−20.5070	−0.784678	−0.392339	−	0.919821i	$-0.628334\pi$
$683$	−20.5070	−0.784678	−0.392339	+	0.919821i	$0.628334\pi$
$684$	−22.7979	−0.871700
$685$	−9.77432	−0.373458
$686$	52.3306	1.99799
$687$	16.2186	0.618778
$688$	95.5702	3.64358
$689$	−64.1301	−2.44316
$690$	15.0741	0.573862
$691$	−10.1438	−0.385889	−0.192944	−	0.981210i	$-0.561804\pi$
$691$	−10.1438	−0.385889	−0.192944	+	0.981210i	$0.561804\pi$
$692$	16.1859	0.615297
$693$	5.26296	0.199923
$694$	45.5925	1.73067
$695$	3.63128	0.137742
$696$	−41.2603	−1.56397
$697$	45.8427	1.73642
$698$	56.5187	2.13927
$699$	26.4926	1.00204
$700$	−45.3775	−1.71511
$701$	−1.98691	−0.0750447	−0.0375223	−	0.999296i	$-0.511947\pi$
$701$	−1.98691	−0.0750447	−0.0375223	+	0.999296i	$0.511947\pi$
$702$	−73.2372	−2.76416
$703$	−9.02340	−0.340324
$704$	−7.42705	−0.279918
$705$	7.26861	0.273752
$706$	15.6359	0.588463
$707$	−6.77299	−0.254725
$708$	−31.0184	−1.16574
$709$	−35.8371	−1.34589	−0.672944	−	0.739693i	$-0.734971\pi$
$709$	−35.8371	−1.34589	−0.672944	+	0.739693i	$0.734971\pi$
$710$	9.38727	0.352298
$711$	23.4048	0.877748
$712$	37.2685	1.39670
$713$	26.7404	1.00144
$714$	−22.4802	−0.841300
$715$	5.39309	0.201690
$716$	−88.1658	−3.29491
$717$	−24.3176	−0.908159
$718$	−61.3182	−2.28838
$719$	32.2239	1.20175	0.600874	−	0.799344i	$-0.294819\pi$
$719$	32.2239	1.20175	0.600874	+	0.799344i	$0.294819\pi$
$720$	−12.2957	−0.458234
$721$	−9.06203	−0.337488
$722$	31.3670	1.16736
$723$	0.152224	0.00566128
$724$	9.76396	0.362875
$725$	−23.8401	−0.885401
$726$	25.8964	0.961104
$727$	47.5449	1.76334	0.881671	−	0.471864i	$-0.156419\pi$
$727$	47.5449	1.76334	0.881671	+	0.471864i	$0.156419\pi$
$728$	82.8160	3.06936
$729$	17.2382	0.638451
$730$	20.6269	0.763435
$731$	39.5674	1.46345
$732$	−44.2157	−1.63426
$733$	−29.0099	−1.07150	−0.535752	−	0.844375i	$-0.679972\pi$
$733$	−29.0099	−1.07150	−0.535752	+	0.844375i	$0.679972\pi$
$734$	95.3938	3.52105
$735$	−1.89702	−0.0699727
$736$	64.8621	2.39085
$737$	−17.0429	−0.627783
$738$	58.7030	2.16089
$739$	−9.76169	−0.359090	−0.179545	−	0.983750i	$-0.557462\pi$
$739$	−9.76169	−0.359090	−0.179545	+	0.983750i	$0.557462\pi$
$740$	−12.1835	−0.447875
$741$	−15.3609	−0.564297
$742$	−66.5199	−2.44202
$743$	24.2843	0.890905	0.445453	−	0.895305i	$-0.353043\pi$
$743$	24.2843	0.890905	0.445453	+	0.895305i	$0.353043\pi$
$744$	28.6694	1.05107
$745$	−7.20888	−0.264113
$746$	−84.7710	−3.10369
$747$	−2.56162	−0.0937249
$748$	−23.4056	−0.855795
$749$	−34.4497	−1.25876
$750$	19.8586	0.725132
$751$	11.4807	0.418935	0.209468	−	0.977816i	$-0.432827\pi$
$751$	11.4807	0.418935	0.209468	+	0.977816i	$0.432827\pi$
$752$	80.3468	2.92995
$753$	−7.16230	−0.261009
$754$	75.3089	2.74259
$755$	−11.7803	−0.428728
$756$	−53.4126	−1.94260
$757$	20.4648	0.743807	0.371904	−	0.928271i	$-0.378705\pi$
$757$	20.4648	0.743807	0.371904	+	0.928271i	$0.378705\pi$
$758$	60.2676	2.18902
$759$	10.3197	0.374581
$760$	−14.0000	−0.507834
$761$	41.6218	1.50879	0.754394	−	0.656421i	$-0.227931\pi$
$761$	41.6218	1.50879	0.754394	+	0.656421i	$0.227931\pi$
$762$	59.2889	2.14781
$763$	−11.6548	−0.421933
$764$	−32.3677	−1.17102
$765$	−5.09060	−0.184051
$766$	−48.3285	−1.74618
$767$	32.7091	1.18106
$768$	−22.2629	−0.803345
$769$	13.7739	0.496701	0.248350	−	0.968670i	$-0.420112\pi$
$769$	13.7739	0.496701	0.248350	+	0.968670i	$0.420112\pi$
$770$	5.59407	0.201596
$771$	4.88899	0.176073
$772$	−11.5160	−0.414471
$773$	32.5514	1.17079	0.585396	−	0.810748i	$-0.300939\pi$
$773$	32.5514	1.17079	0.585396	+	0.810748i	$0.300939\pi$
$774$	50.6672	1.82120
$775$	16.5652	0.595038
$776$	82.1937	2.95058
$777$	−8.01099	−0.287393
$778$	−82.7790	−2.96777
$779$	32.4921	1.16415
$780$	−20.7405	−0.742629
$781$	6.42649	0.229958
$782$	68.9865	2.46695
$783$	−28.0616	−1.00284
$784$	−20.9696	−0.748914
$785$	−6.97053	−0.248789
$786$	−33.8304	−1.20669
$787$	53.9797	1.92417	0.962085	−	0.272751i	$-0.0879335\pi$
$787$	53.9797	1.92417	0.962085	+	0.272751i	$0.0879335\pi$
$788$	−70.7283	−2.51959
$789$	−30.0268	−1.06898
$790$	24.8772	0.885092
$791$	−8.28871	−0.294713
$792$	−17.3159	−0.615294
$793$	46.6258	1.65573
$794$	−68.1863	−2.41984
$795$	9.62482	0.341357
$796$	20.2600	0.718095
$797$	13.1508	0.465824	0.232912	−	0.972498i	$-0.425175\pi$
$797$	13.1508	0.465824	0.232912	+	0.972498i	$0.425175\pi$
$798$	−15.9333	−0.564034
$799$	33.2647	1.17682
$800$	40.1808	1.42061
$801$	9.60483	0.339370
$802$	−1.66688	−0.0588596
$803$	14.1211	0.498322
$804$	65.5427	2.31151
$805$	−11.5929	−0.408597
$806$	−52.3279	−1.84317
$807$	−31.0678	−1.09364
$808$	22.2841	0.783954
$809$	−14.0199	−0.492913	−0.246457	−	0.969154i	$-0.579266\pi$
$809$	−14.0199	−0.492913	−0.246457	+	0.969154i	$0.579266\pi$
$810$	0.307834	0.0108162
$811$	20.4895	0.719485	0.359742	−	0.933052i	$-0.382865\pi$
$811$	20.4895	0.719485	0.359742	+	0.933052i	$0.382865\pi$
$812$	54.9235	1.92744
$813$	−18.9287	−0.663858
$814$	−11.8627	−0.415789
$815$	5.46335	0.191373
$816$	35.9549	1.25867
$817$	28.0443	0.981146
$818$	47.3174	1.65441
$819$	21.3433	0.745795
$820$	43.8712	1.53205
$821$	−43.3836	−1.51410	−0.757050	−	0.653357i	$-0.773360\pi$
$821$	−43.3836	−1.51410	−0.757050	+	0.653357i	$0.773360\pi$
$822$	36.5999	1.27657
$823$	0.608462	0.0212096	0.0106048	−	0.999944i	$-0.496624\pi$
$823$	0.608462	0.0212096	0.0106048	+	0.999944i	$0.496624\pi$
$824$	29.8154	1.03867
$825$	6.39284	0.222570
$826$	33.9280	1.18051
$827$	22.5602	0.784496	0.392248	−	0.919859i	$-0.371697\pi$
$827$	22.5602	0.784496	0.392248	+	0.919859i	$0.371697\pi$
$828$	62.1121	2.15854
$829$	21.9917	0.763803	0.381901	−	0.924203i	$-0.375269\pi$
$829$	21.9917	0.763803	0.381901	+	0.924203i	$0.375269\pi$
$830$	−2.72278	−0.0945091
$831$	−16.2149	−0.562488
$832$	−30.1195	−1.04421
$833$	−8.68171	−0.300803
$834$	−13.5973	−0.470837
$835$	2.16278	0.0748459
$836$	−16.5893	−0.573752
$837$	19.4984	0.673963
$838$	14.2094	0.490856
$839$	6.33472	0.218699	0.109349	−	0.994003i	$-0.465123\pi$
$839$	6.33472	0.218699	0.109349	+	0.994003i	$0.465123\pi$
$840$	−12.4292	−0.428850
$841$	−0.144654	−0.00498808
$842$	−2.42340	−0.0835159
$843$	2.33889	0.0805556
$844$	87.7108	3.01913
$845$	12.1261	0.417151
$846$	42.5964	1.46450
$847$	−19.9159	−0.684320
$848$	106.392	3.65353
$849$	−26.8594	−0.921812
$850$	42.7358	1.46583
$851$	24.5839	0.842725
$852$	−24.7147	−0.846711
$853$	24.3078	0.832284	0.416142	−	0.909300i	$-0.363382\pi$
$853$	24.3078	0.832284	0.416142	+	0.909300i	$0.363382\pi$
$854$	48.3633	1.65496
$855$	−3.60808	−0.123394
$856$	113.344	3.87403
$857$	−58.2558	−1.98998	−0.994990	−	0.0999711i	$-0.968125\pi$
$857$	−58.2558	−1.98998	−0.994990	+	0.0999711i	$0.968125\pi$
$858$	−20.1944	−0.689427
$859$	−2.40797	−0.0821590	−0.0410795	−	0.999156i	$-0.513080\pi$
$859$	−2.40797	−0.0821590	−0.0410795	+	0.999156i	$0.513080\pi$
$860$	37.8658	1.29121
$861$	28.8465	0.983087
$862$	19.5787	0.666852
$863$	−32.6585	−1.11171	−0.555855	−	0.831279i	$-0.687609\pi$
$863$	−32.6585	−1.11171	−0.555855	+	0.831279i	$0.687609\pi$
$864$	47.2957	1.60903
$865$	2.56164	0.0870984
$866$	−100.108	−3.40181
$867$	−3.49907	−0.118835
$868$	−38.1632	−1.29534
$869$	17.0309	0.577733
$870$	−11.3026	−0.383193
$871$	−69.1154	−2.34188
$872$	38.3461	1.29856
$873$	21.1829	0.716934
$874$	48.8957	1.65392
$875$	−15.2725	−0.516304
$876$	−54.3062	−1.83484
$877$	3.58565	0.121079	0.0605394	−	0.998166i	$-0.480718\pi$
$877$	3.58565	0.121079	0.0605394	+	0.998166i	$0.480718\pi$
$878$	2.73304	0.0922355
$879$	27.4268	0.925084
$880$	−8.94718	−0.301609
$881$	24.8449	0.837046	0.418523	−	0.908206i	$-0.362548\pi$
$881$	24.8449	0.837046	0.418523	+	0.908206i	$0.362548\pi$
$882$	−11.1172	−0.374335
$883$	−36.9256	−1.24264	−0.621322	−	0.783555i	$-0.713404\pi$
$883$	−36.9256	−1.24264	−0.621322	+	0.783555i	$0.713404\pi$
$884$	−94.9188	−3.19246
$885$	−4.90908	−0.165017
$886$	−72.6004	−2.43906
$887$	47.4016	1.59159	0.795795	−	0.605567i	$-0.207053\pi$
$887$	47.4016	1.59159	0.795795	+	0.605567i	$0.207053\pi$
$888$	26.3574	0.884495
$889$	−45.5969	−1.52927
$890$	10.2091	0.342210
$891$	0.210742	0.00706012
$892$	9.35520	0.313235
$893$	23.5771	0.788978
$894$	26.9937	0.902803
$895$	−13.9534	−0.466411
$896$	7.84615	0.262122
$897$	41.8502	1.39734
$898$	22.3583	0.746105
$899$	−20.0499	−0.668703
$900$	38.4772	1.28257
$901$	44.0479	1.46745
$902$	42.7161	1.42229
$903$	24.8978	0.828547
$904$	27.2711	0.907023
$905$	1.54528	0.0513668
$906$	44.1112	1.46550
$907$	−7.99303	−0.265404	−0.132702	−	0.991156i	$-0.542365\pi$
$907$	−7.99303	−0.265404	−0.132702	+	0.991156i	$0.542365\pi$
$908$	−86.6179	−2.87452
$909$	5.74306	0.190485
$910$	22.6861	0.752036
$911$	3.00986	0.0997213	0.0498606	−	0.998756i	$-0.484122\pi$
$911$	3.00986	0.0997213	0.0498606	+	0.998756i	$0.484122\pi$
$912$	25.4839	0.843855
$913$	−1.86401	−0.0616896
$914$	−65.7012	−2.17320
$915$	−6.99773	−0.231338
$916$	71.0322	2.34697
$917$	26.0177	0.859180
$918$	50.3031	1.66025
$919$	21.3037	0.702746	0.351373	−	0.936236i	$-0.385715\pi$
$919$	21.3037	0.702746	0.351373	+	0.936236i	$0.385715\pi$
$920$	38.1425	1.25752
$921$	14.5790	0.480395
$922$	75.8200	2.49700
$923$	26.0618	0.857836
$924$	−14.7280	−0.484515
$925$	15.2293	0.500735
$926$	46.0452	1.51314
$927$	7.68402	0.252376
$928$	−48.6336	−1.59648
$929$	14.8078	0.485827	0.242914	−	0.970048i	$-0.421897\pi$
$929$	14.8078	0.485827	0.242914	+	0.970048i	$0.421897\pi$
$930$	7.85351	0.257527
$931$	−6.15335	−0.201668
$932$	116.029	3.80066
$933$	8.98663	0.294209
$934$	43.3639	1.41891
$935$	−3.70426	−0.121142
$936$	−70.2226	−2.29530
$937$	−34.5264	−1.12793	−0.563965	−	0.825799i	$-0.690725\pi$
$937$	−34.5264	−1.12793	−0.563965	+	0.825799i	$0.690725\pi$
$938$	−71.6909	−2.34079
$939$	0.446544	0.0145724
$940$	31.8341	1.03831
$941$	−39.5370	−1.28887	−0.644435	−	0.764660i	$-0.722907\pi$
$941$	−39.5370	−1.28887	−0.644435	+	0.764660i	$0.722907\pi$
$942$	26.1011	0.850421
$943$	−88.5234	−2.88272
$944$	−54.2647	−1.76616
$945$	−8.45327	−0.274985
$946$	36.8688	1.19871
$947$	18.2910	0.594377	0.297189	−	0.954819i	$-0.403951\pi$
$947$	18.2910	0.594377	0.297189	+	0.954819i	$0.403951\pi$
$948$	−65.4965	−2.12723
$949$	57.2664	1.85894
$950$	30.2900	0.982737
$951$	32.1117	1.04129
$952$	−56.8823	−1.84357
$953$	−47.1751	−1.52815	−0.764075	−	0.645127i	$-0.776804\pi$
$953$	−47.1751	−1.52815	−0.764075	+	0.645127i	$0.776804\pi$
$954$	56.4046	1.82617
$955$	−5.12262	−0.165764
$956$	−106.503	−3.44456
$957$	−7.73769	−0.250124
$958$	−51.3214	−1.65812
$959$	−28.1477	−0.908935
$960$	4.52042	0.145896
$961$	−17.0684	−0.550595
$962$	−48.1079	−1.55106
$963$	29.2111	0.941314
$964$	0.666692	0.0214727
$965$	−1.82257	−0.0586706
$966$	43.4098	1.39669
$967$	2.57144	0.0826918	0.0413459	−	0.999145i	$-0.486835\pi$
$967$	2.57144	0.0826918	0.0413459	+	0.999145i	$0.486835\pi$
$968$	65.5264	2.10610
$969$	10.5507	0.338937
$970$	22.5156	0.722932
$971$	51.7560	1.66093	0.830464	−	0.557072i	$-0.188075\pi$
$971$	51.7560	1.66093	0.830464	+	0.557072i	$0.188075\pi$
$972$	73.4187	2.35491
$973$	10.4572	0.335243
$974$	70.4362	2.25692
$975$	25.9254	0.830277
$976$	−77.3526	−2.47600
$977$	8.24030	0.263630	0.131815	−	0.991274i	$-0.457919\pi$
$977$	8.24030	0.263630	0.131815	+	0.991274i	$0.457919\pi$
$978$	−20.4575	−0.654159
$979$	6.98911	0.223373
$980$	−8.30834	−0.265400
$981$	9.88255	0.315525
$982$	−1.02174	−0.0326052
$983$	57.4953	1.83382	0.916908	−	0.399099i	$-0.130677\pi$
$983$	57.4953	1.83382	0.916908	+	0.399099i	$0.130677\pi$
$984$	−94.9094	−3.02560
$985$	−11.1937	−0.356661
$986$	−51.7261	−1.64729
$987$	20.9318	0.666267
$988$	−67.2758	−2.14033
$989$	−76.4056	−2.42956
$990$	−4.74341	−0.150755
$991$	45.5934	1.44832	0.724160	−	0.689632i	$-0.242228\pi$
$991$	45.5934	1.44832	0.724160	+	0.689632i	$0.242228\pi$
$992$	33.7927	1.07292
$993$	33.8940	1.07559
$994$	27.0330	0.857436
$995$	3.20641	0.101650
$996$	7.16851	0.227143
$997$	8.52491	0.269986	0.134993	−	0.990847i	$-0.456899\pi$
$997$	8.52491	0.269986	0.134993	+	0.990847i	$0.456899\pi$
$998$	53.4506	1.69195
$999$	17.9259	0.567151

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4019.2.a.a.1.6	✓	149

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4019.2.a.a.1.6	✓	149	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:	\( N \)	\(=\)	\( 4019 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4019.a (trivial)

\(f(q)\)	\(=\)	\(q-2.59547 q^{2} +1.08147 q^{3} +4.73647 q^{4} +0.749609 q^{5} -2.80691 q^{6} +2.15869 q^{7} -7.10242 q^{8} -1.83043 q^{9} +O(q^{10})\)	\(q-2.59547 q^{2} +1.08147 q^{3} +4.73647 q^{4} +0.749609 q^{5} -2.80691 q^{6} +2.15869 q^{7} -7.10242 q^{8} -1.83043 q^{9} -1.94559 q^{10} -1.33194 q^{11} +5.12233 q^{12} -5.40153 q^{13} -5.60282 q^{14} +0.810677 q^{15} +8.96118 q^{16} +3.71006 q^{17} +4.75083 q^{18} +2.62958 q^{19} +3.55050 q^{20} +2.33455 q^{21} +3.45702 q^{22} -7.16420 q^{23} -7.68102 q^{24} -4.43809 q^{25} +14.0195 q^{26} -5.22395 q^{27} +10.2246 q^{28} +5.37172 q^{29} -2.10409 q^{30} -3.73250 q^{31} -9.05364 q^{32} -1.44045 q^{33} -9.62934 q^{34} +1.61818 q^{35} -8.66978 q^{36} -3.43149 q^{37} -6.82501 q^{38} -5.84157 q^{39} -5.32404 q^{40} +12.3564 q^{41} -6.05926 q^{42} +10.6649 q^{43} -6.30870 q^{44} -1.37211 q^{45} +18.5945 q^{46} +8.96610 q^{47} +9.69121 q^{48} -2.34005 q^{49} +11.5189 q^{50} +4.01230 q^{51} -25.5842 q^{52} +11.8726 q^{53} +13.5586 q^{54} -0.998437 q^{55} -15.3319 q^{56} +2.84381 q^{57} -13.9421 q^{58} -6.05553 q^{59} +3.83974 q^{60} -8.63196 q^{61} +9.68759 q^{62} -3.95134 q^{63} +5.57610 q^{64} -4.04904 q^{65} +3.73865 q^{66} +12.7955 q^{67} +17.5726 q^{68} -7.74784 q^{69} -4.19993 q^{70} -4.82490 q^{71} +13.0005 q^{72} -10.6019 q^{73} +8.90634 q^{74} -4.79964 q^{75} +12.4549 q^{76} -2.87526 q^{77} +15.1616 q^{78} -12.7865 q^{79} +6.71739 q^{80} -0.158221 q^{81} -32.0705 q^{82} +1.39946 q^{83} +11.0575 q^{84} +2.78109 q^{85} -27.6805 q^{86} +5.80933 q^{87} +9.46002 q^{88} -5.24730 q^{89} +3.56127 q^{90} -11.6603 q^{91} -33.9330 q^{92} -4.03657 q^{93} -23.2712 q^{94} +1.97116 q^{95} -9.79120 q^{96} -11.5726 q^{97} +6.07352 q^{98} +2.43803 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 149 q - 8 q^{2} - 12 q^{3} + 124 q^{4} - 36 q^{5} - 45 q^{6} - 32 q^{7} - 21 q^{8} + 115 q^{9}+O(q^{10}) \) 149 * q - 8 * q^2 - 12 * q^3 + 124 * q^4 - 36 * q^5 - 45 * q^6 - 32 * q^7 - 21 * q^8 + 115 * q^9	\( 149 q - 8 q^{2} - 12 q^{3} + 124 q^{4} - 36 q^{5} - 45 q^{6} - 32 q^{7} - 21 q^{8} + 115 q^{9} - 58 q^{10} - 33 q^{11} - 33 q^{12} - 107 q^{13} - 28 q^{14} - 24 q^{15} + 74 q^{16} - 39 q^{17} - 33 q^{18} - 93 q^{19} - 63 q^{20} - 113 q^{21} - 38 q^{22} - 11 q^{23} - 130 q^{24} + 85 q^{25} - 33 q^{26} - 30 q^{27} - 94 q^{28} - 85 q^{29} - 16 q^{30} - 129 q^{31} - 35 q^{32} - 64 q^{33} - 78 q^{34} - 27 q^{35} + 79 q^{36} - 135 q^{37} - 11 q^{38} - 73 q^{39} - 146 q^{40} - 101 q^{41} + 4 q^{42} - 55 q^{43} - 82 q^{44} - 168 q^{45} - 113 q^{46} - 40 q^{47} - 65 q^{48} + 27 q^{49} - 5 q^{50} - 49 q^{51} - 177 q^{52} - 32 q^{53} - 155 q^{54} - 128 q^{55} - 44 q^{56} - 47 q^{57} - 46 q^{58} - 53 q^{59} - 11 q^{60} - 347 q^{61} - 11 q^{62} - 73 q^{63} + q^{64} - 31 q^{65} - 37 q^{66} - 40 q^{67} - 80 q^{68} - 175 q^{69} - 61 q^{70} - 31 q^{71} - 68 q^{72} - 193 q^{73} - 33 q^{74} - 56 q^{75} - 248 q^{76} - 84 q^{77} + 40 q^{78} - 111 q^{79} - 54 q^{80} + 49 q^{81} - 74 q^{82} - 24 q^{83} - 159 q^{84} - 258 q^{85} - q^{86} - 66 q^{87} - 97 q^{88} - 76 q^{89} - 75 q^{90} - 134 q^{91} + 31 q^{92} - 97 q^{93} - 111 q^{94} - 14 q^{95} - 216 q^{96} - 140 q^{97} - 13 q^{98} - 116 q^{99}+O(q^{100}) \) 149 * q - 8 * q^2 - 12 * q^3 + 124 * q^4 - 36 * q^5 - 45 * q^6 - 32 * q^7 - 21 * q^8 + 115 * q^9 - 58 * q^10 - 33 * q^11 - 33 * q^12 - 107 * q^13 - 28 * q^14 - 24 * q^15 + 74 * q^16 - 39 * q^17 - 33 * q^18 - 93 * q^19 - 63 * q^20 - 113 * q^21 - 38 * q^22 - 11 * q^23 - 130 * q^24 + 85 * q^25 - 33 * q^26 - 30 * q^27 - 94 * q^28 - 85 * q^29 - 16 * q^30 - 129 * q^31 - 35 * q^32 - 64 * q^33 - 78 * q^34 - 27 * q^35 + 79 * q^36 - 135 * q^37 - 11 * q^38 - 73 * q^39 - 146 * q^40 - 101 * q^41 + 4 * q^42 - 55 * q^43 - 82 * q^44 - 168 * q^45 - 113 * q^46 - 40 * q^47 - 65 * q^48 + 27 * q^49 - 5 * q^50 - 49 * q^51 - 177 * q^52 - 32 * q^53 - 155 * q^54 - 128 * q^55 - 44 * q^56 - 47 * q^57 - 46 * q^58 - 53 * q^59 - 11 * q^60 - 347 * q^61 - 11 * q^62 - 73 * q^63 + q^64 - 31 * q^65 - 37 * q^66 - 40 * q^67 - 80 * q^68 - 175 * q^69 - 61 * q^70 - 31 * q^71 - 68 * q^72 - 193 * q^73 - 33 * q^74 - 56 * q^75 - 248 * q^76 - 84 * q^77 + 40 * q^78 - 111 * q^79 - 54 * q^80 + 49 * q^81 - 74 * q^82 - 24 * q^83 - 159 * q^84 - 258 * q^85 - q^86 - 66 * q^87 - 97 * q^88 - 76 * q^89 - 75 * q^90 - 134 * q^91 + 31 * q^92 - 97 * q^93 - 111 * q^94 - 14 * q^95 - 216 * q^96 - 140 * q^97 - 13 * q^98 - 116 * q^99

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