LMFDB - Embedded newform 6019.2.a.d.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6019,2,Mod(1,6019)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6019, 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("6019.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6019 = 13 \cdot 463 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6019.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:	$48.0619569766$
Analytic rank:	$0$
Dimension:	$123$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	6019.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.17075 q^{2} -1.42264 q^{3} +2.71217 q^{4} -2.44924 q^{5} +3.08820 q^{6} +1.96298 q^{7} -1.54596 q^{8} -0.976102 q^{9} +O(q^{10})$	\(q-2.17075 q^{2} -1.42264 q^{3} +2.71217 q^{4} -2.44924 q^{5} +3.08820 q^{6} +1.96298 q^{7} -1.54596 q^{8} -0.976102 q^{9} +5.31670 q^{10} +0.687870 q^{11} -3.85844 q^{12} -1.00000 q^{13} -4.26114 q^{14} +3.48438 q^{15} -2.06846 q^{16} +2.73867 q^{17} +2.11888 q^{18} -2.73534 q^{19} -6.64276 q^{20} -2.79261 q^{21} -1.49320 q^{22} +1.29423 q^{23} +2.19934 q^{24} +0.998773 q^{25} +2.17075 q^{26} +5.65655 q^{27} +5.32394 q^{28} -3.31618 q^{29} -7.56373 q^{30} -3.43661 q^{31} +7.58203 q^{32} -0.978590 q^{33} -5.94498 q^{34} -4.80780 q^{35} -2.64736 q^{36} -5.31574 q^{37} +5.93776 q^{38} +1.42264 q^{39} +3.78642 q^{40} -1.76876 q^{41} +6.06206 q^{42} +7.72318 q^{43} +1.86562 q^{44} +2.39071 q^{45} -2.80945 q^{46} +11.9341 q^{47} +2.94267 q^{48} -3.14672 q^{49} -2.16809 q^{50} -3.89614 q^{51} -2.71217 q^{52} -6.52597 q^{53} -12.2790 q^{54} -1.68476 q^{55} -3.03468 q^{56} +3.89140 q^{57} +7.19861 q^{58} +8.26965 q^{59} +9.45025 q^{60} -4.66279 q^{61} +7.46003 q^{62} -1.91607 q^{63} -12.3218 q^{64} +2.44924 q^{65} +2.12428 q^{66} +5.33383 q^{67} +7.42775 q^{68} -1.84122 q^{69} +10.4366 q^{70} -14.4771 q^{71} +1.50901 q^{72} +6.03305 q^{73} +11.5392 q^{74} -1.42089 q^{75} -7.41873 q^{76} +1.35027 q^{77} -3.08820 q^{78} +6.90267 q^{79} +5.06615 q^{80} -5.11892 q^{81} +3.83954 q^{82} -1.55528 q^{83} -7.57403 q^{84} -6.70766 q^{85} -16.7651 q^{86} +4.71772 q^{87} -1.06342 q^{88} -7.58241 q^{89} -5.18964 q^{90} -1.96298 q^{91} +3.51018 q^{92} +4.88904 q^{93} -25.9059 q^{94} +6.69951 q^{95} -10.7865 q^{96} -4.21992 q^{97} +6.83075 q^{98} -0.671431 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 123 q + 10 q^{2} + q^{3} + 136 q^{4} + 46 q^{5} + 16 q^{6} + 12 q^{7} + 30 q^{8} + 154 q^{9}+O(q^{10}) $ 123 * q + 10 * q^2 + q^3 + 136 * q^4 + 46 * q^5 + 16 * q^6 + 12 * q^7 + 30 * q^8 + 154 * q^9	\( 123 q + 10 q^{2} + q^{3} + 136 q^{4} + 46 q^{5} + 16 q^{6} + 12 q^{7} + 30 q^{8} + 154 q^{9} + 5 q^{10} + 53 q^{11} - 6 q^{12} - 123 q^{13} + 21 q^{14} + 29 q^{15} + 166 q^{16} - 35 q^{17} + 28 q^{18} + 23 q^{19} + 93 q^{20} + 72 q^{21} + 8 q^{22} + 42 q^{23} + 55 q^{24} + 153 q^{25} - 10 q^{26} + 7 q^{27} + 39 q^{28} + 86 q^{29} + 44 q^{30} + 16 q^{31} + 70 q^{32} + 40 q^{33} + 10 q^{34} + 6 q^{35} + 222 q^{36} + 52 q^{37} + 12 q^{38} - q^{39} + 14 q^{40} + 80 q^{41} + 29 q^{42} + 2 q^{43} + 143 q^{44} + 137 q^{45} + 39 q^{46} + 45 q^{47} - 27 q^{48} + 163 q^{49} + 102 q^{50} + 48 q^{51} - 136 q^{52} + 117 q^{53} + 75 q^{54} + 20 q^{55} + 88 q^{56} + 67 q^{57} + 56 q^{58} + 88 q^{59} + 96 q^{60} + 57 q^{61} - 13 q^{62} + 48 q^{63} + 228 q^{64} - 46 q^{65} + 28 q^{66} + 43 q^{67} - 56 q^{68} + 92 q^{69} + 14 q^{70} + 90 q^{71} + 98 q^{72} + 25 q^{73} + 80 q^{74} + 21 q^{75} + 75 q^{76} + 112 q^{77} - 16 q^{78} + 36 q^{79} + 208 q^{80} + 231 q^{81} - 27 q^{82} + 93 q^{83} + 175 q^{84} + 77 q^{85} + 199 q^{86} + 15 q^{87} + 43 q^{88} + 140 q^{89} + 11 q^{90} - 12 q^{91} + 93 q^{92} + 140 q^{93} + 4 q^{94} + 23 q^{95} + 105 q^{96} + 43 q^{97} + 67 q^{98} + 140 q^{99}+O(q^{100}) \) 123 * q + 10 * q^2 + q^3 + 136 * q^4 + 46 * q^5 + 16 * q^6 + 12 * q^7 + 30 * q^8 + 154 * q^9 + 5 * q^10 + 53 * q^11 - 6 * q^12 - 123 * q^13 + 21 * q^14 + 29 * q^15 + 166 * q^16 - 35 * q^17 + 28 * q^18 + 23 * q^19 + 93 * q^20 + 72 * q^21 + 8 * q^22 + 42 * q^23 + 55 * q^24 + 153 * q^25 - 10 * q^26 + 7 * q^27 + 39 * q^28 + 86 * q^29 + 44 * q^30 + 16 * q^31 + 70 * q^32 + 40 * q^33 + 10 * q^34 + 6 * q^35 + 222 * q^36 + 52 * q^37 + 12 * q^38 - q^39 + 14 * q^40 + 80 * q^41 + 29 * q^42 + 2 * q^43 + 143 * q^44 + 137 * q^45 + 39 * q^46 + 45 * q^47 - 27 * q^48 + 163 * q^49 + 102 * q^50 + 48 * q^51 - 136 * q^52 + 117 * q^53 + 75 * q^54 + 20 * q^55 + 88 * q^56 + 67 * q^57 + 56 * q^58 + 88 * q^59 + 96 * q^60 + 57 * q^61 - 13 * q^62 + 48 * q^63 + 228 * q^64 - 46 * q^65 + 28 * q^66 + 43 * q^67 - 56 * q^68 + 92 * q^69 + 14 * q^70 + 90 * q^71 + 98 * q^72 + 25 * q^73 + 80 * q^74 + 21 * q^75 + 75 * q^76 + 112 * q^77 - 16 * q^78 + 36 * q^79 + 208 * q^80 + 231 * q^81 - 27 * q^82 + 93 * q^83 + 175 * q^84 + 77 * q^85 + 199 * q^86 + 15 * q^87 + 43 * q^88 + 140 * q^89 + 11 * q^90 - 12 * q^91 + 93 * q^92 + 140 * q^93 + 4 * q^94 + 23 * q^95 + 105 * q^96 + 43 * q^97 + 67 * q^98 + 140 * 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 $

$2$	−2.17075	−1.53496	−0.767478	−	0.641076i	$-0.778488\pi$
$2$	−2.17075	−1.53496	−0.767478	+	0.641076i	$0.778488\pi$
$3$	−1.42264	−0.821360	−0.410680	−	0.911779i	$-0.634709\pi$
$3$	−1.42264	−0.821360	−0.410680	+	0.911779i	$0.634709\pi$
$4$	2.71217	1.35609
$5$	−2.44924	−1.09533	−0.547667	−	0.836697i	$-0.684484\pi$
$5$	−2.44924	−1.09533	−0.547667	+	0.836697i	$0.684484\pi$
$6$	3.08820	1.26075
$7$	1.96298	0.741936	0.370968	−	0.928646i	$-0.379026\pi$
$7$	1.96298	0.741936	0.370968	+	0.928646i	$0.379026\pi$
$8$	−1.54596	−0.546578
$9$	−0.976102	−0.325367
$10$	5.31670	1.68129
$11$	0.687870	0.207401	0.103700	−	0.994609i	$-0.466932\pi$
$11$	0.687870	0.207401	0.103700	+	0.994609i	$0.466932\pi$
$12$	−3.85844	−1.11384
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−4.26114	−1.13884
$15$	3.48438	0.899663
$16$	−2.06846	−0.517115
$17$	2.73867	0.664225	0.332113	−	0.943240i	$-0.392239\pi$
$17$	2.73867	0.664225	0.332113	+	0.943240i	$0.392239\pi$
$18$	2.11888	0.499424
$19$	−2.73534	−0.627531	−0.313765	−	0.949501i	$-0.601591\pi$
$19$	−2.73534	−0.627531	−0.313765	+	0.949501i	$0.601591\pi$
$20$	−6.64276	−1.48537
$21$	−2.79261	−0.609397
$22$	−1.49320	−0.318351
$23$	1.29423	0.269866	0.134933	−	0.990855i	$-0.456918\pi$
$23$	1.29423	0.269866	0.134933	+	0.990855i	$0.456918\pi$
$24$	2.19934	0.448937
$25$	0.998773	0.199755
$26$	2.17075	0.425720
$27$	5.65655	1.08860
$28$	5.32394	1.00613
$29$	−3.31618	−0.615799	−0.307900	−	0.951419i	$-0.599626\pi$
$29$	−3.31618	−0.615799	−0.307900	+	0.951419i	$0.599626\pi$
$30$	−7.56373	−1.38094
$31$	−3.43661	−0.617233	−0.308616	−	0.951187i	$-0.599866\pi$
$31$	−3.43661	−0.617233	−0.308616	+	0.951187i	$0.599866\pi$
$32$	7.58203	1.34033
$33$	−0.978590	−0.170351
$34$	−5.94498	−1.01956
$35$	−4.80780	−0.812667
$36$	−2.64736	−0.441227
$37$	−5.31574	−0.873903	−0.436951	−	0.899485i	$-0.643942\pi$
$37$	−5.31574	−0.873903	−0.436951	+	0.899485i	$0.643942\pi$
$38$	5.93776	0.963232
$39$	1.42264	0.227804
$40$	3.78642	0.598685
$41$	−1.76876	−0.276233	−0.138117	−	0.990416i	$-0.544105\pi$
$41$	−1.76876	−0.276233	−0.138117	+	0.990416i	$0.544105\pi$
$42$	6.06206	0.935396
$43$	7.72318	1.17777	0.588887	−	0.808215i	$-0.299566\pi$
$43$	7.72318	1.17777	0.588887	+	0.808215i	$0.299566\pi$
$44$	1.86562	0.281253
$45$	2.39071	0.356386
$46$	−2.80945	−0.414231
$47$	11.9341	1.74076	0.870380	−	0.492380i	$-0.163873\pi$
$47$	11.9341	1.74076	0.870380	+	0.492380i	$0.163873\pi$
$48$	2.94267	0.424737
$49$	−3.14672	−0.449531
$50$	−2.16809	−0.306614
$51$	−3.89614	−0.545568
$52$	−2.71217	−0.376111
$53$	−6.52597	−0.896412	−0.448206	−	0.893930i	$-0.647937\pi$
$53$	−6.52597	−0.896412	−0.448206	+	0.893930i	$0.647937\pi$
$54$	−12.2790	−1.67096
$55$	−1.68476	−0.227173
$56$	−3.03468	−0.405526
$57$	3.89140	0.515429
$58$	7.19861	0.945224
$59$	8.26965	1.07662	0.538309	−	0.842748i	$-0.319063\pi$
$59$	8.26965	1.07662	0.538309	+	0.842748i	$0.319063\pi$
$60$	9.45025	1.22002
$61$	−4.66279	−0.597008	−0.298504	−	0.954408i	$-0.596488\pi$
$61$	−4.66279	−0.597008	−0.298504	+	0.954408i	$0.596488\pi$
$62$	7.46003	0.947424
$63$	−1.91607	−0.241402
$64$	−12.3218	−1.54023
$65$	2.44924	0.303791
$66$	2.12428	0.261481
$67$	5.33383	0.651631	0.325816	−	0.945433i	$-0.394361\pi$
$67$	5.33383	0.651631	0.325816	+	0.945433i	$0.394361\pi$
$68$	7.42775	0.900747
$69$	−1.84122	−0.221657
$70$	10.4366	1.24741
$71$	−14.4771	−1.71812	−0.859060	−	0.511875i	$-0.828951\pi$
$71$	−14.4771	−1.71812	−0.859060	+	0.511875i	$0.828951\pi$
$72$	1.50901	0.177839
$73$	6.03305	0.706115	0.353057	−	0.935602i	$-0.385142\pi$
$73$	6.03305	0.706115	0.353057	+	0.935602i	$0.385142\pi$
$74$	11.5392	1.34140
$75$	−1.42089	−0.164071
$76$	−7.41873	−0.850987
$77$	1.35027	0.153878
$78$	−3.08820	−0.349669
$79$	6.90267	0.776611	0.388305	−	0.921531i	$-0.373061\pi$
$79$	6.90267	0.776611	0.388305	+	0.921531i	$0.373061\pi$
$80$	5.06615	0.566413
$81$	−5.11892	−0.568769
$82$	3.83954	0.424006
$83$	−1.55528	−0.170714	−0.0853572	−	0.996350i	$-0.527203\pi$
$83$	−1.55528	−0.170714	−0.0853572	+	0.996350i	$0.527203\pi$
$84$	−7.57403	−0.826395
$85$	−6.70766	−0.727548
$86$	−16.7651	−1.80783
$87$	4.71772	0.505793
$88$	−1.06342	−0.113361
$89$	−7.58241	−0.803734	−0.401867	−	0.915698i	$-0.631639\pi$
$89$	−7.58241	−0.803734	−0.401867	+	0.915698i	$0.631639\pi$
$90$	−5.18964	−0.547036
$91$	−1.96298	−0.205776
$92$	3.51018	0.365961
$93$	4.88904	0.506970
$94$	−25.9059	−2.67199
$95$	6.69951	0.687355
$96$	−10.7865	−1.10089
$97$	−4.21992	−0.428468	−0.214234	−	0.976782i	$-0.568726\pi$
$97$	−4.21992	−0.428468	−0.214234	+	0.976782i	$0.568726\pi$
$98$	6.83075	0.690010
$99$	−0.671431	−0.0674814
$100$	2.70885	0.270885
$101$	16.6732	1.65904	0.829522	−	0.558475i	$-0.188613\pi$
$101$	16.6732	1.65904	0.829522	+	0.558475i	$0.188613\pi$
$102$	8.45756	0.837423
$103$	4.15545	0.409449	0.204724	−	0.978820i	$-0.434370\pi$
$103$	4.15545	0.409449	0.204724	+	0.978820i	$0.434370\pi$
$104$	1.54596	0.151593
$105$	6.83976	0.667492
$106$	14.1663	1.37595
$107$	−0.924726	−0.0893966	−0.0446983	−	0.999001i	$-0.514233\pi$
$107$	−0.924726	−0.0893966	−0.0446983	+	0.999001i	$0.514233\pi$
$108$	15.3416	1.47624
$109$	−4.86888	−0.466354	−0.233177	−	0.972434i	$-0.574912\pi$
$109$	−4.86888	−0.466354	−0.233177	+	0.972434i	$0.574912\pi$
$110$	3.65720	0.348700
$111$	7.56238	0.717789
$112$	−4.06034	−0.383666
$113$	−4.65629	−0.438026	−0.219013	−	0.975722i	$-0.570284\pi$
$113$	−4.65629	−0.438026	−0.219013	+	0.975722i	$0.570284\pi$
$114$	−8.44728	−0.791160
$115$	−3.16988	−0.295593
$116$	−8.99406	−0.835077
$117$	0.976102	0.0902407
$118$	−17.9514	−1.65256
$119$	5.37595	0.492813
$120$	−5.38670	−0.491736
$121$	−10.5268	−0.956985
$122$	10.1218	0.916381
$123$	2.51630	0.226887
$124$	−9.32067	−0.837021
$125$	9.79996	0.876535
$126$	4.15931	0.370541
$127$	−15.7610	−1.39856	−0.699281	−	0.714847i	$-0.746497\pi$
$127$	−15.7610	−1.39856	−0.699281	+	0.714847i	$0.746497\pi$
$128$	11.5836	1.02385
$129$	−10.9873	−0.967377
$130$	−5.31670	−0.466305
$131$	19.9594	1.74386	0.871930	−	0.489631i	$-0.162868\pi$
$131$	19.9594	1.74386	0.871930	+	0.489631i	$0.162868\pi$
$132$	−2.65411	−0.231010
$133$	−5.36942	−0.465588
$134$	−11.5784	−1.00022
$135$	−13.8543	−1.19238
$136$	−4.23386	−0.363051
$137$	−22.3171	−1.90668	−0.953339	−	0.301903i	$-0.902378\pi$
$137$	−22.3171	−1.90668	−0.953339	+	0.301903i	$0.902378\pi$
$138$	3.99684	0.340233
$139$	−13.8322	−1.17323	−0.586617	−	0.809864i	$-0.699541\pi$
$139$	−13.8322	−1.17323	−0.586617	+	0.809864i	$0.699541\pi$
$140$	−13.0396	−1.10205
$141$	−16.9778	−1.42979
$142$	31.4263	2.63724
$143$	−0.687870	−0.0575226
$144$	2.01903	0.168252
$145$	8.12212	0.674505
$146$	−13.0963	−1.08385
$147$	4.47664	0.369227
$148$	−14.4172	−1.18509
$149$	17.3181	1.41875	0.709377	−	0.704829i	$-0.248976\pi$
$149$	17.3181	1.41875	0.709377	+	0.704829i	$0.248976\pi$
$150$	3.08441	0.251841
$151$	18.8936	1.53754	0.768770	−	0.639525i	$-0.220869\pi$
$151$	18.8936	1.53754	0.768770	+	0.639525i	$0.220869\pi$
$152$	4.22872	0.342995
$153$	−2.67322	−0.216117
$154$	−2.93111	−0.236196
$155$	8.41707	0.676075
$156$	3.85844	0.308923
$157$	−10.9121	−0.870883	−0.435441	−	0.900217i	$-0.643408\pi$
$157$	−10.9121	−0.870883	−0.435441	+	0.900217i	$0.643408\pi$
$158$	−14.9840	−1.19206
$159$	9.28410	0.736277
$160$	−18.5702	−1.46810
$161$	2.54054	0.200223
$162$	11.1119	0.873034
$163$	−4.86565	−0.381107	−0.190553	−	0.981677i	$-0.561028\pi$
$163$	−4.86565	−0.381107	−0.190553	+	0.981677i	$0.561028\pi$
$164$	−4.79718	−0.374596
$165$	2.39680	0.186591
$166$	3.37613	0.262039
$167$	−16.3573	−1.26577	−0.632883	−	0.774247i	$-0.718129\pi$
$167$	−16.3573	−1.26577	−0.632883	+	0.774247i	$0.718129\pi$
$168$	4.31725	0.333083
$169$	1.00000	0.0769231
$170$	14.5607	1.11675
$171$	2.66997	0.204178
$172$	20.9466	1.59716
$173$	−11.1185	−0.845322	−0.422661	−	0.906288i	$-0.638904\pi$
$173$	−11.1185	−0.845322	−0.422661	+	0.906288i	$0.638904\pi$
$174$	−10.2410	−0.776370
$175$	1.96057	0.148205
$176$	−1.42283	−0.107250
$177$	−11.7647	−0.884291
$178$	16.4596	1.23370
$179$	4.17929	0.312375	0.156187	−	0.987727i	$-0.450080\pi$
$179$	4.17929	0.312375	0.156187	+	0.987727i	$0.450080\pi$
$180$	6.48402	0.483290
$181$	11.3116	0.840784	0.420392	−	0.907343i	$-0.361893\pi$
$181$	11.3116	0.840784	0.420392	+	0.907343i	$0.361893\pi$
$182$	4.26114	0.315857
$183$	6.63345	0.490359
$184$	−2.00082	−0.147503
$185$	13.0195	0.957215
$186$	−10.6129	−0.778177
$187$	1.88385	0.137761
$188$	32.3672	2.36062
$189$	11.1037	0.807674
$190$	−14.5430	−1.05506
$191$	−13.6480	−0.987533	−0.493767	−	0.869594i	$-0.664380\pi$
$191$	−13.6480	−0.987533	−0.493767	+	0.869594i	$0.664380\pi$
$192$	17.5295	1.26508
$193$	−23.8114	−1.71398	−0.856991	−	0.515331i	$-0.827669\pi$
$193$	−23.8114	−1.71398	−0.856991	+	0.515331i	$0.827669\pi$
$194$	9.16041	0.657679
$195$	−3.48438	−0.249522
$196$	−8.53445	−0.609604
$197$	−10.9048	−0.776935	−0.388467	−	0.921462i	$-0.626995\pi$
$197$	−10.9048	−0.776935	−0.388467	+	0.921462i	$0.626995\pi$
$198$	1.45751	0.103581
$199$	−14.3115	−1.01451	−0.507256	−	0.861795i	$-0.669340\pi$
$199$	−14.3115	−1.01451	−0.507256	+	0.861795i	$0.669340\pi$
$200$	−1.54406	−0.109181
$201$	−7.58811	−0.535224
$202$	−36.1934	−2.54656
$203$	−6.50959	−0.456883
$204$	−10.5670	−0.739838
$205$	4.33211	0.302568
$206$	−9.02046	−0.628486
$207$	−1.26330	−0.0878054
$208$	2.06846	0.143422
$209$	−1.88156	−0.130150
$210$	−14.8474	−1.02457
$211$	−19.9259	−1.37175	−0.685876	−	0.727718i	$-0.740581\pi$
$211$	−19.9259	−1.37175	−0.685876	+	0.727718i	$0.740581\pi$
$212$	−17.6996	−1.21561
$213$	20.5957	1.41120
$214$	2.00735	0.137220
$215$	−18.9159	−1.29005
$216$	−8.74478	−0.595007
$217$	−6.74598	−0.457947
$218$	10.5691	0.715833
$219$	−8.58284	−0.579975
$220$	−4.56936	−0.308066
$221$	−2.73867	−0.184223
$222$	−16.4161	−1.10177
$223$	2.47573	0.165787	0.0828937	−	0.996558i	$-0.473584\pi$
$223$	2.47573	0.165787	0.0828937	+	0.996558i	$0.473584\pi$
$224$	14.8833	0.994436
$225$	−0.974905	−0.0649936
$226$	10.1077	0.672351
$227$	21.0996	1.40043	0.700216	−	0.713931i	$-0.253087\pi$
$227$	21.0996	1.40043	0.700216	+	0.713931i	$0.253087\pi$
$228$	10.5542	0.698966
$229$	−16.8988	−1.11671	−0.558353	−	0.829604i	$-0.688566\pi$
$229$	−16.8988	−1.11671	−0.558353	+	0.829604i	$0.688566\pi$
$230$	6.88103	0.453721
$231$	−1.92095	−0.126389
$232$	5.12667	0.336582
$233$	19.0321	1.24683	0.623416	−	0.781890i	$-0.285744\pi$
$233$	19.0321	1.24683	0.623416	+	0.781890i	$0.285744\pi$
$234$	−2.11888	−0.138515
$235$	−29.2294	−1.90671
$236$	22.4287	1.45999
$237$	−9.81999	−0.637877
$238$	−11.6699	−0.756445
$239$	15.3945	0.995786	0.497893	−	0.867238i	$-0.334107\pi$
$239$	15.3945	0.995786	0.497893	+	0.867238i	$0.334107\pi$
$240$	−7.20730	−0.465229
$241$	−4.32294	−0.278465	−0.139232	−	0.990260i	$-0.544464\pi$
$241$	−4.32294	−0.278465	−0.139232	+	0.990260i	$0.544464\pi$
$242$	22.8512	1.46893
$243$	−9.68729	−0.621440
$244$	−12.6463	−0.809596
$245$	7.70707	0.492386
$246$	−5.46227	−0.348261
$247$	2.73534	0.174046
$248$	5.31284	0.337366
$249$	2.21260	0.140218
$250$	−21.2733	−1.34544
$251$	15.2693	0.963792	0.481896	−	0.876228i	$-0.339948\pi$
$251$	15.2693	0.963792	0.481896	+	0.876228i	$0.339948\pi$
$252$	−5.19671	−0.327362
$253$	0.890262	0.0559703
$254$	34.2133	2.14673
$255$	9.54257	0.597579
$256$	−0.501440	−0.0313400
$257$	17.0061	1.06081	0.530405	−	0.847744i	$-0.322040\pi$
$257$	17.0061	1.06081	0.530405	+	0.847744i	$0.322040\pi$
$258$	23.8507	1.48488
$259$	−10.4347	−0.648380
$260$	6.64276	0.411967
$261$	3.23693	0.200361
$262$	−43.3269	−2.67675
$263$	9.40555	0.579971	0.289985	−	0.957031i	$-0.406350\pi$
$263$	9.40555	0.579971	0.289985	+	0.957031i	$0.406350\pi$
$264$	1.51286	0.0931099
$265$	15.9837	0.981869
$266$	11.6557	0.714656
$267$	10.7870	0.660155
$268$	14.4663	0.883669
$269$	−28.3577	−1.72900	−0.864501	−	0.502632i	$-0.832365\pi$
$269$	−28.3577	−1.72900	−0.864501	+	0.502632i	$0.832365\pi$
$270$	30.0742	1.83026
$271$	15.1540	0.920541	0.460271	−	0.887779i	$-0.347752\pi$
$271$	15.1540	0.920541	0.460271	+	0.887779i	$0.347752\pi$
$272$	−5.66483	−0.343481
$273$	2.79261	0.169016
$274$	48.4449	2.92666
$275$	0.687026	0.0414292
$276$	−4.99371	−0.300586
$277$	−1.46800	−0.0882034	−0.0441017	−	0.999027i	$-0.514043\pi$
$277$	−1.46800	−0.0882034	−0.0441017	+	0.999027i	$0.514043\pi$
$278$	30.0264	1.80086
$279$	3.35448	0.200827
$280$	7.43265	0.444186
$281$	−17.0749	−1.01860	−0.509302	−	0.860588i	$-0.670096\pi$
$281$	−17.0749	−1.01860	−0.509302	+	0.860588i	$0.670096\pi$
$282$	36.8547	2.19467
$283$	−18.5994	−1.10562	−0.552809	−	0.833308i	$-0.686444\pi$
$283$	−18.5994	−1.10562	−0.552809	+	0.833308i	$0.686444\pi$
$284$	−39.2645	−2.32992
$285$	−9.53098	−0.564566
$286$	1.49320	0.0882946
$287$	−3.47203	−0.204947
$288$	−7.40083	−0.436098
$289$	−9.49968	−0.558805
$290$	−17.6311	−1.03534
$291$	6.00342	0.351927
$292$	16.3627	0.957553
$293$	−17.0533	−0.996264	−0.498132	−	0.867101i	$-0.665980\pi$
$293$	−17.0533	−0.996264	−0.498132	+	0.867101i	$0.665980\pi$
$294$	−9.71769	−0.566747
$295$	−20.2544	−1.17925
$296$	8.21791	0.477656
$297$	3.89097	0.225777
$298$	−37.5933	−2.17772
$299$	−1.29423	−0.0748472
$300$	−3.85371	−0.222494
$301$	15.1604	0.873833
$302$	−41.0134	−2.36006
$303$	−23.7199	−1.36267
$304$	5.65794	0.324505
$305$	11.4203	0.653923
$306$	5.80291	0.331730
$307$	20.9113	1.19347	0.596735	−	0.802438i	$-0.296464\pi$
$307$	20.9113	1.19347	0.596735	+	0.802438i	$0.296464\pi$
$308$	3.66218	0.208672
$309$	−5.91170	−0.336305
$310$	−18.2714	−1.03775
$311$	0.331320	0.0187874	0.00939370	−	0.999956i	$-0.497010\pi$
$311$	0.331320	0.0187874	0.00939370	+	0.999956i	$0.497010\pi$
$312$	−2.19934	−0.124513
$313$	0.219632	0.0124143	0.00620716	−	0.999981i	$-0.498024\pi$
$313$	0.219632	0.0124143	0.00620716	+	0.999981i	$0.498024\pi$
$314$	23.6876	1.33677
$315$	4.69291	0.264415
$316$	18.7212	1.05315
$317$	23.5718	1.32393	0.661963	−	0.749536i	$-0.269724\pi$
$317$	23.5718	1.32393	0.661963	+	0.749536i	$0.269724\pi$
$318$	−20.1535	−1.13015
$319$	−2.28110	−0.127717
$320$	30.1790	1.68706
$321$	1.31555	0.0734268
$322$	−5.51490	−0.307333
$323$	−7.49121	−0.416822
$324$	−13.8834	−0.771300
$325$	−0.998773	−0.0554020
$326$	10.5621	0.584982
$327$	6.92666	0.383045
$328$	2.73442	0.150983
$329$	23.4263	1.29153
$330$	−5.20287	−0.286408
$331$	10.2523	0.563520	0.281760	−	0.959485i	$-0.409082\pi$
$331$	10.2523	0.563520	0.281760	+	0.959485i	$0.409082\pi$
$332$	−4.21820	−0.231504
$333$	5.18871	0.284340
$334$	35.5077	1.94289
$335$	−13.0638	−0.713753
$336$	5.77639	0.315128
$337$	−27.3602	−1.49040	−0.745201	−	0.666839i	$-0.767647\pi$
$337$	−27.3602	−1.49040	−0.745201	+	0.666839i	$0.767647\pi$
$338$	−2.17075	−0.118073
$339$	6.62421	0.359778
$340$	−18.1923	−0.986619
$341$	−2.36394	−0.128014
$342$	−5.79586	−0.313404
$343$	−19.9178	−1.07546
$344$	−11.9397	−0.643745
$345$	4.50959	0.242788
$346$	24.1355	1.29753
$347$	27.3775	1.46970	0.734850	−	0.678229i	$-0.237252\pi$
$347$	27.3775	1.46970	0.734850	+	0.678229i	$0.237252\pi$
$348$	12.7953	0.685899
$349$	0.476966	0.0255314	0.0127657	−	0.999919i	$-0.495936\pi$
$349$	0.476966	0.0255314	0.0127657	+	0.999919i	$0.495936\pi$
$350$	−4.25591	−0.227488
$351$	−5.65655	−0.301924
$352$	5.21545	0.277984
$353$	−15.4143	−0.820420	−0.410210	−	0.911991i	$-0.634545\pi$
$353$	−15.4143	−0.820420	−0.410210	+	0.911991i	$0.634545\pi$
$354$	25.5383	1.35735
$355$	35.4580	1.88191
$356$	−20.5648	−1.08993
$357$	−7.64803	−0.404777
$358$	−9.07221	−0.479481
$359$	12.3089	0.649637	0.324819	−	0.945776i	$-0.394697\pi$
$359$	12.3089	0.649637	0.324819	+	0.945776i	$0.394697\pi$
$360$	−3.69593	−0.194793
$361$	−11.5179	−0.606205
$362$	−24.5547	−1.29057
$363$	14.9759	0.786029
$364$	−5.32394	−0.279050
$365$	−14.7764	−0.773431
$366$	−14.3996	−0.752679
$367$	17.7278	0.925385	0.462693	−	0.886519i	$-0.346883\pi$
$367$	17.7278	0.925385	0.462693	+	0.886519i	$0.346883\pi$
$368$	−2.67706	−0.139551
$369$	1.72649	0.0898773
$370$	−28.2622	−1.46928
$371$	−12.8103	−0.665080
$372$	13.2599	0.687496
$373$	−15.2348	−0.788826	−0.394413	−	0.918933i	$-0.629052\pi$
$373$	−15.2348	−0.788826	−0.394413	+	0.918933i	$0.629052\pi$
$374$	−4.08938	−0.211457
$375$	−13.9418	−0.719951
$376$	−18.4495	−0.951462
$377$	3.31618	0.170792
$378$	−24.1034	−1.23974
$379$	4.91904	0.252674	0.126337	−	0.991987i	$-0.459678\pi$
$379$	4.91904	0.252674	0.126337	+	0.991987i	$0.459678\pi$
$380$	18.1702	0.932114
$381$	22.4222	1.14872
$382$	29.6264	1.51582
$383$	17.0778	0.872634	0.436317	−	0.899793i	$-0.356283\pi$
$383$	17.0778	0.872634	0.436317	+	0.899793i	$0.356283\pi$
$384$	−16.4792	−0.840950
$385$	−3.30714	−0.168548
$386$	51.6887	2.63089
$387$	−7.53861	−0.383209
$388$	−11.4452	−0.581040
$389$	20.8856	1.05894	0.529471	−	0.848328i	$-0.322390\pi$
$389$	20.8856	1.05894	0.529471	+	0.848328i	$0.322390\pi$
$390$	7.56373	0.383005
$391$	3.54447	0.179252
$392$	4.86469	0.245704
$393$	−28.3950	−1.43234
$394$	23.6716	1.19256
$395$	−16.9063	−0.850647
$396$	−1.82104	−0.0915107
$397$	34.9606	1.75462	0.877312	−	0.479921i	$-0.159335\pi$
$397$	34.9606	1.75462	0.877312	+	0.479921i	$0.159335\pi$
$398$	31.0667	1.55723
$399$	7.63874	0.382415
$400$	−2.06592	−0.103296
$401$	9.76456	0.487619	0.243809	−	0.969823i	$-0.421603\pi$
$401$	9.76456	0.487619	0.243809	+	0.969823i	$0.421603\pi$
$402$	16.4719	0.821545
$403$	3.43661	0.171190
$404$	45.2206	2.24981
$405$	12.5375	0.622991
$406$	14.1307	0.701296
$407$	−3.65654	−0.181248
$408$	6.02326	0.298196
$409$	34.1938	1.69077	0.845387	−	0.534155i	$-0.179370\pi$
$409$	34.1938	1.69077	0.845387	+	0.534155i	$0.179370\pi$
$410$	−9.40394	−0.464428
$411$	31.7491	1.56607
$412$	11.2703	0.555248
$413$	16.2331	0.798781
$414$	2.74231	0.134777
$415$	3.80926	0.186989
$416$	−7.58203	−0.371739
$417$	19.6783	0.963648
$418$	4.08441	0.199775
$419$	0.300770	0.0146936	0.00734680	−	0.999973i	$-0.497661\pi$
$419$	0.300770	0.0146936	0.00734680	+	0.999973i	$0.497661\pi$
$420$	18.5506	0.905178
$421$	−34.2375	−1.66863	−0.834316	−	0.551286i	$-0.814137\pi$
$421$	−34.2375	−1.66863	−0.834316	+	0.551286i	$0.814137\pi$
$422$	43.2541	2.10558
$423$	−11.6489	−0.566387
$424$	10.0889	0.489959
$425$	2.73531	0.132682
$426$	−44.7083	−2.16612
$427$	−9.15294	−0.442942
$428$	−2.50802	−0.121230
$429$	0.978590	0.0472468
$430$	41.0618	1.98018
$431$	32.5636	1.56853	0.784267	−	0.620424i	$-0.213039\pi$
$431$	32.5636	1.56853	0.784267	+	0.620424i	$0.213039\pi$
$432$	−11.7003	−0.562933
$433$	−34.3843	−1.65240	−0.826202	−	0.563375i	$-0.809503\pi$
$433$	−34.3843	−1.65240	−0.826202	+	0.563375i	$0.809503\pi$
$434$	14.6439	0.702928
$435$	−11.5548	−0.554012
$436$	−13.2053	−0.632417
$437$	−3.54016	−0.169349
$438$	18.6312	0.890235
$439$	−2.83187	−0.135158	−0.0675788	−	0.997714i	$-0.521527\pi$
$439$	−2.83187	−0.135158	−0.0675788	+	0.997714i	$0.521527\pi$
$440$	2.60456	0.124168
$441$	3.07152	0.146263
$442$	5.94498	0.282774
$443$	39.9561	1.89837	0.949187	−	0.314713i	$-0.101908\pi$
$443$	39.9561	1.89837	0.949187	+	0.314713i	$0.101908\pi$
$444$	20.5105	0.973385
$445$	18.5711	0.880356
$446$	−5.37421	−0.254476
$447$	−24.6374	−1.16531
$448$	−24.1874	−1.14275
$449$	15.3085	0.722454	0.361227	−	0.932478i	$-0.382358\pi$
$449$	15.3085	0.722454	0.361227	+	0.932478i	$0.382358\pi$
$450$	2.11628	0.0997623
$451$	−1.21667	−0.0572910
$452$	−12.6287	−0.594002
$453$	−26.8788	−1.26287
$454$	−45.8021	−2.14960
$455$	4.80780	0.225393
$456$	−6.01594	−0.281722
$457$	−2.48675	−0.116325	−0.0581627	−	0.998307i	$-0.518524\pi$
$457$	−2.48675	−0.116325	−0.0581627	+	0.998307i	$0.518524\pi$
$458$	36.6832	1.71409
$459$	15.4914	0.723078
$460$	−8.59726	−0.400849
$461$	6.31991	0.294347	0.147174	−	0.989111i	$-0.452982\pi$
$461$	6.31991	0.294347	0.147174	+	0.989111i	$0.452982\pi$
$462$	4.16991	0.194002
$463$	1.00000	0.0464739
$463$	1.00000	0.0464739
$464$	6.85938	0.318439
$465$	−11.9744	−0.555301
$466$	−41.3140	−1.91383
$467$	−0.208385	−0.00964290	−0.00482145	−	0.999988i	$-0.501535\pi$
$467$	−0.208385	−0.00964290	−0.00482145	+	0.999988i	$0.501535\pi$
$468$	2.64736	0.122374
$469$	10.4702	0.483469
$470$	63.4498	2.92672
$471$	15.5240	0.715309
$472$	−12.7845	−0.588455
$473$	5.31254	0.244271
$474$	21.3168	0.979113
$475$	−2.73199	−0.125352
$476$	14.5805	0.668297
$477$	6.37002	0.291663
$478$	−33.4176	−1.52849
$479$	−37.3166	−1.70504	−0.852519	−	0.522697i	$-0.824926\pi$
$479$	−37.3166	−1.70504	−0.852519	+	0.522697i	$0.824926\pi$
$480$	26.4187	1.20584
$481$	5.31574	0.242377
$482$	9.38404	0.427431
$483$	−3.61427	−0.164455
$484$	−28.5506	−1.29776
$485$	10.3356	0.469315
$486$	21.0287	0.953883
$487$	4.85944	0.220202	0.110101	−	0.993920i	$-0.464883\pi$
$487$	4.85944	0.220202	0.110101	+	0.993920i	$0.464883\pi$
$488$	7.20846	0.326312
$489$	6.92205	0.313026
$490$	−16.7302	−0.755791
$491$	35.0990	1.58400	0.791999	−	0.610523i	$-0.209041\pi$
$491$	35.0990	1.58400	0.791999	+	0.610523i	$0.209041\pi$
$492$	6.82464	0.307679
$493$	−9.08193	−0.409029
$494$	−5.93776	−0.267152
$495$	1.64450	0.0739146
$496$	7.10848	0.319180
$497$	−28.4183	−1.27474
$498$	−4.80302	−0.215228
$499$	−38.0501	−1.70336	−0.851679	−	0.524064i	$-0.824415\pi$
$499$	−38.0501	−1.70336	−0.851679	+	0.524064i	$0.824415\pi$
$500$	26.5792	1.18866
$501$	23.2705	1.03965
$502$	−33.1460	−1.47938
$503$	32.6166	1.45430	0.727150	−	0.686479i	$-0.240844\pi$
$503$	32.6166	1.45430	0.727150	+	0.686479i	$0.240844\pi$
$504$	2.96215	0.131945
$505$	−40.8366	−1.81720
$506$	−1.93254	−0.0859119
$507$	−1.42264	−0.0631816
$508$	−42.7466	−1.89657
$509$	33.0157	1.46339	0.731697	−	0.681630i	$-0.238729\pi$
$509$	33.0157	1.46339	0.731697	+	0.681630i	$0.238729\pi$
$510$	−20.7146	−0.917257
$511$	11.8427	0.523892
$512$	−22.0786	−0.975745
$513$	−15.4726	−0.683133
$514$	−36.9160	−1.62830
$515$	−10.1777	−0.448483
$516$	−29.7994	−1.31185
$517$	8.20908	0.361035
$518$	22.6511	0.995234
$519$	15.8176	0.694314
$520$	−3.78642	−0.166045
$521$	−7.84823	−0.343837	−0.171919	−	0.985111i	$-0.554997\pi$
$521$	−7.84823	−0.343837	−0.171919	+	0.985111i	$0.554997\pi$
$522$	−7.02658	−0.307545
$523$	−30.8459	−1.34880	−0.674399	−	0.738367i	$-0.735597\pi$
$523$	−30.8459	−1.34880	−0.674399	+	0.738367i	$0.735597\pi$
$524$	54.1333	2.36483
$525$	−2.78918	−0.121730
$526$	−20.4171	−0.890229
$527$	−9.41173	−0.409982
$528$	2.02417	0.0880908
$529$	−21.3250	−0.927173
$530$	−34.6966	−1.50713
$531$	−8.07203	−0.350296
$532$	−14.5628	−0.631377
$533$	1.76876	0.0766133
$534$	−23.4160	−1.01331
$535$	2.26487	0.0979191
$536$	−8.24587	−0.356167
$537$	−5.94561	−0.256572
$538$	61.5577	2.65394
$539$	−2.16453	−0.0932331
$540$	−37.5751	−1.61698
$541$	36.9694	1.58944	0.794720	−	0.606977i	$-0.207618\pi$
$541$	36.9694	1.58944	0.794720	+	0.606977i	$0.207618\pi$
$542$	−32.8957	−1.41299
$543$	−16.0923	−0.690586
$544$	20.7647	0.890278
$545$	11.9251	0.510813
$546$	−6.06206	−0.259432
$547$	8.47834	0.362508	0.181254	−	0.983436i	$-0.441984\pi$
$547$	8.47834	0.362508	0.181254	+	0.983436i	$0.441984\pi$
$548$	−60.5278	−2.58562
$549$	4.55135	0.194247
$550$	−1.49137	−0.0635920
$551$	9.07089	0.386433
$552$	2.84644	0.121153
$553$	13.5498	0.576195
$554$	3.18666	0.135388
$555$	−18.5221	−0.786218
$556$	−37.5154	−1.59101
$557$	−1.39424	−0.0590757	−0.0295378	−	0.999564i	$-0.509404\pi$
$557$	−1.39424	−0.0590757	−0.0295378	+	0.999564i	$0.509404\pi$
$558$	−7.28175	−0.308261
$559$	−7.72318	−0.326656
$560$	9.94474	0.420242
$561$	−2.68004	−0.113151
$562$	37.0655	1.56351
$563$	−40.8035	−1.71966	−0.859830	−	0.510580i	$-0.829431\pi$
$563$	−40.8035	−1.71966	−0.859830	+	0.510580i	$0.829431\pi$
$564$	−46.0469	−1.93892
$565$	11.4044	0.479785
$566$	40.3747	1.69708
$567$	−10.0483	−0.421990
$568$	22.3810	0.939087
$569$	24.5119	1.02759	0.513797	−	0.857912i	$-0.328238\pi$
$569$	24.5119	1.02759	0.513797	+	0.857912i	$0.328238\pi$
$570$	20.6894	0.866584
$571$	26.6565	1.11554	0.557770	−	0.829995i	$-0.311657\pi$
$571$	26.6565	1.11554	0.557770	+	0.829995i	$0.311657\pi$
$572$	−1.86562	−0.0780056
$573$	19.4161	0.811121
$574$	7.53692	0.314585
$575$	1.29264	0.0539069
$576$	12.0273	0.501139
$577$	11.1560	0.464431	0.232216	−	0.972664i	$-0.425402\pi$
$577$	11.1560	0.464431	0.232216	+	0.972664i	$0.425402\pi$
$578$	20.6215	0.857740
$579$	33.8750	1.40780
$580$	22.0286	0.914688
$581$	−3.05298	−0.126659
$582$	−13.0319	−0.540192
$583$	−4.48902	−0.185916
$584$	−9.32682	−0.385947
$585$	−2.39071	−0.0988436
$586$	37.0185	1.52922
$587$	−41.7373	−1.72268	−0.861341	−	0.508028i	$-0.830375\pi$
$587$	−41.7373	−1.72268	−0.861341	+	0.508028i	$0.830375\pi$
$588$	12.1414	0.500704
$589$	9.40030	0.387332
$590$	43.9672	1.81010
$591$	15.5136	0.638143
$592$	10.9954	0.451908
$593$	−40.5272	−1.66425	−0.832126	−	0.554586i	$-0.812877\pi$
$593$	−40.5272	−1.66425	−0.832126	+	0.554586i	$0.812877\pi$
$594$	−8.44635	−0.346558
$595$	−13.1670	−0.539794
$596$	46.9697	1.92395
$597$	20.3600	0.833280
$598$	2.80945	0.114887
$599$	10.7130	0.437722	0.218861	−	0.975756i	$-0.429766\pi$
$599$	10.7130	0.437722	0.218861	+	0.975756i	$0.429766\pi$
$600$	2.19664	0.0896773
$601$	30.0986	1.22775	0.613874	−	0.789404i	$-0.289610\pi$
$601$	30.0986	1.22775	0.613874	+	0.789404i	$0.289610\pi$
$602$	−32.9096	−1.34129
$603$	−5.20636	−0.212020
$604$	51.2428	2.08504
$605$	25.7827	1.04822
$606$	51.4901	2.09164
$607$	20.8675	0.846984	0.423492	−	0.905900i	$-0.360804\pi$
$607$	20.8675	0.846984	0.423492	+	0.905900i	$0.360804\pi$
$608$	−20.7394	−0.841096
$609$	9.26078	0.375266
$610$	−24.7906	−1.00374
$611$	−11.9341	−0.482800
$612$	−7.25025	−0.293074
$613$	28.2560	1.14125	0.570625	−	0.821210i	$-0.306701\pi$
$613$	28.2560	1.14125	0.570625	+	0.821210i	$0.306701\pi$
$614$	−45.3933	−1.83192
$615$	−6.16302	−0.248517
$616$	−2.08746	−0.0841063
$617$	34.0543	1.37098	0.685488	−	0.728084i	$-0.259589\pi$
$617$	34.0543	1.37098	0.685488	+	0.728084i	$0.259589\pi$
$618$	12.8329	0.516213
$619$	13.2646	0.533148	0.266574	−	0.963815i	$-0.414108\pi$
$619$	13.2646	0.533148	0.266574	+	0.963815i	$0.414108\pi$
$620$	22.8286	0.916817
$621$	7.32088	0.293777
$622$	−0.719213	−0.0288378
$623$	−14.8841	−0.596319
$624$	−2.94267	−0.117801
$625$	−28.9963	−1.15985
$626$	−0.476767	−0.0190554
$627$	2.67678	0.106900
$628$	−29.5956	−1.18099
$629$	−14.5581	−0.580468
$630$	−10.1871	−0.405866
$631$	38.3824	1.52798	0.763989	−	0.645230i	$-0.223238\pi$
$631$	38.3824	1.52798	0.763989	+	0.645230i	$0.223238\pi$
$632$	−10.6712	−0.424478
$633$	28.3473	1.12670
$634$	−51.1687	−2.03217
$635$	38.6025	1.53189
$636$	25.1801	0.998456
$637$	3.14672	0.124678
$638$	4.95171	0.196040
$639$	14.1312	0.559020
$640$	−28.3709	−1.12146
$641$	−24.2555	−0.958034	−0.479017	−	0.877806i	$-0.659007\pi$
$641$	−24.2555	−0.958034	−0.479017	+	0.877806i	$0.659007\pi$
$642$	−2.85573	−0.112707
$643$	16.8482	0.664427	0.332214	−	0.943204i	$-0.392205\pi$
$643$	16.8482	0.664427	0.332214	+	0.943204i	$0.392205\pi$
$644$	6.89040	0.271520
$645$	26.9105	1.05960
$646$	16.2616	0.639803
$647$	20.1598	0.792565	0.396282	−	0.918129i	$-0.370300\pi$
$647$	20.1598	0.792565	0.396282	+	0.918129i	$0.370300\pi$
$648$	7.91362	0.310876
$649$	5.68845	0.223291
$650$	2.16809	0.0850395
$651$	9.59709	0.376139
$652$	−13.1965	−0.516814
$653$	−42.7675	−1.67362	−0.836811	−	0.547492i	$-0.815583\pi$
$653$	−42.7675	−1.67362	−0.836811	+	0.547492i	$0.815583\pi$
$654$	−15.0361	−0.587957
$655$	−48.8853	−1.91011
$656$	3.65860	0.142844
$657$	−5.88887	−0.229747
$658$	−50.8527	−1.98244
$659$	44.6039	1.73752	0.868760	−	0.495233i	$-0.164917\pi$
$659$	44.6039	1.73752	0.868760	+	0.495233i	$0.164917\pi$
$660$	6.50054	0.253033
$661$	11.1957	0.435461	0.217731	−	0.976009i	$-0.430135\pi$
$661$	11.1957	0.435461	0.217731	+	0.976009i	$0.430135\pi$
$662$	−22.2553	−0.864978
$663$	3.89614	0.151313
$664$	2.40440	0.0933087
$665$	13.1510	0.509973
$666$	−11.2634	−0.436448
$667$	−4.29190	−0.166183
$668$	−44.3639	−1.71649
$669$	−3.52207	−0.136171
$670$	28.3584	1.09558
$671$	−3.20739	−0.123820
$672$	−21.1736	−0.816790
$673$	−16.8600	−0.649906	−0.324953	−	0.945730i	$-0.605349\pi$
$673$	−16.8600	−0.649906	−0.324953	+	0.945730i	$0.605349\pi$
$674$	59.3922	2.28770
$675$	5.64961	0.217454
$676$	2.71217	0.104314
$677$	23.3760	0.898414	0.449207	−	0.893428i	$-0.351707\pi$
$677$	23.3760	0.898414	0.449207	+	0.893428i	$0.351707\pi$
$678$	−14.3795	−0.552242
$679$	−8.28361	−0.317896
$680$	10.3697	0.397662
$681$	−30.0171	−1.15026
$682$	5.13153	0.196496
$683$	24.9038	0.952919	0.476459	−	0.879196i	$-0.341920\pi$
$683$	24.9038	0.952919	0.476459	+	0.879196i	$0.341920\pi$
$684$	7.24144	0.276883
$685$	54.6599	2.08845
$686$	43.2366	1.65078
$687$	24.0409	0.917218
$688$	−15.9751	−0.609044
$689$	6.52597	0.248620
$690$	−9.78921	−0.372669
$691$	1.90479	0.0724617	0.0362309	−	0.999343i	$-0.488465\pi$
$691$	1.90479	0.0724617	0.0362309	+	0.999343i	$0.488465\pi$
$692$	−30.1552	−1.14633
$693$	−1.31800	−0.0500669
$694$	−59.4298	−2.25592
$695$	33.8785	1.28508
$696$	−7.29339	−0.276455
$697$	−4.84404	−0.183481
$698$	−1.03537	−0.0391895
$699$	−27.0757	−1.02410
$700$	5.31741	0.200979
$701$	41.6419	1.57279	0.786396	−	0.617722i	$-0.211944\pi$
$701$	41.6419	1.57279	0.786396	+	0.617722i	$0.211944\pi$
$702$	12.2790	0.463440
$703$	14.5404	0.548401
$704$	−8.47580	−0.319444
$705$	41.5828	1.56610
$706$	33.4606	1.25931
$707$	32.7291	1.23090
$708$	−31.9080	−1.19918
$709$	33.0793	1.24232	0.621160	−	0.783684i	$-0.286662\pi$
$709$	33.0793	1.24232	0.621160	+	0.783684i	$0.286662\pi$
$710$	−76.9706	−2.88865
$711$	−6.73771	−0.252684
$712$	11.7221	0.439303
$713$	−4.44776	−0.166570
$714$	16.6020	0.621314
$715$	1.68476	0.0630064
$716$	11.3350	0.423607
$717$	−21.9008	−0.817899
$718$	−26.7195	−0.997164
$719$	−24.2975	−0.906143	−0.453072	−	0.891474i	$-0.649672\pi$
$719$	−24.2975	−0.906143	−0.453072	+	0.891474i	$0.649672\pi$
$720$	−4.94508	−0.184292
$721$	8.15706	0.303785
$722$	25.0025	0.930498
$723$	6.14998	0.228720
$724$	30.6790	1.14018
$725$	−3.31211	−0.123009
$726$	−32.5089	−1.20652
$727$	1.76215	0.0653544	0.0326772	−	0.999466i	$-0.489597\pi$
$727$	1.76215	0.0653544	0.0326772	+	0.999466i	$0.489597\pi$
$728$	3.03468	0.112473
$729$	29.1383	1.07919
$730$	32.0759	1.18718
$731$	21.1512	0.782307
$732$	17.9911	0.664970
$733$	34.5167	1.27490	0.637452	−	0.770490i	$-0.279988\pi$
$733$	34.5167	1.27490	0.637452	+	0.770490i	$0.279988\pi$
$734$	−38.4828	−1.42042
$735$	−10.9644	−0.404427
$736$	9.81288	0.361708
$737$	3.66898	0.135149
$738$	−3.74778	−0.137958
$739$	51.3579	1.88923	0.944615	−	0.328180i	$-0.106435\pi$
$739$	51.3579	1.88923	0.944615	+	0.328180i	$0.106435\pi$
$740$	35.3112	1.29807
$741$	−3.89140	−0.142954
$742$	27.8081	1.02087
$743$	34.2090	1.25500	0.627502	−	0.778615i	$-0.284077\pi$
$743$	34.2090	1.25500	0.627502	+	0.778615i	$0.284077\pi$
$744$	−7.55825	−0.277099
$745$	−42.4162	−1.55401
$746$	33.0709	1.21081
$747$	1.51811	0.0555449
$748$	5.10933	0.186816
$749$	−1.81522	−0.0663265
$750$	30.2642	1.10509
$751$	8.30110	0.302911	0.151456	−	0.988464i	$-0.451604\pi$
$751$	8.30110	0.302911	0.151456	+	0.988464i	$0.451604\pi$
$752$	−24.6851	−0.900173
$753$	−21.7227	−0.791621
$754$	−7.19861	−0.262158
$755$	−46.2750	−1.68412
$756$	30.1151	1.09528
$757$	22.9026	0.832408	0.416204	−	0.909271i	$-0.363360\pi$
$757$	22.9026	0.832408	0.416204	+	0.909271i	$0.363360\pi$
$758$	−10.6780	−0.387843
$759$	−1.26652	−0.0459718
$760$	−10.3571	−0.375693
$761$	30.7446	1.11449	0.557246	−	0.830347i	$-0.311858\pi$
$761$	30.7446	1.11449	0.557246	+	0.830347i	$0.311858\pi$
$762$	−48.6731	−1.76324
$763$	−9.55751	−0.346005
$764$	−37.0157	−1.33918
$765$	6.54736	0.236720
$766$	−37.0717	−1.33945
$767$	−8.26965	−0.298600
$768$	0.713367	0.0257414
$769$	44.2710	1.59645	0.798226	−	0.602358i	$-0.205772\pi$
$769$	44.2710	1.59645	0.798226	+	0.602358i	$0.205772\pi$
$770$	7.17900	0.258713
$771$	−24.1935	−0.871307
$772$	−64.5807	−2.32431
$773$	27.3618	0.984134	0.492067	−	0.870557i	$-0.336241\pi$
$773$	27.3618	0.984134	0.492067	+	0.870557i	$0.336241\pi$
$774$	16.3645	0.588209
$775$	−3.43239	−0.123295
$776$	6.52381	0.234191
$777$	14.8448	0.532553
$778$	−45.3375	−1.62543
$779$	4.83816	0.173345
$780$	−9.45025	−0.338373
$781$	−9.95839	−0.356339
$782$	−7.69417	−0.275143
$783$	−18.7581	−0.670362
$784$	6.50886	0.232459
$785$	26.7264	0.953907
$786$	61.6385	2.19857
$787$	23.7142	0.845318	0.422659	−	0.906289i	$-0.361097\pi$
$787$	23.7142	0.845318	0.422659	+	0.906289i	$0.361097\pi$
$788$	−29.5757	−1.05359
$789$	−13.3807	−0.476365
$790$	36.6994	1.30571
$791$	−9.14018	−0.324988
$792$	1.03800	0.0368838
$793$	4.66279	0.165580
$794$	−75.8909	−2.69327
$795$	−22.7390	−0.806468
$796$	−38.8152	−1.37577
$797$	35.7531	1.26644	0.633220	−	0.773972i	$-0.281733\pi$
$797$	35.7531	1.26644	0.633220	+	0.773972i	$0.281733\pi$
$798$	−16.5818	−0.586990
$799$	32.6835	1.15626
$800$	7.57273	0.267736
$801$	7.40121	0.261509
$802$	−21.1965	−0.748473
$803$	4.14995	0.146449
$804$	−20.5803	−0.725811
$805$	−6.22240	−0.219311
$806$	−7.46003	−0.262768
$807$	40.3428	1.42013
$808$	−25.7760	−0.906796
$809$	−0.833218	−0.0292944	−0.0146472	−	0.999893i	$-0.504663\pi$
$809$	−0.833218	−0.0292944	−0.0146472	+	0.999893i	$0.504663\pi$
$810$	−27.2157	−0.956264
$811$	−18.7063	−0.656867	−0.328434	−	0.944527i	$-0.606521\pi$
$811$	−18.7063	−0.656867	−0.328434	+	0.944527i	$0.606521\pi$
$812$	−17.6551	−0.619574
$813$	−21.5587	−0.756096
$814$	7.93745	0.278208
$815$	11.9171	0.417439
$816$	8.05900	0.282121
$817$	−21.1255	−0.739089
$818$	−74.2263	−2.59526
$819$	1.91607	0.0669528
$820$	11.7494	0.410308
$821$	−22.1035	−0.771419	−0.385710	−	0.922620i	$-0.626043\pi$
$821$	−22.1035	−0.771419	−0.385710	+	0.922620i	$0.626043\pi$
$822$	−68.9196	−2.40385
$823$	27.7961	0.968912	0.484456	−	0.874816i	$-0.339018\pi$
$823$	27.7961	0.968912	0.484456	+	0.874816i	$0.339018\pi$
$824$	−6.42414	−0.223796
$825$	−0.977389	−0.0340283
$826$	−35.2382	−1.22609
$827$	−6.50909	−0.226343	−0.113172	−	0.993575i	$-0.536101\pi$
$827$	−6.50909	−0.226343	−0.113172	+	0.993575i	$0.536101\pi$
$828$	−3.42629	−0.119072
$829$	41.7440	1.44983	0.724915	−	0.688838i	$-0.241879\pi$
$829$	41.7440	1.44983	0.724915	+	0.688838i	$0.241879\pi$
$830$	−8.26896	−0.287020
$831$	2.08843	0.0724467
$832$	12.3218	0.427182
$833$	−8.61783	−0.298590
$834$	−42.7167	−1.47916
$835$	40.0629	1.38644
$836$	−5.10312	−0.176495
$837$	−19.4393	−0.671922
$838$	−0.652898	−0.0225540
$839$	−17.6754	−0.610221	−0.305111	−	0.952317i	$-0.598693\pi$
$839$	−17.6754	−0.610221	−0.305111	+	0.952317i	$0.598693\pi$
$840$	−10.5740	−0.364837
$841$	−18.0029	−0.620791
$842$	74.3212	2.56128
$843$	24.2914	0.836641
$844$	−54.0424	−1.86022
$845$	−2.44924	−0.0842564
$846$	25.2868	0.869378
$847$	−20.6639	−0.710021
$848$	13.4987	0.463547
$849$	26.4602	0.908111
$850$	−5.93769	−0.203661
$851$	−6.87979	−0.235836
$852$	55.8592	1.91370
$853$	−19.5170	−0.668251	−0.334125	−	0.942529i	$-0.608441\pi$
$853$	−19.5170	−0.668251	−0.334125	+	0.942529i	$0.608441\pi$
$854$	19.8688	0.679896
$855$	−6.53941	−0.223643
$856$	1.42958	0.0488622
$857$	−22.9564	−0.784176	−0.392088	−	0.919928i	$-0.628247\pi$
$857$	−22.9564	−0.784176	−0.392088	+	0.919928i	$0.628247\pi$
$858$	−2.12428	−0.0725217
$859$	8.37463	0.285739	0.142869	−	0.989742i	$-0.454367\pi$
$859$	8.37463	0.285739	0.142869	+	0.989742i	$0.454367\pi$
$860$	−51.3033	−1.74943
$861$	4.93944	0.168336
$862$	−70.6876	−2.40763
$863$	−44.4884	−1.51440	−0.757202	−	0.653181i	$-0.773434\pi$
$863$	−44.4884	−1.51440	−0.757202	+	0.653181i	$0.773434\pi$
$864$	42.8881	1.45908
$865$	27.2318	0.925909
$866$	74.6398	2.53636
$867$	13.5146	0.458980
$868$	−18.2963	−0.621016
$869$	4.74814	0.161070
$870$	25.0827	0.850383
$871$	−5.33383	−0.180730
$872$	7.52708	0.254899
$873$	4.11907	0.139410
$874$	7.68482	0.259943
$875$	19.2371	0.650333
$876$	−23.2782	−0.786496
$877$	44.7614	1.51148	0.755742	−	0.654870i	$-0.227276\pi$
$877$	44.7614	1.51148	0.755742	+	0.654870i	$0.227276\pi$
$878$	6.14729	0.207461
$879$	24.2606	0.818291
$880$	3.48485	0.117474
$881$	−49.2043	−1.65773	−0.828867	−	0.559446i	$-0.811014\pi$
$881$	−49.2043	−1.65773	−0.828867	+	0.559446i	$0.811014\pi$
$882$	−6.66751	−0.224507
$883$	3.03342	0.102083	0.0510414	−	0.998697i	$-0.483746\pi$
$883$	3.03342	0.102083	0.0510414	+	0.998697i	$0.483746\pi$
$884$	−7.42775	−0.249822
$885$	28.8146	0.968593
$886$	−86.7350	−2.91392
$887$	7.16404	0.240545	0.120272	−	0.992741i	$-0.461623\pi$
$887$	7.16404	0.240545	0.120272	+	0.992741i	$0.461623\pi$
$888$	−11.6911	−0.392328
$889$	−30.9385	−1.03764
$890$	−40.3134	−1.35131
$891$	−3.52115	−0.117963
$892$	6.71462	0.224822
$893$	−32.6437	−1.09238
$894$	53.4817	1.78870
$895$	−10.2361	−0.342154
$896$	22.7383	0.759632
$897$	1.84122	0.0614765
$898$	−33.2310	−1.10893
$899$	11.3964	0.380091
$900$	−2.64411	−0.0881371
$901$	−17.8725	−0.595419
$902$	2.64110	0.0879391
$903$	−21.5678	−0.717731
$904$	7.19841	0.239416
$905$	−27.7048	−0.920938
$906$	58.3472	1.93846
$907$	−33.9295	−1.12661	−0.563305	−	0.826249i	$-0.690471\pi$
$907$	−33.9295	−1.12661	−0.563305	+	0.826249i	$0.690471\pi$
$908$	57.2259	1.89911
$909$	−16.2747	−0.539799
$910$	−10.4366	−0.345968
$911$	−45.9181	−1.52133	−0.760667	−	0.649142i	$-0.775128\pi$
$911$	−45.9181	−1.52133	−0.760667	+	0.649142i	$0.775128\pi$
$912$	−8.04920	−0.266536
$913$	−1.06983	−0.0354063
$914$	5.39813	0.178554
$915$	−16.2469	−0.537106
$916$	−45.8326	−1.51435
$917$	39.1798	1.29383
$918$	−33.6281	−1.10989
$919$	25.8228	0.851814	0.425907	−	0.904767i	$-0.359955\pi$
$919$	25.8228	0.851814	0.425907	+	0.904767i	$0.359955\pi$
$920$	4.90049	0.161564
$921$	−29.7492	−0.980269
$922$	−13.7190	−0.451810
$923$	14.4771	0.476521
$924$	−5.20995	−0.171395
$925$	−5.30922	−0.174566
$926$	−2.17075	−0.0713354
$927$	−4.05614	−0.133221
$928$	−25.1434	−0.825371
$929$	−53.4712	−1.75433	−0.877167	−	0.480185i	$-0.840570\pi$
$929$	−53.4712	−1.75433	−0.877167	+	0.480185i	$0.840570\pi$
$930$	25.9936	0.852363
$931$	8.60736	0.282095
$932$	51.6183	1.69081
$933$	−0.471348	−0.0154312
$934$	0.452352	0.0148014
$935$	−4.61400	−0.150894
$936$	−1.50901	−0.0493236
$937$	−40.8889	−1.33578	−0.667891	−	0.744259i	$-0.732803\pi$
$937$	−40.8889	−1.33578	−0.667891	+	0.744259i	$0.732803\pi$
$938$	−22.7282	−0.742103
$939$	−0.312456	−0.0101966
$940$	−79.2751	−2.58567
$941$	2.95965	0.0964818	0.0482409	−	0.998836i	$-0.484638\pi$
$941$	2.95965	0.0964818	0.0482409	+	0.998836i	$0.484638\pi$
$942$	−33.6988	−1.09797
$943$	−2.28918	−0.0745458
$944$	−17.1054	−0.556735
$945$	−27.1956	−0.884672
$946$	−11.5322	−0.374945
$947$	9.14920	0.297309	0.148655	−	0.988889i	$-0.452506\pi$
$947$	9.14920	0.297309	0.148655	+	0.988889i	$0.452506\pi$
$948$	−26.6335	−0.865017
$949$	−6.03305	−0.195841
$950$	5.93047	0.192410
$951$	−33.5342	−1.08742
$952$	−8.31098	−0.269360
$953$	−1.23136	−0.0398876	−0.0199438	−	0.999801i	$-0.506349\pi$
$953$	−1.23136	−0.0398876	−0.0199438	+	0.999801i	$0.506349\pi$
$954$	−13.8277	−0.447690
$955$	33.4272	1.08168
$956$	41.7525	1.35037
$957$	3.24518	0.104902
$958$	81.0051	2.61716
$959$	−43.8079	−1.41463
$960$	−42.9338	−1.38568
$961$	−19.1897	−0.619024
$962$	−11.5392	−0.372038
$963$	0.902627	0.0290867
$964$	−11.7246	−0.377623
$965$	58.3198	1.87738
$966$	7.84570	0.252431
$967$	8.34195	0.268259	0.134130	−	0.990964i	$-0.457176\pi$
$967$	8.34195	0.268259	0.134130	+	0.990964i	$0.457176\pi$
$968$	16.2740	0.523067
$969$	10.6573	0.342361
$970$	−22.4360	−0.720378
$971$	50.1608	1.60974	0.804869	−	0.593453i	$-0.202236\pi$
$971$	50.1608	1.60974	0.804869	+	0.593453i	$0.202236\pi$
$972$	−26.2736	−0.842727
$973$	−27.1524	−0.870465
$974$	−10.5487	−0.338001
$975$	1.42089	0.0455050
$976$	9.64478	0.308722
$977$	43.0229	1.37642	0.688211	−	0.725510i	$-0.258396\pi$
$977$	43.0229	1.37642	0.688211	+	0.725510i	$0.258396\pi$
$978$	−15.0261	−0.480481
$979$	−5.21571	−0.166695
$980$	20.9029	0.667719
$981$	4.75253	0.151736
$982$	−76.1914	−2.43137
$983$	−25.3564	−0.808744	−0.404372	−	0.914595i	$-0.632510\pi$
$983$	−25.3564	−0.808744	−0.404372	+	0.914595i	$0.632510\pi$
$984$	−3.89009	−0.124011
$985$	26.7085	0.851002
$986$	19.7146	0.627842
$987$	−33.3271	−1.06081
$988$	7.41873	0.236021
$989$	9.99557	0.317841
$990$	−3.56980	−0.113456
$991$	−47.9962	−1.52465	−0.762325	−	0.647194i	$-0.775942\pi$
$991$	−47.9962	−1.52465	−0.762325	+	0.647194i	$0.775942\pi$
$992$	−26.0564	−0.827293
$993$	−14.5854	−0.462853
$994$	61.6892	1.95666
$995$	35.0522	1.11123
$996$	6.00096	0.190148
$997$	26.3203	0.833571	0.416785	−	0.909005i	$-0.363157\pi$
$997$	26.3203	0.833571	0.416785	+	0.909005i	$0.363157\pi$
$998$	82.5975	2.61458
$999$	−30.0688	−0.951334

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6019.2.a.d.1.17	✓	123

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6019.2.a.d.1.17	✓	123	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:	\( N \)	\(=\)	\( 6019 = 13 \cdot 463 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6019.a (trivial)

\(f(q)\)	\(=\)	\(q-2.17075 q^{2} -1.42264 q^{3} +2.71217 q^{4} -2.44924 q^{5} +3.08820 q^{6} +1.96298 q^{7} -1.54596 q^{8} -0.976102 q^{9} +O(q^{10})\)	\(q-2.17075 q^{2} -1.42264 q^{3} +2.71217 q^{4} -2.44924 q^{5} +3.08820 q^{6} +1.96298 q^{7} -1.54596 q^{8} -0.976102 q^{9} +5.31670 q^{10} +0.687870 q^{11} -3.85844 q^{12} -1.00000 q^{13} -4.26114 q^{14} +3.48438 q^{15} -2.06846 q^{16} +2.73867 q^{17} +2.11888 q^{18} -2.73534 q^{19} -6.64276 q^{20} -2.79261 q^{21} -1.49320 q^{22} +1.29423 q^{23} +2.19934 q^{24} +0.998773 q^{25} +2.17075 q^{26} +5.65655 q^{27} +5.32394 q^{28} -3.31618 q^{29} -7.56373 q^{30} -3.43661 q^{31} +7.58203 q^{32} -0.978590 q^{33} -5.94498 q^{34} -4.80780 q^{35} -2.64736 q^{36} -5.31574 q^{37} +5.93776 q^{38} +1.42264 q^{39} +3.78642 q^{40} -1.76876 q^{41} +6.06206 q^{42} +7.72318 q^{43} +1.86562 q^{44} +2.39071 q^{45} -2.80945 q^{46} +11.9341 q^{47} +2.94267 q^{48} -3.14672 q^{49} -2.16809 q^{50} -3.89614 q^{51} -2.71217 q^{52} -6.52597 q^{53} -12.2790 q^{54} -1.68476 q^{55} -3.03468 q^{56} +3.89140 q^{57} +7.19861 q^{58} +8.26965 q^{59} +9.45025 q^{60} -4.66279 q^{61} +7.46003 q^{62} -1.91607 q^{63} -12.3218 q^{64} +2.44924 q^{65} +2.12428 q^{66} +5.33383 q^{67} +7.42775 q^{68} -1.84122 q^{69} +10.4366 q^{70} -14.4771 q^{71} +1.50901 q^{72} +6.03305 q^{73} +11.5392 q^{74} -1.42089 q^{75} -7.41873 q^{76} +1.35027 q^{77} -3.08820 q^{78} +6.90267 q^{79} +5.06615 q^{80} -5.11892 q^{81} +3.83954 q^{82} -1.55528 q^{83} -7.57403 q^{84} -6.70766 q^{85} -16.7651 q^{86} +4.71772 q^{87} -1.06342 q^{88} -7.58241 q^{89} -5.18964 q^{90} -1.96298 q^{91} +3.51018 q^{92} +4.88904 q^{93} -25.9059 q^{94} +6.69951 q^{95} -10.7865 q^{96} -4.21992 q^{97} +6.83075 q^{98} -0.671431 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 123 q + 10 q^{2} + q^{3} + 136 q^{4} + 46 q^{5} + 16 q^{6} + 12 q^{7} + 30 q^{8} + 154 q^{9}+O(q^{10}) \) 123 * q + 10 * q^2 + q^3 + 136 * q^4 + 46 * q^5 + 16 * q^6 + 12 * q^7 + 30 * q^8 + 154 * q^9	\( 123 q + 10 q^{2} + q^{3} + 136 q^{4} + 46 q^{5} + 16 q^{6} + 12 q^{7} + 30 q^{8} + 154 q^{9} + 5 q^{10} + 53 q^{11} - 6 q^{12} - 123 q^{13} + 21 q^{14} + 29 q^{15} + 166 q^{16} - 35 q^{17} + 28 q^{18} + 23 q^{19} + 93 q^{20} + 72 q^{21} + 8 q^{22} + 42 q^{23} + 55 q^{24} + 153 q^{25} - 10 q^{26} + 7 q^{27} + 39 q^{28} + 86 q^{29} + 44 q^{30} + 16 q^{31} + 70 q^{32} + 40 q^{33} + 10 q^{34} + 6 q^{35} + 222 q^{36} + 52 q^{37} + 12 q^{38} - q^{39} + 14 q^{40} + 80 q^{41} + 29 q^{42} + 2 q^{43} + 143 q^{44} + 137 q^{45} + 39 q^{46} + 45 q^{47} - 27 q^{48} + 163 q^{49} + 102 q^{50} + 48 q^{51} - 136 q^{52} + 117 q^{53} + 75 q^{54} + 20 q^{55} + 88 q^{56} + 67 q^{57} + 56 q^{58} + 88 q^{59} + 96 q^{60} + 57 q^{61} - 13 q^{62} + 48 q^{63} + 228 q^{64} - 46 q^{65} + 28 q^{66} + 43 q^{67} - 56 q^{68} + 92 q^{69} + 14 q^{70} + 90 q^{71} + 98 q^{72} + 25 q^{73} + 80 q^{74} + 21 q^{75} + 75 q^{76} + 112 q^{77} - 16 q^{78} + 36 q^{79} + 208 q^{80} + 231 q^{81} - 27 q^{82} + 93 q^{83} + 175 q^{84} + 77 q^{85} + 199 q^{86} + 15 q^{87} + 43 q^{88} + 140 q^{89} + 11 q^{90} - 12 q^{91} + 93 q^{92} + 140 q^{93} + 4 q^{94} + 23 q^{95} + 105 q^{96} + 43 q^{97} + 67 q^{98} + 140 q^{99}+O(q^{100}) \) 123 * q + 10 * q^2 + q^3 + 136 * q^4 + 46 * q^5 + 16 * q^6 + 12 * q^7 + 30 * q^8 + 154 * q^9 + 5 * q^10 + 53 * q^11 - 6 * q^12 - 123 * q^13 + 21 * q^14 + 29 * q^15 + 166 * q^16 - 35 * q^17 + 28 * q^18 + 23 * q^19 + 93 * q^20 + 72 * q^21 + 8 * q^22 + 42 * q^23 + 55 * q^24 + 153 * q^25 - 10 * q^26 + 7 * q^27 + 39 * q^28 + 86 * q^29 + 44 * q^30 + 16 * q^31 + 70 * q^32 + 40 * q^33 + 10 * q^34 + 6 * q^35 + 222 * q^36 + 52 * q^37 + 12 * q^38 - q^39 + 14 * q^40 + 80 * q^41 + 29 * q^42 + 2 * q^43 + 143 * q^44 + 137 * q^45 + 39 * q^46 + 45 * q^47 - 27 * q^48 + 163 * q^49 + 102 * q^50 + 48 * q^51 - 136 * q^52 + 117 * q^53 + 75 * q^54 + 20 * q^55 + 88 * q^56 + 67 * q^57 + 56 * q^58 + 88 * q^59 + 96 * q^60 + 57 * q^61 - 13 * q^62 + 48 * q^63 + 228 * q^64 - 46 * q^65 + 28 * q^66 + 43 * q^67 - 56 * q^68 + 92 * q^69 + 14 * q^70 + 90 * q^71 + 98 * q^72 + 25 * q^73 + 80 * q^74 + 21 * q^75 + 75 * q^76 + 112 * q^77 - 16 * q^78 + 36 * q^79 + 208 * q^80 + 231 * q^81 - 27 * q^82 + 93 * q^83 + 175 * q^84 + 77 * q^85 + 199 * q^86 + 15 * q^87 + 43 * q^88 + 140 * q^89 + 11 * q^90 - 12 * q^91 + 93 * q^92 + 140 * q^93 + 4 * q^94 + 23 * q^95 + 105 * q^96 + 43 * q^97 + 67 * q^98 + 140 * q^99

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