LMFDB - Embedded newform 6019.2.a.d.1.18

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			1.18
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)

$f(q)$	$=$	$q-2.16481 q^{2} +1.72504 q^{3} +2.68638 q^{4} -0.175994 q^{5} -3.73438 q^{6} -2.81780 q^{7} -1.48588 q^{8} -0.0242310 q^{9} +O(q^{10})$	\(q-2.16481 q^{2} +1.72504 q^{3} +2.68638 q^{4} -0.175994 q^{5} -3.73438 q^{6} -2.81780 q^{7} -1.48588 q^{8} -0.0242310 q^{9} +0.380992 q^{10} -6.25768 q^{11} +4.63412 q^{12} -1.00000 q^{13} +6.09998 q^{14} -0.303597 q^{15} -2.15612 q^{16} -2.35463 q^{17} +0.0524554 q^{18} +2.44294 q^{19} -0.472786 q^{20} -4.86082 q^{21} +13.5467 q^{22} -8.13195 q^{23} -2.56321 q^{24} -4.96903 q^{25} +2.16481 q^{26} -5.21692 q^{27} -7.56968 q^{28} -4.80208 q^{29} +0.657227 q^{30} -10.5971 q^{31} +7.63934 q^{32} -10.7948 q^{33} +5.09731 q^{34} +0.495915 q^{35} -0.0650937 q^{36} +9.12667 q^{37} -5.28849 q^{38} -1.72504 q^{39} +0.261506 q^{40} +5.99292 q^{41} +10.5227 q^{42} -8.70438 q^{43} -16.8105 q^{44} +0.00426451 q^{45} +17.6041 q^{46} +6.58109 q^{47} -3.71939 q^{48} +0.939986 q^{49} +10.7570 q^{50} -4.06183 q^{51} -2.68638 q^{52} +9.00946 q^{53} +11.2936 q^{54} +1.10131 q^{55} +4.18692 q^{56} +4.21417 q^{57} +10.3956 q^{58} +4.24568 q^{59} -0.815576 q^{60} +7.24107 q^{61} +22.9406 q^{62} +0.0682781 q^{63} -12.2254 q^{64} +0.175994 q^{65} +23.3686 q^{66} -11.5105 q^{67} -6.32543 q^{68} -14.0279 q^{69} -1.07356 q^{70} -2.37904 q^{71} +0.0360044 q^{72} -0.649719 q^{73} -19.7575 q^{74} -8.57178 q^{75} +6.56267 q^{76} +17.6329 q^{77} +3.73438 q^{78} -7.06044 q^{79} +0.379463 q^{80} -8.92672 q^{81} -12.9735 q^{82} +2.72549 q^{83} -13.0580 q^{84} +0.414400 q^{85} +18.8433 q^{86} -8.28379 q^{87} +9.29818 q^{88} +2.65796 q^{89} -0.00923182 q^{90} +2.81780 q^{91} -21.8455 q^{92} -18.2804 q^{93} -14.2468 q^{94} -0.429942 q^{95} +13.1782 q^{96} +1.87141 q^{97} -2.03489 q^{98} +0.151630 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.16481	−1.53075	−0.765374	−	0.643585i	$-0.777446\pi$
$2$	−2.16481	−1.53075	−0.765374	+	0.643585i	$0.777446\pi$
$3$	1.72504	0.995953	0.497977	−	0.867190i	$-0.334077\pi$
$3$	1.72504	0.995953	0.497977	+	0.867190i	$0.334077\pi$
$4$	2.68638	1.34319
$5$	−0.175994	−0.0787068	−0.0393534	−	0.999225i	$-0.512530\pi$
$5$	−0.175994	−0.0787068	−0.0393534	+	0.999225i	$0.512530\pi$
$6$	−3.73438	−1.52455
$7$	−2.81780	−1.06503	−0.532514	−	0.846421i	$-0.678753\pi$
$7$	−2.81780	−1.06503	−0.532514	+	0.846421i	$0.678753\pi$
$8$	−1.48588	−0.525339
$9$	−0.0242310	−0.00807700
$10$	0.380992	0.120480
$11$	−6.25768	−1.88676	−0.943381	−	0.331712i	$-0.892374\pi$
$11$	−6.25768	−1.88676	−0.943381	+	0.331712i	$0.892374\pi$
$12$	4.63412	1.33776
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	6.09998	1.63029
$15$	−0.303597	−0.0783883
$16$	−2.15612	−0.539029
$17$	−2.35463	−0.571081	−0.285540	−	0.958367i	$-0.592173\pi$
$17$	−2.35463	−0.571081	−0.285540	+	0.958367i	$0.592173\pi$
$18$	0.0524554	0.0123639
$19$	2.44294	0.560449	0.280224	−	0.959935i	$-0.409591\pi$
$19$	2.44294	0.560449	0.280224	+	0.959935i	$0.409591\pi$
$20$	−0.472786	−0.105718
$21$	−4.86082	−1.06072
$22$	13.5467	2.88816
$23$	−8.13195	−1.69563	−0.847814	−	0.530293i	$-0.822082\pi$
$23$	−8.13195	−1.69563	−0.847814	+	0.530293i	$0.822082\pi$
$24$	−2.56321	−0.523213
$25$	−4.96903	−0.993805
$26$	2.16481	0.424553
$27$	−5.21692	−1.00400
$28$	−7.56968	−1.43054
$29$	−4.80208	−0.891724	−0.445862	−	0.895102i	$-0.647103\pi$
$29$	−4.80208	−0.891724	−0.445862	+	0.895102i	$0.647103\pi$
$30$	0.657227	0.119993
$31$	−10.5971	−1.90329	−0.951645	−	0.307200i	$-0.900608\pi$
$31$	−10.5971	−1.90329	−0.951645	+	0.307200i	$0.900608\pi$
$32$	7.63934	1.35046
$33$	−10.7948	−1.87913
$34$	5.09731	0.874181
$35$	0.495915	0.0838249
$36$	−0.0650937	−0.0108490
$37$	9.12667	1.50042	0.750208	−	0.661202i	$-0.229953\pi$
$37$	9.12667	1.50042	0.750208	+	0.661202i	$0.229953\pi$
$38$	−5.28849	−0.857906
$39$	−1.72504	−0.276228
$40$	0.261506	0.0413477
$41$	5.99292	0.935936	0.467968	−	0.883745i	$-0.344986\pi$
$41$	5.99292	0.935936	0.467968	+	0.883745i	$0.344986\pi$
$42$	10.5227	1.62369
$43$	−8.70438	−1.32740	−0.663702	−	0.747997i	$-0.731016\pi$
$43$	−8.70438	−1.32740	−0.663702	+	0.747997i	$0.731016\pi$
$44$	−16.8105	−2.53428
$45$	0.00426451	0.000635715 0
$46$	17.6041	2.59558
$47$	6.58109	0.959950	0.479975	−	0.877282i	$-0.340646\pi$
$47$	6.58109	0.959950	0.479975	+	0.877282i	$0.340646\pi$
$48$	−3.71939	−0.536848
$49$	0.939986	0.134284
$50$	10.7570	1.52127
$51$	−4.06183	−0.568770
$52$	−2.68638	−0.372534
$53$	9.00946	1.23755	0.618773	−	0.785570i	$-0.287630\pi$
$53$	9.00946	1.23755	0.618773	+	0.785570i	$0.287630\pi$
$54$	11.2936	1.53687
$55$	1.10131	0.148501
$56$	4.18692	0.559500
$57$	4.21417	0.558181
$58$	10.3956	1.36501
$59$	4.24568	0.552740	0.276370	−	0.961051i	$-0.410868\pi$
$59$	4.24568	0.552740	0.276370	+	0.961051i	$0.410868\pi$
$60$	−0.815576	−0.105290
$61$	7.24107	0.927124	0.463562	−	0.886064i	$-0.346571\pi$
$61$	7.24107	0.927124	0.463562	+	0.886064i	$0.346571\pi$
$62$	22.9406	2.91346
$63$	0.0682781	0.00860223
$64$	−12.2254	−1.52818
$65$	0.175994	0.0218293
$66$	23.3686	2.87647
$67$	−11.5105	−1.40623	−0.703116	−	0.711075i	$-0.748208\pi$
$67$	−11.5105	−1.40623	−0.703116	+	0.711075i	$0.748208\pi$
$68$	−6.32543	−0.767071
$69$	−14.0279	−1.68877
$70$	−1.07356	−0.128315
$71$	−2.37904	−0.282340	−0.141170	−	0.989985i	$-0.545086\pi$
$71$	−2.37904	−0.282340	−0.141170	+	0.989985i	$0.545086\pi$
$72$	0.0360044	0.00424316
$73$	−0.649719	−0.0760439	−0.0380219	−	0.999277i	$-0.512106\pi$
$73$	−0.649719	−0.0760439	−0.0380219	+	0.999277i	$0.512106\pi$
$74$	−19.7575	−2.29676
$75$	−8.57178	−0.989784
$76$	6.56267	0.752789
$77$	17.6329	2.00945
$78$	3.73438	0.422835
$79$	−7.06044	−0.794362	−0.397181	−	0.917740i	$-0.630011\pi$
$79$	−7.06044	−0.794362	−0.397181	+	0.917740i	$0.630011\pi$
$80$	0.379463	0.0424253
$81$	−8.92672	−0.991858
$82$	−12.9735	−1.43268
$83$	2.72549	0.299162	0.149581	−	0.988750i	$-0.452208\pi$
$83$	2.72549	0.299162	0.149581	+	0.988750i	$0.452208\pi$
$84$	−13.0580	−1.42475
$85$	0.414400	0.0449479
$86$	18.8433	2.03192
$87$	−8.28379	−0.888116
$88$	9.29818	0.991189
$89$	2.65796	0.281743	0.140872	−	0.990028i	$-0.455010\pi$
$89$	2.65796	0.281743	0.140872	+	0.990028i	$0.455010\pi$
$90$	−0.00923182	−0.000973120 0
$91$	2.81780	0.295386
$92$	−21.8455	−2.27755
$93$	−18.2804	−1.89559
$94$	−14.2468	−1.46944
$95$	−0.429942	−0.0441111
$96$	13.1782	1.34499
$97$	1.87141	0.190013	0.0950066	−	0.995477i	$-0.469713\pi$
$97$	1.87141	0.190013	0.0950066	+	0.995477i	$0.469713\pi$
$98$	−2.03489	−0.205555
$99$	0.151630	0.0152394
$100$	−13.3487	−1.33487
$101$	15.5625	1.54852	0.774262	−	0.632866i	$-0.218121\pi$
$101$	15.5625	1.54852	0.774262	+	0.632866i	$0.218121\pi$
$102$	8.79307	0.870644
$103$	−0.773066	−0.0761724	−0.0380862	−	0.999274i	$-0.512126\pi$
$103$	−0.773066	−0.0761724	−0.0380862	+	0.999274i	$0.512126\pi$
$104$	1.48588	0.145703
$105$	0.855474	0.0834857
$106$	−19.5037	−1.89437
$107$	5.96832	0.576979	0.288490	−	0.957483i	$-0.406847\pi$
$107$	5.96832	0.576979	0.288490	+	0.957483i	$0.406847\pi$
$108$	−14.0147	−1.34856
$109$	3.62302	0.347023	0.173511	−	0.984832i	$-0.444489\pi$
$109$	3.62302	0.347023	0.173511	+	0.984832i	$0.444489\pi$
$110$	−2.38413	−0.227318
$111$	15.7439	1.49434
$112$	6.07550	0.574081
$113$	4.34249	0.408507	0.204253	−	0.978918i	$-0.434523\pi$
$113$	4.34249	0.408507	0.204253	+	0.978918i	$0.434523\pi$
$114$	−9.12286	−0.854434
$115$	1.43117	0.133457
$116$	−12.9002	−1.19776
$117$	0.0242310	0.00224016
$118$	−9.19107	−0.846106
$119$	6.63486	0.608217
$120$	0.451109	0.0411804
$121$	28.1586	2.55987
$122$	−15.6755	−1.41919
$123$	10.3380	0.932149
$124$	−28.4678	−2.55648
$125$	1.75449	0.156926
$126$	−0.147809	−0.0131678
$127$	−5.79478	−0.514204	−0.257102	−	0.966384i	$-0.582768\pi$
$127$	−5.79478	−0.514204	−0.257102	+	0.966384i	$0.582768\pi$
$128$	11.1870	0.988803
$129$	−15.0154	−1.32203
$130$	−0.380992	−0.0334152
$131$	−22.4926	−1.96519	−0.982595	−	0.185762i	$-0.940525\pi$
$131$	−22.4926	−1.96519	−0.982595	+	0.185762i	$0.940525\pi$
$132$	−28.9988	−2.52403
$133$	−6.88371	−0.596893
$134$	24.9180	2.15259
$135$	0.918146	0.0790214
$136$	3.49870	0.300011
$137$	15.1504	1.29438	0.647192	−	0.762327i	$-0.275943\pi$
$137$	15.1504	1.29438	0.647192	+	0.762327i	$0.275943\pi$
$138$	30.3678	2.58508
$139$	0.974884	0.0826885	0.0413443	−	0.999145i	$-0.486836\pi$
$139$	0.974884	0.0826885	0.0413443	+	0.999145i	$0.486836\pi$
$140$	1.33222	0.112593
$141$	11.3527	0.956066
$142$	5.15016	0.432192
$143$	6.25768	0.523293
$144$	0.0522449	0.00435374
$145$	0.845136	0.0701848
$146$	1.40652	0.116404
$147$	1.62152	0.133740
$148$	24.5177	2.01535
$149$	−5.64603	−0.462541	−0.231270	−	0.972890i	$-0.574288\pi$
$149$	−5.64603	−0.462541	−0.231270	+	0.972890i	$0.574288\pi$
$150$	18.5562	1.51511
$151$	−2.16297	−0.176020	−0.0880099	−	0.996120i	$-0.528051\pi$
$151$	−2.16297	−0.176020	−0.0880099	+	0.996120i	$0.528051\pi$
$152$	−3.62992	−0.294425
$153$	0.0570550	0.00461262
$154$	−38.1717	−3.07597
$155$	1.86502	0.149802
$156$	−4.63412	−0.371027
$157$	−9.68490	−0.772939	−0.386470	−	0.922302i	$-0.626306\pi$
$157$	−9.68490	−0.772939	−0.386470	+	0.922302i	$0.626306\pi$
$158$	15.2845	1.21597
$159$	15.5417	1.23254
$160$	−1.34448	−0.106290
$161$	22.9142	1.80589
$162$	19.3246	1.51828
$163$	18.8641	1.47755	0.738775	−	0.673952i	$-0.235404\pi$
$163$	18.8641	1.47755	0.738775	+	0.673952i	$0.235404\pi$
$164$	16.0993	1.25714
$165$	1.89981	0.147900
$166$	−5.90016	−0.457941
$167$	−20.8393	−1.61259	−0.806297	−	0.591511i	$-0.798532\pi$
$167$	−20.8393	−1.61259	−0.806297	+	0.591511i	$0.798532\pi$
$168$	7.22261	0.557236
$169$	1.00000	0.0769231
$170$	−0.897094	−0.0688040
$171$	−0.0591949	−0.00452674
$172$	−23.3833	−1.78296
$173$	7.43241	0.565076	0.282538	−	0.959256i	$-0.408824\pi$
$173$	7.43241	0.565076	0.282538	+	0.959256i	$0.408824\pi$
$174$	17.9328	1.35948
$175$	14.0017	1.05843
$176$	13.4923	1.01702
$177$	7.32397	0.550504
$178$	−5.75396	−0.431278
$179$	14.6658	1.09618	0.548088	−	0.836420i	$-0.315356\pi$
$179$	14.6658	1.09618	0.548088	+	0.836420i	$0.315356\pi$
$180$	0.0114561	0.000853886 0
$181$	0.593907	0.0441448	0.0220724	−	0.999756i	$-0.492974\pi$
$181$	0.593907	0.0441448	0.0220724	+	0.999756i	$0.492974\pi$
$182$	−6.09998	−0.452161
$183$	12.4912	0.923373
$184$	12.0831	0.890780
$185$	−1.60624	−0.118093
$186$	39.5735	2.90167
$187$	14.7345	1.07749
$188$	17.6793	1.28940
$189$	14.7002	1.06929
$190$	0.930741	0.0675230
$191$	8.14653	0.589462	0.294731	−	0.955580i	$-0.404770\pi$
$191$	8.14653	0.589462	0.294731	+	0.955580i	$0.404770\pi$
$192$	−21.0894	−1.52200
$193$	22.7084	1.63459	0.817294	−	0.576221i	$-0.195473\pi$
$193$	22.7084	1.63459	0.817294	+	0.576221i	$0.195473\pi$
$194$	−4.05125	−0.290862
$195$	0.303597	0.0217410
$196$	2.52516	0.180369
$197$	−6.30874	−0.449479	−0.224739	−	0.974419i	$-0.572153\pi$
$197$	−6.30874	−0.449479	−0.224739	+	0.974419i	$0.572153\pi$
$198$	−0.328249	−0.0233277
$199$	−22.0982	−1.56650	−0.783250	−	0.621707i	$-0.786439\pi$
$199$	−22.0982	−1.56650	−0.783250	+	0.621707i	$0.786439\pi$
$200$	7.38339	0.522085
$201$	−19.8561	−1.40054
$202$	−33.6897	−2.37040
$203$	13.5313	0.949711
$204$	−10.9116	−0.763967
$205$	−1.05472	−0.0736646
$206$	1.67354	0.116601
$207$	0.197045	0.0136956
$208$	2.15612	0.149500
$209$	−15.2871	−1.05743
$210$	−1.85193	−0.127796
$211$	2.57027	0.176945	0.0884725	−	0.996079i	$-0.471801\pi$
$211$	2.57027	0.176945	0.0884725	+	0.996079i	$0.471801\pi$
$212$	24.2029	1.66226
$213$	−4.10394	−0.281198
$214$	−12.9202	−0.883210
$215$	1.53192	0.104476
$216$	7.75174	0.527439
$217$	29.8604	2.02706
$218$	−7.84314	−0.531205
$219$	−1.12079	−0.0757361
$220$	2.95855	0.199465
$221$	2.35463	0.158389
$222$	−34.0825	−2.28747
$223$	5.80939	0.389026	0.194513	−	0.980900i	$-0.437687\pi$
$223$	5.80939	0.389026	0.194513	+	0.980900i	$0.437687\pi$
$224$	−21.5261	−1.43827
$225$	0.120405	0.00802697
$226$	−9.40064	−0.625321
$227$	−14.5842	−0.967988	−0.483994	−	0.875071i	$-0.660814\pi$
$227$	−14.5842	−0.967988	−0.483994	+	0.875071i	$0.660814\pi$
$228$	11.3209	0.749743
$229$	−12.5515	−0.829423	−0.414712	−	0.909953i	$-0.636118\pi$
$229$	−12.5515	−0.829423	−0.414712	+	0.909953i	$0.636118\pi$
$230$	−3.09821	−0.204290
$231$	30.4175	2.00132
$232$	7.13533	0.468457
$233$	11.5179	0.754564	0.377282	−	0.926098i	$-0.376859\pi$
$233$	11.5179	0.754564	0.377282	+	0.926098i	$0.376859\pi$
$234$	−0.0524554	−0.00342912
$235$	−1.15823	−0.0755546
$236$	11.4055	0.742436
$237$	−12.1796	−0.791147
$238$	−14.3632	−0.931027
$239$	−18.5157	−1.19768	−0.598840	−	0.800869i	$-0.704371\pi$
$239$	−18.5157	−1.19768	−0.598840	+	0.800869i	$0.704371\pi$
$240$	0.654590	0.0422536
$241$	13.5661	0.873871	0.436936	−	0.899493i	$-0.356064\pi$
$241$	13.5661	0.873871	0.436936	+	0.899493i	$0.356064\pi$
$242$	−60.9578	−3.91852
$243$	0.251810	0.0161536
$244$	19.4523	1.24531
$245$	−0.165432	−0.0105690
$246$	−22.3798	−1.42689
$247$	−2.44294	−0.155440
$248$	15.7460	0.999872
$249$	4.70159	0.297951
$250$	−3.79812	−0.240214
$251$	8.87966	0.560479	0.280239	−	0.959930i	$-0.409586\pi$
$251$	8.87966	0.560479	0.280239	+	0.959930i	$0.409586\pi$
$252$	0.183421	0.0115544
$253$	50.8871	3.19925
$254$	12.5446	0.787116
$255$	0.714857	0.0447661
$256$	0.233144	0.0145715
$257$	−11.3632	−0.708816	−0.354408	−	0.935091i	$-0.615318\pi$
$257$	−11.3632	−0.708816	−0.354408	+	0.935091i	$0.615318\pi$
$258$	32.5054	2.02370
$259$	−25.7171	−1.59798
$260$	0.472786	0.0293210
$261$	0.116359	0.00720246
$262$	48.6921	3.00821
$263$	−23.8540	−1.47090	−0.735451	−	0.677578i	$-0.763029\pi$
$263$	−23.8540	−1.47090	−0.735451	+	0.677578i	$0.763029\pi$
$264$	16.0397	0.987178
$265$	−1.58561	−0.0974032
$266$	14.9019	0.913693
$267$	4.58509	0.280603
$268$	−30.9216	−1.88884
$269$	−14.6135	−0.891004	−0.445502	−	0.895281i	$-0.646975\pi$
$269$	−14.6135	−0.891004	−0.445502	+	0.895281i	$0.646975\pi$
$270$	−1.98761	−0.120962
$271$	28.3657	1.72309	0.861547	−	0.507677i	$-0.169496\pi$
$271$	28.3657	1.72309	0.861547	+	0.507677i	$0.169496\pi$
$272$	5.07685	0.307829
$273$	4.86082	0.294190
$274$	−32.7976	−1.98138
$275$	31.0946	1.87507
$276$	−37.6844	−2.26834
$277$	−30.8602	−1.85421	−0.927106	−	0.374800i	$-0.877711\pi$
$277$	−30.8602	−1.85421	−0.927106	+	0.374800i	$0.877711\pi$
$278$	−2.11043	−0.126575
$279$	0.256778	0.0153729
$280$	−0.736871	−0.0440365
$281$	−14.3725	−0.857391	−0.428696	−	0.903449i	$-0.641027\pi$
$281$	−14.3725	−0.857391	−0.428696	+	0.903449i	$0.641027\pi$
$282$	−24.5763	−1.46350
$283$	−28.8583	−1.71545	−0.857724	−	0.514110i	$-0.828122\pi$
$283$	−28.8583	−1.71545	−0.857724	+	0.514110i	$0.828122\pi$
$284$	−6.39101	−0.379237
$285$	−0.741668	−0.0439326
$286$	−13.5467	−0.801031
$287$	−16.8868	−0.996798
$288$	−0.185109	−0.0109076
$289$	−11.4557	−0.673867
$290$	−1.82956	−0.107435
$291$	3.22827	0.189244
$292$	−1.74539	−0.102141
$293$	28.8888	1.68770	0.843851	−	0.536578i	$-0.180283\pi$
$293$	28.8888	1.68770	0.843851	+	0.536578i	$0.180283\pi$
$294$	−3.51026	−0.204723
$295$	−0.747213	−0.0435044
$296$	−13.5612	−0.788227
$297$	32.6458	1.89430
$298$	12.2226	0.708034
$299$	8.13195	0.470283
$300$	−23.0271	−1.32947
$301$	24.5272	1.41372
$302$	4.68241	0.269442
$303$	26.8459	1.54226
$304$	−5.26726	−0.302098
$305$	−1.27438	−0.0729710
$306$	−0.123513	−0.00706076
$307$	−2.82291	−0.161112	−0.0805559	−	0.996750i	$-0.525670\pi$
$307$	−2.82291	−0.161112	−0.0805559	+	0.996750i	$0.525670\pi$
$308$	47.3686	2.69908
$309$	−1.33357	−0.0758642
$310$	−4.03740	−0.229309
$311$	−12.6393	−0.716711	−0.358356	−	0.933585i	$-0.616662\pi$
$311$	−12.6393	−0.716711	−0.358356	+	0.933585i	$0.616662\pi$
$312$	2.56321	0.145113
$313$	−2.47792	−0.140060	−0.0700302	−	0.997545i	$-0.522310\pi$
$313$	−2.47792	−0.140060	−0.0700302	+	0.997545i	$0.522310\pi$
$314$	20.9659	1.18318
$315$	−0.0120165	−0.000677054 0
$316$	−18.9670	−1.06698
$317$	10.9964	0.617620	0.308810	−	0.951124i	$-0.400069\pi$
$317$	10.9964	0.617620	0.308810	+	0.951124i	$0.400069\pi$
$318$	−33.6448	−1.88670
$319$	30.0499	1.68247
$320$	2.15160	0.120278
$321$	10.2956	0.574644
$322$	−49.6048	−2.76436
$323$	−5.75221	−0.320061
$324$	−23.9806	−1.33225
$325$	4.96903	0.275632
$326$	−40.8371	−2.26176
$327$	6.24987	0.345618
$328$	−8.90477	−0.491684
$329$	−18.5442	−1.02237
$330$	−4.11272	−0.226398
$331$	−8.36710	−0.459898	−0.229949	−	0.973203i	$-0.573856\pi$
$331$	−8.36710	−0.459898	−0.229949	+	0.973203i	$0.573856\pi$
$332$	7.32171	0.401831
$333$	−0.221148	−0.0121189
$334$	45.1130	2.46847
$335$	2.02578	0.110680
$336$	10.4805	0.571758
$337$	−23.5767	−1.28430	−0.642151	−	0.766578i	$-0.721958\pi$
$337$	−23.5767	−1.28430	−0.642151	+	0.766578i	$0.721958\pi$
$338$	−2.16481	−0.117750
$339$	7.49097	0.406854
$340$	1.11324	0.0603737
$341$	66.3131	3.59105
$342$	0.128145	0.00692931
$343$	17.0759	0.922012
$344$	12.9337	0.697337
$345$	2.46883	0.132917
$346$	−16.0897	−0.864989
$347$	32.5565	1.74773	0.873864	−	0.486171i	$-0.161607\pi$
$347$	32.5565	1.74773	0.873864	+	0.486171i	$0.161607\pi$
$348$	−22.2534	−1.19291
$349$	−13.5011	−0.722697	−0.361348	−	0.932431i	$-0.617683\pi$
$349$	−13.5011	−0.722697	−0.361348	+	0.932431i	$0.617683\pi$
$350$	−30.3110	−1.62019
$351$	5.21692	0.278459
$352$	−47.8045	−2.54799
$353$	0.325842	0.0173428	0.00867142	−	0.999962i	$-0.497240\pi$
$353$	0.325842	0.0173428	0.00867142	+	0.999962i	$0.497240\pi$
$354$	−15.8550	−0.842682
$355$	0.418696	0.0222221
$356$	7.14029	0.378435
$357$	11.4454	0.605756
$358$	−31.7487	−1.67797
$359$	23.5881	1.24493	0.622467	−	0.782646i	$-0.286131\pi$
$359$	23.5881	1.24493	0.622467	+	0.782646i	$0.286131\pi$
$360$	−0.00633655	−0.000333966 0
$361$	−13.0321	−0.685897
$362$	−1.28569	−0.0675745
$363$	48.5747	2.54951
$364$	7.56968	0.396759
$365$	0.114346	0.00598517
$366$	−27.0409	−1.41345
$367$	32.6378	1.70368	0.851838	−	0.523805i	$-0.175488\pi$
$367$	32.6378	1.70368	0.851838	+	0.523805i	$0.175488\pi$
$368$	17.5334	0.913993
$369$	−0.145214	−0.00755956
$370$	3.47719	0.180771
$371$	−25.3869	−1.31802
$372$	−49.1081	−2.54614
$373$	−31.4355	−1.62767	−0.813835	−	0.581096i	$-0.802624\pi$
$373$	−31.4355	−1.62767	−0.813835	+	0.581096i	$0.802624\pi$
$374$	−31.8973	−1.64937
$375$	3.02656	0.156291
$376$	−9.77872	−0.504299
$377$	4.80208	0.247320
$378$	−31.8232	−1.63681
$379$	−35.3269	−1.81462	−0.907310	−	0.420462i	$-0.861868\pi$
$379$	−35.3269	−1.81462	−0.907310	+	0.420462i	$0.861868\pi$
$380$	−1.15499	−0.0592496
$381$	−9.99624	−0.512123
$382$	−17.6357	−0.902319
$383$	−34.2734	−1.75129	−0.875644	−	0.482958i	$-0.839562\pi$
$383$	−34.2734	−1.75129	−0.875644	+	0.482958i	$0.839562\pi$
$384$	19.2981	0.984802
$385$	−3.10328	−0.158158
$386$	−49.1593	−2.50214
$387$	0.210916	0.0107215
$388$	5.02733	0.255224
$389$	−6.06369	−0.307441	−0.153721	−	0.988114i	$-0.549126\pi$
$389$	−6.06369	−0.307441	−0.153721	+	0.988114i	$0.549126\pi$
$390$	−0.657227	−0.0332800
$391$	19.1477	0.968341
$392$	−1.39671	−0.0705445
$393$	−38.8007	−1.95724
$394$	13.6572	0.688039
$395$	1.24259	0.0625217
$396$	0.407336	0.0204694
$397$	−1.99614	−0.100183	−0.0500916	−	0.998745i	$-0.515951\pi$
$397$	−1.99614	−0.100183	−0.0500916	+	0.998745i	$0.515951\pi$
$398$	47.8383	2.39792
$399$	−11.8747	−0.594478
$400$	10.7138	0.535690
$401$	−20.2325	−1.01036	−0.505182	−	0.863013i	$-0.668575\pi$
$401$	−20.2325	−1.01036	−0.505182	+	0.863013i	$0.668575\pi$
$402$	42.9846	2.14388
$403$	10.5971	0.527878
$404$	41.8067	2.07996
$405$	1.57105	0.0780659
$406$	−29.2926	−1.45377
$407$	−57.1118	−2.83093
$408$	6.03540	0.298797
$409$	11.5390	0.570567	0.285283	−	0.958443i	$-0.407912\pi$
$409$	11.5390	0.570567	0.285283	+	0.958443i	$0.407912\pi$
$410$	2.28325	0.112762
$411$	26.1350	1.28915
$412$	−2.07675	−0.102314
$413$	−11.9635	−0.588684
$414$	−0.426565	−0.0209645
$415$	−0.479670	−0.0235461
$416$	−7.63934	−0.374549
$417$	1.68171	0.0823539
$418$	33.0937	1.61866
$419$	34.7339	1.69686	0.848430	−	0.529307i	$-0.177548\pi$
$419$	34.7339	1.69686	0.848430	+	0.529307i	$0.177548\pi$
$420$	2.29813	0.112137
$421$	−21.2519	−1.03575	−0.517877	−	0.855455i	$-0.673278\pi$
$421$	−21.2519	−1.03575	−0.517877	+	0.855455i	$0.673278\pi$
$422$	−5.56414	−0.270858
$423$	−0.159466	−0.00775352
$424$	−13.3870	−0.650131
$425$	11.7002	0.567543
$426$	8.88424	0.430443
$427$	−20.4039	−0.987413
$428$	16.0332	0.774993
$429$	10.7948	0.521176
$430$	−3.31630	−0.159926
$431$	30.0000	1.44505	0.722525	−	0.691345i	$-0.242981\pi$
$431$	30.0000	1.44505	0.722525	+	0.691345i	$0.242981\pi$
$432$	11.2483	0.541184
$433$	−1.66204	−0.0798725	−0.0399363	−	0.999202i	$-0.512715\pi$
$433$	−1.66204	−0.0798725	−0.0399363	+	0.999202i	$0.512715\pi$
$434$	−64.6420	−3.10291
$435$	1.45790	0.0699007
$436$	9.73282	0.466118
$437$	−19.8659	−0.950313
$438$	2.42630	0.115933
$439$	0.219588	0.0104804	0.00524018	−	0.999986i	$-0.498332\pi$
$439$	0.219588	0.0104804	0.00524018	+	0.999986i	$0.498332\pi$
$440$	−1.63642	−0.0780133
$441$	−0.0227768	−0.00108461
$442$	−5.09731	−0.242454
$443$	−11.1142	−0.528051	−0.264026	−	0.964516i	$-0.585050\pi$
$443$	−11.1142	−0.528051	−0.264026	+	0.964516i	$0.585050\pi$
$444$	42.2941	2.00719
$445$	−0.467784	−0.0221751
$446$	−12.5762	−0.595500
$447$	−9.73964	−0.460669
$448$	34.4488	1.62755
$449$	−18.4658	−0.871453	−0.435726	−	0.900079i	$-0.643508\pi$
$449$	−18.4658	−0.871453	−0.435726	+	0.900079i	$0.643508\pi$
$450$	−0.260652	−0.0122873
$451$	−37.5018	−1.76589
$452$	11.6656	0.548703
$453$	−3.73121	−0.175308
$454$	31.5720	1.48175
$455$	−0.495915	−0.0232488
$456$	−6.26176	−0.293234
$457$	−1.86200	−0.0871008	−0.0435504	−	0.999051i	$-0.513867\pi$
$457$	−1.86200	−0.0871008	−0.0435504	+	0.999051i	$0.513867\pi$
$458$	27.1714	1.26964
$459$	12.2839	0.573364
$460$	3.84467	0.179259
$461$	−29.0093	−1.35110	−0.675549	−	0.737315i	$-0.736093\pi$
$461$	−29.0093	−1.35110	−0.675549	+	0.737315i	$0.736093\pi$
$462$	−65.8479	−3.06352
$463$	1.00000	0.0464739
$463$	1.00000	0.0464739
$464$	10.3538	0.480665
$465$	3.21723	0.149196
$466$	−24.9341	−1.15505
$467$	−28.5745	−1.32227	−0.661136	−	0.750266i	$-0.729925\pi$
$467$	−28.5745	−1.32227	−0.661136	+	0.750266i	$0.729925\pi$
$468$	0.0650937	0.00300896
$469$	32.4343	1.49768
$470$	2.50734	0.115655
$471$	−16.7069	−0.769812
$472$	−6.30858	−0.290376
$473$	54.4692	2.50450
$474$	26.3664	1.21105
$475$	−12.1390	−0.556977
$476$	17.8238	0.816951
$477$	−0.218308	−0.00999565
$478$	40.0828	1.83335
$479$	−5.10099	−0.233070	−0.116535	−	0.993187i	$-0.537179\pi$
$479$	−5.10099	−0.233070	−0.116535	+	0.993187i	$0.537179\pi$
$480$	−2.31928	−0.105860
$481$	−9.12667	−0.416141
$482$	−29.3680	−1.33768
$483$	39.5279	1.79858
$484$	75.6446	3.43839
$485$	−0.329357	−0.0149553
$486$	−0.545119	−0.0247271
$487$	−12.5950	−0.570736	−0.285368	−	0.958418i	$-0.592116\pi$
$487$	−12.5950	−0.570736	−0.285368	+	0.958418i	$0.592116\pi$
$488$	−10.7594	−0.487055
$489$	32.5414	1.47157
$490$	0.358127	0.0161785
$491$	17.8252	0.804439	0.402219	−	0.915543i	$-0.368239\pi$
$491$	17.8252	0.804439	0.402219	+	0.915543i	$0.368239\pi$
$492$	27.7719	1.25205
$493$	11.3071	0.509247
$494$	5.28849	0.237940
$495$	−0.0266859	−0.00119944
$496$	22.8485	1.02593
$497$	6.70366	0.300700
$498$	−10.1780	−0.456088
$499$	−13.0042	−0.582150	−0.291075	−	0.956700i	$-0.594013\pi$
$499$	−13.0042	−0.582150	−0.291075	+	0.956700i	$0.594013\pi$
$500$	4.71322	0.210782
$501$	−35.9487	−1.60607
$502$	−19.2227	−0.857952
$503$	−12.0565	−0.537574	−0.268787	−	0.963200i	$-0.586623\pi$
$503$	−12.0565	−0.537574	−0.268787	+	0.963200i	$0.586623\pi$
$504$	−0.101453	−0.00451909
$505$	−2.73890	−0.121879
$506$	−110.161	−4.89724
$507$	1.72504	0.0766118
$508$	−15.5670	−0.690673
$509$	31.8100	1.40995	0.704976	−	0.709231i	$-0.250958\pi$
$509$	31.8100	1.40995	0.704976	+	0.709231i	$0.250958\pi$
$510$	−1.54753	−0.0685256
$511$	1.83078	0.0809888
$512$	−22.8788	−1.01111
$513$	−12.7446	−0.562689
$514$	24.5991	1.08502
$515$	0.136055	0.00599529
$516$	−40.3371	−1.77574
$517$	−41.1823	−1.81120
$518$	55.6726	2.44611
$519$	12.8212	0.562789
$520$	−0.261506	−0.0114678
$521$	12.3330	0.540316	0.270158	−	0.962816i	$-0.412924\pi$
$521$	12.3330	0.540316	0.270158	+	0.962816i	$0.412924\pi$
$522$	−0.251895	−0.0110252
$523$	−36.6562	−1.60286	−0.801432	−	0.598086i	$-0.795928\pi$
$523$	−36.6562	−1.60286	−0.801432	+	0.598086i	$0.795928\pi$
$524$	−60.4238	−2.63962
$525$	24.1535	1.05415
$526$	51.6393	2.25158
$527$	24.9521	1.08693
$528$	23.2748	1.01290
$529$	43.1286	1.87516
$530$	3.43254	0.149100
$531$	−0.102877	−0.00446448
$532$	−18.4923	−0.801741
$533$	−5.99292	−0.259582
$534$	−9.92583	−0.429533
$535$	−1.05039	−0.0454122
$536$	17.1033	0.738748
$537$	25.2992	1.09174
$538$	31.6355	1.36390
$539$	−5.88213	−0.253361
$540$	2.46649	0.106141
$541$	−31.2802	−1.34484	−0.672421	−	0.740169i	$-0.734745\pi$
$541$	−31.2802	−1.34484	−0.672421	+	0.740169i	$0.734745\pi$
$542$	−61.4062	−2.63762
$543$	1.02451	0.0439661
$544$	−17.9878	−0.771220
$545$	−0.637630	−0.0273130
$546$	−10.5227	−0.450331
$547$	7.34384	0.314000	0.157000	−	0.987599i	$-0.449818\pi$
$547$	7.34384	0.314000	0.157000	+	0.987599i	$0.449818\pi$
$548$	40.6997	1.73860
$549$	−0.175458	−0.00748839
$550$	−67.3137	−2.87027
$551$	−11.7312	−0.499766
$552$	20.8439	0.887175
$553$	19.8949	0.846017
$554$	66.8064	2.83833
$555$	−2.77083	−0.117615
$556$	2.61891	0.111067
$557$	22.0382	0.933788	0.466894	−	0.884313i	$-0.345373\pi$
$557$	22.0382	0.933788	0.466894	+	0.884313i	$0.345373\pi$
$558$	−0.555874	−0.0235320
$559$	8.70438	0.368156
$560$	−1.06925	−0.0451841
$561$	25.4176	1.07313
$562$	31.1137	1.31245
$563$	12.4601	0.525129	0.262564	−	0.964915i	$-0.415432\pi$
$563$	12.4601	0.525129	0.262564	+	0.964915i	$0.415432\pi$
$564$	30.4976	1.28418
$565$	−0.764251	−0.0321523
$566$	62.4726	2.62592
$567$	25.1537	1.05636
$568$	3.53498	0.148324
$569$	4.34089	0.181980	0.0909898	−	0.995852i	$-0.470997\pi$
$569$	4.34089	0.181980	0.0909898	+	0.995852i	$0.470997\pi$
$570$	1.60557	0.0672498
$571$	−47.1894	−1.97482	−0.987408	−	0.158196i	$-0.949432\pi$
$571$	−47.1894	−1.97482	−0.987408	+	0.158196i	$0.949432\pi$
$572$	16.8105	0.702883
$573$	14.0531	0.587077
$574$	36.5567	1.52585
$575$	40.4079	1.68512
$576$	0.296235	0.0123431
$577$	16.1456	0.672148	0.336074	−	0.941836i	$-0.390901\pi$
$577$	16.1456	0.672148	0.336074	+	0.941836i	$0.390901\pi$
$578$	24.7994	1.03152
$579$	39.1730	1.62797
$580$	2.27036	0.0942715
$581$	−7.67989	−0.318615
$582$	−6.98857	−0.289685
$583$	−56.3783	−2.33495
$584$	0.965406	0.0399488
$585$	−0.00426451	−0.000176316 0
$586$	−62.5386	−2.58345
$587$	−3.29230	−0.135888	−0.0679440	−	0.997689i	$-0.521644\pi$
$587$	−3.29230	−0.135888	−0.0679440	+	0.997689i	$0.521644\pi$
$588$	4.35601	0.179639
$589$	−25.8880	−1.06670
$590$	1.61757	0.0665943
$591$	−10.8828	−0.447660
$592$	−19.6782	−0.808768
$593$	−15.4839	−0.635847	−0.317923	−	0.948116i	$-0.602985\pi$
$593$	−15.4839	−0.635847	−0.317923	+	0.948116i	$0.602985\pi$
$594$	−70.6719	−2.89970
$595$	−1.16769	−0.0478708
$596$	−15.1674	−0.621281
$597$	−38.1203	−1.56016
$598$	−17.6041	−0.719885
$599$	8.36064	0.341607	0.170803	−	0.985305i	$-0.445364\pi$
$599$	8.36064	0.341607	0.170803	+	0.985305i	$0.445364\pi$
$600$	12.7367	0.519972
$601$	29.6302	1.20864	0.604320	−	0.796742i	$-0.293445\pi$
$601$	29.6302	1.20864	0.604320	+	0.796742i	$0.293445\pi$
$602$	−53.0966	−2.16405
$603$	0.278911	0.0113581
$604$	−5.81056	−0.236428
$605$	−4.95573	−0.201479
$606$	−58.1162	−2.36081
$607$	4.34668	0.176426	0.0882132	−	0.996102i	$-0.471884\pi$
$607$	4.34668	0.176426	0.0882132	+	0.996102i	$0.471884\pi$
$608$	18.6624	0.756862
$609$	23.3421	0.945868
$610$	2.75879	0.111700
$611$	−6.58109	−0.266242
$612$	0.153271	0.00619563
$613$	−1.53209	−0.0618805	−0.0309402	−	0.999521i	$-0.509850\pi$
$613$	−1.53209	−0.0618805	−0.0309402	+	0.999521i	$0.509850\pi$
$614$	6.11105	0.246622
$615$	−1.81943	−0.0733665
$616$	−26.2004	−1.05564
$617$	24.4918	0.986002	0.493001	−	0.870029i	$-0.335900\pi$
$617$	24.4918	0.986002	0.493001	+	0.870029i	$0.335900\pi$
$618$	2.88692	0.116129
$619$	−7.73692	−0.310973	−0.155487	−	0.987838i	$-0.549695\pi$
$619$	−7.73692	−0.310973	−0.155487	+	0.987838i	$0.549695\pi$
$620$	5.01015	0.201212
$621$	42.4238	1.70241
$622$	27.3617	1.09710
$623$	−7.48959	−0.300064
$624$	3.71939	0.148895
$625$	24.5364	0.981454
$626$	5.36422	0.214397
$627$	−26.3709	−1.05315
$628$	−26.0173	−1.03821
$629$	−21.4899	−0.856859
$630$	0.0260134	0.00103640
$631$	−12.0714	−0.480554	−0.240277	−	0.970704i	$-0.577238\pi$
$631$	−12.0714	−0.480554	−0.240277	+	0.970704i	$0.577238\pi$
$632$	10.4910	0.417309
$633$	4.43383	0.176229
$634$	−23.8051	−0.945421
$635$	1.01984	0.0404713
$636$	41.7509	1.65553
$637$	−0.939986	−0.0372436
$638$	−65.0522	−2.57544
$639$	0.0576466	0.00228046
$640$	−1.96885	−0.0778255
$641$	47.2248	1.86527	0.932635	−	0.360822i	$-0.117504\pi$
$641$	47.2248	1.86527	0.932635	+	0.360822i	$0.117504\pi$
$642$	−22.2880	−0.879636
$643$	−8.10344	−0.319568	−0.159784	−	0.987152i	$-0.551080\pi$
$643$	−8.10344	−0.319568	−0.159784	+	0.987152i	$0.551080\pi$
$644$	61.5563	2.42566
$645$	2.64262	0.104053
$646$	12.4524	0.489934
$647$	16.0074	0.629314	0.314657	−	0.949205i	$-0.398110\pi$
$647$	16.0074	0.629314	0.314657	+	0.949205i	$0.398110\pi$
$648$	13.2641	0.521061
$649$	−26.5681	−1.04289
$650$	−10.7570	−0.421923
$651$	51.5104	2.01885
$652$	50.6762	1.98463
$653$	−33.9725	−1.32944	−0.664722	−	0.747090i	$-0.731450\pi$
$653$	−33.9725	−1.32944	−0.664722	+	0.747090i	$0.731450\pi$
$654$	−13.5297	−0.529055
$655$	3.95856	0.154674
$656$	−12.9214	−0.504497
$657$	0.0157433	0.000614206 0
$658$	40.1445	1.56500
$659$	13.1455	0.512077	0.256038	−	0.966667i	$-0.417583\pi$
$659$	13.1455	0.512077	0.256038	+	0.966667i	$0.417583\pi$
$660$	5.10361	0.198658
$661$	−3.02627	−0.117708	−0.0588541	−	0.998267i	$-0.518745\pi$
$661$	−3.02627	−0.117708	−0.0588541	+	0.998267i	$0.518745\pi$
$662$	18.1132	0.703988
$663$	4.06183	0.157748
$664$	−4.04976	−0.157161
$665$	1.21149	0.0469796
$666$	0.478743	0.0185509
$667$	39.0503	1.51203
$668$	−55.9823	−2.16602
$669$	10.0214	0.387451
$670$	−4.38541	−0.169423
$671$	−45.3123	−1.74926
$672$	−37.1334	−1.43245
$673$	−40.3681	−1.55608	−0.778038	−	0.628217i	$-0.783785\pi$
$673$	−40.3681	−1.55608	−0.778038	+	0.628217i	$0.783785\pi$
$674$	51.0389	1.96594
$675$	25.9230	0.997778
$676$	2.68638	0.103322
$677$	−14.0961	−0.541755	−0.270878	−	0.962614i	$-0.587314\pi$
$677$	−14.0961	−0.541755	−0.270878	+	0.962614i	$0.587314\pi$
$678$	−16.2165	−0.622791
$679$	−5.27326	−0.202369
$680$	−0.615749	−0.0236129
$681$	−25.1584	−0.964071
$682$	−143.555	−5.49700
$683$	17.1542	0.656386	0.328193	−	0.944611i	$-0.393560\pi$
$683$	17.1542	0.656386	0.328193	+	0.944611i	$0.393560\pi$
$684$	−0.159020	−0.00608028
$685$	−2.66637	−0.101877
$686$	−36.9660	−1.41137
$687$	−21.6518	−0.826067
$688$	18.7676	0.715510
$689$	−9.00946	−0.343233
$690$	−5.34454	−0.203463
$691$	11.7605	0.447389	0.223694	−	0.974659i	$-0.428188\pi$
$691$	11.7605	0.447389	0.223694	+	0.974659i	$0.428188\pi$
$692$	19.9663	0.759005
$693$	−0.427262	−0.0162304
$694$	−70.4786	−2.67533
$695$	−0.171573	−0.00650815
$696$	12.3087	0.466562
$697$	−14.1111	−0.534495
$698$	29.2272	1.10627
$699$	19.8689	0.751511
$700$	37.6139	1.42167
$701$	27.4150	1.03545	0.517725	−	0.855547i	$-0.326779\pi$
$701$	27.4150	1.03545	0.517725	+	0.855547i	$0.326779\pi$
$702$	−11.2936	−0.426250
$703$	22.2959	0.840906
$704$	76.5029	2.88331
$705$	−1.99800	−0.0752489
$706$	−0.705385	−0.0265475
$707$	−43.8519	−1.64922
$708$	19.6750	0.739431
$709$	28.3979	1.06651	0.533253	−	0.845956i	$-0.320969\pi$
$709$	28.3979	1.06651	0.533253	+	0.845956i	$0.320969\pi$
$710$	−0.906396	−0.0340164
$711$	0.171082	0.00641606
$712$	−3.94941	−0.148011
$713$	86.1748	3.22727
$714$	−24.7771	−0.927260
$715$	−1.10131	−0.0411868
$716$	39.3981	1.47237
$717$	−31.9403	−1.19283
$718$	−51.0637	−1.90568
$719$	18.1160	0.675612	0.337806	−	0.941216i	$-0.390315\pi$
$719$	18.1160	0.675612	0.337806	+	0.941216i	$0.390315\pi$
$720$	−0.00919477	−0.000342669 0
$721$	2.17834	0.0811257
$722$	28.2119	1.04994
$723$	23.4021	0.870335
$724$	1.59546	0.0592949
$725$	23.8617	0.886200
$726$	−105.155	−3.90266
$727$	46.3498	1.71902	0.859509	−	0.511120i	$-0.170769\pi$
$727$	46.3498	1.71902	0.859509	+	0.511120i	$0.170769\pi$
$728$	−4.18692	−0.155177
$729$	27.2145	1.00795
$730$	−0.247538	−0.00916179
$731$	20.4956	0.758056
$732$	33.5560	1.24027
$733$	−21.4775	−0.793288	−0.396644	−	0.917973i	$-0.629825\pi$
$733$	−21.4775	−0.793288	−0.396644	+	0.917973i	$0.629825\pi$
$734$	−70.6544	−2.60790
$735$	−0.285377	−0.0105263
$736$	−62.1227	−2.28987
$737$	72.0290	2.65322
$738$	0.314361	0.0115718
$739$	−3.19049	−0.117364	−0.0586820	−	0.998277i	$-0.518690\pi$
$739$	−3.19049	−0.117364	−0.0586820	+	0.998277i	$0.518690\pi$
$740$	−4.31497	−0.158621
$741$	−4.21417	−0.154811
$742$	54.9576	2.01756
$743$	41.3154	1.51572	0.757858	−	0.652419i	$-0.226246\pi$
$743$	41.3154	1.51572	0.757858	+	0.652419i	$0.226246\pi$
$744$	27.1625	0.995826
$745$	0.993666	0.0364051
$746$	68.0518	2.49155
$747$	−0.0660414	−0.00241633
$748$	39.5825	1.44728
$749$	−16.8175	−0.614499
$750$	−6.55192	−0.239242
$751$	27.1055	0.989092	0.494546	−	0.869151i	$-0.335334\pi$
$751$	27.1055	0.989092	0.494546	+	0.869151i	$0.335334\pi$
$752$	−14.1896	−0.517441
$753$	15.3178	0.558211
$754$	−10.3956	−0.378584
$755$	0.380669	0.0138540
$756$	39.4905	1.43625
$757$	25.4469	0.924885	0.462443	−	0.886649i	$-0.346973\pi$
$757$	25.4469	0.924885	0.462443	+	0.886649i	$0.346973\pi$
$758$	76.4758	2.77773
$759$	87.7824	3.18630
$760$	0.638843	0.0231733
$761$	20.6248	0.747647	0.373823	−	0.927500i	$-0.378047\pi$
$761$	20.6248	0.747647	0.373823	+	0.927500i	$0.378047\pi$
$762$	21.6399	0.783931
$763$	−10.2089	−0.369589
$764$	21.8847	0.791761
$765$	−0.0100413	−0.000363045 0
$766$	74.1952	2.68078
$767$	−4.24568	−0.153303
$768$	0.402184	0.0145126
$769$	24.0538	0.867403	0.433701	−	0.901057i	$-0.357207\pi$
$769$	24.0538	0.867403	0.433701	+	0.901057i	$0.357207\pi$
$770$	6.71799	0.242100
$771$	−19.6020	−0.705948
$772$	61.0035	2.19556
$773$	0.330467	0.0118861	0.00594303	−	0.999982i	$-0.498108\pi$
$773$	0.330467	0.0118861	0.00594303	+	0.999982i	$0.498108\pi$
$774$	−0.456592	−0.0164118
$775$	52.6571	1.89150
$776$	−2.78070	−0.0998213
$777$	−44.3631	−1.59152
$778$	13.1267	0.470615
$779$	14.6403	0.524544
$780$	0.815576	0.0292023
$781$	14.8873	0.532709
$782$	−41.4510	−1.48229
$783$	25.0521	0.895289
$784$	−2.02672	−0.0723829
$785$	1.70448	0.0608356
$786$	83.9960	2.99604
$787$	−3.54644	−0.126417	−0.0632085	−	0.998000i	$-0.520133\pi$
$787$	−3.54644	−0.126417	−0.0632085	+	0.998000i	$0.520133\pi$
$788$	−16.9477	−0.603736
$789$	−41.1492	−1.46495
$790$	−2.68997	−0.0957049
$791$	−12.2363	−0.435071
$792$	−0.225304	−0.00800584
$793$	−7.24107	−0.257138
$794$	4.32125	0.153355
$795$	−2.73524	−0.0970090
$796$	−59.3642	−2.10411
$797$	11.9880	0.424638	0.212319	−	0.977200i	$-0.431898\pi$
$797$	11.9880	0.424638	0.212319	+	0.977200i	$0.431898\pi$
$798$	25.7064	0.909996
$799$	−15.4960	−0.548209
$800$	−37.9601	−1.34209
$801$	−0.0644050	−0.00227564
$802$	43.7995	1.54661
$803$	4.06573	0.143477
$804$	−53.3411	−1.88119
$805$	−4.03275	−0.142136
$806$	−22.9406	−0.808048
$807$	−25.2090	−0.887398
$808$	−23.1240	−0.813499
$809$	−26.4740	−0.930776	−0.465388	−	0.885107i	$-0.654085\pi$
$809$	−26.4740	−0.930776	−0.465388	+	0.885107i	$0.654085\pi$
$810$	−3.40101	−0.119499
$811$	−24.1015	−0.846317	−0.423159	−	0.906056i	$-0.639079\pi$
$811$	−24.1015	−0.846317	−0.423159	+	0.906056i	$0.639079\pi$
$812$	36.3502	1.27564
$813$	48.9320	1.71612
$814$	123.636	4.33344
$815$	−3.31996	−0.116293
$816$	8.75778	0.306584
$817$	−21.2643	−0.743942
$818$	−24.9797	−0.873394
$819$	−0.0682781	−0.00238583
$820$	−2.83337	−0.0989456
$821$	32.9858	1.15121	0.575606	−	0.817727i	$-0.304766\pi$
$821$	32.9858	1.15121	0.575606	+	0.817727i	$0.304766\pi$
$822$	−56.5772	−1.97336
$823$	−5.61946	−0.195882	−0.0979410	−	0.995192i	$-0.531226\pi$
$823$	−5.61946	−0.195882	−0.0979410	+	0.995192i	$0.531226\pi$
$824$	1.14868	0.0400163
$825$	53.6394	1.86749
$826$	25.8986	0.901127
$827$	35.6095	1.23826	0.619131	−	0.785287i	$-0.287485\pi$
$827$	35.6095	1.23826	0.619131	+	0.785287i	$0.287485\pi$
$828$	0.529339	0.0183958
$829$	−5.96323	−0.207111	−0.103556	−	0.994624i	$-0.533022\pi$
$829$	−5.96323	−0.207111	−0.103556	+	0.994624i	$0.533022\pi$
$830$	1.03839	0.0360431
$831$	−53.2352	−1.84671
$832$	12.2254	0.423841
$833$	−2.21332	−0.0766869
$834$	−3.64059	−0.126063
$835$	3.66759	0.126922
$836$	−41.0671	−1.42033
$837$	55.2841	1.91090
$838$	−75.1921	−2.59747
$839$	6.85044	0.236503	0.118252	−	0.992984i	$-0.462271\pi$
$839$	6.85044	0.236503	0.118252	+	0.992984i	$0.462271\pi$
$840$	−1.27113	−0.0438583
$841$	−5.94001	−0.204828
$842$	46.0063	1.58548
$843$	−24.7932	−0.853922
$844$	6.90474	0.237671
$845$	−0.175994	−0.00605437
$846$	0.345214	0.0118687
$847$	−79.3451	−2.72633
$848$	−19.4255	−0.667073
$849$	−49.7818	−1.70851
$850$	−25.3287	−0.868766
$851$	−74.2176	−2.54415
$852$	−11.0248	−0.377702
$853$	25.3738	0.868783	0.434391	−	0.900724i	$-0.356963\pi$
$853$	25.3738	0.868783	0.434391	+	0.900724i	$0.356963\pi$
$854$	44.1704	1.51148
$855$	0.0104179	0.000356286 0
$856$	−8.86822	−0.303110
$857$	−38.0120	−1.29846	−0.649232	−	0.760591i	$-0.724910\pi$
$857$	−38.0120	−1.29846	−0.649232	+	0.760591i	$0.724910\pi$
$858$	−23.3686	−0.797789
$859$	49.9701	1.70496	0.852479	−	0.522762i	$-0.175098\pi$
$859$	49.9701	1.70496	0.852479	+	0.522762i	$0.175098\pi$
$860$	4.11531	0.140331
$861$	−29.1305	−0.992764
$862$	−64.9442	−2.21201
$863$	6.75267	0.229864	0.114932	−	0.993373i	$-0.463335\pi$
$863$	6.75267	0.229864	0.114932	+	0.993373i	$0.463335\pi$
$864$	−39.8539	−1.35586
$865$	−1.30806	−0.0444753
$866$	3.59799	0.122265
$867$	−19.7616	−0.671140
$868$	80.2164	2.72272
$869$	44.1820	1.49877
$870$	−3.15606	−0.107000
$871$	11.5105	0.390019
$872$	−5.38339	−0.182305
$873$	−0.0453462	−0.00153474
$874$	43.0057	1.45469
$875$	−4.94379	−0.167131
$876$	−3.01088	−0.101728
$877$	31.5942	1.06686	0.533430	−	0.845844i	$-0.320903\pi$
$877$	31.5942	1.06686	0.533430	+	0.845844i	$0.320903\pi$
$878$	−0.475365	−0.0160428
$879$	49.8344	1.68087
$880$	−2.37456	−0.0800463
$881$	17.2108	0.579847	0.289924	−	0.957050i	$-0.406370\pi$
$881$	17.2108	0.579847	0.289924	+	0.957050i	$0.406370\pi$
$882$	0.0493074	0.00166027
$883$	−27.9879	−0.941869	−0.470935	−	0.882168i	$-0.656083\pi$
$883$	−27.9879	−0.941869	−0.470935	+	0.882168i	$0.656083\pi$
$884$	6.32543	0.212747
$885$	−1.28897	−0.0433284
$886$	24.0601	0.808313
$887$	37.1118	1.24609	0.623046	−	0.782185i	$-0.285895\pi$
$887$	37.1118	1.24609	0.623046	+	0.782185i	$0.285895\pi$
$888$	−23.3936	−0.785037
$889$	16.3285	0.547641
$890$	1.01266	0.0339445
$891$	55.8606	1.87140
$892$	15.6062	0.522536
$893$	16.0772	0.538003
$894$	21.0844	0.705168
$895$	−2.58110	−0.0862766
$896$	−31.5228	−1.05310
$897$	14.0279	0.468380
$898$	39.9748	1.33398
$899$	50.8880	1.69721
$900$	0.323452	0.0107817
$901$	−21.2139	−0.706738
$902$	81.1840	2.70313
$903$	42.3104	1.40800
$904$	−6.45243	−0.214605
$905$	−0.104524	−0.00347449
$906$	8.07734	0.268352
$907$	−24.5547	−0.815325	−0.407663	−	0.913133i	$-0.633656\pi$
$907$	−24.5547	−0.815325	−0.407663	+	0.913133i	$0.633656\pi$
$908$	−39.1788	−1.30019
$909$	−0.377094	−0.0125074
$910$	1.07356	0.0355881
$911$	14.6274	0.484629	0.242314	−	0.970198i	$-0.422093\pi$
$911$	14.6274	0.484629	0.242314	+	0.970198i	$0.422093\pi$
$912$	−9.08625	−0.300876
$913$	−17.0553	−0.564447
$914$	4.03087	0.133329
$915$	−2.19837	−0.0726757
$916$	−33.7180	−1.11407
$917$	63.3797	2.09298
$918$	−26.5923	−0.877676
$919$	−19.5595	−0.645207	−0.322603	−	0.946534i	$-0.604558\pi$
$919$	−19.5595	−0.645207	−0.322603	+	0.946534i	$0.604558\pi$
$920$	−2.12655	−0.0701104
$921$	−4.86963	−0.160460
$922$	62.7995	2.06819
$923$	2.37904	0.0783071
$924$	81.7129	2.68816
$925$	−45.3507	−1.49112
$926$	−2.16481	−0.0711399
$927$	0.0187322	0.000615245 0
$928$	−36.6847	−1.20424
$929$	−41.2299	−1.35271	−0.676354	−	0.736576i	$-0.736441\pi$
$929$	−41.2299	−1.35271	−0.676354	+	0.736576i	$0.736441\pi$
$930$	−6.96468	−0.228381
$931$	2.29633	0.0752591
$932$	30.9415	1.01352
$933$	−21.8034	−0.713811
$934$	61.8583	2.02406
$935$	−2.59318	−0.0848061
$936$	−0.0360044	−0.00117684
$937$	−56.2922	−1.83899	−0.919494	−	0.393105i	$-0.871401\pi$
$937$	−56.2922	−1.83899	−0.919494	+	0.393105i	$0.871401\pi$
$938$	−70.2139	−2.29256
$939$	−4.27452	−0.139494
$940$	−3.11145	−0.101484
$941$	33.6403	1.09664	0.548322	−	0.836267i	$-0.315267\pi$
$941$	33.6403	1.09664	0.548322	+	0.836267i	$0.315267\pi$
$942$	36.1671	1.17839
$943$	−48.7341	−1.58700
$944$	−9.15418	−0.297943
$945$	−2.58715	−0.0841600
$946$	−117.915	−3.83375
$947$	−35.0026	−1.13743	−0.568716	−	0.822534i	$-0.692560\pi$
$947$	−35.0026	−1.13743	−0.568716	+	0.822534i	$0.692560\pi$
$948$	−32.7189	−1.06266
$949$	0.649719	0.0210908
$950$	26.2786	0.852591
$951$	18.9693	0.615121
$952$	−9.85863	−0.319520
$953$	22.7028	0.735417	0.367708	−	0.929941i	$-0.380142\pi$
$953$	22.7028	0.735417	0.367708	+	0.929941i	$0.380142\pi$
$954$	0.472595	0.0153008
$955$	−1.43374	−0.0463947
$956$	−49.7402	−1.60871
$957$	51.8373	1.67566
$958$	11.0427	0.356772
$959$	−42.6907	−1.37855
$960$	3.71160	0.119791
$961$	81.2979	2.62251
$962$	19.7575	0.637006
$963$	−0.144618	−0.00466026
$964$	36.4438	1.17378
$965$	−3.99654	−0.128653
$966$	−85.5703	−2.75318
$967$	−29.6590	−0.953770	−0.476885	−	0.878966i	$-0.658234\pi$
$967$	−29.6590	−0.953770	−0.476885	+	0.878966i	$0.658234\pi$
$968$	−41.8403	−1.34480
$969$	−9.92280	−0.318766
$970$	0.712994	0.0228929
$971$	24.2366	0.777790	0.388895	−	0.921282i	$-0.372857\pi$
$971$	24.2366	0.777790	0.388895	+	0.921282i	$0.372857\pi$
$972$	0.676457	0.0216974
$973$	−2.74703	−0.0880656
$974$	27.2658	0.873653
$975$	8.57178	0.274517
$976$	−15.6126	−0.499747
$977$	−0.284545	−0.00910342	−0.00455171	−	0.999990i	$-0.501449\pi$
$977$	−0.284545	−0.00910342	−0.00455171	+	0.999990i	$0.501449\pi$
$978$	−70.4457	−2.25261
$979$	−16.6327	−0.531582
$980$	−0.444413	−0.0141962
$981$	−0.0877895	−0.00280290
$982$	−38.5880	−1.23139
$983$	23.4631	0.748357	0.374179	−	0.927357i	$-0.377925\pi$
$983$	23.4631	0.748357	0.374179	+	0.927357i	$0.377925\pi$
$984$	−15.3611	−0.489694
$985$	1.11030	0.0353770
$986$	−24.4777	−0.779529
$987$	−31.9895	−1.01824
$988$	−6.56267	−0.208786
$989$	70.7835	2.25079
$990$	0.0577698	0.00183604
$991$	−44.3917	−1.41015	−0.705074	−	0.709134i	$-0.749086\pi$
$991$	−44.3917	−1.41015	−0.705074	+	0.709134i	$0.749086\pi$
$992$	−80.9546	−2.57031
$993$	−14.4336	−0.458037
$994$	−14.5121	−0.460296
$995$	3.88914	0.123294
$996$	12.6303	0.400205
$997$	49.5381	1.56889	0.784443	−	0.620201i	$-0.212949\pi$
$997$	49.5381	1.56889	0.784443	+	0.620201i	$0.212949\pi$
$998$	28.1516	0.891125
$999$	−47.6132	−1.50641

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6019.2.a.d.1.18	✓	123

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6019.2.a.d.1.18	✓	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)

\(f(q)\)	\(=\)	\(q-2.16481 q^{2} +1.72504 q^{3} +2.68638 q^{4} -0.175994 q^{5} -3.73438 q^{6} -2.81780 q^{7} -1.48588 q^{8} -0.0242310 q^{9} +O(q^{10})\)	\(q-2.16481 q^{2} +1.72504 q^{3} +2.68638 q^{4} -0.175994 q^{5} -3.73438 q^{6} -2.81780 q^{7} -1.48588 q^{8} -0.0242310 q^{9} +0.380992 q^{10} -6.25768 q^{11} +4.63412 q^{12} -1.00000 q^{13} +6.09998 q^{14} -0.303597 q^{15} -2.15612 q^{16} -2.35463 q^{17} +0.0524554 q^{18} +2.44294 q^{19} -0.472786 q^{20} -4.86082 q^{21} +13.5467 q^{22} -8.13195 q^{23} -2.56321 q^{24} -4.96903 q^{25} +2.16481 q^{26} -5.21692 q^{27} -7.56968 q^{28} -4.80208 q^{29} +0.657227 q^{30} -10.5971 q^{31} +7.63934 q^{32} -10.7948 q^{33} +5.09731 q^{34} +0.495915 q^{35} -0.0650937 q^{36} +9.12667 q^{37} -5.28849 q^{38} -1.72504 q^{39} +0.261506 q^{40} +5.99292 q^{41} +10.5227 q^{42} -8.70438 q^{43} -16.8105 q^{44} +0.00426451 q^{45} +17.6041 q^{46} +6.58109 q^{47} -3.71939 q^{48} +0.939986 q^{49} +10.7570 q^{50} -4.06183 q^{51} -2.68638 q^{52} +9.00946 q^{53} +11.2936 q^{54} +1.10131 q^{55} +4.18692 q^{56} +4.21417 q^{57} +10.3956 q^{58} +4.24568 q^{59} -0.815576 q^{60} +7.24107 q^{61} +22.9406 q^{62} +0.0682781 q^{63} -12.2254 q^{64} +0.175994 q^{65} +23.3686 q^{66} -11.5105 q^{67} -6.32543 q^{68} -14.0279 q^{69} -1.07356 q^{70} -2.37904 q^{71} +0.0360044 q^{72} -0.649719 q^{73} -19.7575 q^{74} -8.57178 q^{75} +6.56267 q^{76} +17.6329 q^{77} +3.73438 q^{78} -7.06044 q^{79} +0.379463 q^{80} -8.92672 q^{81} -12.9735 q^{82} +2.72549 q^{83} -13.0580 q^{84} +0.414400 q^{85} +18.8433 q^{86} -8.28379 q^{87} +9.29818 q^{88} +2.65796 q^{89} -0.00923182 q^{90} +2.81780 q^{91} -21.8455 q^{92} -18.2804 q^{93} -14.2468 q^{94} -0.429942 q^{95} +13.1782 q^{96} +1.87141 q^{97} -2.03489 q^{98} +0.151630 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 123 q + 10 q^{2} + q^{3} + 136 q^{4} + 46 q^{5} + 16 q^{6} + 12 q^{7} + 30 q^{8} + 154 q^{9}+O(q^{10}) \) 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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