LMFDB - Embedded newform 6033.2.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6033,2,Mod(1,6033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6033, 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("6033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6033 = 3 \cdot 2011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6033.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:	$48.1737475394$
Analytic rank:	$1$
Dimension:	$84$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	6033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.82117 q^{2} -1.00000 q^{3} +5.95898 q^{4} -2.46990 q^{5} +2.82117 q^{6} +0.575292 q^{7} -11.1689 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.82117 q^{2} -1.00000 q^{3} +5.95898 q^{4} -2.46990 q^{5} +2.82117 q^{6} +0.575292 q^{7} -11.1689 q^{8} +1.00000 q^{9} +6.96801 q^{10} +2.39367 q^{11} -5.95898 q^{12} +1.09645 q^{13} -1.62299 q^{14} +2.46990 q^{15} +19.5915 q^{16} +4.80807 q^{17} -2.82117 q^{18} +7.61959 q^{19} -14.7181 q^{20} -0.575292 q^{21} -6.75293 q^{22} +2.74159 q^{23} +11.1689 q^{24} +1.10043 q^{25} -3.09328 q^{26} -1.00000 q^{27} +3.42816 q^{28} -10.1232 q^{29} -6.96801 q^{30} +5.86378 q^{31} -32.9330 q^{32} -2.39367 q^{33} -13.5644 q^{34} -1.42092 q^{35} +5.95898 q^{36} -6.47587 q^{37} -21.4961 q^{38} -1.09645 q^{39} +27.5862 q^{40} -4.56908 q^{41} +1.62299 q^{42} -7.41198 q^{43} +14.2638 q^{44} -2.46990 q^{45} -7.73450 q^{46} -11.6577 q^{47} -19.5915 q^{48} -6.66904 q^{49} -3.10450 q^{50} -4.80807 q^{51} +6.53375 q^{52} +4.21799 q^{53} +2.82117 q^{54} -5.91213 q^{55} -6.42541 q^{56} -7.61959 q^{57} +28.5593 q^{58} +12.7131 q^{59} +14.7181 q^{60} -9.72353 q^{61} -16.5427 q^{62} +0.575292 q^{63} +53.7265 q^{64} -2.70814 q^{65} +6.75293 q^{66} +0.423568 q^{67} +28.6512 q^{68} -2.74159 q^{69} +4.00864 q^{70} -3.16764 q^{71} -11.1689 q^{72} -9.73683 q^{73} +18.2695 q^{74} -1.10043 q^{75} +45.4050 q^{76} +1.37706 q^{77} +3.09328 q^{78} +11.1560 q^{79} -48.3891 q^{80} +1.00000 q^{81} +12.8901 q^{82} -3.77878 q^{83} -3.42816 q^{84} -11.8755 q^{85} +20.9104 q^{86} +10.1232 q^{87} -26.7347 q^{88} +6.63225 q^{89} +6.96801 q^{90} +0.630782 q^{91} +16.3371 q^{92} -5.86378 q^{93} +32.8883 q^{94} -18.8197 q^{95} +32.9330 q^{96} -5.97894 q^{97} +18.8145 q^{98} +2.39367 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 13 q^{2} - 84 q^{3} + 81 q^{4} - 10 q^{5} + 13 q^{6} - 32 q^{7} - 39 q^{8} + 84 q^{9}+O(q^{10}) $ 84 * q - 13 * q^2 - 84 * q^3 + 81 * q^4 - 10 * q^5 + 13 * q^6 - 32 * q^7 - 39 * q^8 + 84 * q^9	\( 84 q - 13 q^{2} - 84 q^{3} + 81 q^{4} - 10 q^{5} + 13 q^{6} - 32 q^{7} - 39 q^{8} + 84 q^{9} + 13 q^{10} - 20 q^{11} - 81 q^{12} + 7 q^{13} - 9 q^{14} + 10 q^{15} + 83 q^{16} - 39 q^{17} - 13 q^{18} + 13 q^{19} - 26 q^{20} + 32 q^{21} - 21 q^{22} - 93 q^{23} + 39 q^{24} + 66 q^{25} - 34 q^{26} - 84 q^{27} - 59 q^{28} - 39 q^{29} - 13 q^{30} + 8 q^{31} - 96 q^{32} + 20 q^{33} - 69 q^{35} + 81 q^{36} + 6 q^{37} - 59 q^{38} - 7 q^{39} + 28 q^{40} - 23 q^{41} + 9 q^{42} - 74 q^{43} - 43 q^{44} - 10 q^{45} - 6 q^{46} - 77 q^{47} - 83 q^{48} + 100 q^{49} - 74 q^{50} + 39 q^{51} - 44 q^{52} - 66 q^{53} + 13 q^{54} - 60 q^{55} - 31 q^{56} - 13 q^{57} - 39 q^{58} - 36 q^{59} + 26 q^{60} + 104 q^{61} - 53 q^{62} - 32 q^{63} + 85 q^{64} - 47 q^{65} + 21 q^{66} - 65 q^{67} - 118 q^{68} + 93 q^{69} - 3 q^{70} - 68 q^{71} - 39 q^{72} + 8 q^{73} - 30 q^{74} - 66 q^{75} + 71 q^{76} - 83 q^{77} + 34 q^{78} - 24 q^{79} - 67 q^{80} + 84 q^{81} - 9 q^{82} - 95 q^{83} + 59 q^{84} + 24 q^{85} - 32 q^{86} + 39 q^{87} - 65 q^{88} - 44 q^{89} + 13 q^{90} + 8 q^{91} - 184 q^{92} - 8 q^{93} + 61 q^{94} - 153 q^{95} + 96 q^{96} + 19 q^{97} - 67 q^{98} - 20 q^{99}+O(q^{100}) \) 84 * q - 13 * q^2 - 84 * q^3 + 81 * q^4 - 10 * q^5 + 13 * q^6 - 32 * q^7 - 39 * q^8 + 84 * q^9 + 13 * q^10 - 20 * q^11 - 81 * q^12 + 7 * q^13 - 9 * q^14 + 10 * q^15 + 83 * q^16 - 39 * q^17 - 13 * q^18 + 13 * q^19 - 26 * q^20 + 32 * q^21 - 21 * q^22 - 93 * q^23 + 39 * q^24 + 66 * q^25 - 34 * q^26 - 84 * q^27 - 59 * q^28 - 39 * q^29 - 13 * q^30 + 8 * q^31 - 96 * q^32 + 20 * q^33 - 69 * q^35 + 81 * q^36 + 6 * q^37 - 59 * q^38 - 7 * q^39 + 28 * q^40 - 23 * q^41 + 9 * q^42 - 74 * q^43 - 43 * q^44 - 10 * q^45 - 6 * q^46 - 77 * q^47 - 83 * q^48 + 100 * q^49 - 74 * q^50 + 39 * q^51 - 44 * q^52 - 66 * q^53 + 13 * q^54 - 60 * q^55 - 31 * q^56 - 13 * q^57 - 39 * q^58 - 36 * q^59 + 26 * q^60 + 104 * q^61 - 53 * q^62 - 32 * q^63 + 85 * q^64 - 47 * q^65 + 21 * q^66 - 65 * q^67 - 118 * q^68 + 93 * q^69 - 3 * q^70 - 68 * q^71 - 39 * q^72 + 8 * q^73 - 30 * q^74 - 66 * q^75 + 71 * q^76 - 83 * q^77 + 34 * q^78 - 24 * q^79 - 67 * q^80 + 84 * q^81 - 9 * q^82 - 95 * q^83 + 59 * q^84 + 24 * q^85 - 32 * q^86 + 39 * q^87 - 65 * q^88 - 44 * q^89 + 13 * q^90 + 8 * q^91 - 184 * q^92 - 8 * q^93 + 61 * q^94 - 153 * q^95 + 96 * q^96 + 19 * q^97 - 67 * q^98 - 20 * 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 $

$2$	−2.82117	−1.99487	−0.997433	−	0.0716049i	$-0.977188\pi$
$2$	−2.82117	−1.99487	−0.997433	+	0.0716049i	$0.977188\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	5.95898	2.97949
$5$	−2.46990	−1.10458	−0.552288	−	0.833654i	$-0.686245\pi$
$5$	−2.46990	−1.10458	−0.552288	+	0.833654i	$0.686245\pi$
$6$	2.82117	1.15174
$7$	0.575292	0.217440	0.108720	−	0.994072i	$-0.465325\pi$
$7$	0.575292	0.217440	0.108720	+	0.994072i	$0.465325\pi$
$8$	−11.1689	−3.94882
$9$	1.00000	0.333333
$10$	6.96801	2.20348
$11$	2.39367	0.721718	0.360859	−	0.932620i	$-0.382484\pi$
$11$	2.39367	0.721718	0.360859	+	0.932620i	$0.382484\pi$
$12$	−5.95898	−1.72021
$13$	1.09645	0.304102	0.152051	−	0.988373i	$-0.451412\pi$
$13$	1.09645	0.304102	0.152051	+	0.988373i	$0.451412\pi$
$14$	−1.62299	−0.433764
$15$	2.46990	0.637727
$16$	19.5915	4.89788
$17$	4.80807	1.16613	0.583064	−	0.812426i	$-0.301854\pi$
$17$	4.80807	1.16613	0.583064	+	0.812426i	$0.301854\pi$
$18$	−2.82117	−0.664955
$19$	7.61959	1.74805	0.874027	−	0.485877i	$-0.161500\pi$
$19$	7.61959	1.74805	0.874027	+	0.485877i	$0.161500\pi$
$20$	−14.7181	−3.29107
$21$	−0.575292	−0.125539
$22$	−6.75293	−1.43973
$23$	2.74159	0.571662	0.285831	−	0.958280i	$-0.407730\pi$
$23$	2.74159	0.571662	0.285831	+	0.958280i	$0.407730\pi$
$24$	11.1689	2.27985
$25$	1.10043	0.220086
$26$	−3.09328	−0.606642
$27$	−1.00000	−0.192450
$28$	3.42816	0.647860
$29$	−10.1232	−1.87983	−0.939917	−	0.341402i	$-0.889098\pi$
$29$	−10.1232	−1.87983	−0.939917	+	0.341402i	$0.889098\pi$
$30$	−6.96801	−1.27218
$31$	5.86378	1.05317	0.526583	−	0.850124i	$-0.323473\pi$
$31$	5.86378	1.05317	0.526583	+	0.850124i	$0.323473\pi$
$32$	−32.9330	−5.82179
$33$	−2.39367	−0.416684
$34$	−13.5644	−2.32627
$35$	−1.42092	−0.240179
$36$	5.95898	0.993164
$37$	−6.47587	−1.06463	−0.532313	−	0.846548i	$-0.678677\pi$
$37$	−6.47587	−1.06463	−0.532313	+	0.846548i	$0.678677\pi$
$38$	−21.4961	−3.48713
$39$	−1.09645	−0.175573
$40$	27.5862	4.36177
$41$	−4.56908	−0.713570	−0.356785	−	0.934187i	$-0.616127\pi$
$41$	−4.56908	−0.713570	−0.356785	+	0.934187i	$0.616127\pi$
$42$	1.62299	0.250434
$43$	−7.41198	−1.13032	−0.565158	−	0.824983i	$-0.691185\pi$
$43$	−7.41198	−1.13032	−0.565158	+	0.824983i	$0.691185\pi$
$44$	14.2638	2.15035
$45$	−2.46990	−0.368192
$46$	−7.73450	−1.14039
$47$	−11.6577	−1.70045	−0.850226	−	0.526418i	$-0.823535\pi$
$47$	−11.6577	−1.70045	−0.850226	+	0.526418i	$0.823535\pi$
$48$	−19.5915	−2.82779
$49$	−6.66904	−0.952720
$50$	−3.10450	−0.439042
$51$	−4.80807	−0.673264
$52$	6.53375	0.906068
$53$	4.21799	0.579386	0.289693	−	0.957120i	$-0.406447\pi$
$53$	4.21799	0.579386	0.289693	+	0.957120i	$0.406447\pi$
$54$	2.82117	0.383912
$55$	−5.91213	−0.797191
$56$	−6.42541	−0.858631
$57$	−7.61959	−1.00924
$58$	28.5593	3.75002
$59$	12.7131	1.65511	0.827555	−	0.561384i	$-0.189731\pi$
$59$	12.7131	1.65511	0.827555	+	0.561384i	$0.189731\pi$
$60$	14.7181	1.90010
$61$	−9.72353	−1.24497	−0.622486	−	0.782631i	$-0.713877\pi$
$61$	−9.72353	−1.24497	−0.622486	+	0.782631i	$0.713877\pi$
$62$	−16.5427	−2.10093
$63$	0.575292	0.0724800
$64$	53.7265	6.71581
$65$	−2.70814	−0.335903
$66$	6.75293	0.831228
$67$	0.423568	0.0517470	0.0258735	−	0.999665i	$-0.491763\pi$
$67$	0.423568	0.0517470	0.0258735	+	0.999665i	$0.491763\pi$
$68$	28.6512	3.47447
$69$	−2.74159	−0.330049
$70$	4.00864	0.479124
$71$	−3.16764	−0.375930	−0.187965	−	0.982176i	$-0.560189\pi$
$71$	−3.16764	−0.375930	−0.187965	+	0.982176i	$0.560189\pi$
$72$	−11.1689	−1.31627
$73$	−9.73683	−1.13961	−0.569805	−	0.821780i	$-0.692981\pi$
$73$	−9.73683	−1.13961	−0.569805	+	0.821780i	$0.692981\pi$
$74$	18.2695	2.12379
$75$	−1.10043	−0.127067
$76$	45.4050	5.20831
$77$	1.37706	0.156930
$78$	3.09328	0.350245
$79$	11.1560	1.25515	0.627576	−	0.778555i	$-0.284047\pi$
$79$	11.1560	1.25515	0.627576	+	0.778555i	$0.284047\pi$
$80$	−48.3891	−5.41007
$81$	1.00000	0.111111
$82$	12.8901	1.42348
$83$	−3.77878	−0.414775	−0.207387	−	0.978259i	$-0.566496\pi$
$83$	−3.77878	−0.414775	−0.207387	+	0.978259i	$0.566496\pi$
$84$	−3.42816	−0.374042
$85$	−11.8755	−1.28808
$86$	20.9104	2.25483
$87$	10.1232	1.08532
$88$	−26.7347	−2.84993
$89$	6.63225	0.703017	0.351509	−	0.936185i	$-0.385669\pi$
$89$	6.63225	0.703017	0.351509	+	0.936185i	$0.385669\pi$
$90$	6.96801	0.734493
$91$	0.630782	0.0661239
$92$	16.3371	1.70326
$93$	−5.86378	−0.608046
$94$	32.8883	3.39217
$95$	−18.8197	−1.93086
$96$	32.9330	3.36121
$97$	−5.97894	−0.607069	−0.303534	−	0.952820i	$-0.598167\pi$
$97$	−5.97894	−0.607069	−0.303534	+	0.952820i	$0.598167\pi$
$98$	18.8145	1.90055
$99$	2.39367	0.240573
$100$	6.55744	0.655744
$101$	−11.8409	−1.17821	−0.589104	−	0.808057i	$-0.700519\pi$
$101$	−11.8409	−1.17821	−0.589104	+	0.808057i	$0.700519\pi$
$102$	13.5644	1.34307
$103$	2.80291	0.276179	0.138090	−	0.990420i	$-0.455904\pi$
$103$	2.80291	0.276179	0.138090	+	0.990420i	$0.455904\pi$
$104$	−12.2462	−1.20084
$105$	1.42092	0.138667
$106$	−11.8997	−1.15580
$107$	14.7664	1.42752	0.713761	−	0.700390i	$-0.246990\pi$
$107$	14.7664	1.42752	0.713761	+	0.700390i	$0.246990\pi$
$108$	−5.95898	−0.573403
$109$	−1.28680	−0.123253	−0.0616267	−	0.998099i	$-0.519629\pi$
$109$	−1.28680	−0.123253	−0.0616267	+	0.998099i	$0.519629\pi$
$110$	16.6791	1.59029
$111$	6.47587	0.614662
$112$	11.2708	1.06499
$113$	−4.77469	−0.449165	−0.224582	−	0.974455i	$-0.572102\pi$
$113$	−4.77469	−0.449165	−0.224582	+	0.974455i	$0.572102\pi$
$114$	21.4961	2.01330
$115$	−6.77148	−0.631444
$116$	−60.3241	−5.60095
$117$	1.09645	0.101367
$118$	−35.8659	−3.30172
$119$	2.76604	0.253563
$120$	−27.5862	−2.51827
$121$	−5.27036	−0.479124
$122$	27.4317	2.48355
$123$	4.56908	0.411980
$124$	34.9422	3.13790
$125$	9.63157	0.861474
$126$	−1.62299	−0.144588
$127$	−12.2358	−1.08575	−0.542875	−	0.839814i	$-0.682664\pi$
$127$	−12.2358	−1.08575	−0.542875	+	0.839814i	$0.682664\pi$
$128$	−85.7054	−7.57535
$129$	7.41198	0.652588
$130$	7.64011	0.670082
$131$	17.4874	1.52788	0.763941	−	0.645286i	$-0.223262\pi$
$131$	17.4874	1.52788	0.763941	+	0.645286i	$0.223262\pi$
$132$	−14.2638	−1.24151
$133$	4.38349	0.380097
$134$	−1.19496	−0.103228
$135$	2.46990	0.212576
$136$	−53.7011	−4.60483
$137$	19.3099	1.64976	0.824878	−	0.565311i	$-0.191244\pi$
$137$	19.3099	1.64976	0.824878	+	0.565311i	$0.191244\pi$
$138$	7.73450	0.658404
$139$	4.48410	0.380336	0.190168	−	0.981752i	$-0.439097\pi$
$139$	4.48410	0.380336	0.190168	+	0.981752i	$0.439097\pi$
$140$	−8.46722	−0.715610
$141$	11.6577	0.981756
$142$	8.93644	0.749930
$143$	2.62455	0.219476
$144$	19.5915	1.63263
$145$	25.0034	2.07642
$146$	27.4692	2.27337
$147$	6.66904	0.550053
$148$	−38.5896	−3.17204
$149$	−19.2968	−1.58085	−0.790427	−	0.612556i	$-0.790141\pi$
$149$	−19.2968	−1.58085	−0.790427	+	0.612556i	$0.790141\pi$
$150$	3.10450	0.253481
$151$	6.08328	0.495050	0.247525	−	0.968882i	$-0.420383\pi$
$151$	6.08328	0.495050	0.247525	+	0.968882i	$0.420383\pi$
$152$	−85.1028	−6.90275
$153$	4.80807	0.388709
$154$	−3.88491	−0.313055
$155$	−14.4830	−1.16330
$156$	−6.53375	−0.523119
$157$	−6.07279	−0.484661	−0.242331	−	0.970194i	$-0.577912\pi$
$157$	−6.07279	−0.484661	−0.242331	+	0.970194i	$0.577912\pi$
$158$	−31.4730	−2.50386
$159$	−4.21799	−0.334509
$160$	81.3414	6.43060
$161$	1.57722	0.124302
$162$	−2.82117	−0.221652
$163$	14.6361	1.14639	0.573196	−	0.819419i	$-0.305704\pi$
$163$	14.6361	1.14639	0.573196	+	0.819419i	$0.305704\pi$
$164$	−27.2270	−2.12608
$165$	5.91213	0.460259
$166$	10.6606	0.827420
$167$	−18.5643	−1.43655	−0.718273	−	0.695762i	$-0.755067\pi$
$167$	−18.5643	−1.43655	−0.718273	+	0.695762i	$0.755067\pi$
$168$	6.42541	0.495731
$169$	−11.7978	−0.907522
$170$	33.5027	2.56954
$171$	7.61959	0.582685
$172$	−44.1679	−3.36777
$173$	3.93428	0.299118	0.149559	−	0.988753i	$-0.452215\pi$
$173$	3.93428	0.299118	0.149559	+	0.988753i	$0.452215\pi$
$174$	−28.5593	−2.16507
$175$	0.633069	0.0478555
$176$	46.8955	3.53488
$177$	−12.7131	−0.955579
$178$	−18.7107	−1.40242
$179$	9.02845	0.674818	0.337409	−	0.941358i	$-0.390449\pi$
$179$	9.02845	0.674818	0.337409	+	0.941358i	$0.390449\pi$
$180$	−14.7181	−1.09702
$181$	−11.1921	−0.831902	−0.415951	−	0.909387i	$-0.636551\pi$
$181$	−11.1921	−0.831902	−0.415951	+	0.909387i	$0.636551\pi$
$182$	−1.77954	−0.131908
$183$	9.72353	0.718784
$184$	−30.6207	−2.25739
$185$	15.9948	1.17596
$186$	16.5427	1.21297
$187$	11.5089	0.841615
$188$	−69.4681	−5.06648
$189$	−0.575292	−0.0418463
$190$	53.0934	3.85180
$191$	−11.6060	−0.839778	−0.419889	−	0.907575i	$-0.637931\pi$
$191$	−11.6060	−0.839778	−0.419889	+	0.907575i	$0.637931\pi$
$192$	−53.7265	−3.87737
$193$	21.4336	1.54282	0.771412	−	0.636336i	$-0.219551\pi$
$193$	21.4336	1.54282	0.771412	+	0.636336i	$0.219551\pi$
$194$	16.8676	1.21102
$195$	2.70814	0.193934
$196$	−39.7407	−2.83862
$197$	−11.5515	−0.823007	−0.411503	−	0.911408i	$-0.634996\pi$
$197$	−11.5515	−0.823007	−0.411503	+	0.911408i	$0.634996\pi$
$198$	−6.75293	−0.479910
$199$	−7.57160	−0.536736	−0.268368	−	0.963316i	$-0.586484\pi$
$199$	−7.57160	−0.536736	−0.268368	+	0.963316i	$0.586484\pi$
$200$	−12.2906	−0.869080
$201$	−0.423568	−0.0298762
$202$	33.4050	2.35037
$203$	−5.82381	−0.408751
$204$	−28.6512	−2.00598
$205$	11.2852	0.788192
$206$	−7.90749	−0.550941
$207$	2.74159	0.190554
$208$	21.4812	1.48945
$209$	18.2388	1.26160
$210$	−4.00864	−0.276623
$211$	20.6740	1.42326	0.711629	−	0.702556i	$-0.247958\pi$
$211$	20.6740	1.42326	0.711629	+	0.702556i	$0.247958\pi$
$212$	25.1349	1.72627
$213$	3.16764	0.217043
$214$	−41.6585	−2.84771
$215$	18.3069	1.24852
$216$	11.1689	0.759951
$217$	3.37339	0.229000
$218$	3.63029	0.245874
$219$	9.73683	0.657954
$220$	−35.2303	−2.37522
$221$	5.27183	0.354621
$222$	−18.2695	−1.22617
$223$	−15.2460	−1.02095	−0.510473	−	0.859894i	$-0.670530\pi$
$223$	−15.2460	−1.02095	−0.510473	+	0.859894i	$0.670530\pi$
$224$	−18.9461	−1.26589
$225$	1.10043	0.0733620
$226$	13.4702	0.896023
$227$	11.4597	0.760605	0.380303	−	0.924862i	$-0.375820\pi$
$227$	11.4597	0.760605	0.380303	+	0.924862i	$0.375820\pi$
$228$	−45.4050	−3.00702
$229$	9.93394	0.656453	0.328227	−	0.944599i	$-0.393549\pi$
$229$	9.93394	0.656453	0.328227	+	0.944599i	$0.393549\pi$
$230$	19.1035	1.25965
$231$	−1.37706	−0.0906037
$232$	113.066	7.42313
$233$	−16.8832	−1.10605	−0.553027	−	0.833163i	$-0.686527\pi$
$233$	−16.8832	−1.10605	−0.553027	+	0.833163i	$0.686527\pi$
$234$	−3.09328	−0.202214
$235$	28.7934	1.87828
$236$	75.7574	4.93139
$237$	−11.1560	−0.724663
$238$	−7.80347	−0.505824
$239$	−3.86602	−0.250072	−0.125036	−	0.992152i	$-0.539905\pi$
$239$	−3.86602	−0.250072	−0.125036	+	0.992152i	$0.539905\pi$
$240$	48.3891	3.12351
$241$	−25.2277	−1.62506	−0.812529	−	0.582921i	$-0.801910\pi$
$241$	−25.2277	−1.62506	−0.812529	+	0.582921i	$0.801910\pi$
$242$	14.8686	0.955788
$243$	−1.00000	−0.0641500
$244$	−57.9424	−3.70938
$245$	16.4719	1.05235
$246$	−12.8901	−0.821845
$247$	8.35454	0.531586
$248$	−65.4923	−4.15876
$249$	3.77878	0.239470
$250$	−27.1723	−1.71852
$251$	−20.8672	−1.31712	−0.658562	−	0.752526i	$-0.728835\pi$
$251$	−20.8672	−1.31712	−0.658562	+	0.752526i	$0.728835\pi$
$252$	3.42816	0.215953
$253$	6.56246	0.412579
$254$	34.5192	2.16593
$255$	11.8755	0.743671
$256$	134.336	8.39601
$257$	−28.4501	−1.77467	−0.887333	−	0.461129i	$-0.847445\pi$
$257$	−28.4501	−1.77467	−0.887333	+	0.461129i	$0.847445\pi$
$258$	−20.9104	−1.30183
$259$	−3.72551	−0.231492
$260$	−16.1377	−1.00082
$261$	−10.1232	−0.626612
$262$	−49.3349	−3.04792
$263$	−3.17681	−0.195890	−0.0979451	−	0.995192i	$-0.531227\pi$
$263$	−3.17681	−0.195890	−0.0979451	+	0.995192i	$0.531227\pi$
$264$	26.7347	1.64541
$265$	−10.4180	−0.639975
$266$	−12.3666	−0.758242
$267$	−6.63225	−0.405887
$268$	2.52403	0.154180
$269$	−10.5839	−0.645311	−0.322655	−	0.946517i	$-0.604575\pi$
$269$	−10.5839	−0.645311	−0.322655	+	0.946517i	$0.604575\pi$
$270$	−6.96801	−0.424060
$271$	3.59111	0.218144	0.109072	−	0.994034i	$-0.465212\pi$
$271$	3.59111	0.218144	0.109072	+	0.994034i	$0.465212\pi$
$272$	94.1973	5.71155
$273$	−0.630782	−0.0381766
$274$	−54.4764	−3.29104
$275$	2.63406	0.158840
$276$	−16.3371	−0.983379
$277$	−16.0385	−0.963658	−0.481829	−	0.876265i	$-0.660027\pi$
$277$	−16.0385	−0.963658	−0.481829	+	0.876265i	$0.660027\pi$
$278$	−12.6504	−0.758720
$279$	5.86378	0.351055
$280$	15.8701	0.948423
$281$	33.0786	1.97331	0.986653	−	0.162839i	$-0.0520652\pi$
$281$	33.0786	1.97331	0.986653	+	0.162839i	$0.0520652\pi$
$282$	−32.8883	−1.95847
$283$	−16.3363	−0.971090	−0.485545	−	0.874212i	$-0.661379\pi$
$283$	−16.3363	−0.971090	−0.485545	+	0.874212i	$0.661379\pi$
$284$	−18.8759	−1.12008
$285$	18.8197	1.11478
$286$	−7.40428	−0.437824
$287$	−2.62855	−0.155159
$288$	−32.9330	−1.94060
$289$	6.11751	0.359853
$290$	−70.5387	−4.14218
$291$	5.97894	0.350491
$292$	−58.0216	−3.39546
$293$	−11.4112	−0.666648	−0.333324	−	0.942812i	$-0.608170\pi$
$293$	−11.4112	−0.666648	−0.333324	+	0.942812i	$0.608170\pi$
$294$	−18.8145	−1.09728
$295$	−31.4003	−1.82819
$296$	72.3286	4.20401
$297$	−2.39367	−0.138895
$298$	54.4395	3.15359
$299$	3.00603	0.173843
$300$	−6.55744	−0.378594
$301$	−4.26405	−0.245776
$302$	−17.1619	−0.987559
$303$	11.8409	0.680239
$304$	149.279	8.56175
$305$	24.0162	1.37516
$306$	−13.5644	−0.775423
$307$	0.513818	0.0293251	0.0146626	−	0.999892i	$-0.495333\pi$
$307$	0.513818	0.0293251	0.0146626	+	0.999892i	$0.495333\pi$
$308$	8.20586	0.467572
$309$	−2.80291	−0.159452
$310$	40.8589	2.32063
$311$	12.1082	0.686595	0.343298	−	0.939227i	$-0.388456\pi$
$311$	12.1082	0.686595	0.343298	+	0.939227i	$0.388456\pi$
$312$	12.2462	0.693307
$313$	16.4181	0.928005	0.464003	−	0.885834i	$-0.346413\pi$
$313$	16.4181	0.928005	0.464003	+	0.885834i	$0.346413\pi$
$314$	17.1323	0.966834
$315$	−1.42092	−0.0800596
$316$	66.4786	3.73971
$317$	0.995569	0.0559167	0.0279584	−	0.999609i	$-0.491099\pi$
$317$	0.995569	0.0559167	0.0279584	+	0.999609i	$0.491099\pi$
$318$	11.8997	0.667300
$319$	−24.2316	−1.35671
$320$	−132.699	−7.41812
$321$	−14.7664	−0.824180
$322$	−4.44959	−0.247966
$323$	36.6355	2.03845
$324$	5.95898	0.331055
$325$	1.20657	0.0669285
$326$	−41.2910	−2.28690
$327$	1.28680	0.0711604
$328$	51.0318	2.81776
$329$	−6.70659	−0.369746
$330$	−16.6791	−0.918154
$331$	3.01857	0.165916	0.0829579	−	0.996553i	$-0.473563\pi$
$331$	3.01857	0.165916	0.0829579	+	0.996553i	$0.473563\pi$
$332$	−22.5177	−1.23582
$333$	−6.47587	−0.354875
$334$	52.3729	2.86572
$335$	−1.04617	−0.0571585
$336$	−11.2708	−0.614875
$337$	21.8470	1.19008	0.595040	−	0.803696i	$-0.297136\pi$
$337$	21.8470	1.19008	0.595040	+	0.803696i	$0.297136\pi$
$338$	33.2835	1.81039
$339$	4.77469	0.259325
$340$	−70.7657	−3.83781
$341$	14.0359	0.760088
$342$	−21.4961	−1.16238
$343$	−7.86369	−0.424599
$344$	82.7840	4.46342
$345$	6.77148	0.364564
$346$	−11.0993	−0.596699
$347$	−31.2927	−1.67988	−0.839940	−	0.542680i	$-0.817410\pi$
$347$	−31.2927	−1.67988	−0.839940	+	0.542680i	$0.817410\pi$
$348$	60.3241	3.23371
$349$	−15.1015	−0.808363	−0.404181	−	0.914679i	$-0.632444\pi$
$349$	−15.1015	−0.808363	−0.404181	+	0.914679i	$0.632444\pi$
$350$	−1.78599	−0.0954653
$351$	−1.09645	−0.0585244
$352$	−78.8306	−4.20169
$353$	−16.5401	−0.880338	−0.440169	−	0.897915i	$-0.645082\pi$
$353$	−16.5401	−0.880338	−0.440169	+	0.897915i	$0.645082\pi$
$354$	35.8659	1.90625
$355$	7.82377	0.415243
$356$	39.5215	2.09463
$357$	−2.76604	−0.146395
$358$	−25.4708	−1.34617
$359$	19.5452	1.03155	0.515777	−	0.856723i	$-0.327503\pi$
$359$	19.5452	1.03155	0.515777	+	0.856723i	$0.327503\pi$
$360$	27.5862	1.45392
$361$	39.0582	2.05569
$362$	31.5748	1.65953
$363$	5.27036	0.276622
$364$	3.75882	0.197015
$365$	24.0491	1.25879
$366$	−27.4317	−1.43388
$367$	7.46562	0.389702	0.194851	−	0.980833i	$-0.437578\pi$
$367$	7.46562	0.389702	0.194851	+	0.980833i	$0.437578\pi$
$368$	53.7120	2.79993
$369$	−4.56908	−0.237857
$370$	−45.1239	−2.34588
$371$	2.42658	0.125982
$372$	−34.9422	−1.81167
$373$	23.9994	1.24264	0.621322	−	0.783556i	$-0.286596\pi$
$373$	23.9994	1.24264	0.621322	+	0.783556i	$0.286596\pi$
$374$	−32.4686	−1.67891
$375$	−9.63157	−0.497372
$376$	130.204	6.71478
$377$	−11.0997	−0.571661
$378$	1.62299	0.0834779
$379$	2.30114	0.118202	0.0591009	−	0.998252i	$-0.481177\pi$
$379$	2.30114	0.118202	0.0591009	+	0.998252i	$0.481177\pi$
$380$	−112.146	−5.75297
$381$	12.2358	0.626858
$382$	32.7424	1.67524
$383$	7.91730	0.404555	0.202278	−	0.979328i	$-0.435166\pi$
$383$	7.91730	0.404555	0.202278	+	0.979328i	$0.435166\pi$
$384$	85.7054	4.37363
$385$	−3.40120	−0.173341
$386$	−60.4677	−3.07773
$387$	−7.41198	−0.376772
$388$	−35.6284	−1.80876
$389$	30.6759	1.55533	0.777664	−	0.628680i	$-0.216404\pi$
$389$	30.6759	1.55533	0.777664	+	0.628680i	$0.216404\pi$
$390$	−7.64011	−0.386872
$391$	13.1818	0.666631
$392$	74.4862	3.76212
$393$	−17.4874	−0.882124
$394$	32.5886	1.64179
$395$	−27.5544	−1.38641
$396$	14.2638	0.716784
$397$	23.1335	1.16104	0.580519	−	0.814247i	$-0.302850\pi$
$397$	23.1335	1.16104	0.580519	+	0.814247i	$0.302850\pi$
$398$	21.3607	1.07072
$399$	−4.38349	−0.219449
$400$	21.5591	1.07795
$401$	−0.902443	−0.0450658	−0.0225329	−	0.999746i	$-0.507173\pi$
$401$	−0.902443	−0.0450658	−0.0225329	+	0.999746i	$0.507173\pi$
$402$	1.19496	0.0595990
$403$	6.42937	0.320270
$404$	−70.5594	−3.51046
$405$	−2.46990	−0.122731
$406$	16.4299	0.815404
$407$	−15.5011	−0.768359
$408$	53.7011	2.65860
$409$	−13.4577	−0.665438	−0.332719	−	0.943026i	$-0.607966\pi$
$409$	−13.4577	−0.665438	−0.332719	+	0.943026i	$0.607966\pi$
$410$	−31.8374	−1.57234
$411$	−19.3099	−0.952487
$412$	16.7025	0.822874
$413$	7.31377	0.359887
$414$	−7.73450	−0.380130
$415$	9.33322	0.458150
$416$	−36.1095	−1.77042
$417$	−4.48410	−0.219587
$418$	−51.4546	−2.51673
$419$	−25.8410	−1.26242	−0.631208	−	0.775614i	$-0.717440\pi$
$419$	−25.8410	−1.26242	−0.631208	+	0.775614i	$0.717440\pi$
$420$	8.46722	0.413158
$421$	17.8350	0.869225	0.434612	−	0.900618i	$-0.356885\pi$
$421$	17.8350	0.869225	0.434612	+	0.900618i	$0.356885\pi$
$422$	−58.3248	−2.83921
$423$	−11.6577	−0.566817
$424$	−47.1105	−2.28789
$425$	5.29094	0.256648
$426$	−8.93644	−0.432972
$427$	−5.59387	−0.270706
$428$	87.9927	4.25329
$429$	−2.62455	−0.126714
$430$	−51.6468	−2.49063
$431$	13.7434	0.661995	0.330998	−	0.943632i	$-0.392615\pi$
$431$	13.7434	0.661995	0.330998	+	0.943632i	$0.392615\pi$
$432$	−19.5915	−0.942597
$433$	−26.2380	−1.26092	−0.630458	−	0.776224i	$-0.717133\pi$
$433$	−26.2380	−1.26092	−0.630458	+	0.776224i	$0.717133\pi$
$434$	−9.51689	−0.456825
$435$	−25.0034	−1.19882
$436$	−7.66804	−0.367233
$437$	20.8898	0.999296
$438$	−27.4692	−1.31253
$439$	−39.1347	−1.86780	−0.933898	−	0.357540i	$-0.883616\pi$
$439$	−39.1347	−1.86780	−0.933898	+	0.357540i	$0.883616\pi$
$440$	66.0323	3.14796
$441$	−6.66904	−0.317573
$442$	−14.8727	−0.707422
$443$	−19.1519	−0.909935	−0.454967	−	0.890508i	$-0.650349\pi$
$443$	−19.1519	−0.909935	−0.454967	+	0.890508i	$0.650349\pi$
$444$	38.5896	1.83138
$445$	−16.3810	−0.776535
$446$	43.0115	2.03665
$447$	19.2968	0.912707
$448$	30.9084	1.46029
$449$	−30.0908	−1.42007	−0.710037	−	0.704164i	$-0.751322\pi$
$449$	−30.0908	−1.42007	−0.710037	+	0.704164i	$0.751322\pi$
$450$	−3.10450	−0.146347
$451$	−10.9368	−0.514996
$452$	−28.4523	−1.33828
$453$	−6.08328	−0.285817
$454$	−32.3297	−1.51731
$455$	−1.55797	−0.0730388
$456$	85.1028	3.98531
$457$	−21.9239	−1.02556	−0.512779	−	0.858521i	$-0.671384\pi$
$457$	−21.9239	−1.02556	−0.512779	+	0.858521i	$0.671384\pi$
$458$	−28.0253	−1.30954
$459$	−4.80807	−0.224421
$460$	−40.3511	−1.88138
$461$	−8.80930	−0.410290	−0.205145	−	0.978732i	$-0.565767\pi$
$461$	−8.80930	−0.410290	−0.205145	+	0.978732i	$0.565767\pi$
$462$	3.88491	0.180742
$463$	−29.4010	−1.36638	−0.683191	−	0.730240i	$-0.739408\pi$
$463$	−29.4010	−1.36638	−0.683191	+	0.730240i	$0.739408\pi$
$464$	−198.329	−9.20720
$465$	14.4830	0.671632
$466$	47.6303	2.20643
$467$	19.0843	0.883118	0.441559	−	0.897232i	$-0.354426\pi$
$467$	19.0843	0.883118	0.441559	+	0.897232i	$0.354426\pi$
$468$	6.53375	0.302023
$469$	0.243675	0.0112519
$470$	−81.2311	−3.74691
$471$	6.07279	0.279819
$472$	−141.992	−6.53573
$473$	−17.7418	−0.815769
$474$	31.4730	1.44560
$475$	8.38483	0.384722
$476$	16.4828	0.755488
$477$	4.21799	0.193129
$478$	10.9067	0.498860
$479$	20.1261	0.919584	0.459792	−	0.888027i	$-0.347924\pi$
$479$	20.1261	0.919584	0.459792	+	0.888027i	$0.347924\pi$
$480$	−81.3414	−3.71271
$481$	−7.10049	−0.323755
$482$	71.1715	3.24177
$483$	−1.57722	−0.0717659
$484$	−31.4060	−1.42754
$485$	14.7674	0.670553
$486$	2.82117	0.127971
$487$	11.1327	0.504469	0.252235	−	0.967666i	$-0.418835\pi$
$487$	11.1327	0.504469	0.252235	+	0.967666i	$0.418835\pi$
$488$	108.602	4.91617
$489$	−14.6361	−0.661869
$490$	−46.4700	−2.09930
$491$	25.7024	1.15993	0.579966	−	0.814640i	$-0.303066\pi$
$491$	25.7024	1.15993	0.579966	+	0.814640i	$0.303066\pi$
$492$	27.2270	1.22749
$493$	−48.6731	−2.19213
$494$	−23.5695	−1.06044
$495$	−5.91213	−0.265730
$496$	114.880	5.15828
$497$	−1.82232	−0.0817422
$498$	−10.6606	−0.477711
$499$	14.2822	0.639361	0.319680	−	0.947525i	$-0.396424\pi$
$499$	14.2822	0.639361	0.319680	+	0.947525i	$0.396424\pi$
$500$	57.3943	2.56675
$501$	18.5643	0.829390
$502$	58.8698	2.62749
$503$	35.1783	1.56852	0.784262	−	0.620430i	$-0.213042\pi$
$503$	35.1783	1.56852	0.784262	+	0.620430i	$0.213042\pi$
$504$	−6.42541	−0.286210
$505$	29.2458	1.30142
$506$	−18.5138	−0.823039
$507$	11.7978	0.523958
$508$	−72.9128	−3.23498
$509$	−8.64514	−0.383189	−0.191594	−	0.981474i	$-0.561366\pi$
$509$	−8.64514	−0.383189	−0.191594	+	0.981474i	$0.561366\pi$
$510$	−33.5027	−1.48352
$511$	−5.60152	−0.247797
$512$	−207.574	−9.17356
$513$	−7.61959	−0.336413
$514$	80.2624	3.54022
$515$	−6.92293	−0.305061
$516$	44.1679	1.94438
$517$	−27.9047	−1.22725
$518$	10.5103	0.461796
$519$	−3.93428	−0.172696
$520$	30.2471	1.32642
$521$	−28.9001	−1.26614	−0.633069	−	0.774095i	$-0.718205\pi$
$521$	−28.9001	−1.26614	−0.633069	+	0.774095i	$0.718205\pi$
$522$	28.5593	1.25001
$523$	3.16756	0.138508	0.0692538	−	0.997599i	$-0.477938\pi$
$523$	3.16756	0.138508	0.0692538	+	0.997599i	$0.477938\pi$
$524$	104.207	4.55231
$525$	−0.633069	−0.0276294
$526$	8.96230	0.390775
$527$	28.1934	1.22813
$528$	−46.8955	−2.04087
$529$	−15.4837	−0.673203
$530$	29.3910	1.27666
$531$	12.7131	0.551704
$532$	26.1211	1.13250
$533$	−5.00978	−0.216998
$534$	18.7107	0.809690
$535$	−36.4716	−1.57680
$536$	−4.73081	−0.204340
$537$	−9.02845	−0.389606
$538$	29.8589	1.28731
$539$	−15.9635	−0.687595
$540$	14.7181	0.633367
$541$	−45.7574	−1.96726	−0.983632	−	0.180187i	$-0.942330\pi$
$541$	−45.7574	−1.96726	−0.983632	+	0.180187i	$0.942330\pi$
$542$	−10.1311	−0.435169
$543$	11.1921	0.480299
$544$	−158.344	−6.78895
$545$	3.17828	0.136143
$546$	1.77954	0.0761573
$547$	−12.4461	−0.532157	−0.266079	−	0.963951i	$-0.585728\pi$
$547$	−12.4461	−0.532157	−0.266079	+	0.963951i	$0.585728\pi$
$548$	115.067	4.91543
$549$	−9.72353	−0.414990
$550$	−7.43113	−0.316864
$551$	−77.1348	−3.28605
$552$	30.6207	1.30330
$553$	6.41798	0.272920
$554$	45.2472	1.92237
$555$	−15.9948	−0.678940
$556$	26.7207	1.13321
$557$	9.57176	0.405568	0.202784	−	0.979223i	$-0.435001\pi$
$557$	9.57176	0.405568	0.202784	+	0.979223i	$0.435001\pi$
$558$	−16.5427	−0.700308
$559$	−8.12690	−0.343731
$560$	−27.8379	−1.17637
$561$	−11.5089	−0.485907
$562$	−93.3203	−3.93648
$563$	−5.09656	−0.214794	−0.107397	−	0.994216i	$-0.534252\pi$
$563$	−5.09656	−0.214794	−0.107397	+	0.994216i	$0.534252\pi$
$564$	69.4681	2.92513
$565$	11.7930	0.496136
$566$	46.0873	1.93719
$567$	0.575292	0.0241600
$568$	35.3792	1.48448
$569$	−24.4313	−1.02421	−0.512107	−	0.858922i	$-0.671135\pi$
$569$	−24.4313	−1.02421	−0.512107	+	0.858922i	$0.671135\pi$
$570$	−53.0934	−2.22384
$571$	−8.84719	−0.370243	−0.185122	−	0.982716i	$-0.559268\pi$
$571$	−8.84719	−0.370243	−0.185122	+	0.982716i	$0.559268\pi$
$572$	15.6396	0.653925
$573$	11.6060	0.484846
$574$	7.41559	0.309521
$575$	3.01693	0.125815
$576$	53.7265	2.23860
$577$	−0.584232	−0.0243219	−0.0121609	−	0.999926i	$-0.503871\pi$
$577$	−0.584232	−0.0243219	−0.0121609	+	0.999926i	$0.503871\pi$
$578$	−17.2585	−0.717859
$579$	−21.4336	−0.890750
$580$	148.995	6.18667
$581$	−2.17390	−0.0901886
$582$	−16.8676	−0.699183
$583$	10.0965	0.418153
$584$	108.750	4.50012
$585$	−2.70814	−0.111968
$586$	32.1928	1.32987
$587$	34.5348	1.42540	0.712702	−	0.701467i	$-0.247471\pi$
$587$	34.5348	1.42540	0.712702	+	0.701467i	$0.247471\pi$
$588$	39.7407	1.63888
$589$	44.6796	1.84099
$590$	88.5854	3.64700
$591$	11.5515	0.475163
$592$	−126.872	−5.21440
$593$	9.42860	0.387186	0.193593	−	0.981082i	$-0.437986\pi$
$593$	9.42860	0.387186	0.193593	+	0.981082i	$0.437986\pi$
$594$	6.75293	0.277076
$595$	−6.83186	−0.280079
$596$	−114.989	−4.71014
$597$	7.57160	0.309885
$598$	−8.48052	−0.346794
$599$	21.2847	0.869668	0.434834	−	0.900511i	$-0.356807\pi$
$599$	21.2847	0.869668	0.434834	+	0.900511i	$0.356807\pi$
$600$	12.2906	0.501763
$601$	−0.830807	−0.0338893	−0.0169447	−	0.999856i	$-0.505394\pi$
$601$	−0.830807	−0.0338893	−0.0169447	+	0.999856i	$0.505394\pi$
$602$	12.0296	0.490290
$603$	0.423568	0.0172490
$604$	36.2501	1.47500
$605$	13.0173	0.529228
$606$	−33.4050	−1.35699
$607$	5.20818	0.211393	0.105697	−	0.994398i	$-0.466293\pi$
$607$	5.20818	0.211393	0.105697	+	0.994398i	$0.466293\pi$
$608$	−250.936	−10.1768
$609$	5.82381	0.235993
$610$	−67.7537	−2.74327
$611$	−12.7821	−0.517110
$612$	28.6512	1.15816
$613$	−36.7346	−1.48370	−0.741849	−	0.670567i	$-0.766051\pi$
$613$	−36.7346	−1.48370	−0.741849	+	0.670567i	$0.766051\pi$
$614$	−1.44956	−0.0584997
$615$	−11.2852	−0.455063
$616$	−15.3803	−0.619689
$617$	−3.39937	−0.136853	−0.0684267	−	0.997656i	$-0.521798\pi$
$617$	−3.39937	−0.136853	−0.0684267	+	0.997656i	$0.521798\pi$
$618$	7.90749	0.318086
$619$	−21.9967	−0.884124	−0.442062	−	0.896985i	$-0.645753\pi$
$619$	−21.9967	−0.884124	−0.442062	+	0.896985i	$0.645753\pi$
$620$	−86.3038	−3.46604
$621$	−2.74159	−0.110016
$622$	−34.1594	−1.36967
$623$	3.81548	0.152864
$624$	−21.4812	−0.859936
$625$	−29.2912	−1.17165
$626$	−46.3182	−1.85125
$627$	−18.2388	−0.728386
$628$	−36.1876	−1.44404
$629$	−31.1364	−1.24149
$630$	4.00864	0.159708
$631$	−1.15512	−0.0459844	−0.0229922	−	0.999736i	$-0.507319\pi$
$631$	−1.15512	−0.0459844	−0.0229922	+	0.999736i	$0.507319\pi$
$632$	−124.601	−4.95637
$633$	−20.6740	−0.821718
$634$	−2.80867	−0.111546
$635$	30.2212	1.19929
$636$	−25.1349	−0.996665
$637$	−7.31230	−0.289724
$638$	68.3614	2.70645
$639$	−3.16764	−0.125310
$640$	211.684	8.36755
$641$	−4.52515	−0.178733	−0.0893663	−	0.995999i	$-0.528484\pi$
$641$	−4.52515	−0.178733	−0.0893663	+	0.995999i	$0.528484\pi$
$642$	41.6585	1.64413
$643$	−8.40133	−0.331316	−0.165658	−	0.986183i	$-0.552975\pi$
$643$	−8.40133	−0.331316	−0.165658	+	0.986183i	$0.552975\pi$
$644$	9.39861	0.370357
$645$	−18.3069	−0.720833
$646$	−103.355	−4.06644
$647$	−9.24179	−0.363332	−0.181666	−	0.983360i	$-0.558149\pi$
$647$	−9.24179	−0.363332	−0.181666	+	0.983360i	$0.558149\pi$
$648$	−11.1689	−0.438758
$649$	30.4310	1.19452
$650$	−3.40394	−0.133513
$651$	−3.37339	−0.132213
$652$	87.2165	3.41566
$653$	7.00999	0.274322	0.137161	−	0.990549i	$-0.456202\pi$
$653$	7.00999	0.274322	0.137161	+	0.990549i	$0.456202\pi$
$654$	−3.63029	−0.141956
$655$	−43.1923	−1.68766
$656$	−89.5151	−3.49498
$657$	−9.73683	−0.379870
$658$	18.9204	0.737594
$659$	0.117110	0.00456195	0.00228097	−	0.999997i	$-0.499274\pi$
$659$	0.117110	0.00456195	0.00228097	+	0.999997i	$0.499274\pi$
$660$	35.2303	1.37134
$661$	−29.6943	−1.15497	−0.577487	−	0.816400i	$-0.695967\pi$
$661$	−29.6943	−1.15497	−0.577487	+	0.816400i	$0.695967\pi$
$662$	−8.51589	−0.330980
$663$	−5.27183	−0.204741
$664$	42.2050	1.63787
$665$	−10.8268	−0.419846
$666$	18.2695	0.707929
$667$	−27.7538	−1.07463
$668$	−110.624	−4.28017
$669$	15.2460	0.589444
$670$	2.95143	0.114024
$671$	−23.2749	−0.898517
$672$	18.9461	0.730861
$673$	−36.4230	−1.40400	−0.702002	−	0.712175i	$-0.747710\pi$
$673$	−36.4230	−1.40400	−0.702002	+	0.712175i	$0.747710\pi$
$674$	−61.6340	−2.37405
$675$	−1.10043	−0.0423556
$676$	−70.3028	−2.70395
$677$	0.977651	0.0375742	0.0187871	−	0.999824i	$-0.494020\pi$
$677$	0.977651	0.0375742	0.0187871	+	0.999824i	$0.494020\pi$
$678$	−13.4702	−0.517319
$679$	−3.43963	−0.132001
$680$	132.636	5.08638
$681$	−11.4597	−0.439136
$682$	−39.5977	−1.51627
$683$	36.2609	1.38748	0.693742	−	0.720223i	$-0.255961\pi$
$683$	36.2609	1.38748	0.693742	+	0.720223i	$0.255961\pi$
$684$	45.4050	1.73610
$685$	−47.6936	−1.82228
$686$	22.1848	0.847019
$687$	−9.93394	−0.379003
$688$	−145.212	−5.53615
$689$	4.62484	0.176192
$690$	−19.1035	−0.727257
$691$	11.6239	0.442196	0.221098	−	0.975252i	$-0.429036\pi$
$691$	11.6239	0.442196	0.221098	+	0.975252i	$0.429036\pi$
$692$	23.4443	0.891218
$693$	1.37706	0.0523101
$694$	88.2819	3.35113
$695$	−11.0753	−0.420110
$696$	−113.066	−4.28575
$697$	−21.9684	−0.832114
$698$	42.6038	1.61258
$699$	16.8832	0.638580
$700$	3.77244	0.142585
$701$	10.9129	0.412176	0.206088	−	0.978533i	$-0.433927\pi$
$701$	10.9129	0.412176	0.206088	+	0.978533i	$0.433927\pi$
$702$	3.09328	0.116748
$703$	−49.3435	−1.86102
$704$	128.603	4.84692
$705$	−28.7934	−1.08442
$706$	46.6623	1.75616
$707$	−6.81195	−0.256190
$708$	−75.7574	−2.84714
$709$	33.5313	1.25929	0.629646	−	0.776882i	$-0.283200\pi$
$709$	33.5313	1.25929	0.629646	+	0.776882i	$0.283200\pi$
$710$	−22.0722	−0.828354
$711$	11.1560	0.418384
$712$	−74.0753	−2.77609
$713$	16.0761	0.602055
$714$	7.80347	0.292037
$715$	−6.48238	−0.242427
$716$	53.8004	2.01061
$717$	3.86602	0.144379
$718$	−55.1401	−2.05781
$719$	44.7740	1.66979	0.834894	−	0.550410i	$-0.185529\pi$
$719$	44.7740	1.66979	0.834894	+	0.550410i	$0.185529\pi$
$720$	−48.3891	−1.80336
$721$	1.61249	0.0600524
$722$	−110.190	−4.10083
$723$	25.2277	0.938227
$724$	−66.6935	−2.47864
$725$	−11.1399	−0.413725
$726$	−14.8686	−0.551824
$727$	5.90842	0.219131	0.109566	−	0.993980i	$-0.465054\pi$
$727$	5.90842	0.219131	0.109566	+	0.993980i	$0.465054\pi$
$728$	−7.04517	−0.261111
$729$	1.00000	0.0370370
$730$	−67.8464	−2.51111
$731$	−35.6373	−1.31809
$732$	57.9424	2.14161
$733$	3.24840	0.119982	0.0599911	−	0.998199i	$-0.480893\pi$
$733$	3.24840	0.119982	0.0599911	+	0.998199i	$0.480893\pi$
$734$	−21.0618	−0.777403
$735$	−16.4719	−0.607575
$736$	−90.2889	−3.32809
$737$	1.01388	0.0373468
$738$	12.8901	0.474492
$739$	−10.3228	−0.379730	−0.189865	−	0.981810i	$-0.560805\pi$
$739$	−10.3228	−0.379730	−0.189865	+	0.981810i	$0.560805\pi$
$740$	95.3125	3.50376
$741$	−8.35454	−0.306912
$742$	−6.84578	−0.251316
$743$	1.44521	0.0530196	0.0265098	−	0.999649i	$-0.491561\pi$
$743$	1.44521	0.0530196	0.0265098	+	0.999649i	$0.491561\pi$
$744$	65.4923	2.40106
$745$	47.6612	1.74617
$746$	−67.7064	−2.47891
$747$	−3.77878	−0.138258
$748$	68.5814	2.50758
$749$	8.49499	0.310400
$750$	27.1723	0.992191
$751$	−44.7037	−1.63126	−0.815630	−	0.578574i	$-0.803609\pi$
$751$	−44.7037	−1.63126	−0.815630	+	0.578574i	$0.803609\pi$
$752$	−228.392	−8.32860
$753$	20.8672	0.760442
$754$	31.3140	1.14039
$755$	−15.0251	−0.546820
$756$	−3.42816	−0.124681
$757$	−49.9797	−1.81654	−0.908272	−	0.418380i	$-0.862598\pi$
$757$	−49.9797	−1.81654	−0.908272	+	0.418380i	$0.862598\pi$
$758$	−6.49191	−0.235797
$759$	−6.56246	−0.238202
$760$	210.196	7.62461
$761$	21.7784	0.789466	0.394733	−	0.918796i	$-0.370837\pi$
$761$	21.7784	0.789466	0.394733	+	0.918796i	$0.370837\pi$
$762$	−34.5192	−1.25050
$763$	−0.740288	−0.0268002
$764$	−69.1597	−2.50211
$765$	−11.8755	−0.429358
$766$	−22.3360	−0.807034
$767$	13.9394	0.503322
$768$	−134.336	−4.84744
$769$	36.8891	1.33026	0.665128	−	0.746729i	$-0.268377\pi$
$769$	36.8891	1.33026	0.665128	+	0.746729i	$0.268377\pi$
$770$	9.59535	0.345793
$771$	28.4501	1.02460
$772$	127.722	4.59683
$773$	20.5668	0.739735	0.369867	−	0.929085i	$-0.379403\pi$
$773$	20.5668	0.739735	0.369867	+	0.929085i	$0.379403\pi$
$774$	20.9104	0.751610
$775$	6.45268	0.231787
$776$	66.7784	2.39721
$777$	3.72551	0.133652
$778$	−86.5418	−3.10267
$779$	−34.8145	−1.24736
$780$	16.1377	0.577824
$781$	−7.58228	−0.271315
$782$	−37.1880	−1.32984
$783$	10.1232	0.361774
$784$	−130.656	−4.66630
$785$	14.9992	0.535344
$786$	49.3349	1.75972
$787$	38.9980	1.39013	0.695064	−	0.718948i	$-0.255376\pi$
$787$	38.9980	1.39013	0.695064	+	0.718948i	$0.255376\pi$
$788$	−68.8349	−2.45214
$789$	3.17681	0.113097
$790$	77.7354	2.76570
$791$	−2.74684	−0.0976664
$792$	−26.7347	−0.949978
$793$	−10.6614	−0.378598
$794$	−65.2635	−2.31611
$795$	10.4180	0.369490
$796$	−45.1190	−1.59920
$797$	−46.5167	−1.64770	−0.823852	−	0.566805i	$-0.808179\pi$
$797$	−46.5167	−1.64770	−0.823852	+	0.566805i	$0.808179\pi$
$798$	12.3666	0.437771
$799$	−56.0511	−1.98294
$800$	−36.2404	−1.28129
$801$	6.63225	0.234339
$802$	2.54594	0.0899003
$803$	−23.3067	−0.822477
$804$	−2.52403	−0.0890158
$805$	−3.89558	−0.137301
$806$	−18.1383	−0.638895
$807$	10.5839	0.372570
$808$	132.250	4.65253
$809$	9.05448	0.318338	0.159169	−	0.987251i	$-0.449118\pi$
$809$	9.05448	0.318338	0.159169	+	0.987251i	$0.449118\pi$
$810$	6.96801	0.244831
$811$	44.5879	1.56569	0.782846	−	0.622216i	$-0.213767\pi$
$811$	44.5879	1.56569	0.782846	+	0.622216i	$0.213767\pi$
$812$	−34.7040	−1.21787
$813$	−3.59111	−0.125946
$814$	43.7311	1.53277
$815$	−36.1499	−1.26627
$816$	−94.1973	−3.29756
$817$	−56.4763	−1.97585
$818$	37.9663	1.32746
$819$	0.630782	0.0220413
$820$	67.2482	2.34841
$821$	11.1350	0.388613	0.194306	−	0.980941i	$-0.437754\pi$
$821$	11.1350	0.388613	0.194306	+	0.980941i	$0.437754\pi$
$822$	54.4764	1.90008
$823$	−56.4150	−1.96650	−0.983252	−	0.182253i	$-0.941661\pi$
$823$	−56.4150	−1.96650	−0.983252	+	0.182253i	$0.941661\pi$
$824$	−31.3056	−1.09058
$825$	−2.63406	−0.0917063
$826$	−20.6334	−0.717927
$827$	−11.9681	−0.416171	−0.208085	−	0.978111i	$-0.566723\pi$
$827$	−11.9681	−0.416171	−0.208085	+	0.978111i	$0.566723\pi$
$828$	16.3371	0.567754
$829$	54.7852	1.90277	0.951385	−	0.308004i	$-0.0996611\pi$
$829$	54.7852	1.90277	0.951385	+	0.308004i	$0.0996611\pi$
$830$	−26.3306	−0.913948
$831$	16.0385	0.556368
$832$	58.9086	2.04229
$833$	−32.0652	−1.11099
$834$	12.6504	0.438047
$835$	45.8520	1.58677
$836$	108.684	3.75893
$837$	−5.86378	−0.202682
$838$	72.9018	2.51835
$839$	−17.4742	−0.603275	−0.301637	−	0.953423i	$-0.597533\pi$
$839$	−17.4742	−0.603275	−0.301637	+	0.953423i	$0.597533\pi$
$840$	−15.8701	−0.547572
$841$	73.4796	2.53378
$842$	−50.3155	−1.73399
$843$	−33.0786	−1.13929
$844$	123.196	4.24058
$845$	29.1394	1.00243
$846$	32.8883	1.13072
$847$	−3.03200	−0.104181
$848$	82.6368	2.83776
$849$	16.3363	0.560659
$850$	−14.9266	−0.511979
$851$	−17.7542	−0.608606
$852$	18.8759	0.646678
$853$	2.67339	0.0915350	0.0457675	−	0.998952i	$-0.485427\pi$
$853$	2.67339	0.0915350	0.0457675	+	0.998952i	$0.485427\pi$
$854$	15.7812	0.540023
$855$	−18.8197	−0.643619
$856$	−164.925	−5.63703
$857$	8.17371	0.279209	0.139604	−	0.990207i	$-0.455417\pi$
$857$	8.17371	0.279209	0.139604	+	0.990207i	$0.455417\pi$
$858$	7.40428	0.252778
$859$	−47.7434	−1.62899	−0.814493	−	0.580174i	$-0.802985\pi$
$859$	−47.7434	−1.62899	−0.814493	+	0.580174i	$0.802985\pi$
$860$	109.090	3.71995
$861$	2.62855	0.0895809
$862$	−38.7724	−1.32059
$863$	−11.1869	−0.380808	−0.190404	−	0.981706i	$-0.560980\pi$
$863$	−11.1869	−0.380808	−0.190404	+	0.981706i	$0.560980\pi$
$864$	32.9330	1.12040
$865$	−9.71729	−0.330398
$866$	74.0216	2.51536
$867$	−6.11751	−0.207761
$868$	20.1019	0.682305
$869$	26.7038	0.905865
$870$	70.5387	2.39149
$871$	0.464423	0.0157364
$872$	14.3722	0.486706
$873$	−5.97894	−0.202356
$874$	−58.9337	−1.99346
$875$	5.54096	0.187319
$876$	58.0216	1.96037
$877$	23.8509	0.805388	0.402694	−	0.915335i	$-0.368074\pi$
$877$	23.8509	0.805388	0.402694	+	0.915335i	$0.368074\pi$
$878$	110.405	3.72600
$879$	11.4112	0.384890
$880$	−115.827	−3.90454
$881$	−51.6961	−1.74169	−0.870843	−	0.491561i	$-0.836426\pi$
$881$	−51.6961	−1.74169	−0.870843	+	0.491561i	$0.836426\pi$
$882$	18.8145	0.633516
$883$	2.03425	0.0684581	0.0342291	−	0.999414i	$-0.489102\pi$
$883$	2.03425	0.0684581	0.0342291	+	0.999414i	$0.489102\pi$
$884$	31.4147	1.05659
$885$	31.4003	1.05551
$886$	54.0307	1.81520
$887$	−18.8254	−0.632095	−0.316047	−	0.948743i	$-0.602356\pi$
$887$	−18.8254	−0.632095	−0.316047	+	0.948743i	$0.602356\pi$
$888$	−72.3286	−2.42719
$889$	−7.03915	−0.236085
$890$	46.2136	1.54908
$891$	2.39367	0.0801908
$892$	−90.8505	−3.04190
$893$	−88.8270	−2.97248
$894$	−54.4395	−1.82073
$895$	−22.2994	−0.745387
$896$	−49.3056	−1.64718
$897$	−3.00603	−0.100369
$898$	84.8913	2.83286
$899$	−59.3603	−1.97978
$900$	6.55744	0.218581
$901$	20.2804	0.675638
$902$	30.8547	1.02735
$903$	4.26405	0.141899
$904$	53.3282	1.77367
$905$	27.6434	0.918898
$906$	17.1619	0.570167
$907$	10.7711	0.357649	0.178824	−	0.983881i	$-0.442771\pi$
$907$	10.7711	0.357649	0.178824	+	0.983881i	$0.442771\pi$
$908$	68.2880	2.26622
$909$	−11.8409	−0.392736
$910$	4.39529	0.145703
$911$	−13.0150	−0.431207	−0.215604	−	0.976481i	$-0.569172\pi$
$911$	−13.0150	−0.431207	−0.215604	+	0.976481i	$0.569172\pi$
$912$	−149.279	−4.94313
$913$	−9.04514	−0.299350
$914$	61.8510	2.04585
$915$	−24.0162	−0.793951
$916$	59.1961	1.95590
$917$	10.0604	0.332223
$918$	13.5644	0.447691
$919$	−51.0007	−1.68236	−0.841179	−	0.540757i	$-0.818138\pi$
$919$	−51.0007	−1.68236	−0.841179	+	0.540757i	$0.818138\pi$
$920$	75.6303	2.49346
$921$	−0.513818	−0.0169309
$922$	24.8525	0.818473
$923$	−3.47317	−0.114321
$924$	−8.20586	−0.269953
$925$	−7.12623	−0.234309
$926$	82.9452	2.72575
$927$	2.80291	0.0920598
$928$	333.388	10.9440
$929$	−44.7310	−1.46758	−0.733788	−	0.679378i	$-0.762250\pi$
$929$	−44.7310	−1.46758	−0.733788	+	0.679378i	$0.762250\pi$
$930$	−40.8589	−1.33982
$931$	−50.8154	−1.66541
$932$	−100.607	−3.29548
$933$	−12.1082	−0.396406
$934$	−53.8401	−1.76170
$935$	−28.4259	−0.929627
$936$	−12.2462	−0.400281
$937$	12.8574	0.420034	0.210017	−	0.977698i	$-0.432648\pi$
$937$	12.8574	0.420034	0.210017	+	0.977698i	$0.432648\pi$
$938$	−0.687448	−0.0224460
$939$	−16.4181	−0.535784
$940$	171.580	5.59631
$941$	43.3461	1.41304	0.706521	−	0.707692i	$-0.250264\pi$
$941$	43.3461	1.41304	0.706521	+	0.707692i	$0.250264\pi$
$942$	−17.1323	−0.558202
$943$	−12.5266	−0.407921
$944$	249.070	8.10653
$945$	1.42092	0.0462224
$946$	50.0526	1.62735
$947$	29.4673	0.957560	0.478780	−	0.877935i	$-0.341079\pi$
$947$	29.4673	0.957560	0.478780	+	0.877935i	$0.341079\pi$
$948$	−66.4786	−2.15913
$949$	−10.6760	−0.346557
$950$	−23.6550	−0.767469
$951$	−0.995569	−0.0322835
$952$	−30.8938	−1.00127
$953$	−12.4383	−0.402917	−0.201459	−	0.979497i	$-0.564568\pi$
$953$	−12.4383	−0.402917	−0.201459	+	0.979497i	$0.564568\pi$
$954$	−11.8997	−0.385266
$955$	28.6656	0.927598
$956$	−23.0375	−0.745087
$957$	24.2316	0.783297
$958$	−56.7791	−1.83445
$959$	11.1088	0.358723
$960$	132.699	4.28285
$961$	3.38392	0.109159
$962$	20.0317	0.645847
$963$	14.7664	0.475841
$964$	−150.331	−4.84184
$965$	−52.9389	−1.70416
$966$	4.44959	0.143163
$967$	−19.2788	−0.619963	−0.309981	−	0.950743i	$-0.600323\pi$
$967$	−19.2788	−0.619963	−0.309981	+	0.950743i	$0.600323\pi$
$968$	58.8644	1.89197
$969$	−36.6355	−1.17690
$970$	−41.6613	−1.33766
$971$	49.1323	1.57673	0.788366	−	0.615207i	$-0.210928\pi$
$971$	49.1323	1.57673	0.788366	+	0.615207i	$0.210928\pi$
$972$	−5.95898	−0.191134
$973$	2.57967	0.0827003
$974$	−31.4071	−1.00635
$975$	−1.20657	−0.0386412
$976$	−190.499	−6.09771
$977$	56.4854	1.80713	0.903563	−	0.428454i	$-0.140942\pi$
$977$	56.4854	1.80713	0.903563	+	0.428454i	$0.140942\pi$
$978$	41.2910	1.32034
$979$	15.8754	0.507380
$980$	98.1557	3.13547
$981$	−1.28680	−0.0410845
$982$	−72.5107	−2.31391
$983$	54.6443	1.74288	0.871442	−	0.490499i	$-0.163185\pi$
$983$	54.6443	1.74288	0.871442	+	0.490499i	$0.163185\pi$
$984$	−51.0318	−1.62683
$985$	28.5310	0.909073
$986$	137.315	4.37300
$987$	6.70659	0.213473
$988$	49.7845	1.58386
$989$	−20.3206	−0.646159
$990$	16.6791	0.530097
$991$	33.9458	1.07832	0.539162	−	0.842202i	$-0.318741\pi$
$991$	33.9458	1.07832	0.539162	+	0.842202i	$0.318741\pi$
$992$	−193.112	−6.13131
$993$	−3.01857	−0.0957915
$994$	5.14107	0.163065
$995$	18.7011	0.592865
$996$	22.5177	0.713500
$997$	0.716823	0.0227020	0.0113510	−	0.999936i	$-0.496387\pi$
$997$	0.716823	0.0227020	0.0113510	+	0.999936i	$0.496387\pi$
$998$	−40.2926	−1.27544
$999$	6.47587	0.204887

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6033.2.a.d.1.1	✓	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6033.2.a.d.1.1	✓	84	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:	\( N \)	\(=\)	\( 6033 = 3 \cdot 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6033.a (trivial)

\(f(q)\)	\(=\)	\(q-2.82117 q^{2} -1.00000 q^{3} +5.95898 q^{4} -2.46990 q^{5} +2.82117 q^{6} +0.575292 q^{7} -11.1689 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.82117 q^{2} -1.00000 q^{3} +5.95898 q^{4} -2.46990 q^{5} +2.82117 q^{6} +0.575292 q^{7} -11.1689 q^{8} +1.00000 q^{9} +6.96801 q^{10} +2.39367 q^{11} -5.95898 q^{12} +1.09645 q^{13} -1.62299 q^{14} +2.46990 q^{15} +19.5915 q^{16} +4.80807 q^{17} -2.82117 q^{18} +7.61959 q^{19} -14.7181 q^{20} -0.575292 q^{21} -6.75293 q^{22} +2.74159 q^{23} +11.1689 q^{24} +1.10043 q^{25} -3.09328 q^{26} -1.00000 q^{27} +3.42816 q^{28} -10.1232 q^{29} -6.96801 q^{30} +5.86378 q^{31} -32.9330 q^{32} -2.39367 q^{33} -13.5644 q^{34} -1.42092 q^{35} +5.95898 q^{36} -6.47587 q^{37} -21.4961 q^{38} -1.09645 q^{39} +27.5862 q^{40} -4.56908 q^{41} +1.62299 q^{42} -7.41198 q^{43} +14.2638 q^{44} -2.46990 q^{45} -7.73450 q^{46} -11.6577 q^{47} -19.5915 q^{48} -6.66904 q^{49} -3.10450 q^{50} -4.80807 q^{51} +6.53375 q^{52} +4.21799 q^{53} +2.82117 q^{54} -5.91213 q^{55} -6.42541 q^{56} -7.61959 q^{57} +28.5593 q^{58} +12.7131 q^{59} +14.7181 q^{60} -9.72353 q^{61} -16.5427 q^{62} +0.575292 q^{63} +53.7265 q^{64} -2.70814 q^{65} +6.75293 q^{66} +0.423568 q^{67} +28.6512 q^{68} -2.74159 q^{69} +4.00864 q^{70} -3.16764 q^{71} -11.1689 q^{72} -9.73683 q^{73} +18.2695 q^{74} -1.10043 q^{75} +45.4050 q^{76} +1.37706 q^{77} +3.09328 q^{78} +11.1560 q^{79} -48.3891 q^{80} +1.00000 q^{81} +12.8901 q^{82} -3.77878 q^{83} -3.42816 q^{84} -11.8755 q^{85} +20.9104 q^{86} +10.1232 q^{87} -26.7347 q^{88} +6.63225 q^{89} +6.96801 q^{90} +0.630782 q^{91} +16.3371 q^{92} -5.86378 q^{93} +32.8883 q^{94} -18.8197 q^{95} +32.9330 q^{96} -5.97894 q^{97} +18.8145 q^{98} +2.39367 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 13 q^{2} - 84 q^{3} + 81 q^{4} - 10 q^{5} + 13 q^{6} - 32 q^{7} - 39 q^{8} + 84 q^{9}+O(q^{10}) \) 84 * q - 13 * q^2 - 84 * q^3 + 81 * q^4 - 10 * q^5 + 13 * q^6 - 32 * q^7 - 39 * q^8 + 84 * q^9	\( 84 q - 13 q^{2} - 84 q^{3} + 81 q^{4} - 10 q^{5} + 13 q^{6} - 32 q^{7} - 39 q^{8} + 84 q^{9} + 13 q^{10} - 20 q^{11} - 81 q^{12} + 7 q^{13} - 9 q^{14} + 10 q^{15} + 83 q^{16} - 39 q^{17} - 13 q^{18} + 13 q^{19} - 26 q^{20} + 32 q^{21} - 21 q^{22} - 93 q^{23} + 39 q^{24} + 66 q^{25} - 34 q^{26} - 84 q^{27} - 59 q^{28} - 39 q^{29} - 13 q^{30} + 8 q^{31} - 96 q^{32} + 20 q^{33} - 69 q^{35} + 81 q^{36} + 6 q^{37} - 59 q^{38} - 7 q^{39} + 28 q^{40} - 23 q^{41} + 9 q^{42} - 74 q^{43} - 43 q^{44} - 10 q^{45} - 6 q^{46} - 77 q^{47} - 83 q^{48} + 100 q^{49} - 74 q^{50} + 39 q^{51} - 44 q^{52} - 66 q^{53} + 13 q^{54} - 60 q^{55} - 31 q^{56} - 13 q^{57} - 39 q^{58} - 36 q^{59} + 26 q^{60} + 104 q^{61} - 53 q^{62} - 32 q^{63} + 85 q^{64} - 47 q^{65} + 21 q^{66} - 65 q^{67} - 118 q^{68} + 93 q^{69} - 3 q^{70} - 68 q^{71} - 39 q^{72} + 8 q^{73} - 30 q^{74} - 66 q^{75} + 71 q^{76} - 83 q^{77} + 34 q^{78} - 24 q^{79} - 67 q^{80} + 84 q^{81} - 9 q^{82} - 95 q^{83} + 59 q^{84} + 24 q^{85} - 32 q^{86} + 39 q^{87} - 65 q^{88} - 44 q^{89} + 13 q^{90} + 8 q^{91} - 184 q^{92} - 8 q^{93} + 61 q^{94} - 153 q^{95} + 96 q^{96} + 19 q^{97} - 67 q^{98} - 20 q^{99}+O(q^{100}) \) 84 * q - 13 * q^2 - 84 * q^3 + 81 * q^4 - 10 * q^5 + 13 * q^6 - 32 * q^7 - 39 * q^8 + 84 * q^9 + 13 * q^10 - 20 * q^11 - 81 * q^12 + 7 * q^13 - 9 * q^14 + 10 * q^15 + 83 * q^16 - 39 * q^17 - 13 * q^18 + 13 * q^19 - 26 * q^20 + 32 * q^21 - 21 * q^22 - 93 * q^23 + 39 * q^24 + 66 * q^25 - 34 * q^26 - 84 * q^27 - 59 * q^28 - 39 * q^29 - 13 * q^30 + 8 * q^31 - 96 * q^32 + 20 * q^33 - 69 * q^35 + 81 * q^36 + 6 * q^37 - 59 * q^38 - 7 * q^39 + 28 * q^40 - 23 * q^41 + 9 * q^42 - 74 * q^43 - 43 * q^44 - 10 * q^45 - 6 * q^46 - 77 * q^47 - 83 * q^48 + 100 * q^49 - 74 * q^50 + 39 * q^51 - 44 * q^52 - 66 * q^53 + 13 * q^54 - 60 * q^55 - 31 * q^56 - 13 * q^57 - 39 * q^58 - 36 * q^59 + 26 * q^60 + 104 * q^61 - 53 * q^62 - 32 * q^63 + 85 * q^64 - 47 * q^65 + 21 * q^66 - 65 * q^67 - 118 * q^68 + 93 * q^69 - 3 * q^70 - 68 * q^71 - 39 * q^72 + 8 * q^73 - 30 * q^74 - 66 * q^75 + 71 * q^76 - 83 * q^77 + 34 * q^78 - 24 * q^79 - 67 * q^80 + 84 * q^81 - 9 * q^82 - 95 * q^83 + 59 * q^84 + 24 * q^85 - 32 * q^86 + 39 * q^87 - 65 * q^88 - 44 * q^89 + 13 * q^90 + 8 * q^91 - 184 * q^92 - 8 * q^93 + 61 * q^94 - 153 * q^95 + 96 * q^96 + 19 * q^97 - 67 * q^98 - 20 * q^99

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