LMFDB - Embedded newform 6018.2.a.y.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6018,2,Mod(1,6018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6018, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("6018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6018 = 2 \cdot 3 \cdot 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6018.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:	$48.0539719364$
Analytic rank:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - 33x^{8} + 53x^{7} + 356x^{6} - 433x^{5} - 1296x^{4} + 1135x^{3} + 930x^{2} - 186x - 104 $ x^10 - 2x^9 - 33x^8 + 53x^7 + 356x^6 - 433x^5 - 1296x^4 + 1135x^3 + 930x^2 - 186*x - 104
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$-3.49703$ of defining polynomial
Character	$\chi$	$=$	6018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.49703 q^{5} -1.00000 q^{6} -4.54363 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.49703 q^{5} -1.00000 q^{6} -4.54363 q^{7} -1.00000 q^{8} +1.00000 q^{9} -3.49703 q^{10} -4.43900 q^{11} +1.00000 q^{12} -0.549811 q^{13} +4.54363 q^{14} +3.49703 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} +7.86381 q^{19} +3.49703 q^{20} -4.54363 q^{21} +4.43900 q^{22} -0.106779 q^{23} -1.00000 q^{24} +7.22922 q^{25} +0.549811 q^{26} +1.00000 q^{27} -4.54363 q^{28} -9.87626 q^{29} -3.49703 q^{30} +2.98829 q^{31} -1.00000 q^{32} -4.43900 q^{33} +1.00000 q^{34} -15.8892 q^{35} +1.00000 q^{36} -6.87634 q^{37} -7.86381 q^{38} -0.549811 q^{39} -3.49703 q^{40} +7.13275 q^{41} +4.54363 q^{42} -11.0012 q^{43} -4.43900 q^{44} +3.49703 q^{45} +0.106779 q^{46} +6.14847 q^{47} +1.00000 q^{48} +13.6446 q^{49} -7.22922 q^{50} -1.00000 q^{51} -0.549811 q^{52} +13.0995 q^{53} -1.00000 q^{54} -15.5233 q^{55} +4.54363 q^{56} +7.86381 q^{57} +9.87626 q^{58} +1.00000 q^{59} +3.49703 q^{60} -6.91367 q^{61} -2.98829 q^{62} -4.54363 q^{63} +1.00000 q^{64} -1.92271 q^{65} +4.43900 q^{66} -13.4729 q^{67} -1.00000 q^{68} -0.106779 q^{69} +15.8892 q^{70} -13.7110 q^{71} -1.00000 q^{72} +4.03219 q^{73} +6.87634 q^{74} +7.22922 q^{75} +7.86381 q^{76} +20.1692 q^{77} +0.549811 q^{78} -2.01574 q^{79} +3.49703 q^{80} +1.00000 q^{81} -7.13275 q^{82} -3.43030 q^{83} -4.54363 q^{84} -3.49703 q^{85} +11.0012 q^{86} -9.87626 q^{87} +4.43900 q^{88} -0.242414 q^{89} -3.49703 q^{90} +2.49814 q^{91} -0.106779 q^{92} +2.98829 q^{93} -6.14847 q^{94} +27.5000 q^{95} -1.00000 q^{96} +0.142690 q^{97} -13.6446 q^{98} -4.43900 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{2} + 10 q^{3} + 10 q^{4} - 2 q^{5} - 10 q^{6} - 6 q^{7} - 10 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q - 10 * q^2 + 10 * q^3 + 10 * q^4 - 2 * q^5 - 10 * q^6 - 6 * q^7 - 10 * q^8 + 10 * q^9	\( 10 q - 10 q^{2} + 10 q^{3} + 10 q^{4} - 2 q^{5} - 10 q^{6} - 6 q^{7} - 10 q^{8} + 10 q^{9} + 2 q^{10} - 3 q^{11} + 10 q^{12} - 10 q^{13} + 6 q^{14} - 2 q^{15} + 10 q^{16} - 10 q^{17} - 10 q^{18} + 8 q^{19} - 2 q^{20} - 6 q^{21} + 3 q^{22} - 9 q^{23} - 10 q^{24} + 20 q^{25} + 10 q^{26} + 10 q^{27} - 6 q^{28} - 24 q^{29} + 2 q^{30} - 7 q^{31} - 10 q^{32} - 3 q^{33} + 10 q^{34} - 22 q^{35} + 10 q^{36} - 4 q^{37} - 8 q^{38} - 10 q^{39} + 2 q^{40} - 9 q^{41} + 6 q^{42} - 11 q^{43} - 3 q^{44} - 2 q^{45} + 9 q^{46} - 18 q^{47} + 10 q^{48} + 6 q^{49} - 20 q^{50} - 10 q^{51} - 10 q^{52} - 9 q^{53} - 10 q^{54} + q^{55} + 6 q^{56} + 8 q^{57} + 24 q^{58} + 10 q^{59} - 2 q^{60} - 25 q^{61} + 7 q^{62} - 6 q^{63} + 10 q^{64} - 28 q^{65} + 3 q^{66} + 2 q^{67} - 10 q^{68} - 9 q^{69} + 22 q^{70} - 30 q^{71} - 10 q^{72} - 11 q^{73} + 4 q^{74} + 20 q^{75} + 8 q^{76} + 4 q^{77} + 10 q^{78} + 3 q^{79} - 2 q^{80} + 10 q^{81} + 9 q^{82} - q^{83} - 6 q^{84} + 2 q^{85} + 11 q^{86} - 24 q^{87} + 3 q^{88} - 14 q^{89} + 2 q^{90} - 13 q^{91} - 9 q^{92} - 7 q^{93} + 18 q^{94} - 35 q^{95} - 10 q^{96} - 10 q^{97} - 6 q^{98} - 3 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 + 10 * q^3 + 10 * q^4 - 2 * q^5 - 10 * q^6 - 6 * q^7 - 10 * q^8 + 10 * q^9 + 2 * q^10 - 3 * q^11 + 10 * q^12 - 10 * q^13 + 6 * q^14 - 2 * q^15 + 10 * q^16 - 10 * q^17 - 10 * q^18 + 8 * q^19 - 2 * q^20 - 6 * q^21 + 3 * q^22 - 9 * q^23 - 10 * q^24 + 20 * q^25 + 10 * q^26 + 10 * q^27 - 6 * q^28 - 24 * q^29 + 2 * q^30 - 7 * q^31 - 10 * q^32 - 3 * q^33 + 10 * q^34 - 22 * q^35 + 10 * q^36 - 4 * q^37 - 8 * q^38 - 10 * q^39 + 2 * q^40 - 9 * q^41 + 6 * q^42 - 11 * q^43 - 3 * q^44 - 2 * q^45 + 9 * q^46 - 18 * q^47 + 10 * q^48 + 6 * q^49 - 20 * q^50 - 10 * q^51 - 10 * q^52 - 9 * q^53 - 10 * q^54 + q^55 + 6 * q^56 + 8 * q^57 + 24 * q^58 + 10 * q^59 - 2 * q^60 - 25 * q^61 + 7 * q^62 - 6 * q^63 + 10 * q^64 - 28 * q^65 + 3 * q^66 + 2 * q^67 - 10 * q^68 - 9 * q^69 + 22 * q^70 - 30 * q^71 - 10 * q^72 - 11 * q^73 + 4 * q^74 + 20 * q^75 + 8 * q^76 + 4 * q^77 + 10 * q^78 + 3 * q^79 - 2 * q^80 + 10 * q^81 + 9 * q^82 - q^83 - 6 * q^84 + 2 * q^85 + 11 * q^86 - 24 * q^87 + 3 * q^88 - 14 * q^89 + 2 * q^90 - 13 * q^91 - 9 * q^92 - 7 * q^93 + 18 * q^94 - 35 * q^95 - 10 * q^96 - 10 * q^97 - 6 * q^98 - 3 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	3.49703	1.56392	0.781960	−	0.623329i	$-0.214220\pi$
$5$	3.49703	1.56392	0.781960	+	0.623329i	$0.214220\pi$
$6$	−1.00000	−0.408248
$7$	−4.54363	−1.71733	−0.858666	−	0.512536i	$-0.828706\pi$
$7$	−4.54363	−1.71733	−0.858666	+	0.512536i	$0.828706\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−3.49703	−1.10586
$11$	−4.43900	−1.33841	−0.669205	−	0.743078i	$-0.733365\pi$
$11$	−4.43900	−1.33841	−0.669205	+	0.743078i	$0.733365\pi$
$12$	1.00000	0.288675
$13$	−0.549811	−0.152490	−0.0762451	−	0.997089i	$-0.524293\pi$
$13$	−0.549811	−0.152490	−0.0762451	+	0.997089i	$0.524293\pi$
$14$	4.54363	1.21434
$15$	3.49703	0.902929
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.00000	−0.235702
$19$	7.86381	1.80408	0.902041	−	0.431651i	$-0.142069\pi$
$19$	7.86381	1.80408	0.902041	+	0.431651i	$0.142069\pi$
$20$	3.49703	0.781960
$21$	−4.54363	−0.991502
$22$	4.43900	0.946399
$23$	−0.106779	−0.0222651	−0.0111325	−	0.999938i	$-0.503544\pi$
$23$	−0.106779	−0.0222651	−0.0111325	+	0.999938i	$0.503544\pi$
$24$	−1.00000	−0.204124
$25$	7.22922	1.44584
$26$	0.549811	0.107827
$27$	1.00000	0.192450
$28$	−4.54363	−0.858666
$29$	−9.87626	−1.83398	−0.916988	−	0.398915i	$-0.869387\pi$
$29$	−9.87626	−1.83398	−0.916988	+	0.398915i	$0.869387\pi$
$30$	−3.49703	−0.638467
$31$	2.98829	0.536713	0.268357	−	0.963320i	$-0.413519\pi$
$31$	2.98829	0.536713	0.268357	+	0.963320i	$0.413519\pi$
$32$	−1.00000	−0.176777
$33$	−4.43900	−0.772731
$34$	1.00000	0.171499
$35$	−15.8892	−2.68577
$36$	1.00000	0.166667
$37$	−6.87634	−1.13046	−0.565232	−	0.824932i	$-0.691213\pi$
$37$	−6.87634	−1.13046	−0.565232	+	0.824932i	$0.691213\pi$
$38$	−7.86381	−1.27568
$39$	−0.549811	−0.0880403
$40$	−3.49703	−0.552929
$41$	7.13275	1.11395	0.556974	−	0.830530i	$-0.311962\pi$
$41$	7.13275	1.11395	0.556974	+	0.830530i	$0.311962\pi$
$42$	4.54363	0.701098
$43$	−11.0012	−1.67767	−0.838837	−	0.544383i	$-0.816764\pi$
$43$	−11.0012	−1.67767	−0.838837	+	0.544383i	$0.816764\pi$
$44$	−4.43900	−0.669205
$45$	3.49703	0.521307
$46$	0.106779	0.0157438
$47$	6.14847	0.896847	0.448423	−	0.893821i	$-0.351986\pi$
$47$	6.14847	0.896847	0.448423	+	0.893821i	$0.351986\pi$
$48$	1.00000	0.144338
$49$	13.6446	1.94923
$50$	−7.22922	−1.02237
$51$	−1.00000	−0.140028
$52$	−0.549811	−0.0762451
$53$	13.0995	1.79935	0.899677	−	0.436555i	$-0.143802\pi$
$53$	13.0995	1.79935	0.899677	+	0.436555i	$0.143802\pi$
$54$	−1.00000	−0.136083
$55$	−15.5233	−2.09317
$56$	4.54363	0.607168
$57$	7.86381	1.04159
$58$	9.87626	1.29682
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	3.49703	0.451465
$61$	−6.91367	−0.885205	−0.442603	−	0.896718i	$-0.645945\pi$
$61$	−6.91367	−0.885205	−0.442603	+	0.896718i	$0.645945\pi$
$62$	−2.98829	−0.379513
$63$	−4.54363	−0.572444
$64$	1.00000	0.125000
$65$	−1.92271	−0.238482
$66$	4.43900	0.546404
$67$	−13.4729	−1.64597	−0.822986	−	0.568061i	$-0.807694\pi$
$67$	−13.4729	−1.64597	−0.822986	+	0.568061i	$0.807694\pi$
$68$	−1.00000	−0.121268
$69$	−0.106779	−0.0128547
$70$	15.8892	1.89912
$71$	−13.7110	−1.62720	−0.813598	−	0.581428i	$-0.802494\pi$
$71$	−13.7110	−1.62720	−0.813598	+	0.581428i	$0.802494\pi$
$72$	−1.00000	−0.117851
$73$	4.03219	0.471932	0.235966	−	0.971761i	$-0.424175\pi$
$73$	4.03219	0.471932	0.235966	+	0.971761i	$0.424175\pi$
$74$	6.87634	0.799359
$75$	7.22922	0.834759
$76$	7.86381	0.902041
$77$	20.1692	2.29849
$78$	0.549811	0.0622539
$79$	−2.01574	−0.226789	−0.113394	−	0.993550i	$-0.536172\pi$
$79$	−2.01574	−0.226789	−0.113394	+	0.993550i	$0.536172\pi$
$80$	3.49703	0.390980
$81$	1.00000	0.111111
$82$	−7.13275	−0.787681
$83$	−3.43030	−0.376524	−0.188262	−	0.982119i	$-0.560285\pi$
$83$	−3.43030	−0.376524	−0.188262	+	0.982119i	$0.560285\pi$
$84$	−4.54363	−0.495751
$85$	−3.49703	−0.379306
$86$	11.0012	1.18629
$87$	−9.87626	−1.05885
$88$	4.43900	0.473199
$89$	−0.242414	−0.0256958	−0.0128479	−	0.999917i	$-0.504090\pi$
$89$	−0.242414	−0.0256958	−0.0128479	+	0.999917i	$0.504090\pi$
$90$	−3.49703	−0.368619
$91$	2.49814	0.261876
$92$	−0.106779	−0.0111325
$93$	2.98829	0.309871
$94$	−6.14847	−0.634166
$95$	27.5000	2.82144
$96$	−1.00000	−0.102062
$97$	0.142690	0.0144880	0.00724399	−	0.999974i	$-0.497694\pi$
$97$	0.142690	0.0144880	0.00724399	+	0.999974i	$0.497694\pi$
$98$	−13.6446	−1.37831
$99$	−4.43900	−0.446137
$100$	7.22922	0.722922
$101$	−4.01752	−0.399758	−0.199879	−	0.979821i	$-0.564055\pi$
$101$	−4.01752	−0.399758	−0.199879	+	0.979821i	$0.564055\pi$
$102$	1.00000	0.0990148
$103$	11.4507	1.12827	0.564136	−	0.825682i	$-0.309209\pi$
$103$	11.4507	1.12827	0.564136	+	0.825682i	$0.309209\pi$
$104$	0.549811	0.0539134
$105$	−15.8892	−1.55063
$106$	−13.0995	−1.27234
$107$	−8.12821	−0.785784	−0.392892	−	0.919585i	$-0.628525\pi$
$107$	−8.12821	−0.785784	−0.392892	+	0.919585i	$0.628525\pi$
$108$	1.00000	0.0962250
$109$	3.85341	0.369089	0.184545	−	0.982824i	$-0.440919\pi$
$109$	3.85341	0.369089	0.184545	+	0.982824i	$0.440919\pi$
$110$	15.5233	1.48009
$111$	−6.87634	−0.652674
$112$	−4.54363	−0.429333
$113$	−12.6675	−1.19166	−0.595830	−	0.803111i	$-0.703177\pi$
$113$	−12.6675	−1.19166	−0.595830	+	0.803111i	$0.703177\pi$
$114$	−7.86381	−0.736513
$115$	−0.373411	−0.0348208
$116$	−9.87626	−0.916988
$117$	−0.549811	−0.0508301
$118$	−1.00000	−0.0920575
$119$	4.54363	0.416514
$120$	−3.49703	−0.319234
$121$	8.70475	0.791341
$122$	6.91367	0.625935
$123$	7.13275	0.643139
$124$	2.98829	0.268357
$125$	7.79566	0.697265
$126$	4.54363	0.404779
$127$	−19.7922	−1.75628	−0.878138	−	0.478407i	$-0.841214\pi$
$127$	−19.7922	−1.75628	−0.878138	+	0.478407i	$0.841214\pi$
$128$	−1.00000	−0.0883883
$129$	−11.0012	−0.968606
$130$	1.92271	0.168633
$131$	−11.5248	−1.00693	−0.503463	−	0.864017i	$-0.667941\pi$
$131$	−11.5248	−1.00693	−0.503463	+	0.864017i	$0.667941\pi$
$132$	−4.43900	−0.386366
$133$	−35.7302	−3.09821
$134$	13.4729	1.16388
$135$	3.49703	0.300976
$136$	1.00000	0.0857493
$137$	−11.4144	−0.975197	−0.487598	−	0.873068i	$-0.662127\pi$
$137$	−11.4144	−0.975197	−0.487598	+	0.873068i	$0.662127\pi$
$138$	0.106779	0.00908967
$139$	11.5440	0.979146	0.489573	−	0.871962i	$-0.337153\pi$
$139$	11.5440	0.979146	0.489573	+	0.871962i	$0.337153\pi$
$140$	−15.8892	−1.34288
$141$	6.14847	0.517795
$142$	13.7110	1.15060
$143$	2.44061	0.204094
$144$	1.00000	0.0833333
$145$	−34.5376	−2.86819
$146$	−4.03219	−0.333707
$147$	13.6446	1.12539
$148$	−6.87634	−0.565232
$149$	−15.8894	−1.30171	−0.650856	−	0.759202i	$-0.725590\pi$
$149$	−15.8894	−1.30171	−0.650856	+	0.759202i	$0.725590\pi$
$150$	−7.22922	−0.590263
$151$	−20.7685	−1.69011	−0.845057	−	0.534676i	$-0.820434\pi$
$151$	−20.7685	−1.69011	−0.845057	+	0.534676i	$0.820434\pi$
$152$	−7.86381	−0.637839
$153$	−1.00000	−0.0808452
$154$	−20.1692	−1.62528
$155$	10.4501	0.839376
$156$	−0.549811	−0.0440201
$157$	−1.95157	−0.155752	−0.0778762	−	0.996963i	$-0.524814\pi$
$157$	−1.95157	−0.155752	−0.0778762	+	0.996963i	$0.524814\pi$
$158$	2.01574	0.160364
$159$	13.0995	1.03886
$160$	−3.49703	−0.276465
$161$	0.485167	0.0382365
$162$	−1.00000	−0.0785674
$163$	−11.2556	−0.881604	−0.440802	−	0.897604i	$-0.645306\pi$
$163$	−11.2556	−0.881604	−0.440802	+	0.897604i	$0.645306\pi$
$164$	7.13275	0.556974
$165$	−15.5233	−1.20849
$166$	3.43030	0.266243
$167$	−23.5704	−1.82393	−0.911966	−	0.410265i	$-0.865436\pi$
$167$	−23.5704	−1.82393	−0.911966	+	0.410265i	$0.865436\pi$
$168$	4.54363	0.350549
$169$	−12.6977	−0.976747
$170$	3.49703	0.268210
$171$	7.86381	0.601360
$172$	−11.0012	−0.838837
$173$	8.32355	0.632827	0.316414	−	0.948621i	$-0.397521\pi$
$173$	8.32355	0.632827	0.316414	+	0.948621i	$0.397521\pi$
$174$	9.87626	0.748718
$175$	−32.8469	−2.48299
$176$	−4.43900	−0.334602
$177$	1.00000	0.0751646
$178$	0.242414	0.0181697
$179$	18.3227	1.36950	0.684751	−	0.728777i	$-0.259911\pi$
$179$	18.3227	1.36950	0.684751	+	0.728777i	$0.259911\pi$
$180$	3.49703	0.260653
$181$	−17.7514	−1.31945	−0.659724	−	0.751508i	$-0.729327\pi$
$181$	−17.7514	−1.31945	−0.659724	+	0.751508i	$0.729327\pi$
$182$	−2.49814	−0.185174
$183$	−6.91367	−0.511074
$184$	0.106779	0.00787189
$185$	−24.0468	−1.76795
$186$	−2.98829	−0.219112
$187$	4.43900	0.324612
$188$	6.14847	0.448423
$189$	−4.54363	−0.330501
$190$	−27.5000	−1.99506
$191$	−10.4835	−0.758558	−0.379279	−	0.925282i	$-0.623828\pi$
$191$	−10.4835	−0.758558	−0.379279	+	0.925282i	$0.623828\pi$
$192$	1.00000	0.0721688
$193$	22.2709	1.60309	0.801547	−	0.597932i	$-0.204011\pi$
$193$	22.2709	1.60309	0.801547	+	0.597932i	$0.204011\pi$
$194$	−0.142690	−0.0102445
$195$	−1.92271	−0.137688
$196$	13.6446	0.974613
$197$	0.00114879	8.18480e−5 0	4.09240e−5	−	1.00000i	$-0.499987\pi$
$197$	0.00114879	8.18480e−5 0	4.09240e−5		1.00000i	$0.499987\pi$
$198$	4.43900	0.315466
$199$	7.73765	0.548507	0.274254	−	0.961657i	$-0.411569\pi$
$199$	7.73765	0.548507	0.274254	+	0.961657i	$0.411569\pi$
$200$	−7.22922	−0.511183
$201$	−13.4729	−0.950303
$202$	4.01752	0.282672
$203$	44.8741	3.14954
$204$	−1.00000	−0.0700140
$205$	24.9435	1.74213
$206$	−11.4507	−0.797809
$207$	−0.106779	−0.00742169
$208$	−0.549811	−0.0381226
$209$	−34.9075	−2.41460
$210$	15.8892	1.09646
$211$	−7.53974	−0.519057	−0.259529	−	0.965735i	$-0.583567\pi$
$211$	−7.53974	−0.519057	−0.259529	+	0.965735i	$0.583567\pi$
$212$	13.0995	0.899677
$213$	−13.7110	−0.939462
$214$	8.12821	0.555633
$215$	−38.4717	−2.62375
$216$	−1.00000	−0.0680414
$217$	−13.5777	−0.921714
$218$	−3.85341	−0.260986
$219$	4.03219	0.272470
$220$	−15.5233	−1.04658
$221$	0.549811	0.0369843
$222$	6.87634	0.461510
$223$	−11.3959	−0.763125	−0.381562	−	0.924343i	$-0.624614\pi$
$223$	−11.3959	−0.763125	−0.381562	+	0.924343i	$0.624614\pi$
$224$	4.54363	0.303584
$225$	7.22922	0.481948
$226$	12.6675	0.842631
$227$	−27.1548	−1.80232	−0.901162	−	0.433482i	$-0.857285\pi$
$227$	−27.1548	−1.80232	−0.901162	+	0.433482i	$0.857285\pi$
$228$	7.86381	0.520793
$229$	21.2799	1.40622	0.703108	−	0.711083i	$-0.251795\pi$
$229$	21.2799	1.40622	0.703108	+	0.711083i	$0.251795\pi$
$230$	0.373411	0.0246220
$231$	20.1692	1.32704
$232$	9.87626	0.648408
$233$	−8.95969	−0.586969	−0.293484	−	0.955964i	$-0.594815\pi$
$233$	−8.95969	−0.586969	−0.293484	+	0.955964i	$0.594815\pi$
$234$	0.549811	0.0359423
$235$	21.5014	1.40260
$236$	1.00000	0.0650945
$237$	−2.01574	−0.130937
$238$	−4.54363	−0.294520
$239$	3.80631	0.246210	0.123105	−	0.992394i	$-0.460715\pi$
$239$	3.80631	0.246210	0.123105	+	0.992394i	$0.460715\pi$
$240$	3.49703	0.225732
$241$	−3.69048	−0.237725	−0.118862	−	0.992911i	$-0.537925\pi$
$241$	−3.69048	−0.237725	−0.118862	+	0.992911i	$0.537925\pi$
$242$	−8.70475	−0.559563
$243$	1.00000	0.0641500
$244$	−6.91367	−0.442603
$245$	47.7155	3.04843
$246$	−7.13275	−0.454768
$247$	−4.32361	−0.275105
$248$	−2.98829	−0.189757
$249$	−3.43030	−0.217387
$250$	−7.79566	−0.493041
$251$	29.3558	1.85292	0.926462	−	0.376387i	$-0.122834\pi$
$251$	29.3558	1.85292	0.926462	+	0.376387i	$0.122834\pi$
$252$	−4.54363	−0.286222
$253$	0.473994	0.0297998
$254$	19.7922	1.24187
$255$	−3.49703	−0.218993
$256$	1.00000	0.0625000
$257$	5.58117	0.348144	0.174072	−	0.984733i	$-0.444307\pi$
$257$	5.58117	0.348144	0.174072	+	0.984733i	$0.444307\pi$
$258$	11.0012	0.684908
$259$	31.2436	1.94138
$260$	−1.92271	−0.119241
$261$	−9.87626	−0.611325
$262$	11.5248	0.712005
$263$	−26.5801	−1.63900	−0.819500	−	0.573079i	$-0.805749\pi$
$263$	−26.5801	−1.63900	−0.819500	+	0.573079i	$0.805749\pi$
$264$	4.43900	0.273202
$265$	45.8094	2.81405
$266$	35.7302	2.19076
$267$	−0.242414	−0.0148355
$268$	−13.4729	−0.822986
$269$	8.38333	0.511141	0.255570	−	0.966790i	$-0.417737\pi$
$269$	8.38333	0.511141	0.255570	+	0.966790i	$0.417737\pi$
$270$	−3.49703	−0.212822
$271$	−12.9011	−0.783683	−0.391842	−	0.920033i	$-0.628162\pi$
$271$	−12.9011	−0.783683	−0.391842	+	0.920033i	$0.628162\pi$
$272$	−1.00000	−0.0606339
$273$	2.49814	0.151194
$274$	11.4144	0.689568
$275$	−32.0905	−1.93513
$276$	−0.106779	−0.00642737
$277$	21.8402	1.31225	0.656126	−	0.754651i	$-0.272194\pi$
$277$	21.8402	1.31225	0.656126	+	0.754651i	$0.272194\pi$
$278$	−11.5440	−0.692361
$279$	2.98829	0.178904
$280$	15.8892	0.949562
$281$	7.04426	0.420225	0.210113	−	0.977677i	$-0.432617\pi$
$281$	7.04426	0.420225	0.210113	+	0.977677i	$0.432617\pi$
$282$	−6.14847	−0.366136
$283$	14.5750	0.866394	0.433197	−	0.901299i	$-0.357385\pi$
$283$	14.5750	0.866394	0.433197	+	0.901299i	$0.357385\pi$
$284$	−13.7110	−0.813598
$285$	27.5000	1.62896
$286$	−2.44061	−0.144317
$287$	−32.4086	−1.91302
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	34.5376	2.02812
$291$	0.142690	0.00836464
$292$	4.03219	0.235966
$293$	1.00168	0.0585186	0.0292593	−	0.999572i	$-0.490685\pi$
$293$	1.00168	0.0585186	0.0292593	+	0.999572i	$0.490685\pi$
$294$	−13.6446	−0.795768
$295$	3.49703	0.203605
$296$	6.87634	0.399679
$297$	−4.43900	−0.257577
$298$	15.8894	0.920449
$299$	0.0587086	0.00339520
$300$	7.22922	0.417379
$301$	49.9856	2.88112
$302$	20.7685	1.19509
$303$	−4.01752	−0.230800
$304$	7.86381	0.451020
$305$	−24.1773	−1.38439
$306$	1.00000	0.0571662
$307$	3.84621	0.219515	0.109758	−	0.993958i	$-0.464993\pi$
$307$	3.84621	0.219515	0.109758	+	0.993958i	$0.464993\pi$
$308$	20.1692	1.14925
$309$	11.4507	0.651409
$310$	−10.4501	−0.593529
$311$	2.74079	0.155416	0.0777079	−	0.996976i	$-0.475240\pi$
$311$	2.74079	0.155416	0.0777079	+	0.996976i	$0.475240\pi$
$312$	0.549811	0.0311269
$313$	10.1837	0.575617	0.287809	−	0.957688i	$-0.407073\pi$
$313$	10.1837	0.575617	0.287809	+	0.957688i	$0.407073\pi$
$314$	1.95157	0.110134
$315$	−15.8892	−0.895256
$316$	−2.01574	−0.113394
$317$	21.0229	1.18076	0.590381	−	0.807125i	$-0.298978\pi$
$317$	21.0229	1.18076	0.590381	+	0.807125i	$0.298978\pi$
$318$	−13.0995	−0.734584
$319$	43.8408	2.45461
$320$	3.49703	0.195490
$321$	−8.12821	−0.453673
$322$	−0.485167	−0.0270373
$323$	−7.86381	−0.437554
$324$	1.00000	0.0555556
$325$	−3.97471	−0.220477
$326$	11.2556	0.623388
$327$	3.85341	0.213094
$328$	−7.13275	−0.393840
$329$	−27.9364	−1.54018
$330$	15.5233	0.854531
$331$	6.16842	0.339047	0.169524	−	0.985526i	$-0.445777\pi$
$331$	6.16842	0.339047	0.169524	+	0.985526i	$0.445777\pi$
$332$	−3.43030	−0.188262
$333$	−6.87634	−0.376821
$334$	23.5704	1.28972
$335$	−47.1150	−2.57417
$336$	−4.54363	−0.247875
$337$	−17.1161	−0.932373	−0.466186	−	0.884687i	$-0.654372\pi$
$337$	−17.1161	−0.932373	−0.466186	+	0.884687i	$0.654372\pi$
$338$	12.6977	0.690664
$339$	−12.6675	−0.688005
$340$	−3.49703	−0.189653
$341$	−13.2650	−0.718342
$342$	−7.86381	−0.425226
$343$	−30.1905	−1.63014
$344$	11.0012	0.593147
$345$	−0.373411	−0.0201038
$346$	−8.32355	−0.447477
$347$	−31.0317	−1.66587	−0.832935	−	0.553371i	$-0.813341\pi$
$347$	−31.0317	−1.66587	−0.832935	+	0.553371i	$0.813341\pi$
$348$	−9.87626	−0.529423
$349$	0.644419	0.0344949	0.0172475	−	0.999851i	$-0.494510\pi$
$349$	0.644419	0.0344949	0.0172475	+	0.999851i	$0.494510\pi$
$350$	32.8469	1.75574
$351$	−0.549811	−0.0293468
$352$	4.43900	0.236600
$353$	−15.5533	−0.827819	−0.413909	−	0.910318i	$-0.635837\pi$
$353$	−15.5533	−0.827819	−0.413909	+	0.910318i	$0.635837\pi$
$354$	−1.00000	−0.0531494
$355$	−47.9478	−2.54480
$356$	−0.242414	−0.0128479
$357$	4.54363	0.240474
$358$	−18.3227	−0.968384
$359$	33.6438	1.77565	0.887826	−	0.460179i	$-0.152215\pi$
$359$	33.6438	1.77565	0.887826	+	0.460179i	$0.152215\pi$
$360$	−3.49703	−0.184310
$361$	42.8395	2.25471
$362$	17.7514	0.932991
$363$	8.70475	0.456881
$364$	2.49814	0.130938
$365$	14.1007	0.738064
$366$	6.91367	0.361384
$367$	−8.40764	−0.438875	−0.219438	−	0.975627i	$-0.570422\pi$
$367$	−8.40764	−0.438875	−0.219438	+	0.975627i	$0.570422\pi$
$368$	−0.106779	−0.00556626
$369$	7.13275	0.371316
$370$	24.0468	1.25013
$371$	−59.5193	−3.09009
$372$	2.98829	0.154936
$373$	−4.69009	−0.242844	−0.121422	−	0.992601i	$-0.538745\pi$
$373$	−4.69009	−0.242844	−0.121422	+	0.992601i	$0.538745\pi$
$374$	−4.43900	−0.229535
$375$	7.79566	0.402566
$376$	−6.14847	−0.317083
$377$	5.43008	0.279663
$378$	4.54363	0.233699
$379$	0.347165	0.0178327	0.00891633	−	0.999960i	$-0.497162\pi$
$379$	0.347165	0.0178327	0.00891633	+	0.999960i	$0.497162\pi$
$380$	27.5000	1.41072
$381$	−19.7922	−1.01399
$382$	10.4835	0.536382
$383$	−6.55251	−0.334818	−0.167409	−	0.985888i	$-0.553540\pi$
$383$	−6.55251	−0.334818	−0.167409	+	0.985888i	$0.553540\pi$
$384$	−1.00000	−0.0510310
$385$	70.5323	3.59466
$386$	−22.2709	−1.13356
$387$	−11.0012	−0.559225
$388$	0.142690	0.00724399
$389$	−23.6612	−1.19967	−0.599835	−	0.800124i	$-0.704767\pi$
$389$	−23.6612	−1.19967	−0.599835	+	0.800124i	$0.704767\pi$
$390$	1.92271	0.0973600
$391$	0.106779	0.00540007
$392$	−13.6446	−0.689156
$393$	−11.5248	−0.581349
$394$	−0.00114879	−5.78753e−5 0
$395$	−7.04912	−0.354680
$396$	−4.43900	−0.223068
$397$	−29.4955	−1.48033	−0.740167	−	0.672423i	$-0.765254\pi$
$397$	−29.4955	−1.48033	−0.740167	+	0.672423i	$0.765254\pi$
$398$	−7.73765	−0.387853
$399$	−35.7302	−1.78875
$400$	7.22922	0.361461
$401$	15.7260	0.785320	0.392660	−	0.919684i	$-0.371555\pi$
$401$	15.7260	0.785320	0.392660	+	0.919684i	$0.371555\pi$
$402$	13.4729	0.671965
$403$	−1.64300	−0.0818435
$404$	−4.01752	−0.199879
$405$	3.49703	0.173769
$406$	−44.8741	−2.22706
$407$	30.5241	1.51302
$408$	1.00000	0.0495074
$409$	31.1286	1.53921	0.769606	−	0.638519i	$-0.220453\pi$
$409$	31.1286	1.53921	0.769606	+	0.638519i	$0.220453\pi$
$410$	−24.9435	−1.23187
$411$	−11.4144	−0.563030
$412$	11.4507	0.564136
$413$	−4.54363	−0.223577
$414$	0.106779	0.00524792
$415$	−11.9959	−0.588854
$416$	0.549811	0.0269567
$417$	11.5440	0.565310
$418$	34.9075	1.70738
$419$	−25.0841	−1.22544	−0.612718	−	0.790301i	$-0.709924\pi$
$419$	−25.0841	−1.22544	−0.612718	+	0.790301i	$0.709924\pi$
$420$	−15.8892	−0.775314
$421$	25.7424	1.25461	0.627305	−	0.778774i	$-0.284158\pi$
$421$	25.7424	1.25461	0.627305	+	0.778774i	$0.284158\pi$
$422$	7.53974	0.367029
$423$	6.14847	0.298949
$424$	−13.0995	−0.636168
$425$	−7.22922	−0.350669
$426$	13.7110	0.664300
$427$	31.4132	1.52019
$428$	−8.12821	−0.392892
$429$	2.44061	0.117834
$430$	38.4717	1.85527
$431$	−16.8356	−0.810944	−0.405472	−	0.914107i	$-0.632893\pi$
$431$	−16.8356	−0.810944	−0.405472	+	0.914107i	$0.632893\pi$
$432$	1.00000	0.0481125
$433$	15.6481	0.752001	0.376001	−	0.926619i	$-0.377299\pi$
$433$	15.6481	0.752001	0.376001	+	0.926619i	$0.377299\pi$
$434$	13.5777	0.651750
$435$	−34.5376	−1.65595
$436$	3.85341	0.184545
$437$	−0.839693	−0.0401680
$438$	−4.03219	−0.192666
$439$	13.1713	0.628633	0.314317	−	0.949318i	$-0.398225\pi$
$439$	13.1713	0.628633	0.314317	+	0.949318i	$0.398225\pi$
$440$	15.5233	0.740046
$441$	13.6446	0.649742
$442$	−0.549811	−0.0261519
$443$	−39.6436	−1.88352	−0.941761	−	0.336282i	$-0.890830\pi$
$443$	−39.6436	−1.88352	−0.941761	+	0.336282i	$0.890830\pi$
$444$	−6.87634	−0.326337
$445$	−0.847729	−0.0401862
$446$	11.3959	0.539611
$447$	−15.8894	−0.751543
$448$	−4.54363	−0.214666
$449$	−17.8751	−0.843579	−0.421789	−	0.906694i	$-0.638598\pi$
$449$	−17.8751	−0.843579	−0.421789	+	0.906694i	$0.638598\pi$
$450$	−7.22922	−0.340789
$451$	−31.6623	−1.49092
$452$	−12.6675	−0.595830
$453$	−20.7685	−0.975788
$454$	27.1548	1.27444
$455$	8.73607	0.409553
$456$	−7.86381	−0.368257
$457$	35.3211	1.65225	0.826126	−	0.563486i	$-0.190540\pi$
$457$	35.3211	1.65225	0.826126	+	0.563486i	$0.190540\pi$
$458$	−21.2799	−0.994344
$459$	−1.00000	−0.0466760
$460$	−0.373411	−0.0174104
$461$	−22.0633	−1.02759	−0.513795	−	0.857913i	$-0.671761\pi$
$461$	−22.0633	−1.02759	−0.513795	+	0.857913i	$0.671761\pi$
$462$	−20.1692	−0.938356
$463$	−22.0904	−1.02663	−0.513315	−	0.858200i	$-0.671583\pi$
$463$	−22.0904	−1.02663	−0.513315	+	0.858200i	$0.671583\pi$
$464$	−9.87626	−0.458494
$465$	10.4501	0.484614
$466$	8.95969	0.415050
$467$	0.985515	0.0456042	0.0228021	−	0.999740i	$-0.492741\pi$
$467$	0.985515	0.0456042	0.0228021	+	0.999740i	$0.492741\pi$
$468$	−0.549811	−0.0254150
$469$	61.2157	2.82668
$470$	−21.5014	−0.991785
$471$	−1.95157	−0.0899236
$472$	−1.00000	−0.0460287
$473$	48.8346	2.24542
$474$	2.01574	0.0925862
$475$	56.8492	2.60842
$476$	4.54363	0.208257
$477$	13.0995	0.599785
$478$	−3.80631	−0.174097
$479$	−5.15309	−0.235451	−0.117725	−	0.993046i	$-0.537560\pi$
$479$	−5.15309	−0.235451	−0.117725	+	0.993046i	$0.537560\pi$
$480$	−3.49703	−0.159617
$481$	3.78069	0.172385
$482$	3.69048	0.168097
$483$	0.485167	0.0220758
$484$	8.70475	0.395671
$485$	0.498991	0.0226580
$486$	−1.00000	−0.0453609
$487$	10.4063	0.471555	0.235778	−	0.971807i	$-0.424236\pi$
$487$	10.4063	0.471555	0.235778	+	0.971807i	$0.424236\pi$
$488$	6.91367	0.312967
$489$	−11.2556	−0.508994
$490$	−47.7155	−2.15557
$491$	16.8014	0.758237	0.379119	−	0.925348i	$-0.376227\pi$
$491$	16.8014	0.758237	0.379119	+	0.925348i	$0.376227\pi$
$492$	7.13275	0.321569
$493$	9.87626	0.444805
$494$	4.32361	0.194528
$495$	−15.5233	−0.697722
$496$	2.98829	0.134178
$497$	62.2977	2.79443
$498$	3.43030	0.153715
$499$	24.3768	1.09125	0.545627	−	0.838028i	$-0.316292\pi$
$499$	24.3768	1.09125	0.545627	+	0.838028i	$0.316292\pi$
$500$	7.79566	0.348632
$501$	−23.5704	−1.05305
$502$	−29.3558	−1.31022
$503$	37.6036	1.67666	0.838332	−	0.545161i	$-0.183531\pi$
$503$	37.6036	1.67666	0.838332	+	0.545161i	$0.183531\pi$
$504$	4.54363	0.202389
$505$	−14.0494	−0.625190
$506$	−0.473994	−0.0210716
$507$	−12.6977	−0.563925
$508$	−19.7922	−0.878138
$509$	−25.3321	−1.12283	−0.561413	−	0.827536i	$-0.689742\pi$
$509$	−25.3321	−1.12283	−0.561413	+	0.827536i	$0.689742\pi$
$510$	3.49703	0.154851
$511$	−18.3208	−0.810464
$512$	−1.00000	−0.0441942
$513$	7.86381	0.347196
$514$	−5.58117	−0.246175
$515$	40.0435	1.76453
$516$	−11.0012	−0.484303
$517$	−27.2931	−1.20035
$518$	−31.2436	−1.37276
$519$	8.32355	0.365363
$520$	1.92271	0.0843163
$521$	34.0247	1.49065	0.745324	−	0.666702i	$-0.232295\pi$
$521$	34.0247	1.49065	0.745324	+	0.666702i	$0.232295\pi$
$522$	9.87626	0.432272
$523$	11.1201	0.486250	0.243125	−	0.969995i	$-0.421827\pi$
$523$	11.1201	0.486250	0.243125	+	0.969995i	$0.421827\pi$
$524$	−11.5248	−0.503463
$525$	−32.8469	−1.43356
$526$	26.5801	1.15895
$527$	−2.98829	−0.130172
$528$	−4.43900	−0.193183
$529$	−22.9886	−0.999504
$530$	−45.8094	−1.98983
$531$	1.00000	0.0433963
$532$	−35.7302	−1.54910
$533$	−3.92167	−0.169866
$534$	0.242414	0.0104903
$535$	−28.4246	−1.22890
$536$	13.4729	0.581939
$537$	18.3227	0.790682
$538$	−8.38333	−0.361431
$539$	−60.5684	−2.60886
$540$	3.49703	0.150488
$541$	−15.1854	−0.652871	−0.326436	−	0.945219i	$-0.605848\pi$
$541$	−15.1854	−0.652871	−0.326436	+	0.945219i	$0.605848\pi$
$542$	12.9011	0.554148
$543$	−17.7514	−0.761784
$544$	1.00000	0.0428746
$545$	13.4755	0.577226
$546$	−2.49814	−0.106911
$547$	28.1806	1.20492	0.602458	−	0.798150i	$-0.294188\pi$
$547$	28.1806	1.20492	0.602458	+	0.798150i	$0.294188\pi$
$548$	−11.4144	−0.487598
$549$	−6.91367	−0.295068
$550$	32.0905	1.36835
$551$	−77.6650	−3.30864
$552$	0.106779	0.00454484
$553$	9.15880	0.389472
$554$	−21.8402	−0.927902
$555$	−24.0468	−1.02073
$556$	11.5440	0.489573
$557$	41.4024	1.75428	0.877138	−	0.480239i	$-0.159450\pi$
$557$	41.4024	1.75428	0.877138	+	0.480239i	$0.159450\pi$
$558$	−2.98829	−0.126504
$559$	6.04861	0.255829
$560$	−15.8892	−0.671442
$561$	4.43900	0.187415
$562$	−7.04426	−0.297144
$563$	41.5417	1.75078	0.875388	−	0.483421i	$-0.160606\pi$
$563$	41.5417	1.75078	0.875388	+	0.483421i	$0.160606\pi$
$564$	6.14847	0.258897
$565$	−44.2987	−1.86366
$566$	−14.5750	−0.612633
$567$	−4.54363	−0.190815
$568$	13.7110	0.575301
$569$	28.8197	1.20819	0.604093	−	0.796914i	$-0.293536\pi$
$569$	28.8197	1.20819	0.604093	+	0.796914i	$0.293536\pi$
$570$	−27.5000	−1.15185
$571$	−8.78426	−0.367610	−0.183805	−	0.982963i	$-0.558841\pi$
$571$	−8.78426	−0.367610	−0.183805	+	0.982963i	$0.558841\pi$
$572$	2.44061	0.102047
$573$	−10.4835	−0.437954
$574$	32.4086	1.35271
$575$	−0.771932	−0.0321918
$576$	1.00000	0.0416667
$577$	20.1421	0.838525	0.419263	−	0.907865i	$-0.362289\pi$
$577$	20.1421	0.838525	0.419263	+	0.907865i	$0.362289\pi$
$578$	−1.00000	−0.0415945
$579$	22.2709	0.925547
$580$	−34.5376	−1.43410
$581$	15.5860	0.646617
$582$	−0.142690	−0.00591469
$583$	−58.1487	−2.40827
$584$	−4.03219	−0.166853
$585$	−1.92271	−0.0794941
$586$	−1.00168	−0.0413789
$587$	−15.6295	−0.645097	−0.322548	−	0.946553i	$-0.604540\pi$
$587$	−15.6295	−0.645097	−0.322548	+	0.946553i	$0.604540\pi$
$588$	13.6446	0.562693
$589$	23.4994	0.968274
$590$	−3.49703	−0.143970
$591$	0.00114879	4.72549e−5 0
$592$	−6.87634	−0.282616
$593$	12.5128	0.513841	0.256921	−	0.966433i	$-0.417292\pi$
$593$	12.5128	0.513841	0.256921	+	0.966433i	$0.417292\pi$
$594$	4.43900	0.182135
$595$	15.8892	0.651394
$596$	−15.8894	−0.650856
$597$	7.73765	0.316681
$598$	−0.0587086	−0.00240077
$599$	20.2320	0.826657	0.413328	−	0.910582i	$-0.364366\pi$
$599$	20.2320	0.826657	0.413328	+	0.910582i	$0.364366\pi$
$600$	−7.22922	−0.295132
$601$	18.9160	0.771600	0.385800	−	0.922582i	$-0.373925\pi$
$601$	18.9160	0.771600	0.385800	+	0.922582i	$0.373925\pi$
$602$	−49.9856	−2.03726
$603$	−13.4729	−0.548657
$604$	−20.7685	−0.845057
$605$	30.4408	1.23759
$606$	4.01752	0.163201
$607$	−38.6728	−1.56968	−0.784841	−	0.619697i	$-0.787255\pi$
$607$	−38.6728	−1.56968	−0.784841	+	0.619697i	$0.787255\pi$
$608$	−7.86381	−0.318920
$609$	44.8741	1.81839
$610$	24.1773	0.978912
$611$	−3.38050	−0.136760
$612$	−1.00000	−0.0404226
$613$	7.81414	0.315610	0.157805	−	0.987470i	$-0.449558\pi$
$613$	7.81414	0.315610	0.157805	+	0.987470i	$0.449558\pi$
$614$	−3.84621	−0.155221
$615$	24.9435	1.00582
$616$	−20.1692	−0.812640
$617$	−30.2985	−1.21977	−0.609885	−	0.792490i	$-0.708784\pi$
$617$	−30.2985	−1.21977	−0.609885	+	0.792490i	$0.708784\pi$
$618$	−11.4507	−0.460615
$619$	24.0852	0.968065	0.484033	−	0.875050i	$-0.339172\pi$
$619$	24.0852	0.968065	0.484033	+	0.875050i	$0.339172\pi$
$620$	10.4501	0.419688
$621$	−0.106779	−0.00428491
$622$	−2.74079	−0.109896
$623$	1.10144	0.0441282
$624$	−0.549811	−0.0220101
$625$	−8.88446	−0.355378
$626$	−10.1837	−0.407023
$627$	−34.9075	−1.39407
$628$	−1.95157	−0.0778762
$629$	6.87634	0.274178
$630$	15.8892	0.633042
$631$	−14.8283	−0.590307	−0.295153	−	0.955450i	$-0.595371\pi$
$631$	−14.8283	−0.590307	−0.295153	+	0.955450i	$0.595371\pi$
$632$	2.01574	0.0801820
$633$	−7.53974	−0.299678
$634$	−21.0229	−0.834924
$635$	−69.2140	−2.74667
$636$	13.0995	0.519429
$637$	−7.50195	−0.297238
$638$	−43.8408	−1.73567
$639$	−13.7110	−0.542399
$640$	−3.49703	−0.138232
$641$	−43.3697	−1.71300	−0.856501	−	0.516146i	$-0.827366\pi$
$641$	−43.3697	−1.71300	−0.856501	+	0.516146i	$0.827366\pi$
$642$	8.12821	0.320795
$643$	−4.37166	−0.172401	−0.0862006	−	0.996278i	$-0.527473\pi$
$643$	−4.37166	−0.172401	−0.0862006	+	0.996278i	$0.527473\pi$
$644$	0.485167	0.0191182
$645$	−38.4717	−1.51482
$646$	7.86381	0.309397
$647$	21.7143	0.853676	0.426838	−	0.904328i	$-0.359627\pi$
$647$	21.7143	0.853676	0.426838	+	0.904328i	$0.359627\pi$
$648$	−1.00000	−0.0392837
$649$	−4.43900	−0.174246
$650$	3.97471	0.155901
$651$	−13.5777	−0.532152
$652$	−11.2556	−0.440802
$653$	−39.7397	−1.55513	−0.777567	−	0.628800i	$-0.783546\pi$
$653$	−39.7397	−1.55513	−0.777567	+	0.628800i	$0.783546\pi$
$654$	−3.85341	−0.150680
$655$	−40.3026	−1.57475
$656$	7.13275	0.278487
$657$	4.03219	0.157311
$658$	27.9364	1.08907
$659$	20.2193	0.787630	0.393815	−	0.919190i	$-0.371155\pi$
$659$	20.2193	0.787630	0.393815	+	0.919190i	$0.371155\pi$
$660$	−15.5233	−0.604245
$661$	17.0555	0.663384	0.331692	−	0.943388i	$-0.392381\pi$
$661$	17.0555	0.663384	0.331692	+	0.943388i	$0.392381\pi$
$662$	−6.16842	−0.239743
$663$	0.549811	0.0213529
$664$	3.43030	0.133122
$665$	−124.950	−4.84534
$666$	6.87634	0.266453
$667$	1.05458	0.0408336
$668$	−23.5704	−0.911966
$669$	−11.3959	−0.440590
$670$	47.1150	1.82021
$671$	30.6898	1.18477
$672$	4.54363	0.175274
$673$	4.03032	0.155357	0.0776786	−	0.996978i	$-0.475249\pi$
$673$	4.03032	0.155357	0.0776786	+	0.996978i	$0.475249\pi$
$674$	17.1161	0.659287
$675$	7.22922	0.278253
$676$	−12.6977	−0.488373
$677$	−8.48311	−0.326033	−0.163016	−	0.986623i	$-0.552122\pi$
$677$	−8.48311	−0.326033	−0.163016	+	0.986623i	$0.552122\pi$
$678$	12.6675	0.486493
$679$	−0.648331	−0.0248807
$680$	3.49703	0.134105
$681$	−27.1548	−1.04057
$682$	13.2650	0.507945
$683$	−6.63614	−0.253925	−0.126962	−	0.991908i	$-0.540523\pi$
$683$	−6.63614	−0.253925	−0.126962	+	0.991908i	$0.540523\pi$
$684$	7.86381	0.300680
$685$	−39.9165	−1.52513
$686$	30.1905	1.15268
$687$	21.2799	0.811879
$688$	−11.0012	−0.419419
$689$	−7.20225	−0.274384
$690$	0.373411	0.0142155
$691$	42.8448	1.62989	0.814946	−	0.579537i	$-0.196766\pi$
$691$	42.8448	1.62989	0.814946	+	0.579537i	$0.196766\pi$
$692$	8.32355	0.316414
$693$	20.1692	0.766164
$694$	31.0317	1.17795
$695$	40.3696	1.53131
$696$	9.87626	0.374359
$697$	−7.13275	−0.270172
$698$	−0.644419	−0.0243916
$699$	−8.95969	−0.338887
$700$	−32.8469	−1.24150
$701$	10.4930	0.396315	0.198157	−	0.980170i	$-0.436504\pi$
$701$	10.4930	0.396315	0.198157	+	0.980170i	$0.436504\pi$
$702$	0.549811	0.0207513
$703$	−54.0742	−2.03945
$704$	−4.43900	−0.167301
$705$	21.5014	0.809789
$706$	15.5533	0.585356
$707$	18.2541	0.686517
$708$	1.00000	0.0375823
$709$	36.8084	1.38237	0.691184	−	0.722678i	$-0.257089\pi$
$709$	36.8084	1.38237	0.691184	+	0.722678i	$0.257089\pi$
$710$	47.9478	1.79945
$711$	−2.01574	−0.0755963
$712$	0.242414	0.00908484
$713$	−0.319088	−0.0119499
$714$	−4.54363	−0.170041
$715$	8.53490	0.319187
$716$	18.3227	0.684751
$717$	3.80631	0.142149
$718$	−33.6438	−1.25558
$719$	−43.7664	−1.63221	−0.816106	−	0.577903i	$-0.803871\pi$
$719$	−43.7664	−1.63221	−0.816106	+	0.577903i	$0.803871\pi$
$720$	3.49703	0.130327
$721$	−52.0278	−1.93762
$722$	−42.8395	−1.59432
$723$	−3.69048	−0.137250
$724$	−17.7514	−0.659724
$725$	−71.3977	−2.65164
$726$	−8.70475	−0.323064
$727$	46.1130	1.71024	0.855118	−	0.518433i	$-0.173484\pi$
$727$	46.1130	1.71024	0.855118	+	0.518433i	$0.173484\pi$
$728$	−2.49814	−0.0925872
$729$	1.00000	0.0370370
$730$	−14.1007	−0.521890
$731$	11.0012	0.406896
$732$	−6.91367	−0.255537
$733$	14.3130	0.528663	0.264331	−	0.964432i	$-0.414849\pi$
$733$	14.3130	0.528663	0.264331	+	0.964432i	$0.414849\pi$
$734$	8.40764	0.310332
$735$	47.7155	1.76001
$736$	0.106779	0.00393594
$737$	59.8061	2.20299
$738$	−7.13275	−0.262560
$739$	17.2210	0.633487	0.316743	−	0.948511i	$-0.397411\pi$
$739$	17.2210	0.633487	0.316743	+	0.948511i	$0.397411\pi$
$740$	−24.0468	−0.883977
$741$	−4.32361	−0.158832
$742$	59.5193	2.18502
$743$	−25.0469	−0.918883	−0.459441	−	0.888208i	$-0.651950\pi$
$743$	−25.0469	−0.918883	−0.459441	+	0.888208i	$0.651950\pi$
$744$	−2.98829	−0.109556
$745$	−55.5657	−2.03577
$746$	4.69009	0.171716
$747$	−3.43030	−0.125508
$748$	4.43900	0.162306
$749$	36.9316	1.34945
$750$	−7.79566	−0.284657
$751$	−24.8091	−0.905298	−0.452649	−	0.891689i	$-0.649521\pi$
$751$	−24.8091	−0.905298	−0.452649	+	0.891689i	$0.649521\pi$
$752$	6.14847	0.224212
$753$	29.3558	1.06979
$754$	−5.43008	−0.197752
$755$	−72.6280	−2.64320
$756$	−4.54363	−0.165250
$757$	10.2790	0.373597	0.186798	−	0.982398i	$-0.440189\pi$
$757$	10.2790	0.373597	0.186798	+	0.982398i	$0.440189\pi$
$758$	−0.347165	−0.0126096
$759$	0.473994	0.0172049
$760$	−27.5000	−0.997529
$761$	−46.0792	−1.67037	−0.835185	−	0.549969i	$-0.814640\pi$
$761$	−46.0792	−1.67037	−0.835185	+	0.549969i	$0.814640\pi$
$762$	19.7922	0.716997
$763$	−17.5085	−0.633849
$764$	−10.4835	−0.379279
$765$	−3.49703	−0.126435
$766$	6.55251	0.236752
$767$	−0.549811	−0.0198525
$768$	1.00000	0.0360844
$769$	12.4170	0.447769	0.223884	−	0.974616i	$-0.428126\pi$
$769$	12.4170	0.447769	0.223884	+	0.974616i	$0.428126\pi$
$770$	−70.5323	−2.54181
$771$	5.58117	0.201001
$772$	22.2709	0.801547
$773$	−5.23743	−0.188377	−0.0941887	−	0.995554i	$-0.530026\pi$
$773$	−5.23743	−0.188377	−0.0941887	+	0.995554i	$0.530026\pi$
$774$	11.0012	0.395432
$775$	21.6030	0.776004
$776$	−0.142690	−0.00512227
$777$	31.2436	1.12086
$778$	23.6612	0.848295
$779$	56.0906	2.00965
$780$	−1.92271	−0.0688440
$781$	60.8632	2.17785
$782$	−0.106779	−0.00381843
$783$	−9.87626	−0.352949
$784$	13.6446	0.487307
$785$	−6.82470	−0.243584
$786$	11.5248	0.411076
$787$	−32.7170	−1.16624	−0.583118	−	0.812387i	$-0.698168\pi$
$787$	−32.7170	−1.16624	−0.583118	+	0.812387i	$0.698168\pi$
$788$	0.00114879	4.09240e−5 0
$789$	−26.5801	−0.946277
$790$	7.04912	0.250796
$791$	57.5565	2.04648
$792$	4.43900	0.157733
$793$	3.80122	0.134985
$794$	29.4955	1.04675
$795$	45.8094	1.62469
$796$	7.73765	0.274254
$797$	−48.0116	−1.70066	−0.850330	−	0.526250i	$-0.823598\pi$
$797$	−48.0116	−1.70066	−0.850330	+	0.526250i	$0.823598\pi$
$798$	35.7302	1.26484
$799$	−6.14847	−0.217517
$800$	−7.22922	−0.255592
$801$	−0.242414	−0.00856527
$802$	−15.7260	−0.555305
$803$	−17.8989	−0.631639
$804$	−13.4729	−0.475151
$805$	1.69664	0.0597988
$806$	1.64300	0.0578721
$807$	8.38333	0.295107
$808$	4.01752	0.141336
$809$	−14.5106	−0.510167	−0.255083	−	0.966919i	$-0.582103\pi$
$809$	−14.5106	−0.510167	−0.255083	+	0.966919i	$0.582103\pi$
$810$	−3.49703	−0.122873
$811$	−29.4819	−1.03525	−0.517624	−	0.855608i	$-0.673183\pi$
$811$	−29.4819	−1.03525	−0.517624	+	0.855608i	$0.673183\pi$
$812$	44.8741	1.57477
$813$	−12.9011	−0.452460
$814$	−30.5241	−1.06987
$815$	−39.3610	−1.37876
$816$	−1.00000	−0.0350070
$817$	−86.5117	−3.02666
$818$	−31.1286	−1.08839
$819$	2.49814	0.0872921
$820$	24.9435	0.871063
$821$	46.5662	1.62517	0.812586	−	0.582841i	$-0.198059\pi$
$821$	46.5662	1.62517	0.812586	+	0.582841i	$0.198059\pi$
$822$	11.4144	0.398122
$823$	−2.48852	−0.0867443	−0.0433721	−	0.999059i	$-0.513810\pi$
$823$	−2.48852	−0.0867443	−0.0433721	+	0.999059i	$0.513810\pi$
$824$	−11.4507	−0.398905
$825$	−32.0905	−1.11725
$826$	4.54363	0.158093
$827$	11.6229	0.404169	0.202085	−	0.979368i	$-0.435228\pi$
$827$	11.6229	0.404169	0.202085	+	0.979368i	$0.435228\pi$
$828$	−0.106779	−0.00371084
$829$	−11.3809	−0.395276	−0.197638	−	0.980275i	$-0.563327\pi$
$829$	−11.3809	−0.395276	−0.197638	+	0.980275i	$0.563327\pi$
$830$	11.9959	0.416383
$831$	21.8402	0.757629
$832$	−0.549811	−0.0190613
$833$	−13.6446	−0.472757
$834$	−11.5440	−0.399735
$835$	−82.4264	−2.85248
$836$	−34.9075	−1.20730
$837$	2.98829	0.103290
$838$	25.0841	0.866514
$839$	−7.32370	−0.252842	−0.126421	−	0.991977i	$-0.540349\pi$
$839$	−7.32370	−0.252842	−0.126421	+	0.991977i	$0.540349\pi$
$840$	15.8892	0.548230
$841$	68.5406	2.36347
$842$	−25.7424	−0.887143
$843$	7.04426	0.242617
$844$	−7.53974	−0.259529
$845$	−44.4043	−1.52755
$846$	−6.14847	−0.211389
$847$	−39.5512	−1.35900
$848$	13.0995	0.449839
$849$	14.5750	0.500213
$850$	7.22922	0.247960
$851$	0.734252	0.0251698
$852$	−13.7110	−0.469731
$853$	−8.20684	−0.280997	−0.140498	−	0.990081i	$-0.544870\pi$
$853$	−8.20684	−0.280997	−0.140498	+	0.990081i	$0.544870\pi$
$854$	−31.4132	−1.07494
$855$	27.5000	0.940479
$856$	8.12821	0.277817
$857$	−0.318981	−0.0108962	−0.00544808	−	0.999985i	$-0.501734\pi$
$857$	−0.318981	−0.0108962	−0.00544808	+	0.999985i	$0.501734\pi$
$858$	−2.44061	−0.0833212
$859$	25.3747	0.865774	0.432887	−	0.901448i	$-0.357495\pi$
$859$	25.3747	0.865774	0.432887	+	0.901448i	$0.357495\pi$
$860$	−38.4717	−1.31187
$861$	−32.4086	−1.10448
$862$	16.8356	0.573424
$863$	−14.9442	−0.508707	−0.254354	−	0.967111i	$-0.581863\pi$
$863$	−14.9442	−0.508707	−0.254354	+	0.967111i	$0.581863\pi$
$864$	−1.00000	−0.0340207
$865$	29.1077	0.989691
$866$	−15.6481	−0.531745
$867$	1.00000	0.0339618
$868$	−13.5777	−0.460857
$869$	8.94790	0.303537
$870$	34.5376	1.17093
$871$	7.40753	0.250995
$872$	−3.85341	−0.130493
$873$	0.142690	0.00482933
$874$	0.839693	0.0284030
$875$	−35.4206	−1.19743
$876$	4.03219	0.136235
$877$	15.4799	0.522718	0.261359	−	0.965242i	$-0.415829\pi$
$877$	15.4799	0.522718	0.261359	+	0.965242i	$0.415829\pi$
$878$	−13.1713	−0.444511
$879$	1.00168	0.0337857
$880$	−15.5233	−0.523291
$881$	−45.4649	−1.53175	−0.765876	−	0.642989i	$-0.777694\pi$
$881$	−45.4649	−1.53175	−0.765876	+	0.642989i	$0.777694\pi$
$882$	−13.6446	−0.459437
$883$	−48.0019	−1.61539	−0.807696	−	0.589599i	$-0.799286\pi$
$883$	−48.0019	−1.61539	−0.807696	+	0.589599i	$0.799286\pi$
$884$	0.549811	0.0184922
$885$	3.49703	0.117551
$886$	39.6436	1.33185
$887$	17.9476	0.602622	0.301311	−	0.953526i	$-0.402576\pi$
$887$	17.9476	0.602622	0.301311	+	0.953526i	$0.402576\pi$
$888$	6.87634	0.230755
$889$	89.9286	3.01611
$890$	0.847729	0.0284159
$891$	−4.43900	−0.148712
$892$	−11.3959	−0.381562
$893$	48.3504	1.61798
$894$	15.8894	0.531421
$895$	64.0750	2.14179
$896$	4.54363	0.151792
$897$	0.0587086	0.00196022
$898$	17.8751	0.596500
$899$	−29.5132	−0.984319
$900$	7.22922	0.240974
$901$	−13.0995	−0.436408
$902$	31.6623	1.05424
$903$	49.9856	1.66342
$904$	12.6675	0.421316
$905$	−62.0770	−2.06351
$906$	20.7685	0.689986
$907$	8.84309	0.293630	0.146815	−	0.989164i	$-0.453098\pi$
$907$	8.84309	0.293630	0.146815	+	0.989164i	$0.453098\pi$
$908$	−27.1548	−0.901162
$909$	−4.01752	−0.133253
$910$	−8.73607	−0.289598
$911$	6.73627	0.223183	0.111591	−	0.993754i	$-0.464405\pi$
$911$	6.73627	0.223183	0.111591	+	0.993754i	$0.464405\pi$
$912$	7.86381	0.260397
$913$	15.2271	0.503944
$914$	−35.3211	−1.16832
$915$	−24.1773	−0.799278
$916$	21.2799	0.703108
$917$	52.3645	1.72923
$918$	1.00000	0.0330049
$919$	−27.1856	−0.896770	−0.448385	−	0.893841i	$-0.648001\pi$
$919$	−27.1856	−0.896770	−0.448385	+	0.893841i	$0.648001\pi$
$920$	0.373411	0.0123110
$921$	3.84621	0.126737
$922$	22.0633	0.726616
$923$	7.53846	0.248131
$924$	20.1692	0.663518
$925$	−49.7106	−1.63447
$926$	22.0904	0.725937
$927$	11.4507	0.376091
$928$	9.87626	0.324204
$929$	27.4609	0.900962	0.450481	−	0.892786i	$-0.351252\pi$
$929$	27.4609	0.900962	0.450481	+	0.892786i	$0.351252\pi$
$930$	−10.4501	−0.342674
$931$	107.298	3.51656
$932$	−8.95969	−0.293484
$933$	2.74079	0.0897293
$934$	−0.985515	−0.0322470
$935$	15.5233	0.507667
$936$	0.549811	0.0179711
$937$	−1.62448	−0.0530694	−0.0265347	−	0.999648i	$-0.508447\pi$
$937$	−1.62448	−0.0530694	−0.0265347	+	0.999648i	$0.508447\pi$
$938$	−61.2157	−1.99876
$939$	10.1837	0.332333
$940$	21.5014	0.701298
$941$	43.5628	1.42011	0.710053	−	0.704148i	$-0.248671\pi$
$941$	43.5628	1.42011	0.710053	+	0.704148i	$0.248671\pi$
$942$	1.95157	0.0635856
$943$	−0.761632	−0.0248021
$944$	1.00000	0.0325472
$945$	−15.8892	−0.516876
$946$	−48.8346	−1.58775
$947$	41.8049	1.35848	0.679238	−	0.733918i	$-0.262310\pi$
$947$	41.8049	1.35848	0.679238	+	0.733918i	$0.262310\pi$
$948$	−2.01574	−0.0654683
$949$	−2.21694	−0.0719651
$950$	−56.8492	−1.84443
$951$	21.0229	0.681713
$952$	−4.54363	−0.147260
$953$	−15.8893	−0.514704	−0.257352	−	0.966318i	$-0.582850\pi$
$953$	−15.8893	−0.514704	−0.257352	+	0.966318i	$0.582850\pi$
$954$	−13.0995	−0.424112
$955$	−36.6611	−1.18632
$956$	3.80631	0.123105
$957$	43.8408	1.41717
$958$	5.15309	0.166489
$959$	51.8628	1.67474
$960$	3.49703	0.112866
$961$	−22.0701	−0.711939
$962$	−3.78069	−0.121894
$963$	−8.12821	−0.261928
$964$	−3.69048	−0.118862
$965$	77.8820	2.50711
$966$	−0.485167	−0.0156100
$967$	44.2108	1.42172	0.710862	−	0.703332i	$-0.248305\pi$
$967$	44.2108	1.42172	0.710862	+	0.703332i	$0.248305\pi$
$968$	−8.70475	−0.279781
$969$	−7.86381	−0.252622
$970$	−0.498991	−0.0160217
$971$	−6.76712	−0.217167	−0.108584	−	0.994087i	$-0.534632\pi$
$971$	−6.76712	−0.217167	−0.108584	+	0.994087i	$0.534632\pi$
$972$	1.00000	0.0320750
$973$	−52.4515	−1.68152
$974$	−10.4063	−0.333440
$975$	−3.97471	−0.127293
$976$	−6.91367	−0.221301
$977$	50.4514	1.61408	0.807042	−	0.590494i	$-0.201067\pi$
$977$	50.4514	1.61408	0.807042	+	0.590494i	$0.201067\pi$
$978$	11.2556	0.359913
$979$	1.07608	0.0343915
$980$	47.7155	1.52422
$981$	3.85341	0.123030
$982$	−16.8014	−0.536155
$983$	−40.9847	−1.30721	−0.653604	−	0.756836i	$-0.726744\pi$
$983$	−40.9847	−1.30721	−0.653604	+	0.756836i	$0.726744\pi$
$984$	−7.13275	−0.227384
$985$	0.00401736	0.000128004 0
$986$	−9.87626	−0.314524
$987$	−27.9364	−0.889225
$988$	−4.32361	−0.137552
$989$	1.17471	0.0373535
$990$	15.5233	0.493364
$991$	23.4956	0.746363	0.373182	−	0.927758i	$-0.378267\pi$
$991$	23.4956	0.746363	0.373182	+	0.927758i	$0.378267\pi$
$992$	−2.98829	−0.0948784
$993$	6.16842	0.195749
$994$	−62.2977	−1.97596
$995$	27.0588	0.857821
$996$	−3.43030	−0.108693
$997$	−3.77133	−0.119439	−0.0597197	−	0.998215i	$-0.519021\pi$
$997$	−3.77133	−0.119439	−0.0597197	+	0.998215i	$0.519021\pi$
$998$	−24.3768	−0.771633
$999$	−6.87634	−0.217558

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.y.1.10	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.y.1.10	✓	10	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:	\( N \)	\(=\)	\( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6018.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.49703 q^{5} -1.00000 q^{6} -4.54363 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.49703 q^{5} -1.00000 q^{6} -4.54363 q^{7} -1.00000 q^{8} +1.00000 q^{9} -3.49703 q^{10} -4.43900 q^{11} +1.00000 q^{12} -0.549811 q^{13} +4.54363 q^{14} +3.49703 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} +7.86381 q^{19} +3.49703 q^{20} -4.54363 q^{21} +4.43900 q^{22} -0.106779 q^{23} -1.00000 q^{24} +7.22922 q^{25} +0.549811 q^{26} +1.00000 q^{27} -4.54363 q^{28} -9.87626 q^{29} -3.49703 q^{30} +2.98829 q^{31} -1.00000 q^{32} -4.43900 q^{33} +1.00000 q^{34} -15.8892 q^{35} +1.00000 q^{36} -6.87634 q^{37} -7.86381 q^{38} -0.549811 q^{39} -3.49703 q^{40} +7.13275 q^{41} +4.54363 q^{42} -11.0012 q^{43} -4.43900 q^{44} +3.49703 q^{45} +0.106779 q^{46} +6.14847 q^{47} +1.00000 q^{48} +13.6446 q^{49} -7.22922 q^{50} -1.00000 q^{51} -0.549811 q^{52} +13.0995 q^{53} -1.00000 q^{54} -15.5233 q^{55} +4.54363 q^{56} +7.86381 q^{57} +9.87626 q^{58} +1.00000 q^{59} +3.49703 q^{60} -6.91367 q^{61} -2.98829 q^{62} -4.54363 q^{63} +1.00000 q^{64} -1.92271 q^{65} +4.43900 q^{66} -13.4729 q^{67} -1.00000 q^{68} -0.106779 q^{69} +15.8892 q^{70} -13.7110 q^{71} -1.00000 q^{72} +4.03219 q^{73} +6.87634 q^{74} +7.22922 q^{75} +7.86381 q^{76} +20.1692 q^{77} +0.549811 q^{78} -2.01574 q^{79} +3.49703 q^{80} +1.00000 q^{81} -7.13275 q^{82} -3.43030 q^{83} -4.54363 q^{84} -3.49703 q^{85} +11.0012 q^{86} -9.87626 q^{87} +4.43900 q^{88} -0.242414 q^{89} -3.49703 q^{90} +2.49814 q^{91} -0.106779 q^{92} +2.98829 q^{93} -6.14847 q^{94} +27.5000 q^{95} -1.00000 q^{96} +0.142690 q^{97} -13.6446 q^{98} -4.43900 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{2} + 10 q^{3} + 10 q^{4} - 2 q^{5} - 10 q^{6} - 6 q^{7} - 10 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q - 10 * q^2 + 10 * q^3 + 10 * q^4 - 2 * q^5 - 10 * q^6 - 6 * q^7 - 10 * q^8 + 10 * q^9	\( 10 q - 10 q^{2} + 10 q^{3} + 10 q^{4} - 2 q^{5} - 10 q^{6} - 6 q^{7} - 10 q^{8} + 10 q^{9} + 2 q^{10} - 3 q^{11} + 10 q^{12} - 10 q^{13} + 6 q^{14} - 2 q^{15} + 10 q^{16} - 10 q^{17} - 10 q^{18} + 8 q^{19} - 2 q^{20} - 6 q^{21} + 3 q^{22} - 9 q^{23} - 10 q^{24} + 20 q^{25} + 10 q^{26} + 10 q^{27} - 6 q^{28} - 24 q^{29} + 2 q^{30} - 7 q^{31} - 10 q^{32} - 3 q^{33} + 10 q^{34} - 22 q^{35} + 10 q^{36} - 4 q^{37} - 8 q^{38} - 10 q^{39} + 2 q^{40} - 9 q^{41} + 6 q^{42} - 11 q^{43} - 3 q^{44} - 2 q^{45} + 9 q^{46} - 18 q^{47} + 10 q^{48} + 6 q^{49} - 20 q^{50} - 10 q^{51} - 10 q^{52} - 9 q^{53} - 10 q^{54} + q^{55} + 6 q^{56} + 8 q^{57} + 24 q^{58} + 10 q^{59} - 2 q^{60} - 25 q^{61} + 7 q^{62} - 6 q^{63} + 10 q^{64} - 28 q^{65} + 3 q^{66} + 2 q^{67} - 10 q^{68} - 9 q^{69} + 22 q^{70} - 30 q^{71} - 10 q^{72} - 11 q^{73} + 4 q^{74} + 20 q^{75} + 8 q^{76} + 4 q^{77} + 10 q^{78} + 3 q^{79} - 2 q^{80} + 10 q^{81} + 9 q^{82} - q^{83} - 6 q^{84} + 2 q^{85} + 11 q^{86} - 24 q^{87} + 3 q^{88} - 14 q^{89} + 2 q^{90} - 13 q^{91} - 9 q^{92} - 7 q^{93} + 18 q^{94} - 35 q^{95} - 10 q^{96} - 10 q^{97} - 6 q^{98} - 3 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 + 10 * q^3 + 10 * q^4 - 2 * q^5 - 10 * q^6 - 6 * q^7 - 10 * q^8 + 10 * q^9 + 2 * q^10 - 3 * q^11 + 10 * q^12 - 10 * q^13 + 6 * q^14 - 2 * q^15 + 10 * q^16 - 10 * q^17 - 10 * q^18 + 8 * q^19 - 2 * q^20 - 6 * q^21 + 3 * q^22 - 9 * q^23 - 10 * q^24 + 20 * q^25 + 10 * q^26 + 10 * q^27 - 6 * q^28 - 24 * q^29 + 2 * q^30 - 7 * q^31 - 10 * q^32 - 3 * q^33 + 10 * q^34 - 22 * q^35 + 10 * q^36 - 4 * q^37 - 8 * q^38 - 10 * q^39 + 2 * q^40 - 9 * q^41 + 6 * q^42 - 11 * q^43 - 3 * q^44 - 2 * q^45 + 9 * q^46 - 18 * q^47 + 10 * q^48 + 6 * q^49 - 20 * q^50 - 10 * q^51 - 10 * q^52 - 9 * q^53 - 10 * q^54 + q^55 + 6 * q^56 + 8 * q^57 + 24 * q^58 + 10 * q^59 - 2 * q^60 - 25 * q^61 + 7 * q^62 - 6 * q^63 + 10 * q^64 - 28 * q^65 + 3 * q^66 + 2 * q^67 - 10 * q^68 - 9 * q^69 + 22 * q^70 - 30 * q^71 - 10 * q^72 - 11 * q^73 + 4 * q^74 + 20 * q^75 + 8 * q^76 + 4 * q^77 + 10 * q^78 + 3 * q^79 - 2 * q^80 + 10 * q^81 + 9 * q^82 - q^83 - 6 * q^84 + 2 * q^85 + 11 * q^86 - 24 * q^87 + 3 * q^88 - 14 * q^89 + 2 * q^90 - 13 * q^91 - 9 * q^92 - 7 * q^93 + 18 * q^94 - 35 * q^95 - 10 * q^96 - 10 * q^97 - 6 * q^98 - 3 * q^99

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