LMFDB - Embedded newform 6018.2.a.bb.1.5

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:	$0$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 4 x^{12} - 41 x^{11} + 179 x^{10} + 540 x^{9} - 2773 x^{8} - 2260 x^{7} + 17621 x^{6} + \cdots + 128 $ x^13 - 4x^12 - 41x^11 + 179x^10 + 540x^9 - 2773x^8 - 2260x^7 + 17621x^6 - 838x^5 - 44478x^4 + 16472x^3 + 29944x^2 - 6856x + 128
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			1.5
Root			$-0.877543$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.877543 q^{5} +1.00000 q^{6} -4.30430 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.877543 q^{5} +1.00000 q^{6} -4.30430 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.877543 q^{10} +2.30359 q^{11} +1.00000 q^{12} +5.05151 q^{13} -4.30430 q^{14} -0.877543 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} +6.89366 q^{19} -0.877543 q^{20} -4.30430 q^{21} +2.30359 q^{22} -3.74016 q^{23} +1.00000 q^{24} -4.22992 q^{25} +5.05151 q^{26} +1.00000 q^{27} -4.30430 q^{28} -2.11743 q^{29} -0.877543 q^{30} -3.57444 q^{31} +1.00000 q^{32} +2.30359 q^{33} +1.00000 q^{34} +3.77721 q^{35} +1.00000 q^{36} -5.04033 q^{37} +6.89366 q^{38} +5.05151 q^{39} -0.877543 q^{40} +2.42727 q^{41} -4.30430 q^{42} +1.15789 q^{43} +2.30359 q^{44} -0.877543 q^{45} -3.74016 q^{46} +4.76221 q^{47} +1.00000 q^{48} +11.5270 q^{49} -4.22992 q^{50} +1.00000 q^{51} +5.05151 q^{52} +9.00329 q^{53} +1.00000 q^{54} -2.02150 q^{55} -4.30430 q^{56} +6.89366 q^{57} -2.11743 q^{58} -1.00000 q^{59} -0.877543 q^{60} -0.436886 q^{61} -3.57444 q^{62} -4.30430 q^{63} +1.00000 q^{64} -4.43292 q^{65} +2.30359 q^{66} +10.9173 q^{67} +1.00000 q^{68} -3.74016 q^{69} +3.77721 q^{70} -3.56848 q^{71} +1.00000 q^{72} +10.4703 q^{73} -5.04033 q^{74} -4.22992 q^{75} +6.89366 q^{76} -9.91536 q^{77} +5.05151 q^{78} -2.70149 q^{79} -0.877543 q^{80} +1.00000 q^{81} +2.42727 q^{82} +14.9440 q^{83} -4.30430 q^{84} -0.877543 q^{85} +1.15789 q^{86} -2.11743 q^{87} +2.30359 q^{88} +12.3753 q^{89} -0.877543 q^{90} -21.7432 q^{91} -3.74016 q^{92} -3.57444 q^{93} +4.76221 q^{94} -6.04948 q^{95} +1.00000 q^{96} -0.796735 q^{97} +11.5270 q^{98} +2.30359 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q + 13 q^{2} + 13 q^{3} + 13 q^{4} + 4 q^{5} + 13 q^{6} + 11 q^{7} + 13 q^{8} + 13 q^{9}+O(q^{10}) $ 13 * q + 13 * q^2 + 13 * q^3 + 13 * q^4 + 4 * q^5 + 13 * q^6 + 11 * q^7 + 13 * q^8 + 13 * q^9	\( 13 q + 13 q^{2} + 13 q^{3} + 13 q^{4} + 4 q^{5} + 13 q^{6} + 11 q^{7} + 13 q^{8} + 13 q^{9} + 4 q^{10} + 7 q^{11} + 13 q^{12} + 6 q^{13} + 11 q^{14} + 4 q^{15} + 13 q^{16} + 13 q^{17} + 13 q^{18} + 9 q^{19} + 4 q^{20} + 11 q^{21} + 7 q^{22} + 2 q^{23} + 13 q^{24} + 33 q^{25} + 6 q^{26} + 13 q^{27} + 11 q^{28} + 14 q^{29} + 4 q^{30} - 5 q^{31} + 13 q^{32} + 7 q^{33} + 13 q^{34} + 24 q^{35} + 13 q^{36} + 4 q^{37} + 9 q^{38} + 6 q^{39} + 4 q^{40} + 28 q^{41} + 11 q^{42} + q^{43} + 7 q^{44} + 4 q^{45} + 2 q^{46} + 12 q^{47} + 13 q^{48} + 32 q^{49} + 33 q^{50} + 13 q^{51} + 6 q^{52} + 22 q^{53} + 13 q^{54} - 7 q^{55} + 11 q^{56} + 9 q^{57} + 14 q^{58} - 13 q^{59} + 4 q^{60} - 9 q^{61} - 5 q^{62} + 11 q^{63} + 13 q^{64} + 34 q^{65} + 7 q^{66} + 26 q^{67} + 13 q^{68} + 2 q^{69} + 24 q^{70} + 8 q^{71} + 13 q^{72} + 4 q^{73} + 4 q^{74} + 33 q^{75} + 9 q^{76} + 38 q^{77} + 6 q^{78} - 17 q^{79} + 4 q^{80} + 13 q^{81} + 28 q^{82} + 14 q^{83} + 11 q^{84} + 4 q^{85} + q^{86} + 14 q^{87} + 7 q^{88} + 19 q^{89} + 4 q^{90} - 5 q^{91} + 2 q^{92} - 5 q^{93} + 12 q^{94} + 25 q^{95} + 13 q^{96} - 5 q^{97} + 32 q^{98} + 7 q^{99}+O(q^{100}) \) 13 * q + 13 * q^2 + 13 * q^3 + 13 * q^4 + 4 * q^5 + 13 * q^6 + 11 * q^7 + 13 * q^8 + 13 * q^9 + 4 * q^10 + 7 * q^11 + 13 * q^12 + 6 * q^13 + 11 * q^14 + 4 * q^15 + 13 * q^16 + 13 * q^17 + 13 * q^18 + 9 * q^19 + 4 * q^20 + 11 * q^21 + 7 * q^22 + 2 * q^23 + 13 * q^24 + 33 * q^25 + 6 * q^26 + 13 * q^27 + 11 * q^28 + 14 * q^29 + 4 * q^30 - 5 * q^31 + 13 * q^32 + 7 * q^33 + 13 * q^34 + 24 * q^35 + 13 * q^36 + 4 * q^37 + 9 * q^38 + 6 * q^39 + 4 * q^40 + 28 * q^41 + 11 * q^42 + q^43 + 7 * q^44 + 4 * q^45 + 2 * q^46 + 12 * q^47 + 13 * q^48 + 32 * q^49 + 33 * q^50 + 13 * q^51 + 6 * q^52 + 22 * q^53 + 13 * q^54 - 7 * q^55 + 11 * q^56 + 9 * q^57 + 14 * q^58 - 13 * q^59 + 4 * q^60 - 9 * q^61 - 5 * q^62 + 11 * q^63 + 13 * q^64 + 34 * q^65 + 7 * q^66 + 26 * q^67 + 13 * q^68 + 2 * q^69 + 24 * q^70 + 8 * q^71 + 13 * q^72 + 4 * q^73 + 4 * q^74 + 33 * q^75 + 9 * q^76 + 38 * q^77 + 6 * q^78 - 17 * q^79 + 4 * q^80 + 13 * q^81 + 28 * q^82 + 14 * q^83 + 11 * q^84 + 4 * q^85 + q^86 + 14 * q^87 + 7 * q^88 + 19 * q^89 + 4 * q^90 - 5 * q^91 + 2 * q^92 - 5 * q^93 + 12 * q^94 + 25 * q^95 + 13 * q^96 - 5 * q^97 + 32 * q^98 + 7 * 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
$5$	−0.877543	−0.392449	−0.196225	−	0.980559i	$-0.562868\pi$
$5$	−0.877543	−0.392449	−0.196225	+	0.980559i	$0.562868\pi$
$6$	1.00000	0.408248
$7$	−4.30430	−1.62687	−0.813436	−	0.581655i	$-0.802405\pi$
$7$	−4.30430	−1.62687	−0.813436	+	0.581655i	$0.802405\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−0.877543	−0.277503
$11$	2.30359	0.694560	0.347280	−	0.937761i	$-0.387105\pi$
$11$	2.30359	0.694560	0.347280	+	0.937761i	$0.387105\pi$
$12$	1.00000	0.288675
$13$	5.05151	1.40104	0.700519	−	0.713634i	$-0.252952\pi$
$13$	5.05151	1.40104	0.700519	+	0.713634i	$0.252952\pi$
$14$	−4.30430	−1.15037
$15$	−0.877543	−0.226581
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	1.00000	0.235702
$19$	6.89366	1.58151	0.790757	−	0.612130i	$-0.209687\pi$
$19$	6.89366	1.58151	0.790757	+	0.612130i	$0.209687\pi$
$20$	−0.877543	−0.196225
$21$	−4.30430	−0.939275
$22$	2.30359	0.491128
$23$	−3.74016	−0.779878	−0.389939	−	0.920841i	$-0.627504\pi$
$23$	−3.74016	−0.779878	−0.389939	+	0.920841i	$0.627504\pi$
$24$	1.00000	0.204124
$25$	−4.22992	−0.845984
$26$	5.05151	0.990683
$27$	1.00000	0.192450
$28$	−4.30430	−0.813436
$29$	−2.11743	−0.393196	−0.196598	−	0.980484i	$-0.562989\pi$
$29$	−2.11743	−0.393196	−0.196598	+	0.980484i	$0.562989\pi$
$30$	−0.877543	−0.160217
$31$	−3.57444	−0.641988	−0.320994	−	0.947081i	$-0.604017\pi$
$31$	−3.57444	−0.641988	−0.320994	+	0.947081i	$0.604017\pi$
$32$	1.00000	0.176777
$33$	2.30359	0.401004
$34$	1.00000	0.171499
$35$	3.77721	0.638464
$36$	1.00000	0.166667
$37$	−5.04033	−0.828626	−0.414313	−	0.910135i	$-0.635978\pi$
$37$	−5.04033	−0.828626	−0.414313	+	0.910135i	$0.635978\pi$
$38$	6.89366	1.11830
$39$	5.05151	0.808890
$40$	−0.877543	−0.138752
$41$	2.42727	0.379076	0.189538	−	0.981873i	$-0.439301\pi$
$41$	2.42727	0.379076	0.189538	+	0.981873i	$0.439301\pi$
$42$	−4.30430	−0.664167
$43$	1.15789	0.176577	0.0882886	−	0.996095i	$-0.471860\pi$
$43$	1.15789	0.176577	0.0882886	+	0.996095i	$0.471860\pi$
$44$	2.30359	0.347280
$45$	−0.877543	−0.130816
$46$	−3.74016	−0.551457
$47$	4.76221	0.694640	0.347320	−	0.937747i	$-0.387092\pi$
$47$	4.76221	0.694640	0.347320	+	0.937747i	$0.387092\pi$
$48$	1.00000	0.144338
$49$	11.5270	1.64671
$50$	−4.22992	−0.598201
$51$	1.00000	0.140028
$52$	5.05151	0.700519
$53$	9.00329	1.23670	0.618349	−	0.785904i	$-0.287802\pi$
$53$	9.00329	1.23670	0.618349	+	0.785904i	$0.287802\pi$
$54$	1.00000	0.136083
$55$	−2.02150	−0.272579
$56$	−4.30430	−0.575186
$57$	6.89366	0.913087
$58$	−2.11743	−0.278032
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	−0.877543	−0.113290
$61$	−0.436886	−0.0559376	−0.0279688	−	0.999609i	$-0.508904\pi$
$61$	−0.436886	−0.0559376	−0.0279688	+	0.999609i	$0.508904\pi$
$62$	−3.57444	−0.453954
$63$	−4.30430	−0.542290
$64$	1.00000	0.125000
$65$	−4.43292	−0.549836
$66$	2.30359	0.283553
$67$	10.9173	1.33376	0.666879	−	0.745166i	$-0.267630\pi$
$67$	10.9173	1.33376	0.666879	+	0.745166i	$0.267630\pi$
$68$	1.00000	0.121268
$69$	−3.74016	−0.450263
$70$	3.77721	0.451462
$71$	−3.56848	−0.423501	−0.211750	−	0.977324i	$-0.567916\pi$
$71$	−3.56848	−0.423501	−0.211750	+	0.977324i	$0.567916\pi$
$72$	1.00000	0.117851
$73$	10.4703	1.22546	0.612729	−	0.790293i	$-0.290072\pi$
$73$	10.4703	1.22546	0.612729	+	0.790293i	$0.290072\pi$
$74$	−5.04033	−0.585927
$75$	−4.22992	−0.488429
$76$	6.89366	0.790757
$77$	−9.91536	−1.12996
$78$	5.05151	0.571971
$79$	−2.70149	−0.303942	−0.151971	−	0.988385i	$-0.548562\pi$
$79$	−2.70149	−0.303942	−0.151971	+	0.988385i	$0.548562\pi$
$80$	−0.877543	−0.0981123
$81$	1.00000	0.111111
$82$	2.42727	0.268047
$83$	14.9440	1.64032	0.820158	−	0.572136i	$-0.193885\pi$
$83$	14.9440	1.64032	0.820158	+	0.572136i	$0.193885\pi$
$84$	−4.30430	−0.469637
$85$	−0.877543	−0.0951829
$86$	1.15789	0.124859
$87$	−2.11743	−0.227012
$88$	2.30359	0.245564
$89$	12.3753	1.31178	0.655889	−	0.754857i	$-0.272294\pi$
$89$	12.3753	1.31178	0.655889	+	0.754857i	$0.272294\pi$
$90$	−0.877543	−0.0925011
$91$	−21.7432	−2.27931
$92$	−3.74016	−0.389939
$93$	−3.57444	−0.370652
$94$	4.76221	0.491184
$95$	−6.04948	−0.620664
$96$	1.00000	0.102062
$97$	−0.796735	−0.0808962	−0.0404481	−	0.999182i	$-0.512879\pi$
$97$	−0.796735	−0.0808962	−0.0404481	+	0.999182i	$0.512879\pi$
$98$	11.5270	1.16440
$99$	2.30359	0.231520
$100$	−4.22992	−0.422992
$101$	16.5586	1.64764	0.823819	−	0.566852i	$-0.191839\pi$
$101$	16.5586	1.64764	0.823819	+	0.566852i	$0.191839\pi$
$102$	1.00000	0.0990148
$103$	18.6957	1.84214	0.921071	−	0.389395i	$-0.127316\pi$
$103$	18.6957	1.84214	0.921071	+	0.389395i	$0.127316\pi$
$104$	5.05151	0.495342
$105$	3.77721	0.368617
$106$	9.00329	0.874477
$107$	−5.14856	−0.497730	−0.248865	−	0.968538i	$-0.580058\pi$
$107$	−5.14856	−0.497730	−0.248865	+	0.968538i	$0.580058\pi$
$108$	1.00000	0.0962250
$109$	−8.89420	−0.851910	−0.425955	−	0.904744i	$-0.640062\pi$
$109$	−8.89420	−0.851910	−0.425955	+	0.904744i	$0.640062\pi$
$110$	−2.02150	−0.192743
$111$	−5.04033	−0.478407
$112$	−4.30430	−0.406718
$113$	−4.07890	−0.383710	−0.191855	−	0.981423i	$-0.561450\pi$
$113$	−4.07890	−0.383710	−0.191855	+	0.981423i	$0.561450\pi$
$114$	6.89366	0.645650
$115$	3.28215	0.306062
$116$	−2.11743	−0.196598
$117$	5.05151	0.467013
$118$	−1.00000	−0.0920575
$119$	−4.30430	−0.394574
$120$	−0.877543	−0.0801083
$121$	−5.69345	−0.517586
$122$	−0.436886	−0.0395538
$123$	2.42727	0.218860
$124$	−3.57444	−0.320994
$125$	8.09965	0.724455
$126$	−4.30430	−0.383457
$127$	−12.8459	−1.13989	−0.569945	−	0.821683i	$-0.693035\pi$
$127$	−12.8459	−1.13989	−0.569945	+	0.821683i	$0.693035\pi$
$128$	1.00000	0.0883883
$129$	1.15789	0.101947
$130$	−4.43292	−0.388793
$131$	7.90167	0.690372	0.345186	−	0.938534i	$-0.387816\pi$
$131$	7.90167	0.690372	0.345186	+	0.938534i	$0.387816\pi$
$132$	2.30359	0.200502
$133$	−29.6724	−2.57292
$134$	10.9173	0.943109
$135$	−0.877543	−0.0755269
$136$	1.00000	0.0857493
$137$	−12.8283	−1.09599	−0.547997	−	0.836481i	$-0.684609\pi$
$137$	−12.8283	−1.09599	−0.547997	+	0.836481i	$0.684609\pi$
$138$	−3.74016	−0.318384
$139$	3.73772	0.317029	0.158515	−	0.987357i	$-0.449330\pi$
$139$	3.73772	0.317029	0.158515	+	0.987357i	$0.449330\pi$
$140$	3.77721	0.319232
$141$	4.76221	0.401050
$142$	−3.56848	−0.299460
$143$	11.6366	0.973105
$144$	1.00000	0.0833333
$145$	1.85813	0.154310
$146$	10.4703	0.866530
$147$	11.5270	0.950729
$148$	−5.04033	−0.414313
$149$	−7.05125	−0.577661	−0.288830	−	0.957380i	$-0.593266\pi$
$149$	−7.05125	−0.577661	−0.288830	+	0.957380i	$0.593266\pi$
$150$	−4.22992	−0.345371
$151$	6.95671	0.566129	0.283065	−	0.959101i	$-0.408649\pi$
$151$	6.95671	0.566129	0.283065	+	0.959101i	$0.408649\pi$
$152$	6.89366	0.559150
$153$	1.00000	0.0808452
$154$	−9.91536	−0.799002
$155$	3.13672	0.251948
$156$	5.05151	0.404445
$157$	−10.0668	−0.803418	−0.401709	−	0.915767i	$-0.631584\pi$
$157$	−10.0668	−0.803418	−0.401709	+	0.915767i	$0.631584\pi$
$158$	−2.70149	−0.214919
$159$	9.00329	0.714008
$160$	−0.877543	−0.0693759
$161$	16.0988	1.26876
$162$	1.00000	0.0785674
$163$	17.0589	1.33616	0.668078	−	0.744091i	$-0.267117\pi$
$163$	17.0589	1.33616	0.668078	+	0.744091i	$0.267117\pi$
$164$	2.42727	0.189538
$165$	−2.02150	−0.157374
$166$	14.9440	1.15988
$167$	−0.675722	−0.0522889	−0.0261445	−	0.999658i	$-0.508323\pi$
$167$	−0.675722	−0.0522889	−0.0261445	+	0.999658i	$0.508323\pi$
$168$	−4.30430	−0.332084
$169$	12.5178	0.962907
$170$	−0.877543	−0.0673045
$171$	6.89366	0.527171
$172$	1.15789	0.0882886
$173$	7.42906	0.564821	0.282411	−	0.959294i	$-0.408866\pi$
$173$	7.42906	0.564821	0.282411	+	0.959294i	$0.408866\pi$
$174$	−2.11743	−0.160522
$175$	18.2068	1.37631
$176$	2.30359	0.173640
$177$	−1.00000	−0.0751646
$178$	12.3753	0.927567
$179$	−1.63402	−0.122132	−0.0610661	−	0.998134i	$-0.519450\pi$
$179$	−1.63402	−0.122132	−0.0610661	+	0.998134i	$0.519450\pi$
$180$	−0.877543	−0.0654082
$181$	23.0051	1.70996	0.854979	−	0.518662i	$-0.173570\pi$
$181$	23.0051	1.70996	0.854979	+	0.518662i	$0.173570\pi$
$182$	−21.7432	−1.61171
$183$	−0.436886	−0.0322956
$184$	−3.74016	−0.275729
$185$	4.42311	0.325193
$186$	−3.57444	−0.262091
$187$	2.30359	0.168456
$188$	4.76221	0.347320
$189$	−4.30430	−0.313092
$190$	−6.04948	−0.438875
$191$	−18.4009	−1.33144	−0.665721	−	0.746201i	$-0.731876\pi$
$191$	−18.4009	−1.33144	−0.665721	+	0.746201i	$0.731876\pi$
$192$	1.00000	0.0721688
$193$	22.1825	1.59673	0.798365	−	0.602174i	$-0.205699\pi$
$193$	22.1825	1.59673	0.798365	+	0.602174i	$0.205699\pi$
$194$	−0.796735	−0.0572023
$195$	−4.43292	−0.317448
$196$	11.5270	0.823355
$197$	−7.77988	−0.554294	−0.277147	−	0.960828i	$-0.589389\pi$
$197$	−7.77988	−0.554294	−0.277147	+	0.960828i	$0.589389\pi$
$198$	2.30359	0.163709
$199$	−1.09109	−0.0773452	−0.0386726	−	0.999252i	$-0.512313\pi$
$199$	−1.09109	−0.0773452	−0.0386726	+	0.999252i	$0.512313\pi$
$200$	−4.22992	−0.299100
$201$	10.9173	0.770045
$202$	16.5586	1.16506
$203$	9.11404	0.639680
$204$	1.00000	0.0700140
$205$	−2.13004	−0.148768
$206$	18.6957	1.30259
$207$	−3.74016	−0.259959
$208$	5.05151	0.350259
$209$	15.8802	1.09846
$210$	3.77721	0.260652
$211$	18.1556	1.24988	0.624940	−	0.780673i	$-0.285123\pi$
$211$	18.1556	1.24988	0.624940	+	0.780673i	$0.285123\pi$
$212$	9.00329	0.618349
$213$	−3.56848	−0.244508
$214$	−5.14856	−0.351948
$215$	−1.01610	−0.0692976
$216$	1.00000	0.0680414
$217$	15.3855	1.04443
$218$	−8.89420	−0.602392
$219$	10.4703	0.707519
$220$	−2.02150	−0.136290
$221$	5.05151	0.339802
$222$	−5.04033	−0.338285
$223$	−12.1629	−0.814488	−0.407244	−	0.913319i	$-0.633510\pi$
$223$	−12.1629	−0.814488	−0.407244	+	0.913319i	$0.633510\pi$
$224$	−4.30430	−0.287593
$225$	−4.22992	−0.281995
$226$	−4.07890	−0.271324
$227$	−10.1522	−0.673823	−0.336911	−	0.941536i	$-0.609382\pi$
$227$	−10.1522	−0.673823	−0.336911	+	0.941536i	$0.609382\pi$
$228$	6.89366	0.456544
$229$	3.11633	0.205933	0.102966	−	0.994685i	$-0.467167\pi$
$229$	3.11633	0.205933	0.102966	+	0.994685i	$0.467167\pi$
$230$	3.28215	0.216419
$231$	−9.91536	−0.652383
$232$	−2.11743	−0.139016
$233$	−21.2854	−1.39446	−0.697228	−	0.716850i	$-0.745583\pi$
$233$	−21.2854	−1.39446	−0.697228	+	0.716850i	$0.745583\pi$
$234$	5.05151	0.330228
$235$	−4.17904	−0.272611
$236$	−1.00000	−0.0650945
$237$	−2.70149	−0.175481
$238$	−4.30430	−0.279006
$239$	−7.96108	−0.514959	−0.257480	−	0.966284i	$-0.582892\pi$
$239$	−7.96108	−0.514959	−0.257480	+	0.966284i	$0.582892\pi$
$240$	−0.877543	−0.0566451
$241$	18.2076	1.17286	0.586429	−	0.810001i	$-0.300533\pi$
$241$	18.2076	1.17286	0.586429	+	0.810001i	$0.300533\pi$
$242$	−5.69345	−0.365989
$243$	1.00000	0.0641500
$244$	−0.436886	−0.0279688
$245$	−10.1154	−0.646250
$246$	2.42727	0.154757
$247$	34.8234	2.21576
$248$	−3.57444	−0.226977
$249$	14.9440	0.947037
$250$	8.09965	0.512267
$251$	−14.8296	−0.936038	−0.468019	−	0.883719i	$-0.655032\pi$
$251$	−14.8296	−0.936038	−0.468019	+	0.883719i	$0.655032\pi$
$252$	−4.30430	−0.271145
$253$	−8.61582	−0.541672
$254$	−12.8459	−0.806023
$255$	−0.877543	−0.0549539
$256$	1.00000	0.0625000
$257$	19.6495	1.22570	0.612851	−	0.790198i	$-0.290023\pi$
$257$	19.6495	1.22570	0.612851	+	0.790198i	$0.290023\pi$
$258$	1.15789	0.0720874
$259$	21.6951	1.34807
$260$	−4.43292	−0.274918
$261$	−2.11743	−0.131065
$262$	7.90167	0.488167
$263$	24.3818	1.50345	0.751724	−	0.659478i	$-0.229223\pi$
$263$	24.3818	1.50345	0.751724	+	0.659478i	$0.229223\pi$
$264$	2.30359	0.141776
$265$	−7.90078	−0.485341
$266$	−29.6724	−1.81933
$267$	12.3753	0.757355
$268$	10.9173	0.666879
$269$	21.8406	1.33165	0.665824	−	0.746109i	$-0.268080\pi$
$269$	21.8406	1.33165	0.665824	+	0.746109i	$0.268080\pi$
$270$	−0.877543	−0.0534056
$271$	−19.6792	−1.19542	−0.597712	−	0.801711i	$-0.703923\pi$
$271$	−19.6792	−1.19542	−0.597712	+	0.801711i	$0.703923\pi$
$272$	1.00000	0.0606339
$273$	−21.7432	−1.31596
$274$	−12.8283	−0.774984
$275$	−9.74402	−0.587586
$276$	−3.74016	−0.225131
$277$	26.3177	1.58128	0.790639	−	0.612282i	$-0.209748\pi$
$277$	26.3177	1.58128	0.790639	+	0.612282i	$0.209748\pi$
$278$	3.73772	0.224173
$279$	−3.57444	−0.213996
$280$	3.77721	0.225731
$281$	19.7053	1.17552	0.587759	−	0.809036i	$-0.300010\pi$
$281$	19.7053	1.17552	0.587759	+	0.809036i	$0.300010\pi$
$282$	4.76221	0.283585
$283$	−22.4304	−1.33335	−0.666675	−	0.745349i	$-0.732283\pi$
$283$	−22.4304	−1.33335	−0.666675	+	0.745349i	$0.732283\pi$
$284$	−3.56848	−0.211750
$285$	−6.04948	−0.358340
$286$	11.6366	0.688089
$287$	−10.4477	−0.616708
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	1.85813	0.109113
$291$	−0.796735	−0.0467055
$292$	10.4703	0.612729
$293$	16.0364	0.936857	0.468429	−	0.883501i	$-0.344820\pi$
$293$	16.0364	0.936857	0.468429	+	0.883501i	$0.344820\pi$
$294$	11.5270	0.672267
$295$	0.877543	0.0510925
$296$	−5.04033	−0.292963
$297$	2.30359	0.133668
$298$	−7.05125	−0.408468
$299$	−18.8935	−1.09264
$300$	−4.22992	−0.244214
$301$	−4.98392	−0.287269
$302$	6.95671	0.400314
$303$	16.5586	0.951265
$304$	6.89366	0.395378
$305$	0.383387	0.0219526
$306$	1.00000	0.0571662
$307$	−26.3214	−1.50224	−0.751122	−	0.660163i	$-0.770487\pi$
$307$	−26.3214	−1.50224	−0.751122	+	0.660163i	$0.770487\pi$
$308$	−9.91536	−0.564980
$309$	18.6957	1.06356
$310$	3.13672	0.178154
$311$	−9.60875	−0.544862	−0.272431	−	0.962175i	$-0.587828\pi$
$311$	−9.60875	−0.544862	−0.272431	+	0.962175i	$0.587828\pi$
$312$	5.05151	0.285986
$313$	3.49992	0.197827	0.0989137	−	0.995096i	$-0.468463\pi$
$313$	3.49992	0.197827	0.0989137	+	0.995096i	$0.468463\pi$
$314$	−10.0668	−0.568103
$315$	3.77721	0.212821
$316$	−2.70149	−0.151971
$317$	5.51016	0.309482	0.154741	−	0.987955i	$-0.450546\pi$
$317$	5.51016	0.309482	0.154741	+	0.987955i	$0.450546\pi$
$318$	9.00329	0.504880
$319$	−4.87769	−0.273098
$320$	−0.877543	−0.0490561
$321$	−5.14856	−0.287365
$322$	16.0988	0.897150
$323$	6.89366	0.383573
$324$	1.00000	0.0555556
$325$	−21.3675	−1.18526
$326$	17.0589	0.944805
$327$	−8.89420	−0.491851
$328$	2.42727	0.134024
$329$	−20.4980	−1.13009
$330$	−2.02150	−0.111280
$331$	−25.9542	−1.42657	−0.713287	−	0.700872i	$-0.752794\pi$
$331$	−25.9542	−1.42657	−0.713287	+	0.700872i	$0.752794\pi$
$332$	14.9440	0.820158
$333$	−5.04033	−0.276209
$334$	−0.675722	−0.0369739
$335$	−9.58038	−0.523432
$336$	−4.30430	−0.234819
$337$	−12.3722	−0.673959	−0.336980	−	0.941512i	$-0.609405\pi$
$337$	−12.3722	−0.673959	−0.336980	+	0.941512i	$0.609405\pi$
$338$	12.5178	0.680878
$339$	−4.07890	−0.221535
$340$	−0.877543	−0.0475914
$341$	−8.23406	−0.445899
$342$	6.89366	0.372766
$343$	−19.4854	−1.05212
$344$	1.15789	0.0624295
$345$	3.28215	0.176705
$346$	7.42906	0.399389
$347$	−29.5835	−1.58812	−0.794062	−	0.607837i	$-0.792037\pi$
$347$	−29.5835	−1.58812	−0.794062	+	0.607837i	$0.792037\pi$
$348$	−2.11743	−0.113506
$349$	−20.6380	−1.10473	−0.552364	−	0.833603i	$-0.686274\pi$
$349$	−20.6380	−1.10473	−0.552364	+	0.833603i	$0.686274\pi$
$350$	18.2068	0.973196
$351$	5.05151	0.269630
$352$	2.30359	0.122782
$353$	1.62624	0.0865561	0.0432781	−	0.999063i	$-0.486220\pi$
$353$	1.62624	0.0865561	0.0432781	+	0.999063i	$0.486220\pi$
$354$	−1.00000	−0.0531494
$355$	3.13150	0.166203
$356$	12.3753	0.655889
$357$	−4.30430	−0.227808
$358$	−1.63402	−0.0863605
$359$	−22.3190	−1.17795	−0.588977	−	0.808150i	$-0.700469\pi$
$359$	−22.3190	−1.17795	−0.588977	+	0.808150i	$0.700469\pi$
$360$	−0.877543	−0.0462506
$361$	28.5225	1.50119
$362$	23.0051	1.20912
$363$	−5.69345	−0.298829
$364$	−21.7432	−1.13965
$365$	−9.18816	−0.480930
$366$	−0.436886	−0.0228364
$367$	−18.2295	−0.951570	−0.475785	−	0.879562i	$-0.657836\pi$
$367$	−18.2295	−0.951570	−0.475785	+	0.879562i	$0.657836\pi$
$368$	−3.74016	−0.194970
$369$	2.42727	0.126359
$370$	4.42311	0.229946
$371$	−38.7528	−2.01195
$372$	−3.57444	−0.185326
$373$	−1.94774	−0.100850	−0.0504251	−	0.998728i	$-0.516058\pi$
$373$	−1.94774	−0.100850	−0.0504251	+	0.998728i	$0.516058\pi$
$374$	2.30359	0.119116
$375$	8.09965	0.418264
$376$	4.76221	0.245592
$377$	−10.6962	−0.550883
$378$	−4.30430	−0.221389
$379$	19.9168	1.02306	0.511528	−	0.859267i	$-0.329080\pi$
$379$	19.9168	1.02306	0.511528	+	0.859267i	$0.329080\pi$
$380$	−6.04948	−0.310332
$381$	−12.8459	−0.658115
$382$	−18.4009	−0.941472
$383$	24.1839	1.23574	0.617870	−	0.786280i	$-0.287996\pi$
$383$	24.1839	1.23574	0.617870	+	0.786280i	$0.287996\pi$
$384$	1.00000	0.0510310
$385$	8.70115	0.443452
$386$	22.1825	1.12906
$387$	1.15789	0.0588591
$388$	−0.796735	−0.0404481
$389$	8.69795	0.441003	0.220502	−	0.975387i	$-0.429231\pi$
$389$	8.69795	0.441003	0.220502	+	0.975387i	$0.429231\pi$
$390$	−4.43292	−0.224470
$391$	−3.74016	−0.189148
$392$	11.5270	0.582200
$393$	7.90167	0.398587
$394$	−7.77988	−0.391945
$395$	2.37068	0.119282
$396$	2.30359	0.115760
$397$	0.936843	0.0470188	0.0235094	−	0.999724i	$-0.492516\pi$
$397$	0.936843	0.0470188	0.0235094	+	0.999724i	$0.492516\pi$
$398$	−1.09109	−0.0546913
$399$	−29.6724	−1.48548
$400$	−4.22992	−0.211496
$401$	32.9290	1.64440	0.822199	−	0.569201i	$-0.192747\pi$
$401$	32.9290	1.64440	0.822199	+	0.569201i	$0.192747\pi$
$402$	10.9173	0.544504
$403$	−18.0563	−0.899450
$404$	16.5586	0.823819
$405$	−0.877543	−0.0436055
$406$	9.11404	0.452322
$407$	−11.6109	−0.575530
$408$	1.00000	0.0495074
$409$	5.02080	0.248263	0.124131	−	0.992266i	$-0.460386\pi$
$409$	5.02080	0.248263	0.124131	+	0.992266i	$0.460386\pi$
$410$	−2.13004	−0.105195
$411$	−12.8283	−0.632772
$412$	18.6957	0.921071
$413$	4.30430	0.211801
$414$	−3.74016	−0.183819
$415$	−13.1140	−0.643741
$416$	5.05151	0.247671
$417$	3.73772	0.183037
$418$	15.8802	0.776726
$419$	31.5902	1.54328	0.771640	−	0.636059i	$-0.219437\pi$
$419$	31.5902	1.54328	0.771640	+	0.636059i	$0.219437\pi$
$420$	3.77721	0.184309
$421$	−25.3368	−1.23484	−0.617419	−	0.786634i	$-0.711822\pi$
$421$	−25.3368	−1.23484	−0.617419	+	0.786634i	$0.711822\pi$
$422$	18.1556	0.883799
$423$	4.76221	0.231547
$424$	9.00329	0.437239
$425$	−4.22992	−0.205181
$426$	−3.56848	−0.172893
$427$	1.88049	0.0910032
$428$	−5.14856	−0.248865
$429$	11.6366	0.561822
$430$	−1.01610	−0.0490008
$431$	−11.9267	−0.574489	−0.287245	−	0.957857i	$-0.592739\pi$
$431$	−11.9267	−0.574489	−0.287245	+	0.957857i	$0.592739\pi$
$432$	1.00000	0.0481125
$433$	−40.3348	−1.93837	−0.969184	−	0.246339i	$-0.920772\pi$
$433$	−40.3348	−1.93837	−0.969184	+	0.246339i	$0.920772\pi$
$434$	15.3855	0.738525
$435$	1.85813	0.0890907
$436$	−8.89420	−0.425955
$437$	−25.7834	−1.23339
$438$	10.4703	0.500291
$439$	−32.0919	−1.53166	−0.765832	−	0.643040i	$-0.777673\pi$
$439$	−32.0919	−1.53166	−0.765832	+	0.643040i	$0.777673\pi$
$440$	−2.02150	−0.0963714
$441$	11.5270	0.548904
$442$	5.05151	0.240276
$443$	−6.45303	−0.306593	−0.153296	−	0.988180i	$-0.548989\pi$
$443$	−6.45303	−0.306593	−0.153296	+	0.988180i	$0.548989\pi$
$444$	−5.04033	−0.239204
$445$	−10.8598	−0.514806
$446$	−12.1629	−0.575930
$447$	−7.05125	−0.333513
$448$	−4.30430	−0.203359
$449$	24.7264	1.16691	0.583456	−	0.812145i	$-0.301700\pi$
$449$	24.7264	1.16691	0.583456	+	0.812145i	$0.301700\pi$
$450$	−4.22992	−0.199400
$451$	5.59145	0.263291
$452$	−4.07890	−0.191855
$453$	6.95671	0.326855
$454$	−10.1522	−0.476465
$455$	19.0806	0.894512
$456$	6.89366	0.322825
$457$	−14.9141	−0.697652	−0.348826	−	0.937187i	$-0.613420\pi$
$457$	−14.9141	−0.697652	−0.348826	+	0.937187i	$0.613420\pi$
$458$	3.11633	0.145617
$459$	1.00000	0.0466760
$460$	3.28215	0.153031
$461$	−35.2317	−1.64090	−0.820451	−	0.571716i	$-0.806278\pi$
$461$	−35.2317	−1.64090	−0.820451	+	0.571716i	$0.806278\pi$
$462$	−9.91536	−0.461304
$463$	34.8659	1.62036	0.810178	−	0.586184i	$-0.199370\pi$
$463$	34.8659	1.62036	0.810178	+	0.586184i	$0.199370\pi$
$464$	−2.11743	−0.0982991
$465$	3.13672	0.145462
$466$	−21.2854	−0.986029
$467$	29.3445	1.35790	0.678951	−	0.734183i	$-0.262435\pi$
$467$	29.3445	1.35790	0.678951	+	0.734183i	$0.262435\pi$
$468$	5.05151	0.233506
$469$	−46.9912	−2.16985
$470$	−4.17904	−0.192765
$471$	−10.0668	−0.463854
$472$	−1.00000	−0.0460287
$473$	2.66732	0.122644
$474$	−2.70149	−0.124084
$475$	−29.1596	−1.33793
$476$	−4.30430	−0.197287
$477$	9.00329	0.412232
$478$	−7.96108	−0.364131
$479$	−32.4605	−1.48316	−0.741579	−	0.670866i	$-0.765923\pi$
$479$	−32.4605	−1.48316	−0.741579	+	0.670866i	$0.765923\pi$
$480$	−0.877543	−0.0400542
$481$	−25.4613	−1.16094
$482$	18.2076	0.829335
$483$	16.0988	0.732520
$484$	−5.69345	−0.258793
$485$	0.699169	0.0317476
$486$	1.00000	0.0453609
$487$	16.8915	0.765425	0.382712	−	0.923868i	$-0.374990\pi$
$487$	16.8915	0.765425	0.382712	+	0.923868i	$0.374990\pi$
$488$	−0.436886	−0.0197769
$489$	17.0589	0.771430
$490$	−10.1154	−0.456968
$491$	−21.5669	−0.973302	−0.486651	−	0.873597i	$-0.661782\pi$
$491$	−21.5669	−0.973302	−0.486651	+	0.873597i	$0.661782\pi$
$492$	2.42727	0.109430
$493$	−2.11743	−0.0953641
$494$	34.8234	1.56678
$495$	−2.02150	−0.0908598
$496$	−3.57444	−0.160497
$497$	15.3598	0.688981
$498$	14.9440	0.669657
$499$	−28.9628	−1.29655	−0.648276	−	0.761405i	$-0.724510\pi$
$499$	−28.9628	−1.29655	−0.648276	+	0.761405i	$0.724510\pi$
$500$	8.09965	0.362227
$501$	−0.675722	−0.0301890
$502$	−14.8296	−0.661879
$503$	23.2254	1.03557	0.517785	−	0.855511i	$-0.326757\pi$
$503$	23.2254	1.03557	0.517785	+	0.855511i	$0.326757\pi$
$504$	−4.30430	−0.191729
$505$	−14.5308	−0.646614
$506$	−8.61582	−0.383020
$507$	12.5178	0.555934
$508$	−12.8459	−0.569945
$509$	0.646995	0.0286775	0.0143388	−	0.999897i	$-0.495436\pi$
$509$	0.646995	0.0286775	0.0143388	+	0.999897i	$0.495436\pi$
$510$	−0.877543	−0.0388583
$511$	−45.0674	−1.99366
$512$	1.00000	0.0441942
$513$	6.89366	0.304362
$514$	19.6495	0.866702
$515$	−16.4063	−0.722947
$516$	1.15789	0.0509735
$517$	10.9702	0.482469
$518$	21.6951	0.953228
$519$	7.42906	0.326100
$520$	−4.43292	−0.194396
$521$	13.6146	0.596469	0.298234	−	0.954493i	$-0.403602\pi$
$521$	13.6146	0.596469	0.298234	+	0.954493i	$0.403602\pi$
$522$	−2.11743	−0.0926773
$523$	−38.1995	−1.67035	−0.835173	−	0.549987i	$-0.814633\pi$
$523$	−38.1995	−1.67035	−0.835173	+	0.549987i	$0.814633\pi$
$524$	7.90167	0.345186
$525$	18.2068	0.794611
$526$	24.3818	1.06310
$527$	−3.57444	−0.155705
$528$	2.30359	0.100251
$529$	−9.01117	−0.391790
$530$	−7.90078	−0.343188
$531$	−1.00000	−0.0433963
$532$	−29.6724	−1.28646
$533$	12.2614	0.531100
$534$	12.3753	0.535531
$535$	4.51808	0.195334
$536$	10.9173	0.471555
$537$	−1.63402	−0.0705130
$538$	21.8406	0.941617
$539$	26.5535	1.14374
$540$	−0.877543	−0.0377634
$541$	−39.0417	−1.67853	−0.839266	−	0.543721i	$-0.817015\pi$
$541$	−39.0417	−1.67853	−0.839266	+	0.543721i	$0.817015\pi$
$542$	−19.6792	−0.845292
$543$	23.0051	0.987245
$544$	1.00000	0.0428746
$545$	7.80505	0.334331
$546$	−21.7432	−0.930524
$547$	−6.83309	−0.292162	−0.146081	−	0.989273i	$-0.546666\pi$
$547$	−6.83309	−0.292162	−0.146081	+	0.989273i	$0.546666\pi$
$548$	−12.8283	−0.547997
$549$	−0.436886	−0.0186459
$550$	−9.74402	−0.415486
$551$	−14.5968	−0.621845
$552$	−3.74016	−0.159192
$553$	11.6280	0.494474
$554$	26.3177	1.11813
$555$	4.42311	0.187751
$556$	3.73772	0.158515
$557$	−21.2603	−0.900828	−0.450414	−	0.892820i	$-0.648724\pi$
$557$	−21.2603	−0.900828	−0.450414	+	0.892820i	$0.648724\pi$
$558$	−3.57444	−0.151318
$559$	5.84912	0.247391
$560$	3.77721	0.159616
$561$	2.30359	0.0972579
$562$	19.7053	0.831216
$563$	−10.5885	−0.446251	−0.223126	−	0.974790i	$-0.571626\pi$
$563$	−10.5885	−0.446251	−0.223126	+	0.974790i	$0.571626\pi$
$564$	4.76221	0.200525
$565$	3.57941	0.150587
$566$	−22.4304	−0.942821
$567$	−4.30430	−0.180763
$568$	−3.56848	−0.149730
$569$	−7.64211	−0.320374	−0.160187	−	0.987087i	$-0.551210\pi$
$569$	−7.64211	−0.320374	−0.160187	+	0.987087i	$0.551210\pi$
$570$	−6.04948	−0.253385
$571$	−14.8389	−0.620988	−0.310494	−	0.950575i	$-0.600494\pi$
$571$	−14.8389	−0.620988	−0.310494	+	0.950575i	$0.600494\pi$
$572$	11.6366	0.486552
$573$	−18.4009	−0.768709
$574$	−10.4477	−0.436079
$575$	15.8206	0.659764
$576$	1.00000	0.0416667
$577$	9.47090	0.394279	0.197139	−	0.980375i	$-0.436835\pi$
$577$	9.47090	0.394279	0.197139	+	0.980375i	$0.436835\pi$
$578$	1.00000	0.0415945
$579$	22.1825	0.921873
$580$	1.85813	0.0771548
$581$	−64.3234	−2.66858
$582$	−0.796735	−0.0330257
$583$	20.7399	0.858961
$584$	10.4703	0.433265
$585$	−4.43292	−0.183279
$586$	16.0364	0.662458
$587$	−11.0480	−0.455998	−0.227999	−	0.973661i	$-0.573218\pi$
$587$	−11.0480	−0.455998	−0.227999	+	0.973661i	$0.573218\pi$
$588$	11.5270	0.475364
$589$	−24.6410	−1.01531
$590$	0.877543	0.0361279
$591$	−7.77988	−0.320022
$592$	−5.04033	−0.207156
$593$	−7.50287	−0.308106	−0.154053	−	0.988063i	$-0.549233\pi$
$593$	−7.50287	−0.308106	−0.154053	+	0.988063i	$0.549233\pi$
$594$	2.30359	0.0945176
$595$	3.77721	0.154850
$596$	−7.05125	−0.288830
$597$	−1.09109	−0.0446553
$598$	−18.8935	−0.772612
$599$	33.0055	1.34857	0.674284	−	0.738473i	$-0.264453\pi$
$599$	33.0055	1.34857	0.674284	+	0.738473i	$0.264453\pi$
$600$	−4.22992	−0.172686
$601$	−0.974548	−0.0397526	−0.0198763	−	0.999802i	$-0.506327\pi$
$601$	−0.974548	−0.0397526	−0.0198763	+	0.999802i	$0.506327\pi$
$602$	−4.98392	−0.203130
$603$	10.9173	0.444586
$604$	6.95671	0.283065
$605$	4.99625	0.203126
$606$	16.5586	0.672646
$607$	1.17832	0.0478266	0.0239133	−	0.999714i	$-0.492387\pi$
$607$	1.17832	0.0478266	0.0239133	+	0.999714i	$0.492387\pi$
$608$	6.89366	0.279575
$609$	9.11404	0.369319
$610$	0.383387	0.0155229
$611$	24.0564	0.973216
$612$	1.00000	0.0404226
$613$	0.515565	0.0208235	0.0104117	−	0.999946i	$-0.496686\pi$
$613$	0.515565	0.0208235	0.0104117	+	0.999946i	$0.496686\pi$
$614$	−26.3214	−1.06225
$615$	−2.13004	−0.0858913
$616$	−9.91536	−0.399501
$617$	−2.97725	−0.119860	−0.0599298	−	0.998203i	$-0.519088\pi$
$617$	−2.97725	−0.119860	−0.0599298	+	0.998203i	$0.519088\pi$
$618$	18.6957	0.752051
$619$	0.590071	0.0237170	0.0118585	−	0.999930i	$-0.496225\pi$
$619$	0.590071	0.0237170	0.0118585	+	0.999930i	$0.496225\pi$
$620$	3.13672	0.125974
$621$	−3.74016	−0.150088
$622$	−9.60875	−0.385276
$623$	−53.2669	−2.13409
$624$	5.05151	0.202222
$625$	14.0418	0.561672
$626$	3.49992	0.139885
$627$	15.8802	0.634194
$628$	−10.0668	−0.401709
$629$	−5.04033	−0.200971
$630$	3.77721	0.150487
$631$	−19.8553	−0.790426	−0.395213	−	0.918590i	$-0.629329\pi$
$631$	−19.8553	−0.790426	−0.395213	+	0.918590i	$0.629329\pi$
$632$	−2.70149	−0.107460
$633$	18.1556	0.721618
$634$	5.51016	0.218837
$635$	11.2728	0.447348
$636$	9.00329	0.357004
$637$	58.2287	2.30710
$638$	−4.87769	−0.193110
$639$	−3.56848	−0.141167
$640$	−0.877543	−0.0346879
$641$	−20.2960	−0.801643	−0.400822	−	0.916156i	$-0.631275\pi$
$641$	−20.2960	−0.801643	−0.400822	+	0.916156i	$0.631275\pi$
$642$	−5.14856	−0.203197
$643$	7.76284	0.306136	0.153068	−	0.988216i	$-0.451085\pi$
$643$	7.76284	0.306136	0.153068	+	0.988216i	$0.451085\pi$
$644$	16.0988	0.634381
$645$	−1.01610	−0.0400090
$646$	6.89366	0.271227
$647$	−13.7200	−0.539390	−0.269695	−	0.962946i	$-0.586923\pi$
$647$	−13.7200	−0.539390	−0.269695	+	0.962946i	$0.586923\pi$
$648$	1.00000	0.0392837
$649$	−2.30359	−0.0904240
$650$	−21.3675	−0.838102
$651$	15.3855	0.603003
$652$	17.0589	0.668078
$653$	25.0489	0.980239	0.490119	−	0.871655i	$-0.336953\pi$
$653$	25.0489	0.980239	0.490119	+	0.871655i	$0.336953\pi$
$654$	−8.89420	−0.347791
$655$	−6.93406	−0.270936
$656$	2.42727	0.0947691
$657$	10.4703	0.408486
$658$	−20.4980	−0.799094
$659$	4.58884	0.178756	0.0893779	−	0.995998i	$-0.471512\pi$
$659$	4.58884	0.178756	0.0893779	+	0.995998i	$0.471512\pi$
$660$	−2.02150	−0.0786869
$661$	−35.4885	−1.38034	−0.690170	−	0.723647i	$-0.742464\pi$
$661$	−35.4885	−1.38034	−0.690170	+	0.723647i	$0.742464\pi$
$662$	−25.9542	−1.00874
$663$	5.05151	0.196185
$664$	14.9440	0.579940
$665$	26.0388	1.00974
$666$	−5.04033	−0.195309
$667$	7.91953	0.306645
$668$	−0.675722	−0.0261445
$669$	−12.1629	−0.470245
$670$	−9.58038	−0.370122
$671$	−1.00641	−0.0388520
$672$	−4.30430	−0.166042
$673$	9.89513	0.381429	0.190715	−	0.981646i	$-0.438920\pi$
$673$	9.89513	0.381429	0.190715	+	0.981646i	$0.438920\pi$
$674$	−12.3722	−0.476561
$675$	−4.22992	−0.162810
$676$	12.5178	0.481453
$677$	−24.4100	−0.938153	−0.469076	−	0.883158i	$-0.655413\pi$
$677$	−24.4100	−0.938153	−0.469076	+	0.883158i	$0.655413\pi$
$678$	−4.07890	−0.156649
$679$	3.42939	0.131608
$680$	−0.877543	−0.0336522
$681$	−10.1522	−0.389032
$682$	−8.23406	−0.315299
$683$	−37.3398	−1.42877	−0.714384	−	0.699754i	$-0.753293\pi$
$683$	−37.3398	−1.42877	−0.714384	+	0.699754i	$0.753293\pi$
$684$	6.89366	0.263586
$685$	11.2574	0.430122
$686$	−19.4854	−0.743958
$687$	3.11633	0.118895
$688$	1.15789	0.0441443
$689$	45.4803	1.73266
$690$	3.28215	0.124949
$691$	−9.17164	−0.348906	−0.174453	−	0.984666i	$-0.555816\pi$
$691$	−9.17164	−0.348906	−0.174453	+	0.984666i	$0.555816\pi$
$692$	7.42906	0.282411
$693$	−9.91536	−0.376653
$694$	−29.5835	−1.12297
$695$	−3.28001	−0.124418
$696$	−2.11743	−0.0802609
$697$	2.42727	0.0919395
$698$	−20.6380	−0.781161
$699$	−21.2854	−0.805089
$700$	18.2068	0.688153
$701$	31.2541	1.18045	0.590225	−	0.807239i	$-0.299039\pi$
$701$	31.2541	1.18045	0.590225	+	0.807239i	$0.299039\pi$
$702$	5.05151	0.190657
$703$	−34.7463	−1.31048
$704$	2.30359	0.0868200
$705$	−4.17904	−0.157392
$706$	1.62624	0.0612044
$707$	−71.2730	−2.68050
$708$	−1.00000	−0.0375823
$709$	−39.8669	−1.49723	−0.748616	−	0.663004i	$-0.769281\pi$
$709$	−39.8669	−1.49723	−0.748616	+	0.663004i	$0.769281\pi$
$710$	3.13150	0.117523
$711$	−2.70149	−0.101314
$712$	12.3753	0.463784
$713$	13.3690	0.500673
$714$	−4.30430	−0.161084
$715$	−10.2117	−0.381894
$716$	−1.63402	−0.0610661
$717$	−7.96108	−0.297312
$718$	−22.3190	−0.832939
$719$	12.6263	0.470882	0.235441	−	0.971889i	$-0.424347\pi$
$719$	12.6263	0.470882	0.235441	+	0.971889i	$0.424347\pi$
$720$	−0.877543	−0.0327041
$721$	−80.4719	−2.99693
$722$	28.5225	1.06150
$723$	18.2076	0.677150
$724$	23.0051	0.854979
$725$	8.95654	0.332638
$726$	−5.69345	−0.211304
$727$	−41.5133	−1.53964	−0.769821	−	0.638260i	$-0.779654\pi$
$727$	−41.5133	−1.53964	−0.769821	+	0.638260i	$0.779654\pi$
$728$	−21.7432	−0.805857
$729$	1.00000	0.0370370
$730$	−9.18816	−0.340069
$731$	1.15789	0.0428263
$732$	−0.436886	−0.0161478
$733$	26.6946	0.985989	0.492995	−	0.870032i	$-0.335902\pi$
$733$	26.6946	0.985989	0.492995	+	0.870032i	$0.335902\pi$
$734$	−18.2295	−0.672861
$735$	−10.1154	−0.373113
$736$	−3.74016	−0.137864
$737$	25.1490	0.926375
$738$	2.42727	0.0893491
$739$	−32.1480	−1.18258	−0.591292	−	0.806458i	$-0.701382\pi$
$739$	−32.1480	−1.18258	−0.591292	+	0.806458i	$0.701382\pi$
$740$	4.42311	0.162597
$741$	34.8234	1.27927
$742$	−38.7528	−1.42266
$743$	48.1861	1.76778	0.883889	−	0.467697i	$-0.154916\pi$
$743$	48.1861	1.76778	0.883889	+	0.467697i	$0.154916\pi$
$744$	−3.57444	−0.131045
$745$	6.18777	0.226702
$746$	−1.94774	−0.0713119
$747$	14.9440	0.546772
$748$	2.30359	0.0842278
$749$	22.1609	0.809743
$750$	8.09965	0.295757
$751$	10.3964	0.379369	0.189685	−	0.981845i	$-0.439253\pi$
$751$	10.3964	0.379369	0.189685	+	0.981845i	$0.439253\pi$
$752$	4.76221	0.173660
$753$	−14.8296	−0.540422
$754$	−10.6962	−0.389533
$755$	−6.10481	−0.222177
$756$	−4.30430	−0.156546
$757$	−38.5582	−1.40142	−0.700711	−	0.713445i	$-0.747134\pi$
$757$	−38.5582	−1.40142	−0.700711	+	0.713445i	$0.747134\pi$
$758$	19.9168	0.723409
$759$	−8.61582	−0.312735
$760$	−6.04948	−0.219438
$761$	43.6976	1.58404	0.792019	−	0.610497i	$-0.209030\pi$
$761$	43.6976	1.58404	0.792019	+	0.610497i	$0.209030\pi$
$762$	−12.8459	−0.465358
$763$	38.2833	1.38595
$764$	−18.4009	−0.665721
$765$	−0.877543	−0.0317276
$766$	24.1839	0.873800
$767$	−5.05151	−0.182400
$768$	1.00000	0.0360844
$769$	15.8159	0.570336	0.285168	−	0.958478i	$-0.407951\pi$
$769$	15.8159	0.570336	0.285168	+	0.958478i	$0.407951\pi$
$770$	8.70115	0.313568
$771$	19.6495	0.707659
$772$	22.1825	0.798365
$773$	29.1380	1.04802	0.524010	−	0.851712i	$-0.324436\pi$
$773$	29.1380	1.04802	0.524010	+	0.851712i	$0.324436\pi$
$774$	1.15789	0.0416197
$775$	15.1196	0.543112
$776$	−0.796735	−0.0286011
$777$	21.6951	0.778307
$778$	8.69795	0.311836
$779$	16.7328	0.599514
$780$	−4.43292	−0.158724
$781$	−8.22033	−0.294147
$782$	−3.74016	−0.133748
$783$	−2.11743	−0.0756707
$784$	11.5270	0.411678
$785$	8.83405	0.315301
$786$	7.90167	0.281843
$787$	15.5557	0.554500	0.277250	−	0.960798i	$-0.410577\pi$
$787$	15.5557	0.554500	0.277250	+	0.960798i	$0.410577\pi$
$788$	−7.77988	−0.277147
$789$	24.3818	0.868016
$790$	2.37068	0.0843448
$791$	17.5568	0.624247
$792$	2.30359	0.0818547
$793$	−2.20694	−0.0783706
$794$	0.936843	0.0332473
$795$	−7.90078	−0.280212
$796$	−1.09109	−0.0386726
$797$	−54.8428	−1.94263	−0.971316	−	0.237791i	$-0.923577\pi$
$797$	−54.8428	−1.94263	−0.971316	+	0.237791i	$0.923577\pi$
$798$	−29.6724	−1.05039
$799$	4.76221	0.168475
$800$	−4.22992	−0.149550
$801$	12.3753	0.437259
$802$	32.9290	1.16276
$803$	24.1194	0.851155
$804$	10.9173	0.385023
$805$	−14.1274	−0.497924
$806$	−18.0563	−0.636007
$807$	21.8406	0.768827
$808$	16.5586	0.582528
$809$	6.31641	0.222073	0.111037	−	0.993816i	$-0.464583\pi$
$809$	6.31641	0.222073	0.111037	+	0.993816i	$0.464583\pi$
$810$	−0.877543	−0.0308337
$811$	31.0815	1.09142	0.545709	−	0.837975i	$-0.316260\pi$
$811$	31.0815	1.09142	0.545709	+	0.837975i	$0.316260\pi$
$812$	9.11404	0.319840
$813$	−19.6792	−0.690178
$814$	−11.6109	−0.406961
$815$	−14.9699	−0.524373
$816$	1.00000	0.0350070
$817$	7.98213	0.279259
$818$	5.02080	0.175548
$819$	−21.7432	−0.759769
$820$	−2.13004	−0.0743841
$821$	48.2338	1.68337	0.841685	−	0.539969i	$-0.181564\pi$
$821$	48.2338	1.68337	0.841685	+	0.539969i	$0.181564\pi$
$822$	−12.8283	−0.447437
$823$	12.7848	0.445651	0.222825	−	0.974858i	$-0.428472\pi$
$823$	12.7848	0.445651	0.222825	+	0.974858i	$0.428472\pi$
$824$	18.6957	0.651296
$825$	−9.74402	−0.339243
$826$	4.30430	0.149766
$827$	−18.5328	−0.644450	−0.322225	−	0.946663i	$-0.604431\pi$
$827$	−18.5328	−0.644450	−0.322225	+	0.946663i	$0.604431\pi$
$828$	−3.74016	−0.129980
$829$	−14.8456	−0.515608	−0.257804	−	0.966197i	$-0.582999\pi$
$829$	−14.8456	−0.515608	−0.257804	+	0.966197i	$0.582999\pi$
$830$	−13.1140	−0.455194
$831$	26.3177	0.912952
$832$	5.05151	0.175130
$833$	11.5270	0.399386
$834$	3.73772	0.129427
$835$	0.592975	0.0205207
$836$	15.8802	0.549228
$837$	−3.57444	−0.123551
$838$	31.5902	1.09126
$839$	15.9710	0.551380	0.275690	−	0.961247i	$-0.411094\pi$
$839$	15.9710	0.551380	0.275690	+	0.961247i	$0.411094\pi$
$840$	3.77721	0.130326
$841$	−24.5165	−0.845397
$842$	−25.3368	−0.873162
$843$	19.7053	0.678685
$844$	18.1556	0.624940
$845$	−10.9849	−0.377892
$846$	4.76221	0.163728
$847$	24.5063	0.842047
$848$	9.00329	0.309174
$849$	−22.4304	−0.769810
$850$	−4.22992	−0.145085
$851$	18.8517	0.646227
$852$	−3.56848	−0.122254
$853$	−47.3944	−1.62275	−0.811377	−	0.584523i	$-0.801282\pi$
$853$	−47.3944	−1.62275	−0.811377	+	0.584523i	$0.801282\pi$
$854$	1.88049	0.0643490
$855$	−6.04948	−0.206888
$856$	−5.14856	−0.175974
$857$	6.98682	0.238665	0.119333	−	0.992854i	$-0.461925\pi$
$857$	6.98682	0.238665	0.119333	+	0.992854i	$0.461925\pi$
$858$	11.6366	0.397268
$859$	−35.4872	−1.21081	−0.605404	−	0.795919i	$-0.706988\pi$
$859$	−35.4872	−1.21081	−0.605404	+	0.795919i	$0.706988\pi$
$860$	−1.01610	−0.0346488
$861$	−10.4477	−0.356057
$862$	−11.9267	−0.406225
$863$	15.0125	0.511031	0.255516	−	0.966805i	$-0.417755\pi$
$863$	15.0125	0.511031	0.255516	+	0.966805i	$0.417755\pi$
$864$	1.00000	0.0340207
$865$	−6.51932	−0.221664
$866$	−40.3348	−1.37063
$867$	1.00000	0.0339618
$868$	15.3855	0.522216
$869$	−6.22314	−0.211106
$870$	1.85813	0.0629966
$871$	55.1488	1.86865
$872$	−8.89420	−0.301196
$873$	−0.796735	−0.0269654
$874$	−25.7834	−0.872137
$875$	−34.8633	−1.17859
$876$	10.4703	0.353759
$877$	7.38172	0.249263	0.124631	−	0.992203i	$-0.460225\pi$
$877$	7.38172	0.249263	0.124631	+	0.992203i	$0.460225\pi$
$878$	−32.0919	−1.08305
$879$	16.0364	0.540895
$880$	−2.02150	−0.0681449
$881$	2.86488	0.0965203	0.0482601	−	0.998835i	$-0.484632\pi$
$881$	2.86488	0.0965203	0.0482601	+	0.998835i	$0.484632\pi$
$882$	11.5270	0.388133
$883$	−46.5673	−1.56712	−0.783558	−	0.621319i	$-0.786597\pi$
$883$	−46.5673	−1.56712	−0.783558	+	0.621319i	$0.786597\pi$
$884$	5.05151	0.169901
$885$	0.877543	0.0294983
$886$	−6.45303	−0.216794
$887$	24.1809	0.811914	0.405957	−	0.913892i	$-0.366938\pi$
$887$	24.1809	0.811914	0.405957	+	0.913892i	$0.366938\pi$
$888$	−5.04033	−0.169143
$889$	55.2926	1.85445
$890$	−10.8598	−0.364023
$891$	2.30359	0.0771733
$892$	−12.1629	−0.407244
$893$	32.8290	1.09858
$894$	−7.05125	−0.235829
$895$	1.43392	0.0479306
$896$	−4.30430	−0.143796
$897$	−18.8935	−0.630835
$898$	24.7264	0.825132
$899$	7.56862	0.252428
$900$	−4.22992	−0.140997
$901$	9.00329	0.299943
$902$	5.59145	0.186175
$903$	−4.98392	−0.165855
$904$	−4.07890	−0.135662
$905$	−20.1880	−0.671072
$906$	6.95671	0.231121
$907$	41.8560	1.38981	0.694903	−	0.719104i	$-0.255447\pi$
$907$	41.8560	1.38981	0.694903	+	0.719104i	$0.255447\pi$
$908$	−10.1522	−0.336911
$909$	16.5586	0.549213
$910$	19.0806	0.632516
$911$	11.4859	0.380546	0.190273	−	0.981731i	$-0.439063\pi$
$911$	11.4859	0.380546	0.190273	+	0.981731i	$0.439063\pi$
$912$	6.89366	0.228272
$913$	34.4249	1.13930
$914$	−14.9141	−0.493315
$915$	0.383387	0.0126744
$916$	3.11633	0.102966
$917$	−34.0112	−1.12315
$918$	1.00000	0.0330049
$919$	−16.9946	−0.560599	−0.280300	−	0.959913i	$-0.590434\pi$
$919$	−16.9946	−0.560599	−0.280300	+	0.959913i	$0.590434\pi$
$920$	3.28215	0.108209
$921$	−26.3214	−0.867321
$922$	−35.2317	−1.16029
$923$	−18.0262	−0.593341
$924$	−9.91536	−0.326191
$925$	21.3202	0.701004
$926$	34.8659	1.14576
$927$	18.6957	0.614047
$928$	−2.11743	−0.0695080
$929$	43.6825	1.43318	0.716589	−	0.697496i	$-0.245702\pi$
$929$	43.6825	1.43318	0.716589	+	0.697496i	$0.245702\pi$
$930$	3.13672	0.102857
$931$	79.4630	2.60430
$932$	−21.2854	−0.697228
$933$	−9.60875	−0.314576
$934$	29.3445	0.960182
$935$	−2.02150	−0.0661102
$936$	5.05151	0.165114
$937$	0.189310	0.00618448	0.00309224	−	0.999995i	$-0.499016\pi$
$937$	0.189310	0.00618448	0.00309224	+	0.999995i	$0.499016\pi$
$938$	−46.9912	−1.53432
$939$	3.49992	0.114216
$940$	−4.17904	−0.136305
$941$	−46.2506	−1.50773	−0.753864	−	0.657031i	$-0.771812\pi$
$941$	−46.2506	−1.50773	−0.753864	+	0.657031i	$0.771812\pi$
$942$	−10.0668	−0.327994
$943$	−9.07840	−0.295633
$944$	−1.00000	−0.0325472
$945$	3.77721	0.122872
$946$	2.66732	0.0867221
$947$	−38.5273	−1.25197	−0.625985	−	0.779835i	$-0.715303\pi$
$947$	−38.5273	−1.25197	−0.625985	+	0.779835i	$0.715303\pi$
$948$	−2.70149	−0.0877404
$949$	52.8910	1.71691
$950$	−29.1596	−0.946063
$951$	5.51016	0.178679
$952$	−4.30430	−0.139503
$953$	12.5850	0.407669	0.203834	−	0.979005i	$-0.434660\pi$
$953$	12.5850	0.407669	0.203834	+	0.979005i	$0.434660\pi$
$954$	9.00329	0.291492
$955$	16.1476	0.522523
$956$	−7.96108	−0.257480
$957$	−4.87769	−0.157673
$958$	−32.4605	−1.04875
$959$	55.2167	1.78304
$960$	−0.877543	−0.0283226
$961$	−18.2234	−0.587851
$962$	−25.4613	−0.820906
$963$	−5.14856	−0.165910
$964$	18.2076	0.586429
$965$	−19.4661	−0.626635
$966$	16.0988	0.517970
$967$	12.3696	0.397780	0.198890	−	0.980022i	$-0.436266\pi$
$967$	12.3696	0.397780	0.198890	+	0.980022i	$0.436266\pi$
$968$	−5.69345	−0.182994
$969$	6.89366	0.221456
$970$	0.699169	0.0224490
$971$	−30.4025	−0.975663	−0.487831	−	0.872938i	$-0.662212\pi$
$971$	−30.4025	−0.975663	−0.487831	+	0.872938i	$0.662212\pi$
$972$	1.00000	0.0320750
$973$	−16.0882	−0.515766
$974$	16.8915	0.541237
$975$	−21.3675	−0.684307
$976$	−0.436886	−0.0139844
$977$	4.37150	0.139857	0.0699284	−	0.997552i	$-0.477723\pi$
$977$	4.37150	0.139857	0.0699284	+	0.997552i	$0.477723\pi$
$978$	17.0589	0.545483
$979$	28.5076	0.911108
$980$	−10.1154	−0.323125
$981$	−8.89420	−0.283970
$982$	−21.5669	−0.688228
$983$	11.1613	0.355991	0.177996	−	0.984031i	$-0.443039\pi$
$983$	11.1613	0.355991	0.177996	+	0.984031i	$0.443039\pi$
$984$	2.42727	0.0773786
$985$	6.82718	0.217532
$986$	−2.11743	−0.0674326
$987$	−20.4980	−0.652458
$988$	34.8234	1.10788
$989$	−4.33072	−0.137709
$990$	−2.02150	−0.0642476
$991$	6.11662	0.194301	0.0971504	−	0.995270i	$-0.469027\pi$
$991$	6.11662	0.194301	0.0971504	+	0.995270i	$0.469027\pi$
$992$	−3.57444	−0.113489
$993$	−25.9542	−0.823633
$994$	15.3598	0.487183
$995$	0.957477	0.0303541
$996$	14.9440	0.473519
$997$	61.5992	1.95087	0.975434	−	0.220293i	$-0.0707012\pi$
$997$	61.5992	1.95087	0.975434	+	0.220293i	$0.0707012\pi$
$998$	−28.9628	−0.916801
$999$	−5.04033	−0.159469

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.bb.1.5	✓	13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.bb.1.5	✓	13	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.877543 q^{5} +1.00000 q^{6} -4.30430 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.877543 q^{5} +1.00000 q^{6} -4.30430 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.877543 q^{10} +2.30359 q^{11} +1.00000 q^{12} +5.05151 q^{13} -4.30430 q^{14} -0.877543 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} +6.89366 q^{19} -0.877543 q^{20} -4.30430 q^{21} +2.30359 q^{22} -3.74016 q^{23} +1.00000 q^{24} -4.22992 q^{25} +5.05151 q^{26} +1.00000 q^{27} -4.30430 q^{28} -2.11743 q^{29} -0.877543 q^{30} -3.57444 q^{31} +1.00000 q^{32} +2.30359 q^{33} +1.00000 q^{34} +3.77721 q^{35} +1.00000 q^{36} -5.04033 q^{37} +6.89366 q^{38} +5.05151 q^{39} -0.877543 q^{40} +2.42727 q^{41} -4.30430 q^{42} +1.15789 q^{43} +2.30359 q^{44} -0.877543 q^{45} -3.74016 q^{46} +4.76221 q^{47} +1.00000 q^{48} +11.5270 q^{49} -4.22992 q^{50} +1.00000 q^{51} +5.05151 q^{52} +9.00329 q^{53} +1.00000 q^{54} -2.02150 q^{55} -4.30430 q^{56} +6.89366 q^{57} -2.11743 q^{58} -1.00000 q^{59} -0.877543 q^{60} -0.436886 q^{61} -3.57444 q^{62} -4.30430 q^{63} +1.00000 q^{64} -4.43292 q^{65} +2.30359 q^{66} +10.9173 q^{67} +1.00000 q^{68} -3.74016 q^{69} +3.77721 q^{70} -3.56848 q^{71} +1.00000 q^{72} +10.4703 q^{73} -5.04033 q^{74} -4.22992 q^{75} +6.89366 q^{76} -9.91536 q^{77} +5.05151 q^{78} -2.70149 q^{79} -0.877543 q^{80} +1.00000 q^{81} +2.42727 q^{82} +14.9440 q^{83} -4.30430 q^{84} -0.877543 q^{85} +1.15789 q^{86} -2.11743 q^{87} +2.30359 q^{88} +12.3753 q^{89} -0.877543 q^{90} -21.7432 q^{91} -3.74016 q^{92} -3.57444 q^{93} +4.76221 q^{94} -6.04948 q^{95} +1.00000 q^{96} -0.796735 q^{97} +11.5270 q^{98} +2.30359 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 13 q^{2} + 13 q^{3} + 13 q^{4} + 4 q^{5} + 13 q^{6} + 11 q^{7} + 13 q^{8} + 13 q^{9}+O(q^{10}) \) 13 * q + 13 * q^2 + 13 * q^3 + 13 * q^4 + 4 * q^5 + 13 * q^6 + 11 * q^7 + 13 * q^8 + 13 * q^9	\( 13 q + 13 q^{2} + 13 q^{3} + 13 q^{4} + 4 q^{5} + 13 q^{6} + 11 q^{7} + 13 q^{8} + 13 q^{9} + 4 q^{10} + 7 q^{11} + 13 q^{12} + 6 q^{13} + 11 q^{14} + 4 q^{15} + 13 q^{16} + 13 q^{17} + 13 q^{18} + 9 q^{19} + 4 q^{20} + 11 q^{21} + 7 q^{22} + 2 q^{23} + 13 q^{24} + 33 q^{25} + 6 q^{26} + 13 q^{27} + 11 q^{28} + 14 q^{29} + 4 q^{30} - 5 q^{31} + 13 q^{32} + 7 q^{33} + 13 q^{34} + 24 q^{35} + 13 q^{36} + 4 q^{37} + 9 q^{38} + 6 q^{39} + 4 q^{40} + 28 q^{41} + 11 q^{42} + q^{43} + 7 q^{44} + 4 q^{45} + 2 q^{46} + 12 q^{47} + 13 q^{48} + 32 q^{49} + 33 q^{50} + 13 q^{51} + 6 q^{52} + 22 q^{53} + 13 q^{54} - 7 q^{55} + 11 q^{56} + 9 q^{57} + 14 q^{58} - 13 q^{59} + 4 q^{60} - 9 q^{61} - 5 q^{62} + 11 q^{63} + 13 q^{64} + 34 q^{65} + 7 q^{66} + 26 q^{67} + 13 q^{68} + 2 q^{69} + 24 q^{70} + 8 q^{71} + 13 q^{72} + 4 q^{73} + 4 q^{74} + 33 q^{75} + 9 q^{76} + 38 q^{77} + 6 q^{78} - 17 q^{79} + 4 q^{80} + 13 q^{81} + 28 q^{82} + 14 q^{83} + 11 q^{84} + 4 q^{85} + q^{86} + 14 q^{87} + 7 q^{88} + 19 q^{89} + 4 q^{90} - 5 q^{91} + 2 q^{92} - 5 q^{93} + 12 q^{94} + 25 q^{95} + 13 q^{96} - 5 q^{97} + 32 q^{98} + 7 q^{99}+O(q^{100}) \) 13 * q + 13 * q^2 + 13 * q^3 + 13 * q^4 + 4 * q^5 + 13 * q^6 + 11 * q^7 + 13 * q^8 + 13 * q^9 + 4 * q^10 + 7 * q^11 + 13 * q^12 + 6 * q^13 + 11 * q^14 + 4 * q^15 + 13 * q^16 + 13 * q^17 + 13 * q^18 + 9 * q^19 + 4 * q^20 + 11 * q^21 + 7 * q^22 + 2 * q^23 + 13 * q^24 + 33 * q^25 + 6 * q^26 + 13 * q^27 + 11 * q^28 + 14 * q^29 + 4 * q^30 - 5 * q^31 + 13 * q^32 + 7 * q^33 + 13 * q^34 + 24 * q^35 + 13 * q^36 + 4 * q^37 + 9 * q^38 + 6 * q^39 + 4 * q^40 + 28 * q^41 + 11 * q^42 + q^43 + 7 * q^44 + 4 * q^45 + 2 * q^46 + 12 * q^47 + 13 * q^48 + 32 * q^49 + 33 * q^50 + 13 * q^51 + 6 * q^52 + 22 * q^53 + 13 * q^54 - 7 * q^55 + 11 * q^56 + 9 * q^57 + 14 * q^58 - 13 * q^59 + 4 * q^60 - 9 * q^61 - 5 * q^62 + 11 * q^63 + 13 * q^64 + 34 * q^65 + 7 * q^66 + 26 * q^67 + 13 * q^68 + 2 * q^69 + 24 * q^70 + 8 * q^71 + 13 * q^72 + 4 * q^73 + 4 * q^74 + 33 * q^75 + 9 * q^76 + 38 * q^77 + 6 * q^78 - 17 * q^79 + 4 * q^80 + 13 * q^81 + 28 * q^82 + 14 * q^83 + 11 * q^84 + 4 * q^85 + q^86 + 14 * q^87 + 7 * q^88 + 19 * q^89 + 4 * q^90 - 5 * q^91 + 2 * q^92 - 5 * q^93 + 12 * q^94 + 25 * q^95 + 13 * q^96 - 5 * q^97 + 32 * q^98 + 7 * q^99

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