LMFDB - Embedded newform 6018.2.a.bc.1.8

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:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 2 x^{13} - 49 x^{12} + 79 x^{11} + 956 x^{10} - 1179 x^{9} - 9396 x^{8} + 8315 x^{7} + \cdots - 43744 $ x^14 - 2x^13 - 49x^12 + 79x^11 + 956x^10 - 1179x^9 - 9396x^8 + 8315x^7 + 48570x^6 - 28124x^5 - 125592x^4 + 40576x^3 + 138096x^2 - 22032*x - 43744
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$0.800423$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.800423 q^{5} -1.00000 q^{6} -4.52948 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.800423 q^{5} -1.00000 q^{6} -4.52948 q^{7} +1.00000 q^{8} +1.00000 q^{9} +0.800423 q^{10} -4.93150 q^{11} -1.00000 q^{12} +6.52527 q^{13} -4.52948 q^{14} -0.800423 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} -7.08202 q^{19} +0.800423 q^{20} +4.52948 q^{21} -4.93150 q^{22} +2.86224 q^{23} -1.00000 q^{24} -4.35932 q^{25} +6.52527 q^{26} -1.00000 q^{27} -4.52948 q^{28} +5.23795 q^{29} -0.800423 q^{30} -6.12633 q^{31} +1.00000 q^{32} +4.93150 q^{33} +1.00000 q^{34} -3.62550 q^{35} +1.00000 q^{36} -4.16347 q^{37} -7.08202 q^{38} -6.52527 q^{39} +0.800423 q^{40} +4.90976 q^{41} +4.52948 q^{42} +8.25459 q^{43} -4.93150 q^{44} +0.800423 q^{45} +2.86224 q^{46} +4.64397 q^{47} -1.00000 q^{48} +13.5162 q^{49} -4.35932 q^{50} -1.00000 q^{51} +6.52527 q^{52} -2.60293 q^{53} -1.00000 q^{54} -3.94729 q^{55} -4.52948 q^{56} +7.08202 q^{57} +5.23795 q^{58} +1.00000 q^{59} -0.800423 q^{60} +7.15643 q^{61} -6.12633 q^{62} -4.52948 q^{63} +1.00000 q^{64} +5.22298 q^{65} +4.93150 q^{66} +7.55334 q^{67} +1.00000 q^{68} -2.86224 q^{69} -3.62550 q^{70} +6.13669 q^{71} +1.00000 q^{72} -8.65932 q^{73} -4.16347 q^{74} +4.35932 q^{75} -7.08202 q^{76} +22.3371 q^{77} -6.52527 q^{78} +8.55362 q^{79} +0.800423 q^{80} +1.00000 q^{81} +4.90976 q^{82} -4.79003 q^{83} +4.52948 q^{84} +0.800423 q^{85} +8.25459 q^{86} -5.23795 q^{87} -4.93150 q^{88} -1.75496 q^{89} +0.800423 q^{90} -29.5560 q^{91} +2.86224 q^{92} +6.12633 q^{93} +4.64397 q^{94} -5.66861 q^{95} -1.00000 q^{96} -15.5706 q^{97} +13.5162 q^{98} -4.93150 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 14 q^{2} - 14 q^{3} + 14 q^{4} + 2 q^{5} - 14 q^{6} + q^{7} + 14 q^{8} + 14 q^{9}+O(q^{10}) $ 14 * q + 14 * q^2 - 14 * q^3 + 14 * q^4 + 2 * q^5 - 14 * q^6 + q^7 + 14 * q^8 + 14 * q^9	\( 14 q + 14 q^{2} - 14 q^{3} + 14 q^{4} + 2 q^{5} - 14 q^{6} + q^{7} + 14 q^{8} + 14 q^{9} + 2 q^{10} + 3 q^{11} - 14 q^{12} + 16 q^{13} + q^{14} - 2 q^{15} + 14 q^{16} + 14 q^{17} + 14 q^{18} + 13 q^{19} + 2 q^{20} - q^{21} + 3 q^{22} + 4 q^{23} - 14 q^{24} + 32 q^{25} + 16 q^{26} - 14 q^{27} + q^{28} - 2 q^{30} - 13 q^{31} + 14 q^{32} - 3 q^{33} + 14 q^{34} + 14 q^{36} + 12 q^{37} + 13 q^{38} - 16 q^{39} + 2 q^{40} - 18 q^{41} - q^{42} + 29 q^{43} + 3 q^{44} + 2 q^{45} + 4 q^{46} - 14 q^{48} + 49 q^{49} + 32 q^{50} - 14 q^{51} + 16 q^{52} + 24 q^{53} - 14 q^{54} + 15 q^{55} + q^{56} - 13 q^{57} + 14 q^{59} - 2 q^{60} + 29 q^{61} - 13 q^{62} + q^{63} + 14 q^{64} + 6 q^{65} - 3 q^{66} + 4 q^{67} + 14 q^{68} - 4 q^{69} - 10 q^{71} + 14 q^{72} + 18 q^{73} + 12 q^{74} - 32 q^{75} + 13 q^{76} + 20 q^{77} - 16 q^{78} + 7 q^{79} + 2 q^{80} + 14 q^{81} - 18 q^{82} + 28 q^{83} - q^{84} + 2 q^{85} + 29 q^{86} + 3 q^{88} + 23 q^{89} + 2 q^{90} + 9 q^{91} + 4 q^{92} + 13 q^{93} + 5 q^{95} - 14 q^{96} - 7 q^{97} + 49 q^{98} + 3 q^{99}+O(q^{100}) \) 14 * q + 14 * q^2 - 14 * q^3 + 14 * q^4 + 2 * q^5 - 14 * q^6 + q^7 + 14 * q^8 + 14 * q^9 + 2 * q^10 + 3 * q^11 - 14 * q^12 + 16 * q^13 + q^14 - 2 * q^15 + 14 * q^16 + 14 * q^17 + 14 * q^18 + 13 * q^19 + 2 * q^20 - q^21 + 3 * q^22 + 4 * q^23 - 14 * q^24 + 32 * q^25 + 16 * q^26 - 14 * q^27 + q^28 - 2 * q^30 - 13 * q^31 + 14 * q^32 - 3 * q^33 + 14 * q^34 + 14 * q^36 + 12 * q^37 + 13 * q^38 - 16 * q^39 + 2 * q^40 - 18 * q^41 - q^42 + 29 * q^43 + 3 * q^44 + 2 * q^45 + 4 * q^46 - 14 * q^48 + 49 * q^49 + 32 * q^50 - 14 * q^51 + 16 * q^52 + 24 * q^53 - 14 * q^54 + 15 * q^55 + q^56 - 13 * q^57 + 14 * q^59 - 2 * q^60 + 29 * q^61 - 13 * q^62 + q^63 + 14 * q^64 + 6 * q^65 - 3 * q^66 + 4 * q^67 + 14 * q^68 - 4 * q^69 - 10 * q^71 + 14 * q^72 + 18 * q^73 + 12 * q^74 - 32 * q^75 + 13 * q^76 + 20 * q^77 - 16 * q^78 + 7 * q^79 + 2 * q^80 + 14 * q^81 - 18 * q^82 + 28 * q^83 - q^84 + 2 * q^85 + 29 * q^86 + 3 * q^88 + 23 * q^89 + 2 * q^90 + 9 * q^91 + 4 * q^92 + 13 * q^93 + 5 * q^95 - 14 * q^96 - 7 * q^97 + 49 * 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
$5$	0.800423	0.357960	0.178980	−	0.983853i	$-0.442720\pi$
$5$	0.800423	0.357960	0.178980	+	0.983853i	$0.442720\pi$
$6$	−1.00000	−0.408248
$7$	−4.52948	−1.71198	−0.855991	−	0.516991i	$-0.827052\pi$
$7$	−4.52948	−1.71198	−0.855991	+	0.516991i	$0.827052\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	0.800423	0.253116
$11$	−4.93150	−1.48690	−0.743452	−	0.668790i	$-0.766813\pi$
$11$	−4.93150	−1.48690	−0.743452	+	0.668790i	$0.766813\pi$
$12$	−1.00000	−0.288675
$13$	6.52527	1.80978	0.904892	−	0.425642i	$-0.139952\pi$
$13$	6.52527	1.80978	0.904892	+	0.425642i	$0.139952\pi$
$14$	−4.52948	−1.21055
$15$	−0.800423	−0.206668
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	1.00000	0.235702
$19$	−7.08202	−1.62473	−0.812363	−	0.583152i	$-0.801819\pi$
$19$	−7.08202	−1.62473	−0.812363	+	0.583152i	$0.801819\pi$
$20$	0.800423	0.178980
$21$	4.52948	0.988413
$22$	−4.93150	−1.05140
$23$	2.86224	0.596818	0.298409	−	0.954438i	$-0.403544\pi$
$23$	2.86224	0.596818	0.298409	+	0.954438i	$0.403544\pi$
$24$	−1.00000	−0.204124
$25$	−4.35932	−0.871865
$26$	6.52527	1.27971
$27$	−1.00000	−0.192450
$28$	−4.52948	−0.855991
$29$	5.23795	0.972663	0.486331	−	0.873774i	$-0.338335\pi$
$29$	5.23795	0.972663	0.486331	+	0.873774i	$0.338335\pi$
$30$	−0.800423	−0.146137
$31$	−6.12633	−1.10032	−0.550161	−	0.835059i	$-0.685434\pi$
$31$	−6.12633	−1.10032	−0.550161	+	0.835059i	$0.685434\pi$
$32$	1.00000	0.176777
$33$	4.93150	0.858464
$34$	1.00000	0.171499
$35$	−3.62550	−0.612821
$36$	1.00000	0.166667
$37$	−4.16347	−0.684470	−0.342235	−	0.939614i	$-0.611184\pi$
$37$	−4.16347	−0.684470	−0.342235	+	0.939614i	$0.611184\pi$
$38$	−7.08202	−1.14886
$39$	−6.52527	−1.04488
$40$	0.800423	0.126558
$41$	4.90976	0.766776	0.383388	−	0.923587i	$-0.374757\pi$
$41$	4.90976	0.766776	0.383388	+	0.923587i	$0.374757\pi$
$42$	4.52948	0.698913
$43$	8.25459	1.25881	0.629407	−	0.777076i	$-0.283298\pi$
$43$	8.25459	1.25881	0.629407	+	0.777076i	$0.283298\pi$
$44$	−4.93150	−0.743452
$45$	0.800423	0.119320
$46$	2.86224	0.422014
$47$	4.64397	0.677392	0.338696	−	0.940896i	$-0.390014\pi$
$47$	4.64397	0.677392	0.338696	+	0.940896i	$0.390014\pi$
$48$	−1.00000	−0.144338
$49$	13.5162	1.93088
$50$	−4.35932	−0.616501
$51$	−1.00000	−0.140028
$52$	6.52527	0.904892
$53$	−2.60293	−0.357539	−0.178770	−	0.983891i	$-0.557212\pi$
$53$	−2.60293	−0.357539	−0.178770	+	0.983891i	$0.557212\pi$
$54$	−1.00000	−0.136083
$55$	−3.94729	−0.532252
$56$	−4.52948	−0.605277
$57$	7.08202	0.938036
$58$	5.23795	0.687776
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	−0.800423	−0.103334
$61$	7.15643	0.916287	0.458144	−	0.888878i	$-0.348515\pi$
$61$	7.15643	0.916287	0.458144	+	0.888878i	$0.348515\pi$
$62$	−6.12633	−0.778045
$63$	−4.52948	−0.570660
$64$	1.00000	0.125000
$65$	5.22298	0.647830
$66$	4.93150	0.607026
$67$	7.55334	0.922787	0.461394	−	0.887195i	$-0.347350\pi$
$67$	7.55334	0.922787	0.461394	+	0.887195i	$0.347350\pi$
$68$	1.00000	0.121268
$69$	−2.86224	−0.344573
$70$	−3.62550	−0.433330
$71$	6.13669	0.728291	0.364145	−	0.931342i	$-0.381361\pi$
$71$	6.13669	0.728291	0.364145	+	0.931342i	$0.381361\pi$
$72$	1.00000	0.117851
$73$	−8.65932	−1.01350	−0.506749	−	0.862094i	$-0.669153\pi$
$73$	−8.65932	−1.01350	−0.506749	+	0.862094i	$0.669153\pi$
$74$	−4.16347	−0.483994
$75$	4.35932	0.503371
$76$	−7.08202	−0.812363
$77$	22.3371	2.54555
$78$	−6.52527	−0.738841
$79$	8.55362	0.962357	0.481179	−	0.876623i	$-0.340209\pi$
$79$	8.55362	0.962357	0.481179	+	0.876623i	$0.340209\pi$
$80$	0.800423	0.0894900
$81$	1.00000	0.111111
$82$	4.90976	0.542193
$83$	−4.79003	−0.525774	−0.262887	−	0.964827i	$-0.584675\pi$
$83$	−4.79003	−0.525774	−0.262887	+	0.964827i	$0.584675\pi$
$84$	4.52948	0.494206
$85$	0.800423	0.0868181
$86$	8.25459	0.890115
$87$	−5.23795	−0.561567
$88$	−4.93150	−0.525700
$89$	−1.75496	−0.186026	−0.0930129	−	0.995665i	$-0.529650\pi$
$89$	−1.75496	−0.186026	−0.0930129	+	0.995665i	$0.529650\pi$
$90$	0.800423	0.0843720
$91$	−29.5560	−3.09832
$92$	2.86224	0.298409
$93$	6.12633	0.635271
$94$	4.64397	0.478989
$95$	−5.66861	−0.581587
$96$	−1.00000	−0.102062
$97$	−15.5706	−1.58096	−0.790479	−	0.612489i	$-0.790169\pi$
$97$	−15.5706	−1.58096	−0.790479	+	0.612489i	$0.790169\pi$
$98$	13.5162	1.36534
$99$	−4.93150	−0.495635
$100$	−4.35932	−0.435932
$101$	1.84783	0.183865	0.0919327	−	0.995765i	$-0.470696\pi$
$101$	1.84783	0.183865	0.0919327	+	0.995765i	$0.470696\pi$
$102$	−1.00000	−0.0990148
$103$	9.86585	0.972111	0.486055	−	0.873928i	$-0.338435\pi$
$103$	9.86585	0.972111	0.486055	+	0.873928i	$0.338435\pi$
$104$	6.52527	0.639855
$105$	3.62550	0.353812
$106$	−2.60293	−0.252819
$107$	−15.4998	−1.49842	−0.749209	−	0.662334i	$-0.769566\pi$
$107$	−15.4998	−1.49842	−0.749209	+	0.662334i	$0.769566\pi$
$108$	−1.00000	−0.0962250
$109$	−0.198490	−0.0190119	−0.00950595	−	0.999955i	$-0.503026\pi$
$109$	−0.198490	−0.0190119	−0.00950595	+	0.999955i	$0.503026\pi$
$110$	−3.94729	−0.376359
$111$	4.16347	0.395179
$112$	−4.52948	−0.427995
$113$	20.0727	1.88828	0.944142	−	0.329540i	$-0.106894\pi$
$113$	20.0727	1.88828	0.944142	+	0.329540i	$0.106894\pi$
$114$	7.08202	0.663292
$115$	2.29100	0.213637
$116$	5.23795	0.486331
$117$	6.52527	0.603261
$118$	1.00000	0.0920575
$119$	−4.52948	−0.415216
$120$	−0.800423	−0.0730683
$121$	13.3197	1.21088
$122$	7.15643	0.647913
$123$	−4.90976	−0.442698
$124$	−6.12633	−0.550161
$125$	−7.49142	−0.670053
$126$	−4.52948	−0.403518
$127$	1.61717	0.143501	0.0717503	−	0.997423i	$-0.477142\pi$
$127$	1.61717	0.143501	0.0717503	+	0.997423i	$0.477142\pi$
$128$	1.00000	0.0883883
$129$	−8.25459	−0.726776
$130$	5.22298	0.458085
$131$	17.3695	1.51758	0.758788	−	0.651338i	$-0.225792\pi$
$131$	17.3695	1.51758	0.758788	+	0.651338i	$0.225792\pi$
$132$	4.93150	0.429232
$133$	32.0778	2.78150
$134$	7.55334	0.652509
$135$	−0.800423	−0.0688895
$136$	1.00000	0.0857493
$137$	−7.57839	−0.647466	−0.323733	−	0.946149i	$-0.604938\pi$
$137$	−7.57839	−0.647466	−0.323733	+	0.946149i	$0.604938\pi$
$138$	−2.86224	−0.243650
$139$	11.3645	0.963923	0.481961	−	0.876192i	$-0.339925\pi$
$139$	11.3645	0.963923	0.481961	+	0.876192i	$0.339925\pi$
$140$	−3.62550	−0.306411
$141$	−4.64397	−0.391093
$142$	6.13669	0.514979
$143$	−32.1794	−2.69097
$144$	1.00000	0.0833333
$145$	4.19258	0.348175
$146$	−8.65932	−0.716651
$147$	−13.5162	−1.11479
$148$	−4.16347	−0.342235
$149$	17.2520	1.41334	0.706668	−	0.707545i	$-0.250197\pi$
$149$	17.2520	1.41334	0.706668	+	0.707545i	$0.250197\pi$
$150$	4.35932	0.355937
$151$	16.5589	1.34755	0.673773	−	0.738938i	$-0.264672\pi$
$151$	16.5589	1.34755	0.673773	+	0.738938i	$0.264672\pi$
$152$	−7.08202	−0.574428
$153$	1.00000	0.0808452
$154$	22.3371	1.79998
$155$	−4.90366	−0.393871
$156$	−6.52527	−0.522440
$157$	7.16638	0.571939	0.285970	−	0.958239i	$-0.407684\pi$
$157$	7.16638	0.571939	0.285970	+	0.958239i	$0.407684\pi$
$158$	8.55362	0.680489
$159$	2.60293	0.206425
$160$	0.800423	0.0632790
$161$	−12.9644	−1.02174
$162$	1.00000	0.0785674
$163$	−1.41302	−0.110676	−0.0553380	−	0.998468i	$-0.517624\pi$
$163$	−1.41302	−0.110676	−0.0553380	+	0.998468i	$0.517624\pi$
$164$	4.90976	0.383388
$165$	3.94729	0.307296
$166$	−4.79003	−0.371778
$167$	19.8396	1.53523	0.767617	−	0.640908i	$-0.221442\pi$
$167$	19.8396	1.53523	0.767617	+	0.640908i	$0.221442\pi$
$168$	4.52948	0.349457
$169$	29.5791	2.27532
$170$	0.800423	0.0613897
$171$	−7.08202	−0.541576
$172$	8.25459	0.629407
$173$	−4.43468	−0.337163	−0.168581	−	0.985688i	$-0.553919\pi$
$173$	−4.43468	−0.337163	−0.168581	+	0.985688i	$0.553919\pi$
$174$	−5.23795	−0.397088
$175$	19.7454	1.49262
$176$	−4.93150	−0.371726
$177$	−1.00000	−0.0751646
$178$	−1.75496	−0.131540
$179$	−0.823345	−0.0615397	−0.0307698	−	0.999526i	$-0.509796\pi$
$179$	−0.823345	−0.0615397	−0.0307698	+	0.999526i	$0.509796\pi$
$180$	0.800423	0.0596600
$181$	19.5683	1.45450	0.727251	−	0.686372i	$-0.240798\pi$
$181$	19.5683	1.45450	0.727251	+	0.686372i	$0.240798\pi$
$182$	−29.5560	−2.19084
$183$	−7.15643	−0.529019
$184$	2.86224	0.211007
$185$	−3.33254	−0.245013
$186$	6.12633	0.449205
$187$	−4.93150	−0.360627
$188$	4.64397	0.338696
$189$	4.52948	0.329471
$190$	−5.66861	−0.411244
$191$	0.470035	0.0340105	0.0170053	−	0.999855i	$-0.494587\pi$
$191$	0.470035	0.0340105	0.0170053	+	0.999855i	$0.494587\pi$
$192$	−1.00000	−0.0721688
$193$	3.84313	0.276635	0.138317	−	0.990388i	$-0.455831\pi$
$193$	3.84313	0.276635	0.138317	+	0.990388i	$0.455831\pi$
$194$	−15.5706	−1.11791
$195$	−5.22298	−0.374025
$196$	13.5162	0.965440
$197$	5.61341	0.399939	0.199970	−	0.979802i	$-0.435916\pi$
$197$	5.61341	0.399939	0.199970	+	0.979802i	$0.435916\pi$
$198$	−4.93150	−0.350467
$199$	10.4808	0.742965	0.371482	−	0.928440i	$-0.378850\pi$
$199$	10.4808	0.742965	0.371482	+	0.928440i	$0.378850\pi$
$200$	−4.35932	−0.308251
$201$	−7.55334	−0.532772
$202$	1.84783	0.130013
$203$	−23.7252	−1.66518
$204$	−1.00000	−0.0700140
$205$	3.92989	0.274475
$206$	9.86585	0.687386
$207$	2.86224	0.198939
$208$	6.52527	0.452446
$209$	34.9250	2.41581
$210$	3.62550	0.250183
$211$	−26.1553	−1.80061	−0.900303	−	0.435265i	$-0.856655\pi$
$211$	−26.1553	−1.80061	−0.900303	+	0.435265i	$0.856655\pi$
$212$	−2.60293	−0.178770
$213$	−6.13669	−0.420479
$214$	−15.4998	−1.05954
$215$	6.60717	0.450605
$216$	−1.00000	−0.0680414
$217$	27.7491	1.88373
$218$	−0.198490	−0.0134434
$219$	8.65932	0.585143
$220$	−3.94729	−0.266126
$221$	6.52527	0.438937
$222$	4.16347	0.279434
$223$	−17.7903	−1.19133	−0.595663	−	0.803235i	$-0.703111\pi$
$223$	−17.7903	−1.19133	−0.595663	+	0.803235i	$0.703111\pi$
$224$	−4.52948	−0.302638
$225$	−4.35932	−0.290622
$226$	20.0727	1.33522
$227$	5.75967	0.382283	0.191141	−	0.981563i	$-0.438781\pi$
$227$	5.75967	0.382283	0.191141	+	0.981563i	$0.438781\pi$
$228$	7.08202	0.469018
$229$	22.1948	1.46668	0.733338	−	0.679864i	$-0.237961\pi$
$229$	22.1948	1.46668	0.733338	+	0.679864i	$0.237961\pi$
$230$	2.29100	0.151064
$231$	−22.3371	−1.46967
$232$	5.23795	0.343888
$233$	2.69400	0.176490	0.0882449	−	0.996099i	$-0.471874\pi$
$233$	2.69400	0.176490	0.0882449	+	0.996099i	$0.471874\pi$
$234$	6.52527	0.426570
$235$	3.71714	0.242479
$236$	1.00000	0.0650945
$237$	−8.55362	−0.555617
$238$	−4.52948	−0.293602
$239$	10.6746	0.690480	0.345240	−	0.938515i	$-0.387798\pi$
$239$	10.6746	0.690480	0.345240	+	0.938515i	$0.387798\pi$
$240$	−0.800423	−0.0516671
$241$	−22.4145	−1.44385	−0.721924	−	0.691972i	$-0.756742\pi$
$241$	−22.4145	−1.44385	−0.721924	+	0.691972i	$0.756742\pi$
$242$	13.3197	0.856223
$243$	−1.00000	−0.0641500
$244$	7.15643	0.458144
$245$	10.8186	0.691178
$246$	−4.90976	−0.313035
$247$	−46.2121	−2.94040
$248$	−6.12633	−0.389023
$249$	4.79003	0.303556
$250$	−7.49142	−0.473799
$251$	28.0985	1.77356	0.886780	−	0.462192i	$-0.152937\pi$
$251$	28.0985	1.77356	0.886780	+	0.462192i	$0.152937\pi$
$252$	−4.52948	−0.285330
$253$	−14.1151	−0.887411
$254$	1.61717	0.101470
$255$	−0.800423	−0.0501244
$256$	1.00000	0.0625000
$257$	1.13957	0.0710846	0.0355423	−	0.999368i	$-0.488684\pi$
$257$	1.13957	0.0710846	0.0355423	+	0.999368i	$0.488684\pi$
$258$	−8.25459	−0.513908
$259$	18.8583	1.17180
$260$	5.22298	0.323915
$261$	5.23795	0.324221
$262$	17.3695	1.07309
$263$	12.7281	0.784851	0.392425	−	0.919784i	$-0.371636\pi$
$263$	12.7281	0.784851	0.392425	+	0.919784i	$0.371636\pi$
$264$	4.93150	0.303513
$265$	−2.08344	−0.127985
$266$	32.0778	1.96682
$267$	1.75496	0.107402
$268$	7.55334	0.461394
$269$	−23.4706	−1.43103	−0.715514	−	0.698598i	$-0.753807\pi$
$269$	−23.4706	−1.43103	−0.715514	+	0.698598i	$0.753807\pi$
$270$	−0.800423	−0.0487122
$271$	−7.07963	−0.430057	−0.215028	−	0.976608i	$-0.568984\pi$
$271$	−7.07963	−0.430057	−0.215028	+	0.976608i	$0.568984\pi$
$272$	1.00000	0.0606339
$273$	29.5560	1.78881
$274$	−7.57839	−0.457827
$275$	21.4980	1.29638
$276$	−2.86224	−0.172287
$277$	−11.6986	−0.702901	−0.351451	−	0.936206i	$-0.614312\pi$
$277$	−11.6986	−0.702901	−0.351451	+	0.936206i	$0.614312\pi$
$278$	11.3645	0.681596
$279$	−6.12633	−0.366774
$280$	−3.62550	−0.216665
$281$	−24.5335	−1.46355	−0.731773	−	0.681549i	$-0.761307\pi$
$281$	−24.5335	−1.46355	−0.731773	+	0.681549i	$0.761307\pi$
$282$	−4.64397	−0.276544
$283$	−3.26289	−0.193959	−0.0969794	−	0.995286i	$-0.530918\pi$
$283$	−3.26289	−0.193959	−0.0969794	+	0.995286i	$0.530918\pi$
$284$	6.13669	0.364145
$285$	5.66861	0.335780
$286$	−32.1794	−1.90281
$287$	−22.2387	−1.31271
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	4.19258	0.246197
$291$	15.5706	0.912767
$292$	−8.65932	−0.506749
$293$	−16.4188	−0.959197	−0.479598	−	0.877488i	$-0.659218\pi$
$293$	−16.4188	−0.959197	−0.479598	+	0.877488i	$0.659218\pi$
$294$	−13.5162	−0.788278
$295$	0.800423	0.0466024
$296$	−4.16347	−0.241997
$297$	4.93150	0.286155
$298$	17.2520	0.999380
$299$	18.6769	1.08011
$300$	4.35932	0.251686
$301$	−37.3890	−2.15506
$302$	16.5589	0.952859
$303$	−1.84783	−0.106155
$304$	−7.08202	−0.406182
$305$	5.72817	0.327994
$306$	1.00000	0.0571662
$307$	−9.16557	−0.523106	−0.261553	−	0.965189i	$-0.584235\pi$
$307$	−9.16557	−0.523106	−0.261553	+	0.965189i	$0.584235\pi$
$308$	22.3371	1.27278
$309$	−9.86585	−0.561248
$310$	−4.90366	−0.278509
$311$	−12.2264	−0.693294	−0.346647	−	0.937996i	$-0.612680\pi$
$311$	−12.2264	−0.693294	−0.346647	+	0.937996i	$0.612680\pi$
$312$	−6.52527	−0.369421
$313$	19.3046	1.09116	0.545579	−	0.838059i	$-0.316310\pi$
$313$	19.3046	1.09116	0.545579	+	0.838059i	$0.316310\pi$
$314$	7.16638	0.404422
$315$	−3.62550	−0.204274
$316$	8.55362	0.481179
$317$	27.1196	1.52319	0.761595	−	0.648053i	$-0.224417\pi$
$317$	27.1196	1.52319	0.761595	+	0.648053i	$0.224417\pi$
$318$	2.60293	0.145965
$319$	−25.8310	−1.44626
$320$	0.800423	0.0447450
$321$	15.4998	0.865112
$322$	−12.9644	−0.722480
$323$	−7.08202	−0.394054
$324$	1.00000	0.0555556
$325$	−28.4457	−1.57789
$326$	−1.41302	−0.0782597
$327$	0.198490	0.0109765
$328$	4.90976	0.271096
$329$	−21.0347	−1.15968
$330$	3.94729	0.217291
$331$	−4.82675	−0.265302	−0.132651	−	0.991163i	$-0.542349\pi$
$331$	−4.82675	−0.265302	−0.132651	+	0.991163i	$0.542349\pi$
$332$	−4.79003	−0.262887
$333$	−4.16347	−0.228157
$334$	19.8396	1.08557
$335$	6.04587	0.330321
$336$	4.52948	0.247103
$337$	−22.5431	−1.22800	−0.614000	−	0.789306i	$-0.710441\pi$
$337$	−22.5431	−1.22800	−0.614000	+	0.789306i	$0.710441\pi$
$338$	29.5791	1.60889
$339$	−20.0727	−1.09020
$340$	0.800423	0.0434090
$341$	30.2120	1.63607
$342$	−7.08202	−0.382952
$343$	−29.5148	−1.59365
$344$	8.25459	0.445058
$345$	−2.29100	−0.123343
$346$	−4.43468	−0.238410
$347$	−21.9232	−1.17690	−0.588448	−	0.808535i	$-0.700261\pi$
$347$	−21.9232	−1.17690	−0.588448	+	0.808535i	$0.700261\pi$
$348$	−5.23795	−0.280784
$349$	17.0438	0.912333	0.456166	−	0.889894i	$-0.349222\pi$
$349$	17.0438	0.912333	0.456166	+	0.889894i	$0.349222\pi$
$350$	19.7454	1.05544
$351$	−6.52527	−0.348293
$352$	−4.93150	−0.262850
$353$	10.3980	0.553430	0.276715	−	0.960952i	$-0.410754\pi$
$353$	10.3980	0.553430	0.276715	+	0.960952i	$0.410754\pi$
$354$	−1.00000	−0.0531494
$355$	4.91195	0.260699
$356$	−1.75496	−0.0930129
$357$	4.52948	0.239725
$358$	−0.823345	−0.0435151
$359$	4.47636	0.236253	0.118127	−	0.992999i	$-0.462311\pi$
$359$	4.47636	0.236253	0.118127	+	0.992999i	$0.462311\pi$
$360$	0.800423	0.0421860
$361$	31.1550	1.63974
$362$	19.5683	1.02849
$363$	−13.3197	−0.699103
$364$	−29.5560	−1.54916
$365$	−6.93112	−0.362792
$366$	−7.15643	−0.374073
$367$	31.8272	1.66136	0.830682	−	0.556747i	$-0.187951\pi$
$367$	31.8272	1.66136	0.830682	+	0.556747i	$0.187951\pi$
$368$	2.86224	0.149205
$369$	4.90976	0.255592
$370$	−3.33254	−0.173250
$371$	11.7899	0.612101
$372$	6.12633	0.317636
$373$	21.2779	1.10173	0.550865	−	0.834595i	$-0.314298\pi$
$373$	21.2779	1.10173	0.550865	+	0.834595i	$0.314298\pi$
$374$	−4.93150	−0.255002
$375$	7.49142	0.386855
$376$	4.64397	0.239494
$377$	34.1790	1.76031
$378$	4.52948	0.232971
$379$	−6.19092	−0.318006	−0.159003	−	0.987278i	$-0.550828\pi$
$379$	−6.19092	−0.318006	−0.159003	+	0.987278i	$0.550828\pi$
$380$	−5.66861	−0.290794
$381$	−1.61717	−0.0828501
$382$	0.470035	0.0240491
$383$	29.9444	1.53009	0.765043	−	0.643979i	$-0.222717\pi$
$383$	29.9444	1.53009	0.765043	+	0.643979i	$0.222717\pi$
$384$	−1.00000	−0.0510310
$385$	17.8791	0.911206
$386$	3.84313	0.195610
$387$	8.25459	0.419604
$388$	−15.5706	−0.790479
$389$	9.10606	0.461696	0.230848	−	0.972990i	$-0.425850\pi$
$389$	9.10606	0.461696	0.230848	+	0.972990i	$0.425850\pi$
$390$	−5.22298	−0.264476
$391$	2.86224	0.144750
$392$	13.5162	0.682669
$393$	−17.3695	−0.876173
$394$	5.61341	0.282800
$395$	6.84651	0.344486
$396$	−4.93150	−0.247817
$397$	13.3424	0.669637	0.334818	−	0.942283i	$-0.391325\pi$
$397$	13.3424	0.669637	0.334818	+	0.942283i	$0.391325\pi$
$398$	10.4808	0.525355
$399$	−32.0778	−1.60590
$400$	−4.35932	−0.217966
$401$	−29.5062	−1.47347	−0.736734	−	0.676183i	$-0.763633\pi$
$401$	−29.5062	−1.47347	−0.736734	+	0.676183i	$0.763633\pi$
$402$	−7.55334	−0.376726
$403$	−39.9760	−1.99134
$404$	1.84783	0.0919327
$405$	0.800423	0.0397734
$406$	−23.7252	−1.17746
$407$	20.5322	1.01774
$408$	−1.00000	−0.0495074
$409$	34.3121	1.69663	0.848313	−	0.529495i	$-0.177619\pi$
$409$	34.3121	1.69663	0.848313	+	0.529495i	$0.177619\pi$
$410$	3.92989	0.194083
$411$	7.57839	0.373814
$412$	9.86585	0.486055
$413$	−4.52948	−0.222881
$414$	2.86224	0.140671
$415$	−3.83405	−0.188206
$416$	6.52527	0.319928
$417$	−11.3645	−0.556521
$418$	34.9250	1.70824
$419$	−15.7960	−0.771684	−0.385842	−	0.922565i	$-0.626089\pi$
$419$	−15.7960	−0.771684	−0.385842	+	0.922565i	$0.626089\pi$
$420$	3.62550	0.176906
$421$	−32.4334	−1.58071	−0.790354	−	0.612651i	$-0.790103\pi$
$421$	−32.4334	−1.58071	−0.790354	+	0.612651i	$0.790103\pi$
$422$	−26.1553	−1.27322
$423$	4.64397	0.225797
$424$	−2.60293	−0.126409
$425$	−4.35932	−0.211458
$426$	−6.13669	−0.297323
$427$	−32.4149	−1.56867
$428$	−15.4998	−0.749209
$429$	32.1794	1.55363
$430$	6.60717	0.318626
$431$	−11.3099	−0.544777	−0.272389	−	0.962187i	$-0.587814\pi$
$431$	−11.3099	−0.544777	−0.272389	+	0.962187i	$0.587814\pi$
$432$	−1.00000	−0.0481125
$433$	21.7722	1.04631	0.523153	−	0.852239i	$-0.324756\pi$
$433$	21.7722	1.04631	0.523153	+	0.852239i	$0.324756\pi$
$434$	27.7491	1.33200
$435$	−4.19258	−0.201019
$436$	−0.198490	−0.00950595
$437$	−20.2704	−0.969666
$438$	8.65932	0.413758
$439$	−6.22232	−0.296975	−0.148488	−	0.988914i	$-0.547441\pi$
$439$	−6.22232	−0.296975	−0.148488	+	0.988914i	$0.547441\pi$
$440$	−3.94729	−0.188180
$441$	13.5162	0.643626
$442$	6.52527	0.310375
$443$	−4.11568	−0.195542	−0.0977709	−	0.995209i	$-0.531171\pi$
$443$	−4.11568	−0.195542	−0.0977709	+	0.995209i	$0.531171\pi$
$444$	4.16347	0.197590
$445$	−1.40471	−0.0665898
$446$	−17.7903	−0.842395
$447$	−17.2520	−0.815990
$448$	−4.52948	−0.213998
$449$	−17.3833	−0.820369	−0.410184	−	0.912003i	$-0.634536\pi$
$449$	−17.3833	−0.820369	−0.410184	+	0.912003i	$0.634536\pi$
$450$	−4.35932	−0.205500
$451$	−24.2125	−1.14012
$452$	20.0727	0.944142
$453$	−16.5589	−0.778006
$454$	5.75967	0.270315
$455$	−23.6573	−1.10907
$456$	7.08202	0.331646
$457$	−5.96344	−0.278958	−0.139479	−	0.990225i	$-0.544543\pi$
$457$	−5.96344	−0.278958	−0.139479	+	0.990225i	$0.544543\pi$
$458$	22.1948	1.03710
$459$	−1.00000	−0.0466760
$460$	2.29100	0.106819
$461$	−38.7873	−1.80651	−0.903253	−	0.429109i	$-0.858828\pi$
$461$	−38.7873	−1.80651	−0.903253	+	0.429109i	$0.858828\pi$
$462$	−22.3371	−1.03922
$463$	30.2839	1.40741	0.703707	−	0.710490i	$-0.251527\pi$
$463$	30.2839	1.40741	0.703707	+	0.710490i	$0.251527\pi$
$464$	5.23795	0.243166
$465$	4.90366	0.227402
$466$	2.69400	0.124797
$467$	10.8580	0.502448	0.251224	−	0.967929i	$-0.419167\pi$
$467$	10.8580	0.502448	0.251224	+	0.967929i	$0.419167\pi$
$468$	6.52527	0.301631
$469$	−34.2127	−1.57979
$470$	3.71714	0.171459
$471$	−7.16638	−0.330209
$472$	1.00000	0.0460287
$473$	−40.7075	−1.87173
$474$	−8.55362	−0.392881
$475$	30.8728	1.41654
$476$	−4.52948	−0.207608
$477$	−2.60293	−0.119180
$478$	10.6746	0.488243
$479$	6.77582	0.309595	0.154798	−	0.987946i	$-0.450527\pi$
$479$	6.77582	0.309595	0.154798	+	0.987946i	$0.450527\pi$
$480$	−0.800423	−0.0365342
$481$	−27.1678	−1.23874
$482$	−22.4145	−1.02095
$483$	12.9644	0.589903
$484$	13.3197	0.605441
$485$	−12.4631	−0.565920
$486$	−1.00000	−0.0453609
$487$	−20.1083	−0.911196	−0.455598	−	0.890186i	$-0.650574\pi$
$487$	−20.1083	−0.911196	−0.455598	+	0.890186i	$0.650574\pi$
$488$	7.15643	0.323956
$489$	1.41302	0.0638988
$490$	10.8186	0.488737
$491$	30.2566	1.36546	0.682731	−	0.730669i	$-0.260792\pi$
$491$	30.2566	1.36546	0.682731	+	0.730669i	$0.260792\pi$
$492$	−4.90976	−0.221349
$493$	5.23795	0.235905
$494$	−46.2121	−2.07918
$495$	−3.94729	−0.177417
$496$	−6.12633	−0.275080
$497$	−27.7960	−1.24682
$498$	4.79003	0.214646
$499$	20.9423	0.937508	0.468754	−	0.883329i	$-0.344703\pi$
$499$	20.9423	0.937508	0.468754	+	0.883329i	$0.344703\pi$
$500$	−7.49142	−0.335026
$501$	−19.8396	−0.886368
$502$	28.0985	1.25410
$503$	33.6848	1.50193	0.750965	−	0.660342i	$-0.229589\pi$
$503$	33.6848	1.50193	0.750965	+	0.660342i	$0.229589\pi$
$504$	−4.52948	−0.201759
$505$	1.47904	0.0658165
$506$	−14.1151	−0.627494
$507$	−29.5791	−1.31365
$508$	1.61717	0.0717503
$509$	18.4173	0.816332	0.408166	−	0.912908i	$-0.366168\pi$
$509$	18.4173	0.816332	0.408166	+	0.912908i	$0.366168\pi$
$510$	−0.800423	−0.0354433
$511$	39.2222	1.73509
$512$	1.00000	0.0441942
$513$	7.08202	0.312679
$514$	1.13957	0.0502644
$515$	7.89685	0.347977
$516$	−8.25459	−0.363388
$517$	−22.9017	−1.00722
$518$	18.8583	0.828588
$519$	4.43468	0.194661
$520$	5.22298	0.229043
$521$	−7.42944	−0.325489	−0.162745	−	0.986668i	$-0.552035\pi$
$521$	−7.42944	−0.325489	−0.162745	+	0.986668i	$0.552035\pi$
$522$	5.23795	0.229259
$523$	32.1318	1.40502	0.702512	−	0.711672i	$-0.252062\pi$
$523$	32.1318	1.40502	0.702512	+	0.711672i	$0.252062\pi$
$524$	17.3695	0.758788
$525$	−19.7454	−0.861762
$526$	12.7281	0.554973
$527$	−6.12633	−0.266867
$528$	4.93150	0.214616
$529$	−14.8076	−0.643808
$530$	−2.08344	−0.0904990
$531$	1.00000	0.0433963
$532$	32.0778	1.39075
$533$	32.0375	1.38770
$534$	1.75496	0.0759447
$535$	−12.4064	−0.536374
$536$	7.55334	0.326255
$537$	0.823345	0.0355300
$538$	−23.4706	−1.01189
$539$	−66.6549	−2.87103
$540$	−0.800423	−0.0344447
$541$	34.5958	1.48739	0.743695	−	0.668519i	$-0.233071\pi$
$541$	34.5958	1.48739	0.743695	+	0.668519i	$0.233071\pi$
$542$	−7.07963	−0.304096
$543$	−19.5683	−0.839757
$544$	1.00000	0.0428746
$545$	−0.158876	−0.00680551
$546$	29.5560	1.26488
$547$	−24.9050	−1.06486	−0.532431	−	0.846473i	$-0.678721\pi$
$547$	−24.9050	−1.06486	−0.532431	+	0.846473i	$0.678721\pi$
$548$	−7.57839	−0.323733
$549$	7.15643	0.305429
$550$	21.4980	0.916678
$551$	−37.0953	−1.58031
$552$	−2.86224	−0.121825
$553$	−38.7434	−1.64754
$554$	−11.6986	−0.497026
$555$	3.33254	0.141458
$556$	11.3645	0.481961
$557$	−19.0739	−0.808188	−0.404094	−	0.914718i	$-0.632413\pi$
$557$	−19.0739	−0.808188	−0.404094	+	0.914718i	$0.632413\pi$
$558$	−6.12633	−0.259348
$559$	53.8634	2.27818
$560$	−3.62550	−0.153205
$561$	4.93150	0.208208
$562$	−24.5335	−1.03488
$563$	22.0719	0.930219	0.465110	−	0.885253i	$-0.346015\pi$
$563$	22.0719	0.930219	0.465110	+	0.885253i	$0.346015\pi$
$564$	−4.64397	−0.195546
$565$	16.0667	0.675930
$566$	−3.26289	−0.137150
$567$	−4.52948	−0.190220
$568$	6.13669	0.257490
$569$	−12.1877	−0.510935	−0.255467	−	0.966818i	$-0.582229\pi$
$569$	−12.1877	−0.510935	−0.255467	+	0.966818i	$0.582229\pi$
$570$	5.66861	0.237432
$571$	−27.2573	−1.14068	−0.570341	−	0.821408i	$-0.693189\pi$
$571$	−27.2573	−1.14068	−0.570341	+	0.821408i	$0.693189\pi$
$572$	−32.1794	−1.34549
$573$	−0.470035	−0.0196360
$574$	−22.2387	−0.928223
$575$	−12.4774	−0.520345
$576$	1.00000	0.0416667
$577$	−8.50508	−0.354071	−0.177036	−	0.984204i	$-0.556651\pi$
$577$	−8.50508	−0.354071	−0.177036	+	0.984204i	$0.556651\pi$
$578$	1.00000	0.0415945
$579$	−3.84313	−0.159715
$580$	4.19258	0.174087
$581$	21.6963	0.900115
$582$	15.5706	0.645424
$583$	12.8363	0.531627
$584$	−8.65932	−0.358325
$585$	5.22298	0.215943
$586$	−16.4188	−0.678255
$587$	−34.3632	−1.41832	−0.709160	−	0.705048i	$-0.750925\pi$
$587$	−34.3632	−1.41832	−0.709160	+	0.705048i	$0.750925\pi$
$588$	−13.5162	−0.557397
$589$	43.3868	1.78772
$590$	0.800423	0.0329529
$591$	−5.61341	−0.230905
$592$	−4.16347	−0.171118
$593$	−27.8519	−1.14374	−0.571871	−	0.820344i	$-0.693782\pi$
$593$	−27.8519	−1.14374	−0.571871	+	0.820344i	$0.693782\pi$
$594$	4.93150	0.202342
$595$	−3.62550	−0.148631
$596$	17.2520	0.706668
$597$	−10.4808	−0.428951
$598$	18.6769	0.763754
$599$	38.7841	1.58467	0.792337	−	0.610083i	$-0.208864\pi$
$599$	38.7841	1.58467	0.792337	+	0.610083i	$0.208864\pi$
$600$	4.35932	0.177969
$601$	34.5942	1.41113	0.705563	−	0.708647i	$-0.250694\pi$
$601$	34.5942	1.41113	0.705563	+	0.708647i	$0.250694\pi$
$602$	−37.3890	−1.52386
$603$	7.55334	0.307596
$604$	16.5589	0.673773
$605$	10.6614	0.433448
$606$	−1.84783	−0.0750628
$607$	−6.43344	−0.261125	−0.130563	−	0.991440i	$-0.541678\pi$
$607$	−6.43344	−0.261125	−0.130563	+	0.991440i	$0.541678\pi$
$608$	−7.08202	−0.287214
$609$	23.7252	0.961392
$610$	5.72817	0.231927
$611$	30.3031	1.22593
$612$	1.00000	0.0404226
$613$	36.1298	1.45927	0.729635	−	0.683837i	$-0.239690\pi$
$613$	36.1298	1.45927	0.729635	+	0.683837i	$0.239690\pi$
$614$	−9.16557	−0.369892
$615$	−3.92989	−0.158468
$616$	22.3371	0.899988
$617$	25.2406	1.01615	0.508073	−	0.861314i	$-0.330358\pi$
$617$	25.2406	1.01615	0.508073	+	0.861314i	$0.330358\pi$
$618$	−9.86585	−0.396863
$619$	19.0657	0.766315	0.383158	−	0.923683i	$-0.374837\pi$
$619$	19.0657	0.766315	0.383158	+	0.923683i	$0.374837\pi$
$620$	−4.90366	−0.196936
$621$	−2.86224	−0.114858
$622$	−12.2264	−0.490233
$623$	7.94907	0.318473
$624$	−6.52527	−0.261220
$625$	15.8003	0.632012
$626$	19.3046	0.771565
$627$	−34.9250	−1.39477
$628$	7.16638	0.285970
$629$	−4.16347	−0.166008
$630$	−3.62550	−0.144443
$631$	−32.1725	−1.28077	−0.640383	−	0.768056i	$-0.721224\pi$
$631$	−32.1725	−1.28077	−0.640383	+	0.768056i	$0.721224\pi$
$632$	8.55362	0.340245
$633$	26.1553	1.03958
$634$	27.1196	1.07706
$635$	1.29442	0.0513675
$636$	2.60293	0.103213
$637$	88.1965	3.49447
$638$	−25.8310	−1.02266
$639$	6.13669	0.242764
$640$	0.800423	0.0316395
$641$	−19.1244	−0.755367	−0.377684	−	0.925935i	$-0.623279\pi$
$641$	−19.1244	−0.755367	−0.377684	+	0.925935i	$0.623279\pi$
$642$	15.4998	0.611727
$643$	−13.7377	−0.541764	−0.270882	−	0.962613i	$-0.587315\pi$
$643$	−13.7377	−0.541764	−0.270882	+	0.962613i	$0.587315\pi$
$644$	−12.9644	−0.510871
$645$	−6.60717	−0.260157
$646$	−7.08202	−0.278638
$647$	9.14854	0.359666	0.179833	−	0.983697i	$-0.442444\pi$
$647$	9.14854	0.359666	0.179833	+	0.983697i	$0.442444\pi$
$648$	1.00000	0.0392837
$649$	−4.93150	−0.193578
$650$	−28.4457	−1.11573
$651$	−27.7491	−1.08757
$652$	−1.41302	−0.0553380
$653$	2.27852	0.0891654	0.0445827	−	0.999006i	$-0.485804\pi$
$653$	2.27852	0.0891654	0.0445827	+	0.999006i	$0.485804\pi$
$654$	0.198490	0.00776158
$655$	13.9029	0.543232
$656$	4.90976	0.191694
$657$	−8.65932	−0.337832
$658$	−21.0347	−0.820019
$659$	−36.2363	−1.41156	−0.705782	−	0.708429i	$-0.749404\pi$
$659$	−36.2363	−1.41156	−0.705782	+	0.708429i	$0.749404\pi$
$660$	3.94729	0.153648
$661$	17.8640	0.694829	0.347414	−	0.937712i	$-0.387060\pi$
$661$	17.8640	0.694829	0.347414	+	0.937712i	$0.387060\pi$
$662$	−4.82675	−0.187597
$663$	−6.52527	−0.253420
$664$	−4.79003	−0.185889
$665$	25.6758	0.995667
$666$	−4.16347	−0.161331
$667$	14.9923	0.580503
$668$	19.8396	0.767617
$669$	17.7903	0.687812
$670$	6.04587	0.233572
$671$	−35.2920	−1.36243
$672$	4.52948	0.174728
$673$	−38.5217	−1.48490	−0.742452	−	0.669899i	$-0.766337\pi$
$673$	−38.5217	−1.48490	−0.742452	+	0.669899i	$0.766337\pi$
$674$	−22.5431	−0.868328
$675$	4.35932	0.167790
$676$	29.5791	1.13766
$677$	−17.1856	−0.660497	−0.330248	−	0.943894i	$-0.607133\pi$
$677$	−17.1856	−0.660497	−0.330248	+	0.943894i	$0.607133\pi$
$678$	−20.0727	−0.770888
$679$	70.5268	2.70657
$680$	0.800423	0.0306948
$681$	−5.75967	−0.220711
$682$	30.2120	1.15688
$683$	7.40031	0.283165	0.141583	−	0.989926i	$-0.454781\pi$
$683$	7.40031	0.283165	0.141583	+	0.989926i	$0.454781\pi$
$684$	−7.08202	−0.270788
$685$	−6.06592	−0.231767
$686$	−29.5148	−1.12688
$687$	−22.1948	−0.846786
$688$	8.25459	0.314703
$689$	−16.9848	−0.647069
$690$	−2.29100	−0.0872170
$691$	−20.7835	−0.790641	−0.395320	−	0.918543i	$-0.629366\pi$
$691$	−20.7835	−0.790641	−0.395320	+	0.918543i	$0.629366\pi$
$692$	−4.43468	−0.168581
$693$	22.3371	0.848517
$694$	−21.9232	−0.832192
$695$	9.09640	0.345046
$696$	−5.23795	−0.198544
$697$	4.90976	0.185971
$698$	17.0438	0.645117
$699$	−2.69400	−0.101896
$700$	19.7454	0.746308
$701$	−28.8169	−1.08840	−0.544200	−	0.838955i	$-0.683167\pi$
$701$	−28.8169	−1.08840	−0.544200	+	0.838955i	$0.683167\pi$
$702$	−6.52527	−0.246280
$703$	29.4858	1.11208
$704$	−4.93150	−0.185863
$705$	−3.71714	−0.139996
$706$	10.3980	0.391334
$707$	−8.36968	−0.314774
$708$	−1.00000	−0.0375823
$709$	−4.71002	−0.176889	−0.0884443	−	0.996081i	$-0.528190\pi$
$709$	−4.71002	−0.176889	−0.0884443	+	0.996081i	$0.528190\pi$
$710$	4.91195	0.184342
$711$	8.55362	0.320786
$712$	−1.75496	−0.0657701
$713$	−17.5350	−0.656692
$714$	4.52948	0.169511
$715$	−25.7571	−0.963261
$716$	−0.823345	−0.0307698
$717$	−10.6746	−0.398649
$718$	4.47636	0.167056
$719$	−41.4948	−1.54750	−0.773748	−	0.633494i	$-0.781620\pi$
$719$	−41.4948	−1.54750	−0.773748	+	0.633494i	$0.781620\pi$
$720$	0.800423	0.0298300
$721$	−44.6871	−1.66424
$722$	31.1550	1.15947
$723$	22.4145	0.833606
$724$	19.5683	0.727251
$725$	−22.8339	−0.848030
$726$	−13.3197	−0.494341
$727$	15.3249	0.568370	0.284185	−	0.958770i	$-0.408277\pi$
$727$	15.3249	0.568370	0.284185	+	0.958770i	$0.408277\pi$
$728$	−29.5560	−1.09542
$729$	1.00000	0.0370370
$730$	−6.93112	−0.256532
$731$	8.25459	0.305307
$732$	−7.15643	−0.264509
$733$	−18.2264	−0.673206	−0.336603	−	0.941647i	$-0.609278\pi$
$733$	−18.2264	−0.673206	−0.336603	+	0.941647i	$0.609278\pi$
$734$	31.8272	1.17476
$735$	−10.8186	−0.399052
$736$	2.86224	0.105504
$737$	−37.2493	−1.37210
$738$	4.90976	0.180731
$739$	6.21315	0.228555	0.114277	−	0.993449i	$-0.463545\pi$
$739$	6.21315	0.228555	0.114277	+	0.993449i	$0.463545\pi$
$740$	−3.33254	−0.122507
$741$	46.2121	1.69764
$742$	11.7899	0.432821
$743$	−6.91426	−0.253660	−0.126830	−	0.991924i	$-0.540480\pi$
$743$	−6.91426	−0.253660	−0.126830	+	0.991924i	$0.540480\pi$
$744$	6.12633	0.224602
$745$	13.8089	0.505918
$746$	21.2779	0.779040
$747$	−4.79003	−0.175258
$748$	−4.93150	−0.180314
$749$	70.2058	2.56526
$750$	7.49142	0.273548
$751$	13.7927	0.503303	0.251652	−	0.967818i	$-0.419026\pi$
$751$	13.7927	0.503303	0.251652	+	0.967818i	$0.419026\pi$
$752$	4.64397	0.169348
$753$	−28.0985	−1.02397
$754$	34.1790	1.24473
$755$	13.2542	0.482368
$756$	4.52948	0.164735
$757$	−3.42758	−0.124577	−0.0622887	−	0.998058i	$-0.519840\pi$
$757$	−3.42758	−0.124577	−0.0622887	+	0.998058i	$0.519840\pi$
$758$	−6.19092	−0.224864
$759$	14.1151	0.512347
$760$	−5.66861	−0.205622
$761$	8.88342	0.322024	0.161012	−	0.986952i	$-0.448524\pi$
$761$	8.88342	0.322024	0.161012	+	0.986952i	$0.448524\pi$
$762$	−1.61717	−0.0585839
$763$	0.899056	0.0325480
$764$	0.470035	0.0170053
$765$	0.800423	0.0289394
$766$	29.9444	1.08193
$767$	6.52527	0.235614
$768$	−1.00000	−0.0360844
$769$	−23.4631	−0.846101	−0.423050	−	0.906106i	$-0.639041\pi$
$769$	−23.4631	−0.846101	−0.423050	+	0.906106i	$0.639041\pi$
$770$	17.8791	0.644320
$771$	−1.13957	−0.0410407
$772$	3.84313	0.138317
$773$	−44.5987	−1.60410	−0.802052	−	0.597254i	$-0.796259\pi$
$773$	−44.5987	−1.60410	−0.802052	+	0.597254i	$0.796259\pi$
$774$	8.25459	0.296705
$775$	26.7067	0.959332
$776$	−15.5706	−0.558953
$777$	−18.8583	−0.676539
$778$	9.10606	0.326468
$779$	−34.7710	−1.24580
$780$	−5.22298	−0.187013
$781$	−30.2631	−1.08290
$782$	2.86224	0.102353
$783$	−5.23795	−0.187189
$784$	13.5162	0.482720
$785$	5.73614	0.204732
$786$	−17.3695	−0.619548
$787$	−33.4315	−1.19170	−0.595852	−	0.803094i	$-0.703186\pi$
$787$	−33.4315	−1.19170	−0.595852	+	0.803094i	$0.703186\pi$
$788$	5.61341	0.199970
$789$	−12.7281	−0.453134
$790$	6.84651	0.243588
$791$	−90.9189	−3.23271
$792$	−4.93150	−0.175233
$793$	46.6976	1.65828
$794$	13.3424	0.473505
$795$	2.08344	0.0738921
$796$	10.4808	0.371482
$797$	−41.5332	−1.47118	−0.735590	−	0.677427i	$-0.763095\pi$
$797$	−41.5332	−1.47118	−0.735590	+	0.677427i	$0.763095\pi$
$798$	−32.0778	−1.13554
$799$	4.64397	0.164292
$800$	−4.35932	−0.154125
$801$	−1.75496	−0.0620086
$802$	−29.5062	−1.04190
$803$	42.7035	1.50697
$804$	−7.55334	−0.266386
$805$	−10.3770	−0.365743
$806$	−39.9760	−1.40809
$807$	23.4706	0.826204
$808$	1.84783	0.0650063
$809$	45.0669	1.58447	0.792234	−	0.610217i	$-0.208918\pi$
$809$	45.0669	1.58447	0.792234	+	0.610217i	$0.208918\pi$
$810$	0.800423	0.0281240
$811$	−46.9819	−1.64976	−0.824878	−	0.565311i	$-0.808756\pi$
$811$	−46.9819	−1.64976	−0.824878	+	0.565311i	$0.808756\pi$
$812$	−23.7252	−0.832590
$813$	7.07963	0.248293
$814$	20.5322	0.719652
$815$	−1.13101	−0.0396176
$816$	−1.00000	−0.0350070
$817$	−58.4592	−2.04523
$818$	34.3121	1.19970
$819$	−29.5560	−1.03277
$820$	3.92989	0.137238
$821$	41.9693	1.46474	0.732370	−	0.680907i	$-0.238414\pi$
$821$	41.9693	1.46474	0.732370	+	0.680907i	$0.238414\pi$
$822$	7.57839	0.264327
$823$	49.4079	1.72225	0.861125	−	0.508393i	$-0.169760\pi$
$823$	49.4079	1.72225	0.861125	+	0.508393i	$0.169760\pi$
$824$	9.86585	0.343693
$825$	−21.4980	−0.748464
$826$	−4.52948	−0.157601
$827$	16.4944	0.573567	0.286783	−	0.957995i	$-0.407414\pi$
$827$	16.4944	0.573567	0.286783	+	0.957995i	$0.407414\pi$
$828$	2.86224	0.0994697
$829$	30.6977	1.06617	0.533087	−	0.846060i	$-0.321032\pi$
$829$	30.6977	1.06617	0.533087	+	0.846060i	$0.321032\pi$
$830$	−3.83405	−0.133082
$831$	11.6986	0.405820
$832$	6.52527	0.226223
$833$	13.5162	0.468307
$834$	−11.3645	−0.393520
$835$	15.8801	0.549553
$836$	34.9250	1.20791
$837$	6.12633	0.211757
$838$	−15.7960	−0.545663
$839$	−34.2696	−1.18312	−0.591559	−	0.806262i	$-0.701487\pi$
$839$	−34.2696	−1.18312	−0.591559	+	0.806262i	$0.701487\pi$
$840$	3.62550	0.125092
$841$	−1.56389	−0.0539271
$842$	−32.4334	−1.11773
$843$	24.5335	0.844979
$844$	−26.1553	−0.900303
$845$	23.6758	0.814473
$846$	4.64397	0.159663
$847$	−60.3313	−2.07301
$848$	−2.60293	−0.0893848
$849$	3.26289	0.111982
$850$	−4.35932	−0.149524
$851$	−11.9169	−0.408504
$852$	−6.13669	−0.210239
$853$	14.2914	0.489329	0.244665	−	0.969608i	$-0.421322\pi$
$853$	14.2914	0.489329	0.244665	+	0.969608i	$0.421322\pi$
$854$	−32.4149	−1.10921
$855$	−5.66861	−0.193862
$856$	−15.4998	−0.529771
$857$	−45.8257	−1.56538	−0.782688	−	0.622414i	$-0.786152\pi$
$857$	−45.8257	−1.56538	−0.782688	+	0.622414i	$0.786152\pi$
$858$	32.1794	1.09859
$859$	10.2347	0.349205	0.174602	−	0.984639i	$-0.444136\pi$
$859$	10.2347	0.349205	0.174602	+	0.984639i	$0.444136\pi$
$860$	6.60717	0.225303
$861$	22.2387	0.757891
$862$	−11.3099	−0.385216
$863$	7.00941	0.238603	0.119302	−	0.992858i	$-0.461934\pi$
$863$	7.00941	0.238603	0.119302	+	0.992858i	$0.461934\pi$
$864$	−1.00000	−0.0340207
$865$	−3.54962	−0.120691
$866$	21.7722	0.739850
$867$	−1.00000	−0.0339618
$868$	27.7491	0.941865
$869$	−42.1822	−1.43093
$870$	−4.19258	−0.142142
$871$	49.2876	1.67005
$872$	−0.198490	−0.00672172
$873$	−15.5706	−0.526986
$874$	−20.2704	−0.685658
$875$	33.9322	1.14712
$876$	8.65932	0.292571
$877$	39.4490	1.33210	0.666049	−	0.745908i	$-0.267984\pi$
$877$	39.4490	1.33210	0.666049	+	0.745908i	$0.267984\pi$
$878$	−6.22232	−0.209993
$879$	16.4188	0.553793
$880$	−3.94729	−0.133063
$881$	−44.9688	−1.51504	−0.757519	−	0.652813i	$-0.773589\pi$
$881$	−44.9688	−1.51504	−0.757519	+	0.652813i	$0.773589\pi$
$882$	13.5162	0.455113
$883$	−56.2006	−1.89130	−0.945650	−	0.325186i	$-0.894573\pi$
$883$	−56.2006	−1.89130	−0.945650	+	0.325186i	$0.894573\pi$
$884$	6.52527	0.219469
$885$	−0.800423	−0.0269059
$886$	−4.11568	−0.138269
$887$	−18.7974	−0.631154	−0.315577	−	0.948900i	$-0.602198\pi$
$887$	−18.7974	−0.631154	−0.315577	+	0.948900i	$0.602198\pi$
$888$	4.16347	0.139717
$889$	−7.32493	−0.245670
$890$	−1.40471	−0.0470861
$891$	−4.93150	−0.165212
$892$	−17.7903	−0.595663
$893$	−32.8887	−1.10058
$894$	−17.2520	−0.576992
$895$	−0.659024	−0.0220288
$896$	−4.52948	−0.151319
$897$	−18.6769	−0.623603
$898$	−17.3833	−0.580088
$899$	−32.0894	−1.07024
$900$	−4.35932	−0.145311
$901$	−2.60293	−0.0867160
$902$	−24.2125	−0.806188
$903$	37.3890	1.24423
$904$	20.0727	0.667609
$905$	15.6629	0.520654
$906$	−16.5589	−0.550134
$907$	57.5335	1.91037	0.955185	−	0.296010i	$-0.0956562\pi$
$907$	57.5335	1.91037	0.955185	+	0.296010i	$0.0956562\pi$
$908$	5.75967	0.191141
$909$	1.84783	0.0612885
$910$	−23.6573	−0.784233
$911$	33.7037	1.11665	0.558326	−	0.829621i	$-0.311444\pi$
$911$	33.7037	1.11665	0.558326	+	0.829621i	$0.311444\pi$
$912$	7.08202	0.234509
$913$	23.6220	0.781776
$914$	−5.96344	−0.197253
$915$	−5.72817	−0.189368
$916$	22.1948	0.733338
$917$	−78.6745	−2.59806
$918$	−1.00000	−0.0330049
$919$	48.6587	1.60510	0.802552	−	0.596583i	$-0.203475\pi$
$919$	48.6587	1.60510	0.802552	+	0.596583i	$0.203475\pi$
$920$	2.29100	0.0755321
$921$	9.16557	0.302016
$922$	−38.7873	−1.27739
$923$	40.0435	1.31805
$924$	−22.3371	−0.734837
$925$	18.1499	0.596765
$926$	30.2839	0.995192
$927$	9.86585	0.324037
$928$	5.23795	0.171944
$929$	−5.40454	−0.177317	−0.0886586	−	0.996062i	$-0.528258\pi$
$929$	−5.40454	−0.177317	−0.0886586	+	0.996062i	$0.528258\pi$
$930$	4.90366	0.160797
$931$	−95.7217	−3.13715
$932$	2.69400	0.0882449
$933$	12.2264	0.400273
$934$	10.8580	0.355285
$935$	−3.94729	−0.129090
$936$	6.52527	0.213285
$937$	53.7631	1.75637	0.878183	−	0.478325i	$-0.158756\pi$
$937$	53.7631	1.75637	0.878183	+	0.478325i	$0.158756\pi$
$938$	−34.2127	−1.11708
$939$	−19.3046	−0.629980
$940$	3.71714	0.121240
$941$	−44.7190	−1.45780	−0.728899	−	0.684621i	$-0.759968\pi$
$941$	−44.7190	−1.45780	−0.728899	+	0.684621i	$0.759968\pi$
$942$	−7.16638	−0.233493
$943$	14.0529	0.457626
$944$	1.00000	0.0325472
$945$	3.62550	0.117937
$946$	−40.7075	−1.32352
$947$	34.5912	1.12406	0.562032	−	0.827115i	$-0.310020\pi$
$947$	34.5912	1.12406	0.562032	+	0.827115i	$0.310020\pi$
$948$	−8.55362	−0.277809
$949$	−56.5044	−1.83421
$950$	30.8728	1.00165
$951$	−27.1196	−0.879414
$952$	−4.52948	−0.146801
$953$	−29.7204	−0.962740	−0.481370	−	0.876518i	$-0.659861\pi$
$953$	−29.7204	−0.962740	−0.481370	+	0.876518i	$0.659861\pi$
$954$	−2.60293	−0.0842728
$955$	0.376227	0.0121744
$956$	10.6746	0.345240
$957$	25.8310	0.834996
$958$	6.77582	0.218917
$959$	34.3261	1.10845
$960$	−0.800423	−0.0258335
$961$	6.53195	0.210708
$962$	−27.1678	−0.875924
$963$	−15.4998	−0.499473
$964$	−22.4145	−0.721924
$965$	3.07613	0.0990242
$966$	12.9644	0.417124
$967$	19.5009	0.627107	0.313554	−	0.949571i	$-0.398480\pi$
$967$	19.5009	0.627107	0.313554	+	0.949571i	$0.398480\pi$
$968$	13.3197	0.428111
$969$	7.08202	0.227507
$970$	−12.4631	−0.400166
$971$	−16.4411	−0.527622	−0.263811	−	0.964574i	$-0.584979\pi$
$971$	−16.4411	−0.527622	−0.263811	+	0.964574i	$0.584979\pi$
$972$	−1.00000	−0.0320750
$973$	−51.4752	−1.65022
$974$	−20.1083	−0.644313
$975$	28.4457	0.910993
$976$	7.15643	0.229072
$977$	−34.9120	−1.11693	−0.558467	−	0.829527i	$-0.688610\pi$
$977$	−34.9120	−1.11693	−0.558467	+	0.829527i	$0.688610\pi$
$978$	1.41302	0.0451833
$979$	8.65461	0.276602
$980$	10.8186	0.345589
$981$	−0.198490	−0.00633730
$982$	30.2566	0.965528
$983$	48.6975	1.55321	0.776605	−	0.629988i	$-0.216940\pi$
$983$	48.6975	1.55321	0.776605	+	0.629988i	$0.216940\pi$
$984$	−4.90976	−0.156518
$985$	4.49311	0.143162
$986$	5.23795	0.166810
$987$	21.0347	0.669543
$988$	−46.2121	−1.47020
$989$	23.6266	0.751283
$990$	−3.94729	−0.125453
$991$	34.6401	1.10038	0.550189	−	0.835040i	$-0.314555\pi$
$991$	34.6401	1.10038	0.550189	+	0.835040i	$0.314555\pi$
$992$	−6.12633	−0.194511
$993$	4.82675	0.153172
$994$	−27.7960	−0.881635
$995$	8.38908	0.265952
$996$	4.79003	0.151778
$997$	2.42236	0.0767168	0.0383584	−	0.999264i	$-0.487787\pi$
$997$	2.42236	0.0767168	0.0383584	+	0.999264i	$0.487787\pi$
$998$	20.9423	0.662918
$999$	4.16347	0.131726

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.bc.1.8	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.bc.1.8	✓	14	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.800423 q^{5} -1.00000 q^{6} -4.52948 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.800423 q^{5} -1.00000 q^{6} -4.52948 q^{7} +1.00000 q^{8} +1.00000 q^{9} +0.800423 q^{10} -4.93150 q^{11} -1.00000 q^{12} +6.52527 q^{13} -4.52948 q^{14} -0.800423 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} -7.08202 q^{19} +0.800423 q^{20} +4.52948 q^{21} -4.93150 q^{22} +2.86224 q^{23} -1.00000 q^{24} -4.35932 q^{25} +6.52527 q^{26} -1.00000 q^{27} -4.52948 q^{28} +5.23795 q^{29} -0.800423 q^{30} -6.12633 q^{31} +1.00000 q^{32} +4.93150 q^{33} +1.00000 q^{34} -3.62550 q^{35} +1.00000 q^{36} -4.16347 q^{37} -7.08202 q^{38} -6.52527 q^{39} +0.800423 q^{40} +4.90976 q^{41} +4.52948 q^{42} +8.25459 q^{43} -4.93150 q^{44} +0.800423 q^{45} +2.86224 q^{46} +4.64397 q^{47} -1.00000 q^{48} +13.5162 q^{49} -4.35932 q^{50} -1.00000 q^{51} +6.52527 q^{52} -2.60293 q^{53} -1.00000 q^{54} -3.94729 q^{55} -4.52948 q^{56} +7.08202 q^{57} +5.23795 q^{58} +1.00000 q^{59} -0.800423 q^{60} +7.15643 q^{61} -6.12633 q^{62} -4.52948 q^{63} +1.00000 q^{64} +5.22298 q^{65} +4.93150 q^{66} +7.55334 q^{67} +1.00000 q^{68} -2.86224 q^{69} -3.62550 q^{70} +6.13669 q^{71} +1.00000 q^{72} -8.65932 q^{73} -4.16347 q^{74} +4.35932 q^{75} -7.08202 q^{76} +22.3371 q^{77} -6.52527 q^{78} +8.55362 q^{79} +0.800423 q^{80} +1.00000 q^{81} +4.90976 q^{82} -4.79003 q^{83} +4.52948 q^{84} +0.800423 q^{85} +8.25459 q^{86} -5.23795 q^{87} -4.93150 q^{88} -1.75496 q^{89} +0.800423 q^{90} -29.5560 q^{91} +2.86224 q^{92} +6.12633 q^{93} +4.64397 q^{94} -5.66861 q^{95} -1.00000 q^{96} -15.5706 q^{97} +13.5162 q^{98} -4.93150 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 14 q^{2} - 14 q^{3} + 14 q^{4} + 2 q^{5} - 14 q^{6} + q^{7} + 14 q^{8} + 14 q^{9}+O(q^{10}) \) 14 * q + 14 * q^2 - 14 * q^3 + 14 * q^4 + 2 * q^5 - 14 * q^6 + q^7 + 14 * q^8 + 14 * q^9	\( 14 q + 14 q^{2} - 14 q^{3} + 14 q^{4} + 2 q^{5} - 14 q^{6} + q^{7} + 14 q^{8} + 14 q^{9} + 2 q^{10} + 3 q^{11} - 14 q^{12} + 16 q^{13} + q^{14} - 2 q^{15} + 14 q^{16} + 14 q^{17} + 14 q^{18} + 13 q^{19} + 2 q^{20} - q^{21} + 3 q^{22} + 4 q^{23} - 14 q^{24} + 32 q^{25} + 16 q^{26} - 14 q^{27} + q^{28} - 2 q^{30} - 13 q^{31} + 14 q^{32} - 3 q^{33} + 14 q^{34} + 14 q^{36} + 12 q^{37} + 13 q^{38} - 16 q^{39} + 2 q^{40} - 18 q^{41} - q^{42} + 29 q^{43} + 3 q^{44} + 2 q^{45} + 4 q^{46} - 14 q^{48} + 49 q^{49} + 32 q^{50} - 14 q^{51} + 16 q^{52} + 24 q^{53} - 14 q^{54} + 15 q^{55} + q^{56} - 13 q^{57} + 14 q^{59} - 2 q^{60} + 29 q^{61} - 13 q^{62} + q^{63} + 14 q^{64} + 6 q^{65} - 3 q^{66} + 4 q^{67} + 14 q^{68} - 4 q^{69} - 10 q^{71} + 14 q^{72} + 18 q^{73} + 12 q^{74} - 32 q^{75} + 13 q^{76} + 20 q^{77} - 16 q^{78} + 7 q^{79} + 2 q^{80} + 14 q^{81} - 18 q^{82} + 28 q^{83} - q^{84} + 2 q^{85} + 29 q^{86} + 3 q^{88} + 23 q^{89} + 2 q^{90} + 9 q^{91} + 4 q^{92} + 13 q^{93} + 5 q^{95} - 14 q^{96} - 7 q^{97} + 49 q^{98} + 3 q^{99}+O(q^{100}) \) 14 * q + 14 * q^2 - 14 * q^3 + 14 * q^4 + 2 * q^5 - 14 * q^6 + q^7 + 14 * q^8 + 14 * q^9 + 2 * q^10 + 3 * q^11 - 14 * q^12 + 16 * q^13 + q^14 - 2 * q^15 + 14 * q^16 + 14 * q^17 + 14 * q^18 + 13 * q^19 + 2 * q^20 - q^21 + 3 * q^22 + 4 * q^23 - 14 * q^24 + 32 * q^25 + 16 * q^26 - 14 * q^27 + q^28 - 2 * q^30 - 13 * q^31 + 14 * q^32 - 3 * q^33 + 14 * q^34 + 14 * q^36 + 12 * q^37 + 13 * q^38 - 16 * q^39 + 2 * q^40 - 18 * q^41 - q^42 + 29 * q^43 + 3 * q^44 + 2 * q^45 + 4 * q^46 - 14 * q^48 + 49 * q^49 + 32 * q^50 - 14 * q^51 + 16 * q^52 + 24 * q^53 - 14 * q^54 + 15 * q^55 + q^56 - 13 * q^57 + 14 * q^59 - 2 * q^60 + 29 * q^61 - 13 * q^62 + q^63 + 14 * q^64 + 6 * q^65 - 3 * q^66 + 4 * q^67 + 14 * q^68 - 4 * q^69 - 10 * q^71 + 14 * q^72 + 18 * q^73 + 12 * q^74 - 32 * q^75 + 13 * q^76 + 20 * q^77 - 16 * q^78 + 7 * q^79 + 2 * q^80 + 14 * q^81 - 18 * q^82 + 28 * q^83 - q^84 + 2 * q^85 + 29 * q^86 + 3 * q^88 + 23 * q^89 + 2 * q^90 + 9 * q^91 + 4 * q^92 + 13 * q^93 + 5 * q^95 - 14 * q^96 - 7 * q^97 + 49 * q^98 + 3 * q^99

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