LMFDB - Embedded newform 6018.2.a.u.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:	$1$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 4x^{8} - 16x^{7} + 37x^{6} + 97x^{5} - 72x^{4} - 182x^{3} + 24x^{2} + 70x - 19 $ x^9 - 4x^8 - 16x^7 + 37x^6 + 97x^5 - 72x^4 - 182x^3 + 24x^2 + 70x - 19
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$-1.72522$ of defining polynomial
Character	$\chi$	$=$	6018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.17259 q^{5} +1.00000 q^{6} -4.61193 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.17259 q^{5} +1.00000 q^{6} -4.61193 q^{7} -1.00000 q^{8} +1.00000 q^{9} -3.17259 q^{10} -0.697022 q^{11} -1.00000 q^{12} +2.07427 q^{13} +4.61193 q^{14} -3.17259 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} -4.21524 q^{19} +3.17259 q^{20} +4.61193 q^{21} +0.697022 q^{22} +1.76787 q^{23} +1.00000 q^{24} +5.06531 q^{25} -2.07427 q^{26} -1.00000 q^{27} -4.61193 q^{28} -2.67126 q^{29} +3.17259 q^{30} +2.74610 q^{31} -1.00000 q^{32} +0.697022 q^{33} -1.00000 q^{34} -14.6318 q^{35} +1.00000 q^{36} +6.98827 q^{37} +4.21524 q^{38} -2.07427 q^{39} -3.17259 q^{40} -9.67750 q^{41} -4.61193 q^{42} -0.221360 q^{43} -0.697022 q^{44} +3.17259 q^{45} -1.76787 q^{46} +4.09351 q^{47} -1.00000 q^{48} +14.2699 q^{49} -5.06531 q^{50} -1.00000 q^{51} +2.07427 q^{52} -4.12004 q^{53} +1.00000 q^{54} -2.21136 q^{55} +4.61193 q^{56} +4.21524 q^{57} +2.67126 q^{58} +1.00000 q^{59} -3.17259 q^{60} +3.42864 q^{61} -2.74610 q^{62} -4.61193 q^{63} +1.00000 q^{64} +6.58080 q^{65} -0.697022 q^{66} -9.96569 q^{67} +1.00000 q^{68} -1.76787 q^{69} +14.6318 q^{70} +3.78324 q^{71} -1.00000 q^{72} -2.02937 q^{73} -6.98827 q^{74} -5.06531 q^{75} -4.21524 q^{76} +3.21462 q^{77} +2.07427 q^{78} +3.39812 q^{79} +3.17259 q^{80} +1.00000 q^{81} +9.67750 q^{82} +3.65024 q^{83} +4.61193 q^{84} +3.17259 q^{85} +0.221360 q^{86} +2.67126 q^{87} +0.697022 q^{88} -3.75248 q^{89} -3.17259 q^{90} -9.56639 q^{91} +1.76787 q^{92} -2.74610 q^{93} -4.09351 q^{94} -13.3732 q^{95} +1.00000 q^{96} +7.20410 q^{97} -14.2699 q^{98} -0.697022 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 9 q^{2} - 9 q^{3} + 9 q^{4} + 2 q^{5} + 9 q^{6} - 5 q^{7} - 9 q^{8} + 9 q^{9}+O(q^{10}) $ 9 * q - 9 * q^2 - 9 * q^3 + 9 * q^4 + 2 * q^5 + 9 * q^6 - 5 * q^7 - 9 * q^8 + 9 * q^9	\( 9 q - 9 q^{2} - 9 q^{3} + 9 q^{4} + 2 q^{5} + 9 q^{6} - 5 q^{7} - 9 q^{8} + 9 q^{9} - 2 q^{10} - q^{11} - 9 q^{12} - 4 q^{13} + 5 q^{14} - 2 q^{15} + 9 q^{16} + 9 q^{17} - 9 q^{18} - 7 q^{19} + 2 q^{20} + 5 q^{21} + q^{22} - 8 q^{23} + 9 q^{24} + 5 q^{25} + 4 q^{26} - 9 q^{27} - 5 q^{28} + 6 q^{29} + 2 q^{30} - 17 q^{31} - 9 q^{32} + q^{33} - 9 q^{34} + 10 q^{35} + 9 q^{36} + 2 q^{37} + 7 q^{38} + 4 q^{39} - 2 q^{40} + 14 q^{41} - 5 q^{42} - 27 q^{43} - q^{44} + 2 q^{45} + 8 q^{46} - 18 q^{47} - 9 q^{48} + 18 q^{49} - 5 q^{50} - 9 q^{51} - 4 q^{52} + 4 q^{53} + 9 q^{54} - 27 q^{55} + 5 q^{56} + 7 q^{57} - 6 q^{58} + 9 q^{59} - 2 q^{60} + 5 q^{61} + 17 q^{62} - 5 q^{63} + 9 q^{64} + 2 q^{65} - q^{66} - 22 q^{67} + 9 q^{68} + 8 q^{69} - 10 q^{70} + 16 q^{71} - 9 q^{72} - 12 q^{73} - 2 q^{74} - 5 q^{75} - 7 q^{76} + 6 q^{77} - 4 q^{78} - 9 q^{79} + 2 q^{80} + 9 q^{81} - 14 q^{82} + 10 q^{83} + 5 q^{84} + 2 q^{85} + 27 q^{86} - 6 q^{87} + q^{88} + 15 q^{89} - 2 q^{90} + 3 q^{91} - 8 q^{92} + 17 q^{93} + 18 q^{94} - 9 q^{95} + 9 q^{96} - 33 q^{97} - 18 q^{98} - q^{99}+O(q^{100}) \) 9 * q - 9 * q^2 - 9 * q^3 + 9 * q^4 + 2 * q^5 + 9 * q^6 - 5 * q^7 - 9 * q^8 + 9 * q^9 - 2 * q^10 - q^11 - 9 * q^12 - 4 * q^13 + 5 * q^14 - 2 * q^15 + 9 * q^16 + 9 * q^17 - 9 * q^18 - 7 * q^19 + 2 * q^20 + 5 * q^21 + q^22 - 8 * q^23 + 9 * q^24 + 5 * q^25 + 4 * q^26 - 9 * q^27 - 5 * q^28 + 6 * q^29 + 2 * q^30 - 17 * q^31 - 9 * q^32 + q^33 - 9 * q^34 + 10 * q^35 + 9 * q^36 + 2 * q^37 + 7 * q^38 + 4 * q^39 - 2 * q^40 + 14 * q^41 - 5 * q^42 - 27 * q^43 - q^44 + 2 * q^45 + 8 * q^46 - 18 * q^47 - 9 * q^48 + 18 * q^49 - 5 * q^50 - 9 * q^51 - 4 * q^52 + 4 * q^53 + 9 * q^54 - 27 * q^55 + 5 * q^56 + 7 * q^57 - 6 * q^58 + 9 * q^59 - 2 * q^60 + 5 * q^61 + 17 * q^62 - 5 * q^63 + 9 * q^64 + 2 * q^65 - q^66 - 22 * q^67 + 9 * q^68 + 8 * q^69 - 10 * q^70 + 16 * q^71 - 9 * q^72 - 12 * q^73 - 2 * q^74 - 5 * q^75 - 7 * q^76 + 6 * q^77 - 4 * q^78 - 9 * q^79 + 2 * q^80 + 9 * q^81 - 14 * q^82 + 10 * q^83 + 5 * q^84 + 2 * q^85 + 27 * q^86 - 6 * q^87 + q^88 + 15 * q^89 - 2 * q^90 + 3 * q^91 - 8 * q^92 + 17 * q^93 + 18 * q^94 - 9 * q^95 + 9 * q^96 - 33 * q^97 - 18 * q^98 - q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	3.17259	1.41882	0.709412	−	0.704794i	$-0.248961\pi$
$5$	3.17259	1.41882	0.709412	+	0.704794i	$0.248961\pi$
$6$	1.00000	0.408248
$7$	−4.61193	−1.74315	−0.871573	−	0.490266i	$-0.836900\pi$
$7$	−4.61193	−1.74315	−0.871573	+	0.490266i	$0.836900\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−3.17259	−1.00326
$11$	−0.697022	−0.210160	−0.105080	−	0.994464i	$-0.533510\pi$
$11$	−0.697022	−0.210160	−0.105080	+	0.994464i	$0.533510\pi$
$12$	−1.00000	−0.288675
$13$	2.07427	0.575299	0.287649	−	0.957736i	$-0.407126\pi$
$13$	2.07427	0.575299	0.287649	+	0.957736i	$0.407126\pi$
$14$	4.61193	1.23259
$15$	−3.17259	−0.819158
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.00000	−0.235702
$19$	−4.21524	−0.967042	−0.483521	−	0.875333i	$-0.660642\pi$
$19$	−4.21524	−0.967042	−0.483521	+	0.875333i	$0.660642\pi$
$20$	3.17259	0.709412
$21$	4.61193	1.00641
$22$	0.697022	0.148606
$23$	1.76787	0.368627	0.184314	−	0.982867i	$-0.440994\pi$
$23$	1.76787	0.368627	0.184314	+	0.982867i	$0.440994\pi$
$24$	1.00000	0.204124
$25$	5.06531	1.01306
$26$	−2.07427	−0.406798
$27$	−1.00000	−0.192450
$28$	−4.61193	−0.871573
$29$	−2.67126	−0.496041	−0.248021	−	0.968755i	$-0.579780\pi$
$29$	−2.67126	−0.496041	−0.248021	+	0.968755i	$0.579780\pi$
$30$	3.17259	0.579232
$31$	2.74610	0.493214	0.246607	−	0.969116i	$-0.420684\pi$
$31$	2.74610	0.493214	0.246607	+	0.969116i	$0.420684\pi$
$32$	−1.00000	−0.176777
$33$	0.697022	0.121336
$34$	−1.00000	−0.171499
$35$	−14.6318	−2.47322
$36$	1.00000	0.166667
$37$	6.98827	1.14886	0.574432	−	0.818552i	$-0.305223\pi$
$37$	6.98827	1.14886	0.574432	+	0.818552i	$0.305223\pi$
$38$	4.21524	0.683802
$39$	−2.07427	−0.332149
$40$	−3.17259	−0.501630
$41$	−9.67750	−1.51137	−0.755686	−	0.654935i	$-0.772696\pi$
$41$	−9.67750	−1.51137	−0.755686	+	0.654935i	$0.772696\pi$
$42$	−4.61193	−0.711636
$43$	−0.221360	−0.0337571	−0.0168785	−	0.999858i	$-0.505373\pi$
$43$	−0.221360	−0.0337571	−0.0168785	+	0.999858i	$0.505373\pi$
$44$	−0.697022	−0.105080
$45$	3.17259	0.472941
$46$	−1.76787	−0.260659
$47$	4.09351	0.597100	0.298550	−	0.954394i	$-0.403497\pi$
$47$	4.09351	0.597100	0.298550	+	0.954394i	$0.403497\pi$
$48$	−1.00000	−0.144338
$49$	14.2699	2.03856
$50$	−5.06531	−0.716343
$51$	−1.00000	−0.140028
$52$	2.07427	0.287649
$53$	−4.12004	−0.565931	−0.282965	−	0.959130i	$-0.591318\pi$
$53$	−4.12004	−0.565931	−0.282965	+	0.959130i	$0.591318\pi$
$54$	1.00000	0.136083
$55$	−2.21136	−0.298180
$56$	4.61193	0.616295
$57$	4.21524	0.558322
$58$	2.67126	0.350754
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	−3.17259	−0.409579
$61$	3.42864	0.438992	0.219496	−	0.975613i	$-0.429559\pi$
$61$	3.42864	0.438992	0.219496	+	0.975613i	$0.429559\pi$
$62$	−2.74610	−0.348755
$63$	−4.61193	−0.581049
$64$	1.00000	0.125000
$65$	6.58080	0.816248
$66$	−0.697022	−0.0857975
$67$	−9.96569	−1.21750	−0.608751	−	0.793361i	$-0.708329\pi$
$67$	−9.96569	−1.21750	−0.608751	+	0.793361i	$0.708329\pi$
$68$	1.00000	0.121268
$69$	−1.76787	−0.212827
$70$	14.6318	1.74883
$71$	3.78324	0.448988	0.224494	−	0.974475i	$-0.427927\pi$
$71$	3.78324	0.448988	0.224494	+	0.974475i	$0.427927\pi$
$72$	−1.00000	−0.117851
$73$	−2.02937	−0.237519	−0.118760	−	0.992923i	$-0.537892\pi$
$73$	−2.02937	−0.237519	−0.118760	+	0.992923i	$0.537892\pi$
$74$	−6.98827	−0.812370
$75$	−5.06531	−0.584891
$76$	−4.21524	−0.483521
$77$	3.21462	0.366340
$78$	2.07427	0.234865
$79$	3.39812	0.382318	0.191159	−	0.981559i	$-0.438775\pi$
$79$	3.39812	0.382318	0.191159	+	0.981559i	$0.438775\pi$
$80$	3.17259	0.354706
$81$	1.00000	0.111111
$82$	9.67750	1.06870
$83$	3.65024	0.400666	0.200333	−	0.979728i	$-0.435798\pi$
$83$	3.65024	0.400666	0.200333	+	0.979728i	$0.435798\pi$
$84$	4.61193	0.503203
$85$	3.17259	0.344115
$86$	0.221360	0.0238698
$87$	2.67126	0.286389
$88$	0.697022	0.0743028
$89$	−3.75248	−0.397762	−0.198881	−	0.980024i	$-0.563731\pi$
$89$	−3.75248	−0.397762	−0.198881	+	0.980024i	$0.563731\pi$
$90$	−3.17259	−0.334420
$91$	−9.56639	−1.00283
$92$	1.76787	0.184314
$93$	−2.74610	−0.284757
$94$	−4.09351	−0.422213
$95$	−13.3732	−1.37206
$96$	1.00000	0.102062
$97$	7.20410	0.731465	0.365733	−	0.930720i	$-0.380818\pi$
$97$	7.20410	0.731465	0.365733	+	0.930720i	$0.380818\pi$
$98$	−14.2699	−1.44148
$99$	−0.697022	−0.0700534
$100$	5.06531	0.506531
$101$	8.94213	0.889775	0.444888	−	0.895586i	$-0.353244\pi$
$101$	8.94213	0.889775	0.444888	+	0.895586i	$0.353244\pi$
$102$	1.00000	0.0990148
$103$	−8.97892	−0.884720	−0.442360	−	0.896838i	$-0.645859\pi$
$103$	−8.97892	−0.884720	−0.442360	+	0.896838i	$0.645859\pi$
$104$	−2.07427	−0.203399
$105$	14.6318	1.42791
$106$	4.12004	0.400174
$107$	−8.68135	−0.839257	−0.419629	−	0.907696i	$-0.637840\pi$
$107$	−8.68135	−0.839257	−0.419629	+	0.907696i	$0.637840\pi$
$108$	−1.00000	−0.0962250
$109$	10.4807	1.00387	0.501933	−	0.864906i	$-0.332622\pi$
$109$	10.4807	1.00387	0.501933	+	0.864906i	$0.332622\pi$
$110$	2.21136	0.210845
$111$	−6.98827	−0.663297
$112$	−4.61193	−0.435787
$113$	−9.37509	−0.881934	−0.440967	−	0.897523i	$-0.645364\pi$
$113$	−9.37509	−0.881934	−0.440967	+	0.897523i	$0.645364\pi$
$114$	−4.21524	−0.394793
$115$	5.60873	0.523017
$116$	−2.67126	−0.248021
$117$	2.07427	0.191766
$118$	−1.00000	−0.0920575
$119$	−4.61193	−0.422775
$120$	3.17259	0.289616
$121$	−10.5142	−0.955833
$122$	−3.42864	−0.310414
$123$	9.67750	0.872591
$124$	2.74610	0.246607
$125$	0.207194	0.0185320
$126$	4.61193	0.410863
$127$	−7.25265	−0.643568	−0.321784	−	0.946813i	$-0.604283\pi$
$127$	−7.25265	−0.643568	−0.321784	+	0.946813i	$0.604283\pi$
$128$	−1.00000	−0.0883883
$129$	0.221360	0.0194896
$130$	−6.58080	−0.577174
$131$	−5.99034	−0.523379	−0.261689	−	0.965152i	$-0.584280\pi$
$131$	−5.99034	−0.523379	−0.261689	+	0.965152i	$0.584280\pi$
$132$	0.697022	0.0606680
$133$	19.4404	1.68569
$134$	9.96569	0.860904
$135$	−3.17259	−0.273053
$136$	−1.00000	−0.0857493
$137$	−22.2170	−1.89813	−0.949064	−	0.315084i	$-0.897967\pi$
$137$	−22.2170	−1.89813	−0.949064	+	0.315084i	$0.897967\pi$
$138$	1.76787	0.150491
$139$	−12.3095	−1.04407	−0.522037	−	0.852923i	$-0.674828\pi$
$139$	−12.3095	−1.04407	−0.522037	+	0.852923i	$0.674828\pi$
$140$	−14.6318	−1.23661
$141$	−4.09351	−0.344736
$142$	−3.78324	−0.317483
$143$	−1.44581	−0.120905
$144$	1.00000	0.0833333
$145$	−8.47481	−0.703795
$146$	2.02937	0.167951
$147$	−14.2699	−1.17696
$148$	6.98827	0.574432
$149$	−3.07162	−0.251637	−0.125818	−	0.992053i	$-0.540156\pi$
$149$	−3.07162	−0.251637	−0.125818	+	0.992053i	$0.540156\pi$
$150$	5.06531	0.413581
$151$	6.44348	0.524363	0.262181	−	0.965019i	$-0.415558\pi$
$151$	6.44348	0.524363	0.262181	+	0.965019i	$0.415558\pi$
$152$	4.21524	0.341901
$153$	1.00000	0.0808452
$154$	−3.21462	−0.259041
$155$	8.71223	0.699783
$156$	−2.07427	−0.166074
$157$	−0.400382	−0.0319540	−0.0159770	−	0.999872i	$-0.505086\pi$
$157$	−0.400382	−0.0319540	−0.0159770	+	0.999872i	$0.505086\pi$
$158$	−3.39812	−0.270340
$159$	4.12004	0.326740
$160$	−3.17259	−0.250815
$161$	−8.15331	−0.642571
$162$	−1.00000	−0.0785674
$163$	−9.23737	−0.723527	−0.361763	−	0.932270i	$-0.617825\pi$
$163$	−9.23737	−0.723527	−0.361763	+	0.932270i	$0.617825\pi$
$164$	−9.67750	−0.755686
$165$	2.21136	0.172154
$166$	−3.65024	−0.283314
$167$	−8.75120	−0.677188	−0.338594	−	0.940933i	$-0.609951\pi$
$167$	−8.75120	−0.677188	−0.338594	+	0.940933i	$0.609951\pi$
$168$	−4.61193	−0.355818
$169$	−8.69741	−0.669031
$170$	−3.17259	−0.243326
$171$	−4.21524	−0.322347
$172$	−0.221360	−0.0168785
$173$	−12.9483	−0.984439	−0.492220	−	0.870471i	$-0.663814\pi$
$173$	−12.9483	−0.984439	−0.492220	+	0.870471i	$0.663814\pi$
$174$	−2.67126	−0.202508
$175$	−23.3608	−1.76591
$176$	−0.697022	−0.0525400
$177$	−1.00000	−0.0751646
$178$	3.75248	0.281260
$179$	19.2985	1.44244	0.721219	−	0.692707i	$-0.243582\pi$
$179$	19.2985	1.44244	0.721219	+	0.692707i	$0.243582\pi$
$180$	3.17259	0.236471
$181$	13.1597	0.978153	0.489076	−	0.872241i	$-0.337334\pi$
$181$	13.1597	0.978153	0.489076	+	0.872241i	$0.337334\pi$
$182$	9.56639	0.709108
$183$	−3.42864	−0.253452
$184$	−1.76787	−0.130329
$185$	22.1709	1.63004
$186$	2.74610	0.201354
$187$	−0.697022	−0.0509713
$188$	4.09351	0.298550
$189$	4.61193	0.335469
$190$	13.3732	0.970194
$191$	11.0165	0.797123	0.398562	−	0.917142i	$-0.369509\pi$
$191$	11.0165	0.797123	0.398562	+	0.917142i	$0.369509\pi$
$192$	−1.00000	−0.0721688
$193$	−6.89410	−0.496248	−0.248124	−	0.968728i	$-0.579814\pi$
$193$	−6.89410	−0.496248	−0.248124	+	0.968728i	$0.579814\pi$
$194$	−7.20410	−0.517224
$195$	−6.58080	−0.471261
$196$	14.2699	1.01928
$197$	12.1568	0.866135	0.433067	−	0.901362i	$-0.357431\pi$
$197$	12.1568	0.866135	0.433067	+	0.901362i	$0.357431\pi$
$198$	0.697022	0.0495352
$199$	−13.8801	−0.983933	−0.491967	−	0.870614i	$-0.663722\pi$
$199$	−13.8801	−0.983933	−0.491967	+	0.870614i	$0.663722\pi$
$200$	−5.06531	−0.358171
$201$	9.96569	0.702925
$202$	−8.94213	−0.629166
$203$	12.3197	0.864672
$204$	−1.00000	−0.0700140
$205$	−30.7027	−2.14437
$206$	8.97892	0.625591
$207$	1.76787	0.122876
$208$	2.07427	0.143825
$209$	2.93811	0.203234
$210$	−14.6318	−1.00969
$211$	−13.4608	−0.926682	−0.463341	−	0.886180i	$-0.653349\pi$
$211$	−13.4608	−0.926682	−0.463341	+	0.886180i	$0.653349\pi$
$212$	−4.12004	−0.282965
$213$	−3.78324	−0.259223
$214$	8.68135	0.593445
$215$	−0.702283	−0.0478953
$216$	1.00000	0.0680414
$217$	−12.6648	−0.859743
$218$	−10.4807	−0.709841
$219$	2.02937	0.137132
$220$	−2.21136	−0.149090
$221$	2.07427	0.139530
$222$	6.98827	0.469022
$223$	−3.13791	−0.210130	−0.105065	−	0.994465i	$-0.533505\pi$
$223$	−3.13791	−0.210130	−0.105065	+	0.994465i	$0.533505\pi$
$224$	4.61193	0.308148
$225$	5.06531	0.337687
$226$	9.37509	0.623622
$227$	−6.01614	−0.399305	−0.199653	−	0.979867i	$-0.563981\pi$
$227$	−6.01614	−0.399305	−0.199653	+	0.979867i	$0.563981\pi$
$228$	4.21524	0.279161
$229$	1.24858	0.0825088	0.0412544	−	0.999149i	$-0.486865\pi$
$229$	1.24858	0.0825088	0.0412544	+	0.999149i	$0.486865\pi$
$230$	−5.60873	−0.369829
$231$	−3.21462	−0.211506
$232$	2.67126	0.175377
$233$	21.9229	1.43621	0.718107	−	0.695932i	$-0.245009\pi$
$233$	21.9229	1.43621	0.718107	+	0.695932i	$0.245009\pi$
$234$	−2.07427	−0.135599
$235$	12.9870	0.847179
$236$	1.00000	0.0650945
$237$	−3.39812	−0.220732
$238$	4.61193	0.298947
$239$	9.73172	0.629493	0.314746	−	0.949176i	$-0.398081\pi$
$239$	9.73172	0.629493	0.314746	+	0.949176i	$0.398081\pi$
$240$	−3.17259	−0.204790
$241$	6.50044	0.418730	0.209365	−	0.977838i	$-0.432860\pi$
$241$	6.50044	0.418730	0.209365	+	0.977838i	$0.432860\pi$
$242$	10.5142	0.675876
$243$	−1.00000	−0.0641500
$244$	3.42864	0.219496
$245$	45.2725	2.89236
$246$	−9.67750	−0.617015
$247$	−8.74354	−0.556338
$248$	−2.74610	−0.174377
$249$	−3.65024	−0.231325
$250$	−0.207194	−0.0131041
$251$	−13.6593	−0.862165	−0.431082	−	0.902313i	$-0.641868\pi$
$251$	−13.6593	−0.862165	−0.431082	+	0.902313i	$0.641868\pi$
$252$	−4.61193	−0.290524
$253$	−1.23225	−0.0774707
$254$	7.25265	0.455072
$255$	−3.17259	−0.198675
$256$	1.00000	0.0625000
$257$	1.73754	0.108385	0.0541925	−	0.998531i	$-0.482742\pi$
$257$	1.73754	0.108385	0.0541925	+	0.998531i	$0.482742\pi$
$258$	−0.221360	−0.0137813
$259$	−32.2294	−2.00264
$260$	6.58080	0.408124
$261$	−2.67126	−0.165347
$262$	5.99034	0.370085
$263$	−17.7588	−1.09506	−0.547528	−	0.836787i	$-0.684431\pi$
$263$	−17.7588	−1.09506	−0.547528	+	0.836787i	$0.684431\pi$
$264$	−0.697022	−0.0428988
$265$	−13.0712	−0.802956
$266$	−19.4404	−1.19197
$267$	3.75248	0.229648
$268$	−9.96569	−0.608751
$269$	26.5153	1.61667	0.808334	−	0.588724i	$-0.200370\pi$
$269$	26.5153	1.61667	0.808334	+	0.588724i	$0.200370\pi$
$270$	3.17259	0.193077
$271$	−16.3215	−0.991458	−0.495729	−	0.868477i	$-0.665099\pi$
$271$	−16.3215	−0.991458	−0.495729	+	0.868477i	$0.665099\pi$
$272$	1.00000	0.0606339
$273$	9.56639	0.578984
$274$	22.2170	1.34218
$275$	−3.53063	−0.212905
$276$	−1.76787	−0.106413
$277$	15.7904	0.948752	0.474376	−	0.880322i	$-0.342674\pi$
$277$	15.7904	0.948752	0.474376	+	0.880322i	$0.342674\pi$
$278$	12.3095	0.738272
$279$	2.74610	0.164405
$280$	14.6318	0.874414
$281$	16.3853	0.977466	0.488733	−	0.872433i	$-0.337459\pi$
$281$	16.3853	0.977466	0.488733	+	0.872433i	$0.337459\pi$
$282$	4.09351	0.243765
$283$	−25.1596	−1.49558	−0.747791	−	0.663934i	$-0.768886\pi$
$283$	−25.1596	−1.49558	−0.747791	+	0.663934i	$0.768886\pi$
$284$	3.78324	0.224494
$285$	13.3732	0.792160
$286$	1.44581	0.0854927
$287$	44.6320	2.63454
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	8.47481	0.497658
$291$	−7.20410	−0.422312
$292$	−2.02937	−0.118760
$293$	−3.59198	−0.209846	−0.104923	−	0.994480i	$-0.533460\pi$
$293$	−3.59198	−0.209846	−0.104923	+	0.994480i	$0.533460\pi$
$294$	14.2699	0.832238
$295$	3.17259	0.184715
$296$	−6.98827	−0.406185
$297$	0.697022	0.0404453
$298$	3.07162	0.177934
$299$	3.66705	0.212071
$300$	−5.06531	−0.292446
$301$	1.02090	0.0588435
$302$	−6.44348	−0.370780
$303$	−8.94213	−0.513712
$304$	−4.21524	−0.241760
$305$	10.8777	0.622853
$306$	−1.00000	−0.0571662
$307$	−14.9408	−0.852717	−0.426358	−	0.904554i	$-0.640204\pi$
$307$	−14.9408	−0.852717	−0.426358	+	0.904554i	$0.640204\pi$
$308$	3.21462	0.183170
$309$	8.97892	0.510793
$310$	−8.71223	−0.494821
$311$	−5.41262	−0.306921	−0.153461	−	0.988155i	$-0.549042\pi$
$311$	−5.41262	−0.306921	−0.153461	+	0.988155i	$0.549042\pi$
$312$	2.07427	0.117432
$313$	−8.10497	−0.458120	−0.229060	−	0.973412i	$-0.573565\pi$
$313$	−8.10497	−0.458120	−0.229060	+	0.973412i	$0.573565\pi$
$314$	0.400382	0.0225949
$315$	−14.6318	−0.824406
$316$	3.39812	0.191159
$317$	−14.6654	−0.823693	−0.411847	−	0.911253i	$-0.635116\pi$
$317$	−14.6654	−0.823693	−0.411847	+	0.911253i	$0.635116\pi$
$318$	−4.12004	−0.231040
$319$	1.86193	0.104248
$320$	3.17259	0.177353
$321$	8.68135	0.484545
$322$	8.15331	0.454366
$323$	−4.21524	−0.234542
$324$	1.00000	0.0555556
$325$	10.5068	0.582813
$326$	9.23737	0.511611
$327$	−10.4807	−0.579583
$328$	9.67750	0.534350
$329$	−18.8790	−1.04083
$330$	−2.21136	−0.121732
$331$	1.61826	0.0889476	0.0444738	−	0.999011i	$-0.485839\pi$
$331$	1.61826	0.0889476	0.0444738	+	0.999011i	$0.485839\pi$
$332$	3.65024	0.200333
$333$	6.98827	0.382955
$334$	8.75120	0.478844
$335$	−31.6170	−1.72742
$336$	4.61193	0.251601
$337$	−12.7459	−0.694316	−0.347158	−	0.937807i	$-0.612853\pi$
$337$	−12.7459	−0.694316	−0.347158	+	0.937807i	$0.612853\pi$
$338$	8.69741	0.473076
$339$	9.37509	0.509185
$340$	3.17259	0.172058
$341$	−1.91409	−0.103654
$342$	4.21524	0.227934
$343$	−33.5283	−1.81036
$344$	0.221360	0.0119349
$345$	−5.60873	−0.301964
$346$	12.9483	0.696104
$347$	0.819977	0.0440187	0.0220093	−	0.999758i	$-0.492994\pi$
$347$	0.819977	0.0440187	0.0220093	+	0.999758i	$0.492994\pi$
$348$	2.67126	0.143195
$349$	−18.8438	−1.00869	−0.504343	−	0.863503i	$-0.668265\pi$
$349$	−18.8438	−1.00869	−0.504343	+	0.863503i	$0.668265\pi$
$350$	23.3608	1.24869
$351$	−2.07427	−0.110716
$352$	0.697022	0.0371514
$353$	−10.8447	−0.577205	−0.288603	−	0.957449i	$-0.593191\pi$
$353$	−10.8447	−0.577205	−0.288603	+	0.957449i	$0.593191\pi$
$354$	1.00000	0.0531494
$355$	12.0027	0.637035
$356$	−3.75248	−0.198881
$357$	4.61193	0.244089
$358$	−19.2985	−1.01996
$359$	3.73184	0.196959	0.0984795	−	0.995139i	$-0.468602\pi$
$359$	3.73184	0.196959	0.0984795	+	0.995139i	$0.468602\pi$
$360$	−3.17259	−0.167210
$361$	−1.23178	−0.0648306
$362$	−13.1597	−0.691659
$363$	10.5142	0.551850
$364$	−9.56639	−0.501415
$365$	−6.43834	−0.336998
$366$	3.42864	0.179218
$367$	−0.914900	−0.0477574	−0.0238787	−	0.999715i	$-0.507602\pi$
$367$	−0.914900	−0.0477574	−0.0238787	+	0.999715i	$0.507602\pi$
$368$	1.76787	0.0921568
$369$	−9.67750	−0.503790
$370$	−22.1709	−1.15261
$371$	19.0013	0.986500
$372$	−2.74610	−0.142378
$373$	−14.2855	−0.739675	−0.369838	−	0.929096i	$-0.620587\pi$
$373$	−14.2855	−0.739675	−0.369838	+	0.929096i	$0.620587\pi$
$374$	0.697022	0.0360422
$375$	−0.207194	−0.0106995
$376$	−4.09351	−0.211107
$377$	−5.54092	−0.285372
$378$	−4.61193	−0.237212
$379$	11.3516	0.583095	0.291547	−	0.956556i	$-0.405830\pi$
$379$	11.3516	0.583095	0.291547	+	0.956556i	$0.405830\pi$
$380$	−13.3732	−0.686031
$381$	7.25265	0.371564
$382$	−11.0165	−0.563651
$383$	10.2583	0.524172	0.262086	−	0.965044i	$-0.415590\pi$
$383$	10.2583	0.524172	0.262086	+	0.965044i	$0.415590\pi$
$384$	1.00000	0.0510310
$385$	10.1987	0.519772
$386$	6.89410	0.350901
$387$	−0.221360	−0.0112524
$388$	7.20410	0.365733
$389$	−19.8997	−1.00896	−0.504478	−	0.863425i	$-0.668315\pi$
$389$	−19.8997	−1.00896	−0.504478	+	0.863425i	$0.668315\pi$
$390$	6.58080	0.333232
$391$	1.76787	0.0894052
$392$	−14.2699	−0.720739
$393$	5.99034	0.302173
$394$	−12.1568	−0.612450
$395$	10.7808	0.542442
$396$	−0.697022	−0.0350267
$397$	4.31177	0.216401	0.108201	−	0.994129i	$-0.465491\pi$
$397$	4.31177	0.216401	0.108201	+	0.994129i	$0.465491\pi$
$398$	13.8801	0.695746
$399$	−19.4404	−0.973236
$400$	5.06531	0.253265
$401$	9.70256	0.484523	0.242261	−	0.970211i	$-0.422111\pi$
$401$	9.70256	0.484523	0.242261	+	0.970211i	$0.422111\pi$
$402$	−9.96569	−0.497043
$403$	5.69614	0.283745
$404$	8.94213	0.444888
$405$	3.17259	0.157647
$406$	−12.3197	−0.611416
$407$	−4.87098	−0.241446
$408$	1.00000	0.0495074
$409$	−13.8045	−0.682586	−0.341293	−	0.939957i	$-0.610865\pi$
$409$	−13.8045	−0.682586	−0.341293	+	0.939957i	$0.610865\pi$
$410$	30.7027	1.51630
$411$	22.2170	1.09588
$412$	−8.97892	−0.442360
$413$	−4.61193	−0.226938
$414$	−1.76787	−0.0868863
$415$	11.5807	0.568475
$416$	−2.07427	−0.101699
$417$	12.3095	0.602797
$418$	−2.93811	−0.143708
$419$	−15.1389	−0.739585	−0.369793	−	0.929114i	$-0.620571\pi$
$419$	−15.1389	−0.739585	−0.369793	+	0.929114i	$0.620571\pi$
$420$	14.6318	0.713956
$421$	−21.7817	−1.06158	−0.530789	−	0.847504i	$-0.678104\pi$
$421$	−21.7817	−1.06158	−0.530789	+	0.847504i	$0.678104\pi$
$422$	13.4608	0.655263
$423$	4.09351	0.199033
$424$	4.12004	0.200087
$425$	5.06531	0.245704
$426$	3.78324	0.183299
$427$	−15.8126	−0.765228
$428$	−8.68135	−0.419629
$429$	1.44581	0.0698045
$430$	0.702283	0.0338671
$431$	7.49178	0.360867	0.180433	−	0.983587i	$-0.442250\pi$
$431$	7.49178	0.360867	0.180433	+	0.983587i	$0.442250\pi$
$432$	−1.00000	−0.0481125
$433$	−5.68976	−0.273432	−0.136716	−	0.990610i	$-0.543655\pi$
$433$	−5.68976	−0.273432	−0.136716	+	0.990610i	$0.543655\pi$
$434$	12.6648	0.607930
$435$	8.47481	0.406336
$436$	10.4807	0.501933
$437$	−7.45201	−0.356478
$438$	−2.02937	−0.0969668
$439$	3.65697	0.174538	0.0872689	−	0.996185i	$-0.472186\pi$
$439$	3.65697	0.174538	0.0872689	+	0.996185i	$0.472186\pi$
$440$	2.21136	0.105423
$441$	14.2699	0.679519
$442$	−2.07427	−0.0986629
$443$	−15.3617	−0.729854	−0.364927	−	0.931036i	$-0.618906\pi$
$443$	−15.3617	−0.729854	−0.364927	+	0.931036i	$0.618906\pi$
$444$	−6.98827	−0.331649
$445$	−11.9051	−0.564355
$446$	3.13791	0.148584
$447$	3.07162	0.145283
$448$	−4.61193	−0.217893
$449$	−38.8200	−1.83203	−0.916014	−	0.401145i	$-0.868612\pi$
$449$	−38.8200	−1.83203	−0.916014	+	0.401145i	$0.868612\pi$
$450$	−5.06531	−0.238781
$451$	6.74543	0.317630
$452$	−9.37509	−0.440967
$453$	−6.44348	−0.302741
$454$	6.01614	0.282352
$455$	−30.3502	−1.42284
$456$	−4.21524	−0.197397
$457$	10.3618	0.484703	0.242352	−	0.970188i	$-0.422081\pi$
$457$	10.3618	0.484703	0.242352	+	0.970188i	$0.422081\pi$
$458$	−1.24858	−0.0583425
$459$	−1.00000	−0.0466760
$460$	5.60873	0.261509
$461$	25.0884	1.16849	0.584243	−	0.811579i	$-0.301392\pi$
$461$	25.0884	1.16849	0.584243	+	0.811579i	$0.301392\pi$
$462$	3.21462	0.149558
$463$	−16.3874	−0.761586	−0.380793	−	0.924660i	$-0.624349\pi$
$463$	−16.3874	−0.761586	−0.380793	+	0.924660i	$0.624349\pi$
$464$	−2.67126	−0.124010
$465$	−8.71223	−0.404020
$466$	−21.9229	−1.01556
$467$	−7.35003	−0.340119	−0.170059	−	0.985434i	$-0.554396\pi$
$467$	−7.35003	−0.340119	−0.170059	+	0.985434i	$0.554396\pi$
$468$	2.07427	0.0958831
$469$	45.9611	2.12228
$470$	−12.9870	−0.599046
$471$	0.400382	0.0184486
$472$	−1.00000	−0.0460287
$473$	0.154293	0.00709439
$474$	3.39812	0.156081
$475$	−21.3515	−0.979673
$476$	−4.61193	−0.211388
$477$	−4.12004	−0.188644
$478$	−9.73172	−0.445119
$479$	22.9794	1.04996	0.524978	−	0.851116i	$-0.324074\pi$
$479$	22.9794	1.04996	0.524978	+	0.851116i	$0.324074\pi$
$480$	3.17259	0.144808
$481$	14.4956	0.660941
$482$	−6.50044	−0.296087
$483$	8.15331	0.370989
$484$	−10.5142	−0.477916
$485$	22.8556	1.03782
$486$	1.00000	0.0453609
$487$	34.8341	1.57849	0.789243	−	0.614081i	$-0.210473\pi$
$487$	34.8341	1.57849	0.789243	+	0.614081i	$0.210473\pi$
$488$	−3.42864	−0.155207
$489$	9.23737	0.417728
$490$	−45.2725	−2.04520
$491$	0.710144	0.0320484	0.0160242	−	0.999872i	$-0.494899\pi$
$491$	0.710144	0.0320484	0.0160242	+	0.999872i	$0.494899\pi$
$492$	9.67750	0.436295
$493$	−2.67126	−0.120308
$494$	8.74354	0.393390
$495$	−2.21136	−0.0993934
$496$	2.74610	0.123303
$497$	−17.4480	−0.782652
$498$	3.65024	0.163571
$499$	−28.5446	−1.27783	−0.638917	−	0.769276i	$-0.720617\pi$
$499$	−28.5446	−1.27783	−0.638917	+	0.769276i	$0.720617\pi$
$500$	0.207194	0.00926600
$501$	8.75120	0.390975
$502$	13.6593	0.609643
$503$	−35.2382	−1.57119	−0.785596	−	0.618739i	$-0.787644\pi$
$503$	−35.2382	−1.57119	−0.785596	+	0.618739i	$0.787644\pi$
$504$	4.61193	0.205432
$505$	28.3697	1.26243
$506$	1.23225	0.0547801
$507$	8.69741	0.386265
$508$	−7.25265	−0.321784
$509$	23.1864	1.02772	0.513859	−	0.857875i	$-0.328216\pi$
$509$	23.1864	1.02772	0.513859	+	0.857875i	$0.328216\pi$
$510$	3.17259	0.140485
$511$	9.35929	0.414031
$512$	−1.00000	−0.0441942
$513$	4.21524	0.186107
$514$	−1.73754	−0.0766398
$515$	−28.4864	−1.25526
$516$	0.221360	0.00974482
$517$	−2.85327	−0.125487
$518$	32.2294	1.41608
$519$	12.9483	0.568366
$520$	−6.58080	−0.288587
$521$	34.3890	1.50661	0.753306	−	0.657671i	$-0.228458\pi$
$521$	34.3890	1.50661	0.753306	+	0.657671i	$0.228458\pi$
$522$	2.67126	0.116918
$523$	−38.5019	−1.68357	−0.841785	−	0.539812i	$-0.818495\pi$
$523$	−38.5019	−1.68357	−0.841785	+	0.539812i	$0.818495\pi$
$524$	−5.99034	−0.261689
$525$	23.3608	1.01955
$526$	17.7588	0.774321
$527$	2.74610	0.119622
$528$	0.697022	0.0303340
$529$	−19.8746	−0.864114
$530$	13.0712	0.567776
$531$	1.00000	0.0433963
$532$	19.4404	0.842847
$533$	−20.0737	−0.869490
$534$	−3.75248	−0.162386
$535$	−27.5423	−1.19076
$536$	9.96569	0.430452
$537$	−19.2985	−0.832793
$538$	−26.5153	−1.14316
$539$	−9.94644	−0.428424
$540$	−3.17259	−0.136526
$541$	0.983049	0.0422646	0.0211323	−	0.999777i	$-0.493273\pi$
$541$	0.983049	0.0422646	0.0211323	+	0.999777i	$0.493273\pi$
$542$	16.3215	0.701067
$543$	−13.1597	−0.564737
$544$	−1.00000	−0.0428746
$545$	33.2509	1.42431
$546$	−9.56639	−0.409404
$547$	−20.4155	−0.872905	−0.436452	−	0.899727i	$-0.643765\pi$
$547$	−20.4155	−0.872905	−0.436452	+	0.899727i	$0.643765\pi$
$548$	−22.2170	−0.949064
$549$	3.42864	0.146331
$550$	3.53063	0.150547
$551$	11.2600	0.479692
$552$	1.76787	0.0752457
$553$	−15.6719	−0.666437
$554$	−15.7904	−0.670869
$555$	−22.1709	−0.941102
$556$	−12.3095	−0.522037
$557$	−37.6392	−1.59482	−0.797411	−	0.603437i	$-0.793798\pi$
$557$	−37.6392	−1.59482	−0.797411	+	0.603437i	$0.793798\pi$
$558$	−2.74610	−0.116252
$559$	−0.459160	−0.0194204
$560$	−14.6318	−0.618304
$561$	0.697022	0.0294283
$562$	−16.3853	−0.691173
$563$	−15.8961	−0.669940	−0.334970	−	0.942229i	$-0.608726\pi$
$563$	−15.8961	−0.669940	−0.334970	+	0.942229i	$0.608726\pi$
$564$	−4.09351	−0.172368
$565$	−29.7433	−1.25131
$566$	25.1596	1.05754
$567$	−4.61193	−0.193683
$568$	−3.78324	−0.158741
$569$	−35.8197	−1.50164	−0.750819	−	0.660508i	$-0.770341\pi$
$569$	−35.8197	−1.50164	−0.750819	+	0.660508i	$0.770341\pi$
$570$	−13.3732	−0.560142
$571$	−23.6635	−0.990285	−0.495142	−	0.868812i	$-0.664884\pi$
$571$	−23.6635	−0.990285	−0.495142	+	0.868812i	$0.664884\pi$
$572$	−1.44581	−0.0604524
$573$	−11.0165	−0.460219
$574$	−44.6320	−1.86290
$575$	8.95482	0.373442
$576$	1.00000	0.0416667
$577$	−19.3111	−0.803933	−0.401967	−	0.915654i	$-0.631673\pi$
$577$	−19.3111	−0.803933	−0.401967	+	0.915654i	$0.631673\pi$
$578$	−1.00000	−0.0415945
$579$	6.89410	0.286509
$580$	−8.47481	−0.351898
$581$	−16.8347	−0.698419
$582$	7.20410	0.298619
$583$	2.87176	0.118936
$584$	2.02937	0.0839757
$585$	6.58080	0.272083
$586$	3.59198	0.148383
$587$	41.4115	1.70924	0.854618	−	0.519257i	$-0.173791\pi$
$587$	41.4115	1.70924	0.854618	+	0.519257i	$0.173791\pi$
$588$	−14.2699	−0.588481
$589$	−11.5754	−0.476958
$590$	−3.17259	−0.130613
$591$	−12.1568	−0.500063
$592$	6.98827	0.287216
$593$	−3.54104	−0.145413	−0.0727066	−	0.997353i	$-0.523164\pi$
$593$	−3.54104	−0.145413	−0.0727066	+	0.997353i	$0.523164\pi$
$594$	−0.697022	−0.0285992
$595$	−14.6318	−0.599843
$596$	−3.07162	−0.125818
$597$	13.8801	0.568074
$598$	−3.66705	−0.149957
$599$	4.35724	0.178032	0.0890160	−	0.996030i	$-0.471628\pi$
$599$	4.35724	0.178032	0.0890160	+	0.996030i	$0.471628\pi$
$600$	5.06531	0.206790
$601$	−11.2613	−0.459357	−0.229679	−	0.973267i	$-0.573768\pi$
$601$	−11.2613	−0.459357	−0.229679	+	0.973267i	$0.573768\pi$
$602$	−1.02090	−0.0416086
$603$	−9.96569	−0.405834
$604$	6.44348	0.262181
$605$	−33.3571	−1.35616
$606$	8.94213	0.363249
$607$	−7.70508	−0.312739	−0.156370	−	0.987699i	$-0.549979\pi$
$607$	−7.70508	−0.312739	−0.156370	+	0.987699i	$0.549979\pi$
$608$	4.21524	0.170950
$609$	−12.3197	−0.499219
$610$	−10.8777	−0.440423
$611$	8.49104	0.343511
$612$	1.00000	0.0404226
$613$	20.2947	0.819693	0.409847	−	0.912154i	$-0.365582\pi$
$613$	20.2947	0.819693	0.409847	+	0.912154i	$0.365582\pi$
$614$	14.9408	0.602962
$615$	30.7027	1.23805
$616$	−3.21462	−0.129521
$617$	−1.39455	−0.0561423	−0.0280712	−	0.999606i	$-0.508937\pi$
$617$	−1.39455	−0.0561423	−0.0280712	+	0.999606i	$0.508937\pi$
$618$	−8.97892	−0.361185
$619$	0.865295	0.0347791	0.0173896	−	0.999849i	$-0.494464\pi$
$619$	0.865295	0.0347791	0.0173896	+	0.999849i	$0.494464\pi$
$620$	8.71223	0.349892
$621$	−1.76787	−0.0709423
$622$	5.41262	0.217026
$623$	17.3062	0.693358
$624$	−2.07427	−0.0830372
$625$	−24.6692	−0.986768
$626$	8.10497	0.323940
$627$	−2.93811	−0.117337
$628$	−0.400382	−0.0159770
$629$	6.98827	0.278641
$630$	14.6318	0.582943
$631$	−9.63053	−0.383385	−0.191693	−	0.981455i	$-0.561398\pi$
$631$	−9.63053	−0.383385	−0.191693	+	0.981455i	$0.561398\pi$
$632$	−3.39812	−0.135170
$633$	13.4608	0.535020
$634$	14.6654	0.582439
$635$	−23.0097	−0.913110
$636$	4.12004	0.163370
$637$	29.5996	1.17278
$638$	−1.86193	−0.0737145
$639$	3.78324	0.149663
$640$	−3.17259	−0.125408
$641$	42.6368	1.68405	0.842026	−	0.539436i	$-0.181363\pi$
$641$	42.6368	1.68405	0.842026	+	0.539436i	$0.181363\pi$
$642$	−8.68135	−0.342625
$643$	28.6274	1.12895	0.564477	−	0.825449i	$-0.309078\pi$
$643$	28.6274	1.12895	0.564477	+	0.825449i	$0.309078\pi$
$644$	−8.15331	−0.321285
$645$	0.702283	0.0276524
$646$	4.21524	0.165846
$647$	0.899317	0.0353558	0.0176779	−	0.999844i	$-0.494373\pi$
$647$	0.899317	0.0353558	0.0176779	+	0.999844i	$0.494373\pi$
$648$	−1.00000	−0.0392837
$649$	−0.697022	−0.0273605
$650$	−10.5068	−0.412111
$651$	12.6648	0.496373
$652$	−9.23737	−0.361763
$653$	−33.1462	−1.29711	−0.648555	−	0.761168i	$-0.724626\pi$
$653$	−33.1462	−1.29711	−0.648555	+	0.761168i	$0.724626\pi$
$654$	10.4807	0.409827
$655$	−19.0049	−0.742582
$656$	−9.67750	−0.377843
$657$	−2.02937	−0.0791731
$658$	18.8790	0.735979
$659$	11.6363	0.453285	0.226643	−	0.973978i	$-0.427225\pi$
$659$	11.6363	0.453285	0.226643	+	0.973978i	$0.427225\pi$
$660$	2.21136	0.0860772
$661$	−13.3896	−0.520795	−0.260397	−	0.965502i	$-0.583854\pi$
$661$	−13.3896	−0.520795	−0.260397	+	0.965502i	$0.583854\pi$
$662$	−1.61826	−0.0628955
$663$	−2.07427	−0.0805580
$664$	−3.65024	−0.141657
$665$	61.6763	2.39170
$666$	−6.98827	−0.270790
$667$	−4.72246	−0.182854
$668$	−8.75120	−0.338594
$669$	3.13791	0.121319
$670$	31.6170	1.22147
$671$	−2.38984	−0.0922587
$672$	−4.61193	−0.177909
$673$	−12.5689	−0.484495	−0.242247	−	0.970215i	$-0.577885\pi$
$673$	−12.5689	−0.484495	−0.242247	+	0.970215i	$0.577885\pi$
$674$	12.7459	0.490955
$675$	−5.06531	−0.194964
$676$	−8.69741	−0.334516
$677$	−7.29573	−0.280398	−0.140199	−	0.990123i	$-0.544774\pi$
$677$	−7.29573	−0.280398	−0.140199	+	0.990123i	$0.544774\pi$
$678$	−9.37509	−0.360048
$679$	−33.2248	−1.27505
$680$	−3.17259	−0.121663
$681$	6.01614	0.230539
$682$	1.91409	0.0732943
$683$	−50.3284	−1.92576	−0.962881	−	0.269926i	$-0.913001\pi$
$683$	−50.3284	−1.92576	−0.962881	+	0.269926i	$0.913001\pi$
$684$	−4.21524	−0.161174
$685$	−70.4854	−2.69311
$686$	33.5283	1.28012
$687$	−1.24858	−0.0476365
$688$	−0.221360	−0.00843926
$689$	−8.54607	−0.325579
$690$	5.60873	0.213521
$691$	−31.9426	−1.21515	−0.607577	−	0.794261i	$-0.707858\pi$
$691$	−31.9426	−1.21515	−0.607577	+	0.794261i	$0.707858\pi$
$692$	−12.9483	−0.492220
$693$	3.21462	0.122113
$694$	−0.819977	−0.0311259
$695$	−39.0528	−1.48136
$696$	−2.67126	−0.101254
$697$	−9.67750	−0.366561
$698$	18.8438	0.713249
$699$	−21.9229	−0.829199
$700$	−23.3608	−0.882957
$701$	−30.5685	−1.15456	−0.577279	−	0.816547i	$-0.695885\pi$
$701$	−30.5685	−1.15456	−0.577279	+	0.816547i	$0.695885\pi$
$702$	2.07427	0.0782883
$703$	−29.4572	−1.11100
$704$	−0.697022	−0.0262700
$705$	−12.9870	−0.489119
$706$	10.8447	0.408146
$707$	−41.2405	−1.55101
$708$	−1.00000	−0.0375823
$709$	−2.79645	−0.105023	−0.0525115	−	0.998620i	$-0.516723\pi$
$709$	−2.79645	−0.105023	−0.0525115	+	0.998620i	$0.516723\pi$
$710$	−12.0027	−0.450452
$711$	3.39812	0.127439
$712$	3.75248	0.140630
$713$	4.85475	0.181812
$714$	−4.61193	−0.172597
$715$	−4.58696	−0.171543
$716$	19.2985	0.721219
$717$	−9.73172	−0.363438
$718$	−3.73184	−0.139271
$719$	24.6666	0.919909	0.459955	−	0.887942i	$-0.347866\pi$
$719$	24.6666	0.919909	0.459955	+	0.887942i	$0.347866\pi$
$720$	3.17259	0.118235
$721$	41.4102	1.54220
$722$	1.23178	0.0458422
$723$	−6.50044	−0.241754
$724$	13.1597	0.489076
$725$	−13.5308	−0.502520
$726$	−10.5142	−0.390217
$727$	15.8720	0.588659	0.294329	−	0.955704i	$-0.404904\pi$
$727$	15.8720	0.588659	0.294329	+	0.955704i	$0.404904\pi$
$728$	9.56639	0.354554
$729$	1.00000	0.0370370
$730$	6.43834	0.238294
$731$	−0.221360	−0.00818729
$732$	−3.42864	−0.126726
$733$	−6.99751	−0.258459	−0.129229	−	0.991615i	$-0.541250\pi$
$733$	−6.99751	−0.258459	−0.129229	+	0.991615i	$0.541250\pi$
$734$	0.914900	0.0337696
$735$	−45.2725	−1.66990
$736$	−1.76787	−0.0651647
$737$	6.94631	0.255870
$738$	9.67750	0.356234
$739$	3.19806	0.117642	0.0588212	−	0.998269i	$-0.481266\pi$
$739$	3.19806	0.117642	0.0588212	+	0.998269i	$0.481266\pi$
$740$	22.1709	0.815018
$741$	8.74354	0.321202
$742$	−19.0013	−0.697561
$743$	−42.9011	−1.57389	−0.786944	−	0.617024i	$-0.788338\pi$
$743$	−42.9011	−1.57389	−0.786944	+	0.617024i	$0.788338\pi$
$744$	2.74610	0.100677
$745$	−9.74498	−0.357028
$746$	14.2855	0.523030
$747$	3.65024	0.133555
$748$	−0.697022	−0.0254857
$749$	40.0378	1.46295
$750$	0.207194	0.00756566
$751$	15.8096	0.576901	0.288450	−	0.957495i	$-0.406860\pi$
$751$	15.8096	0.576901	0.288450	+	0.957495i	$0.406860\pi$
$752$	4.09351	0.149275
$753$	13.6593	0.497771
$754$	5.54092	0.201788
$755$	20.4425	0.743978
$756$	4.61193	0.167734
$757$	−18.8560	−0.685334	−0.342667	−	0.939457i	$-0.611330\pi$
$757$	−18.8560	−0.685334	−0.342667	+	0.939457i	$0.611330\pi$
$758$	−11.3516	−0.412310
$759$	1.23225	0.0447277
$760$	13.3732	0.485097
$761$	−12.3501	−0.447693	−0.223846	−	0.974624i	$-0.571861\pi$
$761$	−12.3501	−0.447693	−0.223846	+	0.974624i	$0.571861\pi$
$762$	−7.25265	−0.262736
$763$	−48.3362	−1.74989
$764$	11.0165	0.398562
$765$	3.17259	0.114705
$766$	−10.2583	−0.370646
$767$	2.07427	0.0748975
$768$	−1.00000	−0.0360844
$769$	−4.72877	−0.170524	−0.0852619	−	0.996359i	$-0.527173\pi$
$769$	−4.72877	−0.170524	−0.0852619	+	0.996359i	$0.527173\pi$
$770$	−10.1987	−0.367534
$771$	−1.73754	−0.0625761
$772$	−6.89410	−0.248124
$773$	−22.2320	−0.799629	−0.399814	−	0.916596i	$-0.630925\pi$
$773$	−22.2320	−0.799629	−0.399814	+	0.916596i	$0.630925\pi$
$774$	0.221360	0.00795661
$775$	13.9098	0.499656
$776$	−7.20410	−0.258612
$777$	32.2294	1.15622
$778$	19.8997	0.713439
$779$	40.7929	1.46156
$780$	−6.58080	−0.235630
$781$	−2.63700	−0.0943594
$782$	−1.76787	−0.0632190
$783$	2.67126	0.0954632
$784$	14.2699	0.509640
$785$	−1.27025	−0.0453371
$786$	−5.99034	−0.213668
$787$	−40.2536	−1.43489	−0.717443	−	0.696617i	$-0.754688\pi$
$787$	−40.2536	−1.43489	−0.717443	+	0.696617i	$0.754688\pi$
$788$	12.1568	0.433067
$789$	17.7588	0.632231
$790$	−10.7808	−0.383565
$791$	43.2373	1.53734
$792$	0.697022	0.0247676
$793$	7.11192	0.252552
$794$	−4.31177	−0.153019
$795$	13.0712	0.463587
$796$	−13.8801	−0.491967
$797$	24.9899	0.885189	0.442594	−	0.896722i	$-0.354058\pi$
$797$	24.9899	0.885189	0.442594	+	0.896722i	$0.354058\pi$
$798$	19.4404	0.688182
$799$	4.09351	0.144818
$800$	−5.06531	−0.179086
$801$	−3.75248	−0.132587
$802$	−9.70256	−0.342609
$803$	1.41451	0.0499171
$804$	9.96569	0.351463
$805$	−25.8671	−0.911695
$806$	−5.69614	−0.200638
$807$	−26.5153	−0.933384
$808$	−8.94213	−0.314583
$809$	−30.3671	−1.06765	−0.533825	−	0.845595i	$-0.679246\pi$
$809$	−30.3671	−1.06765	−0.533825	+	0.845595i	$0.679246\pi$
$810$	−3.17259	−0.111473
$811$	−20.6401	−0.724770	−0.362385	−	0.932028i	$-0.618038\pi$
$811$	−20.6401	−0.724770	−0.362385	+	0.932028i	$0.618038\pi$
$812$	12.3197	0.432336
$813$	16.3215	0.572418
$814$	4.87098	0.170728
$815$	−29.3064	−1.02656
$816$	−1.00000	−0.0350070
$817$	0.933084	0.0326445
$818$	13.8045	0.482661
$819$	−9.56639	−0.334277
$820$	−30.7027	−1.07218
$821$	−31.8233	−1.11064	−0.555320	−	0.831637i	$-0.687404\pi$
$821$	−31.8233	−1.11064	−0.555320	+	0.831637i	$0.687404\pi$
$822$	−22.2170	−0.774907
$823$	47.8948	1.66951	0.834755	−	0.550622i	$-0.185609\pi$
$823$	47.8948	1.66951	0.834755	+	0.550622i	$0.185609\pi$
$824$	8.97892	0.312796
$825$	3.53063	0.122921
$826$	4.61193	0.160470
$827$	29.6401	1.03069	0.515344	−	0.856983i	$-0.327664\pi$
$827$	29.6401	1.03069	0.515344	+	0.856983i	$0.327664\pi$
$828$	1.76787	0.0614379
$829$	−1.60209	−0.0556429	−0.0278214	−	0.999613i	$-0.508857\pi$
$829$	−1.60209	−0.0556429	−0.0278214	+	0.999613i	$0.508857\pi$
$830$	−11.5807	−0.401972
$831$	−15.7904	−0.547762
$832$	2.07427	0.0719124
$833$	14.2699	0.494423
$834$	−12.3095	−0.426242
$835$	−27.7639	−0.960810
$836$	2.93811	0.101617
$837$	−2.74610	−0.0949190
$838$	15.1389	0.522966
$839$	9.79637	0.338208	0.169104	−	0.985598i	$-0.445913\pi$
$839$	9.79637	0.338208	0.169104	+	0.985598i	$0.445913\pi$
$840$	−14.6318	−0.504843
$841$	−21.8644	−0.753943
$842$	21.7817	0.750649
$843$	−16.3853	−0.564340
$844$	−13.4608	−0.463341
$845$	−27.5933	−0.949237
$846$	−4.09351	−0.140738
$847$	48.4906	1.66616
$848$	−4.12004	−0.141483
$849$	25.1596	0.863475
$850$	−5.06531	−0.173739
$851$	12.3544	0.423503
$852$	−3.78324	−0.129612
$853$	−10.0556	−0.344298	−0.172149	−	0.985071i	$-0.555071\pi$
$853$	−10.0556	−0.344298	−0.172149	+	0.985071i	$0.555071\pi$
$854$	15.8126	0.541098
$855$	−13.3732	−0.457354
$856$	8.68135	0.296722
$857$	31.6627	1.08158	0.540788	−	0.841159i	$-0.318126\pi$
$857$	31.6627	1.08158	0.540788	+	0.841159i	$0.318126\pi$
$858$	−1.44581	−0.0493592
$859$	−8.09553	−0.276216	−0.138108	−	0.990417i	$-0.544102\pi$
$859$	−8.09553	−0.276216	−0.138108	+	0.990417i	$0.544102\pi$
$860$	−0.702283	−0.0239477
$861$	−44.6320	−1.52105
$862$	−7.49178	−0.255171
$863$	−41.2490	−1.40413	−0.702065	−	0.712112i	$-0.747739\pi$
$863$	−41.2490	−1.40413	−0.702065	+	0.712112i	$0.747739\pi$
$864$	1.00000	0.0340207
$865$	−41.0795	−1.39675
$866$	5.68976	0.193346
$867$	−1.00000	−0.0339618
$868$	−12.6648	−0.429872
$869$	−2.36856	−0.0803481
$870$	−8.47481	−0.287323
$871$	−20.6715	−0.700428
$872$	−10.4807	−0.354921
$873$	7.20410	0.243822
$874$	7.45201	0.252068
$875$	−0.955565	−0.0323040
$876$	2.02937	0.0685659
$877$	−54.3282	−1.83453	−0.917266	−	0.398275i	$-0.869609\pi$
$877$	−54.3282	−1.83453	−0.917266	+	0.398275i	$0.869609\pi$
$878$	−3.65697	−0.123417
$879$	3.59198	0.121154
$880$	−2.21136	−0.0745450
$881$	52.4513	1.76713	0.883565	−	0.468309i	$-0.155136\pi$
$881$	52.4513	1.76713	0.883565	+	0.468309i	$0.155136\pi$
$882$	−14.2699	−0.480493
$883$	50.8930	1.71269	0.856343	−	0.516408i	$-0.172731\pi$
$883$	50.8930	1.71269	0.856343	+	0.516408i	$0.172731\pi$
$884$	2.07427	0.0697652
$885$	−3.17259	−0.106645
$886$	15.3617	0.516085
$887$	28.0490	0.941792	0.470896	−	0.882189i	$-0.343931\pi$
$887$	28.0490	0.941792	0.470896	+	0.882189i	$0.343931\pi$
$888$	6.98827	0.234511
$889$	33.4487	1.12183
$890$	11.9051	0.399059
$891$	−0.697022	−0.0233511
$892$	−3.13791	−0.105065
$893$	−17.2551	−0.577420
$894$	−3.07162	−0.102730
$895$	61.2262	2.04657
$896$	4.61193	0.154074
$897$	−3.66705	−0.122439
$898$	38.8200	1.29544
$899$	−7.33555	−0.244654
$900$	5.06531	0.168844
$901$	−4.12004	−0.137258
$902$	−6.74543	−0.224598
$903$	−1.02090	−0.0339733
$904$	9.37509	0.311811
$905$	41.7503	1.38783
$906$	6.44348	0.214070
$907$	10.6337	0.353088	0.176544	−	0.984293i	$-0.443508\pi$
$907$	10.6337	0.353088	0.176544	+	0.984293i	$0.443508\pi$
$908$	−6.01614	−0.199653
$909$	8.94213	0.296592
$910$	30.3502	1.00610
$911$	14.5627	0.482484	0.241242	−	0.970465i	$-0.422445\pi$
$911$	14.5627	0.482484	0.241242	+	0.970465i	$0.422445\pi$
$912$	4.21524	0.139580
$913$	−2.54430	−0.0842040
$914$	−10.3618	−0.342737
$915$	−10.8777	−0.359604
$916$	1.24858	0.0412544
$917$	27.6270	0.912325
$918$	1.00000	0.0330049
$919$	23.8556	0.786922	0.393461	−	0.919341i	$-0.371278\pi$
$919$	23.8556	0.786922	0.393461	+	0.919341i	$0.371278\pi$
$920$	−5.60873	−0.184914
$921$	14.9408	0.492316
$922$	−25.0884	−0.826244
$923$	7.84746	0.258302
$924$	−3.21462	−0.105753
$925$	35.3977	1.16387
$926$	16.3874	0.538523
$927$	−8.97892	−0.294907
$928$	2.67126	0.0876885
$929$	37.4867	1.22990	0.614950	−	0.788566i	$-0.289176\pi$
$929$	37.4867	1.22990	0.614950	+	0.788566i	$0.289176\pi$
$930$	8.71223	0.285685
$931$	−60.1510	−1.97137
$932$	21.9229	0.718107
$933$	5.41262	0.177201
$934$	7.35003	0.240500
$935$	−2.21136	−0.0723193
$936$	−2.07427	−0.0677996
$937$	15.1401	0.494604	0.247302	−	0.968938i	$-0.420456\pi$
$937$	15.1401	0.494604	0.247302	+	0.968938i	$0.420456\pi$
$938$	−45.9611	−1.50068
$939$	8.10497	0.264496
$940$	12.9870	0.423590
$941$	27.2813	0.889343	0.444672	−	0.895694i	$-0.353320\pi$
$941$	27.2813	0.889343	0.444672	+	0.895694i	$0.353320\pi$
$942$	−0.400382	−0.0130452
$943$	−17.1086	−0.557132
$944$	1.00000	0.0325472
$945$	14.6318	0.475971
$946$	−0.154293	−0.00501649
$947$	−14.1345	−0.459309	−0.229655	−	0.973272i	$-0.573760\pi$
$947$	−14.1345	−0.459309	−0.229655	+	0.973272i	$0.573760\pi$
$948$	−3.39812	−0.110366
$949$	−4.20945	−0.136645
$950$	21.3515	0.692733
$951$	14.6654	0.475559
$952$	4.61193	0.149474
$953$	−7.50195	−0.243012	−0.121506	−	0.992591i	$-0.538772\pi$
$953$	−7.50195	−0.243012	−0.121506	+	0.992591i	$0.538772\pi$
$954$	4.12004	0.133391
$955$	34.9507	1.13098
$956$	9.73172	0.314746
$957$	−1.86193	−0.0601876
$958$	−22.9794	−0.742431
$959$	102.463	3.30871
$960$	−3.17259	−0.102395
$961$	−23.4590	−0.756740
$962$	−14.4956	−0.467356
$963$	−8.68135	−0.279752
$964$	6.50044	0.209365
$965$	−21.8721	−0.704089
$966$	−8.15331	−0.262329
$967$	−27.1182	−0.872061	−0.436031	−	0.899932i	$-0.643616\pi$
$967$	−27.1182	−0.872061	−0.436031	+	0.899932i	$0.643616\pi$
$968$	10.5142	0.337938
$969$	4.21524	0.135413
$970$	−22.8556	−0.733850
$971$	−35.2458	−1.13109	−0.565546	−	0.824717i	$-0.691335\pi$
$971$	−35.2458	−1.13109	−0.565546	+	0.824717i	$0.691335\pi$
$972$	−1.00000	−0.0320750
$973$	56.7704	1.81997
$974$	−34.8341	−1.11616
$975$	−10.5068	−0.336487
$976$	3.42864	0.109748
$977$	27.3569	0.875226	0.437613	−	0.899163i	$-0.355824\pi$
$977$	27.3569	0.875226	0.437613	+	0.899163i	$0.355824\pi$
$978$	−9.23737	−0.295378
$979$	2.61556	0.0835938
$980$	45.2725	1.44618
$981$	10.4807	0.334622
$982$	−0.710144	−0.0226616
$983$	−1.53138	−0.0488436	−0.0244218	−	0.999702i	$-0.507774\pi$
$983$	−1.53138	−0.0488436	−0.0244218	+	0.999702i	$0.507774\pi$
$984$	−9.67750	−0.308507
$985$	38.5684	1.22889
$986$	2.67126	0.0850704
$987$	18.8790	0.600925
$988$	−8.74354	−0.278169
$989$	−0.391336	−0.0124438
$990$	2.21136	0.0702817
$991$	48.2633	1.53313	0.766567	−	0.642164i	$-0.221963\pi$
$991$	48.2633	1.53313	0.766567	+	0.642164i	$0.221963\pi$
$992$	−2.74610	−0.0871887
$993$	−1.61826	−0.0513539
$994$	17.4480	0.553418
$995$	−44.0358	−1.39603
$996$	−3.65024	−0.115662
$997$	−33.1059	−1.04847	−0.524237	−	0.851572i	$-0.675649\pi$
$997$	−33.1059	−1.04847	−0.524237	+	0.851572i	$0.675649\pi$
$998$	28.5446	0.903565
$999$	−6.98827	−0.221099

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.u.1.8	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.u.1.8	✓	9	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6018.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.17259 q^{5} +1.00000 q^{6} -4.61193 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.17259 q^{5} +1.00000 q^{6} -4.61193 q^{7} -1.00000 q^{8} +1.00000 q^{9} -3.17259 q^{10} -0.697022 q^{11} -1.00000 q^{12} +2.07427 q^{13} +4.61193 q^{14} -3.17259 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} -4.21524 q^{19} +3.17259 q^{20} +4.61193 q^{21} +0.697022 q^{22} +1.76787 q^{23} +1.00000 q^{24} +5.06531 q^{25} -2.07427 q^{26} -1.00000 q^{27} -4.61193 q^{28} -2.67126 q^{29} +3.17259 q^{30} +2.74610 q^{31} -1.00000 q^{32} +0.697022 q^{33} -1.00000 q^{34} -14.6318 q^{35} +1.00000 q^{36} +6.98827 q^{37} +4.21524 q^{38} -2.07427 q^{39} -3.17259 q^{40} -9.67750 q^{41} -4.61193 q^{42} -0.221360 q^{43} -0.697022 q^{44} +3.17259 q^{45} -1.76787 q^{46} +4.09351 q^{47} -1.00000 q^{48} +14.2699 q^{49} -5.06531 q^{50} -1.00000 q^{51} +2.07427 q^{52} -4.12004 q^{53} +1.00000 q^{54} -2.21136 q^{55} +4.61193 q^{56} +4.21524 q^{57} +2.67126 q^{58} +1.00000 q^{59} -3.17259 q^{60} +3.42864 q^{61} -2.74610 q^{62} -4.61193 q^{63} +1.00000 q^{64} +6.58080 q^{65} -0.697022 q^{66} -9.96569 q^{67} +1.00000 q^{68} -1.76787 q^{69} +14.6318 q^{70} +3.78324 q^{71} -1.00000 q^{72} -2.02937 q^{73} -6.98827 q^{74} -5.06531 q^{75} -4.21524 q^{76} +3.21462 q^{77} +2.07427 q^{78} +3.39812 q^{79} +3.17259 q^{80} +1.00000 q^{81} +9.67750 q^{82} +3.65024 q^{83} +4.61193 q^{84} +3.17259 q^{85} +0.221360 q^{86} +2.67126 q^{87} +0.697022 q^{88} -3.75248 q^{89} -3.17259 q^{90} -9.56639 q^{91} +1.76787 q^{92} -2.74610 q^{93} -4.09351 q^{94} -13.3732 q^{95} +1.00000 q^{96} +7.20410 q^{97} -14.2699 q^{98} -0.697022 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 9 q^{2} - 9 q^{3} + 9 q^{4} + 2 q^{5} + 9 q^{6} - 5 q^{7} - 9 q^{8} + 9 q^{9}+O(q^{10}) \) 9 * q - 9 * q^2 - 9 * q^3 + 9 * q^4 + 2 * q^5 + 9 * q^6 - 5 * q^7 - 9 * q^8 + 9 * q^9	\( 9 q - 9 q^{2} - 9 q^{3} + 9 q^{4} + 2 q^{5} + 9 q^{6} - 5 q^{7} - 9 q^{8} + 9 q^{9} - 2 q^{10} - q^{11} - 9 q^{12} - 4 q^{13} + 5 q^{14} - 2 q^{15} + 9 q^{16} + 9 q^{17} - 9 q^{18} - 7 q^{19} + 2 q^{20} + 5 q^{21} + q^{22} - 8 q^{23} + 9 q^{24} + 5 q^{25} + 4 q^{26} - 9 q^{27} - 5 q^{28} + 6 q^{29} + 2 q^{30} - 17 q^{31} - 9 q^{32} + q^{33} - 9 q^{34} + 10 q^{35} + 9 q^{36} + 2 q^{37} + 7 q^{38} + 4 q^{39} - 2 q^{40} + 14 q^{41} - 5 q^{42} - 27 q^{43} - q^{44} + 2 q^{45} + 8 q^{46} - 18 q^{47} - 9 q^{48} + 18 q^{49} - 5 q^{50} - 9 q^{51} - 4 q^{52} + 4 q^{53} + 9 q^{54} - 27 q^{55} + 5 q^{56} + 7 q^{57} - 6 q^{58} + 9 q^{59} - 2 q^{60} + 5 q^{61} + 17 q^{62} - 5 q^{63} + 9 q^{64} + 2 q^{65} - q^{66} - 22 q^{67} + 9 q^{68} + 8 q^{69} - 10 q^{70} + 16 q^{71} - 9 q^{72} - 12 q^{73} - 2 q^{74} - 5 q^{75} - 7 q^{76} + 6 q^{77} - 4 q^{78} - 9 q^{79} + 2 q^{80} + 9 q^{81} - 14 q^{82} + 10 q^{83} + 5 q^{84} + 2 q^{85} + 27 q^{86} - 6 q^{87} + q^{88} + 15 q^{89} - 2 q^{90} + 3 q^{91} - 8 q^{92} + 17 q^{93} + 18 q^{94} - 9 q^{95} + 9 q^{96} - 33 q^{97} - 18 q^{98} - q^{99}+O(q^{100}) \) 9 * q - 9 * q^2 - 9 * q^3 + 9 * q^4 + 2 * q^5 + 9 * q^6 - 5 * q^7 - 9 * q^8 + 9 * q^9 - 2 * q^10 - q^11 - 9 * q^12 - 4 * q^13 + 5 * q^14 - 2 * q^15 + 9 * q^16 + 9 * q^17 - 9 * q^18 - 7 * q^19 + 2 * q^20 + 5 * q^21 + q^22 - 8 * q^23 + 9 * q^24 + 5 * q^25 + 4 * q^26 - 9 * q^27 - 5 * q^28 + 6 * q^29 + 2 * q^30 - 17 * q^31 - 9 * q^32 + q^33 - 9 * q^34 + 10 * q^35 + 9 * q^36 + 2 * q^37 + 7 * q^38 + 4 * q^39 - 2 * q^40 + 14 * q^41 - 5 * q^42 - 27 * q^43 - q^44 + 2 * q^45 + 8 * q^46 - 18 * q^47 - 9 * q^48 + 18 * q^49 - 5 * q^50 - 9 * q^51 - 4 * q^52 + 4 * q^53 + 9 * q^54 - 27 * q^55 + 5 * q^56 + 7 * q^57 - 6 * q^58 + 9 * q^59 - 2 * q^60 + 5 * q^61 + 17 * q^62 - 5 * q^63 + 9 * q^64 + 2 * q^65 - q^66 - 22 * q^67 + 9 * q^68 + 8 * q^69 - 10 * q^70 + 16 * q^71 - 9 * q^72 - 12 * q^73 - 2 * q^74 - 5 * q^75 - 7 * q^76 + 6 * q^77 - 4 * q^78 - 9 * q^79 + 2 * q^80 + 9 * q^81 - 14 * q^82 + 10 * q^83 + 5 * q^84 + 2 * q^85 + 27 * q^86 - 6 * q^87 + q^88 + 15 * q^89 - 2 * q^90 + 3 * q^91 - 8 * q^92 + 17 * q^93 + 18 * q^94 - 9 * q^95 + 9 * q^96 - 33 * q^97 - 18 * q^98 - q^99

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