LMFDB - Embedded newform 6018.2.a.x.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:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} - 34x^{8} + 30x^{7} + 341x^{6} - 276x^{5} - 1032x^{4} + 1176x^{3} + 416x^{2} - 896x + 272 $ x^10 - x^9 - 34x^8 + 30x^7 + 341x^6 - 276x^5 - 1032x^4 + 1176x^3 + 416x^2 - 896x + 272
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$1.39621$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.39621 q^{5} +1.00000 q^{6} -1.23174 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.39621 q^{5} +1.00000 q^{6} -1.23174 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.39621 q^{10} +1.33294 q^{11} -1.00000 q^{12} +3.02185 q^{13} +1.23174 q^{14} -1.39621 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} +2.38520 q^{19} +1.39621 q^{20} +1.23174 q^{21} -1.33294 q^{22} +5.24380 q^{23} +1.00000 q^{24} -3.05059 q^{25} -3.02185 q^{26} -1.00000 q^{27} -1.23174 q^{28} +5.12161 q^{29} +1.39621 q^{30} +0.238960 q^{31} -1.00000 q^{32} -1.33294 q^{33} -1.00000 q^{34} -1.71978 q^{35} +1.00000 q^{36} +5.99937 q^{37} -2.38520 q^{38} -3.02185 q^{39} -1.39621 q^{40} +6.44784 q^{41} -1.23174 q^{42} +5.24123 q^{43} +1.33294 q^{44} +1.39621 q^{45} -5.24380 q^{46} -5.48284 q^{47} -1.00000 q^{48} -5.48281 q^{49} +3.05059 q^{50} -1.00000 q^{51} +3.02185 q^{52} -6.85752 q^{53} +1.00000 q^{54} +1.86107 q^{55} +1.23174 q^{56} -2.38520 q^{57} -5.12161 q^{58} -1.00000 q^{59} -1.39621 q^{60} -4.09141 q^{61} -0.238960 q^{62} -1.23174 q^{63} +1.00000 q^{64} +4.21915 q^{65} +1.33294 q^{66} +14.4176 q^{67} +1.00000 q^{68} -5.24380 q^{69} +1.71978 q^{70} +2.45847 q^{71} -1.00000 q^{72} -9.84343 q^{73} -5.99937 q^{74} +3.05059 q^{75} +2.38520 q^{76} -1.64184 q^{77} +3.02185 q^{78} +1.35868 q^{79} +1.39621 q^{80} +1.00000 q^{81} -6.44784 q^{82} +0.183267 q^{83} +1.23174 q^{84} +1.39621 q^{85} -5.24123 q^{86} -5.12161 q^{87} -1.33294 q^{88} -9.50534 q^{89} -1.39621 q^{90} -3.72215 q^{91} +5.24380 q^{92} -0.238960 q^{93} +5.48284 q^{94} +3.33024 q^{95} +1.00000 q^{96} +1.31659 q^{97} +5.48281 q^{98} +1.33294 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{2} - 10 q^{3} + 10 q^{4} + q^{5} + 10 q^{6} + 10 q^{7} - 10 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q - 10 * q^2 - 10 * q^3 + 10 * q^4 + q^5 + 10 * q^6 + 10 * q^7 - 10 * q^8 + 10 * q^9	\( 10 q - 10 q^{2} - 10 q^{3} + 10 q^{4} + q^{5} + 10 q^{6} + 10 q^{7} - 10 q^{8} + 10 q^{9} - q^{10} + 2 q^{11} - 10 q^{12} - 10 q^{14} - q^{15} + 10 q^{16} + 10 q^{17} - 10 q^{18} + 15 q^{19} + q^{20} - 10 q^{21} - 2 q^{22} + 19 q^{23} + 10 q^{24} + 19 q^{25} - 10 q^{27} + 10 q^{28} - q^{29} + q^{30} + 15 q^{31} - 10 q^{32} - 2 q^{33} - 10 q^{34} - 14 q^{35} + 10 q^{36} + q^{37} - 15 q^{38} - q^{40} - 5 q^{41} + 10 q^{42} + 26 q^{43} + 2 q^{44} + q^{45} - 19 q^{46} + 14 q^{47} - 10 q^{48} + 20 q^{49} - 19 q^{50} - 10 q^{51} - 2 q^{53} + 10 q^{54} + 4 q^{55} - 10 q^{56} - 15 q^{57} + q^{58} - 10 q^{59} - q^{60} + 4 q^{61} - 15 q^{62} + 10 q^{63} + 10 q^{64} - 20 q^{65} + 2 q^{66} + 15 q^{67} + 10 q^{68} - 19 q^{69} + 14 q^{70} + 14 q^{71} - 10 q^{72} + 43 q^{73} - q^{74} - 19 q^{75} + 15 q^{76} + 20 q^{77} + q^{80} + 10 q^{81} + 5 q^{82} - 4 q^{83} - 10 q^{84} + q^{85} - 26 q^{86} + q^{87} - 2 q^{88} - 22 q^{89} - q^{90} - q^{91} + 19 q^{92} - 15 q^{93} - 14 q^{94} - 37 q^{95} + 10 q^{96} + 37 q^{97} - 20 q^{98} + 2 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 - 10 * q^3 + 10 * q^4 + q^5 + 10 * q^6 + 10 * q^7 - 10 * q^8 + 10 * q^9 - q^10 + 2 * q^11 - 10 * q^12 - 10 * q^14 - q^15 + 10 * q^16 + 10 * q^17 - 10 * q^18 + 15 * q^19 + q^20 - 10 * q^21 - 2 * q^22 + 19 * q^23 + 10 * q^24 + 19 * q^25 - 10 * q^27 + 10 * q^28 - q^29 + q^30 + 15 * q^31 - 10 * q^32 - 2 * q^33 - 10 * q^34 - 14 * q^35 + 10 * q^36 + q^37 - 15 * q^38 - q^40 - 5 * q^41 + 10 * q^42 + 26 * q^43 + 2 * q^44 + q^45 - 19 * q^46 + 14 * q^47 - 10 * q^48 + 20 * q^49 - 19 * q^50 - 10 * q^51 - 2 * q^53 + 10 * q^54 + 4 * q^55 - 10 * q^56 - 15 * q^57 + q^58 - 10 * q^59 - q^60 + 4 * q^61 - 15 * q^62 + 10 * q^63 + 10 * q^64 - 20 * q^65 + 2 * q^66 + 15 * q^67 + 10 * q^68 - 19 * q^69 + 14 * q^70 + 14 * q^71 - 10 * q^72 + 43 * q^73 - q^74 - 19 * q^75 + 15 * q^76 + 20 * q^77 + q^80 + 10 * q^81 + 5 * q^82 - 4 * q^83 - 10 * q^84 + q^85 - 26 * q^86 + q^87 - 2 * q^88 - 22 * q^89 - q^90 - q^91 + 19 * q^92 - 15 * q^93 - 14 * q^94 - 37 * q^95 + 10 * q^96 + 37 * q^97 - 20 * q^98 + 2 * 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
$5$	1.39621	0.624406	0.312203	−	0.950015i	$-0.398933\pi$
$5$	1.39621	0.624406	0.312203	+	0.950015i	$0.398933\pi$
$6$	1.00000	0.408248
$7$	−1.23174	−0.465556	−0.232778	−	0.972530i	$-0.574781\pi$
$7$	−1.23174	−0.465556	−0.232778	+	0.972530i	$0.574781\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−1.39621	−0.441521
$11$	1.33294	0.401897	0.200948	−	0.979602i	$-0.435598\pi$
$11$	1.33294	0.401897	0.200948	+	0.979602i	$0.435598\pi$
$12$	−1.00000	−0.288675
$13$	3.02185	0.838111	0.419056	−	0.907961i	$-0.362361\pi$
$13$	3.02185	0.838111	0.419056	+	0.907961i	$0.362361\pi$
$14$	1.23174	0.329197
$15$	−1.39621	−0.360501
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.00000	−0.235702
$19$	2.38520	0.547201	0.273601	−	0.961843i	$-0.411785\pi$
$19$	2.38520	0.547201	0.273601	+	0.961843i	$0.411785\pi$
$20$	1.39621	0.312203
$21$	1.23174	0.268789
$22$	−1.33294	−0.284184
$23$	5.24380	1.09341	0.546704	−	0.837326i	$-0.315882\pi$
$23$	5.24380	1.09341	0.546704	+	0.837326i	$0.315882\pi$
$24$	1.00000	0.204124
$25$	−3.05059	−0.610118
$26$	−3.02185	−0.592634
$27$	−1.00000	−0.192450
$28$	−1.23174	−0.232778
$29$	5.12161	0.951059	0.475530	−	0.879700i	$-0.342256\pi$
$29$	5.12161	0.951059	0.475530	+	0.879700i	$0.342256\pi$
$30$	1.39621	0.254913
$31$	0.238960	0.0429186	0.0214593	−	0.999770i	$-0.493169\pi$
$31$	0.238960	0.0429186	0.0214593	+	0.999770i	$0.493169\pi$
$32$	−1.00000	−0.176777
$33$	−1.33294	−0.232035
$34$	−1.00000	−0.171499
$35$	−1.71978	−0.290696
$36$	1.00000	0.166667
$37$	5.99937	0.986291	0.493145	−	0.869947i	$-0.335847\pi$
$37$	5.99937	0.986291	0.493145	+	0.869947i	$0.335847\pi$
$38$	−2.38520	−0.386930
$39$	−3.02185	−0.483884
$40$	−1.39621	−0.220761
$41$	6.44784	1.00698	0.503492	−	0.864000i	$-0.332048\pi$
$41$	6.44784	1.00698	0.503492	+	0.864000i	$0.332048\pi$
$42$	−1.23174	−0.190062
$43$	5.24123	0.799280	0.399640	−	0.916672i	$-0.369135\pi$
$43$	5.24123	0.799280	0.399640	+	0.916672i	$0.369135\pi$
$44$	1.33294	0.200948
$45$	1.39621	0.208135
$46$	−5.24380	−0.773156
$47$	−5.48284	−0.799755	−0.399877	−	0.916569i	$-0.630947\pi$
$47$	−5.48284	−0.799755	−0.399877	+	0.916569i	$0.630947\pi$
$48$	−1.00000	−0.144338
$49$	−5.48281	−0.783258
$50$	3.05059	0.431418
$51$	−1.00000	−0.140028
$52$	3.02185	0.419056
$53$	−6.85752	−0.941952	−0.470976	−	0.882146i	$-0.656098\pi$
$53$	−6.85752	−0.941952	−0.470976	+	0.882146i	$0.656098\pi$
$54$	1.00000	0.136083
$55$	1.86107	0.250947
$56$	1.23174	0.164599
$57$	−2.38520	−0.315927
$58$	−5.12161	−0.672500
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	−1.39621	−0.180250
$61$	−4.09141	−0.523851	−0.261925	−	0.965088i	$-0.584357\pi$
$61$	−4.09141	−0.523851	−0.261925	+	0.965088i	$0.584357\pi$
$62$	−0.238960	−0.0303480
$63$	−1.23174	−0.155185
$64$	1.00000	0.125000
$65$	4.21915	0.523321
$66$	1.33294	0.164074
$67$	14.4176	1.76139	0.880693	−	0.473687i	$-0.157077\pi$
$67$	14.4176	1.76139	0.880693	+	0.473687i	$0.157077\pi$
$68$	1.00000	0.121268
$69$	−5.24380	−0.631280
$70$	1.71978	0.205553
$71$	2.45847	0.291766	0.145883	−	0.989302i	$-0.453398\pi$
$71$	2.45847	0.291766	0.145883	+	0.989302i	$0.453398\pi$
$72$	−1.00000	−0.117851
$73$	−9.84343	−1.15209	−0.576043	−	0.817419i	$-0.695404\pi$
$73$	−9.84343	−1.15209	−0.576043	+	0.817419i	$0.695404\pi$
$74$	−5.99937	−0.697413
$75$	3.05059	0.352252
$76$	2.38520	0.273601
$77$	−1.64184	−0.187105
$78$	3.02185	0.342157
$79$	1.35868	0.152863	0.0764316	−	0.997075i	$-0.475647\pi$
$79$	1.35868	0.152863	0.0764316	+	0.997075i	$0.475647\pi$
$80$	1.39621	0.156101
$81$	1.00000	0.111111
$82$	−6.44784	−0.712045
$83$	0.183267	0.0201162	0.0100581	−	0.999949i	$-0.496798\pi$
$83$	0.183267	0.0201162	0.0100581	+	0.999949i	$0.496798\pi$
$84$	1.23174	0.134394
$85$	1.39621	0.151441
$86$	−5.24123	−0.565176
$87$	−5.12161	−0.549094
$88$	−1.33294	−0.142092
$89$	−9.50534	−1.00756	−0.503782	−	0.863831i	$-0.668058\pi$
$89$	−9.50534	−1.00756	−0.503782	+	0.863831i	$0.668058\pi$
$90$	−1.39621	−0.147174
$91$	−3.72215	−0.390187
$92$	5.24380	0.546704
$93$	−0.238960	−0.0247790
$94$	5.48284	0.565512
$95$	3.33024	0.341676
$96$	1.00000	0.102062
$97$	1.31659	0.133679	0.0668395	−	0.997764i	$-0.478708\pi$
$97$	1.31659	0.133679	0.0668395	+	0.997764i	$0.478708\pi$
$98$	5.48281	0.553847
$99$	1.33294	0.133966
$100$	−3.05059	−0.305059
$101$	−3.12325	−0.310775	−0.155387	−	0.987854i	$-0.549663\pi$
$101$	−3.12325	−0.310775	−0.155387	+	0.987854i	$0.549663\pi$
$102$	1.00000	0.0990148
$103$	15.3042	1.50796	0.753982	−	0.656895i	$-0.228130\pi$
$103$	15.3042	1.50796	0.753982	+	0.656895i	$0.228130\pi$
$104$	−3.02185	−0.296317
$105$	1.71978	0.167833
$106$	6.85752	0.666061
$107$	19.5560	1.89055	0.945277	−	0.326270i	$-0.105792\pi$
$107$	19.5560	1.89055	0.945277	+	0.326270i	$0.105792\pi$
$108$	−1.00000	−0.0962250
$109$	10.3763	0.993870	0.496935	−	0.867788i	$-0.334459\pi$
$109$	10.3763	0.993870	0.496935	+	0.867788i	$0.334459\pi$
$110$	−1.86107	−0.177446
$111$	−5.99937	−0.569435
$112$	−1.23174	−0.116389
$113$	−9.34541	−0.879142	−0.439571	−	0.898208i	$-0.644869\pi$
$113$	−9.34541	−0.879142	−0.439571	+	0.898208i	$0.644869\pi$
$114$	2.38520	0.223394
$115$	7.32147	0.682730
$116$	5.12161	0.475530
$117$	3.02185	0.279370
$118$	1.00000	0.0920575
$119$	−1.23174	−0.112914
$120$	1.39621	0.127456
$121$	−9.22327	−0.838479
$122$	4.09141	0.370419
$123$	−6.44784	−0.581382
$124$	0.238960	0.0214593
$125$	−11.2403	−1.00537
$126$	1.23174	0.109732
$127$	−9.30279	−0.825489	−0.412744	−	0.910847i	$-0.635430\pi$
$127$	−9.30279	−0.825489	−0.412744	+	0.910847i	$0.635430\pi$
$128$	−1.00000	−0.0883883
$129$	−5.24123	−0.461464
$130$	−4.21915	−0.370044
$131$	0.579803	0.0506577	0.0253288	−	0.999679i	$-0.491937\pi$
$131$	0.579803	0.0506577	0.0253288	+	0.999679i	$0.491937\pi$
$132$	−1.33294	−0.116018
$133$	−2.93795	−0.254753
$134$	−14.4176	−1.24549
$135$	−1.39621	−0.120167
$136$	−1.00000	−0.0857493
$137$	−9.81475	−0.838530	−0.419265	−	0.907864i	$-0.637712\pi$
$137$	−9.81475	−0.838530	−0.419265	+	0.907864i	$0.637712\pi$
$138$	5.24380	0.446382
$139$	−1.30210	−0.110443	−0.0552213	−	0.998474i	$-0.517586\pi$
$139$	−1.30210	−0.110443	−0.0552213	+	0.998474i	$0.517586\pi$
$140$	−1.71978	−0.145348
$141$	5.48284	0.461739
$142$	−2.45847	−0.206310
$143$	4.02795	0.336834
$144$	1.00000	0.0833333
$145$	7.15086	0.593847
$146$	9.84343	0.814648
$147$	5.48281	0.452214
$148$	5.99937	0.493145
$149$	−7.26871	−0.595476	−0.297738	−	0.954648i	$-0.596232\pi$
$149$	−7.26871	−0.595476	−0.297738	+	0.954648i	$0.596232\pi$
$150$	−3.05059	−0.249079
$151$	−4.46621	−0.363455	−0.181727	−	0.983349i	$-0.558169\pi$
$151$	−4.46621	−0.363455	−0.181727	+	0.983349i	$0.558169\pi$
$152$	−2.38520	−0.193465
$153$	1.00000	0.0808452
$154$	1.64184	0.132303
$155$	0.333640	0.0267986
$156$	−3.02185	−0.241942
$157$	14.8615	1.18608	0.593039	−	0.805174i	$-0.297928\pi$
$157$	14.8615	1.18608	0.593039	+	0.805174i	$0.297928\pi$
$158$	−1.35868	−0.108091
$159$	6.85752	0.543836
$160$	−1.39621	−0.110380
$161$	−6.45902	−0.509042
$162$	−1.00000	−0.0785674
$163$	7.24912	0.567795	0.283897	−	0.958855i	$-0.408372\pi$
$163$	7.24912	0.567795	0.283897	+	0.958855i	$0.408372\pi$
$164$	6.44784	0.503492
$165$	−1.86107	−0.144884
$166$	−0.183267	−0.0142243
$167$	16.8368	1.30287	0.651437	−	0.758703i	$-0.274167\pi$
$167$	16.8368	1.30287	0.651437	+	0.758703i	$0.274167\pi$
$168$	−1.23174	−0.0950311
$169$	−3.86841	−0.297570
$170$	−1.39621	−0.107085
$171$	2.38520	0.182400
$172$	5.24123	0.399640
$173$	−12.5264	−0.952366	−0.476183	−	0.879346i	$-0.657980\pi$
$173$	−12.5264	−0.952366	−0.476183	+	0.879346i	$0.657980\pi$
$174$	5.12161	0.388268
$175$	3.75754	0.284044
$176$	1.33294	0.100474
$177$	1.00000	0.0751646
$178$	9.50534	0.712455
$179$	17.6585	1.31986	0.659931	−	0.751326i	$-0.270586\pi$
$179$	17.6585	1.31986	0.659931	+	0.751326i	$0.270586\pi$
$180$	1.39621	0.104068
$181$	1.52082	0.113041	0.0565207	−	0.998401i	$-0.481999\pi$
$181$	1.52082	0.113041	0.0565207	+	0.998401i	$0.481999\pi$
$182$	3.72215	0.275904
$183$	4.09141	0.302445
$184$	−5.24380	−0.386578
$185$	8.37641	0.615846
$186$	0.238960	0.0175214
$187$	1.33294	0.0974743
$188$	−5.48284	−0.399877
$189$	1.23174	0.0895962
$190$	−3.33024	−0.241601
$191$	2.16514	0.156664	0.0783319	−	0.996927i	$-0.475041\pi$
$191$	2.16514	0.156664	0.0783319	+	0.996927i	$0.475041\pi$
$192$	−1.00000	−0.0721688
$193$	25.9722	1.86952	0.934758	−	0.355284i	$-0.115616\pi$
$193$	25.9722	1.86952	0.934758	+	0.355284i	$0.115616\pi$
$194$	−1.31659	−0.0945253
$195$	−4.21915	−0.302140
$196$	−5.48281	−0.391629
$197$	−19.9099	−1.41852	−0.709261	−	0.704946i	$-0.750971\pi$
$197$	−19.9099	−1.41852	−0.709261	+	0.704946i	$0.750971\pi$
$198$	−1.33294	−0.0947280
$199$	−10.8532	−0.769362	−0.384681	−	0.923050i	$-0.625689\pi$
$199$	−10.8532	−0.769362	−0.384681	+	0.923050i	$0.625689\pi$
$200$	3.05059	0.215709
$201$	−14.4176	−1.01694
$202$	3.12325	0.219751
$203$	−6.30851	−0.442771
$204$	−1.00000	−0.0700140
$205$	9.00256	0.628766
$206$	−15.3042	−1.06629
$207$	5.24380	0.364469
$208$	3.02185	0.209528
$209$	3.17932	0.219918
$210$	−1.71978	−0.118676
$211$	−6.02741	−0.414944	−0.207472	−	0.978241i	$-0.566524\pi$
$211$	−6.02741	−0.414944	−0.207472	+	0.978241i	$0.566524\pi$
$212$	−6.85752	−0.470976
$213$	−2.45847	−0.168451
$214$	−19.5560	−1.33682
$215$	7.31787	0.499075
$216$	1.00000	0.0680414
$217$	−0.294338	−0.0199810
$218$	−10.3763	−0.702772
$219$	9.84343	0.665157
$220$	1.86107	0.125473
$221$	3.02185	0.203272
$222$	5.99937	0.402652
$223$	−6.10343	−0.408716	−0.204358	−	0.978896i	$-0.565511\pi$
$223$	−6.10343	−0.408716	−0.204358	+	0.978896i	$0.565511\pi$
$224$	1.23174	0.0822994
$225$	−3.05059	−0.203373
$226$	9.34541	0.621647
$227$	−22.7438	−1.50956	−0.754780	−	0.655978i	$-0.772256\pi$
$227$	−22.7438	−1.50956	−0.754780	+	0.655978i	$0.772256\pi$
$228$	−2.38520	−0.157963
$229$	29.1330	1.92516	0.962582	−	0.270989i	$-0.0873508\pi$
$229$	29.1330	1.92516	0.962582	+	0.270989i	$0.0873508\pi$
$230$	−7.32147	−0.482763
$231$	1.64184	0.108025
$232$	−5.12161	−0.336250
$233$	19.7915	1.29658	0.648291	−	0.761392i	$-0.275484\pi$
$233$	19.7915	1.29658	0.648291	+	0.761392i	$0.275484\pi$
$234$	−3.02185	−0.197545
$235$	−7.65522	−0.499371
$236$	−1.00000	−0.0650945
$237$	−1.35868	−0.0882556
$238$	1.23174	0.0798421
$239$	−20.7500	−1.34221	−0.671104	−	0.741363i	$-0.734180\pi$
$239$	−20.7500	−1.34221	−0.671104	+	0.741363i	$0.734180\pi$
$240$	−1.39621	−0.0901252
$241$	−14.6805	−0.945655	−0.472827	−	0.881155i	$-0.656767\pi$
$241$	−14.6805	−0.945655	−0.472827	+	0.881155i	$0.656767\pi$
$242$	9.22327	0.592894
$243$	−1.00000	−0.0641500
$244$	−4.09141	−0.261925
$245$	−7.65517	−0.489071
$246$	6.44784	0.411099
$247$	7.20771	0.458616
$248$	−0.238960	−0.0151740
$249$	−0.183267	−0.0116141
$250$	11.2403	0.710901
$251$	15.2730	0.964024	0.482012	−	0.876165i	$-0.339906\pi$
$251$	15.2730	0.964024	0.482012	+	0.876165i	$0.339906\pi$
$252$	−1.23174	−0.0775926
$253$	6.98968	0.439437
$254$	9.30279	0.583709
$255$	−1.39621	−0.0874343
$256$	1.00000	0.0625000
$257$	8.63132	0.538407	0.269204	−	0.963083i	$-0.413240\pi$
$257$	8.63132	0.538407	0.269204	+	0.963083i	$0.413240\pi$
$258$	5.24123	0.326305
$259$	−7.38969	−0.459173
$260$	4.21915	0.261661
$261$	5.12161	0.317020
$262$	−0.579803	−0.0358204
$263$	15.4180	0.950713	0.475357	−	0.879793i	$-0.342319\pi$
$263$	15.4180	0.950713	0.475357	+	0.879793i	$0.342319\pi$
$264$	1.33294	0.0820368
$265$	−9.57456	−0.588160
$266$	2.93795	0.180137
$267$	9.50534	0.581717
$268$	14.4176	0.880693
$269$	−0.513904	−0.0313333	−0.0156666	−	0.999877i	$-0.504987\pi$
$269$	−0.513904	−0.0313333	−0.0156666	+	0.999877i	$0.504987\pi$
$270$	1.39621	0.0849709
$271$	0.211744	0.0128625	0.00643127	−	0.999979i	$-0.497953\pi$
$271$	0.211744	0.0128625	0.00643127	+	0.999979i	$0.497953\pi$
$272$	1.00000	0.0606339
$273$	3.72215	0.225275
$274$	9.81475	0.592931
$275$	−4.06625	−0.245204
$276$	−5.24380	−0.315640
$277$	25.6652	1.54207	0.771037	−	0.636790i	$-0.219738\pi$
$277$	25.6652	1.54207	0.771037	+	0.636790i	$0.219738\pi$
$278$	1.30210	0.0780947
$279$	0.238960	0.0143062
$280$	1.71978	0.102776
$281$	−20.1926	−1.20459	−0.602295	−	0.798274i	$-0.705747\pi$
$281$	−20.1926	−1.20459	−0.602295	+	0.798274i	$0.705747\pi$
$282$	−5.48284	−0.326499
$283$	23.5657	1.40083	0.700417	−	0.713734i	$-0.252998\pi$
$283$	23.5657	1.40083	0.700417	+	0.713734i	$0.252998\pi$
$284$	2.45847	0.145883
$285$	−3.33024	−0.197267
$286$	−4.02795	−0.238178
$287$	−7.94209	−0.468807
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	−7.15086	−0.419913
$291$	−1.31659	−0.0771796
$292$	−9.84343	−0.576043
$293$	−8.18650	−0.478261	−0.239130	−	0.970987i	$-0.576862\pi$
$293$	−8.18650	−0.478261	−0.239130	+	0.970987i	$0.576862\pi$
$294$	−5.48281	−0.319764
$295$	−1.39621	−0.0812907
$296$	−5.99937	−0.348706
$297$	−1.33294	−0.0773451
$298$	7.26871	0.421065
$299$	15.8460	0.916398
$300$	3.05059	0.176126
$301$	−6.45585	−0.372109
$302$	4.46621	0.257001
$303$	3.12325	0.179426
$304$	2.38520	0.136800
$305$	−5.71248	−0.327095
$306$	−1.00000	−0.0571662
$307$	−0.820077	−0.0468043	−0.0234021	−	0.999726i	$-0.507450\pi$
$307$	−0.820077	−0.0468043	−0.0234021	+	0.999726i	$0.507450\pi$
$308$	−1.64184	−0.0935526
$309$	−15.3042	−0.870624
$310$	−0.333640	−0.0189495
$311$	−0.565621	−0.0320734	−0.0160367	−	0.999871i	$-0.505105\pi$
$311$	−0.565621	−0.0320734	−0.0160367	+	0.999871i	$0.505105\pi$
$312$	3.02185	0.171079
$313$	3.77250	0.213234	0.106617	−	0.994300i	$-0.465998\pi$
$313$	3.77250	0.213234	0.106617	+	0.994300i	$0.465998\pi$
$314$	−14.8615	−0.838683
$315$	−1.71978	−0.0968985
$316$	1.35868	0.0764316
$317$	13.8954	0.780443	0.390221	−	0.920721i	$-0.372398\pi$
$317$	13.8954	0.780443	0.390221	+	0.920721i	$0.372398\pi$
$318$	−6.85752	−0.384550
$319$	6.82680	0.382227
$320$	1.39621	0.0780507
$321$	−19.5560	−1.09151
$322$	6.45902	0.359947
$323$	2.38520	0.132716
$324$	1.00000	0.0555556
$325$	−9.21843	−0.511346
$326$	−7.24912	−0.401492
$327$	−10.3763	−0.573811
$328$	−6.44784	−0.356022
$329$	6.75346	0.372330
$330$	1.86107	0.102449
$331$	26.2630	1.44355	0.721774	−	0.692129i	$-0.243327\pi$
$331$	26.2630	1.44355	0.721774	+	0.692129i	$0.243327\pi$
$332$	0.183267	0.0100581
$333$	5.99937	0.328764
$334$	−16.8368	−0.921271
$335$	20.1300	1.09982
$336$	1.23174	0.0671972
$337$	−26.4216	−1.43927	−0.719637	−	0.694350i	$-0.755692\pi$
$337$	−26.4216	−1.43927	−0.719637	+	0.694350i	$0.755692\pi$
$338$	3.86841	0.210414
$339$	9.34541	0.507573
$340$	1.39621	0.0757203
$341$	0.318520	0.0172488
$342$	−2.38520	−0.128977
$343$	15.3756	0.830206
$344$	−5.24123	−0.282588
$345$	−7.32147	−0.394175
$346$	12.5264	0.673425
$347$	−33.1388	−1.77898	−0.889492	−	0.456952i	$-0.848941\pi$
$347$	−33.1388	−1.77898	−0.889492	+	0.456952i	$0.848941\pi$
$348$	−5.12161	−0.274547
$349$	−28.3322	−1.51659	−0.758294	−	0.651912i	$-0.773967\pi$
$349$	−28.3322	−1.51659	−0.758294	+	0.651912i	$0.773967\pi$
$350$	−3.75754	−0.200849
$351$	−3.02185	−0.161295
$352$	−1.33294	−0.0710460
$353$	11.7666	0.626271	0.313136	−	0.949708i	$-0.398621\pi$
$353$	11.7666	0.626271	0.313136	+	0.949708i	$0.398621\pi$
$354$	−1.00000	−0.0531494
$355$	3.43254	0.182181
$356$	−9.50534	−0.503782
$357$	1.23174	0.0651908
$358$	−17.6585	−0.933283
$359$	−26.2799	−1.38700	−0.693500	−	0.720457i	$-0.743932\pi$
$359$	−26.2799	−1.38700	−0.693500	+	0.720457i	$0.743932\pi$
$360$	−1.39621	−0.0735869
$361$	−13.3108	−0.700571
$362$	−1.52082	−0.0799323
$363$	9.22327	0.484096
$364$	−3.72215	−0.195094
$365$	−13.7435	−0.719369
$366$	−4.09141	−0.213861
$367$	1.49221	0.0778927	0.0389464	−	0.999241i	$-0.487600\pi$
$367$	1.49221	0.0778927	0.0389464	+	0.999241i	$0.487600\pi$
$368$	5.24380	0.273352
$369$	6.44784	0.335661
$370$	−8.37641	−0.435469
$371$	8.44670	0.438531
$372$	−0.238960	−0.0123895
$373$	17.2112	0.891161	0.445581	−	0.895242i	$-0.352997\pi$
$373$	17.2112	0.891161	0.445581	+	0.895242i	$0.352997\pi$
$374$	−1.33294	−0.0689247
$375$	11.2403	0.580449
$376$	5.48284	0.282756
$377$	15.4767	0.797093
$378$	−1.23174	−0.0633541
$379$	18.4947	0.950011	0.475006	−	0.879983i	$-0.342446\pi$
$379$	18.4947	0.950011	0.475006	+	0.879983i	$0.342446\pi$
$380$	3.33024	0.170838
$381$	9.30279	0.476596
$382$	−2.16514	−0.110778
$383$	−29.8949	−1.52756	−0.763780	−	0.645477i	$-0.776659\pi$
$383$	−29.8949	−1.52756	−0.763780	+	0.645477i	$0.776659\pi$
$384$	1.00000	0.0510310
$385$	−2.29236	−0.116830
$386$	−25.9722	−1.32195
$387$	5.24123	0.266427
$388$	1.31659	0.0668395
$389$	9.84584	0.499204	0.249602	−	0.968348i	$-0.419700\pi$
$389$	9.84584	0.499204	0.249602	+	0.968348i	$0.419700\pi$
$390$	4.21915	0.213645
$391$	5.24380	0.265190
$392$	5.48281	0.276924
$393$	−0.579803	−0.0292472
$394$	19.9099	1.00305
$395$	1.89700	0.0954487
$396$	1.33294	0.0669828
$397$	−27.0890	−1.35956	−0.679780	−	0.733416i	$-0.737925\pi$
$397$	−27.0890	−1.35956	−0.679780	+	0.733416i	$0.737925\pi$
$398$	10.8532	0.544021
$399$	2.93795	0.147081
$400$	−3.05059	−0.152529
$401$	38.2155	1.90839	0.954195	−	0.299186i	$-0.0967152\pi$
$401$	38.2155	1.90839	0.954195	+	0.299186i	$0.0967152\pi$
$402$	14.4176	0.719083
$403$	0.722103	0.0359705
$404$	−3.12325	−0.155387
$405$	1.39621	0.0693784
$406$	6.30851	0.313086
$407$	7.99681	0.396387
$408$	1.00000	0.0495074
$409$	11.5634	0.571772	0.285886	−	0.958264i	$-0.407712\pi$
$409$	11.5634	0.571772	0.285886	+	0.958264i	$0.407712\pi$
$410$	−9.00256	−0.444605
$411$	9.81475	0.484126
$412$	15.3042	0.753982
$413$	1.23174	0.0606102
$414$	−5.24380	−0.257719
$415$	0.255880	0.0125607
$416$	−3.02185	−0.148159
$417$	1.30210	0.0637641
$418$	−3.17932	−0.155506
$419$	−19.3900	−0.947263	−0.473632	−	0.880723i	$-0.657057\pi$
$419$	−19.3900	−0.947263	−0.473632	+	0.880723i	$0.657057\pi$
$420$	1.71978	0.0839166
$421$	38.4482	1.87385	0.936924	−	0.349532i	$-0.113659\pi$
$421$	38.4482	1.87385	0.936924	+	0.349532i	$0.113659\pi$
$422$	6.02741	0.293410
$423$	−5.48284	−0.266585
$424$	6.85752	0.333030
$425$	−3.05059	−0.147975
$426$	2.45847	0.119113
$427$	5.03957	0.243882
$428$	19.5560	0.945277
$429$	−4.02795	−0.194471
$430$	−7.31787	−0.352899
$431$	19.4651	0.937599	0.468800	−	0.883304i	$-0.344687\pi$
$431$	19.4651	0.937599	0.468800	+	0.883304i	$0.344687\pi$
$432$	−1.00000	−0.0481125
$433$	21.4455	1.03060	0.515302	−	0.857008i	$-0.327680\pi$
$433$	21.4455	1.03060	0.515302	+	0.857008i	$0.327680\pi$
$434$	0.294338	0.0141287
$435$	−7.15086	−0.342858
$436$	10.3763	0.496935
$437$	12.5075	0.598315
$438$	−9.84343	−0.470337
$439$	−12.0458	−0.574913	−0.287457	−	0.957794i	$-0.592810\pi$
$439$	−12.0458	−0.574913	−0.287457	+	0.957794i	$0.592810\pi$
$440$	−1.86107	−0.0887230
$441$	−5.48281	−0.261086
$442$	−3.02185	−0.143735
$443$	35.4527	1.68441	0.842204	−	0.539159i	$-0.181258\pi$
$443$	35.4527	1.68441	0.842204	+	0.539159i	$0.181258\pi$
$444$	−5.99937	−0.284718
$445$	−13.2715	−0.629128
$446$	6.10343	0.289006
$447$	7.26871	0.343798
$448$	−1.23174	−0.0581944
$449$	10.4628	0.493769	0.246885	−	0.969045i	$-0.420593\pi$
$449$	10.4628	0.493769	0.246885	+	0.969045i	$0.420593\pi$
$450$	3.05059	0.143806
$451$	8.59459	0.404703
$452$	−9.34541	−0.439571
$453$	4.46621	0.209841
$454$	22.7438	1.06742
$455$	−5.19692	−0.243635
$456$	2.38520	0.111697
$457$	25.8809	1.21066	0.605330	−	0.795975i	$-0.293041\pi$
$457$	25.8809	1.21066	0.605330	+	0.795975i	$0.293041\pi$
$458$	−29.1330	−1.36130
$459$	−1.00000	−0.0466760
$460$	7.32147	0.341365
$461$	−13.0148	−0.606158	−0.303079	−	0.952965i	$-0.598015\pi$
$461$	−13.0148	−0.606158	−0.303079	+	0.952965i	$0.598015\pi$
$462$	−1.64184	−0.0763854
$463$	35.2018	1.63596	0.817982	−	0.575243i	$-0.195093\pi$
$463$	35.2018	1.63596	0.817982	+	0.575243i	$0.195093\pi$
$464$	5.12161	0.237765
$465$	−0.333640	−0.0154722
$466$	−19.7915	−0.916822
$467$	−25.3681	−1.17390	−0.586949	−	0.809624i	$-0.699671\pi$
$467$	−25.3681	−1.17390	−0.586949	+	0.809624i	$0.699671\pi$
$468$	3.02185	0.139685
$469$	−17.7588	−0.820023
$470$	7.65522	0.353109
$471$	−14.8615	−0.684782
$472$	1.00000	0.0460287
$473$	6.98624	0.321228
$474$	1.35868	0.0624061
$475$	−7.27625	−0.333857
$476$	−1.23174	−0.0564569
$477$	−6.85752	−0.313984
$478$	20.7500	0.949085
$479$	−6.29957	−0.287835	−0.143917	−	0.989590i	$-0.545970\pi$
$479$	−6.29957	−0.287835	−0.143917	+	0.989590i	$0.545970\pi$
$480$	1.39621	0.0637281
$481$	18.1292	0.826621
$482$	14.6805	0.668679
$483$	6.45902	0.293896
$484$	−9.22327	−0.419240
$485$	1.83823	0.0834699
$486$	1.00000	0.0453609
$487$	−1.07461	−0.0486953	−0.0243476	−	0.999704i	$-0.507751\pi$
$487$	−1.07461	−0.0486953	−0.0243476	+	0.999704i	$0.507751\pi$
$488$	4.09141	0.185209
$489$	−7.24912	−0.327816
$490$	7.65517	0.345825
$491$	−15.9517	−0.719891	−0.359945	−	0.932973i	$-0.617205\pi$
$491$	−15.9517	−0.719891	−0.359945	+	0.932973i	$0.617205\pi$
$492$	−6.44784	−0.290691
$493$	5.12161	0.230666
$494$	−7.20771	−0.324290
$495$	1.86107	0.0836489
$496$	0.238960	0.0107296
$497$	−3.02820	−0.135833
$498$	0.183267	0.00821241
$499$	32.3491	1.44815	0.724073	−	0.689723i	$-0.242268\pi$
$499$	32.3491	1.44815	0.724073	+	0.689723i	$0.242268\pi$
$500$	−11.2403	−0.502683
$501$	−16.8368	−0.752215
$502$	−15.2730	−0.681668
$503$	11.5567	0.515286	0.257643	−	0.966240i	$-0.417054\pi$
$503$	11.5567	0.515286	0.257643	+	0.966240i	$0.417054\pi$
$504$	1.23174	0.0548662
$505$	−4.36072	−0.194050
$506$	−6.98968	−0.310729
$507$	3.86841	0.171802
$508$	−9.30279	−0.412744
$509$	31.6757	1.40400	0.702000	−	0.712177i	$-0.252290\pi$
$509$	31.6757	1.40400	0.702000	+	0.712177i	$0.252290\pi$
$510$	1.39621	0.0618254
$511$	12.1246	0.536360
$512$	−1.00000	−0.0441942
$513$	−2.38520	−0.105309
$514$	−8.63132	−0.380711
$515$	21.3679	0.941582
$516$	−5.24123	−0.230732
$517$	−7.30830	−0.321419
$518$	7.38969	0.324684
$519$	12.5264	0.549849
$520$	−4.21915	−0.185022
$521$	−31.9605	−1.40022	−0.700108	−	0.714037i	$-0.746865\pi$
$521$	−31.9605	−1.40022	−0.700108	+	0.714037i	$0.746865\pi$
$522$	−5.12161	−0.224167
$523$	17.3949	0.760625	0.380313	−	0.924858i	$-0.375816\pi$
$523$	17.3949	0.760625	0.380313	+	0.924858i	$0.375816\pi$
$524$	0.579803	0.0253288
$525$	−3.75754	−0.163993
$526$	−15.4180	−0.672256
$527$	0.238960	0.0104093
$528$	−1.33294	−0.0580088
$529$	4.49746	0.195542
$530$	9.57456	0.415892
$531$	−1.00000	−0.0433963
$532$	−2.93795	−0.127376
$533$	19.4844	0.843964
$534$	−9.50534	−0.411336
$535$	27.3044	1.18047
$536$	−14.4176	−0.622744
$537$	−17.6585	−0.762022
$538$	0.513904	0.0221560
$539$	−7.30825	−0.314789
$540$	−1.39621	−0.0600835
$541$	−27.1614	−1.16776	−0.583880	−	0.811840i	$-0.698466\pi$
$541$	−27.1614	−1.16776	−0.583880	+	0.811840i	$0.698466\pi$
$542$	−0.211744	−0.00909519
$543$	−1.52082	−0.0652645
$544$	−1.00000	−0.0428746
$545$	14.4875	0.620578
$546$	−3.72215	−0.159293
$547$	28.7298	1.22840	0.614198	−	0.789152i	$-0.289480\pi$
$547$	28.7298	1.22840	0.614198	+	0.789152i	$0.289480\pi$
$548$	−9.81475	−0.419265
$549$	−4.09141	−0.174617
$550$	4.06625	0.173386
$551$	12.2160	0.520421
$552$	5.24380	0.223191
$553$	−1.67354	−0.0711663
$554$	−25.6652	−1.09041
$555$	−8.37641	−0.355559
$556$	−1.30210	−0.0552213
$557$	24.7181	1.04734	0.523670	−	0.851921i	$-0.324562\pi$
$557$	24.7181	1.04734	0.523670	+	0.851921i	$0.324562\pi$
$558$	−0.238960	−0.0101160
$559$	15.8382	0.669885
$560$	−1.71978	−0.0726739
$561$	−1.33294	−0.0562768
$562$	20.1926	0.851773
$563$	−6.51171	−0.274436	−0.137218	−	0.990541i	$-0.543816\pi$
$563$	−6.51171	−0.274436	−0.137218	+	0.990541i	$0.543816\pi$
$564$	5.48284	0.230869
$565$	−13.0482	−0.548941
$566$	−23.5657	−0.990539
$567$	−1.23174	−0.0517284
$568$	−2.45847	−0.103155
$569$	−24.9423	−1.04564	−0.522818	−	0.852445i	$-0.675119\pi$
$569$	−24.9423	−1.04564	−0.522818	+	0.852445i	$0.675119\pi$
$570$	3.33024	0.139488
$571$	27.8848	1.16694	0.583472	−	0.812133i	$-0.301694\pi$
$571$	27.8848	1.16694	0.583472	+	0.812133i	$0.301694\pi$
$572$	4.02795	0.168417
$573$	−2.16514	−0.0904498
$574$	7.94209	0.331496
$575$	−15.9967	−0.667108
$576$	1.00000	0.0416667
$577$	12.4115	0.516698	0.258349	−	0.966052i	$-0.416822\pi$
$577$	12.4115	0.516698	0.258349	+	0.966052i	$0.416822\pi$
$578$	−1.00000	−0.0415945
$579$	−25.9722	−1.07937
$580$	7.15086	0.296923
$581$	−0.225739	−0.00936521
$582$	1.31659	0.0545742
$583$	−9.14066	−0.378567
$584$	9.84343	0.407324
$585$	4.21915	0.174440
$586$	8.18650	0.338181
$587$	44.3772	1.83164	0.915821	−	0.401587i	$-0.131541\pi$
$587$	44.3772	1.83164	0.915821	+	0.401587i	$0.131541\pi$
$588$	5.48281	0.226107
$589$	0.569967	0.0234851
$590$	1.39621	0.0574812
$591$	19.9099	0.818984
$592$	5.99937	0.246573
$593$	26.2219	1.07681	0.538403	−	0.842688i	$-0.319028\pi$
$593$	26.2219	1.07681	0.538403	+	0.842688i	$0.319028\pi$
$594$	1.33294	0.0546912
$595$	−1.71978	−0.0705040
$596$	−7.26871	−0.297738
$597$	10.8532	0.444192
$598$	−15.8460	−0.647991
$599$	34.0986	1.39323	0.696616	−	0.717444i	$-0.254688\pi$
$599$	34.0986	1.39323	0.696616	+	0.717444i	$0.254688\pi$
$600$	−3.05059	−0.124540
$601$	20.7898	0.848033	0.424017	−	0.905654i	$-0.360620\pi$
$601$	20.7898	0.848033	0.424017	+	0.905654i	$0.360620\pi$
$602$	6.45585	0.263121
$603$	14.4176	0.587129
$604$	−4.46621	−0.181727
$605$	−12.8777	−0.523551
$606$	−3.12325	−0.126873
$607$	41.4237	1.68134	0.840668	−	0.541550i	$-0.182162\pi$
$607$	41.4237	1.68134	0.840668	+	0.541550i	$0.182162\pi$
$608$	−2.38520	−0.0967325
$609$	6.30851	0.255634
$610$	5.71248	0.231291
$611$	−16.5683	−0.670283
$612$	1.00000	0.0404226
$613$	−3.82735	−0.154585	−0.0772926	−	0.997008i	$-0.524628\pi$
$613$	−3.82735	−0.154585	−0.0772926	+	0.997008i	$0.524628\pi$
$614$	0.820077	0.0330956
$615$	−9.00256	−0.363018
$616$	1.64184	0.0661517
$617$	−27.9532	−1.12535	−0.562677	−	0.826677i	$-0.690229\pi$
$617$	−27.9532	−1.12535	−0.562677	+	0.826677i	$0.690229\pi$
$618$	15.3042	0.615624
$619$	9.63003	0.387064	0.193532	−	0.981094i	$-0.438006\pi$
$619$	9.63003	0.387064	0.193532	+	0.981094i	$0.438006\pi$
$620$	0.333640	0.0133993
$621$	−5.24380	−0.210427
$622$	0.565621	0.0226793
$623$	11.7081	0.469077
$624$	−3.02185	−0.120971
$625$	−0.440976	−0.0176390
$626$	−3.77250	−0.150779
$627$	−3.17932	−0.126970
$628$	14.8615	0.593039
$629$	5.99937	0.239211
$630$	1.71978	0.0685176
$631$	29.6927	1.18205	0.591025	−	0.806653i	$-0.298724\pi$
$631$	29.6927	1.18205	0.591025	+	0.806653i	$0.298724\pi$
$632$	−1.35868	−0.0540453
$633$	6.02741	0.239568
$634$	−13.8954	−0.551856
$635$	−12.9887	−0.515440
$636$	6.85752	0.271918
$637$	−16.5682	−0.656457
$638$	−6.82680	−0.270276
$639$	2.45847	0.0972554
$640$	−1.39621	−0.0551902
$641$	−42.4598	−1.67706	−0.838531	−	0.544854i	$-0.816585\pi$
$641$	−42.4598	−1.67706	−0.838531	+	0.544854i	$0.816585\pi$
$642$	19.5560	0.771815
$643$	21.5021	0.847960	0.423980	−	0.905672i	$-0.360633\pi$
$643$	21.5021	0.847960	0.423980	+	0.905672i	$0.360633\pi$
$644$	−6.45902	−0.254521
$645$	−7.31787	−0.288141
$646$	−2.38520	−0.0938443
$647$	−1.56383	−0.0614806	−0.0307403	−	0.999527i	$-0.509786\pi$
$647$	−1.56383	−0.0614806	−0.0307403	+	0.999527i	$0.509786\pi$
$648$	−1.00000	−0.0392837
$649$	−1.33294	−0.0523225
$650$	9.21843	0.361576
$651$	0.294338	0.0115360
$652$	7.24912	0.283897
$653$	−33.6465	−1.31669	−0.658344	−	0.752717i	$-0.728743\pi$
$653$	−33.6465	−1.31669	−0.658344	+	0.752717i	$0.728743\pi$
$654$	10.3763	0.405746
$655$	0.809529	0.0316309
$656$	6.44784	0.251746
$657$	−9.84343	−0.384029
$658$	−6.75346	−0.263277
$659$	40.8857	1.59268	0.796340	−	0.604850i	$-0.206767\pi$
$659$	40.8857	1.59268	0.796340	+	0.604850i	$0.206767\pi$
$660$	−1.86107	−0.0724420
$661$	−26.0265	−1.01231	−0.506157	−	0.862442i	$-0.668934\pi$
$661$	−26.0265	−1.01231	−0.506157	+	0.862442i	$0.668934\pi$
$662$	−26.2630	−1.02074
$663$	−3.02185	−0.117359
$664$	−0.183267	−0.00711215
$665$	−4.10201	−0.159069
$666$	−5.99937	−0.232471
$667$	26.8567	1.03990
$668$	16.8368	0.651437
$669$	6.10343	0.235972
$670$	−20.1300	−0.777690
$671$	−5.45360	−0.210534
$672$	−1.23174	−0.0475156
$673$	22.1661	0.854439	0.427220	−	0.904148i	$-0.359493\pi$
$673$	22.1661	0.854439	0.427220	+	0.904148i	$0.359493\pi$
$674$	26.4216	1.01772
$675$	3.05059	0.117417
$676$	−3.86841	−0.148785
$677$	−42.7753	−1.64399	−0.821994	−	0.569497i	$-0.807138\pi$
$677$	−42.7753	−1.64399	−0.821994	+	0.569497i	$0.807138\pi$
$678$	−9.34541	−0.358908
$679$	−1.62170	−0.0622350
$680$	−1.39621	−0.0535423
$681$	22.7438	0.871544
$682$	−0.318520	−0.0121968
$683$	−40.0387	−1.53204	−0.766020	−	0.642817i	$-0.777765\pi$
$683$	−40.0387	−1.53204	−0.766020	+	0.642817i	$0.777765\pi$
$684$	2.38520	0.0912002
$685$	−13.7035	−0.523583
$686$	−15.3756	−0.587044
$687$	−29.1330	−1.11149
$688$	5.24123	0.199820
$689$	−20.7224	−0.789461
$690$	7.32147	0.278723
$691$	−0.691794	−0.0263171	−0.0131585	−	0.999913i	$-0.504189\pi$
$691$	−0.691794	−0.0263171	−0.0131585	+	0.999913i	$0.504189\pi$
$692$	−12.5264	−0.476183
$693$	−1.64184	−0.0623684
$694$	33.1388	1.25793
$695$	−1.81801	−0.0689610
$696$	5.12161	0.194134
$697$	6.44784	0.244229
$698$	28.3322	1.07239
$699$	−19.7915	−0.748582
$700$	3.75754	0.142022
$701$	37.5727	1.41910	0.709550	−	0.704655i	$-0.248898\pi$
$701$	37.5727	1.41910	0.709550	+	0.704655i	$0.248898\pi$
$702$	3.02185	0.114052
$703$	14.3097	0.539700
$704$	1.33294	0.0502371
$705$	7.65522	0.288312
$706$	−11.7666	−0.442841
$707$	3.84704	0.144683
$708$	1.00000	0.0375823
$709$	14.0912	0.529205	0.264603	−	0.964358i	$-0.414759\pi$
$709$	14.0912	0.529205	0.264603	+	0.964358i	$0.414759\pi$
$710$	−3.43254	−0.128821
$711$	1.35868	0.0509544
$712$	9.50534	0.356228
$713$	1.25306	0.0469275
$714$	−1.23174	−0.0460969
$715$	5.62388	0.210321
$716$	17.6585	0.659931
$717$	20.7500	0.774924
$718$	26.2799	0.980757
$719$	−8.23341	−0.307055	−0.153527	−	0.988144i	$-0.549063\pi$
$719$	−8.23341	−0.307055	−0.153527	+	0.988144i	$0.549063\pi$
$720$	1.39621	0.0520338
$721$	−18.8508	−0.702041
$722$	13.3108	0.495378
$723$	14.6805	0.545974
$724$	1.52082	0.0565207
$725$	−15.6239	−0.580258
$726$	−9.22327	−0.342308
$727$	−19.1597	−0.710592	−0.355296	−	0.934754i	$-0.615620\pi$
$727$	−19.1597	−0.710592	−0.355296	+	0.934754i	$0.615620\pi$
$728$	3.72215	0.137952
$729$	1.00000	0.0370370
$730$	13.7435	0.508671
$731$	5.24123	0.193854
$732$	4.09141	0.151223
$733$	40.9223	1.51150	0.755750	−	0.654860i	$-0.227272\pi$
$733$	40.9223	1.51150	0.755750	+	0.654860i	$0.227272\pi$
$734$	−1.49221	−0.0550785
$735$	7.65517	0.282365
$736$	−5.24380	−0.193289
$737$	19.2178	0.707895
$738$	−6.44784	−0.237348
$739$	15.9018	0.584955	0.292478	−	0.956272i	$-0.405520\pi$
$739$	15.9018	0.584955	0.292478	+	0.956272i	$0.405520\pi$
$740$	8.37641	0.307923
$741$	−7.20771	−0.264782
$742$	−8.44670	−0.310088
$743$	29.0634	1.06623	0.533116	−	0.846042i	$-0.321021\pi$
$743$	29.0634	1.06623	0.533116	+	0.846042i	$0.321021\pi$
$744$	0.238960	0.00876072
$745$	−10.1487	−0.371819
$746$	−17.2112	−0.630146
$747$	0.183267	0.00670540
$748$	1.33294	0.0487371
$749$	−24.0880	−0.880157
$750$	−11.2403	−0.410439
$751$	10.3721	0.378484	0.189242	−	0.981930i	$-0.439397\pi$
$751$	10.3721	0.378484	0.189242	+	0.981930i	$0.439397\pi$
$752$	−5.48284	−0.199939
$753$	−15.2730	−0.556579
$754$	−15.4767	−0.563630
$755$	−6.23578	−0.226943
$756$	1.23174	0.0447981
$757$	41.6545	1.51396	0.756979	−	0.653439i	$-0.226674\pi$
$757$	41.6545	1.51396	0.756979	+	0.653439i	$0.226674\pi$
$758$	−18.4947	−0.671759
$759$	−6.98968	−0.253709
$760$	−3.33024	−0.120801
$761$	42.9826	1.55812	0.779059	−	0.626951i	$-0.215697\pi$
$761$	42.9826	1.55812	0.779059	+	0.626951i	$0.215697\pi$
$762$	−9.30279	−0.337004
$763$	−12.7810	−0.462702
$764$	2.16514	0.0783319
$765$	1.39621	0.0504802
$766$	29.8949	1.08015
$767$	−3.02185	−0.109113
$768$	−1.00000	−0.0360844
$769$	−46.8981	−1.69119	−0.845595	−	0.533825i	$-0.820754\pi$
$769$	−46.8981	−1.69119	−0.845595	+	0.533825i	$0.820754\pi$
$770$	2.29236	0.0826110
$771$	−8.63132	−0.310850
$772$	25.9722	0.934758
$773$	34.8556	1.25367	0.626834	−	0.779153i	$-0.284350\pi$
$773$	34.8556	1.25367	0.626834	+	0.779153i	$0.284350\pi$
$774$	−5.24123	−0.188392
$775$	−0.728970	−0.0261854
$776$	−1.31659	−0.0472627
$777$	7.38969	0.265104
$778$	−9.84584	−0.352991
$779$	15.3794	0.551023
$780$	−4.21915	−0.151070
$781$	3.27699	0.117260
$782$	−5.24380	−0.187518
$783$	−5.12161	−0.183031
$784$	−5.48281	−0.195815
$785$	20.7498	0.740594
$786$	0.579803	0.0206809
$787$	9.81117	0.349730	0.174865	−	0.984592i	$-0.444051\pi$
$787$	9.81117	0.349730	0.174865	+	0.984592i	$0.444051\pi$
$788$	−19.9099	−0.709261
$789$	−15.4180	−0.548895
$790$	−1.89700	−0.0674924
$791$	11.5111	0.409289
$792$	−1.33294	−0.0473640
$793$	−12.3636	−0.439045
$794$	27.0890	0.961354
$795$	9.57456	0.339575
$796$	−10.8532	−0.384681
$797$	4.43107	0.156956	0.0784782	−	0.996916i	$-0.474994\pi$
$797$	4.43107	0.156956	0.0784782	+	0.996916i	$0.474994\pi$
$798$	−2.93795	−0.104002
$799$	−5.48284	−0.193969
$800$	3.05059	0.107855
$801$	−9.50534	−0.335855
$802$	−38.2155	−1.34944
$803$	−13.1207	−0.463020
$804$	−14.4176	−0.508469
$805$	−9.01817	−0.317849
$806$	−0.722103	−0.0254350
$807$	0.513904	0.0180903
$808$	3.12325	0.109875
$809$	−0.121244	−0.00426270	−0.00213135	−	0.999998i	$-0.500678\pi$
$809$	−0.121244	−0.00426270	−0.00213135	+	0.999998i	$0.500678\pi$
$810$	−1.39621	−0.0490579
$811$	39.1636	1.37522	0.687609	−	0.726081i	$-0.258660\pi$
$811$	39.1636	1.37522	0.687609	+	0.726081i	$0.258660\pi$
$812$	−6.30851	−0.221385
$813$	−0.211744	−0.00742619
$814$	−7.99681	−0.280288
$815$	10.1213	0.354534
$816$	−1.00000	−0.0350070
$817$	12.5013	0.437367
$818$	−11.5634	−0.404304
$819$	−3.72215	−0.130062
$820$	9.00256	0.314383
$821$	−22.4498	−0.783505	−0.391752	−	0.920071i	$-0.628131\pi$
$821$	−22.4498	−0.783505	−0.391752	+	0.920071i	$0.628131\pi$
$822$	−9.81475	−0.342329
$823$	−17.1175	−0.596678	−0.298339	−	0.954460i	$-0.596433\pi$
$823$	−17.1175	−0.596678	−0.298339	+	0.954460i	$0.596433\pi$
$824$	−15.3042	−0.533146
$825$	4.06625	0.141569
$826$	−1.23174	−0.0428579
$827$	−44.2346	−1.53819	−0.769094	−	0.639136i	$-0.779292\pi$
$827$	−44.2346	−1.53819	−0.769094	+	0.639136i	$0.779292\pi$
$828$	5.24380	0.182235
$829$	55.3045	1.92081	0.960403	−	0.278614i	$-0.0898752\pi$
$829$	55.3045	1.92081	0.960403	+	0.278614i	$0.0898752\pi$
$830$	−0.255880	−0.00888174
$831$	−25.6652	−0.890317
$832$	3.02185	0.104764
$833$	−5.48281	−0.189968
$834$	−1.30210	−0.0450880
$835$	23.5078	0.813522
$836$	3.17932	0.109959
$837$	−0.238960	−0.00825968
$838$	19.3900	0.669816
$839$	−43.0150	−1.48504	−0.742521	−	0.669823i	$-0.766370\pi$
$839$	−43.0150	−1.48504	−0.742521	+	0.669823i	$0.766370\pi$
$840$	−1.71978	−0.0593380
$841$	−2.76911	−0.0954866
$842$	−38.4482	−1.32501
$843$	20.1926	0.695470
$844$	−6.02741	−0.207472
$845$	−5.40112	−0.185804
$846$	5.48284	0.188504
$847$	11.3607	0.390359
$848$	−6.85752	−0.235488
$849$	−23.5657	−0.808771
$850$	3.05059	0.104634
$851$	31.4595	1.07842
$852$	−2.45847	−0.0842257
$853$	5.97823	0.204691	0.102345	−	0.994749i	$-0.467365\pi$
$853$	5.97823	0.204691	0.102345	+	0.994749i	$0.467365\pi$
$854$	−5.03957	−0.172450
$855$	3.33024	0.113892
$856$	−19.5560	−0.668411
$857$	−8.12750	−0.277630	−0.138815	−	0.990318i	$-0.544329\pi$
$857$	−8.12750	−0.277630	−0.138815	+	0.990318i	$0.544329\pi$
$858$	4.02795	0.137512
$859$	23.2508	0.793307	0.396653	−	0.917968i	$-0.370171\pi$
$859$	23.2508	0.793307	0.396653	+	0.917968i	$0.370171\pi$
$860$	7.31787	0.249537
$861$	7.94209	0.270666
$862$	−19.4651	−0.662983
$863$	−28.3579	−0.965312	−0.482656	−	0.875810i	$-0.660328\pi$
$863$	−28.3579	−0.965312	−0.482656	+	0.875810i	$0.660328\pi$
$864$	1.00000	0.0340207
$865$	−17.4896	−0.594663
$866$	−21.4455	−0.728747
$867$	−1.00000	−0.0339618
$868$	−0.294338	−0.00999049
$869$	1.81104	0.0614352
$870$	7.15086	0.242437
$871$	43.5678	1.47624
$872$	−10.3763	−0.351386
$873$	1.31659	0.0445597
$874$	−12.5075	−0.423072
$875$	13.8452	0.468054
$876$	9.84343	0.332579
$877$	31.9525	1.07896	0.539480	−	0.841999i	$-0.318621\pi$
$877$	31.9525	1.07896	0.539480	+	0.841999i	$0.318621\pi$
$878$	12.0458	0.406525
$879$	8.18650	0.276124
$880$	1.86107	0.0627366
$881$	−8.29509	−0.279469	−0.139734	−	0.990189i	$-0.544625\pi$
$881$	−8.29509	−0.279469	−0.139734	+	0.990189i	$0.544625\pi$
$882$	5.48281	0.184616
$883$	−47.1516	−1.58678	−0.793389	−	0.608715i	$-0.791685\pi$
$883$	−47.1516	−1.58678	−0.793389	+	0.608715i	$0.791685\pi$
$884$	3.02185	0.101636
$885$	1.39621	0.0469332
$886$	−35.4527	−1.19106
$887$	42.5563	1.42890	0.714450	−	0.699686i	$-0.246677\pi$
$887$	42.5563	1.42890	0.714450	+	0.699686i	$0.246677\pi$
$888$	5.99937	0.201326
$889$	11.4587	0.384311
$890$	13.2715	0.444861
$891$	1.33294	0.0446552
$892$	−6.10343	−0.204358
$893$	−13.0777	−0.437627
$894$	−7.26871	−0.243102
$895$	24.6551	0.824129
$896$	1.23174	0.0411497
$897$	−15.8460	−0.529082
$898$	−10.4628	−0.349148
$899$	1.22386	0.0408181
$900$	−3.05059	−0.101686
$901$	−6.85752	−0.228457
$902$	−8.59459	−0.286168
$903$	6.45585	0.214837
$904$	9.34541	0.310824
$905$	2.12338	0.0705837
$906$	−4.46621	−0.148380
$907$	−17.5953	−0.584242	−0.292121	−	0.956381i	$-0.594361\pi$
$907$	−17.5953	−0.584242	−0.292121	+	0.956381i	$0.594361\pi$
$908$	−22.7438	−0.754780
$909$	−3.12325	−0.103592
$910$	5.19692	0.172276
$911$	−7.12161	−0.235949	−0.117975	−	0.993017i	$-0.537640\pi$
$911$	−7.12161	−0.235949	−0.117975	+	0.993017i	$0.537640\pi$
$912$	−2.38520	−0.0789817
$913$	0.244285	0.00808464
$914$	−25.8809	−0.856065
$915$	5.71248	0.188849
$916$	29.1330	0.962582
$917$	−0.714169	−0.0235839
$918$	1.00000	0.0330049
$919$	−44.8470	−1.47936	−0.739682	−	0.672956i	$-0.765024\pi$
$919$	−44.8470	−1.47936	−0.739682	+	0.672956i	$0.765024\pi$
$920$	−7.32147	−0.241382
$921$	0.820077	0.0270225
$922$	13.0148	0.428619
$923$	7.42912	0.244533
$924$	1.64184	0.0540126
$925$	−18.3016	−0.601753
$926$	−35.2018	−1.15680
$927$	15.3042	0.502655
$928$	−5.12161	−0.168125
$929$	43.1047	1.41422	0.707110	−	0.707104i	$-0.249999\pi$
$929$	43.1047	1.41422	0.707110	+	0.707104i	$0.249999\pi$
$930$	0.333640	0.0109405
$931$	−13.0776	−0.428600
$932$	19.7915	0.648291
$933$	0.565621	0.0185176
$934$	25.3681	0.830071
$935$	1.86107	0.0608635
$936$	−3.02185	−0.0987723
$937$	5.56059	0.181657	0.0908283	−	0.995867i	$-0.471049\pi$
$937$	5.56059	0.181657	0.0908283	+	0.995867i	$0.471049\pi$
$938$	17.7588	0.579844
$939$	−3.77250	−0.123111
$940$	−7.65522	−0.249686
$941$	−27.1729	−0.885810	−0.442905	−	0.896569i	$-0.646052\pi$
$941$	−27.1729	−0.885810	−0.442905	+	0.896569i	$0.646052\pi$
$942$	14.8615	0.484214
$943$	33.8112	1.10104
$944$	−1.00000	−0.0325472
$945$	1.71978	0.0559444
$946$	−6.98624	−0.227142
$947$	−13.2653	−0.431065	−0.215532	−	0.976497i	$-0.569149\pi$
$947$	−13.2653	−0.431065	−0.215532	+	0.976497i	$0.569149\pi$
$948$	−1.35868	−0.0441278
$949$	−29.7454	−0.965576
$950$	7.27625	0.236073
$951$	−13.8954	−0.450589
$952$	1.23174	0.0399211
$953$	−13.2911	−0.430541	−0.215270	−	0.976555i	$-0.569063\pi$
$953$	−13.2911	−0.430541	−0.215270	+	0.976555i	$0.569063\pi$
$954$	6.85752	0.222020
$955$	3.02299	0.0978217
$956$	−20.7500	−0.671104
$957$	−6.82680	−0.220679
$958$	6.29957	0.203530
$959$	12.0893	0.390382
$960$	−1.39621	−0.0450626
$961$	−30.9429	−0.998158
$962$	−18.1292	−0.584509
$963$	19.5560	0.630184
$964$	−14.6805	−0.472827
$965$	36.2627	1.16734
$966$	−6.45902	−0.207816
$967$	−31.8430	−1.02400	−0.512002	−	0.858984i	$-0.671096\pi$
$967$	−31.8430	−1.02400	−0.512002	+	0.858984i	$0.671096\pi$
$968$	9.22327	0.296447
$969$	−2.38520	−0.0766235
$970$	−1.83823	−0.0590222
$971$	−19.2626	−0.618167	−0.309084	−	0.951035i	$-0.600022\pi$
$971$	−19.2626	−0.618167	−0.309084	+	0.951035i	$0.600022\pi$
$972$	−1.00000	−0.0320750
$973$	1.60385	0.0514172
$974$	1.07461	0.0344328
$975$	9.21843	0.295226
$976$	−4.09141	−0.130963
$977$	24.4202	0.781271	0.390635	−	0.920545i	$-0.372255\pi$
$977$	24.4202	0.781271	0.390635	+	0.920545i	$0.372255\pi$
$978$	7.24912	0.231801
$979$	−12.6700	−0.404936
$980$	−7.65517	−0.244535
$981$	10.3763	0.331290
$982$	15.9517	0.509040
$983$	−14.7485	−0.470404	−0.235202	−	0.971947i	$-0.575575\pi$
$983$	−14.7485	−0.470404	−0.235202	+	0.971947i	$0.575575\pi$
$984$	6.44784	0.205550
$985$	−27.7985	−0.885733
$986$	−5.12161	−0.163105
$987$	−6.75346	−0.214965
$988$	7.20771	0.229308
$989$	27.4840	0.873939
$990$	−1.86107	−0.0591487
$991$	−56.4977	−1.79471	−0.897355	−	0.441310i	$-0.854514\pi$
$991$	−56.4977	−1.79471	−0.897355	+	0.441310i	$0.854514\pi$
$992$	−0.238960	−0.00758700
$993$	−26.2630	−0.833433
$994$	3.02820	0.0960487
$995$	−15.1534	−0.480394
$996$	−0.183267	−0.00580705
$997$	−41.1781	−1.30412	−0.652061	−	0.758166i	$-0.726095\pi$
$997$	−41.1781	−1.30412	−0.652061	+	0.758166i	$0.726095\pi$
$998$	−32.3491	−1.02399
$999$	−5.99937	−0.189812

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.x.1.8	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.x.1.8	✓	10	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.39621 q^{5} +1.00000 q^{6} -1.23174 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.39621 q^{5} +1.00000 q^{6} -1.23174 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.39621 q^{10} +1.33294 q^{11} -1.00000 q^{12} +3.02185 q^{13} +1.23174 q^{14} -1.39621 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} +2.38520 q^{19} +1.39621 q^{20} +1.23174 q^{21} -1.33294 q^{22} +5.24380 q^{23} +1.00000 q^{24} -3.05059 q^{25} -3.02185 q^{26} -1.00000 q^{27} -1.23174 q^{28} +5.12161 q^{29} +1.39621 q^{30} +0.238960 q^{31} -1.00000 q^{32} -1.33294 q^{33} -1.00000 q^{34} -1.71978 q^{35} +1.00000 q^{36} +5.99937 q^{37} -2.38520 q^{38} -3.02185 q^{39} -1.39621 q^{40} +6.44784 q^{41} -1.23174 q^{42} +5.24123 q^{43} +1.33294 q^{44} +1.39621 q^{45} -5.24380 q^{46} -5.48284 q^{47} -1.00000 q^{48} -5.48281 q^{49} +3.05059 q^{50} -1.00000 q^{51} +3.02185 q^{52} -6.85752 q^{53} +1.00000 q^{54} +1.86107 q^{55} +1.23174 q^{56} -2.38520 q^{57} -5.12161 q^{58} -1.00000 q^{59} -1.39621 q^{60} -4.09141 q^{61} -0.238960 q^{62} -1.23174 q^{63} +1.00000 q^{64} +4.21915 q^{65} +1.33294 q^{66} +14.4176 q^{67} +1.00000 q^{68} -5.24380 q^{69} +1.71978 q^{70} +2.45847 q^{71} -1.00000 q^{72} -9.84343 q^{73} -5.99937 q^{74} +3.05059 q^{75} +2.38520 q^{76} -1.64184 q^{77} +3.02185 q^{78} +1.35868 q^{79} +1.39621 q^{80} +1.00000 q^{81} -6.44784 q^{82} +0.183267 q^{83} +1.23174 q^{84} +1.39621 q^{85} -5.24123 q^{86} -5.12161 q^{87} -1.33294 q^{88} -9.50534 q^{89} -1.39621 q^{90} -3.72215 q^{91} +5.24380 q^{92} -0.238960 q^{93} +5.48284 q^{94} +3.33024 q^{95} +1.00000 q^{96} +1.31659 q^{97} +5.48281 q^{98} +1.33294 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{2} - 10 q^{3} + 10 q^{4} + q^{5} + 10 q^{6} + 10 q^{7} - 10 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q - 10 * q^2 - 10 * q^3 + 10 * q^4 + q^5 + 10 * q^6 + 10 * q^7 - 10 * q^8 + 10 * q^9	\( 10 q - 10 q^{2} - 10 q^{3} + 10 q^{4} + q^{5} + 10 q^{6} + 10 q^{7} - 10 q^{8} + 10 q^{9} - q^{10} + 2 q^{11} - 10 q^{12} - 10 q^{14} - q^{15} + 10 q^{16} + 10 q^{17} - 10 q^{18} + 15 q^{19} + q^{20} - 10 q^{21} - 2 q^{22} + 19 q^{23} + 10 q^{24} + 19 q^{25} - 10 q^{27} + 10 q^{28} - q^{29} + q^{30} + 15 q^{31} - 10 q^{32} - 2 q^{33} - 10 q^{34} - 14 q^{35} + 10 q^{36} + q^{37} - 15 q^{38} - q^{40} - 5 q^{41} + 10 q^{42} + 26 q^{43} + 2 q^{44} + q^{45} - 19 q^{46} + 14 q^{47} - 10 q^{48} + 20 q^{49} - 19 q^{50} - 10 q^{51} - 2 q^{53} + 10 q^{54} + 4 q^{55} - 10 q^{56} - 15 q^{57} + q^{58} - 10 q^{59} - q^{60} + 4 q^{61} - 15 q^{62} + 10 q^{63} + 10 q^{64} - 20 q^{65} + 2 q^{66} + 15 q^{67} + 10 q^{68} - 19 q^{69} + 14 q^{70} + 14 q^{71} - 10 q^{72} + 43 q^{73} - q^{74} - 19 q^{75} + 15 q^{76} + 20 q^{77} + q^{80} + 10 q^{81} + 5 q^{82} - 4 q^{83} - 10 q^{84} + q^{85} - 26 q^{86} + q^{87} - 2 q^{88} - 22 q^{89} - q^{90} - q^{91} + 19 q^{92} - 15 q^{93} - 14 q^{94} - 37 q^{95} + 10 q^{96} + 37 q^{97} - 20 q^{98} + 2 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 - 10 * q^3 + 10 * q^4 + q^5 + 10 * q^6 + 10 * q^7 - 10 * q^8 + 10 * q^9 - q^10 + 2 * q^11 - 10 * q^12 - 10 * q^14 - q^15 + 10 * q^16 + 10 * q^17 - 10 * q^18 + 15 * q^19 + q^20 - 10 * q^21 - 2 * q^22 + 19 * q^23 + 10 * q^24 + 19 * q^25 - 10 * q^27 + 10 * q^28 - q^29 + q^30 + 15 * q^31 - 10 * q^32 - 2 * q^33 - 10 * q^34 - 14 * q^35 + 10 * q^36 + q^37 - 15 * q^38 - q^40 - 5 * q^41 + 10 * q^42 + 26 * q^43 + 2 * q^44 + q^45 - 19 * q^46 + 14 * q^47 - 10 * q^48 + 20 * q^49 - 19 * q^50 - 10 * q^51 - 2 * q^53 + 10 * q^54 + 4 * q^55 - 10 * q^56 - 15 * q^57 + q^58 - 10 * q^59 - q^60 + 4 * q^61 - 15 * q^62 + 10 * q^63 + 10 * q^64 - 20 * q^65 + 2 * q^66 + 15 * q^67 + 10 * q^68 - 19 * q^69 + 14 * q^70 + 14 * q^71 - 10 * q^72 + 43 * q^73 - q^74 - 19 * q^75 + 15 * q^76 + 20 * q^77 + q^80 + 10 * q^81 + 5 * q^82 - 4 * q^83 - 10 * q^84 + q^85 - 26 * q^86 + q^87 - 2 * q^88 - 22 * q^89 - q^90 - q^91 + 19 * q^92 - 15 * q^93 - 14 * q^94 - 37 * q^95 + 10 * q^96 + 37 * q^97 - 20 * q^98 + 2 * q^99

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