LMFDB - Embedded newform 6018.2.a.u.1.1

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			1.1
Root			$-1.12576$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.14251 q^{5} +1.00000 q^{6} -1.86106 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.14251 q^{5} +1.00000 q^{6} -1.86106 q^{7} -1.00000 q^{8} +1.00000 q^{9} +3.14251 q^{10} -1.90868 q^{11} -1.00000 q^{12} -0.598620 q^{13} +1.86106 q^{14} +3.14251 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} -2.79804 q^{19} -3.14251 q^{20} +1.86106 q^{21} +1.90868 q^{22} +6.06631 q^{23} +1.00000 q^{24} +4.87539 q^{25} +0.598620 q^{26} -1.00000 q^{27} -1.86106 q^{28} -0.0580368 q^{29} -3.14251 q^{30} -9.30117 q^{31} -1.00000 q^{32} +1.90868 q^{33} -1.00000 q^{34} +5.84842 q^{35} +1.00000 q^{36} -1.53439 q^{37} +2.79804 q^{38} +0.598620 q^{39} +3.14251 q^{40} +12.3401 q^{41} -1.86106 q^{42} +1.47691 q^{43} -1.90868 q^{44} -3.14251 q^{45} -6.06631 q^{46} +2.09247 q^{47} -1.00000 q^{48} -3.53644 q^{49} -4.87539 q^{50} -1.00000 q^{51} -0.598620 q^{52} -7.58796 q^{53} +1.00000 q^{54} +5.99804 q^{55} +1.86106 q^{56} +2.79804 q^{57} +0.0580368 q^{58} +1.00000 q^{59} +3.14251 q^{60} +15.1201 q^{61} +9.30117 q^{62} -1.86106 q^{63} +1.00000 q^{64} +1.88117 q^{65} -1.90868 q^{66} +10.7010 q^{67} +1.00000 q^{68} -6.06631 q^{69} -5.84842 q^{70} +1.96132 q^{71} -1.00000 q^{72} +1.82049 q^{73} +1.53439 q^{74} -4.87539 q^{75} -2.79804 q^{76} +3.55217 q^{77} -0.598620 q^{78} -11.9342 q^{79} -3.14251 q^{80} +1.00000 q^{81} -12.3401 q^{82} +16.2029 q^{83} +1.86106 q^{84} -3.14251 q^{85} -1.47691 q^{86} +0.0580368 q^{87} +1.90868 q^{88} +5.45500 q^{89} +3.14251 q^{90} +1.11407 q^{91} +6.06631 q^{92} +9.30117 q^{93} -2.09247 q^{94} +8.79288 q^{95} +1.00000 q^{96} +1.87586 q^{97} +3.53644 q^{98} -1.90868 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−3.14251	−1.40537	−0.702687	−	0.711499i	$-0.748017\pi$
$5$	−3.14251	−1.40537	−0.702687	+	0.711499i	$0.748017\pi$
$6$	1.00000	0.408248
$7$	−1.86106	−0.703416	−0.351708	−	0.936110i	$-0.614399\pi$
$7$	−1.86106	−0.703416	−0.351708	+	0.936110i	$0.614399\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	3.14251	0.993750
$11$	−1.90868	−0.575488	−0.287744	−	0.957707i	$-0.592905\pi$
$11$	−1.90868	−0.575488	−0.287744	+	0.957707i	$0.592905\pi$
$12$	−1.00000	−0.288675
$13$	−0.598620	−0.166027	−0.0830137	−	0.996548i	$-0.526455\pi$
$13$	−0.598620	−0.166027	−0.0830137	+	0.996548i	$0.526455\pi$
$14$	1.86106	0.497390
$15$	3.14251	0.811393
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.00000	−0.235702
$19$	−2.79804	−0.641914	−0.320957	−	0.947094i	$-0.604005\pi$
$19$	−2.79804	−0.641914	−0.320957	+	0.947094i	$0.604005\pi$
$20$	−3.14251	−0.702687
$21$	1.86106	0.406118
$22$	1.90868	0.406931
$23$	6.06631	1.26491	0.632456	−	0.774596i	$-0.282047\pi$
$23$	6.06631	1.26491	0.632456	+	0.774596i	$0.282047\pi$
$24$	1.00000	0.204124
$25$	4.87539	0.975078
$26$	0.598620	0.117399
$27$	−1.00000	−0.192450
$28$	−1.86106	−0.351708
$29$	−0.0580368	−0.0107772	−0.00538858	−	0.999985i	$-0.501715\pi$
$29$	−0.0580368	−0.0107772	−0.00538858	+	0.999985i	$0.501715\pi$
$30$	−3.14251	−0.573742
$31$	−9.30117	−1.67054	−0.835270	−	0.549840i	$-0.814689\pi$
$31$	−9.30117	−1.67054	−0.835270	+	0.549840i	$0.814689\pi$
$32$	−1.00000	−0.176777
$33$	1.90868	0.332258
$34$	−1.00000	−0.171499
$35$	5.84842	0.988564
$36$	1.00000	0.166667
$37$	−1.53439	−0.252252	−0.126126	−	0.992014i	$-0.540254\pi$
$37$	−1.53439	−0.252252	−0.126126	+	0.992014i	$0.540254\pi$
$38$	2.79804	0.453902
$39$	0.598620	0.0958559
$40$	3.14251	0.496875
$41$	12.3401	1.92721	0.963603	−	0.267336i	$-0.0861434\pi$
$41$	12.3401	1.92721	0.963603	+	0.267336i	$0.0861434\pi$
$42$	−1.86106	−0.287169
$43$	1.47691	0.225227	0.112613	−	0.993639i	$-0.464078\pi$
$43$	1.47691	0.225227	0.112613	+	0.993639i	$0.464078\pi$
$44$	−1.90868	−0.287744
$45$	−3.14251	−0.468458
$46$	−6.06631	−0.894428
$47$	2.09247	0.305218	0.152609	−	0.988287i	$-0.451232\pi$
$47$	2.09247	0.305218	0.152609	+	0.988287i	$0.451232\pi$
$48$	−1.00000	−0.144338
$49$	−3.53644	−0.505205
$50$	−4.87539	−0.689484
$51$	−1.00000	−0.140028
$52$	−0.598620	−0.0830137
$53$	−7.58796	−1.04229	−0.521143	−	0.853469i	$-0.674494\pi$
$53$	−7.58796	−1.04229	−0.521143	+	0.853469i	$0.674494\pi$
$54$	1.00000	0.136083
$55$	5.99804	0.808776
$56$	1.86106	0.248695
$57$	2.79804	0.370609
$58$	0.0580368	0.00762060
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	3.14251	0.405697
$61$	15.1201	1.93593	0.967964	−	0.251090i	$-0.0807891\pi$
$61$	15.1201	1.93593	0.967964	+	0.251090i	$0.0807891\pi$
$62$	9.30117	1.18125
$63$	−1.86106	−0.234472
$64$	1.00000	0.125000
$65$	1.88117	0.233331
$66$	−1.90868	−0.234942
$67$	10.7010	1.30734	0.653669	−	0.756781i	$-0.273229\pi$
$67$	10.7010	1.30734	0.653669	+	0.756781i	$0.273229\pi$
$68$	1.00000	0.121268
$69$	−6.06631	−0.730298
$70$	−5.84842	−0.699020
$71$	1.96132	0.232765	0.116383	−	0.993204i	$-0.462870\pi$
$71$	1.96132	0.232765	0.116383	+	0.993204i	$0.462870\pi$
$72$	−1.00000	−0.117851
$73$	1.82049	0.213072	0.106536	−	0.994309i	$-0.466024\pi$
$73$	1.82049	0.213072	0.106536	+	0.994309i	$0.466024\pi$
$74$	1.53439	0.178369
$75$	−4.87539	−0.562962
$76$	−2.79804	−0.320957
$77$	3.55217	0.404807
$78$	−0.598620	−0.0677804
$79$	−11.9342	−1.34271	−0.671353	−	0.741138i	$-0.734286\pi$
$79$	−11.9342	−1.34271	−0.671353	+	0.741138i	$0.734286\pi$
$80$	−3.14251	−0.351344
$81$	1.00000	0.111111
$82$	−12.3401	−1.36274
$83$	16.2029	1.77850	0.889250	−	0.457422i	$-0.151227\pi$
$83$	16.2029	1.77850	0.889250	+	0.457422i	$0.151227\pi$
$84$	1.86106	0.203059
$85$	−3.14251	−0.340853
$86$	−1.47691	−0.159259
$87$	0.0580368	0.00622220
$88$	1.90868	0.203466
$89$	5.45500	0.578229	0.289115	−	0.957295i	$-0.406639\pi$
$89$	5.45500	0.578229	0.289115	+	0.957295i	$0.406639\pi$
$90$	3.14251	0.331250
$91$	1.11407	0.116786
$92$	6.06631	0.632456
$93$	9.30117	0.964487
$94$	−2.09247	−0.215822
$95$	8.79288	0.902130
$96$	1.00000	0.102062
$97$	1.87586	0.190465	0.0952323	−	0.995455i	$-0.469641\pi$
$97$	1.87586	0.190465	0.0952323	+	0.995455i	$0.469641\pi$
$98$	3.53644	0.357234
$99$	−1.90868	−0.191829
$100$	4.87539	0.487539
$101$	−0.354613	−0.0352853	−0.0176427	−	0.999844i	$-0.505616\pi$
$101$	−0.354613	−0.0352853	−0.0176427	+	0.999844i	$0.505616\pi$
$102$	1.00000	0.0990148
$103$	−14.9092	−1.46905	−0.734525	−	0.678581i	$-0.762595\pi$
$103$	−14.9092	−1.46905	−0.734525	+	0.678581i	$0.762595\pi$
$104$	0.598620	0.0586995
$105$	−5.84842	−0.570747
$106$	7.58796	0.737008
$107$	8.18027	0.790817	0.395408	−	0.918505i	$-0.370603\pi$
$107$	8.18027	0.790817	0.395408	+	0.918505i	$0.370603\pi$
$108$	−1.00000	−0.0962250
$109$	16.3901	1.56989	0.784943	−	0.619568i	$-0.212692\pi$
$109$	16.3901	1.56989	0.784943	+	0.619568i	$0.212692\pi$
$110$	−5.99804	−0.571891
$111$	1.53439	0.145638
$112$	−1.86106	−0.175854
$113$	0.272035	0.0255909	0.0127954	−	0.999918i	$-0.495927\pi$
$113$	0.272035	0.0255909	0.0127954	+	0.999918i	$0.495927\pi$
$114$	−2.79804	−0.262060
$115$	−19.0635	−1.77768
$116$	−0.0580368	−0.00538858
$117$	−0.598620	−0.0553425
$118$	−1.00000	−0.0920575
$119$	−1.86106	−0.170604
$120$	−3.14251	−0.286871
$121$	−7.35695	−0.668814
$122$	−15.1201	−1.36891
$123$	−12.3401	−1.11267
$124$	−9.30117	−0.835270
$125$	0.391588	0.0350247
$126$	1.86106	0.165797
$127$	−16.3022	−1.44659	−0.723294	−	0.690540i	$-0.757373\pi$
$127$	−16.3022	−1.44659	−0.723294	+	0.690540i	$0.757373\pi$
$128$	−1.00000	−0.0883883
$129$	−1.47691	−0.130035
$130$	−1.88117	−0.164990
$131$	21.4814	1.87684	0.938421	−	0.345493i	$-0.112288\pi$
$131$	21.4814	1.87684	0.938421	+	0.345493i	$0.112288\pi$
$132$	1.90868	0.166129
$133$	5.20733	0.451533
$134$	−10.7010	−0.924427
$135$	3.14251	0.270464
$136$	−1.00000	−0.0857493
$137$	6.72615	0.574654	0.287327	−	0.957833i	$-0.407233\pi$
$137$	6.72615	0.574654	0.287327	+	0.957833i	$0.407233\pi$
$138$	6.06631	0.516399
$139$	5.74712	0.487464	0.243732	−	0.969843i	$-0.421628\pi$
$139$	5.74712	0.487464	0.243732	+	0.969843i	$0.421628\pi$
$140$	5.84842	0.494282
$141$	−2.09247	−0.176218
$142$	−1.96132	−0.164590
$143$	1.14257	0.0955467
$144$	1.00000	0.0833333
$145$	0.182381	0.0151460
$146$	−1.82049	−0.150665
$147$	3.53644	0.291680
$148$	−1.53439	−0.126126
$149$	−4.15571	−0.340449	−0.170224	−	0.985405i	$-0.554449\pi$
$149$	−4.15571	−0.340449	−0.170224	+	0.985405i	$0.554449\pi$
$150$	4.87539	0.398074
$151$	3.76515	0.306403	0.153202	−	0.988195i	$-0.451042\pi$
$151$	3.76515	0.306403	0.153202	+	0.988195i	$0.451042\pi$
$152$	2.79804	0.226951
$153$	1.00000	0.0808452
$154$	−3.55217	−0.286242
$155$	29.2291	2.34773
$156$	0.598620	0.0479280
$157$	−11.4685	−0.915284	−0.457642	−	0.889136i	$-0.651306\pi$
$157$	−11.4685	−0.915284	−0.457642	+	0.889136i	$0.651306\pi$
$158$	11.9342	0.949436
$159$	7.58796	0.601764
$160$	3.14251	0.248437
$161$	−11.2898	−0.889760
$162$	−1.00000	−0.0785674
$163$	−7.29454	−0.571352	−0.285676	−	0.958326i	$-0.592218\pi$
$163$	−7.29454	−0.571352	−0.285676	+	0.958326i	$0.592218\pi$
$164$	12.3401	0.963603
$165$	−5.99804	−0.466947
$166$	−16.2029	−1.25759
$167$	−17.7398	−1.37275	−0.686374	−	0.727249i	$-0.740799\pi$
$167$	−17.7398	−1.37275	−0.686374	+	0.727249i	$0.740799\pi$
$168$	−1.86106	−0.143584
$169$	−12.6417	−0.972435
$170$	3.14251	0.241020
$171$	−2.79804	−0.213971
$172$	1.47691	0.112613
$173$	6.87128	0.522414	0.261207	−	0.965283i	$-0.415879\pi$
$173$	6.87128	0.522414	0.261207	+	0.965283i	$0.415879\pi$
$174$	−0.0580368	−0.00439976
$175$	−9.07342	−0.685886
$176$	−1.90868	−0.143872
$177$	−1.00000	−0.0751646
$178$	−5.45500	−0.408870
$179$	−19.6437	−1.46824	−0.734121	−	0.679018i	$-0.762406\pi$
$179$	−19.6437	−1.46824	−0.734121	+	0.679018i	$0.762406\pi$
$180$	−3.14251	−0.234229
$181$	1.41315	0.105039	0.0525193	−	0.998620i	$-0.483275\pi$
$181$	1.41315	0.105039	0.0525193	+	0.998620i	$0.483275\pi$
$182$	−1.11407	−0.0825804
$183$	−15.1201	−1.11771
$184$	−6.06631	−0.447214
$185$	4.82184	0.354509
$186$	−9.30117	−0.681995
$187$	−1.90868	−0.139576
$188$	2.09247	0.152609
$189$	1.86106	0.135373
$190$	−8.79288	−0.637902
$191$	4.57387	0.330953	0.165477	−	0.986214i	$-0.447084\pi$
$191$	4.57387	0.330953	0.165477	+	0.986214i	$0.447084\pi$
$192$	−1.00000	−0.0721688
$193$	24.6726	1.77598	0.887988	−	0.459867i	$-0.152103\pi$
$193$	24.6726	1.77598	0.887988	+	0.459867i	$0.152103\pi$
$194$	−1.87586	−0.134679
$195$	−1.88117	−0.134714
$196$	−3.53644	−0.252603
$197$	3.81498	0.271806	0.135903	−	0.990722i	$-0.456606\pi$
$197$	3.81498	0.271806	0.135903	+	0.990722i	$0.456606\pi$
$198$	1.90868	0.135644
$199$	1.86102	0.131924	0.0659621	−	0.997822i	$-0.478988\pi$
$199$	1.86102	0.131924	0.0659621	+	0.997822i	$0.478988\pi$
$200$	−4.87539	−0.344742
$201$	−10.7010	−0.754792
$202$	0.354613	0.0249505
$203$	0.108010	0.00758083
$204$	−1.00000	−0.0700140
$205$	−38.7791	−2.70845
$206$	14.9092	1.03878
$207$	6.06631	0.421638
$208$	−0.598620	−0.0415068
$209$	5.34055	0.369414
$210$	5.84842	0.403579
$211$	7.91425	0.544839	0.272420	−	0.962179i	$-0.412176\pi$
$211$	7.91425	0.544839	0.272420	+	0.962179i	$0.412176\pi$
$212$	−7.58796	−0.521143
$213$	−1.96132	−0.134387
$214$	−8.18027	−0.559192
$215$	−4.64121	−0.316528
$216$	1.00000	0.0680414
$217$	17.3101	1.17508
$218$	−16.3901	−1.11008
$219$	−1.82049	−0.123017
$220$	5.99804	0.404388
$221$	−0.598620	−0.0402675
$222$	−1.53439	−0.102982
$223$	−18.3666	−1.22992	−0.614959	−	0.788559i	$-0.710827\pi$
$223$	−18.3666	−1.22992	−0.614959	+	0.788559i	$0.710827\pi$
$224$	1.86106	0.124348
$225$	4.87539	0.325026
$226$	−0.272035	−0.0180955
$227$	−4.93993	−0.327875	−0.163937	−	0.986471i	$-0.552419\pi$
$227$	−4.93993	−0.327875	−0.163937	+	0.986471i	$0.552419\pi$
$228$	2.79804	0.185305
$229$	−5.78391	−0.382212	−0.191106	−	0.981569i	$-0.561207\pi$
$229$	−5.78391	−0.382212	−0.191106	+	0.981569i	$0.561207\pi$
$230$	19.0635	1.25701
$231$	−3.55217	−0.233716
$232$	0.0580368	0.00381030
$233$	−16.2536	−1.06481	−0.532405	−	0.846490i	$-0.678712\pi$
$233$	−16.2536	−1.06481	−0.532405	+	0.846490i	$0.678712\pi$
$234$	0.598620	0.0391330
$235$	−6.57561	−0.428946
$236$	1.00000	0.0650945
$237$	11.9342	0.775211
$238$	1.86106	0.120635
$239$	7.83325	0.506691	0.253345	−	0.967376i	$-0.418469\pi$
$239$	7.83325	0.506691	0.253345	+	0.967376i	$0.418469\pi$
$240$	3.14251	0.202848
$241$	−5.49476	−0.353949	−0.176974	−	0.984215i	$-0.556631\pi$
$241$	−5.49476	−0.353949	−0.176974	+	0.984215i	$0.556631\pi$
$242$	7.35695	0.472923
$243$	−1.00000	−0.0641500
$244$	15.1201	0.967964
$245$	11.1133	0.710003
$246$	12.3401	0.786779
$247$	1.67496	0.106575
$248$	9.30117	0.590625
$249$	−16.2029	−1.02682
$250$	−0.391588	−0.0247662
$251$	−11.2099	−0.707560	−0.353780	−	0.935329i	$-0.615104\pi$
$251$	−11.2099	−0.707560	−0.353780	+	0.935329i	$0.615104\pi$
$252$	−1.86106	−0.117236
$253$	−11.5786	−0.727942
$254$	16.3022	1.02289
$255$	3.14251	0.196792
$256$	1.00000	0.0625000
$257$	−13.6981	−0.854466	−0.427233	−	0.904142i	$-0.640512\pi$
$257$	−13.6981	−0.854466	−0.427233	+	0.904142i	$0.640512\pi$
$258$	1.47691	0.0919485
$259$	2.85560	0.177438
$260$	1.88117	0.116665
$261$	−0.0580368	−0.00359239
$262$	−21.4814	−1.32713
$263$	−18.5784	−1.14560	−0.572798	−	0.819697i	$-0.694142\pi$
$263$	−18.5784	−1.14560	−0.572798	+	0.819697i	$0.694142\pi$
$264$	−1.90868	−0.117471
$265$	23.8453	1.46480
$266$	−5.20733	−0.319282
$267$	−5.45500	−0.333841
$268$	10.7010	0.653669
$269$	28.1773	1.71800	0.859001	−	0.511973i	$-0.171085\pi$
$269$	28.1773	1.71800	0.859001	+	0.511973i	$0.171085\pi$
$270$	−3.14251	−0.191247
$271$	15.3524	0.932590	0.466295	−	0.884629i	$-0.345589\pi$
$271$	15.3524	0.932590	0.466295	+	0.884629i	$0.345589\pi$
$272$	1.00000	0.0606339
$273$	−1.11407	−0.0674266
$274$	−6.72615	−0.406342
$275$	−9.30554	−0.561145
$276$	−6.06631	−0.365149
$277$	−7.29924	−0.438569	−0.219284	−	0.975661i	$-0.570372\pi$
$277$	−7.29924	−0.438569	−0.219284	+	0.975661i	$0.570372\pi$
$278$	−5.74712	−0.344689
$279$	−9.30117	−0.556847
$280$	−5.84842	−0.349510
$281$	−10.2946	−0.614126	−0.307063	−	0.951689i	$-0.599346\pi$
$281$	−10.2946	−0.614126	−0.307063	+	0.951689i	$0.599346\pi$
$282$	2.09247	0.124605
$283$	−11.1593	−0.663350	−0.331675	−	0.943394i	$-0.607614\pi$
$283$	−11.1593	−0.663350	−0.331675	+	0.943394i	$0.607614\pi$
$284$	1.96132	0.116383
$285$	−8.79288	−0.520845
$286$	−1.14257	−0.0675617
$287$	−22.9658	−1.35563
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	−0.182381	−0.0107098
$291$	−1.87586	−0.109965
$292$	1.82049	0.106536
$293$	−3.53990	−0.206803	−0.103401	−	0.994640i	$-0.532973\pi$
$293$	−3.53990	−0.206803	−0.103401	+	0.994640i	$0.532973\pi$
$294$	−3.53644	−0.206249
$295$	−3.14251	−0.182964
$296$	1.53439	0.0891846
$297$	1.90868	0.110753
$298$	4.15571	0.240734
$299$	−3.63141	−0.210010
$300$	−4.87539	−0.281481
$301$	−2.74863	−0.158428
$302$	−3.76515	−0.216660
$303$	0.354613	0.0203720
$304$	−2.79804	−0.160479
$305$	−47.5150	−2.72070
$306$	−1.00000	−0.0571662
$307$	15.1451	0.864378	0.432189	−	0.901783i	$-0.357741\pi$
$307$	15.1451	0.864378	0.432189	+	0.901783i	$0.357741\pi$
$308$	3.55217	0.202404
$309$	14.9092	0.848157
$310$	−29.2291	−1.66010
$311$	−27.9857	−1.58692	−0.793461	−	0.608621i	$-0.791723\pi$
$311$	−27.9857	−1.58692	−0.793461	+	0.608621i	$0.791723\pi$
$312$	−0.598620	−0.0338902
$313$	−18.6629	−1.05489	−0.527444	−	0.849590i	$-0.676850\pi$
$313$	−18.6629	−1.05489	−0.527444	+	0.849590i	$0.676850\pi$
$314$	11.4685	0.647204
$315$	5.84842	0.329521
$316$	−11.9342	−0.671353
$317$	−5.33071	−0.299403	−0.149701	−	0.988731i	$-0.547831\pi$
$317$	−5.33071	−0.299403	−0.149701	+	0.988731i	$0.547831\pi$
$318$	−7.58796	−0.425512
$319$	0.110773	0.00620212
$320$	−3.14251	−0.175672
$321$	−8.18027	−0.456578
$322$	11.2898	0.629156
$323$	−2.79804	−0.155687
$324$	1.00000	0.0555556
$325$	−2.91851	−0.161890
$326$	7.29454	0.404007
$327$	−16.3901	−0.906374
$328$	−12.3401	−0.681370
$329$	−3.89422	−0.214695
$330$	5.99804	0.330181
$331$	−6.46188	−0.355177	−0.177588	−	0.984105i	$-0.556830\pi$
$331$	−6.46188	−0.355177	−0.177588	+	0.984105i	$0.556830\pi$
$332$	16.2029	0.889250
$333$	−1.53439	−0.0840841
$334$	17.7398	0.970680
$335$	−33.6281	−1.83730
$336$	1.86106	0.101529
$337$	9.86479	0.537370	0.268685	−	0.963228i	$-0.413411\pi$
$337$	9.86479	0.537370	0.268685	+	0.963228i	$0.413411\pi$
$338$	12.6417	0.687615
$339$	−0.272035	−0.0147749
$340$	−3.14251	−0.170427
$341$	17.7529	0.961375
$342$	2.79804	0.151301
$343$	19.6090	1.05879
$344$	−1.47691	−0.0796297
$345$	19.0635	1.02634
$346$	−6.87128	−0.369403
$347$	9.75055	0.523437	0.261718	−	0.965144i	$-0.415711\pi$
$347$	9.75055	0.523437	0.261718	+	0.965144i	$0.415711\pi$
$348$	0.0580368	0.00311110
$349$	2.64990	0.141846	0.0709230	−	0.997482i	$-0.477406\pi$
$349$	2.64990	0.141846	0.0709230	+	0.997482i	$0.477406\pi$
$350$	9.07342	0.484995
$351$	0.598620	0.0319520
$352$	1.90868	0.101733
$353$	0.895285	0.0476512	0.0238256	−	0.999716i	$-0.492415\pi$
$353$	0.895285	0.0476512	0.0238256	+	0.999716i	$0.492415\pi$
$354$	1.00000	0.0531494
$355$	−6.16346	−0.327123
$356$	5.45500	0.289115
$357$	1.86106	0.0984980
$358$	19.6437	1.03820
$359$	24.1820	1.27627	0.638137	−	0.769923i	$-0.279705\pi$
$359$	24.1820	1.27627	0.638137	+	0.769923i	$0.279705\pi$
$360$	3.14251	0.165625
$361$	−11.1710	−0.587946
$362$	−1.41315	−0.0742735
$363$	7.35695	0.386140
$364$	1.11407	0.0583932
$365$	−5.72091	−0.299446
$366$	15.1201	0.790339
$367$	−7.64468	−0.399049	−0.199525	−	0.979893i	$-0.563940\pi$
$367$	−7.64468	−0.399049	−0.199525	+	0.979893i	$0.563940\pi$
$368$	6.06631	0.316228
$369$	12.3401	0.642402
$370$	−4.82184	−0.250676
$371$	14.1217	0.733161
$372$	9.30117	0.482243
$373$	0.359609	0.0186199	0.00930993	−	0.999957i	$-0.497037\pi$
$373$	0.359609	0.0186199	0.00930993	+	0.999957i	$0.497037\pi$
$374$	1.90868	0.0986953
$375$	−0.391588	−0.0202215
$376$	−2.09247	−0.107911
$377$	0.0347420	0.00178930
$378$	−1.86106	−0.0957228
$379$	26.7145	1.37223	0.686117	−	0.727491i	$-0.259314\pi$
$379$	26.7145	1.37223	0.686117	+	0.727491i	$0.259314\pi$
$380$	8.79288	0.451065
$381$	16.3022	0.835188
$382$	−4.57387	−0.234019
$383$	−6.58131	−0.336289	−0.168145	−	0.985762i	$-0.553778\pi$
$383$	−6.58131	−0.336289	−0.168145	+	0.985762i	$0.553778\pi$
$384$	1.00000	0.0510310
$385$	−11.1627	−0.568906
$386$	−24.6726	−1.25580
$387$	1.47691	0.0750756
$388$	1.87586	0.0952323
$389$	−39.1368	−1.98432	−0.992158	−	0.124990i	$-0.960110\pi$
$389$	−39.1368	−1.98432	−0.992158	+	0.124990i	$0.960110\pi$
$390$	1.88117	0.0952568
$391$	6.06631	0.306786
$392$	3.53644	0.178617
$393$	−21.4814	−1.08360
$394$	−3.81498	−0.192196
$395$	37.5035	1.88700
$396$	−1.90868	−0.0959146
$397$	19.8735	0.997420	0.498710	−	0.866769i	$-0.333807\pi$
$397$	19.8735	0.997420	0.498710	+	0.866769i	$0.333807\pi$
$398$	−1.86102	−0.0932845
$399$	−5.20733	−0.260693
$400$	4.87539	0.243770
$401$	−23.6493	−1.18099	−0.590495	−	0.807041i	$-0.701067\pi$
$401$	−23.6493	−1.18099	−0.590495	+	0.807041i	$0.701067\pi$
$402$	10.7010	0.533718
$403$	5.56787	0.277355
$404$	−0.354613	−0.0176427
$405$	−3.14251	−0.156153
$406$	−0.108010	−0.00536046
$407$	2.92865	0.145168
$408$	1.00000	0.0495074
$409$	−11.5307	−0.570158	−0.285079	−	0.958504i	$-0.592020\pi$
$409$	−11.5307	−0.570158	−0.285079	+	0.958504i	$0.592020\pi$
$410$	38.7791	1.91516
$411$	−6.72615	−0.331777
$412$	−14.9092	−0.734525
$413$	−1.86106	−0.0915770
$414$	−6.06631	−0.298143
$415$	−50.9178	−2.49946
$416$	0.598620	0.0293498
$417$	−5.74712	−0.281438
$418$	−5.34055	−0.261215
$419$	−6.47921	−0.316530	−0.158265	−	0.987397i	$-0.550590\pi$
$419$	−6.47921	−0.316530	−0.158265	+	0.987397i	$0.550590\pi$
$420$	−5.84842	−0.285374
$421$	−1.57699	−0.0768580	−0.0384290	−	0.999261i	$-0.512235\pi$
$421$	−1.57699	−0.0768580	−0.0384290	+	0.999261i	$0.512235\pi$
$422$	−7.91425	−0.385259
$423$	2.09247	0.101739
$424$	7.58796	0.368504
$425$	4.87539	0.236491
$426$	1.96132	0.0950261
$427$	−28.1394	−1.36176
$428$	8.18027	0.395408
$429$	−1.14257	−0.0551639
$430$	4.64121	0.223819
$431$	19.5195	0.940222	0.470111	−	0.882607i	$-0.344214\pi$
$431$	19.5195	0.940222	0.470111	+	0.882607i	$0.344214\pi$
$432$	−1.00000	−0.0481125
$433$	−23.7483	−1.14127	−0.570636	−	0.821203i	$-0.693303\pi$
$433$	−23.7483	−1.14127	−0.570636	+	0.821203i	$0.693303\pi$
$434$	−17.3101	−0.830911
$435$	−0.182381	−0.00874452
$436$	16.3901	0.784943
$437$	−16.9738	−0.811966
$438$	1.82049	0.0869863
$439$	−35.8678	−1.71188	−0.855938	−	0.517079i	$-0.827019\pi$
$439$	−35.8678	−1.71188	−0.855938	+	0.517079i	$0.827019\pi$
$440$	−5.99804	−0.285945
$441$	−3.53644	−0.168402
$442$	0.598620	0.0284735
$443$	−30.7025	−1.45872	−0.729360	−	0.684131i	$-0.760182\pi$
$443$	−30.7025	−1.45872	−0.729360	+	0.684131i	$0.760182\pi$
$444$	1.53439	0.0728189
$445$	−17.1424	−0.812628
$446$	18.3666	0.869683
$447$	4.15571	0.196558
$448$	−1.86106	−0.0879270
$449$	−3.86029	−0.182178	−0.0910892	−	0.995843i	$-0.529035\pi$
$449$	−3.86029	−0.182178	−0.0910892	+	0.995843i	$0.529035\pi$
$450$	−4.87539	−0.229828
$451$	−23.5533	−1.10908
$452$	0.272035	0.0127954
$453$	−3.76515	−0.176902
$454$	4.93993	0.231842
$455$	−3.50098	−0.164129
$456$	−2.79804	−0.131030
$457$	−30.6656	−1.43447	−0.717237	−	0.696829i	$-0.754594\pi$
$457$	−30.6656	−1.43447	−0.717237	+	0.696829i	$0.754594\pi$
$458$	5.78391	0.270264
$459$	−1.00000	−0.0466760
$460$	−19.0635	−0.888838
$461$	33.1352	1.54326	0.771630	−	0.636072i	$-0.219442\pi$
$461$	33.1352	1.54326	0.771630	+	0.636072i	$0.219442\pi$
$462$	3.55217	0.165262
$463$	−26.9844	−1.25407	−0.627036	−	0.778990i	$-0.715732\pi$
$463$	−26.9844	−1.25407	−0.627036	+	0.778990i	$0.715732\pi$
$464$	−0.0580368	−0.00269429
$465$	−29.2291	−1.35546
$466$	16.2536	0.752935
$467$	19.8835	0.920098	0.460049	−	0.887894i	$-0.347832\pi$
$467$	19.8835	0.920098	0.460049	+	0.887894i	$0.347832\pi$
$468$	−0.598620	−0.0276712
$469$	−19.9153	−0.919603
$470$	6.57561	0.303310
$471$	11.4685	0.528440
$472$	−1.00000	−0.0460287
$473$	−2.81895	−0.129615
$474$	−11.9342	−0.548157
$475$	−13.6415	−0.625917
$476$	−1.86106	−0.0853018
$477$	−7.58796	−0.347429
$478$	−7.83325	−0.358284
$479$	3.62156	0.165473	0.0827366	−	0.996571i	$-0.473634\pi$
$479$	3.62156	0.165473	0.0827366	+	0.996571i	$0.473634\pi$
$480$	−3.14251	−0.143435
$481$	0.918517	0.0418808
$482$	5.49476	0.250280
$483$	11.2898	0.513703
$484$	−7.35695	−0.334407
$485$	−5.89491	−0.267674
$486$	1.00000	0.0453609
$487$	−3.29761	−0.149429	−0.0747145	−	0.997205i	$-0.523805\pi$
$487$	−3.29761	−0.149429	−0.0747145	+	0.997205i	$0.523805\pi$
$488$	−15.1201	−0.684454
$489$	7.29454	0.329870
$490$	−11.1133	−0.502048
$491$	3.68978	0.166518	0.0832588	−	0.996528i	$-0.473467\pi$
$491$	3.68978	0.166518	0.0832588	+	0.996528i	$0.473467\pi$
$492$	−12.3401	−0.556337
$493$	−0.0580368	−0.00261385
$494$	−1.67496	−0.0753601
$495$	5.99804	0.269592
$496$	−9.30117	−0.417635
$497$	−3.65014	−0.163731
$498$	16.2029	0.726069
$499$	20.7578	0.929246	0.464623	−	0.885508i	$-0.346190\pi$
$499$	20.7578	0.929246	0.464623	+	0.885508i	$0.346190\pi$
$500$	0.391588	0.0175123
$501$	17.7398	0.792557
$502$	11.2099	0.500321
$503$	−35.7200	−1.59268	−0.796338	−	0.604852i	$-0.793232\pi$
$503$	−35.7200	−1.59268	−0.796338	+	0.604852i	$0.793232\pi$
$504$	1.86106	0.0828984
$505$	1.11438	0.0495891
$506$	11.5786	0.514733
$507$	12.6417	0.561436
$508$	−16.3022	−0.723294
$509$	36.2571	1.60707	0.803533	−	0.595260i	$-0.202951\pi$
$509$	36.2571	1.60707	0.803533	+	0.595260i	$0.202951\pi$
$510$	−3.14251	−0.139153
$511$	−3.38805	−0.149878
$512$	−1.00000	−0.0441942
$513$	2.79804	0.123536
$514$	13.6981	0.604198
$515$	46.8525	2.06457
$516$	−1.47691	−0.0650174
$517$	−3.99385	−0.175649
$518$	−2.85560	−0.125468
$519$	−6.87128	−0.301616
$520$	−1.88117	−0.0824948
$521$	3.29763	0.144472	0.0722360	−	0.997388i	$-0.476987\pi$
$521$	3.29763	0.144472	0.0722360	+	0.997388i	$0.476987\pi$
$522$	0.0580368	0.00254020
$523$	−0.897541	−0.0392467	−0.0196234	−	0.999807i	$-0.506247\pi$
$523$	−0.897541	−0.0392467	−0.0196234	+	0.999807i	$0.506247\pi$
$524$	21.4814	0.938421
$525$	9.07342	0.395996
$526$	18.5784	0.810059
$527$	−9.30117	−0.405165
$528$	1.90868	0.0830645
$529$	13.8001	0.600005
$530$	−23.8453	−1.03577
$531$	1.00000	0.0433963
$532$	5.20733	0.225767
$533$	−7.38706	−0.319969
$534$	5.45500	0.236061
$535$	−25.7066	−1.11139
$536$	−10.7010	−0.462214
$537$	19.6437	0.847690
$538$	−28.1773	−1.21481
$539$	6.74992	0.290740
$540$	3.14251	0.135232
$541$	1.03530	0.0445110	0.0222555	−	0.999752i	$-0.492915\pi$
$541$	1.03530	0.0445110	0.0222555	+	0.999752i	$0.492915\pi$
$542$	−15.3524	−0.659441
$543$	−1.41315	−0.0606440
$544$	−1.00000	−0.0428746
$545$	−51.5061	−2.20628
$546$	1.11407	0.0476778
$547$	10.3399	0.442104	0.221052	−	0.975262i	$-0.429051\pi$
$547$	10.3399	0.442104	0.221052	+	0.975262i	$0.429051\pi$
$548$	6.72615	0.287327
$549$	15.1201	0.645309
$550$	9.30554	0.396790
$551$	0.162389	0.00691802
$552$	6.06631	0.258199
$553$	22.2104	0.944481
$554$	7.29924	0.310115
$555$	−4.82184	−0.204676
$556$	5.74712	0.243732
$557$	3.20934	0.135984	0.0679920	−	0.997686i	$-0.478341\pi$
$557$	3.20934	0.135984	0.0679920	+	0.997686i	$0.478341\pi$
$558$	9.30117	0.393750
$559$	−0.884109	−0.0373938
$560$	5.84842	0.247141
$561$	1.90868	0.0805844
$562$	10.2946	0.434252
$563$	41.9631	1.76853	0.884267	−	0.466982i	$-0.154659\pi$
$563$	41.9631	1.76853	0.884267	+	0.466982i	$0.154659\pi$
$564$	−2.09247	−0.0881089
$565$	−0.854872	−0.0359648
$566$	11.1593	0.469060
$567$	−1.86106	−0.0781574
$568$	−1.96132	−0.0822950
$569$	−1.36078	−0.0570467	−0.0285233	−	0.999593i	$-0.509080\pi$
$569$	−1.36078	−0.0570467	−0.0285233	+	0.999593i	$0.509080\pi$
$570$	8.79288	0.368293
$571$	−25.8025	−1.07980	−0.539901	−	0.841728i	$-0.681538\pi$
$571$	−25.8025	−1.07980	−0.539901	+	0.841728i	$0.681538\pi$
$572$	1.14257	0.0477733
$573$	−4.57387	−0.191076
$574$	22.9658	0.958574
$575$	29.5756	1.23339
$576$	1.00000	0.0416667
$577$	24.2000	1.00746	0.503730	−	0.863861i	$-0.331961\pi$
$577$	24.2000	1.00746	0.503730	+	0.863861i	$0.331961\pi$
$578$	−1.00000	−0.0415945
$579$	−24.6726	−1.02536
$580$	0.182381	0.00757298
$581$	−30.1546	−1.25103
$582$	1.87586	0.0777569
$583$	14.4830	0.599823
$584$	−1.82049	−0.0753324
$585$	1.88117	0.0777769
$586$	3.53990	0.146232
$587$	−4.68153	−0.193228	−0.0966138	−	0.995322i	$-0.530801\pi$
$587$	−4.68153	−0.193228	−0.0966138	+	0.995322i	$0.530801\pi$
$588$	3.53644	0.145840
$589$	26.0250	1.07234
$590$	3.14251	0.129375
$591$	−3.81498	−0.156927
$592$	−1.53439	−0.0630630
$593$	−3.54913	−0.145745	−0.0728727	−	0.997341i	$-0.523217\pi$
$593$	−3.54913	−0.145745	−0.0728727	+	0.997341i	$0.523217\pi$
$594$	−1.90868	−0.0783140
$595$	5.84842	0.239762
$596$	−4.15571	−0.170224
$597$	−1.86102	−0.0761665
$598$	3.63141	0.148500
$599$	−9.71087	−0.396775	−0.198388	−	0.980124i	$-0.563570\pi$
$599$	−9.71087	−0.396775	−0.198388	+	0.980124i	$0.563570\pi$
$600$	4.87539	0.199037
$601$	41.2484	1.68256	0.841280	−	0.540600i	$-0.181803\pi$
$601$	41.2484	1.68256	0.841280	+	0.540600i	$0.181803\pi$
$602$	2.74863	0.112026
$603$	10.7010	0.435779
$604$	3.76515	0.153202
$605$	23.1193	0.939934
$606$	−0.354613	−0.0144052
$607$	10.7455	0.436148	0.218074	−	0.975932i	$-0.430023\pi$
$607$	10.7455	0.436148	0.218074	+	0.975932i	$0.430023\pi$
$608$	2.79804	0.113476
$609$	−0.108010	−0.00437680
$610$	47.5150	1.92383
$611$	−1.25259	−0.0506745
$612$	1.00000	0.0404226
$613$	−42.8545	−1.73088	−0.865439	−	0.501015i	$-0.832960\pi$
$613$	−42.8545	−1.73088	−0.865439	+	0.501015i	$0.832960\pi$
$614$	−15.1451	−0.611207
$615$	38.7791	1.56372
$616$	−3.55217	−0.143121
$617$	12.5734	0.506186	0.253093	−	0.967442i	$-0.418552\pi$
$617$	12.5734	0.506186	0.253093	+	0.967442i	$0.418552\pi$
$618$	−14.9092	−0.599737
$619$	−30.9707	−1.24482	−0.622409	−	0.782692i	$-0.713846\pi$
$619$	−30.9707	−1.24482	−0.622409	+	0.782692i	$0.713846\pi$
$620$	29.2291	1.17387
$621$	−6.06631	−0.243433
$622$	27.9857	1.12212
$623$	−10.1521	−0.406736
$624$	0.598620	0.0239640
$625$	−25.6075	−1.02430
$626$	18.6629	0.745918
$627$	−5.34055	−0.213281
$628$	−11.4685	−0.457642
$629$	−1.53439	−0.0611801
$630$	−5.84842	−0.233007
$631$	36.5580	1.45535	0.727676	−	0.685921i	$-0.240601\pi$
$631$	36.5580	1.45535	0.727676	+	0.685921i	$0.240601\pi$
$632$	11.9342	0.474718
$633$	−7.91425	−0.314563
$634$	5.33071	0.211710
$635$	51.2299	2.03300
$636$	7.58796	0.300882
$637$	2.11698	0.0838779
$638$	−0.110773	−0.00438556
$639$	1.96132	0.0775885
$640$	3.14251	0.124219
$641$	−48.2160	−1.90442	−0.952208	−	0.305451i	$-0.901193\pi$
$641$	−48.2160	−1.90442	−0.952208	+	0.305451i	$0.901193\pi$
$642$	8.18027	0.322850
$643$	−5.90006	−0.232675	−0.116338	−	0.993210i	$-0.537115\pi$
$643$	−5.90006	−0.232675	−0.116338	+	0.993210i	$0.537115\pi$
$644$	−11.2898	−0.444880
$645$	4.64121	0.182748
$646$	2.79804	0.110087
$647$	−41.2781	−1.62281	−0.811406	−	0.584483i	$-0.801297\pi$
$647$	−41.2781	−1.62281	−0.811406	+	0.584483i	$0.801297\pi$
$648$	−1.00000	−0.0392837
$649$	−1.90868	−0.0749221
$650$	2.91851	0.114473
$651$	−17.3101	−0.678436
$652$	−7.29454	−0.285676
$653$	41.0822	1.60767	0.803834	−	0.594853i	$-0.202790\pi$
$653$	41.0822	1.60767	0.803834	+	0.594853i	$0.202790\pi$
$654$	16.3901	0.640903
$655$	−67.5057	−2.63767
$656$	12.3401	0.481802
$657$	1.82049	0.0710240
$658$	3.89422	0.151813
$659$	−9.72224	−0.378725	−0.189362	−	0.981907i	$-0.560642\pi$
$659$	−9.72224	−0.378725	−0.189362	+	0.981907i	$0.560642\pi$
$660$	−5.99804	−0.233473
$661$	48.5684	1.88909	0.944547	−	0.328377i	$-0.106502\pi$
$661$	48.5684	1.88909	0.944547	+	0.328377i	$0.106502\pi$
$662$	6.46188	0.251148
$663$	0.598620	0.0232485
$664$	−16.2029	−0.628795
$665$	−16.3641	−0.634573
$666$	1.53439	0.0594564
$667$	−0.352069	−0.0136322
$668$	−17.7398	−0.686374
$669$	18.3666	0.710094
$670$	33.6281	1.29917
$671$	−28.8593	−1.11410
$672$	−1.86106	−0.0717921
$673$	30.9484	1.19297	0.596486	−	0.802624i	$-0.296563\pi$
$673$	30.9484	1.19297	0.596486	+	0.802624i	$0.296563\pi$
$674$	−9.86479	−0.379978
$675$	−4.87539	−0.187654
$676$	−12.6417	−0.486217
$677$	−21.5578	−0.828533	−0.414267	−	0.910156i	$-0.635962\pi$
$677$	−21.5578	−0.828533	−0.414267	+	0.910156i	$0.635962\pi$
$678$	0.272035	0.0104474
$679$	−3.49110	−0.133976
$680$	3.14251	0.120510
$681$	4.93993	0.189299
$682$	−17.7529	−0.679795
$683$	−48.8989	−1.87107	−0.935533	−	0.353240i	$-0.885080\pi$
$683$	−48.8989	−1.87107	−0.935533	+	0.353240i	$0.885080\pi$
$684$	−2.79804	−0.106986
$685$	−21.1370	−0.807604
$686$	−19.6090	−0.748675
$687$	5.78391	0.220670
$688$	1.47691	0.0563067
$689$	4.54230	0.173048
$690$	−19.0635	−0.725733
$691$	−41.5151	−1.57931	−0.789654	−	0.613552i	$-0.789740\pi$
$691$	−41.5151	−1.57931	−0.789654	+	0.613552i	$0.789740\pi$
$692$	6.87128	0.261207
$693$	3.55217	0.134936
$694$	−9.75055	−0.370126
$695$	−18.0604	−0.685070
$696$	−0.0580368	−0.00219988
$697$	12.3401	0.467416
$698$	−2.64990	−0.100300
$699$	16.2536	0.614769
$700$	−9.07342	−0.342943
$701$	15.8052	0.596953	0.298476	−	0.954417i	$-0.403522\pi$
$701$	15.8052	0.596953	0.298476	+	0.954417i	$0.403522\pi$
$702$	−0.598620	−0.0225935
$703$	4.29329	0.161924
$704$	−1.90868	−0.0719360
$705$	6.57561	0.247652
$706$	−0.895285	−0.0336945
$707$	0.659958	0.0248203
$708$	−1.00000	−0.0375823
$709$	2.50063	0.0939130	0.0469565	−	0.998897i	$-0.485048\pi$
$709$	2.50063	0.0939130	0.0469565	+	0.998897i	$0.485048\pi$
$710$	6.16346	0.231311
$711$	−11.9342	−0.447568
$712$	−5.45500	−0.204435
$713$	−56.4238	−2.11309
$714$	−1.86106	−0.0696486
$715$	−3.59055	−0.134279
$716$	−19.6437	−0.734121
$717$	−7.83325	−0.292538
$718$	−24.1820	−0.902462
$719$	1.43858	0.0536500	0.0268250	−	0.999640i	$-0.491460\pi$
$719$	1.43858	0.0536500	0.0268250	+	0.999640i	$0.491460\pi$
$720$	−3.14251	−0.117115
$721$	27.7471	1.03335
$722$	11.1710	0.415741
$723$	5.49476	0.204352
$724$	1.41315	0.0525193
$725$	−0.282952	−0.0105086
$726$	−7.35695	−0.273042
$727$	−25.5769	−0.948595	−0.474297	−	0.880365i	$-0.657298\pi$
$727$	−25.5769	−0.948595	−0.474297	+	0.880365i	$0.657298\pi$
$728$	−1.11407	−0.0412902
$729$	1.00000	0.0370370
$730$	5.72091	0.211740
$731$	1.47691	0.0546255
$732$	−15.1201	−0.558854
$733$	−33.2668	−1.22874	−0.614368	−	0.789020i	$-0.710589\pi$
$733$	−33.2668	−1.22874	−0.614368	+	0.789020i	$0.710589\pi$
$734$	7.64468	0.282170
$735$	−11.1133	−0.409920
$736$	−6.06631	−0.223607
$737$	−20.4248	−0.752357
$738$	−12.3401	−0.454247
$739$	40.7673	1.49965	0.749824	−	0.661637i	$-0.230138\pi$
$739$	40.7673	1.49965	0.749824	+	0.661637i	$0.230138\pi$
$740$	4.82184	0.177254
$741$	−1.67496	−0.0615313
$742$	−14.1217	−0.518423
$743$	−10.3232	−0.378723	−0.189362	−	0.981907i	$-0.560642\pi$
$743$	−10.3232	−0.378723	−0.189362	+	0.981907i	$0.560642\pi$
$744$	−9.30117	−0.340997
$745$	13.0594	0.478458
$746$	−0.359609	−0.0131662
$747$	16.2029	0.592833
$748$	−1.90868	−0.0697881
$749$	−15.2240	−0.556274
$750$	0.391588	0.0142988
$751$	13.2524	0.483585	0.241793	−	0.970328i	$-0.422265\pi$
$751$	13.2524	0.483585	0.241793	+	0.970328i	$0.422265\pi$
$752$	2.09247	0.0763045
$753$	11.2099	0.408510
$754$	−0.0347420	−0.00126523
$755$	−11.8320	−0.430612
$756$	1.86106	0.0676863
$757$	−35.5662	−1.29268	−0.646338	−	0.763051i	$-0.723700\pi$
$757$	−35.5662	−1.29268	−0.646338	+	0.763051i	$0.723700\pi$
$758$	−26.7145	−0.970316
$759$	11.5786	0.420277
$760$	−8.79288	−0.318951
$761$	6.12212	0.221927	0.110963	−	0.993825i	$-0.464606\pi$
$761$	6.12212	0.221927	0.110963	+	0.993825i	$0.464606\pi$
$762$	−16.3022	−0.590567
$763$	−30.5030	−1.10428
$764$	4.57387	0.165477
$765$	−3.14251	−0.113618
$766$	6.58131	0.237792
$767$	−0.598620	−0.0216149
$768$	−1.00000	−0.0360844
$769$	20.7532	0.748380	0.374190	−	0.927352i	$-0.377921\pi$
$769$	20.7532	0.748380	0.374190	+	0.927352i	$0.377921\pi$
$770$	11.1627	0.402277
$771$	13.6981	0.493326
$772$	24.6726	0.887988
$773$	−11.0940	−0.399022	−0.199511	−	0.979896i	$-0.563935\pi$
$773$	−11.0940	−0.399022	−0.199511	+	0.979896i	$0.563935\pi$
$774$	−1.47691	−0.0530865
$775$	−45.3468	−1.62891
$776$	−1.87586	−0.0673394
$777$	−2.85560	−0.102444
$778$	39.1368	1.40312
$779$	−34.5282	−1.23710
$780$	−1.88117	−0.0673568
$781$	−3.74352	−0.133954
$782$	−6.06631	−0.216931
$783$	0.0580368	0.00207407
$784$	−3.53644	−0.126301
$785$	36.0399	1.28632
$786$	21.4814	0.766218
$787$	−43.6838	−1.55716	−0.778579	−	0.627546i	$-0.784059\pi$
$787$	−43.6838	−1.55716	−0.778579	+	0.627546i	$0.784059\pi$
$788$	3.81498	0.135903
$789$	18.5784	0.661410
$790$	−37.5035	−1.33431
$791$	−0.506274	−0.0180010
$792$	1.90868	0.0678219
$793$	−9.05118	−0.321417
$794$	−19.8735	−0.705283
$795$	−23.8453	−0.845704
$796$	1.86102	0.0659621
$797$	30.6357	1.08517	0.542586	−	0.840001i	$-0.317445\pi$
$797$	30.6357	1.08517	0.542586	+	0.840001i	$0.317445\pi$
$798$	5.20733	0.184338
$799$	2.09247	0.0740262
$800$	−4.87539	−0.172371
$801$	5.45500	0.192743
$802$	23.6493	0.835086
$803$	−3.47472	−0.122620
$804$	−10.7010	−0.377396
$805$	35.4783	1.25045
$806$	−5.56787	−0.196120
$807$	−28.1773	−0.991889
$808$	0.354613	0.0124752
$809$	−34.8608	−1.22564	−0.612820	−	0.790222i	$-0.709965\pi$
$809$	−34.8608	−1.22564	−0.612820	+	0.790222i	$0.709965\pi$
$810$	3.14251	0.110417
$811$	−44.8939	−1.57644	−0.788220	−	0.615394i	$-0.788997\pi$
$811$	−44.8939	−1.57644	−0.788220	+	0.615394i	$0.788997\pi$
$812$	0.108010	0.00379042
$813$	−15.3524	−0.538431
$814$	−2.92865	−0.102649
$815$	22.9232	0.802964
$816$	−1.00000	−0.0350070
$817$	−4.13246	−0.144576
$818$	11.5307	0.403162
$819$	1.11407	0.0389288
$820$	−38.7791	−1.35422
$821$	−30.2437	−1.05551	−0.527756	−	0.849396i	$-0.676967\pi$
$821$	−30.2437	−1.05551	−0.527756	+	0.849396i	$0.676967\pi$
$822$	6.72615	0.234602
$823$	5.02773	0.175256	0.0876279	−	0.996153i	$-0.472071\pi$
$823$	5.02773	0.175256	0.0876279	+	0.996153i	$0.472071\pi$
$824$	14.9092	0.519388
$825$	9.30554	0.323977
$826$	1.86106	0.0647547
$827$	−15.8411	−0.550848	−0.275424	−	0.961323i	$-0.588818\pi$
$827$	−15.8411	−0.550848	−0.275424	+	0.961323i	$0.588818\pi$
$828$	6.06631	0.210819
$829$	35.0633	1.21780	0.608899	−	0.793248i	$-0.291612\pi$
$829$	35.0633	1.21780	0.608899	+	0.793248i	$0.291612\pi$
$830$	50.9178	1.76738
$831$	7.29924	0.253208
$832$	−0.598620	−0.0207534
$833$	−3.53644	−0.122530
$834$	5.74712	0.199006
$835$	55.7476	1.92923
$836$	5.34055	0.184707
$837$	9.30117	0.321496
$838$	6.47921	0.223821
$839$	28.9036	0.997863	0.498931	−	0.866641i	$-0.333726\pi$
$839$	28.9036	0.997863	0.498931	+	0.866641i	$0.333726\pi$
$840$	5.84842	0.201790
$841$	−28.9966	−0.999884
$842$	1.57699	0.0543468
$843$	10.2946	0.354566
$844$	7.91425	0.272420
$845$	39.7266	1.36664
$846$	−2.09247	−0.0719406
$847$	13.6918	0.470455
$848$	−7.58796	−0.260572
$849$	11.1593	0.382986
$850$	−4.87539	−0.167225
$851$	−9.30809	−0.319077
$852$	−1.96132	−0.0671936
$853$	−51.9757	−1.77961	−0.889807	−	0.456337i	$-0.849161\pi$
$853$	−51.9757	−1.77961	−0.889807	+	0.456337i	$0.849161\pi$
$854$	28.1394	0.962912
$855$	8.79288	0.300710
$856$	−8.18027	−0.279596
$857$	−15.1236	−0.516612	−0.258306	−	0.966063i	$-0.583164\pi$
$857$	−15.1236	−0.516612	−0.258306	+	0.966063i	$0.583164\pi$
$858$	1.14257	0.0390068
$859$	−23.2044	−0.791724	−0.395862	−	0.918310i	$-0.629554\pi$
$859$	−23.2044	−0.791724	−0.395862	+	0.918310i	$0.629554\pi$
$860$	−4.64121	−0.158264
$861$	22.9658	0.782673
$862$	−19.5195	−0.664837
$863$	−6.78838	−0.231079	−0.115540	−	0.993303i	$-0.536860\pi$
$863$	−6.78838	−0.231079	−0.115540	+	0.993303i	$0.536860\pi$
$864$	1.00000	0.0340207
$865$	−21.5931	−0.734188
$866$	23.7483	0.807001
$867$	−1.00000	−0.0339618
$868$	17.3101	0.587542
$869$	22.7786	0.772710
$870$	0.182381	0.00618331
$871$	−6.40585	−0.217054
$872$	−16.3901	−0.555039
$873$	1.87586	0.0634882
$874$	16.9738	0.574147
$875$	−0.728770	−0.0246369
$876$	−1.82049	−0.0615086
$877$	22.4067	0.756621	0.378310	−	0.925679i	$-0.376505\pi$
$877$	22.4067	0.756621	0.378310	+	0.925679i	$0.376505\pi$
$878$	35.8678	1.21048
$879$	3.53990	0.119398
$880$	5.99804	0.202194
$881$	34.1130	1.14930	0.574649	−	0.818400i	$-0.305139\pi$
$881$	34.1130	1.14930	0.574649	+	0.818400i	$0.305139\pi$
$882$	3.53644	0.119078
$883$	−22.8326	−0.768378	−0.384189	−	0.923254i	$-0.625519\pi$
$883$	−22.8326	−0.768378	−0.384189	+	0.923254i	$0.625519\pi$
$884$	−0.598620	−0.0201338
$885$	3.14251	0.105634
$886$	30.7025	1.03147
$887$	12.2213	0.410350	0.205175	−	0.978725i	$-0.434224\pi$
$887$	12.2213	0.410350	0.205175	+	0.978725i	$0.434224\pi$
$888$	−1.53439	−0.0514908
$889$	30.3395	1.01755
$890$	17.1424	0.574615
$891$	−1.90868	−0.0639431
$892$	−18.3666	−0.614959
$893$	−5.85481	−0.195924
$894$	−4.15571	−0.138988
$895$	61.7307	2.06343
$896$	1.86106	0.0621738
$897$	3.63141	0.121249
$898$	3.86029	0.128820
$899$	0.539810	0.0180037
$900$	4.87539	0.162513
$901$	−7.58796	−0.252792
$902$	23.5533	0.784241
$903$	2.74863	0.0914686
$904$	−0.272035	−0.00904774
$905$	−4.44084	−0.147619
$906$	3.76515	0.125089
$907$	−4.63566	−0.153925	−0.0769623	−	0.997034i	$-0.524522\pi$
$907$	−4.63566	−0.153925	−0.0769623	+	0.997034i	$0.524522\pi$
$908$	−4.93993	−0.163937
$909$	−0.354613	−0.0117618
$910$	3.50098	0.116056
$911$	−41.8449	−1.38638	−0.693192	−	0.720753i	$-0.743796\pi$
$911$	−41.8449	−1.38638	−0.693192	+	0.720753i	$0.743796\pi$
$912$	2.79804	0.0926524
$913$	−30.9261	−1.02350
$914$	30.6656	1.01433
$915$	47.5150	1.57080
$916$	−5.78391	−0.191106
$917$	−39.9784	−1.32020
$918$	1.00000	0.0330049
$919$	14.9079	0.491765	0.245882	−	0.969300i	$-0.420922\pi$
$919$	14.9079	0.491765	0.245882	+	0.969300i	$0.420922\pi$
$920$	19.0635	0.628504
$921$	−15.1451	−0.499049
$922$	−33.1352	−1.09125
$923$	−1.17408	−0.0386454
$924$	−3.55217	−0.116858
$925$	−7.48075	−0.245966
$926$	26.9844	0.886763
$927$	−14.9092	−0.489684
$928$	0.0580368	0.00190515
$929$	7.90774	0.259444	0.129722	−	0.991550i	$-0.458591\pi$
$929$	7.90774	0.259444	0.129722	+	0.991550i	$0.458591\pi$
$930$	29.2291	0.958458
$931$	9.89509	0.324299
$932$	−16.2536	−0.532405
$933$	27.9857	0.916210
$934$	−19.8835	−0.650607
$935$	5.99804	0.196157
$936$	0.598620	0.0195665
$937$	18.9798	0.620041	0.310021	−	0.950730i	$-0.399664\pi$
$937$	18.9798	0.620041	0.310021	+	0.950730i	$0.399664\pi$
$938$	19.9153	0.650257
$939$	18.6629	0.609040
$940$	−6.57561	−0.214473
$941$	7.83769	0.255501	0.127751	−	0.991806i	$-0.459224\pi$
$941$	7.83769	0.255501	0.127751	+	0.991806i	$0.459224\pi$
$942$	−11.4685	−0.373663
$943$	74.8591	2.43775
$944$	1.00000	0.0325472
$945$	−5.84842	−0.190249
$946$	2.81895	0.0916518
$947$	46.2923	1.50430	0.752150	−	0.658993i	$-0.229017\pi$
$947$	46.2923	1.50430	0.752150	+	0.658993i	$0.229017\pi$
$948$	11.9342	0.387606
$949$	−1.08978	−0.0353758
$950$	13.6415	0.442590
$951$	5.33071	0.172860
$952$	1.86106	0.0603175
$953$	13.3168	0.431373	0.215687	−	0.976463i	$-0.430801\pi$
$953$	13.3168	0.431373	0.215687	+	0.976463i	$0.430801\pi$
$954$	7.58796	0.245669
$955$	−14.3734	−0.465113
$956$	7.83325	0.253345
$957$	−0.110773	−0.00358080
$958$	−3.62156	−0.117007
$959$	−12.5178	−0.404221
$960$	3.14251	0.101424
$961$	55.5118	1.79070
$962$	−0.918517	−0.0296142
$963$	8.18027	0.263606
$964$	−5.49476	−0.176974
$965$	−77.5341	−2.49591
$966$	−11.2898	−0.363243
$967$	−37.2363	−1.19744	−0.598719	−	0.800959i	$-0.704324\pi$
$967$	−37.2363	−1.19744	−0.598719	+	0.800959i	$0.704324\pi$
$968$	7.35695	0.236461
$969$	2.79804	0.0898860
$970$	5.89491	0.189274
$971$	43.0354	1.38107	0.690536	−	0.723298i	$-0.257375\pi$
$971$	43.0354	1.38107	0.690536	+	0.723298i	$0.257375\pi$
$972$	−1.00000	−0.0320750
$973$	−10.6958	−0.342890
$974$	3.29761	0.105662
$975$	2.91851	0.0934670
$976$	15.1201	0.483982
$977$	−24.7135	−0.790653	−0.395327	−	0.918541i	$-0.629369\pi$
$977$	−24.7135	−0.790653	−0.395327	+	0.918541i	$0.629369\pi$
$978$	−7.29454	−0.233254
$979$	−10.4118	−0.332764
$980$	11.1133	0.355001
$981$	16.3901	0.523295
$982$	−3.68978	−0.117746
$983$	−4.57592	−0.145949	−0.0729745	−	0.997334i	$-0.523249\pi$
$983$	−4.57592	−0.145949	−0.0729745	+	0.997334i	$0.523249\pi$
$984$	12.3401	0.393389
$985$	−11.9886	−0.381989
$986$	0.0580368	0.00184827
$987$	3.89422	0.123954
$988$	1.67496	0.0532877
$989$	8.95940	0.284892
$990$	−5.99804	−0.190630
$991$	−35.6719	−1.13315	−0.566577	−	0.824009i	$-0.691733\pi$
$991$	−35.6719	−1.13315	−0.566577	+	0.824009i	$0.691733\pi$
$992$	9.30117	0.295312
$993$	6.46188	0.205061
$994$	3.65014	0.115775
$995$	−5.84828	−0.185403
$996$	−16.2029	−0.513409
$997$	−17.3650	−0.549956	−0.274978	−	0.961451i	$-0.588671\pi$
$997$	−17.3650	−0.549956	−0.274978	+	0.961451i	$0.588671\pi$
$998$	−20.7578	−0.657076
$999$	1.53439	0.0485460

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.u.1.1	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.14251 q^{5} +1.00000 q^{6} -1.86106 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.14251 q^{5} +1.00000 q^{6} -1.86106 q^{7} -1.00000 q^{8} +1.00000 q^{9} +3.14251 q^{10} -1.90868 q^{11} -1.00000 q^{12} -0.598620 q^{13} +1.86106 q^{14} +3.14251 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} -2.79804 q^{19} -3.14251 q^{20} +1.86106 q^{21} +1.90868 q^{22} +6.06631 q^{23} +1.00000 q^{24} +4.87539 q^{25} +0.598620 q^{26} -1.00000 q^{27} -1.86106 q^{28} -0.0580368 q^{29} -3.14251 q^{30} -9.30117 q^{31} -1.00000 q^{32} +1.90868 q^{33} -1.00000 q^{34} +5.84842 q^{35} +1.00000 q^{36} -1.53439 q^{37} +2.79804 q^{38} +0.598620 q^{39} +3.14251 q^{40} +12.3401 q^{41} -1.86106 q^{42} +1.47691 q^{43} -1.90868 q^{44} -3.14251 q^{45} -6.06631 q^{46} +2.09247 q^{47} -1.00000 q^{48} -3.53644 q^{49} -4.87539 q^{50} -1.00000 q^{51} -0.598620 q^{52} -7.58796 q^{53} +1.00000 q^{54} +5.99804 q^{55} +1.86106 q^{56} +2.79804 q^{57} +0.0580368 q^{58} +1.00000 q^{59} +3.14251 q^{60} +15.1201 q^{61} +9.30117 q^{62} -1.86106 q^{63} +1.00000 q^{64} +1.88117 q^{65} -1.90868 q^{66} +10.7010 q^{67} +1.00000 q^{68} -6.06631 q^{69} -5.84842 q^{70} +1.96132 q^{71} -1.00000 q^{72} +1.82049 q^{73} +1.53439 q^{74} -4.87539 q^{75} -2.79804 q^{76} +3.55217 q^{77} -0.598620 q^{78} -11.9342 q^{79} -3.14251 q^{80} +1.00000 q^{81} -12.3401 q^{82} +16.2029 q^{83} +1.86106 q^{84} -3.14251 q^{85} -1.47691 q^{86} +0.0580368 q^{87} +1.90868 q^{88} +5.45500 q^{89} +3.14251 q^{90} +1.11407 q^{91} +6.06631 q^{92} +9.30117 q^{93} -2.09247 q^{94} +8.79288 q^{95} +1.00000 q^{96} +1.87586 q^{97} +3.53644 q^{98} -1.90868 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 9 q^{2} - 9 q^{3} + 9 q^{4} + 2 q^{5} + 9 q^{6} - 5 q^{7} - 9 q^{8} + 9 q^{9}+O(q^{10}) \) 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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