LMFDB - Embedded newform 6018.2.a.t.1.4

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:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 15x^{6} + 14x^{5} + 84x^{4} + 9x^{3} - 158x^{2} - 142x - 35 $ x^8 - 2x^7 - 15x^6 + 14x^5 + 84x^4 + 9x^3 - 158x^2 - 142*x - 35
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			1.4
Root			$3.51784$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.98195 q^{5} -1.00000 q^{6} -2.53589 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.98195 q^{5} -1.00000 q^{6} -2.53589 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.98195 q^{10} +6.11492 q^{11} +1.00000 q^{12} -1.71429 q^{13} +2.53589 q^{14} -1.98195 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} +4.16864 q^{19} -1.98195 q^{20} -2.53589 q^{21} -6.11492 q^{22} -8.88922 q^{23} -1.00000 q^{24} -1.07187 q^{25} +1.71429 q^{26} +1.00000 q^{27} -2.53589 q^{28} +2.92115 q^{29} +1.98195 q^{30} -6.42050 q^{31} -1.00000 q^{32} +6.11492 q^{33} -1.00000 q^{34} +5.02601 q^{35} +1.00000 q^{36} +0.684941 q^{37} -4.16864 q^{38} -1.71429 q^{39} +1.98195 q^{40} +6.28450 q^{41} +2.53589 q^{42} +0.490978 q^{43} +6.11492 q^{44} -1.98195 q^{45} +8.88922 q^{46} -2.59102 q^{47} +1.00000 q^{48} -0.569249 q^{49} +1.07187 q^{50} +1.00000 q^{51} -1.71429 q^{52} -8.69189 q^{53} -1.00000 q^{54} -12.1195 q^{55} +2.53589 q^{56} +4.16864 q^{57} -2.92115 q^{58} -1.00000 q^{59} -1.98195 q^{60} +2.45772 q^{61} +6.42050 q^{62} -2.53589 q^{63} +1.00000 q^{64} +3.39763 q^{65} -6.11492 q^{66} -2.32984 q^{67} +1.00000 q^{68} -8.88922 q^{69} -5.02601 q^{70} -6.70088 q^{71} -1.00000 q^{72} +13.8160 q^{73} -0.684941 q^{74} -1.07187 q^{75} +4.16864 q^{76} -15.5068 q^{77} +1.71429 q^{78} +3.42675 q^{79} -1.98195 q^{80} +1.00000 q^{81} -6.28450 q^{82} -0.548934 q^{83} -2.53589 q^{84} -1.98195 q^{85} -0.490978 q^{86} +2.92115 q^{87} -6.11492 q^{88} -14.1501 q^{89} +1.98195 q^{90} +4.34724 q^{91} -8.88922 q^{92} -6.42050 q^{93} +2.59102 q^{94} -8.26203 q^{95} -1.00000 q^{96} -4.28648 q^{97} +0.569249 q^{98} +6.11492 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + 8 q^{3} + 8 q^{4} - 6 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q - 8 * q^2 + 8 * q^3 + 8 * q^4 - 6 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^8 + 8 * q^9	\( 8 q - 8 q^{2} + 8 q^{3} + 8 q^{4} - 6 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{8} + 8 q^{9} + 6 q^{10} + q^{11} + 8 q^{12} - 2 q^{13} + 4 q^{14} - 6 q^{15} + 8 q^{16} + 8 q^{17} - 8 q^{18} + 4 q^{19} - 6 q^{20} - 4 q^{21} - q^{22} - 11 q^{23} - 8 q^{24} + 6 q^{25} + 2 q^{26} + 8 q^{27} - 4 q^{28} - 12 q^{29} + 6 q^{30} - 9 q^{31} - 8 q^{32} + q^{33} - 8 q^{34} - 28 q^{35} + 8 q^{36} - 22 q^{37} - 4 q^{38} - 2 q^{39} + 6 q^{40} - 19 q^{41} + 4 q^{42} - 5 q^{43} + q^{44} - 6 q^{45} + 11 q^{46} - 26 q^{47} + 8 q^{48} - 6 q^{50} + 8 q^{51} - 2 q^{52} - 21 q^{53} - 8 q^{54} - 13 q^{55} + 4 q^{56} + 4 q^{57} + 12 q^{58} - 8 q^{59} - 6 q^{60} + 9 q^{61} + 9 q^{62} - 4 q^{63} + 8 q^{64} + 14 q^{65} - q^{66} + 26 q^{67} + 8 q^{68} - 11 q^{69} + 28 q^{70} - 14 q^{71} - 8 q^{72} + 17 q^{73} + 22 q^{74} + 6 q^{75} + 4 q^{76} - 18 q^{77} + 2 q^{78} - 39 q^{79} - 6 q^{80} + 8 q^{81} + 19 q^{82} - 11 q^{83} - 4 q^{84} - 6 q^{85} + 5 q^{86} - 12 q^{87} - q^{88} + 6 q^{90} + 11 q^{91} - 11 q^{92} - 9 q^{93} + 26 q^{94} - 15 q^{95} - 8 q^{96} + 16 q^{97} + q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 + 8 * q^3 + 8 * q^4 - 6 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^8 + 8 * q^9 + 6 * q^10 + q^11 + 8 * q^12 - 2 * q^13 + 4 * q^14 - 6 * q^15 + 8 * q^16 + 8 * q^17 - 8 * q^18 + 4 * q^19 - 6 * q^20 - 4 * q^21 - q^22 - 11 * q^23 - 8 * q^24 + 6 * q^25 + 2 * q^26 + 8 * q^27 - 4 * q^28 - 12 * q^29 + 6 * q^30 - 9 * q^31 - 8 * q^32 + q^33 - 8 * q^34 - 28 * q^35 + 8 * q^36 - 22 * q^37 - 4 * q^38 - 2 * q^39 + 6 * q^40 - 19 * q^41 + 4 * q^42 - 5 * q^43 + q^44 - 6 * q^45 + 11 * q^46 - 26 * q^47 + 8 * q^48 - 6 * q^50 + 8 * q^51 - 2 * q^52 - 21 * q^53 - 8 * q^54 - 13 * q^55 + 4 * q^56 + 4 * q^57 + 12 * q^58 - 8 * q^59 - 6 * q^60 + 9 * q^61 + 9 * q^62 - 4 * q^63 + 8 * q^64 + 14 * q^65 - q^66 + 26 * q^67 + 8 * q^68 - 11 * q^69 + 28 * q^70 - 14 * q^71 - 8 * q^72 + 17 * q^73 + 22 * q^74 + 6 * q^75 + 4 * q^76 - 18 * q^77 + 2 * q^78 - 39 * q^79 - 6 * q^80 + 8 * q^81 + 19 * q^82 - 11 * q^83 - 4 * q^84 - 6 * q^85 + 5 * q^86 - 12 * q^87 - q^88 + 6 * q^90 + 11 * q^91 - 11 * q^92 - 9 * q^93 + 26 * q^94 - 15 * q^95 - 8 * q^96 + 16 * q^97 + 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
$5$	−1.98195	−0.886355	−0.443178	−	0.896434i	$-0.646149\pi$
$5$	−1.98195	−0.886355	−0.443178	+	0.896434i	$0.646149\pi$
$6$	−1.00000	−0.408248
$7$	−2.53589	−0.958477	−0.479239	−	0.877685i	$-0.659087\pi$
$7$	−2.53589	−0.958477	−0.479239	+	0.877685i	$0.659087\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	1.98195	0.626748
$11$	6.11492	1.84372	0.921859	−	0.387525i	$-0.126670\pi$
$11$	6.11492	1.84372	0.921859	+	0.387525i	$0.126670\pi$
$12$	1.00000	0.288675
$13$	−1.71429	−0.475457	−0.237729	−	0.971332i	$-0.576403\pi$
$13$	−1.71429	−0.475457	−0.237729	+	0.971332i	$0.576403\pi$
$14$	2.53589	0.677746
$15$	−1.98195	−0.511738
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.00000	−0.235702
$19$	4.16864	0.956351	0.478175	−	0.878264i	$-0.341298\pi$
$19$	4.16864	0.956351	0.478175	+	0.878264i	$0.341298\pi$
$20$	−1.98195	−0.443178
$21$	−2.53589	−0.553377
$22$	−6.11492	−1.30371
$23$	−8.88922	−1.85353	−0.926765	−	0.375641i	$-0.877423\pi$
$23$	−8.88922	−1.85353	−0.926765	+	0.375641i	$0.877423\pi$
$24$	−1.00000	−0.204124
$25$	−1.07187	−0.214374
$26$	1.71429	0.336199
$27$	1.00000	0.192450
$28$	−2.53589	−0.479239
$29$	2.92115	0.542444	0.271222	−	0.962517i	$-0.412572\pi$
$29$	2.92115	0.542444	0.271222	+	0.962517i	$0.412572\pi$
$30$	1.98195	0.361853
$31$	−6.42050	−1.15316	−0.576578	−	0.817042i	$-0.695612\pi$
$31$	−6.42050	−1.15316	−0.576578	+	0.817042i	$0.695612\pi$
$32$	−1.00000	−0.176777
$33$	6.11492	1.06447
$34$	−1.00000	−0.171499
$35$	5.02601	0.849552
$36$	1.00000	0.166667
$37$	0.684941	0.112604	0.0563018	−	0.998414i	$-0.482069\pi$
$37$	0.684941	0.112604	0.0563018	+	0.998414i	$0.482069\pi$
$38$	−4.16864	−0.676242
$39$	−1.71429	−0.274505
$40$	1.98195	0.313374
$41$	6.28450	0.981474	0.490737	−	0.871308i	$-0.336728\pi$
$41$	6.28450	0.981474	0.490737	+	0.871308i	$0.336728\pi$
$42$	2.53589	0.391297
$43$	0.490978	0.0748734	0.0374367	−	0.999299i	$-0.488081\pi$
$43$	0.490978	0.0748734	0.0374367	+	0.999299i	$0.488081\pi$
$44$	6.11492	0.921859
$45$	−1.98195	−0.295452
$46$	8.88922	1.31064
$47$	−2.59102	−0.377939	−0.188969	−	0.981983i	$-0.560515\pi$
$47$	−2.59102	−0.377939	−0.188969	+	0.981983i	$0.560515\pi$
$48$	1.00000	0.144338
$49$	−0.569249	−0.0813213
$50$	1.07187	0.151585
$51$	1.00000	0.140028
$52$	−1.71429	−0.237729
$53$	−8.69189	−1.19392	−0.596961	−	0.802270i	$-0.703625\pi$
$53$	−8.69189	−1.19392	−0.596961	+	0.802270i	$0.703625\pi$
$54$	−1.00000	−0.136083
$55$	−12.1195	−1.63419
$56$	2.53589	0.338873
$57$	4.16864	0.552149
$58$	−2.92115	−0.383566
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	−1.98195	−0.255869
$61$	2.45772	0.314679	0.157339	−	0.987545i	$-0.449708\pi$
$61$	2.45772	0.314679	0.157339	+	0.987545i	$0.449708\pi$
$62$	6.42050	0.815404
$63$	−2.53589	−0.319492
$64$	1.00000	0.125000
$65$	3.39763	0.421424
$66$	−6.11492	−0.752695
$67$	−2.32984	−0.284635	−0.142317	−	0.989821i	$-0.545455\pi$
$67$	−2.32984	−0.284635	−0.142317	+	0.989821i	$0.545455\pi$
$68$	1.00000	0.121268
$69$	−8.88922	−1.07014
$70$	−5.02601	−0.600724
$71$	−6.70088	−0.795248	−0.397624	−	0.917549i	$-0.630165\pi$
$71$	−6.70088	−0.795248	−0.397624	+	0.917549i	$0.630165\pi$
$72$	−1.00000	−0.117851
$73$	13.8160	1.61704	0.808520	−	0.588469i	$-0.200269\pi$
$73$	13.8160	1.61704	0.808520	+	0.588469i	$0.200269\pi$
$74$	−0.684941	−0.0796228
$75$	−1.07187	−0.123769
$76$	4.16864	0.478175
$77$	−15.5068	−1.76716
$78$	1.71429	0.194105
$79$	3.42675	0.385540	0.192770	−	0.981244i	$-0.438253\pi$
$79$	3.42675	0.385540	0.192770	+	0.981244i	$0.438253\pi$
$80$	−1.98195	−0.221589
$81$	1.00000	0.111111
$82$	−6.28450	−0.694007
$83$	−0.548934	−0.0602534	−0.0301267	−	0.999546i	$-0.509591\pi$
$83$	−0.548934	−0.0602534	−0.0301267	+	0.999546i	$0.509591\pi$
$84$	−2.53589	−0.276689
$85$	−1.98195	−0.214973
$86$	−0.490978	−0.0529435
$87$	2.92115	0.313180
$88$	−6.11492	−0.651853
$89$	−14.1501	−1.49991	−0.749955	−	0.661489i	$-0.769925\pi$
$89$	−14.1501	−1.49991	−0.749955	+	0.661489i	$0.769925\pi$
$90$	1.98195	0.208916
$91$	4.34724	0.455715
$92$	−8.88922	−0.926765
$93$	−6.42050	−0.665775
$94$	2.59102	0.267243
$95$	−8.26203	−0.847667
$96$	−1.00000	−0.102062
$97$	−4.28648	−0.435227	−0.217613	−	0.976035i	$-0.569827\pi$
$97$	−4.28648	−0.435227	−0.217613	+	0.976035i	$0.569827\pi$
$98$	0.569249	0.0575029
$99$	6.11492	0.614573
$100$	−1.07187	−0.107187
$101$	15.5776	1.55003	0.775017	−	0.631941i	$-0.217741\pi$
$101$	15.5776	1.55003	0.775017	+	0.631941i	$0.217741\pi$
$102$	−1.00000	−0.0990148
$103$	13.4015	1.32048	0.660242	−	0.751053i	$-0.270454\pi$
$103$	13.4015	1.32048	0.660242	+	0.751053i	$0.270454\pi$
$104$	1.71429	0.168100
$105$	5.02601	0.490489
$106$	8.69189	0.844231
$107$	4.50493	0.435508	0.217754	−	0.976004i	$-0.430127\pi$
$107$	4.50493	0.435508	0.217754	+	0.976004i	$0.430127\pi$
$108$	1.00000	0.0962250
$109$	8.89417	0.851907	0.425954	−	0.904745i	$-0.359939\pi$
$109$	8.89417	0.851907	0.425954	+	0.904745i	$0.359939\pi$
$110$	12.1195	1.15555
$111$	0.684941	0.0650117
$112$	−2.53589	−0.239619
$113$	1.75660	0.165247	0.0826234	−	0.996581i	$-0.473670\pi$
$113$	1.75660	0.165247	0.0826234	+	0.996581i	$0.473670\pi$
$114$	−4.16864	−0.390428
$115$	17.6180	1.64289
$116$	2.92115	0.271222
$117$	−1.71429	−0.158486
$118$	1.00000	0.0920575
$119$	−2.53589	−0.232465
$120$	1.98195	0.180927
$121$	26.3923	2.39930
$122$	−2.45772	−0.222511
$123$	6.28450	0.566654
$124$	−6.42050	−0.576578
$125$	12.0341	1.07637
$126$	2.53589	0.225915
$127$	14.5290	1.28924	0.644621	−	0.764502i	$-0.277015\pi$
$127$	14.5290	1.28924	0.644621	+	0.764502i	$0.277015\pi$
$128$	−1.00000	−0.0883883
$129$	0.490978	0.0432282
$130$	−3.39763	−0.297992
$131$	−8.60199	−0.751559	−0.375780	−	0.926709i	$-0.622625\pi$
$131$	−8.60199	−0.751559	−0.375780	+	0.926709i	$0.622625\pi$
$132$	6.11492	0.532236
$133$	−10.5712	−0.916640
$134$	2.32984	0.201267
$135$	−1.98195	−0.170579
$136$	−1.00000	−0.0857493
$137$	−6.97343	−0.595781	−0.297890	−	0.954600i	$-0.596283\pi$
$137$	−6.97343	−0.595781	−0.297890	+	0.954600i	$0.596283\pi$
$138$	8.88922	0.756701
$139$	−17.3609	−1.47253	−0.736266	−	0.676692i	$-0.763413\pi$
$139$	−17.3609	−1.47253	−0.736266	+	0.676692i	$0.763413\pi$
$140$	5.02601	0.424776
$141$	−2.59102	−0.218203
$142$	6.70088	0.562325
$143$	−10.4827	−0.876609
$144$	1.00000	0.0833333
$145$	−5.78958	−0.480798
$146$	−13.8160	−1.14342
$147$	−0.569249	−0.0469509
$148$	0.684941	0.0563018
$149$	−7.98343	−0.654028	−0.327014	−	0.945019i	$-0.606042\pi$
$149$	−7.98343	−0.654028	−0.327014	+	0.945019i	$0.606042\pi$
$150$	1.07187	0.0875178
$151$	0.789521	0.0642503	0.0321251	−	0.999484i	$-0.489772\pi$
$151$	0.789521	0.0642503	0.0321251	+	0.999484i	$0.489772\pi$
$152$	−4.16864	−0.338121
$153$	1.00000	0.0808452
$154$	15.5068	1.24957
$155$	12.7251	1.02211
$156$	−1.71429	−0.137253
$157$	−11.8748	−0.947712	−0.473856	−	0.880602i	$-0.657138\pi$
$157$	−11.8748	−0.947712	−0.473856	+	0.880602i	$0.657138\pi$
$158$	−3.42675	−0.272618
$159$	−8.69189	−0.689312
$160$	1.98195	0.156687
$161$	22.5421	1.77657
$162$	−1.00000	−0.0785674
$163$	−14.4631	−1.13283	−0.566417	−	0.824119i	$-0.691671\pi$
$163$	−14.4631	−1.13283	−0.566417	+	0.824119i	$0.691671\pi$
$164$	6.28450	0.490737
$165$	−12.1195	−0.943500
$166$	0.548934	0.0426056
$167$	−21.2926	−1.64767	−0.823836	−	0.566829i	$-0.808170\pi$
$167$	−21.2926	−1.64767	−0.823836	+	0.566829i	$0.808170\pi$
$168$	2.53589	0.195648
$169$	−10.0612	−0.773940
$170$	1.98195	0.152009
$171$	4.16864	0.318784
$172$	0.490978	0.0374367
$173$	−17.7535	−1.34977	−0.674886	−	0.737922i	$-0.735807\pi$
$173$	−17.7535	−1.34977	−0.674886	+	0.737922i	$0.735807\pi$
$174$	−2.92115	−0.221452
$175$	2.71815	0.205473
$176$	6.11492	0.460930
$177$	−1.00000	−0.0751646
$178$	14.1501	1.06060
$179$	0.878112	0.0656332	0.0328166	−	0.999461i	$-0.489552\pi$
$179$	0.878112	0.0656332	0.0328166	+	0.999461i	$0.489552\pi$
$180$	−1.98195	−0.147726
$181$	−20.6530	−1.53513	−0.767564	−	0.640972i	$-0.778531\pi$
$181$	−20.6530	−1.53513	−0.767564	+	0.640972i	$0.778531\pi$
$182$	−4.34724	−0.322239
$183$	2.45772	0.181680
$184$	8.88922	0.655322
$185$	−1.35752	−0.0998069
$186$	6.42050	0.470774
$187$	6.11492	0.447167
$188$	−2.59102	−0.188969
$189$	−2.53589	−0.184459
$190$	8.26203	0.599391
$191$	−0.812845	−0.0588154	−0.0294077	−	0.999567i	$-0.509362\pi$
$191$	−0.812845	−0.0588154	−0.0294077	+	0.999567i	$0.509362\pi$
$192$	1.00000	0.0721688
$193$	−11.7174	−0.843438	−0.421719	−	0.906727i	$-0.638573\pi$
$193$	−11.7174	−0.843438	−0.421719	+	0.906727i	$0.638573\pi$
$194$	4.28648	0.307752
$195$	3.39763	0.243309
$196$	−0.569249	−0.0406607
$197$	−18.5124	−1.31895	−0.659475	−	0.751726i	$-0.729222\pi$
$197$	−18.5124	−1.31895	−0.659475	+	0.751726i	$0.729222\pi$
$198$	−6.11492	−0.434569
$199$	26.2585	1.86142	0.930708	−	0.365763i	$-0.119192\pi$
$199$	26.2585	1.86142	0.930708	+	0.365763i	$0.119192\pi$
$200$	1.07187	0.0757927
$201$	−2.32984	−0.164334
$202$	−15.5776	−1.09604
$203$	−7.40772	−0.519920
$204$	1.00000	0.0700140
$205$	−12.4556	−0.869935
$206$	−13.4015	−0.933724
$207$	−8.88922	−0.617844
$208$	−1.71429	−0.118864
$209$	25.4909	1.76324
$210$	−5.02601	−0.346828
$211$	−10.2801	−0.707714	−0.353857	−	0.935300i	$-0.615130\pi$
$211$	−10.2801	−0.707714	−0.353857	+	0.935300i	$0.615130\pi$
$212$	−8.69189	−0.596961
$213$	−6.70088	−0.459136
$214$	−4.50493	−0.307950
$215$	−0.973094	−0.0663644
$216$	−1.00000	−0.0680414
$217$	16.2817	1.10527
$218$	−8.89417	−0.602389
$219$	13.8160	0.933598
$220$	−12.1195	−0.817095
$221$	−1.71429	−0.115315
$222$	−0.684941	−0.0459702
$223$	14.6130	0.978558	0.489279	−	0.872127i	$-0.337260\pi$
$223$	14.6130	0.978558	0.489279	+	0.872127i	$0.337260\pi$
$224$	2.53589	0.169436
$225$	−1.07187	−0.0714580
$226$	−1.75660	−0.116847
$227$	−11.9386	−0.792390	−0.396195	−	0.918166i	$-0.629670\pi$
$227$	−11.9386	−0.792390	−0.396195	+	0.918166i	$0.629670\pi$
$228$	4.16864	0.276075
$229$	−7.88952	−0.521354	−0.260677	−	0.965426i	$-0.583946\pi$
$229$	−7.88952	−0.521354	−0.260677	+	0.965426i	$0.583946\pi$
$230$	−17.6180	−1.16170
$231$	−15.5068	−1.02027
$232$	−2.92115	−0.191783
$233$	−4.34628	−0.284734	−0.142367	−	0.989814i	$-0.545471\pi$
$233$	−4.34628	−0.284734	−0.142367	+	0.989814i	$0.545471\pi$
$234$	1.71429	0.112066
$235$	5.13527	0.334988
$236$	−1.00000	−0.0650945
$237$	3.42675	0.222591
$238$	2.53589	0.164377
$239$	−10.3872	−0.671891	−0.335945	−	0.941881i	$-0.609056\pi$
$239$	−10.3872	−0.671891	−0.335945	+	0.941881i	$0.609056\pi$
$240$	−1.98195	−0.127934
$241$	−17.1707	−1.10606	−0.553031	−	0.833161i	$-0.686529\pi$
$241$	−17.1707	−1.10606	−0.553031	+	0.833161i	$0.686529\pi$
$242$	−26.3923	−1.69656
$243$	1.00000	0.0641500
$244$	2.45772	0.157339
$245$	1.12822	0.0720796
$246$	−6.28450	−0.400685
$247$	−7.14623	−0.454704
$248$	6.42050	0.407702
$249$	−0.548934	−0.0347873
$250$	−12.0341	−0.761106
$251$	4.17427	0.263477	0.131739	−	0.991284i	$-0.457944\pi$
$251$	4.17427	0.263477	0.131739	+	0.991284i	$0.457944\pi$
$252$	−2.53589	−0.159746
$253$	−54.3569	−3.41739
$254$	−14.5290	−0.911632
$255$	−1.98195	−0.124115
$256$	1.00000	0.0625000
$257$	−11.6636	−0.727553	−0.363777	−	0.931486i	$-0.618513\pi$
$257$	−11.6636	−0.727553	−0.363777	+	0.931486i	$0.618513\pi$
$258$	−0.490978	−0.0305669
$259$	−1.73694	−0.107928
$260$	3.39763	0.210712
$261$	2.92115	0.180815
$262$	8.60199	0.531433
$263$	−18.6856	−1.15220	−0.576102	−	0.817378i	$-0.695427\pi$
$263$	−18.6856	−1.15220	−0.576102	+	0.817378i	$0.695427\pi$
$264$	−6.11492	−0.376347
$265$	17.2269	1.05824
$266$	10.5712	0.648163
$267$	−14.1501	−0.865973
$268$	−2.32984	−0.142317
$269$	−17.3736	−1.05929	−0.529644	−	0.848220i	$-0.677675\pi$
$269$	−17.3736	−1.05929	−0.529644	+	0.848220i	$0.677675\pi$
$270$	1.98195	0.120618
$271$	−13.3491	−0.810899	−0.405449	−	0.914118i	$-0.632885\pi$
$271$	−13.3491	−0.810899	−0.405449	+	0.914118i	$0.632885\pi$
$272$	1.00000	0.0606339
$273$	4.34724	0.263107
$274$	6.97343	0.421281
$275$	−6.55440	−0.395245
$276$	−8.88922	−0.535068
$277$	17.5884	1.05678	0.528392	−	0.849000i	$-0.322795\pi$
$277$	17.5884	1.05678	0.528392	+	0.849000i	$0.322795\pi$
$278$	17.3609	1.04124
$279$	−6.42050	−0.384385
$280$	−5.02601	−0.300362
$281$	−30.1045	−1.79588	−0.897941	−	0.440115i	$-0.854938\pi$
$281$	−30.1045	−1.79588	−0.897941	+	0.440115i	$0.854938\pi$
$282$	2.59102	0.154293
$283$	−3.26407	−0.194029	−0.0970144	−	0.995283i	$-0.530929\pi$
$283$	−3.26407	−0.194029	−0.0970144	+	0.995283i	$0.530929\pi$
$284$	−6.70088	−0.397624
$285$	−8.26203	−0.489400
$286$	10.4827	0.619856
$287$	−15.9368	−0.940721
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	5.78958	0.339976
$291$	−4.28648	−0.251278
$292$	13.8160	0.808520
$293$	−28.4323	−1.66103	−0.830515	−	0.556996i	$-0.811954\pi$
$293$	−28.4323	−1.66103	−0.830515	+	0.556996i	$0.811954\pi$
$294$	0.569249	0.0331993
$295$	1.98195	0.115394
$296$	−0.684941	−0.0398114
$297$	6.11492	0.354824
$298$	7.98343	0.462468
$299$	15.2387	0.881275
$300$	−1.07187	−0.0618845
$301$	−1.24507	−0.0717644
$302$	−0.789521	−0.0454318
$303$	15.5776	0.894912
$304$	4.16864	0.239088
$305$	−4.87108	−0.278917
$306$	−1.00000	−0.0571662
$307$	22.0522	1.25858	0.629292	−	0.777169i	$-0.283345\pi$
$307$	22.0522	1.25858	0.629292	+	0.777169i	$0.283345\pi$
$308$	−15.5068	−0.883581
$309$	13.4015	0.762382
$310$	−12.7251	−0.722738
$311$	−25.3155	−1.43551	−0.717756	−	0.696295i	$-0.754831\pi$
$311$	−25.3155	−1.43551	−0.717756	+	0.696295i	$0.754831\pi$
$312$	1.71429	0.0970523
$313$	4.68133	0.264605	0.132302	−	0.991209i	$-0.457763\pi$
$313$	4.68133	0.264605	0.132302	+	0.991209i	$0.457763\pi$
$314$	11.8748	0.670134
$315$	5.02601	0.283184
$316$	3.42675	0.192770
$317$	4.79577	0.269357	0.134679	−	0.990889i	$-0.457000\pi$
$317$	4.79577	0.269357	0.134679	+	0.990889i	$0.457000\pi$
$318$	8.69189	0.487417
$319$	17.8626	1.00011
$320$	−1.98195	−0.110794
$321$	4.50493	0.251440
$322$	−22.5421	−1.25622
$323$	4.16864	0.231949
$324$	1.00000	0.0555556
$325$	1.83749	0.101926
$326$	14.4631	0.801034
$327$	8.89417	0.491849
$328$	−6.28450	−0.347003
$329$	6.57054	0.362245
$330$	12.1195	0.667155
$331$	−20.8182	−1.14427	−0.572136	−	0.820159i	$-0.693885\pi$
$331$	−20.8182	−1.14427	−0.572136	+	0.820159i	$0.693885\pi$
$332$	−0.548934	−0.0301267
$333$	0.684941	0.0375345
$334$	21.2926	1.16508
$335$	4.61762	0.252288
$336$	−2.53589	−0.138344
$337$	15.5792	0.848656	0.424328	−	0.905509i	$-0.360510\pi$
$337$	15.5792	0.848656	0.424328	+	0.905509i	$0.360510\pi$
$338$	10.0612	0.547259
$339$	1.75660	0.0954053
$340$	−1.98195	−0.107486
$341$	−39.2609	−2.12609
$342$	−4.16864	−0.225414
$343$	19.1948	1.03642
$344$	−0.490978	−0.0264717
$345$	17.6180	0.948521
$346$	17.7535	0.954432
$347$	13.5483	0.727311	0.363655	−	0.931534i	$-0.381529\pi$
$347$	13.5483	0.727311	0.363655	+	0.931534i	$0.381529\pi$
$348$	2.92115	0.156590
$349$	9.98156	0.534301	0.267150	−	0.963655i	$-0.413918\pi$
$349$	9.98156	0.534301	0.267150	+	0.963655i	$0.413918\pi$
$350$	−2.71815	−0.145291
$351$	−1.71429	−0.0915018
$352$	−6.11492	−0.325926
$353$	−6.11437	−0.325435	−0.162717	−	0.986673i	$-0.552026\pi$
$353$	−6.11437	−0.325435	−0.162717	+	0.986673i	$0.552026\pi$
$354$	1.00000	0.0531494
$355$	13.2808	0.704872
$356$	−14.1501	−0.749955
$357$	−2.53589	−0.134214
$358$	−0.878112	−0.0464097
$359$	23.4658	1.23848	0.619240	−	0.785202i	$-0.287441\pi$
$359$	23.4658	1.23848	0.619240	+	0.785202i	$0.287441\pi$
$360$	1.98195	0.104458
$361$	−1.62248	−0.0853936
$362$	20.6530	1.08550
$363$	26.3923	1.38523
$364$	4.34724	0.227857
$365$	−27.3826	−1.43327
$366$	−2.45772	−0.128467
$367$	−33.1741	−1.73167	−0.865837	−	0.500326i	$-0.833214\pi$
$367$	−33.1741	−1.73167	−0.865837	+	0.500326i	$0.833214\pi$
$368$	−8.88922	−0.463383
$369$	6.28450	0.327158
$370$	1.35752	0.0705741
$371$	22.0417	1.14435
$372$	−6.42050	−0.332887
$373$	−24.8570	−1.28705	−0.643524	−	0.765426i	$-0.722528\pi$
$373$	−24.8570	−1.28705	−0.643524	+	0.765426i	$0.722528\pi$
$374$	−6.11492	−0.316195
$375$	12.0341	0.621441
$376$	2.59102	0.133621
$377$	−5.00769	−0.257909
$378$	2.53589	0.130432
$379$	−9.53862	−0.489966	−0.244983	−	0.969527i	$-0.578782\pi$
$379$	−9.53862	−0.489966	−0.244983	+	0.969527i	$0.578782\pi$
$380$	−8.26203	−0.423833
$381$	14.5290	0.744344
$382$	0.812845	0.0415888
$383$	−23.7671	−1.21444	−0.607221	−	0.794533i	$-0.707716\pi$
$383$	−23.7671	−1.21444	−0.607221	+	0.794533i	$0.707716\pi$
$384$	−1.00000	−0.0510310
$385$	30.7337	1.56633
$386$	11.7174	0.596400
$387$	0.490978	0.0249578
$388$	−4.28648	−0.217613
$389$	−20.2240	−1.02540	−0.512699	−	0.858568i	$-0.671354\pi$
$389$	−20.2240	−1.02540	−0.512699	+	0.858568i	$0.671354\pi$
$390$	−3.39763	−0.172046
$391$	−8.88922	−0.449547
$392$	0.569249	0.0287514
$393$	−8.60199	−0.433913
$394$	18.5124	0.932639
$395$	−6.79166	−0.341725
$396$	6.11492	0.307286
$397$	−18.8087	−0.943982	−0.471991	−	0.881603i	$-0.656464\pi$
$397$	−18.8087	−0.943982	−0.471991	+	0.881603i	$0.656464\pi$
$398$	−26.2585	−1.31622
$399$	−10.5712	−0.529222
$400$	−1.07187	−0.0535935
$401$	13.2635	0.662348	0.331174	−	0.943570i	$-0.392555\pi$
$401$	13.2635	0.662348	0.331174	+	0.943570i	$0.392555\pi$
$402$	2.32984	0.116202
$403$	11.0066	0.548276
$404$	15.5776	0.775017
$405$	−1.98195	−0.0984839
$406$	7.40772	0.367639
$407$	4.18836	0.207609
$408$	−1.00000	−0.0495074
$409$	24.4677	1.20985	0.604925	−	0.796282i	$-0.293203\pi$
$409$	24.4677	1.20985	0.604925	+	0.796282i	$0.293203\pi$
$410$	12.4556	0.615137
$411$	−6.97343	−0.343974
$412$	13.4015	0.660242
$413$	2.53589	0.124783
$414$	8.88922	0.436881
$415$	1.08796	0.0534059
$416$	1.71429	0.0840498
$417$	−17.3609	−0.850167
$418$	−25.4909	−1.24680
$419$	−27.3552	−1.33639	−0.668194	−	0.743987i	$-0.732932\pi$
$419$	−27.3552	−1.33639	−0.668194	+	0.743987i	$0.732932\pi$
$420$	5.02601	0.245244
$421$	8.99127	0.438208	0.219104	−	0.975702i	$-0.429687\pi$
$421$	8.99127	0.438208	0.219104	+	0.975702i	$0.429687\pi$
$422$	10.2801	0.500429
$423$	−2.59102	−0.125980
$424$	8.69189	0.422115
$425$	−1.07187	−0.0519933
$426$	6.70088	0.324658
$427$	−6.23251	−0.301612
$428$	4.50493	0.217754
$429$	−10.4827	−0.506111
$430$	0.973094	0.0469267
$431$	35.1492	1.69308	0.846538	−	0.532329i	$-0.178683\pi$
$431$	35.1492	1.69308	0.846538	+	0.532329i	$0.178683\pi$
$432$	1.00000	0.0481125
$433$	−0.639007	−0.0307087	−0.0153544	−	0.999882i	$-0.504888\pi$
$433$	−0.639007	−0.0307087	−0.0153544	+	0.999882i	$0.504888\pi$
$434$	−16.2817	−0.781547
$435$	−5.78958	−0.277589
$436$	8.89417	0.425954
$437$	−37.0559	−1.77263
$438$	−13.8160	−0.660153
$439$	31.9049	1.52274	0.761369	−	0.648319i	$-0.224528\pi$
$439$	31.9049	1.52274	0.761369	+	0.648319i	$0.224528\pi$
$440$	12.1195	0.577773
$441$	−0.569249	−0.0271071
$442$	1.71429	0.0815402
$443$	−2.55401	−0.121345	−0.0606723	−	0.998158i	$-0.519324\pi$
$443$	−2.55401	−0.121345	−0.0606723	+	0.998158i	$0.519324\pi$
$444$	0.684941	0.0325059
$445$	28.0448	1.32945
$446$	−14.6130	−0.691945
$447$	−7.98343	−0.377603
$448$	−2.53589	−0.119810
$449$	2.32417	0.109684	0.0548422	−	0.998495i	$-0.482534\pi$
$449$	2.32417	0.109684	0.0548422	+	0.998495i	$0.482534\pi$
$450$	1.07187	0.0505284
$451$	38.4292	1.80956
$452$	1.75660	0.0826234
$453$	0.789521	0.0370949
$454$	11.9386	0.560305
$455$	−8.61602	−0.403925
$456$	−4.16864	−0.195214
$457$	4.44849	0.208092	0.104046	−	0.994573i	$-0.466821\pi$
$457$	4.44849	0.208092	0.104046	+	0.994573i	$0.466821\pi$
$458$	7.88952	0.368653
$459$	1.00000	0.0466760
$460$	17.6180	0.821444
$461$	31.5586	1.46983	0.734916	−	0.678159i	$-0.237222\pi$
$461$	31.5586	1.46983	0.734916	+	0.678159i	$0.237222\pi$
$462$	15.5068	0.721441
$463$	−33.9587	−1.57819	−0.789097	−	0.614269i	$-0.789451\pi$
$463$	−33.9587	−1.57819	−0.789097	+	0.614269i	$0.789451\pi$
$464$	2.92115	0.135611
$465$	12.7251	0.590113
$466$	4.34628	0.201337
$467$	−39.8442	−1.84377	−0.921885	−	0.387463i	$-0.873352\pi$
$467$	−39.8442	−1.84377	−0.921885	+	0.387463i	$0.873352\pi$
$468$	−1.71429	−0.0792429
$469$	5.90822	0.272816
$470$	−5.13527	−0.236872
$471$	−11.8748	−0.547162
$472$	1.00000	0.0460287
$473$	3.00229	0.138045
$474$	−3.42675	−0.157396
$475$	−4.46824	−0.205017
$476$	−2.53589	−0.116232
$477$	−8.69189	−0.397974
$478$	10.3872	0.475098
$479$	−6.89494	−0.315038	−0.157519	−	0.987516i	$-0.550350\pi$
$479$	−6.89494	−0.315038	−0.157519	+	0.987516i	$0.550350\pi$
$480$	1.98195	0.0904633
$481$	−1.17418	−0.0535382
$482$	17.1707	0.782104
$483$	22.5421	1.02570
$484$	26.3923	1.19965
$485$	8.49560	0.385765
$486$	−1.00000	−0.0453609
$487$	9.59035	0.434580	0.217290	−	0.976107i	$-0.430278\pi$
$487$	9.59035	0.434580	0.217290	+	0.976107i	$0.430278\pi$
$488$	−2.45772	−0.111256
$489$	−14.4631	−0.654042
$490$	−1.12822	−0.0509680
$491$	6.82051	0.307805	0.153903	−	0.988086i	$-0.450816\pi$
$491$	6.82051	0.307805	0.153903	+	0.988086i	$0.450816\pi$
$492$	6.28450	0.283327
$493$	2.92115	0.131562
$494$	7.14623	0.321524
$495$	−12.1195	−0.544730
$496$	−6.42050	−0.288289
$497$	16.9927	0.762227
$498$	0.548934	0.0245983
$499$	6.86311	0.307235	0.153618	−	0.988130i	$-0.450908\pi$
$499$	6.86311	0.307235	0.153618	+	0.988130i	$0.450908\pi$
$500$	12.0341	0.538184
$501$	−21.2926	−0.951284
$502$	−4.17427	−0.186307
$503$	−1.11995	−0.0499359	−0.0249680	−	0.999688i	$-0.507948\pi$
$503$	−1.11995	−0.0499359	−0.0249680	+	0.999688i	$0.507948\pi$
$504$	2.53589	0.112958
$505$	−30.8741	−1.37388
$506$	54.3569	2.41646
$507$	−10.0612	−0.446835
$508$	14.5290	0.644621
$509$	5.52002	0.244671	0.122335	−	0.992489i	$-0.460962\pi$
$509$	5.52002	0.244671	0.122335	+	0.992489i	$0.460962\pi$
$510$	1.98195	0.0877623
$511$	−35.0359	−1.54990
$512$	−1.00000	−0.0441942
$513$	4.16864	0.184050
$514$	11.6636	0.514458
$515$	−26.5610	−1.17042
$516$	0.490978	0.0216141
$517$	−15.8439	−0.696812
$518$	1.73694	0.0763166
$519$	−17.7535	−0.779291
$520$	−3.39763	−0.148996
$521$	39.6425	1.73677	0.868385	−	0.495891i	$-0.165158\pi$
$521$	39.6425	1.73677	0.868385	+	0.495891i	$0.165158\pi$
$522$	−2.92115	−0.127855
$523$	37.2866	1.63043	0.815215	−	0.579158i	$-0.196619\pi$
$523$	37.2866	1.63043	0.815215	+	0.579158i	$0.196619\pi$
$524$	−8.60199	−0.375780
$525$	2.71815	0.118630
$526$	18.6856	0.814731
$527$	−6.42050	−0.279681
$528$	6.11492	0.266118
$529$	56.0182	2.43558
$530$	−17.2269	−0.748289
$531$	−1.00000	−0.0433963
$532$	−10.5712	−0.458320
$533$	−10.7734	−0.466649
$534$	14.1501	0.612335
$535$	−8.92854	−0.386015
$536$	2.32984	0.100634
$537$	0.878112	0.0378933
$538$	17.3736	0.749030
$539$	−3.48092	−0.149934
$540$	−1.98195	−0.0852896
$541$	24.1767	1.03944	0.519718	−	0.854338i	$-0.326037\pi$
$541$	24.1767	1.03944	0.519718	+	0.854338i	$0.326037\pi$
$542$	13.3491	0.573392
$543$	−20.6530	−0.886306
$544$	−1.00000	−0.0428746
$545$	−17.6278	−0.755093
$546$	−4.34724	−0.186045
$547$	−40.3365	−1.72467	−0.862333	−	0.506342i	$-0.830997\pi$
$547$	−40.3365	−1.72467	−0.862333	+	0.506342i	$0.830997\pi$
$548$	−6.97343	−0.297890
$549$	2.45772	0.104893
$550$	6.55440	0.279481
$551$	12.1772	0.518767
$552$	8.88922	0.378350
$553$	−8.68988	−0.369531
$554$	−17.5884	−0.747259
$555$	−1.35752	−0.0576235
$556$	−17.3609	−0.736266
$557$	−3.77673	−0.160025	−0.0800127	−	0.996794i	$-0.525496\pi$
$557$	−3.77673	−0.160025	−0.0800127	+	0.996794i	$0.525496\pi$
$558$	6.42050	0.271801
$559$	−0.841676	−0.0355991
$560$	5.02601	0.212388
$561$	6.11492	0.258172
$562$	30.1045	1.26988
$563$	−28.5886	−1.20486	−0.602432	−	0.798170i	$-0.705802\pi$
$563$	−28.5886	−1.20486	−0.602432	+	0.798170i	$0.705802\pi$
$564$	−2.59102	−0.109101
$565$	−3.48149	−0.146467
$566$	3.26407	0.137199
$567$	−2.53589	−0.106497
$568$	6.70088	0.281162
$569$	7.58964	0.318174	0.159087	−	0.987265i	$-0.449145\pi$
$569$	7.58964	0.318174	0.159087	+	0.987265i	$0.449145\pi$
$570$	8.26203	0.346058
$571$	−2.07405	−0.0867963	−0.0433982	−	0.999058i	$-0.513818\pi$
$571$	−2.07405	−0.0867963	−0.0433982	+	0.999058i	$0.513818\pi$
$572$	−10.4827	−0.438305
$573$	−0.812845	−0.0339571
$574$	15.9368	0.665190
$575$	9.52809	0.397349
$576$	1.00000	0.0416667
$577$	−21.9136	−0.912274	−0.456137	−	0.889910i	$-0.650767\pi$
$577$	−21.9136	−0.912274	−0.456137	+	0.889910i	$0.650767\pi$
$578$	−1.00000	−0.0415945
$579$	−11.7174	−0.486959
$580$	−5.78958	−0.240399
$581$	1.39204	0.0577515
$582$	4.28648	0.177681
$583$	−53.1502	−2.20126
$584$	−13.8160	−0.571710
$585$	3.39763	0.140475
$586$	28.4323	1.17453
$587$	26.5266	1.09487	0.547436	−	0.836848i	$-0.315604\pi$
$587$	26.5266	1.09487	0.547436	+	0.836848i	$0.315604\pi$
$588$	−0.569249	−0.0234754
$589$	−26.7647	−1.10282
$590$	−1.98195	−0.0815956
$591$	−18.5124	−0.761497
$592$	0.684941	0.0281509
$593$	15.6637	0.643231	0.321616	−	0.946870i	$-0.395774\pi$
$593$	15.6637	0.643231	0.321616	+	0.946870i	$0.395774\pi$
$594$	−6.11492	−0.250898
$595$	5.02601	0.206047
$596$	−7.98343	−0.327014
$597$	26.2585	1.07469
$598$	−15.2387	−0.623155
$599$	5.97584	0.244166	0.122083	−	0.992520i	$-0.461043\pi$
$599$	5.97584	0.244166	0.122083	+	0.992520i	$0.461043\pi$
$600$	1.07187	0.0437589
$601$	14.8377	0.605243	0.302621	−	0.953111i	$-0.402138\pi$
$601$	14.8377	0.605243	0.302621	+	0.953111i	$0.402138\pi$
$602$	1.24507	0.0507451
$603$	−2.32984	−0.0948783
$604$	0.789521	0.0321251
$605$	−52.3082	−2.12663
$606$	−15.5776	−0.632799
$607$	10.8039	0.438518	0.219259	−	0.975667i	$-0.429636\pi$
$607$	10.8039	0.438518	0.219259	+	0.975667i	$0.429636\pi$
$608$	−4.16864	−0.169060
$609$	−7.40772	−0.300176
$610$	4.87108	0.197224
$611$	4.44174	0.179694
$612$	1.00000	0.0404226
$613$	5.67485	0.229205	0.114602	−	0.993411i	$-0.463441\pi$
$613$	5.67485	0.229205	0.114602	+	0.993411i	$0.463441\pi$
$614$	−22.0522	−0.889953
$615$	−12.4556	−0.502257
$616$	15.5068	0.624786
$617$	−0.791937	−0.0318822	−0.0159411	−	0.999873i	$-0.505074\pi$
$617$	−0.791937	−0.0318822	−0.0159411	+	0.999873i	$0.505074\pi$
$618$	−13.4015	−0.539086
$619$	11.1603	0.448570	0.224285	−	0.974524i	$-0.427995\pi$
$619$	11.1603	0.448570	0.224285	+	0.974524i	$0.427995\pi$
$620$	12.7251	0.511053
$621$	−8.88922	−0.356712
$622$	25.3155	1.01506
$623$	35.8832	1.43763
$624$	−1.71429	−0.0686263
$625$	−18.4917	−0.739670
$626$	−4.68133	−0.187104
$627$	25.4909	1.01801
$628$	−11.8748	−0.473856
$629$	0.684941	0.0273104
$630$	−5.02601	−0.200241
$631$	36.6940	1.46077	0.730383	−	0.683038i	$-0.239342\pi$
$631$	36.6940	1.46077	0.730383	+	0.683038i	$0.239342\pi$
$632$	−3.42675	−0.136309
$633$	−10.2801	−0.408599
$634$	−4.79577	−0.190464
$635$	−28.7958	−1.14273
$636$	−8.69189	−0.344656
$637$	0.975856	0.0386648
$638$	−17.8626	−0.707187
$639$	−6.70088	−0.265083
$640$	1.98195	0.0783435
$641$	7.00182	0.276555	0.138278	−	0.990394i	$-0.455843\pi$
$641$	7.00182	0.276555	0.138278	+	0.990394i	$0.455843\pi$
$642$	−4.50493	−0.177795
$643$	41.1626	1.62330	0.811648	−	0.584147i	$-0.198571\pi$
$643$	41.1626	1.62330	0.811648	+	0.584147i	$0.198571\pi$
$644$	22.5421	0.888284
$645$	−0.973094	−0.0383155
$646$	−4.16864	−0.164013
$647$	−45.6014	−1.79278	−0.896389	−	0.443269i	$-0.853819\pi$
$647$	−45.6014	−1.79278	−0.896389	+	0.443269i	$0.853819\pi$
$648$	−1.00000	−0.0392837
$649$	−6.11492	−0.240032
$650$	−1.83749	−0.0720723
$651$	16.2817	0.638130
$652$	−14.4631	−0.566417
$653$	27.3240	1.06927	0.534634	−	0.845083i	$-0.320449\pi$
$653$	27.3240	1.06927	0.534634	+	0.845083i	$0.320449\pi$
$654$	−8.89417	−0.347790
$655$	17.0487	0.666149
$656$	6.28450	0.245369
$657$	13.8160	0.539013
$658$	−6.57054	−0.256146
$659$	−36.1773	−1.40927	−0.704634	−	0.709571i	$-0.748889\pi$
$659$	−36.1773	−1.40927	−0.704634	+	0.709571i	$0.748889\pi$
$660$	−12.1195	−0.471750
$661$	−14.7850	−0.575070	−0.287535	−	0.957770i	$-0.592836\pi$
$661$	−14.7850	−0.575070	−0.287535	+	0.957770i	$0.592836\pi$
$662$	20.8182	0.809122
$663$	−1.71429	−0.0665773
$664$	0.548934	0.0213028
$665$	20.9516	0.812469
$666$	−0.684941	−0.0265409
$667$	−25.9668	−1.00544
$668$	−21.2926	−0.823836
$669$	14.6130	0.564971
$670$	−4.61762	−0.178394
$671$	15.0288	0.580179
$672$	2.53589	0.0978242
$673$	−7.44733	−0.287073	−0.143537	−	0.989645i	$-0.545848\pi$
$673$	−7.44733	−0.287073	−0.143537	+	0.989645i	$0.545848\pi$
$674$	−15.5792	−0.600090
$675$	−1.07187	−0.0412563
$676$	−10.0612	−0.386970
$677$	0.360414	0.0138518	0.00692591	−	0.999976i	$-0.497795\pi$
$677$	0.360414	0.0138518	0.00692591	+	0.999976i	$0.497795\pi$
$678$	−1.75660	−0.0674618
$679$	10.8701	0.417155
$680$	1.98195	0.0760044
$681$	−11.9386	−0.457487
$682$	39.2609	1.50338
$683$	−3.70335	−0.141705	−0.0708523	−	0.997487i	$-0.522572\pi$
$683$	−3.70335	−0.141705	−0.0708523	+	0.997487i	$0.522572\pi$
$684$	4.16864	0.159392
$685$	13.8210	0.528073
$686$	−19.1948	−0.732861
$687$	−7.88952	−0.301004
$688$	0.490978	0.0187183
$689$	14.9004	0.567659
$690$	−17.6180	−0.670706
$691$	−29.0679	−1.10579	−0.552897	−	0.833250i	$-0.686478\pi$
$691$	−29.0679	−1.10579	−0.552897	+	0.833250i	$0.686478\pi$
$692$	−17.7535	−0.674886
$693$	−15.5068	−0.589054
$694$	−13.5483	−0.514286
$695$	34.4084	1.30519
$696$	−2.92115	−0.110726
$697$	6.28450	0.238042
$698$	−9.98156	−0.377808
$699$	−4.34628	−0.164391
$700$	2.71815	0.102736
$701$	−7.73448	−0.292127	−0.146064	−	0.989275i	$-0.546660\pi$
$701$	−7.73448	−0.292127	−0.146064	+	0.989275i	$0.546660\pi$
$702$	1.71429	0.0647015
$703$	2.85527	0.107689
$704$	6.11492	0.230465
$705$	5.13527	0.193405
$706$	6.11437	0.230117
$707$	−39.5032	−1.48567
$708$	−1.00000	−0.0375823
$709$	5.32057	0.199818	0.0999091	−	0.994997i	$-0.468145\pi$
$709$	5.32057	0.199818	0.0999091	+	0.994997i	$0.468145\pi$
$710$	−13.2808	−0.498420
$711$	3.42675	0.128513
$712$	14.1501	0.530298
$713$	57.0732	2.13741
$714$	2.53589	0.0949034
$715$	20.7762	0.776987
$716$	0.878112	0.0328166
$717$	−10.3872	−0.387916
$718$	−23.4658	−0.875738
$719$	−12.3648	−0.461130	−0.230565	−	0.973057i	$-0.574057\pi$
$719$	−12.3648	−0.461130	−0.230565	+	0.973057i	$0.574057\pi$
$720$	−1.98195	−0.0738630
$721$	−33.9847	−1.26565
$722$	1.62248	0.0603824
$723$	−17.1707	−0.638585
$724$	−20.6530	−0.767564
$725$	−3.13109	−0.116286
$726$	−26.3923	−0.979509
$727$	−4.04734	−0.150108	−0.0750538	−	0.997179i	$-0.523913\pi$
$727$	−4.04734	−0.150108	−0.0750538	+	0.997179i	$0.523913\pi$
$728$	−4.34724	−0.161120
$729$	1.00000	0.0370370
$730$	27.3826	1.01348
$731$	0.490978	0.0181595
$732$	2.45772	0.0908399
$733$	−22.1465	−0.817999	−0.409000	−	0.912535i	$-0.634122\pi$
$733$	−22.1465	−0.817999	−0.409000	+	0.912535i	$0.634122\pi$
$734$	33.1741	1.22448
$735$	1.12822	0.0416152
$736$	8.88922	0.327661
$737$	−14.2468	−0.524787
$738$	−6.28450	−0.231336
$739$	12.8708	0.473462	0.236731	−	0.971575i	$-0.423924\pi$
$739$	12.8708	0.473462	0.236731	+	0.971575i	$0.423924\pi$
$740$	−1.35752	−0.0499034
$741$	−7.14623	−0.262523
$742$	−22.0417	−0.809176
$743$	−11.9626	−0.438866	−0.219433	−	0.975628i	$-0.570421\pi$
$743$	−11.9626	−0.438866	−0.219433	+	0.975628i	$0.570421\pi$
$744$	6.42050	0.235387
$745$	15.8228	0.579702
$746$	24.8570	0.910080
$747$	−0.548934	−0.0200845
$748$	6.11492	0.223584
$749$	−11.4240	−0.417424
$750$	−12.0341	−0.439425
$751$	−2.07552	−0.0757366	−0.0378683	−	0.999283i	$-0.512057\pi$
$751$	−2.07552	−0.0757366	−0.0378683	+	0.999283i	$0.512057\pi$
$752$	−2.59102	−0.0944846
$753$	4.17427	0.152119
$754$	5.00769	0.182369
$755$	−1.56479	−0.0569486
$756$	−2.53589	−0.0922295
$757$	37.9832	1.38052	0.690261	−	0.723561i	$-0.257496\pi$
$757$	37.9832	1.38052	0.690261	+	0.723561i	$0.257496\pi$
$758$	9.53862	0.346458
$759$	−54.3569	−1.97303
$760$	8.26203	0.299695
$761$	29.1446	1.05649	0.528246	−	0.849092i	$-0.322850\pi$
$761$	29.1446	1.05649	0.528246	+	0.849092i	$0.322850\pi$
$762$	−14.5290	−0.526331
$763$	−22.5547	−0.816534
$764$	−0.812845	−0.0294077
$765$	−1.98195	−0.0716576
$766$	23.7671	0.858740
$767$	1.71429	0.0618993
$768$	1.00000	0.0360844
$769$	−48.0089	−1.73124	−0.865622	−	0.500697i	$-0.833077\pi$
$769$	−48.0089	−1.73124	−0.865622	+	0.500697i	$0.833077\pi$
$770$	−30.7337	−1.10757
$771$	−11.6636	−0.420053
$772$	−11.7174	−0.421719
$773$	7.59811	0.273285	0.136643	−	0.990620i	$-0.456369\pi$
$773$	7.59811	0.273285	0.136643	+	0.990620i	$0.456369\pi$
$774$	−0.490978	−0.0176478
$775$	6.88194	0.247207
$776$	4.28648	0.153876
$777$	−1.73694	−0.0623123
$778$	20.2240	0.725066
$779$	26.1978	0.938633
$780$	3.39763	0.121655
$781$	−40.9753	−1.46621
$782$	8.88922	0.317878
$783$	2.92115	0.104393
$784$	−0.569249	−0.0203303
$785$	23.5353	0.840010
$786$	8.60199	0.306823
$787$	41.2769	1.47136	0.735682	−	0.677327i	$-0.236862\pi$
$787$	41.2769	1.47136	0.735682	+	0.677327i	$0.236862\pi$
$788$	−18.5124	−0.659475
$789$	−18.6856	−0.665225
$790$	6.79166	0.241636
$791$	−4.45454	−0.158385
$792$	−6.11492	−0.217284
$793$	−4.21323	−0.149616
$794$	18.8087	0.667496
$795$	17.2269	0.610975
$796$	26.2585	0.930708
$797$	14.0847	0.498904	0.249452	−	0.968387i	$-0.419749\pi$
$797$	14.0847	0.498904	0.249452	+	0.968387i	$0.419749\pi$
$798$	10.5712	0.374217
$799$	−2.59102	−0.0916636
$800$	1.07187	0.0378963
$801$	−14.1501	−0.499970
$802$	−13.2635	−0.468351
$803$	84.4837	2.98136
$804$	−2.32984	−0.0821670
$805$	−44.6774	−1.57467
$806$	−11.0066	−0.387690
$807$	−17.3736	−0.611581
$808$	−15.5776	−0.548020
$809$	−36.2715	−1.27524	−0.637618	−	0.770352i	$-0.720080\pi$
$809$	−36.2715	−1.27524	−0.637618	+	0.770352i	$0.720080\pi$
$810$	1.98195	0.0696387
$811$	−39.7728	−1.39661	−0.698306	−	0.715799i	$-0.746063\pi$
$811$	−39.7728	−1.39661	−0.698306	+	0.715799i	$0.746063\pi$
$812$	−7.40772	−0.259960
$813$	−13.3491	−0.468173
$814$	−4.18836	−0.146802
$815$	28.6651	1.00409
$816$	1.00000	0.0350070
$817$	2.04671	0.0716052
$818$	−24.4677	−0.855493
$819$	4.34724	0.151905
$820$	−12.4556	−0.434967
$821$	53.2431	1.85820	0.929098	−	0.369834i	$-0.120585\pi$
$821$	53.2431	1.85820	0.929098	+	0.369834i	$0.120585\pi$
$822$	6.97343	0.243226
$823$	45.9233	1.60079	0.800394	−	0.599475i	$-0.204624\pi$
$823$	45.9233	1.60079	0.800394	+	0.599475i	$0.204624\pi$
$824$	−13.4015	−0.466862
$825$	−6.55440	−0.228195
$826$	−2.53589	−0.0882350
$827$	14.4885	0.503816	0.251908	−	0.967751i	$-0.418942\pi$
$827$	14.4885	0.503816	0.251908	+	0.967751i	$0.418942\pi$
$828$	−8.88922	−0.308922
$829$	−18.3729	−0.638119	−0.319059	−	0.947735i	$-0.603367\pi$
$829$	−18.3729	−0.638119	−0.319059	+	0.947735i	$0.603367\pi$
$830$	−1.08796	−0.0377637
$831$	17.5884	0.610135
$832$	−1.71429	−0.0594322
$833$	−0.569249	−0.0197233
$834$	17.3609	0.601159
$835$	42.2009	1.46042
$836$	25.4909	0.881620
$837$	−6.42050	−0.221925
$838$	27.3552	0.944969
$839$	−2.76959	−0.0956168	−0.0478084	−	0.998857i	$-0.515224\pi$
$839$	−2.76959	−0.0956168	−0.0478084	+	0.998857i	$0.515224\pi$
$840$	−5.02601	−0.173414
$841$	−20.4669	−0.705755
$842$	−8.99127	−0.309860
$843$	−30.1045	−1.03685
$844$	−10.2801	−0.353857
$845$	19.9409	0.685986
$846$	2.59102	0.0890810
$847$	−66.9280	−2.29967
$848$	−8.69189	−0.298481
$849$	−3.26407	−0.112023
$850$	1.07187	0.0367648
$851$	−6.08859	−0.208714
$852$	−6.70088	−0.229568
$853$	−34.0927	−1.16731	−0.583656	−	0.812001i	$-0.698378\pi$
$853$	−34.0927	−1.16731	−0.583656	+	0.812001i	$0.698378\pi$
$854$	6.23251	0.213272
$855$	−8.26203	−0.282556
$856$	−4.50493	−0.153975
$857$	55.7049	1.90284	0.951421	−	0.307893i	$-0.0996240\pi$
$857$	55.7049	1.90284	0.951421	+	0.307893i	$0.0996240\pi$
$858$	10.4827	0.357874
$859$	−31.6275	−1.07912	−0.539559	−	0.841948i	$-0.681409\pi$
$859$	−31.6275	−1.07912	−0.539559	+	0.841948i	$0.681409\pi$
$860$	−0.973094	−0.0331822
$861$	−15.9368	−0.543125
$862$	−35.1492	−1.19718
$863$	−23.0423	−0.784371	−0.392185	−	0.919886i	$-0.628281\pi$
$863$	−23.0423	−0.784371	−0.392185	+	0.919886i	$0.628281\pi$
$864$	−1.00000	−0.0340207
$865$	35.1865	1.19638
$866$	0.639007	0.0217143
$867$	1.00000	0.0339618
$868$	16.2817	0.552637
$869$	20.9543	0.710827
$870$	5.78958	0.196285
$871$	3.99401	0.135332
$872$	−8.89417	−0.301195
$873$	−4.28648	−0.145076
$874$	37.0559	1.25344
$875$	−30.5173	−1.03167
$876$	13.8160	0.466799
$877$	25.3932	0.857467	0.428734	−	0.903431i	$-0.358960\pi$
$877$	25.3932	0.857467	0.428734	+	0.903431i	$0.358960\pi$
$878$	−31.9049	−1.07674
$879$	−28.4323	−0.958996
$880$	−12.1195	−0.408547
$881$	−44.0535	−1.48420	−0.742100	−	0.670289i	$-0.766170\pi$
$881$	−44.0535	−1.48420	−0.742100	+	0.670289i	$0.766170\pi$
$882$	0.569249	0.0191676
$883$	−43.9011	−1.47739	−0.738695	−	0.674040i	$-0.764557\pi$
$883$	−43.9011	−1.47739	−0.738695	+	0.674040i	$0.764557\pi$
$884$	−1.71429	−0.0576577
$885$	1.98195	0.0666226
$886$	2.55401	0.0858036
$887$	46.4482	1.55958	0.779789	−	0.626043i	$-0.215326\pi$
$887$	46.4482	1.55958	0.779789	+	0.626043i	$0.215326\pi$
$888$	−0.684941	−0.0229851
$889$	−36.8440	−1.23571
$890$	−28.0448	−0.940065
$891$	6.11492	0.204858
$892$	14.6130	0.489279
$893$	−10.8010	−0.361442
$894$	7.98343	0.267006
$895$	−1.74038	−0.0581743
$896$	2.53589	0.0847182
$897$	15.2387	0.508804
$898$	−2.32417	−0.0775586
$899$	−18.7552	−0.625523
$900$	−1.07187	−0.0357290
$901$	−8.69189	−0.289569
$902$	−38.4292	−1.27955
$903$	−1.24507	−0.0414332
$904$	−1.75660	−0.0584236
$905$	40.9333	1.36067
$906$	−0.789521	−0.0262301
$907$	−23.1072	−0.767261	−0.383631	−	0.923487i	$-0.625326\pi$
$907$	−23.1072	−0.767261	−0.383631	+	0.923487i	$0.625326\pi$
$908$	−11.9386	−0.396195
$909$	15.5776	0.516678
$910$	8.61602	0.285618
$911$	27.9080	0.924632	0.462316	−	0.886715i	$-0.347019\pi$
$911$	27.9080	0.924632	0.462316	+	0.886715i	$0.347019\pi$
$912$	4.16864	0.138037
$913$	−3.35669	−0.111090
$914$	−4.44849	−0.147143
$915$	−4.87108	−0.161033
$916$	−7.88952	−0.260677
$917$	21.8137	0.720352
$918$	−1.00000	−0.0330049
$919$	−9.43064	−0.311088	−0.155544	−	0.987829i	$-0.549713\pi$
$919$	−9.43064	−0.311088	−0.155544	+	0.987829i	$0.549713\pi$
$920$	−17.6180	−0.580848
$921$	22.0522	0.726643
$922$	−31.5586	−1.03933
$923$	11.4872	0.378106
$924$	−15.5068	−0.510136
$925$	−0.734168	−0.0241393
$926$	33.9587	1.11595
$927$	13.4015	0.440162
$928$	−2.92115	−0.0958915
$929$	25.2676	0.829002	0.414501	−	0.910049i	$-0.363956\pi$
$929$	25.2676	0.829002	0.414501	+	0.910049i	$0.363956\pi$
$930$	−12.7251	−0.417273
$931$	−2.37299	−0.0777717
$932$	−4.34628	−0.142367
$933$	−25.3155	−0.828793
$934$	39.8442	1.30374
$935$	−12.1195	−0.396349
$936$	1.71429	0.0560332
$937$	15.4694	0.505364	0.252682	−	0.967549i	$-0.418687\pi$
$937$	15.4694	0.505364	0.252682	+	0.967549i	$0.418687\pi$
$938$	−5.90822	−0.192910
$939$	4.68133	0.152770
$940$	5.13527	0.167494
$941$	59.4665	1.93855	0.969276	−	0.245977i	$-0.0791089\pi$
$941$	59.4665	1.93855	0.969276	+	0.245977i	$0.0791089\pi$
$942$	11.8748	0.386902
$943$	−55.8643	−1.81919
$944$	−1.00000	−0.0325472
$945$	5.02601	0.163496
$946$	−3.00229	−0.0976129
$947$	−3.90103	−0.126766	−0.0633832	−	0.997989i	$-0.520189\pi$
$947$	−3.90103	−0.126766	−0.0633832	+	0.997989i	$0.520189\pi$
$948$	3.42675	0.111296
$949$	−23.6845	−0.768833
$950$	4.46824	0.144969
$951$	4.79577	0.155514
$952$	2.53589	0.0821887
$953$	−45.3850	−1.47017	−0.735083	−	0.677978i	$-0.762857\pi$
$953$	−45.3850	−1.47017	−0.735083	+	0.677978i	$0.762857\pi$
$954$	8.69189	0.281410
$955$	1.61102	0.0521314
$956$	−10.3872	−0.335945
$957$	17.8626	0.577416
$958$	6.89494	0.222766
$959$	17.6839	0.571042
$960$	−1.98195	−0.0639672
$961$	10.2228	0.329769
$962$	1.17418	0.0378572
$963$	4.50493	0.145169
$964$	−17.1707	−0.553031
$965$	23.2233	0.747585
$966$	−22.5421	−0.725280
$967$	36.6887	1.17983	0.589915	−	0.807466i	$-0.299161\pi$
$967$	36.6887	1.17983	0.589915	+	0.807466i	$0.299161\pi$
$968$	−26.3923	−0.848280
$969$	4.16864	0.133916
$970$	−8.49560	−0.272777
$971$	29.1417	0.935200	0.467600	−	0.883940i	$-0.345119\pi$
$971$	29.1417	0.935200	0.467600	+	0.883940i	$0.345119\pi$
$972$	1.00000	0.0320750
$973$	44.0254	1.41139
$974$	−9.59035	−0.307295
$975$	1.83749	0.0588468
$976$	2.45772	0.0786697
$977$	−6.24037	−0.199647	−0.0998236	−	0.995005i	$-0.531828\pi$
$977$	−6.24037	−0.199647	−0.0998236	+	0.995005i	$0.531828\pi$
$978$	14.4631	0.462477
$979$	−86.5269	−2.76541
$980$	1.12822	0.0360398
$981$	8.89417	0.283969
$982$	−6.82051	−0.217651
$983$	−23.3817	−0.745759	−0.372880	−	0.927880i	$-0.621630\pi$
$983$	−23.3817	−0.745759	−0.372880	+	0.927880i	$0.621630\pi$
$984$	−6.28450	−0.200343
$985$	36.6906	1.16906
$986$	−2.92115	−0.0930284
$987$	6.57054	0.209143
$988$	−7.14623	−0.227352
$989$	−4.36441	−0.138780
$990$	12.1195	0.385182
$991$	−25.4564	−0.808650	−0.404325	−	0.914615i	$-0.632493\pi$
$991$	−25.4564	−0.808650	−0.404325	+	0.914615i	$0.632493\pi$
$992$	6.42050	0.203851
$993$	−20.8182	−0.660645
$994$	−16.9927	−0.538976
$995$	−52.0431	−1.64988
$996$	−0.548934	−0.0173936
$997$	−16.8530	−0.533738	−0.266869	−	0.963733i	$-0.585989\pi$
$997$	−16.8530	−0.533738	−0.266869	+	0.963733i	$0.585989\pi$
$998$	−6.86311	−0.217248
$999$	0.684941	0.0216706

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.t.1.4	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.t.1.4	✓	8	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.98195 q^{5} -1.00000 q^{6} -2.53589 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.98195 q^{5} -1.00000 q^{6} -2.53589 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.98195 q^{10} +6.11492 q^{11} +1.00000 q^{12} -1.71429 q^{13} +2.53589 q^{14} -1.98195 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} +4.16864 q^{19} -1.98195 q^{20} -2.53589 q^{21} -6.11492 q^{22} -8.88922 q^{23} -1.00000 q^{24} -1.07187 q^{25} +1.71429 q^{26} +1.00000 q^{27} -2.53589 q^{28} +2.92115 q^{29} +1.98195 q^{30} -6.42050 q^{31} -1.00000 q^{32} +6.11492 q^{33} -1.00000 q^{34} +5.02601 q^{35} +1.00000 q^{36} +0.684941 q^{37} -4.16864 q^{38} -1.71429 q^{39} +1.98195 q^{40} +6.28450 q^{41} +2.53589 q^{42} +0.490978 q^{43} +6.11492 q^{44} -1.98195 q^{45} +8.88922 q^{46} -2.59102 q^{47} +1.00000 q^{48} -0.569249 q^{49} +1.07187 q^{50} +1.00000 q^{51} -1.71429 q^{52} -8.69189 q^{53} -1.00000 q^{54} -12.1195 q^{55} +2.53589 q^{56} +4.16864 q^{57} -2.92115 q^{58} -1.00000 q^{59} -1.98195 q^{60} +2.45772 q^{61} +6.42050 q^{62} -2.53589 q^{63} +1.00000 q^{64} +3.39763 q^{65} -6.11492 q^{66} -2.32984 q^{67} +1.00000 q^{68} -8.88922 q^{69} -5.02601 q^{70} -6.70088 q^{71} -1.00000 q^{72} +13.8160 q^{73} -0.684941 q^{74} -1.07187 q^{75} +4.16864 q^{76} -15.5068 q^{77} +1.71429 q^{78} +3.42675 q^{79} -1.98195 q^{80} +1.00000 q^{81} -6.28450 q^{82} -0.548934 q^{83} -2.53589 q^{84} -1.98195 q^{85} -0.490978 q^{86} +2.92115 q^{87} -6.11492 q^{88} -14.1501 q^{89} +1.98195 q^{90} +4.34724 q^{91} -8.88922 q^{92} -6.42050 q^{93} +2.59102 q^{94} -8.26203 q^{95} -1.00000 q^{96} -4.28648 q^{97} +0.569249 q^{98} +6.11492 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 8 q^{3} + 8 q^{4} - 6 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q - 8 * q^2 + 8 * q^3 + 8 * q^4 - 6 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^8 + 8 * q^9	\( 8 q - 8 q^{2} + 8 q^{3} + 8 q^{4} - 6 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{8} + 8 q^{9} + 6 q^{10} + q^{11} + 8 q^{12} - 2 q^{13} + 4 q^{14} - 6 q^{15} + 8 q^{16} + 8 q^{17} - 8 q^{18} + 4 q^{19} - 6 q^{20} - 4 q^{21} - q^{22} - 11 q^{23} - 8 q^{24} + 6 q^{25} + 2 q^{26} + 8 q^{27} - 4 q^{28} - 12 q^{29} + 6 q^{30} - 9 q^{31} - 8 q^{32} + q^{33} - 8 q^{34} - 28 q^{35} + 8 q^{36} - 22 q^{37} - 4 q^{38} - 2 q^{39} + 6 q^{40} - 19 q^{41} + 4 q^{42} - 5 q^{43} + q^{44} - 6 q^{45} + 11 q^{46} - 26 q^{47} + 8 q^{48} - 6 q^{50} + 8 q^{51} - 2 q^{52} - 21 q^{53} - 8 q^{54} - 13 q^{55} + 4 q^{56} + 4 q^{57} + 12 q^{58} - 8 q^{59} - 6 q^{60} + 9 q^{61} + 9 q^{62} - 4 q^{63} + 8 q^{64} + 14 q^{65} - q^{66} + 26 q^{67} + 8 q^{68} - 11 q^{69} + 28 q^{70} - 14 q^{71} - 8 q^{72} + 17 q^{73} + 22 q^{74} + 6 q^{75} + 4 q^{76} - 18 q^{77} + 2 q^{78} - 39 q^{79} - 6 q^{80} + 8 q^{81} + 19 q^{82} - 11 q^{83} - 4 q^{84} - 6 q^{85} + 5 q^{86} - 12 q^{87} - q^{88} + 6 q^{90} + 11 q^{91} - 11 q^{92} - 9 q^{93} + 26 q^{94} - 15 q^{95} - 8 q^{96} + 16 q^{97} + q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 + 8 * q^3 + 8 * q^4 - 6 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^8 + 8 * q^9 + 6 * q^10 + q^11 + 8 * q^12 - 2 * q^13 + 4 * q^14 - 6 * q^15 + 8 * q^16 + 8 * q^17 - 8 * q^18 + 4 * q^19 - 6 * q^20 - 4 * q^21 - q^22 - 11 * q^23 - 8 * q^24 + 6 * q^25 + 2 * q^26 + 8 * q^27 - 4 * q^28 - 12 * q^29 + 6 * q^30 - 9 * q^31 - 8 * q^32 + q^33 - 8 * q^34 - 28 * q^35 + 8 * q^36 - 22 * q^37 - 4 * q^38 - 2 * q^39 + 6 * q^40 - 19 * q^41 + 4 * q^42 - 5 * q^43 + q^44 - 6 * q^45 + 11 * q^46 - 26 * q^47 + 8 * q^48 - 6 * q^50 + 8 * q^51 - 2 * q^52 - 21 * q^53 - 8 * q^54 - 13 * q^55 + 4 * q^56 + 4 * q^57 + 12 * q^58 - 8 * q^59 - 6 * q^60 + 9 * q^61 + 9 * q^62 - 4 * q^63 + 8 * q^64 + 14 * q^65 - q^66 + 26 * q^67 + 8 * q^68 - 11 * q^69 + 28 * q^70 - 14 * q^71 - 8 * q^72 + 17 * q^73 + 22 * q^74 + 6 * q^75 + 4 * q^76 - 18 * q^77 + 2 * q^78 - 39 * q^79 - 6 * q^80 + 8 * q^81 + 19 * q^82 - 11 * q^83 - 4 * q^84 - 6 * q^85 + 5 * q^86 - 12 * q^87 - q^88 + 6 * q^90 + 11 * q^91 - 11 * q^92 - 9 * q^93 + 26 * q^94 - 15 * q^95 - 8 * q^96 + 16 * q^97 + q^99

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