LMFDB - Embedded newform 6042.2.a.v.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6042,2,Mod(1,6042)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6042, 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("6042.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6042 = 2 \cdot 3 \cdot 19 \cdot 53 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6042.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:	$48.2456129013$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.21848308.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} - 4x^{4} + 9x^{3} + 6x^{2} - 4x - 2 $ x^6 - 3x^5 - 4x^4 + 9x^3 + 6x^2 - 4*x - 2
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			$3.24366$ of defining polynomial
Character	$\chi$	$=$	6042.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.840706 q^{5} -1.00000 q^{6} -3.39143 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.840706 q^{5} -1.00000 q^{6} -3.39143 q^{7} -1.00000 q^{8} +1.00000 q^{9} -0.840706 q^{10} +5.97063 q^{11} +1.00000 q^{12} +0.0340297 q^{13} +3.39143 q^{14} +0.840706 q^{15} +1.00000 q^{16} -4.77731 q^{17} -1.00000 q^{18} +1.00000 q^{19} +0.840706 q^{20} -3.39143 q^{21} -5.97063 q^{22} -0.864244 q^{23} -1.00000 q^{24} -4.29321 q^{25} -0.0340297 q^{26} +1.00000 q^{27} -3.39143 q^{28} -7.98112 q^{29} -0.840706 q^{30} +10.2054 q^{31} -1.00000 q^{32} +5.97063 q^{33} +4.77731 q^{34} -2.85120 q^{35} +1.00000 q^{36} -4.18377 q^{37} -1.00000 q^{38} +0.0340297 q^{39} -0.840706 q^{40} -4.94060 q^{41} +3.39143 q^{42} -5.10560 q^{43} +5.97063 q^{44} +0.840706 q^{45} +0.864244 q^{46} -2.95109 q^{47} +1.00000 q^{48} +4.50181 q^{49} +4.29321 q^{50} -4.77731 q^{51} +0.0340297 q^{52} -1.00000 q^{53} -1.00000 q^{54} +5.01955 q^{55} +3.39143 q^{56} +1.00000 q^{57} +7.98112 q^{58} -9.09303 q^{59} +0.840706 q^{60} -1.02211 q^{61} -10.2054 q^{62} -3.39143 q^{63} +1.00000 q^{64} +0.0286090 q^{65} -5.97063 q^{66} -14.0735 q^{67} -4.77731 q^{68} -0.864244 q^{69} +2.85120 q^{70} -2.68465 q^{71} -1.00000 q^{72} -0.0692174 q^{73} +4.18377 q^{74} -4.29321 q^{75} +1.00000 q^{76} -20.2490 q^{77} -0.0340297 q^{78} +3.25089 q^{79} +0.840706 q^{80} +1.00000 q^{81} +4.94060 q^{82} +15.1475 q^{83} -3.39143 q^{84} -4.01631 q^{85} +5.10560 q^{86} -7.98112 q^{87} -5.97063 q^{88} +13.5725 q^{89} -0.840706 q^{90} -0.115409 q^{91} -0.864244 q^{92} +10.2054 q^{93} +2.95109 q^{94} +0.840706 q^{95} -1.00000 q^{96} -17.6530 q^{97} -4.50181 q^{98} +5.97063 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} + 6 q^{3} + 6 q^{4} + 3 q^{5} - 6 q^{6} - 7 q^{7} - 6 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 + 6 * q^3 + 6 * q^4 + 3 * q^5 - 6 * q^6 - 7 * q^7 - 6 * q^8 + 6 * q^9	\( 6 q - 6 q^{2} + 6 q^{3} + 6 q^{4} + 3 q^{5} - 6 q^{6} - 7 q^{7} - 6 q^{8} + 6 q^{9} - 3 q^{10} + q^{11} + 6 q^{12} - 13 q^{13} + 7 q^{14} + 3 q^{15} + 6 q^{16} - 5 q^{17} - 6 q^{18} + 6 q^{19} + 3 q^{20} - 7 q^{21} - q^{22} + 9 q^{23} - 6 q^{24} - 5 q^{25} + 13 q^{26} + 6 q^{27} - 7 q^{28} - 12 q^{29} - 3 q^{30} - 2 q^{31} - 6 q^{32} + q^{33} + 5 q^{34} - 14 q^{35} + 6 q^{36} - 7 q^{37} - 6 q^{38} - 13 q^{39} - 3 q^{40} - 18 q^{41} + 7 q^{42} - 11 q^{43} + q^{44} + 3 q^{45} - 9 q^{46} - 5 q^{47} + 6 q^{48} + 3 q^{49} + 5 q^{50} - 5 q^{51} - 13 q^{52} - 6 q^{53} - 6 q^{54} + 8 q^{55} + 7 q^{56} + 6 q^{57} + 12 q^{58} + 2 q^{59} + 3 q^{60} - 12 q^{61} + 2 q^{62} - 7 q^{63} + 6 q^{64} - 5 q^{65} - q^{66} - 9 q^{67} - 5 q^{68} + 9 q^{69} + 14 q^{70} + 18 q^{71} - 6 q^{72} - 31 q^{73} + 7 q^{74} - 5 q^{75} + 6 q^{76} + q^{77} + 13 q^{78} - 17 q^{79} + 3 q^{80} + 6 q^{81} + 18 q^{82} - 9 q^{83} - 7 q^{84} - 32 q^{85} + 11 q^{86} - 12 q^{87} - q^{88} + 18 q^{89} - 3 q^{90} + 9 q^{92} - 2 q^{93} + 5 q^{94} + 3 q^{95} - 6 q^{96} - 7 q^{97} - 3 q^{98} + q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 + 6 * q^3 + 6 * q^4 + 3 * q^5 - 6 * q^6 - 7 * q^7 - 6 * q^8 + 6 * q^9 - 3 * q^10 + q^11 + 6 * q^12 - 13 * q^13 + 7 * q^14 + 3 * q^15 + 6 * q^16 - 5 * q^17 - 6 * q^18 + 6 * q^19 + 3 * q^20 - 7 * q^21 - q^22 + 9 * q^23 - 6 * q^24 - 5 * q^25 + 13 * q^26 + 6 * q^27 - 7 * q^28 - 12 * q^29 - 3 * q^30 - 2 * q^31 - 6 * q^32 + q^33 + 5 * q^34 - 14 * q^35 + 6 * q^36 - 7 * q^37 - 6 * q^38 - 13 * q^39 - 3 * q^40 - 18 * q^41 + 7 * q^42 - 11 * q^43 + q^44 + 3 * q^45 - 9 * q^46 - 5 * q^47 + 6 * q^48 + 3 * q^49 + 5 * q^50 - 5 * q^51 - 13 * q^52 - 6 * q^53 - 6 * q^54 + 8 * q^55 + 7 * q^56 + 6 * q^57 + 12 * q^58 + 2 * q^59 + 3 * q^60 - 12 * q^61 + 2 * q^62 - 7 * q^63 + 6 * q^64 - 5 * q^65 - q^66 - 9 * q^67 - 5 * q^68 + 9 * q^69 + 14 * q^70 + 18 * q^71 - 6 * q^72 - 31 * q^73 + 7 * q^74 - 5 * q^75 + 6 * q^76 + q^77 + 13 * q^78 - 17 * q^79 + 3 * q^80 + 6 * q^81 + 18 * q^82 - 9 * q^83 - 7 * q^84 - 32 * q^85 + 11 * q^86 - 12 * q^87 - q^88 + 18 * q^89 - 3 * q^90 + 9 * q^92 - 2 * q^93 + 5 * q^94 + 3 * q^95 - 6 * q^96 - 7 * q^97 - 3 * 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
$5$	0.840706	0.375975	0.187988	−	0.982171i	$-0.439804\pi$
$5$	0.840706	0.375975	0.187988	+	0.982171i	$0.439804\pi$
$6$	−1.00000	−0.408248
$7$	−3.39143	−1.28184	−0.640920	−	0.767607i	$-0.721447\pi$
$7$	−3.39143	−1.28184	−0.640920	+	0.767607i	$0.721447\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−0.840706	−0.265855
$11$	5.97063	1.80021	0.900107	−	0.435670i	$-0.143488\pi$
$11$	5.97063	1.80021	0.900107	+	0.435670i	$0.143488\pi$
$12$	1.00000	0.288675
$13$	0.0340297	0.00943814	0.00471907	−	0.999989i	$-0.498498\pi$
$13$	0.0340297	0.00943814	0.00471907	+	0.999989i	$0.498498\pi$
$14$	3.39143	0.906398
$15$	0.840706	0.217069
$16$	1.00000	0.250000
$17$	−4.77731	−1.15867	−0.579334	−	0.815090i	$-0.696687\pi$
$17$	−4.77731	−1.15867	−0.579334	+	0.815090i	$0.696687\pi$
$18$	−1.00000	−0.235702
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	0.840706	0.187988
$21$	−3.39143	−0.740071
$22$	−5.97063	−1.27294
$23$	−0.864244	−0.180207	−0.0901037	−	0.995932i	$-0.528720\pi$
$23$	−0.864244	−0.180207	−0.0901037	+	0.995932i	$0.528720\pi$
$24$	−1.00000	−0.204124
$25$	−4.29321	−0.858643
$26$	−0.0340297	−0.00667377
$27$	1.00000	0.192450
$28$	−3.39143	−0.640920
$29$	−7.98112	−1.48206	−0.741029	−	0.671473i	$-0.765662\pi$
$29$	−7.98112	−1.48206	−0.741029	+	0.671473i	$0.765662\pi$
$30$	−0.840706	−0.153491
$31$	10.2054	1.83294	0.916469	−	0.400105i	$-0.131026\pi$
$31$	10.2054	1.83294	0.916469	+	0.400105i	$0.131026\pi$
$32$	−1.00000	−0.176777
$33$	5.97063	1.03935
$34$	4.77731	0.819302
$35$	−2.85120	−0.481940
$36$	1.00000	0.166667
$37$	−4.18377	−0.687808	−0.343904	−	0.939005i	$-0.611750\pi$
$37$	−4.18377	−0.687808	−0.343904	+	0.939005i	$0.611750\pi$
$38$	−1.00000	−0.162221
$39$	0.0340297	0.00544911
$40$	−0.840706	−0.132927
$41$	−4.94060	−0.771591	−0.385796	−	0.922584i	$-0.626073\pi$
$41$	−4.94060	−0.771591	−0.385796	+	0.922584i	$0.626073\pi$
$42$	3.39143	0.523309
$43$	−5.10560	−0.778596	−0.389298	−	0.921112i	$-0.627282\pi$
$43$	−5.10560	−0.778596	−0.389298	+	0.921112i	$0.627282\pi$
$44$	5.97063	0.900107
$45$	0.840706	0.125325
$46$	0.864244	0.127426
$47$	−2.95109	−0.430460	−0.215230	−	0.976563i	$-0.569050\pi$
$47$	−2.95109	−0.430460	−0.215230	+	0.976563i	$0.569050\pi$
$48$	1.00000	0.144338
$49$	4.50181	0.643116
$50$	4.29321	0.607152
$51$	−4.77731	−0.668957
$52$	0.0340297	0.00471907
$53$	−1.00000	−0.137361
$53$	−1.00000	−0.137361
$54$	−1.00000	−0.136083
$55$	5.01955	0.676835
$56$	3.39143	0.453199
$57$	1.00000	0.132453
$58$	7.98112	1.04797
$59$	−9.09303	−1.18381	−0.591906	−	0.806007i	$-0.701624\pi$
$59$	−9.09303	−1.18381	−0.591906	+	0.806007i	$0.701624\pi$
$60$	0.840706	0.108535
$61$	−1.02211	−0.130868	−0.0654340	−	0.997857i	$-0.520843\pi$
$61$	−1.02211	−0.130868	−0.0654340	+	0.997857i	$0.520843\pi$
$62$	−10.2054	−1.29608
$63$	−3.39143	−0.427280
$64$	1.00000	0.125000
$65$	0.0286090	0.00354851
$66$	−5.97063	−0.734934
$67$	−14.0735	−1.71935	−0.859677	−	0.510839i	$-0.829335\pi$
$67$	−14.0735	−1.71935	−0.859677	+	0.510839i	$0.829335\pi$
$68$	−4.77731	−0.579334
$69$	−0.864244	−0.104043
$70$	2.85120	0.340783
$71$	−2.68465	−0.318609	−0.159304	−	0.987230i	$-0.550925\pi$
$71$	−2.68465	−0.318609	−0.159304	+	0.987230i	$0.550925\pi$
$72$	−1.00000	−0.117851
$73$	−0.0692174	−0.00810129	−0.00405064	−	0.999992i	$-0.501289\pi$
$73$	−0.0692174	−0.00810129	−0.00405064	+	0.999992i	$0.501289\pi$
$74$	4.18377	0.486354
$75$	−4.29321	−0.495738
$76$	1.00000	0.114708
$77$	−20.2490	−2.30759
$78$	−0.0340297	−0.00385311
$79$	3.25089	0.365754	0.182877	−	0.983136i	$-0.441459\pi$
$79$	3.25089	0.365754	0.182877	+	0.983136i	$0.441459\pi$
$80$	0.840706	0.0939938
$81$	1.00000	0.111111
$82$	4.94060	0.545598
$83$	15.1475	1.66266	0.831329	−	0.555780i	$-0.187580\pi$
$83$	15.1475	1.66266	0.831329	+	0.555780i	$0.187580\pi$
$84$	−3.39143	−0.370036
$85$	−4.01631	−0.435630
$86$	5.10560	0.550551
$87$	−7.98112	−0.855666
$88$	−5.97063	−0.636472
$89$	13.5725	1.43868	0.719340	−	0.694659i	$-0.244445\pi$
$89$	13.5725	1.43868	0.719340	+	0.694659i	$0.244445\pi$
$90$	−0.840706	−0.0886182
$91$	−0.115409	−0.0120982
$92$	−0.864244	−0.0901037
$93$	10.2054	1.05825
$94$	2.95109	0.304381
$95$	0.840706	0.0862546
$96$	−1.00000	−0.102062
$97$	−17.6530	−1.79239	−0.896195	−	0.443660i	$-0.853680\pi$
$97$	−17.6530	−1.79239	−0.896195	+	0.443660i	$0.853680\pi$
$98$	−4.50181	−0.454752
$99$	5.97063	0.600071
$100$	−4.29321	−0.429321
$101$	−2.43532	−0.242323	−0.121162	−	0.992633i	$-0.538662\pi$
$101$	−2.43532	−0.242323	−0.121162	+	0.992633i	$0.538662\pi$
$102$	4.77731	0.473024
$103$	14.5415	1.43282	0.716410	−	0.697679i	$-0.245784\pi$
$103$	14.5415	1.43282	0.716410	+	0.697679i	$0.245784\pi$
$104$	−0.0340297	−0.00333689
$105$	−2.85120	−0.278248
$106$	1.00000	0.0971286
$107$	0.770697	0.0745061	0.0372531	−	0.999306i	$-0.488139\pi$
$107$	0.770697	0.0745061	0.0372531	+	0.999306i	$0.488139\pi$
$108$	1.00000	0.0962250
$109$	3.37503	0.323269	0.161635	−	0.986851i	$-0.448323\pi$
$109$	3.37503	0.323269	0.161635	+	0.986851i	$0.448323\pi$
$110$	−5.01955	−0.478595
$111$	−4.18377	−0.397106
$112$	−3.39143	−0.320460
$113$	−1.04169	−0.0979935	−0.0489968	−	0.998799i	$-0.515602\pi$
$113$	−1.04169	−0.0979935	−0.0489968	+	0.998799i	$0.515602\pi$
$114$	−1.00000	−0.0936586
$115$	−0.726575	−0.0677535
$116$	−7.98112	−0.741029
$117$	0.0340297	0.00314605
$118$	9.09303	0.837081
$119$	16.2019	1.48523
$120$	−0.840706	−0.0767456
$121$	24.6484	2.24077
$122$	1.02211	0.0925376
$123$	−4.94060	−0.445479
$124$	10.2054	0.916469
$125$	−7.81286	−0.698803
$126$	3.39143	0.302133
$127$	11.0957	0.984580	0.492290	−	0.870431i	$-0.336160\pi$
$127$	11.0957	0.984580	0.492290	+	0.870431i	$0.336160\pi$
$128$	−1.00000	−0.0883883
$129$	−5.10560	−0.449523
$130$	−0.0286090	−0.00250917
$131$	−1.60845	−0.140531	−0.0702655	−	0.997528i	$-0.522385\pi$
$131$	−1.60845	−0.140531	−0.0702655	+	0.997528i	$0.522385\pi$
$132$	5.97063	0.519677
$133$	−3.39143	−0.294074
$134$	14.0735	1.21577
$135$	0.840706	0.0723564
$136$	4.77731	0.409651
$137$	−4.08856	−0.349309	−0.174654	−	0.984630i	$-0.555881\pi$
$137$	−4.08856	−0.349309	−0.174654	+	0.984630i	$0.555881\pi$
$138$	0.864244	0.0735694
$139$	−15.3512	−1.30207	−0.651037	−	0.759046i	$-0.725666\pi$
$139$	−15.3512	−1.30207	−0.651037	+	0.759046i	$0.725666\pi$
$140$	−2.85120	−0.240970
$141$	−2.95109	−0.248526
$142$	2.68465	0.225290
$143$	0.203179	0.0169907
$144$	1.00000	0.0833333
$145$	−6.70978	−0.557217
$146$	0.0692174	0.00572848
$147$	4.50181	0.371303
$148$	−4.18377	−0.343904
$149$	−14.6758	−1.20229	−0.601143	−	0.799141i	$-0.705288\pi$
$149$	−14.6758	−1.20229	−0.601143	+	0.799141i	$0.705288\pi$
$150$	4.29321	0.350539
$151$	14.7576	1.20096	0.600479	−	0.799640i	$-0.294976\pi$
$151$	14.7576	1.20096	0.600479	+	0.799640i	$0.294976\pi$
$152$	−1.00000	−0.0811107
$153$	−4.77731	−0.386222
$154$	20.2490	1.63171
$155$	8.57971	0.689139
$156$	0.0340297	0.00272456
$157$	4.00171	0.319371	0.159686	−	0.987168i	$-0.448952\pi$
$157$	4.00171	0.319371	0.159686	+	0.987168i	$0.448952\pi$
$158$	−3.25089	−0.258627
$159$	−1.00000	−0.0793052
$160$	−0.840706	−0.0664636
$161$	2.93103	0.230997
$162$	−1.00000	−0.0785674
$163$	−7.98342	−0.625309	−0.312655	−	0.949867i	$-0.601218\pi$
$163$	−7.98342	−0.625309	−0.312655	+	0.949867i	$0.601218\pi$
$164$	−4.94060	−0.385796
$165$	5.01955	0.390771
$166$	−15.1475	−1.17568
$167$	−20.1975	−1.56293	−0.781464	−	0.623951i	$-0.785527\pi$
$167$	−20.1975	−1.56293	−0.781464	+	0.623951i	$0.785527\pi$
$168$	3.39143	0.261655
$169$	−12.9988	−0.999911
$170$	4.01631	0.308037
$171$	1.00000	0.0764719
$172$	−5.10560	−0.389298
$173$	−5.82596	−0.442939	−0.221470	−	0.975167i	$-0.571085\pi$
$173$	−5.82596	−0.442939	−0.221470	+	0.975167i	$0.571085\pi$
$174$	7.98112	0.605047
$175$	14.5601	1.10064
$176$	5.97063	0.450053
$177$	−9.09303	−0.683474
$178$	−13.5725	−1.01730
$179$	10.4147	0.778433	0.389216	−	0.921146i	$-0.372746\pi$
$179$	10.4147	0.778433	0.389216	+	0.921146i	$0.372746\pi$
$180$	0.840706	0.0626625
$181$	−26.4059	−1.96274	−0.981369	−	0.192133i	$-0.938459\pi$
$181$	−26.4059	−1.96274	−0.981369	+	0.192133i	$0.938459\pi$
$182$	0.115409	0.00855472
$183$	−1.02211	−0.0755566
$184$	0.864244	0.0637129
$185$	−3.51732	−0.258599
$186$	−10.2054	−0.748294
$187$	−28.5235	−2.08585
$188$	−2.95109	−0.215230
$189$	−3.39143	−0.246690
$190$	−0.840706	−0.0609912
$191$	26.6628	1.92926	0.964628	−	0.263616i	$-0.0849151\pi$
$191$	26.6628	1.92926	0.964628	+	0.263616i	$0.0849151\pi$
$192$	1.00000	0.0721688
$193$	6.09321	0.438599	0.219299	−	0.975658i	$-0.429623\pi$
$193$	6.09321	0.438599	0.219299	+	0.975658i	$0.429623\pi$
$194$	17.6530	1.26741
$195$	0.0286090	0.00204873
$196$	4.50181	0.321558
$197$	13.2533	0.944259	0.472129	−	0.881529i	$-0.343486\pi$
$197$	13.2533	0.944259	0.472129	+	0.881529i	$0.343486\pi$
$198$	−5.97063	−0.424314
$199$	−22.8313	−1.61846	−0.809232	−	0.587489i	$-0.800117\pi$
$199$	−22.8313	−1.61846	−0.809232	+	0.587489i	$0.800117\pi$
$200$	4.29321	0.303576
$201$	−14.0735	−0.992669
$202$	2.43532	0.171348
$203$	27.0674	1.89976
$204$	−4.77731	−0.334478
$205$	−4.15359	−0.290099
$206$	−14.5415	−1.01316
$207$	−0.864244	−0.0600691
$208$	0.0340297	0.00235954
$209$	5.97063	0.412997
$210$	2.85120	0.196751
$211$	−21.1410	−1.45541	−0.727704	−	0.685891i	$-0.759413\pi$
$211$	−21.1410	−1.45541	−0.727704	+	0.685891i	$0.759413\pi$
$212$	−1.00000	−0.0686803
$213$	−2.68465	−0.183949
$214$	−0.770697	−0.0526838
$215$	−4.29230	−0.292733
$216$	−1.00000	−0.0680414
$217$	−34.6108	−2.34954
$218$	−3.37503	−0.228586
$219$	−0.0692174	−0.00467728
$220$	5.01955	0.338418
$221$	−0.162570	−0.0109357
$222$	4.18377	0.280797
$223$	−8.86230	−0.593464	−0.296732	−	0.954961i	$-0.595897\pi$
$223$	−8.86230	−0.593464	−0.296732	+	0.954961i	$0.595897\pi$
$224$	3.39143	0.226600
$225$	−4.29321	−0.286214
$226$	1.04169	0.0692919
$227$	−23.2370	−1.54230	−0.771148	−	0.636656i	$-0.780317\pi$
$227$	−23.2370	−1.54230	−0.771148	+	0.636656i	$0.780317\pi$
$228$	1.00000	0.0662266
$229$	−7.46821	−0.493513	−0.246757	−	0.969078i	$-0.579365\pi$
$229$	−7.46821	−0.493513	−0.246757	+	0.969078i	$0.579365\pi$
$230$	0.726575	0.0479090
$231$	−20.2490	−1.33229
$232$	7.98112	0.523986
$233$	−4.94567	−0.324001	−0.162001	−	0.986791i	$-0.551795\pi$
$233$	−4.94567	−0.324001	−0.162001	+	0.986791i	$0.551795\pi$
$234$	−0.0340297	−0.00222459
$235$	−2.48100	−0.161842
$236$	−9.09303	−0.591906
$237$	3.25089	0.211168
$238$	−16.2019	−1.05021
$239$	−6.57642	−0.425393	−0.212697	−	0.977118i	$-0.568225\pi$
$239$	−6.57642	−0.425393	−0.212697	+	0.977118i	$0.568225\pi$
$240$	0.840706	0.0542673
$241$	−4.78458	−0.308202	−0.154101	−	0.988055i	$-0.549248\pi$
$241$	−4.78458	−0.308202	−0.154101	+	0.988055i	$0.549248\pi$
$242$	−24.6484	−1.58446
$243$	1.00000	0.0641500
$244$	−1.02211	−0.0654340
$245$	3.78470	0.241796
$246$	4.94060	0.315001
$247$	0.0340297	0.00216526
$248$	−10.2054	−0.648042
$249$	15.1475	0.959936
$250$	7.81286	0.494129
$251$	18.8261	1.18829	0.594145	−	0.804358i	$-0.297491\pi$
$251$	18.8261	1.18829	0.594145	+	0.804358i	$0.297491\pi$
$252$	−3.39143	−0.213640
$253$	−5.16009	−0.324412
$254$	−11.0957	−0.696203
$255$	−4.01631	−0.251511
$256$	1.00000	0.0625000
$257$	27.1661	1.69457	0.847287	−	0.531135i	$-0.178234\pi$
$257$	27.1661	1.69457	0.847287	+	0.531135i	$0.178234\pi$
$258$	5.10560	0.317861
$259$	14.1890	0.881661
$260$	0.0286090	0.00177425
$261$	−7.98112	−0.494019
$262$	1.60845	0.0993704
$263$	−16.7153	−1.03071	−0.515355	−	0.856977i	$-0.672340\pi$
$263$	−16.7153	−1.03071	−0.515355	+	0.856977i	$0.672340\pi$
$264$	−5.97063	−0.367467
$265$	−0.840706	−0.0516441
$266$	3.39143	0.207942
$267$	13.5725	0.830622
$268$	−14.0735	−0.859677
$269$	17.9745	1.09592	0.547962	−	0.836503i	$-0.315404\pi$
$269$	17.9745	1.09592	0.547962	+	0.836503i	$0.315404\pi$
$270$	−0.840706	−0.0511637
$271$	−0.972520	−0.0590764	−0.0295382	−	0.999564i	$-0.509404\pi$
$271$	−0.972520	−0.0590764	−0.0295382	+	0.999564i	$0.509404\pi$
$272$	−4.77731	−0.289667
$273$	−0.115409	−0.00698490
$274$	4.08856	0.246999
$275$	−25.6332	−1.54574
$276$	−0.864244	−0.0520214
$277$	12.1981	0.732912	0.366456	−	0.930435i	$-0.380571\pi$
$277$	12.1981	0.732912	0.366456	+	0.930435i	$0.380571\pi$
$278$	15.3512	0.920705
$279$	10.2054	0.610979
$280$	2.85120	0.170392
$281$	−10.6768	−0.636924	−0.318462	−	0.947936i	$-0.603166\pi$
$281$	−10.6768	−0.636924	−0.318462	+	0.947936i	$0.603166\pi$
$282$	2.95109	0.175735
$283$	−11.7540	−0.698700	−0.349350	−	0.936992i	$-0.613598\pi$
$283$	−11.7540	−0.698700	−0.349350	+	0.936992i	$0.613598\pi$
$284$	−2.68465	−0.159304
$285$	0.840706	0.0497991
$286$	−0.203179	−0.0120142
$287$	16.7557	0.989057
$288$	−1.00000	−0.0589256
$289$	5.82267	0.342510
$290$	6.70978	0.394012
$291$	−17.6530	−1.03484
$292$	−0.0692174	−0.00405064
$293$	−3.84968	−0.224900	−0.112450	−	0.993657i	$-0.535870\pi$
$293$	−3.84968	−0.224900	−0.112450	+	0.993657i	$0.535870\pi$
$294$	−4.50181	−0.262551
$295$	−7.64456	−0.445083
$296$	4.18377	0.243177
$297$	5.97063	0.346451
$298$	14.6758	0.850145
$299$	−0.0294100	−0.00170082
$300$	−4.29321	−0.247869
$301$	17.3153	0.998036
$302$	−14.7576	−0.849206
$303$	−2.43532	−0.139905
$304$	1.00000	0.0573539
$305$	−0.859295	−0.0492031
$306$	4.77731	0.273101
$307$	−22.0677	−1.25947	−0.629736	−	0.776809i	$-0.716837\pi$
$307$	−22.0677	−1.25947	−0.629736	+	0.776809i	$0.716837\pi$
$308$	−20.2490	−1.15379
$309$	14.5415	0.827239
$310$	−8.57971	−0.487295
$311$	14.8666	0.843008	0.421504	−	0.906826i	$-0.361502\pi$
$311$	14.8666	0.843008	0.421504	+	0.906826i	$0.361502\pi$
$312$	−0.0340297	−0.00192655
$313$	−19.2359	−1.08728	−0.543640	−	0.839319i	$-0.682954\pi$
$313$	−19.2359	−1.08728	−0.543640	+	0.839319i	$0.682954\pi$
$314$	−4.00171	−0.225830
$315$	−2.85120	−0.160647
$316$	3.25089	0.182877
$317$	−27.8704	−1.56536	−0.782679	−	0.622425i	$-0.786148\pi$
$317$	−27.8704	−1.56536	−0.782679	+	0.622425i	$0.786148\pi$
$318$	1.00000	0.0560772
$319$	−47.6523	−2.66802
$320$	0.840706	0.0469969
$321$	0.770697	0.0430161
$322$	−2.93103	−0.163340
$323$	−4.77731	−0.265817
$324$	1.00000	0.0555556
$325$	−0.146097	−0.00810399
$326$	7.98342	0.442161
$327$	3.37503	0.186639
$328$	4.94060	0.272799
$329$	10.0084	0.551782
$330$	−5.01955	−0.276317
$331$	−24.4069	−1.34152	−0.670761	−	0.741674i	$-0.734032\pi$
$331$	−24.4069	−1.34152	−0.670761	+	0.741674i	$0.734032\pi$
$332$	15.1475	0.831329
$333$	−4.18377	−0.229269
$334$	20.1975	1.10516
$335$	−11.8317	−0.646434
$336$	−3.39143	−0.185018
$337$	0.383394	0.0208848	0.0104424	−	0.999945i	$-0.496676\pi$
$337$	0.383394	0.0208848	0.0104424	+	0.999945i	$0.496676\pi$
$338$	12.9988	0.707044
$339$	−1.04169	−0.0565766
$340$	−4.01631	−0.217815
$341$	60.9325	3.29968
$342$	−1.00000	−0.0540738
$343$	8.47243	0.457468
$344$	5.10560	0.275275
$345$	−0.726575	−0.0391175
$346$	5.82596	0.313205
$347$	−4.39537	−0.235956	−0.117978	−	0.993016i	$-0.537641\pi$
$347$	−4.39537	−0.235956	−0.117978	+	0.993016i	$0.537641\pi$
$348$	−7.98112	−0.427833
$349$	−18.0900	−0.968333	−0.484167	−	0.874976i	$-0.660877\pi$
$349$	−18.0900	−0.968333	−0.484167	+	0.874976i	$0.660877\pi$
$350$	−14.5601	−0.778272
$351$	0.0340297	0.00181637
$352$	−5.97063	−0.318236
$353$	−31.2278	−1.66209	−0.831044	−	0.556206i	$-0.812256\pi$
$353$	−31.2278	−1.66209	−0.831044	+	0.556206i	$0.812256\pi$
$354$	9.09303	0.483289
$355$	−2.25700	−0.119789
$356$	13.5725	0.719340
$357$	16.2019	0.857496
$358$	−10.4147	−0.550435
$359$	−5.23517	−0.276302	−0.138151	−	0.990411i	$-0.544116\pi$
$359$	−5.23517	−0.276302	−0.138151	+	0.990411i	$0.544116\pi$
$360$	−0.840706	−0.0443091
$361$	1.00000	0.0526316
$362$	26.4059	1.38787
$363$	24.6484	1.29371
$364$	−0.115409	−0.00604910
$365$	−0.0581915	−0.00304588
$366$	1.02211	0.0534266
$367$	2.08727	0.108955	0.0544773	−	0.998515i	$-0.482651\pi$
$367$	2.08727	0.108955	0.0544773	+	0.998515i	$0.482651\pi$
$368$	−0.864244	−0.0450519
$369$	−4.94060	−0.257197
$370$	3.51732	0.182857
$371$	3.39143	0.176074
$372$	10.2054	0.529124
$373$	−14.7594	−0.764213	−0.382107	−	0.924118i	$-0.624801\pi$
$373$	−14.7594	−0.764213	−0.382107	+	0.924118i	$0.624801\pi$
$374$	28.5235	1.47492
$375$	−7.81286	−0.403454
$376$	2.95109	0.152191
$377$	−0.271595	−0.0139879
$378$	3.39143	0.174436
$379$	9.08121	0.466471	0.233235	−	0.972420i	$-0.425069\pi$
$379$	9.08121	0.466471	0.233235	+	0.972420i	$0.425069\pi$
$380$	0.840706	0.0431273
$381$	11.0957	0.568448
$382$	−26.6628	−1.36419
$383$	28.2968	1.44590	0.722949	−	0.690902i	$-0.242786\pi$
$383$	28.2968	1.44590	0.722949	+	0.690902i	$0.242786\pi$
$384$	−1.00000	−0.0510310
$385$	−17.0234	−0.867595
$386$	−6.09321	−0.310136
$387$	−5.10560	−0.259532
$388$	−17.6530	−0.896195
$389$	0.813679	0.0412552	0.0206276	−	0.999787i	$-0.493434\pi$
$389$	0.813679	0.0412552	0.0206276	+	0.999787i	$0.493434\pi$
$390$	−0.0286090	−0.00144867
$391$	4.12876	0.208800
$392$	−4.50181	−0.227376
$393$	−1.60845	−0.0811356
$394$	−13.2533	−0.667692
$395$	2.73304	0.137514
$396$	5.97063	0.300036
$397$	19.4933	0.978338	0.489169	−	0.872189i	$-0.337300\pi$
$397$	19.4933	0.978338	0.489169	+	0.872189i	$0.337300\pi$
$398$	22.8313	1.14443
$399$	−3.39143	−0.169784
$400$	−4.29321	−0.214661
$401$	30.1940	1.50782	0.753909	−	0.656979i	$-0.228166\pi$
$401$	30.1940	1.50782	0.753909	+	0.656979i	$0.228166\pi$
$402$	14.0735	0.701923
$403$	0.347286	0.0172995
$404$	−2.43532	−0.121162
$405$	0.840706	0.0417750
$406$	−27.0674	−1.34333
$407$	−24.9798	−1.23820
$408$	4.77731	0.236512
$409$	26.0228	1.28675	0.643373	−	0.765552i	$-0.277534\pi$
$409$	26.0228	1.28675	0.643373	+	0.765552i	$0.277534\pi$
$410$	4.15359	0.205131
$411$	−4.08856	−0.201674
$412$	14.5415	0.716410
$413$	30.8384	1.51746
$414$	0.864244	0.0424753
$415$	12.7346	0.625118
$416$	−0.0340297	−0.00166844
$417$	−15.3512	−0.751752
$418$	−5.97063	−0.292033
$419$	25.6185	1.25154	0.625772	−	0.780006i	$-0.284784\pi$
$419$	25.6185	1.25154	0.625772	+	0.780006i	$0.284784\pi$
$420$	−2.85120	−0.139124
$421$	3.97461	0.193711	0.0968554	−	0.995298i	$-0.469122\pi$
$421$	3.97461	0.193711	0.0968554	+	0.995298i	$0.469122\pi$
$422$	21.1410	1.02913
$423$	−2.95109	−0.143487
$424$	1.00000	0.0485643
$425$	20.5100	0.994881
$426$	2.68465	0.130072
$427$	3.46642	0.167752
$428$	0.770697	0.0372531
$429$	0.203179	0.00980957
$430$	4.29230	0.206993
$431$	−14.4706	−0.697022	−0.348511	−	0.937305i	$-0.613313\pi$
$431$	−14.4706	−0.697022	−0.348511	+	0.937305i	$0.613313\pi$
$432$	1.00000	0.0481125
$433$	18.4519	0.886740	0.443370	−	0.896339i	$-0.353783\pi$
$433$	18.4519	0.886740	0.443370	+	0.896339i	$0.353783\pi$
$434$	34.6108	1.66137
$435$	−6.70978	−0.321709
$436$	3.37503	0.161635
$437$	−0.864244	−0.0413424
$438$	0.0692174	0.00330734
$439$	−11.7638	−0.561457	−0.280729	−	0.959787i	$-0.590576\pi$
$439$	−11.7638	−0.561457	−0.280729	+	0.959787i	$0.590576\pi$
$440$	−5.01955	−0.239297
$441$	4.50181	0.214372
$442$	0.162570	0.00773269
$443$	33.9566	1.61333	0.806663	−	0.591012i	$-0.201271\pi$
$443$	33.9566	1.61333	0.806663	+	0.591012i	$0.201271\pi$
$444$	−4.18377	−0.198553
$445$	11.4105	0.540907
$446$	8.86230	0.419642
$447$	−14.6758	−0.694140
$448$	−3.39143	−0.160230
$449$	0.723945	0.0341651	0.0170825	−	0.999854i	$-0.494562\pi$
$449$	0.723945	0.0341651	0.0170825	+	0.999854i	$0.494562\pi$
$450$	4.29321	0.202384
$451$	−29.4985	−1.38903
$452$	−1.04169	−0.0489968
$453$	14.7576	0.693374
$454$	23.2370	1.09057
$455$	−0.0970254	−0.00454862
$456$	−1.00000	−0.0468293
$457$	17.5869	0.822682	0.411341	−	0.911482i	$-0.365061\pi$
$457$	17.5869	0.822682	0.411341	+	0.911482i	$0.365061\pi$
$458$	7.46821	0.348966
$459$	−4.77731	−0.222986
$460$	−0.726575	−0.0338767
$461$	3.52857	0.164342	0.0821710	−	0.996618i	$-0.473815\pi$
$461$	3.52857	0.164342	0.0821710	+	0.996618i	$0.473815\pi$
$462$	20.2490	0.942068
$463$	−24.5177	−1.13944	−0.569718	−	0.821840i	$-0.692948\pi$
$463$	−24.5177	−1.13944	−0.569718	+	0.821840i	$0.692948\pi$
$464$	−7.98112	−0.370514
$465$	8.57971	0.397875
$466$	4.94567	0.229104
$467$	20.3281	0.940673	0.470336	−	0.882487i	$-0.344133\pi$
$467$	20.3281	0.940673	0.470336	+	0.882487i	$0.344133\pi$
$468$	0.0340297	0.00157302
$469$	47.7294	2.20394
$470$	2.48100	0.114440
$471$	4.00171	0.184389
$472$	9.09303	0.418540
$473$	−30.4836	−1.40164
$474$	−3.25089	−0.149318
$475$	−4.29321	−0.196986
$476$	16.2019	0.742614
$477$	−1.00000	−0.0457869
$478$	6.57642	0.300799
$479$	20.5448	0.938714	0.469357	−	0.883009i	$-0.344486\pi$
$479$	20.5448	0.938714	0.469357	+	0.883009i	$0.344486\pi$
$480$	−0.840706	−0.0383728
$481$	−0.142373	−0.00649163
$482$	4.78458	0.217932
$483$	2.93103	0.133366
$484$	24.6484	1.12038
$485$	−14.8410	−0.673894
$486$	−1.00000	−0.0453609
$487$	−20.2193	−0.916222	−0.458111	−	0.888895i	$-0.651474\pi$
$487$	−20.2193	−0.916222	−0.458111	+	0.888895i	$0.651474\pi$
$488$	1.02211	0.0462688
$489$	−7.98342	−0.361023
$490$	−3.78470	−0.170975
$491$	−18.1298	−0.818185	−0.409092	−	0.912493i	$-0.634155\pi$
$491$	−18.1298	−0.818185	−0.409092	+	0.912493i	$0.634155\pi$
$492$	−4.94060	−0.222739
$493$	38.1283	1.71721
$494$	−0.0340297	−0.00153107
$495$	5.01955	0.225612
$496$	10.2054	0.458235
$497$	9.10480	0.408406
$498$	−15.1475	−0.678778
$499$	−38.6098	−1.72841	−0.864207	−	0.503137i	$-0.832179\pi$
$499$	−38.6098	−1.72841	−0.864207	+	0.503137i	$0.832179\pi$
$500$	−7.81286	−0.349402
$501$	−20.1975	−0.902356
$502$	−18.8261	−0.840248
$503$	4.39243	0.195849	0.0979243	−	0.995194i	$-0.468780\pi$
$503$	4.39243	0.195849	0.0979243	+	0.995194i	$0.468780\pi$
$504$	3.39143	0.151066
$505$	−2.04739	−0.0911074
$506$	5.16009	0.229394
$507$	−12.9988	−0.577299
$508$	11.0957	0.492290
$509$	−8.68393	−0.384909	−0.192454	−	0.981306i	$-0.561645\pi$
$509$	−8.68393	−0.384909	−0.192454	+	0.981306i	$0.561645\pi$
$510$	4.01631	0.177845
$511$	0.234746	0.0103846
$512$	−1.00000	−0.0441942
$513$	1.00000	0.0441511
$514$	−27.1661	−1.19824
$515$	12.2252	0.538705
$516$	−5.10560	−0.224761
$517$	−17.6199	−0.774920
$518$	−14.1890	−0.623428
$519$	−5.82596	−0.255731
$520$	−0.0286090	−0.00125459
$521$	23.0900	1.01159	0.505795	−	0.862654i	$-0.331199\pi$
$521$	23.0900	1.01159	0.505795	+	0.862654i	$0.331199\pi$
$522$	7.98112	0.349324
$523$	−34.8538	−1.52405	−0.762026	−	0.647546i	$-0.775795\pi$
$523$	−34.8538	−1.52405	−0.762026	+	0.647546i	$0.775795\pi$
$524$	−1.60845	−0.0702655
$525$	14.5601	0.635457
$526$	16.7153	0.728822
$527$	−48.7542	−2.12377
$528$	5.97063	0.259838
$529$	−22.2531	−0.967525
$530$	0.840706	0.0365179
$531$	−9.09303	−0.394604
$532$	−3.39143	−0.147037
$533$	−0.168127	−0.00728239
$534$	−13.5725	−0.587338
$535$	0.647930	0.0280124
$536$	14.0735	0.607883
$537$	10.4147	0.449428
$538$	−17.9745	−0.774936
$539$	26.8787	1.15775
$540$	0.840706	0.0361782
$541$	−15.8105	−0.679747	−0.339874	−	0.940471i	$-0.610384\pi$
$541$	−15.8105	−0.679747	−0.339874	+	0.940471i	$0.610384\pi$
$542$	0.972520	0.0417733
$543$	−26.4059	−1.13319
$544$	4.77731	0.204825
$545$	2.83741	0.121541
$546$	0.115409	0.00493907
$547$	−4.20791	−0.179917	−0.0899587	−	0.995945i	$-0.528673\pi$
$547$	−4.20791	−0.179917	−0.0899587	+	0.995945i	$0.528673\pi$
$548$	−4.08856	−0.174654
$549$	−1.02211	−0.0436226
$550$	25.6332	1.09300
$551$	−7.98112	−0.340007
$552$	0.864244	0.0367847
$553$	−11.0252	−0.468838
$554$	−12.1981	−0.518247
$555$	−3.51732	−0.149302
$556$	−15.3512	−0.651037
$557$	32.5265	1.37819	0.689095	−	0.724671i	$-0.258008\pi$
$557$	32.5265	1.37819	0.689095	+	0.724671i	$0.258008\pi$
$558$	−10.2054	−0.432028
$559$	−0.173742	−0.00734850
$560$	−2.85120	−0.120485
$561$	−28.5235	−1.20427
$562$	10.6768	0.450373
$563$	−39.7437	−1.67500	−0.837498	−	0.546441i	$-0.815982\pi$
$563$	−39.7437	−1.67500	−0.837498	+	0.546441i	$0.815982\pi$
$564$	−2.95109	−0.124263
$565$	−0.875751	−0.0368431
$566$	11.7540	0.494055
$567$	−3.39143	−0.142427
$568$	2.68465	0.112645
$569$	−23.9365	−1.00347	−0.501735	−	0.865021i	$-0.667305\pi$
$569$	−23.9365	−1.00347	−0.501735	+	0.865021i	$0.667305\pi$
$570$	−0.840706	−0.0352133
$571$	−23.5276	−0.984600	−0.492300	−	0.870426i	$-0.663844\pi$
$571$	−23.5276	−0.984600	−0.492300	+	0.870426i	$0.663844\pi$
$572$	0.203179	0.00849534
$573$	26.6628	1.11386
$574$	−16.7557	−0.699369
$575$	3.71039	0.154734
$576$	1.00000	0.0416667
$577$	−25.4824	−1.06084	−0.530422	−	0.847734i	$-0.677967\pi$
$577$	−25.4824	−1.06084	−0.530422	+	0.847734i	$0.677967\pi$
$578$	−5.82267	−0.242191
$579$	6.09321	0.253225
$580$	−6.70978	−0.278608
$581$	−51.3719	−2.13126
$582$	17.6530	0.731740
$583$	−5.97063	−0.247278
$584$	0.0692174	0.00286424
$585$	0.0286090	0.00118284
$586$	3.84968	0.159029
$587$	7.90127	0.326120	0.163060	−	0.986616i	$-0.447864\pi$
$587$	7.90127	0.326120	0.163060	+	0.986616i	$0.447864\pi$
$588$	4.50181	0.185652
$589$	10.2054	0.420505
$590$	7.64456	0.314722
$591$	13.2533	0.545168
$592$	−4.18377	−0.171952
$593$	−19.7516	−0.811100	−0.405550	−	0.914073i	$-0.632920\pi$
$593$	−19.7516	−0.811100	−0.405550	+	0.914073i	$0.632920\pi$
$594$	−5.97063	−0.244978
$595$	13.6210	0.558408
$596$	−14.6758	−0.601143
$597$	−22.8313	−0.934421
$598$	0.0294100	0.00120266
$599$	31.3037	1.27903	0.639517	−	0.768777i	$-0.279134\pi$
$599$	31.3037	1.27903	0.639517	+	0.768777i	$0.279134\pi$
$600$	4.29321	0.175270
$601$	42.1839	1.72072	0.860359	−	0.509688i	$-0.170239\pi$
$601$	42.1839	1.72072	0.860359	+	0.509688i	$0.170239\pi$
$602$	−17.3153	−0.705718
$603$	−14.0735	−0.573118
$604$	14.7576	0.600479
$605$	20.7221	0.842473
$606$	2.43532	0.0989280
$607$	−24.9868	−1.01418	−0.507092	−	0.861892i	$-0.669280\pi$
$607$	−24.9868	−1.01418	−0.507092	+	0.861892i	$0.669280\pi$
$608$	−1.00000	−0.0405554
$609$	27.0674	1.09683
$610$	0.859295	0.0347918
$611$	−0.100425	−0.00406275
$612$	−4.77731	−0.193111
$613$	42.6651	1.72323	0.861613	−	0.507565i	$-0.169454\pi$
$613$	42.6651	1.72323	0.861613	+	0.507565i	$0.169454\pi$
$614$	22.0677	0.890582
$615$	−4.15359	−0.167489
$616$	20.2490	0.815855
$617$	−5.88364	−0.236866	−0.118433	−	0.992962i	$-0.537787\pi$
$617$	−5.88364	−0.236866	−0.118433	+	0.992962i	$0.537787\pi$
$618$	−14.5415	−0.584947
$619$	−30.8472	−1.23985	−0.619927	−	0.784659i	$-0.712838\pi$
$619$	−30.8472	−1.23985	−0.619927	+	0.784659i	$0.712838\pi$
$620$	8.57971	0.344570
$621$	−0.864244	−0.0346809
$622$	−14.8666	−0.596097
$623$	−46.0301	−1.84416
$624$	0.0340297	0.00136228
$625$	14.8978	0.595910
$626$	19.2359	0.768823
$627$	5.97063	0.238444
$628$	4.00171	0.159686
$629$	19.9872	0.796941
$630$	2.85120	0.113594
$631$	20.9562	0.834254	0.417127	−	0.908848i	$-0.363037\pi$
$631$	20.9562	0.834254	0.417127	+	0.908848i	$0.363037\pi$
$632$	−3.25089	−0.129314
$633$	−21.1410	−0.840280
$634$	27.8704	1.10688
$635$	9.32818	0.370178
$636$	−1.00000	−0.0396526
$637$	0.153195	0.00606982
$638$	47.6523	1.88657
$639$	−2.68465	−0.106203
$640$	−0.840706	−0.0332318
$641$	−1.68807	−0.0666746	−0.0333373	−	0.999444i	$-0.510614\pi$
$641$	−1.68807	−0.0666746	−0.0333373	+	0.999444i	$0.510614\pi$
$642$	−0.770697	−0.0304170
$643$	11.1155	0.438351	0.219176	−	0.975685i	$-0.429663\pi$
$643$	11.1155	0.438351	0.219176	+	0.975685i	$0.429663\pi$
$644$	2.93103	0.115499
$645$	−4.29230	−0.169009
$646$	4.77731	0.187961
$647$	−30.4737	−1.19805	−0.599023	−	0.800732i	$-0.704444\pi$
$647$	−30.4737	−1.19805	−0.599023	+	0.800732i	$0.704444\pi$
$648$	−1.00000	−0.0392837
$649$	−54.2911	−2.13111
$650$	0.146097	0.00573039
$651$	−34.6108	−1.35650
$652$	−7.98342	−0.312655
$653$	−26.7107	−1.04527	−0.522636	−	0.852556i	$-0.675051\pi$
$653$	−26.7107	−1.04527	−0.522636	+	0.852556i	$0.675051\pi$
$654$	−3.37503	−0.131974
$655$	−1.35223	−0.0528361
$656$	−4.94060	−0.192898
$657$	−0.0692174	−0.00270043
$658$	−10.0084	−0.390168
$659$	−25.5240	−0.994274	−0.497137	−	0.867672i	$-0.665615\pi$
$659$	−25.5240	−0.994274	−0.497137	+	0.867672i	$0.665615\pi$
$660$	5.01955	0.195386
$661$	−11.5398	−0.448846	−0.224423	−	0.974492i	$-0.572050\pi$
$661$	−11.5398	−0.448846	−0.224423	+	0.974492i	$0.572050\pi$
$662$	24.4069	0.948599
$663$	−0.162570	−0.00631371
$664$	−15.1475	−0.587839
$665$	−2.85120	−0.110565
$666$	4.18377	0.162118
$667$	6.89764	0.267078
$668$	−20.1975	−0.781464
$669$	−8.86230	−0.342636
$670$	11.8317	0.457098
$671$	−6.10265	−0.235590
$672$	3.39143	0.130827
$673$	−23.7139	−0.914104	−0.457052	−	0.889440i	$-0.651095\pi$
$673$	−23.7139	−0.914104	−0.457052	+	0.889440i	$0.651095\pi$
$674$	−0.383394	−0.0147678
$675$	−4.29321	−0.165246
$676$	−12.9988	−0.499955
$677$	−18.3311	−0.704523	−0.352261	−	0.935902i	$-0.614587\pi$
$677$	−18.3311	−0.704523	−0.352261	+	0.935902i	$0.614587\pi$
$678$	1.04169	0.0400057
$679$	59.8689	2.29756
$680$	4.01631	0.154018
$681$	−23.2370	−0.890445
$682$	−60.9325	−2.33323
$683$	0.174825	0.00668950	0.00334475	−	0.999994i	$-0.498935\pi$
$683$	0.174825	0.00668950	0.00334475	+	0.999994i	$0.498935\pi$
$684$	1.00000	0.0382360
$685$	−3.43727	−0.131331
$686$	−8.47243	−0.323479
$687$	−7.46821	−0.284930
$688$	−5.10560	−0.194649
$689$	−0.0340297	−0.00129643
$690$	0.726575	0.0276603
$691$	5.04318	0.191852	0.0959259	−	0.995388i	$-0.469419\pi$
$691$	5.04318	0.191852	0.0959259	+	0.995388i	$0.469419\pi$
$692$	−5.82596	−0.221470
$693$	−20.2490	−0.769196
$694$	4.39537	0.166846
$695$	−12.9059	−0.489547
$696$	7.98112	0.302524
$697$	23.6027	0.894018
$698$	18.0900	0.684715
$699$	−4.94567	−0.187062
$700$	14.5601	0.550322
$701$	19.4931	0.736243	0.368122	−	0.929778i	$-0.380001\pi$
$701$	19.4931	0.736243	0.368122	+	0.929778i	$0.380001\pi$
$702$	−0.0340297	−0.00128437
$703$	−4.18377	−0.157794
$704$	5.97063	0.225027
$705$	−2.48100	−0.0934397
$706$	31.2278	1.17527
$707$	8.25921	0.310620
$708$	−9.09303	−0.341737
$709$	26.1541	0.982237	0.491118	−	0.871093i	$-0.336588\pi$
$709$	26.1541	0.982237	0.491118	+	0.871093i	$0.336588\pi$
$710$	2.25700	0.0847036
$711$	3.25089	0.121918
$712$	−13.5725	−0.508650
$713$	−8.81993	−0.330309
$714$	−16.2019	−0.606342
$715$	0.170814	0.00638807
$716$	10.4147	0.389216
$717$	−6.57642	−0.245601
$718$	5.23517	0.195375
$719$	39.1185	1.45887	0.729437	−	0.684048i	$-0.239782\pi$
$719$	39.1185	1.45887	0.729437	+	0.684048i	$0.239782\pi$
$720$	0.840706	0.0313313
$721$	−49.3166	−1.83665
$722$	−1.00000	−0.0372161
$723$	−4.78458	−0.177940
$724$	−26.4059	−0.981369
$725$	34.2647	1.27256
$726$	−24.6484	−0.914790
$727$	−7.72933	−0.286665	−0.143332	−	0.989675i	$-0.545782\pi$
$727$	−7.72933	−0.286665	−0.143332	+	0.989675i	$0.545782\pi$
$728$	0.115409	0.00427736
$729$	1.00000	0.0370370
$730$	0.0581915	0.00215376
$731$	24.3910	0.902134
$732$	−1.02211	−0.0377783
$733$	48.4571	1.78980	0.894902	−	0.446263i	$-0.147245\pi$
$733$	48.4571	1.78980	0.894902	+	0.446263i	$0.147245\pi$
$734$	−2.08727	−0.0770425
$735$	3.78470	0.139601
$736$	0.864244	0.0318565
$737$	−84.0278	−3.09520
$738$	4.94060	0.181866
$739$	28.1569	1.03577	0.517884	−	0.855451i	$-0.326720\pi$
$739$	28.1569	1.03577	0.517884	+	0.855451i	$0.326720\pi$
$740$	−3.51732	−0.129299
$741$	0.0340297	0.00125011
$742$	−3.39143	−0.124503
$743$	−24.2352	−0.889102	−0.444551	−	0.895753i	$-0.646637\pi$
$743$	−24.2352	−0.889102	−0.444551	+	0.895753i	$0.646637\pi$
$744$	−10.2054	−0.374147
$745$	−12.3380	−0.452030
$746$	14.7594	0.540380
$747$	15.1475	0.554220
$748$	−28.5235	−1.04292
$749$	−2.61377	−0.0955050
$750$	7.81286	0.285285
$751$	−43.1309	−1.57387	−0.786934	−	0.617037i	$-0.788333\pi$
$751$	−43.1309	−1.57387	−0.786934	+	0.617037i	$0.788333\pi$
$752$	−2.95109	−0.107615
$753$	18.8261	0.686060
$754$	0.271595	0.00989092
$755$	12.4068	0.451531
$756$	−3.39143	−0.123345
$757$	22.5509	0.819626	0.409813	−	0.912170i	$-0.365594\pi$
$757$	22.5509	0.819626	0.409813	+	0.912170i	$0.365594\pi$
$758$	−9.08121	−0.329845
$759$	−5.16009	−0.187299
$760$	−0.840706	−0.0304956
$761$	8.98099	0.325561	0.162780	−	0.986662i	$-0.447954\pi$
$761$	8.98099	0.325561	0.162780	+	0.986662i	$0.447954\pi$
$762$	−11.0957	−0.401953
$763$	−11.4462	−0.414379
$764$	26.6628	0.964628
$765$	−4.01631	−0.145210
$766$	−28.2968	−1.02240
$767$	−0.309433	−0.0111730
$768$	1.00000	0.0360844
$769$	19.8747	0.716700	0.358350	−	0.933587i	$-0.383339\pi$
$769$	19.8747	0.716700	0.358350	+	0.933587i	$0.383339\pi$
$770$	17.0234	0.613482
$771$	27.1661	0.978363
$772$	6.09321	0.219299
$773$	28.8387	1.03726	0.518629	−	0.855000i	$-0.326443\pi$
$773$	28.8387	1.03726	0.518629	+	0.855000i	$0.326443\pi$
$774$	5.10560	0.183517
$775$	−43.8138	−1.57384
$776$	17.6530	0.633706
$777$	14.1890	0.509027
$778$	−0.813679	−0.0291718
$779$	−4.94060	−0.177015
$780$	0.0286090	0.00102437
$781$	−16.0290	−0.573564
$782$	−4.12876	−0.147644
$783$	−7.98112	−0.285222
$784$	4.50181	0.160779
$785$	3.36426	0.120076
$786$	1.60845	0.0573715
$787$	−16.7788	−0.598098	−0.299049	−	0.954238i	$-0.596669\pi$
$787$	−16.7788	−0.598098	−0.299049	+	0.954238i	$0.596669\pi$
$788$	13.2533	0.472129
$789$	−16.7153	−0.595081
$790$	−2.73304	−0.0972373
$791$	3.53281	0.125612
$792$	−5.97063	−0.212157
$793$	−0.0347821	−0.00123515
$794$	−19.4933	−0.691790
$795$	−0.840706	−0.0298168
$796$	−22.8313	−0.809232
$797$	−6.81803	−0.241507	−0.120753	−	0.992683i	$-0.538531\pi$
$797$	−6.81803	−0.241507	−0.120753	+	0.992683i	$0.538531\pi$
$798$	3.39143	0.120055
$799$	14.0983	0.498760
$800$	4.29321	0.151788
$801$	13.5725	0.479560
$802$	−30.1940	−1.06619
$803$	−0.413272	−0.0145840
$804$	−14.0735	−0.496335
$805$	2.46413	0.0868492
$806$	−0.347286	−0.0122326
$807$	17.9745	0.632732
$808$	2.43532	0.0856742
$809$	−11.9782	−0.421132	−0.210566	−	0.977580i	$-0.567531\pi$
$809$	−11.9782	−0.421132	−0.210566	+	0.977580i	$0.567531\pi$
$810$	−0.840706	−0.0295394
$811$	−9.82898	−0.345142	−0.172571	−	0.984997i	$-0.555207\pi$
$811$	−9.82898	−0.345142	−0.172571	+	0.984997i	$0.555207\pi$
$812$	27.0674	0.949881
$813$	−0.972520	−0.0341078
$814$	24.9798	0.875541
$815$	−6.71170	−0.235101
$816$	−4.77731	−0.167239
$817$	−5.10560	−0.178622
$818$	−26.0228	−0.909867
$819$	−0.115409	−0.00403273
$820$	−4.15359	−0.145050
$821$	−7.63649	−0.266515	−0.133258	−	0.991081i	$-0.542544\pi$
$821$	−7.63649	−0.266515	−0.133258	+	0.991081i	$0.542544\pi$
$822$	4.08856	0.142605
$823$	−9.19427	−0.320492	−0.160246	−	0.987077i	$-0.551229\pi$
$823$	−9.19427	−0.320492	−0.160246	+	0.987077i	$0.551229\pi$
$824$	−14.5415	−0.506579
$825$	−25.6332	−0.892433
$826$	−30.8384	−1.07300
$827$	4.57245	0.159000	0.0794998	−	0.996835i	$-0.474668\pi$
$827$	4.57245	0.159000	0.0794998	+	0.996835i	$0.474668\pi$
$828$	−0.864244	−0.0300346
$829$	−42.6741	−1.48213	−0.741067	−	0.671432i	$-0.765680\pi$
$829$	−42.6741	−1.48213	−0.741067	+	0.671432i	$0.765680\pi$
$830$	−12.7346	−0.442025
$831$	12.1981	0.423147
$832$	0.0340297	0.00117977
$833$	−21.5065	−0.745158
$834$	15.3512	0.531569
$835$	−16.9801	−0.587622
$836$	5.97063	0.206499
$837$	10.2054	0.352749
$838$	−25.6185	−0.884975
$839$	55.0455	1.90038	0.950191	−	0.311669i	$-0.100888\pi$
$839$	55.0455	1.90038	0.950191	+	0.311669i	$0.100888\pi$
$840$	2.85120	0.0983756
$841$	34.6983	1.19649
$842$	−3.97461	−0.136974
$843$	−10.6768	−0.367728
$844$	−21.1410	−0.727704
$845$	−10.9282	−0.375942
$846$	2.95109	0.101460
$847$	−83.5935	−2.87231
$848$	−1.00000	−0.0343401
$849$	−11.7540	−0.403395
$850$	−20.5100	−0.703487
$851$	3.61580	0.123948
$852$	−2.68465	−0.0919745
$853$	10.1555	0.347717	0.173858	−	0.984771i	$-0.444377\pi$
$853$	10.1555	0.347717	0.173858	+	0.984771i	$0.444377\pi$
$854$	−3.46642	−0.118618
$855$	0.840706	0.0287515
$856$	−0.770697	−0.0263419
$857$	20.2939	0.693228	0.346614	−	0.938008i	$-0.387331\pi$
$857$	20.2939	0.693228	0.346614	+	0.938008i	$0.387331\pi$
$858$	−0.203179	−0.00693641
$859$	43.4026	1.48088	0.740439	−	0.672124i	$-0.234618\pi$
$859$	43.4026	1.48088	0.740439	+	0.672124i	$0.234618\pi$
$860$	−4.29230	−0.146366
$861$	16.7557	0.571033
$862$	14.4706	0.492869
$863$	27.3747	0.931846	0.465923	−	0.884825i	$-0.345722\pi$
$863$	27.3747	0.931846	0.465923	+	0.884825i	$0.345722\pi$
$864$	−1.00000	−0.0340207
$865$	−4.89792	−0.166534
$866$	−18.4519	−0.627020
$867$	5.82267	0.197748
$868$	−34.6108	−1.17477
$869$	19.4099	0.658435
$870$	6.70978	0.227483
$871$	−0.478918	−0.0162275
$872$	−3.37503	−0.114293
$873$	−17.6530	−0.597463
$874$	0.864244	0.0292335
$875$	26.4968	0.895755
$876$	−0.0692174	−0.00233864
$877$	−56.0192	−1.89163	−0.945817	−	0.324700i	$-0.894737\pi$
$877$	−56.0192	−1.89163	−0.945817	+	0.324700i	$0.894737\pi$
$878$	11.7638	0.397010
$879$	−3.84968	−0.129846
$880$	5.01955	0.169209
$881$	−28.6772	−0.966160	−0.483080	−	0.875576i	$-0.660482\pi$
$881$	−28.6772	−0.966160	−0.483080	+	0.875576i	$0.660482\pi$
$882$	−4.50181	−0.151584
$883$	0.715816	0.0240891	0.0120446	−	0.999927i	$-0.496166\pi$
$883$	0.715816	0.0240891	0.0120446	+	0.999927i	$0.496166\pi$
$884$	−0.162570	−0.00546783
$885$	−7.64456	−0.256969
$886$	−33.9566	−1.14079
$887$	2.96448	0.0995375	0.0497688	−	0.998761i	$-0.484152\pi$
$887$	2.96448	0.0995375	0.0497688	+	0.998761i	$0.484152\pi$
$888$	4.18377	0.140398
$889$	−37.6302	−1.26208
$890$	−11.4105	−0.382479
$891$	5.97063	0.200024
$892$	−8.86230	−0.296732
$893$	−2.95109	−0.0987544
$894$	14.6758	0.490831
$895$	8.75571	0.292671
$896$	3.39143	0.113300
$897$	−0.0294100	−0.000981971 0
$898$	−0.723945	−0.0241584
$899$	−81.4503	−2.71652
$900$	−4.29321	−0.143107
$901$	4.77731	0.159155
$902$	29.4985	0.982192
$903$	17.3153	0.576217
$904$	1.04169	0.0346459
$905$	−22.1996	−0.737940
$906$	−14.7576	−0.490289
$907$	13.5828	0.451008	0.225504	−	0.974242i	$-0.427597\pi$
$907$	13.5828	0.451008	0.225504	+	0.974242i	$0.427597\pi$
$908$	−23.2370	−0.771148
$909$	−2.43532	−0.0807744
$910$	0.0970254	0.00321636
$911$	52.4655	1.73826	0.869130	−	0.494583i	$-0.164679\pi$
$911$	52.4655	1.73826	0.869130	+	0.494583i	$0.164679\pi$
$912$	1.00000	0.0331133
$913$	90.4404	2.99314
$914$	−17.5869	−0.581724
$915$	−0.859295	−0.0284074
$916$	−7.46821	−0.246757
$917$	5.45495	0.180138
$918$	4.77731	0.157675
$919$	35.8802	1.18358	0.591789	−	0.806093i	$-0.298422\pi$
$919$	35.8802	1.18358	0.591789	+	0.806093i	$0.298422\pi$
$920$	0.726575	0.0239545
$921$	−22.0677	−0.727157
$922$	−3.52857	−0.116207
$923$	−0.0913577	−0.00300708
$924$	−20.2490	−0.666143
$925$	17.9618	0.590581
$926$	24.5177	0.805703
$927$	14.5415	0.477607
$928$	7.98112	0.261993
$929$	−43.8598	−1.43899	−0.719497	−	0.694496i	$-0.755628\pi$
$929$	−43.8598	−1.43899	−0.719497	+	0.694496i	$0.755628\pi$
$930$	−8.57971	−0.281340
$931$	4.50181	0.147541
$932$	−4.94567	−0.162001
$933$	14.8666	0.486711
$934$	−20.3281	−0.665156
$935$	−23.9799	−0.784227
$936$	−0.0340297	−0.00111230
$937$	32.0721	1.04775	0.523876	−	0.851795i	$-0.324486\pi$
$937$	32.0721	1.04775	0.523876	+	0.851795i	$0.324486\pi$
$938$	−47.7294	−1.55842
$939$	−19.2359	−0.627741
$940$	−2.48100	−0.0809212
$941$	35.4879	1.15687	0.578436	−	0.815728i	$-0.303663\pi$
$941$	35.4879	1.15687	0.578436	+	0.815728i	$0.303663\pi$
$942$	−4.00171	−0.130383
$943$	4.26988	0.139046
$944$	−9.09303	−0.295953
$945$	−2.85120	−0.0927494
$946$	30.4836	0.991109
$947$	−5.29568	−0.172086	−0.0860432	−	0.996291i	$-0.527422\pi$
$947$	−5.29568	−0.172086	−0.0860432	+	0.996291i	$0.527422\pi$
$948$	3.25089	0.105584
$949$	−0.00235545	−7.64611e−5 0
$950$	4.29321	0.139290
$951$	−27.8704	−0.903760
$952$	−16.2019	−0.525107
$953$	8.30400	0.268993	0.134496	−	0.990914i	$-0.457058\pi$
$953$	8.30400	0.268993	0.134496	+	0.990914i	$0.457058\pi$
$954$	1.00000	0.0323762
$955$	22.4156	0.725352
$956$	−6.57642	−0.212697
$957$	−47.6523	−1.54038
$958$	−20.5448	−0.663771
$959$	13.8661	0.447758
$960$	0.840706	0.0271337
$961$	73.1495	2.35966
$962$	0.142373	0.00459028
$963$	0.770697	0.0248354
$964$	−4.78458	−0.154101
$965$	5.12259	0.164902
$966$	−2.93103	−0.0943042
$967$	−56.4042	−1.81384	−0.906918	−	0.421308i	$-0.861571\pi$
$967$	−56.4042	−1.81384	−0.906918	+	0.421308i	$0.861571\pi$
$968$	−24.6484	−0.792231
$969$	−4.77731	−0.153469
$970$	14.8410	0.476515
$971$	56.0348	1.79824	0.899121	−	0.437700i	$-0.144207\pi$
$971$	56.0348	1.79824	0.899121	+	0.437700i	$0.144207\pi$
$972$	1.00000	0.0320750
$973$	52.0626	1.66905
$974$	20.2193	0.647867
$975$	−0.146097	−0.00467884
$976$	−1.02211	−0.0327170
$977$	−47.0743	−1.50604	−0.753020	−	0.657998i	$-0.771404\pi$
$977$	−47.0743	−1.50604	−0.753020	+	0.657998i	$0.771404\pi$
$978$	7.98342	0.255282
$979$	81.0362	2.58993
$980$	3.78470	0.120898
$981$	3.37503	0.107756
$982$	18.1298	0.578544
$983$	−0.838034	−0.0267291	−0.0133646	−	0.999911i	$-0.504254\pi$
$983$	−0.838034	−0.0267291	−0.0133646	+	0.999911i	$0.504254\pi$
$984$	4.94060	0.157500
$985$	11.1421	0.355018
$986$	−38.1283	−1.21425
$987$	10.0084	0.318571
$988$	0.0340297	0.00108263
$989$	4.41248	0.140309
$990$	−5.01955	−0.159532
$991$	−36.0441	−1.14498	−0.572489	−	0.819913i	$-0.694022\pi$
$991$	−36.0441	−1.14498	−0.572489	+	0.819913i	$0.694022\pi$
$992$	−10.2054	−0.324021
$993$	−24.4069	−0.774528
$994$	−9.10480	−0.288787
$995$	−19.1944	−0.608502
$996$	15.1475	0.479968
$997$	−20.6303	−0.653367	−0.326684	−	0.945134i	$-0.605931\pi$
$997$	−20.6303	−0.653367	−0.326684	+	0.945134i	$0.605931\pi$
$998$	38.6098	1.22217
$999$	−4.18377	−0.132369

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6042.2.a.v.1.4	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6042.2.a.v.1.4	✓	6	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:	\( N \)	\(=\)	\( 6042 = 2 \cdot 3 \cdot 19 \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6042.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.840706 q^{5} -1.00000 q^{6} -3.39143 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.840706 q^{5} -1.00000 q^{6} -3.39143 q^{7} -1.00000 q^{8} +1.00000 q^{9} -0.840706 q^{10} +5.97063 q^{11} +1.00000 q^{12} +0.0340297 q^{13} +3.39143 q^{14} +0.840706 q^{15} +1.00000 q^{16} -4.77731 q^{17} -1.00000 q^{18} +1.00000 q^{19} +0.840706 q^{20} -3.39143 q^{21} -5.97063 q^{22} -0.864244 q^{23} -1.00000 q^{24} -4.29321 q^{25} -0.0340297 q^{26} +1.00000 q^{27} -3.39143 q^{28} -7.98112 q^{29} -0.840706 q^{30} +10.2054 q^{31} -1.00000 q^{32} +5.97063 q^{33} +4.77731 q^{34} -2.85120 q^{35} +1.00000 q^{36} -4.18377 q^{37} -1.00000 q^{38} +0.0340297 q^{39} -0.840706 q^{40} -4.94060 q^{41} +3.39143 q^{42} -5.10560 q^{43} +5.97063 q^{44} +0.840706 q^{45} +0.864244 q^{46} -2.95109 q^{47} +1.00000 q^{48} +4.50181 q^{49} +4.29321 q^{50} -4.77731 q^{51} +0.0340297 q^{52} -1.00000 q^{53} -1.00000 q^{54} +5.01955 q^{55} +3.39143 q^{56} +1.00000 q^{57} +7.98112 q^{58} -9.09303 q^{59} +0.840706 q^{60} -1.02211 q^{61} -10.2054 q^{62} -3.39143 q^{63} +1.00000 q^{64} +0.0286090 q^{65} -5.97063 q^{66} -14.0735 q^{67} -4.77731 q^{68} -0.864244 q^{69} +2.85120 q^{70} -2.68465 q^{71} -1.00000 q^{72} -0.0692174 q^{73} +4.18377 q^{74} -4.29321 q^{75} +1.00000 q^{76} -20.2490 q^{77} -0.0340297 q^{78} +3.25089 q^{79} +0.840706 q^{80} +1.00000 q^{81} +4.94060 q^{82} +15.1475 q^{83} -3.39143 q^{84} -4.01631 q^{85} +5.10560 q^{86} -7.98112 q^{87} -5.97063 q^{88} +13.5725 q^{89} -0.840706 q^{90} -0.115409 q^{91} -0.864244 q^{92} +10.2054 q^{93} +2.95109 q^{94} +0.840706 q^{95} -1.00000 q^{96} -17.6530 q^{97} -4.50181 q^{98} +5.97063 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} + 6 q^{3} + 6 q^{4} + 3 q^{5} - 6 q^{6} - 7 q^{7} - 6 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 + 6 * q^3 + 6 * q^4 + 3 * q^5 - 6 * q^6 - 7 * q^7 - 6 * q^8 + 6 * q^9	\( 6 q - 6 q^{2} + 6 q^{3} + 6 q^{4} + 3 q^{5} - 6 q^{6} - 7 q^{7} - 6 q^{8} + 6 q^{9} - 3 q^{10} + q^{11} + 6 q^{12} - 13 q^{13} + 7 q^{14} + 3 q^{15} + 6 q^{16} - 5 q^{17} - 6 q^{18} + 6 q^{19} + 3 q^{20} - 7 q^{21} - q^{22} + 9 q^{23} - 6 q^{24} - 5 q^{25} + 13 q^{26} + 6 q^{27} - 7 q^{28} - 12 q^{29} - 3 q^{30} - 2 q^{31} - 6 q^{32} + q^{33} + 5 q^{34} - 14 q^{35} + 6 q^{36} - 7 q^{37} - 6 q^{38} - 13 q^{39} - 3 q^{40} - 18 q^{41} + 7 q^{42} - 11 q^{43} + q^{44} + 3 q^{45} - 9 q^{46} - 5 q^{47} + 6 q^{48} + 3 q^{49} + 5 q^{50} - 5 q^{51} - 13 q^{52} - 6 q^{53} - 6 q^{54} + 8 q^{55} + 7 q^{56} + 6 q^{57} + 12 q^{58} + 2 q^{59} + 3 q^{60} - 12 q^{61} + 2 q^{62} - 7 q^{63} + 6 q^{64} - 5 q^{65} - q^{66} - 9 q^{67} - 5 q^{68} + 9 q^{69} + 14 q^{70} + 18 q^{71} - 6 q^{72} - 31 q^{73} + 7 q^{74} - 5 q^{75} + 6 q^{76} + q^{77} + 13 q^{78} - 17 q^{79} + 3 q^{80} + 6 q^{81} + 18 q^{82} - 9 q^{83} - 7 q^{84} - 32 q^{85} + 11 q^{86} - 12 q^{87} - q^{88} + 18 q^{89} - 3 q^{90} + 9 q^{92} - 2 q^{93} + 5 q^{94} + 3 q^{95} - 6 q^{96} - 7 q^{97} - 3 q^{98} + q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 + 6 * q^3 + 6 * q^4 + 3 * q^5 - 6 * q^6 - 7 * q^7 - 6 * q^8 + 6 * q^9 - 3 * q^10 + q^11 + 6 * q^12 - 13 * q^13 + 7 * q^14 + 3 * q^15 + 6 * q^16 - 5 * q^17 - 6 * q^18 + 6 * q^19 + 3 * q^20 - 7 * q^21 - q^22 + 9 * q^23 - 6 * q^24 - 5 * q^25 + 13 * q^26 + 6 * q^27 - 7 * q^28 - 12 * q^29 - 3 * q^30 - 2 * q^31 - 6 * q^32 + q^33 + 5 * q^34 - 14 * q^35 + 6 * q^36 - 7 * q^37 - 6 * q^38 - 13 * q^39 - 3 * q^40 - 18 * q^41 + 7 * q^42 - 11 * q^43 + q^44 + 3 * q^45 - 9 * q^46 - 5 * q^47 + 6 * q^48 + 3 * q^49 + 5 * q^50 - 5 * q^51 - 13 * q^52 - 6 * q^53 - 6 * q^54 + 8 * q^55 + 7 * q^56 + 6 * q^57 + 12 * q^58 + 2 * q^59 + 3 * q^60 - 12 * q^61 + 2 * q^62 - 7 * q^63 + 6 * q^64 - 5 * q^65 - q^66 - 9 * q^67 - 5 * q^68 + 9 * q^69 + 14 * q^70 + 18 * q^71 - 6 * q^72 - 31 * q^73 + 7 * q^74 - 5 * q^75 + 6 * q^76 + q^77 + 13 * q^78 - 17 * q^79 + 3 * q^80 + 6 * q^81 + 18 * q^82 - 9 * q^83 - 7 * q^84 - 32 * q^85 + 11 * q^86 - 12 * q^87 - q^88 + 18 * q^89 - 3 * q^90 + 9 * q^92 - 2 * q^93 + 5 * q^94 + 3 * q^95 - 6 * q^96 - 7 * q^97 - 3 * q^98 + q^99

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