LMFDB - Embedded newform 6018.2.a.ba.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6018,2,Mod(1,6018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6018, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.0539719364$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} - 31 x^{10} + 111 x^{9} + 381 x^{8} - 1101 x^{7} - 2301 x^{6} + 4690 x^{5} + \cdots + 5653 $ x^12 - 4x^11 - 31x^10 + 111x^9 + 381x^8 - 1101x^7 - 2301x^6 + 4690x^5 + 6915x^4 - 8325x^3 - 10082x^2 + 5149*x + 5653
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$-2.56401$ of defining polynomial
Character	$\chi$	$=$	6018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.56401 q^{5} +1.00000 q^{6} -2.46585 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.56401 q^{5} +1.00000 q^{6} -2.46585 q^{7} +1.00000 q^{8} +1.00000 q^{9} +3.56401 q^{10} +2.23727 q^{11} +1.00000 q^{12} +6.98778 q^{13} -2.46585 q^{14} +3.56401 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} -3.26299 q^{19} +3.56401 q^{20} -2.46585 q^{21} +2.23727 q^{22} -0.970280 q^{23} +1.00000 q^{24} +7.70218 q^{25} +6.98778 q^{26} +1.00000 q^{27} -2.46585 q^{28} +5.56947 q^{29} +3.56401 q^{30} +2.91738 q^{31} +1.00000 q^{32} +2.23727 q^{33} -1.00000 q^{34} -8.78831 q^{35} +1.00000 q^{36} -6.24983 q^{37} -3.26299 q^{38} +6.98778 q^{39} +3.56401 q^{40} -5.50288 q^{41} -2.46585 q^{42} -6.05959 q^{43} +2.23727 q^{44} +3.56401 q^{45} -0.970280 q^{46} +0.503679 q^{47} +1.00000 q^{48} -0.919592 q^{49} +7.70218 q^{50} -1.00000 q^{51} +6.98778 q^{52} +11.1097 q^{53} +1.00000 q^{54} +7.97366 q^{55} -2.46585 q^{56} -3.26299 q^{57} +5.56947 q^{58} +1.00000 q^{59} +3.56401 q^{60} +6.17244 q^{61} +2.91738 q^{62} -2.46585 q^{63} +1.00000 q^{64} +24.9045 q^{65} +2.23727 q^{66} +2.12053 q^{67} -1.00000 q^{68} -0.970280 q^{69} -8.78831 q^{70} -3.41104 q^{71} +1.00000 q^{72} -1.74528 q^{73} -6.24983 q^{74} +7.70218 q^{75} -3.26299 q^{76} -5.51677 q^{77} +6.98778 q^{78} -0.425901 q^{79} +3.56401 q^{80} +1.00000 q^{81} -5.50288 q^{82} -11.9283 q^{83} -2.46585 q^{84} -3.56401 q^{85} -6.05959 q^{86} +5.56947 q^{87} +2.23727 q^{88} -10.1559 q^{89} +3.56401 q^{90} -17.2308 q^{91} -0.970280 q^{92} +2.91738 q^{93} +0.503679 q^{94} -11.6293 q^{95} +1.00000 q^{96} +7.98124 q^{97} -0.919592 q^{98} +2.23727 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{2} + 12 q^{3} + 12 q^{4} + 8 q^{5} + 12 q^{6} + 5 q^{7} + 12 q^{8} + 12 q^{9}+O(q^{10}) $ 12 * q + 12 * q^2 + 12 * q^3 + 12 * q^4 + 8 * q^5 + 12 * q^6 + 5 * q^7 + 12 * q^8 + 12 * q^9	\( 12 q + 12 q^{2} + 12 q^{3} + 12 q^{4} + 8 q^{5} + 12 q^{6} + 5 q^{7} + 12 q^{8} + 12 q^{9} + 8 q^{10} + 11 q^{11} + 12 q^{12} + 6 q^{13} + 5 q^{14} + 8 q^{15} + 12 q^{16} - 12 q^{17} + 12 q^{18} + 3 q^{19} + 8 q^{20} + 5 q^{21} + 11 q^{22} + 22 q^{23} + 12 q^{24} + 22 q^{25} + 6 q^{26} + 12 q^{27} + 5 q^{28} + 26 q^{29} + 8 q^{30} + q^{31} + 12 q^{32} + 11 q^{33} - 12 q^{34} + 24 q^{35} + 12 q^{36} + 10 q^{37} + 3 q^{38} + 6 q^{39} + 8 q^{40} + 16 q^{41} + 5 q^{42} + 23 q^{43} + 11 q^{44} + 8 q^{45} + 22 q^{46} + 6 q^{47} + 12 q^{48} + 11 q^{49} + 22 q^{50} - 12 q^{51} + 6 q^{52} + 10 q^{53} + 12 q^{54} + 15 q^{55} + 5 q^{56} + 3 q^{57} + 26 q^{58} + 12 q^{59} + 8 q^{60} + 15 q^{61} + q^{62} + 5 q^{63} + 12 q^{64} + 4 q^{65} + 11 q^{66} + 4 q^{67} - 12 q^{68} + 22 q^{69} + 24 q^{70} + 10 q^{71} + 12 q^{72} + 24 q^{73} + 10 q^{74} + 22 q^{75} + 3 q^{76} + 24 q^{77} + 6 q^{78} + 23 q^{79} + 8 q^{80} + 12 q^{81} + 16 q^{82} + 5 q^{84} - 8 q^{85} + 23 q^{86} + 26 q^{87} + 11 q^{88} + 13 q^{89} + 8 q^{90} + 3 q^{91} + 22 q^{92} + q^{93} + 6 q^{94} + 11 q^{95} + 12 q^{96} + 13 q^{97} + 11 q^{98} + 11 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 12 * q^3 + 12 * q^4 + 8 * q^5 + 12 * q^6 + 5 * q^7 + 12 * q^8 + 12 * q^9 + 8 * q^10 + 11 * q^11 + 12 * q^12 + 6 * q^13 + 5 * q^14 + 8 * q^15 + 12 * q^16 - 12 * q^17 + 12 * q^18 + 3 * q^19 + 8 * q^20 + 5 * q^21 + 11 * q^22 + 22 * q^23 + 12 * q^24 + 22 * q^25 + 6 * q^26 + 12 * q^27 + 5 * q^28 + 26 * q^29 + 8 * q^30 + q^31 + 12 * q^32 + 11 * q^33 - 12 * q^34 + 24 * q^35 + 12 * q^36 + 10 * q^37 + 3 * q^38 + 6 * q^39 + 8 * q^40 + 16 * q^41 + 5 * q^42 + 23 * q^43 + 11 * q^44 + 8 * q^45 + 22 * q^46 + 6 * q^47 + 12 * q^48 + 11 * q^49 + 22 * q^50 - 12 * q^51 + 6 * q^52 + 10 * q^53 + 12 * q^54 + 15 * q^55 + 5 * q^56 + 3 * q^57 + 26 * q^58 + 12 * q^59 + 8 * q^60 + 15 * q^61 + q^62 + 5 * q^63 + 12 * q^64 + 4 * q^65 + 11 * q^66 + 4 * q^67 - 12 * q^68 + 22 * q^69 + 24 * q^70 + 10 * q^71 + 12 * q^72 + 24 * q^73 + 10 * q^74 + 22 * q^75 + 3 * q^76 + 24 * q^77 + 6 * q^78 + 23 * q^79 + 8 * q^80 + 12 * q^81 + 16 * q^82 + 5 * q^84 - 8 * q^85 + 23 * q^86 + 26 * q^87 + 11 * q^88 + 13 * q^89 + 8 * q^90 + 3 * q^91 + 22 * q^92 + q^93 + 6 * q^94 + 11 * q^95 + 12 * q^96 + 13 * q^97 + 11 * q^98 + 11 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	3.56401	1.59387	0.796937	−	0.604062i	$-0.206452\pi$
$5$	3.56401	1.59387	0.796937	+	0.604062i	$0.206452\pi$
$6$	1.00000	0.408248
$7$	−2.46585	−0.932003	−0.466002	−	0.884784i	$-0.654306\pi$
$7$	−2.46585	−0.932003	−0.466002	+	0.884784i	$0.654306\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	3.56401	1.12704
$11$	2.23727	0.674563	0.337281	−	0.941404i	$-0.390493\pi$
$11$	2.23727	0.674563	0.337281	+	0.941404i	$0.390493\pi$
$12$	1.00000	0.288675
$13$	6.98778	1.93806	0.969031	−	0.246939i	$-0.0794246\pi$
$13$	6.98778	1.93806	0.969031	+	0.246939i	$0.0794246\pi$
$14$	−2.46585	−0.659026
$15$	3.56401	0.920224
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.00000	0.235702
$19$	−3.26299	−0.748582	−0.374291	−	0.927311i	$-0.622114\pi$
$19$	−3.26299	−0.748582	−0.374291	+	0.927311i	$0.622114\pi$
$20$	3.56401	0.796937
$21$	−2.46585	−0.538092
$22$	2.23727	0.476988
$23$	−0.970280	−0.202317	−0.101159	−	0.994870i	$-0.532255\pi$
$23$	−0.970280	−0.202317	−0.101159	+	0.994870i	$0.532255\pi$
$24$	1.00000	0.204124
$25$	7.70218	1.54044
$26$	6.98778	1.37042
$27$	1.00000	0.192450
$28$	−2.46585	−0.466002
$29$	5.56947	1.03422	0.517112	−	0.855918i	$-0.327007\pi$
$29$	5.56947	1.03422	0.517112	+	0.855918i	$0.327007\pi$
$30$	3.56401	0.650697
$31$	2.91738	0.523978	0.261989	−	0.965071i	$-0.415622\pi$
$31$	2.91738	0.523978	0.261989	+	0.965071i	$0.415622\pi$
$32$	1.00000	0.176777
$33$	2.23727	0.389459
$34$	−1.00000	−0.171499
$35$	−8.78831	−1.48550
$36$	1.00000	0.166667
$37$	−6.24983	−1.02747	−0.513733	−	0.857950i	$-0.671738\pi$
$37$	−6.24983	−1.02747	−0.513733	+	0.857950i	$0.671738\pi$
$38$	−3.26299	−0.529327
$39$	6.98778	1.11894
$40$	3.56401	0.563520
$41$	−5.50288	−0.859405	−0.429702	−	0.902971i	$-0.641382\pi$
$41$	−5.50288	−0.859405	−0.429702	+	0.902971i	$0.641382\pi$
$42$	−2.46585	−0.380489
$43$	−6.05959	−0.924079	−0.462040	−	0.886859i	$-0.652882\pi$
$43$	−6.05959	−0.924079	−0.462040	+	0.886859i	$0.652882\pi$
$44$	2.23727	0.337281
$45$	3.56401	0.531292
$46$	−0.970280	−0.143060
$47$	0.503679	0.0734691	0.0367346	−	0.999325i	$-0.488304\pi$
$47$	0.503679	0.0734691	0.0367346	+	0.999325i	$0.488304\pi$
$48$	1.00000	0.144338
$49$	−0.919592	−0.131370
$50$	7.70218	1.08925
$51$	−1.00000	−0.140028
$52$	6.98778	0.969031
$53$	11.1097	1.52604	0.763018	−	0.646378i	$-0.223717\pi$
$53$	11.1097	1.52604	0.763018	+	0.646378i	$0.223717\pi$
$54$	1.00000	0.136083
$55$	7.97366	1.07517
$56$	−2.46585	−0.329513
$57$	−3.26299	−0.432194
$58$	5.56947	0.731307
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	3.56401	0.460112
$61$	6.17244	0.790300	0.395150	−	0.918617i	$-0.370693\pi$
$61$	6.17244	0.790300	0.395150	+	0.918617i	$0.370693\pi$
$62$	2.91738	0.370508
$63$	−2.46585	−0.310668
$64$	1.00000	0.125000
$65$	24.9045	3.08903
$66$	2.23727	0.275389
$67$	2.12053	0.259064	0.129532	−	0.991575i	$-0.458652\pi$
$67$	2.12053	0.259064	0.129532	+	0.991575i	$0.458652\pi$
$68$	−1.00000	−0.121268
$69$	−0.970280	−0.116808
$70$	−8.78831	−1.05040
$71$	−3.41104	−0.404816	−0.202408	−	0.979301i	$-0.564877\pi$
$71$	−3.41104	−0.404816	−0.202408	+	0.979301i	$0.564877\pi$
$72$	1.00000	0.117851
$73$	−1.74528	−0.204269	−0.102135	−	0.994771i	$-0.532567\pi$
$73$	−1.74528	−0.204269	−0.102135	+	0.994771i	$0.532567\pi$
$74$	−6.24983	−0.726528
$75$	7.70218	0.889371
$76$	−3.26299	−0.374291
$77$	−5.51677	−0.628695
$78$	6.98778	0.791211
$79$	−0.425901	−0.0479176	−0.0239588	−	0.999713i	$-0.507627\pi$
$79$	−0.425901	−0.0479176	−0.0239588	+	0.999713i	$0.507627\pi$
$80$	3.56401	0.398469
$81$	1.00000	0.111111
$82$	−5.50288	−0.607691
$83$	−11.9283	−1.30930	−0.654651	−	0.755932i	$-0.727184\pi$
$83$	−11.9283	−1.30930	−0.654651	+	0.755932i	$0.727184\pi$
$84$	−2.46585	−0.269046
$85$	−3.56401	−0.386571
$86$	−6.05959	−0.653423
$87$	5.56947	0.597109
$88$	2.23727	0.238494
$89$	−10.1559	−1.07652	−0.538261	−	0.842778i	$-0.680919\pi$
$89$	−10.1559	−1.07652	−0.538261	+	0.842778i	$0.680919\pi$
$90$	3.56401	0.375680
$91$	−17.2308	−1.80628
$92$	−0.970280	−0.101159
$93$	2.91738	0.302519
$94$	0.503679	0.0519505
$95$	−11.6293	−1.19315
$96$	1.00000	0.102062
$97$	7.98124	0.810372	0.405186	−	0.914234i	$-0.367207\pi$
$97$	7.98124	0.810372	0.405186	+	0.914234i	$0.367207\pi$
$98$	−0.919592	−0.0928928
$99$	2.23727	0.224854
$100$	7.70218	0.770218
$101$	4.04456	0.402449	0.201224	−	0.979545i	$-0.435508\pi$
$101$	4.04456	0.402449	0.201224	+	0.979545i	$0.435508\pi$
$102$	−1.00000	−0.0990148
$103$	−2.26499	−0.223176	−0.111588	−	0.993755i	$-0.535594\pi$
$103$	−2.26499	−0.223176	−0.111588	+	0.993755i	$0.535594\pi$
$104$	6.98778	0.685208
$105$	−8.78831	−0.857652
$106$	11.1097	1.07907
$107$	0.130964	0.0126608	0.00633040	−	0.999980i	$-0.497985\pi$
$107$	0.130964	0.0126608	0.00633040	+	0.999980i	$0.497985\pi$
$108$	1.00000	0.0962250
$109$	−3.89539	−0.373111	−0.186556	−	0.982444i	$-0.559732\pi$
$109$	−3.89539	−0.373111	−0.186556	+	0.982444i	$0.559732\pi$
$110$	7.97366	0.760259
$111$	−6.24983	−0.593208
$112$	−2.46585	−0.233001
$113$	−17.3075	−1.62815	−0.814074	−	0.580761i	$-0.802755\pi$
$113$	−17.3075	−1.62815	−0.814074	+	0.580761i	$0.802755\pi$
$114$	−3.26299	−0.305607
$115$	−3.45809	−0.322469
$116$	5.56947	0.517112
$117$	6.98778	0.646021
$118$	1.00000	0.0920575
$119$	2.46585	0.226044
$120$	3.56401	0.325348
$121$	−5.99461	−0.544965
$122$	6.17244	0.558826
$123$	−5.50288	−0.496178
$124$	2.91738	0.261989
$125$	9.63061	0.861388
$126$	−2.46585	−0.219675
$127$	2.96617	0.263205	0.131603	−	0.991303i	$-0.457988\pi$
$127$	2.96617	0.263205	0.131603	+	0.991303i	$0.457988\pi$
$128$	1.00000	0.0883883
$129$	−6.05959	−0.533517
$130$	24.9045	2.18427
$131$	18.6351	1.62816	0.814079	−	0.580754i	$-0.197242\pi$
$131$	18.6351	1.62816	0.814079	+	0.580754i	$0.197242\pi$
$132$	2.23727	0.194730
$133$	8.04605	0.697681
$134$	2.12053	0.183186
$135$	3.56401	0.306741
$136$	−1.00000	−0.0857493
$137$	−3.67411	−0.313901	−0.156950	−	0.987606i	$-0.550166\pi$
$137$	−3.67411	−0.313901	−0.156950	+	0.987606i	$0.550166\pi$
$138$	−0.970280	−0.0825957
$139$	−1.97821	−0.167789	−0.0838947	−	0.996475i	$-0.526736\pi$
$139$	−1.97821	−0.167789	−0.0838947	+	0.996475i	$0.526736\pi$
$140$	−8.78831	−0.742748
$141$	0.503679	0.0424174
$142$	−3.41104	−0.286248
$143$	15.6336	1.30734
$144$	1.00000	0.0833333
$145$	19.8496	1.64842
$146$	−1.74528	−0.144440
$147$	−0.919592	−0.0758466
$148$	−6.24983	−0.513733
$149$	−1.77398	−0.145330	−0.0726649	−	0.997356i	$-0.523150\pi$
$149$	−1.77398	−0.145330	−0.0726649	+	0.997356i	$0.523150\pi$
$150$	7.70218	0.628881
$151$	3.59720	0.292736	0.146368	−	0.989230i	$-0.453242\pi$
$151$	3.59720	0.292736	0.146368	+	0.989230i	$0.453242\pi$
$152$	−3.26299	−0.264664
$153$	−1.00000	−0.0808452
$154$	−5.51677	−0.444554
$155$	10.3976	0.835155
$156$	6.98778	0.559470
$157$	22.8722	1.82540	0.912698	−	0.408634i	$-0.133995\pi$
$157$	22.8722	1.82540	0.912698	+	0.408634i	$0.133995\pi$
$158$	−0.425901	−0.0338829
$159$	11.1097	0.881057
$160$	3.56401	0.281760
$161$	2.39256	0.188560
$162$	1.00000	0.0785674
$163$	−4.78554	−0.374832	−0.187416	−	0.982281i	$-0.560011\pi$
$163$	−4.78554	−0.374832	−0.187416	+	0.982281i	$0.560011\pi$
$164$	−5.50288	−0.429702
$165$	7.97366	0.620749
$166$	−11.9283	−0.925816
$167$	−19.4990	−1.50888	−0.754438	−	0.656372i	$-0.772090\pi$
$167$	−19.4990	−1.50888	−0.754438	+	0.656372i	$0.772090\pi$
$168$	−2.46585	−0.190244
$169$	35.8291	2.75609
$170$	−3.56401	−0.273347
$171$	−3.26299	−0.249527
$172$	−6.05959	−0.462040
$173$	20.1747	1.53385	0.766926	−	0.641735i	$-0.221785\pi$
$173$	20.1747	1.53385	0.766926	+	0.641735i	$0.221785\pi$
$174$	5.56947	0.422220
$175$	−18.9924	−1.43569
$176$	2.23727	0.168641
$177$	1.00000	0.0751646
$178$	−10.1559	−0.761216
$179$	−8.03098	−0.600263	−0.300132	−	0.953898i	$-0.597031\pi$
$179$	−8.03098	−0.600263	−0.300132	+	0.953898i	$0.597031\pi$
$180$	3.56401	0.265646
$181$	1.21353	0.0902010	0.0451005	−	0.998982i	$-0.485639\pi$
$181$	1.21353	0.0902010	0.0451005	+	0.998982i	$0.485639\pi$
$182$	−17.2308	−1.27723
$183$	6.17244	0.456280
$184$	−0.970280	−0.0715300
$185$	−22.2745	−1.63765
$186$	2.91738	0.213913
$187$	−2.23727	−0.163606
$188$	0.503679	0.0367346
$189$	−2.46585	−0.179364
$190$	−11.6293	−0.843681
$191$	−24.2520	−1.75481	−0.877405	−	0.479750i	$-0.840727\pi$
$191$	−24.2520	−1.75481	−0.877405	+	0.479750i	$0.840727\pi$
$192$	1.00000	0.0721688
$193$	−8.35509	−0.601413	−0.300706	−	0.953717i	$-0.597222\pi$
$193$	−8.35509	−0.601413	−0.300706	+	0.953717i	$0.597222\pi$
$194$	7.98124	0.573020
$195$	24.9045	1.78345
$196$	−0.919592	−0.0656851
$197$	19.5537	1.39314	0.696571	−	0.717488i	$-0.254708\pi$
$197$	19.5537	1.39314	0.696571	+	0.717488i	$0.254708\pi$
$198$	2.23727	0.158996
$199$	14.9285	1.05825	0.529127	−	0.848543i	$-0.322519\pi$
$199$	14.9285	1.05825	0.529127	+	0.848543i	$0.322519\pi$
$200$	7.70218	0.544627
$201$	2.12053	0.149571
$202$	4.04456	0.284574
$203$	−13.7335	−0.963900
$204$	−1.00000	−0.0700140
$205$	−19.6123	−1.36978
$206$	−2.26499	−0.157809
$207$	−0.970280	−0.0674391
$208$	6.98778	0.484516
$209$	−7.30020	−0.504965
$210$	−8.78831	−0.606451
$211$	19.3548	1.33244	0.666219	−	0.745757i	$-0.267912\pi$
$211$	19.3548	1.33244	0.666219	+	0.745757i	$0.267912\pi$
$212$	11.1097	0.763018
$213$	−3.41104	−0.233721
$214$	0.130964	0.00895254
$215$	−21.5965	−1.47287
$216$	1.00000	0.0680414
$217$	−7.19383	−0.488349
$218$	−3.89539	−0.263829
$219$	−1.74528	−0.117935
$220$	7.97366	0.537584
$221$	−6.98778	−0.470049
$222$	−6.24983	−0.419461
$223$	8.77171	0.587397	0.293699	−	0.955898i	$-0.405114\pi$
$223$	8.77171	0.587397	0.293699	+	0.955898i	$0.405114\pi$
$224$	−2.46585	−0.164756
$225$	7.70218	0.513479
$226$	−17.3075	−1.15127
$227$	−27.6135	−1.83277	−0.916386	−	0.400296i	$-0.868907\pi$
$227$	−27.6135	−1.83277	−0.916386	+	0.400296i	$0.868907\pi$
$228$	−3.26299	−0.216097
$229$	−14.1022	−0.931898	−0.465949	−	0.884812i	$-0.654287\pi$
$229$	−14.1022	−0.931898	−0.465949	+	0.884812i	$0.654287\pi$
$230$	−3.45809	−0.228020
$231$	−5.51677	−0.362977
$232$	5.56947	0.365653
$233$	24.3452	1.59491	0.797453	−	0.603381i	$-0.206180\pi$
$233$	24.3452	1.59491	0.797453	+	0.603381i	$0.206180\pi$
$234$	6.98778	0.456806
$235$	1.79512	0.117101
$236$	1.00000	0.0650945
$237$	−0.425901	−0.0276653
$238$	2.46585	0.159837
$239$	4.93536	0.319242	0.159621	−	0.987178i	$-0.448973\pi$
$239$	4.93536	0.319242	0.159621	+	0.987178i	$0.448973\pi$
$240$	3.56401	0.230056
$241$	−20.9104	−1.34696	−0.673478	−	0.739208i	$-0.735200\pi$
$241$	−20.9104	−1.34696	−0.673478	+	0.739208i	$0.735200\pi$
$242$	−5.99461	−0.385348
$243$	1.00000	0.0641500
$244$	6.17244	0.395150
$245$	−3.27744	−0.209388
$246$	−5.50288	−0.350851
$247$	−22.8011	−1.45080
$248$	2.91738	0.185254
$249$	−11.9283	−0.755925
$250$	9.63061	0.609093
$251$	−11.7534	−0.741870	−0.370935	−	0.928659i	$-0.620963\pi$
$251$	−11.7534	−0.741870	−0.370935	+	0.928659i	$0.620963\pi$
$252$	−2.46585	−0.155334
$253$	−2.17078	−0.136476
$254$	2.96617	0.186114
$255$	−3.56401	−0.223187
$256$	1.00000	0.0625000
$257$	−26.4509	−1.64996	−0.824981	−	0.565161i	$-0.808814\pi$
$257$	−26.4509	−1.64996	−0.824981	+	0.565161i	$0.808814\pi$
$258$	−6.05959	−0.377254
$259$	15.4111	0.957602
$260$	24.9045	1.54451
$261$	5.56947	0.344741
$262$	18.6351	1.15128
$263$	29.3182	1.80784	0.903918	−	0.427706i	$-0.140678\pi$
$263$	29.3182	1.80784	0.903918	+	0.427706i	$0.140678\pi$
$264$	2.23727	0.137695
$265$	39.5951	2.43231
$266$	8.04605	0.493335
$267$	−10.1559	−0.621530
$268$	2.12053	0.129532
$269$	7.38146	0.450056	0.225028	−	0.974352i	$-0.427753\pi$
$269$	7.38146	0.450056	0.225028	+	0.974352i	$0.427753\pi$
$270$	3.56401	0.216899
$271$	2.56015	0.155518	0.0777590	−	0.996972i	$-0.475224\pi$
$271$	2.56015	0.155518	0.0777590	+	0.996972i	$0.475224\pi$
$272$	−1.00000	−0.0606339
$273$	−17.2308	−1.04286
$274$	−3.67411	−0.221961
$275$	17.2319	1.03912
$276$	−0.970280	−0.0584040
$277$	1.02187	0.0613979	0.0306990	−	0.999529i	$-0.490227\pi$
$277$	1.02187	0.0613979	0.0306990	+	0.999529i	$0.490227\pi$
$278$	−1.97821	−0.118645
$279$	2.91738	0.174659
$280$	−8.78831	−0.525202
$281$	−12.1185	−0.722928	−0.361464	−	0.932386i	$-0.617723\pi$
$281$	−12.1185	−0.722928	−0.361464	+	0.932386i	$0.617723\pi$
$282$	0.503679	0.0299936
$283$	−19.3973	−1.15305	−0.576524	−	0.817080i	$-0.695591\pi$
$283$	−19.3973	−1.15305	−0.576524	+	0.817080i	$0.695591\pi$
$284$	−3.41104	−0.202408
$285$	−11.6293	−0.688863
$286$	15.6336	0.924432
$287$	13.5693	0.800968
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	19.8496	1.16561
$291$	7.98124	0.467869
$292$	−1.74528	−0.102135
$293$	5.56354	0.325026	0.162513	−	0.986706i	$-0.448040\pi$
$293$	5.56354	0.325026	0.162513	+	0.986706i	$0.448040\pi$
$294$	−0.919592	−0.0536317
$295$	3.56401	0.207505
$296$	−6.24983	−0.363264
$297$	2.23727	0.129820
$298$	−1.77398	−0.102764
$299$	−6.78011	−0.392104
$300$	7.70218	0.444686
$301$	14.9420	0.861245
$302$	3.59720	0.206995
$303$	4.04456	0.232354
$304$	−3.26299	−0.187145
$305$	21.9986	1.25964
$306$	−1.00000	−0.0571662
$307$	−1.43170	−0.0817115	−0.0408557	−	0.999165i	$-0.513008\pi$
$307$	−1.43170	−0.0817115	−0.0408557	+	0.999165i	$0.513008\pi$
$308$	−5.51677	−0.314347
$309$	−2.26499	−0.128851
$310$	10.3976	0.590544
$311$	−17.5004	−0.992356	−0.496178	−	0.868221i	$-0.665264\pi$
$311$	−17.5004	−0.992356	−0.496178	+	0.868221i	$0.665264\pi$
$312$	6.98778	0.395605
$313$	21.8387	1.23440	0.617199	−	0.786807i	$-0.288267\pi$
$313$	21.8387	1.23440	0.617199	+	0.786807i	$0.288267\pi$
$314$	22.8722	1.29075
$315$	−8.78831	−0.495165
$316$	−0.425901	−0.0239588
$317$	16.2873	0.914784	0.457392	−	0.889265i	$-0.348784\pi$
$317$	16.2873	0.914784	0.457392	+	0.889265i	$0.348784\pi$
$318$	11.1097	0.623001
$319$	12.4604	0.697649
$320$	3.56401	0.199234
$321$	0.130964	0.00730972
$322$	2.39256	0.133332
$323$	3.26299	0.181558
$324$	1.00000	0.0555556
$325$	53.8212	2.98546
$326$	−4.78554	−0.265047
$327$	−3.89539	−0.215416
$328$	−5.50288	−0.303845
$329$	−1.24200	−0.0684735
$330$	7.97366	0.438936
$331$	−2.52898	−0.139005	−0.0695027	−	0.997582i	$-0.522141\pi$
$331$	−2.52898	−0.139005	−0.0695027	+	0.997582i	$0.522141\pi$
$332$	−11.9283	−0.654651
$333$	−6.24983	−0.342489
$334$	−19.4990	−1.06694
$335$	7.55761	0.412916
$336$	−2.46585	−0.134523
$337$	−19.2350	−1.04780	−0.523899	−	0.851780i	$-0.675523\pi$
$337$	−19.2350	−1.04780	−0.523899	+	0.851780i	$0.675523\pi$
$338$	35.8291	1.94885
$339$	−17.3075	−0.940012
$340$	−3.56401	−0.193286
$341$	6.52698	0.353456
$342$	−3.26299	−0.176442
$343$	19.5285	1.05444
$344$	−6.05959	−0.326711
$345$	−3.45809	−0.186177
$346$	20.1747	1.08460
$347$	28.3599	1.52244	0.761218	−	0.648495i	$-0.224601\pi$
$347$	28.3599	1.52244	0.761218	+	0.648495i	$0.224601\pi$
$348$	5.56947	0.298555
$349$	−6.82397	−0.365279	−0.182639	−	0.983180i	$-0.558464\pi$
$349$	−6.82397	−0.365279	−0.182639	+	0.983180i	$0.558464\pi$
$350$	−18.9924	−1.01519
$351$	6.98778	0.372980
$352$	2.23727	0.119247
$353$	−20.8545	−1.10997	−0.554986	−	0.831860i	$-0.687276\pi$
$353$	−20.8545	−1.10997	−0.554986	+	0.831860i	$0.687276\pi$
$354$	1.00000	0.0531494
$355$	−12.1570	−0.645226
$356$	−10.1559	−0.538261
$357$	2.46585	0.130507
$358$	−8.03098	−0.424450
$359$	−22.9948	−1.21362	−0.606809	−	0.794847i	$-0.707551\pi$
$359$	−22.9948	−1.21362	−0.606809	+	0.794847i	$0.707551\pi$
$360$	3.56401	0.187840
$361$	−8.35288	−0.439625
$362$	1.21353	0.0637817
$363$	−5.99461	−0.314636
$364$	−17.2308	−0.903140
$365$	−6.22020	−0.325580
$366$	6.17244	0.322639
$367$	−11.6246	−0.606799	−0.303399	−	0.952864i	$-0.598122\pi$
$367$	−11.6246	−0.606799	−0.303399	+	0.952864i	$0.598122\pi$
$368$	−0.970280	−0.0505794
$369$	−5.50288	−0.286468
$370$	−22.2745	−1.15800
$371$	−27.3948	−1.42227
$372$	2.91738	0.151259
$373$	7.27027	0.376440	0.188220	−	0.982127i	$-0.439728\pi$
$373$	7.27027	0.376440	0.188220	+	0.982127i	$0.439728\pi$
$374$	−2.23727	−0.115687
$375$	9.63061	0.497323
$376$	0.503679	0.0259753
$377$	38.9182	2.00439
$378$	−2.46585	−0.126830
$379$	5.79634	0.297738	0.148869	−	0.988857i	$-0.452437\pi$
$379$	5.79634	0.297738	0.148869	+	0.988857i	$0.452437\pi$
$380$	−11.6293	−0.596573
$381$	2.96617	0.151962
$382$	−24.2520	−1.24084
$383$	−33.9636	−1.73546	−0.867729	−	0.497038i	$-0.834421\pi$
$383$	−33.9636	−1.73546	−0.867729	+	0.497038i	$0.834421\pi$
$384$	1.00000	0.0510310
$385$	−19.6618	−1.00206
$386$	−8.35509	−0.425263
$387$	−6.05959	−0.308026
$388$	7.98124	0.405186
$389$	−2.46577	−0.125019	−0.0625097	−	0.998044i	$-0.519910\pi$
$389$	−2.46577	−0.125019	−0.0625097	+	0.998044i	$0.519910\pi$
$390$	24.9045	1.26109
$391$	0.970280	0.0490692
$392$	−0.919592	−0.0464464
$393$	18.6351	0.940017
$394$	19.5537	0.985100
$395$	−1.51792	−0.0763747
$396$	2.23727	0.112427
$397$	0.0972268	0.00487967	0.00243984	−	0.999997i	$-0.499223\pi$
$397$	0.0972268	0.00487967	0.00243984	+	0.999997i	$0.499223\pi$
$398$	14.9285	0.748299
$399$	8.04605	0.402806
$400$	7.70218	0.385109
$401$	−16.1431	−0.806147	−0.403074	−	0.915168i	$-0.632058\pi$
$401$	−16.1431	−0.806147	−0.403074	+	0.915168i	$0.632058\pi$
$402$	2.12053	0.105763
$403$	20.3860	1.01550
$404$	4.04456	0.201224
$405$	3.56401	0.177097
$406$	−13.7335	−0.681580
$407$	−13.9826	−0.693090
$408$	−1.00000	−0.0495074
$409$	35.0033	1.73080	0.865401	−	0.501079i	$-0.167063\pi$
$409$	35.0033	1.73080	0.865401	+	0.501079i	$0.167063\pi$
$410$	−19.6123	−0.968583
$411$	−3.67411	−0.181231
$412$	−2.26499	−0.111588
$413$	−2.46585	−0.121336
$414$	−0.970280	−0.0476867
$415$	−42.5126	−2.08686
$416$	6.98778	0.342604
$417$	−1.97821	−0.0968733
$418$	−7.30020	−0.357065
$419$	−17.6489	−0.862207	−0.431104	−	0.902302i	$-0.641876\pi$
$419$	−17.6489	−0.862207	−0.431104	+	0.902302i	$0.641876\pi$
$420$	−8.78831	−0.428826
$421$	−16.4817	−0.803269	−0.401635	−	0.915800i	$-0.631558\pi$
$421$	−16.4817	−0.803269	−0.401635	+	0.915800i	$0.631558\pi$
$422$	19.3548	0.942175
$423$	0.503679	0.0244897
$424$	11.1097	0.539535
$425$	−7.70218	−0.373611
$426$	−3.41104	−0.165265
$427$	−15.2203	−0.736562
$428$	0.130964	0.00633040
$429$	15.6336	0.754796
$430$	−21.5965	−1.04147
$431$	−13.6301	−0.656539	−0.328270	−	0.944584i	$-0.606465\pi$
$431$	−13.6301	−0.656539	−0.328270	+	0.944584i	$0.606465\pi$
$432$	1.00000	0.0481125
$433$	9.39726	0.451603	0.225802	−	0.974173i	$-0.427500\pi$
$433$	9.39726	0.451603	0.225802	+	0.974173i	$0.427500\pi$
$434$	−7.19383	−0.345315
$435$	19.8496	0.951717
$436$	−3.89539	−0.186556
$437$	3.16602	0.151451
$438$	−1.74528	−0.0833927
$439$	12.4607	0.594718	0.297359	−	0.954766i	$-0.403894\pi$
$439$	12.4607	0.594718	0.297359	+	0.954766i	$0.403894\pi$
$440$	7.97366	0.380130
$441$	−0.919592	−0.0437901
$442$	−6.98778	−0.332375
$443$	−2.00234	−0.0951342	−0.0475671	−	0.998868i	$-0.515147\pi$
$443$	−2.00234	−0.0951342	−0.0475671	+	0.998868i	$0.515147\pi$
$444$	−6.24983	−0.296604
$445$	−36.1957	−1.71584
$446$	8.77171	0.415352
$447$	−1.77398	−0.0839062
$448$	−2.46585	−0.116500
$449$	18.9313	0.893425	0.446712	−	0.894678i	$-0.352595\pi$
$449$	18.9313	0.893425	0.446712	+	0.894678i	$0.352595\pi$
$450$	7.70218	0.363084
$451$	−12.3114	−0.579723
$452$	−17.3075	−0.814074
$453$	3.59720	0.169011
$454$	−27.6135	−1.29597
$455$	−61.4108	−2.87898
$456$	−3.26299	−0.152804
$457$	−9.83853	−0.460227	−0.230114	−	0.973164i	$-0.573910\pi$
$457$	−9.83853	−0.460227	−0.230114	+	0.973164i	$0.573910\pi$
$458$	−14.1022	−0.658951
$459$	−1.00000	−0.0466760
$460$	−3.45809	−0.161234
$461$	−30.0975	−1.40178	−0.700890	−	0.713270i	$-0.747214\pi$
$461$	−30.0975	−1.40178	−0.700890	+	0.713270i	$0.747214\pi$
$462$	−5.51677	−0.256664
$463$	10.0107	0.465237	0.232618	−	0.972568i	$-0.425271\pi$
$463$	10.0107	0.465237	0.232618	+	0.972568i	$0.425271\pi$
$464$	5.56947	0.258556
$465$	10.3976	0.482177
$466$	24.3452	1.12777
$467$	−34.0902	−1.57751	−0.788753	−	0.614710i	$-0.789273\pi$
$467$	−34.0902	−1.57751	−0.788753	+	0.614710i	$0.789273\pi$
$468$	6.98778	0.323010
$469$	−5.22891	−0.241449
$470$	1.79512	0.0828026
$471$	22.8722	1.05389
$472$	1.00000	0.0460287
$473$	−13.5570	−0.623349
$474$	−0.425901	−0.0195623
$475$	−25.1322	−1.15314
$476$	2.46585	0.113022
$477$	11.1097	0.508678
$478$	4.93536	0.225738
$479$	35.5996	1.62659	0.813294	−	0.581853i	$-0.197672\pi$
$479$	35.5996	1.62659	0.813294	+	0.581853i	$0.197672\pi$
$480$	3.56401	0.162674
$481$	−43.6725	−1.99129
$482$	−20.9104	−0.952441
$483$	2.39256	0.108865
$484$	−5.99461	−0.272482
$485$	28.4452	1.29163
$486$	1.00000	0.0453609
$487$	−2.41684	−0.109518	−0.0547588	−	0.998500i	$-0.517439\pi$
$487$	−2.41684	−0.109518	−0.0547588	+	0.998500i	$0.517439\pi$
$488$	6.17244	0.279413
$489$	−4.78554	−0.216410
$490$	−3.27744	−0.148059
$491$	0.934422	0.0421699	0.0210849	−	0.999778i	$-0.493288\pi$
$491$	0.934422	0.0421699	0.0210849	+	0.999778i	$0.493288\pi$
$492$	−5.50288	−0.248089
$493$	−5.56947	−0.250836
$494$	−22.8011	−1.02587
$495$	7.97366	0.358390
$496$	2.91738	0.130994
$497$	8.41111	0.377290
$498$	−11.9283	−0.534520
$499$	−21.3492	−0.955723	−0.477862	−	0.878435i	$-0.658588\pi$
$499$	−21.3492	−0.955723	−0.477862	+	0.878435i	$0.658588\pi$
$500$	9.63061	0.430694
$501$	−19.4990	−0.871150
$502$	−11.7534	−0.524582
$503$	−30.6887	−1.36834	−0.684171	−	0.729321i	$-0.739836\pi$
$503$	−30.6887	−1.36834	−0.684171	+	0.729321i	$0.739836\pi$
$504$	−2.46585	−0.109838
$505$	14.4149	0.641453
$506$	−2.17078	−0.0965030
$507$	35.8291	1.59123
$508$	2.96617	0.131603
$509$	26.4320	1.17158	0.585790	−	0.810463i	$-0.300784\pi$
$509$	26.4320	1.17158	0.585790	+	0.810463i	$0.300784\pi$
$510$	−3.56401	−0.157817
$511$	4.30359	0.190380
$512$	1.00000	0.0441942
$513$	−3.26299	−0.144065
$514$	−26.4509	−1.16670
$515$	−8.07244	−0.355714
$516$	−6.05959	−0.266759
$517$	1.12687	0.0495595
$518$	15.4111	0.677127
$519$	20.1747	0.885570
$520$	24.9045	1.09214
$521$	16.0017	0.701047	0.350523	−	0.936554i	$-0.386004\pi$
$521$	16.0017	0.701047	0.350523	+	0.936554i	$0.386004\pi$
$522$	5.56947	0.243769
$523$	13.2972	0.581445	0.290722	−	0.956807i	$-0.406104\pi$
$523$	13.2972	0.581445	0.290722	+	0.956807i	$0.406104\pi$
$524$	18.6351	0.814079
$525$	−18.9924	−0.828897
$526$	29.3182	1.27833
$527$	−2.91738	−0.127083
$528$	2.23727	0.0973648
$529$	−22.0586	−0.959068
$530$	39.5951	1.71990
$531$	1.00000	0.0433963
$532$	8.04605	0.348840
$533$	−38.4529	−1.66558
$534$	−10.1559	−0.439488
$535$	0.466759	0.0201797
$536$	2.12053	0.0915931
$537$	−8.03098	−0.346562
$538$	7.38146	0.318237
$539$	−2.05738	−0.0886175
$540$	3.56401	0.153371
$541$	−25.9174	−1.11428	−0.557139	−	0.830419i	$-0.688101\pi$
$541$	−25.9174	−1.11428	−0.557139	+	0.830419i	$0.688101\pi$
$542$	2.56015	0.109968
$543$	1.21353	0.0520776
$544$	−1.00000	−0.0428746
$545$	−13.8832	−0.594692
$546$	−17.2308	−0.737411
$547$	−27.3248	−1.16832	−0.584161	−	0.811638i	$-0.698576\pi$
$547$	−27.3248	−1.16832	−0.584161	+	0.811638i	$0.698576\pi$
$548$	−3.67411	−0.156950
$549$	6.17244	0.263433
$550$	17.2319	0.734770
$551$	−18.1731	−0.774201
$552$	−0.970280	−0.0412979
$553$	1.05021	0.0446594
$554$	1.02187	0.0434149
$555$	−22.2745	−0.945499
$556$	−1.97821	−0.0838947
$557$	36.0840	1.52893	0.764463	−	0.644667i	$-0.223004\pi$
$557$	36.0840	1.52893	0.764463	+	0.644667i	$0.223004\pi$
$558$	2.91738	0.123503
$559$	−42.3431	−1.79092
$560$	−8.78831	−0.371374
$561$	−2.23727	−0.0944577
$562$	−12.1185	−0.511187
$563$	29.2996	1.23483	0.617415	−	0.786637i	$-0.288180\pi$
$563$	29.2996	1.23483	0.617415	+	0.786637i	$0.288180\pi$
$564$	0.503679	0.0212087
$565$	−61.6840	−2.59506
$566$	−19.3973	−0.815328
$567$	−2.46585	−0.103556
$568$	−3.41104	−0.143124
$569$	45.5909	1.91127	0.955635	−	0.294553i	$-0.0951707\pi$
$569$	45.5909	1.91127	0.955635	+	0.294553i	$0.0951707\pi$
$570$	−11.6293	−0.487100
$571$	5.19206	0.217281	0.108640	−	0.994081i	$-0.465350\pi$
$571$	5.19206	0.217281	0.108640	+	0.994081i	$0.465350\pi$
$572$	15.6336	0.653672
$573$	−24.2520	−1.01314
$574$	13.5693	0.566370
$575$	−7.47328	−0.311657
$576$	1.00000	0.0416667
$577$	−32.3119	−1.34516	−0.672580	−	0.740024i	$-0.734814\pi$
$577$	−32.3119	−1.34516	−0.672580	+	0.740024i	$0.734814\pi$
$578$	1.00000	0.0415945
$579$	−8.35509	−0.347226
$580$	19.8496	0.824212
$581$	29.4134	1.22027
$582$	7.98124	0.330833
$583$	24.8554	1.02941
$584$	−1.74528	−0.0722202
$585$	24.9045	1.02968
$586$	5.56354	0.229828
$587$	−5.50467	−0.227202	−0.113601	−	0.993526i	$-0.536239\pi$
$587$	−5.50467	−0.227202	−0.113601	+	0.993526i	$0.536239\pi$
$588$	−0.919592	−0.0379233
$589$	−9.51940	−0.392240
$590$	3.56401	0.146728
$591$	19.5537	0.804331
$592$	−6.24983	−0.256867
$593$	28.3579	1.16452	0.582259	−	0.813003i	$-0.302169\pi$
$593$	28.3579	1.16452	0.582259	+	0.813003i	$0.302169\pi$
$594$	2.23727	0.0917964
$595$	8.78831	0.360286
$596$	−1.77398	−0.0726649
$597$	14.9285	0.610983
$598$	−6.78011	−0.277259
$599$	4.64367	0.189735	0.0948675	−	0.995490i	$-0.469757\pi$
$599$	4.64367	0.189735	0.0948675	+	0.995490i	$0.469757\pi$
$600$	7.70218	0.314440
$601$	−15.5633	−0.634838	−0.317419	−	0.948285i	$-0.602816\pi$
$601$	−15.5633	−0.634838	−0.317419	+	0.948285i	$0.602816\pi$
$602$	14.9420	0.608992
$603$	2.12053	0.0863548
$604$	3.59720	0.146368
$605$	−21.3649	−0.868606
$606$	4.04456	0.164299
$607$	34.1616	1.38658	0.693288	−	0.720660i	$-0.256161\pi$
$607$	34.1616	1.38658	0.693288	+	0.720660i	$0.256161\pi$
$608$	−3.26299	−0.132332
$609$	−13.7335	−0.556508
$610$	21.9986	0.890699
$611$	3.51960	0.142388
$612$	−1.00000	−0.0404226
$613$	−37.7588	−1.52506	−0.762532	−	0.646951i	$-0.776044\pi$
$613$	−37.7588	−1.52506	−0.762532	+	0.646951i	$0.776044\pi$
$614$	−1.43170	−0.0577788
$615$	−19.6123	−0.790845
$616$	−5.51677	−0.222277
$617$	25.3885	1.02210	0.511051	−	0.859551i	$-0.329256\pi$
$617$	25.3885	1.02210	0.511051	+	0.859551i	$0.329256\pi$
$618$	−2.26499	−0.0911111
$619$	17.5385	0.704932	0.352466	−	0.935825i	$-0.385343\pi$
$619$	17.5385	0.704932	0.352466	+	0.935825i	$0.385343\pi$
$620$	10.3976	0.417577
$621$	−0.970280	−0.0389360
$622$	−17.5004	−0.701702
$623$	25.0429	1.00332
$624$	6.98778	0.279735
$625$	−4.18729	−0.167492
$626$	21.8387	0.872851
$627$	−7.30020	−0.291542
$628$	22.8722	0.912698
$629$	6.24983	0.249197
$630$	−8.78831	−0.350135
$631$	−15.1224	−0.602013	−0.301006	−	0.953622i	$-0.597323\pi$
$631$	−15.1224	−0.602013	−0.301006	+	0.953622i	$0.597323\pi$
$632$	−0.425901	−0.0169414
$633$	19.3548	0.769283
$634$	16.2873	0.646850
$635$	10.5715	0.419516
$636$	11.1097	0.440528
$637$	−6.42591	−0.254604
$638$	12.4604	0.493312
$639$	−3.41104	−0.134939
$640$	3.56401	0.140880
$641$	4.20350	0.166028	0.0830142	−	0.996548i	$-0.473545\pi$
$641$	4.20350	0.166028	0.0830142	+	0.996548i	$0.473545\pi$
$642$	0.130964	0.00516875
$643$	−19.0056	−0.749506	−0.374753	−	0.927125i	$-0.622272\pi$
$643$	−19.0056	−0.749506	−0.374753	+	0.927125i	$0.622272\pi$
$644$	2.39256	0.0942802
$645$	−21.5965	−0.850360
$646$	3.26299	0.128381
$647$	41.8033	1.64346	0.821730	−	0.569878i	$-0.193009\pi$
$647$	41.8033	1.64346	0.821730	+	0.569878i	$0.193009\pi$
$648$	1.00000	0.0392837
$649$	2.23727	0.0878206
$650$	53.8212	2.11104
$651$	−7.19383	−0.281948
$652$	−4.78554	−0.187416
$653$	27.2763	1.06740	0.533701	−	0.845673i	$-0.320801\pi$
$653$	27.2763	1.06740	0.533701	+	0.845673i	$0.320801\pi$
$654$	−3.89539	−0.152322
$655$	66.4158	2.59508
$656$	−5.50288	−0.214851
$657$	−1.74528	−0.0680898
$658$	−1.24200	−0.0484180
$659$	4.33960	0.169047	0.0845235	−	0.996421i	$-0.473063\pi$
$659$	4.33960	0.169047	0.0845235	+	0.996421i	$0.473063\pi$
$660$	7.97366	0.310374
$661$	12.0803	0.469870	0.234935	−	0.972011i	$-0.424512\pi$
$661$	12.0803	0.469870	0.234935	+	0.972011i	$0.424512\pi$
$662$	−2.52898	−0.0982916
$663$	−6.98778	−0.271383
$664$	−11.9283	−0.462908
$665$	28.6762	1.11202
$666$	−6.24983	−0.242176
$667$	−5.40394	−0.209241
$668$	−19.4990	−0.754438
$669$	8.77171	0.339134
$670$	7.55761	0.291976
$671$	13.8094	0.533107
$672$	−2.46585	−0.0951222
$673$	−34.4949	−1.32968	−0.664841	−	0.746985i	$-0.731501\pi$
$673$	−34.4949	−1.32968	−0.664841	+	0.746985i	$0.731501\pi$
$674$	−19.2350	−0.740905
$675$	7.70218	0.296457
$676$	35.8291	1.37804
$677$	19.7677	0.759735	0.379868	−	0.925041i	$-0.375970\pi$
$677$	19.7677	0.759735	0.379868	+	0.925041i	$0.375970\pi$
$678$	−17.3075	−0.664689
$679$	−19.6805	−0.755269
$680$	−3.56401	−0.136674
$681$	−27.6135	−1.05815
$682$	6.52698	0.249931
$683$	−44.5128	−1.70323	−0.851617	−	0.524165i	$-0.824377\pi$
$683$	−44.5128	−1.70323	−0.851617	+	0.524165i	$0.824377\pi$
$684$	−3.26299	−0.124764
$685$	−13.0946	−0.500318
$686$	19.5285	0.745602
$687$	−14.1022	−0.538032
$688$	−6.05959	−0.231020
$689$	77.6322	2.95755
$690$	−3.45809	−0.131647
$691$	−14.6291	−0.556517	−0.278259	−	0.960506i	$-0.589757\pi$
$691$	−14.6291	−0.556517	−0.278259	+	0.960506i	$0.589757\pi$
$692$	20.1747	0.766926
$693$	−5.51677	−0.209565
$694$	28.3599	1.07653
$695$	−7.05036	−0.267435
$696$	5.56947	0.211110
$697$	5.50288	0.208436
$698$	−6.82397	−0.258291
$699$	24.3452	0.920819
$700$	−18.9924	−0.717846
$701$	−14.8437	−0.560640	−0.280320	−	0.959907i	$-0.590441\pi$
$701$	−14.8437	−0.560640	−0.280320	+	0.959907i	$0.590441\pi$
$702$	6.98778	0.263737
$703$	20.3932	0.769143
$704$	2.23727	0.0843204
$705$	1.79512	0.0676081
$706$	−20.8545	−0.784868
$707$	−9.97328	−0.375084
$708$	1.00000	0.0375823
$709$	13.0860	0.491454	0.245727	−	0.969339i	$-0.420973\pi$
$709$	13.0860	0.491454	0.245727	+	0.969339i	$0.420973\pi$
$710$	−12.1570	−0.456244
$711$	−0.425901	−0.0159725
$712$	−10.1559	−0.380608
$713$	−2.83068	−0.106010
$714$	2.46585	0.0922821
$715$	55.7182	2.08374
$716$	−8.03098	−0.300132
$717$	4.93536	0.184314
$718$	−22.9948	−0.858158
$719$	51.1607	1.90797	0.953985	−	0.299853i	$-0.0969376\pi$
$719$	51.1607	1.90797	0.953985	+	0.299853i	$0.0969376\pi$
$720$	3.56401	0.132823
$721$	5.58511	0.208000
$722$	−8.35288	−0.310862
$723$	−20.9104	−0.777665
$724$	1.21353	0.0451005
$725$	42.8970	1.59316
$726$	−5.99461	−0.222481
$727$	2.47646	0.0918468	0.0459234	−	0.998945i	$-0.485377\pi$
$727$	2.47646	0.0918468	0.0459234	+	0.998945i	$0.485377\pi$
$728$	−17.2308	−0.638616
$729$	1.00000	0.0370370
$730$	−6.22020	−0.230220
$731$	6.05959	0.224122
$732$	6.17244	0.228140
$733$	−16.2732	−0.601064	−0.300532	−	0.953772i	$-0.597164\pi$
$733$	−16.2732	−0.601064	−0.300532	+	0.953772i	$0.597164\pi$
$734$	−11.6246	−0.429071
$735$	−3.27744	−0.120890
$736$	−0.970280	−0.0357650
$737$	4.74421	0.174755
$738$	−5.50288	−0.202564
$739$	3.32574	0.122339	0.0611697	−	0.998127i	$-0.480517\pi$
$739$	3.32574	0.122339	0.0611697	+	0.998127i	$0.480517\pi$
$740$	−22.2745	−0.818826
$741$	−22.8011	−0.837619
$742$	−27.3948	−1.00570
$743$	−36.6746	−1.34546	−0.672731	−	0.739887i	$-0.734879\pi$
$743$	−36.6746	−1.34546	−0.672731	+	0.739887i	$0.734879\pi$
$744$	2.91738	0.106956
$745$	−6.32247	−0.231637
$746$	7.27027	0.266183
$747$	−11.9283	−0.436434
$748$	−2.23727	−0.0818028
$749$	−0.322938	−0.0117999
$750$	9.63061	0.351660
$751$	−30.9525	−1.12947	−0.564737	−	0.825271i	$-0.691022\pi$
$751$	−30.9525	−1.12947	−0.564737	+	0.825271i	$0.691022\pi$
$752$	0.503679	0.0183673
$753$	−11.7534	−0.428319
$754$	38.9182	1.41732
$755$	12.8205	0.466584
$756$	−2.46585	−0.0896820
$757$	36.7118	1.33431	0.667156	−	0.744918i	$-0.267511\pi$
$757$	36.7118	1.33431	0.667156	+	0.744918i	$0.267511\pi$
$758$	5.79634	0.210533
$759$	−2.17078	−0.0787943
$760$	−11.6293	−0.421841
$761$	−31.3805	−1.13754	−0.568772	−	0.822495i	$-0.692581\pi$
$761$	−31.3805	−1.13754	−0.568772	+	0.822495i	$0.692581\pi$
$762$	2.96617	0.107453
$763$	9.60545	0.347741
$764$	−24.2520	−0.877405
$765$	−3.56401	−0.128857
$766$	−33.9636	−1.22715
$767$	6.98778	0.252314
$768$	1.00000	0.0360844
$769$	−31.6190	−1.14021	−0.570105	−	0.821572i	$-0.693098\pi$
$769$	−31.6190	−1.14021	−0.570105	+	0.821572i	$0.693098\pi$
$770$	−19.6618	−0.708564
$771$	−26.4509	−0.952606
$772$	−8.35509	−0.300706
$773$	−26.2808	−0.945255	−0.472628	−	0.881262i	$-0.656694\pi$
$773$	−26.2808	−0.945255	−0.472628	+	0.881262i	$0.656694\pi$
$774$	−6.05959	−0.217808
$775$	22.4702	0.807154
$776$	7.98124	0.286510
$777$	15.4111	0.552872
$778$	−2.46577	−0.0884020
$779$	17.9558	0.643335
$780$	24.9045	0.891726
$781$	−7.63142	−0.273074
$782$	0.970280	0.0346971
$783$	5.56947	0.199036
$784$	−0.919592	−0.0328426
$785$	81.5166	2.90945
$786$	18.6351	0.664693
$787$	−40.5050	−1.44385	−0.721923	−	0.691974i	$-0.756741\pi$
$787$	−40.5050	−1.44385	−0.721923	+	0.691974i	$0.756741\pi$
$788$	19.5537	0.696571
$789$	29.3182	1.04375
$790$	−1.51792	−0.0540051
$791$	42.6776	1.51744
$792$	2.23727	0.0794980
$793$	43.1317	1.53165
$794$	0.0972268	0.00345045
$795$	39.5951	1.40429
$796$	14.9285	0.529127
$797$	−24.3614	−0.862925	−0.431463	−	0.902131i	$-0.642002\pi$
$797$	−24.3614	−0.862925	−0.431463	+	0.902131i	$0.642002\pi$
$798$	8.04605	0.284827
$799$	−0.503679	−0.0178189
$800$	7.70218	0.272313
$801$	−10.1559	−0.358841
$802$	−16.1431	−0.570032
$803$	−3.90466	−0.137793
$804$	2.12053	0.0747854
$805$	8.52713	0.300542
$806$	20.3860	0.718068
$807$	7.38146	0.259840
$808$	4.04456	0.142287
$809$	42.9433	1.50981	0.754903	−	0.655837i	$-0.227684\pi$
$809$	42.9433	1.50981	0.754903	+	0.655837i	$0.227684\pi$
$810$	3.56401	0.125227
$811$	−16.6348	−0.584128	−0.292064	−	0.956399i	$-0.594342\pi$
$811$	−16.6348	−0.584128	−0.292064	+	0.956399i	$0.594342\pi$
$812$	−13.7335	−0.481950
$813$	2.56015	0.0897884
$814$	−13.9826	−0.490089
$815$	−17.0557	−0.597436
$816$	−1.00000	−0.0350070
$817$	19.7724	0.691749
$818$	35.0033	1.22386
$819$	−17.2308	−0.602093
$820$	−19.6123	−0.684892
$821$	−50.3562	−1.75744	−0.878722	−	0.477334i	$-0.841603\pi$
$821$	−50.3562	−1.75744	−0.878722	+	0.477334i	$0.841603\pi$
$822$	−3.67411	−0.128149
$823$	−41.4562	−1.44507	−0.722536	−	0.691333i	$-0.757024\pi$
$823$	−41.4562	−1.44507	−0.722536	+	0.691333i	$0.757024\pi$
$824$	−2.26499	−0.0789045
$825$	17.2319	0.599937
$826$	−2.46585	−0.0857978
$827$	−28.9887	−1.00803	−0.504017	−	0.863694i	$-0.668145\pi$
$827$	−28.9887	−1.00803	−0.504017	+	0.863694i	$0.668145\pi$
$828$	−0.970280	−0.0337196
$829$	−17.1173	−0.594507	−0.297254	−	0.954799i	$-0.596071\pi$
$829$	−17.1173	−0.594507	−0.297254	+	0.954799i	$0.596071\pi$
$830$	−42.5126	−1.47563
$831$	1.02187	0.0354481
$832$	6.98778	0.242258
$833$	0.919592	0.0318620
$834$	−1.97821	−0.0684998
$835$	−69.4946	−2.40496
$836$	−7.30020	−0.252483
$837$	2.91738	0.100840
$838$	−17.6489	−0.609673
$839$	4.67921	0.161544	0.0807722	−	0.996733i	$-0.474261\pi$
$839$	4.67921	0.161544	0.0807722	+	0.996733i	$0.474261\pi$
$840$	−8.78831	−0.303226
$841$	2.01894	0.0696187
$842$	−16.4817	−0.567997
$843$	−12.1185	−0.417383
$844$	19.3548	0.666219
$845$	127.695	4.39285
$846$	0.503679	0.0173168
$847$	14.7818	0.507909
$848$	11.1097	0.381509
$849$	−19.3973	−0.665712
$850$	−7.70218	−0.264183
$851$	6.06409	0.207874
$852$	−3.41104	−0.116860
$853$	21.1123	0.722871	0.361435	−	0.932397i	$-0.382287\pi$
$853$	21.1123	0.722871	0.361435	+	0.932397i	$0.382287\pi$
$854$	−15.2203	−0.520828
$855$	−11.6293	−0.397715
$856$	0.130964	0.00447627
$857$	−3.67335	−0.125479	−0.0627396	−	0.998030i	$-0.519984\pi$
$857$	−3.67335	−0.125479	−0.0627396	+	0.998030i	$0.519984\pi$
$858$	15.6336	0.533721
$859$	25.1176	0.857003	0.428501	−	0.903541i	$-0.359042\pi$
$859$	25.1176	0.857003	0.428501	+	0.903541i	$0.359042\pi$
$860$	−21.5965	−0.736433
$861$	13.5693	0.462439
$862$	−13.6301	−0.464243
$863$	32.0621	1.09141	0.545704	−	0.837978i	$-0.316262\pi$
$863$	32.0621	1.09141	0.545704	+	0.837978i	$0.316262\pi$
$864$	1.00000	0.0340207
$865$	71.9028	2.44477
$866$	9.39726	0.319332
$867$	1.00000	0.0339618
$868$	−7.19383	−0.244174
$869$	−0.952857	−0.0323234
$870$	19.8496	0.672966
$871$	14.8178	0.502083
$872$	−3.89539	−0.131915
$873$	7.98124	0.270124
$874$	3.16602	0.107092
$875$	−23.7476	−0.802816
$876$	−1.74528	−0.0589675
$877$	−31.4730	−1.06277	−0.531384	−	0.847131i	$-0.678328\pi$
$877$	−31.4730	−1.06277	−0.531384	+	0.847131i	$0.678328\pi$
$878$	12.4607	0.420529
$879$	5.56354	0.187654
$880$	7.97366	0.268792
$881$	−11.4002	−0.384084	−0.192042	−	0.981387i	$-0.561511\pi$
$881$	−11.4002	−0.384084	−0.192042	+	0.981387i	$0.561511\pi$
$882$	−0.919592	−0.0309643
$883$	−14.7324	−0.495784	−0.247892	−	0.968788i	$-0.579738\pi$
$883$	−14.7324	−0.495784	−0.247892	+	0.968788i	$0.579738\pi$
$884$	−6.98778	−0.235025
$885$	3.56401	0.119803
$886$	−2.00234	−0.0672700
$887$	11.7191	0.393490	0.196745	−	0.980455i	$-0.436963\pi$
$887$	11.7191	0.393490	0.196745	+	0.980455i	$0.436963\pi$
$888$	−6.24983	−0.209731
$889$	−7.31413	−0.245308
$890$	−36.1957	−1.21328
$891$	2.23727	0.0749514
$892$	8.77171	0.293699
$893$	−1.64350	−0.0549977
$894$	−1.77398	−0.0593306
$895$	−28.6225	−0.956745
$896$	−2.46585	−0.0823782
$897$	−6.78011	−0.226381
$898$	18.9313	0.631747
$899$	16.2483	0.541910
$900$	7.70218	0.256739
$901$	−11.1097	−0.370118
$902$	−12.3114	−0.409926
$903$	14.9420	0.497240
$904$	−17.3075	−0.575637
$905$	4.32504	0.143769
$906$	3.59720	0.119509
$907$	−11.4540	−0.380324	−0.190162	−	0.981753i	$-0.560901\pi$
$907$	−11.4540	−0.380324	−0.190162	+	0.981753i	$0.560901\pi$
$908$	−27.6135	−0.916386
$909$	4.04456	0.134150
$910$	−61.4108	−2.03575
$911$	−15.9765	−0.529326	−0.264663	−	0.964341i	$-0.585261\pi$
$911$	−15.9765	−0.529326	−0.264663	+	0.964341i	$0.585261\pi$
$912$	−3.26299	−0.108048
$913$	−26.6869	−0.883206
$914$	−9.83853	−0.325430
$915$	21.9986	0.727253
$916$	−14.1022	−0.465949
$917$	−45.9514	−1.51745
$918$	−1.00000	−0.0330049
$919$	9.98033	0.329221	0.164610	−	0.986359i	$-0.447363\pi$
$919$	9.98033	0.329221	0.164610	+	0.986359i	$0.447363\pi$
$920$	−3.45809	−0.114010
$921$	−1.43170	−0.0471762
$922$	−30.0975	−0.991208
$923$	−23.8356	−0.784558
$924$	−5.51677	−0.181489
$925$	−48.1374	−1.58275
$926$	10.0107	0.328972
$927$	−2.26499	−0.0743919
$928$	5.56947	0.182827
$929$	−21.3469	−0.700370	−0.350185	−	0.936681i	$-0.613881\pi$
$929$	−21.3469	−0.700370	−0.350185	+	0.936681i	$0.613881\pi$
$930$	10.3976	0.340950
$931$	3.00062	0.0983414
$932$	24.3452	0.797453
$933$	−17.5004	−0.572937
$934$	−34.0902	−1.11547
$935$	−7.97366	−0.260767
$936$	6.98778	0.228403
$937$	−11.5092	−0.375989	−0.187995	−	0.982170i	$-0.560199\pi$
$937$	−11.5092	−0.375989	−0.187995	+	0.982170i	$0.560199\pi$
$938$	−5.22891	−0.170730
$939$	21.8387	0.712680
$940$	1.79512	0.0585503
$941$	39.6200	1.29157	0.645787	−	0.763517i	$-0.276529\pi$
$941$	39.6200	1.29157	0.645787	+	0.763517i	$0.276529\pi$
$942$	22.8722	0.745215
$943$	5.33933	0.173873
$944$	1.00000	0.0325472
$945$	−8.78831	−0.285884
$946$	−13.5570	−0.440775
$947$	−16.3697	−0.531944	−0.265972	−	0.963981i	$-0.585693\pi$
$947$	−16.3697	−0.531944	−0.265972	+	0.963981i	$0.585693\pi$
$948$	−0.425901	−0.0138326
$949$	−12.1956	−0.395887
$950$	−25.1322	−0.815395
$951$	16.2873	0.528151
$952$	2.46585	0.0799186
$953$	−8.12107	−0.263067	−0.131534	−	0.991312i	$-0.541990\pi$
$953$	−8.12107	−0.263067	−0.131534	+	0.991312i	$0.541990\pi$
$954$	11.1097	0.359690
$955$	−86.4343	−2.79695
$956$	4.93536	0.159621
$957$	12.4604	0.402788
$958$	35.5996	1.15017
$959$	9.05981	0.292556
$960$	3.56401	0.115028
$961$	−22.4889	−0.725447
$962$	−43.6725	−1.40806
$963$	0.130964	0.00422027
$964$	−20.9104	−0.673478
$965$	−29.7776	−0.958576
$966$	2.39256	0.0769795
$967$	4.75678	0.152968	0.0764838	−	0.997071i	$-0.475631\pi$
$967$	4.75678	0.152968	0.0764838	+	0.997071i	$0.475631\pi$
$968$	−5.99461	−0.192674
$969$	3.26299	0.104822
$970$	28.4452	0.913321
$971$	40.8894	1.31220	0.656102	−	0.754672i	$-0.272204\pi$
$971$	40.8894	1.31220	0.656102	+	0.754672i	$0.272204\pi$
$972$	1.00000	0.0320750
$973$	4.87796	0.156380
$974$	−2.41684	−0.0774407
$975$	53.8212	1.72366
$976$	6.17244	0.197575
$977$	16.3248	0.522277	0.261138	−	0.965301i	$-0.415902\pi$
$977$	16.3248	0.522277	0.261138	+	0.965301i	$0.415902\pi$
$978$	−4.78554	−0.153025
$979$	−22.7215	−0.726182
$980$	−3.27744	−0.104694
$981$	−3.89539	−0.124370
$982$	0.934422	0.0298186
$983$	22.8757	0.729622	0.364811	−	0.931082i	$-0.381134\pi$
$983$	22.8757	0.729622	0.364811	+	0.931082i	$0.381134\pi$
$984$	−5.50288	−0.175425
$985$	69.6896	2.22049
$986$	−5.56947	−0.177368
$987$	−1.24200	−0.0395332
$988$	−22.8011	−0.725399
$989$	5.87950	0.186957
$990$	7.97366	0.253420
$991$	−58.4060	−1.85533	−0.927664	−	0.373417i	$-0.878186\pi$
$991$	−58.4060	−1.85533	−0.927664	+	0.373417i	$0.878186\pi$
$992$	2.91738	0.0926270
$993$	−2.52898	−0.0802548
$994$	8.41111	0.266784
$995$	53.2054	1.68672
$996$	−11.9283	−0.377963
$997$	30.3108	0.959954	0.479977	−	0.877281i	$-0.340645\pi$
$997$	30.3108	0.959954	0.479977	+	0.877281i	$0.340645\pi$
$998$	−21.3492	−0.675798
$999$	−6.24983	−0.197736

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.ba.1.10	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.ba.1.10	✓	12	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.56401 q^{5} +1.00000 q^{6} -2.46585 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.56401 q^{5} +1.00000 q^{6} -2.46585 q^{7} +1.00000 q^{8} +1.00000 q^{9} +3.56401 q^{10} +2.23727 q^{11} +1.00000 q^{12} +6.98778 q^{13} -2.46585 q^{14} +3.56401 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} -3.26299 q^{19} +3.56401 q^{20} -2.46585 q^{21} +2.23727 q^{22} -0.970280 q^{23} +1.00000 q^{24} +7.70218 q^{25} +6.98778 q^{26} +1.00000 q^{27} -2.46585 q^{28} +5.56947 q^{29} +3.56401 q^{30} +2.91738 q^{31} +1.00000 q^{32} +2.23727 q^{33} -1.00000 q^{34} -8.78831 q^{35} +1.00000 q^{36} -6.24983 q^{37} -3.26299 q^{38} +6.98778 q^{39} +3.56401 q^{40} -5.50288 q^{41} -2.46585 q^{42} -6.05959 q^{43} +2.23727 q^{44} +3.56401 q^{45} -0.970280 q^{46} +0.503679 q^{47} +1.00000 q^{48} -0.919592 q^{49} +7.70218 q^{50} -1.00000 q^{51} +6.98778 q^{52} +11.1097 q^{53} +1.00000 q^{54} +7.97366 q^{55} -2.46585 q^{56} -3.26299 q^{57} +5.56947 q^{58} +1.00000 q^{59} +3.56401 q^{60} +6.17244 q^{61} +2.91738 q^{62} -2.46585 q^{63} +1.00000 q^{64} +24.9045 q^{65} +2.23727 q^{66} +2.12053 q^{67} -1.00000 q^{68} -0.970280 q^{69} -8.78831 q^{70} -3.41104 q^{71} +1.00000 q^{72} -1.74528 q^{73} -6.24983 q^{74} +7.70218 q^{75} -3.26299 q^{76} -5.51677 q^{77} +6.98778 q^{78} -0.425901 q^{79} +3.56401 q^{80} +1.00000 q^{81} -5.50288 q^{82} -11.9283 q^{83} -2.46585 q^{84} -3.56401 q^{85} -6.05959 q^{86} +5.56947 q^{87} +2.23727 q^{88} -10.1559 q^{89} +3.56401 q^{90} -17.2308 q^{91} -0.970280 q^{92} +2.91738 q^{93} +0.503679 q^{94} -11.6293 q^{95} +1.00000 q^{96} +7.98124 q^{97} -0.919592 q^{98} +2.23727 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{2} + 12 q^{3} + 12 q^{4} + 8 q^{5} + 12 q^{6} + 5 q^{7} + 12 q^{8} + 12 q^{9}+O(q^{10}) \) 12 * q + 12 * q^2 + 12 * q^3 + 12 * q^4 + 8 * q^5 + 12 * q^6 + 5 * q^7 + 12 * q^8 + 12 * q^9	\( 12 q + 12 q^{2} + 12 q^{3} + 12 q^{4} + 8 q^{5} + 12 q^{6} + 5 q^{7} + 12 q^{8} + 12 q^{9} + 8 q^{10} + 11 q^{11} + 12 q^{12} + 6 q^{13} + 5 q^{14} + 8 q^{15} + 12 q^{16} - 12 q^{17} + 12 q^{18} + 3 q^{19} + 8 q^{20} + 5 q^{21} + 11 q^{22} + 22 q^{23} + 12 q^{24} + 22 q^{25} + 6 q^{26} + 12 q^{27} + 5 q^{28} + 26 q^{29} + 8 q^{30} + q^{31} + 12 q^{32} + 11 q^{33} - 12 q^{34} + 24 q^{35} + 12 q^{36} + 10 q^{37} + 3 q^{38} + 6 q^{39} + 8 q^{40} + 16 q^{41} + 5 q^{42} + 23 q^{43} + 11 q^{44} + 8 q^{45} + 22 q^{46} + 6 q^{47} + 12 q^{48} + 11 q^{49} + 22 q^{50} - 12 q^{51} + 6 q^{52} + 10 q^{53} + 12 q^{54} + 15 q^{55} + 5 q^{56} + 3 q^{57} + 26 q^{58} + 12 q^{59} + 8 q^{60} + 15 q^{61} + q^{62} + 5 q^{63} + 12 q^{64} + 4 q^{65} + 11 q^{66} + 4 q^{67} - 12 q^{68} + 22 q^{69} + 24 q^{70} + 10 q^{71} + 12 q^{72} + 24 q^{73} + 10 q^{74} + 22 q^{75} + 3 q^{76} + 24 q^{77} + 6 q^{78} + 23 q^{79} + 8 q^{80} + 12 q^{81} + 16 q^{82} + 5 q^{84} - 8 q^{85} + 23 q^{86} + 26 q^{87} + 11 q^{88} + 13 q^{89} + 8 q^{90} + 3 q^{91} + 22 q^{92} + q^{93} + 6 q^{94} + 11 q^{95} + 12 q^{96} + 13 q^{97} + 11 q^{98} + 11 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 12 * q^3 + 12 * q^4 + 8 * q^5 + 12 * q^6 + 5 * q^7 + 12 * q^8 + 12 * q^9 + 8 * q^10 + 11 * q^11 + 12 * q^12 + 6 * q^13 + 5 * q^14 + 8 * q^15 + 12 * q^16 - 12 * q^17 + 12 * q^18 + 3 * q^19 + 8 * q^20 + 5 * q^21 + 11 * q^22 + 22 * q^23 + 12 * q^24 + 22 * q^25 + 6 * q^26 + 12 * q^27 + 5 * q^28 + 26 * q^29 + 8 * q^30 + q^31 + 12 * q^32 + 11 * q^33 - 12 * q^34 + 24 * q^35 + 12 * q^36 + 10 * q^37 + 3 * q^38 + 6 * q^39 + 8 * q^40 + 16 * q^41 + 5 * q^42 + 23 * q^43 + 11 * q^44 + 8 * q^45 + 22 * q^46 + 6 * q^47 + 12 * q^48 + 11 * q^49 + 22 * q^50 - 12 * q^51 + 6 * q^52 + 10 * q^53 + 12 * q^54 + 15 * q^55 + 5 * q^56 + 3 * q^57 + 26 * q^58 + 12 * q^59 + 8 * q^60 + 15 * q^61 + q^62 + 5 * q^63 + 12 * q^64 + 4 * q^65 + 11 * q^66 + 4 * q^67 - 12 * q^68 + 22 * q^69 + 24 * q^70 + 10 * q^71 + 12 * q^72 + 24 * q^73 + 10 * q^74 + 22 * q^75 + 3 * q^76 + 24 * q^77 + 6 * q^78 + 23 * q^79 + 8 * q^80 + 12 * q^81 + 16 * q^82 + 5 * q^84 - 8 * q^85 + 23 * q^86 + 26 * q^87 + 11 * q^88 + 13 * q^89 + 8 * q^90 + 3 * q^91 + 22 * q^92 + q^93 + 6 * q^94 + 11 * q^95 + 12 * q^96 + 13 * q^97 + 11 * q^98 + 11 * q^99

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