LMFDB - Embedded newform 6042.2.a.v.1.6

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			1.6
Root			$-0.422254$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.50346 q^{5} -1.00000 q^{6} -3.58336 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.50346 q^{5} -1.00000 q^{6} -3.58336 q^{7} -1.00000 q^{8} +1.00000 q^{9} -3.50346 q^{10} -1.90161 q^{11} +1.00000 q^{12} -2.97719 q^{13} +3.58336 q^{14} +3.50346 q^{15} +1.00000 q^{16} -2.57905 q^{17} -1.00000 q^{18} +1.00000 q^{19} +3.50346 q^{20} -3.58336 q^{21} +1.90161 q^{22} +6.52444 q^{23} -1.00000 q^{24} +7.27423 q^{25} +2.97719 q^{26} +1.00000 q^{27} -3.58336 q^{28} -7.14911 q^{29} -3.50346 q^{30} -7.42118 q^{31} -1.00000 q^{32} -1.90161 q^{33} +2.57905 q^{34} -12.5542 q^{35} +1.00000 q^{36} +5.70263 q^{37} -1.00000 q^{38} -2.97719 q^{39} -3.50346 q^{40} -1.70988 q^{41} +3.58336 q^{42} +5.28754 q^{43} -1.90161 q^{44} +3.50346 q^{45} -6.52444 q^{46} -6.76059 q^{47} +1.00000 q^{48} +5.84050 q^{49} -7.27423 q^{50} -2.57905 q^{51} -2.97719 q^{52} -1.00000 q^{53} -1.00000 q^{54} -6.66220 q^{55} +3.58336 q^{56} +1.00000 q^{57} +7.14911 q^{58} +1.16330 q^{59} +3.50346 q^{60} +14.8469 q^{61} +7.42118 q^{62} -3.58336 q^{63} +1.00000 q^{64} -10.4305 q^{65} +1.90161 q^{66} -7.07719 q^{67} -2.57905 q^{68} +6.52444 q^{69} +12.5542 q^{70} +8.69087 q^{71} -1.00000 q^{72} -2.90929 q^{73} -5.70263 q^{74} +7.27423 q^{75} +1.00000 q^{76} +6.81414 q^{77} +2.97719 q^{78} -15.4858 q^{79} +3.50346 q^{80} +1.00000 q^{81} +1.70988 q^{82} -6.97395 q^{83} -3.58336 q^{84} -9.03559 q^{85} -5.28754 q^{86} -7.14911 q^{87} +1.90161 q^{88} -3.72029 q^{89} -3.50346 q^{90} +10.6684 q^{91} +6.52444 q^{92} -7.42118 q^{93} +6.76059 q^{94} +3.50346 q^{95} -1.00000 q^{96} +9.35502 q^{97} -5.84050 q^{98} -1.90161 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	3.50346	1.56679	0.783397	−	0.621521i	$-0.213485\pi$
$5$	3.50346	1.56679	0.783397	+	0.621521i	$0.213485\pi$
$6$	−1.00000	−0.408248
$7$	−3.58336	−1.35438	−0.677192	−	0.735806i	$-0.736803\pi$
$7$	−3.58336	−1.35438	−0.677192	+	0.735806i	$0.736803\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−3.50346	−1.10789
$11$	−1.90161	−0.573355	−0.286678	−	0.958027i	$-0.592551\pi$
$11$	−1.90161	−0.573355	−0.286678	+	0.958027i	$0.592551\pi$
$12$	1.00000	0.288675
$13$	−2.97719	−0.825725	−0.412862	−	0.910793i	$-0.635471\pi$
$13$	−2.97719	−0.825725	−0.412862	+	0.910793i	$0.635471\pi$
$14$	3.58336	0.957694
$15$	3.50346	0.904590
$16$	1.00000	0.250000
$17$	−2.57905	−0.625511	−0.312756	−	0.949834i	$-0.601252\pi$
$17$	−2.57905	−0.625511	−0.312756	+	0.949834i	$0.601252\pi$
$18$	−1.00000	−0.235702
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	3.50346	0.783397
$21$	−3.58336	−0.781954
$22$	1.90161	0.405424
$23$	6.52444	1.36044	0.680220	−	0.733008i	$-0.261884\pi$
$23$	6.52444	1.36044	0.680220	+	0.733008i	$0.261884\pi$
$24$	−1.00000	−0.204124
$25$	7.27423	1.45485
$26$	2.97719	0.583876
$27$	1.00000	0.192450
$28$	−3.58336	−0.677192
$29$	−7.14911	−1.32756	−0.663778	−	0.747930i	$-0.731048\pi$
$29$	−7.14911	−1.32756	−0.663778	+	0.747930i	$0.731048\pi$
$30$	−3.50346	−0.639641
$31$	−7.42118	−1.33288	−0.666442	−	0.745557i	$-0.732184\pi$
$31$	−7.42118	−1.33288	−0.666442	+	0.745557i	$0.732184\pi$
$32$	−1.00000	−0.176777
$33$	−1.90161	−0.331027
$34$	2.57905	0.442303
$35$	−12.5542	−2.12204
$36$	1.00000	0.166667
$37$	5.70263	0.937506	0.468753	−	0.883329i	$-0.344703\pi$
$37$	5.70263	0.937506	0.468753	+	0.883329i	$0.344703\pi$
$38$	−1.00000	−0.162221
$39$	−2.97719	−0.476732
$40$	−3.50346	−0.553946
$41$	−1.70988	−0.267038	−0.133519	−	0.991046i	$-0.542628\pi$
$41$	−1.70988	−0.267038	−0.133519	+	0.991046i	$0.542628\pi$
$42$	3.58336	0.552925
$43$	5.28754	0.806342	0.403171	−	0.915125i	$-0.367908\pi$
$43$	5.28754	0.806342	0.403171	+	0.915125i	$0.367908\pi$
$44$	−1.90161	−0.286678
$45$	3.50346	0.522265
$46$	−6.52444	−0.961977
$47$	−6.76059	−0.986134	−0.493067	−	0.869991i	$-0.664124\pi$
$47$	−6.76059	−0.986134	−0.493067	+	0.869991i	$0.664124\pi$
$48$	1.00000	0.144338
$49$	5.84050	0.834357
$50$	−7.27423	−1.02873
$51$	−2.57905	−0.361139
$52$	−2.97719	−0.412862
$53$	−1.00000	−0.137361
$53$	−1.00000	−0.137361
$54$	−1.00000	−0.136083
$55$	−6.66220	−0.898331
$56$	3.58336	0.478847
$57$	1.00000	0.132453
$58$	7.14911	0.938724
$59$	1.16330	0.151449	0.0757244	−	0.997129i	$-0.475873\pi$
$59$	1.16330	0.151449	0.0757244	+	0.997129i	$0.475873\pi$
$60$	3.50346	0.452295
$61$	14.8469	1.90095	0.950475	−	0.310801i	$-0.100597\pi$
$61$	14.8469	1.90095	0.950475	+	0.310801i	$0.100597\pi$
$62$	7.42118	0.942491
$63$	−3.58336	−0.451461
$64$	1.00000	0.125000
$65$	−10.4305	−1.29374
$66$	1.90161	0.234071
$67$	−7.07719	−0.864617	−0.432308	−	0.901726i	$-0.642301\pi$
$67$	−7.07719	−0.864617	−0.432308	+	0.901726i	$0.642301\pi$
$68$	−2.57905	−0.312756
$69$	6.52444	0.785451
$70$	12.5542	1.50051
$71$	8.69087	1.03142	0.515708	−	0.856764i	$-0.327529\pi$
$71$	8.69087	1.03142	0.515708	+	0.856764i	$0.327529\pi$
$72$	−1.00000	−0.117851
$73$	−2.90929	−0.340507	−0.170253	−	0.985400i	$-0.554459\pi$
$73$	−2.90929	−0.340507	−0.170253	+	0.985400i	$0.554459\pi$
$74$	−5.70263	−0.662917
$75$	7.27423	0.839956
$76$	1.00000	0.114708
$77$	6.81414	0.776544
$78$	2.97719	0.337101
$79$	−15.4858	−1.74228	−0.871142	−	0.491032i	$-0.836620\pi$
$79$	−15.4858	−1.74228	−0.871142	+	0.491032i	$0.836620\pi$
$80$	3.50346	0.391699
$81$	1.00000	0.111111
$82$	1.70988	0.188825
$83$	−6.97395	−0.765490	−0.382745	−	0.923854i	$-0.625021\pi$
$83$	−6.97395	−0.765490	−0.382745	+	0.923854i	$0.625021\pi$
$84$	−3.58336	−0.390977
$85$	−9.03559	−0.980048
$86$	−5.28754	−0.570170
$87$	−7.14911	−0.766465
$88$	1.90161	0.202712
$89$	−3.72029	−0.394350	−0.197175	−	0.980368i	$-0.563177\pi$
$89$	−3.72029	−0.394350	−0.197175	+	0.980368i	$0.563177\pi$
$90$	−3.50346	−0.369297
$91$	10.6684	1.11835
$92$	6.52444	0.680220
$93$	−7.42118	−0.769541
$94$	6.76059	0.697302
$95$	3.50346	0.359447
$96$	−1.00000	−0.102062
$97$	9.35502	0.949858	0.474929	−	0.880024i	$-0.342474\pi$
$97$	9.35502	0.949858	0.474929	+	0.880024i	$0.342474\pi$
$98$	−5.84050	−0.589979
$99$	−1.90161	−0.191118
$100$	7.27423	0.727423
$101$	−10.7483	−1.06949	−0.534746	−	0.845013i	$-0.679593\pi$
$101$	−10.7483	−1.06949	−0.534746	+	0.845013i	$0.679593\pi$
$102$	2.57905	0.255364
$103$	−11.5753	−1.14055	−0.570273	−	0.821455i	$-0.693163\pi$
$103$	−11.5753	−1.14055	−0.570273	+	0.821455i	$0.693163\pi$
$104$	2.97719	0.291938
$105$	−12.5542	−1.22516
$106$	1.00000	0.0971286
$107$	−9.31621	−0.900632	−0.450316	−	0.892869i	$-0.648689\pi$
$107$	−9.31621	−0.900632	−0.450316	+	0.892869i	$0.648689\pi$
$108$	1.00000	0.0962250
$109$	14.9363	1.43064	0.715319	−	0.698798i	$-0.246281\pi$
$109$	14.9363	1.43064	0.715319	+	0.698798i	$0.246281\pi$
$110$	6.66220	0.635216
$111$	5.70263	0.541269
$112$	−3.58336	−0.338596
$113$	−12.3029	−1.15736	−0.578680	−	0.815555i	$-0.696432\pi$
$113$	−12.3029	−1.15736	−0.578680	+	0.815555i	$0.696432\pi$
$114$	−1.00000	−0.0936586
$115$	22.8581	2.13153
$116$	−7.14911	−0.663778
$117$	−2.97719	−0.275242
$118$	−1.16330	−0.107090
$119$	9.24167	0.847182
$120$	−3.50346	−0.319821
$121$	−7.38390	−0.671263
$122$	−14.8469	−1.34417
$123$	−1.70988	−0.154175
$124$	−7.42118	−0.666442
$125$	7.96768	0.712651
$126$	3.58336	0.319231
$127$	−20.1914	−1.79170	−0.895849	−	0.444359i	$-0.853431\pi$
$127$	−20.1914	−1.79170	−0.895849	+	0.444359i	$0.853431\pi$
$128$	−1.00000	−0.0883883
$129$	5.28754	0.465542
$130$	10.4305	0.914813
$131$	−0.0765693	−0.00668989	−0.00334495	−	0.999994i	$-0.501065\pi$
$131$	−0.0765693	−0.00668989	−0.00334495	+	0.999994i	$0.501065\pi$
$132$	−1.90161	−0.165513
$133$	−3.58336	−0.310717
$134$	7.07719	0.611376
$135$	3.50346	0.301530
$136$	2.57905	0.221152
$137$	−9.15679	−0.782317	−0.391159	−	0.920323i	$-0.627926\pi$
$137$	−9.15679	−0.782317	−0.391159	+	0.920323i	$0.627926\pi$
$138$	−6.52444	−0.555398
$139$	−21.6224	−1.83399	−0.916993	−	0.398903i	$-0.869391\pi$
$139$	−21.6224	−1.83399	−0.916993	+	0.398903i	$0.869391\pi$
$140$	−12.5542	−1.06102
$141$	−6.76059	−0.569345
$142$	−8.69087	−0.729322
$143$	5.66145	0.473434
$144$	1.00000	0.0833333
$145$	−25.0466	−2.08001
$146$	2.90929	0.240775
$147$	5.84050	0.481716
$148$	5.70263	0.468753
$149$	−6.51870	−0.534033	−0.267016	−	0.963692i	$-0.586038\pi$
$149$	−6.51870	−0.534033	−0.267016	+	0.963692i	$0.586038\pi$
$150$	−7.27423	−0.593939
$151$	−18.1269	−1.47514	−0.737571	−	0.675269i	$-0.764027\pi$
$151$	−18.1269	−1.47514	−0.737571	+	0.675269i	$0.764027\pi$
$152$	−1.00000	−0.0811107
$153$	−2.57905	−0.208504
$154$	−6.81414	−0.549099
$155$	−25.9998	−2.08836
$156$	−2.97719	−0.238366
$157$	−2.12825	−0.169853	−0.0849264	−	0.996387i	$-0.527066\pi$
$157$	−2.12825	−0.169853	−0.0849264	+	0.996387i	$0.527066\pi$
$158$	15.4858	1.23198
$159$	−1.00000	−0.0793052
$160$	−3.50346	−0.276973
$161$	−23.3795	−1.84256
$162$	−1.00000	−0.0785674
$163$	12.3774	0.969475	0.484737	−	0.874660i	$-0.338915\pi$
$163$	12.3774	0.969475	0.484737	+	0.874660i	$0.338915\pi$
$164$	−1.70988	−0.133519
$165$	−6.66220	−0.518651
$166$	6.97395	0.541284
$167$	−11.7689	−0.910704	−0.455352	−	0.890312i	$-0.650487\pi$
$167$	−11.7689	−0.910704	−0.455352	+	0.890312i	$0.650487\pi$
$168$	3.58336	0.276463
$169$	−4.13632	−0.318179
$170$	9.03559	0.692998
$171$	1.00000	0.0764719
$172$	5.28754	0.403171
$173$	−4.42126	−0.336142	−0.168071	−	0.985775i	$-0.553754\pi$
$173$	−4.42126	−0.336142	−0.168071	+	0.985775i	$0.553754\pi$
$174$	7.14911	0.541972
$175$	−26.0662	−1.97042
$176$	−1.90161	−0.143339
$177$	1.16330	0.0874389
$178$	3.72029	0.278848
$179$	4.08100	0.305028	0.152514	−	0.988301i	$-0.451263\pi$
$179$	4.08100	0.305028	0.152514	+	0.988301i	$0.451263\pi$
$180$	3.50346	0.261132
$181$	14.1814	1.05409	0.527046	−	0.849837i	$-0.323299\pi$
$181$	14.1814	1.05409	0.527046	+	0.849837i	$0.323299\pi$
$182$	−10.6684	−0.790792
$183$	14.8469	1.09751
$184$	−6.52444	−0.480988
$185$	19.9789	1.46888
$186$	7.42118	0.544148
$187$	4.90433	0.358640
$188$	−6.76059	−0.493067
$189$	−3.58336	−0.260651
$190$	−3.50346	−0.254168
$191$	−9.15755	−0.662617	−0.331308	−	0.943522i	$-0.607490\pi$
$191$	−9.15755	−0.662617	−0.331308	+	0.943522i	$0.607490\pi$
$192$	1.00000	0.0721688
$193$	−19.6666	−1.41564	−0.707818	−	0.706395i	$-0.750320\pi$
$193$	−19.6666	−1.41564	−0.707818	+	0.706395i	$0.750320\pi$
$194$	−9.35502	−0.671651
$195$	−10.4305	−0.746942
$196$	5.84050	0.417178
$197$	14.6849	1.04626	0.523128	−	0.852254i	$-0.324765\pi$
$197$	14.6849	1.04626	0.523128	+	0.852254i	$0.324765\pi$
$198$	1.90161	0.135141
$199$	−7.58984	−0.538030	−0.269015	−	0.963136i	$-0.586698\pi$
$199$	−7.58984	−0.538030	−0.269015	+	0.963136i	$0.586698\pi$
$200$	−7.27423	−0.514366
$201$	−7.07719	−0.499187
$202$	10.7483	0.756246
$203$	25.6179	1.79802
$204$	−2.57905	−0.180569
$205$	−5.99050	−0.418395
$206$	11.5753	0.806488
$207$	6.52444	0.453480
$208$	−2.97719	−0.206431
$209$	−1.90161	−0.131537
$210$	12.5542	0.866320
$211$	4.17434	0.287373	0.143687	−	0.989623i	$-0.454104\pi$
$211$	4.17434	0.287373	0.143687	+	0.989623i	$0.454104\pi$
$212$	−1.00000	−0.0686803
$213$	8.69087	0.595489
$214$	9.31621	0.636843
$215$	18.5247	1.26337
$216$	−1.00000	−0.0680414
$217$	26.5928	1.80524
$218$	−14.9363	−1.01161
$219$	−2.90929	−0.196592
$220$	−6.66220	−0.449165
$221$	7.67832	0.516500
$222$	−5.70263	−0.382735
$223$	−3.78490	−0.253456	−0.126728	−	0.991938i	$-0.540447\pi$
$223$	−3.78490	−0.253456	−0.126728	+	0.991938i	$0.540447\pi$
$224$	3.58336	0.239424
$225$	7.27423	0.484949
$226$	12.3029	0.818377
$227$	−11.2276	−0.745203	−0.372601	−	0.927992i	$-0.621534\pi$
$227$	−11.2276	−0.745203	−0.372601	+	0.927992i	$0.621534\pi$
$228$	1.00000	0.0662266
$229$	−22.7748	−1.50500	−0.752499	−	0.658593i	$-0.771152\pi$
$229$	−22.7748	−1.50500	−0.752499	+	0.658593i	$0.771152\pi$
$230$	−22.8581	−1.50722
$231$	6.81414	0.448338
$232$	7.14911	0.469362
$233$	−1.30731	−0.0856446	−0.0428223	−	0.999083i	$-0.513635\pi$
$233$	−1.30731	−0.0856446	−0.0428223	+	0.999083i	$0.513635\pi$
$234$	2.97719	0.194625
$235$	−23.6855	−1.54507
$236$	1.16330	0.0757244
$237$	−15.4858	−1.00591
$238$	−9.24167	−0.599048
$239$	20.6089	1.33308	0.666540	−	0.745469i	$-0.267774\pi$
$239$	20.6089	1.33308	0.666540	+	0.745469i	$0.267774\pi$
$240$	3.50346	0.226147
$241$	0.961523	0.0619371	0.0309686	−	0.999520i	$-0.490141\pi$
$241$	0.961523	0.0619371	0.0309686	+	0.999520i	$0.490141\pi$
$242$	7.38390	0.474655
$243$	1.00000	0.0641500
$244$	14.8469	0.950475
$245$	20.4619	1.30727
$246$	1.70988	0.109018
$247$	−2.97719	−0.189434
$248$	7.42118	0.471246
$249$	−6.97395	−0.441956
$250$	−7.96768	−0.503921
$251$	28.8026	1.81801	0.909004	−	0.416788i	$-0.136844\pi$
$251$	28.8026	1.81801	0.909004	+	0.416788i	$0.136844\pi$
$252$	−3.58336	−0.225731
$253$	−12.4069	−0.780016
$254$	20.1914	1.26692
$255$	−9.03559	−0.565831
$256$	1.00000	0.0625000
$257$	18.4466	1.15067	0.575333	−	0.817920i	$-0.304873\pi$
$257$	18.4466	1.15067	0.575333	+	0.817920i	$0.304873\pi$
$258$	−5.28754	−0.329188
$259$	−20.4346	−1.26974
$260$	−10.4305	−0.646871
$261$	−7.14911	−0.442519
$262$	0.0765693	0.00473047
$263$	23.3384	1.43911	0.719553	−	0.694438i	$-0.244347\pi$
$263$	23.3384	1.43911	0.719553	+	0.694438i	$0.244347\pi$
$264$	1.90161	0.117036
$265$	−3.50346	−0.215216
$266$	3.58336	0.219710
$267$	−3.72029	−0.227678
$268$	−7.07719	−0.432308
$269$	−9.55201	−0.582396	−0.291198	−	0.956663i	$-0.594054\pi$
$269$	−9.55201	−0.582396	−0.291198	+	0.956663i	$0.594054\pi$
$270$	−3.50346	−0.213214
$271$	18.5178	1.12488	0.562439	−	0.826838i	$-0.309863\pi$
$271$	18.5178	1.12488	0.562439	+	0.826838i	$0.309863\pi$
$272$	−2.57905	−0.156378
$273$	10.6684	0.645679
$274$	9.15679	0.553182
$275$	−13.8327	−0.834144
$276$	6.52444	0.392725
$277$	−22.9640	−1.37977	−0.689887	−	0.723917i	$-0.742340\pi$
$277$	−22.9640	−1.37977	−0.689887	+	0.723917i	$0.742340\pi$
$278$	21.6224	1.29682
$279$	−7.42118	−0.444295
$280$	12.5542	0.750255
$281$	−16.2480	−0.969273	−0.484637	−	0.874716i	$-0.661048\pi$
$281$	−16.2480	−0.969273	−0.484637	+	0.874716i	$0.661048\pi$
$282$	6.76059	0.402587
$283$	−4.10361	−0.243934	−0.121967	−	0.992534i	$-0.538920\pi$
$283$	−4.10361	−0.243934	−0.121967	+	0.992534i	$0.538920\pi$
$284$	8.69087	0.515708
$285$	3.50346	0.207527
$286$	−5.66145	−0.334768
$287$	6.12712	0.361673
$288$	−1.00000	−0.0589256
$289$	−10.3485	−0.608736
$290$	25.0466	1.47079
$291$	9.35502	0.548401
$292$	−2.90929	−0.170253
$293$	−24.1237	−1.40932	−0.704661	−	0.709544i	$-0.748901\pi$
$293$	−24.1237	−1.40932	−0.704661	+	0.709544i	$0.748901\pi$
$294$	−5.84050	−0.340625
$295$	4.07557	0.237289
$296$	−5.70263	−0.331458
$297$	−1.90161	−0.110342
$298$	6.51870	0.377618
$299$	−19.4245	−1.12335
$300$	7.27423	0.419978
$301$	−18.9472	−1.09210
$302$	18.1269	1.04308
$303$	−10.7483	−0.617472
$304$	1.00000	0.0573539
$305$	52.0155	2.97840
$306$	2.57905	0.147434
$307$	10.8191	0.617481	0.308741	−	0.951146i	$-0.400093\pi$
$307$	10.8191	0.617481	0.308741	+	0.951146i	$0.400093\pi$
$308$	6.81414	0.388272
$309$	−11.5753	−0.658495
$310$	25.9998	1.47669
$311$	16.1233	0.914268	0.457134	−	0.889398i	$-0.348876\pi$
$311$	16.1233	0.914268	0.457134	+	0.889398i	$0.348876\pi$
$312$	2.97719	0.168550
$313$	27.9539	1.58005	0.790023	−	0.613077i	$-0.210068\pi$
$313$	27.9539	1.58005	0.790023	+	0.613077i	$0.210068\pi$
$314$	2.12825	0.120104
$315$	−12.5542	−0.707347
$316$	−15.4858	−0.871142
$317$	30.9328	1.73736	0.868679	−	0.495376i	$-0.164970\pi$
$317$	30.9328	1.73736	0.868679	+	0.495376i	$0.164970\pi$
$318$	1.00000	0.0560772
$319$	13.5948	0.761161
$320$	3.50346	0.195849
$321$	−9.31621	−0.519980
$322$	23.3795	1.30289
$323$	−2.57905	−0.143502
$324$	1.00000	0.0555556
$325$	−21.6568	−1.20130
$326$	−12.3774	−0.685522
$327$	14.9363	0.825979
$328$	1.70988	0.0944124
$329$	24.2257	1.33560
$330$	6.66220	0.366742
$331$	−17.7106	−0.973462	−0.486731	−	0.873552i	$-0.661811\pi$
$331$	−17.7106	−0.973462	−0.486731	+	0.873552i	$0.661811\pi$
$332$	−6.97395	−0.382745
$333$	5.70263	0.312502
$334$	11.7689	0.643965
$335$	−24.7947	−1.35468
$336$	−3.58336	−0.195489
$337$	−13.1309	−0.715285	−0.357642	−	0.933859i	$-0.616419\pi$
$337$	−13.1309	−0.715285	−0.357642	+	0.933859i	$0.616419\pi$
$338$	4.13632	0.224986
$339$	−12.3029	−0.668202
$340$	−9.03559	−0.490024
$341$	14.1122	0.764216
$342$	−1.00000	−0.0540738
$343$	4.15492	0.224345
$344$	−5.28754	−0.285085
$345$	22.8581	1.23064
$346$	4.42126	0.237688
$347$	−34.1291	−1.83215	−0.916073	−	0.401011i	$-0.868659\pi$
$347$	−34.1291	−1.83215	−0.916073	+	0.401011i	$0.868659\pi$
$348$	−7.14911	−0.383232
$349$	9.83622	0.526521	0.263260	−	0.964725i	$-0.415202\pi$
$349$	9.83622	0.526521	0.263260	+	0.964725i	$0.415202\pi$
$350$	26.0662	1.39330
$351$	−2.97719	−0.158911
$352$	1.90161	0.101356
$353$	−25.0775	−1.33474	−0.667371	−	0.744725i	$-0.732580\pi$
$353$	−25.0775	−1.33474	−0.667371	+	0.744725i	$0.732580\pi$
$354$	−1.16330	−0.0618287
$355$	30.4481	1.61602
$356$	−3.72029	−0.197175
$357$	9.24167	0.489121
$358$	−4.08100	−0.215687
$359$	−4.22146	−0.222800	−0.111400	−	0.993776i	$-0.535534\pi$
$359$	−4.22146	−0.222800	−0.111400	+	0.993776i	$0.535534\pi$
$360$	−3.50346	−0.184649
$361$	1.00000	0.0526316
$362$	−14.1814	−0.745356
$363$	−7.38390	−0.387554
$364$	10.6684	0.559174
$365$	−10.1926	−0.533504
$366$	−14.8469	−0.776060
$367$	−25.6885	−1.34093	−0.670464	−	0.741942i	$-0.733905\pi$
$367$	−25.6885	−1.34093	−0.670464	+	0.741942i	$0.733905\pi$
$368$	6.52444	0.340110
$369$	−1.70988	−0.0890128
$370$	−19.9789	−1.03865
$371$	3.58336	0.186039
$372$	−7.42118	−0.384770
$373$	32.2219	1.66839	0.834194	−	0.551471i	$-0.185933\pi$
$373$	32.2219	1.66839	0.834194	+	0.551471i	$0.185933\pi$
$374$	−4.90433	−0.253597
$375$	7.96768	0.411449
$376$	6.76059	0.348651
$377$	21.2843	1.09620
$378$	3.58336	0.184308
$379$	−32.6376	−1.67648	−0.838240	−	0.545302i	$-0.816415\pi$
$379$	−32.6376	−1.67648	−0.838240	+	0.545302i	$0.816415\pi$
$380$	3.50346	0.179724
$381$	−20.1914	−1.03444
$382$	9.15755	0.468541
$383$	28.5124	1.45691	0.728457	−	0.685092i	$-0.240238\pi$
$383$	28.5124	1.45691	0.728457	+	0.685092i	$0.240238\pi$
$384$	−1.00000	−0.0510310
$385$	23.8731	1.21668
$386$	19.6666	1.00101
$387$	5.28754	0.268781
$388$	9.35502	0.474929
$389$	33.7547	1.71143	0.855715	−	0.517447i	$-0.173117\pi$
$389$	33.7547	1.71143	0.855715	+	0.517447i	$0.173117\pi$
$390$	10.4305	0.528168
$391$	−16.8269	−0.850971
$392$	−5.84050	−0.294990
$393$	−0.0765693	−0.00386241
$394$	−14.6849	−0.739815
$395$	−54.2537	−2.72980
$396$	−1.90161	−0.0955592
$397$	16.3934	0.822759	0.411379	−	0.911464i	$-0.365047\pi$
$397$	16.3934	0.822759	0.411379	+	0.911464i	$0.365047\pi$
$398$	7.58984	0.380444
$399$	−3.58336	−0.179393
$400$	7.27423	0.363712
$401$	32.4317	1.61956	0.809782	−	0.586731i	$-0.199585\pi$
$401$	32.4317	1.61956	0.809782	+	0.586731i	$0.199585\pi$
$402$	7.07719	0.352978
$403$	22.0943	1.10060
$404$	−10.7483	−0.534746
$405$	3.50346	0.174088
$406$	−25.6179	−1.27139
$407$	−10.8441	−0.537524
$408$	2.57905	0.127682
$409$	29.5884	1.46305	0.731527	−	0.681813i	$-0.238808\pi$
$409$	29.5884	1.46305	0.731527	+	0.681813i	$0.238808\pi$
$410$	5.99050	0.295850
$411$	−9.15679	−0.451671
$412$	−11.5753	−0.570273
$413$	−4.16853	−0.205120
$414$	−6.52444	−0.320659
$415$	−24.4330	−1.19937
$416$	2.97719	0.145969
$417$	−21.6224	−1.05885
$418$	1.90161	0.0930105
$419$	−21.3127	−1.04119	−0.520597	−	0.853803i	$-0.674291\pi$
$419$	−21.3127	−1.04119	−0.520597	+	0.853803i	$0.674291\pi$
$420$	−12.5542	−0.612581
$421$	−0.0512792	−0.00249920	−0.00124960	−	0.999999i	$-0.500398\pi$
$421$	−0.0512792	−0.00249920	−0.00124960	+	0.999999i	$0.500398\pi$
$422$	−4.17434	−0.203204
$423$	−6.76059	−0.328711
$424$	1.00000	0.0485643
$425$	−18.7606	−0.910023
$426$	−8.69087	−0.421074
$427$	−53.2018	−2.57462
$428$	−9.31621	−0.450316
$429$	5.66145	0.273337
$430$	−18.5247	−0.893339
$431$	29.2367	1.40828	0.704141	−	0.710060i	$-0.251332\pi$
$431$	29.2367	1.40828	0.704141	+	0.710060i	$0.251332\pi$
$432$	1.00000	0.0481125
$433$	11.0106	0.529135	0.264567	−	0.964367i	$-0.414771\pi$
$433$	11.0106	0.529135	0.264567	+	0.964367i	$0.414771\pi$
$434$	−26.5928	−1.27650
$435$	−25.0466	−1.20089
$436$	14.9363	0.715319
$437$	6.52444	0.312107
$438$	2.90929	0.139011
$439$	2.68593	0.128192	0.0640962	−	0.997944i	$-0.479584\pi$
$439$	2.68593	0.128192	0.0640962	+	0.997944i	$0.479584\pi$
$440$	6.66220	0.317608
$441$	5.84050	0.278119
$442$	−7.67832	−0.365221
$443$	1.08140	0.0513786	0.0256893	−	0.999670i	$-0.491822\pi$
$443$	1.08140	0.0513786	0.0256893	+	0.999670i	$0.491822\pi$
$444$	5.70263	0.270635
$445$	−13.0339	−0.617866
$446$	3.78490	0.179220
$447$	−6.51870	−0.308324
$448$	−3.58336	−0.169298
$449$	−1.83002	−0.0863642	−0.0431821	−	0.999067i	$-0.513750\pi$
$449$	−1.83002	−0.0863642	−0.0431821	+	0.999067i	$0.513750\pi$
$450$	−7.27423	−0.342911
$451$	3.25152	0.153108
$452$	−12.3029	−0.578680
$453$	−18.1269	−0.851674
$454$	11.2276	0.526938
$455$	37.3762	1.75222
$456$	−1.00000	−0.0468293
$457$	5.81295	0.271918	0.135959	−	0.990714i	$-0.456588\pi$
$457$	5.81295	0.271918	0.135959	+	0.990714i	$0.456588\pi$
$458$	22.7748	1.06419
$459$	−2.57905	−0.120380
$460$	22.8581	1.06577
$461$	5.40387	0.251684	0.125842	−	0.992050i	$-0.459837\pi$
$461$	5.40387	0.251684	0.125842	+	0.992050i	$0.459837\pi$
$462$	−6.81414	−0.317023
$463$	−13.0554	−0.606737	−0.303368	−	0.952873i	$-0.598111\pi$
$463$	−13.0554	−0.606737	−0.303368	+	0.952873i	$0.598111\pi$
$464$	−7.14911	−0.331889
$465$	−25.9998	−1.20571
$466$	1.30731	0.0605599
$467$	25.4467	1.17753	0.588766	−	0.808303i	$-0.299614\pi$
$467$	25.4467	1.17753	0.588766	+	0.808303i	$0.299614\pi$
$468$	−2.97719	−0.137621
$469$	25.3602	1.17102
$470$	23.6855	1.09253
$471$	−2.12825	−0.0980646
$472$	−1.16330	−0.0535452
$473$	−10.0548	−0.462321
$474$	15.4858	0.711284
$475$	7.27423	0.333765
$476$	9.24167	0.423591
$477$	−1.00000	−0.0457869
$478$	−20.6089	−0.942630
$479$	8.79014	0.401632	0.200816	−	0.979629i	$-0.435641\pi$
$479$	8.79014	0.401632	0.200816	+	0.979629i	$0.435641\pi$
$480$	−3.50346	−0.159910
$481$	−16.9778	−0.774122
$482$	−0.961523	−0.0437962
$483$	−23.3795	−1.06380
$484$	−7.38390	−0.335632
$485$	32.7749	1.48823
$486$	−1.00000	−0.0453609
$487$	−37.3743	−1.69359	−0.846796	−	0.531917i	$-0.821472\pi$
$487$	−37.3743	−1.69359	−0.846796	+	0.531917i	$0.821472\pi$
$488$	−14.8469	−0.672087
$489$	12.3774	0.559726
$490$	−20.4619	−0.924376
$491$	26.3515	1.18922	0.594612	−	0.804013i	$-0.297306\pi$
$491$	26.3515	1.18922	0.594612	+	0.804013i	$0.297306\pi$
$492$	−1.70988	−0.0770874
$493$	18.4379	0.830401
$494$	2.97719	0.133950
$495$	−6.66220	−0.299444
$496$	−7.42118	−0.333221
$497$	−31.1425	−1.39693
$498$	6.97395	0.312510
$499$	−1.41265	−0.0632389	−0.0316195	−	0.999500i	$-0.510066\pi$
$499$	−1.41265	−0.0632389	−0.0316195	+	0.999500i	$0.510066\pi$
$500$	7.96768	0.356326
$501$	−11.7689	−0.525795
$502$	−28.8026	−1.28553
$503$	−20.4994	−0.914021	−0.457010	−	0.889461i	$-0.651080\pi$
$503$	−20.4994	−0.914021	−0.457010	+	0.889461i	$0.651080\pi$
$504$	3.58336	0.159616
$505$	−37.6561	−1.67568
$506$	12.4069	0.551555
$507$	−4.13632	−0.183701
$508$	−20.1914	−0.895849
$509$	−11.5834	−0.513424	−0.256712	−	0.966488i	$-0.582639\pi$
$509$	−11.5834	−0.513424	−0.256712	+	0.966488i	$0.582639\pi$
$510$	9.03559	0.400103
$511$	10.4251	0.461177
$512$	−1.00000	−0.0441942
$513$	1.00000	0.0441511
$514$	−18.4466	−0.813643
$515$	−40.5535	−1.78700
$516$	5.28754	0.232771
$517$	12.8560	0.565405
$518$	20.4346	0.897844
$519$	−4.42126	−0.194072
$520$	10.4305	0.457407
$521$	15.1699	0.664606	0.332303	−	0.943173i	$-0.392174\pi$
$521$	15.1699	0.664606	0.332303	+	0.943173i	$0.392174\pi$
$522$	7.14911	0.312908
$523$	25.9237	1.13356	0.566781	−	0.823868i	$-0.308188\pi$
$523$	25.9237	1.13356	0.566781	+	0.823868i	$0.308188\pi$
$524$	−0.0765693	−0.00334495
$525$	−26.0662	−1.13762
$526$	−23.3384	−1.01760
$527$	19.1396	0.833734
$528$	−1.90161	−0.0827567
$529$	19.5684	0.850799
$530$	3.50346	0.152181
$531$	1.16330	0.0504829
$532$	−3.58336	−0.155359
$533$	5.09064	0.220500
$534$	3.72029	0.160993
$535$	−32.6390	−1.41111
$536$	7.07719	0.305688
$537$	4.08100	0.176108
$538$	9.55201	0.411816
$539$	−11.1063	−0.478383
$540$	3.50346	0.150765
$541$	36.9817	1.58997	0.794985	−	0.606629i	$-0.207479\pi$
$541$	36.9817	1.58997	0.794985	+	0.606629i	$0.207479\pi$
$542$	−18.5178	−0.795409
$543$	14.1814	0.608581
$544$	2.57905	0.110576
$545$	52.3287	2.24152
$546$	−10.6684	−0.456564
$547$	−10.7605	−0.460084	−0.230042	−	0.973181i	$-0.573886\pi$
$547$	−10.7605	−0.460084	−0.230042	+	0.973181i	$0.573886\pi$
$548$	−9.15679	−0.391159
$549$	14.8469	0.633650
$550$	13.8327	0.589829
$551$	−7.14911	−0.304562
$552$	−6.52444	−0.277699
$553$	55.4911	2.35972
$554$	22.9640	0.975647
$555$	19.9789	0.848058
$556$	−21.6224	−0.916993
$557$	32.7528	1.38778	0.693890	−	0.720081i	$-0.255895\pi$
$557$	32.7528	1.38778	0.693890	+	0.720081i	$0.255895\pi$
$558$	7.42118	0.314164
$559$	−15.7420	−0.665816
$560$	−12.5542	−0.530511
$561$	4.90433	0.207061
$562$	16.2480	0.685380
$563$	−21.6039	−0.910495	−0.455247	−	0.890365i	$-0.650449\pi$
$563$	−21.6039	−0.910495	−0.455247	+	0.890365i	$0.650449\pi$
$564$	−6.76059	−0.284672
$565$	−43.1027	−1.81335
$566$	4.10361	0.172488
$567$	−3.58336	−0.150487
$568$	−8.69087	−0.364661
$569$	40.0854	1.68047	0.840233	−	0.542225i	$-0.182418\pi$
$569$	40.0854	1.68047	0.840233	+	0.542225i	$0.182418\pi$
$570$	−3.50346	−0.146744
$571$	26.2522	1.09862	0.549311	−	0.835618i	$-0.314890\pi$
$571$	26.2522	1.09862	0.549311	+	0.835618i	$0.314890\pi$
$572$	5.66145	0.236717
$573$	−9.15755	−0.382562
$574$	−6.12712	−0.255741
$575$	47.4603	1.97923
$576$	1.00000	0.0416667
$577$	−39.3879	−1.63974	−0.819869	−	0.572550i	$-0.805954\pi$
$577$	−39.3879	−1.63974	−0.819869	+	0.572550i	$0.805954\pi$
$578$	10.3485	0.430441
$579$	−19.6666	−0.817318
$580$	−25.0466	−1.04000
$581$	24.9902	1.03677
$582$	−9.35502	−0.387778
$583$	1.90161	0.0787564
$584$	2.90929	0.120387
$585$	−10.4305	−0.431247
$586$	24.1237	0.996541
$587$	−8.44150	−0.348418	−0.174209	−	0.984709i	$-0.555737\pi$
$587$	−8.44150	−0.348418	−0.174209	+	0.984709i	$0.555737\pi$
$588$	5.84050	0.240858
$589$	−7.42118	−0.305785
$590$	−4.07557	−0.167789
$591$	14.6849	0.604056
$592$	5.70263	0.234376
$593$	37.5722	1.54290	0.771452	−	0.636288i	$-0.219531\pi$
$593$	37.5722	1.54290	0.771452	+	0.636288i	$0.219531\pi$
$594$	1.90161	0.0780238
$595$	32.3778	1.32736
$596$	−6.51870	−0.267016
$597$	−7.58984	−0.310632
$598$	19.4245	0.794328
$599$	−39.3246	−1.60676	−0.803380	−	0.595467i	$-0.796967\pi$
$599$	−39.3246	−1.60676	−0.803380	+	0.595467i	$0.796967\pi$
$600$	−7.27423	−0.296969
$601$	−21.5371	−0.878517	−0.439259	−	0.898361i	$-0.644759\pi$
$601$	−21.5371	−0.878517	−0.439259	+	0.898361i	$0.644759\pi$
$602$	18.9472	0.772229
$603$	−7.07719	−0.288206
$604$	−18.1269	−0.737571
$605$	−25.8692	−1.05173
$606$	10.7483	0.436619
$607$	−30.1514	−1.22381	−0.611903	−	0.790933i	$-0.709596\pi$
$607$	−30.1514	−1.22381	−0.611903	+	0.790933i	$0.709596\pi$
$608$	−1.00000	−0.0405554
$609$	25.6179	1.03809
$610$	−52.0155	−2.10605
$611$	20.1276	0.814275
$612$	−2.57905	−0.104252
$613$	24.6108	0.994020	0.497010	−	0.867745i	$-0.334431\pi$
$613$	24.6108	0.994020	0.497010	+	0.867745i	$0.334431\pi$
$614$	−10.8191	−0.436625
$615$	−5.99050	−0.241560
$616$	−6.81414	−0.274550
$617$	−41.1287	−1.65578	−0.827890	−	0.560891i	$-0.810459\pi$
$617$	−41.1287	−1.65578	−0.827890	+	0.560891i	$0.810459\pi$
$618$	11.5753	0.465626
$619$	36.6802	1.47430	0.737150	−	0.675729i	$-0.236171\pi$
$619$	36.6802	1.47430	0.737150	+	0.675729i	$0.236171\pi$
$620$	−25.9998	−1.04418
$621$	6.52444	0.261817
$622$	−16.1233	−0.646485
$623$	13.3312	0.534102
$624$	−2.97719	−0.119183
$625$	−8.45670	−0.338268
$626$	−27.9539	−1.11726
$627$	−1.90161	−0.0759428
$628$	−2.12825	−0.0849264
$629$	−14.7073	−0.586420
$630$	12.5542	0.500170
$631$	−3.07258	−0.122318	−0.0611588	−	0.998128i	$-0.519480\pi$
$631$	−3.07258	−0.122318	−0.0611588	+	0.998128i	$0.519480\pi$
$632$	15.4858	0.615990
$633$	4.17434	0.165915
$634$	−30.9328	−1.22850
$635$	−70.7398	−2.80722
$636$	−1.00000	−0.0396526
$637$	−17.3883	−0.688949
$638$	−13.5948	−0.538222
$639$	8.69087	0.343805
$640$	−3.50346	−0.138486
$641$	23.5055	0.928411	0.464205	−	0.885728i	$-0.346340\pi$
$641$	23.5055	0.928411	0.464205	+	0.885728i	$0.346340\pi$
$642$	9.31621	0.367681
$643$	−15.4345	−0.608678	−0.304339	−	0.952564i	$-0.598436\pi$
$643$	−15.4345	−0.608678	−0.304339	+	0.952564i	$0.598436\pi$
$644$	−23.3795	−0.921280
$645$	18.5247	0.729408
$646$	2.57905	0.101471
$647$	−30.1790	−1.18646	−0.593229	−	0.805034i	$-0.702147\pi$
$647$	−30.1790	−1.18646	−0.593229	+	0.805034i	$0.702147\pi$
$648$	−1.00000	−0.0392837
$649$	−2.21214	−0.0868339
$650$	21.6568	0.849449
$651$	26.5928	1.04225
$652$	12.3774	0.484737
$653$	−0.641649	−0.0251097	−0.0125548	−	0.999921i	$-0.503996\pi$
$653$	−0.641649	−0.0251097	−0.0125548	+	0.999921i	$0.503996\pi$
$654$	−14.9363	−0.584056
$655$	−0.268258	−0.0104817
$656$	−1.70988	−0.0667596
$657$	−2.90929	−0.113502
$658$	−24.2257	−0.944415
$659$	−11.8788	−0.462732	−0.231366	−	0.972867i	$-0.574319\pi$
$659$	−11.8788	−0.462732	−0.231366	+	0.972867i	$0.574319\pi$
$660$	−6.66220	−0.259326
$661$	11.5988	0.451141	0.225570	−	0.974227i	$-0.427575\pi$
$661$	11.5988	0.451141	0.225570	+	0.974227i	$0.427575\pi$
$662$	17.7106	0.688342
$663$	7.67832	0.298201
$664$	6.97395	0.270642
$665$	−12.5542	−0.486830
$666$	−5.70263	−0.220972
$667$	−46.6440	−1.80606
$668$	−11.7689	−0.455352
$669$	−3.78490	−0.146333
$670$	24.7947	0.957901
$671$	−28.2329	−1.08992
$672$	3.58336	0.138231
$673$	−19.3515	−0.745946	−0.372973	−	0.927842i	$-0.621662\pi$
$673$	−19.3515	−0.745946	−0.372973	+	0.927842i	$0.621662\pi$
$674$	13.1309	0.505783
$675$	7.27423	0.279985
$676$	−4.13632	−0.159089
$677$	27.0204	1.03848	0.519240	−	0.854629i	$-0.326215\pi$
$677$	27.0204	1.03848	0.519240	+	0.854629i	$0.326215\pi$
$678$	12.3029	0.472490
$679$	−33.5224	−1.28647
$680$	9.03559	0.346499
$681$	−11.2276	−0.430243
$682$	−14.1122	−0.540383
$683$	15.2633	0.584033	0.292016	−	0.956413i	$-0.405674\pi$
$683$	15.2633	0.584033	0.292016	+	0.956413i	$0.405674\pi$
$684$	1.00000	0.0382360
$685$	−32.0804	−1.22573
$686$	−4.15492	−0.158636
$687$	−22.7748	−0.868912
$688$	5.28754	0.201585
$689$	2.97719	0.113422
$690$	−22.8581	−0.870194
$691$	−43.0940	−1.63937	−0.819686	−	0.572813i	$-0.805852\pi$
$691$	−43.0940	−1.63937	−0.819686	+	0.572813i	$0.805852\pi$
$692$	−4.42126	−0.168071
$693$	6.81414	0.258848
$694$	34.1291	1.29552
$695$	−75.7531	−2.87348
$696$	7.14911	0.270986
$697$	4.40986	0.167035
$698$	−9.83622	−0.372306
$699$	−1.30731	−0.0494470
$700$	−26.0662	−0.985211
$701$	45.3963	1.71459	0.857297	−	0.514823i	$-0.172142\pi$
$701$	45.3963	1.71459	0.857297	+	0.514823i	$0.172142\pi$
$702$	2.97719	0.112367
$703$	5.70263	0.215079
$704$	−1.90161	−0.0716694
$705$	−23.6855	−0.892046
$706$	25.0775	0.943805
$707$	38.5150	1.44850
$708$	1.16330	0.0437195
$709$	−20.0626	−0.753468	−0.376734	−	0.926321i	$-0.622953\pi$
$709$	−20.0626	−0.753468	−0.376734	+	0.926321i	$0.622953\pi$
$710$	−30.4481	−1.14270
$711$	−15.4858	−0.580761
$712$	3.72029	0.139424
$713$	−48.4191	−1.81331
$714$	−9.24167	−0.345861
$715$	19.8346	0.741774
$716$	4.08100	0.152514
$717$	20.6089	0.769654
$718$	4.22146	0.157544
$719$	0.809817	0.0302011	0.0151005	−	0.999886i	$-0.495193\pi$
$719$	0.809817	0.0302011	0.0151005	+	0.999886i	$0.495193\pi$
$720$	3.50346	0.130566
$721$	41.4785	1.54474
$722$	−1.00000	−0.0372161
$723$	0.961523	0.0357594
$724$	14.1814	0.527046
$725$	−52.0043	−1.93139
$726$	7.38390	0.274042
$727$	−35.4678	−1.31543	−0.657714	−	0.753268i	$-0.728477\pi$
$727$	−35.4678	−1.31543	−0.657714	+	0.753268i	$0.728477\pi$
$728$	−10.6684	−0.395396
$729$	1.00000	0.0370370
$730$	10.1926	0.377245
$731$	−13.6368	−0.504376
$732$	14.8469	0.548757
$733$	−9.71770	−0.358931	−0.179466	−	0.983764i	$-0.557437\pi$
$733$	−9.71770	−0.358931	−0.179466	+	0.983764i	$0.557437\pi$
$734$	25.6885	0.948179
$735$	20.4619	0.754750
$736$	−6.52444	−0.240494
$737$	13.4580	0.495733
$738$	1.70988	0.0629416
$739$	−1.99259	−0.0732985	−0.0366492	−	0.999328i	$-0.511668\pi$
$739$	−1.99259	−0.0732985	−0.0366492	+	0.999328i	$0.511668\pi$
$740$	19.9789	0.734440
$741$	−2.97719	−0.109370
$742$	−3.58336	−0.131549
$743$	−1.06080	−0.0389170	−0.0194585	−	0.999811i	$-0.506194\pi$
$743$	−1.06080	−0.0389170	−0.0194585	+	0.999811i	$0.506194\pi$
$744$	7.42118	0.272074
$745$	−22.8380	−0.836720
$746$	−32.2219	−1.17973
$747$	−6.97395	−0.255163
$748$	4.90433	0.179320
$749$	33.3834	1.21980
$750$	−7.96768	−0.290939
$751$	12.4679	0.454962	0.227481	−	0.973783i	$-0.426951\pi$
$751$	12.4679	0.454962	0.227481	+	0.973783i	$0.426951\pi$
$752$	−6.76059	−0.246533
$753$	28.8026	1.04963
$754$	−21.2843	−0.775127
$755$	−63.5067	−2.31125
$756$	−3.58336	−0.130326
$757$	−23.7392	−0.862817	−0.431409	−	0.902157i	$-0.641983\pi$
$757$	−23.7392	−0.862817	−0.431409	+	0.902157i	$0.641983\pi$
$758$	32.6376	1.18545
$759$	−12.4069	−0.450343
$760$	−3.50346	−0.127084
$761$	6.32819	0.229397	0.114698	−	0.993400i	$-0.463410\pi$
$761$	6.32819	0.229397	0.114698	+	0.993400i	$0.463410\pi$
$762$	20.1914	0.731457
$763$	−53.5222	−1.93763
$764$	−9.15755	−0.331308
$765$	−9.03559	−0.326683
$766$	−28.5124	−1.03019
$767$	−3.46337	−0.125055
$768$	1.00000	0.0360844
$769$	−28.1623	−1.01556	−0.507780	−	0.861487i	$-0.669534\pi$
$769$	−28.1623	−1.01556	−0.507780	+	0.861487i	$0.669534\pi$
$770$	−23.8731	−0.860326
$771$	18.4466	0.664337
$772$	−19.6666	−0.707818
$773$	−3.44108	−0.123767	−0.0618835	−	0.998083i	$-0.519711\pi$
$773$	−3.44108	−0.123767	−0.0618835	+	0.998083i	$0.519711\pi$
$774$	−5.28754	−0.190057
$775$	−53.9834	−1.93914
$776$	−9.35502	−0.335826
$777$	−20.4346	−0.733086
$778$	−33.7547	−1.21016
$779$	−1.70988	−0.0612628
$780$	−10.4305	−0.373471
$781$	−16.5266	−0.591368
$782$	16.8269	0.601727
$783$	−7.14911	−0.255488
$784$	5.84050	0.208589
$785$	−7.45624	−0.266125
$786$	0.0765693	0.00273114
$787$	26.3808	0.940373	0.470187	−	0.882567i	$-0.344187\pi$
$787$	26.3808	0.940373	0.470187	+	0.882567i	$0.344187\pi$
$788$	14.6849	0.523128
$789$	23.3384	0.830868
$790$	54.2537	1.93026
$791$	44.0858	1.56751
$792$	1.90161	0.0675706
$793$	−44.2021	−1.56966
$794$	−16.3934	−0.581778
$795$	−3.50346	−0.124255
$796$	−7.58984	−0.269015
$797$	−36.5326	−1.29405	−0.647026	−	0.762468i	$-0.723987\pi$
$797$	−36.5326	−1.29405	−0.647026	+	0.762468i	$0.723987\pi$
$798$	3.58336	0.126850
$799$	17.4359	0.616838
$800$	−7.27423	−0.257183
$801$	−3.72029	−0.131450
$802$	−32.4317	−1.14520
$803$	5.53232	0.195231
$804$	−7.07719	−0.249593
$805$	−81.9090	−2.88691
$806$	−22.0943	−0.778238
$807$	−9.55201	−0.336247
$808$	10.7483	0.378123
$809$	0.943754	0.0331806	0.0165903	−	0.999862i	$-0.494719\pi$
$809$	0.943754	0.0331806	0.0165903	+	0.999862i	$0.494719\pi$
$810$	−3.50346	−0.123099
$811$	43.1587	1.51551	0.757753	−	0.652542i	$-0.226297\pi$
$811$	43.1587	1.51551	0.757753	+	0.652542i	$0.226297\pi$
$812$	25.6179	0.899010
$813$	18.5178	0.649449
$814$	10.8441	0.380087
$815$	43.3638	1.51897
$816$	−2.57905	−0.0902847
$817$	5.28754	0.184988
$818$	−29.5884	−1.03453
$819$	10.6684	0.372783
$820$	−5.99050	−0.209197
$821$	47.2184	1.64793	0.823967	−	0.566638i	$-0.191756\pi$
$821$	47.2184	1.64793	0.823967	+	0.566638i	$0.191756\pi$
$822$	9.15679	0.319380
$823$	10.9256	0.380844	0.190422	−	0.981702i	$-0.439014\pi$
$823$	10.9256	0.380844	0.190422	+	0.981702i	$0.439014\pi$
$824$	11.5753	0.403244
$825$	−13.8327	−0.481593
$826$	4.16853	0.145042
$827$	−5.37585	−0.186937	−0.0934683	−	0.995622i	$-0.529795\pi$
$827$	−5.37585	−0.186937	−0.0934683	+	0.995622i	$0.529795\pi$
$828$	6.52444	0.226740
$829$	−6.49429	−0.225556	−0.112778	−	0.993620i	$-0.535975\pi$
$829$	−6.49429	−0.225556	−0.112778	+	0.993620i	$0.535975\pi$
$830$	24.4330	0.848080
$831$	−22.9640	−0.796613
$832$	−2.97719	−0.103216
$833$	−15.0629	−0.521899
$834$	21.6224	0.748722
$835$	−41.2318	−1.42689
$836$	−1.90161	−0.0657684
$837$	−7.42118	−0.256514
$838$	21.3127	0.736235
$839$	36.6522	1.26537	0.632686	−	0.774408i	$-0.281952\pi$
$839$	36.6522	1.26537	0.632686	+	0.774408i	$0.281952\pi$
$840$	12.5542	0.433160
$841$	22.1097	0.762404
$842$	0.0512792	0.00176720
$843$	−16.2480	−0.559610
$844$	4.17434	0.143687
$845$	−14.4914	−0.498521
$846$	6.76059	0.232434
$847$	26.4592	0.909149
$848$	−1.00000	−0.0343401
$849$	−4.10361	−0.140836
$850$	18.7606	0.643483
$851$	37.2065	1.27542
$852$	8.69087	0.297744
$853$	−43.0853	−1.47521	−0.737606	−	0.675231i	$-0.764044\pi$
$853$	−43.0853	−1.47521	−0.737606	+	0.675231i	$0.764044\pi$
$854$	53.2018	1.82053
$855$	3.50346	0.119816
$856$	9.31621	0.318421
$857$	−20.6307	−0.704732	−0.352366	−	0.935862i	$-0.614623\pi$
$857$	−20.6307	−0.704732	−0.352366	+	0.935862i	$0.614623\pi$
$858$	−5.66145	−0.193279
$859$	−18.5611	−0.633298	−0.316649	−	0.948543i	$-0.602558\pi$
$859$	−18.5611	−0.633298	−0.316649	+	0.948543i	$0.602558\pi$
$860$	18.5247	0.631686
$861$	6.12712	0.208812
$862$	−29.2367	−0.995805
$863$	−9.01186	−0.306767	−0.153384	−	0.988167i	$-0.549017\pi$
$863$	−9.01186	−0.306767	−0.153384	+	0.988167i	$0.549017\pi$
$864$	−1.00000	−0.0340207
$865$	−15.4897	−0.526665
$866$	−11.0106	−0.374155
$867$	−10.3485	−0.351454
$868$	26.5928	0.902619
$869$	29.4478	0.998948
$870$	25.0466	0.849160
$871$	21.0702	0.713935
$872$	−14.9363	−0.505807
$873$	9.35502	0.316619
$874$	−6.52444	−0.220693
$875$	−28.5511	−0.965204
$876$	−2.90929	−0.0982959
$877$	30.2155	1.02031	0.510153	−	0.860084i	$-0.329589\pi$
$877$	30.2155	1.02031	0.510153	+	0.860084i	$0.329589\pi$
$878$	−2.68593	−0.0906457
$879$	−24.1237	−0.813673
$880$	−6.66220	−0.224583
$881$	20.8960	0.704005	0.352002	−	0.935999i	$-0.385501\pi$
$881$	20.8960	0.704005	0.352002	+	0.935999i	$0.385501\pi$
$882$	−5.84050	−0.196660
$883$	−46.3894	−1.56113	−0.780565	−	0.625075i	$-0.785068\pi$
$883$	−46.3894	−1.56113	−0.780565	+	0.625075i	$0.785068\pi$
$884$	7.67832	0.258250
$885$	4.07557	0.136999
$886$	−1.08140	−0.0363302
$887$	8.12503	0.272812	0.136406	−	0.990653i	$-0.456445\pi$
$887$	8.12503	0.272812	0.136406	+	0.990653i	$0.456445\pi$
$888$	−5.70263	−0.191368
$889$	72.3532	2.42665
$890$	13.0339	0.436897
$891$	−1.90161	−0.0637062
$892$	−3.78490	−0.126728
$893$	−6.76059	−0.226235
$894$	6.51870	0.218018
$895$	14.2976	0.477916
$896$	3.58336	0.119712
$897$	−19.4245	−0.648566
$898$	1.83002	0.0610687
$899$	53.0548	1.76948
$900$	7.27423	0.242474
$901$	2.57905	0.0859205
$902$	−3.25152	−0.108264
$903$	−18.9472	−0.630522
$904$	12.3029	0.409189
$905$	49.6839	1.65155
$906$	18.1269	0.602224
$907$	15.0241	0.498866	0.249433	−	0.968392i	$-0.419756\pi$
$907$	15.0241	0.498866	0.249433	+	0.968392i	$0.419756\pi$
$908$	−11.2276	−0.372601
$909$	−10.7483	−0.356498
$910$	−37.3762	−1.23901
$911$	−24.9868	−0.827849	−0.413924	−	0.910311i	$-0.635842\pi$
$911$	−24.9868	−0.827849	−0.413924	+	0.910311i	$0.635842\pi$
$912$	1.00000	0.0331133
$913$	13.2617	0.438898
$914$	−5.81295	−0.192275
$915$	52.0155	1.71958
$916$	−22.7748	−0.752499
$917$	0.274376	0.00906068
$918$	2.57905	0.0851213
$919$	−13.3338	−0.439841	−0.219920	−	0.975518i	$-0.570580\pi$
$919$	−13.3338	−0.439841	−0.219920	+	0.975518i	$0.570580\pi$
$920$	−22.8581	−0.753610
$921$	10.8191	0.356503
$922$	−5.40387	−0.177967
$923$	−25.8744	−0.851666
$924$	6.81414	0.224169
$925$	41.4822	1.36393
$926$	13.0554	0.429028
$927$	−11.5753	−0.380182
$928$	7.14911	0.234681
$929$	11.7501	0.385508	0.192754	−	0.981247i	$-0.438258\pi$
$929$	11.7501	0.385508	0.192754	+	0.981247i	$0.438258\pi$
$930$	25.9998	0.852568
$931$	5.84050	0.191415
$932$	−1.30731	−0.0428223
$933$	16.1233	0.527853
$934$	−25.4467	−0.832641
$935$	17.1821	0.561916
$936$	2.97719	0.0973126
$937$	−26.5589	−0.867642	−0.433821	−	0.900999i	$-0.642835\pi$
$937$	−26.5589	−0.867642	−0.433821	+	0.900999i	$0.642835\pi$
$938$	−25.3602	−0.828039
$939$	27.9539	0.912240
$940$	−23.6855	−0.772535
$941$	50.3819	1.64240	0.821202	−	0.570638i	$-0.193304\pi$
$941$	50.3819	1.64240	0.821202	+	0.570638i	$0.193304\pi$
$942$	2.12825	0.0693421
$943$	−11.1560	−0.363290
$944$	1.16330	0.0378622
$945$	−12.5542	−0.408387
$946$	10.0548	0.326910
$947$	40.2268	1.30720	0.653598	−	0.756842i	$-0.273259\pi$
$947$	40.2268	1.30720	0.653598	+	0.756842i	$0.273259\pi$
$948$	−15.4858	−0.502954
$949$	8.66152	0.281165
$950$	−7.27423	−0.236007
$951$	30.9328	1.00306
$952$	−9.24167	−0.299524
$953$	−28.7733	−0.932059	−0.466030	−	0.884769i	$-0.654316\pi$
$953$	−28.7733	−0.932059	−0.466030	+	0.884769i	$0.654316\pi$
$954$	1.00000	0.0323762
$955$	−32.0831	−1.03818
$956$	20.6089	0.666540
$957$	13.5948	0.439457
$958$	−8.79014	−0.283997
$959$	32.8121	1.05956
$960$	3.50346	0.113074
$961$	24.0740	0.776580
$962$	16.9778	0.547387
$963$	−9.31621	−0.300211
$964$	0.961523	0.0309686
$965$	−68.9013	−2.21801
$966$	23.3795	0.752222
$967$	34.5677	1.11162	0.555812	−	0.831308i	$-0.312408\pi$
$967$	34.5677	1.11162	0.555812	+	0.831308i	$0.312408\pi$
$968$	7.38390	0.237327
$969$	−2.57905	−0.0828510
$970$	−32.7749	−1.05234
$971$	−14.8679	−0.477133	−0.238566	−	0.971126i	$-0.576677\pi$
$971$	−14.8679	−0.477133	−0.238566	+	0.971126i	$0.576677\pi$
$972$	1.00000	0.0320750
$973$	77.4808	2.48392
$974$	37.3743	1.19755
$975$	−21.6568	−0.693572
$976$	14.8469	0.475238
$977$	−21.1048	−0.675204	−0.337602	−	0.941289i	$-0.609616\pi$
$977$	−21.1048	−0.675204	−0.337602	+	0.941289i	$0.609616\pi$
$978$	−12.3774	−0.395786
$979$	7.07453	0.226103
$980$	20.4619	0.653633
$981$	14.9363	0.476879
$982$	−26.3515	−0.840909
$983$	−13.0086	−0.414911	−0.207456	−	0.978244i	$-0.566518\pi$
$983$	−13.0086	−0.414911	−0.207456	+	0.978244i	$0.566518\pi$
$984$	1.70988	0.0545090
$985$	51.4480	1.63927
$986$	−18.4379	−0.587182
$987$	24.2257	0.771111
$988$	−2.97719	−0.0947171
$989$	34.4982	1.09698
$990$	6.66220	0.211739
$991$	32.9690	1.04730	0.523648	−	0.851935i	$-0.324571\pi$
$991$	32.9690	1.04730	0.523648	+	0.851935i	$0.324571\pi$
$992$	7.42118	0.235623
$993$	−17.7106	−0.562029
$994$	31.1425	0.987782
$995$	−26.5907	−0.842982
$996$	−6.97395	−0.220978
$997$	38.5634	1.22131	0.610657	−	0.791895i	$-0.290905\pi$
$997$	38.5634	1.22131	0.610657	+	0.791895i	$0.290905\pi$
$998$	1.41265	0.0447167
$999$	5.70263	0.180423

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6042.2.a.v.1.6	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6042.2.a.v.1.6	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.50346 q^{5} -1.00000 q^{6} -3.58336 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.50346 q^{5} -1.00000 q^{6} -3.58336 q^{7} -1.00000 q^{8} +1.00000 q^{9} -3.50346 q^{10} -1.90161 q^{11} +1.00000 q^{12} -2.97719 q^{13} +3.58336 q^{14} +3.50346 q^{15} +1.00000 q^{16} -2.57905 q^{17} -1.00000 q^{18} +1.00000 q^{19} +3.50346 q^{20} -3.58336 q^{21} +1.90161 q^{22} +6.52444 q^{23} -1.00000 q^{24} +7.27423 q^{25} +2.97719 q^{26} +1.00000 q^{27} -3.58336 q^{28} -7.14911 q^{29} -3.50346 q^{30} -7.42118 q^{31} -1.00000 q^{32} -1.90161 q^{33} +2.57905 q^{34} -12.5542 q^{35} +1.00000 q^{36} +5.70263 q^{37} -1.00000 q^{38} -2.97719 q^{39} -3.50346 q^{40} -1.70988 q^{41} +3.58336 q^{42} +5.28754 q^{43} -1.90161 q^{44} +3.50346 q^{45} -6.52444 q^{46} -6.76059 q^{47} +1.00000 q^{48} +5.84050 q^{49} -7.27423 q^{50} -2.57905 q^{51} -2.97719 q^{52} -1.00000 q^{53} -1.00000 q^{54} -6.66220 q^{55} +3.58336 q^{56} +1.00000 q^{57} +7.14911 q^{58} +1.16330 q^{59} +3.50346 q^{60} +14.8469 q^{61} +7.42118 q^{62} -3.58336 q^{63} +1.00000 q^{64} -10.4305 q^{65} +1.90161 q^{66} -7.07719 q^{67} -2.57905 q^{68} +6.52444 q^{69} +12.5542 q^{70} +8.69087 q^{71} -1.00000 q^{72} -2.90929 q^{73} -5.70263 q^{74} +7.27423 q^{75} +1.00000 q^{76} +6.81414 q^{77} +2.97719 q^{78} -15.4858 q^{79} +3.50346 q^{80} +1.00000 q^{81} +1.70988 q^{82} -6.97395 q^{83} -3.58336 q^{84} -9.03559 q^{85} -5.28754 q^{86} -7.14911 q^{87} +1.90161 q^{88} -3.72029 q^{89} -3.50346 q^{90} +10.6684 q^{91} +6.52444 q^{92} -7.42118 q^{93} +6.76059 q^{94} +3.50346 q^{95} -1.00000 q^{96} +9.35502 q^{97} -5.84050 q^{98} -1.90161 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} + 6 q^{3} + 6 q^{4} + 3 q^{5} - 6 q^{6} - 7 q^{7} - 6 q^{8} + 6 q^{9}+O(q^{10}) \) 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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