LMFDB - Embedded newform 6034.2.a.n.1.24

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6034,2,Mod(1,6034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6034, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("6034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6034 = 2 \cdot 7 \cdot 431 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6034.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:	$48.1817325796$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.24
Character	$\chi$	$=$	6034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +3.44887 q^{3} +1.00000 q^{4} +2.88493 q^{5} -3.44887 q^{6} -1.00000 q^{7} -1.00000 q^{8} +8.89471 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +3.44887 q^{3} +1.00000 q^{4} +2.88493 q^{5} -3.44887 q^{6} -1.00000 q^{7} -1.00000 q^{8} +8.89471 q^{9} -2.88493 q^{10} +1.39981 q^{11} +3.44887 q^{12} -0.813710 q^{13} +1.00000 q^{14} +9.94975 q^{15} +1.00000 q^{16} +1.51622 q^{17} -8.89471 q^{18} -0.506954 q^{19} +2.88493 q^{20} -3.44887 q^{21} -1.39981 q^{22} -1.49483 q^{23} -3.44887 q^{24} +3.32281 q^{25} +0.813710 q^{26} +20.3301 q^{27} -1.00000 q^{28} +4.17292 q^{29} -9.94975 q^{30} -8.18728 q^{31} -1.00000 q^{32} +4.82776 q^{33} -1.51622 q^{34} -2.88493 q^{35} +8.89471 q^{36} +10.9769 q^{37} +0.506954 q^{38} -2.80638 q^{39} -2.88493 q^{40} -3.91904 q^{41} +3.44887 q^{42} -3.82119 q^{43} +1.39981 q^{44} +25.6606 q^{45} +1.49483 q^{46} +7.25695 q^{47} +3.44887 q^{48} +1.00000 q^{49} -3.32281 q^{50} +5.22925 q^{51} -0.813710 q^{52} -14.1345 q^{53} -20.3301 q^{54} +4.03835 q^{55} +1.00000 q^{56} -1.74842 q^{57} -4.17292 q^{58} -12.1773 q^{59} +9.94975 q^{60} +6.62877 q^{61} +8.18728 q^{62} -8.89471 q^{63} +1.00000 q^{64} -2.34749 q^{65} -4.82776 q^{66} +13.6748 q^{67} +1.51622 q^{68} -5.15546 q^{69} +2.88493 q^{70} +13.9997 q^{71} -8.89471 q^{72} -8.75839 q^{73} -10.9769 q^{74} +11.4600 q^{75} -0.506954 q^{76} -1.39981 q^{77} +2.80638 q^{78} -0.807708 q^{79} +2.88493 q^{80} +43.4317 q^{81} +3.91904 q^{82} +13.2321 q^{83} -3.44887 q^{84} +4.37419 q^{85} +3.82119 q^{86} +14.3919 q^{87} -1.39981 q^{88} +6.69640 q^{89} -25.6606 q^{90} +0.813710 q^{91} -1.49483 q^{92} -28.2369 q^{93} -7.25695 q^{94} -1.46253 q^{95} -3.44887 q^{96} -13.9283 q^{97} -1.00000 q^{98} +12.4509 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{2} + 7 q^{3} + 24 q^{4} + 8 q^{5} - 7 q^{6} - 24 q^{7} - 24 q^{8} + 19 q^{9}+O(q^{10}) $ 24 * q - 24 * q^2 + 7 * q^3 + 24 * q^4 + 8 * q^5 - 7 * q^6 - 24 * q^7 - 24 * q^8 + 19 * q^9	\( 24 q - 24 q^{2} + 7 q^{3} + 24 q^{4} + 8 q^{5} - 7 q^{6} - 24 q^{7} - 24 q^{8} + 19 q^{9} - 8 q^{10} + 15 q^{11} + 7 q^{12} - 7 q^{13} + 24 q^{14} + 13 q^{15} + 24 q^{16} - 5 q^{17} - 19 q^{18} + 6 q^{19} + 8 q^{20} - 7 q^{21} - 15 q^{22} + 3 q^{23} - 7 q^{24} + 12 q^{25} + 7 q^{26} + 22 q^{27} - 24 q^{28} + 5 q^{29} - 13 q^{30} + 13 q^{31} - 24 q^{32} - 8 q^{33} + 5 q^{34} - 8 q^{35} + 19 q^{36} + 2 q^{37} - 6 q^{38} + 7 q^{39} - 8 q^{40} + 25 q^{41} + 7 q^{42} - 15 q^{43} + 15 q^{44} + 41 q^{45} - 3 q^{46} + 35 q^{47} + 7 q^{48} + 24 q^{49} - 12 q^{50} + 31 q^{51} - 7 q^{52} + 2 q^{53} - 22 q^{54} + 14 q^{55} + 24 q^{56} - 13 q^{57} - 5 q^{58} + 35 q^{59} + 13 q^{60} - 7 q^{61} - 13 q^{62} - 19 q^{63} + 24 q^{64} - 4 q^{65} + 8 q^{66} + 10 q^{67} - 5 q^{68} + 6 q^{69} + 8 q^{70} + 58 q^{71} - 19 q^{72} + 9 q^{73} - 2 q^{74} + 7 q^{75} + 6 q^{76} - 15 q^{77} - 7 q^{78} + 31 q^{79} + 8 q^{80} + 16 q^{81} - 25 q^{82} - q^{83} - 7 q^{84} - 4 q^{85} + 15 q^{86} + 30 q^{87} - 15 q^{88} + 45 q^{89} - 41 q^{90} + 7 q^{91} + 3 q^{92} + 25 q^{93} - 35 q^{94} - 10 q^{95} - 7 q^{96} - 9 q^{97} - 24 q^{98} + 64 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 + 7 * q^3 + 24 * q^4 + 8 * q^5 - 7 * q^6 - 24 * q^7 - 24 * q^8 + 19 * q^9 - 8 * q^10 + 15 * q^11 + 7 * q^12 - 7 * q^13 + 24 * q^14 + 13 * q^15 + 24 * q^16 - 5 * q^17 - 19 * q^18 + 6 * q^19 + 8 * q^20 - 7 * q^21 - 15 * q^22 + 3 * q^23 - 7 * q^24 + 12 * q^25 + 7 * q^26 + 22 * q^27 - 24 * q^28 + 5 * q^29 - 13 * q^30 + 13 * q^31 - 24 * q^32 - 8 * q^33 + 5 * q^34 - 8 * q^35 + 19 * q^36 + 2 * q^37 - 6 * q^38 + 7 * q^39 - 8 * q^40 + 25 * q^41 + 7 * q^42 - 15 * q^43 + 15 * q^44 + 41 * q^45 - 3 * q^46 + 35 * q^47 + 7 * q^48 + 24 * q^49 - 12 * q^50 + 31 * q^51 - 7 * q^52 + 2 * q^53 - 22 * q^54 + 14 * q^55 + 24 * q^56 - 13 * q^57 - 5 * q^58 + 35 * q^59 + 13 * q^60 - 7 * q^61 - 13 * q^62 - 19 * q^63 + 24 * q^64 - 4 * q^65 + 8 * q^66 + 10 * q^67 - 5 * q^68 + 6 * q^69 + 8 * q^70 + 58 * q^71 - 19 * q^72 + 9 * q^73 - 2 * q^74 + 7 * q^75 + 6 * q^76 - 15 * q^77 - 7 * q^78 + 31 * q^79 + 8 * q^80 + 16 * q^81 - 25 * q^82 - q^83 - 7 * q^84 - 4 * q^85 + 15 * q^86 + 30 * q^87 - 15 * q^88 + 45 * q^89 - 41 * q^90 + 7 * q^91 + 3 * q^92 + 25 * q^93 - 35 * q^94 - 10 * q^95 - 7 * q^96 - 9 * q^97 - 24 * q^98 + 64 * 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
$3$	3.44887	1.99121	0.995603	−	0.0936715i	$-0.0298603\pi$
$3$	3.44887	1.99121	0.995603	+	0.0936715i	$0.0298603\pi$
$4$	1.00000	0.500000
$5$	2.88493	1.29018	0.645090	−	0.764107i	$-0.276820\pi$
$5$	2.88493	1.29018	0.645090	+	0.764107i	$0.276820\pi$
$6$	−3.44887	−1.40800
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	8.89471	2.96490
$10$	−2.88493	−0.912295
$11$	1.39981	0.422058	0.211029	−	0.977480i	$-0.432319\pi$
$11$	1.39981	0.422058	0.211029	+	0.977480i	$0.432319\pi$
$12$	3.44887	0.995603
$13$	−0.813710	−0.225682	−0.112841	−	0.993613i	$-0.535995\pi$
$13$	−0.813710	−0.225682	−0.112841	+	0.993613i	$0.535995\pi$
$14$	1.00000	0.267261
$15$	9.94975	2.56901
$16$	1.00000	0.250000
$17$	1.51622	0.367738	0.183869	−	0.982951i	$-0.441138\pi$
$17$	1.51622	0.367738	0.183869	+	0.982951i	$0.441138\pi$
$18$	−8.89471	−2.09650
$19$	−0.506954	−0.116303	−0.0581516	−	0.998308i	$-0.518521\pi$
$19$	−0.506954	−0.116303	−0.0581516	+	0.998308i	$0.518521\pi$
$20$	2.88493	0.645090
$21$	−3.44887	−0.752605
$22$	−1.39981	−0.298440
$23$	−1.49483	−0.311693	−0.155846	−	0.987781i	$-0.549811\pi$
$23$	−1.49483	−0.311693	−0.155846	+	0.987781i	$0.549811\pi$
$24$	−3.44887	−0.703998
$25$	3.32281	0.664563
$26$	0.813710	0.159582
$27$	20.3301	3.91253
$28$	−1.00000	−0.188982
$29$	4.17292	0.774892	0.387446	−	0.921892i	$-0.373357\pi$
$29$	4.17292	0.774892	0.387446	+	0.921892i	$0.373357\pi$
$30$	−9.94975	−1.81657
$31$	−8.18728	−1.47048	−0.735239	−	0.677808i	$-0.762930\pi$
$31$	−8.18728	−1.47048	−0.735239	+	0.677808i	$0.762930\pi$
$32$	−1.00000	−0.176777
$33$	4.82776	0.840405
$34$	−1.51622	−0.260030
$35$	−2.88493	−0.487642
$36$	8.89471	1.48245
$37$	10.9769	1.80459	0.902296	−	0.431117i	$-0.141880\pi$
$37$	10.9769	1.80459	0.902296	+	0.431117i	$0.141880\pi$
$38$	0.506954	0.0822388
$39$	−2.80638	−0.449380
$40$	−2.88493	−0.456147
$41$	−3.91904	−0.612052	−0.306026	−	0.952023i	$-0.598999\pi$
$41$	−3.91904	−0.612052	−0.306026	+	0.952023i	$0.598999\pi$
$42$	3.44887	0.532172
$43$	−3.82119	−0.582726	−0.291363	−	0.956613i	$-0.594109\pi$
$43$	−3.82119	−0.582726	−0.291363	+	0.956613i	$0.594109\pi$
$44$	1.39981	0.211029
$45$	25.6606	3.82526
$46$	1.49483	0.220400
$47$	7.25695	1.05854	0.529268	−	0.848455i	$-0.322467\pi$
$47$	7.25695	1.05854	0.529268	+	0.848455i	$0.322467\pi$
$48$	3.44887	0.497802
$49$	1.00000	0.142857
$50$	−3.32281	−0.469917
$51$	5.22925	0.732242
$52$	−0.813710	−0.112841
$53$	−14.1345	−1.94153	−0.970764	−	0.240035i	$-0.922841\pi$
$53$	−14.1345	−1.94153	−0.970764	+	0.240035i	$0.922841\pi$
$54$	−20.3301	−2.76657
$55$	4.03835	0.544531
$56$	1.00000	0.133631
$57$	−1.74842	−0.231584
$58$	−4.17292	−0.547932
$59$	−12.1773	−1.58534	−0.792672	−	0.609648i	$-0.791311\pi$
$59$	−12.1773	−1.58534	−0.792672	+	0.609648i	$0.791311\pi$
$60$	9.94975	1.28451
$61$	6.62877	0.848727	0.424363	−	0.905492i	$-0.360498\pi$
$61$	6.62877	0.848727	0.424363	+	0.905492i	$0.360498\pi$
$62$	8.18728	1.03979
$63$	−8.89471	−1.12063
$64$	1.00000	0.125000
$65$	−2.34749	−0.291171
$66$	−4.82776	−0.594256
$67$	13.6748	1.67064	0.835319	−	0.549766i	$-0.185283\pi$
$67$	13.6748	1.67064	0.835319	+	0.549766i	$0.185283\pi$
$68$	1.51622	0.183869
$69$	−5.15546	−0.620645
$70$	2.88493	0.344815
$71$	13.9997	1.66146	0.830731	−	0.556673i	$-0.187923\pi$
$71$	13.9997	1.66146	0.830731	+	0.556673i	$0.187923\pi$
$72$	−8.89471	−1.04825
$73$	−8.75839	−1.02509	−0.512546	−	0.858660i	$-0.671298\pi$
$73$	−8.75839	−1.02509	−0.512546	+	0.858660i	$0.671298\pi$
$74$	−10.9769	−1.27604
$75$	11.4600	1.32328
$76$	−0.506954	−0.0581516
$77$	−1.39981	−0.159523
$78$	2.80638	0.317760
$79$	−0.807708	−0.0908742	−0.0454371	−	0.998967i	$-0.514468\pi$
$79$	−0.807708	−0.0908742	−0.0454371	+	0.998967i	$0.514468\pi$
$80$	2.88493	0.322545
$81$	43.4317	4.82574
$82$	3.91904	0.432786
$83$	13.2321	1.45242	0.726209	−	0.687474i	$-0.241281\pi$
$83$	13.2321	1.45242	0.726209	+	0.687474i	$0.241281\pi$
$84$	−3.44887	−0.376303
$85$	4.37419	0.474448
$86$	3.82119	0.412050
$87$	14.3919	1.54297
$88$	−1.39981	−0.149220
$89$	6.69640	0.709817	0.354909	−	0.934901i	$-0.384512\pi$
$89$	6.69640	0.709817	0.354909	+	0.934901i	$0.384512\pi$
$90$	−25.6606	−2.70486
$91$	0.813710	0.0853000
$92$	−1.49483	−0.155846
$93$	−28.2369	−2.92803
$94$	−7.25695	−0.748498
$95$	−1.46253	−0.150052
$96$	−3.44887	−0.351999
$97$	−13.9283	−1.41421	−0.707103	−	0.707110i	$-0.749998\pi$
$97$	−13.9283	−1.41421	−0.707103	+	0.707110i	$0.749998\pi$
$98$	−1.00000	−0.101015
$99$	12.4509	1.25136
$100$	3.32281	0.332281
$101$	−9.00761	−0.896291	−0.448146	−	0.893961i	$-0.647915\pi$
$101$	−9.00761	−0.896291	−0.448146	+	0.893961i	$0.647915\pi$
$102$	−5.22925	−0.517773
$103$	2.96859	0.292504	0.146252	−	0.989247i	$-0.453279\pi$
$103$	2.96859	0.292504	0.146252	+	0.989247i	$0.453279\pi$
$104$	0.813710	0.0797908
$105$	−9.94975	−0.970996
$106$	14.1345	1.37287
$107$	−17.7096	−1.71206	−0.856028	−	0.516929i	$-0.827075\pi$
$107$	−17.7096	−1.71206	−0.856028	+	0.516929i	$0.827075\pi$
$108$	20.3301	1.95626
$109$	11.2137	1.07408	0.537040	−	0.843557i	$-0.319542\pi$
$109$	11.2137	1.07408	0.537040	+	0.843557i	$0.319542\pi$
$110$	−4.03835	−0.385041
$111$	37.8579	3.59332
$112$	−1.00000	−0.0944911
$113$	−3.15063	−0.296387	−0.148193	−	0.988958i	$-0.547346\pi$
$113$	−3.15063	−0.296387	−0.148193	+	0.988958i	$0.547346\pi$
$114$	1.74842	0.163755
$115$	−4.31247	−0.402140
$116$	4.17292	0.387446
$117$	−7.23771	−0.669127
$118$	12.1773	1.12101
$119$	−1.51622	−0.138992
$120$	−9.94975	−0.908283
$121$	−9.04053	−0.821867
$122$	−6.62877	−0.600141
$123$	−13.5163	−1.21872
$124$	−8.18728	−0.735239
$125$	−4.83856	−0.432774
$126$	8.89471	0.792404
$127$	11.7063	1.03877	0.519383	−	0.854542i	$-0.326162\pi$
$127$	11.7063	1.03877	0.519383	+	0.854542i	$0.326162\pi$
$128$	−1.00000	−0.0883883
$129$	−13.1788	−1.16033
$130$	2.34749	0.205889
$131$	−12.7309	−1.11230	−0.556152	−	0.831081i	$-0.687723\pi$
$131$	−12.7309	−1.11230	−0.556152	+	0.831081i	$0.687723\pi$
$132$	4.82776	0.420203
$133$	0.506954	0.0439585
$134$	−13.6748	−1.18132
$135$	58.6508	5.04786
$136$	−1.51622	−0.130015
$137$	−16.7561	−1.43157	−0.715787	−	0.698319i	$-0.753932\pi$
$137$	−16.7561	−1.43157	−0.715787	+	0.698319i	$0.753932\pi$
$138$	5.15546	0.438862
$139$	−1.19318	−0.101205	−0.0506023	−	0.998719i	$-0.516114\pi$
$139$	−1.19318	−0.101205	−0.0506023	+	0.998719i	$0.516114\pi$
$140$	−2.88493	−0.243821
$141$	25.0283	2.10776
$142$	−13.9997	−1.17483
$143$	−1.13904	−0.0952512
$144$	8.89471	0.741226
$145$	12.0386	0.999750
$146$	8.75839	0.724850
$147$	3.44887	0.284458
$148$	10.9769	0.902296
$149$	−3.75485	−0.307609	−0.153805	−	0.988101i	$-0.549153\pi$
$149$	−3.75485	−0.307609	−0.153805	+	0.988101i	$0.549153\pi$
$150$	−11.4600	−0.935701
$151$	−24.1670	−1.96669	−0.983343	−	0.181761i	$-0.941820\pi$
$151$	−24.1670	−1.96669	−0.983343	+	0.181761i	$0.941820\pi$
$152$	0.506954	0.0411194
$153$	13.4863	1.09031
$154$	1.39981	0.112800
$155$	−23.6197	−1.89718
$156$	−2.80638	−0.224690
$157$	10.2895	0.821188	0.410594	−	0.911818i	$-0.365321\pi$
$157$	10.2895	0.821188	0.410594	+	0.911818i	$0.365321\pi$
$158$	0.807708	0.0642578
$159$	−48.7482	−3.86598
$160$	−2.88493	−0.228074
$161$	1.49483	0.117809
$162$	−43.4317	−3.41232
$163$	18.7442	1.46816	0.734080	−	0.679063i	$-0.237614\pi$
$163$	18.7442	1.46816	0.734080	+	0.679063i	$0.237614\pi$
$164$	−3.91904	−0.306026
$165$	13.9277	1.08427
$166$	−13.2321	−1.02701
$167$	11.9597	0.925467	0.462733	−	0.886498i	$-0.346869\pi$
$167$	11.9597	0.925467	0.462733	+	0.886498i	$0.346869\pi$
$168$	3.44887	0.266086
$169$	−12.3379	−0.949067
$170$	−4.37419	−0.335485
$171$	−4.50921	−0.344828
$172$	−3.82119	−0.291363
$173$	15.8121	1.20217	0.601084	−	0.799185i	$-0.294736\pi$
$173$	15.8121	1.20217	0.601084	+	0.799185i	$0.294736\pi$
$174$	−14.3919	−1.09105
$175$	−3.32281	−0.251181
$176$	1.39981	0.105515
$177$	−41.9978	−3.15675
$178$	−6.69640	−0.501916
$179$	17.5074	1.30856	0.654282	−	0.756250i	$-0.272971\pi$
$179$	17.5074	1.30856	0.654282	+	0.756250i	$0.272971\pi$
$180$	25.6606	1.91263
$181$	−5.12015	−0.380578	−0.190289	−	0.981728i	$-0.560943\pi$
$181$	−5.12015	−0.380578	−0.190289	+	0.981728i	$0.560943\pi$
$182$	−0.813710	−0.0603162
$183$	22.8618	1.68999
$184$	1.49483	0.110200
$185$	31.6676	2.32825
$186$	28.2369	2.07043
$187$	2.12242	0.155207
$188$	7.25695	0.529268
$189$	−20.3301	−1.47880
$190$	1.46253	0.106103
$191$	−6.44084	−0.466043	−0.233022	−	0.972472i	$-0.574861\pi$
$191$	−6.44084	−0.466043	−0.233022	+	0.972472i	$0.574861\pi$
$192$	3.44887	0.248901
$193$	−11.4848	−0.826694	−0.413347	−	0.910574i	$-0.635640\pi$
$193$	−11.4848	−0.826694	−0.413347	+	0.910574i	$0.635640\pi$
$194$	13.9283	0.999995
$195$	−8.09621	−0.579781
$196$	1.00000	0.0714286
$197$	12.5723	0.895739	0.447869	−	0.894099i	$-0.352183\pi$
$197$	12.5723	0.895739	0.447869	+	0.894099i	$0.352183\pi$
$198$	−12.4509	−0.884846
$199$	−8.40944	−0.596130	−0.298065	−	0.954546i	$-0.596341\pi$
$199$	−8.40944	−0.596130	−0.298065	+	0.954546i	$0.596341\pi$
$200$	−3.32281	−0.234958
$201$	47.1625	3.32658
$202$	9.00761	0.633773
$203$	−4.17292	−0.292882
$204$	5.22925	0.366121
$205$	−11.3062	−0.789657
$206$	−2.96859	−0.206832
$207$	−13.2960	−0.924139
$208$	−0.813710	−0.0564206
$209$	−0.709639	−0.0490868
$210$	9.94975	0.686598
$211$	20.3180	1.39875	0.699375	−	0.714755i	$-0.253462\pi$
$211$	20.3180	1.39875	0.699375	+	0.714755i	$0.253462\pi$
$212$	−14.1345	−0.970764
$213$	48.2833	3.30832
$214$	17.7096	1.21061
$215$	−11.0239	−0.751821
$216$	−20.3301	−1.38329
$217$	8.18728	0.555789
$218$	−11.2137	−0.759490
$219$	−30.2066	−2.04117
$220$	4.03835	0.272265
$221$	−1.23376	−0.0829920
$222$	−37.8579	−2.54086
$223$	16.8144	1.12597	0.562987	−	0.826465i	$-0.309652\pi$
$223$	16.8144	1.12597	0.562987	+	0.826465i	$0.309652\pi$
$224$	1.00000	0.0668153
$225$	29.5555	1.97036
$226$	3.15063	0.209577
$227$	0.765435	0.0508037	0.0254019	−	0.999677i	$-0.491913\pi$
$227$	0.765435	0.0508037	0.0254019	+	0.999677i	$0.491913\pi$
$228$	−1.74842	−0.115792
$229$	2.13892	0.141344	0.0706718	−	0.997500i	$-0.477486\pi$
$229$	2.13892	0.141344	0.0706718	+	0.997500i	$0.477486\pi$
$230$	4.31247	0.284356
$231$	−4.82776	−0.317643
$232$	−4.17292	−0.273966
$233$	−15.6844	−1.02752	−0.513759	−	0.857934i	$-0.671748\pi$
$233$	−15.6844	−1.02752	−0.513759	+	0.857934i	$0.671748\pi$
$234$	7.23771	0.473144
$235$	20.9358	1.36570
$236$	−12.1773	−0.792672
$237$	−2.78568	−0.180949
$238$	1.51622	0.0982820
$239$	−23.5404	−1.52270	−0.761351	−	0.648340i	$-0.775463\pi$
$239$	−23.5404	−1.52270	−0.761351	+	0.648340i	$0.775463\pi$
$240$	9.94975	0.642253
$241$	18.6125	1.19894	0.599470	−	0.800397i	$-0.295378\pi$
$241$	18.6125	1.19894	0.599470	+	0.800397i	$0.295378\pi$
$242$	9.04053	0.581148
$243$	88.8001	5.69653
$244$	6.62877	0.424363
$245$	2.88493	0.184311
$246$	13.5163	0.861766
$247$	0.412514	0.0262476
$248$	8.18728	0.519893
$249$	45.6360	2.89206
$250$	4.83856	0.306018
$251$	−5.61168	−0.354206	−0.177103	−	0.984192i	$-0.556673\pi$
$251$	−5.61168	−0.354206	−0.177103	+	0.984192i	$0.556673\pi$
$252$	−8.89471	−0.560314
$253$	−2.09247	−0.131553
$254$	−11.7063	−0.734518
$255$	15.0860	0.944723
$256$	1.00000	0.0625000
$257$	15.3370	0.956697	0.478349	−	0.878170i	$-0.341236\pi$
$257$	15.3370	0.956697	0.478349	+	0.878170i	$0.341236\pi$
$258$	13.1788	0.820476
$259$	−10.9769	−0.682072
$260$	−2.34749	−0.145585
$261$	37.1169	2.29748
$262$	12.7309	0.786517
$263$	15.4310	0.951514	0.475757	−	0.879577i	$-0.342174\pi$
$263$	15.4310	0.951514	0.475757	+	0.879577i	$0.342174\pi$
$264$	−4.82776	−0.297128
$265$	−40.7771	−2.50492
$266$	−0.506954	−0.0310834
$267$	23.0950	1.41339
$268$	13.6748	0.835319
$269$	−9.37756	−0.571760	−0.285880	−	0.958265i	$-0.592286\pi$
$269$	−9.37756	−0.571760	−0.285880	+	0.958265i	$0.592286\pi$
$270$	−58.6508	−3.56938
$271$	7.35841	0.446992	0.223496	−	0.974705i	$-0.428253\pi$
$271$	7.35841	0.446992	0.223496	+	0.974705i	$0.428253\pi$
$272$	1.51622	0.0919344
$273$	2.80638	0.169850
$274$	16.7561	1.01228
$275$	4.65130	0.280484
$276$	−5.15546	−0.310323
$277$	−33.0042	−1.98303	−0.991516	−	0.129984i	$-0.958508\pi$
$277$	−33.0042	−1.98303	−0.991516	+	0.129984i	$0.958508\pi$
$278$	1.19318	0.0715624
$279$	−72.8234	−4.35982
$280$	2.88493	0.172407
$281$	−19.8839	−1.18618	−0.593088	−	0.805138i	$-0.702091\pi$
$281$	−19.8839	−1.18618	−0.593088	+	0.805138i	$0.702091\pi$
$282$	−25.0283	−1.49041
$283$	−6.61804	−0.393401	−0.196701	−	0.980464i	$-0.563023\pi$
$283$	−6.61804	−0.393401	−0.196701	+	0.980464i	$0.563023\pi$
$284$	13.9997	0.830731
$285$	−5.04407	−0.298785
$286$	1.13904	0.0673527
$287$	3.91904	0.231334
$288$	−8.89471	−0.524126
$289$	−14.7011	−0.864769
$290$	−12.0386	−0.706930
$291$	−48.0370	−2.81598
$292$	−8.75839	−0.512546
$293$	−24.9643	−1.45843	−0.729215	−	0.684285i	$-0.760115\pi$
$293$	−24.9643	−1.45843	−0.729215	+	0.684285i	$0.760115\pi$
$294$	−3.44887	−0.201142
$295$	−35.1305	−2.04538
$296$	−10.9769	−0.638020
$297$	28.4582	1.65131
$298$	3.75485	0.217513
$299$	1.21636	0.0703436
$300$	11.4600	0.661641
$301$	3.82119	0.220250
$302$	24.1670	1.39066
$303$	−31.0661	−1.78470
$304$	−0.506954	−0.0290758
$305$	19.1235	1.09501
$306$	−13.4863	−0.770963
$307$	−17.3748	−0.991634	−0.495817	−	0.868427i	$-0.665131\pi$
$307$	−17.3748	−0.991634	−0.495817	+	0.868427i	$0.665131\pi$
$308$	−1.39981	−0.0797615
$309$	10.2383	0.582436
$310$	23.6197	1.34151
$311$	26.8490	1.52247	0.761235	−	0.648476i	$-0.224594\pi$
$311$	26.8490	1.52247	0.761235	+	0.648476i	$0.224594\pi$
$312$	2.80638	0.158880
$313$	1.42080	0.0803083	0.0401542	−	0.999193i	$-0.487215\pi$
$313$	1.42080	0.0803083	0.0401542	+	0.999193i	$0.487215\pi$
$314$	−10.2895	−0.580667
$315$	−25.6606	−1.44581
$316$	−0.807708	−0.0454371
$317$	−3.99781	−0.224539	−0.112270	−	0.993678i	$-0.535812\pi$
$317$	−3.99781	−0.224539	−0.112270	+	0.993678i	$0.535812\pi$
$318$	48.7482	2.73366
$319$	5.84130	0.327050
$320$	2.88493	0.161272
$321$	−61.0783	−3.40906
$322$	−1.49483	−0.0833035
$323$	−0.768655	−0.0427691
$324$	43.4317	2.41287
$325$	−2.70381	−0.149980
$326$	−18.7442	−1.03815
$327$	38.6747	2.13872
$328$	3.91904	0.216393
$329$	−7.25695	−0.400089
$330$	−13.9277	−0.766697
$331$	−3.98507	−0.219039	−0.109520	−	0.993985i	$-0.534931\pi$
$331$	−3.98507	−0.219039	−0.109520	+	0.993985i	$0.534931\pi$
$332$	13.2321	0.726209
$333$	97.6364	5.35044
$334$	−11.9597	−0.654404
$335$	39.4507	2.15542
$336$	−3.44887	−0.188151
$337$	−9.93820	−0.541368	−0.270684	−	0.962668i	$-0.587250\pi$
$337$	−9.93820	−0.541368	−0.270684	+	0.962668i	$0.587250\pi$
$338$	12.3379	0.671092
$339$	−10.8661	−0.590167
$340$	4.37419	0.237224
$341$	−11.4606	−0.620628
$342$	4.50921	0.243830
$343$	−1.00000	−0.0539949
$344$	3.82119	0.206025
$345$	−14.8731	−0.800743
$346$	−15.8121	−0.850062
$347$	−8.02651	−0.430886	−0.215443	−	0.976516i	$-0.569120\pi$
$347$	−8.02651	−0.430886	−0.215443	+	0.976516i	$0.569120\pi$
$348$	14.3919	0.771485
$349$	−6.42460	−0.343901	−0.171951	−	0.985106i	$-0.555007\pi$
$349$	−6.42460	−0.343901	−0.171951	+	0.985106i	$0.555007\pi$
$350$	3.32281	0.177612
$351$	−16.5428	−0.882989
$352$	−1.39981	−0.0746101
$353$	−16.0561	−0.854580	−0.427290	−	0.904115i	$-0.640532\pi$
$353$	−16.0561	−0.854580	−0.427290	+	0.904115i	$0.640532\pi$
$354$	41.9978	2.23216
$355$	40.3882	2.14359
$356$	6.69640	0.354909
$357$	−5.22925	−0.276761
$358$	−17.5074	−0.925295
$359$	−7.31339	−0.385986	−0.192993	−	0.981200i	$-0.561819\pi$
$359$	−7.31339	−0.385986	−0.192993	+	0.981200i	$0.561819\pi$
$360$	−25.6606	−1.35243
$361$	−18.7430	−0.986474
$362$	5.12015	0.269109
$363$	−31.1796	−1.63651
$364$	0.813710	0.0426500
$365$	−25.2673	−1.32255
$366$	−22.8618	−1.19500
$367$	32.4639	1.69460	0.847301	−	0.531113i	$-0.178226\pi$
$367$	32.4639	1.69460	0.847301	+	0.531113i	$0.178226\pi$
$368$	−1.49483	−0.0779232
$369$	−34.8588	−1.81467
$370$	−31.6676	−1.64632
$371$	14.1345	0.733829
$372$	−28.2369	−1.46401
$373$	−0.0279538	−0.00144739	−0.000723697	−	1.00000i	$-0.500230\pi$
$373$	−0.0279538	−0.00144739	−0.000723697		1.00000i	$0.500230\pi$
$374$	−2.12242	−0.109748
$375$	−16.6876	−0.861743
$376$	−7.25695	−0.374249
$377$	−3.39555	−0.174880
$378$	20.3301	1.04567
$379$	20.3187	1.04370	0.521850	−	0.853037i	$-0.325242\pi$
$379$	20.3187	1.04370	0.521850	+	0.853037i	$0.325242\pi$
$380$	−1.46253	−0.0750260
$381$	40.3735	2.06840
$382$	6.44084	0.329542
$383$	2.82960	0.144586	0.0722928	−	0.997383i	$-0.476968\pi$
$383$	2.82960	0.144586	0.0722928	+	0.997383i	$0.476968\pi$
$384$	−3.44887	−0.175999
$385$	−4.03835	−0.205813
$386$	11.4848	0.584561
$387$	−33.9884	−1.72773
$388$	−13.9283	−0.707103
$389$	3.78486	0.191900	0.0959501	−	0.995386i	$-0.469411\pi$
$389$	3.78486	0.191900	0.0959501	+	0.995386i	$0.469411\pi$
$390$	8.09621	0.409967
$391$	−2.26649	−0.114621
$392$	−1.00000	−0.0505076
$393$	−43.9072	−2.21483
$394$	−12.5723	−0.633383
$395$	−2.33018	−0.117244
$396$	12.4509	0.625681
$397$	−4.39957	−0.220808	−0.110404	−	0.993887i	$-0.535214\pi$
$397$	−4.39957	−0.220808	−0.110404	+	0.993887i	$0.535214\pi$
$398$	8.40944	0.421527
$399$	1.74842	0.0875305
$400$	3.32281	0.166141
$401$	−5.72679	−0.285982	−0.142991	−	0.989724i	$-0.545672\pi$
$401$	−5.72679	−0.285982	−0.142991	+	0.989724i	$0.545672\pi$
$402$	−47.1625	−2.35225
$403$	6.66207	0.331861
$404$	−9.00761	−0.448146
$405$	125.297	6.22608
$406$	4.17292	0.207099
$407$	15.3656	0.761643
$408$	−5.22925	−0.258887
$409$	−1.26583	−0.0625912	−0.0312956	−	0.999510i	$-0.509963\pi$
$409$	−1.26583	−0.0625912	−0.0312956	+	0.999510i	$0.509963\pi$
$410$	11.3062	0.558372
$411$	−57.7898	−2.85056
$412$	2.96859	0.146252
$413$	12.1773	0.599204
$414$	13.2960	0.653465
$415$	38.1738	1.87388
$416$	0.813710	0.0398954
$417$	−4.11514	−0.201519
$418$	0.709639	0.0347096
$419$	29.4486	1.43866	0.719330	−	0.694669i	$-0.244449\pi$
$419$	29.4486	1.43866	0.719330	+	0.694669i	$0.244449\pi$
$420$	−9.94975	−0.485498
$421$	−5.95829	−0.290389	−0.145195	−	0.989403i	$-0.546381\pi$
$421$	−5.95829	−0.290389	−0.145195	+	0.989403i	$0.546381\pi$
$422$	−20.3180	−0.989065
$423$	64.5485	3.13845
$424$	14.1345	0.686434
$425$	5.03812	0.244385
$426$	−48.2833	−2.33933
$427$	−6.62877	−0.320789
$428$	−17.7096	−0.856028
$429$	−3.92840	−0.189665
$430$	11.0239	0.531618
$431$	1.00000	0.0481683
$431$	1.00000	0.0481683
$432$	20.3301	0.978132
$433$	−41.1373	−1.97693	−0.988465	−	0.151447i	$-0.951607\pi$
$433$	−41.1373	−1.97693	−0.988465	+	0.151447i	$0.951607\pi$
$434$	−8.18728	−0.393002
$435$	41.5195	1.99071
$436$	11.2137	0.537040
$437$	0.757809	0.0362509
$438$	30.2066	1.44333
$439$	20.2397	0.965988	0.482994	−	0.875624i	$-0.339549\pi$
$439$	20.2397	0.965988	0.482994	+	0.875624i	$0.339549\pi$
$440$	−4.03835	−0.192521
$441$	8.89471	0.423558
$442$	1.23376	0.0586842
$443$	−15.4176	−0.732513	−0.366257	−	0.930514i	$-0.619361\pi$
$443$	−15.4176	−0.732513	−0.366257	+	0.930514i	$0.619361\pi$
$444$	37.8579	1.79666
$445$	19.3186	0.915791
$446$	−16.8144	−0.796184
$447$	−12.9500	−0.612513
$448$	−1.00000	−0.0472456
$449$	−38.0610	−1.79621	−0.898106	−	0.439779i	$-0.855057\pi$
$449$	−38.0610	−1.79621	−0.898106	+	0.439779i	$0.855057\pi$
$450$	−29.5555	−1.39326
$451$	−5.48591	−0.258322
$452$	−3.15063	−0.148193
$453$	−83.3490	−3.91608
$454$	−0.765435	−0.0359237
$455$	2.34749	0.110052
$456$	1.74842	0.0818773
$457$	−35.0062	−1.63752	−0.818760	−	0.574136i	$-0.805338\pi$
$457$	−35.0062	−1.63752	−0.818760	+	0.574136i	$0.805338\pi$
$458$	−2.13892	−0.0999450
$459$	30.8249	1.43878
$460$	−4.31247	−0.201070
$461$	35.8238	1.66848	0.834241	−	0.551401i	$-0.185906\pi$
$461$	35.8238	1.66848	0.834241	+	0.551401i	$0.185906\pi$
$462$	4.82776	0.224608
$463$	−10.0545	−0.467271	−0.233636	−	0.972324i	$-0.575062\pi$
$463$	−10.0545	−0.467271	−0.233636	+	0.972324i	$0.575062\pi$
$464$	4.17292	0.193723
$465$	−81.4613	−3.77768
$466$	15.6844	0.726565
$467$	−9.40099	−0.435026	−0.217513	−	0.976057i	$-0.569794\pi$
$467$	−9.40099	−0.435026	−0.217513	+	0.976057i	$0.569794\pi$
$468$	−7.23771	−0.334563
$469$	−13.6748	−0.631442
$470$	−20.9358	−0.965696
$471$	35.4870	1.63515
$472$	12.1773	0.560504
$473$	−5.34894	−0.245944
$474$	2.78568	0.127950
$475$	−1.68451	−0.0772908
$476$	−1.51622	−0.0694959
$477$	−125.723	−5.75644
$478$	23.5404	1.07671
$479$	−22.0023	−1.00531	−0.502656	−	0.864487i	$-0.667644\pi$
$479$	−22.0023	−1.00531	−0.502656	+	0.864487i	$0.667644\pi$
$480$	−9.94975	−0.454142
$481$	−8.93202	−0.407265
$482$	−18.6125	−0.847778
$483$	5.15546	0.234582
$484$	−9.04053	−0.410933
$485$	−40.1822	−1.82458
$486$	−88.8001	−4.02805
$487$	7.40984	0.335772	0.167886	−	0.985806i	$-0.446306\pi$
$487$	7.40984	0.335772	0.167886	+	0.985806i	$0.446306\pi$
$488$	−6.62877	−0.300070
$489$	64.6464	2.92341
$490$	−2.88493	−0.130328
$491$	4.49072	0.202663	0.101332	−	0.994853i	$-0.467690\pi$
$491$	4.49072	0.202663	0.101332	+	0.994853i	$0.467690\pi$
$492$	−13.5163	−0.609361
$493$	6.32708	0.284957
$494$	−0.412514	−0.0185599
$495$	35.9199	1.61448
$496$	−8.18728	−0.367620
$497$	−13.9997	−0.627974
$498$	−45.6360	−2.04500
$499$	10.8954	0.487745	0.243872	−	0.969807i	$-0.421582\pi$
$499$	10.8954	0.487745	0.243872	+	0.969807i	$0.421582\pi$
$500$	−4.83856	−0.216387
$501$	41.2473	1.84279
$502$	5.61168	0.250461
$503$	−22.6049	−1.00790	−0.503952	−	0.863732i	$-0.668121\pi$
$503$	−22.6049	−1.00790	−0.503952	+	0.863732i	$0.668121\pi$
$504$	8.89471	0.396202
$505$	−25.9863	−1.15638
$506$	2.09247	0.0930217
$507$	−42.5517	−1.88979
$508$	11.7063	0.519383
$509$	21.5103	0.953425	0.476713	−	0.879059i	$-0.341828\pi$
$509$	21.5103	0.953425	0.476713	+	0.879059i	$0.341828\pi$
$510$	−15.0860	−0.668020
$511$	8.75839	0.387449
$512$	−1.00000	−0.0441942
$513$	−10.3064	−0.455040
$514$	−15.3370	−0.676487
$515$	8.56418	0.377383
$516$	−13.1788	−0.580164
$517$	10.1584	0.446764
$518$	10.9769	0.482298
$519$	54.5338	2.39377
$520$	2.34749	0.102944
$521$	−12.3513	−0.541121	−0.270561	−	0.962703i	$-0.587209\pi$
$521$	−12.3513	−0.541121	−0.270561	+	0.962703i	$0.587209\pi$
$522$	−37.1169	−1.62456
$523$	−28.7508	−1.25719	−0.628593	−	0.777735i	$-0.716369\pi$
$523$	−28.7508	−1.25719	−0.628593	+	0.777735i	$0.716369\pi$
$524$	−12.7309	−0.556152
$525$	−11.4600	−0.500153
$526$	−15.4310	−0.672822
$527$	−12.4137	−0.540750
$528$	4.82776	0.210101
$529$	−20.7655	−0.902847
$530$	40.7771	1.77125
$531$	−108.313	−4.70039
$532$	0.506954	0.0219793
$533$	3.18896	0.138129
$534$	−23.0950	−0.999419
$535$	−51.0911	−2.20886
$536$	−13.6748	−0.590660
$537$	60.3808	2.60562
$538$	9.37756	0.404295
$539$	1.39981	0.0602940
$540$	58.6508	2.52393
$541$	23.3418	1.00354	0.501772	−	0.865000i	$-0.332682\pi$
$541$	23.3418	1.00354	0.501772	+	0.865000i	$0.332682\pi$
$542$	−7.35841	−0.316071
$543$	−17.6587	−0.757809
$544$	−1.51622	−0.0650075
$545$	32.3508	1.38576
$546$	−2.80638	−0.120102
$547$	−15.1423	−0.647437	−0.323718	−	0.946153i	$-0.604933\pi$
$547$	−15.1423	−0.647437	−0.323718	+	0.946153i	$0.604933\pi$
$548$	−16.7561	−0.715787
$549$	58.9610	2.51639
$550$	−4.65130	−0.198332
$551$	−2.11548	−0.0901225
$552$	5.15546	0.219431
$553$	0.807708	0.0343472
$554$	33.0042	1.40222
$555$	109.217	4.63602
$556$	−1.19318	−0.0506023
$557$	19.9462	0.845146	0.422573	−	0.906329i	$-0.361127\pi$
$557$	19.9462	0.845146	0.422573	+	0.906329i	$0.361127\pi$
$558$	72.8234	3.08286
$559$	3.10934	0.131511
$560$	−2.88493	−0.121910
$561$	7.31995	0.309049
$562$	19.8839	0.838752
$563$	−30.5479	−1.28744	−0.643721	−	0.765260i	$-0.722610\pi$
$563$	−30.5479	−1.28744	−0.643721	+	0.765260i	$0.722610\pi$
$564$	25.0283	1.05388
$565$	−9.08935	−0.382392
$566$	6.61804	0.278177
$567$	−43.4317	−1.82396
$568$	−13.9997	−0.587416
$569$	10.8653	0.455498	0.227749	−	0.973720i	$-0.426863\pi$
$569$	10.8653	0.455498	0.227749	+	0.973720i	$0.426863\pi$
$570$	5.04407	0.211273
$571$	−19.3945	−0.811635	−0.405818	−	0.913954i	$-0.633013\pi$
$571$	−19.3945	−0.811635	−0.405818	+	0.913954i	$0.633013\pi$
$572$	−1.13904	−0.0476256
$573$	−22.2136	−0.927988
$574$	−3.91904	−0.163578
$575$	−4.96703	−0.207140
$576$	8.89471	0.370613
$577$	−28.5494	−1.18853	−0.594263	−	0.804271i	$-0.702556\pi$
$577$	−28.5494	−1.18853	−0.594263	+	0.804271i	$0.702556\pi$
$578$	14.7011	0.611484
$579$	−39.6096	−1.64612
$580$	12.0386	0.499875
$581$	−13.2321	−0.548962
$582$	48.0370	1.99120
$583$	−19.7857	−0.819438
$584$	8.75839	0.362425
$585$	−20.8803	−0.863293
$586$	24.9643	1.03127
$587$	20.2952	0.837673	0.418836	−	0.908062i	$-0.362438\pi$
$587$	20.2952	0.837673	0.418836	+	0.908062i	$0.362438\pi$
$588$	3.44887	0.142229
$589$	4.15057	0.171021
$590$	35.1305	1.44630
$591$	43.3602	1.78360
$592$	10.9769	0.451148
$593$	23.5236	0.965997	0.482998	−	0.875621i	$-0.339548\pi$
$593$	23.5236	0.965997	0.482998	+	0.875621i	$0.339548\pi$
$594$	−28.4582	−1.16766
$595$	−4.37419	−0.179324
$596$	−3.75485	−0.153805
$597$	−29.0031	−1.18702
$598$	−1.21636	−0.0497405
$599$	25.2716	1.03257	0.516285	−	0.856417i	$-0.327315\pi$
$599$	25.2716	1.03257	0.516285	+	0.856417i	$0.327315\pi$
$600$	−11.4600	−0.467851
$601$	−41.2633	−1.68317	−0.841583	−	0.540127i	$-0.818376\pi$
$601$	−41.2633	−1.68317	−0.841583	+	0.540127i	$0.818376\pi$
$602$	−3.82119	−0.155740
$603$	121.633	4.95328
$604$	−24.1670	−0.983343
$605$	−26.0813	−1.06036
$606$	31.0661	1.26197
$607$	−30.0189	−1.21843	−0.609214	−	0.793006i	$-0.708515\pi$
$607$	−30.0189	−1.21843	−0.609214	+	0.793006i	$0.708515\pi$
$608$	0.506954	0.0205597
$609$	−14.3919	−0.583188
$610$	−19.1235	−0.774289
$611$	−5.90505	−0.238893
$612$	13.4863	0.545153
$613$	−10.9740	−0.443235	−0.221618	−	0.975134i	$-0.571134\pi$
$613$	−10.9740	−0.443235	−0.221618	+	0.975134i	$0.571134\pi$
$614$	17.3748	0.701191
$615$	−38.9935	−1.57237
$616$	1.39981	0.0563999
$617$	35.3320	1.42241	0.711207	−	0.702983i	$-0.248149\pi$
$617$	35.3320	1.42241	0.711207	+	0.702983i	$0.248149\pi$
$618$	−10.2383	−0.411845
$619$	42.1930	1.69588	0.847940	−	0.530092i	$-0.177843\pi$
$619$	42.1930	1.69588	0.847940	+	0.530092i	$0.177843\pi$
$620$	−23.6197	−0.948590
$621$	−30.3900	−1.21951
$622$	−26.8490	−1.07655
$623$	−6.69640	−0.268286
$624$	−2.80638	−0.112345
$625$	−30.5730	−1.22292
$626$	−1.42080	−0.0567866
$627$	−2.44745	−0.0977419
$628$	10.2895	0.410594
$629$	16.6434	0.663617
$630$	25.6606	1.02234
$631$	25.3937	1.01091	0.505453	−	0.862854i	$-0.331325\pi$
$631$	25.3937	1.01091	0.505453	+	0.862854i	$0.331325\pi$
$632$	0.807708	0.0321289
$633$	70.0742	2.78520
$634$	3.99781	0.158773
$635$	33.7718	1.34019
$636$	−48.7482	−1.93299
$637$	−0.813710	−0.0322404
$638$	−5.84130	−0.231259
$639$	124.524	4.92608
$640$	−2.88493	−0.114037
$641$	39.3977	1.55611	0.778057	−	0.628193i	$-0.216205\pi$
$641$	39.3977	1.55611	0.778057	+	0.628193i	$0.216205\pi$
$642$	61.0783	2.41057
$643$	−16.1099	−0.635311	−0.317656	−	0.948206i	$-0.602896\pi$
$643$	−16.1099	−0.635311	−0.317656	+	0.948206i	$0.602896\pi$
$644$	1.49483	0.0589044
$645$	−38.0199	−1.49703
$646$	0.768655	0.0302423
$647$	0.347065	0.0136446	0.00682228	−	0.999977i	$-0.497828\pi$
$647$	0.347065	0.0136446	0.00682228	+	0.999977i	$0.497828\pi$
$648$	−43.4317	−1.70616
$649$	−17.0458	−0.669108
$650$	2.70381	0.106052
$651$	28.2369	1.10669
$652$	18.7442	0.734080
$653$	20.7225	0.810936	0.405468	−	0.914109i	$-0.367109\pi$
$653$	20.7225	0.810936	0.405468	+	0.914109i	$0.367109\pi$
$654$	−38.6747	−1.51230
$655$	−36.7277	−1.43507
$656$	−3.91904	−0.153013
$657$	−77.9034	−3.03930
$658$	7.25695	0.282906
$659$	−37.4476	−1.45875	−0.729375	−	0.684114i	$-0.760189\pi$
$659$	−37.4476	−1.45875	−0.729375	+	0.684114i	$0.760189\pi$
$660$	13.9277	0.542137
$661$	10.1868	0.396220	0.198110	−	0.980180i	$-0.436520\pi$
$661$	10.1868	0.396220	0.198110	+	0.980180i	$0.436520\pi$
$662$	3.98507	0.154884
$663$	−4.25509	−0.165254
$664$	−13.2321	−0.513507
$665$	1.46253	0.0567144
$666$	−97.6364	−3.78333
$667$	−6.23780	−0.241529
$668$	11.9597	0.462733
$669$	57.9907	2.24205
$670$	−39.4507	−1.52411
$671$	9.27901	0.358212
$672$	3.44887	0.133043
$673$	10.1635	0.391774	0.195887	−	0.980627i	$-0.437241\pi$
$673$	10.1635	0.391774	0.195887	+	0.980627i	$0.437241\pi$
$674$	9.93820	0.382805
$675$	67.5531	2.60012
$676$	−12.3379	−0.474534
$677$	15.9137	0.611611	0.305806	−	0.952094i	$-0.401074\pi$
$677$	15.9137	0.611611	0.305806	+	0.952094i	$0.401074\pi$
$678$	10.8661	0.417311
$679$	13.9283	0.534520
$680$	−4.37419	−0.167743
$681$	2.63989	0.101161
$682$	11.4606	0.438850
$683$	7.27962	0.278547	0.139274	−	0.990254i	$-0.455523\pi$
$683$	7.27962	0.278547	0.139274	+	0.990254i	$0.455523\pi$
$684$	−4.50921	−0.172414
$685$	−48.3403	−1.84699
$686$	1.00000	0.0381802
$687$	7.37685	0.281444
$688$	−3.82119	−0.145682
$689$	11.5014	0.438169
$690$	14.8731	0.566211
$691$	45.2006	1.71951	0.859756	−	0.510705i	$-0.170616\pi$
$691$	45.2006	1.71951	0.859756	+	0.510705i	$0.170616\pi$
$692$	15.8121	0.601084
$693$	−12.4509	−0.472970
$694$	8.02651	0.304682
$695$	−3.44225	−0.130572
$696$	−14.3919	−0.545523
$697$	−5.94214	−0.225075
$698$	6.42460	0.243175
$699$	−54.0934	−2.04600
$700$	−3.32281	−0.125591
$701$	8.69132	0.328267	0.164133	−	0.986438i	$-0.447517\pi$
$701$	8.69132	0.328267	0.164133	+	0.986438i	$0.447517\pi$
$702$	16.5428	0.624367
$703$	−5.56479	−0.209880
$704$	1.39981	0.0527573
$705$	72.2049	2.71939
$706$	16.0561	0.604279
$707$	9.00761	0.338766
$708$	−41.9978	−1.57837
$709$	−40.7256	−1.52948	−0.764740	−	0.644339i	$-0.777133\pi$
$709$	−40.7256	−1.52948	−0.764740	+	0.644339i	$0.777133\pi$
$710$	−40.3882	−1.51574
$711$	−7.18432	−0.269433
$712$	−6.69640	−0.250958
$713$	12.2386	0.458338
$714$	5.22925	0.195700
$715$	−3.28604	−0.122891
$716$	17.5074	0.654282
$717$	−81.1878	−3.03201
$718$	7.31339	0.272933
$719$	13.8921	0.518087	0.259044	−	0.965866i	$-0.416593\pi$
$719$	13.8921	0.518087	0.259044	+	0.965866i	$0.416593\pi$
$720$	25.6606	0.956314
$721$	−2.96859	−0.110556
$722$	18.7430	0.697542
$723$	64.1923	2.38734
$724$	−5.12015	−0.190289
$725$	13.8658	0.514965
$726$	31.1796	1.15718
$727$	−4.78903	−0.177615	−0.0888077	−	0.996049i	$-0.528306\pi$
$727$	−4.78903	−0.177615	−0.0888077	+	0.996049i	$0.528306\pi$
$728$	−0.813710	−0.0301581
$729$	175.965	6.51722
$730$	25.2673	0.935186
$731$	−5.79377	−0.214290
$732$	22.8618	0.844995
$733$	13.0004	0.480180	0.240090	−	0.970751i	$-0.422823\pi$
$733$	13.0004	0.480180	0.240090	+	0.970751i	$0.422823\pi$
$734$	−32.4639	−1.19826
$735$	9.94975	0.367002
$736$	1.49483	0.0551001
$737$	19.1421	0.705107
$738$	34.8588	1.28317
$739$	−32.1791	−1.18373	−0.591864	−	0.806038i	$-0.701608\pi$
$739$	−32.1791	−1.18373	−0.591864	+	0.806038i	$0.701608\pi$
$740$	31.6676	1.16412
$741$	1.42271	0.0522644
$742$	−14.1345	−0.518895
$743$	−1.21978	−0.0447494	−0.0223747	−	0.999750i	$-0.507123\pi$
$743$	−1.21978	−0.0447494	−0.0223747	+	0.999750i	$0.507123\pi$
$744$	28.2369	1.03521
$745$	−10.8325	−0.396871
$746$	0.0279538	0.00102346
$747$	117.696	4.30628
$748$	2.12242	0.0776034
$749$	17.7096	0.647096
$750$	16.6876	0.609344
$751$	−8.95682	−0.326839	−0.163419	−	0.986557i	$-0.552252\pi$
$751$	−8.95682	−0.326839	−0.163419	+	0.986557i	$0.552252\pi$
$752$	7.25695	0.264634
$753$	−19.3539	−0.705297
$754$	3.39555	0.123659
$755$	−69.7202	−2.53738
$756$	−20.3301	−0.739398
$757$	9.97200	0.362438	0.181219	−	0.983443i	$-0.441996\pi$
$757$	9.97200	0.362438	0.181219	+	0.983443i	$0.441996\pi$
$758$	−20.3187	−0.738008
$759$	−7.21667	−0.261948
$760$	1.46253	0.0530514
$761$	6.63713	0.240596	0.120298	−	0.992738i	$-0.461615\pi$
$761$	6.63713	0.240596	0.120298	+	0.992738i	$0.461615\pi$
$762$	−40.3735	−1.46258
$763$	−11.2137	−0.405964
$764$	−6.44084	−0.233022
$765$	38.9071	1.40669
$766$	−2.82960	−0.102238
$767$	9.90876	0.357785
$768$	3.44887	0.124450
$769$	39.5679	1.42686	0.713428	−	0.700729i	$-0.247142\pi$
$769$	39.5679	1.42686	0.713428	+	0.700729i	$0.247142\pi$
$770$	4.03835	0.145532
$771$	52.8954	1.90498
$772$	−11.4848	−0.413347
$773$	13.2797	0.477639	0.238820	−	0.971064i	$-0.423240\pi$
$773$	13.2797	0.477639	0.238820	+	0.971064i	$0.423240\pi$
$774$	33.9884	1.22169
$775$	−27.2048	−0.977225
$776$	13.9283	0.499997
$777$	−37.8579	−1.35815
$778$	−3.78486	−0.135694
$779$	1.98678	0.0711836
$780$	−8.09621	−0.289891
$781$	19.5970	0.701234
$782$	2.26649	0.0810495
$783$	84.8359	3.03179
$784$	1.00000	0.0357143
$785$	29.6843	1.05948
$786$	43.9072	1.56612
$787$	−14.6636	−0.522701	−0.261351	−	0.965244i	$-0.584168\pi$
$787$	−14.6636	−0.522701	−0.261351	+	0.965244i	$0.584168\pi$
$788$	12.5723	0.447869
$789$	53.2194	1.89466
$790$	2.33018	0.0829040
$791$	3.15063	0.112024
$792$	−12.4509	−0.442423
$793$	−5.39389	−0.191543
$794$	4.39957	0.156135
$795$	−140.635	−4.98781
$796$	−8.40944	−0.298065
$797$	−42.6633	−1.51121	−0.755606	−	0.655026i	$-0.772658\pi$
$797$	−42.6633	−1.51121	−0.755606	+	0.655026i	$0.772658\pi$
$798$	−1.74842	−0.0618934
$799$	11.0031	0.389263
$800$	−3.32281	−0.117479
$801$	59.5625	2.10454
$802$	5.72679	0.202220
$803$	−12.2601	−0.432649
$804$	47.1625	1.66329
$805$	4.31247	0.151995
$806$	−6.66207	−0.234661
$807$	−32.3420	−1.13849
$808$	9.00761	0.316887
$809$	22.6563	0.796554	0.398277	−	0.917265i	$-0.369608\pi$
$809$	22.6563	0.796554	0.398277	+	0.917265i	$0.369608\pi$
$810$	−125.297	−4.40250
$811$	13.9754	0.490742	0.245371	−	0.969429i	$-0.421090\pi$
$811$	13.9754	0.490742	0.245371	+	0.969429i	$0.421090\pi$
$812$	−4.17292	−0.146441
$813$	25.3782	0.890053
$814$	−15.3656	−0.538563
$815$	54.0757	1.89419
$816$	5.22925	0.183060
$817$	1.93717	0.0677730
$818$	1.26583	0.0442586
$819$	7.23771	0.252906
$820$	−11.3062	−0.394828
$821$	−22.6258	−0.789645	−0.394822	−	0.918757i	$-0.629194\pi$
$821$	−22.6258	−0.789645	−0.394822	+	0.918757i	$0.629194\pi$
$822$	57.7898	2.01565
$823$	19.6399	0.684605	0.342302	−	0.939590i	$-0.388793\pi$
$823$	19.6399	0.684605	0.342302	+	0.939590i	$0.388793\pi$
$824$	−2.96859	−0.103416
$825$	16.0417	0.558502
$826$	−12.1773	−0.423701
$827$	34.0024	1.18238	0.591189	−	0.806533i	$-0.298659\pi$
$827$	34.0024	1.18238	0.591189	+	0.806533i	$0.298659\pi$
$828$	−13.2960	−0.462070
$829$	2.03878	0.0708097	0.0354048	−	0.999373i	$-0.488728\pi$
$829$	2.03878	0.0708097	0.0354048	+	0.999373i	$0.488728\pi$
$830$	−38.1738	−1.32503
$831$	−113.827	−3.94863
$832$	−0.813710	−0.0282103
$833$	1.51622	0.0525340
$834$	4.11514	0.142496
$835$	34.5028	1.19402
$836$	−0.709639	−0.0245434
$837$	−166.448	−5.75329
$838$	−29.4486	−1.01729
$839$	3.99221	0.137827	0.0689133	−	0.997623i	$-0.478047\pi$
$839$	3.99221	0.137827	0.0689133	+	0.997623i	$0.478047\pi$
$840$	9.94975	0.343299
$841$	−11.5867	−0.399542
$842$	5.95829	0.205336
$843$	−68.5771	−2.36192
$844$	20.3180	0.699375
$845$	−35.5939	−1.22447
$846$	−64.5485	−2.21922
$847$	9.04053	0.310636
$848$	−14.1345	−0.485382
$849$	−22.8248	−0.783343
$850$	−5.03812	−0.172806
$851$	−16.4086	−0.562479
$852$	48.2833	1.65416
$853$	21.2578	0.727853	0.363927	−	0.931428i	$-0.381436\pi$
$853$	21.2578	0.727853	0.363927	+	0.931428i	$0.381436\pi$
$854$	6.62877	0.226832
$855$	−13.0087	−0.444890
$856$	17.7096	0.605303
$857$	−26.3946	−0.901622	−0.450811	−	0.892619i	$-0.648865\pi$
$857$	−26.3946	−0.901622	−0.450811	+	0.892619i	$0.648865\pi$
$858$	3.92840	0.134113
$859$	7.35153	0.250831	0.125416	−	0.992104i	$-0.459974\pi$
$859$	7.35153	0.250831	0.125416	+	0.992104i	$0.459974\pi$
$860$	−11.0239	−0.375911
$861$	13.5163	0.460633
$862$	−1.00000	−0.0340601
$863$	−8.80994	−0.299894	−0.149947	−	0.988694i	$-0.547910\pi$
$863$	−8.80994	−0.299894	−0.149947	+	0.988694i	$0.547910\pi$
$864$	−20.3301	−0.691644
$865$	45.6167	1.55101
$866$	41.1373	1.39790
$867$	−50.7021	−1.72193
$868$	8.18728	0.277894
$869$	−1.13064	−0.0383542
$870$	−41.5195	−1.40764
$871$	−11.1273	−0.377034
$872$	−11.2137	−0.379745
$873$	−123.888	−4.19298
$874$	−0.757809	−0.0256333
$875$	4.83856	0.163573
$876$	−30.2066	−1.02059
$877$	16.1128	0.544091	0.272046	−	0.962284i	$-0.412300\pi$
$877$	16.1128	0.544091	0.272046	+	0.962284i	$0.412300\pi$
$878$	−20.2397	−0.683057
$879$	−86.0987	−2.90404
$880$	4.03835	0.136133
$881$	1.18723	0.0399989	0.0199995	−	0.999800i	$-0.493634\pi$
$881$	1.18723	0.0399989	0.0199995	+	0.999800i	$0.493634\pi$
$882$	−8.89471	−0.299500
$883$	−43.5460	−1.46544	−0.732720	−	0.680531i	$-0.761749\pi$
$883$	−43.5460	−1.46544	−0.732720	+	0.680531i	$0.761749\pi$
$884$	−1.23376	−0.0414960
$885$	−121.161	−4.07277
$886$	15.4176	0.517965
$887$	13.4084	0.450210	0.225105	−	0.974334i	$-0.427727\pi$
$887$	13.4084	0.450210	0.225105	+	0.974334i	$0.427727\pi$
$888$	−37.8579	−1.27043
$889$	−11.7063	−0.392617
$890$	−19.3186	−0.647562
$891$	60.7961	2.03675
$892$	16.8144	0.562987
$893$	−3.67894	−0.123111
$894$	12.9500	0.433112
$895$	50.5076	1.68828
$896$	1.00000	0.0334077
$897$	4.19505	0.140069
$898$	38.0610	1.27011
$899$	−34.1649	−1.13946
$900$	29.5555	0.985182
$901$	−21.4311	−0.713973
$902$	5.48591	0.182661
$903$	13.1788	0.438563
$904$	3.15063	0.104788
$905$	−14.7713	−0.491014
$906$	83.3490	2.76908
$907$	3.33376	0.110696	0.0553479	−	0.998467i	$-0.482373\pi$
$907$	3.33376	0.110696	0.0553479	+	0.998467i	$0.482373\pi$
$908$	0.765435	0.0254019
$909$	−80.1201	−2.65742
$910$	−2.34749	−0.0778187
$911$	20.0045	0.662778	0.331389	−	0.943494i	$-0.392483\pi$
$911$	20.0045	0.662778	0.331389	+	0.943494i	$0.392483\pi$
$912$	−1.74842	−0.0578960
$913$	18.5225	0.613005
$914$	35.0062	1.15790
$915$	65.9546	2.18039
$916$	2.13892	0.0706718
$917$	12.7309	0.420411
$918$	−30.8249	−1.01737
$919$	15.5179	0.511888	0.255944	−	0.966692i	$-0.417614\pi$
$919$	15.5179	0.511888	0.255944	+	0.966692i	$0.417614\pi$
$920$	4.31247	0.142178
$921$	−59.9236	−1.97455
$922$	−35.8238	−1.17979
$923$	−11.3917	−0.374963
$924$	−4.82776	−0.158822
$925$	36.4742	1.19926
$926$	10.0545	0.330411
$927$	26.4048	0.867247
$928$	−4.17292	−0.136983
$929$	39.7803	1.30515	0.652575	−	0.757724i	$-0.273689\pi$
$929$	39.7803	1.30515	0.652575	+	0.757724i	$0.273689\pi$
$930$	81.4613	2.67122
$931$	−0.506954	−0.0166148
$932$	−15.6844	−0.513759
$933$	92.5989	3.03155
$934$	9.40099	0.307610
$935$	6.12303	0.200245
$936$	7.23771	0.236572
$937$	20.0017	0.653427	0.326714	−	0.945123i	$-0.394059\pi$
$937$	20.0017	0.653427	0.326714	+	0.945123i	$0.394059\pi$
$938$	13.6748	0.446497
$939$	4.90015	0.159910
$940$	20.9358	0.682850
$941$	−4.93655	−0.160927	−0.0804635	−	0.996758i	$-0.525640\pi$
$941$	−4.93655	−0.160927	−0.0804635	+	0.996758i	$0.525640\pi$
$942$	−35.4870	−1.15623
$943$	5.85829	0.190772
$944$	−12.1773	−0.396336
$945$	−58.6508	−1.90791
$946$	5.34894	0.173909
$947$	10.0072	0.325189	0.162594	−	0.986693i	$-0.448014\pi$
$947$	10.0072	0.325189	0.162594	+	0.986693i	$0.448014\pi$
$948$	−2.78568	−0.0904746
$949$	7.12679	0.231345
$950$	1.68451	0.0546529
$951$	−13.7879	−0.447104
$952$	1.51622	0.0491410
$953$	29.3799	0.951709	0.475855	−	0.879524i	$-0.342139\pi$
$953$	29.3799	0.951709	0.475855	+	0.879524i	$0.342139\pi$
$954$	125.723	4.07042
$955$	−18.5814	−0.601279
$956$	−23.5404	−0.761351
$957$	20.1459	0.651224
$958$	22.0023	0.710863
$959$	16.7561	0.541084
$960$	9.94975	0.321127
$961$	36.0315	1.16231
$962$	8.93202	0.287980
$963$	−157.522	−5.07608
$964$	18.6125	0.599470
$965$	−33.1328	−1.06658
$966$	−5.15546	−0.165874
$967$	35.9698	1.15671	0.578355	−	0.815785i	$-0.303695\pi$
$967$	35.9698	1.15671	0.578355	+	0.815785i	$0.303695\pi$
$968$	9.04053	0.290574
$969$	−2.65099	−0.0851621
$970$	40.1822	1.29017
$971$	−6.85280	−0.219917	−0.109958	−	0.993936i	$-0.535072\pi$
$971$	−6.85280	−0.219917	−0.109958	+	0.993936i	$0.535072\pi$
$972$	88.8001	2.84826
$973$	1.19318	0.0382517
$974$	−7.40984	−0.237427
$975$	−9.32508	−0.298641
$976$	6.62877	0.212182
$977$	−27.8112	−0.889759	−0.444879	−	0.895590i	$-0.646753\pi$
$977$	−27.8112	−0.889759	−0.444879	+	0.895590i	$0.646753\pi$
$978$	−64.6464	−2.06716
$979$	9.37368	0.299584
$980$	2.88493	0.0921557
$981$	99.7429	3.18454
$982$	−4.49072	−0.143305
$983$	−39.1304	−1.24807	−0.624033	−	0.781398i	$-0.714507\pi$
$983$	−39.1304	−1.24807	−0.624033	+	0.781398i	$0.714507\pi$
$984$	13.5163	0.430883
$985$	36.2702	1.15566
$986$	−6.32708	−0.201495
$987$	−25.0283	−0.796659
$988$	0.412514	0.0131238
$989$	5.71202	0.181632
$990$	−35.9199	−1.14161
$991$	−20.5780	−0.653682	−0.326841	−	0.945079i	$-0.605984\pi$
$991$	−20.5780	−0.653682	−0.326841	+	0.945079i	$0.605984\pi$
$992$	8.18728	0.259946
$993$	−13.7440	−0.436152
$994$	13.9997	0.444045
$995$	−24.2606	−0.769114
$996$	45.6360	1.44603
$997$	−56.9024	−1.80212	−0.901059	−	0.433697i	$-0.857209\pi$
$997$	−56.9024	−1.80212	−0.901059	+	0.433697i	$0.857209\pi$
$998$	−10.8954	−0.344887
$999$	223.161	7.06052

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.n.1.24	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.n.1.24	✓	24	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:	\( N \)	\(=\)	\( 6034 = 2 \cdot 7 \cdot 431 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +3.44887 q^{3} +1.00000 q^{4} +2.88493 q^{5} -3.44887 q^{6} -1.00000 q^{7} -1.00000 q^{8} +8.89471 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +3.44887 q^{3} +1.00000 q^{4} +2.88493 q^{5} -3.44887 q^{6} -1.00000 q^{7} -1.00000 q^{8} +8.89471 q^{9} -2.88493 q^{10} +1.39981 q^{11} +3.44887 q^{12} -0.813710 q^{13} +1.00000 q^{14} +9.94975 q^{15} +1.00000 q^{16} +1.51622 q^{17} -8.89471 q^{18} -0.506954 q^{19} +2.88493 q^{20} -3.44887 q^{21} -1.39981 q^{22} -1.49483 q^{23} -3.44887 q^{24} +3.32281 q^{25} +0.813710 q^{26} +20.3301 q^{27} -1.00000 q^{28} +4.17292 q^{29} -9.94975 q^{30} -8.18728 q^{31} -1.00000 q^{32} +4.82776 q^{33} -1.51622 q^{34} -2.88493 q^{35} +8.89471 q^{36} +10.9769 q^{37} +0.506954 q^{38} -2.80638 q^{39} -2.88493 q^{40} -3.91904 q^{41} +3.44887 q^{42} -3.82119 q^{43} +1.39981 q^{44} +25.6606 q^{45} +1.49483 q^{46} +7.25695 q^{47} +3.44887 q^{48} +1.00000 q^{49} -3.32281 q^{50} +5.22925 q^{51} -0.813710 q^{52} -14.1345 q^{53} -20.3301 q^{54} +4.03835 q^{55} +1.00000 q^{56} -1.74842 q^{57} -4.17292 q^{58} -12.1773 q^{59} +9.94975 q^{60} +6.62877 q^{61} +8.18728 q^{62} -8.89471 q^{63} +1.00000 q^{64} -2.34749 q^{65} -4.82776 q^{66} +13.6748 q^{67} +1.51622 q^{68} -5.15546 q^{69} +2.88493 q^{70} +13.9997 q^{71} -8.89471 q^{72} -8.75839 q^{73} -10.9769 q^{74} +11.4600 q^{75} -0.506954 q^{76} -1.39981 q^{77} +2.80638 q^{78} -0.807708 q^{79} +2.88493 q^{80} +43.4317 q^{81} +3.91904 q^{82} +13.2321 q^{83} -3.44887 q^{84} +4.37419 q^{85} +3.82119 q^{86} +14.3919 q^{87} -1.39981 q^{88} +6.69640 q^{89} -25.6606 q^{90} +0.813710 q^{91} -1.49483 q^{92} -28.2369 q^{93} -7.25695 q^{94} -1.46253 q^{95} -3.44887 q^{96} -13.9283 q^{97} -1.00000 q^{98} +12.4509 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{2} + 7 q^{3} + 24 q^{4} + 8 q^{5} - 7 q^{6} - 24 q^{7} - 24 q^{8} + 19 q^{9}+O(q^{10}) \) 24 * q - 24 * q^2 + 7 * q^3 + 24 * q^4 + 8 * q^5 - 7 * q^6 - 24 * q^7 - 24 * q^8 + 19 * q^9	\( 24 q - 24 q^{2} + 7 q^{3} + 24 q^{4} + 8 q^{5} - 7 q^{6} - 24 q^{7} - 24 q^{8} + 19 q^{9} - 8 q^{10} + 15 q^{11} + 7 q^{12} - 7 q^{13} + 24 q^{14} + 13 q^{15} + 24 q^{16} - 5 q^{17} - 19 q^{18} + 6 q^{19} + 8 q^{20} - 7 q^{21} - 15 q^{22} + 3 q^{23} - 7 q^{24} + 12 q^{25} + 7 q^{26} + 22 q^{27} - 24 q^{28} + 5 q^{29} - 13 q^{30} + 13 q^{31} - 24 q^{32} - 8 q^{33} + 5 q^{34} - 8 q^{35} + 19 q^{36} + 2 q^{37} - 6 q^{38} + 7 q^{39} - 8 q^{40} + 25 q^{41} + 7 q^{42} - 15 q^{43} + 15 q^{44} + 41 q^{45} - 3 q^{46} + 35 q^{47} + 7 q^{48} + 24 q^{49} - 12 q^{50} + 31 q^{51} - 7 q^{52} + 2 q^{53} - 22 q^{54} + 14 q^{55} + 24 q^{56} - 13 q^{57} - 5 q^{58} + 35 q^{59} + 13 q^{60} - 7 q^{61} - 13 q^{62} - 19 q^{63} + 24 q^{64} - 4 q^{65} + 8 q^{66} + 10 q^{67} - 5 q^{68} + 6 q^{69} + 8 q^{70} + 58 q^{71} - 19 q^{72} + 9 q^{73} - 2 q^{74} + 7 q^{75} + 6 q^{76} - 15 q^{77} - 7 q^{78} + 31 q^{79} + 8 q^{80} + 16 q^{81} - 25 q^{82} - q^{83} - 7 q^{84} - 4 q^{85} + 15 q^{86} + 30 q^{87} - 15 q^{88} + 45 q^{89} - 41 q^{90} + 7 q^{91} + 3 q^{92} + 25 q^{93} - 35 q^{94} - 10 q^{95} - 7 q^{96} - 9 q^{97} - 24 q^{98} + 64 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 + 7 * q^3 + 24 * q^4 + 8 * q^5 - 7 * q^6 - 24 * q^7 - 24 * q^8 + 19 * q^9 - 8 * q^10 + 15 * q^11 + 7 * q^12 - 7 * q^13 + 24 * q^14 + 13 * q^15 + 24 * q^16 - 5 * q^17 - 19 * q^18 + 6 * q^19 + 8 * q^20 - 7 * q^21 - 15 * q^22 + 3 * q^23 - 7 * q^24 + 12 * q^25 + 7 * q^26 + 22 * q^27 - 24 * q^28 + 5 * q^29 - 13 * q^30 + 13 * q^31 - 24 * q^32 - 8 * q^33 + 5 * q^34 - 8 * q^35 + 19 * q^36 + 2 * q^37 - 6 * q^38 + 7 * q^39 - 8 * q^40 + 25 * q^41 + 7 * q^42 - 15 * q^43 + 15 * q^44 + 41 * q^45 - 3 * q^46 + 35 * q^47 + 7 * q^48 + 24 * q^49 - 12 * q^50 + 31 * q^51 - 7 * q^52 + 2 * q^53 - 22 * q^54 + 14 * q^55 + 24 * q^56 - 13 * q^57 - 5 * q^58 + 35 * q^59 + 13 * q^60 - 7 * q^61 - 13 * q^62 - 19 * q^63 + 24 * q^64 - 4 * q^65 + 8 * q^66 + 10 * q^67 - 5 * q^68 + 6 * q^69 + 8 * q^70 + 58 * q^71 - 19 * q^72 + 9 * q^73 - 2 * q^74 + 7 * q^75 + 6 * q^76 - 15 * q^77 - 7 * q^78 + 31 * q^79 + 8 * q^80 + 16 * q^81 - 25 * q^82 - q^83 - 7 * q^84 - 4 * q^85 + 15 * q^86 + 30 * q^87 - 15 * q^88 + 45 * q^89 - 41 * q^90 + 7 * q^91 + 3 * q^92 + 25 * q^93 - 35 * q^94 - 10 * q^95 - 7 * q^96 - 9 * q^97 - 24 * q^98 + 64 * q^99

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