LMFDB - Embedded newform 6018.2.a.ba.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("6018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			1.6
Root			$1.26686$ of defining polynomial
Character	$\chi$	$=$	6018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.266858 q^{5} +1.00000 q^{6} +0.661205 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.266858 q^{5} +1.00000 q^{6} +0.661205 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.266858 q^{10} +6.00384 q^{11} +1.00000 q^{12} +4.92511 q^{13} +0.661205 q^{14} -0.266858 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} +2.93564 q^{19} -0.266858 q^{20} +0.661205 q^{21} +6.00384 q^{22} +3.23768 q^{23} +1.00000 q^{24} -4.92879 q^{25} +4.92511 q^{26} +1.00000 q^{27} +0.661205 q^{28} +2.82398 q^{29} -0.266858 q^{30} +3.09749 q^{31} +1.00000 q^{32} +6.00384 q^{33} -1.00000 q^{34} -0.176448 q^{35} +1.00000 q^{36} -8.66526 q^{37} +2.93564 q^{38} +4.92511 q^{39} -0.266858 q^{40} -2.52649 q^{41} +0.661205 q^{42} +7.24921 q^{43} +6.00384 q^{44} -0.266858 q^{45} +3.23768 q^{46} -7.06213 q^{47} +1.00000 q^{48} -6.56281 q^{49} -4.92879 q^{50} -1.00000 q^{51} +4.92511 q^{52} -12.8630 q^{53} +1.00000 q^{54} -1.60217 q^{55} +0.661205 q^{56} +2.93564 q^{57} +2.82398 q^{58} +1.00000 q^{59} -0.266858 q^{60} -5.51956 q^{61} +3.09749 q^{62} +0.661205 q^{63} +1.00000 q^{64} -1.31430 q^{65} +6.00384 q^{66} +9.08239 q^{67} -1.00000 q^{68} +3.23768 q^{69} -0.176448 q^{70} +0.403782 q^{71} +1.00000 q^{72} -8.85398 q^{73} -8.66526 q^{74} -4.92879 q^{75} +2.93564 q^{76} +3.96977 q^{77} +4.92511 q^{78} -3.21467 q^{79} -0.266858 q^{80} +1.00000 q^{81} -2.52649 q^{82} +5.07674 q^{83} +0.661205 q^{84} +0.266858 q^{85} +7.24921 q^{86} +2.82398 q^{87} +6.00384 q^{88} +9.29193 q^{89} -0.266858 q^{90} +3.25651 q^{91} +3.23768 q^{92} +3.09749 q^{93} -7.06213 q^{94} -0.783399 q^{95} +1.00000 q^{96} -9.48859 q^{97} -6.56281 q^{98} +6.00384 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{2} + 12 q^{3} + 12 q^{4} + 8 q^{5} + 12 q^{6} + 5 q^{7} + 12 q^{8} + 12 q^{9}+O(q^{10}) $ 12 * q + 12 * q^2 + 12 * q^3 + 12 * q^4 + 8 * q^5 + 12 * q^6 + 5 * q^7 + 12 * q^8 + 12 * q^9	\( 12 q + 12 q^{2} + 12 q^{3} + 12 q^{4} + 8 q^{5} + 12 q^{6} + 5 q^{7} + 12 q^{8} + 12 q^{9} + 8 q^{10} + 11 q^{11} + 12 q^{12} + 6 q^{13} + 5 q^{14} + 8 q^{15} + 12 q^{16} - 12 q^{17} + 12 q^{18} + 3 q^{19} + 8 q^{20} + 5 q^{21} + 11 q^{22} + 22 q^{23} + 12 q^{24} + 22 q^{25} + 6 q^{26} + 12 q^{27} + 5 q^{28} + 26 q^{29} + 8 q^{30} + q^{31} + 12 q^{32} + 11 q^{33} - 12 q^{34} + 24 q^{35} + 12 q^{36} + 10 q^{37} + 3 q^{38} + 6 q^{39} + 8 q^{40} + 16 q^{41} + 5 q^{42} + 23 q^{43} + 11 q^{44} + 8 q^{45} + 22 q^{46} + 6 q^{47} + 12 q^{48} + 11 q^{49} + 22 q^{50} - 12 q^{51} + 6 q^{52} + 10 q^{53} + 12 q^{54} + 15 q^{55} + 5 q^{56} + 3 q^{57} + 26 q^{58} + 12 q^{59} + 8 q^{60} + 15 q^{61} + q^{62} + 5 q^{63} + 12 q^{64} + 4 q^{65} + 11 q^{66} + 4 q^{67} - 12 q^{68} + 22 q^{69} + 24 q^{70} + 10 q^{71} + 12 q^{72} + 24 q^{73} + 10 q^{74} + 22 q^{75} + 3 q^{76} + 24 q^{77} + 6 q^{78} + 23 q^{79} + 8 q^{80} + 12 q^{81} + 16 q^{82} + 5 q^{84} - 8 q^{85} + 23 q^{86} + 26 q^{87} + 11 q^{88} + 13 q^{89} + 8 q^{90} + 3 q^{91} + 22 q^{92} + q^{93} + 6 q^{94} + 11 q^{95} + 12 q^{96} + 13 q^{97} + 11 q^{98} + 11 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 12 * q^3 + 12 * q^4 + 8 * q^5 + 12 * q^6 + 5 * q^7 + 12 * q^8 + 12 * q^9 + 8 * q^10 + 11 * q^11 + 12 * q^12 + 6 * q^13 + 5 * q^14 + 8 * q^15 + 12 * q^16 - 12 * q^17 + 12 * q^18 + 3 * q^19 + 8 * q^20 + 5 * q^21 + 11 * q^22 + 22 * q^23 + 12 * q^24 + 22 * q^25 + 6 * q^26 + 12 * q^27 + 5 * q^28 + 26 * q^29 + 8 * q^30 + q^31 + 12 * q^32 + 11 * q^33 - 12 * q^34 + 24 * q^35 + 12 * q^36 + 10 * q^37 + 3 * q^38 + 6 * q^39 + 8 * q^40 + 16 * q^41 + 5 * q^42 + 23 * q^43 + 11 * q^44 + 8 * q^45 + 22 * q^46 + 6 * q^47 + 12 * q^48 + 11 * q^49 + 22 * q^50 - 12 * q^51 + 6 * q^52 + 10 * q^53 + 12 * q^54 + 15 * q^55 + 5 * q^56 + 3 * q^57 + 26 * q^58 + 12 * q^59 + 8 * q^60 + 15 * q^61 + q^62 + 5 * q^63 + 12 * q^64 + 4 * q^65 + 11 * q^66 + 4 * q^67 - 12 * q^68 + 22 * q^69 + 24 * q^70 + 10 * q^71 + 12 * q^72 + 24 * q^73 + 10 * q^74 + 22 * q^75 + 3 * q^76 + 24 * q^77 + 6 * q^78 + 23 * q^79 + 8 * q^80 + 12 * q^81 + 16 * q^82 + 5 * q^84 - 8 * q^85 + 23 * q^86 + 26 * q^87 + 11 * q^88 + 13 * q^89 + 8 * q^90 + 3 * q^91 + 22 * q^92 + q^93 + 6 * q^94 + 11 * q^95 + 12 * q^96 + 13 * q^97 + 11 * q^98 + 11 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−0.266858	−0.119342	−0.0596712	−	0.998218i	$-0.519005\pi$
$5$	−0.266858	−0.119342	−0.0596712	+	0.998218i	$0.519005\pi$
$6$	1.00000	0.408248
$7$	0.661205	0.249912	0.124956	−	0.992162i	$-0.460121\pi$
$7$	0.661205	0.249912	0.124956	+	0.992162i	$0.460121\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−0.266858	−0.0843878
$11$	6.00384	1.81023	0.905113	−	0.425171i	$-0.139786\pi$
$11$	6.00384	1.81023	0.905113	+	0.425171i	$0.139786\pi$
$12$	1.00000	0.288675
$13$	4.92511	1.36598	0.682990	−	0.730427i	$-0.260679\pi$
$13$	4.92511	1.36598	0.682990	+	0.730427i	$0.260679\pi$
$14$	0.661205	0.176714
$15$	−0.266858	−0.0689024
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.00000	0.235702
$19$	2.93564	0.673483	0.336742	−	0.941597i	$-0.390675\pi$
$19$	2.93564	0.673483	0.336742	+	0.941597i	$0.390675\pi$
$20$	−0.266858	−0.0596712
$21$	0.661205	0.144287
$22$	6.00384	1.28002
$23$	3.23768	0.675104	0.337552	−	0.941307i	$-0.390401\pi$
$23$	3.23768	0.675104	0.337552	+	0.941307i	$0.390401\pi$
$24$	1.00000	0.204124
$25$	−4.92879	−0.985757
$26$	4.92511	0.965894
$27$	1.00000	0.192450
$28$	0.661205	0.124956
$29$	2.82398	0.524401	0.262200	−	0.965013i	$-0.415552\pi$
$29$	2.82398	0.524401	0.262200	+	0.965013i	$0.415552\pi$
$30$	−0.266858	−0.0487213
$31$	3.09749	0.556325	0.278163	−	0.960534i	$-0.410275\pi$
$31$	3.09749	0.556325	0.278163	+	0.960534i	$0.410275\pi$
$32$	1.00000	0.176777
$33$	6.00384	1.04513
$34$	−1.00000	−0.171499
$35$	−0.176448	−0.0298251
$36$	1.00000	0.166667
$37$	−8.66526	−1.42456	−0.712280	−	0.701896i	$-0.752337\pi$
$37$	−8.66526	−1.42456	−0.712280	+	0.701896i	$0.752337\pi$
$38$	2.93564	0.476224
$39$	4.92511	0.788649
$40$	−0.266858	−0.0421939
$41$	−2.52649	−0.394572	−0.197286	−	0.980346i	$-0.563213\pi$
$41$	−2.52649	−0.394572	−0.197286	+	0.980346i	$0.563213\pi$
$42$	0.661205	0.102026
$43$	7.24921	1.10549	0.552747	−	0.833349i	$-0.313580\pi$
$43$	7.24921	1.10549	0.552747	+	0.833349i	$0.313580\pi$
$44$	6.00384	0.905113
$45$	−0.266858	−0.0397808
$46$	3.23768	0.477370
$47$	−7.06213	−1.03012	−0.515059	−	0.857155i	$-0.672230\pi$
$47$	−7.06213	−1.03012	−0.515059	+	0.857155i	$0.672230\pi$
$48$	1.00000	0.144338
$49$	−6.56281	−0.937544
$50$	−4.92879	−0.697036
$51$	−1.00000	−0.140028
$52$	4.92511	0.682990
$53$	−12.8630	−1.76687	−0.883436	−	0.468552i	$-0.844776\pi$
$53$	−12.8630	−1.76687	−0.883436	+	0.468552i	$0.844776\pi$
$54$	1.00000	0.136083
$55$	−1.60217	−0.216037
$56$	0.661205	0.0883572
$57$	2.93564	0.388836
$58$	2.82398	0.370807
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	−0.266858	−0.0344512
$61$	−5.51956	−0.706707	−0.353353	−	0.935490i	$-0.614959\pi$
$61$	−5.51956	−0.706707	−0.353353	+	0.935490i	$0.614959\pi$
$62$	3.09749	0.393381
$63$	0.661205	0.0833040
$64$	1.00000	0.125000
$65$	−1.31430	−0.163019
$66$	6.00384	0.739022
$67$	9.08239	1.10959	0.554795	−	0.831987i	$-0.312797\pi$
$67$	9.08239	1.10959	0.554795	+	0.831987i	$0.312797\pi$
$68$	−1.00000	−0.121268
$69$	3.23768	0.389771
$70$	−0.176448	−0.0210895
$71$	0.403782	0.0479201	0.0239601	−	0.999713i	$-0.492373\pi$
$71$	0.403782	0.0479201	0.0239601	+	0.999713i	$0.492373\pi$
$72$	1.00000	0.117851
$73$	−8.85398	−1.03628	−0.518140	−	0.855296i	$-0.673375\pi$
$73$	−8.85398	−1.03628	−0.518140	+	0.855296i	$0.673375\pi$
$74$	−8.66526	−1.00732
$75$	−4.92879	−0.569127
$76$	2.93564	0.336742
$77$	3.96977	0.452397
$78$	4.92511	0.557659
$79$	−3.21467	−0.361679	−0.180839	−	0.983513i	$-0.557881\pi$
$79$	−3.21467	−0.361679	−0.180839	+	0.983513i	$0.557881\pi$
$80$	−0.266858	−0.0298356
$81$	1.00000	0.111111
$82$	−2.52649	−0.279004
$83$	5.07674	0.557245	0.278622	−	0.960401i	$-0.410122\pi$
$83$	5.07674	0.557245	0.278622	+	0.960401i	$0.410122\pi$
$84$	0.661205	0.0721433
$85$	0.266858	0.0289448
$86$	7.24921	0.781702
$87$	2.82398	0.302763
$88$	6.00384	0.640012
$89$	9.29193	0.984943	0.492471	−	0.870329i	$-0.336094\pi$
$89$	9.29193	0.984943	0.492471	+	0.870329i	$0.336094\pi$
$90$	−0.266858	−0.0281293
$91$	3.25651	0.341375
$92$	3.23768	0.337552
$93$	3.09749	0.321194
$94$	−7.06213	−0.728403
$95$	−0.783399	−0.0803751
$96$	1.00000	0.102062
$97$	−9.48859	−0.963420	−0.481710	−	0.876331i	$-0.659984\pi$
$97$	−9.48859	−0.963420	−0.481710	+	0.876331i	$0.659984\pi$
$98$	−6.56281	−0.662944
$99$	6.00384	0.603409
$100$	−4.92879	−0.492879
$101$	−12.8268	−1.27631	−0.638155	−	0.769908i	$-0.720302\pi$
$101$	−12.8268	−1.27631	−0.638155	+	0.769908i	$0.720302\pi$
$102$	−1.00000	−0.0990148
$103$	−0.894509	−0.0881386	−0.0440693	−	0.999028i	$-0.514032\pi$
$103$	−0.894509	−0.0881386	−0.0440693	+	0.999028i	$0.514032\pi$
$104$	4.92511	0.482947
$105$	−0.176448	−0.0172195
$106$	−12.8630	−1.24937
$107$	11.3681	1.09900	0.549498	−	0.835495i	$-0.314819\pi$
$107$	11.3681	1.09900	0.549498	+	0.835495i	$0.314819\pi$
$108$	1.00000	0.0962250
$109$	19.2501	1.84383	0.921913	−	0.387397i	$-0.126626\pi$
$109$	19.2501	1.84383	0.921913	+	0.387397i	$0.126626\pi$
$110$	−1.60217	−0.152761
$111$	−8.66526	−0.822470
$112$	0.661205	0.0624780
$113$	−4.44265	−0.417930	−0.208965	−	0.977923i	$-0.567009\pi$
$113$	−4.44265	−0.417930	−0.208965	+	0.977923i	$0.567009\pi$
$114$	2.93564	0.274948
$115$	−0.864001	−0.0805685
$116$	2.82398	0.262200
$117$	4.92511	0.455327
$118$	1.00000	0.0920575
$119$	−0.661205	−0.0606125
$120$	−0.266858	−0.0243607
$121$	25.0461	2.27692
$122$	−5.51956	−0.499717
$123$	−2.52649	−0.227806
$124$	3.09749	0.278163
$125$	2.64957	0.236985
$126$	0.661205	0.0589048
$127$	8.01394	0.711122	0.355561	−	0.934653i	$-0.384290\pi$
$127$	8.01394	0.711122	0.355561	+	0.934653i	$0.384290\pi$
$128$	1.00000	0.0883883
$129$	7.24921	0.638257
$130$	−1.31430	−0.115272
$131$	−6.36369	−0.555998	−0.277999	−	0.960581i	$-0.589671\pi$
$131$	−6.36369	−0.555998	−0.277999	+	0.960581i	$0.589671\pi$
$132$	6.00384	0.522567
$133$	1.94106	0.168311
$134$	9.08239	0.784599
$135$	−0.266858	−0.0229675
$136$	−1.00000	−0.0857493
$137$	7.11365	0.607760	0.303880	−	0.952710i	$-0.401718\pi$
$137$	7.11365	0.607760	0.303880	+	0.952710i	$0.401718\pi$
$138$	3.23768	0.275610
$139$	−15.2946	−1.29727	−0.648636	−	0.761099i	$-0.724660\pi$
$139$	−15.2946	−1.29727	−0.648636	+	0.761099i	$0.724660\pi$
$140$	−0.176448	−0.0149125
$141$	−7.06213	−0.594739
$142$	0.403782	0.0338847
$143$	29.5696	2.47273
$144$	1.00000	0.0833333
$145$	−0.753602	−0.0625832
$146$	−8.85398	−0.732760
$147$	−6.56281	−0.541291
$148$	−8.66526	−0.712280
$149$	−15.0061	−1.22935	−0.614673	−	0.788782i	$-0.710712\pi$
$149$	−15.0061	−1.22935	−0.614673	+	0.788782i	$0.710712\pi$
$150$	−4.92879	−0.402434
$151$	2.51014	0.204272	0.102136	−	0.994770i	$-0.467432\pi$
$151$	2.51014	0.204272	0.102136	+	0.994770i	$0.467432\pi$
$152$	2.93564	0.238112
$153$	−1.00000	−0.0808452
$154$	3.96977	0.319893
$155$	−0.826588	−0.0663932
$156$	4.92511	0.394325
$157$	−22.7560	−1.81613	−0.908063	−	0.418834i	$-0.862439\pi$
$157$	−22.7560	−1.81613	−0.908063	+	0.418834i	$0.862439\pi$
$158$	−3.21467	−0.255746
$159$	−12.8630	−1.02010
$160$	−0.266858	−0.0210970
$161$	2.14077	0.168716
$162$	1.00000	0.0785674
$163$	7.62401	0.597159	0.298579	−	0.954385i	$-0.403487\pi$
$163$	7.62401	0.597159	0.298579	+	0.954385i	$0.403487\pi$
$164$	−2.52649	−0.197286
$165$	−1.60217	−0.124729
$166$	5.07674	0.394031
$167$	15.8838	1.22912	0.614562	−	0.788869i	$-0.289333\pi$
$167$	15.8838	1.22912	0.614562	+	0.788869i	$0.289333\pi$
$168$	0.661205	0.0510130
$169$	11.2567	0.865903
$170$	0.266858	0.0204671
$171$	2.93564	0.224494
$172$	7.24921	0.552747
$173$	1.42019	0.107975	0.0539875	−	0.998542i	$-0.482807\pi$
$173$	1.42019	0.107975	0.0539875	+	0.998542i	$0.482807\pi$
$174$	2.82398	0.214086
$175$	−3.25894	−0.246352
$176$	6.00384	0.452557
$177$	1.00000	0.0751646
$178$	9.29193	0.696460
$179$	12.2426	0.915055	0.457527	−	0.889196i	$-0.348735\pi$
$179$	12.2426	0.915055	0.457527	+	0.889196i	$0.348735\pi$
$180$	−0.266858	−0.0198904
$181$	−13.2624	−0.985790	−0.492895	−	0.870089i	$-0.664061\pi$
$181$	−13.2624	−0.985790	−0.492895	+	0.870089i	$0.664061\pi$
$182$	3.25651	0.241388
$183$	−5.51956	−0.408017
$184$	3.23768	0.238685
$185$	2.31239	0.170010
$186$	3.09749	0.227119
$187$	−6.00384	−0.439044
$188$	−7.06213	−0.515059
$189$	0.661205	0.0480956
$190$	−0.783399	−0.0568338
$191$	−0.345969	−0.0250334	−0.0125167	−	0.999922i	$-0.503984\pi$
$191$	−0.345969	−0.0250334	−0.0125167	+	0.999922i	$0.503984\pi$
$192$	1.00000	0.0721688
$193$	0.855597	0.0615872	0.0307936	−	0.999526i	$-0.490197\pi$
$193$	0.855597	0.0615872	0.0307936	+	0.999526i	$0.490197\pi$
$194$	−9.48859	−0.681241
$195$	−1.31430	−0.0941193
$196$	−6.56281	−0.468772
$197$	0.150212	0.0107022	0.00535108	−	0.999986i	$-0.498297\pi$
$197$	0.150212	0.0107022	0.00535108	+	0.999986i	$0.498297\pi$
$198$	6.00384	0.426674
$199$	−11.7644	−0.833960	−0.416980	−	0.908916i	$-0.636911\pi$
$199$	−11.7644	−0.833960	−0.416980	+	0.908916i	$0.636911\pi$
$200$	−4.92879	−0.348518
$201$	9.08239	0.640623
$202$	−12.8268	−0.902487
$203$	1.86723	0.131054
$204$	−1.00000	−0.0700140
$205$	0.674214	0.0470892
$206$	−0.894509	−0.0623234
$207$	3.23768	0.225035
$208$	4.92511	0.341495
$209$	17.6251	1.21916
$210$	−0.176448	−0.0121760
$211$	−7.86508	−0.541454	−0.270727	−	0.962656i	$-0.587264\pi$
$211$	−7.86508	−0.541454	−0.270727	+	0.962656i	$0.587264\pi$
$212$	−12.8630	−0.883436
$213$	0.403782	0.0276667
$214$	11.3681	0.777108
$215$	−1.93451	−0.131932
$216$	1.00000	0.0680414
$217$	2.04807	0.139032
$218$	19.2501	1.30378
$219$	−8.85398	−0.598296
$220$	−1.60217	−0.108018
$221$	−4.92511	−0.331299
$222$	−8.66526	−0.581574
$223$	7.87497	0.527347	0.263673	−	0.964612i	$-0.415066\pi$
$223$	7.87497	0.527347	0.263673	+	0.964612i	$0.415066\pi$
$224$	0.661205	0.0441786
$225$	−4.92879	−0.328586
$226$	−4.44265	−0.295521
$227$	4.93665	0.327657	0.163829	−	0.986489i	$-0.447616\pi$
$227$	4.93665	0.327657	0.163829	+	0.986489i	$0.447616\pi$
$228$	2.93564	0.194418
$229$	19.5860	1.29428	0.647140	−	0.762371i	$-0.275965\pi$
$229$	19.5860	1.29428	0.647140	+	0.762371i	$0.275965\pi$
$230$	−0.864001	−0.0569705
$231$	3.96977	0.261192
$232$	2.82398	0.185404
$233$	4.95773	0.324791	0.162396	−	0.986726i	$-0.448078\pi$
$233$	4.95773	0.324791	0.162396	+	0.986726i	$0.448078\pi$
$234$	4.92511	0.321965
$235$	1.88458	0.122937
$236$	1.00000	0.0650945
$237$	−3.21467	−0.208815
$238$	−0.661205	−0.0428595
$239$	4.15922	0.269037	0.134519	−	0.990911i	$-0.457051\pi$
$239$	4.15922	0.269037	0.134519	+	0.990911i	$0.457051\pi$
$240$	−0.266858	−0.0172256
$241$	7.21863	0.464993	0.232497	−	0.972597i	$-0.425311\pi$
$241$	7.21863	0.464993	0.232497	+	0.972597i	$0.425311\pi$
$242$	25.0461	1.61003
$243$	1.00000	0.0641500
$244$	−5.51956	−0.353353
$245$	1.75134	0.111889
$246$	−2.52649	−0.161083
$247$	14.4584	0.919965
$248$	3.09749	0.196691
$249$	5.07674	0.321725
$250$	2.64957	0.167574
$251$	−6.74208	−0.425557	−0.212778	−	0.977101i	$-0.568251\pi$
$251$	−6.74208	−0.425557	−0.212778	+	0.977101i	$0.568251\pi$
$252$	0.661205	0.0416520
$253$	19.4385	1.22209
$254$	8.01394	0.502839
$255$	0.266858	0.0167113
$256$	1.00000	0.0625000
$257$	10.8482	0.676693	0.338346	−	0.941022i	$-0.390132\pi$
$257$	10.8482	0.676693	0.338346	+	0.941022i	$0.390132\pi$
$258$	7.24921	0.451316
$259$	−5.72951	−0.356014
$260$	−1.31430	−0.0815097
$261$	2.82398	0.174800
$262$	−6.36369	−0.393150
$263$	5.15305	0.317751	0.158875	−	0.987299i	$-0.449213\pi$
$263$	5.15305	0.317751	0.158875	+	0.987299i	$0.449213\pi$
$264$	6.00384	0.369511
$265$	3.43260	0.210863
$266$	1.94106	0.119014
$267$	9.29193	0.568657
$268$	9.08239	0.554795
$269$	21.6255	1.31853	0.659264	−	0.751912i	$-0.270868\pi$
$269$	21.6255	1.31853	0.659264	+	0.751912i	$0.270868\pi$
$270$	−0.266858	−0.0162404
$271$	−10.7533	−0.653219	−0.326609	−	0.945159i	$-0.605906\pi$
$271$	−10.7533	−0.653219	−0.326609	+	0.945159i	$0.605906\pi$
$272$	−1.00000	−0.0606339
$273$	3.25651	0.197093
$274$	7.11365	0.429752
$275$	−29.5917	−1.78444
$276$	3.23768	0.194886
$277$	−5.03758	−0.302679	−0.151340	−	0.988482i	$-0.548359\pi$
$277$	−5.03758	−0.302679	−0.151340	+	0.988482i	$0.548359\pi$
$278$	−15.2946	−0.917310
$279$	3.09749	0.185442
$280$	−0.176448	−0.0105448
$281$	−17.6986	−1.05581	−0.527906	−	0.849303i	$-0.677022\pi$
$281$	−17.6986	−1.05581	−0.527906	+	0.849303i	$0.677022\pi$
$282$	−7.06213	−0.420544
$283$	−11.7605	−0.699089	−0.349544	−	0.936920i	$-0.613664\pi$
$283$	−11.7605	−0.699089	−0.349544	+	0.936920i	$0.613664\pi$
$284$	0.403782	0.0239601
$285$	−0.783399	−0.0464046
$286$	29.5696	1.74849
$287$	−1.67053	−0.0986082
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	−0.753602	−0.0442530
$291$	−9.48859	−0.556231
$292$	−8.85398	−0.518140
$293$	−23.5534	−1.37600	−0.688001	−	0.725709i	$-0.741512\pi$
$293$	−23.5534	−1.37600	−0.688001	+	0.725709i	$0.741512\pi$
$294$	−6.56281	−0.382751
$295$	−0.266858	−0.0155371
$296$	−8.66526	−0.503658
$297$	6.00384	0.348378
$298$	−15.0061	−0.869280
$299$	15.9460	0.922179
$300$	−4.92879	−0.284564
$301$	4.79321	0.276276
$302$	2.51014	0.144442
$303$	−12.8268	−0.736878
$304$	2.93564	0.168371
$305$	1.47294	0.0843401
$306$	−1.00000	−0.0571662
$307$	24.5020	1.39840	0.699201	−	0.714925i	$-0.253539\pi$
$307$	24.5020	1.39840	0.699201	+	0.714925i	$0.253539\pi$
$308$	3.96977	0.226199
$309$	−0.894509	−0.0508868
$310$	−0.826588	−0.0469471
$311$	−9.53146	−0.540480	−0.270240	−	0.962793i	$-0.587103\pi$
$311$	−9.53146	−0.540480	−0.270240	+	0.962793i	$0.587103\pi$
$312$	4.92511	0.278830
$313$	21.1981	1.19819	0.599095	−	0.800678i	$-0.295527\pi$
$313$	21.1981	1.19819	0.599095	+	0.800678i	$0.295527\pi$
$314$	−22.7560	−1.28419
$315$	−0.176448	−0.00994169
$316$	−3.21467	−0.180839
$317$	16.8520	0.946502	0.473251	−	0.880928i	$-0.343080\pi$
$317$	16.8520	0.946502	0.473251	+	0.880928i	$0.343080\pi$
$318$	−12.8630	−0.721323
$319$	16.9548	0.949284
$320$	−0.266858	−0.0149178
$321$	11.3681	0.634506
$322$	2.14077	0.119301
$323$	−2.93564	−0.163344
$324$	1.00000	0.0555556
$325$	−24.2748	−1.34653
$326$	7.62401	0.422255
$327$	19.2501	1.06453
$328$	−2.52649	−0.139502
$329$	−4.66951	−0.257439
$330$	−1.60217	−0.0881966
$331$	−3.03642	−0.166897	−0.0834483	−	0.996512i	$-0.526593\pi$
$331$	−3.03642	−0.166897	−0.0834483	+	0.996512i	$0.526593\pi$
$332$	5.07674	0.278622
$333$	−8.66526	−0.474853
$334$	15.8838	0.869121
$335$	−2.42371	−0.132421
$336$	0.661205	0.0360717
$337$	−17.4906	−0.952774	−0.476387	−	0.879236i	$-0.658054\pi$
$337$	−17.4906	−0.952774	−0.476387	+	0.879236i	$0.658054\pi$
$338$	11.2567	0.612286
$339$	−4.44265	−0.241292
$340$	0.266858	0.0144724
$341$	18.5968	1.00707
$342$	2.93564	0.158741
$343$	−8.96779	−0.484215
$344$	7.24921	0.390851
$345$	−0.864001	−0.0465162
$346$	1.42019	0.0763499
$347$	−36.4841	−1.95857	−0.979284	−	0.202493i	$-0.935096\pi$
$347$	−36.4841	−1.95857	−0.979284	+	0.202493i	$0.935096\pi$
$348$	2.82398	0.151381
$349$	11.7623	0.629621	0.314810	−	0.949155i	$-0.398059\pi$
$349$	11.7623	0.629621	0.314810	+	0.949155i	$0.398059\pi$
$350$	−3.25894	−0.174197
$351$	4.92511	0.262883
$352$	6.00384	0.320006
$353$	13.2836	0.707013	0.353506	−	0.935432i	$-0.384989\pi$
$353$	13.2836	0.707013	0.353506	+	0.935432i	$0.384989\pi$
$354$	1.00000	0.0531494
$355$	−0.107752	−0.00571890
$356$	9.29193	0.492471
$357$	−0.661205	−0.0349947
$358$	12.2426	0.647041
$359$	19.9451	1.05266	0.526331	−	0.850280i	$-0.323567\pi$
$359$	19.9451	1.05266	0.526331	+	0.850280i	$0.323567\pi$
$360$	−0.266858	−0.0140646
$361$	−10.3820	−0.546421
$362$	−13.2624	−0.697059
$363$	25.0461	1.31458
$364$	3.25651	0.170687
$365$	2.36275	0.123672
$366$	−5.51956	−0.288512
$367$	34.2762	1.78920	0.894601	−	0.446866i	$-0.147460\pi$
$367$	34.2762	1.78920	0.894601	+	0.446866i	$0.147460\pi$
$368$	3.23768	0.168776
$369$	−2.52649	−0.131524
$370$	2.31239	0.120215
$371$	−8.50509	−0.441562
$372$	3.09749	0.160597
$373$	3.56633	0.184657	0.0923287	−	0.995729i	$-0.470569\pi$
$373$	3.56633	0.184657	0.0923287	+	0.995729i	$0.470569\pi$
$374$	−6.00384	−0.310451
$375$	2.64957	0.136823
$376$	−7.06213	−0.364202
$377$	13.9084	0.716321
$378$	0.661205	0.0340087
$379$	−34.5976	−1.77716	−0.888580	−	0.458721i	$-0.848308\pi$
$379$	−34.5976	−1.77716	−0.888580	+	0.458721i	$0.848308\pi$
$380$	−0.783399	−0.0401875
$381$	8.01394	0.410566
$382$	−0.345969	−0.0177013
$383$	27.5035	1.40536	0.702682	−	0.711504i	$-0.251986\pi$
$383$	27.5035	1.40536	0.702682	+	0.711504i	$0.251986\pi$
$384$	1.00000	0.0510310
$385$	−1.05936	−0.0539901
$386$	0.855597	0.0435487
$387$	7.24921	0.368498
$388$	−9.48859	−0.481710
$389$	−29.5188	−1.49666	−0.748332	−	0.663325i	$-0.769145\pi$
$389$	−29.5188	−1.49666	−0.748332	+	0.663325i	$0.769145\pi$
$390$	−1.31430	−0.0665524
$391$	−3.23768	−0.163737
$392$	−6.56281	−0.331472
$393$	−6.36369	−0.321006
$394$	0.150212	0.00756757
$395$	0.857860	0.0431636
$396$	6.00384	0.301704
$397$	−26.0865	−1.30924	−0.654621	−	0.755957i	$-0.727172\pi$
$397$	−26.0865	−1.30924	−0.654621	+	0.755957i	$0.727172\pi$
$398$	−11.7644	−0.589699
$399$	1.94106	0.0971746
$400$	−4.92879	−0.246439
$401$	−15.1338	−0.755744	−0.377872	−	0.925858i	$-0.623344\pi$
$401$	−15.1338	−0.755744	−0.377872	+	0.925858i	$0.623344\pi$
$402$	9.08239	0.452989
$403$	15.2555	0.759929
$404$	−12.8268	−0.638155
$405$	−0.266858	−0.0132603
$406$	1.86723	0.0926692
$407$	−52.0248	−2.57877
$408$	−1.00000	−0.0495074
$409$	−23.9312	−1.18332	−0.591660	−	0.806188i	$-0.701527\pi$
$409$	−23.9312	−1.18332	−0.591660	+	0.806188i	$0.701527\pi$
$410$	0.674214	0.0332971
$411$	7.11365	0.350891
$412$	−0.894509	−0.0440693
$413$	0.661205	0.0325358
$414$	3.23768	0.159123
$415$	−1.35477	−0.0665029
$416$	4.92511	0.241474
$417$	−15.2946	−0.748981
$418$	17.6251	0.862074
$419$	19.8667	0.970551	0.485276	−	0.874361i	$-0.338719\pi$
$419$	19.8667	0.970551	0.485276	+	0.874361i	$0.338719\pi$
$420$	−0.176448	−0.00860976
$421$	−20.6847	−1.00811	−0.504054	−	0.863672i	$-0.668159\pi$
$421$	−20.6847	−1.00811	−0.504054	+	0.863672i	$0.668159\pi$
$422$	−7.86508	−0.382866
$423$	−7.06213	−0.343372
$424$	−12.8630	−0.624684
$425$	4.92879	0.239081
$426$	0.403782	0.0195633
$427$	−3.64956	−0.176614
$428$	11.3681	0.549498
$429$	29.5696	1.42763
$430$	−1.93451	−0.0932902
$431$	−1.51475	−0.0729631	−0.0364815	−	0.999334i	$-0.511615\pi$
$431$	−1.51475	−0.0729631	−0.0364815	+	0.999334i	$0.511615\pi$
$432$	1.00000	0.0481125
$433$	−23.9247	−1.14975	−0.574873	−	0.818242i	$-0.694949\pi$
$433$	−23.9247	−1.14975	−0.574873	+	0.818242i	$0.694949\pi$
$434$	2.04807	0.0983107
$435$	−0.753602	−0.0361325
$436$	19.2501	0.921913
$437$	9.50469	0.454671
$438$	−8.85398	−0.423059
$439$	−12.4977	−0.596482	−0.298241	−	0.954491i	$-0.596400\pi$
$439$	−12.4977	−0.596482	−0.298241	+	0.954491i	$0.596400\pi$
$440$	−1.60217	−0.0763805
$441$	−6.56281	−0.312515
$442$	−4.92511	−0.234264
$443$	35.9030	1.70580	0.852901	−	0.522073i	$-0.174841\pi$
$443$	35.9030	1.70580	0.852901	+	0.522073i	$0.174841\pi$
$444$	−8.66526	−0.411235
$445$	−2.47962	−0.117545
$446$	7.87497	0.372890
$447$	−15.0061	−0.709764
$448$	0.661205	0.0312390
$449$	21.3015	1.00528	0.502640	−	0.864496i	$-0.332362\pi$
$449$	21.3015	1.00528	0.502640	+	0.864496i	$0.332362\pi$
$450$	−4.92879	−0.232345
$451$	−15.1687	−0.714265
$452$	−4.44265	−0.208965
$453$	2.51014	0.117937
$454$	4.93665	0.231689
$455$	−0.869024	−0.0407405
$456$	2.93564	0.137474
$457$	−35.4470	−1.65814	−0.829069	−	0.559146i	$-0.811129\pi$
$457$	−35.4470	−1.65814	−0.829069	+	0.559146i	$0.811129\pi$
$458$	19.5860	0.915194
$459$	−1.00000	−0.0466760
$460$	−0.864001	−0.0402842
$461$	−19.8860	−0.926183	−0.463092	−	0.886310i	$-0.653260\pi$
$461$	−19.8860	−0.926183	−0.463092	+	0.886310i	$0.653260\pi$
$462$	3.96977	0.184690
$463$	−29.9893	−1.39372	−0.696861	−	0.717207i	$-0.745420\pi$
$463$	−29.9893	−1.39372	−0.696861	+	0.717207i	$0.745420\pi$
$464$	2.82398	0.131100
$465$	−0.826588	−0.0383321
$466$	4.95773	0.229662
$467$	23.9764	1.10949	0.554747	−	0.832019i	$-0.312815\pi$
$467$	23.9764	1.10949	0.554747	+	0.832019i	$0.312815\pi$
$468$	4.92511	0.227663
$469$	6.00532	0.277300
$470$	1.88458	0.0869294
$471$	−22.7560	−1.04854
$472$	1.00000	0.0460287
$473$	43.5231	2.00119
$474$	−3.21467	−0.147655
$475$	−14.4692	−0.663891
$476$	−0.661205	−0.0303063
$477$	−12.8630	−0.588957
$478$	4.15922	0.190238
$479$	31.5251	1.44042	0.720208	−	0.693758i	$-0.244046\pi$
$479$	31.5251	1.44042	0.720208	+	0.693758i	$0.244046\pi$
$480$	−0.266858	−0.0121803
$481$	−42.6774	−1.94592
$482$	7.21863	0.328800
$483$	2.14077	0.0974085
$484$	25.0461	1.13846
$485$	2.53210	0.114977
$486$	1.00000	0.0453609
$487$	12.0173	0.544557	0.272279	−	0.962218i	$-0.412223\pi$
$487$	12.0173	0.544557	0.272279	+	0.962218i	$0.412223\pi$
$488$	−5.51956	−0.249859
$489$	7.62401	0.344770
$490$	1.75134	0.0791173
$491$	−31.1824	−1.40724	−0.703620	−	0.710576i	$-0.748434\pi$
$491$	−31.1824	−1.40724	−0.703620	+	0.710576i	$0.748434\pi$
$492$	−2.52649	−0.113903
$493$	−2.82398	−0.127186
$494$	14.4584	0.650513
$495$	−1.60217	−0.0720123
$496$	3.09749	0.139081
$497$	0.266983	0.0119758
$498$	5.07674	0.227494
$499$	−1.51830	−0.0679682	−0.0339841	−	0.999422i	$-0.510820\pi$
$499$	−1.51830	−0.0679682	−0.0339841	+	0.999422i	$0.510820\pi$
$500$	2.64957	0.118493
$501$	15.8838	0.709635
$502$	−6.74208	−0.300914
$503$	−36.5833	−1.63117	−0.815585	−	0.578637i	$-0.803585\pi$
$503$	−36.5833	−1.63117	−0.815585	+	0.578637i	$0.803585\pi$
$504$	0.661205	0.0294524
$505$	3.42292	0.152318
$506$	19.4385	0.864149
$507$	11.2567	0.499930
$508$	8.01394	0.355561
$509$	14.0540	0.622935	0.311467	−	0.950257i	$-0.399180\pi$
$509$	14.0540	0.622935	0.311467	+	0.950257i	$0.399180\pi$
$510$	0.266858	0.0118167
$511$	−5.85429	−0.258979
$512$	1.00000	0.0441942
$513$	2.93564	0.129612
$514$	10.8482	0.478494
$515$	0.238707	0.0105187
$516$	7.24921	0.319129
$517$	−42.3999	−1.86475
$518$	−5.72951	−0.251740
$519$	1.42019	0.0623394
$520$	−1.31430	−0.0576361
$521$	3.78717	0.165919	0.0829595	−	0.996553i	$-0.473563\pi$
$521$	3.78717	0.165919	0.0829595	+	0.996553i	$0.473563\pi$
$522$	2.82398	0.123602
$523$	−6.29287	−0.275168	−0.137584	−	0.990490i	$-0.543934\pi$
$523$	−6.29287	−0.275168	−0.137584	+	0.990490i	$0.543934\pi$
$524$	−6.36369	−0.277999
$525$	−3.25894	−0.142232
$526$	5.15305	0.224684
$527$	−3.09749	−0.134929
$528$	6.00384	0.261284
$529$	−12.5174	−0.544235
$530$	3.43260	0.149102
$531$	1.00000	0.0433963
$532$	1.94106	0.0841557
$533$	−12.4433	−0.538978
$534$	9.29193	0.402101
$535$	−3.03367	−0.131157
$536$	9.08239	0.392300
$537$	12.2426	0.528307
$538$	21.6255	0.932340
$539$	−39.4021	−1.69717
$540$	−0.266858	−0.0114837
$541$	−34.0482	−1.46384	−0.731922	−	0.681388i	$-0.761377\pi$
$541$	−34.0482	−1.46384	−0.731922	+	0.681388i	$0.761377\pi$
$542$	−10.7533	−0.461895
$543$	−13.2624	−0.569146
$544$	−1.00000	−0.0428746
$545$	−5.13704	−0.220047
$546$	3.25651	0.139366
$547$	14.4283	0.616909	0.308454	−	0.951239i	$-0.400188\pi$
$547$	14.4283	0.616909	0.308454	+	0.951239i	$0.400188\pi$
$548$	7.11365	0.303880
$549$	−5.51956	−0.235569
$550$	−29.5917	−1.26179
$551$	8.29021	0.353175
$552$	3.23768	0.137805
$553$	−2.12556	−0.0903878
$554$	−5.03758	−0.214026
$555$	2.31239	0.0981555
$556$	−15.2946	−0.648636
$557$	5.53277	0.234431	0.117216	−	0.993106i	$-0.462603\pi$
$557$	5.53277	0.234431	0.117216	+	0.993106i	$0.462603\pi$
$558$	3.09749	0.131127
$559$	35.7032	1.51008
$560$	−0.176448	−0.00745627
$561$	−6.00384	−0.253482
$562$	−17.6986	−0.746571
$563$	−20.1239	−0.848121	−0.424061	−	0.905634i	$-0.639396\pi$
$563$	−20.1239	−0.848121	−0.424061	+	0.905634i	$0.639396\pi$
$564$	−7.06213	−0.297369
$565$	1.18556	0.0498767
$566$	−11.7605	−0.494330
$567$	0.661205	0.0277680
$568$	0.403782	0.0169423
$569$	−31.5034	−1.32069	−0.660346	−	0.750961i	$-0.729591\pi$
$569$	−31.5034	−1.32069	−0.660346	+	0.750961i	$0.729591\pi$
$570$	−0.783399	−0.0328130
$571$	5.76822	0.241392	0.120696	−	0.992689i	$-0.461487\pi$
$571$	5.76822	0.241392	0.120696	+	0.992689i	$0.461487\pi$
$572$	29.5696	1.23637
$573$	−0.345969	−0.0144531
$574$	−1.67053	−0.0697265
$575$	−15.9579	−0.665488
$576$	1.00000	0.0416667
$577$	−23.8183	−0.991568	−0.495784	−	0.868446i	$-0.665119\pi$
$577$	−23.8183	−0.991568	−0.495784	+	0.868446i	$0.665119\pi$
$578$	1.00000	0.0415945
$579$	0.855597	0.0355574
$580$	−0.753602	−0.0312916
$581$	3.35676	0.139262
$582$	−9.48859	−0.393315
$583$	−77.2276	−3.19844
$584$	−8.85398	−0.366380
$585$	−1.31430	−0.0543398
$586$	−23.5534	−0.972981
$587$	−34.7330	−1.43358	−0.716792	−	0.697287i	$-0.754390\pi$
$587$	−34.7330	−1.43358	−0.716792	+	0.697287i	$0.754390\pi$
$588$	−6.56281	−0.270646
$589$	9.09312	0.374676
$590$	−0.266858	−0.0109864
$591$	0.150212	0.00617889
$592$	−8.66526	−0.356140
$593$	21.2877	0.874180	0.437090	−	0.899418i	$-0.356009\pi$
$593$	21.2877	0.874180	0.437090	+	0.899418i	$0.356009\pi$
$594$	6.00384	0.246341
$595$	0.176448	0.00723364
$596$	−15.0061	−0.614673
$597$	−11.7644	−0.481487
$598$	15.9460	0.652079
$599$	−38.6559	−1.57944	−0.789718	−	0.613470i	$-0.789773\pi$
$599$	−38.6559	−1.57944	−0.789718	+	0.613470i	$0.789773\pi$
$600$	−4.92879	−0.201217
$601$	19.4430	0.793095	0.396547	−	0.918014i	$-0.370208\pi$
$601$	19.4430	0.793095	0.396547	+	0.918014i	$0.370208\pi$
$602$	4.79321	0.195357
$603$	9.08239	0.369864
$604$	2.51014	0.102136
$605$	−6.68375	−0.271733
$606$	−12.8268	−0.521051
$607$	17.0375	0.691531	0.345765	−	0.938321i	$-0.387619\pi$
$607$	17.0375	0.691531	0.345765	+	0.938321i	$0.387619\pi$
$608$	2.93564	0.119056
$609$	1.86723	0.0756640
$610$	1.47294	0.0596374
$611$	−34.7818	−1.40712
$612$	−1.00000	−0.0404226
$613$	−30.5394	−1.23347	−0.616737	−	0.787169i	$-0.711546\pi$
$613$	−30.5394	−1.23347	−0.616737	+	0.787169i	$0.711546\pi$
$614$	24.5020	0.988820
$615$	0.674214	0.0271869
$616$	3.96977	0.159947
$617$	48.5577	1.95486	0.977431	−	0.211257i	$-0.0677557\pi$
$617$	48.5577	1.95486	0.977431	+	0.211257i	$0.0677557\pi$
$618$	−0.894509	−0.0359824
$619$	7.99948	0.321526	0.160763	−	0.986993i	$-0.448604\pi$
$619$	7.99948	0.321526	0.160763	+	0.986993i	$0.448604\pi$
$620$	−0.826588	−0.0331966
$621$	3.23768	0.129924
$622$	−9.53146	−0.382177
$623$	6.14387	0.246149
$624$	4.92511	0.197162
$625$	23.9369	0.957475
$626$	21.1981	0.847248
$627$	17.6251	0.703880
$628$	−22.7560	−0.908063
$629$	8.66526	0.345506
$630$	−0.176448	−0.00702984
$631$	42.3140	1.68450	0.842248	−	0.539091i	$-0.181232\pi$
$631$	42.3140	1.68450	0.842248	+	0.539091i	$0.181232\pi$
$632$	−3.21467	−0.127873
$633$	−7.86508	−0.312609
$634$	16.8520	0.669278
$635$	−2.13858	−0.0848670
$636$	−12.8630	−0.510052
$637$	−32.3226	−1.28067
$638$	16.9548	0.671245
$639$	0.403782	0.0159734
$640$	−0.266858	−0.0105485
$641$	15.8779	0.627138	0.313569	−	0.949565i	$-0.398475\pi$
$641$	15.8779	0.627138	0.313569	+	0.949565i	$0.398475\pi$
$642$	11.3681	0.448664
$643$	−14.6659	−0.578367	−0.289184	−	0.957274i	$-0.593384\pi$
$643$	−14.6659	−0.578367	−0.289184	+	0.957274i	$0.593384\pi$
$644$	2.14077	0.0843582
$645$	−1.93451	−0.0761712
$646$	−2.93564	−0.115501
$647$	22.8934	0.900031	0.450016	−	0.893021i	$-0.351418\pi$
$647$	22.8934	0.900031	0.450016	+	0.893021i	$0.351418\pi$
$648$	1.00000	0.0392837
$649$	6.00384	0.235671
$650$	−24.2748	−0.952137
$651$	2.04807	0.0802703
$652$	7.62401	0.298579
$653$	−3.06282	−0.119857	−0.0599287	−	0.998203i	$-0.519087\pi$
$653$	−3.06282	−0.119857	−0.0599287	+	0.998203i	$0.519087\pi$
$654$	19.2501	0.752739
$655$	1.69820	0.0663542
$656$	−2.52649	−0.0986430
$657$	−8.85398	−0.345426
$658$	−4.66951	−0.182037
$659$	0.188838	0.00735608	0.00367804	−	0.999993i	$-0.498829\pi$
$659$	0.188838	0.00735608	0.00367804	+	0.999993i	$0.498829\pi$
$660$	−1.60217	−0.0623644
$661$	27.5958	1.07335	0.536675	−	0.843789i	$-0.319680\pi$
$661$	27.5958	1.07335	0.536675	+	0.843789i	$0.319680\pi$
$662$	−3.03642	−0.118014
$663$	−4.92511	−0.191276
$664$	5.07674	0.197016
$665$	−0.517987	−0.0200867
$666$	−8.66526	−0.335772
$667$	9.14317	0.354025
$668$	15.8838	0.614562
$669$	7.87497	0.304464
$670$	−2.42371	−0.0936359
$671$	−33.1385	−1.27930
$672$	0.661205	0.0255065
$673$	−14.0278	−0.540731	−0.270366	−	0.962758i	$-0.587145\pi$
$673$	−14.0278	−0.540731	−0.270366	+	0.962758i	$0.587145\pi$
$674$	−17.4906	−0.673713
$675$	−4.92879	−0.189709
$676$	11.2567	0.432952
$677$	9.36427	0.359898	0.179949	−	0.983676i	$-0.442407\pi$
$677$	9.36427	0.359898	0.179949	+	0.983676i	$0.442407\pi$
$678$	−4.44265	−0.170619
$679$	−6.27390	−0.240770
$680$	0.266858	0.0102335
$681$	4.93665	0.189173
$682$	18.5968	0.712109
$683$	46.9014	1.79463	0.897317	−	0.441387i	$-0.145513\pi$
$683$	46.9014	1.79463	0.897317	+	0.441387i	$0.145513\pi$
$684$	2.93564	0.112247
$685$	−1.89833	−0.0725316
$686$	−8.96779	−0.342392
$687$	19.5860	0.747253
$688$	7.24921	0.276374
$689$	−63.3519	−2.41351
$690$	−0.864001	−0.0328919
$691$	−25.6181	−0.974560	−0.487280	−	0.873246i	$-0.662011\pi$
$691$	−25.6181	−0.974560	−0.487280	+	0.873246i	$0.662011\pi$
$692$	1.42019	0.0539875
$693$	3.96977	0.150799
$694$	−36.4841	−1.38492
$695$	4.08149	0.154820
$696$	2.82398	0.107043
$697$	2.52649	0.0956978
$698$	11.7623	0.445209
$699$	4.95773	0.187518
$700$	−3.25894	−0.123176
$701$	5.25519	0.198486	0.0992428	−	0.995063i	$-0.468358\pi$
$701$	5.25519	0.198486	0.0992428	+	0.995063i	$0.468358\pi$
$702$	4.92511	0.185886
$703$	−25.4381	−0.959416
$704$	6.00384	0.226278
$705$	1.88458	0.0709775
$706$	13.2836	0.499934
$707$	−8.48111	−0.318965
$708$	1.00000	0.0375823
$709$	44.2306	1.66111	0.830557	−	0.556934i	$-0.188022\pi$
$709$	44.2306	1.66111	0.830557	+	0.556934i	$0.188022\pi$
$710$	−0.107752	−0.00404388
$711$	−3.21467	−0.120560
$712$	9.29193	0.348230
$713$	10.0287	0.375577
$714$	−0.661205	−0.0247450
$715$	−7.89088	−0.295102
$716$	12.2426	0.457527
$717$	4.15922	0.155329
$718$	19.9451	0.744344
$719$	−43.0889	−1.60695	−0.803473	−	0.595341i	$-0.797017\pi$
$719$	−43.0889	−1.60695	−0.803473	+	0.595341i	$0.797017\pi$
$720$	−0.266858	−0.00994520
$721$	−0.591454	−0.0220269
$722$	−10.3820	−0.386378
$723$	7.21863	0.268464
$724$	−13.2624	−0.492895
$725$	−13.9188	−0.516932
$726$	25.0461	0.929549
$727$	5.09075	0.188805	0.0944027	−	0.995534i	$-0.469906\pi$
$727$	5.09075	0.188805	0.0944027	+	0.995534i	$0.469906\pi$
$728$	3.25651	0.120694
$729$	1.00000	0.0370370
$730$	2.36275	0.0874494
$731$	−7.24921	−0.268122
$732$	−5.51956	−0.204009
$733$	22.2846	0.823099	0.411550	−	0.911387i	$-0.364988\pi$
$733$	22.2846	0.823099	0.411550	+	0.911387i	$0.364988\pi$
$734$	34.2762	1.26516
$735$	1.75134	0.0645990
$736$	3.23768	0.119343
$737$	54.5292	2.00861
$738$	−2.52649	−0.0930015
$739$	44.6618	1.64291	0.821456	−	0.570272i	$-0.193162\pi$
$739$	44.6618	1.64291	0.821456	+	0.570272i	$0.193162\pi$
$740$	2.31239	0.0850052
$741$	14.4584	0.531142
$742$	−8.50509	−0.312232
$743$	13.9784	0.512818	0.256409	−	0.966568i	$-0.417461\pi$
$743$	13.9784	0.512818	0.256409	+	0.966568i	$0.417461\pi$
$744$	3.09749	0.113559
$745$	4.00449	0.146713
$746$	3.56633	0.130573
$747$	5.07674	0.185748
$748$	−6.00384	−0.219522
$749$	7.51665	0.274652
$750$	2.64957	0.0967487
$751$	16.6687	0.608251	0.304125	−	0.952632i	$-0.401636\pi$
$751$	16.6687	0.608251	0.304125	+	0.952632i	$0.401636\pi$
$752$	−7.06213	−0.257529
$753$	−6.74208	−0.245695
$754$	13.9084	0.506516
$755$	−0.669851	−0.0243784
$756$	0.661205	0.0240478
$757$	−17.9384	−0.651983	−0.325991	−	0.945373i	$-0.605698\pi$
$757$	−17.9384	−0.651983	−0.325991	+	0.945373i	$0.605698\pi$
$758$	−34.5976	−1.25664
$759$	19.4385	0.705574
$760$	−0.783399	−0.0284169
$761$	8.54466	0.309744	0.154872	−	0.987935i	$-0.450504\pi$
$761$	8.54466	0.309744	0.154872	+	0.987935i	$0.450504\pi$
$762$	8.01394	0.290314
$763$	12.7283	0.460794
$764$	−0.345969	−0.0125167
$765$	0.266858	0.00964826
$766$	27.5035	0.993742
$767$	4.92511	0.177836
$768$	1.00000	0.0360844
$769$	−19.8230	−0.714836	−0.357418	−	0.933945i	$-0.616343\pi$
$769$	−19.8230	−0.714836	−0.357418	+	0.933945i	$0.616343\pi$
$770$	−1.05936	−0.0381768
$771$	10.8482	0.390689
$772$	0.855597	0.0307936
$773$	−5.31287	−0.191091	−0.0955453	−	0.995425i	$-0.530459\pi$
$773$	−5.31287	−0.191091	−0.0955453	+	0.995425i	$0.530459\pi$
$774$	7.24921	0.260567
$775$	−15.2669	−0.548402
$776$	−9.48859	−0.340620
$777$	−5.72951	−0.205545
$778$	−29.5188	−1.05830
$779$	−7.41689	−0.265737
$780$	−1.31430	−0.0470597
$781$	2.42424	0.0867463
$782$	−3.23768	−0.115779
$783$	2.82398	0.100921
$784$	−6.56281	−0.234386
$785$	6.07261	0.216741
$786$	−6.36369	−0.226985
$787$	3.66522	0.130651	0.0653255	−	0.997864i	$-0.479191\pi$
$787$	3.66522	0.130651	0.0653255	+	0.997864i	$0.479191\pi$
$788$	0.150212	0.00535108
$789$	5.15305	0.183454
$790$	0.857860	0.0305213
$791$	−2.93750	−0.104446
$792$	6.00384	0.213337
$793$	−27.1844	−0.965348
$794$	−26.0865	−0.925775
$795$	3.43260	0.121742
$796$	−11.7644	−0.416980
$797$	51.1997	1.81359	0.906794	−	0.421574i	$-0.138522\pi$
$797$	51.1997	1.81359	0.906794	+	0.421574i	$0.138522\pi$
$798$	1.94106	0.0687128
$799$	7.06213	0.249840
$800$	−4.92879	−0.174259
$801$	9.29193	0.328314
$802$	−15.1338	−0.534391
$803$	−53.1579	−1.87590
$804$	9.08239	0.320311
$805$	−0.571281	−0.0201350
$806$	15.2555	0.537351
$807$	21.6255	0.761252
$808$	−12.8268	−0.451244
$809$	23.8655	0.839065	0.419533	−	0.907740i	$-0.362194\pi$
$809$	23.8655	0.839065	0.419533	+	0.907740i	$0.362194\pi$
$810$	−0.266858	−0.00937642
$811$	−40.3600	−1.41723	−0.708615	−	0.705595i	$-0.750680\pi$
$811$	−40.3600	−1.41723	−0.708615	+	0.705595i	$0.750680\pi$
$812$	1.86723	0.0655270
$813$	−10.7533	−0.377136
$814$	−52.0248	−1.82347
$815$	−2.03453	−0.0712664
$816$	−1.00000	−0.0350070
$817$	21.2811	0.744532
$818$	−23.9312	−0.836733
$819$	3.25651	0.113792
$820$	0.674214	0.0235446
$821$	−23.1200	−0.806893	−0.403446	−	0.915003i	$-0.632188\pi$
$821$	−23.1200	−0.806893	−0.403446	+	0.915003i	$0.632188\pi$
$822$	7.11365	0.248117
$823$	44.9932	1.56836	0.784182	−	0.620531i	$-0.213083\pi$
$823$	44.9932	1.56836	0.784182	+	0.620531i	$0.213083\pi$
$824$	−0.894509	−0.0311617
$825$	−29.5917	−1.03025
$826$	0.661205	0.0230063
$827$	27.8210	0.967430	0.483715	−	0.875226i	$-0.339287\pi$
$827$	27.8210	0.967430	0.483715	+	0.875226i	$0.339287\pi$
$828$	3.23768	0.112517
$829$	−24.3391	−0.845333	−0.422667	−	0.906285i	$-0.638906\pi$
$829$	−24.3391	−0.845333	−0.422667	+	0.906285i	$0.638906\pi$
$830$	−1.35477	−0.0470247
$831$	−5.03758	−0.174752
$832$	4.92511	0.170748
$833$	6.56281	0.227388
$834$	−15.2946	−0.529609
$835$	−4.23871	−0.146686
$836$	17.6251	0.609578
$837$	3.09749	0.107065
$838$	19.8667	0.686283
$839$	−7.29246	−0.251764	−0.125882	−	0.992045i	$-0.540176\pi$
$839$	−7.29246	−0.251764	−0.125882	+	0.992045i	$0.540176\pi$
$840$	−0.176448	−0.00608802
$841$	−21.0251	−0.725004
$842$	−20.6847	−0.712840
$843$	−17.6986	−0.609573
$844$	−7.86508	−0.270727
$845$	−3.00395	−0.103339
$846$	−7.06213	−0.242801
$847$	16.5606	0.569029
$848$	−12.8630	−0.441718
$849$	−11.7605	−0.403619
$850$	4.92879	0.169056
$851$	−28.0554	−0.961725
$852$	0.403782	0.0138334
$853$	−31.6434	−1.08345	−0.541724	−	0.840556i	$-0.682228\pi$
$853$	−31.6434	−1.08345	−0.541724	+	0.840556i	$0.682228\pi$
$854$	−3.64956	−0.124885
$855$	−0.783399	−0.0267917
$856$	11.3681	0.388554
$857$	−25.1941	−0.860614	−0.430307	−	0.902683i	$-0.641595\pi$
$857$	−25.1941	−0.860614	−0.430307	+	0.902683i	$0.641595\pi$
$858$	29.5696	1.00949
$859$	−11.2532	−0.383953	−0.191976	−	0.981400i	$-0.561490\pi$
$859$	−11.2532	−0.383953	−0.191976	+	0.981400i	$0.561490\pi$
$860$	−1.93451	−0.0659662
$861$	−1.67053	−0.0569315
$862$	−1.51475	−0.0515927
$863$	22.5196	0.766576	0.383288	−	0.923629i	$-0.374792\pi$
$863$	22.5196	0.766576	0.383288	+	0.923629i	$0.374792\pi$
$864$	1.00000	0.0340207
$865$	−0.378988	−0.0128860
$866$	−23.9247	−0.812994
$867$	1.00000	0.0339618
$868$	2.04807	0.0695161
$869$	−19.3004	−0.654721
$870$	−0.753602	−0.0255495
$871$	44.7318	1.51568
$872$	19.2501	0.651891
$873$	−9.48859	−0.321140
$874$	9.50469	0.321501
$875$	1.75191	0.0592254
$876$	−8.85398	−0.299148
$877$	−3.39291	−0.114571	−0.0572853	−	0.998358i	$-0.518244\pi$
$877$	−3.39291	−0.114571	−0.0572853	+	0.998358i	$0.518244\pi$
$878$	−12.4977	−0.421776
$879$	−23.5534	−0.794436
$880$	−1.60217	−0.0540092
$881$	−38.6819	−1.30323	−0.651613	−	0.758551i	$-0.725907\pi$
$881$	−38.6819	−1.30323	−0.651613	+	0.758551i	$0.725907\pi$
$882$	−6.56281	−0.220981
$883$	−40.4331	−1.36068	−0.680342	−	0.732895i	$-0.738169\pi$
$883$	−40.4331	−1.36068	−0.680342	+	0.732895i	$0.738169\pi$
$884$	−4.92511	−0.165649
$885$	−0.266858	−0.00897032
$886$	35.9030	1.20618
$887$	−15.7393	−0.528475	−0.264237	−	0.964458i	$-0.585120\pi$
$887$	−15.7393	−0.528475	−0.264237	+	0.964458i	$0.585120\pi$
$888$	−8.66526	−0.290787
$889$	5.29885	0.177718
$890$	−2.47962	−0.0831172
$891$	6.00384	0.201136
$892$	7.87497	0.263673
$893$	−20.7319	−0.693767
$894$	−15.0061	−0.501879
$895$	−3.26703	−0.109205
$896$	0.661205	0.0220893
$897$	15.9460	0.532420
$898$	21.3015	0.710840
$899$	8.74726	0.291737
$900$	−4.92879	−0.164293
$901$	12.8630	0.428529
$902$	−15.1687	−0.505061
$903$	4.79321	0.159508
$904$	−4.44265	−0.147760
$905$	3.53919	0.117647
$906$	2.51014	0.0833939
$907$	7.68155	0.255062	0.127531	−	0.991835i	$-0.459295\pi$
$907$	7.68155	0.255062	0.127531	+	0.991835i	$0.459295\pi$
$908$	4.93665	0.163829
$909$	−12.8268	−0.425436
$910$	−0.869024	−0.0288079
$911$	3.41016	0.112984	0.0564918	−	0.998403i	$-0.482009\pi$
$911$	3.41016	0.112984	0.0564918	+	0.998403i	$0.482009\pi$
$912$	2.93564	0.0972089
$913$	30.4799	1.00874
$914$	−35.4470	−1.17248
$915$	1.47294	0.0486938
$916$	19.5860	0.647140
$917$	−4.20770	−0.138951
$918$	−1.00000	−0.0330049
$919$	−28.1331	−0.928027	−0.464013	−	0.885828i	$-0.653591\pi$
$919$	−28.1331	−0.928027	−0.464013	+	0.885828i	$0.653591\pi$
$920$	−0.864001	−0.0284853
$921$	24.5020	0.807368
$922$	−19.8860	−0.654911
$923$	1.98867	0.0654580
$924$	3.96977	0.130596
$925$	42.7092	1.40427
$926$	−29.9893	−0.985510
$927$	−0.894509	−0.0293795
$928$	2.82398	0.0927018
$929$	52.5381	1.72372	0.861859	−	0.507148i	$-0.169300\pi$
$929$	52.5381	1.72372	0.861859	+	0.507148i	$0.169300\pi$
$930$	−0.826588	−0.0271049
$931$	−19.2661	−0.631420
$932$	4.95773	0.162396
$933$	−9.53146	−0.312046
$934$	23.9764	0.784531
$935$	1.60217	0.0523966
$936$	4.92511	0.160982
$937$	14.3085	0.467438	0.233719	−	0.972304i	$-0.424910\pi$
$937$	14.3085	0.467438	0.233719	+	0.972304i	$0.424910\pi$
$938$	6.00532	0.196081
$939$	21.1981	0.691775
$940$	1.88458	0.0614683
$941$	23.7941	0.775664	0.387832	−	0.921730i	$-0.373224\pi$
$941$	23.7941	0.775664	0.387832	+	0.921730i	$0.373224\pi$
$942$	−22.7560	−0.741430
$943$	−8.17999	−0.266377
$944$	1.00000	0.0325472
$945$	−0.176448	−0.00573984
$946$	43.5231	1.41506
$947$	14.8478	0.482488	0.241244	−	0.970465i	$-0.422445\pi$
$947$	14.8478	0.482488	0.241244	+	0.970465i	$0.422445\pi$
$948$	−3.21467	−0.104408
$949$	−43.6068	−1.41554
$950$	−14.4692	−0.469442
$951$	16.8520	0.546463
$952$	−0.661205	−0.0214298
$953$	26.7663	0.867045	0.433523	−	0.901143i	$-0.357270\pi$
$953$	26.7663	0.867045	0.433523	+	0.901143i	$0.357270\pi$
$954$	−12.8630	−0.416456
$955$	0.0923245	0.00298755
$956$	4.15922	0.134519
$957$	16.9548	0.548069
$958$	31.5251	1.01853
$959$	4.70358	0.151887
$960$	−0.266858	−0.00861280
$961$	−21.4056	−0.690502
$962$	−42.6774	−1.37597
$963$	11.3681	0.366332
$964$	7.21863	0.232497
$965$	−0.228323	−0.00734997
$966$	2.14077	0.0688782
$967$	32.5923	1.04810	0.524049	−	0.851688i	$-0.324421\pi$
$967$	32.5923	1.04810	0.524049	+	0.851688i	$0.324421\pi$
$968$	25.0461	0.805013
$969$	−2.93564	−0.0943065
$970$	2.53210	0.0813009
$971$	32.6578	1.04804	0.524020	−	0.851706i	$-0.324432\pi$
$971$	32.6578	1.04804	0.524020	+	0.851706i	$0.324432\pi$
$972$	1.00000	0.0320750
$973$	−10.1129	−0.324204
$974$	12.0173	0.385060
$975$	−24.2748	−0.777417
$976$	−5.51956	−0.176677
$977$	−47.4842	−1.51915	−0.759576	−	0.650418i	$-0.774594\pi$
$977$	−47.4842	−1.51915	−0.759576	+	0.650418i	$0.774594\pi$
$978$	7.62401	0.243789
$979$	55.7873	1.78297
$980$	1.75134	0.0559444
$981$	19.2501	0.614609
$982$	−31.1824	−0.995069
$983$	−55.6826	−1.77600	−0.888000	−	0.459844i	$-0.847905\pi$
$983$	−55.6826	−1.77600	−0.888000	+	0.459844i	$0.847905\pi$
$984$	−2.52649	−0.0805417
$985$	−0.0400852	−0.00127722
$986$	−2.82398	−0.0899340
$987$	−4.66951	−0.148632
$988$	14.4584	0.459982
$989$	23.4707	0.746323
$990$	−1.60217	−0.0509204
$991$	23.9067	0.759422	0.379711	−	0.925105i	$-0.376023\pi$
$991$	23.9067	0.759422	0.379711	+	0.925105i	$0.376023\pi$
$992$	3.09749	0.0983453
$993$	−3.03642	−0.0963578
$994$	0.266983	0.00846818
$995$	3.13943	0.0995268
$996$	5.07674	0.160863
$997$	7.74167	0.245181	0.122591	−	0.992457i	$-0.460880\pi$
$997$	7.74167	0.245181	0.122591	+	0.992457i	$0.460880\pi$
$998$	−1.51830	−0.0480608
$999$	−8.66526	−0.274157

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.ba.1.6	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.ba.1.6	✓	12	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.266858 q^{5} +1.00000 q^{6} +0.661205 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.266858 q^{5} +1.00000 q^{6} +0.661205 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.266858 q^{10} +6.00384 q^{11} +1.00000 q^{12} +4.92511 q^{13} +0.661205 q^{14} -0.266858 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} +2.93564 q^{19} -0.266858 q^{20} +0.661205 q^{21} +6.00384 q^{22} +3.23768 q^{23} +1.00000 q^{24} -4.92879 q^{25} +4.92511 q^{26} +1.00000 q^{27} +0.661205 q^{28} +2.82398 q^{29} -0.266858 q^{30} +3.09749 q^{31} +1.00000 q^{32} +6.00384 q^{33} -1.00000 q^{34} -0.176448 q^{35} +1.00000 q^{36} -8.66526 q^{37} +2.93564 q^{38} +4.92511 q^{39} -0.266858 q^{40} -2.52649 q^{41} +0.661205 q^{42} +7.24921 q^{43} +6.00384 q^{44} -0.266858 q^{45} +3.23768 q^{46} -7.06213 q^{47} +1.00000 q^{48} -6.56281 q^{49} -4.92879 q^{50} -1.00000 q^{51} +4.92511 q^{52} -12.8630 q^{53} +1.00000 q^{54} -1.60217 q^{55} +0.661205 q^{56} +2.93564 q^{57} +2.82398 q^{58} +1.00000 q^{59} -0.266858 q^{60} -5.51956 q^{61} +3.09749 q^{62} +0.661205 q^{63} +1.00000 q^{64} -1.31430 q^{65} +6.00384 q^{66} +9.08239 q^{67} -1.00000 q^{68} +3.23768 q^{69} -0.176448 q^{70} +0.403782 q^{71} +1.00000 q^{72} -8.85398 q^{73} -8.66526 q^{74} -4.92879 q^{75} +2.93564 q^{76} +3.96977 q^{77} +4.92511 q^{78} -3.21467 q^{79} -0.266858 q^{80} +1.00000 q^{81} -2.52649 q^{82} +5.07674 q^{83} +0.661205 q^{84} +0.266858 q^{85} +7.24921 q^{86} +2.82398 q^{87} +6.00384 q^{88} +9.29193 q^{89} -0.266858 q^{90} +3.25651 q^{91} +3.23768 q^{92} +3.09749 q^{93} -7.06213 q^{94} -0.783399 q^{95} +1.00000 q^{96} -9.48859 q^{97} -6.56281 q^{98} +6.00384 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{2} + 12 q^{3} + 12 q^{4} + 8 q^{5} + 12 q^{6} + 5 q^{7} + 12 q^{8} + 12 q^{9}+O(q^{10}) \) 12 * q + 12 * q^2 + 12 * q^3 + 12 * q^4 + 8 * q^5 + 12 * q^6 + 5 * q^7 + 12 * q^8 + 12 * q^9	\( 12 q + 12 q^{2} + 12 q^{3} + 12 q^{4} + 8 q^{5} + 12 q^{6} + 5 q^{7} + 12 q^{8} + 12 q^{9} + 8 q^{10} + 11 q^{11} + 12 q^{12} + 6 q^{13} + 5 q^{14} + 8 q^{15} + 12 q^{16} - 12 q^{17} + 12 q^{18} + 3 q^{19} + 8 q^{20} + 5 q^{21} + 11 q^{22} + 22 q^{23} + 12 q^{24} + 22 q^{25} + 6 q^{26} + 12 q^{27} + 5 q^{28} + 26 q^{29} + 8 q^{30} + q^{31} + 12 q^{32} + 11 q^{33} - 12 q^{34} + 24 q^{35} + 12 q^{36} + 10 q^{37} + 3 q^{38} + 6 q^{39} + 8 q^{40} + 16 q^{41} + 5 q^{42} + 23 q^{43} + 11 q^{44} + 8 q^{45} + 22 q^{46} + 6 q^{47} + 12 q^{48} + 11 q^{49} + 22 q^{50} - 12 q^{51} + 6 q^{52} + 10 q^{53} + 12 q^{54} + 15 q^{55} + 5 q^{56} + 3 q^{57} + 26 q^{58} + 12 q^{59} + 8 q^{60} + 15 q^{61} + q^{62} + 5 q^{63} + 12 q^{64} + 4 q^{65} + 11 q^{66} + 4 q^{67} - 12 q^{68} + 22 q^{69} + 24 q^{70} + 10 q^{71} + 12 q^{72} + 24 q^{73} + 10 q^{74} + 22 q^{75} + 3 q^{76} + 24 q^{77} + 6 q^{78} + 23 q^{79} + 8 q^{80} + 12 q^{81} + 16 q^{82} + 5 q^{84} - 8 q^{85} + 23 q^{86} + 26 q^{87} + 11 q^{88} + 13 q^{89} + 8 q^{90} + 3 q^{91} + 22 q^{92} + q^{93} + 6 q^{94} + 11 q^{95} + 12 q^{96} + 13 q^{97} + 11 q^{98} + 11 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 12 * q^3 + 12 * q^4 + 8 * q^5 + 12 * q^6 + 5 * q^7 + 12 * q^8 + 12 * q^9 + 8 * q^10 + 11 * q^11 + 12 * q^12 + 6 * q^13 + 5 * q^14 + 8 * q^15 + 12 * q^16 - 12 * q^17 + 12 * q^18 + 3 * q^19 + 8 * q^20 + 5 * q^21 + 11 * q^22 + 22 * q^23 + 12 * q^24 + 22 * q^25 + 6 * q^26 + 12 * q^27 + 5 * q^28 + 26 * q^29 + 8 * q^30 + q^31 + 12 * q^32 + 11 * q^33 - 12 * q^34 + 24 * q^35 + 12 * q^36 + 10 * q^37 + 3 * q^38 + 6 * q^39 + 8 * q^40 + 16 * q^41 + 5 * q^42 + 23 * q^43 + 11 * q^44 + 8 * q^45 + 22 * q^46 + 6 * q^47 + 12 * q^48 + 11 * q^49 + 22 * q^50 - 12 * q^51 + 6 * q^52 + 10 * q^53 + 12 * q^54 + 15 * q^55 + 5 * q^56 + 3 * q^57 + 26 * q^58 + 12 * q^59 + 8 * q^60 + 15 * q^61 + q^62 + 5 * q^63 + 12 * q^64 + 4 * q^65 + 11 * q^66 + 4 * q^67 - 12 * q^68 + 22 * q^69 + 24 * q^70 + 10 * q^71 + 12 * q^72 + 24 * q^73 + 10 * q^74 + 22 * q^75 + 3 * q^76 + 24 * q^77 + 6 * q^78 + 23 * q^79 + 8 * q^80 + 12 * q^81 + 16 * q^82 + 5 * q^84 - 8 * q^85 + 23 * q^86 + 26 * q^87 + 11 * q^88 + 13 * q^89 + 8 * q^90 + 3 * q^91 + 22 * q^92 + q^93 + 6 * q^94 + 11 * q^95 + 12 * q^96 + 13 * q^97 + 11 * q^98 + 11 * q^99

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