LMFDB - Embedded newform 6045.2.a.bh.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6045,2,Mod(1,6045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6045, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("6045.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6045 = 3 \cdot 5 \cdot 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6045.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:	$48.2695680219$
Analytic rank:	$0$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 2 x^{16} - 25 x^{15} + 47 x^{14} + 252 x^{13} - 437 x^{12} - 1319 x^{11} + 2056 x^{10} + \cdots + 8 $ x^17 - 2x^16 - 25x^15 + 47x^14 + 252x^13 - 437x^12 - 1319x^11 + 2056x^10 + 3854x^9 - 5201x^8 - 6304x^7 + 6915x^6 + 5469x^5 - 4238x^4 - 2198x^3 + 760x^2 + 306x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$1.15560$ of defining polynomial
Character	$\chi$	$=$	6045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.15560 q^{2} -1.00000 q^{3} -0.664588 q^{4} +1.00000 q^{5} -1.15560 q^{6} +3.45180 q^{7} -3.07920 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.15560 q^{2} -1.00000 q^{3} -0.664588 q^{4} +1.00000 q^{5} -1.15560 q^{6} +3.45180 q^{7} -3.07920 q^{8} +1.00000 q^{9} +1.15560 q^{10} +3.68267 q^{11} +0.664588 q^{12} +1.00000 q^{13} +3.98890 q^{14} -1.00000 q^{15} -2.22915 q^{16} +5.55902 q^{17} +1.15560 q^{18} +7.37771 q^{19} -0.664588 q^{20} -3.45180 q^{21} +4.25569 q^{22} -2.65936 q^{23} +3.07920 q^{24} +1.00000 q^{25} +1.15560 q^{26} -1.00000 q^{27} -2.29402 q^{28} -7.40999 q^{29} -1.15560 q^{30} +1.00000 q^{31} +3.58239 q^{32} -3.68267 q^{33} +6.42401 q^{34} +3.45180 q^{35} -0.664588 q^{36} +6.10362 q^{37} +8.52569 q^{38} -1.00000 q^{39} -3.07920 q^{40} +3.82913 q^{41} -3.98890 q^{42} +4.86623 q^{43} -2.44745 q^{44} +1.00000 q^{45} -3.07316 q^{46} -7.44601 q^{47} +2.22915 q^{48} +4.91491 q^{49} +1.15560 q^{50} -5.55902 q^{51} -0.664588 q^{52} -5.58500 q^{53} -1.15560 q^{54} +3.68267 q^{55} -10.6288 q^{56} -7.37771 q^{57} -8.56299 q^{58} -5.32340 q^{59} +0.664588 q^{60} +0.0429733 q^{61} +1.15560 q^{62} +3.45180 q^{63} +8.59811 q^{64} +1.00000 q^{65} -4.25569 q^{66} +8.97401 q^{67} -3.69446 q^{68} +2.65936 q^{69} +3.98890 q^{70} +6.99933 q^{71} -3.07920 q^{72} -10.0956 q^{73} +7.05335 q^{74} -1.00000 q^{75} -4.90314 q^{76} +12.7118 q^{77} -1.15560 q^{78} -16.2880 q^{79} -2.22915 q^{80} +1.00000 q^{81} +4.42495 q^{82} -7.76523 q^{83} +2.29402 q^{84} +5.55902 q^{85} +5.62342 q^{86} +7.40999 q^{87} -11.3397 q^{88} +4.35728 q^{89} +1.15560 q^{90} +3.45180 q^{91} +1.76738 q^{92} -1.00000 q^{93} -8.60462 q^{94} +7.37771 q^{95} -3.58239 q^{96} +0.514614 q^{97} +5.67967 q^{98} +3.68267 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q + 2 q^{2} - 17 q^{3} + 20 q^{4} + 17 q^{5} - 2 q^{6} + 18 q^{7} + 9 q^{8} + 17 q^{9}+O(q^{10}) $ 17 * q + 2 * q^2 - 17 * q^3 + 20 * q^4 + 17 * q^5 - 2 * q^6 + 18 * q^7 + 9 * q^8 + 17 * q^9	\( 17 q + 2 q^{2} - 17 q^{3} + 20 q^{4} + 17 q^{5} - 2 q^{6} + 18 q^{7} + 9 q^{8} + 17 q^{9} + 2 q^{10} + 3 q^{11} - 20 q^{12} + 17 q^{13} + q^{14} - 17 q^{15} + 26 q^{16} + 2 q^{18} + 10 q^{19} + 20 q^{20} - 18 q^{21} + 5 q^{22} + 16 q^{23} - 9 q^{24} + 17 q^{25} + 2 q^{26} - 17 q^{27} + 36 q^{28} - 3 q^{29} - 2 q^{30} + 17 q^{31} + 20 q^{32} - 3 q^{33} + q^{34} + 18 q^{35} + 20 q^{36} + 14 q^{37} + 22 q^{38} - 17 q^{39} + 9 q^{40} - 6 q^{41} - q^{42} + 24 q^{43} - 15 q^{44} + 17 q^{45} + 6 q^{46} + 25 q^{47} - 26 q^{48} + 31 q^{49} + 2 q^{50} + 20 q^{52} - 15 q^{53} - 2 q^{54} + 3 q^{55} + 31 q^{56} - 10 q^{57} + 44 q^{58} + 16 q^{59} - 20 q^{60} - 5 q^{61} + 2 q^{62} + 18 q^{63} + 35 q^{64} + 17 q^{65} - 5 q^{66} + 50 q^{67} + 13 q^{68} - 16 q^{69} + q^{70} + 16 q^{71} + 9 q^{72} + 33 q^{73} + 2 q^{74} - 17 q^{75} + 9 q^{77} - 2 q^{78} - 10 q^{79} + 26 q^{80} + 17 q^{81} + 61 q^{82} + 27 q^{83} - 36 q^{84} - 12 q^{86} + 3 q^{87} + 23 q^{88} - 24 q^{89} + 2 q^{90} + 18 q^{91} - 21 q^{92} - 17 q^{93} + 6 q^{94} + 10 q^{95} - 20 q^{96} + 48 q^{97} + 14 q^{98} + 3 q^{99}+O(q^{100}) \) 17 * q + 2 * q^2 - 17 * q^3 + 20 * q^4 + 17 * q^5 - 2 * q^6 + 18 * q^7 + 9 * q^8 + 17 * q^9 + 2 * q^10 + 3 * q^11 - 20 * q^12 + 17 * q^13 + q^14 - 17 * q^15 + 26 * q^16 + 2 * q^18 + 10 * q^19 + 20 * q^20 - 18 * q^21 + 5 * q^22 + 16 * q^23 - 9 * q^24 + 17 * q^25 + 2 * q^26 - 17 * q^27 + 36 * q^28 - 3 * q^29 - 2 * q^30 + 17 * q^31 + 20 * q^32 - 3 * q^33 + q^34 + 18 * q^35 + 20 * q^36 + 14 * q^37 + 22 * q^38 - 17 * q^39 + 9 * q^40 - 6 * q^41 - q^42 + 24 * q^43 - 15 * q^44 + 17 * q^45 + 6 * q^46 + 25 * q^47 - 26 * q^48 + 31 * q^49 + 2 * q^50 + 20 * q^52 - 15 * q^53 - 2 * q^54 + 3 * q^55 + 31 * q^56 - 10 * q^57 + 44 * q^58 + 16 * q^59 - 20 * q^60 - 5 * q^61 + 2 * q^62 + 18 * q^63 + 35 * q^64 + 17 * q^65 - 5 * q^66 + 50 * q^67 + 13 * q^68 - 16 * q^69 + q^70 + 16 * q^71 + 9 * q^72 + 33 * q^73 + 2 * q^74 - 17 * q^75 + 9 * q^77 - 2 * q^78 - 10 * q^79 + 26 * q^80 + 17 * q^81 + 61 * q^82 + 27 * q^83 - 36 * q^84 - 12 * q^86 + 3 * q^87 + 23 * q^88 - 24 * q^89 + 2 * q^90 + 18 * q^91 - 21 * q^92 - 17 * q^93 + 6 * q^94 + 10 * q^95 - 20 * q^96 + 48 * q^97 + 14 * q^98 + 3 * 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 $

$2$	1.15560	0.817133	0.408566	−	0.912729i	$-0.366029\pi$
$2$	1.15560	0.817133	0.408566	+	0.912729i	$0.366029\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.664588	−0.332294
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.15560	−0.471772
$7$	3.45180	1.30466	0.652328	−	0.757936i	$-0.273792\pi$
$7$	3.45180	1.30466	0.652328	+	0.757936i	$0.273792\pi$
$8$	−3.07920	−1.08866
$9$	1.00000	0.333333
$10$	1.15560	0.365433
$11$	3.68267	1.11037	0.555183	−	0.831728i	$-0.312648\pi$
$11$	3.68267	1.11037	0.555183	+	0.831728i	$0.312648\pi$
$12$	0.664588	0.191850
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	3.98890	1.06608
$15$	−1.00000	−0.258199
$16$	−2.22915	−0.557287
$17$	5.55902	1.34826	0.674130	−	0.738613i	$-0.264519\pi$
$17$	5.55902	1.34826	0.674130	+	0.738613i	$0.264519\pi$
$18$	1.15560	0.272378
$19$	7.37771	1.69256	0.846282	−	0.532736i	$-0.178836\pi$
$19$	7.37771	1.69256	0.846282	+	0.532736i	$0.178836\pi$
$20$	−0.664588	−0.148606
$21$	−3.45180	−0.753244
$22$	4.25569	0.907316
$23$	−2.65936	−0.554515	−0.277258	−	0.960796i	$-0.589426\pi$
$23$	−2.65936	−0.554515	−0.277258	+	0.960796i	$0.589426\pi$
$24$	3.07920	0.628539
$25$	1.00000	0.200000
$26$	1.15560	0.226632
$27$	−1.00000	−0.192450
$28$	−2.29402	−0.433529
$29$	−7.40999	−1.37600	−0.688001	−	0.725710i	$-0.741511\pi$
$29$	−7.40999	−1.37600	−0.688001	+	0.725710i	$0.741511\pi$
$30$	−1.15560	−0.210983
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	3.58239	0.633283
$33$	−3.68267	−0.641070
$34$	6.42401	1.10171
$35$	3.45180	0.583460
$36$	−0.664588	−0.110765
$37$	6.10362	1.00343	0.501715	−	0.865033i	$-0.332703\pi$
$37$	6.10362	1.00343	0.501715	+	0.865033i	$0.332703\pi$
$38$	8.52569	1.38305
$39$	−1.00000	−0.160128
$40$	−3.07920	−0.486864
$41$	3.82913	0.598010	0.299005	−	0.954251i	$-0.403345\pi$
$41$	3.82913	0.598010	0.299005	+	0.954251i	$0.403345\pi$
$42$	−3.98890	−0.615501
$43$	4.86623	0.742093	0.371047	−	0.928614i	$-0.378999\pi$
$43$	4.86623	0.742093	0.371047	+	0.928614i	$0.378999\pi$
$44$	−2.44745	−0.368968
$45$	1.00000	0.149071
$46$	−3.07316	−0.453112
$47$	−7.44601	−1.08611	−0.543056	−	0.839696i	$-0.682733\pi$
$47$	−7.44601	−1.08611	−0.543056	+	0.839696i	$0.682733\pi$
$48$	2.22915	0.321750
$49$	4.91491	0.702130
$50$	1.15560	0.163427
$51$	−5.55902	−0.778418
$52$	−0.664588	−0.0921617
$53$	−5.58500	−0.767159	−0.383580	−	0.923508i	$-0.625309\pi$
$53$	−5.58500	−0.767159	−0.383580	+	0.923508i	$0.625309\pi$
$54$	−1.15560	−0.157257
$55$	3.68267	0.496571
$56$	−10.6288	−1.42033
$57$	−7.37771	−0.977202
$58$	−8.56299	−1.12438
$59$	−5.32340	−0.693048	−0.346524	−	0.938041i	$-0.612638\pi$
$59$	−5.32340	−0.693048	−0.346524	+	0.938041i	$0.612638\pi$
$60$	0.664588	0.0857979
$61$	0.0429733	0.00550217	0.00275109	−	0.999996i	$-0.499124\pi$
$61$	0.0429733	0.00550217	0.00275109	+	0.999996i	$0.499124\pi$
$62$	1.15560	0.146761
$63$	3.45180	0.434886
$64$	8.59811	1.07476
$65$	1.00000	0.124035
$66$	−4.25569	−0.523839
$67$	8.97401	1.09635	0.548175	−	0.836364i	$-0.315323\pi$
$67$	8.97401	1.09635	0.548175	+	0.836364i	$0.315323\pi$
$68$	−3.69446	−0.448019
$69$	2.65936	0.320149
$70$	3.98890	0.476765
$71$	6.99933	0.830667	0.415334	−	0.909669i	$-0.363665\pi$
$71$	6.99933	0.830667	0.415334	+	0.909669i	$0.363665\pi$
$72$	−3.07920	−0.362887
$73$	−10.0956	−1.18160	−0.590801	−	0.806818i	$-0.701188\pi$
$73$	−10.0956	−1.18160	−0.590801	+	0.806818i	$0.701188\pi$
$74$	7.05335	0.819935
$75$	−1.00000	−0.115470
$76$	−4.90314	−0.562428
$77$	12.7118	1.44865
$78$	−1.15560	−0.130846
$79$	−16.2880	−1.83254	−0.916271	−	0.400559i	$-0.868816\pi$
$79$	−16.2880	−1.83254	−0.916271	+	0.400559i	$0.868816\pi$
$80$	−2.22915	−0.249226
$81$	1.00000	0.111111
$82$	4.42495	0.488654
$83$	−7.76523	−0.852344	−0.426172	−	0.904642i	$-0.640138\pi$
$83$	−7.76523	−0.852344	−0.426172	+	0.904642i	$0.640138\pi$
$84$	2.29402	0.250298
$85$	5.55902	0.602960
$86$	5.62342	0.606389
$87$	7.40999	0.794435
$88$	−11.3397	−1.20881
$89$	4.35728	0.461871	0.230936	−	0.972969i	$-0.425821\pi$
$89$	4.35728	0.461871	0.230936	+	0.972969i	$0.425821\pi$
$90$	1.15560	0.121811
$91$	3.45180	0.361847
$92$	1.76738	0.184262
$93$	−1.00000	−0.103695
$94$	−8.60462	−0.887498
$95$	7.37771	0.756937
$96$	−3.58239	−0.365626
$97$	0.514614	0.0522511	0.0261256	−	0.999659i	$-0.491683\pi$
$97$	0.514614	0.0522511	0.0261256	+	0.999659i	$0.491683\pi$
$98$	5.67967	0.573733
$99$	3.68267	0.370122
$100$	−0.664588	−0.0664588
$101$	5.49389	0.546662	0.273331	−	0.961920i	$-0.411875\pi$
$101$	5.49389	0.546662	0.273331	+	0.961920i	$0.411875\pi$
$102$	−6.42401	−0.636071
$103$	0.794455	0.0782800	0.0391400	−	0.999234i	$-0.487538\pi$
$103$	0.794455	0.0782800	0.0391400	+	0.999234i	$0.487538\pi$
$104$	−3.07920	−0.301940
$105$	−3.45180	−0.336861
$106$	−6.45403	−0.626871
$107$	3.91613	0.378587	0.189293	−	0.981921i	$-0.439380\pi$
$107$	3.91613	0.378587	0.189293	+	0.981921i	$0.439380\pi$
$108$	0.664588	0.0639500
$109$	11.9042	1.14021	0.570107	−	0.821570i	$-0.306902\pi$
$109$	11.9042	1.14021	0.570107	+	0.821570i	$0.306902\pi$
$110$	4.25569	0.405764
$111$	−6.10362	−0.579330
$112$	−7.69457	−0.727068
$113$	−4.70375	−0.442491	−0.221246	−	0.975218i	$-0.571012\pi$
$113$	−4.70375	−0.442491	−0.221246	+	0.975218i	$0.571012\pi$
$114$	−8.52569	−0.798504
$115$	−2.65936	−0.247987
$116$	4.92459	0.457237
$117$	1.00000	0.0924500
$118$	−6.15172	−0.566312
$119$	19.1886	1.75902
$120$	3.07920	0.281091
$121$	2.56203	0.232912
$122$	0.0496600	0.00449601
$123$	−3.82913	−0.345261
$124$	−0.664588	−0.0596817
$125$	1.00000	0.0894427
$126$	3.98890	0.355359
$127$	−5.46072	−0.484560	−0.242280	−	0.970206i	$-0.577895\pi$
$127$	−5.46072	−0.484560	−0.242280	+	0.970206i	$0.577895\pi$
$128$	2.77120	0.244941
$129$	−4.86623	−0.428448
$130$	1.15560	0.101353
$131$	−19.7147	−1.72248	−0.861242	−	0.508195i	$-0.830313\pi$
$131$	−19.7147	−1.72248	−0.861242	+	0.508195i	$0.830313\pi$
$132$	2.44745	0.213024
$133$	25.4664	2.20821
$134$	10.3704	0.895863
$135$	−1.00000	−0.0860663
$136$	−17.1173	−1.46780
$137$	14.5229	1.24078	0.620388	−	0.784295i	$-0.286975\pi$
$137$	14.5229	1.24078	0.620388	+	0.784295i	$0.286975\pi$
$138$	3.07316	0.261605
$139$	19.4720	1.65160	0.825798	−	0.563966i	$-0.190725\pi$
$139$	19.4720	1.65160	0.825798	+	0.563966i	$0.190725\pi$
$140$	−2.29402	−0.193880
$141$	7.44601	0.627067
$142$	8.08842	0.678766
$143$	3.68267	0.307960
$144$	−2.22915	−0.185762
$145$	−7.40999	−0.615366
$146$	−11.6665	−0.965525
$147$	−4.91491	−0.405375
$148$	−4.05639	−0.333433
$149$	−10.7211	−0.878306	−0.439153	−	0.898412i	$-0.644721\pi$
$149$	−10.7211	−0.878306	−0.439153	+	0.898412i	$0.644721\pi$
$150$	−1.15560	−0.0943544
$151$	2.00613	0.163256	0.0816282	−	0.996663i	$-0.473988\pi$
$151$	2.00613	0.163256	0.0816282	+	0.996663i	$0.473988\pi$
$152$	−22.7174	−1.84263
$153$	5.55902	0.449420
$154$	14.6898	1.18374
$155$	1.00000	0.0803219
$156$	0.664588	0.0532096
$157$	14.7473	1.17696	0.588482	−	0.808511i	$-0.299726\pi$
$157$	14.7473	1.17696	0.588482	+	0.808511i	$0.299726\pi$
$158$	−18.8224	−1.49743
$159$	5.58500	0.442920
$160$	3.58239	0.283213
$161$	−9.17958	−0.723452
$162$	1.15560	0.0907925
$163$	−13.3734	−1.04749	−0.523744	−	0.851876i	$-0.675465\pi$
$163$	−13.3734	−1.04749	−0.523744	+	0.851876i	$0.675465\pi$
$164$	−2.54479	−0.198715
$165$	−3.68267	−0.286695
$166$	−8.97350	−0.696479
$167$	4.77435	0.369451	0.184725	−	0.982790i	$-0.440860\pi$
$167$	4.77435	0.369451	0.184725	+	0.982790i	$0.440860\pi$
$168$	10.6288	0.820028
$169$	1.00000	0.0769231
$170$	6.42401	0.492699
$171$	7.37771	0.564188
$172$	−3.23404	−0.246593
$173$	15.2716	1.16107	0.580537	−	0.814234i	$-0.302843\pi$
$173$	15.2716	1.16107	0.580537	+	0.814234i	$0.302843\pi$
$174$	8.56299	0.649159
$175$	3.45180	0.260931
$176$	−8.20921	−0.618792
$177$	5.32340	0.400131
$178$	5.03528	0.377410
$179$	−25.0704	−1.87385	−0.936926	−	0.349527i	$-0.886342\pi$
$179$	−25.0704	−1.87385	−0.936926	+	0.349527i	$0.886342\pi$
$180$	−0.664588	−0.0495354
$181$	−20.5638	−1.52849	−0.764247	−	0.644924i	$-0.776889\pi$
$181$	−20.5638	−1.52849	−0.764247	+	0.644924i	$0.776889\pi$
$182$	3.98890	0.295677
$183$	−0.0429733	−0.00317668
$184$	8.18870	0.603679
$185$	6.10362	0.448747
$186$	−1.15560	−0.0847327
$187$	20.4720	1.49706
$188$	4.94853	0.360908
$189$	−3.45180	−0.251081
$190$	8.52569	0.618518
$191$	15.7412	1.13899	0.569495	−	0.821995i	$-0.307139\pi$
$191$	15.7412	1.13899	0.569495	+	0.821995i	$0.307139\pi$
$192$	−8.59811	−0.620515
$193$	−1.22423	−0.0881222	−0.0440611	−	0.999029i	$-0.514030\pi$
$193$	−1.22423	−0.0881222	−0.0440611	+	0.999029i	$0.514030\pi$
$194$	0.594688	0.0426961
$195$	−1.00000	−0.0716115
$196$	−3.26639	−0.233313
$197$	4.49584	0.320315	0.160158	−	0.987091i	$-0.448800\pi$
$197$	4.49584	0.320315	0.160158	+	0.987091i	$0.448800\pi$
$198$	4.25569	0.302439
$199$	19.9721	1.41579	0.707894	−	0.706319i	$-0.249645\pi$
$199$	19.9721	1.41579	0.707894	+	0.706319i	$0.249645\pi$
$200$	−3.07920	−0.217732
$201$	−8.97401	−0.632978
$202$	6.34874	0.446696
$203$	−25.5778	−1.79521
$204$	3.69446	0.258664
$205$	3.82913	0.267438
$206$	0.918072	0.0639651
$207$	−2.65936	−0.184838
$208$	−2.22915	−0.154564
$209$	27.1696	1.87936
$210$	−3.98890	−0.275260
$211$	10.1027	0.695499	0.347750	−	0.937587i	$-0.386946\pi$
$211$	10.1027	0.695499	0.347750	+	0.937587i	$0.386946\pi$
$212$	3.71172	0.254922
$213$	−6.99933	−0.479586
$214$	4.52548	0.309356
$215$	4.86623	0.331874
$216$	3.07920	0.209513
$217$	3.45180	0.234323
$218$	13.7565	0.931706
$219$	10.0956	0.682198
$220$	−2.44745	−0.165007
$221$	5.55902	0.373940
$222$	−7.05335	−0.473390
$223$	19.0499	1.27567	0.637837	−	0.770172i	$-0.279829\pi$
$223$	19.0499	1.27567	0.637837	+	0.770172i	$0.279829\pi$
$224$	12.3657	0.826218
$225$	1.00000	0.0666667
$226$	−5.43565	−0.361574
$227$	−5.26928	−0.349734	−0.174867	−	0.984592i	$-0.555950\pi$
$227$	−5.26928	−0.349734	−0.174867	+	0.984592i	$0.555950\pi$
$228$	4.90314	0.324718
$229$	4.78252	0.316038	0.158019	−	0.987436i	$-0.449489\pi$
$229$	4.78252	0.316038	0.158019	+	0.987436i	$0.449489\pi$
$230$	−3.07316	−0.202638
$231$	−12.7118	−0.836376
$232$	22.8168	1.49800
$233$	16.6051	1.08784	0.543919	−	0.839138i	$-0.316940\pi$
$233$	16.6051	1.08784	0.543919	+	0.839138i	$0.316940\pi$
$234$	1.15560	0.0755440
$235$	−7.44601	−0.485724
$236$	3.53787	0.230295
$237$	16.2880	1.05802
$238$	22.1744	1.43735
$239$	9.11652	0.589698	0.294849	−	0.955544i	$-0.404731\pi$
$239$	9.11652	0.589698	0.294849	+	0.955544i	$0.404731\pi$
$240$	2.22915	0.143891
$241$	7.03305	0.453038	0.226519	−	0.974007i	$-0.427265\pi$
$241$	7.03305	0.453038	0.226519	+	0.974007i	$0.427265\pi$
$242$	2.96068	0.190320
$243$	−1.00000	−0.0641500
$244$	−0.0285596	−0.00182834
$245$	4.91491	0.314002
$246$	−4.42495	−0.282124
$247$	7.37771	0.469433
$248$	−3.07920	−0.195529
$249$	7.76523	0.492101
$250$	1.15560	0.0730866
$251$	−0.731078	−0.0461453	−0.0230726	−	0.999734i	$-0.507345\pi$
$251$	−0.731078	−0.0461453	−0.0230726	+	0.999734i	$0.507345\pi$
$252$	−2.29402	−0.144510
$253$	−9.79354	−0.615714
$254$	−6.31040	−0.395950
$255$	−5.55902	−0.348119
$256$	−13.9938	−0.874614
$257$	5.08032	0.316901	0.158451	−	0.987367i	$-0.449350\pi$
$257$	5.08032	0.316901	0.158451	+	0.987367i	$0.449350\pi$
$258$	−5.62342	−0.350099
$259$	21.0685	1.30913
$260$	−0.664588	−0.0412160
$261$	−7.40999	−0.458667
$262$	−22.7824	−1.40750
$263$	12.4367	0.766878	0.383439	−	0.923566i	$-0.374740\pi$
$263$	12.4367	0.766878	0.383439	+	0.923566i	$0.374740\pi$
$264$	11.3397	0.697908
$265$	−5.58500	−0.343084
$266$	29.4289	1.80440
$267$	−4.35728	−0.266661
$268$	−5.96401	−0.364310
$269$	−17.6601	−1.07676	−0.538378	−	0.842704i	$-0.680963\pi$
$269$	−17.6601	−1.07676	−0.538378	+	0.842704i	$0.680963\pi$
$270$	−1.15560	−0.0703276
$271$	6.24082	0.379103	0.189551	−	0.981871i	$-0.439297\pi$
$271$	6.24082	0.379103	0.189551	+	0.981871i	$0.439297\pi$
$272$	−12.3919	−0.751368
$273$	−3.45180	−0.208912
$274$	16.7827	1.01388
$275$	3.68267	0.222073
$276$	−1.76738	−0.106384
$277$	6.62059	0.397793	0.198896	−	0.980021i	$-0.436264\pi$
$277$	6.62059	0.397793	0.198896	+	0.980021i	$0.436264\pi$
$278$	22.5019	1.34957
$279$	1.00000	0.0598684
$280$	−10.6288	−0.635191
$281$	16.0010	0.954540	0.477270	−	0.878757i	$-0.341626\pi$
$281$	16.0010	0.954540	0.477270	+	0.878757i	$0.341626\pi$
$282$	8.60462	0.512397
$283$	−17.8454	−1.06080	−0.530401	−	0.847747i	$-0.677958\pi$
$283$	−17.8454	−1.06080	−0.530401	+	0.847747i	$0.677958\pi$
$284$	−4.65167	−0.276026
$285$	−7.37771	−0.437018
$286$	4.25569	0.251644
$287$	13.2174	0.780198
$288$	3.58239	0.211094
$289$	13.9027	0.817806
$290$	−8.56299	−0.502836
$291$	−0.514614	−0.0301672
$292$	6.70941	0.392639
$293$	26.6384	1.55623	0.778116	−	0.628120i	$-0.216175\pi$
$293$	26.6384	1.55623	0.778116	+	0.628120i	$0.216175\pi$
$294$	−5.67967	−0.331245
$295$	−5.32340	−0.309940
$296$	−18.7943	−1.09239
$297$	−3.68267	−0.213690
$298$	−12.3893	−0.717693
$299$	−2.65936	−0.153795
$300$	0.664588	0.0383700
$301$	16.7972	0.968177
$302$	2.31828	0.133402
$303$	−5.49389	−0.315616
$304$	−16.4460	−0.943244
$305$	0.0429733	0.00246065
$306$	6.42401	0.367236
$307$	−24.7994	−1.41538	−0.707689	−	0.706524i	$-0.750262\pi$
$307$	−24.7994	−1.41538	−0.707689	+	0.706524i	$0.750262\pi$
$308$	−8.44812	−0.481376
$309$	−0.794455	−0.0451950
$310$	1.15560	0.0656337
$311$	−28.3490	−1.60753	−0.803763	−	0.594950i	$-0.797172\pi$
$311$	−28.3490	−1.60753	−0.803763	+	0.594950i	$0.797172\pi$
$312$	3.07920	0.174325
$313$	5.31496	0.300420	0.150210	−	0.988654i	$-0.452005\pi$
$313$	5.31496	0.300420	0.150210	+	0.988654i	$0.452005\pi$
$314$	17.0420	0.961736
$315$	3.45180	0.194487
$316$	10.8248	0.608942
$317$	−27.7691	−1.55967	−0.779833	−	0.625988i	$-0.784696\pi$
$317$	−27.7691	−1.55967	−0.779833	+	0.625988i	$0.784696\pi$
$318$	6.45403	0.361924
$319$	−27.2885	−1.52786
$320$	8.59811	0.480649
$321$	−3.91613	−0.218577
$322$	−10.6079	−0.591156
$323$	41.0128	2.28202
$324$	−0.664588	−0.0369215
$325$	1.00000	0.0554700
$326$	−15.4543	−0.855937
$327$	−11.9042	−0.658303
$328$	−11.7907	−0.651031
$329$	−25.7021	−1.41700
$330$	−4.25569	−0.234268
$331$	22.7349	1.24962	0.624812	−	0.780775i	$-0.285176\pi$
$331$	22.7349	1.24962	0.624812	+	0.780775i	$0.285176\pi$
$332$	5.16067	0.283229
$333$	6.10362	0.334477
$334$	5.51725	0.301890
$335$	8.97401	0.490302
$336$	7.69457	0.419773
$337$	−7.58767	−0.413327	−0.206663	−	0.978412i	$-0.566261\pi$
$337$	−7.58767	−0.413327	−0.206663	+	0.978412i	$0.566261\pi$
$338$	1.15560	0.0628564
$339$	4.70375	0.255472
$340$	−3.69446	−0.200360
$341$	3.68267	0.199428
$342$	8.52569	0.461016
$343$	−7.19731	−0.388618
$344$	−14.9841	−0.807888
$345$	2.65936	0.143175
$346$	17.6478	0.948752
$347$	17.4202	0.935166	0.467583	−	0.883949i	$-0.345125\pi$
$347$	17.4202	0.935166	0.467583	+	0.883949i	$0.345125\pi$
$348$	−4.92459	−0.263986
$349$	−36.0401	−1.92918	−0.964590	−	0.263753i	$-0.915040\pi$
$349$	−36.0401	−1.92918	−0.964590	+	0.263753i	$0.915040\pi$
$350$	3.98890	0.213216
$351$	−1.00000	−0.0533761
$352$	13.1928	0.703176
$353$	−25.6193	−1.36358	−0.681789	−	0.731548i	$-0.738798\pi$
$353$	−25.6193	−1.36358	−0.681789	+	0.731548i	$0.738798\pi$
$354$	6.15172	0.326960
$355$	6.99933	0.371486
$356$	−2.89580	−0.153477
$357$	−19.1886	−1.01557
$358$	−28.9714	−1.53119
$359$	6.87756	0.362984	0.181492	−	0.983392i	$-0.441907\pi$
$359$	6.87756	0.362984	0.181492	+	0.983392i	$0.441907\pi$
$360$	−3.07920	−0.162288
$361$	35.4306	1.86477
$362$	−23.7635	−1.24898
$363$	−2.56203	−0.134472
$364$	−2.29402	−0.120239
$365$	−10.0956	−0.528428
$366$	−0.0496600	−0.00259577
$367$	−6.24011	−0.325731	−0.162866	−	0.986648i	$-0.552074\pi$
$367$	−6.24011	−0.325731	−0.162866	+	0.986648i	$0.552074\pi$
$368$	5.92811	0.309024
$369$	3.82913	0.199337
$370$	7.05335	0.366686
$371$	−19.2783	−1.00088
$372$	0.664588	0.0344573
$373$	15.4603	0.800506	0.400253	−	0.916405i	$-0.368922\pi$
$373$	15.4603	0.800506	0.400253	+	0.916405i	$0.368922\pi$
$374$	23.6575	1.22330
$375$	−1.00000	−0.0516398
$376$	22.9278	1.18241
$377$	−7.40999	−0.381634
$378$	−3.98890	−0.205167
$379$	6.99678	0.359401	0.179700	−	0.983721i	$-0.442487\pi$
$379$	6.99678	0.359401	0.179700	+	0.983721i	$0.442487\pi$
$380$	−4.90314	−0.251526
$381$	5.46072	0.279761
$382$	18.1905	0.930706
$383$	−11.6416	−0.594856	−0.297428	−	0.954744i	$-0.596129\pi$
$383$	−11.6416	−0.594856	−0.297428	+	0.954744i	$0.596129\pi$
$384$	−2.77120	−0.141417
$385$	12.7118	0.647854
$386$	−1.41472	−0.0720075
$387$	4.86623	0.247364
$388$	−0.342006	−0.0173627
$389$	5.75465	0.291772	0.145886	−	0.989301i	$-0.453397\pi$
$389$	5.75465	0.291772	0.145886	+	0.989301i	$0.453397\pi$
$390$	−1.15560	−0.0585161
$391$	−14.7834	−0.747631
$392$	−15.1340	−0.764381
$393$	19.7147	0.994477
$394$	5.19539	0.261740
$395$	−16.2880	−0.819538
$396$	−2.44745	−0.122989
$397$	1.61697	0.0811532	0.0405766	−	0.999176i	$-0.487081\pi$
$397$	1.61697	0.0811532	0.0405766	+	0.999176i	$0.487081\pi$
$398$	23.0798	1.15689
$399$	−25.4664	−1.27491
$400$	−2.22915	−0.111457
$401$	−5.59014	−0.279158	−0.139579	−	0.990211i	$-0.544575\pi$
$401$	−5.59014	−0.279158	−0.139579	+	0.990211i	$0.544575\pi$
$402$	−10.3704	−0.517227
$403$	1.00000	0.0498135
$404$	−3.65117	−0.181652
$405$	1.00000	0.0496904
$406$	−29.5577	−1.46692
$407$	22.4776	1.11417
$408$	17.1173	0.847434
$409$	−9.60922	−0.475145	−0.237573	−	0.971370i	$-0.576352\pi$
$409$	−9.60922	−0.475145	−0.237573	+	0.971370i	$0.576352\pi$
$410$	4.42495	0.218533
$411$	−14.5229	−0.716363
$412$	−0.527985	−0.0260119
$413$	−18.3753	−0.904190
$414$	−3.07316	−0.151037
$415$	−7.76523	−0.381180
$416$	3.58239	0.175641
$417$	−19.4720	−0.953549
$418$	31.3973	1.53569
$419$	25.3461	1.23824	0.619120	−	0.785296i	$-0.287489\pi$
$419$	25.3461	1.23824	0.619120	+	0.785296i	$0.287489\pi$
$420$	2.29402	0.111937
$421$	−23.2753	−1.13437	−0.567185	−	0.823590i	$-0.691968\pi$
$421$	−23.2753	−1.13437	−0.567185	+	0.823590i	$0.691968\pi$
$422$	11.6747	0.568315
$423$	−7.44601	−0.362038
$424$	17.1973	0.835177
$425$	5.55902	0.269652
$426$	−8.08842	−0.391885
$427$	0.148335	0.00717845
$428$	−2.60261	−0.125802
$429$	−3.68267	−0.177801
$430$	5.62342	0.271185
$431$	13.1766	0.634694	0.317347	−	0.948309i	$-0.397208\pi$
$431$	13.1766	0.634694	0.317347	+	0.948309i	$0.397208\pi$
$432$	2.22915	0.107250
$433$	31.4111	1.50952	0.754761	−	0.655999i	$-0.227753\pi$
$433$	31.4111	1.50952	0.754761	+	0.655999i	$0.227753\pi$
$434$	3.98890	0.191473
$435$	7.40999	0.355282
$436$	−7.91137	−0.378886
$437$	−19.6200	−0.938552
$438$	11.6665	0.557446
$439$	−7.35849	−0.351202	−0.175601	−	0.984461i	$-0.556187\pi$
$439$	−7.35849	−0.351202	−0.175601	+	0.984461i	$0.556187\pi$
$440$	−11.3397	−0.540597
$441$	4.91491	0.234043
$442$	6.42401	0.305559
$443$	−4.32041	−0.205269	−0.102634	−	0.994719i	$-0.532727\pi$
$443$	−4.32041	−0.205269	−0.102634	+	0.994719i	$0.532727\pi$
$444$	4.05639	0.192508
$445$	4.35728	0.206555
$446$	22.0140	1.04239
$447$	10.7211	0.507090
$448$	29.6789	1.40220
$449$	35.4081	1.67101	0.835507	−	0.549480i	$-0.185174\pi$
$449$	35.4081	1.67101	0.835507	+	0.549480i	$0.185174\pi$
$450$	1.15560	0.0544755
$451$	14.1014	0.664010
$452$	3.12605	0.147037
$453$	−2.00613	−0.0942561
$454$	−6.08918	−0.285779
$455$	3.45180	0.161823
$456$	22.7174	1.06384
$457$	−36.1045	−1.68890	−0.844449	−	0.535637i	$-0.820072\pi$
$457$	−36.1045	−1.68890	−0.844449	+	0.535637i	$0.820072\pi$
$458$	5.52668	0.258245
$459$	−5.55902	−0.259473
$460$	1.76738	0.0824044
$461$	−25.0978	−1.16892	−0.584460	−	0.811423i	$-0.698694\pi$
$461$	−25.0978	−1.16892	−0.584460	+	0.811423i	$0.698694\pi$
$462$	−14.6898	−0.683431
$463$	23.4002	1.08750	0.543750	−	0.839248i	$-0.317004\pi$
$463$	23.4002	1.08750	0.543750	+	0.839248i	$0.317004\pi$
$464$	16.5180	0.766828
$465$	−1.00000	−0.0463739
$466$	19.1889	0.888909
$467$	−7.05419	−0.326429	−0.163214	−	0.986591i	$-0.552186\pi$
$467$	−7.05419	−0.326429	−0.163214	+	0.986591i	$0.552186\pi$
$468$	−0.664588	−0.0307206
$469$	30.9765	1.43036
$470$	−8.60462	−0.396901
$471$	−14.7473	−0.679520
$472$	16.3918	0.754494
$473$	17.9207	0.823995
$474$	18.8224	0.864542
$475$	7.37771	0.338513
$476$	−12.7525	−0.584510
$477$	−5.58500	−0.255720
$478$	10.5350	0.481862
$479$	26.2079	1.19747	0.598734	−	0.800948i	$-0.295671\pi$
$479$	26.2079	1.19747	0.598734	+	0.800948i	$0.295671\pi$
$480$	−3.58239	−0.163513
$481$	6.10362	0.278301
$482$	8.12739	0.370193
$483$	9.17958	0.417685
$484$	−1.70269	−0.0773951
$485$	0.514614	0.0233674
$486$	−1.15560	−0.0524191
$487$	−6.16762	−0.279482	−0.139741	−	0.990188i	$-0.544627\pi$
$487$	−6.16762	−0.279482	−0.139741	+	0.990188i	$0.544627\pi$
$488$	−0.132323	−0.00599000
$489$	13.3734	0.604767
$490$	5.67967	0.256581
$491$	−4.91056	−0.221611	−0.110805	−	0.993842i	$-0.535343\pi$
$491$	−4.91056	−0.221611	−0.110805	+	0.993842i	$0.535343\pi$
$492$	2.54479	0.114728
$493$	−41.1923	−1.85521
$494$	8.52569	0.383589
$495$	3.68267	0.165524
$496$	−2.22915	−0.100092
$497$	24.1603	1.08374
$498$	8.97350	0.402112
$499$	13.0487	0.584142	0.292071	−	0.956397i	$-0.405656\pi$
$499$	13.0487	0.584142	0.292071	+	0.956397i	$0.405656\pi$
$500$	−0.664588	−0.0297213
$501$	−4.77435	−0.213302
$502$	−0.844835	−0.0377068
$503$	−9.58960	−0.427579	−0.213790	−	0.976880i	$-0.568581\pi$
$503$	−9.58960	−0.427579	−0.213790	+	0.976880i	$0.568581\pi$
$504$	−10.6288	−0.473443
$505$	5.49389	0.244475
$506$	−11.3174	−0.503120
$507$	−1.00000	−0.0444116
$508$	3.62912	0.161016
$509$	−10.4382	−0.462666	−0.231333	−	0.972875i	$-0.574309\pi$
$509$	−10.4382	−0.462666	−0.231333	+	0.972875i	$0.574309\pi$
$510$	−6.42401	−0.284460
$511$	−34.8480	−1.54158
$512$	−21.7137	−0.959617
$513$	−7.37771	−0.325734
$514$	5.87081	0.258951
$515$	0.794455	0.0350079
$516$	3.23404	0.142371
$517$	−27.4212	−1.20598
$518$	24.3467	1.06973
$519$	−15.2716	−0.670347
$520$	−3.07920	−0.135032
$521$	15.1474	0.663618	0.331809	−	0.943347i	$-0.392341\pi$
$521$	15.1474	0.663618	0.331809	+	0.943347i	$0.392341\pi$
$522$	−8.56299	−0.374792
$523$	12.2904	0.537423	0.268712	−	0.963221i	$-0.413402\pi$
$523$	12.2904	0.537423	0.268712	+	0.963221i	$0.413402\pi$
$524$	13.1022	0.572371
$525$	−3.45180	−0.150649
$526$	14.3718	0.626641
$527$	5.55902	0.242155
$528$	8.20921	0.357260
$529$	−15.9278	−0.692513
$530$	−6.45403	−0.280345
$531$	−5.32340	−0.231016
$532$	−16.9246	−0.733776
$533$	3.82913	0.165858
$534$	−5.03528	−0.217898
$535$	3.91613	0.169309
$536$	−27.6327	−1.19355
$537$	25.0704	1.08187
$538$	−20.4080	−0.879852
$539$	18.1000	0.779621
$540$	0.664588	0.0285993
$541$	16.0209	0.688791	0.344396	−	0.938825i	$-0.388084\pi$
$541$	16.0209	0.688791	0.344396	+	0.938825i	$0.388084\pi$
$542$	7.21189	0.309777
$543$	20.5638	0.882476
$544$	19.9146	0.853831
$545$	11.9042	0.509919
$546$	−3.98890	−0.170709
$547$	−27.1899	−1.16256	−0.581278	−	0.813705i	$-0.697447\pi$
$547$	−27.1899	−1.16256	−0.581278	+	0.813705i	$0.697447\pi$
$548$	−9.65175	−0.412302
$549$	0.0429733	0.00183406
$550$	4.25569	0.181463
$551$	−54.6688	−2.32897
$552$	−8.18870	−0.348534
$553$	−56.2228	−2.39084
$554$	7.65076	0.325050
$555$	−6.10362	−0.259084
$556$	−12.9409	−0.548815
$557$	−41.1493	−1.74355	−0.871776	−	0.489906i	$-0.837031\pi$
$557$	−41.1493	−1.74355	−0.871776	+	0.489906i	$0.837031\pi$
$558$	1.15560	0.0489205
$559$	4.86623	0.205820
$560$	−7.69457	−0.325155
$561$	−20.4720	−0.864329
$562$	18.4908	0.779986
$563$	−31.3227	−1.32009	−0.660047	−	0.751224i	$-0.729464\pi$
$563$	−31.3227	−1.32009	−0.660047	+	0.751224i	$0.729464\pi$
$564$	−4.94853	−0.208371
$565$	−4.70375	−0.197888
$566$	−20.6222	−0.866816
$567$	3.45180	0.144962
$568$	−21.5523	−0.904315
$569$	−12.9484	−0.542823	−0.271412	−	0.962463i	$-0.587490\pi$
$569$	−12.9484	−0.542823	−0.271412	+	0.962463i	$0.587490\pi$
$570$	−8.52569	−0.357102
$571$	38.5692	1.61407	0.807035	−	0.590504i	$-0.201071\pi$
$571$	38.5692	1.61407	0.807035	+	0.590504i	$0.201071\pi$
$572$	−2.44745	−0.102333
$573$	−15.7412	−0.657596
$574$	15.2740	0.637526
$575$	−2.65936	−0.110903
$576$	8.59811	0.358255
$577$	24.3701	1.01454	0.507269	−	0.861788i	$-0.330655\pi$
$577$	24.3701	1.01454	0.507269	+	0.861788i	$0.330655\pi$
$578$	16.0660	0.668256
$579$	1.22423	0.0508774
$580$	4.92459	0.204482
$581$	−26.8040	−1.11202
$582$	−0.594688	−0.0246506
$583$	−20.5677	−0.851827
$584$	31.0864	1.28636
$585$	1.00000	0.0413449
$586$	30.7834	1.27165
$587$	19.1381	0.789912	0.394956	−	0.918700i	$-0.370760\pi$
$587$	19.1381	0.789912	0.394956	+	0.918700i	$0.370760\pi$
$588$	3.26639	0.134704
$589$	7.37771	0.303993
$590$	−6.15172	−0.253262
$591$	−4.49584	−0.184934
$592$	−13.6059	−0.559198
$593$	33.9960	1.39605	0.698024	−	0.716075i	$-0.254063\pi$
$593$	33.9960	1.39605	0.698024	+	0.716075i	$0.254063\pi$
$594$	−4.25569	−0.174613
$595$	19.1886	0.786656
$596$	7.12510	0.291856
$597$	−19.9721	−0.817406
$598$	−3.07316	−0.125671
$599$	−19.8530	−0.811173	−0.405586	−	0.914057i	$-0.632933\pi$
$599$	−19.8530	−0.811173	−0.405586	+	0.914057i	$0.632933\pi$
$600$	3.07920	0.125708
$601$	−43.6759	−1.78158	−0.890788	−	0.454419i	$-0.849847\pi$
$601$	−43.6759	−1.78158	−0.890788	+	0.454419i	$0.849847\pi$
$602$	19.4109	0.791129
$603$	8.97401	0.365450
$604$	−1.33325	−0.0542491
$605$	2.56203	0.104161
$606$	−6.34874	−0.257900
$607$	−1.81031	−0.0734781	−0.0367391	−	0.999325i	$-0.511697\pi$
$607$	−1.81031	−0.0734781	−0.0367391	+	0.999325i	$0.511697\pi$
$608$	26.4299	1.07187
$609$	25.5778	1.03646
$610$	0.0496600	0.00201068
$611$	−7.44601	−0.301233
$612$	−3.69446	−0.149340
$613$	−4.54994	−0.183770	−0.0918851	−	0.995770i	$-0.529289\pi$
$613$	−4.54994	−0.183770	−0.0918851	+	0.995770i	$0.529289\pi$
$614$	−28.6582	−1.15655
$615$	−3.82913	−0.154406
$616$	−39.1422	−1.57708
$617$	21.1795	0.852653	0.426326	−	0.904569i	$-0.359808\pi$
$617$	21.1795	0.852653	0.426326	+	0.904569i	$0.359808\pi$
$618$	−0.918072	−0.0369303
$619$	30.2565	1.21611	0.608055	−	0.793895i	$-0.291950\pi$
$619$	30.2565	1.21611	0.608055	+	0.793895i	$0.291950\pi$
$620$	−0.664588	−0.0266905
$621$	2.65936	0.106716
$622$	−32.7601	−1.31356
$623$	15.0405	0.602583
$624$	2.22915	0.0892374
$625$	1.00000	0.0400000
$626$	6.14198	0.245483
$627$	−27.1696	−1.08505
$628$	−9.80088	−0.391098
$629$	33.9302	1.35288
$630$	3.98890	0.158922
$631$	−17.1054	−0.680955	−0.340478	−	0.940253i	$-0.610589\pi$
$631$	−17.1054	−0.680955	−0.340478	+	0.940253i	$0.610589\pi$
$632$	50.1540	1.99502
$633$	−10.1027	−0.401547
$634$	−32.0899	−1.27445
$635$	−5.46072	−0.216702
$636$	−3.71172	−0.147179
$637$	4.91491	0.194736
$638$	−31.5346	−1.24847
$639$	6.99933	0.276889
$640$	2.77120	0.109541
$641$	−28.7831	−1.13687	−0.568433	−	0.822730i	$-0.692450\pi$
$641$	−28.7831	−1.13687	−0.568433	+	0.822730i	$0.692450\pi$
$642$	−4.52548	−0.178607
$643$	−31.6754	−1.24916	−0.624579	−	0.780962i	$-0.714729\pi$
$643$	−31.6754	−1.24916	−0.624579	+	0.780962i	$0.714729\pi$
$644$	6.10063	0.240399
$645$	−4.86623	−0.191608
$646$	47.3945	1.86471
$647$	−10.3237	−0.405868	−0.202934	−	0.979192i	$-0.565048\pi$
$647$	−10.3237	−0.405868	−0.202934	+	0.979192i	$0.565048\pi$
$648$	−3.07920	−0.120962
$649$	−19.6043	−0.769536
$650$	1.15560	0.0453264
$651$	−3.45180	−0.135287
$652$	8.88781	0.348074
$653$	16.6251	0.650589	0.325294	−	0.945613i	$-0.394537\pi$
$653$	16.6251	0.650589	0.325294	+	0.945613i	$0.394537\pi$
$654$	−13.7565	−0.537921
$655$	−19.7147	−0.770319
$656$	−8.53571	−0.333263
$657$	−10.0956	−0.393867
$658$	−29.7014	−1.15788
$659$	−19.1340	−0.745354	−0.372677	−	0.927961i	$-0.621560\pi$
$659$	−19.1340	−0.745354	−0.372677	+	0.927961i	$0.621560\pi$
$660$	2.44745	0.0952670
$661$	−6.71511	−0.261188	−0.130594	−	0.991436i	$-0.541688\pi$
$661$	−6.71511	−0.261188	−0.130594	+	0.991436i	$0.541688\pi$
$662$	26.2725	1.02111
$663$	−5.55902	−0.215894
$664$	23.9107	0.927914
$665$	25.4664	0.987543
$666$	7.05335	0.273312
$667$	19.7058	0.763013
$668$	−3.17298	−0.122766
$669$	−19.0499	−0.736511
$670$	10.3704	0.400642
$671$	0.158256	0.00610942
$672$	−12.3657	−0.477017
$673$	−21.9106	−0.844593	−0.422297	−	0.906458i	$-0.638776\pi$
$673$	−21.9106	−0.844593	−0.422297	+	0.906458i	$0.638776\pi$
$674$	−8.76832	−0.337743
$675$	−1.00000	−0.0384900
$676$	−0.664588	−0.0255611
$677$	−6.44124	−0.247557	−0.123779	−	0.992310i	$-0.539501\pi$
$677$	−6.44124	−0.247557	−0.123779	+	0.992310i	$0.539501\pi$
$678$	5.43565	0.208755
$679$	1.77634	0.0681698
$680$	−17.1173	−0.656419
$681$	5.26928	0.201919
$682$	4.25569	0.162959
$683$	43.1468	1.65096	0.825482	−	0.564428i	$-0.190903\pi$
$683$	43.1468	1.65096	0.825482	+	0.564428i	$0.190903\pi$
$684$	−4.90314	−0.187476
$685$	14.5229	0.554892
$686$	−8.31722	−0.317553
$687$	−4.78252	−0.182464
$688$	−10.8476	−0.413559
$689$	−5.58500	−0.212772
$690$	3.07316	0.116993
$691$	18.3927	0.699691	0.349846	−	0.936807i	$-0.386234\pi$
$691$	18.3927	0.699691	0.349846	+	0.936807i	$0.386234\pi$
$692$	−10.1493	−0.385818
$693$	12.7118	0.482882
$694$	20.1308	0.764155
$695$	19.4720	0.738616
$696$	−22.8168	−0.864870
$697$	21.2862	0.806274
$698$	−41.6479	−1.57640
$699$	−16.6051	−0.628064
$700$	−2.29402	−0.0867059
$701$	44.3865	1.67645	0.838227	−	0.545322i	$-0.183593\pi$
$701$	44.3865	1.67645	0.838227	+	0.545322i	$0.183593\pi$
$702$	−1.15560	−0.0436153
$703$	45.0308	1.69837
$704$	31.6640	1.19338
$705$	7.44601	0.280433
$706$	−29.6057	−1.11423
$707$	18.9638	0.713207
$708$	−3.53787	−0.132961
$709$	−44.4583	−1.66967	−0.834834	−	0.550502i	$-0.814436\pi$
$709$	−44.4583	−1.66967	−0.834834	+	0.550502i	$0.814436\pi$
$710$	8.08842	0.303553
$711$	−16.2880	−0.610847
$712$	−13.4169	−0.502821
$713$	−2.65936	−0.0995938
$714$	−22.1744	−0.829855
$715$	3.68267	0.137724
$716$	16.6615	0.622670
$717$	−9.11652	−0.340463
$718$	7.94771	0.296606
$719$	−35.1784	−1.31193	−0.655967	−	0.754790i	$-0.727739\pi$
$719$	−35.1784	−1.31193	−0.655967	+	0.754790i	$0.727739\pi$
$720$	−2.22915	−0.0830755
$721$	2.74230	0.102129
$722$	40.9437	1.52376
$723$	−7.03305	−0.261562
$724$	13.6664	0.507909
$725$	−7.40999	−0.275200
$726$	−2.96068	−0.109881
$727$	−9.88501	−0.366615	−0.183307	−	0.983056i	$-0.558680\pi$
$727$	−9.88501	−0.366615	−0.183307	+	0.983056i	$0.558680\pi$
$728$	−10.6288	−0.393928
$729$	1.00000	0.0370370
$730$	−11.6665	−0.431796
$731$	27.0515	1.00053
$732$	0.0285596	0.00105559
$733$	−21.9263	−0.809867	−0.404934	−	0.914346i	$-0.632705\pi$
$733$	−21.9263	−0.809867	−0.404934	+	0.914346i	$0.632705\pi$
$734$	−7.21107	−0.266166
$735$	−4.91491	−0.181289
$736$	−9.52687	−0.351165
$737$	33.0483	1.21735
$738$	4.42495	0.162885
$739$	−17.5982	−0.647360	−0.323680	−	0.946167i	$-0.604920\pi$
$739$	−17.5982	−0.647360	−0.323680	+	0.946167i	$0.604920\pi$
$740$	−4.05639	−0.149116
$741$	−7.37771	−0.271027
$742$	−22.2780	−0.817852
$743$	−33.6860	−1.23582	−0.617909	−	0.786250i	$-0.712020\pi$
$743$	−33.6860	−1.23582	−0.617909	+	0.786250i	$0.712020\pi$
$744$	3.07920	0.112889
$745$	−10.7211	−0.392790
$746$	17.8660	0.654120
$747$	−7.76523	−0.284115
$748$	−13.6054	−0.497464
$749$	13.5177	0.493926
$750$	−1.15560	−0.0421966
$751$	27.7482	1.01255	0.506273	−	0.862373i	$-0.331023\pi$
$751$	27.7482	1.01255	0.506273	+	0.862373i	$0.331023\pi$
$752$	16.5983	0.605276
$753$	0.731078	0.0266420
$754$	−8.56299	−0.311846
$755$	2.00613	0.0730105
$756$	2.29402	0.0834328
$757$	−8.83493	−0.321111	−0.160556	−	0.987027i	$-0.551329\pi$
$757$	−8.83493	−0.321111	−0.160556	+	0.987027i	$0.551329\pi$
$758$	8.08548	0.293678
$759$	9.79354	0.355483
$760$	−22.7174	−0.824048
$761$	−45.4008	−1.64578	−0.822890	−	0.568201i	$-0.807640\pi$
$761$	−45.4008	−1.64578	−0.822890	+	0.568201i	$0.807640\pi$
$762$	6.31040	0.228602
$763$	41.0908	1.48759
$764$	−10.4614	−0.378479
$765$	5.55902	0.200987
$766$	−13.4530	−0.486076
$767$	−5.32340	−0.192217
$768$	13.9938	0.504959
$769$	−35.8632	−1.29326	−0.646629	−	0.762805i	$-0.723822\pi$
$769$	−35.8632	−1.29326	−0.646629	+	0.762805i	$0.723822\pi$
$770$	14.6898	0.529383
$771$	−5.08032	−0.182963
$772$	0.813610	0.0292825
$773$	−32.5414	−1.17043	−0.585216	−	0.810877i	$-0.698990\pi$
$773$	−32.5414	−1.17043	−0.585216	+	0.810877i	$0.698990\pi$
$774$	5.62342	0.202130
$775$	1.00000	0.0359211
$776$	−1.58460	−0.0568838
$777$	−21.0685	−0.755827
$778$	6.65007	0.238417
$779$	28.2502	1.01217
$780$	0.664588	0.0237961
$781$	25.7762	0.922344
$782$	−17.0837	−0.610914
$783$	7.40999	0.264812
$784$	−10.9561	−0.391288
$785$	14.7473	0.526354
$786$	22.7824	0.812620
$787$	−27.7949	−0.990782	−0.495391	−	0.868670i	$-0.664975\pi$
$787$	−27.7949	−0.990782	−0.495391	+	0.868670i	$0.664975\pi$
$788$	−2.98788	−0.106439
$789$	−12.4367	−0.442757
$790$	−18.8224	−0.669671
$791$	−16.2364	−0.577299
$792$	−11.3397	−0.402937
$793$	0.0429733	0.00152603
$794$	1.86857	0.0663129
$795$	5.58500	0.198080
$796$	−13.2732	−0.470458
$797$	33.0703	1.17141	0.585706	−	0.810524i	$-0.300817\pi$
$797$	33.0703	1.17141	0.585706	+	0.810524i	$0.300817\pi$
$798$	−29.4289	−1.04177
$799$	−41.3925	−1.46436
$800$	3.58239	0.126657
$801$	4.35728	0.153957
$802$	−6.45996	−0.228109
$803$	−37.1787	−1.31201
$804$	5.96401	0.210334
$805$	−9.17958	−0.323538
$806$	1.15560	0.0407043
$807$	17.6601	0.621665
$808$	−16.9168	−0.595130
$809$	52.8271	1.85730	0.928651	−	0.370954i	$-0.120969\pi$
$809$	52.8271	1.85730	0.928651	+	0.370954i	$0.120969\pi$
$810$	1.15560	0.0406037
$811$	15.5481	0.545969	0.272985	−	0.962018i	$-0.411989\pi$
$811$	15.5481	0.545969	0.272985	+	0.962018i	$0.411989\pi$
$812$	16.9987	0.596537
$813$	−6.24082	−0.218875
$814$	25.9751	0.910428
$815$	−13.3734	−0.468451
$816$	12.3919	0.433803
$817$	35.9016	1.25604
$818$	−11.1044	−0.388257
$819$	3.45180	0.120616
$820$	−2.54479	−0.0888681
$821$	14.3184	0.499717	0.249858	−	0.968282i	$-0.419616\pi$
$821$	14.3184	0.499717	0.249858	+	0.968282i	$0.419616\pi$
$822$	−16.7827	−0.585364
$823$	38.2689	1.33397	0.666984	−	0.745072i	$-0.267585\pi$
$823$	38.2689	1.33397	0.666984	+	0.745072i	$0.267585\pi$
$824$	−2.44628	−0.0852204
$825$	−3.68267	−0.128214
$826$	−21.2345	−0.738843
$827$	16.8828	0.587073	0.293536	−	0.955948i	$-0.405168\pi$
$827$	16.8828	0.587073	0.293536	+	0.955948i	$0.405168\pi$
$828$	1.76738	0.0614206
$829$	−41.1300	−1.42850	−0.714252	−	0.699888i	$-0.753233\pi$
$829$	−41.1300	−1.42850	−0.714252	+	0.699888i	$0.753233\pi$
$830$	−8.97350	−0.311475
$831$	−6.62059	−0.229666
$832$	8.59811	0.298086
$833$	27.3221	0.946654
$834$	−22.5019	−0.779177
$835$	4.77435	0.165223
$836$	−18.0566	−0.624501
$837$	−1.00000	−0.0345651
$838$	29.2900	1.01181
$839$	−22.4091	−0.773649	−0.386824	−	0.922153i	$-0.626428\pi$
$839$	−22.4091	−0.773649	−0.386824	+	0.922153i	$0.626428\pi$
$840$	10.6288	0.366727
$841$	25.9080	0.893380
$842$	−26.8970	−0.926932
$843$	−16.0010	−0.551104
$844$	−6.71413	−0.231110
$845$	1.00000	0.0344010
$846$	−8.60462	−0.295833
$847$	8.84360	0.303870
$848$	12.4498	0.427528
$849$	17.8454	0.612454
$850$	6.42401	0.220342
$851$	−16.2317	−0.556417
$852$	4.65167	0.159363
$853$	50.3096	1.72257	0.861285	−	0.508123i	$-0.169660\pi$
$853$	50.3096	1.72257	0.861285	+	0.508123i	$0.169660\pi$
$854$	0.171416	0.00586575
$855$	7.37771	0.252312
$856$	−12.0585	−0.412153
$857$	−6.48158	−0.221406	−0.110703	−	0.993854i	$-0.535310\pi$
$857$	−6.48158	−0.221406	−0.110703	+	0.993854i	$0.535310\pi$
$858$	−4.25569	−0.145287
$859$	46.8165	1.59736	0.798679	−	0.601757i	$-0.205532\pi$
$859$	46.8165	1.59736	0.798679	+	0.601757i	$0.205532\pi$
$860$	−3.23404	−0.110280
$861$	−13.2174	−0.450448
$862$	15.2269	0.518629
$863$	−23.1513	−0.788081	−0.394041	−	0.919093i	$-0.628923\pi$
$863$	−23.1513	−0.788081	−0.394041	+	0.919093i	$0.628923\pi$
$864$	−3.58239	−0.121875
$865$	15.2716	0.519248
$866$	36.2987	1.23348
$867$	−13.9027	−0.472160
$868$	−2.29402	−0.0778642
$869$	−59.9832	−2.03479
$870$	8.56299	0.290313
$871$	8.97401	0.304073
$872$	−36.6553	−1.24131
$873$	0.514614	0.0174170
$874$	−22.6729	−0.766921
$875$	3.45180	0.116692
$876$	−6.70941	−0.226690
$877$	38.5019	1.30012	0.650059	−	0.759884i	$-0.274744\pi$
$877$	38.5019	1.30012	0.650059	+	0.759884i	$0.274744\pi$
$878$	−8.50348	−0.286979
$879$	−26.6384	−0.898491
$880$	−8.20921	−0.276732
$881$	−30.2785	−1.02011	−0.510054	−	0.860142i	$-0.670375\pi$
$881$	−30.2785	−1.02011	−0.510054	+	0.860142i	$0.670375\pi$
$882$	5.67967	0.191244
$883$	44.8646	1.50981	0.754907	−	0.655832i	$-0.227682\pi$
$883$	44.8646	1.50981	0.754907	+	0.655832i	$0.227682\pi$
$884$	−3.69446	−0.124258
$885$	5.32340	0.178944
$886$	−4.99266	−0.167732
$887$	−22.4361	−0.753330	−0.376665	−	0.926349i	$-0.622929\pi$
$887$	−22.4361	−0.753330	−0.376665	+	0.926349i	$0.622929\pi$
$888$	18.7943	0.630694
$889$	−18.8493	−0.632185
$890$	5.03528	0.168783
$891$	3.68267	0.123374
$892$	−12.6603	−0.423898
$893$	−54.9345	−1.83831
$894$	12.3893	0.414360
$895$	−25.0704	−0.838012
$896$	9.56561	0.319565
$897$	2.65936	0.0887935
$898$	40.9177	1.36544
$899$	−7.40999	−0.247137
$900$	−0.664588	−0.0221529
$901$	−31.0471	−1.03433
$902$	16.2956	0.542584
$903$	−16.7972	−0.558977
$904$	14.4838	0.481723
$905$	−20.5638	−0.683563
$906$	−2.31828	−0.0770198
$907$	58.4534	1.94091	0.970456	−	0.241279i	$-0.0775669\pi$
$907$	58.4534	1.94091	0.970456	+	0.241279i	$0.0775669\pi$
$908$	3.50190	0.116214
$909$	5.49389	0.182221
$910$	3.98890	0.132231
$911$	−25.5846	−0.847656	−0.423828	−	0.905743i	$-0.639314\pi$
$911$	−25.5846	−0.847656	−0.423828	+	0.905743i	$0.639314\pi$
$912$	16.4460	0.544582
$913$	−28.5967	−0.946414
$914$	−41.7224	−1.38005
$915$	−0.0429733	−0.00142066
$916$	−3.17840	−0.105017
$917$	−68.0513	−2.24725
$918$	−6.42401	−0.212024
$919$	−2.87386	−0.0947999	−0.0474000	−	0.998876i	$-0.515094\pi$
$919$	−2.87386	−0.0947999	−0.0474000	+	0.998876i	$0.515094\pi$
$920$	8.18870	0.269973
$921$	24.7994	0.817169
$922$	−29.0030	−0.955163
$923$	6.99933	0.230386
$924$	8.44812	0.277923
$925$	6.10362	0.200686
$926$	27.0413	0.888631
$927$	0.794455	0.0260933
$928$	−26.5455	−0.871399
$929$	9.42928	0.309365	0.154682	−	0.987964i	$-0.450565\pi$
$929$	9.42928	0.309365	0.154682	+	0.987964i	$0.450565\pi$
$930$	−1.15560	−0.0378936
$931$	36.2608	1.18840
$932$	−11.0356	−0.361482
$933$	28.3490	0.928105
$934$	−8.15182	−0.266736
$935$	20.4720	0.669506
$936$	−3.07920	−0.100647
$937$	24.5194	0.801015	0.400507	−	0.916294i	$-0.368834\pi$
$937$	24.5194	0.801015	0.400507	+	0.916294i	$0.368834\pi$
$938$	35.7964	1.16879
$939$	−5.31496	−0.173447
$940$	4.94853	0.161403
$941$	20.0909	0.654944	0.327472	−	0.944861i	$-0.393803\pi$
$941$	20.0909	0.654944	0.327472	+	0.944861i	$0.393803\pi$
$942$	−17.0420	−0.555258
$943$	−10.1830	−0.331606
$944$	11.8667	0.386227
$945$	−3.45180	−0.112287
$946$	20.7092	0.673313
$947$	−38.4246	−1.24863	−0.624316	−	0.781172i	$-0.714622\pi$
$947$	−38.4246	−1.24863	−0.624316	+	0.781172i	$0.714622\pi$
$948$	−10.8248	−0.351573
$949$	−10.0956	−0.327717
$950$	8.52569	0.276610
$951$	27.7691	0.900473
$952$	−59.0855	−1.91497
$953$	−23.8105	−0.771298	−0.385649	−	0.922646i	$-0.626022\pi$
$953$	−23.8105	−0.771298	−0.385649	+	0.922646i	$0.626022\pi$
$954$	−6.45403	−0.208957
$955$	15.7412	0.509372
$956$	−6.05872	−0.195953
$957$	27.2885	0.882113
$958$	30.2858	0.978491
$959$	50.1302	1.61879
$960$	−8.59811	−0.277503
$961$	1.00000	0.0322581
$962$	7.05335	0.227409
$963$	3.91613	0.126196
$964$	−4.67408	−0.150542
$965$	−1.22423	−0.0394094
$966$	10.6079	0.341304
$967$	25.9292	0.833828	0.416914	−	0.908946i	$-0.363112\pi$
$967$	25.9292	0.833828	0.416914	+	0.908946i	$0.363112\pi$
$968$	−7.88899	−0.253562
$969$	−41.0128	−1.31752
$970$	0.594688	0.0190943
$971$	−13.6795	−0.438997	−0.219498	−	0.975613i	$-0.570442\pi$
$971$	−13.6795	−0.438997	−0.219498	+	0.975613i	$0.570442\pi$
$972$	0.664588	0.0213167
$973$	67.2135	2.15477
$974$	−7.12731	−0.228374
$975$	−1.00000	−0.0320256
$976$	−0.0957940	−0.00306629
$977$	−37.7088	−1.20641	−0.603205	−	0.797586i	$-0.706110\pi$
$977$	−37.7088	−1.20641	−0.603205	+	0.797586i	$0.706110\pi$
$978$	15.4543	0.494175
$979$	16.0464	0.512846
$980$	−3.26639	−0.104341
$981$	11.9042	0.380071
$982$	−5.67465	−0.181085
$983$	−5.50069	−0.175445	−0.0877224	−	0.996145i	$-0.527959\pi$
$983$	−5.50069	−0.175445	−0.0877224	+	0.996145i	$0.527959\pi$
$984$	11.7907	0.375873
$985$	4.49584	0.143249
$986$	−47.6018	−1.51595
$987$	25.7021	0.818108
$988$	−4.90314	−0.155990
$989$	−12.9411	−0.411502
$990$	4.25569	0.135255
$991$	−2.49122	−0.0791361	−0.0395681	−	0.999217i	$-0.512598\pi$
$991$	−2.49122	−0.0791361	−0.0395681	+	0.999217i	$0.512598\pi$
$992$	3.58239	0.113741
$993$	−22.7349	−0.721471
$994$	27.9196	0.885556
$995$	19.9721	0.633160
$996$	−5.16067	−0.163522
$997$	−42.6734	−1.35148	−0.675740	−	0.737140i	$-0.736176\pi$
$997$	−42.6734	−1.35148	−0.675740	+	0.737140i	$0.736176\pi$
$998$	15.0791	0.477322
$999$	−6.10362	−0.193110

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6045.2.a.bh.1.11	✓	17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6045.2.a.bh.1.11	✓	17	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:	\( N \)	\(=\)	\( 6045 = 3 \cdot 5 \cdot 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6045.a (trivial)

\(f(q)\)	\(=\)	\(q+1.15560 q^{2} -1.00000 q^{3} -0.664588 q^{4} +1.00000 q^{5} -1.15560 q^{6} +3.45180 q^{7} -3.07920 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.15560 q^{2} -1.00000 q^{3} -0.664588 q^{4} +1.00000 q^{5} -1.15560 q^{6} +3.45180 q^{7} -3.07920 q^{8} +1.00000 q^{9} +1.15560 q^{10} +3.68267 q^{11} +0.664588 q^{12} +1.00000 q^{13} +3.98890 q^{14} -1.00000 q^{15} -2.22915 q^{16} +5.55902 q^{17} +1.15560 q^{18} +7.37771 q^{19} -0.664588 q^{20} -3.45180 q^{21} +4.25569 q^{22} -2.65936 q^{23} +3.07920 q^{24} +1.00000 q^{25} +1.15560 q^{26} -1.00000 q^{27} -2.29402 q^{28} -7.40999 q^{29} -1.15560 q^{30} +1.00000 q^{31} +3.58239 q^{32} -3.68267 q^{33} +6.42401 q^{34} +3.45180 q^{35} -0.664588 q^{36} +6.10362 q^{37} +8.52569 q^{38} -1.00000 q^{39} -3.07920 q^{40} +3.82913 q^{41} -3.98890 q^{42} +4.86623 q^{43} -2.44745 q^{44} +1.00000 q^{45} -3.07316 q^{46} -7.44601 q^{47} +2.22915 q^{48} +4.91491 q^{49} +1.15560 q^{50} -5.55902 q^{51} -0.664588 q^{52} -5.58500 q^{53} -1.15560 q^{54} +3.68267 q^{55} -10.6288 q^{56} -7.37771 q^{57} -8.56299 q^{58} -5.32340 q^{59} +0.664588 q^{60} +0.0429733 q^{61} +1.15560 q^{62} +3.45180 q^{63} +8.59811 q^{64} +1.00000 q^{65} -4.25569 q^{66} +8.97401 q^{67} -3.69446 q^{68} +2.65936 q^{69} +3.98890 q^{70} +6.99933 q^{71} -3.07920 q^{72} -10.0956 q^{73} +7.05335 q^{74} -1.00000 q^{75} -4.90314 q^{76} +12.7118 q^{77} -1.15560 q^{78} -16.2880 q^{79} -2.22915 q^{80} +1.00000 q^{81} +4.42495 q^{82} -7.76523 q^{83} +2.29402 q^{84} +5.55902 q^{85} +5.62342 q^{86} +7.40999 q^{87} -11.3397 q^{88} +4.35728 q^{89} +1.15560 q^{90} +3.45180 q^{91} +1.76738 q^{92} -1.00000 q^{93} -8.60462 q^{94} +7.37771 q^{95} -3.58239 q^{96} +0.514614 q^{97} +5.67967 q^{98} +3.68267 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 2 q^{2} - 17 q^{3} + 20 q^{4} + 17 q^{5} - 2 q^{6} + 18 q^{7} + 9 q^{8} + 17 q^{9}+O(q^{10}) \) 17 * q + 2 * q^2 - 17 * q^3 + 20 * q^4 + 17 * q^5 - 2 * q^6 + 18 * q^7 + 9 * q^8 + 17 * q^9	\( 17 q + 2 q^{2} - 17 q^{3} + 20 q^{4} + 17 q^{5} - 2 q^{6} + 18 q^{7} + 9 q^{8} + 17 q^{9} + 2 q^{10} + 3 q^{11} - 20 q^{12} + 17 q^{13} + q^{14} - 17 q^{15} + 26 q^{16} + 2 q^{18} + 10 q^{19} + 20 q^{20} - 18 q^{21} + 5 q^{22} + 16 q^{23} - 9 q^{24} + 17 q^{25} + 2 q^{26} - 17 q^{27} + 36 q^{28} - 3 q^{29} - 2 q^{30} + 17 q^{31} + 20 q^{32} - 3 q^{33} + q^{34} + 18 q^{35} + 20 q^{36} + 14 q^{37} + 22 q^{38} - 17 q^{39} + 9 q^{40} - 6 q^{41} - q^{42} + 24 q^{43} - 15 q^{44} + 17 q^{45} + 6 q^{46} + 25 q^{47} - 26 q^{48} + 31 q^{49} + 2 q^{50} + 20 q^{52} - 15 q^{53} - 2 q^{54} + 3 q^{55} + 31 q^{56} - 10 q^{57} + 44 q^{58} + 16 q^{59} - 20 q^{60} - 5 q^{61} + 2 q^{62} + 18 q^{63} + 35 q^{64} + 17 q^{65} - 5 q^{66} + 50 q^{67} + 13 q^{68} - 16 q^{69} + q^{70} + 16 q^{71} + 9 q^{72} + 33 q^{73} + 2 q^{74} - 17 q^{75} + 9 q^{77} - 2 q^{78} - 10 q^{79} + 26 q^{80} + 17 q^{81} + 61 q^{82} + 27 q^{83} - 36 q^{84} - 12 q^{86} + 3 q^{87} + 23 q^{88} - 24 q^{89} + 2 q^{90} + 18 q^{91} - 21 q^{92} - 17 q^{93} + 6 q^{94} + 10 q^{95} - 20 q^{96} + 48 q^{97} + 14 q^{98} + 3 q^{99}+O(q^{100}) \) 17 * q + 2 * q^2 - 17 * q^3 + 20 * q^4 + 17 * q^5 - 2 * q^6 + 18 * q^7 + 9 * q^8 + 17 * q^9 + 2 * q^10 + 3 * q^11 - 20 * q^12 + 17 * q^13 + q^14 - 17 * q^15 + 26 * q^16 + 2 * q^18 + 10 * q^19 + 20 * q^20 - 18 * q^21 + 5 * q^22 + 16 * q^23 - 9 * q^24 + 17 * q^25 + 2 * q^26 - 17 * q^27 + 36 * q^28 - 3 * q^29 - 2 * q^30 + 17 * q^31 + 20 * q^32 - 3 * q^33 + q^34 + 18 * q^35 + 20 * q^36 + 14 * q^37 + 22 * q^38 - 17 * q^39 + 9 * q^40 - 6 * q^41 - q^42 + 24 * q^43 - 15 * q^44 + 17 * q^45 + 6 * q^46 + 25 * q^47 - 26 * q^48 + 31 * q^49 + 2 * q^50 + 20 * q^52 - 15 * q^53 - 2 * q^54 + 3 * q^55 + 31 * q^56 - 10 * q^57 + 44 * q^58 + 16 * q^59 - 20 * q^60 - 5 * q^61 + 2 * q^62 + 18 * q^63 + 35 * q^64 + 17 * q^65 - 5 * q^66 + 50 * q^67 + 13 * q^68 - 16 * q^69 + q^70 + 16 * q^71 + 9 * q^72 + 33 * q^73 + 2 * q^74 - 17 * q^75 + 9 * q^77 - 2 * q^78 - 10 * q^79 + 26 * q^80 + 17 * q^81 + 61 * q^82 + 27 * q^83 - 36 * q^84 - 12 * q^86 + 3 * q^87 + 23 * q^88 - 24 * q^89 + 2 * q^90 + 18 * q^91 - 21 * q^92 - 17 * q^93 + 6 * q^94 + 10 * q^95 - 20 * q^96 + 48 * q^97 + 14 * q^98 + 3 * q^99

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