LMFDB - Embedded newform 6010.2.a.g.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6010,2,Mod(1,6010)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6010, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6010.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6010 = 2 \cdot 5 \cdot 601 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6010.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:	$47.9900916148$
Analytic rank:	$0$
Dimension:	$27$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	6010.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.03782 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.03782 q^{6} -3.65688 q^{7} -1.00000 q^{8} -1.92294 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.03782 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.03782 q^{6} -3.65688 q^{7} -1.00000 q^{8} -1.92294 q^{9} -1.00000 q^{10} +3.37688 q^{11} +1.03782 q^{12} +3.74747 q^{13} +3.65688 q^{14} +1.03782 q^{15} +1.00000 q^{16} -0.215513 q^{17} +1.92294 q^{18} -3.16754 q^{19} +1.00000 q^{20} -3.79517 q^{21} -3.37688 q^{22} +5.41020 q^{23} -1.03782 q^{24} +1.00000 q^{25} -3.74747 q^{26} -5.10911 q^{27} -3.65688 q^{28} +0.812402 q^{29} -1.03782 q^{30} +2.01579 q^{31} -1.00000 q^{32} +3.50458 q^{33} +0.215513 q^{34} -3.65688 q^{35} -1.92294 q^{36} -1.23319 q^{37} +3.16754 q^{38} +3.88919 q^{39} -1.00000 q^{40} -2.22559 q^{41} +3.79517 q^{42} +6.28835 q^{43} +3.37688 q^{44} -1.92294 q^{45} -5.41020 q^{46} -2.31372 q^{47} +1.03782 q^{48} +6.37279 q^{49} -1.00000 q^{50} -0.223663 q^{51} +3.74747 q^{52} +3.87618 q^{53} +5.10911 q^{54} +3.37688 q^{55} +3.65688 q^{56} -3.28733 q^{57} -0.812402 q^{58} -13.5212 q^{59} +1.03782 q^{60} +10.9507 q^{61} -2.01579 q^{62} +7.03195 q^{63} +1.00000 q^{64} +3.74747 q^{65} -3.50458 q^{66} +0.202415 q^{67} -0.215513 q^{68} +5.61479 q^{69} +3.65688 q^{70} +4.07678 q^{71} +1.92294 q^{72} -14.6244 q^{73} +1.23319 q^{74} +1.03782 q^{75} -3.16754 q^{76} -12.3488 q^{77} -3.88919 q^{78} +13.1650 q^{79} +1.00000 q^{80} +0.466492 q^{81} +2.22559 q^{82} +11.3538 q^{83} -3.79517 q^{84} -0.215513 q^{85} -6.28835 q^{86} +0.843125 q^{87} -3.37688 q^{88} -10.8782 q^{89} +1.92294 q^{90} -13.7041 q^{91} +5.41020 q^{92} +2.09202 q^{93} +2.31372 q^{94} -3.16754 q^{95} -1.03782 q^{96} -11.0319 q^{97} -6.37279 q^{98} -6.49352 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 27 q - 27 q^{2} + 6 q^{3} + 27 q^{4} + 27 q^{5} - 6 q^{6} - 27 q^{8} + 37 q^{9}+O(q^{10}) $ 27 * q - 27 * q^2 + 6 * q^3 + 27 * q^4 + 27 * q^5 - 6 * q^6 - 27 * q^8 + 37 * q^9	\( 27 q - 27 q^{2} + 6 q^{3} + 27 q^{4} + 27 q^{5} - 6 q^{6} - 27 q^{8} + 37 q^{9} - 27 q^{10} + 18 q^{11} + 6 q^{12} - 6 q^{13} + 6 q^{15} + 27 q^{16} + 3 q^{17} - 37 q^{18} + 27 q^{19} + 27 q^{20} + 16 q^{21} - 18 q^{22} + 15 q^{23} - 6 q^{24} + 27 q^{25} + 6 q^{26} + 27 q^{27} + 25 q^{29} - 6 q^{30} + 9 q^{31} - 27 q^{32} + 11 q^{33} - 3 q^{34} + 37 q^{36} - 16 q^{37} - 27 q^{38} + 20 q^{39} - 27 q^{40} + 39 q^{41} - 16 q^{42} + 9 q^{43} + 18 q^{44} + 37 q^{45} - 15 q^{46} + 31 q^{47} + 6 q^{48} + 27 q^{49} - 27 q^{50} + 39 q^{51} - 6 q^{52} - 5 q^{53} - 27 q^{54} + 18 q^{55} - 10 q^{57} - 25 q^{58} + 46 q^{59} + 6 q^{60} + 18 q^{61} - 9 q^{62} + 23 q^{63} + 27 q^{64} - 6 q^{65} - 11 q^{66} + 11 q^{67} + 3 q^{68} + 17 q^{69} + 50 q^{71} - 37 q^{72} - 29 q^{73} + 16 q^{74} + 6 q^{75} + 27 q^{76} - 6 q^{77} - 20 q^{78} + 56 q^{79} + 27 q^{80} + 51 q^{81} - 39 q^{82} + 44 q^{83} + 16 q^{84} + 3 q^{85} - 9 q^{86} + 42 q^{87} - 18 q^{88} + 34 q^{89} - 37 q^{90} + 43 q^{91} + 15 q^{92} - 20 q^{93} - 31 q^{94} + 27 q^{95} - 6 q^{96} - 37 q^{97} - 27 q^{98} + 67 q^{99}+O(q^{100}) \) 27 * q - 27 * q^2 + 6 * q^3 + 27 * q^4 + 27 * q^5 - 6 * q^6 - 27 * q^8 + 37 * q^9 - 27 * q^10 + 18 * q^11 + 6 * q^12 - 6 * q^13 + 6 * q^15 + 27 * q^16 + 3 * q^17 - 37 * q^18 + 27 * q^19 + 27 * q^20 + 16 * q^21 - 18 * q^22 + 15 * q^23 - 6 * q^24 + 27 * q^25 + 6 * q^26 + 27 * q^27 + 25 * q^29 - 6 * q^30 + 9 * q^31 - 27 * q^32 + 11 * q^33 - 3 * q^34 + 37 * q^36 - 16 * q^37 - 27 * q^38 + 20 * q^39 - 27 * q^40 + 39 * q^41 - 16 * q^42 + 9 * q^43 + 18 * q^44 + 37 * q^45 - 15 * q^46 + 31 * q^47 + 6 * q^48 + 27 * q^49 - 27 * q^50 + 39 * q^51 - 6 * q^52 - 5 * q^53 - 27 * q^54 + 18 * q^55 - 10 * q^57 - 25 * q^58 + 46 * q^59 + 6 * q^60 + 18 * q^61 - 9 * q^62 + 23 * q^63 + 27 * q^64 - 6 * q^65 - 11 * q^66 + 11 * q^67 + 3 * q^68 + 17 * q^69 + 50 * q^71 - 37 * q^72 - 29 * q^73 + 16 * q^74 + 6 * q^75 + 27 * q^76 - 6 * q^77 - 20 * q^78 + 56 * q^79 + 27 * q^80 + 51 * q^81 - 39 * q^82 + 44 * q^83 + 16 * q^84 + 3 * q^85 - 9 * q^86 + 42 * q^87 - 18 * q^88 + 34 * q^89 - 37 * q^90 + 43 * q^91 + 15 * q^92 - 20 * q^93 - 31 * q^94 + 27 * q^95 - 6 * q^96 - 37 * q^97 - 27 * q^98 + 67 * 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
$3$	1.03782	0.599184	0.299592	−	0.954067i	$-0.403149\pi$
$3$	1.03782	0.599184	0.299592	+	0.954067i	$0.403149\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.03782	−0.423687
$7$	−3.65688	−1.38217	−0.691086	−	0.722773i	$-0.742867\pi$
$7$	−3.65688	−1.38217	−0.691086	+	0.722773i	$0.742867\pi$
$8$	−1.00000	−0.353553
$9$	−1.92294	−0.640979
$10$	−1.00000	−0.316228
$11$	3.37688	1.01817	0.509083	−	0.860717i	$-0.329984\pi$
$11$	3.37688	1.01817	0.509083	+	0.860717i	$0.329984\pi$
$12$	1.03782	0.299592
$13$	3.74747	1.03936	0.519681	−	0.854361i	$-0.326051\pi$
$13$	3.74747	1.03936	0.519681	+	0.854361i	$0.326051\pi$
$14$	3.65688	0.977343
$15$	1.03782	0.267963
$16$	1.00000	0.250000
$17$	−0.215513	−0.0522697	−0.0261348	−	0.999658i	$-0.508320\pi$
$17$	−0.215513	−0.0522697	−0.0261348	+	0.999658i	$0.508320\pi$
$18$	1.92294	0.453240
$19$	−3.16754	−0.726685	−0.363342	−	0.931656i	$-0.618364\pi$
$19$	−3.16754	−0.726685	−0.363342	+	0.931656i	$0.618364\pi$
$20$	1.00000	0.223607
$21$	−3.79517	−0.828175
$22$	−3.37688	−0.719953
$23$	5.41020	1.12810	0.564052	−	0.825739i	$-0.309242\pi$
$23$	5.41020	1.12810	0.564052	+	0.825739i	$0.309242\pi$
$24$	−1.03782	−0.211843
$25$	1.00000	0.200000
$26$	−3.74747	−0.734939
$27$	−5.10911	−0.983248
$28$	−3.65688	−0.691086
$29$	0.812402	0.150859	0.0754297	−	0.997151i	$-0.475967\pi$
$29$	0.812402	0.150859	0.0754297	+	0.997151i	$0.475967\pi$
$30$	−1.03782	−0.189479
$31$	2.01579	0.362047	0.181024	−	0.983479i	$-0.442059\pi$
$31$	2.01579	0.362047	0.181024	+	0.983479i	$0.442059\pi$
$32$	−1.00000	−0.176777
$33$	3.50458	0.610069
$34$	0.215513	0.0369602
$35$	−3.65688	−0.618126
$36$	−1.92294	−0.320489
$37$	−1.23319	−0.202736	−0.101368	−	0.994849i	$-0.532322\pi$
$37$	−1.23319	−0.202736	−0.101368	+	0.994849i	$0.532322\pi$
$38$	3.16754	0.513844
$39$	3.88919	0.622768
$40$	−1.00000	−0.158114
$41$	−2.22559	−0.347578	−0.173789	−	0.984783i	$-0.555601\pi$
$41$	−2.22559	−0.347578	−0.173789	+	0.984783i	$0.555601\pi$
$42$	3.79517	0.585608
$43$	6.28835	0.958964	0.479482	−	0.877552i	$-0.340825\pi$
$43$	6.28835	0.958964	0.479482	+	0.877552i	$0.340825\pi$
$44$	3.37688	0.509083
$45$	−1.92294	−0.286654
$46$	−5.41020	−0.797690
$47$	−2.31372	−0.337491	−0.168745	−	0.985660i	$-0.553972\pi$
$47$	−2.31372	−0.337491	−0.168745	+	0.985660i	$0.553972\pi$
$48$	1.03782	0.149796
$49$	6.37279	0.910398
$50$	−1.00000	−0.141421
$51$	−0.223663	−0.0313192
$52$	3.74747	0.519681
$53$	3.87618	0.532434	0.266217	−	0.963913i	$-0.414226\pi$
$53$	3.87618	0.532434	0.266217	+	0.963913i	$0.414226\pi$
$54$	5.10911	0.695261
$55$	3.37688	0.455338
$56$	3.65688	0.488671
$57$	−3.28733	−0.435418
$58$	−0.812402	−0.106674
$59$	−13.5212	−1.76031	−0.880153	−	0.474690i	$-0.842560\pi$
$59$	−13.5212	−1.76031	−0.880153	+	0.474690i	$0.842560\pi$
$60$	1.03782	0.133982
$61$	10.9507	1.40209	0.701046	−	0.713116i	$-0.252717\pi$
$61$	10.9507	1.40209	0.701046	+	0.713116i	$0.252717\pi$
$62$	−2.01579	−0.256006
$63$	7.03195	0.885943
$64$	1.00000	0.125000
$65$	3.74747	0.464816
$66$	−3.50458	−0.431384
$67$	0.202415	0.0247289	0.0123645	−	0.999924i	$-0.496064\pi$
$67$	0.202415	0.0247289	0.0123645	+	0.999924i	$0.496064\pi$
$68$	−0.215513	−0.0261348
$69$	5.61479	0.675942
$70$	3.65688	0.437081
$71$	4.07678	0.483825	0.241912	−	0.970298i	$-0.422225\pi$
$71$	4.07678	0.483825	0.241912	+	0.970298i	$0.422225\pi$
$72$	1.92294	0.226620
$73$	−14.6244	−1.71166	−0.855831	−	0.517256i	$-0.826954\pi$
$73$	−14.6244	−1.71166	−0.855831	+	0.517256i	$0.826954\pi$
$74$	1.23319	0.143356
$75$	1.03782	0.119837
$76$	−3.16754	−0.363342
$77$	−12.3488	−1.40728
$78$	−3.88919	−0.440364
$79$	13.1650	1.48117	0.740587	−	0.671961i	$-0.234548\pi$
$79$	13.1650	1.48117	0.740587	+	0.671961i	$0.234548\pi$
$80$	1.00000	0.111803
$81$	0.466492	0.0518325
$82$	2.22559	0.245775
$83$	11.3538	1.24625	0.623123	−	0.782124i	$-0.285864\pi$
$83$	11.3538	1.24625	0.623123	+	0.782124i	$0.285864\pi$
$84$	−3.79517	−0.414087
$85$	−0.215513	−0.0233757
$86$	−6.28835	−0.678090
$87$	0.843125	0.0903925
$88$	−3.37688	−0.359976
$89$	−10.8782	−1.15309	−0.576546	−	0.817065i	$-0.695600\pi$
$89$	−10.8782	−1.15309	−0.576546	+	0.817065i	$0.695600\pi$
$90$	1.92294	0.202695
$91$	−13.7041	−1.43658
$92$	5.41020	0.564052
$93$	2.09202	0.216933
$94$	2.31372	0.238642
$95$	−3.16754	−0.324983
$96$	−1.03782	−0.105922
$97$	−11.0319	−1.12012	−0.560059	−	0.828453i	$-0.689222\pi$
$97$	−11.0319	−1.12012	−0.560059	+	0.828453i	$0.689222\pi$
$98$	−6.37279	−0.643749
$99$	−6.49352	−0.652623
$100$	1.00000	0.100000
$101$	6.63126	0.659835	0.329918	−	0.944010i	$-0.392979\pi$
$101$	6.63126	0.659835	0.329918	+	0.944010i	$0.392979\pi$
$102$	0.223663	0.0221460
$103$	3.21287	0.316573	0.158287	−	0.987393i	$-0.449403\pi$
$103$	3.21287	0.316573	0.158287	+	0.987393i	$0.449403\pi$
$104$	−3.74747	−0.367470
$105$	−3.79517	−0.370371
$106$	−3.87618	−0.376488
$107$	−15.5948	−1.50760	−0.753801	−	0.657102i	$-0.771782\pi$
$107$	−15.5948	−1.50760	−0.753801	+	0.657102i	$0.771782\pi$
$108$	−5.10911	−0.491624
$109$	9.74833	0.933721	0.466860	−	0.884331i	$-0.345385\pi$
$109$	9.74833	0.933721	0.466860	+	0.884331i	$0.345385\pi$
$110$	−3.37688	−0.321973
$111$	−1.27983	−0.121476
$112$	−3.65688	−0.345543
$113$	4.69211	0.441397	0.220698	−	0.975342i	$-0.429166\pi$
$113$	4.69211	0.441397	0.220698	+	0.975342i	$0.429166\pi$
$114$	3.28733	0.307887
$115$	5.41020	0.504503
$116$	0.812402	0.0754297
$117$	−7.20615	−0.666208
$118$	13.5212	1.24472
$119$	0.788107	0.0722457
$120$	−1.03782	−0.0947393
$121$	0.403297	0.0366634
$122$	−10.9507	−0.991428
$123$	−2.30975	−0.208263
$124$	2.01579	0.181024
$125$	1.00000	0.0894427
$126$	−7.03195	−0.626456
$127$	13.3627	1.18575	0.592874	−	0.805296i	$-0.297993\pi$
$127$	13.3627	1.18575	0.592874	+	0.805296i	$0.297993\pi$
$128$	−1.00000	−0.0883883
$129$	6.52615	0.574596
$130$	−3.74747	−0.328675
$131$	11.5136	1.00595	0.502973	−	0.864302i	$-0.332240\pi$
$131$	11.5136	1.00595	0.502973	+	0.864302i	$0.332240\pi$
$132$	3.50458	0.305035
$133$	11.5833	1.00440
$134$	−0.202415	−0.0174860
$135$	−5.10911	−0.439722
$136$	0.215513	0.0184801
$137$	17.7664	1.51789	0.758945	−	0.651155i	$-0.225715\pi$
$137$	17.7664	1.51789	0.758945	+	0.651155i	$0.225715\pi$
$138$	−5.61479	−0.477963
$139$	5.17338	0.438800	0.219400	−	0.975635i	$-0.429590\pi$
$139$	5.17338	0.438800	0.219400	+	0.975635i	$0.429590\pi$
$140$	−3.65688	−0.309063
$141$	−2.40122	−0.202219
$142$	−4.07678	−0.342116
$143$	12.6547	1.05824
$144$	−1.92294	−0.160245
$145$	0.812402	0.0674663
$146$	14.6244	1.21033
$147$	6.61378	0.545496
$148$	−1.23319	−0.101368
$149$	8.93665	0.732119	0.366060	−	0.930591i	$-0.380707\pi$
$149$	8.93665	0.732119	0.366060	+	0.930591i	$0.380707\pi$
$150$	−1.03782	−0.0847374
$151$	−3.91214	−0.318365	−0.159183	−	0.987249i	$-0.550886\pi$
$151$	−3.91214	−0.318365	−0.159183	+	0.987249i	$0.550886\pi$
$152$	3.16754	0.256922
$153$	0.414419	0.0335038
$154$	12.3488	0.995098
$155$	2.01579	0.161912
$156$	3.88919	0.311384
$157$	13.0752	1.04351	0.521756	−	0.853095i	$-0.325277\pi$
$157$	13.0752	1.04351	0.521756	+	0.853095i	$0.325277\pi$
$158$	−13.1650	−1.04735
$159$	4.02276	0.319026
$160$	−1.00000	−0.0790569
$161$	−19.7845	−1.55923
$162$	−0.466492	−0.0366511
$163$	−2.24469	−0.175818	−0.0879089	−	0.996129i	$-0.528018\pi$
$163$	−2.24469	−0.175818	−0.0879089	+	0.996129i	$0.528018\pi$
$164$	−2.22559	−0.173789
$165$	3.50458	0.272831
$166$	−11.3538	−0.881229
$167$	−19.8554	−1.53646	−0.768228	−	0.640176i	$-0.778861\pi$
$167$	−19.8554	−1.53646	−0.768228	+	0.640176i	$0.778861\pi$
$168$	3.79517	0.292804
$169$	1.04353	0.0802717
$170$	0.215513	0.0165291
$171$	6.09099	0.465789
$172$	6.28835	0.479482
$173$	−5.76255	−0.438119	−0.219059	−	0.975712i	$-0.570299\pi$
$173$	−5.76255	−0.438119	−0.219059	+	0.975712i	$0.570299\pi$
$174$	−0.843125	−0.0639171
$175$	−3.65688	−0.276434
$176$	3.37688	0.254542
$177$	−14.0325	−1.05475
$178$	10.8782	0.815359
$179$	15.8613	1.18553	0.592765	−	0.805376i	$-0.298036\pi$
$179$	15.8613	1.18553	0.592765	+	0.805376i	$0.298036\pi$
$180$	−1.92294	−0.143327
$181$	9.47492	0.704265	0.352132	−	0.935950i	$-0.385457\pi$
$181$	9.47492	0.704265	0.352132	+	0.935950i	$0.385457\pi$
$182$	13.7041	1.01581
$183$	11.3648	0.840110
$184$	−5.41020	−0.398845
$185$	−1.23319	−0.0906661
$186$	−2.09202	−0.153395
$187$	−0.727762	−0.0532193
$188$	−2.31372	−0.168745
$189$	18.6834	1.35902
$190$	3.16754	0.229798
$191$	14.6508	1.06010	0.530049	−	0.847967i	$-0.322173\pi$
$191$	14.6508	1.06010	0.530049	+	0.847967i	$0.322173\pi$
$192$	1.03782	0.0748980
$193$	−17.4298	−1.25463	−0.627313	−	0.778767i	$-0.715846\pi$
$193$	−17.4298	−1.25463	−0.627313	+	0.778767i	$0.715846\pi$
$194$	11.0319	0.792043
$195$	3.88919	0.278511
$196$	6.37279	0.455199
$197$	5.43621	0.387314	0.193657	−	0.981069i	$-0.437965\pi$
$197$	5.43621	0.387314	0.193657	+	0.981069i	$0.437965\pi$
$198$	6.49352	0.461474
$199$	24.7689	1.75582	0.877911	−	0.478824i	$-0.158937\pi$
$199$	24.7689	1.75582	0.877911	+	0.478824i	$0.158937\pi$
$200$	−1.00000	−0.0707107
$201$	0.210069	0.0148172
$202$	−6.63126	−0.466574
$203$	−2.97086	−0.208513
$204$	−0.223663	−0.0156596
$205$	−2.22559	−0.155442
$206$	−3.21287	−0.223851
$207$	−10.4035	−0.723091
$208$	3.74747	0.259840
$209$	−10.6964	−0.739886
$210$	3.79517	0.261892
$211$	27.0025	1.85893	0.929465	−	0.368911i	$-0.120269\pi$
$211$	27.0025	1.85893	0.929465	+	0.368911i	$0.120269\pi$
$212$	3.87618	0.266217
$213$	4.23095	0.289900
$214$	15.5948	1.06604
$215$	6.28835	0.428862
$216$	5.10911	0.347631
$217$	−7.37152	−0.500411
$218$	−9.74833	−0.660240
$219$	−15.1775	−1.02560
$220$	3.37688	0.227669
$221$	−0.807630	−0.0543271
$222$	1.27983	0.0858964
$223$	3.92520	0.262851	0.131425	−	0.991326i	$-0.458045\pi$
$223$	3.92520	0.262851	0.131425	+	0.991326i	$0.458045\pi$
$224$	3.65688	0.244336
$225$	−1.92294	−0.128196
$226$	−4.69211	−0.312115
$227$	22.6128	1.50087	0.750433	−	0.660946i	$-0.229845\pi$
$227$	22.6128	1.50087	0.750433	+	0.660946i	$0.229845\pi$
$228$	−3.28733	−0.217709
$229$	26.1728	1.72955	0.864774	−	0.502161i	$-0.167462\pi$
$229$	26.1728	1.72955	0.864774	+	0.502161i	$0.167462\pi$
$230$	−5.41020	−0.356738
$231$	−12.8158	−0.843220
$232$	−0.812402	−0.0533368
$233$	0.751493	0.0492319	0.0246160	−	0.999697i	$-0.492164\pi$
$233$	0.751493	0.0492319	0.0246160	+	0.999697i	$0.492164\pi$
$234$	7.20615	0.471080
$235$	−2.31372	−0.150930
$236$	−13.5212	−0.880153
$237$	13.6628	0.887495
$238$	−0.788107	−0.0510854
$239$	−7.58600	−0.490698	−0.245349	−	0.969435i	$-0.578903\pi$
$239$	−7.58600	−0.490698	−0.245349	+	0.969435i	$0.578903\pi$
$240$	1.03782	0.0669908
$241$	26.0437	1.67762	0.838811	−	0.544423i	$-0.183251\pi$
$241$	26.0437	1.67762	0.838811	+	0.544423i	$0.183251\pi$
$242$	−0.403297	−0.0259249
$243$	15.8115	1.01431
$244$	10.9507	0.701046
$245$	6.37279	0.407142
$246$	2.30975	0.147264
$247$	−11.8703	−0.755288
$248$	−2.01579	−0.128003
$249$	11.7832	0.746730
$250$	−1.00000	−0.0632456
$251$	11.7263	0.740158	0.370079	−	0.929000i	$-0.379331\pi$
$251$	11.7263	0.740158	0.370079	+	0.929000i	$0.379331\pi$
$252$	7.03195	0.442971
$253$	18.2696	1.14860
$254$	−13.3627	−0.838450
$255$	−0.223663	−0.0140064
$256$	1.00000	0.0625000
$257$	18.6346	1.16240	0.581198	−	0.813763i	$-0.302584\pi$
$257$	18.6346	1.16240	0.581198	+	0.813763i	$0.302584\pi$
$258$	−6.52615	−0.406301
$259$	4.50964	0.280215
$260$	3.74747	0.232408
$261$	−1.56220	−0.0966976
$262$	−11.5136	−0.711311
$263$	−12.6650	−0.780959	−0.390479	−	0.920612i	$-0.627691\pi$
$263$	−12.6650	−0.780959	−0.390479	+	0.920612i	$0.627691\pi$
$264$	−3.50458	−0.215692
$265$	3.87618	0.238112
$266$	−11.5833	−0.710220
$267$	−11.2896	−0.690914
$268$	0.202415	0.0123645
$269$	6.82885	0.416363	0.208181	−	0.978090i	$-0.433246\pi$
$269$	6.82885	0.416363	0.208181	+	0.978090i	$0.433246\pi$
$270$	5.10911	0.310930
$271$	19.4095	1.17905	0.589523	−	0.807752i	$-0.299316\pi$
$271$	19.4095	1.17905	0.589523	+	0.807752i	$0.299316\pi$
$272$	−0.215513	−0.0130674
$273$	−14.2223	−0.860773
$274$	−17.7664	−1.07331
$275$	3.37688	0.203633
$276$	5.61479	0.337971
$277$	−29.0790	−1.74719	−0.873594	−	0.486655i	$-0.838217\pi$
$277$	−29.0790	−1.74719	−0.873594	+	0.486655i	$0.838217\pi$
$278$	−5.17338	−0.310279
$279$	−3.87624	−0.232064
$280$	3.65688	0.218541
$281$	28.2649	1.68614	0.843070	−	0.537803i	$-0.180746\pi$
$281$	28.2649	1.68614	0.843070	+	0.537803i	$0.180746\pi$
$282$	2.40122	0.142990
$283$	3.28111	0.195042	0.0975208	−	0.995233i	$-0.468909\pi$
$283$	3.28111	0.195042	0.0975208	+	0.995233i	$0.468909\pi$
$284$	4.07678	0.241912
$285$	−3.28733	−0.194725
$286$	−12.6547	−0.748291
$287$	8.13871	0.480413
$288$	1.92294	0.113310
$289$	−16.9536	−0.997268
$290$	−0.812402	−0.0477059
$291$	−11.4491	−0.671157
$292$	−14.6244	−0.855831
$293$	−25.2458	−1.47487	−0.737437	−	0.675416i	$-0.763964\pi$
$293$	−25.2458	−1.47487	−0.737437	+	0.675416i	$0.763964\pi$
$294$	−6.61378	−0.385724
$295$	−13.5212	−0.787233
$296$	1.23319	0.0716779
$297$	−17.2528	−1.00111
$298$	−8.93665	−0.517686
$299$	20.2746	1.17251
$300$	1.03782	0.0599184
$301$	−22.9957	−1.32545
$302$	3.91214	0.225118
$303$	6.88203	0.395362
$304$	−3.16754	−0.181671
$305$	10.9507	0.627034
$306$	−0.414419	−0.0236907
$307$	21.3000	1.21565	0.607826	−	0.794070i	$-0.292042\pi$
$307$	21.3000	1.21565	0.607826	+	0.794070i	$0.292042\pi$
$308$	−12.3488	−0.703640
$309$	3.33437	0.189686
$310$	−2.01579	−0.114489
$311$	−11.3248	−0.642172	−0.321086	−	0.947050i	$-0.604048\pi$
$311$	−11.3248	−0.642172	−0.321086	+	0.947050i	$0.604048\pi$
$312$	−3.88919	−0.220182
$313$	24.5480	1.38754	0.693768	−	0.720199i	$-0.255950\pi$
$313$	24.5480	1.38754	0.693768	+	0.720199i	$0.255950\pi$
$314$	−13.0752	−0.737874
$315$	7.03195	0.396206
$316$	13.1650	0.740587
$317$	−6.12633	−0.344089	−0.172045	−	0.985089i	$-0.555037\pi$
$317$	−6.12633	−0.344089	−0.172045	+	0.985089i	$0.555037\pi$
$318$	−4.02276	−0.225585
$319$	2.74338	0.153600
$320$	1.00000	0.0559017
$321$	−16.1845	−0.903331
$322$	19.7845	1.10254
$323$	0.682648	0.0379836
$324$	0.466492	0.0259162
$325$	3.74747	0.207872
$326$	2.24469	0.124322
$327$	10.1170	0.559470
$328$	2.22559	0.122887
$329$	8.46100	0.466470
$330$	−3.50458	−0.192921
$331$	−0.250410	−0.0137638	−0.00688189	−	0.999976i	$-0.502191\pi$
$331$	−0.250410	−0.0137638	−0.00688189	+	0.999976i	$0.502191\pi$
$332$	11.3538	0.623123
$333$	2.37135	0.129949
$334$	19.8554	1.08644
$335$	0.202415	0.0110591
$336$	−3.79517	−0.207044
$337$	10.7313	0.584569	0.292284	−	0.956331i	$-0.405585\pi$
$337$	10.7313	0.584569	0.292284	+	0.956331i	$0.405585\pi$
$338$	−1.04353	−0.0567607
$339$	4.86955	0.264478
$340$	−0.215513	−0.0116879
$341$	6.80708	0.368624
$342$	−6.09099	−0.329363
$343$	2.29365	0.123845
$344$	−6.28835	−0.339045
$345$	5.61479	0.302290
$346$	5.76255	0.309797
$347$	−36.1651	−1.94144	−0.970722	−	0.240204i	$-0.922786\pi$
$347$	−36.1651	−1.94144	−0.970722	+	0.240204i	$0.922786\pi$
$348$	0.843125	0.0451962
$349$	−34.5414	−1.84896	−0.924478	−	0.381235i	$-0.875499\pi$
$349$	−34.5414	−1.84896	−0.924478	+	0.381235i	$0.875499\pi$
$350$	3.65688	0.195469
$351$	−19.1462	−1.02195
$352$	−3.37688	−0.179988
$353$	9.77851	0.520458	0.260229	−	0.965547i	$-0.416202\pi$
$353$	9.77851	0.520458	0.260229	+	0.965547i	$0.416202\pi$
$354$	14.0325	0.745819
$355$	4.07678	0.216373
$356$	−10.8782	−0.576546
$357$	0.817911	0.0432884
$358$	−15.8613	−0.838296
$359$	−2.30879	−0.121854	−0.0609268	−	0.998142i	$-0.519406\pi$
$359$	−2.30879	−0.121854	−0.0609268	+	0.998142i	$0.519406\pi$
$360$	1.92294	0.101348
$361$	−8.96666	−0.471930
$362$	−9.47492	−0.497991
$363$	0.418549	0.0219681
$364$	−13.7041	−0.718288
$365$	−14.6244	−0.765478
$366$	−11.3648	−0.594048
$367$	−32.3313	−1.68768	−0.843839	−	0.536596i	$-0.819710\pi$
$367$	−32.3313	−1.68768	−0.843839	+	0.536596i	$0.819710\pi$
$368$	5.41020	0.282026
$369$	4.27966	0.222790
$370$	1.23319	0.0641106
$371$	−14.1747	−0.735915
$372$	2.09202	0.108466
$373$	−10.2869	−0.532637	−0.266319	−	0.963885i	$-0.585807\pi$
$373$	−10.2869	−0.532637	−0.266319	+	0.963885i	$0.585807\pi$
$374$	0.727762	0.0376317
$375$	1.03782	0.0535926
$376$	2.31372	0.119321
$377$	3.04445	0.156797
$378$	−18.6834	−0.960970
$379$	−10.7646	−0.552940	−0.276470	−	0.961023i	$-0.589165\pi$
$379$	−10.7646	−0.552940	−0.276470	+	0.961023i	$0.589165\pi$
$380$	−3.16754	−0.162492
$381$	13.8680	0.710480
$382$	−14.6508	−0.749603
$383$	−5.30417	−0.271030	−0.135515	−	0.990775i	$-0.543269\pi$
$383$	−5.30417	−0.271030	−0.135515	+	0.990775i	$0.543269\pi$
$384$	−1.03782	−0.0529609
$385$	−12.3488	−0.629355
$386$	17.4298	0.887155
$387$	−12.0921	−0.614676
$388$	−11.0319	−0.560059
$389$	−9.53656	−0.483523	−0.241761	−	0.970336i	$-0.577725\pi$
$389$	−9.53656	−0.483523	−0.241761	+	0.970336i	$0.577725\pi$
$390$	−3.88919	−0.196937
$391$	−1.16597	−0.0589656
$392$	−6.37279	−0.321874
$393$	11.9490	0.602746
$394$	−5.43621	−0.273872
$395$	13.1650	0.662401
$396$	−6.49352	−0.326312
$397$	−18.9346	−0.950300	−0.475150	−	0.879905i	$-0.657606\pi$
$397$	−18.9346	−0.950300	−0.475150	+	0.879905i	$0.657606\pi$
$398$	−24.7689	−1.24155
$399$	12.0214	0.601822
$400$	1.00000	0.0500000
$401$	−0.0627506	−0.00313361	−0.00156681	−	0.999999i	$-0.500499\pi$
$401$	−0.0627506	−0.00313361	−0.00156681	+	0.999999i	$0.500499\pi$
$402$	−0.210069	−0.0104773
$403$	7.55412	0.376298
$404$	6.63126	0.329918
$405$	0.466492	0.0231802
$406$	2.97086	0.147441
$407$	−4.16434	−0.206419
$408$	0.223663	0.0110730
$409$	−4.26183	−0.210734	−0.105367	−	0.994433i	$-0.533602\pi$
$409$	−4.26183	−0.210734	−0.105367	+	0.994433i	$0.533602\pi$
$410$	2.22559	0.109914
$411$	18.4383	0.909495
$412$	3.21287	0.158287
$413$	49.4453	2.43304
$414$	10.4035	0.511302
$415$	11.3538	0.557338
$416$	−3.74747	−0.183735
$417$	5.36902	0.262922
$418$	10.6964	0.523178
$419$	−2.69655	−0.131735	−0.0658674	−	0.997828i	$-0.520981\pi$
$419$	−2.69655	−0.131735	−0.0658674	+	0.997828i	$0.520981\pi$
$420$	−3.79517	−0.185186
$421$	−20.7655	−1.01205	−0.506025	−	0.862519i	$-0.668886\pi$
$421$	−20.7655	−1.01205	−0.506025	+	0.862519i	$0.668886\pi$
$422$	−27.0025	−1.31446
$423$	4.44913	0.216324
$424$	−3.87618	−0.188244
$425$	−0.215513	−0.0104539
$426$	−4.23095	−0.204990
$427$	−40.0454	−1.93793
$428$	−15.5948	−0.753801
$429$	13.1333	0.634082
$430$	−6.28835	−0.303251
$431$	−1.62083	−0.0780728	−0.0390364	−	0.999238i	$-0.512429\pi$
$431$	−1.62083	−0.0780728	−0.0390364	+	0.999238i	$0.512429\pi$
$432$	−5.10911	−0.245812
$433$	−5.50288	−0.264451	−0.132226	−	0.991220i	$-0.542212\pi$
$433$	−5.50288	−0.264451	−0.132226	+	0.991220i	$0.542212\pi$
$434$	7.37152	0.353844
$435$	0.843125	0.0404247
$436$	9.74833	0.466860
$437$	−17.1370	−0.819776
$438$	15.1775	0.725209
$439$	11.8038	0.563363	0.281682	−	0.959508i	$-0.409108\pi$
$439$	11.8038	0.563363	0.281682	+	0.959508i	$0.409108\pi$
$440$	−3.37688	−0.160986
$441$	−12.2545	−0.583546
$442$	0.807630	0.0384150
$443$	37.9919	1.80505	0.902525	−	0.430638i	$-0.141711\pi$
$443$	37.9919	1.80505	0.902525	+	0.430638i	$0.141711\pi$
$444$	−1.27983	−0.0607380
$445$	−10.8782	−0.515678
$446$	−3.92520	−0.185863
$447$	9.27461	0.438674
$448$	−3.65688	−0.172771
$449$	−14.7413	−0.695687	−0.347843	−	0.937553i	$-0.613086\pi$
$449$	−14.7413	−0.695687	−0.347843	+	0.937553i	$0.613086\pi$
$450$	1.92294	0.0906481
$451$	−7.51553	−0.353893
$452$	4.69211	0.220698
$453$	−4.06008	−0.190759
$454$	−22.6128	−1.06127
$455$	−13.7041	−0.642456
$456$	3.28733	0.153943
$457$	20.5518	0.961370	0.480685	−	0.876893i	$-0.340388\pi$
$457$	20.5518	0.961370	0.480685	+	0.876893i	$0.340388\pi$
$458$	−26.1728	−1.22298
$459$	1.10108	0.0513941
$460$	5.41020	0.252252
$461$	26.0399	1.21280	0.606399	−	0.795160i	$-0.292613\pi$
$461$	26.0399	1.21280	0.606399	+	0.795160i	$0.292613\pi$
$462$	12.8158	0.596247
$463$	−40.3534	−1.87538	−0.937692	−	0.347468i	$-0.887042\pi$
$463$	−40.3534	−1.87538	−0.937692	+	0.347468i	$0.887042\pi$
$464$	0.812402	0.0377148
$465$	2.09202	0.0970153
$466$	−0.751493	−0.0348122
$467$	19.0057	0.879479	0.439740	−	0.898125i	$-0.355071\pi$
$467$	19.0057	0.879479	0.439740	+	0.898125i	$0.355071\pi$
$468$	−7.20615	−0.333104
$469$	−0.740207	−0.0341796
$470$	2.31372	0.106724
$471$	13.5696	0.625255
$472$	13.5212	0.622362
$473$	21.2350	0.976385
$474$	−13.6628	−0.627554
$475$	−3.16754	−0.145337
$476$	0.788107	0.0361228
$477$	−7.45364	−0.341279
$478$	7.58600	0.346976
$479$	−4.99765	−0.228349	−0.114174	−	0.993461i	$-0.536422\pi$
$479$	−4.99765	−0.228349	−0.114174	+	0.993461i	$0.536422\pi$
$480$	−1.03782	−0.0473696
$481$	−4.62135	−0.210716
$482$	−26.0437	−1.18626
$483$	−20.5326	−0.934267
$484$	0.403297	0.0183317
$485$	−11.0319	−0.500932
$486$	−15.8115	−0.717222
$487$	33.5250	1.51916	0.759581	−	0.650413i	$-0.225404\pi$
$487$	33.5250	1.51916	0.759581	+	0.650413i	$0.225404\pi$
$488$	−10.9507	−0.495714
$489$	−2.32958	−0.105347
$490$	−6.37279	−0.287893
$491$	−8.90643	−0.401941	−0.200971	−	0.979597i	$-0.564410\pi$
$491$	−8.90643	−0.401941	−0.200971	+	0.979597i	$0.564410\pi$
$492$	−2.30975	−0.104132
$493$	−0.175084	−0.00788537
$494$	11.8703	0.534069
$495$	−6.49352	−0.291862
$496$	2.01579	0.0905118
$497$	−14.9083	−0.668729
$498$	−11.7832	−0.528018
$499$	−13.3307	−0.596764	−0.298382	−	0.954447i	$-0.596447\pi$
$499$	−13.3307	−0.596764	−0.298382	+	0.954447i	$0.596447\pi$
$500$	1.00000	0.0447214
$501$	−20.6063	−0.920620
$502$	−11.7263	−0.523371
$503$	41.1360	1.83417	0.917083	−	0.398697i	$-0.130538\pi$
$503$	41.1360	1.83417	0.917083	+	0.398697i	$0.130538\pi$
$504$	−7.03195	−0.313228
$505$	6.63126	0.295087
$506$	−18.2696	−0.812181
$507$	1.08300	0.0480975
$508$	13.3627	0.592874
$509$	19.6597	0.871400	0.435700	−	0.900092i	$-0.356501\pi$
$509$	19.6597	0.871400	0.435700	+	0.900092i	$0.356501\pi$
$510$	0.223663	0.00990399
$511$	53.4799	2.36581
$512$	−1.00000	−0.0441942
$513$	16.1833	0.714511
$514$	−18.6346	−0.821937
$515$	3.21287	0.141576
$516$	6.52615	0.287298
$517$	−7.81314	−0.343622
$518$	−4.50964	−0.198142
$519$	−5.98048	−0.262514
$520$	−3.74747	−0.164337
$521$	−9.43214	−0.413230	−0.206615	−	0.978422i	$-0.566245\pi$
$521$	−9.43214	−0.413230	−0.206615	+	0.978422i	$0.566245\pi$
$522$	1.56220	0.0683755
$523$	−2.68428	−0.117376	−0.0586878	−	0.998276i	$-0.518692\pi$
$523$	−2.68428	−0.117376	−0.0586878	+	0.998276i	$0.518692\pi$
$524$	11.5136	0.502973
$525$	−3.79517	−0.165635
$526$	12.6650	0.552221
$527$	−0.434430	−0.0189241
$528$	3.50458	0.152517
$529$	6.27023	0.272619
$530$	−3.87618	−0.168370
$531$	26.0003	1.12832
$532$	11.5833	0.502201
$533$	−8.34032	−0.361259
$534$	11.2896	0.488550
$535$	−15.5948	−0.674220
$536$	−0.202415	−0.00874299
$537$	16.4611	0.710350
$538$	−6.82885	−0.294413
$539$	21.5201	0.926937
$540$	−5.10911	−0.219861
$541$	−10.0571	−0.432389	−0.216194	−	0.976350i	$-0.569365\pi$
$541$	−10.0571	−0.432389	−0.216194	+	0.976350i	$0.569365\pi$
$542$	−19.4095	−0.833711
$543$	9.83323	0.421984
$544$	0.215513	0.00924006
$545$	9.74833	0.417573
$546$	14.2223	0.608658
$547$	−24.7023	−1.05619	−0.528097	−	0.849184i	$-0.677094\pi$
$547$	−24.7023	−1.05619	−0.528097	+	0.849184i	$0.677094\pi$
$548$	17.7664	0.758945
$549$	−21.0575	−0.898711
$550$	−3.37688	−0.143991
$551$	−2.57332	−0.109627
$552$	−5.61479	−0.238981
$553$	−48.1427	−2.04724
$554$	29.0790	1.23545
$555$	−1.27983	−0.0543257
$556$	5.17338	0.219400
$557$	−27.0631	−1.14670	−0.573349	−	0.819311i	$-0.694356\pi$
$557$	−27.0631	−1.14670	−0.573349	+	0.819311i	$0.694356\pi$
$558$	3.87624	0.164094
$559$	23.5654	0.996710
$560$	−3.65688	−0.154531
$561$	−0.755284	−0.0318881
$562$	−28.2649	−1.19228
$563$	38.3795	1.61750	0.808751	−	0.588152i	$-0.200144\pi$
$563$	38.3795	1.61750	0.808751	+	0.588152i	$0.200144\pi$
$564$	−2.40122	−0.101109
$565$	4.69211	0.197399
$566$	−3.28111	−0.137915
$567$	−1.70591	−0.0716414
$568$	−4.07678	−0.171058
$569$	39.1862	1.64277	0.821386	−	0.570373i	$-0.193201\pi$
$569$	39.1862	1.64277	0.821386	+	0.570373i	$0.193201\pi$
$570$	3.28733	0.137691
$571$	30.6549	1.28287	0.641434	−	0.767178i	$-0.278340\pi$
$571$	30.6549	1.28287	0.641434	+	0.767178i	$0.278340\pi$
$572$	12.6547	0.529121
$573$	15.2049	0.635194
$574$	−8.13871	−0.339703
$575$	5.41020	0.225621
$576$	−1.92294	−0.0801223
$577$	24.5919	1.02377	0.511887	−	0.859053i	$-0.328947\pi$
$577$	24.5919	1.02377	0.511887	+	0.859053i	$0.328947\pi$
$578$	16.9536	0.705175
$579$	−18.0890	−0.751752
$580$	0.812402	0.0337332
$581$	−41.5196	−1.72252
$582$	11.4491	0.474579
$583$	13.0894	0.542106
$584$	14.6244	0.605164
$585$	−7.20615	−0.297937
$586$	25.2458	1.04289
$587$	22.9989	0.949265	0.474632	−	0.880184i	$-0.342581\pi$
$587$	22.9989	0.949265	0.474632	+	0.880184i	$0.342581\pi$
$588$	6.61378	0.272748
$589$	−6.38511	−0.263094
$590$	13.5212	0.556658
$591$	5.64179	0.232072
$592$	−1.23319	−0.0506839
$593$	−31.7364	−1.30326	−0.651630	−	0.758537i	$-0.725914\pi$
$593$	−31.7364	−1.30326	−0.651630	+	0.758537i	$0.725914\pi$
$594$	17.2528	0.707892
$595$	0.788107	0.0323092
$596$	8.93665	0.366060
$597$	25.7056	1.05206
$598$	−20.2746	−0.829088
$599$	43.9098	1.79411	0.897053	−	0.441923i	$-0.145704\pi$
$599$	43.9098	1.79411	0.897053	+	0.441923i	$0.145704\pi$
$600$	−1.03782	−0.0423687
$601$	−1.00000	−0.0407909
$601$	−1.00000	−0.0407909
$602$	22.9957	0.937237
$603$	−0.389231	−0.0158507
$604$	−3.91214	−0.159183
$605$	0.403297	0.0163964
$606$	−6.88203	−0.279563
$607$	−32.6908	−1.32688	−0.663440	−	0.748229i	$-0.730904\pi$
$607$	−32.6908	−1.32688	−0.663440	+	0.748229i	$0.730904\pi$
$608$	3.16754	0.128461
$609$	−3.08321	−0.124938
$610$	−10.9507	−0.443380
$611$	−8.67059	−0.350775
$612$	0.414419	0.0167519
$613$	−30.8105	−1.24442	−0.622212	−	0.782848i	$-0.713766\pi$
$613$	−30.8105	−1.24442	−0.622212	+	0.782848i	$0.713766\pi$
$614$	−21.3000	−0.859596
$615$	−2.30975	−0.0931382
$616$	12.3488	0.497549
$617$	34.6123	1.39344	0.696719	−	0.717344i	$-0.254642\pi$
$617$	34.6123	1.39344	0.696719	+	0.717344i	$0.254642\pi$
$618$	−3.33437	−0.134128
$619$	3.78119	0.151979	0.0759895	−	0.997109i	$-0.475788\pi$
$619$	3.78119	0.151979	0.0759895	+	0.997109i	$0.475788\pi$
$620$	2.01579	0.0809562
$621$	−27.6413	−1.10921
$622$	11.3248	0.454084
$623$	39.7805	1.59377
$624$	3.88919	0.155692
$625$	1.00000	0.0400000
$626$	−24.5480	−0.981135
$627$	−11.1009	−0.443328
$628$	13.0752	0.521756
$629$	0.265770	0.0105969
$630$	−7.03195	−0.280160
$631$	19.0714	0.759221	0.379610	−	0.925146i	$-0.376058\pi$
$631$	19.0714	0.759221	0.379610	+	0.925146i	$0.376058\pi$
$632$	−13.1650	−0.523674
$633$	28.0237	1.11384
$634$	6.12633	0.243308
$635$	13.3627	0.530282
$636$	4.02276	0.159513
$637$	23.8818	0.946232
$638$	−2.74338	−0.108612
$639$	−7.83939	−0.310121
$640$	−1.00000	−0.0395285
$641$	0.227937	0.00900295	0.00450148	−	0.999990i	$-0.498567\pi$
$641$	0.227937	0.00900295	0.00450148	+	0.999990i	$0.498567\pi$
$642$	16.1845	0.638752
$643$	−1.27126	−0.0501336	−0.0250668	−	0.999686i	$-0.507980\pi$
$643$	−1.27126	−0.0501336	−0.0250668	+	0.999686i	$0.507980\pi$
$644$	−19.7845	−0.779617
$645$	6.52615	0.256967
$646$	−0.682648	−0.0268584
$647$	−34.8403	−1.36972	−0.684858	−	0.728677i	$-0.740136\pi$
$647$	−34.8403	−1.36972	−0.684858	+	0.728677i	$0.740136\pi$
$648$	−0.466492	−0.0183255
$649$	−45.6593	−1.79228
$650$	−3.74747	−0.146988
$651$	−7.65028	−0.299838
$652$	−2.24469	−0.0879089
$653$	−27.4648	−1.07478	−0.537391	−	0.843333i	$-0.680590\pi$
$653$	−27.4648	−1.07478	−0.537391	+	0.843333i	$0.680590\pi$
$654$	−10.1170	−0.395605
$655$	11.5136	0.449873
$656$	−2.22559	−0.0868946
$657$	28.1219	1.09714
$658$	−8.46100	−0.329844
$659$	30.0151	1.16922	0.584611	−	0.811314i	$-0.301247\pi$
$659$	30.0151	1.16922	0.584611	+	0.811314i	$0.301247\pi$
$660$	3.50458	0.136416
$661$	10.0503	0.390911	0.195455	−	0.980713i	$-0.437382\pi$
$661$	10.0503	0.390911	0.195455	+	0.980713i	$0.437382\pi$
$662$	0.250410	0.00973246
$663$	−0.838172	−0.0325519
$664$	−11.3538	−0.440614
$665$	11.5833	0.449182
$666$	−2.37135	−0.0918880
$667$	4.39526	0.170185
$668$	−19.8554	−0.768228
$669$	4.07364	0.157496
$670$	−0.202415	−0.00781996
$671$	36.9791	1.42756
$672$	3.79517	0.146402
$673$	−10.4797	−0.403964	−0.201982	−	0.979389i	$-0.564738\pi$
$673$	−10.4797	−0.403964	−0.201982	+	0.979389i	$0.564738\pi$
$674$	−10.7313	−0.413353
$675$	−5.10911	−0.196650
$676$	1.04353	0.0401358
$677$	40.5800	1.55962	0.779809	−	0.626018i	$-0.215316\pi$
$677$	40.5800	1.55962	0.779809	+	0.626018i	$0.215316\pi$
$678$	−4.86955	−0.187014
$679$	40.3423	1.54820
$680$	0.215513	0.00826456
$681$	23.4680	0.899295
$682$	−6.80708	−0.260657
$683$	−7.62692	−0.291836	−0.145918	−	0.989297i	$-0.546614\pi$
$683$	−7.62692	−0.291836	−0.145918	+	0.989297i	$0.546614\pi$
$684$	6.09099	0.232895
$685$	17.7664	0.678821
$686$	−2.29365	−0.0875718
$687$	27.1626	1.03632
$688$	6.28835	0.239741
$689$	14.5259	0.553391
$690$	−5.61479	−0.213752
$691$	−5.46159	−0.207769	−0.103884	−	0.994589i	$-0.533127\pi$
$691$	−5.46159	−0.207769	−0.103884	+	0.994589i	$0.533127\pi$
$692$	−5.76255	−0.219059
$693$	23.7460	0.902037
$694$	36.1651	1.37281
$695$	5.17338	0.196237
$696$	−0.843125	−0.0319586
$697$	0.479644	0.0181678
$698$	34.5414	1.30741
$699$	0.779912	0.0294990
$700$	−3.65688	−0.138217
$701$	−2.74812	−0.103795	−0.0518976	−	0.998652i	$-0.516527\pi$
$701$	−2.74812	−0.103795	−0.0518976	+	0.998652i	$0.516527\pi$
$702$	19.1462	0.722628
$703$	3.90619	0.147325
$704$	3.37688	0.127271
$705$	−2.40122	−0.0904350
$706$	−9.77851	−0.368019
$707$	−24.2497	−0.912005
$708$	−14.0325	−0.527373
$709$	−21.5202	−0.808209	−0.404104	−	0.914713i	$-0.632417\pi$
$709$	−21.5202	−0.808209	−0.404104	+	0.914713i	$0.632417\pi$
$710$	−4.07678	−0.152999
$711$	−25.3154	−0.949400
$712$	10.8782	0.407680
$713$	10.9058	0.408427
$714$	−0.817911	−0.0306095
$715$	12.6547	0.473261
$716$	15.8613	0.592765
$717$	−7.87288	−0.294018
$718$	2.30879	0.0861635
$719$	30.9846	1.15553	0.577765	−	0.816203i	$-0.303925\pi$
$719$	30.9846	1.15553	0.577765	+	0.816203i	$0.303925\pi$
$720$	−1.92294	−0.0716636
$721$	−11.7491	−0.437559
$722$	8.96666	0.333705
$723$	27.0286	1.00520
$724$	9.47492	0.352132
$725$	0.812402	0.0301719
$726$	−0.418549	−0.0155338
$727$	−23.4729	−0.870561	−0.435281	−	0.900295i	$-0.643351\pi$
$727$	−23.4729	−0.870561	−0.435281	+	0.900295i	$0.643351\pi$
$728$	13.7041	0.507906
$729$	15.0099	0.555923
$730$	14.6244	0.541275
$731$	−1.35522	−0.0501248
$732$	11.3648	0.420055
$733$	−2.37074	−0.0875654	−0.0437827	−	0.999041i	$-0.513941\pi$
$733$	−2.37074	−0.0875654	−0.0437827	+	0.999041i	$0.513941\pi$
$734$	32.3313	1.19337
$735$	6.61378	0.243953
$736$	−5.41020	−0.199423
$737$	0.683530	0.0251781
$738$	−4.27966	−0.157537
$739$	−11.9266	−0.438726	−0.219363	−	0.975643i	$-0.570398\pi$
$739$	−11.9266	−0.438726	−0.219363	+	0.975643i	$0.570398\pi$
$740$	−1.23319	−0.0453331
$741$	−12.3192	−0.452556
$742$	14.1747	0.520370
$743$	15.2883	0.560872	0.280436	−	0.959873i	$-0.409521\pi$
$743$	15.2883	0.560872	0.280436	+	0.959873i	$0.409521\pi$
$744$	−2.09202	−0.0766973
$745$	8.93665	0.327414
$746$	10.2869	0.376632
$747$	−21.8327	−0.798817
$748$	−0.727762	−0.0266096
$749$	57.0282	2.08377
$750$	−1.03782	−0.0378957
$751$	−23.6972	−0.864724	−0.432362	−	0.901700i	$-0.642320\pi$
$751$	−23.6972	−0.864724	−0.432362	+	0.901700i	$0.642320\pi$
$752$	−2.31372	−0.0843726
$753$	12.1698	0.443491
$754$	−3.04445	−0.110872
$755$	−3.91214	−0.142377
$756$	18.6834	0.679509
$757$	−41.4932	−1.50810	−0.754048	−	0.656820i	$-0.771901\pi$
$757$	−41.4932	−1.50810	−0.754048	+	0.656820i	$0.771901\pi$
$758$	10.7646	0.390987
$759$	18.9605	0.688221
$760$	3.16754	0.114899
$761$	8.50542	0.308321	0.154161	−	0.988046i	$-0.450733\pi$
$761$	8.50542	0.308321	0.154161	+	0.988046i	$0.450733\pi$
$762$	−13.8680	−0.502386
$763$	−35.6485	−1.29056
$764$	14.6508	0.530049
$765$	0.414419	0.0149833
$766$	5.30417	0.191647
$767$	−50.6702	−1.82959
$768$	1.03782	0.0374490
$769$	6.47655	0.233551	0.116775	−	0.993158i	$-0.462744\pi$
$769$	6.47655	0.233551	0.116775	+	0.993158i	$0.462744\pi$
$770$	12.3488	0.445021
$771$	19.3393	0.696488
$772$	−17.4298	−0.627313
$773$	−8.66929	−0.311813	−0.155906	−	0.987772i	$-0.549830\pi$
$773$	−8.66929	−0.311813	−0.155906	+	0.987772i	$0.549830\pi$
$774$	12.0921	0.434641
$775$	2.01579	0.0724094
$776$	11.0319	0.396021
$777$	4.68018	0.167901
$778$	9.53656	0.341902
$779$	7.04964	0.252580
$780$	3.88919	0.139255
$781$	13.7668	0.492614
$782$	1.16597	0.0416950
$783$	−4.15065	−0.148332
$784$	6.37279	0.227600
$785$	13.0752	0.466673
$786$	−11.9490	−0.426206
$787$	−9.01728	−0.321431	−0.160716	−	0.987001i	$-0.551380\pi$
$787$	−9.01728	−0.321431	−0.160716	+	0.987001i	$0.551380\pi$
$788$	5.43621	0.193657
$789$	−13.1440	−0.467938
$790$	−13.1650	−0.468388
$791$	−17.1585	−0.610086
$792$	6.49352	0.230737
$793$	41.0374	1.45728
$794$	18.9346	0.671964
$795$	4.02276	0.142673
$796$	24.7689	0.877911
$797$	43.3680	1.53617	0.768086	−	0.640347i	$-0.221209\pi$
$797$	43.3680	1.53617	0.768086	+	0.640347i	$0.221209\pi$
$798$	−12.0214	−0.425552
$799$	0.498637	0.0176405
$800$	−1.00000	−0.0353553
$801$	20.9182	0.739107
$802$	0.0627506	0.00221580
$803$	−49.3849	−1.74276
$804$	0.210069	0.00740858
$805$	−19.7845	−0.697310
$806$	−7.55412	−0.266083
$807$	7.08710	0.249478
$808$	−6.63126	−0.233287
$809$	9.04658	0.318061	0.159030	−	0.987274i	$-0.449163\pi$
$809$	9.04658	0.318061	0.159030	+	0.987274i	$0.449163\pi$
$810$	−0.466492	−0.0163909
$811$	20.6201	0.724070	0.362035	−	0.932164i	$-0.382082\pi$
$811$	20.6201	0.724070	0.362035	+	0.932164i	$0.382082\pi$
$812$	−2.97086	−0.104257
$813$	20.1435	0.706465
$814$	4.16434	0.145960
$815$	−2.24469	−0.0786281
$816$	−0.223663	−0.00782979
$817$	−19.9186	−0.696864
$818$	4.26183	0.149011
$819$	26.3520	0.920814
$820$	−2.22559	−0.0777209
$821$	−29.1302	−1.01665	−0.508325	−	0.861165i	$-0.669735\pi$
$821$	−29.1302	−1.01665	−0.508325	+	0.861165i	$0.669735\pi$
$822$	−18.4383	−0.643110
$823$	−8.47428	−0.295395	−0.147697	−	0.989033i	$-0.547186\pi$
$823$	−8.47428	−0.295395	−0.147697	+	0.989033i	$0.547186\pi$
$824$	−3.21287	−0.111926
$825$	3.50458	0.122014
$826$	−49.4453	−1.72042
$827$	38.8715	1.35169	0.675847	−	0.737042i	$-0.263778\pi$
$827$	38.8715	1.35169	0.675847	+	0.737042i	$0.263778\pi$
$828$	−10.4035	−0.361545
$829$	−33.5907	−1.16665	−0.583327	−	0.812238i	$-0.698249\pi$
$829$	−33.5907	−1.16665	−0.583327	+	0.812238i	$0.698249\pi$
$830$	−11.3538	−0.394097
$831$	−30.1787	−1.04689
$832$	3.74747	0.129920
$833$	−1.37342	−0.0475862
$834$	−5.36902	−0.185914
$835$	−19.8554	−0.687124
$836$	−10.6964	−0.369943
$837$	−10.2989	−0.355982
$838$	2.69655	0.0931506
$839$	−26.5267	−0.915802	−0.457901	−	0.889003i	$-0.651399\pi$
$839$	−26.5267	−0.915802	−0.457901	+	0.889003i	$0.651399\pi$
$840$	3.79517	0.130946
$841$	−28.3400	−0.977241
$842$	20.7655	0.715627
$843$	29.3338	1.01031
$844$	27.0025	0.929465
$845$	1.04353	0.0358986
$846$	−4.44913	−0.152964
$847$	−1.47481	−0.0506751
$848$	3.87618	0.133108
$849$	3.40519	0.116866
$850$	0.215513	0.00739205
$851$	−6.67182	−0.228707
$852$	4.23095	0.144950
$853$	40.1425	1.37445	0.687226	−	0.726444i	$-0.258828\pi$
$853$	40.1425	1.37445	0.687226	+	0.726444i	$0.258828\pi$
$854$	40.0454	1.37032
$855$	6.09099	0.208307
$856$	15.5948	0.533018
$857$	−1.04928	−0.0358427	−0.0179213	−	0.999839i	$-0.505705\pi$
$857$	−1.04928	−0.0358427	−0.0179213	+	0.999839i	$0.505705\pi$
$858$	−13.1333	−0.448364
$859$	37.4295	1.27708	0.638540	−	0.769589i	$-0.279539\pi$
$859$	37.4295	1.27708	0.638540	+	0.769589i	$0.279539\pi$
$860$	6.28835	0.214431
$861$	8.44649	0.287856
$862$	1.62083	0.0552058
$863$	−39.2898	−1.33744	−0.668721	−	0.743514i	$-0.733158\pi$
$863$	−39.2898	−1.33744	−0.668721	+	0.743514i	$0.733158\pi$
$864$	5.10911	0.173815
$865$	−5.76255	−0.195933
$866$	5.50288	0.186995
$867$	−17.5947	−0.597547
$868$	−7.37152	−0.250206
$869$	44.4564	1.50808
$870$	−0.843125	−0.0285846
$871$	0.758543	0.0257023
$872$	−9.74833	−0.330120
$873$	21.2136	0.717972
$874$	17.1370	0.579669
$875$	−3.65688	−0.123625
$876$	−15.1775	−0.512800
$877$	12.4506	0.420428	0.210214	−	0.977655i	$-0.432584\pi$
$877$	12.4506	0.420428	0.210214	+	0.977655i	$0.432584\pi$
$878$	−11.8038	−0.398358
$879$	−26.2005	−0.883720
$880$	3.37688	0.113834
$881$	−27.7485	−0.934871	−0.467436	−	0.884027i	$-0.654822\pi$
$881$	−27.7485	−0.934871	−0.467436	+	0.884027i	$0.654822\pi$
$882$	12.2545	0.412629
$883$	−32.3580	−1.08893	−0.544467	−	0.838782i	$-0.683268\pi$
$883$	−32.3580	−1.08893	−0.544467	+	0.838782i	$0.683268\pi$
$884$	−0.807630	−0.0271635
$885$	−14.0325	−0.471697
$886$	−37.9919	−1.27636
$887$	46.3314	1.55566	0.777829	−	0.628476i	$-0.216321\pi$
$887$	46.3314	1.55566	0.777829	+	0.628476i	$0.216321\pi$
$888$	1.27983	0.0429482
$889$	−48.8658	−1.63891
$890$	10.8782	0.364640
$891$	1.57529	0.0527741
$892$	3.92520	0.131425
$893$	7.32881	0.245249
$894$	−9.27461	−0.310189
$895$	15.8613	0.530185
$896$	3.65688	0.122168
$897$	21.0413	0.702548
$898$	14.7413	0.491925
$899$	1.63763	0.0546182
$900$	−1.92294	−0.0640979
$901$	−0.835368	−0.0278302
$902$	7.51553	0.250240
$903$	−23.8654	−0.794190
$904$	−4.69211	−0.156057
$905$	9.47492	0.314957
$906$	4.06008	0.134887
$907$	−26.1113	−0.867012	−0.433506	−	0.901151i	$-0.642724\pi$
$907$	−26.1113	−0.867012	−0.433506	+	0.901151i	$0.642724\pi$
$908$	22.6128	0.750433
$909$	−12.7515	−0.422940
$910$	13.7041	0.454285
$911$	8.88789	0.294469	0.147234	−	0.989102i	$-0.452963\pi$
$911$	8.88789	0.294469	0.147234	+	0.989102i	$0.452963\pi$
$912$	−3.28733	−0.108854
$913$	38.3405	1.26889
$914$	−20.5518	−0.679792
$915$	11.3648	0.375709
$916$	26.1728	0.864774
$917$	−42.1038	−1.39039
$918$	−1.10108	−0.0363411
$919$	3.18645	0.105111	0.0525557	−	0.998618i	$-0.483263\pi$
$919$	3.18645	0.105111	0.0525557	+	0.998618i	$0.483263\pi$
$920$	−5.41020	−0.178369
$921$	22.1054	0.728399
$922$	−26.0399	−0.857578
$923$	15.2776	0.502869
$924$	−12.8158	−0.421610
$925$	−1.23319	−0.0405471
$926$	40.3534	1.32610
$927$	−6.17814	−0.202917
$928$	−0.812402	−0.0266684
$929$	−60.2598	−1.97706	−0.988530	−	0.151024i	$-0.951743\pi$
$929$	−60.2598	−1.97706	−0.988530	+	0.151024i	$0.951743\pi$
$930$	−2.09202	−0.0686001
$931$	−20.1861	−0.661572
$932$	0.751493	0.0246160
$933$	−11.7531	−0.384779
$934$	−19.0057	−0.621886
$935$	−0.727762	−0.0238004
$936$	7.20615	0.235540
$937$	54.5953	1.78355	0.891775	−	0.452479i	$-0.149460\pi$
$937$	54.5953	1.78355	0.891775	+	0.452479i	$0.149460\pi$
$938$	0.740207	0.0241686
$939$	25.4763	0.831389
$940$	−2.31372	−0.0754652
$941$	−17.8167	−0.580807	−0.290403	−	0.956904i	$-0.593789\pi$
$941$	−17.8167	−0.580807	−0.290403	+	0.956904i	$0.593789\pi$
$942$	−13.5696	−0.442122
$943$	−12.0409	−0.392104
$944$	−13.5212	−0.440076
$945$	18.6834	0.607771
$946$	−21.2350	−0.690409
$947$	−57.0959	−1.85537	−0.927683	−	0.373368i	$-0.878203\pi$
$947$	−57.0959	−1.85537	−0.927683	+	0.373368i	$0.878203\pi$
$948$	13.6628	0.443747
$949$	−54.8047	−1.77903
$950$	3.16754	0.102769
$951$	−6.35801	−0.206173
$952$	−0.788107	−0.0255427
$953$	−12.3794	−0.401008	−0.200504	−	0.979693i	$-0.564258\pi$
$953$	−12.3794	−0.401008	−0.200504	+	0.979693i	$0.564258\pi$
$954$	7.45364	0.241321
$955$	14.6508	0.474090
$956$	−7.58600	−0.245349
$957$	2.84713	0.0920346
$958$	4.99765	0.161467
$959$	−64.9698	−2.09798
$960$	1.03782	0.0334954
$961$	−26.9366	−0.868922
$962$	4.62135	0.148998
$963$	29.9877	0.966341
$964$	26.0437	0.838811
$965$	−17.4298	−0.561086
$966$	20.5326	0.660627
$967$	57.8777	1.86122	0.930611	−	0.366009i	$-0.119276\pi$
$967$	57.8777	1.86122	0.930611	+	0.366009i	$0.119276\pi$
$968$	−0.403297	−0.0129625
$969$	0.708464	0.0227591
$970$	11.0319	0.354212
$971$	26.4547	0.848971	0.424485	−	0.905435i	$-0.360455\pi$
$971$	26.4547	0.848971	0.424485	+	0.905435i	$0.360455\pi$
$972$	15.8115	0.507153
$973$	−18.9184	−0.606497
$974$	−33.5250	−1.07421
$975$	3.88919	0.124554
$976$	10.9507	0.350523
$977$	−9.41195	−0.301115	−0.150557	−	0.988601i	$-0.548107\pi$
$977$	−9.41195	−0.301115	−0.150557	+	0.988601i	$0.548107\pi$
$978$	2.32958	0.0744917
$979$	−36.7345	−1.17404
$980$	6.37279	0.203571
$981$	−18.7454	−0.598495
$982$	8.90643	0.284216
$983$	−25.7156	−0.820199	−0.410100	−	0.912041i	$-0.634506\pi$
$983$	−25.7156	−0.820199	−0.410100	+	0.912041i	$0.634506\pi$
$984$	2.30975	0.0736322
$985$	5.43621	0.173212
$986$	0.175084	0.00557580
$987$	8.78096	0.279501
$988$	−11.8703	−0.377644
$989$	34.0212	1.08181
$990$	6.49352	0.206378
$991$	16.4151	0.521443	0.260722	−	0.965414i	$-0.416040\pi$
$991$	16.4151	0.521443	0.260722	+	0.965414i	$0.416040\pi$
$992$	−2.01579	−0.0640015
$993$	−0.259880	−0.00824703
$994$	14.9083	0.472863
$995$	24.7689	0.785227
$996$	11.7832	0.373365
$997$	−30.2357	−0.957574	−0.478787	−	0.877931i	$-0.658923\pi$
$997$	−30.2357	−0.957574	−0.478787	+	0.877931i	$0.658923\pi$
$998$	13.3307	0.421976
$999$	6.30051	0.199339

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6010.2.a.g.1.15	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6010.2.a.g.1.15	✓	27	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:	\( N \)	\(=\)	\( 6010 = 2 \cdot 5 \cdot 601 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6010.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.03782 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.03782 q^{6} -3.65688 q^{7} -1.00000 q^{8} -1.92294 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.03782 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.03782 q^{6} -3.65688 q^{7} -1.00000 q^{8} -1.92294 q^{9} -1.00000 q^{10} +3.37688 q^{11} +1.03782 q^{12} +3.74747 q^{13} +3.65688 q^{14} +1.03782 q^{15} +1.00000 q^{16} -0.215513 q^{17} +1.92294 q^{18} -3.16754 q^{19} +1.00000 q^{20} -3.79517 q^{21} -3.37688 q^{22} +5.41020 q^{23} -1.03782 q^{24} +1.00000 q^{25} -3.74747 q^{26} -5.10911 q^{27} -3.65688 q^{28} +0.812402 q^{29} -1.03782 q^{30} +2.01579 q^{31} -1.00000 q^{32} +3.50458 q^{33} +0.215513 q^{34} -3.65688 q^{35} -1.92294 q^{36} -1.23319 q^{37} +3.16754 q^{38} +3.88919 q^{39} -1.00000 q^{40} -2.22559 q^{41} +3.79517 q^{42} +6.28835 q^{43} +3.37688 q^{44} -1.92294 q^{45} -5.41020 q^{46} -2.31372 q^{47} +1.03782 q^{48} +6.37279 q^{49} -1.00000 q^{50} -0.223663 q^{51} +3.74747 q^{52} +3.87618 q^{53} +5.10911 q^{54} +3.37688 q^{55} +3.65688 q^{56} -3.28733 q^{57} -0.812402 q^{58} -13.5212 q^{59} +1.03782 q^{60} +10.9507 q^{61} -2.01579 q^{62} +7.03195 q^{63} +1.00000 q^{64} +3.74747 q^{65} -3.50458 q^{66} +0.202415 q^{67} -0.215513 q^{68} +5.61479 q^{69} +3.65688 q^{70} +4.07678 q^{71} +1.92294 q^{72} -14.6244 q^{73} +1.23319 q^{74} +1.03782 q^{75} -3.16754 q^{76} -12.3488 q^{77} -3.88919 q^{78} +13.1650 q^{79} +1.00000 q^{80} +0.466492 q^{81} +2.22559 q^{82} +11.3538 q^{83} -3.79517 q^{84} -0.215513 q^{85} -6.28835 q^{86} +0.843125 q^{87} -3.37688 q^{88} -10.8782 q^{89} +1.92294 q^{90} -13.7041 q^{91} +5.41020 q^{92} +2.09202 q^{93} +2.31372 q^{94} -3.16754 q^{95} -1.03782 q^{96} -11.0319 q^{97} -6.37279 q^{98} -6.49352 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q - 27 q^{2} + 6 q^{3} + 27 q^{4} + 27 q^{5} - 6 q^{6} - 27 q^{8} + 37 q^{9}+O(q^{10}) \) 27 * q - 27 * q^2 + 6 * q^3 + 27 * q^4 + 27 * q^5 - 6 * q^6 - 27 * q^8 + 37 * q^9	\( 27 q - 27 q^{2} + 6 q^{3} + 27 q^{4} + 27 q^{5} - 6 q^{6} - 27 q^{8} + 37 q^{9} - 27 q^{10} + 18 q^{11} + 6 q^{12} - 6 q^{13} + 6 q^{15} + 27 q^{16} + 3 q^{17} - 37 q^{18} + 27 q^{19} + 27 q^{20} + 16 q^{21} - 18 q^{22} + 15 q^{23} - 6 q^{24} + 27 q^{25} + 6 q^{26} + 27 q^{27} + 25 q^{29} - 6 q^{30} + 9 q^{31} - 27 q^{32} + 11 q^{33} - 3 q^{34} + 37 q^{36} - 16 q^{37} - 27 q^{38} + 20 q^{39} - 27 q^{40} + 39 q^{41} - 16 q^{42} + 9 q^{43} + 18 q^{44} + 37 q^{45} - 15 q^{46} + 31 q^{47} + 6 q^{48} + 27 q^{49} - 27 q^{50} + 39 q^{51} - 6 q^{52} - 5 q^{53} - 27 q^{54} + 18 q^{55} - 10 q^{57} - 25 q^{58} + 46 q^{59} + 6 q^{60} + 18 q^{61} - 9 q^{62} + 23 q^{63} + 27 q^{64} - 6 q^{65} - 11 q^{66} + 11 q^{67} + 3 q^{68} + 17 q^{69} + 50 q^{71} - 37 q^{72} - 29 q^{73} + 16 q^{74} + 6 q^{75} + 27 q^{76} - 6 q^{77} - 20 q^{78} + 56 q^{79} + 27 q^{80} + 51 q^{81} - 39 q^{82} + 44 q^{83} + 16 q^{84} + 3 q^{85} - 9 q^{86} + 42 q^{87} - 18 q^{88} + 34 q^{89} - 37 q^{90} + 43 q^{91} + 15 q^{92} - 20 q^{93} - 31 q^{94} + 27 q^{95} - 6 q^{96} - 37 q^{97} - 27 q^{98} + 67 q^{99}+O(q^{100}) \) 27 * q - 27 * q^2 + 6 * q^3 + 27 * q^4 + 27 * q^5 - 6 * q^6 - 27 * q^8 + 37 * q^9 - 27 * q^10 + 18 * q^11 + 6 * q^12 - 6 * q^13 + 6 * q^15 + 27 * q^16 + 3 * q^17 - 37 * q^18 + 27 * q^19 + 27 * q^20 + 16 * q^21 - 18 * q^22 + 15 * q^23 - 6 * q^24 + 27 * q^25 + 6 * q^26 + 27 * q^27 + 25 * q^29 - 6 * q^30 + 9 * q^31 - 27 * q^32 + 11 * q^33 - 3 * q^34 + 37 * q^36 - 16 * q^37 - 27 * q^38 + 20 * q^39 - 27 * q^40 + 39 * q^41 - 16 * q^42 + 9 * q^43 + 18 * q^44 + 37 * q^45 - 15 * q^46 + 31 * q^47 + 6 * q^48 + 27 * q^49 - 27 * q^50 + 39 * q^51 - 6 * q^52 - 5 * q^53 - 27 * q^54 + 18 * q^55 - 10 * q^57 - 25 * q^58 + 46 * q^59 + 6 * q^60 + 18 * q^61 - 9 * q^62 + 23 * q^63 + 27 * q^64 - 6 * q^65 - 11 * q^66 + 11 * q^67 + 3 * q^68 + 17 * q^69 + 50 * q^71 - 37 * q^72 - 29 * q^73 + 16 * q^74 + 6 * q^75 + 27 * q^76 - 6 * q^77 - 20 * q^78 + 56 * q^79 + 27 * q^80 + 51 * q^81 - 39 * q^82 + 44 * q^83 + 16 * q^84 + 3 * q^85 - 9 * q^86 + 42 * q^87 - 18 * q^88 + 34 * q^89 - 37 * q^90 + 43 * q^91 + 15 * q^92 - 20 * q^93 - 31 * q^94 + 27 * q^95 - 6 * q^96 - 37 * q^97 - 27 * q^98 + 67 * q^99

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