LMFDB - Embedded newform 6018.2.a.q.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("6018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$48.0539719364$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.5173625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 8x^{4} + 8x^{3} + 10x^{2} - 7x + 1 $ x^6 - x^5 - 8x^4 + 8x^3 + 10x^2 - 7x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$1.72409$ of defining polynomial
Character	$\chi$	$=$	6018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.724086 q^{5} -1.00000 q^{6} -0.160419 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.724086 q^{5} -1.00000 q^{6} -0.160419 q^{7} +1.00000 q^{8} +1.00000 q^{9} +0.724086 q^{10} +4.82765 q^{11} -1.00000 q^{12} -5.08721 q^{13} -0.160419 q^{14} -0.724086 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} +0.132892 q^{19} +0.724086 q^{20} +0.160419 q^{21} +4.82765 q^{22} -6.42468 q^{23} -1.00000 q^{24} -4.47570 q^{25} -5.08721 q^{26} -1.00000 q^{27} -0.160419 q^{28} -2.70370 q^{29} -0.724086 q^{30} -1.82907 q^{31} +1.00000 q^{32} -4.82765 q^{33} -1.00000 q^{34} -0.116157 q^{35} +1.00000 q^{36} +5.23531 q^{37} +0.132892 q^{38} +5.08721 q^{39} +0.724086 q^{40} -6.47973 q^{41} +0.160419 q^{42} -9.83882 q^{43} +4.82765 q^{44} +0.724086 q^{45} -6.42468 q^{46} -10.4908 q^{47} -1.00000 q^{48} -6.97427 q^{49} -4.47570 q^{50} +1.00000 q^{51} -5.08721 q^{52} +3.55964 q^{53} -1.00000 q^{54} +3.49563 q^{55} -0.160419 q^{56} -0.132892 q^{57} -2.70370 q^{58} +1.00000 q^{59} -0.724086 q^{60} +14.5199 q^{61} -1.82907 q^{62} -0.160419 q^{63} +1.00000 q^{64} -3.68358 q^{65} -4.82765 q^{66} -0.809137 q^{67} -1.00000 q^{68} +6.42468 q^{69} -0.116157 q^{70} -11.3019 q^{71} +1.00000 q^{72} -1.36030 q^{73} +5.23531 q^{74} +4.47570 q^{75} +0.132892 q^{76} -0.774446 q^{77} +5.08721 q^{78} +10.0286 q^{79} +0.724086 q^{80} +1.00000 q^{81} -6.47973 q^{82} +2.50692 q^{83} +0.160419 q^{84} -0.724086 q^{85} -9.83882 q^{86} +2.70370 q^{87} +4.82765 q^{88} +7.70320 q^{89} +0.724086 q^{90} +0.816085 q^{91} -6.42468 q^{92} +1.82907 q^{93} -10.4908 q^{94} +0.0962251 q^{95} -1.00000 q^{96} -1.86281 q^{97} -6.97427 q^{98} +4.82765 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} - 6 q^{3} + 6 q^{4} - 5 q^{5} - 6 q^{6} - q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 - 6 * q^3 + 6 * q^4 - 5 * q^5 - 6 * q^6 - q^7 + 6 * q^8 + 6 * q^9	$ 6 q + 6 q^{2} - 6 q^{3} + 6 q^{4} - 5 q^{5} - 6 q^{6} - q^{7} + 6 q^{8} + 6 q^{9} - 5 q^{10} - 6 q^{12} + 2 q^{13} - q^{14} + 5 q^{15} + 6 q^{16} - 6 q^{17} + 6 q^{18} - 5 q^{20} + q^{21} - 10 q^{23} - 6 q^{24} - 9 q^{25} + 2 q^{26} - 6 q^{27} - q^{28} - 3 q^{29} + 5 q^{30} - 7 q^{31} + 6 q^{32} - 6 q^{34} + 6 q^{35} + 6 q^{36} - 23 q^{37} - 2 q^{39} - 5 q^{40} - 12 q^{41} + q^{42} - 18 q^{43} - 5 q^{45} - 10 q^{46} - 14 q^{47} - 6 q^{48} + 9 q^{49} - 9 q^{50} + 6 q^{51} + 2 q^{52} + 21 q^{53} - 6 q^{54} + 4 q^{55} - q^{56} - 3 q^{58} + 6 q^{59} + 5 q^{60} - 2 q^{61} - 7 q^{62} - q^{63} + 6 q^{64} - 6 q^{65} + q^{67} - 6 q^{68} + 10 q^{69} + 6 q^{70} + 4 q^{71} + 6 q^{72} - 38 q^{73} - 23 q^{74} + 9 q^{75} - 22 q^{77} - 2 q^{78} - 30 q^{79} - 5 q^{80} + 6 q^{81} - 12 q^{82} + 23 q^{83} + q^{84} + 5 q^{85} - 18 q^{86} + 3 q^{87} - 7 q^{89} - 5 q^{90} - 5 q^{91} - 10 q^{92} + 7 q^{93} - 14 q^{94} - 7 q^{95} - 6 q^{96} - 10 q^{97} + 9 q^{98}+O(q^{100}) $ 6 * q + 6 * q^2 - 6 * q^3 + 6 * q^4 - 5 * q^5 - 6 * q^6 - q^7 + 6 * q^8 + 6 * q^9 - 5 * q^10 - 6 * q^12 + 2 * q^13 - q^14 + 5 * q^15 + 6 * q^16 - 6 * q^17 + 6 * q^18 - 5 * q^20 + q^21 - 10 * q^23 - 6 * q^24 - 9 * q^25 + 2 * q^26 - 6 * q^27 - q^28 - 3 * q^29 + 5 * q^30 - 7 * q^31 + 6 * q^32 - 6 * q^34 + 6 * q^35 + 6 * q^36 - 23 * q^37 - 2 * q^39 - 5 * q^40 - 12 * q^41 + q^42 - 18 * q^43 - 5 * q^45 - 10 * q^46 - 14 * q^47 - 6 * q^48 + 9 * q^49 - 9 * q^50 + 6 * q^51 + 2 * q^52 + 21 * q^53 - 6 * q^54 + 4 * q^55 - q^56 - 3 * q^58 + 6 * q^59 + 5 * q^60 - 2 * q^61 - 7 * q^62 - q^63 + 6 * q^64 - 6 * q^65 + q^67 - 6 * q^68 + 10 * q^69 + 6 * q^70 + 4 * q^71 + 6 * q^72 - 38 * q^73 - 23 * q^74 + 9 * q^75 - 22 * q^77 - 2 * q^78 - 30 * q^79 - 5 * q^80 + 6 * q^81 - 12 * q^82 + 23 * q^83 + q^84 + 5 * q^85 - 18 * q^86 + 3 * q^87 - 7 * q^89 - 5 * q^90 - 5 * q^91 - 10 * q^92 + 7 * q^93 - 14 * q^94 - 7 * q^95 - 6 * q^96 - 10 * q^97 + 9 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	0.724086	0.323821	0.161911	−	0.986805i	$-0.448234\pi$
$5$	0.724086	0.323821	0.161911	+	0.986805i	$0.448234\pi$
$6$	−1.00000	−0.408248
$7$	−0.160419	−0.0606327	−0.0303164	−	0.999540i	$-0.509651\pi$
$7$	−0.160419	−0.0606327	−0.0303164	+	0.999540i	$0.509651\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	0.724086	0.228976
$11$	4.82765	1.45559	0.727795	−	0.685795i	$-0.240545\pi$
$11$	4.82765	1.45559	0.727795	+	0.685795i	$0.240545\pi$
$12$	−1.00000	−0.288675
$13$	−5.08721	−1.41094	−0.705469	−	0.708741i	$-0.749264\pi$
$13$	−5.08721	−1.41094	−0.705469	+	0.708741i	$0.749264\pi$
$14$	−0.160419	−0.0428738
$15$	−0.724086	−0.186958
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.00000	0.235702
$19$	0.132892	0.0304875	0.0152437	−	0.999884i	$-0.495148\pi$
$19$	0.132892	0.0304875	0.0152437	+	0.999884i	$0.495148\pi$
$20$	0.724086	0.161911
$21$	0.160419	0.0350063
$22$	4.82765	1.02926
$23$	−6.42468	−1.33964	−0.669819	−	0.742525i	$-0.733628\pi$
$23$	−6.42468	−1.33964	−0.669819	+	0.742525i	$0.733628\pi$
$24$	−1.00000	−0.204124
$25$	−4.47570	−0.895140
$26$	−5.08721	−0.997684
$27$	−1.00000	−0.192450
$28$	−0.160419	−0.0303164
$29$	−2.70370	−0.502065	−0.251033	−	0.967979i	$-0.580770\pi$
$29$	−2.70370	−0.502065	−0.251033	+	0.967979i	$0.580770\pi$
$30$	−0.724086	−0.132199
$31$	−1.82907	−0.328510	−0.164255	−	0.986418i	$-0.552522\pi$
$31$	−1.82907	−0.328510	−0.164255	+	0.986418i	$0.552522\pi$
$32$	1.00000	0.176777
$33$	−4.82765	−0.840385
$34$	−1.00000	−0.171499
$35$	−0.116157	−0.0196342
$36$	1.00000	0.166667
$37$	5.23531	0.860680	0.430340	−	0.902667i	$-0.358394\pi$
$37$	5.23531	0.860680	0.430340	+	0.902667i	$0.358394\pi$
$38$	0.132892	0.0215579
$39$	5.08721	0.814606
$40$	0.724086	0.114488
$41$	−6.47973	−1.01196	−0.505982	−	0.862544i	$-0.668870\pi$
$41$	−6.47973	−1.01196	−0.505982	+	0.862544i	$0.668870\pi$
$42$	0.160419	0.0247532
$43$	−9.83882	−1.50041	−0.750203	−	0.661207i	$-0.770044\pi$
$43$	−9.83882	−1.50041	−0.750203	+	0.661207i	$0.770044\pi$
$44$	4.82765	0.727795
$45$	0.724086	0.107940
$46$	−6.42468	−0.947267
$47$	−10.4908	−1.53025	−0.765123	−	0.643884i	$-0.777322\pi$
$47$	−10.4908	−1.53025	−0.765123	+	0.643884i	$0.777322\pi$
$48$	−1.00000	−0.144338
$49$	−6.97427	−0.996324
$50$	−4.47570	−0.632959
$51$	1.00000	0.140028
$52$	−5.08721	−0.705469
$53$	3.55964	0.488954	0.244477	−	0.969655i	$-0.421384\pi$
$53$	3.55964	0.488954	0.244477	+	0.969655i	$0.421384\pi$
$54$	−1.00000	−0.136083
$55$	3.49563	0.471351
$56$	−0.160419	−0.0214369
$57$	−0.132892	−0.0176020
$58$	−2.70370	−0.355014
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	−0.724086	−0.0934791
$61$	14.5199	1.85908	0.929540	−	0.368720i	$-0.120204\pi$
$61$	14.5199	1.85908	0.929540	+	0.368720i	$0.120204\pi$
$62$	−1.82907	−0.232292
$63$	−0.160419	−0.0202109
$64$	1.00000	0.125000
$65$	−3.68358	−0.456892
$66$	−4.82765	−0.594242
$67$	−0.809137	−0.0988518	−0.0494259	−	0.998778i	$-0.515739\pi$
$67$	−0.809137	−0.0988518	−0.0494259	+	0.998778i	$0.515739\pi$
$68$	−1.00000	−0.121268
$69$	6.42468	0.773440
$70$	−0.116157	−0.0138834
$71$	−11.3019	−1.34129	−0.670646	−	0.741778i	$-0.733983\pi$
$71$	−11.3019	−1.34129	−0.670646	+	0.741778i	$0.733983\pi$
$72$	1.00000	0.117851
$73$	−1.36030	−0.159211	−0.0796055	−	0.996826i	$-0.525366\pi$
$73$	−1.36030	−0.159211	−0.0796055	+	0.996826i	$0.525366\pi$
$74$	5.23531	0.608592
$75$	4.47570	0.516809
$76$	0.132892	0.0152437
$77$	−0.774446	−0.0882564
$78$	5.08721	0.576013
$79$	10.0286	1.12830	0.564151	−	0.825672i	$-0.309204\pi$
$79$	10.0286	1.12830	0.564151	+	0.825672i	$0.309204\pi$
$80$	0.724086	0.0809553
$81$	1.00000	0.111111
$82$	−6.47973	−0.715567
$83$	2.50692	0.275170	0.137585	−	0.990490i	$-0.456066\pi$
$83$	2.50692	0.275170	0.137585	+	0.990490i	$0.456066\pi$
$84$	0.160419	0.0175032
$85$	−0.724086	−0.0785382
$86$	−9.83882	−1.06095
$87$	2.70370	0.289867
$88$	4.82765	0.514629
$89$	7.70320	0.816538	0.408269	−	0.912862i	$-0.366133\pi$
$89$	7.70320	0.816538	0.408269	+	0.912862i	$0.366133\pi$
$90$	0.724086	0.0763254
$91$	0.816085	0.0855490
$92$	−6.42468	−0.669819
$93$	1.82907	0.189665
$94$	−10.4908	−1.08205
$95$	0.0962251	0.00987249
$96$	−1.00000	−0.102062
$97$	−1.86281	−0.189140	−0.0945700	−	0.995518i	$-0.530148\pi$
$97$	−1.86281	−0.189140	−0.0945700	+	0.995518i	$0.530148\pi$
$98$	−6.97427	−0.704507
$99$	4.82765	0.485197
$100$	−4.47570	−0.447570
$101$	1.46236	0.145511	0.0727553	−	0.997350i	$-0.476821\pi$
$101$	1.46236	0.145511	0.0727553	+	0.997350i	$0.476821\pi$
$102$	1.00000	0.0990148
$103$	4.49374	0.442782	0.221391	−	0.975185i	$-0.428940\pi$
$103$	4.49374	0.442782	0.221391	+	0.975185i	$0.428940\pi$
$104$	−5.08721	−0.498842
$105$	0.116157	0.0113358
$106$	3.55964	0.345742
$107$	1.25261	0.121095	0.0605473	−	0.998165i	$-0.480715\pi$
$107$	1.25261	0.121095	0.0605473	+	0.998165i	$0.480715\pi$
$108$	−1.00000	−0.0962250
$109$	−5.43680	−0.520751	−0.260376	−	0.965507i	$-0.583846\pi$
$109$	−5.43680	−0.520751	−0.260376	+	0.965507i	$0.583846\pi$
$110$	3.49563	0.333295
$111$	−5.23531	−0.496914
$112$	−0.160419	−0.0151582
$113$	−14.0883	−1.32532	−0.662659	−	0.748921i	$-0.730572\pi$
$113$	−14.0883	−1.32532	−0.662659	+	0.748921i	$0.730572\pi$
$114$	−0.132892	−0.0124465
$115$	−4.65202	−0.433803
$116$	−2.70370	−0.251033
$117$	−5.08721	−0.470313
$118$	1.00000	0.0920575
$119$	0.160419	0.0147056
$120$	−0.724086	−0.0660997
$121$	12.3062	1.11874
$122$	14.5199	1.31457
$123$	6.47973	0.584258
$124$	−1.82907	−0.164255
$125$	−6.86122	−0.613686
$126$	−0.160419	−0.0142913
$127$	−19.5170	−1.73186	−0.865929	−	0.500167i	$-0.833272\pi$
$127$	−19.5170	−1.73186	−0.865929	+	0.500167i	$0.833272\pi$
$128$	1.00000	0.0883883
$129$	9.83882	0.866260
$130$	−3.68358	−0.323071
$131$	6.35748	0.555456	0.277728	−	0.960660i	$-0.410419\pi$
$131$	6.35748	0.555456	0.277728	+	0.960660i	$0.410419\pi$
$132$	−4.82765	−0.420193
$133$	−0.0213184	−0.00184854
$134$	−0.809137	−0.0698988
$135$	−0.724086	−0.0623194
$136$	−1.00000	−0.0857493
$137$	−19.7080	−1.68377	−0.841885	−	0.539657i	$-0.818554\pi$
$137$	−19.7080	−1.68377	−0.841885	+	0.539657i	$0.818554\pi$
$138$	6.42468	0.546905
$139$	1.22873	0.104220	0.0521099	−	0.998641i	$-0.483405\pi$
$139$	1.22873	0.104220	0.0521099	+	0.998641i	$0.483405\pi$
$140$	−0.116157	−0.00981708
$141$	10.4908	0.883488
$142$	−11.3019	−0.948437
$143$	−24.5593	−2.05375
$144$	1.00000	0.0833333
$145$	−1.95771	−0.162579
$146$	−1.36030	−0.112579
$147$	6.97427	0.575228
$148$	5.23531	0.430340
$149$	4.68593	0.383887	0.191943	−	0.981406i	$-0.438521\pi$
$149$	4.68593	0.383887	0.191943	+	0.981406i	$0.438521\pi$
$150$	4.47570	0.365439
$151$	3.92717	0.319589	0.159794	−	0.987150i	$-0.448917\pi$
$151$	3.92717	0.319589	0.159794	+	0.987150i	$0.448917\pi$
$152$	0.132892	0.0107789
$153$	−1.00000	−0.0808452
$154$	−0.774446	−0.0624067
$155$	−1.32440	−0.106378
$156$	5.08721	0.407303
$157$	2.43991	0.194726	0.0973632	−	0.995249i	$-0.468959\pi$
$157$	2.43991	0.194726	0.0973632	+	0.995249i	$0.468959\pi$
$158$	10.0286	0.797830
$159$	−3.55964	−0.282297
$160$	0.724086	0.0572440
$161$	1.03064	0.0812259
$162$	1.00000	0.0785674
$163$	5.60848	0.439290	0.219645	−	0.975580i	$-0.429510\pi$
$163$	5.60848	0.439290	0.219645	+	0.975580i	$0.429510\pi$
$164$	−6.47973	−0.505982
$165$	−3.49563	−0.272135
$166$	2.50692	0.194575
$167$	12.2187	0.945508	0.472754	−	0.881194i	$-0.343260\pi$
$167$	12.2187	0.945508	0.472754	+	0.881194i	$0.343260\pi$
$168$	0.160419	0.0123766
$169$	12.8797	0.990746
$170$	−0.724086	−0.0555349
$171$	0.132892	0.0101625
$172$	−9.83882	−0.750203
$173$	14.0403	1.06746	0.533732	−	0.845654i	$-0.320789\pi$
$173$	14.0403	1.06746	0.533732	+	0.845654i	$0.320789\pi$
$174$	2.70370	0.204967
$175$	0.717987	0.0542748
$176$	4.82765	0.363898
$177$	−1.00000	−0.0751646
$178$	7.70320	0.577379
$179$	−5.78153	−0.432132	−0.216066	−	0.976379i	$-0.569323\pi$
$179$	−5.78153	−0.432132	−0.216066	+	0.976379i	$0.569323\pi$
$180$	0.724086	0.0539702
$181$	−24.5169	−1.82232	−0.911162	−	0.412048i	$-0.864813\pi$
$181$	−24.5169	−1.82232	−0.911162	+	0.412048i	$0.864813\pi$
$182$	0.816085	0.0604923
$183$	−14.5199	−1.07334
$184$	−6.42468	−0.473633
$185$	3.79082	0.278706
$186$	1.82907	0.134114
$187$	−4.82765	−0.353032
$188$	−10.4908	−0.765123
$189$	0.160419	0.0116688
$190$	0.0962251	0.00698090
$191$	−21.7785	−1.57584	−0.787919	−	0.615779i	$-0.788841\pi$
$191$	−21.7785	−1.57584	−0.787919	+	0.615779i	$0.788841\pi$
$192$	−1.00000	−0.0721688
$193$	16.8243	1.21104	0.605519	−	0.795831i	$-0.292966\pi$
$193$	16.8243	1.21104	0.605519	+	0.795831i	$0.292966\pi$
$194$	−1.86281	−0.133742
$195$	3.68358	0.263786
$196$	−6.97427	−0.498162
$197$	−15.4289	−1.09926	−0.549630	−	0.835408i	$-0.685231\pi$
$197$	−15.4289	−1.09926	−0.549630	+	0.835408i	$0.685231\pi$
$198$	4.82765	0.343086
$199$	10.4900	0.743615	0.371808	−	0.928310i	$-0.378738\pi$
$199$	10.4900	0.743615	0.371808	+	0.928310i	$0.378738\pi$
$200$	−4.47570	−0.316480
$201$	0.809137	0.0570721
$202$	1.46236	0.102892
$203$	0.433726	0.0304416
$204$	1.00000	0.0700140
$205$	−4.69188	−0.327695
$206$	4.49374	0.313094
$207$	−6.42468	−0.446546
$208$	−5.08721	−0.352735
$209$	0.641555	0.0443773
$210$	0.116157	0.00801561
$211$	−10.1715	−0.700236	−0.350118	−	0.936706i	$-0.613858\pi$
$211$	−10.1715	−0.700236	−0.350118	+	0.936706i	$0.613858\pi$
$212$	3.55964	0.244477
$213$	11.3019	0.774395
$214$	1.25261	0.0856268
$215$	−7.12415	−0.485863
$216$	−1.00000	−0.0680414
$217$	0.293417	0.0199185
$218$	−5.43680	−0.368227
$219$	1.36030	0.0919205
$220$	3.49563	0.235675
$221$	5.08721	0.342203
$222$	−5.23531	−0.351371
$223$	14.6397	0.980348	0.490174	−	0.871625i	$-0.336933\pi$
$223$	14.6397	0.980348	0.490174	+	0.871625i	$0.336933\pi$
$224$	−0.160419	−0.0107184
$225$	−4.47570	−0.298380
$226$	−14.0883	−0.937141
$227$	−0.350448	−0.0232600	−0.0116300	−	0.999932i	$-0.503702\pi$
$227$	−0.350448	−0.0232600	−0.0116300	+	0.999932i	$0.503702\pi$
$228$	−0.132892	−0.00880098
$229$	22.4296	1.48219	0.741095	−	0.671400i	$-0.234307\pi$
$229$	22.4296	1.48219	0.741095	+	0.671400i	$0.234307\pi$
$230$	−4.65202	−0.306745
$231$	0.774446	0.0509548
$232$	−2.70370	−0.177507
$233$	−14.6131	−0.957335	−0.478668	−	0.877996i	$-0.658880\pi$
$233$	−14.6131	−0.957335	−0.478668	+	0.877996i	$0.658880\pi$
$234$	−5.08721	−0.332561
$235$	−7.59627	−0.495526
$236$	1.00000	0.0650945
$237$	−10.0286	−0.651425
$238$	0.160419	0.0103984
$239$	7.04964	0.456003	0.228002	−	0.973661i	$-0.426781\pi$
$239$	7.04964	0.456003	0.228002	+	0.973661i	$0.426781\pi$
$240$	−0.724086	−0.0467396
$241$	−20.9919	−1.35221	−0.676104	−	0.736806i	$-0.736333\pi$
$241$	−20.9919	−1.35221	−0.676104	+	0.736806i	$0.736333\pi$
$242$	12.3062	0.791071
$243$	−1.00000	−0.0641500
$244$	14.5199	0.929540
$245$	−5.04997	−0.322631
$246$	6.47973	0.413133
$247$	−0.676049	−0.0430159
$248$	−1.82907	−0.116146
$249$	−2.50692	−0.158870
$250$	−6.86122	−0.433942
$251$	31.4984	1.98816	0.994082	−	0.108633i	$-0.0346473\pi$
$251$	31.4984	1.98816	0.994082	+	0.108633i	$0.0346473\pi$
$252$	−0.160419	−0.0101055
$253$	−31.0161	−1.94996
$254$	−19.5170	−1.22461
$255$	0.724086	0.0453440
$256$	1.00000	0.0625000
$257$	2.47851	0.154605	0.0773027	−	0.997008i	$-0.475369\pi$
$257$	2.47851	0.154605	0.0773027	+	0.997008i	$0.475369\pi$
$258$	9.83882	0.612538
$259$	−0.839844	−0.0521853
$260$	−3.68358	−0.228446
$261$	−2.70370	−0.167355
$262$	6.35748	0.392767
$263$	−22.3403	−1.37756	−0.688781	−	0.724969i	$-0.741854\pi$
$263$	−22.3403	−1.37756	−0.688781	+	0.724969i	$0.741854\pi$
$264$	−4.82765	−0.297121
$265$	2.57748	0.158333
$266$	−0.0213184	−0.00130711
$267$	−7.70320	−0.471428
$268$	−0.809137	−0.0494259
$269$	−2.37907	−0.145055	−0.0725273	−	0.997366i	$-0.523106\pi$
$269$	−2.37907	−0.145055	−0.0725273	+	0.997366i	$0.523106\pi$
$270$	−0.724086	−0.0440665
$271$	−28.5587	−1.73482	−0.867408	−	0.497597i	$-0.834216\pi$
$271$	−28.5587	−1.73482	−0.867408	+	0.497597i	$0.834216\pi$
$272$	−1.00000	−0.0606339
$273$	−0.816085	−0.0493917
$274$	−19.7080	−1.19061
$275$	−21.6071	−1.30296
$276$	6.42468	0.386720
$277$	−15.9823	−0.960283	−0.480142	−	0.877191i	$-0.659415\pi$
$277$	−15.9823	−0.960283	−0.480142	+	0.877191i	$0.659415\pi$
$278$	1.22873	0.0736945
$279$	−1.82907	−0.109503
$280$	−0.116157	−0.00694172
$281$	−1.02714	−0.0612742	−0.0306371	−	0.999531i	$-0.509754\pi$
$281$	−1.02714	−0.0612742	−0.0306371	+	0.999531i	$0.509754\pi$
$282$	10.4908	0.624721
$283$	10.0453	0.597130	0.298565	−	0.954389i	$-0.403492\pi$
$283$	10.0453	0.597130	0.298565	+	0.954389i	$0.403492\pi$
$284$	−11.3019	−0.670646
$285$	−0.0962251	−0.00569988
$286$	−24.5593	−1.45222
$287$	1.03947	0.0613581
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	−1.95771	−0.114961
$291$	1.86281	0.109200
$292$	−1.36030	−0.0796055
$293$	33.5729	1.96135	0.980675	−	0.195646i	$-0.0626804\pi$
$293$	33.5729	1.96135	0.980675	+	0.195646i	$0.0626804\pi$
$294$	6.97427	0.406747
$295$	0.724086	0.0421579
$296$	5.23531	0.304296
$297$	−4.82765	−0.280128
$298$	4.68593	0.271449
$299$	32.6837	1.89015
$300$	4.47570	0.258405
$301$	1.57833	0.0909737
$302$	3.92717	0.225984
$303$	−1.46236	−0.0840106
$304$	0.132892	0.00762187
$305$	10.5136	0.602010
$306$	−1.00000	−0.0571662
$307$	−26.1118	−1.49028	−0.745140	−	0.666909i	$-0.767617\pi$
$307$	−26.1118	−1.49028	−0.745140	+	0.666909i	$0.767617\pi$
$308$	−0.774446	−0.0441282
$309$	−4.49374	−0.255640
$310$	−1.32440	−0.0752210
$311$	−17.4325	−0.988509	−0.494254	−	0.869317i	$-0.664559\pi$
$311$	−17.4325	−0.988509	−0.494254	+	0.869317i	$0.664559\pi$
$312$	5.08721	0.288007
$313$	17.9350	1.01374	0.506872	−	0.862021i	$-0.330802\pi$
$313$	17.9350	1.01374	0.506872	+	0.862021i	$0.330802\pi$
$314$	2.43991	0.137692
$315$	−0.116157	−0.00654472
$316$	10.0286	0.564151
$317$	−19.9883	−1.12266	−0.561328	−	0.827593i	$-0.689710\pi$
$317$	−19.9883	−1.12266	−0.561328	+	0.827593i	$0.689710\pi$
$318$	−3.55964	−0.199614
$319$	−13.0525	−0.730801
$320$	0.724086	0.0404776
$321$	−1.25261	−0.0699140
$322$	1.03064	0.0574354
$323$	−0.132892	−0.00739430
$324$	1.00000	0.0555556
$325$	22.7688	1.26299
$326$	5.60848	0.310625
$327$	5.43680	0.300656
$328$	−6.47973	−0.357783
$329$	1.68293	0.0927830
$330$	−3.49563	−0.192428
$331$	−0.494779	−0.0271955	−0.0135978	−	0.999908i	$-0.504328\pi$
$331$	−0.494779	−0.0271955	−0.0135978	+	0.999908i	$0.504328\pi$
$332$	2.50692	0.137585
$333$	5.23531	0.286893
$334$	12.2187	0.668575
$335$	−0.585885	−0.0320103
$336$	0.160419	0.00875158
$337$	−29.1507	−1.58794	−0.793969	−	0.607959i	$-0.791989\pi$
$337$	−29.1507	−1.58794	−0.793969	+	0.607959i	$0.791989\pi$
$338$	12.8797	0.700564
$339$	14.0883	0.765173
$340$	−0.724086	−0.0392691
$341$	−8.83009	−0.478176
$342$	0.132892	0.00718597
$343$	2.24174	0.121043
$344$	−9.83882	−0.530474
$345$	4.65202	0.250456
$346$	14.0403	0.754811
$347$	7.66357	0.411402	0.205701	−	0.978615i	$-0.434053\pi$
$347$	7.66357	0.411402	0.205701	+	0.978615i	$0.434053\pi$
$348$	2.70370	0.144934
$349$	0.863673	0.0462313	0.0231157	−	0.999733i	$-0.492641\pi$
$349$	0.863673	0.0462313	0.0231157	+	0.999733i	$0.492641\pi$
$350$	0.717987	0.0383780
$351$	5.08721	0.271535
$352$	4.82765	0.257314
$353$	12.4621	0.663289	0.331644	−	0.943405i	$-0.392397\pi$
$353$	12.4621	0.663289	0.331644	+	0.943405i	$0.392397\pi$
$354$	−1.00000	−0.0531494
$355$	−8.18357	−0.434339
$356$	7.70320	0.408269
$357$	−0.160419	−0.00849028
$358$	−5.78153	−0.305563
$359$	26.9482	1.42227	0.711137	−	0.703054i	$-0.248181\pi$
$359$	26.9482	1.42227	0.711137	+	0.703054i	$0.248181\pi$
$360$	0.724086	0.0381627
$361$	−18.9823	−0.999071
$362$	−24.5169	−1.28858
$363$	−12.3062	−0.645906
$364$	0.816085	0.0427745
$365$	−0.984974	−0.0515559
$366$	−14.5199	−0.758966
$367$	−4.79310	−0.250198	−0.125099	−	0.992144i	$-0.539925\pi$
$367$	−4.79310	−0.250198	−0.125099	+	0.992144i	$0.539925\pi$
$368$	−6.42468	−0.334909
$369$	−6.47973	−0.337321
$370$	3.79082	0.197075
$371$	−0.571033	−0.0296466
$372$	1.82907	0.0948327
$373$	−7.02669	−0.363828	−0.181914	−	0.983314i	$-0.558229\pi$
$373$	−7.02669	−0.363828	−0.181914	+	0.983314i	$0.558229\pi$
$374$	−4.82765	−0.249632
$375$	6.86122	0.354312
$376$	−10.4908	−0.541024
$377$	13.7543	0.708383
$378$	0.160419	0.00825107
$379$	−20.2760	−1.04151	−0.520755	−	0.853706i	$-0.674350\pi$
$379$	−20.2760	−1.04151	−0.520755	+	0.853706i	$0.674350\pi$
$380$	0.0962251	0.00493624
$381$	19.5170	0.999889
$382$	−21.7785	−1.11429
$383$	29.9280	1.52925	0.764625	−	0.644476i	$-0.222924\pi$
$383$	29.9280	1.52925	0.764625	+	0.644476i	$0.222924\pi$
$384$	−1.00000	−0.0510310
$385$	−0.560766	−0.0285793
$386$	16.8243	0.856333
$387$	−9.83882	−0.500135
$388$	−1.86281	−0.0945700
$389$	−16.8429	−0.853967	−0.426983	−	0.904260i	$-0.640424\pi$
$389$	−16.8429	−0.853967	−0.426983	+	0.904260i	$0.640424\pi$
$390$	3.68358	0.186525
$391$	6.42468	0.324910
$392$	−6.97427	−0.352254
$393$	−6.35748	−0.320693
$394$	−15.4289	−0.777294
$395$	7.26154	0.365368
$396$	4.82765	0.242598
$397$	−28.3715	−1.42392	−0.711962	−	0.702218i	$-0.752193\pi$
$397$	−28.3715	−1.42392	−0.711962	+	0.702218i	$0.752193\pi$
$398$	10.4900	0.525815
$399$	0.0213184	0.00106725
$400$	−4.47570	−0.223785
$401$	4.72404	0.235907	0.117954	−	0.993019i	$-0.462367\pi$
$401$	4.72404	0.235907	0.117954	+	0.993019i	$0.462367\pi$
$402$	0.809137	0.0403561
$403$	9.30485	0.463507
$404$	1.46236	0.0727553
$405$	0.724086	0.0359801
$406$	0.433726	0.0215254
$407$	25.2742	1.25280
$408$	1.00000	0.0495074
$409$	−22.2550	−1.10044	−0.550219	−	0.835020i	$-0.685456\pi$
$409$	−22.2550	−1.10044	−0.550219	+	0.835020i	$0.685456\pi$
$410$	−4.69188	−0.231716
$411$	19.7080	0.972125
$412$	4.49374	0.221391
$413$	−0.160419	−0.00789371
$414$	−6.42468	−0.315756
$415$	1.81523	0.0891059
$416$	−5.08721	−0.249421
$417$	−1.22873	−0.0601713
$418$	0.641555	0.0313795
$419$	7.94052	0.387920	0.193960	−	0.981009i	$-0.437867\pi$
$419$	7.94052	0.387920	0.193960	+	0.981009i	$0.437867\pi$
$420$	0.116157	0.00566789
$421$	−12.8526	−0.626396	−0.313198	−	0.949688i	$-0.601400\pi$
$421$	−12.8526	−0.626396	−0.313198	+	0.949688i	$0.601400\pi$
$422$	−10.1715	−0.495141
$423$	−10.4908	−0.510082
$424$	3.55964	0.172871
$425$	4.47570	0.217103
$426$	11.3019	0.547580
$427$	−2.32927	−0.112721
$428$	1.25261	0.0605473
$429$	24.5593	1.18573
$430$	−7.12415	−0.343557
$431$	12.8090	0.616985	0.308493	−	0.951227i	$-0.400175\pi$
$431$	12.8090	0.616985	0.308493	+	0.951227i	$0.400175\pi$
$432$	−1.00000	−0.0481125
$433$	−27.5091	−1.32200	−0.661001	−	0.750385i	$-0.729868\pi$
$433$	−27.5091	−1.32200	−0.661001	+	0.750385i	$0.729868\pi$
$434$	0.293417	0.0140845
$435$	1.95771	0.0938652
$436$	−5.43680	−0.260376
$437$	−0.853787	−0.0408422
$438$	1.36030	0.0649976
$439$	36.2855	1.73181	0.865907	−	0.500206i	$-0.166742\pi$
$439$	36.2855	1.73181	0.865907	+	0.500206i	$0.166742\pi$
$440$	3.49563	0.166648
$441$	−6.97427	−0.332108
$442$	5.08721	0.241974
$443$	−3.64689	−0.173269	−0.0866345	−	0.996240i	$-0.527611\pi$
$443$	−3.64689	−0.173269	−0.0866345	+	0.996240i	$0.527611\pi$
$444$	−5.23531	−0.248457
$445$	5.57778	0.264412
$446$	14.6397	0.693210
$447$	−4.68593	−0.221637
$448$	−0.160419	−0.00757909
$449$	−18.9265	−0.893197	−0.446598	−	0.894735i	$-0.647365\pi$
$449$	−18.9265	−0.893197	−0.446598	+	0.894735i	$0.647365\pi$
$450$	−4.47570	−0.210986
$451$	−31.2819	−1.47300
$452$	−14.0883	−0.662659
$453$	−3.92717	−0.184515
$454$	−0.350448	−0.0164473
$455$	0.590916	0.0277026
$456$	−0.132892	−0.00622323
$457$	2.62956	0.123006	0.0615029	−	0.998107i	$-0.480411\pi$
$457$	2.62956	0.123006	0.0615029	+	0.998107i	$0.480411\pi$
$458$	22.4296	1.04807
$459$	1.00000	0.0466760
$460$	−4.65202	−0.216901
$461$	−5.27867	−0.245852	−0.122926	−	0.992416i	$-0.539228\pi$
$461$	−5.27867	−0.245852	−0.122926	+	0.992416i	$0.539228\pi$
$462$	0.774446	0.0360305
$463$	8.41650	0.391148	0.195574	−	0.980689i	$-0.437343\pi$
$463$	8.41650	0.391148	0.195574	+	0.980689i	$0.437343\pi$
$464$	−2.70370	−0.125516
$465$	1.32440	0.0614177
$466$	−14.6131	−0.676938
$467$	10.4623	0.484136	0.242068	−	0.970259i	$-0.422174\pi$
$467$	10.4623	0.484136	0.242068	+	0.970259i	$0.422174\pi$
$468$	−5.08721	−0.235156
$469$	0.129801	0.00599365
$470$	−7.59627	−0.350390
$471$	−2.43991	−0.112425
$472$	1.00000	0.0460287
$473$	−47.4984	−2.18398
$474$	−10.0286	−0.460627
$475$	−0.594784	−0.0272906
$476$	0.160419	0.00735280
$477$	3.55964	0.162985
$478$	7.04964	0.322443
$479$	−13.7977	−0.630431	−0.315216	−	0.949020i	$-0.602077\pi$
$479$	−13.7977	−0.630431	−0.315216	+	0.949020i	$0.602077\pi$
$480$	−0.724086	−0.0330499
$481$	−26.6331	−1.21437
$482$	−20.9919	−0.956156
$483$	−1.03064	−0.0468958
$484$	12.3062	0.559371
$485$	−1.34884	−0.0612476
$486$	−1.00000	−0.0453609
$487$	7.22225	0.327272	0.163636	−	0.986521i	$-0.447678\pi$
$487$	7.22225	0.327272	0.163636	+	0.986521i	$0.447678\pi$
$488$	14.5199	0.657284
$489$	−5.60848	−0.253624
$490$	−5.04997	−0.228134
$491$	40.0807	1.80882	0.904409	−	0.426667i	$-0.140312\pi$
$491$	40.0807	1.80882	0.904409	+	0.426667i	$0.140312\pi$
$492$	6.47973	0.292129
$493$	2.70370	0.121769
$494$	−0.676049	−0.0304169
$495$	3.49563	0.157117
$496$	−1.82907	−0.0821275
$497$	1.81304	0.0813262
$498$	−2.50692	−0.112338
$499$	−3.59868	−0.161099	−0.0805494	−	0.996751i	$-0.525667\pi$
$499$	−3.59868	−0.161099	−0.0805494	+	0.996751i	$0.525667\pi$
$500$	−6.86122	−0.306843
$501$	−12.2187	−0.545889
$502$	31.4984	1.40584
$503$	−18.6726	−0.832571	−0.416286	−	0.909234i	$-0.636668\pi$
$503$	−18.6726	−0.832571	−0.416286	+	0.909234i	$0.636668\pi$
$504$	−0.160419	−0.00714563
$505$	1.05888	0.0471194
$506$	−31.0161	−1.37883
$507$	−12.8797	−0.572008
$508$	−19.5170	−0.865929
$509$	−7.19060	−0.318718	−0.159359	−	0.987221i	$-0.550943\pi$
$509$	−7.19060	−0.318718	−0.159359	+	0.987221i	$0.550943\pi$
$510$	0.724086	0.0320631
$511$	0.218218	0.00965340
$512$	1.00000	0.0441942
$513$	−0.132892	−0.00586732
$514$	2.47851	0.109323
$515$	3.25386	0.143382
$516$	9.83882	0.433130
$517$	−50.6461	−2.22741
$518$	−0.839844	−0.0369006
$519$	−14.0403	−0.616301
$520$	−3.68358	−0.161536
$521$	0.900853	0.0394671	0.0197335	−	0.999805i	$-0.493718\pi$
$521$	0.900853	0.0394671	0.0197335	+	0.999805i	$0.493718\pi$
$522$	−2.70370	−0.118338
$523$	6.81692	0.298083	0.149042	−	0.988831i	$-0.452381\pi$
$523$	6.81692	0.298083	0.149042	+	0.988831i	$0.452381\pi$
$524$	6.35748	0.277728
$525$	−0.717987	−0.0313355
$526$	−22.3403	−0.974083
$527$	1.82907	0.0796754
$528$	−4.82765	−0.210096
$529$	18.2765	0.794629
$530$	2.57748	0.111959
$531$	1.00000	0.0433963
$532$	−0.0213184	−0.000924269 0
$533$	32.9638	1.42782
$534$	−7.70320	−0.333350
$535$	0.906999	0.0392130
$536$	−0.809137	−0.0349494
$537$	5.78153	0.249491
$538$	−2.37907	−0.102569
$539$	−33.6693	−1.45024
$540$	−0.724086	−0.0311597
$541$	25.6318	1.10200	0.550999	−	0.834506i	$-0.314247\pi$
$541$	25.6318	1.10200	0.550999	+	0.834506i	$0.314247\pi$
$542$	−28.5587	−1.22670
$543$	24.5169	1.05212
$544$	−1.00000	−0.0428746
$545$	−3.93671	−0.168630
$546$	−0.816085	−0.0349252
$547$	0.750215	0.0320769	0.0160384	−	0.999871i	$-0.494895\pi$
$547$	0.750215	0.0320769	0.0160384	+	0.999871i	$0.494895\pi$
$548$	−19.7080	−0.841885
$549$	14.5199	0.619694
$550$	−21.6071	−0.921330
$551$	−0.359300	−0.0153067
$552$	6.42468	0.273452
$553$	−1.60877	−0.0684120
$554$	−15.9823	−0.679023
$555$	−3.79082	−0.160911
$556$	1.22873	0.0521099
$557$	4.50132	0.190727	0.0953635	−	0.995443i	$-0.469599\pi$
$557$	4.50132	0.190727	0.0953635	+	0.995443i	$0.469599\pi$
$558$	−1.82907	−0.0774306
$559$	50.0522	2.11698
$560$	−0.116157	−0.00490854
$561$	4.82765	0.203823
$562$	−1.02714	−0.0433274
$563$	0.734054	0.0309367	0.0154684	−	0.999880i	$-0.495076\pi$
$563$	0.734054	0.0309367	0.0154684	+	0.999880i	$0.495076\pi$
$564$	10.4908	0.441744
$565$	−10.2012	−0.429166
$566$	10.0453	0.422235
$567$	−0.160419	−0.00673697
$568$	−11.3019	−0.474218
$569$	43.9151	1.84102	0.920509	−	0.390721i	$-0.127774\pi$
$569$	43.9151	1.84102	0.920509	+	0.390721i	$0.127774\pi$
$570$	−0.0962251	−0.00403043
$571$	1.12565	0.0471071	0.0235535	−	0.999723i	$-0.492502\pi$
$571$	1.12565	0.0471071	0.0235535	+	0.999723i	$0.492502\pi$
$572$	−24.5593	−1.02687
$573$	21.7785	0.909810
$574$	1.03947	0.0433867
$575$	28.7549	1.19916
$576$	1.00000	0.0416667
$577$	−38.8145	−1.61587	−0.807934	−	0.589273i	$-0.799414\pi$
$577$	−38.8145	−1.61587	−0.807934	+	0.589273i	$0.799414\pi$
$578$	1.00000	0.0415945
$579$	−16.8243	−0.699193
$580$	−1.95771	−0.0812897
$581$	−0.402158	−0.0166843
$582$	1.86281	0.0772161
$583$	17.1847	0.711716
$584$	−1.36030	−0.0562896
$585$	−3.68358	−0.152297
$586$	33.5729	1.38688
$587$	6.67218	0.275390	0.137695	−	0.990475i	$-0.456031\pi$
$587$	6.67218	0.275390	0.137695	+	0.990475i	$0.456031\pi$
$588$	6.97427	0.287614
$589$	−0.243068	−0.0100154
$590$	0.724086	0.0298102
$591$	15.4289	0.634658
$592$	5.23531	0.215170
$593$	18.0547	0.741418	0.370709	−	0.928749i	$-0.379115\pi$
$593$	18.0547	0.741418	0.370709	+	0.928749i	$0.379115\pi$
$594$	−4.82765	−0.198081
$595$	0.116157	0.00476198
$596$	4.68593	0.191943
$597$	−10.4900	−0.429327
$598$	32.6837	1.33653
$599$	18.1466	0.741450	0.370725	−	0.928743i	$-0.379109\pi$
$599$	18.1466	0.741450	0.370725	+	0.928743i	$0.379109\pi$
$600$	4.47570	0.182720
$601$	4.37754	0.178563	0.0892817	−	0.996006i	$-0.471543\pi$
$601$	4.37754	0.178563	0.0892817	+	0.996006i	$0.471543\pi$
$602$	1.57833	0.0643281
$603$	−0.809137	−0.0329506
$604$	3.92717	0.159794
$605$	8.91073	0.362273
$606$	−1.46236	−0.0594045
$607$	33.2895	1.35118	0.675590	−	0.737277i	$-0.263889\pi$
$607$	33.2895	1.35118	0.675590	+	0.737277i	$0.263889\pi$
$608$	0.132892	0.00538947
$609$	−0.433726	−0.0175754
$610$	10.5136	0.425685
$611$	53.3691	2.15908
$612$	−1.00000	−0.0404226
$613$	36.6330	1.47959	0.739796	−	0.672832i	$-0.234922\pi$
$613$	36.6330	1.47959	0.739796	+	0.672832i	$0.234922\pi$
$614$	−26.1118	−1.05379
$615$	4.69188	0.189195
$616$	−0.774446	−0.0312033
$617$	24.1468	0.972113	0.486056	−	0.873927i	$-0.338435\pi$
$617$	24.1468	0.972113	0.486056	+	0.873927i	$0.338435\pi$
$618$	−4.49374	−0.180765
$619$	5.56033	0.223489	0.111744	−	0.993737i	$-0.464356\pi$
$619$	5.56033	0.223489	0.111744	+	0.993737i	$0.464356\pi$
$620$	−1.32440	−0.0531892
$621$	6.42468	0.257813
$622$	−17.4325	−0.698981
$623$	−1.23574	−0.0495089
$624$	5.08721	0.203651
$625$	17.4104	0.696415
$626$	17.9350	0.716826
$627$	−0.641555	−0.0256212
$628$	2.43991	0.0973632
$629$	−5.23531	−0.208745
$630$	−0.116157	−0.00462781
$631$	6.55991	0.261146	0.130573	−	0.991439i	$-0.458318\pi$
$631$	6.55991	0.261146	0.130573	+	0.991439i	$0.458318\pi$
$632$	10.0286	0.398915
$633$	10.1715	0.404281
$634$	−19.9883	−0.793838
$635$	−14.1320	−0.560812
$636$	−3.55964	−0.141149
$637$	35.4796	1.40575
$638$	−13.0525	−0.516754
$639$	−11.3019	−0.447097
$640$	0.724086	0.0286220
$641$	11.6822	0.461418	0.230709	−	0.973023i	$-0.425896\pi$
$641$	11.6822	0.461418	0.230709	+	0.973023i	$0.425896\pi$
$642$	−1.25261	−0.0494367
$643$	11.4322	0.450843	0.225422	−	0.974261i	$-0.427624\pi$
$643$	11.4322	0.450843	0.225422	+	0.974261i	$0.427624\pi$
$644$	1.03064	0.0406129
$645$	7.12415	0.280513
$646$	−0.132892	−0.00522856
$647$	−35.5315	−1.39689	−0.698444	−	0.715665i	$-0.746124\pi$
$647$	−35.5315	−1.39689	−0.698444	+	0.715665i	$0.746124\pi$
$648$	1.00000	0.0392837
$649$	4.82765	0.189502
$650$	22.7688	0.893067
$651$	−0.293417	−0.0114999
$652$	5.60848	0.219645
$653$	−19.9264	−0.779782	−0.389891	−	0.920861i	$-0.627487\pi$
$653$	−19.9264	−0.779782	−0.389891	+	0.920861i	$0.627487\pi$
$654$	5.43680	0.212596
$655$	4.60336	0.179868
$656$	−6.47973	−0.252991
$657$	−1.36030	−0.0530704
$658$	1.68293	0.0656075
$659$	−4.44214	−0.173041	−0.0865207	−	0.996250i	$-0.527575\pi$
$659$	−4.44214	−0.173041	−0.0865207	+	0.996250i	$0.527575\pi$
$660$	−3.49563	−0.136067
$661$	20.2824	0.788895	0.394447	−	0.918919i	$-0.370936\pi$
$661$	20.2824	0.788895	0.394447	+	0.918919i	$0.370936\pi$
$662$	−0.494779	−0.0192301
$663$	−5.08721	−0.197571
$664$	2.50692	0.0972873
$665$	−0.0154363	−0.000598596 0
$666$	5.23531	0.202864
$667$	17.3704	0.672585
$668$	12.2187	0.472754
$669$	−14.6397	−0.566004
$670$	−0.585885	−0.0226347
$671$	70.0969	2.70606
$672$	0.160419	0.00618830
$673$	−35.0743	−1.35202	−0.676008	−	0.736894i	$-0.736292\pi$
$673$	−35.0743	−1.35202	−0.676008	+	0.736894i	$0.736292\pi$
$674$	−29.1507	−1.12284
$675$	4.47570	0.172270
$676$	12.8797	0.495373
$677$	−18.9191	−0.727120	−0.363560	−	0.931571i	$-0.618439\pi$
$677$	−18.9191	−0.727120	−0.363560	+	0.931571i	$0.618439\pi$
$678$	14.0883	0.541059
$679$	0.298831	0.0114681
$680$	−0.724086	−0.0277674
$681$	0.350448	0.0134292
$682$	−8.83009	−0.338121
$683$	−16.2148	−0.620442	−0.310221	−	0.950664i	$-0.600403\pi$
$683$	−16.2148	−0.620442	−0.310221	+	0.950664i	$0.600403\pi$
$684$	0.132892	0.00508125
$685$	−14.2703	−0.545240
$686$	2.24174	0.0855900
$687$	−22.4296	−0.855742
$688$	−9.83882	−0.375102
$689$	−18.1086	−0.689883
$690$	4.65202	0.177099
$691$	16.6812	0.634581	0.317291	−	0.948328i	$-0.397227\pi$
$691$	16.6812	0.634581	0.317291	+	0.948328i	$0.397227\pi$
$692$	14.0403	0.533732
$693$	−0.774446	−0.0294188
$694$	7.66357	0.290905
$695$	0.889708	0.0337486
$696$	2.70370	0.102484
$697$	6.47973	0.245437
$698$	0.863673	0.0326905
$699$	14.6131	0.552718
$700$	0.717987	0.0271374
$701$	31.2672	1.18095	0.590473	−	0.807057i	$-0.298941\pi$
$701$	31.2672	1.18095	0.590473	+	0.807057i	$0.298941\pi$
$702$	5.08721	0.192004
$703$	0.695730	0.0262399
$704$	4.82765	0.181949
$705$	7.59627	0.286092
$706$	12.4621	0.469016
$707$	−0.234591	−0.00882270
$708$	−1.00000	−0.0375823
$709$	43.0467	1.61665	0.808327	−	0.588734i	$-0.200373\pi$
$709$	43.0467	1.61665	0.808327	+	0.588734i	$0.200373\pi$
$710$	−8.18357	−0.307124
$711$	10.0286	0.376100
$712$	7.70320	0.288690
$713$	11.7512	0.440084
$714$	−0.160419	−0.00600353
$715$	−17.7830	−0.665047
$716$	−5.78153	−0.216066
$717$	−7.04964	−0.263274
$718$	26.9482	1.00570
$719$	24.6310	0.918582	0.459291	−	0.888286i	$-0.348104\pi$
$719$	24.6310	0.918582	0.459291	+	0.888286i	$0.348104\pi$
$720$	0.724086	0.0269851
$721$	−0.720882	−0.0268471
$722$	−18.9823	−0.706450
$723$	20.9919	0.780698
$724$	−24.5169	−0.911162
$725$	12.1010	0.449419
$726$	−12.3062	−0.456725
$727$	36.7878	1.36438	0.682192	−	0.731173i	$-0.261027\pi$
$727$	36.7878	1.36438	0.682192	+	0.731173i	$0.261027\pi$
$728$	0.816085	0.0302461
$729$	1.00000	0.0370370
$730$	−0.984974	−0.0364555
$731$	9.83882	0.363902
$732$	−14.5199	−0.536670
$733$	−10.4410	−0.385647	−0.192823	−	0.981233i	$-0.561764\pi$
$733$	−10.4410	−0.385647	−0.192823	+	0.981233i	$0.561764\pi$
$734$	−4.79310	−0.176917
$735$	5.04997	0.186271
$736$	−6.42468	−0.236817
$737$	−3.90623	−0.143888
$738$	−6.47973	−0.238522
$739$	−34.4849	−1.26855	−0.634273	−	0.773109i	$-0.718700\pi$
$739$	−34.4849	−1.26855	−0.634273	+	0.773109i	$0.718700\pi$
$740$	3.79082	0.139353
$741$	0.676049	0.0248353
$742$	−0.571033	−0.0209633
$743$	−4.28953	−0.157368	−0.0786838	−	0.996900i	$-0.525072\pi$
$743$	−4.28953	−0.157368	−0.0786838	+	0.996900i	$0.525072\pi$
$744$	1.82907	0.0670568
$745$	3.39302	0.124311
$746$	−7.02669	−0.257265
$747$	2.50692	0.0917234
$748$	−4.82765	−0.176516
$749$	−0.200943	−0.00734229
$750$	6.86122	0.250536
$751$	7.51806	0.274338	0.137169	−	0.990548i	$-0.456200\pi$
$751$	7.51806	0.274338	0.137169	+	0.990548i	$0.456200\pi$
$752$	−10.4908	−0.382562
$753$	−31.4984	−1.14787
$754$	13.7543	0.500902
$755$	2.84361	0.103490
$756$	0.160419	0.00583438
$757$	−28.4843	−1.03528	−0.517640	−	0.855599i	$-0.673189\pi$
$757$	−28.4843	−1.03528	−0.517640	+	0.855599i	$0.673189\pi$
$758$	−20.2760	−0.736459
$759$	31.0161	1.12581
$760$	0.0962251	0.00349045
$761$	−0.474099	−0.0171861	−0.00859304	−	0.999963i	$-0.502735\pi$
$761$	−0.474099	−0.0171861	−0.00859304	+	0.999963i	$0.502735\pi$
$762$	19.5170	0.707028
$763$	0.872167	0.0315745
$764$	−21.7785	−0.787919
$765$	−0.724086	−0.0261794
$766$	29.9280	1.08134
$767$	−5.08721	−0.183689
$768$	−1.00000	−0.0360844
$769$	1.58428	0.0571308	0.0285654	−	0.999592i	$-0.490906\pi$
$769$	1.58428	0.0571308	0.0285654	+	0.999592i	$0.490906\pi$
$770$	−0.560766	−0.0202086
$771$	−2.47851	−0.0892615
$772$	16.8243	0.605519
$773$	7.96773	0.286579	0.143290	−	0.989681i	$-0.454232\pi$
$773$	7.96773	0.286579	0.143290	+	0.989681i	$0.454232\pi$
$774$	−9.83882	−0.353649
$775$	8.18635	0.294062
$776$	−1.86281	−0.0668711
$777$	0.839844	0.0301292
$778$	−16.8429	−0.603846
$779$	−0.861103	−0.0308522
$780$	3.68358	0.131893
$781$	−54.5617	−1.95237
$782$	6.42468	0.229746
$783$	2.70370	0.0966225
$784$	−6.97427	−0.249081
$785$	1.76671	0.0630565
$786$	−6.35748	−0.226764
$787$	−20.2509	−0.721866	−0.360933	−	0.932592i	$-0.617542\pi$
$787$	−20.2509	−0.721866	−0.360933	+	0.932592i	$0.617542\pi$
$788$	−15.4289	−0.549630
$789$	22.3403	0.795336
$790$	7.26154	0.258354
$791$	2.26004	0.0803576
$792$	4.82765	0.171543
$793$	−73.8657	−2.62305
$794$	−28.3715	−1.00687
$795$	−2.57748	−0.0914139
$796$	10.4900	0.371808
$797$	−42.6476	−1.51066	−0.755328	−	0.655347i	$-0.772522\pi$
$797$	−42.6476	−1.51066	−0.755328	+	0.655347i	$0.772522\pi$
$798$	0.0213184	0.000754662 0
$799$	10.4908	0.371139
$800$	−4.47570	−0.158240
$801$	7.70320	0.272179
$802$	4.72404	0.166811
$803$	−6.56705	−0.231746
$804$	0.809137	0.0285361
$805$	0.746272	0.0263026
$806$	9.30485	0.327749
$807$	2.37907	0.0837473
$808$	1.46236	0.0514458
$809$	−53.2128	−1.87086	−0.935431	−	0.353509i	$-0.884988\pi$
$809$	−53.2128	−1.87086	−0.935431	+	0.353509i	$0.884988\pi$
$810$	0.724086	0.0254418
$811$	−53.4961	−1.87850	−0.939250	−	0.343233i	$-0.888478\pi$
$811$	−53.4961	−1.87850	−0.939250	+	0.343233i	$0.888478\pi$
$812$	0.433726	0.0152208
$813$	28.5587	1.00160
$814$	25.2742	0.885861
$815$	4.06102	0.142251
$816$	1.00000	0.0350070
$817$	−1.30750	−0.0457436
$818$	−22.2550	−0.778128
$819$	0.816085	0.0285163
$820$	−4.69188	−0.163848
$821$	−50.0315	−1.74611	−0.873055	−	0.487621i	$-0.837865\pi$
$821$	−50.0315	−1.74611	−0.873055	+	0.487621i	$0.837865\pi$
$822$	19.7080	0.687396
$823$	−31.7653	−1.10727	−0.553634	−	0.832760i	$-0.686759\pi$
$823$	−31.7653	−1.10727	−0.553634	+	0.832760i	$0.686759\pi$
$824$	4.49374	0.156547
$825$	21.6071	0.752262
$826$	−0.160419	−0.00558169
$827$	6.55451	0.227923	0.113961	−	0.993485i	$-0.463646\pi$
$827$	6.55451	0.227923	0.113961	+	0.993485i	$0.463646\pi$
$828$	−6.42468	−0.223273
$829$	−15.7433	−0.546786	−0.273393	−	0.961902i	$-0.588146\pi$
$829$	−15.7433	−0.546786	−0.273393	+	0.961902i	$0.588146\pi$
$830$	1.81523	0.0630074
$831$	15.9823	0.554420
$832$	−5.08721	−0.176367
$833$	6.97427	0.241644
$834$	−1.22873	−0.0425475
$835$	8.84736	0.306176
$836$	0.641555	0.0221886
$837$	1.82907	0.0632218
$838$	7.94052	0.274301
$839$	9.70963	0.335214	0.167607	−	0.985854i	$-0.446396\pi$
$839$	9.70963	0.335214	0.167607	+	0.985854i	$0.446396\pi$
$840$	0.116157	0.00400780
$841$	−21.6900	−0.747931
$842$	−12.8526	−0.442929
$843$	1.02714	0.0353767
$844$	−10.1715	−0.350118
$845$	9.32601	0.320825
$846$	−10.4908	−0.360683
$847$	−1.97414	−0.0678324
$848$	3.55964	0.122238
$849$	−10.0453	−0.344753
$850$	4.47570	0.153515
$851$	−33.6352	−1.15300
$852$	11.3019	0.387198
$853$	2.59073	0.0887047	0.0443524	−	0.999016i	$-0.485878\pi$
$853$	2.59073	0.0887047	0.0443524	+	0.999016i	$0.485878\pi$
$854$	−2.32927	−0.0797058
$855$	0.0962251	0.00329083
$856$	1.25261	0.0428134
$857$	30.5709	1.04428	0.522142	−	0.852859i	$-0.325133\pi$
$857$	30.5709	1.04428	0.522142	+	0.852859i	$0.325133\pi$
$858$	24.5593	0.838439
$859$	35.6255	1.21553	0.607764	−	0.794118i	$-0.292067\pi$
$859$	35.6255	1.21553	0.607764	+	0.794118i	$0.292067\pi$
$860$	−7.12415	−0.242932
$861$	−1.03947	−0.0354251
$862$	12.8090	0.436275
$863$	11.8250	0.402526	0.201263	−	0.979537i	$-0.435495\pi$
$863$	11.8250	0.402526	0.201263	+	0.979537i	$0.435495\pi$
$864$	−1.00000	−0.0340207
$865$	10.1664	0.345668
$866$	−27.5091	−0.934797
$867$	−1.00000	−0.0339618
$868$	0.293417	0.00995923
$869$	48.4144	1.64234
$870$	1.95771	0.0663727
$871$	4.11625	0.139474
$872$	−5.43680	−0.184113
$873$	−1.86281	−0.0630467
$874$	−0.853787	−0.0288798
$875$	1.10067	0.0372095
$876$	1.36030	0.0459603
$877$	34.5530	1.16677	0.583385	−	0.812195i	$-0.301728\pi$
$877$	34.5530	1.16677	0.583385	+	0.812195i	$0.301728\pi$
$878$	36.2855	1.22458
$879$	−33.5729	−1.13239
$880$	3.49563	0.117838
$881$	−6.55674	−0.220902	−0.110451	−	0.993882i	$-0.535230\pi$
$881$	−6.55674	−0.220902	−0.110451	+	0.993882i	$0.535230\pi$
$882$	−6.97427	−0.234836
$883$	−28.7508	−0.967540	−0.483770	−	0.875195i	$-0.660733\pi$
$883$	−28.7508	−0.967540	−0.483770	+	0.875195i	$0.660733\pi$
$884$	5.08721	0.171101
$885$	−0.724086	−0.0243399
$886$	−3.64689	−0.122520
$887$	29.6987	0.997185	0.498592	−	0.866837i	$-0.333851\pi$
$887$	29.6987	0.997185	0.498592	+	0.866837i	$0.333851\pi$
$888$	−5.23531	−0.175686
$889$	3.13091	0.105007
$890$	5.57778	0.186968
$891$	4.82765	0.161732
$892$	14.6397	0.490174
$893$	−1.39415	−0.0466534
$894$	−4.68593	−0.156721
$895$	−4.18632	−0.139933
$896$	−0.160419	−0.00535922
$897$	−32.6837	−1.09128
$898$	−18.9265	−0.631585
$899$	4.94525	0.164933
$900$	−4.47570	−0.149190
$901$	−3.55964	−0.118589
$902$	−31.2819	−1.04157
$903$	−1.57833	−0.0525237
$904$	−14.0883	−0.468571
$905$	−17.7523	−0.590107
$906$	−3.92717	−0.130472
$907$	−48.2474	−1.60203	−0.801015	−	0.598644i	$-0.795706\pi$
$907$	−48.2474	−1.60203	−0.801015	+	0.598644i	$0.795706\pi$
$908$	−0.350448	−0.0116300
$909$	1.46236	0.0485035
$910$	0.590916	0.0195887
$911$	21.8770	0.724816	0.362408	−	0.932020i	$-0.381955\pi$
$911$	21.8770	0.724816	0.362408	+	0.932020i	$0.381955\pi$
$912$	−0.132892	−0.00440049
$913$	12.1025	0.400535
$914$	2.62956	0.0869782
$915$	−10.5136	−0.347570
$916$	22.4296	0.741095
$917$	−1.01986	−0.0336788
$918$	1.00000	0.0330049
$919$	27.9862	0.923179	0.461590	−	0.887094i	$-0.347279\pi$
$919$	27.9862	0.923179	0.461590	+	0.887094i	$0.347279\pi$
$920$	−4.65202	−0.153373
$921$	26.1118	0.860413
$922$	−5.27867	−0.173844
$923$	57.4953	1.89248
$924$	0.774446	0.0254774
$925$	−23.4317	−0.770429
$926$	8.41650	0.276583
$927$	4.49374	0.147594
$928$	−2.70370	−0.0887534
$929$	17.3610	0.569595	0.284798	−	0.958588i	$-0.408074\pi$
$929$	17.3610	0.569595	0.284798	+	0.958588i	$0.408074\pi$
$930$	1.32440	0.0434288
$931$	−0.926823	−0.0303754
$932$	−14.6131	−0.478668
$933$	17.4325	0.570716
$934$	10.4623	0.342336
$935$	−3.49563	−0.114319
$936$	−5.08721	−0.166281
$937$	−11.8634	−0.387560	−0.193780	−	0.981045i	$-0.562075\pi$
$937$	−11.8634	−0.387560	−0.193780	+	0.981045i	$0.562075\pi$
$938$	0.129801	0.00423815
$939$	−17.9350	−0.585286
$940$	−7.59627	−0.247763
$941$	−11.8663	−0.386830	−0.193415	−	0.981117i	$-0.561956\pi$
$941$	−11.8663	−0.386830	−0.193415	+	0.981117i	$0.561956\pi$
$942$	−2.43991	−0.0794967
$943$	41.6302	1.35567
$944$	1.00000	0.0325472
$945$	0.116157	0.00377859
$946$	−47.4984	−1.54430
$947$	29.3440	0.953551	0.476775	−	0.879025i	$-0.341805\pi$
$947$	29.3440	0.953551	0.476775	+	0.879025i	$0.341805\pi$
$948$	−10.0286	−0.325713
$949$	6.92013	0.224637
$950$	−0.594784	−0.0192973
$951$	19.9883	0.648166
$952$	0.160419	0.00519921
$953$	12.2790	0.397756	0.198878	−	0.980024i	$-0.436270\pi$
$953$	12.2790	0.397756	0.198878	+	0.980024i	$0.436270\pi$
$954$	3.55964	0.115247
$955$	−15.7695	−0.510289
$956$	7.04964	0.228002
$957$	13.0525	0.421928
$958$	−13.7977	−0.445782
$959$	3.16154	0.102092
$960$	−0.724086	−0.0233698
$961$	−27.6545	−0.892081
$962$	−26.6331	−0.858686
$963$	1.25261	0.0403649
$964$	−20.9919	−0.676104
$965$	12.1822	0.392159
$966$	−1.03064	−0.0331603
$967$	45.5335	1.46426	0.732130	−	0.681165i	$-0.238526\pi$
$967$	45.5335	1.46426	0.732130	+	0.681165i	$0.238526\pi$
$968$	12.3062	0.395535
$969$	0.132892	0.00426910
$970$	−1.34884	−0.0433086
$971$	−32.6955	−1.04925	−0.524624	−	0.851334i	$-0.675794\pi$
$971$	−32.6955	−1.04925	−0.524624	+	0.851334i	$0.675794\pi$
$972$	−1.00000	−0.0320750
$973$	−0.197112	−0.00631913
$974$	7.22225	0.231416
$975$	−22.7688	−0.729186
$976$	14.5199	0.464770
$977$	−38.0296	−1.21668	−0.608338	−	0.793678i	$-0.708164\pi$
$977$	−38.0296	−1.21668	−0.608338	+	0.793678i	$0.708164\pi$
$978$	−5.60848	−0.179339
$979$	37.1883	1.18854
$980$	−5.04997	−0.161315
$981$	−5.43680	−0.173584
$982$	40.0807	1.27903
$983$	47.1443	1.50367	0.751835	−	0.659351i	$-0.229169\pi$
$983$	47.1443	1.50367	0.751835	+	0.659351i	$0.229169\pi$
$984$	6.47973	0.206566
$985$	−11.1718	−0.355964
$986$	2.70370	0.0861035
$987$	−1.68293	−0.0535683
$988$	−0.676049	−0.0215080
$989$	63.2113	2.01000
$990$	3.49563	0.111098
$991$	35.7034	1.13416	0.567078	−	0.823664i	$-0.308074\pi$
$991$	35.7034	1.13416	0.567078	+	0.823664i	$0.308074\pi$
$992$	−1.82907	−0.0580729
$993$	0.494779	0.0157013
$994$	1.81304	0.0575063
$995$	7.59565	0.240798
$996$	−2.50692	−0.0794348
$997$	59.1779	1.87418	0.937091	−	0.349085i	$-0.113507\pi$
$997$	59.1779	1.87418	0.937091	+	0.349085i	$0.113507\pi$
$998$	−3.59868	−0.113914
$999$	−5.23531	−0.165638

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.q.1.5	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.q.1.5	✓	6	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.724086 q^{5} -1.00000 q^{6} -0.160419 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.724086 q^{5} -1.00000 q^{6} -0.160419 q^{7} +1.00000 q^{8} +1.00000 q^{9} +0.724086 q^{10} +4.82765 q^{11} -1.00000 q^{12} -5.08721 q^{13} -0.160419 q^{14} -0.724086 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} +0.132892 q^{19} +0.724086 q^{20} +0.160419 q^{21} +4.82765 q^{22} -6.42468 q^{23} -1.00000 q^{24} -4.47570 q^{25} -5.08721 q^{26} -1.00000 q^{27} -0.160419 q^{28} -2.70370 q^{29} -0.724086 q^{30} -1.82907 q^{31} +1.00000 q^{32} -4.82765 q^{33} -1.00000 q^{34} -0.116157 q^{35} +1.00000 q^{36} +5.23531 q^{37} +0.132892 q^{38} +5.08721 q^{39} +0.724086 q^{40} -6.47973 q^{41} +0.160419 q^{42} -9.83882 q^{43} +4.82765 q^{44} +0.724086 q^{45} -6.42468 q^{46} -10.4908 q^{47} -1.00000 q^{48} -6.97427 q^{49} -4.47570 q^{50} +1.00000 q^{51} -5.08721 q^{52} +3.55964 q^{53} -1.00000 q^{54} +3.49563 q^{55} -0.160419 q^{56} -0.132892 q^{57} -2.70370 q^{58} +1.00000 q^{59} -0.724086 q^{60} +14.5199 q^{61} -1.82907 q^{62} -0.160419 q^{63} +1.00000 q^{64} -3.68358 q^{65} -4.82765 q^{66} -0.809137 q^{67} -1.00000 q^{68} +6.42468 q^{69} -0.116157 q^{70} -11.3019 q^{71} +1.00000 q^{72} -1.36030 q^{73} +5.23531 q^{74} +4.47570 q^{75} +0.132892 q^{76} -0.774446 q^{77} +5.08721 q^{78} +10.0286 q^{79} +0.724086 q^{80} +1.00000 q^{81} -6.47973 q^{82} +2.50692 q^{83} +0.160419 q^{84} -0.724086 q^{85} -9.83882 q^{86} +2.70370 q^{87} +4.82765 q^{88} +7.70320 q^{89} +0.724086 q^{90} +0.816085 q^{91} -6.42468 q^{92} +1.82907 q^{93} -10.4908 q^{94} +0.0962251 q^{95} -1.00000 q^{96} -1.86281 q^{97} -6.97427 q^{98} +4.82765 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} - 6 q^{3} + 6 q^{4} - 5 q^{5} - 6 q^{6} - q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 - 6 * q^3 + 6 * q^4 - 5 * q^5 - 6 * q^6 - q^7 + 6 * q^8 + 6 * q^9	\( 6 q + 6 q^{2} - 6 q^{3} + 6 q^{4} - 5 q^{5} - 6 q^{6} - q^{7} + 6 q^{8} + 6 q^{9} - 5 q^{10} - 6 q^{12} + 2 q^{13} - q^{14} + 5 q^{15} + 6 q^{16} - 6 q^{17} + 6 q^{18} - 5 q^{20} + q^{21} - 10 q^{23} - 6 q^{24} - 9 q^{25} + 2 q^{26} - 6 q^{27} - q^{28} - 3 q^{29} + 5 q^{30} - 7 q^{31} + 6 q^{32} - 6 q^{34} + 6 q^{35} + 6 q^{36} - 23 q^{37} - 2 q^{39} - 5 q^{40} - 12 q^{41} + q^{42} - 18 q^{43} - 5 q^{45} - 10 q^{46} - 14 q^{47} - 6 q^{48} + 9 q^{49} - 9 q^{50} + 6 q^{51} + 2 q^{52} + 21 q^{53} - 6 q^{54} + 4 q^{55} - q^{56} - 3 q^{58} + 6 q^{59} + 5 q^{60} - 2 q^{61} - 7 q^{62} - q^{63} + 6 q^{64} - 6 q^{65} + q^{67} - 6 q^{68} + 10 q^{69} + 6 q^{70} + 4 q^{71} + 6 q^{72} - 38 q^{73} - 23 q^{74} + 9 q^{75} - 22 q^{77} - 2 q^{78} - 30 q^{79} - 5 q^{80} + 6 q^{81} - 12 q^{82} + 23 q^{83} + q^{84} + 5 q^{85} - 18 q^{86} + 3 q^{87} - 7 q^{89} - 5 q^{90} - 5 q^{91} - 10 q^{92} + 7 q^{93} - 14 q^{94} - 7 q^{95} - 6 q^{96} - 10 q^{97} + 9 q^{98}+O(q^{100}) \) 6 * q + 6 * q^2 - 6 * q^3 + 6 * q^4 - 5 * q^5 - 6 * q^6 - q^7 + 6 * q^8 + 6 * q^9 - 5 * q^10 - 6 * q^12 + 2 * q^13 - q^14 + 5 * q^15 + 6 * q^16 - 6 * q^17 + 6 * q^18 - 5 * q^20 + q^21 - 10 * q^23 - 6 * q^24 - 9 * q^25 + 2 * q^26 - 6 * q^27 - q^28 - 3 * q^29 + 5 * q^30 - 7 * q^31 + 6 * q^32 - 6 * q^34 + 6 * q^35 + 6 * q^36 - 23 * q^37 - 2 * q^39 - 5 * q^40 - 12 * q^41 + q^42 - 18 * q^43 - 5 * q^45 - 10 * q^46 - 14 * q^47 - 6 * q^48 + 9 * q^49 - 9 * q^50 + 6 * q^51 + 2 * q^52 + 21 * q^53 - 6 * q^54 + 4 * q^55 - q^56 - 3 * q^58 + 6 * q^59 + 5 * q^60 - 2 * q^61 - 7 * q^62 - q^63 + 6 * q^64 - 6 * q^65 + q^67 - 6 * q^68 + 10 * q^69 + 6 * q^70 + 4 * q^71 + 6 * q^72 - 38 * q^73 - 23 * q^74 + 9 * q^75 - 22 * q^77 - 2 * q^78 - 30 * q^79 - 5 * q^80 + 6 * q^81 - 12 * q^82 + 23 * q^83 + q^84 + 5 * q^85 - 18 * q^86 + 3 * q^87 - 7 * q^89 - 5 * q^90 - 5 * q^91 - 10 * q^92 + 7 * q^93 - 14 * q^94 - 7 * q^95 - 6 * q^96 - 10 * q^97 + 9 * q^98

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