LMFDB - Embedded newform 6018.2.a.z.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("6018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$48.0539719364$
Analytic rank:	$0$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 4 x^{10} - 27 x^{9} + 117 x^{8} + 200 x^{7} - 1023 x^{6} - 484 x^{5} + 3403 x^{4} + 562 x^{3} + \cdots + 1200 $ x^11 - 4x^10 - 27x^9 + 117x^8 + 200x^7 - 1023x^6 - 484x^5 + 3403x^4 + 562x^3 - 4372x^2 - 692x + 1200
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-1.33314$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.33314 q^{5} -1.00000 q^{6} -3.20872 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.33314 q^{5} -1.00000 q^{6} -3.20872 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.33314 q^{10} -5.27703 q^{11} -1.00000 q^{12} -4.54336 q^{13} -3.20872 q^{14} +1.33314 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} -5.88474 q^{19} -1.33314 q^{20} +3.20872 q^{21} -5.27703 q^{22} +3.53990 q^{23} -1.00000 q^{24} -3.22274 q^{25} -4.54336 q^{26} -1.00000 q^{27} -3.20872 q^{28} +2.80205 q^{29} +1.33314 q^{30} -2.14265 q^{31} +1.00000 q^{32} +5.27703 q^{33} -1.00000 q^{34} +4.27768 q^{35} +1.00000 q^{36} +11.8885 q^{37} -5.88474 q^{38} +4.54336 q^{39} -1.33314 q^{40} -9.10648 q^{41} +3.20872 q^{42} -2.05555 q^{43} -5.27703 q^{44} -1.33314 q^{45} +3.53990 q^{46} -3.47234 q^{47} -1.00000 q^{48} +3.29590 q^{49} -3.22274 q^{50} +1.00000 q^{51} -4.54336 q^{52} +0.774176 q^{53} -1.00000 q^{54} +7.03501 q^{55} -3.20872 q^{56} +5.88474 q^{57} +2.80205 q^{58} -1.00000 q^{59} +1.33314 q^{60} +6.38088 q^{61} -2.14265 q^{62} -3.20872 q^{63} +1.00000 q^{64} +6.05693 q^{65} +5.27703 q^{66} -6.17650 q^{67} -1.00000 q^{68} -3.53990 q^{69} +4.27768 q^{70} +12.7528 q^{71} +1.00000 q^{72} -2.22859 q^{73} +11.8885 q^{74} +3.22274 q^{75} -5.88474 q^{76} +16.9325 q^{77} +4.54336 q^{78} -1.53464 q^{79} -1.33314 q^{80} +1.00000 q^{81} -9.10648 q^{82} +0.352363 q^{83} +3.20872 q^{84} +1.33314 q^{85} -2.05555 q^{86} -2.80205 q^{87} -5.27703 q^{88} +1.42587 q^{89} -1.33314 q^{90} +14.5784 q^{91} +3.53990 q^{92} +2.14265 q^{93} -3.47234 q^{94} +7.84517 q^{95} -1.00000 q^{96} +1.05372 q^{97} +3.29590 q^{98} -5.27703 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q + 11 q^{2} - 11 q^{3} + 11 q^{4} + 4 q^{5} - 11 q^{6} + 3 q^{7} + 11 q^{8} + 11 q^{9}+O(q^{10}) $ 11 * q + 11 * q^2 - 11 * q^3 + 11 * q^4 + 4 * q^5 - 11 * q^6 + 3 * q^7 + 11 * q^8 + 11 * q^9	\( 11 q + 11 q^{2} - 11 q^{3} + 11 q^{4} + 4 q^{5} - 11 q^{6} + 3 q^{7} + 11 q^{8} + 11 q^{9} + 4 q^{10} + 9 q^{11} - 11 q^{12} + 6 q^{13} + 3 q^{14} - 4 q^{15} + 11 q^{16} - 11 q^{17} + 11 q^{18} - q^{19} + 4 q^{20} - 3 q^{21} + 9 q^{22} + 10 q^{23} - 11 q^{24} + 15 q^{25} + 6 q^{26} - 11 q^{27} + 3 q^{28} + 14 q^{29} - 4 q^{30} + 17 q^{31} + 11 q^{32} - 9 q^{33} - 11 q^{34} + 8 q^{35} + 11 q^{36} + 30 q^{37} - q^{38} - 6 q^{39} + 4 q^{40} + 10 q^{41} - 3 q^{42} + 11 q^{43} + 9 q^{44} + 4 q^{45} + 10 q^{46} - 6 q^{47} - 11 q^{48} + 18 q^{49} + 15 q^{50} + 11 q^{51} + 6 q^{52} + 10 q^{53} - 11 q^{54} - 11 q^{55} + 3 q^{56} + q^{57} + 14 q^{58} - 11 q^{59} - 4 q^{60} + 13 q^{61} + 17 q^{62} + 3 q^{63} + 11 q^{64} + 32 q^{65} - 9 q^{66} + 26 q^{67} - 11 q^{68} - 10 q^{69} + 8 q^{70} + 14 q^{71} + 11 q^{72} + 20 q^{73} + 30 q^{74} - 15 q^{75} - q^{76} + 26 q^{77} - 6 q^{78} + 15 q^{79} + 4 q^{80} + 11 q^{81} + 10 q^{82} + 2 q^{83} - 3 q^{84} - 4 q^{85} + 11 q^{86} - 14 q^{87} + 9 q^{88} + q^{89} + 4 q^{90} + 17 q^{91} + 10 q^{92} - 17 q^{93} - 6 q^{94} + 3 q^{95} - 11 q^{96} + 33 q^{97} + 18 q^{98} + 9 q^{99}+O(q^{100}) \) 11 * q + 11 * q^2 - 11 * q^3 + 11 * q^4 + 4 * q^5 - 11 * q^6 + 3 * q^7 + 11 * q^8 + 11 * q^9 + 4 * q^10 + 9 * q^11 - 11 * q^12 + 6 * q^13 + 3 * q^14 - 4 * q^15 + 11 * q^16 - 11 * q^17 + 11 * q^18 - q^19 + 4 * q^20 - 3 * q^21 + 9 * q^22 + 10 * q^23 - 11 * q^24 + 15 * q^25 + 6 * q^26 - 11 * q^27 + 3 * q^28 + 14 * q^29 - 4 * q^30 + 17 * q^31 + 11 * q^32 - 9 * q^33 - 11 * q^34 + 8 * q^35 + 11 * q^36 + 30 * q^37 - q^38 - 6 * q^39 + 4 * q^40 + 10 * q^41 - 3 * q^42 + 11 * q^43 + 9 * q^44 + 4 * q^45 + 10 * q^46 - 6 * q^47 - 11 * q^48 + 18 * q^49 + 15 * q^50 + 11 * q^51 + 6 * q^52 + 10 * q^53 - 11 * q^54 - 11 * q^55 + 3 * q^56 + q^57 + 14 * q^58 - 11 * q^59 - 4 * q^60 + 13 * q^61 + 17 * q^62 + 3 * q^63 + 11 * q^64 + 32 * q^65 - 9 * q^66 + 26 * q^67 - 11 * q^68 - 10 * q^69 + 8 * q^70 + 14 * q^71 + 11 * q^72 + 20 * q^73 + 30 * q^74 - 15 * q^75 - q^76 + 26 * q^77 - 6 * q^78 + 15 * q^79 + 4 * q^80 + 11 * q^81 + 10 * q^82 + 2 * q^83 - 3 * q^84 - 4 * q^85 + 11 * q^86 - 14 * q^87 + 9 * q^88 + q^89 + 4 * q^90 + 17 * q^91 + 10 * q^92 - 17 * q^93 - 6 * q^94 + 3 * q^95 - 11 * q^96 + 33 * q^97 + 18 * q^98 + 9 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	−1.33314	−0.596198	−0.298099	−	0.954535i	$-0.596353\pi$
$5$	−1.33314	−0.596198	−0.298099	+	0.954535i	$0.596353\pi$
$6$	−1.00000	−0.408248
$7$	−3.20872	−1.21278	−0.606392	−	0.795166i	$-0.707384\pi$
$7$	−3.20872	−1.21278	−0.606392	+	0.795166i	$0.707384\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−1.33314	−0.421576
$11$	−5.27703	−1.59108	−0.795542	−	0.605899i	$-0.792814\pi$
$11$	−5.27703	−1.59108	−0.795542	+	0.605899i	$0.792814\pi$
$12$	−1.00000	−0.288675
$13$	−4.54336	−1.26010	−0.630050	−	0.776554i	$-0.716966\pi$
$13$	−4.54336	−1.26010	−0.630050	+	0.776554i	$0.716966\pi$
$14$	−3.20872	−0.857567
$15$	1.33314	0.344215
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.00000	0.235702
$19$	−5.88474	−1.35005	−0.675025	−	0.737794i	$-0.735867\pi$
$19$	−5.88474	−1.35005	−0.675025	+	0.737794i	$0.735867\pi$
$20$	−1.33314	−0.298099
$21$	3.20872	0.700201
$22$	−5.27703	−1.12507
$23$	3.53990	0.738120	0.369060	−	0.929406i	$-0.379680\pi$
$23$	3.53990	0.738120	0.369060	+	0.929406i	$0.379680\pi$
$24$	−1.00000	−0.204124
$25$	−3.22274	−0.644548
$26$	−4.54336	−0.891026
$27$	−1.00000	−0.192450
$28$	−3.20872	−0.606392
$29$	2.80205	0.520327	0.260164	−	0.965565i	$-0.416224\pi$
$29$	2.80205	0.520327	0.260164	+	0.965565i	$0.416224\pi$
$30$	1.33314	0.243397
$31$	−2.14265	−0.384832	−0.192416	−	0.981313i	$-0.561632\pi$
$31$	−2.14265	−0.384832	−0.192416	+	0.981313i	$0.561632\pi$
$32$	1.00000	0.176777
$33$	5.27703	0.918612
$34$	−1.00000	−0.171499
$35$	4.27768	0.723059
$36$	1.00000	0.166667
$37$	11.8885	1.95446	0.977230	−	0.212185i	$-0.0680578\pi$
$37$	11.8885	1.95446	0.977230	+	0.212185i	$0.0680578\pi$
$38$	−5.88474	−0.954630
$39$	4.54336	0.727519
$40$	−1.33314	−0.210788
$41$	−9.10648	−1.42219	−0.711096	−	0.703095i	$-0.751801\pi$
$41$	−9.10648	−1.42219	−0.711096	+	0.703095i	$0.751801\pi$
$42$	3.20872	0.495117
$43$	−2.05555	−0.313468	−0.156734	−	0.987641i	$-0.550097\pi$
$43$	−2.05555	−0.313468	−0.156734	+	0.987641i	$0.550097\pi$
$44$	−5.27703	−0.795542
$45$	−1.33314	−0.198733
$46$	3.53990	0.521930
$47$	−3.47234	−0.506492	−0.253246	−	0.967402i	$-0.581498\pi$
$47$	−3.47234	−0.506492	−0.253246	+	0.967402i	$0.581498\pi$
$48$	−1.00000	−0.144338
$49$	3.29590	0.470843
$50$	−3.22274	−0.455764
$51$	1.00000	0.140028
$52$	−4.54336	−0.630050
$53$	0.774176	0.106341	0.0531706	−	0.998585i	$-0.483067\pi$
$53$	0.774176	0.106341	0.0531706	+	0.998585i	$0.483067\pi$
$54$	−1.00000	−0.136083
$55$	7.03501	0.948601
$56$	−3.20872	−0.428784
$57$	5.88474	0.779452
$58$	2.80205	0.367927
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	1.33314	0.172108
$61$	6.38088	0.816988	0.408494	−	0.912761i	$-0.366054\pi$
$61$	6.38088	0.816988	0.408494	+	0.912761i	$0.366054\pi$
$62$	−2.14265	−0.272117
$63$	−3.20872	−0.404261
$64$	1.00000	0.125000
$65$	6.05693	0.751270
$66$	5.27703	0.649557
$67$	−6.17650	−0.754580	−0.377290	−	0.926095i	$-0.623144\pi$
$67$	−6.17650	−0.754580	−0.377290	+	0.926095i	$0.623144\pi$
$68$	−1.00000	−0.121268
$69$	−3.53990	−0.426154
$70$	4.27768	0.511280
$71$	12.7528	1.51348	0.756741	−	0.653715i	$-0.226791\pi$
$71$	12.7528	1.51348	0.756741	+	0.653715i	$0.226791\pi$
$72$	1.00000	0.117851
$73$	−2.22859	−0.260837	−0.130418	−	0.991459i	$-0.541632\pi$
$73$	−2.22859	−0.260837	−0.130418	+	0.991459i	$0.541632\pi$
$74$	11.8885	1.38201
$75$	3.22274	0.372130
$76$	−5.88474	−0.675025
$77$	16.9325	1.92964
$78$	4.54336	0.514434
$79$	−1.53464	−0.172661	−0.0863305	−	0.996267i	$-0.527514\pi$
$79$	−1.53464	−0.172661	−0.0863305	+	0.996267i	$0.527514\pi$
$80$	−1.33314	−0.149050
$81$	1.00000	0.111111
$82$	−9.10648	−1.00564
$83$	0.352363	0.0386769	0.0193384	−	0.999813i	$-0.493844\pi$
$83$	0.352363	0.0386769	0.0193384	+	0.999813i	$0.493844\pi$
$84$	3.20872	0.350100
$85$	1.33314	0.144599
$86$	−2.05555	−0.221656
$87$	−2.80205	−0.300411
$88$	−5.27703	−0.562533
$89$	1.42587	0.151142	0.0755709	−	0.997140i	$-0.475922\pi$
$89$	1.42587	0.151142	0.0755709	+	0.997140i	$0.475922\pi$
$90$	−1.33314	−0.140525
$91$	14.5784	1.52823
$92$	3.53990	0.369060
$93$	2.14265	0.222183
$94$	−3.47234	−0.358144
$95$	7.84517	0.804898
$96$	−1.00000	−0.102062
$97$	1.05372	0.106989	0.0534944	−	0.998568i	$-0.482964\pi$
$97$	1.05372	0.106989	0.0534944	+	0.998568i	$0.482964\pi$
$98$	3.29590	0.332936
$99$	−5.27703	−0.530361
$100$	−3.22274	−0.322274
$101$	12.7966	1.27331	0.636657	−	0.771147i	$-0.280317\pi$
$101$	12.7966	1.27331	0.636657	+	0.771147i	$0.280317\pi$
$102$	1.00000	0.0990148
$103$	−14.2222	−1.40136	−0.700679	−	0.713477i	$-0.747119\pi$
$103$	−14.2222	−1.40136	−0.700679	+	0.713477i	$0.747119\pi$
$104$	−4.54336	−0.445513
$105$	−4.27768	−0.417458
$106$	0.774176	0.0751946
$107$	15.3758	1.48644	0.743218	−	0.669049i	$-0.233298\pi$
$107$	15.3758	1.48644	0.743218	+	0.669049i	$0.233298\pi$
$108$	−1.00000	−0.0962250
$109$	8.76010	0.839066	0.419533	−	0.907740i	$-0.362194\pi$
$109$	8.76010	0.839066	0.419533	+	0.907740i	$0.362194\pi$
$110$	7.03501	0.670762
$111$	−11.8885	−1.12841
$112$	−3.20872	−0.303196
$113$	−0.300474	−0.0282663	−0.0141331	−	0.999900i	$-0.504499\pi$
$113$	−0.300474	−0.0282663	−0.0141331	+	0.999900i	$0.504499\pi$
$114$	5.88474	0.551156
$115$	−4.71918	−0.440066
$116$	2.80205	0.260164
$117$	−4.54336	−0.420034
$118$	−1.00000	−0.0920575
$119$	3.20872	0.294143
$120$	1.33314	0.121698
$121$	16.8470	1.53155
$122$	6.38088	0.577698
$123$	9.10648	0.821103
$124$	−2.14265	−0.192416
$125$	10.9621	0.980476
$126$	−3.20872	−0.285856
$127$	8.80393	0.781223	0.390611	−	0.920556i	$-0.372264\pi$
$127$	8.80393	0.781223	0.390611	+	0.920556i	$0.372264\pi$
$128$	1.00000	0.0883883
$129$	2.05555	0.180981
$130$	6.05693	0.531228
$131$	−9.49526	−0.829604	−0.414802	−	0.909912i	$-0.636149\pi$
$131$	−9.49526	−0.829604	−0.414802	+	0.909912i	$0.636149\pi$
$132$	5.27703	0.459306
$133$	18.8825	1.63732
$134$	−6.17650	−0.533569
$135$	1.33314	0.114738
$136$	−1.00000	−0.0857493
$137$	−4.01331	−0.342880	−0.171440	−	0.985195i	$-0.554842\pi$
$137$	−4.01331	−0.342880	−0.171440	+	0.985195i	$0.554842\pi$
$138$	−3.53990	−0.301336
$139$	14.3870	1.22029	0.610144	−	0.792290i	$-0.291111\pi$
$139$	14.3870	1.22029	0.610144	+	0.792290i	$0.291111\pi$
$140$	4.27768	0.361530
$141$	3.47234	0.292423
$142$	12.7528	1.07019
$143$	23.9754	2.00492
$144$	1.00000	0.0833333
$145$	−3.73552	−0.310218
$146$	−2.22859	−0.184439
$147$	−3.29590	−0.271841
$148$	11.8885	0.977230
$149$	−22.8693	−1.87353	−0.936765	−	0.349960i	$-0.886195\pi$
$149$	−22.8693	−1.87353	−0.936765	+	0.349960i	$0.886195\pi$
$150$	3.22274	0.263136
$151$	3.34704	0.272378	0.136189	−	0.990683i	$-0.456515\pi$
$151$	3.34704	0.272378	0.136189	+	0.990683i	$0.456515\pi$
$152$	−5.88474	−0.477315
$153$	−1.00000	−0.0808452
$154$	16.9325	1.36446
$155$	2.85646	0.229436
$156$	4.54336	0.363760
$157$	−15.7615	−1.25790	−0.628952	−	0.777444i	$-0.716516\pi$
$157$	−15.7615	−1.25790	−0.628952	+	0.777444i	$0.716516\pi$
$158$	−1.53464	−0.122090
$159$	−0.774176	−0.0613961
$160$	−1.33314	−0.105394
$161$	−11.3586	−0.895179
$162$	1.00000	0.0785674
$163$	−17.8477	−1.39794	−0.698971	−	0.715150i	$-0.746358\pi$
$163$	−17.8477	−1.39794	−0.698971	+	0.715150i	$0.746358\pi$
$164$	−9.10648	−0.711096
$165$	−7.03501	−0.547675
$166$	0.352363	0.0273487
$167$	−17.8906	−1.38442	−0.692208	−	0.721698i	$-0.743362\pi$
$167$	−17.8906	−1.38442	−0.692208	+	0.721698i	$0.743362\pi$
$168$	3.20872	0.247558
$169$	7.64209	0.587853
$170$	1.33314	0.102247
$171$	−5.88474	−0.450017
$172$	−2.05555	−0.156734
$173$	14.2561	1.08387	0.541937	−	0.840419i	$-0.317691\pi$
$173$	14.2561	1.08387	0.541937	+	0.840419i	$0.317691\pi$
$174$	−2.80205	−0.212423
$175$	10.3409	0.781697
$176$	−5.27703	−0.397771
$177$	1.00000	0.0751646
$178$	1.42587	0.106873
$179$	−8.22731	−0.614938	−0.307469	−	0.951558i	$-0.599482\pi$
$179$	−8.22731	−0.614938	−0.307469	+	0.951558i	$0.599482\pi$
$180$	−1.33314	−0.0993664
$181$	1.19896	0.0891182	0.0445591	−	0.999007i	$-0.485812\pi$
$181$	1.19896	0.0891182	0.0445591	+	0.999007i	$0.485812\pi$
$182$	14.5784	1.08062
$183$	−6.38088	−0.471688
$184$	3.53990	0.260965
$185$	−15.8490	−1.16525
$186$	2.14265	0.157107
$187$	5.27703	0.385894
$188$	−3.47234	−0.253246
$189$	3.20872	0.233400
$190$	7.84517	0.569149
$191$	−12.5657	−0.909219	−0.454609	−	0.890691i	$-0.650221\pi$
$191$	−12.5657	−0.909219	−0.454609	+	0.890691i	$0.650221\pi$
$192$	−1.00000	−0.0721688
$193$	6.37688	0.459018	0.229509	−	0.973307i	$-0.426288\pi$
$193$	6.37688	0.459018	0.229509	+	0.973307i	$0.426288\pi$
$194$	1.05372	0.0756525
$195$	−6.05693	−0.433746
$196$	3.29590	0.235421
$197$	−7.23753	−0.515653	−0.257827	−	0.966191i	$-0.583006\pi$
$197$	−7.23753	−0.515653	−0.257827	+	0.966191i	$0.583006\pi$
$198$	−5.27703	−0.375022
$199$	−1.70301	−0.120723	−0.0603615	−	0.998177i	$-0.519225\pi$
$199$	−1.70301	−0.120723	−0.0603615	+	0.998177i	$0.519225\pi$
$200$	−3.22274	−0.227882
$201$	6.17650	0.435657
$202$	12.7966	0.900369
$203$	−8.99099	−0.631044
$204$	1.00000	0.0700140
$205$	12.1402	0.847909
$206$	−14.2222	−0.990909
$207$	3.53990	0.246040
$208$	−4.54336	−0.315025
$209$	31.0539	2.14804
$210$	−4.27768	−0.295188
$211$	−6.38376	−0.439476	−0.219738	−	0.975559i	$-0.570520\pi$
$211$	−6.38376	−0.439476	−0.219738	+	0.975559i	$0.570520\pi$
$212$	0.774176	0.0531706
$213$	−12.7528	−0.873809
$214$	15.3758	1.05107
$215$	2.74034	0.186889
$216$	−1.00000	−0.0680414
$217$	6.87518	0.466718
$218$	8.76010	0.593309
$219$	2.22859	0.150594
$220$	7.03501	0.474300
$221$	4.54336	0.305619
$222$	−11.8885	−0.797905
$223$	28.1041	1.88199	0.940993	−	0.338425i	$-0.109894\pi$
$223$	28.1041	1.88199	0.940993	+	0.338425i	$0.109894\pi$
$224$	−3.20872	−0.214392
$225$	−3.22274	−0.214849
$226$	−0.300474	−0.0199873
$227$	−12.5592	−0.833584	−0.416792	−	0.909002i	$-0.636846\pi$
$227$	−12.5592	−0.833584	−0.416792	+	0.909002i	$0.636846\pi$
$228$	5.88474	0.389726
$229$	16.3707	1.08181	0.540903	−	0.841085i	$-0.318083\pi$
$229$	16.3707	1.08181	0.540903	+	0.841085i	$0.318083\pi$
$230$	−4.71918	−0.311173
$231$	−16.9325	−1.11408
$232$	2.80205	0.183963
$233$	13.5092	0.885014	0.442507	−	0.896765i	$-0.354089\pi$
$233$	13.5092	0.885014	0.442507	+	0.896765i	$0.354089\pi$
$234$	−4.54336	−0.297009
$235$	4.62911	0.301970
$236$	−1.00000	−0.0650945
$237$	1.53464	0.0996858
$238$	3.20872	0.207991
$239$	11.5109	0.744576	0.372288	−	0.928117i	$-0.378573\pi$
$239$	11.5109	0.744576	0.372288	+	0.928117i	$0.378573\pi$
$240$	1.33314	0.0860538
$241$	12.5657	0.809428	0.404714	−	0.914443i	$-0.367371\pi$
$241$	12.5657	0.809428	0.404714	+	0.914443i	$0.367371\pi$
$242$	16.8470	1.08297
$243$	−1.00000	−0.0641500
$244$	6.38088	0.408494
$245$	−4.39389	−0.280716
$246$	9.10648	0.580608
$247$	26.7365	1.70120
$248$	−2.14265	−0.136059
$249$	−0.352363	−0.0223301
$250$	10.9621	0.693301
$251$	0.747213	0.0471637	0.0235818	−	0.999722i	$-0.492493\pi$
$251$	0.747213	0.0471637	0.0235818	+	0.999722i	$0.492493\pi$
$252$	−3.20872	−0.202131
$253$	−18.6801	−1.17441
$254$	8.80393	0.552408
$255$	−1.33314	−0.0834844
$256$	1.00000	0.0625000
$257$	−19.7473	−1.23180	−0.615902	−	0.787823i	$-0.711208\pi$
$257$	−19.7473	−1.23180	−0.615902	+	0.787823i	$0.711208\pi$
$258$	2.05555	0.127973
$259$	−38.1469	−2.37034
$260$	6.05693	0.375635
$261$	2.80205	0.173442
$262$	−9.49526	−0.586619
$263$	−8.44343	−0.520644	−0.260322	−	0.965522i	$-0.583829\pi$
$263$	−8.44343	−0.520644	−0.260322	+	0.965522i	$0.583829\pi$
$264$	5.27703	0.324778
$265$	−1.03208	−0.0634004
$266$	18.8825	1.15776
$267$	−1.42587	−0.0872617
$268$	−6.17650	−0.377290
$269$	−27.1547	−1.65565	−0.827827	−	0.560983i	$-0.810423\pi$
$269$	−27.1547	−1.65565	−0.827827	+	0.560983i	$0.810423\pi$
$270$	1.33314	0.0811323
$271$	−1.40337	−0.0852486	−0.0426243	−	0.999091i	$-0.513572\pi$
$271$	−1.40337	−0.0852486	−0.0426243	+	0.999091i	$0.513572\pi$
$272$	−1.00000	−0.0606339
$273$	−14.5784	−0.882323
$274$	−4.01331	−0.242453
$275$	17.0065	1.02553
$276$	−3.53990	−0.213077
$277$	18.1767	1.09213	0.546066	−	0.837742i	$-0.316125\pi$
$277$	18.1767	1.09213	0.546066	+	0.837742i	$0.316125\pi$
$278$	14.3870	0.862874
$279$	−2.14265	−0.128277
$280$	4.27768	0.255640
$281$	23.7487	1.41673	0.708363	−	0.705848i	$-0.249434\pi$
$281$	23.7487	1.41673	0.708363	+	0.705848i	$0.249434\pi$
$282$	3.47234	0.206775
$283$	−6.38546	−0.379576	−0.189788	−	0.981825i	$-0.560780\pi$
$283$	−6.38546	−0.379576	−0.189788	+	0.981825i	$0.560780\pi$
$284$	12.7528	0.756741
$285$	−7.84517	−0.464708
$286$	23.9754	1.41770
$287$	29.2202	1.72481
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	−3.73552	−0.219357
$291$	−1.05372	−0.0617700
$292$	−2.22859	−0.130418
$293$	−11.2246	−0.655746	−0.327873	−	0.944722i	$-0.606332\pi$
$293$	−11.2246	−0.655746	−0.327873	+	0.944722i	$0.606332\pi$
$294$	−3.29590	−0.192221
$295$	1.33314	0.0776184
$296$	11.8885	0.691006
$297$	5.27703	0.306204
$298$	−22.8693	−1.32479
$299$	−16.0830	−0.930105
$300$	3.22274	0.186065
$301$	6.59569	0.380169
$302$	3.34704	0.192600
$303$	−12.7966	−0.735148
$304$	−5.88474	−0.337513
$305$	−8.50661	−0.487087
$306$	−1.00000	−0.0571662
$307$	10.0228	0.572031	0.286016	−	0.958225i	$-0.407669\pi$
$307$	10.0228	0.572031	0.286016	+	0.958225i	$0.407669\pi$
$308$	16.9325	0.964819
$309$	14.2222	0.809074
$310$	2.85646	0.162236
$311$	0.118857	0.00673976	0.00336988	−	0.999994i	$-0.498927\pi$
$311$	0.118857	0.00673976	0.00336988	+	0.999994i	$0.498927\pi$
$312$	4.54336	0.257217
$313$	−23.3964	−1.32244	−0.661221	−	0.750191i	$-0.729962\pi$
$313$	−23.3964	−1.32244	−0.661221	+	0.750191i	$0.729962\pi$
$314$	−15.7615	−0.889473
$315$	4.27768	0.241020
$316$	−1.53464	−0.0863305
$317$	23.0261	1.29327	0.646637	−	0.762798i	$-0.276175\pi$
$317$	23.0261	1.29327	0.646637	+	0.762798i	$0.276175\pi$
$318$	−0.774176	−0.0434136
$319$	−14.7865	−0.827884
$320$	−1.33314	−0.0745248
$321$	−15.3758	−0.858194
$322$	−11.3586	−0.632987
$323$	5.88474	0.327435
$324$	1.00000	0.0555556
$325$	14.6421	0.812195
$326$	−17.8477	−0.988494
$327$	−8.76010	−0.484435
$328$	−9.10648	−0.502821
$329$	11.1418	0.614265
$330$	−7.03501	−0.387265
$331$	−13.7819	−0.757520	−0.378760	−	0.925495i	$-0.623649\pi$
$331$	−13.7819	−0.757520	−0.378760	+	0.925495i	$0.623649\pi$
$332$	0.352363	0.0193384
$333$	11.8885	0.651486
$334$	−17.8906	−0.978929
$335$	8.23414	0.449879
$336$	3.20872	0.175050
$337$	−15.3451	−0.835899	−0.417950	−	0.908470i	$-0.637251\pi$
$337$	−15.3451	−0.835899	−0.417950	+	0.908470i	$0.637251\pi$
$338$	7.64209	0.415675
$339$	0.300474	0.0163195
$340$	1.33314	0.0722996
$341$	11.3068	0.612299
$342$	−5.88474	−0.318210
$343$	11.8854	0.641753
$344$	−2.05555	−0.110828
$345$	4.71918	0.254072
$346$	14.2561	0.766414
$347$	22.7702	1.22237	0.611185	−	0.791488i	$-0.290693\pi$
$347$	22.7702	1.22237	0.611185	+	0.791488i	$0.290693\pi$
$348$	−2.80205	−0.150205
$349$	33.1748	1.77581	0.887904	−	0.460029i	$-0.152161\pi$
$349$	33.1748	1.77581	0.887904	+	0.460029i	$0.152161\pi$
$350$	10.3409	0.552743
$351$	4.54336	0.242506
$352$	−5.27703	−0.281266
$353$	−6.01006	−0.319883	−0.159942	−	0.987126i	$-0.551131\pi$
$353$	−6.01006	−0.319883	−0.159942	+	0.987126i	$0.551131\pi$
$354$	1.00000	0.0531494
$355$	−17.0013	−0.902335
$356$	1.42587	0.0755709
$357$	−3.20872	−0.169824
$358$	−8.22731	−0.434827
$359$	−35.2935	−1.86272	−0.931360	−	0.364100i	$-0.881377\pi$
$359$	−35.2935	−1.86272	−0.931360	+	0.364100i	$0.881377\pi$
$360$	−1.33314	−0.0702626
$361$	15.6301	0.822638
$362$	1.19896	0.0630161
$363$	−16.8470	−0.884238
$364$	14.5784	0.764114
$365$	2.97102	0.155510
$366$	−6.38088	−0.333534
$367$	−27.3355	−1.42690	−0.713450	−	0.700706i	$-0.752868\pi$
$367$	−27.3355	−1.42690	−0.713450	+	0.700706i	$0.752868\pi$
$368$	3.53990	0.184530
$369$	−9.10648	−0.474064
$370$	−15.8490	−0.823953
$371$	−2.48412	−0.128969
$372$	2.14265	0.111091
$373$	24.2759	1.25696	0.628480	−	0.777825i	$-0.283677\pi$
$373$	24.2759	1.25696	0.628480	+	0.777825i	$0.283677\pi$
$374$	5.27703	0.272869
$375$	−10.9621	−0.566078
$376$	−3.47234	−0.179072
$377$	−12.7307	−0.655664
$378$	3.20872	0.165039
$379$	25.3543	1.30237	0.651183	−	0.758921i	$-0.274273\pi$
$379$	25.3543	1.30237	0.651183	+	0.758921i	$0.274273\pi$
$380$	7.84517	0.402449
$381$	−8.80393	−0.451039
$382$	−12.5657	−0.642915
$383$	3.53263	0.180509	0.0902544	−	0.995919i	$-0.471232\pi$
$383$	3.53263	0.180509	0.0902544	+	0.995919i	$0.471232\pi$
$384$	−1.00000	−0.0510310
$385$	−22.5734	−1.15045
$386$	6.37688	0.324575
$387$	−2.05555	−0.104489
$388$	1.05372	0.0534944
$389$	16.3791	0.830455	0.415228	−	0.909718i	$-0.363702\pi$
$389$	16.3791	0.830455	0.415228	+	0.909718i	$0.363702\pi$
$390$	−6.05693	−0.306705
$391$	−3.53990	−0.179020
$392$	3.29590	0.166468
$393$	9.49526	0.478972
$394$	−7.23753	−0.364622
$395$	2.04589	0.102940
$396$	−5.27703	−0.265181
$397$	10.2742	0.515645	0.257823	−	0.966192i	$-0.416995\pi$
$397$	10.2742	0.515645	0.257823	+	0.966192i	$0.416995\pi$
$398$	−1.70301	−0.0853640
$399$	−18.8825	−0.945307
$400$	−3.22274	−0.161137
$401$	9.08250	0.453558	0.226779	−	0.973946i	$-0.427180\pi$
$401$	9.08250	0.453558	0.226779	+	0.973946i	$0.427180\pi$
$402$	6.17650	0.308056
$403$	9.73484	0.484927
$404$	12.7966	0.636657
$405$	−1.33314	−0.0662442
$406$	−8.99099	−0.446215
$407$	−62.7360	−3.10971
$408$	1.00000	0.0495074
$409$	−26.3211	−1.30149	−0.650746	−	0.759295i	$-0.725544\pi$
$409$	−26.3211	−1.30149	−0.650746	+	0.759295i	$0.725544\pi$
$410$	12.1402	0.599562
$411$	4.01331	0.197962
$412$	−14.2222	−0.700679
$413$	3.20872	0.157891
$414$	3.53990	0.173977
$415$	−0.469749	−0.0230591
$416$	−4.54336	−0.222756
$417$	−14.3870	−0.704534
$418$	31.0539	1.51890
$419$	13.6461	0.666657	0.333329	−	0.942811i	$-0.391828\pi$
$419$	13.6461	0.666657	0.333329	+	0.942811i	$0.391828\pi$
$420$	−4.27768	−0.208729
$421$	36.6883	1.78808	0.894040	−	0.447987i	$-0.147859\pi$
$421$	36.6883	1.78808	0.894040	+	0.447987i	$0.147859\pi$
$422$	−6.38376	−0.310757
$423$	−3.47234	−0.168831
$424$	0.774176	0.0375973
$425$	3.22274	0.156326
$426$	−12.7528	−0.617876
$427$	−20.4745	−0.990830
$428$	15.3758	0.743218
$429$	−23.9754	−1.15754
$430$	2.74034	0.132151
$431$	−16.5386	−0.796638	−0.398319	−	0.917247i	$-0.630406\pi$
$431$	−16.5386	−0.796638	−0.398319	+	0.917247i	$0.630406\pi$
$432$	−1.00000	−0.0481125
$433$	−7.16092	−0.344132	−0.172066	−	0.985085i	$-0.555044\pi$
$433$	−7.16092	−0.344132	−0.172066	+	0.985085i	$0.555044\pi$
$434$	6.87518	0.330019
$435$	3.73552	0.179104
$436$	8.76010	0.419533
$437$	−20.8314	−0.996499
$438$	2.22859	0.106486
$439$	5.73093	0.273523	0.136761	−	0.990604i	$-0.456331\pi$
$439$	5.73093	0.273523	0.136761	+	0.990604i	$0.456331\pi$
$440$	7.03501	0.335381
$441$	3.29590	0.156948
$442$	4.54336	0.216105
$443$	19.0261	0.903955	0.451978	−	0.892029i	$-0.350719\pi$
$443$	19.0261	0.903955	0.451978	+	0.892029i	$0.350719\pi$
$444$	−11.8885	−0.564204
$445$	−1.90088	−0.0901104
$446$	28.1041	1.33077
$447$	22.8693	1.08168
$448$	−3.20872	−0.151598
$449$	5.28529	0.249428	0.124714	−	0.992193i	$-0.460199\pi$
$449$	5.28529	0.249428	0.124714	+	0.992193i	$0.460199\pi$
$450$	−3.22274	−0.151921
$451$	48.0551	2.26283
$452$	−0.300474	−0.0141331
$453$	−3.34704	−0.157257
$454$	−12.5592	−0.589433
$455$	−19.4350	−0.911127
$456$	5.88474	0.275578
$457$	10.3945	0.486234	0.243117	−	0.969997i	$-0.421830\pi$
$457$	10.3945	0.486234	0.243117	+	0.969997i	$0.421830\pi$
$458$	16.3707	0.764952
$459$	1.00000	0.0466760
$460$	−4.71918	−0.220033
$461$	10.1277	0.471692	0.235846	−	0.971790i	$-0.424214\pi$
$461$	10.1277	0.471692	0.235846	+	0.971790i	$0.424214\pi$
$462$	−16.9325	−0.787772
$463$	18.9901	0.882544	0.441272	−	0.897374i	$-0.354527\pi$
$463$	18.9901	0.882544	0.441272	+	0.897374i	$0.354527\pi$
$464$	2.80205	0.130082
$465$	−2.85646	−0.132465
$466$	13.5092	0.625799
$467$	5.39549	0.249674	0.124837	−	0.992177i	$-0.460159\pi$
$467$	5.39549	0.249674	0.124837	+	0.992177i	$0.460159\pi$
$468$	−4.54336	−0.210017
$469$	19.8187	0.915142
$470$	4.62911	0.213525
$471$	15.7615	0.726252
$472$	−1.00000	−0.0460287
$473$	10.8472	0.498754
$474$	1.53464	0.0704885
$475$	18.9650	0.870172
$476$	3.20872	0.147072
$477$	0.774176	0.0354471
$478$	11.5109	0.526495
$479$	−3.73655	−0.170727	−0.0853637	−	0.996350i	$-0.527205\pi$
$479$	−3.73655	−0.170727	−0.0853637	+	0.996350i	$0.527205\pi$
$480$	1.33314	0.0608492
$481$	−54.0138	−2.46282
$482$	12.5657	0.572352
$483$	11.3586	0.516832
$484$	16.8470	0.765773
$485$	−1.40475	−0.0637866
$486$	−1.00000	−0.0453609
$487$	−31.1690	−1.41240	−0.706202	−	0.708011i	$-0.749593\pi$
$487$	−31.1690	−1.41240	−0.706202	+	0.708011i	$0.749593\pi$
$488$	6.38088	0.288849
$489$	17.8477	0.807102
$490$	−4.39389	−0.198496
$491$	−28.1507	−1.27042	−0.635212	−	0.772338i	$-0.719087\pi$
$491$	−28.1507	−1.27042	−0.635212	+	0.772338i	$0.719087\pi$
$492$	9.10648	0.410552
$493$	−2.80205	−0.126198
$494$	26.7365	1.20293
$495$	7.03501	0.316200
$496$	−2.14265	−0.0962080
$497$	−40.9203	−1.83552
$498$	−0.352363	−0.0157898
$499$	25.0049	1.11937	0.559686	−	0.828705i	$-0.310922\pi$
$499$	25.0049	1.11937	0.559686	+	0.828705i	$0.310922\pi$
$500$	10.9621	0.490238
$501$	17.8906	0.799292
$502$	0.747213	0.0333497
$503$	23.5247	1.04891	0.524457	−	0.851437i	$-0.324268\pi$
$503$	23.5247	1.04891	0.524457	+	0.851437i	$0.324268\pi$
$504$	−3.20872	−0.142928
$505$	−17.0597	−0.759147
$506$	−18.6801	−0.830433
$507$	−7.64209	−0.339397
$508$	8.80393	0.390611
$509$	−10.1719	−0.450864	−0.225432	−	0.974259i	$-0.572379\pi$
$509$	−10.1719	−0.450864	−0.225432	+	0.974259i	$0.572379\pi$
$510$	−1.33314	−0.0590324
$511$	7.15092	0.316338
$512$	1.00000	0.0441942
$513$	5.88474	0.259817
$514$	−19.7473	−0.871017
$515$	18.9602	0.835487
$516$	2.05555	0.0904906
$517$	18.3236	0.805871
$518$	−38.1469	−1.67608
$519$	−14.2561	−0.625775
$520$	6.05693	0.265614
$521$	−6.68835	−0.293022	−0.146511	−	0.989209i	$-0.546804\pi$
$521$	−6.68835	−0.293022	−0.146511	+	0.989209i	$0.546804\pi$
$522$	2.80205	0.122642
$523$	4.70891	0.205906	0.102953	−	0.994686i	$-0.467171\pi$
$523$	4.70891	0.205906	0.102953	+	0.994686i	$0.467171\pi$
$524$	−9.49526	−0.414802
$525$	−10.3409	−0.451313
$526$	−8.44343	−0.368151
$527$	2.14265	0.0933354
$528$	5.27703	0.229653
$529$	−10.4691	−0.455179
$530$	−1.03208	−0.0448309
$531$	−1.00000	−0.0433963
$532$	18.8825	0.818659
$533$	41.3740	1.79211
$534$	−1.42587	−0.0617034
$535$	−20.4981	−0.886211
$536$	−6.17650	−0.266784
$537$	8.22731	0.355035
$538$	−27.1547	−1.17072
$539$	−17.3925	−0.749150
$540$	1.33314	0.0573692
$541$	26.4351	1.13653	0.568266	−	0.822845i	$-0.307614\pi$
$541$	26.4351	1.13653	0.568266	+	0.822845i	$0.307614\pi$
$542$	−1.40337	−0.0602799
$543$	−1.19896	−0.0514524
$544$	−1.00000	−0.0428746
$545$	−11.6784	−0.500249
$546$	−14.5784	−0.623897
$547$	−11.6622	−0.498639	−0.249320	−	0.968421i	$-0.580207\pi$
$547$	−11.6622	−0.498639	−0.249320	+	0.968421i	$0.580207\pi$
$548$	−4.01331	−0.171440
$549$	6.38088	0.272329
$550$	17.0065	0.725159
$551$	−16.4893	−0.702468
$552$	−3.53990	−0.150668
$553$	4.92425	0.209400
$554$	18.1767	0.772254
$555$	15.8490	0.672755
$556$	14.3870	0.610144
$557$	−41.2448	−1.74760	−0.873799	−	0.486287i	$-0.838351\pi$
$557$	−41.2448	−1.74760	−0.873799	+	0.486287i	$0.838351\pi$
$558$	−2.14265	−0.0907057
$559$	9.33910	0.395002
$560$	4.27768	0.180765
$561$	−5.27703	−0.222796
$562$	23.7487	1.00178
$563$	22.4107	0.944497	0.472248	−	0.881466i	$-0.343443\pi$
$563$	22.4107	0.944497	0.472248	+	0.881466i	$0.343443\pi$
$564$	3.47234	0.146212
$565$	0.400574	0.0168523
$566$	−6.38546	−0.268401
$567$	−3.20872	−0.134754
$568$	12.7528	0.535096
$569$	−8.15845	−0.342020	−0.171010	−	0.985269i	$-0.554703\pi$
$569$	−8.15845	−0.342020	−0.171010	+	0.985269i	$0.554703\pi$
$570$	−7.84517	−0.328598
$571$	3.54234	0.148242	0.0741212	−	0.997249i	$-0.476385\pi$
$571$	3.54234	0.148242	0.0741212	+	0.997249i	$0.476385\pi$
$572$	23.9754	1.00246
$573$	12.5657	0.524938
$574$	29.2202	1.21963
$575$	−11.4082	−0.475754
$576$	1.00000	0.0416667
$577$	26.9388	1.12148	0.560739	−	0.827992i	$-0.310517\pi$
$577$	26.9388	1.12148	0.560739	+	0.827992i	$0.310517\pi$
$578$	1.00000	0.0415945
$579$	−6.37688	−0.265014
$580$	−3.73552	−0.155109
$581$	−1.13064	−0.0469067
$582$	−1.05372	−0.0436780
$583$	−4.08535	−0.169198
$584$	−2.22859	−0.0922196
$585$	6.05693	0.250423
$586$	−11.2246	−0.463683
$587$	−23.9740	−0.989514	−0.494757	−	0.869031i	$-0.664743\pi$
$587$	−23.9740	−0.989514	−0.494757	+	0.869031i	$0.664743\pi$
$588$	−3.29590	−0.135921
$589$	12.6089	0.519543
$590$	1.33314	0.0548845
$591$	7.23753	0.297712
$592$	11.8885	0.488615
$593$	−13.5603	−0.556854	−0.278427	−	0.960457i	$-0.589813\pi$
$593$	−13.5603	−0.556854	−0.278427	+	0.960457i	$0.589813\pi$
$594$	5.27703	0.216519
$595$	−4.27768	−0.175368
$596$	−22.8693	−0.936765
$597$	1.70301	0.0696994
$598$	−16.0830	−0.657684
$599$	2.15788	0.0881686	0.0440843	−	0.999028i	$-0.485963\pi$
$599$	2.15788	0.0881686	0.0440843	+	0.999028i	$0.485963\pi$
$600$	3.22274	0.131568
$601$	18.8167	0.767547	0.383774	−	0.923427i	$-0.374624\pi$
$601$	18.8167	0.767547	0.383774	+	0.923427i	$0.374624\pi$
$602$	6.59569	0.268820
$603$	−6.17650	−0.251527
$604$	3.34704	0.136189
$605$	−22.4594	−0.913105
$606$	−12.7966	−0.519828
$607$	16.8479	0.683833	0.341917	−	0.939730i	$-0.388924\pi$
$607$	16.8479	0.683833	0.341917	+	0.939730i	$0.388924\pi$
$608$	−5.88474	−0.238658
$609$	8.99099	0.364333
$610$	−8.50661	−0.344422
$611$	15.7761	0.638231
$612$	−1.00000	−0.0404226
$613$	−26.0791	−1.05332	−0.526662	−	0.850075i	$-0.676557\pi$
$613$	−26.0791	−1.05332	−0.526662	+	0.850075i	$0.676557\pi$
$614$	10.0228	0.404487
$615$	−12.1402	−0.489540
$616$	16.9325	0.682230
$617$	−18.5362	−0.746240	−0.373120	−	0.927783i	$-0.621712\pi$
$617$	−18.5362	−0.746240	−0.373120	+	0.927783i	$0.621712\pi$
$618$	14.2222	0.572102
$619$	−2.13884	−0.0859671	−0.0429836	−	0.999076i	$-0.513686\pi$
$619$	−2.13884	−0.0859671	−0.0429836	+	0.999076i	$0.513686\pi$
$620$	2.85646	0.114718
$621$	−3.53990	−0.142051
$622$	0.118857	0.00476573
$623$	−4.57522	−0.183302
$624$	4.54336	0.181880
$625$	1.49974	0.0599895
$626$	−23.3964	−0.935108
$627$	−31.0539	−1.24017
$628$	−15.7615	−0.628952
$629$	−11.8885	−0.474026
$630$	4.27768	0.170427
$631$	−26.5503	−1.05695	−0.528476	−	0.848948i	$-0.677236\pi$
$631$	−26.5503	−1.05695	−0.528476	+	0.848948i	$0.677236\pi$
$632$	−1.53464	−0.0610449
$633$	6.38376	0.253732
$634$	23.0261	0.914482
$635$	−11.7369	−0.465764
$636$	−0.774176	−0.0306981
$637$	−14.9744	−0.593309
$638$	−14.7865	−0.585402
$639$	12.7528	0.504494
$640$	−1.33314	−0.0526970
$641$	−14.7310	−0.581840	−0.290920	−	0.956747i	$-0.593961\pi$
$641$	−14.7310	−0.581840	−0.290920	+	0.956747i	$0.593961\pi$
$642$	−15.3758	−0.606835
$643$	−27.1237	−1.06966	−0.534828	−	0.844961i	$-0.679623\pi$
$643$	−27.1237	−1.06966	−0.534828	+	0.844961i	$0.679623\pi$
$644$	−11.3586	−0.447590
$645$	−2.74034	−0.107901
$646$	5.88474	0.231532
$647$	−34.1230	−1.34151	−0.670756	−	0.741678i	$-0.734030\pi$
$647$	−34.1230	−1.34151	−0.670756	+	0.741678i	$0.734030\pi$
$648$	1.00000	0.0392837
$649$	5.27703	0.207141
$650$	14.6421	0.574309
$651$	−6.87518	−0.269459
$652$	−17.8477	−0.698971
$653$	21.2039	0.829774	0.414887	−	0.909873i	$-0.363821\pi$
$653$	21.2039	0.829774	0.414887	+	0.909873i	$0.363821\pi$
$654$	−8.76010	−0.342547
$655$	12.6585	0.494609
$656$	−9.10648	−0.355548
$657$	−2.22859	−0.0869455
$658$	11.1418	0.434351
$659$	14.2148	0.553730	0.276865	−	0.960909i	$-0.410705\pi$
$659$	14.2148	0.553730	0.276865	+	0.960909i	$0.410705\pi$
$660$	−7.03501	−0.273837
$661$	−37.3006	−1.45083	−0.725413	−	0.688314i	$-0.758351\pi$
$661$	−37.3006	−1.45083	−0.725413	+	0.688314i	$0.758351\pi$
$662$	−13.7819	−0.535648
$663$	−4.54336	−0.176449
$664$	0.352363	0.0136743
$665$	−25.1730	−0.976167
$666$	11.8885	0.460670
$667$	9.91896	0.384064
$668$	−17.8906	−0.692208
$669$	−28.1041	−1.08657
$670$	8.23414	0.318113
$671$	−33.6721	−1.29990
$672$	3.20872	0.123779
$673$	40.0933	1.54548	0.772742	−	0.634720i	$-0.218885\pi$
$673$	40.0933	1.54548	0.772742	+	0.634720i	$0.218885\pi$
$674$	−15.3451	−0.591070
$675$	3.22274	0.124043
$676$	7.64209	0.293927
$677$	39.0613	1.50125	0.750624	−	0.660729i	$-0.229753\pi$
$677$	39.0613	1.50125	0.750624	+	0.660729i	$0.229753\pi$
$678$	0.300474	0.0115397
$679$	−3.38109	−0.129754
$680$	1.33314	0.0511236
$681$	12.5592	0.481270
$682$	11.3068	0.432961
$683$	−35.1070	−1.34333	−0.671666	−	0.740854i	$-0.734421\pi$
$683$	−35.1070	−1.34333	−0.671666	+	0.740854i	$0.734421\pi$
$684$	−5.88474	−0.225008
$685$	5.35030	0.204424
$686$	11.8854	0.453788
$687$	−16.3707	−0.624581
$688$	−2.05555	−0.0783671
$689$	−3.51736	−0.134001
$690$	4.71918	0.179656
$691$	−1.82091	−0.0692706	−0.0346353	−	0.999400i	$-0.511027\pi$
$691$	−1.82091	−0.0692706	−0.0346353	+	0.999400i	$0.511027\pi$
$692$	14.2561	0.541937
$693$	16.9325	0.643213
$694$	22.7702	0.864346
$695$	−19.1799	−0.727534
$696$	−2.80205	−0.106211
$697$	9.10648	0.344932
$698$	33.1748	1.25569
$699$	−13.5092	−0.510963
$700$	10.3409	0.390848
$701$	8.30317	0.313607	0.156803	−	0.987630i	$-0.449881\pi$
$701$	8.30317	0.313607	0.156803	+	0.987630i	$0.449881\pi$
$702$	4.54336	0.171478
$703$	−69.9607	−2.63862
$704$	−5.27703	−0.198885
$705$	−4.62911	−0.174342
$706$	−6.01006	−0.226192
$707$	−41.0609	−1.54425
$708$	1.00000	0.0375823
$709$	−26.4860	−0.994701	−0.497351	−	0.867550i	$-0.665694\pi$
$709$	−26.4860	−0.994701	−0.497351	+	0.867550i	$0.665694\pi$
$710$	−17.0013	−0.638047
$711$	−1.53464	−0.0575536
$712$	1.42587	0.0534367
$713$	−7.58477	−0.284052
$714$	−3.20872	−0.120083
$715$	−31.9626	−1.19533
$716$	−8.22731	−0.307469
$717$	−11.5109	−0.429881
$718$	−35.2935	−1.31714
$719$	19.1091	0.712649	0.356325	−	0.934362i	$-0.384030\pi$
$719$	19.1091	0.712649	0.356325	+	0.934362i	$0.384030\pi$
$720$	−1.33314	−0.0496832
$721$	45.6352	1.69954
$722$	15.6301	0.581693
$723$	−12.5657	−0.467324
$724$	1.19896	0.0445591
$725$	−9.03027	−0.335376
$726$	−16.8470	−0.625251
$727$	35.4874	1.31615	0.658077	−	0.752950i	$-0.271370\pi$
$727$	35.4874	1.31615	0.658077	+	0.752950i	$0.271370\pi$
$728$	14.5784	0.540310
$729$	1.00000	0.0370370
$730$	2.97102	0.109962
$731$	2.05555	0.0760273
$732$	−6.38088	−0.235844
$733$	15.2520	0.563347	0.281674	−	0.959510i	$-0.409110\pi$
$733$	15.2520	0.563347	0.281674	+	0.959510i	$0.409110\pi$
$734$	−27.3355	−1.00897
$735$	4.39389	0.162071
$736$	3.53990	0.130482
$737$	32.5936	1.20060
$738$	−9.10648	−0.335214
$739$	−36.6986	−1.34998	−0.674990	−	0.737827i	$-0.735852\pi$
$739$	−36.6986	−1.34998	−0.674990	+	0.737827i	$0.735852\pi$
$740$	−15.8490	−0.582623
$741$	−26.7365	−0.982188
$742$	−2.48412	−0.0911947
$743$	−30.3799	−1.11453	−0.557265	−	0.830334i	$-0.688149\pi$
$743$	−30.3799	−1.11453	−0.557265	+	0.830334i	$0.688149\pi$
$744$	2.14265	0.0785535
$745$	30.4880	1.11699
$746$	24.2759	0.888805
$747$	0.352363	0.0128923
$748$	5.27703	0.192947
$749$	−49.3367	−1.80272
$750$	−10.9621	−0.400278
$751$	−43.5762	−1.59012	−0.795058	−	0.606533i	$-0.792560\pi$
$751$	−43.5762	−1.59012	−0.795058	+	0.606533i	$0.792560\pi$
$752$	−3.47234	−0.126623
$753$	−0.747213	−0.0272299
$754$	−12.7307	−0.463625
$755$	−4.46207	−0.162391
$756$	3.20872	0.116700
$757$	−8.44983	−0.307114	−0.153557	−	0.988140i	$-0.549073\pi$
$757$	−8.44983	−0.307114	−0.153557	+	0.988140i	$0.549073\pi$
$758$	25.3543	0.920911
$759$	18.6801	0.678046
$760$	7.84517	0.284574
$761$	−38.2416	−1.38626	−0.693129	−	0.720814i	$-0.743768\pi$
$761$	−38.2416	−1.38626	−0.693129	+	0.720814i	$0.743768\pi$
$762$	−8.80393	−0.318933
$763$	−28.1087	−1.01760
$764$	−12.5657	−0.454609
$765$	1.33314	0.0481998
$766$	3.53263	0.127639
$767$	4.54336	0.164051
$768$	−1.00000	−0.0360844
$769$	−10.2056	−0.368023	−0.184012	−	0.982924i	$-0.558908\pi$
$769$	−10.2056	−0.368023	−0.184012	+	0.982924i	$0.558908\pi$
$770$	−22.5734	−0.813489
$771$	19.7473	0.711183
$772$	6.37688	0.229509
$773$	18.4963	0.665264	0.332632	−	0.943057i	$-0.392063\pi$
$773$	18.4963	0.665264	0.332632	+	0.943057i	$0.392063\pi$
$774$	−2.05555	−0.0738852
$775$	6.90521	0.248042
$776$	1.05372	0.0378263
$777$	38.1469	1.36851
$778$	16.3791	0.587220
$779$	53.5892	1.92003
$780$	−6.05693	−0.216873
$781$	−67.2970	−2.40807
$782$	−3.53990	−0.126587
$783$	−2.80205	−0.100137
$784$	3.29590	0.117711
$785$	21.0123	0.749961
$786$	9.49526	0.338685
$787$	29.0456	1.03536	0.517682	−	0.855573i	$-0.326795\pi$
$787$	29.0456	1.03536	0.517682	+	0.855573i	$0.326795\pi$
$788$	−7.23753	−0.257827
$789$	8.44343	0.300594
$790$	2.04589	0.0727897
$791$	0.964139	0.0342808
$792$	−5.27703	−0.187511
$793$	−28.9906	−1.02949
$794$	10.2742	0.364616
$795$	1.03208	0.0366043
$796$	−1.70301	−0.0603615
$797$	34.8204	1.23340	0.616701	−	0.787198i	$-0.288469\pi$
$797$	34.8204	1.23340	0.616701	+	0.787198i	$0.288469\pi$
$798$	−18.8825	−0.668433
$799$	3.47234	0.122842
$800$	−3.22274	−0.113941
$801$	1.42587	0.0503806
$802$	9.08250	0.320714
$803$	11.7603	0.415013
$804$	6.17650	0.217828
$805$	15.1425	0.533704
$806$	9.73484	0.342895
$807$	27.1547	0.955892
$808$	12.7966	0.450184
$809$	−33.7317	−1.18594	−0.592972	−	0.805223i	$-0.702046\pi$
$809$	−33.7317	−1.18594	−0.592972	+	0.805223i	$0.702046\pi$
$810$	−1.33314	−0.0468418
$811$	5.68199	0.199522	0.0997609	−	0.995011i	$-0.468192\pi$
$811$	5.68199	0.199522	0.0997609	+	0.995011i	$0.468192\pi$
$812$	−8.99099	−0.315522
$813$	1.40337	0.0492183
$814$	−62.7360	−2.19889
$815$	23.7935	0.833450
$816$	1.00000	0.0350070
$817$	12.0964	0.423198
$818$	−26.3211	−0.920294
$819$	14.5784	0.509410
$820$	12.1402	0.423954
$821$	−0.629893	−0.0219834	−0.0109917	−	0.999940i	$-0.503499\pi$
$821$	−0.629893	−0.0219834	−0.0109917	+	0.999940i	$0.503499\pi$
$822$	4.01331	0.139980
$823$	41.4837	1.44603	0.723016	−	0.690832i	$-0.242755\pi$
$823$	41.4837	1.44603	0.723016	+	0.690832i	$0.242755\pi$
$824$	−14.2222	−0.495455
$825$	−17.0065	−0.592089
$826$	3.20872	0.111646
$827$	15.6487	0.544158	0.272079	−	0.962275i	$-0.412289\pi$
$827$	15.6487	0.544158	0.272079	+	0.962275i	$0.412289\pi$
$828$	3.53990	0.123020
$829$	9.39901	0.326441	0.163221	−	0.986590i	$-0.447812\pi$
$829$	9.39901	0.326441	0.163221	+	0.986590i	$0.447812\pi$
$830$	−0.469749	−0.0163052
$831$	−18.1767	−0.630542
$832$	−4.54336	−0.157513
$833$	−3.29590	−0.114196
$834$	−14.3870	−0.498181
$835$	23.8507	0.825386
$836$	31.0539	1.07402
$837$	2.14265	0.0740609
$838$	13.6461	0.471398
$839$	20.4182	0.704913	0.352457	−	0.935828i	$-0.385346\pi$
$839$	20.4182	0.704913	0.352457	+	0.935828i	$0.385346\pi$
$840$	−4.27768	−0.147594
$841$	−21.1485	−0.729260
$842$	36.6883	1.26436
$843$	−23.7487	−0.817947
$844$	−6.38376	−0.219738
$845$	−10.1880	−0.350477
$846$	−3.47234	−0.119381
$847$	−54.0573	−1.85743
$848$	0.774176	0.0265853
$849$	6.38546	0.219148
$850$	3.22274	0.110539
$851$	42.0841	1.44263
$852$	−12.7528	−0.436904
$853$	33.0765	1.13252	0.566260	−	0.824227i	$-0.308390\pi$
$853$	33.0765	1.13252	0.566260	+	0.824227i	$0.308390\pi$
$854$	−20.4745	−0.700622
$855$	7.84517	0.268299
$856$	15.3758	0.525535
$857$	−13.6191	−0.465221	−0.232611	−	0.972570i	$-0.574727\pi$
$857$	−13.6191	−0.465221	−0.232611	+	0.972570i	$0.574727\pi$
$858$	−23.9754	−0.818507
$859$	22.8794	0.780635	0.390318	−	0.920680i	$-0.372365\pi$
$859$	22.8794	0.780635	0.390318	+	0.920680i	$0.372365\pi$
$860$	2.74034	0.0934447
$861$	−29.2202	−0.995820
$862$	−16.5386	−0.563308
$863$	−23.5738	−0.802461	−0.401231	−	0.915977i	$-0.631417\pi$
$863$	−23.5738	−0.802461	−0.401231	+	0.915977i	$0.631417\pi$
$864$	−1.00000	−0.0340207
$865$	−19.0054	−0.646203
$866$	−7.16092	−0.243338
$867$	−1.00000	−0.0339618
$868$	6.87518	0.233359
$869$	8.09835	0.274718
$870$	3.73552	0.126646
$871$	28.0621	0.950847
$872$	8.76010	0.296655
$873$	1.05372	0.0356629
$874$	−20.8314	−0.704632
$875$	−35.1742	−1.18911
$876$	2.22859	0.0752970
$877$	3.64679	0.123143	0.0615717	−	0.998103i	$-0.480389\pi$
$877$	3.64679	0.123143	0.0615717	+	0.998103i	$0.480389\pi$
$878$	5.73093	0.193410
$879$	11.2246	0.378595
$880$	7.03501	0.237150
$881$	1.22988	0.0414357	0.0207179	−	0.999785i	$-0.493405\pi$
$881$	1.22988	0.0414357	0.0207179	+	0.999785i	$0.493405\pi$
$882$	3.29590	0.110979
$883$	−6.03513	−0.203098	−0.101549	−	0.994831i	$-0.532380\pi$
$883$	−6.03513	−0.203098	−0.101549	+	0.994831i	$0.532380\pi$
$884$	4.54336	0.152810
$885$	−1.33314	−0.0448130
$886$	19.0261	0.639193
$887$	−15.9812	−0.536597	−0.268299	−	0.963336i	$-0.586461\pi$
$887$	−15.9812	−0.536597	−0.268299	+	0.963336i	$0.586461\pi$
$888$	−11.8885	−0.398952
$889$	−28.2494	−0.947454
$890$	−1.90088	−0.0637177
$891$	−5.27703	−0.176787
$892$	28.1041	0.940993
$893$	20.4338	0.683790
$894$	22.8693	0.764865
$895$	10.9682	0.366625
$896$	−3.20872	−0.107196
$897$	16.0830	0.536997
$898$	5.28529	0.176372
$899$	−6.00381	−0.200238
$900$	−3.22274	−0.107425
$901$	−0.774176	−0.0257915
$902$	48.0551	1.60006
$903$	−6.59569	−0.219491
$904$	−0.300474	−0.00999363
$905$	−1.59838	−0.0531321
$906$	−3.34704	−0.111198
$907$	39.7877	1.32113	0.660564	−	0.750769i	$-0.270317\pi$
$907$	39.7877	1.32113	0.660564	+	0.750769i	$0.270317\pi$
$908$	−12.5592	−0.416792
$909$	12.7966	0.424438
$910$	−19.4350	−0.644264
$911$	−36.1996	−1.19935	−0.599674	−	0.800245i	$-0.704703\pi$
$911$	−36.1996	−1.19935	−0.599674	+	0.800245i	$0.704703\pi$
$912$	5.88474	0.194863
$913$	−1.85943	−0.0615381
$914$	10.3945	0.343820
$915$	8.50661	0.281220
$916$	16.3707	0.540903
$917$	30.4676	1.00613
$918$	1.00000	0.0330049
$919$	34.6403	1.14268	0.571339	−	0.820714i	$-0.306424\pi$
$919$	34.6403	1.14268	0.571339	+	0.820714i	$0.306424\pi$
$920$	−4.71918	−0.155587
$921$	−10.0228	−0.330262
$922$	10.1277	0.333537
$923$	−57.9406	−1.90714
$924$	−16.9325	−0.557039
$925$	−38.3136	−1.25974
$926$	18.9901	0.624053
$927$	−14.2222	−0.467119
$928$	2.80205	0.0919817
$929$	40.9365	1.34308	0.671542	−	0.740966i	$-0.265632\pi$
$929$	40.9365	1.34308	0.671542	+	0.740966i	$0.265632\pi$
$930$	−2.85646	−0.0936669
$931$	−19.3955	−0.635662
$932$	13.5092	0.442507
$933$	−0.118857	−0.00389120
$934$	5.39549	0.176546
$935$	−7.03501	−0.230070
$936$	−4.54336	−0.148504
$937$	44.2680	1.44617	0.723087	−	0.690757i	$-0.242723\pi$
$937$	44.2680	1.44617	0.723087	+	0.690757i	$0.242723\pi$
$938$	19.8187	0.647103
$939$	23.3964	0.763513
$940$	4.62911	0.150985
$941$	−2.43353	−0.0793307	−0.0396654	−	0.999213i	$-0.512629\pi$
$941$	−2.43353	−0.0793307	−0.0396654	+	0.999213i	$0.512629\pi$
$942$	15.7615	0.513538
$943$	−32.2360	−1.04975
$944$	−1.00000	−0.0325472
$945$	−4.27768	−0.139153
$946$	10.8472	0.352673
$947$	−9.22651	−0.299821	−0.149911	−	0.988700i	$-0.547899\pi$
$947$	−9.22651	−0.299821	−0.149911	+	0.988700i	$0.547899\pi$
$948$	1.53464	0.0498429
$949$	10.1253	0.328680
$950$	18.9650	0.615305
$951$	−23.0261	−0.746672
$952$	3.20872	0.103995
$953$	8.10410	0.262518	0.131259	−	0.991348i	$-0.458098\pi$
$953$	8.10410	0.262518	0.131259	+	0.991348i	$0.458098\pi$
$954$	0.774176	0.0250649
$955$	16.7518	0.542074
$956$	11.5109	0.372288
$957$	14.7865	0.477979
$958$	−3.73655	−0.120722
$959$	12.8776	0.415839
$960$	1.33314	0.0430269
$961$	−26.4090	−0.851904
$962$	−54.0138	−1.74147
$963$	15.3758	0.495479
$964$	12.5657	0.404714
$965$	−8.50127	−0.273666
$966$	11.3586	0.365455
$967$	−23.6772	−0.761407	−0.380703	−	0.924697i	$-0.624318\pi$
$967$	−23.6772	−0.761407	−0.380703	+	0.924697i	$0.624318\pi$
$968$	16.8470	0.541483
$969$	−5.88474	−0.189045
$970$	−1.40475	−0.0451039
$971$	−51.3546	−1.64805	−0.824024	−	0.566555i	$-0.808276\pi$
$971$	−51.3546	−1.64805	−0.824024	+	0.566555i	$0.808276\pi$
$972$	−1.00000	−0.0320750
$973$	−46.1639	−1.47995
$974$	−31.1690	−0.998720
$975$	−14.6421	−0.468921
$976$	6.38088	0.204247
$977$	−11.3078	−0.361769	−0.180885	−	0.983504i	$-0.557896\pi$
$977$	−11.3078	−0.361769	−0.180885	+	0.983504i	$0.557896\pi$
$978$	17.8477	0.570707
$979$	−7.52434	−0.240479
$980$	−4.39389	−0.140358
$981$	8.76010	0.279689
$982$	−28.1507	−0.898325
$983$	18.4159	0.587375	0.293687	−	0.955902i	$-0.405118\pi$
$983$	18.4159	0.587375	0.293687	+	0.955902i	$0.405118\pi$
$984$	9.10648	0.290304
$985$	9.64864	0.307431
$986$	−2.80205	−0.0892354
$987$	−11.1418	−0.354646
$988$	26.7365	0.850600
$989$	−7.27644	−0.231377
$990$	7.03501	0.223587
$991$	24.8589	0.789669	0.394834	−	0.918752i	$-0.370802\pi$
$991$	24.8589	0.789669	0.394834	+	0.918752i	$0.370802\pi$
$992$	−2.14265	−0.0680293
$993$	13.7819	0.437355
$994$	−40.9203	−1.29791
$995$	2.27035	0.0719748
$996$	−0.352363	−0.0111651
$997$	−30.3360	−0.960752	−0.480376	−	0.877063i	$-0.659500\pi$
$997$	−30.3360	−0.960752	−0.480376	+	0.877063i	$0.659500\pi$
$998$	25.0049	0.791516
$999$	−11.8885	−0.376136

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.z.1.4	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.z.1.4	✓	11	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.33314 q^{5} -1.00000 q^{6} -3.20872 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.33314 q^{5} -1.00000 q^{6} -3.20872 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.33314 q^{10} -5.27703 q^{11} -1.00000 q^{12} -4.54336 q^{13} -3.20872 q^{14} +1.33314 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} -5.88474 q^{19} -1.33314 q^{20} +3.20872 q^{21} -5.27703 q^{22} +3.53990 q^{23} -1.00000 q^{24} -3.22274 q^{25} -4.54336 q^{26} -1.00000 q^{27} -3.20872 q^{28} +2.80205 q^{29} +1.33314 q^{30} -2.14265 q^{31} +1.00000 q^{32} +5.27703 q^{33} -1.00000 q^{34} +4.27768 q^{35} +1.00000 q^{36} +11.8885 q^{37} -5.88474 q^{38} +4.54336 q^{39} -1.33314 q^{40} -9.10648 q^{41} +3.20872 q^{42} -2.05555 q^{43} -5.27703 q^{44} -1.33314 q^{45} +3.53990 q^{46} -3.47234 q^{47} -1.00000 q^{48} +3.29590 q^{49} -3.22274 q^{50} +1.00000 q^{51} -4.54336 q^{52} +0.774176 q^{53} -1.00000 q^{54} +7.03501 q^{55} -3.20872 q^{56} +5.88474 q^{57} +2.80205 q^{58} -1.00000 q^{59} +1.33314 q^{60} +6.38088 q^{61} -2.14265 q^{62} -3.20872 q^{63} +1.00000 q^{64} +6.05693 q^{65} +5.27703 q^{66} -6.17650 q^{67} -1.00000 q^{68} -3.53990 q^{69} +4.27768 q^{70} +12.7528 q^{71} +1.00000 q^{72} -2.22859 q^{73} +11.8885 q^{74} +3.22274 q^{75} -5.88474 q^{76} +16.9325 q^{77} +4.54336 q^{78} -1.53464 q^{79} -1.33314 q^{80} +1.00000 q^{81} -9.10648 q^{82} +0.352363 q^{83} +3.20872 q^{84} +1.33314 q^{85} -2.05555 q^{86} -2.80205 q^{87} -5.27703 q^{88} +1.42587 q^{89} -1.33314 q^{90} +14.5784 q^{91} +3.53990 q^{92} +2.14265 q^{93} -3.47234 q^{94} +7.84517 q^{95} -1.00000 q^{96} +1.05372 q^{97} +3.29590 q^{98} -5.27703 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 11 q^{2} - 11 q^{3} + 11 q^{4} + 4 q^{5} - 11 q^{6} + 3 q^{7} + 11 q^{8} + 11 q^{9}+O(q^{10}) \) 11 * q + 11 * q^2 - 11 * q^3 + 11 * q^4 + 4 * q^5 - 11 * q^6 + 3 * q^7 + 11 * q^8 + 11 * q^9	\( 11 q + 11 q^{2} - 11 q^{3} + 11 q^{4} + 4 q^{5} - 11 q^{6} + 3 q^{7} + 11 q^{8} + 11 q^{9} + 4 q^{10} + 9 q^{11} - 11 q^{12} + 6 q^{13} + 3 q^{14} - 4 q^{15} + 11 q^{16} - 11 q^{17} + 11 q^{18} - q^{19} + 4 q^{20} - 3 q^{21} + 9 q^{22} + 10 q^{23} - 11 q^{24} + 15 q^{25} + 6 q^{26} - 11 q^{27} + 3 q^{28} + 14 q^{29} - 4 q^{30} + 17 q^{31} + 11 q^{32} - 9 q^{33} - 11 q^{34} + 8 q^{35} + 11 q^{36} + 30 q^{37} - q^{38} - 6 q^{39} + 4 q^{40} + 10 q^{41} - 3 q^{42} + 11 q^{43} + 9 q^{44} + 4 q^{45} + 10 q^{46} - 6 q^{47} - 11 q^{48} + 18 q^{49} + 15 q^{50} + 11 q^{51} + 6 q^{52} + 10 q^{53} - 11 q^{54} - 11 q^{55} + 3 q^{56} + q^{57} + 14 q^{58} - 11 q^{59} - 4 q^{60} + 13 q^{61} + 17 q^{62} + 3 q^{63} + 11 q^{64} + 32 q^{65} - 9 q^{66} + 26 q^{67} - 11 q^{68} - 10 q^{69} + 8 q^{70} + 14 q^{71} + 11 q^{72} + 20 q^{73} + 30 q^{74} - 15 q^{75} - q^{76} + 26 q^{77} - 6 q^{78} + 15 q^{79} + 4 q^{80} + 11 q^{81} + 10 q^{82} + 2 q^{83} - 3 q^{84} - 4 q^{85} + 11 q^{86} - 14 q^{87} + 9 q^{88} + q^{89} + 4 q^{90} + 17 q^{91} + 10 q^{92} - 17 q^{93} - 6 q^{94} + 3 q^{95} - 11 q^{96} + 33 q^{97} + 18 q^{98} + 9 q^{99}+O(q^{100}) \) 11 * q + 11 * q^2 - 11 * q^3 + 11 * q^4 + 4 * q^5 - 11 * q^6 + 3 * q^7 + 11 * q^8 + 11 * q^9 + 4 * q^10 + 9 * q^11 - 11 * q^12 + 6 * q^13 + 3 * q^14 - 4 * q^15 + 11 * q^16 - 11 * q^17 + 11 * q^18 - q^19 + 4 * q^20 - 3 * q^21 + 9 * q^22 + 10 * q^23 - 11 * q^24 + 15 * q^25 + 6 * q^26 - 11 * q^27 + 3 * q^28 + 14 * q^29 - 4 * q^30 + 17 * q^31 + 11 * q^32 - 9 * q^33 - 11 * q^34 + 8 * q^35 + 11 * q^36 + 30 * q^37 - q^38 - 6 * q^39 + 4 * q^40 + 10 * q^41 - 3 * q^42 + 11 * q^43 + 9 * q^44 + 4 * q^45 + 10 * q^46 - 6 * q^47 - 11 * q^48 + 18 * q^49 + 15 * q^50 + 11 * q^51 + 6 * q^52 + 10 * q^53 - 11 * q^54 - 11 * q^55 + 3 * q^56 + q^57 + 14 * q^58 - 11 * q^59 - 4 * q^60 + 13 * q^61 + 17 * q^62 + 3 * q^63 + 11 * q^64 + 32 * q^65 - 9 * q^66 + 26 * q^67 - 11 * q^68 - 10 * q^69 + 8 * q^70 + 14 * q^71 + 11 * q^72 + 20 * q^73 + 30 * q^74 - 15 * q^75 - q^76 + 26 * q^77 - 6 * q^78 + 15 * q^79 + 4 * q^80 + 11 * q^81 + 10 * q^82 + 2 * q^83 - 3 * q^84 - 4 * q^85 + 11 * q^86 - 14 * q^87 + 9 * q^88 + q^89 + 4 * q^90 + 17 * q^91 + 10 * q^92 - 17 * q^93 - 6 * q^94 + 3 * q^95 - 11 * q^96 + 33 * q^97 + 18 * q^98 + 9 * q^99

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