LMFDB - Embedded newform 6018.2.a.r.1.1

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:	6.6.18461324.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} - 4x^{4} + 12x^{3} + 3x^{2} - 6x - 2 $ x^6 - 3x^5 - 4x^4 + 12x^3 + 3x^2 - 6*x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.94685$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.94685 q^{5} +1.00000 q^{6} +2.59293 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.94685 q^{5} +1.00000 q^{6} +2.59293 q^{7} +1.00000 q^{8} +1.00000 q^{9} -2.94685 q^{10} -3.05839 q^{11} +1.00000 q^{12} -4.13766 q^{13} +2.59293 q^{14} -2.94685 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} -2.51055 q^{19} -2.94685 q^{20} +2.59293 q^{21} -3.05839 q^{22} +4.05408 q^{23} +1.00000 q^{24} +3.68393 q^{25} -4.13766 q^{26} +1.00000 q^{27} +2.59293 q^{28} +1.69625 q^{29} -2.94685 q^{30} +8.42100 q^{31} +1.00000 q^{32} -3.05839 q^{33} -1.00000 q^{34} -7.64097 q^{35} +1.00000 q^{36} -4.29414 q^{37} -2.51055 q^{38} -4.13766 q^{39} -2.94685 q^{40} -0.997868 q^{41} +2.59293 q^{42} -1.87209 q^{43} -3.05839 q^{44} -2.94685 q^{45} +4.05408 q^{46} -11.6321 q^{47} +1.00000 q^{48} -0.276726 q^{49} +3.68393 q^{50} -1.00000 q^{51} -4.13766 q^{52} -7.72673 q^{53} +1.00000 q^{54} +9.01260 q^{55} +2.59293 q^{56} -2.51055 q^{57} +1.69625 q^{58} -1.00000 q^{59} -2.94685 q^{60} +0.942941 q^{61} +8.42100 q^{62} +2.59293 q^{63} +1.00000 q^{64} +12.1931 q^{65} -3.05839 q^{66} -4.57867 q^{67} -1.00000 q^{68} +4.05408 q^{69} -7.64097 q^{70} -4.76172 q^{71} +1.00000 q^{72} -12.4692 q^{73} -4.29414 q^{74} +3.68393 q^{75} -2.51055 q^{76} -7.93017 q^{77} -4.13766 q^{78} -4.73788 q^{79} -2.94685 q^{80} +1.00000 q^{81} -0.997868 q^{82} -5.41572 q^{83} +2.59293 q^{84} +2.94685 q^{85} -1.87209 q^{86} +1.69625 q^{87} -3.05839 q^{88} +4.91770 q^{89} -2.94685 q^{90} -10.7287 q^{91} +4.05408 q^{92} +8.42100 q^{93} -11.6321 q^{94} +7.39821 q^{95} +1.00000 q^{96} +18.8346 q^{97} -0.276726 q^{98} -3.05839 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} + 6 q^{3} + 6 q^{4} - 3 q^{5} + 6 q^{6} - 7 q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 + 6 * q^3 + 6 * q^4 - 3 * q^5 + 6 * q^6 - 7 * q^7 + 6 * q^8 + 6 * q^9	\( 6 q + 6 q^{2} + 6 q^{3} + 6 q^{4} - 3 q^{5} + 6 q^{6} - 7 q^{7} + 6 q^{8} + 6 q^{9} - 3 q^{10} - 8 q^{11} + 6 q^{12} - 6 q^{13} - 7 q^{14} - 3 q^{15} + 6 q^{16} - 6 q^{17} + 6 q^{18} - 14 q^{19} - 3 q^{20} - 7 q^{21} - 8 q^{22} - 8 q^{23} + 6 q^{24} - 13 q^{25} - 6 q^{26} + 6 q^{27} - 7 q^{28} - 21 q^{29} - 3 q^{30} - 5 q^{31} + 6 q^{32} - 8 q^{33} - 6 q^{34} - 12 q^{35} + 6 q^{36} - 13 q^{37} - 14 q^{38} - 6 q^{39} - 3 q^{40} - 18 q^{41} - 7 q^{42} - 4 q^{43} - 8 q^{44} - 3 q^{45} - 8 q^{46} - 4 q^{47} + 6 q^{48} + 5 q^{49} - 13 q^{50} - 6 q^{51} - 6 q^{52} - 25 q^{53} + 6 q^{54} - 8 q^{55} - 7 q^{56} - 14 q^{57} - 21 q^{58} - 6 q^{59} - 3 q^{60} - 5 q^{62} - 7 q^{63} + 6 q^{64} + 6 q^{65} - 8 q^{66} - 13 q^{67} - 6 q^{68} - 8 q^{69} - 12 q^{70} - 12 q^{71} + 6 q^{72} - 4 q^{73} - 13 q^{74} - 13 q^{75} - 14 q^{76} + 4 q^{77} - 6 q^{78} - 12 q^{79} - 3 q^{80} + 6 q^{81} - 18 q^{82} + 9 q^{83} - 7 q^{84} + 3 q^{85} - 4 q^{86} - 21 q^{87} - 8 q^{88} - 11 q^{89} - 3 q^{90} - 31 q^{91} - 8 q^{92} - 5 q^{93} - 4 q^{94} + 35 q^{95} + 6 q^{96} + 16 q^{97} + 5 q^{98} - 8 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 + 6 * q^3 + 6 * q^4 - 3 * q^5 + 6 * q^6 - 7 * q^7 + 6 * q^8 + 6 * q^9 - 3 * q^10 - 8 * q^11 + 6 * q^12 - 6 * q^13 - 7 * q^14 - 3 * q^15 + 6 * q^16 - 6 * q^17 + 6 * q^18 - 14 * q^19 - 3 * q^20 - 7 * q^21 - 8 * q^22 - 8 * q^23 + 6 * q^24 - 13 * q^25 - 6 * q^26 + 6 * q^27 - 7 * q^28 - 21 * q^29 - 3 * q^30 - 5 * q^31 + 6 * q^32 - 8 * q^33 - 6 * q^34 - 12 * q^35 + 6 * q^36 - 13 * q^37 - 14 * q^38 - 6 * q^39 - 3 * q^40 - 18 * q^41 - 7 * q^42 - 4 * q^43 - 8 * q^44 - 3 * q^45 - 8 * q^46 - 4 * q^47 + 6 * q^48 + 5 * q^49 - 13 * q^50 - 6 * q^51 - 6 * q^52 - 25 * q^53 + 6 * q^54 - 8 * q^55 - 7 * q^56 - 14 * q^57 - 21 * q^58 - 6 * q^59 - 3 * q^60 - 5 * q^62 - 7 * q^63 + 6 * q^64 + 6 * q^65 - 8 * q^66 - 13 * q^67 - 6 * q^68 - 8 * q^69 - 12 * q^70 - 12 * q^71 + 6 * q^72 - 4 * q^73 - 13 * q^74 - 13 * q^75 - 14 * q^76 + 4 * q^77 - 6 * q^78 - 12 * q^79 - 3 * q^80 + 6 * q^81 - 18 * q^82 + 9 * q^83 - 7 * q^84 + 3 * q^85 - 4 * q^86 - 21 * q^87 - 8 * q^88 - 11 * q^89 - 3 * q^90 - 31 * q^91 - 8 * q^92 - 5 * q^93 - 4 * q^94 + 35 * q^95 + 6 * q^96 + 16 * q^97 + 5 * q^98 - 8 * 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
$5$	−2.94685	−1.31787	−0.658936	−	0.752199i	$-0.728993\pi$
$5$	−2.94685	−1.31787	−0.658936	+	0.752199i	$0.728993\pi$
$6$	1.00000	0.408248
$7$	2.59293	0.980035	0.490017	−	0.871713i	$-0.336990\pi$
$7$	2.59293	0.980035	0.490017	+	0.871713i	$0.336990\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−2.94685	−0.931876
$11$	−3.05839	−0.922138	−0.461069	−	0.887364i	$-0.652534\pi$
$11$	−3.05839	−0.922138	−0.461069	+	0.887364i	$0.652534\pi$
$12$	1.00000	0.288675
$13$	−4.13766	−1.14758	−0.573791	−	0.819002i	$-0.694528\pi$
$13$	−4.13766	−1.14758	−0.573791	+	0.819002i	$0.694528\pi$
$14$	2.59293	0.692989
$15$	−2.94685	−0.760873
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.00000	0.235702
$19$	−2.51055	−0.575959	−0.287979	−	0.957637i	$-0.592983\pi$
$19$	−2.51055	−0.575959	−0.287979	+	0.957637i	$0.592983\pi$
$20$	−2.94685	−0.658936
$21$	2.59293	0.565823
$22$	−3.05839	−0.652050
$23$	4.05408	0.845335	0.422667	−	0.906285i	$-0.361094\pi$
$23$	4.05408	0.845335	0.422667	+	0.906285i	$0.361094\pi$
$24$	1.00000	0.204124
$25$	3.68393	0.736785
$26$	−4.13766	−0.811462
$27$	1.00000	0.192450
$28$	2.59293	0.490017
$29$	1.69625	0.314986	0.157493	−	0.987520i	$-0.449659\pi$
$29$	1.69625	0.314986	0.157493	+	0.987520i	$0.449659\pi$
$30$	−2.94685	−0.538019
$31$	8.42100	1.51246	0.756228	−	0.654308i	$-0.227040\pi$
$31$	8.42100	1.51246	0.756228	+	0.654308i	$0.227040\pi$
$32$	1.00000	0.176777
$33$	−3.05839	−0.532397
$34$	−1.00000	−0.171499
$35$	−7.64097	−1.29156
$36$	1.00000	0.166667
$37$	−4.29414	−0.705952	−0.352976	−	0.935632i	$-0.614830\pi$
$37$	−4.29414	−0.705952	−0.352976	+	0.935632i	$0.614830\pi$
$38$	−2.51055	−0.407265
$39$	−4.13766	−0.662556
$40$	−2.94685	−0.465938
$41$	−0.997868	−0.155841	−0.0779204	−	0.996960i	$-0.524828\pi$
$41$	−0.997868	−0.155841	−0.0779204	+	0.996960i	$0.524828\pi$
$42$	2.59293	0.400097
$43$	−1.87209	−0.285490	−0.142745	−	0.989759i	$-0.545593\pi$
$43$	−1.87209	−0.285490	−0.142745	+	0.989759i	$0.545593\pi$
$44$	−3.05839	−0.461069
$45$	−2.94685	−0.439290
$46$	4.05408	0.597742
$47$	−11.6321	−1.69672	−0.848358	−	0.529423i	$-0.822409\pi$
$47$	−11.6321	−1.69672	−0.848358	+	0.529423i	$0.822409\pi$
$48$	1.00000	0.144338
$49$	−0.276726	−0.0395323
$50$	3.68393	0.520986
$51$	−1.00000	−0.140028
$52$	−4.13766	−0.573791
$53$	−7.72673	−1.06135	−0.530674	−	0.847576i	$-0.678061\pi$
$53$	−7.72673	−1.06135	−0.530674	+	0.847576i	$0.678061\pi$
$54$	1.00000	0.136083
$55$	9.01260	1.21526
$56$	2.59293	0.346495
$57$	−2.51055	−0.332530
$58$	1.69625	0.222729
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	−2.94685	−0.380437
$61$	0.942941	0.120731	0.0603656	−	0.998176i	$-0.480773\pi$
$61$	0.942941	0.120731	0.0603656	+	0.998176i	$0.480773\pi$
$62$	8.42100	1.06947
$63$	2.59293	0.326678
$64$	1.00000	0.125000
$65$	12.1931	1.51236
$66$	−3.05839	−0.376461
$67$	−4.57867	−0.559374	−0.279687	−	0.960091i	$-0.590231\pi$
$67$	−4.57867	−0.559374	−0.279687	+	0.960091i	$0.590231\pi$
$68$	−1.00000	−0.121268
$69$	4.05408	0.488054
$70$	−7.64097	−0.913271
$71$	−4.76172	−0.565113	−0.282556	−	0.959251i	$-0.591182\pi$
$71$	−4.76172	−0.565113	−0.282556	+	0.959251i	$0.591182\pi$
$72$	1.00000	0.117851
$73$	−12.4692	−1.45941	−0.729707	−	0.683760i	$-0.760344\pi$
$73$	−12.4692	−1.45941	−0.729707	+	0.683760i	$0.760344\pi$
$74$	−4.29414	−0.499183
$75$	3.68393	0.425383
$76$	−2.51055	−0.287979
$77$	−7.93017	−0.903727
$78$	−4.13766	−0.468498
$79$	−4.73788	−0.533053	−0.266527	−	0.963828i	$-0.585876\pi$
$79$	−4.73788	−0.533053	−0.266527	+	0.963828i	$0.585876\pi$
$80$	−2.94685	−0.329468
$81$	1.00000	0.111111
$82$	−0.997868	−0.110196
$83$	−5.41572	−0.594452	−0.297226	−	0.954807i	$-0.596061\pi$
$83$	−5.41572	−0.594452	−0.297226	+	0.954807i	$0.596061\pi$
$84$	2.59293	0.282912
$85$	2.94685	0.319631
$86$	−1.87209	−0.201872
$87$	1.69625	0.181857
$88$	−3.05839	−0.326025
$89$	4.91770	0.521275	0.260637	−	0.965437i	$-0.416067\pi$
$89$	4.91770	0.521275	0.260637	+	0.965437i	$0.416067\pi$
$90$	−2.94685	−0.310625
$91$	−10.7287	−1.12467
$92$	4.05408	0.422667
$93$	8.42100	0.873217
$94$	−11.6321	−1.19976
$95$	7.39821	0.759040
$96$	1.00000	0.102062
$97$	18.8346	1.91237	0.956184	−	0.292766i	$-0.0945757\pi$
$97$	18.8346	1.91237	0.956184	+	0.292766i	$0.0945757\pi$
$98$	−0.276726	−0.0279536
$99$	−3.05839	−0.307379
$100$	3.68393	0.368393
$101$	−13.1816	−1.31162	−0.655809	−	0.754927i	$-0.727672\pi$
$101$	−13.1816	−1.31162	−0.655809	+	0.754927i	$0.727672\pi$
$102$	−1.00000	−0.0990148
$103$	8.47277	0.834847	0.417424	−	0.908712i	$-0.362933\pi$
$103$	8.47277	0.834847	0.417424	+	0.908712i	$0.362933\pi$
$104$	−4.13766	−0.405731
$105$	−7.64097	−0.745682
$106$	−7.72673	−0.750487
$107$	−17.5913	−1.70061	−0.850307	−	0.526288i	$-0.823583\pi$
$107$	−17.5913	−1.70061	−0.850307	+	0.526288i	$0.823583\pi$
$108$	1.00000	0.0962250
$109$	−12.2771	−1.17593	−0.587964	−	0.808887i	$-0.700070\pi$
$109$	−12.2771	−1.17593	−0.587964	+	0.808887i	$0.700070\pi$
$110$	9.01260	0.859318
$111$	−4.29414	−0.407581
$112$	2.59293	0.245009
$113$	−11.0614	−1.04057	−0.520284	−	0.853993i	$-0.674174\pi$
$113$	−11.0614	−1.04057	−0.520284	+	0.853993i	$0.674174\pi$
$114$	−2.51055	−0.235134
$115$	−11.9468	−1.11404
$116$	1.69625	0.157493
$117$	−4.13766	−0.382527
$118$	−1.00000	−0.0920575
$119$	−2.59293	−0.237693
$120$	−2.94685	−0.269009
$121$	−1.64628	−0.149662
$122$	0.942941	0.0853699
$123$	−0.997868	−0.0899747
$124$	8.42100	0.756228
$125$	3.87827	0.346883
$126$	2.59293	0.230996
$127$	−4.33664	−0.384815	−0.192407	−	0.981315i	$-0.561630\pi$
$127$	−4.33664	−0.384815	−0.192407	+	0.981315i	$0.561630\pi$
$128$	1.00000	0.0883883
$129$	−1.87209	−0.164828
$130$	12.1931	1.06940
$131$	4.06788	0.355412	0.177706	−	0.984084i	$-0.443132\pi$
$131$	4.06788	0.355412	0.177706	+	0.984084i	$0.443132\pi$
$132$	−3.05839	−0.266198
$133$	−6.50967	−0.564460
$134$	−4.57867	−0.395537
$135$	−2.94685	−0.253624
$136$	−1.00000	−0.0857493
$137$	12.4161	1.06078	0.530391	−	0.847753i	$-0.322045\pi$
$137$	12.4161	1.06078	0.530391	+	0.847753i	$0.322045\pi$
$138$	4.05408	0.345106
$139$	−2.87639	−0.243972	−0.121986	−	0.992532i	$-0.538926\pi$
$139$	−2.87639	−0.243972	−0.121986	+	0.992532i	$0.538926\pi$
$140$	−7.64097	−0.645780
$141$	−11.6321	−0.979600
$142$	−4.76172	−0.399595
$143$	12.6546	1.05823
$144$	1.00000	0.0833333
$145$	−4.99860	−0.415111
$146$	−12.4692	−1.03196
$147$	−0.276726	−0.0228240
$148$	−4.29414	−0.352976
$149$	−16.3327	−1.33803	−0.669014	−	0.743250i	$-0.733283\pi$
$149$	−16.3327	−1.33803	−0.669014	+	0.743250i	$0.733283\pi$
$150$	3.68393	0.300791
$151$	−2.53256	−0.206097	−0.103048	−	0.994676i	$-0.532860\pi$
$151$	−2.53256	−0.206097	−0.103048	+	0.994676i	$0.532860\pi$
$152$	−2.51055	−0.203632
$153$	−1.00000	−0.0808452
$154$	−7.93017	−0.639031
$155$	−24.8154	−1.99322
$156$	−4.13766	−0.331278
$157$	−2.93180	−0.233983	−0.116991	−	0.993133i	$-0.537325\pi$
$157$	−2.93180	−0.233983	−0.116991	+	0.993133i	$0.537325\pi$
$158$	−4.73788	−0.376926
$159$	−7.72673	−0.612770
$160$	−2.94685	−0.232969
$161$	10.5119	0.828457
$162$	1.00000	0.0785674
$163$	0.162854	0.0127557	0.00637786	−	0.999980i	$-0.497970\pi$
$163$	0.162854	0.0127557	0.00637786	+	0.999980i	$0.497970\pi$
$164$	−0.997868	−0.0779204
$165$	9.01260	0.701630
$166$	−5.41572	−0.420341
$167$	−21.7133	−1.68022	−0.840112	−	0.542413i	$-0.817511\pi$
$167$	−21.7133	−1.68022	−0.840112	+	0.542413i	$0.817511\pi$
$168$	2.59293	0.200049
$169$	4.12025	0.316943
$170$	2.94685	0.226013
$171$	−2.51055	−0.191986
$172$	−1.87209	−0.142745
$173$	−3.27074	−0.248669	−0.124335	−	0.992240i	$-0.539680\pi$
$173$	−3.27074	−0.248669	−0.124335	+	0.992240i	$0.539680\pi$
$174$	1.69625	0.128592
$175$	9.55215	0.722075
$176$	−3.05839	−0.230534
$177$	−1.00000	−0.0751646
$178$	4.91770	0.368597
$179$	14.0119	1.04730	0.523651	−	0.851933i	$-0.324570\pi$
$179$	14.0119	1.04730	0.523651	+	0.851933i	$0.324570\pi$
$180$	−2.94685	−0.219645
$181$	1.56428	0.116272	0.0581359	−	0.998309i	$-0.481484\pi$
$181$	1.56428	0.116272	0.0581359	+	0.998309i	$0.481484\pi$
$182$	−10.7287	−0.795261
$183$	0.942941	0.0697042
$184$	4.05408	0.298871
$185$	12.6542	0.930354
$186$	8.42100	0.617458
$187$	3.05839	0.223651
$188$	−11.6321	−0.848358
$189$	2.59293	0.188608
$190$	7.39821	0.536722
$191$	4.89571	0.354241	0.177120	−	0.984189i	$-0.443322\pi$
$191$	4.89571	0.354241	0.177120	+	0.984189i	$0.443322\pi$
$192$	1.00000	0.0721688
$193$	18.7217	1.34761	0.673807	−	0.738907i	$-0.264658\pi$
$193$	18.7217	1.34761	0.673807	+	0.738907i	$0.264658\pi$
$194$	18.8346	1.35225
$195$	12.1931	0.873164
$196$	−0.276726	−0.0197662
$197$	−6.90034	−0.491629	−0.245814	−	0.969317i	$-0.579055\pi$
$197$	−6.90034	−0.491629	−0.245814	+	0.969317i	$0.579055\pi$
$198$	−3.05839	−0.217350
$199$	6.38316	0.452490	0.226245	−	0.974070i	$-0.427355\pi$
$199$	6.38316	0.452490	0.226245	+	0.974070i	$0.427355\pi$
$200$	3.68393	0.260493
$201$	−4.57867	−0.322955
$202$	−13.1816	−0.927454
$203$	4.39826	0.308697
$204$	−1.00000	−0.0700140
$205$	2.94057	0.205378
$206$	8.47277	0.590326
$207$	4.05408	0.281778
$208$	−4.13766	−0.286895
$209$	7.67822	0.531114
$210$	−7.64097	−0.527277
$211$	27.8148	1.91485	0.957424	−	0.288685i	$-0.0932180\pi$
$211$	27.8148	1.91485	0.957424	+	0.288685i	$0.0932180\pi$
$212$	−7.72673	−0.530674
$213$	−4.76172	−0.326268
$214$	−17.5913	−1.20252
$215$	5.51676	0.376240
$216$	1.00000	0.0680414
$217$	21.8350	1.48226
$218$	−12.2771	−0.831507
$219$	−12.4692	−0.842594
$220$	9.01260	0.607630
$221$	4.13766	0.278329
$222$	−4.29414	−0.288204
$223$	−0.0820386	−0.00549371	−0.00274686	−	0.999996i	$-0.500874\pi$
$223$	−0.0820386	−0.00549371	−0.00274686	+	0.999996i	$0.500874\pi$
$224$	2.59293	0.173247
$225$	3.68393	0.245595
$226$	−11.0614	−0.735793
$227$	−26.7816	−1.77756	−0.888780	−	0.458334i	$-0.848446\pi$
$227$	−26.7816	−1.77756	−0.888780	+	0.458334i	$0.848446\pi$
$228$	−2.51055	−0.166265
$229$	25.8246	1.70654	0.853268	−	0.521473i	$-0.174617\pi$
$229$	25.8246	1.70654	0.853268	+	0.521473i	$0.174617\pi$
$230$	−11.9468	−0.787747
$231$	−7.93017	−0.521767
$232$	1.69625	0.111364
$233$	−17.3902	−1.13927	−0.569634	−	0.821898i	$-0.692915\pi$
$233$	−17.3902	−1.13927	−0.569634	+	0.821898i	$0.692915\pi$
$234$	−4.13766	−0.270487
$235$	34.2781	2.23605
$236$	−1.00000	−0.0650945
$237$	−4.73788	−0.307759
$238$	−2.59293	−0.168075
$239$	−5.30771	−0.343327	−0.171664	−	0.985156i	$-0.554914\pi$
$239$	−5.30771	−0.343327	−0.171664	+	0.985156i	$0.554914\pi$
$240$	−2.94685	−0.190218
$241$	9.96044	0.641608	0.320804	−	0.947146i	$-0.396047\pi$
$241$	9.96044	0.641608	0.320804	+	0.947146i	$0.396047\pi$
$242$	−1.64628	−0.105827
$243$	1.00000	0.0641500
$244$	0.942941	0.0603656
$245$	0.815471	0.0520985
$246$	−0.997868	−0.0636217
$247$	10.3878	0.660960
$248$	8.42100	0.534734
$249$	−5.41572	−0.343207
$250$	3.87827	0.245283
$251$	4.38812	0.276976	0.138488	−	0.990364i	$-0.455776\pi$
$251$	4.38812	0.276976	0.138488	+	0.990364i	$0.455776\pi$
$252$	2.59293	0.163339
$253$	−12.3989	−0.779515
$254$	−4.33664	−0.272105
$255$	2.94685	0.184539
$256$	1.00000	0.0625000
$257$	12.3059	0.767623	0.383812	−	0.923411i	$-0.374611\pi$
$257$	12.3059	0.767623	0.383812	+	0.923411i	$0.374611\pi$
$258$	−1.87209	−0.116551
$259$	−11.1344	−0.691857
$260$	12.1931	0.756182
$261$	1.69625	0.104995
$262$	4.06788	0.251314
$263$	−9.63986	−0.594419	−0.297210	−	0.954812i	$-0.596056\pi$
$263$	−9.63986	−0.594419	−0.297210	+	0.954812i	$0.596056\pi$
$264$	−3.05839	−0.188231
$265$	22.7695	1.39872
$266$	−6.50967	−0.399133
$267$	4.91770	0.300958
$268$	−4.57867	−0.279687
$269$	10.3663	0.632046	0.316023	−	0.948752i	$-0.397652\pi$
$269$	10.3663	0.632046	0.316023	+	0.948752i	$0.397652\pi$
$270$	−2.94685	−0.179340
$271$	13.6910	0.831667	0.415833	−	0.909441i	$-0.363490\pi$
$271$	13.6910	0.831667	0.415833	+	0.909441i	$0.363490\pi$
$272$	−1.00000	−0.0606339
$273$	−10.7287	−0.649328
$274$	12.4161	0.750087
$275$	−11.2669	−0.679418
$276$	4.05408	0.244027
$277$	−9.95712	−0.598265	−0.299133	−	0.954212i	$-0.596697\pi$
$277$	−9.95712	−0.598265	−0.299133	+	0.954212i	$0.596697\pi$
$278$	−2.87639	−0.172514
$279$	8.42100	0.504152
$280$	−7.64097	−0.456635
$281$	−0.144941	−0.00864643	−0.00432322	−	0.999991i	$-0.501376\pi$
$281$	−0.144941	−0.00864643	−0.00432322	+	0.999991i	$0.501376\pi$
$282$	−11.6321	−0.692682
$283$	12.5169	0.744051	0.372026	−	0.928222i	$-0.378663\pi$
$283$	12.5169	0.744051	0.372026	+	0.928222i	$0.378663\pi$
$284$	−4.76172	−0.282556
$285$	7.39821	0.438232
$286$	12.6546	0.748280
$287$	−2.58740	−0.152729
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	−4.99860	−0.293528
$291$	18.8346	1.10411
$292$	−12.4692	−0.729707
$293$	10.6978	0.624974	0.312487	−	0.949922i	$-0.398838\pi$
$293$	10.6978	0.624974	0.312487	+	0.949922i	$0.398838\pi$
$294$	−0.276726	−0.0161390
$295$	2.94685	0.171572
$296$	−4.29414	−0.249592
$297$	−3.05839	−0.177466
$298$	−16.3327	−0.946129
$299$	−16.7744	−0.970090
$300$	3.68393	0.212692
$301$	−4.85418	−0.279790
$302$	−2.53256	−0.145732
$303$	−13.1816	−0.757263
$304$	−2.51055	−0.143990
$305$	−2.77871	−0.159108
$306$	−1.00000	−0.0571662
$307$	−20.1410	−1.14951	−0.574753	−	0.818327i	$-0.694902\pi$
$307$	−20.1410	−1.14951	−0.574753	+	0.818327i	$0.694902\pi$
$308$	−7.93017	−0.451863
$309$	8.47277	0.481999
$310$	−24.8154	−1.40942
$311$	−13.7327	−0.778708	−0.389354	−	0.921088i	$-0.627302\pi$
$311$	−13.7327	−0.778708	−0.389354	+	0.921088i	$0.627302\pi$
$312$	−4.13766	−0.234249
$313$	−3.38315	−0.191227	−0.0956136	−	0.995419i	$-0.530481\pi$
$313$	−3.38315	−0.191227	−0.0956136	+	0.995419i	$0.530481\pi$
$314$	−2.93180	−0.165451
$315$	−7.64097	−0.430520
$316$	−4.73788	−0.266527
$317$	−2.09710	−0.117785	−0.0588924	−	0.998264i	$-0.518757\pi$
$317$	−2.09710	−0.117785	−0.0588924	+	0.998264i	$0.518757\pi$
$318$	−7.72673	−0.433294
$319$	−5.18779	−0.290461
$320$	−2.94685	−0.164734
$321$	−17.5913	−0.981849
$322$	10.5119	0.585808
$323$	2.51055	0.139691
$324$	1.00000	0.0555556
$325$	−15.2428	−0.845521
$326$	0.162854	0.00901965
$327$	−12.2771	−0.678923
$328$	−0.997868	−0.0550980
$329$	−30.1612	−1.66284
$330$	9.01260	0.496127
$331$	23.5421	1.29399	0.646996	−	0.762493i	$-0.276025\pi$
$331$	23.5421	1.29399	0.646996	+	0.762493i	$0.276025\pi$
$332$	−5.41572	−0.297226
$333$	−4.29414	−0.235317
$334$	−21.7133	−1.18810
$335$	13.4927	0.737183
$336$	2.59293	0.141456
$337$	10.9276	0.595266	0.297633	−	0.954680i	$-0.403803\pi$
$337$	10.9276	0.595266	0.297633	+	0.954680i	$0.403803\pi$
$338$	4.12025	0.224112
$339$	−11.0614	−0.600772
$340$	2.94685	0.159815
$341$	−25.7547	−1.39469
$342$	−2.51055	−0.135755
$343$	−18.8680	−1.01878
$344$	−1.87209	−0.100936
$345$	−11.9468	−0.643193
$346$	−3.27074	−0.175836
$347$	−25.4728	−1.36745	−0.683726	−	0.729739i	$-0.739642\pi$
$347$	−25.4728	−1.36745	−0.683726	+	0.729739i	$0.739642\pi$
$348$	1.69625	0.0909286
$349$	23.8270	1.27543	0.637714	−	0.770273i	$-0.279880\pi$
$349$	23.8270	1.27543	0.637714	+	0.770273i	$0.279880\pi$
$350$	9.55215	0.510584
$351$	−4.13766	−0.220852
$352$	−3.05839	−0.163012
$353$	11.2371	0.598089	0.299045	−	0.954239i	$-0.403332\pi$
$353$	11.2371	0.598089	0.299045	+	0.954239i	$0.403332\pi$
$354$	−1.00000	−0.0531494
$355$	14.0321	0.744746
$356$	4.91770	0.260637
$357$	−2.59293	−0.137232
$358$	14.0119	0.740554
$359$	−22.2326	−1.17339	−0.586695	−	0.809808i	$-0.699571\pi$
$359$	−22.2326	−1.17339	−0.586695	+	0.809808i	$0.699571\pi$
$360$	−2.94685	−0.155313
$361$	−12.6972	−0.668271
$362$	1.56428	0.0822166
$363$	−1.64628	−0.0864073
$364$	−10.7287	−0.562335
$365$	36.7450	1.92332
$366$	0.942941	0.0492883
$367$	−8.76295	−0.457422	−0.228711	−	0.973494i	$-0.573451\pi$
$367$	−8.76295	−0.457422	−0.228711	+	0.973494i	$0.573451\pi$
$368$	4.05408	0.211334
$369$	−0.997868	−0.0519469
$370$	12.6542	0.657859
$371$	−20.0349	−1.04016
$372$	8.42100	0.436609
$373$	−32.6818	−1.69220	−0.846099	−	0.533025i	$-0.821055\pi$
$373$	−32.6818	−1.69220	−0.846099	+	0.533025i	$0.821055\pi$
$374$	3.05839	0.158145
$375$	3.87827	0.200273
$376$	−11.6321	−0.599880
$377$	−7.01852	−0.361472
$378$	2.59293	0.133366
$379$	17.2143	0.884241	0.442120	−	0.896956i	$-0.354226\pi$
$379$	17.2143	0.884241	0.442120	+	0.896956i	$0.354226\pi$
$380$	7.39821	0.379520
$381$	−4.33664	−0.222173
$382$	4.89571	0.250486
$383$	31.2972	1.59921	0.799607	−	0.600524i	$-0.205041\pi$
$383$	31.2972	1.59921	0.799607	+	0.600524i	$0.205041\pi$
$384$	1.00000	0.0510310
$385$	23.3690	1.19100
$386$	18.7217	0.952907
$387$	−1.87209	−0.0951635
$388$	18.8346	0.956184
$389$	38.4539	1.94969	0.974846	−	0.222878i	$-0.0715453\pi$
$389$	38.4539	1.94969	0.974846	+	0.222878i	$0.0715453\pi$
$390$	12.1931	0.617420
$391$	−4.05408	−0.205024
$392$	−0.276726	−0.0139768
$393$	4.06788	0.205197
$394$	−6.90034	−0.347634
$395$	13.9618	0.702496
$396$	−3.05839	−0.153690
$397$	−18.4829	−0.927630	−0.463815	−	0.885932i	$-0.653520\pi$
$397$	−18.4829	−0.927630	−0.463815	+	0.885932i	$0.653520\pi$
$398$	6.38316	0.319959
$399$	−6.50967	−0.325891
$400$	3.68393	0.184196
$401$	−6.99538	−0.349333	−0.174666	−	0.984628i	$-0.555885\pi$
$401$	−6.99538	−0.349333	−0.174666	+	0.984628i	$0.555885\pi$
$402$	−4.57867	−0.228364
$403$	−34.8433	−1.73567
$404$	−13.1816	−0.655809
$405$	−2.94685	−0.146430
$406$	4.39826	0.218282
$407$	13.1331	0.650985
$408$	−1.00000	−0.0495074
$409$	16.8371	0.832541	0.416271	−	0.909241i	$-0.363337\pi$
$409$	16.8371	0.832541	0.416271	+	0.909241i	$0.363337\pi$
$410$	2.94057	0.145224
$411$	12.4161	0.612443
$412$	8.47277	0.417424
$413$	−2.59293	−0.127590
$414$	4.05408	0.199247
$415$	15.9593	0.783411
$416$	−4.13766	−0.202866
$417$	−2.87639	−0.140857
$418$	7.67822	0.375554
$419$	−12.0786	−0.590079	−0.295040	−	0.955485i	$-0.595333\pi$
$419$	−12.0786	−0.590079	−0.295040	+	0.955485i	$0.595333\pi$
$420$	−7.64097	−0.372841
$421$	39.7490	1.93725	0.968623	−	0.248535i	$-0.0799492\pi$
$421$	39.7490	1.93725	0.968623	+	0.248535i	$0.0799492\pi$
$422$	27.8148	1.35400
$423$	−11.6321	−0.565572
$424$	−7.72673	−0.375243
$425$	−3.68393	−0.178697
$426$	−4.76172	−0.230706
$427$	2.44498	0.118321
$428$	−17.5913	−0.850307
$429$	12.6546	0.610968
$430$	5.51676	0.266042
$431$	3.82406	0.184199	0.0920993	−	0.995750i	$-0.470642\pi$
$431$	3.82406	0.184199	0.0920993	+	0.995750i	$0.470642\pi$
$432$	1.00000	0.0481125
$433$	−1.11814	−0.0537345	−0.0268673	−	0.999639i	$-0.508553\pi$
$433$	−1.11814	−0.0537345	−0.0268673	+	0.999639i	$0.508553\pi$
$434$	21.8350	1.04812
$435$	−4.99860	−0.239664
$436$	−12.2771	−0.587964
$437$	−10.1780	−0.486878
$438$	−12.4692	−0.595804
$439$	25.7165	1.22738	0.613691	−	0.789546i	$-0.289684\pi$
$439$	25.7165	1.22738	0.613691	+	0.789546i	$0.289684\pi$
$440$	9.01260	0.429659
$441$	−0.276726	−0.0131774
$442$	4.13766	0.196809
$443$	−30.8915	−1.46770	−0.733851	−	0.679311i	$-0.762279\pi$
$443$	−30.8915	−1.46770	−0.733851	+	0.679311i	$0.762279\pi$
$444$	−4.29414	−0.203791
$445$	−14.4917	−0.686973
$446$	−0.0820386	−0.00388464
$447$	−16.3327	−0.772511
$448$	2.59293	0.122504
$449$	−24.9899	−1.17935	−0.589673	−	0.807642i	$-0.700743\pi$
$449$	−24.9899	−1.17935	−0.589673	+	0.807642i	$0.700743\pi$
$450$	3.68393	0.173662
$451$	3.05186	0.143707
$452$	−11.0614	−0.520284
$453$	−2.53256	−0.118990
$454$	−26.7816	−1.25692
$455$	31.6158	1.48217
$456$	−2.51055	−0.117567
$457$	14.8183	0.693169	0.346585	−	0.938019i	$-0.387341\pi$
$457$	14.8183	0.693169	0.346585	+	0.938019i	$0.387341\pi$
$458$	25.8246	1.20670
$459$	−1.00000	−0.0466760
$460$	−11.9468	−0.557021
$461$	2.38631	0.111142	0.0555708	−	0.998455i	$-0.482302\pi$
$461$	2.38631	0.111142	0.0555708	+	0.998455i	$0.482302\pi$
$462$	−7.93017	−0.368945
$463$	−20.5562	−0.955327	−0.477664	−	0.878543i	$-0.658516\pi$
$463$	−20.5562	−0.955327	−0.477664	+	0.878543i	$0.658516\pi$
$464$	1.69625	0.0787465
$465$	−24.8154	−1.15079
$466$	−17.3902	−0.805584
$467$	1.51471	0.0700923	0.0350461	−	0.999386i	$-0.488842\pi$
$467$	1.51471	0.0700923	0.0350461	+	0.999386i	$0.488842\pi$
$468$	−4.13766	−0.191264
$469$	−11.8722	−0.548206
$470$	34.2781	1.58113
$471$	−2.93180	−0.135090
$472$	−1.00000	−0.0460287
$473$	5.72556	0.263262
$474$	−4.73788	−0.217618
$475$	−9.24867	−0.424358
$476$	−2.59293	−0.118847
$477$	−7.72673	−0.353783
$478$	−5.30771	−0.242769
$479$	3.78573	0.172975	0.0864873	−	0.996253i	$-0.472436\pi$
$479$	3.78573	0.172975	0.0864873	+	0.996253i	$0.472436\pi$
$480$	−2.94685	−0.134505
$481$	17.7677	0.810137
$482$	9.96044	0.453686
$483$	10.5119	0.478310
$484$	−1.64628	−0.0748309
$485$	−55.5029	−2.52026
$486$	1.00000	0.0453609
$487$	−36.2495	−1.64262	−0.821312	−	0.570480i	$-0.806757\pi$
$487$	−36.2495	−1.64262	−0.821312	+	0.570480i	$0.806757\pi$
$488$	0.942941	0.0426849
$489$	0.162854	0.00736451
$490$	0.815471	0.0368392
$491$	−7.18833	−0.324405	−0.162202	−	0.986758i	$-0.551860\pi$
$491$	−7.18833	−0.324405	−0.162202	+	0.986758i	$0.551860\pi$
$492$	−0.997868	−0.0449873
$493$	−1.69625	−0.0763953
$494$	10.3878	0.467369
$495$	9.01260	0.405086
$496$	8.42100	0.378114
$497$	−12.3468	−0.553830
$498$	−5.41572	−0.242684
$499$	−27.9666	−1.25196	−0.625978	−	0.779841i	$-0.715300\pi$
$499$	−27.9666	−1.25196	−0.625978	+	0.779841i	$0.715300\pi$
$500$	3.87827	0.173442
$501$	−21.7133	−0.970078
$502$	4.38812	0.195851
$503$	29.3335	1.30791	0.653957	−	0.756531i	$-0.273108\pi$
$503$	29.3335	1.30791	0.653957	+	0.756531i	$0.273108\pi$
$504$	2.59293	0.115498
$505$	38.8442	1.72854
$506$	−12.3989	−0.551200
$507$	4.12025	0.182987
$508$	−4.33664	−0.192407
$509$	29.1703	1.29295	0.646476	−	0.762934i	$-0.276242\pi$
$509$	29.1703	1.29295	0.646476	+	0.762934i	$0.276242\pi$
$510$	2.94685	0.130489
$511$	−32.3319	−1.43028
$512$	1.00000	0.0441942
$513$	−2.51055	−0.110843
$514$	12.3059	0.542791
$515$	−24.9680	−1.10022
$516$	−1.87209	−0.0824140
$517$	35.5755	1.56461
$518$	−11.1344	−0.489217
$519$	−3.27074	−0.143569
$520$	12.1931	0.534702
$521$	−27.7345	−1.21507	−0.607535	−	0.794293i	$-0.707842\pi$
$521$	−27.7345	−1.21507	−0.607535	+	0.794293i	$0.707842\pi$
$522$	1.69625	0.0742429
$523$	−10.5391	−0.460842	−0.230421	−	0.973091i	$-0.574010\pi$
$523$	−10.5391	−0.460842	−0.230421	+	0.973091i	$0.574010\pi$
$524$	4.06788	0.177706
$525$	9.55215	0.416890
$526$	−9.63986	−0.420318
$527$	−8.42100	−0.366825
$528$	−3.05839	−0.133099
$529$	−6.56441	−0.285409
$530$	22.7695	0.989045
$531$	−1.00000	−0.0433963
$532$	−6.50967	−0.282230
$533$	4.12884	0.178840
$534$	4.91770	0.212810
$535$	51.8389	2.24119
$536$	−4.57867	−0.197769
$537$	14.0119	0.604660
$538$	10.3663	0.446924
$539$	0.846336	0.0364543
$540$	−2.94685	−0.126812
$541$	10.7190	0.460848	0.230424	−	0.973090i	$-0.425989\pi$
$541$	10.7190	0.460848	0.230424	+	0.973090i	$0.425989\pi$
$542$	13.6910	0.588077
$543$	1.56428	0.0671296
$544$	−1.00000	−0.0428746
$545$	36.1786	1.54972
$546$	−10.7287	−0.459144
$547$	−12.7629	−0.545700	−0.272850	−	0.962057i	$-0.587966\pi$
$547$	−12.7629	−0.545700	−0.272850	+	0.962057i	$0.587966\pi$
$548$	12.4161	0.530391
$549$	0.942941	0.0402437
$550$	−11.2669	−0.480421
$551$	−4.25852	−0.181419
$552$	4.05408	0.172553
$553$	−12.2850	−0.522411
$554$	−9.95712	−0.423037
$555$	12.6542	0.537140
$556$	−2.87639	−0.121986
$557$	11.2765	0.477802	0.238901	−	0.971044i	$-0.423213\pi$
$557$	11.2765	0.477802	0.238901	+	0.971044i	$0.423213\pi$
$558$	8.42100	0.356489
$559$	7.74606	0.327623
$560$	−7.64097	−0.322890
$561$	3.05839	0.129125
$562$	−0.144941	−0.00611395
$563$	−45.3366	−1.91071	−0.955355	−	0.295459i	$-0.904528\pi$
$563$	−45.3366	−1.91071	−0.955355	+	0.295459i	$0.904528\pi$
$564$	−11.6321	−0.489800
$565$	32.5963	1.37134
$566$	12.5169	0.526124
$567$	2.59293	0.108893
$568$	−4.76172	−0.199797
$569$	−15.3889	−0.645135	−0.322568	−	0.946546i	$-0.604546\pi$
$569$	−15.3889	−0.645135	−0.322568	+	0.946546i	$0.604546\pi$
$570$	7.39821	0.309877
$571$	20.4110	0.854174	0.427087	−	0.904210i	$-0.359540\pi$
$571$	20.4110	0.854174	0.427087	+	0.904210i	$0.359540\pi$
$572$	12.6546	0.529114
$573$	4.89571	0.204521
$574$	−2.58740	−0.107996
$575$	14.9349	0.622830
$576$	1.00000	0.0416667
$577$	43.7937	1.82316	0.911578	−	0.411126i	$-0.134864\pi$
$577$	43.7937	1.82316	0.911578	+	0.411126i	$0.134864\pi$
$578$	1.00000	0.0415945
$579$	18.7217	0.778046
$580$	−4.99860	−0.207556
$581$	−14.0426	−0.582583
$582$	18.8346	0.780721
$583$	23.6313	0.978709
$584$	−12.4692	−0.515981
$585$	12.1931	0.504121
$586$	10.6978	0.441923
$587$	−16.7938	−0.693153	−0.346576	−	0.938022i	$-0.612656\pi$
$587$	−16.7938	−0.693153	−0.346576	+	0.938022i	$0.612656\pi$
$588$	−0.276726	−0.0114120
$589$	−21.1413	−0.871113
$590$	2.94685	0.121320
$591$	−6.90034	−0.283842
$592$	−4.29414	−0.176488
$593$	45.6910	1.87631	0.938153	−	0.346220i	$-0.112535\pi$
$593$	45.6910	1.87631	0.938153	+	0.346220i	$0.112535\pi$
$594$	−3.05839	−0.125487
$595$	7.64097	0.313249
$596$	−16.3327	−0.669014
$597$	6.38316	0.261245
$598$	−16.7744	−0.685957
$599$	−22.4711	−0.918143	−0.459072	−	0.888399i	$-0.651818\pi$
$599$	−22.4711	−0.918143	−0.459072	+	0.888399i	$0.651818\pi$
$600$	3.68393	0.150396
$601$	−23.3324	−0.951749	−0.475875	−	0.879513i	$-0.657868\pi$
$601$	−23.3324	−0.951749	−0.475875	+	0.879513i	$0.657868\pi$
$602$	−4.85418	−0.197842
$603$	−4.57867	−0.186458
$604$	−2.53256	−0.103048
$605$	4.85134	0.197235
$606$	−13.1816	−0.535466
$607$	−12.4067	−0.503574	−0.251787	−	0.967783i	$-0.581018\pi$
$607$	−12.4067	−0.503574	−0.251787	+	0.967783i	$0.581018\pi$
$608$	−2.51055	−0.101816
$609$	4.39826	0.178226
$610$	−2.77871	−0.112507
$611$	48.1297	1.94712
$612$	−1.00000	−0.0404226
$613$	43.1067	1.74106	0.870532	−	0.492112i	$-0.163775\pi$
$613$	43.1067	1.74106	0.870532	+	0.492112i	$0.163775\pi$
$614$	−20.1410	−0.812824
$615$	2.94057	0.118575
$616$	−7.93017	−0.319516
$617$	45.5363	1.83322	0.916610	−	0.399782i	$-0.130914\pi$
$617$	45.5363	1.83322	0.916610	+	0.399782i	$0.130914\pi$
$618$	8.47277	0.340825
$619$	0.587507	0.0236139	0.0118070	−	0.999930i	$-0.496242\pi$
$619$	0.587507	0.0236139	0.0118070	+	0.999930i	$0.496242\pi$
$620$	−24.8154	−0.996612
$621$	4.05408	0.162685
$622$	−13.7327	−0.550630
$623$	12.7512	0.510867
$624$	−4.13766	−0.165639
$625$	−29.8483	−1.19393
$626$	−3.38315	−0.135218
$627$	7.67822	0.306639
$628$	−2.93180	−0.116991
$629$	4.29414	0.171218
$630$	−7.64097	−0.304424
$631$	3.37327	0.134288	0.0671438	−	0.997743i	$-0.478611\pi$
$631$	3.37327	0.134288	0.0671438	+	0.997743i	$0.478611\pi$
$632$	−4.73788	−0.188463
$633$	27.8148	1.10554
$634$	−2.09710	−0.0832865
$635$	12.7794	0.507137
$636$	−7.72673	−0.306385
$637$	1.14500	0.0453666
$638$	−5.18779	−0.205387
$639$	−4.76172	−0.188371
$640$	−2.94685	−0.116484
$641$	−43.4496	−1.71616	−0.858078	−	0.513520i	$-0.828341\pi$
$641$	−43.4496	−1.71616	−0.858078	+	0.513520i	$0.828341\pi$
$642$	−17.5913	−0.694272
$643$	−14.2660	−0.562596	−0.281298	−	0.959621i	$-0.590765\pi$
$643$	−14.2660	−0.562596	−0.281298	+	0.959621i	$0.590765\pi$
$644$	10.5119	0.414229
$645$	5.51676	0.217222
$646$	2.51055	0.0987762
$647$	40.3400	1.58593	0.792964	−	0.609269i	$-0.208537\pi$
$647$	40.3400	1.58593	0.792964	+	0.609269i	$0.208537\pi$
$648$	1.00000	0.0392837
$649$	3.05839	0.120052
$650$	−15.2428	−0.597874
$651$	21.8350	0.855783
$652$	0.162854	0.00637786
$653$	13.4087	0.524724	0.262362	−	0.964970i	$-0.415499\pi$
$653$	13.4087	0.524724	0.262362	+	0.964970i	$0.415499\pi$
$654$	−12.2771	−0.480071
$655$	−11.9874	−0.468388
$656$	−0.997868	−0.0389602
$657$	−12.4692	−0.486472
$658$	−30.1612	−1.17581
$659$	6.40762	0.249605	0.124803	−	0.992182i	$-0.460170\pi$
$659$	6.40762	0.249605	0.124803	+	0.992182i	$0.460170\pi$
$660$	9.01260	0.350815
$661$	−27.5510	−1.07161	−0.535804	−	0.844342i	$-0.679991\pi$
$661$	−27.5510	−1.07161	−0.535804	+	0.844342i	$0.679991\pi$
$662$	23.5421	0.914991
$663$	4.13766	0.160694
$664$	−5.41572	−0.210171
$665$	19.1830	0.743885
$666$	−4.29414	−0.166394
$667$	6.87674	0.266269
$668$	−21.7133	−0.840112
$669$	−0.0820386	−0.00317179
$670$	13.4927	0.521267
$671$	−2.88388	−0.111331
$672$	2.59293	0.100024
$673$	−35.2195	−1.35761	−0.678807	−	0.734317i	$-0.737503\pi$
$673$	−35.2195	−1.35761	−0.678807	+	0.734317i	$0.737503\pi$
$674$	10.9276	0.420917
$675$	3.68393	0.141794
$676$	4.12025	0.158471
$677$	2.51579	0.0966896	0.0483448	−	0.998831i	$-0.484605\pi$
$677$	2.51579	0.0966896	0.0483448	+	0.998831i	$0.484605\pi$
$678$	−11.0614	−0.424810
$679$	48.8369	1.87419
$680$	2.94685	0.113007
$681$	−26.7816	−1.02627
$682$	−25.7547	−0.986197
$683$	37.4738	1.43389	0.716947	−	0.697128i	$-0.245539\pi$
$683$	37.4738	1.43389	0.716947	+	0.697128i	$0.245539\pi$
$684$	−2.51055	−0.0959932
$685$	−36.5885	−1.39798
$686$	−18.8680	−0.720385
$687$	25.8246	0.985269
$688$	−1.87209	−0.0713726
$689$	31.9706	1.21798
$690$	−11.9468	−0.454806
$691$	−32.6451	−1.24188	−0.620940	−	0.783858i	$-0.713249\pi$
$691$	−32.6451	−1.24188	−0.620940	+	0.783858i	$0.713249\pi$
$692$	−3.27074	−0.124335
$693$	−7.93017	−0.301242
$694$	−25.4728	−0.966935
$695$	8.47628	0.321524
$696$	1.69625	0.0642962
$697$	0.997868	0.0377969
$698$	23.8270	0.901864
$699$	−17.3902	−0.657757
$700$	9.55215	0.361037
$701$	−24.1040	−0.910396	−0.455198	−	0.890390i	$-0.650431\pi$
$701$	−24.1040	−0.910396	−0.455198	+	0.890390i	$0.650431\pi$
$702$	−4.13766	−0.156166
$703$	10.7806	0.406599
$704$	−3.05839	−0.115267
$705$	34.2781	1.29099
$706$	11.2371	0.422913
$707$	−34.1789	−1.28543
$708$	−1.00000	−0.0375823
$709$	32.5815	1.22363	0.611813	−	0.791003i	$-0.290441\pi$
$709$	32.5815	1.22363	0.611813	+	0.791003i	$0.290441\pi$
$710$	14.0321	0.526615
$711$	−4.73788	−0.177684
$712$	4.91770	0.184298
$713$	34.1394	1.27853
$714$	−2.59293	−0.0970379
$715$	−37.2911	−1.39461
$716$	14.0119	0.523651
$717$	−5.30771	−0.198220
$718$	−22.2326	−0.829712
$719$	20.2718	0.756010	0.378005	−	0.925804i	$-0.376610\pi$
$719$	20.2718	0.756010	0.378005	+	0.925804i	$0.376610\pi$
$720$	−2.94685	−0.109823
$721$	21.9693	0.818179
$722$	−12.6972	−0.472539
$723$	9.96044	0.370433
$724$	1.56428	0.0581359
$725$	6.24887	0.232077
$726$	−1.64628	−0.0610992
$727$	11.1788	0.414598	0.207299	−	0.978278i	$-0.433533\pi$
$727$	11.1788	0.414598	0.207299	+	0.978278i	$0.433533\pi$
$728$	−10.7287	−0.397631
$729$	1.00000	0.0370370
$730$	36.7450	1.35999
$731$	1.87209	0.0692416
$732$	0.942941	0.0348521
$733$	28.6962	1.05992	0.529959	−	0.848024i	$-0.322207\pi$
$733$	28.6962	1.05992	0.529959	+	0.848024i	$0.322207\pi$
$734$	−8.76295	−0.323446
$735$	0.815471	0.0300791
$736$	4.05408	0.149435
$737$	14.0034	0.515820
$738$	−0.997868	−0.0367320
$739$	−15.5944	−0.573650	−0.286825	−	0.957983i	$-0.592600\pi$
$739$	−15.5944	−0.573650	−0.286825	+	0.957983i	$0.592600\pi$
$740$	12.6542	0.465177
$741$	10.3878	0.381605
$742$	−20.0349	−0.735503
$743$	42.6140	1.56335	0.781677	−	0.623683i	$-0.214364\pi$
$743$	42.6140	1.56335	0.781677	+	0.623683i	$0.214364\pi$
$744$	8.42100	0.308729
$745$	48.1301	1.76335
$746$	−32.6818	−1.19657
$747$	−5.41572	−0.198151
$748$	3.05839	0.111826
$749$	−45.6129	−1.66666
$750$	3.87827	0.141614
$751$	−21.6013	−0.788241	−0.394120	−	0.919059i	$-0.628951\pi$
$751$	−21.6013	−0.788241	−0.394120	+	0.919059i	$0.628951\pi$
$752$	−11.6321	−0.424179
$753$	4.38812	0.159912
$754$	−7.01852	−0.255599
$755$	7.46308	0.271609
$756$	2.59293	0.0943039
$757$	32.1947	1.17014	0.585069	−	0.810984i	$-0.301068\pi$
$757$	32.1947	1.17014	0.585069	+	0.810984i	$0.301068\pi$
$758$	17.2143	0.625253
$759$	−12.3989	−0.450053
$760$	7.39821	0.268361
$761$	39.3520	1.42651	0.713254	−	0.700905i	$-0.247221\pi$
$761$	39.3520	1.42651	0.713254	+	0.700905i	$0.247221\pi$
$762$	−4.33664	−0.157100
$763$	−31.8335	−1.15245
$764$	4.89571	0.177120
$765$	2.94685	0.106544
$766$	31.2972	1.13081
$767$	4.13766	0.149402
$768$	1.00000	0.0360844
$769$	−25.4837	−0.918964	−0.459482	−	0.888187i	$-0.651965\pi$
$769$	−25.4837	−0.918964	−0.459482	+	0.888187i	$0.651965\pi$
$770$	23.3690	0.842161
$771$	12.3059	0.443187
$772$	18.7217	0.673807
$773$	36.5661	1.31519	0.657596	−	0.753371i	$-0.271574\pi$
$773$	36.5661	1.31519	0.657596	+	0.753371i	$0.271574\pi$
$774$	−1.87209	−0.0672907
$775$	31.0224	1.11436
$776$	18.8346	0.676124
$777$	−11.1344	−0.399444
$778$	38.4539	1.37864
$779$	2.50519	0.0897579
$780$	12.1931	0.436582
$781$	14.5632	0.521112
$782$	−4.05408	−0.144974
$783$	1.69625	0.0606191
$784$	−0.276726	−0.00988309
$785$	8.63957	0.308359
$786$	4.06788	0.145096
$787$	−30.8736	−1.10053	−0.550263	−	0.834992i	$-0.685472\pi$
$787$	−30.8736	−1.10053	−0.550263	+	0.834992i	$0.685472\pi$
$788$	−6.90034	−0.245814
$789$	−9.63986	−0.343188
$790$	13.9618	0.496740
$791$	−28.6814	−1.01979
$792$	−3.05839	−0.108675
$793$	−3.90157	−0.138549
$794$	−18.4829	−0.655933
$795$	22.7695	0.807552
$796$	6.38316	0.226245
$797$	−14.3979	−0.510000	−0.255000	−	0.966941i	$-0.582076\pi$
$797$	−14.3979	−0.510000	−0.255000	+	0.966941i	$0.582076\pi$
$798$	−6.50967	−0.230440
$799$	11.6321	0.411514
$800$	3.68393	0.130246
$801$	4.91770	0.173758
$802$	−6.99538	−0.247016
$803$	38.1358	1.34578
$804$	−4.57867	−0.161477
$805$	−30.9771	−1.09180
$806$	−34.8433	−1.22730
$807$	10.3663	0.364912
$808$	−13.1816	−0.463727
$809$	27.9819	0.983790	0.491895	−	0.870654i	$-0.336304\pi$
$809$	27.9819	0.983790	0.491895	+	0.870654i	$0.336304\pi$
$810$	−2.94685	−0.103542
$811$	7.69402	0.270174	0.135087	−	0.990834i	$-0.456869\pi$
$811$	7.69402	0.270174	0.135087	+	0.990834i	$0.456869\pi$
$812$	4.39826	0.154349
$813$	13.6910	0.480163
$814$	13.1331	0.460316
$815$	−0.479906	−0.0168104
$816$	−1.00000	−0.0350070
$817$	4.69996	0.164431
$818$	16.8371	0.588695
$819$	−10.7287	−0.374890
$820$	2.94057	0.102689
$821$	−47.8263	−1.66915	−0.834575	−	0.550894i	$-0.814287\pi$
$821$	−47.8263	−1.66915	−0.834575	+	0.550894i	$0.814287\pi$
$822$	12.4161	0.433063
$823$	−11.6637	−0.406569	−0.203285	−	0.979120i	$-0.565162\pi$
$823$	−11.6637	−0.406569	−0.203285	+	0.979120i	$0.565162\pi$
$824$	8.47277	0.295163
$825$	−11.2669	−0.392262
$826$	−2.59293	−0.0902195
$827$	9.96824	0.346630	0.173315	−	0.984866i	$-0.444552\pi$
$827$	9.96824	0.346630	0.173315	+	0.984866i	$0.444552\pi$
$828$	4.05408	0.140889
$829$	21.9871	0.763643	0.381822	−	0.924236i	$-0.375297\pi$
$829$	21.9871	0.763643	0.381822	+	0.924236i	$0.375297\pi$
$830$	15.9593	0.553955
$831$	−9.95712	−0.345409
$832$	−4.13766	−0.143448
$833$	0.276726	0.00958800
$834$	−2.87639	−0.0996012
$835$	63.9858	2.21432
$836$	7.67822	0.265557
$837$	8.42100	0.291072
$838$	−12.0786	−0.417249
$839$	21.3177	0.735969	0.367985	−	0.929832i	$-0.380048\pi$
$839$	21.3177	0.735969	0.367985	+	0.929832i	$0.380048\pi$
$840$	−7.64097	−0.263638
$841$	−26.1227	−0.900784
$842$	39.7490	1.36984
$843$	−0.144941	−0.00499202
$844$	27.8148	0.957424
$845$	−12.1418	−0.417690
$846$	−11.6321	−0.399920
$847$	−4.26868	−0.146674
$848$	−7.72673	−0.265337
$849$	12.5169	0.429578
$850$	−3.68393	−0.126358
$851$	−17.4088	−0.596765
$852$	−4.76172	−0.163134
$853$	−16.9760	−0.581248	−0.290624	−	0.956837i	$-0.593863\pi$
$853$	−16.9760	−0.581248	−0.290624	+	0.956837i	$0.593863\pi$
$854$	2.44498	0.0836654
$855$	7.39821	0.253013
$856$	−17.5913	−0.601258
$857$	−37.7382	−1.28911	−0.644556	−	0.764558i	$-0.722958\pi$
$857$	−37.7382	−1.28911	−0.644556	+	0.764558i	$0.722958\pi$
$858$	12.6546	0.432020
$859$	7.38892	0.252107	0.126053	−	0.992023i	$-0.459769\pi$
$859$	7.38892	0.252107	0.126053	+	0.992023i	$0.459769\pi$
$860$	5.51676	0.188120
$861$	−2.58740	−0.0881783
$862$	3.82406	0.130248
$863$	15.9761	0.543834	0.271917	−	0.962321i	$-0.412342\pi$
$863$	15.9761	0.543834	0.271917	+	0.962321i	$0.412342\pi$
$864$	1.00000	0.0340207
$865$	9.63837	0.327714
$866$	−1.11814	−0.0379961
$867$	1.00000	0.0339618
$868$	21.8350	0.741130
$869$	14.4903	0.491549
$870$	−4.99860	−0.169468
$871$	18.9450	0.641927
$872$	−12.2771	−0.415754
$873$	18.8346	0.637456
$874$	−10.1780	−0.344275
$875$	10.0561	0.339958
$876$	−12.4692	−0.421297
$877$	27.8005	0.938755	0.469378	−	0.882998i	$-0.344478\pi$
$877$	27.8005	0.938755	0.469378	+	0.882998i	$0.344478\pi$
$878$	25.7165	0.867890
$879$	10.6978	0.360829
$880$	9.01260	0.303815
$881$	−0.496845	−0.0167391	−0.00836957	−	0.999965i	$-0.502664\pi$
$881$	−0.496845	−0.0167391	−0.00836957	+	0.999965i	$0.502664\pi$
$882$	−0.276726	−0.00931786
$883$	27.9320	0.939986	0.469993	−	0.882670i	$-0.344256\pi$
$883$	27.9320	0.939986	0.469993	+	0.882670i	$0.344256\pi$
$884$	4.13766	0.139165
$885$	2.94685	0.0990573
$886$	−30.8915	−1.03782
$887$	42.5916	1.43009	0.715043	−	0.699081i	$-0.246407\pi$
$887$	42.5916	1.43009	0.715043	+	0.699081i	$0.246407\pi$
$888$	−4.29414	−0.144102
$889$	−11.2446	−0.377132
$890$	−14.4917	−0.485763
$891$	−3.05839	−0.102460
$892$	−0.0820386	−0.00274686
$893$	29.2029	0.977239
$894$	−16.3327	−0.546248
$895$	−41.2911	−1.38021
$896$	2.59293	0.0866236
$897$	−16.7744	−0.560082
$898$	−24.9899	−0.833923
$899$	14.2841	0.476403
$900$	3.68393	0.122798
$901$	7.72673	0.257415
$902$	3.05186	0.101616
$903$	−4.85418	−0.161537
$904$	−11.0614	−0.367896
$905$	−4.60969	−0.153231
$906$	−2.53256	−0.0841387
$907$	12.9002	0.428346	0.214173	−	0.976796i	$-0.431294\pi$
$907$	12.9002	0.428346	0.214173	+	0.976796i	$0.431294\pi$
$908$	−26.7816	−0.888780
$909$	−13.1816	−0.437206
$910$	31.6158	1.04805
$911$	−4.53163	−0.150139	−0.0750697	−	0.997178i	$-0.523918\pi$
$911$	−4.53163	−0.150139	−0.0750697	+	0.997178i	$0.523918\pi$
$912$	−2.51055	−0.0831325
$913$	16.5633	0.548167
$914$	14.8183	0.490145
$915$	−2.77871	−0.0918612
$916$	25.8246	0.853268
$917$	10.5477	0.348316
$918$	−1.00000	−0.0330049
$919$	31.7408	1.04703	0.523517	−	0.852015i	$-0.324620\pi$
$919$	31.7408	1.04703	0.523517	+	0.852015i	$0.324620\pi$
$920$	−11.9468	−0.393874
$921$	−20.1410	−0.663668
$922$	2.38631	0.0785890
$923$	19.7024	0.648513
$924$	−7.93017	−0.260883
$925$	−15.8193	−0.520135
$926$	−20.5562	−0.675518
$927$	8.47277	0.278282
$928$	1.69625	0.0556822
$929$	42.7452	1.40243	0.701213	−	0.712952i	$-0.252642\pi$
$929$	42.7452	1.40243	0.701213	+	0.712952i	$0.252642\pi$
$930$	−24.8154	−0.813730
$931$	0.694735	0.0227690
$932$	−17.3902	−0.569634
$933$	−13.7327	−0.449587
$934$	1.51471	0.0495627
$935$	−9.01260	−0.294744
$936$	−4.13766	−0.135244
$937$	−11.1322	−0.363672	−0.181836	−	0.983329i	$-0.558204\pi$
$937$	−11.1322	−0.363672	−0.181836	+	0.983329i	$0.558204\pi$
$938$	−11.8722	−0.387640
$939$	−3.38315	−0.110405
$940$	34.2781	1.11803
$941$	−46.5662	−1.51802	−0.759008	−	0.651081i	$-0.774316\pi$
$941$	−46.5662	−1.51802	−0.759008	+	0.651081i	$0.774316\pi$
$942$	−2.93180	−0.0955231
$943$	−4.04544	−0.131738
$944$	−1.00000	−0.0325472
$945$	−7.64097	−0.248561
$946$	5.72556	0.186154
$947$	30.8301	1.00184	0.500922	−	0.865493i	$-0.332994\pi$
$947$	30.8301	1.00184	0.500922	+	0.865493i	$0.332994\pi$
$948$	−4.73788	−0.153879
$949$	51.5935	1.67480
$950$	−9.24867	−0.300066
$951$	−2.09710	−0.0680031
$952$	−2.59293	−0.0840373
$953$	−16.9710	−0.549744	−0.274872	−	0.961481i	$-0.588635\pi$
$953$	−16.9710	−0.549744	−0.274872	+	0.961481i	$0.588635\pi$
$954$	−7.72673	−0.250162
$955$	−14.4269	−0.466844
$956$	−5.30771	−0.171664
$957$	−5.18779	−0.167697
$958$	3.78573	0.122311
$959$	32.1942	1.03960
$960$	−2.94685	−0.0951092
$961$	39.9133	1.28753
$962$	17.7677	0.572853
$963$	−17.5913	−0.566871
$964$	9.96044	0.320804
$965$	−55.1699	−1.77598
$966$	10.5119	0.338216
$967$	−40.6347	−1.30673	−0.653363	−	0.757045i	$-0.726642\pi$
$967$	−40.6347	−1.30673	−0.653363	+	0.757045i	$0.726642\pi$
$968$	−1.64628	−0.0529134
$969$	2.51055	0.0806504
$970$	−55.5029	−1.78209
$971$	28.5208	0.915277	0.457639	−	0.889138i	$-0.348695\pi$
$971$	28.5208	0.915277	0.457639	+	0.889138i	$0.348695\pi$
$972$	1.00000	0.0320750
$973$	−7.45827	−0.239101
$974$	−36.2495	−1.16151
$975$	−15.2428	−0.488162
$976$	0.942941	0.0301828
$977$	−42.1423	−1.34825	−0.674126	−	0.738616i	$-0.735480\pi$
$977$	−42.1423	−1.34825	−0.674126	+	0.738616i	$0.735480\pi$
$978$	0.162854	0.00520750
$979$	−15.0402	−0.480687
$980$	0.815471	0.0260493
$981$	−12.2771	−0.391976
$982$	−7.18833	−0.229389
$983$	40.3522	1.28704	0.643518	−	0.765431i	$-0.277474\pi$
$983$	40.3522	1.28704	0.643518	+	0.765431i	$0.277474\pi$
$984$	−0.997868	−0.0318109
$985$	20.3343	0.647903
$986$	−1.69625	−0.0540197
$987$	−30.1612	−0.960042
$988$	10.3878	0.330480
$989$	−7.58959	−0.241335
$990$	9.01260	0.286439
$991$	29.3802	0.933292	0.466646	−	0.884444i	$-0.345462\pi$
$991$	29.3802	0.933292	0.466646	+	0.884444i	$0.345462\pi$
$992$	8.42100	0.267367
$993$	23.5421	0.747087
$994$	−12.3468	−0.391617
$995$	−18.8102	−0.596324
$996$	−5.41572	−0.171604
$997$	−34.7196	−1.09958	−0.549790	−	0.835303i	$-0.685292\pi$
$997$	−34.7196	−1.09958	−0.549790	+	0.835303i	$0.685292\pi$
$998$	−27.9666	−0.885266
$999$	−4.29414	−0.135860

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.r.1.1	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.94685 q^{5} +1.00000 q^{6} +2.59293 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.94685 q^{5} +1.00000 q^{6} +2.59293 q^{7} +1.00000 q^{8} +1.00000 q^{9} -2.94685 q^{10} -3.05839 q^{11} +1.00000 q^{12} -4.13766 q^{13} +2.59293 q^{14} -2.94685 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} -2.51055 q^{19} -2.94685 q^{20} +2.59293 q^{21} -3.05839 q^{22} +4.05408 q^{23} +1.00000 q^{24} +3.68393 q^{25} -4.13766 q^{26} +1.00000 q^{27} +2.59293 q^{28} +1.69625 q^{29} -2.94685 q^{30} +8.42100 q^{31} +1.00000 q^{32} -3.05839 q^{33} -1.00000 q^{34} -7.64097 q^{35} +1.00000 q^{36} -4.29414 q^{37} -2.51055 q^{38} -4.13766 q^{39} -2.94685 q^{40} -0.997868 q^{41} +2.59293 q^{42} -1.87209 q^{43} -3.05839 q^{44} -2.94685 q^{45} +4.05408 q^{46} -11.6321 q^{47} +1.00000 q^{48} -0.276726 q^{49} +3.68393 q^{50} -1.00000 q^{51} -4.13766 q^{52} -7.72673 q^{53} +1.00000 q^{54} +9.01260 q^{55} +2.59293 q^{56} -2.51055 q^{57} +1.69625 q^{58} -1.00000 q^{59} -2.94685 q^{60} +0.942941 q^{61} +8.42100 q^{62} +2.59293 q^{63} +1.00000 q^{64} +12.1931 q^{65} -3.05839 q^{66} -4.57867 q^{67} -1.00000 q^{68} +4.05408 q^{69} -7.64097 q^{70} -4.76172 q^{71} +1.00000 q^{72} -12.4692 q^{73} -4.29414 q^{74} +3.68393 q^{75} -2.51055 q^{76} -7.93017 q^{77} -4.13766 q^{78} -4.73788 q^{79} -2.94685 q^{80} +1.00000 q^{81} -0.997868 q^{82} -5.41572 q^{83} +2.59293 q^{84} +2.94685 q^{85} -1.87209 q^{86} +1.69625 q^{87} -3.05839 q^{88} +4.91770 q^{89} -2.94685 q^{90} -10.7287 q^{91} +4.05408 q^{92} +8.42100 q^{93} -11.6321 q^{94} +7.39821 q^{95} +1.00000 q^{96} +18.8346 q^{97} -0.276726 q^{98} -3.05839 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + 6 q^{3} + 6 q^{4} - 3 q^{5} + 6 q^{6} - 7 q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 + 6 * q^3 + 6 * q^4 - 3 * q^5 + 6 * q^6 - 7 * q^7 + 6 * q^8 + 6 * q^9	\( 6 q + 6 q^{2} + 6 q^{3} + 6 q^{4} - 3 q^{5} + 6 q^{6} - 7 q^{7} + 6 q^{8} + 6 q^{9} - 3 q^{10} - 8 q^{11} + 6 q^{12} - 6 q^{13} - 7 q^{14} - 3 q^{15} + 6 q^{16} - 6 q^{17} + 6 q^{18} - 14 q^{19} - 3 q^{20} - 7 q^{21} - 8 q^{22} - 8 q^{23} + 6 q^{24} - 13 q^{25} - 6 q^{26} + 6 q^{27} - 7 q^{28} - 21 q^{29} - 3 q^{30} - 5 q^{31} + 6 q^{32} - 8 q^{33} - 6 q^{34} - 12 q^{35} + 6 q^{36} - 13 q^{37} - 14 q^{38} - 6 q^{39} - 3 q^{40} - 18 q^{41} - 7 q^{42} - 4 q^{43} - 8 q^{44} - 3 q^{45} - 8 q^{46} - 4 q^{47} + 6 q^{48} + 5 q^{49} - 13 q^{50} - 6 q^{51} - 6 q^{52} - 25 q^{53} + 6 q^{54} - 8 q^{55} - 7 q^{56} - 14 q^{57} - 21 q^{58} - 6 q^{59} - 3 q^{60} - 5 q^{62} - 7 q^{63} + 6 q^{64} + 6 q^{65} - 8 q^{66} - 13 q^{67} - 6 q^{68} - 8 q^{69} - 12 q^{70} - 12 q^{71} + 6 q^{72} - 4 q^{73} - 13 q^{74} - 13 q^{75} - 14 q^{76} + 4 q^{77} - 6 q^{78} - 12 q^{79} - 3 q^{80} + 6 q^{81} - 18 q^{82} + 9 q^{83} - 7 q^{84} + 3 q^{85} - 4 q^{86} - 21 q^{87} - 8 q^{88} - 11 q^{89} - 3 q^{90} - 31 q^{91} - 8 q^{92} - 5 q^{93} - 4 q^{94} + 35 q^{95} + 6 q^{96} + 16 q^{97} + 5 q^{98} - 8 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 + 6 * q^3 + 6 * q^4 - 3 * q^5 + 6 * q^6 - 7 * q^7 + 6 * q^8 + 6 * q^9 - 3 * q^10 - 8 * q^11 + 6 * q^12 - 6 * q^13 - 7 * q^14 - 3 * q^15 + 6 * q^16 - 6 * q^17 + 6 * q^18 - 14 * q^19 - 3 * q^20 - 7 * q^21 - 8 * q^22 - 8 * q^23 + 6 * q^24 - 13 * q^25 - 6 * q^26 + 6 * q^27 - 7 * q^28 - 21 * q^29 - 3 * q^30 - 5 * q^31 + 6 * q^32 - 8 * q^33 - 6 * q^34 - 12 * q^35 + 6 * q^36 - 13 * q^37 - 14 * q^38 - 6 * q^39 - 3 * q^40 - 18 * q^41 - 7 * q^42 - 4 * q^43 - 8 * q^44 - 3 * q^45 - 8 * q^46 - 4 * q^47 + 6 * q^48 + 5 * q^49 - 13 * q^50 - 6 * q^51 - 6 * q^52 - 25 * q^53 + 6 * q^54 - 8 * q^55 - 7 * q^56 - 14 * q^57 - 21 * q^58 - 6 * q^59 - 3 * q^60 - 5 * q^62 - 7 * q^63 + 6 * q^64 + 6 * q^65 - 8 * q^66 - 13 * q^67 - 6 * q^68 - 8 * q^69 - 12 * q^70 - 12 * q^71 + 6 * q^72 - 4 * q^73 - 13 * q^74 - 13 * q^75 - 14 * q^76 + 4 * q^77 - 6 * q^78 - 12 * q^79 - 3 * q^80 + 6 * q^81 - 18 * q^82 + 9 * q^83 - 7 * q^84 + 3 * q^85 - 4 * q^86 - 21 * q^87 - 8 * q^88 - 11 * q^89 - 3 * q^90 - 31 * q^91 - 8 * q^92 - 5 * q^93 - 4 * q^94 + 35 * q^95 + 6 * q^96 + 16 * q^97 + 5 * q^98 - 8 * q^99

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