LMFDB - Embedded newform 6018.2.a.z.1.2

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			1.2
Root			$-2.64826$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.64826 q^{5} -1.00000 q^{6} +3.55508 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.64826 q^{5} -1.00000 q^{6} +3.55508 q^{7} +1.00000 q^{8} +1.00000 q^{9} -2.64826 q^{10} -1.52226 q^{11} -1.00000 q^{12} +0.735651 q^{13} +3.55508 q^{14} +2.64826 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} +3.99021 q^{19} -2.64826 q^{20} -3.55508 q^{21} -1.52226 q^{22} -4.31835 q^{23} -1.00000 q^{24} +2.01329 q^{25} +0.735651 q^{26} -1.00000 q^{27} +3.55508 q^{28} -0.681423 q^{29} +2.64826 q^{30} +8.45489 q^{31} +1.00000 q^{32} +1.52226 q^{33} -1.00000 q^{34} -9.41479 q^{35} +1.00000 q^{36} +10.9406 q^{37} +3.99021 q^{38} -0.735651 q^{39} -2.64826 q^{40} -0.567568 q^{41} -3.55508 q^{42} +3.56459 q^{43} -1.52226 q^{44} -2.64826 q^{45} -4.31835 q^{46} -12.6874 q^{47} -1.00000 q^{48} +5.63862 q^{49} +2.01329 q^{50} +1.00000 q^{51} +0.735651 q^{52} -2.61343 q^{53} -1.00000 q^{54} +4.03135 q^{55} +3.55508 q^{56} -3.99021 q^{57} -0.681423 q^{58} -1.00000 q^{59} +2.64826 q^{60} -2.02561 q^{61} +8.45489 q^{62} +3.55508 q^{63} +1.00000 q^{64} -1.94820 q^{65} +1.52226 q^{66} -6.71508 q^{67} -1.00000 q^{68} +4.31835 q^{69} -9.41479 q^{70} -0.284372 q^{71} +1.00000 q^{72} +2.98539 q^{73} +10.9406 q^{74} -2.01329 q^{75} +3.99021 q^{76} -5.41177 q^{77} -0.735651 q^{78} +13.7397 q^{79} -2.64826 q^{80} +1.00000 q^{81} -0.567568 q^{82} +11.1306 q^{83} -3.55508 q^{84} +2.64826 q^{85} +3.56459 q^{86} +0.681423 q^{87} -1.52226 q^{88} -0.619345 q^{89} -2.64826 q^{90} +2.61530 q^{91} -4.31835 q^{92} -8.45489 q^{93} -12.6874 q^{94} -10.5671 q^{95} -1.00000 q^{96} -11.7960 q^{97} +5.63862 q^{98} -1.52226 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−2.64826	−1.18434	−0.592169	−	0.805814i	$-0.701728\pi$
$5$	−2.64826	−1.18434	−0.592169	+	0.805814i	$0.701728\pi$
$6$	−1.00000	−0.408248
$7$	3.55508	1.34370	0.671848	−	0.740689i	$-0.265501\pi$
$7$	3.55508	1.34370	0.671848	+	0.740689i	$0.265501\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−2.64826	−0.837454
$11$	−1.52226	−0.458979	−0.229490	−	0.973311i	$-0.573706\pi$
$11$	−1.52226	−0.458979	−0.229490	+	0.973311i	$0.573706\pi$
$12$	−1.00000	−0.288675
$13$	0.735651	0.204033	0.102016	−	0.994783i	$-0.467471\pi$
$13$	0.735651	0.204033	0.102016	+	0.994783i	$0.467471\pi$
$14$	3.55508	0.950136
$15$	2.64826	0.683778
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.00000	0.235702
$19$	3.99021	0.915418	0.457709	−	0.889102i	$-0.348670\pi$
$19$	3.99021	0.915418	0.457709	+	0.889102i	$0.348670\pi$
$20$	−2.64826	−0.592169
$21$	−3.55508	−0.775783
$22$	−1.52226	−0.324547
$23$	−4.31835	−0.900439	−0.450219	−	0.892918i	$-0.648654\pi$
$23$	−4.31835	−0.900439	−0.450219	+	0.892918i	$0.648654\pi$
$24$	−1.00000	−0.204124
$25$	2.01329	0.402658
$26$	0.735651	0.144273
$27$	−1.00000	−0.192450
$28$	3.55508	0.671848
$29$	−0.681423	−0.126537	−0.0632685	−	0.997997i	$-0.520152\pi$
$29$	−0.681423	−0.126537	−0.0632685	+	0.997997i	$0.520152\pi$
$30$	2.64826	0.483504
$31$	8.45489	1.51854	0.759272	−	0.650773i	$-0.225555\pi$
$31$	8.45489	1.51854	0.759272	+	0.650773i	$0.225555\pi$
$32$	1.00000	0.176777
$33$	1.52226	0.264992
$34$	−1.00000	−0.171499
$35$	−9.41479	−1.59139
$36$	1.00000	0.166667
$37$	10.9406	1.79862	0.899312	−	0.437307i	$-0.144068\pi$
$37$	10.9406	1.79862	0.899312	+	0.437307i	$0.144068\pi$
$38$	3.99021	0.647298
$39$	−0.735651	−0.117798
$40$	−2.64826	−0.418727
$41$	−0.567568	−0.0886392	−0.0443196	−	0.999017i	$-0.514112\pi$
$41$	−0.567568	−0.0886392	−0.0443196	+	0.999017i	$0.514112\pi$
$42$	−3.55508	−0.548561
$43$	3.56459	0.543595	0.271798	−	0.962354i	$-0.412382\pi$
$43$	3.56459	0.543595	0.271798	+	0.962354i	$0.412382\pi$
$44$	−1.52226	−0.229490
$45$	−2.64826	−0.394780
$46$	−4.31835	−0.636706
$47$	−12.6874	−1.85065	−0.925326	−	0.379172i	$-0.876209\pi$
$47$	−12.6874	−1.85065	−0.925326	+	0.379172i	$0.876209\pi$
$48$	−1.00000	−0.144338
$49$	5.63862	0.805516
$50$	2.01329	0.284722
$51$	1.00000	0.140028
$52$	0.735651	0.102016
$53$	−2.61343	−0.358983	−0.179491	−	0.983760i	$-0.557445\pi$
$53$	−2.61343	−0.358983	−0.179491	+	0.983760i	$0.557445\pi$
$54$	−1.00000	−0.136083
$55$	4.03135	0.543587
$56$	3.55508	0.475068
$57$	−3.99021	−0.528517
$58$	−0.681423	−0.0894752
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	2.64826	0.341889
$61$	−2.02561	−0.259353	−0.129677	−	0.991556i	$-0.541394\pi$
$61$	−2.02561	−0.259353	−0.129677	+	0.991556i	$0.541394\pi$
$62$	8.45489	1.07377
$63$	3.55508	0.447898
$64$	1.00000	0.125000
$65$	−1.94820	−0.241644
$66$	1.52226	0.187377
$67$	−6.71508	−0.820378	−0.410189	−	0.912001i	$-0.634537\pi$
$67$	−6.71508	−0.820378	−0.410189	+	0.912001i	$0.634537\pi$
$68$	−1.00000	−0.121268
$69$	4.31835	0.519868
$70$	−9.41479	−1.12528
$71$	−0.284372	−0.0337487	−0.0168744	−	0.999858i	$-0.505372\pi$
$71$	−0.284372	−0.0337487	−0.0168744	+	0.999858i	$0.505372\pi$
$72$	1.00000	0.117851
$73$	2.98539	0.349413	0.174707	−	0.984621i	$-0.444102\pi$
$73$	2.98539	0.349413	0.174707	+	0.984621i	$0.444102\pi$
$74$	10.9406	1.27182
$75$	−2.01329	−0.232475
$76$	3.99021	0.457709
$77$	−5.41177	−0.616728
$78$	−0.735651	−0.0832961
$79$	13.7397	1.54583	0.772917	−	0.634507i	$-0.218797\pi$
$79$	13.7397	1.54583	0.772917	+	0.634507i	$0.218797\pi$
$80$	−2.64826	−0.296085
$81$	1.00000	0.111111
$82$	−0.567568	−0.0626774
$83$	11.1306	1.22174	0.610871	−	0.791730i	$-0.290819\pi$
$83$	11.1306	1.22174	0.610871	+	0.791730i	$0.290819\pi$
$84$	−3.55508	−0.387891
$85$	2.64826	0.287244
$86$	3.56459	0.384380
$87$	0.681423	0.0730562
$88$	−1.52226	−0.162274
$89$	−0.619345	−0.0656504	−0.0328252	−	0.999461i	$-0.510450\pi$
$89$	−0.619345	−0.0656504	−0.0328252	+	0.999461i	$0.510450\pi$
$90$	−2.64826	−0.279151
$91$	2.61530	0.274158
$92$	−4.31835	−0.450219
$93$	−8.45489	−0.876732
$94$	−12.6874	−1.30861
$95$	−10.5671	−1.08416
$96$	−1.00000	−0.102062
$97$	−11.7960	−1.19770	−0.598851	−	0.800860i	$-0.704376\pi$
$97$	−11.7960	−1.19770	−0.598851	+	0.800860i	$0.704376\pi$
$98$	5.63862	0.569586
$99$	−1.52226	−0.152993
$100$	2.01329	0.201329
$101$	4.51667	0.449426	0.224713	−	0.974425i	$-0.427856\pi$
$101$	4.51667	0.449426	0.224713	+	0.974425i	$0.427856\pi$
$102$	1.00000	0.0990148
$103$	11.8262	1.16527	0.582636	−	0.812733i	$-0.302021\pi$
$103$	11.8262	1.16527	0.582636	+	0.812733i	$0.302021\pi$
$104$	0.735651	0.0721365
$105$	9.41479	0.918789
$106$	−2.61343	−0.253839
$107$	15.4584	1.49442	0.747209	−	0.664590i	$-0.231394\pi$
$107$	15.4584	1.49442	0.747209	+	0.664590i	$0.231394\pi$
$108$	−1.00000	−0.0962250
$109$	−8.50319	−0.814458	−0.407229	−	0.913326i	$-0.633505\pi$
$109$	−8.50319	−0.814458	−0.407229	+	0.913326i	$0.633505\pi$
$110$	4.03135	0.384374
$111$	−10.9406	−1.03844
$112$	3.55508	0.335924
$113$	15.1110	1.42153	0.710763	−	0.703431i	$-0.248350\pi$
$113$	15.1110	1.42153	0.710763	+	0.703431i	$0.248350\pi$
$114$	−3.99021	−0.373718
$115$	11.4361	1.06642
$116$	−0.681423	−0.0632685
$117$	0.735651	0.0680110
$118$	−1.00000	−0.0920575
$119$	−3.55508	−0.325894
$120$	2.64826	0.241752
$121$	−8.68272	−0.789338
$122$	−2.02561	−0.183390
$123$	0.567568	0.0511759
$124$	8.45489	0.759272
$125$	7.90959	0.707455
$126$	3.55508	0.316712
$127$	−5.32998	−0.472959	−0.236480	−	0.971636i	$-0.575994\pi$
$127$	−5.32998	−0.472959	−0.236480	+	0.971636i	$0.575994\pi$
$128$	1.00000	0.0883883
$129$	−3.56459	−0.313845
$130$	−1.94820	−0.170868
$131$	0.369304	0.0322663	0.0161331	−	0.999870i	$-0.494864\pi$
$131$	0.369304	0.0322663	0.0161331	+	0.999870i	$0.494864\pi$
$132$	1.52226	0.132496
$133$	14.1855	1.23004
$134$	−6.71508	−0.580095
$135$	2.64826	0.227926
$136$	−1.00000	−0.0857493
$137$	5.74535	0.490858	0.245429	−	0.969415i	$-0.421071\pi$
$137$	5.74535	0.490858	0.245429	+	0.969415i	$0.421071\pi$
$138$	4.31835	0.367603
$139$	11.5389	0.978717	0.489358	−	0.872083i	$-0.337231\pi$
$139$	11.5389	0.978717	0.489358	+	0.872083i	$0.337231\pi$
$140$	−9.41479	−0.795695
$141$	12.6874	1.06847
$142$	−0.284372	−0.0238640
$143$	−1.11985	−0.0936469
$144$	1.00000	0.0833333
$145$	1.80459	0.149863
$146$	2.98539	0.247072
$147$	−5.63862	−0.465065
$148$	10.9406	0.899312
$149$	11.4195	0.935519	0.467760	−	0.883856i	$-0.345061\pi$
$149$	11.4195	0.935519	0.467760	+	0.883856i	$0.345061\pi$
$150$	−2.01329	−0.164384
$151$	−10.8207	−0.880572	−0.440286	−	0.897857i	$-0.645123\pi$
$151$	−10.8207	−0.880572	−0.440286	+	0.897857i	$0.645123\pi$
$152$	3.99021	0.323649
$153$	−1.00000	−0.0808452
$154$	−5.41177	−0.436092
$155$	−22.3908	−1.79847
$156$	−0.735651	−0.0588992
$157$	−4.85278	−0.387294	−0.193647	−	0.981071i	$-0.562032\pi$
$157$	−4.85278	−0.387294	−0.193647	+	0.981071i	$0.562032\pi$
$158$	13.7397	1.09307
$159$	2.61343	0.207259
$160$	−2.64826	−0.209363
$161$	−15.3521	−1.20991
$162$	1.00000	0.0785674
$163$	3.86608	0.302814	0.151407	−	0.988471i	$-0.451620\pi$
$163$	3.86608	0.302814	0.151407	+	0.988471i	$0.451620\pi$
$164$	−0.567568	−0.0443196
$165$	−4.03135	−0.313840
$166$	11.1306	0.863902
$167$	3.26831	0.252910	0.126455	−	0.991972i	$-0.459640\pi$
$167$	3.26831	0.252910	0.126455	+	0.991972i	$0.459640\pi$
$168$	−3.55508	−0.274281
$169$	−12.4588	−0.958371
$170$	2.64826	0.203112
$171$	3.99021	0.305139
$172$	3.56459	0.271798
$173$	5.96246	0.453317	0.226659	−	0.973974i	$-0.427220\pi$
$173$	5.96246	0.453317	0.226659	+	0.973974i	$0.427220\pi$
$174$	0.681423	0.0516585
$175$	7.15741	0.541049
$176$	−1.52226	−0.114745
$177$	1.00000	0.0751646
$178$	−0.619345	−0.0464218
$179$	3.87241	0.289438	0.144719	−	0.989473i	$-0.453772\pi$
$179$	3.87241	0.289438	0.144719	+	0.989473i	$0.453772\pi$
$180$	−2.64826	−0.197390
$181$	10.6400	0.790867	0.395434	−	0.918495i	$-0.370594\pi$
$181$	10.6400	0.790867	0.395434	+	0.918495i	$0.370594\pi$
$182$	2.61530	0.193859
$183$	2.02561	0.149738
$184$	−4.31835	−0.318353
$185$	−28.9736	−2.13018
$186$	−8.45489	−0.619943
$187$	1.52226	0.111319
$188$	−12.6874	−0.925326
$189$	−3.55508	−0.258594
$190$	−10.5671	−0.766620
$191$	20.8647	1.50972	0.754859	−	0.655887i	$-0.227705\pi$
$191$	20.8647	1.50972	0.754859	+	0.655887i	$0.227705\pi$
$192$	−1.00000	−0.0721688
$193$	1.81394	0.130570	0.0652852	−	0.997867i	$-0.479204\pi$
$193$	1.81394	0.130570	0.0652852	+	0.997867i	$0.479204\pi$
$194$	−11.7960	−0.846904
$195$	1.94820	0.139513
$196$	5.63862	0.402758
$197$	6.34157	0.451818	0.225909	−	0.974148i	$-0.427465\pi$
$197$	6.34157	0.451818	0.225909	+	0.974148i	$0.427465\pi$
$198$	−1.52226	−0.108182
$199$	−5.95288	−0.421988	−0.210994	−	0.977487i	$-0.567670\pi$
$199$	−5.95288	−0.421988	−0.210994	+	0.977487i	$0.567670\pi$
$200$	2.01329	0.142361
$201$	6.71508	0.473645
$202$	4.51667	0.317792
$203$	−2.42251	−0.170027
$204$	1.00000	0.0700140
$205$	1.50307	0.104979
$206$	11.8262	0.823971
$207$	−4.31835	−0.300146
$208$	0.735651	0.0510082
$209$	−6.07415	−0.420158
$210$	9.41479	0.649682
$211$	−0.810317	−0.0557845	−0.0278923	−	0.999611i	$-0.508880\pi$
$211$	−0.810317	−0.0557845	−0.0278923	+	0.999611i	$0.508880\pi$
$212$	−2.61343	−0.179491
$213$	0.284372	0.0194848
$214$	15.4584	1.05671
$215$	−9.43997	−0.643801
$216$	−1.00000	−0.0680414
$217$	30.0579	2.04046
$218$	−8.50319	−0.575909
$219$	−2.98539	−0.201734
$220$	4.03135	0.271793
$221$	−0.735651	−0.0494853
$222$	−10.9406	−0.734285
$223$	0.528082	0.0353630	0.0176815	−	0.999844i	$-0.494372\pi$
$223$	0.528082	0.0353630	0.0176815	+	0.999844i	$0.494372\pi$
$224$	3.55508	0.237534
$225$	2.01329	0.134219
$226$	15.1110	1.00517
$227$	21.1198	1.40177	0.700884	−	0.713276i	$-0.252789\pi$
$227$	21.1198	1.40177	0.700884	+	0.713276i	$0.252789\pi$
$228$	−3.99021	−0.264258
$229$	−9.32395	−0.616144	−0.308072	−	0.951363i	$-0.599684\pi$
$229$	−9.32395	−0.616144	−0.308072	+	0.951363i	$0.599684\pi$
$230$	11.4361	0.754076
$231$	5.41177	0.356068
$232$	−0.681423	−0.0447376
$233$	8.99292	0.589146	0.294573	−	0.955629i	$-0.404823\pi$
$233$	8.99292	0.589146	0.294573	+	0.955629i	$0.404823\pi$
$234$	0.735651	0.0480910
$235$	33.5996	2.19180
$236$	−1.00000	−0.0650945
$237$	−13.7397	−0.892488
$238$	−3.55508	−0.230442
$239$	11.5727	0.748574	0.374287	−	0.927313i	$-0.377887\pi$
$239$	11.5727	0.748574	0.374287	+	0.927313i	$0.377887\pi$
$240$	2.64826	0.170945
$241$	−2.76620	−0.178187	−0.0890934	−	0.996023i	$-0.528397\pi$
$241$	−2.76620	−0.178187	−0.0890934	+	0.996023i	$0.528397\pi$
$242$	−8.68272	−0.558146
$243$	−1.00000	−0.0641500
$244$	−2.02561	−0.129677
$245$	−14.9325	−0.954004
$246$	0.567568	0.0361868
$247$	2.93541	0.186775
$248$	8.45489	0.536886
$249$	−11.1306	−0.705373
$250$	7.90959	0.500246
$251$	7.96650	0.502841	0.251420	−	0.967878i	$-0.419102\pi$
$251$	7.96650	0.502841	0.251420	+	0.967878i	$0.419102\pi$
$252$	3.55508	0.223949
$253$	6.57366	0.413282
$254$	−5.32998	−0.334433
$255$	−2.64826	−0.165841
$256$	1.00000	0.0625000
$257$	17.2159	1.07390	0.536950	−	0.843614i	$-0.319576\pi$
$257$	17.2159	1.07390	0.536950	+	0.843614i	$0.319576\pi$
$258$	−3.56459	−0.221922
$259$	38.8948	2.41680
$260$	−1.94820	−0.120822
$261$	−0.681423	−0.0421790
$262$	0.369304	0.0228157
$263$	−5.47040	−0.337319	−0.168660	−	0.985674i	$-0.553944\pi$
$263$	−5.47040	−0.337319	−0.168660	+	0.985674i	$0.553944\pi$
$264$	1.52226	0.0936887
$265$	6.92106	0.425157
$266$	14.1855	0.869772
$267$	0.619345	0.0379033
$268$	−6.71508	−0.410189
$269$	−6.39357	−0.389823	−0.194911	−	0.980821i	$-0.562442\pi$
$269$	−6.39357	−0.389823	−0.194911	+	0.980821i	$0.562442\pi$
$270$	2.64826	0.161168
$271$	−15.5891	−0.946972	−0.473486	−	0.880801i	$-0.657005\pi$
$271$	−15.5891	−0.946972	−0.473486	+	0.880801i	$0.657005\pi$
$272$	−1.00000	−0.0606339
$273$	−2.61530	−0.158285
$274$	5.74535	0.347089
$275$	−3.06475	−0.184812
$276$	4.31835	0.259934
$277$	25.7827	1.54913	0.774566	−	0.632493i	$-0.217968\pi$
$277$	25.7827	1.54913	0.774566	+	0.632493i	$0.217968\pi$
$278$	11.5389	0.692057
$279$	8.45489	0.506181
$280$	−9.41479	−0.562641
$281$	−19.4003	−1.15732	−0.578661	−	0.815568i	$-0.696425\pi$
$281$	−19.4003	−1.15732	−0.578661	+	0.815568i	$0.696425\pi$
$282$	12.6874	0.755526
$283$	14.6348	0.869948	0.434974	−	0.900443i	$-0.356758\pi$
$283$	14.6348	0.869948	0.434974	+	0.900443i	$0.356758\pi$
$284$	−0.284372	−0.0168744
$285$	10.5671	0.625943
$286$	−1.11985	−0.0662183
$287$	−2.01775	−0.119104
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	1.80459	0.105969
$291$	11.7960	0.691494
$292$	2.98539	0.174707
$293$	8.28260	0.483874	0.241937	−	0.970292i	$-0.422217\pi$
$293$	8.28260	0.483874	0.241937	+	0.970292i	$0.422217\pi$
$294$	−5.63862	−0.328851
$295$	2.64826	0.154188
$296$	10.9406	0.635910
$297$	1.52226	0.0883306
$298$	11.4195	0.661512
$299$	−3.17680	−0.183719
$300$	−2.01329	−0.116237
$301$	12.6724	0.730426
$302$	−10.8207	−0.622659
$303$	−4.51667	−0.259476
$304$	3.99021	0.228855
$305$	5.36435	0.307162
$306$	−1.00000	−0.0571662
$307$	5.62387	0.320971	0.160485	−	0.987038i	$-0.448694\pi$
$307$	5.62387	0.320971	0.160485	+	0.987038i	$0.448694\pi$
$308$	−5.41177	−0.308364
$309$	−11.8262	−0.672770
$310$	−22.3908	−1.27171
$311$	13.1280	0.744419	0.372209	−	0.928149i	$-0.378600\pi$
$311$	13.1280	0.744419	0.372209	+	0.928149i	$0.378600\pi$
$312$	−0.735651	−0.0416481
$313$	−23.9693	−1.35482	−0.677412	−	0.735604i	$-0.736898\pi$
$313$	−23.9693	−1.35482	−0.677412	+	0.735604i	$0.736898\pi$
$314$	−4.85278	−0.273858
$315$	−9.41479	−0.530463
$316$	13.7397	0.772917
$317$	29.8678	1.67754	0.838771	−	0.544485i	$-0.183275\pi$
$317$	29.8678	1.67754	0.838771	+	0.544485i	$0.183275\pi$
$318$	2.61343	0.146554
$319$	1.03730	0.0580778
$320$	−2.64826	−0.148042
$321$	−15.4584	−0.862802
$322$	−15.3521	−0.855539
$323$	−3.99021	−0.222021
$324$	1.00000	0.0555556
$325$	1.48108	0.0821555
$326$	3.86608	0.214122
$327$	8.50319	0.470228
$328$	−0.567568	−0.0313387
$329$	−45.1049	−2.48671
$330$	−4.03135	−0.221918
$331$	19.1543	1.05282	0.526408	−	0.850232i	$-0.323539\pi$
$331$	19.1543	1.05282	0.526408	+	0.850232i	$0.323539\pi$
$332$	11.1306	0.610871
$333$	10.9406	0.599542
$334$	3.26831	0.178834
$335$	17.7833	0.971605
$336$	−3.55508	−0.193946
$337$	21.6894	1.18149	0.590747	−	0.806857i	$-0.298833\pi$
$337$	21.6894	1.18149	0.590747	+	0.806857i	$0.298833\pi$
$338$	−12.4588	−0.677670
$339$	−15.1110	−0.820718
$340$	2.64826	0.143622
$341$	−12.8706	−0.696980
$342$	3.99021	0.215766
$343$	−4.83984	−0.261327
$344$	3.56459	0.192190
$345$	−11.4361	−0.615700
$346$	5.96246	0.320544
$347$	−21.0091	−1.12783	−0.563913	−	0.825834i	$-0.690705\pi$
$347$	−21.0091	−1.12783	−0.563913	+	0.825834i	$0.690705\pi$
$348$	0.681423	0.0365281
$349$	−17.0187	−0.910991	−0.455496	−	0.890238i	$-0.650538\pi$
$349$	−17.0187	−0.910991	−0.455496	+	0.890238i	$0.650538\pi$
$350$	7.15741	0.382580
$351$	−0.735651	−0.0392662
$352$	−1.52226	−0.0811368
$353$	−13.8340	−0.736310	−0.368155	−	0.929764i	$-0.620010\pi$
$353$	−13.8340	−0.736310	−0.368155	+	0.929764i	$0.620010\pi$
$354$	1.00000	0.0531494
$355$	0.753091	0.0399699
$356$	−0.619345	−0.0328252
$357$	3.55508	0.188155
$358$	3.87241	0.204663
$359$	28.9292	1.52682	0.763412	−	0.645912i	$-0.223523\pi$
$359$	28.9292	1.52682	0.763412	+	0.645912i	$0.223523\pi$
$360$	−2.64826	−0.139576
$361$	−3.07819	−0.162010
$362$	10.6400	0.559228
$363$	8.68272	0.455725
$364$	2.61530	0.137079
$365$	−7.90609	−0.413824
$366$	2.02561	0.105880
$367$	19.3888	1.01209	0.506044	−	0.862508i	$-0.331107\pi$
$367$	19.3888	1.01209	0.506044	+	0.862508i	$0.331107\pi$
$368$	−4.31835	−0.225110
$369$	−0.567568	−0.0295464
$370$	−28.9736	−1.50627
$371$	−9.29098	−0.482363
$372$	−8.45489	−0.438366
$373$	20.0758	1.03948	0.519742	−	0.854323i	$-0.326028\pi$
$373$	20.0758	1.03948	0.519742	+	0.854323i	$0.326028\pi$
$374$	1.52226	0.0787143
$375$	−7.90959	−0.408450
$376$	−12.6874	−0.654304
$377$	−0.501289	−0.0258177
$378$	−3.55508	−0.182854
$379$	22.2150	1.14111	0.570555	−	0.821260i	$-0.306728\pi$
$379$	22.2150	1.14111	0.570555	+	0.821260i	$0.306728\pi$
$380$	−10.5671	−0.542082
$381$	5.32998	0.273063
$382$	20.8647	1.06753
$383$	2.97824	0.152181	0.0760905	−	0.997101i	$-0.475756\pi$
$383$	2.97824	0.152181	0.0760905	+	0.997101i	$0.475756\pi$
$384$	−1.00000	−0.0510310
$385$	14.3318	0.730415
$386$	1.81394	0.0923272
$387$	3.56459	0.181198
$388$	−11.7960	−0.598851
$389$	25.6397	1.29999	0.649993	−	0.759940i	$-0.274772\pi$
$389$	25.6397	1.29999	0.649993	+	0.759940i	$0.274772\pi$
$390$	1.94820	0.0986508
$391$	4.31835	0.218388
$392$	5.63862	0.284793
$393$	−0.369304	−0.0186289
$394$	6.34157	0.319484
$395$	−36.3862	−1.83079
$396$	−1.52226	−0.0764965
$397$	−26.1938	−1.31463	−0.657315	−	0.753616i	$-0.728308\pi$
$397$	−26.1938	−1.31463	−0.657315	+	0.753616i	$0.728308\pi$
$398$	−5.95288	−0.298391
$399$	−14.1855	−0.710165
$400$	2.01329	0.100664
$401$	−5.22997	−0.261172	−0.130586	−	0.991437i	$-0.541686\pi$
$401$	−5.22997	−0.261172	−0.130586	+	0.991437i	$0.541686\pi$
$402$	6.71508	0.334918
$403$	6.21985	0.309833
$404$	4.51667	0.224713
$405$	−2.64826	−0.131593
$406$	−2.42251	−0.120227
$407$	−16.6545	−0.825531
$408$	1.00000	0.0495074
$409$	−4.86369	−0.240494	−0.120247	−	0.992744i	$-0.538369\pi$
$409$	−4.86369	−0.240494	−0.120247	+	0.992744i	$0.538369\pi$
$410$	1.50307	0.0742312
$411$	−5.74535	−0.283397
$412$	11.8262	0.582636
$413$	−3.55508	−0.174934
$414$	−4.31835	−0.212235
$415$	−29.4767	−1.44696
$416$	0.735651	0.0360683
$417$	−11.5389	−0.565062
$418$	−6.07415	−0.297096
$419$	13.5015	0.659591	0.329796	−	0.944052i	$-0.393020\pi$
$419$	13.5015	0.659591	0.329796	+	0.944052i	$0.393020\pi$
$420$	9.41479	0.459395
$421$	12.6660	0.617302	0.308651	−	0.951175i	$-0.400122\pi$
$421$	12.6660	0.617302	0.308651	+	0.951175i	$0.400122\pi$
$422$	−0.810317	−0.0394456
$423$	−12.6874	−0.616884
$424$	−2.61343	−0.126920
$425$	−2.01329	−0.0976589
$426$	0.284372	0.0137779
$427$	−7.20122	−0.348491
$428$	15.4584	0.747209
$429$	1.11985	0.0540670
$430$	−9.43997	−0.455236
$431$	28.6261	1.37887	0.689436	−	0.724347i	$-0.257859\pi$
$431$	28.6261	1.37887	0.689436	+	0.724347i	$0.257859\pi$
$432$	−1.00000	−0.0481125
$433$	2.12024	0.101892	0.0509461	−	0.998701i	$-0.483776\pi$
$433$	2.12024	0.101892	0.0509461	+	0.998701i	$0.483776\pi$
$434$	30.0579	1.44282
$435$	−1.80459	−0.0865233
$436$	−8.50319	−0.407229
$437$	−17.2312	−0.824278
$438$	−2.98539	−0.142647
$439$	−33.4903	−1.59840	−0.799202	−	0.601062i	$-0.794744\pi$
$439$	−33.4903	−1.59840	−0.799202	+	0.601062i	$0.794744\pi$
$440$	4.03135	0.192187
$441$	5.63862	0.268505
$442$	−0.735651	−0.0349914
$443$	−3.66144	−0.173960	−0.0869800	−	0.996210i	$-0.527722\pi$
$443$	−3.66144	−0.173960	−0.0869800	+	0.996210i	$0.527722\pi$
$444$	−10.9406	−0.519218
$445$	1.64019	0.0777523
$446$	0.528082	0.0250054
$447$	−11.4195	−0.540122
$448$	3.55508	0.167962
$449$	3.43094	0.161916	0.0809581	−	0.996718i	$-0.474202\pi$
$449$	3.43094	0.161916	0.0809581	+	0.996718i	$0.474202\pi$
$450$	2.01329	0.0949074
$451$	0.863986	0.0406835
$452$	15.1110	0.710763
$453$	10.8207	0.508399
$454$	21.1198	0.991199
$455$	−6.92600	−0.324696
$456$	−3.99021	−0.186859
$457$	0.458602	0.0214525	0.0107263	−	0.999942i	$-0.496586\pi$
$457$	0.458602	0.0214525	0.0107263	+	0.999942i	$0.496586\pi$
$458$	−9.32395	−0.435679
$459$	1.00000	0.0466760
$460$	11.4361	0.533212
$461$	−35.1056	−1.63503	−0.817515	−	0.575908i	$-0.804649\pi$
$461$	−35.1056	−1.63503	−0.817515	+	0.575908i	$0.804649\pi$
$462$	5.41177	0.251778
$463$	−23.0735	−1.07232	−0.536159	−	0.844117i	$-0.680125\pi$
$463$	−23.0735	−1.07232	−0.536159	+	0.844117i	$0.680125\pi$
$464$	−0.681423	−0.0316343
$465$	22.3908	1.03835
$466$	8.99292	0.416589
$467$	−13.4753	−0.623564	−0.311782	−	0.950154i	$-0.600926\pi$
$467$	−13.4753	−0.623564	−0.311782	+	0.950154i	$0.600926\pi$
$468$	0.735651	0.0340055
$469$	−23.8727	−1.10234
$470$	33.5996	1.54984
$471$	4.85278	0.223604
$472$	−1.00000	−0.0460287
$473$	−5.42624	−0.249499
$474$	−13.7397	−0.631084
$475$	8.03346	0.368600
$476$	−3.55508	−0.162947
$477$	−2.61343	−0.119661
$478$	11.5727	0.529322
$479$	−1.40455	−0.0641756	−0.0320878	−	0.999485i	$-0.510216\pi$
$479$	−1.40455	−0.0641756	−0.0320878	+	0.999485i	$0.510216\pi$
$480$	2.64826	0.120876
$481$	8.04847	0.366979
$482$	−2.76620	−0.125997
$483$	15.3521	0.698545
$484$	−8.68272	−0.394669
$485$	31.2389	1.41849
$486$	−1.00000	−0.0453609
$487$	11.6147	0.526313	0.263157	−	0.964753i	$-0.415236\pi$
$487$	11.6147	0.526313	0.263157	+	0.964753i	$0.415236\pi$
$488$	−2.02561	−0.0916951
$489$	−3.86608	−0.174830
$490$	−14.9325	−0.674583
$491$	−14.1940	−0.640569	−0.320284	−	0.947321i	$-0.603778\pi$
$491$	−14.1940	−0.640569	−0.320284	+	0.947321i	$0.603778\pi$
$492$	0.567568	0.0255879
$493$	0.681423	0.0306897
$494$	2.93541	0.132070
$495$	4.03135	0.181196
$496$	8.45489	0.379636
$497$	−1.01097	−0.0453480
$498$	−11.1306	−0.498774
$499$	−22.6371	−1.01338	−0.506688	−	0.862129i	$-0.669131\pi$
$499$	−22.6371	−1.01338	−0.506688	+	0.862129i	$0.669131\pi$
$500$	7.90959	0.353728
$501$	−3.26831	−0.146017
$502$	7.96650	0.355562
$503$	−16.4807	−0.734840	−0.367420	−	0.930055i	$-0.619759\pi$
$503$	−16.4807	−0.734840	−0.367420	+	0.930055i	$0.619759\pi$
$504$	3.55508	0.158356
$505$	−11.9613	−0.532272
$506$	6.57366	0.292235
$507$	12.4588	0.553315
$508$	−5.32998	−0.236480
$509$	29.0598	1.28805	0.644027	−	0.765003i	$-0.277263\pi$
$509$	29.0598	1.28805	0.644027	+	0.765003i	$0.277263\pi$
$510$	−2.64826	−0.117267
$511$	10.6133	0.469505
$512$	1.00000	0.0441942
$513$	−3.99021	−0.176172
$514$	17.2159	0.759362
$515$	−31.3189	−1.38008
$516$	−3.56459	−0.156922
$517$	19.3136	0.849411
$518$	38.8948	1.70894
$519$	−5.96246	−0.261723
$520$	−1.94820	−0.0854341
$521$	44.9981	1.97140	0.985702	−	0.168496i	$-0.0538911\pi$
$521$	44.9981	1.97140	0.985702	+	0.168496i	$0.0538911\pi$
$522$	−0.681423	−0.0298251
$523$	7.45539	0.326002	0.163001	−	0.986626i	$-0.447883\pi$
$523$	7.45539	0.326002	0.163001	+	0.986626i	$0.447883\pi$
$524$	0.369304	0.0161331
$525$	−7.15741	−0.312375
$526$	−5.47040	−0.238521
$527$	−8.45489	−0.368301
$528$	1.52226	0.0662479
$529$	−4.35184	−0.189210
$530$	6.92106	0.300632
$531$	−1.00000	−0.0433963
$532$	14.1855	0.615021
$533$	−0.417532	−0.0180853
$534$	0.619345	0.0268017
$535$	−40.9378	−1.76990
$536$	−6.71508	−0.290047
$537$	−3.87241	−0.167107
$538$	−6.39357	−0.275646
$539$	−8.58345	−0.369715
$540$	2.64826	0.113963
$541$	33.1221	1.42403	0.712014	−	0.702165i	$-0.247783\pi$
$541$	33.1221	1.42403	0.712014	+	0.702165i	$0.247783\pi$
$542$	−15.5891	−0.669610
$543$	−10.6400	−0.456607
$544$	−1.00000	−0.0428746
$545$	22.5187	0.964594
$546$	−2.61530	−0.111925
$547$	−3.68246	−0.157450	−0.0787252	−	0.996896i	$-0.525085\pi$
$547$	−3.68246	−0.157450	−0.0787252	+	0.996896i	$0.525085\pi$
$548$	5.74535	0.245429
$549$	−2.02561	−0.0864510
$550$	−3.06475	−0.130682
$551$	−2.71902	−0.115834
$552$	4.31835	0.183801
$553$	48.8457	2.07713
$554$	25.7827	1.09540
$555$	28.9736	1.22986
$556$	11.5389	0.489358
$557$	4.15846	0.176199	0.0880997	−	0.996112i	$-0.471921\pi$
$557$	4.15846	0.176199	0.0880997	+	0.996112i	$0.471921\pi$
$558$	8.45489	0.357924
$559$	2.62230	0.110911
$560$	−9.41479	−0.397847
$561$	−1.52226	−0.0642699
$562$	−19.4003	−0.818350
$563$	19.7662	0.833047	0.416523	−	0.909125i	$-0.363248\pi$
$563$	19.7662	0.833047	0.416523	+	0.909125i	$0.363248\pi$
$564$	12.6874	0.534237
$565$	−40.0180	−1.68357
$566$	14.6348	0.615146
$567$	3.55508	0.149299
$568$	−0.284372	−0.0119320
$569$	−19.8483	−0.832084	−0.416042	−	0.909345i	$-0.636583\pi$
$569$	−19.8483	−0.832084	−0.416042	+	0.909345i	$0.636583\pi$
$570$	10.5671	0.442608
$571$	35.1297	1.47013	0.735067	−	0.677994i	$-0.237151\pi$
$571$	35.1297	1.47013	0.735067	+	0.677994i	$0.237151\pi$
$572$	−1.11985	−0.0468234
$573$	−20.8647	−0.871636
$574$	−2.01775	−0.0842193
$575$	−8.69409	−0.362569
$576$	1.00000	0.0416667
$577$	−31.3259	−1.30411	−0.652057	−	0.758170i	$-0.726094\pi$
$577$	−31.3259	−1.30411	−0.652057	+	0.758170i	$0.726094\pi$
$578$	1.00000	0.0415945
$579$	−1.81394	−0.0753848
$580$	1.80459	0.0749313
$581$	39.5702	1.64165
$582$	11.7960	0.488960
$583$	3.97833	0.164766
$584$	2.98539	0.123536
$585$	−1.94820	−0.0805480
$586$	8.28260	0.342151
$587$	−10.5552	−0.435660	−0.217830	−	0.975987i	$-0.569898\pi$
$587$	−10.5552	−0.435660	−0.217830	+	0.975987i	$0.569898\pi$
$588$	−5.63862	−0.232533
$589$	33.7368	1.39010
$590$	2.64826	0.109027
$591$	−6.34157	−0.260857
$592$	10.9406	0.449656
$593$	−11.3785	−0.467258	−0.233629	−	0.972326i	$-0.575060\pi$
$593$	−11.3785	−0.467258	−0.233629	+	0.972326i	$0.575060\pi$
$594$	1.52226	0.0624591
$595$	9.41479	0.385969
$596$	11.4195	0.467760
$597$	5.95288	0.243635
$598$	−3.17680	−0.129909
$599$	−0.00315894	−0.000129071 0	−6.45353e−5	−	1.00000i	$-0.500021\pi$
$599$	−0.00315894	−0.000129071 0	−6.45353e−5		1.00000i	$0.500021\pi$
$600$	−2.01329	−0.0821922
$601$	22.9672	0.936850	0.468425	−	0.883503i	$-0.344822\pi$
$601$	22.9672	0.936850	0.468425	+	0.883503i	$0.344822\pi$
$602$	12.6724	0.516489
$603$	−6.71508	−0.273459
$604$	−10.8207	−0.440286
$605$	22.9941	0.934844
$606$	−4.51667	−0.183477
$607$	−38.9073	−1.57920	−0.789599	−	0.613623i	$-0.789712\pi$
$607$	−38.9073	−1.57920	−0.789599	+	0.613623i	$0.789712\pi$
$608$	3.99021	0.161825
$609$	2.42251	0.0981652
$610$	5.36435	0.217196
$611$	−9.33353	−0.377594
$612$	−1.00000	−0.0404226
$613$	19.3816	0.782817	0.391408	−	0.920217i	$-0.371988\pi$
$613$	19.3816	0.782817	0.391408	+	0.920217i	$0.371988\pi$
$614$	5.62387	0.226961
$615$	−1.50307	−0.0606095
$616$	−5.41177	−0.218046
$617$	1.96197	0.0789859	0.0394930	−	0.999220i	$-0.487426\pi$
$617$	1.96197	0.0789859	0.0394930	+	0.999220i	$0.487426\pi$
$618$	−11.8262	−0.475720
$619$	−6.61678	−0.265951	−0.132975	−	0.991119i	$-0.542453\pi$
$619$	−6.61678	−0.265951	−0.132975	+	0.991119i	$0.542453\pi$
$620$	−22.3908	−0.899235
$621$	4.31835	0.173289
$622$	13.1280	0.526384
$623$	−2.20182	−0.0882141
$624$	−0.735651	−0.0294496
$625$	−31.0131	−1.24052
$626$	−23.9693	−0.958005
$627$	6.07415	0.242578
$628$	−4.85278	−0.193647
$629$	−10.9406	−0.436231
$630$	−9.41479	−0.375094
$631$	34.7767	1.38444	0.692219	−	0.721688i	$-0.256633\pi$
$631$	34.7767	1.38444	0.692219	+	0.721688i	$0.256633\pi$
$632$	13.7397	0.546535
$633$	0.810317	0.0322072
$634$	29.8678	1.18620
$635$	14.1152	0.560144
$636$	2.61343	0.103629
$637$	4.14805	0.164352
$638$	1.03730	0.0410672
$639$	−0.284372	−0.0112496
$640$	−2.64826	−0.104682
$641$	13.4544	0.531416	0.265708	−	0.964054i	$-0.414394\pi$
$641$	13.4544	0.531416	0.265708	+	0.964054i	$0.414394\pi$
$642$	−15.4584	−0.610093
$643$	−45.0759	−1.77762	−0.888811	−	0.458275i	$-0.848468\pi$
$643$	−45.0759	−1.77762	−0.888811	+	0.458275i	$0.848468\pi$
$644$	−15.3521	−0.604957
$645$	9.43997	0.371699
$646$	−3.99021	−0.156993
$647$	−36.8728	−1.44962	−0.724809	−	0.688950i	$-0.758072\pi$
$647$	−36.8728	−1.44962	−0.724809	+	0.688950i	$0.758072\pi$
$648$	1.00000	0.0392837
$649$	1.52226	0.0597540
$650$	1.48108	0.0580927
$651$	−30.0579	−1.17806
$652$	3.86608	0.151407
$653$	−3.48436	−0.136354	−0.0681768	−	0.997673i	$-0.521718\pi$
$653$	−3.48436	−0.136354	−0.0681768	+	0.997673i	$0.521718\pi$
$654$	8.50319	0.332501
$655$	−0.978014	−0.0382142
$656$	−0.567568	−0.0221598
$657$	2.98539	0.116471
$658$	−45.1049	−1.75837
$659$	−50.7261	−1.97601	−0.988003	−	0.154432i	$-0.950645\pi$
$659$	−50.7261	−1.97601	−0.988003	+	0.154432i	$0.950645\pi$
$660$	−4.03135	−0.156920
$661$	−10.5757	−0.411346	−0.205673	−	0.978621i	$-0.565938\pi$
$661$	−10.5757	−0.411346	−0.205673	+	0.978621i	$0.565938\pi$
$662$	19.1543	0.744453
$663$	0.735651	0.0285703
$664$	11.1306	0.431951
$665$	−37.5670	−1.45679
$666$	10.9406	0.423940
$667$	2.94262	0.113939
$668$	3.26831	0.126455
$669$	−0.528082	−0.0204168
$670$	17.7833	0.687029
$671$	3.08351	0.119038
$672$	−3.55508	−0.137140
$673$	−12.6073	−0.485977	−0.242988	−	0.970029i	$-0.578128\pi$
$673$	−12.6073	−0.485977	−0.242988	+	0.970029i	$0.578128\pi$
$674$	21.6894	0.835443
$675$	−2.01329	−0.0774916
$676$	−12.4588	−0.479185
$677$	−36.3846	−1.39837	−0.699187	−	0.714939i	$-0.746454\pi$
$677$	−36.3846	−1.39837	−0.699187	+	0.714939i	$0.746454\pi$
$678$	−15.1110	−0.580336
$679$	−41.9358	−1.60935
$680$	2.64826	0.101556
$681$	−21.1198	−0.809311
$682$	−12.8706	−0.492839
$683$	−1.48495	−0.0568199	−0.0284099	−	0.999596i	$-0.509044\pi$
$683$	−1.48495	−0.0568199	−0.0284099	+	0.999596i	$0.509044\pi$
$684$	3.99021	0.152570
$685$	−15.2152	−0.581342
$686$	−4.83984	−0.184786
$687$	9.32395	0.355731
$688$	3.56459	0.135899
$689$	−1.92258	−0.0732443
$690$	−11.4361	−0.435366
$691$	−18.4355	−0.701321	−0.350660	−	0.936503i	$-0.614043\pi$
$691$	−18.4355	−0.701321	−0.350660	+	0.936503i	$0.614043\pi$
$692$	5.96246	0.226659
$693$	−5.41177	−0.205576
$694$	−21.0091	−0.797493
$695$	−30.5580	−1.15913
$696$	0.681423	0.0258293
$697$	0.567568	0.0214982
$698$	−17.0187	−0.644168
$699$	−8.99292	−0.340143
$700$	7.15741	0.270525
$701$	−14.2428	−0.537943	−0.268971	−	0.963148i	$-0.586684\pi$
$701$	−14.2428	−0.537943	−0.268971	+	0.963148i	$0.586684\pi$
$702$	−0.735651	−0.0277654
$703$	43.6554	1.64649
$704$	−1.52226	−0.0573724
$705$	−33.5996	−1.26544
$706$	−13.8340	−0.520650
$707$	16.0572	0.603891
$708$	1.00000	0.0375823
$709$	−9.82682	−0.369054	−0.184527	−	0.982827i	$-0.559075\pi$
$709$	−9.82682	−0.369054	−0.184527	+	0.982827i	$0.559075\pi$
$710$	0.753091	0.0282630
$711$	13.7397	0.515278
$712$	−0.619345	−0.0232109
$713$	−36.5112	−1.36736
$714$	3.55508	0.133046
$715$	2.96567	0.110910
$716$	3.87241	0.144719
$717$	−11.5727	−0.432190
$718$	28.9292	1.07963
$719$	−31.8716	−1.18861	−0.594305	−	0.804240i	$-0.702573\pi$
$719$	−31.8716	−1.18861	−0.594305	+	0.804240i	$0.702573\pi$
$720$	−2.64826	−0.0986949
$721$	42.0432	1.56577
$722$	−3.07819	−0.114558
$723$	2.76620	0.102876
$724$	10.6400	0.395434
$725$	−1.37190	−0.0509511
$726$	8.68272	0.322246
$727$	−2.76732	−0.102634	−0.0513171	−	0.998682i	$-0.516342\pi$
$727$	−2.76732	−0.102634	−0.0513171	+	0.998682i	$0.516342\pi$
$728$	2.61530	0.0969295
$729$	1.00000	0.0370370
$730$	−7.90609	−0.292617
$731$	−3.56459	−0.131841
$732$	2.02561	0.0748688
$733$	−20.0289	−0.739784	−0.369892	−	0.929075i	$-0.620605\pi$
$733$	−20.0289	−0.739784	−0.369892	+	0.929075i	$0.620605\pi$
$734$	19.3888	0.715654
$735$	14.9325	0.550795
$736$	−4.31835	−0.159177
$737$	10.2221	0.376536
$738$	−0.567568	−0.0208925
$739$	−23.6177	−0.868792	−0.434396	−	0.900722i	$-0.643038\pi$
$739$	−23.6177	−0.868792	−0.434396	+	0.900722i	$0.643038\pi$
$740$	−28.9736	−1.06509
$741$	−2.93541	−0.107835
$742$	−9.29098	−0.341082
$743$	−5.27391	−0.193481	−0.0967404	−	0.995310i	$-0.530842\pi$
$743$	−5.27391	−0.193481	−0.0967404	+	0.995310i	$0.530842\pi$
$744$	−8.45489	−0.309971
$745$	−30.2417	−1.10797
$746$	20.0758	0.735027
$747$	11.1306	0.407247
$748$	1.52226	0.0556594
$749$	54.9558	2.00804
$750$	−7.90959	−0.288817
$751$	−39.3130	−1.43455	−0.717275	−	0.696790i	$-0.754611\pi$
$751$	−39.3130	−1.43455	−0.717275	+	0.696790i	$0.754611\pi$
$752$	−12.6874	−0.462663
$753$	−7.96650	−0.290315
$754$	−0.501289	−0.0182559
$755$	28.6559	1.04290
$756$	−3.55508	−0.129297
$757$	−15.7125	−0.571080	−0.285540	−	0.958367i	$-0.592173\pi$
$757$	−15.7125	−0.571080	−0.285540	+	0.958367i	$0.592173\pi$
$758$	22.2150	0.806886
$759$	−6.57366	−0.238609
$760$	−10.5671	−0.383310
$761$	25.6970	0.931516	0.465758	−	0.884912i	$-0.345782\pi$
$761$	25.6970	0.931516	0.465758	+	0.884912i	$0.345782\pi$
$762$	5.32998	0.193085
$763$	−30.2296	−1.09438
$764$	20.8647	0.754859
$765$	2.64826	0.0957481
$766$	2.97824	0.107608
$767$	−0.735651	−0.0265628
$768$	−1.00000	−0.0360844
$769$	−25.6034	−0.923282	−0.461641	−	0.887067i	$-0.652739\pi$
$769$	−25.6034	−0.923282	−0.461641	+	0.887067i	$0.652739\pi$
$770$	14.3318	0.516481
$771$	−17.2159	−0.620017
$772$	1.81394	0.0652852
$773$	−14.2770	−0.513507	−0.256754	−	0.966477i	$-0.582653\pi$
$773$	−14.2770	−0.513507	−0.256754	+	0.966477i	$0.582653\pi$
$774$	3.56459	0.128127
$775$	17.0222	0.611454
$776$	−11.7960	−0.423452
$777$	−38.8948	−1.39534
$778$	25.6397	0.919229
$779$	−2.26472	−0.0811419
$780$	1.94820	0.0697566
$781$	0.432888	0.0154900
$782$	4.31835	0.154424
$783$	0.681423	0.0243521
$784$	5.63862	0.201379
$785$	12.8514	0.458687
$786$	−0.369304	−0.0131726
$787$	11.5624	0.412157	0.206078	−	0.978535i	$-0.433930\pi$
$787$	11.5624	0.412157	0.206078	+	0.978535i	$0.433930\pi$
$788$	6.34157	0.225909
$789$	5.47040	0.194751
$790$	−36.3862	−1.29456
$791$	53.7210	1.91010
$792$	−1.52226	−0.0540912
$793$	−1.49014	−0.0529166
$794$	−26.1938	−0.929584
$795$	−6.92106	−0.245465
$796$	−5.95288	−0.210994
$797$	12.9504	0.458727	0.229364	−	0.973341i	$-0.426336\pi$
$797$	12.9504	0.458727	0.229364	+	0.973341i	$0.426336\pi$
$798$	−14.1855	−0.502163
$799$	12.6874	0.448849
$800$	2.01329	0.0711805
$801$	−0.619345	−0.0218835
$802$	−5.22997	−0.184677
$803$	−4.54454	−0.160373
$804$	6.71508	0.236823
$805$	40.6564	1.43295
$806$	6.21985	0.219085
$807$	6.39357	0.225064
$808$	4.51667	0.158896
$809$	−10.9856	−0.386233	−0.193116	−	0.981176i	$-0.561859\pi$
$809$	−10.9856	−0.386233	−0.193116	+	0.981176i	$0.561859\pi$
$810$	−2.64826	−0.0930504
$811$	5.42802	0.190604	0.0953018	−	0.995448i	$-0.469618\pi$
$811$	5.42802	0.190604	0.0953018	+	0.995448i	$0.469618\pi$
$812$	−2.42251	−0.0850136
$813$	15.5891	0.546734
$814$	−16.6545	−0.583739
$815$	−10.2384	−0.358635
$816$	1.00000	0.0350070
$817$	14.2235	0.497617
$818$	−4.86369	−0.170055
$819$	2.61530	0.0913860
$820$	1.50307	0.0524894
$821$	29.3331	1.02373	0.511865	−	0.859066i	$-0.328955\pi$
$821$	29.3331	1.02373	0.511865	+	0.859066i	$0.328955\pi$
$822$	−5.74535	−0.200392
$823$	−51.4812	−1.79452	−0.897261	−	0.441501i	$-0.854446\pi$
$823$	−51.4812	−1.79452	−0.897261	+	0.441501i	$0.854446\pi$
$824$	11.8262	0.411986
$825$	3.06475	0.106701
$826$	−3.55508	−0.123697
$827$	−35.0519	−1.21887	−0.609437	−	0.792835i	$-0.708604\pi$
$827$	−35.0519	−1.21887	−0.609437	+	0.792835i	$0.708604\pi$
$828$	−4.31835	−0.150073
$829$	−30.8657	−1.07201	−0.536004	−	0.844215i	$-0.680067\pi$
$829$	−30.8657	−1.07201	−0.536004	+	0.844215i	$0.680067\pi$
$830$	−29.4767	−1.02315
$831$	−25.7827	−0.894392
$832$	0.735651	0.0255041
$833$	−5.63862	−0.195366
$834$	−11.5389	−0.399559
$835$	−8.65535	−0.299531
$836$	−6.07415	−0.210079
$837$	−8.45489	−0.292244
$838$	13.5015	0.466401
$839$	−44.7289	−1.54421	−0.772107	−	0.635493i	$-0.780797\pi$
$839$	−44.7289	−1.54421	−0.772107	+	0.635493i	$0.780797\pi$
$840$	9.41479	0.324841
$841$	−28.5357	−0.983988
$842$	12.6660	0.436498
$843$	19.4003	0.668180
$844$	−0.810317	−0.0278923
$845$	32.9942	1.13504
$846$	−12.6874	−0.436203
$847$	−30.8678	−1.06063
$848$	−2.61343	−0.0897457
$849$	−14.6348	−0.502265
$850$	−2.01329	−0.0690553
$851$	−47.2454	−1.61955
$852$	0.284372	0.00974242
$853$	−19.8373	−0.679215	−0.339608	−	0.940567i	$-0.610294\pi$
$853$	−19.8373	−0.679215	−0.339608	+	0.940567i	$0.610294\pi$
$854$	−7.20122	−0.246421
$855$	−10.5671	−0.361388
$856$	15.4584	0.528356
$857$	−0.863031	−0.0294806	−0.0147403	−	0.999891i	$-0.504692\pi$
$857$	−0.863031	−0.0294806	−0.0147403	+	0.999891i	$0.504692\pi$
$858$	1.11985	0.0382312
$859$	−26.2480	−0.895570	−0.447785	−	0.894141i	$-0.647787\pi$
$859$	−26.2480	−0.895570	−0.447785	+	0.894141i	$0.647787\pi$
$860$	−9.43997	−0.321900
$861$	2.01775	0.0687648
$862$	28.6261	0.975009
$863$	42.7434	1.45500	0.727501	−	0.686106i	$-0.240682\pi$
$863$	42.7434	1.45500	0.727501	+	0.686106i	$0.240682\pi$
$864$	−1.00000	−0.0340207
$865$	−15.7902	−0.536881
$866$	2.12024	0.0720486
$867$	−1.00000	−0.0339618
$868$	30.0579	1.02023
$869$	−20.9154	−0.709505
$870$	−1.80459	−0.0611812
$871$	−4.93996	−0.167384
$872$	−8.50319	−0.287954
$873$	−11.7960	−0.399234
$874$	−17.2312	−0.582852
$875$	28.1193	0.950604
$876$	−2.98539	−0.100867
$877$	−49.9223	−1.68576	−0.842879	−	0.538104i	$-0.819141\pi$
$877$	−49.9223	−1.68576	−0.842879	+	0.538104i	$0.819141\pi$
$878$	−33.4903	−1.13024
$879$	−8.28260	−0.279365
$880$	4.03135	0.135897
$881$	−29.4386	−0.991811	−0.495906	−	0.868376i	$-0.665164\pi$
$881$	−29.4386	−0.991811	−0.495906	+	0.868376i	$0.665164\pi$
$882$	5.63862	0.189862
$883$	−33.2595	−1.11927	−0.559636	−	0.828738i	$-0.689059\pi$
$883$	−33.2595	−1.11927	−0.559636	+	0.828738i	$0.689059\pi$
$884$	−0.735651	−0.0247426
$885$	−2.64826	−0.0890203
$886$	−3.66144	−0.123008
$887$	9.83888	0.330357	0.165179	−	0.986264i	$-0.447180\pi$
$887$	9.83888	0.330357	0.165179	+	0.986264i	$0.447180\pi$
$888$	−10.9406	−0.367143
$889$	−18.9485	−0.635513
$890$	1.64019	0.0549792
$891$	−1.52226	−0.0509977
$892$	0.528082	0.0176815
$893$	−50.6256	−1.69412
$894$	−11.4195	−0.381924
$895$	−10.2552	−0.342792
$896$	3.55508	0.118767
$897$	3.17680	0.106070
$898$	3.43094	0.114492
$899$	−5.76136	−0.192152
$900$	2.01329	0.0671097
$901$	2.61343	0.0870661
$902$	0.863986	0.0287676
$903$	−12.6724	−0.421712
$904$	15.1110	0.502585
$905$	−28.1776	−0.936655
$906$	10.8207	0.359492
$907$	−21.4355	−0.711755	−0.355878	−	0.934533i	$-0.615818\pi$
$907$	−21.4355	−0.711755	−0.355878	+	0.934533i	$0.615818\pi$
$908$	21.1198	0.700884
$909$	4.51667	0.149809
$910$	−6.92600	−0.229595
$911$	−12.4786	−0.413433	−0.206716	−	0.978401i	$-0.566278\pi$
$911$	−12.4786	−0.413433	−0.206716	+	0.978401i	$0.566278\pi$
$912$	−3.99021	−0.132129
$913$	−16.9437	−0.560754
$914$	0.458602	0.0151692
$915$	−5.36435	−0.177340
$916$	−9.32395	−0.308072
$917$	1.31291	0.0433560
$918$	1.00000	0.0330049
$919$	−26.6747	−0.879918	−0.439959	−	0.898018i	$-0.645007\pi$
$919$	−26.6747	−0.879918	−0.439959	+	0.898018i	$0.645007\pi$
$920$	11.4361	0.377038
$921$	−5.62387	−0.185313
$922$	−35.1056	−1.15614
$923$	−0.209199	−0.00688585
$924$	5.41177	0.178034
$925$	22.0266	0.724230
$926$	−23.0735	−0.758243
$927$	11.8262	0.388424
$928$	−0.681423	−0.0223688
$929$	16.5943	0.544442	0.272221	−	0.962235i	$-0.412242\pi$
$929$	16.5943	0.544442	0.272221	+	0.962235i	$0.412242\pi$
$930$	22.3908	0.734222
$931$	22.4993	0.737384
$932$	8.99292	0.294573
$933$	−13.1280	−0.429790
$934$	−13.4753	−0.440926
$935$	−4.03135	−0.131839
$936$	0.735651	0.0240455
$937$	27.9082	0.911720	0.455860	−	0.890051i	$-0.349332\pi$
$937$	27.9082	0.911720	0.455860	+	0.890051i	$0.349332\pi$
$938$	−23.8727	−0.779470
$939$	23.9693	0.782208
$940$	33.5996	1.09590
$941$	−15.8821	−0.517740	−0.258870	−	0.965912i	$-0.583350\pi$
$941$	−15.8821	−0.517740	−0.258870	+	0.965912i	$0.583350\pi$
$942$	4.85278	0.158112
$943$	2.45096	0.0798141
$944$	−1.00000	−0.0325472
$945$	9.41479	0.306263
$946$	−5.42624	−0.176422
$947$	11.4790	0.373018	0.186509	−	0.982453i	$-0.440283\pi$
$947$	11.4790	0.373018	0.186509	+	0.982453i	$0.440283\pi$
$948$	−13.7397	−0.446244
$949$	2.19620	0.0712918
$950$	8.03346	0.260640
$951$	−29.8678	−0.968529
$952$	−3.55508	−0.115221
$953$	28.3295	0.917681	0.458841	−	0.888519i	$-0.348265\pi$
$953$	28.3295	0.917681	0.458841	+	0.888519i	$0.348265\pi$
$954$	−2.61343	−0.0846131
$955$	−55.2552	−1.78802
$956$	11.5727	0.374287
$957$	−1.03730	−0.0335313
$958$	−1.40455	−0.0453790
$959$	20.4252	0.659564
$960$	2.64826	0.0854723
$961$	40.4852	1.30598
$962$	8.04847	0.259493
$963$	15.4584	0.498139
$964$	−2.76620	−0.0890934
$965$	−4.80379	−0.154639
$966$	15.3521	0.493946
$967$	33.9422	1.09151	0.545754	−	0.837946i	$-0.316243\pi$
$967$	33.9422	1.09151	0.545754	+	0.837946i	$0.316243\pi$
$968$	−8.68272	−0.279073
$969$	3.99021	0.128184
$970$	31.2389	1.00302
$971$	30.6285	0.982916	0.491458	−	0.870901i	$-0.336464\pi$
$971$	30.6285	0.982916	0.491458	+	0.870901i	$0.336464\pi$
$972$	−1.00000	−0.0320750
$973$	41.0217	1.31510
$974$	11.6147	0.372159
$975$	−1.48108	−0.0474325
$976$	−2.02561	−0.0648383
$977$	−3.77508	−0.120776	−0.0603878	−	0.998175i	$-0.519234\pi$
$977$	−3.77508	−0.120776	−0.0603878	+	0.998175i	$0.519234\pi$
$978$	−3.86608	−0.123623
$979$	0.942804	0.0301322
$980$	−14.9325	−0.477002
$981$	−8.50319	−0.271486
$982$	−14.1940	−0.452950
$983$	−38.4572	−1.22660	−0.613298	−	0.789852i	$-0.710157\pi$
$983$	−38.4572	−1.22660	−0.613298	+	0.789852i	$0.710157\pi$
$984$	0.567568	0.0180934
$985$	−16.7941	−0.535106
$986$	0.681423	0.0217009
$987$	45.1049	1.43570
$988$	2.93541	0.0933877
$989$	−15.3932	−0.489474
$990$	4.03135	0.128125
$991$	1.41538	0.0449610	0.0224805	−	0.999747i	$-0.492844\pi$
$991$	1.41538	0.0449610	0.0224805	+	0.999747i	$0.492844\pi$
$992$	8.45489	0.268443
$993$	−19.1543	−0.607843
$994$	−1.01097	−0.0320659
$995$	15.7648	0.499777
$996$	−11.1306	−0.352686
$997$	−20.0612	−0.635345	−0.317673	−	0.948200i	$-0.602901\pi$
$997$	−20.0612	−0.635345	−0.317673	+	0.948200i	$0.602901\pi$
$998$	−22.6371	−0.716566
$999$	−10.9406	−0.346145

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.z.1.2	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.z.1.2	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.64826 q^{5} -1.00000 q^{6} +3.55508 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.64826 q^{5} -1.00000 q^{6} +3.55508 q^{7} +1.00000 q^{8} +1.00000 q^{9} -2.64826 q^{10} -1.52226 q^{11} -1.00000 q^{12} +0.735651 q^{13} +3.55508 q^{14} +2.64826 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} +3.99021 q^{19} -2.64826 q^{20} -3.55508 q^{21} -1.52226 q^{22} -4.31835 q^{23} -1.00000 q^{24} +2.01329 q^{25} +0.735651 q^{26} -1.00000 q^{27} +3.55508 q^{28} -0.681423 q^{29} +2.64826 q^{30} +8.45489 q^{31} +1.00000 q^{32} +1.52226 q^{33} -1.00000 q^{34} -9.41479 q^{35} +1.00000 q^{36} +10.9406 q^{37} +3.99021 q^{38} -0.735651 q^{39} -2.64826 q^{40} -0.567568 q^{41} -3.55508 q^{42} +3.56459 q^{43} -1.52226 q^{44} -2.64826 q^{45} -4.31835 q^{46} -12.6874 q^{47} -1.00000 q^{48} +5.63862 q^{49} +2.01329 q^{50} +1.00000 q^{51} +0.735651 q^{52} -2.61343 q^{53} -1.00000 q^{54} +4.03135 q^{55} +3.55508 q^{56} -3.99021 q^{57} -0.681423 q^{58} -1.00000 q^{59} +2.64826 q^{60} -2.02561 q^{61} +8.45489 q^{62} +3.55508 q^{63} +1.00000 q^{64} -1.94820 q^{65} +1.52226 q^{66} -6.71508 q^{67} -1.00000 q^{68} +4.31835 q^{69} -9.41479 q^{70} -0.284372 q^{71} +1.00000 q^{72} +2.98539 q^{73} +10.9406 q^{74} -2.01329 q^{75} +3.99021 q^{76} -5.41177 q^{77} -0.735651 q^{78} +13.7397 q^{79} -2.64826 q^{80} +1.00000 q^{81} -0.567568 q^{82} +11.1306 q^{83} -3.55508 q^{84} +2.64826 q^{85} +3.56459 q^{86} +0.681423 q^{87} -1.52226 q^{88} -0.619345 q^{89} -2.64826 q^{90} +2.61530 q^{91} -4.31835 q^{92} -8.45489 q^{93} -12.6874 q^{94} -10.5671 q^{95} -1.00000 q^{96} -11.7960 q^{97} +5.63862 q^{98} -1.52226 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 11 q^{2} - 11 q^{3} + 11 q^{4} + 4 q^{5} - 11 q^{6} + 3 q^{7} + 11 q^{8} + 11 q^{9}+O(q^{10}) \) 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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