LMFDB - Embedded newform 6018.2.a.u.1.9

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:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 4x^{8} - 16x^{7} + 37x^{6} + 97x^{5} - 72x^{4} - 182x^{3} + 24x^{2} + 70x - 19 $ x^9 - 4x^8 - 16x^7 + 37x^6 + 97x^5 - 72x^4 - 182x^3 + 24x^2 + 70x - 19
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			1.9
Root			$5.15287$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.45787 q^{5} +1.00000 q^{6} +3.88559 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.45787 q^{5} +1.00000 q^{6} +3.88559 q^{7} -1.00000 q^{8} +1.00000 q^{9} -3.45787 q^{10} -5.60139 q^{11} -1.00000 q^{12} -4.12957 q^{13} -3.88559 q^{14} -3.45787 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} -5.92616 q^{19} +3.45787 q^{20} -3.88559 q^{21} +5.60139 q^{22} -3.68458 q^{23} +1.00000 q^{24} +6.95684 q^{25} +4.12957 q^{26} -1.00000 q^{27} +3.88559 q^{28} +5.24594 q^{29} +3.45787 q^{30} -6.53532 q^{31} -1.00000 q^{32} +5.60139 q^{33} -1.00000 q^{34} +13.4358 q^{35} +1.00000 q^{36} +10.4519 q^{37} +5.92616 q^{38} +4.12957 q^{39} -3.45787 q^{40} +0.713032 q^{41} +3.88559 q^{42} -5.70750 q^{43} -5.60139 q^{44} +3.45787 q^{45} +3.68458 q^{46} -5.79742 q^{47} -1.00000 q^{48} +8.09778 q^{49} -6.95684 q^{50} -1.00000 q^{51} -4.12957 q^{52} +5.20130 q^{53} +1.00000 q^{54} -19.3689 q^{55} -3.88559 q^{56} +5.92616 q^{57} -5.24594 q^{58} +1.00000 q^{59} -3.45787 q^{60} -0.310913 q^{61} +6.53532 q^{62} +3.88559 q^{63} +1.00000 q^{64} -14.2795 q^{65} -5.60139 q^{66} +1.06513 q^{67} +1.00000 q^{68} +3.68458 q^{69} -13.4358 q^{70} +10.0903 q^{71} -1.00000 q^{72} -16.5843 q^{73} -10.4519 q^{74} -6.95684 q^{75} -5.92616 q^{76} -21.7647 q^{77} -4.12957 q^{78} -10.1134 q^{79} +3.45787 q^{80} +1.00000 q^{81} -0.713032 q^{82} +11.2226 q^{83} -3.88559 q^{84} +3.45787 q^{85} +5.70750 q^{86} -5.24594 q^{87} +5.60139 q^{88} -9.13347 q^{89} -3.45787 q^{90} -16.0458 q^{91} -3.68458 q^{92} +6.53532 q^{93} +5.79742 q^{94} -20.4919 q^{95} +1.00000 q^{96} -0.689638 q^{97} -8.09778 q^{98} -5.60139 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 9 q^{2} - 9 q^{3} + 9 q^{4} + 2 q^{5} + 9 q^{6} - 5 q^{7} - 9 q^{8} + 9 q^{9}+O(q^{10}) $ 9 * q - 9 * q^2 - 9 * q^3 + 9 * q^4 + 2 * q^5 + 9 * q^6 - 5 * q^7 - 9 * q^8 + 9 * q^9	\( 9 q - 9 q^{2} - 9 q^{3} + 9 q^{4} + 2 q^{5} + 9 q^{6} - 5 q^{7} - 9 q^{8} + 9 q^{9} - 2 q^{10} - q^{11} - 9 q^{12} - 4 q^{13} + 5 q^{14} - 2 q^{15} + 9 q^{16} + 9 q^{17} - 9 q^{18} - 7 q^{19} + 2 q^{20} + 5 q^{21} + q^{22} - 8 q^{23} + 9 q^{24} + 5 q^{25} + 4 q^{26} - 9 q^{27} - 5 q^{28} + 6 q^{29} + 2 q^{30} - 17 q^{31} - 9 q^{32} + q^{33} - 9 q^{34} + 10 q^{35} + 9 q^{36} + 2 q^{37} + 7 q^{38} + 4 q^{39} - 2 q^{40} + 14 q^{41} - 5 q^{42} - 27 q^{43} - q^{44} + 2 q^{45} + 8 q^{46} - 18 q^{47} - 9 q^{48} + 18 q^{49} - 5 q^{50} - 9 q^{51} - 4 q^{52} + 4 q^{53} + 9 q^{54} - 27 q^{55} + 5 q^{56} + 7 q^{57} - 6 q^{58} + 9 q^{59} - 2 q^{60} + 5 q^{61} + 17 q^{62} - 5 q^{63} + 9 q^{64} + 2 q^{65} - q^{66} - 22 q^{67} + 9 q^{68} + 8 q^{69} - 10 q^{70} + 16 q^{71} - 9 q^{72} - 12 q^{73} - 2 q^{74} - 5 q^{75} - 7 q^{76} + 6 q^{77} - 4 q^{78} - 9 q^{79} + 2 q^{80} + 9 q^{81} - 14 q^{82} + 10 q^{83} + 5 q^{84} + 2 q^{85} + 27 q^{86} - 6 q^{87} + q^{88} + 15 q^{89} - 2 q^{90} + 3 q^{91} - 8 q^{92} + 17 q^{93} + 18 q^{94} - 9 q^{95} + 9 q^{96} - 33 q^{97} - 18 q^{98} - q^{99}+O(q^{100}) \) 9 * q - 9 * q^2 - 9 * q^3 + 9 * q^4 + 2 * q^5 + 9 * q^6 - 5 * q^7 - 9 * q^8 + 9 * q^9 - 2 * q^10 - q^11 - 9 * q^12 - 4 * q^13 + 5 * q^14 - 2 * q^15 + 9 * q^16 + 9 * q^17 - 9 * q^18 - 7 * q^19 + 2 * q^20 + 5 * q^21 + q^22 - 8 * q^23 + 9 * q^24 + 5 * q^25 + 4 * q^26 - 9 * q^27 - 5 * q^28 + 6 * q^29 + 2 * q^30 - 17 * q^31 - 9 * q^32 + q^33 - 9 * q^34 + 10 * q^35 + 9 * q^36 + 2 * q^37 + 7 * q^38 + 4 * q^39 - 2 * q^40 + 14 * q^41 - 5 * q^42 - 27 * q^43 - q^44 + 2 * q^45 + 8 * q^46 - 18 * q^47 - 9 * q^48 + 18 * q^49 - 5 * q^50 - 9 * q^51 - 4 * q^52 + 4 * q^53 + 9 * q^54 - 27 * q^55 + 5 * q^56 + 7 * q^57 - 6 * q^58 + 9 * q^59 - 2 * q^60 + 5 * q^61 + 17 * q^62 - 5 * q^63 + 9 * q^64 + 2 * q^65 - q^66 - 22 * q^67 + 9 * q^68 + 8 * q^69 - 10 * q^70 + 16 * q^71 - 9 * q^72 - 12 * q^73 - 2 * q^74 - 5 * q^75 - 7 * q^76 + 6 * q^77 - 4 * q^78 - 9 * q^79 + 2 * q^80 + 9 * q^81 - 14 * q^82 + 10 * q^83 + 5 * q^84 + 2 * q^85 + 27 * q^86 - 6 * q^87 + q^88 + 15 * q^89 - 2 * q^90 + 3 * q^91 - 8 * q^92 + 17 * q^93 + 18 * q^94 - 9 * q^95 + 9 * q^96 - 33 * q^97 - 18 * q^98 - 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
$5$	3.45787	1.54641	0.773203	−	0.634159i	$-0.218654\pi$
$5$	3.45787	1.54641	0.773203	+	0.634159i	$0.218654\pi$
$6$	1.00000	0.408248
$7$	3.88559	1.46861	0.734307	−	0.678818i	$-0.237507\pi$
$7$	3.88559	1.46861	0.734307	+	0.678818i	$0.237507\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−3.45787	−1.09347
$11$	−5.60139	−1.68888	−0.844442	−	0.535648i	$-0.820068\pi$
$11$	−5.60139	−1.68888	−0.844442	+	0.535648i	$0.820068\pi$
$12$	−1.00000	−0.288675
$13$	−4.12957	−1.14534	−0.572668	−	0.819787i	$-0.694092\pi$
$13$	−4.12957	−1.14534	−0.572668	+	0.819787i	$0.694092\pi$
$14$	−3.88559	−1.03847
$15$	−3.45787	−0.892817
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.00000	−0.235702
$19$	−5.92616	−1.35955	−0.679777	−	0.733419i	$-0.737923\pi$
$19$	−5.92616	−1.35955	−0.679777	+	0.733419i	$0.737923\pi$
$20$	3.45787	0.773203
$21$	−3.88559	−0.847904
$22$	5.60139	1.19422
$23$	−3.68458	−0.768287	−0.384144	−	0.923273i	$-0.625503\pi$
$23$	−3.68458	−0.768287	−0.384144	+	0.923273i	$0.625503\pi$
$24$	1.00000	0.204124
$25$	6.95684	1.39137
$26$	4.12957	0.809875
$27$	−1.00000	−0.192450
$28$	3.88559	0.734307
$29$	5.24594	0.974147	0.487073	−	0.873361i	$-0.338064\pi$
$29$	5.24594	0.974147	0.487073	+	0.873361i	$0.338064\pi$
$30$	3.45787	0.631317
$31$	−6.53532	−1.17378	−0.586889	−	0.809668i	$-0.699647\pi$
$31$	−6.53532	−1.17378	−0.586889	+	0.809668i	$0.699647\pi$
$32$	−1.00000	−0.176777
$33$	5.60139	0.975077
$34$	−1.00000	−0.171499
$35$	13.4358	2.27107
$36$	1.00000	0.166667
$37$	10.4519	1.71827	0.859137	−	0.511745i	$-0.171001\pi$
$37$	10.4519	1.71827	0.859137	+	0.511745i	$0.171001\pi$
$38$	5.92616	0.961350
$39$	4.12957	0.661260
$40$	−3.45787	−0.546737
$41$	0.713032	0.111357	0.0556784	−	0.998449i	$-0.482268\pi$
$41$	0.713032	0.111357	0.0556784	+	0.998449i	$0.482268\pi$
$42$	3.88559	0.599559
$43$	−5.70750	−0.870386	−0.435193	−	0.900337i	$-0.643320\pi$
$43$	−5.70750	−0.870386	−0.435193	+	0.900337i	$0.643320\pi$
$44$	−5.60139	−0.844442
$45$	3.45787	0.515468
$46$	3.68458	0.543261
$47$	−5.79742	−0.845640	−0.422820	−	0.906214i	$-0.638960\pi$
$47$	−5.79742	−0.845640	−0.422820	+	0.906214i	$0.638960\pi$
$48$	−1.00000	−0.144338
$49$	8.09778	1.15683
$50$	−6.95684	−0.983846
$51$	−1.00000	−0.140028
$52$	−4.12957	−0.572668
$53$	5.20130	0.714453	0.357226	−	0.934018i	$-0.383722\pi$
$53$	5.20130	0.714453	0.357226	+	0.934018i	$0.383722\pi$
$54$	1.00000	0.136083
$55$	−19.3689	−2.61170
$56$	−3.88559	−0.519233
$57$	5.92616	0.784939
$58$	−5.24594	−0.688826
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	−3.45787	−0.446409
$61$	−0.310913	−0.0398084	−0.0199042	−	0.999802i	$-0.506336\pi$
$61$	−0.310913	−0.0398084	−0.0199042	+	0.999802i	$0.506336\pi$
$62$	6.53532	0.829986
$63$	3.88559	0.489538
$64$	1.00000	0.125000
$65$	−14.2795	−1.77115
$66$	−5.60139	−0.689484
$67$	1.06513	0.130126	0.0650632	−	0.997881i	$-0.479275\pi$
$67$	1.06513	0.130126	0.0650632	+	0.997881i	$0.479275\pi$
$68$	1.00000	0.121268
$69$	3.68458	0.443571
$70$	−13.4358	−1.60589
$71$	10.0903	1.19750	0.598748	−	0.800937i	$-0.295665\pi$
$71$	10.0903	1.19750	0.598748	+	0.800937i	$0.295665\pi$
$72$	−1.00000	−0.117851
$73$	−16.5843	−1.94104	−0.970522	−	0.241011i	$-0.922521\pi$
$73$	−16.5843	−1.94104	−0.970522	+	0.241011i	$0.922521\pi$
$74$	−10.4519	−1.21500
$75$	−6.95684	−0.803307
$76$	−5.92616	−0.679777
$77$	−21.7647	−2.48032
$78$	−4.12957	−0.467581
$79$	−10.1134	−1.13785	−0.568924	−	0.822390i	$-0.692640\pi$
$79$	−10.1134	−1.13785	−0.568924	+	0.822390i	$0.692640\pi$
$80$	3.45787	0.386601
$81$	1.00000	0.111111
$82$	−0.713032	−0.0787412
$83$	11.2226	1.23185	0.615923	−	0.787807i	$-0.288783\pi$
$83$	11.2226	1.23185	0.615923	+	0.787807i	$0.288783\pi$
$84$	−3.88559	−0.423952
$85$	3.45787	0.375058
$86$	5.70750	0.615456
$87$	−5.24594	−0.562424
$88$	5.60139	0.597110
$89$	−9.13347	−0.968146	−0.484073	−	0.875028i	$-0.660843\pi$
$89$	−9.13347	−0.968146	−0.484073	+	0.875028i	$0.660843\pi$
$90$	−3.45787	−0.364491
$91$	−16.0458	−1.68206
$92$	−3.68458	−0.384144
$93$	6.53532	0.677681
$94$	5.79742	0.597958
$95$	−20.4919	−2.10242
$96$	1.00000	0.102062
$97$	−0.689638	−0.0700221	−0.0350110	−	0.999387i	$-0.511147\pi$
$97$	−0.689638	−0.0700221	−0.0350110	+	0.999387i	$0.511147\pi$
$98$	−8.09778	−0.817999
$99$	−5.60139	−0.562961
$100$	6.95684	0.695684
$101$	−8.57709	−0.853452	−0.426726	−	0.904381i	$-0.640333\pi$
$101$	−8.57709	−0.853452	−0.426726	+	0.904381i	$0.640333\pi$
$102$	1.00000	0.0990148
$103$	−4.82911	−0.475827	−0.237913	−	0.971286i	$-0.576463\pi$
$103$	−4.82911	−0.475827	−0.237913	+	0.971286i	$0.576463\pi$
$104$	4.12957	0.404937
$105$	−13.4358	−1.31120
$106$	−5.20130	−0.505194
$107$	−7.66400	−0.740907	−0.370454	−	0.928851i	$-0.620798\pi$
$107$	−7.66400	−0.740907	−0.370454	+	0.928851i	$0.620798\pi$
$108$	−1.00000	−0.0962250
$109$	−6.36294	−0.609459	−0.304729	−	0.952439i	$-0.598566\pi$
$109$	−6.36294	−0.609459	−0.304729	+	0.952439i	$0.598566\pi$
$110$	19.3689	1.84675
$111$	−10.4519	−0.992046
$112$	3.88559	0.367153
$113$	1.70819	0.160693	0.0803467	−	0.996767i	$-0.474397\pi$
$113$	1.70819	0.160693	0.0803467	+	0.996767i	$0.474397\pi$
$114$	−5.92616	−0.555036
$115$	−12.7408	−1.18808
$116$	5.24594	0.487073
$117$	−4.12957	−0.381779
$118$	−1.00000	−0.0920575
$119$	3.88559	0.356191
$120$	3.45787	0.315659
$121$	20.3756	1.85233
$122$	0.310913	0.0281488
$123$	−0.713032	−0.0642919
$124$	−6.53532	−0.586889
$125$	6.76651	0.605215
$126$	−3.88559	−0.346156
$127$	−20.6955	−1.83643	−0.918216	−	0.396081i	$-0.870370\pi$
$127$	−20.6955	−1.83643	−0.918216	+	0.396081i	$0.870370\pi$
$128$	−1.00000	−0.0883883
$129$	5.70750	0.502517
$130$	14.2795	1.25239
$131$	4.04709	0.353596	0.176798	−	0.984247i	$-0.443426\pi$
$131$	4.04709	0.353596	0.176798	+	0.984247i	$0.443426\pi$
$132$	5.60139	0.487539
$133$	−23.0266	−1.99666
$134$	−1.06513	−0.0920132
$135$	−3.45787	−0.297606
$136$	−1.00000	−0.0857493
$137$	4.10036	0.350317	0.175159	−	0.984540i	$-0.443956\pi$
$137$	4.10036	0.350317	0.175159	+	0.984540i	$0.443956\pi$
$138$	−3.68458	−0.313652
$139$	−10.7576	−0.912445	−0.456223	−	0.889866i	$-0.650798\pi$
$139$	−10.7576	−0.912445	−0.456223	+	0.889866i	$0.650798\pi$
$140$	13.4358	1.13554
$141$	5.79742	0.488230
$142$	−10.0903	−0.846758
$143$	23.1313	1.93434
$144$	1.00000	0.0833333
$145$	18.1398	1.50643
$146$	16.5843	1.37253
$147$	−8.09778	−0.667894
$148$	10.4519	0.859137
$149$	−16.8850	−1.38327	−0.691635	−	0.722247i	$-0.743109\pi$
$149$	−16.8850	−1.38327	−0.691635	+	0.722247i	$0.743109\pi$
$150$	6.95684	0.568024
$151$	−17.5452	−1.42781	−0.713906	−	0.700242i	$-0.753076\pi$
$151$	−17.5452	−1.42781	−0.713906	+	0.700242i	$0.753076\pi$
$152$	5.92616	0.480675
$153$	1.00000	0.0808452
$154$	21.7647	1.75385
$155$	−22.5983	−1.81514
$156$	4.12957	0.330630
$157$	19.9483	1.59205	0.796025	−	0.605264i	$-0.206933\pi$
$157$	19.9483	1.59205	0.796025	+	0.605264i	$0.206933\pi$
$158$	10.1134	0.804580
$159$	−5.20130	−0.412490
$160$	−3.45787	−0.273368
$161$	−14.3167	−1.12832
$162$	−1.00000	−0.0785674
$163$	6.93016	0.542812	0.271406	−	0.962465i	$-0.412511\pi$
$163$	6.93016	0.542812	0.271406	+	0.962465i	$0.412511\pi$
$164$	0.713032	0.0556784
$165$	19.3689	1.50786
$166$	−11.2226	−0.871046
$167$	8.51951	0.659260	0.329630	−	0.944110i	$-0.393076\pi$
$167$	8.51951	0.659260	0.329630	+	0.944110i	$0.393076\pi$
$168$	3.88559	0.299779
$169$	4.05332	0.311794
$170$	−3.45787	−0.265206
$171$	−5.92616	−0.453185
$172$	−5.70750	−0.435193
$173$	11.1535	0.847988	0.423994	−	0.905665i	$-0.360628\pi$
$173$	11.1535	0.847988	0.423994	+	0.905665i	$0.360628\pi$
$174$	5.24594	0.397694
$175$	27.0314	2.04338
$176$	−5.60139	−0.422221
$177$	−1.00000	−0.0751646
$178$	9.13347	0.684583
$179$	−4.96069	−0.370779	−0.185390	−	0.982665i	$-0.559355\pi$
$179$	−4.96069	−0.370779	−0.185390	+	0.982665i	$0.559355\pi$
$180$	3.45787	0.257734
$181$	−12.6647	−0.941361	−0.470680	−	0.882304i	$-0.655991\pi$
$181$	−12.6647	−0.941361	−0.470680	+	0.882304i	$0.655991\pi$
$182$	16.0458	1.18939
$183$	0.310913	0.0229834
$184$	3.68458	0.271631
$185$	36.1411	2.65715
$186$	−6.53532	−0.479193
$187$	−5.60139	−0.409614
$188$	−5.79742	−0.422820
$189$	−3.88559	−0.282635
$190$	20.4919	1.48664
$191$	−7.69704	−0.556938	−0.278469	−	0.960445i	$-0.589827\pi$
$191$	−7.69704	−0.556938	−0.278469	+	0.960445i	$0.589827\pi$
$192$	−1.00000	−0.0721688
$193$	−1.14357	−0.0823157	−0.0411579	−	0.999153i	$-0.513105\pi$
$193$	−1.14357	−0.0823157	−0.0411579	+	0.999153i	$0.513105\pi$
$194$	0.689638	0.0495131
$195$	14.2795	1.02258
$196$	8.09778	0.578413
$197$	−24.3600	−1.73558	−0.867788	−	0.496935i	$-0.834459\pi$
$197$	−24.3600	−1.73558	−0.867788	+	0.496935i	$0.834459\pi$
$198$	5.60139	0.398074
$199$	8.28532	0.587330	0.293665	−	0.955908i	$-0.405125\pi$
$199$	8.28532	0.587330	0.293665	+	0.955908i	$0.405125\pi$
$200$	−6.95684	−0.491923
$201$	−1.06513	−0.0751285
$202$	8.57709	0.603482
$203$	20.3836	1.43064
$204$	−1.00000	−0.0700140
$205$	2.46557	0.172203
$206$	4.82911	0.336460
$207$	−3.68458	−0.256096
$208$	−4.12957	−0.286334
$209$	33.1947	2.29613
$210$	13.4358	0.927161
$211$	14.5805	1.00376	0.501882	−	0.864936i	$-0.332641\pi$
$211$	14.5805	1.00376	0.501882	+	0.864936i	$0.332641\pi$
$212$	5.20130	0.357226
$213$	−10.0903	−0.691375
$214$	7.66400	0.523900
$215$	−19.7358	−1.34597
$216$	1.00000	0.0680414
$217$	−25.3935	−1.72383
$218$	6.36294	0.430953
$219$	16.5843	1.12066
$220$	−19.3689	−1.30585
$221$	−4.12957	−0.277785
$222$	10.4519	0.701483
$223$	11.7916	0.789622	0.394811	−	0.918762i	$-0.370810\pi$
$223$	11.7916	0.789622	0.394811	+	0.918762i	$0.370810\pi$
$224$	−3.88559	−0.259617
$225$	6.95684	0.463790
$226$	−1.70819	−0.113627
$227$	−3.42628	−0.227410	−0.113705	−	0.993515i	$-0.536272\pi$
$227$	−3.42628	−0.227410	−0.113705	+	0.993515i	$0.536272\pi$
$228$	5.92616	0.392469
$229$	2.61739	0.172962	0.0864810	−	0.996254i	$-0.472438\pi$
$229$	2.61739	0.172962	0.0864810	+	0.996254i	$0.472438\pi$
$230$	12.7408	0.840102
$231$	21.7647	1.43201
$232$	−5.24594	−0.344413
$233$	2.81899	0.184678	0.0923391	−	0.995728i	$-0.470566\pi$
$233$	2.81899	0.184678	0.0923391	+	0.995728i	$0.470566\pi$
$234$	4.12957	0.269958
$235$	−20.0467	−1.30770
$236$	1.00000	0.0650945
$237$	10.1134	0.656936
$238$	−3.88559	−0.251865
$239$	−14.8334	−0.959490	−0.479745	−	0.877408i	$-0.659271\pi$
$239$	−14.8334	−0.959490	−0.479745	+	0.877408i	$0.659271\pi$
$240$	−3.45787	−0.223204
$241$	−27.7063	−1.78472	−0.892360	−	0.451325i	$-0.850952\pi$
$241$	−27.7063	−1.78472	−0.892360	+	0.451325i	$0.850952\pi$
$242$	−20.3756	−1.30979
$243$	−1.00000	−0.0641500
$244$	−0.310913	−0.0199042
$245$	28.0010	1.78892
$246$	0.713032	0.0454612
$247$	24.4725	1.55715
$248$	6.53532	0.414993
$249$	−11.2226	−0.711206
$250$	−6.76651	−0.427952
$251$	−14.9986	−0.946702	−0.473351	−	0.880874i	$-0.656956\pi$
$251$	−14.9986	−0.946702	−0.473351	+	0.880874i	$0.656956\pi$
$252$	3.88559	0.244769
$253$	20.6388	1.29755
$254$	20.6955	1.29855
$255$	−3.45787	−0.216540
$256$	1.00000	0.0625000
$257$	−22.5998	−1.40974	−0.704868	−	0.709339i	$-0.748994\pi$
$257$	−22.5998	−1.40974	−0.704868	+	0.709339i	$0.748994\pi$
$258$	−5.70750	−0.355333
$259$	40.6116	2.52348
$260$	−14.2795	−0.885577
$261$	5.24594	0.324716
$262$	−4.04709	−0.250030
$263$	15.6141	0.962806	0.481403	−	0.876499i	$-0.340127\pi$
$263$	15.6141	0.962806	0.481403	+	0.876499i	$0.340127\pi$
$264$	−5.60139	−0.344742
$265$	17.9854	1.10483
$266$	23.0266	1.41185
$267$	9.13347	0.558959
$268$	1.06513	0.0650632
$269$	2.14202	0.130601	0.0653007	−	0.997866i	$-0.479199\pi$
$269$	2.14202	0.130601	0.0653007	+	0.997866i	$0.479199\pi$
$270$	3.45787	0.210439
$271$	−22.3597	−1.35826	−0.679128	−	0.734020i	$-0.737642\pi$
$271$	−22.3597	−1.35826	−0.679128	+	0.734020i	$0.737642\pi$
$272$	1.00000	0.0606339
$273$	16.0458	0.971135
$274$	−4.10036	−0.247712
$275$	−38.9680	−2.34986
$276$	3.68458	0.221785
$277$	−7.25233	−0.435750	−0.217875	−	0.975977i	$-0.569913\pi$
$277$	−7.25233	−0.435750	−0.217875	+	0.975977i	$0.569913\pi$
$278$	10.7576	0.645196
$279$	−6.53532	−0.391259
$280$	−13.4358	−0.802945
$281$	27.2419	1.62511	0.812557	−	0.582881i	$-0.198075\pi$
$281$	27.2419	1.62511	0.812557	+	0.582881i	$0.198075\pi$
$282$	−5.79742	−0.345231
$283$	−21.7549	−1.29319	−0.646597	−	0.762832i	$-0.723808\pi$
$283$	−21.7549	−1.29319	−0.646597	+	0.762832i	$0.723808\pi$
$284$	10.0903	0.598748
$285$	20.4919	1.21383
$286$	−23.1313	−1.36778
$287$	2.77055	0.163540
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	−18.1398	−1.06520
$291$	0.689638	0.0404273
$292$	−16.5843	−0.970522
$293$	5.50428	0.321564	0.160782	−	0.986990i	$-0.448598\pi$
$293$	5.50428	0.321564	0.160782	+	0.986990i	$0.448598\pi$
$294$	8.09778	0.472272
$295$	3.45787	0.201325
$296$	−10.4519	−0.607502
$297$	5.60139	0.325026
$298$	16.8850	0.978120
$299$	15.2157	0.879947
$300$	−6.95684	−0.401654
$301$	−22.1770	−1.27826
$302$	17.5452	1.00962
$303$	8.57709	0.492741
$304$	−5.92616	−0.339888
$305$	−1.07510	−0.0615599
$306$	−1.00000	−0.0571662
$307$	24.4677	1.39644	0.698221	−	0.715882i	$-0.253975\pi$
$307$	24.4677	1.39644	0.698221	+	0.715882i	$0.253975\pi$
$308$	−21.7647	−1.24016
$309$	4.82911	0.274719
$310$	22.5983	1.28349
$311$	8.72967	0.495014	0.247507	−	0.968886i	$-0.420389\pi$
$311$	8.72967	0.495014	0.247507	+	0.968886i	$0.420389\pi$
$312$	−4.12957	−0.233791
$313$	−23.7154	−1.34048	−0.670238	−	0.742146i	$-0.733808\pi$
$313$	−23.7154	−1.34048	−0.670238	+	0.742146i	$0.733808\pi$
$314$	−19.9483	−1.12575
$315$	13.4358	0.757024
$316$	−10.1134	−0.568924
$317$	−11.6691	−0.655404	−0.327702	−	0.944781i	$-0.606274\pi$
$317$	−11.6691	−0.655404	−0.327702	+	0.944781i	$0.606274\pi$
$318$	5.20130	0.291674
$319$	−29.3846	−1.64522
$320$	3.45787	0.193301
$321$	7.66400	0.427763
$322$	14.3167	0.797841
$323$	−5.92616	−0.329740
$324$	1.00000	0.0555556
$325$	−28.7288	−1.59358
$326$	−6.93016	−0.383826
$327$	6.36294	0.351871
$328$	−0.713032	−0.0393706
$329$	−22.5264	−1.24192
$330$	−19.3689	−1.06622
$331$	−3.34899	−0.184077	−0.0920385	−	0.995755i	$-0.529338\pi$
$331$	−3.34899	−0.184077	−0.0920385	+	0.995755i	$0.529338\pi$
$332$	11.2226	0.615923
$333$	10.4519	0.572758
$334$	−8.51951	−0.466167
$335$	3.68308	0.201228
$336$	−3.88559	−0.211976
$337$	−28.9538	−1.57722	−0.788608	−	0.614896i	$-0.789198\pi$
$337$	−28.9538	−1.57722	−0.788608	+	0.614896i	$0.789198\pi$
$338$	−4.05332	−0.220472
$339$	−1.70819	−0.0927764
$340$	3.45787	0.187529
$341$	36.6069	1.98237
$342$	5.92616	0.320450
$343$	4.26552	0.230316
$344$	5.70750	0.307728
$345$	12.7408	0.685940
$346$	−11.1535	−0.599618
$347$	12.2510	0.657668	0.328834	−	0.944388i	$-0.393344\pi$
$347$	12.2510	0.657668	0.328834	+	0.944388i	$0.393344\pi$
$348$	−5.24594	−0.281212
$349$	−7.02848	−0.376226	−0.188113	−	0.982147i	$-0.560237\pi$
$349$	−7.02848	−0.376226	−0.188113	+	0.982147i	$0.560237\pi$
$350$	−27.0314	−1.44489
$351$	4.12957	0.220420
$352$	5.60139	0.298555
$353$	20.4224	1.08698	0.543489	−	0.839417i	$-0.317103\pi$
$353$	20.4224	1.08698	0.543489	+	0.839417i	$0.317103\pi$
$354$	1.00000	0.0531494
$355$	34.8909	1.85181
$356$	−9.13347	−0.484073
$357$	−3.88559	−0.205647
$358$	4.96069	0.262181
$359$	23.8475	1.25862	0.629312	−	0.777152i	$-0.283337\pi$
$359$	23.8475	1.25862	0.629312	+	0.777152i	$0.283337\pi$
$360$	−3.45787	−0.182246
$361$	16.1194	0.848387
$362$	12.6647	0.665642
$363$	−20.3756	−1.06944
$364$	−16.0458	−0.841028
$365$	−57.3463	−3.00164
$366$	−0.310913	−0.0162517
$367$	31.6338	1.65127	0.825636	−	0.564204i	$-0.190817\pi$
$367$	31.6338	1.65127	0.825636	+	0.564204i	$0.190817\pi$
$368$	−3.68458	−0.192072
$369$	0.713032	0.0371189
$370$	−36.1411	−1.87889
$371$	20.2101	1.04926
$372$	6.53532	0.338840
$373$	−2.72807	−0.141254	−0.0706270	−	0.997503i	$-0.522500\pi$
$373$	−2.72807	−0.141254	−0.0706270	+	0.997503i	$0.522500\pi$
$374$	5.60139	0.289641
$375$	−6.76651	−0.349421
$376$	5.79742	0.298979
$377$	−21.6635	−1.11572
$378$	3.88559	0.199853
$379$	9.00123	0.462362	0.231181	−	0.972911i	$-0.425741\pi$
$379$	9.00123	0.462362	0.231181	+	0.972911i	$0.425741\pi$
$380$	−20.4919	−1.05121
$381$	20.6955	1.06026
$382$	7.69704	0.393815
$383$	10.9658	0.560327	0.280163	−	0.959952i	$-0.409611\pi$
$383$	10.9658	0.560327	0.280163	+	0.959952i	$0.409611\pi$
$384$	1.00000	0.0510310
$385$	−75.2594	−3.83557
$386$	1.14357	0.0582060
$387$	−5.70750	−0.290129
$388$	−0.689638	−0.0350110
$389$	4.19351	0.212619	0.106310	−	0.994333i	$-0.466097\pi$
$389$	4.19351	0.212619	0.106310	+	0.994333i	$0.466097\pi$
$390$	−14.2795	−0.723070
$391$	−3.68458	−0.186337
$392$	−8.09778	−0.409000
$393$	−4.04709	−0.204149
$394$	24.3600	1.22724
$395$	−34.9708	−1.75957
$396$	−5.60139	−0.281481
$397$	9.06304	0.454861	0.227431	−	0.973794i	$-0.426968\pi$
$397$	9.06304	0.454861	0.227431	+	0.973794i	$0.426968\pi$
$398$	−8.28532	−0.415305
$399$	23.0266	1.15277
$400$	6.95684	0.347842
$401$	−13.4015	−0.669238	−0.334619	−	0.942353i	$-0.608608\pi$
$401$	−13.4015	−0.669238	−0.334619	+	0.942353i	$0.608608\pi$
$402$	1.06513	0.0531238
$403$	26.9880	1.34437
$404$	−8.57709	−0.426726
$405$	3.45787	0.171823
$406$	−20.3836	−1.01162
$407$	−58.5449	−2.90196
$408$	1.00000	0.0495074
$409$	9.06224	0.448099	0.224050	−	0.974578i	$-0.428072\pi$
$409$	9.06224	0.448099	0.224050	+	0.974578i	$0.428072\pi$
$410$	−2.46557	−0.121766
$411$	−4.10036	−0.202256
$412$	−4.82911	−0.237913
$413$	3.88559	0.191197
$414$	3.68458	0.181087
$415$	38.8064	1.90493
$416$	4.12957	0.202469
$417$	10.7576	0.526801
$418$	−33.1947	−1.62361
$419$	21.0139	1.02660	0.513299	−	0.858210i	$-0.328423\pi$
$419$	21.0139	1.02660	0.513299	+	0.858210i	$0.328423\pi$
$420$	−13.4358	−0.655602
$421$	−1.01697	−0.0495640	−0.0247820	−	0.999693i	$-0.507889\pi$
$421$	−1.01697	−0.0495640	−0.0247820	+	0.999693i	$0.507889\pi$
$422$	−14.5805	−0.709768
$423$	−5.79742	−0.281880
$424$	−5.20130	−0.252597
$425$	6.95684	0.337457
$426$	10.0903	0.488876
$427$	−1.20808	−0.0584631
$428$	−7.66400	−0.370454
$429$	−23.1313	−1.11679
$430$	19.7358	0.951744
$431$	−24.6309	−1.18643	−0.593214	−	0.805045i	$-0.702141\pi$
$431$	−24.6309	−1.18643	−0.593214	+	0.805045i	$0.702141\pi$
$432$	−1.00000	−0.0481125
$433$	9.75640	0.468863	0.234431	−	0.972133i	$-0.424677\pi$
$433$	9.75640	0.468863	0.234431	+	0.972133i	$0.424677\pi$
$434$	25.3935	1.21893
$435$	−18.1398	−0.869735
$436$	−6.36294	−0.304729
$437$	21.8354	1.04453
$438$	−16.5843	−0.792428
$439$	0.150788	0.00719671	0.00359836	−	0.999994i	$-0.498855\pi$
$439$	0.150788	0.00719671	0.00359836	+	0.999994i	$0.498855\pi$
$440$	19.3689	0.923375
$441$	8.09778	0.385609
$442$	4.12957	0.196423
$443$	−5.61192	−0.266630	−0.133315	−	0.991074i	$-0.542562\pi$
$443$	−5.61192	−0.266630	−0.133315	+	0.991074i	$0.542562\pi$
$444$	−10.4519	−0.496023
$445$	−31.5823	−1.49715
$446$	−11.7916	−0.558347
$447$	16.8850	0.798631
$448$	3.88559	0.183577
$449$	−17.6168	−0.831387	−0.415694	−	0.909505i	$-0.636461\pi$
$449$	−17.6168	−0.831387	−0.415694	+	0.909505i	$0.636461\pi$
$450$	−6.95684	−0.327949
$451$	−3.99397	−0.188069
$452$	1.70819	0.0803467
$453$	17.5452	0.824348
$454$	3.42628	0.160803
$455$	−55.4842	−2.60114
$456$	−5.92616	−0.277518
$457$	−33.2702	−1.55632	−0.778158	−	0.628069i	$-0.783846\pi$
$457$	−33.2702	−1.55632	−0.778158	+	0.628069i	$0.783846\pi$
$458$	−2.61739	−0.122303
$459$	−1.00000	−0.0466760
$460$	−12.7408	−0.594042
$461$	−32.4362	−1.51070	−0.755351	−	0.655320i	$-0.772534\pi$
$461$	−32.4362	−1.51070	−0.755351	+	0.655320i	$0.772534\pi$
$462$	−21.7647	−1.01259
$463$	−28.5638	−1.32747	−0.663736	−	0.747967i	$-0.731030\pi$
$463$	−28.5638	−1.32747	−0.663736	+	0.747967i	$0.731030\pi$
$464$	5.24594	0.243537
$465$	22.5983	1.04797
$466$	−2.81899	−0.130587
$467$	−29.2683	−1.35438	−0.677188	−	0.735810i	$-0.736802\pi$
$467$	−29.2683	−1.35438	−0.677188	+	0.735810i	$0.736802\pi$
$468$	−4.12957	−0.190889
$469$	4.13865	0.191105
$470$	20.0467	0.924685
$471$	−19.9483	−0.919170
$472$	−1.00000	−0.0460287
$473$	31.9699	1.46998
$474$	−10.1134	−0.464524
$475$	−41.2274	−1.89164
$476$	3.88559	0.178096
$477$	5.20130	0.238151
$478$	14.8334	0.678462
$479$	−15.8350	−0.723519	−0.361759	−	0.932272i	$-0.617824\pi$
$479$	−15.8350	−0.723519	−0.361759	+	0.932272i	$0.617824\pi$
$480$	3.45787	0.157829
$481$	−43.1616	−1.96800
$482$	27.7063	1.26199
$483$	14.3167	0.651434
$484$	20.3756	0.926163
$485$	−2.38468	−0.108283
$486$	1.00000	0.0453609
$487$	−32.3564	−1.46621	−0.733103	−	0.680117i	$-0.761929\pi$
$487$	−32.3564	−1.46621	−0.733103	+	0.680117i	$0.761929\pi$
$488$	0.310913	0.0140744
$489$	−6.93016	−0.313393
$490$	−28.0010	−1.26496
$491$	−13.7048	−0.618488	−0.309244	−	0.950983i	$-0.600076\pi$
$491$	−13.7048	−0.618488	−0.309244	+	0.950983i	$0.600076\pi$
$492$	−0.713032	−0.0321459
$493$	5.24594	0.236265
$494$	−24.4725	−1.10107
$495$	−19.3689	−0.870566
$496$	−6.53532	−0.293444
$497$	39.2067	1.75866
$498$	11.2226	0.502899
$499$	−30.5397	−1.36715	−0.683573	−	0.729883i	$-0.739575\pi$
$499$	−30.5397	−1.36715	−0.683573	+	0.729883i	$0.739575\pi$
$500$	6.76651	0.302607
$501$	−8.51951	−0.380624
$502$	14.9986	0.669420
$503$	27.3515	1.21954	0.609771	−	0.792577i	$-0.291261\pi$
$503$	27.3515	1.21954	0.609771	+	0.792577i	$0.291261\pi$
$504$	−3.88559	−0.173078
$505$	−29.6584	−1.31978
$506$	−20.6388	−0.917505
$507$	−4.05332	−0.180014
$508$	−20.6955	−0.918216
$509$	25.1680	1.11555	0.557776	−	0.829991i	$-0.311655\pi$
$509$	25.1680	1.11555	0.557776	+	0.829991i	$0.311655\pi$
$510$	3.45787	0.153117
$511$	−64.4397	−2.85064
$512$	−1.00000	−0.0441942
$513$	5.92616	0.261646
$514$	22.5998	0.996833
$515$	−16.6984	−0.735821
$516$	5.70750	0.251259
$517$	32.4736	1.42819
$518$	−40.6116	−1.78437
$519$	−11.1535	−0.489586
$520$	14.2795	0.626197
$521$	36.7036	1.60801	0.804007	−	0.594620i	$-0.202698\pi$
$521$	36.7036	1.60801	0.804007	+	0.594620i	$0.202698\pi$
$522$	−5.24594	−0.229609
$523$	28.2743	1.23635	0.618175	−	0.786040i	$-0.287872\pi$
$523$	28.2743	1.23635	0.618175	+	0.786040i	$0.287872\pi$
$524$	4.04709	0.176798
$525$	−27.0314	−1.17975
$526$	−15.6141	−0.680806
$527$	−6.53532	−0.284683
$528$	5.60139	0.243769
$529$	−9.42390	−0.409735
$530$	−17.9854	−0.781235
$531$	1.00000	0.0433963
$532$	−23.0266	−0.998330
$533$	−2.94451	−0.127541
$534$	−9.13347	−0.395244
$535$	−26.5011	−1.14574
$536$	−1.06513	−0.0460066
$537$	4.96069	0.214070
$538$	−2.14202	−0.0923491
$539$	−45.3588	−1.95374
$540$	−3.45787	−0.148803
$541$	−0.725035	−0.0311717	−0.0155858	−	0.999879i	$-0.504961\pi$
$541$	−0.725035	−0.0311717	−0.0155858	+	0.999879i	$0.504961\pi$
$542$	22.3597	0.960431
$543$	12.6647	0.543495
$544$	−1.00000	−0.0428746
$545$	−22.0022	−0.942470
$546$	−16.0458	−0.686696
$547$	−27.3940	−1.17128	−0.585640	−	0.810571i	$-0.699157\pi$
$547$	−27.3940	−1.17128	−0.585640	+	0.810571i	$0.699157\pi$
$548$	4.10036	0.175159
$549$	−0.310913	−0.0132695
$550$	38.9680	1.66160
$551$	−31.0883	−1.32440
$552$	−3.68458	−0.156826
$553$	−39.2965	−1.67106
$554$	7.25233	0.308122
$555$	−36.1411	−1.53411
$556$	−10.7576	−0.456223
$557$	−3.55449	−0.150608	−0.0753042	−	0.997161i	$-0.523993\pi$
$557$	−3.55449	−0.150608	−0.0753042	+	0.997161i	$0.523993\pi$
$558$	6.53532	0.276662
$559$	23.5695	0.996884
$560$	13.4358	0.567768
$561$	5.60139	0.236491
$562$	−27.2419	−1.14913
$563$	42.7640	1.80229	0.901144	−	0.433520i	$-0.142728\pi$
$563$	42.7640	1.80229	0.901144	+	0.433520i	$0.142728\pi$
$564$	5.79742	0.244115
$565$	5.90671	0.248497
$566$	21.7549	0.914426
$567$	3.88559	0.163179
$568$	−10.0903	−0.423379
$569$	8.89396	0.372854	0.186427	−	0.982469i	$-0.440309\pi$
$569$	8.89396	0.372854	0.186427	+	0.982469i	$0.440309\pi$
$570$	−20.4919	−0.858310
$571$	17.2859	0.723393	0.361697	−	0.932296i	$-0.382198\pi$
$571$	17.2859	0.723393	0.361697	+	0.932296i	$0.382198\pi$
$572$	23.1313	0.967169
$573$	7.69704	0.321548
$574$	−2.77055	−0.115640
$575$	−25.6330	−1.06897
$576$	1.00000	0.0416667
$577$	−44.7515	−1.86303	−0.931514	−	0.363705i	$-0.881512\pi$
$577$	−44.7515	−1.86303	−0.931514	+	0.363705i	$0.881512\pi$
$578$	−1.00000	−0.0415945
$579$	1.14357	0.0475250
$580$	18.1398	0.753213
$581$	43.6065	1.80910
$582$	−0.689638	−0.0285864
$583$	−29.1345	−1.20663
$584$	16.5843	0.686263
$585$	−14.2795	−0.590384
$586$	−5.50428	−0.227380
$587$	44.5875	1.84033	0.920163	−	0.391537i	$-0.128056\pi$
$587$	44.5875	1.84033	0.920163	+	0.391537i	$0.128056\pi$
$588$	−8.09778	−0.333947
$589$	38.7293	1.59581
$590$	−3.45787	−0.142358
$591$	24.3600	1.00204
$592$	10.4519	0.429569
$593$	17.5171	0.719340	0.359670	−	0.933080i	$-0.382889\pi$
$593$	17.5171	0.719340	0.359670	+	0.933080i	$0.382889\pi$
$594$	−5.60139	−0.229828
$595$	13.4358	0.550816
$596$	−16.8850	−0.691635
$597$	−8.28532	−0.339095
$598$	−15.2157	−0.622216
$599$	9.43302	0.385423	0.192711	−	0.981255i	$-0.438272\pi$
$599$	9.43302	0.385423	0.192711	+	0.981255i	$0.438272\pi$
$600$	6.95684	0.284012
$601$	31.8344	1.29855	0.649276	−	0.760553i	$-0.275072\pi$
$601$	31.8344	1.29855	0.649276	+	0.760553i	$0.275072\pi$
$602$	22.1770	0.903866
$603$	1.06513	0.0433754
$604$	−17.5452	−0.713906
$605$	70.4561	2.86445
$606$	−8.57709	−0.348420
$607$	−32.3995	−1.31506	−0.657528	−	0.753430i	$-0.728398\pi$
$607$	−32.3995	−1.31506	−0.657528	+	0.753430i	$0.728398\pi$
$608$	5.92616	0.240337
$609$	−20.3836	−0.825983
$610$	1.07510	0.0435294
$611$	23.9408	0.968542
$612$	1.00000	0.0404226
$613$	26.0597	1.05254	0.526271	−	0.850317i	$-0.323590\pi$
$613$	26.0597	1.05254	0.526271	+	0.850317i	$0.323590\pi$
$614$	−24.4677	−0.987434
$615$	−2.46557	−0.0994213
$616$	21.7647	0.876924
$617$	−26.8286	−1.08008	−0.540038	−	0.841640i	$-0.681590\pi$
$617$	−26.8286	−1.08008	−0.540038	+	0.841640i	$0.681590\pi$
$618$	−4.82911	−0.194255
$619$	−8.47796	−0.340758	−0.170379	−	0.985379i	$-0.554499\pi$
$619$	−8.47796	−0.340758	−0.170379	+	0.985379i	$0.554499\pi$
$620$	−22.5983	−0.907568
$621$	3.68458	0.147857
$622$	−8.72967	−0.350028
$623$	−35.4889	−1.42183
$624$	4.12957	0.165315
$625$	−11.3865	−0.455462
$626$	23.7154	0.947860
$627$	−33.1947	−1.32567
$628$	19.9483	0.796025
$629$	10.4519	0.416743
$630$	−13.4358	−0.535297
$631$	37.8105	1.50521	0.752606	−	0.658471i	$-0.228797\pi$
$631$	37.8105	1.50521	0.752606	+	0.658471i	$0.228797\pi$
$632$	10.1134	0.402290
$633$	−14.5805	−0.579523
$634$	11.6691	0.463441
$635$	−71.5624	−2.83987
$636$	−5.20130	−0.206245
$637$	−33.4403	−1.32495
$638$	29.3846	1.16335
$639$	10.0903	0.399166
$640$	−3.45787	−0.136684
$641$	−18.4051	−0.726959	−0.363479	−	0.931602i	$-0.618411\pi$
$641$	−18.4051	−0.726959	−0.363479	+	0.931602i	$0.618411\pi$
$642$	−7.66400	−0.302474
$643$	−10.3111	−0.406630	−0.203315	−	0.979113i	$-0.565172\pi$
$643$	−10.3111	−0.406630	−0.203315	+	0.979113i	$0.565172\pi$
$644$	−14.3167	−0.564159
$645$	19.7358	0.777096
$646$	5.92616	0.233162
$647$	45.3769	1.78395	0.891976	−	0.452083i	$-0.149319\pi$
$647$	45.3769	1.78395	0.891976	+	0.452083i	$0.149319\pi$
$648$	−1.00000	−0.0392837
$649$	−5.60139	−0.219874
$650$	28.7288	1.12683
$651$	25.3935	0.995251
$652$	6.93016	0.271406
$653$	−11.8894	−0.465270	−0.232635	−	0.972564i	$-0.574735\pi$
$653$	−11.8894	−0.465270	−0.232635	+	0.972564i	$0.574735\pi$
$654$	−6.36294	−0.248811
$655$	13.9943	0.546803
$656$	0.713032	0.0278392
$657$	−16.5843	−0.647015
$658$	22.5264	0.878169
$659$	5.06617	0.197350	0.0986751	−	0.995120i	$-0.468540\pi$
$659$	5.06617	0.197350	0.0986751	+	0.995120i	$0.468540\pi$
$660$	19.3689	0.753932
$661$	44.7432	1.74031	0.870154	−	0.492779i	$-0.164019\pi$
$661$	44.7432	1.74031	0.870154	+	0.492779i	$0.164019\pi$
$662$	3.34899	0.130162
$663$	4.12957	0.160379
$664$	−11.2226	−0.435523
$665$	−79.6229	−3.08764
$666$	−10.4519	−0.405001
$667$	−19.3291	−0.748424
$668$	8.51951	0.329630
$669$	−11.7916	−0.455889
$670$	−3.68308	−0.142290
$671$	1.74155	0.0672317
$672$	3.88559	0.149890
$673$	24.9289	0.960940	0.480470	−	0.877011i	$-0.340466\pi$
$673$	24.9289	0.960940	0.480470	+	0.877011i	$0.340466\pi$
$674$	28.9538	1.11526
$675$	−6.95684	−0.267769
$676$	4.05332	0.155897
$677$	−30.9310	−1.18878	−0.594388	−	0.804179i	$-0.702606\pi$
$677$	−30.9310	−1.18878	−0.594388	+	0.804179i	$0.702606\pi$
$678$	1.70819	0.0656028
$679$	−2.67965	−0.102835
$680$	−3.45787	−0.132603
$681$	3.42628	0.131295
$682$	−36.6069	−1.40175
$683$	49.4004	1.89025	0.945127	−	0.326703i	$-0.105938\pi$
$683$	49.4004	1.89025	0.945127	+	0.326703i	$0.105938\pi$
$684$	−5.92616	−0.226592
$685$	14.1785	0.541732
$686$	−4.26552	−0.162858
$687$	−2.61739	−0.0998596
$688$	−5.70750	−0.217596
$689$	−21.4791	−0.818288
$690$	−12.7408	−0.485033
$691$	39.4621	1.50121	0.750604	−	0.660752i	$-0.229763\pi$
$691$	39.4621	1.50121	0.750604	+	0.660752i	$0.229763\pi$
$692$	11.1535	0.423994
$693$	−21.7647	−0.826772
$694$	−12.2510	−0.465041
$695$	−37.1982	−1.41101
$696$	5.24594	0.198847
$697$	0.713032	0.0270080
$698$	7.02848	0.266032
$699$	−2.81899	−0.106624
$700$	27.0314	1.02169
$701$	46.8775	1.77054	0.885269	−	0.465079i	$-0.153974\pi$
$701$	46.8775	1.77054	0.885269	+	0.465079i	$0.153974\pi$
$702$	−4.12957	−0.155860
$703$	−61.9393	−2.33609
$704$	−5.60139	−0.211110
$705$	20.0467	0.755002
$706$	−20.4224	−0.768609
$707$	−33.3270	−1.25339
$708$	−1.00000	−0.0375823
$709$	4.14025	0.155491	0.0777453	−	0.996973i	$-0.475228\pi$
$709$	4.14025	0.155491	0.0777453	+	0.996973i	$0.475228\pi$
$710$	−34.8909	−1.30943
$711$	−10.1134	−0.379282
$712$	9.13347	0.342291
$713$	24.0799	0.901798
$714$	3.88559	0.145414
$715$	79.9850	2.99127
$716$	−4.96069	−0.185390
$717$	14.8334	0.553962
$718$	−23.8475	−0.889982
$719$	−47.5102	−1.77183	−0.885915	−	0.463847i	$-0.846469\pi$
$719$	−47.5102	−1.77183	−0.885915	+	0.463847i	$0.846469\pi$
$720$	3.45787	0.128867
$721$	−18.7639	−0.698805
$722$	−16.1194	−0.599900
$723$	27.7063	1.03041
$724$	−12.6647	−0.470680
$725$	36.4952	1.35540
$726$	20.3756	0.756209
$727$	−29.8335	−1.10646	−0.553232	−	0.833027i	$-0.686606\pi$
$727$	−29.8335	−1.10646	−0.553232	+	0.833027i	$0.686606\pi$
$728$	16.0458	0.594696
$729$	1.00000	0.0370370
$730$	57.3463	2.12248
$731$	−5.70750	−0.211100
$732$	0.310913	0.0114917
$733$	12.2622	0.452913	0.226457	−	0.974021i	$-0.427286\pi$
$733$	12.2622	0.452913	0.226457	+	0.974021i	$0.427286\pi$
$734$	−31.6338	−1.16763
$735$	−28.0010	−1.03283
$736$	3.68458	0.135815
$737$	−5.96621	−0.219768
$738$	−0.713032	−0.0262471
$739$	38.6201	1.42066	0.710332	−	0.703867i	$-0.248545\pi$
$739$	38.6201	1.42066	0.710332	+	0.703867i	$0.248545\pi$
$740$	36.1411	1.32857
$741$	−24.4725	−0.899018
$742$	−20.2101	−0.741935
$743$	−7.05763	−0.258919	−0.129460	−	0.991585i	$-0.541324\pi$
$743$	−7.05763	−0.258919	−0.129460	+	0.991585i	$0.541324\pi$
$744$	−6.53532	−0.239596
$745$	−58.3860	−2.13910
$746$	2.72807	0.0998817
$747$	11.2226	0.410615
$748$	−5.60139	−0.204807
$749$	−29.7791	−1.08811
$750$	6.76651	0.247078
$751$	−45.6229	−1.66480	−0.832402	−	0.554173i	$-0.813035\pi$
$751$	−45.6229	−1.66480	−0.832402	+	0.554173i	$0.813035\pi$
$752$	−5.79742	−0.211410
$753$	14.9986	0.546579
$754$	21.6635	0.788937
$755$	−60.6691	−2.20798
$756$	−3.88559	−0.141317
$757$	−4.70948	−0.171169	−0.0855846	−	0.996331i	$-0.527276\pi$
$757$	−4.70948	−0.171169	−0.0855846	+	0.996331i	$0.527276\pi$
$758$	−9.00123	−0.326939
$759$	−20.6388	−0.749139
$760$	20.4919	0.743318
$761$	13.8767	0.503030	0.251515	−	0.967853i	$-0.419071\pi$
$761$	13.8767	0.503030	0.251515	+	0.967853i	$0.419071\pi$
$762$	−20.6955	−0.749720
$763$	−24.7237	−0.895060
$764$	−7.69704	−0.278469
$765$	3.45787	0.125019
$766$	−10.9658	−0.396211
$767$	−4.12957	−0.149110
$768$	−1.00000	−0.0360844
$769$	48.0506	1.73275	0.866374	−	0.499396i	$-0.166445\pi$
$769$	48.0506	1.73275	0.866374	+	0.499396i	$0.166445\pi$
$770$	75.2594	2.71216
$771$	22.5998	0.813911
$772$	−1.14357	−0.0411579
$773$	31.9555	1.14936	0.574680	−	0.818378i	$-0.305126\pi$
$773$	31.9555	1.14936	0.574680	+	0.818378i	$0.305126\pi$
$774$	5.70750	0.205152
$775$	−45.4652	−1.63316
$776$	0.689638	0.0247565
$777$	−40.6116	−1.45693
$778$	−4.19351	−0.150345
$779$	−4.22554	−0.151396
$780$	14.2795	0.511288
$781$	−56.5196	−2.02243
$782$	3.68458	0.131760
$783$	−5.24594	−0.187475
$784$	8.09778	0.289206
$785$	68.9786	2.46195
$786$	4.04709	0.144355
$787$	26.4236	0.941900	0.470950	−	0.882160i	$-0.343911\pi$
$787$	26.4236	0.941900	0.470950	+	0.882160i	$0.343911\pi$
$788$	−24.3600	−0.867788
$789$	−15.6141	−0.555876
$790$	34.9708	1.24421
$791$	6.63734	0.235997
$792$	5.60139	0.199037
$793$	1.28394	0.0455939
$794$	−9.06304	−0.321635
$795$	−17.9854	−0.637876
$796$	8.28532	0.293665
$797$	−38.9242	−1.37877	−0.689383	−	0.724397i	$-0.742118\pi$
$797$	−38.9242	−1.37877	−0.689383	+	0.724397i	$0.742118\pi$
$798$	−23.0266	−0.815133
$799$	−5.79742	−0.205098
$800$	−6.95684	−0.245962
$801$	−9.13347	−0.322715
$802$	13.4015	0.473223
$803$	92.8951	3.27820
$804$	−1.06513	−0.0375642
$805$	−49.5054	−1.74484
$806$	−26.9880	−0.950613
$807$	−2.14202	−0.0754027
$808$	8.57709	0.301741
$809$	32.3860	1.13863	0.569315	−	0.822120i	$-0.307209\pi$
$809$	32.3860	1.13863	0.569315	+	0.822120i	$0.307209\pi$
$810$	−3.45787	−0.121497
$811$	44.5863	1.56564	0.782819	−	0.622249i	$-0.213781\pi$
$811$	44.5863	1.56564	0.782819	+	0.622249i	$0.213781\pi$
$812$	20.3836	0.715322
$813$	22.3597	0.784189
$814$	58.5449	2.05200
$815$	23.9636	0.839408
$816$	−1.00000	−0.0350070
$817$	33.8236	1.18334
$818$	−9.06224	−0.316854
$819$	−16.0458	−0.560685
$820$	2.46557	0.0861014
$821$	48.8649	1.70540	0.852698	−	0.522404i	$-0.174965\pi$
$821$	48.8649	1.70540	0.852698	+	0.522404i	$0.174965\pi$
$822$	4.10036	0.143016
$823$	40.1238	1.39863	0.699313	−	0.714815i	$-0.253489\pi$
$823$	40.1238	1.39863	0.699313	+	0.714815i	$0.253489\pi$
$824$	4.82911	0.168230
$825$	38.9680	1.35669
$826$	−3.88559	−0.135197
$827$	−10.5229	−0.365917	−0.182958	−	0.983121i	$-0.558567\pi$
$827$	−10.5229	−0.365917	−0.182958	+	0.983121i	$0.558567\pi$
$828$	−3.68458	−0.128048
$829$	10.5285	0.365671	0.182835	−	0.983144i	$-0.441473\pi$
$829$	10.5285	0.365671	0.182835	+	0.983144i	$0.441473\pi$
$830$	−38.8064	−1.34699
$831$	7.25233	0.251580
$832$	−4.12957	−0.143167
$833$	8.09778	0.280571
$834$	−10.7576	−0.372504
$835$	29.4593	1.01948
$836$	33.1947	1.14806
$837$	6.53532	0.225894
$838$	−21.0139	−0.725915
$839$	35.7583	1.23451	0.617257	−	0.786761i	$-0.288244\pi$
$839$	35.7583	1.23451	0.617257	+	0.786761i	$0.288244\pi$
$840$	13.4358	0.463581
$841$	−1.48012	−0.0510385
$842$	1.01697	0.0350470
$843$	−27.2419	−0.938260
$844$	14.5805	0.501882
$845$	14.0158	0.482160
$846$	5.79742	0.199319
$847$	79.1711	2.72035
$848$	5.20130	0.178613
$849$	21.7549	0.746625
$850$	−6.95684	−0.238618
$851$	−38.5107	−1.32013
$852$	−10.0903	−0.345687
$853$	18.3814	0.629368	0.314684	−	0.949196i	$-0.398101\pi$
$853$	18.3814	0.629368	0.314684	+	0.949196i	$0.398101\pi$
$854$	1.20808	0.0413397
$855$	−20.4919	−0.700807
$856$	7.66400	0.261950
$857$	−20.0127	−0.683620	−0.341810	−	0.939769i	$-0.611040\pi$
$857$	−20.0127	−0.683620	−0.341810	+	0.939769i	$0.611040\pi$
$858$	23.1313	0.789690
$859$	−6.95739	−0.237383	−0.118692	−	0.992931i	$-0.537870\pi$
$859$	−6.95739	−0.237383	−0.118692	+	0.992931i	$0.537870\pi$
$860$	−19.7358	−0.672984
$861$	−2.77055	−0.0944199
$862$	24.6309	0.838931
$863$	−15.6671	−0.533314	−0.266657	−	0.963791i	$-0.585919\pi$
$863$	−15.6671	−0.533314	−0.266657	+	0.963791i	$0.585919\pi$
$864$	1.00000	0.0340207
$865$	38.5675	1.31133
$866$	−9.75640	−0.331536
$867$	−1.00000	−0.0339618
$868$	−25.3935	−0.861913
$869$	56.6492	1.92169
$870$	18.1398	0.614996
$871$	−4.39852	−0.149038
$872$	6.36294	0.215476
$873$	−0.689638	−0.0233407
$874$	−21.8354	−0.738593
$875$	26.2918	0.888827
$876$	16.5843	0.560331
$877$	−23.8696	−0.806018	−0.403009	−	0.915196i	$-0.632036\pi$
$877$	−23.8696	−0.806018	−0.403009	+	0.915196i	$0.632036\pi$
$878$	−0.150788	−0.00508884
$879$	−5.50428	−0.185655
$880$	−19.3689	−0.652924
$881$	11.0988	0.373929	0.186964	−	0.982367i	$-0.440135\pi$
$881$	11.0988	0.373929	0.186964	+	0.982367i	$0.440135\pi$
$882$	−8.09778	−0.272666
$883$	−34.4188	−1.15828	−0.579142	−	0.815226i	$-0.696612\pi$
$883$	−34.4188	−1.15828	−0.579142	+	0.815226i	$0.696612\pi$
$884$	−4.12957	−0.138892
$885$	−3.45787	−0.116235
$886$	5.61192	0.188536
$887$	41.3974	1.38999	0.694995	−	0.719015i	$-0.255407\pi$
$887$	41.3974	1.38999	0.694995	+	0.719015i	$0.255407\pi$
$888$	10.4519	0.350741
$889$	−80.4143	−2.69701
$890$	31.5823	1.05864
$891$	−5.60139	−0.187654
$892$	11.7916	0.394811
$893$	34.3564	1.14969
$894$	−16.8850	−0.564718
$895$	−17.1534	−0.573375
$896$	−3.88559	−0.129808
$897$	−15.2157	−0.508038
$898$	17.6168	0.587880
$899$	−34.2839	−1.14343
$900$	6.95684	0.231895
$901$	5.20130	0.173280
$902$	3.99397	0.132985
$903$	22.1770	0.738004
$904$	−1.70819	−0.0568137
$905$	−43.7929	−1.45572
$906$	−17.5452	−0.582902
$907$	−24.0637	−0.799023	−0.399511	−	0.916728i	$-0.630820\pi$
$907$	−24.0637	−0.799023	−0.399511	+	0.916728i	$0.630820\pi$
$908$	−3.42628	−0.113705
$909$	−8.57709	−0.284484
$910$	55.4842	1.83928
$911$	17.3354	0.574347	0.287174	−	0.957879i	$-0.407284\pi$
$911$	17.3354	0.574347	0.287174	+	0.957879i	$0.407284\pi$
$912$	5.92616	0.196235
$913$	−62.8624	−2.08044
$914$	33.2702	1.10048
$915$	1.07510	0.0355416
$916$	2.61739	0.0864810
$917$	15.7253	0.519296
$918$	1.00000	0.0330049
$919$	10.6602	0.351648	0.175824	−	0.984422i	$-0.443741\pi$
$919$	10.6602	0.351648	0.175824	+	0.984422i	$0.443741\pi$
$920$	12.7408	0.420051
$921$	−24.4677	−0.806237
$922$	32.4362	1.06823
$923$	−41.6685	−1.37154
$924$	21.7647	0.716006
$925$	72.7119	2.39075
$926$	28.5638	0.938665
$927$	−4.82911	−0.158609
$928$	−5.24594	−0.172206
$929$	16.8077	0.551443	0.275722	−	0.961238i	$-0.411083\pi$
$929$	16.8077	0.551443	0.275722	+	0.961238i	$0.411083\pi$
$930$	−22.5983	−0.741026
$931$	−47.9887	−1.57277
$932$	2.81899	0.0923391
$933$	−8.72967	−0.285797
$934$	29.2683	0.957689
$935$	−19.3689	−0.633430
$936$	4.12957	0.134979
$937$	−45.8335	−1.49731	−0.748657	−	0.662957i	$-0.769301\pi$
$937$	−45.8335	−1.49731	−0.748657	+	0.662957i	$0.769301\pi$
$938$	−4.13865	−0.135132
$939$	23.7154	0.773924
$940$	−20.0467	−0.653851
$941$	37.2112	1.21305	0.606526	−	0.795064i	$-0.292563\pi$
$941$	37.2112	1.21305	0.606526	+	0.795064i	$0.292563\pi$
$942$	19.9483	0.649951
$943$	−2.62722	−0.0855540
$944$	1.00000	0.0325472
$945$	−13.4358	−0.437068
$946$	−31.9699	−1.03943
$947$	−32.7238	−1.06338	−0.531691	−	0.846939i	$-0.678443\pi$
$947$	−32.7238	−1.06338	−0.531691	+	0.846939i	$0.678443\pi$
$948$	10.1134	0.328468
$949$	68.4860	2.22315
$950$	41.2274	1.33759
$951$	11.6691	0.378398
$952$	−3.88559	−0.125933
$953$	−34.5472	−1.11909	−0.559547	−	0.828798i	$-0.689025\pi$
$953$	−34.5472	−1.11909	−0.559547	+	0.828798i	$0.689025\pi$
$954$	−5.20130	−0.168398
$955$	−26.6153	−0.861252
$956$	−14.8334	−0.479745
$957$	29.3846	0.949868
$958$	15.8350	0.511605
$959$	15.9323	0.514481
$960$	−3.45787	−0.111602
$961$	11.7104	0.377754
$962$	43.1616	1.39159
$963$	−7.66400	−0.246969
$964$	−27.7063	−0.892360
$965$	−3.95430	−0.127293
$966$	−14.3167	−0.460634
$967$	−9.04481	−0.290862	−0.145431	−	0.989368i	$-0.546457\pi$
$967$	−9.04481	−0.290862	−0.145431	+	0.989368i	$0.546457\pi$
$968$	−20.3756	−0.654896
$969$	5.92616	0.190376
$970$	2.38468	0.0765673
$971$	−45.7891	−1.46944	−0.734721	−	0.678370i	$-0.762687\pi$
$971$	−45.7891	−1.46944	−0.734721	+	0.678370i	$0.762687\pi$
$972$	−1.00000	−0.0320750
$973$	−41.7995	−1.34003
$974$	32.3564	1.03676
$975$	28.7288	0.920056
$976$	−0.310913	−0.00995209
$977$	−5.47637	−0.175205	−0.0876024	−	0.996156i	$-0.527920\pi$
$977$	−5.47637	−0.175205	−0.0876024	+	0.996156i	$0.527920\pi$
$978$	6.93016	0.221602
$979$	51.1602	1.63509
$980$	28.0010	0.894461
$981$	−6.36294	−0.203153
$982$	13.7048	0.437337
$983$	23.2145	0.740429	0.370214	−	0.928946i	$-0.379284\pi$
$983$	23.2145	0.740429	0.370214	+	0.928946i	$0.379284\pi$
$984$	0.713032	0.0227306
$985$	−84.2335	−2.68390
$986$	−5.24594	−0.167065
$987$	22.5264	0.717022
$988$	24.4725	0.778573
$989$	21.0297	0.668706
$990$	19.3689	0.615583
$991$	36.0103	1.14390	0.571952	−	0.820287i	$-0.306186\pi$
$991$	36.0103	1.14390	0.571952	+	0.820287i	$0.306186\pi$
$992$	6.53532	0.207497
$993$	3.34899	0.106277
$994$	−39.2067	−1.24356
$995$	28.6495	0.908251
$996$	−11.2226	−0.355603
$997$	−45.1532	−1.43001	−0.715007	−	0.699117i	$-0.753577\pi$
$997$	−45.1532	−1.43001	−0.715007	+	0.699117i	$0.753577\pi$
$998$	30.5397	0.966718
$999$	−10.4519	−0.330682

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.u.1.9	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.u.1.9	✓	9	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.45787 q^{5} +1.00000 q^{6} +3.88559 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.45787 q^{5} +1.00000 q^{6} +3.88559 q^{7} -1.00000 q^{8} +1.00000 q^{9} -3.45787 q^{10} -5.60139 q^{11} -1.00000 q^{12} -4.12957 q^{13} -3.88559 q^{14} -3.45787 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} -5.92616 q^{19} +3.45787 q^{20} -3.88559 q^{21} +5.60139 q^{22} -3.68458 q^{23} +1.00000 q^{24} +6.95684 q^{25} +4.12957 q^{26} -1.00000 q^{27} +3.88559 q^{28} +5.24594 q^{29} +3.45787 q^{30} -6.53532 q^{31} -1.00000 q^{32} +5.60139 q^{33} -1.00000 q^{34} +13.4358 q^{35} +1.00000 q^{36} +10.4519 q^{37} +5.92616 q^{38} +4.12957 q^{39} -3.45787 q^{40} +0.713032 q^{41} +3.88559 q^{42} -5.70750 q^{43} -5.60139 q^{44} +3.45787 q^{45} +3.68458 q^{46} -5.79742 q^{47} -1.00000 q^{48} +8.09778 q^{49} -6.95684 q^{50} -1.00000 q^{51} -4.12957 q^{52} +5.20130 q^{53} +1.00000 q^{54} -19.3689 q^{55} -3.88559 q^{56} +5.92616 q^{57} -5.24594 q^{58} +1.00000 q^{59} -3.45787 q^{60} -0.310913 q^{61} +6.53532 q^{62} +3.88559 q^{63} +1.00000 q^{64} -14.2795 q^{65} -5.60139 q^{66} +1.06513 q^{67} +1.00000 q^{68} +3.68458 q^{69} -13.4358 q^{70} +10.0903 q^{71} -1.00000 q^{72} -16.5843 q^{73} -10.4519 q^{74} -6.95684 q^{75} -5.92616 q^{76} -21.7647 q^{77} -4.12957 q^{78} -10.1134 q^{79} +3.45787 q^{80} +1.00000 q^{81} -0.713032 q^{82} +11.2226 q^{83} -3.88559 q^{84} +3.45787 q^{85} +5.70750 q^{86} -5.24594 q^{87} +5.60139 q^{88} -9.13347 q^{89} -3.45787 q^{90} -16.0458 q^{91} -3.68458 q^{92} +6.53532 q^{93} +5.79742 q^{94} -20.4919 q^{95} +1.00000 q^{96} -0.689638 q^{97} -8.09778 q^{98} -5.60139 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 9 q^{2} - 9 q^{3} + 9 q^{4} + 2 q^{5} + 9 q^{6} - 5 q^{7} - 9 q^{8} + 9 q^{9}+O(q^{10}) \) 9 * q - 9 * q^2 - 9 * q^3 + 9 * q^4 + 2 * q^5 + 9 * q^6 - 5 * q^7 - 9 * q^8 + 9 * q^9	\( 9 q - 9 q^{2} - 9 q^{3} + 9 q^{4} + 2 q^{5} + 9 q^{6} - 5 q^{7} - 9 q^{8} + 9 q^{9} - 2 q^{10} - q^{11} - 9 q^{12} - 4 q^{13} + 5 q^{14} - 2 q^{15} + 9 q^{16} + 9 q^{17} - 9 q^{18} - 7 q^{19} + 2 q^{20} + 5 q^{21} + q^{22} - 8 q^{23} + 9 q^{24} + 5 q^{25} + 4 q^{26} - 9 q^{27} - 5 q^{28} + 6 q^{29} + 2 q^{30} - 17 q^{31} - 9 q^{32} + q^{33} - 9 q^{34} + 10 q^{35} + 9 q^{36} + 2 q^{37} + 7 q^{38} + 4 q^{39} - 2 q^{40} + 14 q^{41} - 5 q^{42} - 27 q^{43} - q^{44} + 2 q^{45} + 8 q^{46} - 18 q^{47} - 9 q^{48} + 18 q^{49} - 5 q^{50} - 9 q^{51} - 4 q^{52} + 4 q^{53} + 9 q^{54} - 27 q^{55} + 5 q^{56} + 7 q^{57} - 6 q^{58} + 9 q^{59} - 2 q^{60} + 5 q^{61} + 17 q^{62} - 5 q^{63} + 9 q^{64} + 2 q^{65} - q^{66} - 22 q^{67} + 9 q^{68} + 8 q^{69} - 10 q^{70} + 16 q^{71} - 9 q^{72} - 12 q^{73} - 2 q^{74} - 5 q^{75} - 7 q^{76} + 6 q^{77} - 4 q^{78} - 9 q^{79} + 2 q^{80} + 9 q^{81} - 14 q^{82} + 10 q^{83} + 5 q^{84} + 2 q^{85} + 27 q^{86} - 6 q^{87} + q^{88} + 15 q^{89} - 2 q^{90} + 3 q^{91} - 8 q^{92} + 17 q^{93} + 18 q^{94} - 9 q^{95} + 9 q^{96} - 33 q^{97} - 18 q^{98} - q^{99}+O(q^{100}) \) 9 * q - 9 * q^2 - 9 * q^3 + 9 * q^4 + 2 * q^5 + 9 * q^6 - 5 * q^7 - 9 * q^8 + 9 * q^9 - 2 * q^10 - q^11 - 9 * q^12 - 4 * q^13 + 5 * q^14 - 2 * q^15 + 9 * q^16 + 9 * q^17 - 9 * q^18 - 7 * q^19 + 2 * q^20 + 5 * q^21 + q^22 - 8 * q^23 + 9 * q^24 + 5 * q^25 + 4 * q^26 - 9 * q^27 - 5 * q^28 + 6 * q^29 + 2 * q^30 - 17 * q^31 - 9 * q^32 + q^33 - 9 * q^34 + 10 * q^35 + 9 * q^36 + 2 * q^37 + 7 * q^38 + 4 * q^39 - 2 * q^40 + 14 * q^41 - 5 * q^42 - 27 * q^43 - q^44 + 2 * q^45 + 8 * q^46 - 18 * q^47 - 9 * q^48 + 18 * q^49 - 5 * q^50 - 9 * q^51 - 4 * q^52 + 4 * q^53 + 9 * q^54 - 27 * q^55 + 5 * q^56 + 7 * q^57 - 6 * q^58 + 9 * q^59 - 2 * q^60 + 5 * q^61 + 17 * q^62 - 5 * q^63 + 9 * q^64 + 2 * q^65 - q^66 - 22 * q^67 + 9 * q^68 + 8 * q^69 - 10 * q^70 + 16 * q^71 - 9 * q^72 - 12 * q^73 - 2 * q^74 - 5 * q^75 - 7 * q^76 + 6 * q^77 - 4 * q^78 - 9 * q^79 + 2 * q^80 + 9 * q^81 - 14 * q^82 + 10 * q^83 + 5 * q^84 + 2 * q^85 + 27 * q^86 - 6 * q^87 + q^88 + 15 * q^89 - 2 * q^90 + 3 * q^91 - 8 * q^92 + 17 * q^93 + 18 * q^94 - 9 * q^95 + 9 * q^96 - 33 * q^97 - 18 * q^98 - q^99

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