LMFDB - Embedded newform 6018.2.a.z.1.7

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			1.7
Root			$2.03178$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.03178 q^{5} -1.00000 q^{6} -2.78135 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.03178 q^{5} -1.00000 q^{6} -2.78135 q^{7} +1.00000 q^{8} +1.00000 q^{9} +2.03178 q^{10} +2.25439 q^{11} -1.00000 q^{12} -0.0372501 q^{13} -2.78135 q^{14} -2.03178 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} -1.18098 q^{19} +2.03178 q^{20} +2.78135 q^{21} +2.25439 q^{22} -5.57535 q^{23} -1.00000 q^{24} -0.871867 q^{25} -0.0372501 q^{26} -1.00000 q^{27} -2.78135 q^{28} +9.92481 q^{29} -2.03178 q^{30} -5.32991 q^{31} +1.00000 q^{32} -2.25439 q^{33} -1.00000 q^{34} -5.65110 q^{35} +1.00000 q^{36} +10.1469 q^{37} -1.18098 q^{38} +0.0372501 q^{39} +2.03178 q^{40} +5.89015 q^{41} +2.78135 q^{42} +0.151772 q^{43} +2.25439 q^{44} +2.03178 q^{45} -5.57535 q^{46} +10.2298 q^{47} -1.00000 q^{48} +0.735932 q^{49} -0.871867 q^{50} +1.00000 q^{51} -0.0372501 q^{52} +7.90996 q^{53} -1.00000 q^{54} +4.58042 q^{55} -2.78135 q^{56} +1.18098 q^{57} +9.92481 q^{58} -1.00000 q^{59} -2.03178 q^{60} -1.98880 q^{61} -5.32991 q^{62} -2.78135 q^{63} +1.00000 q^{64} -0.0756840 q^{65} -2.25439 q^{66} +0.598471 q^{67} -1.00000 q^{68} +5.57535 q^{69} -5.65110 q^{70} +5.04374 q^{71} +1.00000 q^{72} +15.0296 q^{73} +10.1469 q^{74} +0.871867 q^{75} -1.18098 q^{76} -6.27025 q^{77} +0.0372501 q^{78} -16.6292 q^{79} +2.03178 q^{80} +1.00000 q^{81} +5.89015 q^{82} +12.2983 q^{83} +2.78135 q^{84} -2.03178 q^{85} +0.151772 q^{86} -9.92481 q^{87} +2.25439 q^{88} +3.69721 q^{89} +2.03178 q^{90} +0.103606 q^{91} -5.57535 q^{92} +5.32991 q^{93} +10.2298 q^{94} -2.39949 q^{95} -1.00000 q^{96} +6.58331 q^{97} +0.735932 q^{98} +2.25439 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	2.03178	0.908640	0.454320	−	0.890839i	$-0.349882\pi$
$5$	2.03178	0.908640	0.454320	+	0.890839i	$0.349882\pi$
$6$	−1.00000	−0.408248
$7$	−2.78135	−1.05125	−0.525627	−	0.850715i	$-0.676169\pi$
$7$	−2.78135	−1.05125	−0.525627	+	0.850715i	$0.676169\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	2.03178	0.642505
$11$	2.25439	0.679723	0.339861	−	0.940476i	$-0.389620\pi$
$11$	2.25439	0.679723	0.339861	+	0.940476i	$0.389620\pi$
$12$	−1.00000	−0.288675
$13$	−0.0372501	−0.0103313	−0.00516566	−	0.999987i	$-0.501644\pi$
$13$	−0.0372501	−0.0103313	−0.00516566	+	0.999987i	$0.501644\pi$
$14$	−2.78135	−0.743348
$15$	−2.03178	−0.524604
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.00000	0.235702
$19$	−1.18098	−0.270935	−0.135468	−	0.990782i	$-0.543254\pi$
$19$	−1.18098	−0.270935	−0.135468	+	0.990782i	$0.543254\pi$
$20$	2.03178	0.454320
$21$	2.78135	0.606941
$22$	2.25439	0.480637
$23$	−5.57535	−1.16254	−0.581270	−	0.813711i	$-0.697444\pi$
$23$	−5.57535	−1.16254	−0.581270	+	0.813711i	$0.697444\pi$
$24$	−1.00000	−0.204124
$25$	−0.871867	−0.174373
$26$	−0.0372501	−0.00730535
$27$	−1.00000	−0.192450
$28$	−2.78135	−0.525627
$29$	9.92481	1.84299	0.921495	−	0.388389i	$-0.126968\pi$
$29$	9.92481	1.84299	0.921495	+	0.388389i	$0.126968\pi$
$30$	−2.03178	−0.370951
$31$	−5.32991	−0.957280	−0.478640	−	0.878011i	$-0.658870\pi$
$31$	−5.32991	−0.957280	−0.478640	+	0.878011i	$0.658870\pi$
$32$	1.00000	0.176777
$33$	−2.25439	−0.392438
$34$	−1.00000	−0.171499
$35$	−5.65110	−0.955211
$36$	1.00000	0.166667
$37$	10.1469	1.66815	0.834073	−	0.551654i	$-0.186003\pi$
$37$	10.1469	1.66815	0.834073	+	0.551654i	$0.186003\pi$
$38$	−1.18098	−0.191580
$39$	0.0372501	0.00596479
$40$	2.03178	0.321253
$41$	5.89015	0.919887	0.459944	−	0.887948i	$-0.347870\pi$
$41$	5.89015	0.919887	0.459944	+	0.887948i	$0.347870\pi$
$42$	2.78135	0.429172
$43$	0.151772	0.0231450	0.0115725	−	0.999933i	$-0.496316\pi$
$43$	0.151772	0.0231450	0.0115725	+	0.999933i	$0.496316\pi$
$44$	2.25439	0.339861
$45$	2.03178	0.302880
$46$	−5.57535	−0.822040
$47$	10.2298	1.49216	0.746082	−	0.665854i	$-0.231933\pi$
$47$	10.2298	1.49216	0.746082	+	0.665854i	$0.231933\pi$
$48$	−1.00000	−0.144338
$49$	0.735932	0.105133
$50$	−0.871867	−0.123301
$51$	1.00000	0.140028
$52$	−0.0372501	−0.00516566
$53$	7.90996	1.08652	0.543258	−	0.839566i	$-0.317190\pi$
$53$	7.90996	1.08652	0.543258	+	0.839566i	$0.317190\pi$
$54$	−1.00000	−0.136083
$55$	4.58042	0.617623
$56$	−2.78135	−0.371674
$57$	1.18098	0.156425
$58$	9.92481	1.30319
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	−2.03178	−0.262302
$61$	−1.98880	−0.254640	−0.127320	−	0.991862i	$-0.540638\pi$
$61$	−1.98880	−0.254640	−0.127320	+	0.991862i	$0.540638\pi$
$62$	−5.32991	−0.676899
$63$	−2.78135	−0.350418
$64$	1.00000	0.125000
$65$	−0.0756840	−0.00938745
$66$	−2.25439	−0.277496
$67$	0.598471	0.0731149	0.0365575	−	0.999332i	$-0.488361\pi$
$67$	0.598471	0.0731149	0.0365575	+	0.999332i	$0.488361\pi$
$68$	−1.00000	−0.121268
$69$	5.57535	0.671193
$70$	−5.65110	−0.675436
$71$	5.04374	0.598582	0.299291	−	0.954162i	$-0.403250\pi$
$71$	5.04374	0.598582	0.299291	+	0.954162i	$0.403250\pi$
$72$	1.00000	0.117851
$73$	15.0296	1.75908	0.879539	−	0.475827i	$-0.157851\pi$
$73$	15.0296	1.75908	0.879539	+	0.475827i	$0.157851\pi$
$74$	10.1469	1.17956
$75$	0.871867	0.100675
$76$	−1.18098	−0.135468
$77$	−6.27025	−0.714561
$78$	0.0372501	0.00421774
$79$	−16.6292	−1.87093	−0.935463	−	0.353424i	$-0.885017\pi$
$79$	−16.6292	−1.87093	−0.935463	+	0.353424i	$0.885017\pi$
$80$	2.03178	0.227160
$81$	1.00000	0.111111
$82$	5.89015	0.650459
$83$	12.2983	1.34991	0.674954	−	0.737859i	$-0.264163\pi$
$83$	12.2983	1.34991	0.674954	+	0.737859i	$0.264163\pi$
$84$	2.78135	0.303471
$85$	−2.03178	−0.220378
$86$	0.151772	0.0163660
$87$	−9.92481	−1.06405
$88$	2.25439	0.240318
$89$	3.69721	0.391903	0.195952	−	0.980614i	$-0.437220\pi$
$89$	3.69721	0.391903	0.195952	+	0.980614i	$0.437220\pi$
$90$	2.03178	0.214168
$91$	0.103606	0.0108608
$92$	−5.57535	−0.581270
$93$	5.32991	0.552686
$94$	10.2298	1.05512
$95$	−2.39949	−0.246183
$96$	−1.00000	−0.102062
$97$	6.58331	0.668434	0.334217	−	0.942496i	$-0.391528\pi$
$97$	6.58331	0.668434	0.334217	+	0.942496i	$0.391528\pi$
$98$	0.735932	0.0743403
$99$	2.25439	0.226574
$100$	−0.871867	−0.0871867
$101$	−7.88892	−0.784977	−0.392489	−	0.919757i	$-0.628386\pi$
$101$	−7.88892	−0.784977	−0.392489	+	0.919757i	$0.628386\pi$
$102$	1.00000	0.0990148
$103$	−1.85170	−0.182453	−0.0912266	−	0.995830i	$-0.529079\pi$
$103$	−1.85170	−0.182453	−0.0912266	+	0.995830i	$0.529079\pi$
$104$	−0.0372501	−0.00365267
$105$	5.65110	0.551491
$106$	7.90996	0.768283
$107$	−13.1597	−1.27219	−0.636096	−	0.771610i	$-0.719452\pi$
$107$	−13.1597	−1.27219	−0.636096	+	0.771610i	$0.719452\pi$
$108$	−1.00000	−0.0962250
$109$	4.10644	0.393326	0.196663	−	0.980471i	$-0.436990\pi$
$109$	4.10644	0.393326	0.196663	+	0.980471i	$0.436990\pi$
$110$	4.58042	0.436726
$111$	−10.1469	−0.963104
$112$	−2.78135	−0.262813
$113$	9.23405	0.868666	0.434333	−	0.900752i	$-0.356984\pi$
$113$	9.23405	0.868666	0.434333	+	0.900752i	$0.356984\pi$
$114$	1.18098	0.110609
$115$	−11.3279	−1.05633
$116$	9.92481	0.921495
$117$	−0.0372501	−0.00344377
$118$	−1.00000	−0.0920575
$119$	2.78135	0.254966
$120$	−2.03178	−0.185475
$121$	−5.91774	−0.537977
$122$	−1.98880	−0.180058
$123$	−5.89015	−0.531097
$124$	−5.32991	−0.478640
$125$	−11.9303	−1.06708
$126$	−2.78135	−0.247783
$127$	12.9128	1.14583	0.572915	−	0.819615i	$-0.305813\pi$
$127$	12.9128	1.14583	0.572915	+	0.819615i	$0.305813\pi$
$128$	1.00000	0.0883883
$129$	−0.151772	−0.0133628
$130$	−0.0756840	−0.00663793
$131$	21.1277	1.84594	0.922968	−	0.384877i	$-0.125756\pi$
$131$	21.1277	1.84594	0.922968	+	0.384877i	$0.125756\pi$
$132$	−2.25439	−0.196219
$133$	3.28472	0.284822
$134$	0.598471	0.0517001
$135$	−2.03178	−0.174868
$136$	−1.00000	−0.0857493
$137$	3.61782	0.309091	0.154546	−	0.987986i	$-0.450609\pi$
$137$	3.61782	0.309091	0.154546	+	0.987986i	$0.450609\pi$
$138$	5.57535	0.474605
$139$	−14.2864	−1.21176	−0.605880	−	0.795556i	$-0.707179\pi$
$139$	−14.2864	−1.21176	−0.605880	+	0.795556i	$0.707179\pi$
$140$	−5.65110	−0.477605
$141$	−10.2298	−0.861501
$142$	5.04374	0.423261
$143$	−0.0839761	−0.00702243
$144$	1.00000	0.0833333
$145$	20.1650	1.67461
$146$	15.0296	1.24386
$147$	−0.735932	−0.0606986
$148$	10.1469	0.834073
$149$	−1.51653	−0.124239	−0.0621193	−	0.998069i	$-0.519786\pi$
$149$	−1.51653	−0.124239	−0.0621193	+	0.998069i	$0.519786\pi$
$150$	0.871867	0.0711876
$151$	14.0352	1.14217	0.571086	−	0.820891i	$-0.306522\pi$
$151$	14.0352	1.14217	0.571086	+	0.820891i	$0.306522\pi$
$152$	−1.18098	−0.0957901
$153$	−1.00000	−0.0808452
$154$	−6.27025	−0.505271
$155$	−10.8292	−0.869823
$156$	0.0372501	0.00298239
$157$	−13.0866	−1.04442	−0.522211	−	0.852816i	$-0.674893\pi$
$157$	−13.0866	−1.04442	−0.522211	+	0.852816i	$0.674893\pi$
$158$	−16.6292	−1.32294
$159$	−7.90996	−0.627301
$160$	2.03178	0.160626
$161$	15.5070	1.22212
$162$	1.00000	0.0785674
$163$	−9.34353	−0.731842	−0.365921	−	0.930646i	$-0.619246\pi$
$163$	−9.34353	−0.731842	−0.365921	+	0.930646i	$0.619246\pi$
$164$	5.89015	0.459944
$165$	−4.58042	−0.356585
$166$	12.2983	0.954530
$167$	−3.48106	−0.269372	−0.134686	−	0.990888i	$-0.543003\pi$
$167$	−3.48106	−0.269372	−0.134686	+	0.990888i	$0.543003\pi$
$168$	2.78135	0.214586
$169$	−12.9986	−0.999893
$170$	−2.03178	−0.155830
$171$	−1.18098	−0.0903118
$172$	0.151772	0.0115725
$173$	5.45454	0.414701	0.207350	−	0.978267i	$-0.433516\pi$
$173$	5.45454	0.414701	0.207350	+	0.978267i	$0.433516\pi$
$174$	−9.92481	−0.752398
$175$	2.42497	0.183311
$176$	2.25439	0.169931
$177$	1.00000	0.0751646
$178$	3.69721	0.277117
$179$	19.3804	1.44856	0.724280	−	0.689506i	$-0.242172\pi$
$179$	19.3804	1.44856	0.724280	+	0.689506i	$0.242172\pi$
$180$	2.03178	0.151440
$181$	−8.14477	−0.605396	−0.302698	−	0.953087i	$-0.597887\pi$
$181$	−8.14477	−0.605396	−0.302698	+	0.953087i	$0.597887\pi$
$182$	0.103606	0.00767977
$183$	1.98880	0.147017
$184$	−5.57535	−0.411020
$185$	20.6163	1.51574
$186$	5.32991	0.390808
$187$	−2.25439	−0.164857
$188$	10.2298	0.746082
$189$	2.78135	0.202314
$190$	−2.39949	−0.174077
$191$	18.5782	1.34427	0.672135	−	0.740429i	$-0.265378\pi$
$191$	18.5782	1.34427	0.672135	+	0.740429i	$0.265378\pi$
$192$	−1.00000	−0.0721688
$193$	−1.64507	−0.118414	−0.0592072	−	0.998246i	$-0.518857\pi$
$193$	−1.64507	−0.118414	−0.0592072	+	0.998246i	$0.518857\pi$
$194$	6.58331	0.472654
$195$	0.0756840	0.00541985
$196$	0.735932	0.0525666
$197$	2.28114	0.162524	0.0812622	−	0.996693i	$-0.474105\pi$
$197$	2.28114	0.162524	0.0812622	+	0.996693i	$0.474105\pi$
$198$	2.25439	0.160212
$199$	19.6987	1.39640	0.698202	−	0.715901i	$-0.253984\pi$
$199$	19.6987	1.39640	0.698202	+	0.715901i	$0.253984\pi$
$200$	−0.871867	−0.0616503
$201$	−0.598471	−0.0422129
$202$	−7.88892	−0.555063
$203$	−27.6044	−1.93745
$204$	1.00000	0.0700140
$205$	11.9675	0.835847
$206$	−1.85170	−0.129014
$207$	−5.57535	−0.387513
$208$	−0.0372501	−0.00258283
$209$	−2.66239	−0.184161
$210$	5.65110	0.389963
$211$	22.3114	1.53598	0.767991	−	0.640461i	$-0.221257\pi$
$211$	22.3114	1.53598	0.767991	+	0.640461i	$0.221257\pi$
$212$	7.90996	0.543258
$213$	−5.04374	−0.345591
$214$	−13.1597	−0.899576
$215$	0.308368	0.0210305
$216$	−1.00000	−0.0680414
$217$	14.8244	1.00634
$218$	4.10644	0.278123
$219$	−15.0296	−1.01560
$220$	4.58042	0.308812
$221$	0.0372501	0.00250571
$222$	−10.1469	−0.681018
$223$	−10.3040	−0.690008	−0.345004	−	0.938601i	$-0.612122\pi$
$223$	−10.3040	−0.690008	−0.345004	+	0.938601i	$0.612122\pi$
$224$	−2.78135	−0.185837
$225$	−0.871867	−0.0581245
$226$	9.23405	0.614240
$227$	16.5140	1.09608	0.548038	−	0.836454i	$-0.315375\pi$
$227$	16.5140	1.09608	0.548038	+	0.836454i	$0.315375\pi$
$228$	1.18098	0.0782123
$229$	8.61010	0.568971	0.284486	−	0.958680i	$-0.408177\pi$
$229$	8.61010	0.568971	0.284486	+	0.958680i	$0.408177\pi$
$230$	−11.3279	−0.746938
$231$	6.27025	0.412552
$232$	9.92481	0.651596
$233$	6.17877	0.404785	0.202392	−	0.979305i	$-0.435128\pi$
$233$	6.17877	0.404785	0.202392	+	0.979305i	$0.435128\pi$
$234$	−0.0372501	−0.00243512
$235$	20.7846	1.35584
$236$	−1.00000	−0.0650945
$237$	16.6292	1.08018
$238$	2.78135	0.180288
$239$	22.5916	1.46133	0.730663	−	0.682738i	$-0.239211\pi$
$239$	22.5916	1.46133	0.730663	+	0.682738i	$0.239211\pi$
$240$	−2.03178	−0.131151
$241$	−14.4275	−0.929355	−0.464677	−	0.885480i	$-0.653830\pi$
$241$	−14.4275	−0.929355	−0.464677	+	0.885480i	$0.653830\pi$
$242$	−5.91774	−0.380407
$243$	−1.00000	−0.0641500
$244$	−1.98880	−0.127320
$245$	1.49525	0.0955281
$246$	−5.89015	−0.375542
$247$	0.0439916	0.00279912
$248$	−5.32991	−0.338449
$249$	−12.2983	−0.779370
$250$	−11.9303	−0.754541
$251$	−27.5253	−1.73738	−0.868691	−	0.495354i	$-0.835038\pi$
$251$	−27.5253	−1.73738	−0.868691	+	0.495354i	$0.835038\pi$
$252$	−2.78135	−0.175209
$253$	−12.5690	−0.790205
$254$	12.9128	0.810223
$255$	2.03178	0.127235
$256$	1.00000	0.0625000
$257$	24.7589	1.54441	0.772207	−	0.635371i	$-0.219153\pi$
$257$	24.7589	1.54441	0.772207	+	0.635371i	$0.219153\pi$
$258$	−0.151772	−0.00944892
$259$	−28.2222	−1.75364
$260$	−0.0756840	−0.00469372
$261$	9.92481	0.614330
$262$	21.1277	1.30527
$263$	−10.5895	−0.652978	−0.326489	−	0.945201i	$-0.605866\pi$
$263$	−10.5895	−0.652978	−0.326489	+	0.945201i	$0.605866\pi$
$264$	−2.25439	−0.138748
$265$	16.0713	0.987252
$266$	3.28472	0.201399
$267$	−3.69721	−0.226265
$268$	0.598471	0.0365575
$269$	9.52384	0.580679	0.290339	−	0.956924i	$-0.406232\pi$
$269$	9.52384	0.580679	0.290339	+	0.956924i	$0.406232\pi$
$270$	−2.03178	−0.123650
$271$	−1.40167	−0.0851455	−0.0425727	−	0.999093i	$-0.513555\pi$
$271$	−1.40167	−0.0851455	−0.0425727	+	0.999093i	$0.513555\pi$
$272$	−1.00000	−0.0606339
$273$	−0.103606	−0.00627050
$274$	3.61782	0.218560
$275$	−1.96552	−0.118526
$276$	5.57535	0.335596
$277$	−0.830252	−0.0498850	−0.0249425	−	0.999689i	$-0.507940\pi$
$277$	−0.830252	−0.0498850	−0.0249425	+	0.999689i	$0.507940\pi$
$278$	−14.2864	−0.856843
$279$	−5.32991	−0.319093
$280$	−5.65110	−0.337718
$281$	−14.6155	−0.871888	−0.435944	−	0.899974i	$-0.643585\pi$
$281$	−14.6155	−0.871888	−0.435944	+	0.899974i	$0.643585\pi$
$282$	−10.2298	−0.609174
$283$	−25.6174	−1.52280	−0.761399	−	0.648283i	$-0.775487\pi$
$283$	−25.6174	−1.52280	−0.761399	+	0.648283i	$0.775487\pi$
$284$	5.04374	0.299291
$285$	2.39949	0.142134
$286$	−0.0839761	−0.00496561
$287$	−16.3826	−0.967035
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	20.1650	1.18413
$291$	−6.58331	−0.385920
$292$	15.0296	0.879539
$293$	1.15255	0.0673327	0.0336664	−	0.999433i	$-0.489282\pi$
$293$	1.15255	0.0673327	0.0336664	+	0.999433i	$0.489282\pi$
$294$	−0.735932	−0.0429204
$295$	−2.03178	−0.118295
$296$	10.1469	0.589779
$297$	−2.25439	−0.130813
$298$	−1.51653	−0.0878500
$299$	0.207682	0.0120106
$300$	0.871867	0.0503373
$301$	−0.422132	−0.0243313
$302$	14.0352	0.807637
$303$	7.88892	0.453207
$304$	−1.18098	−0.0677339
$305$	−4.04081	−0.231376
$306$	−1.00000	−0.0571662
$307$	−10.9773	−0.626505	−0.313253	−	0.949670i	$-0.601419\pi$
$307$	−10.9773	−0.626505	−0.313253	+	0.949670i	$0.601419\pi$
$308$	−6.27025	−0.357280
$309$	1.85170	0.105339
$310$	−10.8292	−0.615057
$311$	31.5873	1.79115	0.895575	−	0.444911i	$-0.146765\pi$
$311$	31.5873	1.79115	0.895575	+	0.444911i	$0.146765\pi$
$312$	0.0372501	0.00210887
$313$	21.7785	1.23099	0.615497	−	0.788140i	$-0.288955\pi$
$313$	21.7785	1.23099	0.615497	+	0.788140i	$0.288955\pi$
$314$	−13.0866	−0.738518
$315$	−5.65110	−0.318404
$316$	−16.6292	−0.935463
$317$	30.2537	1.69922	0.849610	−	0.527412i	$-0.176838\pi$
$317$	30.2537	1.69922	0.849610	+	0.527412i	$0.176838\pi$
$318$	−7.90996	−0.443568
$319$	22.3743	1.25272
$320$	2.03178	0.113580
$321$	13.1597	0.734501
$322$	15.5070	0.864172
$323$	1.18098	0.0657115
$324$	1.00000	0.0555556
$325$	0.0324771	0.00180151
$326$	−9.34353	−0.517490
$327$	−4.10644	−0.227087
$328$	5.89015	0.325229
$329$	−28.4526	−1.56864
$330$	−4.58042	−0.252144
$331$	−12.9759	−0.713218	−0.356609	−	0.934254i	$-0.616067\pi$
$331$	−12.9759	−0.713218	−0.356609	+	0.934254i	$0.616067\pi$
$332$	12.2983	0.674954
$333$	10.1469	0.556049
$334$	−3.48106	−0.190475
$335$	1.21596	0.0664351
$336$	2.78135	0.151735
$337$	−8.00664	−0.436149	−0.218075	−	0.975932i	$-0.569978\pi$
$337$	−8.00664	−0.436149	−0.218075	+	0.975932i	$0.569978\pi$
$338$	−12.9986	−0.707031
$339$	−9.23405	−0.501525
$340$	−2.03178	−0.110189
$341$	−12.0157	−0.650685
$342$	−1.18098	−0.0638601
$343$	17.4226	0.940732
$344$	0.151772	0.00818301
$345$	11.3279	0.609873
$346$	5.45454	0.293238
$347$	15.6248	0.838781	0.419390	−	0.907806i	$-0.362244\pi$
$347$	15.6248	0.838781	0.419390	+	0.907806i	$0.362244\pi$
$348$	−9.92481	−0.532026
$349$	−33.0941	−1.77148	−0.885742	−	0.464177i	$-0.846350\pi$
$349$	−33.0941	−1.77148	−0.885742	+	0.464177i	$0.846350\pi$
$350$	2.42497	0.129620
$351$	0.0372501	0.00198826
$352$	2.25439	0.120159
$353$	3.84737	0.204775	0.102387	−	0.994745i	$-0.467352\pi$
$353$	3.84737	0.204775	0.102387	+	0.994745i	$0.467352\pi$
$354$	1.00000	0.0531494
$355$	10.2478	0.543895
$356$	3.69721	0.195952
$357$	−2.78135	−0.147205
$358$	19.3804	1.02429
$359$	23.7964	1.25593	0.627964	−	0.778242i	$-0.283889\pi$
$359$	23.7964	1.25593	0.627964	+	0.778242i	$0.283889\pi$
$360$	2.03178	0.107084
$361$	−17.6053	−0.926594
$362$	−8.14477	−0.428080
$363$	5.91774	0.310601
$364$	0.103606	0.00543042
$365$	30.5368	1.59837
$366$	1.98880	0.103956
$367$	14.3639	0.749789	0.374895	−	0.927067i	$-0.377679\pi$
$367$	14.3639	0.749789	0.374895	+	0.927067i	$0.377679\pi$
$368$	−5.57535	−0.290635
$369$	5.89015	0.306629
$370$	20.6163	1.07179
$371$	−22.0004	−1.14220
$372$	5.32991	0.276343
$373$	10.3434	0.535561	0.267780	−	0.963480i	$-0.413710\pi$
$373$	10.3434	0.535561	0.267780	+	0.963480i	$0.413710\pi$
$374$	−2.25439	−0.116572
$375$	11.9303	0.616080
$376$	10.2298	0.527560
$377$	−0.369700	−0.0190405
$378$	2.78135	0.143057
$379$	21.0732	1.08246	0.541230	−	0.840875i	$-0.317959\pi$
$379$	21.0732	1.08246	0.541230	+	0.840875i	$0.317959\pi$
$380$	−2.39949	−0.123091
$381$	−12.9128	−0.661545
$382$	18.5782	0.950542
$383$	−27.4055	−1.40036	−0.700179	−	0.713967i	$-0.746896\pi$
$383$	−27.4055	−1.40036	−0.700179	+	0.713967i	$0.746896\pi$
$384$	−1.00000	−0.0510310
$385$	−12.7398	−0.649279
$386$	−1.64507	−0.0837316
$387$	0.151772	0.00771501
$388$	6.58331	0.334217
$389$	−32.1966	−1.63243	−0.816215	−	0.577748i	$-0.803932\pi$
$389$	−32.1966	−1.63243	−0.816215	+	0.577748i	$0.803932\pi$
$390$	0.0756840	0.00383241
$391$	5.57535	0.281957
$392$	0.735932	0.0371702
$393$	−21.1277	−1.06575
$394$	2.28114	0.114922
$395$	−33.7868	−1.70000
$396$	2.25439	0.113287
$397$	−7.03918	−0.353286	−0.176643	−	0.984275i	$-0.556524\pi$
$397$	−7.03918	−0.353286	−0.176643	+	0.984275i	$0.556524\pi$
$398$	19.6987	0.987407
$399$	−3.28472	−0.164442
$400$	−0.871867	−0.0435933
$401$	−13.9264	−0.695454	−0.347727	−	0.937596i	$-0.613046\pi$
$401$	−13.9264	−0.695454	−0.347727	+	0.937596i	$0.613046\pi$
$402$	−0.598471	−0.0298490
$403$	0.198540	0.00988996
$404$	−7.88892	−0.392489
$405$	2.03178	0.100960
$406$	−27.6044	−1.36998
$407$	22.8751	1.13388
$408$	1.00000	0.0495074
$409$	−28.4417	−1.40635	−0.703175	−	0.711016i	$-0.748235\pi$
$409$	−28.4417	−1.40635	−0.703175	+	0.711016i	$0.748235\pi$
$410$	11.9675	0.591033
$411$	−3.61782	−0.178454
$412$	−1.85170	−0.0912266
$413$	2.78135	0.136861
$414$	−5.57535	−0.274013
$415$	24.9874	1.22658
$416$	−0.0372501	−0.00182634
$417$	14.2864	0.699609
$418$	−2.66239	−0.130222
$419$	−19.3607	−0.945833	−0.472917	−	0.881107i	$-0.656799\pi$
$419$	−19.3607	−0.945833	−0.472917	+	0.881107i	$0.656799\pi$
$420$	5.65110	0.275746
$421$	10.0335	0.489005	0.244503	−	0.969649i	$-0.421375\pi$
$421$	10.0335	0.489005	0.244503	+	0.969649i	$0.421375\pi$
$422$	22.3114	1.08610
$423$	10.2298	0.497388
$424$	7.90996	0.384142
$425$	0.871867	0.0422918
$426$	−5.04374	−0.244370
$427$	5.53157	0.267691
$428$	−13.1597	−0.636096
$429$	0.0839761	0.00405440
$430$	0.308368	0.0148708
$431$	33.6539	1.62105	0.810526	−	0.585703i	$-0.199182\pi$
$431$	33.6539	1.62105	0.810526	+	0.585703i	$0.199182\pi$
$432$	−1.00000	−0.0481125
$433$	25.9459	1.24688	0.623440	−	0.781871i	$-0.285735\pi$
$433$	25.9459	1.24688	0.623440	+	0.781871i	$0.285735\pi$
$434$	14.8244	0.711592
$435$	−20.1650	−0.966839
$436$	4.10644	0.196663
$437$	6.58437	0.314973
$438$	−15.0296	−0.718141
$439$	15.3049	0.730465	0.365233	−	0.930916i	$-0.380989\pi$
$439$	15.3049	0.730465	0.365233	+	0.930916i	$0.380989\pi$
$440$	4.58042	0.218363
$441$	0.735932	0.0350444
$442$	0.0372501	0.00177181
$443$	29.4490	1.39917	0.699583	−	0.714552i	$-0.253369\pi$
$443$	29.4490	1.39917	0.699583	+	0.714552i	$0.253369\pi$
$444$	−10.1469	−0.481552
$445$	7.51191	0.356099
$446$	−10.3040	−0.487910
$447$	1.51653	0.0717292
$448$	−2.78135	−0.131407
$449$	23.9846	1.13190	0.565952	−	0.824438i	$-0.308509\pi$
$449$	23.9846	1.13190	0.565952	+	0.824438i	$0.308509\pi$
$450$	−0.871867	−0.0411002
$451$	13.2787	0.625269
$452$	9.23405	0.434333
$453$	−14.0352	−0.659433
$454$	16.5140	0.775043
$455$	0.210504	0.00986859
$456$	1.18098	0.0553045
$457$	21.4907	1.00529	0.502646	−	0.864492i	$-0.332360\pi$
$457$	21.4907	1.00529	0.502646	+	0.864492i	$0.332360\pi$
$458$	8.61010	0.402324
$459$	1.00000	0.0466760
$460$	−11.3279	−0.528165
$461$	−36.7596	−1.71207	−0.856033	−	0.516921i	$-0.827078\pi$
$461$	−36.7596	−1.71207	−0.856033	+	0.516921i	$0.827078\pi$
$462$	6.27025	0.291718
$463$	−40.4962	−1.88202	−0.941010	−	0.338378i	$-0.890122\pi$
$463$	−40.4962	−1.88202	−0.941010	+	0.338378i	$0.890122\pi$
$464$	9.92481	0.460748
$465$	10.8292	0.502192
$466$	6.17877	0.286226
$467$	−40.3215	−1.86586	−0.932929	−	0.360061i	$-0.882756\pi$
$467$	−40.3215	−1.86586	−0.932929	+	0.360061i	$0.882756\pi$
$468$	−0.0372501	−0.00172189
$469$	−1.66456	−0.0768623
$470$	20.7846	0.958724
$471$	13.0866	0.602997
$472$	−1.00000	−0.0460287
$473$	0.342153	0.0157322
$474$	16.6292	0.763802
$475$	1.02966	0.0472439
$476$	2.78135	0.127483
$477$	7.90996	0.362172
$478$	22.5916	1.03331
$479$	−43.0779	−1.96828	−0.984140	−	0.177392i	$-0.943234\pi$
$479$	−43.0779	−1.96828	−0.984140	+	0.177392i	$0.943234\pi$
$480$	−2.03178	−0.0927377
$481$	−0.377974	−0.0172341
$482$	−14.4275	−0.657153
$483$	−15.5070	−0.705593
$484$	−5.91774	−0.268988
$485$	13.3758	0.607366
$486$	−1.00000	−0.0453609
$487$	13.3110	0.603181	0.301590	−	0.953438i	$-0.402483\pi$
$487$	13.3110	0.603181	0.301590	+	0.953438i	$0.402483\pi$
$488$	−1.98880	−0.0900289
$489$	9.34353	0.422529
$490$	1.49525	0.0675486
$491$	−25.7331	−1.16132	−0.580659	−	0.814147i	$-0.697205\pi$
$491$	−25.7331	−1.16132	−0.580659	+	0.814147i	$0.697205\pi$
$492$	−5.89015	−0.265549
$493$	−9.92481	−0.446991
$494$	0.0439916	0.00197928
$495$	4.58042	0.205874
$496$	−5.32991	−0.239320
$497$	−14.0284	−0.629261
$498$	−12.2983	−0.551098
$499$	−17.7722	−0.795595	−0.397797	−	0.917473i	$-0.630225\pi$
$499$	−17.7722	−0.795595	−0.397797	+	0.917473i	$0.630225\pi$
$500$	−11.9303	−0.533541
$501$	3.48106	0.155522
$502$	−27.5253	−1.22852
$503$	−43.0177	−1.91806	−0.959031	−	0.283300i	$-0.908571\pi$
$503$	−43.0177	−1.91806	−0.959031	+	0.283300i	$0.908571\pi$
$504$	−2.78135	−0.123891
$505$	−16.0286	−0.713262
$506$	−12.5690	−0.558759
$507$	12.9986	0.577289
$508$	12.9128	0.572915
$509$	10.5189	0.466240	0.233120	−	0.972448i	$-0.425106\pi$
$509$	10.5189	0.466240	0.233120	+	0.972448i	$0.425106\pi$
$510$	2.03178	0.0899688
$511$	−41.8026	−1.84924
$512$	1.00000	0.0441942
$513$	1.18098	0.0521415
$514$	24.7589	1.09207
$515$	−3.76224	−0.165784
$516$	−0.151772	−0.00668140
$517$	23.0618	1.01426
$518$	−28.2222	−1.24001
$519$	−5.45454	−0.239428
$520$	−0.0756840	−0.00331896
$521$	−6.03174	−0.264255	−0.132128	−	0.991233i	$-0.542181\pi$
$521$	−6.03174	−0.264255	−0.132128	+	0.991233i	$0.542181\pi$
$522$	9.92481	0.434397
$523$	22.3958	0.979298	0.489649	−	0.871920i	$-0.337125\pi$
$523$	22.3958	0.979298	0.489649	+	0.871920i	$0.337125\pi$
$524$	21.1277	0.922968
$525$	−2.42497	−0.105834
$526$	−10.5895	−0.461725
$527$	5.32991	0.232174
$528$	−2.25439	−0.0981096
$529$	8.08448	0.351499
$530$	16.0713	0.698093
$531$	−1.00000	−0.0433963
$532$	3.28472	0.142411
$533$	−0.219409	−0.00950365
$534$	−3.69721	−0.159994
$535$	−26.7376	−1.15597
$536$	0.598471	0.0258500
$537$	−19.3804	−0.836327
$538$	9.52384	0.410602
$539$	1.65907	0.0714614
$540$	−2.03178	−0.0874339
$541$	−9.76691	−0.419912	−0.209956	−	0.977711i	$-0.567332\pi$
$541$	−9.76691	−0.419912	−0.209956	+	0.977711i	$0.567332\pi$
$542$	−1.40167	−0.0602069
$543$	8.14477	0.349526
$544$	−1.00000	−0.0428746
$545$	8.34339	0.357391
$546$	−0.103606	−0.00443392
$547$	29.3308	1.25409	0.627047	−	0.778981i	$-0.284263\pi$
$547$	29.3308	1.25409	0.627047	+	0.778981i	$0.284263\pi$
$548$	3.61782	0.154546
$549$	−1.98880	−0.0848801
$550$	−1.96552	−0.0838102
$551$	−11.7210	−0.499331
$552$	5.57535	0.237302
$553$	46.2516	1.96682
$554$	−0.830252	−0.0352740
$555$	−20.6163	−0.875115
$556$	−14.2864	−0.605880
$557$	−35.9543	−1.52343	−0.761717	−	0.647910i	$-0.775643\pi$
$557$	−35.9543	−1.52343	−0.761717	+	0.647910i	$0.775643\pi$
$558$	−5.32991	−0.225633
$559$	−0.00565353	−0.000239119 0
$560$	−5.65110	−0.238803
$561$	2.25439	0.0951803
$562$	−14.6155	−0.616518
$563$	15.8750	0.669053	0.334526	−	0.942386i	$-0.391424\pi$
$563$	15.8750	0.669053	0.334526	+	0.942386i	$0.391424\pi$
$564$	−10.2298	−0.430751
$565$	18.7616	0.789305
$566$	−25.6174	−1.07678
$567$	−2.78135	−0.116806
$568$	5.04374	0.211631
$569$	3.60171	0.150992	0.0754958	−	0.997146i	$-0.475946\pi$
$569$	3.60171	0.150992	0.0754958	+	0.997146i	$0.475946\pi$
$570$	2.39949	0.100504
$571$	−25.4611	−1.06551	−0.532757	−	0.846268i	$-0.678844\pi$
$571$	−25.4611	−1.06551	−0.532757	+	0.846268i	$0.678844\pi$
$572$	−0.0839761	−0.00351122
$573$	−18.5782	−0.776114
$574$	−16.3826	−0.683797
$575$	4.86096	0.202716
$576$	1.00000	0.0416667
$577$	13.1523	0.547537	0.273769	−	0.961796i	$-0.411730\pi$
$577$	13.1523	0.547537	0.273769	+	0.961796i	$0.411730\pi$
$578$	1.00000	0.0415945
$579$	1.64507	0.0683666
$580$	20.1650	0.837307
$581$	−34.2058	−1.41910
$582$	−6.58331	−0.272887
$583$	17.8321	0.738530
$584$	15.0296	0.621928
$585$	−0.0756840	−0.00312915
$586$	1.15255	0.0476114
$587$	24.0351	0.992035	0.496017	−	0.868313i	$-0.334795\pi$
$587$	24.0351	0.992035	0.496017	+	0.868313i	$0.334795\pi$
$588$	−0.735932	−0.0303493
$589$	6.29451	0.259361
$590$	−2.03178	−0.0836471
$591$	−2.28114	−0.0938335
$592$	10.1469	0.417036
$593$	25.5162	1.04782	0.523912	−	0.851772i	$-0.324472\pi$
$593$	25.5162	1.04782	0.523912	+	0.851772i	$0.324472\pi$
$594$	−2.25439	−0.0924986
$595$	5.65110	0.231673
$596$	−1.51653	−0.0621193
$597$	−19.6987	−0.806214
$598$	0.207682	0.00849276
$599$	−42.5275	−1.73763	−0.868813	−	0.495141i	$-0.835116\pi$
$599$	−42.5275	−1.73763	−0.868813	+	0.495141i	$0.835116\pi$
$600$	0.871867	0.0355938
$601$	−6.32133	−0.257853	−0.128926	−	0.991654i	$-0.541153\pi$
$601$	−6.32133	−0.257853	−0.128926	+	0.991654i	$0.541153\pi$
$602$	−0.422132	−0.0172048
$603$	0.598471	0.0243716
$604$	14.0352	0.571086
$605$	−12.0236	−0.488827
$606$	7.88892	0.320466
$607$	27.4873	1.11567	0.557837	−	0.829950i	$-0.311631\pi$
$607$	27.4873	1.11567	0.557837	+	0.829950i	$0.311631\pi$
$608$	−1.18098	−0.0478951
$609$	27.6044	1.11859
$610$	−4.04081	−0.163608
$611$	−0.381060	−0.0154160
$612$	−1.00000	−0.0404226
$613$	22.7562	0.919115	0.459557	−	0.888148i	$-0.348008\pi$
$613$	22.7562	0.919115	0.459557	+	0.888148i	$0.348008\pi$
$614$	−10.9773	−0.443006
$615$	−11.9675	−0.482576
$616$	−6.27025	−0.252635
$617$	−10.6856	−0.430187	−0.215093	−	0.976593i	$-0.569006\pi$
$617$	−10.6856	−0.430187	−0.215093	+	0.976593i	$0.569006\pi$
$618$	1.85170	0.0744862
$619$	−4.76483	−0.191515	−0.0957574	−	0.995405i	$-0.530527\pi$
$619$	−4.76483	−0.191515	−0.0957574	+	0.995405i	$0.530527\pi$
$620$	−10.8292	−0.434911
$621$	5.57535	0.223731
$622$	31.5873	1.26653
$623$	−10.2832	−0.411989
$624$	0.0372501	0.00149120
$625$	−19.8805	−0.795221
$626$	21.7785	0.870444
$627$	2.66239	0.106325
$628$	−13.0866	−0.522211
$629$	−10.1469	−0.404585
$630$	−5.65110	−0.225145
$631$	−26.9380	−1.07239	−0.536193	−	0.844095i	$-0.680138\pi$
$631$	−26.9380	−1.07239	−0.536193	+	0.844095i	$0.680138\pi$
$632$	−16.6292	−0.661472
$633$	−22.3114	−0.886799
$634$	30.2537	1.20153
$635$	26.2361	1.04115
$636$	−7.90996	−0.313650
$637$	−0.0274135	−0.00108616
$638$	22.3743	0.885809
$639$	5.04374	0.199527
$640$	2.03178	0.0803132
$641$	−29.1739	−1.15230	−0.576151	−	0.817343i	$-0.695446\pi$
$641$	−29.1739	−1.15230	−0.576151	+	0.817343i	$0.695446\pi$
$642$	13.1597	0.519370
$643$	−8.51754	−0.335899	−0.167949	−	0.985796i	$-0.553715\pi$
$643$	−8.51754	−0.335899	−0.167949	+	0.985796i	$0.553715\pi$
$644$	15.5070	0.611062
$645$	−0.308368	−0.0121420
$646$	1.18098	0.0464650
$647$	−18.2072	−0.715797	−0.357899	−	0.933760i	$-0.616507\pi$
$647$	−18.2072	−0.715797	−0.357899	+	0.933760i	$0.616507\pi$
$648$	1.00000	0.0392837
$649$	−2.25439	−0.0884924
$650$	0.0324771	0.00127386
$651$	−14.8244	−0.581013
$652$	−9.34353	−0.365921
$653$	5.36556	0.209971	0.104985	−	0.994474i	$-0.466520\pi$
$653$	5.36556	0.209971	0.104985	+	0.994474i	$0.466520\pi$
$654$	−4.10644	−0.160575
$655$	42.9269	1.67729
$656$	5.89015	0.229972
$657$	15.0296	0.586359
$658$	−28.4526	−1.10920
$659$	−41.6172	−1.62118	−0.810589	−	0.585616i	$-0.800853\pi$
$659$	−41.6172	−1.62118	−0.810589	+	0.585616i	$0.800853\pi$
$660$	−4.58042	−0.178293
$661$	17.5682	0.683326	0.341663	−	0.939823i	$-0.389010\pi$
$661$	17.5682	0.683326	0.341663	+	0.939823i	$0.389010\pi$
$662$	−12.9759	−0.504321
$663$	−0.0372501	−0.00144667
$664$	12.2983	0.477265
$665$	6.67384	0.258800
$666$	10.1469	0.393186
$667$	−55.3342	−2.14255
$668$	−3.48106	−0.134686
$669$	10.3040	0.398376
$670$	1.21596	0.0469767
$671$	−4.48353	−0.173085
$672$	2.78135	0.107293
$673$	−0.545032	−0.0210094	−0.0105047	−	0.999945i	$-0.503344\pi$
$673$	−0.545032	−0.0210094	−0.0105047	+	0.999945i	$0.503344\pi$
$674$	−8.00664	−0.308404
$675$	0.871867	0.0335582
$676$	−12.9986	−0.499947
$677$	−18.0975	−0.695544	−0.347772	−	0.937579i	$-0.613062\pi$
$677$	−18.0975	−0.695544	−0.347772	+	0.937579i	$0.613062\pi$
$678$	−9.23405	−0.354632
$679$	−18.3105	−0.702693
$680$	−2.03178	−0.0779152
$681$	−16.5140	−0.632820
$682$	−12.0157	−0.460104
$683$	21.1621	0.809747	0.404873	−	0.914373i	$-0.367316\pi$
$683$	21.1621	0.809747	0.404873	+	0.914373i	$0.367316\pi$
$684$	−1.18098	−0.0451559
$685$	7.35062	0.280853
$686$	17.4226	0.665198
$687$	−8.61010	−0.328496
$688$	0.151772	0.00578626
$689$	−0.294647	−0.0112251
$690$	11.3279	0.431245
$691$	10.7258	0.408028	0.204014	−	0.978968i	$-0.434601\pi$
$691$	10.7258	0.408028	0.204014	+	0.978968i	$0.434601\pi$
$692$	5.45454	0.207350
$693$	−6.27025	−0.238187
$694$	15.6248	0.593108
$695$	−29.0269	−1.10105
$696$	−9.92481	−0.376199
$697$	−5.89015	−0.223105
$698$	−33.0941	−1.25263
$699$	−6.17877	−0.233703
$700$	2.42497	0.0916553
$701$	31.7060	1.19752	0.598760	−	0.800929i	$-0.295660\pi$
$701$	31.7060	1.19752	0.598760	+	0.800929i	$0.295660\pi$
$702$	0.0372501	0.00140591
$703$	−11.9833	−0.451960
$704$	2.25439	0.0849654
$705$	−20.7846	−0.782795
$706$	3.84737	0.144798
$707$	21.9419	0.825210
$708$	1.00000	0.0375823
$709$	42.0168	1.57797	0.788987	−	0.614410i	$-0.210606\pi$
$709$	42.0168	1.57797	0.788987	+	0.614410i	$0.210606\pi$
$710$	10.2478	0.384592
$711$	−16.6292	−0.623642
$712$	3.69721	0.138559
$713$	29.7161	1.11288
$714$	−2.78135	−0.104090
$715$	−0.170621	−0.00638087
$716$	19.3804	0.724280
$717$	−22.5916	−0.843697
$718$	23.7964	0.888075
$719$	−43.4201	−1.61930	−0.809648	−	0.586916i	$-0.800342\pi$
$719$	−43.4201	−1.61930	−0.809648	+	0.586916i	$0.800342\pi$
$720$	2.03178	0.0757200
$721$	5.15023	0.191804
$722$	−17.6053	−0.655201
$723$	14.4275	0.536563
$724$	−8.14477	−0.302698
$725$	−8.65311	−0.321368
$726$	5.91774	0.219628
$727$	−27.3644	−1.01489	−0.507445	−	0.861684i	$-0.669410\pi$
$727$	−27.3644	−1.01489	−0.507445	+	0.861684i	$0.669410\pi$
$728$	0.103606	0.00383988
$729$	1.00000	0.0370370
$730$	30.5368	1.13022
$731$	−0.151772	−0.00561350
$732$	1.98880	0.0735083
$733$	8.54735	0.315704	0.157852	−	0.987463i	$-0.449543\pi$
$733$	8.54735	0.315704	0.157852	+	0.987463i	$0.449543\pi$
$734$	14.3639	0.530181
$735$	−1.49525	−0.0551532
$736$	−5.57535	−0.205510
$737$	1.34919	0.0496979
$738$	5.89015	0.216820
$739$	−47.0170	−1.72955	−0.864773	−	0.502162i	$-0.832538\pi$
$739$	−47.0170	−1.72955	−0.864773	+	0.502162i	$0.832538\pi$
$740$	20.6163	0.757872
$741$	−0.0439916	−0.00161607
$742$	−22.0004	−0.807660
$743$	35.4503	1.30055	0.650273	−	0.759700i	$-0.274654\pi$
$743$	35.4503	1.30055	0.650273	+	0.759700i	$0.274654\pi$
$744$	5.32991	0.195404
$745$	−3.08125	−0.112888
$746$	10.3434	0.378699
$747$	12.2983	0.449970
$748$	−2.25439	−0.0824285
$749$	36.6017	1.33740
$750$	11.9303	0.435635
$751$	−5.67770	−0.207182	−0.103591	−	0.994620i	$-0.533033\pi$
$751$	−5.67770	−0.207182	−0.103591	+	0.994620i	$0.533033\pi$
$752$	10.2298	0.373041
$753$	27.5253	1.00308
$754$	−0.369700	−0.0134637
$755$	28.5165	1.03782
$756$	2.78135	0.101157
$757$	13.7223	0.498745	0.249372	−	0.968408i	$-0.419776\pi$
$757$	13.7223	0.498745	0.249372	+	0.968408i	$0.419776\pi$
$758$	21.0732	0.765414
$759$	12.5690	0.456225
$760$	−2.39949	−0.0870387
$761$	−5.71538	−0.207182	−0.103591	−	0.994620i	$-0.533033\pi$
$761$	−5.71538	−0.207182	−0.103591	+	0.994620i	$0.533033\pi$
$762$	−12.9128	−0.467783
$763$	−11.4215	−0.413485
$764$	18.5782	0.672135
$765$	−2.03178	−0.0734592
$766$	−27.4055	−0.990203
$767$	0.0372501	0.00134502
$768$	−1.00000	−0.0360844
$769$	55.1363	1.98827	0.994133	−	0.108161i	$-0.0344962\pi$
$769$	55.1363	1.98827	0.994133	+	0.108161i	$0.0344962\pi$
$770$	−12.7398	−0.459109
$771$	−24.7589	−0.891668
$772$	−1.64507	−0.0592072
$773$	−7.09370	−0.255143	−0.127571	−	0.991829i	$-0.540718\pi$
$773$	−7.09370	−0.255143	−0.127571	+	0.991829i	$0.540718\pi$
$774$	0.151772	0.00545534
$775$	4.64697	0.166924
$776$	6.58331	0.236327
$777$	28.2222	1.01247
$778$	−32.1966	−1.15430
$779$	−6.95615	−0.249230
$780$	0.0756840	0.00270992
$781$	11.3705	0.406870
$782$	5.57535	0.199374
$783$	−9.92481	−0.354684
$784$	0.735932	0.0262833
$785$	−26.5890	−0.949004
$786$	−21.1277	−0.753600
$787$	−42.8679	−1.52808	−0.764038	−	0.645171i	$-0.776786\pi$
$787$	−42.8679	−1.52808	−0.764038	+	0.645171i	$0.776786\pi$
$788$	2.28114	0.0812622
$789$	10.5895	0.376997
$790$	−33.7868	−1.20208
$791$	−25.6832	−0.913188
$792$	2.25439	0.0801061
$793$	0.0740831	0.00263077
$794$	−7.03918	−0.249811
$795$	−16.0713	−0.569990
$796$	19.6987	0.698202
$797$	−27.9382	−0.989622	−0.494811	−	0.869001i	$-0.664763\pi$
$797$	−27.9382	−0.989622	−0.494811	+	0.869001i	$0.664763\pi$
$798$	−3.28472	−0.116278
$799$	−10.2298	−0.361903
$800$	−0.871867	−0.0308251
$801$	3.69721	0.130634
$802$	−13.9264	−0.491760
$803$	33.8825	1.19569
$804$	−0.598471	−0.0211065
$805$	31.5068	1.11047
$806$	0.198540	0.00699326
$807$	−9.52384	−0.335255
$808$	−7.88892	−0.277531
$809$	−54.0870	−1.90160	−0.950799	−	0.309807i	$-0.899735\pi$
$809$	−54.0870	−1.90160	−0.950799	+	0.309807i	$0.899735\pi$
$810$	2.03178	0.0713895
$811$	8.43451	0.296176	0.148088	−	0.988974i	$-0.452688\pi$
$811$	8.43451	0.296176	0.148088	+	0.988974i	$0.452688\pi$
$812$	−27.6044	−0.968725
$813$	1.40167	0.0491588
$814$	22.8751	0.801772
$815$	−18.9840	−0.664981
$816$	1.00000	0.0350070
$817$	−0.179240	−0.00627081
$818$	−28.4417	−0.994440
$819$	0.103606	0.00362028
$820$	11.9675	0.417923
$821$	14.1221	0.492866	0.246433	−	0.969160i	$-0.420742\pi$
$821$	14.1221	0.492866	0.246433	+	0.969160i	$0.420742\pi$
$822$	−3.61782	−0.126186
$823$	36.4697	1.27125	0.635626	−	0.771997i	$-0.280742\pi$
$823$	36.4697	1.27125	0.635626	+	0.771997i	$0.280742\pi$
$824$	−1.85170	−0.0645069
$825$	1.96552	0.0684308
$826$	2.78135	0.0967757
$827$	18.5680	0.645673	0.322836	−	0.946455i	$-0.395364\pi$
$827$	18.5680	0.645673	0.322836	+	0.946455i	$0.395364\pi$
$828$	−5.57535	−0.193757
$829$	16.4444	0.571137	0.285568	−	0.958358i	$-0.407818\pi$
$829$	16.4444	0.571137	0.285568	+	0.958358i	$0.407818\pi$
$830$	24.9874	0.867324
$831$	0.830252	0.0288011
$832$	−0.0372501	−0.00129141
$833$	−0.735932	−0.0254985
$834$	14.2864	0.494699
$835$	−7.07275	−0.244762
$836$	−2.66239	−0.0920805
$837$	5.32991	0.184229
$838$	−19.3607	−0.668805
$839$	−47.0652	−1.62487	−0.812435	−	0.583052i	$-0.801858\pi$
$839$	−47.0652	−1.62487	−0.812435	+	0.583052i	$0.801858\pi$
$840$	5.65110	0.194982
$841$	69.5018	2.39661
$842$	10.0335	0.345779
$843$	14.6155	0.503385
$844$	22.3114	0.767991
$845$	−26.4103	−0.908543
$846$	10.2298	0.351707
$847$	16.4593	0.565550
$848$	7.90996	0.271629
$849$	25.6174	0.879188
$850$	0.871867	0.0299048
$851$	−56.5727	−1.93929
$852$	−5.04374	−0.172796
$853$	47.3699	1.62191	0.810957	−	0.585106i	$-0.198947\pi$
$853$	47.3699	1.62191	0.810957	+	0.585106i	$0.198947\pi$
$854$	5.53157	0.189286
$855$	−2.39949	−0.0820609
$856$	−13.1597	−0.449788
$857$	21.5791	0.737129	0.368565	−	0.929602i	$-0.379849\pi$
$857$	21.5791	0.737129	0.368565	+	0.929602i	$0.379849\pi$
$858$	0.0839761	0.00286690
$859$	6.07787	0.207374	0.103687	−	0.994610i	$-0.466936\pi$
$859$	6.07787	0.207374	0.103687	+	0.994610i	$0.466936\pi$
$860$	0.308368	0.0105153
$861$	16.3826	0.558318
$862$	33.6539	1.14626
$863$	0.0719156	0.00244803	0.00122402	−	0.999999i	$-0.499610\pi$
$863$	0.0719156	0.00244803	0.00122402	+	0.999999i	$0.499610\pi$
$864$	−1.00000	−0.0340207
$865$	11.0824	0.376814
$866$	25.9459	0.881677
$867$	−1.00000	−0.0339618
$868$	14.8244	0.503172
$869$	−37.4885	−1.27171
$870$	−20.1650	−0.683659
$871$	−0.0222931	−0.000755374 0
$872$	4.10644	0.139062
$873$	6.58331	0.222811
$874$	6.58437	0.222720
$875$	33.1825	1.12177
$876$	−15.0296	−0.507802
$877$	13.4348	0.453661	0.226831	−	0.973934i	$-0.427164\pi$
$877$	13.4348	0.453661	0.226831	+	0.973934i	$0.427164\pi$
$878$	15.3049	0.516517
$879$	−1.15255	−0.0388746
$880$	4.58042	0.154406
$881$	10.0121	0.337316	0.168658	−	0.985675i	$-0.446057\pi$
$881$	10.0121	0.337316	0.168658	+	0.985675i	$0.446057\pi$
$882$	0.735932	0.0247801
$883$	−17.2750	−0.581348	−0.290674	−	0.956822i	$-0.593880\pi$
$883$	−17.2750	−0.581348	−0.290674	+	0.956822i	$0.593880\pi$
$884$	0.0372501	0.00125286
$885$	2.03178	0.0682976
$886$	29.4490	0.989359
$887$	−10.2608	−0.344523	−0.172262	−	0.985051i	$-0.555107\pi$
$887$	−10.2608	−0.344523	−0.172262	+	0.985051i	$0.555107\pi$
$888$	−10.1469	−0.340509
$889$	−35.9152	−1.20456
$890$	7.51191	0.251800
$891$	2.25439	0.0755248
$892$	−10.3040	−0.345004
$893$	−12.0811	−0.404280
$894$	1.51653	0.0507202
$895$	39.3768	1.31622
$896$	−2.78135	−0.0929185
$897$	−0.207682	−0.00693431
$898$	23.9846	0.800377
$899$	−52.8983	−1.76426
$900$	−0.871867	−0.0290622
$901$	−7.90996	−0.263519
$902$	13.2787	0.442132
$903$	0.422132	0.0140477
$904$	9.23405	0.307120
$905$	−16.5484	−0.550087
$906$	−14.0352	−0.466289
$907$	−5.63584	−0.187135	−0.0935675	−	0.995613i	$-0.529827\pi$
$907$	−5.63584	−0.187135	−0.0935675	+	0.995613i	$0.529827\pi$
$908$	16.5140	0.548038
$909$	−7.88892	−0.261659
$910$	0.210504	0.00697814
$911$	16.6569	0.551869	0.275934	−	0.961176i	$-0.411013\pi$
$911$	16.6569	0.551869	0.275934	+	0.961176i	$0.411013\pi$
$912$	1.18098	0.0391062
$913$	27.7250	0.917564
$914$	21.4907	0.710849
$915$	4.04081	0.133585
$916$	8.61010	0.284486
$917$	−58.7636	−1.94055
$918$	1.00000	0.0330049
$919$	−21.4854	−0.708738	−0.354369	−	0.935106i	$-0.615304\pi$
$919$	−21.4854	−0.708738	−0.354369	+	0.935106i	$0.615304\pi$
$920$	−11.3279	−0.373469
$921$	10.9773	0.361713
$922$	−36.7596	−1.21061
$923$	−0.187880	−0.00618414
$924$	6.27025	0.206276
$925$	−8.84678	−0.290880
$926$	−40.4962	−1.33079
$927$	−1.85170	−0.0608177
$928$	9.92481	0.325798
$929$	14.2900	0.468840	0.234420	−	0.972135i	$-0.424681\pi$
$929$	14.2900	0.468840	0.234420	+	0.972135i	$0.424681\pi$
$930$	10.8292	0.355104
$931$	−0.869121	−0.0284843
$932$	6.17877	0.202392
$933$	−31.5873	−1.03412
$934$	−40.3215	−1.31936
$935$	−4.58042	−0.149796
$936$	−0.0372501	−0.00121756
$937$	−2.17700	−0.0711194	−0.0355597	−	0.999368i	$-0.511321\pi$
$937$	−2.17700	−0.0711194	−0.0355597	+	0.999368i	$0.511321\pi$
$938$	−1.66456	−0.0543498
$939$	−21.7785	−0.710714
$940$	20.7846	0.677920
$941$	29.2499	0.953518	0.476759	−	0.879034i	$-0.341811\pi$
$941$	29.2499	0.953518	0.476759	+	0.879034i	$0.341811\pi$
$942$	13.0866	0.426384
$943$	−32.8396	−1.06941
$944$	−1.00000	−0.0325472
$945$	5.65110	0.183830
$946$	0.342153	0.0111244
$947$	−1.50415	−0.0488783	−0.0244392	−	0.999701i	$-0.507780\pi$
$947$	−1.50415	−0.0488783	−0.0244392	+	0.999701i	$0.507780\pi$
$948$	16.6292	0.540090
$949$	−0.559853	−0.0181736
$950$	1.02966	0.0334065
$951$	−30.2537	−0.981045
$952$	2.78135	0.0901442
$953$	14.1942	0.459795	0.229898	−	0.973215i	$-0.426161\pi$
$953$	14.1942	0.459795	0.229898	+	0.973215i	$0.426161\pi$
$954$	7.90996	0.256094
$955$	37.7468	1.22146
$956$	22.5916	0.730663
$957$	−22.3743	−0.723260
$958$	−43.0779	−1.39178
$959$	−10.0624	−0.324933
$960$	−2.03178	−0.0655754
$961$	−2.59208	−0.0836156
$962$	−0.377974	−0.0121864
$963$	−13.1597	−0.424064
$964$	−14.4275	−0.464677
$965$	−3.34241	−0.107596
$966$	−15.5070	−0.498930
$967$	−21.2194	−0.682370	−0.341185	−	0.939996i	$-0.610828\pi$
$967$	−21.2194	−0.682370	−0.341185	+	0.939996i	$0.610828\pi$
$968$	−5.91774	−0.190203
$969$	−1.18098	−0.0379385
$970$	13.3758	0.429472
$971$	−22.6082	−0.725533	−0.362767	−	0.931880i	$-0.618168\pi$
$971$	−22.6082	−0.725533	−0.362767	+	0.931880i	$0.618168\pi$
$972$	−1.00000	−0.0320750
$973$	39.7356	1.27387
$974$	13.3110	0.426513
$975$	−0.0324771	−0.00104010
$976$	−1.98880	−0.0636601
$977$	21.9675	0.702803	0.351402	−	0.936225i	$-0.385705\pi$
$977$	21.9675	0.702803	0.351402	+	0.936225i	$0.385705\pi$
$978$	9.34353	0.298773
$979$	8.33493	0.266386
$980$	1.49525	0.0477641
$981$	4.10644	0.131109
$982$	−25.7331	−0.821176
$983$	19.0379	0.607213	0.303607	−	0.952797i	$-0.401809\pi$
$983$	19.0379	0.607213	0.303607	+	0.952797i	$0.401809\pi$
$984$	−5.89015	−0.187771
$985$	4.63477	0.147676
$986$	−9.92481	−0.316070
$987$	28.4526	0.905656
$988$	0.0439916	0.00139956
$989$	−0.846182	−0.0269070
$990$	4.58042	0.145575
$991$	11.3729	0.361272	0.180636	−	0.983550i	$-0.442184\pi$
$991$	11.3729	0.361272	0.180636	+	0.983550i	$0.442184\pi$
$992$	−5.32991	−0.169225
$993$	12.9759	0.411777
$994$	−14.0284	−0.444955
$995$	40.0235	1.26883
$996$	−12.2983	−0.389685
$997$	31.0414	0.983090	0.491545	−	0.870852i	$-0.336432\pi$
$997$	31.0414	0.983090	0.491545	+	0.870852i	$0.336432\pi$
$998$	−17.7722	−0.562571
$999$	−10.1469	−0.321035

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.z.1.7	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.z.1.7	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.03178 q^{5} -1.00000 q^{6} -2.78135 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.03178 q^{5} -1.00000 q^{6} -2.78135 q^{7} +1.00000 q^{8} +1.00000 q^{9} +2.03178 q^{10} +2.25439 q^{11} -1.00000 q^{12} -0.0372501 q^{13} -2.78135 q^{14} -2.03178 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} -1.18098 q^{19} +2.03178 q^{20} +2.78135 q^{21} +2.25439 q^{22} -5.57535 q^{23} -1.00000 q^{24} -0.871867 q^{25} -0.0372501 q^{26} -1.00000 q^{27} -2.78135 q^{28} +9.92481 q^{29} -2.03178 q^{30} -5.32991 q^{31} +1.00000 q^{32} -2.25439 q^{33} -1.00000 q^{34} -5.65110 q^{35} +1.00000 q^{36} +10.1469 q^{37} -1.18098 q^{38} +0.0372501 q^{39} +2.03178 q^{40} +5.89015 q^{41} +2.78135 q^{42} +0.151772 q^{43} +2.25439 q^{44} +2.03178 q^{45} -5.57535 q^{46} +10.2298 q^{47} -1.00000 q^{48} +0.735932 q^{49} -0.871867 q^{50} +1.00000 q^{51} -0.0372501 q^{52} +7.90996 q^{53} -1.00000 q^{54} +4.58042 q^{55} -2.78135 q^{56} +1.18098 q^{57} +9.92481 q^{58} -1.00000 q^{59} -2.03178 q^{60} -1.98880 q^{61} -5.32991 q^{62} -2.78135 q^{63} +1.00000 q^{64} -0.0756840 q^{65} -2.25439 q^{66} +0.598471 q^{67} -1.00000 q^{68} +5.57535 q^{69} -5.65110 q^{70} +5.04374 q^{71} +1.00000 q^{72} +15.0296 q^{73} +10.1469 q^{74} +0.871867 q^{75} -1.18098 q^{76} -6.27025 q^{77} +0.0372501 q^{78} -16.6292 q^{79} +2.03178 q^{80} +1.00000 q^{81} +5.89015 q^{82} +12.2983 q^{83} +2.78135 q^{84} -2.03178 q^{85} +0.151772 q^{86} -9.92481 q^{87} +2.25439 q^{88} +3.69721 q^{89} +2.03178 q^{90} +0.103606 q^{91} -5.57535 q^{92} +5.32991 q^{93} +10.2298 q^{94} -2.39949 q^{95} -1.00000 q^{96} +6.58331 q^{97} +0.735932 q^{98} +2.25439 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 11 q^{2} - 11 q^{3} + 11 q^{4} + 4 q^{5} - 11 q^{6} + 3 q^{7} + 11 q^{8} + 11 q^{9}+O(q^{10}) \) 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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