LMFDB - Embedded newform 6018.2.a.z.1.5

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			1.5
Root			$-0.760310$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.760310 q^{5} -1.00000 q^{6} -1.62737 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.760310 q^{5} -1.00000 q^{6} -1.62737 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.760310 q^{10} +3.63001 q^{11} -1.00000 q^{12} +6.76098 q^{13} -1.62737 q^{14} +0.760310 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} +2.10642 q^{19} -0.760310 q^{20} +1.62737 q^{21} +3.63001 q^{22} +7.89371 q^{23} -1.00000 q^{24} -4.42193 q^{25} +6.76098 q^{26} -1.00000 q^{27} -1.62737 q^{28} -2.99423 q^{29} +0.760310 q^{30} -5.23504 q^{31} +1.00000 q^{32} -3.63001 q^{33} -1.00000 q^{34} +1.23731 q^{35} +1.00000 q^{36} +5.67235 q^{37} +2.10642 q^{38} -6.76098 q^{39} -0.760310 q^{40} +4.04695 q^{41} +1.62737 q^{42} -6.63746 q^{43} +3.63001 q^{44} -0.760310 q^{45} +7.89371 q^{46} -1.45271 q^{47} -1.00000 q^{48} -4.35166 q^{49} -4.42193 q^{50} +1.00000 q^{51} +6.76098 q^{52} +1.88202 q^{53} -1.00000 q^{54} -2.75993 q^{55} -1.62737 q^{56} -2.10642 q^{57} -2.99423 q^{58} -1.00000 q^{59} +0.760310 q^{60} +13.6670 q^{61} -5.23504 q^{62} -1.62737 q^{63} +1.00000 q^{64} -5.14044 q^{65} -3.63001 q^{66} -12.0633 q^{67} -1.00000 q^{68} -7.89371 q^{69} +1.23731 q^{70} +6.36534 q^{71} +1.00000 q^{72} -13.2842 q^{73} +5.67235 q^{74} +4.42193 q^{75} +2.10642 q^{76} -5.90739 q^{77} -6.76098 q^{78} +11.8018 q^{79} -0.760310 q^{80} +1.00000 q^{81} +4.04695 q^{82} +1.53380 q^{83} +1.62737 q^{84} +0.760310 q^{85} -6.63746 q^{86} +2.99423 q^{87} +3.63001 q^{88} +3.89084 q^{89} -0.760310 q^{90} -11.0026 q^{91} +7.89371 q^{92} +5.23504 q^{93} -1.45271 q^{94} -1.60153 q^{95} -1.00000 q^{96} +15.9005 q^{97} -4.35166 q^{98} +3.63001 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−0.760310	−0.340021	−0.170010	−	0.985442i	$-0.554380\pi$
$5$	−0.760310	−0.340021	−0.170010	+	0.985442i	$0.554380\pi$
$6$	−1.00000	−0.408248
$7$	−1.62737	−0.615089	−0.307545	−	0.951534i	$-0.599507\pi$
$7$	−1.62737	−0.615089	−0.307545	+	0.951534i	$0.599507\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−0.760310	−0.240431
$11$	3.63001	1.09449	0.547245	−	0.836972i	$-0.315677\pi$
$11$	3.63001	1.09449	0.547245	+	0.836972i	$0.315677\pi$
$12$	−1.00000	−0.288675
$13$	6.76098	1.87516	0.937580	−	0.347770i	$-0.113061\pi$
$13$	6.76098	1.87516	0.937580	+	0.347770i	$0.113061\pi$
$14$	−1.62737	−0.434934
$15$	0.760310	0.196311
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.00000	0.235702
$19$	2.10642	0.483247	0.241623	−	0.970370i	$-0.422320\pi$
$19$	2.10642	0.483247	0.241623	+	0.970370i	$0.422320\pi$
$20$	−0.760310	−0.170010
$21$	1.62737	0.355122
$22$	3.63001	0.773922
$23$	7.89371	1.64595	0.822976	−	0.568076i	$-0.192312\pi$
$23$	7.89371	1.64595	0.822976	+	0.568076i	$0.192312\pi$
$24$	−1.00000	−0.204124
$25$	−4.42193	−0.884386
$26$	6.76098	1.32594
$27$	−1.00000	−0.192450
$28$	−1.62737	−0.307545
$29$	−2.99423	−0.556014	−0.278007	−	0.960579i	$-0.589674\pi$
$29$	−2.99423	−0.556014	−0.278007	+	0.960579i	$0.589674\pi$
$30$	0.760310	0.138813
$31$	−5.23504	−0.940241	−0.470121	−	0.882602i	$-0.655790\pi$
$31$	−5.23504	−0.940241	−0.470121	+	0.882602i	$0.655790\pi$
$32$	1.00000	0.176777
$33$	−3.63001	−0.631904
$34$	−1.00000	−0.171499
$35$	1.23731	0.209143
$36$	1.00000	0.166667
$37$	5.67235	0.932528	0.466264	−	0.884646i	$-0.345600\pi$
$37$	5.67235	0.932528	0.466264	+	0.884646i	$0.345600\pi$
$38$	2.10642	0.341707
$39$	−6.76098	−1.08262
$40$	−0.760310	−0.120216
$41$	4.04695	0.632028	0.316014	−	0.948755i	$-0.397655\pi$
$41$	4.04695	0.632028	0.316014	+	0.948755i	$0.397655\pi$
$42$	1.62737	0.251109
$43$	−6.63746	−1.01220	−0.506102	−	0.862474i	$-0.668914\pi$
$43$	−6.63746	−1.01220	−0.506102	+	0.862474i	$0.668914\pi$
$44$	3.63001	0.547245
$45$	−0.760310	−0.113340
$46$	7.89371	1.16386
$47$	−1.45271	−0.211900	−0.105950	−	0.994371i	$-0.533788\pi$
$47$	−1.45271	−0.211900	−0.105950	+	0.994371i	$0.533788\pi$
$48$	−1.00000	−0.144338
$49$	−4.35166	−0.621665
$50$	−4.42193	−0.625355
$51$	1.00000	0.140028
$52$	6.76098	0.937580
$53$	1.88202	0.258515	0.129258	−	0.991611i	$-0.458741\pi$
$53$	1.88202	0.258515	0.129258	+	0.991611i	$0.458741\pi$
$54$	−1.00000	−0.136083
$55$	−2.75993	−0.372150
$56$	−1.62737	−0.217467
$57$	−2.10642	−0.279003
$58$	−2.99423	−0.393161
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	0.760310	0.0981556
$61$	13.6670	1.74988	0.874941	−	0.484230i	$-0.160900\pi$
$61$	13.6670	1.74988	0.874941	+	0.484230i	$0.160900\pi$
$62$	−5.23504	−0.664851
$63$	−1.62737	−0.205030
$64$	1.00000	0.125000
$65$	−5.14044	−0.637593
$66$	−3.63001	−0.446824
$67$	−12.0633	−1.47377	−0.736885	−	0.676018i	$-0.763704\pi$
$67$	−12.0633	−1.47377	−0.736885	+	0.676018i	$0.763704\pi$
$68$	−1.00000	−0.121268
$69$	−7.89371	−0.950291
$70$	1.23731	0.147887
$71$	6.36534	0.755426	0.377713	−	0.925923i	$-0.376711\pi$
$71$	6.36534	0.755426	0.377713	+	0.925923i	$0.376711\pi$
$72$	1.00000	0.117851
$73$	−13.2842	−1.55480	−0.777402	−	0.629004i	$-0.783463\pi$
$73$	−13.2842	−1.55480	−0.777402	+	0.629004i	$0.783463\pi$
$74$	5.67235	0.659397
$75$	4.42193	0.510600
$76$	2.10642	0.241623
$77$	−5.90739	−0.673209
$78$	−6.76098	−0.765531
$79$	11.8018	1.32780	0.663901	−	0.747821i	$-0.268900\pi$
$79$	11.8018	1.32780	0.663901	+	0.747821i	$0.268900\pi$
$80$	−0.760310	−0.0850052
$81$	1.00000	0.111111
$82$	4.04695	0.446911
$83$	1.53380	0.168357	0.0841785	−	0.996451i	$-0.473173\pi$
$83$	1.53380	0.168357	0.0841785	+	0.996451i	$0.473173\pi$
$84$	1.62737	0.177561
$85$	0.760310	0.0824672
$86$	−6.63746	−0.715736
$87$	2.99423	0.321015
$88$	3.63001	0.386961
$89$	3.89084	0.412429	0.206214	−	0.978507i	$-0.433886\pi$
$89$	3.89084	0.412429	0.206214	+	0.978507i	$0.433886\pi$
$90$	−0.760310	−0.0801437
$91$	−11.0026	−1.15339
$92$	7.89371	0.822976
$93$	5.23504	0.542848
$94$	−1.45271	−0.149836
$95$	−1.60153	−0.164314
$96$	−1.00000	−0.102062
$97$	15.9005	1.61445	0.807224	−	0.590245i	$-0.200969\pi$
$97$	15.9005	1.61445	0.807224	+	0.590245i	$0.200969\pi$
$98$	−4.35166	−0.439584
$99$	3.63001	0.364830
$100$	−4.42193	−0.442193
$101$	−9.09100	−0.904588	−0.452294	−	0.891869i	$-0.649394\pi$
$101$	−9.09100	−0.904588	−0.452294	+	0.891869i	$0.649394\pi$
$102$	1.00000	0.0990148
$103$	13.9108	1.37068	0.685338	−	0.728225i	$-0.259654\pi$
$103$	13.9108	1.37068	0.685338	+	0.728225i	$0.259654\pi$
$104$	6.76098	0.662969
$105$	−1.23731	−0.120749
$106$	1.88202	0.182798
$107$	−6.47874	−0.626323	−0.313162	−	0.949700i	$-0.601388\pi$
$107$	−6.47874	−0.626323	−0.313162	+	0.949700i	$0.601388\pi$
$108$	−1.00000	−0.0962250
$109$	9.60480	0.919973	0.459987	−	0.887926i	$-0.347854\pi$
$109$	9.60480	0.919973	0.459987	+	0.887926i	$0.347854\pi$
$110$	−2.75993	−0.263149
$111$	−5.67235	−0.538396
$112$	−1.62737	−0.153772
$113$	−13.0169	−1.22453	−0.612264	−	0.790653i	$-0.709741\pi$
$113$	−13.0169	−1.22453	−0.612264	+	0.790653i	$0.709741\pi$
$114$	−2.10642	−0.197285
$115$	−6.00166	−0.559658
$116$	−2.99423	−0.278007
$117$	6.76098	0.625053
$118$	−1.00000	−0.0920575
$119$	1.62737	0.149181
$120$	0.760310	0.0694065
$121$	2.17700	0.197909
$122$	13.6670	1.23735
$123$	−4.04695	−0.364901
$124$	−5.23504	−0.470121
$125$	7.16358	0.640730
$126$	−1.62737	−0.144978
$127$	17.5649	1.55863	0.779316	−	0.626631i	$-0.215567\pi$
$127$	17.5649	1.55863	0.779316	+	0.626631i	$0.215567\pi$
$128$	1.00000	0.0883883
$129$	6.63746	0.584396
$130$	−5.14044	−0.450847
$131$	−13.0849	−1.14323	−0.571616	−	0.820521i	$-0.693683\pi$
$131$	−13.0849	−1.14323	−0.571616	+	0.820521i	$0.693683\pi$
$132$	−3.63001	−0.315952
$133$	−3.42794	−0.297240
$134$	−12.0633	−1.04211
$135$	0.760310	0.0654370
$136$	−1.00000	−0.0857493
$137$	3.13775	0.268076	0.134038	−	0.990976i	$-0.457206\pi$
$137$	3.13775	0.268076	0.134038	+	0.990976i	$0.457206\pi$
$138$	−7.89371	−0.671957
$139$	4.21469	0.357485	0.178742	−	0.983896i	$-0.442797\pi$
$139$	4.21469	0.357485	0.178742	+	0.983896i	$0.442797\pi$
$140$	1.23731	0.104572
$141$	1.45271	0.122340
$142$	6.36534	0.534167
$143$	24.5425	2.05234
$144$	1.00000	0.0833333
$145$	2.27654	0.189056
$146$	−13.2842	−1.09941
$147$	4.35166	0.358918
$148$	5.67235	0.466264
$149$	14.7073	1.20487	0.602433	−	0.798169i	$-0.294198\pi$
$149$	14.7073	1.20487	0.602433	+	0.798169i	$0.294198\pi$
$150$	4.42193	0.361049
$151$	−18.8361	−1.53286	−0.766431	−	0.642327i	$-0.777969\pi$
$151$	−18.8361	−1.53286	−0.766431	+	0.642327i	$0.777969\pi$
$152$	2.10642	0.170854
$153$	−1.00000	−0.0808452
$154$	−5.90739	−0.476031
$155$	3.98025	0.319702
$156$	−6.76098	−0.541312
$157$	4.66776	0.372528	0.186264	−	0.982500i	$-0.440362\pi$
$157$	4.66776	0.372528	0.186264	+	0.982500i	$0.440362\pi$
$158$	11.8018	0.938897
$159$	−1.88202	−0.149254
$160$	−0.760310	−0.0601078
$161$	−12.8460	−1.01241
$162$	1.00000	0.0785674
$163$	4.81393	0.377056	0.188528	−	0.982068i	$-0.439628\pi$
$163$	4.81393	0.377056	0.188528	+	0.982068i	$0.439628\pi$
$164$	4.04695	0.316014
$165$	2.75993	0.214861
$166$	1.53380	0.119046
$167$	15.7377	1.21782	0.608908	−	0.793241i	$-0.291608\pi$
$167$	15.7377	1.21782	0.608908	+	0.793241i	$0.291608\pi$
$168$	1.62737	0.125555
$169$	32.7109	2.51622
$170$	0.760310	0.0583131
$171$	2.10642	0.161082
$172$	−6.63746	−0.506102
$173$	−9.91658	−0.753943	−0.376972	−	0.926225i	$-0.623035\pi$
$173$	−9.91658	−0.753943	−0.376972	+	0.926225i	$0.623035\pi$
$174$	2.99423	0.226992
$175$	7.19613	0.543976
$176$	3.63001	0.273623
$177$	1.00000	0.0751646
$178$	3.89084	0.291631
$179$	−5.63912	−0.421488	−0.210744	−	0.977541i	$-0.567589\pi$
$179$	−5.63912	−0.421488	−0.210744	+	0.977541i	$0.567589\pi$
$180$	−0.760310	−0.0566701
$181$	21.3035	1.58348	0.791739	−	0.610859i	$-0.209176\pi$
$181$	21.3035	1.58348	0.791739	+	0.610859i	$0.209176\pi$
$182$	−11.0026	−0.815570
$183$	−13.6670	−1.01029
$184$	7.89371	0.581932
$185$	−4.31274	−0.317079
$186$	5.23504	0.383852
$187$	−3.63001	−0.265453
$188$	−1.45271	−0.105950
$189$	1.62737	0.118374
$190$	−1.60153	−0.116188
$191$	12.7185	0.920281	0.460140	−	0.887846i	$-0.347799\pi$
$191$	12.7185	0.920281	0.460140	+	0.887846i	$0.347799\pi$
$192$	−1.00000	−0.0721688
$193$	4.43280	0.319080	0.159540	−	0.987191i	$-0.448999\pi$
$193$	4.43280	0.319080	0.159540	+	0.987191i	$0.448999\pi$
$194$	15.9005	1.14159
$195$	5.14044	0.368115
$196$	−4.35166	−0.310833
$197$	19.1487	1.36429	0.682145	−	0.731217i	$-0.261047\pi$
$197$	19.1487	1.36429	0.682145	+	0.731217i	$0.261047\pi$
$198$	3.63001	0.257974
$199$	4.71773	0.334431	0.167216	−	0.985920i	$-0.446522\pi$
$199$	4.71773	0.334431	0.167216	+	0.985920i	$0.446522\pi$
$200$	−4.42193	−0.312678
$201$	12.0633	0.850882
$202$	−9.09100	−0.639640
$203$	4.87272	0.341998
$204$	1.00000	0.0700140
$205$	−3.07694	−0.214903
$206$	13.9108	0.969215
$207$	7.89371	0.548651
$208$	6.76098	0.468790
$209$	7.64635	0.528909
$210$	−1.23731	−0.0853824
$211$	2.79613	0.192493	0.0962467	−	0.995358i	$-0.469316\pi$
$211$	2.79613	0.192493	0.0962467	+	0.995358i	$0.469316\pi$
$212$	1.88202	0.129258
$213$	−6.36534	−0.436146
$214$	−6.47874	−0.442877
$215$	5.04653	0.344170
$216$	−1.00000	−0.0680414
$217$	8.51937	0.578332
$218$	9.60480	0.650519
$219$	13.2842	0.897666
$220$	−2.75993	−0.186075
$221$	−6.76098	−0.454793
$222$	−5.67235	−0.380703
$223$	16.1158	1.07919	0.539597	−	0.841923i	$-0.318577\pi$
$223$	16.1158	1.07919	0.539597	+	0.841923i	$0.318577\pi$
$224$	−1.62737	−0.108733
$225$	−4.42193	−0.294795
$226$	−13.0169	−0.865872
$227$	9.91198	0.657881	0.328941	−	0.944351i	$-0.393308\pi$
$227$	9.91198	0.657881	0.328941	+	0.944351i	$0.393308\pi$
$228$	−2.10642	−0.139501
$229$	−21.8492	−1.44383	−0.721916	−	0.691980i	$-0.756739\pi$
$229$	−21.8492	−1.44383	−0.721916	+	0.691980i	$0.756739\pi$
$230$	−6.00166	−0.395738
$231$	5.90739	0.388678
$232$	−2.99423	−0.196581
$233$	−13.5472	−0.887505	−0.443752	−	0.896149i	$-0.646353\pi$
$233$	−13.5472	−0.887505	−0.443752	+	0.896149i	$0.646353\pi$
$234$	6.76098	0.441979
$235$	1.10451	0.0720503
$236$	−1.00000	−0.0650945
$237$	−11.8018	−0.766606
$238$	1.62737	0.105487
$239$	1.71808	0.111133	0.0555666	−	0.998455i	$-0.482303\pi$
$239$	1.71808	0.111133	0.0555666	+	0.998455i	$0.482303\pi$
$240$	0.760310	0.0490778
$241$	11.4382	0.736800	0.368400	−	0.929667i	$-0.379906\pi$
$241$	11.4382	0.736800	0.368400	+	0.929667i	$0.379906\pi$
$242$	2.17700	0.139943
$243$	−1.00000	−0.0641500
$244$	13.6670	0.874941
$245$	3.30861	0.211379
$246$	−4.04695	−0.258024
$247$	14.2415	0.906165
$248$	−5.23504	−0.332425
$249$	−1.53380	−0.0972009
$250$	7.16358	0.453065
$251$	−28.4694	−1.79697	−0.898487	−	0.439001i	$-0.855333\pi$
$251$	−28.4694	−1.79697	−0.898487	+	0.439001i	$0.855333\pi$
$252$	−1.62737	−0.102515
$253$	28.6543	1.80148
$254$	17.5649	1.10212
$255$	−0.760310	−0.0476124
$256$	1.00000	0.0625000
$257$	7.31711	0.456429	0.228214	−	0.973611i	$-0.426711\pi$
$257$	7.31711	0.456429	0.228214	+	0.973611i	$0.426711\pi$
$258$	6.63746	0.413230
$259$	−9.23103	−0.573588
$260$	−5.14044	−0.318797
$261$	−2.99423	−0.185338
$262$	−13.0849	−0.808387
$263$	16.1806	0.997739	0.498870	−	0.866677i	$-0.333749\pi$
$263$	16.1806	0.997739	0.498870	+	0.866677i	$0.333749\pi$
$264$	−3.63001	−0.223412
$265$	−1.43092	−0.0879006
$266$	−3.42794	−0.210180
$267$	−3.89084	−0.238116
$268$	−12.0633	−0.736885
$269$	21.2237	1.29403	0.647016	−	0.762476i	$-0.276017\pi$
$269$	21.2237	1.29403	0.647016	+	0.762476i	$0.276017\pi$
$270$	0.760310	0.0462710
$271$	−30.6748	−1.86336	−0.931681	−	0.363277i	$-0.881658\pi$
$271$	−30.6748	−1.86336	−0.931681	+	0.363277i	$0.881658\pi$
$272$	−1.00000	−0.0606339
$273$	11.0026	0.665910
$274$	3.13775	0.189558
$275$	−16.0517	−0.967952
$276$	−7.89371	−0.475145
$277$	−23.1354	−1.39007	−0.695036	−	0.718975i	$-0.744611\pi$
$277$	−23.1354	−1.39007	−0.695036	+	0.718975i	$0.744611\pi$
$278$	4.21469	0.252780
$279$	−5.23504	−0.313414
$280$	1.23731	0.0739433
$281$	16.1851	0.965525	0.482763	−	0.875751i	$-0.339633\pi$
$281$	16.1851	0.965525	0.482763	+	0.875751i	$0.339633\pi$
$282$	1.45271	0.0865077
$283$	−13.1301	−0.780502	−0.390251	−	0.920708i	$-0.627612\pi$
$283$	−13.1301	−0.780502	−0.390251	+	0.920708i	$0.627612\pi$
$284$	6.36534	0.377713
$285$	1.60153	0.0948667
$286$	24.5425	1.45123
$287$	−6.58590	−0.388754
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	2.27654	0.133683
$291$	−15.9005	−0.932102
$292$	−13.2842	−0.777402
$293$	−17.6975	−1.03390	−0.516951	−	0.856015i	$-0.672933\pi$
$293$	−17.6975	−1.03390	−0.516951	+	0.856015i	$0.672933\pi$
$294$	4.35166	0.253794
$295$	0.760310	0.0442669
$296$	5.67235	0.329699
$297$	−3.63001	−0.210635
$298$	14.7073	0.851970
$299$	53.3692	3.08642
$300$	4.42193	0.255300
$301$	10.8016	0.622595
$302$	−18.8361	−1.08390
$303$	9.09100	0.522264
$304$	2.10642	0.120812
$305$	−10.3912	−0.594996
$306$	−1.00000	−0.0571662
$307$	9.82541	0.560766	0.280383	−	0.959888i	$-0.409539\pi$
$307$	9.82541	0.560766	0.280383	+	0.959888i	$0.409539\pi$
$308$	−5.90739	−0.336605
$309$	−13.9108	−0.791361
$310$	3.98025	0.226063
$311$	−30.4661	−1.72758	−0.863788	−	0.503856i	$-0.831914\pi$
$311$	−30.4661	−1.72758	−0.863788	+	0.503856i	$0.831914\pi$
$312$	−6.76098	−0.382765
$313$	33.0976	1.87079	0.935395	−	0.353605i	$-0.115044\pi$
$313$	33.0976	1.87079	0.935395	+	0.353605i	$0.115044\pi$
$314$	4.66776	0.263417
$315$	1.23731	0.0697144
$316$	11.8018	0.663901
$317$	17.9222	1.00661	0.503305	−	0.864109i	$-0.332117\pi$
$317$	17.9222	1.00661	0.503305	+	0.864109i	$0.332117\pi$
$318$	−1.88202	−0.105538
$319$	−10.8691	−0.608552
$320$	−0.760310	−0.0425026
$321$	6.47874	0.361608
$322$	−12.8460	−0.715880
$323$	−2.10642	−0.117205
$324$	1.00000	0.0555556
$325$	−29.8966	−1.65836
$326$	4.81393	0.266619
$327$	−9.60480	−0.531147
$328$	4.04695	0.223456
$329$	2.36410	0.130337
$330$	2.75993	0.151929
$331$	−7.50037	−0.412258	−0.206129	−	0.978525i	$-0.566087\pi$
$331$	−7.50037	−0.412258	−0.206129	+	0.978525i	$0.566087\pi$
$332$	1.53380	0.0841785
$333$	5.67235	0.310843
$334$	15.7377	0.861126
$335$	9.17187	0.501113
$336$	1.62737	0.0887805
$337$	28.6815	1.56238	0.781191	−	0.624292i	$-0.214613\pi$
$337$	28.6815	1.56238	0.781191	+	0.624292i	$0.214613\pi$
$338$	32.7109	1.77924
$339$	13.0169	0.706982
$340$	0.760310	0.0412336
$341$	−19.0033	−1.02908
$342$	2.10642	0.113902
$343$	18.4734	0.997469
$344$	−6.63746	−0.357868
$345$	6.00166	0.323119
$346$	−9.91658	−0.533119
$347$	33.0336	1.77334	0.886669	−	0.462404i	$-0.153013\pi$
$347$	33.0336	1.77334	0.886669	+	0.462404i	$0.153013\pi$
$348$	2.99423	0.160507
$349$	−20.6185	−1.10368	−0.551841	−	0.833949i	$-0.686075\pi$
$349$	−20.6185	−1.10368	−0.551841	+	0.833949i	$0.686075\pi$
$350$	7.19613	0.384649
$351$	−6.76098	−0.360875
$352$	3.63001	0.193480
$353$	−25.9945	−1.38355	−0.691775	−	0.722113i	$-0.743171\pi$
$353$	−25.9945	−1.38355	−0.691775	+	0.722113i	$0.743171\pi$
$354$	1.00000	0.0531494
$355$	−4.83963	−0.256861
$356$	3.89084	0.206214
$357$	−1.62737	−0.0861297
$358$	−5.63912	−0.298037
$359$	16.3148	0.861060	0.430530	−	0.902576i	$-0.358327\pi$
$359$	16.3148	0.861060	0.430530	+	0.902576i	$0.358327\pi$
$360$	−0.760310	−0.0400718
$361$	−14.5630	−0.766473
$362$	21.3035	1.11969
$363$	−2.17700	−0.114263
$364$	−11.0026	−0.576695
$365$	10.1001	0.528666
$366$	−13.6670	−0.714386
$367$	−24.8592	−1.29764	−0.648821	−	0.760941i	$-0.724737\pi$
$367$	−24.8592	−1.29764	−0.648821	+	0.760941i	$0.724737\pi$
$368$	7.89371	0.411488
$369$	4.04695	0.210676
$370$	−4.31274	−0.224209
$371$	−3.06275	−0.159010
$372$	5.23504	0.271424
$373$	−0.960167	−0.0497156	−0.0248578	−	0.999691i	$-0.507913\pi$
$373$	−0.960167	−0.0497156	−0.0248578	+	0.999691i	$0.507913\pi$
$374$	−3.63001	−0.187704
$375$	−7.16358	−0.369926
$376$	−1.45271	−0.0749179
$377$	−20.2439	−1.04261
$378$	1.62737	0.0837031
$379$	21.4045	1.09948	0.549738	−	0.835337i	$-0.314728\pi$
$379$	21.4045	1.09948	0.549738	+	0.835337i	$0.314728\pi$
$380$	−1.60153	−0.0821570
$381$	−17.5649	−0.899877
$382$	12.7185	0.650737
$383$	2.36171	0.120678	0.0603388	−	0.998178i	$-0.480782\pi$
$383$	2.36171	0.120678	0.0603388	+	0.998178i	$0.480782\pi$
$384$	−1.00000	−0.0510310
$385$	4.49144	0.228905
$386$	4.43280	0.225624
$387$	−6.63746	−0.337401
$388$	15.9005	0.807224
$389$	−8.71266	−0.441750	−0.220875	−	0.975302i	$-0.570891\pi$
$389$	−8.71266	−0.441750	−0.220875	+	0.975302i	$0.570891\pi$
$390$	5.14044	0.260296
$391$	−7.89371	−0.399202
$392$	−4.35166	−0.219792
$393$	13.0849	0.660045
$394$	19.1487	0.964699
$395$	−8.97299	−0.451480
$396$	3.63001	0.182415
$397$	−16.4192	−0.824057	−0.412029	−	0.911171i	$-0.635180\pi$
$397$	−16.4192	−0.824057	−0.412029	+	0.911171i	$0.635180\pi$
$398$	4.71773	0.236479
$399$	3.42794	0.171612
$400$	−4.42193	−0.221096
$401$	23.1727	1.15719	0.578594	−	0.815615i	$-0.303601\pi$
$401$	23.1727	1.15719	0.578594	+	0.815615i	$0.303601\pi$
$402$	12.0633	0.601664
$403$	−35.3940	−1.76310
$404$	−9.09100	−0.452294
$405$	−0.760310	−0.0377801
$406$	4.87272	0.241829
$407$	20.5907	1.02064
$408$	1.00000	0.0495074
$409$	29.5640	1.46184	0.730922	−	0.682461i	$-0.239090\pi$
$409$	29.5640	1.46184	0.730922	+	0.682461i	$0.239090\pi$
$410$	−3.07694	−0.151959
$411$	−3.13775	−0.154774
$412$	13.9108	0.685338
$413$	1.62737	0.0800778
$414$	7.89371	0.387955
$415$	−1.16617	−0.0572449
$416$	6.76098	0.331485
$417$	−4.21469	−0.206394
$418$	7.64635	0.373995
$419$	−6.58374	−0.321637	−0.160818	−	0.986984i	$-0.551413\pi$
$419$	−6.58374	−0.321637	−0.160818	+	0.986984i	$0.551413\pi$
$420$	−1.23731	−0.0603744
$421$	28.0737	1.36823	0.684114	−	0.729375i	$-0.260189\pi$
$421$	28.0737	1.36823	0.684114	+	0.729375i	$0.260189\pi$
$422$	2.79613	0.136113
$423$	−1.45271	−0.0706332
$424$	1.88202	0.0913990
$425$	4.42193	0.214495
$426$	−6.36534	−0.308402
$427$	−22.2413	−1.07633
$428$	−6.47874	−0.313162
$429$	−24.5425	−1.18492
$430$	5.04653	0.243365
$431$	−39.1100	−1.88386	−0.941931	−	0.335808i	$-0.890991\pi$
$431$	−39.1100	−1.88386	−0.941931	+	0.335808i	$0.890991\pi$
$432$	−1.00000	−0.0481125
$433$	−23.0413	−1.10729	−0.553647	−	0.832751i	$-0.686764\pi$
$433$	−23.0413	−1.10729	−0.553647	+	0.832751i	$0.686764\pi$
$434$	8.51937	0.408943
$435$	−2.27654	−0.109152
$436$	9.60480	0.459987
$437$	16.6275	0.795401
$438$	13.2842	0.634746
$439$	0.621975	0.0296853	0.0148426	−	0.999890i	$-0.495275\pi$
$439$	0.621975	0.0296853	0.0148426	+	0.999890i	$0.495275\pi$
$440$	−2.75993	−0.131575
$441$	−4.35166	−0.207222
$442$	−6.76098	−0.321587
$443$	−28.7111	−1.36410	−0.682052	−	0.731303i	$-0.738912\pi$
$443$	−28.7111	−1.36410	−0.682052	+	0.731303i	$0.738912\pi$
$444$	−5.67235	−0.269198
$445$	−2.95825	−0.140234
$446$	16.1158	0.763106
$447$	−14.7073	−0.695630
$448$	−1.62737	−0.0768862
$449$	−6.66798	−0.314681	−0.157341	−	0.987544i	$-0.550292\pi$
$449$	−6.66798	−0.314681	−0.157341	+	0.987544i	$0.550292\pi$
$450$	−4.42193	−0.208452
$451$	14.6905	0.691748
$452$	−13.0169	−0.612264
$453$	18.8361	0.884998
$454$	9.91198	0.465192
$455$	8.36542	0.392177
$456$	−2.10642	−0.0986423
$457$	23.6303	1.10538	0.552690	−	0.833387i	$-0.313601\pi$
$457$	23.6303	1.10538	0.552690	+	0.833387i	$0.313601\pi$
$458$	−21.8492	−1.02094
$459$	1.00000	0.0466760
$460$	−6.00166	−0.279829
$461$	0.780720	0.0363618	0.0181809	−	0.999835i	$-0.494213\pi$
$461$	0.780720	0.0363618	0.0181809	+	0.999835i	$0.494213\pi$
$462$	5.90739	0.274837
$463$	0.833871	0.0387533	0.0193766	−	0.999812i	$-0.493832\pi$
$463$	0.833871	0.0387533	0.0193766	+	0.999812i	$0.493832\pi$
$464$	−2.99423	−0.139003
$465$	−3.98025	−0.184580
$466$	−13.5472	−0.627561
$467$	−36.4231	−1.68546	−0.842730	−	0.538336i	$-0.819053\pi$
$467$	−36.4231	−1.68546	−0.842730	+	0.538336i	$0.819053\pi$
$468$	6.76098	0.312527
$469$	19.6315	0.906500
$470$	1.10451	0.0509473
$471$	−4.66776	−0.215079
$472$	−1.00000	−0.0460287
$473$	−24.0941	−1.10785
$474$	−11.8018	−0.542073
$475$	−9.31446	−0.427377
$476$	1.62737	0.0745905
$477$	1.88202	0.0861718
$478$	1.71808	0.0785831
$479$	3.13148	0.143081	0.0715405	−	0.997438i	$-0.477208\pi$
$479$	3.13148	0.143081	0.0715405	+	0.997438i	$0.477208\pi$
$480$	0.760310	0.0347032
$481$	38.3507	1.74864
$482$	11.4382	0.520996
$483$	12.8460	0.584514
$484$	2.17700	0.0989545
$485$	−12.0893	−0.548946
$486$	−1.00000	−0.0453609
$487$	−1.19919	−0.0543407	−0.0271703	−	0.999631i	$-0.508650\pi$
$487$	−1.19919	−0.0543407	−0.0271703	+	0.999631i	$0.508650\pi$
$488$	13.6670	0.618676
$489$	−4.81393	−0.217694
$490$	3.30861	0.149468
$491$	−13.9339	−0.628830	−0.314415	−	0.949286i	$-0.601808\pi$
$491$	−13.9339	−0.628830	−0.314415	+	0.949286i	$0.601808\pi$
$492$	−4.04695	−0.182451
$493$	2.99423	0.134853
$494$	14.2415	0.640755
$495$	−2.75993	−0.124050
$496$	−5.23504	−0.235060
$497$	−10.3588	−0.464655
$498$	−1.53380	−0.0687314
$499$	−11.3864	−0.509727	−0.254863	−	0.966977i	$-0.582031\pi$
$499$	−11.3864	−0.509727	−0.254863	+	0.966977i	$0.582031\pi$
$500$	7.16358	0.320365
$501$	−15.7377	−0.703107
$502$	−28.4694	−1.27065
$503$	−11.0211	−0.491406	−0.245703	−	0.969345i	$-0.579019\pi$
$503$	−11.0211	−0.491406	−0.245703	+	0.969345i	$0.579019\pi$
$504$	−1.62737	−0.0724890
$505$	6.91197	0.307579
$506$	28.6543	1.27384
$507$	−32.7109	−1.45274
$508$	17.5649	0.779316
$509$	−10.0579	−0.445807	−0.222903	−	0.974841i	$-0.571553\pi$
$509$	−10.0579	−0.445807	−0.222903	+	0.974841i	$0.571553\pi$
$510$	−0.760310	−0.0336671
$511$	21.6184	0.956343
$512$	1.00000	0.0441942
$513$	−2.10642	−0.0930009
$514$	7.31711	0.322744
$515$	−10.5766	−0.466059
$516$	6.63746	0.292198
$517$	−5.27336	−0.231922
$518$	−9.23103	−0.405588
$519$	9.91658	0.435289
$520$	−5.14044	−0.225423
$521$	−27.1618	−1.18998	−0.594990	−	0.803733i	$-0.702844\pi$
$521$	−27.1618	−1.18998	−0.594990	+	0.803733i	$0.702844\pi$
$522$	−2.99423	−0.131054
$523$	−19.2310	−0.840912	−0.420456	−	0.907313i	$-0.638130\pi$
$523$	−19.2310	−0.840912	−0.420456	+	0.907313i	$0.638130\pi$
$524$	−13.0849	−0.571616
$525$	−7.19613	−0.314065
$526$	16.1806	0.705508
$527$	5.23504	0.228042
$528$	−3.63001	−0.157976
$529$	39.3106	1.70916
$530$	−1.43092	−0.0621551
$531$	−1.00000	−0.0433963
$532$	−3.42794	−0.148620
$533$	27.3614	1.18515
$534$	−3.89084	−0.168373
$535$	4.92585	0.212963
$536$	−12.0633	−0.521056
$537$	5.63912	0.243346
$538$	21.2237	0.915019
$539$	−15.7966	−0.680406
$540$	0.760310	0.0327185
$541$	38.0684	1.63669	0.818343	−	0.574730i	$-0.194893\pi$
$541$	38.0684	1.63669	0.818343	+	0.574730i	$0.194893\pi$
$542$	−30.6748	−1.31760
$543$	−21.3035	−0.914222
$544$	−1.00000	−0.0428746
$545$	−7.30262	−0.312810
$546$	11.0026	0.470870
$547$	20.9084	0.893977	0.446988	−	0.894540i	$-0.352497\pi$
$547$	20.9084	0.893977	0.446988	+	0.894540i	$0.352497\pi$
$548$	3.13775	0.134038
$549$	13.6670	0.583294
$550$	−16.0517	−0.684445
$551$	−6.30711	−0.268692
$552$	−7.89371	−0.335978
$553$	−19.2059	−0.816717
$554$	−23.1354	−0.982929
$555$	4.31274	0.183066
$556$	4.21469	0.178742
$557$	−17.2351	−0.730275	−0.365138	−	0.930954i	$-0.618978\pi$
$557$	−17.2351	−0.730275	−0.365138	+	0.930954i	$0.618978\pi$
$558$	−5.23504	−0.221617
$559$	−44.8758	−1.89804
$560$	1.23731	0.0522858
$561$	3.63001	0.153259
$562$	16.1851	0.682729
$563$	−23.9392	−1.00892	−0.504458	−	0.863436i	$-0.668308\pi$
$563$	−23.9392	−1.00892	−0.504458	+	0.863436i	$0.668308\pi$
$564$	1.45271	0.0611702
$565$	9.89689	0.416365
$566$	−13.1301	−0.551898
$567$	−1.62737	−0.0683433
$568$	6.36534	0.267084
$569$	19.0343	0.797958	0.398979	−	0.916960i	$-0.369365\pi$
$569$	19.0343	0.797958	0.398979	+	0.916960i	$0.369365\pi$
$570$	1.60153	0.0670809
$571$	−6.61480	−0.276821	−0.138410	−	0.990375i	$-0.544199\pi$
$571$	−6.61480	−0.276821	−0.138410	+	0.990375i	$0.544199\pi$
$572$	24.5425	1.02617
$573$	−12.7185	−0.531324
$574$	−6.58590	−0.274890
$575$	−34.9054	−1.45566
$576$	1.00000	0.0416667
$577$	21.8713	0.910516	0.455258	−	0.890360i	$-0.349547\pi$
$577$	21.8713	0.910516	0.455258	+	0.890360i	$0.349547\pi$
$578$	1.00000	0.0415945
$579$	−4.43280	−0.184221
$580$	2.27654	0.0945281
$581$	−2.49607	−0.103555
$582$	−15.9005	−0.659096
$583$	6.83176	0.282943
$584$	−13.2842	−0.549706
$585$	−5.14044	−0.212531
$586$	−17.6975	−0.731079
$587$	20.9831	0.866066	0.433033	−	0.901378i	$-0.357443\pi$
$587$	20.9831	0.866066	0.433033	+	0.901378i	$0.357443\pi$
$588$	4.35166	0.179459
$589$	−11.0272	−0.454368
$590$	0.760310	0.0313015
$591$	−19.1487	−0.787673
$592$	5.67235	0.233132
$593$	−40.4463	−1.66093	−0.830465	−	0.557071i	$-0.811925\pi$
$593$	−40.4463	−1.66093	−0.830465	+	0.557071i	$0.811925\pi$
$594$	−3.63001	−0.148941
$595$	−1.23731	−0.0507247
$596$	14.7073	0.602433
$597$	−4.71773	−0.193084
$598$	53.3692	2.18243
$599$	−17.0129	−0.695128	−0.347564	−	0.937656i	$-0.612991\pi$
$599$	−17.0129	−0.695128	−0.347564	+	0.937656i	$0.612991\pi$
$600$	4.42193	0.180524
$601$	45.2452	1.84559	0.922795	−	0.385291i	$-0.125899\pi$
$601$	45.2452	1.84559	0.922795	+	0.385291i	$0.125899\pi$
$602$	10.8016	0.440241
$603$	−12.0633	−0.491257
$604$	−18.8361	−0.766431
$605$	−1.65519	−0.0672932
$606$	9.09100	0.369297
$607$	−40.3211	−1.63658	−0.818292	−	0.574802i	$-0.805079\pi$
$607$	−40.3211	−1.63658	−0.818292	+	0.574802i	$0.805079\pi$
$608$	2.10642	0.0854268
$609$	−4.87272	−0.197453
$610$	−10.3912	−0.420726
$611$	−9.82176	−0.397346
$612$	−1.00000	−0.0404226
$613$	−13.0033	−0.525198	−0.262599	−	0.964905i	$-0.584580\pi$
$613$	−13.0033	−0.525198	−0.262599	+	0.964905i	$0.584580\pi$
$614$	9.82541	0.396521
$615$	3.07694	0.124074
$616$	−5.90739	−0.238015
$617$	−37.4725	−1.50859	−0.754293	−	0.656538i	$-0.772020\pi$
$617$	−37.4725	−1.50859	−0.754293	+	0.656538i	$0.772020\pi$
$618$	−13.9108	−0.559576
$619$	−18.3333	−0.736877	−0.368438	−	0.929652i	$-0.620107\pi$
$619$	−18.3333	−0.736877	−0.368438	+	0.929652i	$0.620107\pi$
$620$	3.98025	0.159851
$621$	−7.89371	−0.316764
$622$	−30.4661	−1.22158
$623$	−6.33185	−0.253680
$624$	−6.76098	−0.270656
$625$	16.6631	0.666524
$626$	33.0976	1.32285
$627$	−7.64635	−0.305366
$628$	4.66776	0.186264
$629$	−5.67235	−0.226171
$630$	1.23731	0.0492955
$631$	−6.20837	−0.247151	−0.123576	−	0.992335i	$-0.539436\pi$
$631$	−6.20837	−0.247151	−0.123576	+	0.992335i	$0.539436\pi$
$632$	11.8018	0.469449
$633$	−2.79613	−0.111136
$634$	17.9222	0.711781
$635$	−13.3548	−0.529967
$636$	−1.88202	−0.0746270
$637$	−29.4215	−1.16572
$638$	−10.8691	−0.430311
$639$	6.36534	0.251809
$640$	−0.760310	−0.0300539
$641$	27.8091	1.09840	0.549198	−	0.835693i	$-0.314933\pi$
$641$	27.8091	1.09840	0.549198	+	0.835693i	$0.314933\pi$
$642$	6.47874	0.255695
$643$	36.1665	1.42627	0.713133	−	0.701028i	$-0.247275\pi$
$643$	36.1665	1.42627	0.713133	+	0.701028i	$0.247275\pi$
$644$	−12.8460	−0.506204
$645$	−5.04653	−0.198707
$646$	−2.10642	−0.0828761
$647$	−20.5653	−0.808505	−0.404253	−	0.914647i	$-0.632468\pi$
$647$	−20.5653	−0.808505	−0.404253	+	0.914647i	$0.632468\pi$
$648$	1.00000	0.0392837
$649$	−3.63001	−0.142490
$650$	−29.8966	−1.17264
$651$	−8.51937	−0.333900
$652$	4.81393	0.188528
$653$	49.6694	1.94371	0.971857	−	0.235570i	$-0.0756958\pi$
$653$	49.6694	1.94371	0.971857	+	0.235570i	$0.0756958\pi$
$654$	−9.60480	−0.375577
$655$	9.94857	0.388723
$656$	4.04695	0.158007
$657$	−13.2842	−0.518268
$658$	2.36410	0.0921624
$659$	31.4123	1.22365	0.611825	−	0.790994i	$-0.290436\pi$
$659$	31.4123	1.22365	0.611825	+	0.790994i	$0.290436\pi$
$660$	2.75993	0.107430
$661$	11.6492	0.453100	0.226550	−	0.974000i	$-0.427255\pi$
$661$	11.6492	0.453100	0.226550	+	0.974000i	$0.427255\pi$
$662$	−7.50037	−0.291510
$663$	6.76098	0.262575
$664$	1.53380	0.0595232
$665$	2.60629	0.101068
$666$	5.67235	0.219799
$667$	−23.6355	−0.915172
$668$	15.7377	0.608908
$669$	−16.1158	−0.623073
$670$	9.17187	0.354340
$671$	49.6114	1.91523
$672$	1.62737	0.0627773
$673$	−17.8651	−0.688649	−0.344325	−	0.938851i	$-0.611892\pi$
$673$	−17.8651	−0.688649	−0.344325	+	0.938851i	$0.611892\pi$
$674$	28.6815	1.10477
$675$	4.42193	0.170200
$676$	32.7109	1.25811
$677$	13.4427	0.516646	0.258323	−	0.966059i	$-0.416830\pi$
$677$	13.4427	0.516646	0.258323	+	0.966059i	$0.416830\pi$
$678$	13.0169	0.499912
$679$	−25.8760	−0.993030
$680$	0.760310	0.0291565
$681$	−9.91198	−0.379828
$682$	−19.0033	−0.727673
$683$	−16.8098	−0.643209	−0.321604	−	0.946874i	$-0.604222\pi$
$683$	−16.8098	−0.643209	−0.321604	+	0.946874i	$0.604222\pi$
$684$	2.10642	0.0805411
$685$	−2.38566	−0.0911513
$686$	18.4734	0.705317
$687$	21.8492	0.833597
$688$	−6.63746	−0.253051
$689$	12.7243	0.484758
$690$	6.00166	0.228479
$691$	−17.0396	−0.648218	−0.324109	−	0.946020i	$-0.605065\pi$
$691$	−17.0396	−0.648218	−0.324109	+	0.946020i	$0.605065\pi$
$692$	−9.91658	−0.376972
$693$	−5.90739	−0.224403
$694$	33.0336	1.25394
$695$	−3.20447	−0.121552
$696$	2.99423	0.113496
$697$	−4.04695	−0.153289
$698$	−20.6185	−0.780422
$699$	13.5472	0.512401
$700$	7.19613	0.271988
$701$	−20.7107	−0.782234	−0.391117	−	0.920341i	$-0.627911\pi$
$701$	−20.7107	−0.782234	−0.391117	+	0.920341i	$0.627911\pi$
$702$	−6.76098	−0.255177
$703$	11.9484	0.450641
$704$	3.63001	0.136811
$705$	−1.10451	−0.0415983
$706$	−25.9945	−0.978318
$707$	14.7944	0.556402
$708$	1.00000	0.0375823
$709$	−18.2145	−0.684060	−0.342030	−	0.939689i	$-0.611114\pi$
$709$	−18.2145	−0.684060	−0.342030	+	0.939689i	$0.611114\pi$
$710$	−4.83963	−0.181628
$711$	11.8018	0.442600
$712$	3.89084	0.145815
$713$	−41.3239	−1.54759
$714$	−1.62737	−0.0609029
$715$	−18.6599	−0.697840
$716$	−5.63912	−0.210744
$717$	−1.71808	−0.0641628
$718$	16.3148	0.608861
$719$	−28.4924	−1.06259	−0.531294	−	0.847187i	$-0.678294\pi$
$719$	−28.4924	−1.06259	−0.531294	+	0.847187i	$0.678294\pi$
$720$	−0.760310	−0.0283351
$721$	−22.6381	−0.843089
$722$	−14.5630	−0.541978
$723$	−11.4382	−0.425392
$724$	21.3035	0.791739
$725$	13.2403	0.491731
$726$	−2.17700	−0.0807960
$727$	27.0996	1.00507	0.502535	−	0.864557i	$-0.332401\pi$
$727$	27.0996	1.00507	0.502535	+	0.864557i	$0.332401\pi$
$728$	−11.0026	−0.407785
$729$	1.00000	0.0370370
$730$	10.1001	0.373823
$731$	6.63746	0.245495
$732$	−13.6670	−0.505147
$733$	−1.72996	−0.0638975	−0.0319488	−	0.999490i	$-0.510171\pi$
$733$	−1.72996	−0.0638975	−0.0319488	+	0.999490i	$0.510171\pi$
$734$	−24.8592	−0.917571
$735$	−3.30861	−0.122040
$736$	7.89371	0.290966
$737$	−43.7900	−1.61303
$738$	4.04695	0.148970
$739$	31.5143	1.15927	0.579635	−	0.814876i	$-0.303195\pi$
$739$	31.5143	1.15927	0.579635	+	0.814876i	$0.303195\pi$
$740$	−4.31274	−0.158540
$741$	−14.2415	−0.523174
$742$	−3.06275	−0.112437
$743$	12.0144	0.440766	0.220383	−	0.975413i	$-0.429269\pi$
$743$	12.0144	0.440766	0.220383	+	0.975413i	$0.429269\pi$
$744$	5.23504	0.191926
$745$	−11.1821	−0.409680
$746$	−0.960167	−0.0351542
$747$	1.53380	0.0561190
$748$	−3.63001	−0.132726
$749$	10.5433	0.385245
$750$	−7.16358	−0.261577
$751$	24.4977	0.893932	0.446966	−	0.894551i	$-0.352504\pi$
$751$	24.4977	0.893932	0.446966	+	0.894551i	$0.352504\pi$
$752$	−1.45271	−0.0529749
$753$	28.4694	1.03748
$754$	−20.2439	−0.737240
$755$	14.3213	0.521205
$756$	1.62737	0.0591870
$757$	41.6452	1.51362	0.756811	−	0.653634i	$-0.226756\pi$
$757$	41.6452	1.51362	0.756811	+	0.653634i	$0.226756\pi$
$758$	21.4045	0.777447
$759$	−28.6543	−1.04008
$760$	−1.60153	−0.0580938
$761$	48.1386	1.74502	0.872512	−	0.488594i	$-0.162490\pi$
$761$	48.1386	1.74502	0.872512	+	0.488594i	$0.162490\pi$
$762$	−17.5649	−0.636309
$763$	−15.6306	−0.565866
$764$	12.7185	0.460140
$765$	0.760310	0.0274891
$766$	2.36171	0.0853320
$767$	−6.76098	−0.244125
$768$	−1.00000	−0.0360844
$769$	9.40598	0.339188	0.169594	−	0.985514i	$-0.445754\pi$
$769$	9.40598	0.339188	0.169594	+	0.985514i	$0.445754\pi$
$770$	4.49144	0.161860
$771$	−7.31711	−0.263519
$772$	4.43280	0.159540
$773$	39.6916	1.42761	0.713803	−	0.700347i	$-0.246971\pi$
$773$	39.6916	1.42761	0.713803	+	0.700347i	$0.246971\pi$
$774$	−6.63746	−0.238579
$775$	23.1490	0.831536
$776$	15.9005	0.570793
$777$	9.23103	0.331161
$778$	−8.71266	−0.312364
$779$	8.52460	0.305425
$780$	5.14044	0.184057
$781$	23.1063	0.826807
$782$	−7.89371	−0.282278
$783$	2.99423	0.107005
$784$	−4.35166	−0.155416
$785$	−3.54895	−0.126667
$786$	13.0849	0.466723
$787$	11.9056	0.424391	0.212195	−	0.977227i	$-0.431939\pi$
$787$	11.9056	0.424391	0.212195	+	0.977227i	$0.431939\pi$
$788$	19.1487	0.682145
$789$	−16.1806	−0.576045
$790$	−8.97299	−0.319245
$791$	21.1834	0.753194
$792$	3.63001	0.128987
$793$	92.4024	3.28131
$794$	−16.4192	−0.582697
$795$	1.43092	0.0507495
$796$	4.71773	0.167216
$797$	10.0394	0.355615	0.177807	−	0.984065i	$-0.443100\pi$
$797$	10.0394	0.355615	0.177807	+	0.984065i	$0.443100\pi$
$798$	3.42794	0.121348
$799$	1.45271	0.0513932
$800$	−4.42193	−0.156339
$801$	3.89084	0.137476
$802$	23.1727	0.818256
$803$	−48.2220	−1.70172
$804$	12.0633	0.425441
$805$	9.76695	0.344240
$806$	−35.3940	−1.24670
$807$	−21.2237	−0.747110
$808$	−9.09100	−0.319820
$809$	−22.7120	−0.798511	−0.399256	−	0.916840i	$-0.630731\pi$
$809$	−22.7120	−0.798511	−0.399256	+	0.916840i	$0.630731\pi$
$810$	−0.760310	−0.0267146
$811$	30.6184	1.07516	0.537579	−	0.843213i	$-0.319339\pi$
$811$	30.6184	1.07516	0.537579	+	0.843213i	$0.319339\pi$
$812$	4.87272	0.170999
$813$	30.6748	1.07581
$814$	20.5907	0.721704
$815$	−3.66008	−0.128207
$816$	1.00000	0.0350070
$817$	−13.9813	−0.489144
$818$	29.5640	1.03368
$819$	−11.0026	−0.384464
$820$	−3.07694	−0.107451
$821$	−53.7150	−1.87467	−0.937333	−	0.348436i	$-0.886713\pi$
$821$	−53.7150	−1.87467	−0.937333	+	0.348436i	$0.886713\pi$
$822$	−3.13775	−0.109441
$823$	−32.2014	−1.12247	−0.561235	−	0.827657i	$-0.689674\pi$
$823$	−32.2014	−1.12247	−0.561235	+	0.827657i	$0.689674\pi$
$824$	13.9108	0.484607
$825$	16.0517	0.558847
$826$	1.62737	0.0566236
$827$	−26.8042	−0.932074	−0.466037	−	0.884765i	$-0.654319\pi$
$827$	−26.8042	−0.932074	−0.466037	+	0.884765i	$0.654319\pi$
$828$	7.89371	0.274325
$829$	37.6158	1.30645	0.653225	−	0.757164i	$-0.273416\pi$
$829$	37.6158	1.30645	0.653225	+	0.757164i	$0.273416\pi$
$830$	−1.16617	−0.0404782
$831$	23.1354	0.802558
$832$	6.76098	0.234395
$833$	4.35166	0.150776
$834$	−4.21469	−0.145943
$835$	−11.9655	−0.414083
$836$	7.64635	0.264454
$837$	5.23504	0.180949
$838$	−6.58374	−0.227431
$839$	−23.5356	−0.812539	−0.406270	−	0.913753i	$-0.633171\pi$
$839$	−23.5356	−0.812539	−0.406270	+	0.913753i	$0.633171\pi$
$840$	−1.23731	−0.0426912
$841$	−20.0346	−0.690849
$842$	28.0737	0.967484
$843$	−16.1851	−0.557446
$844$	2.79613	0.0962467
$845$	−24.8704	−0.855568
$846$	−1.45271	−0.0499452
$847$	−3.54279	−0.121732
$848$	1.88202	0.0646289
$849$	13.1301	0.450623
$850$	4.42193	0.151671
$851$	44.7759	1.53490
$852$	−6.36534	−0.218073
$853$	−49.0153	−1.67825	−0.839125	−	0.543938i	$-0.816933\pi$
$853$	−49.0153	−1.67825	−0.839125	+	0.543938i	$0.816933\pi$
$854$	−22.2413	−0.761083
$855$	−1.60153	−0.0547713
$856$	−6.47874	−0.221439
$857$	27.2238	0.929948	0.464974	−	0.885324i	$-0.346064\pi$
$857$	27.2238	0.929948	0.464974	+	0.885324i	$0.346064\pi$
$858$	−24.5425	−0.837866
$859$	−19.4563	−0.663839	−0.331920	−	0.943308i	$-0.607696\pi$
$859$	−19.4563	−0.663839	−0.331920	+	0.943308i	$0.607696\pi$
$860$	5.04653	0.172085
$861$	6.58590	0.224447
$862$	−39.1100	−1.33209
$863$	33.7437	1.14865	0.574324	−	0.818628i	$-0.305265\pi$
$863$	33.7437	1.14865	0.574324	+	0.818628i	$0.305265\pi$
$864$	−1.00000	−0.0340207
$865$	7.53967	0.256357
$866$	−23.0413	−0.782975
$867$	−1.00000	−0.0339618
$868$	8.51937	0.289166
$869$	42.8405	1.45327
$870$	−2.27654	−0.0771819
$871$	−81.5600	−2.76355
$872$	9.60480	0.325260
$873$	15.9005	0.538149
$874$	16.6275	0.562433
$875$	−11.6578	−0.394107
$876$	13.2842	0.448833
$877$	−11.1955	−0.378047	−0.189023	−	0.981973i	$-0.560532\pi$
$877$	−11.1955	−0.378047	−0.189023	+	0.981973i	$0.560532\pi$
$878$	0.621975	0.0209906
$879$	17.6975	0.596923
$880$	−2.75993	−0.0930374
$881$	−1.41166	−0.0475602	−0.0237801	−	0.999717i	$-0.507570\pi$
$881$	−1.41166	−0.0475602	−0.0237801	+	0.999717i	$0.507570\pi$
$882$	−4.35166	−0.146528
$883$	38.6523	1.30075	0.650377	−	0.759612i	$-0.274611\pi$
$883$	38.6523	1.30075	0.650377	+	0.759612i	$0.274611\pi$
$884$	−6.76098	−0.227396
$885$	−0.760310	−0.0255575
$886$	−28.7111	−0.964567
$887$	−33.7339	−1.13267	−0.566336	−	0.824174i	$-0.691640\pi$
$887$	−33.7339	−1.13267	−0.566336	+	0.824174i	$0.691640\pi$
$888$	−5.67235	−0.190352
$889$	−28.5846	−0.958698
$890$	−2.95825	−0.0991606
$891$	3.63001	0.121610
$892$	16.1158	0.539597
$893$	−3.06003	−0.102400
$894$	−14.7073	−0.491885
$895$	4.28748	0.143315
$896$	−1.62737	−0.0543667
$897$	−53.3692	−1.78195
$898$	−6.66798	−0.222513
$899$	15.6749	0.522787
$900$	−4.42193	−0.147398
$901$	−1.88202	−0.0626992
$902$	14.6905	0.489140
$903$	−10.8016	−0.359456
$904$	−13.0169	−0.432936
$905$	−16.1973	−0.538416
$906$	18.8361	0.625788
$907$	37.9649	1.26061	0.630303	−	0.776349i	$-0.282931\pi$
$907$	37.9649	1.26061	0.630303	+	0.776349i	$0.282931\pi$
$908$	9.91198	0.328941
$909$	−9.09100	−0.301529
$910$	8.36542	0.277311
$911$	−21.8495	−0.723907	−0.361953	−	0.932196i	$-0.617890\pi$
$911$	−21.8495	−0.723907	−0.361953	+	0.932196i	$0.617890\pi$
$912$	−2.10642	−0.0697507
$913$	5.56773	0.184265
$914$	23.6303	0.781621
$915$	10.3912	0.343521
$916$	−21.8492	−0.721916
$917$	21.2940	0.703190
$918$	1.00000	0.0330049
$919$	−3.53742	−0.116689	−0.0583443	−	0.998297i	$-0.518582\pi$
$919$	−3.53742	−0.116689	−0.0583443	+	0.998297i	$0.518582\pi$
$920$	−6.00166	−0.197869
$921$	−9.82541	−0.323758
$922$	0.780720	0.0257116
$923$	43.0359	1.41655
$924$	5.90739	0.194339
$925$	−25.0827	−0.824715
$926$	0.833871	0.0274027
$927$	13.9108	0.456892
$928$	−2.99423	−0.0982903
$929$	18.5301	0.607952	0.303976	−	0.952680i	$-0.401686\pi$
$929$	18.5301	0.607952	0.303976	+	0.952680i	$0.401686\pi$
$930$	−3.98025	−0.130518
$931$	−9.16643	−0.300418
$932$	−13.5472	−0.443752
$933$	30.4661	0.997416
$934$	−36.4231	−1.19180
$935$	2.75993	0.0902595
$936$	6.76098	0.220990
$937$	5.89175	0.192475	0.0962376	−	0.995358i	$-0.469319\pi$
$937$	5.89175	0.192475	0.0962376	+	0.995358i	$0.469319\pi$
$938$	19.6315	0.640993
$939$	−33.0976	−1.08010
$940$	1.10451	0.0360252
$941$	−32.1850	−1.04920	−0.524601	−	0.851348i	$-0.675786\pi$
$941$	−32.1850	−1.04920	−0.524601	+	0.851348i	$0.675786\pi$
$942$	−4.66776	−0.152084
$943$	31.9455	1.04029
$944$	−1.00000	−0.0325472
$945$	−1.23731	−0.0402496
$946$	−24.0941	−0.783366
$947$	20.6768	0.671905	0.335953	−	0.941879i	$-0.390942\pi$
$947$	20.6768	0.671905	0.335953	+	0.941879i	$0.390942\pi$
$948$	−11.8018	−0.383303
$949$	−89.8146	−2.91551
$950$	−9.31446	−0.302201
$951$	−17.9222	−0.581167
$952$	1.62737	0.0527435
$953$	−21.1557	−0.685300	−0.342650	−	0.939463i	$-0.611324\pi$
$953$	−21.1557	−0.685300	−0.342650	+	0.939463i	$0.611324\pi$
$954$	1.88202	0.0609327
$955$	−9.67002	−0.312915
$956$	1.71808	0.0555666
$957$	10.8691	0.351347
$958$	3.13148	0.101174
$959$	−5.10628	−0.164891
$960$	0.760310	0.0245389
$961$	−3.59435	−0.115947
$962$	38.3507	1.23647
$963$	−6.47874	−0.208774
$964$	11.4382	0.368400
$965$	−3.37030	−0.108494
$966$	12.8460	0.413314
$967$	−45.2397	−1.45481	−0.727405	−	0.686208i	$-0.759274\pi$
$967$	−45.2397	−1.45481	−0.727405	+	0.686208i	$0.759274\pi$
$968$	2.17700	0.0699714
$969$	2.10642	0.0676681
$970$	−12.0893	−0.388163
$971$	21.7060	0.696579	0.348289	−	0.937387i	$-0.386763\pi$
$971$	21.7060	0.696579	0.348289	+	0.937387i	$0.386763\pi$
$972$	−1.00000	−0.0320750
$973$	−6.85887	−0.219885
$974$	−1.19919	−0.0384246
$975$	29.8966	0.957457
$976$	13.6670	0.437470
$977$	−14.8045	−0.473638	−0.236819	−	0.971554i	$-0.576105\pi$
$977$	−14.8045	−0.473638	−0.236819	+	0.971554i	$0.576105\pi$
$978$	−4.81393	−0.153933
$979$	14.1238	0.451399
$980$	3.30861	0.105690
$981$	9.60480	0.306658
$982$	−13.9339	−0.444650
$983$	−24.8315	−0.792003	−0.396001	−	0.918250i	$-0.629602\pi$
$983$	−24.8315	−0.792003	−0.396001	+	0.918250i	$0.629602\pi$
$984$	−4.04695	−0.129012
$985$	−14.5590	−0.463887
$986$	2.99423	0.0953556
$987$	−2.36410	−0.0752503
$988$	14.2415	0.453082
$989$	−52.3942	−1.66604
$990$	−2.75993	−0.0877165
$991$	10.0925	0.320599	0.160299	−	0.987068i	$-0.448754\pi$
$991$	10.0925	0.320599	0.160299	+	0.987068i	$0.448754\pi$
$992$	−5.23504	−0.166213
$993$	7.50037	0.238017
$994$	−10.3588	−0.328561
$995$	−3.58694	−0.113714
$996$	−1.53380	−0.0486005
$997$	−5.58073	−0.176744	−0.0883718	−	0.996088i	$-0.528166\pi$
$997$	−5.58073	−0.176744	−0.0883718	+	0.996088i	$0.528166\pi$
$998$	−11.3864	−0.360431
$999$	−5.67235	−0.179465

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.z.1.5	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.z.1.5	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.760310 q^{5} -1.00000 q^{6} -1.62737 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.760310 q^{5} -1.00000 q^{6} -1.62737 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.760310 q^{10} +3.63001 q^{11} -1.00000 q^{12} +6.76098 q^{13} -1.62737 q^{14} +0.760310 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} +2.10642 q^{19} -0.760310 q^{20} +1.62737 q^{21} +3.63001 q^{22} +7.89371 q^{23} -1.00000 q^{24} -4.42193 q^{25} +6.76098 q^{26} -1.00000 q^{27} -1.62737 q^{28} -2.99423 q^{29} +0.760310 q^{30} -5.23504 q^{31} +1.00000 q^{32} -3.63001 q^{33} -1.00000 q^{34} +1.23731 q^{35} +1.00000 q^{36} +5.67235 q^{37} +2.10642 q^{38} -6.76098 q^{39} -0.760310 q^{40} +4.04695 q^{41} +1.62737 q^{42} -6.63746 q^{43} +3.63001 q^{44} -0.760310 q^{45} +7.89371 q^{46} -1.45271 q^{47} -1.00000 q^{48} -4.35166 q^{49} -4.42193 q^{50} +1.00000 q^{51} +6.76098 q^{52} +1.88202 q^{53} -1.00000 q^{54} -2.75993 q^{55} -1.62737 q^{56} -2.10642 q^{57} -2.99423 q^{58} -1.00000 q^{59} +0.760310 q^{60} +13.6670 q^{61} -5.23504 q^{62} -1.62737 q^{63} +1.00000 q^{64} -5.14044 q^{65} -3.63001 q^{66} -12.0633 q^{67} -1.00000 q^{68} -7.89371 q^{69} +1.23731 q^{70} +6.36534 q^{71} +1.00000 q^{72} -13.2842 q^{73} +5.67235 q^{74} +4.42193 q^{75} +2.10642 q^{76} -5.90739 q^{77} -6.76098 q^{78} +11.8018 q^{79} -0.760310 q^{80} +1.00000 q^{81} +4.04695 q^{82} +1.53380 q^{83} +1.62737 q^{84} +0.760310 q^{85} -6.63746 q^{86} +2.99423 q^{87} +3.63001 q^{88} +3.89084 q^{89} -0.760310 q^{90} -11.0026 q^{91} +7.89371 q^{92} +5.23504 q^{93} -1.45271 q^{94} -1.60153 q^{95} -1.00000 q^{96} +15.9005 q^{97} -4.35166 q^{98} +3.63001 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 11 q^{2} - 11 q^{3} + 11 q^{4} + 4 q^{5} - 11 q^{6} + 3 q^{7} + 11 q^{8} + 11 q^{9}+O(q^{10}) \) 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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