LMFDB - Embedded newform 261.2.k.c.136.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [261,2,Mod(82,261)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(261, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 4]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("261.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 261 = 3^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	261.k (of order $7$, degree $6$, minimal)

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:	no
Analytic conductor:	$2.08409549276$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{7})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 6 x^{17} + 18 x^{16} - 37 x^{15} + 71 x^{14} - 83 x^{13} + 225 x^{12} - 237 x^{11} + 485 x^{10} + \cdots + 64 $ x^18 - 6x^17 + 18x^16 - 37x^15 + 71x^14 - 83x^13 + 225x^12 - 237x^11 + 485x^10 - 319x^9 + 1092x^8 - 1080x^7 + 1833x^6 - 4032x^5 + 6004x^4 - 4480x^3 + 3200x^2 - 576*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 87)
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			136.3
Root			$1.10857 - 1.39010i$ of defining polynomial
Character	$\chi$	$=$	261.136
Dual form			261.2.k.c.190.3

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.50290 - 1.20533i) q^{2} +(3.56470 - 4.46999i) q^{4} +(-2.28635 + 1.10105i) q^{5} +(0.527912 + 0.661981i) q^{7} +(2.29793 - 10.0679i) q^{8} +O(q^{10})$	\(q+(2.50290 - 1.20533i) q^{2} +(3.56470 - 4.46999i) q^{4} +(-2.28635 + 1.10105i) q^{5} +(0.527912 + 0.661981i) q^{7} +(2.29793 - 10.0679i) q^{8} +(-4.39538 + 5.51163i) q^{10} +(0.279921 + 1.22641i) q^{11} +(0.494312 + 2.16572i) q^{13} +(2.11922 + 1.02056i) q^{14} +(-3.83921 - 16.8207i) q^{16} -3.75587 q^{17} +(-1.84230 + 2.31017i) q^{19} +(-3.22848 + 14.1449i) q^{20} +(2.17885 + 2.73219i) q^{22} +(5.78259 + 2.78475i) q^{23} +(0.897653 - 1.12562i) q^{25} +(3.84763 + 4.82478i) q^{26} +4.84090 q^{28} +(-4.24261 + 3.31666i) q^{29} +(-0.518900 + 0.249889i) q^{31} +(-17.0064 - 21.3253i) q^{32} +(-9.40056 + 4.52707i) q^{34} +(-1.93587 - 0.932265i) q^{35} +(0.893407 - 3.91427i) q^{37} +(-1.82657 + 8.00271i) q^{38} +(5.83136 + 25.5489i) q^{40} +9.29991 q^{41} +(-8.60331 - 4.14313i) q^{43} +(6.47989 + 3.12055i) q^{44} +17.8298 q^{46} +(-0.626576 - 2.74521i) q^{47} +(1.39812 - 6.12556i) q^{49} +(0.889987 - 3.89929i) q^{50} +(11.4428 + 5.51058i) q^{52} +(3.55697 - 1.71295i) q^{53} +(-1.99034 - 2.49581i) q^{55} +(7.87785 - 3.79377i) q^{56} +(-6.62115 + 13.4150i) q^{58} -2.24563 q^{59} +(-2.97162 - 3.72629i) q^{61} +(-0.997555 + 1.25089i) q^{62} +(-37.1800 - 17.9050i) q^{64} +(-3.51474 - 4.40735i) q^{65} +(0.0320387 - 0.140371i) q^{67} +(-13.3885 + 16.7887i) q^{68} -5.96898 q^{70} +(-1.13905 - 4.99050i) q^{71} +(-1.24324 - 0.598712i) q^{73} +(-2.48189 - 10.8739i) q^{74} +(3.75920 + 16.4701i) q^{76} +(-0.664089 + 0.832741i) q^{77} +(-0.0599388 + 0.262609i) q^{79} +(27.2982 + 34.2308i) q^{80} +(23.2767 - 11.2095i) q^{82} +(4.26140 - 5.34363i) q^{83} +(8.58724 - 4.13540i) q^{85} -26.5271 q^{86} +12.9906 q^{88} +(-4.15363 + 2.00028i) q^{89} +(-1.17271 + 1.47054i) q^{91} +(33.0610 - 15.9213i) q^{92} +(-4.87715 - 6.11575i) q^{94} +(1.66853 - 7.31033i) q^{95} +(-2.88047 + 3.61199i) q^{97} +(-3.88399 - 17.0169i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 4 q^{2} - 6 q^{4} + q^{5} - 4 q^{7} + 15 q^{8}+O(q^{10}) $ 18 * q + 4 * q^2 - 6 * q^4 + q^5 - 4 * q^7 + 15 * q^8	$ 18 q + 4 q^{2} - 6 q^{4} + q^{5} - 4 q^{7} + 15 q^{8} - 14 q^{10} - 26 q^{11} + 9 q^{13} + 10 q^{14} - 14 q^{16} - 4 q^{17} - 10 q^{19} + q^{20} - 8 q^{22} + 8 q^{23} + 16 q^{25} - 5 q^{26} + 80 q^{28} - 8 q^{29} - 12 q^{31} - 9 q^{32} - 22 q^{34} - 9 q^{35} - 16 q^{37} + 32 q^{38} + 33 q^{40} - 24 q^{41} - 31 q^{43} + 52 q^{44} - 44 q^{46} - 5 q^{47} - 47 q^{49} + 7 q^{50} + 80 q^{52} - 5 q^{53} - 17 q^{55} - 45 q^{56} + 54 q^{58} + 32 q^{59} - 28 q^{61} - 69 q^{62} - 75 q^{64} - 22 q^{65} + 6 q^{67} - 38 q^{68} - 12 q^{70} - 46 q^{71} - q^{73} + 35 q^{74} - 45 q^{76} + 36 q^{77} - 15 q^{79} + 86 q^{80} + 47 q^{82} + 16 q^{83} + 19 q^{85} - 116 q^{86} + 54 q^{88} + 72 q^{89} - 47 q^{91} + 121 q^{92} - 22 q^{94} + 72 q^{95} + 43 q^{97} - 31 q^{98}+O(q^{100}) $ 18 * q + 4 * q^2 - 6 * q^4 + q^5 - 4 * q^7 + 15 * q^8 - 14 * q^10 - 26 * q^11 + 9 * q^13 + 10 * q^14 - 14 * q^16 - 4 * q^17 - 10 * q^19 + q^20 - 8 * q^22 + 8 * q^23 + 16 * q^25 - 5 * q^26 + 80 * q^28 - 8 * q^29 - 12 * q^31 - 9 * q^32 - 22 * q^34 - 9 * q^35 - 16 * q^37 + 32 * q^38 + 33 * q^40 - 24 * q^41 - 31 * q^43 + 52 * q^44 - 44 * q^46 - 5 * q^47 - 47 * q^49 + 7 * q^50 + 80 * q^52 - 5 * q^53 - 17 * q^55 - 45 * q^56 + 54 * q^58 + 32 * q^59 - 28 * q^61 - 69 * q^62 - 75 * q^64 - 22 * q^65 + 6 * q^67 - 38 * q^68 - 12 * q^70 - 46 * q^71 - q^73 + 35 * q^74 - 45 * q^76 + 36 * q^77 - 15 * q^79 + 86 * q^80 + 47 * q^82 + 16 * q^83 + 19 * q^85 - 116 * q^86 + 54 * q^88 + 72 * q^89 - 47 * q^91 + 121 * q^92 - 22 * q^94 + 72 * q^95 + 43 * q^97 - 31 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/261\mathbb{Z}\right)^\times$.

$n$	$118$	$146$
$\chi(n)$	$e\left(\frac{6}{7}\right)$	$1$

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 $

$2$	2.50290	−	1.20533i	1.76982	−	0.852299i	0.803351	−	0.595506i	$-0.203048\pi$
$2$	2.50290	−	1.20533i	1.76982	−	0.852299i	0.966466	−	0.256793i	$-0.0826659\pi$
$3$		0			0
$3$		0			0
$4$	3.56470	−	4.46999i	1.78235	−	2.23500i
$5$	−2.28635	+	1.10105i	−1.02249	+	0.492404i	−0.868511	−	0.495670i	$-0.834923\pi$
$5$	−2.28635	+	1.10105i	−1.02249	+	0.492404i	−0.153977	+	0.988074i	$0.549208\pi$
$6$		0			0
$7$	0.527912	+	0.661981i	0.199532	+	0.250205i	0.871524	−	0.490353i	$-0.163132\pi$
$7$	0.527912	+	0.661981i	0.199532	+	0.250205i	−0.671992	+	0.740559i	$0.734561\pi$
$8$	2.29793	−	10.0679i	0.812440	−	3.55953i
$9$		0			0
$10$	−4.39538	+	5.51163i	−1.38994	+	1.74293i
$11$	0.279921	+	1.22641i	0.0843993	+	0.369778i	0.999436	−	0.0335941i	$-0.0106953\pi$
$11$	0.279921	+	1.22641i	0.0843993	+	0.369778i	−0.915036	+	0.403372i	$0.867838\pi$
$12$		0			0
$13$	0.494312	+	2.16572i	0.137098	+	0.600663i	0.996064	+	0.0886323i	$0.0282496\pi$
$13$	0.494312	+	2.16572i	0.137098	+	0.600663i	−0.858967	+	0.512031i	$0.828893\pi$
$14$	2.11922	+	1.02056i	0.566385	+	0.272757i
$15$		0			0
$16$	−3.83921	−	16.8207i	−0.959802	−	4.20517i
$17$	−3.75587			−0.910932			−0.455466	−	0.890253i	$-0.650527\pi$
$17$	−3.75587			−0.910932			−0.455466	+	0.890253i	$0.650527\pi$
$18$		0			0
$19$	−1.84230	+	2.31017i	−0.422652	+	0.529989i	−0.946879	−	0.321589i	$-0.895783\pi$
$19$	−1.84230	+	2.31017i	−0.422652	+	0.529989i	0.524227	+	0.851579i	$0.324354\pi$
$20$	−3.22848	+	14.1449i	−0.721910	+	3.16289i
$21$		0			0
$22$	2.17885	+	2.73219i	0.464532	+	0.582505i
$23$	5.78259	+	2.78475i	1.20575	+	0.580660i	0.925310	−	0.379211i	$-0.123804\pi$
$23$	5.78259	+	2.78475i	1.20575	+	0.580660i	0.280443	+	0.959871i	$0.409519\pi$
$24$		0			0
$25$	0.897653	−	1.12562i	0.179531	−	0.225124i
$26$	3.84763	+	4.82478i	0.754582	+	0.946216i
$27$		0			0
$28$	4.84090			0.914844
$29$	−4.24261	+	3.31666i	−0.787833	+	0.615889i
$29$	−4.24261	+	3.31666i	−0.787833	+	0.615889i
$30$		0			0
$31$	−0.518900	+	0.249889i	−0.0931972	+	0.0448814i	−0.479902	−	0.877322i	$-0.659328\pi$
$31$	−0.518900	+	0.249889i	−0.0931972	+	0.0448814i	0.386704	+	0.922204i	$0.373613\pi$
$32$	−17.0064	−	21.3253i	−3.00633	−	3.76982i
$33$		0			0
$34$	−9.40056	+	4.52707i	−1.61218	+	0.776386i
$35$	−1.93587	−	0.932265i	−0.327222	−	0.157582i
$36$		0			0
$37$	0.893407	−	3.91427i	0.146875	−	0.643502i	−0.846867	−	0.531805i	$-0.821514\pi$
$37$	0.893407	−	3.91427i	0.146875	−	0.643502i	0.993742	−	0.111698i	$-0.0356288\pi$
$38$	−1.82657	+	8.00271i	−0.296308	+	1.29821i
$39$		0			0
$40$	5.83136	+	25.5489i	0.922019	+	4.03963i
$41$	9.29991			1.45240			0.726201	−	0.687482i	$-0.241284\pi$
$41$	9.29991			1.45240			0.726201	+	0.687482i	$0.241284\pi$
$42$		0			0
$43$	−8.60331	−	4.14313i	−1.31199	−	0.631822i	−0.358582	−	0.933498i	$-0.616740\pi$
$43$	−8.60331	−	4.14313i	−1.31199	−	0.631822i	−0.953410	+	0.301676i	$0.902454\pi$
$44$	6.47989	+	3.12055i	0.976880	+	0.470441i
$45$		0			0
$46$	17.8298			2.62886
$47$	−0.626576	−	2.74521i	−0.0913956	−	0.400430i	0.908450	−	0.417993i	$-0.137266\pi$
$47$	−0.626576	−	2.74521i	−0.0913956	−	0.400430i	−0.999846	+	0.0175630i	$0.994409\pi$
$48$		0			0
$49$	1.39812	−	6.12556i	0.199731	−	0.875080i
$50$	0.889987	−	3.89929i	0.125863	−	0.551443i
$51$		0			0
$52$	11.4428	+	5.51058i	1.58684	+	0.764180i
$53$	3.55697	−	1.71295i	0.488587	−	0.235291i	−0.173336	−	0.984863i	$-0.555455\pi$
$53$	3.55697	−	1.71295i	0.488587	−	0.235291i	0.661923	+	0.749571i	$0.269740\pi$
$54$		0			0
$55$	−1.99034	−	2.49581i	−0.268377	−	0.336535i
$56$	7.87785	−	3.79377i	1.05272	−	0.506964i
$57$		0			0
$58$	−6.62115	+	13.4150i	−0.869400	+	1.76148i
$59$	−2.24563			−0.292356			−0.146178	−	0.989258i	$-0.546697\pi$
$59$	−2.24563			−0.292356			−0.146178	+	0.989258i	$0.546697\pi$
$60$		0			0
$61$	−2.97162	−	3.72629i	−0.380477	−	0.477103i	0.554311	−	0.832310i	$-0.312982\pi$
$61$	−2.97162	−	3.72629i	−0.380477	−	0.477103i	−0.934788	+	0.355207i	$0.884410\pi$
$62$	−0.997555	+	1.25089i	−0.126690	+	0.158864i
$63$		0			0
$64$	−37.1800	−	17.9050i	−4.64750	−	2.23812i
$65$	−3.51474	−	4.40735i	−0.435950	−	0.546664i
$66$		0			0
$67$	0.0320387	−	0.140371i	0.00391415	−	0.0171490i	−0.972933	−	0.231087i	$-0.925772\pi$
$67$	0.0320387	−	0.140371i	0.00391415	−	0.0171490i	0.976847	+	0.213938i	$0.0686290\pi$
$68$	−13.3885	+	16.7887i	−1.62360	+	2.03593i
$69$		0			0
$70$	−5.96898			−0.713429
$71$	−1.13905	−	4.99050i	−0.135180	−	0.592264i	−0.996455	−	0.0841244i	$-0.973191\pi$
$71$	−1.13905	−	4.99050i	−0.135180	−	0.592264i	0.861275	−	0.508139i	$-0.169666\pi$
$72$		0			0
$73$	−1.24324	−	0.598712i	−0.145510	−	0.0700739i	0.359712	−	0.933063i	$-0.382875\pi$
$73$	−1.24324	−	0.598712i	−0.145510	−	0.0700739i	−0.505222	+	0.862990i	$0.668589\pi$
$74$	−2.48189	−	10.8739i	−0.288514	−	1.26406i
$75$		0			0
$76$	3.75920	+	16.4701i	0.431210	+	1.88925i
$77$	−0.664089	+	0.832741i	−0.0756800	+	0.0948997i
$78$		0			0
$79$	−0.0599388	+	0.262609i	−0.00674364	+	0.0295458i	−0.978188	−	0.207722i	$-0.933395\pi$
$79$	−0.0599388	+	0.262609i	−0.00674364	+	0.0295458i	0.971444	+	0.237268i	$0.0762520\pi$
$80$	27.2982	+	34.2308i	3.05203	+	3.82712i
$81$		0			0
$82$	23.2767	−	11.2095i	2.57049	−	1.23788i
$83$	4.26140	−	5.34363i	0.467750	−	0.586540i	−0.490869	−	0.871234i	$-0.663320\pi$
$83$	4.26140	−	5.34363i	0.467750	−	0.586540i	0.958619	+	0.284694i	$0.0918919\pi$
$84$		0			0
$85$	8.58724	−	4.13540i	0.931417	−	0.448547i
$86$	−26.5271			−2.86049
$87$		0			0
$88$	12.9906			1.38480
$89$	−4.15363	+	2.00028i	−0.440284	+	0.212030i	−0.640875	−	0.767645i	$-0.721428\pi$
$89$	−4.15363	+	2.00028i	−0.440284	+	0.212030i	0.200590	+	0.979675i	$0.435714\pi$
$90$		0			0
$91$	−1.17271	+	1.47054i	−0.122934	+	0.154154i
$92$	33.0610	−	15.9213i	3.44685	−	1.65991i
$93$		0			0
$94$	−4.87715	−	6.11575i	−0.503040	−	0.630792i
$95$	1.66853	−	7.31033i	0.171188	−	0.750024i
$96$		0			0
$97$	−2.88047	+	3.61199i	−0.292467	+	0.366742i	−0.906257	−	0.422727i	$-0.861073\pi$
$97$	−2.88047	+	3.61199i	−0.292467	+	0.366742i	0.613790	+	0.789469i	$0.289644\pi$
$98$	−3.88399	−	17.0169i	−0.392342	−	1.71896i
$99$		0			0
$100$	−1.83165	−	8.02500i	−0.183165	−	0.802500i
$101$	−8.21134	−	3.95437i	−0.817059	−	0.393475i	−0.0218131	−	0.999762i	$-0.506944\pi$
$101$	−8.21134	−	3.95437i	−0.817059	−	0.393475i	−0.795246	+	0.606287i	$0.792658\pi$
$102$		0			0
$103$	3.20560	+	14.0446i	0.315857	+	1.38386i	0.844745	+	0.535168i	$0.179752\pi$
$103$	3.20560	+	14.0446i	0.315857	+	1.38386i	−0.528889	+	0.848691i	$0.677391\pi$
$104$	22.9401			2.24946
$105$		0			0
$106$	6.83807	−	8.57466i	0.664172	−	0.832845i
$107$	−0.407981	+	1.78748i	−0.0394410	+	0.172802i	−0.990812	−	0.135244i	$-0.956818\pi$
$107$	−0.407981	+	1.78748i	−0.0394410	+	0.172802i	0.951371	+	0.308046i	$0.0996752\pi$
$108$		0			0
$109$	8.94438	+	11.2159i	0.856716	+	1.07429i	0.996457	+	0.0840999i	$0.0268015\pi$
$109$	8.94438	+	11.2159i	0.856716	+	1.07429i	−0.139741	+	0.990188i	$0.544627\pi$
$110$	−7.98990	−	3.84773i	−0.761807	−	0.366867i
$111$		0			0
$112$	9.10820	−	11.4213i	0.860644	−	1.07921i
$113$	7.34424	+	9.20939i	0.690888	+	0.866346i	0.996306	−	0.0858722i	$-0.0273677\pi$
$113$	7.34424	+	9.20939i	0.690888	+	0.866346i	−0.305418	+	0.952218i	$0.598796\pi$
$114$		0			0
$115$	−16.2872			−1.51879
$116$	−0.298185	+	30.7873i	−0.0276858	+	2.85853i
$117$		0			0
$118$	−5.62059	+	2.70673i	−0.517417	+	0.249175i
$119$	−1.98277	−	2.48631i	−0.181760	−	0.227920i
$120$		0			0
$121$	8.48492	−	4.08612i	0.771357	−	0.371466i
$122$	−11.9291	−	5.74474i	−1.08001	−	0.520104i
$123$		0			0
$124$	−0.732720	+	3.21026i	−0.0658002	+	0.288290i
$125$	2.01043	−	8.80825i	0.179818	−	0.787834i
$126$		0			0
$127$	−2.67677	−	11.7277i	−0.237524	−	1.04066i	−0.943226	−	0.332153i	$-0.892225\pi$
$127$	−2.67677	−	11.7277i	−0.237524	−	1.04066i	0.705701	−	0.708510i	$-0.250632\pi$
$128$	−60.0872			−5.31100
$129$		0			0
$130$	−14.1094	−	6.79471i	−1.23747	−	0.595936i
$131$	−2.14780	−	1.03433i	−0.187654	−	0.0903695i	0.337697	−	0.941255i	$-0.390352\pi$
$131$	−2.14780	−	1.03433i	−0.187654	−	0.0903695i	−0.525352	+	0.850885i	$0.676066\pi$
$132$		0			0
$133$	−2.50186			−0.216939
$134$	−0.0890038	−	0.389951i	−0.00768876	−	0.0336867i
$135$		0			0
$136$	−8.63071	+	37.8136i	−0.740077	+	3.24249i
$137$	−3.01965	+	13.2299i	−0.257986	+	1.13031i	0.665416	+	0.746473i	$0.268254\pi$
$137$	−3.01965	+	13.2299i	−0.257986	+	1.13031i	−0.923401	+	0.383836i	$0.874603\pi$
$138$		0			0
$139$	−18.0033	−	8.66991i	−1.52702	−	0.735373i	−0.533157	−	0.846017i	$-0.678994\pi$
$139$	−18.0033	−	8.66991i	−1.52702	−	0.735373i	−0.993860	+	0.110644i	$0.964709\pi$
$140$	−11.0680	+	5.33007i	−0.935418	+	0.450473i
$141$		0			0
$142$	−8.86614	−	11.1178i	−0.744030	−	0.932984i
$143$	−2.51770	+	1.21246i	−0.210541	+	0.101391i
$144$		0			0
$145$	6.04830	−	12.2544i	0.502284	−	1.01767i
$146$	−3.83335			−0.317250
$147$		0			0
$148$	−14.3120	−	17.9467i	−1.17644	−	1.47521i
$149$	10.0592	−	12.6139i	0.824085	−	1.03337i	−0.174726	−	0.984617i	$-0.555904\pi$
$149$	10.0592	−	12.6139i	0.824085	−	1.03337i	0.998811	−	0.0487523i	$-0.0155245\pi$
$150$		0			0
$151$	−2.52401	−	1.21550i	−0.205401	−	0.0989158i	0.328355	−	0.944554i	$-0.393506\pi$
$151$	−2.52401	−	1.21550i	−0.205401	−	0.0989158i	−0.533756	+	0.845638i	$0.679220\pi$
$152$	19.0250	+	23.8566i	1.54313	+	1.93503i
$153$		0			0
$154$	−0.658418	+	2.88472i	−0.0530568	+	0.232457i
$155$	0.911248	−	1.14267i	0.0731932	−	0.0917814i
$156$		0			0
$157$	8.49632			0.678080			0.339040	−	0.940772i	$-0.389898\pi$
$157$	8.49632			0.678080			0.339040	+	0.940772i	$0.389898\pi$
$158$	0.166510	+	0.729530i	0.0132469	+	0.0580383i
$159$		0			0
$160$	62.3628	+	30.0323i	4.93021	+	2.37426i
$161$	1.20925	+	5.29807i	0.0953022	+	0.417546i
$162$		0			0
$163$	4.61597	+	20.2239i	0.361550	+	1.58406i	0.749261	+	0.662275i	$0.230409\pi$
$163$	4.61597	+	20.2239i	0.361550	+	1.58406i	−0.387711	+	0.921781i	$0.626734\pi$
$164$	33.1514	−	41.5705i	2.58869	−	3.24611i
$165$		0			0
$166$	4.22501	−	18.5110i	0.327924	−	1.43673i
$167$	−6.10998	−	7.66168i	−0.472805	−	0.592878i	0.487051	−	0.873374i	$-0.338073\pi$
$167$	−6.10998	−	7.66168i	−0.472805	−	0.592878i	−0.959855	+	0.280495i	$0.909501\pi$
$168$		0			0
$169$	7.26658	−	3.49940i	0.558968	−	0.269185i
$170$	16.5085	−	20.7010i	1.26614	−	1.58769i
$171$		0			0
$172$	−49.1880	+	23.6877i	−3.75055	+	1.80617i
$173$	20.1246			1.53005			0.765023	−	0.644003i	$-0.222728\pi$
$173$	20.1246			1.53005			0.765023	+	0.644003i	$0.222728\pi$
$174$		0			0
$175$	1.21902			0.0921494
$176$	19.5544	−	9.41691i	1.47397	−	0.709826i
$177$		0			0
$178$	−7.98512	+	10.0130i	−0.598510	+	0.750508i
$179$	−22.1567	+	10.6701i	−1.65607	+	0.797521i	−0.657023	+	0.753871i	$0.728184\pi$
$179$	−22.1567	+	10.6701i	−1.65607	+	0.797521i	−0.999047	+	0.0436504i	$0.986101\pi$
$180$		0			0
$181$	12.1022	+	15.1757i	0.899551	+	1.12800i	0.991221	+	0.132212i	$0.0422079\pi$
$181$	12.1022	+	15.1757i	0.899551	+	1.12800i	−0.0916705	+	0.995789i	$0.529221\pi$
$182$	−1.16270	+	5.09412i	−0.0861850	+	0.377601i
$183$		0			0
$184$	41.3244	−	51.8192i	3.04648	−	3.82016i
$185$	2.26716	+	9.93310i	0.166685	+	0.730296i
$186$		0			0
$187$	−1.05135	−	4.60625i	−0.0768820	−	0.336842i
$188$	−14.5046	−	6.98506i	−1.05786	−	0.509438i
$189$		0			0
$190$	−4.63520	−	20.3082i	−0.336273	−	1.47331i
$191$	0.923161			0.0667976			0.0333988	−	0.999442i	$-0.489367\pi$
$191$	0.923161			0.0667976			0.0333988	+	0.999442i	$0.489367\pi$
$192$		0			0
$193$	6.07588	−	7.61891i	0.437351	−	0.548421i	−0.513492	−	0.858095i	$-0.671648\pi$
$193$	6.07588	−	7.61891i	0.437351	−	0.548421i	0.950843	+	0.309673i	$0.100220\pi$
$194$	−2.85587	+	12.5124i	−0.205039	+	0.898336i
$195$		0			0
$196$	−22.3973	−	28.0854i	−1.59981	−	2.00610i
$197$	−6.73034	−	3.24116i	−0.479517	−	0.230923i	0.178480	−	0.983943i	$-0.442882\pi$
$197$	−6.73034	−	3.24116i	−0.479517	−	0.230923i	−0.657997	+	0.753020i	$0.728596\pi$
$198$		0			0
$199$	16.1636	−	20.2685i	1.14581	−	1.43679i	0.264413	−	0.964410i	$-0.414822\pi$
$199$	16.1636	−	20.2685i	1.14581	−	1.43679i	0.881392	−	0.472385i	$-0.156607\pi$
$200$	−9.26987	−	11.6241i	−0.655479	−	0.821945i
$201$		0			0
$202$	−25.3185			−1.78140
$203$	−4.43530	−	1.05762i	−0.311297	−	0.0742306i
$204$		0			0
$205$	−21.2629	+	10.2397i	−1.48506	+	0.715169i
$206$	24.9518	+	31.2885i	1.73847	+	2.17997i
$207$		0			0
$208$	34.5311	−	16.6293i	2.39430	−	1.15304i
$209$	−3.34892	−	1.61276i	−0.231650	−	0.111557i
$210$		0			0
$211$	−4.28601	+	18.7782i	−0.295061	+	1.29275i	0.582323	+	0.812957i	$0.302144\pi$
$211$	−4.28601	+	18.7782i	−0.295061	+	1.29275i	−0.877384	+	0.479789i	$0.840713\pi$
$212$	5.02267	−	22.0058i	0.344958	−	1.51136i
$213$		0			0
$214$	1.13337	+	4.96563i	0.0774758	+	0.339444i
$215$	24.2320			1.65261
$216$		0			0
$217$	−0.439356	−	0.211583i	−0.0298254	−	0.0143632i
$218$	35.9058	+	17.2913i	2.43185	+	1.17112i
$219$		0			0
$220$	−18.2512			−1.23050
$221$	−1.85657	−	8.13417i	−0.124886	−	0.547163i
$222$		0			0
$223$	0.175370	−	0.768344i	0.0117436	−	0.0514521i	−0.968717	−	0.248170i	$-0.920171\pi$
$223$	0.175370	−	0.768344i	0.0117436	−	0.0514521i	0.980460	+	0.196717i	$0.0630281\pi$
$224$	5.13908	−	22.5158i	0.343369	−	1.50440i
$225$		0			0
$226$	29.4823	+	14.1979i	1.96113	+	0.944431i
$227$	−16.9571	+	8.16610i	−1.12548	+	0.542003i	−0.901581	−	0.432609i	$-0.857593\pi$
$227$	−16.9571	+	8.16610i	−1.12548	+	0.542003i	−0.223899	+	0.974612i	$0.571879\pi$
$228$		0			0
$229$	16.7757	+	21.0360i	1.10857	+	1.39010i	0.912287	+	0.409552i	$0.134315\pi$
$229$	16.7757	+	21.0360i	1.10857	+	1.39010i	0.196281	+	0.980548i	$0.437114\pi$
$230$	−40.7652	+	19.6315i	−2.68798	+	1.29446i
$231$		0			0
$232$	23.6425	+	50.3355i	1.55221	+	3.30469i
$233$	13.1181			0.859393			0.429696	−	0.902973i	$-0.358621\pi$
$233$	13.1181			0.859393			0.429696	+	0.902973i	$0.358621\pi$
$234$		0			0
$235$	4.45519	+	5.58663i	0.290624	+	0.364432i
$236$	−8.00500	+	10.0380i	−0.521081	+	0.653415i
$237$		0			0
$238$	−7.95951	−	3.83310i	−0.515938	−	0.248463i
$239$	−2.52458	−	3.16572i	−0.163302	−	0.204774i	0.693448	−	0.720507i	$-0.256091\pi$
$239$	−2.52458	−	3.16572i	−0.163302	−	0.204774i	−0.856749	+	0.515733i	$0.827519\pi$
$240$		0			0
$241$	−0.896181	+	3.92643i	−0.0577281	+	0.252923i	−0.995555	−	0.0941792i	$-0.969977\pi$
$241$	−0.896181	+	3.92643i	−0.0577281	+	0.252923i	0.937827	+	0.347103i	$0.112834\pi$
$242$	16.3118	−	20.4543i	1.04856	−	1.31485i
$243$		0			0
$244$	−27.2494			−1.74446
$245$	3.54795	+	15.5446i	0.226670	+	0.993108i
$246$		0			0
$247$	−5.91386	−	2.84796i	−0.376290	−	0.181212i
$248$	1.32346	+	5.79845i	0.0840396	+	0.368202i
$249$		0			0
$250$	−5.58498	−	24.4694i	−0.353225	−	1.54758i
$251$	−18.9067	+	23.7083i	−1.19338	+	1.49645i	−0.369939	+	0.929056i	$0.620622\pi$
$251$	−18.9067	+	23.7083i	−1.19338	+	1.49645i	−0.823443	+	0.567399i	$0.807950\pi$
$252$		0			0
$253$	−1.79658	+	7.87135i	−0.112950	+	0.494868i
$254$	−20.8354	−	26.1268i	−1.30733	−	1.63934i
$255$		0			0
$256$	−76.0321	+	36.6151i	−4.75200	+	2.28844i
$257$	5.07958	−	6.36959i	0.316855	−	0.397324i	−0.597743	−	0.801688i	$-0.703936\pi$
$257$	5.07958	−	6.36959i	0.316855	−	0.397324i	0.914598	+	0.404364i	$0.132507\pi$
$258$		0			0
$259$	3.06282	−	1.47497i	0.190314	−	0.0916504i
$260$	−32.2298			−1.99881
$261$		0			0
$262$	−6.62243			−0.409135
$263$	−5.10905	+	2.46039i	−0.315038	+	0.151714i	−0.584720	−	0.811235i	$-0.698796\pi$
$263$	−5.10905	+	2.46039i	−0.315038	+	0.151714i	0.269682	+	0.962949i	$0.413081\pi$
$264$		0			0
$265$	−6.24645	+	7.83280i	−0.383716	+	0.481165i
$266$	−6.26191	+	3.01558i	−0.383942	+	0.184897i
$267$		0			0
$268$	−0.513248	−	0.643592i	−0.0313516	−	0.0393137i
$269$	4.57344	−	20.0376i	0.278848	−	1.22171i	−0.620405	−	0.784282i	$-0.713032\pi$
$269$	4.57344	−	20.0376i	0.278848	−	1.22171i	0.899252	−	0.437430i	$-0.144111\pi$
$270$		0			0
$271$	5.98035	−	7.49912i	0.363280	−	0.455539i	−0.566278	−	0.824214i	$-0.691617\pi$
$271$	5.98035	−	7.49912i	0.363280	−	0.455539i	0.929558	+	0.368675i	$0.120189\pi$
$272$	14.4196	+	63.1762i	0.874314	+	3.83062i
$273$		0			0
$274$	8.38860	+	36.7529i	0.506774	+	2.22032i
$275$	1.63175	+	0.785809i	0.0983982	+	0.0473861i
$276$		0			0
$277$	5.75035	+	25.1939i	0.345505	+	1.51376i	0.787260	+	0.616621i	$0.211499\pi$
$277$	5.75035	+	25.1939i	0.345505	+	1.51376i	−0.441755	+	0.897136i	$0.645644\pi$
$278$	−55.5105			−3.32930
$279$		0			0
$280$	−13.8344	+	17.3478i	−0.826764	+	1.03673i
$281$	−4.07233	+	17.8421i	−0.242935	+	1.06437i	0.695395	+	0.718627i	$0.255229\pi$
$281$	−4.07233	+	17.8421i	−0.242935	+	1.06437i	−0.938330	+	0.345740i	$0.887628\pi$
$282$		0			0
$283$	−8.60447	−	10.7897i	−0.511483	−	0.641379i	0.457293	−	0.889316i	$-0.348819\pi$
$283$	−8.60447	−	10.7897i	−0.511483	−	0.641379i	−0.968776	+	0.247937i	$0.920247\pi$
$284$	−26.3679	−	12.6981i	−1.56465	−	0.753494i
$285$		0			0
$286$	−4.84014	+	6.06934i	−0.286203	+	0.358888i
$287$	4.90954	+	6.15637i	0.289801	+	0.363399i
$288$		0			0
$289$	−2.89345			−0.170203
$290$	0.367672	−	37.9617i	0.0215904	−	2.22919i
$291$		0			0
$292$	−7.10800	+	3.42303i	−0.415964	+	0.200318i
$293$	8.24552	+	10.3396i	0.481708	+	0.604043i	0.961995	−	0.273069i	$-0.0880387\pi$
$293$	8.24552	+	10.3396i	0.481708	+	0.604043i	−0.480286	+	0.877112i	$0.659467\pi$
$294$		0			0
$295$	5.13431	−	2.47255i	0.298931	−	0.143958i
$296$	−37.3554	−	17.9894i	−2.17124	−	1.04561i
$297$		0			0
$298$	9.97333	−	43.6960i	0.577739	−	2.53124i
$299$	−3.17259	+	13.9000i	−0.183476	+	0.803859i
$300$		0			0
$301$	−1.79912	−	7.88244i	−0.103699	−	0.454336i
$302$	−7.78241			−0.447828
$303$		0			0
$304$	45.9316	+	22.1195i	2.63436	+	1.26864i
$305$	10.8970	+	5.24772i	0.623960	+	0.300483i
$306$		0			0
$307$	23.3280			1.33140			0.665698	−	0.746221i	$-0.268134\pi$
$307$	23.3280			1.33140			0.665698	+	0.746221i	$0.268134\pi$
$308$	1.35507	+	5.93694i	0.0772122	+	0.338289i
$309$		0			0
$310$	0.903466	−	3.95834i	0.0513134	−	0.224819i
$311$	−1.26488	+	5.54181i	−0.0717249	+	0.314247i	−0.998046	−	0.0624884i	$-0.980096\pi$
$311$	−1.26488	+	5.54181i	−0.0717249	+	0.314247i	0.926321	+	0.376736i	$0.122953\pi$
$312$		0			0
$313$	−3.59647	−	1.73197i	−0.203284	−	0.0978966i	0.329472	−	0.944165i	$-0.393129\pi$
$313$	−3.59647	−	1.73197i	−0.203284	−	0.0978966i	−0.532756	+	0.846269i	$0.678844\pi$
$314$	21.2654	−	10.2409i	1.20008	−	0.577927i
$315$		0			0
$316$	0.960196	+	1.20405i	0.0540153	+	0.0677330i
$317$	11.0688	−	5.33046i	0.621687	−	0.299389i	−0.0963994	−	0.995343i	$-0.530733\pi$
$317$	11.0688	−	5.33046i	0.621687	−	0.299389i	0.718086	+	0.695954i	$0.245018\pi$
$318$		0			0
$319$	−5.25519	−	4.27479i	−0.294234	−	0.239342i
$320$	104.721			5.85408
$321$		0			0
$322$	9.41257	+	11.8030i	0.524542	+	0.657755i
$323$	6.91943	−	8.67669i	0.385007	−	0.482784i
$324$		0			0
$325$	2.88150	+	1.38766i	0.159837	+	0.0769735i
$326$	35.9298	+	45.0545i	1.98997	+	2.49534i
$327$		0			0
$328$	21.3705	−	93.6303i	1.17999	−	5.16987i
$329$	1.48650	−	1.86401i	0.0819534	−	0.102766i
$330$		0			0
$331$	−15.4931			−0.851579			−0.425790	−	0.904822i	$-0.640004\pi$
$331$	−15.4931			−0.851579			−0.425790	+	0.904822i	$0.640004\pi$
$332$	−8.69537	−	38.0969i	−0.477220	−	2.09084i
$333$		0			0
$334$	−24.5275	−	11.8118i	−1.34209	−	0.646315i
$335$	0.0813034	+	0.356213i	0.00444208	+	0.0194620i
$336$		0			0
$337$	0.00717696	+	0.0314443i	0.000390954	+	0.00171288i	0.975123	−	0.221664i	$-0.0711489\pi$
$337$	0.00717696	+	0.0314443i	0.000390954	+	0.00171288i	−0.974732	+	0.223377i	$0.928292\pi$
$338$	13.9696	−	17.5173i	0.759845	−	0.952816i
$339$		0			0
$340$	12.1257	−	53.1264i	0.657611	−	2.88118i
$341$	−0.451718	−	0.566437i	−0.0244619	−	0.0306743i
$342$		0			0
$343$	10.1331	−	4.87983i	0.547135	−	0.263486i
$344$	−61.4823	+	77.0964i	−3.31490	+	4.15676i
$345$		0			0
$346$	50.3699	−	24.2568i	2.70790	−	1.30406i
$347$	4.44819			0.238791			0.119396	−	0.992847i	$-0.461904\pi$
$347$	4.44819			0.238791			0.119396	+	0.992847i	$0.461904\pi$
$348$		0			0
$349$	−17.0567			−0.913024			−0.456512	−	0.889717i	$-0.650901\pi$
$349$	−17.0567			−0.913024			−0.456512	+	0.889717i	$0.650901\pi$
$350$	3.05109	−	1.46933i	0.163088	−	0.0785389i
$351$		0			0
$352$	21.3932	−	26.8262i	1.14026	−	1.42984i
$353$	−7.89583	+	3.80243i	−0.420252	+	0.202383i	−0.632045	−	0.774932i	$-0.717784\pi$
$353$	−7.89583	+	3.80243i	−0.420252	+	0.202383i	0.211792	+	0.977315i	$0.432070\pi$
$354$		0			0
$355$	8.09906	+	10.1559i	0.429854	+	0.539019i
$356$	−5.86520	+	25.6971i	−0.310855	+	1.36194i
$357$		0			0
$358$	−42.5950	+	53.4124i	−2.25121	+	2.82293i
$359$	0.501253	+	2.19613i	0.0264551	+	0.115907i	0.986431	−	0.164174i	$-0.0524958\pi$
$359$	0.501253	+	2.19613i	0.0264551	+	0.115907i	−0.959976	+	0.280081i	$0.909639\pi$
$360$		0			0
$361$	2.28508	+	10.0116i	0.120267	+	0.526925i
$362$	48.5824	+	23.3961i	2.55344	+	1.22967i
$363$		0			0
$364$	2.39292	+	10.4840i	0.125423	+	0.549513i
$365$	3.50169			0.183287
$366$		0			0
$367$	5.57199	−	6.98706i	0.290856	−	0.364721i	−0.614839	−	0.788653i	$-0.710779\pi$
$367$	5.57199	−	6.98706i	0.290856	−	0.364721i	0.905694	+	0.423932i	$0.139350\pi$
$368$	24.6408	−	107.958i	1.28449	−	5.62771i
$369$		0			0
$370$	17.6472	+	22.1289i	0.917433	+	1.15042i
$371$	3.01171	+	1.45036i	0.156360	+	0.0752990i
$372$		0			0
$373$	−2.98091	+	3.73794i	−0.154346	+	0.193543i	−0.852992	−	0.521924i	$-0.825215\pi$
$373$	−2.98091	+	3.73794i	−0.154346	+	0.193543i	0.698647	+	0.715467i	$0.253786\pi$
$374$	−8.18347	−	10.2618i	−0.423157	−	0.530623i
$375$		0			0
$376$	−29.0783			−1.49960
$377$	−9.28014	−	7.54886i	−0.477952	−	0.388786i
$378$		0			0
$379$	−30.8943	+	14.8779i	−1.58693	+	0.764226i	−0.999001	−	0.0446854i	$-0.985771\pi$
$379$	−30.8943	+	14.8779i	−1.58693	+	0.764226i	−0.587931	+	0.808911i	$0.700057\pi$
$380$	−26.7293	−	33.5175i	−1.37118	−	1.71941i
$381$		0			0
$382$	2.31058	−	1.11272i	0.118220	−	0.0569315i
$383$	21.4436	+	10.3267i	1.09572	+	0.527669i	0.892309	−	0.451426i	$-0.149084\pi$
$383$	21.4436	+	10.3267i	1.09572	+	0.527669i	0.203407	+	0.979094i	$0.434799\pi$
$384$		0			0
$385$	0.601453	−	2.63514i	0.0306529	−	0.134299i
$386$	6.02399	−	26.3928i	0.306613	−	1.34336i
$387$		0			0
$388$	5.87757	+	25.7513i	0.298388	+	1.30733i
$389$	−18.5239			−0.939198			−0.469599	−	0.882880i	$-0.655601\pi$
$389$	−18.5239			−0.939198			−0.469599	+	0.882880i	$0.655601\pi$
$390$		0			0
$391$	−21.7186	−	10.4591i	−1.09836	−	0.528942i
$392$	−58.4586	−	28.1522i	−2.95260	−	1.42190i
$393$		0			0
$394$	−20.7521			−1.04547
$395$	−0.152104	−	0.666413i	−0.00765320	−	0.0335309i
$396$		0			0
$397$	2.41408	−	10.5768i	0.121159	−	0.530833i	−0.877524	−	0.479533i	$-0.840806\pi$
$397$	2.41408	−	10.5768i	0.121159	−	0.530833i	0.998683	−	0.0513005i	$-0.0163366\pi$
$398$	16.0255	−	70.2125i	0.803287	−	3.51943i
$399$		0			0
$400$	−22.3800	−	10.7776i	−1.11900	−	0.538881i
$401$	25.8578	−	12.4525i	1.29128	−	0.621846i	0.343013	−	0.939331i	$-0.388553\pi$
$401$	25.8578	−	12.4525i	1.29128	−	0.621846i	0.948263	+	0.317485i	$0.102838\pi$
$402$		0			0
$403$	−0.797689	−	1.00027i	−0.0397357	−	0.0498270i
$404$	−46.9470	+	22.6085i	−2.33570	+	1.12481i
$405$		0			0
$406$	−12.3759	+	2.69888i	−0.614205	+	0.133943i
$407$	5.05060			0.250349
$408$		0			0
$409$	−15.7089	−	19.6984i	−0.776756	−	0.974021i	0.223244	−	0.974763i	$-0.428335\pi$
$409$	−15.7089	−	19.6984i	−0.776756	−	0.974021i	−1.00000		0.000741524i	$0.999764\pi$
$410$	−40.8767	+	51.2577i	−2.01875	+	2.53144i
$411$		0			0
$412$	74.2064	+	35.7359i	3.65589	+	1.76058i
$413$	−1.18550	−	1.48657i	−0.0583345	−	0.0731491i
$414$		0			0
$415$	−3.85947	+	16.9095i	−0.189454	+	0.830052i
$416$	37.7782	−	47.3724i	1.85223	−	2.32262i
$417$		0			0
$418$	−10.3259			−0.505057
$419$	2.88089	+	12.6220i	0.140741	+	0.616625i	0.995264	+	0.0972114i	$0.0309923\pi$
$419$	2.88089	+	12.6220i	0.140741	+	0.616625i	−0.854523	+	0.519413i	$0.826151\pi$
$420$		0			0
$421$	−17.6399	−	8.49493i	−0.859716	−	0.414018i	−0.0485414	−	0.998821i	$-0.515457\pi$
$421$	−17.6399	−	8.49493i	−0.859716	−	0.414018i	−0.811175	+	0.584804i	$0.801172\pi$
$422$	11.9066	+	52.1661i	0.579602	+	2.53940i
$423$		0			0
$424$	−9.07207	−	39.7473i	−0.440579	−	1.93030i
$425$	−3.37147	+	4.22769i	−0.163540	+	0.205073i
$426$		0			0
$427$	0.897981	−	3.93431i	0.0434563	−	0.190395i
$428$	6.53569	+	8.19550i	0.315915	+	0.396144i
$429$		0			0
$430$	60.6503	−	29.2076i	2.92482	−	1.40852i
$431$	2.24797	−	2.81887i	0.108281	−	0.135780i	−0.724738	−	0.689025i	$-0.758039\pi$
$431$	2.24797	−	2.81887i	0.108281	−	0.135780i	0.833019	+	0.553245i	$0.186611\pi$
$432$		0			0
$433$	4.33066	−	2.08554i	0.208118	−	0.100225i	−0.326921	−	0.945052i	$-0.606011\pi$
$433$	4.33066	−	2.08554i	0.208118	−	0.100225i	0.535039	+	0.844827i	$0.320297\pi$
$434$	−1.35469			−0.0650272
$435$		0			0
$436$	82.0190			3.92800
$437$	−17.0865	+	8.22842i	−0.817358	+	0.393619i
$438$		0			0
$439$	4.70521	−	5.90014i	0.224567	−	0.281599i	−0.656765	−	0.754095i	$-0.728076\pi$
$439$	4.70521	−	5.90014i	0.224567	−	0.281599i	0.881332	+	0.472497i	$0.156647\pi$
$440$	−29.7011	+	14.3033i	−1.41595	+	0.681884i
$441$		0			0
$442$	−14.4512	−	18.1212i	−0.687373	−	0.861939i
$443$	5.07740	−	22.2456i	0.241235	−	1.05692i	−0.698660	−	0.715454i	$-0.746220\pi$
$443$	5.07740	−	22.2456i	0.241235	−	1.05692i	0.939895	−	0.341465i	$-0.110923\pi$
$444$		0			0
$445$	7.29426	−	9.14672i	0.345781	−	0.433596i
$446$	−0.487178	−	2.13447i	−0.0230686	−	0.101070i
$447$		0			0
$448$	−7.77505	−	34.0647i	−0.367337	−	1.60941i
$449$	−11.7896	−	5.67759i	−0.556388	−	0.267942i	0.134489	−	0.990915i	$-0.457061\pi$
$449$	−11.7896	−	5.67759i	−0.556388	−	0.267942i	−0.690876	+	0.722973i	$0.742775\pi$
$450$		0			0
$451$	2.60324	+	11.4055i	0.122582	+	0.537066i
$452$	67.3459			3.16768
$453$		0			0
$454$	−32.5990	+	40.8778i	−1.52995	+	1.91849i
$455$	1.06210	−	4.65339i	0.0497922	−	0.218154i
$456$		0			0
$457$	−19.5401	−	24.5025i	−0.914048	−	1.14618i	−0.988840	−	0.148981i	$-0.952401\pi$
$457$	−19.5401	−	24.5025i	−0.914048	−	1.14618i	0.0747922	−	0.997199i	$-0.476171\pi$
$458$	67.3432	+	32.4308i	3.14674	+	1.51539i
$459$		0			0
$460$	−58.0589	+	72.8036i	−2.70701	+	3.39448i
$461$	−23.7681	−	29.8043i	−1.10699	−	1.38813i	−0.913410	−	0.407042i	$-0.866560\pi$
$461$	−23.7681	−	29.8043i	−1.10699	−	1.38813i	−0.193584	−	0.981084i	$-0.562011\pi$
$462$		0			0
$463$	39.1593			1.81989			0.909944	−	0.414732i	$-0.136125\pi$
$463$	39.1593			1.81989			0.909944	+	0.414732i	$0.136125\pi$
$464$	72.0767	+	58.6302i	3.34608	+	2.72184i
$465$		0			0
$466$	32.8332	−	15.8116i	1.52097	−	0.732460i
$467$	−8.74298	−	10.9633i	−0.404577	−	0.507323i	0.537249	−	0.843423i	$-0.319463\pi$
$467$	−8.74298	−	10.9633i	−0.404577	−	0.507323i	−0.941826	+	0.336100i	$0.890892\pi$
$468$		0			0
$469$	0.109836	−	0.0528945i	0.00507178	−	0.00244244i
$470$	17.8846	+	8.61279i	0.824957	+	0.397278i
$471$		0			0
$472$	−5.16029	+	22.6087i	−0.237522	+	1.04065i
$473$	2.67295	−	11.7110i	0.122902	−	0.538471i
$474$		0			0
$475$	0.946631	+	4.14746i	0.0434344	+	0.190299i
$476$	−18.1818			−0.833361
$477$		0			0
$478$	−10.1345	−	4.88053i	−0.463542	−	0.223230i
$479$	−37.6742	−	18.1430i	−1.72138	−	0.828973i	−0.988971	−	0.148107i	$-0.952682\pi$
$479$	−37.6742	−	18.1430i	−1.72138	−	0.828973i	−0.732408	−	0.680866i	$-0.761604\pi$
$480$		0			0
$481$	8.91885			0.406665
$482$	2.48960	+	10.9077i	0.113398	+	0.496830i
$483$		0			0
$484$	11.9813	−	52.4933i	0.544603	−	2.38606i
$485$	2.60878	−	11.4298i	0.118459	−	0.519002i
$486$		0			0
$487$	−12.7105	−	6.12107i	−0.575969	−	0.277372i	0.123138	−	0.992390i	$-0.460704\pi$
$487$	−12.7105	−	6.12107i	−0.575969	−	0.277372i	−0.699106	+	0.715018i	$0.746419\pi$
$488$	−44.3444	+	21.3551i	−2.00738	+	0.966701i
$489$		0			0
$490$	27.6166	+	34.6301i	1.24759	+	1.56443i
$491$	23.9429	−	11.5303i	1.08053	−	0.520354i	0.193041	−	0.981191i	$-0.438165\pi$
$491$	23.9429	−	11.5303i	1.08053	−	0.520354i	0.887485	+	0.460837i	$0.152451\pi$
$492$		0			0
$493$	15.9347	−	12.4569i	0.717662	−	0.561033i
$494$	−18.2345			−0.820411
$495$		0			0
$496$	6.19546	+	7.76887i	0.278185	+	0.348832i
$497$	2.70230	−	3.38858i	0.121215	−	0.151998i
$498$		0			0
$499$	−17.2217	−	8.29352i	−0.770948	−	0.371269i	0.00669320	−	0.999978i	$-0.497869\pi$
$499$	−17.2217	−	8.29352i	−0.770948	−	0.371269i	−0.777641	+	0.628709i	$0.783584\pi$
$500$	−32.2063	−	40.3854i	−1.44031	−	1.80609i
$501$		0			0
$502$	−18.7453	+	82.1284i	−0.836642	+	3.66557i
$503$	−10.0746	+	12.6332i	−0.449206	+	0.563287i	−0.953944	−	0.299986i	$-0.903018\pi$
$503$	−10.0746	+	12.6332i	−0.449206	+	0.563287i	0.504737	+	0.863273i	$0.331589\pi$
$504$		0			0
$505$	23.1280			1.02918
$506$	4.99093	+	21.8667i	0.221874	+	0.972093i
$507$		0			0
$508$	−61.9645	−	29.8405i	−2.74923	−	1.32396i
$509$	−5.58653	−	24.4762i	−0.247619	−	1.08489i	−0.933895	−	0.357548i	$-0.883613\pi$
$509$	−5.58653	−	24.4762i	−0.247619	−	1.08489i	0.686276	−	0.727341i	$-0.259244\pi$
$510$		0			0
$511$	−0.259985	−	1.13907i	−0.0115010	−	0.0503894i
$512$	−71.2398	+	89.3318i	−3.14838	+	3.94795i
$513$		0			0
$514$	5.03620	−	22.0650i	0.222137	−	0.973246i
$515$	−22.7930	−	28.5815i	−1.00438	−	1.25945i
$516$		0			0
$517$	3.19137	−	1.53688i	0.140356	−	0.0675921i
$518$	5.88808	−	7.38342i	0.258708	−	0.324409i
$519$		0			0
$520$	−52.4492	+	25.2582i	−2.30005	+	1.10765i
$521$	−2.82291			−0.123674			−0.0618370	−	0.998086i	$-0.519696\pi$
$521$	−2.82291			−0.123674			−0.0618370	+	0.998086i	$0.519696\pi$
$522$		0			0
$523$	30.2113			1.32105			0.660523	−	0.750805i	$-0.270334\pi$
$523$	30.2113			1.32105			0.660523	+	0.750805i	$0.270334\pi$
$524$	−12.2797	+	5.91359i	−0.536441	+	0.258336i
$525$		0			0
$526$	−9.82186	+	12.3162i	−0.428253	+	0.537013i
$527$	1.94892	−	0.938550i	0.0848963	−	0.0408839i
$528$		0			0
$529$	11.3432	+	14.2240i	0.493184	+	0.618433i
$530$	−6.19311	+	27.1338i	−0.269011	+	1.17862i
$531$		0			0
$532$	−8.91839	+	11.1833i	−0.386661	+	0.484858i
$533$	4.59706	+	20.1410i	0.199121	+	0.872405i
$534$		0			0
$535$	−1.03532	−	4.53602i	−0.0447606	−	0.196109i
$536$	−1.33961	−	0.645123i	−0.0578625	−	0.0278651i
$537$		0			0
$538$	−12.7051	−	55.6645i	−0.547754	−	2.39987i
$539$	7.90383			0.340442
$540$		0			0
$541$	8.40733	−	10.5425i	0.361459	−	0.453256i	−0.567535	−	0.823349i	$-0.692103\pi$
$541$	8.40733	−	10.5425i	0.361459	−	0.453256i	0.928995	+	0.370094i	$0.120674\pi$
$542$	5.92928	−	25.9779i	0.254684	−	1.11584i
$543$		0			0
$544$	63.8736	+	80.0950i	2.73856	+	3.43405i
$545$	−32.7993	−	15.7953i	−1.40497	−	0.676596i
$546$		0			0
$547$	14.5525	−	18.2482i	0.622219	−	0.780238i	−0.366436	−	0.930443i	$-0.619422\pi$
$547$	14.5525	−	18.2482i	0.622219	−	0.780238i	0.988655	+	0.150206i	$0.0479935\pi$
$548$	48.3736	+	60.6585i	2.06642	+	2.59120i
$549$		0			0
$550$	5.03126			0.214534
$551$	0.154107	−	15.9114i	0.00656520	−	0.677850i
$552$		0			0
$553$	−0.205485	+	0.0989562i	−0.00873810	+	0.00420805i
$554$	44.7596	+	56.1268i	1.90165	+	2.38460i
$555$		0			0
$556$	−102.931	+	49.5688i	−4.36523	+	2.10219i
$557$	3.00534	+	1.44729i	0.127340	+	0.0613238i	0.496469	−	0.868054i	$-0.334630\pi$
$557$	3.00534	+	1.44729i	0.127340	+	0.0613238i	−0.369129	+	0.929378i	$0.620344\pi$
$558$		0			0
$559$	4.72016	−	20.6804i	0.199642	−	0.874687i
$560$	−8.24912	+	36.1418i	−0.348589	+	1.52727i
$561$		0			0
$562$	11.3130	+	49.5654i	0.477209	+	2.09079i
$563$	−7.82895			−0.329951			−0.164976	−	0.986298i	$-0.552755\pi$
$563$	−7.82895			−0.329951			−0.164976	+	0.986298i	$0.552755\pi$
$564$		0			0
$565$	−26.9315	−	12.9695i	−1.13302	−	0.545633i
$566$	−34.5413	−	16.6342i	−1.45188	−	0.699188i
$567$		0			0
$568$	−52.8612			−2.21801
$569$	0.0380192	+	0.166573i	0.00159385	+	0.00698310i	0.975719	−	0.219028i	$-0.0702886\pi$
$569$	0.0380192	+	0.166573i	0.00159385	+	0.00698310i	−0.974125	+	0.226011i	$0.927431\pi$
$570$		0			0
$571$	−5.95314	+	26.0824i	−0.249131	+	1.09152i	0.683291	+	0.730146i	$0.260548\pi$
$571$	−5.95314	+	26.0824i	−0.249131	+	1.09152i	−0.932423	+	0.361370i	$0.882309\pi$
$572$	−3.55516	+	15.5762i	−0.148649	+	0.651273i
$573$		0			0
$574$	19.7086	+	9.49114i	0.822619	+	0.396153i
$575$	8.32533	−	4.00927i	0.347190	−	0.167198i
$576$		0			0
$577$	−24.4227	−	30.6252i	−1.01673	−	1.27494i	−0.961015	−	0.276495i	$-0.910827\pi$
$577$	−24.4227	−	30.6252i	−1.01673	−	1.27494i	−0.0557170	−	0.998447i	$-0.517744\pi$
$578$	−7.24202	+	3.48757i	−0.301228	+	0.145064i
$579$		0			0
$580$	−33.2166	−	70.7191i	−1.37925	−	2.93645i
$581$	5.78703			0.240087
$582$		0			0
$583$	3.09645	+	3.88283i	0.128242	+	0.160810i
$584$	−8.88462	+	11.1410i	−0.367648	+	0.461016i
$585$		0			0
$586$	33.1003	+	15.9403i	1.36736	+	0.658486i
$587$	1.30417	+	1.63538i	0.0538290	+	0.0674994i	0.808017	−	0.589159i	$-0.200541\pi$
$587$	1.30417	+	1.63538i	0.0538290	+	0.0674994i	−0.754188	+	0.656658i	$0.771969\pi$
$588$		0			0
$589$	0.378683	−	1.65912i	0.0156033	−	0.0683627i
$590$	9.87041	−	12.3771i	0.406358	−	0.509557i
$591$		0			0
$592$	−69.2706			−2.84701
$593$	4.80876	+	21.0685i	0.197472	+	0.865181i	0.972435	+	0.233174i	$0.0749113\pi$
$593$	4.80876	+	21.0685i	0.197472	+	0.865181i	−0.774963	+	0.632007i	$0.782232\pi$
$594$		0			0
$595$	7.27087	+	3.50147i	0.298077	+	0.143546i
$596$	−20.5258	−	89.9294i	−0.840769	−	3.68365i
$597$		0			0
$598$	8.81348	+	38.6144i	0.360410	+	1.57906i
$599$	6.19230	−	7.76490i	0.253011	−	0.317265i	−0.639064	−	0.769154i	$-0.720678\pi$
$599$	6.19230	−	7.76490i	0.253011	−	0.317265i	0.892074	+	0.451888i	$0.149249\pi$
$600$		0			0
$601$	−3.45048	+	15.1175i	−0.140748	+	0.616657i	0.854514	+	0.519428i	$0.173855\pi$
$601$	−3.45048	+	15.1175i	−0.140748	+	0.616657i	−0.995262	+	0.0972287i	$0.969002\pi$
$602$	−14.0040	−	17.5604i	−0.570759	−	0.715710i
$603$		0			0
$604$	−14.4306	+	6.94941i	−0.587172	+	0.282767i
$605$	−14.9005	+	18.6846i	−0.605792	+	0.759639i
$606$		0			0
$607$	−0.363257	+	0.174936i	−0.0147442	+	0.00710042i	−0.441241	−	0.897388i	$-0.645462\pi$
$607$	−0.363257	+	0.174936i	−0.0147442	+	0.00710042i	0.426497	+	0.904489i	$0.359747\pi$
$608$	80.5959			3.26859
$609$		0			0
$610$	33.5993			1.36040
$611$	5.63564	−	2.71398i	0.227994	−	0.109796i
$612$		0			0
$613$	−9.22408	+	11.5666i	−0.372557	+	0.467172i	−0.932401	−	0.361426i	$-0.882290\pi$
$613$	−9.22408	+	11.5666i	−0.372557	+	0.467172i	0.559843	+	0.828598i	$0.310861\pi$
$614$	58.3875	−	28.1180i	2.35633	−	1.13475i
$615$		0			0
$616$	6.85791	+	8.59954i	0.276313	+	0.346485i
$617$	0.133056	−	0.582958i	0.00535665	−	0.0234690i	−0.972179	−	0.234239i	$-0.924740\pi$
$617$	0.133056	−	0.582958i	0.00535665	−	0.0234690i	0.977536	+	0.210770i	$0.0675972\pi$
$618$		0			0
$619$	3.30388	−	4.14293i	0.132794	−	0.166518i	−0.710989	−	0.703204i	$-0.751752\pi$
$619$	3.30388	−	4.14293i	0.132794	−	0.166518i	0.843783	+	0.536685i	$0.180324\pi$
$620$	−1.85940	−	8.14655i	−0.0746751	−	0.327173i
$621$		0			0
$622$	3.51385	+	15.3952i	0.140893	+	0.617291i
$623$	−3.51691	−	1.69365i	−0.140902	−	0.0678548i
$624$		0			0
$625$	6.70362	+	29.3705i	0.268145	+	1.17482i
$626$	−11.0892			−0.443214
$627$		0			0
$628$	30.2868	−	37.9785i	1.20858	−	1.51551i
$629$	−3.35552	+	14.7015i	−0.133793	+	0.586187i
$630$		0			0
$631$	−16.5526	−	20.7564i	−0.658950	−	0.826298i	0.334278	−	0.942474i	$-0.391508\pi$
$631$	−16.5526	−	20.7564i	−0.658950	−	0.826298i	−0.993229	+	0.116177i	$0.962936\pi$
$632$	2.50618	+	1.20691i	0.0996904	+	0.0480084i
$633$		0			0
$634$	21.2792	−	26.6832i	0.845104	−	1.05973i
$635$	19.0328	+	23.8664i	0.755293	+	0.947108i
$636$		0			0
$637$	13.9574			0.553011
$638$	−18.3058	−	4.36512i	−0.724732	−	0.172817i
$639$		0			0
$640$	137.381	−	66.1590i	5.43044	−	2.61516i
$641$	−3.27345	−	4.10477i	−0.129293	−	0.162129i	0.712971	−	0.701194i	$-0.247349\pi$
$641$	−3.27345	−	4.10477i	−0.129293	−	0.162129i	−0.842264	+	0.539065i	$0.818778\pi$
$642$		0			0
$643$	−16.1356	+	7.77051i	−0.636327	+	0.306439i	−0.724093	−	0.689702i	$-0.757742\pi$
$643$	−16.1356	+	7.77051i	−0.636327	+	0.306439i	0.0877660	+	0.996141i	$0.472027\pi$
$644$	27.9929	+	13.4807i	1.10308	+	0.531213i
$645$		0			0
$646$	6.86034	−	30.0571i	0.269916	−	1.18258i
$647$	−7.79104	+	34.1348i	−0.306297	+	1.34198i	0.554141	+	0.832423i	$0.313047\pi$
$647$	−7.79104	+	34.1348i	−0.306297	+	1.34198i	−0.860439	+	0.509554i	$0.829810\pi$
$648$		0			0
$649$	−0.628599	−	2.75407i	−0.0246747	−	0.108107i
$650$	8.88471			0.348487
$651$		0			0
$652$	106.855	+	51.4587i	4.18477	+	2.01528i
$653$	16.7006	+	8.04260i	0.653546	+	0.314731i	0.731113	−	0.682256i	$-0.239001\pi$
$653$	16.7006	+	8.04260i	0.653546	+	0.314731i	−0.0775675	+	0.996987i	$0.524715\pi$
$654$		0			0
$655$	6.04947			0.236372
$656$	−35.7043	−	156.431i	−1.39402	−	6.10759i
$657$		0			0
$658$	1.47381	−	6.45717i	0.0574549	−	0.251727i
$659$	−0.290833	+	1.27422i	−0.0113293	+	0.0496367i	−0.980277	−	0.197630i	$-0.936675\pi$
$659$	−0.290833	+	1.27422i	−0.0113293	+	0.0496367i	0.968947	+	0.247267i	$0.0795325\pi$
$660$		0			0
$661$	−30.7540	−	14.8103i	−1.19619	−	0.576055i	−0.273603	−	0.961843i	$-0.588215\pi$
$661$	−30.7540	−	14.8103i	−1.19619	−	0.576055i	−0.922588	+	0.385788i	$0.873930\pi$
$662$	−38.7777	+	18.6744i	−1.50714	+	0.725800i
$663$		0			0
$664$	−44.0066	−	55.1826i	−1.70779	−	2.14150i
$665$	5.72014	−	2.75467i	0.221818	−	0.106822i
$666$		0			0
$667$	−33.7693	+	7.36429i	−1.30755	+	0.285146i
$668$	−56.0279			−2.16778
$669$		0			0
$670$	0.632850	+	0.793569i	0.0244491	+	0.0306582i
$671$	3.73815	−	4.68750i	0.144310	−	0.180959i
$672$		0			0
$673$	17.1253	+	8.24713i	0.660134	+	0.317904i	0.733786	−	0.679380i	$-0.237751\pi$
$673$	17.1253	+	8.24713i	0.660134	+	0.317904i	−0.0736527	+	0.997284i	$0.523466\pi$
$674$	0.0558641	+	0.0700513i	0.00215180	+	0.00269828i
$675$		0			0
$676$	10.2609	−	44.9559i	0.394650	−	1.72907i
$677$	−14.7723	+	18.5239i	−0.567746	+	0.711930i	−0.979968	−	0.199153i	$-0.936181\pi$
$677$	−14.7723	+	18.5239i	−0.567746	+	0.711930i	0.412223	+	0.911083i	$0.364752\pi$
$678$		0			0
$679$	−3.91170			−0.150117
$680$	−21.9018	−	95.9581i	−0.839896	−	3.67983i
$681$		0			0
$682$	−1.81335	−	0.873263i	−0.0694368	−	0.0334390i
$683$	3.23113	+	14.1565i	0.123636	+	0.541683i	0.998370	+	0.0570798i	$0.0181789\pi$
$683$	3.23113	+	14.1565i	0.123636	+	0.541683i	−0.874734	+	0.484603i	$0.838964\pi$
$684$		0			0
$685$	−7.66284	−	33.5731i	−0.292782	−	1.28276i
$686$	19.4803	−	24.4275i	0.743760	−	0.932645i
$687$		0			0
$688$	−36.6604	+	160.620i	−1.39766	+	6.12357i
$689$	5.46802	+	6.85668i	0.208315	+	0.261219i
$690$		0			0
$691$	11.3521	−	5.46688i	0.431854	−	0.207970i	−0.205312	−	0.978697i	$-0.565821\pi$
$691$	11.3521	−	5.46688i	0.431854	−	0.207970i	0.637166	+	0.770727i	$0.280107\pi$
$692$	71.7382	−	89.9568i	2.72708	−	3.41964i
$693$		0			0
$694$	11.1334	−	5.36155i	0.422617	−	0.203522i
$695$	50.7078			1.92346
$696$		0			0
$697$	−34.9292			−1.32304
$698$	−42.6912	+	20.5590i	−1.61588	+	0.778169i
$699$		0			0
$700$	4.34545	−	5.44902i	0.164243	−	0.205954i
$701$	32.7410	−	15.7672i	1.23661	−	0.595521i	0.302721	−	0.953079i	$-0.402105\pi$
$701$	32.7410	−	15.7672i	1.23661	−	0.595521i	0.933891	+	0.357559i	$0.116391\pi$
$702$		0			0
$703$	7.39671	+	9.27518i	0.278972	+	0.349820i
$704$	11.5514	−	50.6101i	0.435360	−	1.90744i
$705$		0			0
$706$	−15.1793	+	19.0342i	−0.571279	+	0.716362i
$707$	−1.71715	−	7.52332i	−0.0645800	−	0.282943i
$708$		0			0
$709$	4.48293	+	19.6410i	0.168360	+	0.737633i	0.986654	+	0.162833i	$0.0520630\pi$
$709$	4.48293	+	19.6410i	0.168360	+	0.737633i	−0.818294	+	0.574800i	$0.805080\pi$
$710$	32.5124	+	15.6571i	1.22017	+	0.587602i
$711$		0			0
$712$	10.5939	+	46.4148i	0.397022	+	1.73947i
$713$	−3.69646			−0.138434
$714$		0			0
$715$	4.42138	−	5.54423i	0.165350	−	0.207343i
$716$	−31.2867	+	137.076i	−1.16924	+	5.12277i
$717$		0			0
$718$	3.90165	+	4.89252i	0.145608	+	0.182587i
$719$	−17.5840	−	8.46801i	−0.655773	−	0.315804i	0.0762449	−	0.997089i	$-0.475707\pi$
$719$	−17.5840	−	8.46801i	−0.655773	−	0.315804i	−0.732018	+	0.681286i	$0.761421\pi$
$720$		0			0
$721$	−7.60501	+	9.53639i	−0.283226	+	0.355154i
$722$	17.7866	+	22.3037i	0.661949	+	0.830058i
$723$		0			0
$724$	110.976			4.12439
$725$	−0.0750882	+	7.75279i	−0.00278871	+	0.287931i
$726$		0			0
$727$	0.886876	−	0.427097i	0.0328924	−	0.0158401i	−0.417365	−	0.908739i	$-0.637046\pi$
$727$	0.886876	−	0.427097i	0.0328924	−	0.0158401i	0.450258	+	0.892899i	$0.351332\pi$
$728$	12.1104	+	15.1859i	0.448840	+	0.562828i
$729$		0			0
$730$	8.76438	−	4.22070i	0.324384	−	0.156215i
$731$	32.3129	+	15.5611i	1.19514	+	0.575547i
$732$		0			0
$733$	7.34197	−	32.1673i	0.271182	−	1.18812i	−0.637438	−	0.770501i	$-0.720006\pi$
$733$	7.34197	−	32.1673i	0.271182	−	1.18812i	0.908620	−	0.417624i	$-0.137137\pi$
$734$	5.52441	−	24.2040i	0.203910	−	0.893386i
$735$		0			0
$736$	−38.9552	−	170.674i	−1.43591	−	6.29112i
$737$	0.181121			0.00667167
$738$		0			0
$739$	−19.6077	−	9.44255i	−0.721279	−	0.347350i	0.0369684	−	0.999316i	$-0.488230\pi$
$739$	−19.6077	−	9.44255i	−0.721279	−	0.347350i	−0.758248	+	0.651967i	$0.773944\pi$
$740$	52.4826	+	25.2743i	1.92930	+	0.929102i
$741$		0			0
$742$	9.28617			0.340906
$743$	−3.81650	−	16.7212i	−0.140014	−	0.613440i	−0.995430	−	0.0954983i	$-0.969556\pi$
$743$	−3.81650	−	16.7212i	−0.140014	−	0.613440i	0.855416	−	0.517942i	$-0.173302\pi$
$744$		0			0
$745$	−9.11045	+	39.9155i	−0.333781	+	1.46239i
$746$	−2.95545	+	12.9487i	−0.108207	+	0.474085i
$747$		0			0
$748$	−24.3376	−	11.7204i	−0.889871	−	0.428540i
$749$	−1.39866	+	0.673557i	−0.0511058	+	0.0246112i
$750$		0			0
$751$	23.4475	+	29.4022i	0.855610	+	1.07290i	0.996559	+	0.0828839i	$0.0264131\pi$
$751$	23.4475	+	29.4022i	0.855610	+	1.07290i	−0.140949	+	0.990017i	$0.545015\pi$
$752$	−43.7707	+	21.0789i	−1.59615	+	0.768667i
$753$		0			0
$754$	−32.3262	−	7.70836i	−1.17725	−	0.280722i
$755$	7.10910			0.258726
$756$		0			0
$757$	15.4259	+	19.3435i	0.560664	+	0.703050i	0.978680	−	0.205389i	$-0.0658460\pi$
$757$	15.4259	+	19.3435i	0.560664	+	0.703050i	−0.418017	+	0.908439i	$0.637275\pi$
$758$	−59.3924	+	74.4757i	−2.15723	+	2.70508i
$759$		0			0
$760$	−69.7653	−	33.5972i	−2.53065	−	1.21870i
$761$	14.7384	+	18.4813i	0.534266	+	0.669948i	0.973570	−	0.228391i	$-0.0733463\pi$
$761$	14.7384	+	18.4813i	0.534266	+	0.669948i	−0.439304	+	0.898338i	$0.644775\pi$
$762$		0			0
$763$	−2.70286	+	11.8420i	−0.0978503	+	0.428710i
$764$	3.29079	−	4.12652i	0.119057	−	0.149292i
$765$		0			0
$766$	66.1182			2.38895
$767$	−1.11004	−	4.86341i	−0.0400813	−	0.175608i
$768$		0			0
$769$	1.87153	+	0.901284i	0.0674893	+	0.0325011i	0.467324	−	0.884086i	$-0.345218\pi$
$769$	1.87153	+	0.901284i	0.0674893	+	0.0325011i	−0.399835	+	0.916587i	$0.630932\pi$
$770$	−1.67084	−	7.32043i	−0.0602129	−	0.263810i
$771$		0			0
$772$	−12.3978	−	54.3183i	−0.446206	−	1.95496i
$773$	−8.08528	+	10.1386i	−0.290807	+	0.364661i	−0.905677	−	0.423968i	$-0.860637\pi$
$773$	−8.08528	+	10.1386i	−0.290807	+	0.364661i	0.614870	+	0.788628i	$0.289208\pi$
$774$		0			0
$775$	−0.184512	+	0.808398i	−0.00662786	+	0.0290385i
$776$	29.7460	+	37.3003i	1.06782	+	1.33900i
$777$		0			0
$778$	−46.3634	+	22.3274i	−1.66221	+	0.800478i
$779$	−17.1332	+	21.4844i	−0.613861	+	0.769758i
$780$		0			0
$781$	5.80158	−	2.79389i	0.207597	−	0.0999733i
$782$	−66.9663			−2.39471
$783$		0			0
$784$	−108.404			−3.87156
$785$	−19.4256	+	9.35487i	−0.693329	+	0.333890i
$786$		0			0
$787$	−4.28528	+	5.37357i	−0.152754	+	0.191547i	−0.852320	−	0.523020i	$-0.824805\pi$
$787$	−4.28528	+	5.37357i	−0.152754	+	0.191547i	0.699566	+	0.714568i	$0.253377\pi$
$788$	−38.4796	+	18.5308i	−1.37078	+	0.660133i
$789$		0			0
$790$	−1.18395	−	1.48463i	−0.0421231	−	0.0528207i
$791$	−2.21933	+	9.72350i	−0.0789101	+	0.345728i
$792$		0			0
$793$	6.60120	−	8.27765i	0.234416	−	0.293948i
$794$	−6.70634	−	29.3824i	−0.237999	−	1.04274i
$795$		0			0
$796$	−32.9817	−	144.502i	−1.16900	−	5.12174i
$797$	−12.1118	−	5.83274i	−0.429023	−	0.206606i	0.206895	−	0.978363i	$-0.433664\pi$
$797$	−12.1118	−	5.83274i	−0.429023	−	0.206606i	−0.635918	+	0.771757i	$0.719378\pi$
$798$		0			0
$799$	2.35334	+	10.3106i	0.0832551	+	0.364765i
$800$	−39.2700			−1.38840
$801$		0			0
$802$	49.7101	−	62.3345i	1.75532	−	2.20111i
$803$	0.386260	−	1.69232i	0.0136308	−	0.0597205i
$804$		0			0
$805$	−8.59821	−	10.7818i	−0.303047	−	0.380009i
$806$	−3.20219	−	1.54210i	−0.112792	−	0.0543180i
$807$		0			0
$808$	−58.6812	+	73.5839i	−2.06440	+	2.58867i
$809$	−22.3326	−	28.0043i	−0.785174	−	0.984577i	−0.999969	−	0.00791779i	$-0.997480\pi$
$809$	−22.3326	−	28.0043i	−0.785174	−	0.984577i	0.214795	−	0.976659i	$-0.431092\pi$
$810$		0			0
$811$	−42.0554			−1.47677			−0.738383	−	0.674382i	$-0.764410\pi$
$811$	−42.0554			−1.47677			−0.738383	+	0.674382i	$0.764410\pi$
$812$	−20.5381	+	16.0556i	−0.720745	+	0.563442i
$813$		0			0
$814$	12.6411	−	6.08765i	0.443072	−	0.213372i
$815$	−32.8212	−	41.1565i	−1.14968	−	1.44165i
$816$		0			0
$817$	25.4212	−	12.2422i	0.889376	−	0.428301i
$818$	−63.0609	−	30.3685i	−2.20487	−	1.06181i
$819$		0			0
$820$	−30.0246	+	131.546i	−1.04850	+	4.59380i
$821$	−4.17288	+	18.2826i	−0.145635	+	0.638067i	0.848433	+	0.529303i	$0.177546\pi$
$821$	−4.17288	+	18.2826i	−0.145635	+	0.638067i	−0.994068	+	0.108764i	$0.965311\pi$
$822$		0			0
$823$	4.43930	+	19.4498i	0.154744	+	0.677978i	0.991468	+	0.130353i	$0.0416110\pi$
$823$	4.43930	+	19.4498i	0.154744	+	0.677978i	−0.836724	+	0.547626i	$0.815532\pi$
$824$	148.766			5.18251
$825$		0			0
$826$	−4.75899	−	2.29181i	−0.165586	−	0.0797422i
$827$	13.3371	+	6.42279i	0.463775	+	0.223342i	0.651154	−	0.758945i	$-0.274285\pi$
$827$	13.3371	+	6.42279i	0.463775	+	0.223342i	−0.187379	+	0.982288i	$0.559999\pi$
$828$		0			0
$829$	−33.7345			−1.17165			−0.585824	−	0.810438i	$-0.699229\pi$
$829$	−33.7345			−1.17165			−0.585824	+	0.810438i	$0.699229\pi$
$830$	10.7216	+	46.9746i	0.372154	+	1.63051i
$831$		0			0
$832$	20.3986	−	89.3723i	0.707196	−	3.09843i
$833$	−5.25115	+	23.0068i	−0.181942	+	0.797138i
$834$		0			0
$835$	22.4055	+	10.7899i	0.775373	+	0.373400i
$836$	−19.1469	+	9.22066i	−0.662209	+	0.318903i
$837$		0			0
$838$	22.4243	+	28.1191i	0.774634	+	0.971360i
$839$	16.9843	−	8.17920i	0.586363	−	0.282377i	−0.117088	−	0.993122i	$-0.537356\pi$
$839$	16.9843	−	8.17920i	0.586363	−	0.282377i	0.703451	+	0.710744i	$0.251642\pi$
$840$		0			0
$841$	6.99951	−	28.1426i	0.241362	−	0.970435i
$842$	−54.3901			−1.87441
$843$		0			0
$844$	68.6602	+	86.0971i	2.36338	+	2.96358i
$845$	−12.7610	+	16.0017i	−0.438991	+	0.550477i
$846$		0			0
$847$	7.18423	+	3.45974i	0.246853	+	0.118878i
$848$	−42.4688	−	53.2542i	−1.45839	−	1.82876i
$849$		0			0
$850$	−3.34267	+	14.6452i	−0.114653	+	0.502327i
$851$	16.0665	−	20.1467i	0.550751	−	0.690620i
$852$		0			0
$853$	50.4469			1.72727			0.863634	−	0.504119i	$-0.168183\pi$
$853$	50.4469			1.72727			0.863634	+	0.504119i	$0.168183\pi$
$854$	−2.49460	−	10.9295i	−0.0853634	−	0.374001i
$855$		0			0
$856$	17.0586	+	8.21499i	0.583051	+	0.280783i
$857$	12.6515	+	55.4299i	0.432168	+	1.89345i	0.448884	+	0.893590i	$0.351822\pi$
$857$	12.6515	+	55.4299i	0.432168	+	1.89345i	−0.0167160	+	0.999860i	$0.505321\pi$
$858$		0			0
$859$	3.91095	+	17.1350i	0.133440	+	0.584638i	0.996792	+	0.0800362i	$0.0255036\pi$
$859$	3.91095	+	17.1350i	0.133440	+	0.584638i	−0.863352	+	0.504602i	$0.831639\pi$
$860$	86.3798	−	108.317i	2.94553	−	3.69357i
$861$		0			0
$862$	2.22877	−	9.76490i	0.0759123	−	0.332594i
$863$	19.5746	+	24.5458i	0.666329	+	0.835550i	0.994016	−	0.109237i	$-0.0348406\pi$
$863$	19.5746	+	24.5458i	0.666329	+	0.835550i	−0.327687	+	0.944786i	$0.606269\pi$
$864$		0			0
$865$	−46.0120	+	22.1582i	−1.56445	+	0.753401i
$866$	8.32545	−	10.4398i	0.282910	−	0.354758i
$867$		0			0
$868$	−2.51194	+	1.20969i	−0.0852609	+	0.0410595i
$869$	−0.338845			−0.0114945
$870$		0			0
$871$	0.319841			0.0108374
$872$	133.474	−	64.2776i	4.51999	−	2.17671i
$873$		0			0
$874$	−32.8478	+	41.1898i	−1.11109	+	1.39327i
$875$	6.89223	−	3.31912i	0.233000	−	0.112207i
$876$		0			0
$877$	18.1826	+	22.8002i	0.613981	+	0.769908i	0.987484	−	0.157721i	$-0.0504146\pi$
$877$	18.1826	+	22.8002i	0.613981	+	0.769908i	−0.373502	+	0.927629i	$0.621843\pi$
$878$	4.66502	−	20.4388i	0.157437	−	0.689776i
$879$		0			0
$880$	−34.3398	+	43.0608i	−1.15760	+	1.45158i
$881$	−1.37959	−	6.04439i	−0.0464796	−	0.203641i	0.946357	−	0.323124i	$-0.104733\pi$
$881$	−1.37959	−	6.04439i	−0.0464796	−	0.203641i	−0.992836	+	0.119484i	$0.961876\pi$
$882$		0			0
$883$	11.6283	+	50.9468i	0.391322	+	1.71450i	0.660000	+	0.751265i	$0.270556\pi$
$883$	11.6283	+	50.9468i	0.391322	+	1.71450i	−0.268678	+	0.963230i	$0.586587\pi$
$884$	−42.9778	−	20.6970i	−1.44550	−	0.696116i
$885$		0			0
$886$	−14.1051	−	61.7984i	−0.473869	−	2.07616i
$887$	26.4724			0.888855			0.444428	−	0.895815i	$-0.353407\pi$
$887$	26.4724			0.888855			0.444428	+	0.895815i	$0.353407\pi$
$888$		0			0
$889$	6.35040	−	7.96315i	0.212986	−	0.267076i
$890$	7.23197	−	31.6853i	0.242416	−	1.06209i
$891$		0			0
$892$	−2.80935	−	3.52282i	−0.0940641	−	0.117953i
$893$	7.49624	+	3.61000i	0.250852	+	0.120804i
$894$		0			0
$895$	38.9097	−	48.7913i	1.30061	−	1.63091i
$896$	−31.7208	−	39.7766i	−1.05972	−	1.32884i
$897$		0			0
$898$	−36.3517			−1.21307
$899$	1.37269	−	2.78120i	0.0457819	−	0.0927581i
$900$		0			0
$901$	−13.3595	+	6.43360i	−0.445070	+	0.214334i
$902$	20.2631	+	25.4091i	0.674688	+	0.846032i
$903$		0			0
$904$	109.595	−	52.7784i	3.64509	−	1.75538i
$905$	−44.3792	−	21.3719i	−1.47521	−	0.710425i
$906$		0			0
$907$	4.33990	−	19.0144i	0.144104	−	0.631362i	−0.850352	−	0.526214i	$-0.823611\pi$
$907$	4.33990	−	19.0144i	0.144104	−	0.631362i	0.994457	−	0.105148i	$-0.0335316\pi$
$908$	−23.9445	+	104.908i	−0.794626	+	3.48148i
$909$		0			0
$910$	−2.95054	−	12.9271i	−0.0978093	−	0.428531i
$911$	−26.8766			−0.890461			−0.445231	−	0.895416i	$-0.646878\pi$
$911$	−26.8766			−0.890461			−0.445231	+	0.895416i	$0.646878\pi$
$912$		0			0
$913$	7.74636	+	3.73045i	0.256367	+	0.123460i
$914$	−78.4406	−	37.7750i	−2.59459	−	1.24949i
$915$		0			0
$916$	153.831			5.08272
$917$	−0.449146	−	1.96784i	−0.0148321	−	0.0649837i
$918$		0			0
$919$	5.24040	−	22.9597i	0.172865	−	0.757370i	−0.811945	−	0.583734i	$-0.801591\pi$
$919$	5.24040	−	22.9597i	0.172865	−	0.757370i	0.984810	−	0.173636i	$-0.0555517\pi$
$920$	−37.4268	+	163.977i	−1.23392	+	5.40617i
$921$		0			0
$922$	−95.4134	−	45.9487i	−3.14227	−	1.51324i
$923$	10.2450	−	4.93373i	0.337218	−	0.162396i
$924$		0			0
$925$	−3.60402	−	4.51930i	−0.118499	−	0.148594i
$926$	98.0118	−	47.2000i	3.22087	−	1.55109i
$927$		0			0
$928$	142.880	+	34.0706i	4.69027	+	1.11842i
$929$	26.2377			0.860831			0.430416	−	0.902631i	$-0.358367\pi$
$929$	26.2377			0.860831			0.430416	+	0.902631i	$0.358367\pi$
$930$		0			0
$931$	11.5753	+	14.5150i	0.379366	+	0.475710i
$932$	46.7619	−	58.6376i	1.53174	−	1.92074i
$933$		0			0
$934$	−35.0973	−	16.9020i	−1.14842	−	0.553049i
$935$	7.47546	+	9.37393i	0.244474	+	0.306560i
$936$		0			0
$937$	−9.73863	+	42.6677i	−0.318147	+	1.39389i	0.522651	+	0.852546i	$0.324943\pi$
$937$	−9.73863	+	42.6677i	−0.318147	+	1.39389i	−0.840799	+	0.541348i	$0.817914\pi$
$938$	0.211154	−	0.264779i	0.00689443	−	0.00864534i
$939$		0			0
$940$	40.8536			1.33250
$941$	3.40693	+	14.9267i	0.111063	+	0.486597i	0.999613	+	0.0278180i	$0.00885589\pi$
$941$	3.40693	+	14.9267i	0.111063	+	0.486597i	−0.888550	+	0.458779i	$0.848287\pi$
$942$		0			0
$943$	53.7776	+	25.8979i	1.75124	+	0.843352i
$944$	8.62144	+	37.7730i	0.280604	+	1.22941i
$945$		0			0
$946$	−7.42548	−	32.5332i	−0.241423	−	1.05774i
$947$	7.57022	−	9.49275i	0.245999	−	0.308473i	−0.643467	−	0.765474i	$-0.722505\pi$
$947$	7.57022	−	9.49275i	0.245999	−	0.308473i	0.889466	+	0.457000i	$0.151076\pi$
$948$		0			0
$949$	0.682096	−	2.98846i	0.0221418	−	0.0970095i
$950$	7.36839	+	9.23967i	0.239062	+	0.299775i
$951$		0			0
$952$	−29.5882	+	14.2489i	−0.958958	+	0.461810i
$953$	8.91546	−	11.1796i	0.288800	−	0.362144i	−0.616174	−	0.787610i	$-0.711318\pi$
$953$	8.91546	−	11.1796i	0.288800	−	0.362144i	0.904974	+	0.425466i	$0.139890\pi$
$954$		0			0
$955$	−2.11067	+	1.01645i	−0.0682998	+	0.0328914i
$956$	−23.1501			−0.748729
$957$		0			0
$958$	−116.163			−3.75306
$959$	−10.3521	+	4.98530i	−0.334286	+	0.160984i
$960$		0			0
$961$	−19.1214	+	23.9774i	−0.616818	+	0.773466i
$962$	22.3230	−	10.7502i	0.719722	−	0.346600i
$963$		0			0
$964$	14.3565	+	18.0025i	0.462391	+	0.579820i
$965$	−5.50281	+	24.1094i	−0.177142	+	0.776108i
$966$		0			0
$967$	−7.56263	+	9.48324i	−0.243198	+	0.304960i	−0.888417	−	0.459037i	$-0.848195\pi$
$967$	−7.56263	+	9.48324i	−0.243198	+	0.304960i	0.645219	+	0.763997i	$0.276766\pi$
$968$	−21.6408	−	94.8147i	−0.695563	−	3.04746i
$969$		0			0
$970$	−7.24722	−	31.7521i	−0.232694	−	1.01950i
$971$	−47.0955	−	22.6800i	−1.51137	−	0.727836i	−0.519423	−	0.854517i	$-0.673853\pi$
$971$	−47.0955	−	22.6800i	−1.51137	−	0.727836i	−0.991943	+	0.126681i	$0.959568\pi$
$972$		0			0
$973$	−3.76483	−	16.4948i	−0.120695	−	0.528798i
$974$	−39.1911			−1.25576
$975$		0			0
$976$	−51.2700	+	64.2906i	−1.64111	+	2.05789i
$977$	9.93012	−	43.5067i	0.317693	−	1.39190i	−0.523896	−	0.851782i	$-0.675522\pi$
$977$	9.93012	−	43.5067i	0.317693	−	1.39190i	0.841588	−	0.540120i	$-0.181621\pi$
$978$		0			0
$979$	−3.61586	−	4.53415i	−0.115564	−	0.144912i
$980$	82.1316	+	39.5525i	2.62360	+	1.26346i
$981$		0			0
$982$	46.0288	−	57.7182i	1.46884	−	1.84186i
$983$	−3.24886	−	4.07394i	−0.103622	−	0.129938i	0.727316	−	0.686303i	$-0.240767\pi$
$983$	−3.24886	−	4.07394i	−0.103622	−	0.129938i	−0.830939	+	0.556364i	$0.812196\pi$
$984$		0			0
$985$	18.9566			0.604008
$986$	24.8682	−	50.3851i	0.791964	−	1.60459i
$987$		0			0
$988$	−33.8115	+	16.2828i	−1.07569	+	0.518024i
$989$	−38.2118	−	47.9161i	−1.21506	−	1.52364i
$990$		0			0
$991$	−34.5135	+	16.6208i	−1.09636	+	0.527978i	−0.892511	−	0.451025i	$-0.851059\pi$
$991$	−34.5135	+	16.6208i	−1.09636	+	0.527978i	−0.203846	+	0.979003i	$0.565344\pi$
$992$	14.1536	+	6.81599i	0.449376	+	0.216408i
$993$		0			0
$994$	2.67922	−	11.7384i	0.0849798	−	0.372321i
$995$	−14.6390	+	64.1378i	−0.464089	+	2.03331i
$996$		0			0
$997$	−2.54648	−	11.1568i	−0.0806477	−	0.353341i	0.918463	−	0.395507i	$-0.129431\pi$
$997$	−2.54648	−	11.1568i	−0.0806477	−	0.353341i	−0.999111	+	0.0421665i	$0.986574\pi$
$998$	−53.1005			−1.68087
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	261.2.k.c.136.3		18
3.2	odd	2		87.2.g.a.49.1	yes	18
29.4	even	14		7569.2.a.bm.1.9		9
29.16	even	7	inner	261.2.k.c.190.3		18
29.25	even	7		7569.2.a.bj.1.1		9
87.62	odd	14		2523.2.a.o.1.1		9
87.74	odd	14		87.2.g.a.16.1	✓	18
87.83	odd	14		2523.2.a.r.1.9		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
87.2.g.a.16.1	✓	18	87.74	odd	14
87.2.g.a.49.1	yes	18	3.2	odd	2
261.2.k.c.136.3		18	1.1	even	1	trivial
261.2.k.c.190.3		18	29.16	even	7	inner
2523.2.a.o.1.1		9	87.62	odd	14
2523.2.a.r.1.9		9	87.83	odd	14
7569.2.a.bj.1.1		9	29.25	even	7
7569.2.a.bm.1.9		9	29.4	even	14

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:	\( N \)	\(=\)	\( 261 = 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	261.k (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(2.50290 - 1.20533i) q^{2} +(3.56470 - 4.46999i) q^{4} +(-2.28635 + 1.10105i) q^{5} +(0.527912 + 0.661981i) q^{7} +(2.29793 - 10.0679i) q^{8} +O(q^{10})\)	\(q+(2.50290 - 1.20533i) q^{2} +(3.56470 - 4.46999i) q^{4} +(-2.28635 + 1.10105i) q^{5} +(0.527912 + 0.661981i) q^{7} +(2.29793 - 10.0679i) q^{8} +(-4.39538 + 5.51163i) q^{10} +(0.279921 + 1.22641i) q^{11} +(0.494312 + 2.16572i) q^{13} +(2.11922 + 1.02056i) q^{14} +(-3.83921 - 16.8207i) q^{16} -3.75587 q^{17} +(-1.84230 + 2.31017i) q^{19} +(-3.22848 + 14.1449i) q^{20} +(2.17885 + 2.73219i) q^{22} +(5.78259 + 2.78475i) q^{23} +(0.897653 - 1.12562i) q^{25} +(3.84763 + 4.82478i) q^{26} +4.84090 q^{28} +(-4.24261 + 3.31666i) q^{29} +(-0.518900 + 0.249889i) q^{31} +(-17.0064 - 21.3253i) q^{32} +(-9.40056 + 4.52707i) q^{34} +(-1.93587 - 0.932265i) q^{35} +(0.893407 - 3.91427i) q^{37} +(-1.82657 + 8.00271i) q^{38} +(5.83136 + 25.5489i) q^{40} +9.29991 q^{41} +(-8.60331 - 4.14313i) q^{43} +(6.47989 + 3.12055i) q^{44} +17.8298 q^{46} +(-0.626576 - 2.74521i) q^{47} +(1.39812 - 6.12556i) q^{49} +(0.889987 - 3.89929i) q^{50} +(11.4428 + 5.51058i) q^{52} +(3.55697 - 1.71295i) q^{53} +(-1.99034 - 2.49581i) q^{55} +(7.87785 - 3.79377i) q^{56} +(-6.62115 + 13.4150i) q^{58} -2.24563 q^{59} +(-2.97162 - 3.72629i) q^{61} +(-0.997555 + 1.25089i) q^{62} +(-37.1800 - 17.9050i) q^{64} +(-3.51474 - 4.40735i) q^{65} +(0.0320387 - 0.140371i) q^{67} +(-13.3885 + 16.7887i) q^{68} -5.96898 q^{70} +(-1.13905 - 4.99050i) q^{71} +(-1.24324 - 0.598712i) q^{73} +(-2.48189 - 10.8739i) q^{74} +(3.75920 + 16.4701i) q^{76} +(-0.664089 + 0.832741i) q^{77} +(-0.0599388 + 0.262609i) q^{79} +(27.2982 + 34.2308i) q^{80} +(23.2767 - 11.2095i) q^{82} +(4.26140 - 5.34363i) q^{83} +(8.58724 - 4.13540i) q^{85} -26.5271 q^{86} +12.9906 q^{88} +(-4.15363 + 2.00028i) q^{89} +(-1.17271 + 1.47054i) q^{91} +(33.0610 - 15.9213i) q^{92} +(-4.87715 - 6.11575i) q^{94} +(1.66853 - 7.31033i) q^{95} +(-2.88047 + 3.61199i) q^{97} +(-3.88399 - 17.0169i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 4 q^{2} - 6 q^{4} + q^{5} - 4 q^{7} + 15 q^{8}+O(q^{10}) \) 18 * q + 4 * q^2 - 6 * q^4 + q^5 - 4 * q^7 + 15 * q^8	\( 18 q + 4 q^{2} - 6 q^{4} + q^{5} - 4 q^{7} + 15 q^{8} - 14 q^{10} - 26 q^{11} + 9 q^{13} + 10 q^{14} - 14 q^{16} - 4 q^{17} - 10 q^{19} + q^{20} - 8 q^{22} + 8 q^{23} + 16 q^{25} - 5 q^{26} + 80 q^{28} - 8 q^{29} - 12 q^{31} - 9 q^{32} - 22 q^{34} - 9 q^{35} - 16 q^{37} + 32 q^{38} + 33 q^{40} - 24 q^{41} - 31 q^{43} + 52 q^{44} - 44 q^{46} - 5 q^{47} - 47 q^{49} + 7 q^{50} + 80 q^{52} - 5 q^{53} - 17 q^{55} - 45 q^{56} + 54 q^{58} + 32 q^{59} - 28 q^{61} - 69 q^{62} - 75 q^{64} - 22 q^{65} + 6 q^{67} - 38 q^{68} - 12 q^{70} - 46 q^{71} - q^{73} + 35 q^{74} - 45 q^{76} + 36 q^{77} - 15 q^{79} + 86 q^{80} + 47 q^{82} + 16 q^{83} + 19 q^{85} - 116 q^{86} + 54 q^{88} + 72 q^{89} - 47 q^{91} + 121 q^{92} - 22 q^{94} + 72 q^{95} + 43 q^{97} - 31 q^{98}+O(q^{100}) \) 18 * q + 4 * q^2 - 6 * q^4 + q^5 - 4 * q^7 + 15 * q^8 - 14 * q^10 - 26 * q^11 + 9 * q^13 + 10 * q^14 - 14 * q^16 - 4 * q^17 - 10 * q^19 + q^20 - 8 * q^22 + 8 * q^23 + 16 * q^25 - 5 * q^26 + 80 * q^28 - 8 * q^29 - 12 * q^31 - 9 * q^32 - 22 * q^34 - 9 * q^35 - 16 * q^37 + 32 * q^38 + 33 * q^40 - 24 * q^41 - 31 * q^43 + 52 * q^44 - 44 * q^46 - 5 * q^47 - 47 * q^49 + 7 * q^50 + 80 * q^52 - 5 * q^53 - 17 * q^55 - 45 * q^56 + 54 * q^58 + 32 * q^59 - 28 * q^61 - 69 * q^62 - 75 * q^64 - 22 * q^65 + 6 * q^67 - 38 * q^68 - 12 * q^70 - 46 * q^71 - q^73 + 35 * q^74 - 45 * q^76 + 36 * q^77 - 15 * q^79 + 86 * q^80 + 47 * q^82 + 16 * q^83 + 19 * q^85 - 116 * q^86 + 54 * q^88 + 72 * q^89 - 47 * q^91 + 121 * q^92 - 22 * q^94 + 72 * q^95 + 43 * q^97 - 31 * q^98

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