LMFDB - Embedded newform 552.2.f.d.277.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(277,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 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("552.277");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.f (of order $2$, degree $1$, 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:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} + 2 x^{18} - 2 x^{17} + x^{16} - 4 x^{15} + 16 x^{14} - 24 x^{13} + 32 x^{12} + \cdots + 1024 $ x^20 - 2x^19 + 2x^18 - 2x^17 + x^16 - 4x^15 + 16x^14 - 24x^13 + 32x^12 - 16x^11 - 16x^10 - 32x^9 + 128x^8 - 192x^7 + 256x^6 - 128x^5 + 64x^4 - 256x^3 + 512x^2 - 1024x + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{9} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			277.14
Root			$-0.238838 - 1.39390i$ of defining polynomial
Character	$\chi$	$=$	552.277
Dual form			552.2.f.d.277.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.238838 + 1.39390i) q^{2} -1.00000i q^{3} +(-1.88591 + 0.665833i) q^{4} +4.08024i q^{5} +(1.39390 - 0.238838i) q^{6} -1.92513 q^{7} +(-1.37853 - 2.46975i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(0.238838 + 1.39390i) q^{2} -1.00000i q^{3} +(-1.88591 + 0.665833i) q^{4} +4.08024i q^{5} +(1.39390 - 0.238838i) q^{6} -1.92513 q^{7} +(-1.37853 - 2.46975i) q^{8} -1.00000 q^{9} +(-5.68744 + 0.974516i) q^{10} +3.31713i q^{11} +(0.665833 + 1.88591i) q^{12} -3.23474i q^{13} +(-0.459794 - 2.68344i) q^{14} +4.08024 q^{15} +(3.11333 - 2.51140i) q^{16} -5.13964 q^{17} +(-0.238838 - 1.39390i) q^{18} -5.11222i q^{19} +(-2.71676 - 7.69498i) q^{20} +1.92513i q^{21} +(-4.62374 + 0.792256i) q^{22} +1.00000 q^{23} +(-2.46975 + 1.37853i) q^{24} -11.6484 q^{25} +(4.50890 - 0.772579i) q^{26} +1.00000i q^{27} +(3.63062 - 1.28181i) q^{28} +7.41361i q^{29} +(0.974516 + 5.68744i) q^{30} -1.83802 q^{31} +(4.24423 + 3.73986i) q^{32} +3.31713 q^{33} +(-1.22754 - 7.16414i) q^{34} -7.85499i q^{35} +(1.88591 - 0.665833i) q^{36} +7.80968i q^{37} +(7.12592 - 1.22099i) q^{38} -3.23474 q^{39} +(10.0772 - 5.62474i) q^{40} -11.9521 q^{41} +(-2.68344 + 0.459794i) q^{42} +2.04224i q^{43} +(-2.20865 - 6.25581i) q^{44} -4.08024i q^{45} +(0.238838 + 1.39390i) q^{46} +10.9404 q^{47} +(-2.51140 - 3.11333i) q^{48} -3.29388 q^{49} +(-2.78207 - 16.2366i) q^{50} +5.13964i q^{51} +(2.15379 + 6.10044i) q^{52} +3.69447i q^{53} +(-1.39390 + 0.238838i) q^{54} -13.5347 q^{55} +(2.65385 + 4.75458i) q^{56} -5.11222 q^{57} +(-10.3338 + 1.77065i) q^{58} -10.0230i q^{59} +(-7.69498 + 2.71676i) q^{60} +3.89795i q^{61} +(-0.438988 - 2.56201i) q^{62} +1.92513 q^{63} +(-4.19930 + 6.80925i) q^{64} +13.1985 q^{65} +(0.792256 + 4.62374i) q^{66} +11.4934i q^{67} +(9.69291 - 3.42214i) q^{68} -1.00000i q^{69} +(10.9491 - 1.87607i) q^{70} +1.12076 q^{71} +(1.37853 + 2.46975i) q^{72} +12.8000 q^{73} +(-10.8859 + 1.86525i) q^{74} +11.6484i q^{75} +(3.40388 + 9.64120i) q^{76} -6.38590i q^{77} +(-0.772579 - 4.50890i) q^{78} +3.52506 q^{79} +(10.2471 + 12.7031i) q^{80} +1.00000 q^{81} +(-2.85462 - 16.6601i) q^{82} +10.1903i q^{83} +(-1.28181 - 3.63062i) q^{84} -20.9709i q^{85} +(-2.84668 + 0.487765i) q^{86} +7.41361 q^{87} +(8.19246 - 4.57276i) q^{88} -5.70580 q^{89} +(5.68744 - 0.974516i) q^{90} +6.22729i q^{91} +(-1.88591 + 0.665833i) q^{92} +1.83802i q^{93} +(2.61298 + 15.2498i) q^{94} +20.8591 q^{95} +(3.73986 - 4.24423i) q^{96} +0.894897 q^{97} +(-0.786704 - 4.59134i) q^{98} -3.31713i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} + 2 q^{6} - 8 q^{7} - 2 q^{8} - 20 q^{9}+O(q^{10}) $ 20 * q - 2 * q^2 + 2 * q^6 - 8 * q^7 - 2 * q^8 - 20 * q^9	$ 20 q - 2 q^{2} + 2 q^{6} - 8 q^{7} - 2 q^{8} - 20 q^{9} - 12 q^{10} + 2 q^{14} + 4 q^{15} + 4 q^{16} + 32 q^{17} + 2 q^{18} + 20 q^{20} + 14 q^{22} + 20 q^{23} + 10 q^{24} - 28 q^{25} + 18 q^{28} - 22 q^{32} + 28 q^{33} - 26 q^{34} + 16 q^{38} + 4 q^{40} - 40 q^{41} + 14 q^{42} + 10 q^{44} - 2 q^{46} + 40 q^{47} + 12 q^{49} - 14 q^{50} + 20 q^{52} - 2 q^{54} - 8 q^{55} + 6 q^{56} - 44 q^{57} - 32 q^{58} - 24 q^{60} + 20 q^{62} + 8 q^{63} - 48 q^{64} + 8 q^{65} + 10 q^{66} + 22 q^{68} + 80 q^{70} - 40 q^{71} + 2 q^{72} - 16 q^{73} - 30 q^{74} + 44 q^{76} - 36 q^{78} - 16 q^{79} + 4 q^{80} + 20 q^{81} - 32 q^{82} + 6 q^{84} - 4 q^{86} + 8 q^{87} - 70 q^{88} - 40 q^{89} + 12 q^{90} + 64 q^{94} - 40 q^{95} + 2 q^{96} + 32 q^{97} - 26 q^{98}+O(q^{100}) $ 20 * q - 2 * q^2 + 2 * q^6 - 8 * q^7 - 2 * q^8 - 20 * q^9 - 12 * q^10 + 2 * q^14 + 4 * q^15 + 4 * q^16 + 32 * q^17 + 2 * q^18 + 20 * q^20 + 14 * q^22 + 20 * q^23 + 10 * q^24 - 28 * q^25 + 18 * q^28 - 22 * q^32 + 28 * q^33 - 26 * q^34 + 16 * q^38 + 4 * q^40 - 40 * q^41 + 14 * q^42 + 10 * q^44 - 2 * q^46 + 40 * q^47 + 12 * q^49 - 14 * q^50 + 20 * q^52 - 2 * q^54 - 8 * q^55 + 6 * q^56 - 44 * q^57 - 32 * q^58 - 24 * q^60 + 20 * q^62 + 8 * q^63 - 48 * q^64 + 8 * q^65 + 10 * q^66 + 22 * q^68 + 80 * q^70 - 40 * q^71 + 2 * q^72 - 16 * q^73 - 30 * q^74 + 44 * q^76 - 36 * q^78 - 16 * q^79 + 4 * q^80 + 20 * q^81 - 32 * q^82 + 6 * q^84 - 4 * q^86 + 8 * q^87 - 70 * q^88 - 40 * q^89 + 12 * q^90 + 64 * q^94 - 40 * q^95 + 2 * q^96 + 32 * q^97 - 26 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$1$	$1$	$-1$	$1$

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 $

$2$	0.238838	+	1.39390i	0.168884	+	0.985636i
$2$	0.238838	+	1.39390i	0.168884	+	0.985636i
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	−1.88591	+	0.665833i	−0.942956	+	0.332916i
$5$			4.08024i			1.82474i	0.409368	+	0.912369i	$0.365749\pi$
$5$			4.08024i			1.82474i	−0.409368	+	0.912369i	$0.634251\pi$
$6$	1.39390	−	0.238838i	0.569057	−	0.0975052i
$7$	−1.92513			−0.727630			−0.363815	−	0.931471i	$-0.618526\pi$
$7$	−1.92513			−0.727630			−0.363815	+	0.931471i	$0.618526\pi$
$8$	−1.37853	−	2.46975i	−0.487384	−	0.873187i
$9$	−1.00000			−0.333333
$10$	−5.68744	+	0.974516i	−1.79853	+	0.308169i
$11$			3.31713i			1.00015i	0.865982	+	0.500076i	$0.166694\pi$
$11$			3.31713i			1.00015i	−0.865982	+	0.500076i	$0.833306\pi$
$12$	0.665833	+	1.88591i	0.192209	+	0.544416i
$13$		−	3.23474i		−	0.897155i	−0.893744	−	0.448578i	$-0.851931\pi$
$13$		−	3.23474i		−	0.897155i	0.893744	−	0.448578i	$-0.148069\pi$
$14$	−0.459794	−	2.68344i	−0.122885	−	0.717179i
$15$	4.08024			1.05351
$16$	3.11333	−	2.51140i	0.778334	−	0.627851i
$17$	−5.13964			−1.24655			−0.623273	−	0.782005i	$-0.714197\pi$
$17$	−5.13964			−1.24655			−0.623273	+	0.782005i	$0.714197\pi$
$18$	−0.238838	−	1.39390i	−0.0562947	−	0.328545i
$19$		−	5.11222i		−	1.17282i	−0.810013	−	0.586412i	$-0.800540\pi$
$19$		−	5.11222i		−	1.17282i	0.810013	−	0.586412i	$-0.199460\pi$
$20$	−2.71676	−	7.69498i	−0.607485	−	1.72065i
$21$			1.92513i			0.420098i
$22$	−4.62374	+	0.792256i	−0.985785	+	0.168910i
$23$	1.00000			0.208514
$23$	1.00000			0.208514
$24$	−2.46975	+	1.37853i	−0.504135	+	0.281392i
$25$	−11.6484			−2.32967
$26$	4.50890	−	0.772579i	0.884268	−	0.151515i
$27$			1.00000i			0.192450i
$28$	3.63062	−	1.28181i	0.686124	−	0.242240i
$29$			7.41361i			1.37667i	0.725391	+	0.688337i	$0.241659\pi$
$29$			7.41361i			1.37667i	−0.725391	+	0.688337i	$0.758341\pi$
$30$	0.974516	+	5.68744i	0.177922	+	1.03838i
$31$	−1.83802			−0.330117			−0.165059	−	0.986284i	$-0.552781\pi$
$31$	−1.83802			−0.330117			−0.165059	+	0.986284i	$0.552781\pi$
$32$	4.24423	+	3.73986i	0.750281	+	0.661120i
$33$	3.31713			0.577438
$34$	−1.22754	−	7.16414i	−0.210521	−	1.22864i
$35$		−	7.85499i		−	1.32773i
$36$	1.88591	−	0.665833i	0.314319	−	0.110972i
$37$			7.80968i			1.28390i	0.766745	+	0.641952i	$0.221875\pi$
$37$			7.80968i			1.28390i	−0.766745	+	0.641952i	$0.778125\pi$
$38$	7.12592	−	1.22099i	1.15598	−	0.198071i
$39$	−3.23474			−0.517973
$40$	10.0772	−	5.62474i	1.59334	−	0.889349i
$41$	−11.9521			−1.86661			−0.933304	−	0.359087i	$-0.883088\pi$
$41$	−11.9521			−1.86661			−0.933304	+	0.359087i	$0.883088\pi$
$42$	−2.68344	+	0.459794i	−0.414063	+	0.0709477i
$43$			2.04224i			0.311439i	0.987801	+	0.155719i	$0.0497695\pi$
$43$			2.04224i			0.311439i	−0.987801	+	0.155719i	$0.950230\pi$
$44$	−2.20865	−	6.25581i	−0.332967	−	0.943099i
$45$		−	4.08024i		−	0.608246i
$46$	0.238838	+	1.39390i	0.0352147	+	0.205519i
$47$	10.9404			1.59582			0.797909	−	0.602778i	$-0.205940\pi$
$47$	10.9404			1.59582			0.797909	+	0.602778i	$0.205940\pi$
$48$	−2.51140	−	3.11333i	−0.362490	−	0.449371i
$49$	−3.29388			−0.470554
$50$	−2.78207	−	16.2366i	−0.393444	−	2.29621i
$51$			5.13964i			0.719693i
$52$	2.15379	+	6.10044i	0.298678	+	0.845978i
$53$			3.69447i			0.507474i	0.967273	+	0.253737i	$0.0816597\pi$
$53$			3.69447i			0.507474i	−0.967273	+	0.253737i	$0.918340\pi$
$54$	−1.39390	+	0.238838i	−0.189686	+	0.0325017i
$55$	−13.5347			−1.82501
$56$	2.65385	+	4.75458i	0.354636	+	0.635358i
$57$	−5.11222			−0.677130
$58$	−10.3338	+	1.77065i	−1.35690	+	0.232498i
$59$		−	10.0230i		−	1.30489i	−0.757838	−	0.652443i	$-0.773744\pi$
$59$		−	10.0230i		−	1.30489i	0.757838	−	0.652443i	$-0.226256\pi$
$60$	−7.69498	+	2.71676i	−0.993417	+	0.350732i
$61$			3.89795i			0.499081i	0.968364	+	0.249541i	$0.0802797\pi$
$61$			3.89795i			0.499081i	−0.968364	+	0.249541i	$0.919720\pi$
$62$	−0.438988	−	2.56201i	−0.0557515	−	0.325375i
$63$	1.92513			0.242543
$64$	−4.19930	+	6.80925i	−0.524913	+	0.851156i
$65$	13.1985			1.63707
$66$	0.792256	+	4.62374i	0.0975200	+	0.569143i
$67$			11.4934i			1.40415i	0.712105	+	0.702073i	$0.247742\pi$
$67$			11.4934i			1.40415i	−0.712105	+	0.702073i	$0.752258\pi$
$68$	9.69291	−	3.42214i	1.17544	−	0.414995i
$69$		−	1.00000i		−	0.120386i
$70$	10.9491	−	1.87607i	1.30866	−	0.224233i
$71$	1.12076			0.133009			0.0665046	−	0.997786i	$-0.478815\pi$
$71$	1.12076			0.133009			0.0665046	+	0.997786i	$0.478815\pi$
$72$	1.37853	+	2.46975i	0.162461	+	0.291062i
$73$	12.8000			1.49813			0.749066	−	0.662495i	$-0.230503\pi$
$73$	12.8000			1.49813			0.749066	+	0.662495i	$0.230503\pi$
$74$	−10.8859	+	1.86525i	−1.26546	+	0.216831i
$75$			11.6484i			1.34504i
$76$	3.40388	+	9.64120i	0.390452	+	1.10592i
$77$		−	6.38590i		−	0.727740i
$78$	−0.772579	−	4.50890i	−0.0874773	−	0.510533i
$79$	3.52506			0.396600			0.198300	−	0.980141i	$-0.436458\pi$
$79$	3.52506			0.396600			0.198300	+	0.980141i	$0.436458\pi$
$80$	10.2471	+	12.7031i	1.14566	+	1.42026i
$81$	1.00000			0.111111
$82$	−2.85462	−	16.6601i	−0.315240	−	1.83980i
$83$			10.1903i			1.11853i	0.828988	+	0.559266i	$0.188917\pi$
$83$			10.1903i			1.11853i	−0.828988	+	0.559266i	$0.811083\pi$
$84$	−1.28181	−	3.63062i	−0.139857	−	0.396134i
$85$		−	20.9709i		−	2.27462i
$86$	−2.84668	+	0.487765i	−0.306965	+	0.0525970i
$87$	7.41361			0.794823
$88$	8.19246	−	4.57276i	0.873320	−	0.487458i
$89$	−5.70580			−0.604813			−0.302407	−	0.953179i	$-0.597790\pi$
$89$	−5.70580			−0.604813			−0.302407	+	0.953179i	$0.597790\pi$
$90$	5.68744	−	0.974516i	0.599509	−	0.102723i
$91$			6.22729i			0.652797i
$92$	−1.88591	+	0.665833i	−0.196620	+	0.0694178i
$93$			1.83802i			0.190593i
$94$	2.61298	+	15.2498i	0.269508	+	1.57290i
$95$	20.8591			2.14010
$96$	3.73986	−	4.24423i	0.381698	−	0.433175i
$97$	0.894897			0.0908630			0.0454315	−	0.998967i	$-0.485534\pi$
$97$	0.894897			0.0908630			0.0454315	+	0.998967i	$0.485534\pi$
$98$	−0.786704	−	4.59134i	−0.0794691	−	0.463795i
$99$		−	3.31713i		−	0.333384i
$100$	21.9678	−	7.75585i	2.19678	−	0.775585i
$101$		−	0.154427i		−	0.0153661i	−0.999970	−	0.00768303i	$-0.997554\pi$
$101$		−	0.154427i		−	0.0153661i	0.999970	−	0.00768303i	$-0.00244561\pi$
$102$	−7.16414	+	1.22754i	−0.709355	+	0.121545i
$103$	3.94598			0.388809			0.194405	−	0.980921i	$-0.437722\pi$
$103$	3.94598			0.388809			0.194405	+	0.980921i	$0.437722\pi$
$104$	−7.98899	+	4.45919i	−0.783385	+	0.437259i
$105$	−7.85499			−0.766568
$106$	−5.14971	+	0.882379i	−0.500184	+	0.0857042i
$107$			0.972312i			0.0939969i	0.998895	+	0.0469985i	$0.0149656\pi$
$107$			0.972312i			0.0939969i	−0.998895	+	0.0469985i	$0.985034\pi$
$108$	−0.665833	−	1.88591i	−0.0640698	−	0.181472i
$109$		−	0.105755i		−	0.0101295i	−0.999987	−	0.00506477i	$-0.998388\pi$
$109$		−	0.105755i		−	0.0101295i	0.999987	−	0.00506477i	$-0.00161217\pi$
$110$	−3.23259	−	18.8660i	−0.308216	−	1.79880i
$111$	7.80968			0.741262
$112$	−5.99357	+	4.83478i	−0.566339	+	0.456843i
$113$	5.59603			0.526430			0.263215	−	0.964737i	$-0.415217\pi$
$113$	5.59603			0.526430			0.263215	+	0.964737i	$0.415217\pi$
$114$	−1.22099	−	7.12592i	−0.114356	−	0.667403i
$115$			4.08024i			0.380484i
$116$	−4.93623	−	13.9814i	−0.458317	−	1.29814i
$117$			3.23474i			0.299052i
$118$	13.9711	−	2.39388i	1.28614	−	0.220374i
$119$	9.89446			0.907024
$120$	−5.62474	−	10.0772i	−0.513466	−	0.919915i
$121$	−0.00332879			−0.000302617
$122$	−5.43335	+	0.930979i	−0.491913	+	0.0842869i
$123$			11.9521i			1.07769i
$124$	3.46634	−	1.22381i	0.311286	−	0.109901i
$125$		−	27.1269i		−	2.42630i
$126$	0.459794	+	2.68344i	0.0409617	+	0.239060i
$127$	−12.5841			−1.11666			−0.558330	−	0.829619i	$-0.688558\pi$
$127$	−12.5841			−1.11666			−0.558330	+	0.829619i	$0.688558\pi$
$128$	−10.4944	−	4.22710i	−0.927579	−	0.373626i
$129$	2.04224			0.179809
$130$	3.15231	+	18.3974i	0.276476	+	1.61356i
$131$			8.63751i			0.754663i	0.926078	+	0.377332i	$0.123158\pi$
$131$			8.63751i			0.754663i	−0.926078	+	0.377332i	$0.876842\pi$
$132$	−6.25581	+	2.20865i	−0.544498	+	0.192238i
$133$			9.84168i			0.853382i
$134$	−16.0207	+	2.74507i	−1.38398	+	0.237138i
$135$	−4.08024			−0.351171
$136$	7.08515	+	12.6936i	0.607547	+	1.08847i
$137$	13.0277			1.11303			0.556514	−	0.830838i	$-0.312139\pi$
$137$	13.0277			1.11303			0.556514	+	0.830838i	$0.312139\pi$
$138$	1.39390	−	0.238838i	0.118657	−	0.0203312i
$139$			5.78691i			0.490839i	0.969417	+	0.245420i	$0.0789257\pi$
$139$			5.78691i			0.490839i	−0.969417	+	0.245420i	$0.921074\pi$
$140$	5.23010	+	14.8138i	0.442025	+	1.25200i
$141$		−	10.9404i		−	0.921346i
$142$	0.267679	+	1.56222i	0.0224631	+	0.131099i
$143$	10.7300			0.897291
$144$	−3.11333	+	2.51140i	−0.259445	+	0.209284i
$145$	−30.2493			−2.51207
$146$	3.05714	+	17.8420i	0.253011	+	1.47661i
$147$			3.29388i			0.271675i
$148$	−5.19994	−	14.7284i	−0.427432	−	1.21067i
$149$			5.29865i			0.434083i	0.976162	+	0.217041i	$0.0696406\pi$
$149$			5.29865i			0.434083i	−0.976162	+	0.217041i	$0.930359\pi$
$150$	−16.2366	+	2.78207i	−1.32572	+	0.227155i
$151$	−9.39903			−0.764882			−0.382441	−	0.923980i	$-0.624917\pi$
$151$	−9.39903			−0.764882			−0.382441	+	0.923980i	$0.624917\pi$
$152$	−12.6259	+	7.04735i	−1.02409	+	0.571616i
$153$	5.13964			0.415515
$154$	8.90130	−	1.52519i	0.717287	−	0.122904i
$155$		−	7.49954i		−	0.602378i
$156$	6.10044	−	2.15379i	0.488426	−	0.172442i
$157$			16.1651i			1.29011i	0.764135	+	0.645057i	$0.223166\pi$
$157$			16.1651i			1.29011i	−0.764135	+	0.645057i	$0.776834\pi$
$158$	0.841918	+	4.91358i	0.0669794	+	0.390903i
$159$	3.69447			0.292990
$160$	−15.2595	+	17.3175i	−1.20637	+	1.36907i
$161$	−1.92513			−0.151721
$162$	0.238838	+	1.39390i	0.0187649	+	0.109515i
$163$			5.09700i			0.399227i	0.979875	+	0.199614i	$0.0639687\pi$
$163$			5.09700i			0.399227i	−0.979875	+	0.199614i	$0.936031\pi$
$164$	22.5407	−	7.95811i	1.76013	−	0.621424i
$165$			13.5347i			1.05367i
$166$	−14.2043	+	2.43383i	−1.10247	+	0.188902i
$167$	−18.3213			−1.41774			−0.708871	−	0.705338i	$-0.750795\pi$
$167$	−18.3213			−1.41774			−0.708871	+	0.705338i	$0.750795\pi$
$168$	4.75458	−	2.65385i	0.366824	−	0.204749i
$169$	2.53646			0.195113
$170$	29.2314	−	5.00866i	2.24195	−	0.384147i
$171$			5.11222i			0.390941i
$172$	−1.35979	−	3.85149i	−0.103683	−	0.293673i
$173$			25.3158i			1.92472i	0.271776	+	0.962361i	$0.412389\pi$
$173$			25.3158i			1.92472i	−0.271776	+	0.962361i	$0.587611\pi$
$174$	1.77065	+	10.3338i	0.134233	+	0.783406i
$175$	22.4246			1.69514
$176$	8.33065	+	10.3273i	0.627946	+	0.778451i
$177$	−10.0230			−0.753376
$178$	−1.36276	−	7.95331i	−0.102143	−	0.596126i
$179$		−	19.5389i		−	1.46041i	−0.683229	−	0.730205i	$-0.739425\pi$
$179$		−	19.5389i		−	1.46041i	0.683229	−	0.730205i	$-0.260575\pi$
$180$	2.71676	+	7.69498i	0.202495	+	0.573550i
$181$			0.895809i			0.0665850i	0.999446	+	0.0332925i	$0.0105993\pi$
$181$			0.895809i			0.0665850i	−0.999446	+	0.0332925i	$0.989401\pi$
$182$	−8.68022	+	1.48731i	−0.643420	+	0.110247i
$183$	3.89795			0.288145
$184$	−1.37853	−	2.46975i	−0.101627	−	0.182072i
$185$	−31.8654			−2.34279
$186$	−2.56201	+	0.438988i	−0.187856	+	0.0321882i
$187$		−	17.0488i		−	1.24673i
$188$	−20.6326	+	7.28446i	−1.50479	+	0.531274i
$189$		−	1.92513i		−	0.140033i
$190$	4.98194	+	29.0755i	0.361428	+	2.10936i
$191$	6.97535			0.504718			0.252359	−	0.967634i	$-0.418794\pi$
$191$	6.97535			0.504718			0.252359	+	0.967634i	$0.418794\pi$
$192$	6.80925	+	4.19930i	0.491415	+	0.303059i
$193$	−12.7853			−0.920307			−0.460153	−	0.887839i	$-0.652206\pi$
$193$	−12.7853			−0.920307			−0.460153	+	0.887839i	$0.652206\pi$
$194$	0.213735	+	1.24740i	0.0153453	+	0.0895579i
$195$		−	13.1985i		−	0.945165i
$196$	6.21197	−	2.19317i	0.443712	−	0.156655i
$197$		−	0.521510i		−	0.0371560i	−0.999827	−	0.0185780i	$-0.994086\pi$
$197$		−	0.521510i		−	0.0371560i	0.999827	−	0.0185780i	$-0.00591391\pi$
$198$	4.62374	−	0.792256i	0.328595	−	0.0563032i
$199$	1.33738			0.0948042			0.0474021	−	0.998876i	$-0.484906\pi$
$199$	1.33738			0.0948042			0.0474021	+	0.998876i	$0.484906\pi$
$200$	16.0576	+	28.7685i	1.13545	+	2.03424i
$201$	11.4934			0.810684
$202$	0.215256	−	0.0368830i	0.0151453	−	0.00259508i
$203$		−	14.2722i		−	1.00171i
$204$	−3.42214	−	9.69291i	−0.239598	−	0.678639i
$205$		−	48.7675i		−	3.40607i
$206$	0.942451	+	5.50031i	0.0656637	+	0.383225i
$207$	−1.00000			−0.0695048
$208$	−8.12374	−	10.0708i	−0.563280	−	0.698286i
$209$	16.9579			1.17300
$210$	−1.87607	−	10.9491i	−0.129461	−	0.755557i
$211$		−	23.2302i		−	1.59923i	−0.600510	−	0.799617i	$-0.705036\pi$
$211$		−	23.2302i		−	1.59923i	0.600510	−	0.799617i	$-0.294964\pi$
$212$	−2.45990	−	6.96744i	−0.168946	−	0.478526i
$213$		−	1.12076i		−	0.0767929i
$214$	−1.35531	+	0.232225i	−0.0926468	+	0.0158746i
$215$	−8.33283			−0.568294
$216$	2.46975	−	1.37853i	0.168045	−	0.0937972i
$217$	3.53842			0.240203
$218$	0.147413	−	0.0252584i	0.00998404	−	0.00171072i
$219$		−	12.8000i		−	0.864947i
$220$	25.5252	−	9.01182i	1.72091	−	0.607577i
$221$			16.6254i			1.11834i
$222$	1.86525	+	10.8859i	0.125187	+	0.730615i
$223$	17.7737			1.19022			0.595108	−	0.803645i	$-0.297109\pi$
$223$	17.7737			1.19022			0.595108	+	0.803645i	$0.297109\pi$
$224$	−8.17069	−	7.19971i	−0.545927	−	0.481051i
$225$	11.6484			0.776557
$226$	1.33654	+	7.80030i	0.0889056	+	0.518869i
$227$		−	24.1023i		−	1.59972i	−0.600184	−	0.799862i	$-0.704906\pi$
$227$		−	24.1023i		−	1.59972i	0.600184	−	0.799862i	$-0.295094\pi$
$228$	9.64120	−	3.40388i	0.638504	−	0.225428i
$229$		−	15.5589i		−	1.02816i	−0.857743	−	0.514079i	$-0.828134\pi$
$229$		−	15.5589i		−	1.02816i	0.857743	−	0.514079i	$-0.171866\pi$
$230$	−5.68744	+	0.974516i	−0.375019	+	0.0642577i
$231$	−6.38590			−0.420161
$232$	18.3098	−	10.2199i	1.20209	−	0.670969i
$233$	−17.7810			−1.16487			−0.582437	−	0.812876i	$-0.697901\pi$
$233$	−17.7810			−1.16487			−0.582437	+	0.812876i	$0.697901\pi$
$234$	−4.50890	+	0.772579i	−0.294756	+	0.0505050i
$235$			44.6393i			2.91195i
$236$	6.67365	+	18.9025i	0.434418	+	1.23045i
$237$		−	3.52506i		−	0.228977i
$238$	2.36317	+	13.7919i	0.153182	+	0.893995i
$239$	−17.9002			−1.15787			−0.578933	−	0.815375i	$-0.696531\pi$
$239$	−17.9002			−1.15787			−0.578933	+	0.815375i	$0.696531\pi$
$240$	12.7031	−	10.2471i	0.819985	−	0.661449i
$241$	−8.00122			−0.515404			−0.257702	−	0.966224i	$-0.582965\pi$
$241$	−8.00122			−0.515404			−0.257702	+	0.966224i	$0.582965\pi$
$242$	−0.000795041	−	0.00464000i	−5.11072e−5	−	0.000298270i
$243$		−	1.00000i		−	0.0641500i
$244$	−2.59538	−	7.35120i	−0.166152	−	0.470612i
$245$		−	13.4398i		−	0.858638i
$246$	−16.6601	+	2.85462i	−1.06221	+	0.182004i
$247$	−16.5367			−1.05220
$248$	2.53376	+	4.53943i	0.160894	+	0.288254i
$249$	10.1903			0.645785
$250$	37.8121	−	6.47893i	2.39145	−	0.409763i
$251$			12.4116i			0.783414i	0.920090	+	0.391707i	$0.128115\pi$
$251$			12.4116i			0.783414i	−0.920090	+	0.391707i	$0.871885\pi$
$252$	−3.63062	+	1.28181i	−0.228708	+	0.0807466i
$253$			3.31713i			0.208546i
$254$	−3.00557	−	17.5410i	−0.188586	−	1.10062i
$255$	−20.9709			−1.31325
$256$	3.38570	−	15.6377i	0.211606	−	0.977355i
$257$	24.5211			1.52959			0.764793	−	0.644276i	$-0.222841\pi$
$257$	24.5211			1.52959			0.764793	+	0.644276i	$0.222841\pi$
$258$	0.487765	+	2.84668i	0.0303669	+	0.177226i
$259$		−	15.0346i		−	0.934207i
$260$	−24.8912	+	8.78800i	−1.54369	+	0.545008i
$261$		−	7.41361i		−	0.458891i
$262$	−12.0398	+	2.06297i	−0.743823	+	0.127451i
$263$	−18.7706			−1.15745			−0.578724	−	0.815524i	$-0.696449\pi$
$263$	−18.7706			−1.15745			−0.578724	+	0.815524i	$0.696449\pi$
$264$	−4.57276	−	8.19246i	−0.281434	−	0.504211i
$265$	−15.0743			−0.926007
$266$	−13.7183	+	2.35057i	−0.841124	+	0.144123i
$267$			5.70580i			0.349189i
$268$	−7.65270	−	21.6756i	−0.467463	−	1.32405i
$269$			20.6183i			1.25712i	0.777761	+	0.628560i	$0.216355\pi$
$269$			20.6183i			1.25712i	−0.777761	+	0.628560i	$0.783645\pi$
$270$	−0.974516	−	5.68744i	−0.0593072	−	0.346127i
$271$	−3.31648			−0.201462			−0.100731	−	0.994914i	$-0.532118\pi$
$271$	−3.31648			−0.201462			−0.100731	+	0.994914i	$0.532118\pi$
$272$	−16.0014	+	12.9077i	−0.970228	+	0.782645i
$273$	6.22729			0.376893
$274$	3.11150	+	18.1592i	0.187973	+	1.09704i
$275$		−	38.6391i		−	2.33002i
$276$	0.665833	+	1.88591i	0.0400784	+	0.113519i
$277$		−	12.3940i		−	0.744683i	−0.928096	−	0.372342i	$-0.878555\pi$
$277$		−	12.3940i		−	0.744683i	0.928096	−	0.372342i	$-0.121445\pi$
$278$	−8.06637	+	1.38213i	−0.483789	+	0.0828949i
$279$	1.83802			0.110039
$280$	−19.3998	+	10.8283i	−1.15936	+	0.647117i
$281$	19.4045			1.15757			0.578786	−	0.815479i	$-0.303527\pi$
$281$	19.4045			1.15757			0.578786	+	0.815479i	$0.303527\pi$
$282$	15.2498	−	2.61298i	0.908112	−	0.155601i
$283$		−	16.9344i		−	1.00664i	−0.864099	−	0.503322i	$-0.832111\pi$
$283$		−	16.9344i		−	1.00664i	0.864099	−	0.503322i	$-0.167889\pi$
$284$	−2.11365	+	0.746236i	−0.125422	+	0.0442810i
$285$		−	20.8591i		−	1.23558i
$286$	2.56274	+	14.9566i	0.151538	+	0.884402i
$287$	23.0094			1.35820
$288$	−4.24423	−	3.73986i	−0.250094	−	0.220373i
$289$	9.41587			0.553874
$290$	−7.22469	−	42.1645i	−0.424248	−	2.47599i
$291$		−	0.894897i		−	0.0524598i
$292$	−24.1398	+	8.52269i	−1.41267	+	0.498753i
$293$		−	19.2392i		−	1.12397i	−0.827148	−	0.561984i	$-0.810038\pi$
$293$		−	19.2392i		−	1.12397i	0.827148	−	0.561984i	$-0.189962\pi$
$294$	−4.59134	+	0.786704i	−0.267772	+	0.0458815i
$295$	40.8963			2.38108
$296$	19.2879	−	10.7659i	1.12109	−	0.625755i
$297$	−3.31713			−0.192479
$298$	−7.38579	+	1.26552i	−0.427848	+	0.0733096i
$299$		−	3.23474i		−	0.187070i
$300$	−7.75585	−	21.9678i	−0.447784	−	1.26831i
$301$		−	3.93157i		−	0.226612i
$302$	−2.24485	−	13.1013i	−0.129176	−	0.753895i
$303$	−0.154427			−0.00887159
$304$	−12.8388	−	15.9160i	−0.736358	−	0.912848i
$305$	−15.9046			−0.910693
$306$	1.22754	+	7.16414i	0.0701738	+	0.409547i
$307$		−	13.1991i		−	0.753314i	−0.926353	−	0.376657i	$-0.877074\pi$
$307$		−	13.1991i		−	0.753314i	0.926353	−	0.376657i	$-0.122926\pi$
$308$	4.25194	+	12.0432i	0.242277	+	0.686227i
$309$		−	3.94598i		−	0.224479i
$310$	10.4536	−	1.79118i	0.593725	−	0.101732i
$311$	31.9088			1.80938			0.904691	−	0.426069i	$-0.140102\pi$
$311$	31.9088			1.80938			0.904691	+	0.426069i	$0.140102\pi$
$312$	4.45919	+	7.98899i	0.252452	+	0.452287i
$313$	17.2307			0.973934			0.486967	−	0.873420i	$-0.338103\pi$
$313$	17.2307			0.973934			0.486967	+	0.873420i	$0.338103\pi$
$314$	−22.5325	+	3.86083i	−1.27158	+	0.217879i
$315$			7.85499i			0.442578i
$316$	−6.64795	+	2.34710i	−0.373977	+	0.132035i
$317$			29.5721i			1.66094i	0.557066	+	0.830468i	$0.311927\pi$
$317$			29.5721i			1.66094i	−0.557066	+	0.830468i	$0.688073\pi$
$318$	0.882379	+	5.14971i	0.0494813	+	0.288782i
$319$	−24.5919			−1.37688
$320$	−27.7834	−	17.1342i	−1.55314	−	0.957829i
$321$	0.972312			0.0542692
$322$	−0.459794	−	2.68344i	−0.0256233	−	0.149542i
$323$			26.2749i			1.46198i
$324$	−1.88591	+	0.665833i	−0.104773	+	0.0369907i
$325$			37.6794i			2.09008i
$326$	−7.10470	+	1.21736i	−0.393493	+	0.0674231i
$327$	−0.105755			−0.00584829
$328$	16.4764	+	29.5187i	0.909756	+	1.62990i
$329$	−21.0616			−1.16117
$330$	−18.8660	+	3.23259i	−1.03854	+	0.177948i
$331$		−	14.3757i		−	0.790161i	−0.918647	−	0.395080i	$-0.870717\pi$
$331$		−	14.3757i		−	0.790161i	0.918647	−	0.395080i	$-0.129283\pi$
$332$	−6.78504	−	19.2180i	−0.372377	−	1.05473i
$333$		−	7.80968i		−	0.427968i
$334$	−4.37581	−	25.5380i	−0.239434	−	1.39738i
$335$	−46.8959			−2.56220
$336$	4.83478	+	5.99357i	0.263759	+	0.326976i
$337$	14.0736			0.766637			0.383319	−	0.923616i	$-0.374781\pi$
$337$	14.0736			0.766637			0.383319	+	0.923616i	$0.374781\pi$
$338$	0.605804	+	3.53558i	0.0329514	+	0.192310i
$339$		−	5.59603i		−	0.303935i
$340$	13.9631	+	39.5494i	0.757258	+	2.14487i
$341$		−	6.09693i		−	0.330167i
$342$	−7.12592	+	1.22099i	−0.385326	+	0.0660237i
$343$	19.8170			1.07002
$344$	5.04382	−	2.81529i	0.271944	−	0.151790i
$345$	4.08024			0.219673
$346$	−35.2876	+	6.04636i	−1.89707	+	0.325055i
$347$			28.2414i			1.51608i	0.652209	+	0.758039i	$0.273842\pi$
$347$			28.2414i			1.51608i	−0.652209	+	0.758039i	$0.726158\pi$
$348$	−13.9814	+	4.93623i	−0.749483	+	0.264609i
$349$		−	22.9236i		−	1.22707i	−0.789666	−	0.613537i	$-0.789746\pi$
$349$		−	22.9236i		−	1.22707i	0.789666	−	0.613537i	$-0.210254\pi$
$350$	5.35584	+	31.2576i	0.286282	+	1.67079i
$351$	3.23474			0.172658
$352$	−12.4056	+	14.0786i	−0.661220	+	0.750394i
$353$	0.954617			0.0508091			0.0254046	−	0.999677i	$-0.491913\pi$
$353$	0.954617			0.0508091			0.0254046	+	0.999677i	$0.491913\pi$
$354$	−2.39388	−	13.9711i	−0.127233	−	0.742555i
$355$			4.57295i			0.242707i
$356$	10.7606	−	3.79910i	0.570312	−	0.201352i
$357$		−	9.89446i		−	0.523670i
$358$	27.2353	−	4.66664i	1.43943	−	0.246640i
$359$	−8.13384			−0.429288			−0.214644	−	0.976692i	$-0.568859\pi$
$359$	−8.13384			−0.429288			−0.214644	+	0.976692i	$0.568859\pi$
$360$	−10.0772	+	5.62474i	−0.531113	+	0.296450i
$361$	−7.13477			−0.375514
$362$	−1.24867	+	0.213953i	−0.0656285	+	0.0112451i
$363$			0.00332879i			0.000174716i
$364$	−4.14633	−	11.7441i	−0.217327	−	0.615559i
$365$			52.2273i			2.73370i
$366$	0.930979	+	5.43335i	0.0486630	+	0.284006i
$367$	11.5663			0.603754			0.301877	−	0.953347i	$-0.402387\pi$
$367$	11.5663			0.603754			0.301877	+	0.953347i	$0.402387\pi$
$368$	3.11333	−	2.51140i	0.162294	−	0.130916i
$369$	11.9521			0.622203
$370$	−7.61066	−	44.4171i	−0.395659	−	2.30914i
$371$		−	7.11232i		−	0.369253i
$372$	−1.22381	−	3.46634i	−0.0634516	−	0.179721i
$373$		−	6.53297i		−	0.338264i	−0.985593	−	0.169132i	$-0.945904\pi$
$373$		−	6.53297i		−	0.338264i	0.985593	−	0.169132i	$-0.0540965\pi$
$374$	23.7644	−	4.07191i	1.22883	−	0.210553i
$375$	−27.1269			−1.40083
$376$	−15.0817	−	27.0200i	−0.777777	−	1.39345i
$377$	23.9811			1.23509
$378$	2.68344	−	0.459794i	0.138021	−	0.0236492i
$379$			26.3450i			1.35325i	0.736326	+	0.676627i	$0.236559\pi$
$379$			26.3450i			1.35325i	−0.736326	+	0.676627i	$0.763441\pi$
$380$	−39.3384	+	13.8886i	−2.01802	+	0.712473i
$381$			12.5841i			0.644704i
$382$	1.66598	+	9.72293i	0.0852388	+	0.497468i
$383$	4.71284			0.240815			0.120407	−	0.992725i	$-0.461580\pi$
$383$	4.71284			0.240815			0.120407	+	0.992725i	$0.461580\pi$
$384$	−4.22710	+	10.4944i	−0.215713	+	0.535538i
$385$	26.0560			1.32794
$386$	−3.05362	−	17.8214i	−0.155425	−	0.907088i
$387$		−	2.04224i		−	0.103813i
$388$	−1.68770	+	0.595852i	−0.0856799	+	0.0302498i
$389$			0.597157i			0.0302771i	0.999885	+	0.0151385i	$0.00481893\pi$
$389$			0.597157i			0.0302771i	−0.999885	+	0.0151385i	$0.995181\pi$
$390$	18.3974	−	3.15231i	0.931588	−	0.159623i
$391$	−5.13964			−0.259923
$392$	4.54072	+	8.13505i	0.229341	+	0.410882i
$393$	8.63751			0.435705
$394$	0.726933	−	0.124556i	0.0366223	−	0.00627506i
$395$			14.3831i			0.723691i
$396$	2.20865	+	6.25581i	0.110989	+	0.314366i
$397$			28.7445i			1.44264i	0.692600	+	0.721321i	$0.256465\pi$
$397$			28.7445i			1.44264i	−0.692600	+	0.721321i	$0.743535\pi$
$398$	0.319417	+	1.86417i	0.0160109	+	0.0934424i
$399$	9.84168			0.492700
$400$	−36.2652	+	29.2537i	−1.81326	+	1.46269i
$401$	−14.0440			−0.701322			−0.350661	−	0.936502i	$-0.614043\pi$
$401$	−14.0440			−0.701322			−0.350661	+	0.936502i	$0.614043\pi$
$402$	2.74507	+	16.0207i	0.136912	+	0.799039i
$403$			5.94550i			0.296166i
$404$	0.102822	+	0.291236i	0.00511561	+	0.0144895i
$405$			4.08024i			0.202749i
$406$	19.8940	−	3.40873i	0.987321	−	0.169173i
$407$	−25.9057			−1.28410
$408$	12.6936	−	7.08515i	0.628427	−	0.350767i
$409$	−7.87046			−0.389169			−0.194585	−	0.980886i	$-0.562336\pi$
$409$	−7.87046			−0.389169			−0.194585	+	0.980886i	$0.562336\pi$
$410$	67.9770	−	11.6475i	3.35715	−	0.575231i
$411$		−	13.0277i		−	0.642607i
$412$	−7.44178	+	2.62736i	−0.366630	+	0.129441i
$413$			19.2956i			0.949475i
$414$	−0.238838	−	1.39390i	−0.0117382	−	0.0685064i
$415$	−41.5789			−2.04103
$416$	12.0975	−	13.7290i	0.593127	−	0.673118i
$417$	5.78691			0.283386
$418$	4.05019	+	23.6376i	0.198101	+	1.15615i
$419$			17.2220i			0.841349i	0.907212	+	0.420674i	$0.138206\pi$
$419$			17.2220i			0.841349i	−0.907212	+	0.420674i	$0.861794\pi$
$420$	14.8138	−	5.23010i	0.722840	−	0.255203i
$421$		−	16.8128i		−	0.819404i	−0.912220	−	0.409702i	$-0.865633\pi$
$421$		−	16.8128i		−	0.819404i	0.912220	−	0.409702i	$-0.134367\pi$
$422$	32.3806	−	5.54826i	1.57626	−	0.270085i
$423$	−10.9404			−0.531939
$424$	9.12440	−	5.09294i	0.443120	−	0.247335i
$425$	59.8683			2.90404
$426$	1.56222	−	0.267679i	0.0756899	−	0.0129691i
$427$		−	7.50406i		−	0.363147i
$428$	−0.647397	−	1.83370i	−0.0312931	−	0.0886350i
$429$		−	10.7300i		−	0.518051i
$430$	−1.99020	−	11.6151i	−0.0959758	−	0.560131i
$431$	15.9583			0.768683			0.384341	−	0.923191i	$-0.374429\pi$
$431$	15.9583			0.768683			0.384341	+	0.923191i	$0.374429\pi$
$432$	2.51140	+	3.11333i	0.120830	+	0.149790i
$433$	−30.1498			−1.44891			−0.724453	−	0.689324i	$-0.757908\pi$
$433$	−30.1498			−1.44891			−0.724453	+	0.689324i	$0.757908\pi$
$434$	0.845108	+	4.93220i	0.0405665	+	0.236753i
$435$			30.2493i			1.45034i
$436$	0.0704154	+	0.199446i	0.00337229	+	0.00955171i
$437$		−	5.11222i		−	0.244551i
$438$	17.8420	−	3.05714i	0.852523	−	0.146076i
$439$	−6.77425			−0.323317			−0.161659	−	0.986847i	$-0.551684\pi$
$439$	−6.77425			−0.323317			−0.161659	+	0.986847i	$0.551684\pi$
$440$	18.6580	+	33.4272i	0.889484	+	1.59358i
$441$	3.29388			0.156851
$442$	−23.1741	+	3.97077i	−1.10228	+	0.188870i
$443$		−	7.38479i		−	0.350862i	−0.984492	−	0.175431i	$-0.943868\pi$
$443$		−	7.38479i		−	0.350862i	0.984492	−	0.175431i	$-0.0561319\pi$
$444$	−14.7284	+	5.19994i	−0.698978	+	0.246778i
$445$		−	23.2810i		−	1.10363i
$446$	4.24504	+	24.7748i	0.201009	+	1.17312i
$447$	5.29865			0.250618
$448$	8.08420	−	13.1087i	0.381942	−	0.619327i
$449$	−7.22755			−0.341089			−0.170545	−	0.985350i	$-0.554553\pi$
$449$	−7.22755			−0.341089			−0.170545	+	0.985350i	$0.554553\pi$
$450$	2.78207	+	16.2366i	0.131148	+	0.765402i
$451$		−	39.6467i		−	1.86689i
$452$	−10.5536	+	3.72602i	−0.496401	+	0.175257i
$453$			9.39903i			0.441605i
$454$	33.5961	−	5.75654i	1.57674	−	0.270168i
$455$	−25.4088			−1.19118
$456$	7.04735	+	12.6259i	0.330023	+	0.591261i
$457$	−18.5420			−0.867360			−0.433680	−	0.901067i	$-0.642785\pi$
$457$	−18.5420			−0.867360			−0.433680	+	0.901067i	$0.642785\pi$
$458$	21.6875	−	3.71605i	1.01339	−	0.173640i
$459$		−	5.13964i		−	0.239898i
$460$	−2.71676	−	7.69498i	−0.126669	−	0.358780i
$461$		−	19.9468i		−	0.929014i	−0.885569	−	0.464507i	$-0.846232\pi$
$461$		−	19.9468i		−	0.929014i	0.885569	−	0.464507i	$-0.153768\pi$
$462$	−1.52519	−	8.90130i	−0.0709585	−	0.414126i
$463$	−12.5401			−0.582786			−0.291393	−	0.956603i	$-0.594119\pi$
$463$	−12.5401			−0.582786			−0.291393	+	0.956603i	$0.594119\pi$
$464$	18.6186	+	23.0811i	0.864346	+	1.07151i
$465$	−7.49954			−0.347783
$466$	−4.24678	−	24.7850i	−0.196728	−	1.14814i
$467$		−	31.8637i		−	1.47448i	−0.675632	−	0.737239i	$-0.736129\pi$
$467$		−	31.8637i		−	1.47448i	0.675632	−	0.737239i	$-0.263871\pi$
$468$	−2.15379	−	6.10044i	−0.0995592	−	0.281993i
$469$		−	22.1263i		−	1.02170i
$470$	−62.2228	+	10.6616i	−2.87012	+	0.491782i
$471$	16.1651			0.744847
$472$	−24.7543	+	13.8171i	−1.13941	+	0.635981i
$473$	−6.77437			−0.311486
$474$	4.91358	−	0.841918i	0.225688	−	0.0386706i
$475$			59.5489i			2.73229i
$476$	−18.6601	+	6.58805i	−0.855284	+	0.301963i
$477$		−	3.69447i		−	0.169158i
$478$	−4.27524	−	24.9510i	−0.195545	−	1.14123i
$479$	−35.6996			−1.63116			−0.815578	−	0.578647i	$-0.803581\pi$
$479$	−35.6996			−1.63116			−0.815578	+	0.578647i	$0.803581\pi$
$480$	17.3175	+	15.2595i	0.790431	+	0.696498i
$481$	25.2623			1.15186
$482$	−1.91100	−	11.1529i	−0.0870435	−	0.508001i
$483$			1.92513i			0.0875964i
$484$	0.00627780	−	0.00221641i	0.000285355	−	0.000100746i
$485$			3.65139i			0.165801i
$486$	1.39390	−	0.238838i	0.0632286	−	0.0108339i
$487$	9.00670			0.408133			0.204066	−	0.978957i	$-0.434584\pi$
$487$	9.00670			0.408133			0.204066	+	0.978957i	$0.434584\pi$
$488$	9.62695	−	5.37345i	0.435792	−	0.243245i
$489$	5.09700			0.230494
$490$	18.7338	−	3.20994i	0.846305	−	0.145010i
$491$			16.5070i			0.744951i	0.928042	+	0.372476i	$0.121491\pi$
$491$			16.5070i			0.744951i	−0.928042	+	0.372476i	$0.878509\pi$
$492$	−7.95811	−	22.5407i	−0.358779	−	1.01621i
$493$		−	38.1033i		−	1.71609i
$494$	−3.94959	−	23.0505i	−0.177700	−	1.03709i
$495$	13.5347			0.608338
$496$	−5.72236	+	4.61600i	−0.256941	+	0.207264i
$497$	−2.15760			−0.0967816
$498$	2.43383	+	14.2043i	0.109063	+	0.636508i
$499$		−	9.39150i		−	0.420421i	−0.977656	−	0.210211i	$-0.932585\pi$
$499$		−	9.39150i		−	0.420421i	0.977656	−	0.210211i	$-0.0674150\pi$
$500$	18.0620	+	51.1589i	0.807755	+	2.28790i
$501$			18.3213i			0.818533i
$502$	−17.3005	+	2.96436i	−0.772161	+	0.132306i
$503$	7.80178			0.347864			0.173932	−	0.984758i	$-0.444353\pi$
$503$	7.80178			0.347864			0.173932	+	0.984758i	$0.444353\pi$
$504$	−2.65385	−	4.75458i	−0.118212	−	0.211786i
$505$	0.630099			0.0280390
$506$	−4.62374	+	0.792256i	−0.205550	+	0.0352201i
$507$		−	2.53646i		−	0.112648i
$508$	23.7326	−	8.37892i	1.05296	−	0.371754i
$509$			27.4596i			1.21712i	0.793506	+	0.608562i	$0.208253\pi$
$509$			27.4596i			1.21712i	−0.793506	+	0.608562i	$0.791747\pi$
$510$	−5.00866	−	29.2314i	−0.221787	−	1.29439i
$511$	−24.6417			−1.09009
$512$	22.6060	+	0.984451i	0.999053	+	0.0435070i
$513$	5.11222			0.225710
$514$	5.85658	+	34.1800i	0.258322	+	1.50761i
$515$			16.1006i			0.709476i
$516$	−3.85149	+	1.35979i	−0.169552	+	0.0598614i
$517$			36.2906i			1.59606i
$518$	20.9568	−	3.59084i	0.920788	−	0.157773i
$519$	25.3158			1.11124
$520$	−18.1946	−	32.5970i	−0.797884	−	1.42947i
$521$	−23.8179			−1.04348			−0.521740	−	0.853105i	$-0.674717\pi$
$521$	−23.8179			−1.04348			−0.521740	+	0.853105i	$0.674717\pi$
$522$	10.3338	−	1.77065i	0.452300	−	0.0774994i
$523$		−	11.9451i		−	0.522324i	−0.965295	−	0.261162i	$-0.915894\pi$
$523$		−	11.9451i		−	0.522324i	0.965295	−	0.261162i	$-0.0841057\pi$
$524$	−5.75114	−	16.2896i	−0.251240	−	0.711614i
$525$		−	22.4246i		−	0.978689i
$526$	−4.48314	−	26.1644i	−0.195474	−	1.14082i
$527$	9.44673			0.411506
$528$	10.3273	−	8.33065i	0.449439	−	0.362545i
$529$	1.00000			0.0434783
$530$	−3.60032	−	21.0121i	−0.156388	−	0.912706i
$531$			10.0230i			0.434962i
$532$	−6.55291	−	18.5605i	−0.284105	−	0.804702i
$533$			38.6620i			1.67464i
$534$	−7.95331	+	1.36276i	−0.344173	+	0.0589724i
$535$	−3.96727			−0.171520
$536$	28.3859	−	15.8440i	1.22608	−	0.684359i
$537$	−19.5389			−0.843168
$538$	−28.7398	+	4.92443i	−1.23906	+	0.212307i
$539$		−	10.9262i		−	0.470625i
$540$	7.69498	−	2.71676i	0.331139	−	0.116911i
$541$		−	5.79103i		−	0.248976i	−0.992221	−	0.124488i	$-0.960271\pi$
$541$		−	5.79103i		−	0.248976i	0.992221	−	0.124488i	$-0.0397288\pi$
$542$	−0.792102	−	4.62284i	−0.0340237	−	0.198568i
$543$	0.895809			0.0384428
$544$	−21.8138	−	19.2215i	−0.935259	−	0.824115i
$545$	0.431508			0.0184838
$546$	1.48731	+	8.68022i	0.0636511	+	0.371479i
$547$			27.5144i			1.17643i	0.808704	+	0.588216i	$0.200169\pi$
$547$			27.5144i			1.17643i	−0.808704	+	0.588216i	$0.799831\pi$
$548$	−24.5690	+	8.67424i	−1.04954	+	0.370545i
$549$		−	3.89795i		−	0.166360i
$550$	53.8590	−	9.22848i	2.29655	−	0.393504i
$551$	37.9000			1.61459
$552$	−2.46975	+	1.37853i	−0.105119	+	0.0586742i
$553$	−6.78619			−0.288578
$554$	17.2760	−	2.96016i	0.733987	−	0.125765i
$555$			31.8654i			1.35261i
$556$	−3.85311	−	10.9136i	−0.163408	−	0.462840i
$557$			28.3196i			1.19994i	0.800023	+	0.599969i	$0.204821\pi$
$557$			28.3196i			1.19994i	−0.800023	+	0.599969i	$0.795179\pi$
$558$	0.438988	+	2.56201i	0.0185838	+	0.108458i
$559$	6.60611			0.279409
$560$	−19.7270	−	24.4552i	−0.833620	−	1.03342i
$561$	−17.0488			−0.719802
$562$	4.63452	+	27.0479i	0.195495	+	1.14095i
$563$			1.04911i			0.0442146i	0.999756	+	0.0221073i	$0.00703755\pi$
$563$			1.04911i			0.0442146i	−0.999756	+	0.0221073i	$0.992962\pi$
$564$	7.28446	+	20.6326i	0.306731	+	0.868789i
$565$			22.8331i			0.960597i
$566$	23.6048	−	4.04457i	0.992185	−	0.170006i
$567$	−1.92513			−0.0808478
$568$	−1.54500	−	2.76798i	−0.0648267	−	0.116142i
$569$	19.5828			0.820954			0.410477	−	0.911871i	$-0.365362\pi$
$569$	19.5828			0.820954			0.410477	+	0.911871i	$0.365362\pi$
$570$	29.0755	−	4.98194i	1.21784	−	0.208671i
$571$			19.2897i			0.807248i	0.914925	+	0.403624i	$0.132250\pi$
$571$			19.2897i			0.807248i	−0.914925	+	0.403624i	$0.867750\pi$
$572$	−20.2359	+	7.14441i	−0.846106	+	0.298723i
$573$		−	6.97535i		−	0.291399i
$574$	5.49551	+	32.0728i	0.229378	+	1.33869i
$575$	−11.6484			−0.485770
$576$	4.19930	−	6.80925i	0.174971	−	0.283719i
$577$	23.7854			0.990200			0.495100	−	0.868836i	$-0.335131\pi$
$577$	23.7854			0.990200			0.495100	+	0.868836i	$0.335131\pi$
$578$	2.24887	+	13.1248i	0.0935405	+	0.545919i
$579$			12.7853i			0.531339i
$580$	57.0476	−	20.1410i	2.36877	−	0.836309i
$581$		−	19.6177i		−	0.813877i
$582$	1.24740	−	0.213735i	0.0517063	−	0.00885962i
$583$	−12.2550			−0.507551
$584$	−17.6453	−	31.6129i	−0.730166	−	1.30815i
$585$	−13.1985			−0.545691
$586$	26.8175	−	4.59506i	1.10782	−	0.189820i
$587$		−	36.3860i		−	1.50181i	−0.660411	−	0.750905i	$-0.729618\pi$
$587$		−	36.3860i		−	1.50181i	0.660411	−	0.750905i	$-0.270382\pi$
$588$	−2.19317	−	6.21197i	−0.0904449	−	0.256177i
$589$			9.39633i			0.387169i
$590$	9.76760	+	57.0054i	0.402126	+	2.34687i
$591$	−0.521510			−0.0214521
$592$	19.6133	+	24.3141i	0.806100	+	0.999305i
$593$	−14.3327			−0.588572			−0.294286	−	0.955717i	$-0.595082\pi$
$593$	−14.3327			−0.588572			−0.294286	+	0.955717i	$0.595082\pi$
$594$	−0.792256	−	4.62374i	−0.0325067	−	0.189714i
$595$			40.3718i			1.65508i
$596$	−3.52802	−	9.99280i	−0.144513	−	0.409321i
$597$		−	1.33738i		−	0.0547352i
$598$	4.50890	−	0.772579i	0.184383	−	0.0315931i
$599$	11.0889			0.453082			0.226541	−	0.974002i	$-0.427258\pi$
$599$	11.0889			0.453082			0.226541	+	0.974002i	$0.427258\pi$
$600$	28.7685	−	16.0576i	1.17447	−	0.655550i
$601$	48.2043			1.96630			0.983148	−	0.182811i	$-0.0585195\pi$
$601$	48.2043			1.96630			0.983148	+	0.182811i	$0.0585195\pi$
$602$	5.48022	−	0.939010i	0.223357	−	0.0382712i
$603$		−	11.4934i		−	0.468049i
$604$	17.7258	−	6.25818i	0.721251	−	0.254642i
$605$		−	0.0135822i		−	0.000552197i
$606$	−0.0368830	−	0.215256i	−0.00149827	−	0.00874416i
$607$	11.4142			0.463288			0.231644	−	0.972801i	$-0.425589\pi$
$607$	11.4142			0.463288			0.231644	+	0.972801i	$0.425589\pi$
$608$	19.1190	−	21.6974i	0.775376	−	0.879947i
$609$	−14.2722			−0.578337
$610$	−3.79862	−	22.1694i	−0.153802	−	0.897612i
$611$		−	35.3893i		−	1.43170i
$612$	−9.69291	+	3.42214i	−0.391813	+	0.138332i
$613$			43.4698i			1.75573i	0.478909	+	0.877864i	$0.341032\pi$
$613$			43.4698i			1.75573i	−0.478909	+	0.877864i	$0.658968\pi$
$614$	18.3983	−	3.15245i	0.742493	−	0.127223i
$615$	−48.7675			−1.96650
$616$	−15.7715	+	8.80316i	−0.635454	+	0.354689i
$617$	−1.84391			−0.0742332			−0.0371166	−	0.999311i	$-0.511817\pi$
$617$	−1.84391			−0.0742332			−0.0371166	+	0.999311i	$0.511817\pi$
$618$	5.50031	−	0.942451i	0.221255	−	0.0379109i
$619$		−	19.4509i		−	0.781799i	−0.920433	−	0.390900i	$-0.872164\pi$
$619$		−	19.4509i		−	0.781799i	0.920433	−	0.390900i	$-0.127836\pi$
$620$	4.99344	+	14.1435i	0.200541	+	0.568016i
$621$			1.00000i			0.0401286i
$622$	7.62103	+	44.4776i	0.305576	+	1.78339i
$623$	10.9844			0.440080
$624$	−10.0708	+	8.12374i	−0.403156	+	0.325210i
$625$	52.4424			2.09769
$626$	4.11534	+	24.0178i	0.164482	+	0.959945i
$627$		−	16.9579i		−	0.677232i
$628$	−10.7632	−	30.4859i	−0.429500	−	1.21652i
$629$		−	40.1389i		−	1.60044i
$630$	−10.9491	+	1.87607i	−0.436221	+	0.0747444i
$631$	−13.5872			−0.540897			−0.270449	−	0.962734i	$-0.587172\pi$
$631$	−13.5872			−0.540897			−0.270449	+	0.962734i	$0.587172\pi$
$632$	−4.85940	−	8.70600i	−0.193297	−	0.346306i
$633$	−23.2302			−0.923318
$634$	−41.2206	+	7.06295i	−1.63708	+	0.280506i
$635$		−	51.3462i		−	2.03761i
$636$	−6.96744	+	2.45990i	−0.276277	+	0.0975412i
$637$			10.6548i			0.422160i
$638$	−5.87348	−	34.2786i	−0.232533	−	1.35710i
$639$	−1.12076			−0.0443364
$640$	17.2476	−	42.8195i	0.681770	−	1.69259i
$641$	32.1785			1.27097			0.635487	−	0.772111i	$-0.280799\pi$
$641$	32.1785			1.27097			0.635487	+	0.772111i	$0.280799\pi$
$642$	0.232225	+	1.35531i	0.00916519	+	0.0534896i
$643$		−	11.0232i		−	0.434711i	−0.976093	−	0.217355i	$-0.930257\pi$
$643$		−	11.0232i		−	0.434711i	0.976093	−	0.217355i	$-0.0697431\pi$
$644$	3.63062	−	1.28181i	0.143067	−	0.0505105i
$645$			8.33283i			0.328105i
$646$	−36.6246	+	6.27546i	−1.44098	+	0.246905i
$647$	−15.4900			−0.608974			−0.304487	−	0.952516i	$-0.598485\pi$
$647$	−15.4900			−0.608974			−0.304487	+	0.952516i	$0.598485\pi$
$648$	−1.37853	−	2.46975i	−0.0541538	−	0.0970208i
$649$	33.2476			1.30508
$650$	−52.5213	+	8.99927i	−2.06005	+	0.352980i
$651$		−	3.53842i		−	0.138681i
$652$	−3.39375	−	9.61249i	−0.132909	−	0.376454i
$653$			4.68969i			0.183522i	0.995781	+	0.0917609i	$0.0292495\pi$
$653$			4.68969i			0.183522i	−0.995781	+	0.0917609i	$0.970750\pi$
$654$	−0.0252584	−	0.147413i	−0.000987683	−	0.00576429i
$655$	−35.2431			−1.37706
$656$	−37.2110	+	30.0166i	−1.45284	+	1.17195i
$657$	−12.8000			−0.499377
$658$	−5.03032	−	29.3578i	−0.196102	−	1.14449i
$659$			0.419811i			0.0163535i	0.999967	+	0.00817675i	$0.00260277\pi$
$659$			0.419811i			0.0163535i	−0.999967	+	0.00817675i	$0.997397\pi$
$660$	−9.01182	−	25.5252i	−0.350785	−	0.993567i
$661$			12.2432i			0.476206i	0.971240	+	0.238103i	$0.0765256\pi$
$661$			12.2432i			0.476206i	−0.971240	+	0.238103i	$0.923474\pi$
$662$	20.0383	−	3.43347i	0.778811	−	0.133445i
$663$	16.6254			0.645676
$664$	25.1675	−	14.0477i	0.976688	−	0.545155i
$665$	−40.1564			−1.55720
$666$	10.8859	−	1.86525i	0.421821	−	0.0722769i
$667$			7.41361i			0.287056i
$668$	34.5523	−	12.1989i	1.33687	−	0.471989i
$669$		−	17.7737i		−	0.687172i
$670$	−11.2005	−	65.3682i	−0.432714	−	2.52539i
$671$	−12.9300			−0.499157
$672$	−7.19971	+	8.17069i	−0.277735	+	0.315191i
$673$	40.6490			1.56691			0.783453	−	0.621452i	$-0.213457\pi$
$673$	40.6490			1.56691			0.783453	+	0.621452i	$0.213457\pi$
$674$	3.36131	+	19.6172i	0.129473	+	0.755625i
$675$		−	11.6484i		−	0.448345i
$676$	−4.78355	+	1.68886i	−0.183983	+	0.0649562i
$677$			19.3500i			0.743681i	0.928297	+	0.371840i	$0.121273\pi$
$677$			19.3500i			0.743681i	−0.928297	+	0.371840i	$0.878727\pi$
$678$	7.80030	−	1.33654i	0.299569	−	0.0513297i
$679$	−1.72279			−0.0661147
$680$	−51.7929	+	28.9091i	−1.98617	+	1.10861i
$681$	−24.1023			−0.923601
$682$	8.49851	−	1.45618i	0.325425	−	0.0557600i
$683$			33.9615i			1.29950i	0.760147	+	0.649751i	$0.225127\pi$
$683$			33.9615i			1.29950i	−0.760147	+	0.649751i	$0.774873\pi$
$684$	−3.40388	−	9.64120i	−0.130151	−	0.368640i
$685$			53.1559i			2.03098i
$686$	4.73306	+	27.6230i	0.180709	+	1.05465i
$687$	−15.5589			−0.593608
$688$	5.12889	+	6.35818i	0.195537	+	0.242403i
$689$	11.9506			0.455283
$690$	0.974516	+	5.68744i	0.0370992	+	0.216517i
$691$			13.8308i			0.526150i	0.964775	+	0.263075i	$0.0847367\pi$
$691$			13.8308i			0.526150i	−0.964775	+	0.263075i	$0.915263\pi$
$692$	−16.8561	−	47.7433i	−0.640771	−	1.81493i
$693$			6.38590i			0.242580i
$694$	−39.3657	+	6.74512i	−1.49430	+	0.256041i
$695$	−23.6120			−0.895653
$696$	−10.2199	−	18.3098i	−0.387384	−	0.694029i
$697$	61.4296			2.32681
$698$	31.9532	−	5.47503i	1.20945	−	0.207233i
$699$			17.7810i			0.672540i
$700$	−42.2908	+	14.9310i	−1.59844	+	0.564339i
$701$		−	21.2319i		−	0.801918i	−0.916096	−	0.400959i	$-0.868677\pi$
$701$		−	21.2319i		−	0.801918i	0.916096	−	0.400959i	$-0.131323\pi$
$702$	0.772579	+	4.50890i	0.0291591	+	0.170178i
$703$	39.9248			1.50579
$704$	−22.5871	−	13.9296i	−0.851285	−	0.524992i
$705$	44.6393			1.68122
$706$	0.227999	+	1.33064i	0.00858085	+	0.0500793i
$707$			0.297292i			0.0111808i
$708$	18.9025	−	6.67365i	0.710401	−	0.250811i
$709$		−	9.49852i		−	0.356725i	−0.983965	−	0.178362i	$-0.942920\pi$
$709$		−	9.49852i		−	0.356725i	0.983965	−	0.178362i	$-0.0570799\pi$
$710$	−6.37424	+	1.09220i	−0.239221	+	0.0409894i
$711$	−3.52506			−0.132200
$712$	7.86562	+	14.0919i	0.294777	+	0.528115i
$713$	−1.83802			−0.0688342
$714$	13.7919	−	2.36317i	0.516148	−	0.0884396i
$715$			43.7811i			1.63732i
$716$	13.0097	+	36.8487i	0.486194	+	1.37710i
$717$			17.9002i			0.668494i
$718$	−1.94267	−	11.3378i	−0.0724998	−	0.423121i
$719$	34.2920			1.27888			0.639438	−	0.768843i	$-0.279167\pi$
$719$	34.2920			1.27888			0.639438	+	0.768843i	$0.279167\pi$
$720$	−10.2471	−	12.7031i	−0.381888	−	0.473418i
$721$	−7.59653			−0.282909
$722$	−1.70406	−	9.94516i	−0.0634184	−	0.370120i
$723$			8.00122i			0.297569i
$724$	−0.596459	−	1.68942i	−0.0221672	−	0.0627867i
$725$		−	86.3564i		−	3.20720i
$726$	−0.00464000		0.000795041i	−0.000172206		2.95067e-5i
$727$	5.75020			0.213263			0.106631	−	0.994299i	$-0.465993\pi$
$727$	5.75020			0.213263			0.106631	+	0.994299i	$0.465993\pi$
$728$	15.3798	−	8.58451i	0.570014	−	0.318163i
$729$	−1.00000			−0.0370370
$730$	−72.7996	+	12.4739i	−2.69443	+	0.461678i
$731$		−	10.4964i		−	0.388222i
$732$	−7.35120	+	2.59538i	−0.271708	+	0.0959281i
$733$			42.8684i			1.58338i	0.610923	+	0.791690i	$0.290799\pi$
$733$			42.8684i			1.58338i	−0.610923	+	0.791690i	$0.709201\pi$
$734$	2.76247	+	16.1222i	0.101964	+	0.595082i
$735$	−13.4398			−0.495735
$736$	4.24423	+	3.73986i	0.156444	+	0.137853i
$737$	−38.1252			−1.40436
$738$	2.85462	+	16.6601i	0.105080	+	0.613265i
$739$		−	9.76913i		−	0.359363i	−0.983725	−	0.179682i	$-0.942493\pi$
$739$		−	9.76913i		−	0.359363i	0.983725	−	0.179682i	$-0.0575067\pi$
$740$	60.0953	−	21.2170i	2.20915	−	0.779952i
$741$			16.5367i			0.607491i
$742$	9.91386	−	1.69869i	0.363949	−	0.0623610i
$743$	47.7415			1.75146			0.875732	−	0.482797i	$-0.160379\pi$
$743$	47.7415			1.75146			0.875732	+	0.482797i	$0.160379\pi$
$744$	4.53943	−	2.53376i	0.166424	−	0.0928922i
$745$	−21.6198			−0.792087
$746$	9.10631	−	1.56032i	0.333406	−	0.0571275i
$747$		−	10.1903i		−	0.372844i
$748$	11.3517	+	32.1526i	0.415058	+	1.17562i
$749$		−	1.87183i		−	0.0683950i
$750$	−6.47893	−	37.8121i	−0.236577	−	1.38070i
$751$	11.8095			0.430934			0.215467	−	0.976511i	$-0.430873\pi$
$751$	11.8095			0.430934			0.215467	+	0.976511i	$0.430873\pi$
$752$	34.0610	−	27.4757i	1.24208	−	1.00194i
$753$	12.4116			0.452304
$754$	5.72760	+	33.4273i	0.208587	+	1.21735i
$755$		−	38.3503i		−	1.39571i
$756$	1.28181	+	3.63062i	0.0466191	+	0.132045i
$757$		−	24.5255i		−	0.891396i	−0.895183	−	0.445698i	$-0.852956\pi$
$757$		−	24.5255i		−	0.891396i	0.895183	−	0.445698i	$-0.147044\pi$
$758$	−36.7223	+	6.29220i	−1.33382	+	0.228543i
$759$	3.31713			0.120404
$760$	−28.7549	−	51.5166i	−1.04305	−	1.86870i
$761$	8.83638			0.320318			0.160159	−	0.987091i	$-0.448799\pi$
$761$	8.83638			0.320318			0.160159	+	0.987091i	$0.448799\pi$
$762$	−17.5410	+	3.00557i	−0.635444	+	0.108880i
$763$			0.203593i			0.00737056i
$764$	−13.1549	+	4.64441i	−0.475927	+	0.168029i
$765$			20.9709i			0.758206i
$766$	1.12561	+	6.56923i	0.0406698	+	0.237356i
$767$	−32.4219			−1.17069
$768$	−15.6377	−	3.38570i	−0.564276	−	0.122171i
$769$	−10.8352			−0.390728			−0.195364	−	0.980731i	$-0.562589\pi$
$769$	−10.8352			−0.390728			−0.195364	+	0.980731i	$0.562589\pi$
$770$	6.22316	+	36.3194i	0.224267	+	1.30886i
$771$		−	24.5211i		−	0.883107i
$772$	24.1120	−	8.51288i	0.867809	−	0.306385i
$773$			43.8425i			1.57691i	0.615095	+	0.788453i	$0.289118\pi$
$773$			43.8425i			1.57691i	−0.615095	+	0.788453i	$0.710882\pi$
$774$	2.84668	−	0.487765i	0.102322	−	0.0175323i
$775$	21.4098			0.769064
$776$	−1.23364	−	2.21017i	−0.0442852	−	0.0793405i
$777$	−15.0346			−0.539365
$778$	−0.832377	+	0.142624i	−0.0298422	+	0.00511331i
$779$			61.1019i			2.18920i
$780$	8.78800	+	24.8912i	0.314661	+	0.891249i
$781$			3.71769i			0.133029i
$782$	−1.22754	−	7.16414i	−0.0438968	−	0.256189i
$783$	−7.41361			−0.264941
$784$	−10.2549	+	8.27226i	−0.366248	+	0.295438i
$785$	−65.9574			−2.35412
$786$	2.06297	+	12.0398i	0.0735836	+	0.429446i
$787$		−	17.2645i		−	0.615413i	−0.951481	−	0.307707i	$-0.900438\pi$
$787$		−	17.2645i		−	0.615413i	0.951481	−	0.307707i	$-0.0995615\pi$
$788$	0.347238	+	0.983522i	0.0123699	+	0.0350365i
$789$			18.7706i			0.668253i
$790$	−20.0486	+	3.43523i	−0.713296	+	0.122220i
$791$	−10.7731			−0.383047
$792$	−8.19246	+	4.57276i	−0.291107	+	0.162486i
$793$	12.6089			0.447754
$794$	−40.0669	+	6.86527i	−1.42192	+	0.243639i
$795$			15.0743i			0.534630i
$796$	−2.52218	+	0.890470i	−0.0893962	+	0.0315619i
$797$		−	53.2281i		−	1.88544i	−0.333590	−	0.942718i	$-0.608260\pi$
$797$		−	53.2281i		−	1.88544i	0.333590	−	0.942718i	$-0.391740\pi$
$798$	2.35057	+	13.7183i	0.0832092	+	0.485623i
$799$	−56.2296			−1.98926
$800$	−49.4383	−	43.5632i	−1.74791	−	1.54019i
$801$	5.70580			0.201604
$802$	−3.35423	−	19.5759i	−0.118442	−	0.691248i
$803$			42.4594i			1.49836i
$804$	−21.6756	+	7.65270i	−0.764439	+	0.269890i
$805$		−	7.85499i		−	0.276852i
$806$	−8.28743	+	1.42001i	−0.291912	+	0.0500178i
$807$	20.6183			0.725798
$808$	−0.381395	+	0.212882i	−0.0134174	+	0.00748917i
$809$	−45.8144			−1.61075			−0.805375	−	0.592766i	$-0.798036\pi$
$809$	−45.8144			−1.61075			−0.805375	+	0.592766i	$0.798036\pi$
$810$	−5.68744	+	0.974516i	−0.199836	+	0.0342410i
$811$		−	28.9020i		−	1.01489i	−0.861685	−	0.507443i	$-0.830591\pi$
$811$		−	28.9020i		−	1.01489i	0.861685	−	0.507443i	$-0.169409\pi$
$812$	9.50287	+	26.9161i	0.333485	+	0.944568i
$813$			3.31648i			0.116314i
$814$	−6.18727	−	36.1099i	−0.216864	−	1.26565i
$815$	−20.7970			−0.728486
$816$	12.9077	+	16.0014i	0.451860	+	0.560161i
$817$	10.4404			0.365263
$818$	−1.87977	−	10.9706i	−0.0657244	−	0.383579i
$819$		−	6.22729i		−	0.217599i
$820$	32.4710	+	91.9713i	1.13394	+	3.21178i
$821$		−	21.4773i		−	0.749561i	−0.927113	−	0.374781i	$-0.877718\pi$
$821$		−	21.4773i		−	0.749561i	0.927113	−	0.374781i	$-0.122282\pi$
$822$	18.1592	−	3.11150i	0.633376	−	0.108526i
$823$	1.06437			0.0371017			0.0185509	−	0.999828i	$-0.494095\pi$
$823$	1.06437			0.0371017			0.0185509	+	0.999828i	$0.494095\pi$
$824$	−5.43966	−	9.74558i	−0.189500	−	0.339504i
$825$	−38.6391			−1.34524
$826$	−26.8961	+	4.60852i	−0.935836	+	0.160351i
$827$			6.65816i			0.231527i	0.993277	+	0.115764i	$0.0369315\pi$
$827$			6.65816i			0.231527i	−0.993277	+	0.115764i	$0.963069\pi$
$828$	1.88591	−	0.665833i	0.0655400	−	0.0231393i
$829$			11.1460i			0.387117i	0.981089	+	0.193559i	$0.0620029\pi$
$829$			11.1460i			0.387117i	−0.981089	+	0.193559i	$0.937997\pi$
$830$	−9.93062	−	57.9568i	−0.344697	−	2.01171i
$831$	−12.3940			−0.429943
$832$	22.0261	+	13.5836i	0.763619	+	0.470928i
$833$	16.9293			0.586567
$834$	1.38213	+	8.06637i	0.0478594	+	0.279316i
$835$		−	74.7551i		−	2.58701i
$836$	−31.9811	+	11.2911i	−1.10609	+	0.390511i
$837$		−	1.83802i		−	0.0635311i
$838$	−24.0057	+	4.11326i	−0.829263	+	0.142090i
$839$	45.5904			1.57396			0.786979	−	0.616980i	$-0.211644\pi$
$839$	45.5904			1.57396			0.786979	+	0.616980i	$0.211644\pi$
$840$	10.8283	+	19.3998i	0.373613	+	0.669358i
$841$	−25.9617			−0.895230
$842$	23.4353	−	4.01553i	0.807634	−	0.138384i
$843$		−	19.4045i		−	0.668325i
$844$	15.4674	+	43.8102i	0.532411	+	1.50801i
$845$			10.3494i			0.356029i
$846$	−2.61298	−	15.2498i	−0.0898360	−	0.524298i
$847$	0.00640834			0.000220193
$848$	9.27830	+	11.5021i	0.318618	+	0.394984i
$849$	−16.9344			−0.581186
$850$	14.2988	+	83.4504i	0.490446	+	2.86233i
$851$			7.80968i			0.267712i
$852$	0.746236	+	2.11365i	0.0255656	+	0.0724124i
$853$			39.3936i			1.34881i	0.738362	+	0.674405i	$0.235600\pi$
$853$			39.3936i			1.34881i	−0.738362	+	0.674405i	$0.764400\pi$
$854$	10.4599	−	1.79225i	0.357931	−	0.0613297i
$855$	−20.8591			−0.713365
$856$	2.40136	−	1.34036i	0.0820770	−	0.0458127i
$857$	8.67083			0.296190			0.148095	−	0.988973i	$-0.452686\pi$
$857$	8.67083			0.296190			0.148095	+	0.988973i	$0.452686\pi$
$858$	14.9566	−	2.56274i	0.510610	−	0.0874905i
$859$			27.1809i			0.927402i	0.885992	+	0.463701i	$0.153479\pi$
$859$			27.1809i			0.927402i	−0.885992	+	0.463701i	$0.846521\pi$
$860$	15.7150	−	5.54827i	0.535877	−	0.189194i
$861$		−	23.0094i		−	0.784157i
$862$	3.81144	+	22.2442i	0.129818	+	0.757641i
$863$	−48.5298			−1.65198			−0.825988	−	0.563688i	$-0.809382\pi$
$863$	−48.5298			−1.65198			−0.825988	+	0.563688i	$0.809382\pi$
$864$	−3.73986	+	4.24423i	−0.127233	+	0.144392i
$865$	−103.294			−3.51211
$866$	−7.20091	−	42.0258i	−0.244697	−	1.42809i
$867$		−	9.41587i		−	0.319780i
$868$	−6.67314	+	2.35599i	−0.226501	+	0.0799676i
$869$			11.6931i			0.396660i
$870$	−42.1645	+	7.22469i	−1.42951	+	0.244940i
$871$	37.1782			1.25974
$872$	−0.261189	+	0.145787i	−0.00884499	+	0.00493698i
$873$	−0.894897			−0.0302877
$874$	7.12592	−	1.22099i	0.241038	−	0.0413007i
$875$			52.2227i			1.76545i
$876$	8.52269	+	24.1398i	0.287955	+	0.815607i
$877$		−	16.5665i		−	0.559410i	−0.960086	−	0.279705i	$-0.909763\pi$
$877$		−	16.5665i		−	0.559410i	0.960086	−	0.279705i	$-0.0902367\pi$
$878$	−1.61795	−	9.44262i	−0.0546031	−	0.318673i
$879$	−19.2392			−0.648923
$880$	−42.1380	+	33.9910i	−1.42047	+	1.14584i
$881$	−6.96876			−0.234783			−0.117392	−	0.993086i	$-0.537453\pi$
$881$	−6.96876			−0.234783			−0.117392	+	0.993086i	$0.537453\pi$
$882$	0.786704	+	4.59134i	0.0264897	+	0.154598i
$883$		−	16.7729i		−	0.564452i	−0.959348	−	0.282226i	$-0.908927\pi$
$883$		−	16.7729i		−	0.564452i	0.959348	−	0.282226i	$-0.0910728\pi$
$884$	−11.0697	−	31.3540i	−0.372315	−	1.05455i
$885$		−	40.8963i		−	1.37472i
$886$	10.2937	−	1.76377i	0.345822	−	0.0592550i
$887$	−28.5330			−0.958046			−0.479023	−	0.877802i	$-0.659009\pi$
$887$	−28.5330			−0.958046			−0.479023	+	0.877802i	$0.659009\pi$
$888$	−10.7659	−	19.2879i	−0.361280	−	0.647261i
$889$	24.2261			0.812516
$890$	32.4514	−	5.56039i	1.08777	−	0.186385i
$891$			3.31713i			0.111128i
$892$	−33.5197	+	11.8343i	−1.12232	+	0.396243i
$893$		−	55.9296i		−	1.87161i
$894$	1.26552	+	7.38579i	0.0423253	+	0.247018i
$895$	79.7236			2.66486
$896$	20.2030	+	8.13771i	0.674935	+	0.271862i
$897$	−3.23474			−0.108005
$898$	−1.72621	−	10.0745i	−0.0576045	−	0.336190i
$899$		−	13.6263i		−	0.454464i
$900$	−21.9678	+	7.75585i	−0.732259	+	0.258528i
$901$		−	18.9882i		−	0.632589i
$902$	55.2635	−	9.46914i	1.84007	−	0.315288i
$903$	−3.93157			−0.130835
$904$	−7.71430	−	13.8208i	−0.256574	−	0.459672i
$905$	−3.65512			−0.121500
$906$	−13.1013	+	2.24485i	−0.435262	+	0.0745800i
$907$			9.28967i			0.308458i	0.988035	+	0.154229i	$0.0492894\pi$
$907$			9.28967i			0.308458i	−0.988035	+	0.154229i	$0.950711\pi$
$908$	16.0481	+	45.4548i	0.532574	+	1.50847i
$909$			0.154427i			0.00512202i
$910$	−6.06859	−	35.4174i	−0.201172	−	1.17407i
$911$	−24.2874			−0.804679			−0.402339	−	0.915491i	$-0.631803\pi$
$911$	−24.2874			−0.804679			−0.402339	+	0.915491i	$0.631803\pi$
$912$	−15.9160	+	12.8388i	−0.527033	+	0.425137i
$913$	−33.8025			−1.11870
$914$	−4.42854	−	25.8457i	−0.146483	−	0.854901i
$915$			15.9046i			0.525789i
$916$	10.3596	+	29.3427i	0.342291	+	0.969509i
$917$		−	16.6283i		−	0.549116i
$918$	7.16414	−	1.22754i	0.236452	−	0.0405149i
$919$	−49.6916			−1.63917			−0.819587	−	0.572955i	$-0.805797\pi$
$919$	−49.6916			−1.63917			−0.819587	+	0.572955i	$0.805797\pi$
$920$	10.0772	−	5.62474i	0.332234	−	0.185442i
$921$	−13.1991			−0.434926
$922$	27.8038	−	4.76405i	0.915669	−	0.156896i
$923$		−	3.62535i		−	0.119330i
$924$	12.0432	−	4.25194i	0.396194	−	0.139878i
$925$		−	90.9699i		−	2.99107i
$926$	−2.99504	−	17.4796i	−0.0984232	−	0.574415i
$927$	−3.94598			−0.129603
$928$	−27.7259	+	31.4651i	−0.910146	+	1.03289i
$929$	24.4855			0.803342			0.401671	−	0.915784i	$-0.368430\pi$
$929$	24.4855			0.803342			0.401671	+	0.915784i	$0.368430\pi$
$930$	−1.79118	−	10.4536i	−0.0587350	−	0.342787i
$931$			16.8390i			0.551877i
$932$	33.5334	−	11.8392i	1.09842	−	0.387805i
$933$		−	31.9088i		−	1.04465i
$934$	44.4149	−	7.61027i	1.45330	−	0.249016i
$935$	69.5633			2.27496
$936$	7.98899	−	4.45919i	0.261128	−	0.145753i
$937$	33.7468			1.10246			0.551230	−	0.834353i	$-0.314159\pi$
$937$	33.7468			1.10246			0.551230	+	0.834353i	$0.314159\pi$
$938$	30.8419	−	5.28461i	1.00702	−	0.172549i
$939$		−	17.2307i		−	0.562301i
$940$	−29.7223	−	84.1859i	−0.969436	−	2.74584i
$941$		−	3.28150i		−	0.106974i	−0.998569	−	0.0534869i	$-0.982966\pi$
$941$		−	3.28150i		−	0.106974i	0.998569	−	0.0534869i	$-0.0170335\pi$
$942$	3.86083	+	22.5325i	0.125793	+	0.734148i
$943$	−11.9521			−0.389215
$944$	−25.1719	−	31.2050i	−0.819274	−	1.01564i
$945$	7.85499			0.255523
$946$	−1.61798	−	9.44279i	−0.0526050	−	0.307012i
$947$		−	46.6662i		−	1.51645i	−0.651993	−	0.758225i	$-0.726067\pi$
$947$		−	46.6662i		−	1.51645i	0.651993	−	0.758225i	$-0.273933\pi$
$948$	2.34710	+	6.64795i	0.0762302	+	0.215915i
$949$		−	41.4048i		−	1.34406i
$950$	−83.0052	+	14.2225i	−2.69305	+	0.461440i
$951$	29.5721			0.958942
$952$	−13.6398	−	24.4368i	−0.442069	−	0.792002i
$953$	45.2546			1.46594			0.732970	−	0.680261i	$-0.238133\pi$
$953$	45.2546			1.46594			0.732970	+	0.680261i	$0.238133\pi$
$954$	5.14971	−	0.882379i	0.166728	−	0.0285681i
$955$			28.4611i			0.920979i
$956$	33.7581	−	11.9185i	1.09182	−	0.385472i
$957$			24.5919i			0.794943i
$958$	−8.52642	−	49.7616i	−0.275476	−	1.60773i
$959$	−25.0799			−0.809873
$960$	−17.1342	+	27.7834i	−0.553003	+	0.896704i
$961$	−27.6217			−0.891023
$962$	6.03359	+	35.2131i	0.194531	+	1.13532i
$963$		−	0.972312i		−	0.0313323i
$964$	15.0896	−	5.32747i	0.486004	−	0.171586i
$965$		−	52.1671i		−	1.67932i
$966$	−2.68344	+	0.459794i	−0.0863381	+	0.0147936i
$967$	41.0528			1.32017			0.660084	−	0.751192i	$-0.270521\pi$
$967$	41.0528			1.32017			0.660084	+	0.751192i	$0.270521\pi$
$968$	0.00458884	+	0.00822126i	0.000147491	+	0.000264241i
$969$	26.2749			0.844073
$970$	−5.08968	+	0.872092i	−0.163420	+	0.0280012i
$971$		−	21.9250i		−	0.703605i	−0.936074	−	0.351803i	$-0.885569\pi$
$971$		−	21.9250i		−	0.703605i	0.936074	−	0.351803i	$-0.114431\pi$
$972$	0.665833	+	1.88591i	0.0213566	+	0.0604907i
$973$		−	11.1405i		−	0.357149i
$974$	2.15114	+	12.5544i	0.0689271	+	0.402270i
$975$	37.6794			1.20671
$976$	9.78933	+	12.1356i	0.313349	+	0.388452i
$977$	−3.69255			−0.118135			−0.0590676	−	0.998254i	$-0.518813\pi$
$977$	−3.69255			−0.118135			−0.0590676	+	0.998254i	$0.518813\pi$
$978$	1.21736	+	7.10470i	0.0389268	+	0.227183i
$979$		−	18.9268i		−	0.604905i
$980$	8.94867	+	25.3463i	0.285855	+	0.809659i
$981$			0.105755i			0.00337651i
$982$	−23.0091	+	3.94250i	−0.734251	+	0.125810i
$983$	−2.61252			−0.0833264			−0.0416632	−	0.999132i	$-0.513266\pi$
$983$	−2.61252			−0.0833264			−0.0416632	+	0.999132i	$0.513266\pi$
$984$	29.5187	−	16.4764i	0.941022	−	0.525248i
$985$	2.12789			0.0678001
$986$	53.1122	−	9.10051i	1.69144	−	0.289819i
$987$			21.0616i			0.670399i
$988$	31.1868	−	11.0107i	0.992183	−	0.350296i
$989$			2.04224i			0.0649395i
$990$	3.23259	+	18.8660i	0.102739	+	0.599600i
$991$	−4.00303			−0.127161			−0.0635803	−	0.997977i	$-0.520252\pi$
$991$	−4.00303			−0.127161			−0.0635803	+	0.997977i	$0.520252\pi$
$992$	−7.80096	−	6.87391i	−0.247681	−	0.218247i
$993$	−14.3757			−0.456199
$994$	−0.515317	−	3.00748i	−0.0163449	−	0.0953914i
$995$			5.45682i			0.172993i
$996$	−19.2180	+	6.78504i	−0.608947	+	0.214992i
$997$			31.8616i			1.00907i	0.863392	+	0.504534i	$0.168336\pi$
$997$			31.8616i			1.00907i	−0.863392	+	0.504534i	$0.831664\pi$
$998$	13.0908	−	2.24305i	0.414382	−	0.0710024i
$999$	−7.80968			−0.247087

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.f.d.277.14	yes	20
4.3	odd	2		2208.2.f.d.1105.20		20
8.3	odd	2		2208.2.f.d.1105.1		20
8.5	even	2	inner	552.2.f.d.277.13	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.f.d.277.13	✓	20	8.5	even	2	inner
552.2.f.d.277.14	yes	20	1.1	even	1	trivial
2208.2.f.d.1105.1		20	8.3	odd	2
2208.2.f.d.1105.20		20	4.3	odd	2

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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.238838 + 1.39390i) q^{2} -1.00000i q^{3} +(-1.88591 + 0.665833i) q^{4} +4.08024i q^{5} +(1.39390 - 0.238838i) q^{6} -1.92513 q^{7} +(-1.37853 - 2.46975i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(0.238838 + 1.39390i) q^{2} -1.00000i q^{3} +(-1.88591 + 0.665833i) q^{4} +4.08024i q^{5} +(1.39390 - 0.238838i) q^{6} -1.92513 q^{7} +(-1.37853 - 2.46975i) q^{8} -1.00000 q^{9} +(-5.68744 + 0.974516i) q^{10} +3.31713i q^{11} +(0.665833 + 1.88591i) q^{12} -3.23474i q^{13} +(-0.459794 - 2.68344i) q^{14} +4.08024 q^{15} +(3.11333 - 2.51140i) q^{16} -5.13964 q^{17} +(-0.238838 - 1.39390i) q^{18} -5.11222i q^{19} +(-2.71676 - 7.69498i) q^{20} +1.92513i q^{21} +(-4.62374 + 0.792256i) q^{22} +1.00000 q^{23} +(-2.46975 + 1.37853i) q^{24} -11.6484 q^{25} +(4.50890 - 0.772579i) q^{26} +1.00000i q^{27} +(3.63062 - 1.28181i) q^{28} +7.41361i q^{29} +(0.974516 + 5.68744i) q^{30} -1.83802 q^{31} +(4.24423 + 3.73986i) q^{32} +3.31713 q^{33} +(-1.22754 - 7.16414i) q^{34} -7.85499i q^{35} +(1.88591 - 0.665833i) q^{36} +7.80968i q^{37} +(7.12592 - 1.22099i) q^{38} -3.23474 q^{39} +(10.0772 - 5.62474i) q^{40} -11.9521 q^{41} +(-2.68344 + 0.459794i) q^{42} +2.04224i q^{43} +(-2.20865 - 6.25581i) q^{44} -4.08024i q^{45} +(0.238838 + 1.39390i) q^{46} +10.9404 q^{47} +(-2.51140 - 3.11333i) q^{48} -3.29388 q^{49} +(-2.78207 - 16.2366i) q^{50} +5.13964i q^{51} +(2.15379 + 6.10044i) q^{52} +3.69447i q^{53} +(-1.39390 + 0.238838i) q^{54} -13.5347 q^{55} +(2.65385 + 4.75458i) q^{56} -5.11222 q^{57} +(-10.3338 + 1.77065i) q^{58} -10.0230i q^{59} +(-7.69498 + 2.71676i) q^{60} +3.89795i q^{61} +(-0.438988 - 2.56201i) q^{62} +1.92513 q^{63} +(-4.19930 + 6.80925i) q^{64} +13.1985 q^{65} +(0.792256 + 4.62374i) q^{66} +11.4934i q^{67} +(9.69291 - 3.42214i) q^{68} -1.00000i q^{69} +(10.9491 - 1.87607i) q^{70} +1.12076 q^{71} +(1.37853 + 2.46975i) q^{72} +12.8000 q^{73} +(-10.8859 + 1.86525i) q^{74} +11.6484i q^{75} +(3.40388 + 9.64120i) q^{76} -6.38590i q^{77} +(-0.772579 - 4.50890i) q^{78} +3.52506 q^{79} +(10.2471 + 12.7031i) q^{80} +1.00000 q^{81} +(-2.85462 - 16.6601i) q^{82} +10.1903i q^{83} +(-1.28181 - 3.63062i) q^{84} -20.9709i q^{85} +(-2.84668 + 0.487765i) q^{86} +7.41361 q^{87} +(8.19246 - 4.57276i) q^{88} -5.70580 q^{89} +(5.68744 - 0.974516i) q^{90} +6.22729i q^{91} +(-1.88591 + 0.665833i) q^{92} +1.83802i q^{93} +(2.61298 + 15.2498i) q^{94} +20.8591 q^{95} +(3.73986 - 4.24423i) q^{96} +0.894897 q^{97} +(-0.786704 - 4.59134i) q^{98} -3.31713i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} + 2 q^{6} - 8 q^{7} - 2 q^{8} - 20 q^{9}+O(q^{10}) \) 20 * q - 2 * q^2 + 2 * q^6 - 8 * q^7 - 2 * q^8 - 20 * q^9	\( 20 q - 2 q^{2} + 2 q^{6} - 8 q^{7} - 2 q^{8} - 20 q^{9} - 12 q^{10} + 2 q^{14} + 4 q^{15} + 4 q^{16} + 32 q^{17} + 2 q^{18} + 20 q^{20} + 14 q^{22} + 20 q^{23} + 10 q^{24} - 28 q^{25} + 18 q^{28} - 22 q^{32} + 28 q^{33} - 26 q^{34} + 16 q^{38} + 4 q^{40} - 40 q^{41} + 14 q^{42} + 10 q^{44} - 2 q^{46} + 40 q^{47} + 12 q^{49} - 14 q^{50} + 20 q^{52} - 2 q^{54} - 8 q^{55} + 6 q^{56} - 44 q^{57} - 32 q^{58} - 24 q^{60} + 20 q^{62} + 8 q^{63} - 48 q^{64} + 8 q^{65} + 10 q^{66} + 22 q^{68} + 80 q^{70} - 40 q^{71} + 2 q^{72} - 16 q^{73} - 30 q^{74} + 44 q^{76} - 36 q^{78} - 16 q^{79} + 4 q^{80} + 20 q^{81} - 32 q^{82} + 6 q^{84} - 4 q^{86} + 8 q^{87} - 70 q^{88} - 40 q^{89} + 12 q^{90} + 64 q^{94} - 40 q^{95} + 2 q^{96} + 32 q^{97} - 26 q^{98}+O(q^{100}) \) 20 * q - 2 * q^2 + 2 * q^6 - 8 * q^7 - 2 * q^8 - 20 * q^9 - 12 * q^10 + 2 * q^14 + 4 * q^15 + 4 * q^16 + 32 * q^17 + 2 * q^18 + 20 * q^20 + 14 * q^22 + 20 * q^23 + 10 * q^24 - 28 * q^25 + 18 * q^28 - 22 * q^32 + 28 * q^33 - 26 * q^34 + 16 * q^38 + 4 * q^40 - 40 * q^41 + 14 * q^42 + 10 * q^44 - 2 * q^46 + 40 * q^47 + 12 * q^49 - 14 * q^50 + 20 * q^52 - 2 * q^54 - 8 * q^55 + 6 * q^56 - 44 * q^57 - 32 * q^58 - 24 * q^60 + 20 * q^62 + 8 * q^63 - 48 * q^64 + 8 * q^65 + 10 * q^66 + 22 * q^68 + 80 * q^70 - 40 * q^71 + 2 * q^72 - 16 * q^73 - 30 * q^74 + 44 * q^76 - 36 * q^78 - 16 * q^79 + 4 * q^80 + 20 * q^81 - 32 * q^82 + 6 * q^84 - 4 * q^86 + 8 * q^87 - 70 * q^88 - 40 * q^89 + 12 * q^90 + 64 * q^94 - 40 * q^95 + 2 * q^96 + 32 * q^97 - 26 * q^98

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