LMFDB - Embedded newform 55.2.b.a.34.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [55,2,Mod(34,55)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(55, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("55.34");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 55 = 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	55.b (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:	$0.439177211117$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-11})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2x^{2} - 3x + 9 $ x^4 - x^3 - 2x^2 - 3x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			34.1
Root			$-1.18614 + 1.26217i$ of defining polynomial
Character	$\chi$	$=$	55.34
Dual form			55.2.b.a.34.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.52434i q^{2} +0.792287i q^{3} -4.37228 q^{4} +(0.686141 - 2.12819i) q^{5} +2.00000 q^{6} +3.46410i q^{7} +5.98844i q^{8} +2.37228 q^{9} +O(q^{10})$	\(q-2.52434i q^{2} +0.792287i q^{3} -4.37228 q^{4} +(0.686141 - 2.12819i) q^{5} +2.00000 q^{6} +3.46410i q^{7} +5.98844i q^{8} +2.37228 q^{9} +(-5.37228 - 1.73205i) q^{10} -1.00000 q^{11} -3.46410i q^{12} +8.74456 q^{14} +(1.68614 + 0.543620i) q^{15} +6.37228 q^{16} +1.58457i q^{17} -5.98844i q^{18} -4.00000 q^{19} +(-3.00000 + 9.30506i) q^{20} -2.74456 q^{21} +2.52434i q^{22} -0.792287i q^{23} -4.74456 q^{24} +(-4.05842 - 2.92048i) q^{25} +4.25639i q^{27} -15.1460i q^{28} -8.74456 q^{29} +(1.37228 - 4.25639i) q^{30} +3.37228 q^{31} -4.10891i q^{32} -0.792287i q^{33} +4.00000 q^{34} +(7.37228 + 2.37686i) q^{35} -10.3723 q^{36} -1.08724i q^{37} +10.0974i q^{38} +(12.7446 + 4.10891i) q^{40} +8.74456 q^{41} +6.92820i q^{42} -3.46410i q^{43} +4.37228 q^{44} +(1.62772 - 5.04868i) q^{45} -2.00000 q^{46} -6.63325i q^{47} +5.04868i q^{48} -5.00000 q^{49} +(-7.37228 + 10.2448i) q^{50} -1.25544 q^{51} -10.0974i q^{53} +10.7446 q^{54} +(-0.686141 + 2.12819i) q^{55} -20.7446 q^{56} -3.16915i q^{57} +22.0742i q^{58} +7.37228 q^{59} +(-7.37228 - 2.37686i) q^{60} -0.744563 q^{61} -8.51278i q^{62} +8.21782i q^{63} +2.37228 q^{64} -2.00000 q^{66} +9.30506i q^{67} -6.92820i q^{68} +0.627719 q^{69} +(6.00000 - 18.6101i) q^{70} -10.1168 q^{71} +14.2063i q^{72} +6.92820i q^{73} -2.74456 q^{74} +(2.31386 - 3.21543i) q^{75} +17.4891 q^{76} -3.46410i q^{77} -1.25544 q^{79} +(4.37228 - 13.5615i) q^{80} +3.74456 q^{81} -22.0742i q^{82} -6.63325i q^{83} +12.0000 q^{84} +(3.37228 + 1.08724i) q^{85} -8.74456 q^{86} -6.92820i q^{87} -5.98844i q^{88} -1.37228 q^{89} +(-12.7446 - 4.10891i) q^{90} +3.46410i q^{92} +2.67181i q^{93} -16.7446 q^{94} +(-2.74456 + 8.51278i) q^{95} +3.25544 q^{96} +5.84096i q^{97} +12.6217i q^{98} -2.37228 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 6 q^{4} - 3 q^{5} + 8 q^{6} - 2 q^{9}+O(q^{10}) $ 4 * q - 6 * q^4 - 3 * q^5 + 8 * q^6 - 2 * q^9	$ 4 q - 6 q^{4} - 3 q^{5} + 8 q^{6} - 2 q^{9} - 10 q^{10} - 4 q^{11} + 12 q^{14} + q^{15} + 14 q^{16} - 16 q^{19} - 12 q^{20} + 12 q^{21} + 4 q^{24} + q^{25} - 12 q^{29} - 6 q^{30} + 2 q^{31} + 16 q^{34} + 18 q^{35} - 30 q^{36} + 28 q^{40} + 12 q^{41} + 6 q^{44} + 18 q^{45} - 8 q^{46} - 20 q^{49} - 18 q^{50} - 28 q^{51} + 20 q^{54} + 3 q^{55} - 60 q^{56} + 18 q^{59} - 18 q^{60} + 20 q^{61} - 2 q^{64} - 8 q^{66} + 14 q^{69} + 24 q^{70} - 6 q^{71} + 12 q^{74} + 15 q^{75} + 24 q^{76} - 28 q^{79} + 6 q^{80} - 8 q^{81} + 48 q^{84} + 2 q^{85} - 12 q^{86} + 6 q^{89} - 28 q^{90} - 44 q^{94} + 12 q^{95} + 36 q^{96} + 2 q^{99}+O(q^{100}) $ 4 * q - 6 * q^4 - 3 * q^5 + 8 * q^6 - 2 * q^9 - 10 * q^10 - 4 * q^11 + 12 * q^14 + q^15 + 14 * q^16 - 16 * q^19 - 12 * q^20 + 12 * q^21 + 4 * q^24 + q^25 - 12 * q^29 - 6 * q^30 + 2 * q^31 + 16 * q^34 + 18 * q^35 - 30 * q^36 + 28 * q^40 + 12 * q^41 + 6 * q^44 + 18 * q^45 - 8 * q^46 - 20 * q^49 - 18 * q^50 - 28 * q^51 + 20 * q^54 + 3 * q^55 - 60 * q^56 + 18 * q^59 - 18 * q^60 + 20 * q^61 - 2 * q^64 - 8 * q^66 + 14 * q^69 + 24 * q^70 - 6 * q^71 + 12 * q^74 + 15 * q^75 + 24 * q^76 - 28 * q^79 + 6 * q^80 - 8 * q^81 + 48 * q^84 + 2 * q^85 - 12 * q^86 + 6 * q^89 - 28 * q^90 - 44 * q^94 + 12 * q^95 + 36 * q^96 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/55\mathbb{Z}\right)^\times$.

$n$	$12$	$46$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	2.52434i		−	1.78498i	−0.451071	−	0.892488i	$-0.648958\pi$
$2$		−	2.52434i		−	1.78498i	0.451071	−	0.892488i	$-0.351042\pi$
$3$			0.792287i			0.457427i	0.973494	+	0.228714i	$0.0734519\pi$
$3$			0.792287i			0.457427i	−0.973494	+	0.228714i	$0.926548\pi$
$4$	−4.37228			−2.18614
$5$	0.686141	−	2.12819i	0.306851	−	0.951757i
$5$	0.686141	−	2.12819i	0.306851	−	0.951757i
$6$	2.00000			0.816497
$7$			3.46410i			1.30931i	0.755929	+	0.654654i	$0.227186\pi$
$7$			3.46410i			1.30931i	−0.755929	+	0.654654i	$0.772814\pi$
$8$			5.98844i			2.11723i
$9$	2.37228			0.790760
$10$	−5.37228	−	1.73205i	−1.69886	−	0.547723i
$11$	−1.00000			−0.301511
$11$	−1.00000			−0.301511
$12$		−	3.46410i		−	1.00000i
$13$		0			0		1.00000			$0$
$13$		0			0		−1.00000			$\pi$
$14$	8.74456			2.33708
$15$	1.68614	+	0.543620i	0.435360	+	0.140362i
$16$	6.37228			1.59307
$17$			1.58457i			0.384316i	0.981364	+	0.192158i	$0.0615486\pi$
$17$			1.58457i			0.384316i	−0.981364	+	0.192158i	$0.938451\pi$
$18$		−	5.98844i		−	1.41149i
$19$	−4.00000			−0.917663			−0.458831	−	0.888523i	$-0.651732\pi$
$19$	−4.00000			−0.917663			−0.458831	+	0.888523i	$0.651732\pi$
$20$	−3.00000	+	9.30506i	−0.670820	+	2.08068i
$21$	−2.74456			−0.598913
$22$			2.52434i			0.538191i
$23$		−	0.792287i		−	0.165203i	−0.996583	−	0.0826016i	$-0.973677\pi$
$23$		−	0.792287i		−	0.165203i	0.996583	−	0.0826016i	$-0.0263229\pi$
$24$	−4.74456			−0.968480
$25$	−4.05842	−	2.92048i	−0.811684	−	0.584096i
$26$		0			0
$27$			4.25639i			0.819142i
$28$		−	15.1460i		−	2.86233i
$29$	−8.74456			−1.62382			−0.811912	−	0.583779i	$-0.801573\pi$
$29$	−8.74456			−1.62382			−0.811912	+	0.583779i	$0.801573\pi$
$30$	1.37228	−	4.25639i	0.250543	−	0.777107i
$31$	3.37228			0.605680			0.302840	−	0.953041i	$-0.402065\pi$
$31$	3.37228			0.605680			0.302840	+	0.953041i	$0.402065\pi$
$32$		−	4.10891i		−	0.726360i
$33$		−	0.792287i		−	0.137919i
$34$	4.00000			0.685994
$35$	7.37228	+	2.37686i	1.24614	+	0.401763i
$36$	−10.3723			−1.72871
$37$		−	1.08724i		−	0.178741i	−0.995998	−	0.0893706i	$-0.971514\pi$
$37$		−	1.08724i		−	0.178741i	0.995998	−	0.0893706i	$-0.0284856\pi$
$38$			10.0974i			1.63801i
$39$		0			0
$40$	12.7446	+	4.10891i	2.01509	+	0.649676i
$41$	8.74456			1.36567			0.682836	−	0.730572i	$-0.260747\pi$
$41$	8.74456			1.36567			0.682836	+	0.730572i	$0.260747\pi$
$42$			6.92820i			1.06904i
$43$		−	3.46410i		−	0.528271i	−0.964486	−	0.264135i	$-0.914913\pi$
$43$		−	3.46410i		−	0.528271i	0.964486	−	0.264135i	$-0.0850865\pi$
$44$	4.37228			0.659146
$45$	1.62772	−	5.04868i	0.242646	−	0.752612i
$46$	−2.00000			−0.294884
$47$		−	6.63325i		−	0.967559i	−0.875190	−	0.483779i	$-0.839264\pi$
$47$		−	6.63325i		−	0.967559i	0.875190	−	0.483779i	$-0.160736\pi$
$48$			5.04868i			0.728714i
$49$	−5.00000			−0.714286
$50$	−7.37228	+	10.2448i	−1.04260	+	1.44884i
$51$	−1.25544			−0.175796
$52$		0			0
$53$		−	10.0974i		−	1.38698i	−0.720467	−	0.693489i	$-0.756073\pi$
$53$		−	10.0974i		−	1.38698i	0.720467	−	0.693489i	$-0.243927\pi$
$54$	10.7446			1.46215
$55$	−0.686141	+	2.12819i	−0.0925192	+	0.286966i
$56$	−20.7446			−2.77211
$57$		−	3.16915i		−	0.419764i
$58$			22.0742i			2.89849i
$59$	7.37228			0.959789			0.479895	−	0.877326i	$-0.340675\pi$
$59$	7.37228			0.959789			0.479895	+	0.877326i	$0.340675\pi$
$60$	−7.37228	−	2.37686i	−0.951757	−	0.306851i
$61$	−0.744563			−0.0953315			−0.0476657	−	0.998863i	$-0.515178\pi$
$61$	−0.744563			−0.0953315			−0.0476657	+	0.998863i	$0.515178\pi$
$62$		−	8.51278i		−	1.08112i
$63$			8.21782i			1.03535i
$64$	2.37228			0.296535
$65$		0			0
$66$	−2.00000			−0.246183
$67$			9.30506i			1.13679i	0.822754	+	0.568397i	$0.192436\pi$
$67$			9.30506i			1.13679i	−0.822754	+	0.568397i	$0.807564\pi$
$68$		−	6.92820i		−	0.840168i
$69$	0.627719			0.0755684
$70$	6.00000	−	18.6101i	0.717137	−	2.22434i
$71$	−10.1168			−1.20065			−0.600324	−	0.799757i	$-0.704962\pi$
$71$	−10.1168			−1.20065			−0.600324	+	0.799757i	$0.704962\pi$
$72$			14.2063i			1.67422i
$73$			6.92820i			0.810885i	0.914121	+	0.405442i	$0.132883\pi$
$73$			6.92820i			0.810885i	−0.914121	+	0.405442i	$0.867117\pi$
$74$	−2.74456			−0.319049
$75$	2.31386	−	3.21543i	0.267181	−	0.371286i
$76$	17.4891			2.00614
$77$		−	3.46410i		−	0.394771i
$78$		0			0
$79$	−1.25544			−0.141248			−0.0706239	−	0.997503i	$-0.522499\pi$
$79$	−1.25544			−0.141248			−0.0706239	+	0.997503i	$0.522499\pi$
$80$	4.37228	−	13.5615i	0.488836	−	1.51622i
$81$	3.74456			0.416063
$82$		−	22.0742i		−	2.43769i
$83$		−	6.63325i		−	0.728094i	−0.931381	−	0.364047i	$-0.881395\pi$
$83$		−	6.63325i		−	0.728094i	0.931381	−	0.364047i	$-0.118605\pi$
$84$	12.0000			1.30931
$85$	3.37228	+	1.08724i	0.365775	+	0.117928i
$86$	−8.74456			−0.942950
$87$		−	6.92820i		−	0.742781i
$88$		−	5.98844i		−	0.638370i
$89$	−1.37228			−0.145462			−0.0727308	−	0.997352i	$-0.523171\pi$
$89$	−1.37228			−0.145462			−0.0727308	+	0.997352i	$0.523171\pi$
$90$	−12.7446	−	4.10891i	−1.34339	−	0.433117i
$91$		0			0
$92$			3.46410i			0.361158i
$93$			2.67181i			0.277054i
$94$	−16.7446			−1.72707
$95$	−2.74456	+	8.51278i	−0.281586	+	0.873393i
$96$	3.25544			0.332257
$97$			5.84096i			0.593060i	0.955024	+	0.296530i	$0.0958295\pi$
$97$			5.84096i			0.593060i	−0.955024	+	0.296530i	$0.904171\pi$
$98$			12.6217i			1.27498i
$99$	−2.37228			−0.238423
$100$	17.7446	+	12.7692i	1.77446	+	1.27692i
$101$	6.00000			0.597022			0.298511	−	0.954406i	$-0.403510\pi$
$101$	6.00000			0.597022			0.298511	+	0.954406i	$0.403510\pi$
$102$			3.16915i			0.313792i
$103$			10.3923i			1.02398i	0.858990	+	0.511992i	$0.171092\pi$
$103$			10.3923i			1.02398i	−0.858990	+	0.511992i	$0.828908\pi$
$104$		0			0
$105$	−1.88316	+	5.84096i	−0.183777	+	0.570020i
$106$	−25.4891			−2.47572
$107$		−	6.63325i		−	0.641260i	−0.947204	−	0.320630i	$-0.896105\pi$
$107$		−	6.63325i		−	0.641260i	0.947204	−	0.320630i	$-0.103895\pi$
$108$		−	18.6101i		−	1.79076i
$109$	−10.0000			−0.957826			−0.478913	−	0.877862i	$-0.658969\pi$
$109$	−10.0000			−0.957826			−0.478913	+	0.877862i	$0.658969\pi$
$110$	5.37228	+	1.73205i	0.512227	+	0.165145i
$111$	0.861407			0.0817611
$112$			22.0742i			2.08582i
$113$			0.497333i			0.0467852i	0.999726	+	0.0233926i	$0.00744677\pi$
$113$			0.497333i			0.0467852i	−0.999726	+	0.0233926i	$0.992553\pi$
$114$	−8.00000			−0.749269
$115$	−1.68614	−	0.543620i	−0.157233	−	0.0506929i
$116$	38.2337			3.54991
$117$		0			0
$118$		−	18.6101i		−	1.71320i
$119$	−5.48913			−0.503187
$120$	−3.25544	+	10.0974i	−0.297179	+	0.921758i
$121$	1.00000			0.0909091
$122$			1.87953i			0.170164i
$123$			6.92820i			0.624695i
$124$	−14.7446			−1.32410
$125$	−9.00000	+	6.63325i	−0.804984	+	0.593296i
$126$	20.7446			1.84807
$127$		−	8.21782i		−	0.729214i	−0.931162	−	0.364607i	$-0.881203\pi$
$127$		−	8.21782i		−	0.729214i	0.931162	−	0.364607i	$-0.118797\pi$
$128$		−	14.2063i		−	1.25567i
$129$	2.74456			0.241645
$130$		0			0
$131$	−2.74456			−0.239794			−0.119897	−	0.992786i	$-0.538256\pi$
$131$	−2.74456			−0.239794			−0.119897	+	0.992786i	$0.538256\pi$
$132$			3.46410i			0.301511i
$133$		−	13.8564i		−	1.20150i
$134$	23.4891			2.02915
$135$	9.05842	+	2.92048i	0.779625	+	0.251355i
$136$	−9.48913			−0.813686
$137$			14.3537i			1.22632i	0.789958	+	0.613161i	$0.210102\pi$
$137$			14.3537i			1.22632i	−0.789958	+	0.613161i	$0.789898\pi$
$138$		−	1.58457i		−	0.134888i
$139$	16.2337			1.37692			0.688462	−	0.725273i	$-0.258286\pi$
$139$	16.2337			1.37692			0.688462	+	0.725273i	$0.258286\pi$
$140$	−32.2337	−	10.3923i	−2.72424	−	0.878310i
$141$	5.25544			0.442588
$142$			25.5383i			2.14313i
$143$		0			0
$144$	15.1168			1.25974
$145$	−6.00000	+	18.6101i	−0.498273	+	1.54549i
$146$	17.4891			1.44741
$147$		−	3.96143i		−	0.326734i
$148$			4.75372i			0.390754i
$149$	11.4891			0.941226			0.470613	−	0.882340i	$-0.344033\pi$
$149$	11.4891			0.941226			0.470613	+	0.882340i	$0.344033\pi$
$150$	−8.11684	−	5.84096i	−0.662738	−	0.476913i
$151$	−12.2337			−0.995563			−0.497782	−	0.867302i	$-0.665852\pi$
$151$	−12.2337			−0.995563			−0.497782	+	0.867302i	$0.665852\pi$
$152$		−	23.9538i		−	1.94291i
$153$			3.75906i			0.303902i
$154$	−8.74456			−0.704657
$155$	2.31386	−	7.17687i	0.185854	−	0.576460i
$156$		0			0
$157$		−	24.4511i		−	1.95141i	−0.219090	−	0.975705i	$-0.570309\pi$
$157$		−	24.4511i		−	1.95141i	0.219090	−	0.975705i	$-0.429691\pi$
$158$			3.16915i			0.252124i
$159$	8.00000			0.634441
$160$	−8.74456	−	2.81929i	−0.691318	−	0.222885i
$161$	2.74456			0.216302
$162$		−	9.45254i		−	0.742662i
$163$			3.46410i			0.271329i	0.990755	+	0.135665i	$0.0433170\pi$
$163$			3.46410i			0.271329i	−0.990755	+	0.135665i	$0.956683\pi$
$164$	−38.2337			−2.98555
$165$	−1.68614	−	0.543620i	−0.131266	−	0.0423208i
$166$	−16.7446			−1.29963
$167$		−	15.7359i		−	1.21768i	−0.793292	−	0.608842i	$-0.791635\pi$
$167$		−	15.7359i		−	1.21768i	0.793292	−	0.608842i	$-0.208365\pi$
$168$		−	16.4356i		−	1.26804i
$169$	13.0000			1.00000
$170$	2.74456	−	8.51278i	0.210498	−	0.652900i
$171$	−9.48913			−0.725652
$172$			15.1460i			1.15487i
$173$			8.51278i			0.647214i	0.946192	+	0.323607i	$0.104896\pi$
$173$			8.51278i			0.647214i	−0.946192	+	0.323607i	$0.895104\pi$
$174$	−17.4891			−1.32585
$175$	10.1168	−	14.0588i	0.764762	−	1.06274i
$176$	−6.37228			−0.480329
$177$			5.84096i			0.439034i
$178$			3.46410i			0.259645i
$179$	−12.8614			−0.961307			−0.480653	−	0.876911i	$-0.659600\pi$
$179$	−12.8614			−0.961307			−0.480653	+	0.876911i	$0.659600\pi$
$180$	−7.11684	+	22.0742i	−0.530458	+	1.64532i
$181$	24.1168			1.79259			0.896295	−	0.443457i	$-0.146248\pi$
$181$	24.1168			1.79259			0.896295	+	0.443457i	$0.146248\pi$
$182$		0			0
$183$		−	0.589907i		−	0.0436072i
$184$	4.74456			0.349774
$185$	−2.31386	−	0.746000i	−0.170118	−	0.0548470i
$186$	6.74456			0.494535
$187$		−	1.58457i		−	0.115876i
$188$			29.0024i			2.11522i
$189$	−14.7446			−1.07251
$190$	21.4891	+	6.92820i	1.55899	+	0.502625i
$191$	−19.3723			−1.40173			−0.700865	−	0.713294i	$-0.747202\pi$
$191$	−19.3723			−1.40173			−0.700865	+	0.713294i	$0.747202\pi$
$192$			1.87953i			0.135643i
$193$			16.4356i			1.18306i	0.806282	+	0.591532i	$0.201477\pi$
$193$			16.4356i			1.18306i	−0.806282	+	0.591532i	$0.798523\pi$
$194$	14.7446			1.05860
$195$		0			0
$196$	21.8614			1.56153
$197$			8.51278i			0.606510i	0.952909	+	0.303255i	$0.0980734\pi$
$197$			8.51278i			0.606510i	−0.952909	+	0.303255i	$0.901927\pi$
$198$			5.98844i			0.425580i
$199$	8.00000			0.567105			0.283552	−	0.958957i	$-0.408487\pi$
$199$	8.00000			0.567105			0.283552	+	0.958957i	$0.408487\pi$
$200$	17.4891	−	24.3036i	1.23667	−	1.71853i
$201$	−7.37228			−0.520001
$202$		−	15.1460i		−	1.06567i
$203$		−	30.2921i		−	2.12609i
$204$	5.48913			0.384316
$205$	6.00000	−	18.6101i	0.419058	−	1.29979i
$206$	26.2337			1.82779
$207$		−	1.87953i		−	0.130636i
$208$		0			0
$209$	4.00000			0.276686
$210$	14.7446	+	4.75372i	1.01747	+	0.328038i
$211$	1.48913			0.102516			0.0512578	−	0.998685i	$-0.483677\pi$
$211$	1.48913			0.102516			0.0512578	+	0.998685i	$0.483677\pi$
$212$			44.1485i			3.03213i
$213$		−	8.01544i		−	0.549209i
$214$	−16.7446			−1.14463
$215$	−7.37228	−	2.37686i	−0.502785	−	0.162101i
$216$	−25.4891			−1.73432
$217$			11.6819i			0.793021i
$218$			25.2434i			1.70970i
$219$	−5.48913			−0.370921
$220$	3.00000	−	9.30506i	0.202260	−	0.627347i
$221$		0			0
$222$		−	2.17448i		−	0.145942i
$223$			2.37686i			0.159166i	0.996828	+	0.0795832i	$0.0253589\pi$
$223$			2.37686i			0.159166i	−0.996828	+	0.0795832i	$0.974641\pi$
$224$	14.2337			0.951028
$225$	−9.62772	−	6.92820i	−0.641848	−	0.461880i
$226$	1.25544			0.0835105
$227$			16.7306i			1.11045i	0.831701	+	0.555224i	$0.187368\pi$
$227$			16.7306i			1.11045i	−0.831701	+	0.555224i	$0.812632\pi$
$228$			13.8564i			0.917663i
$229$	−14.6277			−0.966627			−0.483313	−	0.875447i	$-0.660567\pi$
$229$	−14.6277			−0.966627			−0.483313	+	0.875447i	$0.660567\pi$
$230$	−1.37228	+	4.25639i	−0.0904856	+	0.280658i
$231$	2.74456			0.180579
$232$		−	52.3663i		−	3.43801i
$233$			3.75906i			0.246264i	0.992390	+	0.123132i	$0.0392938\pi$
$233$			3.75906i			0.246264i	−0.992390	+	0.123132i	$0.960706\pi$
$234$		0			0
$235$	−14.1168	−	4.55134i	−0.920881	−	0.296897i
$236$	−32.2337			−2.09823
$237$		−	0.994667i		−	0.0646105i
$238$			13.8564i			0.898177i
$239$	14.7446			0.953746			0.476873	−	0.878972i	$-0.341770\pi$
$239$	14.7446			0.953746			0.476873	+	0.878972i	$0.341770\pi$
$240$	10.7446	+	3.46410i	0.693559	+	0.223607i
$241$	16.7446			1.07861			0.539306	−	0.842110i	$-0.318687\pi$
$241$	16.7446			1.07861			0.539306	+	0.842110i	$0.318687\pi$
$242$		−	2.52434i		−	0.162271i
$243$			15.7359i			1.00946i
$244$	3.25544			0.208408
$245$	−3.43070	+	10.6410i	−0.219180	+	0.679827i
$246$	17.4891			1.11507
$247$		0			0
$248$			20.1947i			1.28236i
$249$	5.25544			0.333050
$250$	16.7446	+	22.7190i	1.05902	+	1.43688i
$251$	−22.1168			−1.39600			−0.698001	−	0.716096i	$-0.745927\pi$
$251$	−22.1168			−1.39600			−0.698001	+	0.716096i	$0.745927\pi$
$252$		−	35.9306i		−	2.26342i
$253$			0.792287i			0.0498107i
$254$	−20.7446			−1.30163
$255$	−0.861407	+	2.67181i	−0.0539434	+	0.167316i
$256$	−31.1168			−1.94480
$257$			10.6873i			0.666653i	0.942811	+	0.333326i	$0.108171\pi$
$257$			10.6873i			0.666653i	−0.942811	+	0.333326i	$0.891829\pi$
$258$		−	6.92820i		−	0.431331i
$259$	3.76631			0.234027
$260$		0			0
$261$	−20.7446			−1.28406
$262$			6.92820i			0.428026i
$263$		−	27.4179i		−	1.69066i	−0.534246	−	0.845329i	$-0.679405\pi$
$263$		−	27.4179i		−	1.69066i	0.534246	−	0.845329i	$-0.320595\pi$
$264$	4.74456			0.292008
$265$	−21.4891	−	6.92820i	−1.32007	−	0.425596i
$266$	−34.9783			−2.14465
$267$		−	1.08724i		−	0.0665380i
$268$		−	40.6844i		−	2.48519i
$269$	11.4891			0.700504			0.350252	−	0.936655i	$-0.386096\pi$
$269$	11.4891			0.700504			0.350252	+	0.936655i	$0.386096\pi$
$270$	7.37228	−	22.8665i	0.448663	−	1.39161i
$271$	13.4891			0.819406			0.409703	−	0.912219i	$-0.365632\pi$
$271$	13.4891			0.819406			0.409703	+	0.912219i	$0.365632\pi$
$272$			10.0974i			0.612242i
$273$		0			0
$274$	36.2337			2.18896
$275$	4.05842	+	2.92048i	0.244732	+	0.176112i
$276$	−2.74456			−0.165203
$277$		−	11.6819i		−	0.701899i	−0.936394	−	0.350949i	$-0.885859\pi$
$277$		−	11.6819i		−	0.701899i	0.936394	−	0.350949i	$-0.114141\pi$
$278$		−	40.9793i		−	2.45778i
$279$	8.00000			0.478947
$280$	−14.2337	+	44.1485i	−0.850626	+	2.63838i
$281$	−0.510875			−0.0304762			−0.0152381	−	0.999884i	$-0.504851\pi$
$281$	−0.510875			−0.0304762			−0.0152381	+	0.999884i	$0.504851\pi$
$282$		−	13.2665i		−	0.790009i
$283$		−	15.1460i		−	0.900338i	−0.892943	−	0.450169i	$-0.851364\pi$
$283$		−	15.1460i		−	0.900338i	0.892943	−	0.450169i	$-0.148636\pi$
$284$	44.2337			2.62479
$285$	−6.74456	−	2.17448i	−0.399513	−	0.128805i
$286$		0			0
$287$			30.2921i			1.78808i
$288$		−	9.74749i		−	0.574377i
$289$	14.4891			0.852301
$290$	46.9783	+	15.1460i	2.75866	+	0.889405i
$291$	−4.62772			−0.271282
$292$		−	30.2921i		−	1.77271i
$293$		−	3.16915i		−	0.185144i	−0.995706	−	0.0925718i	$-0.970491\pi$
$293$		−	3.16915i		−	0.185144i	0.995706	−	0.0925718i	$-0.0295088\pi$
$294$	−10.0000			−0.583212
$295$	5.05842	−	15.6896i	0.294513	−	0.913487i
$296$	6.51087			0.378437
$297$		−	4.25639i		−	0.246981i
$298$		−	29.0024i		−	1.68007i
$299$		0			0
$300$	−10.1168	+	14.0588i	−0.584096	+	0.811684i
$301$	12.0000			0.691669
$302$			30.8820i			1.77706i
$303$			4.75372i			0.273094i
$304$	−25.4891			−1.46190
$305$	−0.510875	+	1.58457i	−0.0292526	+	0.0907324i
$306$	9.48913			0.542457
$307$			31.5817i			1.80246i	0.433340	+	0.901231i	$0.357335\pi$
$307$			31.5817i			1.80246i	−0.433340	+	0.901231i	$0.642665\pi$
$308$			15.1460i			0.863025i
$309$	−8.23369			−0.468398
$310$	−18.1168	−	5.84096i	−1.02897	−	0.331744i
$311$	5.48913			0.311260			0.155630	−	0.987815i	$-0.450259\pi$
$311$	5.48913			0.311260			0.155630	+	0.987815i	$0.450259\pi$
$312$		0			0
$313$			21.8719i			1.23627i	0.786072	+	0.618135i	$0.212112\pi$
$313$			21.8719i			1.23627i	−0.786072	+	0.618135i	$0.787888\pi$
$314$	−61.7228			−3.48322
$315$	17.4891	+	5.63858i	0.985401	+	0.317698i
$316$	5.48913			0.308787
$317$			32.9639i			1.85144i	0.378215	+	0.925718i	$0.376538\pi$
$317$			32.9639i			1.85144i	−0.378215	+	0.925718i	$0.623462\pi$
$318$		−	20.1947i		−	1.13246i
$319$	8.74456			0.489602
$320$	1.62772	−	5.04868i	0.0909922	−	0.282230i
$321$	5.25544			0.293330
$322$		−	6.92820i		−	0.386094i
$323$		−	6.33830i		−	0.352672i
$324$	−16.3723			−0.909571
$325$		0			0
$326$	8.74456			0.484317
$327$		−	7.92287i		−	0.438136i
$328$			52.3663i			2.89144i
$329$	22.9783			1.26683
$330$	−1.37228	+	4.25639i	−0.0755416	+	0.234306i
$331$	−14.1168			−0.775932			−0.387966	−	0.921674i	$-0.626822\pi$
$331$	−14.1168			−0.775932			−0.387966	+	0.921674i	$0.626822\pi$
$332$			29.0024i			1.59172i
$333$		−	2.57924i		−	0.141342i
$334$	−39.7228			−2.17354
$335$	19.8030	+	6.38458i	1.08195	+	0.348827i
$336$	−17.4891			−0.954110
$337$		−	32.4665i		−	1.76856i	−0.466952	−	0.884282i	$-0.654648\pi$
$337$		−	32.4665i		−	1.76856i	0.466952	−	0.884282i	$-0.345352\pi$
$338$		−	32.8164i		−	1.78498i
$339$	−0.394031			−0.0214008
$340$	−14.7446	−	4.75372i	−0.799636	−	0.257807i
$341$	−3.37228			−0.182619
$342$			23.9538i			1.29527i
$343$			6.92820i			0.374088i
$344$	20.7446			1.11847
$345$	0.430703	−	1.33591i	0.0231883	−	0.0719228i
$346$	21.4891			1.15526
$347$		−	22.6641i		−	1.21667i	−0.793679	−	0.608337i	$-0.791837\pi$
$347$		−	22.6641i		−	1.21667i	0.793679	−	0.608337i	$-0.208163\pi$
$348$			30.2921i			1.62382i
$349$	−15.4891			−0.829114			−0.414557	−	0.910023i	$-0.636063\pi$
$349$	−15.4891			−0.829114			−0.414557	+	0.910023i	$0.636063\pi$
$350$	−35.4891	−	25.5383i	−1.89697	−	1.36508i
$351$		0			0
$352$			4.10891i			0.219006i
$353$		−	25.0410i		−	1.33280i	−0.745595	−	0.666399i	$-0.767835\pi$
$353$		−	25.0410i		−	1.33280i	0.745595	−	0.666399i	$-0.232165\pi$
$354$	14.7446			0.783665
$355$	−6.94158	+	21.5306i	−0.368421	+	1.14273i
$356$	6.00000			0.317999
$357$		−	4.34896i		−	0.230172i
$358$			32.4665i			1.71591i
$359$	−29.4891			−1.55638			−0.778188	−	0.628031i	$-0.783861\pi$
$359$	−29.4891			−1.55638			−0.778188	+	0.628031i	$0.783861\pi$
$360$	30.2337	+	9.74749i	1.59346	+	0.513738i
$361$	−3.00000			−0.157895
$362$		−	60.8791i		−	3.19973i
$363$			0.792287i			0.0415843i
$364$		0			0
$365$	14.7446	+	4.75372i	0.771766	+	0.248821i
$366$	−1.48913			−0.0778378
$367$			25.7407i			1.34365i	0.740708	+	0.671827i	$0.234490\pi$
$367$			25.7407i			1.34365i	−0.740708	+	0.671827i	$0.765510\pi$
$368$		−	5.04868i		−	0.263180i
$369$	20.7446			1.07992
$370$	−1.88316	+	5.84096i	−0.0979006	+	0.303657i
$371$	34.9783			1.81598
$372$		−	11.6819i		−	0.605680i
$373$			11.6819i			0.604867i	0.953170	+	0.302434i	$0.0977990\pi$
$373$			11.6819i			0.604867i	−0.953170	+	0.302434i	$0.902201\pi$
$374$	−4.00000			−0.206835
$375$	−5.25544	−	7.13058i	−0.271390	−	0.368222i
$376$	39.7228			2.04855
$377$		0			0
$378$			37.2203i			1.91440i
$379$	0.627719			0.0322437			0.0161219	−	0.999870i	$-0.494868\pi$
$379$	0.627719			0.0322437			0.0161219	+	0.999870i	$0.494868\pi$
$380$	12.0000	−	37.2203i	0.615587	−	1.90936i
$381$	6.51087			0.333562
$382$			48.9022i			2.50205i
$383$			10.8896i			0.556435i	0.960518	+	0.278217i	$0.0897435\pi$
$383$			10.8896i			0.556435i	−0.960518	+	0.278217i	$0.910256\pi$
$384$	11.2554			0.574377
$385$	−7.37228	−	2.37686i	−0.375726	−	0.121136i
$386$	41.4891			2.11174
$387$		−	8.21782i		−	0.417735i
$388$		−	25.5383i		−	1.29651i
$389$	−18.8614			−0.956311			−0.478156	−	0.878275i	$-0.658695\pi$
$389$	−18.8614			−0.956311			−0.478156	+	0.878275i	$0.658695\pi$
$390$		0			0
$391$	1.25544			0.0634902
$392$		−	29.9422i		−	1.51231i
$393$		−	2.17448i		−	0.109688i
$394$	21.4891			1.08261
$395$	−0.861407	+	2.67181i	−0.0433421	+	0.134434i
$396$	10.3723			0.521227
$397$		−	16.4356i		−	0.824881i	−0.910984	−	0.412441i	$-0.864676\pi$
$397$		−	16.4356i		−	0.824881i	0.910984	−	0.412441i	$-0.135324\pi$
$398$		−	20.1947i		−	1.01227i
$399$	10.9783			0.549600
$400$	−25.8614	−	18.6101i	−1.29307	−	0.930506i
$401$	−11.4891			−0.573740			−0.286870	−	0.957970i	$-0.592615\pi$
$401$	−11.4891			−0.573740			−0.286870	+	0.957970i	$0.592615\pi$
$402$			18.6101i			0.928189i
$403$		0			0
$404$	−26.2337			−1.30517
$405$	2.56930	−	7.96916i	0.127669	−	0.395991i
$406$	−76.4674			−3.79501
$407$			1.08724i			0.0538925i
$408$		−	7.51811i		−	0.372202i
$409$	−27.4891			−1.35925			−0.679625	−	0.733560i	$-0.737857\pi$
$409$	−27.4891			−1.35925			−0.679625	+	0.733560i	$0.737857\pi$
$410$	−46.9783	−	15.1460i	−2.32009	−	0.748009i
$411$	−11.3723			−0.560953
$412$		−	45.4381i		−	2.23857i
$413$			25.5383i			1.25666i
$414$	−4.74456			−0.233183
$415$	−14.1168	−	4.55134i	−0.692969	−	0.223417i
$416$		0			0
$417$			12.8617i			0.629842i
$418$		−	10.0974i		−	0.493878i
$419$	22.9783			1.12256			0.561280	−	0.827626i	$-0.310309\pi$
$419$	22.9783			1.12256			0.561280	+	0.827626i	$0.310309\pi$
$420$	8.23369	−	25.5383i	0.401763	−	1.24614i
$421$	8.51087			0.414795			0.207397	−	0.978257i	$-0.433501\pi$
$421$	8.51087			0.414795			0.207397	+	0.978257i	$0.433501\pi$
$422$		−	3.75906i		−	0.182988i
$423$		−	15.7359i		−	0.765107i
$424$	60.4674			2.93656
$425$	4.62772	−	6.43087i	0.224477	−	0.311943i
$426$	−20.2337			−0.980325
$427$		−	2.57924i		−	0.124818i
$428$			29.0024i			1.40189i
$429$		0			0
$430$	−6.00000	+	18.6101i	−0.289346	+	0.897460i
$431$	−25.7228			−1.23902			−0.619512	−	0.784987i	$-0.712670\pi$
$431$	−25.7228			−1.23902			−0.619512	+	0.784987i	$0.712670\pi$
$432$			27.1229i			1.30495i
$433$		−	29.2048i		−	1.40349i	−0.712426	−	0.701747i	$-0.752404\pi$
$433$		−	29.2048i		−	1.40349i	0.712426	−	0.701747i	$-0.247596\pi$
$434$	29.4891			1.41552
$435$	−14.7446	−	4.75372i	−0.706948	−	0.227924i
$436$	43.7228			2.09394
$437$			3.16915i			0.151601i
$438$			13.8564i			0.662085i
$439$	−21.4891			−1.02562			−0.512810	−	0.858502i	$-0.671395\pi$
$439$	−21.4891			−1.02562			−0.512810	+	0.858502i	$0.671395\pi$
$440$	−12.7446	−	4.10891i	−0.607573	−	0.195885i
$441$	−11.8614			−0.564829
$442$		0			0
$443$			31.6742i			1.50489i	0.658656	+	0.752444i	$0.271125\pi$
$443$			31.6742i			1.50489i	−0.658656	+	0.752444i	$0.728875\pi$
$444$	−3.76631			−0.178741
$445$	−0.941578	+	2.92048i	−0.0446351	+	0.138444i
$446$	6.00000			0.284108
$447$			9.10268i			0.430542i
$448$			8.21782i			0.388256i
$449$	−6.86141			−0.323810			−0.161905	−	0.986806i	$-0.551764\pi$
$449$	−6.86141			−0.323810			−0.161905	+	0.986806i	$0.551764\pi$
$450$	−17.4891	+	24.3036i	−0.824445	+	1.14568i
$451$	−8.74456			−0.411765
$452$		−	2.17448i		−	0.102279i
$453$		−	9.69259i		−	0.455398i
$454$	42.2337			1.98213
$455$		0			0
$456$	18.9783			0.888738
$457$		−	20.7846i		−	0.972263i	−0.873886	−	0.486132i	$-0.838408\pi$
$457$		−	20.7846i		−	0.972263i	0.873886	−	0.486132i	$-0.161592\pi$
$458$			36.9253i			1.72541i
$459$	−6.74456			−0.314809
$460$	7.37228	+	2.37686i	0.343734	+	0.110822i
$461$	2.23369			0.104033			0.0520166	−	0.998646i	$-0.483435\pi$
$461$	2.23369			0.104033			0.0520166	+	0.998646i	$0.483435\pi$
$462$		−	6.92820i		−	0.322329i
$463$			30.0897i			1.39839i	0.714933	+	0.699193i	$0.246457\pi$
$463$			30.0897i			1.39839i	−0.714933	+	0.699193i	$0.753543\pi$
$464$	−55.7228			−2.58687
$465$	5.68614	+	1.83324i	0.263688	+	0.0850145i
$466$	9.48913			0.439575
$467$		−	7.72049i		−	0.357262i	−0.983916	−	0.178631i	$-0.942833\pi$
$467$		−	7.72049i		−	0.357262i	0.983916	−	0.178631i	$-0.0571668\pi$
$468$		0			0
$469$	−32.2337			−1.48841
$470$	−11.4891	+	35.6357i	−0.529954	+	1.64375i
$471$	19.3723			0.892628
$472$			44.1485i			2.03210i
$473$			3.46410i			0.159280i
$474$	−2.51087			−0.115328
$475$	16.2337	+	11.6819i	0.744853	+	0.536003i
$476$	24.0000			1.10004
$477$		−	23.9538i		−	1.09677i
$478$		−	37.2203i		−	1.70241i
$479$	5.48913			0.250805			0.125402	−	0.992106i	$-0.459978\pi$
$479$	5.48913			0.250805			0.125402	+	0.992106i	$0.459978\pi$
$480$	2.23369	−	6.92820i	0.101953	−	0.316228i
$481$		0			0
$482$		−	42.2689i		−	1.92530i
$483$			2.17448i			0.0989423i
$484$	−4.37228			−0.198740
$485$	12.4307	+	4.00772i	0.564449	+	0.181981i
$486$	39.7228			1.80186
$487$		−	7.13058i		−	0.323118i	−0.986863	−	0.161559i	$-0.948348\pi$
$487$		−	7.13058i		−	0.323118i	0.986863	−	0.161559i	$-0.0516521\pi$
$488$		−	4.45877i		−	0.201839i
$489$	−2.74456			−0.124113
$490$	26.8614	+	8.66025i	1.21347	+	0.391230i
$491$	6.51087			0.293832			0.146916	−	0.989149i	$-0.453065\pi$
$491$	6.51087			0.293832			0.146916	+	0.989149i	$0.453065\pi$
$492$		−	30.2921i		−	1.36567i
$493$		−	13.8564i		−	0.624061i
$494$		0			0
$495$	−1.62772	+	5.04868i	−0.0731605	+	0.226921i
$496$	21.4891			0.964890
$497$		−	35.0458i		−	1.57202i
$498$		−	13.2665i		−	0.594486i
$499$	20.0000			0.895323			0.447661	−	0.894203i	$-0.352257\pi$
$499$	20.0000			0.895323			0.447661	+	0.894203i	$0.352257\pi$
$500$	39.3505	−	29.0024i	1.75981	−	1.29703i
$501$	12.4674			0.557001
$502$			55.8304i			2.49183i
$503$		−	13.5615i		−	0.604675i	−0.953201	−	0.302338i	$-0.902233\pi$
$503$		−	13.5615i		−	0.604675i	0.953201	−	0.302338i	$-0.0977670\pi$
$504$	−49.2119			−2.19207
$505$	4.11684	−	12.7692i	0.183197	−	0.568220i
$506$	2.00000			0.0889108
$507$			10.2997i			0.457427i
$508$			35.9306i			1.59416i
$509$	−22.6277			−1.00296			−0.501478	−	0.865170i	$-0.667210\pi$
$509$	−22.6277			−1.00296			−0.501478	+	0.865170i	$0.667210\pi$
$510$	6.74456	+	2.17448i	0.298654	+	0.0962876i
$511$	−24.0000			−1.06170
$512$			50.1369i			2.21576i
$513$		−	17.0256i		−	0.751697i
$514$	26.9783			1.18996
$515$	22.1168	+	7.13058i	0.974585	+	0.314211i
$516$	−12.0000			−0.528271
$517$			6.63325i			0.291730i
$518$		−	9.50744i		−	0.417733i
$519$	−6.74456			−0.296053
$520$		0			0
$521$	−21.6060			−0.946575			−0.473287	−	0.880908i	$-0.656933\pi$
$521$	−21.6060			−0.946575			−0.473287	+	0.880908i	$0.656933\pi$
$522$			52.3663i			2.29201i
$523$		−	29.0024i		−	1.26819i	−0.773256	−	0.634094i	$-0.781373\pi$
$523$		−	29.0024i		−	1.26819i	0.773256	−	0.634094i	$-0.218627\pi$
$524$	12.0000			0.524222
$525$	11.1386	+	8.01544i	0.486128	+	0.349823i
$526$	−69.2119			−3.01778
$527$			5.34363i			0.232772i
$528$		−	5.04868i		−	0.219715i
$529$	22.3723			0.972708
$530$	−17.4891	+	54.2458i	−0.759679	+	2.35629i
$531$	17.4891			0.758963
$532$			60.5841i			2.62665i
$533$		0			0
$534$	−2.74456			−0.118769
$535$	−14.1168	−	4.55134i	−0.610324	−	0.196772i
$536$	−55.7228			−2.40686
$537$		−	10.1899i		−	0.439728i
$538$		−	29.0024i		−	1.25038i
$539$	5.00000			0.215365
$540$	−39.6060	−	12.7692i	−1.70437	−	0.549497i
$541$	34.2337			1.47182			0.735911	−	0.677079i	$-0.236754\pi$
$541$	34.2337			1.47182			0.735911	+	0.677079i	$0.236754\pi$
$542$		−	34.0511i		−	1.46262i
$543$			19.1075i			0.819980i
$544$	6.51087			0.279151
$545$	−6.86141	+	21.2819i	−0.293910	+	0.911618i
$546$		0			0
$547$		−	29.0024i		−	1.24005i	−0.784580	−	0.620027i	$-0.787122\pi$
$547$		−	29.0024i		−	1.24005i	0.784580	−	0.620027i	$-0.212878\pi$
$548$		−	62.7586i		−	2.68091i
$549$	−1.76631			−0.0753844
$550$	7.37228	−	10.2448i	0.314355	−	0.436841i
$551$	34.9783			1.49012
$552$			3.75906i			0.159996i
$553$		−	4.34896i		−	0.184937i
$554$	−29.4891			−1.25287
$555$	0.591046	−	1.83324i	0.0250885	−	0.0778167i
$556$	−70.9783			−3.01015
$557$		−	0.994667i		−	0.0421454i	−0.999778	−	0.0210727i	$-0.993292\pi$
$557$		−	0.994667i		−	0.0421454i	0.999778	−	0.0210727i	$-0.00670814\pi$
$558$		−	20.1947i		−	0.854910i
$559$		0			0
$560$	46.9783	+	15.1460i	1.98519	+	0.640036i
$561$	1.25544			0.0530046
$562$			1.28962i			0.0543994i
$563$			18.9051i			0.796754i	0.917222	+	0.398377i	$0.130426\pi$
$563$			18.9051i			0.796754i	−0.917222	+	0.398377i	$0.869574\pi$
$564$	−22.9783			−0.967559
$565$	1.05842	+	0.341241i	0.0445281	+	0.0143561i
$566$	−38.2337			−1.60708
$567$			12.9715i			0.544754i
$568$		−	60.5841i		−	2.54205i
$569$	27.2554			1.14261			0.571304	−	0.820739i	$-0.306438\pi$
$569$	27.2554			1.14261			0.571304	+	0.820739i	$0.306438\pi$
$570$	−5.48913	+	17.0256i	−0.229914	+	0.713122i
$571$	1.48913			0.0623180			0.0311590	−	0.999514i	$-0.490080\pi$
$571$	1.48913			0.0623180			0.0311590	+	0.999514i	$0.490080\pi$
$572$		0			0
$573$		−	15.3484i		−	0.641189i
$574$	76.4674			3.19169
$575$	−2.31386	+	3.21543i	−0.0964946	+	0.134093i
$576$	5.62772			0.234488
$577$			21.8719i			0.910537i	0.890354	+	0.455269i	$0.150457\pi$
$577$			21.8719i			0.910537i	−0.890354	+	0.455269i	$0.849543\pi$
$578$		−	36.5754i		−	1.52134i
$579$	−13.0217			−0.541165
$580$	26.2337	−	81.3687i	1.08929	−	3.37865i
$581$	22.9783			0.953298
$582$			11.6819i			0.484231i
$583$			10.0974i			0.418190i
$584$	−41.4891			−1.71683
$585$		0			0
$586$	−8.00000			−0.330477
$587$		−	41.2743i		−	1.70357i	−0.523890	−	0.851786i	$-0.675520\pi$
$587$		−	41.2743i		−	1.70357i	0.523890	−	0.851786i	$-0.324480\pi$
$588$			17.3205i			0.714286i
$589$	−13.4891			−0.555810
$590$	−39.6060	−	12.7692i	−1.63055	−	0.525698i
$591$	−6.74456			−0.277434
$592$		−	6.92820i		−	0.284747i
$593$			22.7739i			0.935214i	0.883937	+	0.467607i	$0.154884\pi$
$593$			22.7739i			0.935214i	−0.883937	+	0.467607i	$0.845116\pi$
$594$	−10.7446			−0.440855
$595$	−3.76631	+	11.6819i	−0.154404	+	0.478912i
$596$	−50.2337			−2.05765
$597$			6.33830i			0.259409i
$598$		0			0
$599$	−10.9783			−0.448559			−0.224280	−	0.974525i	$-0.572003\pi$
$599$	−10.9783			−0.448559			−0.224280	+	0.974525i	$0.572003\pi$
$600$	19.2554	+	13.8564i	0.786100	+	0.565685i
$601$	−38.4674			−1.56912			−0.784558	−	0.620055i	$-0.787110\pi$
$601$	−38.4674			−1.56912			−0.784558	+	0.620055i	$0.787110\pi$
$602$		−	30.2921i		−	1.23461i
$603$			22.0742i			0.898932i
$604$	53.4891			2.17644
$605$	0.686141	−	2.12819i	0.0278956	−	0.0865234i
$606$	12.0000			0.487467
$607$			3.46410i			0.140604i	0.997526	+	0.0703018i	$0.0223962\pi$
$607$			3.46410i			0.140604i	−0.997526	+	0.0703018i	$0.977604\pi$
$608$			16.4356i			0.666554i
$609$	24.0000			0.972529
$610$	4.00000	+	1.28962i	0.161955	+	0.0522152i
$611$		0			0
$612$		−	16.4356i		−	0.664372i
$613$			4.34896i			0.175653i	0.996136	+	0.0878265i	$0.0279921\pi$
$613$			4.34896i			0.175653i	−0.996136	+	0.0878265i	$0.972008\pi$
$614$	79.7228			3.21735
$615$	14.7446	+	4.75372i	0.594558	+	0.191689i
$616$	20.7446			0.835822
$617$		−	17.0256i		−	0.685423i	−0.939441	−	0.342712i	$-0.888655\pi$
$617$		−	17.0256i		−	0.685423i	0.939441	−	0.342712i	$-0.111345\pi$
$618$			20.7846i			0.836080i
$619$	−14.1168			−0.567404			−0.283702	−	0.958913i	$-0.591563\pi$
$619$	−14.1168			−0.567404			−0.283702	+	0.958913i	$0.591563\pi$
$620$	−10.1168	+	31.3793i	−0.406302	+	1.26022i
$621$	3.37228			0.135325
$622$		−	13.8564i		−	0.555591i
$623$		−	4.75372i		−	0.190454i
$624$		0			0
$625$	7.94158	+	23.7051i	0.317663	+	0.948204i
$626$	55.2119			2.20671
$627$			3.16915i			0.126564i
$628$			106.907i			4.26606i
$629$	1.72281			0.0686931
$630$	14.2337	−	44.1485i	0.567084	−	1.75892i
$631$	23.6060			0.939739			0.469869	−	0.882736i	$-0.344301\pi$
$631$	23.6060			0.939739			0.469869	+	0.882736i	$0.344301\pi$
$632$		−	7.51811i		−	0.299054i
$633$			1.17981i			0.0468934i
$634$	83.2119			3.30477
$635$	−17.4891	−	5.63858i	−0.694035	−	0.223760i
$636$	−34.9783			−1.38698
$637$		0			0
$638$		−	22.0742i		−	0.873927i
$639$	−24.0000			−0.949425
$640$	−30.2337	−	9.74749i	−1.19509	−	0.385304i
$641$	−25.3723			−1.00214			−0.501072	−	0.865405i	$-0.667061\pi$
$641$	−25.3723			−1.00214			−0.501072	+	0.865405i	$0.667061\pi$
$642$		−	13.2665i		−	0.523587i
$643$			30.4944i			1.20258i	0.799030	+	0.601292i	$0.205347\pi$
$643$			30.4944i			1.20258i	−0.799030	+	0.601292i	$0.794653\pi$
$644$	−12.0000			−0.472866
$645$	1.88316	−	5.84096i	0.0741492	−	0.229988i
$646$	−16.0000			−0.629512
$647$		−	21.9817i		−	0.864188i	−0.901829	−	0.432094i	$-0.857775\pi$
$647$		−	21.9817i		−	0.864188i	0.901829	−	0.432094i	$-0.142225\pi$
$648$			22.4241i			0.880901i
$649$	−7.37228			−0.289387
$650$		0			0
$651$	−9.25544			−0.362749
$652$		−	15.1460i		−	0.593164i
$653$			30.7894i			1.20488i	0.798163	+	0.602441i	$0.205805\pi$
$653$			30.7894i			1.20488i	−0.798163	+	0.602441i	$0.794195\pi$
$654$	−20.0000			−0.782062
$655$	−1.88316	+	5.84096i	−0.0735810	+	0.228225i
$656$	55.7228			2.17561
$657$			16.4356i			0.641216i
$658$		−	58.0049i		−	2.26127i
$659$	−21.2554			−0.827994			−0.413997	−	0.910278i	$-0.635868\pi$
$659$	−21.2554			−0.827994			−0.413997	+	0.910278i	$0.635868\pi$
$660$	7.37228	+	2.37686i	0.286966	+	0.0925192i
$661$	−16.3505			−0.635962			−0.317981	−	0.948097i	$-0.603005\pi$
$661$	−16.3505			−0.635962			−0.317981	+	0.948097i	$0.603005\pi$
$662$			35.6357i			1.38502i
$663$		0			0
$664$	39.7228			1.54154
$665$	−29.4891	−	9.50744i	−1.14354	−	0.368683i
$666$	−6.51087			−0.252291
$667$			6.92820i			0.268261i
$668$			68.8019i			2.66203i
$669$	−1.88316			−0.0728070
$670$	16.1168	−	49.9894i	0.622648	−	1.93126i
$671$	0.744563			0.0287435
$672$			11.2772i			0.435026i
$673$		−	18.6101i		−	0.717368i	−0.933459	−	0.358684i	$-0.883226\pi$
$673$		−	18.6101i		−	0.717368i	0.933459	−	0.358684i	$-0.116774\pi$
$674$	−81.9565			−3.15685
$675$	12.4307	−	17.2742i	0.478458	−	0.664885i
$676$	−56.8397			−2.18614
$677$			50.0820i			1.92481i	0.271623	+	0.962404i	$0.412440\pi$
$677$			50.0820i			1.92481i	−0.271623	+	0.962404i	$0.587560\pi$
$678$			0.994667i			0.0381999i
$679$	−20.2337			−0.776498
$680$	−6.51087	+	20.1947i	−0.249681	+	0.774431i
$681$	−13.2554			−0.507949
$682$			8.51278i			0.325971i
$683$		−	17.9104i		−	0.685323i	−0.939459	−	0.342661i	$-0.888672\pi$
$683$		−	17.9104i		−	0.685323i	0.939459	−	0.342661i	$-0.111328\pi$
$684$	41.4891			1.58638
$685$	30.5475	+	9.84868i	1.16716	+	0.376299i
$686$	17.4891			0.667738
$687$		−	11.5894i		−	0.442161i
$688$		−	22.0742i		−	0.841572i
$689$		0			0
$690$	−3.37228	−	1.08724i	−0.128381	−	0.0413905i
$691$	44.8614			1.70661			0.853304	−	0.521413i	$-0.174595\pi$
$691$	44.8614			1.70661			0.853304	+	0.521413i	$0.174595\pi$
$692$		−	37.2203i		−	1.41490i
$693$		−	8.21782i		−	0.312169i
$694$	−57.2119			−2.17174
$695$	11.1386	−	34.5484i	0.422511	−	1.31050i
$696$	41.4891			1.57264
$697$			13.8564i			0.524849i
$698$			39.0998i			1.47995i
$699$	−2.97825			−0.112648
$700$	−44.2337	+	61.4690i	−1.67188	+	2.32331i
$701$	−12.5109			−0.472529			−0.236265	−	0.971689i	$-0.575923\pi$
$701$	−12.5109			−0.472529			−0.236265	+	0.971689i	$0.575923\pi$
$702$		0			0
$703$			4.34896i			0.164024i
$704$	−2.37228			−0.0894087
$705$	3.60597	−	11.1846i	0.135809	−	0.421236i
$706$	−63.2119			−2.37901
$707$			20.7846i			0.781686i
$708$		−	25.5383i		−	0.959789i
$709$	−23.8832			−0.896951			−0.448475	−	0.893795i	$-0.648033\pi$
$709$	−23.8832			−0.896951			−0.448475	+	0.893795i	$0.648033\pi$
$710$	54.3505	+	17.5229i	2.03974	+	0.657622i
$711$	−2.97825			−0.111693
$712$		−	8.21782i		−	0.307976i
$713$		−	2.67181i		−	0.100060i
$714$	−10.9783			−0.410851
$715$		0			0
$716$	56.2337			2.10155
$717$			11.6819i			0.436269i
$718$			74.4405i			2.77810i
$719$	30.3505			1.13188			0.565942	−	0.824445i	$-0.308513\pi$
$719$	30.3505			1.13188			0.565942	+	0.824445i	$0.308513\pi$
$720$	10.3723	−	32.1716i	0.386552	−	1.19896i
$721$	−36.0000			−1.34071
$722$			7.57301i			0.281838i
$723$			13.2665i			0.493386i
$724$	−105.446			−3.91886
$725$	35.4891	+	25.5383i	1.31803	+	0.948470i
$726$	2.00000			0.0742270
$727$			14.0588i			0.521412i	0.965418	+	0.260706i	$0.0839552\pi$
$727$			14.0588i			0.521412i	−0.965418	+	0.260706i	$0.916045\pi$
$728$		0			0
$729$	−1.23369			−0.0456921
$730$	12.0000	−	37.2203i	0.444140	−	1.37758i
$731$	5.48913			0.203023
$732$			2.57924i			0.0953315i
$733$			9.50744i			0.351165i	0.984465	+	0.175583i	$0.0561809\pi$
$733$			9.50744i			0.351165i	−0.984465	+	0.175583i	$0.943819\pi$
$734$	64.9783			2.39839
$735$	−8.43070	−	2.71810i	−0.310971	−	0.100259i
$736$	−3.25544			−0.119997
$737$		−	9.30506i		−	0.342756i
$738$		−	52.3663i		−	1.92763i
$739$	10.7446			0.395245			0.197623	−	0.980278i	$-0.436678\pi$
$739$	10.7446			0.395245			0.197623	+	0.980278i	$0.436678\pi$
$740$	10.1168	+	3.26172i	0.371903	+	0.119903i
$741$		0			0
$742$		−	88.2969i		−	3.24148i
$743$		−	11.3870i		−	0.417747i	−0.977943	−	0.208874i	$-0.933020\pi$
$743$		−	11.3870i		−	0.417747i	0.977943	−	0.208874i	$-0.0669798\pi$
$744$	−16.0000			−0.586588
$745$	7.88316	−	24.4511i	0.288816	−	0.895819i
$746$	29.4891			1.07967
$747$		−	15.7359i		−	0.575748i
$748$			6.92820i			0.253320i
$749$	22.9783			0.839607
$750$	−18.0000	+	13.2665i	−0.657267	+	0.484424i
$751$	27.3723			0.998829			0.499414	−	0.866363i	$-0.333549\pi$
$751$	27.3723			0.998829			0.499414	+	0.866363i	$0.333549\pi$
$752$		−	42.2689i		−	1.54139i
$753$		−	17.5229i		−	0.638570i
$754$		0			0
$755$	−8.39403	+	26.0357i	−0.305490	+	0.947535i
$756$	64.4674			2.34466
$757$			39.7995i			1.44654i	0.690567	+	0.723269i	$0.257361\pi$
$757$			39.7995i			1.44654i	−0.690567	+	0.723269i	$0.742639\pi$
$758$		−	1.58457i		−	0.0575543i
$759$	−0.627719			−0.0227847
$760$	−50.9783	−	16.4356i	−1.84918	−	0.596184i
$761$	32.7446			1.18699			0.593495	−	0.804838i	$-0.297748\pi$
$761$	32.7446			1.18699			0.593495	+	0.804838i	$0.297748\pi$
$762$		−	16.4356i		−	0.595401i
$763$		−	34.6410i		−	1.25409i
$764$	84.7011			3.06438
$765$	8.00000	+	2.57924i	0.289241	+	0.0932526i
$766$	27.4891			0.993222
$767$		0			0
$768$		−	24.6535i		−	0.889605i
$769$	−29.2119			−1.05341			−0.526705	−	0.850048i	$-0.676573\pi$
$769$	−29.2119			−1.05341			−0.526705	+	0.850048i	$0.676573\pi$
$770$	−6.00000	+	18.6101i	−0.216225	+	0.670662i
$771$	−8.46738			−0.304945
$772$		−	71.8613i		−	2.58634i
$773$			17.6155i			0.633584i	0.948495	+	0.316792i	$0.102606\pi$
$773$			17.6155i			0.633584i	−0.948495	+	0.316792i	$0.897394\pi$
$774$	−20.7446			−0.745648
$775$	−13.6861	−	9.84868i	−0.491621	−	0.353775i
$776$	−34.9783			−1.25565
$777$			2.98400i			0.107050i
$778$			47.6126i			1.70699i
$779$	−34.9783			−1.25323
$780$		0			0
$781$	10.1168			0.362009
$782$		−	3.16915i		−	0.113328i
$783$		−	37.2203i		−	1.33014i
$784$	−31.8614			−1.13791
$785$	−52.0367	−	16.7769i	−1.85727	−	0.598793i
$786$	−5.48913			−0.195791
$787$		−	15.1460i		−	0.539898i	−0.962875	−	0.269949i	$-0.912993\pi$
$787$		−	15.1460i		−	0.539898i	0.962875	−	0.269949i	$-0.0870068\pi$
$788$		−	37.2203i		−	1.32592i
$789$	21.7228			0.773353
$790$	6.74456	+	2.17448i	0.239961	+	0.0773646i
$791$	−1.72281			−0.0612562
$792$		−	14.2063i		−	0.504798i
$793$		0			0
$794$	−41.4891			−1.47239
$795$	5.48913	−	17.0256i	0.194679	−	0.603834i
$796$	−34.9783			−1.23977
$797$			5.25106i			0.186002i	0.995666	+	0.0930010i	$0.0296460\pi$
$797$			5.25106i			0.186002i	−0.995666	+	0.0930010i	$0.970354\pi$
$798$		−	27.7128i		−	0.981023i
$799$	10.5109			0.371848
$800$	−12.0000	+	16.6757i	−0.424264	+	0.589575i
$801$	−3.25544			−0.115025
$802$			29.0024i			1.02411i
$803$		−	6.92820i		−	0.244491i
$804$	32.2337			1.13679
$805$	1.88316	−	5.84096i	0.0663725	−	0.205867i
$806$		0			0
$807$			9.10268i			0.320430i
$808$			35.9306i			1.26404i
$809$	32.7446			1.15124			0.575619	−	0.817718i	$-0.304761\pi$
$809$	32.7446			1.15124			0.575619	+	0.817718i	$0.304761\pi$
$810$	−20.1168	−	6.48577i	−0.706834	−	0.227887i
$811$	−0.233688			−0.00820589			−0.00410295	−	0.999992i	$-0.501306\pi$
$811$	−0.233688			−0.00820589			−0.00410295	+	0.999992i	$0.501306\pi$
$812$			132.445i			4.64792i
$813$			10.6873i			0.374819i
$814$	2.74456			0.0961969
$815$	7.37228	+	2.37686i	0.258240	+	0.0832578i
$816$	−8.00000			−0.280056
$817$			13.8564i			0.484774i
$818$			69.3918i			2.42623i
$819$		0			0
$820$	−26.2337	+	81.3687i	−0.916120	+	2.84152i
$821$	−18.0000			−0.628204			−0.314102	−	0.949389i	$-0.601703\pi$
$821$	−18.0000			−0.628204			−0.314102	+	0.949389i	$0.601703\pi$
$822$			28.7075i			1.00129i
$823$		−	56.0328i		−	1.95318i	−0.215111	−	0.976590i	$-0.569011\pi$
$823$		−	56.0328i		−	1.95318i	0.215111	−	0.976590i	$-0.430989\pi$
$824$	−62.2337			−2.16801
$825$	−2.31386	+	3.21543i	−0.0805582	+	0.111947i
$826$	64.4674			2.24311
$827$			28.4125i			0.988000i	0.869462	+	0.494000i	$0.164466\pi$
$827$			28.4125i			0.988000i	−0.869462	+	0.494000i	$0.835534\pi$
$828$			8.21782i			0.285589i
$829$	20.3505			0.706803			0.353402	−	0.935472i	$-0.385025\pi$
$829$	20.3505			0.706803			0.353402	+	0.935472i	$0.385025\pi$
$830$	−11.4891	+	35.6357i	−0.398793	+	1.23693i
$831$	9.25544			0.321068
$832$		0			0
$833$		−	7.92287i		−	0.274511i
$834$	32.4674			1.12425
$835$	−33.4891	−	10.7971i	−1.15894	−	0.373648i
$836$	−17.4891			−0.604874
$837$			14.3537i			0.496138i
$838$		−	58.0049i		−	2.00374i
$839$	10.1168			0.349272			0.174636	−	0.984633i	$-0.444125\pi$
$839$	10.1168			0.349272			0.174636	+	0.984633i	$0.444125\pi$
$840$	−34.9783	−	11.2772i	−1.20686	−	0.389099i
$841$	47.4674			1.63681
$842$		−	21.4843i		−	0.740399i
$843$		−	0.404759i		−	0.0139407i
$844$	−6.51087			−0.224114
$845$	8.91983	−	27.6665i	0.306851	−	0.951757i
$846$	−39.7228			−1.36570
$847$			3.46410i			0.119028i
$848$		−	64.3432i		−	2.20955i
$849$	12.0000			0.411839
$850$	−16.2337	−	11.6819i	−0.556811	−	0.400687i
$851$	−0.861407			−0.0295286
$852$			35.0458i			1.20065i
$853$		−	35.0458i		−	1.19994i	−0.800021	−	0.599972i	$-0.795178\pi$
$853$		−	35.0458i		−	1.19994i	0.800021	−	0.599972i	$-0.204822\pi$
$854$	−6.51087			−0.222798
$855$	−6.51087	+	20.1947i	−0.222667	+	0.690644i
$856$	39.7228			1.35770
$857$		−	23.9538i		−	0.818245i	−0.912480	−	0.409122i	$-0.865835\pi$
$857$		−	23.9538i		−	0.818245i	0.912480	−	0.409122i	$-0.134165\pi$
$858$		0			0
$859$	6.11684			0.208704			0.104352	−	0.994540i	$-0.466723\pi$
$859$	6.11684			0.208704			0.104352	+	0.994540i	$0.466723\pi$
$860$	32.2337	+	10.3923i	1.09916	+	0.354375i
$861$	−24.0000			−0.817918
$862$			64.9331i			2.21163i
$863$			2.87419i			0.0978387i	0.998803	+	0.0489194i	$0.0155777\pi$
$863$			2.87419i			0.0978387i	−0.998803	+	0.0489194i	$0.984422\pi$
$864$	17.4891			0.594992
$865$	18.1168	+	5.84096i	0.615991	+	0.198599i
$866$	−73.7228			−2.50520
$867$			11.4795i			0.389866i
$868$		−	51.0767i		−	1.73365i
$869$	1.25544			0.0425878
$870$	−12.0000	+	37.2203i	−0.406838	+	1.26188i
$871$		0			0
$872$		−	59.8844i		−	2.02794i
$873$			13.8564i			0.468968i
$874$	8.00000			0.270604
$875$	−22.9783	−	31.1769i	−0.776807	−	1.05397i
$876$	24.0000			0.810885
$877$		0			0		1.00000			$0$
$877$		0			0		−1.00000			$\pi$
$878$			54.2458i			1.83071i
$879$	2.51087			0.0846897
$880$	−4.37228	+	13.5615i	−0.147390	+	0.457156i
$881$	−6.86141			−0.231167			−0.115583	−	0.993298i	$-0.536874\pi$
$881$	−6.86141			−0.231167			−0.115583	+	0.993298i	$0.536874\pi$
$882$			29.9422i			1.00821i
$883$		−	24.2487i		−	0.816034i	−0.912974	−	0.408017i	$-0.866220\pi$
$883$		−	24.2487i		−	0.816034i	0.912974	−	0.408017i	$-0.133780\pi$
$884$		0			0
$885$	12.4307	+	4.00772i	0.417854	+	0.134718i
$886$	79.9565			2.68619
$887$		−	27.4179i		−	0.920602i	−0.887763	−	0.460301i	$-0.847742\pi$
$887$		−	27.4179i		−	0.920602i	0.887763	−	0.460301i	$-0.152258\pi$
$888$			5.15848i			0.173107i
$889$	28.4674			0.954765
$890$	7.37228	+	2.37686i	0.247119	+	0.0796726i
$891$	−3.74456			−0.125448
$892$		−	10.3923i		−	0.347960i
$893$			26.5330i			0.887893i
$894$	22.9783			0.768508
$895$	−8.82473	+	27.3716i	−0.294978	+	0.914931i
$896$	49.2119			1.64406
$897$		0			0
$898$			17.3205i			0.577993i
$899$	−29.4891			−0.983517
$900$	42.0951	+	30.2921i	1.40317	+	1.00974i
$901$	16.0000			0.533037
$902$			22.0742i			0.734991i
$903$			9.50744i			0.316388i
$904$	−2.97825			−0.0990551
$905$	16.5475	−	51.3253i	0.550059	−	1.70611i
$906$	−24.4674			−0.812874
$907$		−	19.8997i		−	0.660760i	−0.943848	−	0.330380i	$-0.892823\pi$
$907$		−	19.8997i		−	0.660760i	0.943848	−	0.330380i	$-0.107177\pi$
$908$		−	73.1509i		−	2.42760i
$909$	14.2337			0.472102
$910$		0			0
$911$	−53.4891			−1.77217			−0.886087	−	0.463519i	$-0.846587\pi$
$911$	−53.4891			−1.77217			−0.886087	+	0.463519i	$0.846587\pi$
$912$		−	20.1947i		−	0.668713i
$913$			6.63325i			0.219529i
$914$	−52.4674			−1.73547
$915$	−1.25544	−	0.404759i	−0.0415035	−	0.0133809i
$916$	63.9565			2.11318
$917$		−	9.50744i		−	0.313963i
$918$			17.0256i			0.561927i
$919$	28.2337			0.931343			0.465672	−	0.884958i	$-0.345813\pi$
$919$	28.2337			0.931343			0.465672	+	0.884958i	$0.345813\pi$
$920$	3.25544	−	10.0974i	0.107329	−	0.332900i
$921$	−25.0217			−0.824495
$922$		−	5.63858i		−	0.185697i
$923$		0			0
$924$	−12.0000			−0.394771
$925$	−3.17527	+	4.41248i	−0.104402	+	0.145081i
$926$	75.9565			2.49609
$927$			24.6535i			0.809726i
$928$			35.9306i			1.17948i
$929$	7.02175			0.230376			0.115188	−	0.993344i	$-0.463253\pi$
$929$	7.02175			0.230376			0.115188	+	0.993344i	$0.463253\pi$
$930$	4.62772	−	14.3537i	0.151749	−	0.470678i
$931$	20.0000			0.655474
$932$		−	16.4356i		−	0.538368i
$933$			4.34896i			0.142379i
$934$	−19.4891			−0.637704
$935$	−3.37228	−	1.08724i	−0.110285	−	0.0355566i
$936$		0			0
$937$			53.6559i			1.75286i	0.481527	+	0.876431i	$0.340082\pi$
$937$			53.6559i			1.75286i	−0.481527	+	0.876431i	$0.659918\pi$
$938$			81.3687i			2.65678i
$939$	−17.3288			−0.565503
$940$	61.7228	+	19.8997i	2.01318	+	0.649058i
$941$	−58.4674			−1.90598			−0.952991	−	0.302999i	$-0.902012\pi$
$941$	−58.4674			−1.90598			−0.952991	+	0.302999i	$0.902012\pi$
$942$		−	48.9022i		−	1.59332i
$943$		−	6.92820i		−	0.225613i
$944$	46.9783			1.52901
$945$	−10.1168	+	31.3793i	−0.329101	+	1.02077i
$946$	8.74456			0.284310
$947$		−	26.7354i		−	0.868783i	−0.900724	−	0.434392i	$-0.856963\pi$
$947$		−	26.7354i		−	0.868783i	0.900724	−	0.434392i	$-0.143037\pi$
$948$			4.34896i			0.141248i
$949$		0			0
$950$	29.4891	−	40.9793i	0.956754	−	1.32954i
$951$	−26.1168			−0.846897
$952$		−	32.8713i		−	1.06536i
$953$		−	31.2867i		−	1.01348i	−0.862100	−	0.506738i	$-0.830851\pi$
$953$		−	31.2867i		−	1.01348i	0.862100	−	0.506738i	$-0.169149\pi$
$954$	−60.4674			−1.95770
$955$	−13.2921	+	41.2280i	−0.430123	+	1.33411i
$956$	−64.4674			−2.08502
$957$			6.92820i			0.223957i
$958$		−	13.8564i		−	0.447680i
$959$	−49.7228			−1.60563
$960$	4.00000	+	1.28962i	0.129099	+	0.0416223i
$961$	−19.6277			−0.633152
$962$		0			0
$963$		−	15.7359i		−	0.507083i
$964$	−73.2119			−2.35800
$965$	34.9783	+	11.2772i	1.12599	+	0.363025i
$966$	5.48913			0.176610
$967$		−	26.4232i		−	0.849713i	−0.905261	−	0.424856i	$-0.860325\pi$
$967$		−	26.4232i		−	0.849713i	0.905261	−	0.424856i	$-0.139675\pi$
$968$			5.98844i			0.192476i
$969$	5.02175			0.161322
$970$	10.1168	−	31.3793i	0.324832	−	1.00753i
$971$	−9.09509			−0.291875			−0.145938	−	0.989294i	$-0.546620\pi$
$971$	−9.09509			−0.291875			−0.145938	+	0.989294i	$0.546620\pi$
$972$		−	68.8019i		−	2.20682i
$973$			56.2351i			1.80282i
$974$	−18.0000			−0.576757
$975$		0			0
$976$	−4.74456			−0.151870
$977$		−	50.5793i		−	1.61818i	−0.587687	−	0.809088i	$-0.699962\pi$
$977$		−	50.5793i		−	1.61818i	0.587687	−	0.809088i	$-0.300038\pi$
$978$			6.92820i			0.221540i
$979$	1.37228			0.0438583
$980$	15.0000	−	46.5253i	0.479157	−	1.48620i
$981$	−23.7228			−0.757411
$982$		−	16.4356i		−	0.524483i
$983$			24.7460i			0.789276i	0.918837	+	0.394638i	$0.129130\pi$
$983$			24.7460i			0.789276i	−0.918837	+	0.394638i	$0.870870\pi$
$984$	−41.4891			−1.32263
$985$	18.1168	+	5.84096i	0.577251	+	0.186109i
$986$	−34.9783			−1.11393
$987$			18.2054i			0.579483i
$988$		0			0
$989$	−2.74456			−0.0872720
$990$	12.7446	+	4.10891i	0.405049	+	0.130590i
$991$	18.9783			0.602864			0.301432	−	0.953488i	$-0.402535\pi$
$991$	18.9783			0.602864			0.301432	+	0.953488i	$0.402535\pi$
$992$		−	13.8564i		−	0.439941i
$993$		−	11.1846i		−	0.354932i
$994$	−88.4674			−2.80601
$995$	5.48913	−	17.0256i	0.174017	−	0.539746i
$996$	−22.9783			−0.728094
$997$			2.17448i			0.0688665i	0.999407	+	0.0344333i	$0.0109626\pi$
$997$			2.17448i			0.0688665i	−0.999407	+	0.0344333i	$0.989037\pi$
$998$		−	50.4868i		−	1.59813i
$999$	4.62772			0.146415

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	55.2.b.a.34.1	✓	4
3.2	odd	2		495.2.c.a.199.4		4
4.3	odd	2		880.2.b.h.529.2		4
5.2	odd	4		275.2.a.h.1.4		4
5.3	odd	4		275.2.a.h.1.1		4
5.4	even	2	inner	55.2.b.a.34.4	yes	4
11.2	odd	10		605.2.j.j.444.4		16
11.3	even	5		605.2.j.i.9.1		16
11.4	even	5		605.2.j.i.269.4		16
11.5	even	5		605.2.j.i.124.4		16
11.6	odd	10		605.2.j.j.124.1		16
11.7	odd	10		605.2.j.j.269.1		16
11.8	odd	10		605.2.j.j.9.4		16
11.9	even	5		605.2.j.i.444.1		16
11.10	odd	2		605.2.b.c.364.4		4
15.2	even	4		2475.2.a.bi.1.1		4
15.8	even	4		2475.2.a.bi.1.4		4
15.14	odd	2		495.2.c.a.199.1		4
20.3	even	4		4400.2.a.cc.1.3		4
20.7	even	4		4400.2.a.cc.1.2		4
20.19	odd	2		880.2.b.h.529.3		4
55.4	even	10		605.2.j.i.269.1		16
55.9	even	10		605.2.j.i.444.4		16
55.14	even	10		605.2.j.i.9.4		16
55.19	odd	10		605.2.j.j.9.1		16
55.24	odd	10		605.2.j.j.444.1		16
55.29	odd	10		605.2.j.j.269.4		16
55.32	even	4		3025.2.a.ba.1.1		4
55.39	odd	10		605.2.j.j.124.4		16
55.43	even	4		3025.2.a.ba.1.4		4
55.49	even	10		605.2.j.i.124.1		16
55.54	odd	2		605.2.b.c.364.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.b.a.34.1	✓	4	1.1	even	1	trivial
55.2.b.a.34.4	yes	4	5.4	even	2	inner
275.2.a.h.1.1		4	5.3	odd	4
275.2.a.h.1.4		4	5.2	odd	4
495.2.c.a.199.1		4	15.14	odd	2
495.2.c.a.199.4		4	3.2	odd	2
605.2.b.c.364.1		4	55.54	odd	2
605.2.b.c.364.4		4	11.10	odd	2
605.2.j.i.9.1		16	11.3	even	5
605.2.j.i.9.4		16	55.14	even	10
605.2.j.i.124.1		16	55.49	even	10
605.2.j.i.124.4		16	11.5	even	5
605.2.j.i.269.1		16	55.4	even	10
605.2.j.i.269.4		16	11.4	even	5
605.2.j.i.444.1		16	11.9	even	5
605.2.j.i.444.4		16	55.9	even	10
605.2.j.j.9.1		16	55.19	odd	10
605.2.j.j.9.4		16	11.8	odd	10
605.2.j.j.124.1		16	11.6	odd	10
605.2.j.j.124.4		16	55.39	odd	10
605.2.j.j.269.1		16	11.7	odd	10
605.2.j.j.269.4		16	55.29	odd	10
605.2.j.j.444.1		16	55.24	odd	10
605.2.j.j.444.4		16	11.2	odd	10
880.2.b.h.529.2		4	4.3	odd	2
880.2.b.h.529.3		4	20.19	odd	2
2475.2.a.bi.1.1		4	15.2	even	4
2475.2.a.bi.1.4		4	15.8	even	4
3025.2.a.ba.1.1		4	55.32	even	4
3025.2.a.ba.1.4		4	55.43	even	4
4400.2.a.cc.1.2		4	20.7	even	4
4400.2.a.cc.1.3		4	20.3	even	4

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:	\( N \)	\(=\)	\( 55 = 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	55.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.52434i q^{2} +0.792287i q^{3} -4.37228 q^{4} +(0.686141 - 2.12819i) q^{5} +2.00000 q^{6} +3.46410i q^{7} +5.98844i q^{8} +2.37228 q^{9} +O(q^{10})\)	\(q-2.52434i q^{2} +0.792287i q^{3} -4.37228 q^{4} +(0.686141 - 2.12819i) q^{5} +2.00000 q^{6} +3.46410i q^{7} +5.98844i q^{8} +2.37228 q^{9} +(-5.37228 - 1.73205i) q^{10} -1.00000 q^{11} -3.46410i q^{12} +8.74456 q^{14} +(1.68614 + 0.543620i) q^{15} +6.37228 q^{16} +1.58457i q^{17} -5.98844i q^{18} -4.00000 q^{19} +(-3.00000 + 9.30506i) q^{20} -2.74456 q^{21} +2.52434i q^{22} -0.792287i q^{23} -4.74456 q^{24} +(-4.05842 - 2.92048i) q^{25} +4.25639i q^{27} -15.1460i q^{28} -8.74456 q^{29} +(1.37228 - 4.25639i) q^{30} +3.37228 q^{31} -4.10891i q^{32} -0.792287i q^{33} +4.00000 q^{34} +(7.37228 + 2.37686i) q^{35} -10.3723 q^{36} -1.08724i q^{37} +10.0974i q^{38} +(12.7446 + 4.10891i) q^{40} +8.74456 q^{41} +6.92820i q^{42} -3.46410i q^{43} +4.37228 q^{44} +(1.62772 - 5.04868i) q^{45} -2.00000 q^{46} -6.63325i q^{47} +5.04868i q^{48} -5.00000 q^{49} +(-7.37228 + 10.2448i) q^{50} -1.25544 q^{51} -10.0974i q^{53} +10.7446 q^{54} +(-0.686141 + 2.12819i) q^{55} -20.7446 q^{56} -3.16915i q^{57} +22.0742i q^{58} +7.37228 q^{59} +(-7.37228 - 2.37686i) q^{60} -0.744563 q^{61} -8.51278i q^{62} +8.21782i q^{63} +2.37228 q^{64} -2.00000 q^{66} +9.30506i q^{67} -6.92820i q^{68} +0.627719 q^{69} +(6.00000 - 18.6101i) q^{70} -10.1168 q^{71} +14.2063i q^{72} +6.92820i q^{73} -2.74456 q^{74} +(2.31386 - 3.21543i) q^{75} +17.4891 q^{76} -3.46410i q^{77} -1.25544 q^{79} +(4.37228 - 13.5615i) q^{80} +3.74456 q^{81} -22.0742i q^{82} -6.63325i q^{83} +12.0000 q^{84} +(3.37228 + 1.08724i) q^{85} -8.74456 q^{86} -6.92820i q^{87} -5.98844i q^{88} -1.37228 q^{89} +(-12.7446 - 4.10891i) q^{90} +3.46410i q^{92} +2.67181i q^{93} -16.7446 q^{94} +(-2.74456 + 8.51278i) q^{95} +3.25544 q^{96} +5.84096i q^{97} +12.6217i q^{98} -2.37228 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 6 q^{4} - 3 q^{5} + 8 q^{6} - 2 q^{9}+O(q^{10}) \) 4 * q - 6 * q^4 - 3 * q^5 + 8 * q^6 - 2 * q^9	\( 4 q - 6 q^{4} - 3 q^{5} + 8 q^{6} - 2 q^{9} - 10 q^{10} - 4 q^{11} + 12 q^{14} + q^{15} + 14 q^{16} - 16 q^{19} - 12 q^{20} + 12 q^{21} + 4 q^{24} + q^{25} - 12 q^{29} - 6 q^{30} + 2 q^{31} + 16 q^{34} + 18 q^{35} - 30 q^{36} + 28 q^{40} + 12 q^{41} + 6 q^{44} + 18 q^{45} - 8 q^{46} - 20 q^{49} - 18 q^{50} - 28 q^{51} + 20 q^{54} + 3 q^{55} - 60 q^{56} + 18 q^{59} - 18 q^{60} + 20 q^{61} - 2 q^{64} - 8 q^{66} + 14 q^{69} + 24 q^{70} - 6 q^{71} + 12 q^{74} + 15 q^{75} + 24 q^{76} - 28 q^{79} + 6 q^{80} - 8 q^{81} + 48 q^{84} + 2 q^{85} - 12 q^{86} + 6 q^{89} - 28 q^{90} - 44 q^{94} + 12 q^{95} + 36 q^{96} + 2 q^{99}+O(q^{100}) \) 4 * q - 6 * q^4 - 3 * q^5 + 8 * q^6 - 2 * q^9 - 10 * q^10 - 4 * q^11 + 12 * q^14 + q^15 + 14 * q^16 - 16 * q^19 - 12 * q^20 + 12 * q^21 + 4 * q^24 + q^25 - 12 * q^29 - 6 * q^30 + 2 * q^31 + 16 * q^34 + 18 * q^35 - 30 * q^36 + 28 * q^40 + 12 * q^41 + 6 * q^44 + 18 * q^45 - 8 * q^46 - 20 * q^49 - 18 * q^50 - 28 * q^51 + 20 * q^54 + 3 * q^55 - 60 * q^56 + 18 * q^59 - 18 * q^60 + 20 * q^61 - 2 * q^64 - 8 * q^66 + 14 * q^69 + 24 * q^70 - 6 * q^71 + 12 * q^74 + 15 * q^75 + 24 * q^76 - 28 * q^79 + 6 * q^80 - 8 * q^81 + 48 * q^84 + 2 * q^85 - 12 * q^86 + 6 * q^89 - 28 * q^90 - 44 * q^94 + 12 * q^95 + 36 * q^96 + 2 * q^99

Introduction

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