LMFDB - Embedded newform 273.2.bl.b.88.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(88,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 5]))

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

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

chi := DirichletCharacter("273.88");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.bl (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-7})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - x^{2} - 2x + 4 $ x^4 - x^3 - x^2 - 2*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			88.1
Root			$1.39564 - 0.228425i$ of defining polynomial
Character	$\chi$	$=$	273.88
Dual form			273.2.bl.b.121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.395644 - 0.228425i) q^{2} +1.00000 q^{3} +(-0.895644 - 1.55130i) q^{4} +(-1.50000 + 0.866025i) q^{5} +(-0.395644 - 0.228425i) q^{6} -2.64575i q^{7} +1.73205i q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-0.395644 - 0.228425i) q^{2} +1.00000 q^{3} +(-0.895644 - 1.55130i) q^{4} +(-1.50000 + 0.866025i) q^{5} +(-0.395644 - 0.228425i) q^{6} -2.64575i q^{7} +1.73205i q^{8} +1.00000 q^{9} +0.791288 q^{10} -3.46410i q^{11} +(-0.895644 - 1.55130i) q^{12} +(-1.00000 - 3.46410i) q^{13} +(-0.604356 + 1.04678i) q^{14} +(-1.50000 + 0.866025i) q^{15} +(-1.39564 + 2.41733i) q^{16} +(-0.500000 - 0.866025i) q^{17} +(-0.395644 - 0.228425i) q^{18} -5.29150i q^{19} +(2.68693 + 1.55130i) q^{20} -2.64575i q^{21} +(-0.791288 + 1.37055i) q^{22} +(-0.291288 + 0.504525i) q^{23} +1.73205i q^{24} +(-1.00000 + 1.73205i) q^{25} +(-0.395644 + 1.59898i) q^{26} +1.00000 q^{27} +(-4.10436 + 2.36965i) q^{28} +(3.50000 + 6.06218i) q^{29} +0.791288 q^{30} +(-0.708712 - 0.409175i) q^{31} +(4.10436 - 2.36965i) q^{32} -3.46410i q^{33} +0.456850i q^{34} +(2.29129 + 3.96863i) q^{35} +(-0.895644 - 1.55130i) q^{36} +(3.08258 + 1.77973i) q^{37} +(-1.20871 + 2.09355i) q^{38} +(-1.00000 - 3.46410i) q^{39} +(-1.50000 - 2.59808i) q^{40} +(6.08258 - 3.51178i) q^{41} +(-0.604356 + 1.04678i) q^{42} +(2.29129 - 3.96863i) q^{43} +(-5.37386 + 3.10260i) q^{44} +(-1.50000 + 0.866025i) q^{45} +(0.230493 - 0.133075i) q^{46} +(5.29129 - 3.05493i) q^{47} +(-1.39564 + 2.41733i) q^{48} -7.00000 q^{49} +(0.791288 - 0.456850i) q^{50} +(-0.500000 - 0.866025i) q^{51} +(-4.47822 + 4.65390i) q^{52} +(-6.08258 + 10.5353i) q^{53} +(-0.395644 - 0.228425i) q^{54} +(3.00000 + 5.19615i) q^{55} +4.58258 q^{56} -5.29150i q^{57} -3.19795i q^{58} +(-8.29129 + 4.78698i) q^{59} +(2.68693 + 1.55130i) q^{60} +13.1652 q^{61} +(0.186932 + 0.323775i) q^{62} -2.64575i q^{63} +3.41742 q^{64} +(4.50000 + 4.33013i) q^{65} +(-0.791288 + 1.37055i) q^{66} -7.11890i q^{67} +(-0.895644 + 1.55130i) q^{68} +(-0.291288 + 0.504525i) q^{69} -2.09355i q^{70} +(9.87386 + 5.70068i) q^{71} +1.73205i q^{72} +(7.50000 + 4.33013i) q^{73} +(-0.813068 - 1.40828i) q^{74} +(-1.00000 + 1.73205i) q^{75} +(-8.20871 + 4.73930i) q^{76} -9.16515 q^{77} +(-0.395644 + 1.59898i) q^{78} +(5.29129 + 9.16478i) q^{79} -4.83465i q^{80} +1.00000 q^{81} -3.20871 q^{82} +3.46410i q^{83} +(-4.10436 + 2.36965i) q^{84} +(1.50000 + 0.866025i) q^{85} +(-1.81307 + 1.04678i) q^{86} +(3.50000 + 6.06218i) q^{87} +6.00000 q^{88} +(-13.5000 - 7.79423i) q^{89} +0.791288 q^{90} +(-9.16515 + 2.64575i) q^{91} +1.04356 q^{92} +(-0.708712 - 0.409175i) q^{93} -2.79129 q^{94} +(4.58258 + 7.93725i) q^{95} +(4.10436 - 2.36965i) q^{96} +(-0.0825757 - 0.0476751i) q^{97} +(2.76951 + 1.59898i) q^{98} -3.46410i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 3 q^{2} + 4 q^{3} + q^{4} - 6 q^{5} + 3 q^{6} + 4 q^{9}+O(q^{10}) $ 4 * q + 3 * q^2 + 4 * q^3 + q^4 - 6 * q^5 + 3 * q^6 + 4 * q^9	$ 4 q + 3 q^{2} + 4 q^{3} + q^{4} - 6 q^{5} + 3 q^{6} + 4 q^{9} - 6 q^{10} + q^{12} - 4 q^{13} - 7 q^{14} - 6 q^{15} - q^{16} - 2 q^{17} + 3 q^{18} - 3 q^{20} + 6 q^{22} + 8 q^{23} - 4 q^{25} + 3 q^{26} + 4 q^{27} - 21 q^{28} + 14 q^{29} - 6 q^{30} - 12 q^{31} + 21 q^{32} + q^{36} - 6 q^{37} - 14 q^{38} - 4 q^{39} - 6 q^{40} + 6 q^{41} - 7 q^{42} + 6 q^{44} - 6 q^{45} + 33 q^{46} + 12 q^{47} - q^{48} - 28 q^{49} - 6 q^{50} - 2 q^{51} + 5 q^{52} - 6 q^{53} + 3 q^{54} + 12 q^{55} - 24 q^{59} - 3 q^{60} + 16 q^{61} - 13 q^{62} + 32 q^{64} + 18 q^{65} + 6 q^{66} + q^{68} + 8 q^{69} + 12 q^{71} + 30 q^{73} - 17 q^{74} - 4 q^{75} - 42 q^{76} + 3 q^{78} + 12 q^{79} + 4 q^{81} - 22 q^{82} - 21 q^{84} + 6 q^{85} - 21 q^{86} + 14 q^{87} + 24 q^{88} - 54 q^{89} - 6 q^{90} + 50 q^{92} - 12 q^{93} - 2 q^{94} + 21 q^{96} + 18 q^{97} - 21 q^{98}+O(q^{100}) $ 4 * q + 3 * q^2 + 4 * q^3 + q^4 - 6 * q^5 + 3 * q^6 + 4 * q^9 - 6 * q^10 + q^12 - 4 * q^13 - 7 * q^14 - 6 * q^15 - q^16 - 2 * q^17 + 3 * q^18 - 3 * q^20 + 6 * q^22 + 8 * q^23 - 4 * q^25 + 3 * q^26 + 4 * q^27 - 21 * q^28 + 14 * q^29 - 6 * q^30 - 12 * q^31 + 21 * q^32 + q^36 - 6 * q^37 - 14 * q^38 - 4 * q^39 - 6 * q^40 + 6 * q^41 - 7 * q^42 + 6 * q^44 - 6 * q^45 + 33 * q^46 + 12 * q^47 - q^48 - 28 * q^49 - 6 * q^50 - 2 * q^51 + 5 * q^52 - 6 * q^53 + 3 * q^54 + 12 * q^55 - 24 * q^59 - 3 * q^60 + 16 * q^61 - 13 * q^62 + 32 * q^64 + 18 * q^65 + 6 * q^66 + q^68 + 8 * q^69 + 12 * q^71 + 30 * q^73 - 17 * q^74 - 4 * q^75 - 42 * q^76 + 3 * q^78 + 12 * q^79 + 4 * q^81 - 22 * q^82 - 21 * q^84 + 6 * q^85 - 21 * q^86 + 14 * q^87 + 24 * q^88 - 54 * q^89 - 6 * q^90 + 50 * q^92 - 12 * q^93 - 2 * q^94 + 21 * q^96 + 18 * q^97 - 21 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.395644	−	0.228425i	−0.279763	−	0.161521i	0.353553	−	0.935414i	$-0.384973\pi$
$2$	−0.395644	−	0.228425i	−0.279763	−	0.161521i	−0.633316	+	0.773893i	$0.718307\pi$
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	−0.895644	−	1.55130i	−0.447822	−	0.775650i
$5$	−1.50000	+	0.866025i	−0.670820	+	0.387298i	−0.796387	−	0.604787i	$-0.793258\pi$
$5$	−1.50000	+	0.866025i	−0.670820	+	0.387298i	0.125567	+	0.992085i	$0.459925\pi$
$6$	−0.395644	−	0.228425i	−0.161521	−	0.0932542i
$7$		−	2.64575i		−	1.00000i
$7$		−	2.64575i		−	1.00000i
$8$			1.73205i			0.612372i
$9$	1.00000			0.333333
$10$	0.791288			0.250227
$11$		−	3.46410i		−	1.04447i	−0.852803	−	0.522233i	$-0.825099\pi$
$11$		−	3.46410i		−	1.04447i	0.852803	−	0.522233i	$-0.174901\pi$
$12$	−0.895644	−	1.55130i	−0.258550	−	0.447822i
$13$	−1.00000	−	3.46410i	−0.277350	−	0.960769i
$13$	−1.00000	−	3.46410i	−0.277350	−	0.960769i
$14$	−0.604356	+	1.04678i	−0.161521	+	0.279763i
$15$	−1.50000	+	0.866025i	−0.387298	+	0.223607i
$16$	−1.39564	+	2.41733i	−0.348911	+	0.604332i
$17$	−0.500000	−	0.866025i	−0.121268	−	0.210042i	0.799000	−	0.601331i	$-0.205363\pi$
$17$	−0.500000	−	0.866025i	−0.121268	−	0.210042i	−0.920268	+	0.391289i	$0.872029\pi$
$18$	−0.395644	−	0.228425i	−0.0932542	−	0.0538403i
$19$		−	5.29150i		−	1.21395i	−0.794719	−	0.606977i	$-0.792382\pi$
$19$		−	5.29150i		−	1.21395i	0.794719	−	0.606977i	$-0.207618\pi$
$20$	2.68693	+	1.55130i	0.600816	+	0.346881i
$21$		−	2.64575i		−	0.577350i
$22$	−0.791288	+	1.37055i	−0.168703	+	0.292202i
$23$	−0.291288	+	0.504525i	−0.0607377	+	0.105201i	−0.894795	−	0.446476i	$-0.852679\pi$
$23$	−0.291288	+	0.504525i	−0.0607377	+	0.105201i	0.834058	+	0.551677i	$0.186012\pi$
$24$			1.73205i			0.353553i
$25$	−1.00000	+	1.73205i	−0.200000	+	0.346410i
$26$	−0.395644	+	1.59898i	−0.0775922	+	0.313585i
$27$	1.00000			0.192450
$28$	−4.10436	+	2.36965i	−0.775650	+	0.447822i
$29$	3.50000	+	6.06218i	0.649934	+	1.12572i	0.983138	+	0.182864i	$0.0585367\pi$
$29$	3.50000	+	6.06218i	0.649934	+	1.12572i	−0.333205	+	0.942855i	$0.608130\pi$
$30$	0.791288			0.144469
$31$	−0.708712	−	0.409175i	−0.127288	−	0.0734900i	0.435004	−	0.900429i	$-0.356747\pi$
$31$	−0.708712	−	0.409175i	−0.127288	−	0.0734900i	−0.562292	+	0.826939i	$0.690080\pi$
$32$	4.10436	−	2.36965i	0.725555	−	0.418899i
$33$		−	3.46410i		−	0.603023i
$34$			0.456850i			0.0783492i
$35$	2.29129	+	3.96863i	0.387298	+	0.670820i
$36$	−0.895644	−	1.55130i	−0.149274	−	0.258550i
$37$	3.08258	+	1.77973i	0.506772	+	0.292585i	0.731506	−	0.681835i	$-0.238818\pi$
$37$	3.08258	+	1.77973i	0.506772	+	0.292585i	−0.224734	+	0.974420i	$0.572151\pi$
$38$	−1.20871	+	2.09355i	−0.196079	+	0.339619i
$39$	−1.00000	−	3.46410i	−0.160128	−	0.554700i
$40$	−1.50000	−	2.59808i	−0.237171	−	0.410792i
$41$	6.08258	−	3.51178i	0.949939	−	0.548447i	0.0568768	−	0.998381i	$-0.481886\pi$
$41$	6.08258	−	3.51178i	0.949939	−	0.548447i	0.893062	+	0.449934i	$0.148552\pi$
$42$	−0.604356	+	1.04678i	−0.0932542	+	0.161521i
$43$	2.29129	−	3.96863i	0.349418	−	0.605210i	−0.636728	−	0.771088i	$-0.719713\pi$
$43$	2.29129	−	3.96863i	0.349418	−	0.605210i	0.986146	+	0.165878i	$0.0530460\pi$
$44$	−5.37386	+	3.10260i	−0.810140	+	0.467735i
$45$	−1.50000	+	0.866025i	−0.223607	+	0.129099i
$46$	0.230493	−	0.133075i	0.0339843	−	0.0196208i
$47$	5.29129	−	3.05493i	0.771814	−	0.445607i	−0.0617076	−	0.998094i	$-0.519655\pi$
$47$	5.29129	−	3.05493i	0.771814	−	0.445607i	0.833521	+	0.552487i	$0.186321\pi$
$48$	−1.39564	+	2.41733i	−0.201444	+	0.348911i
$49$	−7.00000			−1.00000
$50$	0.791288	−	0.456850i	0.111905	−	0.0646084i
$51$	−0.500000	−	0.866025i	−0.0700140	−	0.121268i
$52$	−4.47822	+	4.65390i	−0.621017	+	0.645380i
$53$	−6.08258	+	10.5353i	−0.835506	+	1.44714i	0.0581117	+	0.998310i	$0.481492\pi$
$53$	−6.08258	+	10.5353i	−0.835506	+	1.44714i	−0.893618	+	0.448829i	$0.851841\pi$
$54$	−0.395644	−	0.228425i	−0.0538403	−	0.0310847i
$55$	3.00000	+	5.19615i	0.404520	+	0.700649i
$56$	4.58258			0.612372
$57$		−	5.29150i		−	0.700877i
$58$		−	3.19795i		−	0.419912i
$59$	−8.29129	+	4.78698i	−1.07943	+	0.623211i	−0.930744	−	0.365672i	$-0.880839\pi$
$59$	−8.29129	+	4.78698i	−1.07943	+	0.623211i	−0.148690	+	0.988884i	$0.547506\pi$
$60$	2.68693	+	1.55130i	0.346881	+	0.200272i
$61$	13.1652			1.68562			0.842812	−	0.538207i	$-0.180898\pi$
$61$	13.1652			1.68562			0.842812	+	0.538207i	$0.180898\pi$
$62$	0.186932	+	0.323775i	0.0237404	+	0.0411195i
$63$		−	2.64575i		−	0.333333i
$64$	3.41742			0.427178
$65$	4.50000	+	4.33013i	0.558156	+	0.537086i
$66$	−0.791288	+	1.37055i	−0.0974008	+	0.168703i
$67$		−	7.11890i		−	0.869713i	−0.900500	−	0.434856i	$-0.856799\pi$
$67$		−	7.11890i		−	0.869713i	0.900500	−	0.434856i	$-0.143201\pi$
$68$	−0.895644	+	1.55130i	−0.108613	+	0.188123i
$69$	−0.291288	+	0.504525i	−0.0350669	+	0.0607377i
$70$		−	2.09355i		−	0.250227i
$71$	9.87386	+	5.70068i	1.17181	+	0.676546i	0.954106	−	0.299468i	$-0.0968093\pi$
$71$	9.87386	+	5.70068i	1.17181	+	0.676546i	0.217706	+	0.976014i	$0.430143\pi$
$72$			1.73205i			0.204124i
$73$	7.50000	+	4.33013i	0.877809	+	0.506803i	0.869935	−	0.493166i	$-0.164160\pi$
$73$	7.50000	+	4.33013i	0.877809	+	0.506803i	0.00787336	+	0.999969i	$0.497494\pi$
$74$	−0.813068	−	1.40828i	−0.0945173	−	0.163709i
$75$	−1.00000	+	1.73205i	−0.115470	+	0.200000i
$76$	−8.20871	+	4.73930i	−0.941604	+	0.543635i
$77$	−9.16515			−1.04447
$78$	−0.395644	+	1.59898i	−0.0447979	+	0.181048i
$79$	5.29129	+	9.16478i	0.595316	+	1.03112i	0.993502	+	0.113813i	$0.0363066\pi$
$79$	5.29129	+	9.16478i	0.595316	+	1.03112i	−0.398186	+	0.917305i	$0.630360\pi$
$80$		−	4.83465i		−	0.540531i
$81$	1.00000			0.111111
$82$	−3.20871			−0.354343
$83$			3.46410i			0.380235i	0.981761	+	0.190117i	$0.0608868\pi$
$83$			3.46410i			0.380235i	−0.981761	+	0.190117i	$0.939113\pi$
$84$	−4.10436	+	2.36965i	−0.447822	+	0.258550i
$85$	1.50000	+	0.866025i	0.162698	+	0.0939336i
$86$	−1.81307	+	1.04678i	−0.195508	+	0.112877i
$87$	3.50000	+	6.06218i	0.375239	+	0.649934i
$88$	6.00000			0.639602
$89$	−13.5000	−	7.79423i	−1.43100	−	0.826187i	−0.433800	−	0.901009i	$-0.642828\pi$
$89$	−13.5000	−	7.79423i	−1.43100	−	0.826187i	−0.997197	+	0.0748225i	$0.976161\pi$
$90$	0.791288			0.0834091
$91$	−9.16515	+	2.64575i	−0.960769	+	0.277350i
$92$	1.04356			0.108799
$93$	−0.708712	−	0.409175i	−0.0734900	−	0.0424295i
$94$	−2.79129			−0.287899
$95$	4.58258	+	7.93725i	0.470162	+	0.814345i
$96$	4.10436	−	2.36965i	0.418899	−	0.241852i
$97$	−0.0825757	−	0.0476751i	−0.00838429	−	0.00484067i	0.495802	−	0.868436i	$-0.334874\pi$
$97$	−0.0825757	−	0.0476751i	−0.00838429	−	0.00484067i	−0.504186	+	0.863595i	$0.668208\pi$
$98$	2.76951	+	1.59898i	0.279763	+	0.161521i
$99$		−	3.46410i		−	0.348155i
$100$	3.58258			0.358258
$101$	−5.16515			−0.513952			−0.256976	−	0.966418i	$-0.582726\pi$
$101$	−5.16515			−0.513952			−0.256976	+	0.966418i	$0.582726\pi$
$102$			0.456850i			0.0452349i
$103$	−6.29129	−	10.8968i	−0.619899	−	1.07370i	−0.989504	−	0.144507i	$-0.953840\pi$
$103$	−6.29129	−	10.8968i	−0.619899	−	1.07370i	0.369605	−	0.929189i	$-0.379493\pi$
$104$	6.00000	−	1.73205i	0.588348	−	0.169842i
$105$	2.29129	+	3.96863i	0.223607	+	0.387298i
$106$	4.81307	−	2.77883i	0.467487	−	0.269903i
$107$	5.29129	−	9.16478i	0.511528	−	0.885993i	−0.488383	−	0.872630i	$-0.662413\pi$
$107$	5.29129	−	9.16478i	0.511528	−	0.885993i	0.999911	−	0.0133631i	$-0.00425372\pi$
$108$	−0.895644	−	1.55130i	−0.0861834	−	0.149274i
$109$	−1.66515	−	0.961376i	−0.159493	−	0.0920831i	0.418129	−	0.908387i	$-0.362686\pi$
$109$	−1.66515	−	0.961376i	−0.159493	−	0.0920831i	−0.577622	+	0.816304i	$0.696019\pi$
$110$		−	2.74110i		−	0.261354i
$111$	3.08258	+	1.77973i	0.292585	+	0.168924i
$112$	6.39564	+	3.69253i	0.604332	+	0.348911i
$113$	3.08258	−	5.33918i	0.289984	−	0.502268i	−0.683821	−	0.729649i	$-0.739683\pi$
$113$	3.08258	−	5.33918i	0.289984	−	0.502268i	0.973806	+	0.227382i	$0.0730166\pi$
$114$	−1.20871	+	2.09355i	−0.113206	+	0.196079i
$115$		−	1.00905i		−	0.0940945i
$116$	6.26951	−	10.8591i	0.582109	−	1.00824i
$117$	−1.00000	−	3.46410i	−0.0924500	−	0.320256i
$118$	4.37386			0.402647
$119$	−2.29129	+	1.32288i	−0.210042	+	0.121268i
$120$	−1.50000	−	2.59808i	−0.136931	−	0.237171i
$121$	−1.00000			−0.0909091
$122$	−5.20871	−	3.00725i	−0.471575	−	0.272264i
$123$	6.08258	−	3.51178i	0.548447	−	0.316646i
$124$			1.46590i			0.131642i
$125$		−	12.1244i		−	1.08444i
$126$	−0.604356	+	1.04678i	−0.0538403	+	0.0932542i
$127$	1.29129	+	2.23658i	0.114583	+	0.198464i	0.917613	−	0.397475i	$-0.130113\pi$
$127$	1.29129	+	2.23658i	0.114583	+	0.198464i	−0.803030	+	0.595939i	$0.796780\pi$
$128$	−9.56080	−	5.51993i	−0.845063	−	0.487897i
$129$	2.29129	−	3.96863i	0.201737	−	0.349418i
$130$	−0.791288	−	2.74110i	−0.0694005	−	0.240411i
$131$	−5.29129	−	9.16478i	−0.462302	−	0.800730i	0.536773	−	0.843727i	$-0.319643\pi$
$131$	−5.29129	−	9.16478i	−0.462302	−	0.800730i	−0.999075	+	0.0429960i	$0.986310\pi$
$132$	−5.37386	+	3.10260i	−0.467735	+	0.270047i
$133$	−14.0000			−1.21395
$134$	−1.62614	+	2.81655i	−0.140477	+	0.243313i
$135$	−1.50000	+	0.866025i	−0.129099	+	0.0745356i
$136$	1.50000	−	0.866025i	0.128624	−	0.0742611i
$137$	−7.50000	+	4.33013i	−0.640768	+	0.369948i	−0.784910	−	0.619609i	$-0.787291\pi$
$137$	−7.50000	+	4.33013i	−0.640768	+	0.369948i	0.144142	+	0.989557i	$0.453958\pi$
$138$	0.230493	−	0.133075i	0.0196208	−	0.0113281i
$139$	−1.29129	+	2.23658i	−0.109526	+	0.189704i	−0.915578	−	0.402140i	$-0.868266\pi$
$139$	−1.29129	+	2.23658i	−0.109526	+	0.189704i	0.806053	+	0.591844i	$0.201600\pi$
$140$	4.10436	−	7.10895i	0.346881	−	0.600816i
$141$	5.29129	−	3.05493i	0.445607	−	0.257271i
$142$	−2.60436	−	4.51088i	−0.218553	−	0.378544i
$143$	−12.0000	+	3.46410i	−1.00349	+	0.289683i
$144$	−1.39564	+	2.41733i	−0.116304	+	0.201444i
$145$	−10.5000	−	6.06218i	−0.871978	−	0.503436i
$146$	−1.97822	−	3.42638i	−0.163719	−	0.283569i
$147$	−7.00000			−0.577350
$148$		−	6.37600i		−	0.524104i
$149$		−	17.5112i		−	1.43457i	−0.696778	−	0.717287i	$-0.745384\pi$
$149$		−	17.5112i		−	1.43457i	0.696778	−	0.717287i	$-0.254616\pi$
$150$	0.791288	−	0.456850i	0.0646084	−	0.0373017i
$151$	8.45644	+	4.88233i	0.688175	+	0.397318i	0.802928	−	0.596076i	$-0.203274\pi$
$151$	8.45644	+	4.88233i	0.688175	+	0.397318i	−0.114753	+	0.993394i	$0.536608\pi$
$152$	9.16515			0.743392
$153$	−0.500000	−	0.866025i	−0.0404226	−	0.0700140i
$154$	3.62614	+	2.09355i	0.292202	+	0.168703i
$155$	1.41742			0.113850
$156$	−4.47822	+	4.65390i	−0.358545	+	0.372610i
$157$	4.08258	−	7.07123i	0.325825	−	0.564345i	−0.655854	−	0.754888i	$-0.727691\pi$
$157$	4.08258	−	7.07123i	0.325825	−	0.564345i	0.981679	+	0.190542i	$0.0610246\pi$
$158$		−	4.83465i		−	0.384624i
$159$	−6.08258	+	10.5353i	−0.482380	+	0.835506i
$160$	−4.10436	+	7.10895i	−0.324478	+	0.562012i
$161$	1.33485	+	0.770675i	0.105201	+	0.0607377i
$162$	−0.395644	−	0.228425i	−0.0310847	−	0.0179468i
$163$			3.46410i			0.271329i	0.990755	+	0.135665i	$0.0433170\pi$
$163$			3.46410i			0.271329i	−0.990755	+	0.135665i	$0.956683\pi$
$164$	−10.8956	−	6.29060i	−0.850807	−	0.491214i
$165$	3.00000	+	5.19615i	0.233550	+	0.404520i
$166$	0.791288	−	1.37055i	0.0614158	−	0.106375i
$167$	−9.87386	+	5.70068i	−0.764063	+	0.441132i	−0.830752	−	0.556642i	$-0.812089\pi$
$167$	−9.87386	+	5.70068i	−0.764063	+	0.441132i	0.0666899	+	0.997774i	$0.478756\pi$
$168$	4.58258			0.353553
$169$	−11.0000	+	6.92820i	−0.846154	+	0.532939i
$170$	−0.395644	−	0.685275i	−0.0303445	−	0.0525582i
$171$		−	5.29150i		−	0.404651i
$172$	−8.20871			−0.625908
$173$	−12.3303			−0.937456			−0.468728	−	0.883343i	$-0.655287\pi$
$173$	−12.3303			−0.937456			−0.468728	+	0.883343i	$0.655287\pi$
$174$		−	3.19795i		−	0.242436i
$175$	4.58258	+	2.64575i	0.346410	+	0.200000i
$176$	8.37386	+	4.83465i	0.631204	+	0.364426i
$177$	−8.29129	+	4.78698i	−0.623211	+	0.359811i
$178$	3.56080	+	6.16748i	0.266893	+	0.462272i
$179$	19.1652			1.43247			0.716235	−	0.697859i	$-0.245864\pi$
$179$	19.1652			1.43247			0.716235	+	0.697859i	$0.245864\pi$
$180$	2.68693	+	1.55130i	0.200272	+	0.115627i
$181$	22.0000			1.63525			0.817624	−	0.575753i	$-0.195291\pi$
$181$	22.0000			1.63525			0.817624	+	0.575753i	$0.195291\pi$
$182$	4.23049	+	1.04678i	0.313585	+	0.0775922i
$183$	13.1652			0.973196
$184$	−0.873864	−	0.504525i	−0.0644221	−	0.0371941i
$185$	−6.16515			−0.453271
$186$	0.186932	+	0.323775i	0.0137065	+	0.0237404i
$187$	−3.00000	+	1.73205i	−0.219382	+	0.126660i
$188$	−9.47822	−	5.47225i	−0.691270	−	0.399105i
$189$		−	2.64575i		−	0.192450i
$190$		−	4.18710i		−	0.303764i
$191$	22.3303			1.61576			0.807882	−	0.589344i	$-0.200614\pi$
$191$	22.3303			1.61576			0.807882	+	0.589344i	$0.200614\pi$
$192$	3.41742			0.246631
$193$		−	17.5112i		−	1.26048i	−0.776399	−	0.630242i	$-0.782956\pi$
$193$		−	17.5112i		−	1.26048i	0.776399	−	0.630242i	$-0.217044\pi$
$194$	0.0217804	+	0.0377247i	0.00156374	+	0.00270848i
$195$	4.50000	+	4.33013i	0.322252	+	0.310087i
$196$	6.26951	+	10.8591i	0.447822	+	0.775650i
$197$	−12.2477	+	7.07123i	−0.872614	+	0.503804i	−0.868216	−	0.496186i	$-0.834733\pi$
$197$	−12.2477	+	7.07123i	−0.872614	+	0.503804i	−0.00439826	+	0.999990i	$0.501400\pi$
$198$	−0.791288	+	1.37055i	−0.0562344	+	0.0974008i
$199$	3.29129	+	5.70068i	0.233313	+	0.404110i	0.958781	−	0.284146i	$-0.0917099\pi$
$199$	3.29129	+	5.70068i	0.233313	+	0.404110i	−0.725468	+	0.688256i	$0.758377\pi$
$200$	−3.00000	−	1.73205i	−0.212132	−	0.122474i
$201$		−	7.11890i		−	0.502129i
$202$	2.04356	+	1.17985i	0.143784	+	0.0830140i
$203$	16.0390	−	9.26013i	1.12572	−	0.649934i
$204$	−0.895644	+	1.55130i	−0.0627076	+	0.108613i
$205$	−6.08258	+	10.5353i	−0.424826	+	0.735819i
$206$			5.74835i			0.400507i
$207$	−0.291288	+	0.504525i	−0.0202459	+	0.0350669i
$208$	9.76951	+	2.41733i	0.677393	+	0.167611i
$209$	−18.3303			−1.26793
$210$		−	2.09355i		−	0.144469i
$211$	1.29129	+	2.23658i	0.0888959	+	0.153972i	0.907045	−	0.421034i	$-0.138333\pi$
$211$	1.29129	+	2.23658i	0.0888959	+	0.153972i	−0.818149	+	0.575007i	$0.804999\pi$
$212$	21.7913			1.49663
$213$	9.87386	+	5.70068i	0.676546	+	0.390604i
$214$	−4.18693	+	2.41733i	−0.286213	+	0.165245i
$215$			7.93725i			0.541316i
$216$			1.73205i			0.117851i
$217$	−1.08258	+	1.87508i	−0.0734900	+	0.127288i
$218$	0.439205	+	0.760725i	0.0297467	+	0.0515228i
$219$	7.50000	+	4.33013i	0.506803	+	0.292603i
$220$	5.37386	−	9.30780i	0.362306	−	0.627532i
$221$	−2.50000	+	2.59808i	−0.168168	+	0.174766i
$222$	−0.813068	−	1.40828i	−0.0545696	−	0.0945173i
$223$	2.29129	−	1.32288i	0.153436	−	0.0885863i	−0.421316	−	0.906914i	$-0.638432\pi$
$223$	2.29129	−	1.32288i	0.153436	−	0.0885863i	0.574752	+	0.818327i	$0.305098\pi$
$224$	−6.26951	−	10.8591i	−0.418899	−	0.725555i
$225$	−1.00000	+	1.73205i	−0.0666667	+	0.115470i
$226$	−2.43920	+	1.40828i	−0.162253	+	0.0936771i
$227$	17.6216	−	10.1738i	1.16959	−	0.675261i	0.216004	−	0.976393i	$-0.430698\pi$
$227$	17.6216	−	10.1738i	1.16959	−	0.675261i	0.953583	+	0.301132i	$0.0973644\pi$
$228$	−8.20871	+	4.73930i	−0.543635	+	0.313868i
$229$	−0.0825757	+	0.0476751i	−0.00545676	+	0.00315046i	−0.502726	−	0.864446i	$-0.667669\pi$
$229$	−0.0825757	+	0.0476751i	−0.00545676	+	0.00315046i	0.497269	+	0.867596i	$0.334336\pi$
$230$	−0.230493	+	0.399225i	−0.0151982	+	0.0263241i
$231$	−9.16515			−0.603023
$232$	−10.5000	+	6.06218i	−0.689359	+	0.398001i
$233$	−0.917424	−	1.58903i	−0.0601025	−	0.104101i	0.834409	−	0.551146i	$-0.185809\pi$
$233$	−0.917424	−	1.58903i	−0.0601025	−	0.104101i	−0.894511	+	0.447046i	$0.852476\pi$
$234$	−0.395644	+	1.59898i	−0.0258641	+	0.104528i
$235$	−5.29129	+	9.16478i	−0.345166	+	0.597844i
$236$	14.8521	+	8.57485i	0.966788	+	0.558175i
$237$	5.29129	+	9.16478i	0.343706	+	0.595316i
$238$	1.20871			0.0783492
$239$			29.7309i			1.92313i	0.274572	+	0.961566i	$0.411464\pi$
$239$			29.7309i			1.92313i	−0.274572	+	0.961566i	$0.588536\pi$
$240$		−	4.83465i		−	0.312075i
$241$	−15.2477	+	8.80328i	−0.982192	+	0.567069i	−0.902931	−	0.429785i	$-0.858589\pi$
$241$	−15.2477	+	8.80328i	−0.982192	+	0.567069i	−0.0792611	+	0.996854i	$0.525256\pi$
$242$	0.395644	+	0.228425i	0.0254330	+	0.0146837i
$243$	1.00000			0.0641500
$244$	−11.7913	−	20.4231i	−0.754860	−	1.30746i
$245$	10.5000	−	6.06218i	0.670820	−	0.387298i
$246$	−3.20871			−0.204580
$247$	−18.3303	+	5.29150i	−1.16633	+	0.336690i
$248$	0.708712	−	1.22753i	0.0450033	−	0.0779479i
$249$			3.46410i			0.219529i
$250$	−2.76951	+	4.79693i	−0.175159	+	0.303384i
$251$	5.70871	−	9.88778i	0.360331	−	0.624111i	−0.627684	−	0.778468i	$-0.715997\pi$
$251$	5.70871	−	9.88778i	0.360331	−	0.624111i	0.988015	+	0.154357i	$0.0493305\pi$
$252$	−4.10436	+	2.36965i	−0.258550	+	0.149274i
$253$	1.74773	+	1.00905i	0.109879	+	0.0634385i
$254$		−	1.17985i		−	0.0740304i
$255$	1.50000	+	0.866025i	0.0939336	+	0.0542326i
$256$	−0.895644	−	1.55130i	−0.0559777	−	0.0969563i
$257$	−13.6652	+	23.6687i	−0.852409	+	1.47642i	0.0266196	+	0.999646i	$0.491526\pi$
$257$	−13.6652	+	23.6687i	−0.852409	+	1.47642i	−0.879028	+	0.476770i	$0.841808\pi$
$258$	−1.81307	+	1.04678i	−0.112877	+	0.0651694i
$259$	4.70871	−	8.15573i	0.292585	−	0.506772i
$260$	2.68693	−	10.8591i	0.166636	−	0.673453i
$261$	3.50000	+	6.06218i	0.216645	+	0.375239i
$262$			4.83465i			0.298686i
$263$	−23.1652			−1.42842			−0.714212	−	0.699929i	$-0.753215\pi$
$263$	−23.1652			−1.42842			−0.714212	+	0.699929i	$0.753215\pi$
$264$	6.00000			0.369274
$265$		−	21.0707i		−	1.29436i
$266$	5.53901	+	3.19795i	0.339619	+	0.196079i
$267$	−13.5000	−	7.79423i	−0.826187	−	0.476999i
$268$	−11.0436	+	6.37600i	−0.674593	+	0.389476i
$269$	1.08258	+	1.87508i	0.0660058	+	0.114325i	0.897140	−	0.441747i	$-0.145641\pi$
$269$	1.08258	+	1.87508i	0.0660058	+	0.114325i	−0.831134	+	0.556072i	$0.812308\pi$
$270$	0.791288			0.0481562
$271$	22.0390	+	12.7242i	1.33877	+	0.772942i	0.986626	−	0.163002i	$-0.0521177\pi$
$271$	22.0390	+	12.7242i	1.33877	+	0.772942i	0.352149	+	0.935944i	$0.385451\pi$
$272$	2.79129			0.169247
$273$	−9.16515	+	2.64575i	−0.554700	+	0.160128i
$274$	3.95644			0.239017
$275$	6.00000	+	3.46410i	0.361814	+	0.208893i
$276$	1.04356			0.0628150
$277$	13.6652	+	23.6687i	0.821059	+	1.42212i	0.904894	+	0.425637i	$0.139950\pi$
$277$	13.6652	+	23.6687i	0.821059	+	1.42212i	−0.0838347	+	0.996480i	$0.526717\pi$
$278$	1.02178	−	0.589925i	0.0612823	−	0.0353814i
$279$	−0.708712	−	0.409175i	−0.0424295	−	0.0244967i
$280$	−6.87386	+	3.96863i	−0.410792	+	0.237171i
$281$			17.5112i			1.04463i	0.852752	+	0.522316i	$0.174932\pi$
$281$			17.5112i			1.04463i	−0.852752	+	0.522316i	$0.825068\pi$
$282$	−2.79129			−0.166219
$283$	6.33030			0.376297			0.188149	−	0.982141i	$-0.439751\pi$
$283$	6.33030			0.376297			0.188149	+	0.982141i	$0.439751\pi$
$284$		−	20.4231i		−	1.21189i
$285$	4.58258	+	7.93725i	0.271448	+	0.470162i
$286$	5.53901	+	1.37055i	0.327529	+	0.0810424i
$287$	−9.29129	−	16.0930i	−0.548447	−	0.949939i
$288$	4.10436	−	2.36965i	0.241852	−	0.139633i
$289$	8.00000	−	13.8564i	0.470588	−	0.815083i
$290$	2.76951	+	4.79693i	0.162631	+	0.281685i
$291$	−0.0825757	−	0.0476751i	−0.00484067	−	0.00279476i
$292$		−	15.5130i		−	0.907830i
$293$	−19.8303	−	11.4490i	−1.15850	−	0.668860i	−0.207555	−	0.978223i	$-0.566551\pi$
$293$	−19.8303	−	11.4490i	−1.15850	−	0.668860i	−0.950944	+	0.309364i	$0.899884\pi$
$294$	2.76951	+	1.59898i	0.161521	+	0.0932542i
$295$	8.29129	−	14.3609i	0.482737	−	0.836126i
$296$	−3.08258	+	5.33918i	−0.179171	+	0.310333i
$297$		−	3.46410i		−	0.201008i
$298$	−4.00000	+	6.92820i	−0.231714	+	0.401340i
$299$	2.03901	+	0.504525i	0.117919	+	0.0291775i
$300$	3.58258			0.206840
$301$	−10.5000	−	6.06218i	−0.605210	−	0.349418i
$302$	−2.23049	−	3.86333i	−0.128350	−	0.222309i
$303$	−5.16515			−0.296730
$304$	12.7913	+	7.38505i	0.733631	+	0.423562i
$305$	−19.7477	+	11.4014i	−1.13075	+	0.652840i
$306$			0.456850i			0.0261164i
$307$		−	0.190700i		−	0.0108838i	−0.999985	−	0.00544192i	$-0.998268\pi$
$307$		−	0.190700i		−	0.0108838i	0.999985	−	0.00544192i	$-0.00173223\pi$
$308$	8.20871	+	14.2179i	0.467735	+	0.810140i
$309$	−6.29129	−	10.8968i	−0.357899	−	0.619899i
$310$	−0.560795	−	0.323775i	−0.0318510	−	0.0183892i
$311$	−0.291288	+	0.504525i	−0.0165174	+	0.0286090i	−0.874166	−	0.485627i	$-0.838591\pi$
$311$	−0.291288	+	0.504525i	−0.0165174	+	0.0286090i	0.857649	+	0.514236i	$0.171925\pi$
$312$	6.00000	−	1.73205i	0.339683	−	0.0980581i
$313$	16.0826	+	27.8558i	0.909041	+	1.57451i	0.815399	+	0.578899i	$0.196517\pi$
$313$	16.0826	+	27.8558i	0.909041	+	1.57451i	0.0936417	+	0.995606i	$0.470149\pi$
$314$	−3.23049	+	1.86513i	−0.182307	+	0.105255i
$315$	2.29129	+	3.96863i	0.129099	+	0.223607i
$316$	9.47822	−	16.4168i	0.533192	−	0.923515i
$317$	−16.6652	+	9.62163i	−0.936008	+	0.540405i	−0.888707	−	0.458476i	$-0.848395\pi$
$317$	−16.6652	+	9.62163i	−0.936008	+	0.540405i	−0.0473014	+	0.998881i	$0.515062\pi$
$318$	4.81307	−	2.77883i	0.269903	−	0.155829i
$319$	21.0000	−	12.1244i	1.17577	−	0.678834i
$320$	−5.12614	+	2.95958i	−0.286560	+	0.165445i
$321$	5.29129	−	9.16478i	0.295331	−	0.511528i
$322$	−0.352083	−	0.609826i	−0.0196208	−	0.0339843i
$323$	−4.58258	+	2.64575i	−0.254981	+	0.147214i
$324$	−0.895644	−	1.55130i	−0.0497580	−	0.0861834i
$325$	7.00000	+	1.73205i	0.388290	+	0.0960769i
$326$	0.791288	−	1.37055i	0.0438254	−	0.0759078i
$327$	−1.66515	−	0.961376i	−0.0920831	−	0.0531642i
$328$	6.08258	+	10.5353i	0.335854	+	0.581716i
$329$	−8.08258	−	13.9994i	−0.445607	−	0.771814i
$330$		−	2.74110i		−	0.150893i
$331$		−	15.4931i		−	0.851578i	−0.904822	−	0.425789i	$-0.859997\pi$
$331$		−	15.4931i		−	0.851578i	0.904822	−	0.425789i	$-0.140003\pi$
$332$	5.37386	−	3.10260i	0.294929	−	0.170277i
$333$	3.08258	+	1.77973i	0.168924	+	0.0975284i
$334$	5.20871			0.285008
$335$	6.16515	+	10.6784i	0.336838	+	0.583421i
$336$	6.39564	+	3.69253i	0.348911	+	0.201444i
$337$	−31.4955			−1.71567			−0.857833	−	0.513928i	$-0.828190\pi$
$337$	−31.4955			−1.71567			−0.857833	+	0.513928i	$0.828190\pi$
$338$	5.93466	−	0.228425i	0.322803	−	0.0124247i
$339$	3.08258	−	5.33918i	0.167423	−	0.289984i
$340$		−	3.10260i		−	0.168262i
$341$	−1.41742	+	2.45505i	−0.0767578	+	0.132948i
$342$	−1.20871	+	2.09355i	−0.0653597	+	0.113206i
$343$			18.5203i			1.00000i
$344$	6.87386	+	3.96863i	0.370614	+	0.213974i
$345$		−	1.00905i		−	0.0543255i
$346$	4.87841	+	2.81655i	0.262265	+	0.151419i
$347$	−0.873864	−	1.51358i	−0.0469115	−	0.0812530i	0.841616	−	0.540076i	$-0.181605\pi$
$347$	−0.873864	−	1.51358i	−0.0469115	−	0.0812530i	−0.888528	+	0.458823i	$0.848271\pi$
$348$	6.26951	−	10.8591i	0.336081	−	0.582109i
$349$	−0.0825757	+	0.0476751i	−0.00442018	+	0.00255199i	−0.502208	−	0.864747i	$-0.667479\pi$
$349$	−0.0825757	+	0.0476751i	−0.00442018	+	0.00255199i	0.497788	+	0.867299i	$0.334146\pi$
$350$	−1.20871	−	2.09355i	−0.0646084	−	0.111905i
$351$	−1.00000	−	3.46410i	−0.0533761	−	0.184900i
$352$	−8.20871	−	14.2179i	−0.437526	−	0.757817i
$353$		−	12.4104i		−	0.660539i	−0.943887	−	0.330270i	$-0.892860\pi$
$353$		−	12.4104i		−	0.660539i	0.943887	−	0.330270i	$-0.107140\pi$
$354$	4.37386			0.232468
$355$	−19.7477			−1.04810
$356$			27.9234i			1.47994i
$357$	−2.29129	+	1.32288i	−0.121268	+	0.0700140i
$358$	−7.58258	−	4.37780i	−0.400752	−	0.231374i
$359$	16.0390	−	9.26013i	0.846507	−	0.488731i	−0.0129639	−	0.999916i	$-0.504127\pi$
$359$	16.0390	−	9.26013i	0.846507	−	0.488731i	0.859471	+	0.511185i	$0.170793\pi$
$360$	−1.50000	−	2.59808i	−0.0790569	−	0.136931i
$361$	−9.00000			−0.473684
$362$	−8.70417	−	5.02535i	−0.457481	−	0.264127i
$363$	−1.00000			−0.0524864
$364$	12.3131	+	11.8483i	0.645380	+	0.621017i
$365$	−15.0000			−0.785136
$366$	−5.20871	−	3.00725i	−0.272264	−	0.157192i
$367$	−3.16515			−0.165220			−0.0826098	−	0.996582i	$-0.526326\pi$
$367$	−3.16515			−0.165220			−0.0826098	+	0.996582i	$0.526326\pi$
$368$	−0.813068	−	1.40828i	−0.0423841	−	0.0734114i
$369$	6.08258	−	3.51178i	0.316646	−	0.182816i
$370$	2.43920	+	1.40828i	0.126808	+	0.0732128i
$371$	27.8739	+	16.0930i	1.44714	+	0.835506i
$372$			1.46590i			0.0760034i
$373$	−26.0000			−1.34623			−0.673114	−	0.739538i	$-0.735044\pi$
$373$	−26.0000			−1.34623			−0.673114	+	0.739538i	$0.735044\pi$
$374$	1.58258			0.0818330
$375$		−	12.1244i		−	0.626099i
$376$	5.29129	+	9.16478i	0.272877	+	0.472637i
$377$	17.5000	−	18.1865i	0.901296	−	0.936654i
$378$	−0.604356	+	1.04678i	−0.0310847	+	0.0538403i
$379$	−16.0390	+	9.26013i	−0.823869	+	0.475661i	−0.851749	−	0.523950i	$-0.824458\pi$
$379$	−16.0390	+	9.26013i	−0.823869	+	0.475661i	0.0278799	+	0.999611i	$0.491124\pi$
$380$	8.20871	−	14.2179i	0.421098	−	0.729363i
$381$	1.29129	+	2.23658i	0.0661547	+	0.114583i
$382$	−8.83485	−	5.10080i	−0.452030	−	0.260980i
$383$			24.6301i			1.25854i	0.777187	+	0.629270i	$0.216646\pi$
$383$			24.6301i			1.25854i	−0.777187	+	0.629270i	$0.783354\pi$
$384$	−9.56080	−	5.51993i	−0.487897	−	0.281688i
$385$	13.7477	−	7.93725i	0.700649	−	0.404520i
$386$	−4.00000	+	6.92820i	−0.203595	+	0.352636i
$387$	2.29129	−	3.96863i	0.116473	−	0.201737i
$388$			0.170800i			0.00867104i
$389$	4.66515	−	8.08028i	0.236533	−	0.409686i	−0.723184	−	0.690655i	$-0.757322\pi$
$389$	4.66515	−	8.08028i	0.236533	−	0.409686i	0.959717	+	0.280969i	$0.0906557\pi$
$390$	−0.791288	−	2.74110i	−0.0400684	−	0.138801i
$391$	0.582576			0.0294621
$392$		−	12.1244i		−	0.612372i
$393$	−5.29129	−	9.16478i	−0.266910	−	0.462302i
$394$	6.46099			0.325500
$395$	−15.8739	−	9.16478i	−0.798701	−	0.461130i
$396$	−5.37386	+	3.10260i	−0.270047	+	0.155912i
$397$		−	16.0652i		−	0.806290i	−0.915136	−	0.403145i	$-0.867917\pi$
$397$		−	16.0652i		−	0.806290i	0.915136	−	0.403145i	$-0.132083\pi$
$398$		−	3.00725i		−	0.150740i
$399$	−14.0000			−0.700877
$400$	−2.79129	−	4.83465i	−0.139564	−	0.241733i
$401$	20.9174	+	12.0767i	1.04457	+	0.603081i	0.921123	−	0.389271i	$-0.127273\pi$
$401$	20.9174	+	12.0767i	1.04457	+	0.603081i	0.123443	+	0.992352i	$0.460606\pi$
$402$	−1.62614	+	2.81655i	−0.0811043	+	0.140477i
$403$	−0.708712	+	2.86423i	−0.0353035	+	0.142677i
$404$	4.62614	+	8.01270i	0.230159	+	0.398647i
$405$	−1.50000	+	0.866025i	−0.0745356	+	0.0430331i
$406$	−8.46099			−0.419912
$407$	6.16515	−	10.6784i	0.305595	−	0.529306i
$408$	1.50000	−	0.866025i	0.0742611	−	0.0428746i
$409$	17.9174	−	10.3446i	0.885960	−	0.511509i	0.0133409	−	0.999911i	$-0.495753\pi$
$409$	17.9174	−	10.3446i	0.885960	−	0.511509i	0.872619	+	0.488402i	$0.162420\pi$
$410$	4.81307	−	2.77883i	0.237700	−	0.137236i
$411$	−7.50000	+	4.33013i	−0.369948	+	0.213589i
$412$	−11.2695	+	19.5194i	−0.555209	+	0.961650i
$413$	12.6652	+	21.9367i	0.623211	+	1.07943i
$414$	0.230493	−	0.133075i	0.0113281	−	0.00654028i
$415$	−3.00000	−	5.19615i	−0.147264	−	0.255069i
$416$	−12.3131	−	11.8483i	−0.603698	−	0.580909i
$417$	−1.29129	+	2.23658i	−0.0632346	+	0.109526i
$418$	7.25227	+	4.18710i	0.354720	+	0.204798i
$419$	7.87386	+	13.6379i	0.384663	+	0.666257i	0.991722	−	0.128400i	$-0.0409842\pi$
$419$	7.87386	+	13.6379i	0.384663	+	0.666257i	−0.607059	+	0.794657i	$0.707651\pi$
$420$	4.10436	−	7.10895i	0.200272	−	0.346881i
$421$		−	33.5764i		−	1.63641i	−0.574923	−	0.818207i	$-0.694968\pi$
$421$		−	33.5764i		−	1.63641i	0.574923	−	0.818207i	$-0.305032\pi$
$422$		−	1.17985i		−	0.0574342i
$423$	5.29129	−	3.05493i	0.257271	−	0.148536i
$424$	−18.2477	−	10.5353i	−0.886188	−	0.511641i
$425$	2.00000			0.0970143
$426$	−2.60436	−	4.51088i	−0.126181	−	0.218553i
$427$		−	34.8317i		−	1.68562i
$428$	−18.9564			−0.916294
$429$	−12.0000	+	3.46410i	−0.579365	+	0.167248i
$430$	1.81307	−	3.14033i	0.0874339	−	0.151440i
$431$			19.1479i			0.922322i	0.887316	+	0.461161i	$0.152567\pi$
$431$			19.1479i			0.922322i	−0.887316	+	0.461161i	$0.847433\pi$
$432$	−1.39564	+	2.41733i	−0.0671479	+	0.116304i
$433$	−10.6652	+	18.4726i	−0.512534	+	0.887736i	0.487360	+	0.873201i	$0.337960\pi$
$433$	−10.6652	+	18.4726i	−0.512534	+	0.887736i	−0.999894	+	0.0145345i	$0.995373\pi$
$434$	0.856629	−	0.494575i	0.0411195	−	0.0237404i
$435$	−10.5000	−	6.06218i	−0.503436	−	0.290659i
$436$			3.44420i			0.164947i
$437$	2.66970	+	1.54135i	0.127709	+	0.0737328i
$438$	−1.97822	−	3.42638i	−0.0945230	−	0.163719i
$439$	0.708712	−	1.22753i	0.0338250	−	0.0585866i	−0.848617	−	0.529007i	$-0.822564\pi$
$439$	0.708712	−	1.22753i	0.0338250	−	0.0585866i	0.882442	+	0.470421i	$0.155898\pi$
$440$	−9.00000	+	5.19615i	−0.429058	+	0.247717i
$441$	−7.00000			−0.333333
$442$	1.58258	−	0.456850i	0.0752754	−	0.0217302i
$443$	−10.8739	−	18.8341i	−0.516633	−	0.894834i	−0.999813	−	0.0193136i	$-0.993852\pi$
$443$	−10.8739	−	18.8341i	−0.516633	−	0.894834i	0.483181	−	0.875521i	$-0.339481\pi$
$444$		−	6.37600i		−	0.302592i
$445$	27.0000			1.27992
$446$	−1.20871			−0.0572342
$447$		−	17.5112i		−	0.828252i
$448$		−	9.04165i		−	0.427178i
$449$	7.66515	+	4.42548i	0.361741	+	0.208851i	0.669844	−	0.742502i	$-0.266361\pi$
$449$	7.66515	+	4.42548i	0.361741	+	0.208851i	−0.308103	+	0.951353i	$0.599694\pi$
$450$	0.791288	−	0.456850i	0.0373017	−	0.0215361i
$451$	−12.1652	−	21.0707i	−0.572835	−	0.992179i
$452$	−11.0436			−0.519445
$453$	8.45644	+	4.88233i	0.397318	+	0.229392i
$454$	−9.29583			−0.436275
$455$	11.4564	−	11.9059i	0.537086	−	0.558156i
$456$	9.16515			0.429198
$457$	24.2477	+	13.9994i	1.13426	+	0.654866i	0.945003	−	0.327062i	$-0.106058\pi$
$457$	24.2477	+	13.9994i	1.13426	+	0.654866i	0.189258	+	0.981927i	$0.439392\pi$
$458$	0.0435608			0.00203546
$459$	−0.500000	−	0.866025i	−0.0233380	−	0.0404226i
$460$	−1.56534	+	0.903750i	−0.0729844	+	0.0421376i
$461$	18.4129	+	10.6307i	0.857573	+	0.495120i	0.863199	−	0.504864i	$-0.168457\pi$
$461$	18.4129	+	10.6307i	0.857573	+	0.495120i	−0.00562564	+	0.999984i	$0.501791\pi$
$462$	3.62614	+	2.09355i	0.168703	+	0.0974008i
$463$		−	3.84550i		−	0.178716i	−0.996000	−	0.0893578i	$-0.971519\pi$
$463$		−	3.84550i		−	0.178716i	0.996000	−	0.0893578i	$-0.0284815\pi$
$464$	−19.5390			−0.907076
$465$	1.41742			0.0657315
$466$			0.838251i			0.0388312i
$467$	−8.45644	−	14.6470i	−0.391317	−	0.677782i	0.601306	−	0.799019i	$-0.294647\pi$
$467$	−8.45644	−	14.6470i	−0.391317	−	0.677782i	−0.992624	+	0.121237i	$0.961314\pi$
$468$	−4.47822	+	4.65390i	−0.207006	+	0.215127i
$469$	−18.8348			−0.869713
$470$	4.18693	−	2.41733i	0.193129	−	0.111503i
$471$	4.08258	−	7.07123i	0.188115	−	0.325825i
$472$	−8.29129	−	14.3609i	−0.381637	−	0.661015i
$473$	−13.7477	−	7.93725i	−0.632121	−	0.364955i
$474$		−	4.83465i		−	0.222063i
$475$	9.16515	+	5.29150i	0.420526	+	0.242791i
$476$	4.10436	+	2.36965i	0.188123	+	0.108613i
$477$	−6.08258	+	10.5353i	−0.278502	+	0.482380i
$478$	6.79129	−	11.7629i	0.310626	−	0.538020i
$479$			35.2131i			1.60893i	0.594001	+	0.804464i	$0.297547\pi$
$479$			35.2131i			1.60893i	−0.594001	+	0.804464i	$0.702453\pi$
$480$	−4.10436	+	7.10895i	−0.187337	+	0.324478i
$481$	3.08258	−	12.4581i	0.140553	−	0.568040i
$482$	8.04356			0.366374
$483$	1.33485	+	0.770675i	0.0607377	+	0.0350669i
$484$	0.895644	+	1.55130i	0.0407111	+	0.0705137i
$485$	0.165151			0.00749914
$486$	−0.395644	−	0.228425i	−0.0179468	−	0.0103616i
$487$	−32.4564	+	18.7387i	−1.47074	+	0.849133i	−0.999460	−	0.0328498i	$-0.989542\pi$
$487$	−32.4564	+	18.7387i	−1.47074	+	0.849133i	−0.471281	+	0.881983i	$0.656208\pi$
$488$			22.8027i			1.03223i
$489$			3.46410i			0.156652i
$490$	−5.53901			−0.250227
$491$	11.8739	+	20.5661i	0.535860	+	0.928137i	0.999121	+	0.0419149i	$0.0133458\pi$
$491$	11.8739	+	20.5661i	0.535860	+	0.928137i	−0.463261	+	0.886222i	$0.653321\pi$
$492$	−10.8956	−	6.29060i	−0.491214	−	0.283602i
$493$	3.50000	−	6.06218i	0.157632	−	0.273027i
$494$	8.46099	+	2.09355i	0.380678	+	0.0941933i
$495$	3.00000	+	5.19615i	0.134840	+	0.233550i
$496$	1.97822	−	1.14213i	0.0888247	−	0.0512830i
$497$	15.0826	−	26.1238i	0.676546	−	1.17181i
$498$	0.791288	−	1.37055i	0.0354585	−	0.0614158i
$499$	26.2913	−	15.1793i	1.17696	−	0.679518i	0.221650	−	0.975126i	$-0.428856\pi$
$499$	26.2913	−	15.1793i	1.17696	−	0.679518i	0.955309	+	0.295608i	$0.0955223\pi$
$500$	−18.8085	+	10.8591i	−0.841143	+	0.485634i
$501$	−9.87386	+	5.70068i	−0.441132	+	0.254688i
$502$	−4.51723	+	2.60803i	−0.201614	+	0.116402i
$503$	12.8739	−	22.2982i	0.574017	−	0.994227i	−0.422130	−	0.906535i	$-0.638718\pi$
$503$	12.8739	−	22.2982i	0.574017	−	0.994227i	0.996148	−	0.0876919i	$-0.0279491\pi$
$504$	4.58258			0.204124
$505$	7.74773	−	4.47315i	0.344769	−	0.199053i
$506$	−0.460985	−	0.798450i	−0.0204933	−	0.0354954i
$507$	−11.0000	+	6.92820i	−0.488527	+	0.307692i
$508$	2.31307	−	4.00635i	0.102626	−	0.177753i
$509$	3.24773	+	1.87508i	0.143953	+	0.0831113i	0.570247	−	0.821474i	$-0.306848\pi$
$509$	3.24773	+	1.87508i	0.143953	+	0.0831113i	−0.426294	+	0.904585i	$0.640181\pi$
$510$	−0.395644	−	0.685275i	−0.0175194	−	0.0303445i
$511$	11.4564	−	19.8431i	0.506803	−	0.877809i
$512$			22.8981i			1.01196i
$513$		−	5.29150i		−	0.233626i
$514$	10.8131	−	6.24293i	0.476944	−	0.275364i
$515$	18.8739	+	10.8968i	0.831682	+	0.480172i
$516$	−8.20871			−0.361368
$517$	−10.5826	−	18.3296i	−0.465421	−	0.806133i
$518$	−3.72595	+	2.15118i	−0.163709	+	0.0945173i
$519$	−12.3303			−0.541240
$520$	−7.50000	+	7.79423i	−0.328897	+	0.341800i
$521$	16.6652	−	28.8649i	0.730114	−	1.26459i	−0.226721	−	0.973960i	$-0.572800\pi$
$521$	16.6652	−	28.8649i	0.730114	−	1.26459i	0.956834	−	0.290634i	$-0.0938662\pi$
$522$		−	3.19795i		−	0.139971i
$523$	−8.87386	+	15.3700i	−0.388027	+	0.672082i	−0.992184	−	0.124783i	$-0.960177\pi$
$523$	−8.87386	+	15.3700i	−0.388027	+	0.672082i	0.604157	+	0.796865i	$0.293510\pi$
$524$	−9.47822	+	16.4168i	−0.414058	+	0.717169i
$525$	4.58258	+	2.64575i	0.200000	+	0.115470i
$526$	9.16515	+	5.29150i	0.399620	+	0.230720i
$527$			0.818350i			0.0356479i
$528$	8.37386	+	4.83465i	0.364426	+	0.210401i
$529$	11.3303	+	19.6247i	0.492622	+	0.853246i
$530$	−4.81307	+	8.33648i	−0.209066	+	0.362113i
$531$	−8.29129	+	4.78698i	−0.359811	+	0.207737i
$532$	12.5390	+	21.7182i	0.543635	+	0.941604i
$533$	−18.2477	−	17.5589i	−0.790397	−	0.760560i
$534$	3.56080	+	6.16748i	0.154091	+	0.266893i
$535$			18.3296i			0.792456i
$536$	12.3303			0.532588
$537$	19.1652			0.827037
$538$		−	0.989150i		−	0.0426453i
$539$			24.2487i			1.04447i
$540$	2.68693	+	1.55130i	0.115627	+	0.0667574i
$541$	−25.6652	+	14.8178i	−1.10343	+	0.637066i	−0.937120	−	0.349007i	$-0.886519\pi$
$541$	−25.6652	+	14.8178i	−1.10343	+	0.637066i	−0.166311	+	0.986073i	$0.553186\pi$
$542$	−5.81307	−	10.0685i	−0.249693	−	0.432480i
$543$	22.0000			0.944110
$544$	−4.10436	−	2.36965i	−0.175973	−	0.101598i
$545$	3.33030			0.142654
$546$	4.23049	+	1.04678i	0.181048	+	0.0447979i
$547$	−8.00000			−0.342055			−0.171028	−	0.985266i	$-0.554709\pi$
$547$	−8.00000			−0.342055			−0.171028	+	0.985266i	$0.554709\pi$
$548$	13.4347	+	7.75650i	0.573900	+	0.331341i
$549$	13.1652			0.561875
$550$	−1.58258	−	2.74110i	−0.0674813	−	0.116881i
$551$	32.0780	−	18.5203i	1.36657	−	0.788990i
$552$	−0.873864	−	0.504525i	−0.0371941	−	0.0214740i
$553$	24.2477	−	13.9994i	1.03112	−	0.595316i
$554$		−	12.4859i		−	0.530473i
$555$	−6.16515			−0.261696
$556$	4.62614			0.196192
$557$			3.27340i			0.138698i	0.997592	+	0.0693492i	$0.0220923\pi$
$557$			3.27340i			0.138698i	−0.997592	+	0.0693492i	$0.977908\pi$
$558$	0.186932	+	0.323775i	0.00791345	+	0.0137065i
$559$	−16.0390	−	3.96863i	−0.678378	−	0.167855i
$560$	−12.7913			−0.540531
$561$	−3.00000	+	1.73205i	−0.126660	+	0.0731272i
$562$	4.00000	−	6.92820i	0.168730	−	0.292249i
$563$	−7.29129	−	12.6289i	−0.307291	−	0.532244i	0.670478	−	0.741930i	$-0.266089\pi$
$563$	−7.29129	−	12.6289i	−0.307291	−	0.532244i	−0.977769	+	0.209686i	$0.932756\pi$
$564$	−9.47822	−	5.47225i	−0.399105	−	0.230423i
$565$			10.6784i			0.449242i
$566$	−2.50455	−	1.44600i	−0.105274	−	0.0607799i
$567$		−	2.64575i		−	0.111111i
$568$	−9.87386	+	17.1020i	−0.414298	+	0.717585i
$569$	−15.6652	+	27.1328i	−0.656717	+	1.13747i	0.324743	+	0.945802i	$0.394722\pi$
$569$	−15.6652	+	27.1328i	−0.656717	+	1.13747i	−0.981460	+	0.191665i	$0.938611\pi$
$570$		−	4.18710i		−	0.175378i
$571$	−10.1261	+	17.5390i	−0.423766	+	0.733984i	−0.996304	−	0.0858941i	$-0.972625\pi$
$571$	−10.1261	+	17.5390i	−0.423766	+	0.733984i	0.572539	+	0.819878i	$0.305959\pi$
$572$	16.1216	+	15.5130i	0.674078	+	0.648631i
$573$	22.3303			0.932862
$574$			8.48945i			0.354343i
$575$	−0.582576	−	1.00905i	−0.0242951	−	0.0420803i
$576$	3.41742			0.142393
$577$	−2.91742	−	1.68438i	−0.121454	−	0.0701215i	0.438042	−	0.898954i	$-0.355672\pi$
$577$	−2.91742	−	1.68438i	−0.121454	−	0.0701215i	−0.559496	+	0.828833i	$0.689005\pi$
$578$	−6.33030	+	3.65480i	−0.263306	+	0.152020i
$579$		−	17.5112i		−	0.727741i
$580$			21.7182i			0.901800i
$581$	9.16515			0.380235
$582$	0.0217804	+	0.0377247i	0.000902826	+	0.00156374i
$583$	36.4955	+	21.0707i	1.51149	+	0.872658i
$584$	−7.50000	+	12.9904i	−0.310352	+	0.537546i
$585$	4.50000	+	4.33013i	0.186052	+	0.179029i
$586$	5.23049	+	9.05948i	0.216070	+	0.374244i
$587$	−5.12614	+	2.95958i	−0.211578	+	0.122155i	−0.602045	−	0.798462i	$-0.705647\pi$
$587$	−5.12614	+	2.95958i	−0.211578	+	0.122155i	0.390466	+	0.920617i	$0.372314\pi$
$588$	6.26951	+	10.8591i	0.258550	+	0.447822i
$589$	−2.16515	+	3.75015i	−0.0892135	+	0.154522i
$590$	−6.56080	+	3.78788i	−0.270104	+	0.155944i
$591$	−12.2477	+	7.07123i	−0.503804	+	0.290871i
$592$	−8.60436	+	4.96773i	−0.353637	+	0.204172i
$593$	−12.2477	+	7.07123i	−0.502954	+	0.290381i	−0.729933	−	0.683519i	$-0.760449\pi$
$593$	−12.2477	+	7.07123i	−0.502954	+	0.290381i	0.226979	+	0.973900i	$0.427115\pi$
$594$	−0.791288	+	1.37055i	−0.0324669	+	0.0562344i
$595$	2.29129	−	3.96863i	0.0939336	−	0.162698i
$596$	−27.1652	+	15.6838i	−1.11273	+	0.642434i
$597$	3.29129	+	5.70068i	0.134703	+	0.233313i
$598$	−0.691478	−	0.665375i	−0.0282766	−	0.0272092i
$599$	−17.8739	+	30.9584i	−0.730306	+	1.26493i	0.226446	+	0.974024i	$0.427289\pi$
$599$	−17.8739	+	30.9584i	−0.730306	+	1.26493i	−0.956752	+	0.290904i	$0.906044\pi$
$600$	−3.00000	−	1.73205i	−0.122474	−	0.0707107i
$601$	−3.91742	−	6.78518i	−0.159795	−	0.276773i	0.775000	−	0.631962i	$-0.217750\pi$
$601$	−3.91742	−	6.78518i	−0.159795	−	0.276773i	−0.934795	+	0.355189i	$0.884417\pi$
$602$	2.76951	+	4.79693i	0.112877	+	0.195508i
$603$		−	7.11890i		−	0.289904i
$604$		−	17.4913i		−	0.711711i
$605$	1.50000	−	0.866025i	0.0609837	−	0.0352089i
$606$	2.04356	+	1.17985i	0.0830140	+	0.0479281i
$607$	−8.00000			−0.324710			−0.162355	−	0.986732i	$-0.551909\pi$
$607$	−8.00000			−0.324710			−0.162355	+	0.986732i	$0.551909\pi$
$608$	−12.5390	−	21.7182i	−0.508524	−	0.880790i
$609$	16.0390	−	9.26013i	0.649934	−	0.375239i
$610$	10.4174			0.421789
$611$	−15.8739	−	15.2746i	−0.642188	−	0.617945i
$612$	−0.895644	+	1.55130i	−0.0362043	+	0.0627076i
$613$		−	3.27340i		−	0.132211i	−0.997813	−	0.0661057i	$-0.978943\pi$
$613$		−	3.27340i		−	0.132211i	0.997813	−	0.0661057i	$-0.0210575\pi$
$614$	−0.0435608	+	0.0754495i	−0.00175797	+	0.00304489i
$615$	−6.08258	+	10.5353i	−0.245273	+	0.424826i
$616$		−	15.8745i		−	0.639602i
$617$	9.24773	+	5.33918i	0.372299	+	0.214947i	0.674463	−	0.738309i	$-0.264375\pi$
$617$	9.24773	+	5.33918i	0.372299	+	0.214947i	−0.302163	+	0.953256i	$0.597709\pi$
$618$			5.74835i			0.231233i
$619$	−31.0390	−	17.9204i	−1.24756	−	0.720281i	−0.276940	−	0.960887i	$-0.589320\pi$
$619$	−31.0390	−	17.9204i	−1.24756	−	0.720281i	−0.970623	+	0.240606i	$0.922654\pi$
$620$	−1.26951	−	2.19885i	−0.0509846	−	0.0883080i
$621$	−0.291288	+	0.504525i	−0.0116890	+	0.0202459i
$622$	0.230493	−	0.133075i	0.00924191	−	0.00533582i
$623$	−20.6216	+	35.7176i	−0.826187	+	1.43100i
$624$	9.76951	+	2.41733i	0.391093	+	0.0967705i
$625$	5.50000	+	9.52628i	0.220000	+	0.381051i
$626$		−	14.6947i		−	0.587317i
$627$	−18.3303			−0.732042
$628$	−14.6261			−0.583646
$629$		−	3.55945i		−	0.141925i
$630$		−	2.09355i		−	0.0834091i
$631$	−17.1261	−	9.88778i	−0.681781	−	0.393626i	0.118745	−	0.992925i	$-0.462113\pi$
$631$	−17.1261	−	9.88778i	−0.681781	−	0.393626i	−0.800526	+	0.599299i	$0.795446\pi$
$632$	−15.8739	+	9.16478i	−0.631428	+	0.364555i
$633$	1.29129	+	2.23658i	0.0513241	+	0.0888959i
$634$	8.79129			0.349147
$635$	−3.87386	−	2.23658i	−0.153730	−	0.0887558i
$636$	21.7913			0.864081
$637$	7.00000	+	24.2487i	0.277350	+	0.960769i
$638$	−11.0780			−0.438583
$639$	9.87386	+	5.70068i	0.390604	+	0.225515i
$640$	19.1216			0.755847
$641$	−19.2477	−	33.3380i	−0.760240	−	1.31677i	−0.942727	−	0.333565i	$-0.891748\pi$
$641$	−19.2477	−	33.3380i	−0.760240	−	1.31677i	0.182487	−	0.983208i	$-0.441585\pi$
$642$	−4.18693	+	2.41733i	−0.165245	+	0.0954043i
$643$	6.54356	+	3.77793i	0.258053	+	0.148987i	0.623446	−	0.781866i	$-0.285732\pi$
$643$	6.54356	+	3.77793i	0.258053	+	0.148987i	−0.365393	+	0.930853i	$0.619065\pi$
$644$		−	2.76100i		−	0.108799i
$645$			7.93725i			0.312529i
$646$	2.41742			0.0951123
$647$	−1.66970			−0.0656426			−0.0328213	−	0.999461i	$-0.510449\pi$
$647$	−1.66970			−0.0656426			−0.0328213	+	0.999461i	$0.510449\pi$
$648$			1.73205i			0.0680414i
$649$	16.5826	+	28.7219i	0.650923	+	1.12743i
$650$	−2.37386	−	2.28425i	−0.0931106	−	0.0895957i
$651$	−1.08258	+	1.87508i	−0.0424295	+	0.0734900i
$652$	5.37386	−	3.10260i	0.210457	−	0.121507i
$653$	14.2477	−	24.6778i	0.557557	−	0.965716i	−0.440143	−	0.897928i	$-0.645072\pi$
$653$	14.2477	−	24.6778i	0.557557	−	0.965716i	0.997700	−	0.0677888i	$-0.0215944\pi$
$654$	0.439205	+	0.760725i	0.0171743	+	0.0297467i
$655$	15.8739	+	9.16478i	0.620243	+	0.358098i
$656$			19.6048i			0.765437i
$657$	7.50000	+	4.33013i	0.292603	+	0.168934i
$658$			7.38505i			0.287899i
$659$	22.0390	−	38.1727i	0.858518	−	1.48700i	−0.0148242	−	0.999890i	$-0.504719\pi$
$659$	22.0390	−	38.1727i	0.858518	−	1.48700i	0.873342	−	0.487107i	$-0.161948\pi$
$660$	5.37386	−	9.30780i	0.209177	−	0.362306i
$661$			26.2668i			1.02166i	0.859682	+	0.510830i	$0.170662\pi$
$661$			26.2668i			1.02166i	−0.859682	+	0.510830i	$0.829338\pi$
$662$	−3.53901	+	6.12975i	−0.137548	+	0.238240i
$663$	−2.50000	+	2.59808i	−0.0970920	+	0.100901i
$664$	−6.00000			−0.232845
$665$	21.0000	−	12.1244i	0.814345	−	0.470162i
$666$	−0.813068	−	1.40828i	−0.0315058	−	0.0545696i
$667$	−4.07803			−0.157902
$668$	17.6869	+	10.2116i	0.684328	+	0.395097i
$669$	2.29129	−	1.32288i	0.0885863	−	0.0511453i
$670$		−	5.63310i		−	0.217626i
$671$		−	45.6054i		−	1.76058i
$672$	−6.26951	−	10.8591i	−0.241852	−	0.418899i
$673$	−0.665151	−	1.15208i	−0.0256397	−	0.0444093i	0.852921	−	0.522040i	$-0.174829\pi$
$673$	−0.665151	−	1.15208i	−0.0256397	−	0.0444093i	−0.878561	+	0.477631i	$0.841496\pi$
$674$	12.4610	+	7.19435i	0.479979	+	0.277116i
$675$	−1.00000	+	1.73205i	−0.0384900	+	0.0666667i
$676$	20.5998	+	10.8591i	0.792300	+	0.417658i
$677$	−24.0826	−	41.7122i	−0.925569	−	1.60313i	−0.790644	−	0.612276i	$-0.790254\pi$
$677$	−24.0826	−	41.7122i	−0.925569	−	1.60313i	−0.134924	−	0.990856i	$-0.543079\pi$
$678$	−2.43920	+	1.40828i	−0.0936771	+	0.0540845i
$679$	−0.126136	+	0.218475i	−0.00484067	+	0.00838429i
$680$	−1.50000	+	2.59808i	−0.0575224	+	0.0996317i
$681$	17.6216	−	10.1738i	0.675261	−	0.389862i
$682$	1.12159	−	0.647551i	0.0429479	−	0.0247960i
$683$	20.1261	−	11.6198i	0.770105	−	0.444620i	−0.0628069	−	0.998026i	$-0.520005\pi$
$683$	20.1261	−	11.6198i	0.770105	−	0.444620i	0.832912	+	0.553405i	$0.186672\pi$
$684$	−8.20871	+	4.73930i	−0.313868	+	0.181212i
$685$	7.50000	−	12.9904i	0.286560	−	0.496337i
$686$	4.23049	−	7.32743i	0.161521	−	0.279763i
$687$	−0.0825757	+	0.0476751i	−0.00315046	+	0.00181892i
$688$	6.39564	+	11.0776i	0.243832	+	0.422329i
$689$	42.5780	+	10.5353i	1.62209	+	0.401364i
$690$	−0.230493	+	0.399225i	−0.00877470	+	0.0151982i
$691$	−29.4564	−	17.0067i	−1.12058	−	0.646965i	−0.179028	−	0.983844i	$-0.557295\pi$
$691$	−29.4564	−	17.0067i	−1.12058	−	0.646965i	−0.941548	+	0.336879i	$0.890629\pi$
$692$	11.0436	+	19.1280i	0.419813	+	0.727138i
$693$	−9.16515			−0.348155
$694$			0.798450i			0.0303087i
$695$		−	4.47315i		−	0.169676i
$696$	−10.5000	+	6.06218i	−0.398001	+	0.229786i
$697$	−6.08258	−	3.51178i	−0.230394	−	0.133018i
$698$	0.0435608			0.00164880
$699$	−0.917424	−	1.58903i	−0.0347002	−	0.0601025i
$700$		−	9.47860i		−	0.358258i
$701$	34.0000			1.28416			0.642081	−	0.766637i	$-0.278071\pi$
$701$	34.0000			1.28416			0.642081	+	0.766637i	$0.278071\pi$
$702$	−0.395644	+	1.59898i	−0.0149326	+	0.0603495i
$703$	9.41742	−	16.3115i	0.355185	−	0.615198i
$704$		−	11.8383i		−	0.446173i
$705$	−5.29129	+	9.16478i	−0.199281	+	0.345166i
$706$	−2.83485	+	4.91010i	−0.106691	+	0.184794i
$707$			13.6657i			0.513952i
$708$	14.8521	+	8.57485i	0.558175	+	0.322263i
$709$			18.9572i			0.711953i	0.934495	+	0.355976i	$0.115852\pi$
$709$			18.9572i			0.711953i	−0.934495	+	0.355976i	$0.884148\pi$
$710$	7.81307	+	4.51088i	0.293219	+	0.169290i
$711$	5.29129	+	9.16478i	0.198439	+	0.343706i
$712$	13.5000	−	23.3827i	0.505934	−	0.876303i
$713$	0.412878	−	0.238375i	0.0154624	−	0.00892723i
$714$	1.20871			0.0452349
$715$	15.0000	−	15.5885i	0.560968	−	0.582975i
$716$	−17.1652	−	29.7309i	−0.641492	−	1.11110i
$717$			29.7309i			1.11032i
$718$	−8.46099			−0.315761
$719$	2.33030			0.0869056			0.0434528	−	0.999055i	$-0.486164\pi$
$719$	2.33030			0.0869056			0.0434528	+	0.999055i	$0.486164\pi$
$720$		−	4.83465i		−	0.180177i
$721$	−28.8303	+	16.6452i	−1.07370	+	0.619899i
$722$	3.56080	+	2.05583i	0.132519	+	0.0765099i
$723$	−15.2477	+	8.80328i	−0.567069	+	0.327397i
$724$	−19.7042	−	34.1286i	−0.732300	−	1.26838i
$725$	−14.0000			−0.519947
$726$	0.395644	+	0.228425i	0.0146837	+	0.00847765i
$727$	28.0000			1.03846			0.519231	−	0.854634i	$-0.326218\pi$
$727$	28.0000			1.03846			0.519231	+	0.854634i	$0.326218\pi$
$728$	−4.58258	−	15.8745i	−0.169842	−	0.588348i
$729$	1.00000			0.0370370
$730$	5.93466	+	3.42638i	0.219652	+	0.126816i
$731$	−4.58258			−0.169493
$732$	−11.7913	−	20.4231i	−0.435819	−	0.754860i
$733$	−10.8303	+	6.25288i	−0.400026	+	0.230955i	−0.686495	−	0.727134i	$-0.740852\pi$
$733$	−10.8303	+	6.25288i	−0.400026	+	0.230955i	0.286469	+	0.958090i	$0.407518\pi$
$734$	1.25227	+	0.723000i	0.0462222	+	0.0266864i
$735$	10.5000	−	6.06218i	0.387298	−	0.223607i
$736$			2.76100i			0.101772i
$737$	−24.6606			−0.908385
$738$	−3.20871			−0.118114
$739$		−	8.56490i		−	0.315065i	−0.987514	−	0.157533i	$-0.949646\pi$
$739$		−	8.56490i		−	0.315065i	0.987514	−	0.157533i	$-0.0503539\pi$
$740$	5.52178	+	9.56400i	0.202985	+	0.351580i
$741$	−18.3303	+	5.29150i	−0.673380	+	0.194388i
$742$	−7.35208	−	12.7342i	−0.269903	−	0.467487i
$743$	11.2913	−	6.51903i	0.414237	−	0.239160i	−0.278372	−	0.960473i	$-0.589795\pi$
$743$	11.2913	−	6.51903i	0.414237	−	0.239160i	0.692609	+	0.721314i	$0.256461\pi$
$744$	0.708712	−	1.22753i	0.0259826	−	0.0450033i
$745$	15.1652	+	26.2668i	0.555608	+	0.962342i
$746$	10.2867	+	5.93905i	0.376624	+	0.217444i
$747$			3.46410i			0.126745i
$748$	5.37386	+	3.10260i	0.196488	+	0.113442i
$749$	−24.2477	−	13.9994i	−0.885993	−	0.511528i
$750$	−2.76951	+	4.79693i	−0.101128	+	0.175159i
$751$	−16.4564	+	28.5034i	−0.600504	+	1.04010i	0.392241	+	0.919863i	$0.371700\pi$
$751$	−16.4564	+	28.5034i	−0.600504	+	1.04010i	−0.992745	+	0.120241i	$0.961633\pi$
$752$			17.0544i			0.621908i
$753$	5.70871	−	9.88778i	0.208037	−	0.360331i
$754$	−11.0780	+	3.19795i	−0.403438	+	0.116463i
$755$	−16.9129			−0.615523
$756$	−4.10436	+	2.36965i	−0.149274	+	0.0861834i
$757$	25.2477	+	43.7303i	0.917644	+	1.58941i	0.802983	+	0.596002i	$0.203245\pi$
$757$	25.2477	+	43.7303i	0.917644	+	1.58941i	0.114661	+	0.993405i	$0.463422\pi$
$758$	8.46099			0.307317
$759$	1.74773	+	1.00905i	0.0634385	+	0.0366262i
$760$	−13.7477	+	7.93725i	−0.498682	+	0.287914i
$761$		−	33.1950i		−	1.20332i	−0.798753	−	0.601659i	$-0.794507\pi$
$761$		−	33.1950i		−	1.20332i	0.798753	−	0.601659i	$-0.205493\pi$
$762$		−	1.17985i		−	0.0427415i
$763$	−2.54356	+	4.40558i	−0.0920831	+	0.159493i
$764$	−20.0000	−	34.6410i	−0.723575	−	1.25327i
$765$	1.50000	+	0.866025i	0.0542326	+	0.0313112i
$766$	5.62614	−	9.74475i	0.203281	−	0.352092i
$767$	24.8739	+	23.9349i	0.898143	+	0.864239i
$768$	−0.895644	−	1.55130i	−0.0323188	−	0.0559777i
$769$	−12.0826	+	6.97588i	−0.435709	+	0.251557i	−0.701776	−	0.712398i	$-0.747609\pi$
$769$	−12.0826	+	6.97588i	−0.435709	+	0.251557i	0.266067	+	0.963955i	$0.414276\pi$
$770$	−7.25227			−0.261354
$771$	−13.6652	+	23.6687i	−0.492138	+	0.852409i
$772$	−27.1652	+	15.6838i	−0.977695	+	0.564473i
$773$	−6.24773	+	3.60713i	−0.224715	+	0.129739i	−0.608132	−	0.793836i	$-0.708081\pi$
$773$	−6.24773	+	3.60713i	−0.224715	+	0.129739i	0.383417	+	0.923576i	$0.374747\pi$
$774$	−1.81307	+	1.04678i	−0.0651694	+	0.0376256i
$775$	1.41742	−	0.818350i	0.0509154	−	0.0293960i
$776$	0.0825757	−	0.143025i	0.00296429	−	0.00513431i
$777$	4.70871	−	8.15573i	0.168924	−	0.292585i
$778$	−3.69148	+	2.13128i	−0.132346	+	0.0764099i
$779$	−18.5826	−	32.1860i	−0.665790	−	1.15318i
$780$	2.68693	−	10.8591i	0.0962076	−	0.388818i
$781$	19.7477	−	34.2041i	0.706629	−	1.22392i
$782$	−0.230493	−	0.133075i	−0.00824240	−	0.00475875i
$783$	3.50000	+	6.06218i	0.125080	+	0.216645i
$784$	9.76951	−	16.9213i	0.348911	−	0.604332i
$785$			14.1425i			0.504766i
$786$			4.83465i			0.172446i
$787$	−21.7087	+	12.5335i	−0.773832	+	0.446772i	−0.834240	−	0.551402i	$-0.814093\pi$
$787$	−21.7087	+	12.5335i	−0.773832	+	0.446772i	0.0604079	+	0.998174i	$0.480760\pi$
$788$	21.9392	+	12.6666i	0.781552	+	0.451229i
$789$	−23.1652			−0.824701
$790$	4.18693	+	7.25198i	0.148964	+	0.258014i
$791$	−14.1261	−	8.15573i	−0.502268	−	0.289984i
$792$	6.00000			0.213201
$793$	−13.1652	−	45.6054i	−0.467508	−	1.61950i
$794$	−3.66970	+	6.35610i	−0.130233	+	0.225570i
$795$		−	21.0707i		−	0.747299i
$796$	5.89564	−	10.2116i	0.208966	−	0.361939i
$797$	−2.91742	+	5.05313i	−0.103340	+	0.178991i	−0.913059	−	0.407828i	$-0.866286\pi$
$797$	−2.91742	+	5.05313i	−0.103340	+	0.178991i	0.809719	+	0.586818i	$0.199620\pi$
$798$	5.53901	+	3.19795i	0.196079	+	0.113206i
$799$	−5.29129	−	3.05493i	−0.187192	−	0.108076i
$800$			9.47860i			0.335119i
$801$	−13.5000	−	7.79423i	−0.476999	−	0.275396i
$802$	−5.51723	−	9.55613i	−0.194820	−	0.337439i
$803$	15.0000	−	25.9808i	0.529339	−	0.916841i
$804$	−11.0436	+	6.37600i	−0.389476	+	0.224864i
$805$	−2.66970			−0.0940945
$806$	0.934659	−	0.971326i	0.0329220	−	0.0342135i
$807$	1.08258	+	1.87508i	0.0381085	+	0.0660058i
$808$		−	8.94630i		−	0.314730i
$809$	−14.8348			−0.521566			−0.260783	−	0.965398i	$-0.583981\pi$
$809$	−14.8348			−0.521566			−0.260783	+	0.965398i	$0.583981\pi$
$810$	0.791288			0.0278030
$811$			20.9753i			0.736543i	0.929718	+	0.368271i	$0.120050\pi$
$811$			20.9753i			0.736543i	−0.929718	+	0.368271i	$0.879950\pi$
$812$	−28.7305	−	16.5876i	−1.00824	−	0.582109i
$813$	22.0390	+	12.7242i	0.772942	+	0.446258i
$814$	−4.87841	+	2.81655i	−0.170988	+	0.0987201i
$815$	−3.00000	−	5.19615i	−0.105085	−	0.182013i
$816$	2.79129			0.0977146
$817$	−21.0000	−	12.1244i	−0.734697	−	0.424178i
$818$	−9.45189			−0.330478
$819$	−9.16515	+	2.64575i	−0.320256	+	0.0924500i
$820$	21.7913			0.760985
$821$	5.75227	+	3.32108i	0.200756	+	0.115906i	0.597008	−	0.802235i	$-0.296356\pi$
$821$	5.75227	+	3.32108i	0.200756	+	0.115906i	−0.396252	+	0.918142i	$0.629689\pi$
$822$	3.95644			0.137997
$823$	−10.7087	−	18.5480i	−0.373282	−	0.646544i	0.616786	−	0.787131i	$-0.288434\pi$
$823$	−10.7087	−	18.5480i	−0.373282	−	0.646544i	−0.990068	+	0.140587i	$0.955101\pi$
$824$	18.8739	−	10.8968i	0.657502	−	0.379609i
$825$	6.00000	+	3.46410i	0.208893	+	0.120605i
$826$		−	11.5722i		−	0.402647i
$827$		−	4.91010i		−	0.170741i	−0.996349	−	0.0853705i	$-0.972793\pi$
$827$		−	4.91010i		−	0.170741i	0.996349	−	0.0853705i	$-0.0272074\pi$
$828$	1.04356			0.0362662
$829$	26.6606			0.925961			0.462981	−	0.886368i	$-0.346780\pi$
$829$	26.6606			0.925961			0.462981	+	0.886368i	$0.346780\pi$
$830$			2.74110i			0.0951450i
$831$	13.6652	+	23.6687i	0.474039	+	0.821059i
$832$	−3.41742	−	11.8383i	−0.118478	−	0.410419i
$833$	3.50000	+	6.06218i	0.121268	+	0.210042i
$834$	1.02178	−	0.589925i	0.0353814	−	0.0204274i
$835$	9.87386	−	17.1020i	0.341699	−	0.591840i
$836$	16.4174	+	28.4358i	0.567808	+	0.983473i
$837$	−0.708712	−	0.409175i	−0.0244967	−	0.0141432i
$838$		−	7.19435i		−	0.248525i
$839$	−36.8739	−	21.2891i	−1.27303	−	0.734983i	−0.297471	−	0.954731i	$-0.596143\pi$
$839$	−36.8739	−	21.2891i	−1.27303	−	0.734983i	−0.975557	+	0.219748i	$0.929476\pi$
$840$	−6.87386	+	3.96863i	−0.237171	+	0.136931i
$841$	−10.0000	+	17.3205i	−0.344828	+	0.597259i
$842$	−7.66970	+	13.2843i	−0.264315	+	0.457807i
$843$			17.5112i			0.603118i
$844$	2.31307	−	4.00635i	0.0796191	−	0.137904i
$845$	10.5000	−	19.9186i	0.361211	−	0.685220i
$846$	−2.79129			−0.0959665
$847$			2.64575i			0.0909091i
$848$	−16.9782	−	29.4071i	−0.583034	−	1.00985i
$849$	6.33030			0.217255
$850$	−0.791288	−	0.456850i	−0.0271409	−	0.0156698i
$851$	−1.79583	+	1.03683i	−0.0615604	+	0.0355419i
$852$		−	20.4231i		−	0.699684i
$853$		−	52.1522i		−	1.78566i	−0.450396	−	0.892829i	$-0.648717\pi$
$853$		−	52.1522i		−	1.78566i	0.450396	−	0.892829i	$-0.351283\pi$
$854$	−7.95644	+	13.7810i	−0.272264	+	0.471575i
$855$	4.58258	+	7.93725i	0.156721	+	0.271448i
$856$	15.8739	+	9.16478i	0.542557	+	0.313246i
$857$	12.6652	−	21.9367i	0.432633	−	0.749343i	−0.564466	−	0.825456i	$-0.690918\pi$
$857$	12.6652	−	21.9367i	0.432633	−	0.749343i	0.997099	+	0.0761135i	$0.0242511\pi$
$858$	5.53901	+	1.37055i	0.189099	+	0.0467898i
$859$	0.543561	+	0.941475i	0.0185461	+	0.0321227i	0.875149	−	0.483853i	$-0.160763\pi$
$859$	0.543561	+	0.941475i	0.0185461	+	0.0321227i	−0.856603	+	0.515975i	$0.827430\pi$
$860$	12.3131	−	7.10895i	0.419872	−	0.242413i
$861$	−9.29129	−	16.0930i	−0.316646	−	0.548447i
$862$	4.37386	−	7.57575i	0.148974	−	0.258031i
$863$	−5.45644	+	3.15028i	−0.185739	+	0.107237i	−0.589986	−	0.807413i	$-0.700867\pi$
$863$	−5.45644	+	3.15028i	−0.185739	+	0.107237i	0.404247	+	0.914650i	$0.367534\pi$
$864$	4.10436	−	2.36965i	0.139633	−	0.0806172i
$865$	18.4955	−	10.6784i	0.628864	−	0.363075i
$866$	8.43920	−	4.87238i	0.286776	−	0.165570i
$867$	8.00000	−	13.8564i	0.271694	−	0.470588i
$868$	3.87841			0.131642
$869$	31.7477	−	18.3296i	1.07697	−	0.621788i
$870$	2.76951	+	4.79693i	0.0938951	+	0.162631i
$871$	−24.6606	+	7.11890i	−0.835593	+	0.241215i
$872$	1.66515	−	2.88413i	0.0563891	−	0.0976689i
$873$	−0.0825757	−	0.0476751i	−0.00279476	−	0.00161356i
$874$	−0.704166	−	1.21965i	−0.0238188	−	0.0412553i
$875$	−32.0780			−1.08444
$876$		−	15.5130i		−	0.524136i
$877$			36.8498i			1.24433i	0.782886	+	0.622165i	$0.213747\pi$
$877$			36.8498i			1.24433i	−0.782886	+	0.622165i	$0.786253\pi$
$878$	−0.560795	+	0.323775i	−0.0189259	+	0.0109269i
$879$	−19.8303	−	11.4490i	−0.668860	−	0.386166i
$880$	−16.7477			−0.564566
$881$	18.2477	+	31.6060i	0.614782	+	1.06483i	0.990423	+	0.138068i	$0.0440892\pi$
$881$	18.2477	+	31.6060i	0.614782	+	1.06483i	−0.375641	+	0.926765i	$0.622578\pi$
$882$	2.76951	+	1.59898i	0.0932542	+	0.0538403i
$883$	13.6697			0.460022			0.230011	−	0.973188i	$-0.426124\pi$
$883$	13.6697			0.460022			0.230011	+	0.973188i	$0.426124\pi$
$884$	6.26951	+	1.55130i	0.210866	+	0.0521759i
$885$	8.29129	−	14.3609i	0.278709	−	0.482737i
$886$			9.93545i			0.333788i
$887$	23.2913	−	40.3417i	0.782045	−	1.35454i	−0.148704	−	0.988882i	$-0.547510\pi$
$887$	23.2913	−	40.3417i	0.782045	−	1.35454i	0.930749	−	0.365660i	$-0.119157\pi$
$888$	−3.08258	+	5.33918i	−0.103444	+	0.179171i
$889$	5.91742	−	3.41643i	0.198464	−	0.114583i
$890$	−10.6824	−	6.16748i	−0.358074	−	0.206734i
$891$		−	3.46410i		−	0.116052i
$892$	−4.10436	−	2.36965i	−0.137424	−	0.0793418i
$893$	−16.1652	−	27.9989i	−0.540946	−	0.936946i
$894$	−4.00000	+	6.92820i	−0.133780	+	0.231714i
$895$	−28.7477	+	16.5975i	−0.960931	+	0.554794i
$896$	−14.6044	+	25.2955i	−0.487897	+	0.845063i
$897$	2.03901	+	0.504525i	0.0680807	+	0.0168456i
$898$	−2.02178	−	3.50183i	−0.0674677	−	0.116857i
$899$		−	5.72845i		−	0.191055i
$900$	3.58258			0.119419
$901$	12.1652			0.405280
$902$			11.1153i			0.370099i
$903$	−10.5000	−	6.06218i	−0.349418	−	0.201737i
$904$	9.24773	+	5.33918i	0.307575	+	0.177578i
$905$	−33.0000	+	19.0526i	−1.09696	+	0.633328i
$906$	−2.23049	−	3.86333i	−0.0741032	−	0.128350i
$907$	27.1652			0.902004			0.451002	−	0.892523i	$-0.351067\pi$
$907$	27.1652			0.902004			0.451002	+	0.892523i	$0.351067\pi$
$908$	−31.5653	−	18.2243i	−1.04753	−	0.604793i
$909$	−5.16515			−0.171317
$910$	−7.25227	+	2.09355i	−0.240411	+	0.0694005i
$911$	−24.6606			−0.817042			−0.408521	−	0.912749i	$-0.633955\pi$
$911$	−24.6606			−0.817042			−0.408521	+	0.912749i	$0.633955\pi$
$912$	12.7913	+	7.38505i	0.423562	+	0.244544i
$913$	12.0000			0.397142
$914$	−6.39564	−	11.0776i	−0.211549	−	0.366414i
$915$	−19.7477	+	11.4014i	−0.652840	+	0.376917i
$916$	0.147917	+	0.0853998i	0.00488731	+	0.00282169i
$917$	−24.2477	+	13.9994i	−0.800730	+	0.462302i
$918$			0.456850i			0.0150783i
$919$	−23.1652			−0.764148			−0.382074	−	0.924132i	$-0.624790\pi$
$919$	−23.1652			−0.764148			−0.382074	+	0.924132i	$0.624790\pi$
$920$	1.74773			0.0576209
$921$		−	0.190700i		−	0.00628379i
$922$	−4.85663	−	8.41193i	−0.159945	−	0.277032i
$923$	9.87386	−	39.9047i	0.325002	−	1.31348i
$924$	8.20871	+	14.2179i	0.270047	+	0.467735i
$925$	−6.16515	+	3.55945i	−0.202709	+	0.117034i
$926$	−0.878409	+	1.52145i	−0.0288663	+	0.0499979i
$927$	−6.29129	−	10.8968i	−0.206633	−	0.357899i
$928$	28.7305	+	16.5876i	0.943125	+	0.544513i
$929$			42.3320i			1.38887i	0.719556	+	0.694434i	$0.244345\pi$
$929$			42.3320i			1.38887i	−0.719556	+	0.694434i	$0.755655\pi$
$930$	−0.560795	−	0.323775i	−0.0183892	−	0.0106170i
$931$			37.0405i			1.21395i
$932$	−1.64337	+	2.84640i	−0.0538304	+	0.0932370i
$933$	−0.291288	+	0.504525i	−0.00953634	+	0.0165174i
$934$			7.72665i			0.252824i
$935$	3.00000	−	5.19615i	0.0981105	−	0.169932i
$936$	6.00000	−	1.73205i	0.196116	−	0.0566139i
$937$	55.4955			1.81296			0.906479	−	0.422251i	$-0.138760\pi$
$937$	55.4955			1.81296			0.906479	+	0.422251i	$0.138760\pi$
$938$	7.45189	+	4.30235i	0.243313	+	0.140477i
$939$	16.0826	+	27.8558i	0.524835	+	0.909041i
$940$	18.9564			0.618291
$941$	−7.83030	−	4.52083i	−0.255261	−	0.147375i	0.366910	−	0.930256i	$-0.380416\pi$
$941$	−7.83030	−	4.52083i	−0.255261	−	0.147375i	−0.622171	+	0.782882i	$0.713749\pi$
$942$	−3.23049	+	1.86513i	−0.105255	+	0.0607691i
$943$			4.09175i			0.133246i
$944$		−	26.7237i		−	0.869781i
$945$	2.29129	+	3.96863i	0.0745356	+	0.129099i
$946$	3.62614	+	6.28065i	0.117896	+	0.204202i
$947$	19.0390	+	10.9922i	0.618685	+	0.357198i	0.776357	−	0.630294i	$-0.217066\pi$
$947$	19.0390	+	10.9922i	0.618685	+	0.357198i	−0.157672	+	0.987492i	$0.550399\pi$
$948$	9.47822	−	16.4168i	0.307838	−	0.533192i
$949$	7.50000	−	30.3109i	0.243460	−	0.983933i
$950$	−2.41742	−	4.18710i	−0.0784316	−	0.135848i
$951$	−16.6652	+	9.62163i	−0.540405	+	0.312003i
$952$	−2.29129	−	3.96863i	−0.0742611	−	0.128624i
$953$	−5.33485	+	9.24023i	−0.172813	+	0.299320i	−0.939402	−	0.342817i	$-0.888619\pi$
$953$	−5.33485	+	9.24023i	−0.172813	+	0.299320i	0.766589	+	0.642138i	$0.221952\pi$
$954$	4.81307	−	2.77883i	0.155829	−	0.0899678i
$955$	−33.4955	+	19.3386i	−1.08389	+	0.625783i
$956$	46.1216	−	26.6283i	1.49168	−	0.861221i
$957$	21.0000	−	12.1244i	0.678834	−	0.391925i
$958$	8.04356	−	13.9319i	0.259876	−	0.450118i
$959$	11.4564	+	19.8431i	0.369948	+	0.640768i
$960$	−5.12614	+	2.95958i	−0.165445	+	0.0955199i
$961$	−15.1652	−	26.2668i	−0.489198	−	0.847317i
$962$	−4.06534	+	4.22483i	−0.131072	+	0.136214i
$963$	5.29129	−	9.16478i	0.170509	−	0.295331i
$964$	27.3131	+	15.7692i	0.879695	+	0.507892i
$965$	15.1652	+	26.2668i	0.488183	+	0.845559i
$966$	−0.352083	−	0.609826i	−0.0113281	−	0.0196208i
$967$		−	5.29150i		−	0.170163i	−0.996374	−	0.0850816i	$-0.972885\pi$
$967$		−	5.29150i		−	0.170163i	0.996374	−	0.0850816i	$-0.0271151\pi$
$968$		−	1.73205i		−	0.0556702i
$969$	−4.58258	+	2.64575i	−0.147214	+	0.0849938i
$970$	−0.0653411	−	0.0377247i	−0.00209798	−	0.00121127i
$971$	13.6697			0.438681			0.219341	−	0.975648i	$-0.429609\pi$
$971$	13.6697			0.438681			0.219341	+	0.975648i	$0.429609\pi$
$972$	−0.895644	−	1.55130i	−0.0287278	−	0.0497580i
$973$	5.91742	+	3.41643i	0.189704	+	0.109526i
$974$	17.1216			0.548611
$975$	7.00000	+	1.73205i	0.224179	+	0.0554700i
$976$	−18.3739	+	31.8245i	−0.588133	+	1.01868i
$977$			17.5112i			0.560233i	0.959966	+	0.280117i	$0.0903731\pi$
$977$			17.5112i			0.560233i	−0.959966	+	0.280117i	$0.909627\pi$
$978$	0.791288	−	1.37055i	0.0253026	−	0.0438254i
$979$	−27.0000	+	46.7654i	−0.862924	+	1.49463i
$980$	−18.8085	−	10.8591i	−0.600816	−	0.346881i
$981$	−1.66515	−	0.961376i	−0.0531642	−	0.0306944i
$982$		−	10.8492i		−	0.346210i
$983$	−15.7087	−	9.06943i	−0.501030	−	0.289270i	0.228109	−	0.973636i	$-0.426746\pi$
$983$	−15.7087	−	9.06943i	−0.501030	−	0.289270i	−0.729139	+	0.684366i	$0.760079\pi$
$984$	6.08258	+	10.5353i	0.193905	+	0.335854i
$985$	12.2477	−	21.2137i	0.390245	−	0.675924i
$986$	−2.76951	+	1.59898i	−0.0881991	+	0.0509218i
$987$	−8.08258	−	13.9994i	−0.257271	−	0.445607i
$988$	24.6261	+	23.6965i	0.783462	+	0.753886i
$989$	1.33485	+	2.31203i	0.0424457	+	0.0735181i
$990$		−	2.74110i		−	0.0871179i
$991$	−40.6606			−1.29163			−0.645813	−	0.763495i	$-0.723482\pi$
$991$	−40.6606			−1.29163			−0.645813	+	0.763495i	$0.723482\pi$
$992$	−3.87841			−0.123140
$993$		−	15.4931i		−	0.491659i
$994$	−11.9347	+	6.89048i	−0.378544	+	0.218553i
$995$	−9.87386	−	5.70068i	−0.313023	−	0.180724i
$996$	5.37386	−	3.10260i	0.170277	−	0.0983097i
$997$	5.33485	+	9.24023i	0.168956	+	0.292641i	0.938053	−	0.346491i	$-0.112627\pi$
$997$	5.33485	+	9.24023i	0.168956	+	0.292641i	−0.769097	+	0.639132i	$0.779294\pi$
$998$	−13.8693			−0.439026
$999$	3.08258	+	1.77973i	0.0975284	+	0.0563080i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.bl.b.88.1	yes	4
3.2	odd	2		819.2.do.d.361.2		4
7.2	even	3		273.2.t.b.205.2	yes	4
13.4	even	6		273.2.t.b.4.1	✓	4
21.2	odd	6		819.2.bm.d.478.1		4
39.17	odd	6		819.2.bm.d.550.2		4
91.30	even	6	inner	273.2.bl.b.121.1	yes	4
273.212	odd	6		819.2.do.d.667.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.t.b.4.1	✓	4	13.4	even	6
273.2.t.b.205.2	yes	4	7.2	even	3
273.2.bl.b.88.1	yes	4	1.1	even	1	trivial
273.2.bl.b.121.1	yes	4	91.30	even	6	inner
819.2.bm.d.478.1		4	21.2	odd	6
819.2.bm.d.550.2		4	39.17	odd	6
819.2.do.d.361.2		4	3.2	odd	2
819.2.do.d.667.2		4	273.212	odd	6

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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.bl (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.395644 - 0.228425i) q^{2} +1.00000 q^{3} +(-0.895644 - 1.55130i) q^{4} +(-1.50000 + 0.866025i) q^{5} +(-0.395644 - 0.228425i) q^{6} -2.64575i q^{7} +1.73205i q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-0.395644 - 0.228425i) q^{2} +1.00000 q^{3} +(-0.895644 - 1.55130i) q^{4} +(-1.50000 + 0.866025i) q^{5} +(-0.395644 - 0.228425i) q^{6} -2.64575i q^{7} +1.73205i q^{8} +1.00000 q^{9} +0.791288 q^{10} -3.46410i q^{11} +(-0.895644 - 1.55130i) q^{12} +(-1.00000 - 3.46410i) q^{13} +(-0.604356 + 1.04678i) q^{14} +(-1.50000 + 0.866025i) q^{15} +(-1.39564 + 2.41733i) q^{16} +(-0.500000 - 0.866025i) q^{17} +(-0.395644 - 0.228425i) q^{18} -5.29150i q^{19} +(2.68693 + 1.55130i) q^{20} -2.64575i q^{21} +(-0.791288 + 1.37055i) q^{22} +(-0.291288 + 0.504525i) q^{23} +1.73205i q^{24} +(-1.00000 + 1.73205i) q^{25} +(-0.395644 + 1.59898i) q^{26} +1.00000 q^{27} +(-4.10436 + 2.36965i) q^{28} +(3.50000 + 6.06218i) q^{29} +0.791288 q^{30} +(-0.708712 - 0.409175i) q^{31} +(4.10436 - 2.36965i) q^{32} -3.46410i q^{33} +0.456850i q^{34} +(2.29129 + 3.96863i) q^{35} +(-0.895644 - 1.55130i) q^{36} +(3.08258 + 1.77973i) q^{37} +(-1.20871 + 2.09355i) q^{38} +(-1.00000 - 3.46410i) q^{39} +(-1.50000 - 2.59808i) q^{40} +(6.08258 - 3.51178i) q^{41} +(-0.604356 + 1.04678i) q^{42} +(2.29129 - 3.96863i) q^{43} +(-5.37386 + 3.10260i) q^{44} +(-1.50000 + 0.866025i) q^{45} +(0.230493 - 0.133075i) q^{46} +(5.29129 - 3.05493i) q^{47} +(-1.39564 + 2.41733i) q^{48} -7.00000 q^{49} +(0.791288 - 0.456850i) q^{50} +(-0.500000 - 0.866025i) q^{51} +(-4.47822 + 4.65390i) q^{52} +(-6.08258 + 10.5353i) q^{53} +(-0.395644 - 0.228425i) q^{54} +(3.00000 + 5.19615i) q^{55} +4.58258 q^{56} -5.29150i q^{57} -3.19795i q^{58} +(-8.29129 + 4.78698i) q^{59} +(2.68693 + 1.55130i) q^{60} +13.1652 q^{61} +(0.186932 + 0.323775i) q^{62} -2.64575i q^{63} +3.41742 q^{64} +(4.50000 + 4.33013i) q^{65} +(-0.791288 + 1.37055i) q^{66} -7.11890i q^{67} +(-0.895644 + 1.55130i) q^{68} +(-0.291288 + 0.504525i) q^{69} -2.09355i q^{70} +(9.87386 + 5.70068i) q^{71} +1.73205i q^{72} +(7.50000 + 4.33013i) q^{73} +(-0.813068 - 1.40828i) q^{74} +(-1.00000 + 1.73205i) q^{75} +(-8.20871 + 4.73930i) q^{76} -9.16515 q^{77} +(-0.395644 + 1.59898i) q^{78} +(5.29129 + 9.16478i) q^{79} -4.83465i q^{80} +1.00000 q^{81} -3.20871 q^{82} +3.46410i q^{83} +(-4.10436 + 2.36965i) q^{84} +(1.50000 + 0.866025i) q^{85} +(-1.81307 + 1.04678i) q^{86} +(3.50000 + 6.06218i) q^{87} +6.00000 q^{88} +(-13.5000 - 7.79423i) q^{89} +0.791288 q^{90} +(-9.16515 + 2.64575i) q^{91} +1.04356 q^{92} +(-0.708712 - 0.409175i) q^{93} -2.79129 q^{94} +(4.58258 + 7.93725i) q^{95} +(4.10436 - 2.36965i) q^{96} +(-0.0825757 - 0.0476751i) q^{97} +(2.76951 + 1.59898i) q^{98} -3.46410i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 3 q^{2} + 4 q^{3} + q^{4} - 6 q^{5} + 3 q^{6} + 4 q^{9}+O(q^{10}) \) 4 * q + 3 * q^2 + 4 * q^3 + q^4 - 6 * q^5 + 3 * q^6 + 4 * q^9	\( 4 q + 3 q^{2} + 4 q^{3} + q^{4} - 6 q^{5} + 3 q^{6} + 4 q^{9} - 6 q^{10} + q^{12} - 4 q^{13} - 7 q^{14} - 6 q^{15} - q^{16} - 2 q^{17} + 3 q^{18} - 3 q^{20} + 6 q^{22} + 8 q^{23} - 4 q^{25} + 3 q^{26} + 4 q^{27} - 21 q^{28} + 14 q^{29} - 6 q^{30} - 12 q^{31} + 21 q^{32} + q^{36} - 6 q^{37} - 14 q^{38} - 4 q^{39} - 6 q^{40} + 6 q^{41} - 7 q^{42} + 6 q^{44} - 6 q^{45} + 33 q^{46} + 12 q^{47} - q^{48} - 28 q^{49} - 6 q^{50} - 2 q^{51} + 5 q^{52} - 6 q^{53} + 3 q^{54} + 12 q^{55} - 24 q^{59} - 3 q^{60} + 16 q^{61} - 13 q^{62} + 32 q^{64} + 18 q^{65} + 6 q^{66} + q^{68} + 8 q^{69} + 12 q^{71} + 30 q^{73} - 17 q^{74} - 4 q^{75} - 42 q^{76} + 3 q^{78} + 12 q^{79} + 4 q^{81} - 22 q^{82} - 21 q^{84} + 6 q^{85} - 21 q^{86} + 14 q^{87} + 24 q^{88} - 54 q^{89} - 6 q^{90} + 50 q^{92} - 12 q^{93} - 2 q^{94} + 21 q^{96} + 18 q^{97} - 21 q^{98}+O(q^{100}) \) 4 * q + 3 * q^2 + 4 * q^3 + q^4 - 6 * q^5 + 3 * q^6 + 4 * q^9 - 6 * q^10 + q^12 - 4 * q^13 - 7 * q^14 - 6 * q^15 - q^16 - 2 * q^17 + 3 * q^18 - 3 * q^20 + 6 * q^22 + 8 * q^23 - 4 * q^25 + 3 * q^26 + 4 * q^27 - 21 * q^28 + 14 * q^29 - 6 * q^30 - 12 * q^31 + 21 * q^32 + q^36 - 6 * q^37 - 14 * q^38 - 4 * q^39 - 6 * q^40 + 6 * q^41 - 7 * q^42 + 6 * q^44 - 6 * q^45 + 33 * q^46 + 12 * q^47 - q^48 - 28 * q^49 - 6 * q^50 - 2 * q^51 + 5 * q^52 - 6 * q^53 + 3 * q^54 + 12 * q^55 - 24 * q^59 - 3 * q^60 + 16 * q^61 - 13 * q^62 + 32 * q^64 + 18 * q^65 + 6 * q^66 + q^68 + 8 * q^69 + 12 * q^71 + 30 * q^73 - 17 * q^74 - 4 * q^75 - 42 * q^76 + 3 * q^78 + 12 * q^79 + 4 * q^81 - 22 * q^82 - 21 * q^84 + 6 * q^85 - 21 * q^86 + 14 * q^87 + 24 * q^88 - 54 * q^89 - 6 * q^90 + 50 * q^92 - 12 * q^93 - 2 * q^94 + 21 * q^96 + 18 * q^97 - 21 * q^98

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