LMFDB - Embedded newform 273.2.bl.b.121.1

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			121.1
Root			$1.39564 + 0.228425i$ of defining polynomial
Character	$\chi$	$=$	273.121
Dual form			273.2.bl.b.88.1

$q$-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 $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

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

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	−0.633316	−	0.773893i	$-0.718307\pi$
$2$	−0.395644	+	0.228425i	−0.279763	+	0.161521i	0.353553	+	0.935414i	$0.384973\pi$
$3$	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	0.125567	−	0.992085i	$-0.459925\pi$
$5$	−1.50000	−	0.866025i	−0.670820	−	0.387298i	−0.796387	+	0.604787i	$0.793258\pi$
$6$	−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	$0.174901\pi$
$11$			3.46410i			1.04447i	−0.852803	+	0.522233i	$0.825099\pi$
$12$	−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	−0.920268	−	0.391289i	$-0.872029\pi$
$17$	−0.500000	+	0.866025i	−0.121268	+	0.210042i	0.799000	+	0.601331i	$0.205363\pi$
$18$	−0.395644	+	0.228425i	−0.0932542	+	0.0538403i
$19$			5.29150i			1.21395i	0.794719	+	0.606977i	$0.207618\pi$
$19$			5.29150i			1.21395i	−0.794719	+	0.606977i	$0.792382\pi$
$20$	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	0.834058	−	0.551677i	$-0.186012\pi$
$23$	−0.291288	−	0.504525i	−0.0607377	−	0.105201i	−0.894795	+	0.446476i	$0.852679\pi$
$24$		−	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	−0.333205	−	0.942855i	$-0.608130\pi$
$29$	3.50000	−	6.06218i	0.649934	−	1.12572i	0.983138	−	0.182864i	$-0.0585367\pi$
$30$	0.791288			0.144469
$31$	−0.708712	+	0.409175i	−0.127288	+	0.0734900i	−0.562292	−	0.826939i	$-0.690080\pi$
$31$	−0.708712	+	0.409175i	−0.127288	+	0.0734900i	0.435004	+	0.900429i	$0.356747\pi$
$32$	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	−0.224734	−	0.974420i	$-0.572151\pi$
$37$	3.08258	−	1.77973i	0.506772	−	0.292585i	0.731506	+	0.681835i	$0.238818\pi$
$38$	−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	0.893062	−	0.449934i	$-0.148552\pi$
$41$	6.08258	+	3.51178i	0.949939	+	0.548447i	0.0568768	+	0.998381i	$0.481886\pi$
$42$	−0.604356	−	1.04678i	−0.0932542	−	0.161521i
$43$	2.29129	+	3.96863i	0.349418	+	0.605210i	0.986146	−	0.165878i	$-0.0530460\pi$
$43$	2.29129	+	3.96863i	0.349418	+	0.605210i	−0.636728	+	0.771088i	$0.719713\pi$
$44$	−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	0.833521	−	0.552487i	$-0.186321\pi$
$47$	5.29129	+	3.05493i	0.771814	+	0.445607i	−0.0617076	+	0.998094i	$0.519655\pi$
$48$	−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	−0.893618	−	0.448829i	$-0.851841\pi$
$53$	−6.08258	−	10.5353i	−0.835506	−	1.44714i	0.0581117	−	0.998310i	$-0.481492\pi$
$54$	−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	−0.148690	−	0.988884i	$-0.547506\pi$
$59$	−8.29129	−	4.78698i	−1.07943	−	0.623211i	−0.930744	+	0.365672i	$0.880839\pi$
$60$	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	$0.143201\pi$
$67$			7.11890i			0.869713i	−0.900500	+	0.434856i	$0.856799\pi$
$68$	−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	0.217706	−	0.976014i	$-0.430143\pi$
$71$	9.87386	−	5.70068i	1.17181	−	0.676546i	0.954106	+	0.299468i	$0.0968093\pi$
$72$		−	1.73205i		−	0.204124i
$73$	7.50000	−	4.33013i	0.877809	−	0.506803i	0.00787336	−	0.999969i	$-0.497494\pi$
$73$	7.50000	−	4.33013i	0.877809	−	0.506803i	0.869935	+	0.493166i	$0.164160\pi$
$74$	−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	−0.398186	−	0.917305i	$-0.630360\pi$
$79$	5.29129	−	9.16478i	0.595316	−	1.03112i	0.993502	−	0.113813i	$-0.0363066\pi$
$80$			4.83465i			0.540531i
$81$	1.00000			0.111111
$82$	−3.20871			−0.354343
$83$		−	3.46410i		−	0.380235i	−0.981761	−	0.190117i	$-0.939113\pi$
$83$		−	3.46410i		−	0.380235i	0.981761	−	0.190117i	$-0.0608868\pi$
$84$	−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	−0.997197	−	0.0748225i	$-0.976161\pi$
$89$	−13.5000	+	7.79423i	−1.43100	+	0.826187i	−0.433800	+	0.901009i	$0.642828\pi$
$90$	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	−0.504186	−	0.863595i	$-0.668208\pi$
$97$	−0.0825757	+	0.0476751i	−0.00838429	+	0.00484067i	0.495802	+	0.868436i	$0.334874\pi$
$98$	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	0.369605	+	0.929189i	$0.379493\pi$
$103$	−6.29129	+	10.8968i	−0.619899	+	1.07370i	−0.989504	+	0.144507i	$0.953840\pi$
$104$	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	0.999911	+	0.0133631i	$0.00425372\pi$
$107$	5.29129	+	9.16478i	0.511528	+	0.885993i	−0.488383	+	0.872630i	$0.662413\pi$
$108$	−0.895644	+	1.55130i	−0.0861834	+	0.149274i
$109$	−1.66515	+	0.961376i	−0.159493	+	0.0920831i	−0.577622	−	0.816304i	$-0.696019\pi$
$109$	−1.66515	+	0.961376i	−0.159493	+	0.0920831i	0.418129	+	0.908387i	$0.362686\pi$
$110$			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	0.973806	−	0.227382i	$-0.0730166\pi$
$113$	3.08258	+	5.33918i	0.289984	+	0.502268i	−0.683821	+	0.729649i	$0.739683\pi$
$114$	−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	−0.803030	−	0.595939i	$-0.796780\pi$
$127$	1.29129	−	2.23658i	0.114583	−	0.198464i	0.917613	+	0.397475i	$0.130113\pi$
$128$	−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	−0.999075	−	0.0429960i	$-0.986310\pi$
$131$	−5.29129	+	9.16478i	−0.462302	+	0.800730i	0.536773	+	0.843727i	$0.319643\pi$
$132$	−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	0.144142	−	0.989557i	$-0.453958\pi$
$137$	−7.50000	−	4.33013i	−0.640768	−	0.369948i	−0.784910	+	0.619609i	$0.787291\pi$
$138$	0.230493	+	0.133075i	0.0196208	+	0.0113281i
$139$	−1.29129	−	2.23658i	−0.109526	−	0.189704i	0.806053	−	0.591844i	$-0.201600\pi$
$139$	−1.29129	−	2.23658i	−0.109526	−	0.189704i	−0.915578	+	0.402140i	$0.868266\pi$
$140$	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	$0.254616\pi$
$149$			17.5112i			1.43457i	−0.696778	+	0.717287i	$0.745384\pi$
$150$	0.791288	+	0.456850i	0.0646084	+	0.0373017i
$151$	8.45644	−	4.88233i	0.688175	−	0.397318i	−0.114753	−	0.993394i	$-0.536608\pi$
$151$	8.45644	−	4.88233i	0.688175	−	0.397318i	0.802928	+	0.596076i	$0.203274\pi$
$152$	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	0.981679	−	0.190542i	$-0.0610246\pi$
$157$	4.08258	+	7.07123i	0.325825	+	0.564345i	−0.655854	+	0.754888i	$0.727691\pi$
$158$			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	$-0.956683\pi$
$163$		−	3.46410i		−	0.271329i	0.990755	−	0.135665i	$-0.0433170\pi$
$164$	−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	0.0666899	−	0.997774i	$-0.478756\pi$
$167$	−9.87386	−	5.70068i	−0.764063	−	0.441132i	−0.830752	+	0.556642i	$0.812089\pi$
$168$	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	$0.217044\pi$
$193$			17.5112i			1.26048i	−0.776399	+	0.630242i	$0.782956\pi$
$194$	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	−0.00439826	−	0.999990i	$-0.501400\pi$
$197$	−12.2477	−	7.07123i	−0.872614	−	0.503804i	−0.868216	+	0.496186i	$0.834733\pi$
$198$	−0.791288	−	1.37055i	−0.0562344	−	0.0974008i
$199$	3.29129	−	5.70068i	0.233313	−	0.404110i	−0.725468	−	0.688256i	$-0.758377\pi$
$199$	3.29129	−	5.70068i	0.233313	−	0.404110i	0.958781	+	0.284146i	$0.0917099\pi$
$200$	−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	−0.818149	−	0.575007i	$-0.804999\pi$
$211$	1.29129	−	2.23658i	0.0888959	−	0.153972i	0.907045	+	0.421034i	$0.138333\pi$
$212$	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	0.574752	−	0.818327i	$-0.305098\pi$
$223$	2.29129	+	1.32288i	0.153436	+	0.0885863i	−0.421316	+	0.906914i	$0.638432\pi$
$224$	−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	0.953583	−	0.301132i	$-0.0973644\pi$
$227$	17.6216	+	10.1738i	1.16959	+	0.675261i	0.216004	+	0.976393i	$0.430698\pi$
$228$	−8.20871	−	4.73930i	−0.543635	−	0.313868i
$229$	−0.0825757	−	0.0476751i	−0.00545676	−	0.00315046i	0.497269	−	0.867596i	$-0.334336\pi$
$229$	−0.0825757	−	0.0476751i	−0.00545676	−	0.00315046i	−0.502726	+	0.864446i	$0.667669\pi$
$230$	−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	−0.894511	−	0.447046i	$-0.852476\pi$
$233$	−0.917424	+	1.58903i	−0.0601025	+	0.104101i	0.834409	+	0.551146i	$0.185809\pi$
$234$	−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	$-0.588536\pi$
$239$		−	29.7309i		−	1.92313i	0.274572	−	0.961566i	$-0.411464\pi$
$240$			4.83465i			0.312075i
$241$	−15.2477	−	8.80328i	−0.982192	−	0.567069i	−0.0792611	−	0.996854i	$-0.525256\pi$
$241$	−15.2477	−	8.80328i	−0.982192	−	0.567069i	−0.902931	+	0.429785i	$0.858589\pi$
$242$	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	0.988015	−	0.154357i	$-0.0493305\pi$
$251$	5.70871	+	9.88778i	0.360331	+	0.624111i	−0.627684	+	0.778468i	$0.715997\pi$
$252$	−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	−0.879028	−	0.476770i	$-0.841808\pi$
$257$	−13.6652	−	23.6687i	−0.852409	−	1.47642i	0.0266196	−	0.999646i	$-0.491526\pi$
$258$	−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	−0.831134	−	0.556072i	$-0.812308\pi$
$269$	1.08258	−	1.87508i	0.0660058	−	0.114325i	0.897140	+	0.441747i	$0.145641\pi$
$270$	0.791288			0.0481562
$271$	22.0390	−	12.7242i	1.33877	−	0.772942i	0.352149	−	0.935944i	$-0.385451\pi$
$271$	22.0390	−	12.7242i	1.33877	−	0.772942i	0.986626	+	0.163002i	$0.0521177\pi$
$272$	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	−0.0838347	−	0.996480i	$-0.526717\pi$
$277$	13.6652	−	23.6687i	0.821059	−	1.42212i	0.904894	−	0.425637i	$-0.139950\pi$
$278$	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	$-0.825068\pi$
$281$		−	17.5112i		−	1.04463i	0.852752	−	0.522316i	$-0.174932\pi$
$282$	−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	−0.950944	−	0.309364i	$-0.899884\pi$
$293$	−19.8303	+	11.4490i	−1.15850	+	0.668860i	−0.207555	+	0.978223i	$0.566551\pi$
$294$	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	$0.00173223\pi$
$307$			0.190700i			0.0108838i	−0.999985	+	0.00544192i	$0.998268\pi$
$308$	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	0.857649	−	0.514236i	$-0.171925\pi$
$311$	−0.291288	−	0.504525i	−0.0165174	−	0.0286090i	−0.874166	+	0.485627i	$0.838591\pi$
$312$	6.00000	+	1.73205i	0.339683	+	0.0980581i
$313$	16.0826	−	27.8558i	0.909041	−	1.57451i	0.0936417	−	0.995606i	$-0.470149\pi$
$313$	16.0826	−	27.8558i	0.909041	−	1.57451i	0.815399	−	0.578899i	$-0.196517\pi$
$314$	−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	−0.0473014	−	0.998881i	$-0.515062\pi$
$317$	−16.6652	−	9.62163i	−0.936008	−	0.540405i	−0.888707	+	0.458476i	$0.848395\pi$
$318$	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	$0.140003\pi$
$331$			15.4931i			0.851578i	−0.904822	+	0.425789i	$0.859997\pi$
$332$	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	−0.888528	−	0.458823i	$-0.848271\pi$
$347$	−0.873864	+	1.51358i	−0.0469115	+	0.0812530i	0.841616	+	0.540076i	$0.181605\pi$
$348$	6.26951	+	10.8591i	0.336081	+	0.582109i
$349$	−0.0825757	−	0.0476751i	−0.00442018	−	0.00255199i	0.497788	−	0.867299i	$-0.334146\pi$
$349$	−0.0825757	−	0.0476751i	−0.00442018	−	0.00255199i	−0.502208	+	0.864747i	$0.667479\pi$
$350$	−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	$0.107140\pi$
$353$			12.4104i			0.660539i	−0.943887	+	0.330270i	$0.892860\pi$
$354$	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	0.859471	−	0.511185i	$-0.170793\pi$
$359$	16.0390	+	9.26013i	0.846507	+	0.488731i	−0.0129639	+	0.999916i	$0.504127\pi$
$360$	−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	0.0278799	−	0.999611i	$-0.491124\pi$
$379$	−16.0390	−	9.26013i	−0.823869	−	0.475661i	−0.851749	+	0.523950i	$0.824458\pi$
$380$	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	$-0.783354\pi$
$383$		−	24.6301i		−	1.25854i	0.777187	−	0.629270i	$-0.216646\pi$
$384$	−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	0.959717	−	0.280969i	$-0.0906557\pi$
$389$	4.66515	+	8.08028i	0.236533	+	0.409686i	−0.723184	+	0.690655i	$0.757322\pi$
$390$	−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	$0.132083\pi$
$397$			16.0652i			0.806290i	−0.915136	+	0.403145i	$0.867917\pi$
$398$			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	0.123443	−	0.992352i	$-0.460606\pi$
$401$	20.9174	−	12.0767i	1.04457	−	0.603081i	0.921123	+	0.389271i	$0.127273\pi$
$402$	−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	0.872619	−	0.488402i	$-0.162420\pi$
$409$	17.9174	+	10.3446i	0.885960	+	0.511509i	0.0133409	+	0.999911i	$0.495753\pi$
$410$	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	−0.607059	−	0.794657i	$-0.707651\pi$
$419$	7.87386	−	13.6379i	0.384663	−	0.666257i	0.991722	+	0.128400i	$0.0409842\pi$
$420$	4.10436	+	7.10895i	0.200272	+	0.346881i
$421$			33.5764i			1.63641i	0.574923	+	0.818207i	$0.305032\pi$
$421$			33.5764i			1.63641i	−0.574923	+	0.818207i	$0.694968\pi$
$422$			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	$-0.847433\pi$
$431$		−	19.1479i		−	0.922322i	0.887316	−	0.461161i	$-0.152567\pi$
$432$	−1.39564	−	2.41733i	−0.0671479	−	0.116304i
$433$	−10.6652	−	18.4726i	−0.512534	−	0.887736i	−0.999894	−	0.0145345i	$-0.995373\pi$
$433$	−10.6652	−	18.4726i	−0.512534	−	0.887736i	0.487360	−	0.873201i	$-0.337960\pi$
$434$	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	0.882442	−	0.470421i	$-0.155898\pi$
$439$	0.708712	+	1.22753i	0.0338250	+	0.0585866i	−0.848617	+	0.529007i	$0.822564\pi$
$440$	−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	0.483181	+	0.875521i	$0.339481\pi$
$443$	−10.8739	+	18.8341i	−0.516633	+	0.894834i	−0.999813	+	0.0193136i	$0.993852\pi$
$444$			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	−0.308103	−	0.951353i	$-0.599694\pi$
$449$	7.66515	−	4.42548i	0.361741	−	0.208851i	0.669844	+	0.742502i	$0.266361\pi$
$450$	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	0.189258	−	0.981927i	$-0.439392\pi$
$457$	24.2477	−	13.9994i	1.13426	−	0.654866i	0.945003	+	0.327062i	$0.106058\pi$
$458$	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	−0.00562564	−	0.999984i	$-0.501791\pi$
$461$	18.4129	−	10.6307i	0.857573	−	0.495120i	0.863199	+	0.504864i	$0.168457\pi$
$462$	3.62614	−	2.09355i	0.168703	−	0.0974008i
$463$			3.84550i			0.178716i	0.996000	+	0.0893578i	$0.0284815\pi$
$463$			3.84550i			0.178716i	−0.996000	+	0.0893578i	$0.971519\pi$
$464$	−19.5390			−0.907076
$465$	1.41742			0.0657315
$466$		−	0.838251i		−	0.0388312i
$467$	−8.45644	+	14.6470i	−0.391317	+	0.677782i	−0.992624	−	0.121237i	$-0.961314\pi$
$467$	−8.45644	+	14.6470i	−0.391317	+	0.677782i	0.601306	+	0.799019i	$0.294647\pi$
$468$	−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	$-0.702453\pi$
$479$		−	35.2131i		−	1.60893i	0.594001	−	0.804464i	$-0.297547\pi$
$480$	−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	−0.471281	−	0.881983i	$-0.656208\pi$
$487$	−32.4564	−	18.7387i	−1.47074	−	0.849133i	−0.999460	+	0.0328498i	$0.989542\pi$
$488$		−	22.8027i		−	1.03223i
$489$		−	3.46410i		−	0.156652i
$490$	−5.53901			−0.250227
$491$	11.8739	−	20.5661i	0.535860	−	0.928137i	−0.463261	−	0.886222i	$-0.653321\pi$
$491$	11.8739	−	20.5661i	0.535860	−	0.928137i	0.999121	−	0.0419149i	$-0.0133458\pi$
$492$	−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	0.955309	−	0.295608i	$-0.0955223\pi$
$499$	26.2913	+	15.1793i	1.17696	+	0.679518i	0.221650	+	0.975126i	$0.428856\pi$
$500$	−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	0.996148	+	0.0876919i	$0.0279491\pi$
$503$	12.8739	+	22.2982i	0.574017	+	0.994227i	−0.422130	+	0.906535i	$0.638718\pi$
$504$	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	−0.426294	−	0.904585i	$-0.640181\pi$
$509$	3.24773	−	1.87508i	0.143953	−	0.0831113i	0.570247	+	0.821474i	$0.306848\pi$
$510$	−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	0.956834	+	0.290634i	$0.0938662\pi$
$521$	16.6652	+	28.8649i	0.730114	+	1.26459i	−0.226721	+	0.973960i	$0.572800\pi$
$522$			3.19795i			0.139971i
$523$	−8.87386	−	15.3700i	−0.388027	−	0.672082i	0.604157	−	0.796865i	$-0.293510\pi$
$523$	−8.87386	−	15.3700i	−0.388027	−	0.672082i	−0.992184	+	0.124783i	$0.960177\pi$
$524$	−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	−0.166311	−	0.986073i	$-0.553186\pi$
$541$	−25.6652	−	14.8178i	−1.10343	−	0.637066i	−0.937120	+	0.349007i	$0.886519\pi$
$542$	−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	$-0.977908\pi$
$557$		−	3.27340i		−	0.138698i	0.997592	−	0.0693492i	$-0.0220923\pi$
$558$	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	−0.977769	−	0.209686i	$-0.932756\pi$
$563$	−7.29129	+	12.6289i	−0.307291	+	0.532244i	0.670478	+	0.741930i	$0.266089\pi$
$564$	−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	−0.981460	−	0.191665i	$-0.938611\pi$
$569$	−15.6652	−	27.1328i	−0.656717	−	1.13747i	0.324743	−	0.945802i	$-0.394722\pi$
$570$			4.18710i			0.175378i
$571$	−10.1261	−	17.5390i	−0.423766	−	0.733984i	0.572539	−	0.819878i	$-0.305959\pi$
$571$	−10.1261	−	17.5390i	−0.423766	−	0.733984i	−0.996304	+	0.0858941i	$0.972625\pi$
$572$	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	−0.559496	−	0.828833i	$-0.689005\pi$
$577$	−2.91742	+	1.68438i	−0.121454	+	0.0701215i	0.438042	+	0.898954i	$0.355672\pi$
$578$	−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	0.390466	−	0.920617i	$-0.372314\pi$
$587$	−5.12614	−	2.95958i	−0.211578	−	0.122155i	−0.602045	+	0.798462i	$0.705647\pi$
$588$	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	0.226979	−	0.973900i	$-0.427115\pi$
$593$	−12.2477	−	7.07123i	−0.502954	−	0.290381i	−0.729933	+	0.683519i	$0.760449\pi$
$594$	−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	−0.956752	−	0.290904i	$-0.906044\pi$
$599$	−17.8739	−	30.9584i	−0.730306	−	1.26493i	0.226446	−	0.974024i	$-0.427289\pi$
$600$	−3.00000	+	1.73205i	−0.122474	+	0.0707107i
$601$	−3.91742	+	6.78518i	−0.159795	+	0.276773i	−0.934795	−	0.355189i	$-0.884417\pi$
$601$	−3.91742	+	6.78518i	−0.159795	+	0.276773i	0.775000	+	0.631962i	$0.217750\pi$
$602$	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	$0.0210575\pi$
$613$			3.27340i			0.132211i	−0.997813	+	0.0661057i	$0.978943\pi$
$614$	−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	−0.302163	−	0.953256i	$-0.597709\pi$
$617$	9.24773	−	5.33918i	0.372299	−	0.214947i	0.674463	+	0.738309i	$0.264375\pi$
$618$		−	5.74835i		−	0.231233i
$619$	−31.0390	+	17.9204i	−1.24756	+	0.720281i	−0.970623	−	0.240606i	$-0.922654\pi$
$619$	−31.0390	+	17.9204i	−1.24756	+	0.720281i	−0.276940	+	0.960887i	$0.589320\pi$
$620$	−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	−0.800526	−	0.599299i	$-0.795446\pi$
$631$	−17.1261	+	9.88778i	−0.681781	+	0.393626i	0.118745	+	0.992925i	$0.462113\pi$
$632$	−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	0.182487	+	0.983208i	$0.441585\pi$
$641$	−19.2477	+	33.3380i	−0.760240	+	1.31677i	−0.942727	+	0.333565i	$0.891748\pi$
$642$	−4.18693	−	2.41733i	−0.165245	−	0.0954043i
$643$	6.54356	−	3.77793i	0.258053	−	0.148987i	−0.365393	−	0.930853i	$-0.619065\pi$
$643$	6.54356	−	3.77793i	0.258053	−	0.148987i	0.623446	+	0.781866i	$0.285732\pi$
$644$			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	0.997700	+	0.0677888i	$0.0215944\pi$
$653$	14.2477	+	24.6778i	0.557557	+	0.965716i	−0.440143	+	0.897928i	$0.645072\pi$
$654$	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	0.873342	+	0.487107i	$0.161948\pi$
$659$	22.0390	+	38.1727i	0.858518	+	1.48700i	−0.0148242	+	0.999890i	$0.504719\pi$
$660$	5.37386	+	9.30780i	0.209177	+	0.362306i
$661$		−	26.2668i		−	1.02166i	−0.859682	−	0.510830i	$-0.829338\pi$
$661$		−	26.2668i		−	1.02166i	0.859682	−	0.510830i	$-0.170662\pi$
$662$	−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	−0.878561	−	0.477631i	$-0.841496\pi$
$673$	−0.665151	+	1.15208i	−0.0256397	+	0.0444093i	0.852921	+	0.522040i	$0.174829\pi$
$674$	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	−0.134924	+	0.990856i	$0.543079\pi$
$677$	−24.0826	+	41.7122i	−0.925569	+	1.60313i	−0.790644	+	0.612276i	$0.790254\pi$
$678$	−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	0.832912	−	0.553405i	$-0.186672\pi$
$683$	20.1261	+	11.6198i	0.770105	+	0.444620i	−0.0628069	+	0.998026i	$0.520005\pi$
$684$	−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	−0.941548	−	0.336879i	$-0.890629\pi$
$691$	−29.4564	+	17.0067i	−1.12058	+	0.646965i	−0.179028	+	0.983844i	$0.557295\pi$
$692$	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	$-0.884148\pi$
$709$		−	18.9572i		−	0.711953i	0.934495	−	0.355976i	$-0.115852\pi$
$710$	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	0.286469	−	0.958090i	$-0.407518\pi$
$733$	−10.8303	−	6.25288i	−0.400026	−	0.230955i	−0.686495	+	0.727134i	$0.740852\pi$
$734$	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	$0.0503539\pi$
$739$			8.56490i			0.315065i	−0.987514	+	0.157533i	$0.949646\pi$
$740$	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	0.692609	−	0.721314i	$-0.256461\pi$
$743$	11.2913	+	6.51903i	0.414237	+	0.239160i	−0.278372	+	0.960473i	$0.589795\pi$
$744$	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	−0.992745	−	0.120241i	$-0.961633\pi$
$751$	−16.4564	−	28.5034i	−0.600504	−	1.04010i	0.392241	−	0.919863i	$-0.371700\pi$
$752$		−	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	0.114661	−	0.993405i	$-0.463422\pi$
$757$	25.2477	−	43.7303i	0.917644	−	1.58941i	0.802983	−	0.596002i	$-0.203245\pi$
$758$	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	$0.205493\pi$
$761$			33.1950i			1.20332i	−0.798753	+	0.601659i	$0.794507\pi$
$762$			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	0.266067	−	0.963955i	$-0.414276\pi$
$769$	−12.0826	−	6.97588i	−0.435709	−	0.251557i	−0.701776	+	0.712398i	$0.747609\pi$
$770$	−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	0.383417	−	0.923576i	$-0.374747\pi$
$773$	−6.24773	−	3.60713i	−0.224715	−	0.129739i	−0.608132	+	0.793836i	$0.708081\pi$
$774$	−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	0.0604079	−	0.998174i	$-0.480760\pi$
$787$	−21.7087	−	12.5335i	−0.773832	−	0.446772i	−0.834240	+	0.551402i	$0.814093\pi$
$788$	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	0.809719	−	0.586818i	$-0.199620\pi$
$797$	−2.91742	−	5.05313i	−0.103340	−	0.178991i	−0.913059	+	0.407828i	$0.866286\pi$
$798$	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	$-0.879950\pi$
$811$		−	20.9753i		−	0.736543i	0.929718	−	0.368271i	$-0.120050\pi$
$812$	−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	−0.396252	−	0.918142i	$-0.629689\pi$
$821$	5.75227	−	3.32108i	0.200756	−	0.115906i	0.597008	+	0.802235i	$0.296356\pi$
$822$	3.95644			0.137997
$823$	−10.7087	+	18.5480i	−0.373282	+	0.646544i	−0.990068	−	0.140587i	$-0.955101\pi$
$823$	−10.7087	+	18.5480i	−0.373282	+	0.646544i	0.616786	+	0.787131i	$0.288434\pi$
$824$	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	$0.0272074\pi$
$827$			4.91010i			0.170741i	−0.996349	+	0.0853705i	$0.972793\pi$
$828$	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	−0.975557	−	0.219748i	$-0.929476\pi$
$839$	−36.8739	+	21.2891i	−1.27303	+	0.734983i	−0.297471	+	0.954731i	$0.596143\pi$
$840$	−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	$0.351283\pi$
$853$			52.1522i			1.78566i	−0.450396	+	0.892829i	$0.648717\pi$
$854$	−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	0.997099	−	0.0761135i	$-0.0242511\pi$
$857$	12.6652	+	21.9367i	0.432633	+	0.749343i	−0.564466	+	0.825456i	$0.690918\pi$
$858$	5.53901	−	1.37055i	0.189099	−	0.0467898i
$859$	0.543561	−	0.941475i	0.0185461	−	0.0321227i	−0.856603	−	0.515975i	$-0.827430\pi$
$859$	0.543561	−	0.941475i	0.0185461	−	0.0321227i	0.875149	+	0.483853i	$0.160763\pi$
$860$	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	0.404247	−	0.914650i	$-0.367534\pi$
$863$	−5.45644	−	3.15028i	−0.185739	−	0.107237i	−0.589986	+	0.807413i	$0.700867\pi$
$864$	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	$-0.786253\pi$
$877$		−	36.8498i		−	1.24433i	0.782886	−	0.622165i	$-0.213747\pi$
$878$	−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	−0.375641	−	0.926765i	$-0.622578\pi$
$881$	18.2477	−	31.6060i	0.614782	−	1.06483i	0.990423	−	0.138068i	$-0.0440892\pi$
$882$	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	0.930749	+	0.365660i	$0.119157\pi$
$887$	23.2913	+	40.3417i	0.782045	+	1.35454i	−0.148704	+	0.988882i	$0.547510\pi$
$888$	−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	$-0.755655\pi$
$929$		−	42.3320i		−	1.38887i	0.719556	−	0.694434i	$-0.244345\pi$
$930$	−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	−0.622171	−	0.782882i	$-0.713749\pi$
$941$	−7.83030	+	4.52083i	−0.255261	+	0.147375i	0.366910	+	0.930256i	$0.380416\pi$
$942$	−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	−0.157672	−	0.987492i	$-0.550399\pi$
$947$	19.0390	−	10.9922i	0.618685	−	0.357198i	0.776357	+	0.630294i	$0.217066\pi$
$948$	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	0.766589	−	0.642138i	$-0.221952\pi$
$953$	−5.33485	−	9.24023i	−0.172813	−	0.299320i	−0.939402	+	0.342817i	$0.888619\pi$
$954$	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	$0.0271151\pi$
$967$			5.29150i			0.170163i	−0.996374	+	0.0850816i	$0.972885\pi$
$968$			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	$-0.909627\pi$
$977$		−	17.5112i		−	0.560233i	0.959966	−	0.280117i	$-0.0903731\pi$
$978$	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	−0.729139	−	0.684366i	$-0.760079\pi$
$983$	−15.7087	+	9.06943i	−0.501030	+	0.289270i	0.228109	+	0.973636i	$0.426746\pi$
$984$	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	−0.769097	−	0.639132i	$-0.779294\pi$
$997$	5.33485	−	9.24023i	0.168956	−	0.292641i	0.938053	+	0.346491i	$0.112627\pi$
$998$	−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.121.1	yes	4
3.2	odd	2		819.2.do.d.667.2		4
7.4	even	3		273.2.t.b.4.1	✓	4
13.10	even	6		273.2.t.b.205.2	yes	4
21.11	odd	6		819.2.bm.d.550.2		4
39.23	odd	6		819.2.bm.d.478.1		4
91.88	even	6	inner	273.2.bl.b.88.1	yes	4
273.179	odd	6		819.2.do.d.361.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.t.b.4.1	✓	4	7.4	even	3
273.2.t.b.205.2	yes	4	13.10	even	6
273.2.bl.b.88.1	yes	4	91.88	even	6	inner
273.2.bl.b.121.1	yes	4	1.1	even	1	trivial
819.2.bm.d.478.1		4	39.23	odd	6
819.2.bm.d.550.2		4	21.11	odd	6
819.2.do.d.361.2		4	273.179	odd	6
819.2.do.d.667.2		4	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
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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