LMFDB - Embedded newform 273.2.t.b.4.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(4,273)]

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, 1]))

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

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

chi := DirichletCharacter("273.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.t (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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			4.1
Root			$1.39564 - 0.228425i$ of defining polynomial
Character	$\chi$	$=$	273.4
Dual form			273.2.t.b.205.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.456850i q^{2} +(-0.500000 - 0.866025i) q^{3} +1.79129 q^{4} +(1.50000 - 0.866025i) q^{5} +(-0.395644 + 0.228425i) q^{6} +(-2.29129 - 1.32288i) q^{7} -1.73205i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q-0.456850i q^{2} +(-0.500000 - 0.866025i) q^{3} +1.79129 q^{4} +(1.50000 - 0.866025i) q^{5} +(-0.395644 + 0.228425i) q^{6} +(-2.29129 - 1.32288i) q^{7} -1.73205i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.395644 - 0.685275i) q^{10} +(3.00000 - 1.73205i) 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} +2.79129 q^{16} +1.00000 q^{17} +(0.395644 + 0.228425i) q^{18} +(-4.58258 - 2.64575i) q^{19} +(2.68693 - 1.55130i) q^{20} +2.64575i q^{21} +(-0.791288 - 1.37055i) q^{22} +0.582576 q^{23} +(-1.50000 + 0.866025i) q^{24} +(-1.00000 + 1.73205i) q^{25} +(1.58258 + 0.456850i) q^{26} +1.00000 q^{27} +(-4.10436 - 2.36965i) q^{28} +(3.50000 - 6.06218i) q^{29} +(-0.395644 + 0.685275i) q^{30} +(0.708712 + 0.409175i) q^{31} -4.73930i q^{32} +(-3.00000 - 1.73205i) q^{33} -0.456850i q^{34} -4.58258 q^{35} +(-0.895644 + 1.55130i) q^{36} +3.55945i q^{37} +(-1.20871 + 2.09355i) q^{38} +(3.50000 - 0.866025i) q^{39} +(-1.50000 - 2.59808i) q^{40} +(6.08258 + 3.51178i) q^{41} +1.20871 q^{42} +(2.29129 + 3.96863i) q^{43} +(5.37386 - 3.10260i) q^{44} +1.73205i q^{45} -0.266150i q^{46} +(-5.29129 + 3.05493i) q^{47} +(-1.39564 - 2.41733i) q^{48} +(3.50000 + 6.06218i) q^{49} +(0.791288 + 0.456850i) q^{50} +(-0.500000 - 0.866025i) q^{51} +(-1.79129 + 6.20520i) q^{52} +(-6.08258 + 10.5353i) q^{53} -0.456850i q^{54} +(3.00000 - 5.19615i) q^{55} +(-2.29129 + 3.96863i) q^{56} +5.29150i q^{57} +(-2.76951 - 1.59898i) q^{58} +9.57395i q^{59} +(-2.68693 - 1.55130i) q^{60} +(-6.58258 + 11.4014i) q^{61} +(0.186932 - 0.323775i) q^{62} +(2.29129 - 1.32288i) q^{63} +3.41742 q^{64} +(1.50000 + 6.06218i) q^{65} +(-0.791288 + 1.37055i) q^{66} +(6.16515 - 3.55945i) q^{67} +1.79129 q^{68} +(-0.291288 - 0.504525i) q^{69} +2.09355i q^{70} +(9.87386 - 5.70068i) q^{71} +(1.50000 + 0.866025i) q^{72} +(-7.50000 - 4.33013i) q^{73} +1.62614 q^{74} +2.00000 q^{75} +(-8.20871 - 4.73930i) q^{76} -9.16515 q^{77} +(-0.395644 - 1.59898i) q^{78} +(5.29129 + 9.16478i) q^{79} +(4.18693 - 2.41733i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.60436 - 2.77883i) q^{82} -3.46410i q^{83} +4.73930i q^{84} +(1.50000 - 0.866025i) q^{85} +(1.81307 - 1.04678i) q^{86} -7.00000 q^{87} +(-3.00000 - 5.19615i) q^{88} -15.5885i q^{89} +0.791288 q^{90} +(6.87386 - 6.61438i) q^{91} +1.04356 q^{92} -0.818350i q^{93} +(1.39564 + 2.41733i) q^{94} -9.16515 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 - 2 q^{3} - 2 q^{4} + 6 q^{5} + 3 q^{6} - 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^3 - 2 * q^4 + 6 * q^5 + 3 * q^6 - 2 * q^9	$ 4 q - 2 q^{3} - 2 q^{4} + 6 q^{5} + 3 q^{6} - 2 q^{9} + 3 q^{10} + 12 q^{11} + q^{12} - 4 q^{13} - 7 q^{14} - 6 q^{15} + 2 q^{16} + 4 q^{17} - 3 q^{18} - 3 q^{20} + 6 q^{22} - 16 q^{23} - 6 q^{24} - 4 q^{25} - 12 q^{26} + 4 q^{27} - 21 q^{28} + 14 q^{29} + 3 q^{30} + 12 q^{31} - 12 q^{33} + q^{36} - 14 q^{38} + 14 q^{39} - 6 q^{40} + 6 q^{41} + 14 q^{42} - 6 q^{44} - 12 q^{47} - q^{48} + 14 q^{49} - 6 q^{50} - 2 q^{51} + 2 q^{52} - 6 q^{53} + 12 q^{55} + 21 q^{58} + 3 q^{60} - 8 q^{61} - 13 q^{62} + 32 q^{64} + 6 q^{65} + 6 q^{66} - 12 q^{67} - 2 q^{68} + 8 q^{69} + 12 q^{71} + 6 q^{72} - 30 q^{73} + 34 q^{74} + 8 q^{75} - 42 q^{76} + 3 q^{78} + 12 q^{79} + 3 q^{80} - 2 q^{81} + 11 q^{82} + 6 q^{85} + 21 q^{86} - 28 q^{87} - 12 q^{88} - 6 q^{90} + 50 q^{92} + q^{94} - 21 q^{96} + 18 q^{97} - 21 q^{98}+O(q^{100}) $ 4 * q - 2 * q^3 - 2 * q^4 + 6 * q^5 + 3 * q^6 - 2 * q^9 + 3 * q^10 + 12 * q^11 + q^12 - 4 * q^13 - 7 * q^14 - 6 * q^15 + 2 * q^16 + 4 * q^17 - 3 * q^18 - 3 * q^20 + 6 * q^22 - 16 * q^23 - 6 * q^24 - 4 * q^25 - 12 * q^26 + 4 * q^27 - 21 * q^28 + 14 * q^29 + 3 * q^30 + 12 * q^31 - 12 * q^33 + q^36 - 14 * q^38 + 14 * q^39 - 6 * q^40 + 6 * q^41 + 14 * q^42 - 6 * q^44 - 12 * q^47 - q^48 + 14 * q^49 - 6 * q^50 - 2 * q^51 + 2 * q^52 - 6 * q^53 + 12 * q^55 + 21 * q^58 + 3 * q^60 - 8 * q^61 - 13 * q^62 + 32 * q^64 + 6 * q^65 + 6 * q^66 - 12 * q^67 - 2 * q^68 + 8 * q^69 + 12 * q^71 + 6 * q^72 - 30 * q^73 + 34 * q^74 + 8 * q^75 - 42 * q^76 + 3 * q^78 + 12 * q^79 + 3 * q^80 - 2 * q^81 + 11 * q^82 + 6 * q^85 + 21 * q^86 - 28 * q^87 - 12 * q^88 - 6 * q^90 + 50 * q^92 + 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 $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

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

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 $

$2$		−	0.456850i		−	0.323042i	−0.986869	−	0.161521i	$-0.948360\pi$
$2$		−	0.456850i		−	0.323042i	0.986869	−	0.161521i	$-0.0516399\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	1.79129			0.895644
$5$	1.50000	−	0.866025i	0.670820	−	0.387298i	−0.125567	−	0.992085i	$-0.540075\pi$
$5$	1.50000	−	0.866025i	0.670820	−	0.387298i	0.796387	+	0.604787i	$0.206742\pi$
$6$	−0.395644	+	0.228425i	−0.161521	+	0.0932542i
$7$	−2.29129	−	1.32288i	−0.866025	−	0.500000i
$7$	−2.29129	−	1.32288i	−0.866025	−	0.500000i
$8$		−	1.73205i		−	0.612372i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.395644	−	0.685275i	−0.125114	−	0.216703i
$11$	3.00000	−	1.73205i	0.904534	−	0.522233i	0.0258656	−	0.999665i	$-0.491766\pi$
$11$	3.00000	−	1.73205i	0.904534	−	0.522233i	0.878668	+	0.477432i	$0.158432\pi$
$12$	−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
$16$	2.79129			0.697822
$17$	1.00000			0.242536			0.121268	−	0.992620i	$-0.461304\pi$
$17$	1.00000			0.242536			0.121268	+	0.992620i	$0.461304\pi$
$18$	0.395644	+	0.228425i	0.0932542	+	0.0538403i
$19$	−4.58258	−	2.64575i	−1.05131	−	0.606977i	−0.128298	−	0.991736i	$-0.540951\pi$
$19$	−4.58258	−	2.64575i	−1.05131	−	0.606977i	−0.923017	+	0.384759i	$0.874285\pi$
$20$	2.68693	−	1.55130i	0.600816	−	0.346881i
$21$			2.64575i			0.577350i
$22$	−0.791288	−	1.37055i	−0.168703	−	0.292202i
$23$	0.582576			0.121475			0.0607377	−	0.998154i	$-0.480655\pi$
$23$	0.582576			0.121475			0.0607377	+	0.998154i	$0.480655\pi$
$24$	−1.50000	+	0.866025i	−0.306186	+	0.176777i
$25$	−1.00000	+	1.73205i	−0.200000	+	0.346410i
$26$	1.58258	+	0.456850i	0.310369	+	0.0895957i
$27$	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	$-0.0585367\pi$
$30$	−0.395644	+	0.685275i	−0.0722344	+	0.125114i
$31$	0.708712	+	0.409175i	0.127288	+	0.0734900i	0.562292	−	0.826939i	$-0.309920\pi$
$31$	0.708712	+	0.409175i	0.127288	+	0.0734900i	−0.435004	+	0.900429i	$0.643253\pi$
$32$		−	4.73930i		−	0.837798i
$33$	−3.00000	−	1.73205i	−0.522233	−	0.301511i
$34$		−	0.456850i		−	0.0783492i
$35$	−4.58258			−0.774597
$36$	−0.895644	+	1.55130i	−0.149274	+	0.258550i
$37$			3.55945i			0.585170i	0.956239	+	0.292585i	$0.0945155\pi$
$37$			3.55945i			0.585170i	−0.956239	+	0.292585i	$0.905485\pi$
$38$	−1.20871	+	2.09355i	−0.196079	+	0.339619i
$39$	3.50000	−	0.866025i	0.560449	−	0.138675i
$40$	−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	$0.481886\pi$
$42$	1.20871			0.186508
$43$	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
$45$			1.73205i			0.258199i
$46$		−	0.266150i		−	0.0392417i
$47$	−5.29129	+	3.05493i	−0.771814	+	0.445607i	−0.833521	−	0.552487i	$-0.813679\pi$
$47$	−5.29129	+	3.05493i	−0.771814	+	0.445607i	0.0617076	+	0.998094i	$0.480345\pi$
$48$	−1.39564	−	2.41733i	−0.201444	−	0.348911i
$49$	3.50000	+	6.06218i	0.500000	+	0.866025i
$50$	0.791288	+	0.456850i	0.111905	+	0.0646084i
$51$	−0.500000	−	0.866025i	−0.0700140	−	0.121268i
$52$	−1.79129	+	6.20520i	−0.248407	+	0.860507i
$53$	−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	$0.851841\pi$
$54$		−	0.456850i		−	0.0621694i
$55$	3.00000	−	5.19615i	0.404520	−	0.700649i
$56$	−2.29129	+	3.96863i	−0.306186	+	0.530330i
$57$			5.29150i			0.700877i
$58$	−2.76951	−	1.59898i	−0.363654	−	0.209956i
$59$			9.57395i			1.24642i	0.782053	+	0.623211i	$0.214172\pi$
$59$			9.57395i			1.24642i	−0.782053	+	0.623211i	$0.785828\pi$
$60$	−2.68693	−	1.55130i	−0.346881	−	0.200272i
$61$	−6.58258	+	11.4014i	−0.842812	+	1.45979i	0.0446950	+	0.999001i	$0.485768\pi$
$61$	−6.58258	+	11.4014i	−0.842812	+	1.45979i	−0.887507	+	0.460793i	$0.847565\pi$
$62$	0.186932	−	0.323775i	0.0237404	−	0.0411195i
$63$	2.29129	−	1.32288i	0.288675	−	0.166667i
$64$	3.41742			0.427178
$65$	1.50000	+	6.06218i	0.186052	+	0.751921i
$66$	−0.791288	+	1.37055i	−0.0974008	+	0.168703i
$67$	6.16515	−	3.55945i	0.753193	−	0.434856i	−0.0736534	−	0.997284i	$-0.523466\pi$
$67$	6.16515	−	3.55945i	0.753193	−	0.434856i	0.826847	+	0.562428i	$0.190133\pi$
$68$	1.79129			0.217226
$69$	−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	$0.0968093\pi$
$72$	1.50000	+	0.866025i	0.176777	+	0.102062i
$73$	−7.50000	−	4.33013i	−0.877809	−	0.506803i	−0.00787336	−	0.999969i	$-0.502506\pi$
$73$	−7.50000	−	4.33013i	−0.877809	−	0.506803i	−0.869935	+	0.493166i	$0.835840\pi$
$74$	1.62614			0.189035
$75$	2.00000			0.230940
$76$	−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	$0.630360\pi$
$80$	4.18693	−	2.41733i	0.468113	−	0.270265i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	1.60436	−	2.77883i	0.177171	−	0.306870i
$83$		−	3.46410i		−	0.380235i	−0.981761	−	0.190117i	$-0.939113\pi$
$83$		−	3.46410i		−	0.380235i	0.981761	−	0.190117i	$-0.0608868\pi$
$84$			4.73930i			0.517100i
$85$	1.50000	−	0.866025i	0.162698	−	0.0939336i
$86$	1.81307	−	1.04678i	0.195508	−	0.112877i
$87$	−7.00000			−0.750479
$88$	−3.00000	−	5.19615i	−0.319801	−	0.553912i
$89$		−	15.5885i		−	1.65237i	−0.563397	−	0.826187i	$-0.690506\pi$
$89$		−	15.5885i		−	1.65237i	0.563397	−	0.826187i	$-0.309494\pi$
$90$	0.791288			0.0834091
$91$	6.87386	−	6.61438i	0.720577	−	0.693375i
$92$	1.04356			0.108799
$93$		−	0.818350i		−	0.0848590i
$94$	1.39564	+	2.41733i	0.143950	+	0.249328i
$95$	−9.16515			−0.940325
$96$	−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
$100$	−1.79129	+	3.10260i	−0.179129	+	0.310260i
$101$	2.58258	+	4.47315i	0.256976	+	0.445095i	0.965430	−	0.260661i	$-0.0839406\pi$
$101$	2.58258	+	4.47315i	0.256976	+	0.445095i	−0.708454	+	0.705757i	$0.750607\pi$
$102$	−0.395644	+	0.228425i	−0.0391746	+	0.0226175i
$103$	−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
$107$	−10.5826			−1.02306			−0.511528	−	0.859267i	$-0.670920\pi$
$107$	−10.5826			−1.02306			−0.511528	+	0.859267i	$0.670920\pi$
$108$	1.79129			0.172367
$109$	1.66515	+	0.961376i	0.159493	+	0.0920831i	0.577622	−	0.816304i	$-0.303981\pi$
$109$	1.66515	+	0.961376i	0.159493	+	0.0920831i	−0.418129	+	0.908387i	$0.637314\pi$
$110$	−2.37386	−	1.37055i	−0.226339	−	0.130677i
$111$	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	$0.739683\pi$
$114$	2.41742			0.226413
$115$	0.873864	−	0.504525i	0.0814882	−	0.0470472i
$116$	6.26951	−	10.8591i	0.582109	−	1.00824i
$117$	−2.50000	−	2.59808i	−0.231125	−	0.240192i
$118$	4.37386			0.402647
$119$	−2.29129	−	1.32288i	−0.210042	−	0.121268i
$120$	−1.50000	+	2.59808i	−0.136931	+	0.237171i
$121$	0.500000	−	0.866025i	0.0454545	−	0.0787296i
$122$	5.20871	+	3.00725i	0.471575	+	0.272264i
$123$		−	7.02355i		−	0.633292i
$124$	1.26951	+	0.732950i	0.114005	+	0.0658209i
$125$			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	$0.130113\pi$
$128$		−	11.0399i		−	0.975795i
$129$	2.29129	−	3.96863i	0.201737	−	0.349418i
$130$	2.76951	−	0.685275i	0.242902	−	0.0601026i
$131$	−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
$133$	7.00000	+	12.1244i	0.606977	+	1.05131i
$134$	−1.62614	−	2.81655i	−0.140477	−	0.243313i
$135$	1.50000	−	0.866025i	0.129099	−	0.0745356i
$136$		−	1.73205i		−	0.148522i
$137$			8.66025i			0.739895i	0.929053	+	0.369948i	$0.120624\pi$
$137$			8.66025i			0.739895i	−0.929053	+	0.369948i	$0.879376\pi$
$138$	−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	$0.868266\pi$
$140$	−8.20871			−0.693763
$141$	5.29129	+	3.05493i	0.445607	+	0.257271i
$142$	−2.60436	−	4.51088i	−0.218553	−	0.378544i
$143$	3.00000	+	12.1244i	0.250873	+	1.01389i
$144$	−1.39564	+	2.41733i	−0.116304	+	0.201444i
$145$		−	12.1244i		−	1.00687i
$146$	−1.97822	+	3.42638i	−0.163719	+	0.283569i
$147$	3.50000	−	6.06218i	0.288675	−	0.500000i
$148$			6.37600i			0.524104i
$149$	−15.1652	−	8.75560i	−1.24238	−	0.717287i	−0.272800	−	0.962071i	$-0.587950\pi$
$149$	−15.1652	−	8.75560i	−1.24238	−	0.717287i	−0.969578	+	0.244784i	$0.921283\pi$
$150$		−	0.913701i		−	0.0746033i
$151$	−8.45644	−	4.88233i	−0.688175	−	0.397318i	0.114753	−	0.993394i	$-0.463392\pi$
$151$	−8.45644	−	4.88233i	−0.688175	−	0.397318i	−0.802928	+	0.596076i	$0.796726\pi$
$152$	−4.58258	+	7.93725i	−0.371696	+	0.643796i
$153$	−0.500000	+	0.866025i	−0.0404226	+	0.0700140i
$154$			4.18710i			0.337406i
$155$	1.41742			0.113850
$156$	6.26951	−	1.55130i	0.501962	−	0.124203i
$157$	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	$0.0610246\pi$
$158$	4.18693	−	2.41733i	0.333094	−	0.192312i
$159$	12.1652			0.964759
$160$	−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
$163$	3.00000	+	1.73205i	0.234978	+	0.135665i	0.612866	−	0.790186i	$-0.290016\pi$
$163$	3.00000	+	1.73205i	0.234978	+	0.135665i	−0.377888	+	0.925851i	$0.623350\pi$
$164$	10.8956	+	6.29060i	0.850807	+	0.491214i
$165$	−6.00000			−0.467099
$166$	−1.58258			−0.122832
$167$	−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
$171$	4.58258	−	2.64575i	0.350438	−	0.202326i
$172$	4.10436	+	7.10895i	0.312954	+	0.542053i
$173$	6.16515	−	10.6784i	0.468728	−	0.811860i	−0.530633	−	0.847601i	$-0.678046\pi$
$173$	6.16515	−	10.6784i	0.468728	−	0.811860i	0.999361	+	0.0357412i	$0.0113792\pi$
$174$			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
$178$	−7.12159			−0.533786
$179$	−9.58258	−	16.5975i	−0.716235	−	1.24056i	−0.962481	−	0.271349i	$-0.912530\pi$
$179$	−9.58258	−	16.5975i	−0.716235	−	1.24056i	0.246246	−	0.969207i	$-0.420803\pi$
$180$			3.10260i			0.231254i
$181$	22.0000			1.63525			0.817624	−	0.575753i	$-0.195291\pi$
$181$	22.0000			1.63525			0.817624	+	0.575753i	$0.195291\pi$
$182$	−3.02178	−	3.14033i	−0.223989	−	0.232776i
$183$	13.1652			0.973196
$184$		−	1.00905i		−	0.0743882i
$185$	3.08258	+	5.33918i	0.226635	+	0.392544i
$186$	−0.373864			−0.0274130
$187$	3.00000	−	1.73205i	0.219382	−	0.126660i
$188$	−9.47822	+	5.47225i	−0.691270	+	0.399105i
$189$	−2.29129	−	1.32288i	−0.166667	−	0.0962250i
$190$			4.18710i			0.303764i
$191$	−11.1652	+	19.3386i	−0.807882	+	1.39929i	0.106446	+	0.994318i	$0.466053\pi$
$191$	−11.1652	+	19.3386i	−0.807882	+	1.39929i	−0.914328	+	0.404974i	$0.867280\pi$
$192$	−1.70871	−	2.95958i	−0.123316	−	0.213589i
$193$	15.1652	−	8.75560i	1.09161	−	0.630242i	0.157606	−	0.987502i	$-0.449622\pi$
$193$	15.1652	−	8.75560i	1.09161	−	0.630242i	0.934005	+	0.357260i	$0.116289\pi$
$194$	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	$0.834733\pi$
$198$	1.58258			0.112469
$199$	−6.58258			−0.466626			−0.233313	−	0.972402i	$-0.574957\pi$
$199$	−6.58258			−0.466626			−0.233313	+	0.972402i	$0.574957\pi$
$200$	3.00000	+	1.73205i	0.212132	+	0.122474i
$201$	−6.16515	−	3.55945i	−0.434856	−	0.251064i
$202$	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
$205$	12.1652			0.849651
$206$	−4.97822	+	2.87418i	−0.346849	+	0.200253i
$207$	−0.291288	+	0.504525i	−0.0202459	+	0.0350669i
$208$	−2.79129	+	9.66930i	−0.193541	+	0.670446i
$209$	−18.3303			−1.26793
$210$	1.81307	−	1.04678i	0.125114	−	0.0722344i
$211$	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	$0.138333\pi$
$212$	−10.8956	+	18.8718i	−0.748316	+	1.29612i
$213$	−9.87386	−	5.70068i	−0.676546	−	0.390604i
$214$			4.83465i			0.330490i
$215$	6.87386	+	3.96863i	0.468794	+	0.270658i
$216$		−	1.73205i		−	0.117851i
$217$	−1.08258	−	1.87508i	−0.0734900	−	0.127288i
$218$	0.439205	−	0.760725i	0.0297467	−	0.0515228i
$219$			8.66025i			0.585206i
$220$	5.37386	−	9.30780i	0.362306	−	0.627532i
$221$	−1.00000	+	3.46410i	−0.0672673	+	0.233021i
$222$	−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
$227$		−	20.3477i		−	1.35052i	−0.737579	−	0.675261i	$-0.764031\pi$
$227$		−	20.3477i		−	1.35052i	0.737579	−	0.675261i	$-0.235969\pi$
$228$			9.47860i			0.627736i
$229$	0.0825757	−	0.0476751i	0.00545676	−	0.00315046i	−0.497269	−	0.867596i	$-0.665664\pi$
$229$	0.0825757	−	0.0476751i	0.00545676	−	0.00315046i	0.502726	+	0.864446i	$0.332331\pi$
$230$	−0.230493	−	0.399225i	−0.0151982	−	0.0263241i
$231$	4.58258	+	7.93725i	0.301511	+	0.522233i
$232$	−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	$0.852476\pi$
$234$	−1.18693	+	1.14213i	−0.0775922	+	0.0746631i
$235$	−5.29129	+	9.16478i	−0.345166	+	0.597844i
$236$			17.1497i			1.11635i
$237$	5.29129	−	9.16478i	0.343706	−	0.595316i
$238$	−0.604356	+	1.04678i	−0.0391746	+	0.0678524i
$239$		−	29.7309i		−	1.92313i	−0.274572	−	0.961566i	$-0.588536\pi$
$239$		−	29.7309i		−	1.92313i	0.274572	−	0.961566i	$-0.411464\pi$
$240$	−4.18693	−	2.41733i	−0.270265	−	0.156038i
$241$			17.6066i			1.13414i	0.823670	+	0.567069i	$0.191923\pi$
$241$			17.6066i			1.13414i	−0.823670	+	0.567069i	$0.808077\pi$
$242$	−0.395644	−	0.228425i	−0.0254330	−	0.0146837i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−11.7913	+	20.4231i	−0.754860	+	1.30746i
$245$	10.5000	+	6.06218i	0.670820	+	0.387298i
$246$	−3.20871			−0.204580
$247$	13.7477	−	13.2288i	0.874747	−	0.841726i
$248$	0.708712	−	1.22753i	0.0450033	−	0.0779479i
$249$	−3.00000	+	1.73205i	−0.190117	+	0.109764i
$250$	5.53901			0.350318
$251$	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
$254$	−1.02178	−	0.589925i	−0.0641122	−	0.0370152i
$255$	−1.50000	−	0.866025i	−0.0939336	−	0.0542326i
$256$	1.79129			0.111955
$257$	27.3303			1.70482			0.852409	−	0.522876i	$-0.175141\pi$
$257$	27.3303			1.70482			0.852409	+	0.522876i	$0.175141\pi$
$258$	−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
$262$	−4.18693	+	2.41733i	−0.258670	+	0.149343i
$263$	11.5826	+	20.0616i	0.714212	+	1.23705i	0.963263	+	0.268561i	$0.0865482\pi$
$263$	11.5826	+	20.0616i	0.714212	+	1.23705i	−0.249050	+	0.968491i	$0.580118\pi$
$264$	−3.00000	+	5.19615i	−0.184637	+	0.319801i
$265$			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
$269$	−2.16515			−0.132012			−0.0660058	−	0.997819i	$-0.521026\pi$
$269$	−2.16515			−0.132012			−0.0660058	+	0.997819i	$0.521026\pi$
$270$	−0.395644	−	0.685275i	−0.0240781	−	0.0417045i
$271$			25.4485i			1.54588i	0.634477	+	0.772942i	$0.281216\pi$
$271$			25.4485i			1.54588i	−0.634477	+	0.772942i	$0.718784\pi$
$272$	2.79129			0.169247
$273$	−9.16515	−	2.64575i	−0.554700	−	0.160128i
$274$	3.95644			0.239017
$275$			6.92820i			0.417786i
$276$	−0.521780	−	0.903750i	−0.0314075	−	0.0543994i
$277$	−27.3303			−1.64212			−0.821059	−	0.570843i	$-0.806617\pi$
$277$	−27.3303			−1.64212			−0.821059	+	0.570843i	$0.806617\pi$
$278$	−1.02178	+	0.589925i	−0.0612823	+	0.0353814i
$279$	−0.708712	+	0.409175i	−0.0424295	+	0.0244967i
$280$			7.93725i			0.474342i
$281$		−	17.5112i		−	1.04463i	−0.852752	−	0.522316i	$-0.825068\pi$
$281$		−	17.5112i		−	1.04463i	0.852752	−	0.522316i	$-0.174932\pi$
$282$	1.39564	−	2.41733i	0.0831094	−	0.143950i
$283$	−3.16515	−	5.48220i	−0.188149	−	0.325883i	0.756484	−	0.654012i	$-0.226915\pi$
$283$	−3.16515	−	5.48220i	−0.188149	−	0.325883i	−0.944633	+	0.328129i	$0.893582\pi$
$284$	17.6869	−	10.2116i	1.04953	−	0.605944i
$285$	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
$289$	−16.0000			−0.941176
$290$	−5.53901			−0.325262
$291$	0.0825757	+	0.0476751i	0.00484067	+	0.00279476i
$292$	−13.4347	−	7.75650i	−0.786204	−	0.453915i
$293$	−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
$296$	6.16515			0.358342
$297$	3.00000	−	1.73205i	0.174078	−	0.100504i
$298$	−4.00000	+	6.92820i	−0.231714	+	0.401340i
$299$	−0.582576	+	2.01810i	−0.0336912	+	0.116710i
$300$	3.58258			0.206840
$301$		−	12.1244i		−	0.698836i
$302$	−2.23049	+	3.86333i	−0.128350	+	0.222309i
$303$	2.58258	−	4.47315i	0.148365	−	0.256976i
$304$	−12.7913	−	7.38505i	−0.733631	−	0.423562i
$305$			22.8027i			1.30568i
$306$	0.395644	+	0.228425i	0.0226175	+	0.0130582i
$307$			0.190700i			0.0108838i	0.999985	+	0.00544192i	$0.00173223\pi$
$307$			0.190700i			0.0108838i	−0.999985	+	0.00544192i	$0.998268\pi$
$308$	−16.4174			−0.935470
$309$	−6.29129	+	10.8968i	−0.357899	+	0.619899i
$310$		−	0.647551i		−	0.0367784i
$311$	−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	$0.171925\pi$
$312$	−1.50000	−	6.06218i	−0.0849208	−	0.343203i
$313$	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	0.0473014	−	0.998881i	$-0.484938\pi$
$317$	16.6652	−	9.62163i	0.936008	−	0.540405i	0.888707	+	0.458476i	$0.151605\pi$
$318$		−	5.55765i		−	0.311658i
$319$		−	24.2487i		−	1.35767i
$320$	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
$325$	−5.00000	−	5.19615i	−0.277350	−	0.288231i
$326$	0.791288	−	1.37055i	0.0438254	−	0.0759078i
$327$		−	1.92275i		−	0.106328i
$328$	6.08258	−	10.5353i	0.335854	−	0.581716i
$329$	16.1652			0.891214
$330$			2.74110i			0.150893i
$331$	−13.4174	−	7.74655i	−0.737488	−	0.425789i	0.0836671	−	0.996494i	$-0.473337\pi$
$331$	−13.4174	−	7.74655i	−0.737488	−	0.425789i	−0.821155	+	0.570705i	$0.806670\pi$
$332$		−	6.20520i		−	0.340555i
$333$	−3.08258	−	1.77973i	−0.168924	−	0.0975284i
$334$	−2.60436	+	4.51088i	−0.142504	+	0.246824i
$335$	6.16515	−	10.6784i	0.336838	−	0.583421i
$336$			7.38505i			0.402888i
$337$	−31.4955			−1.71567			−0.857833	−	0.513928i	$-0.828190\pi$
$337$	−31.4955			−1.71567			−0.857833	+	0.513928i	$0.828190\pi$
$338$	−3.16515	+	5.02535i	−0.172162	+	0.273343i
$339$	3.08258	−	5.33918i	0.167423	−	0.289984i
$340$	2.68693	−	1.55130i	0.145719	−	0.0841311i
$341$	2.83485			0.153516
$342$	−1.20871	−	2.09355i	−0.0653597	−	0.113206i
$343$		−	18.5203i		−	1.00000i
$344$	6.87386	−	3.96863i	0.370614	−	0.213974i
$345$	−0.873864	−	0.504525i	−0.0470472	−	0.0271627i
$346$	−4.87841	−	2.81655i	−0.262265	−	0.151419i
$347$	1.74773			0.0938229			0.0469115	−	0.998899i	$-0.485062\pi$
$347$	1.74773			0.0938229			0.0469115	+	0.998899i	$0.485062\pi$
$348$	−12.5390			−0.672162
$349$	−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
$353$	10.7477	−	6.20520i	0.572044	−	0.330270i	−0.185921	−	0.982565i	$-0.559527\pi$
$353$	10.7477	−	6.20520i	0.572044	−	0.330270i	0.757965	+	0.652295i	$0.226194\pi$
$354$	−2.18693	−	3.78788i	−0.116234	−	0.201323i
$355$	9.87386	−	17.1020i	0.524050	−	0.907682i
$356$		−	27.9234i		−	1.47994i
$357$			2.64575i			0.140028i
$358$	−7.58258	+	4.37780i	−0.400752	+	0.231374i
$359$	−16.0390	+	9.26013i	−0.846507	+	0.488731i	−0.859471	−	0.511185i	$-0.829207\pi$
$359$	−16.0390	+	9.26013i	−0.846507	+	0.488731i	0.0129639	+	0.999916i	$0.495873\pi$
$360$	3.00000			0.158114
$361$	4.50000	+	7.79423i	0.236842	+	0.410223i
$362$		−	10.0507i		−	0.528253i
$363$	−1.00000			−0.0524864
$364$	12.3131	−	11.8483i	0.645380	−	0.621017i
$365$	−15.0000			−0.785136
$366$		−	6.01450i		−	0.314383i
$367$	1.58258	+	2.74110i	0.0826098	+	0.143084i	0.904370	−	0.426749i	$-0.140341\pi$
$367$	1.58258	+	2.74110i	0.0826098	+	0.143084i	−0.821760	+	0.569833i	$0.807008\pi$
$368$	1.62614			0.0847682
$369$	−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
$373$	13.0000	−	22.5167i	0.673114	−	1.16587i	−0.303902	−	0.952703i	$-0.598289\pi$
$373$	13.0000	−	22.5167i	0.673114	−	1.16587i	0.977016	−	0.213165i	$-0.0683772\pi$
$374$	−0.791288	−	1.37055i	−0.0409165	−	0.0708695i
$375$	10.5000	−	6.06218i	0.542218	−	0.313050i
$376$	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	$0.824458\pi$
$380$	−16.4174			−0.842196
$381$	−2.58258			−0.132309
$382$	8.83485	+	5.10080i	0.452030	+	0.260980i
$383$	21.3303	+	12.3151i	1.08993	+	0.629270i	0.933557	−	0.358429i	$-0.116687\pi$
$383$	21.3303	+	12.3151i	1.08993	+	0.629270i	0.156370	+	0.987698i	$0.450021\pi$
$384$	−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
$387$	−4.58258			−0.232945
$388$	−0.147917	+	0.0853998i	−0.00750934	+	0.00433552i
$389$	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	$0.0906557\pi$
$390$	−1.97822	−	2.05583i	−0.100171	−	0.104101i
$391$	0.582576			0.0294621
$392$	10.5000	−	6.06218i	0.530330	−	0.306186i
$393$	−5.29129	+	9.16478i	−0.266910	+	0.462302i
$394$	−3.23049	+	5.59538i	−0.162750	+	0.281891i
$395$	15.8739	+	9.16478i	0.798701	+	0.461130i
$396$			6.20520i			0.311823i
$397$	−13.9129	−	8.03260i	−0.698267	−	0.403145i	0.108434	−	0.994104i	$-0.465416\pi$
$397$	−13.9129	−	8.03260i	−0.698267	−	0.403145i	−0.806702	+	0.590959i	$0.798750\pi$
$398$			3.00725i			0.150740i
$399$	7.00000	−	12.1244i	0.350438	−	0.606977i
$400$	−2.79129	+	4.83465i	−0.139564	+	0.241733i
$401$			24.1534i			1.20616i	0.797680	+	0.603081i	$0.206060\pi$
$401$			24.1534i			1.20616i	−0.797680	+	0.603081i	$0.793940\pi$
$402$	−1.62614	+	2.81655i	−0.0811043	+	0.140477i
$403$	−2.12614	+	2.04588i	−0.105910	+	0.101912i
$404$	4.62614	+	8.01270i	0.230159	+	0.398647i
$405$	−1.50000	−	0.866025i	−0.0745356	−	0.0430331i
$406$	4.23049	+	7.32743i	0.209956	+	0.363654i
$407$	6.16515	+	10.6784i	0.305595	+	0.529306i
$408$	−1.50000	+	0.866025i	−0.0742611	+	0.0428746i
$409$		−	20.6893i		−	1.02302i	−0.859278	−	0.511509i	$-0.829087\pi$
$409$		−	20.6893i		−	1.02302i	0.859278	−	0.511509i	$-0.170913\pi$
$410$		−	5.55765i		−	0.274473i
$411$	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
$416$	16.4174	+	4.73930i	0.804930	+	0.232363i
$417$	−1.29129	+	2.23658i	−0.0632346	+	0.109526i
$418$			8.37420i			0.409596i
$419$	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	$0.694968\pi$
$422$	−1.02178	−	0.589925i	−0.0497395	−	0.0287171i
$423$		−	6.10985i		−	0.297071i
$424$	18.2477	+	10.5353i	0.886188	+	0.511641i
$425$	−1.00000	+	1.73205i	−0.0485071	+	0.0840168i
$426$	−2.60436	+	4.51088i	−0.126181	+	0.218553i
$427$	30.1652	−	17.4159i	1.45979	−	0.842812i
$428$	−18.9564			−0.916294
$429$	9.00000	−	8.66025i	0.434524	−	0.418121i
$430$	1.81307	−	3.14033i	0.0874339	−	0.151440i
$431$	−16.5826	+	9.57395i	−0.798755	+	0.461161i	−0.843035	−	0.537858i	$-0.819234\pi$
$431$	−16.5826	+	9.57395i	−0.798755	+	0.461161i	0.0442809	+	0.999019i	$0.485900\pi$
$432$	2.79129			0.134296
$433$	−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
$436$	2.98277	+	1.72210i	0.142849	+	0.0824737i
$437$	−2.66970	−	1.54135i	−0.127709	−	0.0737328i
$438$	3.95644			0.189046
$439$	−1.41742			−0.0676500			−0.0338250	−	0.999428i	$-0.510769\pi$
$439$	−1.41742			−0.0676500			−0.0338250	+	0.999428i	$0.510769\pi$
$440$	−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	$-0.339481\pi$
$444$	5.52178	−	3.18800i	0.262052	−	0.151296i
$445$	−13.5000	−	23.3827i	−0.639961	−	1.10845i
$446$	0.604356	−	1.04678i	0.0286171	−	0.0495663i
$447$			17.5112i			0.828252i
$448$	−7.83030	−	4.52083i	−0.369947	−	0.213589i
$449$	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
$451$	24.3303			1.14567
$452$	5.52178	+	9.56400i	0.259723	+	0.449853i
$453$			9.76465i			0.458784i
$454$	−9.29583			−0.436275
$455$	4.58258	−	15.8745i	0.214834	−	0.744208i
$456$	9.16515			0.429198
$457$			27.9989i			1.30973i	0.755745	+	0.654866i	$0.227275\pi$
$457$			27.9989i			1.30973i	−0.755745	+	0.654866i	$0.772725\pi$
$458$	−0.0217804	−	0.0377247i	−0.00101773	−	0.00176276i
$459$	1.00000			0.0466760
$460$	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	$0.971519\pi$
$464$	9.76951	−	16.9213i	0.453538	−	0.785551i
$465$	−0.708712	−	1.22753i	−0.0328657	−	0.0569251i
$466$	−0.725947	+	0.419126i	−0.0336288	+	0.0194156i
$467$	−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
$471$	−8.16515			−0.376230
$472$	16.5826			0.763275
$473$	13.7477	+	7.93725i	0.632121	+	0.364955i
$474$	−4.18693	−	2.41733i	−0.192312	−	0.111031i
$475$	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
$478$	−13.5826			−0.621253
$479$	−30.4955	+	17.6066i	−1.39337	+	0.804464i	−0.993687	−	0.112188i	$-0.964214\pi$
$479$	−30.4955	+	17.6066i	−1.39337	+	0.804464i	−0.399686	+	0.916652i	$0.630881\pi$
$480$	−4.10436	+	7.10895i	−0.187337	+	0.324478i
$481$	−12.3303	−	3.55945i	−0.562213	−	0.162297i
$482$	8.04356			0.366374
$483$			1.54135i			0.0701339i
$484$	0.895644	−	1.55130i	0.0407111	−	0.0705137i
$485$	−0.0825757	+	0.143025i	−0.00374957	+	0.00649444i
$486$	0.395644	+	0.228425i	0.0179468	+	0.0103616i
$487$			37.4775i			1.69827i	0.528179	+	0.849133i	$0.322875\pi$
$487$			37.4775i			1.69827i	−0.528179	+	0.849133i	$0.677125\pi$
$488$	19.7477	+	11.4014i	0.893938	+	0.516115i
$489$		−	3.46410i		−	0.156652i
$490$	2.76951	−	4.79693i	0.125114	−	0.216703i
$491$	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	$-0.0133458\pi$
$492$		−	12.5812i		−	0.567205i
$493$	3.50000	−	6.06218i	0.157632	−	0.273027i
$494$	−6.04356	−	6.28065i	−0.271913	−	0.282580i
$495$	3.00000	+	5.19615i	0.134840	+	0.233550i
$496$	1.97822	+	1.14213i	0.0888247	+	0.0512830i
$497$	−30.1652			−1.35309
$498$	0.791288	+	1.37055i	0.0354585	+	0.0614158i
$499$	−26.2913	+	15.1793i	−1.17696	+	0.679518i	−0.955309	−	0.295608i	$-0.904478\pi$
$499$	−26.2913	+	15.1793i	−1.17696	+	0.679518i	−0.221650	+	0.975126i	$0.571144\pi$
$500$			21.7182i			0.971268i
$501$			11.4014i			0.509375i
$502$	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	$0.638718\pi$
$504$	−2.29129	−	3.96863i	−0.102062	−	0.176777i
$505$	7.74773	+	4.47315i	0.344769	+	0.199053i
$506$	−0.460985	−	0.798450i	−0.0204933	−	0.0354954i
$507$	−0.500000	+	12.9904i	−0.0222058	+	0.576923i
$508$	2.31307	−	4.00635i	0.102626	−	0.177753i
$509$			3.75015i			0.166223i	0.996540	+	0.0831113i	$0.0264857\pi$
$509$			3.75015i			0.166223i	−0.996540	+	0.0831113i	$0.973514\pi$
$510$	−0.395644	+	0.685275i	−0.0175194	+	0.0303445i
$511$	11.4564	+	19.8431i	0.506803	+	0.877809i
$512$		−	22.8981i		−	1.01196i
$513$	−4.58258	−	2.64575i	−0.202326	−	0.116813i
$514$		−	12.4859i		−	0.550727i
$515$	−18.8739	−	10.8968i	−0.831682	−	0.480172i
$516$	4.10436	−	7.10895i	0.180684	−	0.312954i
$517$	−10.5826	+	18.3296i	−0.465421	+	0.806133i
$518$	−3.72595	−	2.15118i	−0.163709	−	0.0945173i
$519$	−12.3303			−0.541240
$520$	10.5000	−	2.59808i	0.460455	−	0.113933i
$521$	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	$-0.0938662\pi$
$522$	2.76951	−	1.59898i	0.121218	−	0.0699853i
$523$	17.7477			0.776054			0.388027	−	0.921648i	$-0.373157\pi$
$523$	17.7477			0.776054			0.388027	+	0.921648i	$0.373157\pi$
$524$	−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
$527$	0.708712	+	0.409175i	0.0308720	+	0.0178239i
$528$	−8.37386	−	4.83465i	−0.364426	−	0.210401i
$529$	−22.6606			−0.985244
$530$	9.62614			0.418133
$531$	−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
$535$	−15.8739	+	9.16478i	−0.686287	+	0.396228i
$536$	−6.16515	−	10.6784i	−0.266294	−	0.461235i
$537$	−9.58258	+	16.5975i	−0.413519	+	0.716235i
$538$			0.989150i			0.0426453i
$539$	21.0000	+	12.1244i	0.904534	+	0.522233i
$540$	2.68693	−	1.55130i	0.115627	−	0.0667574i
$541$	25.6652	−	14.8178i	1.10343	−	0.637066i	0.166311	−	0.986073i	$-0.446814\pi$
$541$	25.6652	−	14.8178i	1.10343	−	0.637066i	0.937120	+	0.349007i	$0.113481\pi$
$542$	11.6261			0.499385
$543$	−11.0000	−	19.0526i	−0.472055	−	0.817624i
$544$		−	4.73930i		−	0.203196i
$545$	3.33030			0.142654
$546$	−1.20871	+	4.18710i	−0.0517281	+	0.179191i
$547$	−8.00000			−0.342055			−0.171028	−	0.985266i	$-0.554709\pi$
$547$	−8.00000			−0.342055			−0.171028	+	0.985266i	$0.554709\pi$
$548$			15.5130i			0.662683i
$549$	−6.58258	−	11.4014i	−0.280937	−	0.486598i
$550$	3.16515			0.134963
$551$	−32.0780	+	18.5203i	−1.36657	+	0.788990i
$552$	−0.873864	+	0.504525i	−0.0371941	+	0.0214740i
$553$		−	27.9989i		−	1.19063i
$554$			12.4859i			0.530473i
$555$	3.08258	−	5.33918i	0.130848	−	0.226635i
$556$	−2.31307	−	4.00635i	−0.0980959	−	0.169907i
$557$	−2.83485	+	1.63670i	−0.120116	+	0.0693492i	−0.558854	−	0.829266i	$-0.688759\pi$
$557$	−2.83485	+	1.63670i	−0.120116	+	0.0693492i	0.438738	+	0.898615i	$0.355426\pi$
$558$	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
$562$	−8.00000			−0.337460
$563$	14.5826			0.614582			0.307291	−	0.951616i	$-0.400577\pi$
$563$	14.5826			0.614582			0.307291	+	0.951616i	$0.400577\pi$
$564$	9.47822	+	5.47225i	0.399105	+	0.230423i
$565$	9.24773	+	5.33918i	0.389055	+	0.224621i
$566$	−2.50455	+	1.44600i	−0.105274	+	0.0607799i
$567$			2.64575i			0.111111i
$568$	−9.87386	−	17.1020i	−0.414298	−	0.717585i
$569$	31.3303			1.31343			0.656717	−	0.754137i	$-0.271944\pi$
$569$	31.3303			1.31343			0.656717	+	0.754137i	$0.271944\pi$
$570$	3.62614	−	2.09355i	0.151882	−	0.0876892i
$571$	−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	$0.305959\pi$
$572$	5.37386	+	21.7182i	0.224693	+	0.908084i
$573$	22.3303			0.932862
$574$	−7.35208	+	4.24473i	−0.306870	+	0.177171i
$575$	−0.582576	+	1.00905i	−0.0242951	+	0.0420803i
$576$	−1.70871	+	2.95958i	−0.0711963	+	0.123316i
$577$	2.91742	+	1.68438i	0.121454	+	0.0701215i	0.559496	−	0.828833i	$-0.310995\pi$
$577$	2.91742	+	1.68438i	0.121454	+	0.0701215i	−0.438042	+	0.898954i	$0.644328\pi$
$578$			7.30960i			0.304039i
$579$	−15.1652	−	8.75560i	−0.630242	−	0.363870i
$580$		−	21.7182i		−	0.901800i
$581$	−4.58258	+	7.93725i	−0.190117	+	0.329293i
$582$	0.0217804	−	0.0377247i	0.000902826	−	0.00156374i
$583$			42.1413i			1.74532i
$584$	−7.50000	+	12.9904i	−0.310352	+	0.537546i
$585$	−6.00000	−	1.73205i	−0.248069	−	0.0716115i
$586$	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
$591$			14.1425i			0.581743i
$592$			9.93545i			0.408345i
$593$	12.2477	−	7.07123i	0.502954	−	0.290381i	−0.226979	−	0.973900i	$-0.572885\pi$
$593$	12.2477	−	7.07123i	0.502954	−	0.290381i	0.729933	+	0.683519i	$0.239551\pi$
$594$	−0.791288	−	1.37055i	−0.0324669	−	0.0562344i
$595$	−4.58258			−0.187867
$596$	−27.1652	−	15.6838i	−1.11273	−	0.642434i
$597$	3.29129	+	5.70068i	0.134703	+	0.233313i
$598$	0.921970	+	0.266150i	0.0377022	+	0.0108837i
$599$	−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	$0.906044\pi$
$600$		−	3.46410i		−	0.141421i
$601$	−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	$0.217750\pi$
$602$	−5.53901			−0.225753
$603$			7.11890i			0.289904i
$604$	−15.1479	−	8.74565i	−0.616360	−	0.355856i
$605$		−	1.73205i		−	0.0704179i
$606$	−2.04356	−	1.17985i	−0.0830140	−	0.0479281i
$607$	4.00000	−	6.92820i	0.162355	−	0.281207i	−0.773358	−	0.633970i	$-0.781424\pi$
$607$	4.00000	−	6.92820i	0.162355	−	0.281207i	0.935713	+	0.352763i	$0.114758\pi$
$608$	−12.5390	+	21.7182i	−0.508524	+	0.880790i
$609$	16.0390	+	9.26013i	0.649934	+	0.375239i
$610$	10.4174			0.421789
$611$	−5.29129	−	21.3845i	−0.214063	−	0.865124i
$612$	−0.895644	+	1.55130i	−0.0362043	+	0.0627076i
$613$	2.83485	−	1.63670i	0.114498	−	0.0661057i	−0.441657	−	0.897184i	$-0.645609\pi$
$613$	2.83485	−	1.63670i	0.114498	−	0.0661057i	0.556156	+	0.831078i	$0.312276\pi$
$614$	0.0871215			0.00351594
$615$	−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	$0.264375\pi$
$618$	4.97822	+	2.87418i	0.200253	+	0.115616i
$619$	31.0390	+	17.9204i	1.24756	+	0.720281i	0.970623	−	0.240606i	$-0.0773462\pi$
$619$	31.0390	+	17.9204i	1.24756	+	0.720281i	0.276940	+	0.960887i	$0.410680\pi$
$620$	2.53901			0.101969
$621$	0.582576			0.0233780
$622$	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
$626$	12.7259	−	7.34733i	0.508631	−	0.293658i
$627$	9.16515	+	15.8745i	0.366021	+	0.633967i
$628$	7.31307	−	12.6666i	0.291823	−	0.505453i
$629$			3.55945i			0.141925i
$630$	−1.81307	−	1.04678i	−0.0722344	−	0.0417045i
$631$	−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
$633$	−2.58258			−0.102648
$634$	−4.39564	−	7.61348i	−0.174573	−	0.302370i
$635$		−	4.47315i		−	0.177512i
$636$	21.7913			0.864081
$637$	−24.5000	+	6.06218i	−0.970725	+	0.240192i
$638$	−11.0780			−0.438583
$639$			11.4014i			0.451031i
$640$	−9.56080	−	16.5598i	−0.377924	−	0.654583i
$641$	38.4955			1.52048			0.760240	−	0.649643i	$-0.225082\pi$
$641$	38.4955			1.52048			0.760240	+	0.649643i	$0.225082\pi$
$642$	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	$0.285732\pi$
$644$	−2.39110	−	1.38050i	−0.0942225	−	0.0543994i
$645$		−	7.93725i		−	0.312529i
$646$	−1.20871	+	2.09355i	−0.0475561	+	0.0823697i
$647$	0.834849	+	1.44600i	0.0328213	+	0.0568481i	0.881969	−	0.471307i	$-0.156217\pi$
$647$	0.834849	+	1.44600i	0.0328213	+	0.0568481i	−0.849148	+	0.528155i	$0.822884\pi$
$648$	−1.50000	+	0.866025i	−0.0589256	+	0.0340207i
$649$	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
$653$	−28.4955			−1.11511			−0.557557	−	0.830139i	$-0.688261\pi$
$653$	−28.4955			−1.11511			−0.557557	+	0.830139i	$0.688261\pi$
$654$	−0.878409			−0.0343485
$655$	−15.8739	−	9.16478i	−0.620243	−	0.358098i
$656$	16.9782	+	9.80238i	0.662888	+	0.382719i
$657$	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	$0.504719\pi$
$660$	−10.7477			−0.418355
$661$	−22.7477	+	13.1334i	−0.884784	+	0.510830i	−0.872233	−	0.489091i	$-0.837329\pi$
$661$	−22.7477	+	13.1334i	−0.884784	+	0.510830i	−0.0125512	+	0.999921i	$0.503995\pi$
$662$	−3.53901	+	6.12975i	−0.137548	+	0.238240i
$663$	3.50000	−	0.866025i	0.135929	−	0.0336336i
$664$	−6.00000			−0.232845
$665$	21.0000	+	12.1244i	0.814345	+	0.470162i
$666$	−0.813068	+	1.40828i	−0.0315058	+	0.0545696i
$667$	2.03901	−	3.53168i	0.0789510	−	0.136747i
$668$	−17.6869	−	10.2116i	−0.684328	−	0.395097i
$669$		−	2.64575i		−	0.102291i
$670$	−4.87841	−	2.81655i	−0.188469	−	0.108813i
$671$			45.6054i			1.76058i
$672$	12.5390			0.483703
$673$	−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	$0.174829\pi$
$674$			14.3887i			0.554232i
$675$	−1.00000	+	1.73205i	−0.0384900	+	0.0666667i
$676$	−19.7042	−	12.4104i	−0.757853	−	0.477323i
$677$	−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
$679$	0.252273			0.00968135
$680$	−1.50000	−	2.59808i	−0.0575224	−	0.0996317i
$681$	−17.6216	+	10.1738i	−0.675261	+	0.389862i
$682$		−	1.29510i		−	0.0495920i
$683$		−	23.2397i		−	0.889241i	−0.895719	−	0.444620i	$-0.853339\pi$
$683$		−	23.2397i		−	0.889241i	0.895719	−	0.444620i	$-0.146661\pi$
$684$	8.20871	−	4.73930i	0.313868	−	0.181212i
$685$	7.50000	+	12.9904i	0.286560	+	0.496337i
$686$	−8.46099			−0.323042
$687$	−0.0825757	−	0.0476751i	−0.00315046	−	0.00181892i
$688$	6.39564	+	11.0776i	0.243832	+	0.422329i
$689$	−30.4129	−	31.6060i	−1.15864	−	1.20409i
$690$	−0.230493	+	0.399225i	−0.00877470	+	0.0151982i
$691$		−	34.0134i		−	1.29393i	−0.762520	−	0.646965i	$-0.776038\pi$
$691$		−	34.0134i		−	1.29393i	0.762520	−	0.646965i	$-0.223962\pi$
$692$	11.0436	−	19.1280i	0.419813	−	0.727138i
$693$	4.58258	−	7.93725i	0.174078	−	0.301511i
$694$		−	0.798450i		−	0.0303087i
$695$	−3.87386	−	2.23658i	−0.146944	−	0.0848382i
$696$			12.1244i			0.459573i
$697$	6.08258	+	3.51178i	0.230394	+	0.133018i
$698$	−0.0217804	+	0.0377247i	−0.000824400	+	0.00142790i
$699$	−0.917424	+	1.58903i	−0.0347002	+	0.0601025i
$700$	8.20871	−	4.73930i	0.310260	−	0.179129i
$701$	34.0000			1.28416			0.642081	−	0.766637i	$-0.278071\pi$
$701$	34.0000			1.28416			0.642081	+	0.766637i	$0.278071\pi$
$702$	1.58258	+	0.456850i	0.0597305	+	0.0172427i
$703$	9.41742	−	16.3115i	0.355185	−	0.615198i
$704$	10.2523	−	5.91915i	0.386397	−	0.223086i
$705$	10.5826			0.398563
$706$	−2.83485	−	4.91010i	−0.106691	−	0.184794i
$707$		−	13.6657i		−	0.513952i
$708$	14.8521	−	8.57485i	0.558175	−	0.322263i
$709$	16.4174	+	9.47860i	0.616569	+	0.355976i	0.775532	−	0.631308i	$-0.217482\pi$
$709$	16.4174	+	9.47860i	0.616569	+	0.355976i	−0.158963	+	0.987285i	$0.550815\pi$
$710$	−7.81307	−	4.51088i	−0.293219	−	0.169290i
$711$	−10.5826			−0.396878
$712$	−27.0000			−1.01187
$713$	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
$717$	−25.7477	+	14.8655i	−0.961566	+	0.555161i
$718$	4.23049	+	7.32743i	0.157881	+	0.273457i
$719$	−1.16515	+	2.01810i	−0.0434528	+	0.0752625i	−0.886934	−	0.461896i	$-0.847169\pi$
$719$	−1.16515	+	2.01810i	−0.0434528	+	0.0752625i	0.843481	+	0.537159i	$0.180502\pi$
$720$			4.83465i			0.180177i
$721$			33.2904i			1.23980i
$722$	3.56080	−	2.05583i	0.132519	−	0.0765099i
$723$	15.2477	−	8.80328i	0.567069	−	0.327397i
$724$	39.4083			1.46460
$725$	7.00000	+	12.1244i	0.259973	+	0.450287i
$726$			0.456850i			0.0169553i
$727$	28.0000			1.03846			0.519231	−	0.854634i	$-0.326218\pi$
$727$	28.0000			1.03846			0.519231	+	0.854634i	$0.326218\pi$
$728$	−11.4564	−	11.9059i	−0.424604	−	0.441261i
$729$	1.00000			0.0370370
$730$			6.85275i			0.253632i
$731$	2.29129	+	3.96863i	0.0847463	+	0.146785i
$732$	23.5826			0.871637
$733$	10.8303	−	6.25288i	0.400026	−	0.230955i	−0.286469	−	0.958090i	$-0.592482\pi$
$733$	10.8303	−	6.25288i	0.400026	−	0.230955i	0.686495	+	0.727134i	$0.259148\pi$
$734$	1.25227	−	0.723000i	0.0462222	−	0.0266864i
$735$		−	12.1244i		−	0.447214i
$736$		−	2.76100i		−	0.101772i
$737$	12.3303	−	21.3567i	0.454193	−	0.786685i
$738$	1.60436	+	2.77883i	0.0590572	+	0.102290i
$739$	7.41742	−	4.28245i	0.272854	−	0.157533i	−0.357330	−	0.933978i	$-0.616313\pi$
$739$	7.41742	−	4.28245i	0.272854	−	0.157533i	0.630184	+	0.776446i	$0.282979\pi$
$740$	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	$0.589795\pi$
$744$	−1.41742			−0.0519653
$745$	−30.3303			−1.11122
$746$	−10.2867	−	5.93905i	−0.376624	−	0.217444i
$747$	3.00000	+	1.73205i	0.109764	+	0.0633724i
$748$	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
$751$	32.9129			1.20101			0.600504	−	0.799622i	$-0.294967\pi$
$751$	32.9129			1.20101			0.600504	+	0.799622i	$0.294967\pi$
$752$	−14.7695	+	8.52718i	−0.538589	+	0.310954i
$753$	5.70871	−	9.88778i	0.208037	−	0.360331i
$754$	8.30852	−	7.99488i	0.302579	−	0.291156i
$755$	−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	$-0.203245\pi$
$758$	−4.23049	+	7.32743i	−0.153658	+	0.266144i
$759$	−1.74773	−	1.00905i	−0.0634385	−	0.0366262i
$760$			15.8745i			0.575829i
$761$	−28.7477	−	16.5975i	−1.04210	−	0.601659i	−0.121676	−	0.992570i	$-0.538827\pi$
$761$	−28.7477	−	16.5975i	−1.04210	−	0.601659i	−0.920429	+	0.390911i	$0.872160\pi$
$762$			1.17985i			0.0427415i
$763$	−2.54356	−	4.40558i	−0.0920831	−	0.159493i
$764$	−20.0000	+	34.6410i	−0.723575	+	1.25327i
$765$			1.73205i			0.0626224i
$766$	5.62614	−	9.74475i	0.203281	−	0.352092i
$767$	−33.1652	−	9.57395i	−1.19752	−	0.345695i
$768$	−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	$0.747609\pi$
$770$	3.62614	+	6.28065i	0.130677	+	0.226339i
$771$	−13.6652	−	23.6687i	−0.492138	−	0.852409i
$772$	27.1652	−	15.6838i	0.977695	−	0.564473i
$773$			7.21425i			0.259479i	0.991548	+	0.129739i	$0.0414141\pi$
$773$			7.21425i			0.259479i	−0.991548	+	0.129739i	$0.958586\pi$
$774$			2.09355i			0.0752511i
$775$	−1.41742	+	0.818350i	−0.0509154	+	0.0293960i
$776$	0.0825757	+	0.143025i	0.00296429	+	0.00513431i
$777$	−9.41742			−0.337848
$778$	−3.69148	−	2.13128i	−0.132346	−	0.0764099i
$779$	−18.5826	−	32.1860i	−0.665790	−	1.15318i
$780$	8.06080	−	7.75650i	0.288623	−	0.277727i
$781$	19.7477	−	34.2041i	0.706629	−	1.22392i
$782$		−	0.266150i		−	0.00951750i
$783$	3.50000	−	6.06218i	0.125080	−	0.216645i
$784$	9.76951	+	16.9213i	0.348911	+	0.604332i
$785$		−	14.1425i		−	0.504766i
$786$	4.18693	+	2.41733i	0.149343	+	0.0862232i
$787$			25.0671i			0.893544i	0.894648	+	0.446772i	$0.147427\pi$
$787$			25.0671i			0.893544i	−0.894648	+	0.446772i	$0.852573\pi$
$788$	−21.9392	−	12.6666i	−0.781552	−	0.451229i
$789$	11.5826	−	20.0616i	0.412351	−	0.714212i
$790$	4.18693	−	7.25198i	0.148964	−	0.258014i
$791$		−	16.3115i		−	0.579969i
$792$	6.00000			0.213201
$793$	−32.9129	−	34.2041i	−1.16877	−	1.21462i
$794$	−3.66970	+	6.35610i	−0.130233	+	0.225570i
$795$	18.2477	−	10.5353i	0.647180	−	0.373650i
$796$	−11.7913			−0.417931
$797$	−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
$800$	8.20871	+	4.73930i	0.290222	+	0.167560i
$801$	13.5000	+	7.79423i	0.476999	+	0.275396i
$802$	11.0345			0.389641
$803$	−30.0000			−1.05868
$804$	−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
$808$	7.74773	−	4.47315i	0.272564	−	0.157365i
$809$	7.41742	+	12.8474i	0.260783	+	0.451689i	0.966450	−	0.256854i	$-0.0826860\pi$
$809$	7.41742	+	12.8474i	0.260783	+	0.451689i	−0.705667	+	0.708543i	$0.749353\pi$
$810$	−0.395644	+	0.685275i	−0.0139015	+	0.0240781i
$811$		−	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
$815$	6.00000			0.210171
$816$	−1.39564	−	2.41733i	−0.0488573	−	0.0846233i
$817$		−	24.2487i		−	0.848355i
$818$	−9.45189			−0.330478
$819$	2.29129	+	9.26013i	0.0800641	+	0.323575i
$820$	21.7913			0.760985
$821$			6.64215i			0.231813i	0.993260	+	0.115906i	$0.0369773\pi$
$821$			6.64215i			0.231813i	−0.993260	+	0.115906i	$0.963023\pi$
$822$	−1.97822	−	3.42638i	−0.0689983	−	0.119509i
$823$	21.4174			0.746564			0.373282	−	0.927718i	$-0.378232\pi$
$823$	21.4174			0.746564			0.373282	+	0.927718i	$0.378232\pi$
$824$	−18.8739	+	10.8968i	−0.657502	+	0.379609i
$825$	6.00000	−	3.46410i	0.208893	−	0.120605i
$826$	−10.0218	−	5.78608i	−0.348702	−	0.201323i
$827$			4.91010i			0.170741i	0.996349	+	0.0853705i	$0.0272074\pi$
$827$			4.91010i			0.170741i	−0.996349	+	0.0853705i	$0.972793\pi$
$828$	−0.521780	+	0.903750i	−0.0181331	+	0.0314075i
$829$	−13.3303	−	23.0888i	−0.462981	−	0.801906i	0.536127	−	0.844137i	$-0.319887\pi$
$829$	−13.3303	−	23.0888i	−0.462981	−	0.801906i	−0.999108	+	0.0422313i	$0.986553\pi$
$830$	−2.37386	+	1.37055i	−0.0823980	+	0.0475725i
$831$	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
$835$	−19.7477			−0.683398
$836$	−32.8348			−1.13562
$837$	0.708712	+	0.409175i	0.0244967	+	0.0141432i
$838$	−6.23049	−	3.59718i	−0.215229	−	0.124262i
$839$	−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
$842$	15.3394			0.528630
$843$	−15.1652	+	8.75560i	−0.522316	+	0.301559i
$844$	2.31307	−	4.00635i	0.0796191	−	0.137904i
$845$	−22.5000	−	0.866025i	−0.774024	−	0.0297922i
$846$	−2.79129			−0.0959665
$847$	−2.29129	+	1.32288i	−0.0787296	+	0.0454545i
$848$	−16.9782	+	29.4071i	−0.583034	+	1.00985i
$849$	−3.16515	+	5.48220i	−0.108628	+	0.188149i
$850$	0.791288	+	0.456850i	0.0271409	+	0.0156698i
$851$			2.07365i			0.0710838i
$852$	−17.6869	−	10.2116i	−0.605944	−	0.349842i
$853$			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
$856$			18.3296i			0.626491i
$857$	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	$0.0242511\pi$
$858$	−3.95644	−	4.11165i	−0.135071	−	0.140369i
$859$	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	−0.404247	−	0.914650i	$-0.632466\pi$
$863$	5.45644	−	3.15028i	0.185739	−	0.107237i	0.589986	+	0.807413i	$0.299133\pi$
$864$		−	4.73930i		−	0.161234i
$865$		−	21.3567i		−	0.726150i
$866$	−8.43920	+	4.87238i	−0.286776	+	0.165570i
$867$	8.00000	+	13.8564i	0.271694	+	0.470588i
$868$	−1.93920	−	3.35880i	−0.0658209	−	0.114005i
$869$	31.7477	+	18.3296i	1.07697	+	0.621788i
$870$	2.76951	+	4.79693i	0.0938951	+	0.162631i
$871$	6.16515	+	24.9162i	0.208898	+	0.844252i
$872$	1.66515	−	2.88413i	0.0563891	−	0.0976689i
$873$		−	0.0953502i		−	0.00322712i
$874$	−0.704166	+	1.21965i	−0.0238188	+	0.0412553i
$875$	16.0390	−	27.7804i	0.542218	−	0.939149i
$876$			15.5130i			0.524136i
$877$	31.9129	+	18.4249i	1.07762	+	0.622165i	0.930254	−	0.366917i	$-0.119587\pi$
$877$	31.9129	+	18.4249i	1.07762	+	0.622165i	0.147368	+	0.989082i	$0.452920\pi$
$878$			0.647551i			0.0218538i
$879$	19.8303	+	11.4490i	0.668860	+	0.386166i
$880$	8.37386	−	14.5040i	0.282283	−	0.488928i
$881$	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	$-0.0440892\pi$
$882$			3.19795i			0.107681i
$883$	13.6697			0.460022			0.230011	−	0.973188i	$-0.426124\pi$
$883$	13.6697			0.460022			0.230011	+	0.973188i	$0.426124\pi$
$884$	−1.79129	+	6.20520i	−0.0602475	+	0.208704i
$885$	8.29129	−	14.3609i	0.278709	−	0.482737i
$886$	−8.60436	+	4.96773i	−0.289069	+	0.166894i
$887$	−46.5826			−1.56409			−0.782045	−	0.623222i	$-0.785823\pi$
$887$	−46.5826			−1.56409			−0.782045	+	0.623222i	$0.785823\pi$
$888$	−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
$891$	−3.00000	−	1.73205i	−0.100504	−	0.0580259i
$892$	4.10436	+	2.36965i	0.137424	+	0.0793418i
$893$	32.3303			1.08189
$894$	8.00000			0.267560
$895$	−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
$899$	4.96099	−	2.86423i	0.165458	−	0.0955273i
$900$	−1.79129	−	3.10260i	−0.0597096	−	0.103420i
$901$	−6.08258	+	10.5353i	−0.202640	+	0.350983i
$902$		−	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
$906$	4.46099			0.148206
$907$	−13.5826	−	23.5257i	−0.451002	−	0.781158i	0.547447	−	0.836841i	$-0.315600\pi$
$907$	−13.5826	−	23.5257i	−0.451002	−	0.781158i	−0.998449	+	0.0556823i	$0.982267\pi$
$908$		−	36.4485i		−	1.20959i
$909$	−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	$0.633955\pi$
$912$			14.7701i			0.489087i
$913$	−6.00000	−	10.3923i	−0.198571	−	0.343935i
$914$	12.7913			0.423098
$915$	19.7477	−	11.4014i	0.652840	−	0.376917i
$916$	0.147917	−	0.0853998i	0.00488731	−	0.00282169i
$917$			27.9989i			0.924604i
$918$		−	0.456850i		−	0.0150783i
$919$	11.5826	−	20.0616i	0.382074	−	0.661771i	−0.609285	−	0.792952i	$-0.708543\pi$
$919$	11.5826	−	20.0616i	0.382074	−	0.661771i	0.991359	+	0.131180i	$0.0418766\pi$
$920$	−0.873864	−	1.51358i	−0.0288104	−	0.0499011i
$921$	0.165151	−	0.0953502i	0.00544192	−	0.00314190i
$922$	−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
$926$	1.75682			0.0577326
$927$	12.5826			0.413266
$928$	−28.7305	−	16.5876i	−0.943125	−	0.544513i
$929$	36.6606	+	21.1660i	1.20280	+	0.694434i	0.961176	−	0.275937i	$-0.0889880\pi$
$929$	36.6606	+	21.1660i	1.20280	+	0.694434i	0.241620	+	0.970371i	$0.422321\pi$
$930$	−0.560795	+	0.323775i	−0.0183892	+	0.0106170i
$931$		−	37.0405i		−	1.21395i
$932$	−1.64337	−	2.84640i	−0.0538304	−	0.0932370i
$933$	0.582576			0.0190727
$934$	−6.69148	+	3.86333i	−0.218952	+	0.126412i
$935$	3.00000	−	5.19615i	0.0981105	−	0.169932i
$936$	−4.50000	+	4.33013i	−0.147087	+	0.141535i
$937$	55.4955			1.81296			0.906479	−	0.422251i	$-0.138760\pi$
$937$	55.4955			1.81296			0.906479	+	0.422251i	$0.138760\pi$
$938$			8.60471i			0.280954i
$939$	16.0826	−	27.8558i	0.524835	−	0.909041i
$940$	−9.47822	+	16.4168i	−0.309145	+	0.535456i
$941$	7.83030	+	4.52083i	0.255261	+	0.147375i	0.622171	−	0.782882i	$-0.286251\pi$
$941$	7.83030	+	4.52083i	0.255261	+	0.147375i	−0.366910	+	0.930256i	$0.619584\pi$
$942$			3.73025i			0.121538i
$943$	3.54356	+	2.04588i	0.115394	+	0.0666229i
$944$			26.7237i			0.869781i
$945$	−4.58258			−0.149071
$946$	3.62614	−	6.28065i	0.117896	−	0.204202i
$947$			21.9844i			0.714396i	0.934029	+	0.357198i	$0.116268\pi$
$947$			21.9844i			0.714396i	−0.934029	+	0.357198i	$0.883732\pi$
$948$	9.47822	−	16.4168i	0.307838	−	0.533192i
$949$	22.5000	−	21.6506i	0.730381	−	0.702809i
$950$	−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
$955$			38.6772i			1.25157i
$956$		−	53.2566i		−	1.72244i
$957$	−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
$962$	−1.62614	+	5.63310i	−0.0524287	+	0.181618i
$963$	5.29129	−	9.16478i	0.170509	−	0.295331i
$964$			31.5384i			1.01578i
$965$	15.1652	−	26.2668i	0.488183	−	0.845559i
$966$	0.704166			0.0226562
$967$			5.29150i			0.170163i	0.996374	+	0.0850816i	$0.0271151\pi$
$967$			5.29150i			0.170163i	−0.996374	+	0.0850816i	$0.972885\pi$
$968$	−1.50000	−	0.866025i	−0.0482118	−	0.0278351i
$969$			5.29150i			0.169988i
$970$	0.0653411	+	0.0377247i	0.00209798	+	0.00121127i
$971$	−6.83485	+	11.8383i	−0.219341	+	0.379909i	−0.954607	−	0.297870i	$-0.903724\pi$
$971$	−6.83485	+	11.8383i	−0.219341	+	0.379909i	0.735266	+	0.677779i	$0.237057\pi$
$972$	−0.895644	+	1.55130i	−0.0287278	+	0.0497580i
$973$			6.83285i			0.219051i
$974$	17.1216			0.548611
$975$	−2.00000	+	6.92820i	−0.0640513	+	0.221880i
$976$	−18.3739	+	31.8245i	−0.588133	+	1.01868i
$977$	−15.1652	+	8.75560i	−0.485176	+	0.280117i	−0.722571	−	0.691297i	$-0.757040\pi$
$977$	−15.1652	+	8.75560i	−0.485176	+	0.280117i	0.237395	+	0.971413i	$0.423706\pi$
$978$	−1.58258			−0.0506052
$979$	−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
$982$	−9.39564	−	5.42458i	−0.299827	−	0.173105i
$983$	15.7087	+	9.06943i	0.501030	+	0.289270i	0.729139	−	0.684366i	$-0.239921\pi$
$983$	15.7087	+	9.06943i	0.501030	+	0.289270i	−0.228109	+	0.973636i	$0.573254\pi$
$984$	−12.1652			−0.387811
$985$	−24.4955			−0.780490
$986$	−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
$990$	2.37386	−	1.37055i	0.0754463	−	0.0435590i
$991$	20.3303	+	35.2131i	0.645813	+	1.11858i	0.984113	+	0.177543i	$0.0568149\pi$
$991$	20.3303	+	35.2131i	0.645813	+	1.11858i	−0.338300	+	0.941038i	$0.609852\pi$
$992$	1.93920	−	3.35880i	0.0615698	−	0.106642i
$993$			15.4931i			0.491659i
$994$			13.7810i			0.437105i
$995$	−9.87386	+	5.70068i	−0.313023	+	0.180724i
$996$	−5.37386	+	3.10260i	−0.170277	+	0.0983097i
$997$	−10.6697			−0.337913			−0.168956	−	0.985624i	$-0.554040\pi$
$997$	−10.6697			−0.337913			−0.168956	+	0.985624i	$0.554040\pi$
$998$	6.93466	+	12.0112i	0.219513	+	0.380207i
$999$			3.55945i			0.112616i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.t.b.4.1	✓	4	1.1	even	1	trivial
273.2.t.b.205.2	yes	4	91.23	even	6	inner
273.2.bl.b.88.1	yes	4	13.10	even	6
273.2.bl.b.121.1	yes	4	7.2	even	3
819.2.bm.d.478.1		4	273.23	odd	6
819.2.bm.d.550.2		4	3.2	odd	2
819.2.do.d.361.2		4	39.23	odd	6
819.2.do.d.667.2		4	21.2	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.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-0.456850i q^{2} +(-0.500000 - 0.866025i) q^{3} +1.79129 q^{4} +(1.50000 - 0.866025i) q^{5} +(-0.395644 + 0.228425i) q^{6} +(-2.29129 - 1.32288i) q^{7} -1.73205i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q-0.456850i q^{2} +(-0.500000 - 0.866025i) q^{3} +1.79129 q^{4} +(1.50000 - 0.866025i) q^{5} +(-0.395644 + 0.228425i) q^{6} +(-2.29129 - 1.32288i) q^{7} -1.73205i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.395644 - 0.685275i) q^{10} +(3.00000 - 1.73205i) 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} +2.79129 q^{16} +1.00000 q^{17} +(0.395644 + 0.228425i) q^{18} +(-4.58258 - 2.64575i) q^{19} +(2.68693 - 1.55130i) q^{20} +2.64575i q^{21} +(-0.791288 - 1.37055i) q^{22} +0.582576 q^{23} +(-1.50000 + 0.866025i) q^{24} +(-1.00000 + 1.73205i) q^{25} +(1.58258 + 0.456850i) q^{26} +1.00000 q^{27} +(-4.10436 - 2.36965i) q^{28} +(3.50000 - 6.06218i) q^{29} +(-0.395644 + 0.685275i) q^{30} +(0.708712 + 0.409175i) q^{31} -4.73930i q^{32} +(-3.00000 - 1.73205i) q^{33} -0.456850i q^{34} -4.58258 q^{35} +(-0.895644 + 1.55130i) q^{36} +3.55945i q^{37} +(-1.20871 + 2.09355i) q^{38} +(3.50000 - 0.866025i) q^{39} +(-1.50000 - 2.59808i) q^{40} +(6.08258 + 3.51178i) q^{41} +1.20871 q^{42} +(2.29129 + 3.96863i) q^{43} +(5.37386 - 3.10260i) q^{44} +1.73205i q^{45} -0.266150i q^{46} +(-5.29129 + 3.05493i) q^{47} +(-1.39564 - 2.41733i) q^{48} +(3.50000 + 6.06218i) q^{49} +(0.791288 + 0.456850i) q^{50} +(-0.500000 - 0.866025i) q^{51} +(-1.79129 + 6.20520i) q^{52} +(-6.08258 + 10.5353i) q^{53} -0.456850i q^{54} +(3.00000 - 5.19615i) q^{55} +(-2.29129 + 3.96863i) q^{56} +5.29150i q^{57} +(-2.76951 - 1.59898i) q^{58} +9.57395i q^{59} +(-2.68693 - 1.55130i) q^{60} +(-6.58258 + 11.4014i) q^{61} +(0.186932 - 0.323775i) q^{62} +(2.29129 - 1.32288i) q^{63} +3.41742 q^{64} +(1.50000 + 6.06218i) q^{65} +(-0.791288 + 1.37055i) q^{66} +(6.16515 - 3.55945i) q^{67} +1.79129 q^{68} +(-0.291288 - 0.504525i) q^{69} +2.09355i q^{70} +(9.87386 - 5.70068i) q^{71} +(1.50000 + 0.866025i) q^{72} +(-7.50000 - 4.33013i) q^{73} +1.62614 q^{74} +2.00000 q^{75} +(-8.20871 - 4.73930i) q^{76} -9.16515 q^{77} +(-0.395644 - 1.59898i) q^{78} +(5.29129 + 9.16478i) q^{79} +(4.18693 - 2.41733i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.60436 - 2.77883i) q^{82} -3.46410i q^{83} +4.73930i q^{84} +(1.50000 - 0.866025i) q^{85} +(1.81307 - 1.04678i) q^{86} -7.00000 q^{87} +(-3.00000 - 5.19615i) q^{88} -15.5885i q^{89} +0.791288 q^{90} +(6.87386 - 6.61438i) q^{91} +1.04356 q^{92} -0.818350i q^{93} +(1.39564 + 2.41733i) q^{94} -9.16515 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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} - 2 q^{4} + 6 q^{5} + 3 q^{6} - 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^3 - 2 * q^4 + 6 * q^5 + 3 * q^6 - 2 * q^9	\( 4 q - 2 q^{3} - 2 q^{4} + 6 q^{5} + 3 q^{6} - 2 q^{9} + 3 q^{10} + 12 q^{11} + q^{12} - 4 q^{13} - 7 q^{14} - 6 q^{15} + 2 q^{16} + 4 q^{17} - 3 q^{18} - 3 q^{20} + 6 q^{22} - 16 q^{23} - 6 q^{24} - 4 q^{25} - 12 q^{26} + 4 q^{27} - 21 q^{28} + 14 q^{29} + 3 q^{30} + 12 q^{31} - 12 q^{33} + q^{36} - 14 q^{38} + 14 q^{39} - 6 q^{40} + 6 q^{41} + 14 q^{42} - 6 q^{44} - 12 q^{47} - q^{48} + 14 q^{49} - 6 q^{50} - 2 q^{51} + 2 q^{52} - 6 q^{53} + 12 q^{55} + 21 q^{58} + 3 q^{60} - 8 q^{61} - 13 q^{62} + 32 q^{64} + 6 q^{65} + 6 q^{66} - 12 q^{67} - 2 q^{68} + 8 q^{69} + 12 q^{71} + 6 q^{72} - 30 q^{73} + 34 q^{74} + 8 q^{75} - 42 q^{76} + 3 q^{78} + 12 q^{79} + 3 q^{80} - 2 q^{81} + 11 q^{82} + 6 q^{85} + 21 q^{86} - 28 q^{87} - 12 q^{88} - 6 q^{90} + 50 q^{92} + q^{94} - 21 q^{96} + 18 q^{97} - 21 q^{98}+O(q^{100}) \) 4 * q - 2 * q^3 - 2 * q^4 + 6 * q^5 + 3 * q^6 - 2 * q^9 + 3 * q^10 + 12 * q^11 + q^12 - 4 * q^13 - 7 * q^14 - 6 * q^15 + 2 * q^16 + 4 * q^17 - 3 * q^18 - 3 * q^20 + 6 * q^22 - 16 * q^23 - 6 * q^24 - 4 * q^25 - 12 * q^26 + 4 * q^27 - 21 * q^28 + 14 * q^29 + 3 * q^30 + 12 * q^31 - 12 * q^33 + q^36 - 14 * q^38 + 14 * q^39 - 6 * q^40 + 6 * q^41 + 14 * q^42 - 6 * q^44 - 12 * q^47 - q^48 + 14 * q^49 - 6 * q^50 - 2 * q^51 + 2 * q^52 - 6 * q^53 + 12 * q^55 + 21 * q^58 + 3 * q^60 - 8 * q^61 - 13 * q^62 + 32 * q^64 + 6 * q^65 + 6 * q^66 - 12 * q^67 - 2 * q^68 + 8 * q^69 + 12 * q^71 + 6 * q^72 - 30 * q^73 + 34 * q^74 + 8 * q^75 - 42 * q^76 + 3 * q^78 + 12 * q^79 + 3 * q^80 - 2 * q^81 + 11 * q^82 + 6 * q^85 + 21 * q^86 - 28 * q^87 - 12 * q^88 - 6 * q^90 + 50 * q^92 + q^94 - 21 * q^96 + 18 * q^97 - 21 * q^98

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