LMFDB - Embedded newform 273.2.bl.a.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:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			121.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	273.121
Dual form			273.2.bl.a.88.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 - 0.866025i) q^{2} -1.00000 q^{3} +(0.500000 - 0.866025i) q^{4} +(3.00000 + 1.73205i) q^{5} +(-1.50000 + 0.866025i) q^{6} +(0.500000 - 2.59808i) q^{7} +1.73205i q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(1.50000 - 0.866025i) q^{2} -1.00000 q^{3} +(0.500000 - 0.866025i) q^{4} +(3.00000 + 1.73205i) q^{5} +(-1.50000 + 0.866025i) q^{6} +(0.500000 - 2.59808i) q^{7} +1.73205i q^{8} +1.00000 q^{9} +6.00000 q^{10} +3.46410i q^{11} +(-0.500000 + 0.866025i) q^{12} +(-2.50000 - 2.59808i) q^{13} +(-1.50000 - 4.33013i) q^{14} +(-3.00000 - 1.73205i) q^{15} +(2.50000 + 4.33013i) q^{16} +(3.00000 - 5.19615i) q^{17} +(1.50000 - 0.866025i) q^{18} -1.73205i q^{19} +(3.00000 - 1.73205i) q^{20} +(-0.500000 + 2.59808i) q^{21} +(3.00000 + 5.19615i) q^{22} +(-3.00000 - 5.19615i) q^{23} -1.73205i q^{24} +(3.50000 + 6.06218i) q^{25} +(-6.00000 - 1.73205i) q^{26} -1.00000 q^{27} +(-2.00000 - 1.73205i) q^{28} +(-3.00000 + 5.19615i) q^{29} -6.00000 q^{30} +(-9.00000 + 5.19615i) q^{31} +(4.50000 + 2.59808i) q^{32} -3.46410i q^{33} -10.3923i q^{34} +(6.00000 - 6.92820i) q^{35} +(0.500000 - 0.866025i) q^{36} +(-1.50000 + 0.866025i) q^{37} +(-1.50000 - 2.59808i) q^{38} +(2.50000 + 2.59808i) q^{39} +(-3.00000 + 5.19615i) q^{40} +(3.00000 + 1.73205i) q^{41} +(1.50000 + 4.33013i) q^{42} +(0.500000 + 0.866025i) q^{43} +(3.00000 + 1.73205i) q^{44} +(3.00000 + 1.73205i) q^{45} +(-9.00000 - 5.19615i) q^{46} +(-9.00000 - 5.19615i) q^{47} +(-2.50000 - 4.33013i) q^{48} +(-6.50000 - 2.59808i) q^{49} +(10.5000 + 6.06218i) q^{50} +(-3.00000 + 5.19615i) q^{51} +(-3.50000 + 0.866025i) q^{52} +(3.00000 + 5.19615i) q^{53} +(-1.50000 + 0.866025i) q^{54} +(-6.00000 + 10.3923i) q^{55} +(4.50000 + 0.866025i) q^{56} +1.73205i q^{57} +10.3923i q^{58} +(-3.00000 - 1.73205i) q^{59} +(-3.00000 + 1.73205i) q^{60} +1.00000 q^{61} +(-9.00000 + 15.5885i) q^{62} +(0.500000 - 2.59808i) q^{63} -1.00000 q^{64} +(-3.00000 - 12.1244i) q^{65} +(-3.00000 - 5.19615i) q^{66} +3.46410i q^{67} +(-3.00000 - 5.19615i) q^{68} +(3.00000 + 5.19615i) q^{69} +(3.00000 - 15.5885i) q^{70} +(3.00000 - 1.73205i) q^{71} +1.73205i q^{72} +(10.5000 - 6.06218i) q^{73} +(-1.50000 + 2.59808i) q^{74} +(-3.50000 - 6.06218i) q^{75} +(-1.50000 - 0.866025i) q^{76} +(9.00000 + 1.73205i) q^{77} +(6.00000 + 1.73205i) q^{78} +(4.00000 - 6.92820i) q^{79} +17.3205i q^{80} +1.00000 q^{81} +6.00000 q^{82} -10.3923i q^{83} +(2.00000 + 1.73205i) q^{84} +(18.0000 - 10.3923i) q^{85} +(1.50000 + 0.866025i) q^{86} +(3.00000 - 5.19615i) q^{87} -6.00000 q^{88} +(9.00000 - 5.19615i) q^{89} +6.00000 q^{90} +(-8.00000 + 5.19615i) q^{91} -6.00000 q^{92} +(9.00000 - 5.19615i) q^{93} -18.0000 q^{94} +(3.00000 - 5.19615i) q^{95} +(-4.50000 - 2.59808i) q^{96} +(-10.5000 + 6.06218i) q^{97} +(-12.0000 + 1.73205i) q^{98} +3.46410i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{2} - 2 q^{3} + q^{4} + 6 q^{5} - 3 q^{6} + q^{7} + 2 q^{9}+O(q^{10}) $ 2 * q + 3 * q^2 - 2 * q^3 + q^4 + 6 * q^5 - 3 * q^6 + q^7 + 2 * q^9	$ 2 q + 3 q^{2} - 2 q^{3} + q^{4} + 6 q^{5} - 3 q^{6} + q^{7} + 2 q^{9} + 12 q^{10} - q^{12} - 5 q^{13} - 3 q^{14} - 6 q^{15} + 5 q^{16} + 6 q^{17} + 3 q^{18} + 6 q^{20} - q^{21} + 6 q^{22} - 6 q^{23} + 7 q^{25} - 12 q^{26} - 2 q^{27} - 4 q^{28} - 6 q^{29} - 12 q^{30} - 18 q^{31} + 9 q^{32} + 12 q^{35} + q^{36} - 3 q^{37} - 3 q^{38} + 5 q^{39} - 6 q^{40} + 6 q^{41} + 3 q^{42} + q^{43} + 6 q^{44} + 6 q^{45} - 18 q^{46} - 18 q^{47} - 5 q^{48} - 13 q^{49} + 21 q^{50} - 6 q^{51} - 7 q^{52} + 6 q^{53} - 3 q^{54} - 12 q^{55} + 9 q^{56} - 6 q^{59} - 6 q^{60} + 2 q^{61} - 18 q^{62} + q^{63} - 2 q^{64} - 6 q^{65} - 6 q^{66} - 6 q^{68} + 6 q^{69} + 6 q^{70} + 6 q^{71} + 21 q^{73} - 3 q^{74} - 7 q^{75} - 3 q^{76} + 18 q^{77} + 12 q^{78} + 8 q^{79} + 2 q^{81} + 12 q^{82} + 4 q^{84} + 36 q^{85} + 3 q^{86} + 6 q^{87} - 12 q^{88} + 18 q^{89} + 12 q^{90} - 16 q^{91} - 12 q^{92} + 18 q^{93} - 36 q^{94} + 6 q^{95} - 9 q^{96} - 21 q^{97} - 24 q^{98}+O(q^{100}) $ 2 * q + 3 * q^2 - 2 * q^3 + q^4 + 6 * q^5 - 3 * q^6 + q^7 + 2 * q^9 + 12 * q^10 - q^12 - 5 * q^13 - 3 * q^14 - 6 * q^15 + 5 * q^16 + 6 * q^17 + 3 * q^18 + 6 * q^20 - q^21 + 6 * q^22 - 6 * q^23 + 7 * q^25 - 12 * q^26 - 2 * q^27 - 4 * q^28 - 6 * q^29 - 12 * q^30 - 18 * q^31 + 9 * q^32 + 12 * q^35 + q^36 - 3 * q^37 - 3 * q^38 + 5 * q^39 - 6 * q^40 + 6 * q^41 + 3 * q^42 + q^43 + 6 * q^44 + 6 * q^45 - 18 * q^46 - 18 * q^47 - 5 * q^48 - 13 * q^49 + 21 * q^50 - 6 * q^51 - 7 * q^52 + 6 * q^53 - 3 * q^54 - 12 * q^55 + 9 * q^56 - 6 * q^59 - 6 * q^60 + 2 * q^61 - 18 * q^62 + q^63 - 2 * q^64 - 6 * q^65 - 6 * q^66 - 6 * q^68 + 6 * q^69 + 6 * q^70 + 6 * q^71 + 21 * q^73 - 3 * q^74 - 7 * q^75 - 3 * q^76 + 18 * q^77 + 12 * q^78 + 8 * q^79 + 2 * q^81 + 12 * q^82 + 4 * q^84 + 36 * q^85 + 3 * q^86 + 6 * q^87 - 12 * q^88 + 18 * q^89 + 12 * q^90 - 16 * q^91 - 12 * q^92 + 18 * q^93 - 36 * q^94 + 6 * q^95 - 9 * q^96 - 21 * q^97 - 24 * 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 $

$2$	1.50000	−	0.866025i	1.06066	−	0.612372i	0.135045	−	0.990839i	$-0.456882\pi$
$2$	1.50000	−	0.866025i	1.06066	−	0.612372i	0.925615	+	0.378467i	$0.123549\pi$
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	3.00000	+	1.73205i	1.34164	+	0.774597i	0.987048	−	0.160424i	$-0.0512862\pi$
$5$	3.00000	+	1.73205i	1.34164	+	0.774597i	0.354593	+	0.935021i	$0.384620\pi$
$6$	−1.50000	+	0.866025i	−0.612372	+	0.353553i
$7$	0.500000	−	2.59808i	0.188982	−	0.981981i
$7$	0.500000	−	2.59808i	0.188982	−	0.981981i
$8$			1.73205i			0.612372i
$9$	1.00000			0.333333
$10$	6.00000			1.89737
$11$			3.46410i			1.04447i	0.852803	+	0.522233i	$0.174901\pi$
$11$			3.46410i			1.04447i	−0.852803	+	0.522233i	$0.825099\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	−2.50000	−	2.59808i	−0.693375	−	0.720577i
$13$	−2.50000	−	2.59808i	−0.693375	−	0.720577i
$14$	−1.50000	−	4.33013i	−0.400892	−	1.15728i
$15$	−3.00000	−	1.73205i	−0.774597	−	0.447214i
$16$	2.50000	+	4.33013i	0.625000	+	1.08253i
$17$	3.00000	−	5.19615i	0.727607	−	1.26025i	−0.230285	−	0.973123i	$-0.573966\pi$
$17$	3.00000	−	5.19615i	0.727607	−	1.26025i	0.957892	−	0.287129i	$-0.0927008\pi$
$18$	1.50000	−	0.866025i	0.353553	−	0.204124i
$19$		−	1.73205i		−	0.397360i	−0.980064	−	0.198680i	$-0.936335\pi$
$19$		−	1.73205i		−	0.397360i	0.980064	−	0.198680i	$-0.0636654\pi$
$20$	3.00000	−	1.73205i	0.670820	−	0.387298i
$21$	−0.500000	+	2.59808i	−0.109109	+	0.566947i
$22$	3.00000	+	5.19615i	0.639602	+	1.10782i
$23$	−3.00000	−	5.19615i	−0.625543	−	1.08347i	−0.988436	−	0.151642i	$-0.951544\pi$
$23$	−3.00000	−	5.19615i	−0.625543	−	1.08347i	0.362892	−	0.931831i	$-0.381789\pi$
$24$		−	1.73205i		−	0.353553i
$25$	3.50000	+	6.06218i	0.700000	+	1.21244i
$26$	−6.00000	−	1.73205i	−1.17670	−	0.339683i
$27$	−1.00000			−0.192450
$28$	−2.00000	−	1.73205i	−0.377964	−	0.327327i
$29$	−3.00000	+	5.19615i	−0.557086	+	0.964901i	0.440652	+	0.897678i	$0.354747\pi$
$29$	−3.00000	+	5.19615i	−0.557086	+	0.964901i	−0.997738	+	0.0672232i	$0.978586\pi$
$30$	−6.00000			−1.09545
$31$	−9.00000	+	5.19615i	−1.61645	+	0.933257i	−0.628619	+	0.777714i	$0.716379\pi$
$31$	−9.00000	+	5.19615i	−1.61645	+	0.933257i	−0.987829	+	0.155543i	$0.950287\pi$
$32$	4.50000	+	2.59808i	0.795495	+	0.459279i
$33$		−	3.46410i		−	0.603023i
$34$		−	10.3923i		−	1.78227i
$35$	6.00000	−	6.92820i	1.01419	−	1.17108i
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	−1.50000	+	0.866025i	−0.246598	+	0.142374i	−0.618206	−	0.786016i	$-0.712140\pi$
$37$	−1.50000	+	0.866025i	−0.246598	+	0.142374i	0.371607	+	0.928390i	$0.378807\pi$
$38$	−1.50000	−	2.59808i	−0.243332	−	0.421464i
$39$	2.50000	+	2.59808i	0.400320	+	0.416025i
$40$	−3.00000	+	5.19615i	−0.474342	+	0.821584i
$41$	3.00000	+	1.73205i	0.468521	+	0.270501i	0.715621	−	0.698489i	$-0.246144\pi$
$41$	3.00000	+	1.73205i	0.468521	+	0.270501i	−0.247099	+	0.968990i	$0.579477\pi$
$42$	1.50000	+	4.33013i	0.231455	+	0.668153i
$43$	0.500000	+	0.866025i	0.0762493	+	0.132068i	0.901629	−	0.432511i	$-0.142372\pi$
$43$	0.500000	+	0.866025i	0.0762493	+	0.132068i	−0.825380	+	0.564578i	$0.809039\pi$
$44$	3.00000	+	1.73205i	0.452267	+	0.261116i
$45$	3.00000	+	1.73205i	0.447214	+	0.258199i
$46$	−9.00000	−	5.19615i	−1.32698	−	0.766131i
$47$	−9.00000	−	5.19615i	−1.31278	−	0.757937i	−0.330228	−	0.943901i	$-0.607126\pi$
$47$	−9.00000	−	5.19615i	−1.31278	−	0.757937i	−0.982556	+	0.185964i	$0.940459\pi$
$48$	−2.50000	−	4.33013i	−0.360844	−	0.625000i
$49$	−6.50000	−	2.59808i	−0.928571	−	0.371154i
$50$	10.5000	+	6.06218i	1.48492	+	0.857321i
$51$	−3.00000	+	5.19615i	−0.420084	+	0.727607i
$52$	−3.50000	+	0.866025i	−0.485363	+	0.120096i
$53$	3.00000	+	5.19615i	0.412082	+	0.713746i	0.995117	−	0.0987002i	$-0.0314685\pi$
$53$	3.00000	+	5.19615i	0.412082	+	0.713746i	−0.583036	+	0.812447i	$0.698135\pi$
$54$	−1.50000	+	0.866025i	−0.204124	+	0.117851i
$55$	−6.00000	+	10.3923i	−0.809040	+	1.40130i
$56$	4.50000	+	0.866025i	0.601338	+	0.115728i
$57$			1.73205i			0.229416i
$58$			10.3923i			1.36458i
$59$	−3.00000	−	1.73205i	−0.390567	−	0.225494i	0.291839	−	0.956467i	$-0.405733\pi$
$59$	−3.00000	−	1.73205i	−0.390567	−	0.225494i	−0.682406	+	0.730974i	$0.739066\pi$
$60$	−3.00000	+	1.73205i	−0.387298	+	0.223607i
$61$	1.00000			0.128037			0.0640184	−	0.997949i	$-0.479608\pi$
$61$	1.00000			0.128037			0.0640184	+	0.997949i	$0.479608\pi$
$62$	−9.00000	+	15.5885i	−1.14300	+	1.97974i
$63$	0.500000	−	2.59808i	0.0629941	−	0.327327i
$64$	−1.00000			−0.125000
$65$	−3.00000	−	12.1244i	−0.372104	−	1.50384i
$66$	−3.00000	−	5.19615i	−0.369274	−	0.639602i
$67$			3.46410i			0.423207i	0.977356	+	0.211604i	$0.0678686\pi$
$67$			3.46410i			0.423207i	−0.977356	+	0.211604i	$0.932131\pi$
$68$	−3.00000	−	5.19615i	−0.363803	−	0.630126i
$69$	3.00000	+	5.19615i	0.361158	+	0.625543i
$70$	3.00000	−	15.5885i	0.358569	−	1.86318i
$71$	3.00000	−	1.73205i	0.356034	−	0.205557i	−0.311305	−	0.950310i	$-0.600766\pi$
$71$	3.00000	−	1.73205i	0.356034	−	0.205557i	0.667340	+	0.744753i	$0.267433\pi$
$72$			1.73205i			0.204124i
$73$	10.5000	−	6.06218i	1.22893	−	0.709524i	0.262126	−	0.965034i	$-0.415577\pi$
$73$	10.5000	−	6.06218i	1.22893	−	0.709524i	0.966807	+	0.255510i	$0.0822432\pi$
$74$	−1.50000	+	2.59808i	−0.174371	+	0.302020i
$75$	−3.50000	−	6.06218i	−0.404145	−	0.700000i
$76$	−1.50000	−	0.866025i	−0.172062	−	0.0993399i
$77$	9.00000	+	1.73205i	1.02565	+	0.197386i
$78$	6.00000	+	1.73205i	0.679366	+	0.196116i
$79$	4.00000	−	6.92820i	0.450035	−	0.779484i	−0.548352	−	0.836247i	$-0.684745\pi$
$79$	4.00000	−	6.92820i	0.450035	−	0.779484i	0.998388	+	0.0567635i	$0.0180781\pi$
$80$			17.3205i			1.93649i
$81$	1.00000			0.111111
$82$	6.00000			0.662589
$83$		−	10.3923i		−	1.14070i	−0.821401	−	0.570352i	$-0.806807\pi$
$83$		−	10.3923i		−	1.14070i	0.821401	−	0.570352i	$-0.193193\pi$
$84$	2.00000	+	1.73205i	0.218218	+	0.188982i
$85$	18.0000	−	10.3923i	1.95237	−	1.12720i
$86$	1.50000	+	0.866025i	0.161749	+	0.0933859i
$87$	3.00000	−	5.19615i	0.321634	−	0.557086i
$88$	−6.00000			−0.639602
$89$	9.00000	−	5.19615i	0.953998	−	0.550791i	0.0596775	−	0.998218i	$-0.480993\pi$
$89$	9.00000	−	5.19615i	0.953998	−	0.550791i	0.894321	+	0.447427i	$0.147659\pi$
$90$	6.00000			0.632456
$91$	−8.00000	+	5.19615i	−0.838628	+	0.544705i
$92$	−6.00000			−0.625543
$93$	9.00000	−	5.19615i	0.933257	−	0.538816i
$94$	−18.0000			−1.85656
$95$	3.00000	−	5.19615i	0.307794	−	0.533114i
$96$	−4.50000	−	2.59808i	−0.459279	−	0.265165i
$97$	−10.5000	+	6.06218i	−1.06611	+	0.615521i	−0.927117	−	0.374772i	$-0.877721\pi$
$97$	−10.5000	+	6.06218i	−1.06611	+	0.615521i	−0.138996	+	0.990293i	$0.544388\pi$
$98$	−12.0000	+	1.73205i	−1.21218	+	0.174964i
$99$			3.46410i			0.348155i
$100$	7.00000			0.700000
$101$	12.0000			1.19404			0.597022	−	0.802225i	$-0.296350\pi$
$101$	12.0000			1.19404			0.597022	+	0.802225i	$0.296350\pi$
$102$			10.3923i			1.02899i
$103$	−5.50000	+	9.52628i	−0.541931	+	0.938652i	0.456862	+	0.889538i	$0.348973\pi$
$103$	−5.50000	+	9.52628i	−0.541931	+	0.938652i	−0.998793	+	0.0491146i	$0.984360\pi$
$104$	4.50000	−	4.33013i	0.441261	−	0.424604i
$105$	−6.00000	+	6.92820i	−0.585540	+	0.676123i
$106$	9.00000	+	5.19615i	0.874157	+	0.504695i
$107$	3.00000	+	5.19615i	0.290021	+	0.502331i	0.973814	−	0.227345i	$-0.0730044\pi$
$107$	3.00000	+	5.19615i	0.290021	+	0.502331i	−0.683793	+	0.729676i	$0.739671\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	−10.5000	+	6.06218i	−1.00572	+	0.580651i	−0.909935	−	0.414751i	$-0.863869\pi$
$109$	−10.5000	+	6.06218i	−1.00572	+	0.580651i	−0.0957826	+	0.995402i	$0.530535\pi$
$110$			20.7846i			1.98173i
$111$	1.50000	−	0.866025i	0.142374	−	0.0821995i
$112$	12.5000	−	4.33013i	1.18114	−	0.409159i
$113$	−6.00000	−	10.3923i	−0.564433	−	0.977626i	−0.997102	−	0.0760733i	$-0.975762\pi$
$113$	−6.00000	−	10.3923i	−0.564433	−	0.977626i	0.432670	−	0.901553i	$-0.357572\pi$
$114$	1.50000	+	2.59808i	0.140488	+	0.243332i
$115$		−	20.7846i		−	1.93817i
$116$	3.00000	+	5.19615i	0.278543	+	0.482451i
$117$	−2.50000	−	2.59808i	−0.231125	−	0.240192i
$118$	−6.00000			−0.552345
$119$	−12.0000	−	10.3923i	−1.10004	−	0.952661i
$120$	3.00000	−	5.19615i	0.273861	−	0.474342i
$121$	−1.00000			−0.0909091
$122$	1.50000	−	0.866025i	0.135804	−	0.0784063i
$123$	−3.00000	−	1.73205i	−0.270501	−	0.156174i
$124$			10.3923i			0.933257i
$125$			6.92820i			0.619677i
$126$	−1.50000	−	4.33013i	−0.133631	−	0.385758i
$127$	5.50000	−	9.52628i	0.488046	−	0.845321i	−0.511859	−	0.859069i	$-0.671043\pi$
$127$	5.50000	−	9.52628i	0.488046	−	0.845321i	0.999905	+	0.0137486i	$0.00437646\pi$
$128$	−10.5000	+	6.06218i	−0.928078	+	0.535826i
$129$	−0.500000	−	0.866025i	−0.0440225	−	0.0762493i
$130$	−15.0000	−	15.5885i	−1.31559	−	1.36720i
$131$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$131$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$132$	−3.00000	−	1.73205i	−0.261116	−	0.150756i
$133$	−4.50000	−	0.866025i	−0.390199	−	0.0750939i
$134$	3.00000	+	5.19615i	0.259161	+	0.448879i
$135$	−3.00000	−	1.73205i	−0.258199	−	0.149071i
$136$	9.00000	+	5.19615i	0.771744	+	0.445566i
$137$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$137$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$138$	9.00000	+	5.19615i	0.766131	+	0.442326i
$139$	2.00000	+	3.46410i	0.169638	+	0.293821i	0.938293	−	0.345843i	$-0.112407\pi$
$139$	2.00000	+	3.46410i	0.169638	+	0.293821i	−0.768655	+	0.639664i	$0.779074\pi$
$140$	−3.00000	−	8.66025i	−0.253546	−	0.731925i
$141$	9.00000	+	5.19615i	0.757937	+	0.437595i
$142$	3.00000	−	5.19615i	0.251754	−	0.436051i
$143$	9.00000	−	8.66025i	0.752618	−	0.724207i
$144$	2.50000	+	4.33013i	0.208333	+	0.360844i
$145$	−18.0000	+	10.3923i	−1.49482	+	0.863034i
$146$	10.5000	−	18.1865i	0.868986	−	1.50513i
$147$	6.50000	+	2.59808i	0.536111	+	0.214286i
$148$			1.73205i			0.142374i
$149$			10.3923i			0.851371i	0.904871	+	0.425685i	$0.139967\pi$
$149$			10.3923i			0.851371i	−0.904871	+	0.425685i	$0.860033\pi$
$150$	−10.5000	−	6.06218i	−0.857321	−	0.494975i
$151$	3.00000	−	1.73205i	0.244137	−	0.140952i	−0.372940	−	0.927855i	$-0.621650\pi$
$151$	3.00000	−	1.73205i	0.244137	−	0.140952i	0.617076	+	0.786903i	$0.288317\pi$
$152$	3.00000			0.243332
$153$	3.00000	−	5.19615i	0.242536	−	0.420084i
$154$	15.0000	−	5.19615i	1.20873	−	0.418718i
$155$	−36.0000			−2.89159
$156$	3.50000	−	0.866025i	0.280224	−	0.0693375i
$157$	6.50000	+	11.2583i	0.518756	+	0.898513i	0.999762	+	0.0217953i	$0.00693820\pi$
$157$	6.50000	+	11.2583i	0.518756	+	0.898513i	−0.481006	+	0.876717i	$0.659728\pi$
$158$		−	13.8564i		−	1.10236i
$159$	−3.00000	−	5.19615i	−0.237915	−	0.412082i
$160$	9.00000	+	15.5885i	0.711512	+	1.23238i
$161$	−15.0000	+	5.19615i	−1.18217	+	0.409514i
$162$	1.50000	−	0.866025i	0.117851	−	0.0680414i
$163$			5.19615i			0.406994i	0.979076	+	0.203497i	$0.0652307\pi$
$163$			5.19615i			0.406994i	−0.979076	+	0.203497i	$0.934769\pi$
$164$	3.00000	−	1.73205i	0.234261	−	0.135250i
$165$	6.00000	−	10.3923i	0.467099	−	0.809040i
$166$	−9.00000	−	15.5885i	−0.698535	−	1.20990i
$167$	18.0000	+	10.3923i	1.39288	+	0.804181i	0.993633	−	0.112662i	$-0.0359378\pi$
$167$	18.0000	+	10.3923i	1.39288	+	0.804181i	0.399248	+	0.916843i	$0.369271\pi$
$168$	−4.50000	−	0.866025i	−0.347183	−	0.0668153i
$169$	−0.500000	+	12.9904i	−0.0384615	+	0.999260i
$170$	18.0000	−	31.1769i	1.38054	−	2.39116i
$171$		−	1.73205i		−	0.132453i
$172$	1.00000			0.0762493
$173$	−12.0000			−0.912343			−0.456172	−	0.889892i	$-0.650780\pi$
$173$	−12.0000			−0.912343			−0.456172	+	0.889892i	$0.650780\pi$
$174$		−	10.3923i		−	0.787839i
$175$	17.5000	−	6.06218i	1.32288	−	0.458258i
$176$	−15.0000	+	8.66025i	−1.13067	+	0.652791i
$177$	3.00000	+	1.73205i	0.225494	+	0.130189i
$178$	9.00000	−	15.5885i	0.674579	−	1.16840i
$179$	24.0000			1.79384			0.896922	−	0.442189i	$-0.145798\pi$
$179$	24.0000			1.79384			0.896922	+	0.442189i	$0.145798\pi$
$180$	3.00000	−	1.73205i	0.223607	−	0.129099i
$181$	5.00000			0.371647			0.185824	−	0.982583i	$-0.440505\pi$
$181$	5.00000			0.371647			0.185824	+	0.982583i	$0.440505\pi$
$182$	−7.50000	+	14.7224i	−0.555937	+	1.09130i
$183$	−1.00000			−0.0739221
$184$	9.00000	−	5.19615i	0.663489	−	0.383065i
$185$	−6.00000			−0.441129
$186$	9.00000	−	15.5885i	0.659912	−	1.14300i
$187$	18.0000	+	10.3923i	1.31629	+	0.759961i
$188$	−9.00000	+	5.19615i	−0.656392	+	0.378968i
$189$	−0.500000	+	2.59808i	−0.0363696	+	0.188982i
$190$		−	10.3923i		−	0.753937i
$191$	−6.00000			−0.434145			−0.217072	−	0.976156i	$-0.569651\pi$
$191$	−6.00000			−0.434145			−0.217072	+	0.976156i	$0.569651\pi$
$192$	1.00000			0.0721688
$193$			12.1244i			0.872730i	0.899770	+	0.436365i	$0.143734\pi$
$193$			12.1244i			0.872730i	−0.899770	+	0.436365i	$0.856266\pi$
$194$	−10.5000	+	18.1865i	−0.753856	+	1.30572i
$195$	3.00000	+	12.1244i	0.214834	+	0.868243i
$196$	−5.50000	+	4.33013i	−0.392857	+	0.309295i
$197$	−3.00000	−	1.73205i	−0.213741	−	0.123404i	0.389308	−	0.921108i	$-0.372714\pi$
$197$	−3.00000	−	1.73205i	−0.213741	−	0.123404i	−0.603049	+	0.797704i	$0.706048\pi$
$198$	3.00000	+	5.19615i	0.213201	+	0.369274i
$199$	5.50000	−	9.52628i	0.389885	−	0.675300i	−0.602549	−	0.798082i	$-0.705848\pi$
$199$	5.50000	−	9.52628i	0.389885	−	0.675300i	0.992434	+	0.122782i	$0.0391815\pi$
$200$	−10.5000	+	6.06218i	−0.742462	+	0.428661i
$201$		−	3.46410i		−	0.244339i
$202$	18.0000	−	10.3923i	1.26648	−	0.731200i
$203$	12.0000	+	10.3923i	0.842235	+	0.729397i
$204$	3.00000	+	5.19615i	0.210042	+	0.363803i
$205$	6.00000	+	10.3923i	0.419058	+	0.725830i
$206$			19.0526i			1.32745i
$207$	−3.00000	−	5.19615i	−0.208514	−	0.361158i
$208$	5.00000	−	17.3205i	0.346688	−	1.20096i
$209$	6.00000			0.415029
$210$	−3.00000	+	15.5885i	−0.207020	+	1.07571i
$211$	2.50000	−	4.33013i	0.172107	−	0.298098i	−0.767049	−	0.641588i	$-0.778276\pi$
$211$	2.50000	−	4.33013i	0.172107	−	0.298098i	0.939156	+	0.343490i	$0.111609\pi$
$212$	6.00000			0.412082
$213$	−3.00000	+	1.73205i	−0.205557	+	0.118678i
$214$	9.00000	+	5.19615i	0.615227	+	0.355202i
$215$			3.46410i			0.236250i
$216$		−	1.73205i		−	0.117851i
$217$	9.00000	+	25.9808i	0.610960	+	1.76369i
$218$	−10.5000	+	18.1865i	−0.711150	+	1.23175i
$219$	−10.5000	+	6.06218i	−0.709524	+	0.409644i
$220$	6.00000	+	10.3923i	0.404520	+	0.700649i
$221$	−21.0000	+	5.19615i	−1.41261	+	0.349531i
$222$	1.50000	−	2.59808i	0.100673	−	0.174371i
$223$	15.0000	+	8.66025i	1.00447	+	0.579934i	0.909569	−	0.415553i	$-0.136412\pi$
$223$	15.0000	+	8.66025i	1.00447	+	0.579934i	0.0949052	+	0.995486i	$0.469745\pi$
$224$	9.00000	−	10.3923i	0.601338	−	0.694365i
$225$	3.50000	+	6.06218i	0.233333	+	0.404145i
$226$	−18.0000	−	10.3923i	−1.19734	−	0.691286i
$227$	6.00000	+	3.46410i	0.398234	+	0.229920i	0.685722	−	0.727864i	$-0.259487\pi$
$227$	6.00000	+	3.46410i	0.398234	+	0.229920i	−0.287488	+	0.957784i	$0.592820\pi$
$228$	1.50000	+	0.866025i	0.0993399	+	0.0573539i
$229$	−4.50000	−	2.59808i	−0.297368	−	0.171686i	0.343892	−	0.939009i	$-0.388255\pi$
$229$	−4.50000	−	2.59808i	−0.297368	−	0.171686i	−0.641260	+	0.767324i	$0.721588\pi$
$230$	−18.0000	−	31.1769i	−1.18688	−	2.05574i
$231$	−9.00000	−	1.73205i	−0.592157	−	0.113961i
$232$	−9.00000	−	5.19615i	−0.590879	−	0.341144i
$233$	6.00000	−	10.3923i	0.393073	−	0.680823i	−0.599780	−	0.800165i	$-0.704745\pi$
$233$	6.00000	−	10.3923i	0.393073	−	0.680823i	0.992853	+	0.119342i	$0.0380786\pi$
$234$	−6.00000	−	1.73205i	−0.392232	−	0.113228i
$235$	−18.0000	−	31.1769i	−1.17419	−	2.03376i
$236$	−3.00000	+	1.73205i	−0.195283	+	0.112747i
$237$	−4.00000	+	6.92820i	−0.259828	+	0.450035i
$238$	−27.0000	−	5.19615i	−1.75015	−	0.336817i
$239$			20.7846i			1.34444i	0.740349	+	0.672222i	$0.234660\pi$
$239$			20.7846i			1.34444i	−0.740349	+	0.672222i	$0.765340\pi$
$240$		−	17.3205i		−	1.11803i
$241$	6.00000	+	3.46410i	0.386494	+	0.223142i	0.680640	−	0.732618i	$-0.261702\pi$
$241$	6.00000	+	3.46410i	0.386494	+	0.223142i	−0.294146	+	0.955761i	$0.595035\pi$
$242$	−1.50000	+	0.866025i	−0.0964237	+	0.0556702i
$243$	−1.00000			−0.0641500
$244$	0.500000	−	0.866025i	0.0320092	−	0.0554416i
$245$	−15.0000	−	19.0526i	−0.958315	−	1.21722i
$246$	−6.00000			−0.382546
$247$	−4.50000	+	4.33013i	−0.286328	+	0.275519i
$248$	−9.00000	−	15.5885i	−0.571501	−	0.989868i
$249$			10.3923i			0.658586i
$250$	6.00000	+	10.3923i	0.379473	+	0.657267i
$251$	−3.00000	−	5.19615i	−0.189358	−	0.327978i	0.755678	−	0.654943i	$-0.227307\pi$
$251$	−3.00000	−	5.19615i	−0.189358	−	0.327978i	−0.945036	+	0.326965i	$0.893974\pi$
$252$	−2.00000	−	1.73205i	−0.125988	−	0.109109i
$253$	18.0000	−	10.3923i	1.13165	−	0.653359i
$254$		−	19.0526i		−	1.19546i
$255$	−18.0000	+	10.3923i	−1.12720	+	0.650791i
$256$	−9.50000	+	16.4545i	−0.593750	+	1.02841i
$257$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$257$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$258$	−1.50000	−	0.866025i	−0.0933859	−	0.0539164i
$259$	1.50000	+	4.33013i	0.0932055	+	0.269061i
$260$	−12.0000	−	3.46410i	−0.744208	−	0.214834i
$261$	−3.00000	+	5.19615i	−0.185695	+	0.321634i
$262$		0			0
$263$		0			0			−	1.00000i	$-0.5\pi$
$263$		0			0				1.00000i	$0.5\pi$
$264$	6.00000			0.369274
$265$			20.7846i			1.27679i
$266$	−7.50000	+	2.59808i	−0.459855	+	0.159298i
$267$	−9.00000	+	5.19615i	−0.550791	+	0.317999i
$268$	3.00000	+	1.73205i	0.183254	+	0.105802i
$269$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$269$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$270$	−6.00000			−0.365148
$271$	−10.5000	+	6.06218i	−0.637830	+	0.368251i	−0.783778	−	0.621041i	$-0.786710\pi$
$271$	−10.5000	+	6.06218i	−0.637830	+	0.368251i	0.145948	+	0.989292i	$0.453377\pi$
$272$	30.0000			1.81902
$273$	8.00000	−	5.19615i	0.484182	−	0.314485i
$274$		0			0
$275$	−21.0000	+	12.1244i	−1.26635	+	0.731126i
$276$	6.00000			0.361158
$277$	9.50000	−	16.4545i	0.570800	−	0.988654i	−0.425684	−	0.904872i	$-0.639967\pi$
$277$	9.50000	−	16.4545i	0.570800	−	0.988654i	0.996484	−	0.0837823i	$-0.0267000\pi$
$278$	6.00000	+	3.46410i	0.359856	+	0.207763i
$279$	−9.00000	+	5.19615i	−0.538816	+	0.311086i
$280$	12.0000	+	10.3923i	0.717137	+	0.621059i
$281$		−	20.7846i		−	1.23991i	−0.784639	−	0.619953i	$-0.787152\pi$
$281$		−	20.7846i		−	1.23991i	0.784639	−	0.619953i	$-0.212848\pi$
$282$	18.0000			1.07188
$283$	−23.0000			−1.36721			−0.683604	−	0.729853i	$-0.739588\pi$
$283$	−23.0000			−1.36721			−0.683604	+	0.729853i	$0.739588\pi$
$284$		−	3.46410i		−	0.205557i
$285$	−3.00000	+	5.19615i	−0.177705	+	0.307794i
$286$	6.00000	−	20.7846i	0.354787	−	1.22902i
$287$	6.00000	−	6.92820i	0.354169	−	0.408959i
$288$	4.50000	+	2.59808i	0.265165	+	0.153093i
$289$	−9.50000	−	16.4545i	−0.558824	−	0.967911i
$290$	−18.0000	+	31.1769i	−1.05700	+	1.83077i
$291$	10.5000	−	6.06218i	0.615521	−	0.355371i
$292$		−	12.1244i		−	0.709524i
$293$	−15.0000	+	8.66025i	−0.876309	+	0.505937i	−0.869440	−	0.494039i	$-0.835520\pi$
$293$	−15.0000	+	8.66025i	−0.876309	+	0.505937i	−0.00686959	+	0.999976i	$0.502187\pi$
$294$	12.0000	−	1.73205i	0.699854	−	0.101015i
$295$	−6.00000	−	10.3923i	−0.349334	−	0.605063i
$296$	−1.50000	−	2.59808i	−0.0871857	−	0.151010i
$297$		−	3.46410i		−	0.201008i
$298$	9.00000	+	15.5885i	0.521356	+	0.903015i
$299$	−6.00000	+	20.7846i	−0.346989	+	1.20201i
$300$	−7.00000			−0.404145
$301$	2.50000	−	0.866025i	0.144098	−	0.0499169i
$302$	3.00000	−	5.19615i	0.172631	−	0.299005i
$303$	−12.0000			−0.689382
$304$	7.50000	−	4.33013i	0.430155	−	0.248350i
$305$	3.00000	+	1.73205i	0.171780	+	0.0991769i
$306$		−	10.3923i		−	0.594089i
$307$			17.3205i			0.988534i	0.869310	+	0.494267i	$0.164563\pi$
$307$			17.3205i			0.988534i	−0.869310	+	0.494267i	$0.835437\pi$
$308$	6.00000	−	6.92820i	0.341882	−	0.394771i
$309$	5.50000	−	9.52628i	0.312884	−	0.541931i
$310$	−54.0000	+	31.1769i	−3.06699	+	1.77073i
$311$	9.00000	+	15.5885i	0.510343	+	0.883940i	0.999928	+	0.0119847i	$0.00381495\pi$
$311$	9.00000	+	15.5885i	0.510343	+	0.883940i	−0.489585	+	0.871956i	$0.662852\pi$
$312$	−4.50000	+	4.33013i	−0.254762	+	0.245145i
$313$	−0.500000	+	0.866025i	−0.0282617	+	0.0489506i	−0.879810	−	0.475325i	$-0.842331\pi$
$313$	−0.500000	+	0.866025i	−0.0282617	+	0.0489506i	0.851549	+	0.524276i	$0.175664\pi$
$314$	19.5000	+	11.2583i	1.10045	+	0.635344i
$315$	6.00000	−	6.92820i	0.338062	−	0.390360i
$316$	−4.00000	−	6.92820i	−0.225018	−	0.389742i
$317$	21.0000	+	12.1244i	1.17948	+	0.680972i	0.955894	−	0.293713i	$-0.0948910\pi$
$317$	21.0000	+	12.1244i	1.17948	+	0.680972i	0.223584	+	0.974685i	$0.428224\pi$
$318$	−9.00000	−	5.19615i	−0.504695	−	0.291386i
$319$	−18.0000	−	10.3923i	−1.00781	−	0.581857i
$320$	−3.00000	−	1.73205i	−0.167705	−	0.0968246i
$321$	−3.00000	−	5.19615i	−0.167444	−	0.290021i
$322$	−18.0000	+	20.7846i	−1.00310	+	1.15828i
$323$	−9.00000	−	5.19615i	−0.500773	−	0.289122i
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$	7.00000	−	24.2487i	0.388290	−	1.34508i
$326$	4.50000	+	7.79423i	0.249232	+	0.431682i
$327$	10.5000	−	6.06218i	0.580651	−	0.335239i
$328$	−3.00000	+	5.19615i	−0.165647	+	0.286910i
$329$	−18.0000	+	20.7846i	−0.992372	+	1.14589i
$330$		−	20.7846i		−	1.14416i
$331$		−	5.19615i		−	0.285606i	−0.989751	−	0.142803i	$-0.954388\pi$
$331$		−	5.19615i		−	0.285606i	0.989751	−	0.142803i	$-0.0456116\pi$
$332$	−9.00000	−	5.19615i	−0.493939	−	0.285176i
$333$	−1.50000	+	0.866025i	−0.0821995	+	0.0474579i
$334$	36.0000			1.96983
$335$	−6.00000	+	10.3923i	−0.327815	+	0.567792i
$336$	−12.5000	+	4.33013i	−0.681931	+	0.236228i
$337$	−29.0000			−1.57973			−0.789865	−	0.613280i	$-0.789850\pi$
$337$	−29.0000			−1.57973			−0.789865	+	0.613280i	$0.789850\pi$
$338$	10.5000	+	19.9186i	0.571125	+	1.08343i
$339$	6.00000	+	10.3923i	0.325875	+	0.564433i
$340$		−	20.7846i		−	1.12720i
$341$	−18.0000	−	31.1769i	−0.974755	−	1.68832i
$342$	−1.50000	−	2.59808i	−0.0811107	−	0.140488i
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$	−1.50000	+	0.866025i	−0.0808746	+	0.0466930i
$345$			20.7846i			1.11901i
$346$	−18.0000	+	10.3923i	−0.967686	+	0.558694i
$347$	9.00000	−	15.5885i	0.483145	−	0.836832i	−0.516667	−	0.856186i	$-0.672828\pi$
$347$	9.00000	−	15.5885i	0.483145	−	0.836832i	0.999813	+	0.0193540i	$0.00616095\pi$
$348$	−3.00000	−	5.19615i	−0.160817	−	0.278543i
$349$	−28.5000	−	16.4545i	−1.52557	−	0.880788i	−0.999540	−	0.0303222i	$-0.990347\pi$
$349$	−28.5000	−	16.4545i	−1.52557	−	0.880788i	−0.526030	−	0.850466i	$-0.676320\pi$
$350$	21.0000	−	24.2487i	1.12250	−	1.29615i
$351$	2.50000	+	2.59808i	0.133440	+	0.138675i
$352$	−9.00000	+	15.5885i	−0.479702	+	0.830868i
$353$			13.8564i			0.737502i	0.929528	+	0.368751i	$0.120215\pi$
$353$			13.8564i			0.737502i	−0.929528	+	0.368751i	$0.879785\pi$
$354$	6.00000			0.318896
$355$	12.0000			0.636894
$356$		−	10.3923i		−	0.550791i
$357$	12.0000	+	10.3923i	0.635107	+	0.550019i
$358$	36.0000	−	20.7846i	1.90266	−	1.09850i
$359$	9.00000	+	5.19615i	0.475002	+	0.274242i	0.718331	−	0.695701i	$-0.244906\pi$
$359$	9.00000	+	5.19615i	0.475002	+	0.274242i	−0.243329	+	0.969944i	$0.578240\pi$
$360$	−3.00000	+	5.19615i	−0.158114	+	0.273861i
$361$	16.0000			0.842105
$362$	7.50000	−	4.33013i	0.394191	−	0.227586i
$363$	1.00000			0.0524864
$364$	0.500000	+	9.52628i	0.0262071	+	0.499313i
$365$	42.0000			2.19838
$366$	−1.50000	+	0.866025i	−0.0784063	+	0.0452679i
$367$	−19.0000			−0.991792			−0.495896	−	0.868382i	$-0.665160\pi$
$367$	−19.0000			−0.991792			−0.495896	+	0.868382i	$0.665160\pi$
$368$	15.0000	−	25.9808i	0.781929	−	1.35434i
$369$	3.00000	+	1.73205i	0.156174	+	0.0901670i
$370$	−9.00000	+	5.19615i	−0.467888	+	0.270135i
$371$	15.0000	−	5.19615i	0.778761	−	0.269771i
$372$		−	10.3923i		−	0.538816i
$373$	22.0000			1.13912			0.569558	−	0.821951i	$-0.307114\pi$
$373$	22.0000			1.13912			0.569558	+	0.821951i	$0.307114\pi$
$374$	36.0000			1.86152
$375$		−	6.92820i		−	0.357771i
$376$	9.00000	−	15.5885i	0.464140	−	0.803913i
$377$	21.0000	−	5.19615i	1.08156	−	0.267615i
$378$	1.50000	+	4.33013i	0.0771517	+	0.222718i
$379$	−9.00000	−	5.19615i	−0.462299	−	0.266908i	0.250711	−	0.968062i	$-0.419335\pi$
$379$	−9.00000	−	5.19615i	−0.462299	−	0.266908i	−0.713010	+	0.701153i	$0.752669\pi$
$380$	−3.00000	−	5.19615i	−0.153897	−	0.266557i
$381$	−5.50000	+	9.52628i	−0.281774	+	0.488046i
$382$	−9.00000	+	5.19615i	−0.460480	+	0.265858i
$383$		−	13.8564i		−	0.708029i	−0.935240	−	0.354015i	$-0.884816\pi$
$383$		−	13.8564i		−	0.708029i	0.935240	−	0.354015i	$-0.115184\pi$
$384$	10.5000	−	6.06218i	0.535826	−	0.309359i
$385$	24.0000	+	20.7846i	1.22315	+	1.05928i
$386$	10.5000	+	18.1865i	0.534436	+	0.925670i
$387$	0.500000	+	0.866025i	0.0254164	+	0.0440225i
$388$			12.1244i			0.615521i
$389$	−3.00000	−	5.19615i	−0.152106	−	0.263455i	0.779895	−	0.625910i	$-0.215272\pi$
$389$	−3.00000	−	5.19615i	−0.152106	−	0.263455i	−0.932002	+	0.362454i	$0.881939\pi$
$390$	15.0000	+	15.5885i	0.759555	+	0.789352i
$391$	−36.0000			−1.82060
$392$	4.50000	−	11.2583i	0.227284	−	0.568632i
$393$		0			0
$394$	−6.00000			−0.302276
$395$	24.0000	−	13.8564i	1.20757	−	0.697191i
$396$	3.00000	+	1.73205i	0.150756	+	0.0870388i
$397$		−	1.73205i		−	0.0869291i	−0.999055	−	0.0434646i	$-0.986160\pi$
$397$		−	1.73205i		−	0.0869291i	0.999055	−	0.0434646i	$-0.0138396\pi$
$398$		−	19.0526i		−	0.955018i
$399$	4.50000	+	0.866025i	0.225282	+	0.0433555i
$400$	−17.5000	+	30.3109i	−0.875000	+	1.51554i
$401$	24.0000	−	13.8564i	1.19850	−	0.691956i	0.238282	−	0.971196i	$-0.423416\pi$
$401$	24.0000	−	13.8564i	1.19850	−	0.691956i	0.960221	+	0.279240i	$0.0900826\pi$
$402$	−3.00000	−	5.19615i	−0.149626	−	0.259161i
$403$	36.0000	+	10.3923i	1.79329	+	0.517678i
$404$	6.00000	−	10.3923i	0.298511	−	0.517036i
$405$	3.00000	+	1.73205i	0.149071	+	0.0860663i
$406$	27.0000	+	5.19615i	1.33999	+	0.257881i
$407$	−3.00000	−	5.19615i	−0.148704	−	0.257564i
$408$	−9.00000	−	5.19615i	−0.445566	−	0.257248i
$409$	−28.5000	−	16.4545i	−1.40923	−	0.813622i	−0.413920	−	0.910313i	$-0.635841\pi$
$409$	−28.5000	−	16.4545i	−1.40923	−	0.813622i	−0.995314	+	0.0966915i	$0.969174\pi$
$410$	18.0000	+	10.3923i	0.888957	+	0.513239i
$411$		0			0
$412$	5.50000	+	9.52628i	0.270966	+	0.469326i
$413$	−6.00000	+	6.92820i	−0.295241	+	0.340915i
$414$	−9.00000	−	5.19615i	−0.442326	−	0.255377i
$415$	18.0000	−	31.1769i	0.883585	−	1.53041i
$416$	−4.50000	−	18.1865i	−0.220631	−	0.891668i
$417$	−2.00000	−	3.46410i	−0.0979404	−	0.169638i
$418$	9.00000	−	5.19615i	0.440204	−	0.254152i
$419$	−12.0000	+	20.7846i	−0.586238	+	1.01539i	0.408481	+	0.912767i	$0.366058\pi$
$419$	−12.0000	+	20.7846i	−0.586238	+	1.01539i	−0.994720	+	0.102628i	$0.967275\pi$
$420$	3.00000	+	8.66025i	0.146385	+	0.422577i
$421$		−	6.92820i		−	0.337660i	−0.985645	−	0.168830i	$-0.946001\pi$
$421$		−	6.92820i		−	0.337660i	0.985645	−	0.168830i	$-0.0539989\pi$
$422$		−	8.66025i		−	0.421575i
$423$	−9.00000	−	5.19615i	−0.437595	−	0.252646i
$424$	−9.00000	+	5.19615i	−0.437079	+	0.252347i
$425$	42.0000			2.03730
$426$	−3.00000	+	5.19615i	−0.145350	+	0.251754i
$427$	0.500000	−	2.59808i	0.0241967	−	0.125730i
$428$	6.00000			0.290021
$429$	−9.00000	+	8.66025i	−0.434524	+	0.418121i
$430$	3.00000	+	5.19615i	0.144673	+	0.250581i
$431$			17.3205i			0.834300i	0.908838	+	0.417150i	$0.136971\pi$
$431$			17.3205i			0.834300i	−0.908838	+	0.417150i	$0.863029\pi$
$432$	−2.50000	−	4.33013i	−0.120281	−	0.208333i
$433$	−17.0000	−	29.4449i	−0.816968	−	1.41503i	−0.907906	−	0.419173i	$-0.862320\pi$
$433$	−17.0000	−	29.4449i	−0.816968	−	1.41503i	0.0909384	−	0.995857i	$-0.471013\pi$
$434$	36.0000	+	31.1769i	1.72806	+	1.49654i
$435$	18.0000	−	10.3923i	0.863034	−	0.498273i
$436$			12.1244i			0.580651i
$437$	−9.00000	+	5.19615i	−0.430528	+	0.248566i
$438$	−10.5000	+	18.1865i	−0.501709	+	0.868986i
$439$	−8.50000	−	14.7224i	−0.405683	−	0.702663i	0.588718	−	0.808339i	$-0.299633\pi$
$439$	−8.50000	−	14.7224i	−0.405683	−	0.702663i	−0.994401	+	0.105675i	$0.966300\pi$
$440$	−18.0000	−	10.3923i	−0.858116	−	0.495434i
$441$	−6.50000	−	2.59808i	−0.309524	−	0.123718i
$442$	−27.0000	+	25.9808i	−1.28426	+	1.23578i
$443$	12.0000	−	20.7846i	0.570137	−	0.987507i	−0.426414	−	0.904528i	$-0.640223\pi$
$443$	12.0000	−	20.7846i	0.570137	−	0.987507i	0.996551	−	0.0829786i	$-0.0264433\pi$
$444$		−	1.73205i		−	0.0821995i
$445$	36.0000			1.70656
$446$	30.0000			1.42054
$447$		−	10.3923i		−	0.491539i
$448$	−0.500000	+	2.59808i	−0.0236228	+	0.122748i
$449$	−9.00000	+	5.19615i	−0.424736	+	0.245222i	−0.697102	−	0.716972i	$-0.745527\pi$
$449$	−9.00000	+	5.19615i	−0.424736	+	0.245222i	0.272365	+	0.962194i	$0.412194\pi$
$450$	10.5000	+	6.06218i	0.494975	+	0.285774i
$451$	−6.00000	+	10.3923i	−0.282529	+	0.489355i
$452$	−12.0000			−0.564433
$453$	−3.00000	+	1.73205i	−0.140952	+	0.0813788i
$454$	12.0000			0.563188
$455$	−33.0000	+	1.73205i	−1.54706	+	0.0811998i
$456$	−3.00000			−0.140488
$457$	−6.00000	+	3.46410i	−0.280668	+	0.162044i	−0.633726	−	0.773558i	$-0.718475\pi$
$457$	−6.00000	+	3.46410i	−0.280668	+	0.162044i	0.353058	+	0.935602i	$0.385142\pi$
$458$	−9.00000			−0.420542
$459$	−3.00000	+	5.19615i	−0.140028	+	0.242536i
$460$	−18.0000	−	10.3923i	−0.839254	−	0.484544i
$461$	−3.00000	+	1.73205i	−0.139724	+	0.0806696i	−0.568232	−	0.822868i	$-0.692373\pi$
$461$	−3.00000	+	1.73205i	−0.139724	+	0.0806696i	0.428508	+	0.903538i	$0.359039\pi$
$462$	−15.0000	+	5.19615i	−0.697863	+	0.241747i
$463$		−	5.19615i		−	0.241486i	−0.992684	−	0.120743i	$-0.961472\pi$
$463$		−	5.19615i		−	0.241486i	0.992684	−	0.120743i	$-0.0385276\pi$
$464$	−30.0000			−1.39272
$465$	36.0000			1.66946
$466$		−	20.7846i		−	0.962828i
$467$	6.00000	−	10.3923i	0.277647	−	0.480899i	−0.693153	−	0.720791i	$-0.743779\pi$
$467$	6.00000	−	10.3923i	0.277647	−	0.480899i	0.970799	+	0.239892i	$0.0771121\pi$
$468$	−3.50000	+	0.866025i	−0.161788	+	0.0400320i
$469$	9.00000	+	1.73205i	0.415581	+	0.0799787i
$470$	−54.0000	−	31.1769i	−2.49083	−	1.43808i
$471$	−6.50000	−	11.2583i	−0.299504	−	0.518756i
$472$	3.00000	−	5.19615i	0.138086	−	0.239172i
$473$	−3.00000	+	1.73205i	−0.137940	+	0.0796398i
$474$			13.8564i			0.636446i
$475$	10.5000	−	6.06218i	0.481773	−	0.278152i
$476$	−15.0000	+	5.19615i	−0.687524	+	0.238165i
$477$	3.00000	+	5.19615i	0.137361	+	0.237915i
$478$	18.0000	+	31.1769i	0.823301	+	1.42600i
$479$			24.2487i			1.10795i	0.832533	+	0.553976i	$0.186890\pi$
$479$			24.2487i			1.10795i	−0.832533	+	0.553976i	$0.813110\pi$
$480$	−9.00000	−	15.5885i	−0.410792	−	0.711512i
$481$	6.00000	+	1.73205i	0.273576	+	0.0789747i
$482$	12.0000			0.546585
$483$	15.0000	−	5.19615i	0.682524	−	0.236433i
$484$	−0.500000	+	0.866025i	−0.0227273	+	0.0393648i
$485$	−42.0000			−1.90712
$486$	−1.50000	+	0.866025i	−0.0680414	+	0.0392837i
$487$	25.5000	+	14.7224i	1.15552	+	0.667137i	0.950225	−	0.311564i	$-0.100853\pi$
$487$	25.5000	+	14.7224i	1.15552	+	0.667137i	0.205290	+	0.978701i	$0.434186\pi$
$488$			1.73205i			0.0784063i
$489$		−	5.19615i		−	0.234978i
$490$	−39.0000	−	15.5885i	−1.76184	−	0.704215i
$491$	6.00000	−	10.3923i	0.270776	−	0.468998i	−0.698285	−	0.715820i	$-0.746053\pi$
$491$	6.00000	−	10.3923i	0.270776	−	0.468998i	0.969061	+	0.246822i	$0.0793863\pi$
$492$	−3.00000	+	1.73205i	−0.135250	+	0.0780869i
$493$	18.0000	+	31.1769i	0.810679	+	1.40414i
$494$	−3.00000	+	10.3923i	−0.134976	+	0.467572i
$495$	−6.00000	+	10.3923i	−0.269680	+	0.467099i
$496$	−45.0000	−	25.9808i	−2.02056	−	1.16657i
$497$	−3.00000	−	8.66025i	−0.134568	−	0.388465i
$498$	9.00000	+	15.5885i	0.403300	+	0.698535i
$499$	−19.5000	−	11.2583i	−0.872940	−	0.503992i	−0.00461581	−	0.999989i	$-0.501469\pi$
$499$	−19.5000	−	11.2583i	−0.872940	−	0.503992i	−0.868324	+	0.495997i	$0.834803\pi$
$500$	6.00000	+	3.46410i	0.268328	+	0.154919i
$501$	−18.0000	−	10.3923i	−0.804181	−	0.464294i
$502$	−9.00000	−	5.19615i	−0.401690	−	0.231916i
$503$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$503$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$504$	4.50000	+	0.866025i	0.200446	+	0.0385758i
$505$	36.0000	+	20.7846i	1.60198	+	0.924903i
$506$	18.0000	−	31.1769i	0.800198	−	1.38598i
$507$	0.500000	−	12.9904i	0.0222058	−	0.576923i
$508$	−5.50000	−	9.52628i	−0.244023	−	0.422660i
$509$	12.0000	−	6.92820i	0.531891	−	0.307087i	−0.209895	−	0.977724i	$-0.567312\pi$
$509$	12.0000	−	6.92820i	0.531891	−	0.307087i	0.741786	+	0.670637i	$0.233979\pi$
$510$	−18.0000	+	31.1769i	−0.797053	+	1.38054i
$511$	−10.5000	−	30.3109i	−0.464493	−	1.34087i
$512$			8.66025i			0.382733i
$513$			1.73205i			0.0764719i
$514$		0			0
$515$	−33.0000	+	19.0526i	−1.45415	+	0.839556i
$516$	−1.00000			−0.0440225
$517$	18.0000	−	31.1769i	0.791639	−	1.37116i
$518$	6.00000	+	5.19615i	0.263625	+	0.228306i
$519$	12.0000			0.526742
$520$	21.0000	−	5.19615i	0.920911	−	0.227866i
$521$	15.0000	+	25.9808i	0.657162	+	1.13824i	0.981347	+	0.192244i	$0.0615766\pi$
$521$	15.0000	+	25.9808i	0.657162	+	1.13824i	−0.324185	+	0.945994i	$0.605090\pi$
$522$			10.3923i			0.454859i
$523$	6.50000	+	11.2583i	0.284225	+	0.492292i	0.972421	−	0.233233i	$-0.0749303\pi$
$523$	6.50000	+	11.2583i	0.284225	+	0.492292i	−0.688196	+	0.725525i	$0.741597\pi$
$524$		0			0
$525$	−17.5000	+	6.06218i	−0.763763	+	0.264575i
$526$		0			0
$527$			62.3538i			2.71618i
$528$	15.0000	−	8.66025i	0.652791	−	0.376889i
$529$	−6.50000	+	11.2583i	−0.282609	+	0.489493i
$530$	18.0000	+	31.1769i	0.781870	+	1.35424i
$531$	−3.00000	−	1.73205i	−0.130189	−	0.0751646i
$532$	−3.00000	+	3.46410i	−0.130066	+	0.150188i
$533$	−3.00000	−	12.1244i	−0.129944	−	0.525164i
$534$	−9.00000	+	15.5885i	−0.389468	+	0.674579i
$535$			20.7846i			0.898597i
$536$	−6.00000			−0.259161
$537$	−24.0000			−1.03568
$538$		0			0
$539$	9.00000	−	22.5167i	0.387657	−	0.969861i
$540$	−3.00000	+	1.73205i	−0.129099	+	0.0745356i
$541$	16.5000	+	9.52628i	0.709390	+	0.409567i	0.810835	−	0.585274i	$-0.199013\pi$
$541$	16.5000	+	9.52628i	0.709390	+	0.409567i	−0.101445	+	0.994841i	$0.532347\pi$
$542$	−10.5000	+	18.1865i	−0.451014	+	0.781179i
$543$	−5.00000			−0.214571
$544$	27.0000	−	15.5885i	1.15762	−	0.668350i
$545$	−42.0000			−1.79908
$546$	7.50000	−	14.7224i	0.320970	−	0.630062i
$547$	−25.0000			−1.06892			−0.534461	−	0.845193i	$-0.679486\pi$
$547$	−25.0000			−1.06892			−0.534461	+	0.845193i	$0.679486\pi$
$548$		0			0
$549$	1.00000			0.0426790
$550$	−21.0000	+	36.3731i	−0.895443	+	1.55095i
$551$	9.00000	+	5.19615i	0.383413	+	0.221364i
$552$	−9.00000	+	5.19615i	−0.383065	+	0.221163i
$553$	−16.0000	−	13.8564i	−0.680389	−	0.589234i
$554$		−	32.9090i		−	1.39817i
$555$	6.00000			0.254686
$556$	4.00000			0.169638
$557$		−	24.2487i		−	1.02745i	−0.857955	−	0.513725i	$-0.828265\pi$
$557$		−	24.2487i		−	1.02745i	0.857955	−	0.513725i	$-0.171735\pi$
$558$	−9.00000	+	15.5885i	−0.381000	+	0.659912i
$559$	1.00000	−	3.46410i	0.0422955	−	0.146516i
$560$	45.0000	+	8.66025i	1.90160	+	0.365963i
$561$	−18.0000	−	10.3923i	−0.759961	−	0.438763i
$562$	−18.0000	−	31.1769i	−0.759284	−	1.31512i
$563$	12.0000	−	20.7846i	0.505740	−	0.875967i	−0.494238	−	0.869326i	$-0.664553\pi$
$563$	12.0000	−	20.7846i	0.505740	−	0.875967i	0.999978	−	0.00664037i	$-0.00211371\pi$
$564$	9.00000	−	5.19615i	0.378968	−	0.218797i
$565$		−	41.5692i		−	1.74883i
$566$	−34.5000	+	19.9186i	−1.45014	+	0.837241i
$567$	0.500000	−	2.59808i	0.0209980	−	0.109109i
$568$	3.00000	+	5.19615i	0.125877	+	0.218026i
$569$	−15.0000	−	25.9808i	−0.628833	−	1.08917i	−0.987786	−	0.155815i	$-0.950200\pi$
$569$	−15.0000	−	25.9808i	−0.628833	−	1.08917i	0.358954	−	0.933355i	$-0.383134\pi$
$570$			10.3923i			0.435286i
$571$	2.50000	+	4.33013i	0.104622	+	0.181210i	0.913584	−	0.406651i	$-0.133303\pi$
$571$	2.50000	+	4.33013i	0.104622	+	0.181210i	−0.808962	+	0.587861i	$0.799970\pi$
$572$	−3.00000	−	12.1244i	−0.125436	−	0.506945i
$573$	6.00000			0.250654
$574$	3.00000	−	15.5885i	0.125218	−	0.650650i
$575$	21.0000	−	36.3731i	0.875761	−	1.51686i
$576$	−1.00000			−0.0416667
$577$	22.5000	−	12.9904i	0.936687	−	0.540797i	0.0477669	−	0.998859i	$-0.484790\pi$
$577$	22.5000	−	12.9904i	0.936687	−	0.540797i	0.888920	+	0.458062i	$0.151456\pi$
$578$	−28.5000	−	16.4545i	−1.18544	−	0.684416i
$579$		−	12.1244i		−	0.503871i
$580$			20.7846i			0.863034i
$581$	−27.0000	−	5.19615i	−1.12015	−	0.215573i
$582$	10.5000	−	18.1865i	0.435239	−	0.753856i
$583$	−18.0000	+	10.3923i	−0.745484	+	0.430405i
$584$	10.5000	+	18.1865i	0.434493	+	0.752564i
$585$	−3.00000	−	12.1244i	−0.124035	−	0.501280i
$586$	−15.0000	+	25.9808i	−0.619644	+	1.07326i
$587$	27.0000	+	15.5885i	1.11441	+	0.643404i	0.939968	−	0.341263i	$-0.110855\pi$
$587$	27.0000	+	15.5885i	1.11441	+	0.643404i	0.174441	+	0.984668i	$0.444188\pi$
$588$	5.50000	−	4.33013i	0.226816	−	0.178571i
$589$	9.00000	+	15.5885i	0.370839	+	0.642311i
$590$	−18.0000	−	10.3923i	−0.741048	−	0.427844i
$591$	3.00000	+	1.73205i	0.123404	+	0.0712470i
$592$	−7.50000	−	4.33013i	−0.308248	−	0.177967i
$593$	6.00000	+	3.46410i	0.246390	+	0.142254i	0.618110	−	0.786091i	$-0.287898\pi$
$593$	6.00000	+	3.46410i	0.246390	+	0.142254i	−0.371720	+	0.928345i	$0.621232\pi$
$594$	−3.00000	−	5.19615i	−0.123091	−	0.213201i
$595$	−18.0000	−	51.9615i	−0.737928	−	2.13021i
$596$	9.00000	+	5.19615i	0.368654	+	0.212843i
$597$	−5.50000	+	9.52628i	−0.225100	+	0.389885i
$598$	9.00000	+	36.3731i	0.368037	+	1.48741i
$599$	9.00000	+	15.5885i	0.367730	+	0.636927i	0.989210	−	0.146503i	$-0.0468017\pi$
$599$	9.00000	+	15.5885i	0.367730	+	0.636927i	−0.621480	+	0.783430i	$0.713468\pi$
$600$	10.5000	−	6.06218i	0.428661	−	0.247487i
$601$	−6.50000	+	11.2583i	−0.265141	+	0.459237i	−0.967600	−	0.252486i	$-0.918752\pi$
$601$	−6.50000	+	11.2583i	−0.265141	+	0.459237i	0.702460	+	0.711723i	$0.252085\pi$
$602$	3.00000	−	3.46410i	0.122271	−	0.141186i
$603$			3.46410i			0.141069i
$604$		−	3.46410i		−	0.140952i
$605$	−3.00000	−	1.73205i	−0.121967	−	0.0704179i
$606$	−18.0000	+	10.3923i	−0.731200	+	0.422159i
$607$	−37.0000			−1.50178			−0.750892	−	0.660425i	$-0.770376\pi$
$607$	−37.0000			−1.50178			−0.750892	+	0.660425i	$0.770376\pi$
$608$	4.50000	−	7.79423i	0.182499	−	0.316098i
$609$	−12.0000	−	10.3923i	−0.486265	−	0.421117i
$610$	6.00000			0.242933
$611$	9.00000	+	36.3731i	0.364101	+	1.47150i
$612$	−3.00000	−	5.19615i	−0.121268	−	0.210042i
$613$			25.9808i			1.04935i	0.851302	+	0.524677i	$0.175814\pi$
$613$			25.9808i			1.04935i	−0.851302	+	0.524677i	$0.824186\pi$
$614$	15.0000	+	25.9808i	0.605351	+	1.04850i
$615$	−6.00000	−	10.3923i	−0.241943	−	0.419058i
$616$	−3.00000	+	15.5885i	−0.120873	+	0.628077i
$617$	−24.0000	+	13.8564i	−0.966204	+	0.557838i	−0.898077	−	0.439839i	$-0.855036\pi$
$617$	−24.0000	+	13.8564i	−0.966204	+	0.557838i	−0.0681269	+	0.997677i	$0.521702\pi$
$618$		−	19.0526i		−	0.766406i
$619$	1.50000	−	0.866025i	0.0602901	−	0.0348085i	−0.469552	−	0.882905i	$-0.655585\pi$
$619$	1.50000	−	0.866025i	0.0602901	−	0.0348085i	0.529842	+	0.848096i	$0.322251\pi$
$620$	−18.0000	+	31.1769i	−0.722897	+	1.25210i
$621$	3.00000	+	5.19615i	0.120386	+	0.208514i
$622$	27.0000	+	15.5885i	1.08260	+	0.625040i
$623$	−9.00000	−	25.9808i	−0.360577	−	1.04090i
$624$	−5.00000	+	17.3205i	−0.200160	+	0.693375i
$625$	5.50000	−	9.52628i	0.220000	−	0.381051i
$626$			1.73205i			0.0692267i
$627$	−6.00000			−0.239617
$628$	13.0000			0.518756
$629$			10.3923i			0.414368i
$630$	3.00000	−	15.5885i	0.119523	−	0.621059i
$631$	−19.5000	+	11.2583i	−0.776283	+	0.448187i	−0.835111	−	0.550081i	$-0.814597\pi$
$631$	−19.5000	+	11.2583i	−0.776283	+	0.448187i	0.0588285	+	0.998268i	$0.481263\pi$
$632$	12.0000	+	6.92820i	0.477334	+	0.275589i
$633$	−2.50000	+	4.33013i	−0.0993661	+	0.172107i
$634$	42.0000			1.66803
$635$	33.0000	−	19.0526i	1.30957	−	0.756078i
$636$	−6.00000			−0.237915
$637$	9.50000	+	23.3827i	0.376404	+	0.926456i
$638$	−36.0000			−1.42525
$639$	3.00000	−	1.73205i	0.118678	−	0.0685189i
$640$	−42.0000			−1.66020
$641$	15.0000	−	25.9808i	0.592464	−	1.02618i	−0.401435	−	0.915888i	$-0.631488\pi$
$641$	15.0000	−	25.9808i	0.592464	−	1.02618i	0.993899	−	0.110291i	$-0.0351782\pi$
$642$	−9.00000	−	5.19615i	−0.355202	−	0.205076i
$643$	31.5000	−	18.1865i	1.24224	−	0.717207i	0.272689	−	0.962102i	$-0.412087\pi$
$643$	31.5000	−	18.1865i	1.24224	−	0.717207i	0.969550	+	0.244895i	$0.0787536\pi$
$644$	−3.00000	+	15.5885i	−0.118217	+	0.614271i
$645$		−	3.46410i		−	0.136399i
$646$	−18.0000			−0.708201
$647$	−36.0000			−1.41531			−0.707653	−	0.706560i	$-0.750246\pi$
$647$	−36.0000			−1.41531			−0.707653	+	0.706560i	$0.750246\pi$
$648$			1.73205i			0.0680414i
$649$	6.00000	−	10.3923i	0.235521	−	0.407934i
$650$	−10.5000	−	42.4352i	−0.411844	−	1.66445i
$651$	−9.00000	−	25.9808i	−0.352738	−	1.01827i
$652$	4.50000	+	2.59808i	0.176234	+	0.101749i
$653$	−18.0000	−	31.1769i	−0.704394	−	1.22005i	−0.966910	−	0.255119i	$-0.917885\pi$
$653$	−18.0000	−	31.1769i	−0.704394	−	1.22005i	0.262515	−	0.964928i	$-0.415448\pi$
$654$	10.5000	−	18.1865i	0.410582	−	0.711150i
$655$		0			0
$656$			17.3205i			0.676252i
$657$	10.5000	−	6.06218i	0.409644	−	0.236508i
$658$	−9.00000	+	46.7654i	−0.350857	+	1.82310i
$659$	9.00000	+	15.5885i	0.350590	+	0.607240i	0.986353	−	0.164644i	$-0.0526477\pi$
$659$	9.00000	+	15.5885i	0.350590	+	0.607240i	−0.635763	+	0.771885i	$0.719314\pi$
$660$	−6.00000	−	10.3923i	−0.233550	−	0.404520i
$661$		0			0		1.00000			$0$
$661$		0			0		−1.00000			$\pi$
$662$	−4.50000	−	7.79423i	−0.174897	−	0.302931i
$663$	21.0000	−	5.19615i	0.815572	−	0.201802i
$664$	18.0000			0.698535
$665$	−12.0000	−	10.3923i	−0.465340	−	0.402996i
$666$	−1.50000	+	2.59808i	−0.0581238	+	0.100673i
$667$	36.0000			1.39393
$668$	18.0000	−	10.3923i	0.696441	−	0.402090i
$669$	−15.0000	−	8.66025i	−0.579934	−	0.334825i
$670$			20.7846i			0.802980i
$671$			3.46410i			0.133730i
$672$	−9.00000	+	10.3923i	−0.347183	+	0.400892i
$673$	−23.5000	+	40.7032i	−0.905858	+	1.56899i	−0.0860977	+	0.996287i	$0.527440\pi$
$673$	−23.5000	+	40.7032i	−0.905858	+	1.56899i	−0.819761	+	0.572706i	$0.805894\pi$
$674$	−43.5000	+	25.1147i	−1.67556	+	0.967384i
$675$	−3.50000	−	6.06218i	−0.134715	−	0.233333i
$676$	11.0000	+	6.92820i	0.423077	+	0.266469i
$677$	−12.0000	+	20.7846i	−0.461197	+	0.798817i	−0.999021	−	0.0442400i	$-0.985913\pi$
$677$	−12.0000	+	20.7846i	−0.461197	+	0.798817i	0.537823	+	0.843057i	$0.319247\pi$
$678$	18.0000	+	10.3923i	0.691286	+	0.399114i
$679$	10.5000	+	30.3109i	0.402953	+	1.16323i
$680$	18.0000	+	31.1769i	0.690268	+	1.19558i
$681$	−6.00000	−	3.46410i	−0.229920	−	0.132745i
$682$	−54.0000	−	31.1769i	−2.06777	−	1.19383i
$683$	21.0000	+	12.1244i	0.803543	+	0.463926i	0.844708	−	0.535227i	$-0.179774\pi$
$683$	21.0000	+	12.1244i	0.803543	+	0.463926i	−0.0411658	+	0.999152i	$0.513107\pi$
$684$	−1.50000	−	0.866025i	−0.0573539	−	0.0331133i
$685$		0			0
$686$	−1.50000	+	32.0429i	−0.0572703	+	1.22341i
$687$	4.50000	+	2.59808i	0.171686	+	0.0991228i
$688$	−2.50000	+	4.33013i	−0.0953116	+	0.165085i
$689$	6.00000	−	20.7846i	0.228582	−	0.791831i
$690$	18.0000	+	31.1769i	0.685248	+	1.18688i
$691$	19.5000	−	11.2583i	0.741815	−	0.428287i	−0.0809139	−	0.996721i	$-0.525784\pi$
$691$	19.5000	−	11.2583i	0.741815	−	0.428287i	0.822729	+	0.568434i	$0.192451\pi$
$692$	−6.00000	+	10.3923i	−0.228086	+	0.395056i
$693$	9.00000	+	1.73205i	0.341882	+	0.0657952i
$694$		−	31.1769i		−	1.18346i
$695$			13.8564i			0.525603i
$696$	9.00000	+	5.19615i	0.341144	+	0.196960i
$697$	18.0000	−	10.3923i	0.681799	−	0.393637i
$698$	−57.0000			−2.15748
$699$	−6.00000	+	10.3923i	−0.226941	+	0.393073i
$700$	3.50000	−	18.1865i	0.132288	−	0.687386i
$701$	−36.0000			−1.35970			−0.679851	−	0.733351i	$-0.737955\pi$
$701$	−36.0000			−1.35970			−0.679851	+	0.733351i	$0.737955\pi$
$702$	6.00000	+	1.73205i	0.226455	+	0.0653720i
$703$	1.50000	+	2.59808i	0.0565736	+	0.0979883i
$704$		−	3.46410i		−	0.130558i
$705$	18.0000	+	31.1769i	0.677919	+	1.17419i
$706$	12.0000	+	20.7846i	0.451626	+	0.782239i
$707$	6.00000	−	31.1769i	0.225653	−	1.17253i
$708$	3.00000	−	1.73205i	0.112747	−	0.0650945i
$709$			29.4449i			1.10583i	0.833239	+	0.552913i	$0.186484\pi$
$709$			29.4449i			1.10583i	−0.833239	+	0.552913i	$0.813516\pi$
$710$	18.0000	−	10.3923i	0.675528	−	0.390016i
$711$	4.00000	−	6.92820i	0.150012	−	0.259828i
$712$	9.00000	+	15.5885i	0.337289	+	0.584202i
$713$	54.0000	+	31.1769i	2.02232	+	1.16758i
$714$	27.0000	+	5.19615i	1.01045	+	0.194461i
$715$	42.0000	−	10.3923i	1.57071	−	0.388650i
$716$	12.0000	−	20.7846i	0.448461	−	0.776757i
$717$		−	20.7846i		−	0.776215i
$718$	18.0000			0.671754
$719$	−30.0000			−1.11881			−0.559406	−	0.828894i	$-0.688971\pi$
$719$	−30.0000			−1.11881			−0.559406	+	0.828894i	$0.688971\pi$
$720$			17.3205i			0.645497i
$721$	22.0000	+	19.0526i	0.819323	+	0.709554i
$722$	24.0000	−	13.8564i	0.893188	−	0.515682i
$723$	−6.00000	−	3.46410i	−0.223142	−	0.128831i
$724$	2.50000	−	4.33013i	0.0929118	−	0.160928i
$725$	−42.0000			−1.55984
$726$	1.50000	−	0.866025i	0.0556702	−	0.0321412i
$727$	−8.00000			−0.296704			−0.148352	−	0.988935i	$-0.547397\pi$
$727$	−8.00000			−0.296704			−0.148352	+	0.988935i	$0.547397\pi$
$728$	−9.00000	−	13.8564i	−0.333562	−	0.513553i
$729$	1.00000			0.0370370
$730$	63.0000	−	36.3731i	2.33173	−	1.34623i
$731$	6.00000			0.221918
$732$	−0.500000	+	0.866025i	−0.0184805	+	0.0320092i
$733$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$733$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$734$	−28.5000	+	16.4545i	−1.05195	+	0.607346i
$735$	15.0000	+	19.0526i	0.553283	+	0.702764i
$736$		−	31.1769i		−	1.14920i
$737$	−12.0000			−0.442026
$738$	6.00000			0.220863
$739$		−	32.9090i		−	1.21058i	−0.796007	−	0.605288i	$-0.793058\pi$
$739$		−	32.9090i		−	1.21058i	0.796007	−	0.605288i	$-0.206942\pi$
$740$	−3.00000	+	5.19615i	−0.110282	+	0.191014i
$741$	4.50000	−	4.33013i	0.165312	−	0.159071i
$742$	18.0000	−	20.7846i	0.660801	−	0.763027i
$743$	33.0000	+	19.0526i	1.21065	+	0.698971i	0.962901	−	0.269853i	$-0.0869752\pi$
$743$	33.0000	+	19.0526i	1.21065	+	0.698971i	0.247751	+	0.968824i	$0.420308\pi$
$744$	9.00000	+	15.5885i	0.329956	+	0.571501i
$745$	−18.0000	+	31.1769i	−0.659469	+	1.14223i
$746$	33.0000	−	19.0526i	1.20822	−	0.697564i
$747$		−	10.3923i		−	0.380235i
$748$	18.0000	−	10.3923i	0.658145	−	0.379980i
$749$	15.0000	−	5.19615i	0.548088	−	0.189863i
$750$	−6.00000	−	10.3923i	−0.219089	−	0.379473i
$751$	−8.50000	−	14.7224i	−0.310169	−	0.537229i	0.668229	−	0.743955i	$-0.267052\pi$
$751$	−8.50000	−	14.7224i	−0.310169	−	0.537229i	−0.978399	+	0.206726i	$0.933719\pi$
$752$		−	51.9615i		−	1.89484i
$753$	3.00000	+	5.19615i	0.109326	+	0.189358i
$754$	27.0000	−	25.9808i	0.983282	−	0.946164i
$755$	12.0000			0.436725
$756$	2.00000	+	1.73205i	0.0727393	+	0.0629941i
$757$	19.0000	−	32.9090i	0.690567	−	1.19610i	−0.281086	−	0.959683i	$-0.590695\pi$
$757$	19.0000	−	32.9090i	0.690567	−	1.19610i	0.971652	−	0.236414i	$-0.0759722\pi$
$758$	−18.0000			−0.653789
$759$	−18.0000	+	10.3923i	−0.653359	+	0.377217i
$760$	9.00000	+	5.19615i	0.326464	+	0.188484i
$761$		−	38.1051i		−	1.38131i	−0.723185	−	0.690655i	$-0.757322\pi$
$761$		−	38.1051i		−	1.38131i	0.723185	−	0.690655i	$-0.242678\pi$
$762$			19.0526i			0.690201i
$763$	10.5000	+	30.3109i	0.380126	+	1.09733i
$764$	−3.00000	+	5.19615i	−0.108536	+	0.187990i
$765$	18.0000	−	10.3923i	0.650791	−	0.375735i
$766$	−12.0000	−	20.7846i	−0.433578	−	0.750978i
$767$	3.00000	+	12.1244i	0.108324	+	0.437785i
$768$	9.50000	−	16.4545i	0.342802	−	0.593750i
$769$	−28.5000	−	16.4545i	−1.02774	−	0.593364i	−0.111401	−	0.993776i	$-0.535534\pi$
$769$	−28.5000	−	16.4545i	−1.02774	−	0.593364i	−0.916335	+	0.400412i	$0.868867\pi$
$770$	54.0000	+	10.3923i	1.94602	+	0.374513i
$771$		0			0
$772$	10.5000	+	6.06218i	0.377903	+	0.218183i
$773$	−42.0000	−	24.2487i	−1.51064	−	0.872166i	−0.999923	−	0.0124137i	$-0.996048\pi$
$773$	−42.0000	−	24.2487i	−1.51064	−	0.872166i	−0.510712	−	0.859752i	$-0.670618\pi$
$774$	1.50000	+	0.866025i	0.0539164	+	0.0311286i
$775$	−63.0000	−	36.3731i	−2.26303	−	1.30656i
$776$	−10.5000	−	18.1865i	−0.376928	−	0.652859i
$777$	−1.50000	−	4.33013i	−0.0538122	−	0.155342i
$778$	−9.00000	−	5.19615i	−0.322666	−	0.186291i
$779$	3.00000	−	5.19615i	0.107486	−	0.186171i
$780$	12.0000	+	3.46410i	0.429669	+	0.124035i
$781$	6.00000	+	10.3923i	0.214697	+	0.371866i
$782$	−54.0000	+	31.1769i	−1.93104	+	1.11488i
$783$	3.00000	−	5.19615i	0.107211	−	0.185695i
$784$	−5.00000	−	34.6410i	−0.178571	−	1.23718i
$785$			45.0333i			1.60731i
$786$		0			0
$787$	4.50000	+	2.59808i	0.160408	+	0.0926114i	0.578055	−	0.815998i	$-0.303812\pi$
$787$	4.50000	+	2.59808i	0.160408	+	0.0926114i	−0.417647	+	0.908609i	$0.637145\pi$
$788$	−3.00000	+	1.73205i	−0.106871	+	0.0617018i
$789$		0			0
$790$	24.0000	−	41.5692i	0.853882	−	1.47897i
$791$	−30.0000	+	10.3923i	−1.06668	+	0.369508i
$792$	−6.00000			−0.213201
$793$	−2.50000	−	2.59808i	−0.0887776	−	0.0922604i
$794$	−1.50000	−	2.59808i	−0.0532330	−	0.0922023i
$795$		−	20.7846i		−	0.737154i
$796$	−5.50000	−	9.52628i	−0.194942	−	0.337650i
$797$	9.00000	+	15.5885i	0.318796	+	0.552171i	0.980237	−	0.197826i	$-0.0633881\pi$
$797$	9.00000	+	15.5885i	0.318796	+	0.552171i	−0.661441	+	0.749997i	$0.730055\pi$
$798$	7.50000	−	2.59808i	0.265497	−	0.0919709i
$799$	−54.0000	+	31.1769i	−1.91038	+	1.10296i
$800$			36.3731i			1.28598i
$801$	9.00000	−	5.19615i	0.317999	−	0.183597i
$802$	24.0000	−	41.5692i	0.847469	−	1.46786i
$803$	21.0000	+	36.3731i	0.741074	+	1.28358i
$804$	−3.00000	−	1.73205i	−0.105802	−	0.0610847i
$805$	−54.0000	−	10.3923i	−1.90325	−	0.366281i
$806$	63.0000	−	15.5885i	2.21908	−	0.549080i
$807$		0			0
$808$			20.7846i			0.731200i
$809$	−6.00000			−0.210949			−0.105474	−	0.994422i	$-0.533636\pi$
$809$	−6.00000			−0.210949			−0.105474	+	0.994422i	$0.533636\pi$
$810$	6.00000			0.210819
$811$		−	36.3731i		−	1.27723i	−0.769526	−	0.638616i	$-0.779507\pi$
$811$		−	36.3731i		−	1.27723i	0.769526	−	0.638616i	$-0.220493\pi$
$812$	15.0000	−	5.19615i	0.526397	−	0.182349i
$813$	10.5000	−	6.06218i	0.368251	−	0.212610i
$814$	−9.00000	−	5.19615i	−0.315450	−	0.182125i
$815$	−9.00000	+	15.5885i	−0.315256	+	0.546040i
$816$	−30.0000			−1.05021
$817$	1.50000	−	0.866025i	0.0524784	−	0.0302984i
$818$	−57.0000			−1.99296
$819$	−8.00000	+	5.19615i	−0.279543	+	0.181568i
$820$	12.0000			0.419058
$821$	33.0000	−	19.0526i	1.15171	−	0.664939i	0.202405	−	0.979302i	$-0.435124\pi$
$821$	33.0000	−	19.0526i	1.15171	−	0.664939i	0.949303	+	0.314363i	$0.101791\pi$
$822$		0			0
$823$	−16.0000	+	27.7128i	−0.557725	+	0.966008i	0.439961	+	0.898017i	$0.354992\pi$
$823$	−16.0000	+	27.7128i	−0.557725	+	0.966008i	−0.997686	+	0.0679910i	$0.978341\pi$
$824$	−16.5000	−	9.52628i	−0.574805	−	0.331864i
$825$	21.0000	−	12.1244i	0.731126	−	0.422116i
$826$	−3.00000	+	15.5885i	−0.104383	+	0.542392i
$827$		−	24.2487i		−	0.843210i	−0.906780	−	0.421605i	$-0.861467\pi$
$827$		−	24.2487i		−	0.843210i	0.906780	−	0.421605i	$-0.138533\pi$
$828$	−6.00000			−0.208514
$829$	−29.0000			−1.00721			−0.503606	−	0.863934i	$-0.667994\pi$
$829$	−29.0000			−1.00721			−0.503606	+	0.863934i	$0.667994\pi$
$830$		−	62.3538i		−	2.16433i
$831$	−9.50000	+	16.4545i	−0.329551	+	0.570800i
$832$	2.50000	+	2.59808i	0.0866719	+	0.0900721i
$833$	−33.0000	+	25.9808i	−1.14338	+	0.900180i
$834$	−6.00000	−	3.46410i	−0.207763	−	0.119952i
$835$	36.0000	+	62.3538i	1.24583	+	2.15784i
$836$	3.00000	−	5.19615i	0.103757	−	0.179713i
$837$	9.00000	−	5.19615i	0.311086	−	0.179605i
$838$			41.5692i			1.43598i
$839$	21.0000	−	12.1244i	0.725001	−	0.418579i	−0.0915899	−	0.995797i	$-0.529195\pi$
$839$	21.0000	−	12.1244i	0.725001	−	0.418579i	0.816590	+	0.577218i	$0.195862\pi$
$840$	−12.0000	−	10.3923i	−0.414039	−	0.358569i
$841$	−3.50000	−	6.06218i	−0.120690	−	0.209041i
$842$	−6.00000	−	10.3923i	−0.206774	−	0.358142i
$843$			20.7846i			0.715860i
$844$	−2.50000	−	4.33013i	−0.0860535	−	0.149049i
$845$	−24.0000	+	38.1051i	−0.825625	+	1.31086i
$846$	−18.0000			−0.618853
$847$	−0.500000	+	2.59808i	−0.0171802	+	0.0892710i
$848$	−15.0000	+	25.9808i	−0.515102	+	0.892183i
$849$	23.0000			0.789358
$850$	63.0000	−	36.3731i	2.16088	−	1.24759i
$851$	9.00000	+	5.19615i	0.308516	+	0.178122i
$852$			3.46410i			0.118678i
$853$		0			0		1.00000			$0$
$853$		0			0		−1.00000			$\pi$
$854$	−1.50000	−	4.33013i	−0.0513289	−	0.148174i
$855$	3.00000	−	5.19615i	0.102598	−	0.177705i
$856$	−9.00000	+	5.19615i	−0.307614	+	0.177601i
$857$	6.00000	+	10.3923i	0.204956	+	0.354994i	0.950119	−	0.311888i	$-0.100962\pi$
$857$	6.00000	+	10.3923i	0.204956	+	0.354994i	−0.745163	+	0.666883i	$0.767628\pi$
$858$	−6.00000	+	20.7846i	−0.204837	+	0.709575i
$859$	−9.50000	+	16.4545i	−0.324136	+	0.561420i	−0.981337	−	0.192295i	$-0.938407\pi$
$859$	−9.50000	+	16.4545i	−0.324136	+	0.561420i	0.657201	+	0.753715i	$0.271740\pi$
$860$	3.00000	+	1.73205i	0.102299	+	0.0590624i
$861$	−6.00000	+	6.92820i	−0.204479	+	0.236113i
$862$	15.0000	+	25.9808i	0.510902	+	0.884908i
$863$	30.0000	+	17.3205i	1.02121	+	0.589597i	0.914455	−	0.404688i	$-0.132620\pi$
$863$	30.0000	+	17.3205i	1.02121	+	0.589597i	0.106757	+	0.994285i	$0.465953\pi$
$864$	−4.50000	−	2.59808i	−0.153093	−	0.0883883i
$865$	−36.0000	−	20.7846i	−1.22404	−	0.706698i
$866$	−51.0000	−	29.4449i	−1.73305	−	1.00058i
$867$	9.50000	+	16.4545i	0.322637	+	0.558824i
$868$	27.0000	+	5.19615i	0.916440	+	0.176369i
$869$	24.0000	+	13.8564i	0.814144	+	0.470046i
$870$	18.0000	−	31.1769i	0.610257	−	1.05700i
$871$	9.00000	−	8.66025i	0.304953	−	0.293442i
$872$	−10.5000	−	18.1865i	−0.355575	−	0.615874i
$873$	−10.5000	+	6.06218i	−0.355371	+	0.205174i
$874$	−9.00000	+	15.5885i	−0.304430	+	0.527287i
$875$	18.0000	+	3.46410i	0.608511	+	0.117108i
$876$			12.1244i			0.409644i
$877$		−	13.8564i		−	0.467898i	−0.972249	−	0.233949i	$-0.924835\pi$
$877$		−	13.8564i		−	0.467898i	0.972249	−	0.233949i	$-0.0751648\pi$
$878$	−25.5000	−	14.7224i	−0.860583	−	0.496858i
$879$	15.0000	−	8.66025i	0.505937	−	0.292103i
$880$	−60.0000			−2.02260
$881$	6.00000	−	10.3923i	0.202145	−	0.350126i	−0.747074	−	0.664741i	$-0.768542\pi$
$881$	6.00000	−	10.3923i	0.202145	−	0.350126i	0.949219	+	0.314615i	$0.101875\pi$
$882$	−12.0000	+	1.73205i	−0.404061	+	0.0583212i
$883$	−41.0000			−1.37976			−0.689880	−	0.723924i	$-0.742337\pi$
$883$	−41.0000			−1.37976			−0.689880	+	0.723924i	$0.742337\pi$
$884$	−6.00000	+	20.7846i	−0.201802	+	0.699062i
$885$	6.00000	+	10.3923i	0.201688	+	0.349334i
$886$		−	41.5692i		−	1.39655i
$887$	21.0000	+	36.3731i	0.705111	+	1.22129i	0.966651	+	0.256096i	$0.0824362\pi$
$887$	21.0000	+	36.3731i	0.705111	+	1.22129i	−0.261540	+	0.965193i	$0.584230\pi$
$888$	1.50000	+	2.59808i	0.0503367	+	0.0871857i
$889$	−22.0000	−	19.0526i	−0.737856	−	0.639002i
$890$	54.0000	−	31.1769i	1.81008	−	1.04505i
$891$			3.46410i			0.116052i
$892$	15.0000	−	8.66025i	0.502237	−	0.289967i
$893$	−9.00000	+	15.5885i	−0.301174	+	0.521648i
$894$	−9.00000	−	15.5885i	−0.301005	−	0.521356i
$895$	72.0000	+	41.5692i	2.40669	+	1.38951i
$896$	10.5000	+	30.3109i	0.350780	+	1.01262i
$897$	6.00000	−	20.7846i	0.200334	−	0.693978i
$898$	−9.00000	+	15.5885i	−0.300334	+	0.520194i
$899$		−	62.3538i		−	2.07962i
$900$	7.00000			0.233333
$901$	36.0000			1.19933
$902$			20.7846i			0.692052i
$903$	−2.50000	+	0.866025i	−0.0831948	+	0.0288195i
$904$	18.0000	−	10.3923i	0.598671	−	0.345643i
$905$	15.0000	+	8.66025i	0.498617	+	0.287877i
$906$	−3.00000	+	5.19615i	−0.0996683	+	0.172631i
$907$	13.0000			0.431658			0.215829	−	0.976431i	$-0.430755\pi$
$907$	13.0000			0.431658			0.215829	+	0.976431i	$0.430755\pi$
$908$	6.00000	−	3.46410i	0.199117	−	0.114960i
$909$	12.0000			0.398015
$910$	−48.0000	+	31.1769i	−1.59118	+	1.03350i
$911$	−36.0000			−1.19273			−0.596367	−	0.802712i	$-0.703390\pi$
$911$	−36.0000			−1.19273			−0.596367	+	0.802712i	$0.703390\pi$
$912$	−7.50000	+	4.33013i	−0.248350	+	0.143385i
$913$	36.0000			1.19143
$914$	−6.00000	+	10.3923i	−0.198462	+	0.343747i
$915$	−3.00000	−	1.73205i	−0.0991769	−	0.0572598i
$916$	−4.50000	+	2.59808i	−0.148684	+	0.0858429i
$917$		0			0
$918$			10.3923i			0.342997i
$919$	1.00000			0.0329870			0.0164935	−	0.999864i	$-0.494750\pi$
$919$	1.00000			0.0329870			0.0164935	+	0.999864i	$0.494750\pi$
$920$	36.0000			1.18688
$921$		−	17.3205i		−	0.570730i
$922$	−3.00000	+	5.19615i	−0.0987997	+	0.171126i
$923$	−12.0000	−	3.46410i	−0.394985	−	0.114022i
$924$	−6.00000	+	6.92820i	−0.197386	+	0.227921i
$925$	−10.5000	−	6.06218i	−0.345238	−	0.199323i
$926$	−4.50000	−	7.79423i	−0.147879	−	0.256134i
$927$	−5.50000	+	9.52628i	−0.180644	+	0.312884i
$928$	−27.0000	+	15.5885i	−0.886318	+	0.511716i
$929$		−	10.3923i		−	0.340960i	−0.985361	−	0.170480i	$-0.945468\pi$
$929$		−	10.3923i		−	0.340960i	0.985361	−	0.170480i	$-0.0545319\pi$
$930$	54.0000	−	31.1769i	1.77073	−	1.02233i
$931$	−4.50000	+	11.2583i	−0.147482	+	0.368977i
$932$	−6.00000	−	10.3923i	−0.196537	−	0.340411i
$933$	−9.00000	−	15.5885i	−0.294647	−	0.510343i
$934$		−	20.7846i		−	0.680093i
$935$	36.0000	+	62.3538i	1.17733	+	2.03919i
$936$	4.50000	−	4.33013i	0.147087	−	0.141535i
$937$	−35.0000			−1.14340			−0.571700	−	0.820463i	$-0.693716\pi$
$937$	−35.0000			−1.14340			−0.571700	+	0.820463i	$0.693716\pi$
$938$	15.0000	−	5.19615i	0.489767	−	0.169660i
$939$	0.500000	−	0.866025i	0.0163169	−	0.0282617i
$940$	−36.0000			−1.17419
$941$	−27.0000	+	15.5885i	−0.880175	+	0.508169i	−0.870716	−	0.491786i	$-0.836344\pi$
$941$	−27.0000	+	15.5885i	−0.880175	+	0.508169i	−0.00945879	+	0.999955i	$0.503011\pi$
$942$	−19.5000	−	11.2583i	−0.635344	−	0.366816i
$943$		−	20.7846i		−	0.676840i
$944$		−	17.3205i		−	0.563735i
$945$	−6.00000	+	6.92820i	−0.195180	+	0.225374i
$946$	−3.00000	+	5.19615i	−0.0975384	+	0.168941i
$947$	12.0000	−	6.92820i	0.389948	−	0.225136i	−0.292190	−	0.956360i	$-0.594384\pi$
$947$	12.0000	−	6.92820i	0.389948	−	0.225136i	0.682137	+	0.731224i	$0.261051\pi$
$948$	4.00000	+	6.92820i	0.129914	+	0.225018i
$949$	−42.0000	−	12.1244i	−1.36338	−	0.393573i
$950$	10.5000	−	18.1865i	0.340665	−	0.590049i
$951$	−21.0000	−	12.1244i	−0.680972	−	0.393159i
$952$	18.0000	−	20.7846i	0.583383	−	0.673633i
$953$	−21.0000	−	36.3731i	−0.680257	−	1.17824i	−0.974902	−	0.222633i	$-0.928535\pi$
$953$	−21.0000	−	36.3731i	−0.680257	−	1.17824i	0.294646	−	0.955607i	$-0.404798\pi$
$954$	9.00000	+	5.19615i	0.291386	+	0.168232i
$955$	−18.0000	−	10.3923i	−0.582466	−	0.336287i
$956$	18.0000	+	10.3923i	0.582162	+	0.336111i
$957$	18.0000	+	10.3923i	0.581857	+	0.335936i
$958$	21.0000	+	36.3731i	0.678479	+	1.17516i
$959$		0			0
$960$	3.00000	+	1.73205i	0.0968246	+	0.0559017i
$961$	38.5000	−	66.6840i	1.24194	−	2.15110i
$962$	10.5000	−	2.59808i	0.338534	−	0.0837653i
$963$	3.00000	+	5.19615i	0.0966736	+	0.167444i
$964$	6.00000	−	3.46410i	0.193247	−	0.111571i
$965$	−21.0000	+	36.3731i	−0.676014	+	1.17089i
$966$	18.0000	−	20.7846i	0.579141	−	0.668734i
$967$			25.9808i			0.835485i	0.908565	+	0.417742i	$0.137179\pi$
$967$			25.9808i			0.835485i	−0.908565	+	0.417742i	$0.862821\pi$
$968$		−	1.73205i		−	0.0556702i
$969$	9.00000	+	5.19615i	0.289122	+	0.166924i
$970$	−63.0000	+	36.3731i	−2.02281	+	1.16787i
$971$	−12.0000			−0.385098			−0.192549	−	0.981287i	$-0.561675\pi$
$971$	−12.0000			−0.385098			−0.192549	+	0.981287i	$0.561675\pi$
$972$	−0.500000	+	0.866025i	−0.0160375	+	0.0277778i
$973$	10.0000	−	3.46410i	0.320585	−	0.111054i
$974$	51.0000			1.63415
$975$	−7.00000	+	24.2487i	−0.224179	+	0.776580i
$976$	2.50000	+	4.33013i	0.0800230	+	0.138604i
$977$		−	10.3923i		−	0.332479i	−0.986085	−	0.166240i	$-0.946837\pi$
$977$		−	10.3923i		−	0.332479i	0.986085	−	0.166240i	$-0.0531625\pi$
$978$	−4.50000	−	7.79423i	−0.143894	−	0.249232i
$979$	18.0000	+	31.1769i	0.575282	+	0.996419i
$980$	−24.0000	+	3.46410i	−0.766652	+	0.110657i
$981$	−10.5000	+	6.06218i	−0.335239	+	0.193550i
$982$		−	20.7846i		−	0.663264i
$983$	−45.0000	+	25.9808i	−1.43528	+	0.828658i	−0.997516	−	0.0704339i	$-0.977562\pi$
$983$	−45.0000	+	25.9808i	−1.43528	+	0.828658i	−0.437761	+	0.899092i	$0.644228\pi$
$984$	3.00000	−	5.19615i	0.0956365	−	0.165647i
$985$	−6.00000	−	10.3923i	−0.191176	−	0.331126i
$986$	54.0000	+	31.1769i	1.71971	+	0.992875i
$987$	18.0000	−	20.7846i	0.572946	−	0.661581i
$988$	1.50000	+	6.06218i	0.0477214	+	0.192864i
$989$	3.00000	−	5.19615i	0.0953945	−	0.165228i
$990$			20.7846i			0.660578i
$991$	−7.00000			−0.222362			−0.111181	−	0.993800i	$-0.535463\pi$
$991$	−7.00000			−0.222362			−0.111181	+	0.993800i	$0.535463\pi$
$992$	−54.0000			−1.71450
$993$			5.19615i			0.164895i
$994$	−12.0000	−	10.3923i	−0.380617	−	0.329624i
$995$	33.0000	−	19.0526i	1.04617	−	0.604007i
$996$	9.00000	+	5.19615i	0.285176	+	0.164646i
$997$	18.5000	−	32.0429i	0.585901	−	1.01481i	−0.408862	−	0.912596i	$-0.634074\pi$
$997$	18.5000	−	32.0429i	0.585901	−	1.01481i	0.994762	−	0.102214i	$-0.0325925\pi$
$998$	−39.0000			−1.23452
$999$	1.50000	−	0.866025i	0.0474579	−	0.0273998i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.bl.a.121.1	yes	2
3.2	odd	2		819.2.do.a.667.1		2
7.4	even	3		273.2.t.a.4.1	✓	2
13.10	even	6		273.2.t.a.205.1	yes	2
21.11	odd	6		819.2.bm.b.550.1		2
39.23	odd	6		819.2.bm.b.478.1		2
91.88	even	6	inner	273.2.bl.a.88.1	yes	2
273.179	odd	6		819.2.do.a.361.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.t.a.4.1	✓	2	7.4	even	3
273.2.t.a.205.1	yes	2	13.10	even	6
273.2.bl.a.88.1	yes	2	91.88	even	6	inner
273.2.bl.a.121.1	yes	2	1.1	even	1	trivial
819.2.bm.b.478.1		2	39.23	odd	6
819.2.bm.b.550.1		2	21.11	odd	6
819.2.do.a.361.1		2	273.179	odd	6
819.2.do.a.667.1		2	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)

\(f(q)\)	\(=\)	\(q+(1.50000 - 0.866025i) q^{2} -1.00000 q^{3} +(0.500000 - 0.866025i) q^{4} +(3.00000 + 1.73205i) q^{5} +(-1.50000 + 0.866025i) q^{6} +(0.500000 - 2.59808i) q^{7} +1.73205i q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(1.50000 - 0.866025i) q^{2} -1.00000 q^{3} +(0.500000 - 0.866025i) q^{4} +(3.00000 + 1.73205i) q^{5} +(-1.50000 + 0.866025i) q^{6} +(0.500000 - 2.59808i) q^{7} +1.73205i q^{8} +1.00000 q^{9} +6.00000 q^{10} +3.46410i q^{11} +(-0.500000 + 0.866025i) q^{12} +(-2.50000 - 2.59808i) q^{13} +(-1.50000 - 4.33013i) q^{14} +(-3.00000 - 1.73205i) q^{15} +(2.50000 + 4.33013i) q^{16} +(3.00000 - 5.19615i) q^{17} +(1.50000 - 0.866025i) q^{18} -1.73205i q^{19} +(3.00000 - 1.73205i) q^{20} +(-0.500000 + 2.59808i) q^{21} +(3.00000 + 5.19615i) q^{22} +(-3.00000 - 5.19615i) q^{23} -1.73205i q^{24} +(3.50000 + 6.06218i) q^{25} +(-6.00000 - 1.73205i) q^{26} -1.00000 q^{27} +(-2.00000 - 1.73205i) q^{28} +(-3.00000 + 5.19615i) q^{29} -6.00000 q^{30} +(-9.00000 + 5.19615i) q^{31} +(4.50000 + 2.59808i) q^{32} -3.46410i q^{33} -10.3923i q^{34} +(6.00000 - 6.92820i) q^{35} +(0.500000 - 0.866025i) q^{36} +(-1.50000 + 0.866025i) q^{37} +(-1.50000 - 2.59808i) q^{38} +(2.50000 + 2.59808i) q^{39} +(-3.00000 + 5.19615i) q^{40} +(3.00000 + 1.73205i) q^{41} +(1.50000 + 4.33013i) q^{42} +(0.500000 + 0.866025i) q^{43} +(3.00000 + 1.73205i) q^{44} +(3.00000 + 1.73205i) q^{45} +(-9.00000 - 5.19615i) q^{46} +(-9.00000 - 5.19615i) q^{47} +(-2.50000 - 4.33013i) q^{48} +(-6.50000 - 2.59808i) q^{49} +(10.5000 + 6.06218i) q^{50} +(-3.00000 + 5.19615i) q^{51} +(-3.50000 + 0.866025i) q^{52} +(3.00000 + 5.19615i) q^{53} +(-1.50000 + 0.866025i) q^{54} +(-6.00000 + 10.3923i) q^{55} +(4.50000 + 0.866025i) q^{56} +1.73205i q^{57} +10.3923i q^{58} +(-3.00000 - 1.73205i) q^{59} +(-3.00000 + 1.73205i) q^{60} +1.00000 q^{61} +(-9.00000 + 15.5885i) q^{62} +(0.500000 - 2.59808i) q^{63} -1.00000 q^{64} +(-3.00000 - 12.1244i) q^{65} +(-3.00000 - 5.19615i) q^{66} +3.46410i q^{67} +(-3.00000 - 5.19615i) q^{68} +(3.00000 + 5.19615i) q^{69} +(3.00000 - 15.5885i) q^{70} +(3.00000 - 1.73205i) q^{71} +1.73205i q^{72} +(10.5000 - 6.06218i) q^{73} +(-1.50000 + 2.59808i) q^{74} +(-3.50000 - 6.06218i) q^{75} +(-1.50000 - 0.866025i) q^{76} +(9.00000 + 1.73205i) q^{77} +(6.00000 + 1.73205i) q^{78} +(4.00000 - 6.92820i) q^{79} +17.3205i q^{80} +1.00000 q^{81} +6.00000 q^{82} -10.3923i q^{83} +(2.00000 + 1.73205i) q^{84} +(18.0000 - 10.3923i) q^{85} +(1.50000 + 0.866025i) q^{86} +(3.00000 - 5.19615i) q^{87} -6.00000 q^{88} +(9.00000 - 5.19615i) q^{89} +6.00000 q^{90} +(-8.00000 + 5.19615i) q^{91} -6.00000 q^{92} +(9.00000 - 5.19615i) q^{93} -18.0000 q^{94} +(3.00000 - 5.19615i) q^{95} +(-4.50000 - 2.59808i) q^{96} +(-10.5000 + 6.06218i) q^{97} +(-12.0000 + 1.73205i) q^{98} +3.46410i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{2} - 2 q^{3} + q^{4} + 6 q^{5} - 3 q^{6} + q^{7} + 2 q^{9}+O(q^{10}) \) 2 * q + 3 * q^2 - 2 * q^3 + q^4 + 6 * q^5 - 3 * q^6 + q^7 + 2 * q^9	\( 2 q + 3 q^{2} - 2 q^{3} + q^{4} + 6 q^{5} - 3 q^{6} + q^{7} + 2 q^{9} + 12 q^{10} - q^{12} - 5 q^{13} - 3 q^{14} - 6 q^{15} + 5 q^{16} + 6 q^{17} + 3 q^{18} + 6 q^{20} - q^{21} + 6 q^{22} - 6 q^{23} + 7 q^{25} - 12 q^{26} - 2 q^{27} - 4 q^{28} - 6 q^{29} - 12 q^{30} - 18 q^{31} + 9 q^{32} + 12 q^{35} + q^{36} - 3 q^{37} - 3 q^{38} + 5 q^{39} - 6 q^{40} + 6 q^{41} + 3 q^{42} + q^{43} + 6 q^{44} + 6 q^{45} - 18 q^{46} - 18 q^{47} - 5 q^{48} - 13 q^{49} + 21 q^{50} - 6 q^{51} - 7 q^{52} + 6 q^{53} - 3 q^{54} - 12 q^{55} + 9 q^{56} - 6 q^{59} - 6 q^{60} + 2 q^{61} - 18 q^{62} + q^{63} - 2 q^{64} - 6 q^{65} - 6 q^{66} - 6 q^{68} + 6 q^{69} + 6 q^{70} + 6 q^{71} + 21 q^{73} - 3 q^{74} - 7 q^{75} - 3 q^{76} + 18 q^{77} + 12 q^{78} + 8 q^{79} + 2 q^{81} + 12 q^{82} + 4 q^{84} + 36 q^{85} + 3 q^{86} + 6 q^{87} - 12 q^{88} + 18 q^{89} + 12 q^{90} - 16 q^{91} - 12 q^{92} + 18 q^{93} - 36 q^{94} + 6 q^{95} - 9 q^{96} - 21 q^{97} - 24 q^{98}+O(q^{100}) \) 2 * q + 3 * q^2 - 2 * q^3 + q^4 + 6 * q^5 - 3 * q^6 + q^7 + 2 * q^9 + 12 * q^10 - q^12 - 5 * q^13 - 3 * q^14 - 6 * q^15 + 5 * q^16 + 6 * q^17 + 3 * q^18 + 6 * q^20 - q^21 + 6 * q^22 - 6 * q^23 + 7 * q^25 - 12 * q^26 - 2 * q^27 - 4 * q^28 - 6 * q^29 - 12 * q^30 - 18 * q^31 + 9 * q^32 + 12 * q^35 + q^36 - 3 * q^37 - 3 * q^38 + 5 * q^39 - 6 * q^40 + 6 * q^41 + 3 * q^42 + q^43 + 6 * q^44 + 6 * q^45 - 18 * q^46 - 18 * q^47 - 5 * q^48 - 13 * q^49 + 21 * q^50 - 6 * q^51 - 7 * q^52 + 6 * q^53 - 3 * q^54 - 12 * q^55 + 9 * q^56 - 6 * q^59 - 6 * q^60 + 2 * q^61 - 18 * q^62 + q^63 - 2 * q^64 - 6 * q^65 - 6 * q^66 - 6 * q^68 + 6 * q^69 + 6 * q^70 + 6 * q^71 + 21 * q^73 - 3 * q^74 - 7 * q^75 - 3 * q^76 + 18 * q^77 + 12 * q^78 + 8 * q^79 + 2 * q^81 + 12 * q^82 + 4 * q^84 + 36 * q^85 + 3 * q^86 + 6 * q^87 - 12 * q^88 + 18 * q^89 + 12 * q^90 - 16 * q^91 - 12 * q^92 + 18 * q^93 - 36 * q^94 + 6 * q^95 - 9 * q^96 - 21 * q^97 - 24 * q^98

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