LMFDB - Embedded newform 462.2.k.a.89.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(89,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 0]))

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

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

chi := DirichletCharacter("462.89");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.k (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:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 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			89.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	462.89
Dual form			462.2.k.a.353.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.866025 + 1.50000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.73205 + 3.00000i) q^{5} -1.73205i q^{6} +(2.00000 + 1.73205i) q^{7} -1.00000i q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.866025 + 1.50000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.73205 + 3.00000i) q^{5} -1.73205i q^{6} +(2.00000 + 1.73205i) q^{7} -1.00000i q^{8} +(-1.50000 + 2.59808i) q^{9} +(3.00000 - 1.73205i) q^{10} +(-0.866025 + 0.500000i) q^{11} +(-0.866025 + 1.50000i) q^{12} -3.46410i q^{13} +(-0.866025 - 2.50000i) q^{14} -6.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.866025 + 1.50000i) q^{17} +(2.59808 - 1.50000i) q^{18} +(-1.50000 - 0.866025i) q^{19} -3.46410 q^{20} +(-0.866025 + 4.50000i) q^{21} +1.00000 q^{22} +(-2.59808 - 1.50000i) q^{23} +(1.50000 - 0.866025i) q^{24} +(-3.50000 - 6.06218i) q^{25} +(-1.73205 + 3.00000i) q^{26} -5.19615 q^{27} +(-0.500000 + 2.59808i) q^{28} +3.00000i q^{29} +(5.19615 + 3.00000i) q^{30} +(3.00000 - 1.73205i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-1.50000 - 0.866025i) q^{33} -1.73205i q^{34} +(-8.66025 + 3.00000i) q^{35} -3.00000 q^{36} +(-3.50000 + 6.06218i) q^{37} +(0.866025 + 1.50000i) q^{38} +(5.19615 - 3.00000i) q^{39} +(3.00000 + 1.73205i) q^{40} +6.92820 q^{41} +(3.00000 - 3.46410i) q^{42} +1.00000 q^{43} +(-0.866025 - 0.500000i) q^{44} +(-5.19615 - 9.00000i) q^{45} +(1.50000 + 2.59808i) q^{46} +(0.866025 - 1.50000i) q^{47} -1.73205 q^{48} +(1.00000 + 6.92820i) q^{49} +7.00000i q^{50} +(-1.50000 + 2.59808i) q^{51} +(3.00000 - 1.73205i) q^{52} +(4.50000 + 2.59808i) q^{54} -3.46410i q^{55} +(1.73205 - 2.00000i) q^{56} -3.00000i q^{57} +(1.50000 - 2.59808i) q^{58} +(-6.06218 - 10.5000i) q^{59} +(-3.00000 - 5.19615i) q^{60} +(9.00000 + 5.19615i) q^{61} -3.46410 q^{62} +(-7.50000 + 2.59808i) q^{63} -1.00000 q^{64} +(10.3923 + 6.00000i) q^{65} +(0.866025 + 1.50000i) q^{66} +(8.00000 + 13.8564i) q^{67} +(-0.866025 + 1.50000i) q^{68} -5.19615i q^{69} +(9.00000 + 1.73205i) q^{70} +15.0000i q^{71} +(2.59808 + 1.50000i) q^{72} +(-12.0000 + 6.92820i) q^{73} +(6.06218 - 3.50000i) q^{74} +(6.06218 - 10.5000i) q^{75} -1.73205i q^{76} +(-2.59808 - 0.500000i) q^{77} -6.00000 q^{78} +(-4.00000 + 6.92820i) q^{79} +(-1.73205 - 3.00000i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-6.00000 - 3.46410i) q^{82} +17.3205 q^{83} +(-4.33013 + 1.50000i) q^{84} -6.00000 q^{85} +(-0.866025 - 0.500000i) q^{86} +(-4.50000 + 2.59808i) q^{87} +(0.500000 + 0.866025i) q^{88} +(5.19615 - 9.00000i) q^{89} +10.3923i q^{90} +(6.00000 - 6.92820i) q^{91} -3.00000i q^{92} +(5.19615 + 3.00000i) q^{93} +(-1.50000 + 0.866025i) q^{94} +(5.19615 - 3.00000i) q^{95} +(1.50000 + 0.866025i) q^{96} -15.5885i q^{97} +(2.59808 - 6.50000i) q^{98} -3.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} + 8 q^{7} - 6 q^{9}+O(q^{10}) $ 4 * q + 2 * q^4 + 8 * q^7 - 6 * q^9	$ 4 q + 2 q^{4} + 8 q^{7} - 6 q^{9} + 12 q^{10} - 24 q^{15} - 2 q^{16} - 6 q^{19} + 4 q^{22} + 6 q^{24} - 14 q^{25} - 2 q^{28} + 12 q^{31} - 6 q^{33} - 12 q^{36} - 14 q^{37} + 12 q^{40} + 12 q^{42} + 4 q^{43} + 6 q^{46} + 4 q^{49} - 6 q^{51} + 12 q^{52} + 18 q^{54} + 6 q^{58} - 12 q^{60} + 36 q^{61} - 30 q^{63} - 4 q^{64} + 32 q^{67} + 36 q^{70} - 48 q^{73} - 24 q^{78} - 16 q^{79} - 18 q^{81} - 24 q^{82} - 24 q^{85} - 18 q^{87} + 2 q^{88} + 24 q^{91} - 6 q^{94} + 6 q^{96}+O(q^{100}) $ 4 * q + 2 * q^4 + 8 * q^7 - 6 * q^9 + 12 * q^10 - 24 * q^15 - 2 * q^16 - 6 * q^19 + 4 * q^22 + 6 * q^24 - 14 * q^25 - 2 * q^28 + 12 * q^31 - 6 * q^33 - 12 * q^36 - 14 * q^37 + 12 * q^40 + 12 * q^42 + 4 * q^43 + 6 * q^46 + 4 * q^49 - 6 * q^51 + 12 * q^52 + 18 * q^54 + 6 * q^58 - 12 * q^60 + 36 * q^61 - 30 * q^63 - 4 * q^64 + 32 * q^67 + 36 * q^70 - 48 * q^73 - 24 * q^78 - 16 * q^79 - 18 * q^81 - 24 * q^82 - 24 * q^85 - 18 * q^87 + 2 * q^88 + 24 * q^91 - 6 * q^94 + 6 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	0.866025	+	1.50000i	0.500000	+	0.866025i
$3$	0.866025	+	1.50000i	0.500000	+	0.866025i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−1.73205	+	3.00000i	−0.774597	+	1.34164i	0.160424	+	0.987048i	$0.448714\pi$
$5$	−1.73205	+	3.00000i	−0.774597	+	1.34164i	−0.935021	+	0.354593i	$0.884620\pi$
$6$		−	1.73205i		−	0.707107i
$7$	2.00000	+	1.73205i	0.755929	+	0.654654i
$7$	2.00000	+	1.73205i	0.755929	+	0.654654i
$8$		−	1.00000i		−	0.353553i
$9$	−1.50000	+	2.59808i	−0.500000	+	0.866025i
$10$	3.00000	−	1.73205i	0.948683	−	0.547723i
$11$	−0.866025	+	0.500000i	−0.261116	+	0.150756i
$11$	−0.866025	+	0.500000i	−0.261116	+	0.150756i
$12$	−0.866025	+	1.50000i	−0.250000	+	0.433013i
$13$		−	3.46410i		−	0.960769i	−0.877058	−	0.480384i	$-0.840497\pi$
$13$		−	3.46410i		−	0.960769i	0.877058	−	0.480384i	$-0.159503\pi$
$14$	−0.866025	−	2.50000i	−0.231455	−	0.668153i
$15$	−6.00000			−1.54919
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.866025	+	1.50000i	0.210042	+	0.363803i	0.951727	−	0.306944i	$-0.0993066\pi$
$17$	0.866025	+	1.50000i	0.210042	+	0.363803i	−0.741685	+	0.670748i	$0.765973\pi$
$18$	2.59808	−	1.50000i	0.612372	−	0.353553i
$19$	−1.50000	−	0.866025i	−0.344124	−	0.198680i	0.317970	−	0.948101i	$-0.396999\pi$
$19$	−1.50000	−	0.866025i	−0.344124	−	0.198680i	−0.662094	+	0.749421i	$0.730332\pi$
$20$	−3.46410			−0.774597
$21$	−0.866025	+	4.50000i	−0.188982	+	0.981981i
$22$	1.00000			0.213201
$23$	−2.59808	−	1.50000i	−0.541736	−	0.312772i	0.204046	−	0.978961i	$-0.434591\pi$
$23$	−2.59808	−	1.50000i	−0.541736	−	0.312772i	−0.745782	+	0.666190i	$0.767924\pi$
$24$	1.50000	−	0.866025i	0.306186	−	0.176777i
$25$	−3.50000	−	6.06218i	−0.700000	−	1.21244i
$26$	−1.73205	+	3.00000i	−0.339683	+	0.588348i
$27$	−5.19615			−1.00000
$28$	−0.500000	+	2.59808i	−0.0944911	+	0.490990i
$29$			3.00000i			0.557086i	0.960424	+	0.278543i	$0.0898515\pi$
$29$			3.00000i			0.557086i	−0.960424	+	0.278543i	$0.910149\pi$
$30$	5.19615	+	3.00000i	0.948683	+	0.547723i
$31$	3.00000	−	1.73205i	0.538816	−	0.311086i	−0.205783	−	0.978598i	$-0.565974\pi$
$31$	3.00000	−	1.73205i	0.538816	−	0.311086i	0.744599	+	0.667512i	$0.232641\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	−1.50000	−	0.866025i	−0.261116	−	0.150756i
$34$		−	1.73205i		−	0.297044i
$35$	−8.66025	+	3.00000i	−1.46385	+	0.507093i
$36$	−3.00000			−0.500000
$37$	−3.50000	+	6.06218i	−0.575396	+	0.996616i	0.420602	+	0.907245i	$0.361819\pi$
$37$	−3.50000	+	6.06218i	−0.575396	+	0.996616i	−0.995998	+	0.0893706i	$0.971514\pi$
$38$	0.866025	+	1.50000i	0.140488	+	0.243332i
$39$	5.19615	−	3.00000i	0.832050	−	0.480384i
$40$	3.00000	+	1.73205i	0.474342	+	0.273861i
$41$	6.92820			1.08200			0.541002	−	0.841021i	$-0.318045\pi$
$41$	6.92820			1.08200			0.541002	+	0.841021i	$0.318045\pi$
$42$	3.00000	−	3.46410i	0.462910	−	0.534522i
$43$	1.00000			0.152499			0.0762493	−	0.997089i	$-0.475706\pi$
$43$	1.00000			0.152499			0.0762493	+	0.997089i	$0.475706\pi$
$44$	−0.866025	−	0.500000i	−0.130558	−	0.0753778i
$45$	−5.19615	−	9.00000i	−0.774597	−	1.34164i
$46$	1.50000	+	2.59808i	0.221163	+	0.383065i
$47$	0.866025	−	1.50000i	0.126323	−	0.218797i	−0.795926	−	0.605393i	$-0.793016\pi$
$47$	0.866025	−	1.50000i	0.126323	−	0.218797i	0.922249	+	0.386596i	$0.126349\pi$
$48$	−1.73205			−0.250000
$49$	1.00000	+	6.92820i	0.142857	+	0.989743i
$50$			7.00000i			0.989949i
$51$	−1.50000	+	2.59808i	−0.210042	+	0.363803i
$52$	3.00000	−	1.73205i	0.416025	−	0.240192i
$53$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$53$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$54$	4.50000	+	2.59808i	0.612372	+	0.353553i
$55$		−	3.46410i		−	0.467099i
$56$	1.73205	−	2.00000i	0.231455	−	0.267261i
$57$		−	3.00000i		−	0.397360i
$58$	1.50000	−	2.59808i	0.196960	−	0.341144i
$59$	−6.06218	−	10.5000i	−0.789228	−	1.36698i	−0.926440	−	0.376442i	$-0.877147\pi$
$59$	−6.06218	−	10.5000i	−0.789228	−	1.36698i	0.137212	−	0.990542i	$-0.456186\pi$
$60$	−3.00000	−	5.19615i	−0.387298	−	0.670820i
$61$	9.00000	+	5.19615i	1.15233	+	0.665299i	0.949454	−	0.313905i	$-0.101637\pi$
$61$	9.00000	+	5.19615i	1.15233	+	0.665299i	0.202878	+	0.979204i	$0.434971\pi$
$62$	−3.46410			−0.439941
$63$	−7.50000	+	2.59808i	−0.944911	+	0.327327i
$64$	−1.00000			−0.125000
$65$	10.3923	+	6.00000i	1.28901	+	0.744208i
$66$	0.866025	+	1.50000i	0.106600	+	0.184637i
$67$	8.00000	+	13.8564i	0.977356	+	1.69283i	0.671932	+	0.740613i	$0.265465\pi$
$67$	8.00000	+	13.8564i	0.977356	+	1.69283i	0.305424	+	0.952217i	$0.401202\pi$
$68$	−0.866025	+	1.50000i	−0.105021	+	0.181902i
$69$		−	5.19615i		−	0.625543i
$70$	9.00000	+	1.73205i	1.07571	+	0.207020i
$71$			15.0000i			1.78017i	0.455792	+	0.890086i	$0.349356\pi$
$71$			15.0000i			1.78017i	−0.455792	+	0.890086i	$0.650644\pi$
$72$	2.59808	+	1.50000i	0.306186	+	0.176777i
$73$	−12.0000	+	6.92820i	−1.40449	+	0.810885i	−0.994850	−	0.101361i	$-0.967680\pi$
$73$	−12.0000	+	6.92820i	−1.40449	+	0.810885i	−0.409644	+	0.912245i	$0.634347\pi$
$74$	6.06218	−	3.50000i	0.704714	−	0.406867i
$75$	6.06218	−	10.5000i	0.700000	−	1.21244i
$76$		−	1.73205i		−	0.198680i
$77$	−2.59808	−	0.500000i	−0.296078	−	0.0569803i
$78$	−6.00000			−0.679366
$79$	−4.00000	+	6.92820i	−0.450035	+	0.779484i	−0.998388	−	0.0567635i	$-0.981922\pi$
$79$	−4.00000	+	6.92820i	−0.450035	+	0.779484i	0.548352	+	0.836247i	$0.315255\pi$
$80$	−1.73205	−	3.00000i	−0.193649	−	0.335410i
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$	−6.00000	−	3.46410i	−0.662589	−	0.382546i
$83$	17.3205			1.90117			0.950586	−	0.310460i	$-0.100483\pi$
$83$	17.3205			1.90117			0.950586	+	0.310460i	$0.100483\pi$
$84$	−4.33013	+	1.50000i	−0.472456	+	0.163663i
$85$	−6.00000			−0.650791
$86$	−0.866025	−	0.500000i	−0.0933859	−	0.0539164i
$87$	−4.50000	+	2.59808i	−0.482451	+	0.278543i
$88$	0.500000	+	0.866025i	0.0533002	+	0.0923186i
$89$	5.19615	−	9.00000i	0.550791	−	0.953998i	−0.447427	−	0.894321i	$-0.647659\pi$
$89$	5.19615	−	9.00000i	0.550791	−	0.953998i	0.998218	−	0.0596775i	$-0.0190072\pi$
$90$			10.3923i			1.09545i
$91$	6.00000	−	6.92820i	0.628971	−	0.726273i
$92$		−	3.00000i		−	0.312772i
$93$	5.19615	+	3.00000i	0.538816	+	0.311086i
$94$	−1.50000	+	0.866025i	−0.154713	+	0.0893237i
$95$	5.19615	−	3.00000i	0.533114	−	0.307794i
$96$	1.50000	+	0.866025i	0.153093	+	0.0883883i
$97$		−	15.5885i		−	1.58277i	−0.611319	−	0.791384i	$-0.709361\pi$
$97$		−	15.5885i		−	1.58277i	0.611319	−	0.791384i	$-0.290639\pi$
$98$	2.59808	−	6.50000i	0.262445	−	0.656599i
$99$		−	3.00000i		−	0.301511i
$100$	3.50000	−	6.06218i	0.350000	−	0.606218i
$101$	−2.59808	−	4.50000i	−0.258518	−	0.447767i	0.707327	−	0.706887i	$-0.249901\pi$
$101$	−2.59808	−	4.50000i	−0.258518	−	0.447767i	−0.965845	+	0.259120i	$0.916568\pi$
$102$	2.59808	−	1.50000i	0.257248	−	0.148522i
$103$	15.0000	+	8.66025i	1.47799	+	0.853320i	0.999691	−	0.0248745i	$-0.00791862\pi$
$103$	15.0000	+	8.66025i	1.47799	+	0.853320i	0.478303	+	0.878195i	$0.341252\pi$
$104$	−3.46410			−0.339683
$105$	−12.0000	−	10.3923i	−1.17108	−	1.01419i
$106$		0			0
$107$	−5.19615	−	3.00000i	−0.502331	−	0.290021i	0.227345	−	0.973814i	$-0.426996\pi$
$107$	−5.19615	−	3.00000i	−0.502331	−	0.290021i	−0.729676	+	0.683793i	$0.760329\pi$
$108$	−2.59808	−	4.50000i	−0.250000	−	0.433013i
$109$	−8.00000	−	13.8564i	−0.766261	−	1.32720i	−0.939577	−	0.342337i	$-0.888782\pi$
$109$	−8.00000	−	13.8564i	−0.766261	−	1.32720i	0.173316	−	0.984866i	$-0.444552\pi$
$110$	−1.73205	+	3.00000i	−0.165145	+	0.286039i
$111$	−12.1244			−1.15079
$112$	−2.50000	+	0.866025i	−0.236228	+	0.0818317i
$113$		−	6.00000i		−	0.564433i	−0.959351	−	0.282216i	$-0.908930\pi$
$113$		−	6.00000i		−	0.564433i	0.959351	−	0.282216i	$-0.0910696\pi$
$114$	−1.50000	+	2.59808i	−0.140488	+	0.243332i
$115$	9.00000	−	5.19615i	0.839254	−	0.484544i
$116$	−2.59808	+	1.50000i	−0.241225	+	0.139272i
$117$	9.00000	+	5.19615i	0.832050	+	0.480384i
$118$			12.1244i			1.11614i
$119$	−0.866025	+	4.50000i	−0.0793884	+	0.412514i
$120$			6.00000i			0.547723i
$121$	0.500000	−	0.866025i	0.0454545	−	0.0787296i
$122$	−5.19615	−	9.00000i	−0.470438	−	0.814822i
$123$	6.00000	+	10.3923i	0.541002	+	0.937043i
$124$	3.00000	+	1.73205i	0.269408	+	0.155543i
$125$	6.92820			0.619677
$126$	7.79423	+	1.50000i	0.694365	+	0.133631i
$127$	11.0000			0.976092			0.488046	−	0.872818i	$-0.337710\pi$
$127$	11.0000			0.976092			0.488046	+	0.872818i	$0.337710\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	0.866025	+	1.50000i	0.0762493	+	0.132068i
$130$	−6.00000	−	10.3923i	−0.526235	−	0.911465i
$131$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$131$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$132$		−	1.73205i		−	0.150756i
$133$	−1.50000	−	4.33013i	−0.130066	−	0.375470i
$134$		−	16.0000i		−	1.38219i
$135$	9.00000	−	15.5885i	0.774597	−	1.34164i
$136$	1.50000	−	0.866025i	0.128624	−	0.0742611i
$137$	15.5885	−	9.00000i	1.33181	−	0.768922i	0.346235	−	0.938148i	$-0.387460\pi$
$137$	15.5885	−	9.00000i	1.33181	−	0.768922i	0.985577	+	0.169226i	$0.0541268\pi$
$138$	−2.59808	+	4.50000i	−0.221163	+	0.383065i
$139$		−	1.73205i		−	0.146911i	−0.997299	−	0.0734553i	$-0.976597\pi$
$139$		−	1.73205i		−	0.146911i	0.997299	−	0.0734553i	$-0.0234026\pi$
$140$	−6.92820	−	6.00000i	−0.585540	−	0.507093i
$141$	3.00000			0.252646
$142$	7.50000	−	12.9904i	0.629386	−	1.09013i
$143$	1.73205	+	3.00000i	0.144841	+	0.250873i
$144$	−1.50000	−	2.59808i	−0.125000	−	0.216506i
$145$	−9.00000	−	5.19615i	−0.747409	−	0.431517i
$146$	13.8564			1.14676
$147$	−9.52628	+	7.50000i	−0.785714	+	0.618590i
$148$	−7.00000			−0.575396
$149$	−7.79423	−	4.50000i	−0.638528	−	0.368654i	0.145519	−	0.989355i	$-0.453515\pi$
$149$	−7.79423	−	4.50000i	−0.638528	−	0.368654i	−0.784047	+	0.620701i	$0.786848\pi$
$150$	−10.5000	+	6.06218i	−0.857321	+	0.494975i
$151$	5.50000	+	9.52628i	0.447584	+	0.775238i	0.998228	−	0.0595022i	$-0.0189513\pi$
$151$	5.50000	+	9.52628i	0.447584	+	0.775238i	−0.550645	+	0.834740i	$0.685618\pi$
$152$	−0.866025	+	1.50000i	−0.0702439	+	0.121666i
$153$	−5.19615			−0.420084
$154$	2.00000	+	1.73205i	0.161165	+	0.139573i
$155$			12.0000i			0.963863i
$156$	5.19615	+	3.00000i	0.416025	+	0.240192i
$157$	4.50000	−	2.59808i	0.359139	−	0.207349i	−0.309564	−	0.950879i	$-0.600183\pi$
$157$	4.50000	−	2.59808i	0.359139	−	0.207349i	0.668703	+	0.743530i	$0.266850\pi$
$158$	6.92820	−	4.00000i	0.551178	−	0.318223i
$159$		0			0
$160$			3.46410i			0.273861i
$161$	−2.59808	−	7.50000i	−0.204757	−	0.591083i
$162$			9.00000i			0.707107i
$163$	−7.00000	+	12.1244i	−0.548282	+	0.949653i	0.450110	+	0.892973i	$0.351385\pi$
$163$	−7.00000	+	12.1244i	−0.548282	+	0.949653i	−0.998392	+	0.0566798i	$0.981949\pi$
$164$	3.46410	+	6.00000i	0.270501	+	0.468521i
$165$	5.19615	−	3.00000i	0.404520	−	0.233550i
$166$	−15.0000	−	8.66025i	−1.16423	−	0.672166i
$167$	24.2487			1.87642			0.938211	−	0.346064i	$-0.112482\pi$
$167$	24.2487			1.87642			0.938211	+	0.346064i	$0.112482\pi$
$168$	4.50000	+	0.866025i	0.347183	+	0.0668153i
$169$	1.00000			0.0769231
$170$	5.19615	+	3.00000i	0.398527	+	0.230089i
$171$	4.50000	−	2.59808i	0.344124	−	0.198680i
$172$	0.500000	+	0.866025i	0.0381246	+	0.0660338i
$173$	−10.3923	+	18.0000i	−0.790112	+	1.36851i	0.135785	+	0.990738i	$0.456644\pi$
$173$	−10.3923	+	18.0000i	−0.790112	+	1.36851i	−0.925897	+	0.377776i	$0.876689\pi$
$174$	5.19615			0.393919
$175$	3.50000	−	18.1865i	0.264575	−	1.37477i
$176$		−	1.00000i		−	0.0753778i
$177$	10.5000	−	18.1865i	0.789228	−	1.36698i
$178$	−9.00000	+	5.19615i	−0.674579	+	0.389468i
$179$	−12.9904	+	7.50000i	−0.970947	+	0.560576i	−0.899525	−	0.436870i	$-0.856087\pi$
$179$	−12.9904	+	7.50000i	−0.970947	+	0.560576i	−0.0714220	+	0.997446i	$0.522754\pi$
$180$	5.19615	−	9.00000i	0.387298	−	0.670820i
$181$			13.8564i			1.02994i	0.857209	+	0.514969i	$0.172197\pi$
$181$			13.8564i			1.02994i	−0.857209	+	0.514969i	$0.827803\pi$
$182$	−8.66025	+	3.00000i	−0.641941	+	0.222375i
$183$			18.0000i			1.33060i
$184$	−1.50000	+	2.59808i	−0.110581	+	0.191533i
$185$	−12.1244	−	21.0000i	−0.891400	−	1.54395i
$186$	−3.00000	−	5.19615i	−0.219971	−	0.381000i
$187$	−1.50000	−	0.866025i	−0.109691	−	0.0633300i
$188$	1.73205			0.126323
$189$	−10.3923	−	9.00000i	−0.755929	−	0.654654i
$190$	−6.00000			−0.435286
$191$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$191$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$192$	−0.866025	−	1.50000i	−0.0625000	−	0.108253i
$193$	−2.00000	−	3.46410i	−0.143963	−	0.249351i	0.785022	−	0.619467i	$-0.212651\pi$
$193$	−2.00000	−	3.46410i	−0.143963	−	0.249351i	−0.928986	+	0.370116i	$0.879318\pi$
$194$	−7.79423	+	13.5000i	−0.559593	+	0.969244i
$195$			20.7846i			1.48842i
$196$	−5.50000	+	4.33013i	−0.392857	+	0.309295i
$197$			9.00000i			0.641223i	0.947211	+	0.320612i	$0.103888\pi$
$197$			9.00000i			0.641223i	−0.947211	+	0.320612i	$0.896112\pi$
$198$	−1.50000	+	2.59808i	−0.106600	+	0.184637i
$199$	−9.00000	+	5.19615i	−0.637993	+	0.368345i	−0.783841	−	0.620962i	$-0.786742\pi$
$199$	−9.00000	+	5.19615i	−0.637993	+	0.368345i	0.145848	+	0.989307i	$0.453409\pi$
$200$	−6.06218	+	3.50000i	−0.428661	+	0.247487i
$201$	−13.8564	+	24.0000i	−0.977356	+	1.69283i
$202$			5.19615i			0.365600i
$203$	−5.19615	+	6.00000i	−0.364698	+	0.421117i
$204$	−3.00000			−0.210042
$205$	−12.0000	+	20.7846i	−0.838116	+	1.45166i
$206$	−8.66025	−	15.0000i	−0.603388	−	1.04510i
$207$	7.79423	−	4.50000i	0.541736	−	0.312772i
$208$	3.00000	+	1.73205i	0.208013	+	0.120096i
$209$	1.73205			0.119808
$210$	5.19615	+	15.0000i	0.358569	+	1.03510i
$211$	4.00000			0.275371			0.137686	−	0.990476i	$-0.456034\pi$
$211$	4.00000			0.275371			0.137686	+	0.990476i	$0.456034\pi$
$212$		0			0
$213$	−22.5000	+	12.9904i	−1.54167	+	0.890086i
$214$	3.00000	+	5.19615i	0.205076	+	0.355202i
$215$	−1.73205	+	3.00000i	−0.118125	+	0.204598i
$216$			5.19615i			0.353553i
$217$	9.00000	+	1.73205i	0.610960	+	0.117579i
$218$			16.0000i			1.08366i
$219$	−20.7846	−	12.0000i	−1.40449	−	0.810885i
$220$	3.00000	−	1.73205i	0.202260	−	0.116775i
$221$	5.19615	−	3.00000i	0.349531	−	0.201802i
$222$	10.5000	+	6.06218i	0.704714	+	0.406867i
$223$		−	10.3923i		−	0.695920i	−0.937509	−	0.347960i	$-0.886874\pi$
$223$		−	10.3923i		−	0.695920i	0.937509	−	0.347960i	$-0.113126\pi$
$224$	2.59808	+	0.500000i	0.173591	+	0.0334077i
$225$	21.0000			1.40000
$226$	−3.00000	+	5.19615i	−0.199557	+	0.345643i
$227$	5.19615	+	9.00000i	0.344881	+	0.597351i	0.985332	−	0.170648i	$-0.0545860\pi$
$227$	5.19615	+	9.00000i	0.344881	+	0.597351i	−0.640451	+	0.767999i	$0.721253\pi$
$228$	2.59808	−	1.50000i	0.172062	−	0.0993399i
$229$	−12.0000	−	6.92820i	−0.792982	−	0.457829i	0.0480291	−	0.998846i	$-0.484706\pi$
$229$	−12.0000	−	6.92820i	−0.792982	−	0.457829i	−0.841011	+	0.541017i	$0.818039\pi$
$230$	−10.3923			−0.685248
$231$	−1.50000	−	4.33013i	−0.0986928	−	0.284901i
$232$	3.00000			0.196960
$233$	23.3827	+	13.5000i	1.53185	+	0.884414i	0.999277	+	0.0380310i	$0.0121086\pi$
$233$	23.3827	+	13.5000i	1.53185	+	0.884414i	0.532574	+	0.846383i	$0.321225\pi$
$234$	−5.19615	−	9.00000i	−0.339683	−	0.588348i
$235$	3.00000	+	5.19615i	0.195698	+	0.338960i
$236$	6.06218	−	10.5000i	0.394614	−	0.683492i
$237$	−13.8564			−0.900070
$238$	3.00000	−	3.46410i	0.194461	−	0.224544i
$239$			6.00000i			0.388108i	0.980991	+	0.194054i	$0.0621637\pi$
$239$			6.00000i			0.388108i	−0.980991	+	0.194054i	$0.937836\pi$
$240$	3.00000	−	5.19615i	0.193649	−	0.335410i
$241$	18.0000	−	10.3923i	1.15948	−	0.669427i	0.208302	−	0.978065i	$-0.433206\pi$
$241$	18.0000	−	10.3923i	1.15948	−	0.669427i	0.951180	+	0.308637i	$0.0998729\pi$
$242$	−0.866025	+	0.500000i	−0.0556702	+	0.0321412i
$243$	7.79423	−	13.5000i	0.500000	−	0.866025i
$244$			10.3923i			0.665299i
$245$	−22.5167	−	9.00000i	−1.43854	−	0.574989i
$246$		−	12.0000i		−	0.765092i
$247$	−3.00000	+	5.19615i	−0.190885	+	0.330623i
$248$	−1.73205	−	3.00000i	−0.109985	−	0.190500i
$249$	15.0000	+	25.9808i	0.950586	+	1.64646i
$250$	−6.00000	−	3.46410i	−0.379473	−	0.219089i
$251$	−12.1244			−0.765283			−0.382641	−	0.923897i	$-0.624985\pi$
$251$	−12.1244			−0.765283			−0.382641	+	0.923897i	$0.624985\pi$
$252$	−6.00000	−	5.19615i	−0.377964	−	0.327327i
$253$	3.00000			0.188608
$254$	−9.52628	−	5.50000i	−0.597732	−	0.345101i
$255$	−5.19615	−	9.00000i	−0.325396	−	0.563602i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−5.19615	+	9.00000i	−0.324127	+	0.561405i	−0.981335	−	0.192304i	$-0.938404\pi$
$257$	−5.19615	+	9.00000i	−0.324127	+	0.561405i	0.657208	+	0.753709i	$0.271737\pi$
$258$		−	1.73205i		−	0.107833i
$259$	−17.5000	+	6.06218i	−1.08740	+	0.376685i
$260$			12.0000i			0.744208i
$261$	−7.79423	−	4.50000i	−0.482451	−	0.278543i
$262$		0			0
$263$	15.5885	−	9.00000i	0.961225	−	0.554964i	0.0646755	−	0.997906i	$-0.479399\pi$
$263$	15.5885	−	9.00000i	0.961225	−	0.554964i	0.896550	+	0.442943i	$0.146065\pi$
$264$	−0.866025	+	1.50000i	−0.0533002	+	0.0923186i
$265$		0			0
$266$	−0.866025	+	4.50000i	−0.0530994	+	0.275913i
$267$	18.0000			1.10158
$268$	−8.00000	+	13.8564i	−0.488678	+	0.846415i
$269$	6.92820	+	12.0000i	0.422420	+	0.731653i	0.996176	−	0.0873736i	$-0.0278474\pi$
$269$	6.92820	+	12.0000i	0.422420	+	0.731653i	−0.573756	+	0.819027i	$0.694514\pi$
$270$	−15.5885	+	9.00000i	−0.948683	+	0.547723i
$271$	−9.00000	−	5.19615i	−0.546711	−	0.315644i	0.201083	−	0.979574i	$-0.435554\pi$
$271$	−9.00000	−	5.19615i	−0.546711	−	0.315644i	−0.747794	+	0.663930i	$0.768887\pi$
$272$	−1.73205			−0.105021
$273$	15.5885	+	3.00000i	0.943456	+	0.181568i
$274$	−18.0000			−1.08742
$275$	6.06218	+	3.50000i	0.365563	+	0.211058i
$276$	4.50000	−	2.59808i	0.270868	−	0.156386i
$277$	−4.00000	−	6.92820i	−0.240337	−	0.416275i	0.720473	−	0.693482i	$-0.243925\pi$
$277$	−4.00000	−	6.92820i	−0.240337	−	0.416275i	−0.960810	+	0.277207i	$0.910591\pi$
$278$	−0.866025	+	1.50000i	−0.0519408	+	0.0899640i
$279$			10.3923i			0.622171i
$280$	3.00000	+	8.66025i	0.179284	+	0.517549i
$281$		−	15.0000i		−	0.894825i	−0.894328	−	0.447412i	$-0.852346\pi$
$281$		−	15.0000i		−	0.894825i	0.894328	−	0.447412i	$-0.147654\pi$
$282$	−2.59808	−	1.50000i	−0.154713	−	0.0893237i
$283$	15.0000	−	8.66025i	0.891657	−	0.514799i	0.0171732	−	0.999853i	$-0.494533\pi$
$283$	15.0000	−	8.66025i	0.891657	−	0.514799i	0.874484	+	0.485054i	$0.161200\pi$
$284$	−12.9904	+	7.50000i	−0.770837	+	0.445043i
$285$	9.00000	+	5.19615i	0.533114	+	0.307794i
$286$		−	3.46410i		−	0.204837i
$287$	13.8564	+	12.0000i	0.817918	+	0.708338i
$288$			3.00000i			0.176777i
$289$	7.00000	−	12.1244i	0.411765	−	0.713197i
$290$	5.19615	+	9.00000i	0.305129	+	0.528498i
$291$	23.3827	−	13.5000i	1.37072	−	0.791384i
$292$	−12.0000	−	6.92820i	−0.702247	−	0.405442i
$293$	−8.66025			−0.505937			−0.252969	−	0.967474i	$-0.581407\pi$
$293$	−8.66025			−0.505937			−0.252969	+	0.967474i	$0.581407\pi$
$294$	12.0000	−	1.73205i	0.699854	−	0.101015i
$295$	42.0000			2.44533
$296$	6.06218	+	3.50000i	0.352357	+	0.203433i
$297$	4.50000	−	2.59808i	0.261116	−	0.150756i
$298$	4.50000	+	7.79423i	0.260678	+	0.451508i
$299$	−5.19615	+	9.00000i	−0.300501	+	0.520483i
$300$	12.1244			0.700000
$301$	2.00000	+	1.73205i	0.115278	+	0.0998337i
$302$		−	11.0000i		−	0.632979i
$303$	4.50000	−	7.79423i	0.258518	−	0.447767i
$304$	1.50000	−	0.866025i	0.0860309	−	0.0496700i
$305$	−31.1769	+	18.0000i	−1.78518	+	1.03068i
$306$	4.50000	+	2.59808i	0.257248	+	0.148522i
$307$		−	17.3205i		−	0.988534i	−0.869310	−	0.494267i	$-0.835437\pi$
$307$		−	17.3205i		−	0.988534i	0.869310	−	0.494267i	$-0.164563\pi$
$308$	−0.866025	−	2.50000i	−0.0493464	−	0.142451i
$309$			30.0000i			1.70664i
$310$	6.00000	−	10.3923i	0.340777	−	0.590243i
$311$	11.2583	+	19.5000i	0.638401	+	1.10574i	0.985784	+	0.168020i	$0.0537373\pi$
$311$	11.2583	+	19.5000i	0.638401	+	1.10574i	−0.347382	+	0.937724i	$0.612929\pi$
$312$	−3.00000	−	5.19615i	−0.169842	−	0.294174i
$313$	−25.5000	−	14.7224i	−1.44135	−	0.832161i	−0.443406	−	0.896321i	$-0.646230\pi$
$313$	−25.5000	−	14.7224i	−1.44135	−	0.832161i	−0.997940	+	0.0641600i	$0.979563\pi$
$314$	−5.19615			−0.293236
$315$	5.19615	−	27.0000i	0.292770	−	1.52128i
$316$	−8.00000			−0.450035
$317$	5.19615	+	3.00000i	0.291845	+	0.168497i	0.638774	−	0.769395i	$-0.279442\pi$
$317$	5.19615	+	3.00000i	0.291845	+	0.168497i	−0.346929	+	0.937892i	$0.612775\pi$
$318$		0			0
$319$	−1.50000	−	2.59808i	−0.0839839	−	0.145464i
$320$	1.73205	−	3.00000i	0.0968246	−	0.167705i
$321$		−	10.3923i		−	0.580042i
$322$	−1.50000	+	7.79423i	−0.0835917	+	0.434355i
$323$		−	3.00000i		−	0.166924i
$324$	4.50000	−	7.79423i	0.250000	−	0.433013i
$325$	−21.0000	+	12.1244i	−1.16487	+	0.672538i
$326$	12.1244	−	7.00000i	0.671506	−	0.387694i
$327$	13.8564	−	24.0000i	0.766261	−	1.32720i
$328$		−	6.92820i		−	0.382546i
$329$	4.33013	−	1.50000i	0.238728	−	0.0826977i
$330$	−6.00000			−0.330289
$331$	−5.00000	+	8.66025i	−0.274825	+	0.476011i	−0.970091	−	0.242742i	$-0.921953\pi$
$331$	−5.00000	+	8.66025i	−0.274825	+	0.476011i	0.695266	+	0.718752i	$0.255287\pi$
$332$	8.66025	+	15.0000i	0.475293	+	0.823232i
$333$	−10.5000	−	18.1865i	−0.575396	−	0.996616i
$334$	−21.0000	−	12.1244i	−1.14907	−	0.663415i
$335$	−55.4256			−3.02823
$336$	−3.46410	−	3.00000i	−0.188982	−	0.163663i
$337$	4.00000			0.217894			0.108947	−	0.994048i	$-0.465252\pi$
$337$	4.00000			0.217894			0.108947	+	0.994048i	$0.465252\pi$
$338$	−0.866025	−	0.500000i	−0.0471056	−	0.0271964i
$339$	9.00000	−	5.19615i	0.488813	−	0.282216i
$340$	−3.00000	−	5.19615i	−0.162698	−	0.281801i
$341$	−1.73205	+	3.00000i	−0.0937958	+	0.162459i
$342$	−5.19615			−0.280976
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$		−	1.00000i		−	0.0539164i
$345$	15.5885	+	9.00000i	0.839254	+	0.484544i
$346$	18.0000	−	10.3923i	0.967686	−	0.558694i
$347$	20.7846	−	12.0000i	1.11578	−	0.644194i	0.175457	−	0.984487i	$-0.443860\pi$
$347$	20.7846	−	12.0000i	1.11578	−	0.644194i	0.940319	+	0.340293i	$0.110526\pi$
$348$	−4.50000	−	2.59808i	−0.241225	−	0.139272i
$349$		−	20.7846i		−	1.11257i	−0.830990	−	0.556287i	$-0.812225\pi$
$349$		−	20.7846i		−	1.11257i	0.830990	−	0.556287i	$-0.187775\pi$
$350$	−12.1244	+	14.0000i	−0.648074	+	0.748331i
$351$			18.0000i			0.960769i
$352$	−0.500000	+	0.866025i	−0.0266501	+	0.0461593i
$353$	−1.73205	−	3.00000i	−0.0921878	−	0.159674i	0.816244	−	0.577708i	$-0.196053\pi$
$353$	−1.73205	−	3.00000i	−0.0921878	−	0.159674i	−0.908431	+	0.418034i	$0.862719\pi$
$354$	−18.1865	+	10.5000i	−0.966603	+	0.558069i
$355$	−45.0000	−	25.9808i	−2.38835	−	1.37892i
$356$	10.3923			0.550791
$357$	−7.50000	+	2.59808i	−0.396942	+	0.137505i
$358$	15.0000			0.792775
$359$	−5.19615	−	3.00000i	−0.274242	−	0.158334i	0.356572	−	0.934268i	$-0.383946\pi$
$359$	−5.19615	−	3.00000i	−0.274242	−	0.158334i	−0.630814	+	0.775934i	$0.717279\pi$
$360$	−9.00000	+	5.19615i	−0.474342	+	0.273861i
$361$	−8.00000	−	13.8564i	−0.421053	−	0.729285i
$362$	6.92820	−	12.0000i	0.364138	−	0.630706i
$363$	1.73205			0.0909091
$364$	9.00000	+	1.73205i	0.471728	+	0.0907841i
$365$		−	48.0000i		−	2.51243i
$366$	9.00000	−	15.5885i	0.470438	−	0.814822i
$367$	−6.00000	+	3.46410i	−0.313197	+	0.180825i	−0.648356	−	0.761337i	$-0.724543\pi$
$367$	−6.00000	+	3.46410i	−0.313197	+	0.180825i	0.335159	+	0.942162i	$0.391210\pi$
$368$	2.59808	−	1.50000i	0.135434	−	0.0781929i
$369$	−10.3923	+	18.0000i	−0.541002	+	0.937043i
$370$			24.2487i			1.26063i
$371$		0			0
$372$			6.00000i			0.311086i
$373$	−7.00000	+	12.1244i	−0.362446	+	0.627775i	−0.988363	−	0.152115i	$-0.951392\pi$
$373$	−7.00000	+	12.1244i	−0.362446	+	0.627775i	0.625917	+	0.779890i	$0.284725\pi$
$374$	0.866025	+	1.50000i	0.0447811	+	0.0775632i
$375$	6.00000	+	10.3923i	0.309839	+	0.536656i
$376$	−1.50000	−	0.866025i	−0.0773566	−	0.0446619i
$377$	10.3923			0.535231
$378$	4.50000	+	12.9904i	0.231455	+	0.668153i
$379$	−20.0000			−1.02733			−0.513665	−	0.857991i	$-0.671713\pi$
$379$	−20.0000			−1.02733			−0.513665	+	0.857991i	$0.671713\pi$
$380$	5.19615	+	3.00000i	0.266557	+	0.153897i
$381$	9.52628	+	16.5000i	0.488046	+	0.845321i
$382$		0			0
$383$	14.7224	−	25.5000i	0.752281	−	1.30299i	−0.194434	−	0.980916i	$-0.562287\pi$
$383$	14.7224	−	25.5000i	0.752281	−	1.30299i	0.946715	−	0.322073i	$-0.104380\pi$
$384$			1.73205i			0.0883883i
$385$	6.00000	−	6.92820i	0.305788	−	0.353094i
$386$			4.00000i			0.203595i
$387$	−1.50000	+	2.59808i	−0.0762493	+	0.132068i
$388$	13.5000	−	7.79423i	0.685359	−	0.395692i
$389$	−15.5885	+	9.00000i	−0.790366	+	0.456318i	−0.840091	−	0.542445i	$-0.817499\pi$
$389$	−15.5885	+	9.00000i	−0.790366	+	0.456318i	0.0497253	+	0.998763i	$0.484165\pi$
$390$	10.3923	−	18.0000i	0.526235	−	0.911465i
$391$		−	5.19615i		−	0.262781i
$392$	6.92820	−	1.00000i	0.349927	−	0.0505076i
$393$		0			0
$394$	4.50000	−	7.79423i	0.226707	−	0.392668i
$395$	−13.8564	−	24.0000i	−0.697191	−	1.20757i
$396$	2.59808	−	1.50000i	0.130558	−	0.0753778i
$397$	−1.50000	−	0.866025i	−0.0752828	−	0.0434646i	0.461886	−	0.886939i	$-0.347173\pi$
$397$	−1.50000	−	0.866025i	−0.0752828	−	0.0434646i	−0.537169	+	0.843475i	$0.680506\pi$
$398$	10.3923			0.520919
$399$	5.19615	−	6.00000i	0.260133	−	0.300376i
$400$	7.00000			0.350000
$401$	−20.7846	−	12.0000i	−1.03793	−	0.599251i	−0.118686	−	0.992932i	$-0.537868\pi$
$401$	−20.7846	−	12.0000i	−1.03793	−	0.599251i	−0.919247	+	0.393680i	$0.871202\pi$
$402$	24.0000	−	13.8564i	1.19701	−	0.691095i
$403$	−6.00000	−	10.3923i	−0.298881	−	0.517678i
$404$	2.59808	−	4.50000i	0.129259	−	0.223883i
$405$	31.1769			1.54919
$406$	7.50000	−	2.59808i	0.372219	−	0.128940i
$407$		−	7.00000i		−	0.346977i
$408$	2.59808	+	1.50000i	0.128624	+	0.0742611i
$409$	12.0000	−	6.92820i	0.593362	−	0.342578i	−0.173064	−	0.984911i	$-0.555367\pi$
$409$	12.0000	−	6.92820i	0.593362	−	0.342578i	0.766426	+	0.642333i	$0.222033\pi$
$410$	20.7846	−	12.0000i	1.02648	−	0.592638i
$411$	27.0000	+	15.5885i	1.33181	+	0.768922i
$412$			17.3205i			0.853320i
$413$	6.06218	−	31.5000i	0.298300	−	1.55001i
$414$	−9.00000			−0.442326
$415$	−30.0000	+	51.9615i	−1.47264	+	2.55069i
$416$	−1.73205	−	3.00000i	−0.0849208	−	0.147087i
$417$	2.59808	−	1.50000i	0.127228	−	0.0734553i
$418$	−1.50000	−	0.866025i	−0.0733674	−	0.0423587i
$419$	−1.73205			−0.0846162			−0.0423081	−	0.999105i	$-0.513471\pi$
$419$	−1.73205			−0.0846162			−0.0423081	+	0.999105i	$0.513471\pi$
$420$	3.00000	−	15.5885i	0.146385	−	0.760639i
$421$	5.00000			0.243685			0.121843	−	0.992549i	$-0.461120\pi$
$421$	5.00000			0.243685			0.121843	+	0.992549i	$0.461120\pi$
$422$	−3.46410	−	2.00000i	−0.168630	−	0.0973585i
$423$	2.59808	+	4.50000i	0.126323	+	0.218797i
$424$		0			0
$425$	6.06218	−	10.5000i	0.294059	−	0.509325i
$426$	25.9808			1.25877
$427$	9.00000	+	25.9808i	0.435541	+	1.25730i
$428$		−	6.00000i		−	0.290021i
$429$	−3.00000	+	5.19615i	−0.144841	+	0.250873i
$430$	3.00000	−	1.73205i	0.144673	−	0.0835269i
$431$	10.3923	−	6.00000i	0.500580	−	0.289010i	−0.228373	−	0.973574i	$-0.573341\pi$
$431$	10.3923	−	6.00000i	0.500580	−	0.289010i	0.728953	+	0.684564i	$0.240007\pi$
$432$	2.59808	−	4.50000i	0.125000	−	0.216506i
$433$		−	8.66025i		−	0.416185i	−0.978109	−	0.208093i	$-0.933274\pi$
$433$		−	8.66025i		−	0.416185i	0.978109	−	0.208093i	$-0.0667255\pi$
$434$	−6.92820	−	6.00000i	−0.332564	−	0.288009i
$435$		−	18.0000i		−	0.863034i
$436$	8.00000	−	13.8564i	0.383131	−	0.663602i
$437$	2.59808	+	4.50000i	0.124283	+	0.215264i
$438$	12.0000	+	20.7846i	0.573382	+	0.993127i
$439$	13.5000	+	7.79423i	0.644320	+	0.371998i	0.786277	−	0.617875i	$-0.212006\pi$
$439$	13.5000	+	7.79423i	0.644320	+	0.371998i	−0.141957	+	0.989873i	$0.545339\pi$
$440$	−3.46410			−0.165145
$441$	−19.5000	−	7.79423i	−0.928571	−	0.371154i
$442$	−6.00000			−0.285391
$443$	7.79423	+	4.50000i	0.370315	+	0.213801i	0.673596	−	0.739100i	$-0.264749\pi$
$443$	7.79423	+	4.50000i	0.370315	+	0.213801i	−0.303281	+	0.952901i	$0.598082\pi$
$444$	−6.06218	−	10.5000i	−0.287698	−	0.498308i
$445$	18.0000	+	31.1769i	0.853282	+	1.47793i
$446$	−5.19615	+	9.00000i	−0.246045	+	0.426162i
$447$		−	15.5885i		−	0.737309i
$448$	−2.00000	−	1.73205i	−0.0944911	−	0.0818317i
$449$		−	12.0000i		−	0.566315i	−0.959073	−	0.283158i	$-0.908618\pi$
$449$		−	12.0000i		−	0.566315i	0.959073	−	0.283158i	$-0.0913819\pi$
$450$	−18.1865	−	10.5000i	−0.857321	−	0.494975i
$451$	−6.00000	+	3.46410i	−0.282529	+	0.163118i
$452$	5.19615	−	3.00000i	0.244406	−	0.141108i
$453$	−9.52628	+	16.5000i	−0.447584	+	0.775238i
$454$		−	10.3923i		−	0.487735i
$455$	10.3923	+	30.0000i	0.487199	+	1.40642i
$456$	−3.00000			−0.140488
$457$	16.0000	−	27.7128i	0.748448	−	1.29635i	−0.200118	−	0.979772i	$-0.564132\pi$
$457$	16.0000	−	27.7128i	0.748448	−	1.29635i	0.948566	−	0.316579i	$-0.102534\pi$
$458$	6.92820	+	12.0000i	0.323734	+	0.560723i
$459$	−4.50000	−	7.79423i	−0.210042	−	0.363803i
$460$	9.00000	+	5.19615i	0.419627	+	0.242272i
$461$	−8.66025			−0.403348			−0.201674	−	0.979453i	$-0.564638\pi$
$461$	−8.66025			−0.403348			−0.201674	+	0.979453i	$0.564638\pi$
$462$	−0.866025	+	4.50000i	−0.0402911	+	0.209359i
$463$	−4.00000			−0.185896			−0.0929479	−	0.995671i	$-0.529629\pi$
$463$	−4.00000			−0.185896			−0.0929479	+	0.995671i	$0.529629\pi$
$464$	−2.59808	−	1.50000i	−0.120613	−	0.0696358i
$465$	−18.0000	+	10.3923i	−0.834730	+	0.481932i
$466$	−13.5000	−	23.3827i	−0.625375	−	1.08318i
$467$	−7.79423	+	13.5000i	−0.360674	+	0.624705i	−0.988072	−	0.153993i	$-0.950787\pi$
$467$	−7.79423	+	13.5000i	−0.360674	+	0.624705i	0.627398	+	0.778699i	$0.284120\pi$
$468$			10.3923i			0.480384i
$469$	−8.00000	+	41.5692i	−0.369406	+	1.91949i
$470$		−	6.00000i		−	0.276759i
$471$	7.79423	+	4.50000i	0.359139	+	0.207349i
$472$	−10.5000	+	6.06218i	−0.483302	+	0.279034i
$473$	−0.866025	+	0.500000i	−0.0398199	+	0.0229900i
$474$	12.0000	+	6.92820i	0.551178	+	0.318223i
$475$			12.1244i			0.556304i
$476$	−4.33013	+	1.50000i	−0.198471	+	0.0687524i
$477$		0			0
$478$	3.00000	−	5.19615i	0.137217	−	0.237666i
$479$	−8.66025	−	15.0000i	−0.395697	−	0.685367i	0.597493	−	0.801874i	$-0.296164\pi$
$479$	−8.66025	−	15.0000i	−0.395697	−	0.685367i	−0.993190	+	0.116507i	$0.962830\pi$
$480$	−5.19615	+	3.00000i	−0.237171	+	0.136931i
$481$	21.0000	+	12.1244i	0.957518	+	0.552823i
$482$	−20.7846			−0.946713
$483$	9.00000	−	10.3923i	0.409514	−	0.472866i
$484$	1.00000			0.0454545
$485$	46.7654	+	27.0000i	2.12351	+	1.22601i
$486$	−13.5000	+	7.79423i	−0.612372	+	0.353553i
$487$	13.0000	+	22.5167i	0.589086	+	1.02033i	0.994352	+	0.106129i	$0.0338455\pi$
$487$	13.0000	+	22.5167i	0.589086	+	1.02033i	−0.405266	+	0.914199i	$0.632821\pi$
$488$	5.19615	−	9.00000i	0.235219	−	0.407411i
$489$	−24.2487			−1.09656
$490$	15.0000	+	19.0526i	0.677631	+	0.860707i
$491$		−	30.0000i		−	1.35388i	−0.736038	−	0.676941i	$-0.763305\pi$
$491$		−	30.0000i		−	1.35388i	0.736038	−	0.676941i	$-0.236695\pi$
$492$	−6.00000	+	10.3923i	−0.270501	+	0.468521i
$493$	−4.50000	+	2.59808i	−0.202670	+	0.117011i
$494$	5.19615	−	3.00000i	0.233786	−	0.134976i
$495$	9.00000	+	5.19615i	0.404520	+	0.233550i
$496$			3.46410i			0.155543i
$497$	−25.9808	+	30.0000i	−1.16540	+	1.34568i
$498$		−	30.0000i		−	1.34433i
$499$	16.0000	−	27.7128i	0.716258	−	1.24060i	−0.246214	−	0.969216i	$-0.579187\pi$
$499$	16.0000	−	27.7128i	0.716258	−	1.24060i	0.962472	−	0.271380i	$-0.0874801\pi$
$500$	3.46410	+	6.00000i	0.154919	+	0.268328i
$501$	21.0000	+	36.3731i	0.938211	+	1.62503i
$502$	10.5000	+	6.06218i	0.468638	+	0.270568i
$503$	17.3205			0.772283			0.386142	−	0.922440i	$-0.373808\pi$
$503$	17.3205			0.772283			0.386142	+	0.922440i	$0.373808\pi$
$504$	2.59808	+	7.50000i	0.115728	+	0.334077i
$505$	18.0000			0.800989
$506$	−2.59808	−	1.50000i	−0.115499	−	0.0666831i
$507$	0.866025	+	1.50000i	0.0384615	+	0.0666173i
$508$	5.50000	+	9.52628i	0.244023	+	0.422660i
$509$	−3.46410	+	6.00000i	−0.153544	+	0.265945i	−0.932528	−	0.361098i	$-0.882402\pi$
$509$	−3.46410	+	6.00000i	−0.153544	+	0.265945i	0.778984	+	0.627044i	$0.215735\pi$
$510$			10.3923i			0.460179i
$511$	−36.0000	−	6.92820i	−1.59255	−	0.306486i
$512$			1.00000i			0.0441942i
$513$	7.79423	+	4.50000i	0.344124	+	0.198680i
$514$	9.00000	−	5.19615i	0.396973	−	0.229192i
$515$	−51.9615	+	30.0000i	−2.28970	+	1.32196i
$516$	−0.866025	+	1.50000i	−0.0381246	+	0.0660338i
$517$			1.73205i			0.0761755i
$518$	18.1865	+	3.50000i	0.799070	+	0.153781i
$519$	−36.0000			−1.58022
$520$	6.00000	−	10.3923i	0.263117	−	0.455733i
$521$	−8.66025	−	15.0000i	−0.379413	−	0.657162i	0.611564	−	0.791195i	$-0.290541\pi$
$521$	−8.66025	−	15.0000i	−0.379413	−	0.657162i	−0.990977	+	0.134033i	$0.957207\pi$
$522$	4.50000	+	7.79423i	0.196960	+	0.341144i
$523$	−15.0000	−	8.66025i	−0.655904	−	0.378686i	0.134810	−	0.990871i	$-0.456957\pi$
$523$	−15.0000	−	8.66025i	−0.655904	−	0.378686i	−0.790715	+	0.612185i	$0.790291\pi$
$524$		0			0
$525$	30.3109	−	10.5000i	1.32288	−	0.458258i
$526$	−18.0000			−0.784837
$527$	5.19615	+	3.00000i	0.226348	+	0.130682i
$528$	1.50000	−	0.866025i	0.0652791	−	0.0376889i
$529$	−7.00000	−	12.1244i	−0.304348	−	0.527146i
$530$		0			0
$531$	36.3731			1.57846
$532$	3.00000	−	3.46410i	0.130066	−	0.150188i
$533$		−	24.0000i		−	1.03956i
$534$	−15.5885	−	9.00000i	−0.674579	−	0.389468i
$535$	18.0000	−	10.3923i	0.778208	−	0.449299i
$536$	13.8564	−	8.00000i	0.598506	−	0.345547i
$537$	−22.5000	−	12.9904i	−0.970947	−	0.560576i
$538$		−	13.8564i		−	0.597392i
$539$	−4.33013	−	5.50000i	−0.186512	−	0.236902i
$540$	18.0000			0.774597
$541$	−10.0000	+	17.3205i	−0.429934	+	0.744667i	−0.996867	−	0.0790969i	$-0.974796\pi$
$541$	−10.0000	+	17.3205i	−0.429934	+	0.744667i	0.566933	+	0.823764i	$0.308130\pi$
$542$	5.19615	+	9.00000i	0.223194	+	0.386583i
$543$	−20.7846	+	12.0000i	−0.891953	+	0.514969i
$544$	1.50000	+	0.866025i	0.0643120	+	0.0371305i
$545$	55.4256			2.37417
$546$	−12.0000	−	10.3923i	−0.513553	−	0.444750i
$547$	−25.0000			−1.06892			−0.534461	−	0.845193i	$-0.679486\pi$
$547$	−25.0000			−1.06892			−0.534461	+	0.845193i	$0.679486\pi$
$548$	15.5885	+	9.00000i	0.665906	+	0.384461i
$549$	−27.0000	+	15.5885i	−1.15233	+	0.665299i
$550$	−3.50000	−	6.06218i	−0.149241	−	0.258492i
$551$	2.59808	−	4.50000i	0.110682	−	0.191706i
$552$	−5.19615			−0.221163
$553$	−20.0000	+	6.92820i	−0.850487	+	0.294617i
$554$			8.00000i			0.339887i
$555$	21.0000	−	36.3731i	0.891400	−	1.54395i
$556$	1.50000	−	0.866025i	0.0636142	−	0.0367277i
$557$	28.5788	−	16.5000i	1.21092	−	0.699127i	0.247964	−	0.968769i	$-0.420239\pi$
$557$	28.5788	−	16.5000i	1.21092	−	0.699127i	0.962961	+	0.269642i	$0.0869053\pi$
$558$	5.19615	−	9.00000i	0.219971	−	0.381000i
$559$		−	3.46410i		−	0.146516i
$560$	1.73205	−	9.00000i	0.0731925	−	0.380319i
$561$		−	3.00000i		−	0.126660i
$562$	−7.50000	+	12.9904i	−0.316368	+	0.547966i
$563$	15.5885	+	27.0000i	0.656975	+	1.13791i	0.981395	+	0.192001i	$0.0614977\pi$
$563$	15.5885	+	27.0000i	0.656975	+	1.13791i	−0.324420	+	0.945913i	$0.605169\pi$
$564$	1.50000	+	2.59808i	0.0631614	+	0.109399i
$565$	18.0000	+	10.3923i	0.757266	+	0.437208i
$566$	−17.3205			−0.728035
$567$	4.50000	−	23.3827i	0.188982	−	0.981981i
$568$	15.0000			0.629386
$569$	−33.7750	−	19.5000i	−1.41592	−	0.817483i	−0.419984	−	0.907532i	$-0.637964\pi$
$569$	−33.7750	−	19.5000i	−1.41592	−	0.817483i	−0.995937	+	0.0900490i	$0.971298\pi$
$570$	−5.19615	−	9.00000i	−0.217643	−	0.376969i
$571$	−11.5000	−	19.9186i	−0.481260	−	0.833567i	0.518509	−	0.855072i	$-0.326487\pi$
$571$	−11.5000	−	19.9186i	−0.481260	−	0.833567i	−0.999769	+	0.0215055i	$0.993154\pi$
$572$	−1.73205	+	3.00000i	−0.0724207	+	0.125436i
$573$		0			0
$574$	−6.00000	−	17.3205i	−0.250435	−	0.722944i
$575$			21.0000i			0.875761i
$576$	1.50000	−	2.59808i	0.0625000	−	0.108253i
$577$	−24.0000	+	13.8564i	−0.999133	+	0.576850i	−0.907992	−	0.418988i	$-0.862385\pi$
$577$	−24.0000	+	13.8564i	−0.999133	+	0.576850i	−0.0911414	+	0.995838i	$0.529052\pi$
$578$	−12.1244	+	7.00000i	−0.504307	+	0.291162i
$579$	3.46410	−	6.00000i	0.143963	−	0.249351i
$580$		−	10.3923i		−	0.431517i
$581$	34.6410	+	30.0000i	1.43715	+	1.24461i
$582$	−27.0000			−1.11919
$583$		0			0
$584$	6.92820	+	12.0000i	0.286691	+	0.496564i
$585$	−31.1769	+	18.0000i	−1.28901	+	0.744208i
$586$	7.50000	+	4.33013i	0.309822	+	0.178876i
$587$	−10.3923			−0.428936			−0.214468	−	0.976731i	$-0.568802\pi$
$587$	−10.3923			−0.428936			−0.214468	+	0.976731i	$0.568802\pi$
$588$	−11.2583	−	4.50000i	−0.464286	−	0.185577i
$589$	−6.00000			−0.247226
$590$	−36.3731	−	21.0000i	−1.49746	−	0.864556i
$591$	−13.5000	+	7.79423i	−0.555316	+	0.320612i
$592$	−3.50000	−	6.06218i	−0.143849	−	0.249154i
$593$	14.7224	−	25.5000i	0.604578	−	1.04716i	−0.387540	−	0.921853i	$-0.626675\pi$
$593$	14.7224	−	25.5000i	0.604578	−	1.04716i	0.992118	−	0.125307i	$-0.0399915\pi$
$594$	−5.19615			−0.213201
$595$	−12.0000	−	10.3923i	−0.491952	−	0.426043i
$596$		−	9.00000i		−	0.368654i
$597$	−15.5885	−	9.00000i	−0.637993	−	0.368345i
$598$	9.00000	−	5.19615i	0.368037	−	0.212486i
$599$	−20.7846	+	12.0000i	−0.849236	+	0.490307i	−0.860393	−	0.509631i	$-0.829782\pi$
$599$	−20.7846	+	12.0000i	−0.849236	+	0.490307i	0.0111569	+	0.999938i	$0.496449\pi$
$600$	−10.5000	−	6.06218i	−0.428661	−	0.247487i
$601$		−	6.92820i		−	0.282607i	−0.989966	−	0.141304i	$-0.954871\pi$
$601$		−	6.92820i		−	0.282607i	0.989966	−	0.141304i	$-0.0451294\pi$
$602$	−0.866025	−	2.50000i	−0.0352966	−	0.101892i
$603$	−48.0000			−1.95471
$604$	−5.50000	+	9.52628i	−0.223792	+	0.387619i
$605$	1.73205	+	3.00000i	0.0704179	+	0.121967i
$606$	−7.79423	+	4.50000i	−0.316619	+	0.182800i
$607$	33.0000	+	19.0526i	1.33943	+	0.773320i	0.986723	−	0.162415i	$-0.0519282\pi$
$607$	33.0000	+	19.0526i	1.33943	+	0.773320i	0.352706	+	0.935734i	$0.385262\pi$
$608$	−1.73205			−0.0702439
$609$	−13.5000	−	2.59808i	−0.547048	−	0.105279i
$610$	36.0000			1.45760
$611$	−5.19615	−	3.00000i	−0.210214	−	0.121367i
$612$	−2.59808	−	4.50000i	−0.105021	−	0.181902i
$613$	−1.00000	−	1.73205i	−0.0403896	−	0.0699569i	0.845124	−	0.534570i	$-0.179527\pi$
$613$	−1.00000	−	1.73205i	−0.0403896	−	0.0699569i	−0.885514	+	0.464614i	$0.846193\pi$
$614$	−8.66025	+	15.0000i	−0.349499	+	0.605351i
$615$	−41.5692			−1.67623
$616$	−0.500000	+	2.59808i	−0.0201456	+	0.104679i
$617$		−	12.0000i		−	0.483102i	−0.970388	−	0.241551i	$-0.922344\pi$
$617$		−	12.0000i		−	0.483102i	0.970388	−	0.241551i	$-0.0776561\pi$
$618$	15.0000	−	25.9808i	0.603388	−	1.04510i
$619$	33.0000	−	19.0526i	1.32638	−	0.765787i	0.341644	−	0.939829i	$-0.389016\pi$
$619$	33.0000	−	19.0526i	1.32638	−	0.765787i	0.984738	+	0.174042i	$0.0556830\pi$
$620$	−10.3923	+	6.00000i	−0.417365	+	0.240966i
$621$	13.5000	+	7.79423i	0.541736	+	0.312772i
$622$		−	22.5167i		−	0.902836i
$623$	25.9808	−	9.00000i	1.04090	−	0.360577i
$624$			6.00000i			0.240192i
$625$	5.50000	−	9.52628i	0.220000	−	0.381051i
$626$	14.7224	+	25.5000i	0.588427	+	1.01918i
$627$	1.50000	+	2.59808i	0.0599042	+	0.103757i
$628$	4.50000	+	2.59808i	0.179570	+	0.103675i
$629$	−12.1244			−0.483430
$630$	−18.0000	+	20.7846i	−0.717137	+	0.828079i
$631$	−22.0000			−0.875806			−0.437903	−	0.899022i	$-0.644279\pi$
$631$	−22.0000			−0.875806			−0.437903	+	0.899022i	$0.644279\pi$
$632$	6.92820	+	4.00000i	0.275589	+	0.159111i
$633$	3.46410	+	6.00000i	0.137686	+	0.238479i
$634$	−3.00000	−	5.19615i	−0.119145	−	0.206366i
$635$	−19.0526	+	33.0000i	−0.756078	+	1.30957i
$636$		0			0
$637$	24.0000	−	3.46410i	0.950915	−	0.137253i
$638$			3.00000i			0.118771i
$639$	−38.9711	−	22.5000i	−1.54167	−	0.890086i
$640$	−3.00000	+	1.73205i	−0.118585	+	0.0684653i
$641$	−41.5692	+	24.0000i	−1.64189	+	0.947943i	−0.661723	+	0.749749i	$0.730174\pi$
$641$	−41.5692	+	24.0000i	−1.64189	+	0.947943i	−0.980163	+	0.198194i	$0.936492\pi$
$642$	−5.19615	+	9.00000i	−0.205076	+	0.355202i
$643$		−	34.6410i		−	1.36611i	−0.730368	−	0.683054i	$-0.760651\pi$
$643$		−	34.6410i		−	1.36611i	0.730368	−	0.683054i	$-0.239349\pi$
$644$	5.19615	−	6.00000i	0.204757	−	0.236433i
$645$	−6.00000			−0.236250
$646$	−1.50000	+	2.59808i	−0.0590167	+	0.102220i
$647$	−5.19615	−	9.00000i	−0.204282	−	0.353827i	0.745622	−	0.666369i	$-0.232153\pi$
$647$	−5.19615	−	9.00000i	−0.204282	−	0.353827i	−0.949904	+	0.312543i	$0.898819\pi$
$648$	−7.79423	+	4.50000i	−0.306186	+	0.176777i
$649$	10.5000	+	6.06218i	0.412161	+	0.237961i
$650$	24.2487			0.951113
$651$	5.19615	+	15.0000i	0.203653	+	0.587896i
$652$	−14.0000			−0.548282
$653$	−5.19615	−	3.00000i	−0.203341	−	0.117399i	0.394872	−	0.918736i	$-0.370789\pi$
$653$	−5.19615	−	3.00000i	−0.203341	−	0.117399i	−0.598213	+	0.801337i	$0.704122\pi$
$654$	−24.0000	+	13.8564i	−0.938474	+	0.541828i
$655$		0			0
$656$	−3.46410	+	6.00000i	−0.135250	+	0.234261i
$657$		−	41.5692i		−	1.62177i
$658$	−4.50000	−	0.866025i	−0.175428	−	0.0337612i
$659$			12.0000i			0.467454i	0.972302	+	0.233727i	$0.0750921\pi$
$659$			12.0000i			0.467454i	−0.972302	+	0.233727i	$0.924908\pi$
$660$	5.19615	+	3.00000i	0.202260	+	0.116775i
$661$	25.5000	−	14.7224i	0.991835	−	0.572636i	0.0860127	−	0.996294i	$-0.472587\pi$
$661$	25.5000	−	14.7224i	0.991835	−	0.572636i	0.905822	+	0.423658i	$0.139254\pi$
$662$	8.66025	−	5.00000i	0.336590	−	0.194331i
$663$	9.00000	+	5.19615i	0.349531	+	0.201802i
$664$		−	17.3205i		−	0.672166i
$665$	15.5885	+	3.00000i	0.604494	+	0.116335i
$666$			21.0000i			0.813733i
$667$	4.50000	−	7.79423i	0.174241	−	0.301794i
$668$	12.1244	+	21.0000i	0.469105	+	0.812514i
$669$	15.5885	−	9.00000i	0.602685	−	0.347960i
$670$	48.0000	+	27.7128i	1.85440	+	1.07064i
$671$	−10.3923			−0.401190
$672$	1.50000	+	4.33013i	0.0578638	+	0.167038i
$673$	22.0000			0.848038			0.424019	−	0.905653i	$-0.360619\pi$
$673$	22.0000			0.848038			0.424019	+	0.905653i	$0.360619\pi$
$674$	−3.46410	−	2.00000i	−0.133432	−	0.0770371i
$675$	18.1865	+	31.5000i	0.700000	+	1.21244i
$676$	0.500000	+	0.866025i	0.0192308	+	0.0333087i
$677$	18.1865	−	31.5000i	0.698965	−	1.21064i	−0.269860	−	0.962899i	$-0.586978\pi$
$677$	18.1865	−	31.5000i	0.698965	−	1.21064i	0.968826	−	0.247744i	$-0.0796891\pi$
$678$	−10.3923			−0.399114
$679$	27.0000	−	31.1769i	1.03616	−	1.19646i
$680$			6.00000i			0.230089i
$681$	−9.00000	+	15.5885i	−0.344881	+	0.597351i
$682$	3.00000	−	1.73205i	0.114876	−	0.0663237i
$683$	−33.7750	+	19.5000i	−1.29236	+	0.746147i	−0.979073	−	0.203510i	$-0.934765\pi$
$683$	−33.7750	+	19.5000i	−1.29236	+	0.746147i	−0.313291	+	0.949657i	$0.601432\pi$
$684$	4.50000	+	2.59808i	0.172062	+	0.0993399i
$685$			62.3538i			2.38242i
$686$	16.4545	−	8.50000i	0.628235	−	0.324532i
$687$		−	24.0000i		−	0.915657i
$688$	−0.500000	+	0.866025i	−0.0190623	+	0.0330169i
$689$		0			0
$690$	−9.00000	−	15.5885i	−0.342624	−	0.593442i
$691$	3.00000	+	1.73205i	0.114125	+	0.0658903i	0.555976	−	0.831198i	$-0.312345\pi$
$691$	3.00000	+	1.73205i	0.114125	+	0.0658903i	−0.441851	+	0.897089i	$0.645678\pi$
$692$	−20.7846			−0.790112
$693$	5.19615	−	6.00000i	0.197386	−	0.227921i
$694$	−24.0000			−0.911028
$695$	5.19615	+	3.00000i	0.197101	+	0.113796i
$696$	2.59808	+	4.50000i	0.0984798	+	0.170572i
$697$	6.00000	+	10.3923i	0.227266	+	0.393637i
$698$	−10.3923	+	18.0000i	−0.393355	+	0.681310i
$699$			46.7654i			1.76883i
$700$	17.5000	−	6.06218i	0.661438	−	0.229129i
$701$		−	3.00000i		−	0.113308i	−0.998394	−	0.0566542i	$-0.981957\pi$
$701$		−	3.00000i		−	0.113308i	0.998394	−	0.0566542i	$-0.0180433\pi$
$702$	9.00000	−	15.5885i	0.339683	−	0.588348i
$703$	10.5000	−	6.06218i	0.396015	−	0.228639i
$704$	0.866025	−	0.500000i	0.0326396	−	0.0188445i
$705$	−5.19615	+	9.00000i	−0.195698	+	0.338960i
$706$			3.46410i			0.130373i
$707$	2.59808	−	13.5000i	0.0977107	−	0.507720i
$708$	21.0000			0.789228
$709$	14.5000	−	25.1147i	0.544559	−	0.943204i	−0.454076	−	0.890963i	$-0.650030\pi$
$709$	14.5000	−	25.1147i	0.544559	−	0.943204i	0.998635	−	0.0522406i	$-0.0166363\pi$
$710$	25.9808	+	45.0000i	0.975041	+	1.68882i
$711$	−12.0000	−	20.7846i	−0.450035	−	0.779484i
$712$	−9.00000	−	5.19615i	−0.337289	−	0.194734i
$713$	−10.3923			−0.389195
$714$	7.79423	+	1.50000i	0.291692	+	0.0561361i
$715$	−12.0000			−0.448775
$716$	−12.9904	−	7.50000i	−0.485473	−	0.280288i
$717$	−9.00000	+	5.19615i	−0.336111	+	0.194054i
$718$	3.00000	+	5.19615i	0.111959	+	0.193919i
$719$	14.7224	−	25.5000i	0.549054	−	0.950990i	−0.449286	−	0.893388i	$-0.648321\pi$
$719$	14.7224	−	25.5000i	0.549054	−	0.950990i	0.998340	−	0.0576013i	$-0.0183452\pi$
$720$	10.3923			0.387298
$721$	15.0000	+	43.3013i	0.558629	+	1.61262i
$722$			16.0000i			0.595458i
$723$	31.1769	+	18.0000i	1.15948	+	0.669427i
$724$	−12.0000	+	6.92820i	−0.445976	+	0.257485i
$725$	18.1865	−	10.5000i	0.675431	−	0.389960i
$726$	−1.50000	−	0.866025i	−0.0556702	−	0.0321412i
$727$			17.3205i			0.642382i	0.947014	+	0.321191i	$0.104083\pi$
$727$			17.3205i			0.642382i	−0.947014	+	0.321191i	$0.895917\pi$
$728$	−6.92820	−	6.00000i	−0.256776	−	0.222375i
$729$	27.0000			1.00000
$730$	−24.0000	+	41.5692i	−0.888280	+	1.53855i
$731$	0.866025	+	1.50000i	0.0320311	+	0.0554795i
$732$	−15.5885	+	9.00000i	−0.576166	+	0.332650i
$733$	3.00000	+	1.73205i	0.110808	+	0.0639748i	0.554380	−	0.832264i	$-0.312956\pi$
$733$	3.00000	+	1.73205i	0.110808	+	0.0639748i	−0.443572	+	0.896239i	$0.646289\pi$
$734$	6.92820			0.255725
$735$	−6.00000	−	41.5692i	−0.221313	−	1.53330i
$736$	−3.00000			−0.110581
$737$	−13.8564	−	8.00000i	−0.510407	−	0.294684i
$738$	18.0000	−	10.3923i	0.662589	−	0.382546i
$739$	14.0000	+	24.2487i	0.514998	+	0.892003i	0.999849	+	0.0174060i	$0.00554079\pi$
$739$	14.0000	+	24.2487i	0.514998	+	0.892003i	−0.484850	+	0.874597i	$0.661126\pi$
$740$	12.1244	−	21.0000i	0.445700	−	0.771975i
$741$	−10.3923			−0.381771
$742$		0			0
$743$			36.0000i			1.32071i	0.750953	+	0.660356i	$0.229595\pi$
$743$			36.0000i			1.32071i	−0.750953	+	0.660356i	$0.770405\pi$
$744$	3.00000	−	5.19615i	0.109985	−	0.190500i
$745$	27.0000	−	15.5885i	0.989203	−	0.571117i
$746$	12.1244	−	7.00000i	0.443904	−	0.256288i
$747$	−25.9808	+	45.0000i	−0.950586	+	1.64646i
$748$		−	1.73205i		−	0.0633300i
$749$	−5.19615	−	15.0000i	−0.189863	−	0.548088i
$750$		−	12.0000i		−	0.438178i
$751$	−26.0000	+	45.0333i	−0.948753	+	1.64329i	−0.200698	+	0.979653i	$0.564321\pi$
$751$	−26.0000	+	45.0333i	−0.948753	+	1.64329i	−0.748056	+	0.663636i	$0.769012\pi$
$752$	0.866025	+	1.50000i	0.0315807	+	0.0546994i
$753$	−10.5000	−	18.1865i	−0.382641	−	0.662754i
$754$	−9.00000	−	5.19615i	−0.327761	−	0.189233i
$755$	−38.1051			−1.38679
$756$	2.59808	−	13.5000i	0.0944911	−	0.490990i
$757$	13.0000			0.472493			0.236247	−	0.971693i	$-0.424083\pi$
$757$	13.0000			0.472493			0.236247	+	0.971693i	$0.424083\pi$
$758$	17.3205	+	10.0000i	0.629109	+	0.363216i
$759$	2.59808	+	4.50000i	0.0943042	+	0.163340i
$760$	−3.00000	−	5.19615i	−0.108821	−	0.188484i
$761$	17.3205	−	30.0000i	0.627868	−	1.08750i	−0.360111	−	0.932910i	$-0.617261\pi$
$761$	17.3205	−	30.0000i	0.627868	−	1.08750i	0.987979	−	0.154590i	$-0.0494055\pi$
$762$		−	19.0526i		−	0.690201i
$763$	8.00000	−	41.5692i	0.289619	−	1.50491i
$764$		0			0
$765$	9.00000	−	15.5885i	0.325396	−	0.563602i
$766$	−25.5000	+	14.7224i	−0.921352	+	0.531943i
$767$	−36.3731	+	21.0000i	−1.31336	+	0.758266i
$768$	0.866025	−	1.50000i	0.0312500	−	0.0541266i
$769$			6.92820i			0.249837i	0.992167	+	0.124919i	$0.0398670\pi$
$769$			6.92820i			0.249837i	−0.992167	+	0.124919i	$0.960133\pi$
$770$	−8.66025	+	3.00000i	−0.312094	+	0.108112i
$771$	−18.0000			−0.648254
$772$	2.00000	−	3.46410i	0.0719816	−	0.124676i
$773$	−6.92820	−	12.0000i	−0.249190	−	0.431610i	0.714111	−	0.700032i	$-0.246831\pi$
$773$	−6.92820	−	12.0000i	−0.249190	−	0.431610i	−0.963301	+	0.268422i	$0.913498\pi$
$774$	2.59808	−	1.50000i	0.0933859	−	0.0539164i
$775$	−21.0000	−	12.1244i	−0.754342	−	0.435520i
$776$	−15.5885			−0.559593
$777$	−24.2487	−	21.0000i	−0.869918	−	0.753371i
$778$	18.0000			0.645331
$779$	−10.3923	−	6.00000i	−0.372343	−	0.214972i
$780$	−18.0000	+	10.3923i	−0.644503	+	0.372104i
$781$	−7.50000	−	12.9904i	−0.268371	−	0.464832i
$782$	−2.59808	+	4.50000i	−0.0929070	+	0.160920i
$783$		−	15.5885i		−	0.557086i
$784$	−6.50000	−	2.59808i	−0.232143	−	0.0927884i
$785$			18.0000i			0.642448i
$786$		0			0
$787$	−31.5000	+	18.1865i	−1.12285	+	0.648280i	−0.942128	−	0.335254i	$-0.891178\pi$
$787$	−31.5000	+	18.1865i	−1.12285	+	0.648280i	−0.180726	+	0.983534i	$0.557845\pi$
$788$	−7.79423	+	4.50000i	−0.277658	+	0.160306i
$789$	27.0000	+	15.5885i	0.961225	+	0.554964i
$790$			27.7128i			0.985978i
$791$	10.3923	−	12.0000i	0.369508	−	0.426671i
$792$	−3.00000			−0.106600
$793$	18.0000	−	31.1769i	0.639199	−	1.10712i
$794$	0.866025	+	1.50000i	0.0307341	+	0.0532330i
$795$		0			0
$796$	−9.00000	−	5.19615i	−0.318997	−	0.184173i
$797$	10.3923			0.368114			0.184057	−	0.982916i	$-0.441077\pi$
$797$	10.3923			0.368114			0.184057	+	0.982916i	$0.441077\pi$
$798$	−7.50000	+	2.59808i	−0.265497	+	0.0919709i
$799$	3.00000			0.106132
$800$	−6.06218	−	3.50000i	−0.214330	−	0.123744i
$801$	15.5885	+	27.0000i	0.550791	+	0.953998i
$802$	12.0000	+	20.7846i	0.423735	+	0.733930i
$803$	6.92820	−	12.0000i	0.244491	−	0.423471i
$804$	−27.7128			−0.977356
$805$	27.0000	+	5.19615i	0.951625	+	0.183140i
$806$			12.0000i			0.422682i
$807$	−12.0000	+	20.7846i	−0.422420	+	0.731653i
$808$	−4.50000	+	2.59808i	−0.158309	+	0.0914000i
$809$	−15.5885	+	9.00000i	−0.548061	+	0.316423i	−0.748340	−	0.663316i	$-0.769149\pi$
$809$	−15.5885	+	9.00000i	−0.548061	+	0.316423i	0.200279	+	0.979739i	$0.435815\pi$
$810$	−27.0000	−	15.5885i	−0.948683	−	0.547723i
$811$		−	10.3923i		−	0.364923i	−0.983213	−	0.182462i	$-0.941593\pi$
$811$		−	10.3923i		−	0.364923i	0.983213	−	0.182462i	$-0.0584065\pi$
$812$	−7.79423	−	1.50000i	−0.273524	−	0.0526397i
$813$		−	18.0000i		−	0.631288i
$814$	−3.50000	+	6.06218i	−0.122675	+	0.212479i
$815$	−24.2487	−	42.0000i	−0.849395	−	1.47120i
$816$	−1.50000	−	2.59808i	−0.0525105	−	0.0909509i
$817$	−1.50000	−	0.866025i	−0.0524784	−	0.0302984i
$818$	−13.8564			−0.484478
$819$	9.00000	+	25.9808i	0.314485	+	0.907841i
$820$	−24.0000			−0.838116
$821$	−25.9808	−	15.0000i	−0.906735	−	0.523504i	−0.0273557	−	0.999626i	$-0.508709\pi$
$821$	−25.9808	−	15.0000i	−0.906735	−	0.523504i	−0.879379	+	0.476122i	$0.842042\pi$
$822$	−15.5885	−	27.0000i	−0.543710	−	0.941733i
$823$	−4.00000	−	6.92820i	−0.139431	−	0.241502i	0.787850	−	0.615867i	$-0.211194\pi$
$823$	−4.00000	−	6.92820i	−0.139431	−	0.241502i	−0.927281	+	0.374365i	$0.877861\pi$
$824$	8.66025	−	15.0000i	0.301694	−	0.522550i
$825$			12.1244i			0.422116i
$826$	−21.0000	+	24.2487i	−0.730683	+	0.843721i
$827$		−	18.0000i		−	0.625921i	−0.949766	−	0.312961i	$-0.898679\pi$
$827$		−	18.0000i		−	0.625921i	0.949766	−	0.312961i	$-0.101321\pi$
$828$	7.79423	+	4.50000i	0.270868	+	0.156386i
$829$	−19.5000	+	11.2583i	−0.677263	+	0.391018i	−0.798823	−	0.601566i	$-0.794544\pi$
$829$	−19.5000	+	11.2583i	−0.677263	+	0.391018i	0.121560	+	0.992584i	$0.461210\pi$
$830$	51.9615	−	30.0000i	1.80361	−	1.04132i
$831$	6.92820	−	12.0000i	0.240337	−	0.416275i
$832$			3.46410i			0.120096i
$833$	−9.52628	+	7.50000i	−0.330066	+	0.259860i
$834$	−3.00000			−0.103882
$835$	−42.0000	+	72.7461i	−1.45347	+	2.51748i
$836$	0.866025	+	1.50000i	0.0299521	+	0.0518786i
$837$	−15.5885	+	9.00000i	−0.538816	+	0.311086i
$838$	1.50000	+	0.866025i	0.0518166	+	0.0299164i
$839$	−17.3205			−0.597970			−0.298985	−	0.954258i	$-0.596648\pi$
$839$	−17.3205			−0.597970			−0.298985	+	0.954258i	$0.596648\pi$
$840$	−10.3923	+	12.0000i	−0.358569	+	0.414039i
$841$	20.0000			0.689655
$842$	−4.33013	−	2.50000i	−0.149226	−	0.0861557i
$843$	22.5000	−	12.9904i	0.774941	−	0.447412i
$844$	2.00000	+	3.46410i	0.0688428	+	0.119239i
$845$	−1.73205	+	3.00000i	−0.0595844	+	0.103203i
$846$		−	5.19615i		−	0.178647i
$847$	2.50000	−	0.866025i	0.0859010	−	0.0297570i
$848$		0			0
$849$	25.9808	+	15.0000i	0.891657	+	0.514799i
$850$	−10.5000	+	6.06218i	−0.360147	+	0.207931i
$851$	18.1865	−	10.5000i	0.623426	−	0.359935i
$852$	−22.5000	−	12.9904i	−0.770837	−	0.445043i
$853$		−	17.3205i		−	0.593043i	−0.955026	−	0.296521i	$-0.904173\pi$
$853$		−	17.3205i		−	0.593043i	0.955026	−	0.296521i	$-0.0958266\pi$
$854$	5.19615	−	27.0000i	0.177809	−	0.923921i
$855$			18.0000i			0.615587i
$856$	−3.00000	+	5.19615i	−0.102538	+	0.177601i
$857$	21.6506	+	37.5000i	0.739572	+	1.28098i	0.952688	+	0.303949i	$0.0983052\pi$
$857$	21.6506	+	37.5000i	0.739572	+	1.28098i	−0.213117	+	0.977027i	$0.568361\pi$
$858$	5.19615	−	3.00000i	0.177394	−	0.102418i
$859$	−27.0000	−	15.5885i	−0.921228	−	0.531871i	−0.0372015	−	0.999308i	$-0.511844\pi$
$859$	−27.0000	−	15.5885i	−0.921228	−	0.531871i	−0.884027	+	0.467436i	$0.845178\pi$
$860$	−3.46410			−0.118125
$861$	−6.00000	+	31.1769i	−0.204479	+	1.06251i
$862$	−12.0000			−0.408722
$863$	31.1769	+	18.0000i	1.06127	+	0.612727i	0.925785	−	0.378052i	$-0.123406\pi$
$863$	31.1769	+	18.0000i	1.06127	+	0.612727i	0.135490	+	0.990779i	$0.456739\pi$
$864$	−4.50000	+	2.59808i	−0.153093	+	0.0883883i
$865$	−36.0000	−	62.3538i	−1.22404	−	2.12009i
$866$	−4.33013	+	7.50000i	−0.147144	+	0.254860i
$867$	24.2487			0.823529
$868$	3.00000	+	8.66025i	0.101827	+	0.293948i
$869$		−	8.00000i		−	0.271381i
$870$	−9.00000	+	15.5885i	−0.305129	+	0.528498i
$871$	48.0000	−	27.7128i	1.62642	−	0.939013i
$872$	−13.8564	+	8.00000i	−0.469237	+	0.270914i
$873$	40.5000	+	23.3827i	1.37072	+	0.791384i
$874$		−	5.19615i		−	0.175762i
$875$	13.8564	+	12.0000i	0.468432	+	0.405674i
$876$		−	24.0000i		−	0.810885i
$877$	5.00000	−	8.66025i	0.168838	−	0.292436i	−0.769174	−	0.639040i	$-0.779332\pi$
$877$	5.00000	−	8.66025i	0.168838	−	0.292436i	0.938012	+	0.346604i	$0.112665\pi$
$878$	−7.79423	−	13.5000i	−0.263042	−	0.455603i
$879$	−7.50000	−	12.9904i	−0.252969	−	0.438155i
$880$	3.00000	+	1.73205i	0.101130	+	0.0583874i
$881$	41.5692			1.40050			0.700251	−	0.713896i	$-0.253071\pi$
$881$	41.5692			1.40050			0.700251	+	0.713896i	$0.253071\pi$
$882$	12.9904	+	16.5000i	0.437409	+	0.555584i
$883$	52.0000			1.74994			0.874970	−	0.484178i	$-0.160881\pi$
$883$	52.0000			1.74994			0.874970	+	0.484178i	$0.160881\pi$
$884$	5.19615	+	3.00000i	0.174766	+	0.100901i
$885$	36.3731	+	63.0000i	1.22267	+	2.11772i
$886$	−4.50000	−	7.79423i	−0.151180	−	0.261852i
$887$	−17.3205	+	30.0000i	−0.581566	+	1.00730i	0.413728	+	0.910400i	$0.364226\pi$
$887$	−17.3205	+	30.0000i	−0.581566	+	1.00730i	−0.995294	+	0.0969010i	$0.969107\pi$
$888$			12.1244i			0.406867i
$889$	22.0000	+	19.0526i	0.737856	+	0.639002i
$890$		−	36.0000i		−	1.20672i
$891$	7.79423	+	4.50000i	0.261116	+	0.150756i
$892$	9.00000	−	5.19615i	0.301342	−	0.173980i
$893$	−2.59808	+	1.50000i	−0.0869413	+	0.0501956i
$894$	−7.79423	+	13.5000i	−0.260678	+	0.451508i
$895$		−	51.9615i		−	1.73688i
$896$	0.866025	+	2.50000i	0.0289319	+	0.0835191i
$897$	−18.0000			−0.601003
$898$	−6.00000	+	10.3923i	−0.200223	+	0.346796i
$899$	5.19615	+	9.00000i	0.173301	+	0.300167i
$900$	10.5000	+	18.1865i	0.350000	+	0.606218i
$901$		0			0
$902$	6.92820			0.230684
$903$	−0.866025	+	4.50000i	−0.0288195	+	0.149751i
$904$	−6.00000			−0.199557
$905$	−41.5692	−	24.0000i	−1.38181	−	0.797787i
$906$	16.5000	−	9.52628i	0.548176	−	0.316489i
$907$	22.0000	+	38.1051i	0.730498	+	1.26526i	0.956671	+	0.291172i	$0.0940453\pi$
$907$	22.0000	+	38.1051i	0.730498	+	1.26526i	−0.226173	+	0.974087i	$0.572621\pi$
$908$	−5.19615	+	9.00000i	−0.172440	+	0.298675i
$909$	15.5885			0.517036
$910$	6.00000	−	31.1769i	0.198898	−	1.03350i
$911$			9.00000i			0.298183i	0.988823	+	0.149092i	$0.0476349\pi$
$911$			9.00000i			0.298183i	−0.988823	+	0.149092i	$0.952365\pi$
$912$	2.59808	+	1.50000i	0.0860309	+	0.0496700i
$913$	−15.0000	+	8.66025i	−0.496428	+	0.286613i
$914$	−27.7128	+	16.0000i	−0.916658	+	0.529233i
$915$	−54.0000	−	31.1769i	−1.78518	−	1.03068i
$916$		−	13.8564i		−	0.457829i
$917$		0			0
$918$			9.00000i			0.297044i
$919$	14.5000	−	25.1147i	0.478311	−	0.828459i	−0.521380	−	0.853325i	$-0.674583\pi$
$919$	14.5000	−	25.1147i	0.478311	−	0.828459i	0.999691	+	0.0248659i	$0.00791589\pi$
$920$	−5.19615	−	9.00000i	−0.171312	−	0.296721i
$921$	25.9808	−	15.0000i	0.856095	−	0.494267i
$922$	7.50000	+	4.33013i	0.246999	+	0.142605i
$923$	51.9615			1.71033
$924$	3.00000	−	3.46410i	0.0986928	−	0.113961i
$925$	49.0000			1.61111
$926$	3.46410	+	2.00000i	0.113837	+	0.0657241i
$927$	−45.0000	+	25.9808i	−1.47799	+	0.853320i
$928$	1.50000	+	2.59808i	0.0492399	+	0.0852860i
$929$	3.46410	−	6.00000i	0.113653	−	0.196854i	−0.803587	−	0.595187i	$-0.797078\pi$
$929$	3.46410	−	6.00000i	0.113653	−	0.196854i	0.917241	+	0.398333i	$0.130411\pi$
$930$	20.7846			0.681554
$931$	4.50000	−	11.2583i	0.147482	−	0.368977i
$932$			27.0000i			0.884414i
$933$	−19.5000	+	33.7750i	−0.638401	+	1.10574i
$934$	13.5000	−	7.79423i	0.441733	−	0.255035i
$935$	5.19615	−	3.00000i	0.169932	−	0.0981105i
$936$	5.19615	−	9.00000i	0.169842	−	0.294174i
$937$			3.46410i			0.113167i	0.998398	+	0.0565836i	$0.0180208\pi$
$937$			3.46410i			0.113167i	−0.998398	+	0.0565836i	$0.981979\pi$
$938$	27.7128	−	32.0000i	0.904855	−	1.04484i
$939$		−	51.0000i		−	1.66432i
$940$	−3.00000	+	5.19615i	−0.0978492	+	0.169480i
$941$	−0.866025	−	1.50000i	−0.0282316	−	0.0488986i	0.851564	−	0.524250i	$-0.175654\pi$
$941$	−0.866025	−	1.50000i	−0.0282316	−	0.0488986i	−0.879796	+	0.475351i	$0.842321\pi$
$942$	−4.50000	−	7.79423i	−0.146618	−	0.253950i
$943$	−18.0000	−	10.3923i	−0.586161	−	0.338420i
$944$	12.1244			0.394614
$945$	45.0000	−	15.5885i	1.46385	−	0.507093i
$946$	1.00000			0.0325128
$947$	2.59808	+	1.50000i	0.0844261	+	0.0487435i	0.541619	−	0.840624i	$-0.317812\pi$
$947$	2.59808	+	1.50000i	0.0844261	+	0.0487435i	−0.457193	+	0.889368i	$0.651145\pi$
$948$	−6.92820	−	12.0000i	−0.225018	−	0.389742i
$949$	24.0000	+	41.5692i	0.779073	+	1.34939i
$950$	6.06218	−	10.5000i	0.196683	−	0.340665i
$951$			10.3923i			0.336994i
$952$	4.50000	+	0.866025i	0.145846	+	0.0280680i
$953$			42.0000i			1.36051i	0.732974	+	0.680257i	$0.238132\pi$
$953$			42.0000i			1.36051i	−0.732974	+	0.680257i	$0.761868\pi$
$954$		0			0
$955$		0			0
$956$	−5.19615	+	3.00000i	−0.168056	+	0.0970269i
$957$	2.59808	−	4.50000i	0.0839839	−	0.145464i
$958$			17.3205i			0.559600i
$959$	46.7654	+	9.00000i	1.51013	+	0.290625i
$960$	6.00000			0.193649
$961$	−9.50000	+	16.4545i	−0.306452	+	0.530790i
$962$	−12.1244	−	21.0000i	−0.390905	−	0.677067i
$963$	15.5885	−	9.00000i	0.502331	−	0.290021i
$964$	18.0000	+	10.3923i	0.579741	+	0.334714i
$965$	13.8564			0.446054
$966$	−12.9904	+	4.50000i	−0.417959	+	0.144785i
$967$	−43.0000			−1.38279			−0.691393	−	0.722478i	$-0.743003\pi$
$967$	−43.0000			−1.38279			−0.691393	+	0.722478i	$0.743003\pi$
$968$	−0.866025	−	0.500000i	−0.0278351	−	0.0160706i
$969$	4.50000	−	2.59808i	0.144561	−	0.0834622i
$970$	−27.0000	−	46.7654i	−0.866918	−	1.50155i
$971$	1.73205	−	3.00000i	0.0555842	−	0.0962746i	−0.836894	−	0.547364i	$-0.815631\pi$
$971$	1.73205	−	3.00000i	0.0555842	−	0.0962746i	0.892479	+	0.451090i	$0.148965\pi$
$972$	15.5885			0.500000
$973$	3.00000	−	3.46410i	0.0961756	−	0.111054i
$974$		−	26.0000i		−	0.833094i
$975$	−36.3731	−	21.0000i	−1.16487	−	0.672538i
$976$	−9.00000	+	5.19615i	−0.288083	+	0.166325i
$977$	−20.7846	+	12.0000i	−0.664959	+	0.383914i	−0.794164	−	0.607704i	$-0.792091\pi$
$977$	−20.7846	+	12.0000i	−0.664959	+	0.383914i	0.129205	+	0.991618i	$0.458757\pi$
$978$	21.0000	+	12.1244i	0.671506	+	0.387694i
$979$			10.3923i			0.332140i
$980$	−3.46410	−	24.0000i	−0.110657	−	0.766652i
$981$	48.0000			1.53252
$982$	−15.0000	+	25.9808i	−0.478669	+	0.829079i
$983$	−0.866025	−	1.50000i	−0.0276219	−	0.0478426i	0.851884	−	0.523731i	$-0.175460\pi$
$983$	−0.866025	−	1.50000i	−0.0276219	−	0.0478426i	−0.879506	+	0.475888i	$0.842127\pi$
$984$	10.3923	−	6.00000i	0.331295	−	0.191273i
$985$	−27.0000	−	15.5885i	−0.860292	−	0.496690i
$986$	5.19615			0.165479
$987$	6.00000	+	5.19615i	0.190982	+	0.165395i
$988$	−6.00000			−0.190885
$989$	−2.59808	−	1.50000i	−0.0826140	−	0.0476972i
$990$	−5.19615	−	9.00000i	−0.165145	−	0.286039i
$991$	10.0000	+	17.3205i	0.317660	+	0.550204i	0.979999	−	0.199000i	$-0.0637695\pi$
$991$	10.0000	+	17.3205i	0.317660	+	0.550204i	−0.662339	+	0.749204i	$0.730436\pi$
$992$	1.73205	−	3.00000i	0.0549927	−	0.0952501i
$993$	−17.3205			−0.549650
$994$	37.5000	−	12.9904i	1.18943	−	0.412030i
$995$		−	36.0000i		−	1.14128i
$996$	−15.0000	+	25.9808i	−0.475293	+	0.823232i
$997$	33.0000	−	19.0526i	1.04512	−	0.603401i	0.123841	−	0.992302i	$-0.460479\pi$
$997$	33.0000	−	19.0526i	1.04512	−	0.603401i	0.921279	+	0.388901i	$0.127145\pi$
$998$	−27.7128	+	16.0000i	−0.877234	+	0.506471i
$999$	18.1865	−	31.5000i	0.575396	−	0.996616i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.k.a.89.1	✓	4
3.2	odd	2	inner	462.2.k.a.89.2	yes	4
7.3	odd	6	inner	462.2.k.a.353.2	yes	4
21.17	even	6	inner	462.2.k.a.353.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.k.a.89.1	✓	4	1.1	even	1	trivial
462.2.k.a.89.2	yes	4	3.2	odd	2	inner
462.2.k.a.353.1	yes	4	21.17	even	6	inner
462.2.k.a.353.2	yes	4	7.3	odd	6	inner

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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.866025 + 1.50000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.73205 + 3.00000i) q^{5} -1.73205i q^{6} +(2.00000 + 1.73205i) q^{7} -1.00000i q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.866025 + 1.50000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.73205 + 3.00000i) q^{5} -1.73205i q^{6} +(2.00000 + 1.73205i) q^{7} -1.00000i q^{8} +(-1.50000 + 2.59808i) q^{9} +(3.00000 - 1.73205i) q^{10} +(-0.866025 + 0.500000i) q^{11} +(-0.866025 + 1.50000i) q^{12} -3.46410i q^{13} +(-0.866025 - 2.50000i) q^{14} -6.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.866025 + 1.50000i) q^{17} +(2.59808 - 1.50000i) q^{18} +(-1.50000 - 0.866025i) q^{19} -3.46410 q^{20} +(-0.866025 + 4.50000i) q^{21} +1.00000 q^{22} +(-2.59808 - 1.50000i) q^{23} +(1.50000 - 0.866025i) q^{24} +(-3.50000 - 6.06218i) q^{25} +(-1.73205 + 3.00000i) q^{26} -5.19615 q^{27} +(-0.500000 + 2.59808i) q^{28} +3.00000i q^{29} +(5.19615 + 3.00000i) q^{30} +(3.00000 - 1.73205i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-1.50000 - 0.866025i) q^{33} -1.73205i q^{34} +(-8.66025 + 3.00000i) q^{35} -3.00000 q^{36} +(-3.50000 + 6.06218i) q^{37} +(0.866025 + 1.50000i) q^{38} +(5.19615 - 3.00000i) q^{39} +(3.00000 + 1.73205i) q^{40} +6.92820 q^{41} +(3.00000 - 3.46410i) q^{42} +1.00000 q^{43} +(-0.866025 - 0.500000i) q^{44} +(-5.19615 - 9.00000i) q^{45} +(1.50000 + 2.59808i) q^{46} +(0.866025 - 1.50000i) q^{47} -1.73205 q^{48} +(1.00000 + 6.92820i) q^{49} +7.00000i q^{50} +(-1.50000 + 2.59808i) q^{51} +(3.00000 - 1.73205i) q^{52} +(4.50000 + 2.59808i) q^{54} -3.46410i q^{55} +(1.73205 - 2.00000i) q^{56} -3.00000i q^{57} +(1.50000 - 2.59808i) q^{58} +(-6.06218 - 10.5000i) q^{59} +(-3.00000 - 5.19615i) q^{60} +(9.00000 + 5.19615i) q^{61} -3.46410 q^{62} +(-7.50000 + 2.59808i) q^{63} -1.00000 q^{64} +(10.3923 + 6.00000i) q^{65} +(0.866025 + 1.50000i) q^{66} +(8.00000 + 13.8564i) q^{67} +(-0.866025 + 1.50000i) q^{68} -5.19615i q^{69} +(9.00000 + 1.73205i) q^{70} +15.0000i q^{71} +(2.59808 + 1.50000i) q^{72} +(-12.0000 + 6.92820i) q^{73} +(6.06218 - 3.50000i) q^{74} +(6.06218 - 10.5000i) q^{75} -1.73205i q^{76} +(-2.59808 - 0.500000i) q^{77} -6.00000 q^{78} +(-4.00000 + 6.92820i) q^{79} +(-1.73205 - 3.00000i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-6.00000 - 3.46410i) q^{82} +17.3205 q^{83} +(-4.33013 + 1.50000i) q^{84} -6.00000 q^{85} +(-0.866025 - 0.500000i) q^{86} +(-4.50000 + 2.59808i) q^{87} +(0.500000 + 0.866025i) q^{88} +(5.19615 - 9.00000i) q^{89} +10.3923i q^{90} +(6.00000 - 6.92820i) q^{91} -3.00000i q^{92} +(5.19615 + 3.00000i) q^{93} +(-1.50000 + 0.866025i) q^{94} +(5.19615 - 3.00000i) q^{95} +(1.50000 + 0.866025i) q^{96} -15.5885i q^{97} +(2.59808 - 6.50000i) q^{98} -3.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} + 8 q^{7} - 6 q^{9}+O(q^{10}) \) 4 * q + 2 * q^4 + 8 * q^7 - 6 * q^9	\( 4 q + 2 q^{4} + 8 q^{7} - 6 q^{9} + 12 q^{10} - 24 q^{15} - 2 q^{16} - 6 q^{19} + 4 q^{22} + 6 q^{24} - 14 q^{25} - 2 q^{28} + 12 q^{31} - 6 q^{33} - 12 q^{36} - 14 q^{37} + 12 q^{40} + 12 q^{42} + 4 q^{43} + 6 q^{46} + 4 q^{49} - 6 q^{51} + 12 q^{52} + 18 q^{54} + 6 q^{58} - 12 q^{60} + 36 q^{61} - 30 q^{63} - 4 q^{64} + 32 q^{67} + 36 q^{70} - 48 q^{73} - 24 q^{78} - 16 q^{79} - 18 q^{81} - 24 q^{82} - 24 q^{85} - 18 q^{87} + 2 q^{88} + 24 q^{91} - 6 q^{94} + 6 q^{96}+O(q^{100}) \) 4 * q + 2 * q^4 + 8 * q^7 - 6 * q^9 + 12 * q^10 - 24 * q^15 - 2 * q^16 - 6 * q^19 + 4 * q^22 + 6 * q^24 - 14 * q^25 - 2 * q^28 + 12 * q^31 - 6 * q^33 - 12 * q^36 - 14 * q^37 + 12 * q^40 + 12 * q^42 + 4 * q^43 + 6 * q^46 + 4 * q^49 - 6 * q^51 + 12 * q^52 + 18 * q^54 + 6 * q^58 - 12 * q^60 + 36 * q^61 - 30 * q^63 - 4 * q^64 + 32 * q^67 + 36 * q^70 - 48 * q^73 - 24 * q^78 - 16 * q^79 - 18 * q^81 - 24 * q^82 - 24 * q^85 - 18 * q^87 + 2 * q^88 + 24 * q^91 - 6 * q^94 + 6 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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