LMFDB - Embedded newform 731.2.m.a.603.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(87,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([7, 0]))

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

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

chi := DirichletCharacter("731.87");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.m (of order $8$, degree $4$, 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:	$5.83706438776$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			603.1
Root			$-0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	731.603
Dual form			731.2.m.a.474.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.292893 + 0.292893i) q^{2} +(-1.00000 + 2.41421i) q^{3} +1.82843i q^{4} +(-3.41421 - 1.41421i) q^{5} +(-0.414214 - 1.00000i) q^{6} +(-2.41421 + 1.00000i) q^{7} +(-1.12132 - 1.12132i) q^{8} +(-2.70711 - 2.70711i) q^{9} +O(q^{10})$	\(q+(-0.292893 + 0.292893i) q^{2} +(-1.00000 + 2.41421i) q^{3} +1.82843i q^{4} +(-3.41421 - 1.41421i) q^{5} +(-0.414214 - 1.00000i) q^{6} +(-2.41421 + 1.00000i) q^{7} +(-1.12132 - 1.12132i) q^{8} +(-2.70711 - 2.70711i) q^{9} +(1.41421 - 0.585786i) q^{10} +(0.292893 + 0.707107i) q^{11} +(-4.41421 - 1.82843i) q^{12} +1.17157i q^{13} +(0.414214 - 1.00000i) q^{14} +(6.82843 - 6.82843i) q^{15} -3.00000 q^{16} +(4.12132 + 0.121320i) q^{17} +1.58579 q^{18} +(-2.00000 + 2.00000i) q^{19} +(2.58579 - 6.24264i) q^{20} -6.82843i q^{21} +(-0.292893 - 0.121320i) q^{22} +(0.121320 + 0.292893i) q^{23} +(3.82843 - 1.58579i) q^{24} +(6.12132 + 6.12132i) q^{25} +(-0.343146 - 0.343146i) q^{26} +(2.00000 - 0.828427i) q^{27} +(-1.82843 - 4.41421i) q^{28} +4.00000i q^{30} +(-0.878680 + 2.12132i) q^{31} +(3.12132 - 3.12132i) q^{32} -2.00000 q^{33} +(-1.24264 + 1.17157i) q^{34} +9.65685 q^{35} +(4.94975 - 4.94975i) q^{36} +(2.24264 - 5.41421i) q^{37} -1.17157i q^{38} +(-2.82843 - 1.17157i) q^{39} +(2.24264 + 5.41421i) q^{40} +(-6.12132 + 2.53553i) q^{41} +(2.00000 + 2.00000i) q^{42} +(0.707107 + 0.707107i) q^{43} +(-1.29289 + 0.535534i) q^{44} +(5.41421 + 13.0711i) q^{45} +(-0.121320 - 0.0502525i) q^{46} +0.242641i q^{47} +(3.00000 - 7.24264i) q^{48} +(-0.121320 + 0.121320i) q^{49} -3.58579 q^{50} +(-4.41421 + 9.82843i) q^{51} -2.14214 q^{52} +(5.82843 - 5.82843i) q^{53} +(-0.343146 + 0.828427i) q^{54} -2.82843i q^{55} +(3.82843 + 1.58579i) q^{56} +(-2.82843 - 6.82843i) q^{57} +(9.48528 + 9.48528i) q^{59} +(12.4853 + 12.4853i) q^{60} +(3.41421 - 1.41421i) q^{61} +(-0.363961 - 0.878680i) q^{62} +(9.24264 + 3.82843i) q^{63} -4.17157i q^{64} +(1.65685 - 4.00000i) q^{65} +(0.585786 - 0.585786i) q^{66} -7.07107 q^{67} +(-0.221825 + 7.53553i) q^{68} -0.828427 q^{69} +(-2.82843 + 2.82843i) q^{70} +(6.07107 - 14.6569i) q^{71} +6.07107i q^{72} +(-12.2426 - 5.07107i) q^{73} +(0.928932 + 2.24264i) q^{74} +(-20.8995 + 8.65685i) q^{75} +(-3.65685 - 3.65685i) q^{76} +(-1.41421 - 1.41421i) q^{77} +(1.17157 - 0.485281i) q^{78} +(2.46447 + 5.94975i) q^{79} +(10.2426 + 4.24264i) q^{80} -5.82843i q^{81} +(1.05025 - 2.53553i) q^{82} +(-1.17157 + 1.17157i) q^{83} +12.4853 q^{84} +(-13.8995 - 6.24264i) q^{85} -0.414214 q^{86} +(0.464466 - 1.12132i) q^{88} -9.17157i q^{89} +(-5.41421 - 2.24264i) q^{90} +(-1.17157 - 2.82843i) q^{91} +(-0.535534 + 0.221825i) q^{92} +(-4.24264 - 4.24264i) q^{93} +(-0.0710678 - 0.0710678i) q^{94} +(9.65685 - 4.00000i) q^{95} +(4.41421 + 10.6569i) q^{96} +(-11.7782 - 4.87868i) q^{97} -0.0710678i q^{98} +(1.12132 - 2.70711i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 4 q^{3} - 8 q^{5} + 4 q^{6} - 4 q^{7} + 4 q^{8} - 8 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 - 4 * q^3 - 8 * q^5 + 4 * q^6 - 4 * q^7 + 4 * q^8 - 8 * q^9	$ 4 q - 4 q^{2} - 4 q^{3} - 8 q^{5} + 4 q^{6} - 4 q^{7} + 4 q^{8} - 8 q^{9} + 4 q^{11} - 12 q^{12} - 4 q^{14} + 16 q^{15} - 12 q^{16} + 8 q^{17} + 12 q^{18} - 8 q^{19} + 16 q^{20} - 4 q^{22} - 8 q^{23} + 4 q^{24} + 16 q^{25} - 24 q^{26} + 8 q^{27} + 4 q^{28} - 12 q^{31} + 4 q^{32} - 8 q^{33} + 12 q^{34} + 16 q^{35} - 8 q^{37} - 8 q^{40} - 16 q^{41} + 8 q^{42} - 8 q^{44} + 16 q^{45} + 8 q^{46} + 12 q^{48} + 8 q^{49} - 20 q^{50} - 12 q^{51} + 48 q^{52} + 12 q^{53} - 24 q^{54} + 4 q^{56} + 4 q^{59} + 16 q^{60} + 8 q^{61} + 24 q^{62} + 20 q^{63} - 16 q^{65} + 8 q^{66} - 32 q^{68} + 8 q^{69} - 4 q^{71} - 32 q^{73} + 32 q^{74} - 44 q^{75} + 8 q^{76} + 16 q^{78} + 24 q^{79} + 24 q^{80} + 24 q^{82} - 16 q^{83} + 16 q^{84} - 16 q^{85} + 4 q^{86} + 16 q^{88} - 16 q^{90} - 16 q^{91} + 12 q^{92} + 28 q^{94} + 16 q^{95} + 12 q^{96} - 16 q^{97} - 4 q^{99}+O(q^{100}) $ 4 * q - 4 * q^2 - 4 * q^3 - 8 * q^5 + 4 * q^6 - 4 * q^7 + 4 * q^8 - 8 * q^9 + 4 * q^11 - 12 * q^12 - 4 * q^14 + 16 * q^15 - 12 * q^16 + 8 * q^17 + 12 * q^18 - 8 * q^19 + 16 * q^20 - 4 * q^22 - 8 * q^23 + 4 * q^24 + 16 * q^25 - 24 * q^26 + 8 * q^27 + 4 * q^28 - 12 * q^31 + 4 * q^32 - 8 * q^33 + 12 * q^34 + 16 * q^35 - 8 * q^37 - 8 * q^40 - 16 * q^41 + 8 * q^42 - 8 * q^44 + 16 * q^45 + 8 * q^46 + 12 * q^48 + 8 * q^49 - 20 * q^50 - 12 * q^51 + 48 * q^52 + 12 * q^53 - 24 * q^54 + 4 * q^56 + 4 * q^59 + 16 * q^60 + 8 * q^61 + 24 * q^62 + 20 * q^63 - 16 * q^65 + 8 * q^66 - 32 * q^68 + 8 * q^69 - 4 * q^71 - 32 * q^73 + 32 * q^74 - 44 * q^75 + 8 * q^76 + 16 * q^78 + 24 * q^79 + 24 * q^80 + 24 * q^82 - 16 * q^83 + 16 * q^84 - 16 * q^85 + 4 * q^86 + 16 * q^88 - 16 * q^90 - 16 * q^91 + 12 * q^92 + 28 * q^94 + 16 * q^95 + 12 * q^96 - 16 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$1$

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 $

$2$	−0.292893	+	0.292893i	−0.207107	+	0.207107i	−0.803037	−	0.595930i	$-0.796784\pi$
$2$	−0.292893	+	0.292893i	−0.207107	+	0.207107i	0.595930	+	0.803037i	$0.296784\pi$
$3$	−1.00000	+	2.41421i	−0.577350	+	1.39385i	0.317832	+	0.948147i	$0.397045\pi$
$3$	−1.00000	+	2.41421i	−0.577350	+	1.39385i	−0.895182	+	0.445700i	$0.852955\pi$
$4$			1.82843i			0.914214i
$5$	−3.41421	−	1.41421i	−1.52688	−	0.632456i	−0.547927	−	0.836526i	$-0.684583\pi$
$5$	−3.41421	−	1.41421i	−1.52688	−	0.632456i	−0.978956	+	0.204071i	$0.934583\pi$
$6$	−0.414214	−	1.00000i	−0.169102	−	0.408248i
$7$	−2.41421	+	1.00000i	−0.912487	+	0.377964i	−0.789008	−	0.614383i	$-0.789405\pi$
$7$	−2.41421	+	1.00000i	−0.912487	+	0.377964i	−0.123479	+	0.992347i	$0.539405\pi$
$8$	−1.12132	−	1.12132i	−0.396447	−	0.396447i
$9$	−2.70711	−	2.70711i	−0.902369	−	0.902369i
$10$	1.41421	−	0.585786i	0.447214	−	0.185242i
$11$	0.292893	+	0.707107i	0.0883106	+	0.213201i	0.961864	−	0.273527i	$-0.0881903\pi$
$11$	0.292893	+	0.707107i	0.0883106	+	0.213201i	−0.873554	+	0.486728i	$0.838190\pi$
$12$	−4.41421	−	1.82843i	−1.27427	−	0.527821i
$13$			1.17157i			0.324936i	0.986714	+	0.162468i	$0.0519454\pi$
$13$			1.17157i			0.324936i	−0.986714	+	0.162468i	$0.948055\pi$
$14$	0.414214	−	1.00000i	0.110703	−	0.267261i
$15$	6.82843	−	6.82843i	1.76309	−	1.76309i
$16$	−3.00000			−0.750000
$17$	4.12132	+	0.121320i	0.999567	+	0.0294245i
$17$	4.12132	+	0.121320i	0.999567	+	0.0294245i
$18$	1.58579			0.373773
$19$	−2.00000	+	2.00000i	−0.458831	+	0.458831i	−0.898272	−	0.439440i	$-0.855177\pi$
$19$	−2.00000	+	2.00000i	−0.458831	+	0.458831i	0.439440	+	0.898272i	$0.355177\pi$
$20$	2.58579	−	6.24264i	0.578199	−	1.39590i
$21$		−	6.82843i		−	1.49008i
$22$	−0.292893	−	0.121320i	−0.0624450	−	0.0258656i
$23$	0.121320	+	0.292893i	0.0252970	+	0.0610725i	0.936023	−	0.351938i	$-0.114477\pi$
$23$	0.121320	+	0.292893i	0.0252970	+	0.0610725i	−0.910726	+	0.413011i	$0.864477\pi$
$24$	3.82843	−	1.58579i	0.781474	−	0.323697i
$25$	6.12132	+	6.12132i	1.22426	+	1.22426i
$26$	−0.343146	−	0.343146i	−0.0672964	−	0.0672964i
$27$	2.00000	−	0.828427i	0.384900	−	0.159431i
$28$	−1.82843	−	4.41421i	−0.345540	−	0.834208i
$29$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$29$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$30$			4.00000i			0.730297i
$31$	−0.878680	+	2.12132i	−0.157816	+	0.381000i	−0.982934	−	0.183960i	$-0.941108\pi$
$31$	−0.878680	+	2.12132i	−0.157816	+	0.381000i	0.825118	+	0.564960i	$0.191108\pi$
$32$	3.12132	−	3.12132i	0.551777	−	0.551777i
$33$	−2.00000			−0.348155
$34$	−1.24264	+	1.17157i	−0.213111	+	0.200923i
$35$	9.65685			1.63231
$36$	4.94975	−	4.94975i	0.824958	−	0.824958i
$37$	2.24264	−	5.41421i	0.368688	−	0.890091i	−0.625278	−	0.780402i	$-0.715014\pi$
$37$	2.24264	−	5.41421i	0.368688	−	0.890091i	0.993966	−	0.109689i	$-0.0349856\pi$
$38$		−	1.17157i		−	0.190054i
$39$	−2.82843	−	1.17157i	−0.452911	−	0.187602i
$40$	2.24264	+	5.41421i	0.354593	+	0.856062i
$41$	−6.12132	+	2.53553i	−0.955990	+	0.395984i	−0.805479	−	0.592625i	$-0.798092\pi$
$41$	−6.12132	+	2.53553i	−0.955990	+	0.395984i	−0.150511	+	0.988608i	$0.548092\pi$
$42$	2.00000	+	2.00000i	0.308607	+	0.308607i
$43$	0.707107	+	0.707107i	0.107833	+	0.107833i
$43$	0.707107	+	0.707107i	0.107833	+	0.107833i
$44$	−1.29289	+	0.535534i	−0.194911	+	0.0807348i
$45$	5.41421	+	13.0711i	0.807103	+	1.94852i
$46$	−0.121320	−	0.0502525i	−0.0178877	−	0.00740933i
$47$			0.242641i			0.0353928i	0.999843	+	0.0176964i	$0.00563323\pi$
$47$			0.242641i			0.0353928i	−0.999843	+	0.0176964i	$0.994367\pi$
$48$	3.00000	−	7.24264i	0.433013	−	1.04539i
$49$	−0.121320	+	0.121320i	−0.0173315	+	0.0173315i
$50$	−3.58579			−0.507107
$51$	−4.41421	+	9.82843i	−0.618114	+	1.37626i
$52$	−2.14214			−0.297061
$53$	5.82843	−	5.82843i	0.800596	−	0.800596i	−0.182593	−	0.983189i	$-0.558449\pi$
$53$	5.82843	−	5.82843i	0.800596	−	0.800596i	0.983189	+	0.182593i	$0.0584489\pi$
$54$	−0.343146	+	0.828427i	−0.0466962	+	0.112735i
$55$		−	2.82843i		−	0.381385i
$56$	3.82843	+	1.58579i	0.511595	+	0.211910i
$57$	−2.82843	−	6.82843i	−0.374634	−	0.904447i
$58$		0			0
$59$	9.48528	+	9.48528i	1.23488	+	1.23488i	0.962068	+	0.272811i	$0.0879533\pi$
$59$	9.48528	+	9.48528i	1.23488	+	1.23488i	0.272811	+	0.962068i	$0.412047\pi$
$60$	12.4853	+	12.4853i	1.61184	+	1.61184i
$61$	3.41421	−	1.41421i	0.437145	−	0.181071i	−0.153247	−	0.988188i	$-0.548973\pi$
$61$	3.41421	−	1.41421i	0.437145	−	0.181071i	0.590392	+	0.807116i	$0.298973\pi$
$62$	−0.363961	−	0.878680i	−0.0462231	−	0.111592i
$63$	9.24264	+	3.82843i	1.16446	+	0.482336i
$64$		−	4.17157i		−	0.521447i
$65$	1.65685	−	4.00000i	0.205507	−	0.496139i
$66$	0.585786	−	0.585786i	0.0721053	−	0.0721053i
$67$	−7.07107			−0.863868			−0.431934	−	0.901905i	$-0.642169\pi$
$67$	−7.07107			−0.863868			−0.431934	+	0.901905i	$0.642169\pi$
$68$	−0.221825	+	7.53553i	−0.0269003	+	0.913818i
$69$	−0.828427			−0.0997309
$70$	−2.82843	+	2.82843i	−0.338062	+	0.338062i
$71$	6.07107	−	14.6569i	0.720503	−	1.73945i	0.0485898	−	0.998819i	$-0.484527\pi$
$71$	6.07107	−	14.6569i	0.720503	−	1.73945i	0.671913	−	0.740630i	$-0.265473\pi$
$72$			6.07107i			0.715482i
$73$	−12.2426	−	5.07107i	−1.43289	−	0.593524i	−0.474829	−	0.880078i	$-0.657490\pi$
$73$	−12.2426	−	5.07107i	−1.43289	−	0.593524i	−0.958064	+	0.286555i	$0.907490\pi$
$74$	0.928932	+	2.24264i	0.107986	+	0.260702i
$75$	−20.8995	+	8.65685i	−2.41327	+	0.999607i
$76$	−3.65685	−	3.65685i	−0.419470	−	0.419470i
$77$	−1.41421	−	1.41421i	−0.161165	−	0.161165i
$78$	1.17157	−	0.485281i	0.132655	−	0.0549473i
$79$	2.46447	+	5.94975i	0.277274	+	0.669399i	0.999758	−	0.0219886i	$-0.00699976\pi$
$79$	2.46447	+	5.94975i	0.277274	+	0.669399i	−0.722484	+	0.691388i	$0.757000\pi$
$80$	10.2426	+	4.24264i	1.14516	+	0.474342i
$81$		−	5.82843i		−	0.647603i
$82$	1.05025	−	2.53553i	0.115981	−	0.280003i
$83$	−1.17157	+	1.17157i	−0.128597	+	0.128597i	−0.768476	−	0.639879i	$-0.778984\pi$
$83$	−1.17157	+	1.17157i	−0.128597	+	0.128597i	0.639879	+	0.768476i	$0.278984\pi$
$84$	12.4853			1.36226
$85$	−13.8995	−	6.24264i	−1.50761	−	0.677109i
$86$	−0.414214			−0.0446658
$87$		0			0
$88$	0.464466	−	1.12132i	0.0495123	−	0.119533i
$89$		−	9.17157i		−	0.972185i	−0.873907	−	0.486092i	$-0.838422\pi$
$89$		−	9.17157i		−	0.972185i	0.873907	−	0.486092i	$-0.161578\pi$
$90$	−5.41421	−	2.24264i	−0.570708	−	0.236395i
$91$	−1.17157	−	2.82843i	−0.122814	−	0.296500i
$92$	−0.535534	+	0.221825i	−0.0558333	+	0.0231269i
$93$	−4.24264	−	4.24264i	−0.439941	−	0.439941i
$94$	−0.0710678	−	0.0710678i	−0.00733009	−	0.00733009i
$95$	9.65685	−	4.00000i	0.990772	−	0.410391i
$96$	4.41421	+	10.6569i	0.450524	+	1.08766i
$97$	−11.7782	−	4.87868i	−1.19589	−	0.495355i	−0.306223	−	0.951960i	$-0.599065\pi$
$97$	−11.7782	−	4.87868i	−1.19589	−	0.495355i	−0.889670	+	0.456605i	$0.849065\pi$
$98$		−	0.0710678i		−	0.00717893i
$99$	1.12132	−	2.70711i	0.112697	−	0.272074i
$100$	−11.1924	+	11.1924i	−1.11924	+	1.11924i
$101$	5.89949			0.587022			0.293511	−	0.955956i	$-0.405176\pi$
$101$	5.89949			0.587022			0.293511	+	0.955956i	$0.405176\pi$
$102$	−1.58579	−	4.17157i	−0.157016	−	0.413047i
$103$	9.89949			0.975426			0.487713	−	0.873004i	$-0.337831\pi$
$103$	9.89949			0.975426			0.487713	+	0.873004i	$0.337831\pi$
$104$	1.31371	−	1.31371i	0.128820	−	0.128820i
$105$	−9.65685	+	23.3137i	−0.942412	+	2.27518i
$106$			3.41421i			0.331618i
$107$	−15.1924	−	6.29289i	−1.46870	−	0.608357i	−0.502141	−	0.864786i	$-0.667454\pi$
$107$	−15.1924	−	6.29289i	−1.46870	−	0.608357i	−0.966563	+	0.256429i	$0.917454\pi$
$108$	1.51472	+	3.65685i	0.145754	+	0.351881i
$109$	−11.3640	+	4.70711i	−1.08847	+	0.450859i	−0.853473	−	0.521137i	$-0.825508\pi$
$109$	−11.3640	+	4.70711i	−1.08847	+	0.450859i	−0.234997	+	0.971996i	$0.575508\pi$
$110$	0.828427	+	0.828427i	0.0789874	+	0.0789874i
$111$	10.8284	+	10.8284i	1.02779	+	1.02779i
$112$	7.24264	−	3.00000i	0.684365	−	0.283473i
$113$	−7.31371	−	17.6569i	−0.688016	−	1.66102i	−0.748741	−	0.662863i	$-0.769341\pi$
$113$	−7.31371	−	17.6569i	−0.688016	−	1.66102i	0.0607252	−	0.998155i	$-0.480659\pi$
$114$	2.82843	+	1.17157i	0.264906	+	0.109728i
$115$		−	1.17157i		−	0.109250i
$116$		0			0
$117$	3.17157	−	3.17157i	0.293212	−	0.293212i
$118$	−5.55635			−0.511503
$119$	−10.0711	+	3.82843i	−0.923213	+	0.350951i
$120$	−15.3137			−1.39794
$121$	7.36396	−	7.36396i	0.669451	−	0.669451i
$122$	−0.585786	+	1.41421i	−0.0530346	+	0.128037i
$123$		−	17.3137i		−	1.56112i
$124$	−3.87868	−	1.60660i	−0.348316	−	0.144277i
$125$	−5.17157	−	12.4853i	−0.462560	−	1.11672i
$126$	−3.82843	+	1.58579i	−0.341063	+	0.141273i
$127$	−5.00000	−	5.00000i	−0.443678	−	0.443678i	0.449568	−	0.893246i	$-0.351578\pi$
$127$	−5.00000	−	5.00000i	−0.443678	−	0.443678i	−0.893246	+	0.449568i	$0.851578\pi$
$128$	7.46447	+	7.46447i	0.659772	+	0.659772i
$129$	−2.41421	+	1.00000i	−0.212560	+	0.0880451i
$130$	0.686292	+	1.65685i	0.0601917	+	0.145316i
$131$	5.82843	+	2.41421i	0.509232	+	0.210931i	0.622480	−	0.782636i	$-0.286125\pi$
$131$	5.82843	+	2.41421i	0.509232	+	0.210931i	−0.113248	+	0.993567i	$0.536125\pi$
$132$		−	3.65685i		−	0.318288i
$133$	2.82843	−	6.82843i	0.245256	−	0.592100i
$134$	2.07107	−	2.07107i	0.178913	−	0.178913i
$135$	−8.00000			−0.688530
$136$	−4.48528	−	4.75736i	−0.384610	−	0.407940i
$137$	−17.6569			−1.50853			−0.754263	−	0.656572i	$-0.772006\pi$
$137$	−17.6569			−1.50853			−0.754263	+	0.656572i	$0.772006\pi$
$138$	0.242641	−	0.242641i	0.0206549	−	0.0206549i
$139$	−0.807612	+	1.94975i	−0.0685007	+	0.165375i	−0.954422	−	0.298460i	$-0.903527\pi$
$139$	−0.807612	+	1.94975i	−0.0685007	+	0.165375i	0.885921	+	0.463835i	$0.153527\pi$
$140$			17.6569i			1.49228i
$141$	−0.585786	−	0.242641i	−0.0493321	−	0.0204340i
$142$	2.51472	+	6.07107i	0.211030	+	0.509473i
$143$	−0.828427	+	0.343146i	−0.0692766	+	0.0286953i
$144$	8.12132	+	8.12132i	0.676777	+	0.676777i
$145$		0			0
$146$	5.07107	−	2.10051i	0.419685	−	0.173839i
$147$	−0.171573	−	0.414214i	−0.0141511	−	0.0341638i
$148$	9.89949	+	4.10051i	0.813733	+	0.337059i
$149$			15.1716i			1.24290i	0.783452	+	0.621452i	$0.213457\pi$
$149$			15.1716i			1.24290i	−0.783452	+	0.621452i	$0.786543\pi$
$150$	3.58579	−	8.65685i	0.292778	−	0.706829i
$151$	−2.00000	+	2.00000i	−0.162758	+	0.162758i	−0.783787	−	0.621029i	$-0.786715\pi$
$151$	−2.00000	+	2.00000i	−0.162758	+	0.162758i	0.621029	+	0.783787i	$0.286715\pi$
$152$	4.48528			0.363804
$153$	−10.8284	−	11.4853i	−0.875426	−	0.928530i
$154$	0.828427			0.0667566
$155$	6.00000	−	6.00000i	0.481932	−	0.481932i
$156$	2.14214	−	5.17157i	0.171508	−	0.414057i
$157$		−	7.65685i		−	0.611083i	−0.952179	−	0.305542i	$-0.901162\pi$
$157$		−	7.65685i		−	0.611083i	0.952179	−	0.305542i	$-0.0988376\pi$
$158$	−2.46447	−	1.02082i	−0.196062	−	0.0812117i
$159$	8.24264	+	19.8995i	0.653684	+	1.57813i
$160$	−15.0711	+	6.24264i	−1.19147	+	0.493524i
$161$	−0.585786	−	0.585786i	−0.0461664	−	0.0461664i
$162$	1.70711	+	1.70711i	0.134123	+	0.134123i
$163$	−12.6569	+	5.24264i	−0.991361	+	0.410635i	−0.818622	−	0.574332i	$-0.805262\pi$
$163$	−12.6569	+	5.24264i	−0.991361	+	0.410635i	−0.172739	+	0.984968i	$0.555262\pi$
$164$	−4.63604	−	11.1924i	−0.362014	−	0.873979i
$165$	6.82843	+	2.82843i	0.531592	+	0.220193i
$166$		−	0.686292i		−	0.0532666i
$167$	4.19239	−	10.1213i	0.324417	−	0.783211i	−0.674570	−	0.738211i	$-0.735671\pi$
$167$	4.19239	−	10.1213i	0.324417	−	0.783211i	0.998987	−	0.0450006i	$-0.0143290\pi$
$168$	−7.65685	+	7.65685i	−0.590739	+	0.590739i
$169$	11.6274			0.894417
$170$	5.89949	−	2.24264i	0.452471	−	0.172003i
$171$	10.8284			0.828071
$172$	−1.29289	+	1.29289i	−0.0985822	+	0.0985822i
$173$	−3.63604	+	8.77817i	−0.276443	+	0.667392i	−0.999732	−	0.0231532i	$-0.992629\pi$
$173$	−3.63604	+	8.77817i	−0.276443	+	0.667392i	0.723289	+	0.690545i	$0.242629\pi$
$174$		0			0
$175$	−20.8995	−	8.65685i	−1.57985	−	0.654397i
$176$	−0.878680	−	2.12132i	−0.0662330	−	0.159901i
$177$	−32.3848	+	13.4142i	−2.43419	+	1.00827i
$178$	2.68629	+	2.68629i	0.201346	+	0.201346i
$179$	7.07107	+	7.07107i	0.528516	+	0.528516i	0.920130	−	0.391613i	$-0.128083\pi$
$179$	7.07107	+	7.07107i	0.528516	+	0.528516i	−0.391613	+	0.920130i	$0.628083\pi$
$180$	−23.8995	+	9.89949i	−1.78136	+	0.737865i
$181$	1.94975	+	4.70711i	0.144924	+	0.349876i	0.979628	−	0.200822i	$-0.0643613\pi$
$181$	1.94975	+	4.70711i	0.144924	+	0.349876i	−0.834704	+	0.550699i	$0.814361\pi$
$182$	1.17157	+	0.485281i	0.0868428	+	0.0359714i
$183$			9.65685i			0.713855i
$184$	0.192388	−	0.464466i	0.0141830	−	0.0342409i
$185$	−15.3137	+	15.3137i	−1.12589	+	1.12589i
$186$	2.48528			0.182230
$187$	1.12132	+	2.94975i	0.0819991	+	0.215707i
$188$	−0.443651			−0.0323566
$189$	−4.00000	+	4.00000i	−0.290957	+	0.290957i
$190$	−1.65685	+	4.00000i	−0.120201	+	0.290191i
$191$			1.51472i			0.109601i	0.998497	+	0.0548006i	$0.0174523\pi$
$191$			1.51472i			0.109601i	−0.998497	+	0.0548006i	$0.982548\pi$
$192$	10.0711	+	4.17157i	0.726817	+	0.301057i
$193$	5.94975	+	14.3640i	0.428272	+	1.03394i	0.979835	+	0.199807i	$0.0640316\pi$
$193$	5.94975	+	14.3640i	0.428272	+	1.03394i	−0.551563	+	0.834133i	$0.685968\pi$
$194$	4.87868	−	2.02082i	0.350269	−	0.145086i
$195$	8.00000	+	8.00000i	0.572892	+	0.572892i
$196$	−0.221825	−	0.221825i	−0.0158447	−	0.0158447i
$197$	−5.77817	+	2.39340i	−0.411678	+	0.170523i	−0.578903	−	0.815396i	$-0.696519\pi$
$197$	−5.77817	+	2.39340i	−0.411678	+	0.170523i	0.167226	+	0.985919i	$0.446519\pi$
$198$	0.464466	+	1.12132i	0.0330082	+	0.0796888i
$199$	−0.414214	−	0.171573i	−0.0293628	−	0.0121625i	0.367954	−	0.929844i	$-0.380058\pi$
$199$	−0.414214	−	0.171573i	−0.0293628	−	0.0121625i	−0.397317	+	0.917682i	$0.630058\pi$
$200$		−	13.7279i		−	0.970711i
$201$	7.07107	−	17.0711i	0.498755	−	1.20410i
$202$	−1.72792	+	1.72792i	−0.121576	+	0.121576i
$203$		0			0
$204$	−17.9706	−	8.07107i	−1.25819	−	0.565088i
$205$	24.4853			1.71013
$206$	−2.89949	+	2.89949i	−0.202017	+	0.202017i
$207$	0.464466	−	1.12132i	0.0322826	−	0.0779372i
$208$		−	3.51472i		−	0.243702i
$209$	−2.00000	−	0.828427i	−0.138343	−	0.0573035i
$210$	−4.00000	−	9.65685i	−0.276026	−	0.666386i
$211$	−16.0711	+	6.65685i	−1.10638	+	0.458277i	−0.859689	−	0.510818i	$-0.829343\pi$
$211$	−16.0711	+	6.65685i	−1.10638	+	0.458277i	−0.246689	+	0.969095i	$0.579343\pi$
$212$	10.6569	+	10.6569i	0.731916	+	0.731916i
$213$	29.3137	+	29.3137i	2.00854	+	2.00854i
$214$	6.29289	−	2.60660i	0.430173	−	0.178184i
$215$	−1.41421	−	3.41421i	−0.0964486	−	0.232847i
$216$	−3.17157	−	1.31371i	−0.215798	−	0.0893865i
$217$		−	6.00000i		−	0.407307i
$218$	1.94975	−	4.70711i	0.132054	−	0.318805i
$219$	24.4853	−	24.4853i	1.65456	−	1.65456i
$220$	5.17157			0.348667
$221$	−0.142136	+	4.82843i	−0.00956108	+	0.324795i
$222$	−6.34315			−0.425724
$223$	0.828427	−	0.828427i	0.0554756	−	0.0554756i	−0.678825	−	0.734300i	$-0.737510\pi$
$223$	0.828427	−	0.828427i	0.0554756	−	0.0554756i	0.734300	+	0.678825i	$0.237510\pi$
$224$	−4.41421	+	10.6569i	−0.294937	+	0.712041i
$225$		−	33.1421i		−	2.20948i
$226$	7.31371	+	3.02944i	0.486501	+	0.201515i
$227$	9.92893	+	23.9706i	0.659006	+	1.59098i	0.799341	+	0.600878i	$0.205182\pi$
$227$	9.92893	+	23.9706i	0.659006	+	1.59098i	−0.140334	+	0.990104i	$0.544818\pi$
$228$	12.4853	−	5.17157i	0.826858	−	0.342496i
$229$	−15.1421	−	15.1421i	−1.00062	−	1.00062i	−1.00000		0.000620680i	$-0.999802\pi$
$229$	−15.1421	−	15.1421i	−1.00062	−	1.00062i	−0.000620680	−	1.00000i	$-0.500198\pi$
$230$	0.343146	+	0.343146i	0.0226264	+	0.0226264i
$231$	4.82843	−	2.00000i	0.317687	−	0.131590i
$232$		0			0
$233$	0.828427	+	0.343146i	0.0542721	+	0.0224802i	0.409654	−	0.912241i	$-0.365649\pi$
$233$	0.828427	+	0.343146i	0.0542721	+	0.0224802i	−0.355382	+	0.934721i	$0.615649\pi$
$234$			1.85786i			0.121452i
$235$	0.343146	−	0.828427i	0.0223844	−	0.0540406i
$236$	−17.3431	+	17.3431i	−1.12894	+	1.12894i
$237$	−16.8284			−1.09312
$238$	1.82843	−	4.07107i	0.118519	−	0.263888i
$239$	26.0000			1.68180			0.840900	−	0.541190i	$-0.182026\pi$
$239$	26.0000			1.68180			0.840900	+	0.541190i	$0.182026\pi$
$240$	−20.4853	+	20.4853i	−1.32232	+	1.32232i
$241$	0.585786	−	1.41421i	0.0377338	−	0.0910975i	−0.903889	−	0.427767i	$-0.859300\pi$
$241$	0.585786	−	1.41421i	0.0377338	−	0.0910975i	0.941623	+	0.336669i	$0.109300\pi$
$242$			4.31371i			0.277296i
$243$	20.0711	+	8.31371i	1.28756	+	0.533325i
$244$	2.58579	+	6.24264i	0.165538	+	0.399644i
$245$	0.585786	−	0.242641i	0.0374245	−	0.0155017i
$246$	5.07107	+	5.07107i	0.323319	+	0.323319i
$247$	−2.34315	−	2.34315i	−0.149091	−	0.149091i
$248$	3.36396	−	1.39340i	0.213612	−	0.0884809i
$249$	−1.65685	−	4.00000i	−0.104999	−	0.253490i
$250$	5.17157	+	2.14214i	0.327079	+	0.135481i
$251$			7.65685i			0.483296i	0.970364	+	0.241648i	$0.0776880\pi$
$251$			7.65685i			0.483296i	−0.970364	+	0.241648i	$0.922312\pi$
$252$	−7.00000	+	16.8995i	−0.440959	+	1.06457i
$253$	−0.171573	+	0.171573i	−0.0107867	+	0.0107867i
$254$	2.92893			0.183778
$255$	28.9706	−	27.3137i	1.81421	−	1.71045i
$256$	3.97056			0.248160
$257$	−6.48528	+	6.48528i	−0.404541	+	0.404541i	−0.879830	−	0.475289i	$-0.842344\pi$
$257$	−6.48528	+	6.48528i	−0.404541	+	0.404541i	0.475289	+	0.879830i	$0.342344\pi$
$258$	0.414214	−	1.00000i	0.0257878	−	0.0622573i
$259$			15.3137i			0.951548i
$260$	7.31371	+	3.02944i	0.453577	+	0.187878i
$261$		0			0
$262$	−2.41421	+	1.00000i	−0.149151	+	0.0617802i
$263$	−18.8284	−	18.8284i	−1.16101	−	1.16101i	−0.984255	−	0.176756i	$-0.943440\pi$
$263$	−18.8284	−	18.8284i	−1.16101	−	1.16101i	−0.176756	−	0.984255i	$-0.556560\pi$
$264$	2.24264	+	2.24264i	0.138025	+	0.138025i
$265$	−28.1421	+	11.6569i	−1.72876	+	0.716075i
$266$	1.17157	+	2.82843i	0.0718337	+	0.173422i
$267$	22.1421	+	9.17157i	1.35508	+	0.561291i
$268$		−	12.9289i		−	0.789760i
$269$	−9.94975	+	24.0208i	−0.606647	+	1.46457i	0.259978	+	0.965615i	$0.416285\pi$
$269$	−9.94975	+	24.0208i	−0.606647	+	1.46457i	−0.866625	+	0.498960i	$0.833715\pi$
$270$	2.34315	−	2.34315i	0.142599	−	0.142599i
$271$	−2.58579			−0.157075			−0.0785377	−	0.996911i	$-0.525025\pi$
$271$	−2.58579			−0.157075			−0.0785377	+	0.996911i	$0.525025\pi$
$272$	−12.3640	−	0.363961i	−0.749675	−	0.0220684i
$273$	8.00000			0.484182
$274$	5.17157	−	5.17157i	0.312426	−	0.312426i
$275$	−2.53553	+	6.12132i	−0.152898	+	0.369130i
$276$		−	1.51472i		−	0.0911753i
$277$	3.65685	+	1.51472i	0.219719	+	0.0910106i	0.489828	−	0.871819i	$-0.337060\pi$
$277$	3.65685	+	1.51472i	0.219719	+	0.0910106i	−0.270109	+	0.962830i	$0.587060\pi$
$278$	−0.334524	−	0.807612i	−0.0200634	−	0.0484373i
$279$	8.12132	−	3.36396i	0.486211	−	0.201395i
$280$	−10.8284	−	10.8284i	−0.647122	−	0.647122i
$281$	−18.3137	−	18.3137i	−1.09250	−	1.09250i	−0.995261	−	0.0972437i	$-0.968997\pi$
$281$	−18.3137	−	18.3137i	−1.09250	−	1.09250i	−0.0972437	−	0.995261i	$-0.531003\pi$
$282$	0.242641	−	0.100505i	0.0144490	−	0.00598499i
$283$	0.292893	+	0.707107i	0.0174107	+	0.0420331i	0.932346	−	0.361568i	$-0.117758\pi$
$283$	0.292893	+	0.707107i	0.0174107	+	0.0420331i	−0.914935	+	0.403601i	$0.867758\pi$
$284$	26.7990	+	11.1005i	1.59023	+	0.658694i
$285$			27.3137i			1.61792i
$286$	0.142136	−	0.343146i	0.00840466	−	0.0202906i
$287$	12.2426	−	12.2426i	0.722660	−	0.722660i
$288$	−16.8995			−0.995812
$289$	16.9706	+	1.00000i	0.998268	+	0.0588235i
$290$		0			0
$291$	23.5563	−	23.5563i	1.38090	−	1.38090i
$292$	9.27208	−	22.3848i	0.542607	−	1.30997i
$293$		−	20.9706i		−	1.22511i	−0.790427	−	0.612557i	$-0.790141\pi$
$293$		−	20.9706i		−	1.22511i	0.790427	−	0.612557i	$-0.209859\pi$
$294$	0.171573	+	0.0710678i	0.0100063	+	0.00414476i
$295$	−18.9706	−	45.7990i	−1.10451	−	2.66652i
$296$	−8.58579	+	3.55635i	−0.499039	+	0.206709i
$297$	1.17157	+	1.17157i	0.0679816	+	0.0679816i
$298$	−4.44365	−	4.44365i	−0.257414	−	0.257414i
$299$	−0.343146	+	0.142136i	−0.0198446	+	0.00821992i
$300$	−15.8284	−	38.2132i	−0.913855	−	2.20624i
$301$	−2.41421	−	1.00000i	−0.139153	−	0.0576390i
$302$		−	1.17157i		−	0.0674164i
$303$	−5.89949	+	14.2426i	−0.338917	+	0.818218i
$304$	6.00000	−	6.00000i	0.344124	−	0.344124i
$305$	−13.6569			−0.781989
$306$	6.53553	+	0.192388i	0.373612	+	0.0109981i
$307$	−13.2132			−0.754117			−0.377059	−	0.926189i	$-0.623064\pi$
$307$	−13.2132			−0.754117			−0.377059	+	0.926189i	$0.623064\pi$
$308$	2.58579	−	2.58579i	0.147339	−	0.147339i
$309$	−9.89949	+	23.8995i	−0.563163	+	1.35959i
$310$			3.51472i			0.199623i
$311$	−18.1924	−	7.53553i	−1.03160	−	0.427301i	−0.198308	−	0.980140i	$-0.563544\pi$
$311$	−18.1924	−	7.53553i	−1.03160	−	0.427301i	−0.833288	+	0.552839i	$0.813544\pi$
$312$	1.85786	+	4.48528i	0.105181	+	0.253929i
$313$	−6.82843	+	2.82843i	−0.385966	+	0.159872i	−0.567224	−	0.823563i	$-0.691983\pi$
$313$	−6.82843	+	2.82843i	−0.385966	+	0.159872i	0.181259	+	0.983435i	$0.441983\pi$
$314$	2.24264	+	2.24264i	0.126560	+	0.126560i
$315$	−26.1421	−	26.1421i	−1.47294	−	1.47294i
$316$	−10.8787	+	4.50610i	−0.611974	+	0.253488i
$317$	−10.8076	−	26.0919i	−0.607016	−	1.46547i	−0.866230	−	0.499646i	$-0.833463\pi$
$317$	−10.8076	−	26.0919i	−0.607016	−	1.46547i	0.259214	−	0.965820i	$-0.416537\pi$
$318$	−8.24264	−	3.41421i	−0.462224	−	0.191460i
$319$		0			0
$320$	−5.89949	+	14.2426i	−0.329792	+	0.796188i
$321$	30.3848	−	30.3848i	1.69591	−	1.69591i
$322$	0.343146			0.0191228
$323$	−8.48528	+	8.00000i	−0.472134	+	0.445132i
$324$	10.6569			0.592047
$325$	−7.17157	+	7.17157i	−0.397807	+	0.397807i
$326$	2.17157	−	5.24264i	0.120272	−	0.290363i
$327$		−	32.1421i		−	1.77746i
$328$	9.70711	+	4.02082i	0.535985	+	0.222012i
$329$	−0.242641	−	0.585786i	−0.0133772	−	0.0322955i
$330$	−2.82843	+	1.17157i	−0.155700	+	0.0644930i
$331$	−15.8995	−	15.8995i	−0.873915	−	0.873915i	0.118981	−	0.992897i	$-0.462037\pi$
$331$	−15.8995	−	15.8995i	−0.873915	−	0.873915i	−0.992897	+	0.118981i	$0.962037\pi$
$332$	−2.14214	−	2.14214i	−0.117565	−	0.117565i
$333$	−20.7279	+	8.58579i	−1.13588	+	0.470498i
$334$	1.73654	+	4.19239i	0.0950195	+	0.229397i
$335$	24.1421	+	10.0000i	1.31903	+	0.546358i
$336$			20.4853i			1.11756i
$337$	9.39340	−	22.6777i	0.511691	−	1.23533i	−0.431208	−	0.902253i	$-0.641912\pi$
$337$	9.39340	−	22.6777i	0.511691	−	1.23533i	0.942899	−	0.333079i	$-0.108088\pi$
$338$	−3.40559	+	3.40559i	−0.185240	+	0.185240i
$339$	49.9411			2.71243
$340$	11.4142	−	25.4142i	0.619023	−	1.37828i
$341$	−1.75736			−0.0951663
$342$	−3.17157	+	3.17157i	−0.171499	+	0.171499i
$343$	7.17157	−	17.3137i	0.387229	−	0.934852i
$344$		−	1.58579i		−	0.0854999i
$345$	2.82843	+	1.17157i	0.152277	+	0.0630754i
$346$	−1.50610	−	3.63604i	−0.0809683	−	0.195475i
$347$	10.0711	−	4.17157i	0.540643	−	0.223942i	−0.0956143	−	0.995418i	$-0.530482\pi$
$347$	10.0711	−	4.17157i	0.540643	−	0.223942i	0.636258	+	0.771477i	$0.280482\pi$
$348$		0			0
$349$	18.2426	+	18.2426i	0.976506	+	0.976506i	0.999730	−	0.0232241i	$-0.00739313\pi$
$349$	18.2426	+	18.2426i	0.976506	+	0.976506i	−0.0232241	+	0.999730i	$0.507393\pi$
$350$	8.65685	−	3.58579i	0.462728	−	0.191668i
$351$	0.970563	+	2.34315i	0.0518048	+	0.125068i
$352$	3.12132	+	1.29289i	0.166367	+	0.0689114i
$353$			13.6569i			0.726881i	0.931617	+	0.363441i	$0.118398\pi$
$353$			13.6569i			0.726881i	−0.931617	+	0.363441i	$0.881602\pi$
$354$	5.55635	−	13.4142i	0.295317	−	0.712957i
$355$	−41.4558	+	41.4558i	−2.20025	+	2.20025i
$356$	16.7696			0.888785
$357$	0.828427	−	28.1421i	0.0438450	−	1.48944i
$358$	−4.14214			−0.218919
$359$	7.07107	−	7.07107i	0.373197	−	0.373197i	−0.495443	−	0.868640i	$-0.664994\pi$
$359$	7.07107	−	7.07107i	0.373197	−	0.373197i	0.868640	+	0.495443i	$0.164994\pi$
$360$	8.58579	−	20.7279i	0.452511	−	1.09246i
$361$			11.0000i			0.578947i
$362$	−1.94975	−	0.807612i	−0.102476	−	0.0424471i
$363$	10.4142	+	25.1421i	0.546604	+	1.31962i
$364$	5.17157	−	2.14214i	0.271064	−	0.112278i
$365$	34.6274	+	34.6274i	1.81248	+	1.81248i
$366$	−2.82843	−	2.82843i	−0.147844	−	0.147844i
$367$	14.0208	−	5.80761i	0.731881	−	0.303155i	0.0145561	−	0.999894i	$-0.495367\pi$
$367$	14.0208	−	5.80761i	0.731881	−	0.303155i	0.717325	+	0.696739i	$0.245367\pi$
$368$	−0.363961	−	0.878680i	−0.0189728	−	0.0458043i
$369$	23.4350	+	9.70711i	1.21998	+	0.505332i
$370$		−	8.97056i		−	0.466357i
$371$	−8.24264	+	19.8995i	−0.427937	+	1.03313i
$372$	7.75736	−	7.75736i	0.402200	−	0.402200i
$373$	−0.485281			−0.0251269			−0.0125635	−	0.999921i	$-0.503999\pi$
$373$	−0.485281			−0.0251269			−0.0125635	+	0.999921i	$0.503999\pi$
$374$	−1.19239	−	0.535534i	−0.0616569	−	0.0276918i
$375$	35.3137			1.82359
$376$	0.272078	−	0.272078i	0.0140313	−	0.0140313i
$377$		0			0
$378$		−	2.34315i		−	0.120518i
$379$	−21.2635	−	8.80761i	−1.09223	−	0.452417i	−0.237446	−	0.971401i	$-0.576310\pi$
$379$	−21.2635	−	8.80761i	−1.09223	−	0.452417i	−0.854784	+	0.518984i	$0.826310\pi$
$380$	7.31371	+	17.6569i	0.375185	+	0.905778i
$381$	17.0711	−	7.07107i	0.874577	−	0.362262i
$382$	−0.443651	−	0.443651i	−0.0226992	−	0.0226992i
$383$	−14.1421	−	14.1421i	−0.722629	−	0.722629i	0.246511	−	0.969140i	$-0.420716\pi$
$383$	−14.1421	−	14.1421i	−0.722629	−	0.722629i	−0.969140	+	0.246511i	$0.920716\pi$
$384$	−25.4853	+	10.5563i	−1.30054	+	0.538701i
$385$	2.82843	+	6.82843i	0.144150	+	0.348009i
$386$	−5.94975	−	2.46447i	−0.302834	−	0.125438i
$387$		−	3.82843i		−	0.194610i
$388$	8.92031	−	21.5355i	0.452860	−	1.09330i
$389$	−0.828427	+	0.828427i	−0.0420029	+	0.0420029i	−0.727796	−	0.685793i	$-0.759455\pi$
$389$	−0.828427	+	0.828427i	−0.0420029	+	0.0420029i	0.685793	+	0.727796i	$0.259455\pi$
$390$	−4.68629			−0.237300
$391$	0.464466	+	1.22183i	0.0234891	+	0.0617904i
$392$	0.272078			0.0137420
$393$	−11.6569	+	11.6569i	−0.588011	+	0.588011i
$394$	0.991378	−	2.39340i	0.0499449	−	0.120578i
$395$		−	23.7990i		−	1.19746i
$396$	4.94975	+	2.05025i	0.248734	+	0.103029i
$397$	−0.464466	−	1.12132i	−0.0233109	−	0.0562775i	0.911795	−	0.410645i	$-0.134696\pi$
$397$	−0.464466	−	1.12132i	−0.0233109	−	0.0562775i	−0.935106	+	0.354367i	$0.884696\pi$
$398$	0.171573	−	0.0710678i	0.00860017	−	0.00356231i
$399$	13.6569	+	13.6569i	0.683698	+	0.683698i
$400$	−18.3640	−	18.3640i	−0.918198	−	0.918198i
$401$	13.6066	−	5.63604i	0.679481	−	0.281450i	−0.0161288	−	0.999870i	$-0.505134\pi$
$401$	13.6066	−	5.63604i	0.679481	−	0.281450i	0.695610	+	0.718420i	$0.255134\pi$
$402$	2.92893	+	7.07107i	0.146082	+	0.352673i
$403$	−2.48528	−	1.02944i	−0.123801	−	0.0512799i
$404$			10.7868i			0.536663i
$405$	−8.24264	+	19.8995i	−0.409580	+	0.988814i
$406$		0			0
$407$	4.48528			0.222327
$408$	15.9706	−	6.07107i	0.790661	−	0.300563i
$409$	−27.4558			−1.35760			−0.678802	−	0.734321i	$-0.737501\pi$
$409$	−27.4558			−1.35760			−0.678802	+	0.734321i	$0.737501\pi$
$410$	−7.17157	+	7.17157i	−0.354179	+	0.354179i
$411$	17.6569	−	42.6274i	0.870948	−	2.10266i
$412$			18.1005i			0.891748i
$413$	−32.3848	−	13.4142i	−1.59355	−	0.660070i
$414$	0.192388	+	0.464466i	0.00945536	+	0.0228273i
$415$	5.65685	−	2.34315i	0.277684	−	0.115021i
$416$	3.65685	+	3.65685i	0.179292	+	0.179292i
$417$	−3.89949	−	3.89949i	−0.190959	−	0.190959i
$418$	0.828427	−	0.343146i	0.0405197	−	0.0167838i
$419$	11.1421	+	26.8995i	0.544329	+	1.31413i	0.921642	+	0.388041i	$0.126848\pi$
$419$	11.1421	+	26.8995i	0.544329	+	1.31413i	−0.377313	+	0.926086i	$0.623152\pi$
$420$	−42.6274	−	17.6569i	−2.08000	−	0.861566i
$421$			26.1421i			1.27409i	0.770827	+	0.637045i	$0.219843\pi$
$421$			26.1421i			1.27409i	−0.770827	+	0.637045i	$0.780157\pi$
$422$	2.75736	−	6.65685i	0.134226	−	0.324051i
$423$	0.656854	−	0.656854i	0.0319373	−	0.0319373i
$424$	−13.0711			−0.634787
$425$	24.4853	+	25.9706i	1.18771	+	1.25976i
$426$	−17.1716			−0.831965
$427$	−6.82843	+	6.82843i	−0.330451	+	0.330451i
$428$	11.5061	−	27.7782i	0.556168	−	1.34271i
$429$		−	2.34315i		−	0.113128i
$430$	1.41421	+	0.585786i	0.0681994	+	0.0282491i
$431$	−8.94975	−	21.6066i	−0.431094	−	1.04075i	−0.978935	−	0.204171i	$-0.934550\pi$
$431$	−8.94975	−	21.6066i	−0.431094	−	1.04075i	0.547841	−	0.836582i	$-0.315450\pi$
$432$	−6.00000	+	2.48528i	−0.288675	+	0.119573i
$433$	23.7990	+	23.7990i	1.14371	+	1.14371i	0.987767	+	0.155940i	$0.0498406\pi$
$433$	23.7990	+	23.7990i	1.14371	+	1.14371i	0.155940	+	0.987767i	$0.450159\pi$
$434$	1.75736	+	1.75736i	0.0843559	+	0.0843559i
$435$		0			0
$436$	−8.60660	−	20.7782i	−0.412181	−	0.995094i
$437$	−0.828427	−	0.343146i	−0.0396290	−	0.0164149i
$438$			14.3431i			0.685342i
$439$	−8.39340	+	20.2635i	−0.400595	+	0.967122i	0.586927	+	0.809640i	$0.300338\pi$
$439$	−8.39340	+	20.2635i	−0.400595	+	0.967122i	−0.987522	+	0.157482i	$0.949662\pi$
$440$	−3.17157	+	3.17157i	−0.151199	+	0.151199i
$441$	0.656854			0.0312788
$442$	−1.37258	−	1.45584i	−0.0652871	−	0.0692474i
$443$	19.6569			0.933925			0.466963	−	0.884277i	$-0.345348\pi$
$443$	19.6569			0.933925			0.466963	+	0.884277i	$0.345348\pi$
$444$	−19.7990	+	19.7990i	−0.939618	+	0.939618i
$445$	−12.9706	+	31.3137i	−0.614864	+	1.48441i
$446$			0.485281i			0.0229787i
$447$	−36.6274	−	15.1716i	−1.73242	−	0.717591i
$448$	4.17157	+	10.0711i	0.197088	+	0.475813i
$449$	17.6569	−	7.31371i	0.833278	−	0.345155i	0.0750787	−	0.997178i	$-0.476079\pi$
$449$	17.6569	−	7.31371i	0.833278	−	0.345155i	0.758200	+	0.652022i	$0.226079\pi$
$450$	9.70711	+	9.70711i	0.457597	+	0.457597i
$451$	−3.58579	−	3.58579i	−0.168848	−	0.168848i
$452$	32.2843	−	13.3726i	1.51852	−	0.628993i
$453$	−2.82843	−	6.82843i	−0.132891	−	0.320827i
$454$	−9.92893	−	4.11270i	−0.465988	−	0.193018i
$455$			11.3137i			0.530395i
$456$	−4.48528	+	10.8284i	−0.210043	+	0.507088i
$457$	10.1421	−	10.1421i	0.474429	−	0.474429i	−0.428916	−	0.903345i	$-0.641104\pi$
$457$	10.1421	−	10.1421i	0.474429	−	0.474429i	0.903345	+	0.428916i	$0.141104\pi$
$458$	8.87006			0.414471
$459$	8.34315	−	3.17157i	0.389425	−	0.148036i
$460$	2.14214			0.0998776
$461$	−11.5563	+	11.5563i	−0.538233	+	0.538233i	−0.923010	−	0.384777i	$-0.874278\pi$
$461$	−11.5563	+	11.5563i	−0.538233	+	0.538233i	0.384777	+	0.923010i	$0.374278\pi$
$462$	−0.828427	+	2.00000i	−0.0385419	+	0.0930484i
$463$			35.6569i			1.65711i	0.559904	+	0.828557i	$0.310838\pi$
$463$			35.6569i			1.65711i	−0.559904	+	0.828557i	$0.689162\pi$
$464$		0			0
$465$	8.48528	+	20.4853i	0.393496	+	0.949982i
$466$	−0.343146	+	0.142136i	−0.0158959	+	0.00658431i
$467$	−28.9706	−	28.9706i	−1.34060	−	1.34060i	−0.895464	−	0.445134i	$-0.853156\pi$
$467$	−28.9706	−	28.9706i	−1.34060	−	1.34060i	−0.445134	−	0.895464i	$-0.646844\pi$
$468$	5.79899	+	5.79899i	0.268058	+	0.268058i
$469$	17.0711	−	7.07107i	0.788269	−	0.326512i
$470$	0.142136	+	0.343146i	0.00655623	+	0.0158281i
$471$	18.4853	+	7.65685i	0.851757	+	0.352809i
$472$		−	21.2721i		−	0.979127i
$473$	−0.292893	+	0.707107i	−0.0134672	+	0.0325128i
$474$	4.92893	−	4.92893i	0.226393	−	0.226393i
$475$	−24.4853			−1.12346
$476$	−7.00000	−	18.4142i	−0.320844	−	0.844014i
$477$	−31.5563			−1.44487
$478$	−7.61522	+	7.61522i	−0.348312	+	0.348312i
$479$	10.6777	−	25.7782i	0.487875	−	1.17783i	−0.467912	−	0.883775i	$-0.654994\pi$
$479$	10.6777	−	25.7782i	0.487875	−	1.17783i	0.955787	−	0.294060i	$-0.0950065\pi$
$480$		−	42.6274i		−	1.94567i
$481$	6.34315	+	2.62742i	0.289223	+	0.119800i
$482$	0.242641	+	0.585786i	0.0110520	+	0.0266818i
$483$	2.00000	−	0.828427i	0.0910032	−	0.0376947i
$484$	13.4645	+	13.4645i	0.612021	+	0.612021i
$485$	33.3137	+	33.3137i	1.51270	+	1.51270i
$486$	−8.31371	+	3.44365i	−0.377117	+	0.156207i
$487$	5.94975	+	14.3640i	0.269609	+	0.650893i	0.999465	−	0.0327075i	$-0.0104130\pi$
$487$	5.94975	+	14.3640i	0.269609	+	0.650893i	−0.729856	+	0.683601i	$0.760413\pi$
$488$	−5.41421	−	2.24264i	−0.245090	−	0.101520i
$489$		−	35.7990i		−	1.61889i
$490$	−0.100505	+	0.242641i	−0.00454036	+	0.0109614i
$491$	−30.4853	+	30.4853i	−1.37578	+	1.37578i	−0.524164	+	0.851617i	$0.675622\pi$
$491$	−30.4853	+	30.4853i	−1.37578	+	1.37578i	−0.851617	+	0.524164i	$0.824378\pi$
$492$	31.6569			1.42720
$493$		0			0
$494$	1.37258			0.0617554
$495$	−7.65685	+	7.65685i	−0.344150	+	0.344150i
$496$	2.63604	−	6.36396i	0.118362	−	0.285750i
$497$			41.4558i			1.85955i
$498$	1.65685	+	0.686292i	0.0742454	+	0.0307535i
$499$	9.72792	+	23.4853i	0.435482	+	1.05135i	0.977492	+	0.210974i	$0.0676634\pi$
$499$	9.72792	+	23.4853i	0.435482	+	1.05135i	−0.542010	+	0.840372i	$0.682337\pi$
$500$	22.8284	−	9.45584i	1.02092	−	0.422878i
$501$	20.2426	+	20.2426i	0.904374	+	0.904374i
$502$	−2.24264	−	2.24264i	−0.100094	−	0.100094i
$503$	23.7279	−	9.82843i	1.05798	−	0.438228i	0.215243	−	0.976560i	$-0.430946\pi$
$503$	23.7279	−	9.82843i	1.05798	−	0.438228i	0.842732	+	0.538333i	$0.180946\pi$
$504$	−6.07107	−	14.6569i	−0.270427	−	0.652868i
$505$	−20.1421	−	8.34315i	−0.896313	−	0.371265i
$506$		−	0.100505i		−	0.00446800i
$507$	−11.6274	+	28.0711i	−0.516392	+	1.24668i
$508$	9.14214	−	9.14214i	0.405617	−	0.405617i
$509$	−9.89949			−0.438787			−0.219394	−	0.975636i	$-0.570408\pi$
$509$	−9.89949			−0.438787			−0.219394	+	0.975636i	$0.570408\pi$
$510$	−0.485281	+	16.4853i	−0.0214886	+	0.729981i
$511$	34.6274			1.53183
$512$	−16.0919	+	16.0919i	−0.711167	+	0.711167i
$513$	−2.34315	+	5.65685i	−0.103452	+	0.249756i
$514$		−	3.79899i		−	0.167566i
$515$	−33.7990	−	14.0000i	−1.48936	−	0.616914i
$516$	−1.82843	−	4.41421i	−0.0804920	−	0.194325i
$517$	−0.171573	+	0.0710678i	−0.00754577	+	0.00312556i
$518$	−4.48528	−	4.48528i	−0.197072	−	0.197072i
$519$	−17.5563	−	17.5563i	−0.770638	−	0.770638i
$520$	−6.34315	+	2.62742i	−0.278165	+	0.115220i
$521$	−7.31371	−	17.6569i	−0.320419	−	0.773561i	−0.999230	−	0.0392470i	$-0.987504\pi$
$521$	−7.31371	−	17.6569i	−0.320419	−	0.773561i	0.678810	−	0.734314i	$-0.262496\pi$
$522$		0			0
$523$		−	26.1421i		−	1.14312i	−0.820562	−	0.571558i	$-0.806339\pi$
$523$		−	26.1421i		−	1.14312i	0.820562	−	0.571558i	$-0.193661\pi$
$524$	−4.41421	+	10.6569i	−0.192836	+	0.465547i
$525$	41.7990	−	41.7990i	1.82426	−	1.82426i
$526$	11.0294			0.480906
$527$	−3.87868	+	8.63604i	−0.168958	+	0.376192i
$528$	6.00000			0.261116
$529$	16.1924	−	16.1924i	0.704017	−	0.704017i
$530$	4.82843	−	11.6569i	0.209733	−	0.506341i
$531$		−	51.3553i		−	2.22863i
$532$	12.4853	+	5.17157i	0.541306	+	0.224216i
$533$	−2.97056	−	7.17157i	−0.128669	−	0.310635i
$534$	−9.17157	+	3.79899i	−0.396893	+	0.164398i
$535$	42.9706	+	42.9706i	1.85778	+	1.85778i
$536$	7.92893	+	7.92893i	0.342478	+	0.342478i
$537$	−24.1421	+	10.0000i	−1.04181	+	0.431532i
$538$	−4.12132	−	9.94975i	−0.177683	−	0.428964i
$539$	−0.121320	−	0.0502525i	−0.00522564	−	0.00216453i
$540$		−	14.6274i		−	0.629464i
$541$	15.9497	−	38.5061i	0.685733	−	1.65551i	−0.0674723	−	0.997721i	$-0.521493\pi$
$541$	15.9497	−	38.5061i	0.685733	−	1.65551i	0.753206	−	0.657785i	$-0.228507\pi$
$542$	0.757359	−	0.757359i	0.0325314	−	0.0325314i
$543$	−13.3137			−0.571346
$544$	13.2426	−	12.4853i	0.567774	−	0.535302i
$545$	45.4558			1.94711
$546$	−2.34315	+	2.34315i	−0.100277	+	0.100277i
$547$	6.12132	−	14.7782i	0.261729	−	0.631869i	−0.737317	−	0.675547i	$-0.763908\pi$
$547$	6.12132	−	14.7782i	0.261729	−	0.631869i	0.999046	+	0.0436779i	$0.0139075\pi$
$548$		−	32.2843i		−	1.37912i
$549$	−13.0711	−	5.41421i	−0.557860	−	0.231073i
$550$	−1.05025	−	2.53553i	−0.0447829	−	0.108116i
$551$		0			0
$552$	0.928932	+	0.928932i	0.0395380	+	0.0395380i
$553$	−11.8995	−	11.8995i	−0.506018	−	0.506018i
$554$	−1.51472	+	0.627417i	−0.0643542	+	0.0266564i
$555$	−21.6569	−	52.2843i	−0.919282	−	2.21934i
$556$	−3.56497	−	1.47666i	−0.151188	−	0.0626243i
$557$		−	0.928932i		−	0.0393601i	−0.999806	−	0.0196801i	$-0.993735\pi$
$557$		−	0.928932i		−	0.0393601i	0.999806	−	0.0196801i	$-0.00626476\pi$
$558$	−1.39340	+	3.36396i	−0.0589873	+	0.142408i
$559$	−0.828427	+	0.828427i	−0.0350387	+	0.0350387i
$560$	−28.9706			−1.22423
$561$	−8.24264	−	0.242641i	−0.348005	−	0.0102443i
$562$	10.7279			0.452530
$563$	9.97056	−	9.97056i	0.420209	−	0.420209i	−0.465067	−	0.885276i	$-0.653970\pi$
$563$	9.97056	−	9.97056i	0.420209	−	0.420209i	0.885276	+	0.465067i	$0.153970\pi$
$564$	0.443651	−	1.07107i	0.0186811	−	0.0451001i
$565$			70.6274i			2.97132i
$566$	−0.292893	−	0.121320i	−0.0123112	−	0.00509947i
$567$	5.82843	+	14.0711i	0.244771	+	0.590929i
$568$	−23.2426	+	9.62742i	−0.975240	+	0.403957i
$569$	−7.31371	−	7.31371i	−0.306607	−	0.306607i	0.536985	−	0.843592i	$-0.319563\pi$
$569$	−7.31371	−	7.31371i	−0.306607	−	0.306607i	−0.843592	+	0.536985i	$0.819563\pi$
$570$	−8.00000	−	8.00000i	−0.335083	−	0.335083i
$571$	−1.34315	+	0.556349i	−0.0562089	+	0.0232825i	−0.410611	−	0.911811i	$-0.634684\pi$
$571$	−1.34315	+	0.556349i	−0.0562089	+	0.0232825i	0.354402	+	0.935093i	$0.384684\pi$
$572$	−0.627417	−	1.51472i	−0.0262336	−	0.0633336i
$573$	−3.65685	−	1.51472i	−0.152767	−	0.0632783i
$574$			7.17157i			0.299336i
$575$	−1.05025	+	2.53553i	−0.0437986	+	0.105739i
$576$	−11.2929	+	11.2929i	−0.470537	+	0.470537i
$577$	−16.6863			−0.694659			−0.347330	−	0.937743i	$-0.612912\pi$
$577$	−16.6863			−0.694659			−0.347330	+	0.937743i	$0.612912\pi$
$578$	−5.26346	+	4.67767i	−0.218931	+	0.194565i
$579$	−40.6274			−1.68842
$580$		0			0
$581$	1.65685	−	4.00000i	0.0687379	−	0.165948i
$582$			13.7990i			0.571987i
$583$	5.82843	+	2.41421i	0.241389	+	0.0999865i
$584$	8.04163	+	19.4142i	0.332765	+	0.803366i
$585$	−15.3137	+	6.34315i	−0.633144	+	0.262257i
$586$	6.14214	+	6.14214i	0.253729	+	0.253729i
$587$	−9.75736	−	9.75736i	−0.402729	−	0.402729i	0.476464	−	0.879194i	$-0.341918\pi$
$587$	−9.75736	−	9.75736i	−0.402729	−	0.402729i	−0.879194	+	0.476464i	$0.841918\pi$
$588$	0.757359	−	0.313708i	0.0312330	−	0.0129371i
$589$	−2.48528	−	6.00000i	−0.102404	−	0.247226i
$590$	18.9706	+	7.85786i	0.781006	+	0.323503i
$591$		−	16.3431i		−	0.672267i
$592$	−6.72792	+	16.2426i	−0.276516	+	0.667568i
$593$	−5.27208	+	5.27208i	−0.216498	+	0.216498i	−0.807021	−	0.590523i	$-0.798922\pi$
$593$	−5.27208	+	5.27208i	−0.216498	+	0.216498i	0.590523	+	0.807021i	$0.298922\pi$
$594$	−0.686292			−0.0281589
$595$	39.7990	+	1.17157i	1.63160	+	0.0480298i
$596$	−27.7401			−1.13628
$597$	0.828427	−	0.828427i	0.0339053	−	0.0339053i
$598$	0.0588745	−	0.142136i	0.00240756	−	0.00581236i
$599$		−	12.9706i		−	0.529963i	−0.964254	−	0.264981i	$-0.914634\pi$
$599$		−	12.9706i		−	0.529963i	0.964254	−	0.264981i	$-0.0853658\pi$
$600$	33.1421	+	13.7279i	1.35302	+	0.560440i
$601$	18.2843	+	44.1421i	0.745831	+	1.80060i	0.580322	+	0.814387i	$0.302927\pi$
$601$	18.2843	+	44.1421i	0.745831	+	1.80060i	0.165509	+	0.986208i	$0.447073\pi$
$602$	1.00000	−	0.414214i	0.0407570	−	0.0168821i
$603$	19.1421	+	19.1421i	0.779528	+	0.779528i
$604$	−3.65685	−	3.65685i	−0.148795	−	0.148795i
$605$	−35.5563	+	14.7279i	−1.44557	+	0.598775i
$606$	−2.44365	−	5.89949i	−0.0992665	−	0.239651i
$607$	−4.07107	−	1.68629i	−0.165240	−	0.0684445i	0.298530	−	0.954400i	$-0.403504\pi$
$607$	−4.07107	−	1.68629i	−0.165240	−	0.0684445i	−0.463770	+	0.885956i	$0.653504\pi$
$608$			12.4853i			0.506345i
$609$		0			0
$610$	4.00000	−	4.00000i	0.161955	−	0.161955i
$611$	−0.284271			−0.0115004
$612$	21.0000	−	19.7990i	0.848875	−	0.800327i
$613$	−15.5563			−0.628315			−0.314158	−	0.949371i	$-0.601722\pi$
$613$	−15.5563			−0.628315			−0.314158	+	0.949371i	$0.601722\pi$
$614$	3.87006	−	3.87006i	0.156183	−	0.156183i
$615$	−24.4853	+	59.1127i	−0.987342	+	2.38365i
$616$			3.17157i			0.127786i
$617$	−9.29289	−	3.84924i	−0.374118	−	0.154965i	0.187698	−	0.982227i	$-0.439897\pi$
$617$	−9.29289	−	3.84924i	−0.374118	−	0.154965i	−0.561816	+	0.827262i	$0.689897\pi$
$618$	−4.10051	−	9.89949i	−0.164947	−	0.398216i
$619$	−13.1213	+	5.43503i	−0.527390	+	0.218452i	−0.630460	−	0.776222i	$-0.717134\pi$
$619$	−13.1213	+	5.43503i	−0.527390	+	0.218452i	0.103069	+	0.994674i	$0.467134\pi$
$620$	10.9706	+	10.9706i	0.440588	+	0.440588i
$621$	0.485281	+	0.485281i	0.0194737	+	0.0194737i
$622$	7.53553	−	3.12132i	0.302147	−	0.125154i
$623$	9.17157	+	22.1421i	0.367451	+	0.887106i
$624$	8.48528	+	3.51472i	0.339683	+	0.140701i
$625$			6.65685i			0.266274i
$626$	1.17157	−	2.82843i	0.0468255	−	0.113047i
$627$	4.00000	−	4.00000i	0.159745	−	0.159745i
$628$	14.0000			0.558661
$629$	9.89949	−	22.0416i	0.394719	−	0.878857i
$630$	15.3137			0.610113
$631$	−9.07107	+	9.07107i	−0.361114	+	0.361114i	−0.864223	−	0.503109i	$-0.832189\pi$
$631$	−9.07107	+	9.07107i	−0.361114	+	0.361114i	0.503109	+	0.864223i	$0.332189\pi$
$632$	3.90812	−	9.43503i	0.155457	−	0.375305i
$633$		−	45.4558i		−	1.80671i
$634$	10.8076	+	4.47666i	0.429225	+	0.177791i
$635$	10.0000	+	24.1421i	0.396838	+	0.958051i
$636$	−36.3848	+	15.0711i	−1.44275	+	0.597607i
$637$	−0.142136	−	0.142136i	−0.00563162	−	0.00563162i
$638$		0			0
$639$	−56.1127	+	23.2426i	−2.21978	+	0.919465i
$640$	−14.9289	−	36.0416i	−0.590118	−	1.42467i
$641$	−16.4853	−	6.82843i	−0.651129	−	0.269707i	0.0325710	−	0.999469i	$-0.489631\pi$
$641$	−16.4853	−	6.82843i	−0.651129	−	0.269707i	−0.683700	+	0.729763i	$0.739631\pi$
$642$			17.7990i			0.702470i
$643$	−0.263456	+	0.636039i	−0.0103897	+	0.0250829i	−0.928989	−	0.370107i	$-0.879321\pi$
$643$	−0.263456	+	0.636039i	−0.0103897	+	0.0250829i	0.918600	+	0.395190i	$0.129321\pi$
$644$	1.07107	−	1.07107i	0.0422060	−	0.0422060i
$645$	9.65685			0.380238
$646$	0.142136	−	4.82843i	0.00559225	−	0.189972i
$647$	−30.1421			−1.18501			−0.592505	−	0.805567i	$-0.701861\pi$
$647$	−30.1421			−1.18501			−0.592505	+	0.805567i	$0.701861\pi$
$648$	−6.53553	+	6.53553i	−0.256740	+	0.256740i
$649$	−3.92893	+	9.48528i	−0.154224	+	0.372330i
$650$		−	4.20101i		−	0.164777i
$651$	14.4853	+	6.00000i	0.567723	+	0.235159i
$652$	−9.58579	−	23.1421i	−0.375408	−	0.906316i
$653$	5.65685	−	2.34315i	0.221370	−	0.0916944i	−0.269242	−	0.963072i	$-0.586773\pi$
$653$	5.65685	−	2.34315i	0.221370	−	0.0916944i	0.490612	+	0.871378i	$0.336773\pi$
$654$	9.41421	+	9.41421i	0.368125	+	0.368125i
$655$	−16.4853	−	16.4853i	−0.644133	−	0.644133i
$656$	18.3640	−	7.60660i	0.716992	−	0.296988i
$657$	19.4142	+	46.8701i	0.757421	+	1.82858i
$658$	0.242641	+	0.100505i	0.00945912	+	0.00391810i
$659$		−	18.5858i		−	0.723999i	−0.932178	−	0.362000i	$-0.882094\pi$
$659$		−	18.5858i		−	0.723999i	0.932178	−	0.362000i	$-0.117906\pi$
$660$	−5.17157	+	12.4853i	−0.201303	+	0.485989i
$661$	−31.5563	+	31.5563i	−1.22740	+	1.22740i	−0.262456	+	0.964944i	$0.584532\pi$
$661$	−31.5563	+	31.5563i	−1.22740	+	1.22740i	−0.964944	+	0.262456i	$0.915468\pi$
$662$	9.31371			0.361988
$663$	−11.5147	−	5.17157i	−0.447195	−	0.200847i
$664$	2.62742			0.101964
$665$	−19.3137	+	19.3137i	−0.748953	+	0.748953i
$666$	3.55635	−	8.58579i	0.137806	−	0.332692i
$667$		0			0
$668$	18.5061	+	7.66548i	0.716022	+	0.296586i
$669$	1.17157	+	2.82843i	0.0452956	+	0.109353i
$670$	−10.0000	+	4.14214i	−0.386334	+	0.160025i
$671$	2.00000	+	2.00000i	0.0772091	+	0.0772091i
$672$	−21.3137	−	21.3137i	−0.822194	−	0.822194i
$673$	6.72792	−	2.78680i	0.259342	−	0.107423i	−0.249224	−	0.968446i	$-0.580176\pi$
$673$	6.72792	−	2.78680i	0.259342	−	0.107423i	0.508567	+	0.861023i	$0.330176\pi$
$674$	3.89087	+	9.39340i	0.149871	+	0.361820i
$675$	17.3137	+	7.17157i	0.666405	+	0.276034i
$676$			21.2599i			0.817688i
$677$	−1.07107	+	2.58579i	−0.0411645	+	0.0993798i	−0.943125	−	0.332440i	$-0.892128\pi$
$677$	−1.07107	+	2.58579i	−0.0411645	+	0.0993798i	0.901960	+	0.431819i	$0.142128\pi$
$678$	−14.6274	+	14.6274i	−0.561763	+	0.561763i
$679$	33.3137			1.27846
$680$	8.58579	+	22.5858i	0.329250	+	0.866125i
$681$	−67.7990			−2.59806
$682$	0.514719	−	0.514719i	0.0197096	−	0.0197096i
$683$	10.7071	−	25.8492i	0.409696	−	0.989094i	−0.575522	−	0.817787i	$-0.695201\pi$
$683$	10.7071	−	25.8492i	0.409696	−	0.989094i	0.985218	−	0.171307i	$-0.0547991\pi$
$684$			19.7990i			0.757033i
$685$	60.2843	+	24.9706i	2.30334	+	0.954076i
$686$	2.97056	+	7.17157i	0.113417	+	0.273812i
$687$	51.6985	−	21.4142i	1.97242	−	0.817003i
$688$	−2.12132	−	2.12132i	−0.0808746	−	0.0808746i
$689$	6.82843	+	6.82843i	0.260142	+	0.260142i
$690$	−1.17157	+	0.485281i	−0.0446010	+	0.0184743i
$691$	16.4142	+	39.6274i	0.624426	+	1.50750i	0.846456	+	0.532458i	$0.178732\pi$
$691$	16.4142	+	39.6274i	0.624426	+	1.50750i	−0.222030	+	0.975040i	$0.571268\pi$
$692$	−16.0503	−	6.64823i	−0.610139	−	0.252728i
$693$			7.65685i			0.290860i
$694$	−1.72792	+	4.17157i	−0.0655910	+	0.158351i
$695$	5.51472	−	5.51472i	0.209185	−	0.209185i
$696$		0			0
$697$	−25.5355	+	9.70711i	−0.967227	+	0.367683i
$698$	−10.6863			−0.404482
$699$	−1.65685	+	1.65685i	−0.0626680	+	0.0626680i
$700$	15.8284	−	38.2132i	0.598258	−	1.44432i
$701$		−	47.7990i		−	1.80534i	−0.430330	−	0.902671i	$-0.641603\pi$
$701$		−	47.7990i		−	1.80534i	0.430330	−	0.902671i	$-0.358397\pi$
$702$	−0.970563	−	0.402020i	−0.0366315	−	0.0151733i
$703$	6.34315	+	15.3137i	0.239236	+	0.577567i
$704$	2.94975	−	1.22183i	0.111173	−	0.0460493i
$705$	1.65685	+	1.65685i	0.0624007	+	0.0624007i
$706$	−4.00000	−	4.00000i	−0.150542	−	0.150542i
$707$	−14.2426	+	5.89949i	−0.535650	+	0.221873i
$708$	−24.5269	−	59.2132i	−0.921778	−	2.22537i
$709$	−38.3345	−	15.8787i	−1.43968	−	0.596336i	−0.479962	−	0.877289i	$-0.659349\pi$
$709$	−38.3345	−	15.8787i	−1.43968	−	0.596336i	−0.959722	+	0.280953i	$0.909349\pi$
$710$		−	24.2843i		−	0.911372i
$711$	9.43503	−	22.7782i	0.353841	−	0.854248i
$712$	−10.2843	+	10.2843i	−0.385419	+	0.385419i
$713$	−0.727922			−0.0272609
$714$	8.00000	+	8.48528i	0.299392	+	0.317554i
$715$	3.31371			0.123926
$716$	−12.9289	+	12.9289i	−0.483177	+	0.483177i
$717$	−26.0000	+	62.7696i	−0.970988	+	2.34417i
$718$			4.14214i			0.154583i
$719$	8.12132	+	3.36396i	0.302874	+	0.125455i	0.528945	−	0.848656i	$-0.322588\pi$
$719$	8.12132	+	3.36396i	0.302874	+	0.125455i	−0.226070	+	0.974111i	$0.572588\pi$
$720$	−16.2426	−	39.2132i	−0.605327	−	1.46139i
$721$	−23.8995	+	9.89949i	−0.890064	+	0.368676i
$722$	−3.22183	−	3.22183i	−0.119904	−	0.119904i
$723$	2.82843	+	2.82843i	0.105190	+	0.105190i
$724$	−8.60660	+	3.56497i	−0.319862	+	0.132491i
$725$		0			0
$726$	−10.4142	−	4.31371i	−0.386508	−	0.160097i
$727$		−	12.2843i		−	0.455598i	−0.973708	−	0.227799i	$-0.926847\pi$
$727$		−	12.2843i		−	0.455598i	0.973708	−	0.227799i	$-0.0731530\pi$
$728$	−1.85786	+	4.48528i	−0.0688570	+	0.166236i
$729$	−27.7782	+	27.7782i	−1.02882	+	1.02882i
$730$	−20.2843			−0.750755
$731$	2.82843	+	3.00000i	0.104613	+	0.110959i
$732$	−17.6569			−0.652616
$733$	−36.7279	+	36.7279i	−1.35658	+	1.35658i	−0.478476	+	0.878100i	$0.658811\pi$
$733$	−36.7279	+	36.7279i	−1.35658	+	1.35658i	−0.878100	+	0.478476i	$0.841189\pi$
$734$	−2.40559	+	5.80761i	−0.0887920	+	0.214363i
$735$			1.65685i			0.0611140i
$736$	1.29289	+	0.535534i	0.0476567	+	0.0197400i
$737$	−2.07107	−	5.00000i	−0.0762888	−	0.184177i
$738$	−9.70711	+	4.02082i	−0.357324	+	0.148008i
$739$	−13.0711	−	13.0711i	−0.480827	−	0.480827i	0.424569	−	0.905396i	$-0.360426\pi$
$739$	−13.0711	−	13.0711i	−0.480827	−	0.480827i	−0.905396	+	0.424569i	$0.860426\pi$
$740$	−28.0000	−	28.0000i	−1.02930	−	1.02930i
$741$	8.00000	−	3.31371i	0.293887	−	0.121732i
$742$	−3.41421	−	8.24264i	−0.125340	−	0.302597i
$743$	36.4558	+	15.1005i	1.33744	+	0.553984i	0.932767	−	0.360480i	$-0.117387\pi$
$743$	36.4558	+	15.1005i	1.33744	+	0.553984i	0.404668	+	0.914464i	$0.367387\pi$
$744$			9.51472i			0.348827i
$745$	21.4558	−	51.7990i	0.786081	−	1.89777i
$746$	0.142136	−	0.142136i	0.00520395	−	0.00520395i
$747$	6.34315			0.232084
$748$	−5.39340	+	2.05025i	−0.197202	+	0.0749647i
$749$	42.9706			1.57011
$750$	−10.3431	+	10.3431i	−0.377678	+	0.377678i
$751$	−10.5563	+	25.4853i	−0.385207	+	0.929971i	0.605734	+	0.795668i	$0.292880\pi$
$751$	−10.5563	+	25.4853i	−0.385207	+	0.929971i	−0.990940	+	0.134304i	$0.957120\pi$
$752$		−	0.727922i		−	0.0265446i
$753$	−18.4853	−	7.65685i	−0.673641	−	0.279031i
$754$		0			0
$755$	9.65685	−	4.00000i	0.351449	−	0.145575i
$756$	−7.31371	−	7.31371i	−0.265997	−	0.265997i
$757$	−20.6274	−	20.6274i	−0.749716	−	0.749716i	0.224710	−	0.974426i	$-0.427857\pi$
$757$	−20.6274	−	20.6274i	−0.749716	−	0.749716i	−0.974426	+	0.224710i	$0.927857\pi$
$758$	8.80761	−	3.64823i	0.319907	−	0.132510i
$759$	−0.242641	−	0.585786i	−0.00880730	−	0.0212627i
$760$	−15.3137	−	6.34315i	−0.555487	−	0.230090i
$761$		−	0.485281i		−	0.0175914i	−0.999961	−	0.00879572i	$-0.997200\pi$
$761$		−	0.485281i		−	0.0175914i	0.999961	−	0.00879572i	$-0.00279980\pi$
$762$	−2.92893	+	7.07107i	−0.106104	+	0.256158i
$763$	22.7279	−	22.7279i	0.822806	−	0.822806i
$764$	−2.76955			−0.100199
$765$	20.7279	+	54.5269i	0.749420	+	1.97142i
$766$	8.28427			0.299323
$767$	−11.1127	+	11.1127i	−0.401256	+	0.401256i
$768$	−3.97056	+	9.58579i	−0.143275	+	0.345897i
$769$			24.9289i			0.898960i	0.893290	+	0.449480i	$0.148391\pi$
$769$			24.9289i			0.898960i	−0.893290	+	0.449480i	$0.851609\pi$
$770$	−2.82843	−	1.17157i	−0.101929	−	0.0422206i
$771$	−9.17157	−	22.1421i	−0.330306	−	0.797430i
$772$	−26.2635	+	10.8787i	−0.945242	+	0.391532i
$773$	24.9706	+	24.9706i	0.898129	+	0.898129i	0.995271	−	0.0971418i	$-0.0309700\pi$
$773$	24.9706	+	24.9706i	0.898129	+	0.898129i	−0.0971418	+	0.995271i	$0.530970\pi$
$774$	1.12132	+	1.12132i	0.0403050	+	0.0403050i
$775$	−18.3640	+	7.60660i	−0.659653	+	0.273237i
$776$	7.73654	+	18.6777i	0.277726	+	0.670489i
$777$	−36.9706	−	15.3137i	−1.32631	−	0.549376i
$778$		−	0.485281i		−	0.0173982i
$779$	7.17157	−	17.3137i	0.256948	−	0.620328i
$780$	−14.6274	+	14.6274i	−0.523746	+	0.523746i
$781$	12.1421			0.434480
$782$	−0.493903	−	0.221825i	−0.0176619	−	0.00793246i
$783$		0			0
$784$	0.363961	−	0.363961i	0.0129986	−	0.0129986i
$785$	−10.8284	+	26.1421i	−0.386483	+	0.933053i
$786$		−	6.82843i		−	0.243562i
$787$	−21.5355	−	8.92031i	−0.767659	−	0.317975i	−0.0357352	−	0.999361i	$-0.511377\pi$
$787$	−21.5355	−	8.92031i	−0.767659	−	0.317975i	−0.731924	+	0.681387i	$0.761377\pi$
$788$	−4.37615	−	10.5650i	−0.155894	−	0.376362i
$789$	64.2843	−	26.6274i	2.28858	−	0.947961i
$790$	6.97056	+	6.97056i	0.248001	+	0.248001i
$791$	35.3137	+	35.3137i	1.25561	+	1.25561i
$792$	−4.29289	+	1.77817i	−0.152541	+	0.0631847i
$793$	1.65685	+	4.00000i	0.0588366	+	0.142044i
$794$	0.464466	+	0.192388i	0.0164833	+	0.00682760i
$795$		−	79.5980i		−	2.82305i
$796$	0.313708	−	0.757359i	0.0111191	−	0.0268439i
$797$	−14.1716	+	14.1716i	−0.501983	+	0.501983i	−0.912054	−	0.410071i	$-0.865504\pi$
$797$	−14.1716	+	14.1716i	−0.501983	+	0.501983i	0.410071	+	0.912054i	$0.365504\pi$
$798$	−8.00000			−0.283197
$799$	−0.0294373	+	1.00000i	−0.00104142	+	0.0353775i
$800$	38.2132			1.35104
$801$	−24.8284	+	24.8284i	−0.877269	+	0.877269i
$802$	−2.33452	+	5.63604i	−0.0824349	+	0.199015i
$803$		−	10.1421i		−	0.357908i
$804$	31.2132	+	12.9289i	1.10080	+	0.455968i
$805$	1.17157	+	2.82843i	0.0412925	+	0.0996890i
$806$	1.02944	−	0.426407i	0.0362604	−	0.0150195i
$807$	−48.0416	−	48.0416i	−1.69115	−	1.69115i
$808$	−6.61522	−	6.61522i	−0.232723	−	0.232723i
$809$	−3.77817	+	1.56497i	−0.132834	+	0.0550215i	−0.448110	−	0.893978i	$-0.647903\pi$
$809$	−3.77817	+	1.56497i	−0.132834	+	0.0550215i	0.315277	+	0.949000i	$0.397903\pi$
$810$	−3.41421	−	8.24264i	−0.119963	−	0.289617i
$811$	−44.7990	−	18.5563i	−1.57311	−	0.651602i	−0.585803	−	0.810454i	$-0.699221\pi$
$811$	−44.7990	−	18.5563i	−1.57311	−	0.651602i	−0.987302	+	0.158852i	$0.949221\pi$
$812$		0			0
$813$	2.58579	−	6.24264i	0.0906875	−	0.218939i
$814$	−1.31371	+	1.31371i	−0.0460455	+	0.0460455i
$815$	50.6274			1.77340
$816$	13.2426	−	29.4853i	0.463585	−	1.03219i
$817$	−2.82843			−0.0989541
$818$	8.04163	−	8.04163i	0.281169	−	0.281169i
$819$	−4.48528	+	10.8284i	−0.156728	+	0.378376i
$820$			44.7696i			1.56342i
$821$	0.221825	+	0.0918831i	0.00774176	+	0.00320674i	0.386551	−	0.922268i	$-0.373666\pi$
$821$	0.221825	+	0.0918831i	0.00774176	+	0.00320674i	−0.378809	+	0.925475i	$0.623666\pi$
$822$	7.31371	+	17.6569i	0.255095	+	0.615854i
$823$	−8.05025	+	3.33452i	−0.280614	+	0.116234i	−0.518552	−	0.855046i	$-0.673529\pi$
$823$	−8.05025	+	3.33452i	−0.280614	+	0.116234i	0.237938	+	0.971280i	$0.423529\pi$
$824$	−11.1005	−	11.1005i	−0.386704	−	0.386704i
$825$	−12.2426	−	12.2426i	−0.426234	−	0.426234i
$826$	13.4142	−	5.55635i	0.466740	−	0.193330i
$827$	18.0208	+	43.5061i	0.626645	+	1.51286i	0.843766	+	0.536711i	$0.180333\pi$
$827$	18.0208	+	43.5061i	0.626645	+	1.51286i	−0.217121	+	0.976145i	$0.569667\pi$
$828$	2.05025	+	0.849242i	0.0712512	+	0.0295132i
$829$		−	1.02944i		−	0.0357538i	−0.999840	−	0.0178769i	$-0.994309\pi$
$829$		−	1.02944i		−	0.0357538i	0.999840	−	0.0178769i	$-0.00569070\pi$
$830$	−0.970563	+	2.34315i	−0.0336887	+	0.0813318i
$831$	−7.31371	+	7.31371i	−0.253710	+	0.253710i
$832$	4.88730			0.169437
$833$	−0.514719	+	0.485281i	−0.0178339	+	0.0168140i
$834$	2.28427			0.0790978
$835$	−28.6274	+	28.6274i	−0.990693	+	0.990693i
$836$	1.51472	−	3.65685i	0.0523876	−	0.126475i
$837$			4.97056i			0.171808i
$838$	−11.1421	−	4.61522i	−0.384899	−	0.159430i
$839$	0.414214	+	1.00000i	0.0143002	+	0.0345238i	0.930868	−	0.365355i	$-0.119052\pi$
$839$	0.414214	+	1.00000i	0.0143002	+	0.0345238i	−0.916568	+	0.399879i	$0.869052\pi$
$840$	36.9706	−	15.3137i	1.27561	−	0.528373i
$841$	−20.5061	−	20.5061i	−0.707107	−	0.707107i
$842$	−7.65685	−	7.65685i	−0.263873	−	0.263873i
$843$	62.5269	−	25.8995i	2.15354	−	0.892026i
$844$	−12.1716	−	29.3848i	−0.418963	−	1.01147i
$845$	−39.6985	−	16.4437i	−1.36567	−	0.565679i
$846$			0.384776i			0.0132289i
$847$	−10.4142	+	25.1421i	−0.357837	+	0.863894i
$848$	−17.4853	+	17.4853i	−0.600447	+	0.600447i
$849$	−2.00000			−0.0686398
$850$	−14.7782	−	0.435029i	−0.506887	−	0.0149214i
$851$	1.85786			0.0636868
$852$	−53.5980	+	53.5980i	−1.83624	+	1.83624i
$853$	2.77817	−	6.70711i	0.0951229	−	0.229647i	−0.869155	−	0.494540i	$-0.835337\pi$
$853$	2.77817	−	6.70711i	0.0951229	−	0.229647i	0.964278	+	0.264893i	$0.0853366\pi$
$854$		−	4.00000i		−	0.136877i
$855$	−36.9706	−	15.3137i	−1.26437	−	0.523718i
$856$	9.97918	+	24.0919i	0.341082	+	0.823444i
$857$	−28.7782	+	11.9203i	−0.983044	+	0.407190i	−0.815552	−	0.578683i	$-0.803567\pi$
$857$	−28.7782	+	11.9203i	−0.983044	+	0.407190i	−0.167491	+	0.985874i	$0.553567\pi$
$858$	0.686292	+	0.686292i	0.0234296	+	0.0234296i
$859$	−1.31371	−	1.31371i	−0.0448232	−	0.0448232i	0.684340	−	0.729163i	$-0.260090\pi$
$859$	−1.31371	−	1.31371i	−0.0448232	−	0.0448232i	−0.729163	+	0.684340i	$0.760090\pi$
$860$	6.24264	−	2.58579i	0.212872	−	0.0881746i
$861$	17.3137	+	41.7990i	0.590050	+	1.42451i
$862$	8.94975	+	3.70711i	0.304830	+	0.126265i
$863$		−	53.5980i		−	1.82450i	−0.409638	−	0.912248i	$-0.634345\pi$
$863$		−	53.5980i		−	1.82450i	0.409638	−	0.912248i	$-0.365655\pi$
$864$	3.65685	−	8.82843i	0.124409	−	0.300349i
$865$	24.8284	−	24.8284i	0.844192	−	0.844192i
$866$	−13.9411			−0.473739
$867$	−19.3848	+	39.9706i	−0.658342	+	1.35747i
$868$	10.9706			0.372365
$869$	−3.48528	+	3.48528i	−0.118230	+	0.118230i
$870$		0			0
$871$		−	8.28427i		−	0.280702i
$872$	18.0208	+	7.46447i	0.610262	+	0.252779i
$873$	18.6777	+	45.0919i	0.632143	+	1.52613i
$874$	0.343146	−	0.142136i	0.0116071	−	0.00480781i
$875$	24.9706	+	24.9706i	0.844159	+	0.844159i
$876$	44.7696	+	44.7696i	1.51262	+	1.51262i
$877$	30.0208	−	12.4350i	1.01373	−	0.419901i	0.186916	−	0.982376i	$-0.440151\pi$
$877$	30.0208	−	12.4350i	1.01373	−	0.419901i	0.826814	+	0.562475i	$0.190151\pi$
$878$	−3.47666	−	8.39340i	−0.117332	−	0.283263i
$879$	50.6274	+	20.9706i	1.70762	+	0.707320i
$880$			8.48528i			0.286039i
$881$	14.4645	−	34.9203i	0.487320	−	1.17650i	−0.468743	−	0.883335i	$-0.655293\pi$
$881$	14.4645	−	34.9203i	0.487320	−	1.17650i	0.956063	−	0.293161i	$-0.0947070\pi$
$882$	−0.192388	+	0.192388i	−0.00647805	+	0.00647805i
$883$	−23.6569			−0.796117			−0.398058	−	0.917360i	$-0.630316\pi$
$883$	−23.6569			−0.796117			−0.398058	+	0.917360i	$0.630316\pi$
$884$	−8.82843	−	0.259885i	−0.296932	−	0.00874087i
$885$	129.539			4.35441
$886$	−5.75736	+	5.75736i	−0.193422	+	0.193422i
$887$	6.69848	−	16.1716i	0.224913	−	0.542988i	−0.770631	−	0.637281i	$-0.780059\pi$
$887$	6.69848	−	16.1716i	0.224913	−	0.542988i	0.995545	+	0.0942929i	$0.0300590\pi$
$888$		−	24.2843i		−	0.814927i
$889$	17.0711	+	7.07107i	0.572545	+	0.237156i
$890$	−5.37258	−	12.9706i	−0.180089	−	0.434774i
$891$	4.12132	−	1.70711i	0.138069	−	0.0571902i
$892$	1.51472	+	1.51472i	0.0507165	+	0.0507165i
$893$	−0.485281	−	0.485281i	−0.0162393	−	0.0162393i
$894$	15.1716	−	6.28427i	0.507413	−	0.210177i
$895$	−14.1421	−	34.1421i	−0.472719	−	1.14125i
$896$	−25.4853	−	10.5563i	−0.851403	−	0.352663i
$897$		−	0.970563i		−	0.0324061i
$898$	−3.02944	+	7.31371i	−0.101094	+	0.244062i
$899$		0			0
$900$	60.5980			2.01993
$901$	24.7279	−	23.3137i	0.823807	−	0.776692i
$902$	2.10051			0.0699392
$903$	4.82843	−	4.82843i	0.160680	−	0.160680i
$904$	−11.5980	+	28.0000i	−0.385743	+	0.931266i
$905$		−	18.8284i		−	0.625878i
$906$	2.82843	+	1.17157i	0.0939682	+	0.0389229i
$907$	19.6066	+	47.3345i	0.651027	+	1.57172i	0.811291	+	0.584643i	$0.198765\pi$
$907$	19.6066	+	47.3345i	0.651027	+	1.57172i	−0.160264	+	0.987074i	$0.551235\pi$
$908$	−43.8284	+	18.1543i	−1.45450	+	0.602473i
$909$	−15.9706	−	15.9706i	−0.529710	−	0.529710i
$910$	−3.31371	−	3.31371i	−0.109848	−	0.109848i
$911$	−12.6569	+	5.24264i	−0.419340	+	0.173696i	−0.582368	−	0.812925i	$-0.697874\pi$
$911$	−12.6569	+	5.24264i	−0.419340	+	0.173696i	0.163028	+	0.986621i	$0.447874\pi$
$912$	8.48528	+	20.4853i	0.280976	+	0.678335i
$913$	−1.17157	−	0.485281i	−0.0387734	−	0.0160605i
$914$			5.94113i			0.196515i
$915$	13.6569	−	32.9706i	0.451482	−	1.08997i
$916$	27.6863	−	27.6863i	0.914781	−	0.914781i
$917$	−16.4853			−0.544392
$918$	−1.51472	+	3.37258i	−0.0499932	+	0.111312i
$919$	−25.9411			−0.855719			−0.427859	−	0.903845i	$-0.640732\pi$
$919$	−25.9411			−0.855719			−0.427859	+	0.903845i	$0.640732\pi$
$920$	−1.31371	+	1.31371i	−0.0433117	+	0.0433117i
$921$	13.2132	−	31.8995i	0.435390	−	1.05112i
$922$		−	6.76955i		−	0.222943i
$923$	17.1716	+	7.11270i	0.565209	+	0.234117i
$924$	3.65685	+	8.82843i	0.120302	+	0.290434i
$925$	46.8701	−	19.4142i	1.54108	−	0.638335i
$926$	−10.4437	−	10.4437i	−0.343200	−	0.343200i
$927$	−26.7990	−	26.7990i	−0.880194	−	0.880194i
$928$		0			0
$929$	−19.5147	−	47.1127i	−0.640257	−	1.54572i	−0.826333	−	0.563182i	$-0.809577\pi$
$929$	−19.5147	−	47.1127i	−0.640257	−	1.54572i	0.186076	−	0.982535i	$-0.440423\pi$
$930$	−8.48528	−	3.51472i	−0.278243	−	0.115252i
$931$		−	0.485281i		−	0.0159045i
$932$	−0.627417	+	1.51472i	−0.0205517	+	0.0496163i
$933$	36.3848	−	36.3848i	1.19118	−	1.19118i
$934$	16.9706			0.555294
$935$	0.343146	−	11.6569i	0.0112221	−	0.381220i
$936$	−7.11270			−0.232486
$937$	−17.2132	+	17.2132i	−0.562331	+	0.562331i	−0.929969	−	0.367638i	$-0.880167\pi$
$937$	−17.2132	+	17.2132i	−0.562331	+	0.562331i	0.367638	+	0.929969i	$0.380167\pi$
$938$	−2.92893	+	7.07107i	−0.0956330	+	0.230879i
$939$		−	19.3137i		−	0.630279i
$940$	1.51472	+	0.627417i	0.0494047	+	0.0204641i
$941$	−3.46447	−	8.36396i	−0.112938	−	0.272657i	0.857297	−	0.514823i	$-0.172142\pi$
$941$	−3.46447	−	8.36396i	−0.112938	−	0.272657i	−0.970235	+	0.242166i	$0.922142\pi$
$942$	−7.65685	+	3.17157i	−0.249474	+	0.103335i
$943$	−1.48528	−	1.48528i	−0.0483674	−	0.0483674i
$944$	−28.4558	−	28.4558i	−0.926159	−	0.926159i
$945$	19.3137	−	8.00000i	0.628275	−	0.260240i
$946$	−0.121320	−	0.292893i	−0.00394446	−	0.00952278i
$947$	−16.0208	−	6.63604i	−0.520607	−	0.215642i	0.106877	−	0.994272i	$-0.465915\pi$
$947$	−16.0208	−	6.63604i	−0.520607	−	0.215642i	−0.627483	+	0.778630i	$0.715915\pi$
$948$		−	30.7696i		−	0.999349i
$949$	5.94113	−	14.3431i	0.192857	−	0.465598i
$950$	7.17157	−	7.17157i	0.232677	−	0.232677i
$951$	73.7990			2.39310
$952$	15.5858	+	7.00000i	0.505138	+	0.226871i
$953$	12.0000			0.388718			0.194359	−	0.980930i	$-0.437737\pi$
$953$	12.0000			0.388718			0.194359	+	0.980930i	$0.437737\pi$
$954$	9.24264	−	9.24264i	0.299242	−	0.299242i
$955$	2.14214	−	5.17157i	0.0693179	−	0.167348i
$956$			47.5391i			1.53752i
$957$		0			0
$958$	4.42284	+	10.6777i	0.142895	+	0.344980i
$959$	42.6274	−	17.6569i	1.37651	−	0.570170i
$960$	−28.4853	−	28.4853i	−0.919359	−	0.919359i
$961$	18.1924	+	18.1924i	0.586851	+	0.586851i
$962$	−2.62742	+	1.08831i	−0.0847113	+	0.0350886i
$963$	24.0919	+	58.1630i	0.776350	+	1.87427i
$964$	2.58579	+	1.07107i	0.0832826	+	0.0344968i
$965$		−	57.4558i		−	1.84957i
$966$	−0.343146	+	0.828427i	−0.0110405	+	0.0266542i
$967$	42.8701	−	42.8701i	1.37861	−	1.37861i	0.531634	−	0.846974i	$-0.321578\pi$
$967$	42.8701	−	42.8701i	1.37861	−	1.37861i	0.846974	−	0.531634i	$-0.178422\pi$
$968$	−16.5147			−0.530803
$969$	−10.8284	−	28.4853i	−0.347859	−	0.915079i
$970$	−19.5147			−0.626580
$971$	−28.0416	+	28.0416i	−0.899899	+	0.899899i	−0.995427	−	0.0955280i	$-0.969546\pi$
$971$	−28.0416	+	28.0416i	−0.899899	+	0.899899i	0.0955280	+	0.995427i	$0.469546\pi$
$972$	−15.2010	+	36.6985i	−0.487573	+	1.17710i
$973$		−	5.51472i		−	0.176794i
$974$	−5.94975	−	2.46447i	−0.190642	−	0.0789666i
$975$	−10.1421	−	24.4853i	−0.324808	−	0.784157i
$976$	−10.2426	+	4.24264i	−0.327859	+	0.135804i
$977$	−38.3848	−	38.3848i	−1.22804	−	1.22804i	−0.964705	−	0.263333i	$-0.915178\pi$
$977$	−38.3848	−	38.3848i	−1.22804	−	1.22804i	−0.263333	−	0.964705i	$-0.584822\pi$
$978$	10.4853	+	10.4853i	0.335282	+	0.335282i
$979$	6.48528	−	2.68629i	0.207270	−	0.0858542i
$980$	0.443651	+	1.07107i	0.0141719	+	0.0342140i
$981$	43.5061	+	18.0208i	1.38904	+	0.575360i
$982$		−	17.8579i		−	0.569867i
$983$	14.6569	−	35.3848i	0.467481	−	1.12860i	−0.497778	−	0.867304i	$-0.665851\pi$
$983$	14.6569	−	35.3848i	0.467481	−	1.12860i	0.965259	−	0.261295i	$-0.0841494\pi$
$984$	−19.4142	+	19.4142i	−0.618903	+	0.618903i
$985$	23.1127			0.736432
$986$		0			0
$987$	1.65685			0.0527383
$988$	4.28427	−	4.28427i	0.136301	−	0.136301i
$989$	−0.121320	+	0.292893i	−0.00385776	+	0.00931346i
$990$		−	4.48528i		−	0.142552i
$991$	−11.4853	−	4.75736i	−0.364842	−	0.151122i	0.192728	−	0.981252i	$-0.438266\pi$
$991$	−11.4853	−	4.75736i	−0.364842	−	0.151122i	−0.557570	+	0.830130i	$0.688266\pi$
$992$	3.87868	+	9.36396i	0.123148	+	0.297306i
$993$	54.2843	−	22.4853i	1.72266	−	0.713549i
$994$	−12.1421	−	12.1421i	−0.385125	−	0.385125i
$995$	1.17157	+	1.17157i	0.0371414	+	0.0371414i
$996$	7.31371	−	3.02944i	0.231744	−	0.0959914i
$997$	−5.89949	−	14.2426i	−0.186839	−	0.451069i	0.802509	−	0.596640i	$-0.203498\pi$
$997$	−5.89949	−	14.2426i	−0.186839	−	0.451069i	−0.989348	+	0.145571i	$0.953498\pi$
$998$	−9.72792	−	4.02944i	−0.307932	−	0.127550i
$999$		−	12.6863i		−	0.401377i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.m.a.603.1	yes	4
17.15	even	8	inner	731.2.m.a.474.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.m.a.474.1	✓	4	17.15	even	8	inner
731.2.m.a.603.1	yes	4	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.m (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.292893 + 0.292893i) q^{2} +(-1.00000 + 2.41421i) q^{3} +1.82843i q^{4} +(-3.41421 - 1.41421i) q^{5} +(-0.414214 - 1.00000i) q^{6} +(-2.41421 + 1.00000i) q^{7} +(-1.12132 - 1.12132i) q^{8} +(-2.70711 - 2.70711i) q^{9} +O(q^{10})\)	\(q+(-0.292893 + 0.292893i) q^{2} +(-1.00000 + 2.41421i) q^{3} +1.82843i q^{4} +(-3.41421 - 1.41421i) q^{5} +(-0.414214 - 1.00000i) q^{6} +(-2.41421 + 1.00000i) q^{7} +(-1.12132 - 1.12132i) q^{8} +(-2.70711 - 2.70711i) q^{9} +(1.41421 - 0.585786i) q^{10} +(0.292893 + 0.707107i) q^{11} +(-4.41421 - 1.82843i) q^{12} +1.17157i q^{13} +(0.414214 - 1.00000i) q^{14} +(6.82843 - 6.82843i) q^{15} -3.00000 q^{16} +(4.12132 + 0.121320i) q^{17} +1.58579 q^{18} +(-2.00000 + 2.00000i) q^{19} +(2.58579 - 6.24264i) q^{20} -6.82843i q^{21} +(-0.292893 - 0.121320i) q^{22} +(0.121320 + 0.292893i) q^{23} +(3.82843 - 1.58579i) q^{24} +(6.12132 + 6.12132i) q^{25} +(-0.343146 - 0.343146i) q^{26} +(2.00000 - 0.828427i) q^{27} +(-1.82843 - 4.41421i) q^{28} +4.00000i q^{30} +(-0.878680 + 2.12132i) q^{31} +(3.12132 - 3.12132i) q^{32} -2.00000 q^{33} +(-1.24264 + 1.17157i) q^{34} +9.65685 q^{35} +(4.94975 - 4.94975i) q^{36} +(2.24264 - 5.41421i) q^{37} -1.17157i q^{38} +(-2.82843 - 1.17157i) q^{39} +(2.24264 + 5.41421i) q^{40} +(-6.12132 + 2.53553i) q^{41} +(2.00000 + 2.00000i) q^{42} +(0.707107 + 0.707107i) q^{43} +(-1.29289 + 0.535534i) q^{44} +(5.41421 + 13.0711i) q^{45} +(-0.121320 - 0.0502525i) q^{46} +0.242641i q^{47} +(3.00000 - 7.24264i) q^{48} +(-0.121320 + 0.121320i) q^{49} -3.58579 q^{50} +(-4.41421 + 9.82843i) q^{51} -2.14214 q^{52} +(5.82843 - 5.82843i) q^{53} +(-0.343146 + 0.828427i) q^{54} -2.82843i q^{55} +(3.82843 + 1.58579i) q^{56} +(-2.82843 - 6.82843i) q^{57} +(9.48528 + 9.48528i) q^{59} +(12.4853 + 12.4853i) q^{60} +(3.41421 - 1.41421i) q^{61} +(-0.363961 - 0.878680i) q^{62} +(9.24264 + 3.82843i) q^{63} -4.17157i q^{64} +(1.65685 - 4.00000i) q^{65} +(0.585786 - 0.585786i) q^{66} -7.07107 q^{67} +(-0.221825 + 7.53553i) q^{68} -0.828427 q^{69} +(-2.82843 + 2.82843i) q^{70} +(6.07107 - 14.6569i) q^{71} +6.07107i q^{72} +(-12.2426 - 5.07107i) q^{73} +(0.928932 + 2.24264i) q^{74} +(-20.8995 + 8.65685i) q^{75} +(-3.65685 - 3.65685i) q^{76} +(-1.41421 - 1.41421i) q^{77} +(1.17157 - 0.485281i) q^{78} +(2.46447 + 5.94975i) q^{79} +(10.2426 + 4.24264i) q^{80} -5.82843i q^{81} +(1.05025 - 2.53553i) q^{82} +(-1.17157 + 1.17157i) q^{83} +12.4853 q^{84} +(-13.8995 - 6.24264i) q^{85} -0.414214 q^{86} +(0.464466 - 1.12132i) q^{88} -9.17157i q^{89} +(-5.41421 - 2.24264i) q^{90} +(-1.17157 - 2.82843i) q^{91} +(-0.535534 + 0.221825i) q^{92} +(-4.24264 - 4.24264i) q^{93} +(-0.0710678 - 0.0710678i) q^{94} +(9.65685 - 4.00000i) q^{95} +(4.41421 + 10.6569i) q^{96} +(-11.7782 - 4.87868i) q^{97} -0.0710678i q^{98} +(1.12132 - 2.70711i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 4 q^{3} - 8 q^{5} + 4 q^{6} - 4 q^{7} + 4 q^{8} - 8 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 - 4 * q^3 - 8 * q^5 + 4 * q^6 - 4 * q^7 + 4 * q^8 - 8 * q^9	\( 4 q - 4 q^{2} - 4 q^{3} - 8 q^{5} + 4 q^{6} - 4 q^{7} + 4 q^{8} - 8 q^{9} + 4 q^{11} - 12 q^{12} - 4 q^{14} + 16 q^{15} - 12 q^{16} + 8 q^{17} + 12 q^{18} - 8 q^{19} + 16 q^{20} - 4 q^{22} - 8 q^{23} + 4 q^{24} + 16 q^{25} - 24 q^{26} + 8 q^{27} + 4 q^{28} - 12 q^{31} + 4 q^{32} - 8 q^{33} + 12 q^{34} + 16 q^{35} - 8 q^{37} - 8 q^{40} - 16 q^{41} + 8 q^{42} - 8 q^{44} + 16 q^{45} + 8 q^{46} + 12 q^{48} + 8 q^{49} - 20 q^{50} - 12 q^{51} + 48 q^{52} + 12 q^{53} - 24 q^{54} + 4 q^{56} + 4 q^{59} + 16 q^{60} + 8 q^{61} + 24 q^{62} + 20 q^{63} - 16 q^{65} + 8 q^{66} - 32 q^{68} + 8 q^{69} - 4 q^{71} - 32 q^{73} + 32 q^{74} - 44 q^{75} + 8 q^{76} + 16 q^{78} + 24 q^{79} + 24 q^{80} + 24 q^{82} - 16 q^{83} + 16 q^{84} - 16 q^{85} + 4 q^{86} + 16 q^{88} - 16 q^{90} - 16 q^{91} + 12 q^{92} + 28 q^{94} + 16 q^{95} + 12 q^{96} - 16 q^{97} - 4 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - 4 * q^3 - 8 * q^5 + 4 * q^6 - 4 * q^7 + 4 * q^8 - 8 * q^9 + 4 * q^11 - 12 * q^12 - 4 * q^14 + 16 * q^15 - 12 * q^16 + 8 * q^17 + 12 * q^18 - 8 * q^19 + 16 * q^20 - 4 * q^22 - 8 * q^23 + 4 * q^24 + 16 * q^25 - 24 * q^26 + 8 * q^27 + 4 * q^28 - 12 * q^31 + 4 * q^32 - 8 * q^33 + 12 * q^34 + 16 * q^35 - 8 * q^37 - 8 * q^40 - 16 * q^41 + 8 * q^42 - 8 * q^44 + 16 * q^45 + 8 * q^46 + 12 * q^48 + 8 * q^49 - 20 * q^50 - 12 * q^51 + 48 * q^52 + 12 * q^53 - 24 * q^54 + 4 * q^56 + 4 * q^59 + 16 * q^60 + 8 * q^61 + 24 * q^62 + 20 * q^63 - 16 * q^65 + 8 * q^66 - 32 * q^68 + 8 * q^69 - 4 * q^71 - 32 * q^73 + 32 * q^74 - 44 * q^75 + 8 * q^76 + 16 * q^78 + 24 * q^79 + 24 * q^80 + 24 * q^82 - 16 * q^83 + 16 * q^84 - 16 * q^85 + 4 * q^86 + 16 * q^88 - 16 * q^90 - 16 * q^91 + 12 * q^92 + 28 * q^94 + 16 * q^95 + 12 * q^96 - 16 * q^97 - 4 * q^99

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