LMFDB - Embedded newform 32.2.g.a.29.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [32,2,Mod(5,32)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(32, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("32.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 32 = 2^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	32.g (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:	$0.255521286468$
Analytic rank:	$0$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			29.1
Root			$-0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	32.29
Dual form			32.2.g.a.21.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421i q^{2} +(-0.707107 - 0.292893i) q^{3} -2.00000 q^{4} +(1.12132 + 2.70711i) q^{5} +(-0.414214 + 1.00000i) q^{6} +(1.00000 - 1.00000i) q^{7} +2.82843i q^{8} +(-1.70711 - 1.70711i) q^{9} +O(q^{10})$	\(q-1.41421i q^{2} +(-0.707107 - 0.292893i) q^{3} -2.00000 q^{4} +(1.12132 + 2.70711i) q^{5} +(-0.414214 + 1.00000i) q^{6} +(1.00000 - 1.00000i) q^{7} +2.82843i q^{8} +(-1.70711 - 1.70711i) q^{9} +(3.82843 - 1.58579i) q^{10} +(-4.12132 + 1.70711i) q^{11} +(1.41421 + 0.585786i) q^{12} +(0.292893 - 0.707107i) q^{13} +(-1.41421 - 1.41421i) q^{14} -2.24264i q^{15} +4.00000 q^{16} -2.82843i q^{17} +(-2.41421 + 2.41421i) q^{18} +(1.53553 - 3.70711i) q^{19} +(-2.24264 - 5.41421i) q^{20} +(-1.00000 + 0.414214i) q^{21} +(2.41421 + 5.82843i) q^{22} +(5.82843 + 5.82843i) q^{23} +(0.828427 - 2.00000i) q^{24} +(-2.53553 + 2.53553i) q^{25} +(-1.00000 - 0.414214i) q^{26} +(1.58579 + 3.82843i) q^{27} +(-2.00000 + 2.00000i) q^{28} +(-3.12132 - 1.29289i) q^{29} -3.17157 q^{30} -4.00000 q^{31} -5.65685i q^{32} +3.41421 q^{33} -4.00000 q^{34} +(3.82843 + 1.58579i) q^{35} +(3.41421 + 3.41421i) q^{36} +(0.292893 + 0.707107i) q^{37} +(-5.24264 - 2.17157i) q^{38} +(-0.414214 + 0.414214i) q^{39} +(-7.65685 + 3.17157i) q^{40} +(-0.171573 - 0.171573i) q^{41} +(0.585786 + 1.41421i) q^{42} +(4.70711 - 1.94975i) q^{43} +(8.24264 - 3.41421i) q^{44} +(2.70711 - 6.53553i) q^{45} +(8.24264 - 8.24264i) q^{46} -0.343146i q^{47} +(-2.82843 - 1.17157i) q^{48} +5.00000i q^{49} +(3.58579 + 3.58579i) q^{50} +(-0.828427 + 2.00000i) q^{51} +(-0.585786 + 1.41421i) q^{52} +(-1.12132 + 0.464466i) q^{53} +(5.41421 - 2.24264i) q^{54} +(-9.24264 - 9.24264i) q^{55} +(2.82843 + 2.82843i) q^{56} +(-2.17157 + 2.17157i) q^{57} +(-1.82843 + 4.41421i) q^{58} +(-1.87868 - 4.53553i) q^{59} +4.48528i q^{60} +(1.70711 + 0.707107i) q^{61} +5.65685i q^{62} -3.41421 q^{63} -8.00000 q^{64} +2.24264 q^{65} -4.82843i q^{66} +(-5.53553 - 2.29289i) q^{67} +5.65685i q^{68} +(-2.41421 - 5.82843i) q^{69} +(2.24264 - 5.41421i) q^{70} +(-5.82843 + 5.82843i) q^{71} +(4.82843 - 4.82843i) q^{72} +(7.00000 + 7.00000i) q^{73} +(1.00000 - 0.414214i) q^{74} +(2.53553 - 1.05025i) q^{75} +(-3.07107 + 7.41421i) q^{76} +(-2.41421 + 5.82843i) q^{77} +(0.585786 + 0.585786i) q^{78} +6.00000i q^{79} +(4.48528 + 10.8284i) q^{80} +4.07107i q^{81} +(-0.242641 + 0.242641i) q^{82} +(1.87868 - 4.53553i) q^{83} +(2.00000 - 0.828427i) q^{84} +(7.65685 - 3.17157i) q^{85} +(-2.75736 - 6.65685i) q^{86} +(1.82843 + 1.82843i) q^{87} +(-4.82843 - 11.6569i) q^{88} +(8.65685 - 8.65685i) q^{89} +(-9.24264 - 3.82843i) q^{90} +(-0.414214 - 1.00000i) q^{91} +(-11.6569 - 11.6569i) q^{92} +(2.82843 + 1.17157i) q^{93} -0.485281 q^{94} +11.7574 q^{95} +(-1.65685 + 4.00000i) q^{96} -18.4853 q^{97} +7.07107 q^{98} +(9.94975 + 4.12132i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 8 q^{4} - 4 q^{5} + 4 q^{6} + 4 q^{7} - 4 q^{9}+O(q^{10}) $ 4 * q - 8 * q^4 - 4 * q^5 + 4 * q^6 + 4 * q^7 - 4 * q^9	$ 4 q - 8 q^{4} - 4 q^{5} + 4 q^{6} + 4 q^{7} - 4 q^{9} + 4 q^{10} - 8 q^{11} + 4 q^{13} + 16 q^{16} - 4 q^{18} - 8 q^{19} + 8 q^{20} - 4 q^{21} + 4 q^{22} + 12 q^{23} - 8 q^{24} + 4 q^{25} - 4 q^{26} + 12 q^{27} - 8 q^{28} - 4 q^{29} - 24 q^{30} - 16 q^{31} + 8 q^{33} - 16 q^{34} + 4 q^{35} + 8 q^{36} + 4 q^{37} - 4 q^{38} + 4 q^{39} - 8 q^{40} - 12 q^{41} + 8 q^{42} + 16 q^{43} + 16 q^{44} + 8 q^{45} + 16 q^{46} + 20 q^{50} + 8 q^{51} - 8 q^{52} + 4 q^{53} + 16 q^{54} - 20 q^{55} - 20 q^{57} + 4 q^{58} - 16 q^{59} + 4 q^{61} - 8 q^{63} - 32 q^{64} - 8 q^{65} - 8 q^{67} - 4 q^{69} - 8 q^{70} - 12 q^{71} + 8 q^{72} + 28 q^{73} + 4 q^{74} - 4 q^{75} + 16 q^{76} - 4 q^{77} + 8 q^{78} - 16 q^{80} + 16 q^{82} + 16 q^{83} + 8 q^{84} + 8 q^{85} - 28 q^{86} - 4 q^{87} - 8 q^{88} + 12 q^{89} - 20 q^{90} + 4 q^{91} - 24 q^{92} + 32 q^{94} + 64 q^{95} + 16 q^{96} - 40 q^{97} + 20 q^{99}+O(q^{100}) $ 4 * q - 8 * q^4 - 4 * q^5 + 4 * q^6 + 4 * q^7 - 4 * q^9 + 4 * q^10 - 8 * q^11 + 4 * q^13 + 16 * q^16 - 4 * q^18 - 8 * q^19 + 8 * q^20 - 4 * q^21 + 4 * q^22 + 12 * q^23 - 8 * q^24 + 4 * q^25 - 4 * q^26 + 12 * q^27 - 8 * q^28 - 4 * q^29 - 24 * q^30 - 16 * q^31 + 8 * q^33 - 16 * q^34 + 4 * q^35 + 8 * q^36 + 4 * q^37 - 4 * q^38 + 4 * q^39 - 8 * q^40 - 12 * q^41 + 8 * q^42 + 16 * q^43 + 16 * q^44 + 8 * q^45 + 16 * q^46 + 20 * q^50 + 8 * q^51 - 8 * q^52 + 4 * q^53 + 16 * q^54 - 20 * q^55 - 20 * q^57 + 4 * q^58 - 16 * q^59 + 4 * q^61 - 8 * q^63 - 32 * q^64 - 8 * q^65 - 8 * q^67 - 4 * q^69 - 8 * q^70 - 12 * q^71 + 8 * q^72 + 28 * q^73 + 4 * q^74 - 4 * q^75 + 16 * q^76 - 4 * q^77 + 8 * q^78 - 16 * q^80 + 16 * q^82 + 16 * q^83 + 8 * q^84 + 8 * q^85 - 28 * q^86 - 4 * q^87 - 8 * q^88 + 12 * q^89 - 20 * q^90 + 4 * q^91 - 24 * q^92 + 32 * q^94 + 64 * q^95 + 16 * q^96 - 40 * q^97 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/32\mathbb{Z}\right)^\times$.

$n$	$5$	$31$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$1$

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 $

$2$		−	1.41421i		−	1.00000i
$2$		−	1.41421i		−	1.00000i
$3$	−0.707107	−	0.292893i	−0.408248	−	0.169102i	0.169102	−	0.985599i	$-0.445913\pi$
$3$	−0.707107	−	0.292893i	−0.408248	−	0.169102i	−0.577350	+	0.816497i	$0.695913\pi$
$4$	−2.00000			−1.00000
$5$	1.12132	+	2.70711i	0.501470	+	1.21065i	0.948683	+	0.316228i	$0.102416\pi$
$5$	1.12132	+	2.70711i	0.501470	+	1.21065i	−0.447214	+	0.894427i	$0.647584\pi$
$6$	−0.414214	+	1.00000i	−0.169102	+	0.408248i
$7$	1.00000	−	1.00000i	0.377964	−	0.377964i	−0.492403	−	0.870367i	$-0.663881\pi$
$7$	1.00000	−	1.00000i	0.377964	−	0.377964i	0.870367	+	0.492403i	$0.163881\pi$
$8$			2.82843i			1.00000i
$9$	−1.70711	−	1.70711i	−0.569036	−	0.569036i
$10$	3.82843	−	1.58579i	1.21065	−	0.501470i
$11$	−4.12132	+	1.70711i	−1.24262	+	0.514712i	−0.904534	−	0.426401i	$-0.859781\pi$
$11$	−4.12132	+	1.70711i	−1.24262	+	0.514712i	−0.338091	+	0.941113i	$0.609781\pi$
$12$	1.41421	+	0.585786i	0.408248	+	0.169102i
$13$	0.292893	−	0.707107i	0.0812340	−	0.196116i	−0.878044	−	0.478580i	$-0.841152\pi$
$13$	0.292893	−	0.707107i	0.0812340	−	0.196116i	0.959278	+	0.282464i	$0.0911517\pi$
$14$	−1.41421	−	1.41421i	−0.377964	−	0.377964i
$15$		−	2.24264i		−	0.579047i
$16$	4.00000			1.00000
$17$		−	2.82843i		−	0.685994i	−0.939336	−	0.342997i	$-0.888558\pi$
$17$		−	2.82843i		−	0.685994i	0.939336	−	0.342997i	$-0.111442\pi$
$18$	−2.41421	+	2.41421i	−0.569036	+	0.569036i
$19$	1.53553	−	3.70711i	0.352276	−	0.850469i	−0.644063	−	0.764973i	$-0.722752\pi$
$19$	1.53553	−	3.70711i	0.352276	−	0.850469i	0.996339	−	0.0854961i	$-0.0272475\pi$
$20$	−2.24264	−	5.41421i	−0.501470	−	1.21065i
$21$	−1.00000	+	0.414214i	−0.218218	+	0.0903888i
$22$	2.41421	+	5.82843i	0.514712	+	1.24262i
$23$	5.82843	+	5.82843i	1.21531	+	1.21531i	0.969256	+	0.246055i	$0.0791345\pi$
$23$	5.82843	+	5.82843i	1.21531	+	1.21531i	0.246055	+	0.969256i	$0.420866\pi$
$24$	0.828427	−	2.00000i	0.169102	−	0.408248i
$25$	−2.53553	+	2.53553i	−0.507107	+	0.507107i
$26$	−1.00000	−	0.414214i	−0.196116	−	0.0812340i
$27$	1.58579	+	3.82843i	0.305185	+	0.736781i
$28$	−2.00000	+	2.00000i	−0.377964	+	0.377964i
$29$	−3.12132	−	1.29289i	−0.579615	−	0.240084i	0.0735609	−	0.997291i	$-0.476564\pi$
$29$	−3.12132	−	1.29289i	−0.579615	−	0.240084i	−0.653176	+	0.757206i	$0.726564\pi$
$30$	−3.17157			−0.579047
$31$	−4.00000			−0.718421			−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000			−0.718421			−0.359211	+	0.933257i	$0.616954\pi$
$32$		−	5.65685i		−	1.00000i
$33$	3.41421			0.594338
$34$	−4.00000			−0.685994
$35$	3.82843	+	1.58579i	0.647122	+	0.268047i
$36$	3.41421	+	3.41421i	0.569036	+	0.569036i
$37$	0.292893	+	0.707107i	0.0481513	+	0.116248i	0.946125	−	0.323802i	$-0.104961\pi$
$37$	0.292893	+	0.707107i	0.0481513	+	0.116248i	−0.897974	+	0.440049i	$0.854961\pi$
$38$	−5.24264	−	2.17157i	−0.850469	−	0.352276i
$39$	−0.414214	+	0.414214i	−0.0663273	+	0.0663273i
$40$	−7.65685	+	3.17157i	−1.21065	+	0.501470i
$41$	−0.171573	−	0.171573i	−0.0267952	−	0.0267952i	0.693582	−	0.720377i	$-0.256031\pi$
$41$	−0.171573	−	0.171573i	−0.0267952	−	0.0267952i	−0.720377	+	0.693582i	$0.756031\pi$
$42$	0.585786	+	1.41421i	0.0903888	+	0.218218i
$43$	4.70711	−	1.94975i	0.717827	−	0.297334i	0.00628798	−	0.999980i	$-0.497998\pi$
$43$	4.70711	−	1.94975i	0.717827	−	0.297334i	0.711539	+	0.702647i	$0.247998\pi$
$44$	8.24264	−	3.41421i	1.24262	−	0.514712i
$45$	2.70711	−	6.53553i	0.403552	−	0.974260i
$46$	8.24264	−	8.24264i	1.21531	−	1.21531i
$47$		−	0.343146i		−	0.0500530i	−0.999687	−	0.0250265i	$-0.992033\pi$
$47$		−	0.343146i		−	0.0500530i	0.999687	−	0.0250265i	$-0.00796701\pi$
$48$	−2.82843	−	1.17157i	−0.408248	−	0.169102i
$49$			5.00000i			0.714286i
$50$	3.58579	+	3.58579i	0.507107	+	0.507107i
$51$	−0.828427	+	2.00000i	−0.116003	+	0.280056i
$52$	−0.585786	+	1.41421i	−0.0812340	+	0.196116i
$53$	−1.12132	+	0.464466i	−0.154025	+	0.0637993i	−0.458364	−	0.888764i	$-0.651564\pi$
$53$	−1.12132	+	0.464466i	−0.154025	+	0.0637993i	0.304339	+	0.952564i	$0.401564\pi$
$54$	5.41421	−	2.24264i	0.736781	−	0.305185i
$55$	−9.24264	−	9.24264i	−1.24628	−	1.24628i
$56$	2.82843	+	2.82843i	0.377964	+	0.377964i
$57$	−2.17157	+	2.17157i	−0.287632	+	0.287632i
$58$	−1.82843	+	4.41421i	−0.240084	+	0.579615i
$59$	−1.87868	−	4.53553i	−0.244583	−	0.590476i	0.753144	−	0.657855i	$-0.228536\pi$
$59$	−1.87868	−	4.53553i	−0.244583	−	0.590476i	−0.997727	+	0.0673793i	$0.978536\pi$
$60$			4.48528i			0.579047i
$61$	1.70711	+	0.707107i	0.218573	+	0.0905357i	0.489283	−	0.872125i	$-0.337259\pi$
$61$	1.70711	+	0.707107i	0.218573	+	0.0905357i	−0.270710	+	0.962661i	$0.587259\pi$
$62$			5.65685i			0.718421i
$63$	−3.41421			−0.430150
$64$	−8.00000			−1.00000
$65$	2.24264			0.278165
$66$		−	4.82843i		−	0.594338i
$67$	−5.53553	−	2.29289i	−0.676273	−	0.280121i	0.0179949	−	0.999838i	$-0.494272\pi$
$67$	−5.53553	−	2.29289i	−0.676273	−	0.280121i	−0.694268	+	0.719717i	$0.744272\pi$
$68$			5.65685i			0.685994i
$69$	−2.41421	−	5.82843i	−0.290637	−	0.701660i
$70$	2.24264	−	5.41421i	0.268047	−	0.647122i
$71$	−5.82843	+	5.82843i	−0.691707	+	0.691707i	−0.962607	−	0.270900i	$-0.912679\pi$
$71$	−5.82843	+	5.82843i	−0.691707	+	0.691707i	0.270900	+	0.962607i	$0.412679\pi$
$72$	4.82843	−	4.82843i	0.569036	−	0.569036i
$73$	7.00000	+	7.00000i	0.819288	+	0.819288i	0.986005	−	0.166717i	$-0.0533166\pi$
$73$	7.00000	+	7.00000i	0.819288	+	0.819288i	−0.166717	+	0.986005i	$0.553317\pi$
$74$	1.00000	−	0.414214i	0.116248	−	0.0481513i
$75$	2.53553	−	1.05025i	0.292778	−	0.121273i
$76$	−3.07107	+	7.41421i	−0.352276	+	0.850469i
$77$	−2.41421	+	5.82843i	−0.275125	+	0.664211i
$78$	0.585786	+	0.585786i	0.0663273	+	0.0663273i
$79$			6.00000i			0.675053i	0.941316	+	0.337526i	$0.109590\pi$
$79$			6.00000i			0.675053i	−0.941316	+	0.337526i	$0.890410\pi$
$80$	4.48528	+	10.8284i	0.501470	+	1.21065i
$81$			4.07107i			0.452341i
$82$	−0.242641	+	0.242641i	−0.0267952	+	0.0267952i
$83$	1.87868	−	4.53553i	0.206212	−	0.497840i	−0.786609	−	0.617452i	$-0.788165\pi$
$83$	1.87868	−	4.53553i	0.206212	−	0.497840i	0.992821	+	0.119612i	$0.0381651\pi$
$84$	2.00000	−	0.828427i	0.218218	−	0.0903888i
$85$	7.65685	−	3.17157i	0.830502	−	0.344005i
$86$	−2.75736	−	6.65685i	−0.297334	−	0.717827i
$87$	1.82843	+	1.82843i	0.196028	+	0.196028i
$88$	−4.82843	−	11.6569i	−0.514712	−	1.24262i
$89$	8.65685	−	8.65685i	0.917625	−	0.917625i	−0.0792315	−	0.996856i	$-0.525247\pi$
$89$	8.65685	−	8.65685i	0.917625	−	0.917625i	0.996856	+	0.0792315i	$0.0252466\pi$
$90$	−9.24264	−	3.82843i	−0.974260	−	0.403552i
$91$	−0.414214	−	1.00000i	−0.0434214	−	0.104828i
$92$	−11.6569	−	11.6569i	−1.21531	−	1.21531i
$93$	2.82843	+	1.17157i	0.293294	+	0.121486i
$94$	−0.485281			−0.0500530
$95$	11.7574			1.20628
$96$	−1.65685	+	4.00000i	−0.169102	+	0.408248i
$97$	−18.4853			−1.87690			−0.938448	−	0.345421i	$-0.887736\pi$
$97$	−18.4853			−1.87690			−0.938448	+	0.345421i	$0.887736\pi$
$98$	7.07107			0.714286
$99$	9.94975	+	4.12132i	0.999987	+	0.414208i
$100$	5.07107	−	5.07107i	0.507107	−	0.507107i
$101$	−1.36396	−	3.29289i	−0.135719	−	0.327655i	0.841379	−	0.540446i	$-0.181745\pi$
$101$	−1.36396	−	3.29289i	−0.135719	−	0.327655i	−0.977098	+	0.212791i	$0.931745\pi$
$102$	2.82843	+	1.17157i	0.280056	+	0.116003i
$103$	9.48528	−	9.48528i	0.934613	−	0.934613i	−0.0633771	−	0.997990i	$-0.520187\pi$
$103$	9.48528	−	9.48528i	0.934613	−	0.934613i	0.997990	+	0.0633771i	$0.0201871\pi$
$104$	2.00000	+	0.828427i	0.196116	+	0.0812340i
$105$	−2.24264	−	2.24264i	−0.218859	−	0.218859i
$106$	0.656854	+	1.58579i	0.0637993	+	0.154025i
$107$	−4.12132	+	1.70711i	−0.398423	+	0.165032i	−0.572893	−	0.819630i	$-0.694179\pi$
$107$	−4.12132	+	1.70711i	−0.398423	+	0.165032i	0.174470	+	0.984663i	$0.444179\pi$
$108$	−3.17157	−	7.65685i	−0.305185	−	0.736781i
$109$	−5.70711	+	13.7782i	−0.546642	+	1.31971i	0.373320	+	0.927702i	$0.378219\pi$
$109$	−5.70711	+	13.7782i	−0.546642	+	1.31971i	−0.919962	+	0.392007i	$0.871781\pi$
$110$	−13.0711	+	13.0711i	−1.24628	+	1.24628i
$111$		−	0.585786i		−	0.0556004i
$112$	4.00000	−	4.00000i	0.377964	−	0.377964i
$113$		−	6.34315i		−	0.596713i	−0.954455	−	0.298356i	$-0.903562\pi$
$113$		−	6.34315i		−	0.596713i	0.954455	−	0.298356i	$-0.0964384\pi$
$114$	3.07107	+	3.07107i	0.287632	+	0.287632i
$115$	−9.24264	+	22.3137i	−0.861881	+	2.08076i
$116$	6.24264	+	2.58579i	0.579615	+	0.240084i
$117$	−1.70711	+	0.707107i	−0.157822	+	0.0653720i
$118$	−6.41421	+	2.65685i	−0.590476	+	0.244583i
$119$	−2.82843	−	2.82843i	−0.259281	−	0.259281i
$120$	6.34315			0.579047
$121$	6.29289	−	6.29289i	0.572081	−	0.572081i
$122$	1.00000	−	2.41421i	0.0905357	−	0.218573i
$123$	0.0710678	+	0.171573i	0.00640797	+	0.0154702i
$124$	8.00000			0.718421
$125$	3.82843	+	1.58579i	0.342425	+	0.141837i
$126$			4.82843i			0.430150i
$127$	12.9706			1.15095			0.575476	−	0.817819i	$-0.304817\pi$
$127$	12.9706			1.15095			0.575476	+	0.817819i	$0.304817\pi$
$128$			11.3137i			1.00000i
$129$	−3.89949			−0.343331
$130$		−	3.17157i		−	0.278165i
$131$	−16.3640	−	6.77817i	−1.42973	−	0.592212i	−0.472442	−	0.881362i	$-0.656627\pi$
$131$	−16.3640	−	6.77817i	−1.42973	−	0.592212i	−0.957284	+	0.289150i	$0.906627\pi$
$132$	−6.82843			−0.594338
$133$	−2.17157	−	5.24264i	−0.188299	−	0.454595i
$134$	−3.24264	+	7.82843i	−0.280121	+	0.676273i
$135$	−8.58579	+	8.58579i	−0.738947	+	0.738947i
$136$	8.00000			0.685994
$137$	−8.65685	−	8.65685i	−0.739605	−	0.739605i	0.232897	−	0.972502i	$-0.425180\pi$
$137$	−8.65685	−	8.65685i	−0.739605	−	0.739605i	−0.972502	+	0.232897i	$0.925180\pi$
$138$	−8.24264	+	3.41421i	−0.701660	+	0.290637i
$139$	13.1924	−	5.46447i	1.11896	−	0.463490i	0.254948	−	0.966955i	$-0.417942\pi$
$139$	13.1924	−	5.46447i	1.11896	−	0.463490i	0.864016	+	0.503465i	$0.167942\pi$
$140$	−7.65685	−	3.17157i	−0.647122	−	0.268047i
$141$	−0.100505	+	0.242641i	−0.00846405	+	0.0204340i
$142$	8.24264	+	8.24264i	0.691707	+	0.691707i
$143$			3.41421i			0.285511i
$144$	−6.82843	−	6.82843i	−0.569036	−	0.569036i
$145$		−	9.89949i		−	0.822108i
$146$	9.89949	−	9.89949i	0.819288	−	0.819288i
$147$	1.46447	−	3.53553i	0.120787	−	0.291606i
$148$	−0.585786	−	1.41421i	−0.0481513	−	0.116248i
$149$	−15.6066	+	6.46447i	−1.27854	+	0.529590i	−0.915551	−	0.402203i	$-0.868245\pi$
$149$	−15.6066	+	6.46447i	−1.27854	+	0.529590i	−0.362992	+	0.931792i	$0.618245\pi$
$150$	−1.48528	−	3.58579i	−0.121273	−	0.292778i
$151$	−1.48528	−	1.48528i	−0.120870	−	0.120870i	0.644084	−	0.764955i	$-0.277239\pi$
$151$	−1.48528	−	1.48528i	−0.120870	−	0.120870i	−0.764955	+	0.644084i	$0.777239\pi$
$152$	10.4853	+	4.34315i	0.850469	+	0.352276i
$153$	−4.82843	+	4.82843i	−0.390355	+	0.390355i
$154$	8.24264	+	3.41421i	0.664211	+	0.275125i
$155$	−4.48528	−	10.8284i	−0.360266	−	0.869760i
$156$	0.828427	−	0.828427i	0.0663273	−	0.0663273i
$157$	1.70711	+	0.707107i	0.136242	+	0.0564333i	0.449763	−	0.893148i	$-0.351509\pi$
$157$	1.70711	+	0.707107i	0.136242	+	0.0564333i	−0.313521	+	0.949581i	$0.601509\pi$
$158$	8.48528			0.675053
$159$	0.928932			0.0736691
$160$	15.3137	−	6.34315i	1.21065	−	0.501470i
$161$	11.6569			0.918689
$162$	5.75736			0.452341
$163$	0.464466	+	0.192388i	0.0363798	+	0.0150690i	0.400799	−	0.916166i	$-0.368733\pi$
$163$	0.464466	+	0.192388i	0.0363798	+	0.0150690i	−0.364419	+	0.931235i	$0.618733\pi$
$164$	0.343146	+	0.343146i	0.0267952	+	0.0267952i
$165$	3.82843	+	9.24264i	0.298043	+	0.719539i
$166$	−6.41421	−	2.65685i	−0.497840	−	0.206212i
$167$	14.6569	−	14.6569i	1.13418	−	1.13418i	0.144707	−	0.989475i	$-0.453776\pi$
$167$	14.6569	−	14.6569i	1.13418	−	1.13418i	0.989475	−	0.144707i	$-0.0462239\pi$
$168$	−1.17157	−	2.82843i	−0.0903888	−	0.218218i
$169$	8.77817	+	8.77817i	0.675244	+	0.675244i
$170$	−4.48528	−	10.8284i	−0.344005	−	0.830502i
$171$	−8.94975	+	3.70711i	−0.684404	+	0.283490i
$172$	−9.41421	+	3.89949i	−0.717827	+	0.297334i
$173$	3.12132	−	7.53553i	0.237310	−	0.572916i	−0.759693	−	0.650282i	$-0.774651\pi$
$173$	3.12132	−	7.53553i	0.237310	−	0.572916i	0.997003	+	0.0773656i	$0.0246509\pi$
$174$	2.58579	−	2.58579i	0.196028	−	0.196028i
$175$			5.07107i			0.383337i
$176$	−16.4853	+	6.82843i	−1.24262	+	0.514712i
$177$			3.75736i			0.282420i
$178$	−12.2426	−	12.2426i	−0.917625	−	0.917625i
$179$	−1.63604	+	3.94975i	−0.122283	+	0.295218i	−0.973153	−	0.230159i	$-0.926076\pi$
$179$	−1.63604	+	3.94975i	−0.122283	+	0.295218i	0.850870	+	0.525377i	$0.176076\pi$
$180$	−5.41421	+	13.0711i	−0.403552	+	0.974260i
$181$	16.1924	−	6.70711i	1.20357	−	0.498535i	0.311420	−	0.950272i	$-0.399196\pi$
$181$	16.1924	−	6.70711i	1.20357	−	0.498535i	0.892151	+	0.451737i	$0.149196\pi$
$182$	−1.41421	+	0.585786i	−0.104828	+	0.0434214i
$183$	−1.00000	−	1.00000i	−0.0739221	−	0.0739221i
$184$	−16.4853	+	16.4853i	−1.21531	+	1.21531i
$185$	−1.58579	+	1.58579i	−0.116589	+	0.116589i
$186$	1.65685	−	4.00000i	0.121486	−	0.293294i
$187$	4.82843	+	11.6569i	0.353090	+	0.852434i
$188$			0.686292i			0.0500530i
$189$	5.41421	+	2.24264i	0.393826	+	0.163128i
$190$		−	16.6274i		−	1.20628i
$191$	−12.0000			−0.868290			−0.434145	−	0.900843i	$-0.642949\pi$
$191$	−12.0000			−0.868290			−0.434145	+	0.900843i	$0.642949\pi$
$192$	5.65685	+	2.34315i	0.408248	+	0.169102i
$193$	−1.51472			−0.109032			−0.0545159	−	0.998513i	$-0.517362\pi$
$193$	−1.51472			−0.109032			−0.0545159	+	0.998513i	$0.517362\pi$
$194$			26.1421i			1.87690i
$195$	−1.58579	−	0.656854i	−0.113561	−	0.0470383i
$196$		−	10.0000i		−	0.714286i
$197$	4.63604	+	11.1924i	0.330304	+	0.797425i	0.998568	+	0.0535002i	$0.0170378\pi$
$197$	4.63604	+	11.1924i	0.330304	+	0.797425i	−0.668264	+	0.743924i	$0.732962\pi$
$198$	5.82843	−	14.0711i	0.414208	−	0.999987i
$199$	−15.9706	+	15.9706i	−1.13212	+	1.13212i	−0.142300	+	0.989824i	$0.545450\pi$
$199$	−15.9706	+	15.9706i	−1.13212	+	1.13212i	−0.989824	+	0.142300i	$0.954550\pi$
$200$	−7.17157	−	7.17157i	−0.507107	−	0.507107i
$201$	3.24264	+	3.24264i	0.228718	+	0.228718i
$202$	−4.65685	+	1.92893i	−0.327655	+	0.135719i
$203$	−4.41421	+	1.82843i	−0.309817	+	0.128330i
$204$	1.65685	−	4.00000i	0.116003	−	0.280056i
$205$	0.272078	−	0.656854i	0.0190027	−	0.0458767i
$206$	−13.4142	−	13.4142i	−0.934613	−	0.934613i
$207$		−	19.8995i		−	1.38311i
$208$	1.17157	−	2.82843i	0.0812340	−	0.196116i
$209$			17.8995i			1.23813i
$210$	−3.17157	+	3.17157i	−0.218859	+	0.218859i
$211$	7.53553	−	18.1924i	0.518768	−	1.25242i	−0.419893	−	0.907574i	$-0.637932\pi$
$211$	7.53553	−	18.1924i	0.518768	−	1.25242i	0.938661	−	0.344842i	$-0.112068\pi$
$212$	2.24264	−	0.928932i	0.154025	−	0.0637993i
$213$	5.82843	−	2.41421i	0.399357	−	0.165419i
$214$	2.41421	+	5.82843i	0.165032	+	0.398423i
$215$	10.5563	+	10.5563i	0.719937	+	0.719937i
$216$	−10.8284	+	4.48528i	−0.736781	+	0.305185i
$217$	−4.00000	+	4.00000i	−0.271538	+	0.271538i
$218$	19.4853	+	8.07107i	1.31971	+	0.546642i
$219$	−2.89949	−	7.00000i	−0.195930	−	0.473016i
$220$	18.4853	+	18.4853i	1.24628	+	1.24628i
$221$	−2.00000	−	0.828427i	−0.134535	−	0.0557260i
$222$	−0.828427			−0.0556004
$223$	−20.9706			−1.40429			−0.702146	−	0.712033i	$-0.747775\pi$
$223$	−20.9706			−1.40429			−0.702146	+	0.712033i	$0.747775\pi$
$224$	−5.65685	−	5.65685i	−0.377964	−	0.377964i
$225$	8.65685			0.577124
$226$	−8.97056			−0.596713
$227$	18.6066	+	7.70711i	1.23496	+	0.511539i	0.902137	−	0.431449i	$-0.141998\pi$
$227$	18.6066	+	7.70711i	1.23496	+	0.511539i	0.332826	+	0.942988i	$0.391998\pi$
$228$	4.34315	−	4.34315i	0.287632	−	0.287632i
$229$	−9.22183	−	22.2635i	−0.609395	−	1.47121i	−0.863659	−	0.504076i	$-0.831833\pi$
$229$	−9.22183	−	22.2635i	−0.609395	−	1.47121i	0.254264	−	0.967135i	$-0.418167\pi$
$230$	31.5563	+	13.0711i	2.08076	+	0.861881i
$231$	3.41421	−	3.41421i	0.224639	−	0.224639i
$232$	3.65685	−	8.82843i	0.240084	−	0.579615i
$233$	−2.65685	−	2.65685i	−0.174056	−	0.174056i	0.614703	−	0.788759i	$-0.289276\pi$
$233$	−2.65685	−	2.65685i	−0.174056	−	0.174056i	−0.788759	+	0.614703i	$0.789276\pi$
$234$	1.00000	+	2.41421i	0.0653720	+	0.157822i
$235$	0.928932	−	0.384776i	0.0605969	−	0.0251000i
$236$	3.75736	+	9.07107i	0.244583	+	0.590476i
$237$	1.75736	−	4.24264i	0.114153	−	0.275589i
$238$	−4.00000	+	4.00000i	−0.259281	+	0.259281i
$239$		−	5.31371i		−	0.343715i	−0.985122	−	0.171858i	$-0.945023\pi$
$239$		−	5.31371i		−	0.343715i	0.985122	−	0.171858i	$-0.0549769\pi$
$240$		−	8.97056i		−	0.579047i
$241$		−	8.48528i		−	0.546585i	−0.961931	−	0.273293i	$-0.911887\pi$
$241$		−	8.48528i		−	0.546585i	0.961931	−	0.273293i	$-0.0881127\pi$
$242$	−8.89949	−	8.89949i	−0.572081	−	0.572081i
$243$	5.94975	−	14.3640i	0.381676	−	0.921449i
$244$	−3.41421	−	1.41421i	−0.218573	−	0.0905357i
$245$	−13.5355	+	5.60660i	−0.864754	+	0.358193i
$246$	0.242641	−	0.100505i	0.0154702	−	0.00640797i
$247$	−2.17157	−	2.17157i	−0.138174	−	0.138174i
$248$		−	11.3137i		−	0.718421i
$249$	−2.65685	+	2.65685i	−0.168371	+	0.168371i
$250$	2.24264	−	5.41421i	0.141837	−	0.342425i
$251$	6.60660	+	15.9497i	0.417005	+	1.00674i	0.983210	+	0.182475i	$0.0584109\pi$
$251$	6.60660	+	15.9497i	0.417005	+	1.00674i	−0.566205	+	0.824264i	$0.691589\pi$
$252$	6.82843			0.430150
$253$	−33.9706	−	14.0711i	−2.13571	−	0.884640i
$254$		−	18.3431i		−	1.15095i
$255$	−6.34315			−0.397223
$256$	16.0000			1.00000
$257$	6.00000			0.374270			0.187135	−	0.982334i	$-0.440080\pi$
$257$	6.00000			0.374270			0.187135	+	0.982334i	$0.440080\pi$
$258$			5.51472i			0.343331i
$259$	1.00000	+	0.414214i	0.0621370	+	0.0257380i
$260$	−4.48528			−0.278165
$261$	3.12132	+	7.53553i	0.193205	+	0.466438i
$262$	−9.58579	+	23.1421i	−0.592212	+	1.42973i
$263$	−5.82843	+	5.82843i	−0.359396	+	0.359396i	−0.863590	−	0.504194i	$-0.831790\pi$
$263$	−5.82843	+	5.82843i	−0.359396	+	0.359396i	0.504194	+	0.863590i	$0.331790\pi$
$264$			9.65685i			0.594338i
$265$	−2.51472	−	2.51472i	−0.154478	−	0.154478i
$266$	−7.41421	+	3.07107i	−0.454595	+	0.188299i
$267$	−8.65685	+	3.58579i	−0.529791	+	0.219447i
$268$	11.0711	+	4.58579i	0.676273	+	0.280121i
$269$	9.12132	−	22.0208i	0.556137	−	1.34263i	−0.356666	−	0.934232i	$-0.616087\pi$
$269$	9.12132	−	22.0208i	0.556137	−	1.34263i	0.912803	−	0.408401i	$-0.133913\pi$
$270$	12.1421	+	12.1421i	0.738947	+	0.738947i
$271$			18.0000i			1.09342i	0.837321	+	0.546711i	$0.184120\pi$
$271$			18.0000i			1.09342i	−0.837321	+	0.546711i	$0.815880\pi$
$272$		−	11.3137i		−	0.685994i
$273$			0.828427i			0.0501387i
$274$	−12.2426	+	12.2426i	−0.739605	+	0.739605i
$275$	6.12132	−	14.7782i	0.369130	−	0.891157i
$276$	4.82843	+	11.6569i	0.290637	+	0.701660i
$277$	1.70711	−	0.707107i	0.102570	−	0.0424859i	−0.330808	−	0.943698i	$-0.607321\pi$
$277$	1.70711	−	0.707107i	0.102570	−	0.0424859i	0.433378	+	0.901212i	$0.357321\pi$
$278$	−7.72792	−	18.6569i	−0.463490	−	1.11896i
$279$	6.82843	+	6.82843i	0.408807	+	0.408807i
$280$	−4.48528	+	10.8284i	−0.268047	+	0.647122i
$281$	−11.8284	+	11.8284i	−0.705625	+	0.705625i	−0.965612	−	0.259987i	$-0.916282\pi$
$281$	−11.8284	+	11.8284i	−0.705625	+	0.705625i	0.259987	+	0.965612i	$0.416282\pi$
$282$	0.343146	+	0.142136i	0.0204340	+	0.00846405i
$283$	5.77817	+	13.9497i	0.343477	+	0.829226i	0.997359	+	0.0726300i	$0.0231392\pi$
$283$	5.77817	+	13.9497i	0.343477	+	0.829226i	−0.653882	+	0.756596i	$0.726861\pi$
$284$	11.6569	−	11.6569i	0.691707	−	0.691707i
$285$	−8.31371	−	3.44365i	−0.492462	−	0.203984i
$286$	4.82843			0.285511
$287$	−0.343146			−0.0202553
$288$	−9.65685	+	9.65685i	−0.569036	+	0.569036i
$289$	9.00000			0.529412
$290$	−14.0000			−0.822108
$291$	13.0711	+	5.41421i	0.766240	+	0.317387i
$292$	−14.0000	−	14.0000i	−0.819288	−	0.819288i
$293$	9.60660	+	23.1924i	0.561224	+	1.35491i	0.908788	+	0.417258i	$0.137009\pi$
$293$	9.60660	+	23.1924i	0.561224	+	1.35491i	−0.347565	+	0.937656i	$0.612991\pi$
$294$	−5.00000	−	2.07107i	−0.291606	−	0.120787i
$295$	10.1716	−	10.1716i	0.592212	−	0.592212i
$296$	−2.00000	+	0.828427i	−0.116248	+	0.0481513i
$297$	−13.0711	−	13.0711i	−0.758460	−	0.758460i
$298$	9.14214	+	22.0711i	0.529590	+	1.27854i
$299$	5.82843	−	2.41421i	0.337067	−	0.139618i
$300$	−5.07107	+	2.10051i	−0.292778	+	0.121273i
$301$	2.75736	−	6.65685i	0.158932	−	0.383695i
$302$	−2.10051	+	2.10051i	−0.120870	+	0.120870i
$303$			2.72792i			0.156715i
$304$	6.14214	−	14.8284i	0.352276	−	0.850469i
$305$			5.41421i			0.310017i
$306$	6.82843	+	6.82843i	0.390355	+	0.390355i
$307$	−6.94975	+	16.7782i	−0.396643	+	0.957581i	0.591813	+	0.806075i	$0.298412\pi$
$307$	−6.94975	+	16.7782i	−0.396643	+	0.957581i	−0.988456	+	0.151506i	$0.951588\pi$
$308$	4.82843	−	11.6569i	0.275125	−	0.664211i
$309$	−9.48528	+	3.92893i	−0.539599	+	0.223509i
$310$	−15.3137	+	6.34315i	−0.869760	+	0.360266i
$311$	−2.65685	−	2.65685i	−0.150656	−	0.150656i	0.627755	−	0.778411i	$-0.283974\pi$
$311$	−2.65685	−	2.65685i	−0.150656	−	0.150656i	−0.778411	+	0.627755i	$0.783974\pi$
$312$	−1.17157	−	1.17157i	−0.0663273	−	0.0663273i
$313$	−7.48528	+	7.48528i	−0.423093	+	0.423093i	−0.886267	−	0.463174i	$-0.846710\pi$
$313$	−7.48528	+	7.48528i	−0.423093	+	0.423093i	0.463174	+	0.886267i	$0.346710\pi$
$314$	1.00000	−	2.41421i	0.0564333	−	0.136242i
$315$	−3.82843	−	9.24264i	−0.215707	−	0.520764i
$316$		−	12.0000i		−	0.675053i
$317$	17.3640	+	7.19239i	0.975257	+	0.403965i	0.812667	−	0.582729i	$-0.198015\pi$
$317$	17.3640	+	7.19239i	0.975257	+	0.403965i	0.162591	+	0.986694i	$0.448015\pi$
$318$		−	1.31371i		−	0.0736691i
$319$	15.0711			0.843818
$320$	−8.97056	−	21.6569i	−0.501470	−	1.21065i
$321$	3.41421			0.190563
$322$		−	16.4853i		−	0.918689i
$323$	−10.4853	−	4.34315i	−0.583417	−	0.241659i
$324$		−	8.14214i		−	0.452341i
$325$	1.05025	+	2.53553i	0.0582575	+	0.140646i
$326$	0.272078	−	0.656854i	0.0150690	−	0.0363798i
$327$	8.07107	−	8.07107i	0.446331	−	0.446331i
$328$	0.485281	−	0.485281i	0.0267952	−	0.0267952i
$329$	−0.343146	−	0.343146i	−0.0189182	−	0.0189182i
$330$	13.0711	−	5.41421i	0.719539	−	0.298043i
$331$	−1.29289	+	0.535534i	−0.0710638	+	0.0294356i	−0.417932	−	0.908478i	$-0.637245\pi$
$331$	−1.29289	+	0.535534i	−0.0710638	+	0.0294356i	0.346868	+	0.937914i	$0.387245\pi$
$332$	−3.75736	+	9.07107i	−0.206212	+	0.497840i
$333$	0.707107	−	1.70711i	0.0387492	−	0.0935489i
$334$	−20.7279	−	20.7279i	−1.13418	−	1.13418i
$335$		−	17.5563i		−	0.959206i
$336$	−4.00000	+	1.65685i	−0.218218	+	0.0903888i
$337$		−	16.9706i		−	0.924445i	−0.886764	−	0.462223i	$-0.847052\pi$
$337$		−	16.9706i		−	0.924445i	0.886764	−	0.462223i	$-0.152948\pi$
$338$	12.4142	−	12.4142i	0.675244	−	0.675244i
$339$	−1.85786	+	4.48528i	−0.100905	+	0.243607i
$340$	−15.3137	+	6.34315i	−0.830502	+	0.344005i
$341$	16.4853	−	6.82843i	0.892728	−	0.369780i
$342$	5.24264	+	12.6569i	0.283490	+	0.684404i
$343$	12.0000	+	12.0000i	0.647939	+	0.647939i
$344$	5.51472	+	13.3137i	0.297334	+	0.717827i
$345$	13.0711	−	13.0711i	0.703723	−	0.703723i
$346$	−10.6569	−	4.41421i	−0.572916	−	0.237310i
$347$	1.63604	+	3.94975i	0.0878272	+	0.212034i	0.961690	−	0.274139i	$-0.0883927\pi$
$347$	1.63604	+	3.94975i	0.0878272	+	0.212034i	−0.873863	+	0.486172i	$0.838393\pi$
$348$	−3.65685	−	3.65685i	−0.196028	−	0.196028i
$349$	24.6777	+	10.2218i	1.32097	+	0.547162i	0.928065	−	0.372419i	$-0.121472\pi$
$349$	24.6777	+	10.2218i	1.32097	+	0.547162i	0.392901	+	0.919581i	$0.371472\pi$
$350$	7.17157			0.383337
$351$	3.17157			0.169286
$352$	9.65685	+	23.3137i	0.514712	+	1.24262i
$353$	6.00000			0.319348			0.159674	−	0.987170i	$-0.448956\pi$
$353$	6.00000			0.319348			0.159674	+	0.987170i	$0.448956\pi$
$354$	5.31371			0.282420
$355$	−22.3137	−	9.24264i	−1.18429	−	0.490548i
$356$	−17.3137	+	17.3137i	−0.917625	+	0.917625i
$357$	1.17157	+	2.82843i	0.0620062	+	0.149696i
$358$	5.58579	+	2.31371i	0.295218	+	0.122283i
$359$	−17.8284	+	17.8284i	−0.940948	+	0.940948i	−0.998351	−	0.0574027i	$-0.981718\pi$
$359$	−17.8284	+	17.8284i	−0.940948	+	0.940948i	0.0574027	+	0.998351i	$0.481718\pi$
$360$	18.4853	+	7.65685i	0.974260	+	0.403552i
$361$	2.05025	+	2.05025i	0.107908	+	0.107908i
$362$	−9.48528	−	22.8995i	−0.498535	−	1.20357i
$363$	−6.29289	+	2.60660i	−0.330291	+	0.136811i
$364$	0.828427	+	2.00000i	0.0434214	+	0.104828i
$365$	−11.1005	+	26.7990i	−0.581027	+	1.40272i
$366$	−1.41421	+	1.41421i	−0.0739221	+	0.0739221i
$367$		−	6.00000i		−	0.313197i	−0.987662	−	0.156599i	$-0.949947\pi$
$367$		−	6.00000i		−	0.313197i	0.987662	−	0.156599i	$-0.0500529\pi$
$368$	23.3137	+	23.3137i	1.21531	+	1.21531i
$369$			0.585786i			0.0304948i
$370$	2.24264	+	2.24264i	0.116589	+	0.116589i
$371$	−0.656854	+	1.58579i	−0.0341022	+	0.0823299i
$372$	−5.65685	−	2.34315i	−0.293294	−	0.121486i
$373$	−10.2929	+	4.26346i	−0.532946	+	0.220753i	−0.632893	−	0.774239i	$-0.718133\pi$
$373$	−10.2929	+	4.26346i	−0.532946	+	0.220753i	0.0999471	+	0.994993i	$0.468133\pi$
$374$	16.4853	−	6.82843i	0.852434	−	0.353090i
$375$	−2.24264	−	2.24264i	−0.115809	−	0.115809i
$376$	0.970563			0.0500530
$377$	−1.82843	+	1.82843i	−0.0941688	+	0.0941688i
$378$	3.17157	−	7.65685i	0.163128	−	0.393826i
$379$	−13.6777	−	33.0208i	−0.702575	−	1.69617i	−0.717769	−	0.696281i	$-0.754837\pi$
$379$	−13.6777	−	33.0208i	−0.702575	−	1.69617i	0.0151948	−	0.999885i	$-0.495163\pi$
$380$	−23.5147			−1.20628
$381$	−9.17157	−	3.79899i	−0.469874	−	0.194628i
$382$			16.9706i			0.868290i
$383$	−16.9706			−0.867155			−0.433578	−	0.901116i	$-0.642749\pi$
$383$	−16.9706			−0.867155			−0.433578	+	0.901116i	$0.642749\pi$
$384$	3.31371	−	8.00000i	0.169102	−	0.408248i
$385$	−18.4853			−0.942097
$386$			2.14214i			0.109032i
$387$	−11.3640	−	4.70711i	−0.577663	−	0.239276i
$388$	36.9706			1.87690
$389$	−8.39340	−	20.2635i	−0.425562	−	1.02740i	−0.980679	−	0.195625i	$-0.937326\pi$
$389$	−8.39340	−	20.2635i	−0.425562	−	1.02740i	0.555117	−	0.831773i	$-0.312674\pi$
$390$	−0.928932	+	2.24264i	−0.0470383	+	0.113561i
$391$	16.4853	−	16.4853i	0.833697	−	0.833697i
$392$	−14.1421			−0.714286
$393$	9.58579	+	9.58579i	0.483539	+	0.483539i
$394$	15.8284	−	6.55635i	0.797425	−	0.330304i
$395$	−16.2426	+	6.72792i	−0.817256	+	0.338518i
$396$	−19.8995	−	8.24264i	−0.999987	−	0.414208i
$397$	−9.22183	+	22.2635i	−0.462830	+	1.11737i	0.504400	+	0.863470i	$0.331714\pi$
$397$	−9.22183	+	22.2635i	−0.462830	+	1.11737i	−0.967230	+	0.253901i	$0.918286\pi$
$398$	22.5858	+	22.5858i	1.13212	+	1.13212i
$399$			4.34315i			0.217429i
$400$	−10.1421	+	10.1421i	−0.507107	+	0.507107i
$401$		−	2.82843i		−	0.141245i	−0.997503	−	0.0706225i	$-0.977501\pi$
$401$		−	2.82843i		−	0.141245i	0.997503	−	0.0706225i	$-0.0224986\pi$
$402$	4.58579	−	4.58579i	0.228718	−	0.228718i
$403$	−1.17157	+	2.82843i	−0.0583602	+	0.140894i
$404$	2.72792	+	6.58579i	0.135719	+	0.327655i
$405$	−11.0208	+	4.56497i	−0.547629	+	0.226835i
$406$	2.58579	+	6.24264i	0.128330	+	0.309817i
$407$	−2.41421	−	2.41421i	−0.119668	−	0.119668i
$408$	−5.65685	−	2.34315i	−0.280056	−	0.116003i
$409$	21.4853	−	21.4853i	1.06238	−	1.06238i	0.0644584	−	0.997920i	$-0.479468\pi$
$409$	21.4853	−	21.4853i	1.06238	−	1.06238i	0.997920	−	0.0644584i	$-0.0205320\pi$
$410$	−0.928932	−	0.384776i	−0.0458767	−	0.0190027i
$411$	3.58579	+	8.65685i	0.176874	+	0.427011i
$412$	−18.9706	+	18.9706i	−0.934613	+	0.934613i
$413$	−6.41421	−	2.65685i	−0.315623	−	0.130735i
$414$	−28.1421			−1.38311
$415$	14.3848			0.706121
$416$	−4.00000	−	1.65685i	−0.196116	−	0.0812340i
$417$	−10.9289			−0.535192
$418$	25.3137			1.23813
$419$	12.6066	+	5.22183i	0.615873	+	0.255103i	0.668737	−	0.743499i	$-0.266835\pi$
$419$	12.6066	+	5.22183i	0.615873	+	0.255103i	−0.0528644	+	0.998602i	$0.516835\pi$
$420$	4.48528	+	4.48528i	0.218859	+	0.218859i
$421$	6.29289	+	15.1924i	0.306697	+	0.740432i	0.999808	+	0.0196009i	$0.00623955\pi$
$421$	6.29289	+	15.1924i	0.306697	+	0.740432i	−0.693111	+	0.720831i	$0.743760\pi$
$422$	−25.7279	−	10.6569i	−1.25242	−	0.518768i
$423$	−0.585786	+	0.585786i	−0.0284819	+	0.0284819i
$424$	−1.31371	−	3.17157i	−0.0637993	−	0.154025i
$425$	7.17157	+	7.17157i	0.347872	+	0.347872i
$426$	−3.41421	−	8.24264i	−0.165419	−	0.399357i
$427$	2.41421	−	1.00000i	0.116832	−	0.0483934i
$428$	8.24264	−	3.41421i	0.398423	−	0.165032i
$429$	1.00000	−	2.41421i	0.0482805	−	0.116559i
$430$	14.9289	−	14.9289i	0.719937	−	0.719937i
$431$		−	12.3431i		−	0.594548i	−0.954792	−	0.297274i	$-0.903922\pi$
$431$		−	12.3431i		−	0.594548i	0.954792	−	0.297274i	$-0.0960775\pi$
$432$	6.34315	+	15.3137i	0.305185	+	0.736781i
$433$		−	15.5147i		−	0.745590i	−0.927914	−	0.372795i	$-0.878400\pi$
$433$		−	15.5147i		−	0.745590i	0.927914	−	0.372795i	$-0.121600\pi$
$434$	5.65685	+	5.65685i	0.271538	+	0.271538i
$435$	−2.89949	+	7.00000i	−0.139020	+	0.335624i
$436$	11.4142	−	27.5563i	0.546642	−	1.31971i
$437$	30.5563	−	12.6569i	1.46171	−	0.605459i
$438$	−9.89949	+	4.10051i	−0.473016	+	0.195930i
$439$	−17.0000	−	17.0000i	−0.811366	−	0.811366i	0.173473	−	0.984839i	$-0.444501\pi$
$439$	−17.0000	−	17.0000i	−0.811366	−	0.811366i	−0.984839	+	0.173473i	$0.944501\pi$
$440$	26.1421	−	26.1421i	1.24628	−	1.24628i
$441$	8.53553	−	8.53553i	0.406454	−	0.406454i
$442$	−1.17157	+	2.82843i	−0.0557260	+	0.134535i
$443$	0.606602	+	1.46447i	0.0288205	+	0.0695789i	0.937635	−	0.347623i	$-0.113011\pi$
$443$	0.606602	+	1.46447i	0.0288205	+	0.0695789i	−0.908814	+	0.417201i	$0.863011\pi$
$444$			1.17157i			0.0556004i
$445$	33.1421	+	13.7279i	1.57109	+	0.650766i
$446$			29.6569i			1.40429i
$447$	12.9289			0.611518
$448$	−8.00000	+	8.00000i	−0.377964	+	0.377964i
$449$	−19.4558			−0.918178			−0.459089	−	0.888390i	$-0.651824\pi$
$449$	−19.4558			−0.918178			−0.459089	+	0.888390i	$0.651824\pi$
$450$		−	12.2426i		−	0.577124i
$451$	1.00000	+	0.414214i	0.0470882	+	0.0195046i
$452$			12.6863i			0.596713i
$453$	0.615224	+	1.48528i	0.0289057	+	0.0697846i
$454$	10.8995	−	26.3137i	0.511539	−	1.23496i
$455$	2.24264	−	2.24264i	0.105137	−	0.105137i
$456$	−6.14214	−	6.14214i	−0.287632	−	0.287632i
$457$	−7.48528	−	7.48528i	−0.350147	−	0.350147i	0.510017	−	0.860164i	$-0.329639\pi$
$457$	−7.48528	−	7.48528i	−0.350147	−	0.350147i	−0.860164	+	0.510017i	$0.829639\pi$
$458$	−31.4853	+	13.0416i	−1.47121	+	0.609395i
$459$	10.8284	−	4.48528i	0.505428	−	0.209355i
$460$	18.4853	−	44.6274i	0.861881	−	2.08076i
$461$	0.636039	−	1.53553i	0.0296233	−	0.0715169i	−0.908376	−	0.418155i	$-0.862677\pi$
$461$	0.636039	−	1.53553i	0.0296233	−	0.0715169i	0.937999	+	0.346638i	$0.112677\pi$
$462$	−4.82843	−	4.82843i	−0.224639	−	0.224639i
$463$			22.9706i			1.06753i	0.845632	+	0.533766i	$0.179224\pi$
$463$			22.9706i			1.06753i	−0.845632	+	0.533766i	$0.820776\pi$
$464$	−12.4853	−	5.17157i	−0.579615	−	0.240084i
$465$			8.97056i			0.416000i
$466$	−3.75736	+	3.75736i	−0.174056	+	0.174056i
$467$	−9.09188	+	21.9497i	−0.420722	+	1.01571i	0.561413	+	0.827536i	$0.310258\pi$
$467$	−9.09188	+	21.9497i	−0.420722	+	1.01571i	−0.982135	+	0.188177i	$0.939742\pi$
$468$	3.41421	−	1.41421i	0.157822	−	0.0653720i
$469$	−7.82843	+	3.24264i	−0.361483	+	0.149731i
$470$	−0.544156	−	1.31371i	−0.0251000	−	0.0605969i
$471$	−1.00000	−	1.00000i	−0.0460776	−	0.0460776i
$472$	12.8284	−	5.31371i	0.590476	−	0.244583i
$473$	−16.0711	+	16.0711i	−0.738948	+	0.738948i
$474$	−6.00000	−	2.48528i	−0.275589	−	0.114153i
$475$	5.50610	+	13.2929i	0.252637	+	0.609920i
$476$	5.65685	+	5.65685i	0.259281	+	0.259281i
$477$	2.70711	+	1.12132i	0.123950	+	0.0513417i
$478$	−7.51472			−0.343715
$479$	28.9706			1.32370			0.661849	−	0.749637i	$-0.269772\pi$
$479$	28.9706			1.32370			0.661849	+	0.749637i	$0.269772\pi$
$480$	−12.6863			−0.579047
$481$	0.585786			0.0267096
$482$	−12.0000			−0.546585
$483$	−8.24264	−	3.41421i	−0.375053	−	0.155352i
$484$	−12.5858	+	12.5858i	−0.572081	+	0.572081i
$485$	−20.7279	−	50.0416i	−0.941206	−	2.27227i
$486$	−20.3137	−	8.41421i	−0.921449	−	0.381676i
$487$	−11.0000	+	11.0000i	−0.498458	+	0.498458i	−0.910958	−	0.412500i	$-0.864656\pi$
$487$	−11.0000	+	11.0000i	−0.498458	+	0.498458i	0.412500	+	0.910958i	$0.364656\pi$
$488$	−2.00000	+	4.82843i	−0.0905357	+	0.218573i
$489$	−0.272078	−	0.272078i	−0.0123038	−	0.0123038i
$490$	7.92893	+	19.1421i	0.358193	+	0.864754i
$491$	39.3345	−	16.2929i	1.77514	−	0.735288i	0.781343	−	0.624102i	$-0.214535\pi$
$491$	39.3345	−	16.2929i	1.77514	−	0.735288i	0.993800	−	0.111186i	$-0.0354648\pi$
$492$	−0.142136	−	0.343146i	−0.00640797	−	0.0154702i
$493$	−3.65685	+	8.82843i	−0.164696	+	0.397612i
$494$	−3.07107	+	3.07107i	−0.138174	+	0.138174i
$495$			31.5563i			1.41835i
$496$	−16.0000			−0.718421
$497$			11.6569i			0.522881i
$498$	3.75736	+	3.75736i	0.168371	+	0.168371i
$499$	−0.949747	+	2.29289i	−0.0425165	+	0.102644i	−0.943711	−	0.330771i	$-0.892691\pi$
$499$	−0.949747	+	2.29289i	−0.0425165	+	0.102644i	0.901195	+	0.433415i	$0.142691\pi$
$500$	−7.65685	−	3.17157i	−0.342425	−	0.141837i
$501$	−14.6569	+	6.07107i	−0.654820	+	0.271235i
$502$	22.5563	−	9.34315i	1.00674	−	0.417005i
$503$	−11.1421	−	11.1421i	−0.496803	−	0.496803i	0.413638	−	0.910441i	$-0.364258\pi$
$503$	−11.1421	−	11.1421i	−0.496803	−	0.496803i	−0.910441	+	0.413638i	$0.864258\pi$
$504$		−	9.65685i		−	0.430150i
$505$	7.38478	−	7.38478i	0.328618	−	0.328618i
$506$	−19.8995	+	48.0416i	−0.884640	+	2.13571i
$507$	−3.63604	−	8.77817i	−0.161482	−	0.389852i
$508$	−25.9411			−1.15095
$509$	−26.0919	−	10.8076i	−1.15650	−	0.479039i	−0.279793	−	0.960060i	$-0.590266\pi$
$509$	−26.0919	−	10.8076i	−1.15650	−	0.479039i	−0.876709	+	0.481021i	$0.840266\pi$
$510$			8.97056i			0.397223i
$511$	14.0000			0.619324
$512$		−	22.6274i		−	1.00000i
$513$	16.6274			0.734118
$514$		−	8.48528i		−	0.374270i
$515$	36.3137	+	15.0416i	1.60017	+	0.662813i
$516$	7.79899			0.343331
$517$	0.585786	+	1.41421i	0.0257629	+	0.0621970i
$518$	0.585786	−	1.41421i	0.0257380	−	0.0621370i
$519$	−4.41421	+	4.41421i	−0.193762	+	0.193762i
$520$			6.34315i			0.278165i
$521$	3.34315	+	3.34315i	0.146466	+	0.146466i	0.776537	−	0.630071i	$-0.216974\pi$
$521$	3.34315	+	3.34315i	0.146466	+	0.146466i	−0.630071	+	0.776537i	$0.716974\pi$
$522$	10.6569	−	4.41421i	0.466438	−	0.193205i
$523$	19.1924	−	7.94975i	0.839225	−	0.347618i	0.0786768	−	0.996900i	$-0.474930\pi$
$523$	19.1924	−	7.94975i	0.839225	−	0.347618i	0.760548	+	0.649282i	$0.224930\pi$
$524$	32.7279	+	13.5563i	1.42973	+	0.592212i
$525$	1.48528	−	3.58579i	0.0648230	−	0.156497i
$526$	8.24264	+	8.24264i	0.359396	+	0.359396i
$527$			11.3137i			0.492833i
$528$	13.6569			0.594338
$529$			44.9411i			1.95396i
$530$	−3.55635	+	3.55635i	−0.154478	+	0.154478i
$531$	−4.53553	+	10.9497i	−0.196825	+	0.475179i
$532$	4.34315	+	10.4853i	0.188299	+	0.454595i
$533$	−0.171573	+	0.0710678i	−0.00743165	+	0.00307829i
$534$	5.07107	+	12.2426i	0.219447	+	0.529791i
$535$	−9.24264	−	9.24264i	−0.399594	−	0.399594i
$536$	6.48528	−	15.6569i	0.280121	−	0.676273i
$537$	2.31371	−	2.31371i	0.0998439	−	0.0998439i
$538$	−31.1421	−	12.8995i	−1.34263	−	0.556137i
$539$	−8.53553	−	20.6066i	−0.367651	−	0.887589i
$540$	17.1716	−	17.1716i	0.738947	−	0.738947i
$541$	−27.2635	−	11.2929i	−1.17215	−	0.485519i	−0.290246	−	0.956952i	$-0.593737\pi$
$541$	−27.2635	−	11.2929i	−1.17215	−	0.485519i	−0.881902	+	0.471433i	$0.843737\pi$
$542$	25.4558			1.09342
$543$	−13.4142			−0.575659
$544$	−16.0000			−0.685994
$545$	−43.6985			−1.87184
$546$	1.17157			0.0501387
$547$	−17.5355	−	7.26346i	−0.749765	−	0.310563i	−0.0251195	−	0.999684i	$-0.507997\pi$
$547$	−17.5355	−	7.26346i	−0.749765	−	0.310563i	−0.724646	+	0.689122i	$0.757997\pi$
$548$	17.3137	+	17.3137i	0.739605	+	0.739605i
$549$	−1.70711	−	4.12132i	−0.0728575	−	0.175894i
$550$	−20.8995	−	8.65685i	−0.891157	−	0.369130i
$551$	−9.58579	+	9.58579i	−0.408368	+	0.408368i
$552$	16.4853	−	6.82843i	0.701660	−	0.290637i
$553$	6.00000	+	6.00000i	0.255146	+	0.255146i
$554$	−1.00000	−	2.41421i	−0.0424859	−	0.102570i
$555$	1.58579	−	0.656854i	0.0673129	−	0.0278819i
$556$	−26.3848	+	10.9289i	−1.11896	+	0.463490i
$557$	15.1213	−	36.5061i	0.640711	−	1.54681i	−0.185012	−	0.982736i	$-0.559232\pi$
$557$	15.1213	−	36.5061i	0.640711	−	1.54681i	0.825722	−	0.564077i	$-0.190768\pi$
$558$	9.65685	−	9.65685i	0.408807	−	0.408807i
$559$		−	3.89949i		−	0.164931i
$560$	15.3137	+	6.34315i	0.647122	+	0.268047i
$561$		−	9.65685i		−	0.407713i
$562$	16.7279	+	16.7279i	0.705625	+	0.705625i
$563$	7.87868	−	19.0208i	0.332047	−	0.801632i	−0.666383	−	0.745610i	$-0.732158\pi$
$563$	7.87868	−	19.0208i	0.332047	−	0.801632i	0.998430	−	0.0560220i	$-0.0178417\pi$
$564$	0.201010	−	0.485281i	0.00846405	−	0.0204340i
$565$	17.1716	−	7.11270i	0.722414	−	0.299233i
$566$	19.7279	−	8.17157i	0.829226	−	0.343477i
$567$	4.07107	+	4.07107i	0.170969	+	0.170969i
$568$	−16.4853	−	16.4853i	−0.691707	−	0.691707i
$569$	14.6569	−	14.6569i	0.614447	−	0.614447i	−0.329654	−	0.944102i	$-0.606932\pi$
$569$	14.6569	−	14.6569i	0.614447	−	0.614447i	0.944102	+	0.329654i	$0.106932\pi$
$570$	−4.87006	+	11.7574i	−0.203984	+	0.492462i
$571$	−2.70711	−	6.53553i	−0.113289	−	0.273504i	0.857058	−	0.515220i	$-0.172290\pi$
$571$	−2.70711	−	6.53553i	−0.113289	−	0.273504i	−0.970347	+	0.241716i	$0.922290\pi$
$572$		−	6.82843i		−	0.285511i
$573$	8.48528	+	3.51472i	0.354478	+	0.146829i
$574$			0.485281i			0.0202553i
$575$	−29.5563			−1.23258
$576$	13.6569	+	13.6569i	0.569036	+	0.569036i
$577$	18.9706			0.789755			0.394877	−	0.918734i	$-0.370787\pi$
$577$	18.9706			0.789755			0.394877	+	0.918734i	$0.370787\pi$
$578$		−	12.7279i		−	0.529412i
$579$	1.07107	+	0.443651i	0.0445121	+	0.0184375i
$580$			19.7990i			0.822108i
$581$	−2.65685	−	6.41421i	−0.110225	−	0.266106i
$582$	7.65685	−	18.4853i	0.317387	−	0.766240i
$583$	3.82843	−	3.82843i	0.158557	−	0.158557i
$584$	−19.7990	+	19.7990i	−0.819288	+	0.819288i
$585$	−3.82843	−	3.82843i	−0.158286	−	0.158286i
$586$	32.7990	−	13.5858i	1.35491	−	0.561224i
$587$	−12.6066	+	5.22183i	−0.520330	+	0.215528i	−0.627362	−	0.778728i	$-0.715865\pi$
$587$	−12.6066	+	5.22183i	−0.520330	+	0.215528i	0.107032	+	0.994256i	$0.465865\pi$
$588$	−2.92893	+	7.07107i	−0.120787	+	0.291606i
$589$	−6.14214	+	14.8284i	−0.253082	+	0.610995i
$590$	−14.3848	−	14.3848i	−0.592212	−	0.592212i
$591$		−	9.27208i		−	0.381402i
$592$	1.17157	+	2.82843i	0.0481513	+	0.116248i
$593$		−	28.2843i		−	1.16150i	−0.814083	−	0.580748i	$-0.802760\pi$
$593$		−	28.2843i		−	1.16150i	0.814083	−	0.580748i	$-0.197240\pi$
$594$	−18.4853	+	18.4853i	−0.758460	+	0.758460i
$595$	4.48528	−	10.8284i	0.183879	−	0.443922i
$596$	31.2132	−	12.9289i	1.27854	−	0.529590i
$597$	15.9706	−	6.61522i	0.653632	−	0.270743i
$598$	−3.41421	−	8.24264i	−0.139618	−	0.337067i
$599$	−26.6569	−	26.6569i	−1.08917	−	1.08917i	−0.995614	−	0.0935555i	$-0.970177\pi$
$599$	−26.6569	−	26.6569i	−1.08917	−	1.08917i	−0.0935555	−	0.995614i	$-0.529823\pi$
$600$	2.97056	+	7.17157i	0.121273	+	0.292778i
$601$	−21.9706	+	21.9706i	−0.896198	+	0.896198i	−0.995097	−	0.0988995i	$-0.968468\pi$
$601$	−21.9706	+	21.9706i	−0.896198	+	0.896198i	0.0988995	+	0.995097i	$0.468468\pi$
$602$	−9.41421	−	3.89949i	−0.383695	−	0.158932i
$603$	5.53553	+	13.3640i	0.225424	+	0.544223i
$604$	2.97056	+	2.97056i	0.120870	+	0.120870i
$605$	24.0919	+	9.97918i	0.979474	+	0.405712i
$606$	3.85786			0.156715
$607$	−32.9706			−1.33823			−0.669117	−	0.743157i	$-0.733327\pi$
$607$	−32.9706			−1.33823			−0.669117	+	0.743157i	$0.733327\pi$
$608$	−20.9706	−	8.68629i	−0.850469	−	0.352276i
$609$	3.65685			0.148183
$610$	7.65685			0.310017
$611$	−0.242641	−	0.100505i	−0.00981619	−	0.00406600i
$612$	9.65685	−	9.65685i	0.390355	−	0.390355i
$613$	1.32233	+	3.19239i	0.0534084	+	0.128939i	0.948332	−	0.317281i	$-0.102770\pi$
$613$	1.32233	+	3.19239i	0.0534084	+	0.128939i	−0.894923	+	0.446220i	$0.852770\pi$
$614$	23.7279	+	9.82843i	0.957581	+	0.396643i
$615$	−0.384776	+	0.384776i	−0.0155157	+	0.0155157i
$616$	−16.4853	−	6.82843i	−0.664211	−	0.275125i
$617$	22.7990	+	22.7990i	0.917853	+	0.917853i	0.996873	−	0.0790202i	$-0.0251792\pi$
$617$	22.7990	+	22.7990i	0.917853	+	0.917853i	−0.0790202	+	0.996873i	$0.525179\pi$
$618$	5.55635	+	13.4142i	0.223509	+	0.539599i
$619$	−21.7782	+	9.02082i	−0.875339	+	0.362577i	−0.774687	−	0.632345i	$-0.782093\pi$
$619$	−21.7782	+	9.02082i	−0.875339	+	0.362577i	−0.100651	+	0.994922i	$0.532093\pi$
$620$	8.97056	+	21.6569i	0.360266	+	0.869760i
$621$	−13.0711	+	31.5563i	−0.524524	+	1.26631i
$622$	−3.75736	+	3.75736i	−0.150656	+	0.150656i
$623$		−	17.3137i		−	0.693659i
$624$	−1.65685	+	1.65685i	−0.0663273	+	0.0663273i
$625$			30.0711i			1.20284i
$626$	10.5858	+	10.5858i	0.423093	+	0.423093i
$627$	5.24264	−	12.6569i	0.209371	−	0.505466i
$628$	−3.41421	−	1.41421i	−0.136242	−	0.0564333i
$629$	2.00000	−	0.828427i	0.0797452	−	0.0330316i
$630$	−13.0711	+	5.41421i	−0.520764	+	0.215707i
$631$	32.4558	+	32.4558i	1.29205	+	1.29205i	0.933519	+	0.358528i	$0.116721\pi$
$631$	32.4558	+	32.4558i	1.29205	+	1.29205i	0.358528	+	0.933519i	$0.383279\pi$
$632$	−16.9706			−0.675053
$633$	−10.6569	+	10.6569i	−0.423572	+	0.423572i
$634$	10.1716	−	24.5563i	0.403965	−	0.975257i
$635$	14.5442	+	35.1127i	0.577167	+	1.39340i
$636$	−1.85786			−0.0736691
$637$	3.53553	+	1.46447i	0.140083	+	0.0580243i
$638$		−	21.3137i		−	0.843818i
$639$	19.8995			0.787212
$640$	−30.6274	+	12.6863i	−1.21065	+	0.501470i
$641$	7.45584			0.294488			0.147244	−	0.989100i	$-0.452960\pi$
$641$	7.45584			0.294488			0.147244	+	0.989100i	$0.452960\pi$
$642$		−	4.82843i		−	0.190563i
$643$	11.4350	+	4.73654i	0.450954	+	0.186791i	0.596588	−	0.802547i	$-0.296522\pi$
$643$	11.4350	+	4.73654i	0.450954	+	0.186791i	−0.145635	+	0.989338i	$0.546522\pi$
$644$	−23.3137			−0.918689
$645$	−4.37258	−	10.5563i	−0.172170	−	0.415656i
$646$	−6.14214	+	14.8284i	−0.241659	+	0.583417i
$647$	6.17157	−	6.17157i	0.242630	−	0.242630i	−0.575308	−	0.817937i	$-0.695118\pi$
$647$	6.17157	−	6.17157i	0.242630	−	0.242630i	0.817937	+	0.575308i	$0.195118\pi$
$648$	−11.5147			−0.452341
$649$	15.4853	+	15.4853i	0.607850	+	0.607850i
$650$	3.58579	−	1.48528i	0.140646	−	0.0582575i
$651$	4.00000	−	1.65685i	0.156772	−	0.0649372i
$652$	−0.928932	−	0.384776i	−0.0363798	−	0.0150690i
$653$	2.09188	−	5.05025i	0.0818617	−	0.197632i	−0.877649	−	0.479304i	$-0.840889\pi$
$653$	2.09188	−	5.05025i	0.0818617	−	0.197632i	0.959511	+	0.281672i	$0.0908891\pi$
$654$	−11.4142	−	11.4142i	−0.446331	−	0.446331i
$655$		−	51.8995i		−	2.02788i
$656$	−0.686292	−	0.686292i	−0.0267952	−	0.0267952i
$657$		−	23.8995i		−	0.932408i
$658$	−0.485281	+	0.485281i	−0.0189182	+	0.0189182i
$659$	−10.1213	+	24.4350i	−0.394271	+	0.951854i	0.594728	+	0.803927i	$0.297260\pi$
$659$	−10.1213	+	24.4350i	−0.394271	+	0.951854i	−0.988998	+	0.147926i	$0.952740\pi$
$660$	−7.65685	−	18.4853i	−0.298043	−	0.719539i
$661$	−41.7487	+	17.2929i	−1.62384	+	0.672616i	−0.994521	−	0.104534i	$-0.966665\pi$
$661$	−41.7487	+	17.2929i	−1.62384	+	0.672616i	−0.629316	+	0.777149i	$0.716665\pi$
$662$	0.757359	+	1.82843i	0.0294356	+	0.0710638i
$663$	1.17157	+	1.17157i	0.0455001	+	0.0455001i
$664$	12.8284	+	5.31371i	0.497840	+	0.206212i
$665$	11.7574	−	11.7574i	0.455931	−	0.455931i
$666$	−2.41421	−	1.00000i	−0.0935489	−	0.0387492i
$667$	−10.6569	−	25.7279i	−0.412635	−	0.996189i
$668$	−29.3137	+	29.3137i	−1.13418	+	1.13418i
$669$	14.8284	+	6.14214i	0.573300	+	0.237469i
$670$	−24.8284			−0.959206
$671$	−8.24264			−0.318204
$672$	2.34315	+	5.65685i	0.0903888	+	0.218218i
$673$	22.4853			0.866744			0.433372	−	0.901215i	$-0.357324\pi$
$673$	22.4853			0.866744			0.433372	+	0.901215i	$0.357324\pi$
$674$	−24.0000			−0.924445
$675$	−13.7279	−	5.68629i	−0.528388	−	0.218865i
$676$	−17.5563	−	17.5563i	−0.675244	−	0.675244i
$677$	15.6066	+	37.6777i	0.599810	+	1.44807i	0.873775	+	0.486331i	$0.161665\pi$
$677$	15.6066	+	37.6777i	0.599810	+	1.44807i	−0.273964	+	0.961740i	$0.588335\pi$
$678$	6.34315	+	2.62742i	0.243607	+	0.100905i
$679$	−18.4853	+	18.4853i	−0.709400	+	0.709400i
$680$	8.97056	+	21.6569i	0.344005	+	0.830502i
$681$	−10.8995	−	10.8995i	−0.417670	−	0.417670i
$682$	−9.65685	−	23.3137i	−0.369780	−	0.892728i
$683$	−10.1213	+	4.19239i	−0.387282	+	0.160417i	−0.567824	−	0.823150i	$-0.692215\pi$
$683$	−10.1213	+	4.19239i	−0.387282	+	0.160417i	0.180543	+	0.983567i	$0.442215\pi$
$684$	17.8995	−	7.41421i	0.684404	−	0.283490i
$685$	13.7279	−	33.1421i	0.524517	−	1.26630i
$686$	16.9706	−	16.9706i	0.647939	−	0.647939i
$687$			18.4437i			0.703669i
$688$	18.8284	−	7.79899i	0.717827	−	0.297334i
$689$			0.928932i			0.0353895i
$690$	−18.4853	−	18.4853i	−0.703723	−	0.703723i
$691$	12.5061	−	30.1924i	0.475754	−	1.14857i	−0.485828	−	0.874055i	$-0.661482\pi$
$691$	12.5061	−	30.1924i	0.475754	−	1.14857i	0.961582	−	0.274518i	$-0.0885183\pi$
$692$	−6.24264	+	15.0711i	−0.237310	+	0.572916i
$693$	14.0711	−	5.82843i	0.534516	−	0.221404i
$694$	5.58579	−	2.31371i	0.212034	−	0.0878272i
$695$	29.5858	+	29.5858i	1.12225	+	1.12225i
$696$	−5.17157	+	5.17157i	−0.196028	+	0.196028i
$697$	−0.485281	+	0.485281i	−0.0183813	+	0.0183813i
$698$	14.4558	−	34.8995i	0.547162	−	1.32097i
$699$	1.10051	+	2.65685i	0.0416249	+	0.100491i
$700$		−	10.1421i		−	0.383337i
$701$	2.87868	+	1.19239i	0.108726	+	0.0450359i	0.436383	−	0.899761i	$-0.356259\pi$
$701$	2.87868	+	1.19239i	0.108726	+	0.0450359i	−0.327657	+	0.944797i	$0.606259\pi$
$702$		−	4.48528i		−	0.169286i
$703$	3.07107			0.115828
$704$	32.9706	−	13.6569i	1.24262	−	0.514712i
$705$	−0.769553			−0.0289830
$706$		−	8.48528i		−	0.319348i
$707$	−4.65685	−	1.92893i	−0.175139	−	0.0725450i
$708$		−	7.51472i		−	0.282420i
$709$	8.77817	+	21.1924i	0.329671	+	0.795897i	0.998616	+	0.0525851i	$0.0167461\pi$
$709$	8.77817	+	21.1924i	0.329671	+	0.795897i	−0.668945	+	0.743312i	$0.733254\pi$
$710$	−13.0711	+	31.5563i	−0.490548	+	1.18429i
$711$	10.2426	−	10.2426i	0.384129	−	0.384129i
$712$	24.4853	+	24.4853i	0.917625	+	0.917625i
$713$	−23.3137	−	23.3137i	−0.873105	−	0.873105i
$714$	4.00000	−	1.65685i	0.149696	−	0.0620062i
$715$	−9.24264	+	3.82843i	−0.345655	+	0.143175i
$716$	3.27208	−	7.89949i	0.122283	−	0.295218i
$717$	−1.55635	+	3.75736i	−0.0581229	+	0.140321i
$718$	25.2132	+	25.2132i	0.940948	+	0.940948i
$719$			35.6569i			1.32978i	0.746943	+	0.664888i	$0.231521\pi$
$719$			35.6569i			1.32978i	−0.746943	+	0.664888i	$0.768479\pi$
$720$	10.8284	−	26.1421i	0.403552	−	0.974260i
$721$		−	18.9706i		−	0.706501i
$722$	2.89949	−	2.89949i	0.107908	−	0.107908i
$723$	−2.48528	+	6.00000i	−0.0924286	+	0.223142i
$724$	−32.3848	+	13.4142i	−1.20357	+	0.498535i
$725$	11.1924	−	4.63604i	0.415675	−	0.172178i
$726$	3.68629	+	8.89949i	0.136811	+	0.330291i
$727$	−9.97056	−	9.97056i	−0.369788	−	0.369788i	0.497612	−	0.867400i	$-0.334210\pi$
$727$	−9.97056	−	9.97056i	−0.369788	−	0.369788i	−0.867400	+	0.497612i	$0.834210\pi$
$728$	2.82843	−	1.17157i	0.104828	−	0.0434214i
$729$	0.221825	−	0.221825i	0.00821576	−	0.00821576i
$730$	37.8995	+	15.6985i	1.40272	+	0.581027i
$731$	−5.51472	−	13.3137i	−0.203969	−	0.492425i
$732$	2.00000	+	2.00000i	0.0739221	+	0.0739221i
$733$	−33.2635	−	13.7782i	−1.22861	−	0.508908i	−0.328475	−	0.944513i	$-0.606535\pi$
$733$	−33.2635	−	13.7782i	−1.22861	−	0.508908i	−0.900138	+	0.435604i	$0.856535\pi$
$734$	−8.48528			−0.313197
$735$	11.2132			0.413605
$736$	32.9706	−	32.9706i	1.21531	−	1.21531i
$737$	26.7279			0.984536
$738$	0.828427			0.0304948
$739$	0.464466	+	0.192388i	0.0170857	+	0.00707711i	0.391210	−	0.920301i	$-0.372057\pi$
$739$	0.464466	+	0.192388i	0.0170857	+	0.00707711i	−0.374124	+	0.927379i	$0.622057\pi$
$740$	3.17157	−	3.17157i	0.116589	−	0.116589i
$741$	0.899495	+	2.17157i	0.0330438	+	0.0797747i
$742$	2.24264	+	0.928932i	0.0823299	+	0.0341022i
$743$	31.6274	−	31.6274i	1.16030	−	1.16030i	0.175887	−	0.984410i	$-0.443721\pi$
$743$	31.6274	−	31.6274i	1.16030	−	1.16030i	0.984410	−	0.175887i	$-0.0562793\pi$
$744$	−3.31371	+	8.00000i	−0.121486	+	0.293294i
$745$	−35.0000	−	35.0000i	−1.28230	−	1.28230i
$746$	6.02944	+	14.5563i	0.220753	+	0.532946i
$747$	−10.9497	+	4.53553i	−0.400630	+	0.165947i
$748$	−9.65685	−	23.3137i	−0.353090	−	0.852434i
$749$	−2.41421	+	5.82843i	−0.0882134	+	0.212966i
$750$	−3.17157	+	3.17157i	−0.115809	+	0.115809i
$751$		−	10.9706i		−	0.400322i	−0.979763	−	0.200161i	$-0.935854\pi$
$751$		−	10.9706i		−	0.400322i	0.979763	−	0.200161i	$-0.0641464\pi$
$752$		−	1.37258i		−	0.0500530i
$753$		−	13.2132i		−	0.481516i
$754$	2.58579	+	2.58579i	0.0941688	+	0.0941688i
$755$	2.35534	−	5.68629i	0.0857196	−	0.206945i
$756$	−10.8284	−	4.48528i	−0.393826	−	0.163128i
$757$	−33.2635	+	13.7782i	−1.20898	+	0.500776i	−0.893890	−	0.448285i	$-0.852035\pi$
$757$	−33.2635	+	13.7782i	−1.20898	+	0.500776i	−0.315090	+	0.949062i	$0.602035\pi$
$758$	−46.6985	+	19.3431i	−1.69617	+	0.702575i
$759$	19.8995	+	19.8995i	0.722306	+	0.722306i
$760$			33.2548i			1.20628i
$761$	−29.8284	+	29.8284i	−1.08128	+	1.08128i	−0.0848892	+	0.996390i	$0.527054\pi$
$761$	−29.8284	+	29.8284i	−1.08128	+	1.08128i	−0.996390	+	0.0848892i	$0.972946\pi$
$762$	−5.37258	+	12.9706i	−0.194628	+	0.469874i
$763$	8.07107	+	19.4853i	0.292192	+	0.705415i
$764$	24.0000			0.868290
$765$	−18.4853	−	7.65685i	−0.668337	−	0.276834i
$766$			24.0000i			0.867155i
$767$	−3.75736			−0.135670
$768$	−11.3137	−	4.68629i	−0.408248	−	0.169102i
$769$	5.51472			0.198866			0.0994329	−	0.995044i	$-0.468297\pi$
$769$	5.51472			0.198866			0.0994329	+	0.995044i	$0.468297\pi$
$770$			26.1421i			0.942097i
$771$	−4.24264	−	1.75736i	−0.152795	−	0.0632897i
$772$	3.02944			0.109032
$773$	12.0919	+	29.1924i	0.434915	+	1.04998i	0.977681	+	0.210094i	$0.0673769\pi$
$773$	12.0919	+	29.1924i	0.434915	+	1.04998i	−0.542766	+	0.839884i	$0.682623\pi$
$774$	−6.65685	+	16.0711i	−0.239276	+	0.577663i
$775$	10.1421	−	10.1421i	0.364316	−	0.364316i
$776$		−	52.2843i		−	1.87690i
$777$	−0.585786	−	0.585786i	−0.0210150	−	0.0210150i
$778$	−28.6569	+	11.8701i	−1.02740	+	0.425562i
$779$	−0.899495	+	0.372583i	−0.0322278	+	0.0133492i
$780$	3.17157	+	1.31371i	0.113561	+	0.0470383i
$781$	14.0711	−	33.9706i	0.503502	−	1.21556i
$782$	−23.3137	−	23.3137i	−0.833697	−	0.833697i
$783$		−	14.0000i		−	0.500319i
$784$			20.0000i			0.714286i
$785$			5.41421i			0.193242i
$786$	13.5563	−	13.5563i	0.483539	−	0.483539i
$787$	−0.949747	+	2.29289i	−0.0338548	+	0.0817328i	−0.939903	−	0.341442i	$-0.889085\pi$
$787$	−0.949747	+	2.29289i	−0.0338548	+	0.0817328i	0.906048	+	0.423175i	$0.139085\pi$
$788$	−9.27208	−	22.3848i	−0.330304	−	0.797425i
$789$	5.82843	−	2.41421i	0.207498	−	0.0859483i
$790$	9.51472	+	22.9706i	0.338518	+	0.817256i
$791$	−6.34315	−	6.34315i	−0.225536	−	0.225536i
$792$	−11.6569	+	28.1421i	−0.414208	+	0.999987i
$793$	1.00000	−	1.00000i	0.0355110	−	0.0355110i
$794$	31.4853	+	13.0416i	1.11737	+	0.462830i
$795$	1.04163	+	2.51472i	0.0369428	+	0.0891879i
$796$	31.9411	−	31.9411i	1.13212	−	1.13212i
$797$	−26.0919	−	10.8076i	−0.924222	−	0.382825i	−0.130738	−	0.991417i	$-0.541735\pi$
$797$	−26.0919	−	10.8076i	−0.924222	−	0.382825i	−0.793484	+	0.608592i	$0.791735\pi$
$798$	6.14214			0.217429
$799$	−0.970563			−0.0343360
$800$	14.3431	+	14.3431i	0.507107	+	0.507107i
$801$	−29.5563			−1.04432
$802$	−4.00000			−0.141245
$803$	−40.7990	−	16.8995i	−1.43977	−	0.596370i
$804$	−6.48528	−	6.48528i	−0.228718	−	0.228718i
$805$	13.0711	+	31.5563i	0.460695	+	1.11222i
$806$	4.00000	+	1.65685i	0.140894	+	0.0583602i
$807$	−12.8995	+	12.8995i	−0.454084	+	0.454084i
$808$	9.31371	−	3.85786i	0.327655	−	0.135719i
$809$	−29.1421	−	29.1421i	−1.02458	−	1.02458i	−0.999690	−	0.0248928i	$-0.992076\pi$
$809$	−29.1421	−	29.1421i	−1.02458	−	1.02458i	−0.0248928	−	0.999690i	$-0.507924\pi$
$810$	6.45584	+	15.5858i	0.226835	+	0.547629i
$811$	−42.2635	+	17.5061i	−1.48407	+	0.614722i	−0.970017	−	0.243036i	$-0.921857\pi$
$811$	−42.2635	+	17.5061i	−1.48407	+	0.614722i	−0.514053	+	0.857758i	$0.671857\pi$
$812$	8.82843	−	3.65685i	0.309817	−	0.128330i
$813$	5.27208	−	12.7279i	0.184900	−	0.446388i
$814$	−3.41421	+	3.41421i	−0.119668	+	0.119668i
$815$			1.47309i			0.0516000i
$816$	−3.31371	+	8.00000i	−0.116003	+	0.280056i
$817$		−	20.4437i		−	0.715233i
$818$	−30.3848	−	30.3848i	−1.06238	−	1.06238i
$819$	−1.00000	+	2.41421i	−0.0349428	+	0.0843594i
$820$	−0.544156	+	1.31371i	−0.0190027	+	0.0458767i
$821$	−21.6066	+	8.94975i	−0.754076	+	0.312348i	−0.726403	−	0.687269i	$-0.758809\pi$
$821$	−21.6066	+	8.94975i	−0.754076	+	0.312348i	−0.0276723	+	0.999617i	$0.508809\pi$
$822$	12.2426	−	5.07107i	0.427011	−	0.176874i
$823$	35.9706	+	35.9706i	1.25385	+	1.25385i	0.953978	+	0.299877i	$0.0969457\pi$
$823$	35.9706	+	35.9706i	1.25385	+	1.25385i	0.299877	+	0.953978i	$0.403054\pi$
$824$	26.8284	+	26.8284i	0.934613	+	0.934613i
$825$	−8.65685	+	8.65685i	−0.301393	+	0.301393i
$826$	−3.75736	+	9.07107i	−0.130735	+	0.315623i
$827$	16.1213	+	38.9203i	0.560593	+	1.35339i	0.909293	+	0.416157i	$0.136623\pi$
$827$	16.1213	+	38.9203i	0.560593	+	1.35339i	−0.348699	+	0.937235i	$0.613377\pi$
$828$			39.7990i			1.38311i
$829$	34.1924	+	14.1630i	1.18755	+	0.491900i	0.886957	−	0.461853i	$-0.152815\pi$
$829$	34.1924	+	14.1630i	1.18755	+	0.491900i	0.300594	+	0.953752i	$0.402815\pi$
$830$		−	20.3431i		−	0.706121i
$831$	−1.41421			−0.0490585
$832$	−2.34315	+	5.65685i	−0.0812340	+	0.196116i
$833$	14.1421			0.489996
$834$			15.4558i			0.535192i
$835$	56.1127	+	23.2426i	1.94186	+	0.804345i
$836$		−	35.7990i		−	1.23813i
$837$	−6.34315	−	15.3137i	−0.219251	−	0.529319i
$838$	7.38478	−	17.8284i	0.255103	−	0.615873i
$839$	9.68629	−	9.68629i	0.334408	−	0.334408i	−0.519850	−	0.854258i	$-0.674012\pi$
$839$	9.68629	−	9.68629i	0.334408	−	0.334408i	0.854258	+	0.519850i	$0.174012\pi$
$840$	6.34315	−	6.34315i	0.218859	−	0.218859i
$841$	−12.4350	−	12.4350i	−0.428794	−	0.428794i
$842$	21.4853	−	8.89949i	0.740432	−	0.306697i
$843$	11.8284	−	4.89949i	0.407393	−	0.168748i
$844$	−15.0711	+	36.3848i	−0.518768	+	1.25242i
$845$	−13.9203	+	33.6066i	−0.478873	+	1.15610i
$846$	0.828427	+	0.828427i	0.0284819	+	0.0284819i
$847$		−	12.5858i		−	0.432453i
$848$	−4.48528	+	1.85786i	−0.154025	+	0.0637993i
$849$		−	11.5563i		−	0.396613i
$850$	10.1421	−	10.1421i	0.347872	−	0.347872i
$851$	−2.41421	+	5.82843i	−0.0827582	+	0.199796i
$852$	−11.6569	+	4.82843i	−0.399357	+	0.165419i
$853$	51.1630	−	21.1924i	1.75179	−	0.725614i	0.754164	−	0.656686i	$-0.228042\pi$
$853$	51.1630	−	21.1924i	1.75179	−	0.725614i	0.997622	−	0.0689279i	$-0.0219579\pi$
$854$	−1.41421	−	3.41421i	−0.0483934	−	0.116832i
$855$	−20.0711	−	20.0711i	−0.686416	−	0.686416i
$856$	−4.82843	−	11.6569i	−0.165032	−	0.398423i
$857$	9.68629	−	9.68629i	0.330877	−	0.330877i	−0.522042	−	0.852920i	$-0.674830\pi$
$857$	9.68629	−	9.68629i	0.330877	−	0.330877i	0.852920	+	0.522042i	$0.174830\pi$
$858$	−3.41421	−	1.41421i	−0.116559	−	0.0482805i
$859$	−1.67767	−	4.05025i	−0.0572413	−	0.138193i	0.892671	−	0.450708i	$-0.148828\pi$
$859$	−1.67767	−	4.05025i	−0.0572413	−	0.138193i	−0.949913	+	0.312515i	$0.898828\pi$
$860$	−21.1127	−	21.1127i	−0.719937	−	0.719937i
$861$	0.242641	+	0.100505i	0.00826917	+	0.00342520i
$862$	−17.4558			−0.594548
$863$	21.9411			0.746885			0.373442	−	0.927653i	$-0.378177\pi$
$863$	21.9411			0.746885			0.373442	+	0.927653i	$0.378177\pi$
$864$	21.6569	−	8.97056i	0.736781	−	0.305185i
$865$	23.8995			0.812607
$866$	−21.9411			−0.745590
$867$	−6.36396	−	2.63604i	−0.216131	−	0.0895246i
$868$	8.00000	−	8.00000i	0.271538	−	0.271538i
$869$	−10.2426	−	24.7279i	−0.347458	−	0.838837i
$870$	9.89949	+	4.10051i	0.335624	+	0.139020i
$871$	−3.24264	+	3.24264i	−0.109873	+	0.109873i
$872$	−38.9706	−	16.1421i	−1.31971	−	0.546642i
$873$	31.5563	+	31.5563i	1.06802	+	1.06802i
$874$	−17.8995	−	43.2132i	−0.605459	−	1.46171i
$875$	5.41421	−	2.24264i	0.183034	−	0.0758151i
$876$	5.79899	+	14.0000i	0.195930	+	0.473016i
$877$	−0.736544	+	1.77817i	−0.0248713	+	0.0600447i	−0.935827	−	0.352459i	$-0.885346\pi$
$877$	−0.736544	+	1.77817i	−0.0248713	+	0.0600447i	0.910956	+	0.412504i	$0.135346\pi$
$878$	−24.0416	+	24.0416i	−0.811366	+	0.811366i
$879$		−	19.2132i		−	0.648045i
$880$	−36.9706	−	36.9706i	−1.24628	−	1.24628i
$881$			22.6274i			0.762337i	0.924506	+	0.381169i	$0.124478\pi$
$881$			22.6274i			0.762337i	−0.924506	+	0.381169i	$0.875522\pi$
$882$	−12.0711	−	12.0711i	−0.406454	−	0.406454i
$883$	20.5650	−	49.6482i	0.692066	−	1.67080i	−0.0485090	−	0.998823i	$-0.515447\pi$
$883$	20.5650	−	49.6482i	0.692066	−	1.67080i	0.740575	−	0.671973i	$-0.234553\pi$
$884$	4.00000	+	1.65685i	0.134535	+	0.0557260i
$885$	−10.1716	+	4.21320i	−0.341914	+	0.141625i
$886$	2.07107	−	0.857864i	0.0695789	−	0.0288205i
$887$	2.31371	+	2.31371i	0.0776867	+	0.0776867i	0.744882	−	0.667196i	$-0.232506\pi$
$887$	2.31371	+	2.31371i	0.0776867	+	0.0776867i	−0.667196	+	0.744882i	$0.732506\pi$
$888$	1.65685			0.0556004
$889$	12.9706	−	12.9706i	0.435019	−	0.435019i
$890$	19.4142	−	46.8701i	0.650766	−	1.57109i
$891$	−6.94975	−	16.7782i	−0.232825	−	0.562090i
$892$	41.9411			1.40429
$893$	−1.27208	−	0.526912i	−0.0425685	−	0.0176324i
$894$		−	18.2843i		−	0.611518i
$895$	−12.5269			−0.418728
$896$	11.3137	+	11.3137i	0.377964	+	0.377964i
$897$	−4.82843			−0.161216
$898$			27.5147i			0.918178i
$899$	12.4853	+	5.17157i	0.416407	+	0.172482i
$900$	−17.3137			−0.577124
$901$	1.31371	+	3.17157i	0.0437660	+	0.105660i
$902$	0.585786	−	1.41421i	0.0195046	−	0.0470882i
$903$	−3.89949	+	3.89949i	−0.129767	+	0.129767i
$904$	17.9411			0.596713
$905$	36.3137	+	36.3137i	1.20711	+	1.20711i
$906$	2.10051	−	0.870058i	0.0697846	−	0.0289057i
$907$	−15.7782	+	6.53553i	−0.523906	+	0.217009i	−0.628932	−	0.777461i	$-0.716507\pi$
$907$	−15.7782	+	6.53553i	−0.523906	+	0.217009i	0.105026	+	0.994469i	$0.466507\pi$
$908$	−37.2132	−	15.4142i	−1.23496	−	0.511539i
$909$	−3.29289	+	7.94975i	−0.109218	+	0.263676i
$910$	−3.17157	−	3.17157i	−0.105137	−	0.105137i
$911$			33.5980i			1.11315i	0.830797	+	0.556575i	$0.187885\pi$
$911$			33.5980i			1.11315i	−0.830797	+	0.556575i	$0.812115\pi$
$912$	−8.68629	+	8.68629i	−0.287632	+	0.287632i
$913$			21.8995i			0.724767i
$914$	−10.5858	+	10.5858i	−0.350147	+	0.350147i
$915$	1.58579	−	3.82843i	0.0524245	−	0.126564i
$916$	18.4437	+	44.5269i	0.609395	+	1.47121i
$917$	−23.1421	+	9.58579i	−0.764221	+	0.316551i
$918$	−6.34315	−	15.3137i	−0.209355	−	0.505428i
$919$	−8.51472	−	8.51472i	−0.280875	−	0.280875i	0.552583	−	0.833458i	$-0.313642\pi$
$919$	−8.51472	−	8.51472i	−0.280875	−	0.280875i	−0.833458	+	0.552583i	$0.813642\pi$
$920$	−63.1127	−	26.1421i	−2.08076	−	0.861881i
$921$	9.82843	−	9.82843i	0.323858	−	0.323858i
$922$	−2.17157	−	0.899495i	−0.0715169	−	0.0296233i
$923$	2.41421	+	5.82843i	0.0794648	+	0.191845i
$924$	−6.82843	+	6.82843i	−0.224639	+	0.224639i
$925$	−2.53553	−	1.05025i	−0.0833678	−	0.0345321i
$926$	32.4853			1.06753
$927$	−32.3848			−1.06366
$928$	−7.31371	+	17.6569i	−0.240084	+	0.579615i
$929$	−9.51472			−0.312168			−0.156084	−	0.987744i	$-0.549887\pi$
$929$	−9.51472			−0.312168			−0.156084	+	0.987744i	$0.549887\pi$
$930$	12.6863			0.416000
$931$	18.5355	+	7.67767i	0.607478	+	0.251625i
$932$	5.31371	+	5.31371i	0.174056	+	0.174056i
$933$	1.10051	+	2.65685i	0.0360289	+	0.0869815i
$934$	31.0416	+	12.8579i	1.01571	+	0.420722i
$935$	−26.1421	+	26.1421i	−0.854939	+	0.854939i
$936$	−2.00000	−	4.82843i	−0.0653720	−	0.157822i
$937$	19.0000	+	19.0000i	0.620703	+	0.620703i	0.945711	−	0.325008i	$-0.105367\pi$
$937$	19.0000	+	19.0000i	0.620703	+	0.620703i	−0.325008	+	0.945711i	$0.605367\pi$
$938$	4.58579	+	11.0711i	0.149731	+	0.361483i
$939$	7.48528	−	3.10051i	0.244273	−	0.101181i
$940$	−1.85786	+	0.769553i	−0.0605969	+	0.0251000i
$941$	0.636039	−	1.53553i	0.0207343	−	0.0500570i	−0.913173	−	0.407571i	$-0.866376\pi$
$941$	0.636039	−	1.53553i	0.0207343	−	0.0500570i	0.933908	+	0.357514i	$0.116376\pi$
$942$	−1.41421	+	1.41421i	−0.0460776	+	0.0460776i
$943$		−	2.00000i		−	0.0651290i
$944$	−7.51472	−	18.1421i	−0.244583	−	0.590476i
$945$			17.1716i			0.558591i
$946$	22.7279	+	22.7279i	0.738948	+	0.738948i
$947$	9.33452	−	22.5355i	0.303331	−	0.732306i	−0.696559	−	0.717499i	$-0.745287\pi$
$947$	9.33452	−	22.5355i	0.303331	−	0.732306i	0.999890	−	0.0148070i	$-0.00471340\pi$
$948$	−3.51472	+	8.48528i	−0.114153	+	0.275589i
$949$	7.00000	−	2.89949i	0.227230	−	0.0941216i
$950$	18.7990	−	7.78680i	0.609920	−	0.252637i
$951$	−10.1716	−	10.1716i	−0.329836	−	0.329836i
$952$	8.00000	−	8.00000i	0.259281	−	0.259281i
$953$	14.6569	−	14.6569i	0.474782	−	0.474782i	−0.428676	−	0.903458i	$-0.641020\pi$
$953$	14.6569	−	14.6569i	0.474782	−	0.474782i	0.903458	+	0.428676i	$0.141020\pi$
$954$	1.58579	−	3.82843i	0.0513417	−	0.123950i
$955$	−13.4558	−	32.4853i	−0.435421	−	1.05120i
$956$			10.6274i			0.343715i
$957$	−10.6569	−	4.41421i	−0.344487	−	0.142691i
$958$		−	40.9706i		−	1.32370i
$959$	−17.3137			−0.559089
$960$			17.9411i			0.579047i
$961$	−15.0000			−0.483871
$962$		−	0.828427i		−	0.0267096i
$963$	9.94975	+	4.12132i	0.320626	+	0.132808i
$964$			16.9706i			0.546585i
$965$	−1.69848	−	4.10051i	−0.0546762	−	0.132000i
$966$	−4.82843	+	11.6569i	−0.155352	+	0.375053i
$967$	−6.02944	+	6.02944i	−0.193894	+	0.193894i	−0.797376	−	0.603483i	$-0.793779\pi$
$967$	−6.02944	+	6.02944i	−0.193894	+	0.193894i	0.603483	+	0.797376i	$0.293779\pi$
$968$	17.7990	+	17.7990i	0.572081	+	0.572081i
$969$	6.14214	+	6.14214i	0.197314	+	0.197314i
$970$	−70.7696	+	29.3137i	−2.27227	+	0.941206i
$971$	22.3640	−	9.26346i	0.717694	−	0.297278i	0.00620964	−	0.999981i	$-0.498023\pi$
$971$	22.3640	−	9.26346i	0.717694	−	0.297278i	0.711484	+	0.702702i	$0.248023\pi$
$972$	−11.8995	+	28.7279i	−0.381676	+	0.921449i
$973$	7.72792	−	18.6569i	0.247746	−	0.598111i
$974$	15.5563	+	15.5563i	0.498458	+	0.498458i
$975$		−	2.10051i		−	0.0672700i
$976$	6.82843	+	2.82843i	0.218573	+	0.0905357i
$977$			14.1421i			0.452447i	0.974075	+	0.226224i	$0.0726380\pi$
$977$			14.1421i			0.452447i	−0.974075	+	0.226224i	$0.927362\pi$
$978$	−0.384776	+	0.384776i	−0.0123038	+	0.0123038i
$979$	−20.8995	+	50.4558i	−0.667951	+	1.61258i
$980$	27.0711	−	11.2132i	0.864754	−	0.358193i
$981$	33.2635	−	13.7782i	1.06202	−	0.439903i
$982$	−23.0416	−	55.6274i	−0.735288	−	1.77514i
$983$	−19.6274	−	19.6274i	−0.626017	−	0.626017i	0.321046	−	0.947064i	$-0.395966\pi$
$983$	−19.6274	−	19.6274i	−0.626017	−	0.626017i	−0.947064	+	0.321046i	$0.895966\pi$
$984$	−0.485281	+	0.201010i	−0.0154702	+	0.00640797i
$985$	−25.1005	+	25.1005i	−0.799769	+	0.799769i
$986$	12.4853	+	5.17157i	0.397612	+	0.164696i
$987$	0.142136	+	0.343146i	0.00452423	+	0.0109224i
$988$	4.34315	+	4.34315i	0.138174	+	0.138174i
$989$	38.7990	+	16.0711i	1.23374	+	0.511030i
$990$	44.6274			1.41835
$991$	−16.0000			−0.508257			−0.254128	−	0.967170i	$-0.581789\pi$
$991$	−16.0000			−0.508257			−0.254128	+	0.967170i	$0.581789\pi$
$992$			22.6274i			0.718421i
$993$	1.07107			0.0339893
$994$	16.4853			0.522881
$995$	−61.1421	−	25.3259i	−1.93834	−	0.802885i
$996$	5.31371	−	5.31371i	0.168371	−	0.168371i
$997$	−20.1924	−	48.7487i	−0.639499	−	1.54389i	−0.827348	−	0.561690i	$-0.810151\pi$
$997$	−20.1924	−	48.7487i	−0.639499	−	1.54389i	0.187848	−	0.982198i	$-0.439849\pi$
$998$	3.24264	+	1.34315i	0.102644	+	0.0425165i
$999$	−2.24264	+	2.24264i	−0.0709540	+	0.0709540i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	32.2.g.a.29.1	yes	4
3.2	odd	2		288.2.v.a.253.1		4
4.3	odd	2		128.2.g.a.81.1		4
5.2	odd	4		800.2.ba.a.349.1		4
5.3	odd	4		800.2.ba.b.349.1		4
5.4	even	2		800.2.y.a.701.1		4
8.3	odd	2		256.2.g.a.161.1		4
8.5	even	2		256.2.g.b.161.1		4
12.11	even	2		1152.2.v.a.721.1		4
16.3	odd	4		512.2.g.b.65.1		4
16.5	even	4		512.2.g.a.65.1		4
16.11	odd	4		512.2.g.c.65.1		4
16.13	even	4		512.2.g.d.65.1		4
32.3	odd	8		512.2.g.c.449.1		4
32.5	even	8		256.2.g.b.97.1		4
32.11	odd	8		128.2.g.a.49.1		4
32.13	even	8		512.2.g.d.449.1		4
32.19	odd	8		512.2.g.b.449.1		4
32.21	even	8	inner	32.2.g.a.21.1	✓	4
32.27	odd	8		256.2.g.a.97.1		4
32.29	even	8		512.2.g.a.449.1		4
64.11	odd	16		4096.2.a.f.1.3		4
64.21	even	16		4096.2.a.e.1.3		4
64.43	odd	16		4096.2.a.f.1.2		4
64.53	even	16		4096.2.a.e.1.2		4
96.11	even	8		1152.2.v.a.433.1		4
96.53	odd	8		288.2.v.a.181.1		4
160.53	odd	8		800.2.ba.a.149.1		4
160.117	odd	8		800.2.ba.b.149.1		4
160.149	even	8		800.2.y.a.501.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.2.g.a.21.1	✓	4	32.21	even	8	inner
32.2.g.a.29.1	yes	4	1.1	even	1	trivial
128.2.g.a.49.1		4	32.11	odd	8
128.2.g.a.81.1		4	4.3	odd	2
256.2.g.a.97.1		4	32.27	odd	8
256.2.g.a.161.1		4	8.3	odd	2
256.2.g.b.97.1		4	32.5	even	8
256.2.g.b.161.1		4	8.5	even	2
288.2.v.a.181.1		4	96.53	odd	8
288.2.v.a.253.1		4	3.2	odd	2
512.2.g.a.65.1		4	16.5	even	4
512.2.g.a.449.1		4	32.29	even	8
512.2.g.b.65.1		4	16.3	odd	4
512.2.g.b.449.1		4	32.19	odd	8
512.2.g.c.65.1		4	16.11	odd	4
512.2.g.c.449.1		4	32.3	odd	8
512.2.g.d.65.1		4	16.13	even	4
512.2.g.d.449.1		4	32.13	even	8
800.2.y.a.501.1		4	160.149	even	8
800.2.y.a.701.1		4	5.4	even	2
800.2.ba.a.149.1		4	160.53	odd	8
800.2.ba.a.349.1		4	5.2	odd	4
800.2.ba.b.149.1		4	160.117	odd	8
800.2.ba.b.349.1		4	5.3	odd	4
1152.2.v.a.433.1		4	96.11	even	8
1152.2.v.a.721.1		4	12.11	even	2
4096.2.a.e.1.2		4	64.53	even	16
4096.2.a.e.1.3		4	64.21	even	16
4096.2.a.f.1.2		4	64.43	odd	16
4096.2.a.f.1.3		4	64.11	odd	16

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:	\( N \)	\(=\)	\( 32 = 2^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	32.g (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q-1.41421i q^{2} +(-0.707107 - 0.292893i) q^{3} -2.00000 q^{4} +(1.12132 + 2.70711i) q^{5} +(-0.414214 + 1.00000i) q^{6} +(1.00000 - 1.00000i) q^{7} +2.82843i q^{8} +(-1.70711 - 1.70711i) q^{9} +O(q^{10})\)	\(q-1.41421i q^{2} +(-0.707107 - 0.292893i) q^{3} -2.00000 q^{4} +(1.12132 + 2.70711i) q^{5} +(-0.414214 + 1.00000i) q^{6} +(1.00000 - 1.00000i) q^{7} +2.82843i q^{8} +(-1.70711 - 1.70711i) q^{9} +(3.82843 - 1.58579i) q^{10} +(-4.12132 + 1.70711i) q^{11} +(1.41421 + 0.585786i) q^{12} +(0.292893 - 0.707107i) q^{13} +(-1.41421 - 1.41421i) q^{14} -2.24264i q^{15} +4.00000 q^{16} -2.82843i q^{17} +(-2.41421 + 2.41421i) q^{18} +(1.53553 - 3.70711i) q^{19} +(-2.24264 - 5.41421i) q^{20} +(-1.00000 + 0.414214i) q^{21} +(2.41421 + 5.82843i) q^{22} +(5.82843 + 5.82843i) q^{23} +(0.828427 - 2.00000i) q^{24} +(-2.53553 + 2.53553i) q^{25} +(-1.00000 - 0.414214i) q^{26} +(1.58579 + 3.82843i) q^{27} +(-2.00000 + 2.00000i) q^{28} +(-3.12132 - 1.29289i) q^{29} -3.17157 q^{30} -4.00000 q^{31} -5.65685i q^{32} +3.41421 q^{33} -4.00000 q^{34} +(3.82843 + 1.58579i) q^{35} +(3.41421 + 3.41421i) q^{36} +(0.292893 + 0.707107i) q^{37} +(-5.24264 - 2.17157i) q^{38} +(-0.414214 + 0.414214i) q^{39} +(-7.65685 + 3.17157i) q^{40} +(-0.171573 - 0.171573i) q^{41} +(0.585786 + 1.41421i) q^{42} +(4.70711 - 1.94975i) q^{43} +(8.24264 - 3.41421i) q^{44} +(2.70711 - 6.53553i) q^{45} +(8.24264 - 8.24264i) q^{46} -0.343146i q^{47} +(-2.82843 - 1.17157i) q^{48} +5.00000i q^{49} +(3.58579 + 3.58579i) q^{50} +(-0.828427 + 2.00000i) q^{51} +(-0.585786 + 1.41421i) q^{52} +(-1.12132 + 0.464466i) q^{53} +(5.41421 - 2.24264i) q^{54} +(-9.24264 - 9.24264i) q^{55} +(2.82843 + 2.82843i) q^{56} +(-2.17157 + 2.17157i) q^{57} +(-1.82843 + 4.41421i) q^{58} +(-1.87868 - 4.53553i) q^{59} +4.48528i q^{60} +(1.70711 + 0.707107i) q^{61} +5.65685i q^{62} -3.41421 q^{63} -8.00000 q^{64} +2.24264 q^{65} -4.82843i q^{66} +(-5.53553 - 2.29289i) q^{67} +5.65685i q^{68} +(-2.41421 - 5.82843i) q^{69} +(2.24264 - 5.41421i) q^{70} +(-5.82843 + 5.82843i) q^{71} +(4.82843 - 4.82843i) q^{72} +(7.00000 + 7.00000i) q^{73} +(1.00000 - 0.414214i) q^{74} +(2.53553 - 1.05025i) q^{75} +(-3.07107 + 7.41421i) q^{76} +(-2.41421 + 5.82843i) q^{77} +(0.585786 + 0.585786i) q^{78} +6.00000i q^{79} +(4.48528 + 10.8284i) q^{80} +4.07107i q^{81} +(-0.242641 + 0.242641i) q^{82} +(1.87868 - 4.53553i) q^{83} +(2.00000 - 0.828427i) q^{84} +(7.65685 - 3.17157i) q^{85} +(-2.75736 - 6.65685i) q^{86} +(1.82843 + 1.82843i) q^{87} +(-4.82843 - 11.6569i) q^{88} +(8.65685 - 8.65685i) q^{89} +(-9.24264 - 3.82843i) q^{90} +(-0.414214 - 1.00000i) q^{91} +(-11.6569 - 11.6569i) q^{92} +(2.82843 + 1.17157i) q^{93} -0.485281 q^{94} +11.7574 q^{95} +(-1.65685 + 4.00000i) q^{96} -18.4853 q^{97} +7.07107 q^{98} +(9.94975 + 4.12132i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 8 q^{4} - 4 q^{5} + 4 q^{6} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 4 * q - 8 * q^4 - 4 * q^5 + 4 * q^6 + 4 * q^7 - 4 * q^9	\( 4 q - 8 q^{4} - 4 q^{5} + 4 q^{6} + 4 q^{7} - 4 q^{9} + 4 q^{10} - 8 q^{11} + 4 q^{13} + 16 q^{16} - 4 q^{18} - 8 q^{19} + 8 q^{20} - 4 q^{21} + 4 q^{22} + 12 q^{23} - 8 q^{24} + 4 q^{25} - 4 q^{26} + 12 q^{27} - 8 q^{28} - 4 q^{29} - 24 q^{30} - 16 q^{31} + 8 q^{33} - 16 q^{34} + 4 q^{35} + 8 q^{36} + 4 q^{37} - 4 q^{38} + 4 q^{39} - 8 q^{40} - 12 q^{41} + 8 q^{42} + 16 q^{43} + 16 q^{44} + 8 q^{45} + 16 q^{46} + 20 q^{50} + 8 q^{51} - 8 q^{52} + 4 q^{53} + 16 q^{54} - 20 q^{55} - 20 q^{57} + 4 q^{58} - 16 q^{59} + 4 q^{61} - 8 q^{63} - 32 q^{64} - 8 q^{65} - 8 q^{67} - 4 q^{69} - 8 q^{70} - 12 q^{71} + 8 q^{72} + 28 q^{73} + 4 q^{74} - 4 q^{75} + 16 q^{76} - 4 q^{77} + 8 q^{78} - 16 q^{80} + 16 q^{82} + 16 q^{83} + 8 q^{84} + 8 q^{85} - 28 q^{86} - 4 q^{87} - 8 q^{88} + 12 q^{89} - 20 q^{90} + 4 q^{91} - 24 q^{92} + 32 q^{94} + 64 q^{95} + 16 q^{96} - 40 q^{97} + 20 q^{99}+O(q^{100}) \) 4 * q - 8 * q^4 - 4 * q^5 + 4 * q^6 + 4 * q^7 - 4 * q^9 + 4 * q^10 - 8 * q^11 + 4 * q^13 + 16 * q^16 - 4 * q^18 - 8 * q^19 + 8 * q^20 - 4 * q^21 + 4 * q^22 + 12 * q^23 - 8 * q^24 + 4 * q^25 - 4 * q^26 + 12 * q^27 - 8 * q^28 - 4 * q^29 - 24 * q^30 - 16 * q^31 + 8 * q^33 - 16 * q^34 + 4 * q^35 + 8 * q^36 + 4 * q^37 - 4 * q^38 + 4 * q^39 - 8 * q^40 - 12 * q^41 + 8 * q^42 + 16 * q^43 + 16 * q^44 + 8 * q^45 + 16 * q^46 + 20 * q^50 + 8 * q^51 - 8 * q^52 + 4 * q^53 + 16 * q^54 - 20 * q^55 - 20 * q^57 + 4 * q^58 - 16 * q^59 + 4 * q^61 - 8 * q^63 - 32 * q^64 - 8 * q^65 - 8 * q^67 - 4 * q^69 - 8 * q^70 - 12 * q^71 + 8 * q^72 + 28 * q^73 + 4 * q^74 - 4 * q^75 + 16 * q^76 - 4 * q^77 + 8 * q^78 - 16 * q^80 + 16 * q^82 + 16 * q^83 + 8 * q^84 + 8 * q^85 - 28 * q^86 - 4 * q^87 - 8 * q^88 + 12 * q^89 - 20 * q^90 + 4 * q^91 - 24 * q^92 + 32 * q^94 + 64 * q^95 + 16 * q^96 - 40 * q^97 + 20 * q^99

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