LMFDB - Embedded newform 800.2.ba.a.149.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [800,2,Mod(149,800)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(800, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 5, 4]))

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

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

chi := DirichletCharacter("800.149");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 800 = 2^{5} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	800.ba (of order $8$, degree $4$, not 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:	$6.38803216170$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 32)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			149.1
Root			$-0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	800.149
Dual form			800.2.ba.a.349.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/800\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$577$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$1$	$-1$

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 $

$2$	1.41421			1.00000
$2$	1.41421			1.00000
$3$	−0.292893	−	0.707107i	−0.169102	−	0.408248i	0.816497	−	0.577350i	$-0.195913\pi$
$3$	−0.292893	−	0.707107i	−0.169102	−	0.408248i	−0.985599	+	0.169102i	$0.945913\pi$
$4$	2.00000			1.00000
$5$		0			0
$5$		0			0
$6$	−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	$0.163881\pi$
$8$	2.82843			1.00000
$9$	1.70711	−	1.70711i	0.569036	−	0.569036i
$10$		0			0
$11$	−4.12132	−	1.70711i	−1.24262	−	0.514712i	−0.338091	−	0.941113i	$-0.609781\pi$
$11$	−4.12132	−	1.70711i	−1.24262	−	0.514712i	−0.904534	+	0.426401i	$0.859781\pi$
$12$	−0.585786	−	1.41421i	−0.169102	−	0.408248i
$13$	−0.707107	+	0.292893i	−0.196116	+	0.0812340i	−0.478580	−	0.878044i	$-0.658848\pi$
$13$	−0.707107	+	0.292893i	−0.196116	+	0.0812340i	0.282464	+	0.959278i	$0.408848\pi$
$14$	1.41421	−	1.41421i	0.377964	−	0.377964i
$15$		0			0
$16$	4.00000			1.00000
$17$	2.82843			0.685994			0.342997	−	0.939336i	$-0.388558\pi$
$17$	2.82843			0.685994			0.342997	+	0.939336i	$0.388558\pi$
$18$	2.41421	−	2.41421i	0.569036	−	0.569036i
$19$	−1.53553	−	3.70711i	−0.352276	−	0.850469i	−0.996339	−	0.0854961i	$-0.972752\pi$
$19$	−1.53553	−	3.70711i	−0.352276	−	0.850469i	0.644063	−	0.764973i	$-0.277248\pi$
$20$		0			0
$21$	−1.00000	−	0.414214i	−0.218218	−	0.0903888i
$22$	−5.82843	−	2.41421i	−1.24262	−	0.514712i
$23$	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
$25$		0			0
$26$	−1.00000	+	0.414214i	−0.196116	+	0.0812340i
$27$	−3.82843	−	1.58579i	−0.736781	−	0.305185i
$28$	2.00000	−	2.00000i	0.377964	−	0.377964i
$29$	3.12132	−	1.29289i	0.579615	−	0.240084i	−0.0735609	−	0.997291i	$-0.523436\pi$
$29$	3.12132	−	1.29289i	0.579615	−	0.240084i	0.653176	+	0.757206i	$0.273436\pi$
$30$		0			0
$31$	−4.00000			−0.718421			−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000			−0.718421			−0.359211	+	0.933257i	$0.616954\pi$
$32$	5.65685			1.00000
$33$			3.41421i			0.594338i
$34$	4.00000			0.685994
$35$		0			0
$36$	3.41421	−	3.41421i	0.569036	−	0.569036i
$37$	−0.707107	−	0.292893i	−0.116248	−	0.0481513i	0.323802	−	0.946125i	$-0.395039\pi$
$37$	−0.707107	−	0.292893i	−0.116248	−	0.0481513i	−0.440049	+	0.897974i	$0.645039\pi$
$38$	−2.17157	−	5.24264i	−0.352276	−	0.850469i
$39$	0.414214	+	0.414214i	0.0663273	+	0.0663273i
$40$		0			0
$41$	−0.171573	+	0.171573i	−0.0267952	+	0.0267952i	−0.720377	−	0.693582i	$-0.756031\pi$
$41$	−0.171573	+	0.171573i	−0.0267952	+	0.0267952i	0.693582	+	0.720377i	$0.256031\pi$
$42$	−1.41421	−	0.585786i	−0.218218	−	0.0903888i
$43$	−1.94975	+	4.70711i	−0.297334	+	0.717827i	0.702647	+	0.711539i	$0.252002\pi$
$43$	−1.94975	+	4.70711i	−0.297334	+	0.717827i	−0.999980	+	0.00628798i	$0.997998\pi$
$44$	−8.24264	−	3.41421i	−1.24262	−	0.514712i
$45$		0			0
$46$	8.24264	+	8.24264i	1.21531	+	1.21531i
$47$	0.343146			0.0500530			0.0250265	−	0.999687i	$-0.492033\pi$
$47$	0.343146			0.0500530			0.0250265	+	0.999687i	$0.492033\pi$
$48$	−1.17157	−	2.82843i	−0.169102	−	0.408248i
$49$			5.00000i			0.714286i
$50$		0			0
$51$	−0.828427	−	2.00000i	−0.116003	−	0.280056i
$52$	−1.41421	+	0.585786i	−0.196116	+	0.0812340i
$53$	0.464466	−	1.12132i	0.0637993	−	0.154025i	−0.888764	−	0.458364i	$-0.848436\pi$
$53$	0.464466	−	1.12132i	0.0637993	−	0.154025i	0.952564	+	0.304339i	$0.0984356\pi$
$54$	−5.41421	−	2.24264i	−0.736781	−	0.305185i
$55$		0			0
$56$	2.82843	−	2.82843i	0.377964	−	0.377964i
$57$	−2.17157	+	2.17157i	−0.287632	+	0.287632i
$58$	4.41421	−	1.82843i	0.579615	−	0.240084i
$59$	1.87868	−	4.53553i	0.244583	−	0.590476i	−0.753144	−	0.657855i	$-0.771464\pi$
$59$	1.87868	−	4.53553i	0.244583	−	0.590476i	0.997727	+	0.0673793i	$0.0214638\pi$
$60$		0			0
$61$	1.70711	−	0.707107i	0.218573	−	0.0905357i	−0.270710	−	0.962661i	$-0.587259\pi$
$61$	1.70711	−	0.707107i	0.218573	−	0.0905357i	0.489283	+	0.872125i	$0.337259\pi$
$62$	−5.65685			−0.718421
$63$		−	3.41421i		−	0.430150i
$64$	8.00000			1.00000
$65$		0			0
$66$			4.82843i			0.594338i
$67$	2.29289	+	5.53553i	0.280121	+	0.676273i	0.999838	−	0.0179949i	$-0.00572826\pi$
$67$	2.29289	+	5.53553i	0.280121	+	0.676273i	−0.719717	+	0.694268i	$0.755728\pi$
$68$	5.65685			0.685994
$69$	2.41421	−	5.82843i	0.290637	−	0.701660i
$70$		0			0
$71$	−5.82843	−	5.82843i	−0.691707	−	0.691707i	0.270900	−	0.962607i	$-0.412679\pi$
$71$	−5.82843	−	5.82843i	−0.691707	−	0.691707i	−0.962607	+	0.270900i	$0.912679\pi$
$72$	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
$75$		0			0
$76$	−3.07107	−	7.41421i	−0.352276	−	0.850469i
$77$	−5.82843	+	2.41421i	−0.664211	+	0.275125i
$78$	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	$0.890410\pi$
$80$		0			0
$81$		−	4.07107i		−	0.452341i
$82$	−0.242641	+	0.242641i	−0.0267952	+	0.0267952i
$83$	−4.53553	+	1.87868i	−0.497840	+	0.206212i	−0.617452	−	0.786609i	$-0.711835\pi$
$83$	−4.53553	+	1.87868i	−0.497840	+	0.206212i	0.119612	+	0.992821i	$0.461835\pi$
$84$	−2.00000	−	0.828427i	−0.218218	−	0.0903888i
$85$		0			0
$86$	−2.75736	+	6.65685i	−0.297334	+	0.717827i
$87$	−1.82843	−	1.82843i	−0.196028	−	0.196028i
$88$	−11.6569	−	4.82843i	−1.24262	−	0.514712i
$89$	−8.65685	−	8.65685i	−0.917625	−	0.917625i	0.0792315	−	0.996856i	$-0.474753\pi$
$89$	−8.65685	−	8.65685i	−0.917625	−	0.917625i	−0.996856	+	0.0792315i	$0.974753\pi$
$90$		0			0
$91$	−0.414214	+	1.00000i	−0.0434214	+	0.104828i
$92$	11.6569	+	11.6569i	1.21531	+	1.21531i
$93$	1.17157	+	2.82843i	0.121486	+	0.293294i
$94$	0.485281			0.0500530
$95$		0			0
$96$	−1.65685	−	4.00000i	−0.169102	−	0.408248i
$97$			18.4853i			1.87690i	0.345421	+	0.938448i	$0.387736\pi$
$97$			18.4853i			1.87690i	−0.345421	+	0.938448i	$0.612264\pi$
$98$			7.07107i			0.714286i
$99$	−9.94975	+	4.12132i	−0.999987	+	0.414208i
$100$		0			0
$101$	−1.36396	+	3.29289i	−0.135719	+	0.327655i	−0.977098	−	0.212791i	$-0.931745\pi$
$101$	−1.36396	+	3.29289i	−0.135719	+	0.327655i	0.841379	+	0.540446i	$0.181745\pi$
$102$	−1.17157	−	2.82843i	−0.116003	−	0.280056i
$103$	−9.48528	+	9.48528i	−0.934613	+	0.934613i	−0.997990	−	0.0633771i	$-0.979813\pi$
$103$	−9.48528	+	9.48528i	−0.934613	+	0.934613i	0.0633771	+	0.997990i	$0.479813\pi$
$104$	−2.00000	+	0.828427i	−0.196116	+	0.0812340i
$105$		0			0
$106$	0.656854	−	1.58579i	0.0637993	−	0.154025i
$107$	−1.70711	+	4.12132i	−0.165032	+	0.398423i	−0.984663	−	0.174470i	$-0.944179\pi$
$107$	−1.70711	+	4.12132i	−0.165032	+	0.398423i	0.819630	+	0.572893i	$0.194179\pi$
$108$	−7.65685	−	3.17157i	−0.736781	−	0.305185i
$109$	5.70711	+	13.7782i	0.546642	+	1.31971i	0.919962	+	0.392007i	$0.128219\pi$
$109$	5.70711	+	13.7782i	0.546642	+	1.31971i	−0.373320	+	0.927702i	$0.621781\pi$
$110$		0			0
$111$			0.585786i			0.0556004i
$112$	4.00000	−	4.00000i	0.377964	−	0.377964i
$113$	−6.34315			−0.596713			−0.298356	−	0.954455i	$-0.596438\pi$
$113$	−6.34315			−0.596713			−0.298356	+	0.954455i	$0.596438\pi$
$114$	−3.07107	+	3.07107i	−0.287632	+	0.287632i
$115$		0			0
$116$	6.24264	−	2.58579i	0.579615	−	0.240084i
$117$	−0.707107	+	1.70711i	−0.0653720	+	0.157822i
$118$	2.65685	−	6.41421i	0.244583	−	0.590476i
$119$	2.82843	−	2.82843i	0.259281	−	0.259281i
$120$		0			0
$121$	6.29289	+	6.29289i	0.572081	+	0.572081i
$122$	2.41421	−	1.00000i	0.218573	−	0.0905357i
$123$	0.171573	+	0.0710678i	0.0154702	+	0.00640797i
$124$	−8.00000			−0.718421
$125$		0			0
$126$		−	4.82843i		−	0.430150i
$127$		−	12.9706i		−	1.15095i	−0.817819	−	0.575476i	$-0.804817\pi$
$127$		−	12.9706i		−	1.15095i	0.817819	−	0.575476i	$-0.195183\pi$
$128$	11.3137			1.00000
$129$	3.89949			0.343331
$130$		0			0
$131$	−16.3640	+	6.77817i	−1.42973	+	0.592212i	−0.957284	−	0.289150i	$-0.906627\pi$
$131$	−16.3640	+	6.77817i	−1.42973	+	0.592212i	−0.472442	+	0.881362i	$0.656627\pi$
$132$			6.82843i			0.594338i
$133$	−5.24264	−	2.17157i	−0.454595	−	0.188299i
$134$	3.24264	+	7.82843i	0.280121	+	0.676273i
$135$		0			0
$136$	8.00000			0.685994
$137$	8.65685	+	8.65685i	0.739605	+	0.739605i	0.972502	−	0.232897i	$-0.0748204\pi$
$137$	8.65685	+	8.65685i	0.739605	+	0.739605i	−0.232897	+	0.972502i	$0.574820\pi$
$138$	3.41421	−	8.24264i	0.290637	−	0.701660i
$139$	−13.1924	−	5.46447i	−1.11896	−	0.463490i	−0.254948	−	0.966955i	$-0.582058\pi$
$139$	−13.1924	−	5.46447i	−1.11896	−	0.463490i	−0.864016	+	0.503465i	$0.832058\pi$
$140$		0			0
$141$	−0.100505	−	0.242641i	−0.00846405	−	0.0204340i
$142$	−8.24264	−	8.24264i	−0.691707	−	0.691707i
$143$	3.41421			0.285511
$144$	6.82843	−	6.82843i	0.569036	−	0.569036i
$145$		0			0
$146$	9.89949	+	9.89949i	0.819288	+	0.819288i
$147$	3.53553	−	1.46447i	0.291606	−	0.120787i
$148$	−1.41421	−	0.585786i	−0.116248	−	0.0481513i
$149$	15.6066	+	6.46447i	1.27854	+	0.529590i	0.915551	−	0.402203i	$-0.131755\pi$
$149$	15.6066	+	6.46447i	1.27854	+	0.529590i	0.362992	+	0.931792i	$0.381755\pi$
$150$		0			0
$151$	−1.48528	+	1.48528i	−0.120870	+	0.120870i	−0.764955	−	0.644084i	$-0.777239\pi$
$151$	−1.48528	+	1.48528i	−0.120870	+	0.120870i	0.644084	+	0.764955i	$0.277239\pi$
$152$	−4.34315	−	10.4853i	−0.352276	−	0.850469i
$153$	4.82843	−	4.82843i	0.390355	−	0.390355i
$154$	−8.24264	+	3.41421i	−0.664211	+	0.275125i
$155$		0			0
$156$	0.828427	+	0.828427i	0.0663273	+	0.0663273i
$157$	−0.707107	−	1.70711i	−0.0564333	−	0.136242i	0.893148	−	0.449763i	$-0.148491\pi$
$157$	−0.707107	−	1.70711i	−0.0564333	−	0.136242i	−0.949581	+	0.313521i	$0.898491\pi$
$158$			8.48528i			0.675053i
$159$	−0.928932			−0.0736691
$160$		0			0
$161$	11.6569			0.918689
$162$		−	5.75736i		−	0.452341i
$163$	0.192388	+	0.464466i	0.0150690	+	0.0363798i	0.931235	−	0.364419i	$-0.118733\pi$
$163$	0.192388	+	0.464466i	0.0150690	+	0.0363798i	−0.916166	+	0.400799i	$0.868733\pi$
$164$	−0.343146	+	0.343146i	−0.0267952	+	0.0267952i
$165$		0			0
$166$	−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	$-0.0462239\pi$
$168$	−2.82843	−	1.17157i	−0.218218	−	0.0903888i
$169$	−8.77817	+	8.77817i	−0.675244	+	0.675244i
$170$		0			0
$171$	−8.94975	−	3.70711i	−0.684404	−	0.283490i
$172$	−3.89949	+	9.41421i	−0.297334	+	0.717827i
$173$	−7.53553	+	3.12132i	−0.572916	+	0.237310i	−0.650282	−	0.759693i	$-0.725349\pi$
$173$	−7.53553	+	3.12132i	−0.572916	+	0.237310i	0.0773656	+	0.997003i	$0.475349\pi$
$174$	−2.58579	−	2.58579i	−0.196028	−	0.196028i
$175$		0			0
$176$	−16.4853	−	6.82843i	−1.24262	−	0.514712i
$177$	−3.75736			−0.282420
$178$	−12.2426	−	12.2426i	−0.917625	−	0.917625i
$179$	1.63604	+	3.94975i	0.122283	+	0.295218i	0.973153	−	0.230159i	$-0.0739245\pi$
$179$	1.63604	+	3.94975i	0.122283	+	0.295218i	−0.850870	+	0.525377i	$0.823924\pi$
$180$		0			0
$181$	16.1924	+	6.70711i	1.20357	+	0.498535i	0.892151	−	0.451737i	$-0.149196\pi$
$181$	16.1924	+	6.70711i	1.20357	+	0.498535i	0.311420	+	0.950272i	$0.399196\pi$
$182$	−0.585786	+	1.41421i	−0.0434214	+	0.104828i
$183$	−1.00000	−	1.00000i	−0.0739221	−	0.0739221i
$184$	16.4853	+	16.4853i	1.21531	+	1.21531i
$185$		0			0
$186$	1.65685	+	4.00000i	0.121486	+	0.293294i
$187$	−11.6569	−	4.82843i	−0.852434	−	0.353090i
$188$	0.686292			0.0500530
$189$	−5.41421	+	2.24264i	−0.393826	+	0.163128i
$190$		0			0
$191$	−12.0000			−0.868290			−0.434145	−	0.900843i	$-0.642949\pi$
$191$	−12.0000			−0.868290			−0.434145	+	0.900843i	$0.642949\pi$
$192$	−2.34315	−	5.65685i	−0.169102	−	0.408248i
$193$		−	1.51472i		−	0.109032i	−0.998513	−	0.0545159i	$-0.982638\pi$
$193$		−	1.51472i		−	0.109032i	0.998513	−	0.0545159i	$-0.0173616\pi$
$194$			26.1421i			1.87690i
$195$		0			0
$196$			10.0000i			0.714286i
$197$	−11.1924	−	4.63604i	−0.797425	−	0.330304i	−0.0535002	−	0.998568i	$-0.517038\pi$
$197$	−11.1924	−	4.63604i	−0.797425	−	0.330304i	−0.743924	+	0.668264i	$0.767038\pi$
$198$	−14.0711	+	5.82843i	−0.999987	+	0.414208i
$199$	15.9706	+	15.9706i	1.13212	+	1.13212i	0.989824	+	0.142300i	$0.0454496\pi$
$199$	15.9706	+	15.9706i	1.13212	+	1.13212i	0.142300	+	0.989824i	$0.454550\pi$
$200$		0			0
$201$	3.24264	−	3.24264i	0.228718	−	0.228718i
$202$	−1.92893	+	4.65685i	−0.135719	+	0.327655i
$203$	1.82843	−	4.41421i	0.128330	−	0.309817i
$204$	−1.65685	−	4.00000i	−0.116003	−	0.280056i
$205$		0			0
$206$	−13.4142	+	13.4142i	−0.934613	+	0.934613i
$207$	19.8995			1.38311
$208$	−2.82843	+	1.17157i	−0.196116	+	0.0812340i
$209$			17.8995i			1.23813i
$210$		0			0
$211$	7.53553	+	18.1924i	0.518768	+	1.25242i	0.938661	+	0.344842i	$0.112068\pi$
$211$	7.53553	+	18.1924i	0.518768	+	1.25242i	−0.419893	+	0.907574i	$0.637932\pi$
$212$	0.928932	−	2.24264i	0.0637993	−	0.154025i
$213$	−2.41421	+	5.82843i	−0.165419	+	0.399357i
$214$	−2.41421	+	5.82843i	−0.165032	+	0.398423i
$215$		0			0
$216$	−10.8284	−	4.48528i	−0.736781	−	0.305185i
$217$	−4.00000	+	4.00000i	−0.271538	+	0.271538i
$218$	8.07107	+	19.4853i	0.546642	+	1.31971i
$219$	2.89949	−	7.00000i	0.195930	−	0.473016i
$220$		0			0
$221$	−2.00000	+	0.828427i	−0.134535	+	0.0557260i
$222$			0.828427i			0.0556004i
$223$		−	20.9706i		−	1.40429i	−0.712033	−	0.702146i	$-0.752225\pi$
$223$		−	20.9706i		−	1.40429i	0.712033	−	0.702146i	$-0.247775\pi$
$224$	5.65685	−	5.65685i	0.377964	−	0.377964i
$225$		0			0
$226$	−8.97056			−0.596713
$227$	−7.70711	−	18.6066i	−0.511539	−	1.23496i	−0.942988	−	0.332826i	$-0.891998\pi$
$227$	−7.70711	−	18.6066i	−0.511539	−	1.23496i	0.431449	−	0.902137i	$-0.358002\pi$
$228$	−4.34315	+	4.34315i	−0.287632	+	0.287632i
$229$	9.22183	−	22.2635i	0.609395	−	1.47121i	−0.254264	−	0.967135i	$-0.581833\pi$
$229$	9.22183	−	22.2635i	0.609395	−	1.47121i	0.863659	−	0.504076i	$-0.168167\pi$
$230$		0			0
$231$	3.41421	+	3.41421i	0.224639	+	0.224639i
$232$	8.82843	−	3.65685i	0.579615	−	0.240084i
$233$	−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			0
$236$	3.75736	−	9.07107i	0.244583	−	0.590476i
$237$	4.24264	−	1.75736i	0.275589	−	0.114153i
$238$	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	$-0.0549769\pi$
$240$		0			0
$241$			8.48528i			0.546585i	0.961931	+	0.273293i	$0.0881127\pi$
$241$			8.48528i			0.546585i	−0.961931	+	0.273293i	$0.911887\pi$
$242$	8.89949	+	8.89949i	0.572081	+	0.572081i
$243$	−14.3640	+	5.94975i	−0.921449	+	0.381676i
$244$	3.41421	−	1.41421i	0.218573	−	0.0905357i
$245$		0			0
$246$	0.242641	+	0.100505i	0.0154702	+	0.00640797i
$247$	2.17157	+	2.17157i	0.138174	+	0.138174i
$248$	−11.3137			−0.718421
$249$	2.65685	+	2.65685i	0.168371	+	0.168371i
$250$		0			0
$251$	6.60660	−	15.9497i	0.417005	−	1.00674i	−0.566205	−	0.824264i	$-0.691589\pi$
$251$	6.60660	−	15.9497i	0.417005	−	1.00674i	0.983210	−	0.182475i	$-0.0584109\pi$
$252$		−	6.82843i		−	0.430150i
$253$	−14.0711	−	33.9706i	−0.884640	−	2.13571i
$254$		−	18.3431i		−	1.15095i
$255$		0			0
$256$	16.0000			1.00000
$257$		−	6.00000i		−	0.374270i	−0.982334	−	0.187135i	$-0.940080\pi$
$257$		−	6.00000i		−	0.374270i	0.982334	−	0.187135i	$-0.0599201\pi$
$258$	5.51472			0.343331
$259$	−1.00000	+	0.414214i	−0.0621370	+	0.0257380i
$260$		0			0
$261$	3.12132	−	7.53553i	0.193205	−	0.466438i
$262$	−23.1421	+	9.58579i	−1.42973	+	0.592212i
$263$	5.82843	−	5.82843i	0.359396	−	0.359396i	−0.504194	−	0.863590i	$-0.668210\pi$
$263$	5.82843	−	5.82843i	0.359396	−	0.359396i	0.863590	+	0.504194i	$0.168210\pi$
$264$			9.65685i			0.594338i
$265$		0			0
$266$	−7.41421	−	3.07107i	−0.454595	−	0.188299i
$267$	−3.58579	+	8.65685i	−0.219447	+	0.529791i
$268$	4.58579	+	11.0711i	0.280121	+	0.676273i
$269$	−9.12132	−	22.0208i	−0.556137	−	1.34263i	−0.912803	−	0.408401i	$-0.866087\pi$
$269$	−9.12132	−	22.0208i	−0.556137	−	1.34263i	0.356666	−	0.934232i	$-0.383913\pi$
$270$		0			0
$271$		−	18.0000i		−	1.09342i	−0.837321	−	0.546711i	$-0.815880\pi$
$271$		−	18.0000i		−	1.09342i	0.837321	−	0.546711i	$-0.184120\pi$
$272$	11.3137			0.685994
$273$	0.828427			0.0501387
$274$	12.2426	+	12.2426i	0.739605	+	0.739605i
$275$		0			0
$276$	4.82843	−	11.6569i	0.290637	−	0.701660i
$277$	0.707107	−	1.70711i	0.0424859	−	0.102570i	−0.901212	−	0.433378i	$-0.857321\pi$
$277$	0.707107	−	1.70711i	0.0424859	−	0.102570i	0.943698	+	0.330808i	$0.107321\pi$
$278$	−18.6569	−	7.72792i	−1.11896	−	0.463490i
$279$	−6.82843	+	6.82843i	−0.408807	+	0.408807i
$280$		0			0
$281$	−11.8284	−	11.8284i	−0.705625	−	0.705625i	0.259987	−	0.965612i	$-0.416282\pi$
$281$	−11.8284	−	11.8284i	−0.705625	−	0.705625i	−0.965612	+	0.259987i	$0.916282\pi$
$282$	−0.142136	−	0.343146i	−0.00846405	−	0.0204340i
$283$	13.9497	+	5.77817i	0.829226	+	0.343477i	0.756596	−	0.653882i	$-0.226861\pi$
$283$	13.9497	+	5.77817i	0.829226	+	0.343477i	0.0726300	+	0.997359i	$0.476861\pi$
$284$	−11.6569	−	11.6569i	−0.691707	−	0.691707i
$285$		0			0
$286$	4.82843			0.285511
$287$			0.343146i			0.0202553i
$288$	9.65685	−	9.65685i	0.569036	−	0.569036i
$289$	−9.00000			−0.529412
$290$		0			0
$291$	13.0711	−	5.41421i	0.766240	−	0.317387i
$292$	14.0000	+	14.0000i	0.819288	+	0.819288i
$293$	23.1924	+	9.60660i	1.35491	+	0.561224i	0.937656	−	0.347565i	$-0.112991\pi$
$293$	23.1924	+	9.60660i	1.35491	+	0.561224i	0.417258	+	0.908788i	$0.362991\pi$
$294$	5.00000	−	2.07107i	0.291606	−	0.120787i
$295$		0			0
$296$	−2.00000	−	0.828427i	−0.116248	−	0.0481513i
$297$	13.0711	+	13.0711i	0.758460	+	0.758460i
$298$	22.0711	+	9.14214i	1.27854	+	0.529590i
$299$	−5.82843	−	2.41421i	−0.337067	−	0.139618i
$300$		0			0
$301$	2.75736	+	6.65685i	0.158932	+	0.383695i
$302$	−2.10051	+	2.10051i	−0.120870	+	0.120870i
$303$	2.72792			0.156715
$304$	−6.14214	−	14.8284i	−0.352276	−	0.850469i
$305$		0			0
$306$	6.82843	−	6.82843i	0.390355	−	0.390355i
$307$	−16.7782	+	6.94975i	−0.957581	+	0.396643i	−0.806075	−	0.591813i	$-0.798412\pi$
$307$	−16.7782	+	6.94975i	−0.957581	+	0.396643i	−0.151506	+	0.988456i	$0.548412\pi$
$308$	−11.6569	+	4.82843i	−0.664211	+	0.275125i
$309$	9.48528	+	3.92893i	0.539599	+	0.223509i
$310$		0			0
$311$	−2.65685	+	2.65685i	−0.150656	+	0.150656i	−0.778411	−	0.627755i	$-0.783974\pi$
$311$	−2.65685	+	2.65685i	−0.150656	+	0.150656i	0.627755	+	0.778411i	$0.283974\pi$
$312$	1.17157	+	1.17157i	0.0663273	+	0.0663273i
$313$	7.48528	−	7.48528i	0.423093	−	0.423093i	−0.463174	−	0.886267i	$-0.653290\pi$
$313$	7.48528	−	7.48528i	0.423093	−	0.423093i	0.886267	+	0.463174i	$0.153290\pi$
$314$	−1.00000	−	2.41421i	−0.0564333	−	0.136242i
$315$		0			0
$316$			12.0000i			0.675053i
$317$	−7.19239	−	17.3640i	−0.403965	−	0.975257i	−0.986694	−	0.162591i	$-0.948015\pi$
$317$	−7.19239	−	17.3640i	−0.403965	−	0.975257i	0.582729	−	0.812667i	$-0.301985\pi$
$318$	−1.31371			−0.0736691
$319$	−15.0711			−0.843818
$320$		0			0
$321$	3.41421			0.190563
$322$	16.4853			0.918689
$323$	−4.34315	−	10.4853i	−0.241659	−	0.583417i
$324$		−	8.14214i		−	0.452341i
$325$		0			0
$326$	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
$330$		0			0
$331$	−1.29289	−	0.535534i	−0.0710638	−	0.0294356i	0.346868	−	0.937914i	$-0.387245\pi$
$331$	−1.29289	−	0.535534i	−0.0710638	−	0.0294356i	−0.417932	+	0.908478i	$0.637245\pi$
$332$	−9.07107	+	3.75736i	−0.497840	+	0.206212i
$333$	−1.70711	+	0.707107i	−0.0935489	+	0.0387492i
$334$	20.7279	−	20.7279i	1.13418	−	1.13418i
$335$		0			0
$336$	−4.00000	−	1.65685i	−0.218218	−	0.0903888i
$337$	16.9706			0.924445			0.462223	−	0.886764i	$-0.347052\pi$
$337$	16.9706			0.924445			0.462223	+	0.886764i	$0.347052\pi$
$338$	−12.4142	+	12.4142i	−0.675244	+	0.675244i
$339$	1.85786	+	4.48528i	0.100905	+	0.243607i
$340$		0			0
$341$	16.4853	+	6.82843i	0.892728	+	0.369780i
$342$	−12.6569	−	5.24264i	−0.684404	−	0.283490i
$343$	12.0000	+	12.0000i	0.647939	+	0.647939i
$344$	−5.51472	+	13.3137i	−0.297334	+	0.717827i
$345$		0			0
$346$	−10.6569	+	4.41421i	−0.572916	+	0.237310i
$347$	−3.94975	−	1.63604i	−0.212034	−	0.0878272i	0.274139	−	0.961690i	$-0.411607\pi$
$347$	−3.94975	−	1.63604i	−0.212034	−	0.0878272i	−0.486172	+	0.873863i	$0.661607\pi$
$348$	−3.65685	−	3.65685i	−0.196028	−	0.196028i
$349$	−24.6777	+	10.2218i	−1.32097	+	0.547162i	−0.928065	−	0.372419i	$-0.878528\pi$
$349$	−24.6777	+	10.2218i	−1.32097	+	0.547162i	−0.392901	+	0.919581i	$0.628528\pi$
$350$		0			0
$351$	3.17157			0.169286
$352$	−23.3137	−	9.65685i	−1.24262	−	0.514712i
$353$			6.00000i			0.319348i	0.987170	+	0.159674i	$0.0510443\pi$
$353$			6.00000i			0.319348i	−0.987170	+	0.159674i	$0.948956\pi$
$354$	−5.31371			−0.282420
$355$		0			0
$356$	−17.3137	−	17.3137i	−0.917625	−	0.917625i
$357$	−2.82843	−	1.17157i	−0.149696	−	0.0620062i
$358$	2.31371	+	5.58579i	0.122283	+	0.295218i
$359$	17.8284	+	17.8284i	0.940948	+	0.940948i	0.998351	−	0.0574027i	$-0.0182819\pi$
$359$	17.8284	+	17.8284i	0.940948	+	0.940948i	−0.0574027	+	0.998351i	$0.518282\pi$
$360$		0			0
$361$	2.05025	−	2.05025i	0.107908	−	0.107908i
$362$	22.8995	+	9.48528i	1.20357	+	0.498535i
$363$	2.60660	−	6.29289i	0.136811	−	0.330291i
$364$	−0.828427	+	2.00000i	−0.0434214	+	0.104828i
$365$		0			0
$366$	−1.41421	−	1.41421i	−0.0739221	−	0.0739221i
$367$	6.00000			0.313197			0.156599	−	0.987662i	$-0.449947\pi$
$367$	6.00000			0.313197			0.156599	+	0.987662i	$0.449947\pi$
$368$	23.3137	+	23.3137i	1.21531	+	1.21531i
$369$			0.585786i			0.0304948i
$370$		0			0
$371$	−0.656854	−	1.58579i	−0.0341022	−	0.0823299i
$372$	2.34315	+	5.65685i	0.121486	+	0.293294i
$373$	4.26346	−	10.2929i	0.220753	−	0.532946i	−0.774239	−	0.632893i	$-0.781867\pi$
$373$	4.26346	−	10.2929i	0.220753	−	0.532946i	0.994993	+	0.0999471i	$0.0318673\pi$
$374$	−16.4853	−	6.82843i	−0.852434	−	0.353090i
$375$		0			0
$376$	0.970563			0.0500530
$377$	−1.82843	+	1.82843i	−0.0941688	+	0.0941688i
$378$	−7.65685	+	3.17157i	−0.393826	+	0.163128i
$379$	13.6777	−	33.0208i	0.702575	−	1.69617i	−0.0151948	−	0.999885i	$-0.504837\pi$
$379$	13.6777	−	33.0208i	0.702575	−	1.69617i	0.717769	−	0.696281i	$-0.245163\pi$
$380$		0			0
$381$	−9.17157	+	3.79899i	−0.469874	+	0.194628i
$382$	−16.9706			−0.868290
$383$		−	16.9706i		−	0.867155i	−0.901116	−	0.433578i	$-0.857251\pi$
$383$		−	16.9706i		−	0.867155i	0.901116	−	0.433578i	$-0.142749\pi$
$384$	−3.31371	−	8.00000i	−0.169102	−	0.408248i
$385$		0			0
$386$		−	2.14214i		−	0.109032i
$387$	4.70711	+	11.3640i	0.239276	+	0.577663i
$388$			36.9706i			1.87690i
$389$	8.39340	−	20.2635i	0.425562	−	1.02740i	−0.555117	−	0.831773i	$-0.687326\pi$
$389$	8.39340	−	20.2635i	0.425562	−	1.02740i	0.980679	−	0.195625i	$-0.0626737\pi$
$390$		0			0
$391$	16.4853	+	16.4853i	0.833697	+	0.833697i
$392$			14.1421i			0.714286i
$393$	9.58579	+	9.58579i	0.483539	+	0.483539i
$394$	−15.8284	−	6.55635i	−0.797425	−	0.330304i
$395$		0			0
$396$	−19.8995	+	8.24264i	−0.999987	+	0.414208i
$397$	−22.2635	+	9.22183i	−1.11737	+	0.462830i	−0.863470	−	0.504400i	$-0.831714\pi$
$397$	−22.2635	+	9.22183i	−1.11737	+	0.462830i	−0.253901	+	0.967230i	$0.581714\pi$
$398$	22.5858	+	22.5858i	1.13212	+	1.13212i
$399$			4.34315i			0.217429i
$400$		0			0
$401$			2.82843i			0.141245i	0.997503	+	0.0706225i	$0.0224986\pi$
$401$			2.82843i			0.141245i	−0.997503	+	0.0706225i	$0.977501\pi$
$402$	4.58579	−	4.58579i	0.228718	−	0.228718i
$403$	2.82843	−	1.17157i	0.140894	−	0.0583602i
$404$	−2.72792	+	6.58579i	−0.135719	+	0.327655i
$405$		0			0
$406$	2.58579	−	6.24264i	0.128330	−	0.309817i
$407$	2.41421	+	2.41421i	0.119668	+	0.119668i
$408$	−2.34315	−	5.65685i	−0.116003	−	0.280056i
$409$	−21.4853	−	21.4853i	−1.06238	−	1.06238i	−0.997920	−	0.0644584i	$-0.979468\pi$
$409$	−21.4853	−	21.4853i	−1.06238	−	1.06238i	−0.0644584	−	0.997920i	$-0.520532\pi$
$410$		0			0
$411$	3.58579	−	8.65685i	0.176874	−	0.427011i
$412$	−18.9706	+	18.9706i	−0.934613	+	0.934613i
$413$	−2.65685	−	6.41421i	−0.130735	−	0.315623i
$414$	28.1421			1.38311
$415$		0			0
$416$	−4.00000	+	1.65685i	−0.196116	+	0.0812340i
$417$			10.9289i			0.535192i
$418$			25.3137i			1.23813i
$419$	−12.6066	+	5.22183i	−0.615873	+	0.255103i	−0.668737	−	0.743499i	$-0.733165\pi$
$419$	−12.6066	+	5.22183i	−0.615873	+	0.255103i	0.0528644	+	0.998602i	$0.483165\pi$
$420$		0			0
$421$	6.29289	−	15.1924i	0.306697	−	0.740432i	−0.693111	−	0.720831i	$-0.743760\pi$
$421$	6.29289	−	15.1924i	0.306697	−	0.740432i	0.999808	−	0.0196009i	$-0.00623955\pi$
$422$	10.6569	+	25.7279i	0.518768	+	1.25242i
$423$	0.585786	−	0.585786i	0.0284819	−	0.0284819i
$424$	1.31371	−	3.17157i	0.0637993	−	0.154025i
$425$		0			0
$426$	−3.41421	+	8.24264i	−0.165419	+	0.399357i
$427$	1.00000	−	2.41421i	0.0483934	−	0.116832i
$428$	−3.41421	+	8.24264i	−0.165032	+	0.398423i
$429$	−1.00000	−	2.41421i	−0.0482805	−	0.116559i
$430$		0			0
$431$			12.3431i			0.594548i	0.954792	+	0.297274i	$0.0960775\pi$
$431$			12.3431i			0.594548i	−0.954792	+	0.297274i	$0.903922\pi$
$432$	−15.3137	−	6.34315i	−0.736781	−	0.305185i
$433$	−15.5147			−0.745590			−0.372795	−	0.927914i	$-0.621600\pi$
$433$	−15.5147			−0.745590			−0.372795	+	0.927914i	$0.621600\pi$
$434$	−5.65685	+	5.65685i	−0.271538	+	0.271538i
$435$		0			0
$436$	11.4142	+	27.5563i	0.546642	+	1.31971i
$437$	12.6569	−	30.5563i	0.605459	−	1.46171i
$438$	4.10051	−	9.89949i	0.195930	−	0.473016i
$439$	17.0000	−	17.0000i	0.811366	−	0.811366i	−0.173473	−	0.984839i	$-0.555499\pi$
$439$	17.0000	−	17.0000i	0.811366	−	0.811366i	0.984839	+	0.173473i	$0.0554989\pi$
$440$		0			0
$441$	8.53553	+	8.53553i	0.406454	+	0.406454i
$442$	−2.82843	+	1.17157i	−0.134535	+	0.0557260i
$443$	1.46447	+	0.606602i	0.0695789	+	0.0288205i	0.417201	−	0.908814i	$-0.363011\pi$
$443$	1.46447	+	0.606602i	0.0695789	+	0.0288205i	−0.347623	+	0.937635i	$0.613011\pi$
$444$			1.17157i			0.0556004i
$445$		0			0
$446$		−	29.6569i		−	1.40429i
$447$		−	12.9289i		−	0.611518i
$448$	8.00000	−	8.00000i	0.377964	−	0.377964i
$449$	19.4558			0.918178			0.459089	−	0.888390i	$-0.348176\pi$
$449$	19.4558			0.918178			0.459089	+	0.888390i	$0.348176\pi$
$450$		0			0
$451$	1.00000	−	0.414214i	0.0470882	−	0.0195046i
$452$	−12.6863			−0.596713
$453$	1.48528	+	0.615224i	0.0697846	+	0.0289057i
$454$	−10.8995	−	26.3137i	−0.511539	−	1.23496i
$455$		0			0
$456$	−6.14214	+	6.14214i	−0.287632	+	0.287632i
$457$	7.48528	+	7.48528i	0.350147	+	0.350147i	0.860164	−	0.510017i	$-0.170361\pi$
$457$	7.48528	+	7.48528i	0.350147	+	0.350147i	−0.510017	+	0.860164i	$0.670361\pi$
$458$	13.0416	−	31.4853i	0.609395	−	1.47121i
$459$	−10.8284	−	4.48528i	−0.505428	−	0.209355i
$460$		0			0
$461$	0.636039	+	1.53553i	0.0296233	+	0.0715169i	0.937999	−	0.346638i	$-0.112677\pi$
$461$	0.636039	+	1.53553i	0.0296233	+	0.0715169i	−0.908376	+	0.418155i	$0.862677\pi$
$462$	4.82843	+	4.82843i	0.224639	+	0.224639i
$463$	22.9706			1.06753			0.533766	−	0.845632i	$-0.320776\pi$
$463$	22.9706			1.06753			0.533766	+	0.845632i	$0.320776\pi$
$464$	12.4853	−	5.17157i	0.579615	−	0.240084i
$465$		0			0
$466$	−3.75736	−	3.75736i	−0.174056	−	0.174056i
$467$	−21.9497	+	9.09188i	−1.01571	+	0.420722i	−0.827536	−	0.561413i	$-0.810258\pi$
$467$	−21.9497	+	9.09188i	−1.01571	+	0.420722i	−0.188177	+	0.982135i	$0.560258\pi$
$468$	−1.41421	+	3.41421i	−0.0653720	+	0.157822i
$469$	7.82843	+	3.24264i	0.361483	+	0.149731i
$470$		0			0
$471$	−1.00000	+	1.00000i	−0.0460776	+	0.0460776i
$472$	5.31371	−	12.8284i	0.244583	−	0.590476i
$473$	16.0711	−	16.0711i	0.738948	−	0.738948i
$474$	6.00000	−	2.48528i	0.275589	−	0.114153i
$475$		0			0
$476$	5.65685	−	5.65685i	0.259281	−	0.259281i
$477$	−1.12132	−	2.70711i	−0.0513417	−	0.123950i
$478$		−	7.51472i		−	0.343715i
$479$	−28.9706			−1.32370			−0.661849	−	0.749637i	$-0.730228\pi$
$479$	−28.9706			−1.32370			−0.661849	+	0.749637i	$0.730228\pi$
$480$		0			0
$481$	0.585786			0.0267096
$482$			12.0000i			0.546585i
$483$	−3.41421	−	8.24264i	−0.155352	−	0.375053i
$484$	12.5858	+	12.5858i	0.572081	+	0.572081i
$485$		0			0
$486$	−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	$0.364656\pi$
$488$	4.82843	−	2.00000i	0.218573	−	0.0905357i
$489$	0.272078	−	0.272078i	0.0123038	−	0.0123038i
$490$		0			0
$491$	39.3345	+	16.2929i	1.77514	+	0.735288i	0.993800	+	0.111186i	$0.0354648\pi$
$491$	39.3345	+	16.2929i	1.77514	+	0.735288i	0.781343	+	0.624102i	$0.214535\pi$
$492$	0.343146	+	0.142136i	0.0154702	+	0.00640797i
$493$	8.82843	−	3.65685i	0.397612	−	0.164696i
$494$	3.07107	+	3.07107i	0.138174	+	0.138174i
$495$		0			0
$496$	−16.0000			−0.718421
$497$	−11.6569			−0.522881
$498$	3.75736	+	3.75736i	0.168371	+	0.168371i
$499$	0.949747	+	2.29289i	0.0425165	+	0.102644i	0.943711	−	0.330771i	$-0.107309\pi$
$499$	0.949747	+	2.29289i	0.0425165	+	0.102644i	−0.901195	+	0.433415i	$0.857309\pi$
$500$		0			0
$501$	−14.6569	−	6.07107i	−0.654820	−	0.271235i
$502$	9.34315	−	22.5563i	0.417005	−	1.00674i
$503$	−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
$505$		0			0
$506$	−19.8995	−	48.0416i	−0.884640	−	2.13571i
$507$	8.77817	+	3.63604i	0.389852	+	0.161482i
$508$		−	25.9411i		−	1.15095i
$509$	26.0919	−	10.8076i	1.15650	−	0.479039i	0.279793	−	0.960060i	$-0.409734\pi$
$509$	26.0919	−	10.8076i	1.15650	−	0.479039i	0.876709	+	0.481021i	$0.159734\pi$
$510$		0			0
$511$	14.0000			0.619324
$512$	22.6274			1.00000
$513$			16.6274i			0.734118i
$514$		−	8.48528i		−	0.374270i
$515$		0			0
$516$	7.79899			0.343331
$517$	−1.41421	−	0.585786i	−0.0621970	−	0.0257629i
$518$	−1.41421	+	0.585786i	−0.0621370	+	0.0257380i
$519$	4.41421	+	4.41421i	0.193762	+	0.193762i
$520$		0			0
$521$	3.34315	−	3.34315i	0.146466	−	0.146466i	−0.630071	−	0.776537i	$-0.716974\pi$
$521$	3.34315	−	3.34315i	0.146466	−	0.146466i	0.776537	+	0.630071i	$0.216974\pi$
$522$	4.41421	−	10.6569i	0.193205	−	0.466438i
$523$	−7.94975	+	19.1924i	−0.347618	+	0.839225i	0.649282	+	0.760548i	$0.275070\pi$
$523$	−7.94975	+	19.1924i	−0.347618	+	0.839225i	−0.996900	+	0.0786768i	$0.974930\pi$
$524$	−32.7279	+	13.5563i	−1.42973	+	0.592212i
$525$		0			0
$526$	8.24264	−	8.24264i	0.359396	−	0.359396i
$527$	−11.3137			−0.492833
$528$			13.6569i			0.594338i
$529$			44.9411i			1.95396i
$530$		0			0
$531$	−4.53553	−	10.9497i	−0.196825	−	0.475179i
$532$	−10.4853	−	4.34315i	−0.454595	−	0.188299i
$533$	0.0710678	−	0.171573i	0.00307829	−	0.00743165i
$534$	−5.07107	+	12.2426i	−0.219447	+	0.529791i
$535$		0			0
$536$	6.48528	+	15.6569i	0.280121	+	0.676273i
$537$	2.31371	−	2.31371i	0.0998439	−	0.0998439i
$538$	−12.8995	−	31.1421i	−0.556137	−	1.34263i
$539$	8.53553	−	20.6066i	0.367651	−	0.887589i
$540$		0			0
$541$	−27.2635	+	11.2929i	−1.17215	+	0.485519i	−0.881902	−	0.471433i	$-0.843737\pi$
$541$	−27.2635	+	11.2929i	−1.17215	+	0.485519i	−0.290246	+	0.956952i	$0.593737\pi$
$542$		−	25.4558i		−	1.09342i
$543$		−	13.4142i		−	0.575659i
$544$	16.0000			0.685994
$545$		0			0
$546$	1.17157			0.0501387
$547$	7.26346	+	17.5355i	0.310563	+	0.749765i	0.999684	+	0.0251195i	$0.00799662\pi$
$547$	7.26346	+	17.5355i	0.310563	+	0.749765i	−0.689122	+	0.724646i	$0.742003\pi$
$548$	17.3137	+	17.3137i	0.739605	+	0.739605i
$549$	1.70711	−	4.12132i	0.0728575	−	0.175894i
$550$		0			0
$551$	−9.58579	−	9.58579i	−0.408368	−	0.408368i
$552$	6.82843	−	16.4853i	0.290637	−	0.701660i
$553$	6.00000	+	6.00000i	0.255146	+	0.255146i
$554$	1.00000	−	2.41421i	0.0424859	−	0.102570i
$555$		0			0
$556$	−26.3848	−	10.9289i	−1.11896	−	0.463490i
$557$	36.5061	−	15.1213i	1.54681	−	0.640711i	0.564077	−	0.825722i	$-0.309232\pi$
$557$	36.5061	−	15.1213i	1.54681	−	0.640711i	0.982736	+	0.185012i	$0.0592323\pi$
$558$	−9.65685	+	9.65685i	−0.408807	+	0.408807i
$559$		−	3.89949i		−	0.164931i
$560$		0			0
$561$			9.65685i			0.407713i
$562$	−16.7279	−	16.7279i	−0.705625	−	0.705625i
$563$	−19.0208	+	7.87868i	−0.801632	+	0.332047i	−0.745610	−	0.666383i	$-0.767842\pi$
$563$	−19.0208	+	7.87868i	−0.801632	+	0.332047i	−0.0560220	+	0.998430i	$0.517842\pi$
$564$	−0.201010	−	0.485281i	−0.00846405	−	0.0204340i
$565$		0			0
$566$	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	$-0.393068\pi$
$569$	−14.6569	−	14.6569i	−0.614447	−	0.614447i	−0.944102	+	0.329654i	$0.893068\pi$
$570$		0			0
$571$	−2.70711	+	6.53553i	−0.113289	+	0.273504i	−0.970347	−	0.241716i	$-0.922290\pi$
$571$	−2.70711	+	6.53553i	−0.113289	+	0.273504i	0.857058	+	0.515220i	$0.172290\pi$
$572$	6.82843			0.285511
$573$	3.51472	+	8.48528i	0.146829	+	0.354478i
$574$			0.485281i			0.0202553i
$575$		0			0
$576$	13.6569	−	13.6569i	0.569036	−	0.569036i
$577$		−	18.9706i		−	0.789755i	−0.918734	−	0.394877i	$-0.870787\pi$
$577$		−	18.9706i		−	0.789755i	0.918734	−	0.394877i	$-0.129213\pi$
$578$	−12.7279			−0.529412
$579$	−1.07107	+	0.443651i	−0.0445121	+	0.0184375i
$580$		0			0
$581$	−2.65685	+	6.41421i	−0.110225	+	0.266106i
$582$	18.4853	−	7.65685i	0.766240	−	0.317387i
$583$	−3.82843	+	3.82843i	−0.158557	+	0.158557i
$584$	19.7990	+	19.7990i	0.819288	+	0.819288i
$585$		0			0
$586$	32.7990	+	13.5858i	1.35491	+	0.561224i
$587$	−5.22183	+	12.6066i	−0.215528	+	0.520330i	−0.994256	−	0.107032i	$-0.965865\pi$
$587$	−5.22183	+	12.6066i	−0.215528	+	0.520330i	0.778728	+	0.627362i	$0.215865\pi$
$588$	7.07107	−	2.92893i	0.291606	−	0.120787i
$589$	6.14214	+	14.8284i	0.253082	+	0.610995i
$590$		0			0
$591$			9.27208i			0.381402i
$592$	−2.82843	−	1.17157i	−0.116248	−	0.0481513i
$593$	−28.2843			−1.16150			−0.580748	−	0.814083i	$-0.697240\pi$
$593$	−28.2843			−1.16150			−0.580748	+	0.814083i	$0.697240\pi$
$594$	18.4853	+	18.4853i	0.758460	+	0.758460i
$595$		0			0
$596$	31.2132	+	12.9289i	1.27854	+	0.529590i
$597$	6.61522	−	15.9706i	0.270743	−	0.653632i
$598$	−8.24264	−	3.41421i	−0.337067	−	0.139618i
$599$	26.6569	−	26.6569i	1.08917	−	1.08917i	0.0935555	−	0.995614i	$-0.470177\pi$
$599$	26.6569	−	26.6569i	1.08917	−	1.08917i	0.995614	−	0.0935555i	$-0.0298232\pi$
$600$		0			0
$601$	−21.9706	−	21.9706i	−0.896198	−	0.896198i	0.0988995	−	0.995097i	$-0.468468\pi$
$601$	−21.9706	−	21.9706i	−0.896198	−	0.896198i	−0.995097	+	0.0988995i	$0.968468\pi$
$602$	3.89949	+	9.41421i	0.158932	+	0.383695i
$603$	13.3640	+	5.53553i	0.544223	+	0.225424i
$604$	−2.97056	+	2.97056i	−0.120870	+	0.120870i
$605$		0			0
$606$	3.85786			0.156715
$607$			32.9706i			1.33823i	0.743157	+	0.669117i	$0.233327\pi$
$607$			32.9706i			1.33823i	−0.743157	+	0.669117i	$0.766673\pi$
$608$	−8.68629	−	20.9706i	−0.352276	−	0.850469i
$609$	−3.65685			−0.148183
$610$		0			0
$611$	−0.242641	+	0.100505i	−0.00981619	+	0.00406600i
$612$	9.65685	−	9.65685i	0.390355	−	0.390355i
$613$	3.19239	+	1.32233i	0.128939	+	0.0534084i	0.446220	−	0.894923i	$-0.352770\pi$
$613$	3.19239	+	1.32233i	0.128939	+	0.0534084i	−0.317281	+	0.948332i	$0.602770\pi$
$614$	−23.7279	+	9.82843i	−0.957581	+	0.396643i
$615$		0			0
$616$	−16.4853	+	6.82843i	−0.664211	+	0.275125i
$617$	−22.7990	−	22.7990i	−0.917853	−	0.917853i	0.0790202	−	0.996873i	$-0.474821\pi$
$617$	−22.7990	−	22.7990i	−0.917853	−	0.917853i	−0.996873	+	0.0790202i	$0.974821\pi$
$618$	13.4142	+	5.55635i	0.539599	+	0.223509i
$619$	21.7782	+	9.02082i	0.875339	+	0.362577i	0.774687	−	0.632345i	$-0.217907\pi$
$619$	21.7782	+	9.02082i	0.875339	+	0.362577i	0.100651	+	0.994922i	$0.467907\pi$
$620$		0			0
$621$	−13.0711	−	31.5563i	−0.524524	−	1.26631i
$622$	−3.75736	+	3.75736i	−0.150656	+	0.150656i
$623$	−17.3137			−0.693659
$624$	1.65685	+	1.65685i	0.0663273	+	0.0663273i
$625$		0			0
$626$	10.5858	−	10.5858i	0.423093	−	0.423093i
$627$	12.6569	−	5.24264i	0.505466	−	0.209371i
$628$	−1.41421	−	3.41421i	−0.0564333	−	0.136242i
$629$	−2.00000	−	0.828427i	−0.0797452	−	0.0330316i
$630$		0			0
$631$	32.4558	−	32.4558i	1.29205	−	1.29205i	0.358528	−	0.933519i	$-0.383279\pi$
$631$	32.4558	−	32.4558i	1.29205	−	1.29205i	0.933519	−	0.358528i	$-0.116721\pi$
$632$			16.9706i			0.675053i
$633$	10.6569	−	10.6569i	0.423572	−	0.423572i
$634$	−10.1716	−	24.5563i	−0.403965	−	0.975257i
$635$		0			0
$636$	−1.85786			−0.0736691
$637$	−1.46447	−	3.53553i	−0.0580243	−	0.140083i
$638$	−21.3137			−0.843818
$639$	−19.8995			−0.787212
$640$		0			0
$641$	7.45584			0.294488			0.147244	−	0.989100i	$-0.452960\pi$
$641$	7.45584			0.294488			0.147244	+	0.989100i	$0.452960\pi$
$642$	4.82843			0.190563
$643$	4.73654	+	11.4350i	0.186791	+	0.450954i	0.989338	−	0.145635i	$-0.0465225\pi$
$643$	4.73654	+	11.4350i	0.186791	+	0.450954i	−0.802547	+	0.596588i	$0.796522\pi$
$644$	23.3137			0.918689
$645$		0			0
$646$	−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	$0.195118\pi$
$648$		−	11.5147i		−	0.452341i
$649$	−15.4853	+	15.4853i	−0.607850	+	0.607850i
$650$		0			0
$651$	4.00000	+	1.65685i	0.156772	+	0.0649372i
$652$	0.384776	+	0.928932i	0.0150690	+	0.0363798i
$653$	−5.05025	+	2.09188i	−0.197632	+	0.0818617i	−0.479304	−	0.877649i	$-0.659111\pi$
$653$	−5.05025	+	2.09188i	−0.197632	+	0.0818617i	0.281672	+	0.959511i	$0.409111\pi$
$654$	11.4142	−	11.4142i	0.446331	−	0.446331i
$655$		0			0
$656$	−0.686292	+	0.686292i	−0.0267952	+	0.0267952i
$657$	23.8995			0.932408
$658$	0.485281	−	0.485281i	0.0189182	−	0.0189182i
$659$	10.1213	+	24.4350i	0.394271	+	0.951854i	0.988998	+	0.147926i	$0.0472599\pi$
$659$	10.1213	+	24.4350i	0.394271	+	0.951854i	−0.594728	+	0.803927i	$0.702740\pi$
$660$		0			0
$661$	−41.7487	−	17.2929i	−1.62384	−	0.672616i	−0.629316	−	0.777149i	$-0.716665\pi$
$661$	−41.7487	−	17.2929i	−1.62384	−	0.672616i	−0.994521	+	0.104534i	$0.966665\pi$
$662$	−1.82843	−	0.757359i	−0.0710638	−	0.0294356i
$663$	1.17157	+	1.17157i	0.0455001	+	0.0455001i
$664$	−12.8284	+	5.31371i	−0.497840	+	0.206212i
$665$		0			0
$666$	−2.41421	+	1.00000i	−0.0935489	+	0.0387492i
$667$	25.7279	+	10.6569i	0.996189	+	0.412635i
$668$	29.3137	−	29.3137i	1.13418	−	1.13418i
$669$	−14.8284	+	6.14214i	−0.573300	+	0.237469i
$670$		0			0
$671$	−8.24264			−0.318204
$672$	−5.65685	−	2.34315i	−0.218218	−	0.0903888i
$673$			22.4853i			0.866744i	0.901215	+	0.433372i	$0.142676\pi$
$673$			22.4853i			0.866744i	−0.901215	+	0.433372i	$0.857324\pi$
$674$	24.0000			0.924445
$675$		0			0
$676$	−17.5563	+	17.5563i	−0.675244	+	0.675244i
$677$	−37.6777	−	15.6066i	−1.44807	−	0.599810i	−0.486331	−	0.873775i	$-0.661665\pi$
$677$	−37.6777	−	15.6066i	−1.44807	−	0.599810i	−0.961740	+	0.273964i	$0.911665\pi$
$678$	2.62742	+	6.34315i	0.100905	+	0.243607i
$679$	18.4853	+	18.4853i	0.709400	+	0.709400i
$680$		0			0
$681$	−10.8995	+	10.8995i	−0.417670	+	0.417670i
$682$	23.3137	+	9.65685i	0.892728	+	0.369780i
$683$	4.19239	−	10.1213i	0.160417	−	0.387282i	−0.823150	−	0.567824i	$-0.807785\pi$
$683$	4.19239	−	10.1213i	0.160417	−	0.387282i	0.983567	+	0.180543i	$0.0577854\pi$
$684$	−17.8995	−	7.41421i	−0.684404	−	0.283490i
$685$		0			0
$686$	16.9706	+	16.9706i	0.647939	+	0.647939i
$687$	−18.4437			−0.703669
$688$	−7.79899	+	18.8284i	−0.297334	+	0.717827i
$689$			0.928932i			0.0353895i
$690$		0			0
$691$	12.5061	+	30.1924i	0.475754	+	1.14857i	0.961582	+	0.274518i	$0.0885183\pi$
$691$	12.5061	+	30.1924i	0.475754	+	1.14857i	−0.485828	+	0.874055i	$0.661482\pi$
$692$	−15.0711	+	6.24264i	−0.572916	+	0.237310i
$693$	−5.82843	+	14.0711i	−0.221404	+	0.534516i
$694$	−5.58579	−	2.31371i	−0.212034	−	0.0878272i
$695$		0			0
$696$	−5.17157	−	5.17157i	−0.196028	−	0.196028i
$697$	−0.485281	+	0.485281i	−0.0183813	+	0.0183813i
$698$	−34.8995	+	14.4558i	−1.32097	+	0.547162i
$699$	−1.10051	+	2.65685i	−0.0416249	+	0.100491i
$700$		0			0
$701$	2.87868	−	1.19239i	0.108726	−	0.0450359i	−0.327657	−	0.944797i	$-0.606259\pi$
$701$	2.87868	−	1.19239i	0.108726	−	0.0450359i	0.436383	+	0.899761i	$0.356259\pi$
$702$	4.48528			0.169286
$703$			3.07107i			0.115828i
$704$	−32.9706	−	13.6569i	−1.24262	−	0.514712i
$705$		0			0
$706$			8.48528i			0.319348i
$707$	1.92893	+	4.65685i	0.0725450	+	0.175139i
$708$	−7.51472			−0.282420
$709$	−8.77817	+	21.1924i	−0.329671	+	0.795897i	0.668945	+	0.743312i	$0.266746\pi$
$709$	−8.77817	+	21.1924i	−0.329671	+	0.795897i	−0.998616	+	0.0525851i	$0.983254\pi$
$710$		0			0
$711$	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
$715$		0			0
$716$	3.27208	+	7.89949i	0.122283	+	0.295218i
$717$	−3.75736	+	1.55635i	−0.140321	+	0.0581229i
$718$	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	$0.768479\pi$
$720$		0			0
$721$			18.9706i			0.706501i
$722$	2.89949	−	2.89949i	0.107908	−	0.107908i
$723$	6.00000	−	2.48528i	0.223142	−	0.0924286i
$724$	32.3848	+	13.4142i	1.20357	+	0.498535i
$725$		0			0
$726$	3.68629	−	8.89949i	0.136811	−	0.330291i
$727$	9.97056	+	9.97056i	0.369788	+	0.369788i	0.867400	−	0.497612i	$-0.165790\pi$
$727$	9.97056	+	9.97056i	0.369788	+	0.369788i	−0.497612	+	0.867400i	$0.665790\pi$
$728$	−1.17157	+	2.82843i	−0.0434214	+	0.104828i
$729$	−0.221825	−	0.221825i	−0.00821576	−	0.00821576i
$730$		0			0
$731$	−5.51472	+	13.3137i	−0.203969	+	0.492425i
$732$	−2.00000	−	2.00000i	−0.0739221	−	0.0739221i
$733$	−13.7782	−	33.2635i	−0.508908	−	1.22861i	−0.944513	−	0.328475i	$-0.893465\pi$
$733$	−13.7782	−	33.2635i	−0.508908	−	1.22861i	0.435604	−	0.900138i	$-0.356535\pi$
$734$	8.48528			0.313197
$735$		0			0
$736$	32.9706	+	32.9706i	1.21531	+	1.21531i
$737$		−	26.7279i		−	0.984536i
$738$			0.828427i			0.0304948i
$739$	−0.464466	+	0.192388i	−0.0170857	+	0.00707711i	−0.391210	−	0.920301i	$-0.627943\pi$
$739$	−0.464466	+	0.192388i	−0.0170857	+	0.00707711i	0.374124	+	0.927379i	$0.377943\pi$
$740$		0			0
$741$	0.899495	−	2.17157i	0.0330438	−	0.0797747i
$742$	−0.928932	−	2.24264i	−0.0341022	−	0.0823299i
$743$	−31.6274	+	31.6274i	−1.16030	+	1.16030i	−0.175887	+	0.984410i	$0.556279\pi$
$743$	−31.6274	+	31.6274i	−1.16030	+	1.16030i	−0.984410	+	0.175887i	$0.943721\pi$
$744$	3.31371	+	8.00000i	0.121486	+	0.293294i
$745$		0			0
$746$	6.02944	−	14.5563i	0.220753	−	0.532946i
$747$	−4.53553	+	10.9497i	−0.165947	+	0.400630i
$748$	−23.3137	−	9.65685i	−0.852434	−	0.353090i
$749$	2.41421	+	5.82843i	0.0882134	+	0.212966i
$750$		0			0
$751$			10.9706i			0.400322i	0.979763	+	0.200161i	$0.0641464\pi$
$751$			10.9706i			0.400322i	−0.979763	+	0.200161i	$0.935854\pi$
$752$	1.37258			0.0500530
$753$	−13.2132			−0.481516
$754$	−2.58579	+	2.58579i	−0.0941688	+	0.0941688i
$755$		0			0
$756$	−10.8284	+	4.48528i	−0.393826	+	0.163128i
$757$	−13.7782	+	33.2635i	−0.500776	+	1.20898i	0.448285	+	0.893890i	$0.352035\pi$
$757$	−13.7782	+	33.2635i	−0.500776	+	1.20898i	−0.949062	+	0.315090i	$0.897965\pi$
$758$	19.3431	−	46.6985i	0.702575	−	1.69617i
$759$	−19.8995	+	19.8995i	−0.722306	+	0.722306i
$760$		0			0
$761$	−29.8284	−	29.8284i	−1.08128	−	1.08128i	−0.996390	−	0.0848892i	$-0.972946\pi$
$761$	−29.8284	−	29.8284i	−1.08128	−	1.08128i	−0.0848892	−	0.996390i	$-0.527054\pi$
$762$	−12.9706	+	5.37258i	−0.469874	+	0.194628i
$763$	19.4853	+	8.07107i	0.705415	+	0.292192i
$764$	−24.0000			−0.868290
$765$		0			0
$766$		−	24.0000i		−	0.867155i
$767$			3.75736i			0.135670i
$768$	−4.68629	−	11.3137i	−0.169102	−	0.408248i
$769$	−5.51472			−0.198866			−0.0994329	−	0.995044i	$-0.531703\pi$
$769$	−5.51472			−0.198866			−0.0994329	+	0.995044i	$0.531703\pi$
$770$		0			0
$771$	−4.24264	+	1.75736i	−0.152795	+	0.0632897i
$772$		−	3.02944i		−	0.109032i
$773$	29.1924	+	12.0919i	1.04998	+	0.434915i	0.839884	−	0.542766i	$-0.182623\pi$
$773$	29.1924	+	12.0919i	1.04998	+	0.434915i	0.210094	+	0.977681i	$0.432623\pi$
$774$	6.65685	+	16.0711i	0.239276	+	0.577663i
$775$		0			0
$776$			52.2843i			1.87690i
$777$	0.585786	+	0.585786i	0.0210150	+	0.0210150i
$778$	11.8701	−	28.6569i	0.425562	−	1.02740i
$779$	0.899495	+	0.372583i	0.0322278	+	0.0133492i
$780$		0			0
$781$	14.0711	+	33.9706i	0.503502	+	1.21556i
$782$	23.3137	+	23.3137i	0.833697	+	0.833697i
$783$	−14.0000			−0.500319
$784$			20.0000i			0.714286i
$785$		0			0
$786$	13.5563	+	13.5563i	0.483539	+	0.483539i
$787$	−2.29289	+	0.949747i	−0.0817328	+	0.0338548i	−0.423175	−	0.906048i	$-0.639085\pi$
$787$	−2.29289	+	0.949747i	−0.0817328	+	0.0338548i	0.341442	+	0.939903i	$0.389085\pi$
$788$	−22.3848	−	9.27208i	−0.797425	−	0.330304i
$789$	−5.82843	−	2.41421i	−0.207498	−	0.0859483i
$790$		0			0
$791$	−6.34315	+	6.34315i	−0.225536	+	0.225536i
$792$	−28.1421	+	11.6569i	−0.999987	+	0.414208i
$793$	−1.00000	+	1.00000i	−0.0355110	+	0.0355110i
$794$	−31.4853	+	13.0416i	−1.11737	+	0.462830i
$795$		0			0
$796$	31.9411	+	31.9411i	1.13212	+	1.13212i
$797$	10.8076	+	26.0919i	0.382825	+	0.924222i	0.991417	+	0.130738i	$0.0417348\pi$
$797$	10.8076	+	26.0919i	0.382825	+	0.924222i	−0.608592	+	0.793484i	$0.708265\pi$
$798$			6.14214i			0.217429i
$799$	0.970563			0.0343360
$800$		0			0
$801$	−29.5563			−1.04432
$802$			4.00000i			0.141245i
$803$	−16.8995	−	40.7990i	−0.596370	−	1.43977i
$804$	6.48528	−	6.48528i	0.228718	−	0.228718i
$805$		0			0
$806$	4.00000	−	1.65685i	0.140894	−	0.0583602i
$807$	−12.8995	+	12.8995i	−0.454084	+	0.454084i
$808$	−3.85786	+	9.31371i	−0.135719	+	0.327655i
$809$	29.1421	−	29.1421i	1.02458	−	1.02458i	0.0248928	−	0.999690i	$-0.492076\pi$
$809$	29.1421	−	29.1421i	1.02458	−	1.02458i	0.999690	−	0.0248928i	$-0.00792444\pi$
$810$		0			0
$811$	−42.2635	−	17.5061i	−1.48407	−	0.614722i	−0.514053	−	0.857758i	$-0.671857\pi$
$811$	−42.2635	−	17.5061i	−1.48407	−	0.614722i	−0.970017	+	0.243036i	$0.921857\pi$
$812$	3.65685	−	8.82843i	0.128330	−	0.309817i
$813$	−12.7279	+	5.27208i	−0.446388	+	0.184900i
$814$	3.41421	+	3.41421i	0.119668	+	0.119668i
$815$		0			0
$816$	−3.31371	−	8.00000i	−0.116003	−	0.280056i
$817$	20.4437			0.715233
$818$	−30.3848	−	30.3848i	−1.06238	−	1.06238i
$819$	1.00000	+	2.41421i	0.0349428	+	0.0843594i
$820$		0			0
$821$	−21.6066	−	8.94975i	−0.754076	−	0.312348i	−0.0276723	−	0.999617i	$-0.508809\pi$
$821$	−21.6066	−	8.94975i	−0.754076	−	0.312348i	−0.726403	+	0.687269i	$0.758809\pi$
$822$	5.07107	−	12.2426i	0.176874	−	0.427011i
$823$	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
$825$		0			0
$826$	−3.75736	−	9.07107i	−0.130735	−	0.315623i
$827$	−38.9203	−	16.1213i	−1.35339	−	0.560593i	−0.416157	−	0.909293i	$-0.636623\pi$
$827$	−38.9203	−	16.1213i	−1.35339	−	0.560593i	−0.937235	+	0.348699i	$0.886623\pi$
$828$	39.7990			1.38311
$829$	−34.1924	+	14.1630i	−1.18755	+	0.491900i	−0.886957	−	0.461853i	$-0.847185\pi$
$829$	−34.1924	+	14.1630i	−1.18755	+	0.491900i	−0.300594	+	0.953752i	$0.597185\pi$
$830$		0			0
$831$	−1.41421			−0.0490585
$832$	−5.65685	+	2.34315i	−0.196116	+	0.0812340i
$833$			14.1421i			0.489996i
$834$			15.4558i			0.535192i
$835$		0			0
$836$			35.7990i			1.23813i
$837$	15.3137	+	6.34315i	0.529319	+	0.219251i
$838$	−17.8284	+	7.38478i	−0.615873	+	0.255103i
$839$	−9.68629	−	9.68629i	−0.334408	−	0.334408i	0.519850	−	0.854258i	$-0.325988\pi$
$839$	−9.68629	−	9.68629i	−0.334408	−	0.334408i	−0.854258	+	0.519850i	$0.825988\pi$
$840$		0			0
$841$	−12.4350	+	12.4350i	−0.428794	+	0.428794i
$842$	8.89949	−	21.4853i	0.306697	−	0.740432i
$843$	−4.89949	+	11.8284i	−0.168748	+	0.407393i
$844$	15.0711	+	36.3848i	0.518768	+	1.25242i
$845$		0			0
$846$	0.828427	−	0.828427i	0.0284819	−	0.0284819i
$847$	12.5858			0.432453
$848$	1.85786	−	4.48528i	0.0637993	−	0.154025i
$849$		−	11.5563i		−	0.396613i
$850$		0			0
$851$	−2.41421	−	5.82843i	−0.0827582	−	0.199796i
$852$	−4.82843	+	11.6569i	−0.165419	+	0.399357i
$853$	−21.1924	+	51.1630i	−0.725614	+	1.75179i	−0.0689279	+	0.997622i	$0.521958\pi$
$853$	−21.1924	+	51.1630i	−0.725614	+	1.75179i	−0.656686	+	0.754164i	$0.728042\pi$
$854$	1.41421	−	3.41421i	0.0483934	−	0.116832i
$855$		0			0
$856$	−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	$0.174830\pi$
$858$	−1.41421	−	3.41421i	−0.0482805	−	0.116559i
$859$	1.67767	−	4.05025i	0.0572413	−	0.138193i	−0.892671	−	0.450708i	$-0.851172\pi$
$859$	1.67767	−	4.05025i	0.0572413	−	0.138193i	0.949913	+	0.312515i	$0.101172\pi$
$860$		0			0
$861$	0.242641	−	0.100505i	0.00826917	−	0.00342520i
$862$			17.4558i			0.594548i
$863$			21.9411i			0.746885i	0.927653	+	0.373442i	$0.121823\pi$
$863$			21.9411i			0.746885i	−0.927653	+	0.373442i	$0.878177\pi$
$864$	−21.6569	−	8.97056i	−0.736781	−	0.305185i
$865$		0			0
$866$	−21.9411			−0.745590
$867$	2.63604	+	6.36396i	0.0895246	+	0.216131i
$868$	−8.00000	+	8.00000i	−0.271538	+	0.271538i
$869$	10.2426	−	24.7279i	0.347458	−	0.838837i
$870$		0			0
$871$	−3.24264	−	3.24264i	−0.109873	−	0.109873i
$872$	16.1421	+	38.9706i	0.546642	+	1.31971i
$873$	31.5563	+	31.5563i	1.06802	+	1.06802i
$874$	17.8995	−	43.2132i	0.605459	−	1.46171i
$875$		0			0
$876$	5.79899	−	14.0000i	0.195930	−	0.473016i
$877$	−1.77817	+	0.736544i	−0.0600447	+	0.0248713i	−0.412504	−	0.910956i	$-0.635346\pi$
$877$	−1.77817	+	0.736544i	−0.0600447	+	0.0248713i	0.352459	+	0.935827i	$0.385346\pi$
$878$	24.0416	−	24.0416i	0.811366	−	0.811366i
$879$		−	19.2132i		−	0.648045i
$880$		0			0
$881$		−	22.6274i		−	0.762337i	−0.924506	−	0.381169i	$-0.875522\pi$
$881$		−	22.6274i		−	0.762337i	0.924506	−	0.381169i	$-0.124478\pi$
$882$	12.0711	+	12.0711i	0.406454	+	0.406454i
$883$	−49.6482	+	20.5650i	−1.67080	+	0.692066i	−0.998823	−	0.0485090i	$-0.984553\pi$
$883$	−49.6482	+	20.5650i	−1.67080	+	0.692066i	−0.671973	+	0.740575i	$0.734553\pi$
$884$	−4.00000	+	1.65685i	−0.134535	+	0.0557260i
$885$		0			0
$886$	2.07107	+	0.857864i	0.0695789	+	0.0288205i
$887$	−2.31371	−	2.31371i	−0.0776867	−	0.0776867i	0.667196	−	0.744882i	$-0.267494\pi$
$887$	−2.31371	−	2.31371i	−0.0776867	−	0.0776867i	−0.744882	+	0.667196i	$0.767494\pi$
$888$			1.65685i			0.0556004i
$889$	−12.9706	−	12.9706i	−0.435019	−	0.435019i
$890$		0			0
$891$	−6.94975	+	16.7782i	−0.232825	+	0.562090i
$892$		−	41.9411i		−	1.40429i
$893$	−0.526912	−	1.27208i	−0.0176324	−	0.0425685i
$894$		−	18.2843i		−	0.611518i
$895$		0			0
$896$	11.3137	−	11.3137i	0.377964	−	0.377964i
$897$			4.82843i			0.161216i
$898$	27.5147			0.918178
$899$	−12.4853	+	5.17157i	−0.416407	+	0.172482i
$900$		0			0
$901$	1.31371	−	3.17157i	0.0437660	−	0.105660i
$902$	1.41421	−	0.585786i	0.0470882	−	0.0195046i
$903$	3.89949	−	3.89949i	0.129767	−	0.129767i
$904$	−17.9411			−0.596713
$905$		0			0
$906$	2.10051	+	0.870058i	0.0697846	+	0.0289057i
$907$	−6.53553	+	15.7782i	−0.217009	+	0.523906i	−0.994469	−	0.105026i	$-0.966507\pi$
$907$	−6.53553	+	15.7782i	−0.217009	+	0.523906i	0.777461	+	0.628932i	$0.216507\pi$
$908$	−15.4142	−	37.2132i	−0.511539	−	1.23496i
$909$	3.29289	+	7.94975i	0.109218	+	0.263676i
$910$		0			0
$911$		−	33.5980i		−	1.11315i	−0.830797	−	0.556575i	$-0.812115\pi$
$911$		−	33.5980i		−	1.11315i	0.830797	−	0.556575i	$-0.187885\pi$
$912$	−8.68629	+	8.68629i	−0.287632	+	0.287632i
$913$	21.8995			0.724767
$914$	10.5858	+	10.5858i	0.350147	+	0.350147i
$915$		0			0
$916$	18.4437	−	44.5269i	0.609395	−	1.47121i
$917$	−9.58579	+	23.1421i	−0.316551	+	0.764221i
$918$	−15.3137	−	6.34315i	−0.505428	−	0.209355i
$919$	8.51472	−	8.51472i	0.280875	−	0.280875i	−0.552583	−	0.833458i	$-0.686358\pi$
$919$	8.51472	−	8.51472i	0.280875	−	0.280875i	0.833458	+	0.552583i	$0.186358\pi$
$920$		0			0
$921$	9.82843	+	9.82843i	0.323858	+	0.323858i
$922$	0.899495	+	2.17157i	0.0296233	+	0.0715169i
$923$	5.82843	+	2.41421i	0.191845	+	0.0794648i
$924$	6.82843	+	6.82843i	0.224639	+	0.224639i
$925$		0			0
$926$	32.4853			1.06753
$927$			32.3848i			1.06366i
$928$	17.6569	−	7.31371i	0.579615	−	0.240084i
$929$	9.51472			0.312168			0.156084	−	0.987744i	$-0.450113\pi$
$929$	9.51472			0.312168			0.156084	+	0.987744i	$0.450113\pi$
$930$		0			0
$931$	18.5355	−	7.67767i	0.607478	−	0.251625i
$932$	−5.31371	−	5.31371i	−0.174056	−	0.174056i
$933$	2.65685	+	1.10051i	0.0869815	+	0.0360289i
$934$	−31.0416	+	12.8579i	−1.01571	+	0.420722i
$935$		0			0
$936$	−2.00000	+	4.82843i	−0.0653720	+	0.157822i
$937$	−19.0000	−	19.0000i	−0.620703	−	0.620703i	0.325008	−	0.945711i	$-0.394633\pi$
$937$	−19.0000	−	19.0000i	−0.620703	−	0.620703i	−0.945711	+	0.325008i	$0.894633\pi$
$938$	11.0711	+	4.58579i	0.361483	+	0.149731i
$939$	−7.48528	−	3.10051i	−0.244273	−	0.101181i
$940$		0			0
$941$	0.636039	+	1.53553i	0.0207343	+	0.0500570i	0.933908	−	0.357514i	$-0.116376\pi$
$941$	0.636039	+	1.53553i	0.0207343	+	0.0500570i	−0.913173	+	0.407571i	$0.866376\pi$
$942$	−1.41421	+	1.41421i	−0.0460776	+	0.0460776i
$943$	−2.00000			−0.0651290
$944$	7.51472	−	18.1421i	0.244583	−	0.590476i
$945$		0			0
$946$	22.7279	−	22.7279i	0.738948	−	0.738948i
$947$	22.5355	−	9.33452i	0.732306	−	0.303331i	0.0148070	−	0.999890i	$-0.495287\pi$
$947$	22.5355	−	9.33452i	0.732306	−	0.303331i	0.717499	+	0.696559i	$0.245287\pi$
$948$	8.48528	−	3.51472i	0.275589	−	0.114153i
$949$	−7.00000	−	2.89949i	−0.227230	−	0.0941216i
$950$		0			0
$951$	−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	−0.903458	−	0.428676i	$-0.858980\pi$
$953$	−14.6569	+	14.6569i	−0.474782	+	0.474782i	0.428676	+	0.903458i	$0.358980\pi$
$954$	−1.58579	−	3.82843i	−0.0513417	−	0.123950i
$955$		0			0
$956$		−	10.6274i		−	0.343715i
$957$	4.41421	+	10.6569i	0.142691	+	0.344487i
$958$	−40.9706			−1.32370
$959$	17.3137			0.559089
$960$		0			0
$961$	−15.0000			−0.483871
$962$	0.828427			0.0267096
$963$	4.12132	+	9.94975i	0.132808	+	0.320626i
$964$			16.9706i			0.546585i
$965$		0			0
$966$	−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
$970$		0			0
$971$	22.3640	+	9.26346i	0.717694	+	0.297278i	0.711484	−	0.702702i	$-0.248023\pi$
$971$	22.3640	+	9.26346i	0.717694	+	0.297278i	0.00620964	+	0.999981i	$0.498023\pi$
$972$	−28.7279	+	11.8995i	−0.921449	+	0.381676i
$973$	−18.6569	+	7.72792i	−0.598111	+	0.247746i
$974$	−15.5563	+	15.5563i	−0.498458	+	0.498458i
$975$		0			0
$976$	6.82843	−	2.82843i	0.218573	−	0.0905357i
$977$	−14.1421			−0.452447			−0.226224	−	0.974075i	$-0.572638\pi$
$977$	−14.1421			−0.452447			−0.226224	+	0.974075i	$0.572638\pi$
$978$	0.384776	−	0.384776i	0.0123038	−	0.0123038i
$979$	20.8995	+	50.4558i	0.667951	+	1.61258i
$980$		0			0
$981$	33.2635	+	13.7782i	1.06202	+	0.439903i
$982$	55.6274	+	23.0416i	1.77514	+	0.735288i
$983$	−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
$985$		0			0
$986$	12.4853	−	5.17157i	0.397612	−	0.164696i
$987$	−0.343146	−	0.142136i	−0.0109224	−	0.00452423i
$988$	4.34315	+	4.34315i	0.138174	+	0.138174i
$989$	−38.7990	+	16.0711i	−1.23374	+	0.511030i
$990$		0			0
$991$	−16.0000			−0.508257			−0.254128	−	0.967170i	$-0.581789\pi$
$991$	−16.0000			−0.508257			−0.254128	+	0.967170i	$0.581789\pi$
$992$	−22.6274			−0.718421
$993$			1.07107i			0.0339893i
$994$	−16.4853			−0.522881
$995$		0			0
$996$	5.31371	+	5.31371i	0.168371	+	0.168371i
$997$	48.7487	+	20.1924i	1.54389	+	0.639499i	0.982198	−	0.187848i	$-0.0601514\pi$
$997$	48.7487	+	20.1924i	1.54389	+	0.639499i	0.561690	+	0.827348i	$0.310151\pi$
$998$	1.34315	+	3.24264i	0.0425165	+	0.102644i
$999$	2.24264	+	2.24264i	0.0709540	+	0.0709540i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	800.2.ba.a.149.1		4
5.2	odd	4		32.2.g.a.21.1	✓	4
5.3	odd	4		800.2.y.a.501.1		4
5.4	even	2		800.2.ba.b.149.1		4
15.2	even	4		288.2.v.a.181.1		4
20.7	even	4		128.2.g.a.49.1		4
32.29	even	8		800.2.ba.b.349.1		4
40.27	even	4		256.2.g.a.97.1		4
40.37	odd	4		256.2.g.b.97.1		4
60.47	odd	4		1152.2.v.a.433.1		4
80.27	even	4		512.2.g.b.449.1		4
80.37	odd	4		512.2.g.d.449.1		4
80.67	even	4		512.2.g.c.449.1		4
80.77	odd	4		512.2.g.a.449.1		4
160.27	even	8		512.2.g.b.65.1		4
160.29	even	8	inner	800.2.ba.a.349.1		4
160.37	odd	8		512.2.g.d.65.1		4
160.67	even	8		128.2.g.a.81.1		4
160.77	odd	8		256.2.g.b.161.1		4
160.93	odd	8		800.2.y.a.701.1		4
160.107	even	8		512.2.g.c.65.1		4
160.117	odd	8		512.2.g.a.65.1		4
160.147	even	8		256.2.g.a.161.1		4
160.157	odd	8		32.2.g.a.29.1	yes	4
320.67	even	16		4096.2.a.f.1.2		4
320.157	odd	16		4096.2.a.e.1.2		4
320.227	even	16		4096.2.a.f.1.3		4
320.317	odd	16		4096.2.a.e.1.3		4
480.227	odd	8		1152.2.v.a.721.1		4
480.317	even	8		288.2.v.a.253.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.2.g.a.21.1	✓	4	5.2	odd	4
32.2.g.a.29.1	yes	4	160.157	odd	8
128.2.g.a.49.1		4	20.7	even	4
128.2.g.a.81.1		4	160.67	even	8
256.2.g.a.97.1		4	40.27	even	4
256.2.g.a.161.1		4	160.147	even	8
256.2.g.b.97.1		4	40.37	odd	4
256.2.g.b.161.1		4	160.77	odd	8
288.2.v.a.181.1		4	15.2	even	4
288.2.v.a.253.1		4	480.317	even	8
512.2.g.a.65.1		4	160.117	odd	8
512.2.g.a.449.1		4	80.77	odd	4
512.2.g.b.65.1		4	160.27	even	8
512.2.g.b.449.1		4	80.27	even	4
512.2.g.c.65.1		4	160.107	even	8
512.2.g.c.449.1		4	80.67	even	4
512.2.g.d.65.1		4	160.37	odd	8
512.2.g.d.449.1		4	80.37	odd	4
800.2.y.a.501.1		4	5.3	odd	4
800.2.y.a.701.1		4	160.93	odd	8
800.2.ba.a.149.1		4	1.1	even	1	trivial
800.2.ba.a.349.1		4	160.29	even	8	inner
800.2.ba.b.149.1		4	5.4	even	2
800.2.ba.b.349.1		4	32.29	even	8
1152.2.v.a.433.1		4	60.47	odd	4
1152.2.v.a.721.1		4	480.227	odd	8
4096.2.a.e.1.2		4	320.157	odd	16
4096.2.a.e.1.3		4	320.317	odd	16
4096.2.a.f.1.2		4	320.67	even	16
4096.2.a.f.1.3		4	320.227	even	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:	\( N \)	\(=\)	\( 800 = 2^{5} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	800.ba (of order \(8\), degree \(4\), not minimal)

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

Introduction

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