LMFDB - Embedded newform 800.2.y.a.501.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [800,2,Mod(101,800)]

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, 1, 0]))

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

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

chi := DirichletCharacter("800.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 800 = 2^{5} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	800.y (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:	$6.38803216170$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 32)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			501.1
Root			$-0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	800.501
Dual form			800.2.y.a.701.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421i q^{2} +(0.707107 - 0.292893i) q^{3} -2.00000 q^{4} +(-0.414214 - 1.00000i) q^{6} +(-1.00000 - 1.00000i) q^{7} +2.82843i q^{8} +(-1.70711 + 1.70711i) q^{9} +O(q^{10})$	\(q-1.41421i q^{2} +(0.707107 - 0.292893i) q^{3} -2.00000 q^{4} +(-0.414214 - 1.00000i) q^{6} +(-1.00000 - 1.00000i) q^{7} +2.82843i q^{8} +(-1.70711 + 1.70711i) q^{9} +(-4.12132 - 1.70711i) q^{11} +(-1.41421 + 0.585786i) q^{12} +(-0.292893 - 0.707107i) q^{13} +(-1.41421 + 1.41421i) q^{14} +4.00000 q^{16} -2.82843i q^{17} +(2.41421 + 2.41421i) q^{18} +(1.53553 + 3.70711i) q^{19} +(-1.00000 - 0.414214i) q^{21} +(-2.41421 + 5.82843i) q^{22} +(-5.82843 + 5.82843i) q^{23} +(0.828427 + 2.00000i) q^{24} +(-1.00000 + 0.414214i) q^{26} +(-1.58579 + 3.82843i) q^{27} +(2.00000 + 2.00000i) q^{28} +(-3.12132 + 1.29289i) q^{29} -4.00000 q^{31} -5.65685i q^{32} -3.41421 q^{33} -4.00000 q^{34} +(3.41421 - 3.41421i) q^{36} +(-0.292893 + 0.707107i) q^{37} +(5.24264 - 2.17157i) q^{38} +(-0.414214 - 0.414214i) q^{39} +(-0.171573 + 0.171573i) q^{41} +(-0.585786 + 1.41421i) q^{42} +(-4.70711 - 1.94975i) q^{43} +(8.24264 + 3.41421i) q^{44} +(8.24264 + 8.24264i) q^{46} -0.343146i q^{47} +(2.82843 - 1.17157i) q^{48} -5.00000i q^{49} +(-0.828427 - 2.00000i) q^{51} +(0.585786 + 1.41421i) q^{52} +(1.12132 + 0.464466i) q^{53} +(5.41421 + 2.24264i) q^{54} +(2.82843 - 2.82843i) q^{56} +(2.17157 + 2.17157i) q^{57} +(1.82843 + 4.41421i) q^{58} +(-1.87868 + 4.53553i) q^{59} +(1.70711 - 0.707107i) q^{61} +5.65685i q^{62} +3.41421 q^{63} -8.00000 q^{64} +4.82843i q^{66} +(5.53553 - 2.29289i) q^{67} +5.65685i 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} +(2.41421 + 5.82843i) q^{77} +(-0.585786 + 0.585786i) q^{78} -6.00000i q^{79} -4.07107i q^{81} +(0.242641 + 0.242641i) q^{82} +(-1.87868 - 4.53553i) q^{83} +(2.00000 + 0.828427i) q^{84} +(-2.75736 + 6.65685i) q^{86} +(-1.82843 + 1.82843i) q^{87} +(4.82843 - 11.6569i) q^{88} +(8.65685 + 8.65685i) q^{89} +(-0.414214 + 1.00000i) q^{91} +(11.6569 - 11.6569i) q^{92} +(-2.82843 + 1.17157i) q^{93} -0.485281 q^{94} +(-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^{6} - 4 q^{7} - 4 q^{9}+O(q^{10}) $ 4 * q - 8 * q^4 + 4 * q^6 - 4 * q^7 - 4 * q^9	$ 4 q - 8 q^{4} + 4 q^{6} - 4 q^{7} - 4 q^{9} - 8 q^{11} - 4 q^{13} + 16 q^{16} + 4 q^{18} - 8 q^{19} - 4 q^{21} - 4 q^{22} - 12 q^{23} - 8 q^{24} - 4 q^{26} - 12 q^{27} + 8 q^{28} - 4 q^{29} - 16 q^{31} - 8 q^{33} - 16 q^{34} + 8 q^{36} - 4 q^{37} + 4 q^{38} + 4 q^{39} - 12 q^{41} - 8 q^{42} - 16 q^{43} + 16 q^{44} + 16 q^{46} + 8 q^{51} + 8 q^{52} - 4 q^{53} + 16 q^{54} + 20 q^{57} - 4 q^{58} - 16 q^{59} + 4 q^{61} + 8 q^{63} - 32 q^{64} + 8 q^{67} - 4 q^{69} - 12 q^{71} - 8 q^{72} - 28 q^{73} + 4 q^{74} + 16 q^{76} + 4 q^{77} - 8 q^{78} - 16 q^{82} - 16 q^{83} + 8 q^{84} - 28 q^{86} + 4 q^{87} + 8 q^{88} + 12 q^{89} + 4 q^{91} + 24 q^{92} + 32 q^{94} + 16 q^{96} + 40 q^{97} + 20 q^{99}+O(q^{100}) $ 4 * q - 8 * q^4 + 4 * q^6 - 4 * q^7 - 4 * q^9 - 8 * q^11 - 4 * q^13 + 16 * q^16 + 4 * q^18 - 8 * q^19 - 4 * q^21 - 4 * q^22 - 12 * q^23 - 8 * q^24 - 4 * q^26 - 12 * q^27 + 8 * q^28 - 4 * q^29 - 16 * q^31 - 8 * q^33 - 16 * q^34 + 8 * q^36 - 4 * q^37 + 4 * q^38 + 4 * q^39 - 12 * q^41 - 8 * q^42 - 16 * q^43 + 16 * q^44 + 16 * q^46 + 8 * q^51 + 8 * q^52 - 4 * q^53 + 16 * q^54 + 20 * q^57 - 4 * q^58 - 16 * q^59 + 4 * q^61 + 8 * q^63 - 32 * q^64 + 8 * q^67 - 4 * q^69 - 12 * q^71 - 8 * q^72 - 28 * q^73 + 4 * q^74 + 16 * q^76 + 4 * q^77 - 8 * q^78 - 16 * q^82 - 16 * q^83 + 8 * q^84 - 28 * q^86 + 4 * q^87 + 8 * q^88 + 12 * q^89 + 4 * q^91 + 24 * q^92 + 32 * q^94 + 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 $\left(\mathbb{Z}/800\mathbb{Z}\right)^\times$.

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

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 $

$2$		−	1.41421i		−	1.00000i
$2$		−	1.41421i		−	1.00000i
$3$	0.707107	−	0.292893i	0.408248	−	0.169102i	−0.169102	−	0.985599i	$-0.554087\pi$
$3$	0.707107	−	0.292893i	0.408248	−	0.169102i	0.577350	+	0.816497i	$0.304087\pi$
$4$	−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	$-0.336119\pi$
$7$	−1.00000	−	1.00000i	−0.377964	−	0.377964i	−0.870367	+	0.492403i	$0.836119\pi$
$8$			2.82843i			1.00000i
$9$	−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	$0.859781\pi$
$12$	−1.41421	+	0.585786i	−0.408248	+	0.169102i
$13$	−0.292893	−	0.707107i	−0.0812340	−	0.196116i	0.878044	−	0.478580i	$-0.158848\pi$
$13$	−0.292893	−	0.707107i	−0.0812340	−	0.196116i	−0.959278	+	0.282464i	$0.908848\pi$
$14$	−1.41421	+	1.41421i	−0.377964	+	0.377964i
$15$		0			0
$16$	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	0.996339	+	0.0854961i	$0.0272475\pi$
$19$	1.53553	+	3.70711i	0.352276	+	0.850469i	−0.644063	+	0.764973i	$0.722752\pi$
$20$		0			0
$21$	−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	−0.246055	+	0.969256i	$0.579134\pi$
$23$	−5.82843	+	5.82843i	−1.21531	+	1.21531i	−0.969256	+	0.246055i	$0.920866\pi$
$24$	0.828427	+	2.00000i	0.169102	+	0.408248i
$25$		0			0
$26$	−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	−0.653176	−	0.757206i	$-0.726564\pi$
$29$	−3.12132	+	1.29289i	−0.579615	+	0.240084i	0.0735609	+	0.997291i	$0.476564\pi$
$30$		0			0
$31$	−4.00000			−0.718421			−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000			−0.718421			−0.359211	+	0.933257i	$0.616954\pi$
$32$		−	5.65685i		−	1.00000i
$33$	−3.41421			−0.594338
$34$	−4.00000			−0.685994
$35$		0			0
$36$	3.41421	−	3.41421i	0.569036	−	0.569036i
$37$	−0.292893	+	0.707107i	−0.0481513	+	0.116248i	−0.946125	−	0.323802i	$-0.895039\pi$
$37$	−0.292893	+	0.707107i	−0.0481513	+	0.116248i	0.897974	+	0.440049i	$0.145039\pi$
$38$	5.24264	−	2.17157i	0.850469	−	0.352276i
$39$	−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	$0.256031\pi$
$42$	−0.585786	+	1.41421i	−0.0903888	+	0.218218i
$43$	−4.70711	−	1.94975i	−0.717827	−	0.297334i	−0.00628798	−	0.999980i	$-0.502002\pi$
$43$	−4.70711	−	1.94975i	−0.717827	−	0.297334i	−0.711539	+	0.702647i	$0.752002\pi$
$44$	8.24264	+	3.41421i	1.24262	+	0.514712i
$45$		0			0
$46$	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
$50$		0			0
$51$	−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	$-0.348436\pi$
$53$	1.12132	+	0.464466i	0.154025	+	0.0637993i	−0.304339	+	0.952564i	$0.598436\pi$
$54$	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
$58$	1.82843	+	4.41421i	0.240084	+	0.579615i
$59$	−1.87868	+	4.53553i	−0.244583	+	0.590476i	−0.997727	−	0.0673793i	$-0.978536\pi$
$59$	−1.87868	+	4.53553i	−0.244583	+	0.590476i	0.753144	+	0.657855i	$0.228536\pi$
$60$		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	$0.337259\pi$
$62$			5.65685i			0.718421i
$63$	3.41421			0.430150
$64$	−8.00000			−1.00000
$65$		0			0
$66$			4.82843i			0.594338i
$67$	5.53553	−	2.29289i	0.676273	−	0.280121i	−0.0179949	−	0.999838i	$-0.505728\pi$
$67$	5.53553	−	2.29289i	0.676273	−	0.280121i	0.694268	+	0.719717i	$0.255728\pi$
$68$			5.65685i			0.685994i
$69$	−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	$-0.946683\pi$
$73$	−7.00000	+	7.00000i	−0.819288	+	0.819288i	0.166717	+	0.986005i	$0.446683\pi$
$74$	1.00000	+	0.414214i	0.116248	+	0.0481513i
$75$		0			0
$76$	−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	$-0.890410\pi$
$79$		−	6.00000i		−	0.675053i	0.941316	−	0.337526i	$-0.109590\pi$
$80$		0			0
$81$		−	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	$-0.211835\pi$
$83$	−1.87868	−	4.53553i	−0.206212	−	0.497840i	−0.992821	+	0.119612i	$0.961835\pi$
$84$	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
$88$	4.82843	−	11.6569i	0.514712	−	1.24262i
$89$	8.65685	+	8.65685i	0.917625	+	0.917625i	0.996856	−	0.0792315i	$-0.0252466\pi$
$89$	8.65685	+	8.65685i	0.917625	+	0.917625i	−0.0792315	+	0.996856i	$0.525247\pi$
$90$		0			0
$91$	−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
$95$		0			0
$96$	−1.65685	−	4.00000i	−0.169102	−	0.408248i
$97$	18.4853			1.87690			0.938448	−	0.345421i	$-0.112264\pi$
$97$	18.4853			1.87690			0.938448	+	0.345421i	$0.112264\pi$
$98$	−7.07107			−0.714286
$99$	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	$0.181745\pi$
$102$	−2.82843	+	1.17157i	−0.280056	+	0.116003i
$103$	−9.48528	−	9.48528i	−0.934613	−	0.934613i	0.0633771	−	0.997990i	$-0.479813\pi$
$103$	−9.48528	−	9.48528i	−0.934613	−	0.934613i	−0.997990	+	0.0633771i	$0.979813\pi$
$104$	2.00000	−	0.828427i	0.196116	−	0.0812340i
$105$		0			0
$106$	0.656854	−	1.58579i	0.0637993	−	0.154025i
$107$	4.12132	+	1.70711i	0.398423	+	0.165032i	0.572893	−	0.819630i	$-0.305821\pi$
$107$	4.12132	+	1.70711i	0.398423	+	0.165032i	−0.174470	+	0.984663i	$0.555821\pi$
$108$	3.17157	−	7.65685i	0.305185	−	0.736781i
$109$	−5.70711	−	13.7782i	−0.546642	−	1.31971i	−0.919962	−	0.392007i	$-0.871781\pi$
$109$	−5.70711	−	13.7782i	−0.546642	−	1.31971i	0.373320	−	0.927702i	$-0.378219\pi$
$110$		0			0
$111$			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
$115$		0			0
$116$	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
$120$		0			0
$121$	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
$125$		0			0
$126$		−	4.82843i		−	0.430150i
$127$	−12.9706			−1.15095			−0.575476	−	0.817819i	$-0.695183\pi$
$127$	−12.9706			−1.15095			−0.575476	+	0.817819i	$0.695183\pi$
$128$			11.3137i			1.00000i
$129$	−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	$0.656627\pi$
$132$	6.82843			0.594338
$133$	2.17157	−	5.24264i	0.188299	−	0.454595i
$134$	−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	−0.232897	−	0.972502i	$-0.574820\pi$
$137$	8.65685	−	8.65685i	0.739605	−	0.739605i	0.972502	+	0.232897i	$0.0748204\pi$
$138$	8.24264	+	3.41421i	0.701660	+	0.290637i
$139$	13.1924	+	5.46447i	1.11896	+	0.463490i	0.864016	−	0.503465i	$-0.167942\pi$
$139$	13.1924	+	5.46447i	1.11896	+	0.463490i	0.254948	+	0.966955i	$0.417942\pi$
$140$		0			0
$141$	−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
$145$		0			0
$146$	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	−0.362992	−	0.931792i	$-0.618245\pi$
$149$	−15.6066	−	6.46447i	−1.27854	−	0.529590i	−0.915551	+	0.402203i	$0.868245\pi$
$150$		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	$0.277239\pi$
$152$	−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
$155$		0			0
$156$	0.828427	+	0.828427i	0.0663273	+	0.0663273i
$157$	−1.70711	+	0.707107i	−0.136242	+	0.0564333i	−0.449763	−	0.893148i	$-0.648491\pi$
$157$	−1.70711	+	0.707107i	−0.136242	+	0.0564333i	0.313521	+	0.949581i	$0.398491\pi$
$158$	−8.48528			−0.675053
$159$	0.928932			0.0736691
$160$		0			0
$161$	11.6569			0.918689
$162$	−5.75736			−0.452341
$163$	−0.464466	+	0.192388i	−0.0363798	+	0.0150690i	−0.400799	−	0.916166i	$-0.631267\pi$
$163$	−0.464466	+	0.192388i	−0.0363798	+	0.0150690i	0.364419	+	0.931235i	$0.381267\pi$
$164$	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	−0.989475	−	0.144707i	$-0.953776\pi$
$167$	−14.6569	−	14.6569i	−1.13418	−	1.13418i	−0.144707	−	0.989475i	$-0.546224\pi$
$168$	1.17157	−	2.82843i	0.0903888	−	0.218218i
$169$	8.77817	−	8.77817i	0.675244	−	0.675244i
$170$		0			0
$171$	−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	$-0.225349\pi$
$173$	−3.12132	−	7.53553i	−0.237310	−	0.572916i	−0.997003	+	0.0773656i	$0.975349\pi$
$174$	2.58579	+	2.58579i	0.196028	+	0.196028i
$175$		0			0
$176$	−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	0.850870	−	0.525377i	$-0.176076\pi$
$179$	−1.63604	−	3.94975i	−0.122283	−	0.295218i	−0.973153	+	0.230159i	$0.926076\pi$
$180$		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	$0.399196\pi$
$182$	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
$185$		0			0
$186$	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
$190$		0			0
$191$	−12.0000			−0.868290			−0.434145	−	0.900843i	$-0.642949\pi$
$191$	−12.0000			−0.868290			−0.434145	+	0.900843i	$0.642949\pi$
$192$	−5.65685	+	2.34315i	−0.408248	+	0.169102i
$193$	1.51472			0.109032			0.0545159	−	0.998513i	$-0.482638\pi$
$193$	1.51472			0.109032			0.0545159	+	0.998513i	$0.482638\pi$
$194$		−	26.1421i		−	1.87690i
$195$		0			0
$196$			10.0000i			0.714286i
$197$	−4.63604	+	11.1924i	−0.330304	+	0.797425i	0.668264	+	0.743924i	$0.267038\pi$
$197$	−4.63604	+	11.1924i	−0.330304	+	0.797425i	−0.998568	+	0.0535002i	$0.982962\pi$
$198$	−5.82843	−	14.0711i	−0.414208	−	0.999987i
$199$	−15.9706	−	15.9706i	−1.13212	−	1.13212i	−0.989824	−	0.142300i	$-0.954550\pi$
$199$	−15.9706	−	15.9706i	−1.13212	−	1.13212i	−0.142300	−	0.989824i	$-0.545450\pi$
$200$		0			0
$201$	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			0
$206$	−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
$210$		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	$0.637932\pi$
$212$	−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
$215$		0			0
$216$	−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
$220$		0			0
$221$	−2.00000	+	0.828427i	−0.134535	+	0.0557260i
$222$	0.828427			0.0556004
$223$	20.9706			1.40429			0.702146	−	0.712033i	$-0.252225\pi$
$223$	20.9706			1.40429			0.702146	+	0.712033i	$0.252225\pi$
$224$	−5.65685	+	5.65685i	−0.377964	+	0.377964i
$225$		0			0
$226$	−8.97056			−0.596713
$227$	−18.6066	+	7.70711i	−1.23496	+	0.511539i	−0.902137	−	0.431449i	$-0.858002\pi$
$227$	−18.6066	+	7.70711i	−1.23496	+	0.511539i	−0.332826	+	0.942988i	$0.608002\pi$
$228$	−4.34315	−	4.34315i	−0.287632	−	0.287632i
$229$	−9.22183	+	22.2635i	−0.609395	+	1.47121i	0.254264	+	0.967135i	$0.418167\pi$
$229$	−9.22183	+	22.2635i	−0.609395	+	1.47121i	−0.863659	+	0.504076i	$0.831833\pi$
$230$		0			0
$231$	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	$-0.710724\pi$
$233$	2.65685	−	2.65685i	0.174056	−	0.174056i	0.788759	+	0.614703i	$0.210724\pi$
$234$	1.00000	−	2.41421i	0.0653720	−	0.157822i
$235$		0			0
$236$	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	$0.0549769\pi$
$239$			5.31371i			0.343715i	−0.985122	+	0.171858i	$0.945023\pi$
$240$		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
$243$	−5.94975	−	14.3640i	−0.381676	−	0.921449i
$244$	−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
$248$		−	11.3137i		−	0.718421i
$249$	−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	$-0.0584109\pi$
$252$	−6.82843			−0.430150
$253$	33.9706	−	14.0711i	2.13571	−	0.884640i
$254$			18.3431i			1.15095i
$255$		0			0
$256$	16.0000			1.00000
$257$	−6.00000			−0.374270			−0.187135	−	0.982334i	$-0.559920\pi$
$257$	−6.00000			−0.374270			−0.187135	+	0.982334i	$0.559920\pi$
$258$			5.51472i			0.343331i
$259$	1.00000	−	0.414214i	0.0621370	−	0.0257380i
$260$		0			0
$261$	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	$-0.168210\pi$
$263$	5.82843	+	5.82843i	0.359396	+	0.359396i	−0.504194	+	0.863590i	$0.668210\pi$
$264$		−	9.65685i		−	0.594338i
$265$		0			0
$266$	−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	0.912803	+	0.408401i	$0.133913\pi$
$269$	9.12132	+	22.0208i	0.556137	+	1.34263i	−0.356666	+	0.934232i	$0.616087\pi$
$270$		0			0
$271$		−	18.0000i		−	1.09342i	−0.837321	−	0.546711i	$-0.815880\pi$
$271$		−	18.0000i		−	1.09342i	0.837321	−	0.546711i	$-0.184120\pi$
$272$		−	11.3137i		−	0.685994i
$273$			0.828427i			0.0501387i
$274$	−12.2426	−	12.2426i	−0.739605	−	0.739605i
$275$		0			0
$276$	4.82843	−	11.6569i	0.290637	−	0.701660i
$277$	−1.70711	−	0.707107i	−0.102570	−	0.0424859i	0.330808	−	0.943698i	$-0.392679\pi$
$277$	−1.70711	−	0.707107i	−0.102570	−	0.0424859i	−0.433378	+	0.901212i	$0.642679\pi$
$278$	7.72792	−	18.6569i	0.463490	−	1.11896i
$279$	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	$0.916282\pi$
$282$	−0.343146	+	0.142136i	−0.0204340	+	0.00846405i
$283$	−5.77817	+	13.9497i	−0.343477	+	0.829226i	0.653882	+	0.756596i	$0.273139\pi$
$283$	−5.77817	+	13.9497i	−0.343477	+	0.829226i	−0.997359	+	0.0726300i	$0.976861\pi$
$284$	11.6569	+	11.6569i	0.691707	+	0.691707i
$285$		0			0
$286$	4.82843			0.285511
$287$	0.343146			0.0202553
$288$	9.65685	+	9.65685i	0.569036	+	0.569036i
$289$	9.00000			0.529412
$290$		0			0
$291$	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	0.347565	+	0.937656i	$0.387009\pi$
$293$	−9.60660	+	23.1924i	−0.561224	+	1.35491i	−0.908788	+	0.417258i	$0.862991\pi$
$294$	−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
$298$	−9.14214	+	22.0711i	−0.529590	+	1.27854i
$299$	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
$303$			2.72792i			0.156715i
$304$	6.14214	+	14.8284i	0.352276	+	0.850469i
$305$		0			0
$306$	6.82843	−	6.82843i	0.390355	−	0.390355i
$307$	6.94975	+	16.7782i	0.396643	+	0.957581i	0.988456	+	0.151506i	$0.0484123\pi$
$307$	6.94975	+	16.7782i	0.396643	+	0.957581i	−0.591813	+	0.806075i	$0.701588\pi$
$308$	−4.82843	−	11.6569i	−0.275125	−	0.664211i
$309$	−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	0.886267	−	0.463174i	$-0.153290\pi$
$313$	7.48528	+	7.48528i	0.423093	+	0.423093i	−0.463174	+	0.886267i	$0.653290\pi$
$314$	1.00000	+	2.41421i	0.0564333	+	0.136242i
$315$		0			0
$316$			12.0000i			0.675053i
$317$	−17.3640	+	7.19239i	−0.975257	+	0.403965i	−0.812667	−	0.582729i	$-0.801985\pi$
$317$	−17.3640	+	7.19239i	−0.975257	+	0.403965i	−0.162591	+	0.986694i	$0.551985\pi$
$318$		−	1.31371i		−	0.0736691i
$319$	15.0711			0.843818
$320$		0			0
$321$	3.41421			0.190563
$322$		−	16.4853i		−	0.918689i
$323$	10.4853	−	4.34315i	0.583417	−	0.241659i
$324$			8.14214i			0.452341i
$325$		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	$0.637245\pi$
$332$	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
$335$		0			0
$336$	−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
$340$		0			0
$341$	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
$345$		0			0
$346$	−10.6569	+	4.41421i	−0.572916	+	0.237310i
$347$	−1.63604	+	3.94975i	−0.0878272	+	0.212034i	−0.961690	−	0.274139i	$-0.911607\pi$
$347$	−1.63604	+	3.94975i	−0.0878272	+	0.212034i	0.873863	+	0.486172i	$0.161607\pi$
$348$	3.65685	−	3.65685i	0.196028	−	0.196028i
$349$	24.6777	−	10.2218i	1.32097	−	0.547162i	0.392901	−	0.919581i	$-0.371472\pi$
$349$	24.6777	−	10.2218i	1.32097	−	0.547162i	0.928065	+	0.372419i	$0.121472\pi$
$350$		0			0
$351$	3.17157			0.169286
$352$	−9.65685	+	23.3137i	−0.514712	+	1.24262i
$353$	−6.00000			−0.319348			−0.159674	−	0.987170i	$-0.551044\pi$
$353$	−6.00000			−0.319348			−0.159674	+	0.987170i	$0.551044\pi$
$354$	5.31371			0.282420
$355$		0			0
$356$	−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	0.0574027	−	0.998351i	$-0.481718\pi$
$359$	−17.8284	−	17.8284i	−0.940948	−	0.940948i	−0.998351	+	0.0574027i	$0.981718\pi$
$360$		0			0
$361$	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
$365$		0			0
$366$	−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
$370$		0			0
$371$	−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	$-0.281867\pi$
$373$	10.2929	+	4.26346i	0.532946	+	0.220753i	−0.0999471	+	0.994993i	$0.531867\pi$
$374$	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
$378$	−3.17157	−	7.65685i	−0.163128	−	0.393826i
$379$	−13.6777	+	33.0208i	−0.702575	+	1.69617i	0.0151948	+	0.999885i	$0.495163\pi$
$379$	−13.6777	+	33.0208i	−0.702575	+	1.69617i	−0.717769	+	0.696281i	$0.754837\pi$
$380$		0			0
$381$	−9.17157	+	3.79899i	−0.469874	+	0.194628i
$382$			16.9706i			0.868290i
$383$	16.9706			0.867155			0.433578	−	0.901116i	$-0.357251\pi$
$383$	16.9706			0.867155			0.433578	+	0.901116i	$0.357251\pi$
$384$	3.31371	+	8.00000i	0.169102	+	0.408248i
$385$		0			0
$386$		−	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	0.555117	+	0.831773i	$0.312674\pi$
$389$	−8.39340	+	20.2635i	−0.425562	+	1.02740i	−0.980679	+	0.195625i	$0.937326\pi$
$390$		0			0
$391$	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
$395$		0			0
$396$	−19.8995	+	8.24264i	−0.999987	+	0.414208i
$397$	9.22183	+	22.2635i	0.462830	+	1.11737i	0.967230	+	0.253901i	$0.0817137\pi$
$397$	9.22183	+	22.2635i	0.462830	+	1.11737i	−0.504400	+	0.863470i	$0.668286\pi$
$398$	−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
$403$	1.17157	+	2.82843i	0.0583602	+	0.140894i
$404$	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
$408$	5.65685	−	2.34315i	0.280056	−	0.116003i
$409$	21.4853	+	21.4853i	1.06238	+	1.06238i	0.997920	+	0.0644584i	$0.0205320\pi$
$409$	21.4853	+	21.4853i	1.06238	+	1.06238i	0.0644584	+	0.997920i	$0.479468\pi$
$410$		0			0
$411$	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
$415$		0			0
$416$	−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	−0.0528644	−	0.998602i	$-0.516835\pi$
$419$	12.6066	−	5.22183i	0.615873	−	0.255103i	0.668737	+	0.743499i	$0.266835\pi$
$420$		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	$-0.00623955\pi$
$422$	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
$425$		0			0
$426$	−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
$430$		0			0
$431$			12.3431i			0.594548i	0.954792	+	0.297274i	$0.0960775\pi$
$431$			12.3431i			0.594548i	−0.954792	+	0.297274i	$0.903922\pi$
$432$	−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
$435$		0			0
$436$	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	−0.984839	−	0.173473i	$-0.944501\pi$
$439$	−17.0000	+	17.0000i	−0.811366	+	0.811366i	0.173473	+	0.984839i	$0.444501\pi$
$440$		0			0
$441$	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	$-0.886989\pi$
$443$	−0.606602	+	1.46447i	−0.0288205	+	0.0695789i	0.908814	+	0.417201i	$0.136989\pi$
$444$		−	1.17157i		−	0.0556004i
$445$		0			0
$446$		−	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	$0.651824\pi$
$450$		0			0
$451$	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
$455$		0			0
$456$	−6.14214	+	6.14214i	−0.287632	+	0.287632i
$457$	7.48528	−	7.48528i	0.350147	−	0.350147i	−0.510017	−	0.860164i	$-0.670361\pi$
$457$	7.48528	−	7.48528i	0.350147	−	0.350147i	0.860164	+	0.510017i	$0.170361\pi$
$458$	31.4853	+	13.0416i	1.47121	+	0.609395i
$459$	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
$463$			22.9706i			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
$465$		0			0
$466$	−3.75736	−	3.75736i	−0.174056	−	0.174056i
$467$	9.09188	+	21.9497i	0.420722	+	1.01571i	0.982135	+	0.188177i	$0.0602580\pi$
$467$	9.09188	+	21.9497i	0.420722	+	1.01571i	−0.561413	+	0.827536i	$0.689742\pi$
$468$	−3.41421	−	1.41421i	−0.157822	−	0.0653720i
$469$	−7.82843	−	3.24264i	−0.361483	−	0.149731i
$470$		0			0
$471$	−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
$475$		0			0
$476$	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	$0.269772\pi$
$480$		0			0
$481$	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
$485$		0			0
$486$	−20.3137	+	8.41421i	−0.921449	+	0.381676i
$487$	11.0000	+	11.0000i	0.498458	+	0.498458i	0.910958	−	0.412500i	$-0.135344\pi$
$487$	11.0000	+	11.0000i	0.498458	+	0.498458i	−0.412500	+	0.910958i	$0.635344\pi$
$488$	2.00000	+	4.82843i	0.0905357	+	0.218573i
$489$	−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	$0.214535\pi$
$492$	0.142136	−	0.343146i	0.00640797	−	0.0154702i
$493$	3.65685	+	8.82843i	0.164696	+	0.397612i
$494$	−3.07107	−	3.07107i	−0.138174	−	0.138174i
$495$		0			0
$496$	−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	0.901195	−	0.433415i	$-0.142691\pi$
$499$	−0.949747	−	2.29289i	−0.0425165	−	0.102644i	−0.943711	+	0.330771i	$0.892691\pi$
$500$		0			0
$501$	−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	$-0.635742\pi$
$503$	11.1421	−	11.1421i	0.496803	−	0.496803i	0.910441	+	0.413638i	$0.135742\pi$
$504$			9.65685i			0.430150i
$505$		0			0
$506$	−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	−0.876709	−	0.481021i	$-0.840266\pi$
$509$	−26.0919	+	10.8076i	−1.15650	+	0.479039i	−0.279793	+	0.960060i	$0.590266\pi$
$510$		0			0
$511$	14.0000			0.619324
$512$		−	22.6274i		−	1.00000i
$513$	−16.6274			−0.734118
$514$			8.48528i			0.374270i
$515$		0			0
$516$	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
$520$		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	$0.216974\pi$
$522$	−10.6569	−	4.41421i	−0.466438	−	0.193205i
$523$	−19.1924	−	7.94975i	−0.839225	−	0.347618i	−0.0786768	−	0.996900i	$-0.525070\pi$
$523$	−19.1924	−	7.94975i	−0.839225	−	0.347618i	−0.760548	+	0.649282i	$0.775070\pi$
$524$	32.7279	−	13.5563i	1.42973	−	0.592212i
$525$		0			0
$526$	8.24264	−	8.24264i	0.359396	−	0.359396i
$527$			11.3137i			0.492833i
$528$	−13.6569			−0.594338
$529$		−	44.9411i		−	1.95396i
$530$		0			0
$531$	−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
$535$		0			0
$536$	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
$540$		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	$0.593737\pi$
$542$	−25.4558			−1.09342
$543$	13.4142			0.575659
$544$	−16.0000			−0.685994
$545$		0			0
$546$	1.17157			0.0501387
$547$	17.5355	−	7.26346i	0.749765	−	0.310563i	0.0251195	−	0.999684i	$-0.492003\pi$
$547$	17.5355	−	7.26346i	0.749765	−	0.310563i	0.724646	+	0.689122i	$0.242003\pi$
$548$	−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
$552$	−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
$555$		0			0
$556$	−26.3848	−	10.9289i	−1.11896	−	0.463490i
$557$	−15.1213	−	36.5061i	−0.640711	−	1.54681i	−0.825722	−	0.564077i	$-0.809232\pi$
$557$	−15.1213	−	36.5061i	−0.640711	−	1.54681i	0.185012	−	0.982736i	$-0.440768\pi$
$558$	−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
$563$	−7.87868	−	19.0208i	−0.332047	−	0.801632i	−0.998430	−	0.0560220i	$-0.982158\pi$
$563$	−7.87868	−	19.0208i	−0.332047	−	0.801632i	0.666383	−	0.745610i	$-0.267842\pi$
$564$	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	0.944102	−	0.329654i	$-0.106932\pi$
$569$	14.6569	+	14.6569i	0.614447	+	0.614447i	−0.329654	+	0.944102i	$0.606932\pi$
$570$		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	$0.172290\pi$
$572$		−	6.82843i		−	0.285511i
$573$	−8.48528	+	3.51472i	−0.354478	+	0.146829i
$574$		−	0.485281i		−	0.0202553i
$575$		0			0
$576$	13.6569	−	13.6569i	0.569036	−	0.569036i
$577$	−18.9706			−0.789755			−0.394877	−	0.918734i	$-0.629213\pi$
$577$	−18.9706			−0.789755			−0.394877	+	0.918734i	$0.629213\pi$
$578$		−	12.7279i		−	0.529412i
$579$	1.07107	−	0.443651i	0.0445121	−	0.0184375i
$580$		0			0
$581$	−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
$585$		0			0
$586$	32.7990	+	13.5858i	1.35491	+	0.561224i
$587$	12.6066	+	5.22183i	0.520330	+	0.215528i	0.627362	−	0.778728i	$-0.284135\pi$
$587$	12.6066	+	5.22183i	0.520330	+	0.215528i	−0.107032	+	0.994256i	$0.534135\pi$
$588$	2.92893	+	7.07107i	0.120787	+	0.291606i
$589$	−6.14214	−	14.8284i	−0.253082	−	0.610995i
$590$		0			0
$591$			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
$595$		0			0
$596$	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	−0.0935555	+	0.995614i	$0.529823\pi$
$599$	−26.6569	+	26.6569i	−1.08917	+	1.08917i	−0.995614	+	0.0935555i	$0.970177\pi$
$600$		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	$0.968468\pi$
$602$	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
$605$		0			0
$606$	3.85786			0.156715
$607$	32.9706			1.33823			0.669117	−	0.743157i	$-0.266673\pi$
$607$	32.9706			1.33823			0.669117	+	0.743157i	$0.266673\pi$
$608$	20.9706	−	8.68629i	0.850469	−	0.352276i
$609$	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
$613$	−1.32233	+	3.19239i	−0.0534084	+	0.128939i	−0.948332	−	0.317281i	$-0.897230\pi$
$613$	−1.32233	+	3.19239i	−0.0534084	+	0.128939i	0.894923	+	0.446220i	$0.147230\pi$
$614$	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	−0.996873	−	0.0790202i	$-0.974821\pi$
$617$	−22.7990	+	22.7990i	−0.917853	+	0.917853i	0.0790202	+	0.996873i	$0.474821\pi$
$618$	−5.55635	+	13.4142i	−0.223509	+	0.539599i
$619$	−21.7782	−	9.02082i	−0.875339	−	0.362577i	−0.100651	−	0.994922i	$-0.532093\pi$
$619$	−21.7782	−	9.02082i	−0.875339	−	0.362577i	−0.774687	+	0.632345i	$0.782093\pi$
$620$		0			0
$621$	−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
$625$		0			0
$626$	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
$630$		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	$-0.116721\pi$
$632$	16.9706			0.675053
$633$	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
$637$	−3.53553	+	1.46447i	−0.140083	+	0.0580243i
$638$		−	21.3137i		−	0.843818i
$639$	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	$0.452960\pi$
$642$		−	4.82843i		−	0.190563i
$643$	−11.4350	+	4.73654i	−0.450954	+	0.186791i	−0.596588	−	0.802547i	$-0.703478\pi$
$643$	−11.4350	+	4.73654i	−0.450954	+	0.186791i	0.145635	+	0.989338i	$0.453478\pi$
$644$	−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	$-0.304882\pi$
$647$	−6.17157	−	6.17157i	−0.242630	−	0.242630i	−0.817937	+	0.575308i	$0.804882\pi$
$648$	11.5147			0.452341
$649$	15.4853	−	15.4853i	0.607850	−	0.607850i
$650$		0			0
$651$	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	$-0.159111\pi$
$653$	−2.09188	−	5.05025i	−0.0818617	−	0.197632i	−0.959511	+	0.281672i	$0.909111\pi$
$654$	−11.4142	+	11.4142i	−0.446331	+	0.446331i
$655$		0			0
$656$	−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	−0.988998	−	0.147926i	$-0.952740\pi$
$659$	−10.1213	−	24.4350i	−0.394271	−	0.951854i	0.594728	−	0.803927i	$-0.297260\pi$
$660$		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	$0.966665\pi$
$662$	−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
$665$		0			0
$666$	−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
$670$		0			0
$671$	−8.24264			−0.318204
$672$	−2.34315	+	5.65685i	−0.0903888	+	0.218218i
$673$	−22.4853			−0.866744			−0.433372	−	0.901215i	$-0.642676\pi$
$673$	−22.4853			−0.866744			−0.433372	+	0.901215i	$0.642676\pi$
$674$	−24.0000			−0.924445
$675$		0			0
$676$	−17.5563	+	17.5563i	−0.675244	+	0.675244i
$677$	−15.6066	+	37.6777i	−0.599810	+	1.44807i	0.273964	+	0.961740i	$0.411665\pi$
$677$	−15.6066	+	37.6777i	−0.599810	+	1.44807i	−0.873775	+	0.486331i	$0.838335\pi$
$678$	−6.34315	+	2.62742i	−0.243607	+	0.100905i
$679$	−18.4853	−	18.4853i	−0.709400	−	0.709400i
$680$		0			0
$681$	−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	$-0.307785\pi$
$683$	10.1213	+	4.19239i	0.387282	+	0.160417i	−0.180543	+	0.983567i	$0.557785\pi$
$684$	17.8995	+	7.41421i	0.684404	+	0.283490i
$685$		0			0
$686$	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
$690$		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	$0.661482\pi$
$692$	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
$695$		0			0
$696$	−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
$700$		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	$0.356259\pi$
$702$		−	4.48528i		−	0.169286i
$703$	−3.07107			−0.115828
$704$	32.9706	+	13.6569i	1.24262	+	0.514712i
$705$		0			0
$706$			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	−0.668945	−	0.743312i	$-0.733254\pi$
$709$	8.77817	−	21.1924i	0.329671	−	0.795897i	0.998616	−	0.0525851i	$-0.0167461\pi$
$710$		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
$717$	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	$-0.768479\pi$
$719$		−	35.6569i		−	1.32978i	0.746943	−	0.664888i	$-0.231521\pi$
$720$		0			0
$721$			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
$725$		0			0
$726$	3.68629	−	8.89949i	0.136811	−	0.330291i
$727$	9.97056	−	9.97056i	0.369788	−	0.369788i	−0.497612	−	0.867400i	$-0.665790\pi$
$727$	9.97056	−	9.97056i	0.369788	−	0.369788i	0.867400	+	0.497612i	$0.165790\pi$
$728$	−2.82843	−	1.17157i	−0.104828	−	0.0434214i
$729$	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
$733$	33.2635	−	13.7782i	1.22861	−	0.508908i	0.328475	−	0.944513i	$-0.393465\pi$
$733$	33.2635	−	13.7782i	1.22861	−	0.508908i	0.900138	+	0.435604i	$0.143465\pi$
$734$	−8.48528			−0.313197
$735$		0			0
$736$	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	−0.374124	−	0.927379i	$-0.622057\pi$
$739$	0.464466	−	0.192388i	0.0170857	−	0.00707711i	0.391210	+	0.920301i	$0.372057\pi$
$740$		0			0
$741$	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	−0.984410	−	0.175887i	$-0.943721\pi$
$743$	−31.6274	−	31.6274i	−1.16030	−	1.16030i	−0.175887	−	0.984410i	$-0.556279\pi$
$744$	−3.31371	−	8.00000i	−0.121486	−	0.293294i
$745$		0			0
$746$	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
$750$		0			0
$751$			10.9706i			0.400322i	0.979763	+	0.200161i	$0.0641464\pi$
$751$			10.9706i			0.400322i	−0.979763	+	0.200161i	$0.935854\pi$
$752$		−	1.37258i		−	0.0500530i
$753$		−	13.2132i		−	0.481516i
$754$	2.58579	−	2.58579i	0.0941688	−	0.0941688i
$755$		0			0
$756$	−10.8284	+	4.48528i	−0.393826	+	0.163128i
$757$	33.2635	+	13.7782i	1.20898	+	0.500776i	0.893890	−	0.448285i	$-0.147965\pi$
$757$	33.2635	+	13.7782i	1.20898	+	0.500776i	0.315090	+	0.949062i	$0.397965\pi$
$758$	46.6985	+	19.3431i	1.69617	+	0.702575i
$759$	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	$-0.527054\pi$
$762$	5.37258	+	12.9706i	0.194628	+	0.469874i
$763$	−8.07107	+	19.4853i	−0.292192	+	0.705415i
$764$	24.0000			0.868290
$765$		0			0
$766$		−	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	$0.468297\pi$
$770$		0			0
$771$	−4.24264	+	1.75736i	−0.152795	+	0.0632897i
$772$	−3.02944			−0.109032
$773$	−12.0919	+	29.1924i	−0.434915	+	1.04998i	0.542766	+	0.839884i	$0.317377\pi$
$773$	−12.0919	+	29.1924i	−0.434915	+	1.04998i	−0.977681	+	0.210094i	$0.932623\pi$
$774$	−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
$778$	28.6569	+	11.8701i	1.02740	+	0.425562i
$779$	−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
$783$		−	14.0000i		−	0.500319i
$784$		−	20.0000i		−	0.714286i
$785$		0			0
$786$	13.5563	+	13.5563i	0.483539	+	0.483539i
$787$	0.949747	+	2.29289i	0.0338548	+	0.0817328i	0.939903	−	0.341442i	$-0.110915\pi$
$787$	0.949747	+	2.29289i	0.0338548	+	0.0817328i	−0.906048	+	0.423175i	$0.860915\pi$
$788$	9.27208	−	22.3848i	0.330304	−	0.797425i
$789$	5.82843	+	2.41421i	0.207498	+	0.0859483i
$790$		0			0
$791$	−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
$795$		0			0
$796$	31.9411	+	31.9411i	1.13212	+	1.13212i
$797$	26.0919	−	10.8076i	0.924222	−	0.382825i	0.130738	−	0.991417i	$-0.458265\pi$
$797$	26.0919	−	10.8076i	0.924222	−	0.382825i	0.793484	+	0.608592i	$0.208265\pi$
$798$	−6.14214			−0.217429
$799$	−0.970563			−0.0343360
$800$		0			0
$801$	−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
$805$		0			0
$806$	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	−0.0248928	+	0.999690i	$0.507924\pi$
$809$	−29.1421	+	29.1421i	−1.02458	+	1.02458i	−0.999690	+	0.0248928i	$0.992076\pi$
$810$		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	$0.921857\pi$
$812$	−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
$815$		0			0
$816$	−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			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	$0.758809\pi$
$822$	−12.2426	−	5.07107i	−0.427011	−	0.176874i
$823$	−35.9706	+	35.9706i	−1.25385	+	1.25385i	−0.299877	+	0.953978i	$0.596946\pi$
$823$	−35.9706	+	35.9706i	−1.25385	+	1.25385i	−0.953978	+	0.299877i	$0.903054\pi$
$824$	26.8284	−	26.8284i	0.934613	−	0.934613i
$825$		0			0
$826$	−3.75736	−	9.07107i	−0.130735	−	0.315623i
$827$	−16.1213	+	38.9203i	−0.560593	+	1.35339i	0.348699	+	0.937235i	$0.386623\pi$
$827$	−16.1213	+	38.9203i	−0.560593	+	1.35339i	−0.909293	+	0.416157i	$0.863377\pi$
$828$			39.7990i			1.38311i
$829$	34.1924	−	14.1630i	1.18755	−	0.491900i	0.300594	−	0.953752i	$-0.402815\pi$
$829$	34.1924	−	14.1630i	1.18755	−	0.491900i	0.886957	+	0.461853i	$0.152815\pi$
$830$		0			0
$831$	−1.41421			−0.0490585
$832$	2.34315	+	5.65685i	0.0812340	+	0.196116i
$833$	−14.1421			−0.489996
$834$		−	15.4558i		−	0.535192i
$835$		0			0
$836$			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	0.854258	−	0.519850i	$-0.174012\pi$
$839$	9.68629	+	9.68629i	0.334408	+	0.334408i	−0.519850	+	0.854258i	$0.674012\pi$
$840$		0			0
$841$	−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
$845$		0			0
$846$	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
$850$		0			0
$851$	−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	−0.997622	−	0.0689279i	$-0.978042\pi$
$853$	−51.1630	−	21.1924i	−1.75179	−	0.725614i	−0.754164	−	0.656686i	$-0.771958\pi$
$854$	−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	$-0.325170\pi$
$857$	−9.68629	−	9.68629i	−0.330877	−	0.330877i	−0.852920	+	0.522042i	$0.825170\pi$
$858$	3.41421	−	1.41421i	0.116559	−	0.0482805i
$859$	−1.67767	+	4.05025i	−0.0572413	+	0.138193i	−0.949913	−	0.312515i	$-0.898828\pi$
$859$	−1.67767	+	4.05025i	−0.0572413	+	0.138193i	0.892671	+	0.450708i	$0.148828\pi$
$860$		0			0
$861$	0.242641	−	0.100505i	0.00826917	−	0.00342520i
$862$	17.4558			0.594548
$863$	−21.9411			−0.746885			−0.373442	−	0.927653i	$-0.621823\pi$
$863$	−21.9411			−0.746885			−0.373442	+	0.927653i	$0.621823\pi$
$864$	21.6569	+	8.97056i	0.736781	+	0.305185i
$865$		0			0
$866$	−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
$870$		0			0
$871$	−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
$875$		0			0
$876$	5.79899	−	14.0000i	0.195930	−	0.473016i
$877$	0.736544	+	1.77817i	0.0248713	+	0.0600447i	0.935827	−	0.352459i	$-0.114654\pi$
$877$	0.736544	+	1.77817i	0.0248713	+	0.0600447i	−0.910956	+	0.412504i	$0.864654\pi$
$878$	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
$883$	−20.5650	−	49.6482i	−0.692066	−	1.67080i	−0.740575	−	0.671973i	$-0.765447\pi$
$883$	−20.5650	−	49.6482i	−0.692066	−	1.67080i	0.0485090	−	0.998823i	$-0.484553\pi$
$884$	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	−0.744882	−	0.667196i	$-0.767494\pi$
$887$	−2.31371	+	2.31371i	−0.0776867	+	0.0776867i	0.667196	+	0.744882i	$0.267494\pi$
$888$	−1.65685			−0.0556004
$889$	12.9706	+	12.9706i	0.435019	+	0.435019i
$890$		0			0
$891$	−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
$895$		0			0
$896$	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
$900$		0			0
$901$	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
$905$		0			0
$906$	2.10051	+	0.870058i	0.0697846	+	0.0289057i
$907$	15.7782	+	6.53553i	0.523906	+	0.217009i	0.628932	−	0.777461i	$-0.283493\pi$
$907$	15.7782	+	6.53553i	0.523906	+	0.217009i	−0.105026	+	0.994469i	$0.533493\pi$
$908$	37.2132	−	15.4142i	1.23496	−	0.511539i
$909$	−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
$913$			21.8995i			0.724767i
$914$	−10.5858	−	10.5858i	−0.350147	−	0.350147i
$915$		0			0
$916$	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	−0.833458	−	0.552583i	$-0.813642\pi$
$919$	−8.51472	+	8.51472i	−0.280875	+	0.280875i	0.552583	+	0.833458i	$0.313642\pi$
$920$		0			0
$921$	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
$925$		0			0
$926$	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	$0.549887\pi$
$930$		0			0
$931$	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
$935$		0			0
$936$	−2.00000	+	4.82843i	−0.0653720	+	0.157822i
$937$	−19.0000	+	19.0000i	−0.620703	+	0.620703i	−0.945711	−	0.325008i	$-0.894633\pi$
$937$	−19.0000	+	19.0000i	−0.620703	+	0.620703i	0.325008	+	0.945711i	$0.394633\pi$
$938$	−4.58579	+	11.0711i	−0.149731	+	0.361483i
$939$	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
$943$		−	2.00000i		−	0.0651290i
$944$	−7.51472	+	18.1421i	−0.244583	+	0.590476i
$945$		0			0
$946$	22.7279	−	22.7279i	0.738948	−	0.738948i
$947$	−9.33452	−	22.5355i	−0.303331	−	0.732306i	−0.999890	−	0.0148070i	$-0.995287\pi$
$947$	−9.33452	−	22.5355i	−0.303331	−	0.732306i	0.696559	−	0.717499i	$-0.254713\pi$
$948$	3.51472	+	8.48528i	0.114153	+	0.275589i
$949$	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	0.428676	−	0.903458i	$-0.358980\pi$
$953$	−14.6569	−	14.6569i	−0.474782	−	0.474782i	−0.903458	+	0.428676i	$0.858980\pi$
$954$	1.58579	+	3.82843i	0.0513417	+	0.123950i
$955$		0			0
$956$		−	10.6274i		−	0.343715i
$957$	10.6569	−	4.41421i	0.344487	−	0.142691i
$958$		−	40.9706i		−	1.32370i
$959$	−17.3137			−0.559089
$960$		0			0
$961$	−15.0000			−0.483871
$962$		−	0.828427i		−	0.0267096i
$963$	−9.94975	+	4.12132i	−0.320626	+	0.132808i
$964$		−	16.9706i		−	0.546585i
$965$		0			0
$966$	−4.82843	−	11.6569i	−0.155352	−	0.375053i
$967$	6.02944	+	6.02944i	0.193894	+	0.193894i	0.797376	−	0.603483i	$-0.206221\pi$
$967$	6.02944	+	6.02944i	0.193894	+	0.193894i	−0.603483	+	0.797376i	$0.706221\pi$
$968$	−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	$0.498023\pi$
$972$	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
$975$		0			0
$976$	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
$980$		0			0
$981$	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	$-0.604034\pi$
$983$	19.6274	−	19.6274i	0.626017	−	0.626017i	0.947064	+	0.321046i	$0.104034\pi$
$984$	−0.485281	−	0.201010i	−0.0154702	−	0.00640797i
$985$		0			0
$986$	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
$990$		0			0
$991$	−16.0000			−0.508257			−0.254128	−	0.967170i	$-0.581789\pi$
$991$	−16.0000			−0.508257			−0.254128	+	0.967170i	$0.581789\pi$
$992$			22.6274i			0.718421i
$993$	−1.07107			−0.0339893
$994$	16.4853			0.522881
$995$		0			0
$996$	5.31371	+	5.31371i	0.168371	+	0.168371i
$997$	20.1924	−	48.7487i	0.639499	−	1.54389i	−0.187848	−	0.982198i	$-0.560151\pi$
$997$	20.1924	−	48.7487i	0.639499	−	1.54389i	0.827348	−	0.561690i	$-0.189849\pi$
$998$	−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	800.2.y.a.501.1		4
5.2	odd	4		800.2.ba.a.149.1		4
5.3	odd	4		800.2.ba.b.149.1		4
5.4	even	2		32.2.g.a.21.1	✓	4
15.14	odd	2		288.2.v.a.181.1		4
20.19	odd	2		128.2.g.a.49.1		4
32.29	even	8	inner	800.2.y.a.701.1		4
40.19	odd	2		256.2.g.a.97.1		4
40.29	even	2		256.2.g.b.97.1		4
60.59	even	2		1152.2.v.a.433.1		4
80.19	odd	4		512.2.g.c.449.1		4
80.29	even	4		512.2.g.a.449.1		4
80.59	odd	4		512.2.g.b.449.1		4
80.69	even	4		512.2.g.d.449.1		4
160.19	odd	8		256.2.g.a.161.1		4
160.29	even	8		32.2.g.a.29.1	yes	4
160.59	odd	8		512.2.g.b.65.1		4
160.69	even	8		512.2.g.d.65.1		4
160.93	odd	8		800.2.ba.a.349.1		4
160.99	odd	8		128.2.g.a.81.1		4
160.109	even	8		256.2.g.b.161.1		4
160.139	odd	8		512.2.g.c.65.1		4
160.149	even	8		512.2.g.a.65.1		4
160.157	odd	8		800.2.ba.b.349.1		4
320.29	even	16		4096.2.a.e.1.2		4
320.99	odd	16		4096.2.a.f.1.3		4
320.189	even	16		4096.2.a.e.1.3		4
320.259	odd	16		4096.2.a.f.1.2		4
480.29	odd	8		288.2.v.a.253.1		4
480.419	even	8		1152.2.v.a.721.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.2.g.a.21.1	✓	4	5.4	even	2
32.2.g.a.29.1	yes	4	160.29	even	8
128.2.g.a.49.1		4	20.19	odd	2
128.2.g.a.81.1		4	160.99	odd	8
256.2.g.a.97.1		4	40.19	odd	2
256.2.g.a.161.1		4	160.19	odd	8
256.2.g.b.97.1		4	40.29	even	2
256.2.g.b.161.1		4	160.109	even	8
288.2.v.a.181.1		4	15.14	odd	2
288.2.v.a.253.1		4	480.29	odd	8
512.2.g.a.65.1		4	160.149	even	8
512.2.g.a.449.1		4	80.29	even	4
512.2.g.b.65.1		4	160.59	odd	8
512.2.g.b.449.1		4	80.59	odd	4
512.2.g.c.65.1		4	160.139	odd	8
512.2.g.c.449.1		4	80.19	odd	4
512.2.g.d.65.1		4	160.69	even	8
512.2.g.d.449.1		4	80.69	even	4
800.2.y.a.501.1		4	1.1	even	1	trivial
800.2.y.a.701.1		4	32.29	even	8	inner
800.2.ba.a.149.1		4	5.2	odd	4
800.2.ba.a.349.1		4	160.93	odd	8
800.2.ba.b.149.1		4	5.3	odd	4
800.2.ba.b.349.1		4	160.157	odd	8
1152.2.v.a.433.1		4	60.59	even	2
1152.2.v.a.721.1		4	480.419	even	8
4096.2.a.e.1.2		4	320.29	even	16
4096.2.a.e.1.3		4	320.189	even	16
4096.2.a.f.1.2		4	320.259	odd	16
4096.2.a.f.1.3		4	320.99	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:	\( N \)	\(=\)	\( 800 = 2^{5} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	800.y (of order \(8\), degree \(4\), minimal)

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

Introduction

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