LMFDB - Embedded newform 800.2.y.a.301.1

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			301.1
Root			$0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	800.301
Dual form			800.2.y.a.101.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421i q^{2} +(-0.707107 + 1.70711i) q^{3} -2.00000 q^{4} +(2.41421 + 1.00000i) q^{6} +(-1.00000 + 1.00000i) q^{7} +2.82843i q^{8} +(-0.292893 - 0.292893i) q^{9} +O(q^{10})$	\(q-1.41421i q^{2} +(-0.707107 + 1.70711i) q^{3} -2.00000 q^{4} +(2.41421 + 1.00000i) q^{6} +(-1.00000 + 1.00000i) q^{7} +2.82843i q^{8} +(-0.292893 - 0.292893i) q^{9} +(0.121320 + 0.292893i) q^{11} +(1.41421 - 3.41421i) q^{12} +(-1.70711 - 0.707107i) q^{13} +(1.41421 + 1.41421i) q^{14} +4.00000 q^{16} -2.82843i q^{17} +(-0.414214 + 0.414214i) q^{18} +(-5.53553 - 2.29289i) q^{19} +(-1.00000 - 2.41421i) q^{21} +(0.414214 - 0.171573i) q^{22} +(-0.171573 - 0.171573i) q^{23} +(-4.82843 - 2.00000i) q^{24} +(-1.00000 + 2.41421i) q^{26} +(-4.41421 + 1.82843i) q^{27} +(2.00000 - 2.00000i) q^{28} +(1.12132 - 2.70711i) q^{29} -4.00000 q^{31} -5.65685i q^{32} -0.585786 q^{33} -4.00000 q^{34} +(0.585786 + 0.585786i) q^{36} +(-1.70711 + 0.707107i) q^{37} +(-3.24264 + 7.82843i) q^{38} +(2.41421 - 2.41421i) q^{39} +(-5.82843 - 5.82843i) q^{41} +(-3.41421 + 1.41421i) q^{42} +(-3.29289 - 7.94975i) q^{43} +(-0.242641 - 0.585786i) q^{44} +(-0.242641 + 0.242641i) q^{46} +11.6569i q^{47} +(-2.82843 + 6.82843i) q^{48} +5.00000i q^{49} +(4.82843 + 2.00000i) q^{51} +(3.41421 + 1.41421i) q^{52} +(-3.12132 - 7.53553i) q^{53} +(2.58579 + 6.24264i) q^{54} +(-2.82843 - 2.82843i) q^{56} +(7.82843 - 7.82843i) q^{57} +(-3.82843 - 1.58579i) q^{58} +(-6.12132 + 2.53553i) q^{59} +(0.292893 - 0.707107i) q^{61} +5.65685i q^{62} +0.585786 q^{63} -8.00000 q^{64} +0.828427i q^{66} +(-1.53553 + 3.70711i) q^{67} +5.65685i q^{68} +(0.414214 - 0.171573i) q^{69} +(-0.171573 + 0.171573i) q^{71} +(0.828427 - 0.828427i) q^{72} +(-7.00000 - 7.00000i) q^{73} +(1.00000 + 2.41421i) q^{74} +(11.0711 + 4.58579i) q^{76} +(-0.414214 - 0.171573i) q^{77} +(-3.41421 - 3.41421i) q^{78} +6.00000i q^{79} -10.0711i q^{81} +(-8.24264 + 8.24264i) q^{82} +(-6.12132 - 2.53553i) q^{83} +(2.00000 + 4.82843i) q^{84} +(-11.2426 + 4.65685i) q^{86} +(3.82843 + 3.82843i) q^{87} +(-0.828427 + 0.343146i) q^{88} +(-2.65685 + 2.65685i) q^{89} +(2.41421 - 1.00000i) q^{91} +(0.343146 + 0.343146i) q^{92} +(2.82843 - 6.82843i) q^{93} +16.4853 q^{94} +(9.65685 + 4.00000i) q^{96} +1.51472 q^{97} +7.07107 q^{98} +(0.0502525 - 0.121320i) 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 $\left(\mathbb{Z}/800\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$577$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$	$1$

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	+	1.70711i	−0.408248	+	0.985599i	0.577350	+	0.816497i	$0.304087\pi$
$3$	−0.707107	+	1.70711i	−0.408248	+	0.985599i	−0.985599	+	0.169102i	$0.945913\pi$
$4$	−2.00000			−1.00000
$5$		0			0
$5$		0			0
$6$	2.41421	+	1.00000i	0.985599	+	0.408248i
$7$	−1.00000	+	1.00000i	−0.377964	+	0.377964i	−0.870367	−	0.492403i	$-0.836119\pi$
$7$	−1.00000	+	1.00000i	−0.377964	+	0.377964i	0.492403	+	0.870367i	$0.336119\pi$
$8$			2.82843i			1.00000i
$9$	−0.292893	−	0.292893i	−0.0976311	−	0.0976311i
$10$		0			0
$11$	0.121320	+	0.292893i	0.0365795	+	0.0883106i	0.941113	−	0.338091i	$-0.109781\pi$
$11$	0.121320	+	0.292893i	0.0365795	+	0.0883106i	−0.904534	+	0.426401i	$0.859781\pi$
$12$	1.41421	−	3.41421i	0.408248	−	0.985599i
$13$	−1.70711	−	0.707107i	−0.473466	−	0.196116i	0.133174	−	0.991093i	$-0.457483\pi$
$13$	−1.70711	−	0.707107i	−0.473466	−	0.196116i	−0.606640	+	0.794977i	$0.707483\pi$
$14$	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	$-0.111442\pi$
$18$	−0.414214	+	0.414214i	−0.0976311	+	0.0976311i
$19$	−5.53553	−	2.29289i	−1.26994	−	0.526026i	−0.356993	−	0.934107i	$-0.616198\pi$
$19$	−5.53553	−	2.29289i	−1.26994	−	0.526026i	−0.912946	+	0.408081i	$0.866198\pi$
$20$		0			0
$21$	−1.00000	−	2.41421i	−0.218218	−	0.526825i
$22$	0.414214	−	0.171573i	0.0883106	−	0.0365795i
$23$	−0.171573	−	0.171573i	−0.0357754	−	0.0357754i	0.688993	−	0.724768i	$-0.258053\pi$
$23$	−0.171573	−	0.171573i	−0.0357754	−	0.0357754i	−0.724768	+	0.688993i	$0.758053\pi$
$24$	−4.82843	−	2.00000i	−0.985599	−	0.408248i
$25$		0			0
$26$	−1.00000	+	2.41421i	−0.196116	+	0.473466i
$27$	−4.41421	+	1.82843i	−0.849516	+	0.351881i
$28$	2.00000	−	2.00000i	0.377964	−	0.377964i
$29$	1.12132	−	2.70711i	0.208224	−	0.502697i	−0.784920	−	0.619598i	$-0.787296\pi$
$29$	1.12132	−	2.70711i	0.208224	−	0.502697i	0.993144	+	0.116900i	$0.0372958\pi$
$30$		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
$33$	−0.585786			−0.101972
$34$	−4.00000			−0.685994
$35$		0			0
$36$	0.585786	+	0.585786i	0.0976311	+	0.0976311i
$37$	−1.70711	+	0.707107i	−0.280647	+	0.116248i	−0.518567	−	0.855037i	$-0.673534\pi$
$37$	−1.70711	+	0.707107i	−0.280647	+	0.116248i	0.237920	+	0.971285i	$0.423534\pi$
$38$	−3.24264	+	7.82843i	−0.526026	+	1.26994i
$39$	2.41421	−	2.41421i	0.386584	−	0.386584i
$40$		0			0
$41$	−5.82843	−	5.82843i	−0.910247	−	0.910247i	0.0860440	−	0.996291i	$-0.472577\pi$
$41$	−5.82843	−	5.82843i	−0.910247	−	0.910247i	−0.996291	+	0.0860440i	$0.972577\pi$
$42$	−3.41421	+	1.41421i	−0.526825	+	0.218218i
$43$	−3.29289	−	7.94975i	−0.502162	−	1.21233i	−0.948304	−	0.317363i	$-0.897203\pi$
$43$	−3.29289	−	7.94975i	−0.502162	−	1.21233i	0.446143	−	0.894962i	$-0.352797\pi$
$44$	−0.242641	−	0.585786i	−0.0365795	−	0.0883106i
$45$		0			0
$46$	−0.242641	+	0.242641i	−0.0357754	+	0.0357754i
$47$			11.6569i			1.70033i	0.526519	+	0.850163i	$0.323497\pi$
$47$			11.6569i			1.70033i	−0.526519	+	0.850163i	$0.676503\pi$
$48$	−2.82843	+	6.82843i	−0.408248	+	0.985599i
$49$			5.00000i			0.714286i
$50$		0			0
$51$	4.82843	+	2.00000i	0.676115	+	0.280056i
$52$	3.41421	+	1.41421i	0.473466	+	0.196116i
$53$	−3.12132	−	7.53553i	−0.428746	−	1.03509i	−0.979686	−	0.200540i	$-0.935730\pi$
$53$	−3.12132	−	7.53553i	−0.428746	−	1.03509i	0.550939	−	0.834545i	$-0.314270\pi$
$54$	2.58579	+	6.24264i	0.351881	+	0.849516i
$55$		0			0
$56$	−2.82843	−	2.82843i	−0.377964	−	0.377964i
$57$	7.82843	−	7.82843i	1.03690	−	1.03690i
$58$	−3.82843	−	1.58579i	−0.502697	−	0.208224i
$59$	−6.12132	+	2.53553i	−0.796928	+	0.330098i	−0.743725	−	0.668485i	$-0.766943\pi$
$59$	−6.12132	+	2.53553i	−0.796928	+	0.330098i	−0.0532027	+	0.998584i	$0.516943\pi$
$60$		0			0
$61$	0.292893	−	0.707107i	0.0375011	−	0.0905357i	−0.904019	−	0.427492i	$-0.859397\pi$
$61$	0.292893	−	0.707107i	0.0375011	−	0.0905357i	0.941520	+	0.336956i	$0.109397\pi$
$62$			5.65685i			0.718421i
$63$	0.585786			0.0738022
$64$	−8.00000			−1.00000
$65$		0			0
$66$			0.828427i			0.101972i
$67$	−1.53553	+	3.70711i	−0.187595	+	0.452895i	−0.989496	−	0.144563i	$-0.953822\pi$
$67$	−1.53553	+	3.70711i	−0.187595	+	0.452895i	0.801900	+	0.597458i	$0.203822\pi$
$68$			5.65685i			0.685994i
$69$	0.414214	−	0.171573i	0.0498655	−	0.0206549i
$70$		0			0
$71$	−0.171573	+	0.171573i	−0.0203620	+	0.0203620i	−0.717214	−	0.696853i	$-0.754583\pi$
$71$	−0.171573	+	0.171573i	−0.0203620	+	0.0203620i	0.696853	+	0.717214i	$0.254583\pi$
$72$	0.828427	−	0.828427i	0.0976311	−	0.0976311i
$73$	−7.00000	−	7.00000i	−0.819288	−	0.819288i	0.166717	−	0.986005i	$-0.446683\pi$
$73$	−7.00000	−	7.00000i	−0.819288	−	0.819288i	−0.986005	+	0.166717i	$0.946683\pi$
$74$	1.00000	+	2.41421i	0.116248	+	0.280647i
$75$		0			0
$76$	11.0711	+	4.58579i	1.26994	+	0.526026i
$77$	−0.414214	−	0.171573i	−0.0472040	−	0.0195525i
$78$	−3.41421	−	3.41421i	−0.386584	−	0.386584i
$79$			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
$81$		−	10.0711i		−	1.11901i
$82$	−8.24264	+	8.24264i	−0.910247	+	0.910247i
$83$	−6.12132	−	2.53553i	−0.671902	−	0.278311i	0.0205350	−	0.999789i	$-0.493463\pi$
$83$	−6.12132	−	2.53553i	−0.671902	−	0.278311i	−0.692437	+	0.721478i	$0.743463\pi$
$84$	2.00000	+	4.82843i	0.218218	+	0.526825i
$85$		0			0
$86$	−11.2426	+	4.65685i	−1.21233	+	0.502162i
$87$	3.82843	+	3.82843i	0.410450	+	0.410450i
$88$	−0.828427	+	0.343146i	−0.0883106	+	0.0365795i
$89$	−2.65685	+	2.65685i	−0.281626	+	0.281626i	−0.833757	−	0.552131i	$-0.813815\pi$
$89$	−2.65685	+	2.65685i	−0.281626	+	0.281626i	0.552131	+	0.833757i	$0.313815\pi$
$90$		0			0
$91$	2.41421	−	1.00000i	0.253078	−	0.104828i
$92$	0.343146	+	0.343146i	0.0357754	+	0.0357754i
$93$	2.82843	−	6.82843i	0.293294	−	0.708075i
$94$	16.4853			1.70033
$95$		0			0
$96$	9.65685	+	4.00000i	0.985599	+	0.408248i
$97$	1.51472			0.153796			0.0768982	−	0.997039i	$-0.475498\pi$
$97$	1.51472			0.153796			0.0768982	+	0.997039i	$0.475498\pi$
$98$	7.07107			0.714286
$99$	0.0502525	−	0.121320i	0.00505057	−	0.0121932i
$100$		0			0
$101$	11.3640	−	4.70711i	1.13076	−	0.468375i	0.262718	−	0.964873i	$-0.415381\pi$
$101$	11.3640	−	4.70711i	1.13076	−	0.468375i	0.868038	+	0.496498i	$0.165381\pi$
$102$	2.82843	−	6.82843i	0.280056	−	0.676115i
$103$	7.48528	−	7.48528i	0.737547	−	0.737547i	−0.234556	−	0.972103i	$-0.575364\pi$
$103$	7.48528	−	7.48528i	0.737547	−	0.737547i	0.972103	+	0.234556i	$0.0753636\pi$
$104$	2.00000	−	4.82843i	0.196116	−	0.473466i
$105$		0			0
$106$	−10.6569	+	4.41421i	−1.03509	+	0.428746i
$107$	−0.121320	−	0.292893i	−0.0117285	−	0.0283151i	0.917907	−	0.396796i	$-0.129878\pi$
$107$	−0.121320	−	0.292893i	−0.0117285	−	0.0283151i	−0.929635	+	0.368481i	$0.879878\pi$
$108$	8.82843	−	3.65685i	0.849516	−	0.351881i
$109$	−4.29289	−	1.77817i	−0.411185	−	0.170318i	0.167496	−	0.985873i	$-0.446432\pi$
$109$	−4.29289	−	1.77817i	−0.411185	−	0.170318i	−0.578680	+	0.815555i	$0.696432\pi$
$110$		0			0
$111$		−	3.41421i		−	0.324063i
$112$	−4.00000	+	4.00000i	−0.377964	+	0.377964i
$113$			17.6569i			1.66102i	0.557006	+	0.830509i	$0.311950\pi$
$113$			17.6569i			1.66102i	−0.557006	+	0.830509i	$0.688050\pi$
$114$	−11.0711	−	11.0711i	−1.03690	−	1.03690i
$115$		0			0
$116$	−2.24264	+	5.41421i	−0.208224	+	0.502697i
$117$	0.292893	+	0.707107i	0.0270780	+	0.0653720i
$118$	3.58579	+	8.65685i	0.330098	+	0.796928i
$119$	2.82843	+	2.82843i	0.259281	+	0.259281i
$120$		0			0
$121$	7.70711	−	7.70711i	0.700646	−	0.700646i
$122$	−1.00000	−	0.414214i	−0.0905357	−	0.0375011i
$123$	14.0711	−	5.82843i	1.26875	−	0.525532i
$124$	8.00000			0.718421
$125$		0			0
$126$		−	0.828427i		−	0.0738022i
$127$	20.9706			1.86084			0.930418	−	0.366499i	$-0.119444\pi$
$127$	20.9706			1.86084			0.930418	+	0.366499i	$0.119444\pi$
$128$			11.3137i			1.00000i
$129$	15.8995			1.39987
$130$		0			0
$131$	−3.63604	+	8.77817i	−0.317682	+	0.766953i	0.681694	+	0.731637i	$0.261244\pi$
$131$	−3.63604	+	8.77817i	−0.317682	+	0.766953i	−0.999376	+	0.0353153i	$0.988756\pi$
$132$	1.17157			0.101972
$133$	7.82843	−	3.24264i	0.678811	−	0.281173i
$134$	5.24264	+	2.17157i	0.452895	+	0.187595i
$135$		0			0
$136$	8.00000			0.685994
$137$	−2.65685	−	2.65685i	−0.226990	−	0.226990i	0.584444	−	0.811434i	$-0.301313\pi$
$137$	−2.65685	−	2.65685i	−0.226990	−	0.226990i	−0.811434	+	0.584444i	$0.801313\pi$
$138$	−0.242641	−	0.585786i	−0.0206549	−	0.0498655i
$139$	−5.19239	−	12.5355i	−0.440413	−	1.06325i	−0.975804	−	0.218646i	$-0.929836\pi$
$139$	−5.19239	−	12.5355i	−0.440413	−	1.06325i	0.535392	−	0.844604i	$-0.320164\pi$
$140$		0			0
$141$	−19.8995	−	8.24264i	−1.67584	−	0.694156i
$142$	0.242641	+	0.242641i	0.0203620	+	0.0203620i
$143$		−	0.585786i		−	0.0489859i
$144$	−1.17157	−	1.17157i	−0.0976311	−	0.0976311i
$145$		0			0
$146$	−9.89949	+	9.89949i	−0.819288	+	0.819288i
$147$	−8.53553	−	3.53553i	−0.703999	−	0.291606i
$148$	3.41421	−	1.41421i	0.280647	−	0.116248i
$149$	5.60660	+	13.5355i	0.459311	+	1.10887i	0.968677	+	0.248324i	$0.0798799\pi$
$149$	5.60660	+	13.5355i	0.459311	+	1.10887i	−0.509366	+	0.860550i	$0.670120\pi$
$150$		0			0
$151$	15.4853	+	15.4853i	1.26017	+	1.26017i	0.951008	+	0.309166i	$0.100050\pi$
$151$	15.4853	+	15.4853i	1.26017	+	1.26017i	0.309166	+	0.951008i	$0.399950\pi$
$152$	6.48528	−	15.6569i	0.526026	−	1.26994i
$153$	−0.828427	+	0.828427i	−0.0669744	+	0.0669744i
$154$	−0.242641	+	0.585786i	−0.0195525	+	0.0472040i
$155$		0			0
$156$	−4.82843	+	4.82843i	−0.386584	+	0.386584i
$157$	−0.292893	+	0.707107i	−0.0233754	+	0.0564333i	−0.935136	−	0.354288i	$-0.884723\pi$
$157$	−0.292893	+	0.707107i	−0.0233754	+	0.0564333i	0.911761	+	0.410722i	$0.134723\pi$
$158$	8.48528			0.675053
$159$	15.0711			1.19521
$160$		0			0
$161$	0.343146			0.0270437
$162$	−14.2426			−1.11901
$163$	−7.53553	+	18.1924i	−0.590229	+	1.42494i	0.293054	+	0.956096i	$0.405329\pi$
$163$	−7.53553	+	18.1924i	−0.590229	+	1.42494i	−0.883282	+	0.468842i	$0.844671\pi$
$164$	11.6569	+	11.6569i	0.910247	+	0.910247i
$165$		0			0
$166$	−3.58579	+	8.65685i	−0.278311	+	0.671902i
$167$	−3.34315	+	3.34315i	−0.258700	+	0.258700i	−0.824525	−	0.565825i	$-0.808558\pi$
$167$	−3.34315	+	3.34315i	−0.258700	+	0.258700i	0.565825	+	0.824525i	$0.308558\pi$
$168$	6.82843	−	2.82843i	0.526825	−	0.218218i
$169$	−6.77817	−	6.77817i	−0.521398	−	0.521398i
$170$		0			0
$171$	0.949747	+	2.29289i	0.0726290	+	0.175342i
$172$	6.58579	+	15.8995i	0.502162	+	1.21233i
$173$	1.12132	+	0.464466i	0.0852524	+	0.0353127i	0.424902	−	0.905239i	$-0.360309\pi$
$173$	1.12132	+	0.464466i	0.0852524	+	0.0353127i	−0.339650	+	0.940552i	$0.610309\pi$
$174$	5.41421	−	5.41421i	0.410450	−	0.410450i
$175$		0			0
$176$	0.485281	+	1.17157i	0.0365795	+	0.0883106i
$177$		−	12.2426i		−	0.920213i
$178$	3.75736	+	3.75736i	0.281626	+	0.281626i
$179$	−14.3640	−	5.94975i	−1.07361	−	0.444705i	−0.225349	−	0.974278i	$-0.572352\pi$
$179$	−14.3640	−	5.94975i	−1.07361	−	0.444705i	−0.848264	+	0.529573i	$0.822352\pi$
$180$		0			0
$181$	−2.19239	−	5.29289i	−0.162959	−	0.393418i	0.821216	−	0.570618i	$-0.193296\pi$
$181$	−2.19239	−	5.29289i	−0.162959	−	0.393418i	−0.984175	+	0.177200i	$0.943296\pi$
$182$	−1.41421	−	3.41421i	−0.104828	−	0.253078i
$183$	1.00000	+	1.00000i	0.0739221	+	0.0739221i
$184$	0.485281	−	0.485281i	0.0357754	−	0.0357754i
$185$		0			0
$186$	−9.65685	−	4.00000i	−0.708075	−	0.293294i
$187$	0.828427	−	0.343146i	0.0605806	−	0.0250933i
$188$		−	23.3137i		−	1.70033i
$189$	2.58579	−	6.24264i	0.188088	−	0.454085i
$190$		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	−	13.6569i	0.408248	−	0.985599i
$193$	18.4853			1.33060			0.665300	−	0.746576i	$-0.268304\pi$
$193$	18.4853			1.33060			0.665300	+	0.746576i	$0.268304\pi$
$194$		−	2.14214i		−	0.153796i
$195$		0			0
$196$		−	10.0000i		−	0.714286i
$197$	−17.3640	+	7.19239i	−1.23713	+	0.512436i	−0.902817	−	0.430025i	$-0.858505\pi$
$197$	−17.3640	+	7.19239i	−1.23713	+	0.512436i	−0.334314	+	0.942462i	$0.608505\pi$
$198$	−0.171573	−	0.0710678i	−0.0121932	−	0.00505057i
$199$	17.9706	−	17.9706i	1.27390	−	1.27390i	0.329875	−	0.944025i	$-0.392994\pi$
$199$	17.9706	−	17.9706i	1.27390	−	1.27390i	0.944025	−	0.329875i	$-0.107006\pi$
$200$		0			0
$201$	−5.24264	−	5.24264i	−0.369787	−	0.369787i
$202$	−6.65685	−	16.0711i	−0.468375	−	1.13076i
$203$	1.58579	+	3.82843i	0.111300	+	0.268703i
$204$	−9.65685	−	4.00000i	−0.676115	−	0.280056i
$205$		0			0
$206$	−10.5858	−	10.5858i	−0.737547	−	0.737547i
$207$			0.100505i			0.00698558i
$208$	−6.82843	−	2.82843i	−0.473466	−	0.196116i
$209$		−	1.89949i		−	0.131391i
$210$		0			0
$211$	0.464466	+	0.192388i	0.0319752	+	0.0132445i	0.398614	−	0.917119i	$-0.369491\pi$
$211$	0.464466	+	0.192388i	0.0319752	+	0.0132445i	−0.366639	+	0.930363i	$0.619491\pi$
$212$	6.24264	+	15.0711i	0.428746	+	1.03509i
$213$	−0.171573	−	0.414214i	−0.0117560	−	0.0283814i
$214$	−0.414214	+	0.171573i	−0.0283151	+	0.0117285i
$215$		0			0
$216$	−5.17157	−	12.4853i	−0.351881	−	0.849516i
$217$	4.00000	−	4.00000i	0.271538	−	0.271538i
$218$	−2.51472	+	6.07107i	−0.170318	+	0.411185i
$219$	16.8995	−	7.00000i	1.14196	−	0.473016i
$220$		0			0
$221$	−2.00000	+	4.82843i	−0.134535	+	0.324795i
$222$	−4.82843			−0.324063
$223$	−12.9706			−0.868573			−0.434287	−	0.900775i	$-0.642999\pi$
$223$	−12.9706			−0.868573			−0.434287	+	0.900775i	$0.642999\pi$
$224$	5.65685	+	5.65685i	0.377964	+	0.377964i
$225$		0			0
$226$	24.9706			1.66102
$227$	2.60660	−	6.29289i	0.173006	−	0.417674i	−0.813464	−	0.581616i	$-0.802421\pi$
$227$	2.60660	−	6.29289i	0.173006	−	0.417674i	0.986470	+	0.163942i	$0.0524208\pi$
$228$	−15.6569	+	15.6569i	−1.03690	+	1.03690i
$229$	−24.7782	+	10.2635i	−1.63739	+	0.678228i	−0.996030	−	0.0890139i	$-0.971628\pi$
$229$	−24.7782	+	10.2635i	−1.63739	+	0.678228i	−0.641357	+	0.767242i	$0.721628\pi$
$230$		0			0
$231$	0.585786	−	0.585786i	0.0385419	−	0.0385419i
$232$	7.65685	+	3.17157i	0.502697	+	0.208224i
$233$	−8.65685	−	8.65685i	−0.567129	−	0.567129i	0.364194	−	0.931323i	$-0.381345\pi$
$233$	−8.65685	−	8.65685i	−0.567129	−	0.567129i	−0.931323	+	0.364194i	$0.881345\pi$
$234$	1.00000	−	0.414214i	0.0653720	−	0.0270780i
$235$		0			0
$236$	12.2426	−	5.07107i	0.796928	−	0.330098i
$237$	−10.2426	−	4.24264i	−0.665331	−	0.275589i
$238$	4.00000	−	4.00000i	0.259281	−	0.259281i
$239$			17.3137i			1.11993i	0.828516	+	0.559965i	$0.189186\pi$
$239$			17.3137i			1.11993i	−0.828516	+	0.559965i	$0.810814\pi$
$240$		0			0
$241$			8.48528i			0.546585i	0.961931	+	0.273293i	$0.0881127\pi$
$241$			8.48528i			0.546585i	−0.961931	+	0.273293i	$0.911887\pi$
$242$	−10.8995	−	10.8995i	−0.700646	−	0.700646i
$243$	3.94975	+	1.63604i	0.253376	+	0.104952i
$244$	−0.585786	+	1.41421i	−0.0375011	+	0.0905357i
$245$		0			0
$246$	−8.24264	−	19.8995i	−0.525532	−	1.26875i
$247$	7.82843	+	7.82843i	0.498111	+	0.498111i
$248$		−	11.3137i		−	0.718421i
$249$	8.65685	−	8.65685i	0.548606	−	0.548606i
$250$		0			0
$251$	−14.6066	+	6.05025i	−0.921961	+	0.381889i	−0.792623	−	0.609712i	$-0.791285\pi$
$251$	−14.6066	+	6.05025i	−0.921961	+	0.381889i	−0.129338	+	0.991601i	$0.541285\pi$
$252$	−1.17157			−0.0738022
$253$	0.0294373	−	0.0710678i	0.00185070	−	0.00446800i
$254$		−	29.6569i		−	1.86084i
$255$		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	$0.559920\pi$
$258$		−	22.4853i		−	1.39987i
$259$	1.00000	−	2.41421i	0.0621370	−	0.150012i
$260$		0			0
$261$	−1.12132	+	0.464466i	−0.0694080	+	0.0287497i
$262$	12.4142	+	5.14214i	0.766953	+	0.317682i
$263$	0.171573	−	0.171573i	0.0105796	−	0.0105796i	−0.701797	−	0.712377i	$-0.747619\pi$
$263$	0.171573	−	0.171573i	0.0105796	−	0.0105796i	0.712377	+	0.701797i	$0.247619\pi$
$264$		−	1.65685i		−	0.101972i
$265$		0			0
$266$	−4.58579	−	11.0711i	−0.281173	−	0.678811i
$267$	−2.65685	−	6.41421i	−0.162597	−	0.392543i
$268$	3.07107	−	7.41421i	0.187595	−	0.452895i
$269$	4.87868	+	2.02082i	0.297458	+	0.123211i	0.526421	−	0.850224i	$-0.323533\pi$
$269$	4.87868	+	2.02082i	0.297458	+	0.123211i	−0.228963	+	0.973435i	$0.573533\pi$
$270$		0			0
$271$			18.0000i			1.09342i	0.837321	+	0.546711i	$0.184120\pi$
$271$			18.0000i			1.09342i	−0.837321	+	0.546711i	$0.815880\pi$
$272$		−	11.3137i		−	0.685994i
$273$			4.82843i			0.292230i
$274$	−3.75736	+	3.75736i	−0.226990	+	0.226990i
$275$		0			0
$276$	−0.828427	+	0.343146i	−0.0498655	+	0.0206549i
$277$	−0.292893	−	0.707107i	−0.0175982	−	0.0424859i	0.914836	−	0.403825i	$-0.132320\pi$
$277$	−0.292893	−	0.707107i	−0.0175982	−	0.0424859i	−0.932434	+	0.361339i	$0.882320\pi$
$278$	−17.7279	+	7.34315i	−1.06325	+	0.440413i
$279$	1.17157	+	1.17157i	0.0701402	+	0.0701402i
$280$		0			0
$281$	−6.17157	+	6.17157i	−0.368165	+	0.368165i	−0.866808	−	0.498643i	$-0.833832\pi$
$281$	−6.17157	+	6.17157i	−0.368165	+	0.368165i	0.498643	+	0.866808i	$0.333832\pi$
$282$	−11.6569	+	28.1421i	−0.694156	+	1.67584i
$283$	9.77817	−	4.05025i	0.581252	−	0.240763i	−0.0726300	−	0.997359i	$-0.523139\pi$
$283$	9.77817	−	4.05025i	0.581252	−	0.240763i	0.653882	+	0.756596i	$0.273139\pi$
$284$	0.343146	−	0.343146i	0.0203620	−	0.0203620i
$285$		0			0
$286$	−0.828427			−0.0489859
$287$	11.6569			0.688082
$288$	−1.65685	+	1.65685i	−0.0976311	+	0.0976311i
$289$	9.00000			0.529412
$290$		0			0
$291$	−1.07107	+	2.58579i	−0.0627871	+	0.151581i
$292$	14.0000	+	14.0000i	0.819288	+	0.819288i
$293$	11.6066	−	4.80761i	0.678065	−	0.280864i	−0.0169528	−	0.999856i	$-0.505397\pi$
$293$	11.6066	−	4.80761i	0.678065	−	0.280864i	0.695018	+	0.718993i	$0.255397\pi$
$294$	−5.00000	+	12.0711i	−0.291606	+	0.703999i
$295$		0			0
$296$	−2.00000	−	4.82843i	−0.116248	−	0.280647i
$297$	−1.07107	−	1.07107i	−0.0621497	−	0.0621497i
$298$	19.1421	−	7.92893i	1.10887	−	0.459311i
$299$	0.171573	+	0.414214i	0.00992232	+	0.0239546i
$300$		0			0
$301$	11.2426	+	4.65685i	0.648015	+	0.268417i
$302$	21.8995	−	21.8995i	1.26017	−	1.26017i
$303$			22.7279i			1.30569i
$304$	−22.1421	−	9.17157i	−1.26994	−	0.526026i
$305$		0			0
$306$	1.17157	+	1.17157i	0.0669744	+	0.0669744i
$307$	−2.94975	−	1.22183i	−0.168351	−	0.0697333i	0.296916	−	0.954904i	$-0.404042\pi$
$307$	−2.94975	−	1.22183i	−0.168351	−	0.0697333i	−0.465267	+	0.885170i	$0.654042\pi$
$308$	0.828427	+	0.343146i	0.0472040	+	0.0195525i
$309$	7.48528	+	18.0711i	0.425823	+	1.02803i
$310$		0			0
$311$	8.65685	+	8.65685i	0.490885	+	0.490885i	0.908585	−	0.417700i	$-0.137164\pi$
$311$	8.65685	+	8.65685i	0.490885	+	0.490885i	−0.417700	+	0.908585i	$0.637164\pi$
$312$	6.82843	+	6.82843i	0.386584	+	0.386584i
$313$	−9.48528	+	9.48528i	−0.536140	+	0.536140i	−0.922393	−	0.386253i	$-0.873769\pi$
$313$	−9.48528	+	9.48528i	−0.536140	+	0.536140i	0.386253	+	0.922393i	$0.373769\pi$
$314$	1.00000	+	0.414214i	0.0564333	+	0.0233754i
$315$		0			0
$316$		−	12.0000i		−	0.675053i
$317$	−4.63604	+	11.1924i	−0.260386	+	0.628627i	−0.998962	−	0.0455425i	$-0.985498\pi$
$317$	−4.63604	+	11.1924i	−0.260386	+	0.628627i	0.738577	+	0.674170i	$0.235498\pi$
$318$		−	21.3137i		−	1.19521i
$319$	0.928932			0.0520102
$320$		0			0
$321$	0.585786			0.0326954
$322$		−	0.485281i		−	0.0270437i
$323$	−6.48528	+	15.6569i	−0.360851	+	0.871171i
$324$			20.1421i			1.11901i
$325$		0			0
$326$	25.7279	+	10.6569i	1.42494	+	0.590229i
$327$	6.07107	−	6.07107i	0.335731	−	0.335731i
$328$	16.4853	−	16.4853i	0.910247	−	0.910247i
$329$	−11.6569	−	11.6569i	−0.642663	−	0.642663i
$330$		0			0
$331$	−2.70711	−	6.53553i	−0.148796	−	0.359225i	0.831854	−	0.554995i	$-0.187280\pi$
$331$	−2.70711	−	6.53553i	−0.148796	−	0.359225i	−0.980650	+	0.195769i	$0.937280\pi$
$332$	12.2426	+	5.07107i	0.671902	+	0.278311i
$333$	0.707107	+	0.292893i	0.0387492	+	0.0160504i
$334$	4.72792	+	4.72792i	0.258700	+	0.258700i
$335$		0			0
$336$	−4.00000	−	9.65685i	−0.218218	−	0.526825i
$337$		−	16.9706i		−	0.924445i	−0.886764	−	0.462223i	$-0.847052\pi$
$337$		−	16.9706i		−	0.924445i	0.886764	−	0.462223i	$-0.152948\pi$
$338$	−9.58579	+	9.58579i	−0.521398	+	0.521398i
$339$	−30.1421	−	12.4853i	−1.63710	−	0.678107i
$340$		0			0
$341$	−0.485281	−	1.17157i	−0.0262795	−	0.0634442i
$342$	3.24264	−	1.34315i	0.175342	−	0.0726290i
$343$	−12.0000	−	12.0000i	−0.647939	−	0.647939i
$344$	22.4853	−	9.31371i	1.21233	−	0.502162i
$345$		0			0
$346$	0.656854	−	1.58579i	0.0353127	−	0.0852524i
$347$	−14.3640	+	5.94975i	−0.771098	+	0.319399i	−0.733317	−	0.679887i	$-0.762029\pi$
$347$	−14.3640	+	5.94975i	−0.771098	+	0.319399i	−0.0377808	+	0.999286i	$0.512029\pi$
$348$	−7.65685	−	7.65685i	−0.410450	−	0.410450i
$349$	−10.6777	+	25.7782i	−0.571563	+	1.37987i	0.328662	+	0.944448i	$0.393402\pi$
$349$	−10.6777	+	25.7782i	−0.571563	+	1.37987i	−0.900224	+	0.435426i	$0.856598\pi$
$350$		0			0
$351$	8.82843			0.471227
$352$	1.65685	−	0.686292i	0.0883106	−	0.0365795i
$353$	−6.00000			−0.319348			−0.159674	−	0.987170i	$-0.551044\pi$
$353$	−6.00000			−0.319348			−0.159674	+	0.987170i	$0.551044\pi$
$354$	−17.3137			−0.920213
$355$		0			0
$356$	5.31371	−	5.31371i	0.281626	−	0.281626i
$357$	−6.82843	+	2.82843i	−0.361399	+	0.149696i
$358$	−8.41421	+	20.3137i	−0.444705	+	1.07361i
$359$	−12.1716	+	12.1716i	−0.642391	+	0.642391i	−0.951143	−	0.308752i	$-0.900089\pi$
$359$	−12.1716	+	12.1716i	−0.642391	+	0.642391i	0.308752	+	0.951143i	$0.400089\pi$
$360$		0			0
$361$	11.9497	+	11.9497i	0.628934	+	0.628934i
$362$	−7.48528	+	3.10051i	−0.393418	+	0.162959i
$363$	7.70711	+	18.6066i	0.404518	+	0.976593i
$364$	−4.82843	+	2.00000i	−0.253078	+	0.104828i
$365$		0			0
$366$	1.41421	−	1.41421i	0.0739221	−	0.0739221i
$367$			6.00000i			0.313197i	0.987662	+	0.156599i	$0.0500529\pi$
$367$			6.00000i			0.313197i	−0.987662	+	0.156599i	$0.949947\pi$
$368$	−0.686292	−	0.686292i	−0.0357754	−	0.0357754i
$369$			3.41421i			0.177737i
$370$		0			0
$371$	10.6569	+	4.41421i	0.553276	+	0.229175i
$372$	−5.65685	+	13.6569i	−0.293294	+	0.708075i
$373$	11.7071	+	28.2635i	0.606171	+	1.46343i	0.867133	+	0.498077i	$0.165960\pi$
$373$	11.7071	+	28.2635i	0.606171	+	1.46343i	−0.260962	+	0.965349i	$0.584040\pi$
$374$	−0.485281	−	1.17157i	−0.0250933	−	0.0605806i
$375$		0			0
$376$	−32.9706			−1.70033
$377$	−3.82843	+	3.82843i	−0.197174	+	0.197174i
$378$	−8.82843	−	3.65685i	−0.454085	−	0.188088i
$379$	21.6777	−	8.97918i	1.11351	−	0.461230i	0.251363	−	0.967893i	$-0.419121\pi$
$379$	21.6777	−	8.97918i	1.11351	−	0.461230i	0.862144	+	0.506663i	$0.169121\pi$
$380$		0			0
$381$	−14.8284	+	35.7990i	−0.759683	+	1.83404i
$382$			16.9706i			0.868290i
$383$	−16.9706			−0.867155			−0.433578	−	0.901116i	$-0.642749\pi$
$383$	−16.9706			−0.867155			−0.433578	+	0.901116i	$0.642749\pi$
$384$	−19.3137	−	8.00000i	−0.985599	−	0.408248i
$385$		0			0
$386$		−	26.1421i		−	1.33060i
$387$	−1.36396	+	3.29289i	−0.0693340	+	0.167387i
$388$	−3.02944			−0.153796
$389$	−29.6066	+	12.2635i	−1.50111	+	0.621782i	−0.973702	−	0.227827i	$-0.926838\pi$
$389$	−29.6066	+	12.2635i	−1.50111	+	0.621782i	−0.527413	+	0.849609i	$0.676838\pi$
$390$		0			0
$391$	−0.485281	+	0.485281i	−0.0245417	+	0.0245417i
$392$	−14.1421			−0.714286
$393$	−12.4142	−	12.4142i	−0.626214	−	0.626214i
$394$	10.1716	+	24.5563i	0.512436	+	1.23713i
$395$		0			0
$396$	−0.100505	+	0.242641i	−0.00505057	+	0.0121932i
$397$	24.7782	+	10.2635i	1.24358	+	0.515108i	0.904832	−	0.425769i	$-0.139996\pi$
$397$	24.7782	+	10.2635i	1.24358	+	0.515108i	0.338749	+	0.940877i	$0.389996\pi$
$398$	−25.4142	−	25.4142i	−1.27390	−	1.27390i
$399$			15.6569i			0.783823i
$400$		0			0
$401$			2.82843i			0.141245i	0.997503	+	0.0706225i	$0.0224986\pi$
$401$			2.82843i			0.141245i	−0.997503	+	0.0706225i	$0.977501\pi$
$402$	−7.41421	+	7.41421i	−0.369787	+	0.369787i
$403$	6.82843	+	2.82843i	0.340148	+	0.140894i
$404$	−22.7279	+	9.41421i	−1.13076	+	0.468375i
$405$		0			0
$406$	5.41421	−	2.24264i	0.268703	−	0.111300i
$407$	−0.414214	−	0.414214i	−0.0205318	−	0.0205318i
$408$	−5.65685	+	13.6569i	−0.280056	+	0.676115i
$409$	4.51472	−	4.51472i	0.223238	−	0.223238i	−0.586622	−	0.809861i	$-0.699543\pi$
$409$	4.51472	−	4.51472i	0.223238	−	0.223238i	0.809861	+	0.586622i	$0.199543\pi$
$410$		0			0
$411$	6.41421	−	2.65685i	0.316390	−	0.131053i
$412$	−14.9706	+	14.9706i	−0.737547	+	0.737547i
$413$	3.58579	−	8.65685i	0.176445	−	0.425976i
$414$	0.142136			0.00698558
$415$		0			0
$416$	−4.00000	+	9.65685i	−0.196116	+	0.473466i
$417$	25.0711			1.22774
$418$	−2.68629			−0.131391
$419$	−8.60660	+	20.7782i	−0.420460	+	1.01508i	0.561752	+	0.827306i	$0.310127\pi$
$419$	−8.60660	+	20.7782i	−0.420460	+	1.01508i	−0.982212	+	0.187775i	$0.939873\pi$
$420$		0			0
$421$	7.70711	−	3.19239i	0.375621	−	0.155587i	−0.186882	−	0.982382i	$-0.559838\pi$
$421$	7.70711	−	3.19239i	0.375621	−	0.155587i	0.562504	+	0.826795i	$0.309838\pi$
$422$	0.272078	−	0.656854i	0.0132445	−	0.0319752i
$423$	3.41421	−	3.41421i	0.166005	−	0.166005i
$424$	21.3137	−	8.82843i	1.03509	−	0.428746i
$425$		0			0
$426$	−0.585786	+	0.242641i	−0.0283814	+	0.0117560i
$427$	0.414214	+	1.00000i	0.0200452	+	0.0483934i
$428$	0.242641	+	0.585786i	0.0117285	+	0.0283151i
$429$	1.00000	+	0.414214i	0.0482805	+	0.0199984i
$430$		0			0
$431$		−	23.6569i		−	1.13951i	−0.821814	−	0.569755i	$-0.807038\pi$
$431$		−	23.6569i		−	1.13951i	0.821814	−	0.569755i	$-0.192962\pi$
$432$	−17.6569	+	7.31371i	−0.849516	+	0.351881i
$433$			32.4853i			1.56114i	0.625067	+	0.780571i	$0.285072\pi$
$433$			32.4853i			1.56114i	−0.625067	+	0.780571i	$0.714928\pi$
$434$	−5.65685	−	5.65685i	−0.271538	−	0.271538i
$435$		0			0
$436$	8.58579	+	3.55635i	0.411185	+	0.170318i
$437$	0.556349	+	1.34315i	0.0266138	+	0.0642514i
$438$	−9.89949	−	23.8995i	−0.473016	−	1.14196i
$439$	−17.0000	−	17.0000i	−0.811366	−	0.811366i	0.173473	−	0.984839i	$-0.444501\pi$
$439$	−17.0000	−	17.0000i	−0.811366	−	0.811366i	−0.984839	+	0.173473i	$0.944501\pi$
$440$		0			0
$441$	1.46447	−	1.46447i	0.0697365	−	0.0697365i
$442$	6.82843	+	2.82843i	0.324795	+	0.134535i
$443$	20.6066	−	8.53553i	0.979049	−	0.405535i	0.164976	−	0.986298i	$-0.447245\pi$
$443$	20.6066	−	8.53553i	0.979049	−	0.405535i	0.814073	+	0.580762i	$0.197245\pi$
$444$			6.82843i			0.324063i
$445$		0			0
$446$			18.3431i			0.868573i
$447$	−27.0711			−1.28042
$448$	8.00000	−	8.00000i	0.377964	−	0.377964i
$449$	31.4558			1.48449			0.742247	−	0.670127i	$-0.233760\pi$
$449$	31.4558			1.48449			0.742247	+	0.670127i	$0.233760\pi$
$450$		0			0
$451$	1.00000	−	2.41421i	0.0470882	−	0.113681i
$452$		−	35.3137i		−	1.66102i
$453$	−37.3848	+	15.4853i	−1.75649	+	0.727562i
$454$	−8.89949	−	3.68629i	−0.417674	−	0.173006i
$455$		0			0
$456$	22.1421	+	22.1421i	1.03690	+	1.03690i
$457$	−9.48528	−	9.48528i	−0.443703	−	0.443703i	0.449552	−	0.893254i	$-0.351584\pi$
$457$	−9.48528	−	9.48528i	−0.443703	−	0.443703i	−0.893254	+	0.449552i	$0.851584\pi$
$458$	14.5147	+	35.0416i	0.678228	+	1.63739i
$459$	5.17157	+	12.4853i	0.241388	+	0.582763i
$460$		0			0
$461$	13.3640	+	5.53553i	0.622422	+	0.257816i	0.671529	−	0.740978i	$-0.265638\pi$
$461$	13.3640	+	5.53553i	0.622422	+	0.257816i	−0.0491076	+	0.998793i	$0.515638\pi$
$462$	−0.828427	−	0.828427i	−0.0385419	−	0.0385419i
$463$			10.9706i			0.509845i	0.966961	+	0.254923i	$0.0820500\pi$
$463$			10.9706i			0.509845i	−0.966961	+	0.254923i	$0.917950\pi$
$464$	4.48528	−	10.8284i	0.208224	−	0.502697i
$465$		0			0
$466$	−12.2426	+	12.2426i	−0.567129	+	0.567129i
$467$	−29.0919	−	12.0503i	−1.34621	−	0.557619i	−0.410977	−	0.911646i	$-0.634812\pi$
$467$	−29.0919	−	12.0503i	−1.34621	−	0.557619i	−0.935235	+	0.354027i	$0.884812\pi$
$468$	−0.585786	−	1.41421i	−0.0270780	−	0.0653720i
$469$	−2.17157	−	5.24264i	−0.100274	−	0.242083i
$470$		0			0
$471$	−1.00000	−	1.00000i	−0.0460776	−	0.0460776i
$472$	−7.17157	−	17.3137i	−0.330098	−	0.796928i
$473$	1.92893	−	1.92893i	0.0886924	−	0.0886924i
$474$	−6.00000	+	14.4853i	−0.275589	+	0.665331i
$475$		0			0
$476$	−5.65685	−	5.65685i	−0.259281	−	0.259281i
$477$	−1.29289	+	3.12132i	−0.0591975	+	0.142915i
$478$	24.4853			1.11993
$479$	−4.97056			−0.227111			−0.113555	−	0.993532i	$-0.536224\pi$
$479$	−4.97056			−0.227111			−0.113555	+	0.993532i	$0.536224\pi$
$480$		0			0
$481$	3.41421			0.155675
$482$	12.0000			0.546585
$483$	−0.242641	+	0.585786i	−0.0110405	+	0.0266542i
$484$	−15.4142	+	15.4142i	−0.700646	+	0.700646i
$485$		0			0
$486$	2.31371	−	5.58579i	0.104952	−	0.253376i
$487$	11.0000	−	11.0000i	0.498458	−	0.498458i	−0.412500	−	0.910958i	$-0.635344\pi$
$487$	11.0000	−	11.0000i	0.498458	−	0.498458i	0.910958	+	0.412500i	$0.135344\pi$
$488$	2.00000	+	0.828427i	0.0905357	+	0.0375011i
$489$	−25.7279	−	25.7279i	−1.16346	−	1.16346i
$490$		0			0
$491$	−7.33452	−	17.7071i	−0.331002	−	0.799111i	−0.998513	−	0.0545104i	$-0.982640\pi$
$491$	−7.33452	−	17.7071i	−0.331002	−	0.799111i	0.667511	−	0.744600i	$-0.267360\pi$
$492$	−28.1421	+	11.6569i	−1.26875	+	0.525532i
$493$	−7.65685	−	3.17157i	−0.344847	−	0.142840i
$494$	11.0711	−	11.0711i	0.498111	−	0.498111i
$495$		0			0
$496$	−16.0000			−0.718421
$497$		−	0.343146i		−	0.0153922i
$498$	−12.2426	−	12.2426i	−0.548606	−	0.548606i
$499$	8.94975	+	3.70711i	0.400646	+	0.165953i	0.573902	−	0.818924i	$-0.305429\pi$
$499$	8.94975	+	3.70711i	0.400646	+	0.165953i	−0.173256	+	0.984877i	$0.555429\pi$
$500$		0			0
$501$	−3.34315	−	8.07107i	−0.149361	−	0.360589i
$502$	8.55635	+	20.6569i	0.381889	+	0.921961i
$503$	−17.1421	−	17.1421i	−0.764330	−	0.764330i	0.212772	−	0.977102i	$-0.431751\pi$
$503$	−17.1421	−	17.1421i	−0.764330	−	0.764330i	−0.977102	+	0.212772i	$0.931751\pi$
$504$			1.65685i			0.0738022i
$505$		0			0
$506$	−0.100505	−	0.0416306i	−0.00446800	−	0.00185070i
$507$	16.3640	−	6.77817i	0.726749	−	0.301029i
$508$	−41.9411			−1.86084
$509$	12.0919	−	29.1924i	0.535963	−	1.29393i	−0.391556	−	0.920154i	$-0.628063\pi$
$509$	12.0919	−	29.1924i	0.535963	−	1.29393i	0.927519	−	0.373776i	$-0.121937\pi$
$510$		0			0
$511$	14.0000			0.619324
$512$		−	22.6274i		−	1.00000i
$513$	28.6274			1.26393
$514$			8.48528i			0.374270i
$515$		0			0
$516$	−31.7990			−1.39987
$517$	−3.41421	+	1.41421i	−0.150157	+	0.0621970i
$518$	−3.41421	−	1.41421i	−0.150012	−	0.0621370i
$519$	−1.58579	+	1.58579i	−0.0696083	+	0.0696083i
$520$		0			0
$521$	14.6569	+	14.6569i	0.642128	+	0.642128i	0.951078	−	0.308950i	$-0.0999775\pi$
$521$	14.6569	+	14.6569i	0.642128	+	0.642128i	−0.308950	+	0.951078i	$0.599978\pi$
$522$	0.656854	+	1.58579i	0.0287497	+	0.0694080i
$523$	−0.807612	−	1.94975i	−0.0353144	−	0.0852565i	0.905238	−	0.424904i	$-0.139692\pi$
$523$	−0.807612	−	1.94975i	−0.0353144	−	0.0852565i	−0.940553	+	0.339648i	$0.889692\pi$
$524$	7.27208	−	17.5563i	0.317682	−	0.766953i
$525$		0			0
$526$	−0.242641	−	0.242641i	−0.0105796	−	0.0105796i
$527$			11.3137i			0.492833i
$528$	−2.34315			−0.101972
$529$		−	22.9411i		−	0.997440i
$530$		0			0
$531$	2.53553	+	1.05025i	0.110033	+	0.0455771i
$532$	−15.6569	+	6.48528i	−0.678811	+	0.281173i
$533$	5.82843	+	14.0711i	0.252457	+	0.609486i
$534$	−9.07107	+	3.75736i	−0.392543	+	0.162597i
$535$		0			0
$536$	−10.4853	−	4.34315i	−0.452895	−	0.187595i
$537$	20.3137	−	20.3137i	0.876601	−	0.876601i
$538$	2.85786	−	6.89949i	0.123211	−	0.297458i
$539$	−1.46447	+	0.606602i	−0.0630790	+	0.0261282i
$540$		0			0
$541$	5.26346	−	12.7071i	0.226294	−	0.546321i	−0.769427	−	0.638735i	$-0.779458\pi$
$541$	5.26346	−	12.7071i	0.226294	−	0.546321i	0.995721	+	0.0924135i	$0.0294582\pi$
$542$	25.4558			1.09342
$543$	10.5858			0.454280
$544$	−16.0000			−0.685994
$545$		0			0
$546$	6.82843			0.292230
$547$	10.4645	−	25.2635i	0.447428	−	1.08019i	−0.525854	−	0.850575i	$-0.676254\pi$
$547$	10.4645	−	25.2635i	0.447428	−	1.08019i	0.973282	−	0.229612i	$-0.0737459\pi$
$548$	5.31371	+	5.31371i	0.226990	+	0.226990i
$549$	−0.292893	+	0.121320i	−0.0125004	+	0.00517783i
$550$		0			0
$551$	−12.4142	+	12.4142i	−0.528863	+	0.528863i
$552$	0.485281	+	1.17157i	0.0206549	+	0.0498655i
$553$	−6.00000	−	6.00000i	−0.255146	−	0.255146i
$554$	−1.00000	+	0.414214i	−0.0424859	+	0.0175982i
$555$		0			0
$556$	10.3848	+	25.0711i	0.440413	+	1.06325i
$557$	−10.8787	−	4.50610i	−0.460944	−	0.190929i	0.140113	−	0.990136i	$-0.455254\pi$
$557$	−10.8787	−	4.50610i	−0.460944	−	0.190929i	−0.601057	+	0.799206i	$0.705254\pi$
$558$	1.65685	−	1.65685i	0.0701402	−	0.0701402i
$559$			15.8995i			0.672477i
$560$		0			0
$561$			1.65685i			0.0699524i
$562$	8.72792	+	8.72792i	0.368165	+	0.368165i
$563$	−12.1213	−	5.02082i	−0.510853	−	0.211602i	0.112341	−	0.993670i	$-0.464165\pi$
$563$	−12.1213	−	5.02082i	−0.510853	−	0.211602i	−0.623194	+	0.782068i	$0.714165\pi$
$564$	39.7990	+	16.4853i	1.67584	+	0.694156i
$565$		0			0
$566$	−5.72792	−	13.8284i	−0.240763	−	0.581252i
$567$	10.0711	+	10.0711i	0.422945	+	0.422945i
$568$	−0.485281	−	0.485281i	−0.0203620	−	0.0203620i
$569$	3.34315	−	3.34315i	0.140152	−	0.140152i	−0.633550	−	0.773702i	$-0.718403\pi$
$569$	3.34315	−	3.34315i	0.140152	−	0.140152i	0.773702	+	0.633550i	$0.218403\pi$
$570$		0			0
$571$	−1.29289	+	0.535534i	−0.0541059	+	0.0224114i	−0.409572	−	0.912278i	$-0.634322\pi$
$571$	−1.29289	+	0.535534i	−0.0541059	+	0.0224114i	0.355466	+	0.934689i	$0.384322\pi$
$572$			1.17157i			0.0489859i
$573$	8.48528	−	20.4853i	0.354478	−	0.855785i
$574$		−	16.4853i		−	0.688082i
$575$		0			0
$576$	2.34315	+	2.34315i	0.0976311	+	0.0976311i
$577$	14.9706			0.623233			0.311616	−	0.950208i	$-0.399130\pi$
$577$	14.9706			0.623233			0.311616	+	0.950208i	$0.399130\pi$
$578$		−	12.7279i		−	0.529412i
$579$	−13.0711	+	31.5563i	−0.543215	+	1.31144i
$580$		0			0
$581$	8.65685	−	3.58579i	0.359147	−	0.148763i
$582$	3.65685	+	1.51472i	0.151581	+	0.0627871i
$583$	1.82843	−	1.82843i	0.0757257	−	0.0757257i
$584$	19.7990	−	19.7990i	0.819288	−	0.819288i
$585$		0			0
$586$	−6.79899	−	16.4142i	−0.280864	−	0.678065i
$587$	−8.60660	−	20.7782i	−0.355232	−	0.857607i	−0.995957	−	0.0898359i	$-0.971366\pi$
$587$	−8.60660	−	20.7782i	−0.355232	−	0.857607i	0.640724	−	0.767771i	$-0.278634\pi$
$588$	17.0711	+	7.07107i	0.703999	+	0.291606i
$589$	22.1421	+	9.17157i	0.912351	+	0.377908i
$590$		0			0
$591$		−	34.7279i		−	1.42852i
$592$	−6.82843	+	2.82843i	−0.280647	+	0.116248i
$593$		−	28.2843i		−	1.16150i	−0.814083	−	0.580748i	$-0.802760\pi$
$593$		−	28.2843i		−	1.16150i	0.814083	−	0.580748i	$-0.197240\pi$
$594$	−1.51472	+	1.51472i	−0.0621497	+	0.0621497i
$595$		0			0
$596$	−11.2132	−	27.0711i	−0.459311	−	1.10887i
$597$	17.9706	+	43.3848i	0.735486	+	1.77562i
$598$	0.585786	−	0.242641i	0.0239546	−	0.00992232i
$599$	−15.3431	−	15.3431i	−0.626904	−	0.626904i	0.320384	−	0.947288i	$-0.396188\pi$
$599$	−15.3431	−	15.3431i	−0.626904	−	0.626904i	−0.947288	+	0.320384i	$0.896188\pi$
$600$		0			0
$601$	11.9706	−	11.9706i	0.488289	−	0.488289i	−0.419477	−	0.907766i	$-0.637786\pi$
$601$	11.9706	−	11.9706i	0.488289	−	0.488289i	0.907766	+	0.419477i	$0.137786\pi$
$602$	6.58579	−	15.8995i	0.268417	−	0.648015i
$603$	1.53553	−	0.636039i	0.0625318	−	0.0259015i
$604$	−30.9706	−	30.9706i	−1.26017	−	1.26017i
$605$		0			0
$606$	32.1421			1.30569
$607$	−0.970563			−0.0393939			−0.0196970	−	0.999806i	$-0.506270\pi$
$607$	−0.970563			−0.0393939			−0.0196970	+	0.999806i	$0.506270\pi$
$608$	−12.9706	+	31.3137i	−0.526026	+	1.26994i
$609$	−7.65685			−0.310271
$610$		0			0
$611$	8.24264	−	19.8995i	0.333462	−	0.805047i
$612$	1.65685	−	1.65685i	0.0669744	−	0.0669744i
$613$	−36.6777	+	15.1924i	−1.48140	+	0.613615i	−0.969425	−	0.245387i	$-0.921085\pi$
$613$	−36.6777	+	15.1924i	−1.48140	+	0.613615i	−0.511972	+	0.859002i	$0.671085\pi$
$614$	−1.72792	+	4.17157i	−0.0697333	+	0.168351i
$615$		0			0
$616$	0.485281	−	1.17157i	0.0195525	−	0.0472040i
$617$	16.7990	+	16.7990i	0.676302	+	0.676302i	0.959161	−	0.282859i	$-0.0912830\pi$
$617$	16.7990	+	16.7990i	0.676302	+	0.676302i	−0.282859	+	0.959161i	$0.591283\pi$
$618$	25.5563	−	10.5858i	1.02803	−	0.425823i
$619$	−6.22183	−	15.0208i	−0.250076	−	0.603738i	0.748133	−	0.663548i	$-0.230950\pi$
$619$	−6.22183	−	15.0208i	−0.250076	−	0.603738i	−0.998210	+	0.0598107i	$0.980950\pi$
$620$		0			0
$621$	1.07107	+	0.443651i	0.0429805	+	0.0178031i
$622$	12.2426	−	12.2426i	0.490885	−	0.490885i
$623$		−	5.31371i		−	0.212889i
$624$	9.65685	−	9.65685i	0.386584	−	0.386584i
$625$		0			0
$626$	13.4142	+	13.4142i	0.536140	+	0.536140i
$627$	3.24264	+	1.34315i	0.129499	+	0.0536401i
$628$	0.585786	−	1.41421i	0.0233754	−	0.0564333i
$629$	2.00000	+	4.82843i	0.0797452	+	0.192522i
$630$		0			0
$631$	−18.4558	−	18.4558i	−0.734716	−	0.734716i	0.236834	−	0.971550i	$-0.423890\pi$
$631$	−18.4558	−	18.4558i	−0.734716	−	0.734716i	−0.971550	+	0.236834i	$0.923890\pi$
$632$	−16.9706			−0.675053
$633$	−0.656854	+	0.656854i	−0.0261076	+	0.0261076i
$634$	15.8284	+	6.55635i	0.628627	+	0.260386i
$635$		0			0
$636$	−30.1421			−1.19521
$637$	3.53553	−	8.53553i	0.140083	−	0.338190i
$638$		−	1.31371i		−	0.0520102i
$639$	0.100505			0.00397592
$640$		0			0
$641$	−43.4558			−1.71640			−0.858201	−	0.513313i	$-0.828418\pi$
$641$	−43.4558			−1.71640			−0.858201	+	0.513313i	$0.828418\pi$
$642$		−	0.828427i		−	0.0326954i
$643$	15.4350	−	37.2635i	0.608698	−	1.46953i	−0.255719	−	0.966751i	$-0.582312\pi$
$643$	15.4350	−	37.2635i	0.608698	−	1.46953i	0.864417	−	0.502776i	$-0.167688\pi$
$644$	−0.686292			−0.0270437
$645$		0			0
$646$	22.1421	+	9.17157i	0.871171	+	0.360851i
$647$	−11.8284	+	11.8284i	−0.465023	+	0.465023i	−0.900298	−	0.435274i	$-0.856651\pi$
$647$	−11.8284	+	11.8284i	−0.465023	+	0.465023i	0.435274	+	0.900298i	$0.356651\pi$
$648$	28.4853			1.11901
$649$	−1.48528	−	1.48528i	−0.0583024	−	0.0583024i
$650$		0			0
$651$	4.00000	+	9.65685i	0.156772	+	0.378482i
$652$	15.0711	−	36.3848i	0.590229	−	1.42494i
$653$	36.0919	+	14.9497i	1.41238	+	0.585029i	0.952935	−	0.303175i	$-0.0980467\pi$
$653$	36.0919	+	14.9497i	1.41238	+	0.585029i	0.459450	+	0.888204i	$0.348047\pi$
$654$	−8.58579	−	8.58579i	−0.335731	−	0.335731i
$655$		0			0
$656$	−23.3137	−	23.3137i	−0.910247	−	0.910247i
$657$			4.10051i			0.159976i
$658$	−16.4853	+	16.4853i	−0.642663	+	0.642663i
$659$	−5.87868	−	2.43503i	−0.229001	−	0.0948553i	0.265233	−	0.964184i	$-0.414551\pi$
$659$	−5.87868	−	2.43503i	−0.229001	−	0.0948553i	−0.494234	+	0.869329i	$0.664551\pi$
$660$		0			0
$661$	7.74874	+	18.7071i	0.301391	+	0.727622i	0.999927	+	0.0120477i	$0.00383499\pi$
$661$	7.74874	+	18.7071i	0.301391	+	0.727622i	−0.698536	+	0.715574i	$0.746165\pi$
$662$	−9.24264	+	3.82843i	−0.359225	+	0.148796i
$663$	−6.82843	−	6.82843i	−0.265194	−	0.265194i
$664$	7.17157	−	17.3137i	0.278311	−	0.671902i
$665$		0			0
$666$	0.414214	−	1.00000i	0.0160504	−	0.0387492i
$667$	−0.656854	+	0.272078i	−0.0254335	+	0.0105349i
$668$	6.68629	−	6.68629i	0.258700	−	0.258700i
$669$	9.17157	−	22.1421i	0.354593	−	0.856064i
$670$		0			0
$671$	0.242641			0.00936704
$672$	−13.6569	+	5.65685i	−0.526825	+	0.218218i
$673$	−5.51472			−0.212577			−0.106288	−	0.994335i	$-0.533897\pi$
$673$	−5.51472			−0.212577			−0.106288	+	0.994335i	$0.533897\pi$
$674$	−24.0000			−0.924445
$675$		0			0
$676$	13.5563	+	13.5563i	0.521398	+	0.521398i
$677$	5.60660	−	2.32233i	0.215479	−	0.0892544i	−0.272333	−	0.962203i	$-0.587795\pi$
$677$	5.60660	−	2.32233i	0.215479	−	0.0892544i	0.487812	+	0.872949i	$0.337795\pi$
$678$	−17.6569	+	42.6274i	−0.678107	+	1.63710i
$679$	−1.51472	+	1.51472i	−0.0581296	+	0.0581296i
$680$		0			0
$681$	8.89949	+	8.89949i	0.341029	+	0.341029i
$682$	−1.65685	+	0.686292i	−0.0634442	+	0.0262795i
$683$	5.87868	+	14.1924i	0.224941	+	0.543057i	0.995548	−	0.0942543i	$-0.0300467\pi$
$683$	5.87868	+	14.1924i	0.224941	+	0.543057i	−0.770607	+	0.637311i	$0.780047\pi$
$684$	−1.89949	−	4.58579i	−0.0726290	−	0.175342i
$685$		0			0
$686$	−16.9706	+	16.9706i	−0.647939	+	0.647939i
$687$		−	49.5563i		−	1.89069i
$688$	−13.1716	−	31.7990i	−0.502162	−	1.21233i
$689$			15.0711i			0.574162i
$690$		0			0
$691$	−28.5061	−	11.8076i	−1.08442	−	0.449183i	−0.232364	−	0.972629i	$-0.574646\pi$
$691$	−28.5061	−	11.8076i	−1.08442	−	0.449183i	−0.852059	+	0.523446i	$0.824646\pi$
$692$	−2.24264	−	0.928932i	−0.0852524	−	0.0353127i
$693$	0.0710678	+	0.171573i	0.00269964	+	0.00651751i
$694$	8.41421	+	20.3137i	0.319399	+	0.771098i
$695$		0			0
$696$	−10.8284	+	10.8284i	−0.410450	+	0.410450i
$697$	−16.4853	+	16.4853i	−0.624425	+	0.624425i
$698$	36.4558	+	15.1005i	1.37987	+	0.571563i
$699$	20.8995	−	8.65685i	0.790491	−	0.327432i
$700$		0			0
$701$	7.12132	−	17.1924i	0.268969	−	0.649348i	−0.730467	−	0.682948i	$-0.760697\pi$
$701$	7.12132	−	17.1924i	0.268969	−	0.649348i	0.999435	+	0.0336007i	$0.0106974\pi$
$702$		−	12.4853i		−	0.471227i
$703$	11.0711			0.417553
$704$	−0.970563	−	2.34315i	−0.0365795	−	0.0883106i
$705$		0			0
$706$			8.48528i			0.319348i
$707$	−6.65685	+	16.0711i	−0.250357	+	0.604415i
$708$			24.4853i			0.920213i
$709$	−6.77817	+	2.80761i	−0.254560	+	0.105442i	−0.506314	−	0.862349i	$-0.668992\pi$
$709$	−6.77817	+	2.80761i	−0.254560	+	0.105442i	0.251755	+	0.967791i	$0.418992\pi$
$710$		0			0
$711$	1.75736	−	1.75736i	0.0659061	−	0.0659061i
$712$	−7.51472	−	7.51472i	−0.281626	−	0.281626i
$713$	0.686292	+	0.686292i	0.0257018	+	0.0257018i
$714$	4.00000	+	9.65685i	0.149696	+	0.361399i
$715$		0			0
$716$	28.7279	+	11.8995i	1.07361	+	0.444705i
$717$	−29.5563	−	12.2426i	−1.10380	−	0.457210i
$718$	17.2132	+	17.2132i	0.642391	+	0.642391i
$719$			24.3431i			0.907846i	0.891041	+	0.453923i	$0.149976\pi$
$719$			24.3431i			0.907846i	−0.891041	+	0.453923i	$0.850024\pi$
$720$		0			0
$721$			14.9706i			0.557533i
$722$	16.8995	−	16.8995i	0.628934	−	0.628934i
$723$	−14.4853	−	6.00000i	−0.538713	−	0.223142i
$724$	4.38478	+	10.5858i	0.162959	+	0.393418i
$725$		0			0
$726$	26.3137	−	10.8995i	0.976593	−	0.404518i
$727$	−23.9706	−	23.9706i	−0.889019	−	0.889019i	0.105410	−	0.994429i	$-0.466385\pi$
$727$	−23.9706	−	23.9706i	−0.889019	−	0.889019i	−0.994429	+	0.105410i	$0.966385\pi$
$728$	2.82843	+	6.82843i	0.104828	+	0.253078i
$729$	15.7782	−	15.7782i	0.584377	−	0.584377i
$730$		0			0
$731$	−22.4853	+	9.31371i	−0.831648	+	0.344480i
$732$	−2.00000	−	2.00000i	−0.0739221	−	0.0739221i
$733$	0.736544	−	1.77817i	0.0272049	−	0.0656784i	−0.909693	−	0.415281i	$-0.863683\pi$
$733$	0.736544	−	1.77817i	0.0272049	−	0.0656784i	0.936898	+	0.349602i	$0.113683\pi$
$734$	8.48528			0.313197
$735$		0			0
$736$	−0.970563	+	0.970563i	−0.0357754	+	0.0357754i
$737$	−1.27208			−0.0468576
$738$	4.82843			0.177737
$739$	7.53553	−	18.1924i	0.277199	−	0.669218i	−0.722557	−	0.691312i	$-0.757033\pi$
$739$	7.53553	−	18.1924i	0.277199	−	0.669218i	0.999756	+	0.0220937i	$0.00703323\pi$
$740$		0			0
$741$	−18.8995	+	7.82843i	−0.694290	+	0.287584i
$742$	6.24264	−	15.0711i	0.229175	−	0.553276i
$743$	13.6274	−	13.6274i	0.499941	−	0.499941i	−0.411478	−	0.911420i	$-0.634987\pi$
$743$	13.6274	−	13.6274i	0.499941	−	0.499941i	0.911420	+	0.411478i	$0.134987\pi$
$744$	19.3137	+	8.00000i	0.708075	+	0.293294i
$745$		0			0
$746$	39.9706	−	16.5563i	1.46343	−	0.606171i
$747$	1.05025	+	2.53553i	0.0384267	+	0.0927703i
$748$	−1.65685	+	0.686292i	−0.0605806	+	0.0250933i
$749$	0.414214	+	0.171573i	0.0151350	+	0.00626914i
$750$		0			0
$751$			22.9706i			0.838208i	0.907938	+	0.419104i	$0.137656\pi$
$751$			22.9706i			0.838208i	−0.907938	+	0.419104i	$0.862344\pi$
$752$			46.6274i			1.70033i
$753$		−	29.2132i		−	1.06459i
$754$	5.41421	+	5.41421i	0.197174	+	0.197174i
$755$		0			0
$756$	−5.17157	+	12.4853i	−0.188088	+	0.454085i
$757$	0.736544	+	1.77817i	0.0267701	+	0.0646289i	0.936699	−	0.350135i	$-0.113864\pi$
$757$	0.736544	+	1.77817i	0.0267701	+	0.0646289i	−0.909929	+	0.414764i	$0.863864\pi$
$758$	−12.6985	−	30.6569i	−0.461230	−	1.11351i
$759$	0.100505	+	0.100505i	0.00364810	+	0.00364810i
$760$		0			0
$761$	−24.1716	+	24.1716i	−0.876219	+	0.876219i	−0.993141	−	0.116922i	$-0.962697\pi$
$761$	−24.1716	+	24.1716i	−0.876219	+	0.876219i	0.116922	+	0.993141i	$0.462697\pi$
$762$	50.6274	+	20.9706i	1.83404	+	0.759683i
$763$	6.07107	−	2.51472i	0.219787	−	0.0910389i
$764$	24.0000			0.868290
$765$		0			0
$766$			24.0000i			0.867155i
$767$	12.2426			0.442056
$768$	−11.3137	+	27.3137i	−0.408248	+	0.985599i
$769$	22.4853			0.810840			0.405420	−	0.914131i	$-0.367125\pi$
$769$	22.4853			0.810840			0.405420	+	0.914131i	$0.367125\pi$
$770$		0			0
$771$	4.24264	−	10.2426i	0.152795	−	0.368880i
$772$	−36.9706			−1.33060
$773$	26.0919	−	10.8076i	0.938460	−	0.388723i	0.139578	−	0.990211i	$-0.455425\pi$
$773$	26.0919	−	10.8076i	0.938460	−	0.388723i	0.798882	+	0.601488i	$0.205425\pi$
$774$	4.65685	+	1.92893i	0.167387	+	0.0693340i
$775$		0			0
$776$			4.28427i			0.153796i
$777$	3.41421	+	3.41421i	0.122484	+	0.122484i
$778$	17.3431	+	41.8701i	0.621782	+	1.50111i
$779$	18.8995	+	45.6274i	0.677145	+	1.63477i
$780$		0			0
$781$	−0.0710678	−	0.0294373i	−0.00254301	−	0.00105335i
$782$	0.686292	+	0.686292i	0.0245417	+	0.0245417i
$783$			14.0000i			0.500319i
$784$			20.0000i			0.714286i
$785$		0			0
$786$	−17.5563	+	17.5563i	−0.626214	+	0.626214i
$787$	−8.94975	−	3.70711i	−0.319024	−	0.132144i	0.217424	−	0.976077i	$-0.430234\pi$
$787$	−8.94975	−	3.70711i	−0.319024	−	0.132144i	−0.536448	+	0.843933i	$0.680234\pi$
$788$	34.7279	−	14.3848i	1.23713	−	0.512436i
$789$	0.171573	+	0.414214i	0.00610816	+	0.0147464i
$790$		0			0
$791$	−17.6569	−	17.6569i	−0.627805	−	0.627805i
$792$	0.343146	+	0.142136i	0.0121932	+	0.00505057i
$793$	−1.00000	+	1.00000i	−0.0355110	+	0.0355110i
$794$	14.5147	−	35.0416i	0.515108	−	1.24358i
$795$		0			0
$796$	−35.9411	+	35.9411i	−1.27390	+	1.27390i
$797$	−12.0919	+	29.1924i	−0.428316	+	1.03405i	0.551505	+	0.834172i	$0.314054\pi$
$797$	−12.0919	+	29.1924i	−0.428316	+	1.03405i	−0.979821	+	0.199876i	$0.935946\pi$
$798$	22.1421			0.783823
$799$	32.9706			1.16641
$800$		0			0
$801$	1.55635			0.0549909
$802$	4.00000			0.141245
$803$	1.20101	−	2.89949i	0.0423827	−	0.102321i
$804$	10.4853	+	10.4853i	0.369787	+	0.369787i
$805$		0			0
$806$	4.00000	−	9.65685i	0.140894	−	0.340148i
$807$	−6.89949	+	6.89949i	−0.242874	+	0.242874i
$808$	13.3137	+	32.1421i	0.468375	+	1.13076i
$809$	−0.857864	−	0.857864i	−0.0301609	−	0.0301609i	0.691865	−	0.722026i	$-0.256789\pi$
$809$	−0.857864	−	0.857864i	−0.0301609	−	0.0301609i	−0.722026	+	0.691865i	$0.756789\pi$
$810$		0			0
$811$	−9.73654	−	23.5061i	−0.341896	−	0.825411i	−0.997524	−	0.0703264i	$-0.977596\pi$
$811$	−9.73654	−	23.5061i	−0.341896	−	0.825411i	0.655628	−	0.755084i	$-0.272404\pi$
$812$	−3.17157	−	7.65685i	−0.111300	−	0.268703i
$813$	−30.7279	−	12.7279i	−1.07768	−	0.446388i
$814$	−0.585786	+	0.585786i	−0.0205318	+	0.0205318i
$815$		0			0
$816$	19.3137	+	8.00000i	0.676115	+	0.280056i
$817$			51.5563i			1.80373i
$818$	−6.38478	−	6.38478i	−0.223238	−	0.223238i
$819$	−1.00000	−	0.414214i	−0.0349428	−	0.0144738i
$820$		0			0
$821$	−0.393398	−	0.949747i	−0.0137297	−	0.0331464i	0.916866	−	0.399195i	$-0.130710\pi$
$821$	−0.393398	−	0.949747i	−0.0137297	−	0.0331464i	−0.930596	+	0.366049i	$0.880710\pi$
$822$	−3.75736	−	9.07107i	−0.131053	−	0.316390i
$823$	−2.02944	−	2.02944i	−0.0707417	−	0.0707417i	0.670851	−	0.741592i	$-0.265929\pi$
$823$	−2.02944	−	2.02944i	−0.0707417	−	0.0707417i	−0.741592	+	0.670851i	$0.765929\pi$
$824$	21.1716	+	21.1716i	0.737547	+	0.737547i
$825$		0			0
$826$	−12.2426	−	5.07107i	−0.425976	−	0.176445i
$827$	−11.8787	+	4.92031i	−0.413062	+	0.171096i	−0.579530	−	0.814951i	$-0.696764\pi$
$827$	−11.8787	+	4.92031i	−0.413062	+	0.171096i	0.166468	+	0.986047i	$0.446764\pi$
$828$		−	0.201010i		−	0.00698558i
$829$	15.8076	−	38.1630i	0.549021	−	1.32545i	−0.369187	−	0.929355i	$-0.620364\pi$
$829$	15.8076	−	38.1630i	0.549021	−	1.32545i	0.918208	−	0.396099i	$-0.129636\pi$
$830$		0			0
$831$	1.41421			0.0490585
$832$	13.6569	+	5.65685i	0.473466	+	0.196116i
$833$	14.1421			0.489996
$834$		−	35.4558i		−	1.22774i
$835$		0			0
$836$			3.79899i			0.131391i
$837$	17.6569	−	7.31371i	0.610310	−	0.252799i
$838$	29.3848	+	12.1716i	1.01508	+	0.420460i
$839$	32.3137	−	32.3137i	1.11559	−	1.11559i	0.123213	−	0.992380i	$-0.460680\pi$
$839$	32.3137	−	32.3137i	1.11559	−	1.11559i	0.992380	−	0.123213i	$-0.0393198\pi$
$840$		0			0
$841$	14.4350	+	14.4350i	0.497760	+	0.497760i
$842$	−4.51472	−	10.8995i	−0.155587	−	0.375621i
$843$	−6.17157	−	14.8995i	−0.212560	−	0.513166i
$844$	−0.928932	−	0.384776i	−0.0319752	−	0.0132445i
$845$		0			0
$846$	−4.82843	−	4.82843i	−0.166005	−	0.166005i
$847$			15.4142i			0.529639i
$848$	−12.4853	−	30.1421i	−0.428746	−	1.03509i
$849$			19.5563i			0.671172i
$850$		0			0
$851$	0.414214	+	0.171573i	0.0141991	+	0.00588144i
$852$	0.343146	+	0.828427i	0.0117560	+	0.0283814i
$853$	1.16295	+	2.80761i	0.0398187	+	0.0961308i	0.942538	−	0.334100i	$-0.108432\pi$
$853$	1.16295	+	2.80761i	0.0398187	+	0.0961308i	−0.902719	+	0.430231i	$0.858432\pi$
$854$	1.41421	−	0.585786i	0.0483934	−	0.0200452i
$855$		0			0
$856$	0.828427	−	0.343146i	0.0283151	−	0.0117285i
$857$	−32.3137	+	32.3137i	−1.10382	+	1.10382i	−0.109869	+	0.993946i	$0.535043\pi$
$857$	−32.3137	+	32.3137i	−1.10382	+	1.10382i	−0.993946	+	0.109869i	$0.964957\pi$
$858$	0.585786	−	1.41421i	0.0199984	−	0.0482805i
$859$	33.6777	−	13.9497i	1.14907	−	0.475959i	0.274847	−	0.961488i	$-0.411373\pi$
$859$	33.6777	−	13.9497i	1.14907	−	0.475959i	0.874221	+	0.485529i	$0.161373\pi$
$860$		0			0
$861$	−8.24264	+	19.8995i	−0.280908	+	0.678173i
$862$	−33.4558			−1.13951
$863$	45.9411			1.56385			0.781927	−	0.623370i	$-0.214237\pi$
$863$	45.9411			1.56385			0.781927	+	0.623370i	$0.214237\pi$
$864$	10.3431	+	24.9706i	0.351881	+	0.849516i
$865$		0			0
$866$	45.9411			1.56114
$867$	−6.36396	+	15.3640i	−0.216131	+	0.521787i
$868$	−8.00000	+	8.00000i	−0.271538	+	0.271538i
$869$	−1.75736	+	0.727922i	−0.0596143	+	0.0246931i
$870$		0			0
$871$	5.24264	−	5.24264i	0.177640	−	0.177640i
$872$	5.02944	−	12.1421i	0.170318	−	0.411185i
$873$	−0.443651	−	0.443651i	−0.0150153	−	0.0150153i
$874$	1.89949	−	0.786797i	0.0642514	−	0.0266138i
$875$		0			0
$876$	−33.7990	+	14.0000i	−1.14196	+	0.473016i
$877$	33.2635	+	13.7782i	1.12323	+	0.465256i	0.865473	−	0.500955i	$-0.167018\pi$
$877$	33.2635	+	13.7782i	1.12323	+	0.465256i	0.257754	+	0.966211i	$0.417018\pi$
$878$	−24.0416	+	24.0416i	−0.811366	+	0.811366i
$879$			23.2132i			0.782962i
$880$		0			0
$881$		−	22.6274i		−	0.762337i	−0.924506	−	0.381169i	$-0.875522\pi$
$881$		−	22.6274i		−	0.762337i	0.924506	−	0.381169i	$-0.124478\pi$
$882$	−2.07107	−	2.07107i	−0.0697365	−	0.0697365i
$883$	−47.4350	−	19.6482i	−1.59632	−	0.661216i	−0.605427	−	0.795901i	$-0.706998\pi$
$883$	−47.4350	−	19.6482i	−1.59632	−	0.661216i	−0.990888	+	0.134685i	$0.956998\pi$
$884$	4.00000	−	9.65685i	0.134535	−	0.324795i
$885$		0			0
$886$	−12.0711	−	29.1421i	−0.405535	−	0.979049i
$887$	20.3137	+	20.3137i	0.682068	+	0.682068i	0.960466	−	0.278398i	$-0.0898035\pi$
$887$	20.3137	+	20.3137i	0.682068	+	0.682068i	−0.278398	+	0.960466i	$0.589803\pi$
$888$	9.65685			0.324063
$889$	−20.9706	+	20.9706i	−0.703330	+	0.703330i
$890$		0			0
$891$	2.94975	−	1.22183i	0.0988203	−	0.0409327i
$892$	25.9411			0.868573
$893$	26.7279	−	64.5269i	0.894416	−	2.15931i
$894$			38.2843i			1.28042i
$895$		0			0
$896$	−11.3137	−	11.3137i	−0.377964	−	0.377964i
$897$	−0.828427			−0.0276604
$898$		−	44.4853i		−	1.48449i
$899$	−4.48528	+	10.8284i	−0.149593	+	0.361148i
$900$		0			0
$901$	−21.3137	+	8.82843i	−0.710063	+	0.294118i
$902$	−3.41421	−	1.41421i	−0.113681	−	0.0470882i
$903$	−15.8995	+	15.8995i	−0.529102	+	0.529102i
$904$	−49.9411			−1.66102
$905$		0			0
$906$	21.8995	+	52.8701i	0.727562	+	1.75649i
$907$	0.221825	+	0.535534i	0.00736559	+	0.0177821i	0.927520	−	0.373775i	$-0.121937\pi$
$907$	0.221825	+	0.535534i	0.00736559	+	0.0177821i	−0.920154	+	0.391557i	$0.871937\pi$
$908$	−5.21320	+	12.5858i	−0.173006	+	0.417674i
$909$	−4.70711	−	1.94975i	−0.156125	−	0.0646690i
$910$		0			0
$911$		−	45.5980i		−	1.51073i	−0.655305	−	0.755364i	$-0.727460\pi$
$911$		−	45.5980i		−	1.51073i	0.655305	−	0.755364i	$-0.272540\pi$
$912$	31.3137	−	31.3137i	1.03690	−	1.03690i
$913$		−	2.10051i		−	0.0695166i
$914$	−13.4142	+	13.4142i	−0.443703	+	0.443703i
$915$		0			0
$916$	49.5563	−	20.5269i	1.63739	−	0.678228i
$917$	−5.14214	−	12.4142i	−0.169808	−	0.409953i
$918$	17.6569	−	7.31371i	0.582763	−	0.241388i
$919$	−25.4853	−	25.4853i	−0.840682	−	0.840682i	0.148266	−	0.988948i	$-0.452631\pi$
$919$	−25.4853	−	25.4853i	−0.840682	−	0.840682i	−0.988948	+	0.148266i	$0.952631\pi$
$920$		0			0
$921$	4.17157	−	4.17157i	0.137458	−	0.137458i
$922$	7.82843	−	18.8995i	0.257816	−	0.622422i
$923$	0.414214	−	0.171573i	0.0136340	−	0.00564739i
$924$	−1.17157	+	1.17157i	−0.0385419	+	0.0385419i
$925$		0			0
$926$	15.5147			0.509845
$927$	−4.38478			−0.144015
$928$	−15.3137	−	6.34315i	−0.502697	−	0.208224i
$929$	−26.4853			−0.868954			−0.434477	−	0.900683i	$-0.643067\pi$
$929$	−26.4853			−0.868954			−0.434477	+	0.900683i	$0.643067\pi$
$930$		0			0
$931$	11.4645	−	27.6777i	0.375733	−	0.907099i
$932$	17.3137	+	17.3137i	0.567129	+	0.567129i
$933$	−20.8995	+	8.65685i	−0.684219	+	0.283413i
$934$	−17.0416	+	41.1421i	−0.557619	+	1.34621i
$935$		0			0
$936$	−2.00000	+	0.828427i	−0.0653720	+	0.0270780i
$937$	−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	$0.894633\pi$
$938$	−7.41421	+	3.07107i	−0.242083	+	0.100274i
$939$	−9.48528	−	22.8995i	−0.309540	−	0.747297i
$940$		0			0
$941$	13.3640	+	5.53553i	0.435653	+	0.180453i	0.589721	−	0.807607i	$-0.299238\pi$
$941$	13.3640	+	5.53553i	0.435653	+	0.180453i	−0.154068	+	0.988060i	$0.549238\pi$
$942$	−1.41421	+	1.41421i	−0.0460776	+	0.0460776i
$943$			2.00000i			0.0651290i
$944$	−24.4853	+	10.1421i	−0.796928	+	0.330098i
$945$		0			0
$946$	−2.72792	−	2.72792i	−0.0886924	−	0.0886924i
$947$	37.3345	+	15.4645i	1.21321	+	0.502528i	0.895245	−	0.445575i	$-0.147001\pi$
$947$	37.3345	+	15.4645i	1.21321	+	0.502528i	0.317964	+	0.948103i	$0.397001\pi$
$948$	20.4853	+	8.48528i	0.665331	+	0.275589i
$949$	7.00000	+	16.8995i	0.227230	+	0.548581i
$950$		0			0
$951$	−15.8284	−	15.8284i	−0.513272	−	0.513272i
$952$	−8.00000	+	8.00000i	−0.259281	+	0.259281i
$953$	−3.34315	+	3.34315i	−0.108295	+	0.108295i	−0.759178	−	0.650883i	$-0.774399\pi$
$953$	−3.34315	+	3.34315i	−0.108295	+	0.108295i	0.650883	+	0.759178i	$0.274399\pi$
$954$	4.41421	+	1.82843i	0.142915	+	0.0591975i
$955$		0			0
$956$		−	34.6274i		−	1.11993i
$957$	−0.656854	+	1.58579i	−0.0212331	+	0.0512612i
$958$			7.02944i			0.227111i
$959$	5.31371			0.171589
$960$		0			0
$961$	−15.0000			−0.483871
$962$		−	4.82843i		−	0.155675i
$963$	−0.0502525	+	0.121320i	−0.00161937	+	0.00390949i
$964$		−	16.9706i		−	0.546585i
$965$		0			0
$966$	0.828427	+	0.343146i	0.0266542	+	0.0110405i
$967$	39.9706	−	39.9706i	1.28537	−	1.28537i	0.347797	−	0.937570i	$-0.386930\pi$
$967$	39.9706	−	39.9706i	1.28537	−	1.28537i	0.937570	−	0.347797i	$-0.113070\pi$
$968$	21.7990	+	21.7990i	0.700646	+	0.700646i
$969$	−22.1421	−	22.1421i	−0.711308	−	0.711308i
$970$		0			0
$971$	9.63604	+	23.2635i	0.309235	+	0.746560i	0.999730	+	0.0232228i	$0.00739270\pi$
$971$	9.63604	+	23.2635i	0.309235	+	0.746560i	−0.690495	+	0.723337i	$0.742607\pi$
$972$	−7.89949	−	3.27208i	−0.253376	−	0.104952i
$973$	17.7279	+	7.34315i	0.568331	+	0.235410i
$974$	−15.5563	−	15.5563i	−0.498458	−	0.498458i
$975$		0			0
$976$	1.17157	−	2.82843i	0.0375011	−	0.0905357i
$977$			14.1421i			0.452447i	0.974075	+	0.226224i	$0.0726380\pi$
$977$			14.1421i			0.452447i	−0.974075	+	0.226224i	$0.927362\pi$
$978$	−36.3848	+	36.3848i	−1.16346	+	1.16346i
$979$	−1.10051	−	0.455844i	−0.0351723	−	0.0145688i
$980$		0			0
$981$	0.736544	+	1.77817i	0.0235160	+	0.0567727i
$982$	−25.0416	+	10.3726i	−0.799111	+	0.331002i
$983$	−25.6274	−	25.6274i	−0.817388	−	0.817388i	0.168341	−	0.985729i	$-0.446159\pi$
$983$	−25.6274	−	25.6274i	−0.817388	−	0.817388i	−0.985729	+	0.168341i	$0.946159\pi$
$984$	16.4853	+	39.7990i	0.525532	+	1.26875i
$985$		0			0
$986$	−4.48528	+	10.8284i	−0.142840	+	0.344847i
$987$	28.1421	−	11.6569i	0.895774	−	0.371042i
$988$	−15.6569	−	15.6569i	−0.498111	−	0.498111i
$989$	−0.798990	+	1.92893i	−0.0254064	+	0.0613365i
$990$		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
$993$	13.0711			0.414798
$994$	−0.485281			−0.0153922
$995$		0			0
$996$	−17.3137	+	17.3137i	−0.548606	+	0.548606i
$997$	1.80761	−	0.748737i	0.0572476	−	0.0237127i	−0.353876	−	0.935292i	$-0.615136\pi$
$997$	1.80761	−	0.748737i	0.0572476	−	0.0237127i	0.411124	+	0.911580i	$0.365136\pi$
$998$	5.24264	−	12.6569i	0.165953	−	0.400646i
$999$	6.24264	−	6.24264i	0.197508	−	0.197508i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	800.2.y.a.301.1		4
5.2	odd	4		800.2.ba.b.749.1		4
5.3	odd	4		800.2.ba.a.749.1		4
5.4	even	2		32.2.g.a.13.1	yes	4
15.14	odd	2		288.2.v.a.109.1		4
20.19	odd	2		128.2.g.a.17.1		4
32.5	even	8	inner	800.2.y.a.101.1		4
40.19	odd	2		256.2.g.a.33.1		4
40.29	even	2		256.2.g.b.33.1		4
60.59	even	2		1152.2.v.a.145.1		4
80.19	odd	4		512.2.g.b.321.1		4
80.29	even	4		512.2.g.d.321.1		4
80.59	odd	4		512.2.g.c.321.1		4
80.69	even	4		512.2.g.a.321.1		4
160.19	odd	8		512.2.g.c.193.1		4
160.29	even	8		512.2.g.d.193.1		4
160.37	odd	8		800.2.ba.a.549.1		4
160.59	odd	8		128.2.g.a.113.1		4
160.69	even	8		32.2.g.a.5.1	✓	4
160.99	odd	8		512.2.g.b.193.1		4
160.109	even	8		512.2.g.a.193.1		4
160.133	odd	8		800.2.ba.b.549.1		4
160.139	odd	8		256.2.g.a.225.1		4
160.149	even	8		256.2.g.b.225.1		4
320.59	odd	16		4096.2.a.f.1.1		4
320.69	even	16		4096.2.a.e.1.4		4
320.219	odd	16		4096.2.a.f.1.4		4
320.229	even	16		4096.2.a.e.1.1		4
480.59	even	8		1152.2.v.a.1009.1		4
480.389	odd	8		288.2.v.a.37.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.2.g.a.5.1	✓	4	160.69	even	8
32.2.g.a.13.1	yes	4	5.4	even	2
128.2.g.a.17.1		4	20.19	odd	2
128.2.g.a.113.1		4	160.59	odd	8
256.2.g.a.33.1		4	40.19	odd	2
256.2.g.a.225.1		4	160.139	odd	8
256.2.g.b.33.1		4	40.29	even	2
256.2.g.b.225.1		4	160.149	even	8
288.2.v.a.37.1		4	480.389	odd	8
288.2.v.a.109.1		4	15.14	odd	2
512.2.g.a.193.1		4	160.109	even	8
512.2.g.a.321.1		4	80.69	even	4
512.2.g.b.193.1		4	160.99	odd	8
512.2.g.b.321.1		4	80.19	odd	4
512.2.g.c.193.1		4	160.19	odd	8
512.2.g.c.321.1		4	80.59	odd	4
512.2.g.d.193.1		4	160.29	even	8
512.2.g.d.321.1		4	80.29	even	4
800.2.y.a.101.1		4	32.5	even	8	inner
800.2.y.a.301.1		4	1.1	even	1	trivial
800.2.ba.a.549.1		4	160.37	odd	8
800.2.ba.a.749.1		4	5.3	odd	4
800.2.ba.b.549.1		4	160.133	odd	8
800.2.ba.b.749.1		4	5.2	odd	4
1152.2.v.a.145.1		4	60.59	even	2
1152.2.v.a.1009.1		4	480.59	even	8
4096.2.a.e.1.1		4	320.229	even	16
4096.2.a.e.1.4		4	320.69	even	16
4096.2.a.f.1.1		4	320.59	odd	16
4096.2.a.f.1.4		4	320.219	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)

\(f(q)\)	\(=\)	\(q-1.41421i q^{2} +(-0.707107 + 1.70711i) q^{3} -2.00000 q^{4} +(2.41421 + 1.00000i) q^{6} +(-1.00000 + 1.00000i) q^{7} +2.82843i q^{8} +(-0.292893 - 0.292893i) q^{9} +O(q^{10})\)	\(q-1.41421i q^{2} +(-0.707107 + 1.70711i) q^{3} -2.00000 q^{4} +(2.41421 + 1.00000i) q^{6} +(-1.00000 + 1.00000i) q^{7} +2.82843i q^{8} +(-0.292893 - 0.292893i) q^{9} +(0.121320 + 0.292893i) q^{11} +(1.41421 - 3.41421i) q^{12} +(-1.70711 - 0.707107i) q^{13} +(1.41421 + 1.41421i) q^{14} +4.00000 q^{16} -2.82843i q^{17} +(-0.414214 + 0.414214i) q^{18} +(-5.53553 - 2.29289i) q^{19} +(-1.00000 - 2.41421i) q^{21} +(0.414214 - 0.171573i) q^{22} +(-0.171573 - 0.171573i) q^{23} +(-4.82843 - 2.00000i) q^{24} +(-1.00000 + 2.41421i) q^{26} +(-4.41421 + 1.82843i) q^{27} +(2.00000 - 2.00000i) q^{28} +(1.12132 - 2.70711i) q^{29} -4.00000 q^{31} -5.65685i q^{32} -0.585786 q^{33} -4.00000 q^{34} +(0.585786 + 0.585786i) q^{36} +(-1.70711 + 0.707107i) q^{37} +(-3.24264 + 7.82843i) q^{38} +(2.41421 - 2.41421i) q^{39} +(-5.82843 - 5.82843i) q^{41} +(-3.41421 + 1.41421i) q^{42} +(-3.29289 - 7.94975i) q^{43} +(-0.242641 - 0.585786i) q^{44} +(-0.242641 + 0.242641i) q^{46} +11.6569i q^{47} +(-2.82843 + 6.82843i) q^{48} +5.00000i q^{49} +(4.82843 + 2.00000i) q^{51} +(3.41421 + 1.41421i) q^{52} +(-3.12132 - 7.53553i) q^{53} +(2.58579 + 6.24264i) q^{54} +(-2.82843 - 2.82843i) q^{56} +(7.82843 - 7.82843i) q^{57} +(-3.82843 - 1.58579i) q^{58} +(-6.12132 + 2.53553i) q^{59} +(0.292893 - 0.707107i) q^{61} +5.65685i q^{62} +0.585786 q^{63} -8.00000 q^{64} +0.828427i q^{66} +(-1.53553 + 3.70711i) q^{67} +5.65685i q^{68} +(0.414214 - 0.171573i) q^{69} +(-0.171573 + 0.171573i) q^{71} +(0.828427 - 0.828427i) q^{72} +(-7.00000 - 7.00000i) q^{73} +(1.00000 + 2.41421i) q^{74} +(11.0711 + 4.58579i) q^{76} +(-0.414214 - 0.171573i) q^{77} +(-3.41421 - 3.41421i) q^{78} +6.00000i q^{79} -10.0711i q^{81} +(-8.24264 + 8.24264i) q^{82} +(-6.12132 - 2.53553i) q^{83} +(2.00000 + 4.82843i) q^{84} +(-11.2426 + 4.65685i) q^{86} +(3.82843 + 3.82843i) q^{87} +(-0.828427 + 0.343146i) q^{88} +(-2.65685 + 2.65685i) q^{89} +(2.41421 - 1.00000i) q^{91} +(0.343146 + 0.343146i) q^{92} +(2.82843 - 6.82843i) q^{93} +16.4853 q^{94} +(9.65685 + 4.00000i) q^{96} +1.51472 q^{97} +7.07107 q^{98} +(0.0502525 - 0.121320i) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more