LMFDB - Embedded newform 800.2.ba.a.749.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("800.149");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 800 = 2^{5} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	800.ba (of order $8$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.38803216170$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 32)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			749.1
Root			$0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	800.749
Dual form			800.2.ba.a.549.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421 q^{2} +(-1.70711 - 0.707107i) q^{3} +2.00000 q^{4} +(2.41421 + 1.00000i) q^{6} +(1.00000 + 1.00000i) q^{7} -2.82843 q^{8} +(0.292893 + 0.292893i) q^{9} +O(q^{10})$	\(q-1.41421 q^{2} +(-1.70711 - 0.707107i) q^{3} +2.00000 q^{4} +(2.41421 + 1.00000i) q^{6} +(1.00000 + 1.00000i) q^{7} -2.82843 q^{8} +(0.292893 + 0.292893i) q^{9} +(0.121320 + 0.292893i) q^{11} +(-3.41421 - 1.41421i) q^{12} +(0.707107 - 1.70711i) q^{13} +(-1.41421 - 1.41421i) q^{14} +4.00000 q^{16} -2.82843 q^{17} +(-0.414214 - 0.414214i) q^{18} +(5.53553 + 2.29289i) q^{19} +(-1.00000 - 2.41421i) q^{21} +(-0.171573 - 0.414214i) q^{22} +(0.171573 - 0.171573i) q^{23} +(4.82843 + 2.00000i) q^{24} +(-1.00000 + 2.41421i) q^{26} +(1.82843 + 4.41421i) q^{27} +(2.00000 + 2.00000i) q^{28} +(-1.12132 + 2.70711i) q^{29} -4.00000 q^{31} -5.65685 q^{32} -0.585786i q^{33} +4.00000 q^{34} +(0.585786 + 0.585786i) q^{36} +(0.707107 + 1.70711i) q^{37} +(-7.82843 - 3.24264i) q^{38} +(-2.41421 + 2.41421i) q^{39} +(-5.82843 - 5.82843i) q^{41} +(1.41421 + 3.41421i) q^{42} +(7.94975 - 3.29289i) q^{43} +(0.242641 + 0.585786i) q^{44} +(-0.242641 + 0.242641i) q^{46} +11.6569 q^{47} +(-6.82843 - 2.82843i) q^{48} -5.00000i q^{49} +(4.82843 + 2.00000i) q^{51} +(1.41421 - 3.41421i) q^{52} +(7.53553 - 3.12132i) q^{53} +(-2.58579 - 6.24264i) q^{54} +(-2.82843 - 2.82843i) q^{56} +(-7.82843 - 7.82843i) q^{57} +(1.58579 - 3.82843i) q^{58} +(6.12132 - 2.53553i) q^{59} +(0.292893 - 0.707107i) q^{61} +5.65685 q^{62} +0.585786i q^{63} +8.00000 q^{64} +0.828427i q^{66} +(3.70711 + 1.53553i) q^{67} -5.65685 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} +(-0.171573 + 0.414214i) q^{77} +(3.41421 - 3.41421i) q^{78} -6.00000i q^{79} -10.0711i q^{81} +(8.24264 + 8.24264i) q^{82} +(2.53553 - 6.12132i) q^{83} +(-2.00000 - 4.82843i) q^{84} +(-11.2426 + 4.65685i) q^{86} +(3.82843 - 3.82843i) q^{87} +(-0.343146 - 0.828427i) q^{88} +(2.65685 - 2.65685i) q^{89} +(2.41421 - 1.00000i) q^{91} +(0.343146 - 0.343146i) q^{92} +(6.82843 + 2.82843i) q^{93} -16.4853 q^{94} +(9.65685 + 4.00000i) q^{96} -1.51472i q^{97} +7.07107i q^{98} +(-0.0502525 + 0.121320i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{3} + 8 q^{4} + 4 q^{6} + 4 q^{7} + 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^3 + 8 * q^4 + 4 * q^6 + 4 * q^7 + 4 * q^9	$ 4 q - 4 q^{3} + 8 q^{4} + 4 q^{6} + 4 q^{7} + 4 q^{9} - 8 q^{11} - 8 q^{12} + 16 q^{16} + 4 q^{18} + 8 q^{19} - 4 q^{21} - 12 q^{22} + 12 q^{23} + 8 q^{24} - 4 q^{26} - 4 q^{27} + 8 q^{28} + 4 q^{29} - 16 q^{31} + 16 q^{34} + 8 q^{36} - 20 q^{38} - 4 q^{39} - 12 q^{41} + 12 q^{43} - 16 q^{44} + 16 q^{46} + 24 q^{47} - 16 q^{48} + 8 q^{51} + 16 q^{53} - 16 q^{54} - 20 q^{57} + 12 q^{58} + 16 q^{59} + 4 q^{61} + 32 q^{64} + 12 q^{67} + 4 q^{69} - 12 q^{71} + 8 q^{72} + 28 q^{73} - 4 q^{74} + 16 q^{76} - 12 q^{77} + 8 q^{78} + 16 q^{82} - 4 q^{83} - 8 q^{84} - 28 q^{86} + 4 q^{87} - 24 q^{88} - 12 q^{89} + 4 q^{91} + 24 q^{92} + 16 q^{93} - 32 q^{94} + 16 q^{96} - 20 q^{99}+O(q^{100}) $ 4 * q - 4 * q^3 + 8 * q^4 + 4 * q^6 + 4 * q^7 + 4 * q^9 - 8 * q^11 - 8 * q^12 + 16 * q^16 + 4 * q^18 + 8 * q^19 - 4 * q^21 - 12 * q^22 + 12 * q^23 + 8 * q^24 - 4 * q^26 - 4 * q^27 + 8 * q^28 + 4 * q^29 - 16 * q^31 + 16 * q^34 + 8 * q^36 - 20 * q^38 - 4 * q^39 - 12 * q^41 + 12 * q^43 - 16 * q^44 + 16 * q^46 + 24 * q^47 - 16 * q^48 + 8 * q^51 + 16 * q^53 - 16 * q^54 - 20 * q^57 + 12 * q^58 + 16 * q^59 + 4 * q^61 + 32 * q^64 + 12 * q^67 + 4 * q^69 - 12 * q^71 + 8 * q^72 + 28 * q^73 - 4 * q^74 + 16 * q^76 - 12 * q^77 + 8 * q^78 + 16 * q^82 - 4 * q^83 - 8 * q^84 - 28 * q^86 + 4 * q^87 - 24 * q^88 - 12 * q^89 + 4 * q^91 + 24 * q^92 + 16 * q^93 - 32 * q^94 + 16 * q^96 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.41421			−1.00000
$2$	−1.41421			−1.00000
$3$	−1.70711	−	0.707107i	−0.985599	−	0.408248i	−0.169102	−	0.985599i	$-0.554087\pi$
$3$	−1.70711	−	0.707107i	−0.985599	−	0.408248i	−0.816497	+	0.577350i	$0.804087\pi$
$4$	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	$-0.163881\pi$
$7$	1.00000	+	1.00000i	0.377964	+	0.377964i	−0.492403	+	0.870367i	$0.663881\pi$
$8$	−2.82843			−1.00000
$9$	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	$0.859781\pi$
$12$	−3.41421	−	1.41421i	−0.985599	−	0.408248i
$13$	0.707107	−	1.70711i	0.196116	−	0.473466i	−0.794977	−	0.606640i	$-0.792517\pi$
$13$	0.707107	−	1.70711i	0.196116	−	0.473466i	0.991093	+	0.133174i	$0.0425169\pi$
$14$	−1.41421	−	1.41421i	−0.377964	−	0.377964i
$15$		0			0
$16$	4.00000			1.00000
$17$	−2.82843			−0.685994			−0.342997	−	0.939336i	$-0.611442\pi$
$17$	−2.82843			−0.685994			−0.342997	+	0.939336i	$0.611442\pi$
$18$	−0.414214	−	0.414214i	−0.0976311	−	0.0976311i
$19$	5.53553	+	2.29289i	1.26994	+	0.526026i	0.912946	−	0.408081i	$-0.133802\pi$
$19$	5.53553	+	2.29289i	1.26994	+	0.526026i	0.356993	+	0.934107i	$0.383802\pi$
$20$		0			0
$21$	−1.00000	−	2.41421i	−0.218218	−	0.526825i
$22$	−0.171573	−	0.414214i	−0.0365795	−	0.0883106i
$23$	0.171573	−	0.171573i	0.0357754	−	0.0357754i	−0.688993	−	0.724768i	$-0.741947\pi$
$23$	0.171573	−	0.171573i	0.0357754	−	0.0357754i	0.724768	+	0.688993i	$0.241947\pi$
$24$	4.82843	+	2.00000i	0.985599	+	0.408248i
$25$		0			0
$26$	−1.00000	+	2.41421i	−0.196116	+	0.473466i
$27$	1.82843	+	4.41421i	0.351881	+	0.849516i
$28$	2.00000	+	2.00000i	0.377964	+	0.377964i
$29$	−1.12132	+	2.70711i	−0.208224	+	0.502697i	−0.993144	−	0.116900i	$-0.962704\pi$
$29$	−1.12132	+	2.70711i	−0.208224	+	0.502697i	0.784920	+	0.619598i	$0.212704\pi$
$30$		0			0
$31$	−4.00000			−0.718421			−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000			−0.718421			−0.359211	+	0.933257i	$0.616954\pi$
$32$	−5.65685			−1.00000
$33$		−	0.585786i		−	0.101972i
$34$	4.00000			0.685994
$35$		0			0
$36$	0.585786	+	0.585786i	0.0976311	+	0.0976311i
$37$	0.707107	+	1.70711i	0.116248	+	0.280647i	0.971285	−	0.237920i	$-0.0764657\pi$
$37$	0.707107	+	1.70711i	0.116248	+	0.280647i	−0.855037	+	0.518567i	$0.826466\pi$
$38$	−7.82843	−	3.24264i	−1.26994	−	0.526026i
$39$	−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	$0.972577\pi$
$42$	1.41421	+	3.41421i	0.218218	+	0.526825i
$43$	7.94975	−	3.29289i	1.21233	−	0.502162i	0.317363	−	0.948304i	$-0.397203\pi$
$43$	7.94975	−	3.29289i	1.21233	−	0.502162i	0.894962	+	0.446143i	$0.147203\pi$
$44$	0.242641	+	0.585786i	0.0365795	+	0.0883106i
$45$		0			0
$46$	−0.242641	+	0.242641i	−0.0357754	+	0.0357754i
$47$	11.6569			1.70033			0.850163	−	0.526519i	$-0.176503\pi$
$47$	11.6569			1.70033			0.850163	+	0.526519i	$0.176503\pi$
$48$	−6.82843	−	2.82843i	−0.985599	−	0.408248i
$49$		−	5.00000i		−	0.714286i
$50$		0			0
$51$	4.82843	+	2.00000i	0.676115	+	0.280056i
$52$	1.41421	−	3.41421i	0.196116	−	0.473466i
$53$	7.53553	−	3.12132i	1.03509	−	0.428746i	0.200540	−	0.979686i	$-0.435730\pi$
$53$	7.53553	−	3.12132i	1.03509	−	0.428746i	0.834545	+	0.550939i	$0.185730\pi$
$54$	−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
$58$	1.58579	−	3.82843i	0.208224	−	0.502697i
$59$	6.12132	−	2.53553i	0.796928	−	0.330098i	0.0532027	−	0.998584i	$-0.483057\pi$
$59$	6.12132	−	2.53553i	0.796928	−	0.330098i	0.743725	+	0.668485i	$0.233057\pi$
$60$		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	$0.109397\pi$
$62$	5.65685			0.718421
$63$			0.585786i			0.0738022i
$64$	8.00000			1.00000
$65$		0			0
$66$			0.828427i			0.101972i
$67$	3.70711	+	1.53553i	0.452895	+	0.187595i	0.597458	−	0.801900i	$-0.296178\pi$
$67$	3.70711	+	1.53553i	0.452895	+	0.187595i	−0.144563	+	0.989496i	$0.546178\pi$
$68$	−5.65685			−0.685994
$69$	−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	$-0.553317\pi$
$73$	7.00000	−	7.00000i	0.819288	−	0.819288i	0.986005	+	0.166717i	$0.0533166\pi$
$74$	−1.00000	−	2.41421i	−0.116248	−	0.280647i
$75$		0			0
$76$	11.0711	+	4.58579i	1.26994	+	0.526026i
$77$	−0.171573	+	0.414214i	−0.0195525	+	0.0472040i
$78$	3.41421	−	3.41421i	0.386584	−	0.386584i
$79$		−	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
$81$		−	10.0711i		−	1.11901i
$82$	8.24264	+	8.24264i	0.910247	+	0.910247i
$83$	2.53553	−	6.12132i	0.278311	−	0.671902i	−0.721478	−	0.692437i	$-0.756537\pi$
$83$	2.53553	−	6.12132i	0.278311	−	0.671902i	0.999789	+	0.0205350i	$0.00653696\pi$
$84$	−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
$88$	−0.343146	−	0.828427i	−0.0365795	−	0.0883106i
$89$	2.65685	−	2.65685i	0.281626	−	0.281626i	−0.552131	−	0.833757i	$-0.686185\pi$
$89$	2.65685	−	2.65685i	0.281626	−	0.281626i	0.833757	+	0.552131i	$0.186185\pi$
$90$		0			0
$91$	2.41421	−	1.00000i	0.253078	−	0.104828i
$92$	0.343146	−	0.343146i	0.0357754	−	0.0357754i
$93$	6.82843	+	2.82843i	0.708075	+	0.293294i
$94$	−16.4853			−1.70033
$95$		0			0
$96$	9.65685	+	4.00000i	0.985599	+	0.408248i
$97$		−	1.51472i		−	0.153796i	−0.997039	−	0.0768982i	$-0.975498\pi$
$97$		−	1.51472i		−	0.153796i	0.997039	−	0.0768982i	$-0.0245016\pi$
$98$			7.07107i			0.714286i
$99$	−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	$0.165381\pi$
$102$	−6.82843	−	2.82843i	−0.676115	−	0.280056i
$103$	7.48528	+	7.48528i	0.737547	+	0.737547i	0.972103	−	0.234556i	$-0.0753636\pi$
$103$	7.48528	+	7.48528i	0.737547	+	0.737547i	−0.234556	+	0.972103i	$0.575364\pi$
$104$	−2.00000	+	4.82843i	−0.196116	+	0.473466i
$105$		0			0
$106$	−10.6569	+	4.41421i	−1.03509	+	0.428746i
$107$	−0.292893	+	0.121320i	−0.0283151	+	0.0117285i	−0.396796	−	0.917907i	$-0.629878\pi$
$107$	−0.292893	+	0.121320i	−0.0283151	+	0.0117285i	0.368481	+	0.929635i	$0.379878\pi$
$108$	3.65685	+	8.82843i	0.351881	+	0.849516i
$109$	4.29289	+	1.77817i	0.411185	+	0.170318i	0.578680	−	0.815555i	$-0.303568\pi$
$109$	4.29289	+	1.77817i	0.411185	+	0.170318i	−0.167496	+	0.985873i	$0.553568\pi$
$110$		0			0
$111$		−	3.41421i		−	0.324063i
$112$	4.00000	+	4.00000i	0.377964	+	0.377964i
$113$	−17.6569			−1.66102			−0.830509	−	0.557006i	$-0.811950\pi$
$113$	−17.6569			−1.66102			−0.830509	+	0.557006i	$0.811950\pi$
$114$	11.0711	+	11.0711i	1.03690	+	1.03690i
$115$		0			0
$116$	−2.24264	+	5.41421i	−0.208224	+	0.502697i
$117$	0.707107	−	0.292893i	0.0653720	−	0.0270780i
$118$	−8.65685	+	3.58579i	−0.796928	+	0.330098i
$119$	−2.82843	−	2.82843i	−0.259281	−	0.259281i
$120$		0			0
$121$	7.70711	−	7.70711i	0.700646	−	0.700646i
$122$	−0.414214	+	1.00000i	−0.0375011	+	0.0905357i
$123$	5.82843	+	14.0711i	0.525532	+	1.26875i
$124$	−8.00000			−0.718421
$125$		0			0
$126$		−	0.828427i		−	0.0738022i
$127$		−	20.9706i		−	1.86084i	−0.366499	−	0.930418i	$-0.619444\pi$
$127$		−	20.9706i		−	1.86084i	0.366499	−	0.930418i	$-0.380556\pi$
$128$	−11.3137			−1.00000
$129$	−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	$0.988756\pi$
$132$		−	1.17157i		−	0.101972i
$133$	3.24264	+	7.82843i	0.281173	+	0.678811i
$134$	−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	−0.811434	−	0.584444i	$-0.801313\pi$
$137$	−2.65685	+	2.65685i	−0.226990	+	0.226990i	0.584444	+	0.811434i	$0.301313\pi$
$138$	0.585786	−	0.242641i	0.0498655	−	0.0206549i
$139$	5.19239	+	12.5355i	0.440413	+	1.06325i	0.975804	+	0.218646i	$0.0701640\pi$
$139$	5.19239	+	12.5355i	0.440413	+	1.06325i	−0.535392	+	0.844604i	$0.679836\pi$
$140$		0			0
$141$	−19.8995	−	8.24264i	−1.67584	−	0.694156i
$142$	0.242641	−	0.242641i	0.0203620	−	0.0203620i
$143$	0.585786			0.0489859
$144$	1.17157	+	1.17157i	0.0976311	+	0.0976311i
$145$		0			0
$146$	−9.89949	+	9.89949i	−0.819288	+	0.819288i
$147$	−3.53553	+	8.53553i	−0.291606	+	0.703999i
$148$	1.41421	+	3.41421i	0.116248	+	0.280647i
$149$	−5.60660	−	13.5355i	−0.459311	−	1.10887i	−0.968677	−	0.248324i	$-0.920120\pi$
$149$	−5.60660	−	13.5355i	−0.459311	−	1.10887i	0.509366	−	0.860550i	$-0.329880\pi$
$150$		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	$0.399950\pi$
$152$	−15.6569	−	6.48528i	−1.26994	−	0.526026i
$153$	−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
$157$	0.707107	+	0.292893i	0.0564333	+	0.0233754i	0.410722	−	0.911761i	$-0.365277\pi$
$157$	0.707107	+	0.292893i	0.0564333	+	0.0233754i	−0.354288	+	0.935136i	$0.615277\pi$
$158$			8.48528i			0.675053i
$159$	−15.0711			−1.19521
$160$		0			0
$161$	0.343146			0.0270437
$162$			14.2426i			1.11901i
$163$	−18.1924	−	7.53553i	−1.42494	−	0.590229i	−0.468842	−	0.883282i	$-0.655329\pi$
$163$	−18.1924	−	7.53553i	−1.42494	−	0.590229i	−0.956096	+	0.293054i	$0.905329\pi$
$164$	−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	$-0.191442\pi$
$167$	3.34315	+	3.34315i	0.258700	+	0.258700i	−0.565825	+	0.824525i	$0.691442\pi$
$168$	2.82843	+	6.82843i	0.218218	+	0.526825i
$169$	6.77817	+	6.77817i	0.521398	+	0.521398i
$170$		0			0
$171$	0.949747	+	2.29289i	0.0726290	+	0.175342i
$172$	15.8995	−	6.58579i	1.21233	−	0.502162i
$173$	−0.464466	+	1.12132i	−0.0353127	+	0.0852524i	−0.940552	−	0.339650i	$-0.889691\pi$
$173$	−0.464466	+	1.12132i	−0.0353127	+	0.0852524i	0.905239	+	0.424902i	$0.139691\pi$
$174$	−5.41421	+	5.41421i	−0.410450	+	0.410450i
$175$		0			0
$176$	0.485281	+	1.17157i	0.0365795	+	0.0883106i
$177$	−12.2426			−0.920213
$178$	−3.75736	+	3.75736i	−0.281626	+	0.281626i
$179$	14.3640	+	5.94975i	1.07361	+	0.444705i	0.848264	−	0.529573i	$-0.177648\pi$
$179$	14.3640	+	5.94975i	1.07361	+	0.444705i	0.225349	+	0.974278i	$0.427648\pi$
$180$		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	$0.943296\pi$
$182$	−3.41421	+	1.41421i	−0.253078	+	0.104828i
$183$	−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
$187$	−0.343146	−	0.828427i	−0.0250933	−	0.0605806i
$188$	23.3137			1.70033
$189$	−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	$0.642949\pi$
$192$	−13.6569	−	5.65685i	−0.985599	−	0.408248i
$193$			18.4853i			1.33060i	0.746576	+	0.665300i	$0.231696\pi$
$193$			18.4853i			1.33060i	−0.746576	+	0.665300i	$0.768304\pi$
$194$			2.14214i			0.153796i
$195$		0			0
$196$		−	10.0000i		−	0.714286i
$197$	7.19239	+	17.3640i	0.512436	+	1.23713i	0.942462	+	0.334314i	$0.108505\pi$
$197$	7.19239	+	17.3640i	0.512436	+	1.23713i	−0.430025	+	0.902817i	$0.641495\pi$
$198$	0.0710678	−	0.171573i	0.00505057	−	0.0121932i
$199$	−17.9706	+	17.9706i	−1.27390	+	1.27390i	−0.329875	+	0.944025i	$0.607006\pi$
$199$	−17.9706	+	17.9706i	−1.27390	+	1.27390i	−0.944025	+	0.329875i	$0.892994\pi$
$200$		0			0
$201$	−5.24264	−	5.24264i	−0.369787	−	0.369787i
$202$	−16.0711	+	6.65685i	−1.13076	+	0.468375i
$203$	−3.82843	+	1.58579i	−0.268703	+	0.111300i
$204$	9.65685	+	4.00000i	0.676115	+	0.280056i
$205$		0			0
$206$	−10.5858	−	10.5858i	−0.737547	−	0.737547i
$207$	0.100505			0.00698558
$208$	2.82843	−	6.82843i	0.196116	−	0.473466i
$209$			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	$0.619491\pi$
$212$	15.0711	−	6.24264i	1.03509	−	0.428746i
$213$	0.414214	−	0.171573i	0.0283814	−	0.0117560i
$214$	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
$218$	−6.07107	−	2.51472i	−0.411185	−	0.170318i
$219$	−16.8995	+	7.00000i	−1.14196	+	0.473016i
$220$		0			0
$221$	−2.00000	+	4.82843i	−0.134535	+	0.324795i
$222$			4.82843i			0.324063i
$223$		−	12.9706i		−	0.868573i	−0.900775	−	0.434287i	$-0.857001\pi$
$223$		−	12.9706i		−	0.868573i	0.900775	−	0.434287i	$-0.142999\pi$
$224$	−5.65685	−	5.65685i	−0.377964	−	0.377964i
$225$		0			0
$226$	24.9706			1.66102
$227$	−6.29289	−	2.60660i	−0.417674	−	0.173006i	0.163942	−	0.986470i	$-0.447579\pi$
$227$	−6.29289	−	2.60660i	−0.417674	−	0.173006i	−0.581616	+	0.813464i	$0.697579\pi$
$228$	−15.6569	−	15.6569i	−1.03690	−	1.03690i
$229$	24.7782	−	10.2635i	1.63739	−	0.678228i	0.641357	−	0.767242i	$-0.278372\pi$
$229$	24.7782	−	10.2635i	1.63739	−	0.678228i	0.996030	+	0.0890139i	$0.0283716\pi$
$230$		0			0
$231$	0.585786	−	0.585786i	0.0385419	−	0.0385419i
$232$	3.17157	−	7.65685i	0.208224	−	0.502697i
$233$	8.65685	−	8.65685i	0.567129	−	0.567129i	−0.364194	−	0.931323i	$-0.618655\pi$
$233$	8.65685	−	8.65685i	0.567129	−	0.567129i	0.931323	+	0.364194i	$0.118655\pi$
$234$	−1.00000	+	0.414214i	−0.0653720	+	0.0270780i
$235$		0			0
$236$	12.2426	−	5.07107i	0.796928	−	0.330098i
$237$	−4.24264	+	10.2426i	−0.275589	+	0.665331i
$238$	4.00000	+	4.00000i	0.259281	+	0.259281i
$239$		−	17.3137i		−	1.11993i	−0.828516	−	0.559965i	$-0.810814\pi$
$239$		−	17.3137i		−	1.11993i	0.828516	−	0.559965i	$-0.189186\pi$
$240$		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
$243$	−1.63604	+	3.94975i	−0.104952	+	0.253376i
$244$	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
$248$	11.3137			0.718421
$249$	−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	$0.541285\pi$
$252$			1.17157i			0.0738022i
$253$	0.0710678	+	0.0294373i	0.00446800	+	0.00185070i
$254$			29.6569i			1.86084i
$255$		0			0
$256$	16.0000			1.00000
$257$			6.00000i			0.374270i	0.982334	+	0.187135i	$0.0599201\pi$
$257$			6.00000i			0.374270i	−0.982334	+	0.187135i	$0.940080\pi$
$258$	22.4853			1.39987
$259$	−1.00000	+	2.41421i	−0.0621370	+	0.150012i
$260$		0			0
$261$	−1.12132	+	0.464466i	−0.0694080	+	0.0287497i
$262$	5.14214	−	12.4142i	0.317682	−	0.766953i
$263$	0.171573	+	0.171573i	0.0105796	+	0.0105796i	0.712377	−	0.701797i	$-0.247619\pi$
$263$	0.171573	+	0.171573i	0.0105796	+	0.0105796i	−0.701797	+	0.712377i	$0.747619\pi$
$264$			1.65685i			0.101972i
$265$		0			0
$266$	−4.58579	−	11.0711i	−0.281173	−	0.678811i
$267$	−6.41421	+	2.65685i	−0.392543	+	0.162597i
$268$	7.41421	+	3.07107i	0.452895	+	0.187595i
$269$	−4.87868	−	2.02082i	−0.297458	−	0.123211i	0.228963	−	0.973435i	$-0.426467\pi$
$269$	−4.87868	−	2.02082i	−0.297458	−	0.123211i	−0.526421	+	0.850224i	$0.676467\pi$
$270$		0			0
$271$			18.0000i			1.09342i	0.837321	+	0.546711i	$0.184120\pi$
$271$			18.0000i			1.09342i	−0.837321	+	0.546711i	$0.815880\pi$
$272$	−11.3137			−0.685994
$273$	−4.82843			−0.292230
$274$	3.75736	−	3.75736i	0.226990	−	0.226990i
$275$		0			0
$276$	−0.828427	+	0.343146i	−0.0498655	+	0.0206549i
$277$	−0.707107	+	0.292893i	−0.0424859	+	0.0175982i	−0.403825	−	0.914836i	$-0.632320\pi$
$277$	−0.707107	+	0.292893i	−0.0424859	+	0.0175982i	0.361339	+	0.932434i	$0.382320\pi$
$278$	−7.34315	−	17.7279i	−0.440413	−	1.06325i
$279$	−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	$0.333832\pi$
$282$	28.1421	+	11.6569i	1.67584	+	0.694156i
$283$	4.05025	+	9.77817i	0.240763	+	0.581252i	0.997359	−	0.0726300i	$-0.0231392\pi$
$283$	4.05025	+	9.77817i	0.240763	+	0.581252i	−0.756596	+	0.653882i	$0.773139\pi$
$284$	−0.343146	+	0.343146i	−0.0203620	+	0.0203620i
$285$		0			0
$286$	−0.828427			−0.0489859
$287$		−	11.6569i		−	0.688082i
$288$	−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
$293$	4.80761	+	11.6066i	0.280864	+	0.678065i	0.999856	−	0.0169528i	$-0.00539650\pi$
$293$	4.80761	+	11.6066i	0.280864	+	0.678065i	−0.718993	+	0.695018i	$0.755397\pi$
$294$	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
$298$	7.92893	+	19.1421i	0.459311	+	1.10887i
$299$	−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
$303$	−22.7279			−1.30569
$304$	22.1421	+	9.17157i	1.26994	+	0.526026i
$305$		0			0
$306$	1.17157	+	1.17157i	0.0669744	+	0.0669744i
$307$	−1.22183	+	2.94975i	−0.0697333	+	0.168351i	−0.954904	−	0.296916i	$-0.904042\pi$
$307$	−1.22183	+	2.94975i	−0.0697333	+	0.168351i	0.885170	+	0.465267i	$0.154042\pi$
$308$	−0.343146	+	0.828427i	−0.0195525	+	0.0472040i
$309$	−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	0.386253	−	0.922393i	$-0.373769\pi$
$313$	−9.48528	−	9.48528i	−0.536140	−	0.536140i	−0.922393	+	0.386253i	$0.873769\pi$
$314$	−1.00000	−	0.414214i	−0.0564333	−	0.0233754i
$315$		0			0
$316$		−	12.0000i		−	0.675053i
$317$	11.1924	+	4.63604i	0.628627	+	0.260386i	0.674170	−	0.738577i	$-0.264502\pi$
$317$	11.1924	+	4.63604i	0.628627	+	0.260386i	−0.0455425	+	0.998962i	$0.514502\pi$
$318$	21.3137			1.19521
$319$	−0.928932			−0.0520102
$320$		0			0
$321$	0.585786			0.0326954
$322$	−0.485281			−0.0270437
$323$	−15.6569	−	6.48528i	−0.871171	−	0.360851i
$324$		−	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	$0.937280\pi$
$332$	5.07107	−	12.2426i	0.278311	−	0.671902i
$333$	−0.292893	+	0.707107i	−0.0160504	+	0.0387492i
$334$	−4.72792	−	4.72792i	−0.258700	−	0.258700i
$335$		0			0
$336$	−4.00000	−	9.65685i	−0.218218	−	0.526825i
$337$	−16.9706			−0.924445			−0.462223	−	0.886764i	$-0.652948\pi$
$337$	−16.9706			−0.924445			−0.462223	+	0.886764i	$0.652948\pi$
$338$	−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
$342$	−1.34315	−	3.24264i	−0.0726290	−	0.175342i
$343$	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
$347$	5.94975	+	14.3640i	0.319399	+	0.771098i	0.999286	+	0.0377808i	$0.0120289\pi$
$347$	5.94975	+	14.3640i	0.319399	+	0.771098i	−0.679887	+	0.733317i	$0.737971\pi$
$348$	7.65685	−	7.65685i	0.410450	−	0.410450i
$349$	10.6777	−	25.7782i	0.571563	−	1.37987i	−0.328662	−	0.944448i	$-0.606598\pi$
$349$	10.6777	−	25.7782i	0.571563	−	1.37987i	0.900224	−	0.435426i	$-0.143402\pi$
$350$		0			0
$351$	8.82843			0.471227
$352$	−0.686292	−	1.65685i	−0.0365795	−	0.0883106i
$353$		−	6.00000i		−	0.319348i	−0.987170	−	0.159674i	$-0.948956\pi$
$353$		−	6.00000i		−	0.319348i	0.987170	−	0.159674i	$-0.0510443\pi$
$354$	17.3137			0.920213
$355$		0			0
$356$	5.31371	−	5.31371i	0.281626	−	0.281626i
$357$	2.82843	+	6.82843i	0.149696	+	0.361399i
$358$	−20.3137	−	8.41421i	−1.07361	−	0.444705i
$359$	12.1716	−	12.1716i	0.642391	−	0.642391i	−0.308752	−	0.951143i	$-0.599911\pi$
$359$	12.1716	−	12.1716i	0.642391	−	0.642391i	0.951143	+	0.308752i	$0.0999112\pi$
$360$		0			0
$361$	11.9497	+	11.9497i	0.628934	+	0.628934i
$362$	3.10051	+	7.48528i	0.162959	+	0.393418i
$363$	−18.6066	+	7.70711i	−0.976593	+	0.404518i
$364$	4.82843	−	2.00000i	0.253078	−	0.104828i
$365$		0			0
$366$	1.41421	−	1.41421i	0.0739221	−	0.0739221i
$367$	6.00000			0.313197			0.156599	−	0.987662i	$-0.449947\pi$
$367$	6.00000			0.313197			0.156599	+	0.987662i	$0.449947\pi$
$368$	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
$372$	13.6569	+	5.65685i	0.708075	+	0.293294i
$373$	−28.2635	+	11.7071i	−1.46343	+	0.606171i	−0.965349	−	0.260962i	$-0.915960\pi$
$373$	−28.2635	+	11.7071i	−1.46343	+	0.606171i	−0.498077	+	0.867133i	$0.665960\pi$
$374$	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
$378$	3.65685	−	8.82843i	0.188088	−	0.454085i
$379$	−21.6777	+	8.97918i	−1.11351	+	0.461230i	−0.862144	−	0.506663i	$-0.830879\pi$
$379$	−21.6777	+	8.97918i	−1.11351	+	0.461230i	−0.251363	+	0.967893i	$0.580879\pi$
$380$		0			0
$381$	−14.8284	+	35.7990i	−0.759683	+	1.83404i
$382$	16.9706			0.868290
$383$		−	16.9706i		−	0.867155i	−0.901116	−	0.433578i	$-0.857251\pi$
$383$		−	16.9706i		−	0.867155i	0.901116	−	0.433578i	$-0.142749\pi$
$384$	19.3137	+	8.00000i	0.985599	+	0.408248i
$385$		0			0
$386$		−	26.1421i		−	1.33060i
$387$	3.29289	+	1.36396i	0.167387	+	0.0693340i
$388$		−	3.02944i		−	0.153796i
$389$	29.6066	−	12.2635i	1.50111	−	0.621782i	0.527413	−	0.849609i	$-0.323162\pi$
$389$	29.6066	−	12.2635i	1.50111	−	0.621782i	0.973702	+	0.227827i	$0.0731622\pi$
$390$		0			0
$391$	−0.485281	+	0.485281i	−0.0245417	+	0.0245417i
$392$			14.1421i			0.714286i
$393$	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
$397$	10.2635	−	24.7782i	0.515108	−	1.24358i	−0.425769	−	0.904832i	$-0.639996\pi$
$397$	10.2635	−	24.7782i	0.515108	−	1.24358i	0.940877	−	0.338749i	$-0.110004\pi$
$398$	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
$403$	−2.82843	+	6.82843i	−0.140894	+	0.340148i
$404$	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
$408$	−13.6569	−	5.65685i	−0.676115	−	0.280056i
$409$	−4.51472	+	4.51472i	−0.223238	+	0.223238i	−0.809861	−	0.586622i	$-0.800457\pi$
$409$	−4.51472	+	4.51472i	−0.223238	+	0.223238i	0.586622	+	0.809861i	$0.300457\pi$
$410$		0			0
$411$	6.41421	−	2.65685i	0.316390	−	0.131053i
$412$	14.9706	+	14.9706i	0.737547	+	0.737547i
$413$	8.65685	+	3.58579i	0.425976	+	0.176445i
$414$	−0.142136			−0.00698558
$415$		0			0
$416$	−4.00000	+	9.65685i	−0.196116	+	0.473466i
$417$		−	25.0711i		−	1.22774i
$418$		−	2.68629i		−	0.131391i
$419$	8.60660	−	20.7782i	0.420460	−	1.01508i	−0.561752	−	0.827306i	$-0.689873\pi$
$419$	8.60660	−	20.7782i	0.420460	−	1.01508i	0.982212	−	0.187775i	$-0.0601275\pi$
$420$		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	$0.309838\pi$
$422$	−0.656854	−	0.272078i	−0.0319752	−	0.0132445i
$423$	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
$427$	1.00000	−	0.414214i	0.0483934	−	0.0200452i
$428$	−0.585786	+	0.242641i	−0.0283151	+	0.0117285i
$429$	−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	$-0.192962\pi$
$432$	7.31371	+	17.6569i	0.351881	+	0.849516i
$433$	−32.4853			−1.56114			−0.780571	−	0.625067i	$-0.785072\pi$
$433$	−32.4853			−1.56114			−0.780571	+	0.625067i	$0.785072\pi$
$434$	5.65685	+	5.65685i	0.271538	+	0.271538i
$435$		0			0
$436$	8.58579	+	3.55635i	0.411185	+	0.170318i
$437$	1.34315	−	0.556349i	0.0642514	−	0.0266138i
$438$	23.8995	−	9.89949i	1.14196	−	0.473016i
$439$	17.0000	+	17.0000i	0.811366	+	0.811366i	0.984839	−	0.173473i	$-0.0554989\pi$
$439$	17.0000	+	17.0000i	0.811366	+	0.811366i	−0.173473	+	0.984839i	$0.555499\pi$
$440$		0			0
$441$	1.46447	−	1.46447i	0.0697365	−	0.0697365i
$442$	2.82843	−	6.82843i	0.134535	−	0.324795i
$443$	8.53553	+	20.6066i	0.405535	+	0.979049i	0.986298	+	0.164976i	$0.0527546\pi$
$443$	8.53553	+	20.6066i	0.405535	+	0.979049i	−0.580762	+	0.814073i	$0.697245\pi$
$444$		−	6.82843i		−	0.324063i
$445$		0			0
$446$			18.3431i			0.868573i
$447$			27.0711i			1.28042i
$448$	8.00000	+	8.00000i	0.377964	+	0.377964i
$449$	−31.4558			−1.48449			−0.742247	−	0.670127i	$-0.766240\pi$
$449$	−31.4558			−1.48449			−0.742247	+	0.670127i	$0.766240\pi$
$450$		0			0
$451$	1.00000	−	2.41421i	0.0470882	−	0.113681i
$452$	−35.3137			−1.66102
$453$	−15.4853	−	37.3848i	−0.727562	−	1.75649i
$454$	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	−0.893254	−	0.449552i	$-0.851584\pi$
$457$	−9.48528	+	9.48528i	−0.443703	+	0.443703i	0.449552	+	0.893254i	$0.351584\pi$
$458$	−35.0416	+	14.5147i	−1.63739	+	0.678228i
$459$	−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
$463$	−10.9706			−0.509845			−0.254923	−	0.966961i	$-0.582050\pi$
$463$	−10.9706			−0.509845			−0.254923	+	0.966961i	$0.582050\pi$
$464$	−4.48528	+	10.8284i	−0.208224	+	0.502697i
$465$		0			0
$466$	−12.2426	+	12.2426i	−0.567129	+	0.567129i
$467$	−12.0503	+	29.0919i	−0.557619	+	1.34621i	0.354027	+	0.935235i	$0.384812\pi$
$467$	−12.0503	+	29.0919i	−0.557619	+	1.34621i	−0.911646	+	0.410977i	$0.865188\pi$
$468$	1.41421	−	0.585786i	0.0653720	−	0.0270780i
$469$	2.17157	+	5.24264i	0.100274	+	0.242083i
$470$		0			0
$471$	−1.00000	−	1.00000i	−0.0460776	−	0.0460776i
$472$	−17.3137	+	7.17157i	−0.796928	+	0.330098i
$473$	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
$477$	3.12132	+	1.29289i	0.142915	+	0.0591975i
$478$			24.4853i			1.11993i
$479$	4.97056			0.227111			0.113555	−	0.993532i	$-0.463776\pi$
$479$	4.97056			0.227111			0.113555	+	0.993532i	$0.463776\pi$
$480$		0			0
$481$	3.41421			0.155675
$482$		−	12.0000i		−	0.546585i
$483$	−0.585786	−	0.242641i	−0.0266542	−	0.0110405i
$484$	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	$-0.364656\pi$
$487$	−11.0000	−	11.0000i	−0.498458	−	0.498458i	−0.910958	+	0.412500i	$0.864656\pi$
$488$	−0.828427	+	2.00000i	−0.0375011	+	0.0905357i
$489$	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	$-0.267360\pi$
$492$	11.6569	+	28.1421i	0.525532	+	1.26875i
$493$	3.17157	−	7.65685i	0.142840	−	0.344847i
$494$	−11.0711	+	11.0711i	−0.498111	+	0.498111i
$495$		0			0
$496$	−16.0000			−0.718421
$497$	−0.343146			−0.0153922
$498$	12.2426	−	12.2426i	0.548606	−	0.548606i
$499$	−8.94975	−	3.70711i	−0.400646	−	0.165953i	0.173256	−	0.984877i	$-0.444571\pi$
$499$	−8.94975	−	3.70711i	−0.400646	−	0.165953i	−0.573902	+	0.818924i	$0.694571\pi$
$500$		0			0
$501$	−3.34315	−	8.07107i	−0.149361	−	0.360589i
$502$	20.6569	−	8.55635i	0.921961	−	0.381889i
$503$	17.1421	−	17.1421i	0.764330	−	0.764330i	−0.212772	−	0.977102i	$-0.568249\pi$
$503$	17.1421	−	17.1421i	0.764330	−	0.764330i	0.977102	+	0.212772i	$0.0682491\pi$
$504$		−	1.65685i		−	0.0738022i
$505$		0			0
$506$	−0.100505	−	0.0416306i	−0.00446800	−	0.00185070i
$507$	−6.77817	−	16.3640i	−0.301029	−	0.726749i
$508$		−	41.9411i		−	1.86084i
$509$	−12.0919	+	29.1924i	−0.535963	+	1.29393i	0.391556	+	0.920154i	$0.371937\pi$
$509$	−12.0919	+	29.1924i	−0.535963	+	1.29393i	−0.927519	+	0.373776i	$0.878063\pi$
$510$		0			0
$511$	14.0000			0.619324
$512$	−22.6274			−1.00000
$513$			28.6274i			1.26393i
$514$		−	8.48528i		−	0.374270i
$515$		0			0
$516$	−31.7990			−1.39987
$517$	1.41421	+	3.41421i	0.0621970	+	0.150157i
$518$	1.41421	−	3.41421i	0.0621370	−	0.150012i
$519$	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	$0.599978\pi$
$522$	1.58579	−	0.656854i	0.0694080	−	0.0287497i
$523$	1.94975	−	0.807612i	0.0852565	−	0.0353144i	−0.339648	−	0.940553i	$-0.610308\pi$
$523$	1.94975	−	0.807612i	0.0852565	−	0.0353144i	0.424904	+	0.905238i	$0.360308\pi$
$524$	−7.27208	+	17.5563i	−0.317682	+	0.766953i
$525$		0			0
$526$	−0.242641	−	0.242641i	−0.0105796	−	0.0105796i
$527$	11.3137			0.492833
$528$		−	2.34315i		−	0.101972i
$529$			22.9411i			0.997440i
$530$		0			0
$531$	2.53553	+	1.05025i	0.110033	+	0.0455771i
$532$	6.48528	+	15.6569i	0.281173	+	0.678811i
$533$	−14.0711	+	5.82843i	−0.609486	+	0.252457i
$534$	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
$538$	6.89949	+	2.85786i	0.297458	+	0.123211i
$539$	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	$0.0294582\pi$
$542$		−	25.4558i		−	1.09342i
$543$			10.5858i			0.454280i
$544$	16.0000			0.685994
$545$		0			0
$546$	6.82843			0.292230
$547$	−25.2635	−	10.4645i	−1.08019	−	0.447428i	−0.229612	−	0.973282i	$-0.573746\pi$
$547$	−25.2635	−	10.4645i	−1.08019	−	0.447428i	−0.850575	+	0.525854i	$0.823746\pi$
$548$	−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
$552$	1.17157	−	0.485281i	0.0498655	−	0.0206549i
$553$	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
$557$	−4.50610	+	10.8787i	−0.190929	+	0.460944i	−0.990136	−	0.140113i	$-0.955254\pi$
$557$	−4.50610	+	10.8787i	−0.190929	+	0.460944i	0.799206	+	0.601057i	$0.205254\pi$
$558$	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
$563$	5.02082	−	12.1213i	0.211602	−	0.510853i	−0.782068	−	0.623194i	$-0.785835\pi$
$563$	5.02082	−	12.1213i	0.211602	−	0.510853i	0.993670	+	0.112341i	$0.0358349\pi$
$564$	−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	−0.773702	−	0.633550i	$-0.781597\pi$
$569$	−3.34315	+	3.34315i	−0.140152	+	0.140152i	0.633550	+	0.773702i	$0.281597\pi$
$570$		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	$0.384322\pi$
$572$	1.17157			0.0489859
$573$	20.4853	+	8.48528i	0.855785	+	0.354478i
$574$			16.4853i			0.688082i
$575$		0			0
$576$	2.34315	+	2.34315i	0.0976311	+	0.0976311i
$577$		−	14.9706i		−	0.623233i	−0.950208	−	0.311616i	$-0.899130\pi$
$577$		−	14.9706i		−	0.623233i	0.950208	−	0.311616i	$-0.100870\pi$
$578$	12.7279			0.529412
$579$	13.0711	−	31.5563i	0.543215	−	1.31144i
$580$		0			0
$581$	8.65685	−	3.58579i	0.359147	−	0.148763i
$582$	1.51472	−	3.65685i	0.0627871	−	0.151581i
$583$	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
$587$	−20.7782	+	8.60660i	−0.857607	+	0.355232i	−0.767771	−	0.640724i	$-0.778634\pi$
$587$	−20.7782	+	8.60660i	−0.857607	+	0.355232i	−0.0898359	+	0.995957i	$0.528634\pi$
$588$	−7.07107	+	17.0711i	−0.291606	+	0.703999i
$589$	−22.1421	−	9.17157i	−0.912351	−	0.377908i
$590$		0			0
$591$		−	34.7279i		−	1.42852i
$592$	2.82843	+	6.82843i	0.116248	+	0.280647i
$593$	28.2843			1.16150			0.580748	−	0.814083i	$-0.302760\pi$
$593$	28.2843			1.16150			0.580748	+	0.814083i	$0.302760\pi$
$594$	1.51472	−	1.51472i	0.0621497	−	0.0621497i
$595$		0			0
$596$	−11.2132	−	27.0711i	−0.459311	−	1.10887i
$597$	43.3848	−	17.9706i	1.77562	−	0.735486i
$598$	0.242641	+	0.585786i	0.00992232	+	0.0239546i
$599$	15.3431	+	15.3431i	0.626904	+	0.626904i	0.947288	−	0.320384i	$-0.103812\pi$
$599$	15.3431	+	15.3431i	0.626904	+	0.626904i	−0.320384	+	0.947288i	$0.603812\pi$
$600$		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	$0.137786\pi$
$602$	−15.8995	−	6.58579i	−0.648015	−	0.268417i
$603$	0.636039	+	1.53553i	0.0259015	+	0.0625318i
$604$	30.9706	+	30.9706i	1.26017	+	1.26017i
$605$		0			0
$606$	32.1421			1.30569
$607$			0.970563i			0.0393939i	0.999806	+	0.0196970i	$0.00627014\pi$
$607$			0.970563i			0.0393939i	−0.999806	+	0.0196970i	$0.993730\pi$
$608$	−31.3137	−	12.9706i	−1.26994	−	0.526026i
$609$	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
$613$	−15.1924	−	36.6777i	−0.613615	−	1.48140i	−0.859002	−	0.511972i	$-0.828915\pi$
$613$	−15.1924	−	36.6777i	−0.613615	−	1.48140i	0.245387	−	0.969425i	$-0.421085\pi$
$614$	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	−0.282859	−	0.959161i	$-0.591283\pi$
$617$	16.7990	−	16.7990i	0.676302	−	0.676302i	0.959161	+	0.282859i	$0.0912830\pi$
$618$	10.5858	+	25.5563i	0.425823	+	1.02803i
$619$	6.22183	+	15.0208i	0.250076	+	0.603738i	0.998210	−	0.0598107i	$-0.0190497\pi$
$619$	6.22183	+	15.0208i	0.250076	+	0.603738i	−0.748133	+	0.663548i	$0.769050\pi$
$620$		0			0
$621$	1.07107	+	0.443651i	0.0429805	+	0.0178031i
$622$	−12.2426	−	12.2426i	−0.490885	−	0.490885i
$623$	5.31371			0.212889
$624$	−9.65685	+	9.65685i	−0.386584	+	0.386584i
$625$		0			0
$626$	13.4142	+	13.4142i	0.536140	+	0.536140i
$627$	1.34315	−	3.24264i	0.0536401	−	0.129499i
$628$	1.41421	+	0.585786i	0.0564333	+	0.0233754i
$629$	−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	$0.923890\pi$
$632$			16.9706i			0.675053i
$633$	−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
$637$	−8.53553	−	3.53553i	−0.338190	−	0.140083i
$638$	1.31371			0.0520102
$639$	−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	$0.828418\pi$
$642$	−0.828427			−0.0326954
$643$	37.2635	+	15.4350i	1.46953	+	0.608698i	0.966751	−	0.255719i	$-0.0823121\pi$
$643$	37.2635	+	15.4350i	1.46953	+	0.608698i	0.502776	+	0.864417i	$0.332312\pi$
$644$	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	$-0.143349\pi$
$647$	11.8284	+	11.8284i	0.465023	+	0.465023i	−0.435274	+	0.900298i	$0.643349\pi$
$648$			28.4853i			1.11901i
$649$	1.48528	+	1.48528i	0.0583024	+	0.0583024i
$650$		0			0
$651$	4.00000	+	9.65685i	0.156772	+	0.378482i
$652$	−36.3848	−	15.0711i	−1.42494	−	0.590229i
$653$	−14.9497	+	36.0919i	−0.585029	+	1.41238i	0.303175	+	0.952935i	$0.401953\pi$
$653$	−14.9497	+	36.0919i	−0.585029	+	1.41238i	−0.888204	+	0.459450i	$0.848047\pi$
$654$	8.58579	+	8.58579i	0.335731	+	0.335731i
$655$		0			0
$656$	−23.3137	−	23.3137i	−0.910247	−	0.910247i
$657$	4.10051			0.159976
$658$	−16.4853	−	16.4853i	−0.642663	−	0.642663i
$659$	5.87868	+	2.43503i	0.229001	+	0.0948553i	0.494234	−	0.869329i	$-0.335449\pi$
$659$	5.87868	+	2.43503i	0.229001	+	0.0948553i	−0.265233	+	0.964184i	$0.585449\pi$
$660$		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	$0.746165\pi$
$662$	3.82843	+	9.24264i	0.148796	+	0.359225i
$663$	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
$667$	0.272078	+	0.656854i	0.0105349	+	0.0254335i
$668$	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
$672$	5.65685	+	13.6569i	0.218218	+	0.526825i
$673$		−	5.51472i		−	0.212577i	−0.994335	−	0.106288i	$-0.966103\pi$
$673$		−	5.51472i		−	0.212577i	0.994335	−	0.106288i	$-0.0338967\pi$
$674$	24.0000			0.924445
$675$		0			0
$676$	13.5563	+	13.5563i	0.521398	+	0.521398i
$677$	−2.32233	−	5.60660i	−0.0892544	−	0.215479i	0.872949	−	0.487812i	$-0.162205\pi$
$677$	−2.32233	−	5.60660i	−0.0892544	−	0.215479i	−0.962203	+	0.272333i	$0.912205\pi$
$678$	−42.6274	−	17.6569i	−1.63710	−	0.678107i
$679$	1.51472	−	1.51472i	0.0581296	−	0.0581296i
$680$		0			0
$681$	8.89949	+	8.89949i	0.341029	+	0.341029i
$682$	0.686292	+	1.65685i	0.0262795	+	0.0634442i
$683$	−14.1924	+	5.87868i	−0.543057	+	0.224941i	−0.637311	−	0.770607i	$-0.719953\pi$
$683$	−14.1924	+	5.87868i	−0.543057	+	0.224941i	0.0942543	+	0.995548i	$0.469953\pi$
$684$	1.89949	+	4.58579i	0.0726290	+	0.175342i
$685$		0			0
$686$	−16.9706	+	16.9706i	−0.647939	+	0.647939i
$687$	−49.5563			−1.89069
$688$	31.7990	−	13.1716i	1.21233	−	0.502162i
$689$		−	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	$0.824646\pi$
$692$	−0.928932	+	2.24264i	−0.0353127	+	0.0852524i
$693$	−0.171573	+	0.0710678i	−0.00651751	+	0.00269964i
$694$	−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
$698$	−15.1005	+	36.4558i	−0.571563	+	1.37987i
$699$	−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	$0.0106974\pi$
$702$	−12.4853			−0.471227
$703$			11.0711i			0.417553i
$704$	0.970563	+	2.34315i	0.0365795	+	0.0883106i
$705$		0			0
$706$			8.48528i			0.319348i
$707$	16.0711	+	6.65685i	0.604415	+	0.250357i
$708$	−24.4853			−0.920213
$709$	6.77817	−	2.80761i	0.254560	−	0.105442i	−0.251755	−	0.967791i	$-0.581008\pi$
$709$	6.77817	−	2.80761i	0.254560	−	0.105442i	0.506314	+	0.862349i	$0.331008\pi$
$710$		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
$717$	−12.2426	+	29.5563i	−0.457210	+	1.10380i
$718$	−17.2132	+	17.2132i	−0.642391	+	0.642391i
$719$		−	24.3431i		−	0.907846i	−0.891041	−	0.453923i	$-0.850024\pi$
$719$		−	24.3431i		−	0.907846i	0.891041	−	0.453923i	$-0.149976\pi$
$720$		0			0
$721$			14.9706i			0.557533i
$722$	−16.8995	−	16.8995i	−0.628934	−	0.628934i
$723$	6.00000	−	14.4853i	0.223142	−	0.538713i
$724$	−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	−0.994429	−	0.105410i	$-0.966385\pi$
$727$	−23.9706	+	23.9706i	−0.889019	+	0.889019i	0.105410	+	0.994429i	$0.466385\pi$
$728$	−6.82843	+	2.82843i	−0.253078	+	0.104828i
$729$	−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
$733$	1.77817	+	0.736544i	0.0656784	+	0.0272049i	0.415281	−	0.909693i	$-0.363683\pi$
$733$	1.77817	+	0.736544i	0.0656784	+	0.0272049i	−0.349602	+	0.936898i	$0.613683\pi$
$734$	−8.48528			−0.313197
$735$		0			0
$736$	−0.970563	+	0.970563i	−0.0357754	+	0.0357754i
$737$			1.27208i			0.0468576i
$738$			4.82843i			0.177737i
$739$	−7.53553	+	18.1924i	−0.277199	+	0.669218i	−0.999756	−	0.0220937i	$-0.992967\pi$
$739$	−7.53553	+	18.1924i	−0.277199	+	0.669218i	0.722557	+	0.691312i	$0.242967\pi$
$740$		0			0
$741$	−18.8995	+	7.82843i	−0.694290	+	0.287584i
$742$	−15.0711	−	6.24264i	−0.553276	−	0.229175i
$743$	13.6274	+	13.6274i	0.499941	+	0.499941i	0.911420	−	0.411478i	$-0.134987\pi$
$743$	13.6274	+	13.6274i	0.499941	+	0.499941i	−0.411478	+	0.911420i	$0.634987\pi$
$744$	−19.3137	−	8.00000i	−0.708075	−	0.293294i
$745$		0			0
$746$	39.9706	−	16.5563i	1.46343	−	0.606171i
$747$	2.53553	−	1.05025i	0.0927703	−	0.0384267i
$748$	−0.686292	−	1.65685i	−0.0250933	−	0.0605806i
$749$	−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	$0.862344\pi$
$752$	46.6274			1.70033
$753$	29.2132			1.06459
$754$	−5.41421	−	5.41421i	−0.197174	−	0.197174i
$755$		0			0
$756$	−5.17157	+	12.4853i	−0.188088	+	0.454085i
$757$	1.77817	−	0.736544i	0.0646289	−	0.0267701i	−0.350135	−	0.936699i	$-0.613864\pi$
$757$	1.77817	−	0.736544i	0.0646289	−	0.0267701i	0.414764	+	0.909929i	$0.363864\pi$
$758$	30.6569	−	12.6985i	1.11351	−	0.461230i
$759$	−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	$0.462697\pi$
$762$	20.9706	−	50.6274i	0.759683	−	1.83404i
$763$	2.51472	+	6.07107i	0.0910389	+	0.219787i
$764$	−24.0000			−0.868290
$765$		0			0
$766$			24.0000i			0.867155i
$767$		−	12.2426i		−	0.442056i
$768$	−27.3137	−	11.3137i	−0.985599	−	0.408248i
$769$	−22.4853			−0.810840			−0.405420	−	0.914131i	$-0.632875\pi$
$769$	−22.4853			−0.810840			−0.405420	+	0.914131i	$0.632875\pi$
$770$		0			0
$771$	4.24264	−	10.2426i	0.152795	−	0.368880i
$772$			36.9706i			1.33060i
$773$	10.8076	+	26.0919i	0.388723	+	0.938460i	0.990211	+	0.139578i	$0.0445747\pi$
$773$	10.8076	+	26.0919i	0.388723	+	0.938460i	−0.601488	+	0.798882i	$0.705425\pi$
$774$	−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
$778$	−41.8701	+	17.3431i	−1.50111	+	0.621782i
$779$	−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
$783$	−14.0000			−0.500319
$784$		−	20.0000i		−	0.714286i
$785$		0			0
$786$	−17.5563	+	17.5563i	−0.626214	+	0.626214i
$787$	−3.70711	+	8.94975i	−0.132144	+	0.319024i	−0.976077	−	0.217424i	$-0.930234\pi$
$787$	−3.70711	+	8.94975i	−0.132144	+	0.319024i	0.843933	+	0.536448i	$0.180234\pi$
$788$	14.3848	+	34.7279i	0.512436	+	1.23713i
$789$	−0.171573	−	0.414214i	−0.00610816	−	0.0147464i
$790$		0			0
$791$	−17.6569	−	17.6569i	−0.627805	−	0.627805i
$792$	0.142136	−	0.343146i	0.00505057	−	0.0121932i
$793$	−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
$797$	29.1924	+	12.0919i	1.03405	+	0.428316i	0.834172	−	0.551505i	$-0.185946\pi$
$797$	29.1924	+	12.0919i	1.03405	+	0.428316i	0.199876	+	0.979821i	$0.435946\pi$
$798$			22.1421i			0.783823i
$799$	−32.9706			−1.16641
$800$		0			0
$801$	1.55635			0.0549909
$802$		−	4.00000i		−	0.141245i
$803$	2.89949	+	1.20101i	0.102321	+	0.0423827i
$804$	−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
$808$	−32.1421	+	13.3137i	−1.13076	+	0.468375i
$809$	0.857864	+	0.857864i	0.0301609	+	0.0301609i	0.722026	−	0.691865i	$-0.243211\pi$
$809$	0.857864	+	0.857864i	0.0301609	+	0.0301609i	−0.691865	+	0.722026i	$0.743211\pi$
$810$		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	$-0.272404\pi$
$812$	−7.65685	+	3.17157i	−0.268703	+	0.111300i
$813$	12.7279	−	30.7279i	0.446388	−	1.07768i
$814$	0.585786	−	0.585786i	0.0205318	−	0.0205318i
$815$		0			0
$816$	19.3137	+	8.00000i	0.676115	+	0.280056i
$817$	51.5563			1.80373
$818$	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	$0.880710\pi$
$822$	−9.07107	+	3.75736i	−0.316390	+	0.131053i
$823$	2.02944	−	2.02944i	0.0707417	−	0.0707417i	−0.670851	−	0.741592i	$-0.734071\pi$
$823$	2.02944	−	2.02944i	0.0707417	−	0.0707417i	0.741592	+	0.670851i	$0.234071\pi$
$824$	−21.1716	−	21.1716i	−0.737547	−	0.737547i
$825$		0			0
$826$	−12.2426	−	5.07107i	−0.425976	−	0.176445i
$827$	4.92031	+	11.8787i	0.171096	+	0.413062i	0.986047	−	0.166468i	$-0.0532362\pi$
$827$	4.92031	+	11.8787i	0.171096	+	0.413062i	−0.814951	+	0.579530i	$0.803236\pi$
$828$	0.201010			0.00698558
$829$	−15.8076	+	38.1630i	−0.549021	+	1.32545i	0.369187	+	0.929355i	$0.379636\pi$
$829$	−15.8076	+	38.1630i	−0.549021	+	1.32545i	−0.918208	+	0.396099i	$0.870364\pi$
$830$		0			0
$831$	1.41421			0.0490585
$832$	5.65685	−	13.6569i	0.196116	−	0.473466i
$833$			14.1421i			0.489996i
$834$			35.4558i			1.22774i
$835$		0			0
$836$			3.79899i			0.131391i
$837$	−7.31371	−	17.6569i	−0.252799	−	0.610310i
$838$	−12.1716	+	29.3848i	−0.420460	+	1.01508i
$839$	−32.3137	+	32.3137i	−1.11559	+	1.11559i	−0.123213	+	0.992380i	$0.539320\pi$
$839$	−32.3137	+	32.3137i	−1.11559	+	1.11559i	−0.992380	+	0.123213i	$0.960680\pi$
$840$		0			0
$841$	14.4350	+	14.4350i	0.497760	+	0.497760i
$842$	−10.8995	+	4.51472i	−0.375621	+	0.155587i
$843$	14.8995	−	6.17157i	0.513166	−	0.212560i
$844$	0.928932	+	0.384776i	0.0319752	+	0.0132445i
$845$		0			0
$846$	−4.82843	−	4.82843i	−0.166005	−	0.166005i
$847$	15.4142			0.529639
$848$	30.1421	−	12.4853i	1.03509	−	0.428746i
$849$		−	19.5563i		−	0.671172i
$850$		0			0
$851$	0.414214	+	0.171573i	0.0141991	+	0.00588144i
$852$	0.828427	−	0.343146i	0.0283814	−	0.0117560i
$853$	−2.80761	+	1.16295i	−0.0961308	+	0.0398187i	−0.430231	−	0.902719i	$-0.641568\pi$
$853$	−2.80761	+	1.16295i	−0.0961308	+	0.0398187i	0.334100	+	0.942538i	$0.391568\pi$
$854$	−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	0.993946	+	0.109869i	$0.0350432\pi$
$857$	32.3137	+	32.3137i	1.10382	+	1.10382i	0.109869	+	0.993946i	$0.464957\pi$
$858$	1.41421	+	0.585786i	0.0482805	+	0.0199984i
$859$	−33.6777	+	13.9497i	−1.14907	+	0.475959i	−0.874221	−	0.485529i	$-0.838627\pi$
$859$	−33.6777	+	13.9497i	−1.14907	+	0.475959i	−0.274847	+	0.961488i	$0.588627\pi$
$860$		0			0
$861$	−8.24264	+	19.8995i	−0.280908	+	0.678173i
$862$			33.4558i			1.13951i
$863$			45.9411i			1.56385i	0.623370	+	0.781927i	$0.285763\pi$
$863$			45.9411i			1.56385i	−0.623370	+	0.781927i	$0.714237\pi$
$864$	−10.3431	−	24.9706i	−0.351881	−	0.849516i
$865$		0			0
$866$	45.9411			1.56114
$867$	15.3640	+	6.36396i	0.521787	+	0.216131i
$868$	−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
$872$	−12.1421	−	5.02944i	−0.411185	−	0.170318i
$873$	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
$877$	13.7782	−	33.2635i	0.465256	−	1.12323i	−0.500955	−	0.865473i	$-0.667018\pi$
$877$	13.7782	−	33.2635i	0.465256	−	1.12323i	0.966211	−	0.257754i	$-0.0829823\pi$
$878$	−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
$883$	19.6482	−	47.4350i	0.661216	−	1.59632i	−0.134685	−	0.990888i	$-0.543002\pi$
$883$	19.6482	−	47.4350i	0.661216	−	1.59632i	0.795901	−	0.605427i	$-0.206998\pi$
$884$	−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	−0.278398	−	0.960466i	$-0.589803\pi$
$887$	20.3137	−	20.3137i	0.682068	−	0.682068i	0.960466	+	0.278398i	$0.0898035\pi$
$888$			9.65685i			0.324063i
$889$	20.9706	−	20.9706i	0.703330	−	0.703330i
$890$		0			0
$891$	2.94975	−	1.22183i	0.0988203	−	0.0409327i
$892$		−	25.9411i		−	0.868573i
$893$	64.5269	+	26.7279i	2.15931	+	0.894416i
$894$		−	38.2843i		−	1.28042i
$895$		0			0
$896$	−11.3137	−	11.3137i	−0.377964	−	0.377964i
$897$			0.828427i			0.0276604i
$898$	44.4853			1.48449
$899$	4.48528	−	10.8284i	0.149593	−	0.361148i
$900$		0			0
$901$	−21.3137	+	8.82843i	−0.710063	+	0.294118i
$902$	−1.41421	+	3.41421i	−0.0470882	+	0.113681i
$903$	−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
$907$	0.535534	−	0.221825i	0.0177821	−	0.00736559i	−0.373775	−	0.927520i	$-0.621937\pi$
$907$	0.535534	−	0.221825i	0.0177821	−	0.00736559i	0.391557	+	0.920154i	$0.371937\pi$
$908$	−12.5858	−	5.21320i	−0.417674	−	0.173006i
$909$	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
$913$	2.10051			0.0695166
$914$	13.4142	−	13.4142i	0.443703	−	0.443703i
$915$		0			0
$916$	49.5563	−	20.5269i	1.63739	−	0.678228i
$917$	−12.4142	+	5.14214i	−0.409953	+	0.169808i
$918$	7.31371	+	17.6569i	0.241388	+	0.582763i
$919$	25.4853	+	25.4853i	0.840682	+	0.840682i	0.988948	−	0.148266i	$-0.0473691\pi$
$919$	25.4853	+	25.4853i	0.840682	+	0.840682i	−0.148266	+	0.988948i	$0.547369\pi$
$920$		0			0
$921$	4.17157	−	4.17157i	0.137458	−	0.137458i
$922$	−18.8995	−	7.82843i	−0.622422	−	0.257816i
$923$	0.171573	+	0.414214i	0.00564739	+	0.0136340i
$924$	1.17157	−	1.17157i	0.0385419	−	0.0385419i
$925$		0			0
$926$	15.5147			0.509845
$927$			4.38478i			0.144015i
$928$	6.34315	−	15.3137i	0.208224	−	0.502697i
$929$	26.4853			0.868954			0.434477	−	0.900683i	$-0.356933\pi$
$929$	26.4853			0.868954			0.434477	+	0.900683i	$0.356933\pi$
$930$		0			0
$931$	11.4645	−	27.6777i	0.375733	−	0.907099i
$932$	17.3137	−	17.3137i	0.567129	−	0.567129i
$933$	−8.65685	−	20.8995i	−0.283413	−	0.684219i
$934$	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	−0.945711	−	0.325008i	$-0.894633\pi$
$937$	−19.0000	+	19.0000i	−0.620703	+	0.620703i	0.325008	+	0.945711i	$0.394633\pi$
$938$	−3.07107	−	7.41421i	−0.100274	−	0.242083i
$939$	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
$943$	−2.00000			−0.0651290
$944$	24.4853	−	10.1421i	0.796928	−	0.330098i
$945$		0			0
$946$	−2.72792	−	2.72792i	−0.0886924	−	0.0886924i
$947$	15.4645	−	37.3345i	0.502528	−	1.21321i	−0.445575	−	0.895245i	$-0.647001\pi$
$947$	15.4645	−	37.3345i	0.502528	−	1.21321i	0.948103	−	0.317964i	$-0.102999\pi$
$948$	−8.48528	+	20.4853i	−0.275589	+	0.665331i
$949$	−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	0.650883	−	0.759178i	$-0.274399\pi$
$953$	−3.34315	−	3.34315i	−0.108295	−	0.108295i	−0.759178	+	0.650883i	$0.774399\pi$
$954$	−4.41421	−	1.82843i	−0.142915	−	0.0591975i
$955$		0			0
$956$		−	34.6274i		−	1.11993i
$957$	1.58579	+	0.656854i	0.0512612	+	0.0212331i
$958$	−7.02944			−0.227111
$959$	−5.31371			−0.171589
$960$		0			0
$961$	−15.0000			−0.483871
$962$	−4.82843			−0.155675
$963$	−0.121320	−	0.0502525i	−0.00390949	−	0.00161937i
$964$			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	−0.937570	−	0.347797i	$-0.886930\pi$
$967$	−39.9706	−	39.9706i	−1.28537	−	1.28537i	−0.347797	−	0.937570i	$-0.613070\pi$
$968$	−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	$0.742607\pi$
$972$	−3.27208	+	7.89949i	−0.104952	+	0.253376i
$973$	−7.34315	+	17.7279i	−0.235410	+	0.568331i
$974$	15.5563	+	15.5563i	0.498458	+	0.498458i
$975$		0			0
$976$	1.17157	−	2.82843i	0.0375011	−	0.0905357i
$977$	14.1421			0.452447			0.226224	−	0.974075i	$-0.427362\pi$
$977$	14.1421			0.452447			0.226224	+	0.974075i	$0.427362\pi$
$978$	−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
$982$	10.3726	+	25.0416i	0.331002	+	0.799111i
$983$	25.6274	−	25.6274i	0.817388	−	0.817388i	−0.168341	−	0.985729i	$-0.553841\pi$
$983$	25.6274	−	25.6274i	0.817388	−	0.817388i	0.985729	+	0.168341i	$0.0538410\pi$
$984$	−16.4853	−	39.7990i	−0.525532	−	1.26875i
$985$		0			0
$986$	−4.48528	+	10.8284i	−0.142840	+	0.344847i
$987$	−11.6569	−	28.1421i	−0.371042	−	0.895774i
$988$	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	$0.581789\pi$
$992$	22.6274			0.718421
$993$			13.0711i			0.414798i
$994$	0.485281			0.0153922
$995$		0			0
$996$	−17.3137	+	17.3137i	−0.548606	+	0.548606i
$997$	−0.748737	−	1.80761i	−0.0237127	−	0.0572476i	0.911580	−	0.411124i	$-0.134864\pi$
$997$	−0.748737	−	1.80761i	−0.0237127	−	0.0572476i	−0.935292	+	0.353876i	$0.884864\pi$
$998$	12.6569	+	5.24264i	0.400646	+	0.165953i
$999$	−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.ba.a.749.1		4
5.2	odd	4		800.2.y.a.301.1		4
5.3	odd	4		32.2.g.a.13.1	yes	4
5.4	even	2		800.2.ba.b.749.1		4
15.8	even	4		288.2.v.a.109.1		4
20.3	even	4		128.2.g.a.17.1		4
32.5	even	8		800.2.ba.b.549.1		4
40.3	even	4		256.2.g.a.33.1		4
40.13	odd	4		256.2.g.b.33.1		4
60.23	odd	4		1152.2.v.a.145.1		4
80.3	even	4		512.2.g.b.321.1		4
80.13	odd	4		512.2.g.d.321.1		4
80.43	even	4		512.2.g.c.321.1		4
80.53	odd	4		512.2.g.a.321.1		4
160.3	even	8		512.2.g.b.193.1		4
160.13	odd	8		512.2.g.a.193.1		4
160.37	odd	8		800.2.y.a.101.1		4
160.43	even	8		256.2.g.a.225.1		4
160.53	odd	8		256.2.g.b.225.1		4
160.69	even	8	inner	800.2.ba.a.549.1		4
160.83	even	8		512.2.g.c.193.1		4
160.93	odd	8		512.2.g.d.193.1		4
160.123	even	8		128.2.g.a.113.1		4
160.133	odd	8		32.2.g.a.5.1	✓	4
320.123	even	16		4096.2.a.f.1.1		4
320.133	odd	16		4096.2.a.e.1.4		4
320.283	even	16		4096.2.a.f.1.4		4
320.293	odd	16		4096.2.a.e.1.1		4
480.293	even	8		288.2.v.a.37.1		4
480.443	odd	8		1152.2.v.a.1009.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.2.g.a.5.1	✓	4	160.133	odd	8
32.2.g.a.13.1	yes	4	5.3	odd	4
128.2.g.a.17.1		4	20.3	even	4
128.2.g.a.113.1		4	160.123	even	8
256.2.g.a.33.1		4	40.3	even	4
256.2.g.a.225.1		4	160.43	even	8
256.2.g.b.33.1		4	40.13	odd	4
256.2.g.b.225.1		4	160.53	odd	8
288.2.v.a.37.1		4	480.293	even	8
288.2.v.a.109.1		4	15.8	even	4
512.2.g.a.193.1		4	160.13	odd	8
512.2.g.a.321.1		4	80.53	odd	4
512.2.g.b.193.1		4	160.3	even	8
512.2.g.b.321.1		4	80.3	even	4
512.2.g.c.193.1		4	160.83	even	8
512.2.g.c.321.1		4	80.43	even	4
512.2.g.d.193.1		4	160.93	odd	8
512.2.g.d.321.1		4	80.13	odd	4
800.2.y.a.101.1		4	160.37	odd	8
800.2.y.a.301.1		4	5.2	odd	4
800.2.ba.a.549.1		4	160.69	even	8	inner
800.2.ba.a.749.1		4	1.1	even	1	trivial
800.2.ba.b.549.1		4	32.5	even	8
800.2.ba.b.749.1		4	5.4	even	2
1152.2.v.a.145.1		4	60.23	odd	4
1152.2.v.a.1009.1		4	480.443	odd	8
4096.2.a.e.1.1		4	320.293	odd	16
4096.2.a.e.1.4		4	320.133	odd	16
4096.2.a.f.1.1		4	320.123	even	16
4096.2.a.f.1.4		4	320.283	even	16

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 800 = 2^{5} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	800.ba (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q-1.41421 q^{2} +(-1.70711 - 0.707107i) q^{3} +2.00000 q^{4} +(2.41421 + 1.00000i) q^{6} +(1.00000 + 1.00000i) q^{7} -2.82843 q^{8} +(0.292893 + 0.292893i) q^{9} +O(q^{10})\)	\(q-1.41421 q^{2} +(-1.70711 - 0.707107i) q^{3} +2.00000 q^{4} +(2.41421 + 1.00000i) q^{6} +(1.00000 + 1.00000i) q^{7} -2.82843 q^{8} +(0.292893 + 0.292893i) q^{9} +(0.121320 + 0.292893i) q^{11} +(-3.41421 - 1.41421i) q^{12} +(0.707107 - 1.70711i) q^{13} +(-1.41421 - 1.41421i) q^{14} +4.00000 q^{16} -2.82843 q^{17} +(-0.414214 - 0.414214i) q^{18} +(5.53553 + 2.29289i) q^{19} +(-1.00000 - 2.41421i) q^{21} +(-0.171573 - 0.414214i) q^{22} +(0.171573 - 0.171573i) q^{23} +(4.82843 + 2.00000i) q^{24} +(-1.00000 + 2.41421i) q^{26} +(1.82843 + 4.41421i) q^{27} +(2.00000 + 2.00000i) q^{28} +(-1.12132 + 2.70711i) q^{29} -4.00000 q^{31} -5.65685 q^{32} -0.585786i q^{33} +4.00000 q^{34} +(0.585786 + 0.585786i) q^{36} +(0.707107 + 1.70711i) q^{37} +(-7.82843 - 3.24264i) q^{38} +(-2.41421 + 2.41421i) q^{39} +(-5.82843 - 5.82843i) q^{41} +(1.41421 + 3.41421i) q^{42} +(7.94975 - 3.29289i) q^{43} +(0.242641 + 0.585786i) q^{44} +(-0.242641 + 0.242641i) q^{46} +11.6569 q^{47} +(-6.82843 - 2.82843i) q^{48} -5.00000i q^{49} +(4.82843 + 2.00000i) q^{51} +(1.41421 - 3.41421i) q^{52} +(7.53553 - 3.12132i) q^{53} +(-2.58579 - 6.24264i) q^{54} +(-2.82843 - 2.82843i) q^{56} +(-7.82843 - 7.82843i) q^{57} +(1.58579 - 3.82843i) q^{58} +(6.12132 - 2.53553i) q^{59} +(0.292893 - 0.707107i) q^{61} +5.65685 q^{62} +0.585786i q^{63} +8.00000 q^{64} +0.828427i q^{66} +(3.70711 + 1.53553i) q^{67} -5.65685 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} +(-0.171573 + 0.414214i) q^{77} +(3.41421 - 3.41421i) q^{78} -6.00000i q^{79} -10.0711i q^{81} +(8.24264 + 8.24264i) q^{82} +(2.53553 - 6.12132i) q^{83} +(-2.00000 - 4.82843i) q^{84} +(-11.2426 + 4.65685i) q^{86} +(3.82843 - 3.82843i) q^{87} +(-0.343146 - 0.828427i) q^{88} +(2.65685 - 2.65685i) q^{89} +(2.41421 - 1.00000i) q^{91} +(0.343146 - 0.343146i) q^{92} +(6.82843 + 2.82843i) q^{93} -16.4853 q^{94} +(9.65685 + 4.00000i) q^{96} -1.51472i q^{97} +7.07107i q^{98} +(-0.0502525 + 0.121320i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{3} + 8 q^{4} + 4 q^{6} + 4 q^{7} + 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^3 + 8 * q^4 + 4 * q^6 + 4 * q^7 + 4 * q^9	\( 4 q - 4 q^{3} + 8 q^{4} + 4 q^{6} + 4 q^{7} + 4 q^{9} - 8 q^{11} - 8 q^{12} + 16 q^{16} + 4 q^{18} + 8 q^{19} - 4 q^{21} - 12 q^{22} + 12 q^{23} + 8 q^{24} - 4 q^{26} - 4 q^{27} + 8 q^{28} + 4 q^{29} - 16 q^{31} + 16 q^{34} + 8 q^{36} - 20 q^{38} - 4 q^{39} - 12 q^{41} + 12 q^{43} - 16 q^{44} + 16 q^{46} + 24 q^{47} - 16 q^{48} + 8 q^{51} + 16 q^{53} - 16 q^{54} - 20 q^{57} + 12 q^{58} + 16 q^{59} + 4 q^{61} + 32 q^{64} + 12 q^{67} + 4 q^{69} - 12 q^{71} + 8 q^{72} + 28 q^{73} - 4 q^{74} + 16 q^{76} - 12 q^{77} + 8 q^{78} + 16 q^{82} - 4 q^{83} - 8 q^{84} - 28 q^{86} + 4 q^{87} - 24 q^{88} - 12 q^{89} + 4 q^{91} + 24 q^{92} + 16 q^{93} - 32 q^{94} + 16 q^{96} - 20 q^{99}+O(q^{100}) \) 4 * q - 4 * q^3 + 8 * q^4 + 4 * q^6 + 4 * q^7 + 4 * q^9 - 8 * q^11 - 8 * q^12 + 16 * q^16 + 4 * q^18 + 8 * q^19 - 4 * q^21 - 12 * q^22 + 12 * q^23 + 8 * q^24 - 4 * q^26 - 4 * q^27 + 8 * q^28 + 4 * q^29 - 16 * q^31 + 16 * q^34 + 8 * q^36 - 20 * q^38 - 4 * q^39 - 12 * q^41 + 12 * q^43 - 16 * q^44 + 16 * q^46 + 24 * q^47 - 16 * q^48 + 8 * q^51 + 16 * q^53 - 16 * q^54 - 20 * q^57 + 12 * q^58 + 16 * q^59 + 4 * q^61 + 32 * q^64 + 12 * q^67 + 4 * q^69 - 12 * q^71 + 8 * q^72 + 28 * q^73 - 4 * q^74 + 16 * q^76 - 12 * q^77 + 8 * q^78 + 16 * q^82 - 4 * q^83 - 8 * q^84 - 28 * q^86 + 4 * q^87 - 24 * q^88 - 12 * q^89 + 4 * q^91 + 24 * q^92 + 16 * q^93 - 32 * q^94 + 16 * q^96 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more