LMFDB - Embedded newform 731.2.m.a.87.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(87,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([7, 0]))

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

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

chi := DirichletCharacter("731.87");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.m (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:	$5.83706438776$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			87.1
Root			$0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	731.87
Dual form			731.2.m.a.689.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.70711 - 1.70711i) q^{2} +(-1.00000 + 0.414214i) q^{3} +3.82843i q^{4} +(-0.585786 - 1.41421i) q^{5} +(2.41421 + 1.00000i) q^{6} +(0.414214 - 1.00000i) q^{7} +(3.12132 - 3.12132i) q^{8} +(-1.29289 + 1.29289i) q^{9} +O(q^{10})$	\(q+(-1.70711 - 1.70711i) q^{2} +(-1.00000 + 0.414214i) q^{3} +3.82843i q^{4} +(-0.585786 - 1.41421i) q^{5} +(2.41421 + 1.00000i) q^{6} +(0.414214 - 1.00000i) q^{7} +(3.12132 - 3.12132i) q^{8} +(-1.29289 + 1.29289i) q^{9} +(-1.41421 + 3.41421i) q^{10} +(1.70711 + 0.707107i) q^{11} +(-1.58579 - 3.82843i) q^{12} -6.82843i q^{13} +(-2.41421 + 1.00000i) q^{14} +(1.17157 + 1.17157i) q^{15} -3.00000 q^{16} +(-0.121320 + 4.12132i) q^{17} +4.41421 q^{18} +(-2.00000 - 2.00000i) q^{19} +(5.41421 - 2.24264i) q^{20} +1.17157i q^{21} +(-1.70711 - 4.12132i) q^{22} +(-4.12132 - 1.70711i) q^{23} +(-1.82843 + 4.41421i) q^{24} +(1.87868 - 1.87868i) q^{25} +(-11.6569 + 11.6569i) q^{26} +(2.00000 - 4.82843i) q^{27} +(3.82843 + 1.58579i) q^{28} -4.00000i q^{30} +(-5.12132 + 2.12132i) q^{31} +(-1.12132 - 1.12132i) q^{32} -2.00000 q^{33} +(7.24264 - 6.82843i) q^{34} -1.65685 q^{35} +(-4.94975 - 4.94975i) q^{36} +(-6.24264 + 2.58579i) q^{37} +6.82843i q^{38} +(2.82843 + 6.82843i) q^{39} +(-6.24264 - 2.58579i) q^{40} +(-1.87868 + 4.53553i) q^{41} +(2.00000 - 2.00000i) q^{42} +(-0.707107 + 0.707107i) q^{43} +(-2.70711 + 6.53553i) q^{44} +(2.58579 + 1.07107i) q^{45} +(4.12132 + 9.94975i) q^{46} +8.24264i q^{47} +(3.00000 - 1.24264i) q^{48} +(4.12132 + 4.12132i) q^{49} -6.41421 q^{50} +(-1.58579 - 4.17157i) q^{51} +26.1421 q^{52} +(0.171573 + 0.171573i) q^{53} +(-11.6569 + 4.82843i) q^{54} -2.82843i q^{55} +(-1.82843 - 4.41421i) q^{56} +(2.82843 + 1.17157i) q^{57} +(-7.48528 + 7.48528i) q^{59} +(-4.48528 + 4.48528i) q^{60} +(0.585786 - 1.41421i) q^{61} +(12.3640 + 5.12132i) q^{62} +(0.757359 + 1.82843i) q^{63} +9.82843i q^{64} +(-9.65685 + 4.00000i) q^{65} +(3.41421 + 3.41421i) q^{66} +7.07107 q^{67} +(-15.7782 - 0.464466i) q^{68} +4.82843 q^{69} +(2.82843 + 2.82843i) q^{70} +(-8.07107 + 3.34315i) q^{71} +8.07107i q^{72} +(-3.75736 - 9.07107i) q^{73} +(15.0711 + 6.24264i) q^{74} +(-1.10051 + 2.65685i) q^{75} +(7.65685 - 7.65685i) q^{76} +(1.41421 - 1.41421i) q^{77} +(6.82843 - 16.4853i) q^{78} +(9.53553 + 3.94975i) q^{79} +(1.75736 + 4.24264i) q^{80} +0.171573i q^{81} +(10.9497 - 4.53553i) q^{82} +(-6.82843 - 6.82843i) q^{83} -4.48528 q^{84} +(5.89949 - 2.24264i) q^{85} +2.41421 q^{86} +(7.53553 - 3.12132i) q^{88} +14.8284i q^{89} +(-2.58579 - 6.24264i) q^{90} +(-6.82843 - 2.82843i) q^{91} +(6.53553 - 15.7782i) q^{92} +(4.24264 - 4.24264i) q^{93} +(14.0711 - 14.0711i) q^{94} +(-1.65685 + 4.00000i) q^{95} +(1.58579 + 0.656854i) q^{96} +(3.77817 + 9.12132i) q^{97} -14.0711i q^{98} +(-3.12132 + 1.29289i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 4 q^{3} - 8 q^{5} + 4 q^{6} - 4 q^{7} + 4 q^{8} - 8 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 - 4 * q^3 - 8 * q^5 + 4 * q^6 - 4 * q^7 + 4 * q^8 - 8 * q^9	$ 4 q - 4 q^{2} - 4 q^{3} - 8 q^{5} + 4 q^{6} - 4 q^{7} + 4 q^{8} - 8 q^{9} + 4 q^{11} - 12 q^{12} - 4 q^{14} + 16 q^{15} - 12 q^{16} + 8 q^{17} + 12 q^{18} - 8 q^{19} + 16 q^{20} - 4 q^{22} - 8 q^{23} + 4 q^{24} + 16 q^{25} - 24 q^{26} + 8 q^{27} + 4 q^{28} - 12 q^{31} + 4 q^{32} - 8 q^{33} + 12 q^{34} + 16 q^{35} - 8 q^{37} - 8 q^{40} - 16 q^{41} + 8 q^{42} - 8 q^{44} + 16 q^{45} + 8 q^{46} + 12 q^{48} + 8 q^{49} - 20 q^{50} - 12 q^{51} + 48 q^{52} + 12 q^{53} - 24 q^{54} + 4 q^{56} + 4 q^{59} + 16 q^{60} + 8 q^{61} + 24 q^{62} + 20 q^{63} - 16 q^{65} + 8 q^{66} - 32 q^{68} + 8 q^{69} - 4 q^{71} - 32 q^{73} + 32 q^{74} - 44 q^{75} + 8 q^{76} + 16 q^{78} + 24 q^{79} + 24 q^{80} + 24 q^{82} - 16 q^{83} + 16 q^{84} - 16 q^{85} + 4 q^{86} + 16 q^{88} - 16 q^{90} - 16 q^{91} + 12 q^{92} + 28 q^{94} + 16 q^{95} + 12 q^{96} - 16 q^{97} - 4 q^{99}+O(q^{100}) $ 4 * q - 4 * q^2 - 4 * q^3 - 8 * q^5 + 4 * q^6 - 4 * q^7 + 4 * q^8 - 8 * q^9 + 4 * q^11 - 12 * q^12 - 4 * q^14 + 16 * q^15 - 12 * q^16 + 8 * q^17 + 12 * q^18 - 8 * q^19 + 16 * q^20 - 4 * q^22 - 8 * q^23 + 4 * q^24 + 16 * q^25 - 24 * q^26 + 8 * q^27 + 4 * q^28 - 12 * q^31 + 4 * q^32 - 8 * q^33 + 12 * q^34 + 16 * q^35 - 8 * q^37 - 8 * q^40 - 16 * q^41 + 8 * q^42 - 8 * q^44 + 16 * q^45 + 8 * q^46 + 12 * q^48 + 8 * q^49 - 20 * q^50 - 12 * q^51 + 48 * q^52 + 12 * q^53 - 24 * q^54 + 4 * q^56 + 4 * q^59 + 16 * q^60 + 8 * q^61 + 24 * q^62 + 20 * q^63 - 16 * q^65 + 8 * q^66 - 32 * q^68 + 8 * q^69 - 4 * q^71 - 32 * q^73 + 32 * q^74 - 44 * q^75 + 8 * q^76 + 16 * q^78 + 24 * q^79 + 24 * q^80 + 24 * q^82 - 16 * q^83 + 16 * q^84 - 16 * q^85 + 4 * q^86 + 16 * q^88 - 16 * q^90 - 16 * q^91 + 12 * q^92 + 28 * q^94 + 16 * q^95 + 12 * q^96 - 16 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.70711	−	1.70711i	−1.20711	−	1.20711i	−0.971960	−	0.235147i	$-0.924443\pi$
$2$	−1.70711	−	1.70711i	−1.20711	−	1.20711i	−0.235147	−	0.971960i	$-0.575557\pi$
$3$	−1.00000	+	0.414214i	−0.577350	+	0.239146i	−0.652198	−	0.758049i	$-0.726153\pi$
$3$	−1.00000	+	0.414214i	−0.577350	+	0.239146i	0.0748477	+	0.997195i	$0.476153\pi$
$4$			3.82843i			1.91421i
$5$	−0.585786	−	1.41421i	−0.261972	−	0.632456i	0.737089	−	0.675796i	$-0.236200\pi$
$5$	−0.585786	−	1.41421i	−0.261972	−	0.632456i	−0.999060	+	0.0433405i	$0.986200\pi$
$6$	2.41421	+	1.00000i	0.985599	+	0.408248i
$7$	0.414214	−	1.00000i	0.156558	−	0.377964i	−0.826066	−	0.563574i	$-0.809426\pi$
$7$	0.414214	−	1.00000i	0.156558	−	0.377964i	0.982624	+	0.185610i	$0.0594260\pi$
$8$	3.12132	−	3.12132i	1.10355	−	1.10355i
$9$	−1.29289	+	1.29289i	−0.430964	+	0.430964i
$10$	−1.41421	+	3.41421i	−0.447214	+	1.07967i
$11$	1.70711	+	0.707107i	0.514712	+	0.213201i	0.624892	−	0.780711i	$-0.285143\pi$
$11$	1.70711	+	0.707107i	0.514712	+	0.213201i	−0.110180	+	0.993912i	$0.535143\pi$
$12$	−1.58579	−	3.82843i	−0.457777	−	1.10517i
$13$		−	6.82843i		−	1.89386i	−0.321433	−	0.946932i	$-0.604164\pi$
$13$		−	6.82843i		−	1.89386i	0.321433	−	0.946932i	$-0.395836\pi$
$14$	−2.41421	+	1.00000i	−0.645226	+	0.267261i
$15$	1.17157	+	1.17157i	0.302499	+	0.302499i
$16$	−3.00000			−0.750000
$17$	−0.121320	+	4.12132i	−0.0294245	+	0.999567i
$17$	−0.121320	+	4.12132i	−0.0294245	+	0.999567i
$18$	4.41421			1.04044
$19$	−2.00000	−	2.00000i	−0.458831	−	0.458831i	0.439440	−	0.898272i	$-0.355177\pi$
$19$	−2.00000	−	2.00000i	−0.458831	−	0.458831i	−0.898272	+	0.439440i	$0.855177\pi$
$20$	5.41421	−	2.24264i	1.21065	−	0.501470i
$21$			1.17157i			0.255658i
$22$	−1.70711	−	4.12132i	−0.363956	−	0.878668i
$23$	−4.12132	−	1.70711i	−0.859355	−	0.355956i	−0.0908996	−	0.995860i	$-0.528974\pi$
$23$	−4.12132	−	1.70711i	−0.859355	−	0.355956i	−0.768455	+	0.639904i	$0.778974\pi$
$24$	−1.82843	+	4.41421i	−0.373226	+	0.901048i
$25$	1.87868	−	1.87868i	0.375736	−	0.375736i
$26$	−11.6569	+	11.6569i	−2.28610	+	2.28610i
$27$	2.00000	−	4.82843i	0.384900	−	0.929231i
$28$	3.82843	+	1.58579i	0.723505	+	0.299685i
$29$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$29$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$30$		−	4.00000i		−	0.730297i
$31$	−5.12132	+	2.12132i	−0.919816	+	0.381000i	−0.791806	−	0.610772i	$-0.790859\pi$
$31$	−5.12132	+	2.12132i	−0.919816	+	0.381000i	−0.128010	+	0.991773i	$0.540859\pi$
$32$	−1.12132	−	1.12132i	−0.198223	−	0.198223i
$33$	−2.00000			−0.348155
$34$	7.24264	−	6.82843i	1.24210	−	1.17107i
$35$	−1.65685			−0.280059
$36$	−4.94975	−	4.94975i	−0.824958	−	0.824958i
$37$	−6.24264	+	2.58579i	−1.02628	+	0.425101i	−0.831370	−	0.555720i	$-0.812443\pi$
$37$	−6.24264	+	2.58579i	−1.02628	+	0.425101i	−0.194914	+	0.980820i	$0.562443\pi$
$38$			6.82843i			1.10772i
$39$	2.82843	+	6.82843i	0.452911	+	1.09342i
$40$	−6.24264	−	2.58579i	−0.987048	−	0.408849i
$41$	−1.87868	+	4.53553i	−0.293400	+	0.708331i	0.706599	+	0.707614i	$0.250228\pi$
$41$	−1.87868	+	4.53553i	−0.293400	+	0.708331i	−1.00000		0.000717467i	$0.999772\pi$
$42$	2.00000	−	2.00000i	0.308607	−	0.308607i
$43$	−0.707107	+	0.707107i	−0.107833	+	0.107833i
$43$	−0.707107	+	0.707107i	−0.107833	+	0.107833i
$44$	−2.70711	+	6.53553i	−0.408112	+	0.985269i
$45$	2.58579	+	1.07107i	0.385466	+	0.159665i
$46$	4.12132	+	9.94975i	0.607656	+	1.46701i
$47$			8.24264i			1.20231i	0.799131	+	0.601156i	$0.205293\pi$
$47$			8.24264i			1.20231i	−0.799131	+	0.601156i	$0.794707\pi$
$48$	3.00000	−	1.24264i	0.433013	−	0.179360i
$49$	4.12132	+	4.12132i	0.588760	+	0.588760i
$50$	−6.41421			−0.907107
$51$	−1.58579	−	4.17157i	−0.222055	−	0.584137i
$52$	26.1421			3.62526
$53$	0.171573	+	0.171573i	0.0235673	+	0.0235673i	0.718792	−	0.695225i	$-0.244695\pi$
$53$	0.171573	+	0.171573i	0.0235673	+	0.0235673i	−0.695225	+	0.718792i	$0.744695\pi$
$54$	−11.6569	+	4.82843i	−1.58630	+	0.657066i
$55$		−	2.82843i		−	0.381385i
$56$	−1.82843	−	4.41421i	−0.244334	−	0.589874i
$57$	2.82843	+	1.17157i	0.374634	+	0.155179i
$58$		0			0
$59$	−7.48528	+	7.48528i	−0.974501	+	0.974501i	−0.999683	−	0.0251822i	$-0.991983\pi$
$59$	−7.48528	+	7.48528i	−0.974501	+	0.974501i	0.0251822	+	0.999683i	$0.491983\pi$
$60$	−4.48528	+	4.48528i	−0.579047	+	0.579047i
$61$	0.585786	−	1.41421i	0.0750023	−	0.181071i	−0.881932	−	0.471377i	$-0.843757\pi$
$61$	0.585786	−	1.41421i	0.0750023	−	0.181071i	0.956934	+	0.290306i	$0.0937570\pi$
$62$	12.3640	+	5.12132i	1.57022	+	0.650408i
$63$	0.757359	+	1.82843i	0.0954183	+	0.230360i
$64$			9.82843i			1.22855i
$65$	−9.65685	+	4.00000i	−1.19779	+	0.496139i
$66$	3.41421	+	3.41421i	0.420261	+	0.420261i
$67$	7.07107			0.863868			0.431934	−	0.901905i	$-0.357831\pi$
$67$	7.07107			0.863868			0.431934	+	0.901905i	$0.357831\pi$
$68$	−15.7782	−	0.464466i	−1.91338	−	0.0563248i
$69$	4.82843			0.581274
$70$	2.82843	+	2.82843i	0.338062	+	0.338062i
$71$	−8.07107	+	3.34315i	−0.957860	+	0.396758i	−0.806179	−	0.591671i	$-0.798468\pi$
$71$	−8.07107	+	3.34315i	−0.957860	+	0.396758i	−0.151680	+	0.988430i	$0.548468\pi$
$72$			8.07107i			0.951184i
$73$	−3.75736	−	9.07107i	−0.439766	−	1.06169i	−0.976030	−	0.217638i	$-0.930165\pi$
$73$	−3.75736	−	9.07107i	−0.439766	−	1.06169i	0.536264	−	0.844050i	$-0.319835\pi$
$74$	15.0711	+	6.24264i	1.75198	+	0.725692i
$75$	−1.10051	+	2.65685i	−0.127075	+	0.306787i
$76$	7.65685	−	7.65685i	0.878301	−	0.878301i
$77$	1.41421	−	1.41421i	0.161165	−	0.161165i
$78$	6.82843	−	16.4853i	0.773167	−	1.86659i
$79$	9.53553	+	3.94975i	1.07283	+	0.444381i	0.847989	−	0.530014i	$-0.177813\pi$
$79$	9.53553	+	3.94975i	1.07283	+	0.444381i	0.224842	+	0.974395i	$0.427813\pi$
$80$	1.75736	+	4.24264i	0.196479	+	0.474342i
$81$			0.171573i			0.0190637i
$82$	10.9497	−	4.53553i	1.20920	−	0.500866i
$83$	−6.82843	−	6.82843i	−0.749517	−	0.749517i	0.224871	−	0.974388i	$-0.427804\pi$
$83$	−6.82843	−	6.82843i	−0.749517	−	0.749517i	−0.974388	+	0.224871i	$0.927804\pi$
$84$	−4.48528			−0.489384
$85$	5.89949	−	2.24264i	0.639890	−	0.243249i
$86$	2.41421			0.260331
$87$		0			0
$88$	7.53553	−	3.12132i	0.803291	−	0.332734i
$89$			14.8284i			1.57181i	0.618347	+	0.785905i	$0.287803\pi$
$89$			14.8284i			1.57181i	−0.618347	+	0.785905i	$0.712197\pi$
$90$	−2.58579	−	6.24264i	−0.272566	−	0.658032i
$91$	−6.82843	−	2.82843i	−0.715814	−	0.296500i
$92$	6.53553	−	15.7782i	0.681377	−	1.64499i
$93$	4.24264	−	4.24264i	0.439941	−	0.439941i
$94$	14.0711	−	14.0711i	1.45132	−	1.45132i
$95$	−1.65685	+	4.00000i	−0.169990	+	0.410391i
$96$	1.58579	+	0.656854i	0.161849	+	0.0670399i
$97$	3.77817	+	9.12132i	0.383616	+	0.926130i	0.991260	+	0.131921i	$0.0421145\pi$
$97$	3.77817	+	9.12132i	0.383616	+	0.926130i	−0.607645	+	0.794209i	$0.707886\pi$
$98$		−	14.0711i		−	1.42139i
$99$	−3.12132	+	1.29289i	−0.313704	+	0.129941i
$100$	7.19239	+	7.19239i	0.719239	+	0.719239i
$101$	−13.8995			−1.38305			−0.691526	−	0.722352i	$-0.743061\pi$
$101$	−13.8995			−1.38305			−0.691526	+	0.722352i	$0.743061\pi$
$102$	−4.41421	+	9.82843i	−0.437072	+	0.973159i
$103$	−9.89949			−0.975426			−0.487713	−	0.873004i	$-0.662169\pi$
$103$	−9.89949			−0.975426			−0.487713	+	0.873004i	$0.662169\pi$
$104$	−21.3137	−	21.3137i	−2.08998	−	2.08998i
$105$	1.65685	−	0.686292i	0.161692	−	0.0669752i
$106$		−	0.585786i		−	0.0568966i
$107$	3.19239	+	7.70711i	0.308620	+	0.745074i	0.999750	+	0.0223442i	$0.00711296\pi$
$107$	3.19239	+	7.70711i	0.308620	+	0.745074i	−0.691131	+	0.722730i	$0.742887\pi$
$108$	18.4853	+	7.65685i	1.77875	+	0.736781i
$109$	1.36396	−	3.29289i	0.130644	−	0.315402i	−0.844999	−	0.534768i	$-0.820399\pi$
$109$	1.36396	−	3.29289i	0.130644	−	0.315402i	0.975643	+	0.219366i	$0.0703989\pi$
$110$	−4.82843	+	4.82843i	−0.460372	+	0.460372i
$111$	5.17157	−	5.17157i	0.490864	−	0.490864i
$112$	−1.24264	+	3.00000i	−0.117419	+	0.283473i
$113$	15.3137	+	6.34315i	1.44059	+	0.596713i	0.959942	−	0.280199i	$-0.0904005\pi$
$113$	15.3137	+	6.34315i	1.44059	+	0.596713i	0.480651	+	0.876912i	$0.340401\pi$
$114$	−2.82843	−	6.82843i	−0.264906	−	0.639541i
$115$			6.82843i			0.636754i
$116$		0			0
$117$	8.82843	+	8.82843i	0.816188	+	0.816188i
$118$	25.5563			2.35265
$119$	4.07107	+	1.82843i	0.373194	+	0.167612i
$120$	7.31371			0.667647
$121$	−5.36396	−	5.36396i	−0.487633	−	0.487633i
$122$	−3.41421	+	1.41421i	−0.309108	+	0.128037i
$123$		−	5.31371i		−	0.479121i
$124$	−8.12132	−	19.6066i	−0.729316	−	1.76072i
$125$	−10.8284	−	4.48528i	−0.968524	−	0.401176i
$126$	1.82843	−	4.41421i	0.162889	−	0.393249i
$127$	−5.00000	+	5.00000i	−0.443678	+	0.443678i	−0.893246	−	0.449568i	$-0.851578\pi$
$127$	−5.00000	+	5.00000i	−0.443678	+	0.443678i	0.449568	+	0.893246i	$0.351578\pi$
$128$	14.5355	−	14.5355i	1.28477	−	1.28477i
$129$	0.414214	−	1.00000i	0.0364695	−	0.0880451i
$130$	23.3137	+	9.65685i	2.04475	+	0.846962i
$131$	0.171573	+	0.414214i	0.0149904	+	0.0361900i	0.931198	−	0.364515i	$-0.118765\pi$
$131$	0.171573	+	0.414214i	0.0149904	+	0.0361900i	−0.916207	+	0.400705i	$0.868765\pi$
$132$		−	7.65685i		−	0.666444i
$133$	−2.82843	+	1.17157i	−0.245256	+	0.101588i
$134$	−12.0711	−	12.0711i	−1.04278	−	1.04278i
$135$	−8.00000			−0.688530
$136$	12.4853	+	13.2426i	1.07060	+	1.13555i
$137$	−6.34315			−0.541932			−0.270966	−	0.962589i	$-0.587343\pi$
$137$	−6.34315			−0.541932			−0.270966	+	0.962589i	$0.587343\pi$
$138$	−8.24264	−	8.24264i	−0.701660	−	0.701660i
$139$	−19.1924	+	7.94975i	−1.62788	+	0.674289i	−0.994992	−	0.0999568i	$-0.968130\pi$
$139$	−19.1924	+	7.94975i	−1.62788	+	0.674289i	−0.632885	+	0.774246i	$0.718130\pi$
$140$		−	6.34315i		−	0.536094i
$141$	−3.41421	−	8.24264i	−0.287529	−	0.694156i
$142$	19.4853	+	8.07107i	1.63517	+	0.677309i
$143$	4.82843	−	11.6569i	0.403773	−	0.974795i
$144$	3.87868	−	3.87868i	0.323223	−	0.323223i
$145$		0			0
$146$	−9.07107	+	21.8995i	−0.750727	+	1.81242i
$147$	−5.82843	−	2.41421i	−0.480721	−	0.199121i
$148$	−9.89949	−	23.8995i	−0.813733	−	1.96453i
$149$		−	20.8284i		−	1.70633i	−0.521640	−	0.853166i	$-0.674680\pi$
$149$		−	20.8284i		−	1.70633i	0.521640	−	0.853166i	$-0.325320\pi$
$150$	6.41421	−	2.65685i	0.523718	−	0.216931i
$151$	−2.00000	−	2.00000i	−0.162758	−	0.162758i	0.621029	−	0.783787i	$-0.286715\pi$
$151$	−2.00000	−	2.00000i	−0.162758	−	0.162758i	−0.783787	+	0.621029i	$0.786715\pi$
$152$	−12.4853			−1.01269
$153$	−5.17157	−	5.48528i	−0.418097	−	0.443459i
$154$	−4.82843			−0.389086
$155$	6.00000	+	6.00000i	0.481932	+	0.481932i
$156$	−26.1421	+	10.8284i	−2.09305	+	0.866968i
$157$		−	3.65685i		−	0.291849i	−0.989296	−	0.145924i	$-0.953384\pi$
$157$		−	3.65685i		−	0.291849i	0.989296	−	0.145924i	$-0.0466156\pi$
$158$	−9.53553	−	23.0208i	−0.758606	−	1.83144i
$159$	−0.242641	−	0.100505i	−0.0192427	−	0.00797057i
$160$	−0.928932	+	2.24264i	−0.0734385	+	0.177296i
$161$	−3.41421	+	3.41421i	−0.269078	+	0.269078i
$162$	0.292893	−	0.292893i	0.0230119	−	0.0230119i
$163$	−1.34315	+	3.24264i	−0.105203	+	0.253983i	−0.967712	−	0.252059i	$-0.918892\pi$
$163$	−1.34315	+	3.24264i	−0.105203	+	0.253983i	0.862508	+	0.506043i	$0.168892\pi$
$164$	−17.3640	−	7.19239i	−1.35590	−	0.561631i
$165$	1.17157	+	2.82843i	0.0912068	+	0.220193i
$166$			23.3137i			1.80949i
$167$	−14.1924	+	5.87868i	−1.09824	+	0.454906i	−0.856873	−	0.515528i	$-0.827596\pi$
$167$	−14.1924	+	5.87868i	−1.09824	+	0.454906i	−0.241367	+	0.970434i	$0.577596\pi$
$168$	3.65685	+	3.65685i	0.282132	+	0.282132i
$169$	−33.6274			−2.58672
$170$	−13.8995	−	6.24264i	−1.06604	−	0.478789i
$171$	5.17157			0.395480
$172$	−2.70711	−	2.70711i	−0.206415	−	0.206415i
$173$	−16.3640	+	6.77817i	−1.24413	+	0.515335i	−0.905003	−	0.425406i	$-0.860131\pi$
$173$	−16.3640	+	6.77817i	−1.24413	+	0.515335i	−0.339126	+	0.940741i	$0.610131\pi$
$174$		0			0
$175$	−1.10051	−	2.65685i	−0.0831904	−	0.200839i
$176$	−5.12132	−	2.12132i	−0.386034	−	0.159901i
$177$	4.38478	−	10.5858i	0.329580	−	0.795676i
$178$	25.3137	−	25.3137i	1.89734	−	1.89734i
$179$	−7.07107	+	7.07107i	−0.528516	+	0.528516i	−0.920130	−	0.391613i	$-0.871917\pi$
$179$	−7.07107	+	7.07107i	−0.528516	+	0.528516i	0.391613	+	0.920130i	$0.371917\pi$
$180$	−4.10051	+	9.89949i	−0.305634	+	0.737865i
$181$	−7.94975	−	3.29289i	−0.590900	−	0.244759i	0.0671377	−	0.997744i	$-0.478613\pi$
$181$	−7.94975	−	3.29289i	−0.590900	−	0.244759i	−0.658038	+	0.752985i	$0.728613\pi$
$182$	6.82843	+	16.4853i	0.506157	+	1.22197i
$183$			1.65685i			0.122478i
$184$	−18.1924	+	7.53553i	−1.34116	+	0.555527i
$185$	7.31371	+	7.31371i	0.537715	+	0.537715i
$186$	−14.4853			−1.06211
$187$	−3.12132	+	6.94975i	−0.228254	+	0.508216i
$188$	−31.5563			−2.30148
$189$	−4.00000	−	4.00000i	−0.290957	−	0.290957i
$190$	9.65685	−	4.00000i	0.700582	−	0.290191i
$191$		−	18.4853i		−	1.33755i	−0.743466	−	0.668774i	$-0.766819\pi$
$191$		−	18.4853i		−	1.33755i	0.743466	−	0.668774i	$-0.233181\pi$
$192$	−4.07107	−	9.82843i	−0.293804	−	0.709306i
$193$	−3.94975	−	1.63604i	−0.284309	−	0.117765i	0.235972	−	0.971760i	$-0.424173\pi$
$193$	−3.94975	−	1.63604i	−0.284309	−	0.117765i	−0.520281	+	0.853995i	$0.674173\pi$
$194$	9.12132	−	22.0208i	0.654873	−	1.58100i
$195$	8.00000	−	8.00000i	0.572892	−	0.572892i
$196$	−15.7782	+	15.7782i	−1.12701	+	1.12701i
$197$	9.77817	−	23.6066i	0.696666	−	1.68190i	−0.0342318	−	0.999414i	$-0.510898\pi$
$197$	9.77817	−	23.6066i	0.696666	−	1.68190i	0.730898	−	0.682487i	$-0.239102\pi$
$198$	7.53553	+	3.12132i	0.535527	+	0.221823i
$199$	2.41421	+	5.82843i	0.171139	+	0.413166i	0.986057	−	0.166411i	$-0.0532178\pi$
$199$	2.41421	+	5.82843i	0.171139	+	0.413166i	−0.814917	+	0.579577i	$0.803218\pi$
$200$		−	11.7279i		−	0.829289i
$201$	−7.07107	+	2.92893i	−0.498755	+	0.206591i
$202$	23.7279	+	23.7279i	1.66949	+	1.66949i
$203$		0			0
$204$	15.9706	−	6.07107i	1.11816	−	0.425060i
$205$	7.51472			0.524851
$206$	16.8995	+	16.8995i	1.17744	+	1.17744i
$207$	7.53553	−	3.12132i	0.523756	−	0.216947i
$208$			20.4853i			1.42040i
$209$	−2.00000	−	4.82843i	−0.138343	−	0.333989i
$210$	−4.00000	−	1.65685i	−0.276026	−	0.114334i
$211$	−1.92893	+	4.65685i	−0.132793	+	0.320591i	−0.976264	−	0.216584i	$-0.930509\pi$
$211$	−1.92893	+	4.65685i	−0.132793	+	0.320591i	0.843471	+	0.537175i	$0.180509\pi$
$212$	−0.656854	+	0.656854i	−0.0451129	+	0.0451129i
$213$	6.68629	−	6.68629i	0.458137	−	0.458137i
$214$	7.70711	−	18.6066i	0.526847	−	1.27192i
$215$	1.41421	+	0.585786i	0.0964486	+	0.0399503i
$216$	−8.82843	−	21.3137i	−0.600698	−	1.45021i
$217$			6.00000i			0.407307i
$218$	−7.94975	+	3.29289i	−0.538425	+	0.223023i
$219$	7.51472	+	7.51472i	0.507798	+	0.507798i
$220$	10.8284			0.730052
$221$	28.1421	+	0.828427i	1.89304	+	0.0557260i
$222$	−17.6569			−1.18505
$223$	−4.82843	−	4.82843i	−0.323335	−	0.323335i	0.526710	−	0.850045i	$-0.323425\pi$
$223$	−4.82843	−	4.82843i	−0.323335	−	0.323335i	−0.850045	+	0.526710i	$0.823425\pi$
$224$	−1.58579	+	0.656854i	−0.105955	+	0.0438879i
$225$			4.85786i			0.323858i
$226$	−15.3137	−	36.9706i	−1.01865	−	2.45925i
$227$	24.0711	+	9.97056i	1.59765	+	0.661769i	0.991081	−	0.133259i	$-0.0425443\pi$
$227$	24.0711	+	9.97056i	1.59765	+	0.661769i	0.606572	+	0.795029i	$0.292544\pi$
$228$	−4.48528	+	10.8284i	−0.297045	+	0.717130i
$229$	13.1421	−	13.1421i	0.868457	−	0.868457i	−0.123845	−	0.992302i	$-0.539523\pi$
$229$	13.1421	−	13.1421i	0.868457	−	0.868457i	0.992302	+	0.123845i	$0.0395225\pi$
$230$	11.6569	−	11.6569i	0.768630	−	0.768630i
$231$	−0.828427	+	2.00000i	−0.0545065	+	0.131590i
$232$		0			0
$233$	−4.82843	−	11.6569i	−0.316321	−	0.763666i	−0.999443	−	0.0333622i	$-0.989379\pi$
$233$	−4.82843	−	11.6569i	−0.316321	−	0.763666i	0.683123	−	0.730304i	$-0.260621\pi$
$234$		−	30.1421i		−	1.97045i
$235$	11.6569	−	4.82843i	0.760409	−	0.314972i
$236$	−28.6569	−	28.6569i	−1.86540	−	1.86540i
$237$	−11.1716			−0.725672
$238$	−3.82843	−	10.0711i	−0.248160	−	0.652810i
$239$	26.0000			1.68180			0.840900	−	0.541190i	$-0.182026\pi$
$239$	26.0000			1.68180			0.840900	+	0.541190i	$0.182026\pi$
$240$	−3.51472	−	3.51472i	−0.226874	−	0.226874i
$241$	3.41421	−	1.41421i	0.219929	−	0.0910975i	−0.269999	−	0.962861i	$-0.587023\pi$
$241$	3.41421	−	1.41421i	0.219929	−	0.0910975i	0.489927	+	0.871763i	$0.337023\pi$
$242$			18.3137i			1.17725i
$243$	5.92893	+	14.3137i	0.380341	+	0.918225i
$244$	5.41421	+	2.24264i	0.346610	+	0.143570i
$245$	3.41421	−	8.24264i	0.218126	−	0.526603i
$246$	−9.07107	+	9.07107i	−0.578350	+	0.578350i
$247$	−13.6569	+	13.6569i	−0.868965	+	0.868965i
$248$	−9.36396	+	22.6066i	−0.594612	+	1.43552i
$249$	9.65685	+	4.00000i	0.611978	+	0.253490i
$250$	10.8284	+	26.1421i	0.684850	+	1.65337i
$251$			3.65685i			0.230819i	0.993318	+	0.115409i	$0.0368180\pi$
$251$			3.65685i			0.230819i	−0.993318	+	0.115409i	$0.963182\pi$
$252$	−7.00000	+	2.89949i	−0.440959	+	0.182651i
$253$	−5.82843	−	5.82843i	−0.366430	−	0.366430i
$254$	17.0711			1.07113
$255$	−4.97056	+	4.68629i	−0.311269	+	0.293467i
$256$	−29.9706			−1.87316
$257$	10.4853	+	10.4853i	0.654054	+	0.654054i	0.953967	−	0.299913i	$-0.0969576\pi$
$257$	10.4853	+	10.4853i	0.654054	+	0.654054i	−0.299913	+	0.953967i	$0.596958\pi$
$258$	−2.41421	+	1.00000i	−0.150302	+	0.0622573i
$259$			7.31371i			0.454452i
$260$	−15.3137	−	36.9706i	−0.949716	−	2.29282i
$261$		0			0
$262$	0.414214	−	1.00000i	0.0255902	−	0.0617802i
$263$	−13.1716	+	13.1716i	−0.812194	+	0.812194i	−0.984962	−	0.172768i	$-0.944729\pi$
$263$	−13.1716	+	13.1716i	−0.812194	+	0.812194i	0.172768	+	0.984962i	$0.444729\pi$
$264$	−6.24264	+	6.24264i	−0.384208	+	0.384208i
$265$	0.142136	−	0.343146i	0.00873132	−	0.0210793i
$266$	6.82843	+	2.82843i	0.418678	+	0.173422i
$267$	−6.14214	−	14.8284i	−0.375893	−	0.907485i
$268$			27.0711i			1.65363i
$269$	−0.0502525	+	0.0208153i	−0.00306395	+	0.00126913i	−0.384215	−	0.923244i	$-0.625528\pi$
$269$	−0.0502525	+	0.0208153i	−0.00306395	+	0.00126913i	0.381151	+	0.924513i	$0.375528\pi$
$270$	13.6569	+	13.6569i	0.831130	+	0.831130i
$271$	−5.41421			−0.328890			−0.164445	−	0.986386i	$-0.552583\pi$
$271$	−5.41421			−0.328890			−0.164445	+	0.986386i	$0.552583\pi$
$272$	0.363961	−	12.3640i	0.0220684	−	0.749675i
$273$	8.00000			0.484182
$274$	10.8284	+	10.8284i	0.654169	+	0.654169i
$275$	4.53553	−	1.87868i	0.273503	−	0.113289i
$276$			18.4853i			1.11268i
$277$	−7.65685	−	18.4853i	−0.460056	−	1.11067i	−0.968374	−	0.249504i	$-0.919733\pi$
$277$	−7.65685	−	18.4853i	−0.460056	−	1.11067i	0.508318	−	0.861169i	$-0.330267\pi$
$278$	46.3345	+	19.1924i	2.77896	+	1.15108i
$279$	3.87868	−	9.36396i	0.232210	−	0.560606i
$280$	−5.17157	+	5.17157i	−0.309061	+	0.309061i
$281$	4.31371	−	4.31371i	0.257334	−	0.257334i	−0.566635	−	0.823969i	$-0.691755\pi$
$281$	4.31371	−	4.31371i	0.257334	−	0.257334i	0.823969	+	0.566635i	$0.191755\pi$
$282$	−8.24264	+	19.8995i	−0.490842	+	1.18500i
$283$	1.70711	+	0.707107i	0.101477	+	0.0420331i	0.432844	−	0.901469i	$-0.357510\pi$
$283$	1.70711	+	0.707107i	0.101477	+	0.0420331i	−0.331367	+	0.943502i	$0.607510\pi$
$284$	−12.7990	−	30.8995i	−0.759480	−	1.83355i
$285$		−	4.68629i		−	0.277592i
$286$	−28.1421	+	11.6569i	−1.66408	+	0.689284i
$287$	3.75736	+	3.75736i	0.221790	+	0.221790i
$288$	2.89949			0.170854
$289$	−16.9706	−	1.00000i	−0.998268	−	0.0588235i
$290$		0			0
$291$	−7.55635	−	7.55635i	−0.442961	−	0.442961i
$292$	34.7279	−	14.3848i	2.03230	−	0.841805i
$293$		−	12.9706i		−	0.757748i	−0.925448	−	0.378874i	$-0.876311\pi$
$293$		−	12.9706i		−	0.757748i	0.925448	−	0.378874i	$-0.123689\pi$
$294$	5.82843	+	14.0711i	0.339921	+	0.820641i
$295$	14.9706	+	6.20101i	0.871620	+	0.361037i
$296$	−11.4142	+	27.5563i	−0.663438	+	1.60168i
$297$	6.82843	−	6.82843i	0.396226	−	0.396226i
$298$	−35.5563	+	35.5563i	−2.05972	+	2.05972i
$299$	−11.6569	+	28.1421i	−0.674133	+	1.62750i
$300$	−10.1716	−	4.21320i	−0.587256	−	0.243249i
$301$	0.414214	+	1.00000i	0.0238749	+	0.0576390i
$302$			6.82843i			0.392932i
$303$	13.8995	−	5.75736i	0.798505	−	0.330752i
$304$	6.00000	+	6.00000i	0.344124	+	0.344124i
$305$	−2.34315			−0.134168
$306$	−0.535534	+	18.1924i	−0.0306144	+	1.03999i
$307$	29.2132			1.66729			0.833643	−	0.552304i	$-0.186251\pi$
$307$	29.2132			1.66729			0.833643	+	0.552304i	$0.186251\pi$
$308$	5.41421	+	5.41421i	0.308503	+	0.308503i
$309$	9.89949	−	4.10051i	0.563163	−	0.233270i
$310$		−	20.4853i		−	1.16349i
$311$	0.192388	+	0.464466i	0.0109093	+	0.0263375i	0.929240	−	0.369476i	$-0.120463\pi$
$311$	0.192388	+	0.464466i	0.0109093	+	0.0263375i	−0.918331	+	0.395813i	$0.870463\pi$
$312$	30.1421	+	12.4853i	1.70646	+	0.706840i
$313$	−1.17157	+	2.82843i	−0.0662212	+	0.159872i	−0.953526	−	0.301312i	$-0.902575\pi$
$313$	−1.17157	+	2.82843i	−0.0662212	+	0.159872i	0.887304	+	0.461184i	$0.152575\pi$
$314$	−6.24264	+	6.24264i	−0.352293	+	0.352293i
$315$	2.14214	−	2.14214i	0.120696	−	0.120696i
$316$	−15.1213	+	36.5061i	−0.850641	+	2.05363i
$317$	−29.1924	−	12.0919i	−1.63961	−	0.679148i	−0.643349	−	0.765573i	$-0.722456\pi$
$317$	−29.1924	−	12.0919i	−1.63961	−	0.679148i	−0.996258	+	0.0864248i	$0.972456\pi$
$318$	0.242641	+	0.585786i	0.0136066	+	0.0328493i
$319$		0			0
$320$	13.8995	−	5.75736i	0.777005	−	0.321846i
$321$	−6.38478	−	6.38478i	−0.356363	−	0.356363i
$322$	11.6569			0.649611
$323$	8.48528	−	8.00000i	0.472134	−	0.445132i
$324$	−0.656854			−0.0364919
$325$	−12.8284	−	12.8284i	−0.711593	−	0.711593i
$326$	7.82843	−	3.24264i	0.433576	−	0.179593i
$327$			3.85786i			0.213340i
$328$	8.29289	+	20.0208i	0.457898	+	1.10546i
$329$	8.24264	+	3.41421i	0.454431	+	0.188232i
$330$	2.82843	−	6.82843i	0.155700	−	0.375893i
$331$	3.89949	−	3.89949i	0.214336	−	0.214336i	−0.591771	−	0.806106i	$-0.701571\pi$
$331$	3.89949	−	3.89949i	0.214336	−	0.214336i	0.806106	+	0.591771i	$0.201571\pi$
$332$	26.1421	−	26.1421i	1.43474	−	1.43474i
$333$	4.72792	−	11.4142i	0.259089	−	0.625495i
$334$	34.2635	+	14.1924i	1.87481	+	0.776573i
$335$	−4.14214	−	10.0000i	−0.226309	−	0.546358i
$336$		−	3.51472i		−	0.191744i
$337$	30.6066	−	12.6777i	1.66725	−	0.690597i	0.668652	−	0.743575i	$-0.266872\pi$
$337$	30.6066	−	12.6777i	1.66725	−	0.690597i	0.998596	+	0.0529787i	$0.0168715\pi$
$338$	57.4056	+	57.4056i	3.12245	+	3.12245i
$339$	−17.9411			−0.974428
$340$	8.58579	+	22.5858i	0.465630	+	1.22489i
$341$	−10.2426			−0.554670
$342$	−8.82843	−	8.82843i	−0.477387	−	0.477387i
$343$	12.8284	−	5.31371i	0.692670	−	0.286913i
$344$			4.41421i			0.237998i
$345$	−2.82843	−	6.82843i	−0.152277	−	0.367630i
$346$	39.5061	+	16.3640i	2.12386	+	0.879732i
$347$	−4.07107	+	9.82843i	−0.218546	+	0.527618i	−0.994687	−	0.102942i	$-0.967174\pi$
$347$	−4.07107	+	9.82843i	−0.218546	+	0.527618i	0.776141	+	0.630559i	$0.217174\pi$
$348$		0			0
$349$	9.75736	−	9.75736i	0.522299	−	0.522299i	−0.395966	−	0.918265i	$-0.629590\pi$
$349$	9.75736	−	9.75736i	0.522299	−	0.522299i	0.918265	+	0.395966i	$0.129590\pi$
$350$	−2.65685	+	6.41421i	−0.142015	+	0.342854i
$351$	−32.9706	−	13.6569i	−1.75984	−	0.728949i
$352$	−1.12132	−	2.70711i	−0.0597666	−	0.144289i
$353$		−	2.34315i		−	0.124713i	−0.998054	−	0.0623565i	$-0.980138\pi$
$353$		−	2.34315i		−	0.124713i	0.998054	−	0.0623565i	$-0.0198616\pi$
$354$	−25.5563	+	10.5858i	−1.35830	+	0.562628i
$355$	9.45584	+	9.45584i	0.501864	+	0.501864i
$356$	−56.7696			−3.00878
$357$	−4.82843	−	0.142136i	−0.255547	−	0.00752261i
$358$	24.1421			1.27595
$359$	−7.07107	−	7.07107i	−0.373197	−	0.373197i	0.495443	−	0.868640i	$-0.335006\pi$
$359$	−7.07107	−	7.07107i	−0.373197	−	0.373197i	−0.868640	+	0.495443i	$0.835006\pi$
$360$	11.4142	−	4.72792i	0.601582	−	0.249183i
$361$		−	11.0000i		−	0.578947i
$362$	7.94975	+	19.1924i	0.417829	+	1.00873i
$363$	7.58579	+	3.14214i	0.398151	+	0.164919i
$364$	10.8284	−	26.1421i	0.567564	−	1.37022i
$365$	−10.6274	+	10.6274i	−0.556264	+	0.556264i
$366$	2.82843	−	2.82843i	0.147844	−	0.147844i
$367$	−10.0208	+	24.1924i	−0.523082	+	1.26283i	0.412897	+	0.910778i	$0.364517\pi$
$367$	−10.0208	+	24.1924i	−0.523082	+	1.26283i	−0.935979	+	0.352055i	$0.885483\pi$
$368$	12.3640	+	5.12132i	0.644516	+	0.266967i
$369$	−3.43503	−	8.29289i	−0.178820	−	0.431711i
$370$		−	24.9706i		−	1.29816i
$371$	0.242641	−	0.100505i	0.0125973	−	0.00521796i
$372$	16.2426	+	16.2426i	0.842142	+	0.842142i
$373$	16.4853			0.853576			0.426788	−	0.904352i	$-0.359645\pi$
$373$	16.4853			0.853576			0.426788	+	0.904352i	$0.359645\pi$
$374$	17.1924	−	6.53553i	0.888997	−	0.337944i
$375$	12.6863			0.655117
$376$	25.7279	+	25.7279i	1.32682	+	1.32682i
$377$		0			0
$378$			13.6569i			0.702433i
$379$	11.2635	+	27.1924i	0.578565	+	1.39678i	0.894101	+	0.447866i	$0.147816\pi$
$379$	11.2635	+	27.1924i	0.578565	+	1.39678i	−0.315536	+	0.948914i	$0.602184\pi$
$380$	−15.3137	−	6.34315i	−0.785577	−	0.325397i
$381$	2.92893	−	7.07107i	0.150054	−	0.362262i
$382$	−31.5563	+	31.5563i	−1.61456	+	1.61456i
$383$	14.1421	−	14.1421i	0.722629	−	0.722629i	−0.246511	−	0.969140i	$-0.579284\pi$
$383$	14.1421	−	14.1421i	0.722629	−	0.722629i	0.969140	+	0.246511i	$0.0792840\pi$
$384$	−8.51472	+	20.5563i	−0.434515	+	1.04901i
$385$	−2.82843	−	1.17157i	−0.144150	−	0.0597089i
$386$	3.94975	+	9.53553i	0.201037	+	0.485346i
$387$		−	1.82843i		−	0.0929442i
$388$	−34.9203	+	14.4645i	−1.77281	+	0.734322i
$389$	4.82843	+	4.82843i	0.244811	+	0.244811i	0.818837	−	0.574026i	$-0.194619\pi$
$389$	4.82843	+	4.82843i	0.244811	+	0.244811i	−0.574026	+	0.818837i	$0.694619\pi$
$390$	−27.3137			−1.38308
$391$	7.53553	−	16.7782i	0.381088	−	0.848509i
$392$	25.7279			1.29946
$393$	−0.343146	−	0.343146i	−0.0173094	−	0.0173094i
$394$	−56.9914	+	23.6066i	−2.87118	+	1.18928i
$395$		−	15.7990i		−	0.794933i
$396$	−4.94975	−	11.9497i	−0.248734	−	0.600497i
$397$	−7.53553	−	3.12132i	−0.378198	−	0.156655i	0.185483	−	0.982647i	$-0.440615\pi$
$397$	−7.53553	−	3.12132i	−0.378198	−	0.156655i	−0.563680	+	0.825993i	$0.690615\pi$
$398$	5.82843	−	14.0711i	0.292153	−	0.705319i
$399$	2.34315	−	2.34315i	0.117304	−	0.117304i
$400$	−5.63604	+	5.63604i	−0.281802	+	0.281802i
$401$	−7.60660	+	18.3640i	−0.379856	+	0.917052i	0.612136	+	0.790752i	$0.290310\pi$
$401$	−7.60660	+	18.3640i	−0.379856	+	0.917052i	−0.991992	+	0.126300i	$0.959690\pi$
$402$	17.0711	+	7.07107i	0.851427	+	0.352673i
$403$	14.4853	+	34.9706i	0.721563	+	1.74201i
$404$		−	53.2132i		−	2.64746i
$405$	0.242641	−	0.100505i	0.0120569	−	0.00499414i
$406$		0			0
$407$	−12.4853			−0.618872
$408$	−17.9706	−	8.07107i	−0.889675	−	0.399577i
$409$	23.4558			1.15982			0.579908	−	0.814682i	$-0.303088\pi$
$409$	23.4558			1.15982			0.579908	+	0.814682i	$0.303088\pi$
$410$	−12.8284	−	12.8284i	−0.633551	−	0.633551i
$411$	6.34315	−	2.62742i	0.312884	−	0.129601i
$412$		−	37.8995i		−	1.86717i
$413$	4.38478	+	10.5858i	0.215761	+	0.520892i
$414$	−18.1924	−	7.53553i	−0.894107	−	0.370351i
$415$	−5.65685	+	13.6569i	−0.277684	+	0.670389i
$416$	−7.65685	+	7.65685i	−0.375408	+	0.375408i
$417$	15.8995	−	15.8995i	0.778602	−	0.778602i
$418$	−4.82843	+	11.6569i	−0.236166	+	0.570155i
$419$	−17.1421	−	7.10051i	−0.837448	−	0.346882i	−0.0776013	−	0.996984i	$-0.524726\pi$
$419$	−17.1421	−	7.10051i	−0.837448	−	0.346882i	−0.759847	+	0.650102i	$0.774726\pi$
$420$	2.62742	+	6.34315i	0.128205	+	0.309514i
$421$			2.14214i			0.104401i	0.998637	+	0.0522007i	$0.0166235\pi$
$421$			2.14214i			0.104401i	−0.998637	+	0.0522007i	$0.983376\pi$
$422$	11.2426	−	4.65685i	0.547283	−	0.226692i
$423$	−10.6569	−	10.6569i	−0.518154	−	0.518154i
$424$	1.07107			0.0520157
$425$	7.51472	+	7.97056i	0.364517	+	0.386629i
$426$	−22.8284			−1.10604
$427$	−1.17157	−	1.17157i	−0.0566964	−	0.0566964i
$428$	−29.5061	+	12.2218i	−1.42623	+	0.590764i
$429$			13.6569i			0.659359i
$430$	−1.41421	−	3.41421i	−0.0681994	−	0.164648i
$431$	0.949747	+	0.393398i	0.0457477	+	0.0189493i	0.405440	−	0.914122i	$-0.367118\pi$
$431$	0.949747	+	0.393398i	0.0457477	+	0.0189493i	−0.359692	+	0.933071i	$0.617118\pi$
$432$	−6.00000	+	14.4853i	−0.288675	+	0.696923i
$433$	−15.7990	+	15.7990i	−0.759251	+	0.759251i	−0.976186	−	0.216935i	$-0.930394\pi$
$433$	−15.7990	+	15.7990i	−0.759251	+	0.759251i	0.216935	+	0.976186i	$0.430394\pi$
$434$	10.2426	−	10.2426i	0.491662	−	0.491662i
$435$		0			0
$436$	12.6066	+	5.22183i	0.603747	+	0.250080i
$437$	4.82843	+	11.6569i	0.230975	+	0.557623i
$438$		−	25.6569i		−	1.22593i
$439$	−29.6066	+	12.2635i	−1.41305	+	0.585303i	−0.953103	−	0.302646i	$-0.902130\pi$
$439$	−29.6066	+	12.2635i	−1.41305	+	0.585303i	−0.459943	+	0.887949i	$0.652130\pi$
$440$	−8.82843	−	8.82843i	−0.420879	−	0.420879i
$441$	−10.6569			−0.507469
$442$	−46.6274	−	49.4558i	−2.21784	−	2.35237i
$443$	8.34315			0.396395			0.198197	−	0.980162i	$-0.436491\pi$
$443$	8.34315			0.396395			0.198197	+	0.980162i	$0.436491\pi$
$444$	19.7990	+	19.7990i	0.939618	+	0.939618i
$445$	20.9706	−	8.68629i	0.994100	−	0.411770i
$446$			16.4853i			0.780601i
$447$	8.62742	+	20.8284i	0.408063	+	0.985151i
$448$	9.82843	+	4.07107i	0.464350	+	0.192340i
$449$	6.34315	−	15.3137i	0.299352	−	0.722699i	−0.700607	−	0.713548i	$-0.747087\pi$
$449$	6.34315	−	15.3137i	0.299352	−	0.722699i	0.999958	−	0.00915081i	$-0.00291283\pi$
$450$	8.29289	−	8.29289i	0.390931	−	0.390931i
$451$	−6.41421	+	6.41421i	−0.302034	+	0.302034i
$452$	−24.2843	+	58.6274i	−1.14224	+	2.75760i
$453$	2.82843	+	1.17157i	0.132891	+	0.0550453i
$454$	−24.0711	−	58.1127i	−1.12971	−	2.72736i
$455$			11.3137i			0.530395i
$456$	12.4853	−	5.17157i	0.584677	−	0.242181i
$457$	−18.1421	−	18.1421i	−0.848653	−	0.848653i	0.141312	−	0.989965i	$-0.454868\pi$
$457$	−18.1421	−	18.1421i	−0.848653	−	0.848653i	−0.989965	+	0.141312i	$0.954868\pi$
$458$	−44.8701			−2.09664
$459$	19.6569	+	8.82843i	0.917503	+	0.412076i
$460$	−26.1421			−1.21888
$461$	19.5563	+	19.5563i	0.910830	+	0.910830i	0.996338	−	0.0855075i	$-0.0272512\pi$
$461$	19.5563	+	19.5563i	0.910830	+	0.910830i	−0.0855075	+	0.996338i	$0.527251\pi$
$462$	4.82843	−	2.00000i	0.224639	−	0.0930484i
$463$		−	24.3431i		−	1.13132i	−0.824638	−	0.565661i	$-0.808621\pi$
$463$		−	24.3431i		−	1.13132i	0.824638	−	0.565661i	$-0.191379\pi$
$464$		0			0
$465$	−8.48528	−	3.51472i	−0.393496	−	0.162991i
$466$	−11.6569	+	28.1421i	−0.539993	+	1.30366i
$467$	4.97056	−	4.97056i	0.230010	−	0.230010i	−0.582687	−	0.812697i	$-0.697999\pi$
$467$	4.97056	−	4.97056i	0.230010	−	0.230010i	0.812697	+	0.582687i	$0.197999\pi$
$468$	−33.7990	+	33.7990i	−1.56236	+	1.56236i
$469$	2.92893	−	7.07107i	0.135246	−	0.326512i
$470$	−28.1421	−	11.6569i	−1.29810	−	0.537691i
$471$	1.51472	+	3.65685i	0.0697946	+	0.168499i
$472$			46.7279i			2.15083i
$473$	−1.70711	+	0.707107i	−0.0784929	+	0.0325128i
$474$	19.0711	+	19.0711i	0.875963	+	0.875963i
$475$	−7.51472			−0.344799
$476$	−7.00000	+	15.5858i	−0.320844	+	0.714373i
$477$	−0.443651			−0.0203134
$478$	−44.3848	−	44.3848i	−2.03011	−	2.03011i
$479$	−24.6777	+	10.2218i	−1.12755	+	0.467047i	−0.866948	−	0.498399i	$-0.833922\pi$
$479$	−24.6777	+	10.2218i	−1.12755	+	0.467047i	−0.260604	+	0.965446i	$0.583922\pi$
$480$		−	2.62742i		−	0.119925i
$481$	17.6569	+	42.6274i	0.805083	+	1.94364i
$482$	−8.24264	−	3.41421i	−0.375442	−	0.155513i
$483$	2.00000	−	4.82843i	0.0910032	−	0.219701i
$484$	20.5355	−	20.5355i	0.933433	−	0.933433i
$485$	10.6863	−	10.6863i	0.485240	−	0.485240i
$486$	14.3137	−	34.5563i	0.649283	−	1.56751i
$487$	−3.94975	−	1.63604i	−0.178980	−	0.0741360i	0.291394	−	0.956603i	$-0.405881\pi$
$487$	−3.94975	−	1.63604i	−0.178980	−	0.0741360i	−0.470374	+	0.882467i	$0.655881\pi$
$488$	−2.58579	−	6.24264i	−0.117053	−	0.282591i
$489$		−	3.79899i		−	0.171796i
$490$	−19.8995	+	8.24264i	−0.898968	+	0.372365i
$491$	−13.5147	−	13.5147i	−0.609911	−	0.609911i	0.333012	−	0.942923i	$-0.391935\pi$
$491$	−13.5147	−	13.5147i	−0.609911	−	0.609911i	−0.942923	+	0.333012i	$0.891935\pi$
$492$	20.3431			0.917140
$493$		0			0
$494$	46.6274			2.09787
$495$	3.65685	+	3.65685i	0.164363	+	0.164363i
$496$	15.3640	−	6.36396i	0.689862	−	0.285750i
$497$			9.45584i			0.424153i
$498$	−9.65685	−	23.3137i	−0.432734	−	1.04471i
$499$	−15.7279	−	6.51472i	−0.704078	−	0.291639i	0.00177328	−	0.999998i	$-0.499436\pi$
$499$	−15.7279	−	6.51472i	−0.704078	−	0.291639i	−0.705852	+	0.708360i	$0.749436\pi$
$500$	17.1716	−	41.4558i	0.767936	−	1.85396i
$501$	11.7574	−	11.7574i	0.525280	−	0.525280i
$502$	6.24264	−	6.24264i	0.278623	−	0.278623i
$503$	−1.72792	+	4.17157i	−0.0770442	+	0.186001i	−0.957709	−	0.287739i	$-0.907096\pi$
$503$	−1.72792	+	4.17157i	−0.0770442	+	0.186001i	0.880665	+	0.473740i	$0.157096\pi$
$504$	8.07107	+	3.34315i	0.359514	+	0.148916i
$505$	8.14214	+	19.6569i	0.362320	+	0.874719i
$506$			19.8995i			0.884640i
$507$	33.6274	−	13.9289i	1.49345	−	0.618606i
$508$	−19.1421	−	19.1421i	−0.849295	−	0.849295i
$509$	9.89949			0.438787			0.219394	−	0.975636i	$-0.429592\pi$
$509$	9.89949			0.438787			0.219394	+	0.975636i	$0.429592\pi$
$510$	16.4853	+	0.485281i	0.729981	+	0.0214886i
$511$	−10.6274			−0.470129
$512$	22.0919	+	22.0919i	0.976333	+	0.976333i
$513$	−13.6569	+	5.65685i	−0.602965	+	0.249756i
$514$		−	35.7990i		−	1.57903i
$515$	5.79899	+	14.0000i	0.255534	+	0.616914i
$516$	3.82843	+	1.58579i	0.168537	+	0.0698104i
$517$	−5.82843	+	14.0711i	−0.256334	+	0.618845i
$518$	12.4853	−	12.4853i	0.548572	−	0.548572i
$519$	13.5563	−	13.5563i	0.595058	−	0.595058i
$520$	−17.6569	+	42.6274i	−0.774304	+	1.86934i
$521$	15.3137	+	6.34315i	0.670906	+	0.277898i	0.692019	−	0.721879i	$-0.256721\pi$
$521$	15.3137	+	6.34315i	0.670906	+	0.277898i	−0.0211137	+	0.999777i	$0.506721\pi$
$522$		0			0
$523$		−	2.14214i		−	0.0936691i	−0.998903	−	0.0468345i	$-0.985087\pi$
$523$		−	2.14214i		−	0.0936691i	0.998903	−	0.0468345i	$-0.0149133\pi$
$524$	−1.58579	+	0.656854i	−0.0692754	+	0.0286948i
$525$	2.20101	+	2.20101i	0.0960600	+	0.0960600i
$526$	44.9706			1.96081
$527$	−8.12132	−	21.3640i	−0.353770	−	0.930629i
$528$	6.00000			0.261116
$529$	−2.19239	−	2.19239i	−0.0953212	−	0.0953212i
$530$	−0.828427	+	0.343146i	−0.0359846	+	0.0149053i
$531$		−	19.3553i		−	0.839950i
$532$	−4.48528	−	10.8284i	−0.194462	−	0.469472i
$533$	30.9706	+	12.8284i	1.34148	+	0.555661i
$534$	−14.8284	+	35.7990i	−0.641689	+	1.54917i
$535$	9.02944	−	9.02944i	0.390377	−	0.390377i
$536$	22.0711	−	22.0711i	0.953325	−	0.953325i
$537$	4.14214	−	10.0000i	0.178746	−	0.431532i
$538$	0.121320	+	0.0502525i	0.00523049	+	0.00216654i
$539$	4.12132	+	9.94975i	0.177518	+	0.428566i
$540$		−	30.6274i		−	1.31799i
$541$	6.05025	−	2.50610i	0.260121	−	0.107746i	−0.248812	−	0.968552i	$-0.580040\pi$
$541$	6.05025	−	2.50610i	0.260121	−	0.107746i	0.508933	+	0.860806i	$0.330040\pi$
$542$	9.24264	+	9.24264i	0.397005	+	0.397005i
$543$	9.31371			0.399689
$544$	4.75736	−	4.48528i	0.203970	−	0.192305i
$545$	−5.45584			−0.233703
$546$	−13.6569	−	13.6569i	−0.584459	−	0.584459i
$547$	1.87868	−	0.778175i	0.0803265	−	0.0332723i	−0.342158	−	0.939642i	$-0.611158\pi$
$547$	1.87868	−	0.778175i	0.0803265	−	0.0332723i	0.422485	+	0.906370i	$0.361158\pi$
$548$		−	24.2843i		−	1.03737i
$549$	1.07107	+	2.58579i	0.0457121	+	0.110359i
$550$	−10.9497	−	4.53553i	−0.466899	−	0.193396i
$551$		0			0
$552$	15.0711	−	15.0711i	0.641467	−	0.641467i
$553$	7.89949	−	7.89949i	0.335921	−	0.335921i
$554$	−18.4853	+	44.6274i	−0.785364	+	1.89604i
$555$	−10.3431	−	4.28427i	−0.439042	−	0.181857i
$556$	−30.4350	−	73.4767i	−1.29073	−	3.11610i
$557$			15.0711i			0.638582i	0.947657	+	0.319291i	$0.103445\pi$
$557$			15.0711i			0.638582i	−0.947657	+	0.319291i	$0.896555\pi$
$558$	−22.6066	+	9.36396i	−0.957014	+	0.396408i
$559$	4.82843	+	4.82843i	0.204221	+	0.204221i
$560$	4.97056			0.210045
$561$	0.242641	−	8.24264i	0.0102443	−	0.348005i
$562$	−14.7279			−0.621260
$563$	−23.9706	−	23.9706i	−1.01024	−	1.01024i	−0.999947	−	0.0102917i	$-0.996724\pi$
$563$	−23.9706	−	23.9706i	−1.01024	−	1.01024i	−0.0102917	−	0.999947i	$-0.503276\pi$
$564$	31.5563	−	13.0711i	1.32876	−	0.550391i
$565$		−	25.3726i		−	1.06743i
$566$	−1.70711	−	4.12132i	−0.0717551	−	0.173232i
$567$	0.171573	+	0.0710678i	0.00720538	+	0.00298457i
$568$	−14.7574	+	35.6274i	−0.619205	+	1.49489i
$569$	15.3137	−	15.3137i	0.641984	−	0.641984i	−0.309059	−	0.951043i	$-0.600014\pi$
$569$	15.3137	−	15.3137i	0.641984	−	0.641984i	0.951043	+	0.309059i	$0.100014\pi$
$570$	−8.00000	+	8.00000i	−0.335083	+	0.335083i
$571$	−12.6569	+	30.5563i	−0.529673	+	1.27874i	0.402065	+	0.915611i	$0.368293\pi$
$571$	−12.6569	+	30.5563i	−0.529673	+	1.27874i	−0.931738	+	0.363132i	$0.881707\pi$
$572$	44.6274	+	18.4853i	1.86597	+	0.772908i
$573$	7.65685	+	18.4853i	0.319870	+	0.772234i
$574$		−	12.8284i		−	0.535448i
$575$	−10.9497	+	4.53553i	−0.456636	+	0.189145i
$576$	−12.7071	−	12.7071i	−0.529463	−	0.529463i
$577$	−39.3137			−1.63665			−0.818326	−	0.574755i	$-0.805097\pi$
$577$	−39.3137			−1.63665			−0.818326	+	0.574755i	$0.805097\pi$
$578$	27.2635	+	30.6777i	1.13401	+	1.27602i
$579$	4.62742			0.192309
$580$		0			0
$581$	−9.65685	+	4.00000i	−0.400634	+	0.165948i
$582$			25.7990i			1.06940i
$583$	0.171573	+	0.414214i	0.00710582	+	0.0171550i
$584$	−40.0416	−	16.5858i	−1.65693	−	0.686325i
$585$	7.31371	−	17.6569i	0.302385	−	0.730021i
$586$	−22.1421	+	22.1421i	−0.914683	+	0.914683i
$587$	−18.2426	+	18.2426i	−0.752954	+	0.752954i	−0.975030	−	0.222075i	$-0.928717\pi$
$587$	−18.2426	+	18.2426i	−0.752954	+	0.752954i	0.222075	+	0.975030i	$0.428717\pi$
$588$	9.24264	−	22.3137i	0.381160	−	0.920202i
$589$	14.4853	+	6.00000i	0.596856	+	0.247226i
$590$	−14.9706	−	36.1421i	−0.616328	−	1.48795i
$591$			27.6569i			1.13765i
$592$	18.7279	−	7.75736i	0.769713	−	0.318826i
$593$	−30.7279	−	30.7279i	−1.26184	−	1.26184i	−0.950198	−	0.311646i	$-0.899120\pi$
$593$	−30.7279	−	30.7279i	−1.26184	−	1.26184i	−0.311646	−	0.950198i	$-0.600880\pi$
$594$	−23.3137			−0.956573
$595$	0.201010	−	6.82843i	0.00824061	−	0.279938i
$596$	79.7401			3.26628
$597$	−4.82843	−	4.82843i	−0.197614	−	0.197614i
$598$	67.9411	−	28.1421i	2.77832	−	1.15082i
$599$		−	20.9706i		−	0.856834i	−0.903581	−	0.428417i	$-0.859071\pi$
$599$		−	20.9706i		−	0.856834i	0.903581	−	0.428417i	$-0.140929\pi$
$600$	4.85786	+	11.7279i	0.198321	+	0.478790i
$601$	−38.2843	−	15.8579i	−1.56165	−	0.646856i	−0.576273	−	0.817257i	$-0.695494\pi$
$601$	−38.2843	−	15.8579i	−1.56165	−	0.646856i	−0.985375	+	0.170401i	$0.945494\pi$
$602$	1.00000	−	2.41421i	0.0407570	−	0.0983960i
$603$	−9.14214	+	9.14214i	−0.372297	+	0.372297i
$604$	7.65685	−	7.65685i	0.311553	−	0.311553i
$605$	−4.44365	+	10.7279i	−0.180660	+	0.436152i
$606$	−33.5563	−	13.8995i	−1.36313	−	0.564628i
$607$	10.0711	+	24.3137i	0.408772	+	0.986863i	0.985461	+	0.169899i	$0.0543443\pi$
$607$	10.0711	+	24.3137i	0.408772	+	0.986863i	−0.576689	+	0.816964i	$0.695656\pi$
$608$			4.48528i			0.181902i
$609$		0			0
$610$	4.00000	+	4.00000i	0.161955	+	0.161955i
$611$	56.2843			2.27702
$612$	21.0000	−	19.7990i	0.848875	−	0.800327i
$613$	15.5563			0.628315			0.314158	−	0.949371i	$-0.398278\pi$
$613$	15.5563			0.628315			0.314158	+	0.949371i	$0.398278\pi$
$614$	−49.8701	−	49.8701i	−2.01259	−	2.01259i
$615$	−7.51472	+	3.11270i	−0.303023	+	0.125516i
$616$		−	8.82843i		−	0.355707i
$617$	−10.7071	−	25.8492i	−0.431052	−	1.04065i	−0.978949	−	0.204106i	$-0.934571\pi$
$617$	−10.7071	−	25.8492i	−0.431052	−	1.04065i	0.547897	−	0.836546i	$-0.315429\pi$
$618$	−23.8995	−	9.89949i	−0.961379	−	0.398216i
$619$	−8.87868	+	21.4350i	−0.356864	+	0.861547i	0.638873	+	0.769312i	$0.279401\pi$
$619$	−8.87868	+	21.4350i	−0.356864	+	0.861547i	−0.995737	+	0.0922344i	$0.970599\pi$
$620$	−22.9706	+	22.9706i	−0.922520	+	0.922520i
$621$	−16.4853	+	16.4853i	−0.661532	+	0.661532i
$622$	0.464466	−	1.12132i	0.0186234	−	0.0449608i
$623$	14.8284	+	6.14214i	0.594088	+	0.246079i
$624$	−8.48528	−	20.4853i	−0.339683	−	0.820068i
$625$			4.65685i			0.186274i
$626$	6.82843	−	2.82843i	0.272919	−	0.113047i
$627$	4.00000	+	4.00000i	0.159745	+	0.159745i
$628$	14.0000			0.558661
$629$	−9.89949	−	26.0416i	−0.394719	−	1.03835i
$630$	−7.31371			−0.291385
$631$	5.07107	+	5.07107i	0.201876	+	0.201876i	0.800803	−	0.598927i	$-0.204406\pi$
$631$	5.07107	+	5.07107i	0.201876	+	0.201876i	−0.598927	+	0.800803i	$0.704406\pi$
$632$	42.0919	−	17.4350i	1.67433	−	0.693528i
$633$		−	5.45584i		−	0.216850i
$634$	29.1924	+	70.4767i	1.15938	+	2.79899i
$635$	10.0000	+	4.14214i	0.396838	+	0.164376i
$636$	0.384776	−	0.928932i	0.0152574	−	0.0368346i
$637$	28.1421	−	28.1421i	1.11503	−	1.11503i
$638$		0			0
$639$	6.11270	−	14.7574i	0.241815	−	0.583792i
$640$	−29.0711	−	12.0416i	−1.14913	−	0.475987i
$641$	0.485281	+	1.17157i	0.0191675	+	0.0462743i	0.933174	−	0.359426i	$-0.117028\pi$
$641$	0.485281	+	1.17157i	0.0191675	+	0.0462743i	−0.914006	+	0.405701i	$0.867028\pi$
$642$			21.7990i			0.860338i
$643$	32.2635	−	13.3640i	1.27235	−	0.527023i	0.358670	−	0.933465i	$-0.383230\pi$
$643$	32.2635	−	13.3640i	1.27235	−	0.527023i	0.913677	+	0.406441i	$0.133230\pi$
$644$	−13.0711	−	13.0711i	−0.515072	−	0.515072i
$645$	−1.65685			−0.0652386
$646$	−28.1421	−	0.828427i	−1.10724	−	0.0325940i
$647$	−1.85786			−0.0730402			−0.0365201	−	0.999333i	$-0.511627\pi$
$647$	−1.85786			−0.0730402			−0.0365201	+	0.999333i	$0.511627\pi$
$648$	0.535534	+	0.535534i	0.0210378	+	0.0210378i
$649$	−18.0711	+	7.48528i	−0.709351	+	0.293823i
$650$			43.7990i			1.71794i
$651$	−2.48528	−	6.00000i	−0.0974059	−	0.235159i
$652$	−12.4142	−	5.14214i	−0.486178	−	0.201382i
$653$	−5.65685	+	13.6569i	−0.221370	+	0.534434i	−0.995076	−	0.0991100i	$-0.968400\pi$
$653$	−5.65685	+	13.6569i	−0.221370	+	0.534434i	0.773707	+	0.633544i	$0.218400\pi$
$654$	6.58579	−	6.58579i	0.257525	−	0.257525i
$655$	0.485281	−	0.485281i	0.0189615	−	0.0189615i
$656$	5.63604	−	13.6066i	0.220050	−	0.531249i
$657$	16.5858	+	6.87006i	0.647073	+	0.268026i
$658$	−8.24264	−	19.8995i	−0.321332	−	0.775763i
$659$			21.4142i			0.834179i	0.908865	+	0.417090i	$0.136950\pi$
$659$			21.4142i			0.834179i	−0.908865	+	0.417090i	$0.863050\pi$
$660$	−10.8284	+	4.48528i	−0.421496	+	0.174589i
$661$	−0.443651	−	0.443651i	−0.0172560	−	0.0172560i	0.698426	−	0.715682i	$-0.253884\pi$
$661$	−0.443651	−	0.443651i	−0.0172560	−	0.0172560i	−0.715682	+	0.698426i	$0.753884\pi$
$662$	−13.3137			−0.517452
$663$	−28.4853	+	10.8284i	−1.10628	+	0.420541i
$664$	−42.6274			−1.65426
$665$	3.31371	+	3.31371i	0.128500	+	0.128500i
$666$	−27.5563	+	11.4142i	−1.06779	+	0.442292i
$667$		0			0
$668$	−22.5061	−	54.3345i	−0.870787	−	2.10227i
$669$	6.82843	+	2.82843i	0.264002	+	0.109353i
$670$	−10.0000	+	24.1421i	−0.386334	+	0.932692i
$671$	2.00000	−	2.00000i	0.0772091	−	0.0772091i
$672$	1.31371	−	1.31371i	0.0506774	−	0.0506774i
$673$	−18.7279	+	45.2132i	−0.721908	+	1.74284i	−0.0540669	+	0.998537i	$0.517218\pi$
$673$	−18.7279	+	45.2132i	−0.721908	+	1.74284i	−0.667841	+	0.744304i	$0.732782\pi$
$674$	−73.8909	−	30.6066i	−2.84617	−	1.17892i
$675$	−5.31371	−	12.8284i	−0.204525	−	0.493766i
$676$		−	128.740i		−	4.95154i
$677$	13.0711	−	5.41421i	0.502362	−	0.208085i	−0.117088	−	0.993122i	$-0.537356\pi$
$677$	13.0711	−	5.41421i	0.502362	−	0.208085i	0.619450	+	0.785036i	$0.287356\pi$
$678$	30.6274	+	30.6274i	1.17624	+	1.17624i
$679$	10.6863			0.410102
$680$	11.4142	−	25.4142i	0.437715	−	0.974591i
$681$	−28.2010			−1.08067
$682$	17.4853	+	17.4853i	0.669546	+	0.669546i
$683$	9.29289	−	3.84924i	0.355583	−	0.147287i	−0.197739	−	0.980255i	$-0.563360\pi$
$683$	9.29289	−	3.84924i	0.355583	−	0.147287i	0.553322	+	0.832967i	$0.313360\pi$
$684$			19.7990i			0.757033i
$685$	3.71573	+	8.97056i	0.141971	+	0.342748i
$686$	−30.9706	−	12.8284i	−1.18246	−	0.489792i
$687$	−7.69848	+	18.5858i	−0.293716	+	0.709092i
$688$	2.12132	−	2.12132i	0.0808746	−	0.0808746i
$689$	1.17157	−	1.17157i	0.0446334	−	0.0446334i
$690$	−6.82843	+	16.4853i	−0.259954	+	0.627584i
$691$	13.5858	+	5.62742i	0.516828	+	0.214077i	0.625823	−	0.779965i	$-0.284763\pi$
$691$	13.5858	+	5.62742i	0.516828	+	0.214077i	−0.108995	+	0.994042i	$0.534763\pi$
$692$	−25.9497	−	62.6482i	−0.986461	−	2.38153i
$693$			3.65685i			0.138912i
$694$	23.7279	−	9.82843i	0.900700	−	0.373082i
$695$	22.4853	+	22.4853i	0.852915	+	0.852915i
$696$		0			0
$697$	−18.4645	−	8.29289i	−0.699392	−	0.314116i
$698$	−33.3137			−1.26094
$699$	9.65685	+	9.65685i	0.365256	+	0.365256i
$700$	10.1716	−	4.21320i	0.384449	−	0.159244i
$701$			8.20101i			0.309748i	0.987934	+	0.154874i	$0.0494971\pi$
$701$			8.20101i			0.309748i	−0.987934	+	0.154874i	$0.950503\pi$
$702$	32.9706	+	79.5980i	1.24439	+	3.00423i
$703$	17.6569	+	7.31371i	0.665941	+	0.275842i
$704$	−6.94975	+	16.7782i	−0.261928	+	0.632351i
$705$	−9.65685	+	9.65685i	−0.363698	+	0.363698i
$706$	−4.00000	+	4.00000i	−0.150542	+	0.150542i
$707$	−5.75736	+	13.8995i	−0.216528	+	0.522744i
$708$	40.5269	+	16.7868i	1.52309	+	0.630886i
$709$	8.33452	+	20.1213i	0.313010	+	0.755672i	0.999590	+	0.0286185i	$0.00911081\pi$
$709$	8.33452	+	20.1213i	0.313010	+	0.755672i	−0.686581	+	0.727054i	$0.740889\pi$
$710$		−	32.2843i		−	1.21161i
$711$	−17.4350	+	7.22183i	−0.653865	+	0.270840i
$712$	46.2843	+	46.2843i	1.73458	+	1.73458i
$713$	24.7279			0.926068
$714$	8.00000	+	8.48528i	0.299392	+	0.317554i
$715$	−19.3137			−0.722292
$716$	−27.0711	−	27.0711i	−1.01169	−	1.01169i
$717$	−26.0000	+	10.7696i	−0.970988	+	0.402196i
$718$			24.1421i			0.900976i
$719$	3.87868	+	9.36396i	0.144650	+	0.349217i	0.979555	−	0.201178i	$-0.0644771\pi$
$719$	3.87868	+	9.36396i	0.144650	+	0.349217i	−0.834904	+	0.550395i	$0.814477\pi$
$720$	−7.75736	−	3.21320i	−0.289100	−	0.119749i
$721$	−4.10051	+	9.89949i	−0.152711	+	0.368676i
$722$	−18.7782	+	18.7782i	−0.698851	+	0.698851i
$723$	−2.82843	+	2.82843i	−0.105190	+	0.105190i
$724$	12.6066	−	30.4350i	0.468521	−	1.13111i
$725$		0			0
$726$	−7.58579	−	18.3137i	−0.281535	−	0.679685i
$727$		−	44.2843i		−	1.64241i	−0.570631	−	0.821206i	$-0.693301\pi$
$727$		−	44.2843i		−	1.64241i	0.570631	−	0.821206i	$-0.306699\pi$
$728$	−30.1421	+	12.4853i	−1.11714	+	0.462735i
$729$	−12.2218	−	12.2218i	−0.452660	−	0.452660i
$730$	36.2843			1.34294
$731$	−2.82843	−	3.00000i	−0.104613	−	0.110959i
$732$	−6.34315			−0.234449
$733$	−11.2721	−	11.2721i	−0.416344	−	0.416344i	0.467598	−	0.883941i	$-0.345120\pi$
$733$	−11.2721	−	11.2721i	−0.416344	−	0.416344i	−0.883941	+	0.467598i	$0.845120\pi$
$734$	58.4056	−	24.1924i	2.15579	−	0.892957i
$735$			9.65685i			0.356198i
$736$	2.70711	+	6.53553i	0.0997853	+	0.240903i
$737$	12.0711	+	5.00000i	0.444643	+	0.184177i
$738$	−8.29289	+	20.0208i	−0.305266	+	0.736976i
$739$	1.07107	−	1.07107i	0.0393999	−	0.0393999i	−0.687132	−	0.726532i	$-0.741131\pi$
$739$	1.07107	−	1.07107i	0.0393999	−	0.0393999i	0.726532	+	0.687132i	$0.241131\pi$
$740$	−28.0000	+	28.0000i	−1.02930	+	1.02930i
$741$	8.00000	−	19.3137i	0.293887	−	0.709507i
$742$	−0.585786	−	0.242641i	−0.0215049	−	0.00890762i
$743$	−14.4558	−	34.8995i	−0.530333	−	1.28034i	−0.931303	−	0.364247i	$-0.881327\pi$
$743$	−14.4558	−	34.8995i	−0.530333	−	1.28034i	0.400969	−	0.916092i	$-0.368673\pi$
$744$		−	26.4853i		−	0.970998i
$745$	−29.4558	+	12.2010i	−1.07918	+	0.447010i
$746$	−28.1421	−	28.1421i	−1.03036	−	1.03036i
$747$	17.6569			0.646031
$748$	−26.6066	−	11.9497i	−0.972834	−	0.436926i
$749$	9.02944			0.329928
$750$	−21.6569	−	21.6569i	−0.790797	−	0.790797i
$751$	20.5563	−	8.51472i	0.750112	−	0.310706i	0.0253246	−	0.999679i	$-0.491938\pi$
$751$	20.5563	−	8.51472i	0.750112	−	0.310706i	0.724787	+	0.688973i	$0.241938\pi$
$752$		−	24.7279i		−	0.901735i
$753$	−1.51472	−	3.65685i	−0.0551994	−	0.133263i
$754$		0			0
$755$	−1.65685	+	4.00000i	−0.0602991	+	0.145575i
$756$	15.3137	−	15.3137i	0.556954	−	0.556954i
$757$	24.6274	−	24.6274i	0.895099	−	0.895099i	−0.0998989	−	0.994998i	$-0.531852\pi$
$757$	24.6274	−	24.6274i	0.895099	−	0.895099i	0.994998	+	0.0998989i	$0.0318519\pi$
$758$	27.1924	−	65.6482i	0.987672	−	2.38445i
$759$	8.24264	+	3.41421i	0.299189	+	0.123928i
$760$	7.31371	+	17.6569i	0.265296	+	0.640481i
$761$		−	16.4853i		−	0.597591i	−0.954317	−	0.298795i	$-0.903415\pi$
$761$		−	16.4853i		−	0.597591i	0.954317	−	0.298795i	$-0.0965848\pi$
$762$	−17.0711	+	7.07107i	−0.618420	+	0.256158i
$763$	−2.72792	−	2.72792i	−0.0987574	−	0.0987574i
$764$	70.7696			2.56035
$765$	−4.72792	+	10.5269i	−0.170938	+	0.380601i
$766$	−48.2843			−1.74458
$767$	51.1127	+	51.1127i	1.84557	+	1.84557i
$768$	29.9706	−	12.4142i	1.08147	−	0.447959i
$769$		−	39.0711i		−	1.40894i	−0.709734	−	0.704469i	$-0.751185\pi$
$769$		−	39.0711i		−	1.40894i	0.709734	−	0.704469i	$-0.248815\pi$
$770$	2.82843	+	6.82843i	0.101929	+	0.246079i
$771$	−14.8284	−	6.14214i	−0.534033	−	0.221204i
$772$	6.26346	−	15.1213i	0.225427	−	0.544228i
$773$	−8.97056	+	8.97056i	−0.322649	+	0.322649i	−0.849782	−	0.527134i	$-0.823267\pi$
$773$	−8.97056	+	8.97056i	−0.322649	+	0.322649i	0.527134	+	0.849782i	$0.323267\pi$
$774$	−3.12132	+	3.12132i	−0.112194	+	0.112194i
$775$	−5.63604	+	13.6066i	−0.202452	+	0.488764i
$776$	40.2635	+	16.6777i	1.44537	+	0.598693i
$777$	−3.02944	−	7.31371i	−0.108680	−	0.262378i
$778$		−	16.4853i		−	0.591026i
$779$	12.8284	−	5.31371i	0.459626	−	0.190383i
$780$	30.6274	+	30.6274i	1.09664	+	1.09664i
$781$	−16.1421			−0.577611
$782$	−41.5061	+	15.7782i	−1.48425	+	0.564226i
$783$		0			0
$784$	−12.3640	−	12.3640i	−0.441570	−	0.441570i
$785$	−5.17157	+	2.14214i	−0.184581	+	0.0764561i
$786$			1.17157i			0.0417886i
$787$	−14.4645	−	34.9203i	−0.515603	−	1.24477i	−0.940580	−	0.339571i	$-0.889718\pi$
$787$	−14.4645	−	34.9203i	−0.515603	−	1.24477i	0.424978	−	0.905204i	$-0.360282\pi$
$788$	90.3762	+	37.4350i	3.21952	+	1.33357i
$789$	7.71573	−	18.6274i	0.274687	−	0.663154i
$790$	−26.9706	+	26.9706i	−0.959570	+	0.959570i
$791$	12.6863	−	12.6863i	0.451073	−	0.451073i
$792$	−5.70711	+	13.7782i	−0.202793	+	0.489586i
$793$	−9.65685	−	4.00000i	−0.342925	−	0.142044i
$794$	7.53553	+	18.1924i	0.267426	+	0.645624i
$795$			0.402020i			0.0142582i
$796$	−22.3137	+	9.24264i	−0.790888	+	0.327597i
$797$	−19.8284	−	19.8284i	−0.702359	−	0.702359i	0.262557	−	0.964916i	$-0.415434\pi$
$797$	−19.8284	−	19.8284i	−0.702359	−	0.702359i	−0.964916	+	0.262557i	$0.915434\pi$
$798$	−8.00000			−0.283197
$799$	−33.9706	−	1.00000i	−1.20179	−	0.0353775i
$800$	−4.21320			−0.148959
$801$	−19.1716	−	19.1716i	−0.677394	−	0.677394i
$802$	44.3345	−	18.3640i	1.56551	−	0.648454i
$803$		−	18.1421i		−	0.640222i
$804$	−11.2132	−	27.0711i	−0.395459	−	0.954723i
$805$	6.82843	+	2.82843i	0.240670	+	0.0996890i
$806$	34.9706	−	84.4264i	1.23179	−	2.97379i
$807$	0.0416306	−	0.0416306i	0.00146547	−	0.00146547i
$808$	−43.3848	+	43.3848i	−1.52627	+	1.52627i
$809$	11.7782	−	28.4350i	0.414099	−	0.999722i	−0.569927	−	0.821695i	$-0.693029\pi$
$809$	11.7782	−	28.4350i	0.414099	−	0.999722i	0.984026	−	0.178027i	$-0.0569715\pi$
$810$	−0.585786	−	0.242641i	−0.0205824	−	0.00852552i
$811$	−5.20101	−	12.5563i	−0.182632	−	0.440913i	0.805875	−	0.592085i	$-0.201695\pi$
$811$	−5.20101	−	12.5563i	−0.182632	−	0.440913i	−0.988507	+	0.151172i	$0.951695\pi$
$812$		0			0
$813$	5.41421	−	2.24264i	0.189885	−	0.0786528i
$814$	21.3137	+	21.3137i	0.747045	+	0.747045i
$815$	5.37258			0.188193
$816$	4.75736	+	12.5147i	0.166541	+	0.438103i
$817$	2.82843			0.0989541
$818$	−40.0416	−	40.0416i	−1.40002	−	1.40002i
$819$	12.4853	−	5.17157i	0.436271	−	0.180709i
$820$			28.7696i			1.00468i
$821$	15.7782	+	38.0919i	0.550662	+	1.32942i	0.916983	+	0.398927i	$0.130617\pi$
$821$	15.7782	+	38.0919i	0.550662	+	1.32942i	−0.366321	+	0.930489i	$0.619383\pi$
$822$	−15.3137	−	6.34315i	−0.534127	−	0.221243i
$823$	−17.9497	+	43.3345i	−0.625689	+	1.51055i	0.219242	+	0.975671i	$0.429642\pi$
$823$	−17.9497	+	43.3345i	−0.625689	+	1.51055i	−0.844931	+	0.534876i	$0.820358\pi$
$824$	−30.8995	+	30.8995i	−1.07643	+	1.07643i
$825$	−3.75736	+	3.75736i	−0.130814	+	0.130814i
$826$	10.5858	−	25.5563i	0.368327	−	0.889219i
$827$	−6.02082	−	2.49390i	−0.209364	−	0.0867215i	0.275537	−	0.961291i	$-0.411144\pi$
$827$	−6.02082	−	2.49390i	−0.209364	−	0.0867215i	−0.484901	+	0.874569i	$0.661144\pi$
$828$	11.9497	+	28.8492i	0.415282	+	1.00258i
$829$			34.9706i			1.21458i	0.794481	+	0.607289i	$0.207743\pi$
$829$			34.9706i			1.21458i	−0.794481	+	0.607289i	$0.792257\pi$
$830$	32.9706	−	13.6569i	1.14442	−	0.474036i
$831$	15.3137	+	15.3137i	0.531227	+	0.531227i
$832$	67.1127			2.32671
$833$	−17.4853	+	16.4853i	−0.605829	+	0.571181i
$834$	−54.2843			−1.87971
$835$	16.6274	+	16.6274i	0.575415	+	0.575415i
$836$	18.4853	−	7.65685i	0.639327	−	0.264818i
$837$			28.9706i			1.00137i
$838$	17.1421	+	41.3848i	0.592165	+	1.42961i
$839$	−2.41421	−	1.00000i	−0.0833479	−	0.0345238i	0.340620	−	0.940201i	$-0.389363\pi$
$839$	−2.41421	−	1.00000i	−0.0833479	−	0.0345238i	−0.423968	+	0.905677i	$0.639363\pi$
$840$	3.02944	−	7.31371i	0.104526	−	0.252347i
$841$	20.5061	−	20.5061i	0.707107	−	0.707107i
$842$	3.65685	−	3.65685i	0.126024	−	0.126024i
$843$	−2.52691	+	6.10051i	−0.0870315	+	0.210113i
$844$	−17.8284	−	7.38478i	−0.613680	−	0.254194i
$845$	19.6985	+	47.5563i	0.677648	+	1.63599i
$846$			36.3848i			1.25093i
$847$	−7.58579	+	3.14214i	−0.260651	+	0.107965i
$848$	−0.514719	−	0.514719i	−0.0176755	−	0.0176755i
$849$	−2.00000			−0.0686398
$850$	0.778175	−	26.4350i	0.0266912	−	0.906714i
$851$	30.1421			1.03326
$852$	25.5980	+	25.5980i	0.876972	+	0.876972i
$853$	−12.7782	+	5.29289i	−0.437516	+	0.181225i	−0.590559	−	0.806994i	$-0.701093\pi$
$853$	−12.7782	+	5.29289i	−0.437516	+	0.181225i	0.153043	+	0.988220i	$0.451093\pi$
$854$			4.00000i			0.136877i
$855$	−3.02944	−	7.31371i	−0.103605	−	0.250124i
$856$	34.0208	+	14.0919i	1.16281	+	0.481651i
$857$	−13.2218	+	31.9203i	−0.451649	+	1.09038i	0.520046	+	0.854138i	$0.325915\pi$
$857$	−13.2218	+	31.9203i	−0.451649	+	1.09038i	−0.971695	+	0.236239i	$0.924085\pi$
$858$	23.3137	−	23.3137i	0.795917	−	0.795917i
$859$	21.3137	−	21.3137i	0.727214	−	0.727214i	−0.242850	−	0.970064i	$-0.578082\pi$
$859$	21.3137	−	21.3137i	0.727214	−	0.727214i	0.970064	+	0.242850i	$0.0780822\pi$
$860$	−2.24264	+	5.41421i	−0.0764734	+	0.184623i
$861$	−5.31371	−	2.20101i	−0.181091	−	0.0750102i
$862$	−0.949747	−	2.29289i	−0.0323485	−	0.0780963i
$863$		−	25.5980i		−	0.871365i	−0.900100	−	0.435683i	$-0.856507\pi$
$863$		−	25.5980i		−	0.871365i	0.900100	−	0.435683i	$-0.143493\pi$
$864$	−7.65685	+	3.17157i	−0.260491	+	0.107899i
$865$	19.1716	+	19.1716i	0.651853	+	0.651853i
$866$	53.9411			1.83299
$867$	17.3848	−	6.02944i	0.590418	−	0.204770i
$868$	−22.9706			−0.779672
$869$	13.4853	+	13.4853i	0.457457	+	0.457457i
$870$		0			0
$871$		−	48.2843i		−	1.63605i
$872$	−6.02082	−	14.5355i	−0.203891	−	0.492235i
$873$	−16.6777	−	6.90812i	−0.564454	−	0.233804i
$874$	11.6569	−	28.1421i	0.394299	−	0.951922i
$875$	−8.97056	+	8.97056i	−0.303260	+	0.303260i
$876$	−28.7696	+	28.7696i	−0.972033	+	0.972033i
$877$	5.97918	−	14.4350i	0.201903	−	0.487436i	−0.790202	−	0.612846i	$-0.790025\pi$
$877$	5.97918	−	14.4350i	0.201903	−	0.487436i	0.992105	+	0.125410i	$0.0400246\pi$
$878$	71.4767	+	29.6066i	2.41222	+	0.999174i
$879$	5.37258	+	12.9706i	0.181213	+	0.437486i
$880$			8.48528i			0.286039i
$881$	21.5355	−	8.92031i	0.725551	−	0.300533i	0.0108284	−	0.999941i	$-0.496553\pi$
$881$	21.5355	−	8.92031i	0.725551	−	0.300533i	0.714722	+	0.699408i	$0.246553\pi$
$882$	18.1924	+	18.1924i	0.612570	+	0.612570i
$883$	−12.3431			−0.415380			−0.207690	−	0.978195i	$-0.566595\pi$
$883$	−12.3431			−0.415380			−0.207690	+	0.978195i	$0.566595\pi$
$884$	−3.17157	+	107.740i	−0.106672	+	3.62369i
$885$	−17.5391			−0.589571
$886$	−14.2426	−	14.2426i	−0.478491	−	0.478491i
$887$	−52.6985	+	21.8284i	−1.76944	+	0.732927i	−0.774489	+	0.632588i	$0.781993\pi$
$887$	−52.6985	+	21.8284i	−1.76944	+	0.732927i	−0.994953	+	0.100339i	$0.968007\pi$
$888$		−	32.2843i		−	1.08339i
$889$	2.92893	+	7.07107i	0.0982332	+	0.237156i
$890$	−50.6274	−	20.9706i	−1.69703	−	0.702935i
$891$	−0.121320	+	0.292893i	−0.00406438	+	0.00981229i
$892$	18.4853	−	18.4853i	0.618933	−	0.618933i
$893$	16.4853	−	16.4853i	0.551659	−	0.551659i
$894$	20.8284	−	50.2843i	0.696607	−	1.68176i
$895$	14.1421	+	5.85786i	0.472719	+	0.195807i
$896$	−8.51472	−	20.5563i	−0.284457	−	0.686739i
$897$		−	32.9706i		−	1.10086i
$898$	−36.9706	+	15.3137i	−1.23372	+	0.511025i
$899$		0			0
$900$	−18.5980			−0.619933
$901$	−0.727922	+	0.686292i	−0.0242506	+	0.0228637i
$902$	21.8995			0.729173
$903$	−0.828427	−	0.828427i	−0.0275683	−	0.0275683i
$904$	67.5980	−	28.0000i	2.24828	−	0.931266i
$905$			13.1716i			0.437838i
$906$	−2.82843	−	6.82843i	−0.0939682	−	0.226859i
$907$	−1.60660	−	0.665476i	−0.0533463	−	0.0220968i	0.355851	−	0.934543i	$-0.384191\pi$
$907$	−1.60660	−	0.665476i	−0.0533463	−	0.0220968i	−0.409197	+	0.912446i	$0.634191\pi$
$908$	−38.1716	+	92.1543i	−1.26677	+	3.05825i
$909$	17.9706	−	17.9706i	0.596046	−	0.596046i
$910$	19.3137	−	19.3137i	0.640243	−	0.640243i
$911$	−1.34315	+	3.24264i	−0.0445004	+	0.107433i	−0.944567	−	0.328319i	$-0.893518\pi$
$911$	−1.34315	+	3.24264i	−0.0445004	+	0.107433i	0.900066	+	0.435753i	$0.143518\pi$
$912$	−8.48528	−	3.51472i	−0.280976	−	0.116384i
$913$	−6.82843	−	16.4853i	−0.225988	−	0.545583i
$914$			61.9411i			2.04883i
$915$	2.34315	−	0.970563i	0.0774620	−	0.0320858i
$916$	50.3137	+	50.3137i	1.66241	+	1.66241i
$917$	0.485281			0.0160254
$918$	−18.4853	−	48.6274i	−0.610105	−	1.60494i
$919$	41.9411			1.38351			0.691755	−	0.722132i	$-0.256838\pi$
$919$	41.9411			1.38351			0.691755	+	0.722132i	$0.256838\pi$
$920$	21.3137	+	21.3137i	0.702692	+	0.702692i
$921$	−29.2132	+	12.1005i	−0.962608	+	0.398725i
$922$		−	66.7696i		−	2.19894i
$923$	22.8284	+	55.1127i	0.751407	+	1.81406i
$924$	−7.65685	−	3.17157i	−0.251892	−	0.104337i
$925$	−6.87006	+	16.5858i	−0.225886	+	0.545337i
$926$	−41.5563	+	41.5563i	−1.36563	+	1.36563i
$927$	12.7990	−	12.7990i	0.420374	−	0.420374i
$928$		0			0
$929$	−36.4853	−	15.1127i	−1.19704	−	0.495832i	−0.307001	−	0.951709i	$-0.599325\pi$
$929$	−36.4853	−	15.1127i	−1.19704	−	0.495832i	−0.890042	+	0.455878i	$0.849325\pi$
$930$	8.48528	+	20.4853i	0.278243	+	0.671739i
$931$		−	16.4853i		−	0.540283i
$932$	44.6274	−	18.4853i	1.46182	−	0.605506i
$933$	−0.384776	−	0.384776i	−0.0125970	−	0.0125970i
$934$	−16.9706			−0.555294
$935$	11.6569	+	0.343146i	0.381220	+	0.0112221i
$936$	55.1127			1.80141
$937$	25.2132	+	25.2132i	0.823679	+	0.823679i	0.986634	−	0.162954i	$-0.0521023\pi$
$937$	25.2132	+	25.2132i	0.823679	+	0.823679i	−0.162954	+	0.986634i	$0.552102\pi$
$938$	−17.0711	+	7.07107i	−0.557390	+	0.230879i
$939$		−	3.31371i		−	0.108139i
$940$	18.4853	+	44.6274i	0.602923	+	1.45559i
$941$	−10.5355	−	4.36396i	−0.343449	−	0.142261i	0.204290	−	0.978910i	$-0.434511\pi$
$941$	−10.5355	−	4.36396i	−0.343449	−	0.142261i	−0.547739	+	0.836649i	$0.684511\pi$
$942$	3.65685	−	8.82843i	0.119147	−	0.287646i
$943$	15.4853	−	15.4853i	0.504270	−	0.504270i
$944$	22.4558	−	22.4558i	0.730875	−	0.730875i
$945$	−3.31371	+	8.00000i	−0.107795	+	0.260240i
$946$	4.12132	+	1.70711i	0.133996	+	0.0555028i
$947$	8.02082	+	19.3640i	0.260641	+	0.629244i	0.998979	−	0.0451877i	$-0.0143886\pi$
$947$	8.02082	+	19.3640i	0.260641	+	0.629244i	−0.738337	+	0.674432i	$0.764389\pi$
$948$		−	42.7696i		−	1.38909i
$949$	−61.9411	+	25.6569i	−2.01069	+	0.832857i
$950$	12.8284	+	12.8284i	0.416209	+	0.416209i
$951$	34.2010			1.10904
$952$	18.4142	−	7.00000i	0.596808	−	0.226871i
$953$	12.0000			0.388718			0.194359	−	0.980930i	$-0.437737\pi$
$953$	12.0000			0.388718			0.194359	+	0.980930i	$0.437737\pi$
$954$	0.757359	+	0.757359i	0.0245204	+	0.0245204i
$955$	−26.1421	+	10.8284i	−0.845940	+	0.350400i
$956$			99.5391i			3.21932i
$957$		0			0
$958$	59.5772	+	24.6777i	1.92485	+	0.797299i
$959$	−2.62742	+	6.34315i	−0.0848437	+	0.204831i
$960$	−11.5147	+	11.5147i	−0.371636	+	0.371636i
$961$	−0.192388	+	0.192388i	−0.00620607	+	0.00620607i
$962$	42.6274	−	102.912i	1.37436	−	3.31801i
$963$	−14.0919	−	5.83705i	−0.454105	−	0.188096i
$964$	5.41421	+	13.0711i	0.174380	+	0.420991i
$965$			6.54416i			0.210664i
$966$	−11.6569	+	4.82843i	−0.375053	+	0.155352i
$967$	−10.8701	−	10.8701i	−0.349557	−	0.349557i	0.510387	−	0.859945i	$-0.329502\pi$
$967$	−10.8701	−	10.8701i	−0.349557	−	0.349557i	−0.859945	+	0.510387i	$0.829502\pi$
$968$	−33.4853			−1.07626
$969$	−5.17157	+	11.5147i	−0.166135	+	0.369906i
$970$	−36.4853			−1.17147
$971$	20.0416	+	20.0416i	0.643167	+	0.643167i	0.951333	−	0.308166i	$-0.0997152\pi$
$971$	20.0416	+	20.0416i	0.643167	+	0.643167i	−0.308166	+	0.951333i	$0.599715\pi$
$972$	−54.7990	+	22.6985i	−1.75768	+	0.728054i
$973$			22.4853i			0.720845i
$974$	3.94975	+	9.53553i	0.126558	+	0.305538i
$975$	18.1421	+	7.51472i	0.581013	+	0.240664i
$976$	−1.75736	+	4.24264i	−0.0562517	+	0.135804i
$977$	−1.61522	+	1.61522i	−0.0516756	+	0.0516756i	−0.732472	−	0.680797i	$-0.761634\pi$
$977$	−1.61522	+	1.61522i	−0.0516756	+	0.0516756i	0.680797	+	0.732472i	$0.261634\pi$
$978$	−6.48528	+	6.48528i	−0.207376	+	0.207376i
$979$	−10.4853	+	25.3137i	−0.335111	+	0.809030i
$980$	31.5563	+	13.0711i	1.00803	+	0.417540i
$981$	2.49390	+	6.02082i	0.0796242	+	0.192230i
$982$			46.1421i			1.47245i
$983$	3.34315	−	1.38478i	0.106630	−	0.0441675i	−0.328731	−	0.944424i	$-0.606621\pi$
$983$	3.34315	−	1.38478i	0.106630	−	0.0441675i	0.435361	+	0.900256i	$0.356621\pi$
$984$	−16.5858	−	16.5858i	−0.528736	−	0.528736i
$985$	−39.1127			−1.24623
$986$		0			0
$987$	−9.65685			−0.307381
$988$	−52.2843	−	52.2843i	−1.66338	−	1.66338i
$989$	4.12132	−	1.70711i	0.131050	−	0.0542828i
$990$		−	12.4853i		−	0.396808i
$991$	5.48528	+	13.2426i	0.174246	+	0.420666i	0.986741	−	0.162301i	$-0.0518916\pi$
$991$	5.48528	+	13.2426i	0.174246	+	0.420666i	−0.812496	+	0.582967i	$0.801892\pi$
$992$	8.12132	+	3.36396i	0.257852	+	0.106806i
$993$	−2.28427	+	5.51472i	−0.0724892	+	0.175004i
$994$	16.1421	−	16.1421i	0.511997	−	0.511997i
$995$	6.82843	−	6.82843i	0.216476	−	0.216476i
$996$	−15.3137	+	36.9706i	−0.485233	+	1.17146i
$997$	13.8995	+	5.75736i	0.440201	+	0.182337i	0.591766	−	0.806110i	$-0.298431\pi$
$997$	13.8995	+	5.75736i	0.440201	+	0.182337i	−0.151564	+	0.988447i	$0.548431\pi$
$998$	15.7279	+	37.9706i	0.497859	+	1.20194i
$999$			35.3137i			1.11728i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.m.a.87.1	✓	4
17.9	even	8	inner	731.2.m.a.689.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.m.a.87.1	✓	4	1.1	even	1	trivial
731.2.m.a.689.1	yes	4	17.9	even	8	inner

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:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.m (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.70711 - 1.70711i) q^{2} +(-1.00000 + 0.414214i) q^{3} +3.82843i q^{4} +(-0.585786 - 1.41421i) q^{5} +(2.41421 + 1.00000i) q^{6} +(0.414214 - 1.00000i) q^{7} +(3.12132 - 3.12132i) q^{8} +(-1.29289 + 1.29289i) q^{9} +O(q^{10})\)	\(q+(-1.70711 - 1.70711i) q^{2} +(-1.00000 + 0.414214i) q^{3} +3.82843i q^{4} +(-0.585786 - 1.41421i) q^{5} +(2.41421 + 1.00000i) q^{6} +(0.414214 - 1.00000i) q^{7} +(3.12132 - 3.12132i) q^{8} +(-1.29289 + 1.29289i) q^{9} +(-1.41421 + 3.41421i) q^{10} +(1.70711 + 0.707107i) q^{11} +(-1.58579 - 3.82843i) q^{12} -6.82843i q^{13} +(-2.41421 + 1.00000i) q^{14} +(1.17157 + 1.17157i) q^{15} -3.00000 q^{16} +(-0.121320 + 4.12132i) q^{17} +4.41421 q^{18} +(-2.00000 - 2.00000i) q^{19} +(5.41421 - 2.24264i) q^{20} +1.17157i q^{21} +(-1.70711 - 4.12132i) q^{22} +(-4.12132 - 1.70711i) q^{23} +(-1.82843 + 4.41421i) q^{24} +(1.87868 - 1.87868i) q^{25} +(-11.6569 + 11.6569i) q^{26} +(2.00000 - 4.82843i) q^{27} +(3.82843 + 1.58579i) q^{28} -4.00000i q^{30} +(-5.12132 + 2.12132i) q^{31} +(-1.12132 - 1.12132i) q^{32} -2.00000 q^{33} +(7.24264 - 6.82843i) q^{34} -1.65685 q^{35} +(-4.94975 - 4.94975i) q^{36} +(-6.24264 + 2.58579i) q^{37} +6.82843i q^{38} +(2.82843 + 6.82843i) q^{39} +(-6.24264 - 2.58579i) q^{40} +(-1.87868 + 4.53553i) q^{41} +(2.00000 - 2.00000i) q^{42} +(-0.707107 + 0.707107i) q^{43} +(-2.70711 + 6.53553i) q^{44} +(2.58579 + 1.07107i) q^{45} +(4.12132 + 9.94975i) q^{46} +8.24264i q^{47} +(3.00000 - 1.24264i) q^{48} +(4.12132 + 4.12132i) q^{49} -6.41421 q^{50} +(-1.58579 - 4.17157i) q^{51} +26.1421 q^{52} +(0.171573 + 0.171573i) q^{53} +(-11.6569 + 4.82843i) q^{54} -2.82843i q^{55} +(-1.82843 - 4.41421i) q^{56} +(2.82843 + 1.17157i) q^{57} +(-7.48528 + 7.48528i) q^{59} +(-4.48528 + 4.48528i) q^{60} +(0.585786 - 1.41421i) q^{61} +(12.3640 + 5.12132i) q^{62} +(0.757359 + 1.82843i) q^{63} +9.82843i q^{64} +(-9.65685 + 4.00000i) q^{65} +(3.41421 + 3.41421i) q^{66} +7.07107 q^{67} +(-15.7782 - 0.464466i) q^{68} +4.82843 q^{69} +(2.82843 + 2.82843i) q^{70} +(-8.07107 + 3.34315i) q^{71} +8.07107i q^{72} +(-3.75736 - 9.07107i) q^{73} +(15.0711 + 6.24264i) q^{74} +(-1.10051 + 2.65685i) q^{75} +(7.65685 - 7.65685i) q^{76} +(1.41421 - 1.41421i) q^{77} +(6.82843 - 16.4853i) q^{78} +(9.53553 + 3.94975i) q^{79} +(1.75736 + 4.24264i) q^{80} +0.171573i q^{81} +(10.9497 - 4.53553i) q^{82} +(-6.82843 - 6.82843i) q^{83} -4.48528 q^{84} +(5.89949 - 2.24264i) q^{85} +2.41421 q^{86} +(7.53553 - 3.12132i) q^{88} +14.8284i q^{89} +(-2.58579 - 6.24264i) q^{90} +(-6.82843 - 2.82843i) q^{91} +(6.53553 - 15.7782i) q^{92} +(4.24264 - 4.24264i) q^{93} +(14.0711 - 14.0711i) q^{94} +(-1.65685 + 4.00000i) q^{95} +(1.58579 + 0.656854i) q^{96} +(3.77817 + 9.12132i) q^{97} -14.0711i q^{98} +(-3.12132 + 1.29289i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 4 q^{3} - 8 q^{5} + 4 q^{6} - 4 q^{7} + 4 q^{8} - 8 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 - 4 * q^3 - 8 * q^5 + 4 * q^6 - 4 * q^7 + 4 * q^8 - 8 * q^9	\( 4 q - 4 q^{2} - 4 q^{3} - 8 q^{5} + 4 q^{6} - 4 q^{7} + 4 q^{8} - 8 q^{9} + 4 q^{11} - 12 q^{12} - 4 q^{14} + 16 q^{15} - 12 q^{16} + 8 q^{17} + 12 q^{18} - 8 q^{19} + 16 q^{20} - 4 q^{22} - 8 q^{23} + 4 q^{24} + 16 q^{25} - 24 q^{26} + 8 q^{27} + 4 q^{28} - 12 q^{31} + 4 q^{32} - 8 q^{33} + 12 q^{34} + 16 q^{35} - 8 q^{37} - 8 q^{40} - 16 q^{41} + 8 q^{42} - 8 q^{44} + 16 q^{45} + 8 q^{46} + 12 q^{48} + 8 q^{49} - 20 q^{50} - 12 q^{51} + 48 q^{52} + 12 q^{53} - 24 q^{54} + 4 q^{56} + 4 q^{59} + 16 q^{60} + 8 q^{61} + 24 q^{62} + 20 q^{63} - 16 q^{65} + 8 q^{66} - 32 q^{68} + 8 q^{69} - 4 q^{71} - 32 q^{73} + 32 q^{74} - 44 q^{75} + 8 q^{76} + 16 q^{78} + 24 q^{79} + 24 q^{80} + 24 q^{82} - 16 q^{83} + 16 q^{84} - 16 q^{85} + 4 q^{86} + 16 q^{88} - 16 q^{90} - 16 q^{91} + 12 q^{92} + 28 q^{94} + 16 q^{95} + 12 q^{96} - 16 q^{97} - 4 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - 4 * q^3 - 8 * q^5 + 4 * q^6 - 4 * q^7 + 4 * q^8 - 8 * q^9 + 4 * q^11 - 12 * q^12 - 4 * q^14 + 16 * q^15 - 12 * q^16 + 8 * q^17 + 12 * q^18 - 8 * q^19 + 16 * q^20 - 4 * q^22 - 8 * q^23 + 4 * q^24 + 16 * q^25 - 24 * q^26 + 8 * q^27 + 4 * q^28 - 12 * q^31 + 4 * q^32 - 8 * q^33 + 12 * q^34 + 16 * q^35 - 8 * q^37 - 8 * q^40 - 16 * q^41 + 8 * q^42 - 8 * q^44 + 16 * q^45 + 8 * q^46 + 12 * q^48 + 8 * q^49 - 20 * q^50 - 12 * q^51 + 48 * q^52 + 12 * q^53 - 24 * q^54 + 4 * q^56 + 4 * q^59 + 16 * q^60 + 8 * q^61 + 24 * q^62 + 20 * q^63 - 16 * q^65 + 8 * q^66 - 32 * q^68 + 8 * q^69 - 4 * q^71 - 32 * q^73 + 32 * q^74 - 44 * q^75 + 8 * q^76 + 16 * q^78 + 24 * q^79 + 24 * q^80 + 24 * q^82 - 16 * q^83 + 16 * q^84 - 16 * q^85 + 4 * q^86 + 16 * q^88 - 16 * q^90 - 16 * q^91 + 12 * q^92 + 28 * q^94 + 16 * q^95 + 12 * q^96 - 16 * q^97 - 4 * q^99

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