LMFDB - Embedded newform 578.2.d.a.155.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [578,2,Mod(155,578)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(578, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([7])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("578.155"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 578 = 2 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	578.d (of order $8$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,-4,0,0,4,-8,0,4,0,8,0,0,0,-8,-4,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(18)] == traces)

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

Self dual:	no
Analytic conductor:	$4.61535323683$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 34)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			155.1
Root			$0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	578.155
Dual form			578.2.d.a.179.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.70711 + 0.707107i) q^{3} +1.00000i q^{4} +(1.41421 + 3.41421i) q^{5} +(1.70711 + 0.707107i) q^{6} +(-0.585786 + 1.41421i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.292893 - 0.292893i) q^{9} +(1.41421 - 3.41421i) q^{10} +(4.12132 + 1.70711i) q^{11} +(-0.707107 - 1.70711i) q^{12} +0.828427i q^{13} +(1.41421 - 0.585786i) q^{14} +(-4.82843 - 4.82843i) q^{15} -1.00000 q^{16} -0.414214 q^{18} +(-0.585786 - 0.585786i) q^{19} +(-3.41421 + 1.41421i) q^{20} -2.82843i q^{21} +(-1.70711 - 4.12132i) q^{22} +(-2.82843 - 1.17157i) q^{23} +(-0.707107 + 1.70711i) q^{24} +(-6.12132 + 6.12132i) q^{25} +(0.585786 - 0.585786i) q^{26} +(1.82843 - 4.41421i) q^{27} +(-1.41421 - 0.585786i) q^{28} +(0.585786 + 1.41421i) q^{29} +6.82843i q^{30} +(-3.41421 + 1.41421i) q^{31} +(0.707107 + 0.707107i) q^{32} -8.24264 q^{33} -5.65685 q^{35} +(0.292893 + 0.292893i) q^{36} +(2.00000 - 0.828427i) q^{37} +0.828427i q^{38} +(-0.585786 - 1.41421i) q^{39} +(3.41421 + 1.41421i) q^{40} +(-4.29289 + 10.3640i) q^{41} +(-2.00000 + 2.00000i) q^{42} +(1.24264 - 1.24264i) q^{43} +(-1.70711 + 4.12132i) q^{44} +(1.41421 + 0.585786i) q^{45} +(1.17157 + 2.82843i) q^{46} -9.65685i q^{47} +(1.70711 - 0.707107i) q^{48} +(3.29289 + 3.29289i) q^{49} +8.65685 q^{50} -0.828427 q^{52} +(-0.585786 - 0.585786i) q^{53} +(-4.41421 + 1.82843i) q^{54} +16.4853i q^{55} +(0.585786 + 1.41421i) q^{56} +(1.41421 + 0.585786i) q^{57} +(0.585786 - 1.41421i) q^{58} +(-0.414214 + 0.414214i) q^{59} +(4.82843 - 4.82843i) q^{60} +(-2.82843 + 6.82843i) q^{61} +(3.41421 + 1.41421i) q^{62} +(0.242641 + 0.585786i) q^{63} -1.00000i q^{64} +(-2.82843 + 1.17157i) q^{65} +(5.82843 + 5.82843i) q^{66} -7.41421 q^{67} +5.65685 q^{69} +(4.00000 + 4.00000i) q^{70} +(2.00000 - 0.828427i) q^{71} -0.414214i q^{72} +(2.05025 + 4.94975i) q^{73} +(-2.00000 - 0.828427i) q^{74} +(6.12132 - 14.7782i) q^{75} +(0.585786 - 0.585786i) q^{76} +(-4.82843 + 4.82843i) q^{77} +(-0.585786 + 1.41421i) q^{78} +(-4.82843 - 2.00000i) q^{79} +(-1.41421 - 3.41421i) q^{80} +10.0711i q^{81} +(10.3640 - 4.29289i) q^{82} +(-4.41421 - 4.41421i) q^{83} +2.82843 q^{84} -1.75736 q^{86} +(-2.00000 - 2.00000i) q^{87} +(4.12132 - 1.70711i) q^{88} -15.0711i q^{89} +(-0.585786 - 1.41421i) q^{90} +(-1.17157 - 0.485281i) q^{91} +(1.17157 - 2.82843i) q^{92} +(4.82843 - 4.82843i) q^{93} +(-6.82843 + 6.82843i) q^{94} +(1.17157 - 2.82843i) q^{95} +(-1.70711 - 0.707107i) q^{96} +(2.12132 + 5.12132i) q^{97} -4.65685i q^{98} +(1.70711 - 0.707107i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{3} + 4 q^{6} - 8 q^{7} + 4 q^{9} + 8 q^{11} - 8 q^{15} - 4 q^{16} + 4 q^{18} - 8 q^{19} - 8 q^{20} - 4 q^{22} - 16 q^{25} + 8 q^{26} - 4 q^{27} + 8 q^{29} - 8 q^{31} - 16 q^{33} + 4 q^{36} + 8 q^{37}+ \cdots + 4 q^{99}+O(q^{100}) $ 4 * q - 4 * q^3 + 4 * q^6 - 8 * q^7 + 4 * q^9 + 8 * q^11 - 8 * q^15 - 4 * q^16 + 4 * q^18 - 8 * q^19 - 8 * q^20 - 4 * q^22 - 16 * q^25 + 8 * q^26 - 4 * q^27 + 8 * q^29 - 8 * q^31 - 16 * q^33 + 4 * q^36 + 8 * q^37 - 8 * q^39 + 8 * q^40 - 20 * q^41 - 8 * q^42 - 12 * q^43 - 4 * q^44 + 16 * q^46 + 4 * q^48 + 16 * q^49 + 12 * q^50 + 8 * q^52 - 8 * q^53 - 12 * q^54 + 8 * q^56 + 8 * q^58 + 4 * q^59 + 8 * q^60 + 8 * q^62 - 16 * q^63 + 12 * q^66 - 24 * q^67 + 16 * q^70 + 8 * q^71 + 28 * q^73 - 8 * q^74 + 16 * q^75 + 8 * q^76 - 8 * q^77 - 8 * q^78 - 8 * q^79 + 16 * q^82 - 12 * q^83 - 24 * q^86 - 8 * q^87 + 8 * q^88 - 8 * q^90 - 16 * q^91 + 16 * q^92 + 8 * q^93 - 16 * q^94 + 16 * q^95 - 4 * q^96 + 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/578\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{7}{8}\right)$

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 $

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	−1.70711	+	0.707107i	−0.985599	+	0.408248i	−0.816497	−	0.577350i	$-0.804087\pi$
$3$	−1.70711	+	0.707107i	−0.985599	+	0.408248i	−0.169102	+	0.985599i	$0.554087\pi$
$4$			1.00000i			0.500000i
$5$	1.41421	+	3.41421i	0.632456	+	1.52688i	0.836526	+	0.547927i	$0.184583\pi$
$5$	1.41421	+	3.41421i	0.632456	+	1.52688i	−0.204071	+	0.978956i	$0.565417\pi$
$6$	1.70711	+	0.707107i	0.696923	+	0.288675i
$7$	−0.585786	+	1.41421i	−0.221406	+	0.534522i	−0.995081	−	0.0990602i	$-0.968416\pi$
$7$	−0.585786	+	1.41421i	−0.221406	+	0.534522i	0.773675	+	0.633583i	$0.218416\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	0.292893	−	0.292893i	0.0976311	−	0.0976311i
$10$	1.41421	−	3.41421i	0.447214	−	1.07967i
$11$	4.12132	+	1.70711i	1.24262	+	0.514712i	0.904534	−	0.426401i	$-0.140219\pi$
$11$	4.12132	+	1.70711i	1.24262	+	0.514712i	0.338091	+	0.941113i	$0.390219\pi$
$12$	−0.707107	−	1.70711i	−0.204124	−	0.492799i
$13$			0.828427i			0.229764i	0.993379	+	0.114882i	$0.0366490\pi$
$13$			0.828427i			0.229764i	−0.993379	+	0.114882i	$0.963351\pi$
$14$	1.41421	−	0.585786i	0.377964	−	0.156558i
$15$	−4.82843	−	4.82843i	−1.24669	−	1.24669i
$16$	−1.00000			−0.250000
$17$		0			0
$17$		0			0
$18$	−0.414214			−0.0976311
$19$	−0.585786	−	0.585786i	−0.134389	−	0.134389i	0.636713	−	0.771101i	$-0.280294\pi$
$19$	−0.585786	−	0.585786i	−0.134389	−	0.134389i	−0.771101	+	0.636713i	$0.780294\pi$
$20$	−3.41421	+	1.41421i	−0.763441	+	0.316228i
$21$		−	2.82843i		−	0.617213i
$22$	−1.70711	−	4.12132i	−0.363956	−	0.878668i
$23$	−2.82843	−	1.17157i	−0.589768	−	0.244290i	0.0677829	−	0.997700i	$-0.478407\pi$
$23$	−2.82843	−	1.17157i	−0.589768	−	0.244290i	−0.657551	+	0.753410i	$0.728407\pi$
$24$	−0.707107	+	1.70711i	−0.144338	+	0.348462i
$25$	−6.12132	+	6.12132i	−1.22426	+	1.22426i
$26$	0.585786	−	0.585786i	0.114882	−	0.114882i
$27$	1.82843	−	4.41421i	0.351881	−	0.849516i
$28$	−1.41421	−	0.585786i	−0.267261	−	0.110703i
$29$	0.585786	+	1.41421i	0.108778	+	0.262613i	0.968890	−	0.247492i	$-0.0796065\pi$
$29$	0.585786	+	1.41421i	0.108778	+	0.262613i	−0.860112	+	0.510105i	$0.829606\pi$
$30$			6.82843i			1.24669i
$31$	−3.41421	+	1.41421i	−0.613211	+	0.254000i	−0.667601	−	0.744520i	$-0.732679\pi$
$31$	−3.41421	+	1.41421i	−0.613211	+	0.254000i	0.0543898	+	0.998520i	$0.482679\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	−8.24264			−1.43486
$34$		0			0
$35$	−5.65685			−0.956183
$36$	0.292893	+	0.292893i	0.0488155	+	0.0488155i
$37$	2.00000	−	0.828427i	0.328798	−	0.136193i	−0.212177	−	0.977231i	$-0.568055\pi$
$37$	2.00000	−	0.828427i	0.328798	−	0.136193i	0.540975	+	0.841039i	$0.318055\pi$
$38$			0.828427i			0.134389i
$39$	−0.585786	−	1.41421i	−0.0938009	−	0.226455i
$40$	3.41421	+	1.41421i	0.539835	+	0.223607i
$41$	−4.29289	+	10.3640i	−0.670437	+	1.61858i	0.110432	+	0.993884i	$0.464777\pi$
$41$	−4.29289	+	10.3640i	−0.670437	+	1.61858i	−0.780869	+	0.624695i	$0.785223\pi$
$42$	−2.00000	+	2.00000i	−0.308607	+	0.308607i
$43$	1.24264	−	1.24264i	0.189501	−	0.189501i	−0.605979	−	0.795480i	$-0.707219\pi$
$43$	1.24264	−	1.24264i	0.189501	−	0.189501i	0.795480	+	0.605979i	$0.207219\pi$
$44$	−1.70711	+	4.12132i	−0.257356	+	0.621312i
$45$	1.41421	+	0.585786i	0.210819	+	0.0873239i
$46$	1.17157	+	2.82843i	0.172739	+	0.417029i
$47$		−	9.65685i		−	1.40860i	−0.709904	−	0.704298i	$-0.751262\pi$
$47$		−	9.65685i		−	1.40860i	0.709904	−	0.704298i	$-0.248738\pi$
$48$	1.70711	−	0.707107i	0.246400	−	0.102062i
$49$	3.29289	+	3.29289i	0.470413	+	0.470413i
$50$	8.65685			1.22426
$51$		0			0
$52$	−0.828427			−0.114882
$53$	−0.585786	−	0.585786i	−0.0804640	−	0.0804640i	0.665729	−	0.746193i	$-0.268121\pi$
$53$	−0.585786	−	0.585786i	−0.0804640	−	0.0804640i	−0.746193	+	0.665729i	$0.768121\pi$
$54$	−4.41421	+	1.82843i	−0.600698	+	0.248817i
$55$			16.4853i			2.22287i
$56$	0.585786	+	1.41421i	0.0782790	+	0.188982i
$57$	1.41421	+	0.585786i	0.187317	+	0.0775893i
$58$	0.585786	−	1.41421i	0.0769175	−	0.185695i
$59$	−0.414214	+	0.414214i	−0.0539260	+	0.0539260i	−0.733556	−	0.679630i	$-0.762141\pi$
$59$	−0.414214	+	0.414214i	−0.0539260	+	0.0539260i	0.679630	+	0.733556i	$0.262141\pi$
$60$	4.82843	−	4.82843i	0.623347	−	0.623347i
$61$	−2.82843	+	6.82843i	−0.362143	+	0.874291i	0.632843	+	0.774280i	$0.281888\pi$
$61$	−2.82843	+	6.82843i	−0.362143	+	0.874291i	−0.994986	+	0.100011i	$0.968112\pi$
$62$	3.41421	+	1.41421i	0.433606	+	0.179605i
$63$	0.242641	+	0.585786i	0.0305699	+	0.0738022i
$64$		−	1.00000i		−	0.125000i
$65$	−2.82843	+	1.17157i	−0.350823	+	0.145316i
$66$	5.82843	+	5.82843i	0.717430	+	0.717430i
$67$	−7.41421			−0.905790			−0.452895	−	0.891564i	$-0.649609\pi$
$67$	−7.41421			−0.905790			−0.452895	+	0.891564i	$0.649609\pi$
$68$		0			0
$69$	5.65685			0.681005
$70$	4.00000	+	4.00000i	0.478091	+	0.478091i
$71$	2.00000	−	0.828427i	0.237356	−	0.0983162i	−0.260835	−	0.965383i	$-0.583998\pi$
$71$	2.00000	−	0.828427i	0.237356	−	0.0983162i	0.498191	+	0.867067i	$0.333998\pi$
$72$		−	0.414214i		−	0.0488155i
$73$	2.05025	+	4.94975i	0.239964	+	0.579324i	0.997279	−	0.0737261i	$-0.0234891\pi$
$73$	2.05025	+	4.94975i	0.239964	+	0.579324i	−0.757315	+	0.653050i	$0.773489\pi$
$74$	−2.00000	−	0.828427i	−0.232495	−	0.0963027i
$75$	6.12132	−	14.7782i	0.706829	−	1.70644i
$76$	0.585786	−	0.585786i	0.0671943	−	0.0671943i
$77$	−4.82843	+	4.82843i	−0.550250	+	0.550250i
$78$	−0.585786	+	1.41421i	−0.0663273	+	0.160128i
$79$	−4.82843	−	2.00000i	−0.543240	−	0.225018i	0.0941507	−	0.995558i	$-0.469986\pi$
$79$	−4.82843	−	2.00000i	−0.543240	−	0.225018i	−0.637391	+	0.770540i	$0.719986\pi$
$80$	−1.41421	−	3.41421i	−0.158114	−	0.381721i
$81$			10.0711i			1.11901i
$82$	10.3640	−	4.29289i	1.14451	−	0.474071i
$83$	−4.41421	−	4.41421i	−0.484523	−	0.484523i	0.422050	−	0.906573i	$-0.361311\pi$
$83$	−4.41421	−	4.41421i	−0.484523	−	0.484523i	−0.906573	+	0.422050i	$0.861311\pi$
$84$	2.82843			0.308607
$85$		0			0
$86$	−1.75736			−0.189501
$87$	−2.00000	−	2.00000i	−0.214423	−	0.214423i
$88$	4.12132	−	1.70711i	0.439334	−	0.181978i
$89$		−	15.0711i		−	1.59753i	−0.601643	−	0.798765i	$-0.705487\pi$
$89$		−	15.0711i		−	1.59753i	0.601643	−	0.798765i	$-0.294513\pi$
$90$	−0.585786	−	1.41421i	−0.0617473	−	0.149071i
$91$	−1.17157	−	0.485281i	−0.122814	−	0.0508713i
$92$	1.17157	−	2.82843i	0.122145	−	0.294884i
$93$	4.82843	−	4.82843i	0.500685	−	0.500685i
$94$	−6.82843	+	6.82843i	−0.704298	+	0.704298i
$95$	1.17157	−	2.82843i	0.120201	−	0.290191i
$96$	−1.70711	−	0.707107i	−0.174231	−	0.0721688i
$97$	2.12132	+	5.12132i	0.215387	+	0.519991i	0.994235	−	0.107222i	$-0.0341955\pi$
$97$	2.12132	+	5.12132i	0.215387	+	0.519991i	−0.778848	+	0.627213i	$0.784196\pi$
$98$		−	4.65685i		−	0.470413i
$99$	1.70711	−	0.707107i	0.171571	−	0.0710669i
$100$	−6.12132	−	6.12132i	−0.612132	−	0.612132i
$101$	4.34315			0.432159			0.216080	−	0.976376i	$-0.430673\pi$
$101$	4.34315			0.432159			0.216080	+	0.976376i	$0.430673\pi$
$102$		0			0
$103$	12.4853			1.23021			0.615106	−	0.788445i	$-0.289113\pi$
$103$	12.4853			1.23021			0.615106	+	0.788445i	$0.289113\pi$
$104$	0.585786	+	0.585786i	0.0574411	+	0.0574411i
$105$	9.65685	−	4.00000i	0.942412	−	0.390360i
$106$			0.828427i			0.0804640i
$107$	−4.46447	−	10.7782i	−0.431596	−	1.04197i	−0.978773	−	0.204948i	$-0.934297\pi$
$107$	−4.46447	−	10.7782i	−0.431596	−	1.04197i	0.547177	−	0.837017i	$-0.315703\pi$
$108$	4.41421	+	1.82843i	0.424758	+	0.175940i
$109$	3.75736	−	9.07107i	0.359890	−	0.868851i	−0.635425	−	0.772163i	$-0.719175\pi$
$109$	3.75736	−	9.07107i	0.359890	−	0.868851i	0.995315	−	0.0966881i	$-0.0308249\pi$
$110$	11.6569	−	11.6569i	1.11144	−	1.11144i
$111$	−2.82843	+	2.82843i	−0.268462	+	0.268462i
$112$	0.585786	−	1.41421i	0.0553516	−	0.133631i
$113$	−8.53553	−	3.53553i	−0.802955	−	0.332595i	−0.0568160	−	0.998385i	$-0.518095\pi$
$113$	−8.53553	−	3.53553i	−0.802955	−	0.332595i	−0.746140	+	0.665790i	$0.768095\pi$
$114$	−0.585786	−	1.41421i	−0.0548639	−	0.132453i
$115$		−	11.3137i		−	1.05501i
$116$	−1.41421	+	0.585786i	−0.131306	+	0.0543889i
$117$	0.242641	+	0.242641i	0.0224321	+	0.0224321i
$118$	0.585786			0.0539260
$119$		0			0
$120$	−6.82843			−0.623347
$121$	6.29289	+	6.29289i	0.572081	+	0.572081i
$122$	6.82843	−	2.82843i	0.618217	−	0.256074i
$123$		−	20.7279i		−	1.86897i
$124$	−1.41421	−	3.41421i	−0.127000	−	0.306605i
$125$	−12.4853	−	5.17157i	−1.11672	−	0.462560i
$126$	0.242641	−	0.585786i	0.0216162	−	0.0521860i
$127$	9.17157	−	9.17157i	0.813845	−	0.813845i	−0.171363	−	0.985208i	$-0.554817\pi$
$127$	9.17157	−	9.17157i	0.813845	−	0.813845i	0.985208	+	0.171363i	$0.0548169\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	−1.24264	+	3.00000i	−0.109408	+	0.264135i
$130$	2.82843	+	1.17157i	0.248069	+	0.102754i
$131$	−0.0502525	−	0.121320i	−0.00439058	−	0.0105998i	0.921669	−	0.387977i	$-0.126826\pi$
$131$	−0.0502525	−	0.121320i	−0.00439058	−	0.0105998i	−0.926060	+	0.377377i	$0.876826\pi$
$132$		−	8.24264i		−	0.717430i
$133$	1.17157	−	0.485281i	0.101588	−	0.0420792i
$134$	5.24264	+	5.24264i	0.452895	+	0.452895i
$135$	17.6569			1.51966
$136$		0			0
$137$	−2.34315			−0.200188			−0.100094	−	0.994978i	$-0.531914\pi$
$137$	−2.34315			−0.200188			−0.100094	+	0.994978i	$0.531914\pi$
$138$	−4.00000	−	4.00000i	−0.340503	−	0.340503i
$139$	−1.70711	+	0.707107i	−0.144795	+	0.0599760i	−0.453904	−	0.891051i	$-0.649969\pi$
$139$	−1.70711	+	0.707107i	−0.144795	+	0.0599760i	0.309109	+	0.951027i	$0.399969\pi$
$140$		−	5.65685i		−	0.478091i
$141$	6.82843	+	16.4853i	0.575057	+	1.38831i
$142$	−2.00000	−	0.828427i	−0.167836	−	0.0695201i
$143$	−1.41421	+	3.41421i	−0.118262	+	0.285511i
$144$	−0.292893	+	0.292893i	−0.0244078	+	0.0244078i
$145$	−4.00000	+	4.00000i	−0.332182	+	0.332182i
$146$	2.05025	−	4.94975i	0.169680	−	0.409644i
$147$	−7.94975	−	3.29289i	−0.655684	−	0.271593i
$148$	0.828427	+	2.00000i	0.0680963	+	0.164399i
$149$			15.6569i			1.28266i	0.767265	+	0.641330i	$0.221617\pi$
$149$			15.6569i			1.28266i	−0.767265	+	0.641330i	$0.778383\pi$
$150$	−14.7782	+	6.12132i	−1.20663	+	0.499804i
$151$	15.6569	+	15.6569i	1.27414	+	1.27414i	0.943897	+	0.330240i	$0.107130\pi$
$151$	15.6569	+	15.6569i	1.27414	+	1.27414i	0.330240	+	0.943897i	$0.392870\pi$
$152$	−0.828427			−0.0671943
$153$		0			0
$154$	6.82843			0.550250
$155$	−9.65685	−	9.65685i	−0.775657	−	0.775657i
$156$	1.41421	−	0.585786i	0.113228	−	0.0469005i
$157$			13.3137i			1.06255i	0.847200	+	0.531275i	$0.178287\pi$
$157$			13.3137i			1.06255i	−0.847200	+	0.531275i	$0.821713\pi$
$158$	2.00000	+	4.82843i	0.159111	+	0.384129i
$159$	1.41421	+	0.585786i	0.112154	+	0.0464559i
$160$	−1.41421	+	3.41421i	−0.111803	+	0.269917i
$161$	3.31371	−	3.31371i	0.261157	−	0.261157i
$162$	7.12132	−	7.12132i	0.559504	−	0.559504i
$163$	−8.70711	+	21.0208i	−0.681993	+	1.64648i	0.0783260	+	0.996928i	$0.475042\pi$
$163$	−8.70711	+	21.0208i	−0.681993	+	1.64648i	−0.760319	+	0.649550i	$0.774958\pi$
$164$	−10.3640	−	4.29289i	−0.809289	−	0.335219i
$165$	−11.6569	−	28.1421i	−0.907485	−	2.19086i
$166$			6.24264i			0.484523i
$167$	−18.2426	+	7.55635i	−1.41166	+	0.584728i	−0.952750	−	0.303756i	$-0.901759\pi$
$167$	−18.2426	+	7.55635i	−1.41166	+	0.584728i	−0.458908	+	0.888484i	$0.651759\pi$
$168$	−2.00000	−	2.00000i	−0.154303	−	0.154303i
$169$	12.3137			0.947208
$170$		0			0
$171$	−0.343146			−0.0262410
$172$	1.24264	+	1.24264i	0.0947505	+	0.0947505i
$173$	−5.41421	+	2.24264i	−0.411635	+	0.170505i	−0.578884	−	0.815410i	$-0.696512\pi$
$173$	−5.41421	+	2.24264i	−0.411635	+	0.170505i	0.167249	+	0.985915i	$0.446512\pi$
$174$			2.82843i			0.214423i
$175$	−5.07107	−	12.2426i	−0.383337	−	0.925457i
$176$	−4.12132	−	1.70711i	−0.310656	−	0.128678i
$177$	0.414214	−	1.00000i	0.0311342	−	0.0751646i
$178$	−10.6569	+	10.6569i	−0.798765	+	0.798765i
$179$	18.2426	−	18.2426i	1.36352	−	1.36352i	0.494132	−	0.869387i	$-0.335486\pi$
$179$	18.2426	−	18.2426i	1.36352	−	1.36352i	0.869387	−	0.494132i	$-0.164514\pi$
$180$	−0.585786	+	1.41421i	−0.0436619	+	0.105409i
$181$	5.65685	+	2.34315i	0.420471	+	0.174165i	0.582879	−	0.812559i	$-0.301926\pi$
$181$	5.65685	+	2.34315i	0.420471	+	0.174165i	−0.162408	+	0.986724i	$0.551926\pi$
$182$	0.485281	+	1.17157i	0.0359714	+	0.0868428i
$183$		−	13.6569i		−	1.00954i
$184$	−2.82843	+	1.17157i	−0.208514	+	0.0863695i
$185$	5.65685	+	5.65685i	0.415900	+	0.415900i
$186$	−6.82843			−0.500685
$187$		0			0
$188$	9.65685			0.704298
$189$	5.17157	+	5.17157i	0.376177	+	0.376177i
$190$	−2.82843	+	1.17157i	−0.205196	+	0.0849948i
$191$			2.82843i			0.204658i	0.994751	+	0.102329i	$0.0326294\pi$
$191$			2.82843i			0.204658i	−0.994751	+	0.102329i	$0.967371\pi$
$192$	0.707107	+	1.70711i	0.0510310	+	0.123200i
$193$	11.3640	+	4.70711i	0.817996	+	0.338825i	0.752139	−	0.659004i	$-0.229022\pi$
$193$	11.3640	+	4.70711i	0.817996	+	0.338825i	0.0658565	+	0.997829i	$0.479022\pi$
$194$	2.12132	−	5.12132i	0.152302	−	0.367689i
$195$	4.00000	−	4.00000i	0.286446	−	0.286446i
$196$	−3.29289	+	3.29289i	−0.235207	+	0.235207i
$197$	7.65685	−	18.4853i	0.545528	−	1.31702i	−0.375246	−	0.926925i	$-0.622442\pi$
$197$	7.65685	−	18.4853i	0.545528	−	1.31702i	0.920774	−	0.390096i	$-0.127558\pi$
$198$	−1.70711	−	0.707107i	−0.121319	−	0.0502519i
$199$	8.00000	+	19.3137i	0.567105	+	1.36911i	0.903985	+	0.427565i	$0.140628\pi$
$199$	8.00000	+	19.3137i	0.567105	+	1.36911i	−0.336880	+	0.941548i	$0.609372\pi$
$200$			8.65685i			0.612132i
$201$	12.6569	−	5.24264i	0.892746	−	0.369787i
$202$	−3.07107	−	3.07107i	−0.216080	−	0.216080i
$203$	−2.34315			−0.164457
$204$		0			0
$205$	−41.4558			−2.89540
$206$	−8.82843	−	8.82843i	−0.615106	−	0.615106i
$207$	−1.17157	+	0.485281i	−0.0814299	+	0.0337294i
$208$		−	0.828427i		−	0.0574411i
$209$	−1.41421	−	3.41421i	−0.0978232	−	0.236166i
$210$	−9.65685	−	4.00000i	−0.666386	−	0.276026i
$211$	0.0502525	−	0.121320i	0.00345953	−	0.00835204i	−0.922140	−	0.386856i	$-0.873561\pi$
$211$	0.0502525	−	0.121320i	0.00345953	−	0.00835204i	0.925600	+	0.378504i	$0.123561\pi$
$212$	0.585786	−	0.585786i	0.0402320	−	0.0402320i
$213$	−2.82843	+	2.82843i	−0.193801	+	0.193801i
$214$	−4.46447	+	10.7782i	−0.305185	+	0.736781i
$215$	6.00000	+	2.48528i	0.409197	+	0.169495i
$216$	−1.82843	−	4.41421i	−0.124409	−	0.300349i
$217$		−	5.65685i		−	0.384012i
$218$	−9.07107	+	3.75736i	−0.614370	+	0.254480i
$219$	−7.00000	−	7.00000i	−0.473016	−	0.473016i
$220$	−16.4853			−1.11144
$221$		0			0
$222$	4.00000			0.268462
$223$	17.3137	+	17.3137i	1.15941	+	1.15941i	0.984602	+	0.174809i	$0.0559309\pi$
$223$	17.3137	+	17.3137i	1.15941	+	1.15941i	0.174809	+	0.984602i	$0.444069\pi$
$224$	−1.41421	+	0.585786i	−0.0944911	+	0.0391395i
$225$			3.58579i			0.239052i
$226$	3.53553	+	8.53553i	0.235180	+	0.567775i
$227$	18.7782	+	7.77817i	1.24635	+	0.516256i	0.905694	−	0.423932i	$-0.139350\pi$
$227$	18.7782	+	7.77817i	1.24635	+	0.516256i	0.340657	+	0.940188i	$0.389350\pi$
$228$	−0.585786	+	1.41421i	−0.0387947	+	0.0936586i
$229$	−13.0711	+	13.0711i	−0.863760	+	0.863760i	−0.991773	−	0.128012i	$-0.959140\pi$
$229$	−13.0711	+	13.0711i	−0.863760	+	0.863760i	0.128012	+	0.991773i	$0.459140\pi$
$230$	−8.00000	+	8.00000i	−0.527504	+	0.527504i
$231$	4.82843	−	11.6569i	0.317687	−	0.766965i
$232$	1.41421	+	0.585786i	0.0928477	+	0.0384588i
$233$	−4.02082	−	9.70711i	−0.263412	−	0.635934i	0.735733	−	0.677272i	$-0.236838\pi$
$233$	−4.02082	−	9.70711i	−0.263412	−	0.635934i	−0.999145	+	0.0413382i	$0.986838\pi$
$234$		−	0.343146i		−	0.0224321i
$235$	32.9706	−	13.6569i	2.15076	−	0.890875i
$236$	−0.414214	−	0.414214i	−0.0269630	−	0.0269630i
$237$	9.65685			0.627280
$238$		0			0
$239$	21.1716			1.36948			0.684738	−	0.728790i	$-0.259917\pi$
$239$	21.1716			1.36948			0.684738	+	0.728790i	$0.259917\pi$
$240$	4.82843	+	4.82843i	0.311674	+	0.311674i
$241$	18.3640	−	7.60660i	1.18293	−	0.489984i	0.297481	−	0.954728i	$-0.403853\pi$
$241$	18.3640	−	7.60660i	1.18293	−	0.489984i	0.885445	+	0.464743i	$0.153853\pi$
$242$		−	8.89949i		−	0.572081i
$243$	−1.63604	−	3.94975i	−0.104952	−	0.253376i
$244$	−6.82843	−	2.82843i	−0.437145	−	0.181071i
$245$	−6.58579	+	15.8995i	−0.420750	+	1.01578i
$246$	−14.6569	+	14.6569i	−0.934487	+	0.934487i
$247$	0.485281	−	0.485281i	0.0308777	−	0.0308777i
$248$	−1.41421	+	3.41421i	−0.0898027	+	0.216803i
$249$	10.6569	+	4.41421i	0.675351	+	0.279739i
$250$	5.17157	+	12.4853i	0.327079	+	0.789639i
$251$			18.7279i			1.18210i	0.806636	+	0.591048i	$0.201286\pi$
$251$			18.7279i			1.18210i	−0.806636	+	0.591048i	$0.798714\pi$
$252$	−0.585786	+	0.242641i	−0.0369011	+	0.0152849i
$253$	−9.65685	−	9.65685i	−0.607121	−	0.607121i
$254$	−12.9706			−0.813845
$255$		0			0
$256$	1.00000			0.0625000
$257$	−5.82843	−	5.82843i	−0.363567	−	0.363567i	0.501557	−	0.865124i	$-0.332761\pi$
$257$	−5.82843	−	5.82843i	−0.363567	−	0.363567i	−0.865124	+	0.501557i	$0.832761\pi$
$258$	3.00000	−	1.24264i	0.186772	−	0.0773634i
$259$			3.31371i			0.205904i
$260$	−1.17157	−	2.82843i	−0.0726579	−	0.175412i
$261$	0.585786	+	0.242641i	0.0362593	+	0.0150191i
$262$	−0.0502525	+	0.121320i	−0.00310461	+	0.00749520i
$263$	−5.65685	+	5.65685i	−0.348817	+	0.348817i	−0.859669	−	0.510852i	$-0.829330\pi$
$263$	−5.65685	+	5.65685i	−0.348817	+	0.348817i	0.510852	+	0.859669i	$0.329330\pi$
$264$	−5.82843	+	5.82843i	−0.358715	+	0.358715i
$265$	1.17157	−	2.82843i	0.0719691	−	0.173749i
$266$	−1.17157	−	0.485281i	−0.0718337	−	0.0297545i
$267$	10.6569	+	25.7279i	0.652189	+	1.57452i
$268$		−	7.41421i		−	0.452895i
$269$	7.07107	−	2.92893i	0.431131	−	0.178580i	−0.156555	−	0.987669i	$-0.550039\pi$
$269$	7.07107	−	2.92893i	0.431131	−	0.178580i	0.587686	+	0.809089i	$0.300039\pi$
$270$	−12.4853	−	12.4853i	−0.759830	−	0.759830i
$271$	−14.8284			−0.900763			−0.450381	−	0.892836i	$-0.648712\pi$
$271$	−14.8284			−0.900763			−0.450381	+	0.892836i	$0.648712\pi$
$272$		0			0
$273$	2.34315			0.141814
$274$	1.65685	+	1.65685i	0.100094	+	0.100094i
$275$	−35.6777	+	14.7782i	−2.15144	+	0.891157i
$276$			5.65685i			0.340503i
$277$	−9.07107	−	21.8995i	−0.545028	−	1.31581i	−0.921137	−	0.389238i	$-0.872738\pi$
$277$	−9.07107	−	21.8995i	−0.545028	−	1.31581i	0.376110	−	0.926575i	$-0.377262\pi$
$278$	1.70711	+	0.707107i	0.102385	+	0.0424094i
$279$	−0.585786	+	1.41421i	−0.0350701	+	0.0846668i
$280$	−4.00000	+	4.00000i	−0.239046	+	0.239046i
$281$	−10.1421	+	10.1421i	−0.605029	+	0.605029i	−0.941643	−	0.336614i	$-0.890718\pi$
$281$	−10.1421	+	10.1421i	−0.605029	+	0.605029i	0.336614	+	0.941643i	$0.390718\pi$
$282$	6.82843	−	16.4853i	0.406627	−	0.981684i
$283$	1.05025	+	0.435029i	0.0624310	+	0.0258598i	0.413680	−	0.910422i	$-0.364243\pi$
$283$	1.05025	+	0.435029i	0.0624310	+	0.0258598i	−0.351249	+	0.936282i	$0.614243\pi$
$284$	0.828427	+	2.00000i	0.0491581	+	0.118678i
$285$			5.65685i			0.335083i
$286$	3.41421	−	1.41421i	0.201887	−	0.0836242i
$287$	−12.1421	−	12.1421i	−0.716728	−	0.716728i
$288$	0.414214			0.0244078
$289$		0			0
$290$	5.65685			0.332182
$291$	−7.24264	−	7.24264i	−0.424571	−	0.424571i
$292$	−4.94975	+	2.05025i	−0.289662	+	0.119982i
$293$			22.0000i			1.28525i	0.766179	+	0.642627i	$0.222155\pi$
$293$			22.0000i			1.28525i	−0.766179	+	0.642627i	$0.777845\pi$
$294$	3.29289	+	7.94975i	0.192045	+	0.463639i
$295$	−2.00000	−	0.828427i	−0.116445	−	0.0482329i
$296$	0.828427	−	2.00000i	0.0481513	−	0.116248i
$297$	15.0711	−	15.0711i	0.874512	−	0.874512i
$298$	11.0711	−	11.0711i	0.641330	−	0.641330i
$299$	0.970563	−	2.34315i	0.0561291	−	0.135508i
$300$	14.7782	+	6.12132i	0.853218	+	0.353415i
$301$	1.02944	+	2.48528i	0.0593358	+	0.143249i
$302$		−	22.1421i		−	1.27414i
$303$	−7.41421	+	3.07107i	−0.425935	+	0.176428i
$304$	0.585786	+	0.585786i	0.0335972	+	0.0335972i
$305$	−27.3137			−1.56398
$306$		0			0
$307$	6.34315			0.362022			0.181011	−	0.983481i	$-0.442063\pi$
$307$	6.34315			0.362022			0.181011	+	0.983481i	$0.442063\pi$
$308$	−4.82843	−	4.82843i	−0.275125	−	0.275125i
$309$	−21.3137	+	8.82843i	−1.21249	+	0.502232i
$310$			13.6569i			0.775657i
$311$	5.75736	+	13.8995i	0.326470	+	0.788168i	0.998849	+	0.0479613i	$0.0152724\pi$
$311$	5.75736	+	13.8995i	0.326470	+	0.788168i	−0.672379	+	0.740207i	$0.734728\pi$
$312$	−1.41421	−	0.585786i	−0.0800641	−	0.0331636i
$313$	−5.19239	+	12.5355i	−0.293491	+	0.708550i	0.706509	+	0.707705i	$0.250269\pi$
$313$	−5.19239	+	12.5355i	−0.293491	+	0.708550i	−1.00000		0.000845724i	$0.999731\pi$
$314$	9.41421	−	9.41421i	0.531275	−	0.531275i
$315$	−1.65685	+	1.65685i	−0.0933532	+	0.0933532i
$316$	2.00000	−	4.82843i	0.112509	−	0.271620i
$317$	20.4853	+	8.48528i	1.15057	+	0.476581i	0.874724	−	0.484622i	$-0.161043\pi$
$317$	20.4853	+	8.48528i	1.15057	+	0.476581i	0.275844	+	0.961202i	$0.411043\pi$
$318$	−0.585786	−	1.41421i	−0.0328493	−	0.0793052i
$319$			6.82843i			0.382319i
$320$	3.41421	−	1.41421i	0.190860	−	0.0790569i
$321$	15.2426	+	15.2426i	0.850761	+	0.850761i
$322$	−4.68629			−0.261157
$323$		0			0
$324$	−10.0711			−0.559504
$325$	−5.07107	−	5.07107i	−0.281292	−	0.281292i
$326$	21.0208	−	8.70711i	1.16424	−	0.482242i
$327$			18.1421i			1.00326i
$328$	4.29289	+	10.3640i	0.237035	+	0.572254i
$329$	13.6569	+	5.65685i	0.752927	+	0.311872i
$330$	−11.6569	+	28.1421i	−0.641689	+	1.54917i
$331$	−19.5858	+	19.5858i	−1.07653	+	1.07653i	−0.0797144	+	0.996818i	$0.525401\pi$
$331$	−19.5858	+	19.5858i	−1.07653	+	1.07653i	−0.996818	+	0.0797144i	$0.974599\pi$
$332$	4.41421	−	4.41421i	0.242261	−	0.242261i
$333$	0.343146	−	0.828427i	0.0188043	−	0.0453975i
$334$	18.2426	+	7.55635i	0.998193	+	0.413465i
$335$	−10.4853	−	25.3137i	−0.572872	−	1.38304i
$336$			2.82843i			0.154303i
$337$	10.7782	−	4.46447i	0.587125	−	0.243195i	−0.0692885	−	0.997597i	$-0.522073\pi$
$337$	10.7782	−	4.46447i	0.587125	−	0.243195i	0.656413	+	0.754402i	$0.272073\pi$
$338$	−8.70711	−	8.70711i	−0.473604	−	0.473604i
$339$	17.0711			0.927173
$340$		0			0
$341$	−16.4853			−0.892728
$342$	0.242641	+	0.242641i	0.0131205	+	0.0131205i
$343$	−16.4853	+	6.82843i	−0.890122	+	0.368700i
$344$		−	1.75736i		−	0.0947505i
$345$	8.00000	+	19.3137i	0.430706	+	1.03982i
$346$	5.41421	+	2.24264i	0.291070	+	0.120565i
$347$	6.19239	−	14.9497i	0.332425	−	0.802544i	−0.665974	−	0.745975i	$-0.731984\pi$
$347$	6.19239	−	14.9497i	0.332425	−	0.802544i	0.998399	−	0.0565694i	$-0.0180162\pi$
$348$	2.00000	−	2.00000i	0.107211	−	0.107211i
$349$	13.8995	−	13.8995i	0.744023	−	0.744023i	−0.229327	−	0.973350i	$-0.573652\pi$
$349$	13.8995	−	13.8995i	0.744023	−	0.744023i	0.973350	+	0.229327i	$0.0736524\pi$
$350$	−5.07107	+	12.2426i	−0.271060	+	0.654397i
$351$	3.65685	+	1.51472i	0.195188	+	0.0808497i
$352$	1.70711	+	4.12132i	0.0909891	+	0.219667i
$353$			14.3848i			0.765624i	0.923826	+	0.382812i	$0.125044\pi$
$353$			14.3848i			0.765624i	−0.923826	+	0.382812i	$0.874956\pi$
$354$	−1.00000	+	0.414214i	−0.0531494	+	0.0220152i
$355$	5.65685	+	5.65685i	0.300235	+	0.300235i
$356$	15.0711			0.798765
$357$		0			0
$358$	−25.7990			−1.36352
$359$	−8.00000	−	8.00000i	−0.422224	−	0.422224i	0.463745	−	0.885969i	$-0.346505\pi$
$359$	−8.00000	−	8.00000i	−0.422224	−	0.422224i	−0.885969	+	0.463745i	$0.846505\pi$
$360$	1.41421	−	0.585786i	0.0745356	−	0.0308737i
$361$		−	18.3137i		−	0.963879i
$362$	−2.34315	−	5.65685i	−0.123153	−	0.297318i
$363$	−15.1924	−	6.29289i	−0.797394	−	0.330291i
$364$	0.485281	−	1.17157i	0.0254357	−	0.0614071i
$365$	−14.0000	+	14.0000i	−0.732793	+	0.732793i
$366$	−9.65685	+	9.65685i	−0.504772	+	0.504772i
$367$	−7.17157	+	17.3137i	−0.374353	+	0.903768i	0.618649	+	0.785668i	$0.287680\pi$
$367$	−7.17157	+	17.3137i	−0.374353	+	0.903768i	−0.993002	+	0.118100i	$0.962320\pi$
$368$	2.82843	+	1.17157i	0.147442	+	0.0610725i
$369$	1.77817	+	4.29289i	0.0925681	+	0.223479i
$370$		−	8.00000i		−	0.415900i
$371$	1.17157	−	0.485281i	0.0608250	−	0.0251946i
$372$	4.82843	+	4.82843i	0.250342	+	0.250342i
$373$	−10.4853			−0.542907			−0.271454	−	0.962452i	$-0.587504\pi$
$373$	−10.4853			−0.542907			−0.271454	+	0.962452i	$0.587504\pi$
$374$		0			0
$375$	24.9706			1.28947
$376$	−6.82843	−	6.82843i	−0.352149	−	0.352149i
$377$	−1.17157	+	0.485281i	−0.0603391	+	0.0249933i
$378$		−	7.31371i		−	0.376177i
$379$	−3.56497	−	8.60660i	−0.183120	−	0.442091i	0.805486	−	0.592614i	$-0.201904\pi$
$379$	−3.56497	−	8.60660i	−0.183120	−	0.442091i	−0.988606	+	0.150523i	$0.951904\pi$
$380$	2.82843	+	1.17157i	0.145095	+	0.0601004i
$381$	−9.17157	+	22.1421i	−0.469874	+	1.13438i
$382$	2.00000	−	2.00000i	0.102329	−	0.102329i
$383$	21.3137	−	21.3137i	1.08908	−	1.08908i	0.0934562	−	0.995623i	$-0.470208\pi$
$383$	21.3137	−	21.3137i	1.08908	−	1.08908i	0.995623	−	0.0934562i	$-0.0297915\pi$
$384$	0.707107	−	1.70711i	0.0360844	−	0.0871154i
$385$	−23.3137	−	9.65685i	−1.18818	−	0.492159i
$386$	−4.70711	−	11.3640i	−0.239585	−	0.578410i
$387$		−	0.727922i		−	0.0370024i
$388$	−5.12132	+	2.12132i	−0.259996	+	0.107694i
$389$	−2.24264	−	2.24264i	−0.113706	−	0.113706i	0.647964	−	0.761671i	$-0.275621\pi$
$389$	−2.24264	−	2.24264i	−0.113706	−	0.113706i	−0.761671	+	0.647964i	$0.775621\pi$
$390$	−5.65685			−0.286446
$391$		0			0
$392$	4.65685			0.235207
$393$	0.171573	+	0.171573i	0.00865471	+	0.00865471i
$394$	−18.4853	+	7.65685i	−0.931275	+	0.385747i
$395$		−	19.3137i		−	0.971778i
$396$	0.707107	+	1.70711i	0.0355335	+	0.0857853i
$397$	7.65685	+	3.17157i	0.384286	+	0.159177i	0.566459	−	0.824090i	$-0.308313\pi$
$397$	7.65685	+	3.17157i	0.384286	+	0.159177i	−0.182173	+	0.983267i	$0.558313\pi$
$398$	8.00000	−	19.3137i	0.401004	−	0.968109i
$399$	−1.65685	+	1.65685i	−0.0829465	+	0.0829465i
$400$	6.12132	−	6.12132i	0.306066	−	0.306066i
$401$	9.19239	−	22.1924i	0.459046	−	1.10823i	−0.509738	−	0.860330i	$-0.670258\pi$
$401$	9.19239	−	22.1924i	0.459046	−	1.10823i	0.968784	−	0.247905i	$-0.0797422\pi$
$402$	−12.6569	−	5.24264i	−0.631267	−	0.261479i
$403$	−1.17157	−	2.82843i	−0.0583602	−	0.140894i
$404$			4.34315i			0.216080i
$405$	−34.3848	+	14.2426i	−1.70859	+	0.707723i
$406$	1.65685	+	1.65685i	0.0822283	+	0.0822283i
$407$	9.65685			0.478672
$408$		0			0
$409$	15.5563			0.769212			0.384606	−	0.923081i	$-0.374337\pi$
$409$	15.5563			0.769212			0.384606	+	0.923081i	$0.374337\pi$
$410$	29.3137	+	29.3137i	1.44770	+	1.44770i
$411$	4.00000	−	1.65685i	0.197305	−	0.0817266i
$412$			12.4853i			0.615106i
$413$	−0.343146	−	0.828427i	−0.0168851	−	0.0407642i
$414$	1.17157	+	0.485281i	0.0575797	+	0.0238503i
$415$	8.82843	−	21.3137i	0.433370	−	1.04625i
$416$	−0.585786	+	0.585786i	−0.0287205	+	0.0287205i
$417$	2.41421	−	2.41421i	0.118225	−	0.118225i
$418$	−1.41421	+	3.41421i	−0.0691714	+	0.166995i
$419$	−15.9497	−	6.60660i	−0.779196	−	0.322754i	−0.0426051	−	0.999092i	$-0.513566\pi$
$419$	−15.9497	−	6.60660i	−0.779196	−	0.322754i	−0.736591	+	0.676338i	$0.763566\pi$
$420$	4.00000	+	9.65685i	0.195180	+	0.471206i
$421$			15.6569i			0.763068i	0.924355	+	0.381534i	$0.124604\pi$
$421$			15.6569i			0.763068i	−0.924355	+	0.381534i	$0.875396\pi$
$422$	−0.121320	+	0.0502525i	−0.00590578	+	0.00244625i
$423$	−2.82843	−	2.82843i	−0.137523	−	0.137523i
$424$	−0.828427			−0.0402320
$425$		0			0
$426$	4.00000			0.193801
$427$	−8.00000	−	8.00000i	−0.387147	−	0.387147i
$428$	10.7782	−	4.46447i	0.520983	−	0.215798i
$429$		−	6.82843i		−	0.329680i
$430$	−2.48528	−	6.00000i	−0.119851	−	0.289346i
$431$	−13.3137	−	5.51472i	−0.641299	−	0.265635i	0.0382464	−	0.999268i	$-0.487823\pi$
$431$	−13.3137	−	5.51472i	−0.641299	−	0.265635i	−0.679545	+	0.733634i	$0.737823\pi$
$432$	−1.82843	+	4.41421i	−0.0879702	+	0.212379i
$433$	9.17157	−	9.17157i	0.440758	−	0.440758i	−0.451509	−	0.892267i	$-0.649114\pi$
$433$	9.17157	−	9.17157i	0.440758	−	0.440758i	0.892267	+	0.451509i	$0.149114\pi$
$434$	−4.00000	+	4.00000i	−0.192006	+	0.192006i
$435$	4.00000	−	9.65685i	0.191785	−	0.463011i
$436$	9.07107	+	3.75736i	0.434425	+	0.179945i
$437$	0.970563	+	2.34315i	0.0464283	+	0.112088i
$438$			9.89949i			0.473016i
$439$	−21.3137	+	8.82843i	−1.01725	+	0.421358i	−0.828094	−	0.560590i	$-0.810575\pi$
$439$	−21.3137	+	8.82843i	−1.01725	+	0.421358i	−0.189154	+	0.981947i	$0.560575\pi$
$440$	11.6569	+	11.6569i	0.555719	+	0.555719i
$441$	1.92893			0.0918539
$442$		0			0
$443$	−36.8701			−1.75175			−0.875875	−	0.482539i	$-0.839715\pi$
$443$	−36.8701			−1.75175			−0.875875	+	0.482539i	$0.839715\pi$
$444$	−2.82843	−	2.82843i	−0.134231	−	0.134231i
$445$	51.4558	−	21.3137i	2.43924	−	1.01037i
$446$		−	24.4853i		−	1.15941i
$447$	−11.0711	−	26.7279i	−0.523644	−	1.26419i
$448$	1.41421	+	0.585786i	0.0668153	+	0.0276758i
$449$	−2.12132	+	5.12132i	−0.100111	+	0.241690i	−0.965998	−	0.258551i	$-0.916755\pi$
$449$	−2.12132	+	5.12132i	−0.100111	+	0.241690i	0.865886	+	0.500241i	$0.166755\pi$
$450$	2.53553	−	2.53553i	0.119526	−	0.119526i
$451$	−35.3848	+	35.3848i	−1.66620	+	1.66620i
$452$	3.53553	−	8.53553i	0.166298	−	0.401478i
$453$	−37.7990	−	15.6569i	−1.77595	−	0.735623i
$454$	−7.77817	−	18.7782i	−0.365048	−	0.881303i
$455$		−	4.68629i		−	0.219697i
$456$	1.41421	−	0.585786i	0.0662266	−	0.0274320i
$457$	−3.51472	−	3.51472i	−0.164412	−	0.164412i	0.620106	−	0.784518i	$-0.287089\pi$
$457$	−3.51472	−	3.51472i	−0.164412	−	0.164412i	−0.784518	+	0.620106i	$0.787089\pi$
$458$	18.4853			0.863760
$459$		0			0
$460$	11.3137			0.527504
$461$	24.7279	+	24.7279i	1.15169	+	1.15169i	0.986213	+	0.165481i	$0.0529177\pi$
$461$	24.7279	+	24.7279i	1.15169	+	1.15169i	0.165481	+	0.986213i	$0.447082\pi$
$462$	−11.6569	+	4.82843i	−0.542326	+	0.224639i
$463$		−	3.31371i		−	0.154001i	−0.997031	−	0.0770005i	$-0.975466\pi$
$463$		−	3.31371i		−	0.154001i	0.997031	−	0.0770005i	$-0.0245343\pi$
$464$	−0.585786	−	1.41421i	−0.0271945	−	0.0656532i
$465$	23.3137	+	9.65685i	1.08115	+	0.447826i
$466$	−4.02082	+	9.70711i	−0.186261	+	0.449673i
$467$	1.75736	−	1.75736i	0.0813209	−	0.0813209i	−0.665276	−	0.746597i	$-0.731686\pi$
$467$	1.75736	−	1.75736i	0.0813209	−	0.0813209i	0.746597	+	0.665276i	$0.231686\pi$
$468$	−0.242641	+	0.242641i	−0.0112161	+	0.0112161i
$469$	4.34315	−	10.4853i	0.200548	−	0.484165i
$470$	−32.9706	−	13.6569i	−1.52082	−	0.629944i
$471$	−9.41421	−	22.7279i	−0.433784	−	1.04725i
$472$			0.585786i			0.0269630i
$473$	7.24264	−	3.00000i	0.333017	−	0.137940i
$474$	−6.82843	−	6.82843i	−0.313640	−	0.313640i
$475$	7.17157			0.329054
$476$		0			0
$477$	−0.343146			−0.0157116
$478$	−14.9706	−	14.9706i	−0.684738	−	0.684738i
$479$	22.9706	−	9.51472i	1.04955	−	0.434739i	0.209820	−	0.977740i	$-0.432712\pi$
$479$	22.9706	−	9.51472i	1.04955	−	0.434739i	0.839732	+	0.543001i	$0.182712\pi$
$480$		−	6.82843i		−	0.311674i
$481$	0.686292	+	1.65685i	0.0312922	+	0.0755461i
$482$	−18.3640	−	7.60660i	−0.836456	−	0.346471i
$483$	−3.31371	+	8.00000i	−0.150779	+	0.364013i
$484$	−6.29289	+	6.29289i	−0.286041	+	0.286041i
$485$	−14.4853	+	14.4853i	−0.657743	+	0.657743i
$486$	−1.63604	+	3.94975i	−0.0742122	+	0.179164i
$487$	20.4853	+	8.48528i	0.928277	+	0.384505i	0.795024	−	0.606577i	$-0.207458\pi$
$487$	20.4853	+	8.48528i	0.928277	+	0.384505i	0.133252	+	0.991082i	$0.457458\pi$
$488$	2.82843	+	6.82843i	0.128037	+	0.309108i
$489$		−	42.0416i		−	1.90119i
$490$	15.8995	−	6.58579i	0.718266	−	0.297516i
$491$	−10.9289	−	10.9289i	−0.493216	−	0.493216i	0.416102	−	0.909318i	$-0.363396\pi$
$491$	−10.9289	−	10.9289i	−0.493216	−	0.493216i	−0.909318	+	0.416102i	$0.863396\pi$
$492$	20.7279			0.934487
$493$		0			0
$494$	−0.686292			−0.0308777
$495$	4.82843	+	4.82843i	0.217022	+	0.217022i
$496$	3.41421	−	1.41421i	0.153303	−	0.0635001i
$497$			3.31371i			0.148640i
$498$	−4.41421	−	10.6569i	−0.197806	−	0.477545i
$499$	−34.0208	−	14.0919i	−1.52298	−	0.630839i	−0.544795	−	0.838569i	$-0.683392\pi$
$499$	−34.0208	−	14.0919i	−1.52298	−	0.630839i	−0.978186	+	0.207730i	$0.933392\pi$
$500$	5.17157	−	12.4853i	0.231280	−	0.558359i
$501$	25.7990	−	25.7990i	1.15261	−	1.15261i
$502$	13.2426	−	13.2426i	0.591048	−	0.591048i
$503$	−4.62742	+	11.1716i	−0.206326	+	0.498116i	−0.992839	−	0.119458i	$-0.961884\pi$
$503$	−4.62742	+	11.1716i	−0.206326	+	0.498116i	0.786513	+	0.617574i	$0.211884\pi$
$504$	0.585786	+	0.242641i	0.0260930	+	0.0108081i
$505$	6.14214	+	14.8284i	0.273321	+	0.659856i
$506$			13.6569i			0.607121i
$507$	−21.0208	+	8.70711i	−0.933567	+	0.386696i
$508$	9.17157	+	9.17157i	0.406923	+	0.406923i
$509$	16.6274			0.736997			0.368499	−	0.929628i	$-0.379872\pi$
$509$	16.6274			0.736997			0.368499	+	0.929628i	$0.379872\pi$
$510$		0			0
$511$	−8.20101			−0.362791
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−3.65685	+	1.51472i	−0.161454	+	0.0668765i
$514$			8.24264i			0.363567i
$515$	17.6569	+	42.6274i	0.778054	+	1.87839i
$516$	−3.00000	−	1.24264i	−0.132068	−	0.0547042i
$517$	16.4853	−	39.7990i	0.725022	−	1.75036i
$518$	2.34315	−	2.34315i	0.102952	−	0.102952i
$519$	7.65685	−	7.65685i	0.336099	−	0.336099i
$520$	−1.17157	+	2.82843i	−0.0513769	+	0.124035i
$521$	32.5061	+	13.4645i	1.42412	+	0.589889i	0.955892	−	0.293720i	$-0.0948932\pi$
$521$	32.5061	+	13.4645i	1.42412	+	0.589889i	0.468226	+	0.883609i	$0.344893\pi$
$522$	−0.242641	−	0.585786i	−0.0106201	−	0.0256392i
$523$		−	23.2132i		−	1.01504i	−0.861639	−	0.507521i	$-0.830562\pi$
$523$		−	23.2132i		−	1.01504i	0.861639	−	0.507521i	$-0.169438\pi$
$524$	0.121320	−	0.0502525i	0.00529990	−	0.00219529i
$525$	17.3137	+	17.3137i	0.755632	+	0.755632i
$526$	8.00000			0.348817
$527$		0			0
$528$	8.24264			0.358715
$529$	−9.63604	−	9.63604i	−0.418958	−	0.418958i
$530$	−2.82843	+	1.17157i	−0.122859	+	0.0508899i
$531$			0.242641i			0.0105297i
$532$	0.485281	+	1.17157i	0.0210396	+	0.0507941i
$533$	−8.58579	−	3.55635i	−0.371892	−	0.154043i
$534$	10.6569	−	25.7279i	0.461167	−	1.11336i
$535$	30.4853	−	30.4853i	1.31799	−	1.31799i
$536$	−5.24264	+	5.24264i	−0.226448	+	0.226448i
$537$	−18.2426	+	44.0416i	−0.787228	+	1.90054i
$538$	−7.07107	−	2.92893i	−0.304855	−	0.126275i
$539$	7.94975	+	19.1924i	0.342420	+	0.826675i
$540$			17.6569i			0.759830i
$541$	18.8284	−	7.79899i	0.809497	−	0.335305i	0.0607439	−	0.998153i	$-0.480653\pi$
$541$	18.8284	−	7.79899i	0.809497	−	0.335305i	0.748753	+	0.662849i	$0.230653\pi$
$542$	10.4853	+	10.4853i	0.450381	+	0.450381i
$543$	−11.3137			−0.485518
$544$		0			0
$545$	36.2843			1.55425
$546$	−1.65685	−	1.65685i	−0.0709068	−	0.0709068i
$547$	−22.6777	+	9.39340i	−0.969627	+	0.401633i	−0.810573	−	0.585637i	$-0.800844\pi$
$547$	−22.6777	+	9.39340i	−0.969627	+	0.401633i	−0.159054	+	0.987270i	$0.550844\pi$
$548$		−	2.34315i		−	0.100094i
$549$	1.17157	+	2.82843i	0.0500015	+	0.120714i
$550$	35.6777	+	14.7782i	1.52130	+	0.630143i
$551$	0.485281	−	1.17157i	0.0206737	−	0.0499107i
$552$	4.00000	−	4.00000i	0.170251	−	0.170251i
$553$	5.65685	−	5.65685i	0.240554	−	0.240554i
$554$	−9.07107	+	21.8995i	−0.385393	+	0.930420i
$555$	−13.6569	−	5.65685i	−0.579701	−	0.240120i
$556$	−0.707107	−	1.70711i	−0.0299880	−	0.0723975i
$557$		−	41.1127i		−	1.74200i	−0.491282	−	0.871000i	$-0.663472\pi$
$557$		−	41.1127i		−	1.74200i	0.491282	−	0.871000i	$-0.336528\pi$
$558$	1.41421	−	0.585786i	0.0598684	−	0.0247983i
$559$	1.02944	+	1.02944i	0.0435406	+	0.0435406i
$560$	5.65685			0.239046
$561$		0			0
$562$	14.3431			0.605029
$563$	5.92893	+	5.92893i	0.249875	+	0.249875i	0.820919	−	0.571044i	$-0.193462\pi$
$563$	5.92893	+	5.92893i	0.249875	+	0.249875i	−0.571044	+	0.820919i	$0.693462\pi$
$564$	−16.4853	+	6.82843i	−0.694156	+	0.287529i
$565$		−	34.1421i		−	1.43637i
$566$	−0.435029	−	1.05025i	−0.0182856	−	0.0441454i
$567$	−14.2426	−	5.89949i	−0.598135	−	0.247755i
$568$	0.828427	−	2.00000i	0.0347600	−	0.0839181i
$569$	−3.48528	+	3.48528i	−0.146111	+	0.146111i	−0.776378	−	0.630267i	$-0.782945\pi$
$569$	−3.48528	+	3.48528i	−0.146111	+	0.146111i	0.630267	+	0.776378i	$0.282945\pi$
$570$	4.00000	−	4.00000i	0.167542	−	0.167542i
$571$	−0.920310	+	2.22183i	−0.0385138	+	0.0929805i	−0.941966	−	0.335708i	$-0.891024\pi$
$571$	−0.920310	+	2.22183i	−0.0385138	+	0.0929805i	0.903452	+	0.428689i	$0.141024\pi$
$572$	−3.41421	−	1.41421i	−0.142755	−	0.0591312i
$573$	−2.00000	−	4.82843i	−0.0835512	−	0.201710i
$574$			17.1716i			0.716728i
$575$	24.4853	−	10.1421i	1.02111	−	0.422956i
$576$	−0.292893	−	0.292893i	−0.0122039	−	0.0122039i
$577$	−16.6274			−0.692208			−0.346104	−	0.938196i	$-0.612496\pi$
$577$	−16.6274			−0.692208			−0.346104	+	0.938196i	$0.612496\pi$
$578$		0			0
$579$	−22.7279			−0.944540
$580$	−4.00000	−	4.00000i	−0.166091	−	0.166091i
$581$	8.82843	−	3.65685i	0.366265	−	0.151712i
$582$			10.2426i			0.424571i
$583$	−1.41421	−	3.41421i	−0.0585707	−	0.141402i
$584$	4.94975	+	2.05025i	0.204822	+	0.0848401i
$585$	−0.485281	+	1.17157i	−0.0200639	+	0.0484386i
$586$	15.5563	−	15.5563i	0.642627	−	0.642627i
$587$	2.14214	−	2.14214i	0.0884154	−	0.0884154i	−0.661516	−	0.749931i	$-0.730087\pi$
$587$	2.14214	−	2.14214i	0.0884154	−	0.0884154i	0.749931	+	0.661516i	$0.230087\pi$
$588$	3.29289	−	7.94975i	0.135797	−	0.327842i
$589$	2.82843	+	1.17157i	0.116543	+	0.0482738i
$590$	0.828427	+	2.00000i	0.0341058	+	0.0823387i
$591$			36.9706i			1.52077i
$592$	−2.00000	+	0.828427i	−0.0821995	+	0.0340481i
$593$	3.00000	+	3.00000i	0.123195	+	0.123195i	0.766016	−	0.642821i	$-0.222236\pi$
$593$	3.00000	+	3.00000i	0.123195	+	0.123195i	−0.642821	+	0.766016i	$0.722236\pi$
$594$	−21.3137			−0.874512
$595$		0			0
$596$	−15.6569			−0.641330
$597$	−27.3137	−	27.3137i	−1.11788	−	1.11788i
$598$	−2.34315	+	0.970563i	−0.0958184	+	0.0396893i
$599$			26.3431i			1.07635i	0.842833	+	0.538176i	$0.180886\pi$
$599$			26.3431i			1.07635i	−0.842833	+	0.538176i	$0.819114\pi$
$600$	−6.12132	−	14.7782i	−0.249902	−	0.603316i
$601$	−17.0208	−	7.05025i	−0.694294	−	0.287586i	0.00749419	−	0.999972i	$-0.497615\pi$
$601$	−17.0208	−	7.05025i	−0.694294	−	0.287586i	−0.701788	+	0.712386i	$0.747615\pi$
$602$	1.02944	−	2.48528i	0.0419567	−	0.101293i
$603$	−2.17157	+	2.17157i	−0.0884333	+	0.0884333i
$604$	−15.6569	+	15.6569i	−0.637068	+	0.637068i
$605$	−12.5858	+	30.3848i	−0.511685	+	1.23532i
$606$	7.41421	+	3.07107i	0.301182	+	0.124754i
$607$	−3.75736	−	9.07107i	−0.152507	−	0.368183i	0.829100	−	0.559101i	$-0.188854\pi$
$607$	−3.75736	−	9.07107i	−0.152507	−	0.368183i	−0.981606	+	0.190918i	$0.938854\pi$
$608$		−	0.828427i		−	0.0335972i
$609$	4.00000	−	1.65685i	0.162088	−	0.0671391i
$610$	19.3137	+	19.3137i	0.781989	+	0.781989i
$611$	8.00000			0.323645
$612$		0			0
$613$	37.7990			1.52669			0.763343	−	0.645993i	$-0.223556\pi$
$613$	37.7990			1.52669			0.763343	+	0.645993i	$0.223556\pi$
$614$	−4.48528	−	4.48528i	−0.181011	−	0.181011i
$615$	70.7696	−	29.3137i	2.85370	−	1.18204i
$616$			6.82843i			0.275125i
$617$	6.92031	+	16.7071i	0.278601	+	0.672603i	0.999797	−	0.0201281i	$-0.00640739\pi$
$617$	6.92031	+	16.7071i	0.278601	+	0.672603i	−0.721196	+	0.692731i	$0.756407\pi$
$618$	21.3137	+	8.82843i	0.857363	+	0.355131i
$619$	−2.12132	+	5.12132i	−0.0852631	+	0.205843i	−0.960760	−	0.277380i	$-0.910534\pi$
$619$	−2.12132	+	5.12132i	−0.0852631	+	0.205843i	0.875497	+	0.483223i	$0.160534\pi$
$620$	9.65685	−	9.65685i	0.387829	−	0.387829i
$621$	−10.3431	+	10.3431i	−0.415056	+	0.415056i
$622$	5.75736	−	13.8995i	0.230849	−	0.557319i
$623$	21.3137	+	8.82843i	0.853916	+	0.353703i
$624$	0.585786	+	1.41421i	0.0234502	+	0.0566139i
$625$		−	6.65685i		−	0.266274i
$626$	12.5355	−	5.19239i	0.501021	−	0.207530i
$627$	4.82843	+	4.82843i	0.192829	+	0.192829i
$628$	−13.3137			−0.531275
$629$		0			0
$630$	2.34315			0.0933532
$631$	21.6569	+	21.6569i	0.862146	+	0.862146i	0.991587	−	0.129441i	$-0.0413184\pi$
$631$	21.6569	+	21.6569i	0.862146	+	0.862146i	−0.129441	+	0.991587i	$0.541318\pi$
$632$	−4.82843	+	2.00000i	−0.192065	+	0.0795557i
$633$			0.242641i			0.00964410i
$634$	−8.48528	−	20.4853i	−0.336994	−	0.813574i
$635$	44.2843	+	18.3431i	1.75737	+	0.727926i
$636$	−0.585786	+	1.41421i	−0.0232279	+	0.0560772i
$637$	−2.72792	+	2.72792i	−0.108084	+	0.108084i
$638$	4.82843	−	4.82843i	0.191159	−	0.191159i
$639$	0.343146	−	0.828427i	0.0135746	−	0.0327721i
$640$	−3.41421	−	1.41421i	−0.134959	−	0.0559017i
$641$	5.56497	+	13.4350i	0.219803	+	0.530652i	0.994862	−	0.101237i	$-0.0322800\pi$
$641$	5.56497	+	13.4350i	0.219803	+	0.530652i	−0.775059	+	0.631889i	$0.782280\pi$
$642$		−	21.5563i		−	0.850761i
$643$	−12.3640	+	5.12132i	−0.487587	+	0.201965i	−0.612913	−	0.790150i	$-0.710002\pi$
$643$	−12.3640	+	5.12132i	−0.487587	+	0.201965i	0.125326	+	0.992116i	$0.460002\pi$
$644$	3.31371	+	3.31371i	0.130578	+	0.130578i
$645$	−12.0000			−0.472500
$646$		0			0
$647$	12.4853			0.490847			0.245424	−	0.969416i	$-0.421073\pi$
$647$	12.4853			0.490847			0.245424	+	0.969416i	$0.421073\pi$
$648$	7.12132	+	7.12132i	0.279752	+	0.279752i
$649$	−2.41421	+	1.00000i	−0.0947662	+	0.0392534i
$650$			7.17157i			0.281292i
$651$	4.00000	+	9.65685i	0.156772	+	0.378482i
$652$	−21.0208	−	8.70711i	−0.823239	−	0.340997i
$653$	9.89949	−	23.8995i	0.387397	−	0.935260i	−0.603092	−	0.797671i	$-0.706065\pi$
$653$	9.89949	−	23.8995i	0.387397	−	0.935260i	0.990490	−	0.137588i	$-0.0439350\pi$
$654$	12.8284	−	12.8284i	0.501631	−	0.501631i
$655$	0.343146	−	0.343146i	0.0134078	−	0.0134078i
$656$	4.29289	−	10.3640i	0.167609	−	0.404645i
$657$	2.05025	+	0.849242i	0.0799880	+	0.0331321i
$658$	−5.65685	−	13.6569i	−0.220527	−	0.532400i
$659$		−	39.3137i		−	1.53144i	−0.643171	−	0.765722i	$-0.722382\pi$
$659$		−	39.3137i		−	1.53144i	0.643171	−	0.765722i	$-0.277618\pi$
$660$	28.1421	−	11.6569i	1.09543	−	0.453742i
$661$	−12.7279	−	12.7279i	−0.495059	−	0.495059i	0.414837	−	0.909896i	$-0.363839\pi$
$661$	−12.7279	−	12.7279i	−0.495059	−	0.495059i	−0.909896	+	0.414837i	$0.863839\pi$
$662$	27.6985			1.07653
$663$		0			0
$664$	−6.24264			−0.242261
$665$	3.31371	+	3.31371i	0.128500	+	0.128500i
$666$	−0.828427	+	0.343146i	−0.0321009	+	0.0132966i
$667$		−	4.68629i		−	0.181454i
$668$	−7.55635	−	18.2426i	−0.292364	−	0.705829i
$669$	−41.7990	−	17.3137i	−1.61604	−	0.669387i
$670$	−10.4853	+	25.3137i	−0.405082	+	0.977954i
$671$	−23.3137	+	23.3137i	−0.900016	+	0.900016i
$672$	2.00000	−	2.00000i	0.0771517	−	0.0771517i
$673$	−0.393398	+	0.949747i	−0.0151644	+	0.0366101i	−0.931280	−	0.364303i	$-0.881307\pi$
$673$	−0.393398	+	0.949747i	−0.0151644	+	0.0366101i	0.916116	+	0.400913i	$0.131307\pi$
$674$	−10.7782	−	4.46447i	−0.415160	−	0.171965i
$675$	15.8284	+	38.2132i	0.609236	+	1.47083i
$676$			12.3137i			0.473604i
$677$	−10.8284	+	4.48528i	−0.416170	+	0.172383i	−0.580936	−	0.813949i	$-0.697313\pi$
$677$	−10.8284	+	4.48528i	−0.416170	+	0.172383i	0.164766	+	0.986333i	$0.447313\pi$
$678$	−12.0711	−	12.0711i	−0.463587	−	0.463587i
$679$	−8.48528			−0.325635
$680$		0			0
$681$	−37.5563			−1.43916
$682$	11.6569	+	11.6569i	0.446364	+	0.446364i
$683$	−10.0208	+	4.15076i	−0.383436	+	0.158824i	−0.566071	−	0.824356i	$-0.691537\pi$
$683$	−10.0208	+	4.15076i	−0.383436	+	0.158824i	0.182635	+	0.983181i	$0.441537\pi$
$684$		−	0.343146i		−	0.0131205i
$685$	−3.31371	−	8.00000i	−0.126610	−	0.305664i
$686$	16.4853	+	6.82843i	0.629411	+	0.260711i
$687$	13.0711	−	31.5563i	0.498692	−	1.20395i
$688$	−1.24264	+	1.24264i	−0.0473752	+	0.0473752i
$689$	0.485281	−	0.485281i	0.0184877	−	0.0184877i
$690$	8.00000	−	19.3137i	0.304555	−	0.735260i
$691$	−43.4350	−	17.9914i	−1.65235	−	0.684424i	−0.654891	−	0.755723i	$-0.727286\pi$
$691$	−43.4350	−	17.9914i	−1.65235	−	0.684424i	−0.997455	+	0.0712988i	$0.977286\pi$
$692$	−2.24264	−	5.41421i	−0.0852524	−	0.205818i
$693$			2.82843i			0.107443i
$694$	−14.9497	+	6.19239i	−0.567485	+	0.235060i
$695$	−4.82843	−	4.82843i	−0.183153	−	0.183153i
$696$	−2.82843			−0.107211
$697$		0			0
$698$	−19.6569			−0.744023
$699$	13.7279	+	13.7279i	0.519238	+	0.519238i
$700$	12.2426	−	5.07107i	0.462728	−	0.191668i
$701$		−	1.51472i		−	0.0572101i	−0.999591	−	0.0286051i	$-0.990893\pi$
$701$		−	1.51472i		−	0.0572101i	0.999591	−	0.0286051i	$-0.00910652\pi$
$702$	−1.51472	−	3.65685i	−0.0571694	−	0.138019i
$703$	−1.65685	−	0.686292i	−0.0624894	−	0.0258840i
$704$	1.70711	−	4.12132i	0.0643390	−	0.155328i
$705$	−46.6274	+	46.6274i	−1.75609	+	1.75609i
$706$	10.1716	−	10.1716i	0.382812	−	0.382812i
$707$	−2.54416	+	6.14214i	−0.0956828	+	0.230999i
$708$	1.00000	+	0.414214i	0.0375823	+	0.0155671i
$709$	2.38478	+	5.75736i	0.0895622	+	0.216222i	0.962313	−	0.271943i	$-0.0876663\pi$
$709$	2.38478	+	5.75736i	0.0895622	+	0.216222i	−0.872751	+	0.488165i	$0.837666\pi$
$710$		−	8.00000i		−	0.300235i
$711$	−2.00000	+	0.828427i	−0.0750059	+	0.0310684i
$712$	−10.6569	−	10.6569i	−0.399382	−	0.399382i
$713$	11.3137			0.423702
$714$		0			0
$715$	−13.6569			−0.510737
$716$	18.2426	+	18.2426i	0.681759	+	0.681759i
$717$	−36.1421	+	14.9706i	−1.34975	+	0.559086i
$718$			11.3137i			0.422224i
$719$	−1.65685	−	4.00000i	−0.0617902	−	0.149175i	0.889969	−	0.456022i	$-0.150726\pi$
$719$	−1.65685	−	4.00000i	−0.0617902	−	0.149175i	−0.951759	+	0.306847i	$0.900726\pi$
$720$	−1.41421	−	0.585786i	−0.0527046	−	0.0218310i
$721$	−7.31371	+	17.6569i	−0.272377	+	0.657576i
$722$	−12.9497	+	12.9497i	−0.481940	+	0.481940i
$723$	−25.9706	+	25.9706i	−0.965856	+	0.965856i
$724$	−2.34315	+	5.65685i	−0.0870823	+	0.210235i
$725$	−12.2426	−	5.07107i	−0.454680	−	0.188335i
$726$	6.29289	+	15.1924i	0.233551	+	0.563842i
$727$			32.2843i			1.19736i	0.800989	+	0.598679i	$0.204307\pi$
$727$			32.2843i			1.19736i	−0.800989	+	0.598679i	$0.795693\pi$
$728$	−1.17157	+	0.485281i	−0.0434214	+	0.0179857i
$729$	−15.7782	−	15.7782i	−0.584377	−	0.584377i
$730$	19.7990			0.732793
$731$		0			0
$732$	13.6569			0.504772
$733$	9.89949	+	9.89949i	0.365646	+	0.365646i	0.865887	−	0.500240i	$-0.166755\pi$
$733$	9.89949	+	9.89949i	0.365646	+	0.365646i	−0.500240	+	0.865887i	$0.666755\pi$
$734$	17.3137	−	7.17157i	0.639061	−	0.264708i
$735$		−	31.7990i		−	1.17292i
$736$	−1.17157	−	2.82843i	−0.0431847	−	0.104257i
$737$	−30.5563	−	12.6569i	−1.12556	−	0.466221i
$738$	1.77817	−	4.29289i	0.0654555	−	0.158024i
$739$	0.485281	−	0.485281i	0.0178514	−	0.0178514i	−0.698125	−	0.715976i	$-0.745982\pi$
$739$	0.485281	−	0.485281i	0.0178514	−	0.0178514i	0.715976	+	0.698125i	$0.245982\pi$
$740$	−5.65685	+	5.65685i	−0.207950	+	0.207950i
$741$	−0.485281	+	1.17157i	−0.0178273	+	0.0430388i
$742$	−1.17157	−	0.485281i	−0.0430098	−	0.0178152i
$743$	−9.89949	−	23.8995i	−0.363177	−	0.876787i	−0.994832	−	0.101537i	$-0.967624\pi$
$743$	−9.89949	−	23.8995i	−0.363177	−	0.876787i	0.631654	−	0.775250i	$-0.282376\pi$
$744$		−	6.82843i		−	0.250342i
$745$	−53.4558	+	22.1421i	−1.95847	+	0.811225i
$746$	7.41421	+	7.41421i	0.271454	+	0.271454i
$747$	−2.58579			−0.0946090
$748$		0			0
$749$	17.8579			0.652512
$750$	−17.6569	−	17.6569i	−0.644737	−	0.644737i
$751$	22.9706	−	9.51472i	0.838208	−	0.347197i	0.0780611	−	0.996949i	$-0.475127\pi$
$751$	22.9706	−	9.51472i	0.838208	−	0.347197i	0.760147	+	0.649752i	$0.225127\pi$
$752$			9.65685i			0.352149i
$753$	−13.2426	−	31.9706i	−0.482589	−	1.16507i
$754$	1.17157	+	0.485281i	0.0426662	+	0.0176729i
$755$	−31.3137	+	75.5980i	−1.13962	+	2.75129i
$756$	−5.17157	+	5.17157i	−0.188088	+	0.188088i
$757$	7.75736	−	7.75736i	0.281946	−	0.281946i	−0.551939	−	0.833885i	$-0.686112\pi$
$757$	7.75736	−	7.75736i	0.281946	−	0.281946i	0.833885	+	0.551939i	$0.186112\pi$
$758$	−3.56497	+	8.60660i	−0.129486	+	0.312606i
$759$	23.3137	+	9.65685i	0.846234	+	0.350522i
$760$	−1.17157	−	2.82843i	−0.0424974	−	0.102598i
$761$			53.2548i			1.93049i	0.261354	+	0.965243i	$0.415831\pi$
$761$			53.2548i			1.93049i	−0.261354	+	0.965243i	$0.584169\pi$
$762$	22.1421	−	9.17157i	0.802125	−	0.332251i
$763$	10.6274	+	10.6274i	0.384738	+	0.384738i
$764$	−2.82843			−0.102329
$765$		0			0
$766$	−30.1421			−1.08908
$767$	−0.343146	−	0.343146i	−0.0123903	−	0.0123903i
$768$	−1.70711	+	0.707107i	−0.0615999	+	0.0255155i
$769$			26.3431i			0.949958i	0.879997	+	0.474979i	$0.157544\pi$
$769$			26.3431i			0.949958i	−0.879997	+	0.474979i	$0.842456\pi$
$770$	9.65685	+	23.3137i	0.348009	+	0.840168i
$771$	14.0711	+	5.82843i	0.506757	+	0.209906i
$772$	−4.70711	+	11.3640i	−0.169412	+	0.408998i
$773$	−2.58579	+	2.58579i	−0.0930043	+	0.0930043i	−0.752078	−	0.659074i	$-0.770948\pi$
$773$	−2.58579	+	2.58579i	−0.0930043	+	0.0930043i	0.659074	+	0.752078i	$0.270948\pi$
$774$	−0.514719	+	0.514719i	−0.0185012	+	0.0185012i
$775$	12.2426	−	29.5563i	0.439769	−	1.06170i
$776$	5.12132	+	2.12132i	0.183845	+	0.0761510i
$777$	−2.34315	−	5.65685i	−0.0840599	−	0.202939i
$778$			3.17157i			0.113706i
$779$	8.58579	−	3.55635i	0.307618	−	0.127419i
$780$	4.00000	+	4.00000i	0.143223	+	0.143223i
$781$	9.65685			0.345549
$782$		0			0
$783$	7.31371			0.261371
$784$	−3.29289	−	3.29289i	−0.117603	−	0.117603i
$785$	−45.4558	+	18.8284i	−1.62239	+	0.672015i
$786$		−	0.242641i		−	0.00865471i
$787$	7.29289	+	17.6066i	0.259964	+	0.627608i	0.998936	−	0.0461286i	$-0.0146884\pi$
$787$	7.29289	+	17.6066i	0.259964	+	0.627608i	−0.738972	+	0.673736i	$0.764688\pi$
$788$	18.4853	+	7.65685i	0.658511	+	0.272764i
$789$	5.65685	−	13.6569i	0.201389	−	0.486197i
$790$	−13.6569	+	13.6569i	−0.485889	+	0.485889i
$791$	10.0000	−	10.0000i	0.355559	−	0.355559i
$792$	0.707107	−	1.70711i	0.0251259	−	0.0606594i
$793$	−5.65685	−	2.34315i	−0.200881	−	0.0832075i
$794$	−3.17157	−	7.65685i	−0.112555	−	0.271732i
$795$			5.65685i			0.200628i
$796$	−19.3137	+	8.00000i	−0.684556	+	0.283552i
$797$	−18.8701	−	18.8701i	−0.668412	−	0.668412i	0.288937	−	0.957348i	$-0.406698\pi$
$797$	−18.8701	−	18.8701i	−0.668412	−	0.668412i	−0.957348	+	0.288937i	$0.906698\pi$
$798$	2.34315			0.0829465
$799$		0			0
$800$	−8.65685			−0.306066
$801$	−4.41421	−	4.41421i	−0.155969	−	0.155969i
$802$	−22.1924	+	9.19239i	−0.783640	+	0.324595i
$803$			23.8995i			0.843395i
$804$	5.24264	+	12.6569i	0.184894	+	0.446373i
$805$	16.0000	+	6.62742i	0.563926	+	0.233586i
$806$	−1.17157	+	2.82843i	−0.0412669	+	0.0996271i
$807$	−10.0000	+	10.0000i	−0.352017	+	0.352017i
$808$	3.07107	−	3.07107i	0.108040	−	0.108040i
$809$	17.8787	−	43.1630i	0.628581	−	1.51753i	−0.212806	−	0.977095i	$-0.568260\pi$
$809$	17.8787	−	43.1630i	0.628581	−	1.51753i	0.841386	−	0.540434i	$-0.181740\pi$
$810$	34.3848	+	14.2426i	1.20816	+	0.500435i
$811$	−18.8492	−	45.5061i	−0.661886	−	1.59794i	−0.794844	−	0.606813i	$-0.792447\pi$
$811$	−18.8492	−	45.5061i	−0.661886	−	1.59794i	0.132958	−	0.991122i	$-0.457553\pi$
$812$		−	2.34315i		−	0.0822283i
$813$	25.3137	−	10.4853i	0.887791	−	0.367735i
$814$	−6.82843	−	6.82843i	−0.239336	−	0.239336i
$815$	−84.0833			−2.94531
$816$		0			0
$817$	−1.45584			−0.0509335
$818$	−11.0000	−	11.0000i	−0.384606	−	0.384606i
$819$	−0.485281	+	0.201010i	−0.0169571	+	0.00702386i
$820$		−	41.4558i		−	1.44770i
$821$	0.142136	+	0.343146i	0.00496057	+	0.0119759i	0.926340	−	0.376687i	$-0.122937\pi$
$821$	0.142136	+	0.343146i	0.00496057	+	0.0119759i	−0.921380	+	0.388663i	$0.872937\pi$
$822$	−4.00000	−	1.65685i	−0.139516	−	0.0577894i
$823$	−16.6863	+	40.2843i	−0.581648	+	1.40422i	0.309671	+	0.950844i	$0.399781\pi$
$823$	−16.6863	+	40.2843i	−0.581648	+	1.40422i	−0.891319	+	0.453378i	$0.850219\pi$
$824$	8.82843	−	8.82843i	0.307553	−	0.307553i
$825$	50.4558	−	50.4558i	1.75665	−	1.75665i
$826$	−0.343146	+	0.828427i	−0.0119396	+	0.0288247i
$827$	−22.0919	−	9.15076i	−0.768210	−	0.318203i	−0.0360629	−	0.999350i	$-0.511482\pi$
$827$	−22.0919	−	9.15076i	−0.768210	−	0.318203i	−0.732147	+	0.681147i	$0.761482\pi$
$828$	−0.485281	−	1.17157i	−0.0168647	−	0.0407150i
$829$		−	20.1421i		−	0.699565i	−0.936831	−	0.349783i	$-0.886255\pi$
$829$		−	20.1421i		−	0.699565i	0.936831	−	0.349783i	$-0.113745\pi$
$830$	−21.3137	+	8.82843i	−0.739810	+	0.306439i
$831$	30.9706	+	30.9706i	1.07436	+	1.07436i
$832$	0.828427			0.0287205
$833$		0			0
$834$	−3.41421			−0.118225
$835$	−51.5980	−	51.5980i	−1.78562	−	1.78562i
$836$	3.41421	−	1.41421i	0.118083	−	0.0489116i
$837$			17.6569i			0.610310i
$838$	6.60660	+	15.9497i	0.228221	+	0.550975i
$839$	44.7279	+	18.5269i	1.54418	+	0.639620i	0.982252	−	0.187566i	$-0.0600600\pi$
$839$	44.7279	+	18.5269i	1.54418	+	0.639620i	0.561927	+	0.827187i	$0.310060\pi$
$840$	4.00000	−	9.65685i	0.138013	−	0.333193i
$841$	18.8492	−	18.8492i	0.649974	−	0.649974i
$842$	11.0711	−	11.0711i	0.381534	−	0.381534i
$843$	10.1421	−	24.4853i	0.349314	−	0.843318i
$844$	0.121320	+	0.0502525i	0.00417602	+	0.00172976i
$845$	17.4142	+	42.0416i	0.599067	+	1.44628i
$846$			4.00000i			0.137523i
$847$	−12.5858	+	5.21320i	−0.432453	+	0.179128i
$848$	0.585786	+	0.585786i	0.0201160	+	0.0201160i
$849$	−2.10051			−0.0720891
$850$		0			0
$851$	−6.62742			−0.227185
$852$	−2.82843	−	2.82843i	−0.0969003	−	0.0969003i
$853$	−35.0711	+	14.5269i	−1.20081	+	0.497392i	−0.891261	−	0.453491i	$-0.850178\pi$
$853$	−35.0711	+	14.5269i	−1.20081	+	0.497392i	−0.309550	+	0.950883i	$0.600178\pi$
$854$			11.3137i			0.387147i
$855$	−0.485281	−	1.17157i	−0.0165963	−	0.0400669i
$856$	−10.7782	−	4.46447i	−0.368390	−	0.152592i
$857$	15.4056	−	37.1924i	0.526245	−	1.27047i	−0.407721	−	0.913106i	$-0.633676\pi$
$857$	15.4056	−	37.1924i	0.526245	−	1.27047i	0.933966	−	0.357361i	$-0.116324\pi$
$858$	−4.82843	+	4.82843i	−0.164840	+	0.164840i
$859$	−0.556349	+	0.556349i	−0.0189824	+	0.0189824i	−0.716534	−	0.697552i	$-0.754273\pi$
$859$	−0.556349	+	0.556349i	−0.0189824	+	0.0189824i	0.697552	+	0.716534i	$0.254273\pi$
$860$	−2.48528	+	6.00000i	−0.0847474	+	0.204598i
$861$	29.3137	+	12.1421i	0.999009	+	0.413803i
$862$	5.51472	+	13.3137i	0.187832	+	0.453467i
$863$		−	0.970563i		−	0.0330383i	−0.999864	−	0.0165192i	$-0.994742\pi$
$863$		−	0.970563i		−	0.0330383i	0.999864	−	0.0165192i	$-0.00525845\pi$
$864$	4.41421	−	1.82843i	0.150175	−	0.0622044i
$865$	−15.3137	−	15.3137i	−0.520682	−	0.520682i
$866$	−12.9706			−0.440758
$867$		0			0
$868$	5.65685			0.192006
$869$	−16.4853	−	16.4853i	−0.559225	−	0.559225i
$870$	−9.65685	+	4.00000i	−0.327398	+	0.135613i
$871$		−	6.14214i		−	0.208118i
$872$	−3.75736	−	9.07107i	−0.127240	−	0.307185i
$873$	2.12132	+	0.878680i	0.0717958	+	0.0297388i
$874$	0.970563	−	2.34315i	0.0328298	−	0.0792581i
$875$	14.6274	−	14.6274i	0.494497	−	0.494497i
$876$	7.00000	−	7.00000i	0.236508	−	0.236508i
$877$	−4.10051	+	9.89949i	−0.138464	+	0.334282i	−0.977867	−	0.209228i	$-0.932905\pi$
$877$	−4.10051	+	9.89949i	−0.138464	+	0.334282i	0.839403	+	0.543510i	$0.182905\pi$
$878$	21.3137	+	8.82843i	0.719303	+	0.297945i
$879$	−15.5563	−	37.5563i	−0.524703	−	1.26674i
$880$		−	16.4853i		−	0.555719i
$881$	−16.7071	+	6.92031i	−0.562877	+	0.233151i	−0.645934	−	0.763394i	$-0.723532\pi$
$881$	−16.7071	+	6.92031i	−0.562877	+	0.233151i	0.0830568	+	0.996545i	$0.473532\pi$
$882$	−1.36396	−	1.36396i	−0.0459270	−	0.0459270i
$883$	34.5269			1.16192			0.580962	−	0.813931i	$-0.302677\pi$
$883$	34.5269			1.16192			0.580962	+	0.813931i	$0.302677\pi$
$884$		0			0
$885$	4.00000			0.134459
$886$	26.0711	+	26.0711i	0.875875	+	0.875875i
$887$	−2.34315	+	0.970563i	−0.0786751	+	0.0325883i	−0.421674	−	0.906748i	$-0.638557\pi$
$887$	−2.34315	+	0.970563i	−0.0786751	+	0.0325883i	0.342999	+	0.939336i	$0.388557\pi$
$888$			4.00000i			0.134231i
$889$	7.59798	+	18.3431i	0.254828	+	0.615209i
$890$	−51.4558	−	21.3137i	−1.72480	−	0.714437i
$891$	−17.1924	+	41.5061i	−0.575967	+	1.39051i
$892$	−17.3137	+	17.3137i	−0.579706	+	0.579706i
$893$	−5.65685	+	5.65685i	−0.189299	+	0.189299i
$894$	−11.0711	+	26.7279i	−0.370272	+	0.893915i
$895$	88.0833	+	36.4853i	2.94430	+	1.21957i
$896$	−0.585786	−	1.41421i	−0.0195698	−	0.0472456i
$897$			4.68629i			0.156471i
$898$	5.12132	−	2.12132i	0.170901	−	0.0707894i
$899$	−4.00000	−	4.00000i	−0.133407	−	0.133407i
$900$	−3.58579			−0.119526
$901$		0			0
$902$	50.0416			1.66620
$903$	−3.51472	−	3.51472i	−0.116963	−	0.116963i
$904$	−8.53553	+	3.53553i	−0.283888	+	0.117590i
$905$			22.6274i			0.752161i
$906$	15.6569	+	37.7990i	0.520164	+	1.25579i
$907$	13.5355	+	5.60660i	0.449440	+	0.186164i	0.595910	−	0.803051i	$-0.296791\pi$
$907$	13.5355	+	5.60660i	0.449440	+	0.186164i	−0.146470	+	0.989215i	$0.546791\pi$
$908$	−7.77817	+	18.7782i	−0.258128	+	0.623176i
$909$	1.27208	−	1.27208i	0.0421922	−	0.0421922i
$910$	−3.31371	+	3.31371i	−0.109848	+	0.109848i
$911$	8.92893	−	21.5563i	0.295829	−	0.714194i	−0.704163	−	0.710039i	$-0.748677\pi$
$911$	8.92893	−	21.5563i	0.295829	−	0.714194i	0.999991	−	0.00415500i	$-0.00132258\pi$
$912$	−1.41421	−	0.585786i	−0.0468293	−	0.0193973i
$913$	−10.6569	−	25.7279i	−0.352690	−	0.851470i
$914$			4.97056i			0.164412i
$915$	46.6274	−	19.3137i	1.54145	−	0.638492i
$916$	−13.0711	−	13.0711i	−0.431880	−	0.431880i
$917$	0.201010			0.00663794
$918$		0			0
$919$	−2.34315			−0.0772932			−0.0386466	−	0.999253i	$-0.512305\pi$
$919$	−2.34315			−0.0772932			−0.0386466	+	0.999253i	$0.512305\pi$
$920$	−8.00000	−	8.00000i	−0.263752	−	0.263752i
$921$	−10.8284	+	4.48528i	−0.356809	+	0.147795i
$922$		−	34.9706i		−	1.15169i
$923$	0.686292	+	1.65685i	0.0225896	+	0.0545360i
$924$	11.6569	+	4.82843i	0.383482	+	0.158844i
$925$	−7.17157	+	17.3137i	−0.235800	+	0.569271i
$926$	−2.34315	+	2.34315i	−0.0770005	+	0.0770005i
$927$	3.65685	−	3.65685i	0.120107	−	0.120107i
$928$	−0.585786	+	1.41421i	−0.0192294	+	0.0464238i
$929$	−8.53553	−	3.53553i	−0.280042	−	0.115997i	0.238242	−	0.971206i	$-0.423429\pi$
$929$	−8.53553	−	3.53553i	−0.280042	−	0.115997i	−0.518284	+	0.855209i	$0.673429\pi$
$930$	−9.65685	−	23.3137i	−0.316661	−	0.764487i
$931$		−	3.85786i		−	0.126436i
$932$	9.70711	−	4.02082i	0.317967	−	0.131706i
$933$	−19.6569	−	19.6569i	−0.643537	−	0.643537i
$934$	−2.48528			−0.0813209
$935$		0			0
$936$	0.343146			0.0112161
$937$	3.75736	+	3.75736i	0.122748	+	0.122748i	0.765812	−	0.643064i	$-0.222337\pi$
$937$	3.75736	+	3.75736i	0.122748	+	0.122748i	−0.643064	+	0.765812i	$0.722337\pi$
$938$	−10.4853	+	4.34315i	−0.342357	+	0.141809i
$939$		−	25.0711i		−	0.818163i
$940$	13.6569	+	32.9706i	0.445437	+	1.07538i
$941$	18.1421	+	7.51472i	0.591417	+	0.244973i	0.658260	−	0.752791i	$-0.271293\pi$
$941$	18.1421	+	7.51472i	0.591417	+	0.244973i	−0.0668433	+	0.997763i	$0.521293\pi$
$942$	−9.41421	+	22.7279i	−0.306732	+	0.740516i
$943$	24.2843	−	24.2843i	0.790805	−	0.790805i
$944$	0.414214	−	0.414214i	0.0134815	−	0.0134815i
$945$	−10.3431	+	24.9706i	−0.336463	+	0.812292i
$946$	−7.24264	−	3.00000i	−0.235479	−	0.0975384i
$947$	20.0208	+	48.3345i	0.650589	+	1.57066i	0.811925	+	0.583761i	$0.198420\pi$
$947$	20.0208	+	48.3345i	0.650589	+	1.57066i	−0.161336	+	0.986900i	$0.551580\pi$
$948$			9.65685i			0.313640i
$949$	−4.10051	+	1.69848i	−0.133108	+	0.0551352i
$950$	−5.07107	−	5.07107i	−0.164527	−	0.164527i
$951$	−40.9706			−1.32856
$952$		0			0
$953$	−11.5563			−0.374347			−0.187173	−	0.982327i	$-0.559933\pi$
$953$	−11.5563			−0.374347			−0.187173	+	0.982327i	$0.559933\pi$
$954$	0.242641	+	0.242641i	0.00785578	+	0.00785578i
$955$	−9.65685	+	4.00000i	−0.312488	+	0.129437i
$956$			21.1716i			0.684738i
$957$	−4.82843	−	11.6569i	−0.156081	−	0.376813i
$958$	−22.9706	−	9.51472i	−0.742145	−	0.307407i
$959$	1.37258	−	3.31371i	0.0443230	−	0.107005i
$960$	−4.82843	+	4.82843i	−0.155837	+	0.155837i
$961$	−12.2635	+	12.2635i	−0.395595	+	0.395595i
$962$	0.686292	−	1.65685i	0.0221269	−	0.0534191i
$963$	−4.46447	−	1.84924i	−0.143865	−	0.0595910i
$964$	7.60660	+	18.3640i	0.244992	+	0.591463i
$965$			45.4558i			1.46328i
$966$	8.00000	−	3.31371i	0.257396	−	0.106617i
$967$	−9.65685	−	9.65685i	−0.310543	−	0.310543i	0.534577	−	0.845120i	$-0.320471\pi$
$967$	−9.65685	−	9.65685i	−0.310543	−	0.310543i	−0.845120	+	0.534577i	$0.820471\pi$
$968$	8.89949			0.286041
$969$		0			0
$970$	20.4853			0.657743
$971$	−15.0416	−	15.0416i	−0.482709	−	0.482709i	0.423287	−	0.905996i	$-0.360876\pi$
$971$	−15.0416	−	15.0416i	−0.482709	−	0.482709i	−0.905996	+	0.423287i	$0.860876\pi$
$972$	3.94975	−	1.63604i	0.126688	−	0.0524760i
$973$		−	2.82843i		−	0.0906752i
$974$	−8.48528	−	20.4853i	−0.271886	−	0.656391i
$975$	12.2426	+	5.07107i	0.392078	+	0.162404i
$976$	2.82843	−	6.82843i	0.0905357	−	0.218573i
$977$	−20.1127	+	20.1127i	−0.643462	+	0.643462i	−0.951405	−	0.307943i	$-0.900359\pi$
$977$	−20.1127	+	20.1127i	−0.643462	+	0.643462i	0.307943	+	0.951405i	$0.400359\pi$
$978$	−29.7279	+	29.7279i	−0.950594	+	0.950594i
$979$	25.7279	−	62.1127i	0.822268	−	1.98513i
$980$	−15.8995	−	6.58579i	−0.507891	−	0.210375i
$981$	−1.55635	−	3.75736i	−0.0496904	−	0.119963i
$982$			15.4558i			0.493216i
$983$	24.9706	−	10.3431i	0.796437	−	0.329895i	0.0529088	−	0.998599i	$-0.483151\pi$
$983$	24.9706	−	10.3431i	0.796437	−	0.329895i	0.743529	+	0.668704i	$0.233151\pi$
$984$	−14.6569	−	14.6569i	−0.467243	−	0.467243i
$985$	73.9411			2.35596
$986$		0			0
$987$	−27.3137			−0.869405
$988$	0.485281	+	0.485281i	0.0154389	+	0.0154389i
$989$	−4.97056	+	2.05887i	−0.158055	+	0.0654684i
$990$		−	6.82843i		−	0.217022i
$991$	17.5147	+	42.2843i	0.556373	+	1.34320i	0.912619	+	0.408812i	$0.134057\pi$
$991$	17.5147	+	42.2843i	0.556373	+	1.34320i	−0.356245	+	0.934392i	$0.615943\pi$
$992$	−3.41421	−	1.41421i	−0.108401	−	0.0449013i
$993$	19.5858	−	47.2843i	0.621536	−	1.50052i
$994$	2.34315	−	2.34315i	0.0743201	−	0.0743201i
$995$	−54.6274	+	54.6274i	−1.73181	+	1.73181i
$996$	−4.41421	+	10.6569i	−0.139870	+	0.337675i
$997$	−10.9706	−	4.54416i	−0.347441	−	0.143915i	0.202137	−	0.979357i	$-0.435211\pi$
$997$	−10.9706	−	4.54416i	−0.347441	−	0.143915i	−0.549578	+	0.835442i	$0.685211\pi$
$998$	14.0919	+	34.0208i	0.446071	+	1.07691i
$999$		−	10.3431i		−	0.327243i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	578.2.d.a.155.1		4
17.2	even	8		34.2.d.a.25.1	yes	4
17.3	odd	16		578.2.a.i.1.1		4
17.4	even	4		578.2.d.b.423.1		4
17.5	odd	16		578.2.b.d.577.1		4
17.6	odd	16		578.2.c.f.327.1		8
17.7	odd	16		578.2.c.f.251.4		8
17.8	even	8		578.2.d.c.179.1		4
17.9	even	8	inner	578.2.d.a.179.1		4
17.10	odd	16		578.2.c.f.251.1		8
17.11	odd	16		578.2.c.f.327.4		8
17.12	odd	16		578.2.b.d.577.4		4
17.13	even	4		34.2.d.a.15.1	✓	4
17.14	odd	16		578.2.a.i.1.4		4
17.15	even	8		578.2.d.b.399.1		4
17.16	even	2		578.2.d.c.155.1		4
51.2	odd	8		306.2.l.c.127.1		4
51.14	even	16		5202.2.a.bw.1.1		4
51.20	even	16		5202.2.a.bw.1.4		4
51.47	odd	4		306.2.l.c.253.1		4
68.3	even	16		4624.2.a.bn.1.4		4
68.19	odd	8		272.2.v.b.161.1		4
68.31	even	16		4624.2.a.bn.1.1		4
68.47	odd	4		272.2.v.b.49.1		4
85.2	odd	8		850.2.o.b.399.1		4
85.13	odd	4		850.2.o.b.49.1		4
85.19	even	8		850.2.l.a.501.1		4
85.47	odd	4		850.2.o.a.49.1		4
85.53	odd	8		850.2.o.a.399.1		4
85.64	even	4		850.2.l.a.151.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
34.2.d.a.15.1	✓	4	17.13	even	4
34.2.d.a.25.1	yes	4	17.2	even	8
272.2.v.b.49.1		4	68.47	odd	4
272.2.v.b.161.1		4	68.19	odd	8
306.2.l.c.127.1		4	51.2	odd	8
306.2.l.c.253.1		4	51.47	odd	4
578.2.a.i.1.1		4	17.3	odd	16
578.2.a.i.1.4		4	17.14	odd	16
578.2.b.d.577.1		4	17.5	odd	16
578.2.b.d.577.4		4	17.12	odd	16
578.2.c.f.251.1		8	17.10	odd	16
578.2.c.f.251.4		8	17.7	odd	16
578.2.c.f.327.1		8	17.6	odd	16
578.2.c.f.327.4		8	17.11	odd	16
578.2.d.a.155.1		4	1.1	even	1	trivial
578.2.d.a.179.1		4	17.9	even	8	inner
578.2.d.b.399.1		4	17.15	even	8
578.2.d.b.423.1		4	17.4	even	4
578.2.d.c.155.1		4	17.16	even	2
578.2.d.c.179.1		4	17.8	even	8
850.2.l.a.151.1		4	85.64	even	4
850.2.l.a.501.1		4	85.19	even	8
850.2.o.a.49.1		4	85.47	odd	4
850.2.o.a.399.1		4	85.53	odd	8
850.2.o.b.49.1		4	85.13	odd	4
850.2.o.b.399.1		4	85.2	odd	8
4624.2.a.bn.1.1		4	68.31	even	16
4624.2.a.bn.1.4		4	68.3	even	16
5202.2.a.bw.1.1		4	51.14	even	16
5202.2.a.bw.1.4		4	51.20	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 578 = 2 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	578.d (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.70711 + 0.707107i) q^{3} +1.00000i q^{4} +(1.41421 + 3.41421i) q^{5} +(1.70711 + 0.707107i) q^{6} +(-0.585786 + 1.41421i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.292893 - 0.292893i) q^{9} +(1.41421 - 3.41421i) q^{10} +(4.12132 + 1.70711i) q^{11} +(-0.707107 - 1.70711i) q^{12} +0.828427i q^{13} +(1.41421 - 0.585786i) q^{14} +(-4.82843 - 4.82843i) q^{15} -1.00000 q^{16} -0.414214 q^{18} +(-0.585786 - 0.585786i) q^{19} +(-3.41421 + 1.41421i) q^{20} -2.82843i q^{21} +(-1.70711 - 4.12132i) q^{22} +(-2.82843 - 1.17157i) q^{23} +(-0.707107 + 1.70711i) q^{24} +(-6.12132 + 6.12132i) q^{25} +(0.585786 - 0.585786i) q^{26} +(1.82843 - 4.41421i) q^{27} +(-1.41421 - 0.585786i) q^{28} +(0.585786 + 1.41421i) q^{29} +6.82843i q^{30} +(-3.41421 + 1.41421i) q^{31} +(0.707107 + 0.707107i) q^{32} -8.24264 q^{33} -5.65685 q^{35} +(0.292893 + 0.292893i) q^{36} +(2.00000 - 0.828427i) q^{37} +0.828427i q^{38} +(-0.585786 - 1.41421i) q^{39} +(3.41421 + 1.41421i) q^{40} +(-4.29289 + 10.3640i) q^{41} +(-2.00000 + 2.00000i) q^{42} +(1.24264 - 1.24264i) q^{43} +(-1.70711 + 4.12132i) q^{44} +(1.41421 + 0.585786i) q^{45} +(1.17157 + 2.82843i) q^{46} -9.65685i q^{47} +(1.70711 - 0.707107i) q^{48} +(3.29289 + 3.29289i) q^{49} +8.65685 q^{50} -0.828427 q^{52} +(-0.585786 - 0.585786i) q^{53} +(-4.41421 + 1.82843i) q^{54} +16.4853i q^{55} +(0.585786 + 1.41421i) q^{56} +(1.41421 + 0.585786i) q^{57} +(0.585786 - 1.41421i) q^{58} +(-0.414214 + 0.414214i) q^{59} +(4.82843 - 4.82843i) q^{60} +(-2.82843 + 6.82843i) q^{61} +(3.41421 + 1.41421i) q^{62} +(0.242641 + 0.585786i) q^{63} -1.00000i q^{64} +(-2.82843 + 1.17157i) q^{65} +(5.82843 + 5.82843i) q^{66} -7.41421 q^{67} +5.65685 q^{69} +(4.00000 + 4.00000i) q^{70} +(2.00000 - 0.828427i) q^{71} -0.414214i q^{72} +(2.05025 + 4.94975i) q^{73} +(-2.00000 - 0.828427i) q^{74} +(6.12132 - 14.7782i) q^{75} +(0.585786 - 0.585786i) q^{76} +(-4.82843 + 4.82843i) q^{77} +(-0.585786 + 1.41421i) q^{78} +(-4.82843 - 2.00000i) q^{79} +(-1.41421 - 3.41421i) q^{80} +10.0711i q^{81} +(10.3640 - 4.29289i) q^{82} +(-4.41421 - 4.41421i) q^{83} +2.82843 q^{84} -1.75736 q^{86} +(-2.00000 - 2.00000i) q^{87} +(4.12132 - 1.70711i) q^{88} -15.0711i q^{89} +(-0.585786 - 1.41421i) q^{90} +(-1.17157 - 0.485281i) q^{91} +(1.17157 - 2.82843i) q^{92} +(4.82843 - 4.82843i) q^{93} +(-6.82843 + 6.82843i) q^{94} +(1.17157 - 2.82843i) q^{95} +(-1.70711 - 0.707107i) q^{96} +(2.12132 + 5.12132i) q^{97} -4.65685i q^{98} +(1.70711 - 0.707107i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{3} + 4 q^{6} - 8 q^{7} + 4 q^{9} + 8 q^{11} - 8 q^{15} - 4 q^{16} + 4 q^{18} - 8 q^{19} - 8 q^{20} - 4 q^{22} - 16 q^{25} + 8 q^{26} - 4 q^{27} + 8 q^{29} - 8 q^{31} - 16 q^{33} + 4 q^{36} + 8 q^{37}+ \cdots + 4 q^{99}+O(q^{100}) \) 4 * q - 4 * q^3 + 4 * q^6 - 8 * q^7 + 4 * q^9 + 8 * q^11 - 8 * q^15 - 4 * q^16 + 4 * q^18 - 8 * q^19 - 8 * q^20 - 4 * q^22 - 16 * q^25 + 8 * q^26 - 4 * q^27 + 8 * q^29 - 8 * q^31 - 16 * q^33 + 4 * q^36 + 8 * q^37 - 8 * q^39 + 8 * q^40 - 20 * q^41 - 8 * q^42 - 12 * q^43 - 4 * q^44 + 16 * q^46 + 4 * q^48 + 16 * q^49 + 12 * q^50 + 8 * q^52 - 8 * q^53 - 12 * q^54 + 8 * q^56 + 8 * q^58 + 4 * q^59 + 8 * q^60 + 8 * q^62 - 16 * q^63 + 12 * q^66 - 24 * q^67 + 16 * q^70 + 8 * q^71 + 28 * q^73 - 8 * q^74 + 16 * q^75 + 8 * q^76 - 8 * q^77 - 8 * q^78 - 8 * q^79 + 16 * q^82 - 12 * q^83 - 24 * q^86 - 8 * q^87 + 8 * q^88 - 8 * q^90 - 16 * q^91 + 16 * q^92 + 8 * q^93 - 16 * q^94 + 16 * q^95 - 4 * q^96 + 4 * q^99

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