LMFDB - Embedded newform 507.2.f.f.437.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(239,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("507.239");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.f (of order $4$, degree $2$, 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.56070144.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 16x^{6} - 34x^{5} + 63x^{4} - 74x^{3} + 70x^{2} - 38x + 13 $ x^8 - 4x^7 + 16x^6 - 34x^5 + 63x^4 - 74x^3 + 70x^2 - 38*x + 13
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 39)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			437.2
Root			$0.500000 + 1.56488i$ of defining polynomial
Character	$\chi$	$=$	507.437
Dual form			507.2.f.f.239.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.06488 + 1.06488i) q^{2} +(1.36603 - 1.06488i) q^{3} -0.267949i q^{4} +(-1.06488 + 1.06488i) q^{5} +(-0.320682 + 2.58863i) q^{6} +(1.00000 - 1.00000i) q^{7} +(-1.84443 - 1.84443i) q^{8} +(0.732051 - 2.90931i) q^{9} +O(q^{10})$	\(q+(-1.06488 + 1.06488i) q^{2} +(1.36603 - 1.06488i) q^{3} -0.267949i q^{4} +(-1.06488 + 1.06488i) q^{5} +(-0.320682 + 2.58863i) q^{6} +(1.00000 - 1.00000i) q^{7} +(-1.84443 - 1.84443i) q^{8} +(0.732051 - 2.90931i) q^{9} -2.26795i q^{10} +(2.90931 + 2.90931i) q^{11} +(-0.285334 - 0.366025i) q^{12} +2.12976i q^{14} +(-0.320682 + 2.58863i) q^{15} +4.46410 q^{16} +5.03908 q^{17} +(2.31853 + 3.87762i) q^{18} +(2.73205 + 2.73205i) q^{19} +(0.285334 + 0.285334i) q^{20} +(0.301143 - 2.43091i) q^{21} -6.19615 q^{22} +(-4.48364 - 0.555437i) q^{24} +2.73205i q^{25} +(-2.09808 - 4.75374i) q^{27} +(-0.267949 - 0.267949i) q^{28} +7.16884i q^{29} +(-2.41510 - 3.09808i) q^{30} +(-2.46410 - 2.46410i) q^{31} +(-1.06488 + 1.06488i) q^{32} +(7.07227 + 0.876119i) q^{33} +(-5.36603 + 5.36603i) q^{34} +2.12976i q^{35} +(-0.779548 - 0.196152i) q^{36} +(3.83013 - 3.83013i) q^{37} -5.81863 q^{38} +3.92820 q^{40} +(3.97420 - 3.97420i) q^{41} +(2.26795 + 2.90931i) q^{42} -2.19615i q^{43} +(0.779548 - 0.779548i) q^{44} +(2.31853 + 3.87762i) q^{45} +(4.25953 + 4.25953i) q^{47} +(6.09808 - 4.75374i) q^{48} +5.00000i q^{49} +(-2.90931 - 2.90931i) q^{50} +(6.88351 - 5.36603i) q^{51} +0.779548i q^{53} +(7.29638 + 2.82797i) q^{54} -6.19615 q^{55} -3.68886 q^{56} +(6.64136 + 0.822738i) q^{57} +(-7.63397 - 7.63397i) q^{58} +(-2.12976 - 2.12976i) q^{59} +(0.693622 + 0.0859264i) q^{60} -7.00000 q^{61} +5.24796 q^{62} +(-2.17726 - 3.64136i) q^{63} +6.66025i q^{64} +(-8.46410 + 6.59817i) q^{66} +(-4.19615 - 4.19615i) q^{67} -1.35022i q^{68} +(-2.26795 - 2.26795i) q^{70} +(2.12976 - 2.12976i) q^{71} +(-6.71624 + 4.01581i) q^{72} +(-0.901924 + 0.901924i) q^{73} +8.15727i q^{74} +(2.90931 + 3.73205i) q^{75} +(0.732051 - 0.732051i) q^{76} +5.81863 q^{77} +2.00000 q^{79} +(-4.75374 + 4.75374i) q^{80} +(-7.92820 - 4.25953i) q^{81} +8.46410i q^{82} +(-2.90931 + 2.90931i) q^{83} +(-0.651360 - 0.0806910i) q^{84} +(-5.36603 + 5.36603i) q^{85} +(2.33864 + 2.33864i) q^{86} +(7.63397 + 9.79282i) q^{87} -10.7321i q^{88} +(6.59817 + 6.59817i) q^{89} +(-6.59817 - 1.66025i) q^{90} +(-5.99000 - 0.742047i) q^{93} -9.07180 q^{94} -5.81863 q^{95} +(-0.320682 + 2.58863i) q^{96} +(-1.19615 - 1.19615i) q^{97} +(-5.32441 - 5.32441i) q^{98} +(10.5939 - 6.33434i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{3} + 16 q^{6} + 8 q^{7} - 8 q^{9}+O(q^{10}) $ 8 * q + 4 * q^3 + 16 * q^6 + 8 * q^7 - 8 * q^9	$ 8 q + 4 q^{3} + 16 q^{6} + 8 q^{7} - 8 q^{9} + 16 q^{15} + 8 q^{16} + 4 q^{18} + 8 q^{19} + 4 q^{21} - 8 q^{22} + 12 q^{24} + 4 q^{27} - 16 q^{28} + 8 q^{31} + 4 q^{33} - 36 q^{34} - 4 q^{37} - 24 q^{40} + 32 q^{42} + 4 q^{45} + 28 q^{48} - 8 q^{54} - 8 q^{55} + 16 q^{57} - 68 q^{58} + 44 q^{60} - 56 q^{61} - 8 q^{63} - 40 q^{66} + 8 q^{67} - 32 q^{70} - 36 q^{72} - 28 q^{73} - 8 q^{76} + 16 q^{79} - 8 q^{81} + 4 q^{84} - 36 q^{85} + 68 q^{87} - 20 q^{93} - 128 q^{94} + 16 q^{96} + 32 q^{97} + 40 q^{99}+O(q^{100}) $ 8 * q + 4 * q^3 + 16 * q^6 + 8 * q^7 - 8 * q^9 + 16 * q^15 + 8 * q^16 + 4 * q^18 + 8 * q^19 + 4 * q^21 - 8 * q^22 + 12 * q^24 + 4 * q^27 - 16 * q^28 + 8 * q^31 + 4 * q^33 - 36 * q^34 - 4 * q^37 - 24 * q^40 + 32 * q^42 + 4 * q^45 + 28 * q^48 - 8 * q^54 - 8 * q^55 + 16 * q^57 - 68 * q^58 + 44 * q^60 - 56 * q^61 - 8 * q^63 - 40 * q^66 + 8 * q^67 - 32 * q^70 - 36 * q^72 - 28 * q^73 - 8 * q^76 + 16 * q^79 - 8 * q^81 + 4 * q^84 - 36 * q^85 + 68 * q^87 - 20 * q^93 - 128 * q^94 + 16 * q^96 + 32 * q^97 + 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.06488	+	1.06488i	−0.752986	+	0.752986i	−0.975035	−	0.222050i	$-0.928725\pi$
$2$	−1.06488	+	1.06488i	−0.752986	+	0.752986i	0.222050	+	0.975035i	$0.428725\pi$
$3$	1.36603	−	1.06488i	0.788675	−	0.614810i
$3$	1.36603	−	1.06488i	0.788675	−	0.614810i
$4$		−	0.267949i		−	0.133975i
$5$	−1.06488	+	1.06488i	−0.476230	+	0.476230i	−0.903924	−	0.427694i	$-0.859326\pi$
$5$	−1.06488	+	1.06488i	−0.476230	+	0.476230i	0.427694	+	0.903924i	$0.359326\pi$
$6$	−0.320682	+	2.58863i	−0.130918	+	1.05680i
$7$	1.00000	−	1.00000i	0.377964	−	0.377964i	−0.492403	−	0.870367i	$-0.663881\pi$
$7$	1.00000	−	1.00000i	0.377964	−	0.377964i	0.870367	+	0.492403i	$0.163881\pi$
$8$	−1.84443	−	1.84443i	−0.652105	−	0.652105i
$9$	0.732051	−	2.90931i	0.244017	−	0.969771i
$10$		−	2.26795i		−	0.717189i
$11$	2.90931	+	2.90931i	0.877191	+	0.877191i	0.993243	−	0.116052i	$-0.0370240\pi$
$11$	2.90931	+	2.90931i	0.877191	+	0.877191i	−0.116052	+	0.993243i	$0.537024\pi$
$12$	−0.285334	−	0.366025i	−0.0823689	−	0.105662i
$13$		0			0
$13$		0			0
$14$			2.12976i			0.569204i
$15$	−0.320682	+	2.58863i	−0.0827997	+	0.668382i
$16$	4.46410			1.11603
$17$	5.03908			1.22216			0.611078	−	0.791570i	$-0.290736\pi$
$17$	5.03908			1.22216			0.611078	+	0.791570i	$0.290736\pi$
$18$	2.31853	+	3.87762i	0.546482	+	0.913965i
$19$	2.73205	+	2.73205i	0.626775	+	0.626775i	0.947255	−	0.320480i	$-0.103844\pi$
$19$	2.73205	+	2.73205i	0.626775	+	0.626775i	−0.320480	+	0.947255i	$0.603844\pi$
$20$	0.285334	+	0.285334i	0.0638027	+	0.0638027i
$21$	0.301143	−	2.43091i	0.0657148	−	0.530468i
$22$	−6.19615			−1.32102
$23$		0			0			−	1.00000i	$-0.5\pi$
$23$		0			0				1.00000i	$0.5\pi$
$24$	−4.48364	−	0.555437i	−0.915219	−	0.113378i
$25$			2.73205i			0.546410i
$26$		0			0
$27$	−2.09808	−	4.75374i	−0.403775	−	0.914858i
$28$	−0.267949	−	0.267949i	−0.0506376	−	0.0506376i
$29$			7.16884i			1.33122i	0.746299	+	0.665610i	$0.231829\pi$
$29$			7.16884i			1.33122i	−0.746299	+	0.665610i	$0.768171\pi$
$30$	−2.41510	−	3.09808i	−0.440935	−	0.565629i
$31$	−2.46410	−	2.46410i	−0.442566	−	0.442566i	0.450308	−	0.892873i	$-0.351314\pi$
$31$	−2.46410	−	2.46410i	−0.442566	−	0.442566i	−0.892873	+	0.450308i	$0.851314\pi$
$32$	−1.06488	+	1.06488i	−0.188246	+	0.188246i
$33$	7.07227	+	0.876119i	1.23112	+	0.152513i
$34$	−5.36603	+	5.36603i	−0.920266	+	0.920266i
$35$			2.12976i			0.359996i
$36$	−0.779548	−	0.196152i	−0.129925	−	0.0326921i
$37$	3.83013	−	3.83013i	0.629669	−	0.629669i	−0.318316	−	0.947985i	$-0.603117\pi$
$37$	3.83013	−	3.83013i	0.629669	−	0.629669i	0.947985	+	0.318316i	$0.103117\pi$
$38$	−5.81863			−0.943906
$39$		0			0
$40$	3.92820			0.621103
$41$	3.97420	−	3.97420i	0.620665	−	0.620665i	−0.325036	−	0.945701i	$-0.605377\pi$
$41$	3.97420	−	3.97420i	0.620665	−	0.620665i	0.945701	+	0.325036i	$0.105377\pi$
$42$	2.26795	+	2.90931i	0.349952	+	0.448917i
$43$		−	2.19615i		−	0.334910i	−0.985880	−	0.167455i	$-0.946445\pi$
$43$		−	2.19615i		−	0.334910i	0.985880	−	0.167455i	$-0.0535549\pi$
$44$	0.779548	−	0.779548i	0.117521	−	0.117521i
$45$	2.31853	+	3.87762i	0.345626	+	0.578042i
$46$		0			0
$47$	4.25953	+	4.25953i	0.621316	+	0.621316i	0.945868	−	0.324552i	$-0.105213\pi$
$47$	4.25953	+	4.25953i	0.621316	+	0.621316i	−0.324552	+	0.945868i	$0.605213\pi$
$48$	6.09808	−	4.75374i	0.880181	−	0.686144i
$49$			5.00000i			0.714286i
$50$	−2.90931	−	2.90931i	−0.411439	−	0.411439i
$51$	6.88351	−	5.36603i	0.963884	−	0.751394i
$52$		0			0
$53$			0.779548i			0.107079i	0.998566	+	0.0535396i	$0.0170503\pi$
$53$			0.779548i			0.107079i	−0.998566	+	0.0535396i	$0.982950\pi$
$54$	7.29638	+	2.82797i	0.992912	+	0.384838i
$55$	−6.19615			−0.835489
$56$	−3.68886			−0.492945
$57$	6.64136	+	0.822738i	0.879670	+	0.108974i
$58$	−7.63397	−	7.63397i	−1.00239	−	1.00239i
$59$	−2.12976	−	2.12976i	−0.277272	−	0.277272i	0.554747	−	0.832019i	$-0.312815\pi$
$59$	−2.12976	−	2.12976i	−0.277272	−	0.277272i	−0.832019	+	0.554747i	$0.812815\pi$
$60$	0.693622	+	0.0859264i	0.0895462	+	0.0110931i
$61$	−7.00000			−0.896258			−0.448129	−	0.893969i	$-0.647910\pi$
$61$	−7.00000			−0.896258			−0.448129	+	0.893969i	$0.647910\pi$
$62$	5.24796			0.666491
$63$	−2.17726	−	3.64136i	−0.274309	−	0.458769i
$64$			6.66025i			0.832532i
$65$		0			0
$66$	−8.46410	+	6.59817i	−1.04186	+	0.812179i
$67$	−4.19615	−	4.19615i	−0.512642	−	0.512642i	0.402693	−	0.915335i	$-0.368074\pi$
$67$	−4.19615	−	4.19615i	−0.512642	−	0.512642i	−0.915335	+	0.402693i	$0.868074\pi$
$68$		−	1.35022i		−	0.163738i
$69$		0			0
$70$	−2.26795	−	2.26795i	−0.271072	−	0.271072i
$71$	2.12976	−	2.12976i	0.252757	−	0.252757i	−0.569343	−	0.822100i	$-0.692802\pi$
$71$	2.12976	−	2.12976i	0.252757	−	0.252757i	0.822100	+	0.569343i	$0.192802\pi$
$72$	−6.71624	+	4.01581i	−0.791517	+	0.473268i
$73$	−0.901924	+	0.901924i	−0.105562	+	0.105562i	−0.757915	−	0.652353i	$-0.773782\pi$
$73$	−0.901924	+	0.901924i	−0.105562	+	0.105562i	0.652353	+	0.757915i	$0.273782\pi$
$74$			8.15727i			0.948263i
$75$	2.90931	+	3.73205i	0.335939	+	0.430940i
$76$	0.732051	−	0.732051i	0.0839720	−	0.0839720i
$77$	5.81863			0.663094
$78$		0			0
$79$	2.00000			0.225018			0.112509	−	0.993651i	$-0.464111\pi$
$79$	2.00000			0.225018			0.112509	+	0.993651i	$0.464111\pi$
$80$	−4.75374	+	4.75374i	−0.531485	+	0.531485i
$81$	−7.92820	−	4.25953i	−0.880911	−	0.473281i
$82$			8.46410i			0.934704i
$83$	−2.90931	+	2.90931i	−0.319339	+	0.319339i	−0.848513	−	0.529174i	$-0.822502\pi$
$83$	−2.90931	+	2.90931i	−0.319339	+	0.319339i	0.529174	+	0.848513i	$0.322502\pi$
$84$	−0.651360	−	0.0806910i	−0.0710692	−	0.00880411i
$85$	−5.36603	+	5.36603i	−0.582027	+	0.582027i
$86$	2.33864	+	2.33864i	0.252182	+	0.252182i
$87$	7.63397	+	9.79282i	0.818448	+	1.04990i
$88$		−	10.7321i		−	1.14404i
$89$	6.59817	+	6.59817i	0.699405	+	0.699405i	0.964282	−	0.264877i	$-0.0853314\pi$
$89$	6.59817	+	6.59817i	0.699405	+	0.699405i	−0.264877	+	0.964282i	$0.585331\pi$
$90$	−6.59817	−	1.66025i	−0.695509	−	0.175006i
$91$		0			0
$92$		0			0
$93$	−5.99000	−	0.742047i	−0.621134	−	0.0769467i
$94$	−9.07180			−0.935684
$95$	−5.81863			−0.596978
$96$	−0.320682	+	2.58863i	−0.0327295	+	0.264201i
$97$	−1.19615	−	1.19615i	−0.121451	−	0.121451i	0.643769	−	0.765220i	$-0.277370\pi$
$97$	−1.19615	−	1.19615i	−0.121451	−	0.121451i	−0.765220	+	0.643769i	$0.777370\pi$
$98$	−5.32441	−	5.32441i	−0.537847	−	0.537847i
$99$	10.5939	−	6.33434i	1.06472	−	0.636625i
$100$	0.732051			0.0732051
$101$	−6.02751			−0.599759			−0.299880	−	0.953977i	$-0.596947\pi$
$101$	−6.02751			−0.599759			−0.299880	+	0.953977i	$0.596947\pi$
$102$	−1.61594	+	13.0443i	−0.160002	+	1.29158i
$103$		−	6.92820i		−	0.682656i	−0.939944	−	0.341328i	$-0.889123\pi$
$103$		−	6.92820i		−	0.682656i	0.939944	−	0.341328i	$-0.110877\pi$
$104$		0			0
$105$	2.26795	+	2.90931i	0.221329	+	0.283920i
$106$	−0.830127	−	0.830127i	−0.0806291	−	0.0806291i
$107$		−	19.0150i		−	1.83825i	−0.393970	−	0.919123i	$-0.628899\pi$
$107$		−	19.0150i		−	1.83825i	0.393970	−	0.919123i	$-0.371101\pi$
$108$	−1.27376	+	0.562178i	−0.122568	+	0.0540956i
$109$	−13.1962	−	13.1962i	−1.26396	−	1.26396i	−0.949156	−	0.314806i	$-0.898060\pi$
$109$	−13.1962	−	13.1962i	−1.26396	−	1.26396i	−0.314806	−	0.949156i	$-0.601940\pi$
$110$	6.59817	−	6.59817i	0.629111	−	0.629111i
$111$	1.15342	−	9.31069i	0.109477	−	0.883731i
$112$	4.46410	−	4.46410i	0.421818	−	0.421818i
$113$		−	10.2870i		−	0.967723i	−0.875145	−	0.483861i	$-0.839234\pi$
$113$		−	10.2870i		−	0.967723i	0.875145	−	0.483861i	$-0.160766\pi$
$114$	−7.94839	+	6.19615i	−0.744435	+	0.580323i
$115$		0			0
$116$	1.92089			0.178350
$117$		0			0
$118$	4.53590			0.417563
$119$	5.03908	−	5.03908i	0.461932	−	0.461932i
$120$	5.36603	−	4.18307i	0.489849	−	0.381861i
$121$			5.92820i			0.538928i
$122$	7.45418	−	7.45418i	0.674869	−	0.674869i
$123$	1.19680	−	9.66090i	0.107912	−	0.871094i
$124$	−0.660254	+	0.660254i	−0.0592926	+	0.0592926i
$125$	−8.23373	−	8.23373i	−0.736447	−	0.736447i
$126$	6.19615	+	1.55910i	0.551997	+	0.138895i
$127$			9.12436i			0.809656i	0.914393	+	0.404828i	$0.132669\pi$
$127$			9.12436i			0.809656i	−0.914393	+	0.404828i	$0.867331\pi$
$128$	−9.22215	−	9.22215i	−0.815131	−	0.815131i
$129$	−2.33864	−	3.00000i	−0.205906	−	0.264135i
$130$		0			0
$131$		−	7.94839i		−	0.694454i	−0.937781	−	0.347227i	$-0.887123\pi$
$131$		−	7.94839i		−	0.694454i	0.937781	−	0.347227i	$-0.112877\pi$
$132$	0.234755	−	1.89501i	0.0204328	−	0.164939i
$133$	5.46410			0.473798
$134$	8.93682			0.772023
$135$	7.29638	+	2.82797i	0.627973	+	0.243393i
$136$	−9.29423	−	9.29423i	−0.796974	−	0.796974i
$137$	4.75374	+	4.75374i	0.406140	+	0.406140i	0.880390	−	0.474250i	$-0.157281\pi$
$137$	4.75374	+	4.75374i	0.406140	+	0.406140i	−0.474250	+	0.880390i	$0.657281\pi$
$138$		0			0
$139$	18.3923			1.56001			0.780007	−	0.625770i	$-0.215215\pi$
$139$	18.3923			1.56001			0.780007	+	0.625770i	$0.215215\pi$
$140$	0.570669			0.0482303
$141$	10.3545	+	1.28273i	0.872008	+	0.108025i
$142$			4.53590i			0.380644i
$143$		0			0
$144$	3.26795	−	12.9875i	0.272329	−	1.08229i
$145$	−7.63397	−	7.63397i	−0.633967	−	0.633967i
$146$		−	1.92089i		−	0.158974i
$147$	5.32441	+	6.83013i	0.439150	+	0.563339i
$148$	−1.02628	−	1.02628i	−0.0843597	−	0.0843597i
$149$	−6.10396	+	6.10396i	−0.500056	+	0.500056i	−0.911455	−	0.411399i	$-0.865040\pi$
$149$	−6.10396	+	6.10396i	−0.500056	+	0.500056i	0.411399	+	0.911455i	$0.365040\pi$
$150$	−7.07227	−	0.876119i	−0.577449	−	0.0715348i
$151$	0.535898	−	0.535898i	0.0436108	−	0.0436108i	−0.684965	−	0.728576i	$-0.740183\pi$
$151$	0.535898	−	0.535898i	0.0436108	−	0.0436108i	0.728576	+	0.684965i	$0.240183\pi$
$152$		−	10.0782i		−	0.817446i
$153$	3.68886	−	14.6603i	0.298227	−	1.18521i
$154$	−6.19615	+	6.19615i	−0.499300	+	0.499300i
$155$	5.24796			0.421526
$156$		0			0
$157$	−4.80385			−0.383389			−0.191694	−	0.981455i	$-0.561398\pi$
$157$	−4.80385			−0.383389			−0.191694	+	0.981455i	$0.561398\pi$
$158$	−2.12976	+	2.12976i	−0.169435	+	0.169435i
$159$	0.830127	+	1.06488i	0.0658334	+	0.0844507i
$160$		−	2.26795i		−	0.179297i
$161$		0			0
$162$	12.9785	−	3.90671i	1.01969	−	0.306940i
$163$	−2.92820	+	2.92820i	−0.229355	+	0.229355i	−0.812423	−	0.583068i	$-0.801852\pi$
$163$	−2.92820	+	2.92820i	−0.229355	+	0.229355i	0.583068	+	0.812423i	$0.301852\pi$
$164$	−1.06488	−	1.06488i	−0.0831533	−	0.0831533i
$165$	−8.46410	+	6.59817i	−0.658929	+	0.513667i
$166$		−	6.19615i		−	0.480915i
$167$	−9.50749	−	9.50749i	−0.735711	−	0.735711i	0.236034	−	0.971745i	$-0.424152\pi$
$167$	−9.50749	−	9.50749i	−0.735711	−	0.735711i	−0.971745	+	0.236034i	$0.924152\pi$
$168$	−5.03908	+	3.92820i	−0.388773	+	0.303067i
$169$		0			0
$170$		−	11.4284i		−	0.876516i
$171$	9.94839	−	5.94839i	0.760772	−	0.454885i
$172$	−0.588457			−0.0448694
$173$	−17.4559			−1.32715			−0.663573	−	0.748112i	$-0.730961\pi$
$173$	−17.4559			−1.32715			−0.663573	+	0.748112i	$0.730961\pi$
$174$	−18.5575	−	2.29892i	−1.40684	−	0.174281i
$175$	2.73205	+	2.73205i	0.206524	+	0.206524i
$176$	12.9875	+	12.9875i	0.978967	+	0.978967i
$177$	−5.17726	−	0.641364i	−0.389147	−	0.0482078i
$178$	−14.0526			−1.05328
$179$	−26.5456			−1.98411			−0.992056	−	0.125798i	$-0.959851\pi$
$179$	−26.5456			−1.98411			−0.992056	+	0.125798i	$0.959851\pi$
$180$	1.03901	−	0.621248i	0.0774430	−	0.0463051i
$181$		−	3.00000i		−	0.222988i	−0.993765	−	0.111494i	$-0.964436\pi$
$181$		−	3.00000i		−	0.222988i	0.993765	−	0.111494i	$-0.0355636\pi$
$182$		0			0
$183$	−9.56218	+	7.45418i	−0.706857	+	0.551029i
$184$		0			0
$185$			8.15727i			0.599734i
$186$	7.16884	−	5.58846i	0.525645	−	0.409766i
$187$	14.6603	+	14.6603i	1.07206	+	1.07206i
$188$	1.14134	−	1.14134i	0.0832406	−	0.0832406i
$189$	−6.85182	−	2.65567i	−0.498397	−	0.193171i
$190$	6.19615	−	6.19615i	0.449516	−	0.449516i
$191$			4.83020i			0.349501i	0.984613	+	0.174750i	$0.0559119\pi$
$191$			4.83020i			0.349501i	−0.984613	+	0.174750i	$0.944088\pi$
$192$	7.09239	+	9.09808i	0.511849	+	0.656597i
$193$	−0.0980762	+	0.0980762i	−0.00705968	+	0.00705968i	−0.710628	−	0.703568i	$-0.751589\pi$
$193$	−0.0980762	+	0.0980762i	−0.00705968	+	0.00705968i	0.703568	+	0.710628i	$0.251589\pi$
$194$	2.54752			0.182902
$195$		0			0
$196$	1.33975			0.0956961
$197$	−2.90931	+	2.90931i	−0.207280	+	0.207280i	−0.803110	−	0.595830i	$-0.796823\pi$
$197$	−2.90931	+	2.90931i	−0.207280	+	0.207280i	0.595830	+	0.803110i	$0.296823\pi$
$198$	−4.53590	+	18.0265i	−0.322352	+	1.28109i
$199$		−	12.9282i		−	0.916456i	−0.888835	−	0.458228i	$-0.848484\pi$
$199$		−	12.9282i		−	0.916456i	0.888835	−	0.458228i	$-0.151516\pi$
$200$	5.03908	−	5.03908i	0.356317	−	0.356317i
$201$	−10.2005	−	1.26364i	−0.719485	−	0.0891304i
$202$	6.41858	−	6.41858i	0.451610	−	0.451610i
$203$	7.16884	+	7.16884i	0.503154	+	0.503154i
$204$	−1.43782	−	1.84443i	−0.100668	−	0.129136i
$205$			8.46410i			0.591158i
$206$	7.37772	+	7.37772i	0.514030	+	0.514030i
$207$		0			0
$208$		0			0
$209$			15.8968i			1.09960i
$210$	−5.51318	−	0.682977i	−0.380445	−	0.0471299i
$211$	−1.80385			−0.124182			−0.0620910	−	0.998070i	$-0.519777\pi$
$211$	−1.80385			−0.124182			−0.0620910	+	0.998070i	$0.519777\pi$
$212$	0.208879			0.0143459
$213$	0.641364	−	5.17726i	0.0439455	−	0.354740i
$214$	20.2487	+	20.2487i	1.38417	+	1.38417i
$215$	2.33864	+	2.33864i	0.159494	+	0.159494i
$216$	−4.89819	+	12.6377i	−0.333280	+	0.859887i
$217$	−4.92820			−0.334548
$218$	28.1047			1.90349
$219$	−0.271608	+	2.19249i	−0.0183536	+	0.148155i
$220$			1.66025i			0.111934i
$221$		0			0
$222$	8.68653	+	11.1430i	0.583002	+	0.747872i
$223$	18.3205	+	18.3205i	1.22683	+	1.22683i	0.965156	+	0.261676i	$0.0842753\pi$
$223$	18.3205	+	18.3205i	1.22683	+	1.22683i	0.261676	+	0.965156i	$0.415725\pi$
$224$			2.12976i			0.142301i
$225$	7.94839	+	2.00000i	0.529893	+	0.133333i
$226$	10.9545	+	10.9545i	0.728681	+	0.728681i
$227$	−14.3377	+	14.3377i	−0.951626	+	0.951626i	−0.998883	−	0.0472572i	$-0.984952\pi$
$227$	−14.3377	+	14.3377i	−0.951626	+	0.951626i	0.0472572	+	0.998883i	$0.484952\pi$
$228$	0.220452	−	1.77955i	0.0145998	−	0.117853i
$229$	−14.1244	+	14.1244i	−0.933364	+	0.933364i	−0.997914	−	0.0645507i	$-0.979439\pi$
$229$	−14.1244	+	14.1244i	−0.933364	+	0.933364i	0.0645507	+	0.997914i	$0.479439\pi$
$230$		0			0
$231$	7.94839	−	6.19615i	0.522966	−	0.407677i
$232$	13.2224	−	13.2224i	0.868095	−	0.868095i
$233$	−17.4559			−1.14357			−0.571786	−	0.820403i	$-0.693749\pi$
$233$	−17.4559			−1.14357			−0.571786	+	0.820403i	$0.693749\pi$
$234$		0			0
$235$	−9.07180			−0.591779
$236$	−0.570669	+	0.570669i	−0.0371474	+	0.0371474i
$237$	2.73205	−	2.12976i	0.177466	−	0.138343i
$238$			10.7321i			0.695656i
$239$	−6.59817	+	6.59817i	−0.426800	+	0.426800i	−0.887537	−	0.460737i	$-0.847585\pi$
$239$	−6.59817	+	6.59817i	−0.426800	+	0.426800i	0.460737	+	0.887537i	$0.347585\pi$
$240$	−1.43156	+	11.5559i	−0.0924066	+	0.745931i
$241$	10.2942	−	10.2942i	0.663110	−	0.663110i	−0.293002	−	0.956112i	$-0.594654\pi$
$241$	10.2942	−	10.2942i	0.663110	−	0.663110i	0.956112	+	0.293002i	$0.0946543\pi$
$242$	−6.31284	−	6.31284i	−0.405805	−	0.405805i
$243$	−15.3660	+	2.62398i	−0.985731	+	0.168328i
$244$			1.87564i			0.120076i
$245$	−5.32441	−	5.32441i	−0.340164	−	0.340164i
$246$	9.01327	+	11.5622i	0.574665	+	0.737178i
$247$		0			0
$248$			9.08973i			0.577198i
$249$	−0.876119	+	7.07227i	−0.0555218	+	0.448187i
$250$	17.5359			1.10907
$251$	0.988427			0.0623890			0.0311945	−	0.999513i	$-0.490069\pi$
$251$	0.988427			0.0623890			0.0311945	+	0.999513i	$0.490069\pi$
$252$	−0.975700	+	0.583396i	−0.0614634	+	0.0367505i
$253$		0			0
$254$	−9.71637	−	9.71637i	−0.609659	−	0.609659i
$255$	−1.61594	+	13.0443i	−0.101194	+	0.816867i
$256$	6.32051			0.395032
$257$	21.5065			1.34154			0.670770	−	0.741665i	$-0.265964\pi$
$257$	21.5065			1.34154			0.670770	+	0.741665i	$0.265964\pi$
$258$	5.68503	+	0.704266i	0.353934	+	0.0438457i
$259$		−	7.66025i		−	0.475985i
$260$		0			0
$261$	20.8564	+	5.24796i	1.29098	+	0.324840i
$262$	8.46410	+	8.46410i	0.522914	+	0.522914i
$263$			22.2861i			1.37422i	0.726554	+	0.687109i	$0.241121\pi$
$263$			22.2861i			1.37422i	−0.726554	+	0.687109i	$0.758879\pi$
$264$	−11.4284	−	14.6603i	−0.703368	−	0.902276i
$265$	−0.830127	−	0.830127i	−0.0509943	−	0.0509943i
$266$	−5.81863	+	5.81863i	−0.356763	+	0.356763i
$267$	16.0396	+	1.98699i	0.981605	+	0.121602i
$268$	−1.12436	+	1.12436i	−0.0686810	+	0.0686810i
$269$		−	14.3377i		−	0.874184i	−0.899417	−	0.437092i	$-0.856008\pi$
$269$		−	14.3377i		−	0.874184i	0.899417	−	0.437092i	$-0.143992\pi$
$270$	−10.7812	+	4.75833i	−0.656126	+	0.289583i
$271$	−5.46410	+	5.46410i	−0.331921	+	0.331921i	−0.853315	−	0.521395i	$-0.825412\pi$
$271$	−5.46410	+	5.46410i	−0.331921	+	0.331921i	0.521395	+	0.853315i	$0.325412\pi$
$272$	22.4950			1.36396
$273$		0			0
$274$	−10.1244			−0.611635
$275$	−7.94839	+	7.94839i	−0.479306	+	0.479306i
$276$		0			0
$277$		−	27.5885i		−	1.65763i	−0.559523	−	0.828815i	$-0.689016\pi$
$277$		−	27.5885i		−	1.65763i	0.559523	−	0.828815i	$-0.310984\pi$
$278$	−19.5856	+	19.5856i	−1.17467	+	1.17467i
$279$	−8.97269	+	5.36500i	−0.537181	+	0.321194i
$280$	3.92820	−	3.92820i	0.234755	−	0.234755i
$281$	12.1315	+	12.1315i	0.723703	+	0.723703i	0.969357	−	0.245655i	$-0.0790030\pi$
$281$	12.1315	+	12.1315i	0.723703	+	0.723703i	−0.245655	+	0.969357i	$0.579003\pi$
$282$	−12.3923	+	9.66040i	−0.737951	+	0.575268i
$283$		−	6.58846i		−	0.391643i	−0.980640	−	0.195822i	$-0.937263\pi$
$283$		−	6.58846i		−	0.391643i	0.980640	−	0.195822i	$-0.0627373\pi$
$284$	−0.570669	−	0.570669i	−0.0338630	−	0.0338630i
$285$	−7.94839	+	6.19615i	−0.470822	+	0.367028i
$286$		0			0
$287$		−	7.94839i		−	0.469179i
$288$	2.31853	+	3.87762i	0.136621	+	0.228491i
$289$	8.39230			0.493665
$290$	16.2586			0.954736
$291$	−2.90774	−	0.360213i	−0.170455	−	0.0211161i
$292$	0.241670	+	0.241670i	0.0141427	+	0.0141427i
$293$	−1.27376	−	1.27376i	−0.0744140	−	0.0744140i	0.668920	−	0.743334i	$-0.266757\pi$
$293$	−1.27376	−	1.27376i	−0.0744140	−	0.0744140i	−0.743334	+	0.668920i	$0.766757\pi$
$294$	−12.9432	−	1.60341i	−0.754860	−	0.0935127i
$295$	4.53590			0.264090
$296$	−14.1288			−0.821220
$297$	7.72617	−	19.9341i	0.448318	−	1.15669i
$298$		−	13.0000i		−	0.753070i
$299$		0			0
$300$	1.00000	−	0.779548i	0.0577350	−	0.0450072i
$301$	−2.19615	−	2.19615i	−0.126584	−	0.126584i
$302$			1.14134i			0.0656766i
$303$	−8.23373	+	6.41858i	−0.473015	+	0.368738i
$304$	12.1962	+	12.1962i	0.699497	+	0.699497i
$305$	7.45418	−	7.45418i	0.426825	−	0.426825i
$306$	11.6832	+	19.5397i	0.667887	+	1.11701i
$307$	8.39230	−	8.39230i	0.478974	−	0.478974i	−0.425829	−	0.904803i	$-0.640018\pi$
$307$	8.39230	−	8.39230i	0.478974	−	0.478974i	0.904803	+	0.425829i	$0.140018\pi$
$308$		−	1.55910i		−	0.0888377i
$309$	−7.37772	−	9.46410i	−0.419704	−	0.538394i
$310$	−5.58846	+	5.58846i	−0.317403	+	0.317403i
$311$	−10.0782			−0.571480			−0.285740	−	0.958307i	$-0.592239\pi$
$311$	−10.0782			−0.571480			−0.285740	+	0.958307i	$0.592239\pi$
$312$		0			0
$313$	2.00000			0.113047			0.0565233	−	0.998401i	$-0.481998\pi$
$313$	2.00000			0.113047			0.0565233	+	0.998401i	$0.481998\pi$
$314$	5.11553	−	5.11553i	0.288686	−	0.288686i
$315$	6.19615	+	1.55910i	0.349114	+	0.0878451i
$316$		−	0.535898i		−	0.0301466i
$317$	11.3519	−	11.3519i	0.637587	−	0.637587i	−0.312373	−	0.949960i	$-0.601124\pi$
$317$	11.3519	−	11.3519i	0.637587	−	0.637587i	0.949960	+	0.312373i	$0.101124\pi$
$318$	−2.01796	−	0.249987i	−0.113162	−	0.0140186i
$319$	−20.8564	+	20.8564i	−1.16773	+	1.16773i
$320$	−7.09239	−	7.09239i	−0.396477	−	0.396477i
$321$	−20.2487	−	25.9749i	−1.13017	−	1.44978i
$322$		0			0
$323$	13.7670	+	13.7670i	0.766017	+	0.766017i
$324$	−1.14134	+	2.12436i	−0.0634076	+	0.118020i
$325$		0			0
$326$		−	6.23638i		−	0.345401i
$327$	−32.0786	−	3.97393i	−1.77395	−	0.219759i
$328$	−14.6603			−0.809477
$329$	8.51906			0.469671
$330$	1.98699	−	16.0396i	0.109380	−	0.882948i
$331$	24.1962	+	24.1962i	1.32994	+	1.32994i	0.905417	+	0.424524i	$0.139559\pi$
$331$	24.1962	+	24.1962i	1.32994	+	1.32994i	0.424524	+	0.905417i	$0.360441\pi$
$332$	0.779548	+	0.779548i	0.0427833	+	0.0427833i
$333$	−8.33919	−	13.9469i	−0.456985	−	0.764285i
$334$	20.2487			1.10796
$335$	8.93682			0.488271
$336$	1.34433	−	10.8518i	0.0733394	−	0.592015i
$337$			18.4641i			1.00580i	0.864344	+	0.502902i	$0.167734\pi$
$337$			18.4641i			1.00580i	−0.864344	+	0.502902i	$0.832266\pi$
$338$		0			0
$339$	−10.9545	−	14.0524i	−0.594966	−	0.763219i
$340$	1.43782	+	1.43782i	0.0779769	+	0.0779769i
$341$		−	14.3377i		−	0.776429i
$342$	−4.25953	+	16.9282i	−0.230329	+	0.915372i
$343$	12.0000	+	12.0000i	0.647939	+	0.647939i
$344$	−4.05065	+	4.05065i	−0.218396	+	0.218396i
$345$		0			0
$346$	18.5885	−	18.5885i	0.999322	−	0.999322i
$347$			20.5741i			1.10447i	0.833687	+	0.552237i	$0.186226\pi$
$347$			20.5741i			1.10447i	−0.833687	+	0.552237i	$0.813774\pi$
$348$	2.62398	−	2.04552i	0.140660	−	0.109651i
$349$	−20.1244	+	20.1244i	−1.07723	+	1.07723i	−0.0804755	+	0.996757i	$0.525644\pi$
$349$	−20.1244	+	20.1244i	−1.07723	+	1.07723i	−0.996757	+	0.0804755i	$0.974356\pi$
$350$	−5.81863			−0.311019
$351$		0			0
$352$	−6.19615			−0.330256
$353$	10.0017	−	10.0017i	0.532337	−	0.532337i	−0.388930	−	0.921267i	$-0.627155\pi$
$353$	10.0017	−	10.0017i	0.532337	−	0.532337i	0.921267	+	0.388930i	$0.127155\pi$
$354$	6.19615	−	4.83020i	0.329322	−	0.256722i
$355$			4.53590i			0.240740i
$356$	1.76798	−	1.76798i	0.0937025	−	0.0937025i
$357$	1.51748	−	12.2495i	0.0803137	−	0.648314i
$358$	28.2679	−	28.2679i	1.49401	−	1.49401i
$359$	−18.2354	−	18.2354i	−0.962429	−	0.962429i	0.0368904	−	0.999319i	$-0.488255\pi$
$359$	−18.2354	−	18.2354i	−0.962429	−	0.962429i	−0.999319	+	0.0368904i	$0.988255\pi$
$360$	2.87564	−	11.4284i	0.151560	−	0.602328i
$361$		−	4.07180i		−	0.214305i
$362$	3.19465	+	3.19465i	0.167907	+	0.167907i
$363$	6.31284	+	8.09808i	0.331338	+	0.425039i
$364$		0			0
$365$		−	1.92089i		−	0.100544i
$366$	2.24477	−	18.1204i	0.117336	−	0.947169i
$367$	30.3923			1.58647			0.793233	−	0.608919i	$-0.208396\pi$
$367$	30.3923			1.58647			0.793233	+	0.608919i	$0.208396\pi$
$368$		0			0
$369$	−8.65286	−	14.4715i	−0.450450	−	0.753356i
$370$	−8.68653	−	8.68653i	−0.451591	−	0.451591i
$371$	0.779548	+	0.779548i	0.0404721	+	0.0404721i
$372$	−0.198831	+	1.60502i	−0.0103089	+	0.0832162i
$373$	11.5885			0.600028			0.300014	−	0.953935i	$-0.403009\pi$
$373$	11.5885			0.600028			0.300014	+	0.953935i	$0.403009\pi$
$374$	−31.2229			−1.61450
$375$	−20.0154	−	2.47953i	−1.03359	−	0.128042i
$376$		−	15.7128i		−	0.810326i
$377$		0			0
$378$	10.1244	−	4.46841i	0.520741	−	0.229830i
$379$	10.4641	+	10.4641i	0.537505	+	0.537505i	0.922795	−	0.385291i	$-0.125899\pi$
$379$	10.4641	+	10.4641i	0.537505	+	0.537505i	−0.385291	+	0.922795i	$0.625899\pi$
$380$			1.55910i			0.0799799i
$381$	9.71637	+	12.4641i	0.497785	+	0.638555i
$382$	−5.14359	−	5.14359i	−0.263169	−	0.263169i
$383$	23.2745	−	23.2745i	1.18927	−	1.18927i	0.212002	−	0.977269i	$-0.432002\pi$
$383$	23.2745	−	23.2745i	1.18927	−	1.18927i	0.977269	−	0.212002i	$-0.0679985\pi$
$384$	−22.4182	−	2.77719i	−1.14402	−	0.141723i
$385$	−6.19615	+	6.19615i	−0.315785	+	0.315785i
$386$		−	0.208879i		−	0.0106317i
$387$	−6.38929	−	1.60770i	−0.324786	−	0.0817237i
$388$	−0.320508	+	0.320508i	−0.0162713	+	0.0162713i
$389$	−22.4950			−1.14054			−0.570270	−	0.821457i	$-0.693161\pi$
$389$	−22.4950			−1.14054			−0.570270	+	0.821457i	$0.693161\pi$
$390$		0			0
$391$		0			0
$392$	9.22215	−	9.22215i	0.465789	−	0.465789i
$393$	−8.46410	−	10.8577i	−0.426957	−	0.547699i
$394$		−	6.19615i		−	0.312158i
$395$	−2.12976	+	2.12976i	−0.107160	+	0.107160i
$396$	−1.69728	−	2.83862i	−0.0852916	−	0.142646i
$397$	−9.73205	+	9.73205i	−0.488438	+	0.488438i	−0.907813	−	0.419375i	$-0.862249\pi$
$397$	−9.73205	+	9.73205i	−0.488438	+	0.488438i	0.419375	+	0.907813i	$0.362249\pi$
$398$	13.7670	+	13.7670i	0.690078	+	0.690078i
$399$	7.46410	−	5.81863i	0.373672	−	0.291296i
$400$			12.1962i			0.609808i
$401$	8.80439	+	8.80439i	0.439670	+	0.439670i	0.891901	−	0.452231i	$-0.149372\pi$
$401$	8.80439	+	8.80439i	0.439670	+	0.439670i	−0.452231	+	0.891901i	$0.649372\pi$
$402$	12.2079	−	9.51666i	0.608876	−	0.474648i
$403$		0			0
$404$			1.61507i			0.0803525i
$405$	12.9785	−	3.90671i	0.644907	−	0.194126i
$406$	−15.2679			−0.757736
$407$	22.2861			1.10468
$408$	−22.5934	−	2.79889i	−1.11854	−	0.138566i
$409$	−21.2224	−	21.2224i	−1.04938	−	1.04938i	−0.998716	−	0.0506661i	$-0.983866\pi$
$409$	−21.2224	−	21.2224i	−1.04938	−	1.04938i	−0.0506661	−	0.998716i	$-0.516134\pi$
$410$	−9.01327	−	9.01327i	−0.445134	−	0.445134i
$411$	11.5559	+	1.43156i	0.570011	+	0.0706135i
$412$	−1.85641			−0.0914586
$413$	−4.25953			−0.209598
$414$		0			0
$415$		−	6.19615i		−	0.304157i
$416$		0			0
$417$	25.1244	−	19.5856i	1.23034	−	0.959113i
$418$	−16.9282	−	16.9282i	−0.827985	−	0.827985i
$419$			9.50749i			0.464471i	0.972660	+	0.232236i	$0.0746040\pi$
$419$			9.50749i			0.464471i	−0.972660	+	0.232236i	$0.925396\pi$
$420$	0.779548	−	0.607695i	0.0380380	−	0.0296525i
$421$	−7.83013	−	7.83013i	−0.381617	−	0.381617i	0.490067	−	0.871685i	$-0.336972\pi$
$421$	−7.83013	−	7.83013i	−0.381617	−	0.381617i	−0.871685	+	0.490067i	$0.836972\pi$
$422$	1.92089	−	1.92089i	0.0935072	−	0.0935072i
$423$	15.5105	−	9.27411i	0.754146	−	0.450923i
$424$	1.43782	−	1.43782i	0.0698268	−	0.0698268i
$425$			13.7670i			0.667798i
$426$	4.83020	+	6.19615i	0.234024	+	0.300205i
$427$	−7.00000	+	7.00000i	−0.338754	+	0.338754i
$428$	−5.09505			−0.246278
$429$		0			0
$430$	−4.98076			−0.240194
$431$	−26.7545	+	26.7545i	−1.28872	+	1.28872i	−0.353152	+	0.935566i	$0.614890\pi$
$431$	−26.7545	+	26.7545i	−1.28872	+	1.28872i	−0.935566	+	0.353152i	$0.885110\pi$
$432$	−9.36603	−	21.2212i	−0.450623	−	1.02101i
$433$			31.0526i			1.49229i	0.665783	+	0.746145i	$0.268098\pi$
$433$			31.0526i			1.49229i	−0.665783	+	0.746145i	$0.731902\pi$
$434$	5.24796	−	5.24796i	0.251910	−	0.251910i
$435$	−18.5575	−	2.29892i	−0.889763	−	0.110225i
$436$	−3.53590	+	3.53590i	−0.169339	+	0.169339i
$437$		0			0
$438$	−2.04552	−	2.62398i	−0.0977386	−	0.125379i
$439$			1.26795i			0.0605159i	0.999542	+	0.0302580i	$0.00963288\pi$
$439$			1.26795i			0.0605159i	−0.999542	+	0.0302580i	$0.990367\pi$
$440$	11.4284	+	11.4284i	0.544826	+	0.544826i
$441$	14.5466	+	3.66025i	0.692694	+	0.174298i
$442$		0			0
$443$			11.2195i			0.533054i	0.963827	+	0.266527i	$0.0858762\pi$
$443$			11.2195i			0.533054i	−0.963827	+	0.266527i	$0.914124\pi$
$444$	−2.49479	−	0.309057i	−0.118398	−	0.0146672i
$445$	−14.0526			−0.666155
$446$	−39.0184			−1.84757
$447$	−1.83816	+	14.8382i	−0.0869422	+	0.701821i
$448$	6.66025	+	6.66025i	0.314667	+	0.314667i
$449$	−14.5466	−	14.5466i	−0.686495	−	0.686495i	0.274961	−	0.961455i	$-0.411335\pi$
$449$	−14.5466	−	14.5466i	−0.686495	−	0.686495i	−0.961455	+	0.274961i	$0.911335\pi$
$450$	−10.5939	+	6.33434i	−0.499400	+	0.298603i
$451$	23.1244			1.08888
$452$	−2.75640			−0.129650
$453$	0.161382	−	1.30272i	0.00758239	−	0.0612071i
$454$		−	30.5359i		−	1.43312i
$455$		0			0
$456$	−10.7321	−	13.7670i	−0.502574	−	0.644700i
$457$	−2.75833	−	2.75833i	−0.129029	−	0.129029i	0.639643	−	0.768672i	$-0.279082\pi$
$457$	−2.75833	−	2.75833i	−0.129029	−	0.129029i	−0.768672	+	0.639643i	$0.779082\pi$
$458$		−	30.0816i		−	1.40562i
$459$	−10.5724	−	23.9545i	−0.493476	−	1.11810i
$460$		0			0
$461$	15.0408	−	15.0408i	0.700519	−	0.700519i	−0.264003	−	0.964522i	$-0.585043\pi$
$461$	15.0408	−	15.0408i	0.700519	−	0.700519i	0.964522	+	0.264003i	$0.0850429\pi$
$462$	−1.86593	+	15.0623i	−0.0868108	+	0.700760i
$463$	23.0526	−	23.0526i	1.07134	−	1.07134i	0.0740918	−	0.997251i	$-0.476394\pi$
$463$	23.0526	−	23.0526i	1.07134	−	1.07134i	0.997251	−	0.0740918i	$-0.0236058\pi$
$464$			32.0024i			1.48568i
$465$	7.16884	−	5.58846i	0.332447	−	0.259159i
$466$	18.5885	−	18.5885i	0.861094	−	0.861094i
$467$	19.1679			0.886984			0.443492	−	0.896278i	$-0.353739\pi$
$467$	19.1679			0.886984			0.443492	+	0.896278i	$0.353739\pi$
$468$		0			0
$469$	−8.39230			−0.387521
$470$	9.66040	−	9.66040i	0.445601	−	0.445601i
$471$	−6.56218	+	5.11553i	−0.302369	+	0.235711i
$472$			7.85641i			0.361620i
$473$	6.38929	−	6.38929i	0.293780	−	0.293780i
$474$	−0.641364	+	5.17726i	−0.0294588	+	0.237800i
$475$	−7.46410	+	7.46410i	−0.342476	+	0.342476i
$476$	−1.35022	−	1.35022i	−0.0618871	−	0.0618871i
$477$	2.26795	+	0.570669i	0.103842	+	0.0261291i
$478$		−	14.0526i		−	0.642749i
$479$	−14.5466	−	14.5466i	−0.664649	−	0.664649i	0.291823	−	0.956472i	$-0.405738\pi$
$479$	−14.5466	−	14.5466i	−0.664649	−	0.664649i	−0.956472	+	0.291823i	$0.905738\pi$
$480$	−2.41510	−	3.09808i	−0.110234	−	0.141407i
$481$		0			0
$482$			21.9243i			0.998624i
$483$		0			0
$484$	1.58846			0.0722026
$485$	2.54752			0.115677
$486$	13.5688	−	19.1572i	0.615492	−	0.868990i
$487$	−4.07180	−	4.07180i	−0.184511	−	0.184511i	0.608807	−	0.793318i	$-0.291648\pi$
$487$	−4.07180	−	4.07180i	−0.184511	−	0.184511i	−0.793318	+	0.608807i	$0.791648\pi$
$488$	12.9110	+	12.9110i	0.584454	+	0.584454i
$489$	−0.881808	+	7.11819i	−0.0398767	+	0.321896i
$490$	11.3397			0.512278
$491$	28.5225			1.28720			0.643600	−	0.765362i	$-0.277440\pi$
$491$	28.5225			1.28720			0.643600	+	0.765362i	$0.277440\pi$
$492$	−2.58863	−	0.320682i	−0.116705	−	0.0144575i
$493$			36.1244i			1.62696i
$494$		0			0
$495$	−4.53590	+	18.0265i	−0.203873	+	0.810233i
$496$	−11.0000	−	11.0000i	−0.493915	−	0.493915i
$497$		−	4.25953i		−	0.191066i
$498$	−6.59817	−	8.46410i	−0.295671	−	0.379285i
$499$	−2.46410	−	2.46410i	−0.110308	−	0.110308i	0.649798	−	0.760107i	$-0.274853\pi$
$499$	−2.46410	−	2.46410i	−0.110308	−	0.110308i	−0.760107	+	0.649798i	$0.774853\pi$
$500$	−2.20622	+	2.20622i	−0.0986652	+	0.0986652i
$501$	−23.1118	−	2.86311i	−1.03256	−	0.127914i
$502$	−1.05256	+	1.05256i	−0.0469780	+	0.0469780i
$503$		−	3.27110i		−	0.145851i	−0.997337	−	0.0729256i	$-0.976766\pi$
$503$		−	3.27110i		−	0.145851i	0.997337	−	0.0729256i	$-0.0232336\pi$
$504$	−2.70043	+	10.7321i	−0.120287	+	0.478044i
$505$	6.41858	−	6.41858i	0.285623	−	0.285623i
$506$		0			0
$507$		0			0
$508$	2.44486			0.108473
$509$	10.3635	−	10.3635i	0.459354	−	0.459354i	−0.439090	−	0.898443i	$-0.644699\pi$
$509$	10.3635	−	10.3635i	0.459354	−	0.459354i	0.898443	+	0.439090i	$0.144699\pi$
$510$	−12.1699	−	15.6114i	−0.538891	−	0.691286i
$511$			1.80385i			0.0797975i
$512$	11.7137	−	11.7137i	0.517678	−	0.517678i
$513$	7.25542	−	18.7195i	0.320335	−	0.826487i
$514$	−22.9019	+	22.9019i	−1.01016	+	1.01016i
$515$	7.37772	+	7.37772i	0.325101	+	0.325101i
$516$	−0.803848	+	0.626638i	−0.0353874	+	0.0275862i
$517$			24.7846i			1.09003i
$518$	8.15727	+	8.15727i	0.358410	+	0.358410i
$519$	−23.8452	+	18.5885i	−1.04669	+	0.815943i
$520$		0			0
$521$			2.49155i			0.109157i	0.998509	+	0.0545785i	$0.0173815\pi$
$521$			2.49155i			0.109157i	−0.998509	+	0.0545785i	$0.982618\pi$
$522$	−27.7981	+	16.6212i	−1.21669	+	0.727489i
$523$	−38.9808			−1.70451			−0.852255	−	0.523127i	$-0.824765\pi$
$523$	−38.9808			−1.70451			−0.852255	+	0.523127i	$0.824765\pi$
$524$	−2.12976			−0.0930392
$525$	6.64136	+	0.822738i	0.289853	+	0.0359072i
$526$	−23.7321	−	23.7321i	−1.03477	−	1.03477i
$527$	−12.4168	−	12.4168i	−0.540884	−	0.540884i
$528$	31.5713	+	3.91108i	1.37397	+	0.170208i
$529$	−23.0000			−1.00000
$530$	1.76798			0.0767959
$531$	−7.75525	+	4.63706i	−0.336549	+	0.201231i
$532$		−	1.46410i		−	0.0634769i
$533$		0			0
$534$	−19.1962	+	14.9643i	−0.830699	+	0.647570i
$535$	20.2487	+	20.2487i	0.875428	+	0.875428i
$536$			15.4790i			0.668592i
$537$	−36.2620	+	28.2679i	−1.56482	+	1.21985i
$538$	15.2679	+	15.2679i	0.658248	+	0.658248i
$539$	−14.5466	+	14.5466i	−0.626565	+	0.626565i
$540$	0.757753	−	1.95506i	0.0326085	−	0.0841324i
$541$	−12.6865	+	12.6865i	−0.545437	+	0.545437i	−0.925118	−	0.379681i	$-0.876034\pi$
$541$	−12.6865	+	12.6865i	−0.545437	+	0.545437i	0.379681	+	0.925118i	$0.376034\pi$
$542$		−	11.6373i		−	0.499863i
$543$	−3.19465	−	4.09808i	−0.137095	−	0.175865i
$544$	−5.36603	+	5.36603i	−0.230066	+	0.230066i
$545$	28.1047			1.20387
$546$		0			0
$547$	2.00000			0.0855138			0.0427569	−	0.999086i	$-0.486386\pi$
$547$	2.00000			0.0855138			0.0427569	+	0.999086i	$0.486386\pi$
$548$	1.27376	−	1.27376i	0.0544124	−	0.0544124i
$549$	−5.12436	+	20.3652i	−0.218702	+	0.869165i
$550$		−	16.9282i		−	0.721821i
$551$	−19.5856	+	19.5856i	−0.834376	+	0.834376i
$552$		0			0
$553$	2.00000	−	2.00000i	0.0850487	−	0.0850487i
$554$	29.3785	+	29.3785i	1.24817	+	1.24817i
$555$	8.68653	+	11.1430i	0.368723	+	0.472996i
$556$		−	4.92820i		−	0.209002i
$557$	−18.1030	−	18.1030i	−0.767049	−	0.767049i	0.210537	−	0.977586i	$-0.432479\pi$
$557$	−18.1030	−	18.1030i	−0.767049	−	0.767049i	−0.977586	+	0.210537i	$0.932479\pi$
$558$	3.84177	−	15.2679i	0.162635	−	0.646344i
$559$		0			0
$560$			9.50749i			0.401765i
$561$	35.6377	+	4.41483i	1.50463	+	0.186394i
$562$	−25.8372			−1.08988
$563$	10.0782			0.424744			0.212372	−	0.977189i	$-0.431881\pi$
$563$	10.0782			0.424744			0.212372	+	0.977189i	$0.431881\pi$
$564$	0.343706	−	2.77449i	0.0144726	−	0.116827i
$565$	10.9545	+	10.9545i	0.460859	+	0.460859i
$566$	7.01593	+	7.01593i	0.294902	+	0.294902i
$567$	−12.1877	+	3.66867i	−0.511837	+	0.154070i
$568$	−7.85641			−0.329647
$569$	2.70043			0.113208			0.0566040	−	0.998397i	$-0.481973\pi$
$569$	2.70043			0.113208			0.0566040	+	0.998397i	$0.481973\pi$
$570$	1.86593	−	15.0623i	0.0781551	−	0.630889i
$571$		−	1.94744i		−	0.0814979i	−0.999169	−	0.0407489i	$-0.987026\pi$
$571$		−	1.94744i		−	0.0814979i	0.999169	−	0.0407489i	$-0.0129744\pi$
$572$		0			0
$573$	5.14359	+	6.59817i	0.214877	+	0.275643i
$574$	8.46410	+	8.46410i	0.353285	+	0.353285i
$575$		0			0
$576$	19.3768	+	4.87564i	0.807365	+	0.203152i
$577$	−22.4904	−	22.4904i	−0.936287	−	0.936287i	0.0618016	−	0.998088i	$-0.480315\pi$
$577$	−22.4904	−	22.4904i	−0.936287	−	0.936287i	−0.998088	+	0.0618016i	$0.980315\pi$
$578$	−8.93682	+	8.93682i	−0.371723	+	0.371723i
$579$	−0.0295350	+	0.238414i	−0.00122743	+	0.00990816i
$580$	−2.04552	+	2.04552i	−0.0849355	+	0.0849355i
$581$			5.81863i			0.241397i
$582$	3.47998	−	2.71281i	0.144250	−	0.112450i
$583$	−2.26795	+	2.26795i	−0.0939289	+	0.0939289i
$584$	3.32707			0.137675
$585$		0			0
$586$	2.71281			0.112065
$587$	13.1963	−	13.1963i	0.544672	−	0.544672i	−0.380223	−	0.924895i	$-0.624153\pi$
$587$	13.1963	−	13.1963i	0.544672	−	0.544672i	0.924895	+	0.380223i	$0.124153\pi$
$588$	1.83013	−	1.42667i	0.0754732	−	0.0588350i
$589$		−	13.4641i		−	0.554779i
$590$	−4.83020	+	4.83020i	−0.198856	+	0.198856i
$591$	−0.876119	+	7.07227i	−0.0360387	+	0.290914i
$592$	17.0981	−	17.0981i	0.702727	−	0.702727i
$593$	−10.3635	−	10.3635i	−0.425578	−	0.425578i	0.461541	−	0.887119i	$-0.347297\pi$
$593$	−10.3635	−	10.3635i	−0.425578	−	0.425578i	−0.887119	+	0.461541i	$0.847297\pi$
$594$	13.0000	+	29.4549i	0.533396	+	1.20855i
$595$			10.7321i			0.439971i
$596$	1.63555	+	1.63555i	0.0669948	+	0.0669948i
$597$	−13.7670	−	17.6603i	−0.563446	−	0.722786i
$598$		0			0
$599$		−	20.7270i		−	0.846881i	−0.905924	−	0.423441i	$-0.860822\pi$
$599$		−	20.7270i		−	0.846881i	0.905924	−	0.423441i	$-0.139178\pi$
$600$	1.51748	−	12.2495i	0.0619510	−	0.500085i
$601$	23.5885			0.962193			0.481097	−	0.876668i	$-0.340239\pi$
$601$	23.5885			0.962193			0.481097	+	0.876668i	$0.340239\pi$
$602$	4.67729			0.190632
$603$	−15.2797	+	9.13612i	−0.622238	+	0.372052i
$604$	−0.143594	−	0.143594i	−0.00584274	−	0.00584274i
$605$	−6.31284	−	6.31284i	−0.256653	−	0.256653i
$606$	1.93291	−	15.6030i	0.0785192	−	0.633828i
$607$	−0.196152			−0.00796158			−0.00398079	−	0.999992i	$-0.501267\pi$
$607$	−0.196152			−0.00796158			−0.00398079	+	0.999992i	$0.501267\pi$
$608$	−5.81863			−0.235976
$609$	17.4268	+	2.15885i	0.706169	+	0.0874809i
$610$			15.8756i			0.642786i
$611$		0			0
$612$	−3.92820	−	0.988427i	−0.158788	−	0.0399548i
$613$	−31.0263	−	31.0263i	−1.25314	−	1.25314i	−0.954305	−	0.298835i	$-0.903402\pi$
$613$	−31.0263	−	31.0263i	−1.25314	−	1.25314i	−0.298835	−	0.954305i	$-0.596598\pi$
$614$			17.8736i			0.721321i
$615$	9.01327	+	11.5622i	0.363450	+	0.466232i
$616$	−10.7321	−	10.7321i	−0.432407	−	0.432407i
$617$	13.0639	−	13.0639i	0.525934	−	0.525934i	−0.393424	−	0.919357i	$-0.628709\pi$
$617$	13.0639	−	13.0639i	0.525934	−	0.525934i	0.919357	+	0.393424i	$0.128709\pi$
$618$	17.9346	+	2.22175i	0.721434	+	0.0893719i
$619$	−31.6603	+	31.6603i	−1.27253	+	1.27253i	−0.327778	+	0.944755i	$0.606300\pi$
$619$	−31.6603	+	31.6603i	−1.27253	+	1.27253i	−0.944755	+	0.327778i	$0.893700\pi$
$620$		−	1.40619i		−	0.0564738i
$621$		0			0
$622$	10.7321	−	10.7321i	0.430316	−	0.430316i
$623$	13.1963			0.528701
$624$		0			0
$625$	3.87564			0.155026
$626$	−2.12976	+	2.12976i	−0.0851225	+	0.0851225i
$627$	16.9282	+	21.7154i	0.676047	+	0.867230i
$628$			1.28719i			0.0513644i
$629$	19.3003	−	19.3003i	0.769554	−	0.769554i
$630$	−8.25843	+	4.93792i	−0.329024	+	0.196731i
$631$	15.6603	−	15.6603i	0.623425	−	0.623425i	−0.322981	−	0.946406i	$-0.604685\pi$
$631$	15.6603	−	15.6603i	0.623425	−	0.623425i	0.946406	+	0.322981i	$0.104685\pi$
$632$	−3.68886	−	3.68886i	−0.146735	−	0.146735i
$633$	−2.46410	+	1.92089i	−0.0979392	+	0.0763483i
$634$			24.1769i			0.960188i
$635$	−9.71637	−	9.71637i	−0.385582	−	0.385582i
$636$	0.285334	−	0.222432i	0.0113142	−	0.00882000i
$637$		0			0
$638$		−	44.4192i		−	1.75857i
$639$	−4.63706	−	7.75525i	−0.183439	−	0.306793i
$640$	19.6410			0.776379
$641$	−45.3517			−1.79128			−0.895642	−	0.444775i	$-0.853284\pi$
$641$	−45.3517			−1.79128			−0.895642	+	0.444775i	$0.853284\pi$
$642$	49.2228	+	6.09776i	1.94267	+	0.240659i
$643$	−5.12436	−	5.12436i	−0.202085	−	0.202085i	0.598808	−	0.800893i	$-0.295641\pi$
$643$	−5.12436	−	5.12436i	−0.202085	−	0.202085i	−0.800893	+	0.598808i	$0.795641\pi$
$644$		0			0
$645$	5.68503	+	0.704266i	0.223848	+	0.0277305i
$646$	−29.3205			−1.15360
$647$	16.4675			0.647402			0.323701	−	0.946159i	$-0.395073\pi$
$647$	16.4675			0.647402			0.323701	+	0.946159i	$0.395073\pi$
$648$	6.76661	+	22.4794i	0.265818	+	0.883075i
$649$		−	12.3923i		−	0.486441i
$650$		0			0
$651$	−6.73205	+	5.24796i	−0.263850	+	0.205684i
$652$	0.784610	+	0.784610i	0.0307277	+	0.0307277i
$653$		−	9.66040i		−	0.378041i	−0.981973	−	0.189020i	$-0.939469\pi$
$653$		−	9.66040i		−	0.378041i	0.981973	−	0.189020i	$-0.0605312\pi$
$654$	38.3917	−	29.9282i	1.50124	−	1.17029i
$655$	8.46410	+	8.46410i	0.330720	+	0.330720i
$656$	17.7412	−	17.7412i	0.692678	−	0.692678i
$657$	1.96372	+	3.28423i	0.0766122	+	0.128130i
$658$	−9.07180	+	9.07180i	−0.353655	+	0.353655i
$659$		−	27.1163i		−	1.05630i	−0.849151	−	0.528150i	$-0.822886\pi$
$659$		−	27.1163i		−	1.05630i	0.849151	−	0.528150i	$-0.177114\pi$
$660$	1.76798	+	2.26795i	0.0688183	+	0.0882798i
$661$	−6.90192	+	6.90192i	−0.268454	+	0.268454i	−0.828477	−	0.560023i	$-0.810792\pi$
$661$	−6.90192	+	6.90192i	−0.268454	+	0.268454i	0.560023	+	0.828477i	$0.310792\pi$
$662$	−51.5321			−2.00285
$663$		0			0
$664$	10.7321			0.416484
$665$	−5.81863	+	5.81863i	−0.225637	+	0.225637i
$666$	23.7321	+	5.97154i	0.919598	+	0.231392i
$667$		0			0
$668$	−2.54752	+	2.54752i	−0.0985666	+	0.0985666i
$669$	44.5355	+	5.51709i	1.72184	+	0.213303i
$670$	−9.51666	+	9.51666i	−0.367661	+	0.367661i
$671$	−20.3652	−	20.3652i	−0.786189	−	0.786189i
$672$	2.26795	+	2.90931i	0.0874880	+	0.112229i
$673$		−	42.7128i		−	1.64646i	−0.567709	−	0.823229i	$-0.692170\pi$
$673$		−	42.7128i		−	1.64646i	0.567709	−	0.823229i	$-0.307830\pi$
$674$	−19.6621	−	19.6621i	−0.757356	−	0.757356i
$675$	12.9875	−	5.73205i	0.499888	−	0.220627i
$676$		0			0
$677$		−	9.66040i		−	0.371279i	−0.982618	−	0.185640i	$-0.940564\pi$
$677$		−	9.66040i		−	0.371279i	0.982618	−	0.185640i	$-0.0594357\pi$
$678$	26.6293	+	3.29887i	1.02269	+	0.126692i
$679$	−2.39230			−0.0918082
$680$	19.7945			0.759085
$681$	−4.31769	+	34.8536i	−0.165454	+	1.33559i
$682$	15.2679	+	15.2679i	0.584640	+	0.584640i
$683$	33.1438	+	33.1438i	1.26821	+	1.26821i	0.947011	+	0.321200i	$0.104086\pi$
$683$	33.1438	+	33.1438i	1.26821	+	1.26821i	0.321200	+	0.947011i	$0.395914\pi$
$684$	−1.59387	−	2.66566i	−0.0609430	−	0.101924i
$685$	−10.1244			−0.386832
$686$	−25.5572			−0.975778
$687$	−4.25345	+	34.3350i	−0.162279	+	1.30996i
$688$		−	9.80385i		−	0.373768i
$689$		0			0
$690$		0			0
$691$	13.3397	+	13.3397i	0.507468	+	0.507468i	0.913748	−	0.406281i	$-0.133174\pi$
$691$	13.3397	+	13.3397i	0.507468	+	0.507468i	−0.406281	+	0.913748i	$0.633174\pi$
$692$			4.67729i			0.177804i
$693$	4.25953	−	16.9282i	0.161806	−	0.643049i
$694$	−21.9090	−	21.9090i	−0.831653	−	0.831653i
$695$	−19.5856	+	19.5856i	−0.742926	+	0.742926i
$696$	3.98184	−	32.1425i	0.150931	−	1.21836i
$697$	20.0263	−	20.0263i	0.758549	−	0.758549i
$698$		−	42.8601i		−	1.62228i
$699$	−23.8452	+	18.5885i	−0.901907	+	0.703080i
$700$	0.732051	−	0.732051i	0.0276689	−	0.0276689i
$701$	−12.7786			−0.482641			−0.241320	−	0.970446i	$-0.577580\pi$
$701$	−12.7786			−0.482641			−0.241320	+	0.970446i	$0.577580\pi$
$702$		0			0
$703$	20.9282			0.789322
$704$	−19.3768	+	19.3768i	−0.730289	+	0.730289i
$705$	−12.3923	+	9.66040i	−0.466721	+	0.363832i
$706$			21.3013i			0.801684i
$707$	−6.02751	+	6.02751i	−0.226688	+	0.226688i
$708$	−0.171853	+	1.38724i	−0.00645863	+	0.0521358i
$709$	−8.29423	+	8.29423i	−0.311496	+	0.311496i	−0.845489	−	0.533993i	$-0.820691\pi$
$709$	−8.29423	+	8.29423i	−0.311496	+	0.311496i	0.533993	+	0.845489i	$0.320691\pi$
$710$	−4.83020	−	4.83020i	−0.181274	−	0.181274i
$711$	1.46410	−	5.81863i	0.0549081	−	0.218216i
$712$		−	24.3397i		−	0.912171i
$713$		0			0
$714$	11.4284	+	14.6603i	0.427696	+	0.548646i
$715$		0			0
$716$			7.11287i			0.265821i
$717$	−1.98699	+	16.0396i	−0.0742056	+	0.599008i
$718$	38.8372			1.44939
$719$	7.37772			0.275143			0.137571	−	0.990492i	$-0.456070\pi$
$719$	7.37772			0.275143			0.137571	+	0.990492i	$0.456070\pi$
$720$	10.3501	+	17.3101i	0.385727	+	0.645110i
$721$	−6.92820	−	6.92820i	−0.258020	−	0.258020i
$722$	4.33598	+	4.33598i	0.161369	+	0.161369i
$723$	3.10003	−	25.0243i	0.115292	−	0.930665i
$724$	−0.803848			−0.0298748
$725$	−19.5856			−0.727392
$726$	−15.3459	−	1.90107i	−0.569541	−	0.0705552i
$727$			19.5167i			0.723833i	0.932211	+	0.361916i	$0.117877\pi$
$727$			19.5167i			0.723833i	−0.932211	+	0.361916i	$0.882123\pi$
$728$		0			0
$729$	−18.1962	+	19.9474i	−0.673932	+	0.738794i
$730$	2.04552	+	2.04552i	0.0757080	+	0.0757080i
$731$		−	11.0666i		−	0.409312i
$732$	1.99734	+	2.56218i	0.0738238	+	0.0947008i
$733$	−6.77757	−	6.77757i	−0.250335	−	0.250335i	0.570773	−	0.821108i	$-0.306644\pi$
$733$	−6.77757	−	6.77757i	−0.250335	−	0.250335i	−0.821108	+	0.570773i	$0.806644\pi$
$734$	−32.3642	+	32.3642i	−1.19459	+	1.19459i
$735$	−12.9432	−	1.60341i	−0.477415	−	0.0591426i
$736$		0			0
$737$		−	24.4158i		−	0.899369i
$738$	24.6247	+	6.19615i	0.906448	+	0.228084i
$739$	8.14359	−	8.14359i	0.299567	−	0.299567i	−0.541277	−	0.840844i	$-0.682059\pi$
$739$	8.14359	−	8.14359i	0.299567	−	0.299567i	0.840844	+	0.541277i	$0.182059\pi$
$740$	2.18573			0.0803492
$741$		0			0
$742$	−1.66025			−0.0609498
$743$	−6.23638	+	6.23638i	−0.228791	+	0.228791i	−0.812187	−	0.583397i	$-0.801723\pi$
$743$	−6.23638	+	6.23638i	−0.228791	+	0.228791i	0.583397	+	0.812187i	$0.301723\pi$
$744$	9.67949	+	12.4168i	0.354867	+	0.455222i
$745$		−	13.0000i		−	0.476283i
$746$	−12.3403	+	12.3403i	−0.451812	+	0.451812i
$747$	6.33434	+	10.5939i	0.231761	+	0.387609i
$748$	3.92820	−	3.92820i	0.143629	−	0.143629i
$749$	−19.0150	−	19.0150i	−0.694792	−	0.694792i
$750$	23.9545	−	18.6737i	0.874694	−	0.681866i
$751$		−	33.8038i		−	1.23352i	−0.787151	−	0.616760i	$-0.788445\pi$
$751$		−	33.8038i		−	1.23352i	0.787151	−	0.616760i	$-0.211555\pi$
$752$	19.0150	+	19.0150i	0.693405	+	0.693405i
$753$	1.35022	−	1.05256i	0.0492046	−	0.0383574i
$754$		0			0
$755$			1.14134i			0.0415375i
$756$	−0.711584	+	1.83594i	−0.0258801	+	0.0667725i
$757$	16.7846			0.610047			0.305024	−	0.952345i	$-0.401336\pi$
$757$	16.7846			0.610047			0.305024	+	0.952345i	$0.401336\pi$
$758$	−22.2861			−0.809467
$759$		0			0
$760$	10.7321	+	10.7321i	0.389292	+	0.389292i
$761$	12.9875	+	12.9875i	0.470795	+	0.470795i	0.902172	−	0.431377i	$-0.141972\pi$
$761$	12.9875	+	12.9875i	0.470795	+	0.470795i	−0.431377	+	0.902172i	$0.641972\pi$
$762$	−23.6196	−	2.92602i	−0.855647	−	0.105998i
$763$	−26.3923			−0.955466
$764$	1.29425			0.0468242
$765$	11.6832	+	19.5397i	0.422409	+	0.706458i
$766$			49.5692i			1.79101i
$767$		0			0
$768$	8.63397	−	6.73060i	0.311552	−	0.242870i
$769$	−29.5885	−	29.5885i	−1.06699	−	1.06699i	−0.997589	−	0.0693980i	$-0.977892\pi$
$769$	−29.5885	−	29.5885i	−1.06699	−	1.06699i	−0.0693980	−	0.997589i	$-0.522108\pi$
$770$		−	13.1963i		−	0.475563i
$771$	29.3785	−	22.9019i	1.05804	−	0.824793i
$772$	0.0262794	+	0.0262794i	0.000945818	+	0.000945818i
$773$	−30.4433	+	30.4433i	−1.09497	+	1.09497i	−0.0999818	+	0.994989i	$0.531878\pi$
$773$	−30.4433	+	30.4433i	−1.09497	+	1.09497i	−0.994989	+	0.0999818i	$0.968122\pi$
$774$	8.51585	−	5.09184i	0.306096	−	0.183022i
$775$	6.73205	−	6.73205i	0.241822	−	0.241822i
$776$			4.41244i			0.158397i
$777$	−8.15727	−	10.4641i	−0.292640	−	0.375398i
$778$	23.9545	−	23.9545i	0.858810	−	0.858810i
$779$	21.7154			0.778035
$780$		0			0
$781$	12.3923			0.443432
$782$		0			0
$783$	34.0788	−	15.0408i	1.21788	−	0.537514i
$784$			22.3205i			0.797161i
$785$	5.11553	−	5.11553i	0.182581	−	0.182581i
$786$	20.5755	+	2.54890i	0.733902	+	0.0909164i
$787$	11.7321	−	11.7321i	0.418202	−	0.418202i	−0.466381	−	0.884584i	$-0.654443\pi$
$787$	11.7321	−	11.7321i	0.418202	−	0.418202i	0.884584	+	0.466381i	$0.154443\pi$
$788$	0.779548	+	0.779548i	0.0277702	+	0.0277702i
$789$	23.7321	+	30.4433i	0.844883	+	1.08381i
$790$		−	4.53590i		−	0.161380i
$791$	−10.2870	−	10.2870i	−0.365765	−	0.365765i
$792$	−31.2229	−	7.85641i	−1.10946	−	0.279165i
$793$		0			0
$794$		−	20.7270i		−	0.735573i
$795$	−2.01796	−	0.249987i	−0.0715697	−	0.00886612i
$796$	−3.46410			−0.122782
$797$	40.3126			1.42795			0.713973	−	0.700173i	$-0.246894\pi$
$797$	40.3126			1.42795			0.713973	+	0.700173i	$0.246894\pi$
$798$	−1.75224	+	14.1445i	−0.0620286	+	0.500711i
$799$	21.4641	+	21.4641i	0.759345	+	0.759345i
$800$	−2.90931	−	2.90931i	−0.102860	−	0.102860i
$801$	24.0264	−	14.3660i	0.848929	−	0.507596i
$802$	−18.7513			−0.662131
$803$	−5.24796			−0.185196
$804$	−0.338592	+	2.73320i	−0.0119412	+	0.0963927i
$805$		0			0
$806$		0			0
$807$	−15.2679	−	19.5856i	−0.537457	−	0.689447i
$808$	11.1173	+	11.1173i	0.391106	+	0.391106i
$809$		−	27.7429i		−	0.975389i	−0.873014	−	0.487694i	$-0.837838\pi$
$809$		−	27.7429i		−	0.975389i	0.873014	−	0.487694i	$-0.162162\pi$
$810$	−9.66040	+	17.9808i	−0.339432	+	0.631780i
$811$	19.0000	+	19.0000i	0.667180	+	0.667180i	0.957062	−	0.289882i	$-0.0936161\pi$
$811$	19.0000	+	19.0000i	0.667180	+	0.667180i	−0.289882	+	0.957062i	$0.593616\pi$
$812$	1.92089	−	1.92089i	0.0674099	−	0.0674099i
$813$	−1.64548	+	13.2827i	−0.0577094	+	0.465846i
$814$	−23.7321	+	23.7321i	−0.831808	+	0.831808i
$815$		−	6.23638i		−	0.218451i
$816$	30.7287	−	23.9545i	1.07572	−	0.838575i
$817$	6.00000	−	6.00000i	0.209913	−	0.209913i
$818$	45.1988			1.58034
$819$		0			0
$820$	2.26795			0.0792002
$821$	−30.4433	+	30.4433i	−1.06248	+	1.06248i	−0.0645667	+	0.997913i	$0.520567\pi$
$821$	−30.4433	+	30.4433i	−1.06248	+	1.06248i	−0.997913	+	0.0645667i	$0.979433\pi$
$822$	−13.8301	+	10.7812i	−0.482381	+	0.376039i
$823$			8.53590i			0.297543i	0.988872	+	0.148771i	$0.0475318\pi$
$823$			8.53590i			0.297543i	−0.988872	+	0.148771i	$0.952468\pi$
$824$	−12.7786	+	12.7786i	−0.445163	+	0.445163i
$825$	−2.39360	+	19.3218i	−0.0833345	+	0.672699i
$826$	4.53590	−	4.53590i	0.157824	−	0.157824i
$827$	31.7936	+	31.7936i	1.10557	+	1.10557i	0.993726	+	0.111845i	$0.0356760\pi$
$827$	31.7936	+	31.7936i	1.10557	+	1.10557i	0.111845	+	0.993726i	$0.464324\pi$
$828$		0			0
$829$			48.1244i			1.67143i	0.549165	+	0.835714i	$0.314946\pi$
$829$			48.1244i			1.67143i	−0.549165	+	0.835714i	$0.685054\pi$
$830$	6.59817	+	6.59817i	0.229026	+	0.229026i
$831$	−29.3785	−	37.6865i	−1.01913	−	1.30733i
$832$		0			0
$833$			25.1954i			0.872968i
$834$	−5.89808	+	47.6109i	−0.204234	+	1.64863i
$835$	20.2487			0.700736
$836$	4.25953			0.147319
$837$	−6.54383	+	16.8836i	−0.226188	+	0.583582i
$838$	−10.1244	−	10.1244i	−0.349740	−	0.349740i
$839$	−7.16884	−	7.16884i	−0.247496	−	0.247496i	0.572446	−	0.819942i	$-0.305995\pi$
$839$	−7.16884	−	7.16884i	−0.247496	−	0.247496i	−0.819942	+	0.572446i	$0.805995\pi$
$840$	1.18295	−	9.54910i	0.0408157	−	0.329475i
$841$	−22.3923			−0.772148
$842$	16.6763			0.574704
$843$	29.4905	+	3.65331i	1.01571	+	0.125827i
$844$			0.483340i			0.0166372i
$845$		0			0
$846$	−6.64102	+	26.3927i	−0.228323	+	0.907400i
$847$	5.92820	+	5.92820i	0.203695	+	0.203695i
$848$			3.47998i			0.119503i
$849$	−7.01593	−	9.00000i	−0.240786	−	0.308879i
$850$	−14.6603	−	14.6603i	−0.502843	−	0.502843i
$851$		0			0
$852$	−1.38724	−	0.171853i	−0.0475262	−	0.00588758i
$853$	−22.3660	+	22.3660i	−0.765798	+	0.765798i	−0.977364	−	0.211566i	$-0.932144\pi$
$853$	−22.3660	+	22.3660i	−0.765798	+	0.765798i	0.211566	+	0.977364i	$0.432144\pi$
$854$		−	14.9084i		−	0.510153i
$855$	−4.25953	+	16.9282i	−0.145673	+	0.578932i
$856$	−35.0718	+	35.0718i	−1.19873	+	1.19873i
$857$	−3.32707			−0.113651			−0.0568253	−	0.998384i	$-0.518098\pi$
$857$	−3.32707			−0.113651			−0.0568253	+	0.998384i	$0.518098\pi$
$858$		0			0
$859$	39.1769			1.33670			0.668350	−	0.743847i	$-0.267001\pi$
$859$	39.1769			1.33670			0.668350	+	0.743847i	$0.267001\pi$
$860$	0.626638	−	0.626638i	0.0213682	−	0.0213682i
$861$	−8.46410	−	10.8577i	−0.288456	−	0.370030i
$862$		−	56.9808i		−	1.94077i
$863$	18.2354	−	18.2354i	0.620741	−	0.620741i	−0.324980	−	0.945721i	$-0.605358\pi$
$863$	18.2354	−	18.2354i	0.620741	−	0.620741i	0.945721	+	0.324980i	$0.105358\pi$
$864$	7.29638	+	2.82797i	0.248228	+	0.0962096i
$865$	18.5885	−	18.5885i	0.632027	−	0.632027i
$866$	−33.0673	−	33.0673i	−1.12367	−	1.12367i
$867$	11.4641	−	8.93682i	0.389341	−	0.303510i
$868$			1.32051i			0.0448210i
$869$	5.81863	+	5.81863i	0.197383	+	0.197383i
$870$	22.2096	−	17.3135i	0.752977	−	0.586981i
$871$		0			0
$872$			48.6788i			1.64847i
$873$	−4.35563	+	2.60434i	−0.147416	+	0.0881435i
$874$		0			0
$875$	−16.4675			−0.556701
$876$	0.587477	+	0.0727771i	0.0198490	+	0.00245891i
$877$	−21.2224	−	21.2224i	−0.716631	−	0.716631i	0.251283	−	0.967914i	$-0.419148\pi$
$877$	−21.2224	−	21.2224i	−0.716631	−	0.716631i	−0.967914	+	0.251283i	$0.919148\pi$
$878$	−1.35022	−	1.35022i	−0.0455676	−	0.0455676i
$879$	−3.09640	−	0.383584i	−0.104439	−	0.0129380i
$880$	−27.6603			−0.932427
$881$	23.4834			0.791175			0.395588	−	0.918428i	$-0.370541\pi$
$881$	23.4834			0.791175			0.395588	+	0.918428i	$0.370541\pi$
$882$	−19.3881	+	11.5926i	−0.652832	+	0.390345i
$883$		−	33.3731i		−	1.12309i	−0.827445	−	0.561547i	$-0.810207\pi$
$883$		−	33.3731i		−	1.12309i	0.827445	−	0.561547i	$-0.189793\pi$
$884$		0			0
$885$	6.19615	−	4.83020i	0.208281	−	0.162365i
$886$	−11.9474	−	11.9474i	−0.401382	−	0.401382i
$887$			25.2514i			0.847858i	0.905696	+	0.423929i	$0.139349\pi$
$887$			25.2514i			0.847858i	−0.905696	+	0.423929i	$0.860651\pi$
$888$	−19.3003	+	15.0455i	−0.647676	+	0.504895i
$889$	9.12436	+	9.12436i	0.306021	+	0.306021i
$890$	14.9643	−	14.9643i	0.501605	−	0.501605i
$891$	−10.6733	−	35.4579i	−0.357570	−	1.18789i
$892$	4.90897	−	4.90897i	0.164364	−	0.164364i
$893$			23.2745i			0.778852i
$894$	−13.8435	−	17.7583i	−0.462995	−	0.593927i
$895$	28.2679	−	28.2679i	0.944893	−	0.944893i
$896$	−18.4443			−0.616181
$897$		0			0
$898$	30.9808			1.03384
$899$	17.6648	−	17.6648i	0.589153	−	0.589153i
$900$	0.535898	−	2.12976i	0.0178633	−	0.0709922i
$901$			3.92820i			0.130867i
$902$	−24.6247	+	24.6247i	−0.819913	+	0.819913i
$903$	−5.33864	−	0.661356i	−0.177659	−	0.0220085i
$904$	−18.9737	+	18.9737i	−0.631057	+	0.631057i
$905$	3.19465	+	3.19465i	0.106194	+	0.106194i
$906$	1.21539	+	1.55910i	0.0403786	+	0.0517975i
$907$		−	17.3205i		−	0.575118i	−0.957763	−	0.287559i	$-0.907156\pi$
$907$		−	17.3205i		−	0.575118i	0.957763	−	0.287559i	$-0.0928437\pi$
$908$	3.84177	+	3.84177i	0.127494	+	0.127494i
$909$	−4.41244	+	17.5359i	−0.146351	+	0.581629i
$910$		0			0
$911$		−	1.55910i		−	0.0516552i	−0.999666	−	0.0258276i	$-0.991778\pi$
$911$		−	1.55910i		−	0.0516552i	0.999666	−	0.0258276i	$-0.00822209\pi$
$912$	29.6477	+	3.67279i	0.981734	+	0.121618i
$913$	−16.9282			−0.560242
$914$	5.87459			0.194314
$915$	2.24477	−	18.1204i	0.0742099	−	0.599043i
$916$	3.78461	+	3.78461i	0.125047	+	0.125047i
$917$	−7.94839	−	7.94839i	−0.262479	−	0.262479i
$918$	36.7670	+	14.2504i	1.21349	+	0.470333i
$919$	13.4115			0.442406			0.221203	−	0.975228i	$-0.429002\pi$
$919$	13.4115			0.442406			0.221203	+	0.975228i	$0.429002\pi$
$920$		0			0
$921$	2.52728	−	20.4009i	0.0832768	−	0.672233i
$922$			32.0333i			1.05496i
$923$		0			0
$924$	−1.66025	−	2.12976i	−0.0546183	−	0.0700641i
$925$	10.4641	+	10.4641i	0.344058	+	0.344058i
$926$			49.0965i			1.61341i
$927$	−20.1563	−	5.07180i	−0.662020	−	0.166580i
$928$	−7.63397	−	7.63397i	−0.250597	−	0.250597i
$929$	14.4141	−	14.4141i	0.472913	−	0.472913i	−0.429943	−	0.902856i	$-0.641466\pi$
$929$	14.4141	−	14.4141i	0.472913	−	0.472913i	0.902856	+	0.429943i	$0.141466\pi$
$930$	−1.68292	+	13.5850i	−0.0551853	+	0.445471i
$931$	−13.6603	+	13.6603i	−0.447697	+	0.447697i
$932$			4.67729i			0.153210i
$933$	−13.7670	+	10.7321i	−0.450712	+	0.351352i
$934$	−20.4115	+	20.4115i	−0.667886	+	0.667886i
$935$	−31.2229			−1.02110
$936$		0			0
$937$	−37.0000			−1.20874			−0.604369	−	0.796705i	$-0.706575\pi$
$937$	−37.0000			−1.20874			−0.604369	+	0.796705i	$0.706575\pi$
$938$	8.93682	−	8.93682i	0.291797	−	0.291797i
$939$	2.73205	−	2.12976i	0.0891571	−	0.0695022i
$940$			2.43078i			0.0792833i
$941$	9.14570	−	9.14570i	0.298141	−	0.298141i	−0.542144	−	0.840285i	$-0.682387\pi$
$941$	9.14570	−	9.14570i	0.298141	−	0.298141i	0.840285	+	0.542144i	$0.182387\pi$
$942$	1.54051	−	12.4354i	0.0501924	−	0.405167i
$943$		0			0
$944$	−9.50749	−	9.50749i	−0.309442	−	0.309442i
$945$	10.1244	−	4.46841i	0.329345	−	0.145357i
$946$			13.6077i			0.442424i
$947$	7.58660	+	7.58660i	0.246531	+	0.246531i	0.819546	−	0.573014i	$-0.194226\pi$
$947$	7.58660	+	7.58660i	0.246531	+	0.246531i	−0.573014	+	0.819546i	$0.694226\pi$
$948$	−0.570669	−	0.732051i	−0.0185345	−	0.0237759i
$949$		0			0
$950$		−	15.8968i		−	0.515760i
$951$	3.41855	−	27.5955i	0.110854	−	0.894844i
$952$	−18.5885			−0.602455
$953$	−1.97685			−0.0640366			−0.0320183	−	0.999487i	$-0.510193\pi$
$953$	−1.97685			−0.0640366			−0.0320183	+	0.999487i	$0.510193\pi$
$954$	−3.02279	+	1.80740i	−0.0978666	+	0.0585169i
$955$	−5.14359	−	5.14359i	−0.166443	−	0.166443i
$956$	1.76798	+	1.76798i	0.0571804	+	0.0571804i
$957$	−6.28076	+	50.7000i	−0.203028	+	1.63890i
$958$	30.9808			1.00094
$959$	9.50749			0.307013
$960$	−17.2409	−	2.13582i	−0.556449	−	0.0689334i
$961$		−	18.8564i		−	0.608271i
$962$		0			0
$963$	−55.3205	−	13.9199i	−1.78268	−	0.448563i
$964$	−2.75833	−	2.75833i	−0.0888398	−	0.0888398i
$965$		−	0.208879i		−	0.00672406i
$966$		0			0
$967$	−27.8564	−	27.8564i	−0.895802	−	0.895802i	0.0992599	−	0.995062i	$-0.468352\pi$
$967$	−27.8564	−	27.8564i	−0.895802	−	0.895802i	−0.995062	+	0.0992599i	$0.968352\pi$
$968$	10.9342	−	10.9342i	0.351437	−	0.351437i
$969$	33.4663	+	4.14584i	1.07509	+	0.133184i
$970$	−2.71281	+	2.71281i	−0.0871032	+	0.0871032i
$971$			47.8433i			1.53536i	0.640832	+	0.767682i	$0.278590\pi$
$971$			47.8433i			1.53536i	−0.640832	+	0.767682i	$0.721410\pi$
$972$	0.703093	+	4.11731i	0.0225517	+	0.132063i
$973$	18.3923	−	18.3923i	0.589630	−	0.589630i
$974$	8.67197			0.277868
$975$		0			0
$976$	−31.2487			−1.00025
$977$	16.7528	−	16.7528i	0.535969	−	0.535969i	−0.386373	−	0.922342i	$-0.626272\pi$
$977$	16.7528	−	16.7528i	0.535969	−	0.535969i	0.922342	+	0.386373i	$0.126272\pi$
$978$	−6.64102	−	8.51906i	−0.212356	−	0.272409i
$979$			38.3923i			1.22702i
$980$	−1.42667	+	1.42667i	−0.0455734	+	0.0455734i
$981$	−48.0520	+	28.7315i	−1.53418	+	0.917326i
$982$	−30.3731	+	30.3731i	−0.969244	+	0.969244i
$983$	30.4433	+	30.4433i	0.970992	+	0.970992i	0.999591	−	0.0285990i	$-0.00910459\pi$
$983$	30.4433	+	30.4433i	0.970992	+	0.970992i	−0.0285990	+	0.999591i	$0.509105\pi$
$984$	−20.0263	+	15.6114i	−0.638414	+	0.497675i
$985$		−	6.19615i		−	0.197426i
$986$	−38.4682	−	38.4682i	−1.22508	−	1.22508i
$987$	11.6373	−	9.07180i	0.370418	−	0.288758i
$988$		0			0
$989$		0			0
$990$	−14.3660	−	24.0264i	−0.456580	−	0.763608i
$991$	−57.5692			−1.82875			−0.914373	−	0.404872i	$-0.867316\pi$
$991$	−57.5692			−1.82875			−0.914373	+	0.404872i	$0.867316\pi$
$992$	5.24796			0.166623
$993$	58.8186	+	7.28650i	1.86655	+	0.231230i
$994$	4.53590	+	4.53590i	0.143870	+	0.143870i
$995$	13.7670	+	13.7670i	0.436444	+	0.436444i
$996$	1.89501	+	0.234755i	0.0600457	+	0.00743851i
$997$	−7.00000			−0.221692			−0.110846	−	0.993838i	$-0.535356\pi$
$997$	−7.00000			−0.221692			−0.110846	+	0.993838i	$0.535356\pi$
$998$	5.24796			0.166121
$999$	−26.2433	−	10.1715i	−0.830303	−	0.321813i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.f.f.437.2		8
3.2	odd	2	inner	507.2.f.f.437.3		8
13.2	odd	12		39.2.k.b.32.1	yes	8
13.3	even	3		507.2.k.e.488.1		8
13.4	even	6		507.2.k.d.89.1		8
13.5	odd	4	inner	507.2.f.f.239.3		8
13.6	odd	12		507.2.k.e.80.2		8
13.7	odd	12		507.2.k.f.80.1		8
13.8	odd	4		507.2.f.e.239.2		8
13.9	even	3		39.2.k.b.11.2	yes	8
13.10	even	6		507.2.k.f.488.2		8
13.11	odd	12		507.2.k.d.188.2		8
13.12	even	2		507.2.f.e.437.3		8
39.2	even	12		39.2.k.b.32.2	yes	8
39.5	even	4	inner	507.2.f.f.239.2		8
39.8	even	4		507.2.f.e.239.3		8
39.11	even	12		507.2.k.d.188.1		8
39.17	odd	6		507.2.k.d.89.2		8
39.20	even	12		507.2.k.f.80.2		8
39.23	odd	6		507.2.k.f.488.1		8
39.29	odd	6		507.2.k.e.488.2		8
39.32	even	12		507.2.k.e.80.1		8
39.35	odd	6		39.2.k.b.11.1	✓	8
39.38	odd	2		507.2.f.e.437.2		8
52.15	even	12		624.2.cn.c.305.1		8
52.35	odd	6		624.2.cn.c.401.2		8
65.2	even	12		975.2.bp.f.149.1		8
65.9	even	6		975.2.bo.d.401.1		8
65.22	odd	12		975.2.bp.e.674.1		8
65.28	even	12		975.2.bp.e.149.2		8
65.48	odd	12		975.2.bp.f.674.2		8
65.54	odd	12		975.2.bo.d.851.2		8
156.35	even	6		624.2.cn.c.401.1		8
156.119	odd	12		624.2.cn.c.305.2		8
195.2	odd	12		975.2.bp.f.149.2		8
195.74	odd	6		975.2.bo.d.401.2		8
195.113	even	12		975.2.bp.f.674.1		8
195.119	even	12		975.2.bo.d.851.1		8
195.152	even	12		975.2.bp.e.674.2		8
195.158	odd	12		975.2.bp.e.149.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.2.k.b.11.1	✓	8	39.35	odd	6
39.2.k.b.11.2	yes	8	13.9	even	3
39.2.k.b.32.1	yes	8	13.2	odd	12
39.2.k.b.32.2	yes	8	39.2	even	12
507.2.f.e.239.2		8	13.8	odd	4
507.2.f.e.239.3		8	39.8	even	4
507.2.f.e.437.2		8	39.38	odd	2
507.2.f.e.437.3		8	13.12	even	2
507.2.f.f.239.2		8	39.5	even	4	inner
507.2.f.f.239.3		8	13.5	odd	4	inner
507.2.f.f.437.2		8	1.1	even	1	trivial
507.2.f.f.437.3		8	3.2	odd	2	inner
507.2.k.d.89.1		8	13.4	even	6
507.2.k.d.89.2		8	39.17	odd	6
507.2.k.d.188.1		8	39.11	even	12
507.2.k.d.188.2		8	13.11	odd	12
507.2.k.e.80.1		8	39.32	even	12
507.2.k.e.80.2		8	13.6	odd	12
507.2.k.e.488.1		8	13.3	even	3
507.2.k.e.488.2		8	39.29	odd	6
507.2.k.f.80.1		8	13.7	odd	12
507.2.k.f.80.2		8	39.20	even	12
507.2.k.f.488.1		8	39.23	odd	6
507.2.k.f.488.2		8	13.10	even	6
624.2.cn.c.305.1		8	52.15	even	12
624.2.cn.c.305.2		8	156.119	odd	12
624.2.cn.c.401.1		8	156.35	even	6
624.2.cn.c.401.2		8	52.35	odd	6
975.2.bo.d.401.1		8	65.9	even	6
975.2.bo.d.401.2		8	195.74	odd	6
975.2.bo.d.851.1		8	195.119	even	12
975.2.bo.d.851.2		8	65.54	odd	12
975.2.bp.e.149.1		8	195.158	odd	12
975.2.bp.e.149.2		8	65.28	even	12
975.2.bp.e.674.1		8	65.22	odd	12
975.2.bp.e.674.2		8	195.152	even	12
975.2.bp.f.149.1		8	65.2	even	12
975.2.bp.f.149.2		8	195.2	odd	12
975.2.bp.f.674.1		8	195.113	even	12
975.2.bp.f.674.2		8	65.48	odd	12

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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.06488 + 1.06488i) q^{2} +(1.36603 - 1.06488i) q^{3} -0.267949i q^{4} +(-1.06488 + 1.06488i) q^{5} +(-0.320682 + 2.58863i) q^{6} +(1.00000 - 1.00000i) q^{7} +(-1.84443 - 1.84443i) q^{8} +(0.732051 - 2.90931i) q^{9} +O(q^{10})\)	\(q+(-1.06488 + 1.06488i) q^{2} +(1.36603 - 1.06488i) q^{3} -0.267949i q^{4} +(-1.06488 + 1.06488i) q^{5} +(-0.320682 + 2.58863i) q^{6} +(1.00000 - 1.00000i) q^{7} +(-1.84443 - 1.84443i) q^{8} +(0.732051 - 2.90931i) q^{9} -2.26795i q^{10} +(2.90931 + 2.90931i) q^{11} +(-0.285334 - 0.366025i) q^{12} +2.12976i q^{14} +(-0.320682 + 2.58863i) q^{15} +4.46410 q^{16} +5.03908 q^{17} +(2.31853 + 3.87762i) q^{18} +(2.73205 + 2.73205i) q^{19} +(0.285334 + 0.285334i) q^{20} +(0.301143 - 2.43091i) q^{21} -6.19615 q^{22} +(-4.48364 - 0.555437i) q^{24} +2.73205i q^{25} +(-2.09808 - 4.75374i) q^{27} +(-0.267949 - 0.267949i) q^{28} +7.16884i q^{29} +(-2.41510 - 3.09808i) q^{30} +(-2.46410 - 2.46410i) q^{31} +(-1.06488 + 1.06488i) q^{32} +(7.07227 + 0.876119i) q^{33} +(-5.36603 + 5.36603i) q^{34} +2.12976i q^{35} +(-0.779548 - 0.196152i) q^{36} +(3.83013 - 3.83013i) q^{37} -5.81863 q^{38} +3.92820 q^{40} +(3.97420 - 3.97420i) q^{41} +(2.26795 + 2.90931i) q^{42} -2.19615i q^{43} +(0.779548 - 0.779548i) q^{44} +(2.31853 + 3.87762i) q^{45} +(4.25953 + 4.25953i) q^{47} +(6.09808 - 4.75374i) q^{48} +5.00000i q^{49} +(-2.90931 - 2.90931i) q^{50} +(6.88351 - 5.36603i) q^{51} +0.779548i q^{53} +(7.29638 + 2.82797i) q^{54} -6.19615 q^{55} -3.68886 q^{56} +(6.64136 + 0.822738i) q^{57} +(-7.63397 - 7.63397i) q^{58} +(-2.12976 - 2.12976i) q^{59} +(0.693622 + 0.0859264i) q^{60} -7.00000 q^{61} +5.24796 q^{62} +(-2.17726 - 3.64136i) q^{63} +6.66025i q^{64} +(-8.46410 + 6.59817i) q^{66} +(-4.19615 - 4.19615i) q^{67} -1.35022i q^{68} +(-2.26795 - 2.26795i) q^{70} +(2.12976 - 2.12976i) q^{71} +(-6.71624 + 4.01581i) q^{72} +(-0.901924 + 0.901924i) q^{73} +8.15727i q^{74} +(2.90931 + 3.73205i) q^{75} +(0.732051 - 0.732051i) q^{76} +5.81863 q^{77} +2.00000 q^{79} +(-4.75374 + 4.75374i) q^{80} +(-7.92820 - 4.25953i) q^{81} +8.46410i q^{82} +(-2.90931 + 2.90931i) q^{83} +(-0.651360 - 0.0806910i) q^{84} +(-5.36603 + 5.36603i) q^{85} +(2.33864 + 2.33864i) q^{86} +(7.63397 + 9.79282i) q^{87} -10.7321i q^{88} +(6.59817 + 6.59817i) q^{89} +(-6.59817 - 1.66025i) q^{90} +(-5.99000 - 0.742047i) q^{93} -9.07180 q^{94} -5.81863 q^{95} +(-0.320682 + 2.58863i) q^{96} +(-1.19615 - 1.19615i) q^{97} +(-5.32441 - 5.32441i) q^{98} +(10.5939 - 6.33434i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3} + 16 q^{6} + 8 q^{7} - 8 q^{9}+O(q^{10}) \) 8 * q + 4 * q^3 + 16 * q^6 + 8 * q^7 - 8 * q^9	\( 8 q + 4 q^{3} + 16 q^{6} + 8 q^{7} - 8 q^{9} + 16 q^{15} + 8 q^{16} + 4 q^{18} + 8 q^{19} + 4 q^{21} - 8 q^{22} + 12 q^{24} + 4 q^{27} - 16 q^{28} + 8 q^{31} + 4 q^{33} - 36 q^{34} - 4 q^{37} - 24 q^{40} + 32 q^{42} + 4 q^{45} + 28 q^{48} - 8 q^{54} - 8 q^{55} + 16 q^{57} - 68 q^{58} + 44 q^{60} - 56 q^{61} - 8 q^{63} - 40 q^{66} + 8 q^{67} - 32 q^{70} - 36 q^{72} - 28 q^{73} - 8 q^{76} + 16 q^{79} - 8 q^{81} + 4 q^{84} - 36 q^{85} + 68 q^{87} - 20 q^{93} - 128 q^{94} + 16 q^{96} + 32 q^{97} + 40 q^{99}+O(q^{100}) \) 8 * q + 4 * q^3 + 16 * q^6 + 8 * q^7 - 8 * q^9 + 16 * q^15 + 8 * q^16 + 4 * q^18 + 8 * q^19 + 4 * q^21 - 8 * q^22 + 12 * q^24 + 4 * q^27 - 16 * q^28 + 8 * q^31 + 4 * q^33 - 36 * q^34 - 4 * q^37 - 24 * q^40 + 32 * q^42 + 4 * q^45 + 28 * q^48 - 8 * q^54 - 8 * q^55 + 16 * q^57 - 68 * q^58 + 44 * q^60 - 56 * q^61 - 8 * q^63 - 40 * q^66 + 8 * q^67 - 32 * q^70 - 36 * q^72 - 28 * q^73 - 8 * q^76 + 16 * q^79 - 8 * q^81 + 4 * q^84 - 36 * q^85 + 68 * q^87 - 20 * q^93 - 128 * q^94 + 16 * q^96 + 32 * q^97 + 40 * q^99

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