LMFDB - Embedded newform 507.2.f.e.239.2

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			239.2
Root			$0.500000 - 1.56488i$ of defining polynomial
Character	$\chi$	$=$	507.239
Dual form			507.2.f.e.437.2

$q$-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} +(-2.58863 - 0.320682i) 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} +(-2.58863 - 0.320682i) q^{15} +4.46410 q^{16} -5.03908 q^{17} +(-3.87762 + 2.31853i) q^{18} +(-2.73205 + 2.73205i) q^{19} +(0.285334 - 0.285334i) q^{20} +(-2.43091 - 0.301143i) q^{21} -6.19615 q^{22} +(-0.555437 + 4.48364i) 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} +(0.876119 - 7.07227i) 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} +(-3.87762 + 2.31853i) 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} +(-2.82797 + 7.29638i) q^{54} -6.19615 q^{55} +3.68886 q^{56} +(-0.822738 + 6.64136i) q^{57} +(7.63397 - 7.63397i) q^{58} +(-2.12976 + 2.12976i) q^{59} +(0.0859264 - 0.693622i) q^{60} -7.00000 q^{61} -5.24796 q^{62} +(-3.64136 + 2.17726i) 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} +(4.01581 + 6.71624i) 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} +(0.0806910 - 0.651360i) 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} +(0.742047 - 5.99000i) q^{93} -9.07180 q^{94} +5.81863 q^{95} +(-2.58863 - 0.320682i) q^{96} +(1.19615 - 1.19615i) q^{97} +(-5.32441 + 5.32441i) q^{98} +(-6.33434 - 10.5939i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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}+ \cdots - 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

Character values

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

$n$	$170$	$340$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

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	0.222050	−	0.975035i	$-0.428725\pi$
$2$	−1.06488	−	1.06488i	−0.752986	−	0.752986i	−0.975035	+	0.222050i	$0.928725\pi$
$3$	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	0.427694	−	0.903924i	$-0.359326\pi$
$5$	−1.06488	−	1.06488i	−0.476230	−	0.476230i	−0.903924	+	0.427694i	$0.859326\pi$
$6$	−2.58863	−	0.320682i	−1.05680	−	0.130918i
$7$	−1.00000	−	1.00000i	−0.377964	−	0.377964i	0.492403	−	0.870367i	$-0.336119\pi$
$7$	−1.00000	−	1.00000i	−0.377964	−	0.377964i	−0.870367	+	0.492403i	$0.836119\pi$
$8$	−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	−0.116052	−	0.993243i	$-0.537024\pi$
$11$	2.90931	−	2.90931i	0.877191	−	0.877191i	0.993243	+	0.116052i	$0.0370240\pi$
$12$	0.285334	+	0.366025i	0.0823689	+	0.105662i
$13$		0			0
$13$		0			0
$14$			2.12976i			0.569204i
$15$	−2.58863	−	0.320682i	−0.668382	−	0.0827997i
$16$	4.46410			1.11603
$17$	−5.03908			−1.22216			−0.611078	−	0.791570i	$-0.709264\pi$
$17$	−5.03908			−1.22216			−0.611078	+	0.791570i	$0.709264\pi$
$18$	−3.87762	+	2.31853i	−0.913965	+	0.546482i
$19$	−2.73205	+	2.73205i	−0.626775	+	0.626775i	−0.947255	−	0.320480i	$-0.896156\pi$
$19$	−2.73205	+	2.73205i	−0.626775	+	0.626775i	0.320480	+	0.947255i	$0.396156\pi$
$20$	0.285334	−	0.285334i	0.0638027	−	0.0638027i
$21$	−2.43091	−	0.301143i	−0.530468	−	0.0657148i
$22$	−6.19615			−1.32102
$23$		0			0			−	1.00000i	$-0.5\pi$
$23$		0			0				1.00000i	$0.5\pi$
$24$	−0.555437	+	4.48364i	−0.113378	+	0.915219i
$25$		−	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	$-0.648686\pi$
$31$	2.46410	−	2.46410i	0.442566	−	0.442566i	0.892873	+	0.450308i	$0.148686\pi$
$32$	−1.06488	−	1.06488i	−0.188246	−	0.188246i
$33$	0.876119	−	7.07227i	0.152513	−	1.23112i
$34$	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	$-0.396883\pi$
$37$	−3.83013	−	3.83013i	−0.629669	−	0.629669i	−0.947985	+	0.318316i	$0.896883\pi$
$38$	5.81863			0.943906
$39$		0			0
$40$	3.92820			0.621103
$41$	3.97420	+	3.97420i	0.620665	+	0.620665i	0.945701	−	0.325036i	$-0.105377\pi$
$41$	3.97420	+	3.97420i	0.620665	+	0.620665i	−0.325036	+	0.945701i	$0.605377\pi$
$42$	2.26795	+	2.90931i	0.349952	+	0.448917i
$43$			2.19615i			0.334910i	0.985880	+	0.167455i	$0.0535549\pi$
$43$			2.19615i			0.334910i	−0.985880	+	0.167455i	$0.946445\pi$
$44$	0.779548	+	0.779548i	0.117521	+	0.117521i
$45$	−3.87762	+	2.31853i	−0.578042	+	0.345626i
$46$		0			0
$47$	4.25953	−	4.25953i	0.621316	−	0.621316i	−0.324552	−	0.945868i	$-0.605213\pi$
$47$	4.25953	−	4.25953i	0.621316	−	0.621316i	0.945868	+	0.324552i	$0.105213\pi$
$48$	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	$0.982950\pi$
$54$	−2.82797	+	7.29638i	−0.384838	+	0.992912i
$55$	−6.19615			−0.835489
$56$	3.68886			0.492945
$57$	−0.822738	+	6.64136i	−0.108974	+	0.879670i
$58$	7.63397	−	7.63397i	1.00239	−	1.00239i
$59$	−2.12976	+	2.12976i	−0.277272	+	0.277272i	−0.832019	−	0.554747i	$-0.812815\pi$
$59$	−2.12976	+	2.12976i	−0.277272	+	0.277272i	0.554747	+	0.832019i	$0.312815\pi$
$60$	0.0859264	−	0.693622i	0.0110931	−	0.0895462i
$61$	−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
$63$	−3.64136	+	2.17726i	−0.458769	+	0.274309i
$64$		−	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	$-0.631926\pi$
$67$	4.19615	−	4.19615i	0.512642	−	0.512642i	0.915335	+	0.402693i	$0.131926\pi$
$68$		−	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	0.822100	−	0.569343i	$-0.192802\pi$
$71$	2.12976	+	2.12976i	0.252757	+	0.252757i	−0.569343	+	0.822100i	$0.692802\pi$
$72$	4.01581	+	6.71624i	0.473268	+	0.791517i
$73$	0.901924	+	0.901924i	0.105562	+	0.105562i	0.757915	−	0.652353i	$-0.226218\pi$
$73$	0.901924	+	0.901924i	0.105562	+	0.105562i	−0.652353	+	0.757915i	$0.726218\pi$
$74$			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	0.529174	−	0.848513i	$-0.322502\pi$
$83$	−2.90931	−	2.90931i	−0.319339	−	0.319339i	−0.848513	+	0.529174i	$0.822502\pi$
$84$	0.0806910	−	0.651360i	0.00880411	−	0.0710692i
$85$	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	−0.264877	−	0.964282i	$-0.585331\pi$
$89$	6.59817	−	6.59817i	0.699405	−	0.699405i	0.964282	+	0.264877i	$0.0853314\pi$
$90$	6.59817	+	1.66025i	0.695509	+	0.175006i
$91$		0			0
$92$		0			0
$93$	0.742047	−	5.99000i	0.0769467	−	0.621134i
$94$	−9.07180			−0.935684
$95$	5.81863			0.596978
$96$	−2.58863	−	0.320682i	−0.264201	−	0.0327295i
$97$	1.19615	−	1.19615i	0.121451	−	0.121451i	−0.643769	−	0.765220i	$-0.722630\pi$
$97$	1.19615	−	1.19615i	0.121451	−	0.121451i	0.765220	+	0.643769i	$0.222630\pi$
$98$	−5.32441	+	5.32441i	−0.537847	+	0.537847i
$99$	−6.33434	−	10.5939i	−0.636625	−	1.06472i
$100$	0.732051			0.0732051
$101$	6.02751			0.599759			0.299880	−	0.953977i	$-0.403053\pi$
$101$	6.02751			0.599759			0.299880	+	0.953977i	$0.403053\pi$
$102$	13.0443	+	1.61594i	1.29158	+	0.160002i
$103$			6.92820i			0.682656i	0.939944	+	0.341328i	$0.110877\pi$
$103$			6.92820i			0.682656i	−0.939944	+	0.341328i	$0.889123\pi$
$104$		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	0.314806	−	0.949156i	$-0.398060\pi$
$109$	13.1962	−	13.1962i	1.26396	−	1.26396i	0.949156	−	0.314806i	$-0.101940\pi$
$110$	6.59817	+	6.59817i	0.629111	+	0.629111i
$111$	−9.31069	−	1.15342i	−0.883731	−	0.109477i
$112$	−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
$123$	9.66090	+	1.19680i	0.871094	+	0.107912i
$124$	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	$-0.867331\pi$
$127$		−	9.12436i		−	0.809656i	0.914393	−	0.404828i	$-0.132669\pi$
$128$	−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	$-0.112877\pi$
$132$	1.89501	+	0.234755i	0.164939	+	0.0204328i
$133$	5.46410			0.473798
$134$	−8.93682			−0.772023
$135$	−2.82797	+	7.29638i	−0.243393	+	0.627973i
$136$	9.29423	−	9.29423i	0.796974	−	0.796974i
$137$	4.75374	−	4.75374i	0.406140	−	0.406140i	−0.474250	−	0.880390i	$-0.657281\pi$
$137$	4.75374	−	4.75374i	0.406140	−	0.406140i	0.880390	+	0.474250i	$0.157281\pi$
$138$		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
$141$	1.28273	−	10.3545i	0.108025	−	0.872008i
$142$		−	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	0.411399	−	0.911455i	$-0.365040\pi$
$149$	−6.10396	−	6.10396i	−0.500056	−	0.500056i	−0.911455	+	0.411399i	$0.865040\pi$
$150$	−0.876119	+	7.07227i	−0.0715348	+	0.577449i
$151$	−0.535898	−	0.535898i	−0.0436108	−	0.0436108i	0.684965	−	0.728576i	$-0.259817\pi$
$151$	−0.535898	−	0.535898i	−0.0436108	−	0.0436108i	−0.728576	+	0.684965i	$0.759817\pi$
$152$		−	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
$162$	3.90671	+	12.9785i	0.306940	+	1.01969i
$163$	2.92820	+	2.92820i	0.229355	+	0.229355i	0.812423	−	0.583068i	$-0.198148\pi$
$163$	2.92820	+	2.92820i	0.229355	+	0.229355i	−0.583068	+	0.812423i	$0.698148\pi$
$164$	−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	−0.971745	−	0.236034i	$-0.924152\pi$
$167$	−9.50749	+	9.50749i	−0.735711	+	0.735711i	0.236034	+	0.971745i	$0.424152\pi$
$168$	5.03908	−	3.92820i	0.388773	−	0.303067i
$169$		0			0
$170$		−	11.4284i		−	0.876516i
$171$	5.94839	+	9.94839i	0.454885	+	0.760772i
$172$	−0.588457			−0.0448694
$173$	17.4559			1.32715			0.663573	−	0.748112i	$-0.269039\pi$
$173$	17.4559			1.32715			0.663573	+	0.748112i	$0.269039\pi$
$174$	2.29892	−	18.5575i	0.174281	−	1.40684i
$175$	−2.73205	+	2.73205i	−0.206524	+	0.206524i
$176$	12.9875	−	12.9875i	0.978967	−	0.978967i
$177$	−0.641364	+	5.17726i	−0.0482078	+	0.389147i
$178$	−14.0526			−1.05328
$179$	26.5456			1.98411			0.992056	−	0.125798i	$-0.0401492\pi$
$179$	26.5456			1.98411			0.992056	+	0.125798i	$0.0401492\pi$
$180$	−0.621248	−	1.03901i	−0.0463051	−	0.0774430i
$181$			3.00000i			0.222988i	0.993765	+	0.111494i	$0.0355636\pi$
$181$			3.00000i			0.222988i	−0.993765	+	0.111494i	$0.964436\pi$
$182$		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
$189$	−2.65567	+	6.85182i	−0.193171	+	0.498397i
$190$	−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	$-0.248411\pi$
$193$	0.0980762	+	0.0980762i	0.00705968	+	0.00705968i	−0.703568	+	0.710628i	$0.748411\pi$
$194$	−2.54752			−0.182902
$195$		0			0
$196$	1.33975			0.0956961
$197$	−2.90931	−	2.90931i	−0.207280	−	0.207280i	0.595830	−	0.803110i	$-0.296823\pi$
$197$	−2.90931	−	2.90931i	−0.207280	−	0.207280i	−0.803110	+	0.595830i	$0.796823\pi$
$198$	−4.53590	+	18.0265i	−0.322352	+	1.28109i
$199$			12.9282i			0.916456i	0.888835	+	0.458228i	$0.151516\pi$
$199$			12.9282i			0.916456i	−0.888835	+	0.458228i	$0.848484\pi$
$200$	5.03908	+	5.03908i	0.356317	+	0.356317i
$201$	1.26364	−	10.2005i	0.0891304	−	0.719485i
$202$	−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
$210$	0.682977	−	5.51318i	0.0471299	−	0.380445i
$211$	−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
$213$	5.17726	+	0.641364i	0.354740	+	0.0439455i
$214$	−20.2487	+	20.2487i	−1.38417	+	1.38417i
$215$	2.33864	−	2.33864i	0.159494	−	0.159494i
$216$	12.6377	+	4.89819i	0.859887	+	0.333280i
$217$	−4.92820			−0.334548
$218$	−28.1047			−1.90349
$219$	2.19249	+	0.271608i	0.148155	+	0.0183536i
$220$		−	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	−0.261676	+	0.965156i	$0.584275\pi$
$223$	−18.3205	+	18.3205i	−1.22683	+	1.22683i	−0.965156	+	0.261676i	$0.915725\pi$
$224$			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	0.0472572	−	0.998883i	$-0.484952\pi$
$227$	−14.3377	−	14.3377i	−0.951626	−	0.951626i	−0.998883	+	0.0472572i	$0.984952\pi$
$228$	−1.77955	−	0.220452i	−0.117853	−	0.0145998i
$229$	14.1244	+	14.1244i	0.933364	+	0.933364i	0.997914	−	0.0645507i	$-0.0205614\pi$
$229$	14.1244	+	14.1244i	0.933364	+	0.933364i	−0.0645507	+	0.997914i	$0.520561\pi$
$230$		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	$-0.306251\pi$
$233$	17.4559			1.14357			0.571786	+	0.820403i	$0.306251\pi$
$234$		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	0.460737	−	0.887537i	$-0.347585\pi$
$239$	−6.59817	−	6.59817i	−0.426800	−	0.426800i	−0.887537	+	0.460737i	$0.847585\pi$
$240$	−11.5559	−	1.43156i	−0.745931	−	0.0924066i
$241$	−10.2942	−	10.2942i	−0.663110	−	0.663110i	0.293002	−	0.956112i	$-0.405346\pi$
$241$	−10.2942	−	10.2942i	−0.663110	−	0.663110i	−0.956112	+	0.293002i	$0.905346\pi$
$242$	−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
$249$	−7.07227	−	0.876119i	−0.448187	−	0.0555218i
$250$	17.5359			1.10907
$251$	−0.988427			−0.0623890			−0.0311945	−	0.999513i	$-0.509931\pi$
$251$	−0.988427			−0.0623890			−0.0311945	+	0.999513i	$0.509931\pi$
$252$	−0.583396	−	0.975700i	−0.0367505	−	0.0614634i
$253$		0			0
$254$	−9.71637	+	9.71637i	−0.609659	+	0.609659i
$255$	13.0443	+	1.61594i	0.816867	+	0.101194i
$256$	6.32051			0.395032
$257$	−21.5065			−1.34154			−0.670770	−	0.741665i	$-0.734036\pi$
$257$	−21.5065			−1.34154			−0.670770	+	0.741665i	$0.734036\pi$
$258$	0.704266	−	5.68503i	0.0438457	−	0.353934i
$259$			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
$267$	1.98699	−	16.0396i	0.121602	−	0.981605i
$268$	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	$-0.174588\pi$
$271$	5.46410	+	5.46410i	0.331921	+	0.331921i	−0.521395	+	0.853315i	$0.674588\pi$
$272$	−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	$0.310984\pi$
$277$			27.5885i			1.65763i	−0.559523	+	0.828815i	$0.689016\pi$
$278$	−19.5856	−	19.5856i	−1.17467	−	1.17467i
$279$	−5.36500	−	8.97269i	−0.321194	−	0.537181i
$280$	−3.92820	−	3.92820i	−0.234755	−	0.234755i
$281$	12.1315	−	12.1315i	0.723703	−	0.723703i	−0.245655	−	0.969357i	$-0.579003\pi$
$281$	12.1315	−	12.1315i	0.723703	−	0.723703i	0.969357	+	0.245655i	$0.0790030\pi$
$282$	−12.3923	+	9.66040i	−0.737951	+	0.575268i
$283$			6.58846i			0.391643i	0.980640	+	0.195822i	$0.0627373\pi$
$283$			6.58846i			0.391643i	−0.980640	+	0.195822i	$0.937263\pi$
$284$	−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
$288$	−3.87762	+	2.31853i	−0.228491	+	0.136621i
$289$	8.39230			0.493665
$290$	−16.2586			−0.954736
$291$	0.360213	−	2.90774i	0.0211161	−	0.170455i
$292$	−0.241670	+	0.241670i	−0.0141427	+	0.0141427i
$293$	−1.27376	+	1.27376i	−0.0744140	+	0.0744140i	−0.743334	−	0.668920i	$-0.766757\pi$
$293$	−1.27376	+	1.27376i	−0.0744140	+	0.0744140i	0.668920	+	0.743334i	$0.266757\pi$
$294$	−1.60341	+	12.9432i	−0.0935127	+	0.754860i
$295$	4.53590			0.264090
$296$	14.1288			0.821220
$297$	−19.9341	−	7.72617i	−1.15669	−	0.448318i
$298$			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
$306$	19.5397	−	11.6832i	1.11701	−	0.667887i
$307$	−8.39230	−	8.39230i	−0.478974	−	0.478974i	0.425829	−	0.904803i	$-0.359982\pi$
$307$	−8.39230	−	8.39230i	−0.478974	−	0.478974i	−0.904803	+	0.425829i	$0.859982\pi$
$308$		−	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	$-0.407761\pi$
$311$	10.0782			0.571480			0.285740	+	0.958307i	$0.407761\pi$
$312$		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	0.949960	−	0.312373i	$-0.101124\pi$
$317$	11.3519	+	11.3519i	0.637587	+	0.637587i	−0.312373	+	0.949960i	$0.601124\pi$
$318$	0.249987	−	2.01796i	0.0140186	−	0.113162i
$319$	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
$327$	3.97393	−	32.0786i	0.219759	−	1.77395i
$328$	−14.6603			−0.809477
$329$	−8.51906			−0.469671
$330$	16.0396	+	1.98699i	0.882948	+	0.109380i
$331$	−24.1962	+	24.1962i	−1.32994	+	1.32994i	−0.424524	+	0.905417i	$0.639559\pi$
$331$	−24.1962	+	24.1962i	−1.32994	+	1.32994i	−0.905417	+	0.424524i	$0.860441\pi$
$332$	0.779548	−	0.779548i	0.0427833	−	0.0427833i
$333$	−13.9469	+	8.33919i	−0.764285	+	0.456985i
$334$	20.2487			1.10796
$335$	−8.93682			−0.488271
$336$	−10.8518	−	1.34433i	−0.592015	−	0.0733394i
$337$		−	18.4641i		−	1.00580i	−0.864344	−	0.502902i	$-0.832266\pi$
$337$		−	18.4641i		−	1.00580i	0.864344	−	0.502902i	$-0.167734\pi$
$338$		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	0.996757	+	0.0804755i	$0.0256439\pi$
$349$	20.1244	+	20.1244i	1.07723	+	1.07723i	0.0804755	+	0.996757i	$0.474356\pi$
$350$	5.81863			0.311019
$351$		0			0
$352$	−6.19615			−0.330256
$353$	10.0017	+	10.0017i	0.532337	+	0.532337i	0.921267	−	0.388930i	$-0.127155\pi$
$353$	10.0017	+	10.0017i	0.532337	+	0.532337i	−0.388930	+	0.921267i	$0.627155\pi$
$354$	6.19615	−	4.83020i	0.329322	−	0.256722i
$355$		−	4.53590i		−	0.240740i
$356$	1.76798	+	1.76798i	0.0937025	+	0.0937025i
$357$	12.2495	+	1.51748i	0.648314	+	0.0803137i
$358$	−28.2679	−	28.2679i	−1.49401	−	1.49401i
$359$	−18.2354	+	18.2354i	−0.962429	+	0.962429i	−0.999319	−	0.0368904i	$-0.988255\pi$
$359$	−18.2354	+	18.2354i	−0.962429	+	0.962429i	0.0368904	+	0.999319i	$0.488255\pi$
$360$	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
$366$	18.1204	+	2.24477i	0.947169	+	0.117336i
$367$	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
$369$	14.4715	−	8.65286i	0.753356	−	0.450450i
$370$	8.68653	−	8.68653i	0.451591	−	0.451591i
$371$	0.779548	−	0.779548i	0.0404721	−	0.0404721i
$372$	1.60502	+	0.198831i	0.0832162	+	0.0103089i
$373$	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
$375$	−2.47953	+	20.0154i	−0.128042	+	1.03359i
$376$			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	$-0.874101\pi$
$379$	−10.4641	+	10.4641i	−0.537505	+	0.537505i	0.385291	+	0.922795i	$0.374101\pi$
$380$			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	0.977269	+	0.212002i	$0.0679985\pi$
$383$	23.2745	+	23.2745i	1.18927	+	1.18927i	0.212002	+	0.977269i	$0.432002\pi$
$384$	−2.77719	+	22.4182i	−0.141723	+	1.14402i
$385$	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	$-0.306839\pi$
$389$	22.4950			1.14054			0.570270	+	0.821457i	$0.306839\pi$
$390$		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
$396$	2.83862	−	1.69728i	0.142646	−	0.0852916i
$397$	9.73205	+	9.73205i	0.488438	+	0.488438i	0.907813	−	0.419375i	$-0.137751\pi$
$397$	9.73205	+	9.73205i	0.488438	+	0.488438i	−0.419375	+	0.907813i	$0.637751\pi$
$398$	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	−0.452231	−	0.891901i	$-0.649372\pi$
$401$	8.80439	−	8.80439i	0.439670	−	0.439670i	0.891901	+	0.452231i	$0.149372\pi$
$402$	−12.2079	+	9.51666i	−0.608876	+	0.474648i
$403$		0			0
$404$			1.61507i			0.0803525i
$405$	3.90671	+	12.9785i	0.194126	+	0.644907i
$406$	−15.2679			−0.757736
$407$	−22.2861			−1.10468
$408$	2.79889	−	22.5934i	0.138566	−	1.11854i
$409$	21.2224	−	21.2224i	1.04938	−	1.04938i	0.0506661	−	0.998716i	$-0.483866\pi$
$409$	21.2224	−	21.2224i	1.04938	−	1.04938i	0.998716	−	0.0506661i	$-0.0161344\pi$
$410$	−9.01327	+	9.01327i	−0.445134	+	0.445134i
$411$	1.43156	−	11.5559i	0.0706135	−	0.570011i
$412$	−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	$-0.663028\pi$
$421$	7.83013	−	7.83013i	0.381617	−	0.381617i	0.871685	+	0.490067i	$0.163028\pi$
$422$	1.92089	+	1.92089i	0.0935072	+	0.0935072i
$423$	−9.27411	−	15.5105i	−0.450923	−	0.754146i
$424$	−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	−0.935566	−	0.353152i	$-0.885110\pi$
$431$	−26.7545	−	26.7545i	−1.28872	−	1.28872i	−0.353152	−	0.935566i	$-0.614890\pi$
$432$	−9.36603	−	21.2212i	−0.450623	−	1.02101i
$433$		−	31.0526i		−	1.49229i	−0.665783	−	0.746145i	$-0.731902\pi$
$433$		−	31.0526i		−	1.49229i	0.665783	−	0.746145i	$-0.268098\pi$
$434$	5.24796	+	5.24796i	0.251910	+	0.251910i
$435$	2.29892	−	18.5575i	0.110225	−	0.889763i
$436$	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	$-0.990367\pi$
$439$		−	1.26795i		−	0.0605159i	0.999542	−	0.0302580i	$-0.00963288\pi$
$440$	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	$0.914124\pi$
$444$	0.309057	−	2.49479i	0.0146672	−	0.118398i
$445$	−14.0526			−0.666155
$446$	39.0184			1.84757
$447$	−14.8382	−	1.83816i	−0.701821	−	0.0869422i
$448$	−6.66025	+	6.66025i	−0.314667	+	0.314667i
$449$	−14.5466	+	14.5466i	−0.686495	+	0.686495i	−0.961455	−	0.274961i	$-0.911335\pi$
$449$	−14.5466	+	14.5466i	−0.686495	+	0.686495i	0.274961	+	0.961455i	$0.411335\pi$
$450$	6.33434	+	10.5939i	0.298603	+	0.499400i
$451$	23.1244			1.08888
$452$	2.75640			0.129650
$453$	−1.30272	−	0.161382i	−0.0612071	−	0.00758239i
$454$			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	$-0.720918\pi$
$457$	2.75833	−	2.75833i	0.129029	−	0.129029i	0.768672	+	0.639643i	$0.220918\pi$
$458$		−	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	0.964522	−	0.264003i	$-0.0850429\pi$
$461$	15.0408	+	15.0408i	0.700519	+	0.700519i	−0.264003	+	0.964522i	$0.585043\pi$
$462$	15.0623	+	1.86593i	0.700760	+	0.0868108i
$463$	−23.0526	−	23.0526i	−1.07134	−	1.07134i	−0.997251	−	0.0740918i	$-0.976394\pi$
$463$	−23.0526	−	23.0526i	−1.07134	−	1.07134i	−0.0740918	−	0.997251i	$-0.523606\pi$
$464$			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	$-0.646261\pi$
$467$	−19.1679			−0.886984			−0.443492	+	0.896278i	$0.646261\pi$
$468$		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
$474$	−5.17726	−	0.641364i	−0.237800	−	0.0294588i
$475$	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	−0.956472	−	0.291823i	$-0.905738\pi$
$479$	−14.5466	+	14.5466i	−0.664649	+	0.664649i	0.291823	+	0.956472i	$0.405738\pi$
$480$	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
$486$	19.1572	+	13.5688i	0.868990	+	0.615492i
$487$	4.07180	−	4.07180i	0.184511	−	0.184511i	−0.608807	−	0.793318i	$-0.708352\pi$
$487$	4.07180	−	4.07180i	0.184511	−	0.184511i	0.793318	+	0.608807i	$0.208352\pi$
$488$	12.9110	−	12.9110i	0.584454	−	0.584454i
$489$	7.11819	+	0.881808i	0.321896	+	0.0398767i
$490$	11.3397			0.512278
$491$	−28.5225			−1.28720			−0.643600	−	0.765362i	$-0.722560\pi$
$491$	−28.5225			−1.28720			−0.643600	+	0.765362i	$0.722560\pi$
$492$	−0.320682	+	2.58863i	−0.0144575	+	0.116705i
$493$		−	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	$-0.725147\pi$
$499$	2.46410	−	2.46410i	0.110308	−	0.110308i	0.760107	+	0.649798i	$0.225147\pi$
$500$	−2.20622	−	2.20622i	−0.0986652	−	0.0986652i
$501$	−2.86311	+	23.1118i	−0.127914	+	1.03256i
$502$	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	0.898443	−	0.439090i	$-0.144699\pi$
$509$	10.3635	+	10.3635i	0.459354	+	0.459354i	−0.439090	+	0.898443i	$0.644699\pi$
$510$	−12.1699	−	15.6114i	−0.538891	−	0.691286i
$511$		−	1.80385i		−	0.0797975i
$512$	11.7137	+	11.7137i	0.517678	+	0.517678i
$513$	18.7195	+	7.25542i	0.826487	+	0.320335i
$514$	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	$0.982618\pi$
$522$	−16.6212	−	27.7981i	−0.727489	−	1.21669i
$523$	−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
$525$	−0.822738	+	6.64136i	−0.0359072	+	0.289853i
$526$	23.7321	−	23.7321i	1.03477	−	1.03477i
$527$	−12.4168	+	12.4168i	−0.540884	+	0.540884i
$528$	3.91108	−	31.5713i	0.170208	−	1.37397i
$529$	−23.0000			−1.00000
$530$	−1.76798			−0.0767959
$531$	4.63706	+	7.75525i	0.201231	+	0.336549i
$532$			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
$540$	−1.95506	−	0.757753i	−0.0841324	−	0.0326085i
$541$	12.6865	+	12.6865i	0.545437	+	0.545437i	0.925118	−	0.379681i	$-0.123966\pi$
$541$	12.6865	+	12.6865i	0.545437	+	0.545437i	−0.379681	+	0.925118i	$0.623966\pi$
$542$		−	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	−0.977586	−	0.210537i	$-0.932479\pi$
$557$	−18.1030	+	18.1030i	−0.767049	+	0.767049i	0.210537	+	0.977586i	$0.432479\pi$
$558$	−3.84177	+	15.2679i	−0.162635	+	0.646344i
$559$		0			0
$560$			9.50749i			0.401765i
$561$	−4.41483	+	35.6377i	−0.186394	+	1.50463i
$562$	−25.8372			−1.08988
$563$	−10.0782			−0.424744			−0.212372	−	0.977189i	$-0.568119\pi$
$563$	−10.0782			−0.424744			−0.212372	+	0.977189i	$0.568119\pi$
$564$	2.77449	+	0.343706i	0.116827	+	0.0144726i
$565$	−10.9545	+	10.9545i	−0.460859	+	0.460859i
$566$	7.01593	−	7.01593i	0.294902	−	0.294902i
$567$	3.66867	+	12.1877i	0.154070	+	0.511837i
$568$	−7.85641			−0.329647
$569$	−2.70043			−0.113208			−0.0566040	−	0.998397i	$-0.518027\pi$
$569$	−2.70043			−0.113208			−0.0566040	+	0.998397i	$0.518027\pi$
$570$	−15.0623	−	1.86593i	−0.630889	−	0.0781551i
$571$			1.94744i			0.0814979i	0.999169	+	0.0407489i	$0.0129744\pi$
$571$			1.94744i			0.0814979i	−0.999169	+	0.0407489i	$0.987026\pi$
$572$		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	$-0.519685\pi$
$577$	22.4904	−	22.4904i	0.936287	−	0.936287i	0.998088	+	0.0618016i	$0.0196846\pi$
$578$	−8.93682	−	8.93682i	−0.371723	−	0.371723i
$579$	0.238414	+	0.0295350i	0.00990816	+	0.00122743i
$580$	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	0.924895	−	0.380223i	$-0.124153\pi$
$587$	13.1963	+	13.1963i	0.544672	+	0.544672i	−0.380223	+	0.924895i	$0.624153\pi$
$588$	1.83013	−	1.42667i	0.0754732	−	0.0588350i
$589$			13.4641i			0.554779i
$590$	−4.83020	−	4.83020i	−0.198856	−	0.198856i
$591$	−7.07227	−	0.876119i	−0.290914	−	0.0360387i
$592$	−17.0981	−	17.0981i	−0.702727	−	0.702727i
$593$	−10.3635	+	10.3635i	−0.425578	+	0.425578i	−0.887119	−	0.461541i	$-0.847297\pi$
$593$	−10.3635	+	10.3635i	−0.425578	+	0.425578i	0.461541	+	0.887119i	$0.347297\pi$
$594$	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	$-0.139178\pi$
$600$	12.2495	+	1.51748i	0.500085	+	0.0619510i
$601$	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
$603$	−9.13612	−	15.2797i	−0.372052	−	0.622238i
$604$	0.143594	−	0.143594i	0.00584274	−	0.00584274i
$605$	−6.31284	+	6.31284i	−0.256653	+	0.256653i
$606$	−15.6030	−	1.93291i	−0.633828	−	0.0785192i
$607$	−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
$609$	2.15885	−	17.4268i	0.0874809	−	0.706169i
$610$		−	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	0.298835	−	0.954305i	$-0.403402\pi$
$613$	31.0263	−	31.0263i	1.25314	−	1.25314i	0.954305	−	0.298835i	$-0.0965979\pi$
$614$			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	0.919357	−	0.393424i	$-0.128709\pi$
$617$	13.0639	+	13.0639i	0.525934	+	0.525934i	−0.393424	+	0.919357i	$0.628709\pi$
$618$	2.22175	−	17.9346i	0.0893719	−	0.721434i
$619$	31.6603	+	31.6603i	1.27253	+	1.27253i	0.944755	+	0.327778i	$0.106300\pi$
$619$	31.6603	+	31.6603i	1.27253	+	1.27253i	0.327778	+	0.944755i	$0.393700\pi$
$620$		−	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
$630$	−4.93792	−	8.25843i	−0.196731	−	0.329024i
$631$	−15.6603	−	15.6603i	−0.623425	−	0.623425i	0.322981	−	0.946406i	$-0.395315\pi$
$631$	−15.6603	−	15.6603i	−0.623425	−	0.623425i	−0.946406	+	0.322981i	$0.895315\pi$
$632$	−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
$639$	7.75525	−	4.63706i	0.306793	−	0.183439i
$640$	19.6410			0.776379
$641$	45.3517			1.79128			0.895642	−	0.444775i	$-0.146716\pi$
$641$	45.3517			1.79128			0.895642	+	0.444775i	$0.146716\pi$
$642$	−6.09776	+	49.2228i	−0.240659	+	1.94267i
$643$	5.12436	−	5.12436i	0.202085	−	0.202085i	−0.598808	−	0.800893i	$-0.704359\pi$
$643$	5.12436	−	5.12436i	0.202085	−	0.202085i	0.800893	+	0.598808i	$0.204359\pi$
$644$		0			0
$645$	0.704266	−	5.68503i	0.0277305	−	0.223848i
$646$	−29.3205			−1.15360
$647$	−16.4675			−0.647402			−0.323701	−	0.946159i	$-0.604927\pi$
$647$	−16.4675			−0.647402			−0.323701	+	0.946159i	$0.604927\pi$
$648$	22.4794	−	6.76661i	0.883075	−	0.265818i
$649$			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
$657$	3.28423	−	1.96372i	0.128130	−	0.0766122i
$658$	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	$-0.189208\pi$
$661$	6.90192	+	6.90192i	0.268454	+	0.268454i	−0.560023	+	0.828477i	$0.689208\pi$
$662$	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
$669$	−5.51709	+	44.5355i	−0.213303	+	1.72184i
$670$	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	$0.307830\pi$
$673$			42.7128i			1.64646i	−0.567709	+	0.823229i	$0.692170\pi$
$674$	−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	$-0.0594357\pi$
$678$	−3.29887	+	26.6293i	−0.126692	+	1.02269i
$679$	−2.39230			−0.0918082
$680$	−19.7945			−0.759085
$681$	−34.8536	−	4.31769i	−1.33559	−	0.165454i
$682$	−15.2679	+	15.2679i	−0.584640	+	0.584640i
$683$	33.1438	−	33.1438i	1.26821	−	1.26821i	0.321200	−	0.947011i	$-0.395914\pi$
$683$	33.1438	−	33.1438i	1.26821	−	1.26821i	0.947011	−	0.321200i	$-0.104086\pi$
$684$	−2.66566	+	1.59387i	−0.101924	+	0.0609430i
$685$	−10.1244			−0.386832
$686$	25.5572			0.975778
$687$	34.3350	+	4.25345i	1.30996	+	0.162279i
$688$			9.80385i			0.373768i
$689$		0			0
$690$		0			0
$691$	−13.3397	+	13.3397i	−0.507468	+	0.507468i	−0.913748	−	0.406281i	$-0.866826\pi$
$691$	−13.3397	+	13.3397i	−0.507468	+	0.507468i	0.406281	+	0.913748i	$0.366826\pi$
$692$			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
$696$	−32.1425	−	3.98184i	−1.21836	−	0.150931i
$697$	−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	$-0.422420\pi$
$701$	12.7786			0.482641			0.241320	+	0.970446i	$0.422420\pi$
$702$		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
$708$	−1.38724	−	0.171853i	−0.0521358	−	0.00645863i
$709$	8.29423	+	8.29423i	0.311496	+	0.311496i	0.845489	−	0.533993i	$-0.179309\pi$
$709$	8.29423	+	8.29423i	0.311496	+	0.311496i	−0.533993	+	0.845489i	$0.679309\pi$
$710$	−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
$717$	−16.0396	−	1.98699i	−0.599008	−	0.0742056i
$718$	38.8372			1.44939
$719$	−7.37772			−0.275143			−0.137571	−	0.990492i	$-0.543930\pi$
$719$	−7.37772			−0.275143			−0.137571	+	0.990492i	$0.543930\pi$
$720$	−17.3101	+	10.3501i	−0.645110	+	0.385727i
$721$	6.92820	−	6.92820i	0.258020	−	0.258020i
$722$	4.33598	−	4.33598i	0.161369	−	0.161369i
$723$	−25.0243	−	3.10003i	−0.930665	−	0.115292i
$724$	−0.803848			−0.0298748
$725$	19.5856			0.727392
$726$	−1.90107	+	15.3459i	−0.0705552	+	0.569541i
$727$		−	19.5167i		−	0.723833i	−0.932211	−	0.361916i	$-0.882123\pi$
$727$		−	19.5167i		−	0.723833i	0.932211	−	0.361916i	$-0.117877\pi$
$728$		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	$-0.693356\pi$
$733$	6.77757	−	6.77757i	0.250335	−	0.250335i	0.821108	+	0.570773i	$0.193356\pi$
$734$	−32.3642	−	32.3642i	−1.19459	−	1.19459i
$735$	−1.60341	+	12.9432i	−0.0591426	+	0.477415i
$736$		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	$-0.317941\pi$
$739$	−8.14359	−	8.14359i	−0.299567	−	0.299567i	−0.840844	+	0.541277i	$0.817941\pi$
$740$	−2.18573			−0.0803492
$741$		0			0
$742$	−1.66025			−0.0609498
$743$	−6.23638	−	6.23638i	−0.228791	−	0.228791i	0.583397	−	0.812187i	$-0.301723\pi$
$743$	−6.23638	−	6.23638i	−0.228791	−	0.228791i	−0.812187	+	0.583397i	$0.801723\pi$
$744$	9.67949	+	12.4168i	0.354867	+	0.455222i
$745$			13.0000i			0.476283i
$746$	−12.3403	−	12.3403i	−0.451812	−	0.451812i
$747$	−10.5939	+	6.33434i	−0.387609	+	0.231761i
$748$	−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	$0.211555\pi$
$751$			33.8038i			1.23352i	−0.787151	+	0.616760i	$0.788445\pi$
$752$	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
$756$	−1.83594	−	0.711584i	−0.0667725	−	0.0258801i
$757$	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	−0.431377	−	0.902172i	$-0.641972\pi$
$761$	12.9875	−	12.9875i	0.470795	−	0.470795i	0.902172	+	0.431377i	$0.141972\pi$
$762$	−2.92602	+	23.6196i	−0.105998	+	0.855647i
$763$	−26.3923			−0.955466
$764$	−1.29425			−0.0468242
$765$	19.5397	−	11.6832i	0.706458	−	0.422409i
$766$		−	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	0.0693980	−	0.997589i	$-0.477892\pi$
$769$	29.5885	−	29.5885i	1.06699	−	1.06699i	0.997589	−	0.0693980i	$-0.0221078\pi$
$770$		−	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	−0.994989	−	0.0999818i	$-0.968122\pi$
$773$	−30.4433	−	30.4433i	−1.09497	−	1.09497i	−0.0999818	−	0.994989i	$-0.531878\pi$
$774$	−5.09184	−	8.51585i	−0.183022	−	0.306096i
$775$	−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
$786$	−2.54890	+	20.5755i	−0.0909164	+	0.733902i
$787$	−11.7321	−	11.7321i	−0.418202	−	0.418202i	0.466381	−	0.884584i	$-0.345557\pi$
$787$	−11.7321	−	11.7321i	−0.418202	−	0.418202i	−0.884584	+	0.466381i	$0.845557\pi$
$788$	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
$795$	0.249987	−	2.01796i	0.00886612	−	0.0715697i
$796$	−3.46410			−0.122782
$797$	−40.3126			−1.42795			−0.713973	−	0.700173i	$-0.753106\pi$
$797$	−40.3126			−1.42795			−0.713973	+	0.700173i	$0.753106\pi$
$798$	−14.1445	−	1.75224i	−0.500711	−	0.0620286i
$799$	−21.4641	+	21.4641i	−0.759345	+	0.759345i
$800$	−2.90931	+	2.90931i	−0.102860	+	0.102860i
$801$	−14.3660	−	24.0264i	−0.507596	−	0.848929i
$802$	−18.7513			−0.662131
$803$	5.24796			0.185196
$804$	2.73320	+	0.338592i	0.0963927	+	0.0119412i
$805$		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	$-0.906384\pi$
$811$	−19.0000	+	19.0000i	−0.667180	+	0.667180i	0.289882	+	0.957062i	$0.406384\pi$
$812$	1.92089	+	1.92089i	0.0674099	+	0.0674099i
$813$	13.2827	+	1.64548i	0.465846	+	0.0577094i
$814$	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	−0.997913	−	0.0645667i	$-0.979433\pi$
$821$	−30.4433	−	30.4433i	−1.06248	−	1.06248i	−0.0645667	−	0.997913i	$-0.520567\pi$
$822$	−13.8301	+	10.7812i	−0.482381	+	0.376039i
$823$		−	8.53590i		−	0.297543i	−0.988872	−	0.148771i	$-0.952468\pi$
$823$		−	8.53590i		−	0.297543i	0.988872	−	0.148771i	$-0.0475318\pi$
$824$	−12.7786	−	12.7786i	−0.445163	−	0.445163i
$825$	−19.3218	−	2.39360i	−0.672699	−	0.0833345i
$826$	−4.53590	−	4.53590i	−0.157824	−	0.157824i
$827$	31.7936	−	31.7936i	1.10557	−	1.10557i	0.111845	−	0.993726i	$-0.464324\pi$
$827$	31.7936	−	31.7936i	1.10557	−	1.10557i	0.993726	−	0.111845i	$-0.0356760\pi$
$828$		0			0
$829$		−	48.1244i		−	1.67143i	−0.549165	−	0.835714i	$-0.685054\pi$
$829$		−	48.1244i		−	1.67143i	0.549165	−	0.835714i	$-0.314946\pi$
$830$	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
$834$	−47.6109	−	5.89808i	−1.64863	−	0.204234i
$835$	20.2487			0.700736
$836$	−4.25953			−0.147319
$837$	−16.8836	−	6.54383i	−0.583582	−	0.226188i
$838$	10.1244	−	10.1244i	0.349740	−	0.349740i
$839$	−7.16884	+	7.16884i	−0.247496	+	0.247496i	−0.819942	−	0.572446i	$-0.805995\pi$
$839$	−7.16884	+	7.16884i	−0.247496	+	0.247496i	0.572446	+	0.819942i	$0.305995\pi$
$840$	−9.54910	−	1.18295i	−0.329475	−	0.0408157i
$841$	−22.3923			−0.772148
$842$	−16.6763			−0.574704
$843$	3.65331	−	29.4905i	0.125827	−	1.01571i
$844$		−	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
$852$	−0.171853	+	1.38724i	−0.00588758	+	0.0475262i
$853$	22.3660	+	22.3660i	0.765798	+	0.765798i	0.977364	−	0.211566i	$-0.0678562\pi$
$853$	22.3660	+	22.3660i	0.765798	+	0.765798i	−0.211566	+	0.977364i	$0.567856\pi$
$854$		−	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	$-0.481902\pi$
$857$	3.32707			0.113651			0.0568253	+	0.998384i	$0.481902\pi$
$858$		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	0.945721	−	0.324980i	$-0.105358\pi$
$863$	18.2354	+	18.2354i	0.620741	+	0.620741i	−0.324980	+	0.945721i	$0.605358\pi$
$864$	−2.82797	+	7.29638i	−0.0962096	+	0.248228i
$865$	−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
$873$	−2.60434	−	4.35563i	−0.0881435	−	0.147416i
$874$		0			0
$875$	16.4675			0.556701
$876$	−0.0727771	+	0.587477i	−0.00245891	+	0.0198490i
$877$	21.2224	−	21.2224i	0.716631	−	0.716631i	−0.251283	−	0.967914i	$-0.580852\pi$
$877$	21.2224	−	21.2224i	0.716631	−	0.716631i	0.967914	+	0.251283i	$0.0808525\pi$
$878$	−1.35022	+	1.35022i	−0.0455676	+	0.0455676i
$879$	−0.383584	+	3.09640i	−0.0129380	+	0.104439i
$880$	−27.6603			−0.932427
$881$	−23.4834			−0.791175			−0.395588	−	0.918428i	$-0.629459\pi$
$881$	−23.4834			−0.791175			−0.395588	+	0.918428i	$0.629459\pi$
$882$	11.5926	+	19.3881i	0.390345	+	0.652832i
$883$			33.3731i			1.12309i	0.827445	+	0.561547i	$0.189793\pi$
$883$			33.3731i			1.12309i	−0.827445	+	0.561547i	$0.810207\pi$
$884$		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
$891$	−35.4579	+	10.6733i	−1.18789	+	0.357570i
$892$	−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
$903$	0.661356	−	5.33864i	0.0220085	−	0.177659i
$904$	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	$0.0928437\pi$
$907$			17.3205i			0.575118i	−0.957763	+	0.287559i	$0.907156\pi$
$908$	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	$-0.00822209\pi$
$912$	−3.67279	+	29.6477i	−0.121618	+	0.981734i
$913$	−16.9282			−0.560242
$914$	−5.87459			−0.194314
$915$	18.1204	+	2.24477i	0.599043	+	0.0742099i
$916$	−3.78461	+	3.78461i	−0.125047	+	0.125047i
$917$	−7.94839	+	7.94839i	−0.262479	+	0.262479i
$918$	14.2504	−	36.7670i	0.470333	−	1.21349i
$919$	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
$921$	−20.4009	−	2.52728i	−0.672233	−	0.0832768i
$922$		−	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	0.902856	−	0.429943i	$-0.141466\pi$
$929$	14.4141	+	14.4141i	0.472913	+	0.472913i	−0.429943	+	0.902856i	$0.641466\pi$
$930$	13.5850	+	1.68292i	0.445471	+	0.0551853i
$931$	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	0.840285	−	0.542144i	$-0.182387\pi$
$941$	9.14570	+	9.14570i	0.298141	+	0.298141i	−0.542144	+	0.840285i	$0.682387\pi$
$942$	12.4354	+	1.54051i	0.405167	+	0.0501924i
$943$		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	−0.573014	−	0.819546i	$-0.694226\pi$
$947$	7.58660	−	7.58660i	0.246531	−	0.246531i	0.819546	+	0.573014i	$0.194226\pi$
$948$	0.570669	+	0.732051i	0.0185345	+	0.0237759i
$949$		0			0
$950$		−	15.8968i		−	0.515760i
$951$	27.5955	+	3.41855i	0.894844	+	0.110854i
$952$	−18.5885			−0.602455
$953$	1.97685			0.0640366			0.0320183	−	0.999487i	$-0.489807\pi$
$953$	1.97685			0.0640366			0.0320183	+	0.999487i	$0.489807\pi$
$954$	−1.80740	−	3.02279i	−0.0585169	−	0.0978666i
$955$	5.14359	−	5.14359i	0.166443	−	0.166443i
$956$	1.76798	−	1.76798i	0.0571804	−	0.0571804i
$957$	50.7000	+	6.28076i	1.63890	+	0.203028i
$958$	30.9808			1.00094
$959$	−9.50749			−0.307013
$960$	−2.13582	+	17.2409i	−0.0689334	+	0.556449i
$961$			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	$-0.531648\pi$
$967$	27.8564	−	27.8564i	0.895802	−	0.895802i	0.995062	+	0.0992599i	$0.0316475\pi$
$968$	10.9342	+	10.9342i	0.351437	+	0.351437i
$969$	4.14584	−	33.4663i	0.133184	−	1.07509i
$970$	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	0.922342	−	0.386373i	$-0.126272\pi$
$977$	16.7528	+	16.7528i	0.535969	+	0.535969i	−0.386373	+	0.922342i	$0.626272\pi$
$978$	−6.64102	−	8.51906i	−0.212356	−	0.272409i
$979$		−	38.3923i		−	1.22702i
$980$	−1.42667	−	1.42667i	−0.0455734	−	0.0455734i
$981$	−28.7315	−	48.0520i	−0.917326	−	1.53418i
$982$	30.3731	+	30.3731i	0.969244	+	0.969244i
$983$	30.4433	−	30.4433i	0.970992	−	0.970992i	−0.0285990	−	0.999591i	$-0.509105\pi$
$983$	30.4433	−	30.4433i	0.970992	−	0.970992i	0.999591	+	0.0285990i	$0.00910459\pi$
$984$	−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
$990$	24.0264	−	14.3660i	0.763608	−	0.456580i
$991$	−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
$993$	−7.28650	+	58.8186i	−0.231230	+	1.86655i
$994$	−4.53590	+	4.53590i	−0.143870	+	0.143870i
$995$	13.7670	−	13.7670i	0.436444	−	0.436444i
$996$	0.234755	−	1.89501i	0.00743851	−	0.0600457i
$997$	−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
$999$	−10.1715	+	26.2433i	−0.321813	+	0.830303i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.f.e.239.2		8
3.2	odd	2	inner	507.2.f.e.239.3		8
13.2	odd	12		507.2.k.e.488.1		8
13.3	even	3		507.2.k.d.188.2		8
13.4	even	6		507.2.k.e.80.2		8
13.5	odd	4		507.2.f.f.437.2		8
13.6	odd	12		39.2.k.b.11.2	yes	8
13.7	odd	12		507.2.k.d.89.1		8
13.8	odd	4	inner	507.2.f.e.437.3		8
13.9	even	3		507.2.k.f.80.1		8
13.10	even	6		39.2.k.b.32.1	yes	8
13.11	odd	12		507.2.k.f.488.2		8
13.12	even	2		507.2.f.f.239.3		8
39.2	even	12		507.2.k.e.488.2		8
39.5	even	4		507.2.f.f.437.3		8
39.8	even	4	inner	507.2.f.e.437.2		8
39.11	even	12		507.2.k.f.488.1		8
39.17	odd	6		507.2.k.e.80.1		8
39.20	even	12		507.2.k.d.89.2		8
39.23	odd	6		39.2.k.b.32.2	yes	8
39.29	odd	6		507.2.k.d.188.1		8
39.32	even	12		39.2.k.b.11.1	✓	8
39.35	odd	6		507.2.k.f.80.2		8
39.38	odd	2		507.2.f.f.239.2		8
52.19	even	12		624.2.cn.c.401.2		8
52.23	odd	6		624.2.cn.c.305.1		8
65.19	odd	12		975.2.bo.d.401.1		8
65.23	odd	12		975.2.bp.e.149.2		8
65.32	even	12		975.2.bp.e.674.1		8
65.49	even	6		975.2.bo.d.851.2		8
65.58	even	12		975.2.bp.f.674.2		8
65.62	odd	12		975.2.bp.f.149.1		8
156.23	even	6		624.2.cn.c.305.2		8
156.71	odd	12		624.2.cn.c.401.1		8
195.23	even	12		975.2.bp.e.149.1		8
195.32	odd	12		975.2.bp.e.674.2		8
195.62	even	12		975.2.bp.f.149.2		8
195.149	even	12		975.2.bo.d.401.2		8
195.179	odd	6		975.2.bo.d.851.1		8
195.188	odd	12		975.2.bp.f.674.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.2.k.b.11.1	✓	8	39.32	even	12
39.2.k.b.11.2	yes	8	13.6	odd	12
39.2.k.b.32.1	yes	8	13.10	even	6
39.2.k.b.32.2	yes	8	39.23	odd	6
507.2.f.e.239.2		8	1.1	even	1	trivial
507.2.f.e.239.3		8	3.2	odd	2	inner
507.2.f.e.437.2		8	39.8	even	4	inner
507.2.f.e.437.3		8	13.8	odd	4	inner
507.2.f.f.239.2		8	39.38	odd	2
507.2.f.f.239.3		8	13.12	even	2
507.2.f.f.437.2		8	13.5	odd	4
507.2.f.f.437.3		8	39.5	even	4
507.2.k.d.89.1		8	13.7	odd	12
507.2.k.d.89.2		8	39.20	even	12
507.2.k.d.188.1		8	39.29	odd	6
507.2.k.d.188.2		8	13.3	even	3
507.2.k.e.80.1		8	39.17	odd	6
507.2.k.e.80.2		8	13.4	even	6
507.2.k.e.488.1		8	13.2	odd	12
507.2.k.e.488.2		8	39.2	even	12
507.2.k.f.80.1		8	13.9	even	3
507.2.k.f.80.2		8	39.35	odd	6
507.2.k.f.488.1		8	39.11	even	12
507.2.k.f.488.2		8	13.11	odd	12
624.2.cn.c.305.1		8	52.23	odd	6
624.2.cn.c.305.2		8	156.23	even	6
624.2.cn.c.401.1		8	156.71	odd	12
624.2.cn.c.401.2		8	52.19	even	12
975.2.bo.d.401.1		8	65.19	odd	12
975.2.bo.d.401.2		8	195.149	even	12
975.2.bo.d.851.1		8	195.179	odd	6
975.2.bo.d.851.2		8	65.49	even	6
975.2.bp.e.149.1		8	195.23	even	12
975.2.bp.e.149.2		8	65.23	odd	12
975.2.bp.e.674.1		8	65.32	even	12
975.2.bp.e.674.2		8	195.32	odd	12
975.2.bp.f.149.1		8	65.62	odd	12
975.2.bp.f.149.2		8	195.62	even	12
975.2.bp.f.674.1		8	195.188	odd	12
975.2.bp.f.674.2		8	65.58	even	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} +(-2.58863 - 0.320682i) 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} +(-2.58863 - 0.320682i) q^{15} +4.46410 q^{16} -5.03908 q^{17} +(-3.87762 + 2.31853i) q^{18} +(-2.73205 + 2.73205i) q^{19} +(0.285334 - 0.285334i) q^{20} +(-2.43091 - 0.301143i) q^{21} -6.19615 q^{22} +(-0.555437 + 4.48364i) 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} +(0.876119 - 7.07227i) 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} +(-3.87762 + 2.31853i) 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} +(-2.82797 + 7.29638i) q^{54} -6.19615 q^{55} +3.68886 q^{56} +(-0.822738 + 6.64136i) q^{57} +(7.63397 - 7.63397i) q^{58} +(-2.12976 + 2.12976i) q^{59} +(0.0859264 - 0.693622i) q^{60} -7.00000 q^{61} -5.24796 q^{62} +(-3.64136 + 2.17726i) 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} +(4.01581 + 6.71624i) 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} +(0.0806910 - 0.651360i) 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} +(0.742047 - 5.99000i) q^{93} -9.07180 q^{94} +5.81863 q^{95} +(-2.58863 - 0.320682i) q^{96} +(1.19615 - 1.19615i) q^{97} +(-5.32441 + 5.32441i) q^{98} +(-6.33434 - 10.5939i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3} - 16 q^{6} - 8 q^{7} - 8 q^{9} - 16 q^{15} + 8 q^{16} - 4 q^{18} - 8 q^{19} - 4 q^{21} - 8 q^{22} - 12 q^{24} + 4 q^{27} + 16 q^{28} - 8 q^{31} - 4 q^{33} + 36 q^{34} + 4 q^{37} - 24 q^{40}+ \cdots - 40 q^{99}+O(q^{100}) \) 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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