LMFDB - Embedded newform 1176.2.c.f.589.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1176,2,Mod(589,1176)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1176, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))

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

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

chi := DirichletCharacter("1176.589");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1176 = 2^{3} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1176.c (of order $2$, degree $1$, 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:	$9.39040727770$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + x^{14} - 2 x^{13} - 2 x^{12} - 4 x^{11} - 2 x^{10} + 16 x^{9} + 8 x^{8} + 32 x^{7} - 8 x^{6} + \cdots + 256 $ x^16 + x^14 - 2x^13 - 2x^12 - 4x^11 - 2x^10 + 16x^9 + 8x^8 + 32x^7 - 8x^6 - 32x^5 - 32x^4 - 64x^3 + 64x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			589.16
Root			$0.284419 + 1.38532i$ of defining polynomial
Character	$\chi$	$=$	1176.589
Dual form			1176.2.c.f.589.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.38532 + 0.284419i) q^{2} -1.00000i q^{3} +(1.83821 + 0.788022i) q^{4} +2.29465i q^{5} +(0.284419 - 1.38532i) q^{6} +(2.32238 + 1.61448i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(1.38532 + 0.284419i) q^{2} -1.00000i q^{3} +(1.83821 + 0.788022i) q^{4} +2.29465i q^{5} +(0.284419 - 1.38532i) q^{6} +(2.32238 + 1.61448i) q^{8} -1.00000 q^{9} +(-0.652642 + 3.17882i) q^{10} +3.88667i q^{11} +(0.788022 - 1.83821i) q^{12} -3.33413i q^{13} +2.29465 q^{15} +(2.75804 + 2.89710i) q^{16} -0.287121 q^{17} +(-1.38532 - 0.284419i) q^{18} +2.78525i q^{19} +(-1.80823 + 4.21805i) q^{20} +(-1.10544 + 5.38428i) q^{22} +6.53425 q^{23} +(1.61448 - 2.32238i) q^{24} -0.265415 q^{25} +(0.948290 - 4.61883i) q^{26} +1.00000i q^{27} +5.53374i q^{29} +(3.17882 + 0.652642i) q^{30} -7.44308 q^{31} +(2.99678 + 4.79785i) q^{32} +3.88667 q^{33} +(-0.397754 - 0.0816627i) q^{34} +(-1.83821 - 0.788022i) q^{36} +5.95539i q^{37} +(-0.792179 + 3.85846i) q^{38} -3.33413 q^{39} +(-3.70467 + 5.32905i) q^{40} +3.51617 q^{41} -11.2465i q^{43} +(-3.06278 + 7.14453i) q^{44} -2.29465i q^{45} +(9.05201 + 1.85847i) q^{46} -0.0870075 q^{47} +(2.89710 - 2.75804i) q^{48} +(-0.367684 - 0.0754890i) q^{50} +0.287121i q^{51} +(2.62737 - 6.12883i) q^{52} -7.05820i q^{53} +(-0.284419 + 1.38532i) q^{54} -8.91855 q^{55} +2.78525 q^{57} +(-1.57390 + 7.66599i) q^{58} +4.35217i q^{59} +(4.21805 + 1.80823i) q^{60} +7.16714i q^{61} +(-10.3110 - 2.11695i) q^{62} +(2.78689 + 7.49888i) q^{64} +7.65066 q^{65} +(5.38428 + 1.10544i) q^{66} -13.0255i q^{67} +(-0.527789 - 0.226257i) q^{68} -6.53425i q^{69} -6.18835 q^{71} +(-2.32238 - 1.61448i) q^{72} +13.8796 q^{73} +(-1.69383 + 8.25010i) q^{74} +0.265415i q^{75} +(-2.19484 + 5.11989i) q^{76} +(-4.61883 - 0.948290i) q^{78} -8.99853 q^{79} +(-6.64783 + 6.32874i) q^{80} +1.00000 q^{81} +(4.87102 + 1.00007i) q^{82} -17.6313i q^{83} -0.658842i q^{85} +(3.19873 - 15.5800i) q^{86} +5.53374 q^{87} +(-6.27497 + 9.02633i) q^{88} +17.1839 q^{89} +(0.652642 - 3.17882i) q^{90} +(12.0113 + 5.14913i) q^{92} +7.44308i q^{93} +(-0.120533 - 0.0247466i) q^{94} -6.39118 q^{95} +(4.79785 - 2.99678i) q^{96} -6.46528 q^{97} -3.88667i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{2} + 2 q^{4} - 8 q^{8} - 16 q^{9}+O(q^{10}) $ 16 * q - 2 * q^2 + 2 * q^4 - 8 * q^8 - 16 * q^9	$ 16 q - 2 q^{2} + 2 q^{4} - 8 q^{8} - 16 q^{9} + 6 q^{10} + 10 q^{16} + 2 q^{18} + 20 q^{20} - 6 q^{22} + 8 q^{23} - 6 q^{24} - 16 q^{25} + 6 q^{26} + 8 q^{30} - 24 q^{31} + 8 q^{32} + 12 q^{34} - 2 q^{36} - 26 q^{38} - 6 q^{40} - 20 q^{44} - 16 q^{46} - 24 q^{47} + 8 q^{48} + 26 q^{50} + 44 q^{52} + 32 q^{55} - 8 q^{57} - 34 q^{58} + 22 q^{60} - 50 q^{62} - 10 q^{64} + 12 q^{66} + 16 q^{68} - 40 q^{71} + 8 q^{72} + 8 q^{73} - 10 q^{74} + 16 q^{76} + 6 q^{78} - 8 q^{79} - 56 q^{80} + 16 q^{81} + 22 q^{86} + 24 q^{87} - 50 q^{88} - 6 q^{90} + 32 q^{92} - 48 q^{94} - 24 q^{95} + 10 q^{96} + 24 q^{97}+O(q^{100}) $ 16 * q - 2 * q^2 + 2 * q^4 - 8 * q^8 - 16 * q^9 + 6 * q^10 + 10 * q^16 + 2 * q^18 + 20 * q^20 - 6 * q^22 + 8 * q^23 - 6 * q^24 - 16 * q^25 + 6 * q^26 + 8 * q^30 - 24 * q^31 + 8 * q^32 + 12 * q^34 - 2 * q^36 - 26 * q^38 - 6 * q^40 - 20 * q^44 - 16 * q^46 - 24 * q^47 + 8 * q^48 + 26 * q^50 + 44 * q^52 + 32 * q^55 - 8 * q^57 - 34 * q^58 + 22 * q^60 - 50 * q^62 - 10 * q^64 + 12 * q^66 + 16 * q^68 - 40 * q^71 + 8 * q^72 + 8 * q^73 - 10 * q^74 + 16 * q^76 + 6 * q^78 - 8 * q^79 - 56 * q^80 + 16 * q^81 + 22 * q^86 + 24 * q^87 - 50 * q^88 - 6 * q^90 + 32 * q^92 - 48 * q^94 - 24 * q^95 + 10 * q^96 + 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1176\mathbb{Z}\right)^\times$.

$n$	$295$	$589$	$785$	$1081$
$\chi(n)$	$1$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$	1.38532	+	0.284419i	0.979568	+	0.201115i
$2$	1.38532	+	0.284419i	0.979568	+	0.201115i
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	1.83821	+	0.788022i	0.919106	+	0.394011i
$5$			2.29465i			1.02620i	0.858329	+	0.513099i	$0.171503\pi$
$5$			2.29465i			1.02620i	−0.858329	+	0.513099i	$0.828497\pi$
$6$	0.284419	−	1.38532i	0.116114	−	0.565554i
$7$		0			0
$7$		0			0
$8$	2.32238	+	1.61448i	0.821085	+	0.570806i
$9$	−1.00000			−0.333333
$10$	−0.652642	+	3.17882i	−0.206384	+	1.00523i
$11$			3.88667i			1.17188i	0.810356	+	0.585938i	$0.199274\pi$
$11$			3.88667i			1.17188i	−0.810356	+	0.585938i	$0.800726\pi$
$12$	0.788022	−	1.83821i	0.227482	−	0.530646i
$13$		−	3.33413i		−	0.924721i	−0.886692	−	0.462361i	$-0.847003\pi$
$13$		−	3.33413i		−	0.924721i	0.886692	−	0.462361i	$-0.152997\pi$
$14$		0			0
$15$	2.29465			0.592476
$16$	2.75804	+	2.89710i	0.689511	+	0.724275i
$17$	−0.287121			−0.0696370			−0.0348185	−	0.999394i	$-0.511085\pi$
$17$	−0.287121			−0.0696370			−0.0348185	+	0.999394i	$0.511085\pi$
$18$	−1.38532	−	0.284419i	−0.326523	−	0.0670382i
$19$			2.78525i			0.638981i	0.947589	+	0.319491i	$0.103512\pi$
$19$			2.78525i			0.638981i	−0.947589	+	0.319491i	$0.896488\pi$
$20$	−1.80823	+	4.21805i	−0.404333	+	0.943185i
$21$		0			0
$22$	−1.10544	+	5.38428i	−0.235681	+	1.14793i
$23$	6.53425			1.36249			0.681243	−	0.732058i	$-0.261440\pi$
$23$	6.53425			1.36249			0.681243	+	0.732058i	$0.261440\pi$
$24$	1.61448	−	2.32238i	0.329555	−	0.474054i
$25$	−0.265415			−0.0530829
$26$	0.948290	−	4.61883i	0.185975	−	0.905827i
$27$			1.00000i			0.192450i
$28$		0			0
$29$			5.53374i			1.02759i	0.857913	+	0.513795i	$0.171761\pi$
$29$			5.53374i			1.02759i	−0.857913	+	0.513795i	$0.828239\pi$
$30$	3.17882	+	0.652642i	0.580370	+	0.119156i
$31$	−7.44308			−1.33682			−0.668408	−	0.743795i	$-0.733024\pi$
$31$	−7.44308			−1.33682			−0.668408	+	0.743795i	$0.733024\pi$
$32$	2.99678	+	4.79785i	0.529760	+	0.848147i
$33$	3.88667			0.676583
$34$	−0.397754	−	0.0816627i	−0.0682142	−	0.0140050i
$35$		0			0
$36$	−1.83821	−	0.788022i	−0.306369	−	0.131337i
$37$			5.95539i			0.979060i	0.871987	+	0.489530i	$0.162832\pi$
$37$			5.95539i			0.979060i	−0.871987	+	0.489530i	$0.837168\pi$
$38$	−0.792179	+	3.85846i	−0.128508	+	0.625925i
$39$	−3.33413			−0.533888
$40$	−3.70467	+	5.32905i	−0.585760	+	0.842596i
$41$	3.51617			0.549134			0.274567	−	0.961568i	$-0.411466\pi$
$41$	3.51617			0.549134			0.274567	+	0.961568i	$0.411466\pi$
$42$		0			0
$43$		−	11.2465i		−	1.71508i	−0.514416	−	0.857541i	$-0.671991\pi$
$43$		−	11.2465i		−	1.71508i	0.514416	−	0.857541i	$-0.328009\pi$
$44$	−3.06278	+	7.14453i	−0.461732	+	1.07708i
$45$		−	2.29465i		−	0.342066i
$46$	9.05201	+	1.85847i	1.33465	+	0.274016i
$47$	−0.0870075			−0.0126913			−0.00634567	−	0.999980i	$-0.502020\pi$
$47$	−0.0870075			−0.0126913			−0.00634567	+	0.999980i	$0.502020\pi$
$48$	2.89710	−	2.75804i	0.418161	−	0.398089i
$49$		0			0
$50$	−0.367684	−	0.0754890i	−0.0519983	−	0.0106758i
$51$			0.287121i			0.0402050i
$52$	2.62737	−	6.12883i	0.364350	−	0.849916i
$53$		−	7.05820i		−	0.969518i	−0.874648	−	0.484759i	$-0.838907\pi$
$53$		−	7.05820i		−	0.969518i	0.874648	−	0.484759i	$-0.161093\pi$
$54$	−0.284419	+	1.38532i	−0.0387045	+	0.188518i
$55$	−8.91855			−1.20258
$56$		0			0
$57$	2.78525			0.368916
$58$	−1.57390	+	7.66599i	−0.206663	+	1.00659i
$59$			4.35217i			0.566605i	0.959031	+	0.283302i	$0.0914300\pi$
$59$			4.35217i			0.566605i	−0.959031	+	0.283302i	$0.908570\pi$
$60$	4.21805	+	1.80823i	0.544548	+	0.233442i
$61$			7.16714i			0.917659i	0.888524	+	0.458829i	$0.151731\pi$
$61$			7.16714i			0.917659i	−0.888524	+	0.458829i	$0.848269\pi$
$62$	−10.3110	−	2.11695i	−1.30950	−	0.268853i
$63$		0			0
$64$	2.78689	+	7.49888i	0.348361	+	0.937360i
$65$	7.65066			0.948947
$66$	5.38428	+	1.10544i	0.662759	+	0.136071i
$67$		−	13.0255i		−	1.59132i	−0.605743	−	0.795661i	$-0.707124\pi$
$67$		−	13.0255i		−	1.59132i	0.605743	−	0.795661i	$-0.292876\pi$
$68$	−0.527789	−	0.226257i	−0.0640038	−	0.0274378i
$69$		−	6.53425i		−	0.786631i
$70$		0			0
$71$	−6.18835			−0.734421			−0.367211	−	0.930138i	$-0.619687\pi$
$71$	−6.18835			−0.734421			−0.367211	+	0.930138i	$0.619687\pi$
$72$	−2.32238	−	1.61448i	−0.273695	−	0.190269i
$73$	13.8796			1.62448			0.812240	−	0.583323i	$-0.198248\pi$
$73$	13.8796			1.62448			0.812240	+	0.583323i	$0.198248\pi$
$74$	−1.69383	+	8.25010i	−0.196903	+	0.959055i
$75$			0.265415i			0.0306474i
$76$	−2.19484	+	5.11989i	−0.251766	+	0.587291i
$77$		0			0
$78$	−4.61883	−	0.948290i	−0.522979	−	0.107373i
$79$	−8.99853			−1.01241			−0.506207	−	0.862412i	$-0.668953\pi$
$79$	−8.99853			−1.01241			−0.506207	+	0.862412i	$0.668953\pi$
$80$	−6.64783	+	6.32874i	−0.743250	+	0.707575i
$81$	1.00000			0.111111
$82$	4.87102	+	1.00007i	0.537914	+	0.110439i
$83$		−	17.6313i		−	1.93529i	−0.252312	−	0.967646i	$-0.581191\pi$
$83$		−	17.6313i		−	1.93529i	0.252312	−	0.967646i	$-0.418809\pi$
$84$		0			0
$85$		−	0.658842i		−	0.0714614i
$86$	3.19873	−	15.5800i	0.344928	−	1.68004i
$87$	5.53374			0.593280
$88$	−6.27497	+	9.02633i	−0.668914	+	0.962210i
$89$	17.1839			1.82149			0.910744	−	0.412972i	$-0.135509\pi$
$89$	17.1839			1.82149			0.910744	+	0.412972i	$0.135509\pi$
$90$	0.652642	−	3.17882i	0.0687945	−	0.335077i
$91$		0			0
$92$	12.0113	+	5.14913i	1.25227	+	0.536834i
$93$			7.44308i			0.771811i
$94$	−0.120533	−	0.0247466i	−0.0124320	−	0.00255242i
$95$	−6.39118			−0.655721
$96$	4.79785	−	2.99678i	0.489678	−	0.305857i
$97$	−6.46528			−0.656450			−0.328225	−	0.944600i	$-0.606450\pi$
$97$	−6.46528			−0.656450			−0.328225	+	0.944600i	$0.606450\pi$
$98$		0			0
$99$		−	3.88667i		−	0.390625i
$100$	−0.487888	−	0.209152i	−0.0487888	−	0.0209152i
$101$		−	11.8461i		−	1.17873i	−0.807867	−	0.589365i	$-0.799378\pi$
$101$		−	11.8461i		−	1.17873i	0.807867	−	0.589365i	$-0.200622\pi$
$102$	−0.0816627	+	0.397754i	−0.00808581	+	0.0393835i
$103$	−1.62190			−0.159810			−0.0799051	−	0.996802i	$-0.525462\pi$
$103$	−1.62190			−0.159810			−0.0799051	+	0.996802i	$0.525462\pi$
$104$	5.38290	−	7.74311i	0.527836	−	0.759275i
$105$		0			0
$106$	2.00749	−	9.77785i	0.194984	−	0.949708i
$107$		−	5.02926i		−	0.486197i	−0.970002	−	0.243098i	$-0.921836\pi$
$107$		−	5.02926i		−	0.486197i	0.970002	−	0.243098i	$-0.0781638\pi$
$108$	−0.788022	+	1.83821i	−0.0758274	+	0.176882i
$109$		−	0.204420i		−	0.0195799i	−0.999952	−	0.00978994i	$-0.996884\pi$
$109$		−	0.204420i		−	0.0195799i	0.999952	−	0.00978994i	$-0.00311628\pi$
$110$	−12.3550	−	2.53661i	−1.17801	−	0.241856i
$111$	5.95539			0.565260
$112$		0			0
$113$	−14.9203			−1.40358			−0.701792	−	0.712382i	$-0.747616\pi$
$113$	−14.9203			−1.40358			−0.701792	+	0.712382i	$0.747616\pi$
$114$	3.85846	+	0.792179i	0.361378	+	0.0741944i
$115$			14.9938i			1.39818i
$116$	−4.36071	+	10.1722i	−0.404882	+	0.944464i
$117$			3.33413i			0.308240i
$118$	−1.23784	+	6.02915i	−0.113953	+	0.555028i
$119$		0			0
$120$	5.32905	+	3.70467i	0.486473	+	0.338189i
$121$	−4.10622			−0.373293
$122$	−2.03847	+	9.92877i	−0.184555	+	0.898909i
$123$		−	3.51617i		−	0.317043i
$124$	−13.6819	−	5.86531i	−1.22868	−	0.526720i
$125$			10.8642i			0.971725i
$126$		0			0
$127$	−6.29267			−0.558384			−0.279192	−	0.960235i	$-0.590067\pi$
$127$	−6.29267			−0.558384			−0.279192	+	0.960235i	$0.590067\pi$
$128$	1.72790	+	11.1810i	0.152726	+	0.988269i
$129$	−11.2465			−0.990203
$130$	10.5986	+	2.17599i	0.929558	+	0.190847i
$131$			1.24096i			0.108423i	0.998529	+	0.0542116i	$0.0172646\pi$
$131$			1.24096i			0.108423i	−0.998529	+	0.0542116i	$0.982735\pi$
$132$	7.14453	+	3.06278i	0.621851	+	0.266581i
$133$		0			0
$134$	3.70471	−	18.0445i	0.320038	−	1.55881i
$135$	−2.29465			−0.197492
$136$	−0.666804	−	0.463552i	−0.0571779	−	0.0397492i
$137$	1.59019			0.135859			0.0679296	−	0.997690i	$-0.478361\pi$
$137$	1.59019			0.135859			0.0679296	+	0.997690i	$0.478361\pi$
$138$	1.85847	−	9.05201i	0.158203	−	0.770559i
$139$		−	1.02981i		−	0.0873470i	−0.999046	−	0.0436735i	$-0.986094\pi$
$139$		−	1.02981i		−	0.0873470i	0.999046	−	0.0436735i	$-0.0139061\pi$
$140$		0			0
$141$			0.0870075i			0.00732735i
$142$	−8.57283	−	1.76008i	−0.719416	−	0.147703i
$143$	12.9587			1.08366
$144$	−2.75804	−	2.89710i	−0.229837	−	0.241425i
$145$	−12.6980			−1.05451
$146$	19.2276	+	3.94761i	1.59129	+	0.326707i
$147$		0			0
$148$	−4.69297	+	10.9473i	−0.385760	+	0.899859i
$149$		−	9.59178i		−	0.785789i	−0.919584	−	0.392895i	$-0.871474\pi$
$149$		−	9.59178i		−	0.785789i	0.919584	−	0.392895i	$-0.128526\pi$
$150$	−0.0754890	+	0.367684i	−0.00616365	+	0.0300212i
$151$	6.99222			0.569019			0.284510	−	0.958673i	$-0.408169\pi$
$151$	6.99222			0.569019			0.284510	+	0.958673i	$0.408169\pi$
$152$	−4.49675	+	6.46842i	−0.364734	+	0.524658i
$153$	0.287121			0.0232123
$154$		0			0
$155$		−	17.0792i		−	1.37184i
$156$	−6.12883	−	2.62737i	−0.490700	−	0.210358i
$157$		−	17.3579i		−	1.38531i	−0.721269	−	0.692655i	$-0.756441\pi$
$157$		−	17.3579i		−	1.38531i	0.721269	−	0.692655i	$-0.243559\pi$
$158$	−12.4658	−	2.55935i	−0.991728	−	0.203611i
$159$	−7.05820			−0.559751
$160$	−11.0094	+	6.87655i	−0.870367	+	0.543639i
$161$		0			0
$162$	1.38532	+	0.284419i	0.108841	+	0.0223461i
$163$		−	15.7220i		−	1.23144i	−0.787965	−	0.615720i	$-0.788865\pi$
$163$		−	15.7220i		−	1.23144i	0.787965	−	0.615720i	$-0.211135\pi$
$164$	6.46347	+	2.77082i	0.504712	+	0.216365i
$165$			8.91855i			0.694308i
$166$	5.01469	−	24.4250i	0.389216	−	1.89575i
$167$	0.102064			0.00789795			0.00394897	−	0.999992i	$-0.498743\pi$
$167$	0.102064			0.00789795			0.00394897	+	0.999992i	$0.498743\pi$
$168$		0			0
$169$	1.88358			0.144891
$170$	0.187387	−	0.912705i	0.0143719	−	0.0700013i
$171$		−	2.78525i		−	0.212994i
$172$	8.86252	−	20.6735i	0.675761	−	1.57634i
$173$			2.28777i			0.173936i	0.996211	+	0.0869678i	$0.0277177\pi$
$173$			2.28777i			0.173936i	−0.996211	+	0.0869678i	$0.972282\pi$
$174$	7.66599	+	1.57390i	0.581158	+	0.119317i
$175$		0			0
$176$	−11.2601	+	10.7196i	−0.848761	+	0.808021i
$177$	4.35217			0.327130
$178$	23.8051	+	4.88742i	1.78427	+	0.366328i
$179$		−	18.6231i		−	1.39196i	−0.718064	−	0.695978i	$-0.754971\pi$
$179$		−	18.6231i		−	1.39196i	0.718064	−	0.695978i	$-0.245029\pi$
$180$	1.80823	−	4.21805i	0.134778	−	0.314395i
$181$			13.6786i			1.01672i	0.861144	+	0.508361i	$0.169748\pi$
$181$			13.6786i			1.01672i	−0.861144	+	0.508361i	$0.830252\pi$
$182$		0			0
$183$	7.16714			0.529810
$184$	15.1750	+	10.5494i	1.11872	+	0.777715i
$185$	−13.6655			−1.00471
$186$	−2.11695	+	10.3110i	−0.155223	+	0.756041i
$187$		−	1.11594i		−	0.0816060i
$188$	−0.159938	−	0.0685638i	−0.0116647	−	0.00500053i
$189$		0			0
$190$	−8.85382	−	1.81777i	−0.642323	−	0.131875i
$191$	−12.6346			−0.914207			−0.457103	−	0.889414i	$-0.651113\pi$
$191$	−12.6346			−0.914207			−0.457103	+	0.889414i	$0.651113\pi$
$192$	7.49888	−	2.78689i	0.541185	−	0.201126i
$193$	2.60582			0.187571			0.0937856	−	0.995592i	$-0.470103\pi$
$193$	2.60582			0.187571			0.0937856	+	0.995592i	$0.470103\pi$
$194$	−8.95647	−	1.83885i	−0.643037	−	0.132022i
$195$		−	7.65066i		−	0.547875i
$196$		0			0
$197$			0.794777i			0.0566255i	0.999599	+	0.0283127i	$0.00901343\pi$
$197$			0.794777i			0.0566255i	−0.999599	+	0.0283127i	$0.990987\pi$
$198$	1.10544	−	5.38428i	0.0785605	−	0.382644i
$199$	−10.7343			−0.760933			−0.380466	−	0.924795i	$-0.624237\pi$
$199$	−10.7343			−0.760933			−0.380466	+	0.924795i	$0.624237\pi$
$200$	−0.616393	−	0.428507i	−0.0435856	−	0.0303001i
$201$	−13.0255			−0.918750
$202$	3.36925	−	16.4106i	0.237060	−	1.15465i
$203$		0			0
$204$	−0.226257	+	0.527789i	−0.0158412	+	0.0369526i
$205$			8.06838i			0.563520i
$206$	−2.24684	−	0.461298i	−0.156545	−	0.0321402i
$207$	−6.53425			−0.454162
$208$	9.65931	−	9.19567i	0.669753	−	0.637605i
$209$	−10.8254			−0.748807
$210$		0			0
$211$			0.556345i			0.0383004i	0.999817	+	0.0191502i	$0.00609607\pi$
$211$			0.556345i			0.0383004i	−0.999817	+	0.0191502i	$0.993904\pi$
$212$	5.56201	−	12.9745i	0.382001	−	0.891090i
$213$			6.18835i			0.424018i
$214$	1.43042	−	6.96712i	0.0977813	−	0.476263i
$215$	25.8069			1.76001
$216$	−1.61448	+	2.32238i	−0.109852	+	0.158018i
$217$		0			0
$218$	0.0581409	−	0.283187i	0.00393780	−	0.0191798i
$219$		−	13.8796i		−	0.937894i
$220$	−16.3942	−	7.02801i	−1.10530	−	0.473828i
$221$			0.957298i			0.0643948i
$222$	8.25010	+	1.69383i	0.553711	+	0.113682i
$223$	−11.1076			−0.743820			−0.371910	−	0.928269i	$-0.621297\pi$
$223$	−11.1076			−0.743820			−0.371910	+	0.928269i	$0.621297\pi$
$224$		0			0
$225$	0.265415			0.0176943
$226$	−20.6694	−	4.24362i	−1.37491	−	0.282281i
$227$			8.76788i			0.581945i	0.956731	+	0.290972i	$0.0939788\pi$
$227$			8.76788i			0.581945i	−0.956731	+	0.290972i	$0.906021\pi$
$228$	5.11989	+	2.19484i	0.339073	+	0.145357i
$229$			20.6962i			1.36764i	0.729648	+	0.683822i	$0.239684\pi$
$229$			20.6962i			1.36764i	−0.729648	+	0.683822i	$0.760316\pi$
$230$	−4.26453	+	20.7712i	−0.281195	+	1.36961i
$231$		0			0
$232$	−8.93414	+	12.8514i	−0.586555	+	0.843739i
$233$	−5.72853			−0.375288			−0.187644	−	0.982237i	$-0.560085\pi$
$233$	−5.72853			−0.375288			−0.187644	+	0.982237i	$0.560085\pi$
$234$	−0.948290	+	4.61883i	−0.0619917	+	0.301942i
$235$		−	0.199652i		−	0.0130238i
$236$	−3.42961	+	8.00022i	−0.223248	+	0.520770i
$237$			8.99853i			0.584517i
$238$		0			0
$239$	2.27651			0.147255			0.0736276	−	0.997286i	$-0.476542\pi$
$239$	2.27651			0.147255			0.0736276	+	0.997286i	$0.476542\pi$
$240$	6.32874	+	6.64783i	0.408519	+	0.429116i
$241$	−23.5850			−1.51925			−0.759623	−	0.650364i	$-0.774616\pi$
$241$	−23.5850			−1.51925			−0.759623	+	0.650364i	$0.774616\pi$
$242$	−5.68842	−	1.16789i	−0.365666	−	0.0750747i
$243$		−	1.00000i		−	0.0641500i
$244$	−5.64786	+	13.1747i	−0.361567	+	0.843425i
$245$		0			0
$246$	1.00007	−	4.87102i	0.0637619	−	0.310565i
$247$	9.28640			0.590879
$248$	−17.2856	−	12.0167i	−1.09764	−	0.763062i
$249$	−17.6313			−1.11734
$250$	−3.08999	+	15.0504i	−0.195428	+	0.951870i
$251$			12.4322i			0.784716i	0.919813	+	0.392358i	$0.128341\pi$
$251$			12.4322i			0.784716i	−0.919813	+	0.392358i	$0.871659\pi$
$252$		0			0
$253$			25.3965i			1.59666i
$254$	−8.71735	−	1.78976i	−0.546975	−	0.112299i
$255$	−0.658842			−0.0412583
$256$	−0.786392	+	15.9807i	−0.0491495	+	0.998791i
$257$	−0.282984			−0.0176521			−0.00882604	−	0.999961i	$-0.502809\pi$
$257$	−0.282984			−0.0176521			−0.00882604	+	0.999961i	$0.502809\pi$
$258$	−15.5800	−	3.19873i	−0.969971	−	0.199144i
$259$		0			0
$260$	14.0635	+	6.02888i	0.872183	+	0.373895i
$261$		−	5.53374i		−	0.342530i
$262$	−0.352953	+	1.71912i	−0.0218055	+	0.106208i
$263$	14.3192			0.882962			0.441481	−	0.897271i	$-0.354453\pi$
$263$	14.3192			0.882962			0.441481	+	0.897271i	$0.354453\pi$
$264$	9.02633	+	6.27497i	0.555532	+	0.386197i
$265$	16.1961			0.994918
$266$		0			0
$267$		−	17.1839i		−	1.05164i
$268$	10.2644	−	23.9437i	0.626998	−	1.46259i
$269$		−	16.8141i		−	1.02517i	−0.858636	−	0.512586i	$-0.828688\pi$
$269$		−	16.8141i		−	1.02517i	0.858636	−	0.512586i	$-0.171312\pi$
$270$	−3.17882	−	0.652642i	−0.193457	−	0.0397185i
$271$	−26.8456			−1.63076			−0.815378	−	0.578929i	$-0.803471\pi$
$271$	−26.8456			−1.63076			−0.815378	+	0.578929i	$0.803471\pi$
$272$	−0.791892	−	0.831818i	−0.0480155	−	0.0504364i
$273$		0			0
$274$	2.20292	+	0.452281i	0.133083	+	0.0273233i
$275$		−	1.03158i		−	0.0622066i
$276$	5.14913	−	12.0113i	0.309941	−	0.722997i
$277$		−	22.5030i		−	1.35207i	−0.736868	−	0.676036i	$-0.763696\pi$
$277$		−	22.5030i		−	1.35207i	0.736868	−	0.676036i	$-0.236304\pi$
$278$	0.292897	−	1.42661i	0.0175668	−	0.0855623i
$279$	7.44308			0.445605
$280$		0			0
$281$	12.8375			0.765824			0.382912	−	0.923785i	$-0.374921\pi$
$281$	12.8375			0.765824			0.382912	+	0.923785i	$0.374921\pi$
$282$	−0.0247466	+	0.120533i	−0.00147364	+	0.00717764i
$283$		−	7.29790i		−	0.433815i	−0.976192	−	0.216908i	$-0.930403\pi$
$283$		−	7.29790i		−	0.433815i	0.976192	−	0.216908i	$-0.0695971\pi$
$284$	−11.3755	−	4.87655i	−0.675011	−	0.289370i
$285$			6.39118i			0.378581i
$286$	17.9519	+	3.68569i	1.06152	+	0.217940i
$287$		0			0
$288$	−2.99678	−	4.79785i	−0.176587	−	0.282716i
$289$	−16.9176			−0.995151
$290$	−17.5908	−	3.61155i	−1.03297	−	0.212078i
$291$			6.46528i			0.379001i
$292$	25.5136	+	10.9374i	1.49307	+	0.640063i
$293$		−	9.95674i		−	0.581679i	−0.956772	−	0.290840i	$-0.906065\pi$
$293$		−	9.95674i		−	0.581679i	0.956772	−	0.290840i	$-0.0939346\pi$
$294$		0			0
$295$	−9.98671			−0.581449
$296$	−9.61487	+	13.8307i	−0.558853	+	0.803891i
$297$	−3.88667			−0.225528
$298$	2.72808	−	13.2877i	0.158034	−	0.769734i
$299$		−	21.7860i		−	1.25992i
$300$	−0.209152	+	0.487888i	−0.0120754	+	0.0281682i
$301$		0			0
$302$	9.68645	+	1.98872i	0.557393	+	0.114438i
$303$	−11.8461			−0.680540
$304$	−8.06916	+	7.68185i	−0.462798	+	0.440584i
$305$	−16.4461			−0.941700
$306$	0.397754	+	0.0816627i	0.0227381	+	0.00466834i
$307$			14.9479i			0.853122i	0.904459	+	0.426561i	$0.140275\pi$
$307$			14.9479i			0.853122i	−0.904459	+	0.426561i	$0.859725\pi$
$308$		0			0
$309$			1.62190i			0.0922664i
$310$	4.85766	−	23.6602i	0.275897	−	1.34381i
$311$	31.2591			1.77254			0.886270	−	0.463169i	$-0.153288\pi$
$311$	31.2591			1.77254			0.886270	+	0.463169i	$0.153288\pi$
$312$	−7.74311	−	5.38290i	−0.438367	−	0.304746i
$313$	3.06468			0.173226			0.0866130	−	0.996242i	$-0.472396\pi$
$313$	3.06468			0.173226			0.0866130	+	0.996242i	$0.472396\pi$
$314$	4.93692	−	24.0462i	0.278606	−	1.35701i
$315$		0			0
$316$	−16.5412	−	7.09104i	−0.930515	−	0.398902i
$317$			16.2981i			0.915391i	0.889109	+	0.457695i	$0.151325\pi$
$317$			16.2981i			0.915391i	−0.889109	+	0.457695i	$0.848675\pi$
$318$	−9.77785	−	2.00749i	−0.548314	−	0.112574i
$319$	−21.5078			−1.20421
$320$	−17.2073	+	6.39493i	−0.961918	+	0.357488i
$321$	−5.02926			−0.280706
$322$		0			0
$323$		−	0.799705i		−	0.0444968i
$324$	1.83821	+	0.788022i	0.102123	+	0.0437790i
$325$			0.884927i			0.0490869i
$326$	4.47163	−	21.7799i	0.247661	−	1.20628i
$327$	−0.204420			−0.0113044
$328$	8.16588	+	5.67680i	0.450885	+	0.313449i
$329$		0			0
$330$	−2.53661	+	12.3550i	−0.139636	+	0.680122i
$331$			2.76307i			0.151872i	0.997113	+	0.0759359i	$0.0241945\pi$
$331$			2.76307i			0.151872i	−0.997113	+	0.0759359i	$0.975806\pi$
$332$	13.8939	−	32.4101i	0.762526	−	1.77874i
$333$		−	5.95539i		−	0.326353i
$334$	0.141391	+	0.0290289i	0.00773657	+	0.00158839i
$335$	29.8890			1.63301
$336$		0			0
$337$	25.8259			1.40682			0.703412	−	0.710782i	$-0.251659\pi$
$337$	25.8259			1.40682			0.703412	+	0.710782i	$0.251659\pi$
$338$	2.60936	+	0.535727i	0.141930	+	0.0291397i
$339$			14.9203i			0.810359i
$340$	0.519182	−	1.21109i	0.0281566	−	0.0656806i
$341$		−	28.9288i		−	1.56658i
$342$	0.792179	−	3.85846i	0.0428362	−	0.208642i
$343$		0			0
$344$	18.1573	−	26.1187i	0.978979	−	1.40823i
$345$	14.9938			0.807240
$346$	−0.650685	+	3.16928i	−0.0349810	+	0.170382i
$347$			12.2755i			0.658984i	0.944158	+	0.329492i	$0.106877\pi$
$347$			12.2755i			0.658984i	−0.944158	+	0.329492i	$0.893123\pi$
$348$	10.1722	+	4.36071i	0.545287	+	0.233759i
$349$			0.209753i			0.0112278i	0.999984	+	0.00561390i	$0.00178697\pi$
$349$			0.209753i			0.0112278i	−0.999984	+	0.00561390i	$0.998213\pi$
$350$		0			0
$351$	3.33413			0.177963
$352$	−18.6477	+	11.6475i	−0.993923	+	0.620813i
$353$	19.5985			1.04312			0.521561	−	0.853214i	$-0.325350\pi$
$353$	19.5985			1.04312			0.521561	+	0.853214i	$0.325350\pi$
$354$	6.02915	+	1.23784i	0.320445	+	0.0657905i
$355$		−	14.2001i		−	0.753662i
$356$	31.5876	+	13.5413i	1.67414	+	0.717686i
$357$		0			0
$358$	5.29676	−	25.7989i	0.279943	−	1.36351i
$359$	−5.71112			−0.301422			−0.150711	−	0.988578i	$-0.548156\pi$
$359$	−5.71112			−0.301422			−0.150711	+	0.988578i	$0.548156\pi$
$360$	3.70467	−	5.32905i	0.195253	−	0.280865i
$361$	11.2424			0.591703
$362$	−3.89045	+	18.9492i	−0.204478	+	0.995948i
$363$			4.10622i			0.215521i
$364$		0			0
$365$			31.8487i			1.66704i
$366$	9.92877	+	2.03847i	0.518985	+	0.106553i
$367$	−28.1275			−1.46824			−0.734122	−	0.679017i	$-0.762406\pi$
$367$	−28.1275			−1.46824			−0.734122	+	0.679017i	$0.762406\pi$
$368$	18.0217	+	18.9304i	0.939448	+	0.986815i
$369$	−3.51617			−0.183045
$370$	−18.9311	−	3.88674i	−0.984181	−	0.202062i
$371$		0			0
$372$	−5.86531	+	13.6819i	−0.304102	+	0.709376i
$373$			17.2035i			0.890764i	0.895341	+	0.445382i	$0.146932\pi$
$373$			17.2035i			0.890764i	−0.895341	+	0.445382i	$0.853068\pi$
$374$	0.317396	−	1.54594i	0.0164122	−	0.0799386i
$375$	10.8642			0.561026
$376$	−0.202064	−	0.140472i	−0.0104207	−	0.00724429i
$377$	18.4502			0.950234
$378$		0			0
$379$		−	10.1872i		−	0.523281i	−0.965165	−	0.261640i	$-0.915737\pi$
$379$		−	10.1872i		−	0.523281i	0.965165	−	0.261640i	$-0.0842635\pi$
$380$	−11.7483	−	5.03639i	−0.602677	−	0.258361i
$381$			6.29267i			0.322383i
$382$	−17.5029	−	3.59352i	−0.895527	−	0.183860i
$383$	19.8433			1.01394			0.506972	−	0.861962i	$-0.330765\pi$
$383$	19.8433			1.01394			0.506972	+	0.861962i	$0.330765\pi$
$384$	11.1810	−	1.72790i	0.570577	−	0.0881766i
$385$		0			0
$386$	3.60989	+	0.741145i	0.183739	+	0.0377233i
$387$			11.2465i			0.571694i
$388$	−11.8846	−	5.09478i	−0.603347	−	0.258648i
$389$			18.5333i			0.939677i	0.882752	+	0.469838i	$0.155688\pi$
$389$			18.5333i			0.939677i	−0.882752	+	0.469838i	$0.844312\pi$
$390$	2.17599	−	10.5986i	0.110186	−	0.536681i
$391$	−1.87612			−0.0948794
$392$		0			0
$393$	1.24096			0.0625982
$394$	−0.226050	+	1.10102i	−0.0113882	+	0.0554685i
$395$		−	20.6485i		−	1.03894i
$396$	3.06278	−	7.14453i	0.153911	−	0.359026i
$397$		−	7.98137i		−	0.400573i	−0.979737	−	0.200287i	$-0.935813\pi$
$397$		−	7.98137i		−	0.400573i	0.979737	−	0.200287i	$-0.0641874\pi$
$398$	−14.8704	−	3.05303i	−0.745385	−	0.153035i
$399$		0			0
$400$	−0.732025	−	0.768933i	−0.0366013	−	0.0384467i
$401$	36.0420			1.79985			0.899925	−	0.436045i	$-0.143621\pi$
$401$	36.0420			1.79985			0.899925	+	0.436045i	$0.143621\pi$
$402$	−18.0445	−	3.70471i	−0.899977	−	0.184774i
$403$			24.8162i			1.23618i
$404$	9.33498	−	21.7756i	0.464432	−	1.08338i
$405$			2.29465i			0.114022i
$406$		0			0
$407$	−23.1466			−1.14734
$408$	−0.463552	+	0.666804i	−0.0229492	+	0.0330117i
$409$	29.5666			1.46197			0.730987	−	0.682391i	$-0.239060\pi$
$409$	29.5666			1.46197			0.730987	+	0.682391i	$0.239060\pi$
$410$	−2.29480	+	11.1773i	−0.113332	+	0.552006i
$411$		−	1.59019i		−	0.0784384i
$412$	−2.98139	−	1.27809i	−0.146882	−	0.0629669i
$413$		0			0
$414$	−9.05201	−	1.85847i	−0.444882	−	0.0913386i
$415$	40.4578			1.98599
$416$	15.9966	−	9.99164i	0.784300	−	0.489880i
$417$	−1.02981			−0.0504298
$418$	−14.9966	−	3.07894i	−0.733507	−	0.150596i
$419$		−	8.73304i		−	0.426637i	−0.976983	−	0.213318i	$-0.931573\pi$
$419$		−	8.73304i		−	0.426637i	0.976983	−	0.213318i	$-0.0684271\pi$
$420$		0			0
$421$		−	1.77349i		−	0.0864344i	−0.999066	−	0.0432172i	$-0.986239\pi$
$421$		−	1.77349i		−	0.0864344i	0.999066	−	0.0432172i	$-0.0137607\pi$
$422$	−0.158235	+	0.770715i	−0.00770277	+	0.0375178i
$423$	0.0870075			0.00423045
$424$	11.3953	−	16.3918i	0.553407	−	0.796057i
$425$	0.0762061			0.00369654
$426$	−1.76008	+	8.57283i	−0.0852763	+	0.415355i
$427$		0			0
$428$	3.96316	−	9.24484i	0.191567	−	0.446866i
$429$		−	12.9587i		−	0.625650i
$430$	35.7507	+	7.33996i	1.72405	+	0.353965i
$431$	28.3672			1.36640			0.683200	−	0.730231i	$-0.260588\pi$
$431$	28.3672			1.36640			0.683200	+	0.730231i	$0.260588\pi$
$432$	−2.89710	+	2.75804i	−0.139387	+	0.132696i
$433$	6.53217			0.313916			0.156958	−	0.987605i	$-0.449831\pi$
$433$	6.53217			0.313916			0.156958	+	0.987605i	$0.449831\pi$
$434$		0			0
$435$			12.6980i			0.608822i
$436$	0.161087	−	0.375767i	0.00771468	−	0.0179960i
$437$			18.1995i			0.870602i
$438$	3.94761	−	19.2276i	0.188624	−	0.918731i
$439$	−0.532322			−0.0254063			−0.0127032	−	0.999919i	$-0.504044\pi$
$439$	−0.532322			−0.0254063			−0.0127032	+	0.999919i	$0.504044\pi$
$440$	−20.7123	−	14.3988i	−0.987418	−	0.686438i
$441$		0			0
$442$	−0.272274	+	1.32616i	−0.0129507	+	0.0630791i
$443$		−	8.51970i		−	0.404783i	−0.979305	−	0.202392i	$-0.935129\pi$
$443$		−	8.51970i		−	0.404783i	0.979305	−	0.202392i	$-0.0648714\pi$
$444$	10.9473	+	4.69297i	0.519534	+	0.222719i
$445$			39.4310i			1.86921i
$446$	−15.3876	−	3.15922i	−0.728622	−	0.149593i
$447$	−9.59178			−0.453676
$448$		0			0
$449$	−15.0180			−0.708745			−0.354373	−	0.935104i	$-0.615306\pi$
$449$	−15.0180			−0.708745			−0.354373	+	0.935104i	$0.615306\pi$
$450$	0.367684	+	0.0754890i	0.0173328	+	0.00355858i
$451$			13.6662i			0.643517i
$452$	−27.4267	−	11.7575i	−1.29004	−	0.553027i
$453$		−	6.99222i		−	0.328523i
$454$	−2.49375	+	12.1463i	−0.117038	+	0.570054i
$455$		0			0
$456$	6.46842	+	4.49675i	0.302911	+	0.210579i
$457$	−31.4552			−1.47141			−0.735705	−	0.677302i	$-0.763149\pi$
$457$	−31.4552			−1.47141			−0.735705	+	0.677302i	$0.763149\pi$
$458$	−5.88640	+	28.6708i	−0.275053	+	1.33970i
$459$		−	0.287121i		−	0.0134017i
$460$	−11.8154	+	27.5618i	−0.550898	+	1.28508i
$461$		−	4.36281i		−	0.203196i	−0.994826	−	0.101598i	$-0.967604\pi$
$461$		−	4.36281i		−	0.203196i	0.994826	−	0.101598i	$-0.0323956\pi$
$462$		0			0
$463$	13.9787			0.649646			0.324823	−	0.945775i	$-0.394695\pi$
$463$	13.9787			0.649646			0.324823	+	0.945775i	$0.394695\pi$
$464$	−16.0318	+	15.2623i	−0.744258	+	0.708535i
$465$	−17.0792			−0.792031
$466$	−7.93584	−	1.62930i	−0.367620	−	0.0754760i
$467$		−	16.5383i		−	0.765302i	−0.923893	−	0.382651i	$-0.875011\pi$
$467$		−	16.5383i		−	0.765302i	0.923893	−	0.382651i	$-0.124989\pi$
$468$	−2.62737	+	6.12883i	−0.121450	+	0.283305i
$469$		0			0
$470$	0.0567847	−	0.276581i	0.00261928	−	0.0127577i
$471$	−17.3579			−0.799810
$472$	−7.02651	+	10.1074i	−0.323421	+	0.465231i
$473$	43.7116			2.00986
$474$	−2.55935	+	12.4658i	−0.117555	+	0.572574i
$475$		−	0.739247i		−	0.0339190i
$476$		0			0
$477$			7.05820i			0.323173i
$478$	3.15369	+	0.647483i	0.144247	+	0.0296152i
$479$	1.18401			0.0540990			0.0270495	−	0.999634i	$-0.491389\pi$
$479$	1.18401			0.0540990			0.0270495	+	0.999634i	$0.491389\pi$
$480$	6.87655	+	11.0094i	0.313870	+	0.502507i
$481$	19.8560			0.905357
$482$	−32.6728	−	6.70803i	−1.48820	−	0.305542i
$483$		0			0
$484$	−7.54810	−	3.23579i	−0.343096	−	0.147081i
$485$		−	14.8356i		−	0.673648i
$486$	0.284419	−	1.38532i	0.0129015	−	0.0628393i
$487$	−24.0896			−1.09160			−0.545801	−	0.837915i	$-0.683775\pi$
$487$	−24.0896			−1.09160			−0.545801	+	0.837915i	$0.683775\pi$
$488$	−11.5712	+	16.6448i	−0.523805	+	0.753476i
$489$	−15.7220			−0.710973
$490$		0			0
$491$			18.4971i			0.834761i	0.908732	+	0.417381i	$0.137052\pi$
$491$			18.4971i			0.834761i	−0.908732	+	0.417381i	$0.862948\pi$
$492$	2.77082	−	6.46347i	0.124918	−	0.291396i
$493$		−	1.58885i		−	0.0715584i
$494$	12.8646	+	2.64123i	0.578806	+	0.118834i
$495$	8.91855			0.400859
$496$	−20.5283	−	21.5633i	−0.921749	−	0.968223i
$497$		0			0
$498$	−24.4250	−	5.01469i	−1.09451	−	0.224714i
$499$		−	12.1283i		−	0.542937i	−0.962447	−	0.271468i	$-0.912491\pi$
$499$		−	12.1283i		−	0.542937i	0.962447	−	0.271468i	$-0.0875092\pi$
$500$	−8.56124	+	19.9707i	−0.382870	+	0.893118i
$501$		−	0.102064i		−	0.00455988i
$502$	−3.53597	+	17.2226i	−0.157818	+	0.768683i
$503$	7.61078			0.339348			0.169674	−	0.985500i	$-0.445729\pi$
$503$	7.61078			0.339348			0.169674	+	0.985500i	$0.445729\pi$
$504$		0			0
$505$	27.1826			1.20961
$506$	−7.22325	+	35.1822i	−0.321112	+	1.56404i
$507$		−	1.88358i		−	0.0836528i
$508$	−11.5673	−	4.95876i	−0.513214	−	0.220009i
$509$			16.0956i			0.713424i	0.934214	+	0.356712i	$0.116102\pi$
$509$			16.0956i			0.713424i	−0.934214	+	0.356712i	$0.883898\pi$
$510$	−0.912705	−	0.187387i	−0.0404153	−	0.00829764i
$511$		0			0
$512$	−5.63461	+	21.9146i	−0.249017	+	0.968499i
$513$	−2.78525			−0.122972
$514$	−0.392023	−	0.0804861i	−0.0172914	−	0.00355009i
$515$		−	3.72168i		−	0.163997i
$516$	−20.6735	−	8.86252i	−0.910101	−	0.390151i
$517$		−	0.338169i		−	0.0148727i
$518$		0			0
$519$	2.28777			0.100422
$520$	17.7677	+	12.3519i	0.779166	+	0.541665i
$521$	19.2934			0.845258			0.422629	−	0.906303i	$-0.361107\pi$
$521$	19.2934			0.845258			0.422629	+	0.906303i	$0.361107\pi$
$522$	1.57390	−	7.66599i	0.0688878	−	0.335531i
$523$			32.2551i			1.41042i	0.709001	+	0.705208i	$0.249146\pi$
$523$			32.2551i			1.41042i	−0.709001	+	0.705208i	$0.750854\pi$
$524$	−0.977904	+	2.28115i	−0.0427199	+	0.0996524i
$525$		0			0
$526$	19.8367	+	4.07266i	0.864921	+	0.177577i
$527$	2.13706			0.0930919
$528$	10.7196	+	11.2601i	0.466511	+	0.490032i
$529$	19.6964			0.856366
$530$	22.4367	+	4.60648i	0.974589	+	0.200093i
$531$		−	4.35217i		−	0.188868i
$532$		0			0
$533$		−	11.7234i		−	0.507796i
$534$	4.88742	−	23.8051i	0.211500	−	1.03015i
$535$	11.5404			0.498934
$536$	21.0295	−	30.2502i	0.908336	−	1.30661i
$537$	−18.6231			−0.803646
$538$	4.78224	−	23.2928i	0.206177	−	1.00423i
$539$		0			0
$540$	−4.21805	−	1.80823i	−0.181516	−	0.0778140i
$541$			3.98877i			0.171491i	0.996317	+	0.0857454i	$0.0273272\pi$
$541$			3.98877i			0.171491i	−0.996317	+	0.0857454i	$0.972673\pi$
$542$	−37.1897	−	7.63541i	−1.59744	−	0.327969i
$543$	13.6786			0.587005
$544$	−0.860437	−	1.37756i	−0.0368909	−	0.0590625i
$545$	0.469072			0.0200928
$546$		0			0
$547$			12.1824i			0.520882i	0.965490	+	0.260441i	$0.0838679\pi$
$547$			12.1824i			0.520882i	−0.965490	+	0.260441i	$0.916132\pi$
$548$	2.92311	+	1.25311i	0.124869	+	0.0535300i
$549$		−	7.16714i		−	0.305886i
$550$	0.293401	−	1.42907i	0.0125107	−	0.0609356i
$551$	−15.4129			−0.656611
$552$	10.5494	−	15.1750i	0.449014	−	0.645891i
$553$		0			0
$554$	6.40027	−	31.1738i	0.271922	−	1.32445i
$555$			13.6655i			0.580069i
$556$	0.811510	−	1.89300i	0.0344157	−	0.0802812i
$557$			2.98826i			0.126617i	0.997994	+	0.0633084i	$0.0201652\pi$
$557$			2.98826i			0.126617i	−0.997994	+	0.0633084i	$0.979835\pi$
$558$	10.3110	+	2.11695i	0.436501	+	0.0896178i
$559$	−37.4974			−1.58597
$560$		0			0
$561$	−1.11594			−0.0471152
$562$	17.7841	+	3.65124i	0.750176	+	0.154018i
$563$			4.41292i			0.185982i	0.995667	+	0.0929911i	$0.0296428\pi$
$563$			4.41292i			0.185982i	−0.995667	+	0.0929911i	$0.970357\pi$
$564$	−0.0685638	+	0.159938i	−0.00288706	+	0.00673461i
$565$		−	34.2368i		−	1.44035i
$566$	2.07566	−	10.1099i	0.0872466	−	0.424952i
$567$		0			0
$568$	−14.3717	−	9.99098i	−0.603022	−	0.419212i
$569$	−12.3086			−0.516005			−0.258002	−	0.966144i	$-0.583064\pi$
$569$	−12.3086			−0.516005			−0.258002	+	0.966144i	$0.583064\pi$
$570$	−1.81777	+	8.85382i	−0.0761382	+	0.370846i
$571$			30.3416i			1.26975i	0.772613	+	0.634877i	$0.218949\pi$
$571$			30.3416i			1.26975i	−0.772613	+	0.634877i	$0.781051\pi$
$572$	23.8208	+	10.2117i	0.995997	+	0.426973i
$573$			12.6346i			0.527818i
$574$		0			0
$575$	−1.73429			−0.0723247
$576$	−2.78689	−	7.49888i	−0.116120	−	0.312453i
$577$	12.0512			0.501697			0.250848	−	0.968026i	$-0.419290\pi$
$577$	12.0512			0.501697			0.250848	+	0.968026i	$0.419290\pi$
$578$	−23.4362	−	4.81168i	−0.974817	−	0.200139i
$579$		−	2.60582i		−	0.108294i
$580$	−23.3416	−	10.0063i	−0.969208	−	0.415489i
$581$		0			0
$582$	−1.83885	+	8.95647i	−0.0762228	+	0.371258i
$583$	27.4329			1.13615
$584$	32.2336	+	22.4083i	1.33384	+	0.927263i
$585$	−7.65066			−0.316316
$586$	2.83189	−	13.7933i	0.116984	−	0.569794i
$587$			5.34331i			0.220542i	0.993902	+	0.110271i	$0.0351719\pi$
$587$			5.34331i			0.220542i	−0.993902	+	0.110271i	$0.964828\pi$
$588$		0			0
$589$		−	20.7309i		−	0.854200i
$590$	−13.8348	−	2.84041i	−0.569569	−	0.116938i
$591$	0.794777			0.0326927
$592$	−17.2534	+	16.4252i	−0.709109	+	0.675072i
$593$	−9.49060			−0.389732			−0.194866	−	0.980830i	$-0.562427\pi$
$593$	−9.49060			−0.389732			−0.194866	+	0.980830i	$0.562427\pi$
$594$	−5.38428	−	1.10544i	−0.220920	−	0.0453569i
$595$		0			0
$596$	7.55853	−	17.6317i	0.309609	−	0.722223i
$597$			10.7343i			0.439325i
$598$	6.19636	−	30.1806i	0.253388	−	1.23418i
$599$	−7.73951			−0.316228			−0.158114	−	0.987421i	$-0.550541\pi$
$599$	−7.73951			−0.316228			−0.158114	+	0.987421i	$0.550541\pi$
$600$	−0.428507	+	0.616393i	−0.0174937	+	0.0251642i
$601$	19.0198			0.775835			0.387917	−	0.921694i	$-0.373195\pi$
$601$	19.0198			0.775835			0.387917	+	0.921694i	$0.373195\pi$
$602$		0			0
$603$			13.0255i			0.530440i
$604$	12.8532	+	5.51002i	0.522989	+	0.224200i
$605$		−	9.42234i		−	0.383072i
$606$	−16.4106	−	3.36925i	−0.666635	−	0.136867i
$607$	−9.19581			−0.373247			−0.186623	−	0.982432i	$-0.559754\pi$
$607$	−9.19581			−0.373247			−0.186623	+	0.982432i	$0.559754\pi$
$608$	−13.3632	+	8.34678i	−0.541950	+	0.338507i
$609$		0			0
$610$	−22.7830	−	4.67758i	−0.922459	−	0.189390i
$611$			0.290094i			0.0117360i
$612$	0.527789	+	0.226257i	0.0213346	+	0.00914592i
$613$			26.4067i			1.06655i	0.845940	+	0.533277i	$0.179040\pi$
$613$			26.4067i			1.06655i	−0.845940	+	0.533277i	$0.820960\pi$
$614$	−4.25147	+	20.7076i	−0.171575	+	0.835691i
$615$	8.06838			0.325348
$616$		0			0
$617$	−45.5837			−1.83513			−0.917565	−	0.397585i	$-0.869848\pi$
$617$	−45.5837			−1.83513			−0.917565	+	0.397585i	$0.869848\pi$
$618$	−0.461298	+	2.24684i	−0.0185561	+	0.0903812i
$619$			49.0337i			1.97083i	0.170169	+	0.985415i	$0.445569\pi$
$619$			49.0337i			1.97083i	−0.170169	+	0.985415i	$0.554431\pi$
$620$	13.4588	−	31.3953i	0.540519	−	1.26086i
$621$			6.53425i			0.262210i
$622$	43.3038	+	8.89068i	1.73632	+	0.356484i
$623$		0			0
$624$	−9.19567	−	9.65931i	−0.368122	−	0.386682i
$625$	−26.2566			−1.05027
$626$	4.24556	+	0.871654i	0.169687	+	0.0348383i
$627$			10.8254i			0.432324i
$628$	13.6784	−	31.9075i	0.545828	−	1.27325i
$629$		−	1.70992i		−	0.0681788i
$630$		0			0
$631$	−12.5801			−0.500804			−0.250402	−	0.968142i	$-0.580563\pi$
$631$	−12.5801			−0.500804			−0.250402	+	0.968142i	$0.580563\pi$
$632$	−20.8980	−	14.5280i	−0.831277	−	0.577892i
$633$	0.556345			0.0221127
$634$	−4.63548	+	22.5780i	−0.184099	+	0.896687i
$635$		−	14.4395i		−	0.573013i
$636$	−12.9745	−	5.56201i	−0.514471	−	0.220548i
$637$		0			0
$638$	−29.7952	−	6.11724i	−1.17960	−	0.242184i
$639$	6.18835			0.244807
$640$	−25.6564	+	3.96493i	−1.01416	+	0.156728i
$641$	−34.2258			−1.35184			−0.675920	−	0.736975i	$-0.736253\pi$
$641$	−34.2258			−1.35184			−0.675920	+	0.736975i	$0.736253\pi$
$642$	−6.96712	−	1.43042i	−0.274970	−	0.0564540i
$643$		−	23.0442i		−	0.908776i	−0.890804	−	0.454388i	$-0.849858\pi$
$643$		−	23.0442i		−	0.908776i	0.890804	−	0.454388i	$-0.150142\pi$
$644$		0			0
$645$		−	25.8069i		−	1.01614i
$646$	0.227451	−	1.10785i	0.00894895	−	0.0435876i
$647$	−15.5820			−0.612590			−0.306295	−	0.951937i	$-0.599089\pi$
$647$	−15.5820			−0.612590			−0.306295	+	0.951937i	$0.599089\pi$
$648$	2.32238	+	1.61448i	0.0912317	+	0.0634229i
$649$	−16.9155			−0.663991
$650$	−0.251690	+	1.22590i	−0.00987210	+	0.0480839i
$651$		0			0
$652$	12.3893	−	28.9003i	0.485201	−	1.13182i
$653$			49.2269i			1.92640i	0.268789	+	0.963199i	$0.413377\pi$
$653$			49.2269i			1.92640i	−0.268789	+	0.963199i	$0.586623\pi$
$654$	−0.283187	−	0.0581409i	−0.0110735	−	0.00227349i
$655$	−2.84757			−0.111264
$656$	9.69775	+	10.1867i	0.378634	+	0.397724i
$657$	−13.8796			−0.541493
$658$		0			0
$659$			5.33204i			0.207707i	0.994593	+	0.103853i	$0.0331173\pi$
$659$			5.33204i			0.207707i	−0.994593	+	0.103853i	$0.966883\pi$
$660$	−7.02801	+	16.3942i	−0.273565	+	0.638143i
$661$			38.6891i			1.50483i	0.658689	+	0.752416i	$0.271111\pi$
$661$			38.6891i			1.50483i	−0.658689	+	0.752416i	$0.728889\pi$
$662$	−0.785869	+	3.82773i	−0.0305437	+	0.148769i
$663$	0.957298			0.0371784
$664$	28.4655	−	40.9467i	1.10468	−	1.58904i
$665$		0			0
$666$	1.69383	−	8.25010i	0.0656344	−	0.319685i
$667$			36.1589i			1.40008i
$668$	0.187615	+	0.0804286i	0.00725905	+	0.00311188i
$669$			11.1076i			0.429445i
$670$	41.4058	+	8.50100i	1.59964	+	0.328422i
$671$	−27.8563			−1.07538
$672$		0			0
$673$	−9.56678			−0.368772			−0.184386	−	0.982854i	$-0.559030\pi$
$673$	−9.56678			−0.368772			−0.184386	+	0.982854i	$0.559030\pi$
$674$	35.7770	+	7.34537i	1.37808	+	0.282933i
$675$		−	0.265415i		−	0.0102158i
$676$	3.46242	+	1.48430i	0.133170	+	0.0570886i
$677$			17.7288i			0.681372i	0.940177	+	0.340686i	$0.110659\pi$
$677$			17.7288i			0.681372i	−0.940177	+	0.340686i	$0.889341\pi$
$678$	−4.24362	+	20.6694i	−0.162975	+	0.793802i
$679$		0			0
$680$	1.06369	−	1.53008i	0.0407906	−	0.0586759i
$681$	8.76788			0.335986
$682$	8.22790	−	40.0756i	0.315063	−	1.53457i
$683$		−	8.77302i		−	0.335690i	−0.985813	−	0.167845i	$-0.946319\pi$
$683$		−	8.77302i		−	0.335690i	0.985813	−	0.167845i	$-0.0536808\pi$
$684$	2.19484	−	5.11989i	0.0839218	−	0.195764i
$685$			3.64893i			0.139418i
$686$		0			0
$687$	20.6962			0.789610
$688$	32.5824	−	31.0184i	1.24219	−	1.18257i
$689$	−23.5329			−0.896534
$690$	20.7712	+	4.26453i	0.790746	+	0.162348i
$691$		−	21.3823i		−	0.813421i	−0.913557	−	0.406710i	$-0.866676\pi$
$691$		−	21.3823i		−	0.813421i	0.913557	−	0.406710i	$-0.133324\pi$
$692$	−1.80281	+	4.20540i	−0.0685326	+	0.159865i
$693$		0			0
$694$	−3.49139	+	17.0055i	−0.132531	+	0.645519i
$695$	2.36304			0.0896354
$696$	12.8514	+	8.93414i	0.487133	+	0.338648i
$697$	−1.00957			−0.0382400
$698$	−0.0596576	+	0.290574i	−0.00225807	+	0.0109984i
$699$			5.72853i			0.216673i
$700$		0			0
$701$			13.4233i			0.506990i	0.967337	+	0.253495i	$0.0815802\pi$
$701$			13.4233i			0.506990i	−0.967337	+	0.253495i	$0.918420\pi$
$702$	4.61883	+	0.948290i	0.174326	+	0.0357909i
$703$	−16.5873			−0.625601
$704$	−29.1457	+	10.8317i	−1.09847	+	0.408236i
$705$	−0.199652			−0.00751931
$706$	27.1501	+	5.57418i	1.02181	+	0.209787i
$707$		0			0
$708$	8.00022	+	3.42961i	0.300667	+	0.128893i
$709$		−	50.6521i		−	1.90228i	−0.308762	−	0.951139i	$-0.599915\pi$
$709$		−	50.6521i		−	1.90228i	0.308762	−	0.951139i	$-0.400085\pi$
$710$	4.03877	−	19.6716i	0.151572	−	0.738263i
$711$	8.99853			0.337471
$712$	39.9075	+	27.7431i	1.49560	+	1.03972i
$713$	−48.6349			−1.82139
$714$		0			0
$715$			29.7356i			1.11205i
$716$	14.6754	−	34.2332i	0.548445	−	1.27935i
$717$		−	2.27651i		−	0.0850179i
$718$	−7.91172	−	1.62435i	−0.295263	−	0.0606203i
$719$	−28.9600			−1.08003			−0.540013	−	0.841657i	$-0.681581\pi$
$719$	−28.9600			−1.08003			−0.540013	+	0.841657i	$0.681581\pi$
$720$	6.64783	−	6.32874i	0.247750	−	0.235858i
$721$		0			0
$722$	15.5742	+	3.19754i	0.579613	+	0.119000i
$723$			23.5850i			0.877137i
$724$	−10.7790	+	25.1441i	−0.400599	+	0.934475i
$725$		−	1.46874i		−	0.0545475i
$726$	−1.16789	+	5.68842i	−0.0433444	+	0.211117i
$727$	10.5092			0.389766			0.194883	−	0.980827i	$-0.437567\pi$
$727$	10.5092			0.389766			0.194883	+	0.980827i	$0.437567\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	−9.05839	+	44.1206i	−0.335266	+	1.63298i
$731$			3.22912i			0.119433i
$732$	13.1747	+	5.64786i	0.486952	+	0.208751i
$733$		−	28.1008i		−	1.03793i	−0.854797	−	0.518963i	$-0.826318\pi$
$733$		−	28.1008i		−	1.03793i	0.854797	−	0.518963i	$-0.173682\pi$
$734$	−38.9655	−	8.00000i	−1.43824	−	0.295285i
$735$		0			0
$736$	19.5817	+	31.3503i	0.721791	+	1.15559i
$737$	50.6259			1.86483
$738$	−4.87102	−	1.00007i	−0.179305	−	0.0368129i
$739$		−	34.8553i		−	1.28217i	−0.767469	−	0.641086i	$-0.778484\pi$
$739$		−	34.8553i		−	1.28217i	0.767469	−	0.641086i	$-0.221516\pi$
$740$	−25.1201	−	10.7687i	−0.923434	−	0.395866i
$741$		−	9.28640i		−	0.341144i
$742$		0			0
$743$	38.4805			1.41171			0.705857	−	0.708354i	$-0.250562\pi$
$743$	38.4805			1.41171			0.705857	+	0.708354i	$0.250562\pi$
$744$	−12.0167	+	17.2856i	−0.440554	+	0.633722i
$745$	22.0098			0.806375
$746$	−4.89301	+	23.8323i	−0.179146	+	0.872564i
$747$			17.6313i			0.645097i
$748$	0.879389	−	2.05134i	0.0321536	−	0.0750045i
$749$		0			0
$750$	15.0504	+	3.08999i	0.549562	+	0.112830i
$751$	0.0225322			0.000822212			0.000411106	−	1.00000i	$-0.499869\pi$
$751$	0.0225322			0.000822212			0.000411106		1.00000i	$0.499869\pi$
$752$	−0.239970	−	0.252069i	−0.00875082	−	0.00919203i
$753$	12.4322			0.453056
$754$	25.5594	+	5.24759i	0.930819	+	0.191106i
$755$			16.0447i			0.583926i
$756$		0			0
$757$		−	30.0479i		−	1.09211i	−0.837749	−	0.546055i	$-0.816129\pi$
$757$		−	30.0479i		−	1.09211i	0.837749	−	0.546055i	$-0.183871\pi$
$758$	2.89743	−	14.1125i	0.105239	−	0.512589i
$759$	25.3965			0.921834
$760$	−14.8427	−	10.3185i	−0.538403	−	0.374290i
$761$	17.1613			0.622096			0.311048	−	0.950394i	$-0.399320\pi$
$761$	17.1613			0.622096			0.311048	+	0.950394i	$0.399320\pi$
$762$	−1.78976	+	8.71735i	−0.0648360	+	0.315796i
$763$		0			0
$764$	−23.2250	−	9.95633i	−0.840253	−	0.360207i
$765$			0.658842i			0.0238205i
$766$	27.4893	+	5.64381i	0.993227	+	0.203919i
$767$	14.5107			0.523952
$768$	15.9807	+	0.786392i	0.576653	+	0.0283765i
$769$	47.2945			1.70548			0.852742	−	0.522332i	$-0.174938\pi$
$769$	47.2945			1.70548			0.852742	+	0.522332i	$0.174938\pi$
$770$		0			0
$771$			0.282984i			0.0101914i
$772$	4.79005	+	2.05344i	0.172398	+	0.0739051i
$773$			42.7753i			1.53852i	0.638935	+	0.769260i	$0.279375\pi$
$773$			42.7753i			1.53852i	−0.638935	+	0.769260i	$0.720625\pi$
$774$	−3.19873	+	15.5800i	−0.114976	+	0.560013i
$775$	1.97550			0.0709621
$776$	−15.0148	−	10.4381i	−0.539001	−	0.374705i
$777$		0			0
$778$	−5.27123	+	25.6745i	−0.188983	+	0.920477i
$779$			9.79343i			0.350886i
$780$	6.02888	−	14.0635i	0.215869	−	0.503555i
$781$		−	24.0521i		−	0.860651i
$782$	−2.59902	−	0.533604i	−0.0929408	−	0.0190816i
$783$	−5.53374			−0.197760
$784$		0			0
$785$	39.8303			1.42160
$786$	1.71912	+	0.352953i	0.0613191	+	0.0125894i
$787$		−	49.4625i		−	1.76315i	−0.472046	−	0.881574i	$-0.656485\pi$
$787$		−	49.4625i		−	1.76315i	0.472046	−	0.881574i	$-0.343515\pi$
$788$	−0.626301	+	1.46097i	−0.0223111	+	0.0520448i
$789$		−	14.3192i		−	0.509778i
$790$	5.87282	−	28.6047i	0.208945	−	1.01771i
$791$		0			0
$792$	6.27497	−	9.02633i	0.222971	−	0.320737i
$793$	23.8962			0.848578
$794$	2.27005	−	11.0567i	0.0805612	−	0.392389i
$795$		−	16.1961i		−	0.574416i
$796$	−19.7319	−	8.45884i	−0.699378	−	0.299816i
$797$			13.3755i			0.473783i	0.971536	+	0.236892i	$0.0761286\pi$
$797$			13.3755i			0.473783i	−0.971536	+	0.236892i	$0.923871\pi$
$798$		0			0
$799$	0.0249817			0.000883788
$800$	−0.795388	−	1.27342i	−0.0281212	−	0.0450221i
$801$	−17.1839			−0.607163
$802$	49.9296	+	10.2510i	1.76307	+	0.361976i
$803$			53.9453i			1.90369i
$804$	−23.9437	−	10.2644i	−0.844428	−	0.361997i
$805$		0			0
$806$	−7.05819	+	34.3783i	−0.248614	+	1.21092i
$807$	−16.8141			−0.591883
$808$	19.1253	−	27.5111i	0.672826	−	0.967838i
$809$	14.2253			0.500136			0.250068	−	0.968228i	$-0.419547\pi$
$809$	14.2253			0.500136			0.250068	+	0.968228i	$0.419547\pi$
$810$	−0.652642	+	3.17882i	−0.0229315	+	0.111692i
$811$		−	20.7849i		−	0.729855i	−0.931036	−	0.364928i	$-0.881094\pi$
$811$		−	20.7849i		−	0.729855i	0.931036	−	0.364928i	$-0.118906\pi$
$812$		0			0
$813$			26.8456i			0.941518i
$814$	−32.0655	−	6.58335i	−1.12389	−	0.230746i
$815$	36.0764			1.26370
$816$	−0.831818	+	0.791892i	−0.0291195	+	0.0277218i
$817$	31.3245			1.09590
$818$	40.9591	+	8.40931i	1.43210	+	0.294025i
$819$		0			0
$820$	−6.35806	+	14.8314i	−0.222033	+	0.517935i
$821$			4.96410i			0.173248i	0.996241	+	0.0866241i	$0.0276079\pi$
$821$			4.96410i			0.173248i	−0.996241	+	0.0866241i	$0.972392\pi$
$822$	0.452281	−	2.20292i	0.0157751	−	0.0768357i
$823$	9.83498			0.342826			0.171413	−	0.985199i	$-0.445167\pi$
$823$	9.83498			0.342826			0.171413	+	0.985199i	$0.445167\pi$
$824$	−3.76666	−	2.61852i	−0.131218	−	0.0912206i
$825$	−1.03158			−0.0359150
$826$		0			0
$827$			41.4331i			1.44077i	0.693574	+	0.720385i	$0.256035\pi$
$827$			41.4331i			1.44077i	−0.693574	+	0.720385i	$0.743965\pi$
$828$	−12.0113	−	5.14913i	−0.417423	−	0.178945i
$829$		−	25.0029i		−	0.868386i	−0.900820	−	0.434193i	$-0.857034\pi$
$829$		−	25.0029i		−	0.868386i	0.900820	−	0.434193i	$-0.142966\pi$
$830$	56.0468	+	11.5070i	1.94541	+	0.399412i
$831$	−22.5030			−0.780619
$832$	25.0022	−	9.29185i	0.866797	−	0.322137i
$833$		0			0
$834$	−1.42661	−	0.292897i	−0.0493994	−	0.0101422i
$835$			0.234201i			0.00810486i
$836$	−19.8993	−	8.53063i	−0.688232	−	0.295038i
$837$		−	7.44308i		−	0.257270i
$838$	2.48384	−	12.0980i	0.0858029	−	0.417920i
$839$	−2.43551			−0.0840833			−0.0420416	−	0.999116i	$-0.513386\pi$
$839$	−2.43551			−0.0840833			−0.0420416	+	0.999116i	$0.513386\pi$
$840$		0			0
$841$	−1.62232			−0.0559420
$842$	0.504413	−	2.45684i	0.0173832	−	0.0846683i
$843$		−	12.8375i		−	0.442148i
$844$	−0.438412	+	1.02268i	−0.0150908	+	0.0352021i
$845$			4.32216i			0.148687i
$846$	0.120533	+	0.0247466i	0.00414401	+	0.000850805i
$847$		0			0
$848$	20.4483	−	19.4668i	0.702198	−	0.668493i
$849$	−7.29790			−0.250463
$850$	0.105570	+	0.0216745i	0.00362101	+	0.000743428i
$851$			38.9140i			1.33395i
$852$	−4.87655	+	11.3755i	−0.167068	+	0.389718i
$853$		−	51.1404i		−	1.75101i	−0.483206	−	0.875507i	$-0.660528\pi$
$853$		−	51.1404i		−	1.75101i	0.483206	−	0.875507i	$-0.339472\pi$
$854$		0			0
$855$	6.39118			0.218574
$856$	8.11965	−	11.6798i	0.277524	−	0.399209i
$857$	−53.4628			−1.82625			−0.913127	−	0.407675i	$-0.866340\pi$
$857$	−53.4628			−1.82625			−0.913127	+	0.407675i	$0.866340\pi$
$858$	3.68569	−	17.9519i	0.125827	−	0.612867i
$859$		−	16.5958i		−	0.566242i	−0.959084	−	0.283121i	$-0.908630\pi$
$859$		−	16.5958i		−	0.566242i	0.959084	−	0.283121i	$-0.0913697\pi$
$860$	47.4385	+	20.3364i	1.61764	+	0.693464i
$861$		0			0
$862$	39.2976	+	8.06817i	1.33848	+	0.274803i
$863$	−40.8512			−1.39059			−0.695296	−	0.718724i	$-0.744727\pi$
$863$	−40.8512			−1.39059			−0.695296	+	0.718724i	$0.744727\pi$
$864$	−4.79785	+	2.99678i	−0.163226	+	0.101952i
$865$	−5.24962			−0.178493
$866$	9.04914	+	1.85787i	0.307502	+	0.0631332i
$867$			16.9176i			0.574551i
$868$		0			0
$869$		−	34.9743i		−	1.18642i
$870$	−3.61155	+	17.5908i	−0.122443	+	0.596383i
$871$	−43.4288			−1.47153
$872$	0.330032	−	0.474740i	0.0111763	−	0.0160767i
$873$	6.46528			0.218817
$874$	−5.17630	+	25.2122i	−0.175091	+	0.852814i
$875$		0			0
$876$	10.9374	−	25.5136i	0.369540	−	0.862024i
$877$			1.51953i			0.0513107i	0.999671	+	0.0256554i	$0.00816725\pi$
$877$			1.51953i			0.0513107i	−0.999671	+	0.0256554i	$0.991833\pi$
$878$	−0.737435	−	0.151402i	−0.0248872	−	0.00510959i
$879$	−9.95674			−0.335833
$880$	−24.5977	−	25.8379i	−0.829190	−	0.870997i
$881$	−12.3299			−0.415406			−0.207703	−	0.978192i	$-0.566599\pi$
$881$	−12.3299			−0.415406			−0.207703	+	0.978192i	$0.566599\pi$
$882$		0			0
$883$		−	12.0145i		−	0.404319i	−0.979353	−	0.202159i	$-0.935204\pi$
$883$		−	12.0145i		−	0.404319i	0.979353	−	0.202159i	$-0.0647959\pi$
$884$	−0.754372	+	1.75972i	−0.0253723	+	0.0591857i
$885$			9.98671i			0.335700i
$886$	2.42316	−	11.8025i	0.0814078	−	0.396512i
$887$	23.0480			0.773875			0.386938	−	0.922106i	$-0.373533\pi$
$887$	23.0480			0.773875			0.386938	+	0.922106i	$0.373533\pi$
$888$	13.8307	+	9.61487i	0.464127	+	0.322654i
$889$		0			0
$890$	−11.2149	+	54.6244i	−0.375925	+	1.83102i
$891$			3.88667i			0.130208i
$892$	−20.4181	−	8.75303i	−0.683650	−	0.293073i
$893$		−	0.242338i		−	0.00810953i
$894$	−13.2877	−	2.72808i	−0.444406	−	0.0912408i
$895$	42.7335			1.42842
$896$		0			0
$897$	−21.7860			−0.727415
$898$	−20.8048	−	4.27142i	−0.694264	−	0.142539i
$899$		−	41.1881i		−	1.37370i
$900$	0.487888	+	0.209152i	0.0162629	+	0.00697175i
$901$			2.02656i			0.0675144i
$902$	−3.88693	+	18.9320i	−0.129421	+	0.630368i
$903$		0			0
$904$	−34.6506	−	24.0886i	−1.15246	−	0.801174i
$905$	−31.3876			−1.04336
$906$	1.98872	−	9.68645i	0.0660709	−	0.321811i
$907$			32.7639i			1.08791i	0.839115	+	0.543954i	$0.183073\pi$
$907$			32.7639i			1.08791i	−0.839115	+	0.543954i	$0.816927\pi$
$908$	−6.90928	+	16.1172i	−0.229293	+	0.534869i
$909$			11.8461i			0.392910i
$910$		0			0
$911$	35.5607			1.17818			0.589090	−	0.808067i	$-0.299486\pi$
$911$	35.5607			1.17818			0.589090	+	0.808067i	$0.299486\pi$
$912$	7.68185	+	8.06916i	0.254372	+	0.267197i
$913$	68.5273			2.26792
$914$	−43.5754	−	8.94645i	−1.44135	−	0.295922i
$915$			16.4461i			0.543691i
$916$	−16.3091	+	38.0440i	−0.538867	+	1.25701i
$917$		0			0
$918$	0.0816627	−	0.397754i	0.00269527	−	0.0131278i
$919$	−27.5241			−0.907937			−0.453969	−	0.891018i	$-0.649992\pi$
$919$	−27.5241			−0.907937			−0.453969	+	0.891018i	$0.649992\pi$
$920$	−24.2073	+	34.8213i	−0.798090	+	1.14802i
$921$	14.9479			0.492550
$922$	1.24087	−	6.04388i	0.0408658	−	0.199045i
$923$			20.6327i			0.679135i
$924$		0			0
$925$		−	1.58065i		−	0.0519713i
$926$	19.3650	+	3.97581i	0.636372	+	0.130653i
$927$	1.62190			0.0532701
$928$	−26.5501	+	16.5834i	−0.871548	+	0.544376i
$929$	−34.9480			−1.14661			−0.573303	−	0.819343i	$-0.694338\pi$
$929$	−34.9480			−1.14661			−0.573303	+	0.819343i	$0.694338\pi$
$930$	−23.6602	−	4.85766i	−0.775848	−	0.159289i
$931$		0			0
$932$	−10.5303	−	4.51421i	−0.344930	−	0.147868i
$933$		−	31.2591i		−	1.02338i
$934$	4.70381	−	22.9108i	0.153913	−	0.749665i
$935$	2.56070			0.0837439
$936$	−5.38290	+	7.74311i	−0.175945	+	0.253092i
$937$	−17.7423			−0.579615			−0.289807	−	0.957085i	$-0.593591\pi$
$937$	−17.7423			−0.579615			−0.289807	+	0.957085i	$0.593591\pi$
$938$		0			0
$939$		−	3.06468i		−	0.100012i
$940$	0.157330	−	0.367002i	0.00513153	−	0.0119703i
$941$			22.5728i			0.735852i	0.929855	+	0.367926i	$0.119932\pi$
$941$			22.5728i			0.735852i	−0.929855	+	0.367926i	$0.880068\pi$
$942$	−24.0462	−	4.93692i	−0.783468	−	0.160853i
$943$	22.9755			0.748187
$944$	−12.6087	+	12.0035i	−0.410378	+	0.390680i
$945$		0			0
$946$	60.5545	+	12.4324i	1.96880	+	0.404213i
$947$			27.2714i			0.886203i	0.896471	+	0.443102i	$0.146122\pi$
$947$			27.2714i			0.886203i	−0.896471	+	0.443102i	$0.853878\pi$
$948$	−7.09104	+	16.5412i	−0.230306	+	0.537233i
$949$		−	46.2763i		−	1.50219i
$950$	0.210256	−	1.02409i	0.00682161	−	0.0332259i
$951$	16.2981			0.528501
$952$		0			0
$953$	−5.90986			−0.191439			−0.0957196	−	0.995408i	$-0.530515\pi$
$953$	−5.90986			−0.191439			−0.0957196	+	0.995408i	$0.530515\pi$
$954$	−2.00749	+	9.77785i	−0.0649948	+	0.316569i
$955$		−	28.9920i		−	0.938157i
$956$	4.18471	+	1.79394i	0.135343	+	0.0580202i
$957$			21.5078i			0.695250i
$958$	1.64024	+	0.336756i	0.0529936	+	0.0108801i
$959$		0			0
$960$	6.39493	+	17.2073i	0.206396	+	0.555363i
$961$	24.3994			0.787077
$962$	27.5069	+	5.64743i	0.886858	+	0.182081i
$963$			5.02926i			0.162066i
$964$	−43.3543	−	18.5855i	−1.39635	−	0.598599i
$965$			5.97945i			0.192485i
$966$		0			0
$967$	14.0032			0.450312			0.225156	−	0.974323i	$-0.427711\pi$
$967$	14.0032			0.450312			0.225156	+	0.974323i	$0.427711\pi$
$968$	−9.53620	−	6.62942i	−0.306505	−	0.213078i
$969$	−0.799705			−0.0256902
$970$	4.21951	−	20.5520i	0.135480	−	0.659884i
$971$			9.13650i			0.293204i	0.989196	+	0.146602i	$0.0468337\pi$
$971$			9.13650i			0.293204i	−0.989196	+	0.146602i	$0.953166\pi$
$972$	0.788022	−	1.83821i	0.0252758	−	0.0589607i
$973$		0			0
$974$	−33.3717	−	6.85153i	−1.06930	−	0.219537i
$975$	0.884927			0.0283403
$976$	−20.7639	+	19.7673i	−0.664638	+	0.632736i
$977$	21.1534			0.676758			0.338379	−	0.941010i	$-0.390121\pi$
$977$	21.1534			0.676758			0.338379	+	0.941010i	$0.390121\pi$
$978$	−21.7799	−	4.47163i	−0.696446	−	0.142987i
$979$			66.7881i			2.13456i
$980$		0			0
$981$			0.204420i			0.00652662i
$982$	−5.26092	+	25.6243i	−0.167883	+	0.817705i
$983$	−46.4009			−1.47996			−0.739979	−	0.672630i	$-0.765164\pi$
$983$	−46.4009			−1.47996			−0.739979	+	0.672630i	$0.765164\pi$
$984$	5.67680	−	8.16588i	0.180970	−	0.260319i
$985$	−1.82373			−0.0581090
$986$	0.451900	−	2.20107i	0.0143914	−	0.0700963i
$987$		0			0
$988$	17.0704	+	7.31788i	0.543081	+	0.232813i
$989$		−	73.4877i		−	2.33677i
$990$	12.3550	+	2.53661i	0.392669	+	0.0806186i
$991$	2.58561			0.0821345			0.0410672	−	0.999156i	$-0.486924\pi$
$991$	2.58561			0.0821345			0.0410672	+	0.999156i	$0.486924\pi$
$992$	−22.3052	−	35.7107i	−0.708192	−	1.13382i
$993$	2.76307			0.0876833
$994$		0			0
$995$		−	24.6314i		−	0.780868i
$996$	−32.4101	−	13.8939i	−1.02695	−	0.440245i
$997$		−	20.7334i		−	0.656635i	−0.944567	−	0.328317i	$-0.893518\pi$
$997$		−	20.7334i		−	0.656635i	0.944567	−	0.328317i	$-0.106482\pi$
$998$	3.44952	−	16.8015i	0.109193	−	0.531843i
$999$	−5.95539			−0.188420

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1176.2.c.f.589.16		16
4.3	odd	2		4704.2.c.f.2353.15		16
7.3	odd	6		168.2.bc.a.37.5	✓	32
7.5	odd	6		168.2.bc.a.109.6	yes	32
7.6	odd	2		1176.2.c.e.589.16		16
8.3	odd	2		4704.2.c.f.2353.2		16
8.5	even	2	inner	1176.2.c.f.589.15		16
21.5	even	6		504.2.cj.e.109.11		32
21.17	even	6		504.2.cj.e.37.12		32
28.3	even	6		672.2.bk.a.625.7		32
28.19	even	6		672.2.bk.a.529.10		32
28.27	even	2		4704.2.c.e.2353.2		16
56.3	even	6		672.2.bk.a.625.10		32
56.5	odd	6		168.2.bc.a.109.5	yes	32
56.13	odd	2		1176.2.c.e.589.15		16
56.19	even	6		672.2.bk.a.529.7		32
56.27	even	2		4704.2.c.e.2353.15		16
56.45	odd	6		168.2.bc.a.37.6	yes	32
84.47	odd	6		2016.2.cr.e.1873.13		32
84.59	odd	6		2016.2.cr.e.1297.4		32
168.5	even	6		504.2.cj.e.109.12		32
168.59	odd	6		2016.2.cr.e.1297.13		32
168.101	even	6		504.2.cj.e.37.11		32
168.131	odd	6		2016.2.cr.e.1873.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.bc.a.37.5	✓	32	7.3	odd	6
168.2.bc.a.37.6	yes	32	56.45	odd	6
168.2.bc.a.109.5	yes	32	56.5	odd	6
168.2.bc.a.109.6	yes	32	7.5	odd	6
504.2.cj.e.37.11		32	168.101	even	6
504.2.cj.e.37.12		32	21.17	even	6
504.2.cj.e.109.11		32	21.5	even	6
504.2.cj.e.109.12		32	168.5	even	6
672.2.bk.a.529.7		32	56.19	even	6
672.2.bk.a.529.10		32	28.19	even	6
672.2.bk.a.625.7		32	28.3	even	6
672.2.bk.a.625.10		32	56.3	even	6
1176.2.c.e.589.15		16	56.13	odd	2
1176.2.c.e.589.16		16	7.6	odd	2
1176.2.c.f.589.15		16	8.5	even	2	inner
1176.2.c.f.589.16		16	1.1	even	1	trivial
2016.2.cr.e.1297.4		32	84.59	odd	6
2016.2.cr.e.1297.13		32	168.59	odd	6
2016.2.cr.e.1873.4		32	168.131	odd	6
2016.2.cr.e.1873.13		32	84.47	odd	6
4704.2.c.e.2353.2		16	28.27	even	2
4704.2.c.e.2353.15		16	56.27	even	2
4704.2.c.f.2353.2		16	8.3	odd	2
4704.2.c.f.2353.15		16	4.3	odd	2

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:	\( N \)	\(=\)	\( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1176.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.38532 + 0.284419i) q^{2} -1.00000i q^{3} +(1.83821 + 0.788022i) q^{4} +2.29465i q^{5} +(0.284419 - 1.38532i) q^{6} +(2.32238 + 1.61448i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(1.38532 + 0.284419i) q^{2} -1.00000i q^{3} +(1.83821 + 0.788022i) q^{4} +2.29465i q^{5} +(0.284419 - 1.38532i) q^{6} +(2.32238 + 1.61448i) q^{8} -1.00000 q^{9} +(-0.652642 + 3.17882i) q^{10} +3.88667i q^{11} +(0.788022 - 1.83821i) q^{12} -3.33413i q^{13} +2.29465 q^{15} +(2.75804 + 2.89710i) q^{16} -0.287121 q^{17} +(-1.38532 - 0.284419i) q^{18} +2.78525i q^{19} +(-1.80823 + 4.21805i) q^{20} +(-1.10544 + 5.38428i) q^{22} +6.53425 q^{23} +(1.61448 - 2.32238i) q^{24} -0.265415 q^{25} +(0.948290 - 4.61883i) q^{26} +1.00000i q^{27} +5.53374i q^{29} +(3.17882 + 0.652642i) q^{30} -7.44308 q^{31} +(2.99678 + 4.79785i) q^{32} +3.88667 q^{33} +(-0.397754 - 0.0816627i) q^{34} +(-1.83821 - 0.788022i) q^{36} +5.95539i q^{37} +(-0.792179 + 3.85846i) q^{38} -3.33413 q^{39} +(-3.70467 + 5.32905i) q^{40} +3.51617 q^{41} -11.2465i q^{43} +(-3.06278 + 7.14453i) q^{44} -2.29465i q^{45} +(9.05201 + 1.85847i) q^{46} -0.0870075 q^{47} +(2.89710 - 2.75804i) q^{48} +(-0.367684 - 0.0754890i) q^{50} +0.287121i q^{51} +(2.62737 - 6.12883i) q^{52} -7.05820i q^{53} +(-0.284419 + 1.38532i) q^{54} -8.91855 q^{55} +2.78525 q^{57} +(-1.57390 + 7.66599i) q^{58} +4.35217i q^{59} +(4.21805 + 1.80823i) q^{60} +7.16714i q^{61} +(-10.3110 - 2.11695i) q^{62} +(2.78689 + 7.49888i) q^{64} +7.65066 q^{65} +(5.38428 + 1.10544i) q^{66} -13.0255i q^{67} +(-0.527789 - 0.226257i) q^{68} -6.53425i q^{69} -6.18835 q^{71} +(-2.32238 - 1.61448i) q^{72} +13.8796 q^{73} +(-1.69383 + 8.25010i) q^{74} +0.265415i q^{75} +(-2.19484 + 5.11989i) q^{76} +(-4.61883 - 0.948290i) q^{78} -8.99853 q^{79} +(-6.64783 + 6.32874i) q^{80} +1.00000 q^{81} +(4.87102 + 1.00007i) q^{82} -17.6313i q^{83} -0.658842i q^{85} +(3.19873 - 15.5800i) q^{86} +5.53374 q^{87} +(-6.27497 + 9.02633i) q^{88} +17.1839 q^{89} +(0.652642 - 3.17882i) q^{90} +(12.0113 + 5.14913i) q^{92} +7.44308i q^{93} +(-0.120533 - 0.0247466i) q^{94} -6.39118 q^{95} +(4.79785 - 2.99678i) q^{96} -6.46528 q^{97} -3.88667i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} + 2 q^{4} - 8 q^{8} - 16 q^{9}+O(q^{10}) \) 16 * q - 2 * q^2 + 2 * q^4 - 8 * q^8 - 16 * q^9	\( 16 q - 2 q^{2} + 2 q^{4} - 8 q^{8} - 16 q^{9} + 6 q^{10} + 10 q^{16} + 2 q^{18} + 20 q^{20} - 6 q^{22} + 8 q^{23} - 6 q^{24} - 16 q^{25} + 6 q^{26} + 8 q^{30} - 24 q^{31} + 8 q^{32} + 12 q^{34} - 2 q^{36} - 26 q^{38} - 6 q^{40} - 20 q^{44} - 16 q^{46} - 24 q^{47} + 8 q^{48} + 26 q^{50} + 44 q^{52} + 32 q^{55} - 8 q^{57} - 34 q^{58} + 22 q^{60} - 50 q^{62} - 10 q^{64} + 12 q^{66} + 16 q^{68} - 40 q^{71} + 8 q^{72} + 8 q^{73} - 10 q^{74} + 16 q^{76} + 6 q^{78} - 8 q^{79} - 56 q^{80} + 16 q^{81} + 22 q^{86} + 24 q^{87} - 50 q^{88} - 6 q^{90} + 32 q^{92} - 48 q^{94} - 24 q^{95} + 10 q^{96} + 24 q^{97}+O(q^{100}) \) 16 * q - 2 * q^2 + 2 * q^4 - 8 * q^8 - 16 * q^9 + 6 * q^10 + 10 * q^16 + 2 * q^18 + 20 * q^20 - 6 * q^22 + 8 * q^23 - 6 * q^24 - 16 * q^25 + 6 * q^26 + 8 * q^30 - 24 * q^31 + 8 * q^32 + 12 * q^34 - 2 * q^36 - 26 * q^38 - 6 * q^40 - 20 * q^44 - 16 * q^46 - 24 * q^47 + 8 * q^48 + 26 * q^50 + 44 * q^52 + 32 * q^55 - 8 * q^57 - 34 * q^58 + 22 * q^60 - 50 * q^62 - 10 * q^64 + 12 * q^66 + 16 * q^68 - 40 * q^71 + 8 * q^72 + 8 * q^73 - 10 * q^74 + 16 * q^76 + 6 * q^78 - 8 * q^79 - 56 * q^80 + 16 * q^81 + 22 * q^86 + 24 * q^87 - 50 * q^88 - 6 * q^90 + 32 * q^92 - 48 * q^94 - 24 * q^95 + 10 * q^96 + 24 * q^97

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