LMFDB - Embedded newform 1170.2.bp.d.289.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1170,2,Mod(289,1170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1170, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("1170.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1170.bp (of order $6$, 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:	$9.34249703649$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 390)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			289.2
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1170.289
Dual form			1170.2.bp.d.919.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-1.23205 + 1.86603i) q^{5} +(-0.633975 - 0.366025i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-1.23205 + 1.86603i) q^{5} +(-0.633975 - 0.366025i) q^{7} -1.00000i q^{8} +(-0.133975 + 2.23205i) q^{10} +(-1.36603 - 2.36603i) q^{11} +(1.59808 - 3.23205i) q^{13} -0.732051 q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.13397 + 1.23205i) q^{17} +(2.36603 - 4.09808i) q^{19} +(1.00000 + 2.00000i) q^{20} +(-2.36603 - 1.36603i) q^{22} +(3.63397 - 2.09808i) q^{23} +(-1.96410 - 4.59808i) q^{25} +(-0.232051 - 3.59808i) q^{26} +(-0.633975 + 0.366025i) q^{28} +(-0.232051 - 0.401924i) q^{29} +4.00000 q^{31} +(-0.866025 - 0.500000i) q^{32} +2.46410 q^{34} +(1.46410 - 0.732051i) q^{35} +(5.13397 - 2.96410i) q^{37} -4.73205i q^{38} +(1.86603 + 1.23205i) q^{40} +(0.598076 + 1.03590i) q^{41} +(5.83013 + 3.36603i) q^{43} -2.73205 q^{44} +(2.09808 - 3.63397i) q^{46} -9.66025i q^{47} +(-3.23205 - 5.59808i) q^{49} +(-4.00000 - 3.00000i) q^{50} +(-2.00000 - 3.00000i) q^{52} -4.26795i q^{53} +(6.09808 + 0.366025i) q^{55} +(-0.366025 + 0.633975i) q^{56} +(-0.401924 - 0.232051i) q^{58} +(-4.19615 + 7.26795i) q^{59} +(-7.06218 + 12.2321i) q^{61} +(3.46410 - 2.00000i) q^{62} -1.00000 q^{64} +(4.06218 + 6.96410i) q^{65} +(8.36603 - 4.83013i) q^{67} +(2.13397 - 1.23205i) q^{68} +(0.901924 - 1.36603i) q^{70} +(2.36603 - 4.09808i) q^{71} +12.6603i q^{73} +(2.96410 - 5.13397i) q^{74} +(-2.36603 - 4.09808i) q^{76} +2.00000i q^{77} -12.0000 q^{79} +(2.23205 + 0.133975i) q^{80} +(1.03590 + 0.598076i) q^{82} -8.73205i q^{83} +(-4.92820 + 2.46410i) q^{85} +6.73205 q^{86} +(-2.36603 + 1.36603i) q^{88} +(-4.46410 - 7.73205i) q^{89} +(-2.19615 + 1.46410i) q^{91} -4.19615i q^{92} +(-4.83013 - 8.36603i) q^{94} +(4.73205 + 9.46410i) q^{95} +(-8.66025 - 5.00000i) q^{97} +(-5.59808 - 3.23205i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} + 2 q^{5} - 6 q^{7}+O(q^{10}) $ 4 * q + 2 * q^4 + 2 * q^5 - 6 * q^7	$ 4 q + 2 q^{4} + 2 q^{5} - 6 q^{7} - 4 q^{10} - 2 q^{11} - 4 q^{13} + 4 q^{14} - 2 q^{16} + 12 q^{17} + 6 q^{19} + 4 q^{20} - 6 q^{22} + 18 q^{23} + 6 q^{25} + 6 q^{26} - 6 q^{28} + 6 q^{29} + 16 q^{31} - 4 q^{34} - 8 q^{35} + 24 q^{37} + 4 q^{40} - 8 q^{41} + 6 q^{43} - 4 q^{44} - 2 q^{46} - 6 q^{49} - 16 q^{50} - 8 q^{52} + 14 q^{55} + 2 q^{56} - 12 q^{58} + 4 q^{59} - 4 q^{61} - 4 q^{64} - 8 q^{65} + 30 q^{67} + 12 q^{68} + 14 q^{70} + 6 q^{71} - 2 q^{74} - 6 q^{76} - 48 q^{79} + 2 q^{80} + 18 q^{82} + 8 q^{85} + 20 q^{86} - 6 q^{88} - 4 q^{89} + 12 q^{91} - 2 q^{94} + 12 q^{95} - 12 q^{98}+O(q^{100}) $ 4 * q + 2 * q^4 + 2 * q^5 - 6 * q^7 - 4 * q^10 - 2 * q^11 - 4 * q^13 + 4 * q^14 - 2 * q^16 + 12 * q^17 + 6 * q^19 + 4 * q^20 - 6 * q^22 + 18 * q^23 + 6 * q^25 + 6 * q^26 - 6 * q^28 + 6 * q^29 + 16 * q^31 - 4 * q^34 - 8 * q^35 + 24 * q^37 + 4 * q^40 - 8 * q^41 + 6 * q^43 - 4 * q^44 - 2 * q^46 - 6 * q^49 - 16 * q^50 - 8 * q^52 + 14 * q^55 + 2 * q^56 - 12 * q^58 + 4 * q^59 - 4 * q^61 - 4 * q^64 - 8 * q^65 + 30 * q^67 + 12 * q^68 + 14 * q^70 + 6 * q^71 - 2 * q^74 - 6 * q^76 - 48 * q^79 + 2 * q^80 + 18 * q^82 + 8 * q^85 + 20 * q^86 - 6 * q^88 - 4 * q^89 + 12 * q^91 - 2 * q^94 + 12 * q^95 - 12 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times$.

$n$	$911$	$937$	$1081$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−1.23205	+	1.86603i	−0.550990	+	0.834512i
$5$	−1.23205	+	1.86603i	−0.550990	+	0.834512i
$6$		0			0
$7$	−0.633975	−	0.366025i	−0.239620	−	0.138345i	0.375382	−	0.926870i	$-0.377511\pi$
$7$	−0.633975	−	0.366025i	−0.239620	−	0.138345i	−0.615002	+	0.788526i	$0.710845\pi$
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	−0.133975	+	2.23205i	−0.0423665	+	0.705836i
$11$	−1.36603	−	2.36603i	−0.411872	−	0.713384i	0.583222	−	0.812313i	$-0.301792\pi$
$11$	−1.36603	−	2.36603i	−0.411872	−	0.713384i	−0.995094	+	0.0989291i	$0.968458\pi$
$12$		0			0
$13$	1.59808	−	3.23205i	0.443227	−	0.896410i
$13$	1.59808	−	3.23205i	0.443227	−	0.896410i
$14$	−0.732051			−0.195649
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.13397	+	1.23205i	0.517565	+	0.298816i	0.735938	−	0.677049i	$-0.236742\pi$
$17$	2.13397	+	1.23205i	0.517565	+	0.298816i	−0.218373	+	0.975865i	$0.570075\pi$
$18$		0			0
$19$	2.36603	−	4.09808i	0.542803	−	0.940163i	−0.455938	−	0.890011i	$-0.650696\pi$
$19$	2.36603	−	4.09808i	0.542803	−	0.940163i	0.998742	−	0.0501517i	$-0.0159705\pi$
$20$	1.00000	+	2.00000i	0.223607	+	0.447214i
$21$		0			0
$22$	−2.36603	−	1.36603i	−0.504438	−	0.291238i
$23$	3.63397	−	2.09808i	0.757736	−	0.437479i	−0.0707462	−	0.997494i	$-0.522538\pi$
$23$	3.63397	−	2.09808i	0.757736	−	0.437479i	0.828482	+	0.560015i	$0.189205\pi$
$24$		0			0
$25$	−1.96410	−	4.59808i	−0.392820	−	0.919615i
$26$	−0.232051	−	3.59808i	−0.0455089	−	0.705641i
$27$		0			0
$28$	−0.633975	+	0.366025i	−0.119810	+	0.0691723i
$29$	−0.232051	−	0.401924i	−0.0430908	−	0.0746354i	0.843676	−	0.536853i	$-0.180387\pi$
$29$	−0.232051	−	0.401924i	−0.0430908	−	0.0746354i	−0.886766	+	0.462218i	$0.847054\pi$
$30$		0			0
$31$	4.00000			0.718421			0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000			0.718421			0.359211	+	0.933257i	$0.383046\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$		0			0
$34$	2.46410			0.422590
$35$	1.46410	−	0.732051i	0.247478	−	0.123739i
$36$		0			0
$37$	5.13397	−	2.96410i	0.844020	−	0.487295i	−0.0146085	−	0.999893i	$-0.504650\pi$
$37$	5.13397	−	2.96410i	0.844020	−	0.487295i	0.858629	+	0.512598i	$0.171317\pi$
$38$		−	4.73205i		−	0.767640i
$39$		0			0
$40$	1.86603	+	1.23205i	0.295045	+	0.194804i
$41$	0.598076	+	1.03590i	0.0934038	+	0.161780i	0.908941	−	0.416924i	$-0.136892\pi$
$41$	0.598076	+	1.03590i	0.0934038	+	0.161780i	−0.815538	+	0.578704i	$0.803559\pi$
$42$		0			0
$43$	5.83013	+	3.36603i	0.889086	+	0.513314i	0.873643	−	0.486567i	$-0.161751\pi$
$43$	5.83013	+	3.36603i	0.889086	+	0.513314i	0.0154426	+	0.999881i	$0.495084\pi$
$44$	−2.73205			−0.411872
$45$		0			0
$46$	2.09808	−	3.63397i	0.309344	−	0.535800i
$47$		−	9.66025i		−	1.40909i	−0.709658	−	0.704546i	$-0.751150\pi$
$47$		−	9.66025i		−	1.40909i	0.709658	−	0.704546i	$-0.248850\pi$
$48$		0			0
$49$	−3.23205	−	5.59808i	−0.461722	−	0.799725i
$50$	−4.00000	−	3.00000i	−0.565685	−	0.424264i
$51$		0			0
$52$	−2.00000	−	3.00000i	−0.277350	−	0.416025i
$53$		−	4.26795i		−	0.586248i	−0.956074	−	0.293124i	$-0.905305\pi$
$53$		−	4.26795i		−	0.586248i	0.956074	−	0.293124i	$-0.0946949\pi$
$54$		0			0
$55$	6.09808	+	0.366025i	0.822264	+	0.0493549i
$56$	−0.366025	+	0.633975i	−0.0489122	+	0.0847184i
$57$		0			0
$58$	−0.401924	−	0.232051i	−0.0527752	−	0.0304698i
$59$	−4.19615	+	7.26795i	−0.546293	+	0.946206i	0.452232	+	0.891900i	$0.350628\pi$
$59$	−4.19615	+	7.26795i	−0.546293	+	0.946206i	−0.998524	+	0.0543060i	$0.982705\pi$
$60$		0			0
$61$	−7.06218	+	12.2321i	−0.904219	+	1.56615i	−0.0822573	+	0.996611i	$0.526213\pi$
$61$	−7.06218	+	12.2321i	−0.904219	+	1.56615i	−0.821962	+	0.569542i	$0.807120\pi$
$62$	3.46410	−	2.00000i	0.439941	−	0.254000i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	4.06218	+	6.96410i	0.503851	+	0.863790i
$66$		0			0
$67$	8.36603	−	4.83013i	1.02207	−	0.590094i	0.107369	−	0.994219i	$-0.465757\pi$
$67$	8.36603	−	4.83013i	1.02207	−	0.590094i	0.914704	+	0.404125i	$0.132424\pi$
$68$	2.13397	−	1.23205i	0.258782	−	0.149408i
$69$		0			0
$70$	0.901924	−	1.36603i	0.107801	−	0.163271i
$71$	2.36603	−	4.09808i	0.280796	−	0.486352i	−0.690785	−	0.723060i	$-0.742735\pi$
$71$	2.36603	−	4.09808i	0.280796	−	0.486352i	0.971581	+	0.236708i	$0.0760684\pi$
$72$		0			0
$73$			12.6603i			1.48177i	0.671632	+	0.740885i	$0.265594\pi$
$73$			12.6603i			1.48177i	−0.671632	+	0.740885i	$0.734406\pi$
$74$	2.96410	−	5.13397i	0.344570	−	0.596812i
$75$		0			0
$76$	−2.36603	−	4.09808i	−0.271402	−	0.470082i
$77$			2.00000i			0.227921i
$78$		0			0
$79$	−12.0000			−1.35011			−0.675053	−	0.737769i	$-0.735879\pi$
$79$	−12.0000			−1.35011			−0.675053	+	0.737769i	$0.735879\pi$
$80$	2.23205	+	0.133975i	0.249551	+	0.0149788i
$81$		0			0
$82$	1.03590	+	0.598076i	0.114396	+	0.0660465i
$83$		−	8.73205i		−	0.958467i	−0.877687	−	0.479234i	$-0.840915\pi$
$83$		−	8.73205i		−	0.958467i	0.877687	−	0.479234i	$-0.159085\pi$
$84$		0			0
$85$	−4.92820	+	2.46410i	−0.534539	+	0.267269i
$86$	6.73205			0.725936
$87$		0			0
$88$	−2.36603	+	1.36603i	−0.252219	+	0.145619i
$89$	−4.46410	−	7.73205i	−0.473194	−	0.819596i	0.526335	−	0.850277i	$-0.323566\pi$
$89$	−4.46410	−	7.73205i	−0.473194	−	0.819596i	−0.999529	+	0.0306813i	$0.990232\pi$
$90$		0			0
$91$	−2.19615	+	1.46410i	−0.230219	+	0.153480i
$92$		−	4.19615i		−	0.437479i
$93$		0			0
$94$	−4.83013	−	8.36603i	−0.498190	−	0.862890i
$95$	4.73205	+	9.46410i	0.485498	+	0.970996i
$96$		0			0
$97$	−8.66025	−	5.00000i	−0.879316	−	0.507673i	−0.00888289	−	0.999961i	$-0.502828\pi$
$97$	−8.66025	−	5.00000i	−0.879316	−	0.507673i	−0.870433	+	0.492287i	$0.836161\pi$
$98$	−5.59808	−	3.23205i	−0.565491	−	0.326486i
$99$		0			0
$100$	−4.96410	−	0.598076i	−0.496410	−	0.0598076i
$101$	0.0358984	+	0.0621778i	0.00357202	+	0.00618692i	0.867806	−	0.496903i	$-0.165530\pi$
$101$	0.0358984	+	0.0621778i	0.00357202	+	0.00618692i	−0.864234	+	0.503090i	$0.832196\pi$
$102$		0			0
$103$			12.7321i			1.25453i	0.778807	+	0.627263i	$0.215825\pi$
$103$			12.7321i			1.25453i	−0.778807	+	0.627263i	$0.784175\pi$
$104$	−3.23205	−	1.59808i	−0.316929	−	0.156704i
$105$		0			0
$106$	−2.13397	−	3.69615i	−0.207270	−	0.359002i
$107$	4.09808	−	2.36603i	0.396176	−	0.228732i	−0.288657	−	0.957433i	$-0.593209\pi$
$107$	4.09808	−	2.36603i	0.396176	−	0.228732i	0.684833	+	0.728700i	$0.259875\pi$
$108$		0			0
$109$	−10.0000			−0.957826			−0.478913	−	0.877862i	$-0.658969\pi$
$109$	−10.0000			−0.957826			−0.478913	+	0.877862i	$0.658969\pi$
$110$	5.46410	−	2.73205i	0.520982	−	0.260491i
$111$		0			0
$112$			0.732051i			0.0691723i
$113$	7.79423	+	4.50000i	0.733219	+	0.423324i	0.819599	−	0.572938i	$-0.194196\pi$
$113$	7.79423	+	4.50000i	0.733219	+	0.423324i	−0.0863794	+	0.996262i	$0.527530\pi$
$114$		0			0
$115$	−0.562178	+	9.36603i	−0.0524234	+	0.873386i
$116$	−0.464102			−0.0430908
$117$		0			0
$118$			8.39230i			0.772574i
$119$	−0.901924	−	1.56218i	−0.0826792	−	0.143205i
$120$		0			0
$121$	1.76795	−	3.06218i	0.160723	−	0.278380i
$122$			14.1244i			1.27876i
$123$		0			0
$124$	2.00000	−	3.46410i	0.179605	−	0.311086i
$125$	11.0000	+	2.00000i	0.983870	+	0.178885i
$126$		0			0
$127$	−3.46410	+	2.00000i	−0.307389	+	0.177471i	−0.645758	−	0.763542i	$-0.723458\pi$
$127$	−3.46410	+	2.00000i	−0.307389	+	0.177471i	0.338368	+	0.941014i	$0.390125\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	7.00000	+	4.00000i	0.613941	+	0.350823i
$131$	−13.8564			−1.21064			−0.605320	−	0.795982i	$-0.706955\pi$
$131$	−13.8564			−1.21064			−0.605320	+	0.795982i	$0.706955\pi$
$132$		0			0
$133$	−3.00000	+	1.73205i	−0.260133	+	0.150188i
$134$	4.83013	−	8.36603i	0.417259	−	0.722715i
$135$		0			0
$136$	1.23205	−	2.13397i	0.105647	−	0.182987i
$137$	−9.99038	−	5.76795i	−0.853536	−	0.492789i	0.00830645	−	0.999966i	$-0.497356\pi$
$137$	−9.99038	−	5.76795i	−0.853536	−	0.492789i	−0.861842	+	0.507176i	$0.830689\pi$
$138$		0			0
$139$	−7.46410	+	12.9282i	−0.633097	+	1.09656i	0.353818	+	0.935314i	$0.384883\pi$
$139$	−7.46410	+	12.9282i	−0.633097	+	1.09656i	−0.986915	+	0.161242i	$0.948450\pi$
$140$	0.0980762	−	1.63397i	0.00828895	−	0.138096i
$141$		0			0
$142$		−	4.73205i		−	0.397105i
$143$	−9.83013	+	0.633975i	−0.822037	+	0.0530156i
$144$		0			0
$145$	1.03590	+	0.0621778i	0.0860267	+	0.00516359i
$146$	6.33013	+	10.9641i	0.523885	+	0.907396i
$147$		0			0
$148$		−	5.92820i		−	0.487295i
$149$	−3.03590	+	5.25833i	−0.248710	+	0.430779i	−0.963168	−	0.268899i	$-0.913340\pi$
$149$	−3.03590	+	5.25833i	−0.248710	+	0.430779i	0.714458	+	0.699679i	$0.246673\pi$
$150$		0			0
$151$	19.1244			1.55632			0.778159	−	0.628067i	$-0.216154\pi$
$151$	19.1244			1.55632			0.778159	+	0.628067i	$0.216154\pi$
$152$	−4.09808	−	2.36603i	−0.332398	−	0.191910i
$153$		0			0
$154$	1.00000	+	1.73205i	0.0805823	+	0.139573i
$155$	−4.92820	+	7.46410i	−0.395843	+	0.599531i
$156$		0			0
$157$			11.3923i			0.909205i	0.890694	+	0.454602i	$0.150219\pi$
$157$			11.3923i			0.909205i	−0.890694	+	0.454602i	$0.849781\pi$
$158$	−10.3923	+	6.00000i	−0.826767	+	0.477334i
$159$		0			0
$160$	2.00000	−	1.00000i	0.158114	−	0.0790569i
$161$	−3.07180			−0.242092
$162$		0			0
$163$	5.66025	+	3.26795i	0.443345	+	0.255966i	0.705016	−	0.709192i	$-0.250940\pi$
$163$	5.66025	+	3.26795i	0.443345	+	0.255966i	−0.261670	+	0.965157i	$0.584273\pi$
$164$	1.19615			0.0934038
$165$		0			0
$166$	−4.36603	−	7.56218i	−0.338869	−	0.586939i
$167$	12.0000	−	6.92820i	0.928588	−	0.536120i	0.0422232	−	0.999108i	$-0.486556\pi$
$167$	12.0000	−	6.92820i	0.928588	−	0.536120i	0.886365	+	0.462988i	$0.153223\pi$
$168$		0			0
$169$	−7.89230	−	10.3301i	−0.607100	−	0.794625i
$170$	−3.03590	+	4.59808i	−0.232843	+	0.352656i
$171$		0			0
$172$	5.83013	−	3.36603i	0.444543	−	0.256657i
$173$	19.7321	+	11.3923i	1.50020	+	0.866141i	1.00000		0.000231036i	$7.35409e-5\pi$
$173$	19.7321	+	11.3923i	1.50020	+	0.866141i	0.500200	+	0.865910i	$0.333260\pi$
$174$		0			0
$175$	−0.437822	+	3.63397i	−0.0330962	+	0.274703i
$176$	−1.36603	+	2.36603i	−0.102968	+	0.178346i
$177$		0			0
$178$	−7.73205	−	4.46410i	−0.579542	−	0.334599i
$179$	−3.90192	−	6.75833i	−0.291643	−	0.505141i	0.682555	−	0.730834i	$-0.260869\pi$
$179$	−3.90192	−	6.75833i	−0.291643	−	0.505141i	−0.974199	+	0.225693i	$0.927535\pi$
$180$		0			0
$181$	8.12436			0.603879			0.301939	−	0.953327i	$-0.402366\pi$
$181$	8.12436			0.603879			0.301939	+	0.953327i	$0.402366\pi$
$182$	−1.16987	+	2.36603i	−0.0867168	+	0.175381i
$183$		0			0
$184$	−2.09808	−	3.63397i	−0.154672	−	0.267900i
$185$	−0.794229	+	13.2321i	−0.0583929	+	0.972840i
$186$		0			0
$187$		−	6.73205i		−	0.492296i
$188$	−8.36603	−	4.83013i	−0.610155	−	0.352273i
$189$		0			0
$190$	8.83013	+	5.83013i	0.640605	+	0.422962i
$191$	−1.26795	+	2.19615i	−0.0917456	+	0.158908i	−0.908246	−	0.418437i	$-0.862578\pi$
$191$	−1.26795	+	2.19615i	−0.0917456	+	0.158908i	0.816500	+	0.577345i	$0.195911\pi$
$192$		0			0
$193$	5.76795	−	3.33013i	0.415186	−	0.239708i	−0.277830	−	0.960630i	$-0.589615\pi$
$193$	5.76795	−	3.33013i	0.415186	−	0.239708i	0.693016	+	0.720923i	$0.256282\pi$
$194$	−10.0000			−0.717958
$195$		0			0
$196$	−6.46410			−0.461722
$197$	−15.4641	+	8.92820i	−1.10177	+	0.636108i	−0.936686	−	0.350171i	$-0.886123\pi$
$197$	−15.4641	+	8.92820i	−1.10177	+	0.636108i	−0.165086	+	0.986279i	$0.552790\pi$
$198$		0			0
$199$	5.02628	−	8.70577i	0.356304	−	0.617136i	−0.631037	−	0.775753i	$-0.717370\pi$
$199$	5.02628	−	8.70577i	0.356304	−	0.617136i	0.987340	+	0.158617i	$0.0507036\pi$
$200$	−4.59808	+	1.96410i	−0.325133	+	0.138883i
$201$		0			0
$202$	0.0621778	+	0.0358984i	0.00437482	+	0.00252580i
$203$			0.339746i			0.0238455i
$204$		0			0
$205$	−2.66987	−	0.160254i	−0.186472	−	0.0111926i
$206$	6.36603	+	11.0263i	0.443542	+	0.768237i
$207$		0			0
$208$	−3.59808	+	0.232051i	−0.249482	+	0.0160898i
$209$	−12.9282			−0.894263
$210$		0			0
$211$	7.26795	+	12.5885i	0.500346	+	0.866625i	1.00000		0.000399869i	$0.000127282\pi$
$211$	7.26795	+	12.5885i	0.500346	+	0.866625i	−0.499654	+	0.866225i	$0.666539\pi$
$212$	−3.69615	−	2.13397i	−0.253853	−	0.146562i
$213$		0			0
$214$	2.36603	−	4.09808i	0.161738	−	0.280139i
$215$	−13.4641	+	6.73205i	−0.918244	+	0.459122i
$216$		0			0
$217$	−2.53590	−	1.46410i	−0.172148	−	0.0993897i
$218$	−8.66025	+	5.00000i	−0.586546	+	0.338643i
$219$		0			0
$220$	3.36603	−	5.09808i	0.226937	−	0.343712i
$221$	7.39230	−	4.92820i	0.497260	−	0.331507i
$222$		0			0
$223$	17.6603	−	10.1962i	1.18262	−	0.682785i	0.225999	−	0.974127i	$-0.427435\pi$
$223$	17.6603	−	10.1962i	1.18262	−	0.682785i	0.956619	+	0.291343i	$0.0941020\pi$
$224$	0.366025	+	0.633975i	0.0244561	+	0.0423592i
$225$		0			0
$226$	9.00000			0.598671
$227$	−5.36603	−	3.09808i	−0.356156	−	0.205627i	0.311237	−	0.950332i	$-0.399257\pi$
$227$	−5.36603	−	3.09808i	−0.356156	−	0.205627i	−0.667393	+	0.744706i	$0.732590\pi$
$228$		0			0
$229$	12.7846			0.844831			0.422415	−	0.906402i	$-0.361182\pi$
$229$	12.7846			0.844831			0.422415	+	0.906402i	$0.361182\pi$
$230$	4.19615	+	8.39230i	0.276686	+	0.553372i
$231$		0			0
$232$	−0.401924	+	0.232051i	−0.0263876	+	0.0152349i
$233$			8.39230i			0.549798i	0.961473	+	0.274899i	$0.0886444\pi$
$233$			8.39230i			0.549798i	−0.961473	+	0.274899i	$0.911356\pi$
$234$		0			0
$235$	18.0263	+	11.9019i	1.17590	+	0.776396i
$236$	4.19615	+	7.26795i	0.273146	+	0.473103i
$237$		0			0
$238$	−1.56218	−	0.901924i	−0.101261	−	0.0584630i
$239$	26.5885			1.71986			0.859932	−	0.510408i	$-0.170506\pi$
$239$	26.5885			1.71986			0.859932	+	0.510408i	$0.170506\pi$
$240$		0			0
$241$	−5.69615	+	9.86603i	−0.366921	+	0.635527i	−0.989083	−	0.147363i	$-0.952922\pi$
$241$	−5.69615	+	9.86603i	−0.366921	+	0.635527i	0.622161	+	0.782889i	$0.286255\pi$
$242$		−	3.53590i		−	0.227296i
$243$		0			0
$244$	7.06218	+	12.2321i	0.452110	+	0.783077i
$245$	14.4282	+	0.866025i	0.921784	+	0.0553283i
$246$		0			0
$247$	−9.46410	−	14.1962i	−0.602186	−	0.903280i
$248$		−	4.00000i		−	0.254000i
$249$		0			0
$250$	10.5263	−	3.76795i	0.665740	−	0.238306i
$251$	−7.26795	+	12.5885i	−0.458749	+	0.794576i	−0.998895	−	0.0469948i	$-0.985036\pi$
$251$	−7.26795	+	12.5885i	−0.458749	+	0.794576i	0.540146	+	0.841571i	$0.318369\pi$
$252$		0			0
$253$	−9.92820	−	5.73205i	−0.624181	−	0.360371i
$254$	−2.00000	+	3.46410i	−0.125491	+	0.217357i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−2.59808	+	1.50000i	−0.162064	+	0.0935674i	−0.578838	−	0.815442i	$-0.696494\pi$
$257$	−2.59808	+	1.50000i	−0.162064	+	0.0935674i	0.416775	+	0.909010i	$0.363160\pi$
$258$		0			0
$259$	−4.33975			−0.269659
$260$	8.06218	−	0.0358984i	0.499995	−	0.00222632i
$261$		0			0
$262$	−12.0000	+	6.92820i	−0.741362	+	0.428026i
$263$	−6.16987	+	3.56218i	−0.380451	+	0.219653i	−0.678014	−	0.735049i	$-0.737159\pi$
$263$	−6.16987	+	3.56218i	−0.380451	+	0.219653i	0.297564	+	0.954702i	$0.403826\pi$
$264$		0			0
$265$	7.96410	+	5.25833i	0.489231	+	0.323017i
$266$	−1.73205	+	3.00000i	−0.106199	+	0.183942i
$267$		0			0
$268$		−	9.66025i		−	0.590094i
$269$	8.19615	−	14.1962i	0.499728	−	0.865555i	−0.500272	−	0.865868i	$-0.666767\pi$
$269$	8.19615	−	14.1962i	0.499728	−	0.865555i	1.00000		0.000313781i	$9.98796e-5\pi$
$270$		0			0
$271$	10.9282	+	18.9282i	0.663841	+	1.14981i	0.979598	+	0.200966i	$0.0644082\pi$
$271$	10.9282	+	18.9282i	0.663841	+	1.14981i	−0.315757	+	0.948840i	$0.602258\pi$
$272$		−	2.46410i		−	0.149408i
$273$		0			0
$274$	−11.5359			−0.696909
$275$	−8.19615	+	10.9282i	−0.494247	+	0.658995i
$276$		0			0
$277$	−19.3301	−	11.1603i	−1.16143	−	0.670555i	−0.209787	−	0.977747i	$-0.567277\pi$
$277$	−19.3301	−	11.1603i	−1.16143	−	0.670555i	−0.951647	+	0.307192i	$0.900610\pi$
$278$			14.9282i			0.895334i
$279$		0			0
$280$	−0.732051	−	1.46410i	−0.0437484	−	0.0874968i
$281$	1.73205			0.103325			0.0516627	−	0.998665i	$-0.483548\pi$
$281$	1.73205			0.103325			0.0516627	+	0.998665i	$0.483548\pi$
$282$		0			0
$283$	−8.36603	+	4.83013i	−0.497309	+	0.287121i	−0.727601	−	0.686000i	$-0.759365\pi$
$283$	−8.36603	+	4.83013i	−0.497309	+	0.287121i	0.230293	+	0.973121i	$0.426032\pi$
$284$	−2.36603	−	4.09808i	−0.140398	−	0.243176i
$285$		0			0
$286$	−8.19615	+	5.46410i	−0.484649	+	0.323099i
$287$		−	0.875644i		−	0.0516877i
$288$		0			0
$289$	−5.46410	−	9.46410i	−0.321418	−	0.556712i
$290$	0.928203	−	0.464102i	0.0545060	−	0.0272530i
$291$		0			0
$292$	10.9641	+	6.33013i	0.641626	+	0.370443i
$293$	8.89230	+	5.13397i	0.519494	+	0.299930i	0.736728	−	0.676190i	$-0.236370\pi$
$293$	8.89230	+	5.13397i	0.519494	+	0.299930i	−0.217234	+	0.976120i	$0.569703\pi$
$294$		0			0
$295$	−8.39230	−	16.7846i	−0.488619	−	0.977238i
$296$	−2.96410	−	5.13397i	−0.172285	−	0.298406i
$297$		0			0
$298$			6.07180i			0.351730i
$299$	−0.973721	−	15.0981i	−0.0563117	−	0.873144i
$300$		0			0
$301$	−2.46410	−	4.26795i	−0.142028	−	0.246001i
$302$	16.5622	−	9.56218i	0.953046	−	0.550242i
$303$		0			0
$304$	−4.73205			−0.271402
$305$	−14.1244	−	28.2487i	−0.808758	−	1.61752i
$306$		0			0
$307$			22.7321i			1.29739i	0.761050	+	0.648693i	$0.224684\pi$
$307$			22.7321i			1.29739i	−0.761050	+	0.648693i	$0.775316\pi$
$308$	1.73205	+	1.00000i	0.0986928	+	0.0569803i
$309$		0			0
$310$	−0.535898	+	8.92820i	−0.0304370	+	0.507088i
$311$	21.1244			1.19785			0.598926	−	0.800804i	$-0.295594\pi$
$311$	21.1244			1.19785			0.598926	+	0.800804i	$0.295594\pi$
$312$		0			0
$313$		−	14.0000i		−	0.791327i	−0.918396	−	0.395663i	$-0.870515\pi$
$313$		−	14.0000i		−	0.791327i	0.918396	−	0.395663i	$-0.129485\pi$
$314$	5.69615	+	9.86603i	0.321452	+	0.556772i
$315$		0			0
$316$	−6.00000	+	10.3923i	−0.337526	+	0.584613i
$317$			26.2679i			1.47536i	0.675153	+	0.737678i	$0.264077\pi$
$317$			26.2679i			1.47536i	−0.675153	+	0.737678i	$0.735923\pi$
$318$		0			0
$319$	−0.633975	+	1.09808i	−0.0354958	+	0.0614805i
$320$	1.23205	−	1.86603i	0.0688737	−	0.104314i
$321$		0			0
$322$	−2.66025	+	1.53590i	−0.148250	+	0.0855923i
$323$	10.0981	−	5.83013i	0.561872	−	0.324397i
$324$		0			0
$325$	−18.0000	−	1.00000i	−0.998460	−	0.0554700i
$326$	6.53590			0.361990
$327$		0			0
$328$	1.03590	−	0.598076i	0.0571979	−	0.0330232i
$329$	−3.53590	+	6.12436i	−0.194940	+	0.337647i
$330$		0			0
$331$	−6.39230	+	11.0718i	−0.351353	+	0.608561i	−0.986487	−	0.163841i	$-0.947612\pi$
$331$	−6.39230	+	11.0718i	−0.351353	+	0.608561i	0.635134	+	0.772402i	$0.280945\pi$
$332$	−7.56218	−	4.36603i	−0.415028	−	0.239617i
$333$		0			0
$334$	6.92820	−	12.0000i	0.379094	−	0.656611i
$335$	−1.29423	+	21.5622i	−0.0707113	+	1.17807i
$336$		0			0
$337$			27.0526i			1.47365i	0.676085	+	0.736823i	$0.263675\pi$
$337$			27.0526i			1.47365i	−0.676085	+	0.736823i	$0.736325\pi$
$338$	−12.0000	−	5.00000i	−0.652714	−	0.271964i
$339$		0			0
$340$	−0.330127	+	5.50000i	−0.0179037	+	0.298279i
$341$	−5.46410	−	9.46410i	−0.295898	−	0.512510i
$342$		0			0
$343$			9.85641i			0.532196i
$344$	3.36603	−	5.83013i	0.181484	−	0.314339i
$345$		0			0
$346$	22.7846			1.22491
$347$	−10.0981	−	5.83013i	−0.542093	−	0.312978i	0.203834	−	0.979006i	$-0.434660\pi$
$347$	−10.0981	−	5.83013i	−0.542093	−	0.312978i	−0.745927	+	0.666028i	$0.767993\pi$
$348$		0			0
$349$	−16.4641	−	28.5167i	−0.881303	−	1.52646i	−0.849893	−	0.526955i	$-0.823334\pi$
$349$	−16.4641	−	28.5167i	−0.881303	−	1.52646i	−0.0314101	−	0.999507i	$-0.510000\pi$
$350$	1.43782	+	3.36603i	0.0768548	+	0.179922i
$351$		0			0
$352$			2.73205i			0.145619i
$353$	−20.1340	+	11.6244i	−1.07162	+	0.618702i	−0.928625	−	0.371021i	$-0.879008\pi$
$353$	−20.1340	+	11.6244i	−1.07162	+	0.618702i	−0.142999	+	0.989723i	$0.545675\pi$
$354$		0			0
$355$	4.73205	+	9.46410i	0.251151	+	0.502302i
$356$	−8.92820			−0.473194
$357$		0			0
$358$	−6.75833	−	3.90192i	−0.357189	−	0.206223i
$359$	33.1244			1.74824			0.874118	−	0.485713i	$-0.161440\pi$
$359$	33.1244			1.74824			0.874118	+	0.485713i	$0.161440\pi$
$360$		0			0
$361$	−1.69615	−	2.93782i	−0.0892712	−	0.154622i
$362$	7.03590	−	4.06218i	0.369799	−	0.213503i
$363$		0			0
$364$	0.169873	+	2.63397i	0.00890376	+	0.138058i
$365$	−23.6244	−	15.5981i	−1.23656	−	0.816441i
$366$		0			0
$367$	16.4378	−	9.49038i	0.858047	−	0.495394i	−0.00531057	−	0.999986i	$-0.501690\pi$
$367$	16.4378	−	9.49038i	0.858047	−	0.495394i	0.863358	+	0.504592i	$0.168357\pi$
$368$	−3.63397	−	2.09808i	−0.189434	−	0.109370i
$369$		0			0
$370$	5.92820	+	11.8564i	0.308193	+	0.616385i
$371$	−1.56218	+	2.70577i	−0.0811042	+	0.140477i
$372$		0			0
$373$	−26.3827	−	15.2321i	−1.36604	−	0.788686i	−0.375624	−	0.926772i	$-0.622571\pi$
$373$	−26.3827	−	15.2321i	−1.36604	−	0.788686i	−0.990420	+	0.138087i	$0.955905\pi$
$374$	−3.36603	−	5.83013i	−0.174053	−	0.301469i
$375$		0			0
$376$	−9.66025			−0.498190
$377$	−1.66987	+	0.107695i	−0.0860028	+	0.00554658i
$378$		0			0
$379$	−11.1244	−	19.2679i	−0.571420	−	0.989728i	−0.996421	−	0.0845351i	$-0.973060\pi$
$379$	−11.1244	−	19.2679i	−0.571420	−	0.989728i	0.425001	−	0.905193i	$-0.360274\pi$
$380$	10.5622	+	0.633975i	0.541828	+	0.0325222i
$381$		0			0
$382$			2.53590i			0.129748i
$383$	11.3205	+	6.53590i	0.578451	+	0.333969i	0.760518	−	0.649317i	$-0.224945\pi$
$383$	11.3205	+	6.53590i	0.578451	+	0.333969i	−0.182067	+	0.983286i	$0.558279\pi$
$384$		0			0
$385$	−3.73205	−	2.46410i	−0.190203	−	0.125582i
$386$	3.33013	−	5.76795i	0.169499	−	0.293581i
$387$		0			0
$388$	−8.66025	+	5.00000i	−0.439658	+	0.253837i
$389$	−37.9282			−1.92304			−0.961518	−	0.274742i	$-0.911408\pi$
$389$	−37.9282			−1.92304			−0.961518	+	0.274742i	$0.911408\pi$
$390$		0			0
$391$	10.3397			0.522903
$392$	−5.59808	+	3.23205i	−0.282746	+	0.163243i
$393$		0			0
$394$	−8.92820	+	15.4641i	−0.449796	+	0.779070i
$395$	14.7846	−	22.3923i	0.743894	−	1.12668i
$396$		0			0
$397$	13.2679	+	7.66025i	0.665899	+	0.384457i	0.794521	−	0.607237i	$-0.207722\pi$
$397$	13.2679	+	7.66025i	0.665899	+	0.384457i	−0.128622	+	0.991694i	$0.541055\pi$
$398$		−	10.0526i		−	0.503889i
$399$		0			0
$400$	−3.00000	+	4.00000i	−0.150000	+	0.200000i
$401$	14.5263	+	25.1603i	0.725408	+	1.25644i	0.958806	+	0.284062i	$0.0916821\pi$
$401$	14.5263	+	25.1603i	0.725408	+	1.25644i	−0.233398	+	0.972381i	$0.574985\pi$
$402$		0			0
$403$	6.39230	−	12.9282i	0.318423	−	0.644000i
$404$	0.0717968			0.00357202
$405$		0			0
$406$	0.169873	+	0.294229i	0.00843065	+	0.0146023i
$407$	−14.0263	−	8.09808i	−0.695257	−	0.401407i
$408$		0			0
$409$	14.9641	−	25.9186i	0.739927	−	1.28159i	−0.212600	−	0.977139i	$-0.568193\pi$
$409$	14.9641	−	25.9186i	0.739927	−	1.28159i	0.952528	−	0.304452i	$-0.0984734\pi$
$410$	−2.39230	+	1.19615i	−0.118148	+	0.0590738i
$411$		0			0
$412$	11.0263	+	6.36603i	0.543226	+	0.313632i
$413$	5.32051	−	3.07180i	0.261805	−	0.151153i
$414$		0			0
$415$	16.2942	+	10.7583i	0.799852	+	0.528106i
$416$	−3.00000	+	2.00000i	−0.147087	+	0.0980581i
$417$		0			0
$418$	−11.1962	+	6.46410i	−0.547622	+	0.316170i
$419$	6.73205	+	11.6603i	0.328882	+	0.569641i	0.982290	−	0.187365i	$-0.0599948\pi$
$419$	6.73205	+	11.6603i	0.328882	+	0.569641i	−0.653408	+	0.757006i	$0.726661\pi$
$420$		0			0
$421$	−21.0526			−1.02604			−0.513019	−	0.858377i	$-0.671473\pi$
$421$	−21.0526			−1.02604			−0.513019	+	0.858377i	$0.671473\pi$
$422$	12.5885	+	7.26795i	0.612797	+	0.353798i
$423$		0			0
$424$	−4.26795			−0.207270
$425$	1.47372	−	12.2321i	0.0714859	−	0.593342i
$426$		0			0
$427$	8.95448	−	5.16987i	0.433338	−	0.250188i
$428$		−	4.73205i		−	0.228732i
$429$		0			0
$430$	−8.29423	+	12.5622i	−0.399983	+	0.605802i
$431$	−9.09808	−	15.7583i	−0.438239	−	0.759052i	0.559315	−	0.828955i	$-0.311064\pi$
$431$	−9.09808	−	15.7583i	−0.438239	−	0.759052i	−0.997554	+	0.0699032i	$0.977731\pi$
$432$		0			0
$433$	21.8205	+	12.5981i	1.04863	+	0.605425i	0.922265	−	0.386559i	$-0.126337\pi$
$433$	21.8205	+	12.5981i	1.04863	+	0.605425i	0.126362	+	0.991984i	$0.459670\pi$
$434$	−2.92820			−0.140558
$435$		0			0
$436$	−5.00000	+	8.66025i	−0.239457	+	0.414751i
$437$		−	19.8564i		−	0.949861i
$438$		0			0
$439$	10.0981	+	17.4904i	0.481955	+	0.834770i	0.999785	−	0.0207128i	$-0.00659358\pi$
$439$	10.0981	+	17.4904i	0.481955	+	0.834770i	−0.517831	+	0.855483i	$0.673260\pi$
$440$	0.366025	−	6.09808i	0.0174496	−	0.290714i
$441$		0			0
$442$	3.93782	−	7.96410i	0.187303	−	0.378814i
$443$			34.6410i			1.64584i	0.568154	+	0.822922i	$0.307658\pi$
$443$			34.6410i			1.64584i	−0.568154	+	0.822922i	$0.692342\pi$
$444$		0			0
$445$	19.9282	+	1.19615i	0.944687	+	0.0567031i
$446$	10.1962	−	17.6603i	0.482802	−	0.836237i
$447$		0			0
$448$	0.633975	+	0.366025i	0.0299525	+	0.0172931i
$449$	−9.92820	+	17.1962i	−0.468541	+	0.811537i	−0.999353	−	0.0359526i	$-0.988553\pi$
$449$	−9.92820	+	17.1962i	−0.468541	+	0.811537i	0.530813	+	0.847489i	$0.321887\pi$
$450$		0			0
$451$	1.63397	−	2.83013i	0.0769409	−	0.133265i
$452$	7.79423	−	4.50000i	0.366610	−	0.211662i
$453$		0			0
$454$	−6.19615			−0.290800
$455$	−0.0262794	−	5.90192i	−0.00123200	−	0.276686i
$456$		0			0
$457$	16.6244	−	9.59808i	0.777655	−	0.448979i	−0.0579439	−	0.998320i	$-0.518454\pi$
$457$	16.6244	−	9.59808i	0.777655	−	0.448979i	0.835598	+	0.549341i	$0.185121\pi$
$458$	11.0718	−	6.39230i	0.517351	−	0.298693i
$459$		0			0
$460$	7.83013	+	5.16987i	0.365082	+	0.241047i
$461$	19.9641	−	34.5788i	0.929821	−	1.61050i	0.146202	−	0.989255i	$-0.453295\pi$
$461$	19.9641	−	34.5788i	0.929821	−	1.61050i	0.783618	−	0.621242i	$-0.213372\pi$
$462$		0			0
$463$		−	23.6603i		−	1.09959i	−0.835301	−	0.549793i	$-0.814707\pi$
$463$		−	23.6603i		−	1.09959i	0.835301	−	0.549793i	$-0.185293\pi$
$464$	−0.232051	+	0.401924i	−0.0107727	+	0.0186588i
$465$		0			0
$466$	4.19615	+	7.26795i	0.194383	+	0.336681i
$467$			16.0526i			0.742824i	0.928468	+	0.371412i	$0.121126\pi$
$467$			16.0526i			0.742824i	−0.928468	+	0.371412i	$0.878874\pi$
$468$		0			0
$469$	−7.07180			−0.326545
$470$	21.5622	+	1.29423i	0.994589	+	0.0596983i
$471$		0			0
$472$	7.26795	+	4.19615i	0.334534	+	0.193144i
$473$		−	18.3923i		−	0.845679i
$474$		0			0
$475$	−23.4904	−	2.83013i	−1.07781	−	0.129855i
$476$	−1.80385			−0.0826792
$477$		0			0
$478$	23.0263	−	13.2942i	1.05320	−	0.608064i
$479$	8.00000	+	13.8564i	0.365529	+	0.633115i	0.988861	−	0.148842i	$-0.0475547\pi$
$479$	8.00000	+	13.8564i	0.365529	+	0.633115i	−0.623332	+	0.781958i	$0.714221\pi$
$480$		0			0
$481$	−1.37564	−	21.3301i	−0.0627240	−	0.972570i
$482$			11.3923i			0.518905i
$483$		0			0
$484$	−1.76795	−	3.06218i	−0.0803613	−	0.139190i
$485$	20.0000	−	10.0000i	0.908153	−	0.454077i
$486$		0			0
$487$	−17.7058	−	10.2224i	−0.802325	−	0.463223i	0.0419584	−	0.999119i	$-0.486640\pi$
$487$	−17.7058	−	10.2224i	−0.802325	−	0.463223i	−0.844284	+	0.535897i	$0.819974\pi$
$488$	12.2321	+	7.06218i	0.553719	+	0.319690i
$489$		0			0
$490$	12.9282	−	6.46410i	0.584037	−	0.292018i
$491$	16.0981	+	27.8827i	0.726496	+	1.25833i	0.958355	+	0.285579i	$0.0921858\pi$
$491$	16.0981	+	27.8827i	0.726496	+	1.25833i	−0.231859	+	0.972749i	$0.574481\pi$
$492$		0			0
$493$		−	1.14359i		−	0.0515049i
$494$	−15.2942	−	7.56218i	−0.688120	−	0.340238i
$495$		0			0
$496$	−2.00000	−	3.46410i	−0.0898027	−	0.155543i
$497$	−3.00000	+	1.73205i	−0.134568	+	0.0776931i
$498$		0			0
$499$	−19.6077			−0.877761			−0.438880	−	0.898545i	$-0.644625\pi$
$499$	−19.6077			−0.877761			−0.438880	+	0.898545i	$0.644625\pi$
$500$	7.23205	−	8.52628i	0.323427	−	0.381307i
$501$		0			0
$502$			14.5359i			0.648769i
$503$	27.8827	+	16.0981i	1.24323	+	0.717778i	0.969750	−	0.244101i	$-0.0784927\pi$
$503$	27.8827	+	16.0981i	1.24323	+	0.717778i	0.273478	+	0.961878i	$0.411826\pi$
$504$		0			0
$505$	−0.160254	−	0.00961894i	−0.00713121	−	0.000428037i
$506$	−11.4641			−0.509641
$507$		0			0
$508$			4.00000i			0.177471i
$509$	−12.3564	−	21.4019i	−0.547688	−	0.948624i	−0.998432	−	0.0559705i	$-0.982175\pi$
$509$	−12.3564	−	21.4019i	−0.547688	−	0.948624i	0.450744	−	0.892653i	$-0.351159\pi$
$510$		0			0
$511$	4.63397	−	8.02628i	0.204995	−	0.355062i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−1.50000	+	2.59808i	−0.0661622	+	0.114596i
$515$	−23.7583	−	15.6865i	−1.04692	−	0.691231i
$516$		0			0
$517$	−22.8564	+	13.1962i	−1.00522	+	0.580366i
$518$	−3.75833	+	2.16987i	−0.165132	+	0.0953387i
$519$		0			0
$520$	6.96410	−	4.06218i	0.305396	−	0.178138i
$521$	−39.4449			−1.72811			−0.864055	−	0.503397i	$-0.832083\pi$
$521$	−39.4449			−1.72811			−0.864055	+	0.503397i	$0.832083\pi$
$522$		0			0
$523$	19.4378	−	11.2224i	0.849957	−	0.490723i	−0.0106796	−	0.999943i	$-0.503399\pi$
$523$	19.4378	−	11.2224i	0.849957	−	0.490723i	0.860636	+	0.509220i	$0.170066\pi$
$524$	−6.92820	+	12.0000i	−0.302660	+	0.524222i
$525$		0			0
$526$	−3.56218	+	6.16987i	−0.155318	+	0.269019i
$527$	8.53590	+	4.92820i	0.371830	+	0.214676i
$528$		0			0
$529$	−2.69615	+	4.66987i	−0.117224	+	0.203038i
$530$	9.52628	+	0.571797i	0.413795	+	0.0248373i
$531$		0			0
$532$			3.46410i			0.150188i
$533$	4.30385	−	0.277568i	0.186420	−	0.0120228i
$534$		0			0
$535$	−0.633975	+	10.5622i	−0.0274091	+	0.456643i
$536$	−4.83013	−	8.36603i	−0.208630	−	0.361357i
$537$		0			0
$538$		−	16.3923i		−	0.706722i
$539$	−8.83013	+	15.2942i	−0.380340	+	0.658769i
$540$		0			0
$541$	9.19615			0.395373			0.197687	−	0.980265i	$-0.436657\pi$
$541$	9.19615			0.395373			0.197687	+	0.980265i	$0.436657\pi$
$542$	18.9282	+	10.9282i	0.813036	+	0.469407i
$543$		0			0
$544$	−1.23205	−	2.13397i	−0.0528237	−	0.0914934i
$545$	12.3205	−	18.6603i	0.527753	−	0.799317i
$546$		0			0
$547$		−	36.1962i		−	1.54764i	−0.633408	−	0.773818i	$-0.718345\pi$
$547$		−	36.1962i		−	1.54764i	0.633408	−	0.773818i	$-0.281655\pi$
$548$	−9.99038	+	5.76795i	−0.426768	+	0.246395i
$549$		0			0
$550$	−1.63397	+	13.5622i	−0.0696729	+	0.578293i
$551$	−2.19615			−0.0935592
$552$		0			0
$553$	7.60770	+	4.39230i	0.323512	+	0.186780i
$554$	−22.3205			−0.948308
$555$		0			0
$556$	7.46410	+	12.9282i	0.316548	+	0.548278i
$557$	2.30385	−	1.33013i	0.0976172	−	0.0563593i	−0.450397	−	0.892829i	$-0.648717\pi$
$557$	2.30385	−	1.33013i	0.0976172	−	0.0563593i	0.548014	+	0.836469i	$0.315384\pi$
$558$		0			0
$559$	20.1962	−	13.4641i	0.854206	−	0.569471i
$560$	−1.36603	−	0.901924i	−0.0577251	−	0.0381132i
$561$		0			0
$562$	1.50000	−	0.866025i	0.0632737	−	0.0365311i
$563$	6.92820	+	4.00000i	0.291989	+	0.168580i	0.638838	−	0.769341i	$-0.279415\pi$
$563$	6.92820	+	4.00000i	0.291989	+	0.168580i	−0.346850	+	0.937921i	$0.612749\pi$
$564$		0			0
$565$	−18.0000	+	9.00000i	−0.757266	+	0.378633i
$566$	−4.83013	+	8.36603i	−0.203025	+	0.351650i
$567$		0			0
$568$	−4.09808	−	2.36603i	−0.171951	−	0.0992762i
$569$	−22.9282	−	39.7128i	−0.961200	−	1.66485i	−0.719494	−	0.694498i	$-0.755626\pi$
$569$	−22.9282	−	39.7128i	−0.961200	−	1.66485i	−0.241706	−	0.970350i	$-0.577707\pi$
$570$		0			0
$571$	−8.33975			−0.349008			−0.174504	−	0.984657i	$-0.555832\pi$
$571$	−8.33975			−0.349008			−0.174504	+	0.984657i	$0.555832\pi$
$572$	−4.36603	+	8.83013i	−0.182553	+	0.369206i
$573$		0			0
$574$	−0.437822	−	0.758330i	−0.0182743	−	0.0316521i
$575$	−16.7846	−	12.5885i	−0.699967	−	0.524975i
$576$		0			0
$577$			27.9808i			1.16485i	0.812883	+	0.582427i	$0.197897\pi$
$577$			27.9808i			1.16485i	−0.812883	+	0.582427i	$0.802103\pi$
$578$	−9.46410	−	5.46410i	−0.393655	−	0.227277i
$579$		0			0
$580$	0.571797	−	0.866025i	0.0237426	−	0.0359597i
$581$	−3.19615	+	5.53590i	−0.132599	+	0.229668i
$582$		0			0
$583$	−10.0981	+	5.83013i	−0.418220	+	0.241459i
$584$	12.6603			0.523885
$585$		0			0
$586$	10.2679			0.424165
$587$	32.7846	−	18.9282i	1.35317	−	0.781251i	0.364474	−	0.931214i	$-0.381249\pi$
$587$	32.7846	−	18.9282i	1.35317	−	0.781251i	0.988692	+	0.149963i	$0.0479155\pi$
$588$		0			0
$589$	9.46410	−	16.3923i	0.389962	−	0.675433i
$590$	−15.6603	−	10.3397i	−0.644722	−	0.425681i
$591$		0			0
$592$	−5.13397	−	2.96410i	−0.211005	−	0.121824i
$593$			1.39230i			0.0571751i	0.999591	+	0.0285876i	$0.00910094\pi$
$593$			1.39230i			0.0571751i	−0.999591	+	0.0285876i	$0.990899\pi$
$594$		0			0
$595$	4.02628	+	0.241670i	0.165061	+	0.00990749i
$596$	3.03590	+	5.25833i	0.124355	+	0.215390i
$597$		0			0
$598$	−8.39230	−	12.5885i	−0.343187	−	0.514780i
$599$	−32.7846			−1.33954			−0.669771	−	0.742567i	$-0.733608\pi$
$599$	−32.7846			−1.33954			−0.669771	+	0.742567i	$0.733608\pi$
$600$		0			0
$601$	−8.50000	−	14.7224i	−0.346722	−	0.600541i	0.638943	−	0.769254i	$-0.279372\pi$
$601$	−8.50000	−	14.7224i	−0.346722	−	0.600541i	−0.985665	+	0.168714i	$0.946039\pi$
$602$	−4.26795	−	2.46410i	−0.173949	−	0.100429i
$603$		0			0
$604$	9.56218	−	16.5622i	0.389079	−	0.673905i
$605$	3.53590	+	7.07180i	0.143755	+	0.287509i
$606$		0			0
$607$	23.9090	+	13.8038i	0.970435	+	0.560281i	0.899369	−	0.437191i	$-0.144027\pi$
$607$	23.9090	+	13.8038i	0.970435	+	0.560281i	0.0710661	+	0.997472i	$0.477360\pi$
$608$	−4.09808	+	2.36603i	−0.166199	+	0.0959550i
$609$		0			0
$610$	−26.3564	−	17.4019i	−1.06714	−	0.704583i
$611$	−31.2224	−	15.4378i	−1.26312	−	0.624547i
$612$		0			0
$613$	−17.1340	+	9.89230i	−0.692035	+	0.399546i	−0.804374	−	0.594123i	$-0.797499\pi$
$613$	−17.1340	+	9.89230i	−0.692035	+	0.399546i	0.112339	+	0.993670i	$0.464166\pi$
$614$	11.3660	+	19.6865i	0.458695	+	0.794484i
$615$		0			0
$616$	2.00000			0.0805823
$617$	−19.6699	−	11.3564i	−0.791879	−	0.457192i	0.0487445	−	0.998811i	$-0.484478\pi$
$617$	−19.6699	−	11.3564i	−0.791879	−	0.457192i	−0.840624	+	0.541620i	$0.817811\pi$
$618$		0			0
$619$	−40.1051			−1.61196			−0.805980	−	0.591942i	$-0.798361\pi$
$619$	−40.1051			−1.61196			−0.805980	+	0.591942i	$0.798361\pi$
$620$	4.00000	+	8.00000i	0.160644	+	0.321288i
$621$		0			0
$622$	18.2942	−	10.5622i	0.733532	−	0.423505i
$623$			6.53590i			0.261855i
$624$		0			0
$625$	−17.2846	+	18.0622i	−0.691384	+	0.722487i
$626$	−7.00000	−	12.1244i	−0.279776	−	0.484587i
$627$		0			0
$628$	9.86603	+	5.69615i	0.393697	+	0.227301i
$629$	14.6077			0.582447
$630$		0			0
$631$	8.92820	−	15.4641i	0.355426	−	0.615616i	−0.631765	−	0.775160i	$-0.717669\pi$
$631$	8.92820	−	15.4641i	0.355426	−	0.615616i	0.987191	+	0.159544i	$0.0510024\pi$
$632$			12.0000i			0.477334i
$633$		0			0
$634$	13.1340	+	22.7487i	0.521617	+	0.903467i
$635$	0.535898	−	8.92820i	0.0212665	−	0.354305i
$636$		0			0
$637$	−23.2583	+	1.50000i	−0.921529	+	0.0594322i
$638$			1.26795i			0.0501986i
$639$		0			0
$640$	0.133975	−	2.23205i	0.00529581	−	0.0882296i
$641$	−14.5263	+	25.1603i	−0.573754	+	0.993770i	0.422422	+	0.906399i	$0.361180\pi$
$641$	−14.5263	+	25.1603i	−0.573754	+	0.993770i	−0.996176	+	0.0873711i	$0.972153\pi$
$642$		0			0
$643$	−28.3923	−	16.3923i	−1.11968	−	0.646449i	−0.178363	−	0.983965i	$-0.557080\pi$
$643$	−28.3923	−	16.3923i	−1.11968	−	0.646449i	−0.941320	+	0.337515i	$0.890414\pi$
$644$	−1.53590	+	2.66025i	−0.0605229	+	0.104829i
$645$		0			0
$646$	5.83013	−	10.0981i	0.229383	−	0.397303i
$647$	9.80385	−	5.66025i	0.385429	−	0.222528i	−0.294749	−	0.955575i	$-0.595236\pi$
$647$	9.80385	−	5.66025i	0.385429	−	0.222528i	0.680178	+	0.733047i	$0.261903\pi$
$648$		0			0
$649$	22.9282			0.900011
$650$	−16.0885	+	8.13397i	−0.631041	+	0.319041i
$651$		0			0
$652$	5.66025	−	3.26795i	0.221673	−	0.127983i
$653$	31.7321	−	18.3205i	1.24177	−	0.716937i	0.272317	−	0.962208i	$-0.412210\pi$
$653$	31.7321	−	18.3205i	1.24177	−	0.716937i	0.969455	+	0.245271i	$0.0788769\pi$
$654$		0			0
$655$	17.0718	−	25.8564i	0.667050	−	1.01029i
$656$	0.598076	−	1.03590i	0.0233510	−	0.0404450i
$657$		0			0
$658$			7.07180i			0.275687i
$659$	17.2679	−	29.9090i	0.672664	−	1.16509i	−0.304482	−	0.952518i	$-0.598483\pi$
$659$	17.2679	−	29.9090i	0.672664	−	1.16509i	0.977146	−	0.212570i	$-0.0681833\pi$
$660$		0			0
$661$	−3.25833	−	5.64359i	−0.126734	−	0.219510i	0.795675	−	0.605724i	$-0.207116\pi$
$661$	−3.25833	−	5.64359i	−0.126734	−	0.219510i	−0.922410	+	0.386213i	$0.873783\pi$
$662$			12.7846i			0.496888i
$663$		0			0
$664$	−8.73205			−0.338869
$665$	0.464102	−	7.73205i	0.0179971	−	0.299836i
$666$		0			0
$667$	−1.68653	−	0.973721i	−0.0653028	−	0.0377026i
$668$		−	13.8564i		−	0.536120i
$669$		0			0
$670$	9.66025	+	19.3205i	0.373208	+	0.746416i
$671$	38.5885			1.48969
$672$		0			0
$673$	11.8923	−	6.86603i	0.458415	−	0.264666i	−0.252963	−	0.967476i	$-0.581405\pi$
$673$	11.8923	−	6.86603i	0.458415	−	0.264666i	0.711377	+	0.702810i	$0.248072\pi$
$674$	13.5263	+	23.4282i	0.521013	+	0.902421i
$675$		0			0
$676$	−12.8923	+	1.66987i	−0.495858	+	0.0642259i
$677$			20.6410i			0.793299i	0.917970	+	0.396649i	$0.129827\pi$
$677$			20.6410i			0.793299i	−0.917970	+	0.396649i	$0.870173\pi$
$678$		0			0
$679$	3.66025	+	6.33975i	0.140468	+	0.243297i
$680$	2.46410	+	4.92820i	0.0944940	+	0.188988i
$681$		0			0
$682$	−9.46410	−	5.46410i	−0.362399	−	0.209231i
$683$	−11.3205	−	6.53590i	−0.433167	−	0.250089i	0.267528	−	0.963550i	$-0.413793\pi$
$683$	−11.3205	−	6.53590i	−0.433167	−	0.250089i	−0.700695	+	0.713461i	$0.747127\pi$
$684$		0			0
$685$	23.0718	−	11.5359i	0.881528	−	0.440764i
$686$	4.92820	+	8.53590i	0.188160	+	0.325902i
$687$		0			0
$688$		−	6.73205i		−	0.256657i
$689$	−13.7942	−	6.82051i	−0.525518	−	0.259841i
$690$		0			0
$691$	−4.70577	−	8.15064i	−0.179016	−	0.310065i	0.762528	−	0.646955i	$-0.223958\pi$
$691$	−4.70577	−	8.15064i	−0.179016	−	0.310065i	−0.941544	+	0.336891i	$0.890625\pi$
$692$	19.7321	−	11.3923i	0.750100	−	0.433070i
$693$		0			0
$694$	−11.6603			−0.442617
$695$	−14.9282	−	29.8564i	−0.566259	−	1.13252i
$696$		0			0
$697$			2.94744i			0.111642i
$698$	−28.5167	−	16.4641i	−1.07937	−	0.623175i
$699$		0			0
$700$	2.92820	+	2.19615i	0.110676	+	0.0830068i
$701$	6.53590			0.246857			0.123429	−	0.992353i	$-0.460611\pi$
$701$	6.53590			0.246857			0.123429	+	0.992353i	$0.460611\pi$
$702$		0			0
$703$		−	28.0526i		−	1.05802i
$704$	1.36603	+	2.36603i	0.0514840	+	0.0891729i
$705$		0			0
$706$	−11.6244	+	20.1340i	−0.437488	+	0.757752i
$707$		−	0.0525589i		−	0.00197668i
$708$		0			0
$709$	−0.526279	+	0.911543i	−0.0197648	+	0.0342337i	−0.875739	−	0.482785i	$-0.839625\pi$
$709$	−0.526279	+	0.911543i	−0.0197648	+	0.0342337i	0.855974	+	0.517019i	$0.172958\pi$
$710$	8.83013	+	5.83013i	0.331389	+	0.218801i
$711$		0			0
$712$	−7.73205	+	4.46410i	−0.289771	+	0.167299i
$713$	14.5359	−	8.39230i	0.544374	−	0.314294i
$714$		0			0
$715$	10.9282	−	19.1244i	0.408692	−	0.715210i
$716$	−7.80385			−0.291643
$717$		0			0
$718$	28.6865	−	16.5622i	1.07057	−	0.618095i
$719$	5.80385	−	10.0526i	0.216447	−	0.374897i	−0.737272	−	0.675596i	$-0.763886\pi$
$719$	5.80385	−	10.0526i	0.216447	−	0.374897i	0.953719	+	0.300699i	$0.0972198\pi$
$720$		0			0
$721$	4.66025	−	8.07180i	0.173557	−	0.300609i
$722$	−2.93782	−	1.69615i	−0.109334	−	0.0631243i
$723$		0			0
$724$	4.06218	−	7.03590i	0.150970	−	0.261487i
$725$	−1.39230	+	1.85641i	−0.0517089	+	0.0689452i
$726$		0			0
$727$			16.7321i			0.620557i	0.950646	+	0.310279i	$0.100422\pi$
$727$			16.7321i			0.620557i	−0.950646	+	0.310279i	$0.899578\pi$
$728$	1.46410	+	2.19615i	0.0542632	+	0.0813948i
$729$		0			0
$730$	−28.2583	−	1.69615i	−1.04589	−	0.0627774i
$731$	8.29423	+	14.3660i	0.306773	+	0.531347i
$732$		0			0
$733$			24.6077i			0.908906i	0.890771	+	0.454453i	$0.150165\pi$
$733$			24.6077i			0.908906i	−0.890771	+	0.454453i	$0.849835\pi$
$734$	9.49038	−	16.4378i	0.350296	−	0.606731i
$735$		0			0
$736$	−4.19615			−0.154672
$737$	−22.8564	−	13.1962i	−0.841927	−	0.486087i
$738$		0			0
$739$	14.9282	+	25.8564i	0.549143	+	0.951143i	0.998334	+	0.0577074i	$0.0183790\pi$
$739$	14.9282	+	25.8564i	0.549143	+	0.951143i	−0.449191	+	0.893436i	$0.648288\pi$
$740$	11.0622	+	7.30385i	0.406654	+	0.268495i
$741$		0			0
$742$			3.12436i			0.114699i
$743$	12.5885	−	7.26795i	0.461826	−	0.266635i	−0.250986	−	0.967991i	$-0.580755\pi$
$743$	12.5885	−	7.26795i	0.461826	−	0.266635i	0.712812	+	0.701356i	$0.247421\pi$
$744$		0			0
$745$	−6.07180	−	12.1436i	−0.222453	−	0.444907i
$746$	−30.4641			−1.11537
$747$		0			0
$748$	−5.83013	−	3.36603i	−0.213171	−	0.123074i
$749$	−3.46410			−0.126576
$750$		0			0
$751$	1.02628	+	1.77757i	0.0374495	+	0.0648644i	0.884143	−	0.467217i	$-0.154743\pi$
$751$	1.02628	+	1.77757i	0.0374495	+	0.0648644i	−0.846693	+	0.532081i	$0.821410\pi$
$752$	−8.36603	+	4.83013i	−0.305078	+	0.176137i
$753$		0			0
$754$	−1.39230	+	0.928203i	−0.0507048	+	0.0338032i
$755$	−23.5622	+	35.6865i	−0.857515	+	1.29877i
$756$		0			0
$757$	−31.2679	+	18.0526i	−1.13645	+	0.656131i	−0.945550	−	0.325477i	$-0.894475\pi$
$757$	−31.2679	+	18.0526i	−1.13645	+	0.656131i	−0.190903	+	0.981609i	$0.561142\pi$
$758$	−19.2679	−	11.1244i	−0.699843	−	0.404055i
$759$		0			0
$760$	9.46410	−	4.73205i	0.343299	−	0.171650i
$761$	18.4641	−	31.9808i	0.669323	−	1.15930i	−0.308771	−	0.951137i	$-0.599918\pi$
$761$	18.4641	−	31.9808i	0.669323	−	1.15930i	0.978094	−	0.208165i	$-0.0667492\pi$
$762$		0			0
$763$	6.33975	+	3.66025i	0.229514	+	0.132510i
$764$	1.26795	+	2.19615i	0.0458728	+	0.0794540i
$765$		0			0
$766$	13.0718			0.472303
$767$	16.7846	+	25.1769i	0.606057	+	0.909086i
$768$		0			0
$769$	19.2679	+	33.3731i	0.694820	+	1.20346i	0.970241	+	0.242140i	$0.0778493\pi$
$769$	19.2679	+	33.3731i	0.694820	+	1.20346i	−0.275421	+	0.961324i	$0.588817\pi$
$770$	−4.46410	−	0.267949i	−0.160875	−	0.00965622i
$771$		0			0
$772$		−	6.66025i		−	0.239708i
$773$	−24.8038	−	14.3205i	−0.892132	−	0.515073i	−0.0174930	−	0.999847i	$-0.505568\pi$
$773$	−24.8038	−	14.3205i	−0.892132	−	0.515073i	−0.874639	+	0.484774i	$0.838902\pi$
$774$		0			0
$775$	−7.85641	−	18.3923i	−0.282210	−	0.660671i
$776$	−5.00000	+	8.66025i	−0.179490	+	0.310885i
$777$		0			0
$778$	−32.8468	+	18.9641i	−1.17761	+	0.679896i
$779$	5.66025			0.202800
$780$		0			0
$781$	−12.9282			−0.462607
$782$	8.95448	−	5.16987i	0.320212	−	0.184874i
$783$		0			0
$784$	−3.23205	+	5.59808i	−0.115430	+	0.199931i
$785$	−21.2583	−	14.0359i	−0.758742	−	0.500963i
$786$		0			0
$787$	13.2679	+	7.66025i	0.472951	+	0.273059i	0.717474	−	0.696585i	$-0.245298\pi$
$787$	13.2679	+	7.66025i	0.472951	+	0.273059i	−0.244523	+	0.969643i	$0.578631\pi$
$788$			17.8564i			0.636108i
$789$		0			0
$790$	1.60770	−	26.7846i	0.0571992	−	0.952954i
$791$	−3.29423	−	5.70577i	−0.117129	−	0.202874i
$792$		0			0
$793$	28.2487	+	42.3731i	1.00314	+	1.50471i
$794$	15.3205			0.543704
$795$		0			0
$796$	−5.02628	−	8.70577i	−0.178152	−	0.308568i
$797$	12.9282	+	7.46410i	0.457940	+	0.264392i	0.711178	−	0.703012i	$-0.248162\pi$
$797$	12.9282	+	7.46410i	0.457940	+	0.264392i	−0.253237	+	0.967404i	$0.581495\pi$
$798$		0			0
$799$	11.9019	−	20.6147i	0.421060	−	0.729297i
$800$	−0.598076	+	4.96410i	−0.0211452	+	0.175507i
$801$		0			0
$802$	25.1603	+	14.5263i	0.888439	+	0.512941i
$803$	29.9545	−	17.2942i	1.05707	−	0.610300i
$804$		0			0
$805$	3.78461	−	5.73205i	0.133390	−	0.202028i
$806$	−0.928203	−	14.3923i	−0.0326946	−	0.506947i
$807$		0			0
$808$	0.0621778	−	0.0358984i	0.00218741	−	0.00126290i
$809$	24.9904	+	43.2846i	0.878615	+	1.52181i	0.852861	+	0.522138i	$0.174865\pi$
$809$	24.9904	+	43.2846i	0.878615	+	1.52181i	0.0257537	+	0.999668i	$0.491801\pi$
$810$		0			0
$811$	−6.14359			−0.215731			−0.107865	−	0.994166i	$-0.534402\pi$
$811$	−6.14359			−0.215731			−0.107865	+	0.994166i	$0.534402\pi$
$812$	0.294229	+	0.169873i	0.0103254	+	0.00596137i
$813$		0			0
$814$	−16.1962			−0.567675
$815$	−13.0718	+	6.53590i	−0.457885	+	0.228943i
$816$		0			0
$817$	27.5885	−	15.9282i	0.965198	−	0.557257i
$818$		−	29.9282i		−	1.04642i
$819$		0			0
$820$	−1.47372	+	2.23205i	−0.0514646	+	0.0779466i
$821$	−19.1244	−	33.1244i	−0.667445	−	1.15605i	−0.978616	−	0.205694i	$-0.934055\pi$
$821$	−19.1244	−	33.1244i	−0.667445	−	1.15605i	0.311172	−	0.950354i	$-0.399279\pi$
$822$		0			0
$823$	16.9808	+	9.80385i	0.591912	+	0.341741i	0.765853	−	0.643015i	$-0.222317\pi$
$823$	16.9808	+	9.80385i	0.591912	+	0.341741i	−0.173941	+	0.984756i	$0.555650\pi$
$824$	12.7321			0.443542
$825$		0			0
$826$	3.07180	−	5.32051i	0.106881	−	0.185124i
$827$			7.21539i			0.250904i	0.992100	+	0.125452i	$0.0400381\pi$
$827$			7.21539i			0.250904i	−0.992100	+	0.125452i	$0.959962\pi$
$828$		0			0
$829$	21.0622	+	36.4808i	0.731520	+	1.26703i	0.956234	+	0.292604i	$0.0945219\pi$
$829$	21.0622	+	36.4808i	0.731520	+	1.26703i	−0.224714	+	0.974425i	$0.572145\pi$
$830$	19.4904	+	1.16987i	0.676521	+	0.0406069i
$831$		0			0
$832$	−1.59808	+	3.23205i	−0.0554033	+	0.112051i
$833$		−	15.9282i		−	0.551880i
$834$		0			0
$835$	−1.85641	+	30.9282i	−0.0642436	+	1.07031i
$836$	−6.46410	+	11.1962i	−0.223566	+	0.387227i
$837$		0			0
$838$	11.6603	+	6.73205i	0.402797	+	0.232555i
$839$	14.0526	−	24.3397i	0.485148	−	0.840301i	−0.514706	−	0.857367i	$-0.672099\pi$
$839$	14.0526	−	24.3397i	0.485148	−	0.840301i	0.999854	+	0.0170653i	$0.00543232\pi$
$840$		0			0
$841$	14.3923	−	24.9282i	0.496286	−	0.859593i
$842$	−18.2321	+	10.5263i	−0.628318	+	0.362760i
$843$		0			0
$844$	14.5359			0.500346
$845$	29.0000	−	2.00000i	0.997630	−	0.0688021i
$846$		0			0
$847$	−2.24167	+	1.29423i	−0.0770247	+	0.0444702i
$848$	−3.69615	+	2.13397i	−0.126926	+	0.0732810i
$849$		0			0
$850$	−4.83975	−	11.3301i	−0.166002	−	0.388620i
$851$	12.4378	−	21.5429i	0.426363	−	0.738482i
$852$		0			0
$853$		−	25.9282i		−	0.887765i	−0.896085	−	0.443882i	$-0.853601\pi$
$853$		−	25.9282i		−	0.887765i	0.896085	−	0.443882i	$-0.146399\pi$
$854$	5.16987	−	8.95448i	0.176909	−	0.306416i
$855$		0			0
$856$	−2.36603	−	4.09808i	−0.0808691	−	0.140069i
$857$		−	9.92820i		−	0.339141i	−0.985518	−	0.169570i	$-0.945762\pi$
$857$		−	9.92820i		−	0.339141i	0.985518	−	0.169570i	$-0.0542380\pi$
$858$		0			0
$859$	−42.3013			−1.44330			−0.721650	−	0.692258i	$-0.756616\pi$
$859$	−42.3013			−1.44330			−0.721650	+	0.692258i	$0.756616\pi$
$860$	−0.901924	+	15.0263i	−0.0307553	+	0.512392i
$861$		0			0
$862$	−15.7583	−	9.09808i	−0.536731	−	0.309882i
$863$			3.12436i			0.106354i	0.998585	+	0.0531772i	$0.0169348\pi$
$863$			3.12436i			0.106354i	−0.998585	+	0.0531772i	$0.983065\pi$
$864$		0			0
$865$	−45.5692	+	22.7846i	−1.54940	+	0.774700i
$866$	25.1962			0.856200
$867$		0			0
$868$	−2.53590	+	1.46410i	−0.0860740	+	0.0496948i
$869$	16.3923	+	28.3923i	0.556071	+	0.963143i
$870$		0			0
$871$	−2.24167	−	34.7583i	−0.0759561	−	1.17774i
$872$			10.0000i			0.338643i
$873$		0			0
$874$	−9.92820	−	17.1962i	−0.335826	−	0.581669i
$875$	−6.24167	−	5.29423i	−0.211007	−	0.178978i
$876$		0			0
$877$	−14.2583	−	8.23205i	−0.481470	−	0.277977i	0.239559	−	0.970882i	$-0.422997\pi$
$877$	−14.2583	−	8.23205i	−0.481470	−	0.277977i	−0.721029	+	0.692905i	$0.756330\pi$
$878$	17.4904	+	10.0981i	0.590272	+	0.340794i
$879$		0			0
$880$	−2.73205	−	5.46410i	−0.0920974	−	0.184195i
$881$	21.0622	+	36.4808i	0.709603	+	1.22907i	0.965005	+	0.262233i	$0.0844589\pi$
$881$	21.0622	+	36.4808i	0.709603	+	1.22907i	−0.255402	+	0.966835i	$0.582208\pi$
$882$		0			0
$883$			30.2487i			1.01795i	0.860781	+	0.508975i	$0.169975\pi$
$883$			30.2487i			1.01795i	−0.860781	+	0.508975i	$0.830025\pi$
$884$	−0.571797	−	8.86603i	−0.0192316	−	0.298197i
$885$		0			0
$886$	17.3205	+	30.0000i	0.581894	+	1.00787i
$887$	37.1769	−	21.4641i	1.24828	−	0.720694i	0.277513	−	0.960722i	$-0.410490\pi$
$887$	37.1769	−	21.4641i	1.24828	−	0.720694i	0.970766	+	0.240028i	$0.0771566\pi$
$888$		0			0
$889$	2.92820			0.0982088
$890$	17.8564	−	8.92820i	0.598548	−	0.299274i
$891$		0			0
$892$		−	20.3923i		−	0.682785i
$893$	−39.5885	−	22.8564i	−1.32478	−	0.764860i
$894$		0			0
$895$	17.4186	+	1.04552i	0.582239	+	0.0349478i
$896$	0.732051			0.0244561
$897$		0			0
$898$			19.8564i			0.662617i
$899$	−0.928203	−	1.60770i	−0.0309573	−	0.0536196i
$900$		0			0
$901$	5.25833	−	9.10770i	0.175180	−	0.303421i
$902$		−	3.26795i		−	0.108811i
$903$		0			0
$904$	4.50000	−	7.79423i	0.149668	−	0.259232i
$905$	−10.0096	+	15.1603i	−0.332731	+	0.503944i
$906$		0			0
$907$	6.00000	−	3.46410i	0.199227	−	0.115024i	−0.397068	−	0.917789i	$-0.629972\pi$
$907$	6.00000	−	3.46410i	0.199227	−	0.115024i	0.596295	+	0.802766i	$0.296639\pi$
$908$	−5.36603	+	3.09808i	−0.178078	+	0.102813i
$909$		0			0
$910$	−2.97372	−	5.09808i	−0.0985779	−	0.169000i
$911$	32.1051			1.06369			0.531845	−	0.846842i	$-0.321499\pi$
$911$	32.1051			1.06369			0.531845	+	0.846842i	$0.321499\pi$
$912$		0			0
$913$	−20.6603	+	11.9282i	−0.683755	+	0.394766i
$914$	9.59808	−	16.6244i	0.317476	−	0.549885i
$915$		0			0
$916$	6.39230	−	11.0718i	0.211208	−	0.365822i
$917$	8.78461	+	5.07180i	0.290093	+	0.167485i
$918$		0			0
$919$	−25.2679	+	43.7654i	−0.833513	+	1.44369i	0.0617229	+	0.998093i	$0.480341\pi$
$919$	−25.2679	+	43.7654i	−0.833513	+	1.44369i	−0.895236	+	0.445593i	$0.852993\pi$
$920$	9.36603	+	0.562178i	0.308789	+	0.0185345i
$921$		0			0
$922$		−	39.9282i		−	1.31497i
$923$	−9.46410	−	14.1962i	−0.311515	−	0.467272i
$924$		0			0
$925$	−23.7128	−	17.7846i	−0.779672	−	0.584754i
$926$	−11.8301	−	20.4904i	−0.388762	−	0.673356i
$927$		0			0
$928$			0.464102i			0.0152349i
$929$	−4.20577	+	7.28461i	−0.137987	+	0.239000i	−0.926734	−	0.375717i	$-0.877397\pi$
$929$	−4.20577	+	7.28461i	−0.137987	+	0.239000i	0.788748	+	0.614717i	$0.210730\pi$
$930$		0			0
$931$	−30.5885			−1.00250
$932$	7.26795	+	4.19615i	0.238070	+	0.137450i
$933$		0			0
$934$	8.02628	+	13.9019i	0.262628	+	0.454885i
$935$	12.5622	+	8.29423i	0.410827	+	0.271250i
$936$		0			0
$937$		−	21.0526i		−	0.687757i	−0.939014	−	0.343879i	$-0.888259\pi$
$937$		−	21.0526i		−	0.687757i	0.939014	−	0.343879i	$-0.111741\pi$
$938$	−6.12436	+	3.53590i	−0.199967	+	0.115451i
$939$		0			0
$940$	19.3205	−	9.66025i	0.630165	−	0.315083i
$941$	8.39230			0.273581			0.136791	−	0.990600i	$-0.456321\pi$
$941$	8.39230			0.273581			0.136791	+	0.990600i	$0.456321\pi$
$942$		0			0
$943$	4.34679	+	2.50962i	0.141551	+	0.0817244i
$944$	8.39230			0.273146
$945$		0			0
$946$	−9.19615	−	15.9282i	−0.298993	−	0.517871i
$947$	−24.0000	+	13.8564i	−0.779895	+	0.450273i	−0.836393	−	0.548130i	$-0.815340\pi$
$947$	−24.0000	+	13.8564i	−0.779895	+	0.450273i	0.0564979	+	0.998403i	$0.482007\pi$
$948$		0			0
$949$	40.9186	+	20.2321i	1.32827	+	0.656760i
$950$	−21.7583	+	9.29423i	−0.705933	+	0.301545i
$951$		0			0
$952$	−1.56218	+	0.901924i	−0.0506305	+	0.0292315i
$953$	15.3397	+	8.85641i	0.496903	+	0.286887i	0.727434	−	0.686178i	$-0.240713\pi$
$953$	15.3397	+	8.85641i	0.496903	+	0.286887i	−0.230531	+	0.973065i	$0.574046\pi$
$954$		0			0
$955$	−2.53590	−	5.07180i	−0.0820597	−	0.164119i
$956$	13.2942	−	23.0263i	0.429966	−	0.744723i
$957$		0			0
$958$	13.8564	+	8.00000i	0.447680	+	0.258468i
$959$	4.22243	+	7.31347i	0.136349	+	0.236164i
$960$		0			0
$961$	−15.0000			−0.483871
$962$	−11.8564	−	17.7846i	−0.382266	−	0.573399i
$963$		0			0
$964$	5.69615	+	9.86603i	0.183461	+	0.317763i
$965$	−0.892305	+	14.8660i	−0.0287243	+	0.478554i
$966$		0			0
$967$		−	14.5885i		−	0.469133i	−0.972100	−	0.234567i	$-0.924633\pi$
$967$		−	14.5885i		−	0.469133i	0.972100	−	0.234567i	$-0.0753671\pi$
$968$	−3.06218	−	1.76795i	−0.0984221	−	0.0568240i
$969$		0			0
$970$	12.3205	−	18.6603i	0.395588	−	0.599145i
$971$	−20.5359	+	35.5692i	−0.659028	+	1.14147i	0.321839	+	0.946794i	$0.395699\pi$
$971$	−20.5359	+	35.5692i	−0.659028	+	1.14147i	−0.980868	+	0.194676i	$0.937634\pi$
$972$		0			0
$973$	9.46410	−	5.46410i	0.303405	−	0.175171i
$974$	−20.4449			−0.655096
$975$		0			0
$976$	14.1244			0.452110
$977$	−23.5981	+	13.6244i	−0.754969	+	0.435882i	−0.827487	−	0.561485i	$-0.810230\pi$
$977$	−23.5981	+	13.6244i	−0.754969	+	0.435882i	0.0725173	+	0.997367i	$0.476897\pi$
$978$		0			0
$979$	−12.1962	+	21.1244i	−0.389791	+	0.675137i
$980$	7.96410	−	12.0622i	0.254404	−	0.385312i
$981$		0			0
$982$	27.8827	+	16.0981i	0.889772	+	0.513710i
$983$		−	23.7128i		−	0.756321i	−0.925740	−	0.378161i	$-0.876557\pi$
$983$		−	23.7128i		−	0.756321i	0.925740	−	0.378161i	$-0.123443\pi$
$984$		0			0
$985$	2.39230	−	39.8564i	0.0762252	−	1.26993i
$986$	−0.571797	−	0.990381i	−0.0182097	−	0.0315402i
$987$		0			0
$988$	−17.0263	+	1.09808i	−0.541678	+	0.0349345i
$989$	28.2487			0.898257
$990$		0			0
$991$	15.0263	+	26.0263i	0.477325	+	0.826752i	0.999662	−	0.0259873i	$-0.00827294\pi$
$991$	15.0263	+	26.0263i	0.477325	+	0.826752i	−0.522337	+	0.852739i	$0.674940\pi$
$992$	−3.46410	−	2.00000i	−0.109985	−	0.0635001i
$993$		0			0
$994$	−1.73205	+	3.00000i	−0.0549373	+	0.0951542i
$995$	10.0526	+	20.1051i	0.318688	+	0.637375i
$996$		0			0
$997$	−1.79423	−	1.03590i	−0.0568238	−	0.0328072i	0.471319	−	0.881963i	$-0.343778\pi$
$997$	−1.79423	−	1.03590i	−0.0568238	−	0.0328072i	−0.528143	+	0.849156i	$0.677111\pi$
$998$	−16.9808	+	9.80385i	−0.537517	+	0.310335i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1170.2.bp.d.289.2		4
3.2	odd	2		390.2.y.b.289.1	yes	4
5.4	even	2		1170.2.bp.e.289.1		4
13.9	even	3		1170.2.bp.e.919.1		4
15.2	even	4		1950.2.i.y.601.2		4
15.8	even	4		1950.2.i.bh.601.1		4
15.14	odd	2		390.2.y.c.289.2	yes	4
39.35	odd	6		390.2.y.c.139.2	yes	4
65.9	even	6	inner	1170.2.bp.d.919.2		4
195.74	odd	6		390.2.y.b.139.1	✓	4
195.113	even	12		1950.2.i.bh.451.1		4
195.152	even	12		1950.2.i.y.451.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.y.b.139.1	✓	4	195.74	odd	6
390.2.y.b.289.1	yes	4	3.2	odd	2
390.2.y.c.139.2	yes	4	39.35	odd	6
390.2.y.c.289.2	yes	4	15.14	odd	2
1170.2.bp.d.289.2		4	1.1	even	1	trivial
1170.2.bp.d.919.2		4	65.9	even	6	inner
1170.2.bp.e.289.1		4	5.4	even	2
1170.2.bp.e.919.1		4	13.9	even	3
1950.2.i.y.451.2		4	195.152	even	12
1950.2.i.y.601.2		4	15.2	even	4
1950.2.i.bh.451.1		4	195.113	even	12
1950.2.i.bh.601.1		4	15.8	even	4

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:	\( N \)	\(=\)	\( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1170.bp (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-1.23205 + 1.86603i) q^{5} +(-0.633975 - 0.366025i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-1.23205 + 1.86603i) q^{5} +(-0.633975 - 0.366025i) q^{7} -1.00000i q^{8} +(-0.133975 + 2.23205i) q^{10} +(-1.36603 - 2.36603i) q^{11} +(1.59808 - 3.23205i) q^{13} -0.732051 q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.13397 + 1.23205i) q^{17} +(2.36603 - 4.09808i) q^{19} +(1.00000 + 2.00000i) q^{20} +(-2.36603 - 1.36603i) q^{22} +(3.63397 - 2.09808i) q^{23} +(-1.96410 - 4.59808i) q^{25} +(-0.232051 - 3.59808i) q^{26} +(-0.633975 + 0.366025i) q^{28} +(-0.232051 - 0.401924i) q^{29} +4.00000 q^{31} +(-0.866025 - 0.500000i) q^{32} +2.46410 q^{34} +(1.46410 - 0.732051i) q^{35} +(5.13397 - 2.96410i) q^{37} -4.73205i q^{38} +(1.86603 + 1.23205i) q^{40} +(0.598076 + 1.03590i) q^{41} +(5.83013 + 3.36603i) q^{43} -2.73205 q^{44} +(2.09808 - 3.63397i) q^{46} -9.66025i q^{47} +(-3.23205 - 5.59808i) q^{49} +(-4.00000 - 3.00000i) q^{50} +(-2.00000 - 3.00000i) q^{52} -4.26795i q^{53} +(6.09808 + 0.366025i) q^{55} +(-0.366025 + 0.633975i) q^{56} +(-0.401924 - 0.232051i) q^{58} +(-4.19615 + 7.26795i) q^{59} +(-7.06218 + 12.2321i) q^{61} +(3.46410 - 2.00000i) q^{62} -1.00000 q^{64} +(4.06218 + 6.96410i) q^{65} +(8.36603 - 4.83013i) q^{67} +(2.13397 - 1.23205i) q^{68} +(0.901924 - 1.36603i) q^{70} +(2.36603 - 4.09808i) q^{71} +12.6603i q^{73} +(2.96410 - 5.13397i) q^{74} +(-2.36603 - 4.09808i) q^{76} +2.00000i q^{77} -12.0000 q^{79} +(2.23205 + 0.133975i) q^{80} +(1.03590 + 0.598076i) q^{82} -8.73205i q^{83} +(-4.92820 + 2.46410i) q^{85} +6.73205 q^{86} +(-2.36603 + 1.36603i) q^{88} +(-4.46410 - 7.73205i) q^{89} +(-2.19615 + 1.46410i) q^{91} -4.19615i q^{92} +(-4.83013 - 8.36603i) q^{94} +(4.73205 + 9.46410i) q^{95} +(-8.66025 - 5.00000i) q^{97} +(-5.59808 - 3.23205i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} + 2 q^{5} - 6 q^{7}+O(q^{10}) \) 4 * q + 2 * q^4 + 2 * q^5 - 6 * q^7	\( 4 q + 2 q^{4} + 2 q^{5} - 6 q^{7} - 4 q^{10} - 2 q^{11} - 4 q^{13} + 4 q^{14} - 2 q^{16} + 12 q^{17} + 6 q^{19} + 4 q^{20} - 6 q^{22} + 18 q^{23} + 6 q^{25} + 6 q^{26} - 6 q^{28} + 6 q^{29} + 16 q^{31} - 4 q^{34} - 8 q^{35} + 24 q^{37} + 4 q^{40} - 8 q^{41} + 6 q^{43} - 4 q^{44} - 2 q^{46} - 6 q^{49} - 16 q^{50} - 8 q^{52} + 14 q^{55} + 2 q^{56} - 12 q^{58} + 4 q^{59} - 4 q^{61} - 4 q^{64} - 8 q^{65} + 30 q^{67} + 12 q^{68} + 14 q^{70} + 6 q^{71} - 2 q^{74} - 6 q^{76} - 48 q^{79} + 2 q^{80} + 18 q^{82} + 8 q^{85} + 20 q^{86} - 6 q^{88} - 4 q^{89} + 12 q^{91} - 2 q^{94} + 12 q^{95} - 12 q^{98}+O(q^{100}) \) 4 * q + 2 * q^4 + 2 * q^5 - 6 * q^7 - 4 * q^10 - 2 * q^11 - 4 * q^13 + 4 * q^14 - 2 * q^16 + 12 * q^17 + 6 * q^19 + 4 * q^20 - 6 * q^22 + 18 * q^23 + 6 * q^25 + 6 * q^26 - 6 * q^28 + 6 * q^29 + 16 * q^31 - 4 * q^34 - 8 * q^35 + 24 * q^37 + 4 * q^40 - 8 * q^41 + 6 * q^43 - 4 * q^44 - 2 * q^46 - 6 * q^49 - 16 * q^50 - 8 * q^52 + 14 * q^55 + 2 * q^56 - 12 * q^58 + 4 * q^59 - 4 * q^61 - 4 * q^64 - 8 * q^65 + 30 * q^67 + 12 * q^68 + 14 * q^70 + 6 * q^71 - 2 * q^74 - 6 * q^76 - 48 * q^79 + 2 * q^80 + 18 * q^82 + 8 * q^85 + 20 * q^86 - 6 * q^88 - 4 * q^89 + 12 * q^91 - 2 * q^94 + 12 * q^95 - 12 * q^98

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