LMFDB - Embedded newform 1170.2.cu.f.431.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1170,2,Mod(71,1170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1170, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 0, 5]))

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

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

chi := DirichletCharacter("1170.71");

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.cu (of order $12$, degree $4$, 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:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
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} - 12x^{14} + 49x^{12} - 12x^{10} - 600x^{8} + 108x^{6} + 4057x^{4} + 18252x^{2} + 28561 $ x^16 - 12x^14 + 49x^12 - 12x^10 - 600x^8 + 108x^6 + 4057x^4 + 18252*x^2 + 28561
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			431.2
Root			$-0.850627 + 1.24273i$ of defining polynomial
Character	$\chi$	$=$	1170.431
Dual form			1170.2.cu.f.1151.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(-0.707107 - 0.707107i) q^{5} +(4.26680 - 1.14329i) q^{7} +(0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(-0.707107 - 0.707107i) q^{5} +(4.26680 - 1.14329i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{10} +(5.38324 + 1.44244i) q^{11} +(-3.06383 - 1.90077i) q^{13} +4.41732i q^{14} +(0.500000 + 0.866025i) q^{16} +(-0.909743 + 1.57572i) q^{17} +(-1.88215 - 7.02429i) q^{19} +(0.258819 + 0.965926i) q^{20} +(-2.78657 + 4.82648i) q^{22} +(-2.07537 - 3.59465i) q^{23} +1.00000i q^{25} +(2.62898 - 2.46748i) q^{26} +(-4.26680 - 1.14329i) q^{28} +(-5.49854 + 3.17458i) q^{29} +(3.75749 - 3.75749i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(-1.28657 - 1.28657i) q^{34} +(-3.82551 - 2.20866i) q^{35} +(2.09443 - 7.81652i) q^{37} +7.27208 q^{38} -1.00000 q^{40} +(-1.03528 + 3.86370i) q^{41} +(6.26630 + 3.61785i) q^{43} +(-3.94081 - 3.94081i) q^{44} +(4.00931 - 1.07429i) q^{46} +(6.08331 - 6.08331i) q^{47} +(10.8363 - 6.25634i) q^{49} +(-0.965926 - 0.258819i) q^{50} +(1.70297 + 3.17803i) q^{52} +5.04732i q^{53} +(-2.78657 - 4.82648i) q^{55} +(2.20866 - 3.82551i) q^{56} +(-1.64329 - 6.13282i) q^{58} +(0.102392 + 0.382131i) q^{59} +(-3.26113 + 5.64845i) q^{61} +(2.65695 + 4.60196i) q^{62} -1.00000i q^{64} +(0.822405 + 3.51051i) q^{65} +(3.04406 + 0.815653i) q^{67} +(1.57572 - 0.909743i) q^{68} +(3.12351 - 3.12351i) q^{70} +(13.8746 - 3.71770i) q^{71} +(-1.33745 - 1.33745i) q^{73} +(7.00810 + 4.04613i) q^{74} +(-1.88215 + 7.02429i) q^{76} +24.6183 q^{77} +4.34474 q^{79} +(0.258819 - 0.965926i) q^{80} +(-3.46410 - 2.00000i) q^{82} +(3.28962 + 3.28962i) q^{83} +(1.75749 - 0.470918i) q^{85} +(-5.11641 + 5.11641i) q^{86} +(4.82648 - 2.78657i) q^{88} +(-5.23972 - 1.40398i) q^{89} +(-15.2459 - 4.60739i) q^{91} +4.15074i q^{92} +(4.30155 + 7.45050i) q^{94} +(-3.63604 + 6.29780i) q^{95} +(1.48272 + 5.53360i) q^{97} +(3.23852 + 12.0863i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{7}+O(q^{10}) $ 16 * q + 12 * q^7	$ 16 q + 12 q^{7} - 8 q^{13} + 8 q^{16} - 52 q^{19} - 8 q^{22} - 12 q^{28} + 36 q^{31} + 16 q^{34} + 8 q^{37} - 16 q^{40} + 72 q^{43} + 32 q^{46} + 60 q^{49} + 12 q^{52} - 8 q^{55} - 8 q^{58} - 12 q^{61} - 12 q^{67} + 12 q^{70} + 8 q^{73} - 52 q^{76} + 8 q^{79} + 4 q^{85} + 24 q^{88} - 84 q^{91} - 16 q^{94} - 96 q^{97}+O(q^{100}) $ 16 * q + 12 * q^7 - 8 * q^13 + 8 * q^16 - 52 * q^19 - 8 * q^22 - 12 * q^28 + 36 * q^31 + 16 * q^34 + 8 * q^37 - 16 * q^40 + 72 * q^43 + 32 * q^46 + 60 * q^49 + 12 * q^52 - 8 * q^55 - 8 * q^58 - 12 * q^61 - 12 * q^67 + 12 * q^70 + 8 * q^73 - 52 * q^76 + 8 * q^79 + 4 * q^85 + 24 * q^88 - 84 * q^91 - 16 * q^94 - 96 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$911$	$937$	$1081$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{12}\right)$

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 $

$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$3$		0			0
$3$		0			0
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	−0.707107	−	0.707107i	−0.316228	−	0.316228i
$5$	−0.707107	−	0.707107i	−0.316228	−	0.316228i
$6$		0			0
$7$	4.26680	−	1.14329i	1.61270	−	0.432121i	0.663853	−	0.747863i	$-0.268920\pi$
$7$	4.26680	−	1.14329i	1.61270	−	0.432121i	0.948845	+	0.315742i	$0.102253\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$		0			0
$10$	0.866025	−	0.500000i	0.273861	−	0.158114i
$11$	5.38324	+	1.44244i	1.62311	+	0.434911i	0.951913	−	0.306370i	$-0.0991143\pi$
$11$	5.38324	+	1.44244i	1.62311	+	0.434911i	0.671196	+	0.741280i	$0.265781\pi$
$12$		0			0
$13$	−3.06383	−	1.90077i	−0.849754	−	0.527180i
$13$	−3.06383	−	1.90077i	−0.849754	−	0.527180i
$14$			4.41732i			1.18058i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−0.909743	+	1.57572i	−0.220645	+	0.382168i	−0.955004	−	0.296593i	$-0.904150\pi$
$17$	−0.909743	+	1.57572i	−0.220645	+	0.382168i	0.734359	+	0.678761i	$0.237483\pi$
$18$		0			0
$19$	−1.88215	−	7.02429i	−0.431795	−	1.61148i	−0.748621	−	0.662998i	$-0.769284\pi$
$19$	−1.88215	−	7.02429i	−0.431795	−	1.61148i	0.316826	−	0.948484i	$-0.397383\pi$
$20$	0.258819	+	0.965926i	0.0578737	+	0.215988i
$21$		0			0
$22$	−2.78657	+	4.82648i	−0.594099	+	1.02901i
$23$	−2.07537	−	3.59465i	−0.432745	−	0.749536i	0.564364	−	0.825526i	$-0.309122\pi$
$23$	−2.07537	−	3.59465i	−0.432745	−	0.749536i	−0.997109	+	0.0759901i	$0.975788\pi$
$24$		0			0
$25$			1.00000i			0.200000i
$26$	2.62898	−	2.46748i	0.515586	−	0.483912i
$27$		0			0
$28$	−4.26680	−	1.14329i	−0.806349	−	0.216061i
$29$	−5.49854	+	3.17458i	−1.02105	+	0.589505i	−0.914409	−	0.404792i	$-0.867344\pi$
$29$	−5.49854	+	3.17458i	−1.02105	+	0.589505i	−0.106644	+	0.994297i	$0.534011\pi$
$30$		0			0
$31$	3.75749	−	3.75749i	0.674865	−	0.674865i	−0.283969	−	0.958834i	$-0.591651\pi$
$31$	3.75749	−	3.75749i	0.674865	−	0.674865i	0.958834	+	0.283969i	$0.0916512\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$		0			0
$34$	−1.28657	−	1.28657i	−0.220645	−	0.220645i
$35$	−3.82551	−	2.20866i	−0.646629	−	0.373331i
$36$		0			0
$37$	2.09443	−	7.81652i	0.344322	−	1.28503i	−0.549079	−	0.835770i	$-0.685022\pi$
$37$	2.09443	−	7.81652i	0.344322	−	1.28503i	0.893402	−	0.449259i	$-0.148312\pi$
$38$	7.27208			1.17969
$39$		0			0
$40$	−1.00000			−0.158114
$41$	−1.03528	+	3.86370i	−0.161683	+	0.603409i	0.836757	+	0.547574i	$0.184449\pi$
$41$	−1.03528	+	3.86370i	−0.161683	+	0.603409i	−0.998440	+	0.0558348i	$0.982218\pi$
$42$		0			0
$43$	6.26630	+	3.61785i	0.955601	+	0.551717i	0.894816	−	0.446434i	$-0.147306\pi$
$43$	6.26630	+	3.61785i	0.955601	+	0.551717i	0.0607848	+	0.998151i	$0.480640\pi$
$44$	−3.94081	−	3.94081i	−0.594099	−	0.594099i
$45$		0			0
$46$	4.00931	−	1.07429i	0.591141	−	0.158396i
$47$	6.08331	−	6.08331i	0.887342	−	0.887342i	−0.106926	−	0.994267i	$-0.534101\pi$
$47$	6.08331	−	6.08331i	0.887342	−	0.887342i	0.994267	+	0.106926i	$0.0341006\pi$
$48$		0			0
$49$	10.8363	−	6.25634i	1.54804	−	0.893763i
$50$	−0.965926	−	0.258819i	−0.136603	−	0.0366025i
$51$		0			0
$52$	1.70297	+	3.17803i	0.236159	+	0.440714i
$53$			5.04732i			0.693303i	0.937994	+	0.346651i	$0.112681\pi$
$53$			5.04732i			0.693303i	−0.937994	+	0.346651i	$0.887319\pi$
$54$		0			0
$55$	−2.78657	−	4.82648i	−0.375741	−	0.650803i
$56$	2.20866	−	3.82551i	0.295144	−	0.511205i
$57$		0			0
$58$	−1.64329	−	6.13282i	−0.215774	−	0.805279i
$59$	0.102392	+	0.382131i	0.0133303	+	0.0497492i	0.972271	−	0.233859i	$-0.0751353\pi$
$59$	0.102392	+	0.382131i	0.0133303	+	0.0497492i	−0.958940	+	0.283608i	$0.908469\pi$
$60$		0			0
$61$	−3.26113	+	5.64845i	−0.417545	+	0.723210i	−0.995692	−	0.0927232i	$-0.970443\pi$
$61$	−3.26113	+	5.64845i	−0.417545	+	0.723210i	0.578147	+	0.815933i	$0.303776\pi$
$62$	2.65695	+	4.60196i	0.337432	+	0.584450i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	0.822405	+	3.51051i	0.102007	+	0.435425i
$66$		0			0
$67$	3.04406	+	0.815653i	0.371891	+	0.0996479i	0.439924	−	0.898035i	$-0.355006\pi$
$67$	3.04406	+	0.815653i	0.371891	+	0.0996479i	−0.0680326	+	0.997683i	$0.521672\pi$
$68$	1.57572	−	0.909743i	0.191084	−	0.110323i
$69$		0			0
$70$	3.12351	−	3.12351i	0.373331	−	0.373331i
$71$	13.8746	−	3.71770i	1.64662	−	0.441210i	0.687955	−	0.725754i	$-0.258509\pi$
$71$	13.8746	−	3.71770i	1.64662	−	0.441210i	0.958663	+	0.284544i	$0.0918421\pi$
$72$		0			0
$73$	−1.33745	−	1.33745i	−0.156536	−	0.156536i	0.624494	−	0.781030i	$-0.285305\pi$
$73$	−1.33745	−	1.33745i	−0.156536	−	0.156536i	−0.781030	+	0.624494i	$0.785305\pi$
$74$	7.00810	+	4.04613i	0.814676	+	0.470353i
$75$		0			0
$76$	−1.88215	+	7.02429i	−0.215898	+	0.805741i
$77$	24.6183			2.80552
$78$		0			0
$79$	4.34474			0.488821			0.244410	−	0.969672i	$-0.421406\pi$
$79$	4.34474			0.488821			0.244410	+	0.969672i	$0.421406\pi$
$80$	0.258819	−	0.965926i	0.0289368	−	0.107994i
$81$		0			0
$82$	−3.46410	−	2.00000i	−0.382546	−	0.220863i
$83$	3.28962	+	3.28962i	0.361083	+	0.361083i	0.864212	−	0.503129i	$-0.167818\pi$
$83$	3.28962	+	3.28962i	0.361083	+	0.361083i	−0.503129	+	0.864212i	$0.667818\pi$
$84$		0			0
$85$	1.75749	−	0.470918i	0.190626	−	0.0510782i
$86$	−5.11641	+	5.11641i	−0.551717	+	0.551717i
$87$		0			0
$88$	4.82648	−	2.78657i	0.514505	−	0.297049i
$89$	−5.23972	−	1.40398i	−0.555409	−	0.148821i	−0.0298129	−	0.999555i	$-0.509491\pi$
$89$	−5.23972	−	1.40398i	−0.555409	−	0.148821i	−0.525596	+	0.850734i	$0.676158\pi$
$90$		0			0
$91$	−15.2459	−	4.60739i	−1.59820	−	0.482985i
$92$			4.15074i			0.432745i
$93$		0			0
$94$	4.30155	+	7.45050i	0.443671	+	0.768460i
$95$	−3.63604	+	6.29780i	−0.373050	+	0.646141i
$96$		0			0
$97$	1.48272	+	5.53360i	0.150548	+	0.561852i	0.999446	+	0.0332948i	$0.0106000\pi$
$97$	1.48272	+	5.53360i	0.150548	+	0.561852i	−0.848898	+	0.528557i	$0.822733\pi$
$98$	3.23852	+	12.0863i	0.327140	+	1.22090i
$99$		0			0
$100$	0.500000	−	0.866025i	0.0500000	−	0.0866025i
$101$	0.873769	+	1.51341i	0.0869432	+	0.150590i	0.906218	−	0.422812i	$-0.138957\pi$
$101$	0.873769	+	1.51341i	0.0869432	+	0.150590i	−0.819274	+	0.573402i	$0.805623\pi$
$102$		0			0
$103$		−	18.8604i		−	1.85838i	−0.369608	−	0.929188i	$-0.620508\pi$
$103$		−	18.8604i		−	1.85838i	0.369608	−	0.929188i	$-0.379492\pi$
$104$	−3.51051	+	0.822405i	−0.344233	+	0.0806435i
$105$		0			0
$106$	−4.87534	−	1.30634i	−0.473535	−	0.126883i
$107$	−4.92179	+	2.84159i	−0.475807	+	0.274707i	−0.718667	−	0.695354i	$-0.755248\pi$
$107$	−4.92179	+	2.84159i	−0.475807	+	0.274707i	0.242860	+	0.970061i	$0.421914\pi$
$108$		0			0
$109$	−5.12766	+	5.12766i	−0.491141	+	0.491141i	−0.908666	−	0.417525i	$-0.862898\pi$
$109$	−5.12766	+	5.12766i	−0.491141	+	0.491141i	0.417525	+	0.908666i	$0.362898\pi$
$110$	5.38324	−	1.44244i	0.513272	−	0.137531i
$111$		0			0
$112$	3.12351	+	3.12351i	0.295144	+	0.295144i
$113$	−4.72163	−	2.72604i	−0.444174	−	0.256444i	0.261193	−	0.965287i	$-0.415884\pi$
$113$	−4.72163	−	2.72604i	−0.444174	−	0.256444i	−0.705366	+	0.708843i	$0.749218\pi$
$114$		0			0
$115$	−1.07429	+	4.00931i	−0.100178	+	0.373870i
$116$	6.34917			0.589505
$117$		0			0
$118$	−0.395611			−0.0364189
$119$	−2.08019	+	7.76338i	−0.190691	+	0.711668i
$120$		0			0
$121$	17.3724	+	10.0300i	1.57931	+	0.911814i
$122$	−4.61194	−	4.61194i	−0.417545	−	0.417545i
$123$		0			0
$124$	−5.13282	+	1.37534i	−0.460941	+	0.123509i
$125$	0.707107	−	0.707107i	0.0632456	−	0.0632456i
$126$		0			0
$127$	−6.63052	+	3.82814i	−0.588364	+	0.339692i	−0.764450	−	0.644683i	$-0.776990\pi$
$127$	−6.63052	+	3.82814i	−0.588364	+	0.339692i	0.176086	+	0.984375i	$0.443656\pi$
$128$	0.965926	+	0.258819i	0.0853766	+	0.0228766i
$129$		0			0
$130$	−3.60374	−	0.114203i	−0.316069	−	0.0100163i
$131$		−	6.95870i		−	0.607985i	−0.952674	−	0.303992i	$-0.901680\pi$
$131$		−	6.95870i		−	0.607985i	0.952674	−	0.303992i	$-0.0983197\pi$
$132$		0			0
$133$	−16.0615	−	27.8194i	−1.39271	−	2.41225i
$134$	−1.57572	+	2.72923i	−0.136122	+	0.235769i
$135$		0			0
$136$	0.470918	+	1.75749i	0.0403809	+	0.150703i
$137$	−5.65041	−	21.0876i	−0.482747	−	1.80164i	−0.589999	−	0.807404i	$-0.700872\pi$
$137$	−5.65041	−	21.0876i	−0.482747	−	1.80164i	0.107252	−	0.994232i	$-0.465795\pi$
$138$		0			0
$139$	−9.87570	+	17.1052i	−0.837646	+	1.45085i	0.0542112	+	0.998529i	$0.482736\pi$
$139$	−9.87570	+	17.1052i	−0.837646	+	1.45085i	−0.891858	+	0.452316i	$0.850598\pi$
$140$	2.20866	+	3.82551i	0.186666	+	0.323314i
$141$		0			0
$142$			14.3641i			1.20541i
$143$	−13.7516	−	14.6517i	−1.14997	−	1.22524i
$144$		0			0
$145$	6.13282	+	1.64329i	0.509303	+	0.136467i
$146$	1.63803	−	0.945717i	0.135564	−	0.0782681i
$147$		0			0
$148$	−5.72209	+	5.72209i	−0.470353	+	0.470353i
$149$	2.17972	−	0.584056i	0.178570	−	0.0478477i	−0.168426	−	0.985714i	$-0.553868\pi$
$149$	2.17972	−	0.584056i	0.178570	−	0.0478477i	0.346996	+	0.937867i	$0.387202\pi$
$150$		0			0
$151$	9.58447	+	9.58447i	0.779973	+	0.779973i	0.979826	−	0.199853i	$-0.0640463\pi$
$151$	9.58447	+	9.58447i	0.779973	+	0.779973i	−0.199853	+	0.979826i	$0.564046\pi$
$152$	−6.29780	−	3.63604i	−0.510819	−	0.294922i
$153$		0			0
$154$	−6.37169	+	23.7795i	−0.513446	+	1.91620i
$155$	−5.31389			−0.426822
$156$		0			0
$157$	12.9292			1.03186			0.515932	−	0.856630i	$-0.327446\pi$
$157$	12.9292			1.03186			0.515932	+	0.856630i	$0.327446\pi$
$158$	−1.12450	+	4.19669i	−0.0894604	+	0.333871i
$159$		0			0
$160$	0.866025	+	0.500000i	0.0684653	+	0.0395285i
$161$	−12.9649	−	12.9649i	−1.02178	−	1.02178i
$162$		0			0
$163$	5.50881	−	1.47608i	0.431483	−	0.115616i	−0.0365391	−	0.999332i	$-0.511633\pi$
$163$	5.50881	−	1.47608i	0.431483	−	0.115616i	0.468022	+	0.883717i	$0.344967\pi$
$164$	2.82843	−	2.82843i	0.220863	−	0.220863i
$165$		0			0
$166$	−4.02895	+	2.32611i	−0.312707	+	0.180541i
$167$	−3.64086	−	0.975565i	−0.281738	−	0.0754915i	0.115183	−	0.993344i	$-0.463255\pi$
$167$	−3.64086	−	0.975565i	−0.281738	−	0.0754915i	−0.396921	+	0.917853i	$0.629921\pi$
$168$		0			0
$169$	5.77412	+	11.6473i	0.444163	+	0.895946i
$170$			1.81949i			0.139548i
$171$		0			0
$172$	−3.61785	−	6.26630i	−0.275858	−	0.477801i
$173$	1.99071	−	3.44801i	0.151351	−	0.262147i	−0.780374	−	0.625314i	$-0.784971\pi$
$173$	1.99071	−	3.44801i	0.151351	−	0.262147i	0.931724	+	0.363167i	$0.118304\pi$
$174$		0			0
$175$	1.14329	+	4.26680i	0.0864243	+	0.322540i
$176$	1.44244	+	5.38324i	0.108728	+	0.405777i
$177$		0			0
$178$	2.71228	−	4.69781i	0.203294	−	0.352115i
$179$	11.6942	+	20.2550i	0.874067	+	1.51393i	0.857754	+	0.514061i	$0.171859\pi$
$179$	11.6942	+	20.2550i	0.874067	+	1.51393i	0.0163127	+	0.999867i	$0.494807\pi$
$180$		0			0
$181$		−	1.18813i		−	0.0883127i	−0.999025	−	0.0441564i	$-0.985940\pi$
$181$		−	1.18813i		−	0.0883127i	0.999025	−	0.0441564i	$-0.0140600\pi$
$182$	8.39632	−	13.5339i	0.622376	−	1.00320i
$183$		0			0
$184$	−4.00931	−	1.07429i	−0.295570	−	0.0791978i
$185$	−7.00810	+	4.04613i	−0.515246	+	0.297477i
$186$		0			0
$187$	−7.17024	+	7.17024i	−0.524340	+	0.524340i
$188$	−8.30995	+	2.22664i	−0.606066	+	0.162395i
$189$		0			0
$190$	−5.14214	−	5.14214i	−0.373050	−	0.373050i
$191$	−11.1791	−	6.45423i	−0.808888	−	0.467012i	0.0376815	−	0.999290i	$-0.488003\pi$
$191$	−11.1791	−	6.45423i	−0.808888	−	0.467012i	−0.846570	+	0.532278i	$0.821336\pi$
$192$		0			0
$193$	1.62753	−	6.07401i	0.117152	−	0.437217i	−0.882287	−	0.470712i	$-0.843997\pi$
$193$	1.62753	−	6.07401i	0.117152	−	0.437217i	0.999439	+	0.0334950i	$0.0106638\pi$
$194$	−5.72880			−0.411304
$195$		0			0
$196$	−12.5127			−0.893763
$197$	−3.93573	+	14.6883i	−0.280409	+	1.04650i	0.671720	+	0.740805i	$0.265556\pi$
$197$	−3.93573	+	14.6883i	−0.280409	+	1.04650i	−0.952129	+	0.305695i	$0.901111\pi$
$198$		0			0
$199$	12.2447	+	7.06950i	0.868006	+	0.501143i	0.866685	−	0.498856i	$-0.166246\pi$
$199$	12.2447	+	7.06950i	0.868006	+	0.501143i	0.00132072	+	0.999999i	$0.499580\pi$
$200$	0.707107	+	0.707107i	0.0500000	+	0.0500000i
$201$		0			0
$202$	−1.68799	+	0.452296i	−0.118767	+	0.0318234i
$203$	−19.8317	+	19.8317i	−1.39191	+	1.39191i
$204$		0			0
$205$	3.46410	−	2.00000i	0.241943	−	0.139686i
$206$	18.2178	+	4.88144i	1.26929	+	0.340106i
$207$		0			0
$208$	0.114203	−	3.60374i	0.00791855	−	0.249875i
$209$		−	40.5283i		−	2.80340i
$210$		0			0
$211$	6.32182	+	10.9497i	0.435212	+	0.753810i	0.997313	−	0.0732592i	$-0.0233400\pi$
$211$	6.32182	+	10.9497i	0.435212	+	0.753810i	−0.562101	+	0.827069i	$0.690007\pi$
$212$	2.52366	−	4.37111i	0.173326	−	0.300209i
$213$		0			0
$214$	−1.47092	−	5.48954i	−0.100550	−	0.375257i
$215$	−1.87274	−	6.98915i	−0.127720	−	0.476656i
$216$		0			0
$217$	11.7366	−	20.3283i	0.796730	−	1.37998i
$218$	−3.62580	−	6.28008i	−0.245570	−	0.425340i
$219$		0			0
$220$			5.57314i			0.375741i
$221$	5.78239	−	3.09853i	0.388965	−	0.208429i
$222$		0			0
$223$	−23.6065	−	6.32533i	−1.58081	−	0.423576i	−0.641630	−	0.767014i	$-0.721742\pi$
$223$	−23.6065	−	6.32533i	−1.58081	−	0.423576i	−0.939175	+	0.343438i	$0.888408\pi$
$224$	−3.82551	+	2.20866i	−0.255602	+	0.147572i
$225$		0			0
$226$	3.85520	−	3.85520i	0.256444	−	0.256444i
$227$	2.95396	−	0.791511i	0.196061	−	0.0525344i	−0.159452	−	0.987206i	$-0.550973\pi$
$227$	2.95396	−	0.791511i	0.196061	−	0.0525344i	0.355513	+	0.934671i	$0.384306\pi$
$228$		0			0
$229$	7.17854	+	7.17854i	0.474371	+	0.474371i	0.903326	−	0.428955i	$-0.141118\pi$
$229$	7.17854	+	7.17854i	0.474371	+	0.474371i	−0.428955	+	0.903326i	$0.641118\pi$
$230$	−3.59465	−	2.07537i	−0.237024	−	0.136846i
$231$		0			0
$232$	−1.64329	+	6.13282i	−0.107887	+	0.402640i
$233$	−8.52268			−0.558339			−0.279170	−	0.960242i	$-0.590059\pi$
$233$	−8.52268			−0.558339			−0.279170	+	0.960242i	$0.590059\pi$
$234$		0			0
$235$	−8.60310			−0.561204
$236$	0.102392	−	0.382131i	0.00666513	−	0.0248746i
$237$		0			0
$238$	−6.96046	−	4.01862i	−0.451179	−	0.260489i
$239$	21.4707	+	21.4707i	1.38882	+	1.38882i	0.827804	+	0.561017i	$0.189590\pi$
$239$	21.4707	+	21.4707i	1.38882	+	1.38882i	0.561017	+	0.827804i	$0.310410\pi$
$240$		0			0
$241$	4.83745	−	1.29619i	0.311607	−	0.0834949i	−0.0996263	−	0.995025i	$-0.531765\pi$
$241$	4.83745	−	1.29619i	0.311607	−	0.0834949i	0.411234	+	0.911530i	$0.365098\pi$
$242$	−14.1845	+	14.1845i	−0.911814	+	0.911814i
$243$		0			0
$244$	5.64845	−	3.26113i	0.361605	−	0.208773i
$245$	−12.0863	−	3.23852i	−0.772167	−	0.206901i
$246$		0			0
$247$	−7.58499	+	25.0988i	−0.482621	+	1.59700i
$248$		−	5.31389i		−	0.337432i
$249$		0			0
$250$	0.500000	+	0.866025i	0.0316228	+	0.0547723i
$251$	0.862488	−	1.49387i	0.0544398	−	0.0942924i	−0.837521	−	0.546405i	$-0.815996\pi$
$251$	0.862488	−	1.49387i	0.0544398	−	0.0942924i	0.891961	+	0.452112i	$0.149329\pi$
$252$		0			0
$253$	−5.98718	−	22.3445i	−0.376411	−	1.40478i
$254$	−1.98159	−	7.39539i	−0.124336	−	0.464028i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	5.50584	+	9.53640i	0.343445	+	0.594864i	0.985070	−	0.172154i	$-0.0550728\pi$
$257$	5.50584	+	9.53640i	0.343445	+	0.594864i	−0.641625	+	0.767018i	$0.721739\pi$
$258$		0			0
$259$		−	35.7461i		−	2.22115i
$260$	1.04303	−	3.45139i	0.0646859	−	0.214046i
$261$		0			0
$262$	6.72159	+	1.80104i	0.415261	+	0.111269i
$263$	6.71821	−	3.87876i	0.414262	−	0.239174i	−0.278357	−	0.960478i	$-0.589790\pi$
$263$	6.71821	−	3.87876i	0.414262	−	0.239174i	0.692619	+	0.721303i	$0.256457\pi$
$264$		0			0
$265$	3.56899	−	3.56899i	0.219242	−	0.219242i
$266$	31.0285	−	8.31406i	1.90248	−	0.509768i
$267$		0			0
$268$	−2.22841	−	2.22841i	−0.136122	−	0.136122i
$269$	−26.3118	−	15.1911i	−1.60426	−	0.926218i	−0.990623	−	0.136627i	$-0.956374\pi$
$269$	−26.3118	−	15.1911i	−1.60426	−	0.926218i	−0.613634	−	0.789591i	$-0.710293\pi$
$270$		0			0
$271$	−8.04544	+	30.0260i	−0.488726	+	1.82395i	0.0739367	+	0.997263i	$0.476444\pi$
$271$	−8.04544	+	30.0260i	−0.488726	+	1.82395i	−0.562663	+	0.826687i	$0.690223\pi$
$272$	−1.81949			−0.110323
$273$		0			0
$274$	21.8315			1.31889
$275$	−1.44244	+	5.38324i	−0.0869821	+	0.324622i
$276$		0			0
$277$	−25.5003	−	14.7226i	−1.53216	−	0.884595i	−0.999262	−	0.0384180i	$-0.987768\pi$
$277$	−25.5003	−	14.7226i	−1.53216	−	0.884595i	−0.532902	−	0.846177i	$-0.678898\pi$
$278$	−13.9664	−	13.9664i	−0.837646	−	0.837646i
$279$		0			0
$280$	−4.26680	+	1.14329i	−0.254990	+	0.0683244i
$281$	−10.6381	+	10.6381i	−0.634615	+	0.634615i	−0.949222	−	0.314607i	$-0.898127\pi$
$281$	−10.6381	+	10.6381i	−0.634615	+	0.634615i	0.314607	+	0.949222i	$0.398127\pi$
$282$		0			0
$283$	−16.0514	+	9.26730i	−0.954159	+	0.550884i	−0.894370	−	0.447327i	$-0.852376\pi$
$283$	−16.0514	+	9.26730i	−0.954159	+	0.550884i	−0.0597885	+	0.998211i	$0.519043\pi$
$284$	−13.8746	−	3.71770i	−0.823309	−	0.220605i
$285$		0			0
$286$	17.7116	−	9.49088i	1.04731	−	0.561208i
$287$			17.6693i			1.04298i
$288$		0			0
$289$	6.84474	+	11.8554i	0.402632	+	0.697378i
$290$	−3.17458	+	5.49854i	−0.186418	+	0.322885i
$291$		0			0
$292$	0.489539	+	1.82699i	0.0286481	+	0.106916i
$293$	−6.57898	−	24.5531i	−0.384348	−	1.43441i	−0.839192	−	0.543835i	$-0.816972\pi$
$293$	−6.57898	−	24.5531i	−0.384348	−	1.43441i	0.454844	−	0.890571i	$-0.349695\pi$
$294$		0			0
$295$	0.197805	−	0.342609i	0.0115167	−	0.0199475i
$296$	−4.04613	−	7.00810i	−0.235177	−	0.407338i
$297$		0			0
$298$			2.25662i			0.130722i
$299$	−0.474027	+	14.9582i	−0.0274137	+	0.865056i
$300$		0			0
$301$	30.8733	+	8.27247i	1.77951	+	0.476817i
$302$	−11.7385	+	6.77725i	−0.675477	+	0.389987i
$303$		0			0
$304$	5.14214	−	5.14214i	0.294922	−	0.294922i
$305$	6.30003	−	1.68809i	0.360738	−	0.0966596i
$306$		0			0
$307$	−15.4918	−	15.4918i	−0.884161	−	0.884161i	0.109793	−	0.993954i	$-0.464981\pi$
$307$	−15.4918	−	15.4918i	−0.884161	−	0.884161i	−0.993954	+	0.109793i	$0.964981\pi$
$308$	−21.3201	−	12.3092i	−1.21483	−	0.701380i
$309$		0			0
$310$	1.37534	−	5.13282i	0.0781138	−	0.291525i
$311$	−19.7445			−1.11961			−0.559804	−	0.828625i	$-0.689123\pi$
$311$	−19.7445			−1.11961			−0.559804	+	0.828625i	$0.689123\pi$
$312$		0			0
$313$	29.1251			1.64625			0.823124	−	0.567862i	$-0.192229\pi$
$313$	29.1251			1.64625			0.823124	+	0.567862i	$0.192229\pi$
$314$	−3.34633	+	12.4887i	−0.188844	+	0.704776i
$315$		0			0
$316$	−3.76265	−	2.17237i	−0.211666	−	0.122205i
$317$	7.55111	+	7.55111i	0.424112	+	0.424112i	0.886617	−	0.462505i	$-0.153049\pi$
$317$	7.55111	+	7.55111i	0.424112	+	0.424112i	−0.462505	+	0.886617i	$0.653049\pi$
$318$		0			0
$319$	−34.1791	+	9.15826i	−1.91366	+	0.512764i
$320$	−0.707107	+	0.707107i	−0.0395285	+	0.0395285i
$321$		0			0
$322$	15.8787	−	9.16757i	0.884885	−	0.510889i
$323$	12.7806	+	3.42455i	0.711131	+	0.190547i
$324$		0			0
$325$	1.90077	−	3.06383i	0.105436	−	0.169951i
$326$			5.70314i			0.315868i
$327$		0			0
$328$	2.00000	+	3.46410i	0.110432	+	0.191273i
$329$	19.0013	−	32.9112i	1.04758	−	1.81445i
$330$		0			0
$331$	3.37054	+	12.5790i	0.185262	+	0.691406i	0.994574	+	0.104028i	$0.0331732\pi$
$331$	3.37054	+	12.5790i	0.185262	+	0.691406i	−0.809313	+	0.587378i	$0.800160\pi$
$332$	−1.20409	−	4.49371i	−0.0660828	−	0.246624i
$333$		0			0
$334$	1.88465	−	3.26430i	0.103123	−	0.178615i
$335$	−1.57572	−	2.72923i	−0.0860908	−	0.149114i
$336$		0			0
$337$			34.1480i			1.86016i	0.367355	+	0.930081i	$0.380263\pi$
$337$			34.1480i			1.86016i	−0.367355	+	0.930081i	$0.619737\pi$
$338$	−12.7449	+	2.56283i	−0.693230	+	0.139399i
$339$		0			0
$340$	−1.75749	−	0.470918i	−0.0953132	−	0.0255391i
$341$	25.6474	−	14.8075i	1.38888	−	0.801873i
$342$		0			0
$343$	17.2189	−	17.2189i	0.929734	−	0.929734i
$344$	6.98915	−	1.87274i	0.376829	−	0.100971i
$345$		0			0
$346$	2.81529	+	2.81529i	0.151351	+	0.151351i
$347$	−27.4249	−	15.8338i	−1.47224	−	0.850000i	−0.472731	−	0.881207i	$-0.656732\pi$
$347$	−27.4249	−	15.8338i	−1.47224	−	0.850000i	−0.999513	+	0.0312067i	$0.990065\pi$
$348$		0			0
$349$	−3.18934	+	11.9028i	−0.170721	+	0.637140i	0.826520	+	0.562908i	$0.190317\pi$
$349$	−3.18934	+	11.9028i	−0.170721	+	0.637140i	−0.997241	+	0.0742326i	$0.976349\pi$
$350$	−4.41732			−0.236115
$351$		0			0
$352$	−5.57314			−0.297049
$353$	−4.75651	+	17.7515i	−0.253163	+	0.944818i	0.715940	+	0.698162i	$0.245998\pi$
$353$	−4.75651	+	17.7515i	−0.253163	+	0.944818i	−0.969103	+	0.246656i	$0.920668\pi$
$354$		0			0
$355$	−12.4397	−	7.18205i	−0.660229	−	0.381183i
$356$	3.83574	+	3.83574i	0.203294	+	0.203294i
$357$		0			0
$358$	−22.5915	+	6.05337i	−1.19400	+	0.319931i
$359$	7.47776	−	7.47776i	0.394661	−	0.394661i	−0.481684	−	0.876345i	$-0.659975\pi$
$359$	7.47776	−	7.47776i	0.394661	−	0.394661i	0.876345	+	0.481684i	$0.159975\pi$
$360$		0			0
$361$	−29.3436	+	16.9416i	−1.54440	+	0.891661i
$362$	1.14764	+	0.307510i	0.0603187	+	0.0161624i
$363$		0			0
$364$	10.8996	+	11.6131i	0.571296	+	0.608689i
$365$			1.89143i			0.0990022i
$366$		0			0
$367$	−10.5767	−	18.3193i	−0.552097	−	0.956260i	−0.998123	−	0.0612398i	$-0.980495\pi$
$367$	−10.5767	−	18.3193i	−0.552097	−	0.956260i	0.446026	−	0.895020i	$-0.352839\pi$
$368$	2.07537	−	3.59465i	0.108186	−	0.187384i
$369$		0			0
$370$	−2.09443	−	7.81652i	−0.108884	−	0.406362i
$371$	5.77053	+	21.5359i	0.299591	+	1.11809i
$372$		0			0
$373$	−10.0170	+	17.3499i	−0.518659	+	0.898344i	0.481106	+	0.876662i	$0.340235\pi$
$373$	−10.0170	+	17.3499i	−0.518659	+	0.898344i	−0.999765	+	0.0216812i	$0.993098\pi$
$374$	−5.07013	−	8.78172i	−0.262170	−	0.454092i
$375$		0			0
$376$		−	8.60310i		−	0.443671i
$377$	22.8808	+	0.725094i	1.17842	+	0.0373442i
$378$		0			0
$379$	−22.6955	−	6.08124i	−1.16579	−	0.312372i	−0.376514	−	0.926411i	$-0.622877\pi$
$379$	−22.6955	−	6.08124i	−1.16579	−	0.312372i	−0.789276	+	0.614039i	$0.789544\pi$
$380$	6.29780	−	3.63604i	0.323071	−	0.186525i
$381$		0			0
$382$	9.12766	−	9.12766i	0.467012	−	0.467012i
$383$	−8.03315	+	2.15247i	−0.410475	+	0.109986i	−0.458146	−	0.888877i	$-0.651486\pi$
$383$	−8.03315	+	2.15247i	−0.410475	+	0.109986i	0.0476719	+	0.998863i	$0.484820\pi$
$384$		0			0
$385$	−17.4078	−	17.4078i	−0.887183	−	0.887183i
$386$	5.44581	+	3.14414i	0.277184	+	0.160033i
$387$		0			0
$388$	1.48272	−	5.53360i	0.0752739	−	0.280926i
$389$	−33.5846			−1.70281			−0.851403	−	0.524511i	$-0.824248\pi$
$389$	−33.5846			−1.70281			−0.851403	+	0.524511i	$0.824248\pi$
$390$		0			0
$391$	7.55222			0.381932
$392$	3.23852	−	12.0863i	0.163570	−	0.610451i
$393$		0			0
$394$	−13.1692	−	7.60324i	−0.663455	−	0.383046i
$395$	−3.07219	−	3.07219i	−0.154579	−	0.154579i
$396$		0			0
$397$	27.6808	−	7.41704i	1.38926	−	0.372250i	0.514782	−	0.857321i	$-0.327873\pi$
$397$	27.6808	−	7.41704i	1.38926	−	0.372250i	0.874475	+	0.485071i	$0.161206\pi$
$398$	−9.99778	+	9.99778i	−0.501143	+	0.501143i
$399$		0			0
$400$	−0.866025	+	0.500000i	−0.0433013	+	0.0250000i
$401$	−26.5627	−	7.11747i	−1.32648	−	0.355429i	−0.475079	−	0.879943i	$-0.657580\pi$
$401$	−26.5627	−	7.11747i	−1.32648	−	0.355429i	−0.851402	+	0.524514i	$0.824247\pi$
$402$		0			0
$403$	−18.6544	+	4.37017i	−0.929244	+	0.217694i
$404$		−	1.74754i		−	0.0869432i
$405$		0			0
$406$	−14.0231	−	24.2888i	−0.695957	−	1.20543i
$407$	22.5497	−	39.0572i	1.11775	−	1.93599i
$408$		0			0
$409$	−1.85172	−	6.91073i	−0.0915619	−	0.341714i	0.904914	−	0.425595i	$-0.139935\pi$
$409$	−1.85172	−	6.91073i	−0.0915619	−	0.341714i	−0.996476	+	0.0838811i	$0.973268\pi$
$410$	1.03528	+	3.86370i	0.0511286	+	0.190815i
$411$		0			0
$412$	−9.43022	+	16.3336i	−0.464594	+	0.804700i
$413$	0.873769	+	1.51341i	0.0429954	+	0.0744701i
$414$		0			0
$415$		−	4.65223i		−	0.228369i
$416$	3.45139	+	1.04303i	0.169218	+	0.0511387i
$417$		0			0
$418$	39.1473	+	10.4895i	1.91476	+	0.513058i
$419$	−26.0222	+	15.0239i	−1.27127	+	0.733966i	−0.975226	−	0.221209i	$-0.929000\pi$
$419$	−26.0222	+	15.0239i	−1.27127	+	0.733966i	−0.296041	+	0.955175i	$0.595666\pi$
$420$		0			0
$421$	−6.76430	+	6.76430i	−0.329672	+	0.329672i	−0.852462	−	0.522790i	$-0.824891\pi$
$421$	−6.76430	+	6.76430i	−0.329672	+	0.329672i	0.522790	+	0.852462i	$0.324891\pi$
$422$	−12.2128	+	3.27242i	−0.594511	+	0.159299i
$423$		0			0
$424$	3.56899	+	3.56899i	0.173326	+	0.173326i
$425$	−1.57572	−	0.909743i	−0.0764337	−	0.0441290i
$426$		0			0
$427$	−7.45681	+	27.8292i	−0.360860	+	1.34675i
$428$	5.68319			0.274707
$429$		0			0
$430$	7.23570			0.348936
$431$	0.103874	−	0.387662i	0.00500342	−	0.0186730i	−0.963379	−	0.268143i	$-0.913590\pi$
$431$	0.103874	−	0.387662i	0.00500342	−	0.0186730i	0.968382	+	0.249470i	$0.0802565\pi$
$432$		0			0
$433$	4.08563	+	2.35884i	0.196343	+	0.113359i	0.594949	−	0.803764i	$-0.297172\pi$
$433$	4.08563	+	2.35884i	0.196343	+	0.113359i	−0.398606	+	0.917122i	$0.630506\pi$
$434$	16.5980	+	16.5980i	0.796730	+	0.796730i
$435$		0			0
$436$	7.00452	−	1.87685i	0.335455	−	0.0898850i
$437$	−21.3437	+	21.3437i	−1.02101	+	1.02101i
$438$		0			0
$439$	21.8959	−	12.6416i	1.04504	−	0.603352i	0.123781	−	0.992310i	$-0.460498\pi$
$439$	21.8959	−	12.6416i	1.04504	−	0.603352i	0.921256	+	0.388957i	$0.127165\pi$
$440$	−5.38324	−	1.44244i	−0.256636	−	0.0687654i
$441$		0			0
$442$	1.49636	+	6.38732i	0.0711744	+	0.303814i
$443$			20.0938i			0.954687i	0.878717	+	0.477344i	$0.158400\pi$
$443$			20.0938i			0.954687i	−0.878717	+	0.477344i	$0.841600\pi$
$444$		0			0
$445$	2.71228	+	4.69781i	0.128574	+	0.222697i
$446$	12.2196	−	21.1650i	0.578615	−	1.00219i
$447$		0			0
$448$	−1.14329	−	4.26680i	−0.0540152	−	0.201587i
$449$	6.64945	+	24.8161i	0.313807	+	1.17114i	0.925095	+	0.379735i	$0.123985\pi$
$449$	6.64945	+	24.8161i	0.313807	+	1.17114i	−0.611288	+	0.791408i	$0.709348\pi$
$450$		0			0
$451$	−11.1463	+	19.3059i	−0.524858	+	0.909081i
$452$	2.72604	+	4.72163i	0.128222	+	0.222087i
$453$		0			0
$454$			3.05816i			0.143527i
$455$	7.52255	+	14.0384i	0.352663	+	0.658129i
$456$		0			0
$457$	25.6393	+	6.87004i	1.19936	+	0.321367i	0.802578	−	0.596547i	$-0.203461\pi$
$457$	25.6393	+	6.87004i	1.19936	+	0.321367i	0.396779	+	0.917914i	$0.370128\pi$
$458$	−8.79188	+	5.07599i	−0.410817	+	0.237186i
$459$		0			0
$460$	2.93502	−	2.93502i	0.136846	−	0.136846i
$461$	−23.6090	+	6.32603i	−1.09958	+	0.294632i	−0.762595	−	0.646876i	$-0.776075\pi$
$461$	−23.6090	+	6.32603i	−1.09958	+	0.294632i	−0.336988	+	0.941509i	$0.609408\pi$
$462$		0			0
$463$	22.5323	+	22.5323i	1.04716	+	1.04716i	0.998831	+	0.0483337i	$0.0153911\pi$
$463$	22.5323	+	22.5323i	1.04716	+	1.04716i	0.0483337	+	0.998831i	$0.484609\pi$
$464$	−5.49854	−	3.17458i	−0.255263	−	0.147376i
$465$		0			0
$466$	2.20583	−	8.23227i	0.102183	−	0.381353i
$467$	27.3009			1.26333			0.631667	−	0.775240i	$-0.282371\pi$
$467$	27.3009			1.26333			0.631667	+	0.775240i	$0.282371\pi$
$468$		0			0
$469$	13.9209			0.642808
$470$	2.22664	−	8.30995i	0.102707	−	0.383309i
$471$		0			0
$472$	0.342609	+	0.197805i	0.0157699	+	0.00910473i
$473$	28.5145	+	28.5145i	1.31110	+	1.31110i
$474$		0			0
$475$	7.02429	−	1.88215i	0.322296	−	0.0863591i
$476$	5.68319	−	5.68319i	0.260489	−	0.260489i
$477$		0			0
$478$	−26.2961	+	15.1820i	−1.20275	+	0.694411i
$479$	20.1538	+	5.40020i	0.920851	+	0.246741i	0.687949	−	0.725759i	$-0.258511\pi$
$479$	20.1538	+	5.40020i	0.920851	+	0.246741i	0.232902	+	0.972500i	$0.425178\pi$
$480$		0			0
$481$	−21.2744	+	19.9675i	−0.970030	+	0.910438i
$482$			5.00809i			0.228112i
$483$		0			0
$484$	−10.0300	−	17.3724i	−0.455907	−	0.789654i
$485$	2.86440	−	4.96129i	0.130066	−	0.225281i
$486$		0			0
$487$	−2.58111	−	9.63282i	−0.116961	−	0.436505i	0.882465	−	0.470378i	$-0.155882\pi$
$487$	−2.58111	−	9.63282i	−0.116961	−	0.436505i	−0.999426	+	0.0338731i	$0.989216\pi$
$488$	1.68809	+	6.30003i	0.0764161	+	0.285189i
$489$		0			0
$490$	6.25634	−	10.8363i	0.282633	−	0.489534i
$491$	−8.09448	−	14.0201i	−0.365299	−	0.632716i	0.623525	−	0.781803i	$-0.285700\pi$
$491$	−8.09448	−	14.0201i	−0.365299	−	0.632716i	−0.988824	+	0.149087i	$0.952367\pi$
$492$		0			0
$493$		−	11.5522i		−	0.520286i
$494$	−22.2804	−	13.8226i	−1.00244	−	0.621907i
$495$		0			0
$496$	5.13282	+	1.37534i	0.230471	+	0.0617544i
$497$	54.9499	−	31.7254i	2.46484	−	1.42308i
$498$		0			0
$499$	24.9871	−	24.9871i	1.11858	−	1.11858i	0.126626	−	0.991951i	$-0.459585\pi$
$499$	24.9871	−	24.9871i	1.11858	−	1.11858i	0.991951	−	0.126626i	$-0.0404148\pi$
$500$	−0.965926	+	0.258819i	−0.0431975	+	0.0115747i
$501$		0			0
$502$	1.21974	+	1.21974i	0.0544398	+	0.0544398i
$503$	22.0359	+	12.7224i	0.982533	+	0.567266i	0.903034	−	0.429569i	$-0.141335\pi$
$503$	22.0359	+	12.7224i	0.982533	+	0.567266i	0.0794993	+	0.996835i	$0.474668\pi$
$504$		0			0
$505$	0.452296	−	1.68799i	0.0201269	−	0.0751146i
$506$	23.1327			1.02837
$507$		0			0
$508$	7.65627			0.339692
$509$	−2.77050	+	10.3397i	−0.122800	+	0.458297i	−0.999752	−	0.0222820i	$-0.992907\pi$
$509$	−2.77050	+	10.3397i	−0.122800	+	0.458297i	0.876951	+	0.480579i	$0.159574\pi$
$510$		0			0
$511$	−7.23570	−	4.17753i	−0.320088	−	0.184803i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$		0			0
$514$	−10.6365	+	2.85003i	−0.469155	+	0.125710i
$515$	−13.3364	+	13.3364i	−0.587670	+	0.587670i
$516$		0			0
$517$	41.5227	−	23.9731i	1.82617	−	1.05434i
$518$	34.5281	+	9.25176i	1.51708	+	0.406499i
$519$		0			0
$520$	3.06383	+	1.90077i	0.134358	+	0.0833544i
$521$		−	10.0995i		−	0.442466i	−0.975221	−	0.221233i	$-0.928992\pi$
$521$		−	10.0995i		−	0.442466i	0.975221	−	0.221233i	$-0.0710081\pi$
$522$		0			0
$523$	−11.1887	−	19.3794i	−0.489247	−	0.847401i	0.510676	−	0.859773i	$-0.329395\pi$
$523$	−11.1887	−	19.3794i	−0.489247	−	0.847401i	−0.999923	+	0.0123720i	$0.996062\pi$
$524$	−3.47935	+	6.02641i	−0.151996	+	0.263265i
$525$		0			0
$526$	2.00779	+	7.49318i	0.0875439	+	0.326718i
$527$	2.50240	+	9.33910i	0.109006	+	0.406818i
$528$		0			0
$529$	2.88566	−	4.99811i	0.125464	−	0.217309i
$530$	2.52366	+	4.37111i	0.109621	+	0.189869i
$531$		0			0
$532$			32.1231i			1.39271i
$533$	10.5159	−	9.86991i	0.455496	−	0.427513i
$534$		0			0
$535$	5.48954	+	1.47092i	0.237333	+	0.0635933i
$536$	2.72923	−	1.57572i	0.117885	−	0.0680608i
$537$		0			0
$538$	21.4835	−	21.4835i	0.926218	−	0.926218i
$539$	67.3588	−	18.0487i	2.90135	−	0.777414i
$540$		0			0
$541$	10.0889	+	10.0889i	0.433754	+	0.433754i	0.889903	−	0.456149i	$-0.150772\pi$
$541$	10.0889	+	10.0889i	0.433754	+	0.433754i	−0.456149	+	0.889903i	$0.650772\pi$
$542$	−26.9206	−	15.5426i	−1.15634	−	0.667612i
$543$		0			0
$544$	0.470918	−	1.75749i	0.0201904	−	0.0753517i
$545$	7.25161			0.310625
$546$		0			0
$547$	−30.3525			−1.29778			−0.648889	−	0.760883i	$-0.724766\pi$
$547$	−30.3525			−1.29778			−0.648889	+	0.760883i	$0.724766\pi$
$548$	−5.65041	+	21.0876i	−0.241373	+	0.900818i
$549$		0			0
$550$	−4.82648	−	2.78657i	−0.205802	−	0.118820i
$551$	32.6483	+	32.6483i	1.39086	+	1.39086i
$552$		0			0
$553$	18.5381	−	4.96727i	0.788321	−	0.211230i
$554$	20.8209	−	20.8209i	0.884595	−	0.884595i
$555$		0			0
$556$	17.1052	−	9.87570i	0.725423	−	0.418823i
$557$	−8.99197	−	2.40939i	−0.381002	−	0.102089i	0.0632345	−	0.997999i	$-0.479858\pi$
$557$	−8.99197	−	2.40939i	−0.381002	−	0.102089i	−0.444237	+	0.895909i	$0.646525\pi$
$558$		0			0
$559$	−12.3222	−	22.9953i	−0.521172	−	0.972597i
$560$		−	4.41732i		−	0.186666i
$561$		0			0
$562$	−7.52227	−	13.0289i	−0.317308	−	0.549593i
$563$	5.33150	−	9.23443i	0.224696	−	0.389185i	−0.731532	−	0.681807i	$-0.761194\pi$
$563$	5.33150	−	9.23443i	0.224696	−	0.389185i	0.956228	+	0.292622i	$0.0945278\pi$
$564$		0			0
$565$	1.41110	+	5.26630i	0.0593654	+	0.221555i
$566$	−4.79711	−	17.9031i	−0.201638	−	0.752521i
$567$		0			0
$568$	7.18205	−	12.4397i	0.301352	−	0.521957i
$569$	4.95673	+	8.58531i	0.207797	+	0.359915i	0.951020	−	0.309129i	$-0.100037\pi$
$569$	4.95673	+	8.58531i	0.207797	+	0.359915i	−0.743223	+	0.669043i	$0.766704\pi$
$570$		0			0
$571$			44.0742i			1.84445i	0.386656	+	0.922224i	$0.373630\pi$
$571$			44.0742i			1.84445i	−0.386656	+	0.922224i	$0.626370\pi$
$572$	4.58338	+	19.5645i	0.191641	+	0.818035i
$573$		0			0
$574$	−17.0672	−	4.57314i	−0.712371	−	0.190879i
$575$	3.59465	−	2.07537i	0.149907	−	0.0865490i
$576$		0			0
$577$	−8.17679	+	8.17679i	−0.340404	+	0.340404i	−0.856519	−	0.516115i	$-0.827378\pi$
$577$	−8.17679	+	8.17679i	−0.340404	+	0.340404i	0.516115	+	0.856519i	$0.327378\pi$
$578$	−13.2230	+	3.54310i	−0.550005	+	0.147373i
$579$		0			0
$580$	−4.48954	−	4.48954i	−0.186418	−	0.186418i
$581$	17.7971	+	10.2752i	0.738349	+	0.426286i
$582$		0			0
$583$	−7.28043	+	27.1709i	−0.301525	+	1.12531i
$584$	−1.89143			−0.0782681
$585$		0			0
$586$	25.4192			1.05006
$587$	−2.94809	+	11.0024i	−0.121681	+	0.454119i	−0.999700	−	0.0245069i	$-0.992198\pi$
$587$	−2.94809	+	11.0024i	−0.121681	+	0.454119i	0.878019	+	0.478626i	$0.158865\pi$
$588$		0			0
$589$	−33.4658	−	19.3215i	−1.37894	−	0.796129i
$590$	0.279739	+	0.279739i	0.0115167	+	0.0115167i
$591$		0			0
$592$	7.81652	−	2.09443i	0.321257	−	0.0860806i
$593$	1.18322	−	1.18322i	0.0485891	−	0.0485891i	−0.682395	−	0.730984i	$-0.739061\pi$
$593$	1.18322	−	1.18322i	0.0485891	−	0.0485891i	0.730984	+	0.682395i	$0.239061\pi$
$594$		0			0
$595$	6.96046	−	4.01862i	0.285351	−	0.164747i
$596$	−2.17972	−	0.584056i	−0.0892850	−	0.0239238i
$597$		0			0
$598$	−14.3258	−	4.32935i	−0.585827	−	0.177040i
$599$		−	36.2200i		−	1.47991i	−0.672657	−	0.739954i	$-0.734847\pi$
$599$		−	36.2200i		−	1.47991i	0.672657	−	0.739954i	$-0.265153\pi$
$600$		0			0
$601$	−1.82381	−	3.15894i	−0.0743949	−	0.128856i	0.826428	−	0.563042i	$-0.190369\pi$
$601$	−1.82381	−	3.15894i	−0.0743949	−	0.128856i	−0.900823	+	0.434187i	$0.857036\pi$
$602$	−15.9812	+	27.6802i	−0.651344	+	1.12816i
$603$		0			0
$604$	−3.50816	−	13.0926i	−0.142745	−	0.532732i
$605$	−5.19189	−	19.3764i	−0.211080	−	0.787762i
$606$		0			0
$607$	6.25647	−	10.8365i	0.253942	−	0.439841i	−0.710665	−	0.703530i	$-0.751606\pi$
$607$	6.25647	−	10.8365i	0.253942	−	0.439841i	0.964608	+	0.263689i	$0.0849393\pi$
$608$	3.63604	+	6.29780i	0.147461	+	0.255410i
$609$		0			0
$610$			6.52227i			0.264079i
$611$	−30.2012	+	7.07523i	−1.22181	+	0.286233i
$612$		0			0
$613$	−0.461463	−	0.123649i	−0.0186383	−	0.00499412i	0.249488	−	0.968378i	$-0.419738\pi$
$613$	−0.461463	−	0.123649i	−0.0186383	−	0.00499412i	−0.268126	+	0.963384i	$0.586404\pi$
$614$	18.9734	−	10.9543i	0.765706	−	0.442081i
$615$		0			0
$616$	17.4078	−	17.4078i	0.701380	−	0.701380i
$617$	2.79759	−	0.749612i	0.112627	−	0.0301782i	−0.202065	−	0.979372i	$-0.564765\pi$
$617$	2.79759	−	0.749612i	0.112627	−	0.0301782i	0.314692	+	0.949194i	$0.398099\pi$
$618$		0			0
$619$	17.1338	+	17.1338i	0.688667	+	0.688667i	0.961937	−	0.273270i	$-0.0881053\pi$
$619$	17.1338	+	17.1338i	0.688667	+	0.688667i	−0.273270	+	0.961937i	$0.588105\pi$
$620$	4.60196	+	2.65695i	0.184819	+	0.106705i
$621$		0			0
$622$	5.11025	−	19.0717i	0.204902	−	0.764706i
$623$	−23.9620			−0.960017
$624$		0			0
$625$	−1.00000			−0.0400000
$626$	−7.53813	+	28.1327i	−0.301284	+	1.12441i
$627$		0			0
$628$	−11.1970	−	6.46460i	−0.446810	−	0.257966i
$629$	10.4113	+	10.4113i	0.415124	+	0.415124i
$630$		0			0
$631$	−0.175763	+	0.0470956i	−0.00699701	+	0.00187484i	−0.262316	−	0.964982i	$-0.584486\pi$
$631$	−0.175763	+	0.0470956i	−0.00699701	+	0.00187484i	0.255319	+	0.966857i	$0.417820\pi$
$632$	3.07219	−	3.07219i	0.122205	−	0.122205i
$633$		0			0
$634$	−9.24818	+	5.33944i	−0.367292	+	0.212056i
$635$	7.39539	+	1.98159i	0.293477	+	0.0786369i
$636$		0			0
$637$	−45.0925	−	1.42899i	−1.78663	−	0.0566184i
$638$		−	35.3848i		−	1.40090i
$639$		0			0
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	13.7638	−	23.8396i	0.543637	−	0.941607i	−0.455054	−	0.890464i	$-0.650380\pi$
$641$	13.7638	−	23.8396i	0.543637	−	0.941607i	0.998691	−	0.0511434i	$-0.0162866\pi$
$642$		0			0
$643$	−5.14710	−	19.2093i	−0.202982	−	0.757539i	−0.990055	−	0.140679i	$-0.955071\pi$
$643$	−5.14710	−	19.2093i	−0.202982	−	0.757539i	0.787073	−	0.616860i	$-0.211595\pi$
$644$	4.74548	+	17.7104i	0.186998	+	0.697887i
$645$		0			0
$646$	−6.61572	+	11.4588i	−0.260292	+	0.450839i
$647$	9.52115	+	16.4911i	0.374315	+	0.648333i	0.990224	−	0.139484i	$-0.0445445\pi$
$647$	9.52115	+	16.4911i	0.374315	+	0.648333i	−0.615909	+	0.787817i	$0.711211\pi$
$648$		0			0
$649$			2.20479i			0.0865458i
$650$	2.46748	+	2.62898i	0.0967824	+	0.103117i
$651$		0			0
$652$	−5.50881	−	1.47608i	−0.215742	−	0.0578078i
$653$	−6.22533	+	3.59420i	−0.243616	+	0.140652i	−0.616838	−	0.787090i	$-0.711586\pi$
$653$	−6.22533	+	3.59420i	−0.243616	+	0.140652i	0.373221	+	0.927742i	$0.378253\pi$
$654$		0			0
$655$	−4.92055	+	4.92055i	−0.192262	+	0.192262i
$656$	−3.86370	+	1.03528i	−0.150852	+	0.0404207i
$657$		0			0
$658$	26.8719	+	26.8719i	1.04758	+	1.04758i
$659$	24.9932	+	14.4298i	0.973597	+	0.562106i	0.900331	−	0.435206i	$-0.143325\pi$
$659$	24.9932	+	14.4298i	0.973597	+	0.562106i	0.0732658	+	0.997312i	$0.476658\pi$
$660$		0			0
$661$	−2.69629	+	10.0627i	−0.104873	+	0.391393i	−0.998331	−	0.0577551i	$-0.981606\pi$
$661$	−2.69629	+	10.0627i	−0.104873	+	0.391393i	0.893457	+	0.449148i	$0.148272\pi$
$662$	−13.0228			−0.506144
$663$		0			0
$664$	4.65223			0.180541
$665$	−8.31406	+	31.0285i	−0.322405	+	1.20323i
$666$		0			0
$667$	22.8230	+	13.1769i	0.883711	+	0.510211i
$668$	2.66529	+	2.66529i	0.103123	+	0.103123i
$669$		0			0
$670$	3.04406	−	0.815653i	0.117602	−	0.0315114i
$671$	−25.7030	+	25.7030i	−0.992253	+	0.992253i
$672$		0			0
$673$	17.6436	−	10.1866i	0.680113	−	0.392663i	−0.119785	−	0.992800i	$-0.538221\pi$
$673$	17.6436	−	10.1866i	0.680113	−	0.392663i	0.799897	+	0.600137i	$0.204887\pi$
$674$	−32.9845	−	8.83816i	−1.27051	−	0.340433i
$675$		0			0
$676$	0.823116	−	12.9739i	0.0316583	−	0.498997i
$677$			24.3407i			0.935489i	0.883864	+	0.467744i	$0.154933\pi$
$677$			24.3407i			0.935489i	−0.883864	+	0.467744i	$0.845067\pi$
$678$		0			0
$679$	12.6530	+	21.9156i	0.485576	+	0.841043i
$680$	0.909743	−	1.57572i	0.0348870	−	0.0604261i
$681$		0			0
$682$	7.66494	+	28.6060i	0.293506	+	1.09538i
$683$	1.88557	+	7.03704i	0.0721493	+	0.269265i	0.992572	−	0.121660i	$-0.0388218\pi$
$683$	1.88557	+	7.03704i	0.0721493	+	0.269265i	−0.920423	+	0.390925i	$0.872155\pi$
$684$		0			0
$685$	−10.9158	+	18.9066i	−0.417069	+	0.722385i
$686$	12.1756	+	21.0888i	0.464867	+	0.805174i
$687$		0			0
$688$			7.23570i			0.275858i
$689$	9.59381	−	15.4641i	0.365495	−	0.589137i
$690$		0			0
$691$	−0.536122	−	0.143654i	−0.0203951	−	0.00546484i	0.248607	−	0.968604i	$-0.420027\pi$
$691$	−0.536122	−	0.143654i	−0.0203951	−	0.00546484i	−0.269002	+	0.963140i	$0.586694\pi$
$692$	−3.44801	+	1.99071i	−0.131074	+	0.0756753i
$693$		0			0
$694$	22.3923	−	22.3923i	0.850000	−	0.850000i
$695$	19.0784	−	5.11204i	0.723685	−	0.193911i
$696$		0			0
$697$	−5.14628	−	5.14628i	−0.194929	−	0.194929i
$698$	−10.6717	−	6.16132i	−0.403931	−	0.233210i
$699$		0			0
$700$	1.14329	−	4.26680i	0.0432121	−	0.161270i
$701$	38.9119			1.46968			0.734842	−	0.678239i	$-0.237256\pi$
$701$	38.9119			1.46968			0.734842	+	0.678239i	$0.237256\pi$
$702$		0			0
$703$	−58.8476			−2.21948
$704$	1.44244	−	5.38324i	0.0543638	−	0.202889i
$705$		0			0
$706$	−15.9156	−	9.18886i	−0.598991	−	0.345827i
$707$	5.45846	+	5.45846i	0.205286	+	0.205286i
$708$		0			0
$709$	−38.5590	+	10.3318i	−1.44811	+	0.388020i	−0.895367	−	0.445330i	$-0.853086\pi$
$709$	−38.5590	+	10.3318i	−1.44811	+	0.388020i	−0.552745	+	0.833350i	$0.686420\pi$
$710$	10.1569	−	10.1569i	0.381183	−	0.381183i
$711$		0			0
$712$	−4.69781	+	2.71228i	−0.176058	+	0.101647i
$713$	−21.3050	−	5.70867i	−0.797880	−	0.213791i
$714$		0			0
$715$	−0.636469	+	20.0842i	−0.0238026	+	0.751105i
$716$		−	23.3884i		−	0.874067i
$717$		0			0
$718$	5.28758	+	9.15835i	0.197331	+	0.341787i
$719$	13.3803	−	23.1754i	0.499002	−	0.864298i	−0.500997	−	0.865449i	$-0.667033\pi$
$719$	13.3803	−	23.1754i	0.499002	−	0.864298i	0.999999	+	0.00115153i	$0.000366543\pi$
$720$		0			0
$721$	−21.5629	−	80.4737i	−0.803043	−	2.99700i
$722$	−8.76959	−	32.7286i	−0.326371	−	1.21803i
$723$		0			0
$724$	−0.594063	+	1.02895i	−0.0220782	+	0.0382405i
$725$	−3.17458	−	5.49854i	−0.117901	−	0.204211i
$726$		0			0
$727$		−	14.2165i		−	0.527261i	−0.964624	−	0.263631i	$-0.915080\pi$
$727$		−	14.2165i		−	0.527261i	0.964624	−	0.263631i	$-0.0849200\pi$
$728$	−14.0384	+	7.52255i	−0.520297	+	0.278804i
$729$		0			0
$730$	−1.82699	−	0.489539i	−0.0676198	−	0.0181187i
$731$	−11.4014	+	6.58262i	−0.421697	+	0.243467i
$732$		0			0
$733$	−1.76745	+	1.76745i	−0.0652821	+	0.0652821i	−0.738994	−	0.673712i	$-0.764699\pi$
$733$	−1.76745	+	1.76745i	−0.0652821	+	0.0652821i	0.673712	+	0.738994i	$0.264699\pi$
$734$	20.4325	−	5.47488i	0.754178	−	0.202081i
$735$		0			0
$736$	2.93502	+	2.93502i	0.108186	+	0.108186i
$737$	15.2104	+	8.78172i	0.560281	+	0.323479i
$738$		0			0
$739$	7.84528	−	29.2790i	0.288593	−	1.07704i	−0.657580	−	0.753384i	$-0.728420\pi$
$739$	7.84528	−	29.2790i	0.288593	−	1.07704i	0.946173	−	0.323660i	$-0.104913\pi$
$740$	8.09226			0.297477
$741$		0			0
$742$	−22.2956			−0.818497
$743$	−4.70116	+	17.5450i	−0.172469	+	0.643663i	0.824500	+	0.565862i	$0.191457\pi$
$743$	−4.70116	+	17.5450i	−0.172469	+	0.643663i	−0.996969	+	0.0778009i	$0.975210\pi$
$744$		0			0
$745$	−1.95429	−	1.12831i	−0.0715996	−	0.0413380i
$746$	−14.1661	−	14.1661i	−0.518659	−	0.518659i
$747$		0			0
$748$	9.79473	−	2.62449i	0.358131	−	0.0959609i
$749$	−17.7515	+	17.7515i	−0.648626	+	0.648626i
$750$		0			0
$751$	12.0508	−	6.95751i	0.439738	−	0.253883i	−0.263748	−	0.964592i	$-0.584959\pi$
$751$	12.0508	−	6.95751i	0.439738	−	0.253883i	0.703487	+	0.710708i	$0.251625\pi$
$752$	8.30995	+	2.22664i	0.303033	+	0.0811974i
$753$		0			0
$754$	−6.62236	+	21.9135i	−0.241172	+	0.798041i
$755$		−	13.5545i		−	0.493298i
$756$		0			0
$757$	−0.423040	−	0.732727i	−0.0153757	−	0.0266314i	0.858235	−	0.513257i	$-0.171561\pi$
$757$	−0.423040	−	0.732727i	−0.0153757	−	0.0266314i	−0.873611	+	0.486625i	$0.838228\pi$
$758$	11.7481	−	20.3482i	0.426709	−	0.739081i
$759$		0			0
$760$	1.88215	+	7.02429i	0.0682728	+	0.254798i
$761$	4.71106	+	17.5819i	0.170776	+	0.637344i	0.997233	+	0.0743441i	$0.0236863\pi$
$761$	4.71106	+	17.5819i	0.170776	+	0.637344i	−0.826457	+	0.563000i	$0.809647\pi$
$762$		0			0
$763$	−16.0163	+	27.7411i	−0.579830	+	1.00429i
$764$	6.45423	+	11.1791i	0.233506	+	0.404444i
$765$		0			0
$766$		−	8.31652i		−	0.300488i
$767$	0.412633	−	1.36541i	0.0148993	−	0.0493020i
$768$		0			0
$769$	−18.8408	−	5.04838i	−0.679417	−	0.182049i	−0.0974240	−	0.995243i	$-0.531060\pi$
$769$	−18.8408	−	5.04838i	−0.679417	−	0.182049i	−0.581993	+	0.813194i	$0.697727\pi$
$770$	21.3201	−	12.3092i	0.768323	−	0.443591i
$771$		0			0
$772$	−4.44649	+	4.44649i	−0.160033	+	0.160033i
$773$	−4.50303	+	1.20658i	−0.161963	+	0.0433978i	−0.338889	−	0.940826i	$-0.610051\pi$
$773$	−4.50303	+	1.20658i	−0.161963	+	0.0433978i	0.176927	+	0.984224i	$0.443384\pi$
$774$		0			0
$775$	3.75749	+	3.75749i	0.134973	+	0.134973i
$776$	4.96129	+	2.86440i	0.178100	+	0.102826i
$777$		0			0
$778$	8.69233	−	32.4402i	0.311635	−	1.16304i
$779$	29.0883			1.04220
$780$		0			0
$781$	80.0531			2.86453
$782$	−1.95466	+	7.29488i	−0.0698984	+	0.260865i
$783$		0			0
$784$	10.8363	+	6.25634i	0.387011	+	0.223441i
$785$	−9.14233	−	9.14233i	−0.326304	−	0.326304i
$786$		0			0
$787$	−11.4239	+	3.06103i	−0.407218	+	0.109114i	−0.456613	−	0.889665i	$-0.650938\pi$
$787$	−11.4239	+	3.06103i	−0.407218	+	0.109114i	0.0493944	+	0.998779i	$0.484271\pi$
$788$	10.7526	−	10.7526i	0.383046	−	0.383046i
$789$		0			0
$790$	3.76265	−	2.17237i	0.133869	−	0.0772894i
$791$	−23.2629	−	6.23327i	−0.827133	−	0.221630i
$792$		0			0
$793$	20.7280	−	11.1072i	0.736072	−	0.394429i
$794$			28.6572i			1.01701i
$795$		0			0
$796$	−7.06950	−	12.2447i	−0.250572	−	0.434003i
$797$	12.3109	−	21.3230i	0.436073	−	0.755301i	−0.561309	−	0.827606i	$-0.689702\pi$
$797$	12.3109	−	21.3230i	0.436073	−	0.755301i	0.997383	+	0.0723052i	$0.0230356\pi$
$798$		0			0
$799$	4.05135	+	15.1198i	0.143326	+	0.534901i
$800$	−0.258819	−	0.965926i	−0.00915064	−	0.0341506i
$801$		0			0
$802$	13.7499	−	23.8155i	0.485526	−	0.840955i
$803$	−5.27062	−	9.12897i	−0.185996	−	0.322154i
$804$		0			0
$805$			18.3351i			0.646229i
$806$	0.606862	−	19.1499i	0.0213758	−	0.674526i
$807$		0			0
$808$	1.68799	+	0.452296i	0.0593833	+	0.0159117i
$809$	27.0698	−	15.6288i	0.951725	−	0.549479i	0.0581084	−	0.998310i	$-0.481493\pi$
$809$	27.0698	−	15.6288i	0.951725	−	0.549479i	0.893616	+	0.448832i	$0.148160\pi$
$810$		0			0
$811$	12.2315	−	12.2315i	0.429508	−	0.429508i	−0.458953	−	0.888461i	$-0.651775\pi$
$811$	12.2315	−	12.2315i	0.429508	−	0.429508i	0.888461	+	0.458953i	$0.151775\pi$
$812$	27.0906	−	7.25891i	0.950694	−	0.254738i
$813$		0			0
$814$	31.8900	+	31.8900i	1.11775	+	1.11775i
$815$	−4.93906	−	2.85157i	−0.173008	−	0.0998861i
$816$		0			0
$817$	13.6187	−	50.8256i	0.476457	−	1.77816i
$818$	7.15452			0.250152
$819$		0			0
$820$	−4.00000			−0.139686
$821$	−5.97161	+	22.2863i	−0.208410	+	0.777799i	0.779972	+	0.625814i	$0.215233\pi$
$821$	−5.97161	+	22.2863i	−0.208410	+	0.777799i	−0.988383	+	0.151985i	$0.951434\pi$
$822$		0			0
$823$	44.4499	+	25.6631i	1.54943	+	0.894561i	0.998185	+	0.0602141i	$0.0191783\pi$
$823$	44.4499	+	25.6631i	1.54943	+	0.894561i	0.551240	+	0.834347i	$0.314155\pi$
$824$	−13.3364	−	13.3364i	−0.464594	−	0.464594i
$825$		0			0
$826$	−1.68799	+	0.452296i	−0.0587327	+	0.0157374i
$827$	−5.09241	+	5.09241i	−0.177081	+	0.177081i	−0.790082	−	0.613001i	$-0.789962\pi$
$827$	−5.09241	+	5.09241i	−0.177081	+	0.177081i	0.613001	+	0.790082i	$0.289962\pi$
$828$		0			0
$829$	23.7406	−	13.7066i	0.824543	−	0.476050i	−0.0274373	−	0.999624i	$-0.508735\pi$
$829$	23.7406	−	13.7066i	0.824543	−	0.476050i	0.851981	+	0.523573i	$0.175401\pi$
$830$	4.49371	+	1.20409i	0.155979	+	0.0417944i
$831$		0			0
$832$	−1.90077	+	3.06383i	−0.0658975	+	0.106219i
$833$			22.7666i			0.788817i
$834$		0			0
$835$	1.88465	+	3.26430i	0.0652209	+	0.112966i
$836$	−20.2642	+	35.0986i	−0.700851	+	1.21391i
$837$		0			0
$838$	−7.77695	−	29.0240i	−0.268650	−	1.00262i
$839$	12.5860	+	46.9715i	0.434516	+	1.62164i	0.742222	+	0.670154i	$0.233772\pi$
$839$	12.5860	+	46.9715i	0.434516	+	1.62164i	−0.307706	+	0.951481i	$0.599561\pi$
$840$		0			0
$841$	5.65596	−	9.79641i	0.195033	−	0.337807i
$842$	−4.78309	−	8.28455i	−0.164836	−	0.285504i
$843$		0			0
$844$		−	12.6436i		−	0.435212i
$845$	4.15297	−	12.3188i	0.142866	−	0.423780i
$846$		0			0
$847$	85.5916	+	22.9342i	2.94096	+	0.788028i
$848$	−4.37111	+	2.52366i	−0.150104	+	0.0866628i
$849$		0			0
$850$	1.28657	−	1.28657i	0.0441290	−	0.0441290i
$851$	−32.4444	+	8.69345i	−1.11218	+	0.298008i
$852$		0			0
$853$	6.27875	+	6.27875i	0.214980	+	0.214980i	0.806379	−	0.591399i	$-0.201424\pi$
$853$	6.27875	+	6.27875i	0.214980	+	0.214980i	−0.591399	+	0.806379i	$0.701424\pi$
$854$	−24.9510	−	14.4055i	−0.853805	−	0.492945i
$855$		0			0
$856$	−1.47092	+	5.48954i	−0.0502749	+	0.187629i
$857$	−53.8336			−1.83892			−0.919460	−	0.393183i	$-0.871374\pi$
$857$	−53.8336			−1.83892			−0.919460	+	0.393183i	$0.871374\pi$
$858$		0			0
$859$	−27.0520			−0.923002			−0.461501	−	0.887140i	$-0.652689\pi$
$859$	−27.0520			−0.923002			−0.461501	+	0.887140i	$0.652689\pi$
$860$	−1.87274	+	6.98915i	−0.0638598	+	0.238328i
$861$		0			0
$862$	0.347568	+	0.200668i	0.0118382	+	0.00683479i
$863$	−28.0041	−	28.0041i	−0.953271	−	0.953271i	0.0456844	−	0.998956i	$-0.485453\pi$
$863$	−28.0041	−	28.0041i	−0.953271	−	0.953271i	−0.998956	+	0.0456844i	$0.985453\pi$
$864$		0			0
$865$	−3.84575	+	1.03047i	−0.130759	+	0.0350369i
$866$	−3.33591	+	3.33591i	−0.113359	+	0.113359i
$867$		0			0
$868$	−20.3283	+	11.7366i	−0.689988	+	0.398365i
$869$	23.3888	+	6.26700i	0.793409	+	0.212593i
$870$		0			0
$871$	−7.77611	−	8.28509i	−0.263483	−	0.280730i
$872$			7.25161i			0.245570i
$873$		0			0
$874$	−15.0923	−	26.1406i	−0.510504	−	0.884218i
$875$	2.20866	−	3.82551i	0.0746663	−	0.129326i
$876$		0			0
$877$	−9.09109	−	33.9284i	−0.306984	−	1.14568i	−0.931224	−	0.364448i	$-0.881258\pi$
$877$	−9.09109	−	33.9284i	−0.306984	−	1.14568i	0.624240	−	0.781233i	$-0.285409\pi$
$878$	6.54379	+	24.4218i	0.220842	+	0.824194i
$879$		0			0
$880$	2.78657	−	4.82648i	0.0939353	−	0.162701i
$881$	25.8681	+	44.8049i	0.871518	+	1.50951i	0.860426	+	0.509576i	$0.170198\pi$
$881$	25.8681	+	44.8049i	0.871518	+	1.50951i	0.0110925	+	0.999938i	$0.496469\pi$
$882$		0			0
$883$		−	8.63529i		−	0.290601i	−0.989388	−	0.145300i	$-0.953585\pi$
$883$		−	8.63529i		−	0.290601i	0.989388	−	0.145300i	$-0.0464148\pi$
$884$	−6.55696	−	0.207791i	−0.220534	−	0.00698876i
$885$		0			0
$886$	−19.4092	−	5.20067i	−0.652063	−	0.174720i
$887$	22.3206	−	12.8868i	0.749454	−	0.432697i	−0.0760426	−	0.997105i	$-0.524229\pi$
$887$	22.3206	−	12.8868i	0.749454	−	0.432697i	0.825497	+	0.564407i	$0.190895\pi$
$888$		0			0
$889$	−23.9145	+	23.9145i	−0.802065	+	0.802065i
$890$	−5.23972	+	1.40398i	−0.175636	+	0.0470615i
$891$		0			0
$892$	17.2811	+	17.2811i	0.578615	+	0.578615i
$893$	−54.1806	−	31.2812i	−1.81308	−	1.04679i
$894$		0			0
$895$	6.05337	−	22.5915i	0.202342	−	0.755150i
$896$	4.41732			0.147572
$897$		0			0
$898$	−25.6915			−0.857337
$899$	−8.73224	+	32.5892i	−0.291236	+	1.08691i
$900$		0			0
$901$	−7.95317	−	4.59176i	−0.264958	−	0.152974i
$902$	−15.7632	−	15.7632i	−0.524858	−	0.524858i
$903$		0			0
$904$	−5.26630	+	1.41110i	−0.175154	+	0.0469325i
$905$	−0.840132	+	0.840132i	−0.0279269	+	0.0279269i
$906$		0			0
$907$	14.3988	−	8.31313i	0.478103	−	0.276033i	−0.241523	−	0.970395i	$-0.577647\pi$
$907$	14.3988	−	8.31313i	0.478103	−	0.276033i	0.719626	+	0.694362i	$0.244313\pi$
$908$	−2.95396	−	0.791511i	−0.0980306	−	0.0262672i
$909$		0			0
$910$	−15.5070	+	3.63282i	−0.514052	+	0.120427i
$911$			7.55296i			0.250241i	0.992142	+	0.125120i	$0.0399317\pi$
$911$			7.55296i			0.250241i	−0.992142	+	0.125120i	$0.960068\pi$
$912$		0			0
$913$	12.9638	+	22.4539i	0.429038	+	0.743115i
$914$	−13.2719	+	22.9876i	−0.438995	+	0.760362i
$915$		0			0
$916$	−2.62753	−	9.80606i	−0.0868159	−	0.324001i
$917$	−7.95578	−	29.6914i	−0.262723	−	0.980496i
$918$		0			0
$919$	−8.02591	+	13.9013i	−0.264750	+	0.458561i	−0.967498	−	0.252878i	$-0.918623\pi$
$919$	−8.02591	+	13.9013i	−0.264750	+	0.458561i	0.702748	+	0.711439i	$0.251956\pi$
$920$	2.07537	+	3.59465i	0.0684230	+	0.118512i
$921$		0			0
$922$		−	24.4419i		−	0.804951i
$923$	−49.5761	−	14.9822i	−1.63182	−	0.493144i
$924$		0			0
$925$	7.81652	+	2.09443i	0.257006	+	0.0688645i
$926$	−27.5963	+	15.9327i	−0.906871	+	0.523582i
$927$		0			0
$928$	4.48954	−	4.48954i	0.147376	−	0.147376i
$929$	−33.4904	+	8.97371i	−1.09878	+	0.294418i	−0.762269	−	0.647261i	$-0.775915\pi$
$929$	−33.4904	+	8.97371i	−1.09878	+	0.294418i	−0.336514	+	0.941678i	$0.609248\pi$
$930$		0			0
$931$	−64.3419	−	64.3419i	−2.10872	−	2.10872i
$932$	7.38086	+	4.26134i	0.241768	+	0.139585i
$933$		0			0
$934$	−7.06599	+	26.3706i	−0.231206	+	0.862873i
$935$	10.1403			0.331622
$936$		0			0
$937$	−42.7348			−1.39609			−0.698043	−	0.716056i	$-0.745945\pi$
$937$	−42.7348			−1.39609			−0.698043	+	0.716056i	$0.745945\pi$
$938$	−3.60300	+	13.4466i	−0.117642	+	0.439046i
$939$		0			0
$940$	7.45050	+	4.30155i	0.243008	+	0.140301i
$941$	−20.1611	−	20.1611i	−0.657233	−	0.657233i	0.297491	−	0.954725i	$-0.403850\pi$
$941$	−20.1611	−	20.1611i	−0.657233	−	0.657233i	−0.954725	+	0.297491i	$0.903850\pi$
$942$		0			0
$943$	16.0372	−	4.29717i	0.522244	−	0.139935i
$944$	−0.279739	+	0.279739i	−0.00910473	+	0.00910473i
$945$		0			0
$946$	−34.9230	+	20.1628i	−1.13544	+	0.655548i
$947$	−1.24826	−	0.334471i	−0.0405631	−	0.0108688i	0.238480	−	0.971147i	$-0.423351\pi$
$947$	−1.24826	−	0.334471i	−0.0405631	−	0.0108688i	−0.279044	+	0.960278i	$0.590017\pi$
$948$		0			0
$949$	1.55553	+	6.63989i	0.0504945	+	0.215540i
$950$			7.27208i			0.235937i
$951$		0			0
$952$	4.01862	+	6.96046i	0.130244	+	0.225590i
$953$	16.0645	−	27.8246i	0.520381	−	0.901327i	−0.479338	−	0.877630i	$-0.659123\pi$
$953$	16.0645	−	27.8246i	0.520381	−	0.901327i	0.999719	−	0.0236964i	$-0.00754351\pi$
$954$		0			0
$955$	3.34096	+	12.4686i	0.108111	+	0.403475i
$956$	−7.85881	−	29.3295i	−0.254172	−	0.948583i
$957$		0			0
$958$	−10.4324	+	18.0694i	−0.337055	+	0.583796i
$959$	−48.2183	−	83.5166i	−1.55705	−	2.69689i
$960$		0			0
$961$			2.76256i			0.0891149i
$962$	−13.7809	−	25.7175i	−0.444313	−	0.829165i
$963$		0			0
$964$	−4.83745	−	1.29619i	−0.155804	−	0.0417475i
$965$	−5.44581	+	3.14414i	−0.175307	+	0.101213i
$966$		0			0
$967$	−17.3091	+	17.3091i	−0.556622	+	0.556622i	−0.928344	−	0.371722i	$-0.878767\pi$
$967$	−17.3091	+	17.3091i	−0.556622	+	0.556622i	0.371722	+	0.928344i	$0.378767\pi$
$968$	19.3764	−	5.19189i	0.622781	−	0.166874i
$969$		0			0
$970$	4.05088	+	4.05088i	0.130066	+	0.130066i
$971$	−28.5156	−	16.4635i	−0.915108	−	0.528338i	−0.0330372	−	0.999454i	$-0.510518\pi$
$971$	−28.5156	−	16.4635i	−0.915108	−	0.528338i	−0.882071	+	0.471116i	$0.843851\pi$
$972$		0			0
$973$	−22.5815	+	84.2753i	−0.723930	+	2.70174i
$974$	9.97263			0.319544
$975$		0			0
$976$	−6.52227			−0.208773
$977$	−7.59567	+	28.3474i	−0.243007	+	0.906915i	0.731368	+	0.681984i	$0.238882\pi$
$977$	−7.59567	+	28.3474i	−0.243007	+	0.906915i	−0.974375	+	0.224931i	$0.927784\pi$
$978$		0			0
$979$	−26.1815	−	15.1159i	−0.836765	−	0.483107i
$980$	8.84780	+	8.84780i	0.282633	+	0.282633i
$981$		0			0
$982$	15.6373	−	4.19001i	0.499008	−	0.133709i
$983$	−0.799524	+	0.799524i	−0.0255009	+	0.0255009i	−0.719742	−	0.694241i	$-0.755740\pi$
$983$	−0.799524	+	0.799524i	−0.0255009	+	0.0255009i	0.694241	+	0.719742i	$0.255740\pi$
$984$		0			0
$985$	13.1692	−	7.60324i	0.419605	−	0.242259i
$986$	11.1586	+	2.98993i	0.355362	+	0.0952189i
$987$		0			0
$988$	19.1182	−	17.9437i	0.608230	−	0.570865i
$989$		−	30.0335i		−	0.955010i
$990$		0			0
$991$	9.92986	+	17.1990i	0.315432	+	0.546345i	0.979529	−	0.201302i	$-0.0645172\pi$
$991$	9.92986	+	17.1990i	0.315432	+	0.546345i	−0.664097	+	0.747646i	$0.731184\pi$
$992$	−2.65695	+	4.60196i	−0.0843581	+	0.146113i
$993$		0			0
$994$	16.4223	+	61.2887i	0.520882	+	1.94396i
$995$	−3.65944	−	13.6572i	−0.116012	−	0.432963i
$996$		0			0
$997$	−0.778102	+	1.34771i	−0.0246427	+	0.0426825i	−0.878084	−	0.478507i	$-0.841178\pi$
$997$	−0.778102	+	1.34771i	−0.0246427	+	0.0426825i	0.853441	+	0.521189i	$0.174511\pi$
$998$	17.6686	+	30.6028i	0.559288	+	0.968716i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1170.2.cu.f.431.2	✓	16
3.2	odd	2	inner	1170.2.cu.f.431.4	yes	16
13.7	odd	12	inner	1170.2.cu.f.1151.4	yes	16
39.20	even	12	inner	1170.2.cu.f.1151.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1170.2.cu.f.431.2	✓	16	1.1	even	1	trivial
1170.2.cu.f.431.4	yes	16	3.2	odd	2	inner
1170.2.cu.f.1151.2	yes	16	39.20	even	12	inner
1170.2.cu.f.1151.4	yes	16	13.7	odd	12	inner

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.cu (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(-0.707107 - 0.707107i) q^{5} +(4.26680 - 1.14329i) q^{7} +(0.707107 - 0.707107i) q^{8} +O(q^{10})\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(-0.707107 - 0.707107i) q^{5} +(4.26680 - 1.14329i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{10} +(5.38324 + 1.44244i) q^{11} +(-3.06383 - 1.90077i) q^{13} +4.41732i q^{14} +(0.500000 + 0.866025i) q^{16} +(-0.909743 + 1.57572i) q^{17} +(-1.88215 - 7.02429i) q^{19} +(0.258819 + 0.965926i) q^{20} +(-2.78657 + 4.82648i) q^{22} +(-2.07537 - 3.59465i) q^{23} +1.00000i q^{25} +(2.62898 - 2.46748i) q^{26} +(-4.26680 - 1.14329i) q^{28} +(-5.49854 + 3.17458i) q^{29} +(3.75749 - 3.75749i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(-1.28657 - 1.28657i) q^{34} +(-3.82551 - 2.20866i) q^{35} +(2.09443 - 7.81652i) q^{37} +7.27208 q^{38} -1.00000 q^{40} +(-1.03528 + 3.86370i) q^{41} +(6.26630 + 3.61785i) q^{43} +(-3.94081 - 3.94081i) q^{44} +(4.00931 - 1.07429i) q^{46} +(6.08331 - 6.08331i) q^{47} +(10.8363 - 6.25634i) q^{49} +(-0.965926 - 0.258819i) q^{50} +(1.70297 + 3.17803i) q^{52} +5.04732i q^{53} +(-2.78657 - 4.82648i) q^{55} +(2.20866 - 3.82551i) q^{56} +(-1.64329 - 6.13282i) q^{58} +(0.102392 + 0.382131i) q^{59} +(-3.26113 + 5.64845i) q^{61} +(2.65695 + 4.60196i) q^{62} -1.00000i q^{64} +(0.822405 + 3.51051i) q^{65} +(3.04406 + 0.815653i) q^{67} +(1.57572 - 0.909743i) q^{68} +(3.12351 - 3.12351i) q^{70} +(13.8746 - 3.71770i) q^{71} +(-1.33745 - 1.33745i) q^{73} +(7.00810 + 4.04613i) q^{74} +(-1.88215 + 7.02429i) q^{76} +24.6183 q^{77} +4.34474 q^{79} +(0.258819 - 0.965926i) q^{80} +(-3.46410 - 2.00000i) q^{82} +(3.28962 + 3.28962i) q^{83} +(1.75749 - 0.470918i) q^{85} +(-5.11641 + 5.11641i) q^{86} +(4.82648 - 2.78657i) q^{88} +(-5.23972 - 1.40398i) q^{89} +(-15.2459 - 4.60739i) q^{91} +4.15074i q^{92} +(4.30155 + 7.45050i) q^{94} +(-3.63604 + 6.29780i) q^{95} +(1.48272 + 5.53360i) q^{97} +(3.23852 + 12.0863i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{7}+O(q^{10}) \) 16 * q + 12 * q^7	\( 16 q + 12 q^{7} - 8 q^{13} + 8 q^{16} - 52 q^{19} - 8 q^{22} - 12 q^{28} + 36 q^{31} + 16 q^{34} + 8 q^{37} - 16 q^{40} + 72 q^{43} + 32 q^{46} + 60 q^{49} + 12 q^{52} - 8 q^{55} - 8 q^{58} - 12 q^{61} - 12 q^{67} + 12 q^{70} + 8 q^{73} - 52 q^{76} + 8 q^{79} + 4 q^{85} + 24 q^{88} - 84 q^{91} - 16 q^{94} - 96 q^{97}+O(q^{100}) \) 16 * q + 12 * q^7 - 8 * q^13 + 8 * q^16 - 52 * q^19 - 8 * q^22 - 12 * q^28 + 36 * q^31 + 16 * q^34 + 8 * q^37 - 16 * q^40 + 72 * q^43 + 32 * q^46 + 60 * q^49 + 12 * q^52 - 8 * q^55 - 8 * q^58 - 12 * q^61 - 12 * q^67 + 12 * q^70 + 8 * q^73 - 52 * q^76 + 8 * q^79 + 4 * q^85 + 24 * q^88 - 84 * q^91 - 16 * q^94 - 96 * q^97

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