LMFDB - Embedded newform 666.2.f.i.343.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [666,2,Mod(343,666)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("666.343"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(666, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 666 = 2 \cdot 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	666.f (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,2,0,-2,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.31803677462$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{11})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 11x^{2} + 121 $ x^4 + 11*x^2 + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			343.2
Root			$1.65831 + 2.87228i$ of defining polynomial
Character	$\chi$	$=$	666.343
Dual form			666.2.f.i.433.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(2.15831 + 3.73831i) q^{7} -1.00000 q^{8} -1.00000 q^{10} +4.31662 q^{11} +(-1.00000 - 1.73205i) q^{13} +4.31662 q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.65831 - 2.87228i) q^{17} +(3.15831 + 5.47036i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(2.15831 - 3.73831i) q^{22} -4.00000 q^{23} +(2.00000 - 3.46410i) q^{25} -2.00000 q^{26} +(2.15831 - 3.73831i) q^{28} +9.63325 q^{29} +4.31662 q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.65831 - 2.87228i) q^{34} +(2.15831 - 3.73831i) q^{35} +(-5.97494 + 1.14023i) q^{37} +6.31662 q^{38} +(0.500000 + 0.866025i) q^{40} +(-5.65831 - 9.80048i) q^{41} -6.31662 q^{43} +(-2.15831 - 3.73831i) q^{44} +(-2.00000 + 3.46410i) q^{46} +2.31662 q^{47} +(-5.81662 + 10.0747i) q^{49} +(-2.00000 - 3.46410i) q^{50} +(-1.00000 + 1.73205i) q^{52} +(4.31662 - 7.47661i) q^{53} +(-2.15831 - 3.73831i) q^{55} +(-2.15831 - 3.73831i) q^{56} +(4.81662 - 8.34264i) q^{58} +(-2.31662 + 4.01251i) q^{59} +(3.65831 + 6.33638i) q^{61} +(2.15831 - 3.73831i) q^{62} +1.00000 q^{64} +(-1.00000 + 1.73205i) q^{65} +(-3.15831 - 5.47036i) q^{67} -3.31662 q^{68} +(-2.15831 - 3.73831i) q^{70} +(3.15831 + 5.47036i) q^{71} -0.633250 q^{73} +(-2.00000 + 5.74456i) q^{74} +(3.15831 - 5.47036i) q^{76} +(9.31662 + 16.1369i) q^{77} +(6.47494 + 11.2149i) q^{79} +1.00000 q^{80} -11.3166 q^{82} +(-2.31662 + 4.01251i) q^{83} -3.31662 q^{85} +(-3.15831 + 5.47036i) q^{86} -4.31662 q^{88} +(-4.65831 + 8.06843i) q^{89} +(4.31662 - 7.47661i) q^{91} +(2.00000 + 3.46410i) q^{92} +(1.15831 - 2.00626i) q^{94} +(3.15831 - 5.47036i) q^{95} +0.366750 q^{97} +(5.81662 + 10.0747i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{4} - 2 q^{5} + 2 q^{7} - 4 q^{8} - 4 q^{10} + 4 q^{11} - 4 q^{13} + 4 q^{14} - 2 q^{16} + 6 q^{19} - 2 q^{20} + 2 q^{22} - 16 q^{23} + 8 q^{25} - 8 q^{26} + 2 q^{28} + 12 q^{29} + 4 q^{31}+ \cdots + 10 q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^4 - 2 * q^5 + 2 * q^7 - 4 * q^8 - 4 * q^10 + 4 * q^11 - 4 * q^13 + 4 * q^14 - 2 * q^16 + 6 * q^19 - 2 * q^20 + 2 * q^22 - 16 * q^23 + 8 * q^25 - 8 * q^26 + 2 * q^28 + 12 * q^29 + 4 * q^31 + 2 * q^32 + 2 * q^35 - 4 * q^37 + 12 * q^38 + 2 * q^40 - 16 * q^41 - 12 * q^43 - 2 * q^44 - 8 * q^46 - 4 * q^47 - 10 * q^49 - 8 * q^50 - 4 * q^52 + 4 * q^53 - 2 * q^55 - 2 * q^56 + 6 * q^58 + 4 * q^59 + 8 * q^61 + 2 * q^62 + 4 * q^64 - 4 * q^65 - 6 * q^67 - 2 * q^70 + 6 * q^71 + 24 * q^73 - 8 * q^74 + 6 * q^76 + 24 * q^77 + 6 * q^79 + 4 * q^80 - 32 * q^82 + 4 * q^83 - 6 * q^86 - 4 * q^88 - 12 * q^89 + 4 * q^91 + 8 * q^92 - 2 * q^94 + 6 * q^95 + 28 * q^97 + 10 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/666\mathbb{Z}\right)^\times$.

$n$	$371$	$631$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i	0.732294	−	0.680989i	$-0.238450\pi$
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i	−0.955901	+	0.293691i	$0.905116\pi$
$6$		0			0
$7$	2.15831	+	3.73831i	0.815765	+	1.41295i	0.908777	+	0.417282i	$0.137017\pi$
$7$	2.15831	+	3.73831i	0.815765	+	1.41295i	−0.0930116	+	0.995665i	$0.529649\pi$
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−1.00000			−0.316228
$11$	4.31662			1.30151			0.650756	−	0.759287i	$-0.274452\pi$
$11$	4.31662			1.30151			0.650756	+	0.759287i	$0.274452\pi$
$12$		0			0
$13$	−1.00000	−	1.73205i	−0.277350	−	0.480384i	0.693375	−	0.720577i	$-0.256123\pi$
$13$	−1.00000	−	1.73205i	−0.277350	−	0.480384i	−0.970725	+	0.240192i	$0.922790\pi$
$14$	4.31662			1.15367
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.65831	−	2.87228i	0.402200	−	0.696631i	−0.591791	−	0.806091i	$-0.701579\pi$
$17$	1.65831	−	2.87228i	0.402200	−	0.696631i	0.993991	+	0.109461i	$0.0349124\pi$
$18$		0			0
$19$	3.15831	+	5.47036i	0.724567	+	1.25499i	0.959152	+	0.282891i	$0.0912933\pi$
$19$	3.15831	+	5.47036i	0.724567	+	1.25499i	−0.234586	+	0.972095i	$0.575373\pi$
$20$	−0.500000	+	0.866025i	−0.111803	+	0.193649i
$21$		0			0
$22$	2.15831	−	3.73831i	0.460154	−	0.797010i
$23$	−4.00000			−0.834058			−0.417029	−	0.908893i	$-0.636929\pi$
$23$	−4.00000			−0.834058			−0.417029	+	0.908893i	$0.636929\pi$
$24$		0			0
$25$	2.00000	−	3.46410i	0.400000	−	0.692820i
$26$	−2.00000			−0.392232
$27$		0			0
$28$	2.15831	−	3.73831i	0.407883	−	0.706474i
$29$	9.63325			1.78885			0.894425	−	0.447218i	$-0.147585\pi$
$29$	9.63325			1.78885			0.894425	+	0.447218i	$0.147585\pi$
$30$		0			0
$31$	4.31662			0.775289			0.387644	−	0.921809i	$-0.373289\pi$
$31$	4.31662			0.775289			0.387644	+	0.921809i	$0.373289\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$	−1.65831	−	2.87228i	−0.284398	−	0.492592i
$35$	2.15831	−	3.73831i	0.364821	−	0.631889i
$36$		0			0
$37$	−5.97494	+	1.14023i	−0.982274	+	0.187453i
$37$	−5.97494	+	1.14023i	−0.982274	+	0.187453i
$38$	6.31662			1.02469
$39$		0			0
$40$	0.500000	+	0.866025i	0.0790569	+	0.136931i
$41$	−5.65831	−	9.80048i	−0.883680	−	1.53058i	−0.847219	−	0.531243i	$-0.821725\pi$
$41$	−5.65831	−	9.80048i	−0.883680	−	1.53058i	−0.0364607	−	0.999335i	$-0.511608\pi$
$42$		0			0
$43$	−6.31662			−0.963276			−0.481638	−	0.876370i	$-0.659958\pi$
$43$	−6.31662			−0.963276			−0.481638	+	0.876370i	$0.659958\pi$
$44$	−2.15831	−	3.73831i	−0.325378	−	0.563571i
$45$		0			0
$46$	−2.00000	+	3.46410i	−0.294884	+	0.510754i
$47$	2.31662			0.337914			0.168957	−	0.985623i	$-0.445960\pi$
$47$	2.31662			0.337914			0.168957	+	0.985623i	$0.445960\pi$
$48$		0			0
$49$	−5.81662	+	10.0747i	−0.830946	+	1.43924i
$50$	−2.00000	−	3.46410i	−0.282843	−	0.489898i
$51$		0			0
$52$	−1.00000	+	1.73205i	−0.138675	+	0.240192i
$53$	4.31662	−	7.47661i	0.592934	−	1.02699i	−0.400901	−	0.916121i	$-0.631303\pi$
$53$	4.31662	−	7.47661i	0.592934	−	1.02699i	0.993835	−	0.110870i	$-0.0353638\pi$
$54$		0			0
$55$	−2.15831	−	3.73831i	−0.291027	−	0.504073i
$56$	−2.15831	−	3.73831i	−0.288417	−	0.499552i
$57$		0			0
$58$	4.81662	−	8.34264i	0.632454	−	1.09544i
$59$	−2.31662	+	4.01251i	−0.301599	+	0.522385i	−0.976498	−	0.215525i	$-0.930854\pi$
$59$	−2.31662	+	4.01251i	−0.301599	+	0.522385i	0.674899	+	0.737910i	$0.264187\pi$
$60$		0			0
$61$	3.65831	+	6.33638i	0.468399	+	0.811291i	0.999348	−	0.0361132i	$-0.0114977\pi$
$61$	3.65831	+	6.33638i	0.468399	+	0.811291i	−0.530949	+	0.847404i	$0.678164\pi$
$62$	2.15831	−	3.73831i	0.274106	−	0.474765i
$63$		0			0
$64$	1.00000			0.125000
$65$	−1.00000	+	1.73205i	−0.124035	+	0.214834i
$66$		0			0
$67$	−3.15831	−	5.47036i	−0.385849	−	0.668311i	0.606037	−	0.795436i	$-0.292758\pi$
$67$	−3.15831	−	5.47036i	−0.385849	−	0.668311i	−0.991887	+	0.127126i	$0.959425\pi$
$68$	−3.31662			−0.402200
$69$		0			0
$70$	−2.15831	−	3.73831i	−0.257968	−	0.446813i
$71$	3.15831	+	5.47036i	0.374823	+	0.649212i	0.990300	−	0.138942i	$-0.0443702\pi$
$71$	3.15831	+	5.47036i	0.374823	+	0.649212i	−0.615478	+	0.788154i	$0.711037\pi$
$72$		0			0
$73$	−0.633250			−0.0741163			−0.0370581	−	0.999313i	$-0.511799\pi$
$73$	−0.633250			−0.0741163			−0.0370581	+	0.999313i	$0.511799\pi$
$74$	−2.00000	+	5.74456i	−0.232495	+	0.667792i
$75$		0			0
$76$	3.15831	−	5.47036i	0.362283	−	0.627493i
$77$	9.31662	+	16.1369i	1.06173	+	1.83897i
$78$		0			0
$79$	6.47494	+	11.2149i	0.728487	+	1.26178i	0.957522	+	0.288359i	$0.0931096\pi$
$79$	6.47494	+	11.2149i	0.728487	+	1.26178i	−0.229035	+	0.973418i	$0.573557\pi$
$80$	1.00000			0.111803
$81$		0			0
$82$	−11.3166			−1.24971
$83$	−2.31662	+	4.01251i	−0.254283	+	0.440430i	−0.964700	−	0.263350i	$-0.915173\pi$
$83$	−2.31662	+	4.01251i	−0.254283	+	0.440430i	0.710418	+	0.703780i	$0.248506\pi$
$84$		0			0
$85$	−3.31662			−0.359738
$86$	−3.15831	+	5.47036i	−0.340570	+	0.589884i
$87$		0			0
$88$	−4.31662			−0.460154
$89$	−4.65831	+	8.06843i	−0.493780	+	0.855252i	−0.999974	−	0.00716726i	$-0.997719\pi$
$89$	−4.65831	+	8.06843i	−0.493780	+	0.855252i	0.506194	+	0.862420i	$0.331052\pi$
$90$		0			0
$91$	4.31662	−	7.47661i	0.452505	−	0.783762i
$92$	2.00000	+	3.46410i	0.208514	+	0.361158i
$93$		0			0
$94$	1.15831	−	2.00626i	0.119471	−	0.206929i
$95$	3.15831	−	5.47036i	0.324036	−	0.561247i
$96$		0			0
$97$	0.366750			0.0372379			0.0186189	−	0.999827i	$-0.494073\pi$
$97$	0.366750			0.0372379			0.0186189	+	0.999827i	$0.494073\pi$
$98$	5.81662	+	10.0747i	0.587568	+	1.01770i
$99$		0			0
$100$	−4.00000			−0.400000
$101$	−18.2665			−1.81758			−0.908792	−	0.417249i	$-0.862994\pi$
$101$	−18.2665			−1.81758			−0.908792	+	0.417249i	$0.862994\pi$
$102$		0			0
$103$	8.94987			0.881857			0.440929	−	0.897542i	$-0.354649\pi$
$103$	8.94987			0.881857			0.440929	+	0.897542i	$0.354649\pi$
$104$	1.00000	+	1.73205i	0.0980581	+	0.169842i
$105$		0			0
$106$	−4.31662	−	7.47661i	−0.419268	−	0.726193i
$107$	−8.79156	−	15.2274i	−0.849912	−	1.47209i	−0.881286	−	0.472584i	$-0.843321\pi$
$107$	−8.79156	−	15.2274i	−0.849912	−	1.47209i	0.0313734	−	0.999508i	$-0.490012\pi$
$108$		0			0
$109$	−4.65831	+	8.06843i	−0.446185	+	0.772816i	−0.998134	−	0.0610624i	$-0.980551\pi$
$109$	−4.65831	+	8.06843i	−0.446185	+	0.772816i	0.551949	+	0.833878i	$0.313884\pi$
$110$	−4.31662			−0.411574
$111$		0			0
$112$	−4.31662			−0.407883
$113$	−5.63325	+	9.75707i	−0.529932	+	0.917868i	0.469459	+	0.882954i	$0.344449\pi$
$113$	−5.63325	+	9.75707i	−0.529932	+	0.917868i	−0.999390	+	0.0349140i	$0.988884\pi$
$114$		0			0
$115$	2.00000	+	3.46410i	0.186501	+	0.323029i
$116$	−4.81662	−	8.34264i	−0.447212	−	0.774595i
$117$		0			0
$118$	2.31662	+	4.01251i	0.213263	+	0.369382i
$119$	14.3166			1.31240
$120$		0			0
$121$	7.63325			0.693932
$122$	7.31662			0.662416
$123$		0			0
$124$	−2.15831	−	3.73831i	−0.193822	−	0.335710i
$125$	−9.00000			−0.804984
$126$		0			0
$127$	8.31662	−	14.4048i	0.737981	−	1.27822i	−0.215422	−	0.976521i	$-0.569113\pi$
$127$	8.31662	−	14.4048i	0.737981	−	1.27822i	0.953403	−	0.301700i	$-0.0975540\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$		0			0
$130$	1.00000	+	1.73205i	0.0877058	+	0.151911i
$131$	−8.63325	+	14.9532i	−0.754291	+	1.30647i	0.191436	+	0.981505i	$0.438686\pi$
$131$	−8.63325	+	14.9532i	−0.754291	+	1.30647i	−0.945726	+	0.324964i	$0.894648\pi$
$132$		0			0
$133$	−13.6332	+	23.6135i	−1.18215	+	2.04755i
$134$	−6.31662			−0.545673
$135$		0			0
$136$	−1.65831	+	2.87228i	−0.142199	+	0.246296i
$137$	−7.31662			−0.625101			−0.312551	−	0.949901i	$-0.601183\pi$
$137$	−7.31662			−0.625101			−0.312551	+	0.949901i	$0.601183\pi$
$138$		0			0
$139$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$139$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$140$	−4.31662			−0.364821
$141$		0			0
$142$	6.31662			0.530079
$143$	−4.31662	−	7.47661i	−0.360974	−	0.625226i
$144$		0			0
$145$	−4.81662	−	8.34264i	−0.399999	−	0.692818i
$146$	−0.316625	+	0.548410i	−0.0262041	+	0.0453868i
$147$		0			0
$148$	3.97494	+	4.60433i	0.326738	+	0.378474i
$149$	6.36675			0.521585			0.260792	−	0.965395i	$-0.416016\pi$
$149$	6.36675			0.521585			0.260792	+	0.965395i	$0.416016\pi$
$150$		0			0
$151$	−10.0000	−	17.3205i	−0.813788	−	1.40952i	−0.910195	−	0.414181i	$-0.864068\pi$
$151$	−10.0000	−	17.3205i	−0.813788	−	1.40952i	0.0964061	−	0.995342i	$-0.469265\pi$
$152$	−3.15831	−	5.47036i	−0.256173	−	0.443705i
$153$		0			0
$154$	18.6332			1.50151
$155$	−2.15831	−	3.73831i	−0.173360	−	0.300268i
$156$		0			0
$157$	−4.65831	+	8.06843i	−0.371774	+	0.643931i	−0.989839	−	0.142196i	$-0.954584\pi$
$157$	−4.65831	+	8.06843i	−0.371774	+	0.643931i	0.618065	+	0.786127i	$0.287917\pi$
$158$	12.9499			1.03024
$159$		0			0
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	−8.63325	−	14.9532i	−0.680395	−	1.17848i
$162$		0			0
$163$	1.15831	−	2.00626i	0.0907260	−	0.157142i	−0.817091	−	0.576509i	$-0.804415\pi$
$163$	1.15831	−	2.00626i	0.0907260	−	0.157142i	0.907817	+	0.419367i	$0.137748\pi$
$164$	−5.65831	+	9.80048i	−0.441840	+	0.765289i
$165$		0			0
$166$	2.31662	+	4.01251i	0.179805	+	0.311431i
$167$	6.00000	+	10.3923i	0.464294	+	0.804181i	0.999169	−	0.0407502i	$-0.0129748\pi$
$167$	6.00000	+	10.3923i	0.464294	+	0.804181i	−0.534875	+	0.844931i	$0.679641\pi$
$168$		0			0
$169$	4.50000	−	7.79423i	0.346154	−	0.599556i
$170$	−1.65831	+	2.87228i	−0.127187	+	0.220294i
$171$		0			0
$172$	3.15831	+	5.47036i	0.240819	+	0.417111i
$173$	0.183375	−	0.317615i	0.0139418	−	0.0241478i	−0.858970	−	0.512025i	$-0.828895\pi$
$173$	0.183375	−	0.317615i	0.0139418	−	0.0241478i	0.872912	+	0.487877i	$0.162229\pi$
$174$		0			0
$175$	17.2665			1.30522
$176$	−2.15831	+	3.73831i	−0.162689	+	0.281785i
$177$		0			0
$178$	4.65831	+	8.06843i	0.349155	+	0.604755i
$179$	−12.6332			−0.944253			−0.472127	−	0.881531i	$-0.656514\pi$
$179$	−12.6332			−0.944253			−0.472127	+	0.881531i	$0.656514\pi$
$180$		0			0
$181$	2.65831	+	4.60433i	0.197591	+	0.342237i	0.947747	−	0.319024i	$-0.103355\pi$
$181$	2.65831	+	4.60433i	0.197591	+	0.342237i	−0.750156	+	0.661261i	$0.770022\pi$
$182$	−4.31662	−	7.47661i	−0.319970	−	0.554203i
$183$		0			0
$184$	4.00000			0.294884
$185$	3.97494	+	4.60433i	0.292243	+	0.338517i
$186$		0			0
$187$	7.15831	−	12.3986i	0.523468	−	0.906673i
$188$	−1.15831	−	2.00626i	−0.0844786	−	0.146321i
$189$		0			0
$190$	−3.15831	−	5.47036i	−0.229128	−	0.396861i
$191$	−24.6332			−1.78240			−0.891200	−	0.453611i	$-0.850135\pi$
$191$	−24.6332			−1.78240			−0.891200	+	0.453611i	$0.850135\pi$
$192$		0			0
$193$	1.00000			0.0719816			0.0359908	−	0.999352i	$-0.488541\pi$
$193$	1.00000			0.0719816			0.0359908	+	0.999352i	$0.488541\pi$
$194$	0.183375	−	0.317615i	0.0131656	−	0.0228034i
$195$		0			0
$196$	11.6332			0.830946
$197$	1.81662	−	3.14649i	0.129429	−	0.224178i	−0.794026	−	0.607883i	$-0.792019\pi$
$197$	1.81662	−	3.14649i	0.129429	−	0.224178i	0.923456	+	0.383705i	$0.125352\pi$
$198$		0			0
$199$	−12.3166			−0.873102			−0.436551	−	0.899679i	$-0.643800\pi$
$199$	−12.3166			−0.873102			−0.436551	+	0.899679i	$0.643800\pi$
$200$	−2.00000	+	3.46410i	−0.141421	+	0.244949i
$201$		0			0
$202$	−9.13325	+	15.8193i	−0.642613	+	1.11304i
$203$	20.7916	+	36.0120i	1.45928	+	2.52755i
$204$		0			0
$205$	−5.65831	+	9.80048i	−0.395194	+	0.684496i
$206$	4.47494	−	7.75082i	0.311784	−	0.540025i
$207$		0			0
$208$	2.00000			0.138675
$209$	13.6332	+	23.6135i	0.943032	+	1.63338i
$210$		0			0
$211$	2.94987			0.203078			0.101539	−	0.994832i	$-0.467623\pi$
$211$	2.94987			0.203078			0.101539	+	0.994832i	$0.467623\pi$
$212$	−8.63325			−0.592934
$213$		0			0
$214$	−17.5831			−1.20196
$215$	3.15831	+	5.47036i	0.215395	+	0.373075i
$216$		0			0
$217$	9.31662	+	16.1369i	0.632454	+	1.09544i
$218$	4.65831	+	8.06843i	0.315501	+	0.546463i
$219$		0			0
$220$	−2.15831	+	3.73831i	−0.145513	+	0.252037i
$221$	−6.63325			−0.446201
$222$		0			0
$223$	12.6332			0.845985			0.422992	−	0.906133i	$-0.360980\pi$
$223$	12.6332			0.845985			0.422992	+	0.906133i	$0.360980\pi$
$224$	−2.15831	+	3.73831i	−0.144208	+	0.249776i
$225$		0			0
$226$	5.63325	+	9.75707i	0.374718	+	0.649031i
$227$	−10.4749	−	18.1431i	−0.695246	−	1.20420i	−0.970098	−	0.242715i	$-0.921962\pi$
$227$	−10.4749	−	18.1431i	−0.695246	−	1.20420i	0.274852	−	0.961487i	$-0.411371\pi$
$228$		0			0
$229$	−10.9749	−	19.0091i	−0.725244	−	1.25616i	−0.958873	−	0.283834i	$-0.908393\pi$
$229$	−10.9749	−	19.0091i	−0.725244	−	1.25616i	0.233629	−	0.972326i	$-0.424940\pi$
$230$	4.00000			0.263752
$231$		0			0
$232$	−9.63325			−0.632454
$233$	13.9499			0.913887			0.456943	−	0.889496i	$-0.348944\pi$
$233$	13.9499			0.913887			0.456943	+	0.889496i	$0.348944\pi$
$234$		0			0
$235$	−1.15831	−	2.00626i	−0.0755600	−	0.130874i
$236$	4.63325			0.301599
$237$		0			0
$238$	7.15831	−	12.3986i	0.464004	−	0.803679i
$239$	0.525063	−	0.909435i	0.0339635	−	0.0588265i	−0.848544	−	0.529125i	$-0.822520\pi$
$239$	0.525063	−	0.909435i	0.0339635	−	0.0588265i	0.882508	+	0.470298i	$0.155854\pi$
$240$		0			0
$241$	−0.316625	−	0.548410i	−0.0203956	−	0.0353262i	0.855647	−	0.517559i	$-0.173159\pi$
$241$	−0.316625	−	0.548410i	−0.0203956	−	0.0353262i	−0.876043	+	0.482233i	$0.839826\pi$
$242$	3.81662	−	6.61059i	0.245342	−	0.424945i
$243$		0			0
$244$	3.65831	−	6.33638i	0.234199	−	0.405645i
$245$	11.6332			0.743221
$246$		0			0
$247$	6.31662	−	10.9407i	0.401917	−	0.696141i
$248$	−4.31662			−0.274106
$249$		0			0
$250$	−4.50000	+	7.79423i	−0.284605	+	0.492950i
$251$	−11.6834			−0.737448			−0.368724	−	0.929539i	$-0.620205\pi$
$251$	−11.6834			−0.737448			−0.368724	+	0.929539i	$0.620205\pi$
$252$		0			0
$253$	−17.2665			−1.08554
$254$	−8.31662	−	14.4048i	−0.521831	−	0.903839i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	8.65831	−	14.9966i	0.540091	−	0.935465i	−0.458808	−	0.888536i	$-0.651723\pi$
$257$	8.65831	−	14.9966i	0.540091	−	0.935465i	0.998898	−	0.0469288i	$-0.0149434\pi$
$258$		0			0
$259$	−17.1583	−	19.8752i	−1.06617	−	1.23498i
$260$	2.00000			0.124035
$261$		0			0
$262$	8.63325	+	14.9532i	0.533364	+	0.923813i
$263$	−3.68338	−	6.37979i	−0.227127	−	0.393395i	0.729829	−	0.683630i	$-0.239600\pi$
$263$	−3.68338	−	6.37979i	−0.227127	−	0.393395i	−0.956955	+	0.290235i	$0.906266\pi$
$264$		0			0
$265$	−8.63325			−0.530336
$266$	13.6332	+	23.6135i	0.835908	+	1.44784i
$267$		0			0
$268$	−3.15831	+	5.47036i	−0.192925	+	0.334155i
$269$	−10.0000			−0.609711			−0.304855	−	0.952399i	$-0.598608\pi$
$269$	−10.0000			−0.609711			−0.304855	+	0.952399i	$0.598608\pi$
$270$		0			0
$271$	4.79156	−	8.29923i	0.291067	−	0.504142i	−0.682996	−	0.730423i	$-0.739323\pi$
$271$	4.79156	−	8.29923i	0.291067	−	0.504142i	0.974062	+	0.226280i	$0.0726565\pi$
$272$	1.65831	+	2.87228i	0.100550	+	0.174158i
$273$		0			0
$274$	−3.65831	+	6.33638i	−0.221007	+	0.382795i
$275$	8.63325	−	14.9532i	0.520605	−	0.901714i
$276$		0			0
$277$	10.3417	+	17.9123i	0.621372	+	1.07625i	0.989231	+	0.146366i	$0.0467577\pi$
$277$	10.3417	+	17.9123i	0.621372	+	1.07625i	−0.367859	+	0.929882i	$0.619909\pi$
$278$		0			0
$279$		0			0
$280$	−2.15831	+	3.73831i	−0.128984	+	0.223407i
$281$	4.34169	−	7.52002i	0.259003	−	0.448607i	−0.706972	−	0.707242i	$-0.749939\pi$
$281$	4.34169	−	7.52002i	0.259003	−	0.448607i	0.965975	+	0.258635i	$0.0832726\pi$
$282$		0			0
$283$	−3.79156	−	6.56718i	−0.225385	−	0.390378i	0.731050	−	0.682324i	$-0.239031\pi$
$283$	−3.79156	−	6.56718i	−0.225385	−	0.390378i	−0.956435	+	0.291946i	$0.905697\pi$
$284$	3.15831	−	5.47036i	0.187411	−	0.324606i
$285$		0			0
$286$	−8.63325			−0.510495
$287$	24.4248	−	42.3050i	1.44175	−	2.49719i
$288$		0			0
$289$	3.00000	+	5.19615i	0.176471	+	0.305656i
$290$	−9.63325			−0.565684
$291$		0			0
$292$	0.316625	+	0.548410i	0.0185291	+	0.0320933i
$293$	−4.18338	−	7.24582i	−0.244395	−	0.423305i	0.717566	−	0.696490i	$-0.245256\pi$
$293$	−4.18338	−	7.24582i	−0.244395	−	0.423305i	−0.961961	+	0.273185i	$0.911923\pi$
$294$		0			0
$295$	4.63325			0.269758
$296$	5.97494	−	1.14023i	0.347286	−	0.0662746i
$297$		0			0
$298$	3.18338	−	5.51377i	0.184408	−	0.319404i
$299$	4.00000	+	6.92820i	0.231326	+	0.400668i
$300$		0			0
$301$	−13.6332	−	23.6135i	−0.785807	−	1.36106i
$302$	−20.0000			−1.15087
$303$		0			0
$304$	−6.31662			−0.362283
$305$	3.65831	−	6.33638i	0.209474	−	0.362820i
$306$		0			0
$307$	−14.9499			−0.853234			−0.426617	−	0.904432i	$-0.640295\pi$
$307$	−14.9499			−0.853234			−0.426617	+	0.904432i	$0.640295\pi$
$308$	9.31662	−	16.1369i	0.530864	−	0.919483i
$309$		0			0
$310$	−4.31662			−0.245168
$311$	−0.841688	+	1.45785i	−0.0477277	+	0.0826668i	−0.888902	−	0.458097i	$-0.848531\pi$
$311$	−0.841688	+	1.45785i	−0.0477277	+	0.0826668i	0.841175	+	0.540764i	$0.181865\pi$
$312$		0			0
$313$	10.1332	−	17.5513i	0.572765	−	0.992058i	−0.423515	−	0.905889i	$-0.639204\pi$
$313$	10.1332	−	17.5513i	0.572765	−	0.992058i	0.996281	−	0.0861694i	$-0.0274626\pi$
$314$	4.65831	+	8.06843i	0.262884	+	0.455328i
$315$		0			0
$316$	6.47494	−	11.2149i	0.364244	−	0.630889i
$317$	−0.866750	+	1.50126i	−0.0486816	+	0.0843189i	−0.889339	−	0.457248i	$-0.848835\pi$
$317$	−0.866750	+	1.50126i	−0.0486816	+	0.0843189i	0.840658	+	0.541567i	$0.182169\pi$
$318$		0			0
$319$	41.5831			2.32821
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$		0			0
$322$	−17.2665			−0.962224
$323$	20.9499			1.16568
$324$		0			0
$325$	−8.00000			−0.443760
$326$	−1.15831	−	2.00626i	−0.0641530	−	0.111116i
$327$		0			0
$328$	5.65831	+	9.80048i	0.312428	+	0.541141i
$329$	5.00000	+	8.66025i	0.275659	+	0.477455i
$330$		0			0
$331$	4.94987	−	8.57343i	0.272070	−	0.471239i	−0.697322	−	0.716758i	$-0.745625\pi$
$331$	4.94987	−	8.57343i	0.272070	−	0.471239i	0.969392	+	0.245520i	$0.0789585\pi$
$332$	4.63325			0.254283
$333$		0			0
$334$	12.0000			0.656611
$335$	−3.15831	+	5.47036i	−0.172557	+	0.298878i
$336$		0			0
$337$	−15.7665	−	27.3084i	−0.858856	−	1.48758i	−0.873021	−	0.487682i	$-0.837842\pi$
$337$	−15.7665	−	27.3084i	−0.858856	−	1.48758i	0.0141652	−	0.999900i	$-0.495491\pi$
$338$	−4.50000	−	7.79423i	−0.244768	−	0.423950i
$339$		0			0
$340$	1.65831	+	2.87228i	0.0899346	+	0.155771i
$341$	18.6332			1.00905
$342$		0			0
$343$	−20.0000			−1.07990
$344$	6.31662			0.340570
$345$		0			0
$346$	−0.183375	−	0.317615i	−0.00985831	−	0.0170751i
$347$	−23.3668			−1.25439			−0.627196	−	0.778861i	$-0.715798\pi$
$347$	−23.3668			−1.25439			−0.627196	+	0.778861i	$0.715798\pi$
$348$		0			0
$349$	−13.6082	+	23.5701i	−0.728430	+	1.26168i	0.229117	+	0.973399i	$0.426416\pi$
$349$	−13.6082	+	23.5701i	−0.728430	+	1.26168i	−0.957547	+	0.288278i	$0.906917\pi$
$350$	8.63325	−	14.9532i	0.461467	−	0.799284i
$351$		0			0
$352$	2.15831	+	3.73831i	0.115038	+	0.199252i
$353$	−3.02506	+	5.23956i	−0.161008	+	0.278874i	−0.935230	−	0.354040i	$-0.884808\pi$
$353$	−3.02506	+	5.23956i	−0.161008	+	0.278874i	0.774223	+	0.632913i	$0.218141\pi$
$354$		0			0
$355$	3.15831	−	5.47036i	0.167626	−	0.290336i
$356$	9.31662			0.493780
$357$		0			0
$358$	−6.31662	+	10.9407i	−0.333844	+	0.578235i
$359$	−11.3668			−0.599914			−0.299957	−	0.953953i	$-0.596972\pi$
$359$	−11.3668			−0.599914			−0.299957	+	0.953953i	$0.596972\pi$
$360$		0			0
$361$	−10.4499	+	18.0997i	−0.549993	+	0.952616i
$362$	5.31662			0.279436
$363$		0			0
$364$	−8.63325			−0.452505
$365$	0.316625	+	0.548410i	0.0165729	+	0.0287051i
$366$		0			0
$367$	14.9499	+	25.8939i	0.780377	+	1.35165i	0.931722	+	0.363172i	$0.118306\pi$
$367$	14.9499	+	25.8939i	0.780377	+	1.35165i	−0.151345	+	0.988481i	$0.548360\pi$
$368$	2.00000	−	3.46410i	0.104257	−	0.180579i
$369$		0			0
$370$	5.97494	−	1.14023i	0.310622	−	0.0592778i
$371$	37.2665			1.93478
$372$		0			0
$373$	−13.9749	−	24.2053i	−0.723595	−	1.25330i	−0.959550	−	0.281539i	$-0.909155\pi$
$373$	−13.9749	−	24.2053i	−0.723595	−	1.25330i	0.235955	−	0.971764i	$-0.424178\pi$
$374$	−7.15831	−	12.3986i	−0.370148	−	0.641114i
$375$		0			0
$376$	−2.31662			−0.119471
$377$	−9.63325	−	16.6853i	−0.496138	−	0.859336i
$378$		0			0
$379$	3.79156	−	6.56718i	0.194759	−	0.337333i	−0.752062	−	0.659092i	$-0.770941\pi$
$379$	3.79156	−	6.56718i	0.194759	−	0.337333i	0.946822	+	0.321759i	$0.104274\pi$
$380$	−6.31662			−0.324036
$381$		0			0
$382$	−12.3166	+	21.3330i	−0.630173	+	1.09149i
$383$	9.79156	+	16.9595i	0.500325	+	0.866589i	1.00000		0.000375832i	$0.000119631\pi$
$383$	9.79156	+	16.9595i	0.500325	+	0.866589i	−0.499674	+	0.866213i	$0.666547\pi$
$384$		0			0
$385$	9.31662	−	16.1369i	0.474819	−	0.822411i
$386$	0.500000	−	0.866025i	0.0254493	−	0.0440795i
$387$		0			0
$388$	−0.183375	−	0.317615i	−0.00930947	−	0.0161245i
$389$	3.50000	+	6.06218i	0.177457	+	0.307365i	0.941009	−	0.338382i	$-0.109880\pi$
$389$	3.50000	+	6.06218i	0.177457	+	0.307365i	−0.763552	+	0.645747i	$0.776546\pi$
$390$		0			0
$391$	−6.63325	+	11.4891i	−0.335458	+	0.581030i
$392$	5.81662	−	10.0747i	0.293784	−	0.508849i
$393$		0			0
$394$	−1.81662	−	3.14649i	−0.0915202	−	0.158518i
$395$	6.47494	−	11.2149i	0.325789	−	0.564284i
$396$		0			0
$397$	−14.5831			−0.731906			−0.365953	−	0.930633i	$-0.619257\pi$
$397$	−14.5831			−0.731906			−0.365953	+	0.930633i	$0.619257\pi$
$398$	−6.15831	+	10.6665i	−0.308688	+	0.534664i
$399$		0			0
$400$	2.00000	+	3.46410i	0.100000	+	0.173205i
$401$	36.5330			1.82437			0.912185	−	0.409778i	$-0.134394\pi$
$401$	36.5330			1.82437			0.912185	+	0.409778i	$0.134394\pi$
$402$		0			0
$403$	−4.31662	−	7.47661i	−0.215026	−	0.372437i
$404$	9.13325	+	15.8193i	0.454396	+	0.787037i
$405$		0			0
$406$	41.5831			2.06374
$407$	−25.7916	+	4.92195i	−1.27844	+	0.243972i
$408$		0			0
$409$	−8.13325	+	14.0872i	−0.402163	+	0.696567i	−0.993987	−	0.109500i	$-0.965075\pi$
$409$	−8.13325	+	14.0872i	−0.402163	+	0.696567i	0.591823	+	0.806068i	$0.298408\pi$
$410$	5.65831	+	9.80048i	0.279444	+	0.484011i
$411$		0			0
$412$	−4.47494	−	7.75082i	−0.220464	−	0.381855i
$413$	−20.0000			−0.984136
$414$		0			0
$415$	4.63325			0.227437
$416$	1.00000	−	1.73205i	0.0490290	−	0.0849208i
$417$		0			0
$418$	27.2665			1.33365
$419$	1.52506	−	2.64149i	0.0745042	−	0.129045i	−0.826366	−	0.563133i	$-0.809596\pi$
$419$	1.52506	−	2.64149i	0.0745042	−	0.129045i	0.900871	+	0.434088i	$0.142929\pi$
$420$		0			0
$421$	35.2164			1.71634			0.858171	−	0.513365i	$-0.171601\pi$
$421$	35.2164			1.71634			0.858171	+	0.513365i	$0.171601\pi$
$422$	1.47494	−	2.55467i	0.0717988	−	0.124359i
$423$		0			0
$424$	−4.31662	+	7.47661i	−0.209634	+	0.363096i
$425$	−6.63325	−	11.4891i	−0.321760	−	0.557304i
$426$		0			0
$427$	−15.7916	+	27.3518i	−0.764207	+	1.32365i
$428$	−8.79156	+	15.2274i	−0.424956	+	0.736046i
$429$		0			0
$430$	6.31662			0.304615
$431$	0.208438	+	0.361025i	0.0100401	+	0.0173900i	0.871002	−	0.491280i	$-0.163471\pi$
$431$	0.208438	+	0.361025i	0.0100401	+	0.0173900i	−0.860962	+	0.508670i	$0.830137\pi$
$432$		0			0
$433$	−28.2665			−1.35840			−0.679201	−	0.733953i	$-0.737673\pi$
$433$	−28.2665			−1.35840			−0.679201	+	0.733953i	$0.737673\pi$
$434$	18.6332			0.894425
$435$		0			0
$436$	9.31662			0.446185
$437$	−12.6332	−	21.8814i	−0.604330	−	1.04673i
$438$		0			0
$439$	7.26650	+	12.5859i	0.346811	+	0.600694i	0.985681	−	0.168620i	$-0.0539312\pi$
$439$	7.26650	+	12.5859i	0.346811	+	0.600694i	−0.638870	+	0.769315i	$0.720598\pi$
$440$	2.15831	+	3.73831i	0.102894	+	0.178217i
$441$		0			0
$442$	−3.31662	+	5.74456i	−0.157756	+	0.273241i
$443$	24.0000			1.14027			0.570137	−	0.821549i	$-0.306890\pi$
$443$	24.0000			1.14027			0.570137	+	0.821549i	$0.306890\pi$
$444$		0			0
$445$	9.31662			0.441650
$446$	6.31662	−	10.9407i	0.299101	−	0.518058i
$447$		0			0
$448$	2.15831	+	3.73831i	0.101971	+	0.176618i
$449$	−2.36675	−	4.09933i	−0.111694	−	0.193459i	0.804759	−	0.593601i	$-0.202294\pi$
$449$	−2.36675	−	4.09933i	−0.111694	−	0.193459i	−0.916453	+	0.400142i	$0.868961\pi$
$450$		0			0
$451$	−24.4248	−	42.3050i	−1.15012	−	1.99207i
$452$	11.2665			0.529932
$453$		0			0
$454$	−20.9499			−0.983226
$455$	−8.63325			−0.404733
$456$		0			0
$457$	−4.18338	−	7.24582i	−0.195690	−	0.338945i	0.751436	−	0.659805i	$-0.229361\pi$
$457$	−4.18338	−	7.24582i	−0.195690	−	0.338945i	−0.947127	+	0.320860i	$0.896028\pi$
$458$	−21.9499			−1.02565
$459$		0			0
$460$	2.00000	−	3.46410i	0.0932505	−	0.161515i
$461$	12.3166	−	21.3330i	0.573642	−	0.993578i	−0.422545	−	0.906342i	$-0.638863\pi$
$461$	12.3166	−	21.3330i	0.573642	−	0.993578i	0.996188	−	0.0872360i	$-0.0278034\pi$
$462$		0			0
$463$	16.4749	+	28.5354i	0.765655	+	1.32615i	0.939899	+	0.341451i	$0.110918\pi$
$463$	16.4749	+	28.5354i	0.765655	+	1.32615i	−0.174244	+	0.984702i	$0.555748\pi$
$464$	−4.81662	+	8.34264i	−0.223606	+	0.387297i
$465$		0			0
$466$	6.97494	−	12.0809i	0.323108	−	0.559639i
$467$	−16.6332			−0.769695			−0.384847	−	0.922980i	$-0.625746\pi$
$467$	−16.6332			−0.769695			−0.384847	+	0.922980i	$0.625746\pi$
$468$		0			0
$469$	13.6332	−	23.6135i	0.629525	−	1.09037i
$470$	−2.31662			−0.106858
$471$		0			0
$472$	2.31662	−	4.01251i	0.106631	−	0.184691i
$473$	−27.2665			−1.25371
$474$		0			0
$475$	25.2665			1.15931
$476$	−7.15831	−	12.3986i	−0.328101	−	0.568287i
$477$		0			0
$478$	−0.525063	−	0.909435i	−0.0240158	−	0.0415966i
$479$	14.0000	−	24.2487i	0.639676	−	1.10795i	−0.345827	−	0.938298i	$-0.612402\pi$
$479$	14.0000	−	24.2487i	0.639676	−	1.10795i	0.985504	−	0.169654i	$-0.0542649\pi$
$480$		0			0
$481$	7.94987	+	9.20866i	0.362483	+	0.419879i
$482$	−0.633250			−0.0288437
$483$		0			0
$484$	−3.81662	−	6.61059i	−0.173483	−	0.300481i
$485$	−0.183375	−	0.317615i	−0.00832664	−	0.0144222i
$486$		0			0
$487$	12.6332			0.572467			0.286234	−	0.958160i	$-0.407597\pi$
$487$	12.6332			0.572467			0.286234	+	0.958160i	$0.407597\pi$
$488$	−3.65831	−	6.33638i	−0.165604	−	0.286835i
$489$		0			0
$490$	5.81662	−	10.0747i	0.262768	−	0.455128i
$491$	7.68338			0.346746			0.173373	−	0.984856i	$-0.444533\pi$
$491$	7.68338			0.346746			0.173373	+	0.984856i	$0.444533\pi$
$492$		0			0
$493$	15.9749	−	27.6694i	0.719475	−	1.24617i
$494$	−6.31662	−	10.9407i	−0.284198	−	0.492246i
$495$		0			0
$496$	−2.15831	+	3.73831i	−0.0969111	+	0.167855i
$497$	−13.6332	+	23.6135i	−0.611535	+	1.05921i
$498$		0			0
$499$	−1.47494	−	2.55467i	−0.0660273	−	0.114363i	0.831122	−	0.556090i	$-0.187699\pi$
$499$	−1.47494	−	2.55467i	−0.0660273	−	0.114363i	−0.897149	+	0.441728i	$0.854366\pi$
$500$	4.50000	+	7.79423i	0.201246	+	0.348569i
$501$		0			0
$502$	−5.84169	+	10.1181i	−0.260727	+	0.451593i
$503$	15.1583	−	26.2550i	0.675876	−	1.17065i	−0.300336	−	0.953833i	$-0.597099\pi$
$503$	15.1583	−	26.2550i	0.675876	−	1.17065i	0.976212	−	0.216818i	$-0.0695677\pi$
$504$		0			0
$505$	9.13325	+	15.8193i	0.406424	+	0.703947i
$506$	−8.63325	+	14.9532i	−0.383795	+	0.664752i
$507$		0			0
$508$	−16.6332			−0.737981
$509$	−19.3997	+	33.6014i	−0.859879	+	1.48935i	0.0121651	+	0.999926i	$0.496128\pi$
$509$	−19.3997	+	33.6014i	−0.859879	+	1.48935i	−0.872044	+	0.489428i	$0.837206\pi$
$510$		0			0
$511$	−1.36675	−	2.36728i	−0.0604615	−	0.104722i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−8.65831	−	14.9966i	−0.381902	−	0.661473i
$515$	−4.47494	−	7.75082i	−0.197189	−	0.341542i
$516$		0			0
$517$	10.0000			0.439799
$518$	−25.7916	+	4.92195i	−1.13322	+	0.216258i
$519$		0			0
$520$	1.00000	−	1.73205i	0.0438529	−	0.0759555i
$521$	21.0000	+	36.3731i	0.920027	+	1.59353i	0.799370	+	0.600839i	$0.205167\pi$
$521$	21.0000	+	36.3731i	0.920027	+	1.59353i	0.120656	+	0.992694i	$0.461500\pi$
$522$		0			0
$523$	14.3166	+	24.7971i	0.626022	+	1.08430i	0.988342	+	0.152249i	$0.0486514\pi$
$523$	14.3166	+	24.7971i	0.626022	+	1.08430i	−0.362320	+	0.932054i	$0.618015\pi$
$524$	17.2665			0.754291
$525$		0			0
$526$	−7.36675			−0.321206
$527$	7.15831	−	12.3986i	0.311821	−	0.540090i
$528$		0			0
$529$	−7.00000			−0.304348
$530$	−4.31662	+	7.47661i	−0.187502	+	0.324763i
$531$		0			0
$532$	27.2665			1.18215
$533$	−11.3166	+	19.6010i	−0.490177	+	0.849012i
$534$		0			0
$535$	−8.79156	+	15.2274i	−0.380092	+	0.658339i
$536$	3.15831	+	5.47036i	0.136418	+	0.236283i
$537$		0			0
$538$	−5.00000	+	8.66025i	−0.215565	+	0.373370i
$539$	−25.1082	+	43.4887i	−1.08149	+	1.87319i
$540$		0			0
$541$	35.3166			1.51838			0.759190	−	0.650869i	$-0.225595\pi$
$541$	35.3166			1.51838			0.759190	+	0.650869i	$0.225595\pi$
$542$	−4.79156	−	8.29923i	−0.205815	−	0.356482i
$543$		0			0
$544$	3.31662			0.142199
$545$	9.31662			0.399080
$546$		0			0
$547$	−26.3166			−1.12522			−0.562609	−	0.826723i	$-0.690202\pi$
$547$	−26.3166			−1.12522			−0.562609	+	0.826723i	$0.690202\pi$
$548$	3.65831	+	6.33638i	0.156275	+	0.270677i
$549$		0			0
$550$	−8.63325	−	14.9532i	−0.368123	−	0.637608i
$551$	30.4248	+	52.6973i	1.29614	+	2.24498i
$552$		0			0
$553$	−27.9499	+	48.4106i	−1.18855	+	2.05863i
$554$	20.6834			0.878752
$555$		0			0
$556$		0			0
$557$	15.4499	−	26.7600i	0.654632	−	1.13386i	−0.327354	−	0.944902i	$-0.606157\pi$
$557$	15.4499	−	26.7600i	0.654632	−	1.13386i	0.981986	−	0.188954i	$-0.0605098\pi$
$558$		0			0
$559$	6.31662	+	10.9407i	0.267165	+	0.462743i
$560$	2.15831	+	3.73831i	0.0912053	+	0.157972i
$561$		0			0
$562$	−4.34169	−	7.52002i	−0.183143	−	0.317213i
$563$	−34.5330			−1.45539			−0.727696	−	0.685900i	$-0.759409\pi$
$563$	−34.5330			−1.45539			−0.727696	+	0.685900i	$0.759409\pi$
$564$		0			0
$565$	11.2665			0.473985
$566$	−7.58312			−0.318742
$567$		0			0
$568$	−3.15831	−	5.47036i	−0.132520	−	0.229531i
$569$	−42.5831			−1.78518			−0.892589	−	0.450872i	$-0.851113\pi$
$569$	−42.5831			−1.78518			−0.892589	+	0.450872i	$0.851113\pi$
$570$		0			0
$571$	−2.00000	+	3.46410i	−0.0836974	+	0.144968i	−0.904835	−	0.425762i	$-0.860006\pi$
$571$	−2.00000	+	3.46410i	−0.0836974	+	0.144968i	0.821138	+	0.570730i	$0.193340\pi$
$572$	−4.31662	+	7.47661i	−0.180487	+	0.312613i
$573$		0			0
$574$	−24.4248	−	42.3050i	−1.01947	−	1.76578i
$575$	−8.00000	+	13.8564i	−0.333623	+	0.577852i
$576$		0			0
$577$	−1.68338	+	2.91569i	−0.0700798	+	0.121382i	−0.898936	−	0.438080i	$-0.855659\pi$
$577$	−1.68338	+	2.91569i	−0.0700798	+	0.121382i	0.828856	+	0.559462i	$0.188992\pi$
$578$	6.00000			0.249567
$579$		0			0
$580$	−4.81662	+	8.34264i	−0.199999	+	0.346409i
$581$	−20.0000			−0.829740
$582$		0			0
$583$	18.6332	−	32.2737i	0.771710	−	1.33664i
$584$	0.633250			0.0262041
$585$		0			0
$586$	−8.36675			−0.345627
$587$	4.63325	+	8.02502i	0.191235	+	0.331228i	0.945660	−	0.325158i	$-0.105418\pi$
$587$	4.63325	+	8.02502i	0.191235	+	0.331228i	−0.754425	+	0.656386i	$0.772084\pi$
$588$		0			0
$589$	13.6332	+	23.6135i	0.561748	+	0.972977i
$590$	2.31662	−	4.01251i	0.0953739	−	0.165192i
$591$		0			0
$592$	2.00000	−	5.74456i	0.0821995	−	0.236100i
$593$	20.0501			0.823360			0.411680	−	0.911328i	$-0.364942\pi$
$593$	20.0501			0.823360			0.411680	+	0.911328i	$0.364942\pi$
$594$		0			0
$595$	−7.15831	−	12.3986i	−0.293462	−	0.508291i
$596$	−3.18338	−	5.51377i	−0.130396	−	0.225853i
$597$		0			0
$598$	8.00000			0.327144
$599$	17.7916	+	30.8159i	0.726944	+	1.25910i	0.958169	+	0.286203i	$0.0923931\pi$
$599$	17.7916	+	30.8159i	0.726944	+	1.25910i	−0.231226	+	0.972900i	$0.574274\pi$
$600$		0			0
$601$	−19.4499	+	33.6882i	−0.793377	+	1.37417i	0.130488	+	0.991450i	$0.458346\pi$
$601$	−19.4499	+	33.6882i	−0.793377	+	1.37417i	−0.923865	+	0.382719i	$0.874988\pi$
$602$	−27.2665			−1.11130
$603$		0			0
$604$	−10.0000	+	17.3205i	−0.406894	+	0.704761i
$605$	−3.81662	−	6.61059i	−0.155168	−	0.268759i
$606$		0			0
$607$	3.20844	−	5.55718i	0.130226	−	0.225559i	−0.793537	−	0.608522i	$-0.791763\pi$
$607$	3.20844	−	5.55718i	0.130226	−	0.225559i	0.923764	+	0.382963i	$0.125096\pi$
$608$	−3.15831	+	5.47036i	−0.128086	+	0.221852i
$609$		0			0
$610$	−3.65831	−	6.33638i	−0.148121	−	0.256553i
$611$	−2.31662	−	4.01251i	−0.0937206	−	0.162329i
$612$		0			0
$613$	−6.29156	+	10.8973i	−0.254114	+	0.440138i	−0.964654	−	0.263518i	$-0.915117\pi$
$613$	−6.29156	+	10.8973i	−0.254114	+	0.440138i	0.710541	+	0.703656i	$0.248450\pi$
$614$	−7.47494	+	12.9470i	−0.301664	+	0.522497i
$615$		0			0
$616$	−9.31662	−	16.1369i	−0.375378	−	0.650173i
$617$	4.63325	−	8.02502i	0.186528	−	0.323075i	−0.757563	−	0.652763i	$-0.773610\pi$
$617$	4.63325	−	8.02502i	0.186528	−	0.323075i	0.944090	+	0.329687i	$0.106943\pi$
$618$		0			0
$619$	17.0501			0.685302			0.342651	−	0.939463i	$-0.388675\pi$
$619$	17.0501			0.685302			0.342651	+	0.939463i	$0.388675\pi$
$620$	−2.15831	+	3.73831i	−0.0866799	+	0.150134i
$621$		0			0
$622$	0.841688	+	1.45785i	0.0337486	+	0.0584543i
$623$	−40.2164			−1.61123
$624$		0			0
$625$	−5.50000	−	9.52628i	−0.220000	−	0.381051i
$626$	−10.1332	−	17.5513i	−0.405006	−	0.701491i
$627$		0			0
$628$	9.31662			0.371774
$629$	−6.63325	+	19.0526i	−0.264485	+	0.759675i
$630$		0			0
$631$	6.00000	−	10.3923i	0.238856	−	0.413711i	−0.721530	−	0.692383i	$-0.756561\pi$
$631$	6.00000	−	10.3923i	0.238856	−	0.413711i	0.960386	+	0.278672i	$0.0898942\pi$
$632$	−6.47494	−	11.2149i	−0.257559	−	0.446106i
$633$		0			0
$634$	0.866750	+	1.50126i	0.0344231	+	0.0596225i
$635$	−16.6332			−0.660070
$636$		0			0
$637$	23.2665			0.921852
$638$	20.7916	−	36.0120i	0.823146	−	1.42573i
$639$		0			0
$640$	−1.00000			−0.0395285
$641$	9.65831	−	16.7287i	0.381480	−	0.660743i	−0.609794	−	0.792560i	$-0.708748\pi$
$641$	9.65831	−	16.7287i	0.381480	−	0.660743i	0.991274	+	0.131817i	$0.0420810\pi$
$642$		0			0
$643$	12.4169			0.489674			0.244837	−	0.969564i	$-0.421266\pi$
$643$	12.4169			0.489674			0.244837	+	0.969564i	$0.421266\pi$
$644$	−8.63325	+	14.9532i	−0.340198	+	0.589240i
$645$		0			0
$646$	10.4749	−	18.1431i	0.412131	−	0.713832i
$647$	−18.7414	−	32.4611i	−0.736802	−	1.27618i	−0.953928	−	0.300035i	$-0.903002\pi$
$647$	−18.7414	−	32.4611i	−0.736802	−	1.27618i	0.217126	−	0.976144i	$-0.430332\pi$
$648$		0			0
$649$	−10.0000	+	17.3205i	−0.392534	+	0.679889i
$650$	−4.00000	+	6.92820i	−0.156893	+	0.271746i
$651$		0			0
$652$	−2.31662			−0.0907260
$653$	9.50000	+	16.4545i	0.371764	+	0.643914i	0.989837	−	0.142207i	$-0.0454198\pi$
$653$	9.50000	+	16.4545i	0.371764	+	0.643914i	−0.618073	+	0.786121i	$0.712086\pi$
$654$		0			0
$655$	17.2665			0.674658
$656$	11.3166			0.441840
$657$		0			0
$658$	10.0000			0.389841
$659$	11.2665	+	19.5141i	0.438880	+	0.760163i	0.997603	−	0.0691911i	$-0.0220418\pi$
$659$	11.2665	+	19.5141i	0.438880	+	0.760163i	−0.558723	+	0.829354i	$0.688708\pi$
$660$		0			0
$661$	−19.2414	−	33.3271i	−0.748405	−	1.29628i	−0.948587	−	0.316517i	$-0.897487\pi$
$661$	−19.2414	−	33.3271i	−0.748405	−	1.29628i	0.200182	−	0.979759i	$-0.435847\pi$
$662$	−4.94987	−	8.57343i	−0.192382	−	0.333216i
$663$		0			0
$664$	2.31662	−	4.01251i	0.0899025	−	0.155716i
$665$	27.2665			1.05735
$666$		0			0
$667$	−38.5330			−1.49200
$668$	6.00000	−	10.3923i	0.232147	−	0.402090i
$669$		0			0
$670$	3.15831	+	5.47036i	0.122016	+	0.211338i
$671$	15.7916	+	27.3518i	0.609626	+	1.05590i
$672$		0			0
$673$	4.94987	+	8.57343i	0.190804	+	0.330482i	0.945517	−	0.325573i	$-0.105557\pi$
$673$	4.94987	+	8.57343i	0.190804	+	0.330482i	−0.754713	+	0.656055i	$0.772224\pi$
$674$	−31.5330			−1.21461
$675$		0			0
$676$	−9.00000			−0.346154
$677$	−28.1662			−1.08252			−0.541258	−	0.840856i	$-0.682052\pi$
$677$	−28.1662			−1.08252			−0.541258	+	0.840856i	$0.682052\pi$
$678$		0			0
$679$	0.791562	+	1.37103i	0.0303774	+	0.0526151i
$680$	3.31662			0.127187
$681$		0			0
$682$	9.31662	−	16.1369i	0.356752	−	0.617913i
$683$	3.52506	−	6.10559i	0.134883	−	0.233624i	−0.790670	−	0.612243i	$-0.790268\pi$
$683$	3.52506	−	6.10559i	0.134883	−	0.233624i	0.925553	+	0.378619i	$0.123601\pi$
$684$		0			0
$685$	3.65831	+	6.33638i	0.139777	+	0.242101i
$686$	−10.0000	+	17.3205i	−0.381802	+	0.661300i
$687$		0			0
$688$	3.15831	−	5.47036i	0.120410	−	0.208555i
$689$	−17.2665			−0.657801
$690$		0			0
$691$	−22.1082	+	38.2925i	−0.841035	+	1.45672i	0.0479854	+	0.998848i	$0.484720\pi$
$691$	−22.1082	+	38.2925i	−0.841035	+	1.45672i	−0.889020	+	0.457867i	$0.848613\pi$
$692$	−0.366750			−0.0139418
$693$		0			0
$694$	−11.6834	+	20.2362i	−0.443495	+	0.768156i
$695$		0			0
$696$		0			0
$697$	−37.5330			−1.42166
$698$	13.6082	+	23.5701i	0.515077	+	0.892140i
$699$		0			0
$700$	−8.63325	−	14.9532i	−0.326306	−	0.565179i
$701$	−0.949874	+	1.64523i	−0.0358763	+	0.0621395i	−0.883406	−	0.468608i	$-0.844756\pi$
$701$	−0.949874	+	1.64523i	−0.0358763	+	0.0621395i	0.847530	+	0.530748i	$0.178089\pi$
$702$		0			0
$703$	−25.1082	−	29.0838i	−0.946973	−	1.09692i
$704$	4.31662			0.162689
$705$		0			0
$706$	3.02506	+	5.23956i	0.113850	+	0.197194i
$707$	−39.4248	−	68.2858i	−1.48272	−	2.56815i
$708$		0			0
$709$	30.5330			1.14669			0.573345	−	0.819314i	$-0.305645\pi$
$709$	30.5330			1.14669			0.573345	+	0.819314i	$0.305645\pi$
$710$	−3.15831	−	5.47036i	−0.118529	−	0.205299i
$711$		0			0
$712$	4.65831	−	8.06843i	0.174578	−	0.302377i
$713$	−17.2665			−0.646635
$714$		0			0
$715$	−4.31662	+	7.47661i	−0.161433	+	0.279609i
$716$	6.31662	+	10.9407i	0.236063	+	0.408874i
$717$		0			0
$718$	−5.68338	+	9.84389i	−0.212102	+	0.367371i
$719$	−21.8997	+	37.9315i	−0.816723	+	1.41461i	0.0913614	+	0.995818i	$0.470878\pi$
$719$	−21.8997	+	37.9315i	−0.816723	+	1.41461i	−0.908084	+	0.418788i	$0.862455\pi$
$720$		0			0
$721$	19.3166	+	33.4574i	0.719389	+	1.24602i
$722$	10.4499	+	18.0997i	0.388904	+	0.673602i
$723$		0			0
$724$	2.65831	−	4.60433i	0.0987954	−	0.171119i
$725$	19.2665	−	33.3706i	0.715540	−	1.23935i
$726$		0			0
$727$	20.9499	+	36.2862i	0.776988	+	1.34578i	0.933670	+	0.358133i	$0.116587\pi$
$727$	20.9499	+	36.2862i	0.776988	+	1.34578i	−0.156683	+	0.987649i	$0.550080\pi$
$728$	−4.31662	+	7.47661i	−0.159985	+	0.277102i
$729$		0			0
$730$	0.633250			0.0234376
$731$	−10.4749	+	18.1431i	−0.387430	+	0.671048i
$732$		0			0
$733$	−7.63325	−	13.2212i	−0.281941	−	0.488335i	0.689922	−	0.723884i	$-0.257645\pi$
$733$	−7.63325	−	13.2212i	−0.281941	−	0.488335i	−0.971863	+	0.235548i	$0.924311\pi$
$734$	29.8997			1.10362
$735$		0			0
$736$	−2.00000	−	3.46410i	−0.0737210	−	0.127688i
$737$	−13.6332	−	23.6135i	−0.502187	−	0.869814i
$738$		0			0
$739$	−38.5330			−1.41746			−0.708730	−	0.705480i	$-0.750731\pi$
$739$	−38.5330			−1.41746			−0.708730	+	0.705480i	$0.750731\pi$
$740$	2.00000	−	5.74456i	0.0735215	−	0.211174i
$741$		0			0
$742$	18.6332	−	32.2737i	0.684048	−	1.18481i
$743$	−0.108187	−	0.187385i	−0.00396899	−	0.00687449i	0.864034	−	0.503433i	$-0.167930\pi$
$743$	−0.108187	−	0.187385i	−0.00396899	−	0.00687449i	−0.868003	+	0.496559i	$0.834597\pi$
$744$		0			0
$745$	−3.18338	−	5.51377i	−0.116630	−	0.202009i
$746$	−27.9499			−1.02332
$747$		0			0
$748$	−14.3166			−0.523468
$749$	37.9499	−	65.7311i	1.38666	−	2.40176i
$750$		0			0
$751$	−3.68338			−0.134408			−0.0672041	−	0.997739i	$-0.521408\pi$
$751$	−3.68338			−0.134408			−0.0672041	+	0.997739i	$0.521408\pi$
$752$	−1.15831	+	2.00626i	−0.0422393	+	0.0731606i
$753$		0			0
$754$	−19.2665			−0.701645
$755$	−10.0000	+	17.3205i	−0.363937	+	0.630358i
$756$		0			0
$757$	4.97494	−	8.61684i	0.180817	−	0.313185i	−0.761342	−	0.648351i	$-0.775459\pi$
$757$	4.97494	−	8.61684i	0.180817	−	0.313185i	0.942159	+	0.335166i	$0.108792\pi$
$758$	−3.79156	−	6.56718i	−0.137716	−	0.238531i
$759$		0			0
$760$	−3.15831	+	5.47036i	−0.114564	+	0.198431i
$761$	−20.9248	+	36.2428i	−0.758524	+	1.31380i	0.185079	+	0.982724i	$0.440746\pi$
$761$	−20.9248	+	36.2428i	−0.758524	+	1.31380i	−0.943603	+	0.331078i	$0.892588\pi$
$762$		0			0
$763$	−40.2164			−1.45593
$764$	12.3166	+	21.3330i	0.445600	+	0.771802i
$765$		0			0
$766$	19.5831			0.707567
$767$	9.26650			0.334594
$768$		0			0
$769$	−11.3668			−0.409896			−0.204948	−	0.978773i	$-0.565702\pi$
$769$	−11.3668			−0.409896			−0.204948	+	0.978773i	$0.565702\pi$
$770$	−9.31662	−	16.1369i	−0.335748	−	0.581532i
$771$		0			0
$772$	−0.500000	−	0.866025i	−0.0179954	−	0.0311689i
$773$	26.4499	+	45.8125i	0.951336	+	1.64776i	0.742539	+	0.669803i	$0.233621\pi$
$773$	26.4499	+	45.8125i	0.951336	+	1.64776i	0.208797	+	0.977959i	$0.433045\pi$
$774$		0			0
$775$	8.63325	−	14.9532i	0.310115	−	0.537136i
$776$	−0.366750			−0.0131656
$777$		0			0
$778$	7.00000			0.250962
$779$	35.7414	−	61.9060i	1.28057	−	2.21801i
$780$		0			0
$781$	13.6332	+	23.6135i	0.487836	+	0.844957i
$782$	6.63325	+	11.4891i	0.237205	+	0.410850i
$783$		0			0
$784$	−5.81662	−	10.0747i	−0.207737	−	0.359810i
$785$	9.31662			0.332525
$786$		0			0
$787$	−51.1662			−1.82388			−0.911940	−	0.410324i	$-0.865416\pi$
$787$	−51.1662			−1.82388			−0.911940	+	0.410324i	$0.865416\pi$
$788$	−3.63325			−0.129429
$789$		0			0
$790$	−6.47494	−	11.2149i	−0.230368	−	0.399009i
$791$	−48.6332			−1.72920
$792$		0			0
$793$	7.31662	−	12.6728i	0.259821	−	0.450023i
$794$	−7.29156	+	12.6294i	−0.258768	+	0.448199i
$795$		0			0
$796$	6.15831	+	10.6665i	0.218276	+	0.378064i
$797$	−3.05013	+	5.28297i	−0.108041	+	0.187132i	−0.914977	−	0.403507i	$-0.867791\pi$
$797$	−3.05013	+	5.28297i	−0.108041	+	0.187132i	0.806936	+	0.590639i	$0.201124\pi$
$798$		0			0
$799$	3.84169	−	6.65400i	0.135909	−	0.235402i
$800$	4.00000			0.141421
$801$		0			0
$802$	18.2665	−	31.6385i	0.645013	−	1.11719i
$803$	−2.73350			−0.0964631
$804$		0			0
$805$	−8.63325	+	14.9532i	−0.304282	+	0.527032i
$806$	−8.63325			−0.304093
$807$		0			0
$808$	18.2665			0.642613
$809$	−1.00000	−	1.73205i	−0.0351581	−	0.0608957i	0.847911	−	0.530139i	$-0.177860\pi$
$809$	−1.00000	−	1.73205i	−0.0351581	−	0.0608957i	−0.883069	+	0.469243i	$0.844527\pi$
$810$		0			0
$811$	−10.9499	−	18.9657i	−0.384502	−	0.665977i	0.607198	−	0.794551i	$-0.292294\pi$
$811$	−10.9499	−	18.9657i	−0.384502	−	0.665977i	−0.991700	+	0.128573i	$0.958960\pi$
$812$	20.7916	−	36.0120i	0.729641	−	1.26377i
$813$		0			0
$814$	−8.63325	+	24.7971i	−0.302595	+	0.869139i
$815$	−2.31662			−0.0811478
$816$		0			0
$817$	−19.9499	−	34.5542i	−0.697958	−	1.20890i
$818$	8.13325	+	14.0872i	0.284372	+	0.492547i
$819$		0			0
$820$	11.3166			0.395194
$821$	1.00000	+	1.73205i	0.0349002	+	0.0604490i	0.882948	−	0.469471i	$-0.155555\pi$
$821$	1.00000	+	1.73205i	0.0349002	+	0.0604490i	−0.848048	+	0.529920i	$0.822222\pi$
$822$		0			0
$823$	−4.31662	+	7.47661i	−0.150468	+	0.260618i	−0.931400	−	0.363998i	$-0.881411\pi$
$823$	−4.31662	+	7.47661i	−0.150468	+	0.260618i	0.780932	+	0.624617i	$0.214745\pi$
$824$	−8.94987			−0.311784
$825$		0			0
$826$	−10.0000	+	17.3205i	−0.347945	+	0.602658i
$827$	25.2665	+	43.7629i	0.878602	+	1.52178i	0.852875	+	0.522115i	$0.174857\pi$
$827$	25.2665	+	43.7629i	0.878602	+	1.52178i	0.0257270	+	0.999669i	$0.491810\pi$
$828$		0			0
$829$	2.36675	−	4.09933i	0.0822006	−	0.142376i	−0.821994	−	0.569496i	$-0.807139\pi$
$829$	2.36675	−	4.09933i	0.0822006	−	0.142376i	0.904195	+	0.427120i	$0.140472\pi$
$830$	2.31662	−	4.01251i	0.0804112	−	0.139276i
$831$		0			0
$832$	−1.00000	−	1.73205i	−0.0346688	−	0.0600481i
$833$	19.2916	+	33.4140i	0.668413	+	1.15773i
$834$		0			0
$835$	6.00000	−	10.3923i	0.207639	−	0.359641i
$836$	13.6332	−	23.6135i	0.471516	−	0.816689i
$837$		0			0
$838$	−1.52506	−	2.64149i	−0.0526824	−	0.0912486i
$839$	−19.5831	+	33.9190i	−0.676085	+	1.17101i	0.300066	+	0.953918i	$0.402991\pi$
$839$	−19.5831	+	33.9190i	−0.676085	+	1.17101i	−0.976151	+	0.217094i	$0.930342\pi$
$840$		0			0
$841$	63.7995			2.19998
$842$	17.6082	−	30.4983i	0.606818	−	1.05104i
$843$		0			0
$844$	−1.47494	−	2.55467i	−0.0507694	−	0.0879352i
$845$	−9.00000			−0.309609
$846$		0			0
$847$	16.4749	+	28.5354i	0.566086	+	0.980489i
$848$	4.31662	+	7.47661i	0.148234	+	0.256748i
$849$		0			0
$850$	−13.2665			−0.455037
$851$	23.8997	−	4.56092i	0.819273	−	0.156346i
$852$		0			0
$853$	12.6082	−	21.8380i	0.431696	−	0.747720i	−0.565323	−	0.824869i	$-0.691249\pi$
$853$	12.6082	−	21.8380i	0.431696	−	0.747720i	0.997020	+	0.0771498i	$0.0245820\pi$
$854$	15.7916	+	27.3518i	0.540376	+	0.935959i
$855$		0			0
$856$	8.79156	+	15.2274i	0.300489	+	0.520463i
$857$	18.4829			0.631363			0.315681	−	0.948865i	$-0.397767\pi$
$857$	18.4829			0.631363			0.315681	+	0.948865i	$0.397767\pi$
$858$		0			0
$859$	33.0501			1.12766			0.563828	−	0.825892i	$-0.309328\pi$
$859$	33.0501			1.12766			0.563828	+	0.825892i	$0.309328\pi$
$860$	3.15831	−	5.47036i	0.107698	−	0.186538i
$861$		0			0
$862$	0.416876			0.0141989
$863$	−6.00000	+	10.3923i	−0.204242	+	0.353758i	−0.949891	−	0.312581i	$-0.898806\pi$
$863$	−6.00000	+	10.3923i	−0.204242	+	0.353758i	0.745649	+	0.666339i	$0.232140\pi$
$864$		0			0
$865$	−0.366750			−0.0124699
$866$	−14.1332	+	24.4795i	−0.480267	+	0.831847i
$867$		0			0
$868$	9.31662	−	16.1369i	0.316227	−	0.547721i
$869$	27.9499	+	48.4106i	0.948135	+	1.64222i
$870$		0			0
$871$	−6.31662	+	10.9407i	−0.214031	+	0.370712i
$872$	4.65831	−	8.06843i	0.157750	−	0.273232i
$873$		0			0
$874$	−25.2665			−0.854652
$875$	−19.4248	−	33.6448i	−0.656678	−	1.13740i
$876$		0			0
$877$	1.94987			0.0658426			0.0329213	−	0.999458i	$-0.489519\pi$
$877$	1.94987			0.0658426			0.0329213	+	0.999458i	$0.489519\pi$
$878$	14.5330			0.490465
$879$		0			0
$880$	4.31662			0.145513
$881$	−22.6583	−	39.2453i	−0.763378	−	1.32221i	−0.941100	−	0.338129i	$-0.890206\pi$
$881$	−22.6583	−	39.2453i	−0.763378	−	1.32221i	0.177722	−	0.984081i	$-0.443127\pi$
$882$		0			0
$883$	−8.63325	−	14.9532i	−0.290532	−	0.503216i	0.683404	−	0.730041i	$-0.260499\pi$
$883$	−8.63325	−	14.9532i	−0.290532	−	0.503216i	−0.973936	+	0.226825i	$0.927166\pi$
$884$	3.31662	+	5.74456i	0.111550	+	0.193211i
$885$		0			0
$886$	12.0000	−	20.7846i	0.403148	−	0.698273i
$887$	57.2665			1.92282			0.961410	−	0.275118i	$-0.0887170\pi$
$887$	57.2665			1.92282			0.961410	+	0.275118i	$0.0887170\pi$
$888$		0			0
$889$	71.7995			2.40808
$890$	4.65831	−	8.06843i	0.156147	−	0.270455i
$891$		0			0
$892$	−6.31662	−	10.9407i	−0.211496	−	0.366322i
$893$	7.31662	+	12.6728i	0.244842	+	0.424078i
$894$		0			0
$895$	6.31662	+	10.9407i	0.211141	+	0.365708i
$896$	4.31662			0.144208
$897$		0			0
$898$	−4.73350			−0.157959
$899$	41.5831			1.38687
$900$		0			0
$901$	−14.3166	−	24.7971i	−0.476956	−	0.826112i
$902$	−48.8496			−1.62651
$903$		0			0
$904$	5.63325	−	9.75707i	0.187359	−	0.324515i
$905$	2.65831	−	4.60433i	0.0883653	−	0.153053i
$906$		0			0
$907$	6.84169	+	11.8502i	0.227175	+	0.393478i	0.956970	−	0.290188i	$-0.0937179\pi$
$907$	6.84169	+	11.8502i	0.227175	+	0.393478i	−0.729795	+	0.683666i	$0.760385\pi$
$908$	−10.4749	+	18.1431i	−0.347623	+	0.602101i
$909$		0			0
$910$	−4.31662	+	7.47661i	−0.143095	+	0.247847i
$911$	17.2665			0.572065			0.286032	−	0.958220i	$-0.407664\pi$
$911$	17.2665			0.572065			0.286032	+	0.958220i	$0.407664\pi$
$912$		0			0
$913$	−10.0000	+	17.3205i	−0.330952	+	0.573225i
$914$	−8.36675			−0.276748
$915$		0			0
$916$	−10.9749	+	19.0091i	−0.362622	+	0.628080i
$917$	−74.5330			−2.46130
$918$		0			0
$919$	39.1662			1.29198			0.645988	−	0.763348i	$-0.276446\pi$
$919$	39.1662			1.29198			0.645988	+	0.763348i	$0.276446\pi$
$920$	−2.00000	−	3.46410i	−0.0659380	−	0.114208i
$921$		0			0
$922$	−12.3166	−	21.3330i	−0.405626	−	0.702566i
$923$	6.31662	−	10.9407i	0.207914	−	0.360118i
$924$		0			0
$925$	−8.00000	+	22.9783i	−0.263038	+	0.755520i
$926$	32.9499			1.08280
$927$		0			0
$928$	4.81662	+	8.34264i	0.158113	+	0.273861i
$929$	−5.39181	−	9.33889i	−0.176900	−	0.306399i	0.763917	−	0.645314i	$-0.223273\pi$
$929$	−5.39181	−	9.33889i	−0.176900	−	0.306399i	−0.940817	+	0.338915i	$0.889940\pi$
$930$		0			0
$931$	−73.4829			−2.40830
$932$	−6.97494	−	12.0809i	−0.228472	−	0.395725i
$933$		0			0
$934$	−8.31662	+	14.4048i	−0.272128	+	0.471340i
$935$	−14.3166			−0.468204
$936$		0			0
$937$	−2.76650	+	4.79172i	−0.0903776	+	0.156539i	−0.907670	−	0.419684i	$-0.862141\pi$
$937$	−2.76650	+	4.79172i	−0.0903776	+	0.156539i	0.817292	+	0.576223i	$0.195474\pi$
$938$	−13.6332	−	23.6135i	−0.445141	−	0.771007i
$939$		0			0
$940$	−1.15831	+	2.00626i	−0.0377800	+	0.0654369i
$941$	2.13325	−	3.69490i	0.0695419	−	0.120450i	−0.829158	−	0.559015i	$-0.811180\pi$
$941$	2.13325	−	3.69490i	0.0695419	−	0.120450i	0.898700	+	0.438564i	$0.144513\pi$
$942$		0			0
$943$	22.6332	+	39.2019i	0.737040	+	1.27659i
$944$	−2.31662	−	4.01251i	−0.0753997	−	0.130596i
$945$		0			0
$946$	−13.6332	+	23.6135i	−0.443255	+	0.767740i
$947$	15.8997	−	27.5392i	0.516672	−	0.894903i	−0.483140	−	0.875543i	$-0.660504\pi$
$947$	15.8997	−	27.5392i	0.516672	−	0.894903i	0.999813	−	0.0193598i	$-0.00616282\pi$
$948$		0			0
$949$	0.633250	+	1.09682i	0.0205562	+	0.0356043i
$950$	12.6332	−	21.8814i	0.409877	−	0.709927i
$951$		0			0
$952$	−14.3166			−0.464004
$953$	14.3668	−	24.8839i	0.465385	−	0.806070i	−0.533834	−	0.845589i	$-0.679249\pi$
$953$	14.3668	−	24.8839i	0.465385	−	0.806070i	0.999219	+	0.0395193i	$0.0125827\pi$
$954$		0			0
$955$	12.3166	+	21.3330i	0.398557	+	0.690320i
$956$	−1.05013			−0.0339635
$957$		0			0
$958$	−14.0000	−	24.2487i	−0.452319	−	0.783440i
$959$	−15.7916	−	27.3518i	−0.509936	−	0.883235i
$960$		0			0
$961$	−12.3668			−0.398927
$962$	11.9499	−	2.28046i	0.385279	−	0.0735250i
$963$		0			0
$964$	−0.316625	+	0.548410i	−0.0101978	+	0.0176631i
$965$	−0.500000	−	0.866025i	−0.0160956	−	0.0278783i
$966$		0			0
$967$	13.8997	+	24.0751i	0.446986	+	0.774202i	0.998188	−	0.0601695i	$-0.0191641\pi$
$967$	13.8997	+	24.0751i	0.446986	+	0.774202i	−0.551202	+	0.834372i	$0.685831\pi$
$968$	−7.63325			−0.245342
$969$		0			0
$970$	−0.366750			−0.0117756
$971$	17.3668	−	30.0801i	0.557326	−	0.965316i	−0.440393	−	0.897805i	$-0.645161\pi$
$971$	17.3668	−	30.0801i	0.557326	−	0.965316i	0.997719	−	0.0675110i	$-0.0215058\pi$
$972$		0			0
$973$		0			0
$974$	6.31662	−	10.9407i	0.202398	−	0.350563i
$975$		0			0
$976$	−7.31662			−0.234199
$977$	23.5330	−	40.7603i	0.752887	−	1.30404i	−0.193530	−	0.981094i	$-0.561994\pi$
$977$	23.5330	−	40.7603i	0.752887	−	1.30404i	0.946418	−	0.322945i	$-0.104673\pi$
$978$		0			0
$979$	−20.1082	+	34.8284i	−0.642660	+	1.11312i
$980$	−5.81662	−	10.0747i	−0.185805	−	0.321824i
$981$		0			0
$982$	3.84169	−	6.65400i	0.122593	−	0.212338i
$983$	24.7414	−	42.8534i	0.789129	−	1.36681i	−0.137372	−	0.990520i	$-0.543865\pi$
$983$	24.7414	−	42.8534i	0.789129	−	1.36681i	0.926501	−	0.376292i	$-0.122801\pi$
$984$		0			0
$985$	−3.63325			−0.115765
$986$	−15.9749	−	27.6694i	−0.508746	−	0.881173i
$987$		0			0
$988$	−12.6332			−0.401917
$989$	25.2665			0.803428
$990$		0			0
$991$	12.9499			0.411366			0.205683	−	0.978619i	$-0.434058\pi$
$991$	12.9499			0.411366			0.205683	+	0.978619i	$0.434058\pi$
$992$	2.15831	+	3.73831i	0.0685265	+	0.118691i
$993$		0			0
$994$	13.6332	+	23.6135i	0.432420	+	0.748974i
$995$	6.15831	+	10.6665i	0.195232	+	0.338151i
$996$		0			0
$997$	−8.36675	+	14.4916i	−0.264978	+	0.458955i	−0.967558	−	0.252650i	$-0.918698\pi$
$997$	−8.36675	+	14.4916i	−0.264978	+	0.458955i	0.702580	+	0.711605i	$0.252031\pi$
$998$	−2.94987			−0.0933766
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.2.f.i.343.2	yes	4
3.2	odd	2		666.2.f.h.343.2	✓	4
37.26	even	3	inner	666.2.f.i.433.2	yes	4
111.26	odd	6		666.2.f.h.433.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
666.2.f.h.343.2	✓	4	3.2	odd	2
666.2.f.h.433.2	yes	4	111.26	odd	6
666.2.f.i.343.2	yes	4	1.1	even	1	trivial
666.2.f.i.433.2	yes	4	37.26	even	3	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	666.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(2.15831 + 3.73831i) q^{7} -1.00000 q^{8} -1.00000 q^{10} +4.31662 q^{11} +(-1.00000 - 1.73205i) q^{13} +4.31662 q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.65831 - 2.87228i) q^{17} +(3.15831 + 5.47036i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(2.15831 - 3.73831i) q^{22} -4.00000 q^{23} +(2.00000 - 3.46410i) q^{25} -2.00000 q^{26} +(2.15831 - 3.73831i) q^{28} +9.63325 q^{29} +4.31662 q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.65831 - 2.87228i) q^{34} +(2.15831 - 3.73831i) q^{35} +(-5.97494 + 1.14023i) q^{37} +6.31662 q^{38} +(0.500000 + 0.866025i) q^{40} +(-5.65831 - 9.80048i) q^{41} -6.31662 q^{43} +(-2.15831 - 3.73831i) q^{44} +(-2.00000 + 3.46410i) q^{46} +2.31662 q^{47} +(-5.81662 + 10.0747i) q^{49} +(-2.00000 - 3.46410i) q^{50} +(-1.00000 + 1.73205i) q^{52} +(4.31662 - 7.47661i) q^{53} +(-2.15831 - 3.73831i) q^{55} +(-2.15831 - 3.73831i) q^{56} +(4.81662 - 8.34264i) q^{58} +(-2.31662 + 4.01251i) q^{59} +(3.65831 + 6.33638i) q^{61} +(2.15831 - 3.73831i) q^{62} +1.00000 q^{64} +(-1.00000 + 1.73205i) q^{65} +(-3.15831 - 5.47036i) q^{67} -3.31662 q^{68} +(-2.15831 - 3.73831i) q^{70} +(3.15831 + 5.47036i) q^{71} -0.633250 q^{73} +(-2.00000 + 5.74456i) q^{74} +(3.15831 - 5.47036i) q^{76} +(9.31662 + 16.1369i) q^{77} +(6.47494 + 11.2149i) q^{79} +1.00000 q^{80} -11.3166 q^{82} +(-2.31662 + 4.01251i) q^{83} -3.31662 q^{85} +(-3.15831 + 5.47036i) q^{86} -4.31662 q^{88} +(-4.65831 + 8.06843i) q^{89} +(4.31662 - 7.47661i) q^{91} +(2.00000 + 3.46410i) q^{92} +(1.15831 - 2.00626i) q^{94} +(3.15831 - 5.47036i) q^{95} +0.366750 q^{97} +(5.81662 + 10.0747i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{4} - 2 q^{5} + 2 q^{7} - 4 q^{8} - 4 q^{10} + 4 q^{11} - 4 q^{13} + 4 q^{14} - 2 q^{16} + 6 q^{19} - 2 q^{20} + 2 q^{22} - 16 q^{23} + 8 q^{25} - 8 q^{26} + 2 q^{28} + 12 q^{29} + 4 q^{31}+ \cdots + 10 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^4 - 2 * q^5 + 2 * q^7 - 4 * q^8 - 4 * q^10 + 4 * q^11 - 4 * q^13 + 4 * q^14 - 2 * q^16 + 6 * q^19 - 2 * q^20 + 2 * q^22 - 16 * q^23 + 8 * q^25 - 8 * q^26 + 2 * q^28 + 12 * q^29 + 4 * q^31 + 2 * q^32 + 2 * q^35 - 4 * q^37 + 12 * q^38 + 2 * q^40 - 16 * q^41 - 12 * q^43 - 2 * q^44 - 8 * q^46 - 4 * q^47 - 10 * q^49 - 8 * q^50 - 4 * q^52 + 4 * q^53 - 2 * q^55 - 2 * q^56 + 6 * q^58 + 4 * q^59 + 8 * q^61 + 2 * q^62 + 4 * q^64 - 4 * q^65 - 6 * q^67 - 2 * q^70 + 6 * q^71 + 24 * q^73 - 8 * q^74 + 6 * q^76 + 24 * q^77 + 6 * q^79 + 4 * q^80 - 32 * q^82 + 4 * q^83 - 6 * q^86 - 4 * q^88 - 12 * q^89 + 4 * q^91 + 8 * q^92 - 2 * q^94 + 6 * q^95 + 28 * q^97 + 10 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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