LMFDB - Embedded newform 189.2.f.a.127.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(64,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("189.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.f (of order $3$, degree $2$, not 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:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			127.3
Root			$0.500000 + 0.224437i$ of defining polynomial
Character	$\chi$	$=$	189.127
Dual form			189.2.f.a.64.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.849814 - 1.47192i) q^{2} +(-0.444368 - 0.769668i) q^{4} +(-1.79418 - 3.10761i) q^{5} +(0.500000 - 0.866025i) q^{7} +1.88874 q^{8} +O(q^{10})$	\(q+(0.849814 - 1.47192i) q^{2} +(-0.444368 - 0.769668i) q^{4} +(-1.79418 - 3.10761i) q^{5} +(0.500000 - 0.866025i) q^{7} +1.88874 q^{8} -6.09888 q^{10} +(-1.40545 + 2.43430i) q^{11} +(-0.500000 - 0.866025i) q^{13} +(-0.849814 - 1.47192i) q^{14} +(2.49381 - 4.31941i) q^{16} +4.11126 q^{17} -0.888736 q^{19} +(-1.59455 + 2.76185i) q^{20} +(2.38874 + 4.13741i) q^{22} +(2.93818 + 5.08907i) q^{23} +(-3.93818 + 6.82112i) q^{25} -1.69963 q^{26} -0.888736 q^{28} +(-0.849814 + 1.47192i) q^{29} +(3.49381 + 6.05146i) q^{31} +(-2.34981 - 4.07000i) q^{32} +(3.49381 - 6.05146i) q^{34} -3.58836 q^{35} +4.76509 q^{37} +(-0.755260 + 1.30815i) q^{38} +(-3.38874 - 5.86946i) q^{40} +(-2.70582 - 4.68661i) q^{41} +(-2.60507 + 4.51212i) q^{43} +2.49814 q^{44} +9.98762 q^{46} +(-1.33310 + 2.30900i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(6.69344 + 11.5934i) q^{50} +(-0.444368 + 0.769668i) q^{52} +0.123644 q^{53} +10.0865 q^{55} +(0.944368 - 1.63569i) q^{56} +(1.44437 + 2.50172i) q^{58} +(-4.43818 - 7.68715i) q^{59} +(-1.93818 + 3.35702i) q^{61} +11.8764 q^{62} +1.98762 q^{64} +(-1.79418 + 3.10761i) q^{65} +(-6.15452 - 10.6599i) q^{67} +(-1.82691 - 3.16431i) q^{68} +(-3.04944 + 5.28179i) q^{70} +2.87636 q^{71} -10.6414 q^{73} +(4.04944 - 7.01384i) q^{74} +(0.394926 + 0.684031i) q^{76} +(1.40545 + 2.43430i) q^{77} +(3.54325 - 6.13709i) q^{79} -17.8974 q^{80} -9.19777 q^{82} +(-2.05563 + 3.56046i) q^{83} +(-7.37636 - 12.7762i) q^{85} +(4.42766 + 7.66893i) q^{86} +(-2.65452 + 4.59776i) q^{88} -9.60940 q^{89} -1.00000 q^{91} +(2.61126 - 4.52284i) q^{92} +(2.26578 + 3.92445i) q^{94} +(1.59455 + 2.76185i) q^{95} +(-3.66071 + 6.34053i) q^{97} -1.69963 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{2} - 3 q^{4} - 5 q^{5} + 3 q^{7} + 12 q^{8}+O(q^{10}) $ 6 * q - q^2 - 3 * q^4 - 5 * q^5 + 3 * q^7 + 12 * q^8	$ 6 q - q^{2} - 3 q^{4} - 5 q^{5} + 3 q^{7} + 12 q^{8} - 2 q^{11} - 3 q^{13} + q^{14} - 3 q^{16} + 24 q^{17} - 6 q^{19} - 16 q^{20} + 15 q^{22} - 6 q^{25} + 2 q^{26} - 6 q^{28} + q^{29} + 3 q^{31} - 8 q^{32} + 3 q^{34} - 10 q^{35} - 6 q^{37} + 8 q^{38} - 21 q^{40} - 22 q^{41} + 3 q^{43} - 46 q^{44} + 24 q^{46} - 9 q^{47} - 3 q^{49} + 10 q^{50} - 3 q^{52} + 36 q^{53} - 12 q^{55} + 6 q^{56} + 9 q^{58} - 9 q^{59} + 6 q^{61} + 36 q^{62} - 24 q^{64} - 5 q^{65} + 6 q^{68} - 18 q^{71} + 6 q^{73} + 6 q^{74} + 21 q^{76} + 2 q^{77} - 15 q^{79} - 22 q^{80} + 18 q^{82} - 12 q^{83} - 9 q^{85} + 34 q^{86} + 21 q^{88} + 4 q^{89} - 6 q^{91} + 15 q^{92} - 24 q^{94} + 16 q^{95} - 3 q^{97} + 2 q^{98}+O(q^{100}) $ 6 * q - q^2 - 3 * q^4 - 5 * q^5 + 3 * q^7 + 12 * q^8 - 2 * q^11 - 3 * q^13 + q^14 - 3 * q^16 + 24 * q^17 - 6 * q^19 - 16 * q^20 + 15 * q^22 - 6 * q^25 + 2 * q^26 - 6 * q^28 + q^29 + 3 * q^31 - 8 * q^32 + 3 * q^34 - 10 * q^35 - 6 * q^37 + 8 * q^38 - 21 * q^40 - 22 * q^41 + 3 * q^43 - 46 * q^44 + 24 * q^46 - 9 * q^47 - 3 * q^49 + 10 * q^50 - 3 * q^52 + 36 * q^53 - 12 * q^55 + 6 * q^56 + 9 * q^58 - 9 * q^59 + 6 * q^61 + 36 * q^62 - 24 * q^64 - 5 * q^65 + 6 * q^68 - 18 * q^71 + 6 * q^73 + 6 * q^74 + 21 * q^76 + 2 * q^77 - 15 * q^79 - 22 * q^80 + 18 * q^82 - 12 * q^83 - 9 * q^85 + 34 * q^86 + 21 * q^88 + 4 * q^89 - 6 * q^91 + 15 * q^92 - 24 * q^94 + 16 * q^95 - 3 * q^97 + 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.849814	−	1.47192i	0.600909	−	1.04081i	−0.391774	−	0.920061i	$-0.628139\pi$
$2$	0.849814	−	1.47192i	0.600909	−	1.04081i	0.992684	−	0.120744i	$-0.0385280\pi$
$3$		0			0
$3$		0			0
$4$	−0.444368	−	0.769668i	−0.222184	−	0.384834i
$5$	−1.79418	−	3.10761i	−0.802383	−	1.38977i	−0.918044	−	0.396479i	$-0.870232\pi$
$5$	−1.79418	−	3.10761i	−0.802383	−	1.38977i	0.115661	−	0.993289i	$-0.463101\pi$
$6$		0			0
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$8$	1.88874			0.667769
$9$		0			0
$10$	−6.09888			−1.92864
$11$	−1.40545	+	2.43430i	−0.423758	+	0.733970i	−0.996304	−	0.0859026i	$-0.972623\pi$
$11$	−1.40545	+	2.43430i	−0.423758	+	0.733970i	0.572546	+	0.819873i	$0.305956\pi$
$12$		0			0
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i	0.788320	−	0.615265i	$-0.210951\pi$
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i	−0.926995	+	0.375073i	$0.877618\pi$
$14$	−0.849814	−	1.47192i	−0.227122	−	0.393387i
$15$		0			0
$16$	2.49381	−	4.31941i	0.623453	−	1.07985i
$17$	4.11126			0.997128			0.498564	−	0.866853i	$-0.333861\pi$
$17$	4.11126			0.997128			0.498564	+	0.866853i	$0.333861\pi$
$18$		0			0
$19$	−0.888736			−0.203890			−0.101945	−	0.994790i	$-0.532507\pi$
$19$	−0.888736			−0.203890			−0.101945	+	0.994790i	$0.532507\pi$
$20$	−1.59455	+	2.76185i	−0.356553	+	0.617568i
$21$		0			0
$22$	2.38874	+	4.13741i	0.509280	+	0.882099i
$23$	2.93818	+	5.08907i	0.612652	+	1.06115i	0.990792	+	0.135396i	$0.0432308\pi$
$23$	2.93818	+	5.08907i	0.612652	+	1.06115i	−0.378139	+	0.925749i	$0.623436\pi$
$24$		0			0
$25$	−3.93818	+	6.82112i	−0.787636	+	1.36422i
$26$	−1.69963			−0.333325
$27$		0			0
$28$	−0.888736			−0.167955
$29$	−0.849814	+	1.47192i	−0.157807	+	0.273329i	−0.934077	−	0.357071i	$-0.883776\pi$
$29$	−0.849814	+	1.47192i	−0.157807	+	0.273329i	0.776271	+	0.630399i	$0.217109\pi$
$30$		0			0
$31$	3.49381	+	6.05146i	0.627507	+	1.08687i	0.988050	+	0.154131i	$0.0492579\pi$
$31$	3.49381	+	6.05146i	0.627507	+	1.08687i	−0.360544	+	0.932742i	$0.617409\pi$
$32$	−2.34981	−	4.07000i	−0.415392	−	0.719481i
$33$		0			0
$34$	3.49381	−	6.05146i	0.599183	−	1.03782i
$35$	−3.58836			−0.606544
$36$		0			0
$37$	4.76509			0.783376			0.391688	−	0.920098i	$-0.371891\pi$
$37$	4.76509			0.783376			0.391688	+	0.920098i	$0.371891\pi$
$38$	−0.755260	+	1.30815i	−0.122519	+	0.212210i
$39$		0			0
$40$	−3.38874	−	5.86946i	−0.535806	−	0.928044i
$41$	−2.70582	−	4.68661i	−0.422578	−	0.731926i	0.573613	−	0.819126i	$-0.305541\pi$
$41$	−2.70582	−	4.68661i	−0.422578	−	0.731926i	−0.996191	+	0.0872002i	$0.972208\pi$
$42$		0			0
$43$	−2.60507	+	4.51212i	−0.397270	+	0.688092i	−0.993388	−	0.114805i	$-0.963376\pi$
$43$	−2.60507	+	4.51212i	−0.397270	+	0.688092i	0.596118	+	0.802897i	$0.296709\pi$
$44$	2.49814			0.376609
$45$		0			0
$46$	9.98762			1.47259
$47$	−1.33310	+	2.30900i	−0.194453	+	0.336803i	−0.946721	−	0.322055i	$-0.895627\pi$
$47$	−1.33310	+	2.30900i	−0.194453	+	0.336803i	0.752268	+	0.658857i	$0.228960\pi$
$48$		0			0
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	6.69344	+	11.5934i	0.946595	+	1.63955i
$51$		0			0
$52$	−0.444368	+	0.769668i	−0.0616227	+	0.106734i
$53$	0.123644			0.0169838			0.00849190	−	0.999964i	$-0.497297\pi$
$53$	0.123644			0.0169838			0.00849190	+	0.999964i	$0.497297\pi$
$54$		0			0
$55$	10.0865			1.36006
$56$	0.944368	−	1.63569i	0.126196	−	0.218579i
$57$		0			0
$58$	1.44437	+	2.50172i	0.189655	+	0.328492i
$59$	−4.43818	−	7.68715i	−0.577802	−	1.00078i	−0.995731	−	0.0923022i	$-0.970577\pi$
$59$	−4.43818	−	7.68715i	−0.577802	−	1.00078i	0.417929	−	0.908479i	$-0.362756\pi$
$60$		0			0
$61$	−1.93818	+	3.35702i	−0.248158	+	0.429823i	−0.963015	−	0.269448i	$-0.913159\pi$
$61$	−1.93818	+	3.35702i	−0.248158	+	0.429823i	0.714857	+	0.699271i	$0.246492\pi$
$62$	11.8764			1.50830
$63$		0			0
$64$	1.98762			0.248453
$65$	−1.79418	+	3.10761i	−0.222541	+	0.385452i
$66$		0			0
$67$	−6.15452	−	10.6599i	−0.751894	−	1.30232i	−0.946904	−	0.321517i	$-0.895807\pi$
$67$	−6.15452	−	10.6599i	−0.751894	−	1.30232i	0.195010	−	0.980801i	$-0.437526\pi$
$68$	−1.82691	−	3.16431i	−0.221546	−	0.383729i
$69$		0			0
$70$	−3.04944	+	5.28179i	−0.364478	+	0.631295i
$71$	2.87636			0.341361			0.170680	−	0.985326i	$-0.445403\pi$
$71$	2.87636			0.341361			0.170680	+	0.985326i	$0.445403\pi$
$72$		0			0
$73$	−10.6414			−1.24549			−0.622744	−	0.782426i	$-0.713982\pi$
$73$	−10.6414			−1.24549			−0.622744	+	0.782426i	$0.713982\pi$
$74$	4.04944	−	7.01384i	0.470738	−	0.815342i
$75$		0			0
$76$	0.394926	+	0.684031i	0.0453011	+	0.0784638i
$77$	1.40545	+	2.43430i	0.160165	+	0.277415i
$78$		0			0
$79$	3.54325	−	6.13709i	0.398647	−	0.690477i	−0.594912	−	0.803791i	$-0.702813\pi$
$79$	3.54325	−	6.13709i	0.398647	−	0.690477i	0.993559	+	0.113314i	$0.0361465\pi$
$80$	−17.8974			−2.00099
$81$		0			0
$82$	−9.19777			−1.01572
$83$	−2.05563	+	3.56046i	−0.225635	+	0.390811i	−0.956510	−	0.291700i	$-0.905779\pi$
$83$	−2.05563	+	3.56046i	−0.225635	+	0.390811i	0.730875	+	0.682512i	$0.239112\pi$
$84$		0			0
$85$	−7.37636	−	12.7762i	−0.800078	−	1.38578i
$86$	4.42766	+	7.66893i	0.477447	+	0.826962i
$87$		0			0
$88$	−2.65452	+	4.59776i	−0.282972	+	0.490123i
$89$	−9.60940			−1.01859			−0.509297	−	0.860591i	$-0.670095\pi$
$89$	−9.60940			−1.01859			−0.509297	+	0.860591i	$0.670095\pi$
$90$		0			0
$91$	−1.00000			−0.104828
$92$	2.61126	−	4.52284i	0.272243	−	0.471539i
$93$		0			0
$94$	2.26578	+	3.92445i	0.233697	+	0.404776i
$95$	1.59455	+	2.76185i	0.163598	+	0.283360i
$96$		0			0
$97$	−3.66071	+	6.34053i	−0.371688	+	0.643783i	−0.989825	−	0.142287i	$-0.954554\pi$
$97$	−3.66071	+	6.34053i	−0.371688	+	0.643783i	0.618137	+	0.786070i	$0.287888\pi$
$98$	−1.69963			−0.171688
$99$		0			0
$100$	7.00000			0.700000
$101$	1.73236	−	3.00054i	0.172376	−	0.298564i	−0.766874	−	0.641798i	$-0.778189\pi$
$101$	1.73236	−	3.00054i	0.172376	−	0.298564i	0.939250	+	0.343233i	$0.111522\pi$
$102$		0			0
$103$	7.93818	+	13.7493i	0.782172	+	1.35476i	0.930674	+	0.365849i	$0.119221\pi$
$103$	7.93818	+	13.7493i	0.782172	+	1.35476i	−0.148502	+	0.988912i	$0.547445\pi$
$104$	−0.944368	−	1.63569i	−0.0926029	−	0.160393i
$105$		0			0
$106$	0.105074	−	0.181994i	0.0102057	−	0.0176768i
$107$	5.35346			0.517538			0.258769	−	0.965939i	$-0.416683\pi$
$107$	5.35346			0.517538			0.258769	+	0.965939i	$0.416683\pi$
$108$		0			0
$109$	−18.8640			−1.80684			−0.903421	−	0.428755i	$-0.858952\pi$
$109$	−18.8640			−1.80684			−0.903421	+	0.428755i	$0.858952\pi$
$110$	8.57165	−	14.8465i	0.817275	−	1.41556i
$111$		0			0
$112$	−2.49381	−	4.31941i	−0.235643	−	0.408145i
$113$	−9.27561	−	16.0658i	−0.872576	−	1.51135i	−0.859322	−	0.511434i	$-0.829114\pi$
$113$	−9.27561	−	16.0658i	−0.872576	−	1.51135i	−0.0132538	−	0.999912i	$-0.504219\pi$
$114$		0			0
$115$	10.5433	−	18.2614i	0.983163	−	1.70289i
$116$	1.51052			0.140248
$117$		0			0
$118$	−15.0865			−1.38883
$119$	2.05563	−	3.56046i	0.188439	−	0.326387i
$120$		0			0
$121$	1.54944	+	2.68371i	0.140858	+	0.243974i
$122$	3.29418	+	5.70569i	0.298241	+	0.516569i
$123$		0			0
$124$	3.10507	−	5.37815i	0.278844	−	0.482972i
$125$	10.3214			0.923175
$126$		0			0
$127$	9.98762			0.886258			0.443129	−	0.896458i	$-0.353868\pi$
$127$	9.98762			0.886258			0.443129	+	0.896458i	$0.353868\pi$
$128$	6.38874	−	11.0656i	0.564690	−	0.978071i
$129$		0			0
$130$	3.04944	+	5.28179i	0.267454	+	0.463244i
$131$	8.02654	+	13.9024i	0.701282	+	1.21466i	0.968017	+	0.250886i	$0.0807220\pi$
$131$	8.02654	+	13.9024i	0.701282	+	1.21466i	−0.266734	+	0.963770i	$0.585945\pi$
$132$		0			0
$133$	−0.444368	+	0.769668i	−0.0385316	+	0.0667387i
$134$	−20.9208			−1.80728
$135$		0			0
$136$	7.76509			0.665851
$137$	−6.49381	+	11.2476i	−0.554804	+	0.960948i	0.443115	+	0.896465i	$0.353873\pi$
$137$	−6.49381	+	11.2476i	−0.554804	+	0.960948i	−0.997919	+	0.0644834i	$0.979460\pi$
$138$		0			0
$139$	−0.555632	−	0.962383i	−0.0471281	−	0.0816283i	0.841499	−	0.540259i	$-0.181674\pi$
$139$	−0.555632	−	0.962383i	−0.0471281	−	0.0816283i	−0.888627	+	0.458630i	$0.848340\pi$
$140$	1.59455	+	2.76185i	0.134764	+	0.233419i
$141$		0			0
$142$	2.44437	−	4.23377i	0.205127	−	0.355290i
$143$	2.81089			0.235059
$144$		0			0
$145$	6.09888			0.506485
$146$	−9.04325	+	15.6634i	−0.748425	+	1.29631i
$147$		0			0
$148$	−2.11745	−	3.66754i	−0.174054	−	0.301470i
$149$	4.21634	+	7.30291i	0.345416	+	0.598278i	0.985429	−	0.170086i	$-0.0544045\pi$
$149$	4.21634	+	7.30291i	0.345416	+	0.598278i	−0.640013	+	0.768364i	$0.721071\pi$
$150$		0			0
$151$	7.42580	−	12.8619i	0.604303	−	1.04668i	−0.387858	−	0.921719i	$-0.626785\pi$
$151$	7.42580	−	12.8619i	0.604303	−	1.04668i	0.992161	−	0.124964i	$-0.0398816\pi$
$152$	−1.67859			−0.136151
$153$		0			0
$154$	4.77747			0.384980
$155$	12.5371	−	21.7148i	1.00700	−	1.74418i
$156$		0			0
$157$	−1.44437	−	2.50172i	−0.115273	−	0.199659i	0.802616	−	0.596496i	$-0.203441\pi$
$157$	−1.44437	−	2.50172i	−0.115273	−	0.199659i	−0.917889	+	0.396837i	$0.870108\pi$
$158$	−6.02221	−	10.4308i	−0.479101	−	0.829828i
$159$		0			0
$160$	−8.43199	+	14.6046i	−0.666607	+	1.15460i
$161$	5.87636			0.463122
$162$		0			0
$163$	−10.3090			−0.807466			−0.403733	−	0.914877i	$-0.632287\pi$
$163$	−10.3090			−0.807466			−0.403733	+	0.914877i	$0.632287\pi$
$164$	−2.40476	+	4.16516i	−0.187780	+	0.325245i
$165$		0			0
$166$	3.49381	+	6.05146i	0.271172	+	0.469684i
$167$	6.07598	+	10.5239i	0.470174	+	0.814365i	0.999418	−	0.0341045i	$-0.0108579\pi$
$167$	6.07598	+	10.5239i	0.470174	+	0.814365i	−0.529244	+	0.848469i	$0.677525\pi$
$168$		0			0
$169$	6.00000	−	10.3923i	0.461538	−	0.799408i
$170$	−25.0741			−1.92310
$171$		0			0
$172$	4.63045			0.353068
$173$	−3.30470	+	5.72391i	−0.251252	+	0.435181i	−0.963871	−	0.266370i	$-0.914176\pi$
$173$	−3.30470	+	5.72391i	−0.251252	+	0.435181i	0.712619	+	0.701551i	$0.247509\pi$
$174$		0			0
$175$	3.93818	+	6.82112i	0.297698	+	0.515629i
$176$	7.00983	+	12.1414i	0.528386	+	0.915191i
$177$		0			0
$178$	−8.16621	+	14.1443i	−0.612083	+	1.06016i
$179$	3.84294			0.287234			0.143617	−	0.989633i	$-0.454127\pi$
$179$	3.84294			0.287234			0.143617	+	0.989633i	$0.454127\pi$
$180$		0			0
$181$	18.5426			1.37826			0.689129	−	0.724639i	$-0.257993\pi$
$181$	18.5426			1.37826			0.689129	+	0.724639i	$0.257993\pi$
$182$	−0.849814	+	1.47192i	−0.0629924	+	0.109106i
$183$		0			0
$184$	5.54944	+	9.61192i	0.409110	+	0.708600i
$185$	−8.54944	−	14.8081i	−0.628567	−	1.08871i
$186$		0			0
$187$	−5.77816	+	10.0081i	−0.422541	+	0.731862i
$188$	2.36955			0.172818
$189$		0			0
$190$	5.42030			0.393230
$191$	2.31708	−	4.01330i	0.167658	−	0.290392i	−0.769938	−	0.638119i	$-0.779713\pi$
$191$	2.31708	−	4.01330i	0.167658	−	0.290392i	0.937596	+	0.347726i	$0.113046\pi$
$192$		0			0
$193$	12.6483	+	21.9075i	0.910446	+	1.57694i	0.813435	+	0.581656i	$0.197595\pi$
$193$	12.6483	+	21.9075i	0.910446	+	1.57694i	0.0970118	+	0.995283i	$0.469072\pi$
$194$	6.22184	+	10.7765i	0.446702	+	0.773711i
$195$		0			0
$196$	−0.444368	+	0.769668i	−0.0317406	+	0.0549763i
$197$	−10.7207			−0.763816			−0.381908	−	0.924200i	$-0.624733\pi$
$197$	−10.7207			−0.763816			−0.381908	+	0.924200i	$0.624733\pi$
$198$		0			0
$199$	−8.76647			−0.621439			−0.310719	−	0.950502i	$-0.600570\pi$
$199$	−8.76647			−0.621439			−0.310719	+	0.950502i	$0.600570\pi$
$200$	−7.43818	+	12.8833i	−0.525959	+	0.910987i
$201$		0			0
$202$	−2.94437	−	5.09979i	−0.207165	−	0.358820i
$203$	0.849814	+	1.47192i	0.0596453	+	0.103309i
$204$		0			0
$205$	−9.70946	+	16.8173i	−0.678138	+	1.17457i
$206$	26.9839			1.88006
$207$		0			0
$208$	−4.98762			−0.345829
$209$	1.24907	−	2.16345i	0.0864000	−	0.149649i
$210$		0			0
$211$	−5.26509	−	9.11941i	−0.362464	−	0.627806i	0.625902	−	0.779902i	$-0.284731\pi$
$211$	−5.26509	−	9.11941i	−0.362464	−	0.627806i	−0.988366	+	0.152096i	$0.951398\pi$
$212$	−0.0549434	−	0.0951647i	−0.00377353	−	0.00653594i
$213$		0			0
$214$	4.54944	−	7.87987i	0.310993	−	0.538656i
$215$	18.6959			1.27505
$216$		0			0
$217$	6.98762			0.474351
$218$	−16.0309	+	27.7663i	−1.08575	+	1.88057i
$219$		0			0
$220$	−4.48212	−	7.76326i	−0.302184	−	0.523399i
$221$	−2.05563	−	3.56046i	−0.138277	−	0.239502i
$222$		0			0
$223$	2.83379	−	4.90827i	0.189765	−	0.328682i	−0.755407	−	0.655256i	$-0.772561\pi$
$223$	2.83379	−	4.90827i	0.189765	−	0.328682i	0.945172	+	0.326574i	$0.105894\pi$
$224$	−4.69963			−0.314007
$225$		0			0
$226$	−31.5302			−2.09736
$227$	−5.54944	+	9.61192i	−0.368329	+	0.637965i	−0.989304	−	0.145865i	$-0.953403\pi$
$227$	−5.54944	+	9.61192i	−0.368329	+	0.637965i	0.620975	+	0.783830i	$0.286737\pi$
$228$		0			0
$229$	−9.82141	−	17.0112i	−0.649017	−	1.12413i	−0.983358	−	0.181679i	$-0.941847\pi$
$229$	−9.82141	−	17.0112i	−0.649017	−	1.12413i	0.334341	−	0.942452i	$-0.391486\pi$
$230$	−17.9196	−	31.0377i	−1.18158	−	2.04656i
$231$		0			0
$232$	−1.60507	+	2.78007i	−0.105378	+	0.182521i
$233$	−8.96286			−0.587177			−0.293588	−	0.955932i	$-0.594849\pi$
$233$	−8.96286			−0.587177			−0.293588	+	0.955932i	$0.594849\pi$
$234$		0			0
$235$	9.56732			0.624103
$236$	−3.94437	+	6.83185i	−0.256756	+	0.444715i
$237$		0			0
$238$	−3.49381	−	6.05146i	−0.226470	−	0.392258i
$239$	5.61126	+	9.71899i	0.362963	+	0.628670i	0.988447	−	0.151567i	$-0.0484320\pi$
$239$	5.61126	+	9.71899i	0.362963	+	0.628670i	−0.625484	+	0.780237i	$0.715099\pi$
$240$		0			0
$241$	3.49312	−	6.05026i	0.225012	−	0.389732i	−0.731311	−	0.682044i	$-0.761091\pi$
$241$	3.49312	−	6.05026i	0.225012	−	0.389732i	0.956323	+	0.292312i	$0.0944246\pi$
$242$	5.26695			0.338572
$243$		0			0
$244$	3.44506			0.220547
$245$	−1.79418	+	3.10761i	−0.114626	+	0.198538i
$246$		0			0
$247$	0.444368	+	0.769668i	0.0282745	+	0.0489728i
$248$	6.59888	+	11.4296i	0.419030	+	0.725781i
$249$		0			0
$250$	8.77128	−	15.1923i	0.554745	−	0.960846i
$251$	−4.62041			−0.291638			−0.145819	−	0.989311i	$-0.546582\pi$
$251$	−4.62041			−0.291638			−0.145819	+	0.989311i	$0.546582\pi$
$252$		0			0
$253$	−16.5178			−1.03847
$254$	8.48762	−	14.7010i	0.532561	−	0.922422i
$255$		0			0
$256$	−8.87085	−	15.3648i	−0.554428	−	0.960298i
$257$	−0.712008	−	1.23323i	−0.0444138	−	0.0769270i	0.842964	−	0.537970i	$-0.180809\pi$
$257$	−0.712008	−	1.23323i	−0.0444138	−	0.0769270i	−0.887378	+	0.461043i	$0.847475\pi$
$258$		0			0
$259$	2.38255	−	4.12669i	0.148044	−	0.256420i
$260$	3.18911			0.197780
$261$		0			0
$262$	27.2843			1.68563
$263$	8.13162	−	14.0844i	0.501417	−	0.868480i	−0.498582	−	0.866843i	$-0.666146\pi$
$263$	8.13162	−	14.0844i	0.501417	−	0.868480i	0.999999	−	0.00163692i	$-0.000521048\pi$
$264$		0			0
$265$	−0.221840	−	0.384237i	−0.0136275	−	0.0236035i
$266$	0.755260	+	1.30815i	0.0463080	+	0.0802078i
$267$		0			0
$268$	−5.46974	+	9.47387i	−0.334118	+	0.578709i
$269$	18.6538			1.13734			0.568672	−	0.822564i	$-0.307457\pi$
$269$	18.6538			1.13734			0.568672	+	0.822564i	$0.307457\pi$
$270$		0			0
$271$	3.96286			0.240727			0.120363	−	0.992730i	$-0.461594\pi$
$271$	3.96286			0.240727			0.120363	+	0.992730i	$0.461594\pi$
$272$	10.2527	−	17.7582i	0.621662	−	1.07675i
$273$		0			0
$274$	11.0371	+	19.1168i	0.666773	+	1.15489i
$275$	−11.0698	−	19.1734i	−0.667534	−	1.15620i
$276$		0			0
$277$	1.16690	−	2.02112i	0.0701120	−	0.121438i	−0.828838	−	0.559488i	$-0.810998\pi$
$277$	1.16690	−	2.02112i	0.0701120	−	0.121438i	0.898950	+	0.438051i	$0.144331\pi$
$278$	−1.88874			−0.113279
$279$		0			0
$280$	−6.77747			−0.405031
$281$	13.9975	−	24.2443i	0.835018	−	1.44629i	−0.0589978	−	0.998258i	$-0.518790\pi$
$281$	13.9975	−	24.2443i	0.835018	−	1.44629i	0.894016	−	0.448035i	$-0.147876\pi$
$282$		0			0
$283$	−5.16002	−	8.93741i	−0.306731	−	0.531274i	0.670914	−	0.741535i	$-0.265902\pi$
$283$	−5.16002	−	8.93741i	−0.306731	−	0.531274i	−0.977645	+	0.210261i	$0.932569\pi$
$284$	−1.27816	−	2.21384i	−0.0758449	−	0.131367i
$285$		0			0
$286$	2.38874	−	4.13741i	0.141249	−	0.244650i
$287$	−5.41164			−0.319439
$288$		0			0
$289$	−0.0975070			−0.00573571
$290$	5.18292	−	8.97708i	0.304351	−	0.527152i
$291$		0			0
$292$	4.72872	+	8.19038i	0.276727	+	0.479306i
$293$	−15.3480	−	26.5834i	−0.896637	−	1.55302i	−0.831765	−	0.555127i	$-0.812670\pi$
$293$	−15.3480	−	26.5834i	−0.896637	−	1.55302i	−0.0648718	−	0.997894i	$-0.520664\pi$
$294$		0			0
$295$	−15.9258	+	27.5843i	−0.927236	+	1.60602i
$296$	9.00000			0.523114
$297$		0			0
$298$	14.3324			0.830255
$299$	2.93818	−	5.08907i	0.169919	−	0.294309i
$300$		0			0
$301$	2.60507	+	4.51212i	0.150154	+	0.260074i
$302$	−12.6211	−	21.8604i	−0.726262	−	1.25792i
$303$		0			0
$304$	−2.21634	+	3.83881i	−0.127116	+	0.220171i
$305$	13.9098			0.796471
$306$		0			0
$307$	−11.4437			−0.653125			−0.326563	−	0.945176i	$-0.605890\pi$
$307$	−11.4437			−0.653125			−0.326563	+	0.945176i	$0.605890\pi$
$308$	1.24907	−	2.16345i	0.0711724	−	0.123274i
$309$		0			0
$310$	−21.3083	−	36.9071i	−1.21023	−	2.09618i
$311$	5.98143	+	10.3601i	0.339176	+	0.587470i	0.984278	−	0.176627i	$-0.0565185\pi$
$311$	5.98143	+	10.3601i	0.339176	+	0.587470i	−0.645102	+	0.764096i	$0.723185\pi$
$312$		0			0
$313$	6.77197	−	11.7294i	0.382774	−	0.662985i	−0.608683	−	0.793413i	$-0.708302\pi$
$313$	6.77197	−	11.7294i	0.382774	−	0.662985i	0.991458	+	0.130429i	$0.0416353\pi$
$314$	−4.90978			−0.277075
$315$		0			0
$316$	−6.29803			−0.354292
$317$	−14.9814	+	25.9486i	−0.841441	+	1.45742i	0.0472355	+	0.998884i	$0.484959\pi$
$317$	−14.9814	+	25.9486i	−0.841441	+	1.45742i	−0.888676	+	0.458535i	$0.848374\pi$
$318$		0			0
$319$	−2.38874	−	4.13741i	−0.133744	−	0.231651i
$320$	−3.56615	−	6.17676i	−0.199354	−	0.345291i
$321$		0			0
$322$	4.99381	−	8.64953i	0.278294	−	0.482020i
$323$	−3.65383			−0.203304
$324$		0			0
$325$	7.87636			0.436902
$326$	−8.76076	+	15.1741i	−0.485214	+	0.840415i
$327$		0			0
$328$	−5.11058	−	8.85178i	−0.282184	−	0.488758i
$329$	1.33310	+	2.30900i	0.0734964	+	0.127299i
$330$		0			0
$331$	−1.04325	+	1.80697i	−0.0573423	+	0.0993198i	−0.893272	−	0.449517i	$-0.851596\pi$
$331$	−1.04325	+	1.80697i	−0.0573423	+	0.0993198i	0.835929	+	0.548837i	$0.184929\pi$
$332$	3.65383			0.200530
$333$		0			0
$334$	20.6538			1.13013
$335$	−22.0846	+	38.2517i	−1.20661	+	2.08992i
$336$		0			0
$337$	8.10439	+	14.0372i	0.441474	+	0.764655i	0.997799	−	0.0663093i	$-0.0211224\pi$
$337$	8.10439	+	14.0372i	0.441474	+	0.764655i	−0.556325	+	0.830965i	$0.687789\pi$
$338$	−10.1978	−	17.6631i	−0.554686	−	0.960743i
$339$		0			0
$340$	−6.55563	+	11.3547i	−0.355529	+	0.615794i
$341$	−19.6414			−1.06364
$342$		0			0
$343$	−1.00000			−0.0539949
$344$	−4.92030	+	8.52220i	−0.265285	+	0.459486i
$345$		0			0
$346$	5.61677	+	9.72852i	0.301959	+	0.523009i
$347$	5.63348	+	9.75747i	0.302421	+	0.523808i	0.976684	−	0.214683i	$-0.0688719\pi$
$347$	5.63348	+	9.75747i	0.302421	+	0.523808i	−0.674263	+	0.738491i	$0.735539\pi$
$348$		0			0
$349$	0.0988844	−	0.171273i	0.00529316	−	0.00916803i	−0.863367	−	0.504577i	$-0.831648\pi$
$349$	0.0988844	−	0.171273i	0.00529316	−	0.00916803i	0.868660	+	0.495409i	$0.164982\pi$
$350$	13.3869			0.715559
$351$		0			0
$352$	13.2101			0.704103
$353$	−6.25093	+	10.8269i	−0.332703	+	0.576259i	−0.983041	−	0.183386i	$-0.941294\pi$
$353$	−6.25093	+	10.8269i	−0.332703	+	0.576259i	0.650338	+	0.759645i	$0.274627\pi$
$354$		0			0
$355$	−5.16071	−	8.93861i	−0.273902	−	0.474412i
$356$	4.27011	+	7.39605i	0.226315	+	0.391990i
$357$		0			0
$358$	3.26578	−	5.65650i	0.172602	−	0.298955i
$359$	−20.0197			−1.05660			−0.528299	−	0.849059i	$-0.677170\pi$
$359$	−20.0197			−1.05660			−0.528299	+	0.849059i	$0.677170\pi$
$360$		0			0
$361$	−18.2101			−0.958429
$362$	15.7577	−	27.2932i	0.828208	−	1.43450i
$363$		0			0
$364$	0.444368	+	0.769668i	0.0232912	+	0.0403416i
$365$	19.0927	+	33.0695i	0.999357	+	1.73094i
$366$		0			0
$367$	−15.0364	+	26.0438i	−0.784892	+	1.35947i	0.144171	+	0.989553i	$0.453948\pi$
$367$	−15.0364	+	26.0438i	−0.784892	+	1.35947i	−0.929063	+	0.369921i	$0.879385\pi$
$368$	29.3090			1.52784
$369$		0			0
$370$	−29.0617			−1.51085
$371$	0.0618219	−	0.107079i	0.00320963	−	0.00555925i
$372$		0			0
$373$	−3.50619	−	6.07290i	−0.181544	−	0.314443i	0.760863	−	0.648913i	$-0.224776\pi$
$373$	−3.50619	−	6.07290i	−0.181544	−	0.314443i	−0.942406	+	0.334470i	$0.891443\pi$
$374$	9.82072	+	17.0100i	0.507818	+	0.879566i
$375$		0			0
$376$	−2.51788	+	4.36110i	−0.129850	+	0.224906i
$377$	1.69963			0.0875353
$378$		0			0
$379$	−19.0741			−0.979772			−0.489886	−	0.871787i	$-0.662962\pi$
$379$	−19.0741			−0.979772			−0.489886	+	0.871787i	$0.662962\pi$
$380$	1.41714	−	2.45455i	0.0726976	−	0.125916i
$381$		0			0
$382$	−3.93818	−	6.82112i	−0.201495	−	0.348999i
$383$	1.60507	+	2.78007i	0.0820155	+	0.142055i	0.904116	−	0.427288i	$-0.140531\pi$
$383$	1.60507	+	2.78007i	0.0820155	+	0.142055i	−0.822100	+	0.569343i	$0.807198\pi$
$384$		0			0
$385$	5.04325	−	8.73517i	0.257028	−	0.445185i
$386$	42.9949			2.18838
$387$		0			0
$388$	6.50680			0.330333
$389$	2.56801	−	4.44793i	0.130203	−	0.225519i	−0.793552	−	0.608503i	$-0.791770\pi$
$389$	2.56801	−	4.44793i	0.130203	−	0.225519i	0.923755	+	0.382984i	$0.125104\pi$
$390$		0			0
$391$	12.0796	+	20.9225i	0.610893	+	1.05810i
$392$	−0.944368	−	1.63569i	−0.0476978	−	0.0826150i
$393$		0			0
$394$	−9.11058	+	15.7800i	−0.458984	+	0.794984i
$395$	−25.4290			−1.27947
$396$		0			0
$397$	22.9381			1.15123			0.575615	−	0.817721i	$-0.304763\pi$
$397$	22.9381			1.15123			0.575615	+	0.817721i	$0.304763\pi$
$398$	−7.44987	+	12.9036i	−0.373428	+	0.646797i
$399$		0			0
$400$	19.6421	+	34.0212i	0.982107	+	1.70106i
$401$	−9.10507	−	15.7705i	−0.454686	−	0.787539i	0.543984	−	0.839095i	$-0.316915\pi$
$401$	−9.10507	−	15.7705i	−0.454686	−	0.787539i	−0.998670	+	0.0515566i	$0.983582\pi$
$402$		0			0
$403$	3.49381	−	6.05146i	0.174039	−	0.301445i
$404$	−3.07922			−0.153197
$405$		0			0
$406$	2.88874			0.143366
$407$	−6.69708	+	11.5997i	−0.331962	+	0.574975i
$408$		0			0
$409$	7.66621	+	13.2783i	0.379070	+	0.656568i	0.990927	−	0.134400i	$-0.0429108\pi$
$409$	7.66621	+	13.2783i	0.379070	+	0.656568i	−0.611858	+	0.790968i	$0.709577\pi$
$410$	16.5025	+	28.5831i	0.814999	+	1.41162i
$411$		0			0
$412$	7.05494	−	12.2195i	0.347572	−	0.602013i
$413$	−8.87636			−0.436777
$414$		0			0
$415$	14.7527			0.724182
$416$	−2.34981	+	4.07000i	−0.115209	+	0.199548i
$417$		0			0
$418$	−2.12296	−	3.67707i	−0.103837	−	0.179851i
$419$	5.28435	+	9.15276i	0.258157	+	0.447142i	0.965748	−	0.259481i	$-0.0835513\pi$
$419$	5.28435	+	9.15276i	0.258157	+	0.447142i	−0.707591	+	0.706622i	$0.750218\pi$
$420$		0			0
$421$	18.0858	−	31.3256i	0.881449	−	1.52671i	0.0317181	−	0.999497i	$-0.489902\pi$
$421$	18.0858	−	31.3256i	0.881449	−	1.52671i	0.849731	−	0.527217i	$-0.176765\pi$
$422$	−17.8974			−0.871232
$423$		0			0
$424$	0.233531			0.0113412
$425$	−16.1909	+	28.0434i	−0.785374	+	1.36031i
$426$		0			0
$427$	1.93818	+	3.35702i	0.0937950	+	0.162458i
$428$	−2.37890	−	4.12038i	−0.114989	−	0.199166i
$429$		0			0
$430$	15.8880	−	27.5189i	0.766190	−	1.32708i
$431$	−35.0989			−1.69065			−0.845327	−	0.534249i	$-0.820594\pi$
$431$	−35.0989			−1.69065			−0.845327	+	0.534249i	$0.820594\pi$
$432$		0			0
$433$	−41.1730			−1.97865			−0.989324	−	0.145731i	$-0.953447\pi$
$433$	−41.1730			−1.97865			−0.989324	+	0.145731i	$0.953447\pi$
$434$	5.93818	−	10.2852i	0.285042	−	0.493707i
$435$		0			0
$436$	8.38255	+	14.5190i	0.401451	+	0.695334i
$437$	−2.61126	−	4.52284i	−0.124914	−	0.216357i
$438$		0			0
$439$	2.33929	−	4.05178i	0.111648	−	0.193381i	−0.804787	−	0.593564i	$-0.797720\pi$
$439$	2.33929	−	4.05178i	0.111648	−	0.193381i	0.916435	+	0.400184i	$0.131054\pi$
$440$	19.0507			0.908209
$441$		0			0
$442$	−6.98762			−0.332367
$443$	15.0865	−	26.1306i	0.716781	−	1.24150i	−0.245487	−	0.969400i	$-0.578948\pi$
$443$	15.0865	−	26.1306i	0.716781	−	1.24150i	0.962268	−	0.272102i	$-0.0877188\pi$
$444$		0			0
$445$	17.2410	+	29.8623i	0.817303	+	1.41561i
$446$	−4.81639	−	8.34224i	−0.228063	−	0.395016i
$447$		0			0
$448$	0.993810	−	1.72133i	0.0469531	−	0.0813252i
$449$	−0.333792			−0.0157526			−0.00787632	−	0.999969i	$-0.502507\pi$
$449$	−0.333792			−0.0157526			−0.00787632	+	0.999969i	$0.502507\pi$
$450$		0			0
$451$	15.2115			0.716283
$452$	−8.24357	+	14.2783i	−0.387745	+	0.671594i
$453$		0			0
$454$	9.43199	+	16.3367i	0.442665	+	0.766719i
$455$	1.79418	+	3.10761i	0.0841125	+	0.145687i
$456$		0			0
$457$	9.65452	−	16.7221i	0.451619	−	0.782227i	−0.546868	−	0.837219i	$-0.684180\pi$
$457$	9.65452	−	16.7221i	0.451619	−	0.782227i	0.998487	+	0.0549917i	$0.0175132\pi$
$458$	−33.3855			−1.56000
$459$		0			0
$460$	−18.7403			−0.873773
$461$	19.5538	−	33.8681i	0.910710	−	1.57740i	0.0976463	−	0.995221i	$-0.468869\pi$
$461$	19.5538	−	33.8681i	0.910710	−	1.57740i	0.813064	−	0.582175i	$-0.197798\pi$
$462$		0			0
$463$	−10.9382	−	18.9455i	−0.508340	−	0.880471i	−0.999953	−	0.00965741i	$-0.996926\pi$
$463$	−10.9382	−	18.9455i	−0.508340	−	0.880471i	0.491613	−	0.870814i	$-0.336407\pi$
$464$	4.23855	+	7.34138i	0.196770	+	0.340815i
$465$		0			0
$466$	−7.61677	+	13.1926i	−0.352840	+	0.611137i
$467$	12.3200			0.570103			0.285052	−	0.958512i	$-0.407989\pi$
$467$	12.3200			0.570103			0.285052	+	0.958512i	$0.407989\pi$
$468$		0			0
$469$	−12.3090			−0.568378
$470$	8.13045	−	14.0823i	0.375029	−	0.649570i
$471$		0			0
$472$	−8.38255	−	14.5190i	−0.385838	−	0.668291i
$473$	−7.32258	−	12.6831i	−0.336693	−	0.583169i
$474$		0			0
$475$	3.50000	−	6.06218i	0.160591	−	0.278152i
$476$	−3.65383			−0.167473
$477$		0			0
$478$	19.0741			0.872430
$479$	6.74474	−	11.6822i	0.308175	−	0.533775i	−0.669788	−	0.742552i	$-0.733615\pi$
$479$	6.74474	−	11.6822i	0.308175	−	0.533775i	0.977963	+	0.208777i	$0.0669484\pi$
$480$		0			0
$481$	−2.38255	−	4.12669i	−0.108635	−	0.188161i
$482$	−5.93701	−	10.2832i	−0.270423	−	0.468387i
$483$		0			0
$484$	1.37704	−	2.38511i	0.0625929	−	0.108414i
$485$	26.2719			1.19295
$486$		0			0
$487$	7.54394			0.341849			0.170924	−	0.985284i	$-0.445325\pi$
$487$	7.54394			0.341849			0.170924	+	0.985284i	$0.445325\pi$
$488$	−3.66071	+	6.34053i	−0.165712	+	0.287022i
$489$		0			0
$490$	3.04944	+	5.28179i	0.137760	+	0.238607i
$491$	−8.06979	−	13.9773i	−0.364185	−	0.630786i	0.624460	−	0.781057i	$-0.285319\pi$
$491$	−8.06979	−	13.9773i	−0.364185	−	0.630786i	−0.988645	+	0.150270i	$0.951986\pi$
$492$		0			0
$493$	−3.49381	+	6.05146i	−0.157353	+	0.272544i
$494$	1.51052			0.0679615
$495$		0			0
$496$	34.8516			1.56488
$497$	1.43818	−	2.49100i	0.0645111	−	0.111737i
$498$		0			0
$499$	15.4327	+	26.7302i	0.690862	+	1.19661i	0.971556	+	0.236810i	$0.0761019\pi$
$499$	15.4327	+	26.7302i	0.690862	+	1.19661i	−0.280694	+	0.959797i	$0.590565\pi$
$500$	−4.58650	−	7.94406i	−0.205115	−	0.355269i
$501$		0			0
$502$	−3.92649	+	6.80088i	−0.175248	+	0.303538i
$503$	−24.6304			−1.09822			−0.549109	−	0.835751i	$-0.685033\pi$
$503$	−24.6304			−1.09822			−0.549109	+	0.835751i	$0.685033\pi$
$504$		0			0
$505$	−12.4327			−0.553247
$506$	−14.0371	+	24.3129i	−0.624024	+	1.08084i
$507$		0			0
$508$	−4.43818	−	7.68715i	−0.196912	−	0.341062i
$509$	6.79487	+	11.7691i	0.301177	+	0.521654i	0.976403	−	0.215957i	$-0.0692870\pi$
$509$	6.79487	+	11.7691i	0.301177	+	0.521654i	−0.675226	+	0.737611i	$0.735954\pi$
$510$		0			0
$511$	−5.32072	+	9.21576i	−0.235375	+	0.407681i
$512$	−4.59937			−0.203265
$513$		0			0
$514$	−2.42030			−0.106755
$515$	28.4851	−	49.3376i	1.25520	−	2.17407i
$516$		0			0
$517$	−3.74721	−	6.49036i	−0.164802	−	0.285446i
$518$	−4.04944	−	7.01384i	−0.177922	−	0.308170i
$519$		0			0
$520$	−3.38874	+	5.86946i	−0.148606	+	0.257393i
$521$	39.1730			1.71620			0.858100	−	0.513482i	$-0.171645\pi$
$521$	39.1730			1.71620			0.858100	+	0.513482i	$0.171645\pi$
$522$		0			0
$523$	19.1236			0.836219			0.418109	−	0.908397i	$-0.362693\pi$
$523$	19.1236			0.836219			0.418109	+	0.908397i	$0.362693\pi$
$524$	7.13348	−	12.3555i	0.311627	−	0.539754i
$525$		0			0
$526$	−13.8207	−	23.9382i	−0.602612	−	1.04375i
$527$	14.3640	+	24.8791i	0.625705	+	1.08375i
$528$		0			0
$529$	−5.76578	+	9.98663i	−0.250686	+	0.434201i
$530$	−0.754090			−0.0327556
$531$		0			0
$532$	0.789851			0.0342444
$533$	−2.70582	+	4.68661i	−0.117202	+	0.203000i
$534$		0			0
$535$	−9.60507	−	16.6365i	−0.415264	−	0.719258i
$536$	−11.6243	−	20.1338i	−0.502091	−	0.869648i
$537$		0			0
$538$	15.8523	−	27.4570i	0.683441	−	1.18375i
$539$	2.81089			0.121074
$540$		0			0
$541$	2.53018			0.108781			0.0543906	−	0.998520i	$-0.482678\pi$
$541$	2.53018			0.108781			0.0543906	+	0.998520i	$0.482678\pi$
$542$	3.36769	−	5.83302i	0.144655	−	0.250550i
$543$		0			0
$544$	−9.66071	−	16.7328i	−0.414199	−	0.717414i
$545$	33.8454	+	58.6220i	1.44978	+	2.51109i
$546$		0			0
$547$	−8.92580	+	15.4599i	−0.381640	+	0.661019i	−0.991297	−	0.131646i	$-0.957974\pi$
$547$	−8.92580	+	15.4599i	−0.381640	+	0.661019i	0.609657	+	0.792665i	$0.291307\pi$
$548$	11.5426			0.493074
$549$		0			0
$550$	−37.6291			−1.60451
$551$	0.755260	−	1.30815i	0.0321752	−	0.0557290i
$552$		0			0
$553$	−3.54325	−	6.13709i	−0.150674	−	0.260976i
$554$	−1.98329	−	3.43516i	−0.0842619	−	0.145946i
$555$		0			0
$556$	−0.493810	+	0.855304i	−0.0209422	+	0.0362730i
$557$	−41.3607			−1.75251			−0.876255	−	0.481847i	$-0.839966\pi$
$557$	−41.3607			−1.75251			−0.876255	+	0.481847i	$0.839966\pi$
$558$		0			0
$559$	5.21015			0.220366
$560$	−8.94870	+	15.4996i	−0.378152	+	0.654978i
$561$		0			0
$562$	−23.7905	−	41.2063i	−1.00354	−	1.73818i
$563$	−10.3683	−	17.9584i	−0.436972	−	0.756858i	0.560482	−	0.828166i	$-0.310616\pi$
$563$	−10.3683	−	17.9584i	−0.436972	−	0.756858i	−0.997454	+	0.0713087i	$0.977282\pi$
$564$		0			0
$565$	−33.2843	+	57.6501i	−1.40028	+	2.42536i
$566$	−17.5402			−0.737271
$567$		0			0
$568$	5.43268			0.227950
$569$	−0.134164	+	0.232379i	−0.00562446	+	0.00974185i	−0.868824	−	0.495121i	$-0.835124\pi$
$569$	−0.134164	+	0.232379i	−0.00562446	+	0.00974185i	0.863199	+	0.504863i	$0.168457\pi$
$570$		0			0
$571$	−17.9684	−	31.1221i	−0.751953	−	1.30242i	−0.946875	−	0.321601i	$-0.895779\pi$
$571$	−17.9684	−	31.1221i	−0.751953	−	1.30242i	0.194923	−	0.980819i	$-0.437554\pi$
$572$	−1.24907	−	2.16345i	−0.0522263	−	0.0904585i
$573$		0			0
$574$	−4.59888	+	7.96550i	−0.191954	+	0.332474i
$575$	−46.2843			−1.93019
$576$		0			0
$577$	5.43130			0.226108			0.113054	−	0.993589i	$-0.463937\pi$
$577$	5.43130			0.226108			0.113054	+	0.993589i	$0.463937\pi$
$578$	−0.0828628	+	0.143523i	−0.00344664	+	0.00596976i
$579$		0			0
$580$	−2.71015	−	4.69412i	−0.112533	−	0.194913i
$581$	2.05563	+	3.56046i	0.0852820	+	0.147713i
$582$		0			0
$583$	−0.173775	+	0.300987i	−0.00719702	+	0.0124656i
$584$	−20.0989			−0.831698
$585$		0			0
$586$	−52.1716			−2.15519
$587$	17.5822	−	30.4532i	0.725694	−	1.25694i	−0.232994	−	0.972478i	$-0.574852\pi$
$587$	17.5822	−	30.4532i	0.725694	−	1.25694i	0.958688	−	0.284461i	$-0.0918145\pi$
$588$		0			0
$589$	−3.10507	−	5.37815i	−0.127942	−	0.221603i
$590$	27.0679	+	46.8830i	1.11437	+	1.93014i
$591$		0			0
$592$	11.8832	−	20.5824i	0.488398	−	0.845930i
$593$	33.5068			1.37596			0.687980	−	0.725730i	$-0.258498\pi$
$593$	33.5068			1.37596			0.687980	+	0.725730i	$0.258498\pi$
$594$		0			0
$595$	−14.7527			−0.604802
$596$	3.74721	−	6.49036i	0.153492	−	0.265856i
$597$		0			0
$598$	−4.99381	−	8.64953i	−0.204212	−	0.353706i
$599$	3.12364	+	5.41031i	0.127629	+	0.221059i	0.922757	−	0.385381i	$-0.125930\pi$
$599$	3.12364	+	5.41031i	0.127629	+	0.221059i	−0.795129	+	0.606441i	$0.792597\pi$
$600$		0			0
$601$	−11.2040	+	19.4058i	−0.457019	+	0.791580i	−0.998802	−	0.0489384i	$-0.984416\pi$
$601$	−11.2040	+	19.4058i	−0.457019	+	0.791580i	0.541783	+	0.840519i	$0.317750\pi$
$602$	8.85532			0.360916
$603$		0			0
$604$	−13.1991			−0.537066
$605$	5.55996	−	9.63014i	0.226045	−	0.391521i
$606$		0			0
$607$	−7.47524	−	12.9475i	−0.303411	−	0.525523i	0.673496	−	0.739191i	$-0.264792\pi$
$607$	−7.47524	−	12.9475i	−0.303411	−	0.525523i	−0.976906	+	0.213669i	$0.931459\pi$
$608$	2.08836	+	3.61715i	0.0846943	+	0.146695i
$609$		0			0
$610$	11.8207	−	20.4741i	0.478607	−	0.828972i
$611$	2.66621			0.107863
$612$		0			0
$613$	35.1978			1.42162			0.710812	−	0.703382i	$-0.248328\pi$
$613$	35.1978			1.42162			0.710812	+	0.703382i	$0.248328\pi$
$614$	−9.72500	+	16.8442i	−0.392469	+	0.679776i
$615$		0			0
$616$	2.65452	+	4.59776i	0.106954	+	0.185249i
$617$	−1.00619	−	1.74277i	−0.0405077	−	0.0701614i	0.845061	−	0.534670i	$-0.179564\pi$
$617$	−1.00619	−	1.74277i	−0.0405077	−	0.0701614i	−0.885568	+	0.464509i	$0.846231\pi$
$618$		0			0
$619$	−19.6909	+	34.1056i	−0.791444	+	1.37082i	0.133629	+	0.991031i	$0.457337\pi$
$619$	−19.6909	+	34.1056i	−0.791444	+	1.37082i	−0.925073	+	0.379789i	$0.875996\pi$
$620$	−22.2843			−0.894958
$621$		0			0
$622$	20.3324			0.815256
$623$	−4.80470	+	8.32199i	−0.192496	+	0.333413i
$624$		0			0
$625$	1.17240	+	2.03065i	0.0468959	+	0.0812261i
$626$	−11.5098	−	19.9356i	−0.460025	−	0.796787i
$627$		0			0
$628$	−1.28366	+	2.22337i	−0.0512237	+	0.0887220i
$629$	19.5906			0.781126
$630$		0			0
$631$	44.3832			1.76687			0.883433	−	0.468558i	$-0.155226\pi$
$631$	44.3832			1.76687			0.883433	+	0.468558i	$0.155226\pi$
$632$	6.69227	−	11.5913i	0.266204	−	0.461079i
$633$		0			0
$634$	25.4629	+	44.1030i	1.01126	+	1.75155i
$635$	−17.9196	−	31.0377i	−0.711118	−	1.23169i
$636$		0			0
$637$	−0.500000	+	0.866025i	−0.0198107	+	0.0343132i
$638$	−8.11993			−0.321471
$639$		0			0
$640$	−45.8502			−1.81239
$641$	−7.49312	+	12.9785i	−0.295961	+	0.512619i	−0.975208	−	0.221291i	$-0.928973\pi$
$641$	−7.49312	+	12.9785i	−0.295961	+	0.512619i	0.679247	+	0.733909i	$0.262306\pi$
$642$		0			0
$643$	5.32691	+	9.22649i	0.210073	+	0.363857i	0.951737	−	0.306914i	$-0.0992965\pi$
$643$	5.32691	+	9.22649i	0.210073	+	0.363857i	−0.741664	+	0.670771i	$0.765963\pi$
$644$	−2.61126	−	4.52284i	−0.102898	−	0.178225i
$645$		0			0
$646$	−3.10507	+	5.37815i	−0.122168	+	0.211600i
$647$	−2.12955			−0.0837213			−0.0418606	−	0.999123i	$-0.513329\pi$
$647$	−2.12955			−0.0837213			−0.0418606	+	0.999123i	$0.513329\pi$
$648$		0			0
$649$	24.9505			0.979392
$650$	6.69344	−	11.5934i	0.262538	−	0.454730i
$651$		0			0
$652$	4.58100	+	7.93453i	0.179406	+	0.310740i
$653$	5.58582	+	9.67492i	0.218590	+	0.378609i	0.954377	−	0.298604i	$-0.0965210\pi$
$653$	5.58582	+	9.67492i	0.218590	+	0.378609i	−0.735787	+	0.677213i	$0.763188\pi$
$654$		0			0
$655$	28.8022	−	49.8868i	1.12539	−	1.94924i
$656$	−26.9912			−1.05383
$657$		0			0
$658$	4.53156			0.176659
$659$	−5.65452	+	9.79391i	−0.220269	+	0.381517i	−0.954890	−	0.296961i	$-0.904027\pi$
$659$	−5.65452	+	9.79391i	−0.220269	+	0.381517i	0.734621	+	0.678478i	$0.237360\pi$
$660$		0			0
$661$	−16.1785	−	28.0220i	−0.629271	−	1.08993i	−0.987698	−	0.156372i	$-0.950020\pi$
$661$	−16.1785	−	28.0220i	−0.629271	−	1.08993i	0.358427	−	0.933558i	$-0.383313\pi$
$662$	1.77314	+	3.07117i	0.0689151	+	0.119364i
$663$		0			0
$664$	−3.88255	+	6.72477i	−0.150672	+	0.260972i
$665$	3.18911			0.123668
$666$		0			0
$667$	−9.98762			−0.386722
$668$	5.39995	−	9.35298i	0.208930	−	0.361878i
$669$		0			0
$670$	37.5357	+	65.0137i	1.45013	+	2.51170i
$671$	−5.44801	−	9.43623i	−0.210318	−	0.364282i
$672$		0			0
$673$	12.0803	−	20.9237i	0.465662	−	0.806550i	−0.533569	−	0.845756i	$-0.679150\pi$
$673$	12.0803	−	20.9237i	0.465662	−	0.806550i	0.999231	+	0.0392063i	$0.0124830\pi$
$674$	27.5489			1.06114
$675$		0			0
$676$	−10.6648			−0.410186
$677$	12.5371	−	21.7148i	0.481838	−	0.834569i	−0.517944	−	0.855414i	$-0.673303\pi$
$677$	12.5371	−	21.7148i	0.481838	−	0.834569i	0.999783	+	0.0208457i	$0.00663587\pi$
$678$		0			0
$679$	3.66071	+	6.34053i	0.140485	+	0.243327i
$680$	−13.9320	−	24.1309i	−0.534267	−	0.925378i
$681$		0			0
$682$	−16.6916	+	28.9107i	−0.639154	+	1.10705i
$683$	47.6784			1.82436			0.912182	−	0.409785i	$-0.134396\pi$
$683$	47.6784			1.82436			0.912182	+	0.409785i	$0.134396\pi$
$684$		0			0
$685$	46.6043			1.78066
$686$	−0.849814	+	1.47192i	−0.0324461	+	0.0561982i
$687$		0			0
$688$	12.9931	+	22.5047i	0.495358	+	0.857985i
$689$	−0.0618219	−	0.107079i	−0.00235523	−	0.00407937i
$690$		0			0
$691$	12.3400	−	21.3735i	0.469435	−	0.813085i	−0.529954	−	0.848026i	$-0.677791\pi$
$691$	12.3400	−	21.3735i	0.469435	−	0.813085i	0.999389	+	0.0349408i	$0.0111243\pi$
$692$	5.87402			0.223297
$693$		0			0
$694$	19.1496			0.726910
$695$	−1.99381	+	3.45338i	−0.0756295	+	0.130994i
$696$		0			0
$697$	−11.1243	−	19.2679i	−0.421364	−	0.729824i
$698$	−0.168067	−	0.291100i	−0.00636142	−	0.0110183i
$699$		0			0
$700$	3.50000	−	6.06218i	0.132288	−	0.229129i
$701$	29.6784			1.12094			0.560469	−	0.828175i	$-0.310621\pi$
$701$	29.6784			1.12094			0.560469	+	0.828175i	$0.310621\pi$
$702$		0			0
$703$	−4.23491			−0.159723
$704$	−2.79349	+	4.83847i	−0.105284	+	0.182357i
$705$		0			0
$706$	10.6243	+	18.4018i	0.399849	+	0.692559i
$707$	−1.73236	−	3.00054i	−0.0651521	−	0.112847i
$708$		0			0
$709$	14.6291	−	25.3383i	0.549406	−	0.951599i	−0.448909	−	0.893577i	$-0.648187\pi$
$709$	14.6291	−	25.3383i	0.549406	−	0.951599i	0.998315	−	0.0580220i	$-0.0184794\pi$
$710$	−17.5426			−0.658361
$711$		0			0
$712$	−18.1496			−0.680186
$713$	−20.5309	+	35.5605i	−0.768887	+	1.33175i
$714$		0			0
$715$	−5.04325	−	8.73517i	−0.188607	−	0.326677i
$716$	−1.70768	−	2.95778i	−0.0638189	−	0.110538i
$717$		0			0
$718$	−17.0130	+	29.4674i	−0.634919	+	1.09971i
$719$	−1.07413			−0.0400581			−0.0200291	−	0.999799i	$-0.506376\pi$
$719$	−1.07413			−0.0400581			−0.0200291	+	0.999799i	$0.506376\pi$
$720$		0			0
$721$	15.8764			0.591266
$722$	−15.4752	+	26.8039i	−0.575929	+	0.997538i
$723$		0			0
$724$	−8.23972	−	14.2716i	−0.306227	−	0.530400i
$725$	−6.69344	−	11.5934i	−0.248588	−	0.430567i
$726$		0			0
$727$	−12.7163	+	22.0253i	−0.471623	+	0.816875i	−0.999473	−	0.0324628i	$-0.989665\pi$
$727$	−12.7163	+	22.0253i	−0.471623	+	0.816875i	0.527850	+	0.849338i	$0.322998\pi$
$728$	−1.88874			−0.0700012
$729$		0			0
$730$	64.9010			2.40209
$731$	−10.7101	+	18.5505i	−0.396129	+	0.686116i
$732$		0			0
$733$	5.69777	+	9.86883i	0.210452	+	0.364513i	0.951856	−	0.306545i	$-0.0991731\pi$
$733$	5.69777	+	9.86883i	0.210452	+	0.364513i	−0.741404	+	0.671059i	$0.765840\pi$
$734$	25.5562	+	44.2647i	0.943298	+	1.63384i
$735$		0			0
$736$	13.8083	−	23.9168i	0.508982	−	0.881583i
$737$	34.5994			1.27448
$738$		0			0
$739$	−29.9395			−1.10134			−0.550671	−	0.834723i	$-0.685628\pi$
$739$	−29.9395			−1.10134			−0.550671	+	0.834723i	$0.685628\pi$
$740$	−7.59820	+	13.1605i	−0.279315	+	0.483788i
$741$		0			0
$742$	−0.105074	−	0.181994i	−0.00385740	−	0.00668121i
$743$	−9.50069	−	16.4557i	−0.348546	−	0.603700i	0.637445	−	0.770496i	$-0.279991\pi$
$743$	−9.50069	−	16.4557i	−0.348546	−	0.603700i	−0.985991	+	0.166796i	$0.946658\pi$
$744$		0			0
$745$	15.1298	−	26.2055i	0.554311	−	0.960096i
$746$	−11.9184			−0.436365
$747$		0			0
$748$	10.2705			0.375527
$749$	2.67673	−	4.63623i	0.0978055	−	0.169404i
$750$		0			0
$751$	−0.0130684	−	0.0226352i	−0.000476873	−	0.000825969i	0.865787	−	0.500413i	$-0.166818\pi$
$751$	−0.0130684	−	0.0226352i	−0.000476873	−	0.000825969i	−0.866264	+	0.499587i	$0.833485\pi$
$752$	6.64902	+	11.5164i	0.242465	+	0.419961i
$753$		0			0
$754$	1.44437	−	2.50172i	0.0526008	−	0.0911072i
$755$	−53.2929			−1.93953
$756$		0			0
$757$	−13.6910			−0.497607			−0.248803	−	0.968554i	$-0.580037\pi$
$757$	−13.6910			−0.497607			−0.248803	+	0.968554i	$0.580037\pi$
$758$	−16.2095	+	28.0756i	−0.588754	+	1.01975i
$759$		0			0
$760$	3.01169	+	5.21640i	0.109246	+	0.189219i
$761$	−7.32141	−	12.6811i	−0.265401	−	0.459688i	0.702268	−	0.711913i	$-0.252171\pi$
$761$	−7.32141	−	12.6811i	−0.265401	−	0.459688i	−0.967669	+	0.252225i	$0.918838\pi$
$762$		0			0
$763$	−9.43199	+	16.3367i	−0.341461	+	0.591428i
$764$	−4.11855			−0.149004
$765$		0			0
$766$	5.45606			0.197135
$767$	−4.43818	+	7.68715i	−0.160253	+	0.277567i
$768$		0			0
$769$	−24.5672	−	42.5517i	−0.885918	−	1.53445i	−0.844658	−	0.535306i	$-0.820196\pi$
$769$	−24.5672	−	42.5517i	−0.885918	−	1.53445i	−0.0412592	−	0.999148i	$-0.513137\pi$
$770$	−8.57165	−	14.8465i	−0.308901	−	0.535032i
$771$		0			0
$772$	11.2410	−	19.4700i	0.404573	−	0.700741i
$773$	−12.4413			−0.447484			−0.223742	−	0.974648i	$-0.571827\pi$
$773$	−12.4413			−0.447484			−0.223742	+	0.974648i	$0.571827\pi$
$774$		0			0
$775$	−55.0370			−1.97699
$776$	−6.91411	+	11.9756i	−0.248202	+	0.429898i
$777$		0			0
$778$	−4.36467	−	7.55982i	−0.156481	−	0.271033i
$779$	2.40476	+	4.16516i	0.0861594	+	0.149232i
$780$		0			0
$781$	−4.04256	+	7.00193i	−0.144654	+	0.250549i
$782$	41.0617			1.46837
$783$		0			0
$784$	−4.98762			−0.178129
$785$	−5.18292	+	8.97708i	−0.184986	+	0.320406i
$786$		0			0
$787$	16.4567	+	28.5038i	0.586617	+	1.01605i	0.994672	+	0.103093i	$0.0328739\pi$
$787$	16.4567	+	28.5038i	0.586617	+	1.01605i	−0.408055	+	0.912957i	$0.633793\pi$
$788$	4.76392	+	8.25135i	0.169708	+	0.293942i
$789$		0			0
$790$	−21.6099	+	37.4294i	−0.768845	+	1.33168i
$791$	−18.5512			−0.659606
$792$		0			0
$793$	3.87636			0.137653
$794$	19.4931	−	33.7631i	0.691785	−	1.19821i
$795$		0			0
$796$	3.89554	+	6.74727i	0.138074	+	0.239151i
$797$	13.1989	+	22.8612i	0.467530	+	0.809786i	0.999312	−	0.0370953i	$-0.0118105\pi$
$797$	13.1989	+	22.8612i	0.467530	+	0.809786i	−0.531781	+	0.846882i	$0.678477\pi$
$798$		0			0
$799$	−5.48074	+	9.49292i	−0.193895	+	0.335835i
$800$	37.0159			1.30871
$801$		0			0
$802$	−30.9505			−1.09290
$803$	14.9560	−	25.9045i	0.527785	−	0.914151i
$804$		0			0
$805$	−10.5433	−	18.2614i	−0.371601	−	0.643631i
$806$	−5.93818	−	10.2852i	−0.209163	−	0.362282i
$807$		0			0
$808$	3.27197	−	5.66722i	0.115108	−	0.199372i
$809$	−35.5919			−1.25135			−0.625673	−	0.780086i	$-0.715175\pi$
$809$	−35.5919			−1.25135			−0.625673	+	0.780086i	$0.715175\pi$
$810$		0			0
$811$	−37.8268			−1.32828			−0.664140	−	0.747608i	$-0.731202\pi$
$811$	−37.8268			−1.32828			−0.664140	+	0.747608i	$0.731202\pi$
$812$	0.755260	−	1.30815i	0.0265044	−	0.0459070i
$813$		0			0
$814$	11.3825	+	19.7151i	0.398958	+	0.691016i
$815$	18.4963	+	32.0365i	0.647896	+	1.12219i
$816$		0			0
$817$	2.31522	−	4.01008i	0.0809994	−	0.140295i
$818$	26.0594			0.911146
$819$		0			0
$820$	17.2583			0.602686
$821$	−9.15638	+	15.8593i	−0.319560	+	0.553494i	−0.980396	−	0.197036i	$-0.936868\pi$
$821$	−9.15638	+	15.8593i	−0.319560	+	0.553494i	0.660836	+	0.750530i	$0.270202\pi$
$822$		0			0
$823$	18.0000	+	31.1769i	0.627441	+	1.08676i	0.988063	+	0.154047i	$0.0492308\pi$
$823$	18.0000	+	31.1769i	0.627441	+	1.08676i	−0.360623	+	0.932712i	$0.617436\pi$
$824$	14.9931	+	25.9688i	0.522310	+	0.904668i
$825$		0			0
$826$	−7.54325	+	13.0653i	−0.262463	+	0.454600i
$827$	28.2115			0.981011			0.490505	−	0.871438i	$-0.336812\pi$
$827$	28.2115			0.981011			0.490505	+	0.871438i	$0.336812\pi$
$828$		0			0
$829$	−11.2843			−0.391919			−0.195960	−	0.980612i	$-0.562782\pi$
$829$	−11.2843			−0.391919			−0.195960	+	0.980612i	$0.562782\pi$
$830$	12.5371	−	21.7148i	0.435168	−	0.753733i
$831$		0			0
$832$	−0.993810	−	1.72133i	−0.0344542	−	0.0596764i
$833$	−2.05563	−	3.56046i	−0.0712234	−	0.123363i
$834$		0			0
$835$	21.8028	−	37.7636i	0.754519	−	1.30686i
$836$	−2.22019			−0.0767868
$837$		0			0
$838$	17.9629			0.620517
$839$	−1.02152	+	1.76933i	−0.0352669	+	0.0610840i	−0.883120	−	0.469147i	$-0.844561\pi$
$839$	−1.02152	+	1.76933i	−0.0352669	+	0.0610840i	0.847853	+	0.530231i	$0.177895\pi$
$840$		0			0
$841$	13.0556	+	22.6130i	0.450194	+	0.779759i
$842$	−30.7392	−	53.2418i	−1.05934	−	1.83483i
$843$		0			0
$844$	−4.67928	+	8.10474i	−0.161067	+	0.278977i
$845$	−43.0604			−1.48132
$846$		0			0
$847$	3.09888			0.106479
$848$	0.308344	−	0.534068i	0.0105886	−	0.0183400i
$849$		0			0
$850$	27.5185	+	47.6634i	0.943877	+	1.63484i
$851$	14.0007	+	24.2499i	0.479937	+	0.831276i
$852$		0			0
$853$	24.2960	−	42.0818i	0.831878	−	1.44085i	−0.0646692	−	0.997907i	$-0.520599\pi$
$853$	24.2960	−	42.0818i	0.831878	−	1.44085i	0.896547	−	0.442948i	$-0.146067\pi$
$854$	6.58836			0.225449
$855$		0			0
$856$	10.1113			0.345596
$857$	−22.4487	+	38.8823i	−0.766833	+	1.32819i	0.172439	+	0.985020i	$0.444835\pi$
$857$	−22.4487	+	38.8823i	−0.766833	+	1.32819i	−0.939272	+	0.343173i	$0.888498\pi$
$858$		0			0
$859$	−14.9065	−	25.8189i	−0.508605	−	0.880929i	−0.999950	−	0.00996438i	$-0.996828\pi$
$859$	−14.9065	−	25.8189i	−0.508605	−	0.880929i	0.491346	−	0.870965i	$-0.336505\pi$
$860$	−8.30786	−	14.3896i	−0.283296	−	0.490683i
$861$		0			0
$862$	−29.8275	+	51.6628i	−1.01593	+	1.75964i
$863$	42.2595			1.43853			0.719265	−	0.694736i	$-0.244479\pi$
$863$	42.2595			1.43853			0.719265	+	0.694736i	$0.244479\pi$
$864$		0			0
$865$	23.7170			0.806401
$866$	−34.9894	+	60.6034i	−1.18899	+	2.05939i
$867$		0			0
$868$	−3.10507	−	5.37815i	−0.105393	−	0.182546i
$869$	9.95970	+	17.2507i	0.337860	+	0.585190i
$870$		0			0
$871$	−6.15452	+	10.6599i	−0.208538	+	0.361198i
$872$	−35.6291			−1.20655
$873$		0			0
$874$	−8.87636			−0.300247
$875$	5.16071	−	8.93861i	0.174464	−	0.302180i
$876$		0			0
$877$	15.2658	+	26.4411i	0.515489	+	0.892853i	0.999838	+	0.0179782i	$0.00572295\pi$
$877$	15.2658	+	26.4411i	0.515489	+	0.892853i	−0.484350	+	0.874875i	$0.660944\pi$
$878$	−3.97593	−	6.88651i	−0.134181	−	0.232409i
$879$		0			0
$880$	25.1538	−	43.5677i	0.847935	−	1.46867i
$881$	13.4079			0.451724			0.225862	−	0.974159i	$-0.427480\pi$
$881$	13.4079			0.451724			0.225862	+	0.974159i	$0.427480\pi$
$882$		0			0
$883$	−14.1250			−0.475345			−0.237672	−	0.971345i	$-0.576384\pi$
$883$	−14.1250			−0.475345			−0.237672	+	0.971345i	$0.576384\pi$
$884$	−1.82691	+	3.16431i	−0.0614458	+	0.106427i
$885$		0			0
$886$	−25.6414	−	44.4123i	−0.861441	−	1.49206i
$887$	−19.9716	−	34.5918i	−0.670581	−	1.16148i	−0.977740	−	0.209822i	$-0.932712\pi$
$887$	−19.9716	−	34.5918i	−0.670581	−	1.16148i	0.307159	−	0.951658i	$-0.400622\pi$
$888$		0			0
$889$	4.99381	−	8.64953i	0.167487	−	0.290096i
$890$	58.6067			1.96450
$891$		0			0
$892$	−5.03699			−0.168651
$893$	1.18478	−	2.05209i	0.0396471	−	0.0686707i
$894$		0			0
$895$	−6.89493	−	11.9424i	−0.230472	−	0.399189i
$896$	−6.38874	−	11.0656i	−0.213433	−	0.369676i
$897$		0			0
$898$	−0.283662	+	0.491316i	−0.00946591	+	0.0163954i
$899$	−11.8764			−0.396099
$900$		0			0
$901$	0.508333			0.0169350
$902$	12.9270	−	22.3902i	0.430421	−	0.745511i
$903$		0			0
$904$	−17.5192	−	30.3441i	−0.582679	−	1.00923i
$905$	−33.2687	−	57.6231i	−1.10589	−	1.91546i
$906$		0			0
$907$	−20.7101	+	35.8710i	−0.687669	+	1.19108i	0.284921	+	0.958551i	$0.408033\pi$
$907$	−20.7101	+	35.8710i	−0.687669	+	1.19108i	−0.972590	+	0.232527i	$0.925301\pi$
$908$	9.86398			0.327348
$909$		0			0
$910$	6.09888			0.202176
$911$	0.894237	−	1.54886i	0.0296274	−	0.0513162i	−0.850832	−	0.525439i	$-0.823901\pi$
$911$	0.894237	−	1.54886i	0.0296274	−	0.0513162i	0.880459	+	0.474122i	$0.157235\pi$
$912$		0			0
$913$	−5.77816	−	10.0081i	−0.191229	−	0.331219i
$914$	−16.4091	−	28.4214i	−0.542764	−	0.940096i
$915$		0			0
$916$	−8.72864	+	15.1185i	−0.288402	+	0.499528i
$917$	16.0531			0.530120
$918$		0			0
$919$	−57.4683			−1.89570			−0.947852	−	0.318711i	$-0.896750\pi$
$919$	−57.4683			−1.89570			−0.947852	+	0.318711i	$0.896750\pi$
$920$	19.9134	−	34.4911i	0.656526	−	1.13714i
$921$		0			0
$922$	−33.2341	−	57.5632i	−1.09451	−	1.89574i
$923$	−1.43818	−	2.49100i	−0.0473382	−	0.0819922i
$924$		0			0
$925$	−18.7658	+	32.5033i	−0.617015	+	1.06870i
$926$	−37.1817			−1.22187
$927$		0			0
$928$	7.98762			0.262206
$929$	17.3676	−	30.0816i	0.569813	−	0.986945i	−0.426771	−	0.904360i	$-0.640349\pi$
$929$	17.3676	−	30.0816i	0.569813	−	0.986945i	0.996584	−	0.0825854i	$-0.0263177\pi$
$930$		0			0
$931$	0.444368	+	0.769668i	0.0145636	+	0.0252248i
$932$	3.98281	+	6.89843i	0.130461	+	0.225965i
$933$		0			0
$934$	10.4697	−	18.1341i	0.342580	−	0.593367i
$935$	41.4683			1.35616
$936$		0			0
$937$	11.6662			0.381118			0.190559	−	0.981676i	$-0.438970\pi$
$937$	11.6662			0.381118			0.190559	+	0.981676i	$0.438970\pi$
$938$	−10.4604	+	18.1179i	−0.341544	+	0.591571i
$939$		0			0
$940$	−4.25141	−	7.36366i	−0.138666	−	0.240176i
$941$	−25.1687	−	43.5934i	−0.820475	−	1.42111i	−0.905329	−	0.424712i	$-0.860375\pi$
$941$	−25.1687	−	43.5934i	−0.820475	−	1.42111i	0.0848531	−	0.996393i	$-0.472958\pi$
$942$		0			0
$943$	15.9004	−	27.5402i	0.517787	−	0.896833i
$944$	−44.2719			−1.44093
$945$		0			0
$946$	−24.8913			−0.809287
$947$	−16.1941	+	28.0491i	−0.526238	+	0.911472i	0.473294	+	0.880904i	$0.343065\pi$
$947$	−16.1941	+	28.0491i	−0.526238	+	0.911472i	−0.999533	+	0.0305673i	$0.990269\pi$
$948$		0			0
$949$	5.32072	+	9.21576i	0.172718	+	0.299156i
$950$	−5.94870	−	10.3034i	−0.193001	−	0.334288i
$951$		0			0
$952$	3.88255	−	6.72477i	0.125834	−	0.217951i
$953$	12.5367			0.406102			0.203051	−	0.979168i	$-0.434914\pi$
$953$	12.5367			0.406102			0.203051	+	0.979168i	$0.434914\pi$
$954$		0			0
$955$	−16.6291			−0.538104
$956$	4.98693	−	8.63762i	0.161289	−	0.279361i
$957$		0			0
$958$	−11.4635	−	19.8555i	−0.370370	−	0.641500i
$959$	6.49381	+	11.2476i	0.209696	+	0.363204i
$960$		0			0
$961$	−8.91342	+	15.4385i	−0.287530	+	0.498016i
$962$	−8.09888			−0.261119
$963$		0			0
$964$	−6.20892			−0.199976
$965$	45.3868	−	78.6122i	1.46105	−	2.53062i
$966$		0			0
$967$	28.9937	+	50.2186i	0.932376	+	1.61492i	0.779248	+	0.626715i	$0.215601\pi$
$967$	28.9937	+	50.2186i	0.932376	+	1.61492i	0.153127	+	0.988206i	$0.451065\pi$
$968$	2.92649	+	5.06882i	0.0940609	+	0.162918i
$969$		0			0
$970$	22.3262	−	38.6702i	0.716852	−	1.24162i
$971$	−28.0370			−0.899750			−0.449875	−	0.893092i	$-0.648531\pi$
$971$	−28.0370			−0.899750			−0.449875	+	0.893092i	$0.648531\pi$
$972$		0			0
$973$	−1.11126			−0.0356255
$974$	6.41095	−	11.1041i	0.205420	−	0.355798i
$975$		0			0
$976$	9.66690	+	16.7436i	0.309430	+	0.535948i
$977$	4.92030	+	8.52220i	0.157414	+	0.272649i	0.933935	−	0.357442i	$-0.116351\pi$
$977$	4.92030	+	8.52220i	0.157414	+	0.272649i	−0.776521	+	0.630091i	$0.783018\pi$
$978$		0			0
$979$	13.5055	−	23.3922i	0.431638	−	0.747618i
$980$	3.18911			0.101872
$981$		0			0
$982$	−27.4313			−0.875368
$983$	−24.3447	+	42.1663i	−0.776476	+	1.34490i	0.157485	+	0.987521i	$0.449661\pi$
$983$	−24.3447	+	42.1663i	−0.776476	+	1.34490i	−0.933961	+	0.357374i	$0.883672\pi$
$984$		0			0
$985$	19.2348	+	33.3157i	0.612873	+	1.06153i
$986$	5.93818	+	10.2852i	0.189110	+	0.327548i
$987$		0			0
$988$	0.394926	−	0.684031i	0.0125643	−	0.0217619i
$989$	−30.6167			−0.973554
$990$		0			0
$991$	2.86398			0.0909772			0.0454886	−	0.998965i	$-0.485516\pi$
$991$	2.86398			0.0909772			0.0454886	+	0.998965i	$0.485516\pi$
$992$	16.4196	−	28.4396i	0.521323	−	0.902958i
$993$		0			0
$994$	−2.44437	−	4.23377i	−0.0775306	−	0.134287i
$995$	15.7286	+	27.2428i	0.498631	+	0.863655i
$996$		0			0
$997$	25.4203	−	44.0292i	0.805069	−	1.39442i	−0.111176	−	0.993801i	$-0.535462\pi$
$997$	25.4203	−	44.0292i	0.805069	−	1.39442i	0.916245	−	0.400619i	$-0.131205\pi$
$998$	52.4596			1.66058
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.f.a.127.3		6
3.2	odd	2		63.2.f.b.43.1	yes	6
4.3	odd	2		3024.2.r.g.2017.1		6
7.2	even	3		1323.2.h.d.802.1		6
7.3	odd	6		1323.2.g.b.667.3		6
7.4	even	3		1323.2.g.c.667.3		6
7.5	odd	6		1323.2.h.e.802.1		6
7.6	odd	2		1323.2.f.c.883.3		6
9.2	odd	6		567.2.a.d.1.3		3
9.4	even	3	inner	189.2.f.a.64.3		6
9.5	odd	6		63.2.f.b.22.1	✓	6
9.7	even	3		567.2.a.g.1.1		3
12.11	even	2		1008.2.r.k.673.1		6
21.2	odd	6		441.2.h.c.214.3		6
21.5	even	6		441.2.h.b.214.3		6
21.11	odd	6		441.2.g.e.79.1		6
21.17	even	6		441.2.g.d.79.1		6
21.20	even	2		441.2.f.d.295.1		6
36.7	odd	6		9072.2.a.cd.1.3		3
36.11	even	6		9072.2.a.bq.1.1		3
36.23	even	6		1008.2.r.k.337.1		6
36.31	odd	6		3024.2.r.g.1009.1		6
63.4	even	3		1323.2.h.d.226.1		6
63.5	even	6		441.2.g.d.67.1		6
63.13	odd	6		1323.2.f.c.442.3		6
63.20	even	6		3969.2.a.m.1.3		3
63.23	odd	6		441.2.g.e.67.1		6
63.31	odd	6		1323.2.h.e.226.1		6
63.32	odd	6		441.2.h.c.373.3		6
63.34	odd	6		3969.2.a.p.1.1		3
63.40	odd	6		1323.2.g.b.361.3		6
63.41	even	6		441.2.f.d.148.1		6
63.58	even	3		1323.2.g.c.361.3		6
63.59	even	6		441.2.h.b.373.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.f.b.22.1	✓	6	9.5	odd	6
63.2.f.b.43.1	yes	6	3.2	odd	2
189.2.f.a.64.3		6	9.4	even	3	inner
189.2.f.a.127.3		6	1.1	even	1	trivial
441.2.f.d.148.1		6	63.41	even	6
441.2.f.d.295.1		6	21.20	even	2
441.2.g.d.67.1		6	63.5	even	6
441.2.g.d.79.1		6	21.17	even	6
441.2.g.e.67.1		6	63.23	odd	6
441.2.g.e.79.1		6	21.11	odd	6
441.2.h.b.214.3		6	21.5	even	6
441.2.h.b.373.3		6	63.59	even	6
441.2.h.c.214.3		6	21.2	odd	6
441.2.h.c.373.3		6	63.32	odd	6
567.2.a.d.1.3		3	9.2	odd	6
567.2.a.g.1.1		3	9.7	even	3
1008.2.r.k.337.1		6	36.23	even	6
1008.2.r.k.673.1		6	12.11	even	2
1323.2.f.c.442.3		6	63.13	odd	6
1323.2.f.c.883.3		6	7.6	odd	2
1323.2.g.b.361.3		6	63.40	odd	6
1323.2.g.b.667.3		6	7.3	odd	6
1323.2.g.c.361.3		6	63.58	even	3
1323.2.g.c.667.3		6	7.4	even	3
1323.2.h.d.226.1		6	63.4	even	3
1323.2.h.d.802.1		6	7.2	even	3
1323.2.h.e.226.1		6	63.31	odd	6
1323.2.h.e.802.1		6	7.5	odd	6
3024.2.r.g.1009.1		6	36.31	odd	6
3024.2.r.g.2017.1		6	4.3	odd	2
3969.2.a.m.1.3		3	63.20	even	6
3969.2.a.p.1.1		3	63.34	odd	6
9072.2.a.bq.1.1		3	36.11	even	6
9072.2.a.cd.1.3		3	36.7	odd	6

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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.f (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.849814 - 1.47192i) q^{2} +(-0.444368 - 0.769668i) q^{4} +(-1.79418 - 3.10761i) q^{5} +(0.500000 - 0.866025i) q^{7} +1.88874 q^{8} +O(q^{10})\)	\(q+(0.849814 - 1.47192i) q^{2} +(-0.444368 - 0.769668i) q^{4} +(-1.79418 - 3.10761i) q^{5} +(0.500000 - 0.866025i) q^{7} +1.88874 q^{8} -6.09888 q^{10} +(-1.40545 + 2.43430i) q^{11} +(-0.500000 - 0.866025i) q^{13} +(-0.849814 - 1.47192i) q^{14} +(2.49381 - 4.31941i) q^{16} +4.11126 q^{17} -0.888736 q^{19} +(-1.59455 + 2.76185i) q^{20} +(2.38874 + 4.13741i) q^{22} +(2.93818 + 5.08907i) q^{23} +(-3.93818 + 6.82112i) q^{25} -1.69963 q^{26} -0.888736 q^{28} +(-0.849814 + 1.47192i) q^{29} +(3.49381 + 6.05146i) q^{31} +(-2.34981 - 4.07000i) q^{32} +(3.49381 - 6.05146i) q^{34} -3.58836 q^{35} +4.76509 q^{37} +(-0.755260 + 1.30815i) q^{38} +(-3.38874 - 5.86946i) q^{40} +(-2.70582 - 4.68661i) q^{41} +(-2.60507 + 4.51212i) q^{43} +2.49814 q^{44} +9.98762 q^{46} +(-1.33310 + 2.30900i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(6.69344 + 11.5934i) q^{50} +(-0.444368 + 0.769668i) q^{52} +0.123644 q^{53} +10.0865 q^{55} +(0.944368 - 1.63569i) q^{56} +(1.44437 + 2.50172i) q^{58} +(-4.43818 - 7.68715i) q^{59} +(-1.93818 + 3.35702i) q^{61} +11.8764 q^{62} +1.98762 q^{64} +(-1.79418 + 3.10761i) q^{65} +(-6.15452 - 10.6599i) q^{67} +(-1.82691 - 3.16431i) q^{68} +(-3.04944 + 5.28179i) q^{70} +2.87636 q^{71} -10.6414 q^{73} +(4.04944 - 7.01384i) q^{74} +(0.394926 + 0.684031i) q^{76} +(1.40545 + 2.43430i) q^{77} +(3.54325 - 6.13709i) q^{79} -17.8974 q^{80} -9.19777 q^{82} +(-2.05563 + 3.56046i) q^{83} +(-7.37636 - 12.7762i) q^{85} +(4.42766 + 7.66893i) q^{86} +(-2.65452 + 4.59776i) q^{88} -9.60940 q^{89} -1.00000 q^{91} +(2.61126 - 4.52284i) q^{92} +(2.26578 + 3.92445i) q^{94} +(1.59455 + 2.76185i) q^{95} +(-3.66071 + 6.34053i) q^{97} -1.69963 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{2} - 3 q^{4} - 5 q^{5} + 3 q^{7} + 12 q^{8}+O(q^{10}) \) 6 * q - q^2 - 3 * q^4 - 5 * q^5 + 3 * q^7 + 12 * q^8	\( 6 q - q^{2} - 3 q^{4} - 5 q^{5} + 3 q^{7} + 12 q^{8} - 2 q^{11} - 3 q^{13} + q^{14} - 3 q^{16} + 24 q^{17} - 6 q^{19} - 16 q^{20} + 15 q^{22} - 6 q^{25} + 2 q^{26} - 6 q^{28} + q^{29} + 3 q^{31} - 8 q^{32} + 3 q^{34} - 10 q^{35} - 6 q^{37} + 8 q^{38} - 21 q^{40} - 22 q^{41} + 3 q^{43} - 46 q^{44} + 24 q^{46} - 9 q^{47} - 3 q^{49} + 10 q^{50} - 3 q^{52} + 36 q^{53} - 12 q^{55} + 6 q^{56} + 9 q^{58} - 9 q^{59} + 6 q^{61} + 36 q^{62} - 24 q^{64} - 5 q^{65} + 6 q^{68} - 18 q^{71} + 6 q^{73} + 6 q^{74} + 21 q^{76} + 2 q^{77} - 15 q^{79} - 22 q^{80} + 18 q^{82} - 12 q^{83} - 9 q^{85} + 34 q^{86} + 21 q^{88} + 4 q^{89} - 6 q^{91} + 15 q^{92} - 24 q^{94} + 16 q^{95} - 3 q^{97} + 2 q^{98}+O(q^{100}) \) 6 * q - q^2 - 3 * q^4 - 5 * q^5 + 3 * q^7 + 12 * q^8 - 2 * q^11 - 3 * q^13 + q^14 - 3 * q^16 + 24 * q^17 - 6 * q^19 - 16 * q^20 + 15 * q^22 - 6 * q^25 + 2 * q^26 - 6 * q^28 + q^29 + 3 * q^31 - 8 * q^32 + 3 * q^34 - 10 * q^35 - 6 * q^37 + 8 * q^38 - 21 * q^40 - 22 * q^41 + 3 * q^43 - 46 * q^44 + 24 * q^46 - 9 * q^47 - 3 * q^49 + 10 * q^50 - 3 * q^52 + 36 * q^53 - 12 * q^55 + 6 * q^56 + 9 * q^58 - 9 * q^59 + 6 * q^61 + 36 * q^62 - 24 * q^64 - 5 * q^65 + 6 * q^68 - 18 * q^71 + 6 * q^73 + 6 * q^74 + 21 * q^76 + 2 * q^77 - 15 * q^79 - 22 * q^80 + 18 * q^82 - 12 * q^83 - 9 * q^85 + 34 * q^86 + 21 * q^88 + 4 * q^89 - 6 * q^91 + 15 * q^92 - 24 * q^94 + 16 * q^95 - 3 * q^97 + 2 * q^98

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