LMFDB - Embedded newform 189.2.o.a.125.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [189,2,Mod(62,189)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(189, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("189.62"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.o (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 7x^{10} + 37x^{8} - 78x^{6} + 123x^{4} - 36x^{2} + 9 $ x^12 - 7x^10 + 37x^8 - 78x^6 + 123x^4 - 36*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			125.5
Root			$-1.29589 - 0.748185i$ of defining polynomial
Character	$\chi$	$=$	189.125
Dual form			189.2.o.a.62.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.97141 - 1.13819i) q^{2} +(1.59097 - 2.75564i) q^{4} +(-0.717144 + 1.24213i) q^{5} +(2.16235 - 1.52455i) q^{7} -2.69056i q^{8} +3.26499i q^{10} +(-2.80150 + 1.61745i) q^{11} +(-4.43334 - 2.55959i) q^{13} +(2.52764 - 5.46668i) q^{14} +(0.119562 + 0.207087i) q^{16} +1.09132 q^{17} +4.48911i q^{19} +(2.28191 + 3.95238i) q^{20} +(-3.68194 + 6.37731i) q^{22} +(-3.47141 - 2.00422i) q^{23} +(1.47141 + 2.54856i) q^{25} -11.6532 q^{26} +(-0.760877 - 8.38418i) q^{28} +(-1.02859 + 0.593857i) q^{29} +(3.24275 + 1.87220i) q^{31} +(5.13160 + 2.96273i) q^{32} +(2.15143 - 1.24213i) q^{34} +(0.342971 + 3.77924i) q^{35} -0.239123 q^{37} +(5.10948 + 8.84988i) q^{38} +(3.34203 + 1.92952i) q^{40} +(3.71620 - 6.43664i) q^{41} +(-3.82326 - 6.62208i) q^{43} +10.2933i q^{44} -9.12476 q^{46} +(-2.11042 - 3.65536i) q^{47} +(2.35150 - 6.59321i) q^{49} +(5.80150 + 3.34950i) q^{50} +(-14.1066 + 8.14447i) q^{52} -7.01414i q^{53} -4.63977i q^{55} +(-4.10189 - 5.81793i) q^{56} +(-1.35185 + 2.34147i) q^{58} +(-4.73531 + 8.20179i) q^{59} +(2.82757 - 1.63250i) q^{61} +8.52371 q^{62} +13.0104 q^{64} +(6.35868 - 3.67119i) q^{65} +(-0.330095 + 0.571741i) q^{67} +(1.73625 - 3.00728i) q^{68} +(4.97764 + 7.06006i) q^{70} -3.82347i q^{71} +7.31073i q^{73} +(-0.471410 + 0.272169i) q^{74} +(12.3704 + 7.14205i) q^{76} +(-3.59195 + 7.76852i) q^{77} +(-1.83009 - 3.16982i) q^{79} -0.342971 q^{80} -16.9190i q^{82} +(-5.45245 - 9.44392i) q^{83} +(-0.782630 + 1.35556i) q^{85} +(-15.0744 - 8.70322i) q^{86} +(4.35185 + 7.53762i) q^{88} +13.6915 q^{89} +(-13.4887 + 1.22412i) q^{91} +(-11.0458 + 6.37731i) q^{92} +(-8.32102 - 4.80415i) q^{94} +(-5.57605 - 3.21934i) q^{95} +(-2.69709 + 1.55716i) q^{97} +(-2.86857 - 15.6744i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{2} + 2 q^{4} - 2 q^{7} + 12 q^{14} + 2 q^{16} - 10 q^{22} - 24 q^{23} - 8 q^{28} - 30 q^{29} + 12 q^{32} - 4 q^{37} - 10 q^{43} - 40 q^{46} + 6 q^{49} + 36 q^{50} - 42 q^{56} + 2 q^{58} + 16 q^{64}+ \cdots - 72 q^{95}+O(q^{100}) $ 12 * q + 6 * q^2 + 2 * q^4 - 2 * q^7 + 12 * q^14 + 2 * q^16 - 10 * q^22 - 24 * q^23 - 8 * q^28 - 30 * q^29 + 12 * q^32 - 4 * q^37 - 10 * q^43 - 40 * q^46 + 6 * q^49 + 36 * q^50 - 42 * q^56 + 2 * q^58 + 16 * q^64 + 78 * q^65 + 12 * q^67 + 18 * q^70 + 12 * q^74 + 24 * q^77 - 6 * q^79 - 6 * q^85 - 96 * q^86 + 34 * q^88 - 24 * q^91 - 30 * q^92 - 72 * q^95

Character values

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

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	1.97141	−	1.13819i	1.39400	−	0.804825i	0.400242	−	0.916409i	$-0.368926\pi$
$2$	1.97141	−	1.13819i	1.39400	−	0.804825i	0.993755	+	0.111585i	$0.0355926\pi$
$3$		0			0
$3$		0			0
$4$	1.59097	−	2.75564i	0.795486	−	1.37782i
$5$	−0.717144	+	1.24213i	−0.320716	+	0.555497i	−0.980636	−	0.195839i	$-0.937257\pi$
$5$	−0.717144	+	1.24213i	−0.320716	+	0.555497i	0.659920	+	0.751336i	$0.270590\pi$
$6$		0			0
$7$	2.16235	−	1.52455i	0.817291	−	0.576225i
$7$	2.16235	−	1.52455i	0.817291	−	0.576225i
$8$		−	2.69056i		−	0.951257i
$9$		0			0
$10$			3.26499i			1.03248i
$11$	−2.80150	+	1.61745i	−0.844686	+	0.487679i	−0.858854	−	0.512220i	$-0.828823\pi$
$11$	−2.80150	+	1.61745i	−0.844686	+	0.487679i	0.0141686	+	0.999900i	$0.495490\pi$
$12$		0			0
$13$	−4.43334	−	2.55959i	−1.22959	−	0.709903i	−0.262644	−	0.964893i	$-0.584594\pi$
$13$	−4.43334	−	2.55959i	−1.22959	−	0.709903i	−0.966944	+	0.254990i	$0.917928\pi$
$14$	2.52764	−	5.46668i	0.675541	−	1.46103i
$15$		0			0
$16$	0.119562	+	0.207087i	0.0298904	+	0.0517717i
$17$	1.09132			0.264683			0.132341	−	0.991204i	$-0.457750\pi$
$17$	1.09132			0.264683			0.132341	+	0.991204i	$0.457750\pi$
$18$		0			0
$19$			4.48911i			1.02987i	0.857228	+	0.514936i	$0.172184\pi$
$19$			4.48911i			1.02987i	−0.857228	+	0.514936i	$0.827816\pi$
$20$	2.28191	+	3.95238i	0.510251	+	0.883780i
$21$		0			0
$22$	−3.68194	+	6.37731i	−0.784993	+	1.35965i
$23$	−3.47141	−	2.00422i	−0.723839	−	0.417909i	0.0923250	−	0.995729i	$-0.470570\pi$
$23$	−3.47141	−	2.00422i	−0.723839	−	0.417909i	−0.816164	+	0.577820i	$0.803903\pi$
$24$		0			0
$25$	1.47141	+	2.54856i	0.294282	+	0.509711i
$26$	−11.6532			−2.28539
$27$		0			0
$28$	−0.760877	−	8.38418i	−0.143792	−	1.58446i
$29$	−1.02859	+	0.593857i	−0.191004	+	0.110276i	−0.592453	−	0.805605i	$-0.701840\pi$
$29$	−1.02859	+	0.593857i	−0.191004	+	0.110276i	0.401448	+	0.915882i	$0.368507\pi$
$30$		0			0
$31$	3.24275	+	1.87220i	0.582414	+	0.336257i	0.762092	−	0.647468i	$-0.224172\pi$
$31$	3.24275	+	1.87220i	0.582414	+	0.336257i	−0.179678	+	0.983726i	$0.557506\pi$
$32$	5.13160	+	2.96273i	0.907147	+	0.523742i
$33$		0			0
$34$	2.15143	−	1.24213i	0.368967	−	0.213023i
$35$	0.342971	+	3.77924i	0.0579728	+	0.638808i
$36$		0			0
$37$	−0.239123			−0.0393116			−0.0196558	−	0.999807i	$-0.506257\pi$
$37$	−0.239123			−0.0393116			−0.0196558	+	0.999807i	$0.506257\pi$
$38$	5.10948	+	8.84988i	0.828867	+	1.43564i
$39$		0			0
$40$	3.34203	+	1.92952i	0.528421	+	0.305084i
$41$	3.71620	−	6.43664i	0.580373	−	1.00523i	−0.415062	−	0.909793i	$-0.636240\pi$
$41$	3.71620	−	6.43664i	0.580373	−	1.00523i	0.995435	−	0.0954418i	$-0.0304264\pi$
$42$		0			0
$43$	−3.82326	−	6.62208i	−0.583041	−	1.00986i	−0.995116	−	0.0987075i	$-0.968529\pi$
$43$	−3.82326	−	6.62208i	−0.583041	−	1.00986i	0.412075	−	0.911150i	$-0.364804\pi$
$44$			10.2933i			1.55177i
$45$		0			0
$46$	−9.12476			−1.34537
$47$	−2.11042	−	3.65536i	−0.307837	−	0.533189i	0.670052	−	0.742314i	$-0.266272\pi$
$47$	−2.11042	−	3.65536i	−0.307837	−	0.533189i	−0.977889	+	0.209125i	$0.932939\pi$
$48$		0			0
$49$	2.35150	−	6.59321i	0.335929	−	0.941887i
$50$	5.80150	+	3.34950i	0.820457	+	0.473691i
$51$		0			0
$52$	−14.1066	+	8.14447i	−1.95624	+	1.12944i
$53$		−	7.01414i		−	0.963466i	−0.876318	−	0.481733i	$-0.840008\pi$
$53$		−	7.01414i		−	0.963466i	0.876318	−	0.481733i	$-0.159992\pi$
$54$		0			0
$55$		−	4.63977i		−	0.625627i
$56$	−4.10189	−	5.81793i	−0.548138	−	0.777454i
$57$		0			0
$58$	−1.35185	+	2.34147i	−0.177506	+	0.307450i
$59$	−4.73531	+	8.20179i	−0.616484	+	1.06778i	0.373638	+	0.927575i	$0.378110\pi$
$59$	−4.73531	+	8.20179i	−0.616484	+	1.06778i	−0.990122	+	0.140208i	$0.955223\pi$
$60$		0			0
$61$	2.82757	−	1.63250i	0.362033	−	0.209020i	−0.307939	−	0.951406i	$-0.599639\pi$
$61$	2.82757	−	1.63250i	0.362033	−	0.209020i	0.669972	+	0.742386i	$0.266306\pi$
$62$	8.52371			1.08251
$63$		0			0
$64$	13.0104			1.62630
$65$	6.35868	−	3.67119i	0.788698	−	0.455355i
$66$		0			0
$67$	−0.330095	+	0.571741i	−0.0403275	+	0.0698493i	−0.885485	−	0.464669i	$-0.846173\pi$
$67$	−0.330095	+	0.571741i	−0.0403275	+	0.0698493i	0.845157	+	0.534518i	$0.179507\pi$
$68$	1.73625	−	3.00728i	0.210552	−	0.364686i
$69$		0			0
$70$	4.97764	+	7.06006i	0.594942	+	0.843838i
$71$		−	3.82347i		−	0.453762i	−0.973922	−	0.226881i	$-0.927147\pi$
$71$		−	3.82347i		−	0.453762i	0.973922	−	0.226881i	$-0.0728529\pi$
$72$		0			0
$73$			7.31073i			0.855656i	0.903860	+	0.427828i	$0.140721\pi$
$73$			7.31073i			0.855656i	−0.903860	+	0.427828i	$0.859279\pi$
$74$	−0.471410	+	0.272169i	−0.0548003	+	0.0316390i
$75$		0			0
$76$	12.3704	+	7.14205i	1.41898	+	0.819249i
$77$	−3.59195	+	7.76852i	−0.409341	+	0.885305i
$78$		0			0
$79$	−1.83009	−	3.16982i	−0.205902	−	0.356632i	0.744518	−	0.667602i	$-0.232679\pi$
$79$	−1.83009	−	3.16982i	−0.205902	−	0.356632i	−0.950420	+	0.310970i	$0.899346\pi$
$80$	−0.342971			−0.0383454
$81$		0			0
$82$		−	16.9190i		−	1.86839i
$83$	−5.45245	−	9.44392i	−0.598484	−	1.03660i	−0.993045	−	0.117735i	$-0.962437\pi$
$83$	−5.45245	−	9.44392i	−0.598484	−	1.03660i	0.394561	−	0.918870i	$-0.370897\pi$
$84$		0			0
$85$	−0.782630	+	1.35556i	−0.0848882	+	0.147031i
$86$	−15.0744	−	8.70322i	−1.62552	−	0.938492i
$87$		0			0
$88$	4.35185	+	7.53762i	0.463909	+	0.803513i
$89$	13.6915			1.45129			0.725646	−	0.688068i	$-0.241541\pi$
$89$	13.6915			1.45129			0.725646	+	0.688068i	$0.241541\pi$
$90$		0			0
$91$	−13.4887	+	1.22412i	−1.41399	+	0.128322i
$92$	−11.0458	+	6.37731i	−1.15161	+	0.664881i
$93$		0			0
$94$	−8.32102	−	4.80415i	−0.858248	−	0.495510i
$95$	−5.57605	−	3.21934i	−0.572091	−	0.330297i
$96$		0			0
$97$	−2.69709	+	1.55716i	−0.273848	+	0.158106i	−0.630635	−	0.776080i	$-0.717205\pi$
$97$	−2.69709	+	1.55716i	−0.273848	+	0.158106i	0.356787	+	0.934186i	$0.383872\pi$
$98$	−2.86857	−	15.6744i	−0.289770	−	1.58335i
$99$		0			0
$100$	9.36389			0.936389
$101$	3.54471	+	6.13962i	0.352712	+	0.610915i	0.986724	−	0.162408i	$-0.0519262\pi$
$101$	3.54471	+	6.13962i	0.352712	+	0.610915i	−0.634012	+	0.773324i	$0.718593\pi$
$102$		0			0
$103$	−1.47529	−	0.851761i	−0.145365	−	0.0839265i	0.425553	−	0.904933i	$-0.360079\pi$
$103$	−1.47529	−	0.851761i	−0.145365	−	0.0839265i	−0.570918	+	0.821007i	$0.693413\pi$
$104$	−6.88674	+	11.9282i	−0.675300	+	1.16965i
$105$		0			0
$106$	−7.98345	−	13.8277i	−0.775421	−	1.34307i
$107$			4.93582i			0.477164i	0.971122	+	0.238582i	$0.0766826\pi$
$107$			4.93582i			0.477164i	−0.971122	+	0.238582i	$0.923317\pi$
$108$		0			0
$109$	8.13844			0.779521			0.389760	−	0.920916i	$-0.372558\pi$
$109$	8.13844			0.779521			0.389760	+	0.920916i	$0.372558\pi$
$110$	−5.28096	−	9.14690i	−0.503520	−	0.872123i
$111$		0			0
$112$	0.574248	+	0.265516i	0.0542613	+	0.0250889i
$113$	3.39699	+	1.96125i	0.319562	+	0.184499i	0.651197	−	0.758908i	$-0.274267\pi$
$113$	3.39699	+	1.96125i	0.319562	+	0.184499i	−0.331635	+	0.943408i	$0.607600\pi$
$114$		0			0
$115$	4.97900	−	2.87463i	0.464294	−	0.268060i
$116$			3.77924i			0.350893i
$117$		0			0
$118$			21.5588i			1.98465i
$119$	2.35981	−	1.66376i	0.216323	−	0.152517i
$120$		0			0
$121$	−0.267713	+	0.463693i	−0.0243376	+	0.0421539i
$122$	3.71620	−	6.43664i	0.336449	−	0.582746i
$123$		0			0
$124$	10.3182	−	5.95724i	0.926605	−	0.534976i
$125$	−11.3923			−1.01896
$126$		0			0
$127$	6.16827			0.547345			0.273673	−	0.961823i	$-0.411761\pi$
$127$	6.16827			0.547345			0.273673	+	0.961823i	$0.411761\pi$
$128$	15.3856	−	8.88290i	1.35991	−	0.785145i
$129$		0			0
$130$	8.35705	−	14.4748i	0.732962	−	1.26953i
$131$	4.13138	−	7.15575i	0.360960	−	0.625201i	−0.627159	−	0.778891i	$-0.715782\pi$
$131$	4.13138	−	7.15575i	0.360960	−	0.625201i	0.988119	+	0.153690i	$0.0491158\pi$
$132$		0			0
$133$	6.84387	+	9.70702i	0.593438	+	0.841706i
$134$			1.50285i			0.129826i
$135$		0			0
$136$		−	2.93625i		−	0.251782i
$137$	8.96169	−	5.17404i	0.765649	−	0.442048i	−0.0656711	−	0.997841i	$-0.520919\pi$
$137$	8.96169	−	5.17404i	0.765649	−	0.442048i	0.831320	+	0.555794i	$0.187585\pi$
$138$		0			0
$139$	−15.4589	−	8.92521i	−1.31121	−	0.757026i	−0.328912	−	0.944361i	$-0.606682\pi$
$139$	−15.4589	−	8.92521i	−1.31121	−	0.757026i	−0.982296	+	0.187334i	$0.940015\pi$
$140$	10.9599	+	5.06755i	0.926280	+	0.428286i
$141$		0			0
$142$	−4.35185	−	7.53762i	−0.365199	−	0.632543i
$143$	16.5600			1.38482
$144$		0			0
$145$		−	1.70352i		−	0.141470i
$146$	8.32102	+	14.4124i	0.688653	+	1.19278i
$147$		0			0
$148$	−0.380438	+	0.658939i	−0.0312718	+	0.0541644i
$149$	15.1758	+	8.76175i	1.24325	+	0.717790i	0.969754	−	0.244083i	$-0.0784869\pi$
$149$	15.1758	+	8.76175i	1.24325	+	0.717790i	0.273495	+	0.961873i	$0.411820\pi$
$150$		0			0
$151$	−0.550343	−	0.953223i	−0.0447863	−	0.0775722i	0.842763	−	0.538284i	$-0.180927\pi$
$151$	−0.550343	−	0.953223i	−0.0447863	−	0.0775722i	−0.887550	+	0.460712i	$0.847594\pi$
$152$	12.0782			0.979674
$153$		0			0
$154$	1.76088	+	19.4033i	0.141895	+	1.56356i
$155$	−4.65103	+	2.68527i	−0.373580	+	0.215686i
$156$		0			0
$157$	8.45150	+	4.87948i	0.674503	+	0.389425i	0.797781	−	0.602947i	$-0.206007\pi$
$157$	8.45150	+	4.87948i	0.674503	+	0.389425i	−0.123277	+	0.992372i	$0.539340\pi$
$158$	−7.21574	−	4.16601i	−0.574053	−	0.331430i
$159$		0			0
$160$	−7.36019	+	4.24941i	−0.581874	+	0.335945i
$161$	−10.5619	+	0.958511i	−0.832397	+	0.0755413i
$162$		0			0
$163$	−7.22545			−0.565941			−0.282970	−	0.959129i	$-0.591320\pi$
$163$	−7.22545			−0.565941			−0.282970	+	0.959129i	$0.591320\pi$
$164$	−11.8247	−	20.4810i	−0.923356	−	1.59930i
$165$		0			0
$166$	−21.4980	−	12.4119i	−1.66857	−	0.963350i
$167$	−8.65419	+	14.9895i	−0.669681	+	1.15992i	0.308312	+	0.951285i	$0.400236\pi$
$167$	−8.65419	+	14.9895i	−0.669681	+	1.15992i	−0.977993	+	0.208637i	$0.933097\pi$
$168$		0			0
$169$	6.60301	+	11.4367i	0.507924	+	0.879750i
$170$			3.56314i			0.273280i
$171$		0			0
$172$	−24.3308			−1.85520
$173$	0.978103	+	1.69412i	0.0743638	+	0.128802i	0.900809	−	0.434215i	$-0.142974\pi$
$173$	0.978103	+	1.69412i	0.0743638	+	0.128802i	−0.826446	+	0.563017i	$0.809641\pi$
$174$		0			0
$175$	7.06710	+	3.26763i	0.534223	+	0.247010i
$176$	−0.669905	−	0.386770i	−0.0504960	−	0.0291539i
$177$		0			0
$178$	26.9915	−	15.5835i	2.02310	−	1.16804i
$179$			23.2017i			1.73418i	0.498152	+	0.867090i	$0.334012\pi$
$179$			23.2017i			1.73418i	−0.498152	+	0.867090i	$0.665988\pi$
$180$		0			0
$181$		−	10.2744i		−	0.763689i	−0.924226	−	0.381845i	$-0.875289\pi$
$181$		−	10.2744i		−	0.763689i	0.924226	−	0.381845i	$-0.124711\pi$
$182$	−25.1984	+	17.7659i	−1.86783	+	1.31690i
$183$		0			0
$184$	−5.39248	+	9.34004i	−0.397539	+	0.688557i
$185$	0.171486	−	0.297022i	0.0126079	−	0.0218375i
$186$		0			0
$187$	−3.05733	+	1.76515i	−0.223574	+	0.129080i
$188$	−13.4305			−0.979520
$189$		0			0
$190$	−14.6569			−1.06332
$191$	−19.6758	+	11.3598i	−1.42369	+	0.821968i	−0.996612	−	0.0822464i	$-0.973791\pi$
$191$	−19.6758	+	11.3598i	−1.42369	+	0.821968i	−0.427079	+	0.904215i	$0.640457\pi$
$192$		0			0
$193$	−8.43598	+	14.6116i	−0.607235	+	1.05176i	0.384459	+	0.923142i	$0.374388\pi$
$193$	−8.43598	+	14.6116i	−0.607235	+	1.05176i	−0.991694	+	0.128620i	$0.958945\pi$
$194$	−3.54471	+	6.13962i	−0.254495	+	0.440799i
$195$		0			0
$196$	−14.4274	−	16.9695i	−1.03053	−	1.21211i
$197$		−	8.94426i		−	0.637252i	−0.947880	−	0.318626i	$-0.896779\pi$
$197$		−	8.94426i		−	0.637252i	0.947880	−	0.318626i	$-0.103221\pi$
$198$		0			0
$199$		−	5.78528i		−	0.410108i	−0.978751	−	0.205054i	$-0.934263\pi$
$199$		−	5.78528i		−	0.410108i	0.978751	−	0.205054i	$-0.0657369\pi$
$200$	6.85705	−	3.95892i	0.484867	−	0.279938i
$201$		0			0
$202$	13.9762	+	8.06914i	0.983359	+	0.567743i
$203$	−1.31881	+	2.85226i	−0.0925621	+	0.200189i
$204$		0			0
$205$	5.33009	+	9.23200i	0.372270	+	0.644791i
$206$	−3.87788			−0.270185
$207$		0			0
$208$		−	1.22412i		−	0.0848771i
$209$	−7.26091	−	12.5763i	−0.502248	−	0.869918i
$210$		0			0
$211$	−12.9451	+	22.4216i	−0.891180	+	1.54357i	−0.0527186	+	0.998609i	$0.516789\pi$
$211$	−12.9451	+	22.4216i	−0.891180	+	1.54357i	−0.838462	+	0.544960i	$0.816545\pi$
$212$	−19.3285	−	11.1593i	−1.32748	−	0.766423i
$213$		0			0
$214$	5.61793	+	9.73053i	0.384034	+	0.665166i
$215$	10.9673			0.747964
$216$		0			0
$217$	9.86621	−	0.895374i	0.669762	−	0.0607819i
$218$	16.0442	−	9.26312i	1.08665	−	0.627378i
$219$		0			0
$220$	−12.7856	−	7.38175i	−0.862003	−	0.497678i
$221$	−4.83818	−	2.79332i	−0.325451	−	0.187899i
$222$		0			0
$223$	−15.4827	+	8.93892i	−1.03680	+	0.598594i	−0.918924	−	0.394435i	$-0.870940\pi$
$223$	−15.4827	+	8.93892i	−1.03680	+	0.598594i	−0.117871	+	0.993029i	$0.537607\pi$
$224$	15.6131	−	1.41692i	1.04320	−	0.0946717i
$225$		0			0
$226$	8.92915			0.593958
$227$	−5.48365	−	9.49796i	−0.363963	−	0.630402i	0.624646	−	0.780908i	$-0.285243\pi$
$227$	−5.48365	−	9.49796i	−0.363963	−	0.630402i	−0.988609	+	0.150506i	$0.951910\pi$
$228$		0			0
$229$	16.8349	+	9.71965i	1.11248	+	0.642293i	0.939471	−	0.342627i	$-0.111317\pi$
$229$	16.8349	+	9.71965i	1.11248	+	0.642293i	0.173012	+	0.984920i	$0.444650\pi$
$230$	6.54377	−	11.3341i	0.431483	−	0.747351i
$231$		0			0
$232$	1.59781	+	2.76748i	0.104901	+	0.181694i
$233$			2.94031i			0.192626i	0.995351	+	0.0963131i	$0.0307050\pi$
$233$			2.94031i			0.192626i	−0.995351	+	0.0963131i	$0.969295\pi$
$234$		0			0
$235$	6.05391			0.394914
$236$	15.0675	+	26.0976i	0.980809	+	1.69881i
$237$		0			0
$238$	2.75846	−	5.96588i	0.178804	−	0.386710i
$239$	10.7255	+	6.19234i	0.693772	+	0.400549i	0.805023	−	0.593243i	$-0.202153\pi$
$239$	10.7255	+	6.19234i	0.693772	+	0.400549i	−0.111252	+	0.993792i	$0.535486\pi$
$240$		0			0
$241$	−11.6943	+	6.75168i	−0.753293	+	0.434914i	−0.826882	−	0.562375i	$-0.809888\pi$
$241$	−11.6943	+	6.75168i	−0.753293	+	0.434914i	0.0735896	+	0.997289i	$0.476555\pi$
$242$			1.21884i			0.0783499i
$243$		0			0
$244$		−	10.3890i		−	0.665089i
$245$	6.50325	+	7.64915i	0.415478	+	0.488686i
$246$		0			0
$247$	11.4903	−	19.9018i	0.731109	−	1.26632i
$248$	5.03727	−	8.72481i	0.319867	−	0.554026i
$249$		0			0
$250$	−22.4589	+	12.9666i	−1.42042	+	0.820082i
$251$	7.51441			0.474305			0.237153	−	0.971472i	$-0.423786\pi$
$251$	7.51441			0.474305			0.237153	+	0.971472i	$0.423786\pi$
$252$		0			0
$253$	12.9669			0.815222
$254$	12.1602	−	7.02069i	0.762998	−	0.440517i
$255$		0			0
$256$	7.21053	−	12.4890i	0.450658	−	0.780563i
$257$	3.87788	−	6.71668i	0.241895	−	0.418975i	−0.719359	−	0.694639i	$-0.755564\pi$
$257$	3.87788	−	6.71668i	0.241895	−	0.418975i	0.961254	+	0.275664i	$0.0888976\pi$
$258$		0			0
$259$	−0.517068	+	0.364555i	−0.0321290	+	0.0226523i
$260$		−	23.3630i		−	1.44891i
$261$		0			0
$262$		−	18.8092i		−	1.16204i
$263$	12.1127	−	6.99329i	0.746903	−	0.431224i	−0.0776710	−	0.996979i	$-0.524748\pi$
$263$	12.1127	−	6.99329i	0.746903	−	0.431224i	0.824574	+	0.565755i	$0.191415\pi$
$264$		0			0
$265$	8.71246	+	5.03014i	0.535202	+	0.308999i
$266$	24.5405	+	11.3469i	1.50468	+	0.695721i
$267$		0			0
$268$	1.05034	+	1.81925i	0.0641599	+	0.111128i
$269$	−25.8321			−1.57501			−0.787505	−	0.616308i	$-0.788628\pi$
$269$	−25.8321			−1.57501			−0.787505	+	0.616308i	$0.788628\pi$
$270$		0			0
$271$			16.6537i			1.01164i	0.862639	+	0.505821i	$0.168810\pi$
$271$			16.6537i			1.01164i	−0.862639	+	0.505821i	$0.831190\pi$
$272$	0.130480	+	0.225997i	0.00791148	+	0.0137031i
$273$		0			0
$274$	11.7781	−	20.4003i	0.711542	−	1.23243i
$275$	−8.24433	−	4.75986i	−0.497152	−	0.287031i
$276$		0			0
$277$	−15.7044	−	27.2008i	−0.943585	−	1.63434i	−0.758560	−	0.651603i	$-0.774097\pi$
$277$	−15.7044	−	27.2008i	−0.943585	−	1.63434i	−0.185025	−	0.982734i	$-0.559237\pi$
$278$	−40.6345			−2.43709
$279$		0			0
$280$	10.1683	−	0.922786i	0.607670	−	0.0551470i
$281$	−8.10464	+	4.67922i	−0.483483	+	0.279139i	−0.721867	−	0.692032i	$-0.756716\pi$
$281$	−8.10464	+	4.67922i	−0.483483	+	0.279139i	0.238384	+	0.971171i	$0.423382\pi$
$282$		0			0
$283$	13.6603	+	7.88676i	0.812018	+	0.468819i	0.847656	−	0.530546i	$-0.178013\pi$
$283$	13.6603	+	7.88676i	0.812018	+	0.468819i	−0.0356380	+	0.999365i	$0.511346\pi$
$284$	−10.5361	−	6.08303i	−0.625203	−	0.360961i
$285$		0			0
$286$	32.6466	−	18.8485i	1.93044	−	1.11454i
$287$	−1.77726	−	19.5838i	−0.104908	−	1.15599i
$288$		0			0
$289$	−15.8090			−0.929943
$290$	−1.93894	−	3.35834i	−0.113858	−	0.197209i
$291$		0			0
$292$	20.1458	+	11.6312i	1.17894	+	0.680662i
$293$	12.4287	−	21.5271i	0.726090	−	1.25762i	−0.232434	−	0.972612i	$-0.574669\pi$
$293$	12.4287	−	21.5271i	0.726090	−	1.25762i	0.958524	−	0.285013i	$-0.0919978\pi$
$294$		0			0
$295$	−6.79179	−	11.7637i	−0.395433	−	0.684911i
$296$			0.643376i			0.0373955i
$297$		0			0
$298$	39.8903			2.31078
$299$	10.2600	+	17.7708i	0.593349	+	1.02771i
$300$		0			0
$301$	−18.3629	−	8.49050i	−1.05842	−	0.489384i
$302$	−2.16991	−	1.25280i	−0.124864	−	0.0720903i
$303$		0			0
$304$	−0.929636	+	0.536725i	−0.0533183	+	0.0307833i
$305$			4.68294i			0.268144i
$306$		0			0
$307$		−	18.8878i		−	1.07799i	−0.842310	−	0.538993i	$-0.818805\pi$
$307$		−	18.8878i		−	1.07799i	0.842310	−	0.538993i	$-0.181195\pi$
$308$	15.6926	+	22.2576i	0.894168	+	1.26825i
$309$		0			0
$310$	−6.11273	+	10.5876i	−0.347179	+	0.601332i
$311$	3.97716	−	6.88864i	0.225524	−	0.390619i	−0.730953	−	0.682428i	$-0.760924\pi$
$311$	3.97716	−	6.88864i	0.225524	−	0.390619i	0.956476	+	0.291809i	$0.0942573\pi$
$312$		0			0
$313$	−9.64210	+	5.56687i	−0.545004	+	0.314658i	−0.747104	−	0.664707i	$-0.768556\pi$
$313$	−9.64210	+	5.56687i	−0.545004	+	0.314658i	0.202101	+	0.979365i	$0.435223\pi$
$314$	22.2152			1.25367
$315$		0			0
$316$	−11.6465			−0.655168
$317$	20.1380	−	11.6267i	1.13107	−	0.653021i	0.186863	−	0.982386i	$-0.440168\pi$
$317$	20.1380	−	11.6267i	1.13107	−	0.653021i	0.944203	+	0.329365i	$0.106835\pi$
$318$		0			0
$319$	1.92107	−	3.32738i	0.107559	−	0.186298i
$320$	−9.33033	+	16.1606i	−0.521581	+	0.903405i
$321$		0			0
$322$	−19.7309	+	13.9111i	−1.09956	+	0.775238i
$323$			4.89904i			0.272590i
$324$		0			0
$325$		−	15.0648i		−	0.835646i
$326$	−14.2443	+	8.22396i	−0.788920	+	0.455483i
$327$		0			0
$328$	−17.3182	−	9.99866i	−0.956237	−	0.552084i
$329$	−10.1363	−	4.68672i	−0.558830	−	0.258387i
$330$		0			0
$331$	9.57962	+	16.5924i	0.526544	+	0.912000i	0.999522	+	0.0309261i	$0.00984566\pi$
$331$	9.57962	+	16.5924i	0.526544	+	0.912000i	−0.472978	+	0.881074i	$0.656821\pi$
$332$	−34.6988			−1.90434
$333$		0			0
$334$			39.4006i			2.15590i
$335$	−0.473451	−	0.820041i	−0.0258674	−	0.0448036i
$336$		0			0
$337$	14.2781	−	24.7304i	0.777779	−	1.34715i	−0.155441	−	0.987845i	$-0.549680\pi$
$337$	14.2781	−	24.7304i	0.777779	−	1.34715i	0.933219	−	0.359307i	$-0.116987\pi$
$338$	26.0345	+	15.0310i	1.41609	+	0.817579i
$339$		0			0
$340$	2.49028	+	4.31330i	0.135055	+	0.233922i
$341$	−12.1128			−0.655943
$342$		0			0
$343$	−4.96690	−	17.8418i	−0.268187	−	0.963367i
$344$	−17.8171	+	10.2867i	−0.960634	+	0.554622i
$345$		0			0
$346$	3.85648	+	2.22654i	0.207326	+	0.119700i
$347$	−2.56690	−	1.48200i	−0.137798	−	0.0795578i	0.429516	−	0.903059i	$-0.358684\pi$
$347$	−2.56690	−	1.48200i	−0.137798	−	0.0795578i	−0.567314	+	0.823501i	$0.692017\pi$
$348$		0			0
$349$	23.3885	−	13.5034i	1.25196	−	0.722818i	0.280460	−	0.959866i	$-0.409513\pi$
$349$	23.3885	−	13.5034i	1.25196	−	0.722818i	0.971498	+	0.237048i	$0.0761797\pi$
$350$	17.6514	−	1.60189i	0.943504	−	0.0856245i
$351$		0			0
$352$	−19.1683			−1.02167
$353$	14.8238	+	25.6755i	0.788990	+	1.36657i	0.926586	+	0.376083i	$0.122729\pi$
$353$	14.8238	+	25.6755i	0.788990	+	1.36657i	−0.137596	+	0.990488i	$0.543937\pi$
$354$		0			0
$355$	4.74924	+	2.74198i	0.252064	+	0.145529i
$356$	21.7827	−	37.7288i	1.15448	−	1.99962i
$357$		0			0
$358$	26.4081	+	45.7401i	1.39571	+	2.41744i
$359$		−	24.6261i		−	1.29972i	−0.760056	−	0.649858i	$-0.774828\pi$
$359$		−	24.6261i		−	1.29972i	0.760056	−	0.649858i	$-0.225172\pi$
$360$		0			0
$361$	−1.15211			−0.0606373
$362$	−11.6943	−	20.2550i	−0.614636	−	1.06458i
$363$		0			0
$364$	−18.0868	+	39.1174i	−0.948008	+	2.05031i
$365$	−9.08087	−	5.24284i	−0.475314	−	0.274423i
$366$		0			0
$367$	4.85598	−	2.80360i	0.253480	−	0.146347i	−0.367877	−	0.929875i	$-0.619915\pi$
$367$	4.85598	−	2.80360i	0.253480	−	0.146347i	0.621357	+	0.783528i	$0.286582\pi$
$368$		−	0.958511i		−	0.0499658i
$369$		0			0
$370$		−	0.780736i		−	0.0405885i
$371$	−10.6934	−	15.1670i	−0.555173	−	0.787432i
$372$		0			0
$373$	1.86677	−	3.23333i	0.0966574	−	0.167416i	−0.813642	−	0.581367i	$-0.802518\pi$
$373$	1.86677	−	3.23333i	0.0966574	−	0.167416i	0.910299	+	0.413951i	$0.135852\pi$
$374$	−4.01816	+	6.95966i	−0.207774	+	0.359876i
$375$		0			0
$376$	−9.83498	+	5.67823i	−0.507200	+	0.292832i
$377$	6.08012			0.313142
$378$		0			0
$379$	−30.4419			−1.56369			−0.781847	−	0.623470i	$-0.785722\pi$
$379$	−30.4419			−1.56369			−0.781847	+	0.623470i	$0.785722\pi$
$380$	−17.7427	+	10.2437i	−0.910181	+	0.525493i
$381$		0			0
$382$	−25.8594	+	44.7897i	−1.32308	+	2.29164i
$383$	−8.49251	+	14.7095i	−0.433947	+	0.751618i	−0.997209	−	0.0746601i	$-0.976213\pi$
$383$	−8.49251	+	14.7095i	−0.433947	+	0.751618i	0.563262	+	0.826278i	$0.309546\pi$
$384$		0			0
$385$	−7.07356	−	10.0328i	−0.360502	−	0.511319i
$386$			38.4071i			1.95487i
$387$		0			0
$388$			9.90962i			0.503085i
$389$	−9.43310	+	5.44621i	−0.478277	+	0.276134i	−0.719698	−	0.694287i	$-0.755720\pi$
$389$	−9.43310	+	5.44621i	−0.478277	+	0.276134i	0.241421	+	0.970420i	$0.422387\pi$
$390$		0			0
$391$	−3.78840	−	2.18724i	−0.191588	−	0.110613i
$392$	−17.7394	−	6.32687i	−0.895977	−	0.319555i
$393$		0			0
$394$	−10.1803	−	17.6328i	−0.512877	−	0.888328i
$395$	5.24976			0.264144
$396$		0			0
$397$			22.3035i			1.11938i	0.828702	+	0.559690i	$0.189080\pi$
$397$			22.3035i			1.11938i	−0.828702	+	0.559690i	$0.810920\pi$
$398$	−6.58477	−	11.4052i	−0.330065	−	0.571689i
$399$		0			0
$400$	−0.351848	+	0.609419i	−0.0175924	+	0.0304710i
$401$	−20.8554	−	12.0409i	−1.04147	−	0.601293i	−0.121221	−	0.992626i	$-0.538681\pi$
$401$	−20.8554	−	12.0409i	−1.04147	−	0.601293i	−0.920249	+	0.391333i	$0.872014\pi$
$402$		0			0
$403$	−9.58414	−	16.6002i	−0.477420	−	0.826915i
$404$	22.5581			1.12231
$405$		0			0
$406$	0.646517	+	7.12403i	0.0320861	+	0.353560i
$407$	0.669905	−	0.386770i	0.0332060	−	0.0191715i
$408$		0			0
$409$	−22.8191	−	13.1746i	−1.12833	−	0.651443i	−0.184817	−	0.982773i	$-0.559169\pi$
$409$	−22.8191	−	13.1746i	−1.12833	−	0.651443i	−0.943515	+	0.331330i	$0.892503\pi$
$410$	21.0156	+	12.1334i	1.03789	+	0.599224i
$411$		0			0
$412$	−4.69430	+	2.71026i	−0.231272	+	0.133525i
$413$	2.26464	+	24.9543i	0.111436	+	1.22792i
$414$		0			0
$415$	15.6408			0.767775
$416$	−15.1668	−	26.2696i	−0.743611	−	1.28797i
$417$		0			0
$418$	−28.6285	−	16.5286i	−1.40026	−	0.808443i
$419$	−16.1761	+	28.0178i	−0.790252	+	1.36876i	0.135558	+	0.990769i	$0.456717\pi$
$419$	−16.1761	+	28.0178i	−0.790252	+	1.36876i	−0.925811	+	0.377988i	$0.876616\pi$
$420$		0			0
$421$	−5.54746	−	9.60849i	−0.270367	−	0.468289i	0.698589	−	0.715523i	$-0.253812\pi$
$421$	−5.54746	−	9.60849i	−0.270367	−	0.468289i	−0.968956	+	0.247234i	$0.920478\pi$
$422$			58.9363i			2.86898i
$423$		0			0
$424$	−18.8720			−0.916504
$425$	1.60577	+	2.78128i	0.0778914	+	0.134912i
$426$		0			0
$427$	3.62537	−	7.84079i	0.175444	−	0.379443i
$428$	13.6014	+	7.85276i	0.657447	+	0.379577i
$429$		0			0
$430$	21.6210	−	12.4829i	1.04266	−	0.601980i
$431$		−	16.3047i		−	0.785368i	−0.919673	−	0.392684i	$-0.871547\pi$
$431$		−	16.3047i		−	0.785368i	0.919673	−	0.392684i	$-0.128453\pi$
$432$		0			0
$433$			12.5359i			0.602438i	0.953555	+	0.301219i	$0.0973936\pi$
$433$			12.5359i			0.602438i	−0.953555	+	0.301219i	$0.902606\pi$
$434$	18.4312	−	12.9948i	0.884728	−	0.623771i
$435$		0			0
$436$	12.9480	−	22.4266i	0.620098	−	1.07404i
$437$	8.99716	−	15.5835i	0.430393	−	0.745462i
$438$		0			0
$439$	16.1276	−	9.31127i	0.769728	−	0.444403i	−0.0630496	−	0.998010i	$-0.520083\pi$
$439$	16.1276	−	9.31127i	0.769728	−	0.444403i	0.832778	+	0.553608i	$0.186749\pi$
$440$	−12.4836			−0.595132
$441$		0			0
$442$	−12.7174			−0.604904
$443$	−4.11436	+	2.37543i	−0.195479	+	0.112860i	−0.594545	−	0.804062i	$-0.702668\pi$
$443$	−4.11436	+	2.37543i	−0.195479	+	0.112860i	0.399066	+	0.916922i	$0.369334\pi$
$444$		0			0
$445$	−9.81875	+	17.0066i	−0.465453	+	0.806189i
$446$	−20.3484	+	35.2445i	−0.963527	+	1.66888i
$447$		0			0
$448$	28.1330	−	19.8350i	1.32916	−	0.937115i
$449$		−	16.2393i		−	0.766379i	−0.923670	−	0.383189i	$-0.874826\pi$
$449$		−	16.2393i		−	0.766379i	0.923670	−	0.383189i	$-0.125174\pi$
$450$		0			0
$451$			24.0431i			1.13214i
$452$	10.8090	−	6.24060i	0.508414	−	0.293533i
$453$		0			0
$454$	−21.6210	−	12.4829i	−1.01473	−	0.585852i
$455$	8.15279	−	17.6325i	0.382209	−	0.826625i
$456$		0			0
$457$	2.87360	+	4.97722i	0.134421	+	0.232825i	0.925376	−	0.379050i	$-0.123749\pi$
$457$	2.87360	+	4.97722i	0.134421	+	0.232825i	−0.790955	+	0.611874i	$0.790416\pi$
$458$	44.2514			2.06773
$459$		0			0
$460$		−	18.2938i		−	0.852953i
$461$	18.1346	+	31.4101i	0.844613	+	1.46291i	0.885957	+	0.463768i	$0.153503\pi$
$461$	18.1346	+	31.4101i	0.844613	+	1.46291i	−0.0413440	+	0.999145i	$0.513164\pi$
$462$		0			0
$463$	14.6202	−	25.3230i	0.679461	−	1.17686i	−0.295683	−	0.955286i	$-0.595547\pi$
$463$	14.6202	−	25.3230i	0.679461	−	1.17686i	0.975144	−	0.221574i	$-0.0711195\pi$
$464$	−0.245960	−	0.142005i	−0.0114184	−	0.00659241i
$465$		0			0
$466$	3.34665	+	5.79656i	0.155030	+	0.268521i
$467$	2.64215			0.122264			0.0611320	−	0.998130i	$-0.480529\pi$
$467$	2.64215			0.122264			0.0611320	+	0.998130i	$0.480529\pi$
$468$		0			0
$469$	0.157867	+	1.73955i	0.00728961	+	0.0803249i
$470$	11.9347	−	6.89053i	0.550508	−	0.317836i
$471$		0			0
$472$	22.0674	+	12.7406i	1.01574	+	0.586435i
$473$	21.4218	+	12.3679i	0.984973	+	0.568675i
$474$		0			0
$475$	−11.4408	+	6.60532i	−0.524938	+	0.303073i
$476$	−0.830357	−	9.14978i	−0.0380593	−	0.419380i
$477$		0			0
$478$	28.1923			1.28949
$479$	−15.5409	−	26.9177i	−0.710083	−	1.22990i	−0.964826	−	0.262891i	$-0.915324\pi$
$479$	−15.5409	−	26.9177i	−0.710083	−	1.22990i	0.254742	−	0.967009i	$-0.418009\pi$
$480$		0			0
$481$	1.06012	+	0.612058i	0.0483371	+	0.0279074i
$482$	−15.3694	+	26.6207i	−0.700059	+	1.21254i
$483$		0			0
$484$	0.851848	+	1.47544i	0.0387204	+	0.0670657i
$485$		−	4.46684i		−	0.202829i
$486$		0			0
$487$	34.8720			1.58020			0.790100	−	0.612978i	$-0.210029\pi$
$487$	34.8720			1.58020			0.790100	+	0.612978i	$0.210029\pi$
$488$	−4.39234	−	7.60775i	−0.198832	−	0.344387i
$489$		0			0
$490$	21.5268	+	7.67765i	0.972482	+	0.346841i
$491$	22.6758	+	13.0919i	1.02334	+	0.590828i	0.915071	−	0.403293i	$-0.132134\pi$
$491$	22.6758	+	13.0919i	1.02334	+	0.590828i	0.108273	+	0.994121i	$0.465468\pi$
$492$		0			0
$493$	−1.12252	+	0.648085i	−0.0505556	+	0.0291883i
$494$		−	52.3127i		−	2.35366i
$495$		0			0
$496$			0.895374i			0.0402035i
$497$	−5.82906	−	8.26767i	−0.261469	−	0.370856i
$498$		0			0
$499$	−6.23912	+	10.8065i	−0.279302	+	0.483764i	−0.971211	−	0.238220i	$-0.923436\pi$
$499$	−6.23912	+	10.8065i	−0.279302	+	0.483764i	0.691910	+	0.721984i	$0.256770\pi$
$500$	−18.1248	+	31.3931i	−0.810566	+	1.40394i
$501$		0			0
$502$	14.8140	−	8.55285i	0.661180	−	0.381733i
$503$	−37.8479			−1.68756			−0.843778	−	0.536693i	$-0.819673\pi$
$503$	−37.8479			−1.68756			−0.843778	+	0.536693i	$0.819673\pi$
$504$		0			0
$505$	−10.1683			−0.452482
$506$	25.5631	−	14.7588i	1.13642	−	0.656111i
$507$		0			0
$508$	9.81354	−	16.9976i	0.435406	−	0.754145i
$509$	17.6924	−	30.6441i	0.784200	−	1.35827i	−0.145276	−	0.989391i	$-0.546407\pi$
$509$	17.6924	−	30.6441i	0.784200	−	1.35827i	0.929476	−	0.368883i	$-0.120260\pi$
$510$		0			0
$511$	11.1456	+	15.8083i	0.493050	+	0.699320i
$512$			2.70367i			0.119486i
$513$		0			0
$514$		−	17.6551i		−	0.778734i
$515$	2.11599	−	1.22167i	0.0932419	−	0.0538332i
$516$		0			0
$517$	11.8247	+	6.82701i	0.520051	+	0.300252i
$518$	−0.604419	+	1.30721i	−0.0265566	+	0.0574356i
$519$		0			0
$520$	−9.87756	−	17.1084i	−0.433160	−	0.750255i
$521$	−2.31879			−0.101588			−0.0507940	−	0.998709i	$-0.516175\pi$
$521$	−2.31879			−0.101588			−0.0507940	+	0.998709i	$0.516175\pi$
$522$		0			0
$523$		−	20.1840i		−	0.882585i	−0.897363	−	0.441293i	$-0.854520\pi$
$523$		−	20.1840i		−	0.882585i	0.897363	−	0.441293i	$-0.145480\pi$
$524$	−13.1458	−	22.7692i	−0.574277	−	0.994677i
$525$		0			0
$526$	15.9194	−	27.5733i	0.694120	−	1.20225i
$527$	3.53886	+	2.04316i	0.154155	+	0.0890015i
$528$		0			0
$529$	−3.46621	−	6.00365i	−0.150705	−	0.261028i
$530$	22.9011			0.994761
$531$		0			0
$532$	37.6375	−	3.41566i	1.63179	−	0.148088i
$533$	−32.9503	+	19.0239i	−1.42724	+	0.824016i
$534$		0			0
$535$	−6.13093	−	3.53970i	−0.265063	−	0.153034i
$536$	1.53831	+	0.888141i	0.0664447	+	0.0383618i
$537$		0			0
$538$	−50.9256	+	29.4019i	−2.19556	+	1.26761i
$539$	4.07644	+	22.2744i	0.175585	+	0.959424i
$540$		0			0
$541$	−22.7713			−0.979014			−0.489507	−	0.871999i	$-0.662823\pi$
$541$	−22.7713			−0.979014			−0.489507	+	0.871999i	$0.662823\pi$
$542$	18.9552	+	32.8313i	0.814194	+	1.41023i
$543$		0			0
$544$	5.60020	+	3.23327i	0.240106	+	0.138626i
$545$	−5.83643	+	10.1090i	−0.250005	+	0.433022i
$546$		0			0
$547$	14.7918	+	25.6201i	0.632451	+	1.09544i	0.987049	+	0.160419i	$0.0512845\pi$
$547$	14.7918	+	25.6201i	0.632451	+	1.09544i	−0.354598	+	0.935019i	$0.615382\pi$
$548$		−	32.9270i		−	1.40657i
$549$		0			0
$550$	−21.6706			−0.924037
$551$	−2.66589	−	4.61745i	−0.113571	−	0.196710i
$552$		0			0
$553$	−8.78984	−	4.06418i	−0.373782	−	0.172827i
$554$	−61.9196	−	35.7493i	−2.63071	−	1.51884i
$555$		0			0
$556$	−49.1894	+	28.3995i	−2.08609	+	1.20441i
$557$			4.71407i			0.199741i	0.995000	+	0.0998707i	$0.0318429\pi$
$557$			4.71407i			0.199741i	−0.995000	+	0.0998707i	$0.968157\pi$
$558$		0			0
$559$			39.1439i			1.65561i
$560$	−0.741624	+	0.522877i	−0.0313393	+	0.0220956i
$561$		0			0
$562$	−10.6517	+	18.4493i	−0.449316	+	0.778238i
$563$	13.6742	−	23.6844i	0.576299	−	0.998179i	−0.419601	−	0.907709i	$-0.637830\pi$
$563$	13.6742	−	23.6844i	0.576299	−	0.998179i	0.995899	−	0.0904697i	$-0.0288368\pi$
$564$		0			0
$565$	−4.87226	+	2.81300i	−0.204977	+	0.118344i
$566$	35.9066			1.50927
$567$		0			0
$568$	−10.2873			−0.431645
$569$	−20.4018	+	11.7790i	−0.855288	+	0.493801i	−0.862432	−	0.506174i	$-0.831059\pi$
$569$	−20.4018	+	11.7790i	−0.855288	+	0.493801i	0.00714355	+	0.999974i	$0.497726\pi$
$570$		0			0
$571$	−9.59385	+	16.6170i	−0.401490	+	0.695401i	−0.993906	−	0.110231i	$-0.964841\pi$
$571$	−9.59385	+	16.6170i	−0.401490	+	0.695401i	0.592416	+	0.805632i	$0.298174\pi$
$572$	26.3465	−	45.6336i	1.10160	−	1.90804i
$573$		0			0
$574$	−25.7939	−	36.5848i	−1.07661	−	1.52702i
$575$		−	11.7961i		−	0.491932i
$576$		0			0
$577$		−	2.23413i		−	0.0930079i	−0.998918	−	0.0465039i	$-0.985192\pi$
$577$		−	2.23413i		−	0.0930079i	0.998918	−	0.0465039i	$-0.0148080\pi$
$578$	−31.1661	+	17.9937i	−1.29634	+	0.748441i
$579$		0			0
$580$	−4.69430	−	2.71026i	−0.194920	−	0.112537i
$581$	−26.1878	−	12.1085i	−1.08645	−	0.502346i
$582$		0			0
$583$	11.3450	+	19.6501i	0.469862	+	0.813826i
$584$	19.6700			0.813949
$585$		0			0
$586$		−	56.5849i		−	2.33750i
$587$	12.9883	+	22.4963i	0.536083	+	0.928522i	0.999110	+	0.0421784i	$0.0134298\pi$
$587$	12.9883	+	22.4963i	0.536083	+	0.928522i	−0.463028	+	0.886344i	$0.653237\pi$
$588$		0			0
$589$	−8.40451	+	14.5570i	−0.346302	+	0.599813i
$590$	−26.7788	−	15.4608i	−1.10247	−	0.636509i
$591$		0			0
$592$	−0.0285900	−	0.0495193i	−0.00117504	−	0.00203523i
$593$	−5.71754			−0.234791			−0.117396	−	0.993085i	$-0.537455\pi$
$593$	−5.71754			−0.234791			−0.117396	+	0.993085i	$0.537455\pi$
$594$		0			0
$595$	0.374290	+	4.12434i	0.0153444	+	0.169081i
$596$	48.2885	−	27.8794i	1.97797	−	1.14198i
$597$		0			0
$598$	40.4532	+	23.3557i	1.65425	+	0.955084i
$599$	−21.8662	−	12.6245i	−0.893429	−	0.515822i	−0.0183665	−	0.999831i	$-0.505847\pi$
$599$	−21.8662	−	12.6245i	−0.893429	−	0.515822i	−0.875063	+	0.484010i	$0.839180\pi$
$600$		0			0
$601$	40.2546	−	23.2410i	1.64202	−	0.948021i	0.661907	−	0.749586i	$-0.269748\pi$
$601$	40.2546	−	23.2410i	1.64202	−	0.948021i	0.980114	−	0.198435i	$-0.0635858\pi$
$602$	−45.8646	+	4.16229i	−1.86930	+	0.169642i
$603$		0			0
$604$	−3.50232			−0.142508
$605$	−0.383978	−	0.665069i	−0.0156109	−	0.0270389i
$606$		0			0
$607$	−6.09405	−	3.51840i	−0.247350	−	0.142808i	0.371200	−	0.928553i	$-0.378946\pi$
$607$	−6.09405	−	3.51840i	−0.247350	−	0.142808i	−0.618550	+	0.785745i	$0.712280\pi$
$608$	−13.3000	+	23.0363i	−0.539387	+	0.934246i
$609$		0			0
$610$	5.33009	+	9.23200i	0.215809	+	0.373793i
$611$			21.6073i			0.874138i
$612$		0			0
$613$	6.54256			0.264252			0.132126	−	0.991233i	$-0.457820\pi$
$613$	6.54256			0.264252			0.132126	+	0.991233i	$0.457820\pi$
$614$	−21.4980	−	37.2357i	−0.867590	−	1.50271i
$615$		0			0
$616$	20.9017	+	9.66437i	0.842153	+	0.389388i
$617$	30.0043	+	17.3230i	1.20793	+	0.697396i	0.962306	−	0.271970i	$-0.0876751\pi$
$617$	30.0043	+	17.3230i	1.20793	+	0.697396i	0.245620	+	0.969366i	$0.421008\pi$
$618$		0			0
$619$	14.7072	−	8.49123i	0.591134	−	0.341291i	−0.174412	−	0.984673i	$-0.555802\pi$
$619$	14.7072	−	8.49123i	0.591134	−	0.341291i	0.765546	+	0.643381i	$0.222469\pi$
$620$			17.0888i			0.686302i
$621$		0			0
$622$		−	18.1071i		−	0.726029i
$623$	29.6057	−	20.8733i	1.18613	−	0.836271i
$624$		0			0
$625$	0.812855	−	1.40791i	0.0325142	−	0.0563162i
$626$	−12.6724	+	21.9492i	−0.506489	+	0.877265i
$627$		0			0
$628$	26.8922	−	15.5262i	1.07312	−	0.619564i
$629$	−0.260959			−0.0104051
$630$		0			0
$631$	26.2438			1.04475			0.522374	−	0.852716i	$-0.325047\pi$
$631$	26.2438			1.04475			0.522374	+	0.852716i	$0.325047\pi$
$632$	−8.52859	+	4.92398i	−0.339249	+	0.195866i
$633$		0			0
$634$	26.4669	−	45.8420i	1.05113	−	1.82062i
$635$	−4.42354	+	7.66179i	−0.175543	+	0.304049i
$636$		0			0
$637$	−27.3009	+	23.2111i	−1.08170	+	0.919656i
$638$		−	8.74619i		−	0.346265i
$639$		0			0
$640$			25.4813i			1.00724i
$641$	−16.5092	+	9.53157i	−0.652073	+	0.376474i	−0.789250	−	0.614072i	$-0.789530\pi$
$641$	−16.5092	+	9.53157i	−0.652073	+	0.376474i	0.137177	+	0.990547i	$0.456197\pi$
$642$		0			0
$643$	15.3447	+	8.85928i	0.605136	+	0.349376i	0.771060	−	0.636763i	$-0.219727\pi$
$643$	15.3447	+	8.85928i	0.605136	+	0.349376i	−0.165923	+	0.986139i	$0.553060\pi$
$644$	−14.1624	+	30.6299i	−0.558077	+	1.20699i
$645$		0			0
$646$	5.57605	+	9.65801i	0.219387	+	0.379989i
$647$	21.7902			0.856661			0.428330	−	0.903622i	$-0.359102\pi$
$647$	21.7902			0.856661			0.428330	+	0.903622i	$0.359102\pi$
$648$		0			0
$649$		−	30.6365i		−	1.20259i
$650$	−17.1467	−	29.6990i	−0.672549	−	1.16489i
$651$		0			0
$652$	−11.4955	+	19.9108i	−0.450198	+	0.779766i
$653$	13.0852	+	7.55475i	0.512064	+	0.295640i	0.733682	−	0.679493i	$-0.237800\pi$
$653$	13.0852	+	7.55475i	0.512064	+	0.295640i	−0.221618	+	0.975134i	$0.571134\pi$
$654$		0			0
$655$	5.92558	+	10.2634i	0.231532	+	0.401024i
$656$	1.77726			0.0693903
$657$		0			0
$658$	−25.3171	+	2.29757i	−0.986964	+	0.0895685i
$659$	27.1850	−	15.6952i	1.05898	−	0.611400i	0.133827	−	0.991005i	$-0.457273\pi$
$659$	27.1850	−	15.6952i	1.05898	−	0.611400i	0.925149	+	0.379605i	$0.123940\pi$
$660$		0			0
$661$	−37.8554	−	21.8558i	−1.47240	−	0.850093i	−0.472885	−	0.881124i	$-0.656787\pi$
$661$	−37.8554	−	21.8558i	−1.47240	−	0.850093i	−0.999518	+	0.0310314i	$0.990121\pi$
$662$	37.7707	+	21.8069i	1.46800	+	0.847551i
$663$		0			0
$664$	−25.4095	+	14.6702i	−0.986078	+	0.569312i
$665$	−16.9654	+	1.53964i	−0.657890	+	0.0597046i
$666$		0			0
$667$	4.76088			0.184342
$668$	27.5371	+	47.6957i	1.06544	+	1.84540i
$669$		0			0
$670$	−1.86673	−	1.07776i	−0.0721181	−	0.0416374i
$671$	−5.28096	+	9.14690i	−0.203869	+	0.353112i
$672$		0			0
$673$	−4.60589	−	7.97763i	−0.177544	−	0.307515i	0.763495	−	0.645814i	$-0.223482\pi$
$673$	−4.60589	−	7.97763i	−0.177544	−	0.307515i	−0.941039	+	0.338299i	$0.890149\pi$
$674$		−	65.0051i		−	2.50390i
$675$		0			0
$676$	42.0208			1.61618
$677$	11.4194	+	19.7789i	0.438882	+	0.760165i	0.997604	−	0.0691899i	$-0.0220414\pi$
$677$	11.4194	+	19.7789i	0.438882	+	0.760165i	−0.558722	+	0.829355i	$0.688708\pi$
$678$		0			0
$679$	−3.45807	+	7.47898i	−0.132709	+	0.287017i
$680$	3.64721	+	2.10571i	0.139864	+	0.0807505i
$681$		0			0
$682$	−23.8792	+	13.7867i	−0.914383	+	0.527919i
$683$			34.1826i			1.30796i	0.756511	+	0.653981i	$0.226902\pi$
$683$			34.1826i			1.30796i	−0.756511	+	0.653981i	$0.773098\pi$
$684$		0			0
$685$			14.8421i			0.567088i
$686$	−30.0992	−	29.5202i	−1.14919	−	1.12709i
$687$		0			0
$688$	0.914230	−	1.58349i	0.0348547	−	0.0603701i
$689$	−17.9533	+	31.0961i	−0.683967	+	1.18467i
$690$		0			0
$691$	−0.224082	+	0.129374i	−0.00852446	+	0.00492160i	−0.504256	−	0.863554i	$-0.668233\pi$
$691$	−0.224082	+	0.129374i	−0.00852446	+	0.00492160i	0.495732	+	0.868476i	$0.334900\pi$
$692$	6.22453			0.236621
$693$		0			0
$694$	−6.74720			−0.256120
$695$	22.1725	−	12.8013i	0.841052	−	0.485582i
$696$		0			0
$697$	4.05555	−	7.02441i	0.153615	−	0.266069i
$698$	30.7389	−	53.2413i	1.16348	−	2.01521i
$699$		0			0
$700$	20.2480	−	14.2757i	0.765302	−	0.539571i
$701$			5.16189i			0.194962i	0.995237	+	0.0974810i	$0.0310785\pi$
$701$			5.16189i			0.194962i	−0.995237	+	0.0974810i	$0.968921\pi$
$702$		0			0
$703$		−	1.07345i		−	0.0404860i
$704$	−36.4487	+	21.0437i	−1.37371	+	0.793113i
$705$		0			0
$706$	58.4475	+	33.7447i	2.19970	+	1.27000i
$707$	17.0251	+	7.87192i	0.640293	+	0.296054i
$708$		0			0
$709$	−11.7472	−	20.3468i	−0.441175	−	0.764138i	0.556602	−	0.830780i	$-0.312105\pi$
$709$	−11.7472	−	20.3468i	−0.441175	−	0.764138i	−0.997777	+	0.0666412i	$0.978772\pi$
$710$	12.4836			0.468501
$711$		0			0
$712$		−	36.8377i		−	1.38055i
$713$	−7.50460	−	12.9984i	−0.281050	−	0.486792i
$714$		0			0
$715$	−11.8759	+	20.5697i	−0.444134	+	0.769263i
$716$	63.9357	+	36.9133i	2.38939	+	1.37952i
$717$		0			0
$718$	−28.0293	−	48.5481i	−1.04604	−	1.81180i
$719$	10.1566			0.378776			0.189388	−	0.981902i	$-0.439350\pi$
$719$	10.1566			0.378776			0.189388	+	0.981902i	$0.439350\pi$
$720$		0			0
$721$	−4.48865	+	0.407352i	−0.167166	+	0.0151706i
$722$	−2.27128	+	1.31132i	−0.0845283	+	0.0488024i
$723$		0			0
$724$	−28.3126	−	16.3463i	−1.05223	−	0.607504i
$725$	−3.02696	−	1.74761i	−0.112418	−	0.0649047i
$726$		0			0
$727$	−5.74874	+	3.31904i	−0.213209	+	0.123096i	−0.602802	−	0.797891i	$-0.705949\pi$
$727$	−5.74874	+	3.31904i	−0.213209	+	0.123096i	0.389593	+	0.920987i	$0.372616\pi$
$728$	3.29356	+	36.2920i	0.122067	+	1.34507i
$729$		0			0
$730$	−23.8695			−0.883449
$731$	−4.17238	−	7.22678i	−0.154321	−	0.267292i
$732$		0			0
$733$	5.20130	+	3.00297i	0.192114	+	0.110917i	0.592972	−	0.805223i	$-0.297954\pi$
$733$	5.20130	+	3.00297i	0.192114	+	0.110917i	−0.400858	+	0.916140i	$0.631288\pi$
$734$	6.38209	−	11.0541i	0.235567	−	0.408014i
$735$		0			0
$736$	−11.8759	−	20.5697i	−0.437752	−	0.758209i
$737$		−	2.13565i		−	0.0786676i
$738$		0			0
$739$	−15.6386			−0.575275			−0.287638	−	0.957739i	$-0.592870\pi$
$739$	−15.6386			−0.575275			−0.287638	+	0.957739i	$0.592870\pi$
$740$	−0.545658	−	0.945107i	−0.0200588	−	0.0347428i
$741$		0			0
$742$	−38.3441	−	17.7292i	−1.40765	−	0.650861i
$743$	−27.3807	−	15.8083i	−1.00450	−	0.579949i	−0.0949246	−	0.995484i	$-0.530261\pi$
$743$	−27.3807	−	15.8083i	−1.00450	−	0.579949i	−0.909577	+	0.415535i	$0.863594\pi$
$744$		0			0
$745$	−21.7664	+	12.5669i	−0.797461	+	0.460414i
$746$		−	8.49897i		−	0.311169i
$747$		0			0
$748$			11.2332i			0.410727i
$749$	7.52490	+	10.6730i	0.274954	+	0.389982i
$750$		0			0
$751$	7.13680	−	12.3613i	0.260426	−	0.451070i	−0.705929	−	0.708282i	$-0.749470\pi$
$751$	7.13680	−	12.3613i	0.260426	−	0.451070i	0.966355	+	0.257212i	$0.0828038\pi$
$752$	0.504652	−	0.874082i	0.0184028	−	0.0318745i
$753$		0			0
$754$	11.9864	−	6.92036i	0.436519	−	0.252025i
$755$	1.57870			0.0574548
$756$		0			0
$757$	−10.8227			−0.393358			−0.196679	−	0.980468i	$-0.563016\pi$
$757$	−10.8227			−0.393358			−0.196679	+	0.980468i	$0.563016\pi$
$758$	−60.0134	+	34.6488i	−2.17979	+	1.25850i
$759$		0			0
$760$	−8.66182	+	15.0027i	−0.314197	+	0.544206i
$761$	−2.93098	+	5.07660i	−0.106248	+	0.184027i	−0.914247	−	0.405157i	$-0.867217\pi$
$761$	−2.93098	+	5.07660i	−0.106248	+	0.184027i	0.808000	+	0.589183i	$0.200550\pi$
$762$		0			0
$763$	17.5981	−	12.4074i	0.637095	−	0.449180i
$764$			72.2926i			2.61546i
$765$		0			0
$766$			38.6645i			1.39701i
$767$	41.9865	−	24.2409i	1.51604	−	0.875288i
$768$		0			0
$769$	27.5683	+	15.9166i	0.994140	+	0.573967i	0.906509	−	0.422186i	$-0.138737\pi$
$769$	27.5683	+	15.9166i	0.994140	+	0.573967i	0.0876307	+	0.996153i	$0.472070\pi$
$770$	−25.3642	−	11.7277i	−0.914061	−	0.422637i
$771$		0			0
$772$	26.8428	+	46.4931i	0.966094	+	1.67332i
$773$	−19.0382			−0.684755			−0.342378	−	0.939562i	$-0.611232\pi$
$773$	−19.0382			−0.684755			−0.342378	+	0.939562i	$0.611232\pi$
$774$		0			0
$775$			11.0191i			0.395818i
$776$	4.18965	+	7.25668i	0.150400	+	0.260500i
$777$		0			0
$778$	−12.3977	+	21.4734i	−0.444478	+	0.769859i
$779$	28.8948	+	16.6824i	1.03526	+	0.597710i
$780$		0			0
$781$	6.18427	+	10.7115i	0.221290	+	0.383286i
$782$	−9.95800			−0.356097
$783$		0			0
$784$	1.64652	−	0.301330i	0.0588042	−	0.0107618i
$785$	−12.1219	+	6.99857i	−0.432649	+	0.249790i
$786$		0			0
$787$	−16.4123	−	9.47564i	−0.585035	−	0.337770i	0.178097	−	0.984013i	$-0.443006\pi$
$787$	−16.4123	−	9.47564i	−0.585035	−	0.337770i	−0.763132	+	0.646243i	$0.776339\pi$
$788$	−24.6472	−	14.2301i	−0.878020	−	0.506925i
$789$		0			0
$790$	10.3494	−	5.97525i	0.368216	−	0.212590i
$791$	10.3355	−	0.937963i	0.367488	−	0.0333501i
$792$		0			0
$793$	−16.7141			−0.593535
$794$	25.3857	+	43.9693i	0.900905	+	1.56041i
$795$		0			0
$796$	−15.9422	−	9.20422i	−0.565055	−	0.326235i
$797$	26.7207	−	46.2816i	0.946497	−	1.63938i	0.193770	−	0.981047i	$-0.437929\pi$
$797$	26.7207	−	46.2816i	0.946497	−	1.63938i	0.752727	−	0.658333i	$-0.228738\pi$
$798$		0			0
$799$	−2.30314	−	3.98916i	−0.0814792	−	0.141126i
$800$			17.4376i			0.616511i
$801$		0			0
$802$	−54.8194			−1.93574
$803$	−11.8247	−	20.4810i	−0.417286	−	0.722760i
$804$		0			0
$805$	6.38383	−	13.8067i	0.225000	−	0.486621i
$806$	−37.7885	−	21.8172i	−1.33104	−	0.768479i
$807$		0			0
$808$	16.5190	−	9.53727i	0.581137	−	0.335520i
$809$		−	2.58095i		−	0.0907413i	−0.998970	−	0.0453706i	$-0.985553\pi$
$809$		−	2.58095i		−	0.0907413i	0.998970	−	0.0453706i	$-0.0144469\pi$
$810$		0			0
$811$		−	6.06938i		−	0.213125i	−0.994306	−	0.106562i	$-0.966016\pi$
$811$		−	6.06938i		−	0.213125i	0.994306	−	0.106562i	$-0.0339844\pi$
$812$	5.76163	+	8.17203i	0.202194	+	0.286782i
$813$		0			0
$814$	0.880438	−	1.52496i	0.0308593	−	0.0534500i
$815$	5.18169	−	8.97494i	0.181507	−	0.314379i
$816$		0			0
$817$	29.7272	−	17.1630i	1.04002	−	0.600458i
$818$	−59.9811			−2.09719
$819$		0			0
$820$	33.9201			1.18454
$821$	−8.03938	+	4.64154i	−0.280576	+	0.161991i	−0.633684	−	0.773592i	$-0.718458\pi$
$821$	−8.03938	+	4.64154i	−0.280576	+	0.161991i	0.353108	+	0.935583i	$0.385125\pi$
$822$		0			0
$823$	−9.03448	+	15.6482i	−0.314922	+	0.545461i	−0.979421	−	0.201828i	$-0.935312\pi$
$823$	−9.03448	+	15.6482i	−0.314922	+	0.545461i	0.664499	+	0.747289i	$0.268645\pi$
$824$	−2.29172	+	3.96937i	−0.0798357	+	0.138280i
$825$		0			0
$826$	32.8674	+	46.6176i	1.14360	+	1.62203i
$827$		−	48.5440i		−	1.68804i	−0.536310	−	0.844021i	$-0.680182\pi$
$827$		−	48.5440i		−	1.68804i	0.536310	−	0.844021i	$-0.319818\pi$
$828$		0			0
$829$			5.44792i			0.189214i	0.995515	+	0.0946071i	$0.0301595\pi$
$829$			5.44792i			0.189214i	−0.995515	+	0.0946071i	$0.969841\pi$
$830$	30.8344	−	17.8022i	1.07028	−	0.617924i
$831$		0			0
$832$	−57.6796	−	33.3013i	−1.99968	−	1.15452i
$833$	2.56623	−	7.19527i	0.0889147	−	0.249302i
$834$		0			0
$835$	−12.4126	−	21.4992i	−0.429556	−	0.744012i
$836$	−46.2076			−1.59812
$837$		0			0
$838$			73.6460i			2.54406i
$839$	24.2673	+	42.0322i	0.837801	+	1.45111i	0.891729	+	0.452569i	$0.149492\pi$
$839$	24.2673	+	42.0322i	0.837801	+	1.45111i	−0.0539281	+	0.998545i	$0.517174\pi$
$840$		0			0
$841$	−13.7947	+	23.8931i	−0.475678	+	0.823899i
$842$	−21.8727	−	12.6282i	−0.753781	−	0.435196i
$843$		0			0
$844$	41.1907	+	71.3444i	1.41784	+	2.45578i
$845$	−18.9412			−0.651598
$846$		0			0
$847$	0.128033	+	1.41081i	0.00439926	+	0.0484759i
$848$	1.45254	−	0.838622i	0.0498803	−	0.0287984i
$849$		0			0
$850$	6.33127	+	3.65536i	0.217161	+	0.125378i
$851$	0.830095	+	0.479256i	0.0284553	+	0.0164287i
$852$		0			0
$853$	−10.7703	+	6.21823i	−0.368768	+	0.212908i	−0.672920	−	0.739715i	$-0.734960\pi$
$853$	−10.7703	+	6.21823i	−0.368768	+	0.212908i	0.304152	+	0.952623i	$0.401627\pi$
$854$	−1.77726	−	19.5838i	−0.0608165	−	0.670144i
$855$		0			0
$856$	13.2801			0.453906
$857$	−5.29077	−	9.16388i	−0.180729	−	0.313032i	0.761400	−	0.648283i	$-0.224512\pi$
$857$	−5.29077	−	9.16388i	−0.180729	−	0.313032i	−0.942129	+	0.335250i	$0.891179\pi$
$858$		0			0
$859$	−28.1452	−	16.2496i	−0.960302	−	0.554431i	−0.0640360	−	0.997948i	$-0.520397\pi$
$859$	−28.1452	−	16.2496i	−0.960302	−	0.554431i	−0.896266	+	0.443517i	$0.853731\pi$
$860$	17.4487	−	30.2220i	0.594995	−	1.03056i
$861$		0			0
$862$	−18.5579	−	32.1432i	−0.632084	−	1.09480i
$863$		−	25.2203i		−	0.858510i	−0.903183	−	0.429255i	$-0.858776\pi$
$863$		−	25.2203i		−	0.858510i	0.903183	−	0.429255i	$-0.141224\pi$
$864$		0			0
$865$	−2.80576			−0.0953987
$866$	14.2683	+	24.7135i	0.484857	+	0.839797i
$867$		0			0
$868$	13.2295	−	28.6123i	0.449040	−	0.971164i
$869$	10.2540	+	5.92017i	0.347844	+	0.200828i
$870$		0			0
$871$	2.92685	−	1.68982i	0.0991724	−	0.0572572i
$872$		−	21.8970i		−	0.741525i
$873$		0			0
$874$		−	40.9621i		−	1.38556i
$875$	−24.6341	+	17.3681i	−0.832784	+	0.587149i
$876$		0			0
$877$	7.47893	−	12.9539i	0.252546	−	0.437422i	−0.711680	−	0.702503i	$-0.752066\pi$
$877$	7.47893	−	12.9539i	0.252546	−	0.437422i	0.964226	+	0.265082i	$0.0853989\pi$
$878$	21.1961	−	36.7127i	0.715333	−	1.23899i
$879$		0			0
$880$	0.960836	−	0.554739i	0.0323898	−	0.0187003i
$881$	36.4482			1.22797			0.613985	−	0.789318i	$-0.289566\pi$
$881$	36.4482			1.22797			0.613985	+	0.789318i	$0.289566\pi$
$882$		0			0
$883$	15.9831			0.537873			0.268936	−	0.963158i	$-0.413328\pi$
$883$	15.9831			0.537873			0.268936	+	0.963158i	$0.413328\pi$
$884$	−15.3948	+	8.88819i	−0.517783	+	0.298942i
$885$		0			0
$886$	−5.40739	+	9.36588i	−0.181665	+	0.314653i
$887$	−24.5208	+	42.4713i	−0.823329	+	1.42605i	0.0798613	+	0.996806i	$0.474552\pi$
$887$	−24.5208	+	42.4713i	−0.823329	+	1.42605i	−0.903190	+	0.429241i	$0.858781\pi$
$888$		0			0
$889$	13.3380	−	9.40383i	0.447341	−	0.315394i
$890$			44.7026i			1.49843i
$891$		0			0
$892$			56.8862i			1.90469i
$893$	16.4093	−	9.47393i	0.549117	−	0.317033i
$894$		0			0
$895$	−28.8196	−	16.6390i	−0.963332	−	0.556180i
$896$	19.7267	−	42.6641i	0.659023	−	1.42531i
$897$		0			0
$898$	−18.4834	−	32.0143i	−0.616801	−	1.06833i
$899$	−4.44728			−0.148325
$900$		0			0
$901$		−	7.65464i		−	0.255013i
$902$	27.3657	+	47.3987i	0.911177	+	1.57820i
$903$		0			0
$904$	5.27687	−	9.13981i	0.175506	−	0.303986i
$905$	12.7621	+	7.36821i	0.424227	+	0.244928i
$906$		0			0
$907$	2.42915	+	4.20741i	0.0806585	+	0.139705i	0.903533	−	0.428519i	$-0.140964\pi$
$907$	2.42915	+	4.20741i	0.0806585	+	0.139705i	−0.822874	+	0.568223i	$0.807631\pi$
$908$	−34.8973			−1.15811
$909$		0			0
$910$	−3.99673	−	44.0404i	−0.132490	−	1.45992i
$911$	−14.4945	+	8.36843i	−0.480226	+	0.277258i	−0.720510	−	0.693444i	$-0.756092\pi$
$911$	−14.4945	+	8.36843i	−0.480226	+	0.277258i	0.240285	+	0.970702i	$0.422759\pi$
$912$		0			0
$913$	30.5501	+	17.6381i	1.01106	+	0.583737i
$914$	11.3301	+	6.54143i	0.374766	+	0.216371i
$915$		0			0
$916$	53.5678	−	30.9274i	1.76993	−	1.02187i
$917$	−1.97582	−	21.7717i	−0.0652472	−	0.718965i
$918$		0			0
$919$	30.6400			1.01072			0.505360	−	0.862909i	$-0.331360\pi$
$919$	30.6400			1.01072			0.505360	+	0.862909i	$0.331360\pi$
$920$	−7.73436	−	13.3963i	−0.254994	−	0.441663i
$921$		0			0
$922$	71.5015	+	41.2814i	2.35478	+	1.35953i
$923$	−9.78651	+	16.9507i	−0.322127	+	0.557940i
$924$		0			0
$925$	−0.351848	−	0.609419i	−0.0115687	−	0.0200376i
$926$		−	66.5627i		−	2.18739i
$927$		0			0
$928$	−7.03775			−0.231025
$929$	−14.8723	−	25.7595i	−0.487943	−	0.845142i	0.511961	−	0.859009i	$-0.328919\pi$
$929$	−14.8723	−	25.7595i	−0.487943	−	0.845142i	−0.999904	+	0.0138670i	$0.995586\pi$
$930$		0			0
$931$	29.5976	+	10.5562i	0.970024	+	0.345964i
$932$	8.10245	+	4.67795i	0.265405	+	0.153231i
$933$		0			0
$934$	5.20876	−	3.00728i	0.170436	−	0.0984011i
$935$		−	5.06346i		−	0.165593i
$936$		0			0
$937$		−	4.03712i		−	0.131887i	−0.997823	−	0.0659434i	$-0.978994\pi$
$937$		−	4.03712i		−	0.131887i	0.997823	−	0.0659434i	$-0.0210057\pi$
$938$	2.29117	+	3.24968i	0.0748092	+	0.106106i
$939$		0			0
$940$	9.63160	−	16.6824i	0.314148	−	0.544121i
$941$	−7.20264	+	12.4753i	−0.234799	+	0.406684i	−0.959214	−	0.282680i	$-0.908777\pi$
$941$	−7.20264	+	12.4753i	−0.234799	+	0.406684i	0.724415	+	0.689364i	$0.242110\pi$
$942$		0			0
$943$	−25.8009	+	14.8962i	−0.840193	+	0.485085i
$944$	−2.26464			−0.0737079
$945$		0			0
$946$	56.3081			1.83073
$947$	−27.0334	+	15.6077i	−0.878467	+	0.507183i	−0.870153	−	0.492782i	$-0.835980\pi$
$947$	−27.0334	+	15.6077i	−0.878467	+	0.507183i	−0.00831468	+	0.999965i	$0.502647\pi$
$948$		0			0
$949$	18.7125	−	32.4109i	0.607432	−	1.05210i
$950$	−15.0363	+	26.0436i	−0.487841	+	0.844966i
$951$		0			0
$952$	−4.47646	−	6.34920i	−0.145083	−	0.205779i
$953$			8.55869i			0.277243i	0.990345	+	0.138622i	$0.0442672\pi$
$953$			8.55869i			0.277243i	−0.990345	+	0.138622i	$0.955733\pi$
$954$		0			0
$955$		−	32.5865i		−	1.05447i
$956$	34.1278	−	19.7037i	1.10377	−	0.637263i
$957$		0			0
$958$	−61.2751	−	35.3772i	−1.97971	−	1.14298i
$959$	11.4902	−	24.8506i	0.371039	−	0.802468i
$960$		0			0
$961$	−8.48973	−	14.7046i	−0.273862	−	0.474343i
$962$	2.78656			0.0898424
$963$		0			0
$964$			42.9669i			1.38387i
$965$	−12.0996	−	20.9572i	−0.389501	−	0.674635i
$966$		0			0
$967$	16.0280	−	27.7614i	0.515427	−	0.892745i	−0.484413	−	0.874840i	$-0.660967\pi$
$967$	16.0280	−	27.7614i	0.515427	−	0.892745i	0.999840	−	0.0179059i	$-0.00569994\pi$
$968$	1.24759	+	0.720299i	0.0400992	+	0.0231513i
$969$		0			0
$970$	−5.08414	−	8.80598i	−0.163242	−	0.282743i
$971$	−33.2366			−1.06661			−0.533307	−	0.845922i	$-0.679051\pi$
$971$	−33.2366			−1.06661			−0.533307	+	0.845922i	$0.679051\pi$
$972$		0			0
$973$	−47.0345	+	4.26845i	−1.50786	+	0.136840i
$974$	68.7469	−	39.6911i	2.20279	−	1.27178i
$975$		0			0
$976$	0.676137	+	0.390368i	0.0216426	+	0.0124954i
$977$	−45.1558	−	26.0707i	−1.44466	−	0.834076i	−0.446507	−	0.894780i	$-0.647332\pi$
$977$	−45.1558	−	26.0707i	−1.44466	−	0.834076i	−0.998156	+	0.0607042i	$0.980665\pi$
$978$		0			0
$979$	−38.3567	+	22.1453i	−1.22589	+	0.707765i
$980$	31.4248	−	5.75107i	1.00383	−	0.183711i
$981$		0			0
$982$	59.6044			1.90205
$983$	12.1192	+	20.9911i	0.386544	+	0.669513i	0.991982	−	0.126379i	$-0.0403356\pi$
$983$	12.1192	+	20.9911i	0.386544	+	0.669513i	−0.605438	+	0.795892i	$0.707002\pi$
$984$		0			0
$985$	11.1099	+	6.41432i	0.353992	+	0.204377i
$986$	−1.47529	+	2.55528i	−0.0469829	+	0.0813768i
$987$		0			0
$988$	−36.5614	−	63.3263i	−1.16317	−	2.01468i
$989$			30.6506i			0.974632i
$990$		0			0
$991$	−24.1981			−0.768678			−0.384339	−	0.923192i	$-0.625571\pi$
$991$	−24.1981			−0.768678			−0.384339	+	0.923192i	$0.625571\pi$
$992$	11.0937	+	19.2148i	0.352224	+	0.610070i
$993$		0			0
$994$	−20.9017	−	9.66437i	−0.662961	−	0.306535i
$995$	7.18607	+	4.14888i	0.227814	+	0.131528i
$996$		0			0
$997$	8.81920	−	5.09177i	0.279307	−	0.161258i	−0.353803	−	0.935320i	$-0.615112\pi$
$997$	8.81920	−	5.09177i	0.279307	−	0.161258i	0.633110	+	0.774062i	$0.281778\pi$
$998$			28.4053i			0.899155i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.o.a.125.5		12
3.2	odd	2		63.2.o.a.41.1	yes	12
4.3	odd	2		3024.2.cc.a.881.3		12
7.2	even	3		1323.2.s.c.962.2		12
7.3	odd	6		1323.2.i.c.1097.6		12
7.4	even	3		1323.2.i.c.1097.5		12
7.5	odd	6		1323.2.s.c.962.1		12
7.6	odd	2	inner	189.2.o.a.125.6		12
9.2	odd	6	inner	189.2.o.a.62.6		12
9.4	even	3		567.2.c.c.566.12		12
9.5	odd	6		567.2.c.c.566.1		12
9.7	even	3		63.2.o.a.20.2	yes	12
12.11	even	2		1008.2.cc.a.545.5		12
21.2	odd	6		441.2.s.c.374.6		12
21.5	even	6		441.2.s.c.374.5		12
21.11	odd	6		441.2.i.c.68.1		12
21.17	even	6		441.2.i.c.68.2		12
21.20	even	2		63.2.o.a.41.2	yes	12
28.27	even	2		3024.2.cc.a.881.4		12
36.7	odd	6		1008.2.cc.a.209.2		12
36.11	even	6		3024.2.cc.a.2897.4		12
63.2	odd	6		1323.2.i.c.521.2		12
63.11	odd	6		1323.2.s.c.656.1		12
63.13	odd	6		567.2.c.c.566.11		12
63.16	even	3		441.2.i.c.227.6		12
63.20	even	6	inner	189.2.o.a.62.5		12
63.25	even	3		441.2.s.c.362.5		12
63.34	odd	6		63.2.o.a.20.1	✓	12
63.38	even	6		1323.2.s.c.656.2		12
63.41	even	6		567.2.c.c.566.2		12
63.47	even	6		1323.2.i.c.521.1		12
63.52	odd	6		441.2.s.c.362.6		12
63.61	odd	6		441.2.i.c.227.5		12
84.83	odd	2		1008.2.cc.a.545.2		12
252.83	odd	6		3024.2.cc.a.2897.3		12
252.223	even	6		1008.2.cc.a.209.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.o.a.20.1	✓	12	63.34	odd	6
63.2.o.a.20.2	yes	12	9.7	even	3
63.2.o.a.41.1	yes	12	3.2	odd	2
63.2.o.a.41.2	yes	12	21.20	even	2
189.2.o.a.62.5		12	63.20	even	6	inner
189.2.o.a.62.6		12	9.2	odd	6	inner
189.2.o.a.125.5		12	1.1	even	1	trivial
189.2.o.a.125.6		12	7.6	odd	2	inner
441.2.i.c.68.1		12	21.11	odd	6
441.2.i.c.68.2		12	21.17	even	6
441.2.i.c.227.5		12	63.61	odd	6
441.2.i.c.227.6		12	63.16	even	3
441.2.s.c.362.5		12	63.25	even	3
441.2.s.c.362.6		12	63.52	odd	6
441.2.s.c.374.5		12	21.5	even	6
441.2.s.c.374.6		12	21.2	odd	6
567.2.c.c.566.1		12	9.5	odd	6
567.2.c.c.566.2		12	63.41	even	6
567.2.c.c.566.11		12	63.13	odd	6
567.2.c.c.566.12		12	9.4	even	3
1008.2.cc.a.209.2		12	36.7	odd	6
1008.2.cc.a.209.5		12	252.223	even	6
1008.2.cc.a.545.2		12	84.83	odd	2
1008.2.cc.a.545.5		12	12.11	even	2
1323.2.i.c.521.1		12	63.47	even	6
1323.2.i.c.521.2		12	63.2	odd	6
1323.2.i.c.1097.5		12	7.4	even	3
1323.2.i.c.1097.6		12	7.3	odd	6
1323.2.s.c.656.1		12	63.11	odd	6
1323.2.s.c.656.2		12	63.38	even	6
1323.2.s.c.962.1		12	7.5	odd	6
1323.2.s.c.962.2		12	7.2	even	3
3024.2.cc.a.881.3		12	4.3	odd	2
3024.2.cc.a.881.4		12	28.27	even	2
3024.2.cc.a.2897.3		12	252.83	odd	6
3024.2.cc.a.2897.4		12	36.11	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.97141 - 1.13819i) q^{2} +(1.59097 - 2.75564i) q^{4} +(-0.717144 + 1.24213i) q^{5} +(2.16235 - 1.52455i) q^{7} -2.69056i q^{8} +3.26499i q^{10} +(-2.80150 + 1.61745i) q^{11} +(-4.43334 - 2.55959i) q^{13} +(2.52764 - 5.46668i) q^{14} +(0.119562 + 0.207087i) q^{16} +1.09132 q^{17} +4.48911i q^{19} +(2.28191 + 3.95238i) q^{20} +(-3.68194 + 6.37731i) q^{22} +(-3.47141 - 2.00422i) q^{23} +(1.47141 + 2.54856i) q^{25} -11.6532 q^{26} +(-0.760877 - 8.38418i) q^{28} +(-1.02859 + 0.593857i) q^{29} +(3.24275 + 1.87220i) q^{31} +(5.13160 + 2.96273i) q^{32} +(2.15143 - 1.24213i) q^{34} +(0.342971 + 3.77924i) q^{35} -0.239123 q^{37} +(5.10948 + 8.84988i) q^{38} +(3.34203 + 1.92952i) q^{40} +(3.71620 - 6.43664i) q^{41} +(-3.82326 - 6.62208i) q^{43} +10.2933i q^{44} -9.12476 q^{46} +(-2.11042 - 3.65536i) q^{47} +(2.35150 - 6.59321i) q^{49} +(5.80150 + 3.34950i) q^{50} +(-14.1066 + 8.14447i) q^{52} -7.01414i q^{53} -4.63977i q^{55} +(-4.10189 - 5.81793i) q^{56} +(-1.35185 + 2.34147i) q^{58} +(-4.73531 + 8.20179i) q^{59} +(2.82757 - 1.63250i) q^{61} +8.52371 q^{62} +13.0104 q^{64} +(6.35868 - 3.67119i) q^{65} +(-0.330095 + 0.571741i) q^{67} +(1.73625 - 3.00728i) q^{68} +(4.97764 + 7.06006i) q^{70} -3.82347i q^{71} +7.31073i q^{73} +(-0.471410 + 0.272169i) q^{74} +(12.3704 + 7.14205i) q^{76} +(-3.59195 + 7.76852i) q^{77} +(-1.83009 - 3.16982i) q^{79} -0.342971 q^{80} -16.9190i q^{82} +(-5.45245 - 9.44392i) q^{83} +(-0.782630 + 1.35556i) q^{85} +(-15.0744 - 8.70322i) q^{86} +(4.35185 + 7.53762i) q^{88} +13.6915 q^{89} +(-13.4887 + 1.22412i) q^{91} +(-11.0458 + 6.37731i) q^{92} +(-8.32102 - 4.80415i) q^{94} +(-5.57605 - 3.21934i) q^{95} +(-2.69709 + 1.55716i) q^{97} +(-2.86857 - 15.6744i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{2} + 2 q^{4} - 2 q^{7} + 12 q^{14} + 2 q^{16} - 10 q^{22} - 24 q^{23} - 8 q^{28} - 30 q^{29} + 12 q^{32} - 4 q^{37} - 10 q^{43} - 40 q^{46} + 6 q^{49} + 36 q^{50} - 42 q^{56} + 2 q^{58} + 16 q^{64}+ \cdots - 72 q^{95}+O(q^{100}) \) 12 * q + 6 * q^2 + 2 * q^4 - 2 * q^7 + 12 * q^14 + 2 * q^16 - 10 * q^22 - 24 * q^23 - 8 * q^28 - 30 * q^29 + 12 * q^32 - 4 * q^37 - 10 * q^43 - 40 * q^46 + 6 * q^49 + 36 * q^50 - 42 * q^56 + 2 * q^58 + 16 * q^64 + 78 * q^65 + 12 * q^67 + 18 * q^70 + 12 * q^74 + 24 * q^77 - 6 * q^79 - 6 * q^85 - 96 * q^86 + 34 * q^88 - 24 * q^91 - 30 * q^92 - 72 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more