LMFDB - Embedded newform 405.2.e.k.271.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [405,2,Mod(136,405)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(405, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("405.136");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	405.e (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:	$3.23394128186$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{13})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 4x^{2} + 3x + 9 $ x^4 - x^3 + 4x^2 + 3x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			271.1
Root			$-0.651388 - 1.12824i$ of defining polynomial
Character	$\chi$	$=$	405.271
Dual form			405.2.e.k.136.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.651388 - 1.12824i) q^{2} +(0.151388 - 0.262211i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-2.30278 - 3.98852i) q^{7} -3.00000 q^{8} +O(q^{10})$	\(q+(-0.651388 - 1.12824i) q^{2} +(0.151388 - 0.262211i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-2.30278 - 3.98852i) q^{7} -3.00000 q^{8} +1.30278 q^{10} +(1.30278 + 2.25647i) q^{11} +(0.302776 - 0.524423i) q^{13} +(-3.00000 + 5.19615i) q^{14} +(1.65139 + 2.86029i) q^{16} -5.60555 q^{17} -3.60555 q^{19} +(0.151388 + 0.262211i) q^{20} +(1.69722 - 2.93968i) q^{22} +(1.50000 - 2.59808i) q^{23} +(-0.500000 - 0.866025i) q^{25} -0.788897 q^{26} -1.39445 q^{28} +(-4.30278 - 7.45263i) q^{29} +(-0.802776 + 1.39045i) q^{31} +(-0.848612 + 1.46984i) q^{32} +(3.65139 + 6.32439i) q^{34} +4.60555 q^{35} +2.00000 q^{37} +(2.34861 + 4.06792i) q^{38} +(1.50000 - 2.59808i) q^{40} +(-1.30278 + 2.25647i) q^{41} +(3.30278 + 5.72058i) q^{43} +0.788897 q^{44} -3.90833 q^{46} +(-2.60555 - 4.51295i) q^{47} +(-7.10555 + 12.3072i) q^{49} +(-0.651388 + 1.12824i) q^{50} +(-0.0916731 - 0.158782i) q^{52} -5.60555 q^{53} -2.60555 q^{55} +(6.90833 + 11.9656i) q^{56} +(-5.60555 + 9.70910i) q^{58} +(4.30278 - 7.45263i) q^{59} +(-5.10555 - 8.84307i) q^{61} +2.09167 q^{62} +8.81665 q^{64} +(0.302776 + 0.524423i) q^{65} +(7.60555 - 13.1732i) q^{67} +(-0.848612 + 1.46984i) q^{68} +(-3.00000 - 5.19615i) q^{70} +14.6056 q^{71} +5.39445 q^{73} +(-1.30278 - 2.25647i) q^{74} +(-0.545837 + 0.945417i) q^{76} +(6.00000 - 10.3923i) q^{77} +(2.19722 + 3.80570i) q^{79} -3.30278 q^{80} +3.39445 q^{82} +(-1.50000 - 2.59808i) q^{83} +(2.80278 - 4.85455i) q^{85} +(4.30278 - 7.45263i) q^{86} +(-3.90833 - 6.76942i) q^{88} +7.81665 q^{89} -2.78890 q^{91} +(-0.454163 - 0.786634i) q^{92} +(-3.39445 + 5.87936i) q^{94} +(1.80278 - 3.12250i) q^{95} +(-4.00000 - 6.92820i) q^{97} +18.5139 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} - 3 q^{4} - 2 q^{5} - 2 q^{7} - 12 q^{8}+O(q^{10}) $ 4 * q + q^2 - 3 * q^4 - 2 * q^5 - 2 * q^7 - 12 * q^8	$ 4 q + q^{2} - 3 q^{4} - 2 q^{5} - 2 q^{7} - 12 q^{8} - 2 q^{10} - 2 q^{11} - 6 q^{13} - 12 q^{14} + 3 q^{16} - 8 q^{17} - 3 q^{20} + 14 q^{22} + 6 q^{23} - 2 q^{25} - 32 q^{26} - 20 q^{28} - 10 q^{29} + 4 q^{31} - 7 q^{32} + 11 q^{34} + 4 q^{35} + 8 q^{37} + 13 q^{38} + 6 q^{40} + 2 q^{41} + 6 q^{43} + 32 q^{44} + 6 q^{46} + 4 q^{47} - 14 q^{49} + q^{50} - 22 q^{52} - 8 q^{53} + 4 q^{55} + 6 q^{56} - 8 q^{58} + 10 q^{59} - 6 q^{61} + 30 q^{62} - 8 q^{64} - 6 q^{65} + 16 q^{67} - 7 q^{68} - 12 q^{70} + 44 q^{71} + 36 q^{73} + 2 q^{74} - 13 q^{76} + 24 q^{77} + 16 q^{79} - 6 q^{80} + 28 q^{82} - 6 q^{83} + 4 q^{85} + 10 q^{86} + 6 q^{88} - 12 q^{89} - 40 q^{91} + 9 q^{92} - 28 q^{94} - 16 q^{97} + 38 q^{98}+O(q^{100}) $ 4 * q + q^2 - 3 * q^4 - 2 * q^5 - 2 * q^7 - 12 * q^8 - 2 * q^10 - 2 * q^11 - 6 * q^13 - 12 * q^14 + 3 * q^16 - 8 * q^17 - 3 * q^20 + 14 * q^22 + 6 * q^23 - 2 * q^25 - 32 * q^26 - 20 * q^28 - 10 * q^29 + 4 * q^31 - 7 * q^32 + 11 * q^34 + 4 * q^35 + 8 * q^37 + 13 * q^38 + 6 * q^40 + 2 * q^41 + 6 * q^43 + 32 * q^44 + 6 * q^46 + 4 * q^47 - 14 * q^49 + q^50 - 22 * q^52 - 8 * q^53 + 4 * q^55 + 6 * q^56 - 8 * q^58 + 10 * q^59 - 6 * q^61 + 30 * q^62 - 8 * q^64 - 6 * q^65 + 16 * q^67 - 7 * q^68 - 12 * q^70 + 44 * q^71 + 36 * q^73 + 2 * q^74 - 13 * q^76 + 24 * q^77 + 16 * q^79 - 6 * q^80 + 28 * q^82 - 6 * q^83 + 4 * q^85 + 10 * q^86 + 6 * q^88 - 12 * q^89 - 40 * q^91 + 9 * q^92 - 28 * q^94 - 16 * q^97 + 38 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.651388	−	1.12824i	−0.460601	−	0.797784i	0.538390	−	0.842696i	$-0.319033\pi$
$2$	−0.651388	−	1.12824i	−0.460601	−	0.797784i	−0.998991	+	0.0449118i	$0.985699\pi$
$3$		0			0
$3$		0			0
$4$	0.151388	−	0.262211i	0.0756939	−	0.131106i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$		0			0
$7$	−2.30278	−	3.98852i	−0.870367	−	1.50752i	−0.861617	−	0.507559i	$-0.830548\pi$
$7$	−2.30278	−	3.98852i	−0.870367	−	1.50752i	−0.00875026	−	0.999962i	$-0.502785\pi$
$8$	−3.00000			−1.06066
$9$		0			0
$10$	1.30278			0.411974
$11$	1.30278	+	2.25647i	0.392802	+	0.680352i	0.992818	−	0.119635i	$-0.0381726\pi$
$11$	1.30278	+	2.25647i	0.392802	+	0.680352i	−0.600016	+	0.799988i	$0.704839\pi$
$12$		0			0
$13$	0.302776	−	0.524423i	0.0839749	−	0.145449i	−0.820979	−	0.570958i	$-0.806572\pi$
$13$	0.302776	−	0.524423i	0.0839749	−	0.145449i	0.904954	+	0.425510i	$0.139905\pi$
$14$	−3.00000	+	5.19615i	−0.801784	+	1.38873i
$15$		0			0
$16$	1.65139	+	2.86029i	0.412847	+	0.715072i
$17$	−5.60555			−1.35955			−0.679773	−	0.733423i	$-0.737922\pi$
$17$	−5.60555			−1.35955			−0.679773	+	0.733423i	$0.737922\pi$
$18$		0			0
$19$	−3.60555			−0.827170			−0.413585	−	0.910465i	$-0.635724\pi$
$19$	−3.60555			−0.827170			−0.413585	+	0.910465i	$0.635724\pi$
$20$	0.151388	+	0.262211i	0.0338513	+	0.0586323i
$21$		0			0
$22$	1.69722	−	2.93968i	0.361849	−	0.626742i
$23$	1.50000	−	2.59808i	0.312772	−	0.541736i	−0.666190	−	0.745782i	$-0.732076\pi$
$23$	1.50000	−	2.59808i	0.312772	−	0.541736i	0.978961	+	0.204046i	$0.0654092\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−0.788897			−0.154716
$27$		0			0
$28$	−1.39445			−0.263526
$29$	−4.30278	−	7.45263i	−0.799005	−	1.38392i	−0.920264	−	0.391297i	$-0.872027\pi$
$29$	−4.30278	−	7.45263i	−0.799005	−	1.38392i	0.121259	−	0.992621i	$-0.461307\pi$
$30$		0			0
$31$	−0.802776	+	1.39045i	−0.144183	+	0.249732i	−0.929068	−	0.369910i	$-0.879389\pi$
$31$	−0.802776	+	1.39045i	−0.144183	+	0.249732i	0.784885	+	0.619641i	$0.212722\pi$
$32$	−0.848612	+	1.46984i	−0.150015	+	0.259833i
$33$		0			0
$34$	3.65139	+	6.32439i	0.626208	+	1.08462i
$35$	4.60555			0.778480
$36$		0			0
$37$	2.00000			0.328798			0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000			0.328798			0.164399	+	0.986394i	$0.447432\pi$
$38$	2.34861	+	4.06792i	0.380995	+	0.659903i
$39$		0			0
$40$	1.50000	−	2.59808i	0.237171	−	0.410792i
$41$	−1.30278	+	2.25647i	−0.203459	+	0.352402i	−0.949641	−	0.313341i	$-0.898552\pi$
$41$	−1.30278	+	2.25647i	−0.203459	+	0.352402i	0.746181	+	0.665743i	$0.231885\pi$
$42$		0			0
$43$	3.30278	+	5.72058i	0.503669	+	0.872380i	0.999991	+	0.00424128i	$0.00135005\pi$
$43$	3.30278	+	5.72058i	0.503669	+	0.872380i	−0.496322	+	0.868138i	$0.665317\pi$
$44$	0.788897			0.118931
$45$		0			0
$46$	−3.90833			−0.576251
$47$	−2.60555	−	4.51295i	−0.380059	−	0.658281i	0.611012	−	0.791622i	$-0.290763\pi$
$47$	−2.60555	−	4.51295i	−0.380059	−	0.658281i	−0.991070	+	0.133341i	$0.957430\pi$
$48$		0			0
$49$	−7.10555	+	12.3072i	−1.01508	+	1.75817i
$50$	−0.651388	+	1.12824i	−0.0921201	+	0.159557i
$51$		0			0
$52$	−0.0916731	−	0.158782i	−0.0127128	−	0.0220192i
$53$	−5.60555			−0.769982			−0.384991	−	0.922920i	$-0.625795\pi$
$53$	−5.60555			−0.769982			−0.384991	+	0.922920i	$0.625795\pi$
$54$		0			0
$55$	−2.60555			−0.351332
$56$	6.90833	+	11.9656i	0.923164	+	1.59897i
$57$		0			0
$58$	−5.60555	+	9.70910i	−0.736045	+	1.27487i
$59$	4.30278	−	7.45263i	0.560174	−	0.970249i	−0.437307	−	0.899312i	$-0.644068\pi$
$59$	4.30278	−	7.45263i	0.560174	−	0.970249i	0.997481	−	0.0709370i	$-0.0225989\pi$
$60$		0			0
$61$	−5.10555	−	8.84307i	−0.653699	−	1.13224i	−0.982218	−	0.187742i	$-0.939883\pi$
$61$	−5.10555	−	8.84307i	−0.653699	−	1.13224i	0.328519	−	0.944497i	$-0.393450\pi$
$62$	2.09167			0.265643
$63$		0			0
$64$	8.81665			1.10208
$65$	0.302776	+	0.524423i	0.0375547	+	0.0650466i
$66$		0			0
$67$	7.60555	−	13.1732i	0.929166	−	1.60936i	0.144446	−	0.989513i	$-0.453860\pi$
$67$	7.60555	−	13.1732i	0.929166	−	1.60936i	0.784720	−	0.619850i	$-0.212807\pi$
$68$	−0.848612	+	1.46984i	−0.102909	+	0.178244i
$69$		0			0
$70$	−3.00000	−	5.19615i	−0.358569	−	0.621059i
$71$	14.6056			1.73336			0.866680	−	0.498864i	$-0.166249\pi$
$71$	14.6056			1.73336			0.866680	+	0.498864i	$0.166249\pi$
$72$		0			0
$73$	5.39445			0.631372			0.315686	−	0.948864i	$-0.397765\pi$
$73$	5.39445			0.631372			0.315686	+	0.948864i	$0.397765\pi$
$74$	−1.30278	−	2.25647i	−0.151445	−	0.262310i
$75$		0			0
$76$	−0.545837	+	0.945417i	−0.0626117	+	0.108447i
$77$	6.00000	−	10.3923i	0.683763	−	1.18431i
$78$		0			0
$79$	2.19722	+	3.80570i	0.247207	+	0.428175i	0.962750	−	0.270394i	$-0.0871539\pi$
$79$	2.19722	+	3.80570i	0.247207	+	0.428175i	−0.715543	+	0.698569i	$0.753821\pi$
$80$	−3.30278			−0.369262
$81$		0			0
$82$	3.39445			0.374854
$83$	−1.50000	−	2.59808i	−0.164646	−	0.285176i	0.771883	−	0.635764i	$-0.219315\pi$
$83$	−1.50000	−	2.59808i	−0.164646	−	0.285176i	−0.936530	+	0.350588i	$0.885982\pi$
$84$		0			0
$85$	2.80278	−	4.85455i	0.304004	−	0.526550i
$86$	4.30278	−	7.45263i	0.463980	−	0.803637i
$87$		0			0
$88$	−3.90833	−	6.76942i	−0.416629	−	0.721623i
$89$	7.81665			0.828564			0.414282	−	0.910149i	$-0.364033\pi$
$89$	7.81665			0.828564			0.414282	+	0.910149i	$0.364033\pi$
$90$		0			0
$91$	−2.78890			−0.292356
$92$	−0.454163	−	0.786634i	−0.0473498	−	0.0820123i
$93$		0			0
$94$	−3.39445	+	5.87936i	−0.350111	+	0.606409i
$95$	1.80278	−	3.12250i	0.184961	−	0.320362i
$96$		0			0
$97$	−4.00000	−	6.92820i	−0.406138	−	0.703452i	0.588315	−	0.808632i	$-0.299792\pi$
$97$	−4.00000	−	6.92820i	−0.406138	−	0.703452i	−0.994453	+	0.105180i	$0.966458\pi$
$98$	18.5139			1.87018
$99$		0			0
$100$	−0.302776			−0.0302776
$101$	−6.00000	−	10.3923i	−0.597022	−	1.03407i	−0.993258	−	0.115924i	$-0.963017\pi$
$101$	−6.00000	−	10.3923i	−0.597022	−	1.03407i	0.396236	−	0.918149i	$-0.370316\pi$
$102$		0			0
$103$	2.00000	−	3.46410i	0.197066	−	0.341328i	−0.750510	−	0.660859i	$-0.770192\pi$
$103$	2.00000	−	3.46410i	0.197066	−	0.341328i	0.947576	+	0.319531i	$0.103525\pi$
$104$	−0.908327	+	1.57327i	−0.0890688	+	0.154272i
$105$		0			0
$106$	3.65139	+	6.32439i	0.354654	+	0.614279i
$107$		0			0			−	1.00000i	$-0.5\pi$
$107$		0			0				1.00000i	$0.5\pi$
$108$		0			0
$109$	−7.00000			−0.670478			−0.335239	−	0.942133i	$-0.608817\pi$
$109$	−7.00000			−0.670478			−0.335239	+	0.942133i	$0.608817\pi$
$110$	1.69722	+	2.93968i	0.161824	+	0.280287i
$111$		0			0
$112$	7.60555	−	13.1732i	0.718657	−	1.24475i
$113$	0.394449	−	0.683205i	0.0371066	−	0.0642705i	−0.846876	−	0.531791i	$-0.821519\pi$
$113$	0.394449	−	0.683205i	0.0371066	−	0.0642705i	0.883982	+	0.467520i	$0.154853\pi$
$114$		0			0
$115$	1.50000	+	2.59808i	0.139876	+	0.242272i
$116$	−2.60555			−0.241919
$117$		0			0
$118$	−11.2111			−1.03207
$119$	12.9083	+	22.3579i	1.18330	+	2.04954i
$120$		0			0
$121$	2.10555	−	3.64692i	0.191414	−	0.331538i
$122$	−6.65139	+	11.5205i	−0.602188	+	1.04302i
$123$		0			0
$124$	0.243061	+	0.420994i	0.0218275	+	0.0378064i
$125$	1.00000			0.0894427
$126$		0			0
$127$	−4.78890			−0.424946			−0.212473	−	0.977167i	$-0.568152\pi$
$127$	−4.78890			−0.424946			−0.212473	+	0.977167i	$0.568152\pi$
$128$	−4.04584	−	7.00759i	−0.357605	−	0.619390i
$129$		0			0
$130$	0.394449	−	0.683205i	0.0345954	−	0.0599211i
$131$	−3.00000	+	5.19615i	−0.262111	+	0.453990i	−0.966803	−	0.255524i	$-0.917752\pi$
$131$	−3.00000	+	5.19615i	−0.262111	+	0.453990i	0.704692	+	0.709514i	$0.251085\pi$
$132$		0			0
$133$	8.30278	+	14.3808i	0.719942	+	1.24698i
$134$	−19.8167			−1.71190
$135$		0			0
$136$	16.8167			1.44202
$137$	2.40833	+	4.17134i	0.205757	+	0.356382i	0.950374	−	0.311111i	$-0.100701\pi$
$137$	2.40833	+	4.17134i	0.205757	+	0.356382i	−0.744616	+	0.667493i	$0.767368\pi$
$138$		0			0
$139$	2.00000	−	3.46410i	0.169638	−	0.293821i	−0.768655	−	0.639664i	$-0.779074\pi$
$139$	2.00000	−	3.46410i	0.169638	−	0.293821i	0.938293	+	0.345843i	$0.112407\pi$
$140$	0.697224	−	1.20763i	0.0589262	−	0.102063i
$141$		0			0
$142$	−9.51388	−	16.4785i	−0.798387	−	1.38285i
$143$	1.57779			0.131942
$144$		0			0
$145$	8.60555			0.714652
$146$	−3.51388	−	6.08622i	−0.290811	−	0.503699i
$147$		0			0
$148$	0.302776	−	0.524423i	0.0248880	−	0.0431073i
$149$	6.51388	−	11.2824i	0.533638	−	0.924288i	−0.465590	−	0.885000i	$-0.654158\pi$
$149$	6.51388	−	11.2824i	0.533638	−	0.924288i	0.999228	−	0.0392872i	$-0.0125087\pi$
$150$		0			0
$151$	7.21110	+	12.4900i	0.586831	+	1.01642i	0.994644	+	0.103356i	$0.0329581\pi$
$151$	7.21110	+	12.4900i	0.586831	+	1.01642i	−0.407813	+	0.913065i	$0.633709\pi$
$152$	10.8167			0.877346
$153$		0			0
$154$	−15.6333			−1.25977
$155$	−0.802776	−	1.39045i	−0.0644805	−	0.111683i
$156$		0			0
$157$	−1.90833	+	3.30532i	−0.152301	+	0.263793i	−0.932073	−	0.362270i	$-0.882002\pi$
$157$	−1.90833	+	3.30532i	−0.152301	+	0.263793i	0.779772	+	0.626064i	$0.215335\pi$
$158$	2.86249	−	4.95798i	0.227728	−	0.394436i
$159$		0			0
$160$	−0.848612	−	1.46984i	−0.0670887	−	0.116201i
$161$	−13.8167			−1.08890
$162$		0			0
$163$	2.00000			0.156652			0.0783260	−	0.996928i	$-0.475042\pi$
$163$	2.00000			0.156652			0.0783260	+	0.996928i	$0.475042\pi$
$164$	0.394449	+	0.683205i	0.0308013	+	0.0533494i
$165$		0			0
$166$	−1.95416	+	3.38471i	−0.151672	+	0.262704i
$167$	1.50000	−	2.59808i	0.116073	−	0.201045i	−0.802135	−	0.597143i	$-0.796303\pi$
$167$	1.50000	−	2.59808i	0.116073	−	0.201045i	0.918208	+	0.396098i	$0.129636\pi$
$168$		0			0
$169$	6.31665	+	10.9408i	0.485896	+	0.841597i
$170$	−7.30278			−0.560097
$171$		0			0
$172$	2.00000			0.152499
$173$	−5.40833	−	9.36750i	−0.411187	−	0.712198i	0.583832	−	0.811874i	$-0.301553\pi$
$173$	−5.40833	−	9.36750i	−0.411187	−	0.712198i	−0.995020	+	0.0996766i	$0.968219\pi$
$174$		0			0
$175$	−2.30278	+	3.98852i	−0.174073	+	0.301504i
$176$	−4.30278	+	7.45263i	−0.324334	+	0.561763i
$177$		0			0
$178$	−5.09167	−	8.81904i	−0.381637	−	0.661015i
$179$	−6.78890			−0.507426			−0.253713	−	0.967280i	$-0.581652\pi$
$179$	−6.78890			−0.507426			−0.253713	+	0.967280i	$0.581652\pi$
$180$		0			0
$181$	−7.00000			−0.520306			−0.260153	−	0.965567i	$-0.583773\pi$
$181$	−7.00000			−0.520306			−0.260153	+	0.965567i	$0.583773\pi$
$182$	1.81665	+	3.14654i	0.134659	+	0.233237i
$183$		0			0
$184$	−4.50000	+	7.79423i	−0.331744	+	0.574598i
$185$	−1.00000	+	1.73205i	−0.0735215	+	0.127343i
$186$		0			0
$187$	−7.30278	−	12.6488i	−0.534032	−	0.924970i
$188$	−1.57779			−0.115073
$189$		0			0
$190$	−4.69722			−0.340772
$191$	−8.21110	−	14.2220i	−0.594135	−	1.02907i	−0.993668	−	0.112353i	$-0.964161\pi$
$191$	−8.21110	−	14.2220i	−0.594135	−	1.02907i	0.399534	−	0.916718i	$-0.369172\pi$
$192$		0			0
$193$	−10.9083	+	18.8938i	−0.785199	+	1.36000i	0.143682	+	0.989624i	$0.454106\pi$
$193$	−10.9083	+	18.8938i	−0.785199	+	1.36000i	−0.928880	+	0.370380i	$0.879228\pi$
$194$	−5.21110	+	9.02589i	−0.374135	+	0.648021i
$195$		0			0
$196$	2.15139	+	3.72631i	0.153671	+	0.266165i
$197$	−1.18335			−0.0843099			−0.0421550	−	0.999111i	$-0.513422\pi$
$197$	−1.18335			−0.0843099			−0.0421550	+	0.999111i	$0.513422\pi$
$198$		0			0
$199$	13.2111			0.936510			0.468255	−	0.883593i	$-0.344883\pi$
$199$	13.2111			0.936510			0.468255	+	0.883593i	$0.344883\pi$
$200$	1.50000	+	2.59808i	0.106066	+	0.183712i
$201$		0			0
$202$	−7.81665	+	13.5388i	−0.549978	+	0.952590i
$203$	−19.8167	+	34.3235i	−1.39086	+	2.40903i
$204$		0			0
$205$	−1.30278	−	2.25647i	−0.0909898	−	0.157599i
$206$	−5.21110			−0.363075
$207$		0			0
$208$	2.00000			0.138675
$209$	−4.69722	−	8.13583i	−0.324914	−	0.562767i
$210$		0			0
$211$	−6.40833	+	11.0995i	−0.441167	+	0.764124i	−0.997776	−	0.0666502i	$-0.978769\pi$
$211$	−6.40833	+	11.0995i	−0.441167	+	0.764124i	0.556609	+	0.830775i	$0.312102\pi$
$212$	−0.848612	+	1.46984i	−0.0582829	+	0.100949i
$213$		0			0
$214$		0			0
$215$	−6.60555			−0.450495
$216$		0			0
$217$	7.39445			0.501968
$218$	4.55971	+	7.89766i	0.308823	+	0.534897i
$219$		0			0
$220$	−0.394449	+	0.683205i	−0.0265937	+	0.0460617i
$221$	−1.69722	+	2.93968i	−0.114168	+	0.197744i
$222$		0			0
$223$	5.00000	+	8.66025i	0.334825	+	0.579934i	0.983451	−	0.181173i	$-0.0579895\pi$
$223$	5.00000	+	8.66025i	0.334825	+	0.579934i	−0.648626	+	0.761107i	$0.724656\pi$
$224$	7.81665			0.522272
$225$		0			0
$226$	−1.02776			−0.0683653
$227$	13.1056	+	22.6995i	0.869846	+	1.50662i	0.862154	+	0.506647i	$0.169115\pi$
$227$	13.1056	+	22.6995i	0.869846	+	1.50662i	0.00769242	+	0.999970i	$0.497551\pi$
$228$		0			0
$229$	3.10555	−	5.37897i	0.205221	−	0.355453i	−0.744982	−	0.667084i	$-0.767542\pi$
$229$	3.10555	−	5.37897i	0.205221	−	0.355453i	0.950203	+	0.311632i	$0.100875\pi$
$230$	1.95416	−	3.38471i	0.128854	−	0.223181i
$231$		0			0
$232$	12.9083	+	22.3579i	0.847473	+	1.46787i
$233$	−18.0000			−1.17922			−0.589610	−	0.807688i	$-0.700718\pi$
$233$	−18.0000			−1.17922			−0.589610	+	0.807688i	$0.700718\pi$
$234$		0			0
$235$	5.21110			0.339935
$236$	−1.30278	−	2.25647i	−0.0848035	−	0.146884i
$237$		0			0
$238$	16.8167	−	29.1273i	1.09006	−	1.88804i
$239$	0.394449	−	0.683205i	0.0255148	−	0.0441929i	−0.852986	−	0.521934i	$-0.825211\pi$
$239$	0.394449	−	0.683205i	0.0255148	−	0.0441929i	0.878501	+	0.477741i	$0.158544\pi$
$240$		0			0
$241$	−14.1056	−	24.4315i	−0.908618	−	1.57377i	−0.815985	−	0.578073i	$-0.803805\pi$
$241$	−14.1056	−	24.4315i	−0.908618	−	1.57377i	−0.0926334	−	0.995700i	$-0.529528\pi$
$242$	−5.48612			−0.352661
$243$		0			0
$244$	−3.09167			−0.197924
$245$	−7.10555	−	12.3072i	−0.453957	−	0.786277i
$246$		0			0
$247$	−1.09167	+	1.89083i	−0.0694615	+	0.120311i
$248$	2.40833	−	4.17134i	0.152929	−	0.264881i
$249$		0			0
$250$	−0.651388	−	1.12824i	−0.0411974	−	0.0713560i
$251$	−15.6333			−0.986766			−0.493383	−	0.869812i	$-0.664240\pi$
$251$	−15.6333			−0.986766			−0.493383	+	0.869812i	$0.664240\pi$
$252$		0			0
$253$	7.81665			0.491429
$254$	3.11943	+	5.40301i	0.195730	+	0.339015i
$255$		0			0
$256$	3.54584	−	6.14157i	0.221615	−	0.383848i
$257$	−11.4083	+	19.7598i	−0.711632	+	1.23258i	0.252612	+	0.967568i	$0.418710\pi$
$257$	−11.4083	+	19.7598i	−0.711632	+	1.23258i	−0.964244	+	0.265015i	$0.914623\pi$
$258$		0			0
$259$	−4.60555	−	7.97705i	−0.286175	−	0.495670i
$260$	0.183346			0.0113706
$261$		0			0
$262$	7.81665			0.482914
$263$	8.60555	+	14.9053i	0.530641	+	0.919097i	0.999361	+	0.0357503i	$0.0113821\pi$
$263$	8.60555	+	14.9053i	0.530641	+	0.919097i	−0.468720	+	0.883347i	$0.655285\pi$
$264$		0			0
$265$	2.80278	−	4.85455i	0.172173	−	0.298213i
$266$	10.8167	−	18.7350i	0.663212	−	1.14872i
$267$		0			0
$268$	−2.30278	−	3.98852i	−0.140664	−	0.243638i
$269$	11.2111			0.683553			0.341776	−	0.939781i	$-0.388971\pi$
$269$	11.2111			0.683553			0.341776	+	0.939781i	$0.388971\pi$
$270$		0			0
$271$	−19.2389			−1.16868			−0.584339	−	0.811510i	$-0.698646\pi$
$271$	−19.2389			−1.16868			−0.584339	+	0.811510i	$0.698646\pi$
$272$	−9.25694	−	16.0335i	−0.561284	−	0.972173i
$273$		0			0
$274$	3.13751	−	5.43433i	0.189544	−	0.328300i
$275$	1.30278	−	2.25647i	0.0785603	−	0.136070i
$276$		0			0
$277$	14.5139	+	25.1388i	0.872054	+	1.51044i	0.859868	+	0.510517i	$0.170546\pi$
$277$	14.5139	+	25.1388i	0.872054	+	1.51044i	0.0121867	+	0.999926i	$0.496121\pi$
$278$	−5.21110			−0.312541
$279$		0			0
$280$	−13.8167			−0.825703
$281$	−0.908327	−	1.57327i	−0.0541862	−	0.0938533i	0.837660	−	0.546192i	$-0.183923\pi$
$281$	−0.908327	−	1.57327i	−0.0541862	−	0.0938533i	−0.891846	+	0.452339i	$0.850590\pi$
$282$		0			0
$283$	−5.30278	+	9.18468i	−0.315217	+	0.545972i	−0.979484	−	0.201524i	$-0.935411\pi$
$283$	−5.30278	+	9.18468i	−0.315217	+	0.545972i	0.664266	+	0.747496i	$0.268744\pi$
$284$	2.21110	−	3.82974i	0.131205	−	0.227253i
$285$		0			0
$286$	−1.02776	−	1.78013i	−0.0607725	−	0.105261i
$287$	12.0000			0.708338
$288$		0			0
$289$	14.4222			0.848365
$290$	−5.60555	−	9.70910i	−0.329169	−	0.570138i
$291$		0			0
$292$	0.816654	−	1.41449i	0.0477911	−	0.0827765i
$293$	14.4083	−	24.9560i	0.841743	−	1.45794i	−0.0466761	−	0.998910i	$-0.514863\pi$
$293$	14.4083	−	24.9560i	0.841743	−	1.45794i	0.888420	−	0.459032i	$-0.151804\pi$
$294$		0			0
$295$	4.30278	+	7.45263i	0.250517	+	0.433909i
$296$	−6.00000			−0.348743
$297$		0			0
$298$	−16.9722			−0.983176
$299$	−0.908327	−	1.57327i	−0.0525299	−	0.0909845i
$300$		0			0
$301$	15.2111	−	26.3464i	0.876753	−	1.51858i
$302$	9.39445	−	16.2717i	0.540590	−	0.936329i
$303$		0			0
$304$	−5.95416	−	10.3129i	−0.341495	−	0.591486i
$305$	10.2111			0.584686
$306$		0			0
$307$	−20.4222			−1.16556			−0.582778	−	0.812631i	$-0.698034\pi$
$307$	−20.4222			−1.16556			−0.582778	+	0.812631i	$0.698034\pi$
$308$	−1.81665	−	3.14654i	−0.103513	−	0.179291i
$309$		0			0
$310$	−1.04584	+	1.81144i	−0.0593995	+	0.102883i
$311$	−6.90833	+	11.9656i	−0.391735	+	0.678505i	−0.992679	−	0.120786i	$-0.961458\pi$
$311$	−6.90833	+	11.9656i	−0.391735	+	0.678505i	0.600943	+	0.799292i	$0.294792\pi$
$312$		0			0
$313$	−11.8167	−	20.4670i	−0.667917	−	1.15687i	−0.978486	−	0.206315i	$-0.933853\pi$
$313$	−11.8167	−	20.4670i	−0.667917	−	1.15687i	0.310569	−	0.950551i	$-0.399480\pi$
$314$	4.97224			0.280600
$315$		0			0
$316$	1.33053			0.0748483
$317$	0.197224	+	0.341603i	0.0110772	+	0.0191863i	0.871511	−	0.490376i	$-0.163141\pi$
$317$	0.197224	+	0.341603i	0.0110772	+	0.0191863i	−0.860434	+	0.509562i	$0.829807\pi$
$318$		0			0
$319$	11.2111	−	19.4182i	0.627701	−	1.08721i
$320$	−4.40833	+	7.63545i	−0.246433	+	0.426834i
$321$		0			0
$322$	9.00000	+	15.5885i	0.501550	+	0.868711i
$323$	20.2111			1.12458
$324$		0			0
$325$	−0.605551			−0.0335899
$326$	−1.30278	−	2.25647i	−0.0721541	−	0.124975i
$327$		0			0
$328$	3.90833	−	6.76942i	0.215801	−	0.373779i
$329$	−12.0000	+	20.7846i	−0.661581	+	1.14589i
$330$		0			0
$331$	−7.39445	−	12.8076i	−0.406436	−	0.703967i	0.588052	−	0.808823i	$-0.299895\pi$
$331$	−7.39445	−	12.8076i	−0.406436	−	0.703967i	−0.994487	+	0.104856i	$0.966562\pi$
$332$	−0.908327			−0.0498509
$333$		0			0
$334$	−3.90833			−0.213854
$335$	7.60555	+	13.1732i	0.415536	+	0.719729i
$336$		0			0
$337$	0.302776	−	0.524423i	0.0164932	−	0.0285671i	−0.857661	−	0.514216i	$-0.828083\pi$
$337$	0.302776	−	0.524423i	0.0164932	−	0.0285671i	0.874154	+	0.485648i	$0.161416\pi$
$338$	8.22918	−	14.2534i	0.447609	−	0.775281i
$339$		0			0
$340$	−0.848612	−	1.46984i	−0.0460225	−	0.0797132i
$341$	−4.18335			−0.226541
$342$		0			0
$343$	33.2111			1.79323
$344$	−9.90833	−	17.1617i	−0.534221	−	0.925298i
$345$		0			0
$346$	−7.04584	+	12.2037i	−0.378787	+	0.656077i
$347$	−0.788897	+	1.36641i	−0.0423502	+	0.0733528i	−0.886424	−	0.462875i	$-0.846818\pi$
$347$	−0.788897	+	1.36641i	−0.0423502	+	0.0733528i	0.844073	+	0.536228i	$0.180151\pi$
$348$		0			0
$349$	−12.9222	−	22.3819i	−0.691710	−	1.19808i	−0.971277	−	0.237950i	$-0.923524\pi$
$349$	−12.9222	−	22.3819i	−0.691710	−	1.19808i	0.279568	−	0.960126i	$-0.409809\pi$
$350$	6.00000			0.320713
$351$		0			0
$352$	−4.42221			−0.235704
$353$	10.8167	+	18.7350i	0.575712	+	0.997163i	0.995964	+	0.0897554i	$0.0286085\pi$
$353$	10.8167	+	18.7350i	0.575712	+	0.997163i	−0.420251	+	0.907408i	$0.638058\pi$
$354$		0			0
$355$	−7.30278	+	12.6488i	−0.387591	+	0.671327i
$356$	1.18335	−	2.04962i	0.0627172	−	0.108629i
$357$		0			0
$358$	4.42221	+	7.65948i	0.233721	+	0.404816i
$359$	33.6333			1.77510			0.887549	−	0.460713i	$-0.152406\pi$
$359$	33.6333			1.77510			0.887549	+	0.460713i	$0.152406\pi$
$360$		0			0
$361$	−6.00000			−0.315789
$362$	4.55971	+	7.89766i	0.239653	+	0.415092i
$363$		0			0
$364$	−0.422205	+	0.731281i	−0.0221296	+	0.0383295i
$365$	−2.69722	+	4.67173i	−0.141179	+	0.244530i
$366$		0			0
$367$	−2.30278	−	3.98852i	−0.120204	−	0.208199i	0.799644	−	0.600474i	$-0.205022\pi$
$367$	−2.30278	−	3.98852i	−0.120204	−	0.208199i	−0.919848	+	0.392275i	$0.871688\pi$
$368$	9.90833			0.516507
$369$		0			0
$370$	2.60555			0.135456
$371$	12.9083	+	22.3579i	0.670167	+	1.16076i
$372$		0			0
$373$	5.39445	−	9.34346i	0.279314	−	0.483786i	−0.691900	−	0.721993i	$-0.743226\pi$
$373$	5.39445	−	9.34346i	0.279314	−	0.483786i	0.971214	+	0.238207i	$0.0765596\pi$
$374$	−9.51388	+	16.4785i	−0.491951	+	0.852084i
$375$		0			0
$376$	7.81665	+	13.5388i	0.403113	+	0.698212i
$377$	−5.21110			−0.268385
$378$		0			0
$379$	14.3944			0.739393			0.369697	−	0.929153i	$-0.379462\pi$
$379$	14.3944			0.739393			0.369697	+	0.929153i	$0.379462\pi$
$380$	−0.545837	−	0.945417i	−0.0280008	−	0.0484988i
$381$		0			0
$382$	−10.6972	+	18.5281i	−0.547318	+	0.947982i
$383$	9.31665	−	16.1369i	0.476059	−	0.824558i	−0.523565	−	0.851986i	$-0.675398\pi$
$383$	9.31665	−	16.1369i	0.476059	−	0.824558i	0.999624	+	0.0274277i	$0.00873162\pi$
$384$		0			0
$385$	6.00000	+	10.3923i	0.305788	+	0.529641i
$386$	28.4222			1.44665
$387$		0			0
$388$	−2.42221			−0.122969
$389$	−2.09167	−	3.62288i	−0.106052	−	0.183688i	0.808116	−	0.589024i	$-0.200488\pi$
$389$	−2.09167	−	3.62288i	−0.106052	−	0.183688i	−0.914168	+	0.405337i	$0.867154\pi$
$390$		0			0
$391$	−8.40833	+	14.5636i	−0.425227	+	0.736515i
$392$	21.3167	−	36.9215i	1.07665	−	1.86482i
$393$		0			0
$394$	0.770817	+	1.33509i	0.0388332	+	0.0672611i
$395$	−4.39445			−0.221109
$396$		0			0
$397$	−12.6056			−0.632654			−0.316327	−	0.948650i	$-0.602450\pi$
$397$	−12.6056			−0.632654			−0.316327	+	0.948650i	$0.602450\pi$
$398$	−8.60555	−	14.9053i	−0.431357	−	0.747133i
$399$		0			0
$400$	1.65139	−	2.86029i	0.0825694	−	0.143014i
$401$	15.0000	−	25.9808i	0.749064	−	1.29742i	−0.199207	−	0.979957i	$-0.563837\pi$
$401$	15.0000	−	25.9808i	0.749064	−	1.29742i	0.948272	−	0.317460i	$-0.102830\pi$
$402$		0			0
$403$	0.486122	+	0.841988i	0.0242155	+	0.0419424i
$404$	−3.63331			−0.180764
$405$		0			0
$406$	51.6333			2.56252
$407$	2.60555	+	4.51295i	0.129152	+	0.223698i
$408$		0			0
$409$	−2.50000	+	4.33013i	−0.123617	+	0.214111i	−0.921192	−	0.389109i	$-0.872783\pi$
$409$	−2.50000	+	4.33013i	−0.123617	+	0.214111i	0.797574	+	0.603220i	$0.206116\pi$
$410$	−1.69722	+	2.93968i	−0.0838199	+	0.145180i
$411$		0			0
$412$	−0.605551	−	1.04885i	−0.0298334	−	0.0516729i
$413$	−39.6333			−1.95023
$414$		0			0
$415$	3.00000			0.147264
$416$	0.513878	+	0.890063i	0.0251950	+	0.0436389i
$417$		0			0
$418$	−6.11943	+	10.5992i	−0.299311	+	0.518422i
$419$	6.51388	−	11.2824i	0.318224	−	0.551180i	−0.661894	−	0.749598i	$-0.730247\pi$
$419$	6.51388	−	11.2824i	0.318224	−	0.551180i	0.980118	+	0.198418i	$0.0635803\pi$
$420$		0			0
$421$	11.7111	+	20.2842i	0.570764	+	0.988593i	0.996488	+	0.0837393i	$0.0266863\pi$
$421$	11.7111	+	20.2842i	0.570764	+	0.988593i	−0.425723	+	0.904853i	$0.639980\pi$
$422$	16.6972			0.812808
$423$		0			0
$424$	16.8167			0.816689
$425$	2.80278	+	4.85455i	0.135955	+	0.235480i
$426$		0			0
$427$	−23.5139	+	40.7272i	−1.13792	+	1.97093i
$428$		0			0
$429$		0			0
$430$	4.30278	+	7.45263i	0.207498	+	0.359398i
$431$	25.8167			1.24354			0.621772	−	0.783198i	$-0.286413\pi$
$431$	25.8167			1.24354			0.621772	+	0.783198i	$0.286413\pi$
$432$		0			0
$433$	−28.2389			−1.35707			−0.678536	−	0.734567i	$-0.737385\pi$
$433$	−28.2389			−1.35707			−0.678536	+	0.734567i	$0.737385\pi$
$434$	−4.81665	−	8.34269i	−0.231207	−	0.400462i
$435$		0			0
$436$	−1.05971	+	1.83548i	−0.0507511	+	0.0879035i
$437$	−5.40833	+	9.36750i	−0.258715	+	0.448108i
$438$		0			0
$439$	−10.1972	−	17.6621i	−0.486687	−	0.842967i	0.513196	−	0.858271i	$-0.328461\pi$
$439$	−10.1972	−	17.6621i	−0.486687	−	0.842967i	−0.999883	+	0.0153049i	$0.995128\pi$
$440$	7.81665			0.372644
$441$		0			0
$442$	4.42221			0.210343
$443$	−9.31665	−	16.1369i	−0.442648	−	0.766688i	0.555237	−	0.831692i	$-0.312627\pi$
$443$	−9.31665	−	16.1369i	−0.442648	−	0.766688i	−0.997885	+	0.0650038i	$0.979294\pi$
$444$		0			0
$445$	−3.90833	+	6.76942i	−0.185272	+	0.320901i
$446$	6.51388	−	11.2824i	0.308441	−	0.534236i
$447$		0			0
$448$	−20.3028	−	35.1654i	−0.959216	−	1.66141i
$449$	−12.2389			−0.577587			−0.288794	−	0.957391i	$-0.593254\pi$
$449$	−12.2389			−0.577587			−0.288794	+	0.957391i	$0.593254\pi$
$450$		0			0
$451$	−6.78890			−0.319677
$452$	−0.119429	−	0.206858i	−0.00561749	−	0.00972978i
$453$		0			0
$454$	17.0736	−	29.5723i	0.801303	−	1.38790i
$455$	1.39445	−	2.41526i	0.0653728	−	0.113229i
$456$		0			0
$457$	−0.605551	−	1.04885i	−0.0283265	−	0.0490629i	0.851515	−	0.524331i	$-0.175684\pi$
$457$	−0.605551	−	1.04885i	−0.0283265	−	0.0490629i	−0.879841	+	0.475268i	$0.842351\pi$
$458$	−8.09167			−0.378099
$459$		0			0
$460$	0.908327			0.0423510
$461$	10.8167	+	18.7350i	0.503782	+	0.872576i	0.999990	+	0.00437236i	$0.00139177\pi$
$461$	10.8167	+	18.7350i	0.503782	+	0.872576i	−0.496209	+	0.868203i	$0.665275\pi$
$462$		0			0
$463$	7.60555	−	13.1732i	0.353460	−	0.612211i	−0.633393	−	0.773830i	$-0.718338\pi$
$463$	7.60555	−	13.1732i	0.353460	−	0.612211i	0.986853	+	0.161620i	$0.0516717\pi$
$464$	14.2111	−	24.6144i	0.659734	−	1.14269i
$465$		0			0
$466$	11.7250	+	20.3083i	0.543149	+	0.940762i
$467$	−2.21110			−0.102318			−0.0511588	−	0.998691i	$-0.516291\pi$
$467$	−2.21110			−0.102318			−0.0511588	+	0.998691i	$0.516291\pi$
$468$		0			0
$469$	−70.0555			−3.23486
$470$	−3.39445	−	5.87936i	−0.156574	−	0.271195i
$471$		0			0
$472$	−12.9083	+	22.3579i	−0.594154	+	1.02910i
$473$	−8.60555	+	14.9053i	−0.395684	+	0.685344i
$474$		0			0
$475$	1.80278	+	3.12250i	0.0827170	+	0.143270i
$476$	7.81665			0.358276
$477$		0			0
$478$	−1.02776			−0.0470085
$479$	8.09167	+	14.0152i	0.369718	+	0.640370i	0.989521	−	0.144387i	$-0.0461210\pi$
$479$	8.09167	+	14.0152i	0.369718	+	0.640370i	−0.619803	+	0.784757i	$0.712788\pi$
$480$		0			0
$481$	0.605551	−	1.04885i	0.0276108	−	0.0478232i
$482$	−18.3764	+	31.8288i	−0.837021	+	1.44976i
$483$		0			0
$484$	−0.637510	−	1.10420i	−0.0289777	−	0.0501909i
$485$	8.00000			0.363261
$486$		0			0
$487$	−8.18335			−0.370823			−0.185411	−	0.982661i	$-0.559362\pi$
$487$	−8.18335			−0.370823			−0.185411	+	0.982661i	$0.559362\pi$
$488$	15.3167	+	26.5292i	0.693352	+	1.20092i
$489$		0			0
$490$	−9.25694	+	16.0335i	−0.418186	+	0.724319i
$491$	−6.39445	+	11.0755i	−0.288577	+	0.499831i	−0.973470	−	0.228813i	$-0.926516\pi$
$491$	−6.39445	+	11.0755i	−0.288577	+	0.499831i	0.684893	+	0.728644i	$0.259849\pi$
$492$		0			0
$493$	24.1194	+	41.7761i	1.08628	+	1.88150i
$494$	2.84441			0.127976
$495$		0			0
$496$	−5.30278			−0.238102
$497$	−33.6333	−	58.2546i	−1.50866	−	2.61308i
$498$		0			0
$499$	13.8028	−	23.9071i	0.617897	−	1.07023i	−0.371972	−	0.928244i	$-0.621318\pi$
$499$	13.8028	−	23.9071i	0.617897	−	1.07023i	0.989869	−	0.141985i	$-0.0453485\pi$
$500$	0.151388	−	0.262211i	0.00677027	−	0.0117265i
$501$		0			0
$502$	10.1833	+	17.6381i	0.454505	+	0.787226i
$503$	31.4222			1.40105			0.700523	−	0.713629i	$-0.252950\pi$
$503$	31.4222			1.40105			0.700523	+	0.713629i	$0.252950\pi$
$504$		0			0
$505$	12.0000			0.533993
$506$	−5.09167	−	8.81904i	−0.226352	−	0.392054i
$507$		0			0
$508$	−0.724981	+	1.25570i	−0.0321658	+	0.0557128i
$509$	−16.4222	+	28.4441i	−0.727901	+	1.26076i	0.229867	+	0.973222i	$0.426171\pi$
$509$	−16.4222	+	28.4441i	−0.727901	+	1.26076i	−0.957769	+	0.287540i	$0.907162\pi$
$510$		0			0
$511$	−12.4222	−	21.5159i	−0.549526	−	0.951807i
$512$	−25.4222			−1.12351
$513$		0			0
$514$	29.7250			1.31111
$515$	2.00000	+	3.46410i	0.0881305	+	0.152647i
$516$		0			0
$517$	6.78890	−	11.7587i	0.298575	−	0.517148i
$518$	−6.00000	+	10.3923i	−0.263625	+	0.456612i
$519$		0			0
$520$	−0.908327	−	1.57327i	−0.0398328	−	0.0689924i
$521$	−21.3944			−0.937308			−0.468654	−	0.883382i	$-0.655261\pi$
$521$	−21.3944			−0.937308			−0.468654	+	0.883382i	$0.655261\pi$
$522$		0			0
$523$	23.3944			1.02297			0.511484	−	0.859293i	$-0.329096\pi$
$523$	23.3944			1.02297			0.511484	+	0.859293i	$0.329096\pi$
$524$	0.908327	+	1.57327i	0.0396804	+	0.0687285i
$525$		0			0
$526$	11.2111	−	19.4182i	0.488827	−	0.846674i
$527$	4.50000	−	7.79423i	0.196023	−	0.339522i
$528$		0			0
$529$	7.00000	+	12.1244i	0.304348	+	0.527146i
$530$	−7.30278			−0.317212
$531$		0			0
$532$	5.02776			0.217981
$533$	0.788897	+	1.36641i	0.0341709	+	0.0591858i
$534$		0			0
$535$		0			0
$536$	−22.8167	+	39.5196i	−0.985529	+	1.70699i
$537$		0			0
$538$	−7.30278	−	12.6488i	−0.314845	−	0.545328i
$539$	−37.0278			−1.59490
$540$		0			0
$541$	−11.5778			−0.497768			−0.248884	−	0.968533i	$-0.580064\pi$
$541$	−11.5778			−0.497768			−0.248884	+	0.968533i	$0.580064\pi$
$542$	12.5320	+	21.7060i	0.538294	+	0.932352i
$543$		0			0
$544$	4.75694	−	8.23926i	0.203952	−	0.353255i
$545$	3.50000	−	6.06218i	0.149924	−	0.259675i
$546$		0			0
$547$	3.30278	+	5.72058i	0.141216	+	0.244594i	0.927955	−	0.372692i	$-0.121565\pi$
$547$	3.30278	+	5.72058i	0.141216	+	0.244594i	−0.786738	+	0.617286i	$0.788232\pi$
$548$	1.45837			0.0622983
$549$		0			0
$550$	−3.39445			−0.144740
$551$	15.5139	+	26.8708i	0.660913	+	1.14474i
$552$		0			0
$553$	10.1194	−	17.5274i	0.430322	−	0.745339i
$554$	18.9083	−	32.7502i	0.803338	−	1.39142i
$555$		0			0
$556$	−0.605551	−	1.04885i	−0.0256811	−	0.0444810i
$557$	−33.6333			−1.42509			−0.712544	−	0.701627i	$-0.752457\pi$
$557$	−33.6333			−1.42509			−0.712544	+	0.701627i	$0.752457\pi$
$558$		0			0
$559$	4.00000			0.169182
$560$	7.60555	+	13.1732i	0.321393	+	0.556669i
$561$		0			0
$562$	−1.18335	+	2.04962i	−0.0499164	+	0.0864578i
$563$	−12.0000	+	20.7846i	−0.505740	+	0.875967i	0.494238	+	0.869326i	$0.335447\pi$
$563$	−12.0000	+	20.7846i	−0.505740	+	0.875967i	−0.999978	+	0.00664037i	$0.997886\pi$
$564$		0			0
$565$	0.394449	+	0.683205i	0.0165946	+	0.0287427i
$566$	13.8167			0.580757
$567$		0			0
$568$	−43.8167			−1.83851
$569$	−18.9083	−	32.7502i	−0.792678	−	1.37296i	−0.924303	−	0.381659i	$-0.875353\pi$
$569$	−18.9083	−	32.7502i	−0.792678	−	1.37296i	0.131625	−	0.991300i	$-0.457981\pi$
$570$		0			0
$571$	18.2250	−	31.5666i	0.762692	−	1.32102i	−0.178767	−	0.983891i	$-0.557211\pi$
$571$	18.2250	−	31.5666i	0.762692	−	1.32102i	0.941458	−	0.337129i	$-0.109456\pi$
$572$	0.238859	−	0.413716i	0.00998719	−	0.0172983i
$573$		0			0
$574$	−7.81665	−	13.5388i	−0.326261	−	0.565100i
$575$	−3.00000			−0.125109
$576$		0			0
$577$	27.8167			1.15802			0.579011	−	0.815320i	$-0.303439\pi$
$577$	27.8167			1.15802			0.579011	+	0.815320i	$0.303439\pi$
$578$	−9.39445	−	16.2717i	−0.390758	−	0.676812i
$579$		0			0
$580$	1.30278	−	2.25647i	0.0540948	−	0.0936950i
$581$	−6.90833	+	11.9656i	−0.286606	+	0.496416i
$582$		0			0
$583$	−7.30278	−	12.6488i	−0.302450	−	0.523859i
$584$	−16.1833			−0.669672
$585$		0			0
$586$	−37.5416			−1.55083
$587$	−10.5000	−	18.1865i	−0.433381	−	0.750639i	0.563781	−	0.825925i	$-0.309346\pi$
$587$	−10.5000	−	18.1865i	−0.433381	−	0.750639i	−0.997162	+	0.0752860i	$0.976013\pi$
$588$		0			0
$589$	2.89445	−	5.01333i	0.119264	−	0.206571i
$590$	5.60555	−	9.70910i	0.230777	−	0.399717i
$591$		0			0
$592$	3.30278	+	5.72058i	0.135743	+	0.235114i
$593$	21.2389			0.872175			0.436088	−	0.899904i	$-0.356364\pi$
$593$	21.2389			0.872175			0.436088	+	0.899904i	$0.356364\pi$
$594$		0			0
$595$	−25.8167			−1.05838
$596$	−1.97224	−	3.41603i	−0.0807862	−	0.139926i
$597$		0			0
$598$	−1.18335	+	2.04962i	−0.0483906	+	0.0838150i
$599$	7.69722	−	13.3320i	0.314500	−	0.544730i	−0.664831	−	0.746994i	$-0.731496\pi$
$599$	7.69722	−	13.3320i	0.314500	−	0.544730i	0.979331	+	0.202264i	$0.0648298\pi$
$600$		0			0
$601$	−16.3167	−	28.2613i	−0.665570	−	1.15280i	−0.979130	−	0.203233i	$-0.934855\pi$
$601$	−16.3167	−	28.2613i	−0.665570	−	1.15280i	0.313560	−	0.949568i	$-0.398478\pi$
$602$	−39.6333			−1.61533
$603$		0			0
$604$	4.36669			0.177678
$605$	2.10555	+	3.64692i	0.0856028	+	0.148268i
$606$		0			0
$607$	−8.69722	+	15.0640i	−0.353009	+	0.611430i	−0.986775	−	0.162095i	$-0.948175\pi$
$607$	−8.69722	+	15.0640i	−0.353009	+	0.611430i	0.633766	+	0.773525i	$0.281508\pi$
$608$	3.05971	−	5.29958i	0.124088	−	0.214926i
$609$		0			0
$610$	−6.65139	−	11.5205i	−0.269307	−	0.466453i
$611$	−3.15559			−0.127661
$612$		0			0
$613$	28.8444			1.16501			0.582507	−	0.812825i	$-0.302072\pi$
$613$	28.8444			1.16501			0.582507	+	0.812825i	$0.302072\pi$
$614$	13.3028	+	23.0411i	0.536856	+	0.929862i
$615$		0			0
$616$	−18.0000	+	31.1769i	−0.725241	+	1.25615i
$617$	13.2250	−	22.9063i	0.532418	−	0.922174i	−0.466866	−	0.884328i	$-0.654617\pi$
$617$	13.2250	−	22.9063i	0.532418	−	0.922174i	0.999284	−	0.0378463i	$-0.0120497\pi$
$618$		0			0
$619$	3.81665	+	6.61064i	0.153404	+	0.265704i	0.932477	−	0.361230i	$-0.117643\pi$
$619$	3.81665	+	6.61064i	0.153404	+	0.265704i	−0.779073	+	0.626934i	$0.784310\pi$
$620$	−0.486122			−0.0195231
$621$		0			0
$622$	18.0000			0.721734
$623$	−18.0000	−	31.1769i	−0.721155	−	1.24908i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−15.3944	+	26.6640i	−0.615286	+	1.06571i
$627$		0			0
$628$	0.577795	+	1.00077i	0.0230565	+	0.0399351i
$629$	−11.2111			−0.447016
$630$		0			0
$631$	30.0278			1.19539			0.597693	−	0.801725i	$-0.296084\pi$
$631$	30.0278			1.19539			0.597693	+	0.801725i	$0.296084\pi$
$632$	−6.59167	−	11.4171i	−0.262203	−	0.454148i
$633$		0			0
$634$	0.256939	−	0.445032i	0.0102044	−	0.0176745i
$635$	2.39445	−	4.14731i	0.0950208	−	0.164581i
$636$		0			0
$637$	4.30278	+	7.45263i	0.170482	+	0.295284i
$638$	−29.2111			−1.15648
$639$		0			0
$640$	8.09167			0.319851
$641$	12.0000	+	20.7846i	0.473972	+	0.820943i	0.999556	−	0.0297987i	$-0.00948663\pi$
$641$	12.0000	+	20.7846i	0.473972	+	0.820943i	−0.525584	+	0.850741i	$0.676153\pi$
$642$		0			0
$643$	11.5139	−	19.9426i	0.454063	−	0.786460i	−0.544571	−	0.838715i	$-0.683307\pi$
$643$	11.5139	−	19.9426i	0.454063	−	0.786460i	0.998634	+	0.0522547i	$0.0166408\pi$
$644$	−2.09167	+	3.62288i	−0.0824235	+	0.142762i
$645$		0			0
$646$	−13.1653	−	22.8029i	−0.517980	−	0.897168i
$647$	38.2111			1.50223			0.751117	−	0.660169i	$-0.229516\pi$
$647$	38.2111			1.50223			0.751117	+	0.660169i	$0.229516\pi$
$648$		0			0
$649$	22.4222			0.880149
$650$	0.394449	+	0.683205i	0.0154716	+	0.0267975i
$651$		0			0
$652$	0.302776	−	0.524423i	0.0118576	−	0.0205380i
$653$	−13.6194	+	23.5895i	−0.532969	+	0.923130i	0.466289	+	0.884632i	$0.345591\pi$
$653$	−13.6194	+	23.5895i	−0.532969	+	0.923130i	−0.999259	+	0.0384979i	$0.987743\pi$
$654$		0			0
$655$	−3.00000	−	5.19615i	−0.117220	−	0.203030i
$656$	−8.60555			−0.335990
$657$		0			0
$658$	31.2666			1.21890
$659$	10.3028	+	17.8449i	0.401339	+	0.695140i	0.993888	−	0.110395i	$-0.0352115\pi$
$659$	10.3028	+	17.8449i	0.401339	+	0.695140i	−0.592549	+	0.805535i	$0.701878\pi$
$660$		0			0
$661$	−11.4222	+	19.7838i	−0.444272	+	0.769502i	−0.998001	−	0.0631948i	$-0.979871\pi$
$661$	−11.4222	+	19.7838i	−0.444272	+	0.769502i	0.553729	+	0.832697i	$0.313204\pi$
$662$	−9.63331	+	16.6854i	−0.374409	+	0.648496i
$663$		0			0
$664$	4.50000	+	7.79423i	0.174634	+	0.302475i
$665$	−16.6056			−0.643936
$666$		0			0
$667$	−25.8167			−0.999625
$668$	−0.454163	−	0.786634i	−0.0175721	−	0.0304358i
$669$		0			0
$670$	9.90833	−	17.1617i	0.382792	−	0.663015i
$671$	13.3028	−	23.0411i	0.513548	−	0.889491i
$672$		0			0
$673$	5.51388	+	9.55032i	0.212544	+	0.368138i	0.952510	−	0.304507i	$-0.0984917\pi$
$673$	5.51388	+	9.55032i	0.212544	+	0.368138i	−0.739966	+	0.672645i	$0.765158\pi$
$674$	−0.788897			−0.0303872
$675$		0			0
$676$	3.82506			0.147118
$677$	10.8167	+	18.7350i	0.415718	+	0.720044i	0.995504	−	0.0947247i	$-0.0301971\pi$
$677$	10.8167	+	18.7350i	0.415718	+	0.720044i	−0.579786	+	0.814769i	$0.696864\pi$
$678$		0			0
$679$	−18.4222	+	31.9082i	−0.706979	+	1.22452i
$680$	−8.40833	+	14.5636i	−0.322445	+	0.558490i
$681$		0			0
$682$	2.72498	+	4.71981i	0.104345	+	0.180731i
$683$	−9.00000			−0.344375			−0.172188	−	0.985064i	$-0.555084\pi$
$683$	−9.00000			−0.344375			−0.172188	+	0.985064i	$0.555084\pi$
$684$		0			0
$685$	−4.81665			−0.184035
$686$	−21.6333	−	37.4700i	−0.825964	−	1.43061i
$687$		0			0
$688$	−10.9083	+	18.8938i	−0.415876	+	0.720318i
$689$	−1.69722	+	2.93968i	−0.0646591	+	0.111993i
$690$		0			0
$691$	−1.19722	−	2.07365i	−0.0455446	−	0.0788855i	0.842354	−	0.538924i	$-0.181169\pi$
$691$	−1.19722	−	2.07365i	−0.0455446	−	0.0788855i	−0.887899	+	0.460038i	$0.847836\pi$
$692$	−3.27502			−0.124498
$693$		0			0
$694$	2.05551			0.0780262
$695$	2.00000	+	3.46410i	0.0758643	+	0.131401i
$696$		0			0
$697$	7.30278	−	12.6488i	0.276612	−	0.479107i
$698$	−16.8347	+	29.1586i	−0.637204	+	1.10367i
$699$		0			0
$700$	0.697224	+	1.20763i	0.0263526	+	0.0456440i
$701$	40.4222			1.52673			0.763363	−	0.645970i	$-0.223547\pi$
$701$	40.4222			1.52673			0.763363	+	0.645970i	$0.223547\pi$
$702$		0			0
$703$	−7.21110			−0.271972
$704$	11.4861	+	19.8945i	0.432900	+	0.749804i
$705$		0			0
$706$	14.0917	−	24.4075i	0.530347	−	0.918588i
$707$	−27.6333	+	47.8623i	−1.03926	+	1.80005i
$708$		0			0
$709$	−17.4222	−	30.1761i	−0.654305	−	1.13329i	−0.982068	−	0.188529i	$-0.939628\pi$
$709$	−17.4222	−	30.1761i	−0.654305	−	1.13329i	0.327763	−	0.944760i	$-0.393705\pi$
$710$	19.0278			0.714099
$711$		0			0
$712$	−23.4500			−0.878824
$713$	2.40833	+	4.17134i	0.0901926	+	0.156218i
$714$		0			0
$715$	−0.788897	+	1.36641i	−0.0295031	+	0.0511009i
$716$	−1.02776	+	1.78013i	−0.0384091	+	0.0665264i
$717$		0			0
$718$	−21.9083	−	37.9463i	−0.817611	−	1.41614i
$719$	−49.2666			−1.83733			−0.918667	−	0.395032i	$-0.870733\pi$
$719$	−49.2666			−1.83733			−0.918667	+	0.395032i	$0.870733\pi$
$720$		0			0
$721$	−18.4222			−0.686079
$722$	3.90833	+	6.76942i	0.145453	+	0.251932i
$723$		0			0
$724$	−1.05971	+	1.83548i	−0.0393840	+	0.0682151i
$725$	−4.30278	+	7.45263i	−0.159801	+	0.276784i
$726$		0			0
$727$	3.81665	+	6.61064i	0.141552	+	0.245175i	0.928081	−	0.372378i	$-0.121457\pi$
$727$	3.81665	+	6.61064i	0.141552	+	0.245175i	−0.786529	+	0.617553i	$0.788124\pi$
$728$	8.36669			0.310090
$729$		0			0
$730$	7.02776			0.260109
$731$	−18.5139	−	32.0670i	−0.684761	−	1.18604i
$732$		0			0
$733$	−16.0000	+	27.7128i	−0.590973	+	1.02360i	0.403128	+	0.915144i	$0.367923\pi$
$733$	−16.0000	+	27.7128i	−0.590973	+	1.02360i	−0.994102	+	0.108453i	$0.965410\pi$
$734$	−3.00000	+	5.19615i	−0.110732	+	0.191793i
$735$		0			0
$736$	2.54584	+	4.40952i	0.0938408	+	0.162537i
$737$	39.6333			1.45991
$738$		0			0
$739$	30.0278			1.10459			0.552294	−	0.833649i	$-0.313752\pi$
$739$	30.0278			1.10459			0.552294	+	0.833649i	$0.313752\pi$
$740$	0.302776	+	0.524423i	0.0111303	+	0.0192782i
$741$		0			0
$742$	16.8167	−	29.1273i	0.617359	−	1.06930i
$743$	17.2111	−	29.8105i	0.631414	−	1.09364i	−0.355849	−	0.934544i	$-0.615808\pi$
$743$	17.2111	−	29.8105i	0.631414	−	1.09364i	0.987263	−	0.159098i	$-0.0508585\pi$
$744$		0			0
$745$	6.51388	+	11.2824i	0.238650	+	0.413354i
$746$	−14.0555			−0.514609
$747$		0			0
$748$	−4.42221			−0.161692
$749$		0			0
$750$		0			0
$751$	−3.01388	+	5.22019i	−0.109978	+	0.190487i	−0.915761	−	0.401723i	$-0.868411\pi$
$751$	−3.01388	+	5.22019i	−0.109978	+	0.190487i	0.805783	+	0.592211i	$0.201745\pi$
$752$	8.60555	−	14.9053i	0.313812	−	0.543539i
$753$		0			0
$754$	3.39445	+	5.87936i	0.123619	+	0.214114i
$755$	−14.4222			−0.524878
$756$		0			0
$757$	31.2111			1.13439			0.567193	−	0.823585i	$-0.308029\pi$
$757$	31.2111			1.13439			0.567193	+	0.823585i	$0.308029\pi$
$758$	−9.37637	−	16.2403i	−0.340565	−	0.589876i
$759$		0			0
$760$	−5.40833	+	9.36750i	−0.196181	+	0.339795i
$761$	26.7250	−	46.2890i	0.968780	−	1.67798i	0.269682	−	0.962949i	$-0.413081\pi$
$761$	26.7250	−	46.2890i	0.968780	−	1.67798i	0.699097	−	0.715027i	$-0.253585\pi$
$762$		0			0
$763$	16.1194	+	27.9197i	0.583563	+	1.01076i
$764$	−4.97224			−0.179889
$765$		0			0
$766$	−24.2750			−0.877092
$767$	−2.60555	−	4.51295i	−0.0940810	−	0.162953i
$768$		0			0
$769$	−20.5000	+	35.5070i	−0.739249	+	1.28042i	0.213585	+	0.976924i	$0.431486\pi$
$769$	−20.5000	+	35.5070i	−0.739249	+	1.28042i	−0.952834	+	0.303492i	$0.901847\pi$
$770$	7.81665	−	13.5388i	0.281693	−	0.487906i
$771$		0			0
$772$	3.30278	+	5.72058i	0.118869	+	0.205888i
$773$	16.8167			0.604853			0.302426	−	0.953173i	$-0.402203\pi$
$773$	16.8167			0.604853			0.302426	+	0.953173i	$0.402203\pi$
$774$		0			0
$775$	1.60555			0.0576731
$776$	12.0000	+	20.7846i	0.430775	+	0.746124i
$777$		0			0
$778$	−2.72498	+	4.71981i	−0.0976953	+	0.169213i
$779$	4.69722	−	8.13583i	0.168296	−	0.291496i
$780$		0			0
$781$	19.0278	+	32.9570i	0.680867	+	1.17930i
$782$	21.9083			0.783440
$783$		0			0
$784$	−46.9361			−1.67629
$785$	−1.90833	−	3.30532i	−0.0681111	−	0.117972i
$786$		0			0
$787$	1.48612	−	2.57404i	0.0529745	−	0.0917546i	−0.838322	−	0.545175i	$-0.816463\pi$
$787$	1.48612	−	2.57404i	0.0529745	−	0.0917546i	0.891297	+	0.453421i	$0.149796\pi$
$788$	−0.179144	+	0.310287i	−0.00638175	+	0.0110535i
$789$		0			0
$790$	2.86249	+	4.95798i	0.101843	+	0.176397i
$791$	−3.63331			−0.129186
$792$		0			0
$793$	−6.18335			−0.219577
$794$	8.21110	+	14.2220i	0.291401	+	0.504722i
$795$		0			0
$796$	2.00000	−	3.46410i	0.0708881	−	0.122782i
$797$	18.8305	−	32.6154i	0.667012	−	1.15530i	−0.311724	−	0.950173i	$-0.600906\pi$
$797$	18.8305	−	32.6154i	0.667012	−	1.15530i	0.978736	−	0.205125i	$-0.0657602\pi$
$798$		0			0
$799$	14.6056	+	25.2976i	0.516707	+	0.894963i
$800$	1.69722			0.0600059
$801$		0			0
$802$	−39.0833			−1.38008
$803$	7.02776	+	12.1724i	0.248004	+	0.429556i
$804$		0			0
$805$	6.90833	−	11.9656i	0.243487	−	0.421731i
$806$	0.633308	−	1.09692i	0.0223073	−	0.0386374i
$807$		0			0
$808$	18.0000	+	31.1769i	0.633238	+	1.09680i
$809$	50.6056			1.77920			0.889598	−	0.456744i	$-0.150984\pi$
$809$	50.6056			1.77920			0.889598	+	0.456744i	$0.150984\pi$
$810$		0			0
$811$	42.4222			1.48965			0.744823	−	0.667263i	$-0.232534\pi$
$811$	42.4222			1.48965			0.744823	+	0.667263i	$0.232534\pi$
$812$	6.00000	+	10.3923i	0.210559	+	0.364698i
$813$		0			0
$814$	3.39445	−	5.87936i	0.118975	−	0.206071i
$815$	−1.00000	+	1.73205i	−0.0350285	+	0.0606711i
$816$		0			0
$817$	−11.9083	−	20.6258i	−0.416620	−	0.721606i
$818$	6.51388			0.227752
$819$		0			0
$820$	−0.788897			−0.0275495
$821$	−15.0000	−	25.9808i	−0.523504	−	0.906735i	−0.999626	−	0.0273557i	$-0.991291\pi$
$821$	−15.0000	−	25.9808i	−0.523504	−	0.906735i	0.476122	−	0.879379i	$-0.342042\pi$
$822$		0			0
$823$	−1.90833	+	3.30532i	−0.0665201	+	0.115216i	−0.897367	−	0.441284i	$-0.854523\pi$
$823$	−1.90833	+	3.30532i	−0.0665201	+	0.115216i	0.830847	+	0.556501i	$0.187856\pi$
$824$	−6.00000	+	10.3923i	−0.209020	+	0.362033i
$825$		0			0
$826$	25.8167	+	44.7158i	0.898276	+	1.55586i
$827$	−33.7889			−1.17496			−0.587478	−	0.809240i	$-0.699879\pi$
$827$	−33.7889			−1.17496			−0.587478	+	0.809240i	$0.699879\pi$
$828$		0			0
$829$	−27.2111			−0.945081			−0.472540	−	0.881309i	$-0.656663\pi$
$829$	−27.2111			−0.945081			−0.472540	+	0.881309i	$0.656663\pi$
$830$	−1.95416	−	3.38471i	−0.0678300	−	0.117485i
$831$		0			0
$832$	2.66947	−	4.62365i	0.0925472	−	0.160296i
$833$	39.8305	−	68.9885i	1.38005	−	2.39031i
$834$		0			0
$835$	1.50000	+	2.59808i	0.0519096	+	0.0899101i
$836$	−2.84441			−0.0983760
$837$		0			0
$838$	−16.9722			−0.586296
$839$	−9.39445	−	16.2717i	−0.324332	−	0.561760i	0.657045	−	0.753852i	$-0.271806\pi$
$839$	−9.39445	−	16.2717i	−0.324332	−	0.561760i	−0.981377	+	0.192092i	$0.938473\pi$
$840$		0			0
$841$	−22.5278	+	39.0192i	−0.776819	+	1.34549i
$842$	15.2569	−	26.4258i	0.525789	−	0.910693i
$843$		0			0
$844$	1.94029	+	3.36067i	0.0667874	+	0.115679i
$845$	−12.6333			−0.434599
$846$		0			0
$847$	−19.3944			−0.666401
$848$	−9.25694	−	16.0335i	−0.317885	−	0.550592i
$849$		0			0
$850$	3.65139	−	6.32439i	0.125242	−	0.216925i
$851$	3.00000	−	5.19615i	0.102839	−	0.178122i
$852$		0			0
$853$	−7.39445	−	12.8076i	−0.253181	−	0.438523i	0.711219	−	0.702971i	$-0.248144\pi$
$853$	−7.39445	−	12.8076i	−0.253181	−	0.438523i	−0.964400	+	0.264448i	$0.914810\pi$
$854$	61.2666			2.09650
$855$		0			0
$856$		0			0
$857$	22.6194	+	39.1780i	0.772665	+	1.33830i	0.936098	+	0.351741i	$0.114410\pi$
$857$	22.6194	+	39.1780i	0.772665	+	1.33830i	−0.163433	+	0.986555i	$0.552257\pi$
$858$		0			0
$859$	−3.01388	+	5.22019i	−0.102832	+	0.178111i	−0.912850	−	0.408294i	$-0.866124\pi$
$859$	−3.01388	+	5.22019i	−0.102832	+	0.178111i	0.810018	+	0.586405i	$0.199457\pi$
$860$	−1.00000	+	1.73205i	−0.0340997	+	0.0590624i
$861$		0			0
$862$	−16.8167	−	29.1273i	−0.572778	−	0.992080i
$863$	15.7889			0.537460			0.268730	−	0.963216i	$-0.413396\pi$
$863$	15.7889			0.537460			0.268730	+	0.963216i	$0.413396\pi$
$864$		0			0
$865$	10.8167			0.367777
$866$	18.3944	+	31.8601i	0.625069	+	1.08265i
$867$		0			0
$868$	1.11943	−	1.93891i	0.0379959	−	0.0658108i
$869$	−5.72498	+	9.91596i	−0.194207	+	0.336376i
$870$		0			0
$871$	−4.60555	−	7.97705i	−0.156053	−	0.270292i
$872$	21.0000			0.711150
$873$		0			0
$874$	14.0917			0.476658
$875$	−2.30278	−	3.98852i	−0.0778480	−	0.134837i
$876$		0			0
$877$	28.3305	−	49.0699i	0.956654	−	1.65697i	0.226117	−	0.974100i	$-0.427397\pi$
$877$	28.3305	−	49.0699i	0.956654	−	1.65697i	0.730537	−	0.682873i	$-0.239270\pi$
$878$	−13.2847	+	23.0098i	−0.448337	+	0.776542i
$879$		0			0
$880$	−4.30278	−	7.45263i	−0.145047	−	0.251228i
$881$	−32.6056			−1.09851			−0.549254	−	0.835655i	$-0.685088\pi$
$881$	−32.6056			−1.09851			−0.549254	+	0.835655i	$0.685088\pi$
$882$		0			0
$883$	−5.81665			−0.195746			−0.0978730	−	0.995199i	$-0.531204\pi$
$883$	−5.81665			−0.195746			−0.0978730	+	0.995199i	$0.531204\pi$
$884$	0.513878	+	0.890063i	0.0172836	+	0.0299361i
$885$		0			0
$886$	−12.1375	+	21.0228i	−0.407768	+	0.706274i
$887$	−6.31665	+	10.9408i	−0.212092	+	0.367355i	−0.952369	−	0.304947i	$-0.901361\pi$
$887$	−6.31665	+	10.9408i	−0.212092	+	0.367355i	0.740277	+	0.672302i	$0.234694\pi$
$888$		0			0
$889$	11.0278	+	19.1006i	0.369859	+	0.640615i
$890$	10.1833			0.341347
$891$		0			0
$892$	3.02776			0.101377
$893$	9.39445	+	16.2717i	0.314373	+	0.544510i
$894$		0			0
$895$	3.39445	−	5.87936i	0.113464	−	0.196525i
$896$	−18.6333	+	32.2738i	−0.622495	+	1.07819i
$897$		0			0
$898$	7.97224	+	13.8083i	0.266037	+	0.460790i
$899$	13.8167			0.460811
$900$		0			0
$901$	31.4222			1.04683
$902$	4.42221	+	7.65948i	0.147243	+	0.255033i
$903$		0			0
$904$	−1.18335	+	2.04962i	−0.0393575	+	0.0681692i
$905$	3.50000	−	6.06218i	0.116344	−	0.201514i
$906$		0			0
$907$	−15.2111	−	26.3464i	−0.505076	−	0.874818i	−0.999983	−	0.00587164i	$-0.998131\pi$
$907$	−15.2111	−	26.3464i	−0.505076	−	0.874818i	0.494906	−	0.868946i	$-0.335202\pi$
$908$	7.93608			0.263368
$909$		0			0
$910$	−3.63331			−0.120443
$911$	−15.5139	−	26.8708i	−0.513998	−	0.890270i	−0.999868	−	0.0162393i	$-0.994831\pi$
$911$	−15.5139	−	26.8708i	−0.513998	−	0.890270i	0.485870	−	0.874031i	$-0.338503\pi$
$912$		0			0
$913$	3.90833	−	6.76942i	0.129347	−	0.224035i
$914$	−0.788897	+	1.36641i	−0.0260944	+	0.0451968i
$915$		0			0
$916$	−0.940285	−	1.62862i	−0.0310679	−	0.0538112i
$917$	27.6333			0.912532
$918$		0			0
$919$	−2.42221			−0.0799012			−0.0399506	−	0.999202i	$-0.512720\pi$
$919$	−2.42221			−0.0799012			−0.0399506	+	0.999202i	$0.512720\pi$
$920$	−4.50000	−	7.79423i	−0.148361	−	0.256968i
$921$		0			0
$922$	14.0917	−	24.4075i	0.464085	−	0.803818i
$923$	4.42221	−	7.65948i	0.145559	−	0.252115i
$924$		0			0
$925$	−1.00000	−	1.73205i	−0.0328798	−	0.0569495i
$926$	−19.8167			−0.651216
$927$		0			0
$928$	14.6056			0.479451
$929$	−13.3028	−	23.0411i	−0.436450	−	0.755953i	0.560963	−	0.827841i	$-0.310431\pi$
$929$	−13.3028	−	23.0411i	−0.436450	−	0.755953i	−0.997413	+	0.0718876i	$0.977098\pi$
$930$		0			0
$931$	25.6194	−	44.3742i	0.839643	−	1.45430i
$932$	−2.72498	+	4.71981i	−0.0892597	+	0.154602i
$933$		0			0
$934$	1.44029	+	2.49465i	0.0471276	+	0.0816274i
$935$	14.6056			0.477653
$936$		0			0
$937$	26.7889			0.875155			0.437578	−	0.899181i	$-0.355837\pi$
$937$	26.7889			0.875155			0.437578	+	0.899181i	$0.355837\pi$
$938$	45.6333	+	79.0392i	1.48998	+	2.58072i
$939$		0			0
$940$	0.788897	−	1.36641i	0.0257310	−	0.0445674i
$941$	−14.2111	+	24.6144i	−0.463269	+	0.802405i	−0.999122	−	0.0419065i	$-0.986657\pi$
$941$	−14.2111	+	24.6144i	−0.463269	+	0.802405i	0.535853	+	0.844311i	$0.319990\pi$
$942$		0			0
$943$	3.90833	+	6.76942i	0.127273	+	0.220443i
$944$	28.4222			0.925064
$945$		0			0
$946$	22.4222			0.729009
$947$	−19.5000	−	33.7750i	−0.633665	−	1.09754i	−0.986796	−	0.161966i	$-0.948217\pi$
$947$	−19.5000	−	33.7750i	−0.633665	−	1.09754i	0.353131	−	0.935574i	$-0.385117\pi$
$948$		0			0
$949$	1.63331	−	2.82897i	0.0530194	−	0.0918323i
$950$	2.34861	−	4.06792i	0.0761990	−	0.131981i
$951$		0			0
$952$	−38.7250	−	67.0736i	−1.25508	−	2.17387i
$953$	26.8444			0.869576			0.434788	−	0.900533i	$-0.356823\pi$
$953$	26.8444			0.869576			0.434788	+	0.900533i	$0.356823\pi$
$954$		0			0
$955$	16.4222			0.531410
$956$	−0.119429	−	0.206858i	−0.00386262	−	0.00669026i
$957$		0			0
$958$	10.5416	−	18.2586i	0.340585	−	0.589910i
$959$	11.0917	−	19.2113i	0.358169	−	0.620367i
$960$		0			0
$961$	14.2111	+	24.6144i	0.458423	+	0.794011i
$962$	−1.57779			−0.0508701
$963$		0			0
$964$	−8.54163			−0.275108
$965$	−10.9083	−	18.8938i	−0.351151	−	0.608212i
$966$		0			0
$967$	−25.0000	+	43.3013i	−0.803946	+	1.39247i	0.113055	+	0.993589i	$0.463936\pi$
$967$	−25.0000	+	43.3013i	−0.803946	+	1.39247i	−0.917000	+	0.398886i	$0.869397\pi$
$968$	−6.31665	+	10.9408i	−0.203025	+	0.351650i
$969$		0			0
$970$	−5.21110	−	9.02589i	−0.167318	−	0.289804i
$971$	−18.0000			−0.577647			−0.288824	−	0.957382i	$-0.593264\pi$
$971$	−18.0000			−0.577647			−0.288824	+	0.957382i	$0.593264\pi$
$972$		0			0
$973$	−18.4222			−0.590589
$974$	5.33053	+	9.23275i	0.170801	+	0.295836i
$975$		0			0
$976$	16.8625	−	29.2067i	0.539755	−	0.934883i
$977$	0.394449	−	0.683205i	0.0126195	−	0.0218577i	−0.859647	−	0.510889i	$-0.829316\pi$
$977$	0.394449	−	0.683205i	0.0126195	−	0.0218577i	0.872266	+	0.489031i	$0.162650\pi$
$978$		0			0
$979$	10.1833	+	17.6381i	0.325461	+	0.563715i
$980$	−4.30278			−0.137447
$981$		0			0
$982$	16.6611			0.531676
$983$	−0.316654	−	0.548461i	−0.0100997	−	0.0174932i	0.860931	−	0.508721i	$-0.169882\pi$
$983$	−0.316654	−	0.548461i	−0.0100997	−	0.0174932i	−0.871031	+	0.491228i	$0.836548\pi$
$984$		0			0
$985$	0.591673	−	1.02481i	0.0188523	−	0.0326531i
$986$	31.4222	−	54.4249i	1.00069	−	1.73324i
$987$		0			0
$988$	0.330532	+	0.572498i	0.0105156	+	0.0182136i
$989$	19.8167			0.630133
$990$		0			0
$991$	−50.8167			−1.61424			−0.807122	−	0.590385i	$-0.798976\pi$
$991$	−50.8167			−1.61424			−0.807122	+	0.590385i	$0.798976\pi$
$992$	−1.36249	−	2.35990i	−0.0432591	−	0.0749270i
$993$		0			0
$994$	−43.8167	+	75.8927i	−1.38978	+	2.40717i
$995$	−6.60555	+	11.4412i	−0.209410	+	0.362709i
$996$		0			0
$997$	−26.9361	−	46.6547i	−0.853074	−	1.47757i	−0.878420	−	0.477889i	$-0.841402\pi$
$997$	−26.9361	−	46.6547i	−0.853074	−	1.47757i	0.0253457	−	0.999679i	$-0.491931\pi$
$998$	−35.9638			−1.13842
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.2.e.k.271.1		4
3.2	odd	2		405.2.e.j.271.2		4
9.2	odd	6		405.2.e.j.136.2		4
9.4	even	3		135.2.a.c.1.2	✓	2
9.5	odd	6		135.2.a.d.1.1	yes	2
9.7	even	3	inner	405.2.e.k.136.1		4
36.23	even	6		2160.2.a.y.1.1		2
36.31	odd	6		2160.2.a.ba.1.1		2
45.4	even	6		675.2.a.p.1.1		2
45.13	odd	12		675.2.b.i.649.2		4
45.14	odd	6		675.2.a.k.1.2		2
45.22	odd	12		675.2.b.i.649.3		4
45.23	even	12		675.2.b.h.649.3		4
45.32	even	12		675.2.b.h.649.2		4
63.13	odd	6		6615.2.a.p.1.2		2
63.41	even	6		6615.2.a.v.1.1		2
72.5	odd	6		8640.2.a.df.1.2		2
72.13	even	6		8640.2.a.cr.1.2		2
72.59	even	6		8640.2.a.cy.1.1		2
72.67	odd	6		8640.2.a.ck.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.a.c.1.2	✓	2	9.4	even	3
135.2.a.d.1.1	yes	2	9.5	odd	6
405.2.e.j.136.2		4	9.2	odd	6
405.2.e.j.271.2		4	3.2	odd	2
405.2.e.k.136.1		4	9.7	even	3	inner
405.2.e.k.271.1		4	1.1	even	1	trivial
675.2.a.k.1.2		2	45.14	odd	6
675.2.a.p.1.1		2	45.4	even	6
675.2.b.h.649.2		4	45.32	even	12
675.2.b.h.649.3		4	45.23	even	12
675.2.b.i.649.2		4	45.13	odd	12
675.2.b.i.649.3		4	45.22	odd	12
2160.2.a.y.1.1		2	36.23	even	6
2160.2.a.ba.1.1		2	36.31	odd	6
6615.2.a.p.1.2		2	63.13	odd	6
6615.2.a.v.1.1		2	63.41	even	6
8640.2.a.ck.1.1		2	72.67	odd	6
8640.2.a.cr.1.2		2	72.13	even	6
8640.2.a.cy.1.1		2	72.59	even	6
8640.2.a.df.1.2		2	72.5	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:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	405.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.651388 - 1.12824i) q^{2} +(0.151388 - 0.262211i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-2.30278 - 3.98852i) q^{7} -3.00000 q^{8} +O(q^{10})\)	\(q+(-0.651388 - 1.12824i) q^{2} +(0.151388 - 0.262211i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-2.30278 - 3.98852i) q^{7} -3.00000 q^{8} +1.30278 q^{10} +(1.30278 + 2.25647i) q^{11} +(0.302776 - 0.524423i) q^{13} +(-3.00000 + 5.19615i) q^{14} +(1.65139 + 2.86029i) q^{16} -5.60555 q^{17} -3.60555 q^{19} +(0.151388 + 0.262211i) q^{20} +(1.69722 - 2.93968i) q^{22} +(1.50000 - 2.59808i) q^{23} +(-0.500000 - 0.866025i) q^{25} -0.788897 q^{26} -1.39445 q^{28} +(-4.30278 - 7.45263i) q^{29} +(-0.802776 + 1.39045i) q^{31} +(-0.848612 + 1.46984i) q^{32} +(3.65139 + 6.32439i) q^{34} +4.60555 q^{35} +2.00000 q^{37} +(2.34861 + 4.06792i) q^{38} +(1.50000 - 2.59808i) q^{40} +(-1.30278 + 2.25647i) q^{41} +(3.30278 + 5.72058i) q^{43} +0.788897 q^{44} -3.90833 q^{46} +(-2.60555 - 4.51295i) q^{47} +(-7.10555 + 12.3072i) q^{49} +(-0.651388 + 1.12824i) q^{50} +(-0.0916731 - 0.158782i) q^{52} -5.60555 q^{53} -2.60555 q^{55} +(6.90833 + 11.9656i) q^{56} +(-5.60555 + 9.70910i) q^{58} +(4.30278 - 7.45263i) q^{59} +(-5.10555 - 8.84307i) q^{61} +2.09167 q^{62} +8.81665 q^{64} +(0.302776 + 0.524423i) q^{65} +(7.60555 - 13.1732i) q^{67} +(-0.848612 + 1.46984i) q^{68} +(-3.00000 - 5.19615i) q^{70} +14.6056 q^{71} +5.39445 q^{73} +(-1.30278 - 2.25647i) q^{74} +(-0.545837 + 0.945417i) q^{76} +(6.00000 - 10.3923i) q^{77} +(2.19722 + 3.80570i) q^{79} -3.30278 q^{80} +3.39445 q^{82} +(-1.50000 - 2.59808i) q^{83} +(2.80278 - 4.85455i) q^{85} +(4.30278 - 7.45263i) q^{86} +(-3.90833 - 6.76942i) q^{88} +7.81665 q^{89} -2.78890 q^{91} +(-0.454163 - 0.786634i) q^{92} +(-3.39445 + 5.87936i) q^{94} +(1.80278 - 3.12250i) q^{95} +(-4.00000 - 6.92820i) q^{97} +18.5139 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} - 3 q^{4} - 2 q^{5} - 2 q^{7} - 12 q^{8}+O(q^{10}) \) 4 * q + q^2 - 3 * q^4 - 2 * q^5 - 2 * q^7 - 12 * q^8	\( 4 q + q^{2} - 3 q^{4} - 2 q^{5} - 2 q^{7} - 12 q^{8} - 2 q^{10} - 2 q^{11} - 6 q^{13} - 12 q^{14} + 3 q^{16} - 8 q^{17} - 3 q^{20} + 14 q^{22} + 6 q^{23} - 2 q^{25} - 32 q^{26} - 20 q^{28} - 10 q^{29} + 4 q^{31} - 7 q^{32} + 11 q^{34} + 4 q^{35} + 8 q^{37} + 13 q^{38} + 6 q^{40} + 2 q^{41} + 6 q^{43} + 32 q^{44} + 6 q^{46} + 4 q^{47} - 14 q^{49} + q^{50} - 22 q^{52} - 8 q^{53} + 4 q^{55} + 6 q^{56} - 8 q^{58} + 10 q^{59} - 6 q^{61} + 30 q^{62} - 8 q^{64} - 6 q^{65} + 16 q^{67} - 7 q^{68} - 12 q^{70} + 44 q^{71} + 36 q^{73} + 2 q^{74} - 13 q^{76} + 24 q^{77} + 16 q^{79} - 6 q^{80} + 28 q^{82} - 6 q^{83} + 4 q^{85} + 10 q^{86} + 6 q^{88} - 12 q^{89} - 40 q^{91} + 9 q^{92} - 28 q^{94} - 16 q^{97} + 38 q^{98}+O(q^{100}) \) 4 * q + q^2 - 3 * q^4 - 2 * q^5 - 2 * q^7 - 12 * q^8 - 2 * q^10 - 2 * q^11 - 6 * q^13 - 12 * q^14 + 3 * q^16 - 8 * q^17 - 3 * q^20 + 14 * q^22 + 6 * q^23 - 2 * q^25 - 32 * q^26 - 20 * q^28 - 10 * q^29 + 4 * q^31 - 7 * q^32 + 11 * q^34 + 4 * q^35 + 8 * q^37 + 13 * q^38 + 6 * q^40 + 2 * q^41 + 6 * q^43 + 32 * q^44 + 6 * q^46 + 4 * q^47 - 14 * q^49 + q^50 - 22 * q^52 - 8 * q^53 + 4 * q^55 + 6 * q^56 - 8 * q^58 + 10 * q^59 - 6 * q^61 + 30 * q^62 - 8 * q^64 - 6 * q^65 + 16 * q^67 - 7 * q^68 - 12 * q^70 + 44 * q^71 + 36 * q^73 + 2 * q^74 - 13 * q^76 + 24 * q^77 + 16 * q^79 - 6 * q^80 + 28 * q^82 - 6 * q^83 + 4 * q^85 + 10 * q^86 + 6 * q^88 - 12 * q^89 - 40 * q^91 + 9 * q^92 - 28 * q^94 - 16 * q^97 + 38 * q^98

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