LMFDB - Embedded newform 2904.1.cj.b.1853.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2904,1,Mod(5,2904)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2904, base_ring=CyclotomicField(110))

chi = DirichletCharacter(H, H._module([0, 55, 55, 74]))

N = Newforms(chi, 1, names="a")

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

chi := DirichletCharacter("2904.5");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 2904 = 2^{3} \cdot 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2904.cj (of order $110$, degree $40$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.44928479669$
Analytic rank:	$0$
Dimension:	$40$
Coefficient field:	$\Q(\zeta_{55})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{40} - x^{39} + x^{35} - x^{34} + x^{30} - x^{28} + x^{25} - x^{23} + x^{20} - x^{17} + x^{15} + \cdots + 1 $ x^40 - x^39 + x^35 - x^34 + x^30 - x^28 + x^25 - x^23 + x^20 - x^17 + x^15 - x^12 + x^10 - x^6 + x^5 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{55}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{55} - \cdots)$

Embedding invariants

Embedding label			1853.1
Root			$-0.362808 + 0.931864i$ of defining polynomial
Character	$\chi$	$=$	2904.1853
Dual form			2904.1.cj.b.1901.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.736741 + 0.676175i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(0.0855750 - 0.996332i) q^{4} +(-0.0556279 + 1.94723i) q^{5} +(0.993482 - 0.113991i) q^{6} +(-0.288416 - 0.546610i) q^{7} +(0.610648 + 0.791902i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.736741 + 0.676175i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(0.0855750 - 0.996332i) q^{4} +(-0.0556279 + 1.94723i) q^{5} +(0.993482 - 0.113991i) q^{6} +(-0.288416 - 0.546610i) q^{7} +(0.610648 + 0.791902i) q^{8} +(0.309017 + 0.951057i) q^{9} +(-1.27568 - 1.47222i) q^{10} +(-0.654861 - 0.755750i) q^{11} +(-0.654861 + 0.755750i) q^{12} +(0.582092 + 0.207690i) q^{14} +(1.18956 - 1.54264i) q^{15} +(-0.985354 - 0.170522i) q^{16} +(-0.870746 - 0.491733i) q^{18} +(1.93533 + 0.222058i) q^{20} +(-0.0879554 + 0.611743i) q^{21} +(0.993482 + 0.113991i) q^{22} +(-0.0285561 - 0.999592i) q^{24} +(-2.79024 - 0.159552i) q^{25} +(0.309017 - 0.951057i) q^{27} +(-0.569286 + 0.240582i) q^{28} +(-1.88062 + 0.107538i) q^{29} +(0.166702 + 1.94088i) q^{30} +(-0.582954 + 0.966721i) q^{31} +(0.841254 - 0.540641i) q^{32} +(0.0855750 + 0.996332i) q^{33} +(1.08042 - 0.531206i) q^{35} +(0.974012 - 0.226497i) q^{36} +(-1.57598 + 1.14502i) q^{40} +(-0.348845 - 0.510170i) q^{42} +(-0.809017 + 0.587785i) q^{44} +(-1.86912 + 0.548822i) q^{45} +(0.696938 + 0.717132i) q^{48} +(0.348845 - 0.510170i) q^{49} +(2.16357 - 1.76914i) q^{50} +(1.94184 - 0.336049i) q^{53} +(0.415415 + 0.909632i) q^{54} +(1.50805 - 1.23312i) q^{55} +(0.256741 - 0.562183i) q^{56} +(1.31281 - 1.35085i) q^{58} +(-0.100971 - 0.498310i) q^{59} +(-1.43519 - 1.31720i) q^{60} +(-0.224186 - 1.10640i) q^{62} +(0.430731 - 0.443212i) q^{63} +(-0.254218 + 0.967147i) q^{64} +(-0.736741 - 0.676175i) q^{66} +(-0.436801 + 1.12191i) q^{70} +(-0.564443 + 0.825472i) q^{72} +(-1.39160 - 1.43192i) q^{73} +(2.16357 + 1.76914i) q^{75} +(-0.224227 + 0.575924i) q^{77} +(0.526814 + 0.770442i) q^{79} +(0.386859 - 1.90922i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(-1.56281 - 0.768383i) q^{83} +(0.601972 + 0.139983i) q^{84} +(1.58466 + 1.01840i) q^{87} +(0.198590 - 0.980083i) q^{88} +(1.00595 - 1.66819i) q^{90} +(1.03984 - 0.439442i) q^{93} +(-0.998369 - 0.0570888i) q^{96} +(-0.0113419 - 0.397019i) q^{97} +(0.0879554 + 0.611743i) q^{98} +(0.516397 - 0.856349i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + q^{2} - 10 q^{3} + q^{4} + 2 q^{5} + q^{6} + 2 q^{7} + q^{8} - 10 q^{9}+O(q^{10}) $ 40 * q + q^2 - 10 * q^3 + q^4 + 2 * q^5 + q^6 + 2 * q^7 + q^8 - 10 * q^9	$ 40 q + q^{2} - 10 q^{3} + q^{4} + 2 q^{5} + q^{6} + 2 q^{7} + q^{8} - 10 q^{9} - 9 q^{10} - 4 q^{11} - 4 q^{12} + 2 q^{14} - 3 q^{15} + q^{16} + q^{18} + 2 q^{20} + 2 q^{21} + q^{22} + q^{24} + 3 q^{25} - 10 q^{27} - 3 q^{28} - 3 q^{29} - 14 q^{30} - 3 q^{31} - 4 q^{32} + q^{33} - q^{35} + q^{36} - 3 q^{40} - 3 q^{42} - 10 q^{44} + 2 q^{45} + q^{48} + 3 q^{49} - 2 q^{50} + 41 q^{53} - 4 q^{54} + 2 q^{55} + 2 q^{56} - 3 q^{58} + 2 q^{59} + 2 q^{60} + 2 q^{62} + 2 q^{63} + q^{64} + q^{66} - q^{70} + q^{72} - 3 q^{73} - 2 q^{75} + 2 q^{77} + 2 q^{79} - 3 q^{80} - 10 q^{81} + 2 q^{83} + 2 q^{84} + 2 q^{87} + q^{88} - 9 q^{90} - 3 q^{93} + q^{96} + 2 q^{97} - 2 q^{98} + q^{99}+O(q^{100}) $ 40 * q + q^2 - 10 * q^3 + q^4 + 2 * q^5 + q^6 + 2 * q^7 + q^8 - 10 * q^9 - 9 * q^10 - 4 * q^11 - 4 * q^12 + 2 * q^14 - 3 * q^15 + q^16 + q^18 + 2 * q^20 + 2 * q^21 + q^22 + q^24 + 3 * q^25 - 10 * q^27 - 3 * q^28 - 3 * q^29 - 14 * q^30 - 3 * q^31 - 4 * q^32 + q^33 - q^35 + q^36 - 3 * q^40 - 3 * q^42 - 10 * q^44 + 2 * q^45 + q^48 + 3 * q^49 - 2 * q^50 + 41 * q^53 - 4 * q^54 + 2 * q^55 + 2 * q^56 - 3 * q^58 + 2 * q^59 + 2 * q^60 + 2 * q^62 + 2 * q^63 + q^64 + q^66 - q^70 + q^72 - 3 * q^73 - 2 * q^75 + 2 * q^77 + 2 * q^79 - 3 * q^80 - 10 * q^81 + 2 * q^83 + 2 * q^84 + 2 * q^87 + q^88 - 9 * q^90 - 3 * q^93 + q^96 + 2 * q^97 - 2 * q^98 + q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2904\mathbb{Z}\right)^\times$.

$n$	$727$	$1453$	$1937$	$2785$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{42}{55}\right)$

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 $

$2$	−0.736741	+	0.676175i	−0.736741	+	0.676175i
$2$	−0.736741	+	0.676175i	−0.736741	+	0.676175i
$3$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$3$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$4$	0.0855750	−	0.996332i	0.0855750	−	0.996332i
$5$	−0.0556279	+	1.94723i	−0.0556279	+	1.94723i	0.198590	+	0.980083i	$0.436364\pi$
$5$	−0.0556279	+	1.94723i	−0.0556279	+	1.94723i	−0.254218	+	0.967147i	$0.581818\pi$
$6$	0.993482	−	0.113991i	0.993482	−	0.113991i
$7$	−0.288416	−	0.546610i	−0.288416	−	0.546610i	0.696938	−	0.717132i	$-0.254545\pi$
$7$	−0.288416	−	0.546610i	−0.288416	−	0.546610i	−0.985354	+	0.170522i	$0.945455\pi$
$8$	0.610648	+	0.791902i	0.610648	+	0.791902i
$9$	0.309017	+	0.951057i	0.309017	+	0.951057i
$10$	−1.27568	−	1.47222i	−1.27568	−	1.47222i
$11$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$11$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$12$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$13$		0			0		−0.921124	−	0.389270i	$-0.872727\pi$
$13$		0			0		0.921124	+	0.389270i	$0.127273\pi$
$14$	0.582092	+	0.207690i	0.582092	+	0.207690i
$15$	1.18956	−	1.54264i	1.18956	−	1.54264i
$16$	−0.985354	−	0.170522i	−0.985354	−	0.170522i
$17$		0			0		−0.254218	−	0.967147i	$-0.581818\pi$
$17$		0			0		0.254218	+	0.967147i	$0.418182\pi$
$18$	−0.870746	−	0.491733i	−0.870746	−	0.491733i
$19$		0			0		−0.362808	−	0.931864i	$-0.618182\pi$
$19$		0			0		0.362808	+	0.931864i	$0.381818\pi$
$20$	1.93533	+	0.222058i	1.93533	+	0.222058i
$21$	−0.0879554	+	0.611743i	−0.0879554	+	0.611743i
$22$	0.993482	+	0.113991i	0.993482	+	0.113991i
$23$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$23$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$24$	−0.0285561	−	0.999592i	−0.0285561	−	0.999592i
$25$	−2.79024	−	0.159552i	−2.79024	−	0.159552i
$26$		0			0
$27$	0.309017	−	0.951057i	0.309017	−	0.951057i
$28$	−0.569286	+	0.240582i	−0.569286	+	0.240582i
$29$	−1.88062	+	0.107538i	−1.88062	+	0.107538i	−0.959493	−	0.281733i	$-0.909091\pi$
$29$	−1.88062	+	0.107538i	−1.88062	+	0.107538i	−0.921124	+	0.389270i	$0.872727\pi$
$30$	0.166702	+	1.94088i	0.166702	+	1.94088i
$31$	−0.582954	+	0.966721i	−0.582954	+	0.966721i	0.415415	+	0.909632i	$0.363636\pi$
$31$	−0.582954	+	0.966721i	−0.582954	+	0.966721i	−0.998369	+	0.0570888i	$0.981818\pi$
$32$	0.841254	−	0.540641i	0.841254	−	0.540641i
$33$	0.0855750	+	0.996332i	0.0855750	+	0.996332i
$34$		0			0
$35$	1.08042	−	0.531206i	1.08042	−	0.531206i
$36$	0.974012	−	0.226497i	0.974012	−	0.226497i
$37$		0			0		−0.974012	−	0.226497i	$-0.927273\pi$
$37$		0			0		0.974012	+	0.226497i	$0.0727273\pi$
$38$		0			0
$39$		0			0
$40$	−1.57598	+	1.14502i	−1.57598	+	1.14502i
$41$		0			0		0.198590	−	0.980083i	$-0.436364\pi$
$41$		0			0		−0.198590	+	0.980083i	$0.563636\pi$
$42$	−0.348845	−	0.510170i	−0.348845	−	0.510170i
$43$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$43$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$44$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$45$	−1.86912	+	0.548822i	−1.86912	+	0.548822i
$46$		0			0
$47$		0			0		0.870746	−	0.491733i	$-0.163636\pi$
$47$		0			0		−0.870746	+	0.491733i	$0.836364\pi$
$48$	0.696938	+	0.717132i	0.696938	+	0.717132i
$49$	0.348845	−	0.510170i	0.348845	−	0.510170i
$50$	2.16357	−	1.76914i	2.16357	−	1.76914i
$51$		0			0
$52$		0			0
$53$	1.94184	−	0.336049i	1.94184	−	0.336049i	0.941844	−	0.336049i	$-0.109091\pi$
$53$	1.94184	−	0.336049i	1.94184	−	0.336049i	1.00000			$0$
$54$	0.415415	+	0.909632i	0.415415	+	0.909632i
$55$	1.50805	−	1.23312i	1.50805	−	1.23312i
$56$	0.256741	−	0.562183i	0.256741	−	0.562183i
$57$		0			0
$58$	1.31281	−	1.35085i	1.31281	−	1.35085i
$59$	−0.100971	−	0.498310i	−0.100971	−	0.498310i	−0.998369	−	0.0570888i	$-0.981818\pi$
$59$	−0.100971	−	0.498310i	−0.100971	−	0.498310i	0.897398	−	0.441221i	$-0.145455\pi$
$60$	−1.43519	−	1.31720i	−1.43519	−	1.31720i
$61$		0			0		−0.736741	−	0.676175i	$-0.763636\pi$
$61$		0			0		0.736741	+	0.676175i	$0.236364\pi$
$62$	−0.224186	−	1.10640i	−0.224186	−	1.10640i
$63$	0.430731	−	0.443212i	0.430731	−	0.443212i
$64$	−0.254218	+	0.967147i	−0.254218	+	0.967147i
$65$		0			0
$66$	−0.736741	−	0.676175i	−0.736741	−	0.676175i
$67$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$67$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$68$		0			0
$69$		0			0
$70$	−0.436801	+	1.12191i	−0.436801	+	1.12191i
$71$		0			0		0.774142	−	0.633012i	$-0.218182\pi$
$71$		0			0		−0.774142	+	0.633012i	$0.781818\pi$
$72$	−0.564443	+	0.825472i	−0.564443	+	0.825472i
$73$	−1.39160	−	1.43192i	−1.39160	−	1.43192i	−0.736741	−	0.676175i	$-0.763636\pi$
$73$	−1.39160	−	1.43192i	−1.39160	−	1.43192i	−0.654861	−	0.755750i	$-0.727273\pi$
$74$		0			0
$75$	2.16357	+	1.76914i	2.16357	+	1.76914i
$76$		0			0
$77$	−0.224227	+	0.575924i	−0.224227	+	0.575924i
$78$		0			0
$79$	0.526814	+	0.770442i	0.526814	+	0.770442i	0.993482	−	0.113991i	$-0.0363636\pi$
$79$	0.526814	+	0.770442i	0.526814	+	0.770442i	−0.466667	+	0.884433i	$0.654545\pi$
$80$	0.386859	−	1.90922i	0.386859	−	1.90922i
$81$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$82$		0			0
$83$	−1.56281	−	0.768383i	−1.56281	−	0.768383i	−0.564443	−	0.825472i	$-0.690909\pi$
$83$	−1.56281	−	0.768383i	−1.56281	−	0.768383i	−0.998369	+	0.0570888i	$0.981818\pi$
$84$	0.601972	+	0.139983i	0.601972	+	0.139983i
$85$		0			0
$86$		0			0
$87$	1.58466	+	1.01840i	1.58466	+	1.01840i
$88$	0.198590	−	0.980083i	0.198590	−	0.980083i
$89$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$89$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$90$	1.00595	−	1.66819i	1.00595	−	1.66819i
$91$		0			0
$92$		0			0
$93$	1.03984	−	0.439442i	1.03984	−	0.439442i
$94$		0			0
$95$		0			0
$96$	−0.998369	−	0.0570888i	−0.998369	−	0.0570888i
$97$	−0.0113419	−	0.397019i	−0.0113419	−	0.397019i	−0.985354	−	0.170522i	$-0.945455\pi$
$97$	−0.0113419	−	0.397019i	−0.0113419	−	0.397019i	0.974012	−	0.226497i	$-0.0727273\pi$
$98$	0.0879554	+	0.611743i	0.0879554	+	0.611743i
$99$	0.516397	−	0.856349i	0.516397	−	0.856349i
$100$	−0.397741	+	2.76635i	−0.397741	+	2.76635i
$101$	−0.720886	−	0.0827139i	−0.720886	−	0.0827139i	−0.254218	−	0.967147i	$-0.581818\pi$
$101$	−0.720886	−	0.0827139i	−0.720886	−	0.0827139i	−0.466667	+	0.884433i	$0.654545\pi$
$102$		0			0
$103$	−1.73014	−	0.977055i	−1.73014	−	0.977055i	−0.921124	−	0.389270i	$-0.872727\pi$
$103$	−1.73014	−	0.977055i	−1.73014	−	0.977055i	−0.809017	−	0.587785i	$-0.800000\pi$
$104$		0			0
$105$	−1.18631	−	0.205299i	−1.18631	−	0.205299i
$106$	−1.20341	+	1.56061i	−1.20341	+	1.56061i
$107$	−1.38779	−	0.495163i	−1.38779	−	0.495163i	−0.466667	−	0.884433i	$-0.654545\pi$
$107$	−1.38779	−	0.495163i	−1.38779	−	0.495163i	−0.921124	+	0.389270i	$0.872727\pi$
$108$	−0.921124	−	0.389270i	−0.921124	−	0.389270i
$109$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$109$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$110$	−0.277233	+	1.92820i	−0.277233	+	1.92820i
$111$		0			0
$112$	0.190983	+	0.587785i	0.190983	+	0.587785i
$113$		0			0		−0.610648	−	0.791902i	$-0.709091\pi$
$113$		0			0		0.610648	+	0.791902i	$0.290909\pi$
$114$		0			0
$115$		0			0
$116$	−0.0537907	+	1.88292i	−0.0537907	+	1.88292i
$117$		0			0
$118$	0.411334	+	0.298852i	0.411334	+	0.298852i
$119$		0			0
$120$	1.94802			1.94802
$121$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$122$		0			0
$123$		0			0
$124$	0.913288	+	0.663543i	0.913288	+	0.663543i
$125$	0.299197	−	3.48348i	0.299197	−	3.48348i
$126$	−0.0176486	+	0.617782i	−0.0176486	+	0.617782i
$127$	0.825414	−	0.0947075i	0.825414	−	0.0947075i	0.309017	−	0.951057i	$-0.400000\pi$
$127$	0.825414	−	0.0947075i	0.825414	−	0.0947075i	0.516397	+	0.856349i	$0.327273\pi$
$128$	−0.466667	−	0.884433i	−0.466667	−	0.884433i
$129$		0			0
$130$		0			0
$131$	−1.01391	−	1.17011i	−1.01391	−	1.17011i	−0.985354	−	0.170522i	$-0.945455\pi$
$131$	−1.01391	−	1.17011i	−1.01391	−	1.17011i	−0.0285561	−	0.999592i	$-0.509091\pi$
$132$	1.00000			1.00000
$133$		0			0
$134$		0			0
$135$	1.83474	+	0.654632i	1.83474	+	0.654632i
$136$		0			0
$137$		0			0		−0.985354	−	0.170522i	$-0.945455\pi$
$137$		0			0		0.985354	+	0.170522i	$0.0545455\pi$
$138$		0			0
$139$		0			0		−0.870746	−	0.491733i	$-0.836364\pi$
$139$		0			0		0.870746	+	0.491733i	$0.163636\pi$
$140$	−0.436801	−	1.12191i	−0.436801	−	1.12191i
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$145$	−0.104786	−	3.66797i	−0.104786	−	3.66797i
$146$	1.99348	+	0.113991i	1.99348	+	0.113991i
$147$	−0.582092	+	0.207690i	−0.582092	+	0.207690i
$148$		0			0
$149$	0.0526073	−	0.0222320i	0.0526073	−	0.0222320i	−0.362808	−	0.931864i	$-0.618182\pi$
$149$	0.0526073	−	0.0222320i	0.0526073	−	0.0222320i	0.415415	+	0.909632i	$0.363636\pi$
$150$	−2.79024	+	0.159552i	−2.79024	+	0.159552i
$151$	0.0339888	+	0.395724i	0.0339888	+	0.395724i	0.993482	+	0.113991i	$0.0363636\pi$
$151$	0.0339888	+	0.395724i	0.0339888	+	0.395724i	−0.959493	+	0.281733i	$0.909091\pi$
$152$		0			0
$153$		0			0
$154$	−0.224227	−	0.575924i	−0.224227	−	0.575924i
$155$	−1.85000	−	1.18892i	−1.85000	−	1.18892i
$156$		0			0
$157$		0			0		0.974012	−	0.226497i	$-0.0727273\pi$
$157$		0			0		−0.974012	+	0.226497i	$0.927273\pi$
$158$	−0.909079	−	0.211397i	−0.909079	−	0.211397i
$159$	−1.76851	−	0.869518i	−1.76851	−	0.869518i
$160$	1.00595	+	1.66819i	1.00595	+	1.66819i
$161$		0			0
$162$	0.198590	−	0.980083i	0.198590	−	0.980083i
$163$		0			0		−0.564443	−	0.825472i	$-0.690909\pi$
$163$		0			0		0.564443	+	0.825472i	$0.309091\pi$
$164$		0			0
$165$	−1.94485	+	0.111210i	−1.94485	+	0.111210i
$166$	1.67095	−	0.490635i	1.67095	−	0.490635i
$167$		0			0		−0.774142	−	0.633012i	$-0.781818\pi$
$167$		0			0		0.774142	+	0.633012i	$0.218182\pi$
$168$	−0.538151	+	0.303908i	−0.538151	+	0.303908i
$169$	0.696938	+	0.717132i	0.696938	+	0.717132i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	0.859717	−	1.62934i	0.859717	−	1.62934i	0.0855750	−	0.996332i	$-0.472727\pi$
$173$	0.859717	−	1.62934i	0.859717	−	1.62934i	0.774142	−	0.633012i	$-0.218182\pi$
$174$	−1.85610	+	0.321211i	−1.85610	+	0.321211i
$175$	0.717538	+	1.57119i	0.717538	+	1.57119i
$176$	0.516397	+	0.856349i	0.516397	+	0.856349i
$177$	−0.211212	+	0.462490i	−0.211212	+	0.462490i
$178$		0			0
$179$	−1.21371	+	1.24888i	−1.21371	+	1.24888i	−0.254218	+	0.967147i	$0.581818\pi$
$179$	−1.21371	+	1.24888i	−1.21371	+	1.24888i	−0.959493	+	0.281733i	$0.909091\pi$
$180$	0.386859	+	1.90922i	0.386859	+	1.90922i
$181$		0			0		−0.736741	−	0.676175i	$-0.763636\pi$
$181$		0			0		0.736741	+	0.676175i	$0.236364\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$	−0.468956	+	1.02687i	−0.468956	+	1.02687i
$187$		0			0
$188$		0			0
$189$	−0.608982	+	0.105389i	−0.608982	+	0.105389i
$190$		0			0
$191$		0			0		0.362808	−	0.931864i	$-0.381818\pi$
$191$		0			0		−0.362808	+	0.931864i	$0.618182\pi$
$192$	0.774142	−	0.633012i	0.774142	−	0.633012i
$193$	1.03984	−	1.52072i	1.03984	−	1.52072i	0.198590	−	0.980083i	$-0.436364\pi$
$193$	1.03984	−	1.52072i	1.03984	−	1.52072i	0.841254	−	0.540641i	$-0.181818\pi$
$194$	0.276810	+	0.284831i	0.276810	+	0.284831i
$195$		0			0
$196$	−0.478446	−	0.391223i	−0.478446	−	0.391223i
$197$	−1.17182	+	0.344079i	−1.17182	+	0.344079i	−0.809017	−	0.587785i	$-0.800000\pi$
$197$	−1.17182	+	0.344079i	−1.17182	+	0.344079i	−0.362808	+	0.931864i	$0.618182\pi$
$198$	0.198590	+	0.980083i	0.198590	+	0.980083i
$199$	−1.33741	−	0.392700i	−1.33741	−	0.392700i	−0.466667	−	0.884433i	$-0.654545\pi$
$199$	−1.33741	−	0.392700i	−1.33741	−	0.392700i	−0.870746	+	0.491733i	$0.836364\pi$
$200$	−1.57750	−	2.30703i	−1.57750	−	2.30703i
$201$		0			0
$202$	0.587035	−	0.426506i	0.587035	−	0.426506i
$203$	0.601181	+	0.996948i	0.601181	+	0.996948i
$204$		0			0
$205$		0			0
$206$	1.93533	−	0.450041i	1.93533	−	0.450041i
$207$		0			0
$208$		0			0
$209$		0			0
$210$	1.01282	−	0.650902i	1.01282	−	0.650902i
$211$		0			0		0.516397	−	0.856349i	$-0.327273\pi$
$211$		0			0		−0.516397	+	0.856349i	$0.672727\pi$
$212$	−0.168643	−	1.96348i	−0.168643	−	1.96348i
$213$		0			0
$214$	1.35726	−	0.573583i	1.35726	−	0.573583i
$215$		0			0
$216$	0.941844	−	0.336049i	0.941844	−	0.336049i
$217$	0.696552	+	0.0398303i	0.696552	+	0.0398303i
$218$		0			0
$219$	0.284165	+	1.97641i	0.284165	+	1.97641i
$220$	−1.09955	−	1.60804i	−1.09955	−	1.60804i
$221$		0			0
$222$		0			0
$223$	−0.443096	−	1.13808i	−0.443096	−	1.13808i	−0.959493	−	0.281733i	$-0.909091\pi$
$223$	−0.443096	−	1.13808i	−0.443096	−	1.13808i	0.516397	−	0.856349i	$-0.327273\pi$
$224$	−0.538151	−	0.303908i	−0.538151	−	0.303908i
$225$	−0.710489	−	2.70298i	−0.710489	−	2.70298i
$226$		0			0
$227$	0.851167	−	1.10381i	0.851167	−	1.10381i	−0.142315	−	0.989821i	$-0.545455\pi$
$227$	0.851167	−	1.10381i	0.851167	−	1.10381i	0.993482	−	0.113991i	$-0.0363636\pi$
$228$		0			0
$229$		0			0		−0.921124	−	0.389270i	$-0.872727\pi$
$229$		0			0		0.921124	+	0.389270i	$0.127273\pi$
$230$		0			0
$231$	0.519923	−	0.334134i	0.519923	−	0.334134i
$232$	−1.23355	−	1.42360i	−1.23355	−	1.42360i
$233$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$233$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$234$		0			0
$235$		0			0
$236$	−0.505123	+	0.0579574i	−0.505123	+	0.0579574i
$237$	0.0266524	−	0.932954i	0.0266524	−	0.932954i
$238$		0			0
$239$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$239$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$240$	−1.43519	+	1.31720i	−1.43519	+	1.31720i
$241$	−0.0571121			−0.0571121			−0.0285561	−	0.999592i	$-0.509091\pi$
$241$	−0.0571121			−0.0571121			−0.0285561	+	0.999592i	$0.509091\pi$
$242$	−0.564443	−	0.825472i	−0.564443	−	0.825472i
$243$	1.00000			1.00000
$244$		0			0
$245$	0.974012	+	0.707661i	0.974012	+	0.707661i
$246$		0			0
$247$		0			0
$248$	−1.12153	+	0.128683i	−1.12153	+	0.128683i
$249$	0.812697	+	1.54023i	0.812697	+	1.54023i
$250$	2.13501	+	2.76873i	2.13501	+	2.76873i
$251$	0.430731	+	1.32565i	0.430731	+	1.32565i	0.897398	+	0.441221i	$0.145455\pi$
$251$	0.430731	+	1.32565i	0.430731	+	1.32565i	−0.466667	+	0.884433i	$0.654545\pi$
$252$	−0.404726	−	0.467079i	−0.404726	−	0.467079i
$253$		0			0
$254$	−0.544078	+	0.627899i	−0.544078	+	0.627899i
$255$		0			0
$256$	0.941844	+	0.336049i	0.941844	+	0.336049i
$257$		0			0		0.610648	−	0.791902i	$-0.290909\pi$
$257$		0			0		−0.610648	+	0.791902i	$0.709091\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−0.683417	−	1.75534i	−0.683417	−	1.75534i
$262$	1.53819	+	0.176491i	1.53819	+	0.176491i
$263$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$263$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$264$	−0.736741	+	0.676175i	−0.736741	+	0.676175i
$265$	0.546345	+	3.79991i	0.546345	+	3.79991i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−0.592999	+	1.82506i	−0.592999	+	1.82506i	−0.0285561	+	0.999592i	$0.509091\pi$
$269$	−0.592999	+	1.82506i	−0.592999	+	1.82506i	−0.564443	+	0.825472i	$0.690909\pi$
$270$	−1.79437	+	0.758307i	−1.79437	+	0.758307i
$271$	1.30759	−	0.0747704i	1.30759	−	0.0747704i	0.610648	−	0.791902i	$-0.290909\pi$
$271$	1.30759	−	0.0747704i	1.30759	−	0.0747704i	0.696938	+	0.717132i	$0.254545\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	1.70664	+	2.21321i	1.70664	+	2.21321i
$276$		0			0
$277$		0			0		0.897398	−	0.441221i	$-0.145455\pi$
$277$		0			0		−0.897398	+	0.441221i	$0.854545\pi$
$278$		0			0
$279$	−1.09955	−	0.255689i	−1.09955	−	0.255689i
$280$	1.08042	+	0.531206i	1.08042	+	0.531206i
$281$		0			0		−0.516397	−	0.856349i	$-0.672727\pi$
$281$		0			0		0.516397	+	0.856349i	$0.327273\pi$
$282$		0			0
$283$		0			0		0.198590	−	0.980083i	$-0.436364\pi$
$283$		0			0		−0.198590	+	0.980083i	$0.563636\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.774142	+	0.633012i	0.774142	+	0.633012i
$289$	−0.870746	+	0.491733i	−0.870746	+	0.491733i
$290$	2.55739	+	2.63149i	2.55739	+	2.63149i
$291$	−0.224186	+	0.327862i	−0.224186	+	0.327862i
$292$	−1.54576	+	1.26396i	−1.54576	+	1.26396i
$293$	0.184465	−	0.473794i	0.184465	−	0.473794i	−0.809017	−	0.587785i	$-0.800000\pi$
$293$	0.184465	−	0.473794i	0.184465	−	0.473794i	0.993482	+	0.113991i	$0.0363636\pi$
$294$	0.288416	−	0.546610i	0.288416	−	0.546610i
$295$	0.975941	−	0.168893i	0.975941	−	0.168893i
$296$		0			0
$297$	−0.921124	+	0.389270i	−0.921124	+	0.389270i
$298$	−0.0237252	+	0.0519510i	−0.0237252	+	0.0519510i
$299$		0			0
$300$	1.94780	−	2.00424i	1.94780	−	2.00424i
$301$		0			0
$302$	−0.292620	−	0.268564i	−0.292620	−	0.268564i
$303$	0.534591	+	0.490643i	0.534591	+	0.490643i
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$307$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$308$	0.554623	+	0.272690i	0.554623	+	0.272690i
$309$	0.825414	+	1.80741i	0.825414	+	1.80741i
$310$	2.16689	−	0.374995i	2.16689	−	0.374995i
$311$		0			0		0.466667	−	0.884433i	$-0.345455\pi$
$311$		0			0		−0.466667	+	0.884433i	$0.654545\pi$
$312$		0			0
$313$	−0.722533	+	0.590812i	−0.722533	+	0.590812i	−0.921124	−	0.389270i	$-0.872727\pi$
$313$	−0.722533	+	0.590812i	−0.722533	+	0.590812i	0.198590	+	0.980083i	$0.436364\pi$
$314$		0			0
$315$	0.839074	+	0.863387i	0.839074	+	0.863387i
$316$	0.812697	−	0.458951i	0.812697	−	0.458951i
$317$	−0.220344	−	0.180174i	−0.220344	−	0.180174i	0.516397	−	0.856349i	$-0.327273\pi$
$317$	−0.220344	−	0.180174i	−0.220344	−	0.180174i	−0.736741	+	0.676175i	$0.763636\pi$
$318$	1.89088	−	0.555213i	1.89088	−	0.555213i
$319$	1.31281	+	1.35085i	1.31281	+	1.35085i
$320$	−1.86912	−	0.548822i	−1.86912	−	0.548822i
$321$	0.831697	+	1.21632i	0.831697	+	1.21632i
$322$		0			0
$323$		0			0
$324$	0.516397	+	0.856349i	0.516397	+	0.856349i
$325$		0			0
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$	1.35765	−	1.39699i	1.35765	−	1.39699i
$331$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$331$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$332$	−0.899302	+	1.49133i	−0.899302	+	1.49133i
$333$		0			0
$334$		0			0
$335$		0			0
$336$	0.190983	−	0.587785i	0.190983	−	0.587785i
$337$	−1.23355	+	0.440131i	−1.23355	+	0.440131i	−0.870746	−	0.491733i	$-0.836364\pi$
$337$	−1.23355	+	0.440131i	−1.23355	+	0.440131i	−0.362808	+	0.931864i	$0.618182\pi$
$338$	−0.998369	−	0.0570888i	−0.998369	−	0.0570888i
$339$		0			0
$340$		0			0
$341$	1.11235	−	0.192500i	1.11235	−	0.192500i
$342$		0			0
$343$	−0.993482	−	0.113991i	−0.993482	−	0.113991i
$344$		0			0
$345$		0			0
$346$	0.468333	+	1.78172i	0.468333	+	1.78172i
$347$	1.94184	+	0.336049i	1.94184	+	0.336049i	1.00000			$0$
$347$	1.94184	+	0.336049i	1.94184	+	0.336049i	0.941844	+	0.336049i	$0.109091\pi$
$348$	1.15027	−	1.49170i	1.15027	−	1.49170i
$349$		0			0		−0.941844	−	0.336049i	$-0.890909\pi$
$349$		0			0		0.941844	+	0.336049i	$0.109091\pi$
$350$	−1.59104	−	0.672378i	−1.59104	−	0.672378i
$351$		0			0
$352$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$353$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$353$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$354$	−0.157116	−	0.483552i	−0.157116	−	0.483552i
$355$		0			0
$356$		0			0
$357$		0			0
$358$	0.0497301	−	1.74078i	0.0497301	−	1.74078i
$359$		0			0		0.0855750	−	0.996332i	$-0.472727\pi$
$359$		0			0		−0.0855750	+	0.996332i	$0.527273\pi$
$360$	−1.57598	−	1.14502i	−1.57598	−	1.14502i
$361$	−0.736741	+	0.676175i	−0.736741	+	0.676175i
$362$		0			0
$363$	0.696938	−	0.717132i	0.696938	−	0.717132i
$364$		0			0
$365$	2.86570	−	2.63011i	2.86570	−	2.63011i
$366$		0			0
$367$	−0.170871	+	1.98941i	−0.170871	+	1.98941i	−0.0285561	+	0.999592i	$0.509091\pi$
$367$	−0.170871	+	1.98941i	−0.170871	+	1.98941i	−0.142315	+	0.989821i	$0.545455\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−0.743747	−	0.964509i	−0.743747	−	0.964509i
$372$	−0.348845	−	1.07363i	−0.348845	−	1.07363i
$373$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$373$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$374$		0			0
$375$	−2.28959	+	2.64233i	−2.28959	+	2.64233i
$376$		0			0
$377$		0			0
$378$	0.377401	−	0.489423i	0.377401	−	0.489423i
$379$		0			0		−0.985354	−	0.170522i	$-0.945455\pi$
$379$		0			0		0.985354	+	0.170522i	$0.0545455\pi$
$380$		0			0
$381$	−0.723442	−	0.408546i	−0.723442	−	0.408546i
$382$		0			0
$383$		0			0		−0.993482	−	0.113991i	$-0.963636\pi$
$383$		0			0		0.993482	+	0.113991i	$0.0363636\pi$
$384$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$385$	−1.10898	−	0.468660i	−1.10898	−	0.468660i
$386$	0.262179	+	1.82350i	0.262179	+	1.82350i
$387$		0			0
$388$	−0.396533	−	0.0226746i	−0.396533	−	0.0226746i
$389$	1.58466	−	0.565405i	1.58466	−	0.565405i	0.610648	−	0.791902i	$-0.290909\pi$
$389$	1.58466	−	0.565405i	1.58466	−	0.565405i	0.974012	+	0.226497i	$0.0727273\pi$
$390$		0			0
$391$		0			0
$392$	0.617026	−	0.0352828i	0.617026	−	0.0352828i
$393$	0.132494	+	1.54260i	0.132494	+	1.54260i
$394$	0.630674	−	1.04586i	0.630674	−	1.04586i
$395$	−1.52953	+	0.982971i	−1.52953	+	0.982971i
$396$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$397$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$397$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$398$	1.25086	−	0.615007i	1.25086	−	0.615007i
$399$		0			0
$400$	2.72217	+	0.633012i	2.72217	+	0.633012i
$401$		0			0		−0.897398	−	0.441221i	$-0.854545\pi$
$401$		0			0		0.897398	+	0.441221i	$0.145455\pi$
$402$		0			0
$403$		0			0
$404$	−0.144100	+	0.711163i	−0.144100	+	0.711163i
$405$	−1.09955	−	1.60804i	−1.09955	−	1.60804i
$406$	−1.11703	−	0.327988i	−1.11703	−	0.327988i
$407$		0			0
$408$		0			0
$409$	−1.25259	−	1.02424i	−1.25259	−	1.02424i	−0.998369	−	0.0570888i	$-0.981818\pi$
$409$	−1.25259	−	1.02424i	−1.25259	−	1.02424i	−0.254218	−	0.967147i	$-0.581818\pi$
$410$		0			0
$411$		0			0
$412$	−1.12153	+	1.64018i	−1.12153	+	1.64018i
$413$	−0.243259	+	0.198912i	−0.243259	+	0.198912i
$414$		0			0
$415$	1.58315	−	3.00041i	1.58315	−	3.00041i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	0.0710983	−	0.155684i	0.0710983	−	0.155684i	−0.870746	−	0.491733i	$-0.836364\pi$
$419$	0.0710983	−	0.155684i	0.0710983	−	0.155684i	0.941844	+	0.336049i	$0.109091\pi$
$420$	−0.306065	+	1.16439i	−0.306065	+	1.16439i
$421$		0			0		0.696938	−	0.717132i	$-0.254545\pi$
$421$		0			0		−0.696938	+	0.717132i	$0.745455\pi$
$422$		0			0
$423$		0			0
$424$	1.45190	+	1.33254i	1.45190	+	1.33254i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	−0.612107	+	1.34033i	−0.612107	+	1.34033i
$429$		0			0
$430$		0			0
$431$		0			0		0.985354	−	0.170522i	$-0.0545455\pi$
$431$		0			0		−0.985354	+	0.170522i	$0.945455\pi$
$432$	−0.466667	+	0.884433i	−0.466667	+	0.884433i
$433$	−0.561729	+	1.44279i	−0.561729	+	1.44279i	0.309017	+	0.951057i	$0.400000\pi$
$433$	−0.561729	+	1.44279i	−0.561729	+	1.44279i	−0.870746	+	0.491733i	$0.836364\pi$
$434$	−0.540111	+	0.441647i	−0.540111	+	0.441647i
$435$	−2.07121	+	3.02904i	−2.07121	+	3.02904i
$436$		0			0
$437$		0			0
$438$	−1.54576	−	1.26396i	−1.54576	−	1.26396i
$439$	−1.48557	+	0.436202i	−1.48557	+	0.436202i	−0.921124	−	0.389270i	$-0.872727\pi$
$439$	−1.48557	+	0.436202i	−1.48557	+	0.436202i	−0.564443	+	0.825472i	$0.690909\pi$
$440$	1.89740	+	0.441221i	1.89740	+	0.441221i
$441$	0.592999	+	0.174120i	0.592999	+	0.174120i
$442$		0			0
$443$	0.205103	−	1.01222i	0.205103	−	1.01222i	−0.736741	−	0.676175i	$-0.763636\pi$
$443$	0.205103	−	1.01222i	0.205103	−	1.01222i	0.941844	−	0.336049i	$-0.109091\pi$
$444$		0			0
$445$		0			0
$446$	1.09599	+	0.538861i	1.09599	+	0.538861i
$447$	−0.0556279	−	0.0129357i	−0.0556279	−	0.0129357i
$448$	0.601972	−	0.139983i	0.601972	−	0.139983i
$449$		0			0		0.897398	−	0.441221i	$-0.145455\pi$
$449$		0			0		−0.897398	+	0.441221i	$0.854545\pi$
$450$	2.35113	+	1.51098i	2.35113	+	1.51098i
$451$		0			0
$452$		0			0
$453$	0.205103	−	0.340126i	0.205103	−	0.340126i
$454$	0.119281	+	1.38876i	0.119281	+	1.38876i
$455$		0			0
$456$		0			0
$457$	−0.224227	+	0.690101i	−0.224227	+	0.690101i	0.774142	+	0.633012i	$0.218182\pi$
$457$	−0.224227	+	0.690101i	−0.224227	+	0.690101i	−0.998369	+	0.0570888i	$0.981818\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	0.186393	+	1.29639i	0.186393	+	1.29639i	0.841254	+	0.540641i	$0.181818\pi$
$461$	0.186393	+	1.29639i	0.186393	+	1.29639i	−0.654861	+	0.755750i	$0.727273\pi$
$462$	−0.157116	+	0.597730i	−0.157116	+	0.597730i
$463$	0.209698	−	1.45848i	0.209698	−	1.45848i	−0.564443	−	0.825472i	$-0.690909\pi$
$463$	0.209698	−	1.45848i	0.209698	−	1.45848i	0.774142	−	0.633012i	$-0.218182\pi$
$464$	1.87141	+	0.214724i	1.87141	+	0.214724i
$465$	0.797850	+	2.04926i	0.797850	+	2.04926i
$466$		0			0
$467$	0.468333	+	1.78172i	0.468333	+	1.78172i	0.610648	+	0.791902i	$0.290909\pi$
$467$	0.468333	+	1.78172i	0.468333	+	1.78172i	−0.142315	+	0.989821i	$0.545455\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	0.332955	−	0.384251i	0.332955	−	0.384251i
$473$		0			0
$474$	0.611204	+	0.705367i	0.611204	+	0.705367i
$475$		0			0
$476$		0			0
$477$	0.919665	+	1.74296i	0.919665	+	1.74296i
$478$		0			0
$479$		0			0		0.0285561	−	0.999592i	$-0.490909\pi$
$479$		0			0		−0.0285561	+	0.999592i	$0.509091\pi$
$480$	0.166702	−	1.94088i	0.166702	−	1.94088i
$481$		0			0
$482$	0.0420768	−	0.0386178i	0.0420768	−	0.0386178i
$483$		0			0
$484$	0.974012	+	0.226497i	0.974012	+	0.226497i
$485$	0.773718			0.773718
$486$	−0.736741	+	0.676175i	−0.736741	+	0.676175i
$487$	1.49041	+	1.08285i	1.49041	+	1.08285i	0.974012	+	0.226497i	$0.0727273\pi$
$487$	1.49041	+	1.08285i	1.49041	+	1.08285i	0.516397	+	0.856349i	$0.327273\pi$
$488$		0			0
$489$		0			0
$490$	−1.19610	+	0.137239i	−1.19610	+	0.137239i
$491$	−0.387721	−	0.734813i	−0.387721	−	0.734813i	0.610648	−	0.791902i	$-0.290909\pi$
$491$	−0.387721	−	0.734813i	−0.387721	−	0.734813i	−0.998369	+	0.0570888i	$0.981818\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$	1.63878	+	1.05318i	1.63878	+	1.05318i
$496$	0.739263	−	0.853155i	0.739263	−	0.853155i
$497$		0			0
$498$	−1.64021	−	0.585227i	−1.64021	−	0.585227i
$499$		0			0		0.610648	−	0.791902i	$-0.290909\pi$
$499$		0			0		−0.610648	+	0.791902i	$0.709091\pi$
$500$	−3.44510	−	0.596198i	−3.44510	−	0.596198i
$501$		0			0
$502$	−1.21371	−	0.685414i	−1.21371	−	0.685414i
$503$		0			0		−0.362808	−	0.931864i	$-0.618182\pi$
$503$		0			0		0.362808	+	0.931864i	$0.381818\pi$
$504$	0.614005	+	0.0704506i	0.614005	+	0.0704506i
$505$	0.201164	−	1.39913i	0.201164	−	1.39913i
$506$		0			0
$507$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$508$	−0.0237252	−	0.830491i	−0.0237252	−	0.830491i
$509$	−1.03111	−	0.0589610i	−1.03111	−	0.0589610i	−0.466667	−	0.884433i	$-0.654545\pi$
$509$	−1.03111	−	0.0589610i	−1.03111	−	0.0589610i	−0.564443	+	0.825472i	$0.690909\pi$
$510$		0			0
$511$	−0.381343	+	1.17365i	−0.381343	+	1.17365i
$512$	−0.921124	+	0.389270i	−0.921124	+	0.389270i
$513$		0			0
$514$		0			0
$515$	1.99879	−	3.31463i	1.99879	−	3.31463i
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−1.65323	+	0.812838i	−1.65323	+	0.812838i
$520$		0			0
$521$		0			0		−0.974012	−	0.226497i	$-0.927273\pi$
$521$		0			0		0.974012	+	0.226497i	$0.0727273\pi$
$522$	1.69042	+	0.831123i	1.69042	+	0.831123i
$523$		0			0		−0.516397	−	0.856349i	$-0.672727\pi$
$523$		0			0		0.516397	+	0.856349i	$0.327273\pi$
$524$	−1.25259	+	0.910058i	−1.25259	+	0.910058i
$525$	0.343021	−	1.69288i	0.343021	−	1.69288i
$526$		0			0
$527$		0			0
$528$	0.0855750	−	0.996332i	0.0855750	−	0.996332i
$529$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$530$	−2.97192	−	2.43013i	−2.97192	−	2.43013i
$531$	0.442719	−	0.250015i	0.442719	−	0.250015i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	1.04140	−	2.67480i	1.04140	−	2.67480i
$536$		0			0
$537$	1.71599	−	0.296963i	1.71599	−	0.296963i
$538$	−0.797176	−	1.74557i	−0.797176	−	1.74557i
$539$	−0.614005	+	0.0704506i	−0.614005	+	0.0704506i
$540$	0.809238	−	1.77198i	0.809238	−	1.77198i
$541$		0			0		0.254218	−	0.967147i	$-0.418182\pi$
$541$		0			0		−0.254218	+	0.967147i	$0.581818\pi$
$542$	−0.912794	+	0.939243i	−0.912794	+	0.939243i
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$		0			0		0.696938	−	0.717132i	$-0.254545\pi$
$547$		0			0		−0.696938	+	0.717132i	$0.745455\pi$
$548$		0			0
$549$		0			0
$550$	−2.75386	−	0.476575i	−2.75386	−	0.476575i
$551$		0			0
$552$		0			0
$553$	0.269189	−	0.510170i	0.269189	−	0.510170i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	1.38479	+	1.42491i	1.38479	+	1.42491i	0.774142	+	0.633012i	$0.218182\pi$
$557$	1.38479	+	1.42491i	1.38479	+	1.42491i	0.610648	+	0.791902i	$0.290909\pi$
$558$	0.982973	−	0.555111i	0.982973	−	0.555111i
$559$		0			0
$560$	−1.15518	+	0.339190i	−1.15518	+	0.339190i
$561$		0			0
$562$		0			0
$563$	1.08316	+	1.58407i	1.08316	+	1.58407i	0.774142	+	0.633012i	$0.218182\pi$
$563$	1.08316	+	1.58407i	1.08316	+	1.58407i	0.309017	+	0.951057i	$0.400000\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	0.554623	+	0.272690i	0.554623	+	0.272690i
$568$		0			0
$569$		0			0		0.974012	−	0.226497i	$-0.0727273\pi$
$569$		0			0		−0.974012	+	0.226497i	$0.927273\pi$
$570$		0			0
$571$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$571$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−0.998369	+	0.0570888i	−0.998369	+	0.0570888i
$577$	0.0526073	−	0.0222320i	0.0526073	−	0.0222320i	−0.362808	−	0.931864i	$-0.618182\pi$
$577$	0.0526073	−	0.0222320i	0.0526073	−	0.0222320i	0.415415	+	0.909632i	$0.363636\pi$
$578$	0.309017	−	0.951057i	0.309017	−	0.951057i
$579$	−1.73511	+	0.619086i	−1.73511	+	0.619086i
$580$	−3.66349	−	0.209486i	−3.66349	−	0.209486i
$581$	0.0307349	+	1.07586i	0.0307349	+	1.07586i
$582$	−0.0565247	−	0.393138i	−0.0565247	−	0.393138i
$583$	−1.52561	−	1.24748i	−1.52561	−	1.24748i
$584$	0.284165	−	1.97641i	0.284165	−	1.97641i
$585$		0			0
$586$	0.184465	+	0.473794i	0.184465	+	0.473794i
$587$	0.812697	+	0.458951i	0.812697	+	0.458951i	0.841254	−	0.540641i	$-0.181818\pi$
$587$	0.812697	+	0.458951i	0.812697	+	0.458951i	−0.0285561	+	0.999592i	$0.509091\pi$
$588$	0.157116	+	0.597730i	0.157116	+	0.597730i
$589$		0			0
$590$	−0.604814	+	0.784337i	−0.604814	+	0.784337i
$591$	1.15027	+	0.410416i	1.15027	+	0.410416i
$592$		0			0
$593$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$593$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$594$	0.415415	−	0.909632i	0.415415	−	0.909632i
$595$		0			0
$596$	−0.0176486	−	0.0543168i	−0.0176486	−	0.0543168i
$597$	0.851167	+	1.10381i	0.851167	+	1.10381i
$598$		0			0
$599$		0			0		0.993482	−	0.113991i	$-0.0363636\pi$
$599$		0			0		−0.993482	+	0.113991i	$0.963636\pi$
$600$	−0.0798084	+	2.79366i	−0.0798084	+	2.79366i
$601$	0.153590	−	1.78821i	0.153590	−	1.78821i	−0.362808	−	0.931864i	$-0.618182\pi$
$601$	0.153590	−	1.78821i	0.153590	−	1.78821i	0.516397	−	0.856349i	$-0.327273\pi$
$602$		0			0
$603$		0			0
$604$	0.397181			0.397181
$605$	−1.91949	−	0.332181i	−1.91949	−	0.332181i
$606$	−0.725615			−0.725615
$607$	−1.23957	+	1.13767i	−1.23957	+	1.13767i	−0.254218	+	0.967147i	$0.581818\pi$
$607$	−1.23957	+	1.13767i	−1.23957	+	1.13767i	−0.985354	+	0.170522i	$0.945455\pi$
$608$		0			0
$609$	0.0996250	−	1.15991i	0.0996250	−	1.15991i
$610$		0			0
$611$		0			0
$612$		0			0
$613$		0			0		−0.610648	−	0.791902i	$-0.709091\pi$
$613$		0			0		0.610648	+	0.791902i	$0.290909\pi$
$614$		0			0
$615$		0			0
$616$	−0.592999	+	0.174120i	−0.592999	+	0.174120i
$617$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$617$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$618$	−1.83024	−	0.773465i	−1.83024	−	0.773465i
$619$		0			0		−0.941844	−	0.336049i	$-0.890909\pi$
$619$		0			0		0.941844	+	0.336049i	$0.109091\pi$
$620$	−1.34287	+	1.74147i	−1.34287	+	1.74147i
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	3.98991	+	0.457800i	3.98991	+	0.457800i
$626$	0.132827	−	0.923835i	0.132827	−	0.923835i
$627$		0			0
$628$		0			0
$629$		0			0
$630$	−1.20198	−	0.0687318i	−1.20198	−	0.0687318i
$631$	−1.64021	+	0.585227i	−1.64021	+	0.585227i	−0.985354	−	0.170522i	$-0.945455\pi$
$631$	−1.64021	+	0.585227i	−1.64021	+	0.585227i	−0.654861	+	0.755750i	$0.727273\pi$
$632$	−0.288416	+	0.887654i	−0.288416	+	0.887654i
$633$		0			0
$634$	0.284165	−	0.0162492i	0.284165	−	0.0162492i
$635$	0.138501	+	1.61254i	0.138501	+	1.61254i
$636$	−1.01767	+	1.68761i	−1.01767	+	1.68761i
$637$		0			0
$638$	−1.88062	−	0.107538i	−1.88062	−	0.107538i
$639$		0			0
$640$	1.74815	−	0.859509i	1.74815	−	0.859509i
$641$		0			0		0.974012	−	0.226497i	$-0.0727273\pi$
$641$		0			0		−0.974012	+	0.226497i	$0.927273\pi$
$642$	−1.43519	−	0.333739i	−1.43519	−	0.333739i
$643$		0			0		−0.897398	−	0.441221i	$-0.854545\pi$
$643$		0			0		0.897398	+	0.441221i	$0.145455\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		−0.564443	−	0.825472i	$-0.690909\pi$
$647$		0			0		0.564443	+	0.825472i	$0.309091\pi$
$648$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$649$	−0.310476	+	0.402632i	−0.310476	+	0.402632i
$650$		0			0
$651$	−0.540111	−	0.441647i	−0.540111	−	0.441647i
$652$		0			0
$653$	0.119281	+	0.122737i	0.119281	+	0.122737i	0.774142	−	0.633012i	$-0.218182\pi$
$653$	0.119281	+	0.122737i	0.119281	+	0.122737i	−0.654861	+	0.755750i	$0.727273\pi$
$654$		0			0
$655$	2.33488	−	1.90922i	2.33488	−	1.90922i
$656$		0			0
$657$	0.931812	−	1.76598i	0.931812	−	1.76598i
$658$		0			0
$659$	0.164995	+	0.361288i	0.164995	+	0.361288i	0.974012	−	0.226497i	$-0.0727273\pi$
$659$	0.164995	+	0.361288i	0.164995	+	0.361288i	−0.809017	+	0.587785i	$0.800000\pi$
$660$	−0.0556279	+	1.94723i	−0.0556279	+	1.94723i
$661$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$661$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$662$		0			0
$663$		0			0
$664$	−0.345844	−	1.70681i	−0.345844	−	1.70681i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$	−0.310476	+	1.18117i	−0.310476	+	1.18117i
$670$		0			0
$671$		0			0
$672$	0.256741	+	0.562183i	0.256741	+	0.562183i
$673$	−1.37346	+	0.237687i	−1.37346	+	0.237687i	−0.809017	−	0.587785i	$-0.800000\pi$
$673$	−1.37346	+	0.237687i	−1.37346	+	0.237687i	−0.564443	+	0.825472i	$0.690909\pi$
$674$	0.611204	−	1.15836i	0.611204	−	1.15836i
$675$	−1.01397	+	2.60437i	−1.01397	+	2.60437i
$676$	0.774142	−	0.633012i	0.774142	−	0.633012i
$677$	−0.873918	+	1.27806i	−0.873918	+	1.27806i	0.0855750	+	0.996332i	$0.472727\pi$
$677$	−0.873918	+	1.27806i	−0.873918	+	1.27806i	−0.959493	+	0.281733i	$0.909091\pi$
$678$		0			0
$679$	−0.213743	+	0.120706i	−0.213743	+	0.120706i
$680$		0			0
$681$	−1.33741	+	0.392700i	−1.33741	+	0.392700i
$682$	−0.689352	+	0.893968i	−0.689352	+	0.893968i
$683$	−1.90648	−	0.559792i	−1.90648	−	0.559792i	−0.985354	−	0.170522i	$-0.945455\pi$
$683$	−1.90648	−	0.559792i	−1.90648	−	0.559792i	−0.921124	−	0.389270i	$-0.872727\pi$
$684$		0			0
$685$		0			0
$686$	0.809017	−	0.587785i	0.809017	−	0.587785i
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$		0			0		0.897398	−	0.441221i	$-0.145455\pi$
$691$		0			0		−0.897398	+	0.441221i	$0.854545\pi$
$692$	−1.54980	−	0.995994i	−1.54980	−	0.995994i
$693$	−0.617026	−	0.0352828i	−0.617026	−	0.0352828i
$694$	−1.65786	+	1.06545i	−1.65786	+	1.06545i
$695$		0			0
$696$	0.161197	+	1.87678i	0.161197	+	1.87678i
$697$		0			0
$698$		0			0
$699$		0			0
$700$	1.62683	−	0.580451i	1.62683	−	0.580451i
$701$	0.284165	+	0.0162492i	0.284165	+	0.0162492i	0.198590	−	0.980083i	$-0.436364\pi$
$701$	0.284165	+	0.0162492i	0.284165	+	0.0162492i	0.0855750	+	0.996332i	$0.472727\pi$
$702$		0			0
$703$		0			0
$704$	0.897398	−	0.441221i	0.897398	−	0.441221i
$705$		0			0
$706$		0			0
$707$	0.162703	+	0.417899i	0.162703	+	0.417899i
$708$	0.442719	+	0.250015i	0.442719	+	0.250015i
$709$		0			0		−0.254218	−	0.967147i	$-0.581818\pi$
$709$		0			0		0.254218	+	0.967147i	$0.418182\pi$
$710$		0			0
$711$	−0.569939	+	0.739110i	−0.569939	+	0.739110i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	1.14043	+	1.31613i	1.14043	+	1.31613i
$717$		0			0
$718$		0			0
$719$		0			0		−0.466667	−	0.884433i	$-0.654545\pi$
$719$		0			0		0.466667	+	0.884433i	$0.345455\pi$
$720$	1.93533	−	0.222058i	1.93533	−	0.222058i
$721$	−0.0350671	+	1.22751i	−0.0350671	+	1.22751i
$722$	0.0855750	−	0.996332i	0.0855750	−	0.996332i
$723$	0.0462047	+	0.0335697i	0.0462047	+	0.0335697i
$724$		0			0
$725$	5.26453			5.26453
$726$	−0.0285561	+	0.999592i	−0.0285561	+	0.999592i
$727$	1.68251			1.68251			0.841254	−	0.540641i	$-0.181818\pi$
$727$	1.68251			1.68251			0.841254	+	0.540641i	$0.181818\pi$
$728$		0			0
$729$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$730$	−0.332861	+	3.87543i	−0.332861	+	3.87543i
$731$		0			0
$732$		0			0
$733$		0			0		−0.466667	−	0.884433i	$-0.654545\pi$
$733$		0			0		0.466667	+	0.884433i	$0.345455\pi$
$734$	−1.21930	−	1.58122i	−1.21930	−	1.58122i
$735$	−0.372039	−	1.14502i	−0.372039	−	1.14502i
$736$		0			0
$737$		0			0
$738$		0			0
$739$		0			0		−0.921124	−	0.389270i	$-0.872727\pi$
$739$		0			0		0.921124	+	0.389270i	$0.127273\pi$
$740$		0			0
$741$		0			0
$742$	1.20013	+	0.207690i	1.20013	+	0.207690i
$743$		0			0		−0.254218	−	0.967147i	$-0.581818\pi$
$743$		0			0		0.254218	+	0.967147i	$0.418182\pi$
$744$	0.982973	+	0.555111i	0.982973	+	0.555111i
$745$	0.0403644	+	0.103675i	0.0403644	+	0.103675i
$746$		0			0
$747$	0.247840	−	1.72377i	0.247840	−	1.72377i
$748$		0			0
$749$	0.129601	+	0.901393i	0.129601	+	0.901393i
$750$	−0.0998407	−	3.49488i	−0.0998407	−	3.49488i
$751$	−0.829475	−	0.0474311i	−0.829475	−	0.0474311i	−0.362808	−	0.931864i	$-0.618182\pi$
$751$	−0.829475	−	0.0474311i	−0.829475	−	0.0474311i	−0.466667	+	0.884433i	$0.654545\pi$
$752$		0			0
$753$	0.430731	−	1.32565i	0.430731	−	1.32565i
$754$		0			0
$755$	−0.772456	+	0.0441706i	−0.772456	+	0.0441706i
$756$	0.0528883	+	0.615767i	0.0528883	+	0.615767i
$757$		0			0		0.516397	−	0.856349i	$-0.327273\pi$
$757$		0			0		−0.516397	+	0.856349i	$0.672727\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$		0			0		0.897398	−	0.441221i	$-0.145455\pi$
$761$		0			0		−0.897398	+	0.441221i	$0.854545\pi$
$762$	0.809238	−	0.188180i	0.809238	−	0.188180i
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−0.564443	−	0.825472i	−0.564443	−	0.825472i
$769$	0.696223	+	0.204429i	0.696223	+	0.204429i	0.610648	−	0.791902i	$-0.290909\pi$
$769$	0.696223	+	0.204429i	0.696223	+	0.204429i	0.0855750	+	0.996332i	$0.472727\pi$
$770$	1.13393	−	0.404585i	1.13393	−	0.404585i
$771$		0			0
$772$	−1.42616	−	1.16617i	−1.42616	−	1.16617i
$773$	−1.64021	+	0.926272i	−1.64021	+	0.926272i	−0.654861	+	0.755750i	$0.727273\pi$
$773$	−1.64021	+	0.926272i	−1.64021	+	0.926272i	−0.985354	+	0.170522i	$0.945455\pi$
$774$		0			0
$775$	1.78082	−	2.60437i	1.78082	−	2.60437i
$776$	0.307474	−	0.251420i	0.307474	−	0.251420i
$777$		0			0
$778$	−0.785171	+	1.48806i	−0.785171	+	1.48806i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−0.478868	+	1.82180i	−0.478868	+	1.82180i
$784$	−0.430731	+	0.443212i	−0.430731	+	0.443212i
$785$		0			0
$786$	−1.14068	−	1.04691i	−1.14068	−	1.04691i
$787$		0			0		−0.736741	−	0.676175i	$-0.763636\pi$
$787$		0			0		0.736741	+	0.676175i	$0.236364\pi$
$788$	0.242538	+	1.19697i	0.242538	+	1.19697i
$789$		0			0
$790$	0.462209	−	1.75843i	0.462209	−	1.75843i
$791$		0			0
$792$	0.993482	−	0.113991i	0.993482	−	0.113991i
$793$		0			0
$794$		0			0
$795$	1.79153	−	3.39533i	1.79153	−	3.39533i
$796$	−0.505709	+	1.29890i	−0.505709	+	1.29890i
$797$	0.799530	−	0.653772i	0.799530	−	0.653772i	−0.142315	−	0.989821i	$-0.545455\pi$
$797$	0.799530	−	0.653772i	0.799530	−	0.653772i	0.941844	+	0.336049i	$0.109091\pi$
$798$		0			0
$799$		0			0
$800$	−2.43356	+	1.37429i	−2.43356	+	1.37429i
$801$		0			0
$802$		0			0
$803$	−0.170871	+	1.98941i	−0.170871	+	1.98941i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	1.55249	−	1.12795i	1.55249	−	1.12795i
$808$	−0.374706	−	0.621380i	−0.374706	−	0.621380i
$809$		0			0		−0.897398	−	0.441221i	$-0.854545\pi$
$809$		0			0		0.897398	+	0.441221i	$0.145455\pi$
$810$	1.89740	+	0.441221i	1.89740	+	0.441221i
$811$		0			0		0.974012	−	0.226497i	$-0.0727273\pi$
$811$		0			0		−0.974012	+	0.226497i	$0.927273\pi$
$812$	1.04474	−	0.513662i	1.04474	−	0.513662i
$813$	−1.10181	−	0.708089i	−1.10181	−	0.708089i
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	1.61540	−	0.0923716i	1.61540	−	0.0923716i
$819$		0			0
$820$		0			0
$821$	−1.38779	+	0.495163i	−1.38779	+	0.495163i	−0.921124	−	0.389270i	$-0.872727\pi$
$821$	−1.38779	+	0.495163i	−1.38779	+	0.495163i	−0.466667	+	0.884433i	$0.654545\pi$
$822$		0			0
$823$	0.0207207	+	0.725319i	0.0207207	+	0.725319i	0.941844	+	0.336049i	$0.109091\pi$
$823$	0.0207207	+	0.725319i	0.0207207	+	0.725319i	−0.921124	+	0.389270i	$0.872727\pi$
$824$	−0.282774	−	1.96674i	−0.282774	−	1.96674i
$825$	−0.0798084	−	2.79366i	−0.0798084	−	2.79366i
$826$	0.0447198	−	0.311033i	0.0447198	−	0.311033i
$827$	−1.83024	−	0.210000i	−1.83024	−	0.210000i	−0.870746	−	0.491733i	$-0.836364\pi$
$827$	−1.83024	−	0.210000i	−1.83024	−	0.210000i	−0.959493	+	0.281733i	$0.909091\pi$
$828$		0			0
$829$		0			0		−0.870746	−	0.491733i	$-0.836364\pi$
$829$		0			0		0.870746	+	0.491733i	$0.163636\pi$
$830$	0.862428	+	3.28101i	0.862428	+	3.28101i
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$	0.739263	+	0.853155i	0.739263	+	0.853155i
$838$	0.0528883	+	0.162773i	0.0528883	+	0.162773i
$839$		0			0		−0.610648	−	0.791902i	$-0.709091\pi$
$839$		0			0		0.610648	+	0.791902i	$0.290909\pi$
$840$	−0.561842	−	1.06481i	−0.561842	−	1.06481i
$841$	2.53167	−	0.290482i	2.53167	−	0.290482i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−1.43519	+	1.31720i	−1.43519	+	1.31720i
$846$		0			0
$847$	0.582092	−	0.207690i	0.582092	−	0.207690i
$848$	−1.97071			−1.97071
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		0.993482	−	0.113991i	$-0.0363636\pi$
$853$		0			0		−0.993482	+	0.113991i	$0.963636\pi$
$854$		0			0
$855$		0			0
$856$	−0.455331	−	1.40136i	−0.455331	−	1.40136i
$857$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$857$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$858$		0			0
$859$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$859$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.985354	−	0.170522i	$-0.945455\pi$
$863$		0			0		0.985354	+	0.170522i	$0.0545455\pi$
$864$	−0.254218	−	0.967147i	−0.254218	−	0.967147i
$865$	3.12488	+	1.76470i	3.12488	+	1.76470i
$866$	−0.561729	−	1.44279i	−0.561729	−	1.44279i
$867$	0.993482	+	0.113991i	0.993482	+	0.113991i
$868$	0.0992917	−	0.690589i	0.0992917	−	0.690589i
$869$	0.237271	−	0.902672i	0.237271	−	0.902672i
$870$	−0.522220	−	3.63212i	−0.522220	−	3.63212i
$871$		0			0
$872$		0			0
$873$	0.374083	−	0.133472i	0.374083	−	0.133472i
$874$		0			0
$875$	−1.99040	+	0.841149i	−1.99040	+	0.841149i
$876$	1.99348	−	0.113991i	1.99348	−	0.113991i
$877$		0			0		−0.0855750	−	0.996332i	$-0.527273\pi$
$877$		0			0		0.0855750	+	0.996332i	$0.472727\pi$
$878$	0.799530	−	1.32587i	0.799530	−	1.32587i
$879$	−0.427724	+	0.274882i	−0.427724	+	0.274882i
$880$	−1.69623	+	0.957907i	−1.69623	+	0.957907i
$881$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$881$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$882$	−0.554623	+	0.272690i	−0.554623	+	0.272690i
$883$		0			0		0.974012	−	0.226497i	$-0.0727273\pi$
$883$		0			0		−0.974012	+	0.226497i	$0.927273\pi$
$884$		0			0
$885$	−0.888825	−	0.437006i	−0.888825	−	0.437006i
$886$	0.533333	+	0.884433i	0.533333	+	0.884433i
$887$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$887$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$888$		0			0
$889$	−0.289831	−	0.423864i	−0.289831	−	0.423864i
$890$		0			0
$891$	0.974012	+	0.226497i	0.974012	+	0.226497i
$892$	−1.17182	+	0.344079i	−1.17182	+	0.344079i
$893$		0			0
$894$	0.0497301	−	0.0280839i	0.0497301	−	0.0280839i
$895$	−2.36434	−	2.43285i	−2.36434	−	2.43285i
$896$	−0.348845	+	0.510170i	−0.348845	+	0.510170i
$897$		0			0
$898$		0			0
$899$	0.992354	−	1.88072i	0.992354	−	1.88072i
$900$	−2.75386	+	0.476575i	−2.75386	+	0.476575i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$	0.0788763	+	0.389270i	0.0788763	+	0.389270i
$907$		0			0		−0.736741	−	0.676175i	$-0.763636\pi$
$907$		0			0		0.736741	+	0.676175i	$0.236364\pi$
$908$	−1.02693	−	0.942503i	−1.02693	−	0.942503i
$909$	−0.144100	−	0.711163i	−0.144100	−	0.711163i
$910$		0			0
$911$		0			0		0.254218	−	0.967147i	$-0.418182\pi$
$911$		0			0		−0.254218	+	0.967147i	$0.581818\pi$
$912$		0			0
$913$	0.442719	+	1.68428i	0.442719	+	1.68428i
$914$	−0.301432	−	0.660043i	−0.301432	−	0.660043i
$915$		0			0
$916$		0			0
$917$	−0.347168	+	0.891693i	−0.347168	+	0.891693i
$918$		0			0
$919$	−0.0966045	+	0.141280i	−0.0966045	+	0.141280i	−0.870746	−	0.491733i	$-0.836364\pi$
$919$	−0.0966045	+	0.141280i	−0.0966045	+	0.141280i	0.774142	+	0.633012i	$0.218182\pi$
$920$		0			0
$921$		0			0
$922$	−1.01391	−	0.829070i	−1.01391	−	0.829070i
$923$		0			0
$924$	−0.288416	−	0.546610i	−0.288416	−	0.546610i
$925$		0			0
$926$	0.831697	+	1.21632i	0.831697	+	1.21632i
$927$	0.394592	−	1.94739i	0.394592	−	1.94739i
$928$	−1.52394	+	1.10720i	−1.52394	+	1.10720i
$929$		0			0		−0.516397	−	0.856349i	$-0.672727\pi$
$929$		0			0		0.516397	+	0.856349i	$0.327273\pi$
$930$	−1.97347	−	0.970288i	−1.97347	−	0.970288i
$931$		0			0
$932$		0			0
$933$		0			0
$934$	−1.54980	−	0.995994i	−1.54980	−	0.995994i
$935$		0			0
$936$		0			0
$937$	−0.582954	+	0.966721i	−0.582954	+	0.966721i	0.415415	+	0.909632i	$0.363636\pi$
$937$	−0.582954	+	0.966721i	−0.582954	+	0.966721i	−0.998369	+	0.0570888i	$0.981818\pi$
$938$		0			0
$939$	0.931812	−	0.0532830i	0.931812	−	0.0532830i
$940$		0			0
$941$	0.519923	−	1.60016i	0.519923	−	1.60016i	−0.254218	−	0.967147i	$-0.581818\pi$
$941$	0.519923	−	1.60016i	0.519923	−	1.60016i	0.774142	−	0.633012i	$-0.218182\pi$
$942$		0			0
$943$		0			0
$944$	0.0145189	+	0.508229i	0.0145189	+	0.508229i
$945$	−0.171339	−	1.19169i	−0.171339	−	1.19169i
$946$		0			0
$947$	0.160657	−	1.11740i	0.160657	−	1.11740i	−0.736741	−	0.676175i	$-0.763636\pi$
$947$	0.160657	−	1.11740i	0.160657	−	1.11740i	0.897398	−	0.441221i	$-0.145455\pi$
$948$	−0.927251	−	0.106392i	−0.927251	−	0.106392i
$949$		0			0
$950$		0			0
$951$	0.0723581	+	0.275279i	0.0723581	+	0.275279i
$952$		0			0
$953$		0			0		0.610648	−	0.791902i	$-0.290909\pi$
$953$		0			0		−0.610648	+	0.791902i	$0.709091\pi$
$954$	−1.85610	−	0.662255i	−1.85610	−	0.662255i
$955$		0			0
$956$		0			0
$957$	−0.268077	−	1.86452i	−0.268077	−	1.86452i
$958$		0			0
$959$		0			0
$960$	1.18956	+	1.54264i	1.18956	+	1.54264i
$961$	−0.128046	−	0.242675i	−0.128046	−	0.242675i
$962$		0			0
$963$	0.0420768	−	1.47288i	0.0420768	−	1.47288i
$964$	−0.00488737	+	0.0569026i	−0.00488737	+	0.0569026i
$965$	2.90335	+	2.10941i	2.90335	+	2.10941i
$966$		0			0
$967$	0.171150			0.171150			0.0855750	−	0.996332i	$-0.472727\pi$
$967$	0.171150			0.171150			0.0855750	+	0.996332i	$0.472727\pi$
$968$	−0.870746	+	0.491733i	−0.870746	+	0.491733i
$969$		0			0
$970$	−0.570030	+	0.523169i	−0.570030	+	0.523169i
$971$	0.230270	+	0.167301i	0.230270	+	0.167301i	0.696938	−	0.717132i	$-0.254545\pi$
$971$	0.230270	+	0.167301i	0.230270	+	0.167301i	−0.466667	+	0.884433i	$0.654545\pi$
$972$	0.0855750	−	0.996332i	0.0855750	−	0.996332i
$973$		0			0
$974$	−1.83024	+	0.210000i	−1.83024	+	0.210000i
$975$		0			0
$976$		0			0
$977$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$977$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$978$		0			0
$979$		0			0
$980$	0.788416	−	0.909881i	0.788416	−	0.909881i
$981$		0			0
$982$	0.782513	+	0.279200i	0.782513	+	0.279200i
$983$		0			0		0.610648	−	0.791902i	$-0.290909\pi$
$983$		0			0		−0.610648	+	0.791902i	$0.709091\pi$
$984$		0			0
$985$	−0.604814	−	2.30095i	−0.604814	−	2.30095i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$	−1.91949	+	0.332181i	−1.91949	+	0.332181i
$991$	−0.0565247	−	0.393138i	−0.0565247	−	0.393138i	−0.998369	−	0.0570888i	$-0.981818\pi$
$991$	−0.0565247	−	0.393138i	−0.0565247	−	0.393138i	0.941844	−	0.336049i	$-0.109091\pi$
$992$	0.0322365	+	1.12843i	0.0322365	+	1.12843i
$993$		0			0
$994$		0			0
$995$	0.839074	−	2.58241i	0.839074	−	2.58241i
$996$	1.60413	−	0.677911i	1.60413	−	0.677911i
$997$		0			0		0.998369	−	0.0570888i	$-0.0181818\pi$
$997$		0			0		−0.998369	+	0.0570888i	$0.981818\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2904.1.cj.b.1853.1	yes	40
3.2	odd	2		2904.1.cj.a.1853.1	✓	40
8.5	even	2		2904.1.cj.a.1853.1	✓	40
24.5	odd	2	CM	2904.1.cj.b.1853.1	yes	40
121.86	even	55	inner	2904.1.cj.b.1901.1	yes	40
363.86	odd	110		2904.1.cj.a.1901.1	yes	40
968.933	even	110		2904.1.cj.a.1901.1	yes	40
2904.1901	odd	110	inner	2904.1.cj.b.1901.1	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2904.1.cj.a.1853.1	✓	40	3.2	odd	2
2904.1.cj.a.1853.1	✓	40	8.5	even	2
2904.1.cj.a.1901.1	yes	40	363.86	odd	110
2904.1.cj.a.1901.1	yes	40	968.933	even	110
2904.1.cj.b.1853.1	yes	40	1.1	even	1	trivial
2904.1.cj.b.1853.1	yes	40	24.5	odd	2	CM
2904.1.cj.b.1901.1	yes	40	121.86	even	55	inner
2904.1.cj.b.1901.1	yes	40	2904.1901	odd	110	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2904 = 2^{3} \cdot 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2904.cj (of order \(110\), degree \(40\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.736741 + 0.676175i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(0.0855750 - 0.996332i) q^{4} +(-0.0556279 + 1.94723i) q^{5} +(0.993482 - 0.113991i) q^{6} +(-0.288416 - 0.546610i) q^{7} +(0.610648 + 0.791902i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.736741 + 0.676175i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(0.0855750 - 0.996332i) q^{4} +(-0.0556279 + 1.94723i) q^{5} +(0.993482 - 0.113991i) q^{6} +(-0.288416 - 0.546610i) q^{7} +(0.610648 + 0.791902i) q^{8} +(0.309017 + 0.951057i) q^{9} +(-1.27568 - 1.47222i) q^{10} +(-0.654861 - 0.755750i) q^{11} +(-0.654861 + 0.755750i) q^{12} +(0.582092 + 0.207690i) q^{14} +(1.18956 - 1.54264i) q^{15} +(-0.985354 - 0.170522i) q^{16} +(-0.870746 - 0.491733i) q^{18} +(1.93533 + 0.222058i) q^{20} +(-0.0879554 + 0.611743i) q^{21} +(0.993482 + 0.113991i) q^{22} +(-0.0285561 - 0.999592i) q^{24} +(-2.79024 - 0.159552i) q^{25} +(0.309017 - 0.951057i) q^{27} +(-0.569286 + 0.240582i) q^{28} +(-1.88062 + 0.107538i) q^{29} +(0.166702 + 1.94088i) q^{30} +(-0.582954 + 0.966721i) q^{31} +(0.841254 - 0.540641i) q^{32} +(0.0855750 + 0.996332i) q^{33} +(1.08042 - 0.531206i) q^{35} +(0.974012 - 0.226497i) q^{36} +(-1.57598 + 1.14502i) q^{40} +(-0.348845 - 0.510170i) q^{42} +(-0.809017 + 0.587785i) q^{44} +(-1.86912 + 0.548822i) q^{45} +(0.696938 + 0.717132i) q^{48} +(0.348845 - 0.510170i) q^{49} +(2.16357 - 1.76914i) q^{50} +(1.94184 - 0.336049i) q^{53} +(0.415415 + 0.909632i) q^{54} +(1.50805 - 1.23312i) q^{55} +(0.256741 - 0.562183i) q^{56} +(1.31281 - 1.35085i) q^{58} +(-0.100971 - 0.498310i) q^{59} +(-1.43519 - 1.31720i) q^{60} +(-0.224186 - 1.10640i) q^{62} +(0.430731 - 0.443212i) q^{63} +(-0.254218 + 0.967147i) q^{64} +(-0.736741 - 0.676175i) q^{66} +(-0.436801 + 1.12191i) q^{70} +(-0.564443 + 0.825472i) q^{72} +(-1.39160 - 1.43192i) q^{73} +(2.16357 + 1.76914i) q^{75} +(-0.224227 + 0.575924i) q^{77} +(0.526814 + 0.770442i) q^{79} +(0.386859 - 1.90922i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(-1.56281 - 0.768383i) q^{83} +(0.601972 + 0.139983i) q^{84} +(1.58466 + 1.01840i) q^{87} +(0.198590 - 0.980083i) q^{88} +(1.00595 - 1.66819i) q^{90} +(1.03984 - 0.439442i) q^{93} +(-0.998369 - 0.0570888i) q^{96} +(-0.0113419 - 0.397019i) q^{97} +(0.0879554 + 0.611743i) q^{98} +(0.516397 - 0.856349i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + q^{2} - 10 q^{3} + q^{4} + 2 q^{5} + q^{6} + 2 q^{7} + q^{8} - 10 q^{9}+O(q^{10}) \) 40 * q + q^2 - 10 * q^3 + q^4 + 2 * q^5 + q^6 + 2 * q^7 + q^8 - 10 * q^9	\( 40 q + q^{2} - 10 q^{3} + q^{4} + 2 q^{5} + q^{6} + 2 q^{7} + q^{8} - 10 q^{9} - 9 q^{10} - 4 q^{11} - 4 q^{12} + 2 q^{14} - 3 q^{15} + q^{16} + q^{18} + 2 q^{20} + 2 q^{21} + q^{22} + q^{24} + 3 q^{25} - 10 q^{27} - 3 q^{28} - 3 q^{29} - 14 q^{30} - 3 q^{31} - 4 q^{32} + q^{33} - q^{35} + q^{36} - 3 q^{40} - 3 q^{42} - 10 q^{44} + 2 q^{45} + q^{48} + 3 q^{49} - 2 q^{50} + 41 q^{53} - 4 q^{54} + 2 q^{55} + 2 q^{56} - 3 q^{58} + 2 q^{59} + 2 q^{60} + 2 q^{62} + 2 q^{63} + q^{64} + q^{66} - q^{70} + q^{72} - 3 q^{73} - 2 q^{75} + 2 q^{77} + 2 q^{79} - 3 q^{80} - 10 q^{81} + 2 q^{83} + 2 q^{84} + 2 q^{87} + q^{88} - 9 q^{90} - 3 q^{93} + q^{96} + 2 q^{97} - 2 q^{98} + q^{99}+O(q^{100}) \) 40 * q + q^2 - 10 * q^3 + q^4 + 2 * q^5 + q^6 + 2 * q^7 + q^8 - 10 * q^9 - 9 * q^10 - 4 * q^11 - 4 * q^12 + 2 * q^14 - 3 * q^15 + q^16 + q^18 + 2 * q^20 + 2 * q^21 + q^22 + q^24 + 3 * q^25 - 10 * q^27 - 3 * q^28 - 3 * q^29 - 14 * q^30 - 3 * q^31 - 4 * q^32 + q^33 - q^35 + q^36 - 3 * q^40 - 3 * q^42 - 10 * q^44 + 2 * q^45 + q^48 + 3 * q^49 - 2 * q^50 + 41 * q^53 - 4 * q^54 + 2 * q^55 + 2 * q^56 - 3 * q^58 + 2 * q^59 + 2 * q^60 + 2 * q^62 + 2 * q^63 + q^64 + q^66 - q^70 + q^72 - 3 * q^73 - 2 * q^75 + 2 * q^77 + 2 * q^79 - 3 * q^80 - 10 * q^81 + 2 * q^83 + 2 * q^84 + 2 * q^87 + q^88 - 9 * q^90 - 3 * q^93 + q^96 + 2 * q^97 - 2 * q^98 + q^99

Introduction

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