LMFDB - Embedded newform 2904.1.cj.b.797.1

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			797.1
Root			$0.974012 + 0.226497i$ of defining polynomial
Character	$\chi$	$=$	2904.797
Dual form			2904.1.cj.b.317.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.897398 - 0.441221i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(0.610648 - 0.791902i) q^{4} +(-1.38779 - 1.27370i) q^{5} +(-0.985354 - 0.170522i) q^{6} +(-0.617026 + 0.0352828i) q^{7} +(0.198590 - 0.980083i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(0.897398 - 0.441221i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(0.610648 - 0.791902i) q^{4} +(-1.38779 - 1.27370i) q^{5} +(-0.985354 - 0.170522i) q^{6} +(-0.617026 + 0.0352828i) q^{7} +(0.198590 - 0.980083i) q^{8} +(0.309017 + 0.951057i) q^{9} +(-1.80739 - 0.530696i) q^{10} +(-0.959493 - 0.281733i) q^{11} +(-0.959493 + 0.281733i) q^{12} +(-0.538151 + 0.303908i) q^{14} +(0.374083 + 1.84617i) q^{15} +(-0.254218 - 0.967147i) q^{16} +(0.696938 + 0.717132i) q^{18} +(-1.85610 + 0.321211i) q^{20} +(0.519923 + 0.334134i) q^{21} +(-0.985354 + 0.170522i) q^{22} +(-0.736741 + 0.676175i) q^{24} +(0.218069 + 2.53894i) q^{25} +(0.309017 - 0.951057i) q^{27} +(-0.348845 + 0.510170i) q^{28} +(-0.149028 + 1.73510i) q^{29} +(1.15027 + 1.49170i) q^{30} +(-0.0567398 - 1.98615i) q^{31} +(-0.654861 - 0.755750i) q^{32} +(0.610648 + 0.791902i) q^{33} +(0.901243 + 0.736943i) q^{35} +(0.941844 + 0.336049i) q^{36} +(-1.52394 + 1.10720i) q^{40} +(0.614005 + 0.0704506i) q^{42} +(-0.809017 + 0.587785i) q^{44} +(0.782513 - 1.71346i) q^{45} +(-0.362808 + 0.931864i) q^{48} +(-0.614005 + 0.0704506i) q^{49} +(1.31593 + 2.18222i) q^{50} +(0.129254 - 0.491733i) q^{53} +(-0.142315 - 0.989821i) q^{54} +(0.972732 + 1.61310i) q^{55} +(-0.0879554 + 0.611743i) q^{56} +(0.631827 + 1.62283i) q^{58} +(0.859717 + 1.62934i) q^{59} +(1.69042 + 0.831123i) q^{60} +(-0.927251 - 1.75734i) q^{62} +(-0.224227 - 0.575924i) q^{63} +(-0.921124 - 0.389270i) q^{64} +(0.897398 + 0.441221i) q^{66} +(1.13393 + 0.263684i) q^{70} +(0.993482 - 0.113991i) q^{72} +(-0.0620945 + 0.159489i) q^{73} +(1.31593 - 2.18222i) q^{75} +(0.601972 + 0.139983i) q^{77} +(-1.98372 - 0.227611i) q^{79} +(-0.879056 + 1.66600i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(1.07906 - 0.882340i) q^{83} +(0.582092 - 0.207690i) q^{84} +(1.14043 - 1.31613i) q^{87} +(-0.466667 + 0.884433i) q^{88} +(-0.0537907 - 1.88292i) q^{90} +(-1.12153 + 1.64018i) q^{93} +(0.0855750 + 0.996332i) q^{96} +(0.687626 - 0.631097i) q^{97} +(-0.519923 + 0.334134i) q^{98} +(-0.0285561 - 0.999592i) 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 $\left(\mathbb{Z}/2904\mathbb{Z}\right)^\times$.

$n$	$727$	$1453$	$1937$	$2785$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{47}{55}\right)$

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 $

$2$	0.897398	−	0.441221i	0.897398	−	0.441221i
$2$	0.897398	−	0.441221i	0.897398	−	0.441221i
$3$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$3$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$4$	0.610648	−	0.791902i	0.610648	−	0.791902i
$5$	−1.38779	−	1.27370i	−1.38779	−	1.27370i	−0.921124	−	0.389270i	$-0.872727\pi$
$5$	−1.38779	−	1.27370i	−1.38779	−	1.27370i	−0.466667	−	0.884433i	$-0.654545\pi$
$6$	−0.985354	−	0.170522i	−0.985354	−	0.170522i
$7$	−0.617026	+	0.0352828i	−0.617026	+	0.0352828i	−0.362808	−	0.931864i	$-0.618182\pi$
$7$	−0.617026	+	0.0352828i	−0.617026	+	0.0352828i	−0.254218	+	0.967147i	$0.581818\pi$
$8$	0.198590	−	0.980083i	0.198590	−	0.980083i
$9$	0.309017	+	0.951057i	0.309017	+	0.951057i
$10$	−1.80739	−	0.530696i	−1.80739	−	0.530696i
$11$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$11$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$12$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$13$		0			0		−0.564443	−	0.825472i	$-0.690909\pi$
$13$		0			0		0.564443	+	0.825472i	$0.309091\pi$
$14$	−0.538151	+	0.303908i	−0.538151	+	0.303908i
$15$	0.374083	+	1.84617i	0.374083	+	1.84617i
$16$	−0.254218	−	0.967147i	−0.254218	−	0.967147i
$17$		0			0		0.921124	−	0.389270i	$-0.127273\pi$
$17$		0			0		−0.921124	+	0.389270i	$0.872727\pi$
$18$	0.696938	+	0.717132i	0.696938	+	0.717132i
$19$		0			0		0.974012	−	0.226497i	$-0.0727273\pi$
$19$		0			0		−0.974012	+	0.226497i	$0.927273\pi$
$20$	−1.85610	+	0.321211i	−1.85610	+	0.321211i
$21$	0.519923	+	0.334134i	0.519923	+	0.334134i
$22$	−0.985354	+	0.170522i	−0.985354	+	0.170522i
$23$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$23$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$24$	−0.736741	+	0.676175i	−0.736741	+	0.676175i
$25$	0.218069	+	2.53894i	0.218069	+	2.53894i
$26$		0			0
$27$	0.309017	−	0.951057i	0.309017	−	0.951057i
$28$	−0.348845	+	0.510170i	−0.348845	+	0.510170i
$29$	−0.149028	+	1.73510i	−0.149028	+	1.73510i	0.415415	+	0.909632i	$0.363636\pi$
$29$	−0.149028	+	1.73510i	−0.149028	+	1.73510i	−0.564443	+	0.825472i	$0.690909\pi$
$30$	1.15027	+	1.49170i	1.15027	+	1.49170i
$31$	−0.0567398	−	1.98615i	−0.0567398	−	1.98615i	−0.142315	−	0.989821i	$-0.545455\pi$
$31$	−0.0567398	−	1.98615i	−0.0567398	−	1.98615i	0.0855750	−	0.996332i	$-0.472727\pi$
$32$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$33$	0.610648	+	0.791902i	0.610648	+	0.791902i
$34$		0			0
$35$	0.901243	+	0.736943i	0.901243	+	0.736943i
$36$	0.941844	+	0.336049i	0.941844	+	0.336049i
$37$		0			0		0.941844	−	0.336049i	$-0.109091\pi$
$37$		0			0		−0.941844	+	0.336049i	$0.890909\pi$
$38$		0			0
$39$		0			0
$40$	−1.52394	+	1.10720i	−1.52394	+	1.10720i
$41$		0			0		0.466667	−	0.884433i	$-0.345455\pi$
$41$		0			0		−0.466667	+	0.884433i	$0.654545\pi$
$42$	0.614005	+	0.0704506i	0.614005	+	0.0704506i
$43$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$43$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$44$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$45$	0.782513	−	1.71346i	0.782513	−	1.71346i
$46$		0			0
$47$		0			0		0.696938	−	0.717132i	$-0.254545\pi$
$47$		0			0		−0.696938	+	0.717132i	$0.745455\pi$
$48$	−0.362808	+	0.931864i	−0.362808	+	0.931864i
$49$	−0.614005	+	0.0704506i	−0.614005	+	0.0704506i
$50$	1.31593	+	2.18222i	1.31593	+	2.18222i
$51$		0			0
$52$		0			0
$53$	0.129254	−	0.491733i	0.129254	−	0.491733i	−0.870746	−	0.491733i	$-0.836364\pi$
$53$	0.129254	−	0.491733i	0.129254	−	0.491733i	1.00000			$0$
$54$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$55$	0.972732	+	1.61310i	0.972732	+	1.61310i
$56$	−0.0879554	+	0.611743i	−0.0879554	+	0.611743i
$57$		0			0
$58$	0.631827	+	1.62283i	0.631827	+	1.62283i
$59$	0.859717	+	1.62934i	0.859717	+	1.62934i	0.774142	+	0.633012i	$0.218182\pi$
$59$	0.859717	+	1.62934i	0.859717	+	1.62934i	0.0855750	+	0.996332i	$0.472727\pi$
$60$	1.69042	+	0.831123i	1.69042	+	0.831123i
$61$		0			0		−0.897398	−	0.441221i	$-0.854545\pi$
$61$		0			0		0.897398	+	0.441221i	$0.145455\pi$
$62$	−0.927251	−	1.75734i	−0.927251	−	1.75734i
$63$	−0.224227	−	0.575924i	−0.224227	−	0.575924i
$64$	−0.921124	−	0.389270i	−0.921124	−	0.389270i
$65$		0			0
$66$	0.897398	+	0.441221i	0.897398	+	0.441221i
$67$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$67$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$68$		0			0
$69$		0			0
$70$	1.13393	+	0.263684i	1.13393	+	0.263684i
$71$		0			0		−0.516397	−	0.856349i	$-0.672727\pi$
$71$		0			0		0.516397	+	0.856349i	$0.327273\pi$
$72$	0.993482	−	0.113991i	0.993482	−	0.113991i
$73$	−0.0620945	+	0.159489i	−0.0620945	+	0.159489i	−0.959493	−	0.281733i	$-0.909091\pi$
$73$	−0.0620945	+	0.159489i	−0.0620945	+	0.159489i	0.897398	+	0.441221i	$0.145455\pi$
$74$		0			0
$75$	1.31593	−	2.18222i	1.31593	−	2.18222i
$76$		0			0
$77$	0.601972	+	0.139983i	0.601972	+	0.139983i
$78$		0			0
$79$	−1.98372	−	0.227611i	−1.98372	−	0.227611i	−0.998369	−	0.0570888i	$-0.981818\pi$
$79$	−1.98372	−	0.227611i	−1.98372	−	0.227611i	−0.985354	−	0.170522i	$-0.945455\pi$
$80$	−0.879056	+	1.66600i	−0.879056	+	1.66600i
$81$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$82$		0			0
$83$	1.07906	−	0.882340i	1.07906	−	0.882340i	0.0855750	−	0.996332i	$-0.472727\pi$
$83$	1.07906	−	0.882340i	1.07906	−	0.882340i	0.993482	+	0.113991i	$0.0363636\pi$
$84$	0.582092	−	0.207690i	0.582092	−	0.207690i
$85$		0			0
$86$		0			0
$87$	1.14043	−	1.31613i	1.14043	−	1.31613i
$88$	−0.466667	+	0.884433i	−0.466667	+	0.884433i
$89$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$89$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$90$	−0.0537907	−	1.88292i	−0.0537907	−	1.88292i
$91$		0			0
$92$		0			0
$93$	−1.12153	+	1.64018i	−1.12153	+	1.64018i
$94$		0			0
$95$		0			0
$96$	0.0855750	+	0.996332i	0.0855750	+	0.996332i
$97$	0.687626	−	0.631097i	0.687626	−	0.631097i	−0.254218	−	0.967147i	$-0.581818\pi$
$97$	0.687626	−	0.631097i	0.687626	−	0.631097i	0.941844	+	0.336049i	$0.109091\pi$
$98$	−0.519923	+	0.334134i	−0.519923	+	0.334134i
$99$	−0.0285561	−	0.999592i	−0.0285561	−	0.999592i
$100$	2.14375	+	1.37771i	2.14375	+	1.37771i
$101$	−1.91949	+	0.332181i	−1.91949	+	0.332181i	−0.998369	−	0.0570888i	$-0.981818\pi$
$101$	−1.91949	+	0.332181i	−1.91949	+	0.332181i	−0.921124	+	0.389270i	$0.872727\pi$
$102$		0			0
$103$	−1.37346	−	1.41326i	−1.37346	−	1.41326i	−0.809017	−	0.587785i	$-0.800000\pi$
$103$	−1.37346	−	1.41326i	−1.37346	−	1.41326i	−0.564443	−	0.825472i	$-0.690909\pi$
$104$		0			0
$105$	−0.295957	−	1.12594i	−0.295957	−	1.12594i
$106$	−0.100971	−	0.498310i	−0.100971	−	0.498310i
$107$	−1.56281	+	0.882561i	−1.56281	+	0.882561i	−0.564443	+	0.825472i	$0.690909\pi$
$107$	−1.56281	+	0.882561i	−1.56281	+	0.882561i	−0.998369	+	0.0570888i	$0.981818\pi$
$108$	−0.564443	−	0.825472i	−0.564443	−	0.825472i
$109$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$109$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$110$	1.58466	+	1.01840i	1.58466	+	1.01840i
$111$		0			0
$112$	0.190983	+	0.587785i	0.190983	+	0.587785i
$113$		0			0		0.198590	−	0.980083i	$-0.436364\pi$
$113$		0			0		−0.198590	+	0.980083i	$0.563636\pi$
$114$		0			0
$115$		0			0
$116$	1.28303	+	1.17755i	1.28303	+	1.17755i
$117$		0			0
$118$	1.49041	+	1.08285i	1.49041	+	1.08285i
$119$		0			0
$120$	1.88369			1.88369
$121$	0.841254	+	0.540641i	0.841254	+	0.540641i
$122$		0			0
$123$		0			0
$124$	−1.60749	−	1.16791i	−1.60749	−	1.16791i
$125$	1.78094	−	2.30957i	1.78094	−	2.30957i
$126$	−0.455331	−	0.417899i	−0.455331	−	0.417899i
$127$	0.280461	+	0.0485357i	0.280461	+	0.0485357i	0.309017	−	0.951057i	$-0.400000\pi$
$127$	0.280461	+	0.0485357i	0.280461	+	0.0485357i	−0.0285561	+	0.999592i	$0.509091\pi$
$128$	−0.998369	+	0.0570888i	−0.998369	+	0.0570888i
$129$		0			0
$130$		0			0
$131$	−0.990959	−	0.290972i	−0.990959	−	0.290972i	−0.254218	−	0.967147i	$-0.581818\pi$
$131$	−0.990959	−	0.290972i	−0.990959	−	0.290972i	−0.736741	+	0.676175i	$0.763636\pi$
$132$	1.00000			1.00000
$133$		0			0
$134$		0			0
$135$	−1.64021	+	0.926272i	−1.64021	+	0.926272i
$136$		0			0
$137$		0			0		−0.254218	−	0.967147i	$-0.581818\pi$
$137$		0			0		0.254218	+	0.967147i	$0.418182\pi$
$138$		0			0
$139$		0			0		−0.696938	−	0.717132i	$-0.745455\pi$
$139$		0			0		0.696938	+	0.717132i	$0.254545\pi$
$140$	1.13393	−	0.263684i	1.13393	−	0.263684i
$141$		0			0
$142$		0			0
$143$		0			0
$144$	0.841254	−	0.540641i	0.841254	−	0.540641i
$145$	2.41683	−	2.21814i	2.41683	−	2.21814i
$146$	0.0146462	+	0.170522i	0.0146462	+	0.170522i
$147$	0.538151	+	0.303908i	0.538151	+	0.303908i
$148$		0			0
$149$	0.831697	−	1.21632i	0.831697	−	1.21632i	−0.142315	−	0.989821i	$-0.545455\pi$
$149$	0.831697	−	1.21632i	0.831697	−	1.21632i	0.974012	−	0.226497i	$-0.0727273\pi$
$150$	0.218069	−	2.53894i	0.218069	−	2.53894i
$151$	−0.569939	−	0.739110i	−0.569939	−	0.739110i	0.415415	−	0.909632i	$-0.363636\pi$
$151$	−0.569939	−	0.739110i	−0.569939	−	0.739110i	−0.985354	+	0.170522i	$0.945455\pi$
$152$		0			0
$153$		0			0
$154$	0.601972	−	0.139983i	0.601972	−	0.139983i
$155$	−2.45103	+	2.82864i	−2.45103	+	2.82864i
$156$		0			0
$157$		0			0		−0.941844	−	0.336049i	$-0.890909\pi$
$157$		0			0		0.941844	+	0.336049i	$0.109091\pi$
$158$	−1.88062	+	0.671003i	−1.88062	+	0.671003i
$159$	−0.393602	+	0.321847i	−0.393602	+	0.321847i
$160$	−0.0537907	+	1.88292i	−0.0537907	+	1.88292i
$161$		0			0
$162$	−0.466667	+	0.884433i	−0.466667	+	0.884433i
$163$		0			0		−0.993482	−	0.113991i	$-0.963636\pi$
$163$		0			0		0.993482	+	0.113991i	$0.0363636\pi$
$164$		0			0
$165$	0.161197	−	1.87678i	0.161197	−	1.87678i
$166$	0.579037	−	1.26791i	0.579037	−	1.26791i
$167$		0			0		0.516397	−	0.856349i	$-0.327273\pi$
$167$		0			0		−0.516397	+	0.856349i	$0.672727\pi$
$168$	0.430731	−	0.443212i	0.430731	−	0.443212i
$169$	−0.362808	+	0.931864i	−0.362808	+	0.931864i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	1.12705	+	0.0644468i	1.12705	+	0.0644468i	0.610648	−	0.791902i	$-0.290909\pi$
$173$	1.12705	+	0.0644468i	1.12705	+	0.0644468i	0.516397	+	0.856349i	$0.327273\pi$
$174$	0.442719	−	1.68428i	0.442719	−	1.68428i
$175$	−0.224135	−	1.55890i	−0.224135	−	1.55890i
$176$	−0.0285561	+	0.999592i	−0.0285561	+	0.999592i
$177$	0.262179	−	1.82350i	0.262179	−	1.82350i
$178$		0			0
$179$	−0.505709	−	1.29890i	−0.505709	−	1.29890i	−0.921124	−	0.389270i	$-0.872727\pi$
$179$	−0.505709	−	1.29890i	−0.505709	−	1.29890i	0.415415	−	0.909632i	$-0.363636\pi$
$180$	−0.879056	−	1.66600i	−0.879056	−	1.66600i
$181$		0			0		−0.897398	−	0.441221i	$-0.854545\pi$
$181$		0			0		0.897398	+	0.441221i	$0.145455\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$	−0.282774	+	1.96674i	−0.282774	+	1.96674i
$187$		0			0
$188$		0			0
$189$	−0.157116	+	0.597730i	−0.157116	+	0.597730i
$190$		0			0
$191$		0			0		−0.974012	−	0.226497i	$-0.927273\pi$
$191$		0			0		0.974012	+	0.226497i	$0.0727273\pi$
$192$	0.516397	+	0.856349i	0.516397	+	0.856349i
$193$	−1.12153	+	0.128683i	−1.12153	+	0.128683i	−0.654861	−	0.755750i	$-0.727273\pi$
$193$	−1.12153	+	0.128683i	−1.12153	+	0.128683i	−0.466667	+	0.884433i	$0.654545\pi$
$194$	0.338621	−	0.869741i	0.338621	−	0.869741i
$195$		0			0
$196$	−0.319151	+	0.529253i	−0.319151	+	0.529253i
$197$	0.164995	−	0.361288i	0.164995	−	0.361288i	−0.809017	−	0.587785i	$-0.800000\pi$
$197$	0.164995	−	0.361288i	0.164995	−	0.361288i	0.974012	+	0.226497i	$0.0727273\pi$
$198$	−0.466667	−	0.884433i	−0.466667	−	0.884433i
$199$	−0.301432	−	0.660043i	−0.301432	−	0.660043i	0.696938	−	0.717132i	$-0.254545\pi$
$199$	−0.301432	−	0.660043i	−0.301432	−	0.660043i	−0.998369	+	0.0570888i	$0.981818\pi$
$200$	2.53167	+	0.290482i	2.53167	+	0.290482i
$201$		0			0
$202$	−1.57598	+	1.14502i	−1.57598	+	1.14502i
$203$	0.0307349	−	1.07586i	0.0307349	−	1.07586i
$204$		0			0
$205$		0			0
$206$	−1.85610	−	0.662255i	−1.85610	−	0.662255i
$207$		0			0
$208$		0			0
$209$		0			0
$210$	−0.762378	−	0.879831i	−0.762378	−	0.879831i
$211$		0			0		−0.0285561	−	0.999592i	$-0.509091\pi$
$211$		0			0		0.0285561	+	0.999592i	$0.490909\pi$
$212$	−0.310476	−	0.402632i	−0.310476	−	0.402632i
$213$		0			0
$214$	−1.01306	+	1.48155i	−1.01306	+	1.48155i
$215$		0			0
$216$	−0.870746	−	0.491733i	−0.870746	−	0.491733i
$217$	0.105087	+	1.22351i	0.105087	+	1.22351i
$218$		0			0
$219$	0.143981	−	0.0925307i	0.143981	−	0.0925307i
$220$	1.87141	+	0.214724i	1.87141	+	0.214724i
$221$		0			0
$222$		0			0
$223$	0.386859	−	0.0899602i	0.386859	−	0.0899602i	−0.0285561	−	0.999592i	$-0.509091\pi$
$223$	0.386859	−	0.0899602i	0.386859	−	0.0899602i	0.415415	+	0.909632i	$0.363636\pi$
$224$	0.430731	+	0.443212i	0.430731	+	0.443212i
$225$	−2.34728	+	0.991970i	−2.34728	+	0.991970i
$226$		0			0
$227$	−0.144100	−	0.711163i	−0.144100	−	0.711163i	−0.985354	−	0.170522i	$-0.945455\pi$
$227$	−0.144100	−	0.711163i	−0.144100	−	0.711163i	0.841254	−	0.540641i	$-0.181818\pi$
$228$		0			0
$229$		0			0		−0.564443	−	0.825472i	$-0.690909\pi$
$229$		0			0		0.564443	+	0.825472i	$0.309091\pi$
$230$		0			0
$231$	−0.404726	−	0.467079i	−0.404726	−	0.467079i
$232$	1.67095	+	0.490635i	1.67095	+	0.490635i
$233$		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
$236$	1.81527	+	0.314144i	1.81527	+	0.314144i
$237$	1.47108	+	1.35014i	1.47108	+	1.35014i
$238$		0			0
$239$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$239$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$240$	1.69042	−	0.831123i	1.69042	−	0.831123i
$241$	−1.47348			−1.47348			−0.736741	−	0.676175i	$-0.763636\pi$
$241$	−1.47348			−1.47348			−0.736741	+	0.676175i	$0.763636\pi$
$242$	0.993482	+	0.113991i	0.993482	+	0.113991i
$243$	1.00000			1.00000
$244$		0			0
$245$	0.941844	+	0.684290i	0.941844	+	0.684290i
$246$		0			0
$247$		0			0
$248$	−1.95786	−	0.338821i	−1.95786	−	0.338821i
$249$	−1.39160	+	0.0795747i	−1.39160	+	0.0795747i
$250$	0.579186	−	2.85839i	0.579186	−	2.85839i
$251$	−0.224227	−	0.690101i	−0.224227	−	0.690101i	−0.998369	−	0.0570888i	$-0.981818\pi$
$251$	−0.224227	−	0.690101i	−0.224227	−	0.690101i	0.774142	−	0.633012i	$-0.218182\pi$
$252$	−0.592999	−	0.174120i	−0.592999	−	0.174120i
$253$		0			0
$254$	0.273100	−	0.0801894i	0.273100	−	0.0801894i
$255$		0			0
$256$	−0.870746	+	0.491733i	−0.870746	+	0.491733i
$257$		0			0		−0.198590	−	0.980083i	$-0.563636\pi$
$257$		0			0		0.198590	+	0.980083i	$0.436364\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−1.69623	+	0.394442i	−1.69623	+	0.394442i
$262$	−1.01767	+	0.176114i	−1.01767	+	0.176114i
$263$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$263$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$264$	0.897398	−	0.441221i	0.897398	−	0.441221i
$265$	−0.805699	+	0.517791i	−0.805699	+	0.517791i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	0.256741	−	0.790166i	0.256741	−	0.790166i	−0.736741	−	0.676175i	$-0.763636\pi$
$269$	0.256741	−	0.790166i	0.256741	−	0.790166i	0.993482	−	0.113991i	$-0.0363636\pi$
$270$	−1.06324	+	1.55493i	−1.06324	+	1.55493i
$271$	−0.164217	+	1.91195i	−0.164217	+	1.91195i	0.198590	+	0.980083i	$0.436364\pi$
$271$	−0.164217	+	1.91195i	−0.164217	+	1.91195i	−0.362808	+	0.931864i	$0.618182\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	0.506065	−	2.49753i	0.506065	−	2.49753i
$276$		0			0
$277$		0			0		−0.774142	−	0.633012i	$-0.781818\pi$
$277$		0			0		0.774142	+	0.633012i	$0.218182\pi$
$278$		0			0
$279$	1.87141	−	0.667718i	1.87141	−	0.667718i
$280$	0.901243	−	0.736943i	0.901243	−	0.736943i
$281$		0			0		0.0285561	−	0.999592i	$-0.490909\pi$
$281$		0			0		−0.0285561	+	0.999592i	$0.509091\pi$
$282$		0			0
$283$		0			0		0.466667	−	0.884433i	$-0.345455\pi$
$283$		0			0		−0.466667	+	0.884433i	$0.654545\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.516397	−	0.856349i	0.516397	−	0.856349i
$289$	0.696938	−	0.717132i	0.696938	−	0.717132i
$290$	1.19016	−	3.05691i	1.19016	−	3.05691i
$291$	−0.927251	+	0.106392i	−0.927251	+	0.106392i
$292$	0.0883814	+	0.146564i	0.0883814	+	0.146564i
$293$	−1.79437	−	0.417263i	−1.79437	−	0.417263i	−0.809017	−	0.587785i	$-0.800000\pi$
$293$	−1.79437	−	0.417263i	−1.79437	−	0.417263i	−0.985354	+	0.170522i	$0.945455\pi$
$294$	0.617026	+	0.0352828i	0.617026	+	0.0352828i
$295$	0.882194	−	3.35621i	0.882194	−	3.35621i
$296$		0			0
$297$	−0.564443	+	0.825472i	−0.564443	+	0.825472i
$298$	0.209698	−	1.45848i	0.209698	−	1.45848i
$299$		0			0
$300$	−0.924537	−	2.37465i	−0.924537	−	2.37465i
$301$		0			0
$302$	−0.837573	−	0.411807i	−0.837573	−	0.411807i
$303$	1.74815	+	0.859509i	1.74815	+	0.859509i
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$307$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$308$	0.478446	−	0.391223i	0.478446	−	0.391223i
$309$	0.280461	+	1.95065i	0.280461	+	1.95065i
$310$	−0.951494	+	3.61986i	−0.951494	+	3.61986i
$311$		0			0		−0.998369	−	0.0570888i	$-0.981818\pi$
$311$		0			0		0.998369	+	0.0570888i	$0.0181818\pi$
$312$		0			0
$313$	−1.03111	−	1.70990i	−1.03111	−	1.70990i	−0.564443	−	0.825472i	$-0.690909\pi$
$313$	−1.03111	−	1.70990i	−1.03111	−	1.70990i	−0.466667	−	0.884433i	$-0.654545\pi$
$314$		0			0
$315$	−0.422375	+	1.08486i	−0.422375	+	1.08486i
$316$	−1.39160	+	1.43192i	−1.39160	+	1.43192i
$317$	0.868842	−	1.44081i	0.868842	−	1.44081i	−0.0285561	−	0.999592i	$-0.509091\pi$
$317$	0.868842	−	1.44081i	0.868842	−	1.44081i	0.897398	−	0.441221i	$-0.145455\pi$
$318$	−0.211212	+	0.462490i	−0.211212	+	0.462490i
$319$	0.631827	−	1.62283i	0.631827	−	1.62283i
$320$	0.782513	+	1.71346i	0.782513	+	1.71346i
$321$	1.78310	+	0.204591i	1.78310	+	0.204591i
$322$		0			0
$323$		0			0
$324$	−0.0285561	+	0.999592i	−0.0285561	+	0.999592i
$325$		0			0
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$	−0.683417	−	1.75534i	−0.683417	−	1.75534i
$331$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$331$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$332$	−0.0398036	−	1.39331i	−0.0398036	−	1.39331i
$333$		0			0
$334$		0			0
$335$		0			0
$336$	0.190983	−	0.587785i	0.190983	−	0.587785i
$337$	1.67095	+	0.943629i	1.67095	+	0.943629i	0.974012	+	0.226497i	$0.0727273\pi$
$337$	1.67095	+	0.943629i	1.67095	+	0.943629i	0.696938	+	0.717132i	$0.254545\pi$
$338$	0.0855750	+	0.996332i	0.0855750	+	0.996332i
$339$		0			0
$340$		0			0
$341$	−0.505123	+	1.92169i	−0.505123	+	1.92169i
$342$		0			0
$343$	0.985354	−	0.170522i	0.985354	−	0.170522i
$344$		0			0
$345$		0			0
$346$	1.03984	−	0.439442i	1.03984	−	0.439442i
$347$	0.129254	+	0.491733i	0.129254	+	0.491733i	1.00000			$0$
$347$	0.129254	+	0.491733i	0.129254	+	0.491733i	−0.870746	+	0.491733i	$0.836364\pi$
$348$	−0.345844	−	1.70681i	−0.345844	−	1.70681i
$349$		0			0		0.870746	−	0.491733i	$-0.163636\pi$
$349$		0			0		−0.870746	+	0.491733i	$0.836364\pi$
$350$	−0.888956	−	1.30006i	−0.888956	−	1.30006i
$351$		0			0
$352$	0.415415	+	0.909632i	0.415415	+	0.909632i
$353$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$353$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$354$	−0.569286	−	1.75208i	−0.569286	−	1.75208i
$355$		0			0
$356$		0			0
$357$		0			0
$358$	−1.02693	−	0.942503i	−1.02693	−	0.942503i
$359$		0			0		0.610648	−	0.791902i	$-0.290909\pi$
$359$		0			0		−0.610648	+	0.791902i	$0.709091\pi$
$360$	−1.52394	−	1.10720i	−1.52394	−	1.10720i
$361$	0.897398	−	0.441221i	0.897398	−	0.441221i
$362$		0			0
$363$	−0.362808	−	0.931864i	−0.362808	−	0.931864i
$364$		0			0
$365$	0.289315	−	0.142247i	0.289315	−	0.142247i
$366$		0			0
$367$	0.104512	−	0.135534i	0.104512	−	0.135534i	−0.736741	−	0.676175i	$-0.763636\pi$
$367$	0.104512	−	0.135534i	0.104512	−	0.135534i	0.841254	+	0.540641i	$0.181818\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−0.0624033	+	0.307972i	−0.0624033	+	0.307972i
$372$	0.614005	+	1.88971i	0.614005	+	1.88971i
$373$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$373$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$374$		0			0
$375$	−2.79835	+	0.821668i	−2.79835	+	0.821668i
$376$		0			0
$377$		0			0
$378$	0.122736	+	0.605724i	0.122736	+	0.605724i
$379$		0			0		−0.254218	−	0.967147i	$-0.581818\pi$
$379$		0			0		0.254218	+	0.967147i	$0.418182\pi$
$380$		0			0
$381$	−0.198369	−	0.204117i	−0.198369	−	0.204117i
$382$		0			0
$383$		0			0		0.985354	−	0.170522i	$-0.0545455\pi$
$383$		0			0		−0.985354	+	0.170522i	$0.945455\pi$
$384$	0.841254	+	0.540641i	0.841254	+	0.540641i
$385$	−0.657116	−	0.961001i	−0.657116	−	0.961001i
$386$	−0.949680	+	0.610322i	−0.949680	+	0.610322i
$387$		0			0
$388$	−0.0798701	−	0.929911i	−0.0798701	−	0.929911i
$389$	1.14043	+	0.644033i	1.14043	+	0.644033i	0.941844	−	0.336049i	$-0.109091\pi$
$389$	1.14043	+	0.644033i	1.14043	+	0.644033i	0.198590	+	0.980083i	$0.436364\pi$
$390$		0			0
$391$		0			0
$392$	−0.0528883	+	0.615767i	−0.0528883	+	0.615767i
$393$	0.630674	+	0.817873i	0.630674	+	0.817873i
$394$	−0.0113419	−	0.397019i	−0.0113419	−	0.397019i
$395$	2.46308	+	2.84255i	2.46308	+	2.84255i
$396$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$397$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$397$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$398$	−0.561729	−	0.459324i	−0.561729	−	0.459324i
$399$		0			0
$400$	2.40009	−	0.856349i	2.40009	−	0.856349i
$401$		0			0		0.774142	−	0.633012i	$-0.218182\pi$
$401$		0			0		−0.774142	+	0.633012i	$0.781818\pi$
$402$		0			0
$403$		0			0
$404$	−0.909079	+	1.72290i	−0.909079	+	1.72290i
$405$	1.87141	+	0.214724i	1.87141	+	0.214724i
$406$	−0.447112	−	0.979038i	−0.447112	−	0.979038i
$407$		0			0
$408$		0			0
$409$	−0.835549	+	1.38560i	−0.835549	+	1.38560i	0.0855750	+	0.996332i	$0.472727\pi$
$409$	−0.835549	+	1.38560i	−0.835549	+	1.38560i	−0.921124	+	0.389270i	$0.872727\pi$
$410$		0			0
$411$		0			0
$412$	−1.95786	+	0.224644i	−1.95786	+	0.224644i
$413$	−0.587955	−	0.975015i	−0.587955	−	0.975015i
$414$		0			0
$415$	−2.62134	−	0.149894i	−2.62134	−	0.149894i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−0.173809	+	1.20886i	−0.173809	+	1.20886i	0.696938	+	0.717132i	$0.254545\pi$
$419$	−0.173809	+	1.20886i	−0.173809	+	1.20886i	−0.870746	+	0.491733i	$0.836364\pi$
$420$	−1.07236	−	0.453182i	−1.07236	−	0.453182i
$421$		0			0		−0.362808	−	0.931864i	$-0.618182\pi$
$421$		0			0		0.362808	+	0.931864i	$0.381818\pi$
$422$		0			0
$423$		0			0
$424$	−0.456270	−	0.224333i	−0.456270	−	0.224333i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	−0.255426	+	1.77653i	−0.255426	+	1.77653i
$429$		0			0
$430$		0			0
$431$		0			0		0.254218	−	0.967147i	$-0.418182\pi$
$431$		0			0		−0.254218	+	0.967147i	$0.581818\pi$
$432$	−0.998369	−	0.0570888i	−0.998369	−	0.0570888i
$433$	1.00595	+	0.233925i	1.00595	+	0.233925i	0.696938	−	0.717132i	$-0.254545\pi$
$433$	1.00595	+	0.233925i	1.00595	+	0.233925i	0.309017	+	0.951057i	$0.400000\pi$
$434$	0.634142	+	1.05161i	0.634142	+	1.05161i
$435$	−3.25905	+	0.373941i	−3.25905	+	0.373941i
$436$		0			0
$437$		0			0
$438$	0.0883814	−	0.146564i	0.0883814	−	0.146564i
$439$	0.429039	−	0.939463i	0.429039	−	0.939463i	−0.564443	−	0.825472i	$-0.690909\pi$
$439$	0.429039	−	0.939463i	0.429039	−	0.939463i	0.993482	−	0.113991i	$-0.0363636\pi$
$440$	1.77414	−	0.633012i	1.77414	−	0.633012i
$441$	−0.256741	−	0.562183i	−0.256741	−	0.562183i
$442$		0			0
$443$	0.0266524	−	0.0505118i	0.0266524	−	0.0505118i	−0.870746	−	0.491733i	$-0.836364\pi$
$443$	0.0266524	−	0.0505118i	0.0266524	−	0.0505118i	0.897398	+	0.441221i	$0.145455\pi$
$444$		0			0
$445$		0			0
$446$	0.307474	−	0.251420i	0.307474	−	0.251420i
$447$	−1.38779	+	0.495163i	−1.38779	+	0.495163i
$448$	0.582092	+	0.207690i	0.582092	+	0.207690i
$449$		0			0		−0.774142	−	0.633012i	$-0.781818\pi$
$449$		0			0		0.774142	+	0.633012i	$0.218182\pi$
$450$	−1.66877	+	1.92586i	−1.66877	+	1.92586i
$451$		0			0
$452$		0			0
$453$	0.0266524	+	0.932954i	0.0266524	+	0.932954i
$454$	−0.443096	−	0.574616i	−0.443096	−	0.574616i
$455$		0			0
$456$		0			0
$457$	0.601972	−	1.85268i	0.601972	−	1.85268i	0.0855750	−	0.996332i	$-0.472727\pi$
$457$	0.601972	−	1.85268i	0.601972	−	1.85268i	0.516397	−	0.856349i	$-0.327273\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−1.61435	+	1.03748i	−1.61435	+	1.03748i	−0.654861	+	0.755750i	$0.727273\pi$
$461$	−1.61435	+	1.03748i	−1.61435	+	1.03748i	−0.959493	+	0.281733i	$0.909091\pi$
$462$	−0.569286	−	0.240582i	−0.569286	−	0.240582i
$463$	1.50988	+	0.970340i	1.50988	+	0.970340i	0.993482	+	0.113991i	$0.0363636\pi$
$463$	1.50988	+	0.970340i	1.50988	+	0.970340i	0.516397	+	0.856349i	$0.327273\pi$
$464$	1.71599	−	0.296963i	1.71599	−	0.296963i
$465$	3.64555	−	0.847737i	3.64555	−	0.847737i
$466$		0			0
$467$	1.03984	−	0.439442i	1.03984	−	0.439442i	0.198590	−	0.980083i	$-0.436364\pi$
$467$	1.03984	−	0.439442i	1.03984	−	0.439442i	0.841254	+	0.540641i	$0.181818\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	1.76762	−	0.519021i	1.76762	−	0.519021i
$473$		0			0
$474$	1.91586	+	0.562546i	1.91586	+	0.562546i
$475$		0			0
$476$		0			0
$477$	0.507607	−	0.0290260i	0.507607	−	0.0290260i
$478$		0			0
$479$		0			0		−0.736741	−	0.676175i	$-0.763636\pi$
$479$		0			0		0.736741	+	0.676175i	$0.236364\pi$
$480$	1.15027	−	1.49170i	1.15027	−	1.49170i
$481$		0			0
$482$	−1.32230	+	0.650131i	−1.32230	+	0.650131i
$483$		0			0
$484$	0.941844	−	0.336049i	0.941844	−	0.336049i
$485$	−1.75811			−1.75811
$486$	0.897398	−	0.441221i	0.897398	−	0.441221i
$487$	0.913288	+	0.663543i	0.913288	+	0.663543i	0.941844	−	0.336049i	$-0.109091\pi$
$487$	0.913288	+	0.663543i	0.913288	+	0.663543i	−0.0285561	+	0.999592i	$0.509091\pi$
$488$		0			0
$489$		0			0
$490$	1.14713	+	0.198519i	1.14713	+	0.198519i
$491$	0.284165	−	0.0162492i	0.284165	−	0.0162492i	0.0855750	−	0.996332i	$-0.472727\pi$
$491$	0.284165	−	0.0162492i	0.284165	−	0.0162492i	0.198590	+	0.980083i	$0.436364\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$	−1.23355	+	1.42360i	−1.23355	+	1.42360i
$496$	−1.90648	+	0.559792i	−1.90648	+	0.559792i
$497$		0			0
$498$	−1.21371	+	0.685414i	−1.21371	+	0.685414i
$499$		0			0		−0.198590	−	0.980083i	$-0.563636\pi$
$499$		0			0		0.198590	+	0.980083i	$0.436364\pi$
$500$	−0.741424	−	2.82067i	−0.741424	−	2.82067i
$501$		0			0
$502$	−0.505709	−	0.520362i	−0.505709	−	0.520362i
$503$		0			0		0.974012	−	0.226497i	$-0.0727273\pi$
$503$		0			0		−0.974012	+	0.226497i	$0.927273\pi$
$504$	−0.608982	+	0.105389i	−0.608982	+	0.105389i
$505$	3.08696	+	1.98387i	3.08696	+	1.98387i
$506$		0			0
$507$	0.841254	−	0.540641i	0.841254	−	0.540641i
$508$	0.209698	−	0.192459i	0.209698	−	0.192459i
$509$	−0.00488737	−	0.0569026i	−0.00488737	−	0.0569026i	0.993482	−	0.113991i	$-0.0363636\pi$
$509$	−0.00488737	−	0.0569026i	−0.00488737	−	0.0569026i	−0.998369	+	0.0570888i	$0.981818\pi$
$510$		0			0
$511$	0.0326867	−	0.100599i	0.0326867	−	0.100599i
$512$	−0.564443	+	0.825472i	−0.564443	+	0.825472i
$513$		0			0
$514$		0			0
$515$	0.106006	+	3.71069i	0.106006	+	3.71069i
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−0.873918	−	0.714599i	−0.873918	−	0.714599i
$520$		0			0
$521$		0			0		0.941844	−	0.336049i	$-0.109091\pi$
$521$		0			0		−0.941844	+	0.336049i	$0.890909\pi$
$522$	−1.34816	+	1.10239i	−1.34816	+	1.10239i
$523$		0			0		0.0285561	−	0.999592i	$-0.490909\pi$
$523$		0			0		−0.0285561	+	0.999592i	$0.509091\pi$
$524$	−0.835549	+	0.607062i	−0.835549	+	0.607062i
$525$	−0.734966	+	1.39292i	−0.734966	+	1.39292i
$526$		0			0
$527$		0			0
$528$	0.610648	−	0.791902i	0.610648	−	0.791902i
$529$	0.415415	−	0.909632i	0.415415	−	0.909632i
$530$	−0.494573	+	0.820157i	−0.494573	+	0.820157i
$531$	−1.28393	+	1.32113i	−1.28393	+	1.32113i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	3.29298	+	0.765749i	3.29298	+	0.765749i
$536$		0			0
$537$	−0.354349	+	1.34808i	−0.354349	+	1.34808i
$538$	−0.118239	−	0.822373i	−0.118239	−	0.822373i
$539$	0.608982	+	0.105389i	0.608982	+	0.105389i
$540$	−0.268077	+	1.86452i	−0.268077	+	1.86452i
$541$		0			0		−0.921124	−	0.389270i	$-0.872727\pi$
$541$		0			0		0.921124	+	0.389270i	$0.127273\pi$
$542$	0.696223	+	1.78823i	0.696223	+	1.78823i
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$		0			0		−0.362808	−	0.931864i	$-0.618182\pi$
$547$		0			0		0.362808	+	0.931864i	$0.381818\pi$
$548$		0			0
$549$		0			0
$550$	−0.647820	−	2.46456i	−0.647820	−	2.46456i
$551$		0			0
$552$		0			0
$553$	1.23204	+	0.0704506i	1.23204	+	0.0704506i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	0.714988	−	1.83643i	0.714988	−	1.83643i	0.198590	−	0.980083i	$-0.436364\pi$
$557$	0.714988	−	1.83643i	0.714988	−	1.83643i	0.516397	−	0.856349i	$-0.327273\pi$
$558$	1.38479	−	1.42491i	1.38479	−	1.42491i
$559$		0			0
$560$	0.483619	−	1.05898i	0.483619	−	1.05898i
$561$		0			0
$562$		0			0
$563$	0.825414	+	0.0947075i	0.825414	+	0.0947075i	0.516397	−	0.856349i	$-0.327273\pi$
$563$	0.825414	+	0.0947075i	0.825414	+	0.0947075i	0.309017	+	0.951057i	$0.400000\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	0.478446	−	0.391223i	0.478446	−	0.391223i
$568$		0			0
$569$		0			0		−0.941844	−	0.336049i	$-0.890909\pi$
$569$		0			0		0.941844	+	0.336049i	$0.109091\pi$
$570$		0			0
$571$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$571$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	0.0855750	−	0.996332i	0.0855750	−	0.996332i
$577$	0.831697	−	1.21632i	0.831697	−	1.21632i	−0.142315	−	0.989821i	$-0.545455\pi$
$577$	0.831697	−	1.21632i	0.831697	−	1.21632i	0.974012	−	0.226497i	$-0.0727273\pi$
$578$	0.309017	−	0.951057i	0.309017	−	0.951057i
$579$	0.982973	+	0.555111i	0.982973	+	0.555111i
$580$	−0.280723	−	3.26840i	−0.280723	−	3.26840i
$581$	−0.634675	+	0.582499i	−0.634675	+	0.582499i
$582$	−0.785171	+	0.504599i	−0.785171	+	0.504599i
$583$	−0.262555	+	0.435399i	−0.262555	+	0.435399i
$584$	0.143981	+	0.0925307i	0.143981	+	0.0925307i
$585$		0			0
$586$	−1.79437	+	0.417263i	−1.79437	+	0.417263i
$587$	−1.39160	−	1.43192i	−1.39160	−	1.43192i	−0.736741	−	0.676175i	$-0.763636\pi$
$587$	−1.39160	−	1.43192i	−1.39160	−	1.43192i	−0.654861	−	0.755750i	$-0.727273\pi$
$588$	0.569286	−	0.240582i	0.569286	−	0.240582i
$589$		0			0
$590$	−0.689153	−	3.40110i	−0.689153	−	3.40110i
$591$	−0.345844	+	0.195307i	−0.345844	+	0.195307i
$592$		0			0
$593$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$593$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$594$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$595$		0			0
$596$	−0.455331	−	1.40136i	−0.455331	−	1.40136i
$597$	−0.144100	+	0.711163i	−0.144100	+	0.711163i
$598$		0			0
$599$		0			0		−0.985354	−	0.170522i	$-0.945455\pi$
$599$		0			0		0.985354	+	0.170522i	$0.0545455\pi$
$600$	−1.87743	−	1.72309i	−1.87743	−	1.72309i
$601$	0.945456	−	1.22609i	0.945456	−	1.22609i	−0.0285561	−	0.999592i	$-0.509091\pi$
$601$	0.945456	−	1.22609i	0.945456	−	1.22609i	0.974012	−	0.226497i	$-0.0727273\pi$
$602$		0			0
$603$		0			0
$604$	−0.933335			−0.933335
$605$	−0.478868	−	1.82180i	−0.478868	−	1.82180i
$606$	1.94802			1.94802
$607$	−1.17534	+	0.577877i	−1.17534	+	0.577877i	−0.921124	−	0.389270i	$-0.872727\pi$
$607$	−1.17534	+	0.577877i	−1.17534	+	0.577877i	−0.254218	+	0.967147i	$0.581818\pi$
$608$		0			0
$609$	−0.657241	+	0.852325i	−0.657241	+	0.852325i
$610$		0			0
$611$		0			0
$612$		0			0
$613$		0			0		0.198590	−	0.980083i	$-0.436364\pi$
$613$		0			0		−0.198590	+	0.980083i	$0.563636\pi$
$614$		0			0
$615$		0			0
$616$	0.256741	−	0.562183i	0.256741	−	0.562183i
$617$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$617$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$618$	1.11235	+	1.62676i	1.11235	+	1.62676i
$619$		0			0		0.870746	−	0.491733i	$-0.163636\pi$
$619$		0			0		−0.870746	+	0.491733i	$0.836364\pi$
$620$	0.743289	+	3.66827i	0.743289	+	3.66827i
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−2.90232	+	0.502267i	−2.90232	+	0.502267i
$626$	−1.67976	−	1.07952i	−1.67976	−	1.07952i
$627$		0			0
$628$		0			0
$629$		0			0
$630$	0.0996250	+	1.15991i	0.0996250	+	1.15991i
$631$	−1.21371	−	0.685414i	−1.21371	−	0.685414i	−0.254218	−	0.967147i	$-0.581818\pi$
$631$	−1.21371	−	0.685414i	−1.21371	−	0.685414i	−0.959493	+	0.281733i	$0.909091\pi$
$632$	−0.617026	+	1.89901i	−0.617026	+	1.89901i
$633$		0			0
$634$	0.143981	−	1.67634i	0.143981	−	1.67634i
$635$	−0.327401	−	0.424581i	−0.327401	−	0.424581i
$636$	0.0145189	+	0.508229i	0.0145189	+	0.508229i
$637$		0			0
$638$	−0.149028	−	1.73510i	−0.149028	−	1.73510i
$639$		0			0
$640$	1.45824	+	1.19240i	1.45824	+	1.19240i
$641$		0			0		−0.941844	−	0.336049i	$-0.890909\pi$
$641$		0			0		0.941844	+	0.336049i	$0.109091\pi$
$642$	1.69042	−	0.603140i	1.69042	−	0.603140i
$643$		0			0		0.774142	−	0.633012i	$-0.218182\pi$
$643$		0			0		−0.774142	+	0.633012i	$0.781818\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		−0.993482	−	0.113991i	$-0.963636\pi$
$647$		0			0		0.993482	+	0.113991i	$0.0363636\pi$
$648$	0.415415	+	0.909632i	0.415415	+	0.909632i
$649$	−0.365853	−	1.80555i	−0.365853	−	1.80555i
$650$		0			0
$651$	0.634142	−	1.05161i	0.634142	−	1.05161i
$652$		0			0
$653$	−0.443096	+	1.13808i	−0.443096	+	1.13808i	0.516397	+	0.856349i	$0.327273\pi$
$653$	−0.443096	+	1.13808i	−0.443096	+	1.13808i	−0.959493	+	0.281733i	$0.909091\pi$
$654$		0			0
$655$	1.00463	+	1.66600i	1.00463	+	1.66600i
$656$		0			0
$657$	−0.170871	−	0.00977075i	−0.170871	−	0.00977075i
$658$		0			0
$659$	0.132827	+	0.923835i	0.132827	+	0.923835i	0.941844	+	0.336049i	$0.109091\pi$
$659$	0.132827	+	0.923835i	0.132827	+	0.923835i	−0.809017	+	0.587785i	$0.800000\pi$
$660$	−1.38779	−	1.27370i	−1.38779	−	1.27370i
$661$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$661$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$662$		0			0
$663$		0			0
$664$	−0.650476	−	1.23279i	−0.650476	−	1.23279i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$	−0.365853	−	0.154611i	−0.365853	−	0.154611i
$670$		0			0
$671$		0			0
$672$	−0.0879554	−	0.611743i	−0.0879554	−	0.611743i
$673$	0.184465	−	0.701777i	0.184465	−	0.701777i	−0.809017	−	0.587785i	$-0.800000\pi$
$673$	0.184465	−	0.701777i	0.184465	−	0.701777i	0.993482	−	0.113991i	$-0.0363636\pi$
$674$	1.91586	+	0.109553i	1.91586	+	0.109553i
$675$	2.48206	+	0.577178i	2.48206	+	0.577178i
$676$	0.516397	+	0.856349i	0.516397	+	0.856349i
$677$	1.02606	−	0.117730i	1.02606	−	0.117730i	0.415415	−	0.909632i	$-0.363636\pi$
$677$	1.02606	−	0.117730i	1.02606	−	0.117730i	0.610648	+	0.791902i	$0.290909\pi$
$678$		0			0
$679$	−0.402016	+	0.413665i	−0.402016	+	0.413665i
$680$		0			0
$681$	−0.301432	+	0.660043i	−0.301432	+	0.660043i
$682$	0.394592	+	1.94739i	0.394592	+	1.94739i
$683$	−0.818662	−	1.79262i	−0.818662	−	1.79262i	−0.564443	−	0.825472i	$-0.690909\pi$
$683$	−0.818662	−	1.79262i	−0.818662	−	1.79262i	−0.254218	−	0.967147i	$-0.581818\pi$
$684$		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		−0.774142	−	0.633012i	$-0.781818\pi$
$691$		0			0		0.774142	+	0.633012i	$0.218182\pi$
$692$	0.739263	−	0.853155i	0.739263	−	0.853155i
$693$	0.0528883	+	0.615767i	0.0528883	+	0.615767i
$694$	0.332955	+	0.384251i	0.332955	+	0.384251i
$695$		0			0
$696$	−1.06344	−	1.37909i	−1.06344	−	1.37909i
$697$		0			0
$698$		0			0
$699$		0			0
$700$	−1.37136	−	0.774443i	−1.37136	−	0.774443i
$701$	0.143981	+	1.67634i	0.143981	+	1.67634i	0.610648	+	0.791902i	$0.290909\pi$
$701$	0.143981	+	1.67634i	0.143981	+	1.67634i	−0.466667	+	0.884433i	$0.654545\pi$
$702$		0			0
$703$		0			0
$704$	0.774142	+	0.633012i	0.774142	+	0.633012i
$705$		0			0
$706$		0			0
$707$	1.17266	−	0.272690i	1.17266	−	0.272690i
$708$	−1.28393	−	1.32113i	−1.28393	−	1.32113i
$709$		0			0		0.921124	−	0.389270i	$-0.127273\pi$
$709$		0			0		−0.921124	+	0.389270i	$0.872727\pi$
$710$		0			0
$711$	−0.396533	−	1.95697i	−0.396533	−	1.95697i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−1.33741	−	0.392700i	−1.33741	−	0.392700i
$717$		0			0
$718$		0			0
$719$		0			0		0.998369	−	0.0570888i	$-0.0181818\pi$
$719$		0			0		−0.998369	+	0.0570888i	$0.981818\pi$
$720$	−1.85610	−	0.321211i	−1.85610	−	0.321211i
$721$	0.897324	+	0.823557i	0.897324	+	0.823557i
$722$	0.610648	−	0.791902i	0.610648	−	0.791902i
$723$	1.19207	+	0.866091i	1.19207	+	0.866091i
$724$		0			0
$725$	−4.43782			−4.43782
$726$	−0.736741	−	0.676175i	−0.736741	−	0.676175i
$727$	−1.30972			−1.30972			−0.654861	−	0.755750i	$-0.727273\pi$
$727$	−1.30972			−1.30972			−0.654861	+	0.755750i	$0.727273\pi$
$728$		0			0
$729$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$730$	0.196869	−	0.255304i	0.196869	−	0.255304i
$731$		0			0
$732$		0			0
$733$		0			0		0.998369	−	0.0570888i	$-0.0181818\pi$
$733$		0			0		−0.998369	+	0.0570888i	$0.981818\pi$
$734$	0.0339888	−	0.167741i	0.0339888	−	0.167741i
$735$	−0.359753	−	1.10720i	−0.359753	−	1.10720i
$736$		0			0
$737$		0			0
$738$		0			0
$739$		0			0		−0.564443	−	0.825472i	$-0.690909\pi$
$739$		0			0		0.564443	+	0.825472i	$0.309091\pi$
$740$		0			0
$741$		0			0
$742$	0.0798833	+	0.303908i	0.0798833	+	0.303908i
$743$		0			0		0.921124	−	0.389270i	$-0.127273\pi$
$743$		0			0		−0.921124	+	0.389270i	$0.872727\pi$
$744$	1.38479	+	1.42491i	1.38479	+	1.42491i
$745$	−2.70345	+	0.628660i	−2.70345	+	0.628660i
$746$		0			0
$747$	1.17260	+	0.753586i	1.17260	+	0.753586i
$748$		0			0
$749$	0.933157	−	0.599703i	0.933157	−	0.599703i
$750$	−2.14869	+	1.97205i	−2.14869	+	1.97205i
$751$	−0.0243572	−	0.283586i	−0.0243572	−	0.283586i	−0.998369	−	0.0570888i	$-0.981818\pi$
$751$	−0.0243572	−	0.283586i	−0.0243572	−	0.283586i	0.974012	−	0.226497i	$-0.0727273\pi$
$752$		0			0
$753$	−0.224227	+	0.690101i	−0.224227	+	0.690101i
$754$		0			0
$755$	−0.150450	+	1.75166i	−0.150450	+	1.75166i
$756$	0.377401	+	0.489423i	0.377401	+	0.489423i
$757$		0			0		−0.0285561	−	0.999592i	$-0.509091\pi$
$757$		0			0		0.0285561	+	0.999592i	$0.490909\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$		0			0		−0.774142	−	0.633012i	$-0.781818\pi$
$761$		0			0		0.774142	+	0.633012i	$0.218182\pi$
$762$	−0.268077	−	0.0956496i	−0.268077	−	0.0956496i
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	0.993482	+	0.113991i	0.993482	+	0.113991i
$769$	0.809238	+	1.77198i	0.809238	+	1.77198i	0.610648	+	0.791902i	$0.290909\pi$
$769$	0.809238	+	1.77198i	0.809238	+	1.77198i	0.198590	+	0.980083i	$0.436364\pi$
$770$	−1.01371	−	0.572467i	−1.01371	−	0.572467i
$771$		0			0
$772$	−0.582954	+	0.966721i	−0.582954	+	0.966721i
$773$	−1.21371	+	1.24888i	−1.21371	+	1.24888i	−0.254218	+	0.967147i	$0.581818\pi$
$773$	−1.21371	+	1.24888i	−1.21371	+	1.24888i	−0.959493	+	0.281733i	$0.909091\pi$
$774$		0			0
$775$	5.03034	−	0.577178i	5.03034	−	0.577178i
$776$	−0.481972	−	0.799260i	−0.481972	−	0.799260i
$777$		0			0
$778$	1.30759	+	0.0747704i	1.30759	+	0.0747704i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	1.60413	+	0.677911i	1.60413	+	0.677911i
$784$	0.224227	+	0.575924i	0.224227	+	0.575924i
$785$		0			0
$786$	0.926829	+	0.455691i	0.926829	+	0.455691i
$787$		0			0		−0.897398	−	0.441221i	$-0.854545\pi$
$787$		0			0		0.897398	+	0.441221i	$0.145455\pi$
$788$	−0.185351	−	0.351280i	−0.185351	−	0.351280i
$789$		0			0
$790$	3.46456	+	1.46414i	3.46456	+	1.46414i
$791$		0			0
$792$	−0.985354	−	0.170522i	−0.985354	−	0.170522i
$793$		0			0
$794$		0			0
$795$	0.956174	+	0.0546760i	0.956174	+	0.0546760i
$796$	−0.706758	−	0.164350i	−0.706758	−	0.164350i
$797$	−0.0294925	−	0.0489079i	−0.0294925	−	0.0489079i	0.841254	−	0.540641i	$-0.181818\pi$
$797$	−0.0294925	−	0.0489079i	−0.0294925	−	0.0489079i	−0.870746	+	0.491733i	$0.836364\pi$
$798$		0			0
$799$		0			0
$800$	1.77599	−	1.82745i	1.77599	−	1.82745i
$801$		0			0
$802$		0			0
$803$	0.104512	−	0.135534i	0.104512	−	0.135534i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−0.672156	+	0.488350i	−0.672156	+	0.488350i
$808$	−0.0556279	+	1.94723i	−0.0556279	+	1.94723i
$809$		0			0		0.774142	−	0.633012i	$-0.218182\pi$
$809$		0			0		−0.774142	+	0.633012i	$0.781818\pi$
$810$	1.77414	−	0.633012i	1.77414	−	0.633012i
$811$		0			0		−0.941844	−	0.336049i	$-0.890909\pi$
$811$		0			0		0.941844	+	0.336049i	$0.109091\pi$
$812$	−0.833210	−	0.681312i	−0.833210	−	0.681312i
$813$	1.25667	−	1.45027i	1.25667	−	1.45027i
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	−0.138463	+	1.61210i	−0.138463	+	1.61210i
$819$		0			0
$820$		0			0
$821$	−1.56281	−	0.882561i	−1.56281	−	0.882561i	−0.998369	−	0.0570888i	$-0.981818\pi$
$821$	−1.56281	−	0.882561i	−1.56281	−	0.882561i	−0.564443	−	0.825472i	$-0.690909\pi$
$822$		0			0
$823$	−1.43519	+	1.31720i	−1.43519	+	1.31720i	−0.564443	+	0.825472i	$0.690909\pi$
$823$	−1.43519	+	1.31720i	−1.43519	+	1.31720i	−0.870746	+	0.491733i	$0.836364\pi$
$824$	−1.65786	+	1.06545i	−1.65786	+	1.06545i
$825$	−1.87743	+	1.72309i	−1.87743	+	1.72309i
$826$	−0.957827	−	0.615558i	−0.957827	−	0.615558i
$827$	1.11235	−	0.192500i	1.11235	−	0.192500i	0.415415	−	0.909632i	$-0.363636\pi$
$827$	1.11235	−	0.192500i	1.11235	−	0.192500i	0.696938	+	0.717132i	$0.254545\pi$
$828$		0			0
$829$		0			0		−0.696938	−	0.717132i	$-0.745455\pi$
$829$		0			0		0.696938	+	0.717132i	$0.254545\pi$
$830$	−2.41853	+	1.02208i	−2.41853	+	1.02208i
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−1.90648	−	0.559792i	−1.90648	−	0.559792i
$838$	0.377401	+	1.16152i	0.377401	+	1.16152i
$839$		0			0		0.198590	−	0.980083i	$-0.436364\pi$
$839$		0			0		−0.198590	+	0.980083i	$0.563636\pi$
$840$	−1.16228	+	0.0664619i	−1.16228	+	0.0664619i
$841$	−2.00302	−	0.346637i	−2.00302	−	0.346637i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	1.69042	−	0.831123i	1.69042	−	0.831123i
$846$		0			0
$847$	−0.538151	−	0.303908i	−0.538151	−	0.303908i
$848$	−0.508437			−0.508437
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		−0.985354	−	0.170522i	$-0.945455\pi$
$853$		0			0		0.985354	+	0.170522i	$0.0545455\pi$
$854$		0			0
$855$		0			0
$856$	0.554623	+	1.70695i	0.554623	+	1.70695i
$857$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$857$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$858$		0			0
$859$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$859$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.254218	−	0.967147i	$-0.581818\pi$
$863$		0			0		0.254218	+	0.967147i	$0.418182\pi$
$864$	−0.921124	+	0.389270i	−0.921124	+	0.389270i
$865$	−1.48202	−	1.52496i	−1.48202	−	1.52496i
$866$	1.00595	−	0.233925i	1.00595	−	0.233925i
$867$	−0.985354	+	0.170522i	−0.985354	+	0.170522i
$868$	1.03307	+	0.663913i	1.03307	+	0.663913i
$869$	1.83924	+	0.777270i	1.83924	+	0.777270i
$870$	−2.75967	+	1.77353i	−2.75967	+	1.77353i
$871$		0			0
$872$		0			0
$873$	0.812697	+	0.458951i	0.812697	+	0.458951i
$874$		0			0
$875$	−1.01740	+	1.48790i	−1.01740	+	1.48790i
$876$	0.0146462	−	0.170522i	0.0146462	−	0.170522i
$877$		0			0		−0.610648	−	0.791902i	$-0.709091\pi$
$877$		0			0		0.610648	+	0.791902i	$0.290909\pi$
$878$	−0.0294925	−	1.03237i	−0.0294925	−	1.03237i
$879$	1.20642	+	1.39228i	1.20642	+	1.39228i
$880$	1.31281	−	1.35085i	1.31281	−	1.35085i
$881$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$881$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$882$	−0.478446	−	0.391223i	−0.478446	−	0.391223i
$883$		0			0		−0.941844	−	0.336049i	$-0.890909\pi$
$883$		0			0		0.941844	+	0.336049i	$0.109091\pi$
$884$		0			0
$885$	−2.68644	+	2.19669i	−2.68644	+	2.19669i
$886$	0.00163090	−	0.0570888i	0.00163090	−	0.0570888i
$887$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$887$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$888$		0			0
$889$	−0.174764	−	0.0200523i	−0.174764	−	0.0200523i
$890$		0			0
$891$	0.941844	−	0.336049i	0.941844	−	0.336049i
$892$	0.164995	−	0.361288i	0.164995	−	0.361288i
$893$		0			0
$894$	−1.02693	+	1.05668i	−1.02693	+	1.05668i
$895$	−0.952598	+	2.44673i	−0.952598	+	2.44673i
$896$	0.614005	−	0.0704506i	0.614005	−	0.0704506i
$897$		0			0
$898$		0			0
$899$	3.45464	+	0.197543i	3.45464	+	0.197543i
$900$	−0.647820	+	2.46456i	−0.647820	+	2.46456i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$	0.435557	+	0.825472i	0.435557	+	0.825472i
$907$		0			0		−0.897398	−	0.441221i	$-0.854545\pi$
$907$		0			0		0.897398	+	0.441221i	$0.145455\pi$
$908$	−0.651166	−	0.320157i	−0.651166	−	0.320157i
$909$	−0.909079	−	1.72290i	−0.909079	−	1.72290i
$910$		0			0
$911$		0			0		−0.921124	−	0.389270i	$-0.872727\pi$
$911$		0			0		0.921124	+	0.389270i	$0.127273\pi$
$912$		0			0
$913$	−1.28393	+	0.542594i	−1.28393	+	0.542594i
$914$	−0.277233	−	1.92820i	−0.277233	−	1.92820i
$915$		0			0
$916$		0			0
$917$	0.621714	+	0.144573i	0.621714	+	0.144573i
$918$		0			0
$919$	1.21334	−	0.139217i	1.21334	−	0.139217i	0.516397	−	0.856349i	$-0.327273\pi$
$919$	1.21334	−	0.139217i	1.21334	−	0.139217i	0.696938	+	0.717132i	$0.254545\pi$
$920$		0			0
$921$		0			0
$922$	−0.990959	+	1.64332i	−0.990959	+	1.64332i
$923$		0			0
$924$	−0.617026	+	0.0352828i	−0.617026	+	0.0352828i
$925$		0			0
$926$	1.78310	+	0.204591i	1.78310	+	0.204591i
$927$	0.919665	−	1.74296i	0.919665	−	1.74296i
$928$	1.40890	−	1.02362i	1.40890	−	1.02362i
$929$		0			0		0.0285561	−	0.999592i	$-0.490909\pi$
$929$		0			0		−0.0285561	+	0.999592i	$0.509091\pi$
$930$	2.89747	−	2.36925i	2.89747	−	2.36925i
$931$		0			0
$932$		0			0
$933$		0			0
$934$	0.739263	−	0.853155i	0.739263	−	0.853155i
$935$		0			0
$936$		0			0
$937$	−0.0567398	−	1.98615i	−0.0567398	−	1.98615i	−0.142315	−	0.989821i	$-0.545455\pi$
$937$	−0.0567398	−	1.98615i	−0.0567398	−	1.98615i	0.0855750	−	0.996332i	$-0.472727\pi$
$938$		0			0
$939$	−0.170871	+	1.98941i	−0.170871	+	1.98941i
$940$		0			0
$941$	−0.404726	+	1.24562i	−0.404726	+	1.24562i	0.516397	+	0.856349i	$0.327273\pi$
$941$	−0.404726	+	1.24562i	−0.404726	+	1.24562i	−0.921124	+	0.389270i	$0.872727\pi$
$942$		0			0
$943$		0			0
$944$	1.35726	−	1.24568i	1.35726	−	1.24568i
$945$	0.979374	−	0.629405i	0.979374	−	0.629405i
$946$		0			0
$947$	1.67154	+	1.07423i	1.67154	+	1.07423i	0.897398	+	0.441221i	$0.145455\pi$
$947$	1.67154	+	1.07423i	1.67154	+	1.07423i	0.774142	+	0.633012i	$0.218182\pi$
$948$	1.96749	−	0.340488i	1.96749	−	0.340488i
$949$		0			0
$950$		0			0
$951$	−1.54980	+	0.654950i	−1.54980	+	0.654950i
$952$		0			0
$953$		0			0		−0.198590	−	0.980083i	$-0.563636\pi$
$953$		0			0		0.198590	+	0.980083i	$0.436364\pi$
$954$	0.442719	−	0.250015i	0.442719	−	0.250015i
$955$		0			0
$956$		0			0
$957$	−1.46504	+	0.941522i	−1.46504	+	0.941522i
$958$		0			0
$959$		0			0
$960$	0.374083	−	1.84617i	0.374083	−	1.84617i
$961$	−2.94322	+	0.168299i	−2.94322	+	0.168299i
$962$		0			0
$963$	−1.32230	−	1.21360i	−1.32230	−	1.21360i
$964$	−0.899779	+	1.16685i	−0.899779	+	1.16685i
$965$	1.72035	+	1.24991i	1.72035	+	1.24991i
$966$		0			0
$967$	1.22130			1.22130			0.610648	−	0.791902i	$-0.290909\pi$
$967$	1.22130			1.22130			0.610648	+	0.791902i	$0.290909\pi$
$968$	0.696938	−	0.717132i	0.696938	−	0.717132i
$969$		0			0
$970$	−1.57773	+	0.775716i	−1.57773	+	0.775716i
$971$	−1.36118	−	0.988953i	−1.36118	−	0.988953i	−0.998369	−	0.0570888i	$-0.981818\pi$
$971$	−1.36118	−	0.988953i	−1.36118	−	0.988953i	−0.362808	−	0.931864i	$-0.618182\pi$
$972$	0.610648	−	0.791902i	0.610648	−	0.791902i
$973$		0			0
$974$	1.11235	+	0.192500i	1.11235	+	0.192500i
$975$		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
$980$	1.11703	−	0.327988i	1.11703	−	0.327988i
$981$		0			0
$982$	0.247840	−	0.139962i	0.247840	−	0.139962i
$983$		0			0		−0.198590	−	0.980083i	$-0.563636\pi$
$983$		0			0		0.198590	+	0.980083i	$0.436364\pi$
$984$		0			0
$985$	−0.689153	+	0.291238i	−0.689153	+	0.291238i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$	−0.478868	+	1.82180i	−0.478868	+	1.82180i
$991$	−0.785171	+	0.504599i	−0.785171	+	0.504599i	−0.870746	−	0.491733i	$-0.836364\pi$
$991$	−0.785171	+	0.504599i	−0.785171	+	0.504599i	0.0855750	+	0.996332i	$0.472727\pi$
$992$	−1.46388	+	1.34353i	−1.46388	+	1.34353i
$993$		0			0
$994$		0			0
$995$	−0.422375	+	1.29994i	−0.422375	+	1.29994i
$996$	−0.786763	+	1.15060i	−0.786763	+	1.15060i
$997$		0			0		0.0855750	−	0.996332i	$-0.472727\pi$
$997$		0			0		−0.0855750	+	0.996332i	$0.527273\pi$
$998$		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.797.1	yes	40
3.2	odd	2		2904.1.cj.a.797.1	yes	40
8.5	even	2		2904.1.cj.a.797.1	yes	40
24.5	odd	2	CM	2904.1.cj.b.797.1	yes	40
121.75	even	55	inner	2904.1.cj.b.317.1	yes	40
363.317	odd	110		2904.1.cj.a.317.1	✓	40
968.317	even	110		2904.1.cj.a.317.1	✓	40
2904.317	odd	110	inner	2904.1.cj.b.317.1	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2904.1.cj.a.317.1	✓	40	363.317	odd	110
2904.1.cj.a.317.1	✓	40	968.317	even	110
2904.1.cj.a.797.1	yes	40	3.2	odd	2
2904.1.cj.a.797.1	yes	40	8.5	even	2
2904.1.cj.b.317.1	yes	40	121.75	even	55	inner
2904.1.cj.b.317.1	yes	40	2904.317	odd	110	inner
2904.1.cj.b.797.1	yes	40	1.1	even	1	trivial
2904.1.cj.b.797.1	yes	40	24.5	odd	2	CM

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)

\(f(q)\)	\(=\)	\(q+(0.897398 - 0.441221i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(0.610648 - 0.791902i) q^{4} +(-1.38779 - 1.27370i) q^{5} +(-0.985354 - 0.170522i) q^{6} +(-0.617026 + 0.0352828i) q^{7} +(0.198590 - 0.980083i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.897398 - 0.441221i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(0.610648 - 0.791902i) q^{4} +(-1.38779 - 1.27370i) q^{5} +(-0.985354 - 0.170522i) q^{6} +(-0.617026 + 0.0352828i) q^{7} +(0.198590 - 0.980083i) q^{8} +(0.309017 + 0.951057i) q^{9} +(-1.80739 - 0.530696i) q^{10} +(-0.959493 - 0.281733i) q^{11} +(-0.959493 + 0.281733i) q^{12} +(-0.538151 + 0.303908i) q^{14} +(0.374083 + 1.84617i) q^{15} +(-0.254218 - 0.967147i) q^{16} +(0.696938 + 0.717132i) q^{18} +(-1.85610 + 0.321211i) q^{20} +(0.519923 + 0.334134i) q^{21} +(-0.985354 + 0.170522i) q^{22} +(-0.736741 + 0.676175i) q^{24} +(0.218069 + 2.53894i) q^{25} +(0.309017 - 0.951057i) q^{27} +(-0.348845 + 0.510170i) q^{28} +(-0.149028 + 1.73510i) q^{29} +(1.15027 + 1.49170i) q^{30} +(-0.0567398 - 1.98615i) q^{31} +(-0.654861 - 0.755750i) q^{32} +(0.610648 + 0.791902i) q^{33} +(0.901243 + 0.736943i) q^{35} +(0.941844 + 0.336049i) q^{36} +(-1.52394 + 1.10720i) q^{40} +(0.614005 + 0.0704506i) q^{42} +(-0.809017 + 0.587785i) q^{44} +(0.782513 - 1.71346i) q^{45} +(-0.362808 + 0.931864i) q^{48} +(-0.614005 + 0.0704506i) q^{49} +(1.31593 + 2.18222i) q^{50} +(0.129254 - 0.491733i) q^{53} +(-0.142315 - 0.989821i) q^{54} +(0.972732 + 1.61310i) q^{55} +(-0.0879554 + 0.611743i) q^{56} +(0.631827 + 1.62283i) q^{58} +(0.859717 + 1.62934i) q^{59} +(1.69042 + 0.831123i) q^{60} +(-0.927251 - 1.75734i) q^{62} +(-0.224227 - 0.575924i) q^{63} +(-0.921124 - 0.389270i) q^{64} +(0.897398 + 0.441221i) q^{66} +(1.13393 + 0.263684i) q^{70} +(0.993482 - 0.113991i) q^{72} +(-0.0620945 + 0.159489i) q^{73} +(1.31593 - 2.18222i) q^{75} +(0.601972 + 0.139983i) q^{77} +(-1.98372 - 0.227611i) q^{79} +(-0.879056 + 1.66600i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(1.07906 - 0.882340i) q^{83} +(0.582092 - 0.207690i) q^{84} +(1.14043 - 1.31613i) q^{87} +(-0.466667 + 0.884433i) q^{88} +(-0.0537907 - 1.88292i) q^{90} +(-1.12153 + 1.64018i) q^{93} +(0.0855750 + 0.996332i) q^{96} +(0.687626 - 0.631097i) q^{97} +(-0.519923 + 0.334134i) q^{98} +(-0.0285561 - 0.999592i) 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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