LMFDB - Embedded newform 600.2.d.g.349.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [600,2,Mod(349,600)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(600, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0, 1]))

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

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

chi := DirichletCharacter("600.349");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 600 = 2^{3} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	600.d (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.79102412128$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.214798336.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 2x^{5} + 9x^{4} - 4x^{3} - 16x + 16 $ x^8 - 2x^7 - 2x^5 + 9x^4 - 4x^3 - 16*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			349.7
Root			$-0.565036 + 1.29643i$ of defining polynomial
Character	$\chi$	$=$	600.349
Dual form			600.2.d.g.349.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.796431 - 1.16863i) q^{2} -1.00000 q^{3} +(-0.731395 - 1.86147i) q^{4} +(-0.796431 + 1.16863i) q^{6} +4.72294i q^{7} +(-2.75787 - 0.627801i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(0.796431 - 1.16863i) q^{2} -1.00000 q^{3} +(-0.731395 - 1.86147i) q^{4} +(-0.796431 + 1.16863i) q^{6} +4.72294i q^{7} +(-2.75787 - 0.627801i) q^{8} +1.00000 q^{9} +3.93012i q^{11} +(0.731395 + 1.86147i) q^{12} +3.46733 q^{13} +(5.51937 + 3.76149i) q^{14} +(-2.93012 + 2.72294i) q^{16} +3.51575i q^{17} +(0.796431 - 1.16863i) q^{18} -5.44133i q^{19} -4.72294i q^{21} +(4.59286 + 3.13007i) q^{22} +7.11585i q^{23} +(2.75787 + 0.627801i) q^{24} +(2.76149 - 4.05203i) q^{26} -1.00000 q^{27} +(8.79159 - 3.45433i) q^{28} -3.66998i q^{29} +5.23414 q^{31} +(0.848464 + 5.59286i) q^{32} -3.93012i q^{33} +(4.10861 + 2.80005i) q^{34} +(-0.731395 - 1.86147i) q^{36} -0.414376 q^{37} +(-6.35890 - 4.33364i) q^{38} -3.46733 q^{39} +3.00454 q^{41} +(-5.51937 - 3.76149i) q^{42} -5.34450 q^{43} +(7.31580 - 2.87447i) q^{44} +(8.31580 + 5.66728i) q^{46} -0.925579i q^{47} +(2.93012 - 2.72294i) q^{48} -15.3061 q^{49} -3.51575i q^{51} +(-2.53599 - 6.45433i) q^{52} +0.233196 q^{53} +(-0.796431 + 1.16863i) q^{54} +(2.96506 - 13.0253i) q^{56} +5.44133i q^{57} +(-4.28885 - 2.92288i) q^{58} +14.3805i q^{59} +0.118290i q^{61} +(4.16863 - 6.11677i) q^{62} +4.72294i q^{63} +(7.21173 + 3.46279i) q^{64} +(-4.59286 - 3.13007i) q^{66} +13.4504 q^{67} +(6.54445 - 2.57140i) q^{68} -7.11585i q^{69} +2.19027 q^{71} +(-2.75787 - 0.627801i) q^{72} +0.563219i q^{73} +(-0.330022 + 0.484253i) q^{74} +(-10.1289 + 3.97976i) q^{76} -18.5617 q^{77} +(-2.76149 + 4.05203i) q^{78} +10.2746 q^{79} +1.00000 q^{81} +(2.39291 - 3.51120i) q^{82} -11.3490 q^{83} +(-8.79159 + 3.45433i) q^{84} +(-4.25653 + 6.24575i) q^{86} +3.66998i q^{87} +(2.46733 - 10.8388i) q^{88} -8.88265 q^{89} +16.3760i q^{91} +(13.2459 - 5.20449i) q^{92} -5.23414 q^{93} +(-1.08166 - 0.737160i) q^{94} +(-0.848464 - 5.59286i) q^{96} +7.27462i q^{97} +(-12.1903 + 17.8872i) q^{98} +3.93012i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} - 8 q^{3} - 4 q^{4} + 2 q^{6} - 8 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 - 8 * q^3 - 4 * q^4 + 2 * q^6 - 8 * q^8 + 8 * q^9	$ 8 q - 2 q^{2} - 8 q^{3} - 4 q^{4} + 2 q^{6} - 8 q^{8} + 8 q^{9} + 4 q^{12} + 6 q^{14} + 8 q^{16} - 2 q^{18} + 20 q^{22} + 8 q^{24} - 2 q^{26} - 8 q^{27} + 24 q^{28} + 8 q^{31} - 12 q^{32} - 12 q^{34} - 4 q^{36} + 14 q^{38} - 6 q^{42} - 8 q^{43} + 12 q^{44} + 20 q^{46} - 8 q^{48} + 24 q^{52} + 8 q^{53} + 2 q^{54} + 8 q^{56} - 20 q^{58} + 26 q^{62} + 32 q^{64} - 20 q^{66} + 24 q^{67} + 36 q^{68} - 40 q^{71} - 8 q^{72} - 8 q^{74} - 20 q^{76} - 24 q^{77} + 2 q^{78} + 16 q^{79} + 8 q^{81} - 16 q^{82} - 32 q^{83} - 24 q^{84} - 18 q^{86} - 8 q^{88} + 28 q^{92} - 8 q^{93} + 4 q^{94} + 12 q^{96} - 40 q^{98}+O(q^{100}) $ 8 * q - 2 * q^2 - 8 * q^3 - 4 * q^4 + 2 * q^6 - 8 * q^8 + 8 * q^9 + 4 * q^12 + 6 * q^14 + 8 * q^16 - 2 * q^18 + 20 * q^22 + 8 * q^24 - 2 * q^26 - 8 * q^27 + 24 * q^28 + 8 * q^31 - 12 * q^32 - 12 * q^34 - 4 * q^36 + 14 * q^38 - 6 * q^42 - 8 * q^43 + 12 * q^44 + 20 * q^46 - 8 * q^48 + 24 * q^52 + 8 * q^53 + 2 * q^54 + 8 * q^56 - 20 * q^58 + 26 * q^62 + 32 * q^64 - 20 * q^66 + 24 * q^67 + 36 * q^68 - 40 * q^71 - 8 * q^72 - 8 * q^74 - 20 * q^76 - 24 * q^77 + 2 * q^78 + 16 * q^79 + 8 * q^81 - 16 * q^82 - 32 * q^83 - 24 * q^84 - 18 * q^86 - 8 * q^88 + 28 * q^92 - 8 * q^93 + 4 * q^94 + 12 * q^96 - 40 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/600\mathbb{Z}\right)^\times$.

$n$	$151$	$301$	$401$	$577$
$\chi(n)$	$1$	$-1$	$1$	$-1$

Coefficient data

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

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

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

$2$	0.796431	−	1.16863i	0.563162	−	0.826347i
$2$	0.796431	−	1.16863i	0.563162	−	0.826347i
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	−0.731395	−	1.86147i	−0.365697	−	0.930734i
$5$		0			0
$5$		0			0
$6$	−0.796431	+	1.16863i	−0.325142	+	0.477091i
$7$			4.72294i			1.78510i	0.450947	+	0.892551i	$0.351086\pi$
$7$			4.72294i			1.78510i	−0.450947	+	0.892551i	$0.648914\pi$
$8$	−2.75787	−	0.627801i	−0.975056	−	0.221961i
$9$	1.00000			0.333333
$10$		0			0
$11$			3.93012i			1.18498i	0.805579	+	0.592488i	$0.201854\pi$
$11$			3.93012i			1.18498i	−0.805579	+	0.592488i	$0.798146\pi$
$12$	0.731395	+	1.86147i	0.211135	+	0.537359i
$13$	3.46733			0.961665			0.480833	−	0.876812i	$-0.340334\pi$
$13$	3.46733			0.961665			0.480833	+	0.876812i	$0.340334\pi$
$14$	5.51937	+	3.76149i	1.47511	+	1.00530i
$15$		0			0
$16$	−2.93012	+	2.72294i	−0.732531	+	0.680734i
$17$			3.51575i			0.852694i	0.904560	+	0.426347i	$0.140200\pi$
$17$			3.51575i			0.852694i	−0.904560	+	0.426347i	$0.859800\pi$
$18$	0.796431	−	1.16863i	0.187721	−	0.275449i
$19$		−	5.44133i		−	1.24833i	−0.781294	−	0.624163i	$-0.785440\pi$
$19$		−	5.44133i		−	1.24833i	0.781294	−	0.624163i	$-0.214560\pi$
$20$		0			0
$21$		−	4.72294i		−	1.03063i
$22$	4.59286	+	3.13007i	0.979202	+	0.667334i
$23$			7.11585i			1.48376i	0.670534	+	0.741878i	$0.266065\pi$
$23$			7.11585i			1.48376i	−0.670534	+	0.741878i	$0.733935\pi$
$24$	2.75787	+	0.627801i	0.562949	+	0.128149i
$25$		0			0
$26$	2.76149	−	4.05203i	0.541573	−	0.794669i
$27$	−1.00000			−0.192450
$28$	8.79159	−	3.45433i	1.66145	−	0.652807i
$29$		−	3.66998i		−	0.681498i	−0.940154	−	0.340749i	$-0.889319\pi$
$29$		−	3.66998i		−	0.681498i	0.940154	−	0.340749i	$-0.110681\pi$
$30$		0			0
$31$	5.23414			0.940079			0.470039	−	0.882645i	$-0.344240\pi$
$31$	5.23414			0.940079			0.470039	+	0.882645i	$0.344240\pi$
$32$	0.848464	+	5.59286i	0.149989	+	0.988688i
$33$		−	3.93012i		−	0.684147i
$34$	4.10861	+	2.80005i	0.704621	+	0.480205i
$35$		0			0
$36$	−0.731395	−	1.86147i	−0.121899	−	0.310245i
$37$	−0.414376			−0.0681231			−0.0340615	−	0.999420i	$-0.510844\pi$
$37$	−0.414376			−0.0681231			−0.0340615	+	0.999420i	$0.510844\pi$
$38$	−6.35890	−	4.33364i	−1.03155	−	0.703010i
$39$	−3.46733			−0.555218
$40$		0			0
$41$	3.00454			0.469231			0.234616	−	0.972088i	$-0.424617\pi$
$41$	3.00454			0.469231			0.234616	+	0.972088i	$0.424617\pi$
$42$	−5.51937	−	3.76149i	−0.851657	−	0.580411i
$43$	−5.34450			−0.815029			−0.407514	−	0.913199i	$-0.633604\pi$
$43$	−5.34450			−0.815029			−0.407514	+	0.913199i	$0.633604\pi$
$44$	7.31580	−	2.87447i	1.10290	−	0.433343i
$45$		0			0
$46$	8.31580	+	5.66728i	1.22610	+	0.835595i
$47$		−	0.925579i		−	0.135010i	−0.997719	−	0.0675048i	$-0.978496\pi$
$47$		−	0.925579i		−	0.135010i	0.997719	−	0.0675048i	$-0.0215038\pi$
$48$	2.93012	−	2.72294i	0.422927	−	0.393022i
$49$	−15.3061			−2.18659
$50$		0			0
$51$		−	3.51575i		−	0.492303i
$52$	−2.53599	−	6.45433i	−0.351679	−	0.895055i
$53$	0.233196			0.0320320			0.0160160	−	0.999872i	$-0.494902\pi$
$53$	0.233196			0.0320320			0.0160160	+	0.999872i	$0.494902\pi$
$54$	−0.796431	+	1.16863i	−0.108381	+	0.159030i
$55$		0			0
$56$	2.96506	−	13.0253i	0.396223	−	1.74057i
$57$			5.44133i			0.720721i
$58$	−4.28885	−	2.92288i	−0.563153	−	0.383794i
$59$			14.3805i			1.87219i	0.351752	+	0.936093i	$0.385586\pi$
$59$			14.3805i			1.87219i	−0.351752	+	0.936093i	$0.614414\pi$
$60$		0			0
$61$			0.118290i			0.0151454i	0.999971	+	0.00757271i	$0.00241049\pi$
$61$			0.118290i			0.0151454i	−0.999971	+	0.00757271i	$0.997590\pi$
$62$	4.16863	−	6.11677i	0.529417	−	0.776831i
$63$			4.72294i			0.595034i
$64$	7.21173	+	3.46279i	0.901467	+	0.432849i
$65$		0			0
$66$	−4.59286	−	3.13007i	−0.565342	−	0.385285i
$67$	13.4504			1.64323			0.821615	−	0.570043i	$-0.193073\pi$
$67$	13.4504			1.64323			0.821615	+	0.570043i	$0.193073\pi$
$68$	6.54445	−	2.57140i	0.793631	−	0.311828i
$69$		−	7.11585i		−	0.856647i
$70$		0			0
$71$	2.19027			0.259937			0.129969	−	0.991518i	$-0.458512\pi$
$71$	2.19027			0.259937			0.129969	+	0.991518i	$0.458512\pi$
$72$	−2.75787	−	0.627801i	−0.325019	−	0.0739870i
$73$			0.563219i			0.0659197i	0.999457	+	0.0329599i	$0.0104934\pi$
$73$			0.563219i			0.0659197i	−0.999457	+	0.0329599i	$0.989507\pi$
$74$	−0.330022	+	0.484253i	−0.0383643	+	0.0562933i
$75$		0			0
$76$	−10.1289	+	3.97976i	−1.16186	+	0.456509i
$77$	−18.5617			−2.11530
$78$	−2.76149	+	4.05203i	−0.312678	+	0.458802i
$79$	10.2746			1.15599			0.577993	−	0.816042i	$-0.303836\pi$
$79$	10.2746			1.15599			0.577993	+	0.816042i	$0.303836\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$	2.39291	−	3.51120i	0.264253	−	0.387747i
$83$	−11.3490			−1.24572			−0.622860	−	0.782334i	$-0.714029\pi$
$83$	−11.3490			−1.24572			−0.622860	+	0.782334i	$0.714029\pi$
$84$	−8.79159	+	3.45433i	−0.959241	+	0.376898i
$85$		0			0
$86$	−4.25653	+	6.24575i	−0.458993	+	0.673496i
$87$			3.66998i			0.393463i
$88$	2.46733	−	10.8388i	0.263019	−	1.15542i
$89$	−8.88265			−0.941559			−0.470780	−	0.882251i	$-0.656027\pi$
$89$	−8.88265			−0.941559			−0.470780	+	0.882251i	$0.656027\pi$
$90$		0			0
$91$			16.3760i			1.71667i
$92$	13.2459	−	5.20449i	1.38098	−	0.542606i
$93$	−5.23414			−0.542755
$94$	−1.08166	−	0.737160i	−0.111565	−	0.0760322i
$95$		0			0
$96$	−0.848464	−	5.59286i	−0.0865960	−	0.570819i
$97$			7.27462i			0.738626i	0.929305	+	0.369313i	$0.120407\pi$
$97$			7.27462i			0.738626i	−0.929305	+	0.369313i	$0.879593\pi$
$98$	−12.1903	+	17.8872i	−1.23140	+	1.80688i
$99$			3.93012i			0.394992i
$100$		0			0
$101$		−	4.23320i		−	0.421219i	−0.977570	−	0.210609i	$-0.932455\pi$
$101$		−	4.23320i		−	0.421219i	0.977570	−	0.210609i	$-0.0675448\pi$
$102$	−4.10861	−	2.80005i	−0.406813	−	0.277246i
$103$		−	0.0429270i		−	0.00422972i	−0.999998	−	0.00211486i	$-0.999327\pi$
$103$		−	0.0429270i		−	0.00422972i	0.999998	−	0.00211486i	$-0.000673181\pi$
$104$	−9.56247	−	2.17679i	−0.937677	−	0.213452i
$105$		0			0
$106$	0.185725	−	0.272520i	0.0180392	−	0.0264695i
$107$	−15.4728			−1.49581			−0.747907	−	0.663804i	$-0.768941\pi$
$107$	−15.4728			−1.49581			−0.747907	+	0.663804i	$0.768941\pi$
$108$	0.731395	+	1.86147i	0.0703785	+	0.179120i
$109$		−	12.9561i		−	1.24097i	−0.784217	−	0.620486i	$-0.786935\pi$
$109$		−	12.9561i		−	1.24097i	0.784217	−	0.620486i	$-0.213065\pi$
$110$		0			0
$111$	0.414376			0.0393309
$112$	−12.8602	−	13.8388i	−1.21518	−	1.30764i
$113$		−	3.86025i		−	0.363141i	−0.983378	−	0.181571i	$-0.941882\pi$
$113$		−	3.86025i		−	0.363141i	0.983378	−	0.181571i	$-0.0581181\pi$
$114$	6.35890	+	4.33364i	0.595566	+	0.405883i
$115$		0			0
$116$	−6.83154	+	2.68420i	−0.634293	+	0.249222i
$117$	3.46733			0.320555
$118$	16.8055	+	11.4531i	1.54708	+	1.05434i
$119$	−16.6046			−1.52215
$120$		0			0
$121$	−4.44587			−0.404170
$122$	0.138237	+	0.0942095i	0.0125154	+	0.00852933i
$123$	−3.00454			−0.270911
$124$	−3.82822	−	9.74318i	−0.343784	−	0.874963i
$125$		0			0
$126$	5.51937	+	3.76149i	0.491704	+	0.335100i
$127$		−	18.3805i		−	1.63101i	−0.578751	−	0.815505i	$-0.696460\pi$
$127$		−	18.3805i		−	1.63101i	0.578751	−	0.815505i	$-0.303540\pi$
$128$	9.79037	−	5.66998i	0.865355	−	0.501160i
$129$	5.34450			0.470557
$130$		0			0
$131$			3.41892i			0.298713i	0.988783	+	0.149356i	$0.0477201\pi$
$131$			3.41892i			0.298713i	−0.988783	+	0.149356i	$0.952280\pi$
$132$	−7.31580	+	2.87447i	−0.636758	+	0.250191i
$133$	25.6990			2.22839
$134$	10.7123	−	15.7186i	0.925404	−	1.35788i
$135$		0			0
$136$	2.20719	−	9.69599i	0.189265	−	0.831424i
$137$		−	16.3714i		−	1.39871i	−0.714776	−	0.699354i	$-0.753471\pi$
$137$		−	16.3714i		−	1.39871i	0.714776	−	0.699354i	$-0.246529\pi$
$138$	−8.31580	−	5.66728i	−0.707888	−	0.482431i
$139$		−	1.95707i		−	0.165997i	−0.996550	−	0.0829984i	$-0.973550\pi$
$139$		−	1.95707i		−	0.165997i	0.996550	−	0.0829984i	$-0.0264496\pi$
$140$		0			0
$141$			0.925579i			0.0779478i
$142$	1.74440	−	2.55962i	0.146387	−	0.214798i
$143$			13.6271i			1.13955i
$144$	−2.93012	+	2.72294i	−0.244177	+	0.226911i
$145$		0			0
$146$	0.658194	+	0.448565i	0.0544726	+	0.0371235i
$147$	15.3061			1.26243
$148$	0.303073	+	0.771348i	0.0249124	+	0.0634044i
$149$			12.0968i			0.991011i	0.868605	+	0.495505i	$0.165017\pi$
$149$			12.0968i			0.991011i	−0.868605	+	0.495505i	$0.834983\pi$
$150$		0			0
$151$	−4.87178			−0.396460			−0.198230	−	0.980156i	$-0.563519\pi$
$151$	−4.87178			−0.396460			−0.198230	+	0.980156i	$0.563519\pi$
$152$	−3.41607	+	15.0065i	−0.277080	+	1.21719i
$153$			3.51575i			0.284231i
$154$	−14.7831	+	21.6918i	−1.19126	+	1.74797i
$155$		0			0
$156$	2.53599	+	6.45433i	0.203042	+	0.516760i
$157$	21.6561			1.72835			0.864173	−	0.503195i	$-0.167842\pi$
$157$	21.6561			1.72835			0.864173	+	0.503195i	$0.167842\pi$
$158$	8.18303	−	12.0072i	0.651007	−	0.955245i
$159$	−0.233196			−0.0184937
$160$		0			0
$161$	−33.6077			−2.64866
$162$	0.796431	−	1.16863i	0.0625735	−	0.0918163i
$163$	−16.2362			−1.27172			−0.635860	−	0.771804i	$-0.719355\pi$
$163$	−16.2362			−1.27172			−0.635860	+	0.771804i	$0.719355\pi$
$164$	−2.19751	−	5.59286i	−0.171597	−	0.436729i
$165$		0			0
$166$	−9.03873	+	13.2628i	−0.701542	+	1.02940i
$167$		−	6.69238i		−	0.517872i	−0.965894	−	0.258936i	$-0.916628\pi$
$167$		−	6.69238i		−	0.517872i	0.965894	−	0.258936i	$-0.0833719\pi$
$168$	−2.96506	+	13.0253i	−0.228759	+	1.00492i
$169$	−0.977595			−0.0751996
$170$		0			0
$171$		−	5.44133i		−	0.416109i
$172$	3.90894	+	9.94861i	0.298054	+	0.758575i
$173$	22.4220			1.70471			0.852355	−	0.522963i	$-0.175173\pi$
$173$	22.4220			1.70471			0.852355	+	0.522963i	$0.175173\pi$
$174$	4.28885	+	2.92288i	0.325137	+	0.221583i
$175$		0			0
$176$	−10.7015	−	11.5157i	−0.806654	−	0.868032i
$177$		−	14.3805i		−	1.08091i
$178$	−7.07442	+	10.3805i	−0.530250	+	0.778054i
$179$		−	0.148842i		−	0.0111250i	−0.999985	−	0.00556249i	$-0.998229\pi$
$179$		−	0.148842i		−	0.0111250i	0.999985	−	0.00556249i	$-0.00177060\pi$
$180$		0			0
$181$		−	10.3929i		−	0.772499i	−0.922394	−	0.386250i	$-0.873770\pi$
$181$		−	10.3929i		−	0.772499i	0.922394	−	0.386250i	$-0.126230\pi$
$182$	19.1375	+	13.0424i	1.41856	+	0.966763i
$183$		−	0.118290i		−	0.00874422i
$184$	4.46733	−	19.6246i	0.329336	−	1.44675i
$185$		0			0
$186$	−4.16863	+	6.11677i	−0.305659	+	0.448504i
$187$	−13.8173			−1.01042
$188$	−1.72294	+	0.676964i	−0.125658	+	0.0493726i
$189$		−	4.72294i		−	0.343543i
$190$		0			0
$191$	6.23320			0.451018			0.225509	−	0.974241i	$-0.427595\pi$
$191$	6.23320			0.451018			0.225509	+	0.974241i	$0.427595\pi$
$192$	−7.21173	−	3.46279i	−0.520462	−	0.249905i
$193$			0.391971i			0.0282147i	0.999900	+	0.0141074i	$0.00449066\pi$
$193$			0.391971i			0.0282147i	−0.999900	+	0.0141074i	$0.995509\pi$
$194$	8.50135	+	5.79374i	0.610361	+	0.415966i
$195$		0			0
$196$	11.1948	+	28.4918i	0.799630	+	2.03513i
$197$	−5.96616			−0.425071			−0.212536	−	0.977153i	$-0.568172\pi$
$197$	−5.96616			−0.425071			−0.212536	+	0.977153i	$0.568172\pi$
$198$	4.59286	+	3.13007i	0.326401	+	0.222445i
$199$	17.9322			1.27118			0.635591	−	0.772026i	$-0.280757\pi$
$199$	17.9322			1.27118			0.635591	+	0.772026i	$0.280757\pi$
$200$		0			0
$201$	−13.4504			−0.948719
$202$	−4.94704	−	3.37145i	−0.348073	−	0.237214i
$203$	17.3331			1.21654
$204$	−6.54445	+	2.57140i	−0.458203	+	0.180034i
$205$		0			0
$206$	−0.0501658	−	0.0341884i	−0.00349521	−	0.00238202i
$207$			7.11585i			0.494586i
$208$	−10.1597	+	9.44133i	−0.704450	+	0.654638i
$209$	21.3851			1.47924
$210$		0			0
$211$		−	6.51575i		−	0.448563i	−0.974524	−	0.224281i	$-0.927997\pi$
$211$		−	6.51575i		−	0.448563i	0.974524	−	0.224281i	$-0.0720034\pi$
$212$	−0.170558	−	0.434087i	−0.0117140	−	0.0298132i
$213$	−2.19027			−0.150075
$214$	−12.3230	+	18.0820i	−0.842385	+	1.23606i
$215$		0			0
$216$	2.75787	+	0.627801i	0.187650	+	0.0427164i
$217$			24.7205i			1.67814i
$218$	−15.1409	−	10.3187i	−1.02547	−	0.698868i
$219$		−	0.563219i		−	0.0380588i
$220$		0			0
$221$			12.1903i			0.820006i
$222$	0.330022	−	0.484253i	0.0221496	−	0.0325009i
$223$		−	3.14640i		−	0.210699i	−0.994435	−	0.105349i	$-0.966404\pi$
$223$		−	3.14640i		−	0.210699i	0.994435	−	0.105349i	$-0.0335961\pi$
$224$	−26.4147	+	4.00724i	−1.76491	+	0.267745i
$225$		0			0
$226$	−4.51120	−	3.07442i	−0.300081	−	0.204507i
$227$	3.92103			0.260248			0.130124	−	0.991498i	$-0.458462\pi$
$227$	3.92103			0.260248			0.130124	+	0.991498i	$0.458462\pi$
$228$	10.1289	−	3.97976i	0.670800	−	0.263566i
$229$			25.6899i			1.69764i	0.528683	+	0.848820i	$0.322686\pi$
$229$			25.6899i			1.69764i	−0.528683	+	0.848820i	$0.677314\pi$
$230$		0			0
$231$	18.5617			1.22127
$232$	−2.30401	+	10.1213i	−0.151266	+	0.664498i
$233$		−	25.7565i		−	1.68737i	−0.536841	−	0.843683i	$-0.680383\pi$
$233$		−	25.7565i		−	1.68737i	0.536841	−	0.843683i	$-0.319617\pi$
$234$	2.76149	−	4.05203i	0.180524	−	0.264890i
$235$		0			0
$236$	26.7689	−	10.5179i	1.74251	−	0.684654i
$237$	−10.2746			−0.667409
$238$	−13.2245	+	19.4047i	−0.857214	+	1.25782i
$239$	15.8727			1.02672			0.513360	−	0.858173i	$-0.328400\pi$
$239$	15.8727			1.02672			0.513360	+	0.858173i	$0.328400\pi$
$240$		0			0
$241$	28.1664			1.81436			0.907178	−	0.420748i	$-0.138232\pi$
$241$	28.1664			1.81436			0.907178	+	0.420748i	$0.138232\pi$
$242$	−3.54083	+	5.19558i	−0.227613	+	0.333985i
$243$	−1.00000			−0.0641500
$244$	0.220192	−	0.0865164i	0.0140964	−	0.00553864i
$245$		0			0
$246$	−2.39291	+	3.51120i	−0.152567	+	0.223866i
$247$		−	18.8669i		−	1.20047i
$248$	−14.4351	−	3.28600i	−0.916629	−	0.208661i
$249$	11.3490			0.719216
$250$		0			0
$251$			4.66004i			0.294139i	0.989126	+	0.147070i	$0.0469842\pi$
$251$			4.66004i			0.294139i	−0.989126	+	0.147070i	$0.953016\pi$
$252$	8.79159	−	3.45433i	0.553818	−	0.217602i
$253$	−27.9662			−1.75822
$254$	−21.4801	−	14.6388i	−1.34778	−	0.918522i
$255$		0			0
$256$	1.17125	−	15.9571i	0.0732029	−	0.997317i
$257$		−	3.33996i		−	0.208341i	−0.994559	−	0.104170i	$-0.966781\pi$
$257$		−	3.33996i		−	0.208341i	0.994559	−	0.104170i	$-0.0332187\pi$
$258$	4.25653	−	6.24575i	0.265000	−	0.388843i
$259$		−	1.95707i		−	0.121607i
$260$		0			0
$261$		−	3.66998i		−	0.227166i
$262$	3.99546	+	2.72294i	0.246840	+	0.168224i
$263$		−	27.5932i		−	1.70147i	−0.525595	−	0.850735i	$-0.676157\pi$
$263$		−	27.5932i		−	1.70147i	0.525595	−	0.850735i	$-0.323843\pi$
$264$	−2.46733	+	10.8388i	−0.151854	+	0.667081i
$265$		0			0
$266$	20.4675	−	30.0327i	1.25494	−	1.84142i
$267$	8.88265			0.543609
$268$	−9.83756	−	25.0375i	−0.600925	−	1.52941i
$269$		−	21.8727i		−	1.33360i	−0.745235	−	0.666802i	$-0.767663\pi$
$269$		−	21.8727i		−	1.33360i	0.745235	−	0.666802i	$-0.232337\pi$
$270$		0			0
$271$	−8.78583			−0.533701			−0.266850	−	0.963738i	$-0.585983\pi$
$271$	−8.78583			−0.533701			−0.266850	+	0.963738i	$0.585983\pi$
$272$	−9.57315	−	10.3016i	−0.580458	−	0.624625i
$273$		−	16.3760i		−	0.991120i
$274$	−19.1322	−	13.0387i	−1.15582	−	0.787699i
$275$		0			0
$276$	−13.2459	+	5.20449i	−0.797311	+	0.313274i
$277$	10.3838			0.623904			0.311952	−	0.950098i	$-0.399017\pi$
$277$	10.3838			0.623904			0.311952	+	0.950098i	$0.399017\pi$
$278$	−2.28710	−	1.55867i	−0.137171	−	0.0934831i
$279$	5.23414			0.313360
$280$		0			0
$281$	17.0584			1.01762			0.508811	−	0.860878i	$-0.330085\pi$
$281$	17.0584			1.01762			0.508811	+	0.860878i	$0.330085\pi$
$282$	1.08166	+	0.737160i	0.0644119	+	0.0438972i
$283$	−3.54724			−0.210862			−0.105431	−	0.994427i	$-0.533622\pi$
$283$	−3.54724			−0.210862			−0.105431	+	0.994427i	$0.533622\pi$
$284$	−1.60195	−	4.07712i	−0.0950583	−	0.241932i
$285$		0			0
$286$	15.9250	+	10.8530i	0.941664	+	0.641752i
$287$			14.1903i			0.837625i
$288$	0.848464	+	5.59286i	0.0499962	+	0.329563i
$289$	4.63952			0.272913
$290$		0			0
$291$		−	7.27462i		−	0.426446i
$292$	1.04841	−	0.411935i	0.0613537	−	0.0241067i
$293$	5.72538			0.334480			0.167240	−	0.985916i	$-0.446515\pi$
$293$	5.72538			0.334480			0.167240	+	0.985916i	$0.446515\pi$
$294$	12.1903	−	17.8872i	0.710951	−	1.04320i
$295$		0			0
$296$	1.14280	+	0.260146i	0.0664238	+	0.0151207i
$297$		−	3.93012i		−	0.228049i
$298$	14.1367	+	9.63429i	0.818918	+	0.558099i
$299$			24.6730i			1.42688i
$300$		0			0
$301$		−	25.2417i		−	1.45491i
$302$	−3.88004	+	5.69331i	−0.223271	+	0.327613i
$303$			4.23320i			0.243191i
$304$	14.8164	+	15.9438i	0.849778	+	0.914437i
$305$		0			0
$306$	4.10861	+	2.80005i	0.234874	+	0.160068i
$307$	−12.3760			−0.706335			−0.353168	−	0.935560i	$-0.614895\pi$
$307$	−12.3760			−0.706335			−0.353168	+	0.935560i	$0.614895\pi$
$308$	13.5759	+	34.5520i	0.773561	+	1.96879i
$309$			0.0429270i			0.00244203i
$310$		0			0
$311$	−18.2746			−1.03626			−0.518129	−	0.855302i	$-0.673371\pi$
$311$	−18.2746			−1.03626			−0.518129	+	0.855302i	$0.673371\pi$
$312$	9.56247	+	2.17679i	0.541368	+	0.123237i
$313$			12.7114i			0.718491i	0.933243	+	0.359246i	$0.116966\pi$
$313$			12.7114i			0.718491i	−0.933243	+	0.359246i	$0.883034\pi$
$314$	17.2476	−	25.3080i	0.973338	−	1.42821i
$315$		0			0
$316$	−7.51481	−	19.1259i	−0.422741	−	1.07591i
$317$	−15.8602			−0.890800			−0.445400	−	0.895332i	$-0.646939\pi$
$317$	−15.8602			−0.890800			−0.445400	+	0.895332i	$0.646939\pi$
$318$	−0.185725	+	0.272520i	−0.0104149	+	0.0152822i
$319$	14.4235			0.807559
$320$		0			0
$321$	15.4728			0.863609
$322$	−26.7662	+	39.2750i	−1.49162	+	2.18871i
$323$	19.1303			1.06444
$324$	−0.731395	−	1.86147i	−0.0406330	−	0.103415i
$325$		0			0
$326$	−12.9310	+	18.9742i	−0.716185	+	1.05088i
$327$			12.9561i			0.716476i
$328$	−8.28615	−	1.88625i	−0.457526	−	0.104151i
$329$	4.37145			0.241006
$330$		0			0
$331$		−	23.0315i		−	1.26593i	−0.774182	−	0.632963i	$-0.781839\pi$
$331$		−	23.0315i		−	1.26593i	0.774182	−	0.632963i	$-0.218161\pi$
$332$	8.30063	+	21.1259i	0.455556	+	1.15943i
$333$	−0.414376			−0.0227077
$334$	−7.82092	−	5.33002i	−0.427942	−	0.291646i
$335$		0			0
$336$	12.8602	+	13.8388i	0.701584	+	0.754968i
$337$		−	0.860247i		−	0.0468606i	−0.999725	−	0.0234303i	$-0.992541\pi$
$337$		−	0.860247i		−	0.0468606i	0.999725	−	0.0234303i	$-0.00745878\pi$
$338$	−0.778587	+	1.14245i	−0.0423496	+	0.0621409i
$339$			3.86025i			0.209660i
$340$		0			0
$341$			20.5708i			1.11397i
$342$	−6.35890	−	4.33364i	−0.343850	−	0.234337i
$343$		−	39.2293i		−	2.11818i
$344$	14.7395	+	3.35528i	0.794698	+	0.180905i
$345$		0			0
$346$	17.8576	−	26.2030i	0.960028	−	1.40868i
$347$	32.2856			1.73318			0.866591	−	0.499019i	$-0.166306\pi$
$347$	32.2856			1.73318			0.866591	+	0.499019i	$0.166306\pi$
$348$	6.83154	−	2.68420i	0.366209	−	0.143888i
$349$			0.742899i			0.0397665i	0.999802	+	0.0198832i	$0.00632945\pi$
$349$			0.742899i			0.0397665i	−0.999802	+	0.0198832i	$0.993671\pi$
$350$		0			0
$351$	−3.46733			−0.185073
$352$	−21.9806	+	3.33457i	−1.17157	+	0.177733i
$353$			32.6392i			1.73721i	0.495506	+	0.868604i	$0.334982\pi$
$353$			32.6392i			1.73721i	−0.495506	+	0.868604i	$0.665018\pi$
$354$	−16.8055	−	11.4531i	−0.893204	−	0.608726i
$355$		0			0
$356$	6.49672	+	16.5348i	0.344326	+	0.876341i
$357$	16.6046			0.878811
$358$	−0.173941	−	0.118542i	−0.00919309	−	0.00626517i
$359$	2.71056			0.143058			0.0715290	−	0.997439i	$-0.477212\pi$
$359$	2.71056			0.143058			0.0715290	+	0.997439i	$0.477212\pi$
$360$		0			0
$361$	−10.6080			−0.558317
$362$	−12.1455	−	8.27724i	−0.638352	−	0.435042i
$363$	4.44587			0.233348
$364$	30.4834	−	11.9773i	1.59776	−	0.627782i
$365$		0			0
$366$	−0.138237	−	0.0942095i	−0.00722575	−	0.00492441i
$367$			0.680008i			0.0354961i	0.999842	+	0.0177481i	$0.00564968\pi$
$367$			0.680008i			0.0354961i	−0.999842	+	0.0177481i	$0.994350\pi$
$368$	−19.3760	−	20.8503i	−1.01004	−	1.08690i
$369$	3.00454			0.156410
$370$		0			0
$371$			1.10137i			0.0571803i
$372$	3.82822	+	9.74318i	0.198484	+	0.505160i
$373$	−3.47642			−0.180002			−0.0900012	−	0.995942i	$-0.528687\pi$
$373$	−3.47642			−0.180002			−0.0900012	+	0.995942i	$0.528687\pi$
$374$	−11.0045	+	16.1473i	−0.569031	+	0.834959i
$375$		0			0
$376$	−0.581079	+	2.55263i	−0.0299669	+	0.131642i
$377$		−	12.7250i		−	0.655373i
$378$	−5.51937	−	3.76149i	−0.283886	−	0.193470i
$379$		−	23.0650i		−	1.18477i	−0.805655	−	0.592385i	$-0.798187\pi$
$379$		−	23.0650i		−	1.18477i	0.805655	−	0.592385i	$-0.201813\pi$
$380$		0			0
$381$			18.3805i			0.941664i
$382$	4.96431	−	7.28430i	0.253996	−	0.372697i
$383$			9.81544i			0.501545i	0.968046	+	0.250773i	$0.0806847\pi$
$383$			9.81544i			0.501545i	−0.968046	+	0.250773i	$0.919315\pi$
$384$	−9.79037	+	5.66998i	−0.499613	+	0.289345i
$385$		0			0
$386$	0.458070	+	0.312178i	0.0233151	+	0.0158895i
$387$	−5.34450			−0.271676
$388$	13.5415	−	5.32062i	0.687464	−	0.270114i
$389$			9.86175i			0.500010i	0.968244	+	0.250005i	$0.0804323\pi$
$389$			9.86175i			0.500010i	−0.968244	+	0.250005i	$0.919568\pi$
$390$		0			0
$391$	−25.0175			−1.26519
$392$	42.2123	+	9.60919i	2.13204	+	0.485337i
$393$		−	3.41892i		−	0.172462i
$394$	−4.75164	+	6.97224i	−0.239384	+	0.351256i
$395$		0			0
$396$	7.31580	−	2.87447i	0.367633	−	0.144448i
$397$	−12.7783			−0.641326			−0.320663	−	0.947193i	$-0.603906\pi$
$397$	−12.7783			−0.641326			−0.320663	+	0.947193i	$0.603906\pi$
$398$	14.2818	−	20.9561i	0.715881	−	1.05044i
$399$	−25.6990			−1.28656
$400$		0			0
$401$	3.17325			0.158465			0.0792323	−	0.996856i	$-0.474753\pi$
$401$	3.17325			0.158465			0.0792323	+	0.996856i	$0.474753\pi$
$402$	−10.7123	+	15.7186i	−0.534282	+	0.783971i
$403$	18.1485			0.904041
$404$	−7.87996	+	3.09614i	−0.392043	+	0.154039i
$405$		0			0
$406$	13.8046	−	20.2560i	0.685111	−	1.00529i
$407$		−	1.62855i		−	0.0807243i
$408$	−2.20719	+	9.69599i	−0.109272	+	0.480023i
$409$	−12.1125			−0.598923			−0.299461	−	0.954108i	$-0.596807\pi$
$409$	−12.1125			−0.598923			−0.299461	+	0.954108i	$0.596807\pi$
$410$		0			0
$411$			16.3714i			0.807544i
$412$	−0.0799071	+	0.0313965i	−0.00393674	+	0.00154680i
$413$	−67.9184			−3.34204
$414$	8.31580	+	5.66728i	0.408699	+	0.278532i
$415$		0			0
$416$	2.94191	+	19.3923i	0.144239	+	0.950787i
$417$			1.95707i			0.0958383i
$418$	17.0317	−	24.9913i	0.833050	−	1.22236i
$419$		−	4.24767i		−	0.207512i	−0.994603	−	0.103756i	$-0.966914\pi$
$419$		−	4.24767i		−	0.207512i	0.994603	−	0.103756i	$-0.0330862\pi$
$420$		0			0
$421$		−	3.77928i		−	0.184191i	−0.995750	−	0.0920953i	$-0.970644\pi$
$421$		−	3.77928i		−	0.184191i	0.995750	−	0.0920953i	$-0.0293564\pi$
$422$	−7.61450	−	5.18934i	−0.370668	−	0.252613i
$423$		−	0.925579i		−	0.0450032i
$424$	−0.643126	−	0.146401i	−0.0312329	−	0.00710985i
$425$		0			0
$426$	−1.74440	+	2.55962i	−0.0845164	+	0.124014i
$427$	−0.558674			−0.0270361
$428$	11.3167	+	28.8022i	0.547015	+	1.39220i
$429$		−	13.6271i		−	0.657920i
$430$		0			0
$431$	25.6271			1.23441			0.617206	−	0.786802i	$-0.288265\pi$
$431$	25.6271			1.23441			0.617206	+	0.786802i	$0.288265\pi$
$432$	2.93012	−	2.72294i	0.140976	−	0.131007i
$433$			2.03149i			0.0976274i	0.998808	+	0.0488137i	$0.0155441\pi$
$433$			2.03149i			0.0976274i	−0.998808	+	0.0488137i	$0.984456\pi$
$434$	28.8891	+	19.6882i	1.38672	+	0.945063i
$435$		0			0
$436$	−24.1174	+	9.47605i	−1.15501	+	0.453820i
$437$	38.7196			1.85221
$438$	−0.658194	−	0.448565i	−0.0314497	−	0.0214333i
$439$	22.4864			1.07322			0.536608	−	0.843832i	$-0.319706\pi$
$439$	22.4864			1.07322			0.536608	+	0.843832i	$0.319706\pi$
$440$		0			0
$441$	−15.3061			−0.728863
$442$	14.2459	+	9.70871i	0.677609	+	0.461796i
$443$	−3.39385			−0.161247			−0.0806234	−	0.996745i	$-0.525691\pi$
$443$	−3.39385			−0.161247			−0.0806234	+	0.996745i	$0.525691\pi$
$444$	−0.303073	−	0.771348i	−0.0143832	−	0.0366066i
$445$		0			0
$446$	−3.67698	−	2.50589i	−0.174110	−	0.118657i
$447$		−	12.0968i		−	0.572160i
$448$	−16.3545	+	34.0605i	−0.772679	+	1.60921i
$449$	2.17780			0.102777			0.0513883	−	0.998679i	$-0.483635\pi$
$449$	2.17780			0.102777			0.0513883	+	0.998679i	$0.483635\pi$
$450$		0			0
$451$			11.8082i			0.556028i
$452$	−7.18572	+	2.82336i	−0.337988	+	0.132800i
$453$	4.87178			0.228896
$454$	3.12283	−	4.58224i	0.146562	−	0.215055i
$455$		0			0
$456$	3.41607	−	15.0065i	0.159972	−	0.702743i
$457$		−	3.57653i		−	0.167303i	−0.996495	−	0.0836516i	$-0.973342\pi$
$457$		−	3.57653i		−	0.167303i	0.996495	−	0.0836516i	$-0.0266583\pi$
$458$	30.0221	+	20.4603i	1.40284	+	0.956046i
$459$		−	3.51575i		−	0.164101i
$460$		0			0
$461$			13.1158i			0.610866i	0.952214	+	0.305433i	$0.0988012\pi$
$461$			13.1158i			0.610866i	−0.952214	+	0.305433i	$0.901199\pi$
$462$	14.7831	−	21.6918i	0.687774	−	1.00919i
$463$			3.21417i			0.149375i	0.997207	+	0.0746877i	$0.0237960\pi$
$463$			3.21417i			0.149375i	−0.997207	+	0.0746877i	$0.976204\pi$
$464$	9.99311	+	10.7535i	0.463919	+	0.499218i
$465$		0			0
$466$	−30.0999	−	20.5133i	−1.39435	−	0.950261i
$467$	−30.3016			−1.40219			−0.701095	−	0.713068i	$-0.747305\pi$
$467$	−30.3016			−1.40219			−0.701095	+	0.713068i	$0.747305\pi$
$468$	−2.53599	−	6.45433i	−0.117226	−	0.298352i
$469$			63.5254i			2.93333i
$470$		0			0
$471$	−21.6561			−0.997861
$472$	9.02811	−	39.6597i	0.415552	−	1.82549i
$473$		−	21.0045i		−	0.965790i
$474$	−8.18303	+	12.0072i	−0.375859	+	0.551511i
$475$		0			0
$476$	12.1446	+	30.9090i	0.556645	+	1.41671i
$477$	0.233196			0.0106773
$478$	12.6415	−	18.5493i	0.578210	−	0.848427i
$479$	−35.0896			−1.60328			−0.801642	−	0.597804i	$-0.796040\pi$
$479$	−35.0896			−1.60328			−0.801642	+	0.597804i	$0.796040\pi$
$480$		0			0
$481$	−1.43678			−0.0655116
$482$	22.4326	−	32.9161i	1.02178	−	1.49929i
$483$	33.6077			1.52920
$484$	3.25169	+	8.27584i	0.147804	+	0.376175i
$485$		0			0
$486$	−0.796431	+	1.16863i	−0.0361269	+	0.0530102i
$487$			36.9117i			1.67263i	0.548250	+	0.836315i	$0.315294\pi$
$487$			36.9117i			1.67263i	−0.548250	+	0.836315i	$0.684706\pi$
$488$	0.0742623	−	0.326228i	0.00336169	−	0.0147676i
$489$	16.2362			0.734228
$490$		0			0
$491$		−	20.9867i		−	0.947116i	−0.880763	−	0.473558i	$-0.842969\pi$
$491$		−	20.9867i		−	0.947116i	0.880763	−	0.473558i	$-0.157031\pi$
$492$	2.19751	+	5.59286i	0.0990713	+	0.252146i
$493$	12.9027			0.581109
$494$	−22.0484	−	15.0262i	−0.992006	−	0.676060i
$495$		0			0
$496$	−15.3367	+	14.2522i	−0.688637	+	0.639943i
$497$			10.3445i			0.464014i
$498$	9.03873	−	13.2628i	0.405035	−	0.594322i
$499$		−	15.9906i		−	0.715836i	−0.933753	−	0.357918i	$-0.883487\pi$
$499$		−	15.9906i		−	0.715836i	0.933753	−	0.357918i	$-0.116513\pi$
$500$		0			0
$501$			6.69238i			0.298994i
$502$	5.44587	+	3.71140i	0.243061	+	0.165648i
$503$			37.6023i			1.67660i	0.545206	+	0.838302i	$0.316451\pi$
$503$			37.6023i			1.67660i	−0.545206	+	0.838302i	$0.683549\pi$
$504$	2.96506	−	13.0253i	0.132074	−	0.580191i
$505$		0			0
$506$	−22.2731	+	32.6821i	−0.990161	+	1.45290i
$507$	0.977595			0.0434165
$508$	−34.2148	+	13.4434i	−1.51804	+	0.596456i
$509$			12.8579i			0.569917i	0.958540	+	0.284958i	$0.0919797\pi$
$509$			12.8579i			0.569917i	−0.958540	+	0.284958i	$0.908020\pi$
$510$		0			0
$511$	−2.66004			−0.117673
$512$	−17.7151	−	14.0775i	−0.782904	−	0.622142i
$513$			5.44133i			0.240240i
$514$	−3.90317	−	2.66004i	−0.172162	−	0.117330i
$515$		0			0
$516$	−3.90894	−	9.94861i	−0.172081	−	0.437963i
$517$	3.63764			0.159983
$518$	−2.28710	−	1.55867i	−0.100489	−	0.0684842i
$519$	−22.4220			−0.984215
$520$		0			0
$521$	37.0015			1.62107			0.810534	−	0.585692i	$-0.199177\pi$
$521$	37.0015			1.62107			0.810534	+	0.585692i	$0.199177\pi$
$522$	−4.28885	−	2.92288i	−0.187718	−	0.127931i
$523$	−17.4952			−0.765013			−0.382506	−	0.923953i	$-0.624939\pi$
$523$	−17.4952			−0.765013			−0.382506	+	0.923953i	$0.624939\pi$
$524$	6.36421	−	2.50058i	0.278022	−	0.109238i
$525$		0			0
$526$	−32.2463	−	21.9761i	−1.40600	−	0.958203i
$527$			18.4019i			0.801600i
$528$	10.7015	+	11.5157i	0.465722	+	0.501159i
$529$	−27.6353			−1.20153
$530$		0			0
$531$			14.3805i			0.624062i
$532$	−18.7961	−	47.8379i	−0.814916	−	2.07404i
$533$	10.4178			0.451243
$534$	7.07442	−	10.3805i	0.306140	−	0.449210i
$535$		0			0
$536$	−37.0945	−	8.44418i	−1.60224	−	0.364733i
$537$			0.148842i			0.00642301i
$538$	−25.5611	−	17.4201i	−1.10202	−	0.751035i
$539$		−	60.1549i		−	2.59106i
$540$		0			0
$541$			38.1225i			1.63901i	0.573069	+	0.819507i	$0.305753\pi$
$541$			38.1225i			1.63901i	−0.573069	+	0.819507i	$0.694247\pi$
$542$	−6.99731	+	10.2674i	−0.300560	+	0.441022i
$543$			10.3929i			0.446003i
$544$	−19.6631	+	2.98298i	−0.843048	+	0.127894i
$545$		0			0
$546$	−19.1375	−	13.0424i	−0.819009	−	0.558161i
$547$	−35.7406			−1.52816			−0.764078	−	0.645124i	$-0.776806\pi$
$547$	−35.7406			−1.52816			−0.764078	+	0.645124i	$0.776806\pi$
$548$	−30.4749	+	11.9740i	−1.30182	+	0.511504i
$549$			0.118290i			0.00504848i
$550$		0			0
$551$	−19.9695			−0.850731
$552$	−4.46733	+	19.6246i	−0.190142	+	0.835279i
$553$			48.5264i			2.06355i
$554$	8.27000	−	12.1349i	0.351359	−	0.515561i
$555$		0			0
$556$	−3.64303	+	1.43139i	−0.154499	+	0.0607046i
$557$	2.65516			0.112503			0.0562514	−	0.998417i	$-0.482085\pi$
$557$	2.65516			0.112503			0.0562514	+	0.998417i	$0.482085\pi$
$558$	4.16863	−	6.11677i	0.176472	−	0.258944i
$559$	−18.5312			−0.783785
$560$		0			0
$561$	13.8173			0.583368
$562$	13.5859	−	19.9350i	0.573086	−	0.840908i
$563$	20.3107			0.855992			0.427996	−	0.903781i	$-0.359220\pi$
$563$	20.3107			0.855992			0.427996	+	0.903781i	$0.359220\pi$
$564$	1.72294	−	0.676964i	0.0725487	−	0.0285053i
$565$		0			0
$566$	−2.82513	+	4.14541i	−0.118749	+	0.174245i
$567$			4.72294i			0.198345i
$568$	−6.04049	−	1.37505i	−0.253453	−	0.0576959i
$569$	28.4274			1.19174			0.595868	−	0.803082i	$-0.296808\pi$
$569$	28.4274			1.19174			0.595868	+	0.803082i	$0.296808\pi$
$570$		0			0
$571$		−	16.1485i		−	0.675794i	−0.941183	−	0.337897i	$-0.890284\pi$
$571$		−	16.1485i		−	0.675794i	0.941183	−	0.337897i	$-0.109716\pi$
$572$	25.3663	−	9.96675i	1.06062	−	0.416731i
$573$	−6.23320			−0.260396
$574$	16.5832	+	11.3016i	0.692169	+	0.471719i
$575$		0			0
$576$	7.21173	+	3.46279i	0.300489	+	0.144283i
$577$		−	30.3600i		−	1.26390i	−0.775008	−	0.631952i	$-0.782254\pi$
$577$		−	30.3600i		−	1.26390i	0.775008	−	0.631952i	$-0.217746\pi$
$578$	3.69506	−	5.42189i	0.153694	−	0.225521i
$579$		−	0.391971i		−	0.0162898i
$580$		0			0
$581$		−	53.6008i		−	2.22374i
$582$	−8.50135	−	5.79374i	−0.352392	−	0.240158i
$583$			0.916490i			0.0379571i
$584$	0.353589	−	1.55329i	0.0146316	−	0.0642754i
$585$		0			0
$586$	4.55987	−	6.69085i	0.188366	−	0.276396i
$587$	−2.74070			−0.113121			−0.0565604	−	0.998399i	$-0.518013\pi$
$587$	−2.74070			−0.113121			−0.0565604	+	0.998399i	$0.518013\pi$
$588$	−11.1948	−	28.4918i	−0.461666	−	1.17498i
$589$		−	28.4807i		−	1.17352i
$590$		0			0
$591$	5.96616			0.245415
$592$	1.21417	−	1.12832i	0.0499022	−	0.0463737i
$593$			22.2586i			0.914053i	0.889453	+	0.457027i	$0.151086\pi$
$593$			22.2586i			0.914053i	−0.889453	+	0.457027i	$0.848914\pi$
$594$	−4.59286	−	3.13007i	−0.188447	−	0.128428i
$595$		0			0
$596$	22.5179	−	8.84755i	0.922367	−	0.362410i
$597$	−17.9322			−0.733917
$598$	28.8336	+	19.6504i	1.17910	+	0.803563i
$599$	−48.4526			−1.97972			−0.989860	−	0.142046i	$-0.954632\pi$
$599$	−48.4526			−1.97972			−0.989860	+	0.142046i	$0.954632\pi$
$600$		0			0
$601$	5.26553			0.214786			0.107393	−	0.994217i	$-0.465750\pi$
$601$	5.26553			0.214786			0.107393	+	0.994217i	$0.465750\pi$
$602$	−29.4983	−	20.1033i	−1.20226	−	0.819349i
$603$	13.4504			0.547743
$604$	3.56319	+	9.06866i	0.144984	+	0.368998i
$605$		0			0
$606$	4.94704	+	3.37145i	0.200960	+	0.136956i
$607$		−	7.38288i		−	0.299662i	−0.988712	−	0.149831i	$-0.952127\pi$
$607$		−	7.38288i		−	0.299662i	0.988712	−	0.149831i	$-0.0478730\pi$
$608$	30.4326	−	4.61677i	1.23420	−	0.187235i
$609$	−17.3331			−0.702371
$610$		0			0
$611$		−	3.20929i		−	0.129834i
$612$	6.54445	−	2.57140i	0.264544	−	0.103943i
$613$	−2.64607			−0.106874			−0.0534369	−	0.998571i	$-0.517018\pi$
$613$	−2.64607			−0.106874			−0.0534369	+	0.998571i	$0.517018\pi$
$614$	−9.85663	+	14.4630i	−0.397781	+	0.583678i
$615$		0			0
$616$	51.1909	+	11.6531i	2.06254	+	0.469515i
$617$		−	21.0136i		−	0.845977i	−0.906135	−	0.422989i	$-0.860981\pi$
$617$		−	21.0136i		−	0.845977i	0.906135	−	0.422989i	$-0.139019\pi$
$618$	0.0501658	+	0.0341884i	0.00201796	+	0.00137526i
$619$		−	24.0874i		−	0.968154i	−0.875025	−	0.484077i	$-0.839155\pi$
$619$		−	24.0874i		−	0.968154i	0.875025	−	0.484077i	$-0.160845\pi$
$620$		0			0
$621$		−	7.11585i		−	0.285549i
$622$	−14.5545	+	21.3563i	−0.583581	+	0.856309i
$623$		−	41.9522i		−	1.68078i
$624$	10.1597	−	9.44133i	0.406714	−	0.377956i
$625$		0			0
$626$	14.8549	+	10.1238i	0.593723	+	0.404627i
$627$	−21.3851			−0.854038
$628$	−15.8392	−	40.3121i	−0.632051	−	1.60863i
$629$		−	1.45684i		−	0.0580881i
$630$		0			0
$631$	25.2094			1.00357			0.501785	−	0.864992i	$-0.332677\pi$
$631$	25.2094			1.00357			0.501785	+	0.864992i	$0.332677\pi$
$632$	−28.3361	−	6.45042i	−1.12715	−	0.256584i
$633$			6.51575i			0.258978i
$634$	−12.6316	+	18.5348i	−0.501665	+	0.736110i
$635$		0			0
$636$	0.170558	+	0.434087i	0.00676308	+	0.0172127i
$637$	−53.0714			−2.10277
$638$	11.4873	−	16.8557i	0.454786	−	0.667324i
$639$	2.19027			0.0866457
$640$		0			0
$641$	−18.4755			−0.729738			−0.364869	−	0.931059i	$-0.618886\pi$
$641$	−18.4755			−0.729738			−0.364869	+	0.931059i	$0.618886\pi$
$642$	12.3230	−	18.0820i	0.486351	−	0.713640i
$643$	−0.636984			−0.0251202			−0.0125601	−	0.999921i	$-0.503998\pi$
$643$	−0.636984			−0.0251202			−0.0125601	+	0.999921i	$0.503998\pi$
$644$	24.5805	+	62.5596i	0.968607	+	2.46519i
$645$		0			0
$646$	15.2360	−	22.3563i	0.599452	−	0.879596i
$647$		−	32.0182i		−	1.25876i	−0.777096	−	0.629382i	$-0.783308\pi$
$647$		−	32.0182i		−	1.25876i	0.777096	−	0.629382i	$-0.216692\pi$
$648$	−2.75787	−	0.627801i	−0.108340	−	0.0246623i
$649$	−56.5173			−2.21850
$650$		0			0
$651$		−	24.7205i		−	0.968873i
$652$	11.8751	+	30.2232i	0.465065	+	1.18363i
$653$	−25.9769			−1.01656			−0.508278	−	0.861193i	$-0.669718\pi$
$653$	−25.9769			−1.01656			−0.508278	+	0.861193i	$0.669718\pi$
$654$	15.1409	+	10.3187i	0.592057	+	0.403492i
$655$		0			0
$656$	−8.80369	+	8.18118i	−0.343726	+	0.319421i
$657$			0.563219i			0.0219732i
$658$	3.48156	−	5.10861i	0.135725	−	0.199154i
$659$			21.3422i			0.831372i	0.909508	+	0.415686i	$0.136459\pi$
$659$			21.3422i			0.831372i	−0.909508	+	0.415686i	$0.863541\pi$
$660$		0			0
$661$			14.8397i			0.577198i	0.957450	+	0.288599i	$0.0931895\pi$
$661$			14.8397i			0.577198i	−0.957450	+	0.288599i	$0.906810\pi$
$662$	−26.9153	−	18.3430i	−1.04609	−	0.712921i
$663$		−	12.1903i		−	0.473431i
$664$	31.2992	+	7.12494i	1.21465	+	0.276501i
$665$		0			0
$666$	−0.330022	+	0.484253i	−0.0127881	+	0.0187644i
$667$	26.1150			1.01118
$668$	−12.4577	+	4.89477i	−0.482001	+	0.189384i
$669$			3.14640i			0.121647i
$670$		0			0
$671$	−0.464893			−0.0179470
$672$	26.4147	−	4.00724i	1.01897	−	0.154583i
$673$			18.1167i			0.698347i	0.937058	+	0.349174i	$0.113538\pi$
$673$			18.1167i			0.698347i	−0.937058	+	0.349174i	$0.886462\pi$
$674$	−1.00531	−	0.685127i	−0.0387231	−	0.0263901i
$675$		0			0
$676$	0.715008	+	1.81976i	0.0275003	+	0.0699908i
$677$	30.5617			1.17458			0.587291	−	0.809376i	$-0.300194\pi$
$677$	30.5617			1.17458			0.587291	+	0.809376i	$0.300194\pi$
$678$	4.51120	+	3.07442i	0.173252	+	0.118072i
$679$	−34.3576			−1.31852
$680$		0			0
$681$	−3.92103			−0.150254
$682$	24.0397	+	16.3832i	0.920527	+	0.627346i
$683$	−22.2027			−0.849564			−0.424782	−	0.905296i	$-0.639649\pi$
$683$	−22.2027			−0.849564			−0.424782	+	0.905296i	$0.639649\pi$
$684$	−10.1289	+	3.97976i	−0.387286	+	0.152170i
$685$		0			0
$686$	−45.8445	−	31.2434i	−1.75035	−	1.19288i
$687$		−	25.6899i		−	0.980132i
$688$	15.6600	−	14.5527i	0.597034	−	0.554818i
$689$	0.808569			0.0308040
$690$		0			0
$691$		−	12.6890i		−	0.482712i	−0.970437	−	0.241356i	$-0.922408\pi$
$691$		−	12.6890i		−	0.482712i	0.970437	−	0.241356i	$-0.0775922\pi$
$692$	−16.3993	−	41.7378i	−0.623408	−	1.58663i
$693$	−18.5617			−0.705101
$694$	25.7133	−	37.7299i	0.976062	−	1.43221i
$695$		0			0
$696$	2.30401	−	10.1213i	0.0873334	−	0.383648i
$697$			10.5632i			0.400110i
$698$	0.868174	+	0.591668i	0.0328609	+	0.0223950i
$699$			25.7565i			0.974202i
$700$		0			0
$701$			34.9241i			1.31906i	0.751676	+	0.659532i	$0.229246\pi$
$701$			34.9241i			1.31906i	−0.751676	+	0.659532i	$0.770754\pi$
$702$	−2.76149	+	4.05203i	−0.104226	+	0.152934i
$703$			2.25476i			0.0850398i
$704$	−13.6092	+	28.3430i	−0.512916	+	1.06822i
$705$		0			0
$706$	38.1431	+	25.9949i	1.43554	+	0.978330i
$707$	19.9931			0.751918
$708$	−26.7689	+	10.5179i	−1.00604	+	0.395285i
$709$		−	5.65610i		−	0.212419i	−0.994344	−	0.106210i	$-0.966129\pi$
$709$		−	5.65610i		−	0.212419i	0.994344	−	0.106210i	$-0.0338715\pi$
$710$		0			0
$711$	10.2746			0.385328
$712$	24.4972	+	5.57653i	0.918073	+	0.208989i
$713$			37.2453i			1.39485i
$714$	13.2245	−	19.4047i	0.494913	−	0.726203i
$715$		0			0
$716$	−0.277065	+	0.108862i	−0.0103544	+	0.00406838i
$717$	−15.8727			−0.592778
$718$	2.15878	−	3.16764i	0.0805648	−	0.118215i
$719$	20.0844			0.749020			0.374510	−	0.927223i	$-0.377811\pi$
$719$	20.0844			0.749020			0.374510	+	0.927223i	$0.377811\pi$
$720$		0			0
$721$	0.202741			0.00755048
$722$	−8.44856	+	12.3969i	−0.314423	+	0.461364i
$723$	−28.1664			−1.04752
$724$	−19.3461	+	7.60132i	−0.718991	+	0.282501i
$725$		0			0
$726$	3.54083	−	5.19558i	0.131413	−	0.192826i
$727$		−	13.0424i		−	0.483715i	−0.970312	−	0.241857i	$-0.922243\pi$
$727$		−	13.0424i		−	0.483715i	0.970312	−	0.241857i	$-0.0777566\pi$
$728$	10.2809	−	45.1629i	0.381034	−	1.67385i
$729$	1.00000			0.0370370
$730$		0			0
$731$		−	18.7899i		−	0.694970i
$732$	−0.220192	+	0.0865164i	−0.00813854	+	0.00319774i
$733$	−34.8917			−1.28876			−0.644378	−	0.764707i	$-0.722884\pi$
$733$	−34.8917			−1.28876			−0.644378	+	0.764707i	$0.722884\pi$
$734$	0.794678	+	0.541580i	0.0293321	+	0.0199901i
$735$		0			0
$736$	−39.7980	+	6.03754i	−1.46697	+	0.222547i
$737$			52.8618i			1.94719i
$738$	2.39291	−	3.51120i	0.0880843	−	0.129249i
$739$			41.5040i			1.52675i	0.645957	+	0.763374i	$0.276459\pi$
$739$			41.5040i			1.52675i	−0.645957	+	0.763374i	$0.723541\pi$
$740$		0			0
$741$			18.8669i			0.693093i
$742$	1.28710	+	0.877166i	0.0472508	+	0.0322018i
$743$			7.63764i			0.280198i	0.990138	+	0.140099i	$0.0447421\pi$
$743$			7.63764i			0.280198i	−0.990138	+	0.140099i	$0.955258\pi$
$744$	14.4351	+	3.28600i	0.529216	+	0.120470i
$745$		0			0
$746$	−2.76873	+	4.06265i	−0.101370	+	0.148744i
$747$	−11.3490			−0.415240
$748$	10.1059	+	25.7205i	0.369509	+	0.940434i
$749$		−	73.0771i		−	2.67018i
$750$		0			0
$751$	−19.4029			−0.708023			−0.354012	−	0.935241i	$-0.615183\pi$
$751$	−19.4029			−0.708023			−0.354012	+	0.935241i	$0.615183\pi$
$752$	2.52029	+	2.71206i	0.0919056	+	0.0988987i
$753$		−	4.66004i		−	0.169821i
$754$	−14.8709	−	10.1346i	−0.541565	−	0.369081i
$755$		0			0
$756$	−8.79159	+	3.45433i	−0.319747	+	0.125633i
$757$	43.7959			1.59179			0.795894	−	0.605436i	$-0.207001\pi$
$757$	43.7959			1.59179			0.795894	+	0.605436i	$0.207001\pi$
$758$	−26.9545	−	18.3697i	−0.979030	−	0.667217i
$759$	27.9662			1.01511
$760$		0			0
$761$	9.95519			0.360875			0.180438	−	0.983586i	$-0.442249\pi$
$761$	9.95519			0.360875			0.180438	+	0.983586i	$0.442249\pi$
$762$	21.4801	+	14.6388i	0.778140	+	0.530309i
$763$	61.1910			2.21526
$764$	−4.55893	−	11.6029i	−0.164936	−	0.419778i
$765$		0			0
$766$	11.4706	+	7.81732i	0.414450	+	0.282451i
$767$			49.8621i			1.80042i
$768$	−1.17125	+	15.9571i	−0.0422637	+	0.575801i
$769$	17.9008			0.645520			0.322760	−	0.946481i	$-0.395389\pi$
$769$	17.9008			0.645520			0.322760	+	0.946481i	$0.395389\pi$
$770$		0			0
$771$			3.33996i			0.120286i
$772$	0.729642	−	0.286686i	0.0262604	−	0.0103180i
$773$	20.8182			0.748777			0.374389	−	0.927272i	$-0.377853\pi$
$773$	20.8182			0.748777			0.374389	+	0.927272i	$0.377853\pi$
$774$	−4.25653	+	6.24575i	−0.152998	+	0.224499i
$775$		0			0
$776$	4.56701	−	20.0625i	0.163946	−	0.720201i
$777$			1.95707i			0.0702096i
$778$	11.5247	+	7.85420i	0.413182	+	0.281587i
$779$		−	16.3487i		−	0.585753i
$780$		0			0
$781$			8.60803i			0.308019i
$782$	−19.9247	+	29.2362i	−0.712507	+	1.04549i
$783$			3.66998i			0.131154i
$784$	44.8488	−	41.6776i	1.60174	−	1.48848i
$785$		0			0
$786$	−3.99546	−	2.72294i	−0.142513	−	0.0971239i
$787$	−27.2047			−0.969744			−0.484872	−	0.874585i	$-0.661134\pi$
$787$	−27.2047			−0.969744			−0.484872	+	0.874585i	$0.661134\pi$
$788$	4.36362	+	11.1058i	0.155448	+	0.395628i
$789$			27.5932i			0.982344i
$790$		0			0
$791$	18.2317			0.648244
$792$	2.46733	−	10.8388i	0.0876729	−	0.385139i
$793$			0.410149i			0.0145648i
$794$	−10.1771	+	14.9332i	−0.361170	+	0.529958i
$795$		0			0
$796$	−13.1155	−	33.3803i	−0.464868	−	1.18313i
$797$	16.4344			0.582138			0.291069	−	0.956702i	$-0.405989\pi$
$797$	16.4344			0.582138			0.291069	+	0.956702i	$0.405989\pi$
$798$	−20.4675	+	30.0327i	−0.724542	+	1.06315i
$799$	3.25410			0.115122
$800$		0			0
$801$	−8.88265			−0.313853
$802$	2.52728	−	3.70836i	0.0892413	−	0.130947i
$803$	−2.21352			−0.0781134
$804$	9.83756	+	25.0375i	0.346944	+	0.883005i
$805$		0			0
$806$	14.4540	−	21.2089i	0.509122	−	0.747052i
$807$			21.8727i			0.769956i
$808$	−2.65760	+	11.6746i	−0.0934942	+	0.410712i
$809$	−28.7698			−1.01149			−0.505747	−	0.862682i	$-0.668783\pi$
$809$	−28.7698			−1.01149			−0.505747	+	0.862682i	$0.668783\pi$
$810$		0			0
$811$			14.3512i			0.503940i	0.967735	+	0.251970i	$0.0810785\pi$
$811$			14.3512i			0.503940i	−0.967735	+	0.251970i	$0.918922\pi$
$812$	−12.6773	−	32.2649i	−0.444887	−	1.13228i
$813$	8.78583			0.308132
$814$	−1.90317	−	1.29703i	−0.0667062	−	0.0454608i
$815$		0			0
$816$	9.57315	+	10.3016i	0.335127	+	0.360627i
$817$			29.0812i			1.01742i
$818$	−9.64675	+	14.1550i	−0.337291	+	0.494918i
$819$			16.3760i			0.572224i
$820$		0			0
$821$			4.97271i			0.173549i	0.996228	+	0.0867744i	$0.0276559\pi$
$821$			4.97271i			0.173549i	−0.996228	+	0.0867744i	$0.972344\pi$
$822$	19.1322	+	13.0387i	0.667311	+	0.454778i
$823$		−	20.3625i		−	0.709791i	−0.934906	−	0.354895i	$-0.884517\pi$
$823$		−	20.3625i		−	0.709791i	0.934906	−	0.354895i	$-0.115483\pi$
$824$	−0.0269496	+	0.118387i	−0.000938833	+	0.00412421i
$825$		0			0
$826$	−54.0923	+	79.3715i	−1.88211	+	2.76169i
$827$	36.0039			1.25198			0.625989	−	0.779832i	$-0.284696\pi$
$827$	36.0039			1.25198			0.625989	+	0.779832i	$0.284696\pi$
$828$	13.2459	−	5.20449i	0.460328	−	0.180869i
$829$			7.68666i			0.266969i	0.991051	+	0.133484i	$0.0426166\pi$
$829$			7.68666i			0.266969i	−0.991051	+	0.133484i	$0.957383\pi$
$830$		0			0
$831$	−10.3838			−0.360211
$832$	25.0055	+	12.0066i	0.866909	+	0.416256i
$833$		−	53.8124i		−	1.86449i
$834$	2.28710	+	1.55867i	0.0791956	+	0.0539725i
$835$		0			0
$836$	−15.6409	−	39.8076i	−0.540953	−	1.37678i
$837$	−5.23414			−0.180918
$838$	−4.96396	−	3.38298i	−0.171477	−	0.116863i
$839$	25.3725			0.875956			0.437978	−	0.898986i	$-0.355695\pi$
$839$	25.3725			0.875956			0.437978	+	0.898986i	$0.355695\pi$
$840$		0			0
$841$	15.5313			0.535561
$842$	−4.41658	−	3.00993i	−0.152205	−	0.103729i
$843$	−17.0584			−0.587524
$844$	−12.1289	+	4.76558i	−0.417492	+	0.164038i
$845$		0			0
$846$	−1.08166	−	0.737160i	−0.0371882	−	0.0253441i
$847$		−	20.9976i		−	0.721485i
$848$	−0.683294	+	0.634978i	−0.0234644	+	0.0218052i
$849$	3.54724			0.121741
$850$		0			0
$851$		−	2.94864i		−	0.101078i
$852$	1.60195	+	4.07712i	0.0548820	+	0.139680i
$853$	20.1365			0.689460			0.344730	−	0.938702i	$-0.387971\pi$
$853$	20.1365			0.689460			0.344730	+	0.938702i	$0.387971\pi$
$854$	−0.444945	+	0.652884i	−0.0152257	+	0.0223412i
$855$		0			0
$856$	42.6721	+	9.71385i	1.45850	+	0.332012i
$857$			42.0380i			1.43599i	0.696047	+	0.717996i	$0.254940\pi$
$857$			42.0380i			1.43599i	−0.696047	+	0.717996i	$0.745060\pi$
$858$	−15.9250	−	10.8530i	−0.543670	−	0.370516i
$859$			12.4095i			0.423406i	0.977334	+	0.211703i	$0.0679010\pi$
$859$			12.4095i			0.423406i	−0.977334	+	0.211703i	$0.932099\pi$
$860$		0			0
$861$		−	14.1903i		−	0.483603i
$862$	20.4102	−	29.9486i	0.695174	−	1.02005i
$863$		−	21.8154i		−	0.742606i	−0.928512	−	0.371303i	$-0.878911\pi$
$863$		−	21.8154i		−	0.742606i	0.928512	−	0.371303i	$-0.121089\pi$
$864$	−0.848464	−	5.59286i	−0.0288653	−	0.190273i
$865$		0			0
$866$	2.37407	+	1.61795i	0.0806740	+	0.0549800i
$867$	−4.63952			−0.157566
$868$	46.0164	−	18.0804i	1.56190	−	0.613690i
$869$			40.3805i			1.36982i
$870$		0			0
$871$	46.6371			1.58024
$872$	−8.13387	+	35.7314i	−0.275448	+	1.21002i
$873$			7.27462i			0.246209i
$874$	30.8375	−	45.2490i	1.04310	−	1.53057i
$875$		0			0
$876$	−1.04841	+	0.411935i	−0.0354226	+	0.0139180i
$877$	−5.83690			−0.197098			−0.0985491	−	0.995132i	$-0.531420\pi$
$877$	−5.83690			−0.197098			−0.0985491	+	0.995132i	$0.531420\pi$
$878$	17.9088	−	26.2782i	0.604394	−	0.886848i
$879$	−5.72538			−0.193112
$880$		0			0
$881$	−11.9613			−0.402986			−0.201493	−	0.979490i	$-0.564579\pi$
$881$	−11.9613			−0.402986			−0.201493	+	0.979490i	$0.564579\pi$
$882$	−12.1903	+	17.8872i	−0.410468	+	0.602293i
$883$	−3.74810			−0.126134			−0.0630668	−	0.998009i	$-0.520088\pi$
$883$	−3.74810			−0.126134			−0.0630668	+	0.998009i	$0.520088\pi$
$884$	22.6918	−	8.91590i	0.763208	−	0.299874i
$885$		0			0
$886$	−2.70297	+	3.96616i	−0.0908081	+	0.133246i
$887$			42.8101i			1.43742i	0.695309	+	0.718711i	$0.255268\pi$
$887$			42.8101i			1.43742i	−0.695309	+	0.718711i	$0.744732\pi$
$888$	−1.14280	−	0.260146i	−0.0383498	−	0.00872992i
$889$	86.8101			2.91152
$890$		0			0
$891$			3.93012i			0.131664i
$892$	−5.85692	+	2.30126i	−0.196104	+	0.0770519i
$893$	−5.03638			−0.168536
$894$	−14.1367	−	9.63429i	−0.472803	−	0.322219i
$895$		0			0
$896$	26.7789	+	46.2393i	0.894622	+	1.54475i
$897$		−	24.6730i		−	0.823808i
$898$	1.73447	−	2.54504i	0.0578799	−	0.0849291i
$899$		−	19.2092i		−	0.640662i
$900$		0			0
$901$			0.819859i			0.0273135i
$902$	13.7995	+	9.40444i	0.459472	+	0.313134i
$903$			25.2417i			0.839992i
$904$	−2.42347	+	10.6461i	−0.0806033	+	0.354083i
$905$		0			0
$906$	3.88004	−	5.69331i	0.128906	−	0.189147i
$907$	−6.97759			−0.231687			−0.115844	−	0.993267i	$-0.536957\pi$
$907$	−6.97759			−0.231687			−0.115844	+	0.993267i	$0.536957\pi$
$908$	−2.86782	−	7.29888i	−0.0951721	−	0.242222i
$909$		−	4.23320i		−	0.140406i
$910$		0			0
$911$	24.2837			0.804555			0.402278	−	0.915518i	$-0.368219\pi$
$911$	24.2837			0.804555			0.402278	+	0.915518i	$0.368219\pi$
$912$	−14.8164	−	15.9438i	−0.490619	−	0.527951i
$913$		−	44.6031i		−	1.47615i
$914$	−4.17965	−	2.84846i	−0.138250	−	0.0942188i
$915$		0			0
$916$	47.8210	−	18.7895i	1.58005	−	0.620822i
$917$	−16.1473			−0.533232
$918$	−4.10861	−	2.80005i	−0.135604	−	0.0924154i
$919$	1.25720			0.0414712			0.0207356	−	0.999785i	$-0.493399\pi$
$919$	1.25720			0.0414712			0.0207356	+	0.999785i	$0.493399\pi$
$920$		0			0
$921$	12.3760			0.407803
$922$	15.3276	+	10.4459i	0.504787	+	0.344016i
$923$	7.59440			0.249973
$924$	−13.5759	−	34.5520i	−0.446616	−	1.13668i
$925$		0			0
$926$	3.75618	+	2.55987i	0.123436	+	0.0841225i
$927$		−	0.0429270i		−	0.00140991i
$928$	20.5257	−	3.11384i	0.673788	−	0.102217i
$929$	−10.4933			−0.344275			−0.172138	−	0.985073i	$-0.555067\pi$
$929$	−10.4933			−0.344275			−0.172138	+	0.985073i	$0.555067\pi$
$930$		0			0
$931$			83.2856i			2.72957i
$932$	−47.9450	+	18.8382i	−1.57049	+	0.617066i
$933$	18.2746			0.598284
$934$	−24.1331	+	35.4113i	−0.789660	+	1.15869i
$935$		0			0
$936$	−9.56247	−	2.17679i	−0.312559	−	0.0711508i
$937$			12.9680i			0.423648i	0.977308	+	0.211824i	$0.0679403\pi$
$937$			12.9680i			0.423648i	−0.977308	+	0.211824i	$0.932060\pi$
$938$	74.2378	+	50.5936i	2.42395	+	1.65194i
$939$		−	12.7114i		−	0.414821i
$940$		0			0
$941$		−	44.9947i		−	1.46678i	−0.679806	−	0.733392i	$-0.737936\pi$
$941$		−	44.9947i		−	1.46678i	0.679806	−	0.733392i	$-0.262064\pi$
$942$	−17.2476	+	25.3080i	−0.561957	+	0.824579i
$943$			21.3799i			0.696225i
$944$	−39.1573	−	42.1368i	−1.27446	−	1.37143i
$945$		0			0
$946$	−24.5466	−	16.7287i	−0.798077	−	0.543896i
$947$	30.6282			0.995283			0.497642	−	0.867383i	$-0.334199\pi$
$947$	30.6282			0.995283			0.497642	+	0.867383i	$0.334199\pi$
$948$	7.51481	+	19.1259i	0.244070	+	0.621180i
$949$			1.95287i			0.0633927i
$950$		0			0
$951$	15.8602			0.514304
$952$	45.7935	+	10.4244i	1.48418	+	0.337857i
$953$		−	17.5717i		−	0.569202i	−0.958646	−	0.284601i	$-0.908139\pi$
$953$		−	17.5717i		−	0.569202i	0.958646	−	0.284601i	$-0.0918610\pi$
$954$	0.185725	−	0.272520i	0.00601306	−	0.00882317i
$955$		0			0
$956$	−11.6092	−	29.5466i	−0.375469	−	0.955604i
$957$	−14.4235			−0.466244
$958$	−27.9465	+	41.0068i	−0.902909	+	1.32487i
$959$	77.3213			2.49683
$960$		0			0
$961$	−3.60380			−0.116252
$962$	−1.14430	+	1.67907i	−0.0368936	+	0.0541353i
$963$	−15.4728			−0.498605
$964$	−20.6007	−	52.4308i	−0.663505	−	1.68868i
$965$		0			0
$966$	26.7662	−	39.2750i	0.861189	−	1.26365i
$967$			4.50932i			0.145010i	0.997368	+	0.0725050i	$0.0230993\pi$
$967$			4.50932i			0.145010i	−0.997368	+	0.0725050i	$0.976901\pi$
$968$	12.2611	+	2.79112i	0.394088	+	0.0897100i
$969$	−19.1303			−0.614555
$970$		0			0
$971$		−	35.8512i		−	1.15052i	−0.817971	−	0.575259i	$-0.804901\pi$
$971$		−	35.8512i		−	1.15052i	0.817971	−	0.575259i	$-0.195099\pi$
$972$	0.731395	+	1.86147i	0.0234595	+	0.0597066i
$973$	9.24313			0.296321
$974$	43.1361	+	29.3976i	1.38217	+	0.941961i
$975$		0			0
$976$	−0.322095	−	0.346603i	−0.0103100	−	0.0110945i
$977$		−	43.9704i		−	1.40674i	−0.710826	−	0.703368i	$-0.751678\pi$
$977$		−	43.9704i		−	1.40674i	0.710826	−	0.703368i	$-0.248322\pi$
$978$	12.9310	−	18.9742i	0.413489	−	0.606727i
$979$		−	34.9099i		−	1.11573i
$980$		0			0
$981$		−	12.9561i		−	0.413657i
$982$	−24.5257	−	16.7144i	−0.782646	−	0.533380i
$983$			4.64187i			0.148053i	0.997256	+	0.0740263i	$0.0235849\pi$
$983$			4.64187i			0.148053i	−0.997256	+	0.0740263i	$0.976415\pi$
$984$	8.28615	+	1.88625i	0.264153	+	0.0601316i
$985$		0			0
$986$	10.2761	−	15.0785i	0.327258	−	0.480197i
$987$	−4.37145			−0.139145
$988$	−35.1201	+	13.7991i	−1.11732	+	0.439009i
$989$		−	38.0307i		−	1.20930i
$990$		0			0
$991$	−52.9117			−1.68080			−0.840398	−	0.541970i	$-0.817679\pi$
$991$	−52.9117			−1.68080			−0.840398	+	0.541970i	$0.817679\pi$
$992$	4.44098	+	29.2738i	0.141001	+	0.929444i
$993$			23.0315i			0.730882i
$994$	12.0889	+	8.23868i	0.383437	+	0.261315i
$995$		0			0
$996$	−8.30063	−	21.1259i	−0.263016	−	0.669399i
$997$	39.4228			1.24853			0.624266	−	0.781211i	$-0.285398\pi$
$997$	39.4228			1.24853			0.624266	+	0.781211i	$0.285398\pi$
$998$	−18.6871	−	12.7354i	−0.591529	−	0.403132i
$999$	0.414376			0.0131103

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	600.2.d.g.349.7		8
3.2	odd	2		1800.2.d.t.1549.2		8
4.3	odd	2		2400.2.d.h.49.1		8
5.2	odd	4		600.2.k.e.301.6	yes	8
5.3	odd	4		600.2.k.d.301.3	✓	8
5.4	even	2		600.2.d.h.349.2		8
8.3	odd	2		2400.2.d.g.49.1		8
8.5	even	2		600.2.d.h.349.1		8
12.11	even	2		7200.2.d.t.2449.1		8
15.2	even	4		1800.2.k.q.901.3		8
15.8	even	4		1800.2.k.t.901.6		8
15.14	odd	2		1800.2.d.s.1549.7		8
20.3	even	4		2400.2.k.d.1201.5		8
20.7	even	4		2400.2.k.e.1201.4		8
20.19	odd	2		2400.2.d.g.49.8		8
24.5	odd	2		1800.2.d.s.1549.8		8
24.11	even	2		7200.2.d.s.2449.1		8
40.3	even	4		2400.2.k.d.1201.1		8
40.13	odd	4		600.2.k.d.301.4	yes	8
40.19	odd	2		2400.2.d.h.49.8		8
40.27	even	4		2400.2.k.e.1201.8		8
40.29	even	2	inner	600.2.d.g.349.8		8
40.37	odd	4		600.2.k.e.301.5	yes	8
60.23	odd	4		7200.2.k.r.3601.2		8
60.47	odd	4		7200.2.k.s.3601.8		8
60.59	even	2		7200.2.d.s.2449.8		8
120.29	odd	2		1800.2.d.t.1549.1		8
120.53	even	4		1800.2.k.t.901.5		8
120.59	even	2		7200.2.d.t.2449.8		8
120.77	even	4		1800.2.k.q.901.4		8
120.83	odd	4		7200.2.k.r.3601.1		8
120.107	odd	4		7200.2.k.s.3601.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
600.2.d.g.349.7		8	1.1	even	1	trivial
600.2.d.g.349.8		8	40.29	even	2	inner
600.2.d.h.349.1		8	8.5	even	2
600.2.d.h.349.2		8	5.4	even	2
600.2.k.d.301.3	✓	8	5.3	odd	4
600.2.k.d.301.4	yes	8	40.13	odd	4
600.2.k.e.301.5	yes	8	40.37	odd	4
600.2.k.e.301.6	yes	8	5.2	odd	4
1800.2.d.s.1549.7		8	15.14	odd	2
1800.2.d.s.1549.8		8	24.5	odd	2
1800.2.d.t.1549.1		8	120.29	odd	2
1800.2.d.t.1549.2		8	3.2	odd	2
1800.2.k.q.901.3		8	15.2	even	4
1800.2.k.q.901.4		8	120.77	even	4
1800.2.k.t.901.5		8	120.53	even	4
1800.2.k.t.901.6		8	15.8	even	4
2400.2.d.g.49.1		8	8.3	odd	2
2400.2.d.g.49.8		8	20.19	odd	2
2400.2.d.h.49.1		8	4.3	odd	2
2400.2.d.h.49.8		8	40.19	odd	2
2400.2.k.d.1201.1		8	40.3	even	4
2400.2.k.d.1201.5		8	20.3	even	4
2400.2.k.e.1201.4		8	20.7	even	4
2400.2.k.e.1201.8		8	40.27	even	4
7200.2.d.s.2449.1		8	24.11	even	2
7200.2.d.s.2449.8		8	60.59	even	2
7200.2.d.t.2449.1		8	12.11	even	2
7200.2.d.t.2449.8		8	120.59	even	2
7200.2.k.r.3601.1		8	120.83	odd	4
7200.2.k.r.3601.2		8	60.23	odd	4
7200.2.k.s.3601.7		8	120.107	odd	4
7200.2.k.s.3601.8		8	60.47	odd	4

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:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	600.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.796431 - 1.16863i) q^{2} -1.00000 q^{3} +(-0.731395 - 1.86147i) q^{4} +(-0.796431 + 1.16863i) q^{6} +4.72294i q^{7} +(-2.75787 - 0.627801i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(0.796431 - 1.16863i) q^{2} -1.00000 q^{3} +(-0.731395 - 1.86147i) q^{4} +(-0.796431 + 1.16863i) q^{6} +4.72294i q^{7} +(-2.75787 - 0.627801i) q^{8} +1.00000 q^{9} +3.93012i q^{11} +(0.731395 + 1.86147i) q^{12} +3.46733 q^{13} +(5.51937 + 3.76149i) q^{14} +(-2.93012 + 2.72294i) q^{16} +3.51575i q^{17} +(0.796431 - 1.16863i) q^{18} -5.44133i q^{19} -4.72294i q^{21} +(4.59286 + 3.13007i) q^{22} +7.11585i q^{23} +(2.75787 + 0.627801i) q^{24} +(2.76149 - 4.05203i) q^{26} -1.00000 q^{27} +(8.79159 - 3.45433i) q^{28} -3.66998i q^{29} +5.23414 q^{31} +(0.848464 + 5.59286i) q^{32} -3.93012i q^{33} +(4.10861 + 2.80005i) q^{34} +(-0.731395 - 1.86147i) q^{36} -0.414376 q^{37} +(-6.35890 - 4.33364i) q^{38} -3.46733 q^{39} +3.00454 q^{41} +(-5.51937 - 3.76149i) q^{42} -5.34450 q^{43} +(7.31580 - 2.87447i) q^{44} +(8.31580 + 5.66728i) q^{46} -0.925579i q^{47} +(2.93012 - 2.72294i) q^{48} -15.3061 q^{49} -3.51575i q^{51} +(-2.53599 - 6.45433i) q^{52} +0.233196 q^{53} +(-0.796431 + 1.16863i) q^{54} +(2.96506 - 13.0253i) q^{56} +5.44133i q^{57} +(-4.28885 - 2.92288i) q^{58} +14.3805i q^{59} +0.118290i q^{61} +(4.16863 - 6.11677i) q^{62} +4.72294i q^{63} +(7.21173 + 3.46279i) q^{64} +(-4.59286 - 3.13007i) q^{66} +13.4504 q^{67} +(6.54445 - 2.57140i) q^{68} -7.11585i q^{69} +2.19027 q^{71} +(-2.75787 - 0.627801i) q^{72} +0.563219i q^{73} +(-0.330022 + 0.484253i) q^{74} +(-10.1289 + 3.97976i) q^{76} -18.5617 q^{77} +(-2.76149 + 4.05203i) q^{78} +10.2746 q^{79} +1.00000 q^{81} +(2.39291 - 3.51120i) q^{82} -11.3490 q^{83} +(-8.79159 + 3.45433i) q^{84} +(-4.25653 + 6.24575i) q^{86} +3.66998i q^{87} +(2.46733 - 10.8388i) q^{88} -8.88265 q^{89} +16.3760i q^{91} +(13.2459 - 5.20449i) q^{92} -5.23414 q^{93} +(-1.08166 - 0.737160i) q^{94} +(-0.848464 - 5.59286i) q^{96} +7.27462i q^{97} +(-12.1903 + 17.8872i) q^{98} +3.93012i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} - 8 q^{3} - 4 q^{4} + 2 q^{6} - 8 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 - 8 * q^3 - 4 * q^4 + 2 * q^6 - 8 * q^8 + 8 * q^9	\( 8 q - 2 q^{2} - 8 q^{3} - 4 q^{4} + 2 q^{6} - 8 q^{8} + 8 q^{9} + 4 q^{12} + 6 q^{14} + 8 q^{16} - 2 q^{18} + 20 q^{22} + 8 q^{24} - 2 q^{26} - 8 q^{27} + 24 q^{28} + 8 q^{31} - 12 q^{32} - 12 q^{34} - 4 q^{36} + 14 q^{38} - 6 q^{42} - 8 q^{43} + 12 q^{44} + 20 q^{46} - 8 q^{48} + 24 q^{52} + 8 q^{53} + 2 q^{54} + 8 q^{56} - 20 q^{58} + 26 q^{62} + 32 q^{64} - 20 q^{66} + 24 q^{67} + 36 q^{68} - 40 q^{71} - 8 q^{72} - 8 q^{74} - 20 q^{76} - 24 q^{77} + 2 q^{78} + 16 q^{79} + 8 q^{81} - 16 q^{82} - 32 q^{83} - 24 q^{84} - 18 q^{86} - 8 q^{88} + 28 q^{92} - 8 q^{93} + 4 q^{94} + 12 q^{96} - 40 q^{98}+O(q^{100}) \) 8 * q - 2 * q^2 - 8 * q^3 - 4 * q^4 + 2 * q^6 - 8 * q^8 + 8 * q^9 + 4 * q^12 + 6 * q^14 + 8 * q^16 - 2 * q^18 + 20 * q^22 + 8 * q^24 - 2 * q^26 - 8 * q^27 + 24 * q^28 + 8 * q^31 - 12 * q^32 - 12 * q^34 - 4 * q^36 + 14 * q^38 - 6 * q^42 - 8 * q^43 + 12 * q^44 + 20 * q^46 - 8 * q^48 + 24 * q^52 + 8 * q^53 + 2 * q^54 + 8 * q^56 - 20 * q^58 + 26 * q^62 + 32 * q^64 - 20 * q^66 + 24 * q^67 + 36 * q^68 - 40 * q^71 - 8 * q^72 - 8 * q^74 - 20 * q^76 - 24 * q^77 + 2 * q^78 + 16 * q^79 + 8 * q^81 - 16 * q^82 - 32 * q^83 - 24 * q^84 - 18 * q^86 - 8 * q^88 + 28 * q^92 - 8 * q^93 + 4 * q^94 + 12 * q^96 - 40 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more