LMFDB - Embedded newform 600.2.k.d.301.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [600,2,Mod(301,600)]

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, 0]))

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

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

chi := DirichletCharacter("600.301");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 600 = 2^{3} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	600.k (of order $2$, degree $1$, 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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			301.4
Root			$-0.565036 + 1.29643i$ of defining polynomial
Character	$\chi$	$=$	600.301
Dual form			600.2.k.d.301.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.16863 + 0.796431i) q^{2} +1.00000i q^{3} +(0.731395 - 1.86147i) q^{4} +(-0.796431 - 1.16863i) q^{6} +4.72294 q^{7} +(0.627801 + 2.75787i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(-1.16863 + 0.796431i) q^{2} +1.00000i q^{3} +(0.731395 - 1.86147i) q^{4} +(-0.796431 - 1.16863i) q^{6} +4.72294 q^{7} +(0.627801 + 2.75787i) q^{8} -1.00000 q^{9} -3.93012i q^{11} +(1.86147 + 0.731395i) q^{12} -3.46733i q^{13} +(-5.51937 + 3.76149i) q^{14} +(-2.93012 - 2.72294i) q^{16} +3.51575 q^{17} +(1.16863 - 0.796431i) q^{18} -5.44133i q^{19} +4.72294i q^{21} +(3.13007 + 4.59286i) q^{22} -7.11585 q^{23} +(-2.75787 + 0.627801i) q^{24} +(2.76149 + 4.05203i) q^{26} -1.00000i q^{27} +(3.45433 - 8.79159i) q^{28} -3.66998i q^{29} +5.23414 q^{31} +(5.59286 + 0.848464i) q^{32} +3.93012 q^{33} +(-4.10861 + 2.80005i) q^{34} +(-0.731395 + 1.86147i) q^{36} -0.414376i q^{37} +(4.33364 + 6.35890i) q^{38} +3.46733 q^{39} +3.00454 q^{41} +(-3.76149 - 5.51937i) q^{42} +5.34450i q^{43} +(-7.31580 - 2.87447i) q^{44} +(8.31580 - 5.66728i) q^{46} -0.925579 q^{47} +(2.72294 - 2.93012i) q^{48} +15.3061 q^{49} +3.51575i q^{51} +(-6.45433 - 2.53599i) q^{52} -0.233196i q^{53} +(0.796431 + 1.16863i) q^{54} +(2.96506 + 13.0253i) q^{56} +5.44133 q^{57} +(2.92288 + 4.28885i) q^{58} +14.3805i q^{59} -0.118290i q^{61} +(-6.11677 + 4.16863i) q^{62} -4.72294 q^{63} +(-7.21173 + 3.46279i) q^{64} +(-4.59286 + 3.13007i) q^{66} +13.4504i q^{67} +(2.57140 - 6.54445i) q^{68} -7.11585i q^{69} +2.19027 q^{71} +(-0.627801 - 2.75787i) q^{72} -0.563219 q^{73} +(0.330022 + 0.484253i) q^{74} +(-10.1289 - 3.97976i) q^{76} -18.5617i q^{77} +(-4.05203 + 2.76149i) q^{78} -10.2746 q^{79} +1.00000 q^{81} +(-3.51120 + 2.39291i) q^{82} +11.3490i q^{83} +(8.79159 + 3.45433i) q^{84} +(-4.25653 - 6.24575i) q^{86} +3.66998 q^{87} +(10.8388 - 2.46733i) q^{88} +8.88265 q^{89} -16.3760i q^{91} +(-5.20449 + 13.2459i) q^{92} +5.23414i q^{93} +(1.08166 - 0.737160i) q^{94} +(-0.848464 + 5.59286i) q^{96} +7.27462 q^{97} +(-17.8872 + 12.1903i) q^{98} +3.93012i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + 4 q^{4} + 2 q^{6} + 8 q^{7} + 4 q^{8} - 8 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 + 4 * q^4 + 2 * q^6 + 8 * q^7 + 4 * q^8 - 8 * q^9	$ 8 q - 2 q^{2} + 4 q^{4} + 2 q^{6} + 8 q^{7} + 4 q^{8} - 8 q^{9} - 6 q^{14} + 8 q^{16} + 2 q^{18} + 12 q^{22} + 8 q^{23} - 8 q^{24} - 2 q^{26} - 4 q^{28} + 8 q^{31} + 28 q^{32} + 12 q^{34} - 4 q^{36} + 30 q^{38} - 6 q^{42} - 12 q^{44} + 20 q^{46} - 8 q^{48} - 20 q^{52} - 2 q^{54} + 8 q^{56} + 8 q^{57} + 12 q^{58} + 30 q^{62} - 8 q^{63} - 32 q^{64} - 20 q^{66} - 28 q^{68} - 40 q^{71} - 4 q^{72} - 16 q^{73} + 8 q^{74} - 20 q^{76} - 22 q^{78} - 16 q^{79} + 8 q^{81} - 24 q^{82} + 24 q^{84} - 18 q^{86} + 24 q^{87} - 8 q^{88} - 36 q^{92} - 4 q^{94} + 12 q^{96} - 8 q^{97} - 48 q^{98}+O(q^{100}) $ 8 * q - 2 * q^2 + 4 * q^4 + 2 * q^6 + 8 * q^7 + 4 * q^8 - 8 * q^9 - 6 * q^14 + 8 * q^16 + 2 * q^18 + 12 * q^22 + 8 * q^23 - 8 * q^24 - 2 * q^26 - 4 * q^28 + 8 * q^31 + 28 * q^32 + 12 * q^34 - 4 * q^36 + 30 * q^38 - 6 * q^42 - 12 * q^44 + 20 * q^46 - 8 * q^48 - 20 * q^52 - 2 * q^54 + 8 * q^56 + 8 * q^57 + 12 * q^58 + 30 * q^62 - 8 * q^63 - 32 * q^64 - 20 * q^66 - 28 * q^68 - 40 * q^71 - 4 * q^72 - 16 * q^73 + 8 * q^74 - 20 * q^76 - 22 * q^78 - 16 * q^79 + 8 * q^81 - 24 * q^82 + 24 * q^84 - 18 * q^86 + 24 * q^87 - 8 * q^88 - 36 * q^92 - 4 * q^94 + 12 * q^96 - 8 * q^97 - 48 * 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 $

$2$	−1.16863	+	0.796431i	−0.826347	+	0.563162i
$2$	−1.16863	+	0.796431i	−0.826347	+	0.563162i
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	0.731395	−	1.86147i	0.365697	−	0.930734i
$5$		0			0
$5$		0			0
$6$	−0.796431	−	1.16863i	−0.325142	−	0.477091i
$7$	4.72294			1.78510			0.892551	−	0.450947i	$-0.148914\pi$
$7$	4.72294			1.78510			0.892551	+	0.450947i	$0.148914\pi$
$8$	0.627801	+	2.75787i	0.221961	+	0.975056i
$9$	−1.00000			−0.333333
$10$		0			0
$11$		−	3.93012i		−	1.18498i	−0.805579	−	0.592488i	$-0.798146\pi$
$11$		−	3.93012i		−	1.18498i	0.805579	−	0.592488i	$-0.201854\pi$
$12$	1.86147	+	0.731395i	0.537359	+	0.211135i
$13$		−	3.46733i		−	0.961665i	−0.876812	−	0.480833i	$-0.840334\pi$
$13$		−	3.46733i		−	0.961665i	0.876812	−	0.480833i	$-0.159666\pi$
$14$	−5.51937	+	3.76149i	−1.47511	+	1.00530i
$15$		0			0
$16$	−2.93012	−	2.72294i	−0.732531	−	0.680734i
$17$	3.51575			0.852694			0.426347	−	0.904560i	$-0.359800\pi$
$17$	3.51575			0.852694			0.426347	+	0.904560i	$0.359800\pi$
$18$	1.16863	−	0.796431i	0.275449	−	0.187721i
$19$		−	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
$22$	3.13007	+	4.59286i	0.667334	+	0.979202i
$23$	−7.11585			−1.48376			−0.741878	−	0.670534i	$-0.766065\pi$
$23$	−7.11585			−1.48376			−0.741878	+	0.670534i	$0.766065\pi$
$24$	−2.75787	+	0.627801i	−0.562949	+	0.128149i
$25$		0			0
$26$	2.76149	+	4.05203i	0.541573	+	0.794669i
$27$		−	1.00000i		−	0.192450i
$28$	3.45433	−	8.79159i	0.652807	−	1.66145i
$29$		−	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	$0.344240\pi$
$32$	5.59286	+	0.848464i	0.988688	+	0.149989i
$33$	3.93012			0.684147
$34$	−4.10861	+	2.80005i	−0.704621	+	0.480205i
$35$		0			0
$36$	−0.731395	+	1.86147i	−0.121899	+	0.310245i
$37$		−	0.414376i		−	0.0681231i	−0.999420	−	0.0340615i	$-0.989156\pi$
$37$		−	0.414376i		−	0.0681231i	0.999420	−	0.0340615i	$-0.0108442\pi$
$38$	4.33364	+	6.35890i	0.703010	+	1.03155i
$39$	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	$0.424617\pi$
$42$	−3.76149	−	5.51937i	−0.580411	−	0.851657i
$43$			5.34450i			0.815029i	0.913199	+	0.407514i	$0.133604\pi$
$43$			5.34450i			0.815029i	−0.913199	+	0.407514i	$0.866396\pi$
$44$	−7.31580	−	2.87447i	−1.10290	−	0.433343i
$45$		0			0
$46$	8.31580	−	5.66728i	1.22610	−	0.835595i
$47$	−0.925579			−0.135010			−0.0675048	−	0.997719i	$-0.521504\pi$
$47$	−0.925579			−0.135010			−0.0675048	+	0.997719i	$0.521504\pi$
$48$	2.72294	−	2.93012i	0.393022	−	0.422927i
$49$	15.3061			2.18659
$50$		0			0
$51$			3.51575i			0.492303i
$52$	−6.45433	−	2.53599i	−0.895055	−	0.351679i
$53$		−	0.233196i		−	0.0320320i	−0.999872	−	0.0160160i	$-0.994902\pi$
$53$		−	0.233196i		−	0.0320320i	0.999872	−	0.0160160i	$-0.00509826\pi$
$54$	0.796431	+	1.16863i	0.108381	+	0.159030i
$55$		0			0
$56$	2.96506	+	13.0253i	0.396223	+	1.74057i
$57$	5.44133			0.720721
$58$	2.92288	+	4.28885i	0.383794	+	0.563153i
$59$			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	$-0.997590\pi$
$61$		−	0.118290i		−	0.0151454i	0.999971	−	0.00757271i	$-0.00241049\pi$
$62$	−6.11677	+	4.16863i	−0.776831	+	0.529417i
$63$	−4.72294			−0.595034
$64$	−7.21173	+	3.46279i	−0.901467	+	0.432849i
$65$		0			0
$66$	−4.59286	+	3.13007i	−0.565342	+	0.385285i
$67$			13.4504i			1.64323i	0.570043	+	0.821615i	$0.306927\pi$
$67$			13.4504i			1.64323i	−0.570043	+	0.821615i	$0.693073\pi$
$68$	2.57140	−	6.54445i	0.311828	−	0.793631i
$69$		−	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	$0.458512\pi$
$72$	−0.627801	−	2.75787i	−0.0739870	−	0.325019i
$73$	−0.563219			−0.0659197			−0.0329599	−	0.999457i	$-0.510493\pi$
$73$	−0.563219			−0.0659197			−0.0329599	+	0.999457i	$0.510493\pi$
$74$	0.330022	+	0.484253i	0.0383643	+	0.0562933i
$75$		0			0
$76$	−10.1289	−	3.97976i	−1.16186	−	0.456509i
$77$		−	18.5617i		−	2.11530i
$78$	−4.05203	+	2.76149i	−0.458802	+	0.312678i
$79$	−10.2746			−1.15599			−0.577993	−	0.816042i	$-0.696164\pi$
$79$	−10.2746			−1.15599			−0.577993	+	0.816042i	$0.696164\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$	−3.51120	+	2.39291i	−0.387747	+	0.264253i
$83$			11.3490i			1.24572i	0.782334	+	0.622860i	$0.214029\pi$
$83$			11.3490i			1.24572i	−0.782334	+	0.622860i	$0.785971\pi$
$84$	8.79159	+	3.45433i	0.959241	+	0.376898i
$85$		0			0
$86$	−4.25653	−	6.24575i	−0.458993	−	0.673496i
$87$	3.66998			0.393463
$88$	10.8388	−	2.46733i	1.15542	−	0.263019i
$89$	8.88265			0.941559			0.470780	−	0.882251i	$-0.343973\pi$
$89$	8.88265			0.941559			0.470780	+	0.882251i	$0.343973\pi$
$90$		0			0
$91$		−	16.3760i		−	1.71667i
$92$	−5.20449	+	13.2459i	−0.542606	+	1.38098i
$93$			5.23414i			0.542755i
$94$	1.08166	−	0.737160i	0.111565	−	0.0760322i
$95$		0			0
$96$	−0.848464	+	5.59286i	−0.0865960	+	0.570819i
$97$	7.27462			0.738626			0.369313	−	0.929305i	$-0.379593\pi$
$97$	7.27462			0.738626			0.369313	+	0.929305i	$0.379593\pi$
$98$	−17.8872	+	12.1903i	−1.80688	+	1.23140i
$99$			3.93012i			0.394992i
$100$		0			0
$101$			4.23320i			0.421219i	0.977570	+	0.210609i	$0.0675448\pi$
$101$			4.23320i			0.421219i	−0.977570	+	0.210609i	$0.932455\pi$
$102$	−2.80005	−	4.10861i	−0.277246	−	0.406813i
$103$	0.0429270			0.00422972			0.00211486	−	0.999998i	$-0.499327\pi$
$103$	0.0429270			0.00422972			0.00211486	+	0.999998i	$0.499327\pi$
$104$	9.56247	−	2.17679i	0.937677	−	0.213452i
$105$		0			0
$106$	0.185725	+	0.272520i	0.0180392	+	0.0264695i
$107$		−	15.4728i		−	1.49581i	−0.663804	−	0.747907i	$-0.731059\pi$
$107$		−	15.4728i		−	1.49581i	0.663804	−	0.747907i	$-0.268941\pi$
$108$	−1.86147	−	0.731395i	−0.179120	−	0.0703785i
$109$		−	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
$112$	−13.8388	−	12.8602i	−1.30764	−	1.21518i
$113$	3.86025			0.363141			0.181571	−	0.983378i	$-0.441882\pi$
$113$	3.86025			0.363141			0.181571	+	0.983378i	$0.441882\pi$
$114$	−6.35890	+	4.33364i	−0.595566	+	0.405883i
$115$		0			0
$116$	−6.83154	−	2.68420i	−0.634293	−	0.249222i
$117$			3.46733i			0.320555i
$118$	−11.4531	−	16.8055i	−1.05434	−	1.54708i
$119$	16.6046			1.52215
$120$		0			0
$121$	−4.44587			−0.404170
$122$	0.0942095	+	0.138237i	0.00852933	+	0.0125154i
$123$			3.00454i			0.270911i
$124$	3.82822	−	9.74318i	0.343784	−	0.874963i
$125$		0			0
$126$	5.51937	−	3.76149i	0.491704	−	0.335100i
$127$	−18.3805			−1.63101			−0.815505	−	0.578751i	$-0.803540\pi$
$127$	−18.3805			−1.63101			−0.815505	+	0.578751i	$0.803540\pi$
$128$	5.66998	−	9.79037i	0.501160	−	0.865355i
$129$	−5.34450			−0.470557
$130$		0			0
$131$		−	3.41892i		−	0.298713i	−0.988783	−	0.149356i	$-0.952280\pi$
$131$		−	3.41892i		−	0.298713i	0.988783	−	0.149356i	$-0.0477201\pi$
$132$	2.87447	−	7.31580i	0.250191	−	0.636758i
$133$		−	25.6990i		−	2.22839i
$134$	−10.7123	−	15.7186i	−0.925404	−	1.35788i
$135$		0			0
$136$	2.20719	+	9.69599i	0.189265	+	0.831424i
$137$	−16.3714			−1.39871			−0.699354	−	0.714776i	$-0.746529\pi$
$137$	−16.3714			−1.39871			−0.699354	+	0.714776i	$0.746529\pi$
$138$	5.66728	+	8.31580i	0.482431	+	0.707888i
$139$		−	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
$142$	−2.55962	+	1.74440i	−0.214798	+	0.146387i
$143$	−13.6271			−1.13955
$144$	2.93012	+	2.72294i	0.244177	+	0.226911i
$145$		0			0
$146$	0.658194	−	0.448565i	0.0544726	−	0.0371235i
$147$			15.3061i			1.26243i
$148$	−0.771348	−	0.303073i	−0.0634044	−	0.0249124i
$149$			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	$0.563519\pi$
$152$	15.0065	−	3.41607i	1.21719	−	0.277080i
$153$	−3.51575			−0.284231
$154$	14.7831	+	21.6918i	1.19126	+	1.74797i
$155$		0			0
$156$	2.53599	−	6.45433i	0.203042	−	0.516760i
$157$			21.6561i			1.72835i	0.503195	+	0.864173i	$0.332158\pi$
$157$			21.6561i			1.72835i	−0.503195	+	0.864173i	$0.667842\pi$
$158$	12.0072	−	8.18303i	0.955245	−	0.651007i
$159$	0.233196			0.0184937
$160$		0			0
$161$	−33.6077			−2.64866
$162$	−1.16863	+	0.796431i	−0.0918163	+	0.0625735i
$163$			16.2362i			1.27172i	0.771804	+	0.635860i	$0.219355\pi$
$163$			16.2362i			1.27172i	−0.771804	+	0.635860i	$0.780645\pi$
$164$	2.19751	−	5.59286i	0.171597	−	0.436729i
$165$		0			0
$166$	−9.03873	−	13.2628i	−0.701542	−	1.02940i
$167$	−6.69238			−0.517872			−0.258936	−	0.965894i	$-0.583372\pi$
$167$	−6.69238			−0.517872			−0.258936	+	0.965894i	$0.583372\pi$
$168$	−13.0253	+	2.96506i	−1.00492	+	0.228759i
$169$	0.977595			0.0751996
$170$		0			0
$171$			5.44133i			0.416109i
$172$	9.94861	+	3.90894i	0.758575	+	0.298054i
$173$		−	22.4220i		−	1.70471i	−0.522963	−	0.852355i	$-0.675173\pi$
$173$		−	22.4220i		−	1.70471i	0.522963	−	0.852355i	$-0.324827\pi$
$174$	−4.28885	+	2.92288i	−0.325137	+	0.221583i
$175$		0			0
$176$	−10.7015	+	11.5157i	−0.806654	+	0.868032i
$177$	−14.3805			−1.08091
$178$	−10.3805	+	7.07442i	−0.778054	+	0.530250i
$179$		−	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	$0.126230\pi$
$181$			10.3929i			0.772499i	−0.922394	+	0.386250i	$0.873770\pi$
$182$	13.0424	+	19.1375i	0.966763	+	1.41856i
$183$	0.118290			0.00874422
$184$	−4.46733	−	19.6246i	−0.329336	−	1.44675i
$185$		0			0
$186$	−4.16863	−	6.11677i	−0.305659	−	0.448504i
$187$		−	13.8173i		−	1.01042i
$188$	−0.676964	+	1.72294i	−0.0493726	+	0.125658i
$189$		−	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	$0.427595\pi$
$192$	−3.46279	−	7.21173i	−0.249905	−	0.520462i
$193$	−0.391971			−0.0282147			−0.0141074	−	0.999900i	$-0.504491\pi$
$193$	−0.391971			−0.0282147			−0.0141074	+	0.999900i	$0.504491\pi$
$194$	−8.50135	+	5.79374i	−0.610361	+	0.415966i
$195$		0			0
$196$	11.1948	−	28.4918i	0.799630	−	2.03513i
$197$		−	5.96616i		−	0.425071i	−0.977153	−	0.212536i	$-0.931828\pi$
$197$		−	5.96616i		−	0.425071i	0.977153	−	0.212536i	$-0.0681722\pi$
$198$	−3.13007	−	4.59286i	−0.222445	−	0.326401i
$199$	−17.9322			−1.27118			−0.635591	−	0.772026i	$-0.719243\pi$
$199$	−17.9322			−1.27118			−0.635591	+	0.772026i	$0.719243\pi$
$200$		0			0
$201$	−13.4504			−0.948719
$202$	−3.37145	−	4.94704i	−0.237214	−	0.348073i
$203$		−	17.3331i		−	1.21654i
$204$	6.54445	+	2.57140i	0.458203	+	0.180034i
$205$		0			0
$206$	−0.0501658	+	0.0341884i	−0.00349521	+	0.00238202i
$207$	7.11585			0.494586
$208$	−9.44133	+	10.1597i	−0.654638	+	0.704450i
$209$	−21.3851			−1.47924
$210$		0			0
$211$			6.51575i			0.448563i	0.974524	+	0.224281i	$0.0720034\pi$
$211$			6.51575i			0.448563i	−0.974524	+	0.224281i	$0.927997\pi$
$212$	−0.434087	−	0.170558i	−0.0298132	−	0.0117140i
$213$			2.19027i			0.150075i
$214$	12.3230	+	18.0820i	0.842385	+	1.23606i
$215$		0			0
$216$	2.75787	−	0.627801i	0.187650	−	0.0427164i
$217$	24.7205			1.67814
$218$	10.3187	+	15.1409i	0.698868	+	1.02547i
$219$		−	0.563219i		−	0.0380588i
$220$		0			0
$221$		−	12.1903i		−	0.820006i
$222$	−0.484253	+	0.330022i	−0.0325009	+	0.0221496i
$223$	3.14640			0.210699			0.105349	−	0.994435i	$-0.466404\pi$
$223$	3.14640			0.210699			0.105349	+	0.994435i	$0.466404\pi$
$224$	26.4147	+	4.00724i	1.76491	+	0.267745i
$225$		0			0
$226$	−4.51120	+	3.07442i	−0.300081	+	0.204507i
$227$			3.92103i			0.260248i	0.991498	+	0.130124i	$0.0415376\pi$
$227$			3.92103i			0.260248i	−0.991498	+	0.130124i	$0.958462\pi$
$228$	3.97976	−	10.1289i	0.263566	−	0.670800i
$229$			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
$232$	10.1213	−	2.30401i	0.664498	−	0.151266i
$233$	25.7565			1.68737			0.843683	−	0.536841i	$-0.180383\pi$
$233$	25.7565			1.68737			0.843683	+	0.536841i	$0.180383\pi$
$234$	−2.76149	−	4.05203i	−0.180524	−	0.264890i
$235$		0			0
$236$	26.7689	+	10.5179i	1.74251	+	0.684654i
$237$		−	10.2746i		−	0.667409i
$238$	−19.4047	+	13.2245i	−1.25782	+	0.857214i
$239$	−15.8727			−1.02672			−0.513360	−	0.858173i	$-0.671600\pi$
$239$	−15.8727			−1.02672			−0.513360	+	0.858173i	$0.671600\pi$
$240$		0			0
$241$	28.1664			1.81436			0.907178	−	0.420748i	$-0.138232\pi$
$241$	28.1664			1.81436			0.907178	+	0.420748i	$0.138232\pi$
$242$	5.19558	−	3.54083i	0.333985	−	0.227613i
$243$			1.00000i			0.0641500i
$244$	−0.220192	−	0.0865164i	−0.0140964	−	0.00553864i
$245$		0			0
$246$	−2.39291	−	3.51120i	−0.152567	−	0.223866i
$247$	−18.8669			−1.20047
$248$	3.28600	+	14.4351i	0.208661	+	0.916629i
$249$	−11.3490			−0.719216
$250$		0			0
$251$		−	4.66004i		−	0.294139i	−0.989126	−	0.147070i	$-0.953016\pi$
$251$		−	4.66004i		−	0.294139i	0.989126	−	0.147070i	$-0.0469842\pi$
$252$	−3.45433	+	8.79159i	−0.217602	+	0.553818i
$253$			27.9662i			1.75822i
$254$	21.4801	−	14.6388i	1.34778	−	0.918522i
$255$		0			0
$256$	1.17125	+	15.9571i	0.0732029	+	0.997317i
$257$	−3.33996			−0.208341			−0.104170	−	0.994559i	$-0.533219\pi$
$257$	−3.33996			−0.208341			−0.104170	+	0.994559i	$0.533219\pi$
$258$	6.24575	−	4.25653i	0.388843	−	0.265000i
$259$		−	1.95707i		−	0.121607i
$260$		0			0
$261$			3.66998i			0.227166i
$262$	2.72294	+	3.99546i	0.168224	+	0.246840i
$263$	27.5932			1.70147			0.850735	−	0.525595i	$-0.176157\pi$
$263$	27.5932			1.70147			0.850735	+	0.525595i	$0.176157\pi$
$264$	2.46733	+	10.8388i	0.151854	+	0.667081i
$265$		0			0
$266$	20.4675	+	30.0327i	1.25494	+	1.84142i
$267$			8.88265i			0.543609i
$268$	25.0375	+	9.83756i	1.52941	+	0.600925i
$269$		−	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	$0.585983\pi$
$272$	−10.3016	−	9.57315i	−0.624625	−	0.580458i
$273$	16.3760			0.991120
$274$	19.1322	−	13.0387i	1.15582	−	0.787699i
$275$		0			0
$276$	−13.2459	−	5.20449i	−0.797311	−	0.313274i
$277$			10.3838i			0.623904i	0.950098	+	0.311952i	$0.100983\pi$
$277$			10.3838i			0.623904i	−0.950098	+	0.311952i	$0.899017\pi$
$278$	1.55867	+	2.28710i	0.0934831	+	0.137171i
$279$	−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	$0.330085\pi$
$282$	0.737160	+	1.08166i	0.0438972	+	0.0644119i
$283$			3.54724i			0.210862i	0.994427	+	0.105431i	$0.0336222\pi$
$283$			3.54724i			0.210862i	−0.994427	+	0.105431i	$0.966378\pi$
$284$	1.60195	−	4.07712i	0.0950583	−	0.241932i
$285$		0			0
$286$	15.9250	−	10.8530i	0.941664	−	0.641752i
$287$	14.1903			0.837625
$288$	−5.59286	−	0.848464i	−0.329563	−	0.0499962i
$289$	−4.63952			−0.272913
$290$		0			0
$291$			7.27462i			0.426446i
$292$	−0.411935	+	1.04841i	−0.0241067	+	0.0613537i
$293$		−	5.72538i		−	0.334480i	−0.985916	−	0.167240i	$-0.946515\pi$
$293$		−	5.72538i		−	0.334480i	0.985916	−	0.167240i	$-0.0534855\pi$
$294$	−12.1903	−	17.8872i	−0.710951	−	1.04320i
$295$		0			0
$296$	1.14280	−	0.260146i	0.0664238	−	0.0151207i
$297$	−3.93012			−0.228049
$298$	−9.63429	−	14.1367i	−0.558099	−	0.818918i
$299$			24.6730i			1.42688i
$300$		0			0
$301$			25.2417i			1.45491i
$302$	5.69331	−	3.88004i	0.327613	−	0.223271i
$303$	−4.23320			−0.243191
$304$	−14.8164	+	15.9438i	−0.849778	+	0.914437i
$305$		0			0
$306$	4.10861	−	2.80005i	0.234874	−	0.160068i
$307$		−	12.3760i		−	0.706335i	−0.935560	−	0.353168i	$-0.885105\pi$
$307$		−	12.3760i		−	0.706335i	0.935560	−	0.353168i	$-0.114895\pi$
$308$	−34.5520	−	13.5759i	−1.96879	−	0.773561i
$309$			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	$0.673371\pi$
$312$	2.17679	+	9.56247i	0.123237	+	0.541368i
$313$	−12.7114			−0.718491			−0.359246	−	0.933243i	$-0.616966\pi$
$313$	−12.7114			−0.718491			−0.359246	+	0.933243i	$0.616966\pi$
$314$	−17.2476	−	25.3080i	−0.973338	−	1.42821i
$315$		0			0
$316$	−7.51481	+	19.1259i	−0.422741	+	1.07591i
$317$		−	15.8602i		−	0.890800i	−0.895332	−	0.445400i	$-0.853061\pi$
$317$		−	15.8602i		−	0.890800i	0.895332	−	0.445400i	$-0.146939\pi$
$318$	−0.272520	+	0.185725i	−0.0152822	+	0.0104149i
$319$	−14.4235			−0.807559
$320$		0			0
$321$	15.4728			0.863609
$322$	39.2750	−	26.7662i	2.18871	−	1.49162i
$323$		−	19.1303i		−	1.06444i
$324$	0.731395	−	1.86147i	0.0406330	−	0.103415i
$325$		0			0
$326$	−12.9310	−	18.9742i	−0.716185	−	1.05088i
$327$	12.9561			0.716476
$328$	1.88625	+	8.28615i	0.104151	+	0.457526i
$329$	−4.37145			−0.241006
$330$		0			0
$331$			23.0315i			1.26593i	0.774182	+	0.632963i	$0.218161\pi$
$331$			23.0315i			1.26593i	−0.774182	+	0.632963i	$0.781839\pi$
$332$	21.1259	+	8.30063i	1.15943	+	0.455556i
$333$			0.414376i			0.0227077i
$334$	7.82092	−	5.33002i	0.427942	−	0.291646i
$335$		0			0
$336$	12.8602	−	13.8388i	0.701584	−	0.754968i
$337$	−0.860247			−0.0468606			−0.0234303	−	0.999725i	$-0.507459\pi$
$337$	−0.860247			−0.0468606			−0.0234303	+	0.999725i	$0.507459\pi$
$338$	−1.14245	+	0.778587i	−0.0621409	+	0.0423496i
$339$			3.86025i			0.209660i
$340$		0			0
$341$		−	20.5708i		−	1.11397i
$342$	−4.33364	−	6.35890i	−0.234337	−	0.343850i
$343$	39.2293			2.11818
$344$	−14.7395	+	3.35528i	−0.794698	+	0.180905i
$345$		0			0
$346$	17.8576	+	26.2030i	0.960028	+	1.40868i
$347$			32.2856i			1.73318i	0.499019	+	0.866591i	$0.333694\pi$
$347$			32.2856i			1.73318i	−0.499019	+	0.866591i	$0.666306\pi$
$348$	2.68420	−	6.83154i	0.143888	−	0.366209i
$349$			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
$352$	3.33457	−	21.9806i	0.177733	−	1.17157i
$353$	−32.6392			−1.73721			−0.868604	−	0.495506i	$-0.834982\pi$
$353$	−32.6392			−1.73721			−0.868604	+	0.495506i	$0.834982\pi$
$354$	16.8055	−	11.4531i	0.893204	−	0.608726i
$355$		0			0
$356$	6.49672	−	16.5348i	0.344326	−	0.876341i
$357$			16.6046i			0.878811i
$358$	0.118542	+	0.173941i	0.00626517	+	0.00919309i
$359$	−2.71056			−0.143058			−0.0715290	−	0.997439i	$-0.522788\pi$
$359$	−2.71056			−0.143058			−0.0715290	+	0.997439i	$0.522788\pi$
$360$		0			0
$361$	−10.6080			−0.558317
$362$	−8.27724	−	12.1455i	−0.435042	−	0.638352i
$363$		−	4.44587i		−	0.233348i
$364$	−30.4834	−	11.9773i	−1.59776	−	0.627782i
$365$		0			0
$366$	−0.138237	+	0.0942095i	−0.00722575	+	0.00492441i
$367$	0.680008			0.0354961			0.0177481	−	0.999842i	$-0.494350\pi$
$367$	0.680008			0.0354961			0.0177481	+	0.999842i	$0.494350\pi$
$368$	20.8503	+	19.3760i	1.08690	+	1.01004i
$369$	−3.00454			−0.156410
$370$		0			0
$371$		−	1.10137i		−	0.0571803i
$372$	9.74318	+	3.82822i	0.505160	+	0.198484i
$373$			3.47642i			0.180002i	0.995942	+	0.0900012i	$0.0286871\pi$
$373$			3.47642i			0.180002i	−0.995942	+	0.0900012i	$0.971313\pi$
$374$	11.0045	+	16.1473i	0.569031	+	0.834959i
$375$		0			0
$376$	−0.581079	−	2.55263i	−0.0299669	−	0.131642i
$377$	−12.7250			−0.655373
$378$	3.76149	+	5.51937i	0.193470	+	0.283886i
$379$		−	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
$382$	−7.28430	+	4.96431i	−0.372697	+	0.253996i
$383$	−9.81544			−0.501545			−0.250773	−	0.968046i	$-0.580685\pi$
$383$	−9.81544			−0.501545			−0.250773	+	0.968046i	$0.580685\pi$
$384$	9.79037	+	5.66998i	0.499613	+	0.289345i
$385$		0			0
$386$	0.458070	−	0.312178i	0.0233151	−	0.0158895i
$387$		−	5.34450i		−	0.271676i
$388$	5.32062	−	13.5415i	0.270114	−	0.687464i
$389$			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
$392$	9.60919	+	42.2123i	0.485337	+	2.13204i
$393$	3.41892			0.172462
$394$	4.75164	+	6.97224i	0.239384	+	0.351256i
$395$		0			0
$396$	7.31580	+	2.87447i	0.367633	+	0.144448i
$397$		−	12.7783i		−	0.641326i	−0.947193	−	0.320663i	$-0.896094\pi$
$397$		−	12.7783i		−	0.641326i	0.947193	−	0.320663i	$-0.103906\pi$
$398$	20.9561	−	14.2818i	1.05044	−	0.715881i
$399$	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	$0.474753\pi$
$402$	15.7186	−	10.7123i	0.783971	−	0.534282i
$403$		−	18.1485i		−	0.904041i
$404$	7.87996	+	3.09614i	0.392043	+	0.154039i
$405$		0			0
$406$	13.8046	+	20.2560i	0.685111	+	1.00529i
$407$	−1.62855			−0.0807243
$408$	−9.69599	+	2.20719i	−0.480023	+	0.109272i
$409$	12.1125			0.598923			0.299461	−	0.954108i	$-0.403193\pi$
$409$	12.1125			0.598923			0.299461	+	0.954108i	$0.403193\pi$
$410$		0			0
$411$		−	16.3714i		−	0.807544i
$412$	0.0313965	−	0.0799071i	0.00154680	−	0.00393674i
$413$			67.9184i			3.34204i
$414$	−8.31580	+	5.66728i	−0.408699	+	0.278532i
$415$		0			0
$416$	2.94191	−	19.3923i	0.144239	−	0.950787i
$417$	1.95707			0.0958383
$418$	24.9913	−	17.0317i	1.22236	−	0.833050i
$419$		−	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	$0.0293564\pi$
$421$			3.77928i			0.184191i	−0.995750	+	0.0920953i	$0.970644\pi$
$422$	−5.18934	−	7.61450i	−0.252613	−	0.370668i
$423$	0.925579			0.0450032
$424$	0.643126	−	0.146401i	0.0312329	−	0.00710985i
$425$		0			0
$426$	−1.74440	−	2.55962i	−0.0845164	−	0.124014i
$427$		−	0.558674i		−	0.0270361i
$428$	−28.8022	−	11.3167i	−1.39220	−	0.547015i
$429$		−	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	$0.288265\pi$
$432$	−2.72294	+	2.93012i	−0.131007	+	0.140976i
$433$	−2.03149			−0.0976274			−0.0488137	−	0.998808i	$-0.515544\pi$
$433$	−2.03149			−0.0976274			−0.0488137	+	0.998808i	$0.515544\pi$
$434$	−28.8891	+	19.6882i	−1.38672	+	0.945063i
$435$		0			0
$436$	−24.1174	−	9.47605i	−1.15501	−	0.453820i
$437$			38.7196i			1.85221i
$438$	0.448565	+	0.658194i	0.0214333	+	0.0314497i
$439$	−22.4864			−1.07322			−0.536608	−	0.843832i	$-0.680294\pi$
$439$	−22.4864			−1.07322			−0.536608	+	0.843832i	$0.680294\pi$
$440$		0			0
$441$	−15.3061			−0.728863
$442$	9.70871	+	14.2459i	0.461796	+	0.677609i
$443$			3.39385i			0.161247i	0.996745	+	0.0806234i	$0.0256911\pi$
$443$			3.39385i			0.161247i	−0.996745	+	0.0806234i	$0.974309\pi$
$444$	0.303073	−	0.771348i	0.0143832	−	0.0366066i
$445$		0			0
$446$	−3.67698	+	2.50589i	−0.174110	+	0.118657i
$447$	−12.0968			−0.572160
$448$	−34.0605	+	16.3545i	−1.60921	+	0.772679i
$449$	−2.17780			−0.102777			−0.0513883	−	0.998679i	$-0.516365\pi$
$449$	−2.17780			−0.102777			−0.0513883	+	0.998679i	$0.516365\pi$
$450$		0			0
$451$		−	11.8082i		−	0.556028i
$452$	2.82336	−	7.18572i	0.132800	−	0.337988i
$453$		−	4.87178i		−	0.228896i
$454$	−3.12283	−	4.58224i	−0.146562	−	0.215055i
$455$		0			0
$456$	3.41607	+	15.0065i	0.159972	+	0.702743i
$457$	−3.57653			−0.167303			−0.0836516	−	0.996495i	$-0.526658\pi$
$457$	−3.57653			−0.167303			−0.0836516	+	0.996495i	$0.526658\pi$
$458$	−20.4603	−	30.0221i	−0.956046	−	1.40284i
$459$		−	3.51575i		−	0.164101i
$460$		0			0
$461$		−	13.1158i		−	0.610866i	−0.952214	−	0.305433i	$-0.901199\pi$
$461$		−	13.1158i		−	0.610866i	0.952214	−	0.305433i	$-0.0988012\pi$
$462$	−21.6918	+	14.7831i	−1.00919	+	0.687774i
$463$	−3.21417			−0.149375			−0.0746877	−	0.997207i	$-0.523796\pi$
$463$	−3.21417			−0.149375			−0.0746877	+	0.997207i	$0.523796\pi$
$464$	−9.99311	+	10.7535i	−0.463919	+	0.499218i
$465$		0			0
$466$	−30.0999	+	20.5133i	−1.39435	+	0.950261i
$467$		−	30.3016i		−	1.40219i	−0.713068	−	0.701095i	$-0.752695\pi$
$467$		−	30.3016i		−	1.40219i	0.713068	−	0.701095i	$-0.247305\pi$
$468$	6.45433	+	2.53599i	0.298352	+	0.117226i
$469$			63.5254i			2.93333i
$470$		0			0
$471$	−21.6561			−0.997861
$472$	−39.6597	+	9.02811i	−1.82549	+	0.415552i
$473$	21.0045			0.965790
$474$	8.18303	+	12.0072i	0.375859	+	0.551511i
$475$		0			0
$476$	12.1446	−	30.9090i	0.556645	−	1.41671i
$477$			0.233196i			0.0106773i
$478$	18.5493	−	12.6415i	0.848427	−	0.578210i
$479$	35.0896			1.60328			0.801642	−	0.597804i	$-0.203960\pi$
$479$	35.0896			1.60328			0.801642	+	0.597804i	$0.203960\pi$
$480$		0			0
$481$	−1.43678			−0.0655116
$482$	−32.9161	+	22.4326i	−1.49929	+	1.02178i
$483$		−	33.6077i		−	1.52920i
$484$	−3.25169	+	8.27584i	−0.147804	+	0.376175i
$485$		0			0
$486$	−0.796431	−	1.16863i	−0.0361269	−	0.0530102i
$487$	36.9117			1.67263			0.836315	−	0.548250i	$-0.184706\pi$
$487$	36.9117			1.67263			0.836315	+	0.548250i	$0.184706\pi$
$488$	0.326228	−	0.0742623i	0.0147676	−	0.00336169i
$489$	−16.2362			−0.734228
$490$		0			0
$491$			20.9867i			0.947116i	0.880763	+	0.473558i	$0.157031\pi$
$491$			20.9867i			0.947116i	−0.880763	+	0.473558i	$0.842969\pi$
$492$	5.59286	+	2.19751i	0.252146	+	0.0990713i
$493$		−	12.9027i		−	0.581109i
$494$	22.0484	−	15.0262i	0.992006	−	0.676060i
$495$		0			0
$496$	−15.3367	−	14.2522i	−0.688637	−	0.639943i
$497$	10.3445			0.464014
$498$	13.2628	−	9.03873i	0.594322	−	0.405035i
$499$		−	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
$502$	3.71140	+	5.44587i	0.165648	+	0.243061i
$503$	−37.6023			−1.67660			−0.838302	−	0.545206i	$-0.816451\pi$
$503$	−37.6023			−1.67660			−0.838302	+	0.545206i	$0.816451\pi$
$504$	−2.96506	−	13.0253i	−0.132074	−	0.580191i
$505$		0			0
$506$	−22.2731	−	32.6821i	−0.990161	−	1.45290i
$507$			0.977595i			0.0434165i
$508$	−13.4434	+	34.2148i	−0.596456	+	1.51804i
$509$			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
$512$	−14.0775	−	17.7151i	−0.622142	−	0.782904i
$513$	−5.44133			−0.240240
$514$	3.90317	−	2.66004i	0.172162	−	0.117330i
$515$		0			0
$516$	−3.90894	+	9.94861i	−0.172081	+	0.437963i
$517$			3.63764i			0.159983i
$518$	1.55867	+	2.28710i	0.0684842	+	0.100489i
$519$	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	$0.199177\pi$
$522$	−2.92288	−	4.28885i	−0.127931	−	0.187718i
$523$			17.4952i			0.765013i	0.923953	+	0.382506i	$0.124939\pi$
$523$			17.4952i			0.765013i	−0.923953	+	0.382506i	$0.875061\pi$
$524$	−6.36421	−	2.50058i	−0.278022	−	0.109238i
$525$		0			0
$526$	−32.2463	+	21.9761i	−1.40600	+	0.958203i
$527$	18.4019			0.801600
$528$	−11.5157	−	10.7015i	−0.501159	−	0.465722i
$529$	27.6353			1.20153
$530$		0			0
$531$		−	14.3805i		−	0.624062i
$532$	−47.8379	−	18.7961i	−2.07404	−	0.814916i
$533$		−	10.4178i		−	0.451243i
$534$	−7.07442	−	10.3805i	−0.306140	−	0.449210i
$535$		0			0
$536$	−37.0945	+	8.44418i	−1.60224	+	0.364733i
$537$	0.148842			0.00642301
$538$	17.4201	+	25.5611i	0.751035	+	1.10202i
$539$		−	60.1549i		−	2.59106i
$540$		0			0
$541$		−	38.1225i		−	1.63901i	−0.573069	−	0.819507i	$-0.694247\pi$
$541$		−	38.1225i		−	1.63901i	0.573069	−	0.819507i	$-0.305753\pi$
$542$	10.2674	−	6.99731i	0.441022	−	0.300560i
$543$	−10.3929			−0.446003
$544$	19.6631	+	2.98298i	0.843048	+	0.127894i
$545$		0			0
$546$	−19.1375	+	13.0424i	−0.819009	+	0.558161i
$547$		−	35.7406i		−	1.52816i	−0.645124	−	0.764078i	$-0.723194\pi$
$547$		−	35.7406i		−	1.52816i	0.645124	−	0.764078i	$-0.276806\pi$
$548$	−11.9740	+	30.4749i	−0.511504	+	1.30182i
$549$			0.118290i			0.00504848i
$550$		0			0
$551$	−19.9695			−0.850731
$552$	19.6246	−	4.46733i	0.835279	−	0.190142i
$553$	−48.5264			−2.06355
$554$	−8.27000	−	12.1349i	−0.351359	−	0.515561i
$555$		0			0
$556$	−3.64303	−	1.43139i	−0.154499	−	0.0607046i
$557$			2.65516i			0.112503i	0.998417	+	0.0562514i	$0.0179148\pi$
$557$			2.65516i			0.112503i	−0.998417	+	0.0562514i	$0.982085\pi$
$558$	6.11677	−	4.16863i	0.258944	−	0.176472i
$559$	18.5312			0.783785
$560$		0			0
$561$	13.8173			0.583368
$562$	−19.9350	+	13.5859i	−0.840908	+	0.573086i
$563$		−	20.3107i		−	0.855992i	−0.903781	−	0.427996i	$-0.859220\pi$
$563$		−	20.3107i		−	0.855992i	0.903781	−	0.427996i	$-0.140780\pi$
$564$	−1.72294	−	0.676964i	−0.0725487	−	0.0285053i
$565$		0			0
$566$	−2.82513	−	4.14541i	−0.118749	−	0.174245i
$567$	4.72294			0.198345
$568$	1.37505	+	6.04049i	0.0576959	+	0.253453i
$569$	−28.4274			−1.19174			−0.595868	−	0.803082i	$-0.703192\pi$
$569$	−28.4274			−1.19174			−0.595868	+	0.803082i	$0.703192\pi$
$570$		0			0
$571$			16.1485i			0.675794i	0.941183	+	0.337897i	$0.109716\pi$
$571$			16.1485i			0.675794i	−0.941183	+	0.337897i	$0.890284\pi$
$572$	−9.96675	+	25.3663i	−0.416731	+	1.06062i
$573$			6.23320i			0.260396i
$574$	−16.5832	+	11.3016i	−0.692169	+	0.471719i
$575$		0			0
$576$	7.21173	−	3.46279i	0.300489	−	0.144283i
$577$	−30.3600			−1.26390			−0.631952	−	0.775008i	$-0.717746\pi$
$577$	−30.3600			−1.26390			−0.631952	+	0.775008i	$0.717746\pi$
$578$	5.42189	−	3.69506i	0.225521	−	0.153694i
$579$		−	0.391971i		−	0.0162898i
$580$		0			0
$581$			53.6008i			2.22374i
$582$	−5.79374	−	8.50135i	−0.240158	−	0.352392i
$583$	−0.916490			−0.0379571
$584$	−0.353589	−	1.55329i	−0.0146316	−	0.0642754i
$585$		0			0
$586$	4.55987	+	6.69085i	0.188366	+	0.276396i
$587$		−	2.74070i		−	0.113121i	−0.998399	−	0.0565604i	$-0.981987\pi$
$587$		−	2.74070i		−	0.113121i	0.998399	−	0.0565604i	$-0.0180133\pi$
$588$	28.4918	+	11.1948i	1.17498	+	0.461666i
$589$		−	28.4807i		−	1.17352i
$590$		0			0
$591$	5.96616			0.245415
$592$	−1.12832	+	1.21417i	−0.0463737	+	0.0499022i
$593$	−22.2586			−0.914053			−0.457027	−	0.889453i	$-0.651086\pi$
$593$	−22.2586			−0.914053			−0.457027	+	0.889453i	$0.651086\pi$
$594$	4.59286	−	3.13007i	0.188447	−	0.128428i
$595$		0			0
$596$	22.5179	+	8.84755i	0.922367	+	0.362410i
$597$		−	17.9322i		−	0.733917i
$598$	−19.6504	−	28.8336i	−0.803563	−	1.17910i
$599$	48.4526			1.97972			0.989860	−	0.142046i	$-0.0453680\pi$
$599$	48.4526			1.97972			0.989860	+	0.142046i	$0.0453680\pi$
$600$		0			0
$601$	5.26553			0.214786			0.107393	−	0.994217i	$-0.465750\pi$
$601$	5.26553			0.214786			0.107393	+	0.994217i	$0.465750\pi$
$602$	−20.1033	−	29.4983i	−0.819349	−	1.20226i
$603$		−	13.4504i		−	0.547743i
$604$	−3.56319	+	9.06866i	−0.144984	+	0.368998i
$605$		0			0
$606$	4.94704	−	3.37145i	0.200960	−	0.136956i
$607$	−7.38288			−0.299662			−0.149831	−	0.988712i	$-0.547873\pi$
$607$	−7.38288			−0.299662			−0.149831	+	0.988712i	$0.547873\pi$
$608$	4.61677	−	30.4326i	0.187235	−	1.23420i
$609$	17.3331			0.702371
$610$		0			0
$611$			3.20929i			0.129834i
$612$	−2.57140	+	6.54445i	−0.103943	+	0.264544i
$613$			2.64607i			0.106874i	0.998571	+	0.0534369i	$0.0170176\pi$
$613$			2.64607i			0.106874i	−0.998571	+	0.0534369i	$0.982982\pi$
$614$	9.85663	+	14.4630i	0.397781	+	0.583678i
$615$		0			0
$616$	51.1909	−	11.6531i	2.06254	−	0.469515i
$617$	−21.0136			−0.845977			−0.422989	−	0.906135i	$-0.639019\pi$
$617$	−21.0136			−0.845977			−0.422989	+	0.906135i	$0.639019\pi$
$618$	−0.0341884	−	0.0501658i	−0.00137526	−	0.00201796i
$619$		−	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
$622$	21.3563	−	14.5545i	0.856309	−	0.583581i
$623$	41.9522			1.68078
$624$	−10.1597	−	9.44133i	−0.406714	−	0.377956i
$625$		0			0
$626$	14.8549	−	10.1238i	0.593723	−	0.404627i
$627$		−	21.3851i		−	0.854038i
$628$	40.3121	+	15.8392i	1.60863	+	0.632051i
$629$		−	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	$0.332677\pi$
$632$	−6.45042	−	28.3361i	−0.256584	−	1.12715i
$633$	−6.51575			−0.258978
$634$	12.6316	+	18.5348i	0.501665	+	0.736110i
$635$		0			0
$636$	0.170558	−	0.434087i	0.00676308	−	0.0172127i
$637$		−	53.0714i		−	2.10277i
$638$	16.8557	−	11.4873i	0.667324	−	0.454786i
$639$	−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	$0.618886\pi$
$642$	−18.0820	+	12.3230i	−0.713640	+	0.486351i
$643$			0.636984i			0.0251202i	0.999921	+	0.0125601i	$0.00399811\pi$
$643$			0.636984i			0.0251202i	−0.999921	+	0.0125601i	$0.996002\pi$
$644$	−24.5805	+	62.5596i	−0.968607	+	2.46519i
$645$		0			0
$646$	15.2360	+	22.3563i	0.599452	+	0.879596i
$647$	−32.0182			−1.25876			−0.629382	−	0.777096i	$-0.716692\pi$
$647$	−32.0182			−1.25876			−0.629382	+	0.777096i	$0.716692\pi$
$648$	0.627801	+	2.75787i	0.0246623	+	0.108340i
$649$	56.5173			2.21850
$650$		0			0
$651$			24.7205i			0.968873i
$652$	30.2232	+	11.8751i	1.18363	+	0.465065i
$653$			25.9769i			1.01656i	0.861193	+	0.508278i	$0.169718\pi$
$653$			25.9769i			1.01656i	−0.861193	+	0.508278i	$0.830282\pi$
$654$	−15.1409	+	10.3187i	−0.592057	+	0.403492i
$655$		0			0
$656$	−8.80369	−	8.18118i	−0.343726	−	0.319421i
$657$	0.563219			0.0219732
$658$	5.10861	−	3.48156i	0.199154	−	0.135725i
$659$			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	$-0.906810\pi$
$661$		−	14.8397i		−	0.577198i	0.957450	−	0.288599i	$-0.0931895\pi$
$662$	−18.3430	−	26.9153i	−0.712921	−	1.04609i
$663$	12.1903			0.473431
$664$	−31.2992	+	7.12494i	−1.21465	+	0.276501i
$665$		0			0
$666$	−0.330022	−	0.484253i	−0.0127881	−	0.0187644i
$667$			26.1150i			1.01118i
$668$	−4.89477	+	12.4577i	−0.189384	+	0.482001i
$669$			3.14640i			0.121647i
$670$		0			0
$671$	−0.464893			−0.0179470
$672$	−4.00724	+	26.4147i	−0.154583	+	1.01897i
$673$	−18.1167			−0.698347			−0.349174	−	0.937058i	$-0.613538\pi$
$673$	−18.1167			−0.698347			−0.349174	+	0.937058i	$0.613538\pi$
$674$	1.00531	−	0.685127i	0.0387231	−	0.0263901i
$675$		0			0
$676$	0.715008	−	1.81976i	0.0275003	−	0.0699908i
$677$			30.5617i			1.17458i	0.809376	+	0.587291i	$0.199806\pi$
$677$			30.5617i			1.17458i	−0.809376	+	0.587291i	$0.800194\pi$
$678$	−3.07442	−	4.51120i	−0.118072	−	0.173252i
$679$	34.3576			1.31852
$680$		0			0
$681$	−3.92103			−0.150254
$682$	16.3832	+	24.0397i	0.627346	+	0.920527i
$683$			22.2027i			0.849564i	0.905296	+	0.424782i	$0.139649\pi$
$683$			22.2027i			0.849564i	−0.905296	+	0.424782i	$0.860351\pi$
$684$	10.1289	+	3.97976i	0.387286	+	0.152170i
$685$		0			0
$686$	−45.8445	+	31.2434i	−1.75035	+	1.19288i
$687$	−25.6899			−0.980132
$688$	14.5527	−	15.6600i	0.554818	−	0.597034i
$689$	−0.808569			−0.0308040
$690$		0			0
$691$			12.6890i			0.482712i	0.970437	+	0.241356i	$0.0775922\pi$
$691$			12.6890i			0.482712i	−0.970437	+	0.241356i	$0.922408\pi$
$692$	−41.7378	−	16.3993i	−1.58663	−	0.623408i
$693$			18.5617i			0.705101i
$694$	−25.7133	−	37.7299i	−0.976062	−	1.43221i
$695$		0			0
$696$	2.30401	+	10.1213i	0.0873334	+	0.383648i
$697$	10.5632			0.400110
$698$	−0.591668	−	0.868174i	−0.0223950	−	0.0328609i
$699$			25.7565i			0.974202i
$700$		0			0
$701$		−	34.9241i		−	1.31906i	−0.751676	−	0.659532i	$-0.770754\pi$
$701$		−	34.9241i		−	1.31906i	0.751676	−	0.659532i	$-0.229246\pi$
$702$	4.05203	−	2.76149i	0.152934	−	0.104226i
$703$	−2.25476			−0.0850398
$704$	13.6092	+	28.3430i	0.512916	+	1.06822i
$705$		0			0
$706$	38.1431	−	25.9949i	1.43554	−	0.978330i
$707$			19.9931i			0.751918i
$708$	−10.5179	+	26.7689i	−0.395285	+	1.00604i
$709$		−	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
$712$	5.57653	+	24.4972i	0.208989	+	0.918073i
$713$	−37.2453			−1.39485
$714$	−13.2245	−	19.4047i	−0.494913	−	0.726203i
$715$		0			0
$716$	−0.277065	−	0.108862i	−0.0103544	−	0.00406838i
$717$		−	15.8727i		−	0.592778i
$718$	3.16764	−	2.15878i	0.118215	−	0.0805648i
$719$	−20.0844			−0.749020			−0.374510	−	0.927223i	$-0.622189\pi$
$719$	−20.0844			−0.749020			−0.374510	+	0.927223i	$0.622189\pi$
$720$		0			0
$721$	0.202741			0.00755048
$722$	12.3969	−	8.44856i	0.461364	−	0.314423i
$723$			28.1664i			1.04752i
$724$	19.3461	+	7.60132i	0.718991	+	0.282501i
$725$		0			0
$726$	3.54083	+	5.19558i	0.131413	+	0.192826i
$727$	−13.0424			−0.483715			−0.241857	−	0.970312i	$-0.577757\pi$
$727$	−13.0424			−0.483715			−0.241857	+	0.970312i	$0.577757\pi$
$728$	45.1629	−	10.2809i	1.67385	−	0.381034i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$			18.7899i			0.694970i
$732$	0.0865164	−	0.220192i	0.00319774	−	0.00813854i
$733$			34.8917i			1.28876i	0.764707	+	0.644378i	$0.222884\pi$
$733$			34.8917i			1.28876i	−0.764707	+	0.644378i	$0.777116\pi$
$734$	−0.794678	+	0.541580i	−0.0293321	+	0.0199901i
$735$		0			0
$736$	−39.7980	−	6.03754i	−1.46697	−	0.222547i
$737$	52.8618			1.94719
$738$	3.51120	−	2.39291i	0.129249	−	0.0880843i
$739$			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
$742$	0.877166	+	1.28710i	0.0322018	+	0.0472508i
$743$	−7.63764			−0.280198			−0.140099	−	0.990138i	$-0.544742\pi$
$743$	−7.63764			−0.280198			−0.140099	+	0.990138i	$0.544742\pi$
$744$	−14.4351	+	3.28600i	−0.529216	+	0.120470i
$745$		0			0
$746$	−2.76873	−	4.06265i	−0.101370	−	0.148744i
$747$		−	11.3490i		−	0.415240i
$748$	−25.7205	−	10.1059i	−0.940434	−	0.369509i
$749$		−	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	$0.615183\pi$
$752$	2.71206	+	2.52029i	0.0988987	+	0.0919056i
$753$	4.66004			0.169821
$754$	14.8709	−	10.1346i	0.541565	−	0.369081i
$755$		0			0
$756$	−8.79159	−	3.45433i	−0.319747	−	0.125633i
$757$			43.7959i			1.59179i	0.605436	+	0.795894i	$0.292999\pi$
$757$			43.7959i			1.59179i	−0.605436	+	0.795894i	$0.707001\pi$
$758$	18.3697	+	26.9545i	0.667217	+	0.979030i
$759$	−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	$0.442249\pi$
$762$	14.6388	+	21.4801i	0.530309	+	0.778140i
$763$		−	61.1910i		−	2.21526i
$764$	4.55893	−	11.6029i	0.164936	−	0.419778i
$765$		0			0
$766$	11.4706	−	7.81732i	0.414450	−	0.282451i
$767$	49.8621			1.80042
$768$	−15.9571	+	1.17125i	−0.575801	+	0.0422637i
$769$	−17.9008			−0.645520			−0.322760	−	0.946481i	$-0.604611\pi$
$769$	−17.9008			−0.645520			−0.322760	+	0.946481i	$0.604611\pi$
$770$		0			0
$771$		−	3.33996i		−	0.120286i
$772$	−0.286686	+	0.729642i	−0.0103180	+	0.0262604i
$773$		−	20.8182i		−	0.748777i	−0.927272	−	0.374389i	$-0.877853\pi$
$773$		−	20.8182i		−	0.748777i	0.927272	−	0.374389i	$-0.122147\pi$
$774$	4.25653	+	6.24575i	0.152998	+	0.224499i
$775$		0			0
$776$	4.56701	+	20.0625i	0.163946	+	0.720201i
$777$	1.95707			0.0702096
$778$	−7.85420	−	11.5247i	−0.281587	−	0.413182i
$779$		−	16.3487i		−	0.585753i
$780$		0			0
$781$		−	8.60803i		−	0.308019i
$782$	29.2362	−	19.9247i	1.04549	−	0.712507i
$783$	−3.66998			−0.131154
$784$	−44.8488	−	41.6776i	−1.60174	−	1.48848i
$785$		0			0
$786$	−3.99546	+	2.72294i	−0.142513	+	0.0971239i
$787$		−	27.2047i		−	0.969744i	−0.874585	−	0.484872i	$-0.838866\pi$
$787$		−	27.2047i		−	0.969744i	0.874585	−	0.484872i	$-0.161134\pi$
$788$	−11.1058	−	4.36362i	−0.395628	−	0.155448i
$789$			27.5932i			0.982344i
$790$		0			0
$791$	18.2317			0.648244
$792$	−10.8388	+	2.46733i	−0.385139	+	0.0876729i
$793$	−0.410149			−0.0145648
$794$	10.1771	+	14.9332i	0.361170	+	0.529958i
$795$		0			0
$796$	−13.1155	+	33.3803i	−0.464868	+	1.18313i
$797$			16.4344i			0.582138i	0.956702	+	0.291069i	$0.0940109\pi$
$797$			16.4344i			0.582138i	−0.956702	+	0.291069i	$0.905989\pi$
$798$	−30.0327	+	20.4675i	−1.06315	+	0.724542i
$799$	−3.25410			−0.115122
$800$		0			0
$801$	−8.88265			−0.313853
$802$	−3.70836	+	2.52728i	−0.130947	+	0.0892413i
$803$			2.21352i			0.0781134i
$804$	−9.83756	+	25.0375i	−0.346944	+	0.883005i
$805$		0			0
$806$	14.4540	+	21.2089i	0.509122	+	0.747052i
$807$	21.8727			0.769956
$808$	−11.6746	+	2.65760i	−0.410712	+	0.0934942i
$809$	28.7698			1.01149			0.505747	−	0.862682i	$-0.331217\pi$
$809$	28.7698			1.01149			0.505747	+	0.862682i	$0.331217\pi$
$810$		0			0
$811$		−	14.3512i		−	0.503940i	−0.967735	−	0.251970i	$-0.918922\pi$
$811$		−	14.3512i		−	0.503940i	0.967735	−	0.251970i	$-0.0810785\pi$
$812$	−32.2649	−	12.6773i	−1.13228	−	0.444887i
$813$		−	8.78583i		−	0.308132i
$814$	1.90317	−	1.29703i	0.0667062	−	0.0454608i
$815$		0			0
$816$	9.57315	−	10.3016i	0.335127	−	0.360627i
$817$	29.0812			1.01742
$818$	−14.1550	+	9.64675i	−0.494918	+	0.337291i
$819$			16.3760i			0.572224i
$820$		0			0
$821$		−	4.97271i		−	0.173549i	−0.996228	−	0.0867744i	$-0.972344\pi$
$821$		−	4.97271i		−	0.173549i	0.996228	−	0.0867744i	$-0.0276559\pi$
$822$	13.0387	+	19.1322i	0.454778	+	0.667311i
$823$	20.3625			0.709791			0.354895	−	0.934906i	$-0.384517\pi$
$823$	20.3625			0.709791			0.354895	+	0.934906i	$0.384517\pi$
$824$	0.0269496	+	0.118387i	0.000938833	+	0.00412421i
$825$		0			0
$826$	−54.0923	−	79.3715i	−1.88211	−	2.76169i
$827$			36.0039i			1.25198i	0.779832	+	0.625989i	$0.215304\pi$
$827$			36.0039i			1.25198i	−0.779832	+	0.625989i	$0.784696\pi$
$828$	5.20449	−	13.2459i	0.180869	−	0.460328i
$829$			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
$832$	12.0066	+	25.0055i	0.416256	+	0.866909i
$833$	53.8124			1.86449
$834$	−2.28710	+	1.55867i	−0.0791956	+	0.0539725i
$835$		0			0
$836$	−15.6409	+	39.8076i	−0.540953	+	1.37678i
$837$		−	5.23414i		−	0.180918i
$838$	3.38298	+	4.96396i	0.116863	+	0.171477i
$839$	−25.3725			−0.875956			−0.437978	−	0.898986i	$-0.644305\pi$
$839$	−25.3725			−0.875956			−0.437978	+	0.898986i	$0.644305\pi$
$840$		0			0
$841$	15.5313			0.535561
$842$	−3.00993	−	4.41658i	−0.103729	−	0.152205i
$843$			17.0584i			0.587524i
$844$	12.1289	+	4.76558i	0.417492	+	0.164038i
$845$		0			0
$846$	−1.08166	+	0.737160i	−0.0371882	+	0.0253441i
$847$	−20.9976			−0.721485
$848$	−0.634978	+	0.683294i	−0.0218052	+	0.0234644i
$849$	−3.54724			−0.121741
$850$		0			0
$851$			2.94864i			0.101078i
$852$	4.07712	+	1.60195i	0.139680	+	0.0548820i
$853$		−	20.1365i		−	0.689460i	−0.938702	−	0.344730i	$-0.887971\pi$
$853$		−	20.1365i		−	0.689460i	0.938702	−	0.344730i	$-0.112029\pi$
$854$	0.444945	+	0.652884i	0.0152257	+	0.0223412i
$855$		0			0
$856$	42.6721	−	9.71385i	1.45850	−	0.332012i
$857$	42.0380			1.43599			0.717996	−	0.696047i	$-0.245060\pi$
$857$	42.0380			1.43599			0.717996	+	0.696047i	$0.245060\pi$
$858$	10.8530	+	15.9250i	0.370516	+	0.543670i
$859$			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
$862$	−29.9486	+	20.4102i	−1.02005	+	0.695174i
$863$	21.8154			0.742606			0.371303	−	0.928512i	$-0.378911\pi$
$863$	21.8154			0.742606			0.371303	+	0.928512i	$0.378911\pi$
$864$	0.848464	−	5.59286i	0.0288653	−	0.190273i
$865$		0			0
$866$	2.37407	−	1.61795i	0.0806740	−	0.0549800i
$867$		−	4.63952i		−	0.157566i
$868$	18.0804	−	46.0164i	0.613690	−	1.56190i
$869$			40.3805i			1.36982i
$870$		0			0
$871$	46.6371			1.58024
$872$	35.7314	−	8.13387i	1.21002	−	0.275448i
$873$	−7.27462			−0.246209
$874$	−30.8375	−	45.2490i	−1.04310	−	1.53057i
$875$		0			0
$876$	−1.04841	−	0.411935i	−0.0354226	−	0.0139180i
$877$		−	5.83690i		−	0.197098i	−0.995132	−	0.0985491i	$-0.968580\pi$
$877$		−	5.83690i		−	0.197098i	0.995132	−	0.0985491i	$-0.0314201\pi$
$878$	26.2782	−	17.9088i	0.886848	−	0.604394i
$879$	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	$0.564579\pi$
$882$	17.8872	−	12.1903i	0.602293	−	0.410468i
$883$			3.74810i			0.126134i	0.998009	+	0.0630668i	$0.0200881\pi$
$883$			3.74810i			0.126134i	−0.998009	+	0.0630668i	$0.979912\pi$
$884$	−22.6918	−	8.91590i	−0.763208	−	0.299874i
$885$		0			0
$886$	−2.70297	−	3.96616i	−0.0908081	−	0.133246i
$887$	42.8101			1.43742			0.718711	−	0.695309i	$-0.244732\pi$
$887$	42.8101			1.43742			0.718711	+	0.695309i	$0.244732\pi$
$888$	0.260146	+	1.14280i	0.00872992	+	0.0383498i
$889$	−86.8101			−2.91152
$890$		0			0
$891$		−	3.93012i		−	0.131664i
$892$	2.30126	−	5.85692i	0.0770519	−	0.196104i
$893$			5.03638i			0.168536i
$894$	14.1367	−	9.63429i	0.472803	−	0.322219i
$895$		0			0
$896$	26.7789	−	46.2393i	0.894622	−	1.54475i
$897$	−24.6730			−0.823808
$898$	2.54504	−	1.73447i	0.0849291	−	0.0578799i
$899$		−	19.2092i		−	0.640662i
$900$		0			0
$901$		−	0.819859i		−	0.0273135i
$902$	9.40444	+	13.7995i	0.313134	+	0.459472i
$903$	−25.2417			−0.839992
$904$	2.42347	+	10.6461i	0.0806033	+	0.354083i
$905$		0			0
$906$	3.88004	+	5.69331i	0.128906	+	0.189147i
$907$		−	6.97759i		−	0.231687i	−0.993267	−	0.115844i	$-0.963043\pi$
$907$		−	6.97759i		−	0.231687i	0.993267	−	0.115844i	$-0.0369571\pi$
$908$	7.29888	+	2.86782i	0.242222	+	0.0951721i
$909$		−	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	$0.368219\pi$
$912$	−15.9438	−	14.8164i	−0.527951	−	0.490619i
$913$	44.6031			1.47615
$914$	4.17965	−	2.84846i	0.138250	−	0.0942188i
$915$		0			0
$916$	47.8210	+	18.7895i	1.58005	+	0.620822i
$917$		−	16.1473i		−	0.533232i
$918$	2.80005	+	4.10861i	0.0924154	+	0.135604i
$919$	−1.25720			−0.0414712			−0.0207356	−	0.999785i	$-0.506601\pi$
$919$	−1.25720			−0.0414712			−0.0207356	+	0.999785i	$0.506601\pi$
$920$		0			0
$921$	12.3760			0.407803
$922$	10.4459	+	15.3276i	0.344016	+	0.504787i
$923$		−	7.59440i		−	0.249973i
$924$	13.5759	−	34.5520i	0.446616	−	1.13668i
$925$		0			0
$926$	3.75618	−	2.55987i	0.123436	−	0.0841225i
$927$	−0.0429270			−0.00140991
$928$	3.11384	−	20.5257i	0.102217	−	0.673788i
$929$	10.4933			0.344275			0.172138	−	0.985073i	$-0.444933\pi$
$929$	10.4933			0.344275			0.172138	+	0.985073i	$0.444933\pi$
$930$		0			0
$931$		−	83.2856i		−	2.72957i
$932$	18.8382	−	47.9450i	0.617066	−	1.57049i
$933$		−	18.2746i		−	0.598284i
$934$	24.1331	+	35.4113i	0.789660	+	1.15869i
$935$		0			0
$936$	−9.56247	+	2.17679i	−0.312559	+	0.0711508i
$937$	12.9680			0.423648			0.211824	−	0.977308i	$-0.432060\pi$
$937$	12.9680			0.423648			0.211824	+	0.977308i	$0.432060\pi$
$938$	−50.5936	−	74.2378i	−1.65194	−	2.42395i
$939$		−	12.7114i		−	0.414821i
$940$		0			0
$941$			44.9947i			1.46678i	0.679806	+	0.733392i	$0.262064\pi$
$941$			44.9947i			1.46678i	−0.679806	+	0.733392i	$0.737936\pi$
$942$	25.3080	−	17.2476i	0.824579	−	0.561957i
$943$	−21.3799			−0.696225
$944$	39.1573	−	42.1368i	1.27446	−	1.37143i
$945$		0			0
$946$	−24.5466	+	16.7287i	−0.798077	+	0.543896i
$947$			30.6282i			0.995283i	0.867383	+	0.497642i	$0.165801\pi$
$947$			30.6282i			0.995283i	−0.867383	+	0.497642i	$0.834199\pi$
$948$	−19.1259	−	7.51481i	−0.621180	−	0.244070i
$949$			1.95287i			0.0633927i
$950$		0			0
$951$	15.8602			0.514304
$952$	10.4244	+	45.7935i	0.337857	+	1.48418i
$953$	17.5717			0.569202			0.284601	−	0.958646i	$-0.408139\pi$
$953$	17.5717			0.569202			0.284601	+	0.958646i	$0.408139\pi$
$954$	−0.185725	−	0.272520i	−0.00601306	−	0.00882317i
$955$		0			0
$956$	−11.6092	+	29.5466i	−0.375469	+	0.955604i
$957$		−	14.4235i		−	0.466244i
$958$	−41.0068	+	27.9465i	−1.32487	+	0.902909i
$959$	−77.3213			−2.49683
$960$		0			0
$961$	−3.60380			−0.116252
$962$	1.67907	−	1.14430i	0.0541353	−	0.0368936i
$963$			15.4728i			0.498605i
$964$	20.6007	−	52.4308i	0.663505	−	1.68868i
$965$		0			0
$966$	26.7662	+	39.2750i	0.861189	+	1.26365i
$967$	4.50932			0.145010			0.0725050	−	0.997368i	$-0.476901\pi$
$967$	4.50932			0.145010			0.0725050	+	0.997368i	$0.476901\pi$
$968$	−2.79112	−	12.2611i	−0.0897100	−	0.394088i
$969$	19.1303			0.614555
$970$		0			0
$971$			35.8512i			1.15052i	0.817971	+	0.575259i	$0.195099\pi$
$971$			35.8512i			1.15052i	−0.817971	+	0.575259i	$0.804901\pi$
$972$	1.86147	+	0.731395i	0.0597066	+	0.0234595i
$973$		−	9.24313i		−	0.296321i
$974$	−43.1361	+	29.3976i	−1.38217	+	0.941961i
$975$		0			0
$976$	−0.322095	+	0.346603i	−0.0103100	+	0.0110945i
$977$	−43.9704			−1.40674			−0.703368	−	0.710826i	$-0.748322\pi$
$977$	−43.9704			−1.40674			−0.703368	+	0.710826i	$0.748322\pi$
$978$	18.9742	−	12.9310i	0.606727	−	0.413489i
$979$		−	34.9099i		−	1.11573i
$980$		0			0
$981$			12.9561i			0.413657i
$982$	−16.7144	−	24.5257i	−0.533380	−	0.782646i
$983$	−4.64187			−0.148053			−0.0740263	−	0.997256i	$-0.523585\pi$
$983$	−4.64187			−0.148053			−0.0740263	+	0.997256i	$0.523585\pi$
$984$	−8.28615	+	1.88625i	−0.264153	+	0.0601316i
$985$		0			0
$986$	10.2761	+	15.0785i	0.327258	+	0.480197i
$987$		−	4.37145i		−	0.139145i
$988$	−13.7991	+	35.1201i	−0.439009	+	1.11732i
$989$		−	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	$0.817679\pi$
$992$	29.2738	+	4.44098i	0.929444	+	0.141001i
$993$	−23.0315			−0.730882
$994$	−12.0889	+	8.23868i	−0.383437	+	0.261315i
$995$		0			0
$996$	−8.30063	+	21.1259i	−0.263016	+	0.669399i
$997$			39.4228i			1.24853i	0.781211	+	0.624266i	$0.214602\pi$
$997$			39.4228i			1.24853i	−0.781211	+	0.624266i	$0.785398\pi$
$998$	12.7354	+	18.6871i	0.403132	+	0.591529i
$999$	−0.414376			−0.0131103

Twists

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

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

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.k (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.16863 + 0.796431i) q^{2} +1.00000i q^{3} +(0.731395 - 1.86147i) q^{4} +(-0.796431 - 1.16863i) q^{6} +4.72294 q^{7} +(0.627801 + 2.75787i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(-1.16863 + 0.796431i) q^{2} +1.00000i q^{3} +(0.731395 - 1.86147i) q^{4} +(-0.796431 - 1.16863i) q^{6} +4.72294 q^{7} +(0.627801 + 2.75787i) q^{8} -1.00000 q^{9} -3.93012i q^{11} +(1.86147 + 0.731395i) q^{12} -3.46733i q^{13} +(-5.51937 + 3.76149i) q^{14} +(-2.93012 - 2.72294i) q^{16} +3.51575 q^{17} +(1.16863 - 0.796431i) q^{18} -5.44133i q^{19} +4.72294i q^{21} +(3.13007 + 4.59286i) q^{22} -7.11585 q^{23} +(-2.75787 + 0.627801i) q^{24} +(2.76149 + 4.05203i) q^{26} -1.00000i q^{27} +(3.45433 - 8.79159i) q^{28} -3.66998i q^{29} +5.23414 q^{31} +(5.59286 + 0.848464i) q^{32} +3.93012 q^{33} +(-4.10861 + 2.80005i) q^{34} +(-0.731395 + 1.86147i) q^{36} -0.414376i q^{37} +(4.33364 + 6.35890i) q^{38} +3.46733 q^{39} +3.00454 q^{41} +(-3.76149 - 5.51937i) q^{42} +5.34450i q^{43} +(-7.31580 - 2.87447i) q^{44} +(8.31580 - 5.66728i) q^{46} -0.925579 q^{47} +(2.72294 - 2.93012i) q^{48} +15.3061 q^{49} +3.51575i q^{51} +(-6.45433 - 2.53599i) q^{52} -0.233196i q^{53} +(0.796431 + 1.16863i) q^{54} +(2.96506 + 13.0253i) q^{56} +5.44133 q^{57} +(2.92288 + 4.28885i) q^{58} +14.3805i q^{59} -0.118290i q^{61} +(-6.11677 + 4.16863i) q^{62} -4.72294 q^{63} +(-7.21173 + 3.46279i) q^{64} +(-4.59286 + 3.13007i) q^{66} +13.4504i q^{67} +(2.57140 - 6.54445i) q^{68} -7.11585i q^{69} +2.19027 q^{71} +(-0.627801 - 2.75787i) q^{72} -0.563219 q^{73} +(0.330022 + 0.484253i) q^{74} +(-10.1289 - 3.97976i) q^{76} -18.5617i q^{77} +(-4.05203 + 2.76149i) q^{78} -10.2746 q^{79} +1.00000 q^{81} +(-3.51120 + 2.39291i) q^{82} +11.3490i q^{83} +(8.79159 + 3.45433i) q^{84} +(-4.25653 - 6.24575i) q^{86} +3.66998 q^{87} +(10.8388 - 2.46733i) q^{88} +8.88265 q^{89} -16.3760i q^{91} +(-5.20449 + 13.2459i) q^{92} +5.23414i q^{93} +(1.08166 - 0.737160i) q^{94} +(-0.848464 + 5.59286i) q^{96} +7.27462 q^{97} +(-17.8872 + 12.1903i) q^{98} +3.93012i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 4 q^{4} + 2 q^{6} + 8 q^{7} + 4 q^{8} - 8 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 + 4 * q^4 + 2 * q^6 + 8 * q^7 + 4 * q^8 - 8 * q^9	\( 8 q - 2 q^{2} + 4 q^{4} + 2 q^{6} + 8 q^{7} + 4 q^{8} - 8 q^{9} - 6 q^{14} + 8 q^{16} + 2 q^{18} + 12 q^{22} + 8 q^{23} - 8 q^{24} - 2 q^{26} - 4 q^{28} + 8 q^{31} + 28 q^{32} + 12 q^{34} - 4 q^{36} + 30 q^{38} - 6 q^{42} - 12 q^{44} + 20 q^{46} - 8 q^{48} - 20 q^{52} - 2 q^{54} + 8 q^{56} + 8 q^{57} + 12 q^{58} + 30 q^{62} - 8 q^{63} - 32 q^{64} - 20 q^{66} - 28 q^{68} - 40 q^{71} - 4 q^{72} - 16 q^{73} + 8 q^{74} - 20 q^{76} - 22 q^{78} - 16 q^{79} + 8 q^{81} - 24 q^{82} + 24 q^{84} - 18 q^{86} + 24 q^{87} - 8 q^{88} - 36 q^{92} - 4 q^{94} + 12 q^{96} - 8 q^{97} - 48 q^{98}+O(q^{100}) \) 8 * q - 2 * q^2 + 4 * q^4 + 2 * q^6 + 8 * q^7 + 4 * q^8 - 8 * q^9 - 6 * q^14 + 8 * q^16 + 2 * q^18 + 12 * q^22 + 8 * q^23 - 8 * q^24 - 2 * q^26 - 4 * q^28 + 8 * q^31 + 28 * q^32 + 12 * q^34 - 4 * q^36 + 30 * q^38 - 6 * q^42 - 12 * q^44 + 20 * q^46 - 8 * q^48 - 20 * q^52 - 2 * q^54 + 8 * q^56 + 8 * q^57 + 12 * q^58 + 30 * q^62 - 8 * q^63 - 32 * q^64 - 20 * q^66 - 28 * q^68 - 40 * q^71 - 4 * q^72 - 16 * q^73 + 8 * q^74 - 20 * q^76 - 22 * q^78 - 16 * q^79 + 8 * q^81 - 24 * q^82 + 24 * q^84 - 18 * q^86 + 24 * q^87 - 8 * q^88 - 36 * q^92 - 4 * q^94 + 12 * q^96 - 8 * q^97 - 48 * q^98

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