LMFDB - Embedded newform 2020.1.bt.c.1059.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2020,1,Mod(279,2020)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2020, base_ring=CyclotomicField(50))

chi = DirichletCharacter(H, H._module([25, 25, 11]))

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

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

chi := DirichletCharacter("2020.279");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 2020 = 2^{2} \cdot 5 \cdot 101 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2020.bt (of order $50$, degree $20$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.00811132552$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$2$ over $\Q(\zeta_{50})$
Coefficient field:	$\Q(\zeta_{100})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{40} - x^{30} + x^{20} - x^{10} + 1 $ x^40 - x^30 + x^20 - x^10 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{50}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{50} - \cdots)$

Embedding invariants

Embedding label			1059.1
Root			$0.844328 + 0.535827i$ of defining polynomial
Character	$\chi$	$=$	2020.1059
Dual form			2020.1.bt.c.639.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.844328 - 0.535827i) q^{2} +(-0.317042 - 1.23480i) q^{3} +(0.425779 + 0.904827i) q^{4} +(-0.535827 - 0.844328i) q^{5} +(-0.393950 + 1.21245i) q^{6} +(0.394502 - 0.996398i) q^{7} +(0.125333 - 0.992115i) q^{8} +(-0.547900 + 0.301210i) q^{9} +O(q^{10})$	\(q+(-0.844328 - 0.535827i) q^{2} +(-0.317042 - 1.23480i) q^{3} +(0.425779 + 0.904827i) q^{4} +(-0.535827 - 0.844328i) q^{5} +(-0.393950 + 1.21245i) q^{6} +(0.394502 - 0.996398i) q^{7} +(0.125333 - 0.992115i) q^{8} +(-0.547900 + 0.301210i) q^{9} +1.00000i q^{10} +(0.982287 - 0.812619i) q^{12} +(-0.866986 + 0.629902i) q^{14} +(-0.872693 + 0.929324i) q^{15} +(-0.637424 + 0.770513i) q^{16} +(0.624004 + 0.0392590i) q^{18} +(0.535827 - 0.844328i) q^{20} +(-1.35542 - 0.171230i) q^{21} +(-0.0859661 - 1.36639i) q^{23} +(-1.26480 + 0.159781i) q^{24} +(-0.425779 + 0.904827i) q^{25} +(-0.327053 - 0.348276i) q^{27} +(1.06954 - 0.0672897i) q^{28} +(-0.621636 - 1.57007i) q^{29} +(1.23480 - 0.317042i) q^{30} +(0.951057 - 0.309017i) q^{32} +(-1.05267 + 0.200808i) q^{35} +(-0.505828 - 0.367505i) q^{36} +(-0.904827 + 0.425779i) q^{40} +(0.700215 + 0.227513i) q^{41} +(1.05267 + 0.870846i) q^{42} +(-0.0931997 + 0.488570i) q^{43} +(0.547900 + 0.301210i) q^{45} +(-0.659566 + 1.19975i) q^{46} +(0.288760 + 1.51373i) q^{47} +(1.15352 + 0.542804i) q^{48} +(-0.108209 - 0.101615i) q^{49} +(0.844328 - 0.535827i) q^{50} +(0.0895243 + 0.469303i) q^{54} +(-0.939097 - 0.516273i) q^{56} +(-0.316423 + 1.65875i) q^{58} +(-1.21245 - 0.393950i) q^{60} +(0.871808 - 0.410241i) q^{61} +(0.0839780 + 0.664754i) q^{63} +(-0.968583 - 0.248690i) q^{64} +(-0.0312307 + 0.121636i) q^{67} +(-1.65996 + 0.539354i) q^{69} +(0.996398 + 0.394502i) q^{70} +(0.230165 + 0.581331i) q^{72} +(1.25227 + 0.238883i) q^{75} +(0.992115 + 0.125333i) q^{80} +(-0.661379 + 1.04217i) q^{81} +(-0.469303 - 0.567290i) q^{82} +(-1.93334 - 0.121636i) q^{83} +(-0.422178 - 1.29933i) q^{84} +(0.340480 - 0.362574i) q^{86} +(-1.74164 + 1.26537i) q^{87} +(0.905793 - 0.749337i) q^{89} +(-0.301210 - 0.547900i) q^{90} +(1.19975 - 0.659566i) q^{92} +(0.567290 - 1.43281i) q^{94} +(-0.683098 - 1.07639i) q^{96} +(0.0369159 + 0.143778i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 10 q^{9}+O(q^{10}) $ 40 * q + 10 * q^9	$ 40 q + 10 q^{9} - 40 q^{21} - 10 q^{29} + 10 q^{30} - 10 q^{36} - 10 q^{45} - 10 q^{46} + 10 q^{49} + 10 q^{54} + 10 q^{61} + 10 q^{70} - 10 q^{81} + 30 q^{84} + 10 q^{94} - 10 q^{96}+O(q^{100}) $ 40 * q + 10 * q^9 - 40 * q^21 - 10 * q^29 + 10 * q^30 - 10 * q^36 - 10 * q^45 - 10 * q^46 + 10 * q^49 + 10 * q^54 + 10 * q^61 + 10 * q^70 - 10 * q^81 + 30 * q^84 + 10 * q^94 - 10 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2020\mathbb{Z}\right)^\times$.

$n$	$1011$	$1617$	$1921$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{9}{50}\right)$

Coefficient data

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

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

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

$2$	−0.844328	−	0.535827i	−0.844328	−	0.535827i
$2$	−0.844328	−	0.535827i	−0.844328	−	0.535827i
$3$	−0.317042	−	1.23480i	−0.317042	−	1.23480i	−0.904827	−	0.425779i	$-0.860000\pi$
$3$	−0.317042	−	1.23480i	−0.317042	−	1.23480i	0.587785	−	0.809017i	$-0.300000\pi$
$4$	0.425779	+	0.904827i	0.425779	+	0.904827i
$5$	−0.535827	−	0.844328i	−0.535827	−	0.844328i
$5$	−0.535827	−	0.844328i	−0.535827	−	0.844328i
$6$	−0.393950	+	1.21245i	−0.393950	+	1.21245i
$7$	0.394502	−	0.996398i	0.394502	−	0.996398i	−0.587785	−	0.809017i	$-0.700000\pi$
$7$	0.394502	−	0.996398i	0.394502	−	0.996398i	0.982287	−	0.187381i	$-0.0600000\pi$
$8$	0.125333	−	0.992115i	0.125333	−	0.992115i
$9$	−0.547900	+	0.301210i	−0.547900	+	0.301210i
$10$			1.00000i			1.00000i
$11$		0			0		−0.481754	−	0.876307i	$-0.660000\pi$
$11$		0			0		0.481754	+	0.876307i	$0.340000\pi$
$12$	0.982287	−	0.812619i	0.982287	−	0.812619i
$13$		0			0		0.929776	−	0.368125i	$-0.120000\pi$
$13$		0			0		−0.929776	+	0.368125i	$0.880000\pi$
$14$	−0.866986	+	0.629902i	−0.866986	+	0.629902i
$15$	−0.872693	+	0.929324i	−0.872693	+	0.929324i
$16$	−0.637424	+	0.770513i	−0.637424	+	0.770513i
$17$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$17$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$18$	0.624004	+	0.0392590i	0.624004	+	0.0392590i
$19$		0			0		−0.637424	−	0.770513i	$-0.720000\pi$
$19$		0			0		0.637424	+	0.770513i	$0.280000\pi$
$20$	0.535827	−	0.844328i	0.535827	−	0.844328i
$21$	−1.35542	−	0.171230i	−1.35542	−	0.171230i
$22$		0			0
$23$	−0.0859661	−	1.36639i	−0.0859661	−	1.36639i	−0.770513	−	0.637424i	$-0.780000\pi$
$23$	−0.0859661	−	1.36639i	−0.0859661	−	1.36639i	0.684547	−	0.728969i	$-0.260000\pi$
$24$	−1.26480	+	0.159781i	−1.26480	+	0.159781i
$25$	−0.425779	+	0.904827i	−0.425779	+	0.904827i
$26$		0			0
$27$	−0.327053	−	0.348276i	−0.327053	−	0.348276i
$28$	1.06954	−	0.0672897i	1.06954	−	0.0672897i
$29$	−0.621636	−	1.57007i	−0.621636	−	1.57007i	−0.809017	−	0.587785i	$-0.800000\pi$
$29$	−0.621636	−	1.57007i	−0.621636	−	1.57007i	0.187381	−	0.982287i	$-0.440000\pi$
$30$	1.23480	−	0.317042i	1.23480	−	0.317042i
$31$		0			0		−0.929776	−	0.368125i	$-0.880000\pi$
$31$		0			0		0.929776	+	0.368125i	$0.120000\pi$
$32$	0.951057	−	0.309017i	0.951057	−	0.309017i
$33$		0			0
$34$		0			0
$35$	−1.05267	+	0.200808i	−1.05267	+	0.200808i
$36$	−0.505828	−	0.367505i	−0.505828	−	0.367505i
$37$		0			0		−0.968583	−	0.248690i	$-0.920000\pi$
$37$		0			0		0.968583	+	0.248690i	$0.0800000\pi$
$38$		0			0
$39$		0			0
$40$	−0.904827	+	0.425779i	−0.904827	+	0.425779i
$41$	0.700215	+	0.227513i	0.700215	+	0.227513i	0.637424	−	0.770513i	$-0.280000\pi$
$41$	0.700215	+	0.227513i	0.700215	+	0.227513i	0.0627905	+	0.998027i	$0.480000\pi$
$42$	1.05267	+	0.870846i	1.05267	+	0.870846i
$43$	−0.0931997	+	0.488570i	−0.0931997	+	0.488570i	0.904827	+	0.425779i	$0.140000\pi$
$43$	−0.0931997	+	0.488570i	−0.0931997	+	0.488570i	−0.998027	+	0.0627905i	$0.980000\pi$
$44$		0			0
$45$	0.547900	+	0.301210i	0.547900	+	0.301210i
$46$	−0.659566	+	1.19975i	−0.659566	+	1.19975i
$47$	0.288760	+	1.51373i	0.288760	+	1.51373i	0.770513	+	0.637424i	$0.220000\pi$
$47$	0.288760	+	1.51373i	0.288760	+	1.51373i	−0.481754	+	0.876307i	$0.660000\pi$
$48$	1.15352	+	0.542804i	1.15352	+	0.542804i
$49$	−0.108209	−	0.101615i	−0.108209	−	0.101615i
$50$	0.844328	−	0.535827i	0.844328	−	0.535827i
$51$		0			0
$52$		0			0
$53$		0			0		−0.904827	−	0.425779i	$-0.860000\pi$
$53$		0			0		0.904827	+	0.425779i	$0.140000\pi$
$54$	0.0895243	+	0.469303i	0.0895243	+	0.469303i
$55$		0			0
$56$	−0.939097	−	0.516273i	−0.939097	−	0.516273i
$57$		0			0
$58$	−0.316423	+	1.65875i	−0.316423	+	1.65875i
$59$		0			0		−0.770513	−	0.637424i	$-0.780000\pi$
$59$		0			0		0.770513	+	0.637424i	$0.220000\pi$
$60$	−1.21245	−	0.393950i	−1.21245	−	0.393950i
$61$	0.871808	−	0.410241i	0.871808	−	0.410241i	0.0627905	−	0.998027i	$-0.480000\pi$
$61$	0.871808	−	0.410241i	0.871808	−	0.410241i	0.809017	+	0.587785i	$0.200000\pi$
$62$		0			0
$63$	0.0839780	+	0.664754i	0.0839780	+	0.664754i
$64$	−0.968583	−	0.248690i	−0.968583	−	0.248690i
$65$		0			0
$66$		0			0
$67$	−0.0312307	+	0.121636i	−0.0312307	+	0.121636i	−0.982287	−	0.187381i	$-0.940000\pi$
$67$	−0.0312307	+	0.121636i	−0.0312307	+	0.121636i	0.951057	+	0.309017i	$0.100000\pi$
$68$		0			0
$69$	−1.65996	+	0.539354i	−1.65996	+	0.539354i
$70$	0.996398	+	0.394502i	0.996398	+	0.394502i
$71$		0			0		0.968583	−	0.248690i	$-0.0800000\pi$
$71$		0			0		−0.968583	+	0.248690i	$0.920000\pi$
$72$	0.230165	+	0.581331i	0.230165	+	0.581331i
$73$		0			0		0.998027	−	0.0627905i	$-0.0200000\pi$
$73$		0			0		−0.998027	+	0.0627905i	$0.980000\pi$
$74$		0			0
$75$	1.25227	+	0.238883i	1.25227	+	0.238883i
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		0.0627905	−	0.998027i	$-0.480000\pi$
$79$		0			0		−0.0627905	+	0.998027i	$0.520000\pi$
$80$	0.992115	+	0.125333i	0.992115	+	0.125333i
$81$	−0.661379	+	1.04217i	−0.661379	+	1.04217i
$82$	−0.469303	−	0.567290i	−0.469303	−	0.567290i
$83$	−1.93334	−	0.121636i	−1.93334	−	0.121636i	−0.951057	−	0.309017i	$-0.900000\pi$
$83$	−1.93334	−	0.121636i	−1.93334	−	0.121636i	−0.982287	+	0.187381i	$0.940000\pi$
$84$	−0.422178	−	1.29933i	−0.422178	−	1.29933i
$85$		0			0
$86$	0.340480	−	0.362574i	0.340480	−	0.362574i
$87$	−1.74164	+	1.26537i	−1.74164	+	1.26537i
$88$		0			0
$89$	0.905793	−	0.749337i	0.905793	−	0.749337i	−0.0627905	−	0.998027i	$-0.520000\pi$
$89$	0.905793	−	0.749337i	0.905793	−	0.749337i	0.968583	+	0.248690i	$0.0800000\pi$
$90$	−0.301210	−	0.547900i	−0.301210	−	0.547900i
$91$		0			0
$92$	1.19975	−	0.659566i	1.19975	−	0.659566i
$93$		0			0
$94$	0.567290	−	1.43281i	0.567290	−	1.43281i
$95$		0			0
$96$	−0.683098	−	1.07639i	−0.683098	−	1.07639i
$97$		0			0		−0.425779	−	0.904827i	$-0.640000\pi$
$97$		0			0		0.425779	+	0.904827i	$0.360000\pi$
$98$	0.0369159	+	0.143778i	0.0369159	+	0.143778i
$99$		0			0
$100$	−1.00000			−1.00000
$101$	0.992115	+	0.125333i	0.992115	+	0.125333i
$101$	0.992115	+	0.125333i	0.992115	+	0.125333i
$102$		0			0
$103$	−1.36615	−	0.866986i	−1.36615	−	0.866986i	−0.368125	−	0.929776i	$-0.620000\pi$
$103$	−1.36615	−	0.866986i	−1.36615	−	0.866986i	−0.998027	+	0.0627905i	$0.980000\pi$
$104$		0			0
$105$	0.581698	+	1.23617i	0.581698	+	1.23617i
$106$		0			0
$107$	−0.559214	+	1.72108i	−0.559214	+	1.72108i	0.125333	+	0.992115i	$0.460000\pi$
$107$	−0.559214	+	1.72108i	−0.559214	+	1.72108i	−0.684547	+	0.728969i	$0.740000\pi$
$108$	0.175877	−	0.444215i	0.175877	−	0.444215i
$109$	−0.193142	+	1.52888i	−0.193142	+	1.52888i	0.535827	+	0.844328i	$0.320000\pi$
$109$	−0.193142	+	1.52888i	−0.193142	+	1.52888i	−0.728969	+	0.684547i	$0.760000\pi$
$110$		0			0
$111$		0			0
$112$	0.516273	+	0.939097i	0.516273	+	0.939097i
$113$		0			0		0.770513	−	0.637424i	$-0.220000\pi$
$113$		0			0		−0.770513	+	0.637424i	$0.780000\pi$
$114$		0			0
$115$	−1.10762	+	0.804733i	−1.10762	+	0.804733i
$116$	1.15596	−	1.23098i	1.15596	−	1.23098i
$117$		0			0
$118$		0			0
$119$		0			0
$120$	0.812619	+	0.982287i	0.812619	+	0.982287i
$121$	−0.535827	+	0.844328i	−0.535827	+	0.844328i
$122$	−0.955910	−	0.120759i	−0.955910	−	0.120759i
$123$	0.0589355	−	0.936754i	0.0589355	−	0.936754i
$124$		0			0
$125$	0.992115	−	0.125333i	0.992115	−	0.125333i
$126$	0.285288	−	0.606268i	0.285288	−	0.606268i
$127$	1.58937	+	0.303189i	1.58937	+	0.303189i	0.904827	−	0.425779i	$-0.140000\pi$
$127$	1.58937	+	0.303189i	1.58937	+	0.303189i	0.684547	+	0.728969i	$0.260000\pi$
$128$	0.684547	+	0.728969i	0.684547	+	0.728969i
$129$	0.632832	−	0.0398144i	0.632832	−	0.0398144i
$130$		0			0
$131$		0			0		0.968583	−	0.248690i	$-0.0800000\pi$
$131$		0			0		−0.968583	+	0.248690i	$0.920000\pi$
$132$		0			0
$133$		0			0
$134$	0.0915446	−	0.0859661i	0.0915446	−	0.0859661i
$135$	−0.118815	+	0.462756i	−0.118815	+	0.462756i
$136$		0			0
$137$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$137$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$138$	1.69055	+	0.434060i	1.69055	+	0.434060i
$139$		0			0		−0.125333	−	0.992115i	$-0.540000\pi$
$139$		0			0		0.125333	+	0.992115i	$0.460000\pi$
$140$	−0.629902	−	0.866986i	−0.629902	−	0.866986i
$141$	1.77760	−	0.836475i	1.77760	−	0.836475i
$142$		0			0
$143$		0			0
$144$	0.117158	−	0.614163i	0.117158	−	0.614163i
$145$	−0.992567	+	1.36615i	−0.992567	+	1.36615i
$146$		0			0
$147$	−0.0911672	+	0.165832i	−0.0911672	+	0.165832i
$148$		0			0
$149$	−1.80608	−	0.849878i	−1.80608	−	0.849878i	−0.929776	−	0.368125i	$-0.880000\pi$
$149$	−1.80608	−	0.849878i	−1.80608	−	0.849878i	−0.876307	−	0.481754i	$-0.840000\pi$
$150$	−0.929324	−	0.872693i	−0.929324	−	0.872693i
$151$		0			0		0.844328	−	0.535827i	$-0.180000\pi$
$151$		0			0		−0.844328	+	0.535827i	$0.820000\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		−0.876307	−	0.481754i	$-0.840000\pi$
$157$		0			0		0.876307	+	0.481754i	$0.160000\pi$
$158$		0			0
$159$		0			0
$160$	−0.770513	−	0.637424i	−0.770513	−	0.637424i
$161$	−1.39539	−	0.453388i	−1.39539	−	0.453388i
$162$	1.11684	−	0.525546i	1.11684	−	0.525546i
$163$	0.0738147	+	0.101597i	0.0738147	+	0.101597i	0.844328	−	0.535827i	$-0.180000\pi$
$163$	0.0738147	+	0.101597i	0.0738147	+	0.101597i	−0.770513	+	0.637424i	$0.780000\pi$
$164$	0.0922765	+	0.730444i	0.0922765	+	0.730444i
$165$		0			0
$166$	1.56720	+	1.13864i	1.56720	+	1.13864i
$167$	1.43211	−	0.273190i	1.43211	−	0.273190i	0.587785	−	0.809017i	$-0.300000\pi$
$167$	1.43211	−	0.273190i	1.43211	−	0.273190i	0.844328	+	0.535827i	$0.180000\pi$
$168$	−0.339759	+	1.32327i	−0.339759	+	1.32327i
$169$	0.728969	−	0.684547i	0.728969	−	0.684547i
$170$		0			0
$171$		0			0
$172$	−0.481754	+	0.123693i	−0.481754	+	0.123693i
$173$		0			0		−0.368125	−	0.929776i	$-0.620000\pi$
$173$		0			0		0.368125	+	0.929776i	$0.380000\pi$
$174$	2.14853	−	0.135174i	2.14853	−	0.135174i
$175$	0.733597	+	0.781202i	0.733597	+	0.781202i
$176$		0			0
$177$		0			0
$178$	−1.16630	+	0.147338i	−1.16630	+	0.147338i
$179$		0			0		−0.0627905	−	0.998027i	$-0.520000\pi$
$179$		0			0		0.0627905	+	0.998027i	$0.480000\pi$
$180$	−0.0392590	+	0.624004i	−0.0392590	+	0.624004i
$181$	1.92189	+	0.242791i	1.92189	+	0.242791i	0.992115	−	0.125333i	$-0.0400000\pi$
$181$	1.92189	+	0.242791i	1.92189	+	0.242791i	0.929776	+	0.368125i	$0.120000\pi$
$182$		0			0
$183$	−0.782964	−	0.946441i	−0.782964	−	0.946441i
$184$	−1.36639	−	0.0859661i	−1.36639	−	0.0859661i
$185$		0			0
$186$		0			0
$187$		0			0
$188$	−1.24672	+	0.905793i	−1.24672	+	0.905793i
$189$	−0.476045	+	0.188479i	−0.476045	+	0.188479i
$190$		0			0
$191$		0			0		−0.481754	−	0.876307i	$-0.660000\pi$
$191$		0			0		0.481754	+	0.876307i	$0.340000\pi$
$192$			1.27485i			1.27485i
$193$		0			0		0.876307	−	0.481754i	$-0.160000\pi$
$193$		0			0		−0.876307	+	0.481754i	$0.840000\pi$
$194$		0			0
$195$		0			0
$196$	0.0458709	−	0.141176i	0.0458709	−	0.141176i
$197$		0			0		−0.535827	−	0.844328i	$-0.680000\pi$
$197$		0			0		0.535827	+	0.844328i	$0.320000\pi$
$198$		0			0
$199$		0			0		−0.248690	−	0.968583i	$-0.580000\pi$
$199$		0			0		0.248690	+	0.968583i	$0.420000\pi$
$200$	0.844328	+	0.535827i	0.844328	+	0.535827i
$201$	0.160097			0.160097
$202$	−0.770513	−	0.637424i	−0.770513	−	0.637424i
$203$	−1.80965			−1.80965
$204$		0			0
$205$	−0.183098	−	0.713118i	−0.183098	−	0.713118i
$206$	0.688925	+	1.46404i	0.688925	+	1.46404i
$207$	0.458672	+	0.722752i	0.458672	+	0.722752i
$208$		0			0
$209$		0			0
$210$	0.171230	−	1.35542i	0.171230	−	1.35542i
$211$		0			0		0.876307	−	0.481754i	$-0.160000\pi$
$211$		0			0		−0.876307	+	0.481754i	$0.840000\pi$
$212$		0			0
$213$		0			0
$214$	1.39436	−	1.15352i	1.39436	−	1.15352i
$215$	0.462452	−	0.183098i	0.462452	−	0.183098i
$216$	−0.386520	+	0.280823i	−0.386520	+	0.280823i
$217$		0			0
$218$	0.982287	−	1.18738i	0.982287	−	1.18738i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	1.94908	+	0.246226i	1.94908	+	0.246226i	0.998027	−	0.0627905i	$-0.0200000\pi$
$223$	1.94908	+	0.246226i	1.94908	+	0.246226i	0.951057	+	0.309017i	$0.100000\pi$
$224$	0.0672897	−	1.06954i	0.0672897	−	1.06954i
$225$	−0.0392590	−	0.624004i	−0.0392590	−	0.624004i
$226$		0			0
$227$	0.849878	−	1.80608i	0.849878	−	1.80608i	0.368125	−	0.929776i	$-0.380000\pi$
$227$	0.849878	−	1.80608i	0.849878	−	1.80608i	0.481754	−	0.876307i	$-0.340000\pi$
$228$		0			0
$229$	−1.30209	−	1.38658i	−1.30209	−	1.38658i	−0.876307	−	0.481754i	$-0.840000\pi$
$229$	−1.30209	−	1.38658i	−1.30209	−	1.38658i	−0.425779	−	0.904827i	$-0.640000\pi$
$230$	1.36639	−	0.0859661i	1.36639	−	0.0859661i
$231$		0			0
$232$	−1.63560	+	0.419952i	−1.63560	+	0.419952i
$233$		0			0		−0.929776	−	0.368125i	$-0.880000\pi$
$233$		0			0		0.929776	+	0.368125i	$0.120000\pi$
$234$		0			0
$235$	1.12336	−	1.05491i	1.12336	−	1.05491i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		−0.968583	−	0.248690i	$-0.920000\pi$
$239$		0			0		0.968583	+	0.248690i	$0.0800000\pi$
$240$	−0.159781	−	1.26480i	−0.159781	−	1.26480i
$241$	−0.566335	−	0.779494i	−0.566335	−	0.779494i	0.425779	−	0.904827i	$-0.360000\pi$
$241$	−0.566335	−	0.779494i	−0.566335	−	0.779494i	−0.992115	+	0.125333i	$0.960000\pi$
$242$	0.904827	−	0.425779i	0.904827	−	0.425779i
$243$	1.04217	+	0.338621i	1.04217	+	0.338621i
$244$	0.742395	+	0.614163i	0.742395	+	0.614163i
$245$	−0.0278151	+	0.145812i	−0.0278151	+	0.145812i
$246$	−0.551699	+	0.759348i	−0.551699	+	0.759348i
$247$		0			0
$248$		0			0
$249$	0.462756	+	2.42585i	0.462756	+	2.42585i
$250$	−0.904827	−	0.425779i	−0.904827	−	0.425779i
$251$		0			0		−0.728969	−	0.684547i	$-0.760000\pi$
$251$		0			0		0.728969	+	0.684547i	$0.240000\pi$
$252$	−0.565732	+	0.359024i	−0.565732	+	0.359024i
$253$		0			0
$254$	−1.17950	−	1.10762i	−1.17950	−	1.10762i
$255$		0			0
$256$	−0.187381	−	0.982287i	−0.187381	−	0.982287i
$257$		0			0		0.481754	−	0.876307i	$-0.340000\pi$
$257$		0			0		−0.481754	+	0.876307i	$0.660000\pi$
$258$	−0.555652	−	0.305472i	−0.555652	−	0.305472i
$259$		0			0
$260$		0			0
$261$	0.813516	+	0.672999i	0.813516	+	0.672999i
$262$		0			0
$263$	−1.79538	+	0.844844i	−1.79538	+	0.844844i	−0.844328	+	0.535827i	$0.820000\pi$
$263$	−1.79538	+	0.844844i	−1.79538	+	0.844844i	−0.951057	+	0.309017i	$0.900000\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−1.21245	−	0.880898i	−1.21245	−	0.880898i
$268$	−0.123357	+	0.0235315i	−0.123357	+	0.0235315i
$269$	0.450043	−	1.75280i	0.450043	−	1.75280i	−0.187381	−	0.982287i	$-0.560000\pi$
$269$	0.450043	−	1.75280i	0.450043	−	1.75280i	0.637424	−	0.770513i	$-0.280000\pi$
$270$	0.348276	−	0.327053i	0.348276	−	0.327053i
$271$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$271$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$	−1.19480	−	1.27233i	−1.19480	−	1.27233i
$277$		0			0		−0.982287	−	0.187381i	$-0.940000\pi$
$277$		0			0		0.982287	+	0.187381i	$0.0600000\pi$
$278$		0			0
$279$		0			0
$280$	0.0672897	+	1.06954i	0.0672897	+	1.06954i
$281$	0.0915446	−	1.45506i	0.0915446	−	1.45506i	−0.637424	−	0.770513i	$-0.720000\pi$
$281$	0.0915446	−	1.45506i	0.0915446	−	1.45506i	0.728969	−	0.684547i	$-0.240000\pi$
$282$	−1.94908	−	0.246226i	−1.94908	−	0.246226i
$283$	0.394502	−	0.621636i	0.394502	−	0.621636i	−0.587785	−	0.809017i	$-0.700000\pi$
$283$	0.394502	−	0.621636i	0.394502	−	0.621636i	0.982287	+	0.187381i	$0.0600000\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	0.502930	−	0.607938i	0.502930	−	0.607938i
$288$	−0.428004	+	0.455778i	−0.428004	+	0.455778i
$289$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$290$	1.57007	−	0.621636i	1.57007	−	0.621636i
$291$		0			0
$292$		0			0
$293$		0			0			−	1.00000i	$-0.5\pi$
$293$		0			0				1.00000i	$0.5\pi$
$294$	0.165832	−	0.0911672i	0.165832	−	0.0911672i
$295$		0			0
$296$		0			0
$297$		0			0
$298$	1.06954	+	1.68532i	1.06954	+	1.68532i
$299$		0			0
$300$	0.317042	+	1.23480i	0.317042	+	1.23480i
$301$	0.450043	+	0.285606i	0.450043	+	0.285606i
$302$		0			0
$303$	−0.159781	−	1.26480i	−0.159781	−	1.26480i
$304$		0			0
$305$	−0.813516	−	0.516273i	−0.813516	−	0.516273i
$306$		0			0
$307$	−0.718995	−	1.52794i	−0.718995	−	1.52794i	−0.844328	−	0.535827i	$-0.820000\pi$
$307$	−0.718995	−	1.52794i	−0.718995	−	1.52794i	0.125333	−	0.992115i	$-0.460000\pi$
$308$		0			0
$309$	−0.637424	+	1.96179i	−0.637424	+	1.96179i
$310$		0			0
$311$		0			0		0.125333	−	0.992115i	$-0.460000\pi$
$311$		0			0		−0.125333	+	0.992115i	$0.540000\pi$
$312$		0			0
$313$		0			0			−	1.00000i	$-0.5\pi$
$313$		0			0				1.00000i	$0.5\pi$
$314$		0			0
$315$	0.516273	−	0.427098i	0.516273	−	0.427098i
$316$		0			0
$317$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$317$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$318$		0			0
$319$		0			0
$320$	0.309017	+	0.951057i	0.309017	+	0.951057i
$321$	2.30248	+	0.144860i	2.30248	+	0.144860i
$322$	0.935225	+	1.13049i	0.935225	+	1.13049i
$323$		0			0
$324$	−1.22458	−	0.154701i	−1.22458	−	0.154701i
$325$		0			0
$326$	−0.00788530	−	0.125333i	−0.00788530	−	0.125333i
$327$	1.94908	−	0.246226i	1.94908	−	0.246226i
$328$	0.313480	−	0.666178i	0.313480	−	0.666178i
$329$	1.62219	+	0.309450i	1.62219	+	0.309450i
$330$		0			0
$331$		0			0		0.998027	−	0.0627905i	$-0.0200000\pi$
$331$		0			0		−0.998027	+	0.0627905i	$0.980000\pi$
$332$	−0.713118	−	1.80113i	−0.713118	−	1.80113i
$333$		0			0
$334$	−1.35556	−	0.536702i	−1.35556	−	0.536702i
$335$	0.119435	−	0.0388067i	0.119435	−	0.0388067i
$336$	0.995914	−	0.935225i	0.995914	−	0.935225i
$337$		0			0		0.248690	−	0.968583i	$-0.420000\pi$
$337$		0			0		−0.248690	+	0.968583i	$0.580000\pi$
$338$	−0.982287	+	0.187381i	−0.982287	+	0.187381i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	0.825723	−	0.388556i	0.825723	−	0.388556i
$344$	0.473036	+	0.153699i	0.473036	+	0.153699i
$345$	1.34484	+	1.11255i	1.34484	+	1.11255i
$346$		0			0
$347$	0.500534	−	0.688925i	0.500534	−	0.688925i	−0.481754	−	0.876307i	$-0.660000\pi$
$347$	0.500534	−	0.688925i	0.500534	−	0.688925i	0.982287	+	0.187381i	$0.0600000\pi$
$348$	−1.88650	−	1.03711i	−1.88650	−	1.03711i
$349$	0.946441	−	1.72157i	0.946441	−	1.72157i	0.309017	−	0.951057i	$-0.400000\pi$
$349$	0.946441	−	1.72157i	0.946441	−	1.72157i	0.637424	−	0.770513i	$-0.280000\pi$
$350$	−0.200808	−	1.05267i	−0.200808	−	1.05267i
$351$		0			0
$352$		0			0
$353$		0			0		0.844328	−	0.535827i	$-0.180000\pi$
$353$		0			0		−0.844328	+	0.535827i	$0.820000\pi$
$354$		0			0
$355$		0			0
$356$	1.06369	+	0.500534i	1.06369	+	0.500534i
$357$		0			0
$358$		0			0
$359$		0			0		−0.876307	−	0.481754i	$-0.840000\pi$
$359$		0			0		0.876307	+	0.481754i	$0.160000\pi$
$360$	0.367505	−	0.505828i	0.367505	−	0.505828i
$361$	−0.187381	+	0.982287i	−0.187381	+	0.982287i
$362$	−1.49261	−	1.23480i	−1.49261	−	1.23480i
$363$	1.21245	+	0.393950i	1.21245	+	0.393950i
$364$		0			0
$365$		0			0
$366$	0.153950	+	1.21864i	0.153950	+	1.21864i
$367$	−1.13864	−	0.292352i	−1.13864	−	0.292352i	−0.368125	−	0.929776i	$-0.620000\pi$
$367$	−1.13864	−	0.292352i	−1.13864	−	0.292352i	−0.770513	+	0.637424i	$0.780000\pi$
$368$	1.10762	+	0.804733i	1.10762	+	0.804733i
$369$	−0.452177	+	0.0862573i	−0.452177	+	0.0862573i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.929776	−	0.368125i	$-0.880000\pi$
$373$		0			0		0.929776	+	0.368125i	$0.120000\pi$
$374$		0			0
$375$	−0.469303	−	1.18532i	−0.469303	−	1.18532i
$376$	1.53799	−	0.0967619i	1.53799	−	0.0967619i
$377$		0			0
$378$	0.502930	+	0.0959390i	0.502930	+	0.0959390i
$379$		0			0		0.425779	−	0.904827i	$-0.360000\pi$
$379$		0			0		−0.425779	+	0.904827i	$0.640000\pi$
$380$		0			0
$381$	−0.129521	−	2.05868i	−0.129521	−	2.05868i
$382$		0			0
$383$	0.248690	+	0.0314168i	0.248690	+	0.0314168i	0.248690	−	0.968583i	$-0.420000\pi$
$383$	0.248690	+	0.0314168i	0.248690	+	0.0314168i			1.00000i	$0.5\pi$
$384$	0.683098	−	1.07639i	0.683098	−	1.07639i
$385$		0			0
$386$		0			0
$387$	−0.0960982	−	0.295760i	−0.0960982	−	0.295760i
$388$		0			0
$389$		0			0		−0.728969	−	0.684547i	$-0.760000\pi$
$389$		0			0		0.728969	+	0.684547i	$0.240000\pi$
$390$		0			0
$391$		0			0
$392$	−0.114376	+	0.0946201i	−0.114376	+	0.0946201i
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$		0			0		0.368125	−	0.929776i	$-0.380000\pi$
$397$		0			0		−0.368125	+	0.929776i	$0.620000\pi$
$398$		0			0
$399$		0			0
$400$	−0.425779	−	0.904827i	−0.425779	−	0.904827i
$401$	0.473036	+	1.84235i	0.473036	+	1.84235i	0.535827	+	0.844328i	$0.320000\pi$
$401$	0.473036	+	1.84235i	0.473036	+	1.84235i	−0.0627905	+	0.998027i	$0.520000\pi$
$402$	−0.135174	−	0.0857841i	−0.135174	−	0.0857841i
$403$		0			0
$404$	0.309017	+	0.951057i	0.309017	+	0.951057i
$405$	1.23432			1.23432
$406$	1.52794	+	0.969661i	1.52794	+	0.969661i
$407$		0			0
$408$		0			0
$409$	−0.781202	−	1.23098i	−0.781202	−	1.23098i	−0.968583	−	0.248690i	$-0.920000\pi$
$409$	−0.781202	−	1.23098i	−0.781202	−	1.23098i	0.187381	−	0.982287i	$-0.440000\pi$
$410$	−0.227513	+	0.700215i	−0.227513	+	0.700215i
$411$		0			0
$412$	0.202793	−	1.60528i	0.202793	−	1.60528i
$413$		0			0
$414$		−	0.856009i		−	0.856009i
$415$	0.933237	+	1.69755i	0.933237	+	1.69755i
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		0.684547	−	0.728969i	$-0.260000\pi$
$419$		0			0		−0.684547	+	0.728969i	$0.740000\pi$
$420$	−0.870846	+	1.05267i	−0.870846	+	1.05267i
$421$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	−0.809017	−	0.587785i	$-0.800000\pi$
$421$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	0.309017	−	0.951057i	$-0.400000\pi$
$422$		0			0
$423$	−0.614163	−	0.742395i	−0.614163	−	0.742395i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−0.0648341	−	1.03051i	−0.0648341	−	1.03051i
$428$	−1.79538	+	0.226810i	−1.79538	+	0.226810i
$429$		0			0
$430$	−0.488570	−	0.0931997i	−0.488570	−	0.0931997i
$431$		0			0		−0.684547	−	0.728969i	$-0.740000\pi$
$431$		0			0		0.684547	+	0.728969i	$0.260000\pi$
$432$	0.476823	−	0.0299991i	0.476823	−	0.0299991i
$433$		0			0		−0.368125	−	0.929776i	$-0.620000\pi$
$433$		0			0		0.368125	+	0.929776i	$0.380000\pi$
$434$		0			0
$435$	2.00160	+	0.792491i	2.00160	+	0.792491i
$436$	−1.46560	+	0.476203i	−1.46560	+	0.476203i
$437$		0			0
$438$		0			0
$439$		0			0		0.982287	−	0.187381i	$-0.0600000\pi$
$439$		0			0		−0.982287	+	0.187381i	$0.940000\pi$
$440$		0			0
$441$	0.0898953	+	0.0230812i	0.0898953	+	0.0230812i
$442$		0			0
$443$	0.363271	+	0.500000i	0.363271	+	0.500000i	0.951057	−	0.309017i	$-0.100000\pi$
$443$	0.363271	+	0.500000i	0.363271	+	0.500000i	−0.587785	+	0.809017i	$0.700000\pi$
$444$		0			0
$445$	−1.11803	−	0.363271i	−1.11803	−	0.363271i
$446$	−1.51373	−	1.25227i	−1.51373	−	1.25227i
$447$	−0.476823	+	2.49959i	−0.476823	+	2.49959i
$448$	−0.629902	+	0.866986i	−0.629902	+	0.866986i
$449$	−1.53583	−	0.844328i	−1.53583	−	0.844328i	−0.535827	−	0.844328i	$-0.680000\pi$
$449$	−1.53583	−	0.844328i	−1.53583	−	0.844328i	−1.00000			$\pi$
$450$	−0.301210	+	0.547900i	−0.301210	+	0.547900i
$451$		0			0
$452$		0			0
$453$		0			0
$454$	−1.68532	+	1.06954i	−1.68532	+	1.06954i
$455$		0			0
$456$		0			0
$457$		0			0		−0.904827	−	0.425779i	$-0.860000\pi$
$457$		0			0		0.904827	+	0.425779i	$0.140000\pi$
$458$	0.356420	+	1.86842i	0.356420	+	1.86842i
$459$		0			0
$460$	−1.19975	−	0.659566i	−1.19975	−	0.659566i
$461$	1.06369	−	1.46404i	1.06369	−	1.46404i	0.187381	−	0.982287i	$-0.440000\pi$
$461$	1.06369	−	1.46404i	1.06369	−	1.46404i	0.876307	−	0.481754i	$-0.160000\pi$
$462$		0			0
$463$	−0.476203	−	0.393950i	−0.476203	−	0.393950i	0.368125	−	0.929776i	$-0.380000\pi$
$463$	−0.476203	−	0.393950i	−0.476203	−	0.393950i	−0.844328	+	0.535827i	$0.820000\pi$
$464$	1.60601	+	0.521823i	1.60601	+	0.521823i
$465$		0			0
$466$		0			0
$467$	0.233064	+	1.84489i	0.233064	+	1.84489i	0.481754	+	0.876307i	$0.340000\pi$
$467$	0.233064	+	1.84489i	0.233064	+	1.84489i	−0.248690	+	0.968583i	$0.580000\pi$
$468$		0			0
$469$	0.108877	+	0.0791038i	0.108877	+	0.0791038i
$470$	−1.51373	+	0.288760i	−1.51373	+	0.288760i
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		−0.982287	−	0.187381i	$-0.940000\pi$
$479$		0			0		0.982287	+	0.187381i	$0.0600000\pi$
$480$	−0.542804	+	1.15352i	−0.542804	+	1.15352i
$481$		0			0
$482$	0.0604991	+	0.961606i	0.0604991	+	0.961606i
$483$	−0.117447	+	1.86676i	−0.117447	+	1.86676i
$484$	−0.992115	−	0.125333i	−0.992115	−	0.125333i
$485$		0			0
$486$	−0.698489	−	0.844328i	−0.698489	−	0.844328i
$487$	1.85588	+	0.116762i	1.85588	+	0.116762i	0.951057	−	0.309017i	$-0.100000\pi$
$487$	1.85588	+	0.116762i	1.85588	+	0.116762i	0.904827	+	0.425779i	$0.140000\pi$
$488$	−0.297740	−	0.916350i	−0.297740	−	0.916350i
$489$	0.102049	−	0.123357i	0.102049	−	0.123357i
$490$	0.101615	−	0.108209i	0.101615	−	0.108209i
$491$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$491$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$492$	0.872693	−	0.345524i	0.872693	−	0.345524i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	0.909118	−	2.29617i	0.909118	−	2.29617i
$499$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$499$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$500$	0.535827	+	0.844328i	0.535827	+	0.844328i
$501$	−0.791374	−	1.68176i	−0.791374	−	1.68176i
$502$		0			0
$503$	1.47978	+	0.939097i	1.47978	+	0.939097i	0.998027	+	0.0627905i	$0.0200000\pi$
$503$	1.47978	+	0.939097i	1.47978	+	0.939097i	0.481754	+	0.876307i	$0.340000\pi$
$504$	0.670038			0.670038
$505$	−0.425779	−	0.904827i	−0.425779	−	0.904827i
$506$		0			0
$507$	−1.07639	−	0.683098i	−1.07639	−	0.683098i
$508$	0.402389	+	1.56720i	0.402389	+	1.56720i
$509$	0.824805	+	1.75280i	0.824805	+	1.75280i	0.637424	+	0.770513i	$0.280000\pi$
$509$	0.824805	+	1.75280i	0.824805	+	1.75280i	0.187381	+	0.982287i	$0.440000\pi$
$510$		0			0
$511$		0			0
$512$	−0.368125	+	0.929776i	−0.368125	+	0.929776i
$513$		0			0
$514$		0			0
$515$			1.61803i			1.61803i
$516$	0.305472	+	0.555652i	0.305472	+	0.555652i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−1.18532	+	1.43281i	−1.18532	+	1.43281i	−0.309017	+	0.951057i	$0.600000\pi$
$521$	−1.18532	+	1.43281i	−1.18532	+	1.43281i	−0.876307	+	0.481754i	$0.840000\pi$
$522$	−0.326263	−	1.00414i	−0.326263	−	1.00414i
$523$	1.74915	+	0.110048i	1.74915	+	0.110048i	0.904827	−	0.425779i	$-0.140000\pi$
$523$	1.74915	+	0.110048i	1.74915	+	0.110048i	0.844328	+	0.535827i	$0.180000\pi$
$524$		0			0
$525$	0.732044	−	1.15352i	0.732044	−	1.15352i
$526$	1.96858	+	0.248690i	1.96858	+	0.248690i
$527$		0			0
$528$		0			0
$529$	−0.867524	+	0.109594i	−0.867524	+	0.109594i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$	0.551699	+	1.39343i	0.551699	+	1.39343i
$535$	1.75280	−	0.450043i	1.75280	−	0.450043i
$536$	0.116762	+	0.0462295i	0.116762	+	0.0462295i
$537$		0			0
$538$	−1.31918	+	1.23879i	−1.31918	+	1.23879i
$539$		0			0
$540$	−0.469303	+	0.0895243i	−0.469303	+	0.0895243i
$541$	−1.50441	−	1.09302i	−1.50441	−	1.09302i	−0.968583	−	0.248690i	$-0.920000\pi$
$541$	−1.50441	−	1.09302i	−1.50441	−	1.09302i	−0.535827	−	0.844328i	$-0.680000\pi$
$542$		0			0
$543$	−0.309522	−	2.45012i	−0.309522	−	2.45012i
$544$		0			0
$545$	1.39436	−	0.656137i	1.39436	−	0.656137i
$546$		0			0
$547$	0.656137	+	0.542804i	0.656137	+	0.542804i	0.904827	−	0.425779i	$-0.140000\pi$
$547$	0.656137	+	0.542804i	0.656137	+	0.542804i	−0.248690	+	0.968583i	$0.580000\pi$
$548$		0			0
$549$	−0.354094	+	0.487369i	−0.354094	+	0.487369i
$550$		0			0
$551$		0			0
$552$	0.327053	+	1.71447i	0.327053	+	1.71447i
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$		0			0		−0.728969	−	0.684547i	$-0.760000\pi$
$557$		0			0		0.728969	+	0.684547i	$0.240000\pi$
$558$		0			0
$559$		0			0
$560$	0.516273	−	0.939097i	0.516273	−	0.939097i
$561$		0			0
$562$	−0.856954	+	1.17950i	−0.856954	+	1.17950i
$563$	−0.220280	+	1.15475i	−0.220280	+	1.15475i	0.684547	+	0.728969i	$0.260000\pi$
$563$	−0.220280	+	1.15475i	−0.220280	+	1.15475i	−0.904827	+	0.425779i	$0.860000\pi$
$564$	1.51373	+	1.25227i	1.51373	+	1.25227i
$565$		0			0
$566$	−0.666178	+	0.313480i	−0.666178	+	0.313480i
$567$	0.777498	+	1.07013i	0.777498	+	1.07013i
$568$		0			0
$569$	1.87631	+	0.481754i	1.87631	+	0.481754i	1.00000			$0$
$569$	1.87631	+	0.481754i	1.87631	+	0.481754i	0.876307	+	0.481754i	$0.160000\pi$
$570$		0			0
$571$		0			0		0.982287	−	0.187381i	$-0.0600000\pi$
$571$		0			0		−0.982287	+	0.187381i	$0.940000\pi$
$572$		0			0
$573$		0			0
$574$	−0.750387	+	0.243816i	−0.750387	+	0.243816i
$575$	1.27295	+	0.503997i	1.27295	+	0.503997i
$576$	0.605594	−	0.155490i	0.605594	−	0.155490i
$577$		0			0		−0.368125	−	0.929776i	$-0.620000\pi$
$577$		0			0		0.368125	+	0.929776i	$0.380000\pi$
$578$	0.998027	−	0.0627905i	0.998027	−	0.0627905i
$579$		0			0
$580$	−1.65875	−	0.316423i	−1.65875	−	0.316423i
$581$	−0.883906	+	1.87839i	−0.883906	+	1.87839i
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$	0.159781	+	0.193142i	0.159781	+	0.193142i	0.844328	−	0.535827i	$-0.180000\pi$
$587$	0.159781	+	0.193142i	0.159781	+	0.193142i	−0.684547	+	0.728969i	$0.740000\pi$
$588$	−0.188867	−	0.0118825i	−0.188867	−	0.0118825i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$		0			0		0.929776	−	0.368125i	$-0.120000\pi$
$593$		0			0		−0.929776	+	0.368125i	$0.880000\pi$
$594$		0			0
$595$		0			0
$596$		−	1.99605i		−	1.99605i
$597$		0			0
$598$		0			0
$599$		0			0		0.368125	−	0.929776i	$-0.380000\pi$
$599$		0			0		−0.368125	+	0.929776i	$0.620000\pi$
$600$	0.393950	−	1.21245i	0.393950	−	1.21245i
$601$	0.331159	+	0.521823i	0.331159	+	0.521823i	0.968583	−	0.248690i	$-0.0800000\pi$
$601$	0.331159	+	0.521823i	0.331159	+	0.521823i	−0.637424	+	0.770513i	$0.720000\pi$
$602$	−0.226948	−	0.482290i	−0.226948	−	0.482290i
$603$	−0.0195266	−	0.0760512i	−0.0195266	−	0.0760512i
$604$		0			0
$605$	1.00000			1.00000
$606$	−0.542804	+	1.15352i	−0.542804	+	1.15352i
$607$	−0.250666			−0.250666			−0.125333	−	0.992115i	$-0.540000\pi$
$607$	−0.250666			−0.250666			−0.125333	+	0.992115i	$0.540000\pi$
$608$		0			0
$609$	0.573736	+	2.23455i	0.573736	+	2.23455i
$610$	0.410241	+	0.871808i	0.410241	+	0.871808i
$611$		0			0
$612$		0			0
$613$		0			0		0.368125	−	0.929776i	$-0.380000\pi$
$613$		0			0		−0.368125	+	0.929776i	$0.620000\pi$
$614$	−0.211645	+	1.67534i	−0.211645	+	1.67534i
$615$	−0.822506	+	0.452177i	−0.822506	+	0.452177i
$616$		0			0
$617$		0			0		−0.481754	−	0.876307i	$-0.660000\pi$
$617$		0			0		0.481754	+	0.876307i	$0.340000\pi$
$618$	1.58937	−	1.31484i	1.58937	−	1.31484i
$619$		0			0		0.929776	−	0.368125i	$-0.120000\pi$
$619$		0			0		−0.929776	+	0.368125i	$0.880000\pi$
$620$		0			0
$621$	−0.447766	+	0.476823i	−0.447766	+	0.476823i
$622$		0			0
$623$	−0.389301	−	1.19815i	−0.389301	−	1.19815i
$624$		0			0
$625$	−0.637424	−	0.770513i	−0.637424	−	0.770513i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$	−0.664754	+	0.0839780i	−0.664754	+	0.0839780i
$631$		0			0		0.425779	−	0.904827i	$-0.360000\pi$
$631$		0			0		−0.425779	+	0.904827i	$0.640000\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−0.595638	−	1.50441i	−0.595638	−	1.50441i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$	0.248690	−	0.968583i	0.248690	−	0.968583i
$641$	−1.15475	+	0.220280i	−1.15475	+	0.220280i	−0.728969	−	0.684547i	$-0.760000\pi$
$641$	−1.15475	+	0.220280i	−1.15475	+	0.220280i	−0.425779	+	0.904827i	$0.640000\pi$
$642$	−1.86643	−	1.35604i	−1.86643	−	1.35604i
$643$		0			0		0.248690	−	0.968583i	$-0.420000\pi$
$643$		0			0		−0.248690	+	0.968583i	$0.580000\pi$
$644$	−0.183888	−	1.45563i	−0.183888	−	1.45563i
$645$	−0.372705	−	0.512984i	−0.372705	−	0.512984i
$646$		0			0
$647$	−0.356420	−	0.115808i	−0.356420	−	0.115808i	0.125333	−	0.992115i	$-0.460000\pi$
$647$	−0.356420	−	0.115808i	−0.356420	−	0.115808i	−0.481754	+	0.876307i	$0.660000\pi$
$648$	0.951057	+	0.786782i	0.951057	+	0.786782i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	−0.0604991	+	0.110048i	−0.0604991	+	0.110048i
$653$		0			0		−0.187381	−	0.982287i	$-0.560000\pi$
$653$		0			0		0.187381	+	0.982287i	$0.440000\pi$
$654$	−1.77760	−	0.836475i	−1.77760	−	0.836475i
$655$		0			0
$656$	−0.621636	+	0.394502i	−0.621636	+	0.394502i
$657$		0			0
$658$	−1.20385	−	1.13049i	−1.20385	−	1.13049i
$659$		0			0		−0.904827	−	0.425779i	$-0.860000\pi$
$659$		0			0		0.904827	+	0.425779i	$0.140000\pi$
$660$		0			0
$661$	0.120759	−	0.219661i	0.120759	−	0.219661i	−0.809017	−	0.587785i	$-0.800000\pi$
$661$	0.120759	−	0.219661i	0.120759	−	0.219661i	0.929776	+	0.368125i	$0.120000\pi$
$662$		0			0
$663$		0			0
$664$	−0.362989	+	1.90285i	−0.362989	+	1.90285i
$665$		0			0
$666$		0			0
$667$	−2.09190	+	0.984371i	−2.09190	+	0.984371i
$668$	0.856954	+	1.17950i	0.856954	+	1.17950i
$669$	−0.313901	−	2.48478i	−0.313901	−	2.48478i
$670$	−0.121636	−	0.0312307i	−0.121636	−	0.0312307i
$671$		0			0
$672$	−1.34200	+	0.255999i	−1.34200	+	0.255999i
$673$		0			0		0.248690	−	0.968583i	$-0.420000\pi$
$673$		0			0		−0.248690	+	0.968583i	$0.580000\pi$
$674$		0			0
$675$	0.454382	−	0.147638i	0.454382	−	0.147638i
$676$	0.929776	+	0.368125i	0.929776	+	0.368125i
$677$		0			0		0.968583	−	0.248690i	$-0.0800000\pi$
$677$		0			0		−0.968583	+	0.248690i	$0.920000\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−2.49959	−	0.476823i	−2.49959	−	0.476823i
$682$		0			0
$683$	−1.94908	+	0.246226i	−1.94908	+	0.246226i	−0.998027	−	0.0627905i	$-0.980000\pi$
$683$	−1.94908	+	0.246226i	−1.94908	+	0.246226i	−0.951057	+	0.309017i	$0.900000\pi$
$684$		0			0
$685$		0			0
$686$	−0.905380	−	0.114376i	−0.905380	−	0.114376i
$687$	−1.29933	+	2.04741i	−1.29933	+	2.04741i
$688$	−0.317042	−	0.383238i	−0.317042	−	0.383238i
$689$		0			0
$690$	−0.539354	−	1.65996i	−0.539354	−	1.65996i
$691$		0			0		0.637424	−	0.770513i	$-0.280000\pi$
$691$		0			0		−0.637424	+	0.770513i	$0.720000\pi$
$692$		0			0
$693$		0			0
$694$	−0.791759	+	0.313480i	−0.791759	+	0.313480i
$695$		0			0
$696$	1.03711	+	1.88650i	1.03711	+	1.88650i
$697$		0			0
$698$	−1.72157	+	0.946441i	−1.72157	+	0.946441i
$699$		0			0
$700$	−0.394502	+	0.996398i	−0.394502	+	0.996398i
$701$	−0.574633	+	1.76854i	−0.574633	+	1.76854i	0.0627905	+	0.998027i	$0.480000\pi$
$701$	−0.574633	+	1.76854i	−0.574633	+	1.76854i	−0.637424	+	0.770513i	$0.720000\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	−1.65875	−	1.05267i	−1.65875	−	1.05267i
$706$		0			0
$707$	0.516273	−	0.939097i	0.516273	−	0.939097i
$708$		0			0
$709$	−0.211645	−	0.134314i	−0.211645	−	0.134314i	0.425779	−	0.904827i	$-0.360000\pi$
$709$	−0.211645	−	0.134314i	−0.211645	−	0.134314i	−0.637424	+	0.770513i	$0.720000\pi$
$710$		0			0
$711$		0			0
$712$	−0.629902	−	0.992567i	−0.629902	−	0.992567i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		0.770513	−	0.637424i	$-0.220000\pi$
$719$		0			0		−0.770513	+	0.637424i	$0.780000\pi$
$720$	−0.581331	+	0.230165i	−0.581331	+	0.230165i
$721$	−1.40281	+	1.01920i	−1.40281	+	1.01920i
$722$	0.684547	−	0.728969i	0.684547	−	0.728969i
$723$	−0.782964	+	0.946441i	−0.782964	+	0.946441i
$724$	0.598617	+	1.84235i	0.598617	+	1.84235i
$725$	1.68532	+	0.106032i	1.68532	+	0.106032i
$726$	−0.812619	−	0.982287i	−0.812619	−	0.982287i
$727$	1.01920	−	1.60601i	1.01920	−	1.60601i	0.248690	−	0.968583i	$-0.420000\pi$
$727$	1.01920	−	1.60601i	1.01920	−	1.60601i	0.770513	−	0.637424i	$-0.220000\pi$
$728$		0			0
$729$	0.0102136	−	0.162341i	0.0102136	−	0.162341i
$730$		0			0
$731$		0			0
$732$	0.522996	−	1.11142i	0.522996	−	1.11142i
$733$		0			0		−0.982287	−	0.187381i	$-0.940000\pi$
$733$		0			0		0.982287	+	0.187381i	$0.0600000\pi$
$734$	0.804733	+	0.856954i	0.804733	+	0.856954i
$735$	0.188867	−	0.0118825i	0.188867	−	0.0118825i
$736$	−0.503997	−	1.27295i	−0.503997	−	1.27295i
$737$		0			0
$738$	0.428004	+	0.169459i	0.428004	+	0.169459i
$739$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$739$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−1.61484	−	1.17325i	−1.61484	−	1.17325i	−0.844328	−	0.535827i	$-0.820000\pi$
$743$	−1.61484	−	1.17325i	−1.61484	−	1.17325i	−0.770513	−	0.637424i	$-0.780000\pi$
$744$		0			0
$745$	0.250172	+	1.98031i	0.250172	+	1.98031i
$746$		0			0
$747$	1.09592	−	0.515699i	1.09592	−	0.515699i
$748$		0			0
$749$	1.49427	+	1.23617i	1.49427	+	1.23617i
$750$	−0.238883	+	1.25227i	−0.238883	+	1.25227i
$751$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$751$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$752$	−1.35041	−	0.742395i	−1.35041	−	0.742395i
$753$		0			0
$754$		0			0
$755$		0			0
$756$	−0.373231	−	0.350487i	−0.373231	−	0.350487i
$757$		0			0		0.844328	−	0.535827i	$-0.180000\pi$
$757$		0			0		−0.844328	+	0.535827i	$0.820000\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−0.371808	−	1.94908i	−0.371808	−	1.94908i	−0.309017	−	0.951057i	$-0.600000\pi$
$761$	−0.371808	−	1.94908i	−0.371808	−	1.94908i	−0.0627905	−	0.998027i	$-0.520000\pi$
$762$	−0.993736	+	1.80760i	−0.993736	+	1.80760i
$763$	1.44717	+	0.795590i	1.44717	+	0.795590i
$764$		0			0
$765$		0			0
$766$	−0.193142	−	0.159781i	−0.193142	−	0.159781i
$767$		0			0
$768$	−1.15352	+	0.542804i	−1.15352	+	0.542804i
$769$	−0.292352	−	0.402389i	−0.292352	−	0.402389i	0.637424	−	0.770513i	$-0.280000\pi$
$769$	−0.292352	−	0.402389i	−0.292352	−	0.402389i	−0.929776	+	0.368125i	$0.880000\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0		0.982287	−	0.187381i	$-0.0600000\pi$
$773$		0			0		−0.982287	+	0.187381i	$0.940000\pi$
$774$	−0.0773377	+	0.301210i	−0.0773377	+	0.301210i
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−0.343511	+	0.729998i	−0.343511	+	0.729998i
$784$	0.147271	−	0.0186046i	0.147271	−	0.0186046i
$785$		0			0
$786$		0			0
$787$	−0.955910	−	0.120759i	−0.955910	−	0.120759i	−0.368125	−	0.929776i	$-0.620000\pi$
$787$	−0.955910	−	0.120759i	−0.955910	−	0.120759i	−0.587785	+	0.809017i	$0.700000\pi$
$788$		0			0
$789$	1.61242	+	1.94908i	1.61242	+	1.94908i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.481754	−	0.876307i	$-0.660000\pi$
$797$		0			0		0.481754	+	0.876307i	$0.340000\pi$
$798$		0			0
$799$		0			0
$800$	−0.125333	+	0.992115i	−0.125333	+	0.992115i
$801$	−0.270575	+	0.683396i	−0.270575	+	0.683396i
$802$	0.587785	−	1.80902i	0.587785	−	1.80902i
$803$		0			0
$804$	0.0681659	+	0.144860i	0.0681659	+	0.144860i
$805$	0.364876	+	1.42110i	0.364876	+	1.42110i
$806$		0			0
$807$	−2.30703			−2.30703
$808$	0.248690	−	0.968583i	0.248690	−	0.968583i
$809$	1.07165			1.07165			0.535827	−	0.844328i	$-0.320000\pi$
$809$	1.07165			1.07165			0.535827	+	0.844328i	$0.320000\pi$
$810$	−1.04217	−	0.661379i	−1.04217	−	0.661379i
$811$		0			0		−0.248690	−	0.968583i	$-0.580000\pi$
$811$		0			0		0.248690	+	0.968583i	$0.420000\pi$
$812$	−0.770513	−	1.63742i	−0.770513	−	1.63742i
$813$		0			0
$814$		0			0
$815$	0.0462295	−	0.116762i	0.0462295	−	0.116762i
$816$		0			0
$817$		0			0
$818$			1.45794i			1.45794i
$819$		0			0
$820$	0.567290	−	0.469303i	0.567290	−	0.469303i
$821$	−1.35556	+	0.536702i	−1.35556	+	0.536702i	−0.929776	−	0.368125i	$-0.880000\pi$
$821$	−1.35556	+	0.536702i	−1.35556	+	0.536702i	−0.425779	+	0.904827i	$0.640000\pi$
$822$		0			0
$823$	0.998027	−	1.06279i	0.998027	−	1.06279i		−	1.00000i	$-0.5\pi$
$823$	0.998027	−	1.06279i	0.998027	−	1.06279i	0.998027	−	0.0627905i	$-0.0200000\pi$
$824$	−1.03137	+	1.24672i	−1.03137	+	1.24672i
$825$		0			0
$826$		0			0
$827$	0.872693	+	1.05491i	0.872693	+	1.05491i	0.998027	+	0.0627905i	$0.0200000\pi$
$827$	0.872693	+	1.05491i	0.872693	+	1.05491i	−0.125333	+	0.992115i	$0.540000\pi$
$828$	−0.458672	+	0.722752i	−0.458672	+	0.722752i
$829$	0.844844	+	0.106729i	0.844844	+	0.106729i	0.535827	−	0.844328i	$-0.320000\pi$
$829$	0.844844	+	0.106729i	0.844844	+	0.106729i	0.309017	+	0.951057i	$0.400000\pi$
$830$	0.121636	−	1.93334i	0.121636	−	1.93334i
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−0.998027	−	1.06279i	−0.998027	−	1.06279i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		−0.929776	−	0.368125i	$-0.880000\pi$
$839$		0			0		0.929776	+	0.368125i	$0.120000\pi$
$840$	1.29933	−	0.422178i	1.29933	−	0.422178i
$841$	−1.34973	+	1.26748i	−1.34973	+	1.26748i
$842$	−0.402389	+	1.56720i	−0.402389	+	1.56720i
$843$	−1.82573	+	0.348276i	−1.82573	+	0.348276i
$844$		0			0
$845$	−0.968583	−	0.248690i	−0.968583	−	0.248690i
$846$	0.120759	+	0.955910i	0.120759	+	0.955910i
$847$	0.629902	+	0.866986i	0.629902	+	0.866986i
$848$		0			0
$849$	−0.892667	−	0.290045i	−0.892667	−	0.290045i
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		−0.876307	−	0.481754i	$-0.840000\pi$
$853$		0			0		0.876307	+	0.481754i	$0.160000\pi$
$854$	−0.497433	+	0.904827i	−0.497433	+	0.904827i
$855$		0			0
$856$	1.63742	+	0.770513i	1.63742	+	0.770513i
$857$		0			0		−0.728969	−	0.684547i	$-0.760000\pi$
$857$		0			0		0.728969	+	0.684547i	$0.240000\pi$
$858$		0			0
$859$		0			0		0.844328	−	0.535827i	$-0.180000\pi$
$859$		0			0		−0.844328	+	0.535827i	$0.820000\pi$
$860$	0.362574	+	0.340480i	0.362574	+	0.340480i
$861$	−0.910129	−	0.428274i	−0.910129	−	0.428274i
$862$		0			0
$863$	0.895846	−	1.62954i	0.895846	−	1.62954i	0.125333	−	0.992115i	$-0.460000\pi$
$863$	0.895846	−	1.62954i	0.895846	−	1.62954i	0.770513	−	0.637424i	$-0.220000\pi$
$864$	−0.418669	−	0.230165i	−0.418669	−	0.230165i
$865$		0			0
$866$		0			0
$867$	0.982287	+	0.812619i	0.982287	+	0.812619i
$868$		0			0
$869$		0			0
$870$	−1.26537	−	1.74164i	−1.26537	−	1.74164i
$871$		0			0
$872$	1.49261	+	0.383238i	1.49261	+	0.383238i
$873$		0			0
$874$		0			0
$875$	0.266509	−	1.03799i	0.266509	−	1.03799i
$876$		0			0
$877$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$877$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	0.734796	−	0.0462295i	0.734796	−	0.0462295i	0.309017	−	0.951057i	$-0.400000\pi$
$881$	0.734796	−	0.0462295i	0.734796	−	0.0462295i	0.425779	+	0.904827i	$0.360000\pi$
$882$	−0.0635336	−	0.0676564i	−0.0635336	−	0.0676564i
$883$	1.82662	+	0.348445i	1.82662	+	0.348445i	0.982287	−	0.187381i	$-0.0600000\pi$
$883$	1.82662	+	0.348445i	1.82662	+	0.348445i	0.844328	+	0.535827i	$0.180000\pi$
$884$		0			0
$885$		0			0
$886$	−0.0388067	−	0.616814i	−0.0388067	−	0.616814i
$887$	0.106032	−	1.68532i	0.106032	−	1.68532i	−0.481754	−	0.876307i	$-0.660000\pi$
$887$	0.106032	−	1.68532i	0.106032	−	1.68532i	0.587785	−	0.809017i	$-0.300000\pi$
$888$		0			0
$889$	0.929109	−	1.46404i	0.929109	−	1.46404i
$890$	0.749337	+	0.905793i	0.749337	+	0.905793i
$891$		0			0
$892$	0.607087	+	1.86842i	0.607087	+	1.86842i
$893$		0			0
$894$	1.74194	−	1.85498i	1.74194	−	1.85498i
$895$		0			0
$896$	0.996398	−	0.394502i	0.996398	−	0.394502i
$897$		0			0
$898$	0.844328	+	1.53583i	0.844328	+	1.53583i
$899$		0			0
$900$	0.547900	−	0.301210i	0.547900	−	0.301210i
$901$		0			0
$902$		0			0
$903$	0.209983	−	0.646260i	0.209983	−	0.646260i
$904$		0			0
$905$	−0.824805	−	1.75280i	−0.824805	−	1.75280i
$906$		0			0
$907$	0.316423	+	0.200808i	0.316423	+	0.200808i	0.684547	−	0.728969i	$-0.260000\pi$
$907$	0.316423	+	0.200808i	0.316423	+	0.200808i	−0.368125	+	0.929776i	$0.620000\pi$
$908$	1.99605			1.99605
$909$	−0.581331	+	0.230165i	−0.581331	+	0.230165i
$910$		0			0
$911$		0			0		−0.844328	−	0.535827i	$-0.820000\pi$
$911$		0			0		0.844328	+	0.535827i	$0.180000\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	−0.379573	+	1.16821i	−0.379573	+	1.16821i
$916$	0.700215	−	1.76854i	0.700215	−	1.76854i
$917$		0			0
$918$		0			0
$919$		0			0			−	1.00000i	$-0.5\pi$
$919$		0			0				1.00000i	$0.5\pi$
$920$	0.659566	+	1.19975i	0.659566	+	1.19975i
$921$	−1.65875	+	1.37223i	−1.65875	+	1.37223i
$922$	−1.68257	+	0.666178i	−1.68257	+	0.666178i
$923$		0			0
$924$		0			0
$925$		0			0
$926$	0.190983	+	0.587785i	0.190983	+	0.587785i
$927$	1.00966	+	0.0635224i	1.00966	+	0.0635224i
$928$	−1.07639	−	1.30113i	−1.07639	−	1.30113i
$929$	−0.996398	+	1.57007i	−0.996398	+	1.57007i	−0.187381	+	0.982287i	$0.560000\pi$
$929$	−0.996398	+	1.57007i	−0.996398	+	1.57007i	−0.809017	+	0.587785i	$0.800000\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$	0.791759	−	1.68257i	0.791759	−	1.68257i
$935$		0			0
$936$		0			0
$937$		0			0		0.998027	−	0.0627905i	$-0.0200000\pi$
$937$		0			0		−0.998027	+	0.0627905i	$0.980000\pi$
$938$	−0.0495420	−	0.125129i	−0.0495420	−	0.125129i
$939$		0			0
$940$	1.43281	+	0.567290i	1.43281	+	0.567290i
$941$	1.89836	−	0.616814i	1.89836	−	0.616814i	0.929776	−	0.368125i	$-0.120000\pi$
$941$	1.89836	−	0.616814i	1.89836	−	0.616814i	0.968583	−	0.248690i	$-0.0800000\pi$
$942$		0			0
$943$	0.250678	−	0.976326i	0.250678	−	0.976326i
$944$		0			0
$945$	0.414216	+	0.300945i	0.414216	+	0.300945i
$946$		0			0
$947$	0.0469702	+	0.371808i	0.0469702	+	0.371808i	0.998027	+	0.0627905i	$0.0200000\pi$
$947$	0.0469702	+	0.371808i	0.0469702	+	0.371808i	−0.951057	+	0.309017i	$0.900000\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$953$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	1.07639	−	0.683098i	1.07639	−	0.683098i
$961$	0.728969	+	0.684547i	0.728969	+	0.684547i
$962$		0			0
$963$	−0.212015	−	1.11142i	−0.212015	−	1.11142i
$964$	0.464173	−	0.844328i	0.464173	−	0.844328i
$965$		0			0
$966$	1.09942	−	1.51323i	1.09942	−	1.51323i
$967$	−0.0469702	+	0.246226i	−0.0469702	+	0.246226i	−0.998027	−	0.0627905i	$-0.980000\pi$
$967$	−0.0469702	+	0.246226i	−0.0469702	+	0.246226i	0.951057	+	0.309017i	$0.100000\pi$
$968$	0.770513	+	0.637424i	0.770513	+	0.637424i
$969$		0			0
$970$		0			0
$971$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$971$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$972$	0.137340	+	1.08716i	0.137340	+	1.08716i
$973$		0			0
$974$	−1.50441	−	1.09302i	−1.50441	−	1.09302i
$975$		0			0
$976$	−0.239615	+	0.933237i	−0.239615	+	0.933237i
$977$		0			0		0.728969	−	0.684547i	$-0.240000\pi$
$977$		0			0		−0.728969	+	0.684547i	$0.760000\pi$
$978$	−0.152261	+	0.0494726i	−0.152261	+	0.0494726i
$979$		0			0
$980$	−0.143778	+	0.0369159i	−0.143778	+	0.0369159i
$981$	−0.354691	−	0.895846i	−0.354691	−	0.895846i
$982$		0			0
$983$	1.27295	+	1.35556i	1.27295	+	1.35556i	0.904827	+	0.425779i	$0.140000\pi$
$983$	1.27295	+	1.35556i	1.27295	+	1.35556i	0.368125	+	0.929776i	$0.380000\pi$
$984$	−0.921980	−	0.175877i	−0.921980	−	0.175877i
$985$		0			0
$986$		0			0
$987$	−0.132196	−	2.10119i	−0.132196	−	2.10119i
$988$		0			0
$989$	0.675590	+	0.0853469i	0.675590	+	0.0853469i
$990$		0			0
$991$		0			0		−0.637424	−	0.770513i	$-0.720000\pi$
$991$		0			0		0.637424	+	0.770513i	$0.280000\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$	−1.99794	+	1.45159i	−1.99794	+	1.45159i
$997$		0			0		0.929776	−	0.368125i	$-0.120000\pi$
$997$		0			0		−0.929776	+	0.368125i	$0.880000\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2020.1.bt.c.1059.1	yes	40
4.3	odd	2	inner	2020.1.bt.c.1059.2	yes	40
5.4	even	2	inner	2020.1.bt.c.1059.2	yes	40
20.19	odd	2	CM	2020.1.bt.c.1059.1	yes	40
101.33	even	50	inner	2020.1.bt.c.639.1	✓	40
404.235	odd	50	inner	2020.1.bt.c.639.2	yes	40
505.134	even	50	inner	2020.1.bt.c.639.2	yes	40
2020.639	odd	50	inner	2020.1.bt.c.639.1	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2020.1.bt.c.639.1	✓	40	101.33	even	50	inner
2020.1.bt.c.639.1	✓	40	2020.639	odd	50	inner
2020.1.bt.c.639.2	yes	40	404.235	odd	50	inner
2020.1.bt.c.639.2	yes	40	505.134	even	50	inner
2020.1.bt.c.1059.1	yes	40	1.1	even	1	trivial
2020.1.bt.c.1059.1	yes	40	20.19	odd	2	CM
2020.1.bt.c.1059.2	yes	40	4.3	odd	2	inner
2020.1.bt.c.1059.2	yes	40	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2020 = 2^{2} \cdot 5 \cdot 101 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2020.bt (of order \(50\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.844328 - 0.535827i) q^{2} +(-0.317042 - 1.23480i) q^{3} +(0.425779 + 0.904827i) q^{4} +(-0.535827 - 0.844328i) q^{5} +(-0.393950 + 1.21245i) q^{6} +(0.394502 - 0.996398i) q^{7} +(0.125333 - 0.992115i) q^{8} +(-0.547900 + 0.301210i) q^{9} +O(q^{10})\)	\(q+(-0.844328 - 0.535827i) q^{2} +(-0.317042 - 1.23480i) q^{3} +(0.425779 + 0.904827i) q^{4} +(-0.535827 - 0.844328i) q^{5} +(-0.393950 + 1.21245i) q^{6} +(0.394502 - 0.996398i) q^{7} +(0.125333 - 0.992115i) q^{8} +(-0.547900 + 0.301210i) q^{9} +1.00000i q^{10} +(0.982287 - 0.812619i) q^{12} +(-0.866986 + 0.629902i) q^{14} +(-0.872693 + 0.929324i) q^{15} +(-0.637424 + 0.770513i) q^{16} +(0.624004 + 0.0392590i) q^{18} +(0.535827 - 0.844328i) q^{20} +(-1.35542 - 0.171230i) q^{21} +(-0.0859661 - 1.36639i) q^{23} +(-1.26480 + 0.159781i) q^{24} +(-0.425779 + 0.904827i) q^{25} +(-0.327053 - 0.348276i) q^{27} +(1.06954 - 0.0672897i) q^{28} +(-0.621636 - 1.57007i) q^{29} +(1.23480 - 0.317042i) q^{30} +(0.951057 - 0.309017i) q^{32} +(-1.05267 + 0.200808i) q^{35} +(-0.505828 - 0.367505i) q^{36} +(-0.904827 + 0.425779i) q^{40} +(0.700215 + 0.227513i) q^{41} +(1.05267 + 0.870846i) q^{42} +(-0.0931997 + 0.488570i) q^{43} +(0.547900 + 0.301210i) q^{45} +(-0.659566 + 1.19975i) q^{46} +(0.288760 + 1.51373i) q^{47} +(1.15352 + 0.542804i) q^{48} +(-0.108209 - 0.101615i) q^{49} +(0.844328 - 0.535827i) q^{50} +(0.0895243 + 0.469303i) q^{54} +(-0.939097 - 0.516273i) q^{56} +(-0.316423 + 1.65875i) q^{58} +(-1.21245 - 0.393950i) q^{60} +(0.871808 - 0.410241i) q^{61} +(0.0839780 + 0.664754i) q^{63} +(-0.968583 - 0.248690i) q^{64} +(-0.0312307 + 0.121636i) q^{67} +(-1.65996 + 0.539354i) q^{69} +(0.996398 + 0.394502i) q^{70} +(0.230165 + 0.581331i) q^{72} +(1.25227 + 0.238883i) q^{75} +(0.992115 + 0.125333i) q^{80} +(-0.661379 + 1.04217i) q^{81} +(-0.469303 - 0.567290i) q^{82} +(-1.93334 - 0.121636i) q^{83} +(-0.422178 - 1.29933i) q^{84} +(0.340480 - 0.362574i) q^{86} +(-1.74164 + 1.26537i) q^{87} +(0.905793 - 0.749337i) q^{89} +(-0.301210 - 0.547900i) q^{90} +(1.19975 - 0.659566i) q^{92} +(0.567290 - 1.43281i) q^{94} +(-0.683098 - 1.07639i) q^{96} +(0.0369159 + 0.143778i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 10 q^{9}+O(q^{10}) \) 40 * q + 10 * q^9	\( 40 q + 10 q^{9} - 40 q^{21} - 10 q^{29} + 10 q^{30} - 10 q^{36} - 10 q^{45} - 10 q^{46} + 10 q^{49} + 10 q^{54} + 10 q^{61} + 10 q^{70} - 10 q^{81} + 30 q^{84} + 10 q^{94} - 10 q^{96}+O(q^{100}) \) 40 * q + 10 * q^9 - 40 * q^21 - 10 * q^29 + 10 * q^30 - 10 * q^36 - 10 * q^45 - 10 * q^46 + 10 * q^49 + 10 * q^54 + 10 * q^61 + 10 * q^70 - 10 * q^81 + 30 * q^84 + 10 * q^94 - 10 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more