LMFDB - Embedded newform 2020.1.bu.a.1179.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2020,1,Mod(19,2020)]

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, 48]))

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

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

chi := DirichletCharacter("2020.19");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 2020 = 2^{2} \cdot 5 \cdot 101 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2020.bu (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:	$20$
Coefficient field:	$\Q(\zeta_{50})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{15} + x^{10} - x^{5} + 1 $ x^20 - x^15 + x^10 - x^5 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{25}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{25} - \cdots)$

Embedding invariants

Embedding label			1179.1
Root			$-0.0627905 - 0.998027i$ of defining polynomial
Character	$\chi$	$=$	2020.1179
Dual form			2020.1.bu.a.759.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.535827 + 0.844328i) q^{2} +(-1.23480 - 0.317042i) q^{3} +(-0.425779 + 0.904827i) q^{4} +(0.535827 - 0.844328i) q^{5} +(-0.393950 - 1.21245i) q^{6} +(-0.996398 + 0.394502i) q^{7} +(-0.992115 + 0.125333i) q^{8} +(0.547900 + 0.301210i) q^{9} +O(q^{10})$	\(q+(0.535827 + 0.844328i) q^{2} +(-1.23480 - 0.317042i) q^{3} +(-0.425779 + 0.904827i) q^{4} +(0.535827 - 0.844328i) q^{5} +(-0.393950 - 1.21245i) q^{6} +(-0.996398 + 0.394502i) q^{7} +(-0.992115 + 0.125333i) q^{8} +(0.547900 + 0.301210i) q^{9} +1.00000 q^{10} +(0.812619 - 0.982287i) q^{12} +(-0.866986 - 0.629902i) q^{14} +(-0.929324 + 0.872693i) q^{15} +(-0.637424 - 0.770513i) q^{16} +(0.0392590 + 0.624004i) q^{18} +(0.535827 + 0.844328i) q^{20} +(1.35542 - 0.171230i) q^{21} +(0.0915446 - 1.45506i) q^{23} +(1.26480 + 0.159781i) q^{24} +(-0.425779 - 0.904827i) q^{25} +(0.348276 + 0.327053i) q^{27} +(0.0672897 - 1.06954i) q^{28} +(-0.996398 - 0.394502i) q^{29} +(-1.23480 - 0.317042i) q^{30} +(0.309017 - 0.951057i) q^{32} +(-0.200808 + 1.05267i) q^{35} +(-0.505828 + 0.367505i) q^{36} +(-0.425779 + 0.904827i) q^{40} +(-0.574633 - 1.76854i) q^{41} +(0.870846 + 1.05267i) q^{42} +(-0.362989 - 1.90285i) q^{43} +(0.547900 - 0.301210i) q^{45} +(1.27760 - 0.702367i) q^{46} +(0.238883 - 1.25227i) q^{47} +(0.542804 + 1.15352i) q^{48} +(0.108209 - 0.101615i) q^{49} +(0.535827 - 0.844328i) q^{50} +(-0.0895243 + 0.469303i) q^{54} +(0.939097 - 0.516273i) q^{56} +(-0.200808 - 1.05267i) q^{58} +(-0.393950 - 1.21245i) q^{60} +(-0.746226 + 1.58581i) q^{61} +(-0.664754 - 0.0839780i) q^{63} +(0.968583 - 0.248690i) q^{64} +(0.121636 - 0.0312307i) q^{67} +(-0.574354 + 1.76768i) q^{69} +(-0.996398 + 0.394502i) q^{70} +(-0.581331 - 0.230165i) q^{72} +(0.238883 + 1.25227i) q^{75} +(-0.992115 + 0.125333i) q^{80} +(-0.661379 - 1.04217i) q^{81} +(1.18532 - 1.43281i) q^{82} +(0.121636 + 1.93334i) q^{83} +(-0.422178 + 1.29933i) q^{84} +(1.41213 - 1.32608i) q^{86} +(1.10528 + 0.803030i) q^{87} +(1.03137 - 1.24672i) q^{89} +(0.547900 + 0.301210i) q^{90} +(1.27760 + 0.702367i) q^{92} +(1.18532 - 0.469303i) q^{94} +(-0.683098 + 1.07639i) q^{96} +(0.143778 + 0.0369159i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 5 q^{3} - 5 q^{7} - 5 q^{9}+O(q^{10}) $ 20 * q - 5 * q^3 - 5 * q^7 - 5 * q^9	$ 20 q - 5 q^{3} - 5 q^{7} - 5 q^{9} + 20 q^{10} + 20 q^{12} + 20 q^{21} - 5 q^{27} - 5 q^{28} - 5 q^{29} - 5 q^{30} - 5 q^{32} - 5 q^{36} - 5 q^{45} - 5 q^{46} - 5 q^{49} - 5 q^{54} - 5 q^{61} - 5 q^{63} - 5 q^{67} - 5 q^{70} - 5 q^{81} - 5 q^{82} - 5 q^{83} + 15 q^{84} - 10 q^{87} - 5 q^{90} - 5 q^{92} - 5 q^{94} - 5 q^{96}+O(q^{100}) $ 20 * q - 5 * q^3 - 5 * q^7 - 5 * q^9 + 20 * q^10 + 20 * q^12 + 20 * q^21 - 5 * q^27 - 5 * q^28 - 5 * q^29 - 5 * q^30 - 5 * q^32 - 5 * q^36 - 5 * q^45 - 5 * q^46 - 5 * q^49 - 5 * q^54 - 5 * q^61 - 5 * q^63 - 5 * q^67 - 5 * q^70 - 5 * q^81 - 5 * q^82 - 5 * q^83 + 15 * q^84 - 10 * q^87 - 5 * q^90 - 5 * q^92 - 5 * q^94 - 5 * q^96

Display 100 coefficients 10 coefficients

Character values

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

$n$	$1011$	$1617$	$1921$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{8}{25}\right)$

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 $

$2$	0.535827	+	0.844328i	0.535827	+	0.844328i
$2$	0.535827	+	0.844328i	0.535827	+	0.844328i
$3$	−1.23480	−	0.317042i	−1.23480	−	0.317042i	−0.425779	−	0.904827i	$-0.640000\pi$
$3$	−1.23480	−	0.317042i	−1.23480	−	0.317042i	−0.809017	+	0.587785i	$0.800000\pi$
$4$	−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
$7$	−0.996398	+	0.394502i	−0.996398	+	0.394502i	−0.809017	−	0.587785i	$-0.800000\pi$
$7$	−0.996398	+	0.394502i	−0.996398	+	0.394502i	−0.187381	+	0.982287i	$0.560000\pi$
$8$	−0.992115	+	0.125333i	−0.992115	+	0.125333i
$9$	0.547900	+	0.301210i	0.547900	+	0.301210i
$10$	1.00000			1.00000
$11$		0			0		−0.876307	−	0.481754i	$-0.840000\pi$
$11$		0			0		0.876307	+	0.481754i	$0.160000\pi$
$12$	0.812619	−	0.982287i	0.812619	−	0.982287i
$13$		0			0		−0.929776	−	0.368125i	$-0.880000\pi$
$13$		0			0		0.929776	+	0.368125i	$0.120000\pi$
$14$	−0.866986	−	0.629902i	−0.866986	−	0.629902i
$15$	−0.929324	+	0.872693i	−0.929324	+	0.872693i
$16$	−0.637424	−	0.770513i	−0.637424	−	0.770513i
$17$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$17$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$18$	0.0392590	+	0.624004i	0.0392590	+	0.624004i
$19$		0			0		0.637424	−	0.770513i	$-0.280000\pi$
$19$		0			0		−0.637424	+	0.770513i	$0.720000\pi$
$20$	0.535827	+	0.844328i	0.535827	+	0.844328i
$21$	1.35542	−	0.171230i	1.35542	−	0.171230i
$22$		0			0
$23$	0.0915446	−	1.45506i	0.0915446	−	1.45506i	−0.637424	−	0.770513i	$-0.720000\pi$
$23$	0.0915446	−	1.45506i	0.0915446	−	1.45506i	0.728969	−	0.684547i	$-0.240000\pi$
$24$	1.26480	+	0.159781i	1.26480	+	0.159781i
$25$	−0.425779	−	0.904827i	−0.425779	−	0.904827i
$26$		0			0
$27$	0.348276	+	0.327053i	0.348276	+	0.327053i
$28$	0.0672897	−	1.06954i	0.0672897	−	1.06954i
$29$	−0.996398	−	0.394502i	−0.996398	−	0.394502i	−0.187381	−	0.982287i	$-0.560000\pi$
$29$	−0.996398	−	0.394502i	−0.996398	−	0.394502i	−0.809017	+	0.587785i	$0.800000\pi$
$30$	−1.23480	−	0.317042i	−1.23480	−	0.317042i
$31$		0			0		0.929776	−	0.368125i	$-0.120000\pi$
$31$		0			0		−0.929776	+	0.368125i	$0.880000\pi$
$32$	0.309017	−	0.951057i	0.309017	−	0.951057i
$33$		0			0
$34$		0			0
$35$	−0.200808	+	1.05267i	−0.200808	+	1.05267i
$36$	−0.505828	+	0.367505i	−0.505828	+	0.367505i
$37$		0			0		0.968583	−	0.248690i	$-0.0800000\pi$
$37$		0			0		−0.968583	+	0.248690i	$0.920000\pi$
$38$		0			0
$39$		0			0
$40$	−0.425779	+	0.904827i	−0.425779	+	0.904827i
$41$	−0.574633	−	1.76854i	−0.574633	−	1.76854i	−0.637424	−	0.770513i	$-0.720000\pi$
$41$	−0.574633	−	1.76854i	−0.574633	−	1.76854i	0.0627905	−	0.998027i	$-0.480000\pi$
$42$	0.870846	+	1.05267i	0.870846	+	1.05267i
$43$	−0.362989	−	1.90285i	−0.362989	−	1.90285i	−0.425779	−	0.904827i	$-0.640000\pi$
$43$	−0.362989	−	1.90285i	−0.362989	−	1.90285i	0.0627905	−	0.998027i	$-0.480000\pi$
$44$		0			0
$45$	0.547900	−	0.301210i	0.547900	−	0.301210i
$46$	1.27760	−	0.702367i	1.27760	−	0.702367i
$47$	0.238883	−	1.25227i	0.238883	−	1.25227i	−0.637424	−	0.770513i	$-0.720000\pi$
$47$	0.238883	−	1.25227i	0.238883	−	1.25227i	0.876307	−	0.481754i	$-0.160000\pi$
$48$	0.542804	+	1.15352i	0.542804	+	1.15352i
$49$	0.108209	−	0.101615i	0.108209	−	0.101615i
$50$	0.535827	−	0.844328i	0.535827	−	0.844328i
$51$		0			0
$52$		0			0
$53$		0			0		−0.425779	−	0.904827i	$-0.640000\pi$
$53$		0			0		0.425779	+	0.904827i	$0.360000\pi$
$54$	−0.0895243	+	0.469303i	−0.0895243	+	0.469303i
$55$		0			0
$56$	0.939097	−	0.516273i	0.939097	−	0.516273i
$57$		0			0
$58$	−0.200808	−	1.05267i	−0.200808	−	1.05267i
$59$		0			0		−0.637424	−	0.770513i	$-0.720000\pi$
$59$		0			0		0.637424	+	0.770513i	$0.280000\pi$
$60$	−0.393950	−	1.21245i	−0.393950	−	1.21245i
$61$	−0.746226	+	1.58581i	−0.746226	+	1.58581i	0.0627905	+	0.998027i	$0.480000\pi$
$61$	−0.746226	+	1.58581i	−0.746226	+	1.58581i	−0.809017	+	0.587785i	$0.800000\pi$
$62$		0			0
$63$	−0.664754	−	0.0839780i	−0.664754	−	0.0839780i
$64$	0.968583	−	0.248690i	0.968583	−	0.248690i
$65$		0			0
$66$		0			0
$67$	0.121636	−	0.0312307i	0.121636	−	0.0312307i	−0.187381	−	0.982287i	$-0.560000\pi$
$67$	0.121636	−	0.0312307i	0.121636	−	0.0312307i	0.309017	+	0.951057i	$0.400000\pi$
$68$		0			0
$69$	−0.574354	+	1.76768i	−0.574354	+	1.76768i
$70$	−0.996398	+	0.394502i	−0.996398	+	0.394502i
$71$		0			0		−0.968583	−	0.248690i	$-0.920000\pi$
$71$		0			0		0.968583	+	0.248690i	$0.0800000\pi$
$72$	−0.581331	−	0.230165i	−0.581331	−	0.230165i
$73$		0			0		0.0627905	−	0.998027i	$-0.480000\pi$
$73$		0			0		−0.0627905	+	0.998027i	$0.520000\pi$
$74$		0			0
$75$	0.238883	+	1.25227i	0.238883	+	1.25227i
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		−0.0627905	−	0.998027i	$-0.520000\pi$
$79$		0			0		0.0627905	+	0.998027i	$0.480000\pi$
$80$	−0.992115	+	0.125333i	−0.992115	+	0.125333i
$81$	−0.661379	−	1.04217i	−0.661379	−	1.04217i
$82$	1.18532	−	1.43281i	1.18532	−	1.43281i
$83$	0.121636	+	1.93334i	0.121636	+	1.93334i	0.309017	+	0.951057i	$0.400000\pi$
$83$	0.121636	+	1.93334i	0.121636	+	1.93334i	−0.187381	+	0.982287i	$0.560000\pi$
$84$	−0.422178	+	1.29933i	−0.422178	+	1.29933i
$85$		0			0
$86$	1.41213	−	1.32608i	1.41213	−	1.32608i
$87$	1.10528	+	0.803030i	1.10528	+	0.803030i
$88$		0			0
$89$	1.03137	−	1.24672i	1.03137	−	1.24672i	0.0627905	−	0.998027i	$-0.480000\pi$
$89$	1.03137	−	1.24672i	1.03137	−	1.24672i	0.968583	−	0.248690i	$-0.0800000\pi$
$90$	0.547900	+	0.301210i	0.547900	+	0.301210i
$91$		0			0
$92$	1.27760	+	0.702367i	1.27760	+	0.702367i
$93$		0			0
$94$	1.18532	−	0.469303i	1.18532	−	0.469303i
$95$		0			0
$96$	−0.683098	+	1.07639i	−0.683098	+	1.07639i
$97$		0			0		0.425779	−	0.904827i	$-0.360000\pi$
$97$		0			0		−0.425779	+	0.904827i	$0.640000\pi$
$98$	0.143778	+	0.0369159i	0.143778	+	0.0369159i
$99$		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
$103$	−0.866986	−	1.36615i	−0.866986	−	1.36615i	−0.929776	−	0.368125i	$-0.880000\pi$
$103$	−0.866986	−	1.36615i	−0.866986	−	1.36615i	0.0627905	−	0.998027i	$-0.480000\pi$
$104$		0			0
$105$	0.581698	−	1.23617i	0.581698	−	1.23617i
$106$		0			0
$107$	−0.263146	−	0.809880i	−0.263146	−	0.809880i	−0.992115	−	0.125333i	$-0.960000\pi$
$107$	−0.263146	−	0.809880i	−0.263146	−	0.809880i	0.728969	−	0.684547i	$-0.240000\pi$
$108$	−0.444215	+	0.175877i	−0.444215	+	0.175877i
$109$	1.26480	−	0.159781i	1.26480	−	0.159781i	0.535827	−	0.844328i	$-0.320000\pi$
$109$	1.26480	−	0.159781i	1.26480	−	0.159781i	0.728969	+	0.684547i	$0.240000\pi$
$110$		0			0
$111$		0			0
$112$	0.939097	+	0.516273i	0.939097	+	0.516273i
$113$		0			0		0.637424	−	0.770513i	$-0.280000\pi$
$113$		0			0		−0.637424	+	0.770513i	$0.720000\pi$
$114$		0			0
$115$	−1.17950	−	0.856954i	−1.17950	−	0.856954i
$116$	0.781202	−	0.733597i	0.781202	−	0.733597i
$117$		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
$122$	−1.73879	+	0.219661i	−1.73879	+	0.219661i
$123$	0.148854	+	2.36597i	0.148854	+	2.36597i
$124$		0			0
$125$	−0.992115	−	0.125333i	−0.992115	−	0.125333i
$126$	−0.285288	−	0.606268i	−0.285288	−	0.606268i
$127$	0.303189	+	1.58937i	0.303189	+	1.58937i	0.728969	+	0.684547i	$0.240000\pi$
$127$	0.303189	+	1.58937i	0.303189	+	1.58937i	−0.425779	+	0.904827i	$0.640000\pi$
$128$	0.728969	+	0.684547i	0.728969	+	0.684547i
$129$	−0.155067	+	2.46472i	−0.155067	+	2.46472i
$130$		0			0
$131$		0			0		−0.968583	−	0.248690i	$-0.920000\pi$
$131$		0			0		0.968583	+	0.248690i	$0.0800000\pi$
$132$		0			0
$133$		0			0
$134$	0.0915446	+	0.0859661i	0.0915446	+	0.0859661i
$135$	0.462756	−	0.118815i	0.462756	−	0.118815i
$136$		0			0
$137$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$137$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$138$	−1.80026	+	0.462227i	−1.80026	+	0.462227i
$139$		0			0		−0.992115	−	0.125333i	$-0.960000\pi$
$139$		0			0		0.992115	+	0.125333i	$0.0400000\pi$
$140$	−0.866986	−	0.629902i	−0.866986	−	0.629902i
$141$	−0.691992	+	1.47056i	−0.691992	+	1.47056i
$142$		0			0
$143$		0			0
$144$	−0.117158	−	0.614163i	−0.117158	−	0.614163i
$145$	−0.866986	+	0.629902i	−0.866986	+	0.629902i
$146$		0			0
$147$	−0.165832	+	0.0911672i	−0.165832	+	0.0911672i
$148$		0			0
$149$	−0.0534698	−	0.113629i	−0.0534698	−	0.113629i	0.876307	−	0.481754i	$-0.160000\pi$
$149$	−0.0534698	−	0.113629i	−0.0534698	−	0.113629i	−0.929776	+	0.368125i	$0.880000\pi$
$150$	−0.929324	+	0.872693i	−0.929324	+	0.872693i
$151$		0			0		0.535827	−	0.844328i	$-0.320000\pi$
$151$		0			0		−0.535827	+	0.844328i	$0.680000\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.876307	−	0.481754i	$-0.160000\pi$
$157$		0			0		−0.876307	+	0.481754i	$0.840000\pi$
$158$		0			0
$159$		0			0
$160$	−0.637424	−	0.770513i	−0.637424	−	0.770513i
$161$	0.482809	+	1.48593i	0.482809	+	1.48593i
$162$	0.525546	−	1.11684i	0.525546	−	1.11684i
$163$	−0.101597	−	0.0738147i	−0.101597	−	0.0738147i	0.535827	−	0.844328i	$-0.320000\pi$
$163$	−0.101597	−	0.0738147i	−0.101597	−	0.0738147i	−0.637424	+	0.770513i	$0.720000\pi$
$164$	1.84489	+	0.233064i	1.84489	+	0.233064i
$165$		0			0
$166$	−1.56720	+	1.13864i	−1.56720	+	1.13864i
$167$	−0.273190	+	1.43211i	−0.273190	+	1.43211i	0.535827	+	0.844328i	$0.320000\pi$
$167$	−0.273190	+	1.43211i	−0.273190	+	1.43211i	−0.809017	+	0.587785i	$0.800000\pi$
$168$	−1.32327	+	0.339759i	−1.32327	+	0.339759i
$169$	0.728969	+	0.684547i	0.728969	+	0.684547i
$170$		0			0
$171$		0			0
$172$	1.87631	+	0.481754i	1.87631	+	0.481754i
$173$		0			0		−0.929776	−	0.368125i	$-0.880000\pi$
$173$		0			0		0.929776	+	0.368125i	$0.120000\pi$
$174$	−0.0857841	+	1.36350i	−0.0857841	+	1.36350i
$175$	0.781202	+	0.733597i	0.781202	+	0.733597i
$176$		0			0
$177$		0			0
$178$	1.60528	+	0.202793i	1.60528	+	0.202793i
$179$		0			0		0.0627905	−	0.998027i	$-0.480000\pi$
$179$		0			0		−0.0627905	+	0.998027i	$0.520000\pi$
$180$	0.0392590	+	0.624004i	0.0392590	+	0.624004i
$181$	−1.92189	+	0.242791i	−1.92189	+	0.242791i	−0.992115	−	0.125333i	$-0.960000\pi$
$181$	−1.92189	+	0.242791i	−1.92189	+	0.242791i	−0.929776	+	0.368125i	$0.880000\pi$
$182$		0			0
$183$	1.42421	−	1.72157i	1.42421	−	1.72157i
$184$	0.0915446	+	1.45506i	0.0915446	+	1.45506i
$185$		0			0
$186$		0			0
$187$		0			0
$188$	1.03137	+	0.749337i	1.03137	+	0.749337i
$189$	−0.476045	−	0.188479i	−0.476045	−	0.188479i
$190$		0			0
$191$		0			0		−0.876307	−	0.481754i	$-0.840000\pi$
$191$		0			0		0.876307	+	0.481754i	$0.160000\pi$
$192$	−1.27485			−1.27485
$193$		0			0		−0.876307	−	0.481754i	$-0.840000\pi$
$193$		0			0		0.876307	+	0.481754i	$0.160000\pi$
$194$		0			0
$195$		0			0
$196$	0.0458709	+	0.141176i	0.0458709	+	0.141176i
$197$		0			0		0.535827	−	0.844328i	$-0.320000\pi$
$197$		0			0		−0.535827	+	0.844328i	$0.680000\pi$
$198$		0			0
$199$		0			0		−0.968583	−	0.248690i	$-0.920000\pi$
$199$		0			0		0.968583	+	0.248690i	$0.0800000\pi$
$200$	0.535827	+	0.844328i	0.535827	+	0.844328i
$201$	−0.160097			−0.160097
$202$	−0.637424	−	0.770513i	−0.637424	−	0.770513i
$203$	1.14844			1.14844
$204$		0			0
$205$	−1.80113	−	0.462452i	−1.80113	−	0.462452i
$206$	0.688925	−	1.46404i	0.688925	−	1.46404i
$207$	0.488437	−	0.769653i	0.488437	−	0.769653i
$208$		0			0
$209$		0			0
$210$	1.35542	−	0.171230i	1.35542	−	0.171230i
$211$		0			0		−0.876307	−	0.481754i	$-0.840000\pi$
$211$		0			0		0.876307	+	0.481754i	$0.160000\pi$
$212$		0			0
$213$		0			0
$214$	0.542804	−	0.656137i	0.542804	−	0.656137i
$215$	−1.80113	−	0.713118i	−1.80113	−	0.713118i
$216$	−0.386520	−	0.280823i	−0.386520	−	0.280823i
$217$		0			0
$218$	0.812619	+	0.982287i	0.812619	+	0.982287i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	0.371808	−	0.0469702i	0.371808	−	0.0469702i	0.0627905	−	0.998027i	$-0.480000\pi$
$223$	0.371808	−	0.0469702i	0.371808	−	0.0469702i	0.309017	+	0.951057i	$0.400000\pi$
$224$	0.0672897	+	1.06954i	0.0672897	+	1.06954i
$225$	0.0392590	−	0.624004i	0.0392590	−	0.624004i
$226$		0			0
$227$	−0.0534698	−	0.113629i	−0.0534698	−	0.113629i	0.876307	−	0.481754i	$-0.160000\pi$
$227$	−0.0534698	−	0.113629i	−0.0534698	−	0.113629i	−0.929776	+	0.368125i	$0.880000\pi$
$228$		0			0
$229$	0.450527	+	0.423073i	0.450527	+	0.423073i	0.876307	−	0.481754i	$-0.160000\pi$
$229$	0.450527	+	0.423073i	0.450527	+	0.423073i	−0.425779	+	0.904827i	$0.640000\pi$
$230$	0.0915446	−	1.45506i	0.0915446	−	1.45506i
$231$		0			0
$232$	1.03799	+	0.266509i	1.03799	+	0.266509i
$233$		0			0		0.929776	−	0.368125i	$-0.120000\pi$
$233$		0			0		−0.929776	+	0.368125i	$0.880000\pi$
$234$		0			0
$235$	−0.929324	−	0.872693i	−0.929324	−	0.872693i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		0.968583	−	0.248690i	$-0.0800000\pi$
$239$		0			0		−0.968583	+	0.248690i	$0.920000\pi$
$240$	1.26480	+	0.159781i	1.26480	+	0.159781i
$241$	−1.41789	−	1.03016i	−1.41789	−	1.03016i	−0.992115	−	0.125333i	$-0.960000\pi$
$241$	−1.41789	−	1.03016i	−1.41789	−	1.03016i	−0.425779	−	0.904827i	$-0.640000\pi$
$242$	−0.425779	+	0.904827i	−0.425779	+	0.904827i
$243$	0.338621	+	1.04217i	0.338621	+	1.04217i
$244$	−1.11716	−	1.35041i	−1.11716	−	1.35041i
$245$	−0.0278151	−	0.145812i	−0.0278151	−	0.145812i
$246$	−1.91789	+	1.39343i	−1.91789	+	1.39343i
$247$		0			0
$248$		0			0
$249$	0.462756	−	2.42585i	0.462756	−	2.42585i
$250$	−0.425779	−	0.904827i	−0.425779	−	0.904827i
$251$		0			0		0.728969	−	0.684547i	$-0.240000\pi$
$251$		0			0		−0.728969	+	0.684547i	$0.760000\pi$
$252$	0.359024	−	0.565732i	0.359024	−	0.565732i
$253$		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		0.876307	−	0.481754i	$-0.160000\pi$
$257$		0			0		−0.876307	+	0.481754i	$0.840000\pi$
$258$	−2.16412	+	1.18974i	−2.16412	+	1.18974i
$259$		0			0
$260$		0			0
$261$	−0.427098	−	0.516273i	−0.427098	−	0.516273i
$262$		0			0
$263$	0.844844	−	1.79538i	0.844844	−	1.79538i	0.309017	−	0.951057i	$-0.400000\pi$
$263$	0.844844	−	1.79538i	0.844844	−	1.79538i	0.535827	−	0.844328i	$-0.320000\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−1.66880	+	1.21245i	−1.66880	+	1.21245i
$268$	−0.0235315	+	0.123357i	−0.0235315	+	0.123357i
$269$	−0.824805	+	0.211774i	−0.824805	+	0.211774i	−0.637424	−	0.770513i	$-0.720000\pi$
$269$	−0.824805	+	0.211774i	−0.824805	+	0.211774i	−0.187381	+	0.982287i	$0.560000\pi$
$270$	0.348276	+	0.327053i	0.348276	+	0.327053i
$271$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$271$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$	−1.35490	−	1.27233i	−1.35490	−	1.27233i
$277$		0			0		−0.187381	−	0.982287i	$-0.560000\pi$
$277$		0			0		0.187381	+	0.982287i	$0.440000\pi$
$278$		0			0
$279$		0			0
$280$	0.0672897	−	1.06954i	0.0672897	−	1.06954i
$281$	0.0915446	+	1.45506i	0.0915446	+	1.45506i	0.728969	+	0.684547i	$0.240000\pi$
$281$	0.0915446	+	1.45506i	0.0915446	+	1.45506i	−0.637424	+	0.770513i	$0.720000\pi$
$282$	−1.61242	+	0.203696i	−1.61242	+	0.203696i
$283$	−0.996398	−	1.57007i	−0.996398	−	1.57007i	−0.809017	−	0.587785i	$-0.800000\pi$
$283$	−0.996398	−	1.57007i	−0.996398	−	1.57007i	−0.187381	−	0.982287i	$-0.560000\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	1.27026	+	1.53548i	1.27026	+	1.53548i
$288$	0.455778	−	0.428004i	0.455778	−	0.428004i
$289$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$290$	−0.996398	−	0.394502i	−0.996398	−	0.394502i
$291$		0			0
$292$		0			0
$293$		0			0		1.00000			$0$
$293$		0			0		−1.00000			$\pi$
$294$	−0.165832	−	0.0911672i	−0.165832	−	0.0911672i
$295$		0			0
$296$		0			0
$297$		0			0
$298$	0.0672897	−	0.106032i	0.0672897	−	0.106032i
$299$		0			0
$300$	−1.23480	−	0.317042i	−1.23480	−	0.317042i
$301$	1.11236	+	1.75280i	1.11236	+	1.75280i
$302$		0			0
$303$	1.26480	+	0.159781i	1.26480	+	0.159781i
$304$		0			0
$305$	0.939097	+	1.47978i	0.939097	+	1.47978i
$306$		0			0
$307$	−0.456288	+	0.969661i	−0.456288	+	0.969661i	0.535827	+	0.844328i	$0.320000\pi$
$307$	−0.456288	+	0.969661i	−0.456288	+	0.969661i	−0.992115	+	0.125333i	$0.960000\pi$
$308$		0			0
$309$	0.637424	+	1.96179i	0.637424	+	1.96179i
$310$		0			0
$311$		0			0		0.992115	−	0.125333i	$-0.0400000\pi$
$311$		0			0		−0.992115	+	0.125333i	$0.960000\pi$
$312$		0			0
$313$		0			0		1.00000			$0$
$313$		0			0		−1.00000			$\pi$
$314$		0			0
$315$	−0.427098	+	0.516273i	−0.427098	+	0.516273i
$316$		0			0
$317$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$317$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$318$		0			0
$319$		0			0
$320$	0.309017	−	0.951057i	0.309017	−	0.951057i
$321$	0.0681659	+	1.08347i	0.0681659	+	1.08347i
$322$	−0.995914	+	1.20385i	−0.995914	+	1.20385i
$323$		0			0
$324$	1.22458	−	0.154701i	1.22458	−	0.154701i
$325$		0			0
$326$	0.00788530	−	0.125333i	0.00788530	−	0.125333i
$327$	−1.61242	−	0.203696i	−1.61242	−	0.203696i
$328$	0.791759	+	1.68257i	0.791759	+	1.68257i
$329$	0.255999	+	1.34200i	0.255999	+	1.34200i
$330$		0			0
$331$		0			0		0.0627905	−	0.998027i	$-0.480000\pi$
$331$		0			0		−0.0627905	+	0.998027i	$0.520000\pi$
$332$	−1.80113	−	0.713118i	−1.80113	−	0.713118i
$333$		0			0
$334$	−1.35556	+	0.536702i	−1.35556	+	0.536702i
$335$	0.0388067	−	0.119435i	0.0388067	−	0.119435i
$336$	−0.995914	−	0.935225i	−0.995914	−	0.935225i
$337$		0			0		0.968583	−	0.248690i	$-0.0800000\pi$
$337$		0			0		−0.968583	+	0.248690i	$0.920000\pi$
$338$	−0.187381	+	0.982287i	−0.187381	+	0.982287i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	0.388556	−	0.825723i	0.388556	−	0.825723i
$344$	0.598617	+	1.84235i	0.598617	+	1.84235i
$345$	1.18475	+	1.43211i	1.18475	+	1.43211i
$346$		0			0
$347$	0.688925	−	0.500534i	0.688925	−	0.500534i	−0.187381	−	0.982287i	$-0.560000\pi$
$347$	0.688925	−	0.500534i	0.688925	−	0.500534i	0.876307	+	0.481754i	$0.160000\pi$
$348$	−1.19721	+	0.658170i	−1.19721	+	0.658170i
$349$	−0.328407	+	0.180543i	−0.328407	+	0.180543i	−0.637424	−	0.770513i	$-0.720000\pi$
$349$	−0.328407	+	0.180543i	−0.328407	+	0.180543i	0.309017	+	0.951057i	$0.400000\pi$
$350$	−0.200808	+	1.05267i	−0.200808	+	1.05267i
$351$		0			0
$352$		0			0
$353$		0			0		0.535827	−	0.844328i	$-0.320000\pi$
$353$		0			0		−0.535827	+	0.844328i	$0.680000\pi$
$354$		0			0
$355$		0			0
$356$	0.688925	+	1.46404i	0.688925	+	1.46404i
$357$		0			0
$358$		0			0
$359$		0			0		0.876307	−	0.481754i	$-0.160000\pi$
$359$		0			0		−0.876307	+	0.481754i	$0.840000\pi$
$360$	−0.505828	+	0.367505i	−0.505828	+	0.367505i
$361$	−0.187381	−	0.982287i	−0.187381	−	0.982287i
$362$	−1.23480	−	1.49261i	−1.23480	−	1.49261i
$363$	−0.393950	−	1.21245i	−0.393950	−	1.21245i
$364$		0			0
$365$		0			0
$366$	2.21670	+	0.280034i	2.21670	+	0.280034i
$367$	−1.56720	+	0.402389i	−1.56720	+	0.402389i	−0.929776	−	0.368125i	$-0.880000\pi$
$367$	−1.56720	+	0.402389i	−1.56720	+	0.402389i	−0.637424	+	0.770513i	$0.720000\pi$
$368$	−1.17950	+	0.856954i	−1.17950	+	0.856954i
$369$	0.217861	−	1.14207i	0.217861	−	1.14207i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.929776	−	0.368125i	$-0.120000\pi$
$373$		0			0		−0.929776	+	0.368125i	$0.880000\pi$
$374$		0			0
$375$	1.18532	+	0.469303i	1.18532	+	0.469303i
$376$	−0.0800484	+	1.27233i	−0.0800484	+	1.27233i
$377$		0			0
$378$	−0.0959390	−	0.502930i	−0.0959390	−	0.502930i
$379$		0			0		−0.425779	−	0.904827i	$-0.640000\pi$
$379$		0			0		0.425779	+	0.904827i	$0.360000\pi$
$380$		0			0
$381$	0.129521	−	2.05868i	0.129521	−	2.05868i
$382$		0			0
$383$	1.96858	−	0.248690i	1.96858	−	0.248690i	0.968583	−	0.248690i	$-0.0800000\pi$
$383$	1.96858	−	0.248690i	1.96858	−	0.248690i	1.00000			$0$
$384$	−0.683098	−	1.07639i	−0.683098	−	1.07639i
$385$		0			0
$386$		0			0
$387$	0.374278	−	1.15191i	0.374278	−	1.15191i
$388$		0			0
$389$	1.45794	−	1.36909i	1.45794	−	1.36909i	0.728969	−	0.684547i	$-0.240000\pi$
$389$	1.45794	−	1.36909i	1.45794	−	1.36909i	0.728969	−	0.684547i	$-0.240000\pi$
$390$		0			0
$391$		0			0
$392$	−0.0946201	+	0.114376i	−0.0946201	+	0.114376i
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$		0			0		0.929776	−	0.368125i	$-0.120000\pi$
$397$		0			0		−0.929776	+	0.368125i	$0.880000\pi$
$398$		0			0
$399$		0			0
$400$	−0.425779	+	0.904827i	−0.425779	+	0.904827i
$401$	0.598617	+	0.153699i	0.598617	+	0.153699i	0.535827	−	0.844328i	$-0.320000\pi$
$401$	0.598617	+	0.153699i	0.598617	+	0.153699i	0.0627905	+	0.998027i	$0.480000\pi$
$402$	−0.0857841	−	0.135174i	−0.0857841	−	0.135174i
$403$		0			0
$404$	0.309017	−	0.951057i	0.309017	−	0.951057i
$405$	−1.23432			−1.23432
$406$	0.615366	+	0.969661i	0.615366	+	0.969661i
$407$		0			0
$408$		0			0
$409$	0.781202	−	1.23098i	0.781202	−	1.23098i	−0.187381	−	0.982287i	$-0.560000\pi$
$409$	0.781202	−	1.23098i	0.781202	−	1.23098i	0.968583	−	0.248690i	$-0.0800000\pi$
$410$	−0.574633	−	1.76854i	−0.574633	−	1.76854i
$411$		0			0
$412$	1.60528	−	0.202793i	1.60528	−	0.202793i
$413$		0			0
$414$	0.911557			0.911557
$415$	1.69755	+	0.933237i	1.69755	+	0.933237i
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		0.728969	−	0.684547i	$-0.240000\pi$
$419$		0			0		−0.728969	+	0.684547i	$0.760000\pi$
$420$	0.870846	+	1.05267i	0.870846	+	1.05267i
$421$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	0.309017	+	0.951057i	$0.400000\pi$
$421$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	−0.809017	+	0.587785i	$0.800000\pi$
$422$		0			0
$423$	0.508080	−	0.614163i	0.508080	−	0.614163i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	0.117933	−	1.87449i	0.117933	−	1.87449i
$428$	0.844844	+	0.106729i	0.844844	+	0.106729i
$429$		0			0
$430$	−0.362989	−	1.90285i	−0.362989	−	1.90285i
$431$		0			0		−0.728969	−	0.684547i	$-0.760000\pi$
$431$		0			0		0.728969	+	0.684547i	$0.240000\pi$
$432$	0.0299991	−	0.476823i	0.0299991	−	0.476823i
$433$		0			0		−0.929776	−	0.368125i	$-0.880000\pi$
$433$		0			0		0.929776	+	0.368125i	$0.120000\pi$
$434$		0			0
$435$	1.27026	−	0.502930i	1.27026	−	0.502930i
$436$	−0.393950	+	1.21245i	−0.393950	+	1.21245i
$437$		0			0
$438$		0			0
$439$		0			0		0.187381	−	0.982287i	$-0.440000\pi$
$439$		0			0		−0.187381	+	0.982287i	$0.560000\pi$
$440$		0			0
$441$	0.0898953	−	0.0230812i	0.0898953	−	0.0230812i
$442$		0			0
$443$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	0.309017	−	0.951057i	$-0.400000\pi$
$443$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	−0.809017	+	0.587785i	$0.800000\pi$
$444$		0			0
$445$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$446$	0.238883	+	0.288760i	0.238883	+	0.288760i
$447$	0.0299991	+	0.157261i	0.0299991	+	0.157261i
$448$	−0.866986	+	0.629902i	−0.866986	+	0.629902i
$449$	1.53583	−	0.844328i	1.53583	−	0.844328i	0.535827	−	0.844328i	$-0.320000\pi$
$449$	1.53583	−	0.844328i	1.53583	−	0.844328i	1.00000			$0$
$450$	0.547900	−	0.301210i	0.547900	−	0.301210i
$451$		0			0
$452$		0			0
$453$		0			0
$454$	0.0672897	−	0.106032i	0.0672897	−	0.106032i
$455$		0			0
$456$		0			0
$457$		0			0		−0.425779	−	0.904827i	$-0.640000\pi$
$457$		0			0		0.425779	+	0.904827i	$0.360000\pi$
$458$	−0.115808	+	0.607087i	−0.115808	+	0.607087i
$459$		0			0
$460$	1.27760	−	0.702367i	1.27760	−	0.702367i
$461$	0.688925	−	0.500534i	0.688925	−	0.500534i	−0.187381	−	0.982287i	$-0.560000\pi$
$461$	0.688925	−	0.500534i	0.688925	−	0.500534i	0.876307	+	0.481754i	$0.160000\pi$
$462$		0			0
$463$	−0.393950	−	0.476203i	−0.393950	−	0.476203i	0.535827	−	0.844328i	$-0.320000\pi$
$463$	−0.393950	−	0.476203i	−0.393950	−	0.476203i	−0.929776	+	0.368125i	$0.880000\pi$
$464$	0.331159	+	1.01920i	0.331159	+	1.01920i
$465$		0			0
$466$		0			0
$467$	1.84489	+	0.233064i	1.84489	+	0.233064i	0.968583	−	0.248690i	$-0.0800000\pi$
$467$	1.84489	+	0.233064i	1.84489	+	0.233064i	0.876307	+	0.481754i	$0.160000\pi$
$468$		0			0
$469$	−0.108877	+	0.0791038i	−0.108877	+	0.0791038i
$470$	0.238883	−	1.25227i	0.238883	−	1.25227i
$471$		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		−0.187381	−	0.982287i	$-0.560000\pi$
$479$		0			0		0.187381	+	0.982287i	$0.440000\pi$
$480$	0.542804	+	1.15352i	0.542804	+	1.15352i
$481$		0			0
$482$	0.110048	−	1.74915i	0.110048	−	1.74915i
$483$	−0.125068	−	1.98790i	−0.125068	−	1.98790i
$484$	−0.992115	+	0.125333i	−0.992115	+	0.125333i
$485$		0			0
$486$	−0.698489	+	0.844328i	−0.698489	+	0.844328i
$487$	−0.116762	−	1.85588i	−0.116762	−	1.85588i	−0.425779	−	0.904827i	$-0.640000\pi$
$487$	−0.116762	−	1.85588i	−0.116762	−	1.85588i	0.309017	−	0.951057i	$-0.400000\pi$
$488$	0.541587	−	1.66683i	0.541587	−	1.66683i
$489$	0.102049	+	0.123357i	0.102049	+	0.123357i
$490$	0.108209	−	0.101615i	0.108209	−	0.101615i
$491$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$491$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$492$	−2.20417	−	0.872693i	−2.20417	−	0.872693i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	2.29617	−	0.909118i	2.29617	−	0.909118i
$499$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$499$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$500$	0.535827	−	0.844328i	0.535827	−	0.844328i
$501$	0.791374	−	1.68176i	0.791374	−	1.68176i
$502$		0			0
$503$	0.939097	+	1.47978i	0.939097	+	1.47978i	0.876307	+	0.481754i	$0.160000\pi$
$503$	0.939097	+	1.47978i	0.939097	+	1.47978i	0.0627905	+	0.998027i	$0.480000\pi$
$504$	0.670038			0.670038
$505$	−0.425779	+	0.904827i	−0.425779	+	0.904827i
$506$		0			0
$507$	−0.683098	−	1.07639i	−0.683098	−	1.07639i
$508$	−1.56720	−	0.402389i	−1.56720	−	0.402389i
$509$	−0.824805	+	1.75280i	−0.824805	+	1.75280i	−0.187381	+	0.982287i	$0.560000\pi$
$509$	−0.824805	+	1.75280i	−0.824805	+	1.75280i	−0.637424	+	0.770513i	$0.720000\pi$
$510$		0			0
$511$		0			0
$512$	−0.929776	+	0.368125i	−0.929776	+	0.368125i
$513$		0			0
$514$		0			0
$515$	−1.61803			−1.61803
$516$	−2.16412	−	1.18974i	−2.16412	−	1.18974i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	1.18532	+	1.43281i	1.18532	+	1.43281i	0.876307	+	0.481754i	$0.160000\pi$
$521$	1.18532	+	1.43281i	1.18532	+	1.43281i	0.309017	+	0.951057i	$0.400000\pi$
$522$	0.207053	−	0.637244i	0.207053	−	0.637244i
$523$	0.110048	+	1.74915i	0.110048	+	1.74915i	0.535827	+	0.844328i	$0.320000\pi$
$523$	0.110048	+	1.74915i	0.110048	+	1.74915i	−0.425779	+	0.904827i	$0.640000\pi$
$524$		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
$529$	−1.11671	−	0.141073i	−1.11671	−	0.141073i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$	−1.91789	−	0.759348i	−1.91789	−	0.759348i
$535$	−0.824805	−	0.211774i	−0.824805	−	0.211774i
$536$	−0.116762	+	0.0462295i	−0.116762	+	0.0462295i
$537$		0			0
$538$	−0.620759	−	0.582932i	−0.620759	−	0.582932i
$539$		0			0
$540$	−0.0895243	+	0.469303i	−0.0895243	+	0.469303i
$541$	1.50441	−	1.09302i	1.50441	−	1.09302i	0.535827	−	0.844328i	$-0.320000\pi$
$541$	1.50441	−	1.09302i	1.50441	−	1.09302i	0.968583	−	0.248690i	$-0.0800000\pi$
$542$		0			0
$543$	2.45012	+	0.309522i	2.45012	+	0.309522i
$544$		0			0
$545$	0.542804	−	1.15352i	0.542804	−	1.15352i
$546$		0			0
$547$	0.542804	+	0.656137i	0.542804	+	0.656137i	0.968583	−	0.248690i	$-0.0800000\pi$
$547$	0.542804	+	0.656137i	0.542804	+	0.656137i	−0.425779	+	0.904827i	$0.640000\pi$
$548$		0			0
$549$	−0.886520	+	0.644095i	−0.886520	+	0.644095i
$550$		0			0
$551$		0			0
$552$	0.348276	−	1.82573i	0.348276	−	1.82573i
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$		0			0		0.728969	−	0.684547i	$-0.240000\pi$
$557$		0			0		−0.728969	+	0.684547i	$0.760000\pi$
$558$		0			0
$559$		0			0
$560$	0.939097	−	0.516273i	0.939097	−	0.516273i
$561$		0			0
$562$	−1.17950	+	0.856954i	−1.17950	+	0.856954i
$563$	0.303189	+	1.58937i	0.303189	+	1.58937i	0.728969	+	0.684547i	$0.240000\pi$
$563$	0.303189	+	1.58937i	0.303189	+	1.58937i	−0.425779	+	0.904827i	$0.640000\pi$
$564$	−1.03597	−	1.25227i	−1.03597	−	1.25227i
$565$		0			0
$566$	0.791759	−	1.68257i	0.791759	−	1.68257i
$567$	1.07013	+	0.777498i	1.07013	+	0.777498i
$568$		0			0
$569$	1.87631	−	0.481754i	1.87631	−	0.481754i	0.876307	−	0.481754i	$-0.160000\pi$
$569$	1.87631	−	0.481754i	1.87631	−	0.481754i	1.00000			$0$
$570$		0			0
$571$		0			0		0.187381	−	0.982287i	$-0.440000\pi$
$571$		0			0		−0.187381	+	0.982287i	$0.560000\pi$
$572$		0			0
$573$		0			0
$574$	−0.615808	+	1.89526i	−0.615808	+	1.89526i
$575$	−1.35556	+	0.536702i	−1.35556	+	0.536702i
$576$	0.605594	+	0.155490i	0.605594	+	0.155490i
$577$		0			0		−0.929776	−	0.368125i	$-0.880000\pi$
$577$		0			0		0.929776	+	0.368125i	$0.120000\pi$
$578$	0.0627905	−	0.998027i	0.0627905	−	0.998027i
$579$		0			0
$580$	−0.200808	−	1.05267i	−0.200808	−	1.05267i
$581$	−0.883906	−	1.87839i	−0.883906	−	1.87839i
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$	1.26480	−	1.52888i	1.26480	−	1.52888i	0.535827	−	0.844328i	$-0.320000\pi$
$587$	1.26480	−	1.52888i	1.26480	−	1.52888i	0.728969	−	0.684547i	$-0.240000\pi$
$588$	−0.0118825	−	0.188867i	−0.0118825	−	0.188867i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$		0			0		−0.929776	−	0.368125i	$-0.880000\pi$
$593$		0			0		0.929776	+	0.368125i	$0.120000\pi$
$594$		0			0
$595$		0			0
$596$	0.125581			0.125581
$597$		0			0
$598$		0			0
$599$		0			0		0.929776	−	0.368125i	$-0.120000\pi$
$599$		0			0		−0.929776	+	0.368125i	$0.880000\pi$
$600$	−0.393950	−	1.21245i	−0.393950	−	1.21245i
$601$	0.331159	−	0.521823i	0.331159	−	0.521823i	−0.637424	−	0.770513i	$-0.720000\pi$
$601$	0.331159	−	0.521823i	0.331159	−	0.521823i	0.968583	+	0.248690i	$0.0800000\pi$
$602$	−0.883906	+	1.87839i	−0.883906	+	1.87839i
$603$	0.0760512	+	0.0195266i	0.0760512	+	0.0195266i
$604$		0			0
$605$	1.00000			1.00000
$606$	0.542804	+	1.15352i	0.542804	+	1.15352i
$607$	−1.98423			−1.98423			−0.992115	−	0.125333i	$-0.960000\pi$
$607$	−1.98423			−1.98423			−0.992115	+	0.125333i	$0.960000\pi$
$608$		0			0
$609$	−1.41809	−	0.364104i	−1.41809	−	0.364104i
$610$	−0.746226	+	1.58581i	−0.746226	+	1.58581i
$611$		0			0
$612$		0			0
$613$		0			0		0.929776	−	0.368125i	$-0.120000\pi$
$613$		0			0		−0.929776	+	0.368125i	$0.880000\pi$
$614$	−1.06320	+	0.134314i	−1.06320	+	0.134314i
$615$	2.07741	+	1.14207i	2.07741	+	1.14207i
$616$		0			0
$617$		0			0		−0.876307	−	0.481754i	$-0.840000\pi$
$617$		0			0		0.876307	+	0.481754i	$0.160000\pi$
$618$	−1.31484	+	1.58937i	−1.31484	+	1.58937i
$619$		0			0		−0.929776	−	0.368125i	$-0.880000\pi$
$619$		0			0		0.929776	+	0.368125i	$0.120000\pi$
$620$		0			0
$621$	0.507765	−	0.476823i	0.507765	−	0.476823i
$622$		0			0
$623$	−0.535827	+	1.64911i	−0.535827	+	1.64911i
$624$		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	$-0.640000\pi$
$631$		0			0		0.425779	+	0.904827i	$0.360000\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	1.50441	+	0.595638i	1.50441	+	0.595638i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$	0.968583	−	0.248690i	0.968583	−	0.248690i
$641$	0.303189	−	1.58937i	0.303189	−	1.58937i	−0.425779	−	0.904827i	$-0.640000\pi$
$641$	0.303189	−	1.58937i	0.303189	−	1.58937i	0.728969	−	0.684547i	$-0.240000\pi$
$642$	−0.878275	+	0.638104i	−0.878275	+	0.638104i
$643$	1.93717	−	0.497380i	1.93717	−	0.497380i	0.968583	−	0.248690i	$-0.0800000\pi$
$643$	1.93717	−	0.497380i	1.93717	−	0.497380i	0.968583	−	0.248690i	$-0.0800000\pi$
$644$	−1.55008	−	0.195821i	−1.55008	−	0.195821i
$645$	1.99794	+	1.45159i	1.99794	+	1.45159i
$646$		0			0
$647$	−0.115808	−	0.356420i	−0.115808	−	0.356420i	0.876307	−	0.481754i	$-0.160000\pi$
$647$	−0.115808	−	0.356420i	−0.115808	−	0.356420i	−0.992115	+	0.125333i	$0.960000\pi$
$648$	0.786782	+	0.951057i	0.786782	+	0.951057i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	0.110048	−	0.0604991i	0.110048	−	0.0604991i
$653$		0			0		0.187381	−	0.982287i	$-0.440000\pi$
$653$		0			0		−0.187381	+	0.982287i	$0.560000\pi$
$654$	−0.691992	−	1.47056i	−0.691992	−	1.47056i
$655$		0			0
$656$	−0.996398	+	1.57007i	−0.996398	+	1.57007i
$657$		0			0
$658$	−0.995914	+	0.935225i	−0.995914	+	0.935225i
$659$		0			0		−0.425779	−	0.904827i	$-0.640000\pi$
$659$		0			0		0.425779	+	0.904827i	$0.360000\pi$
$660$		0			0
$661$	−1.73879	+	0.955910i	−1.73879	+	0.955910i	−0.809017	+	0.587785i	$0.800000\pi$
$661$	−1.73879	+	0.955910i	−1.73879	+	0.955910i	−0.929776	+	0.368125i	$0.880000\pi$
$662$		0			0
$663$		0			0
$664$	−0.362989	−	1.90285i	−0.362989	−	1.90285i
$665$		0			0
$666$		0			0
$667$	−0.665239	+	1.41371i	−0.665239	+	1.41371i
$668$	−1.17950	−	0.856954i	−1.17950	−	0.856954i
$669$	−0.473998	−	0.0598799i	−0.473998	−	0.0598799i
$670$	0.121636	−	0.0312307i	0.121636	−	0.0312307i
$671$		0			0
$672$	0.255999	−	1.34200i	0.255999	−	1.34200i
$673$		0			0		0.968583	−	0.248690i	$-0.0800000\pi$
$673$		0			0		−0.968583	+	0.248690i	$0.920000\pi$
$674$		0			0
$675$	0.147638	−	0.454382i	0.147638	−	0.454382i
$676$	−0.929776	+	0.368125i	−0.929776	+	0.368125i
$677$		0			0		−0.968583	−	0.248690i	$-0.920000\pi$
$677$		0			0		0.968583	+	0.248690i	$0.0800000\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	0.0299991	+	0.157261i	0.0299991	+	0.157261i
$682$		0			0
$683$	0.371808	+	0.0469702i	0.371808	+	0.0469702i	0.309017	−	0.951057i	$-0.400000\pi$
$683$	0.371808	+	0.0469702i	0.371808	+	0.0469702i	0.0627905	+	0.998027i	$0.480000\pi$
$684$		0			0
$685$		0			0
$686$	0.905380	−	0.114376i	0.905380	−	0.114376i
$687$	−0.422178	−	0.665245i	−0.422178	−	0.665245i
$688$	−1.23480	+	1.49261i	−1.23480	+	1.49261i
$689$		0			0
$690$	−0.574354	+	1.76768i	−0.574354	+	1.76768i
$691$		0			0		−0.637424	−	0.770513i	$-0.720000\pi$
$691$		0			0		0.637424	+	0.770513i	$0.280000\pi$
$692$		0			0
$693$		0			0
$694$	0.791759	+	0.313480i	0.791759	+	0.313480i
$695$		0			0
$696$	−1.19721	−	0.658170i	−1.19721	−	0.658170i
$697$		0			0
$698$	−0.328407	−	0.180543i	−0.328407	−	0.180543i
$699$		0			0
$700$	−0.996398	+	0.394502i	−0.996398	+	0.394502i
$701$	−0.574633	−	1.76854i	−0.574633	−	1.76854i	−0.637424	−	0.770513i	$-0.720000\pi$
$701$	−0.574633	−	1.76854i	−0.574633	−	1.76854i	0.0627905	−	0.998027i	$-0.480000\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	0.870846	+	1.37223i	0.870846	+	1.37223i
$706$		0			0
$707$	0.939097	−	0.516273i	0.939097	−	0.516273i
$708$		0			0
$709$	−1.06320	−	1.67534i	−1.06320	−	1.67534i	−0.637424	−	0.770513i	$-0.720000\pi$
$709$	−1.06320	−	1.67534i	−1.06320	−	1.67534i	−0.425779	−	0.904827i	$-0.640000\pi$
$710$		0			0
$711$		0			0
$712$	−0.866986	+	1.36615i	−0.866986	+	1.36615i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		0.637424	−	0.770513i	$-0.280000\pi$
$719$		0			0		−0.637424	+	0.770513i	$0.720000\pi$
$720$	−0.581331	−	0.230165i	−0.581331	−	0.230165i
$721$	1.40281	+	1.01920i	1.40281	+	1.01920i
$722$	0.728969	−	0.684547i	0.728969	−	0.684547i
$723$	1.42421	+	1.72157i	1.42421	+	1.72157i
$724$	0.598617	−	1.84235i	0.598617	−	1.84235i
$725$	0.0672897	+	1.06954i	0.0672897	+	1.06954i
$726$	0.812619	−	0.982287i	0.812619	−	0.982287i
$727$	0.331159	+	0.521823i	0.331159	+	0.521823i	0.968583	−	0.248690i	$-0.0800000\pi$
$727$	0.331159	+	0.521823i	0.331159	+	0.521823i	−0.637424	+	0.770513i	$0.720000\pi$
$728$		0			0
$729$	−0.0102136	−	0.162341i	−0.0102136	−	0.162341i
$730$		0			0
$731$		0			0
$732$	0.951325	+	2.02167i	0.951325	+	2.02167i
$733$		0			0		−0.187381	−	0.982287i	$-0.560000\pi$
$733$		0			0		0.187381	+	0.982287i	$0.440000\pi$
$734$	−1.17950	−	1.10762i	−1.17950	−	1.10762i
$735$	−0.0118825	+	0.188867i	−0.0118825	+	0.188867i
$736$	−1.35556	−	0.536702i	−1.35556	−	0.536702i
$737$		0			0
$738$	1.08102	−	0.428004i	1.08102	−	0.428004i
$739$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$739$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−0.101597	+	0.0738147i	−0.101597	+	0.0738147i	−0.637424	−	0.770513i	$-0.720000\pi$
$743$	−0.101597	+	0.0738147i	−0.101597	+	0.0738147i	0.535827	+	0.844328i	$0.320000\pi$
$744$		0			0
$745$	−0.124591	−	0.0157395i	−0.124591	−	0.0157395i
$746$		0			0
$747$	−0.515699	+	1.09592i	−0.515699	+	1.09592i
$748$		0			0
$749$	0.581698	+	0.703152i	0.581698	+	0.703152i
$750$	0.238883	+	1.25227i	0.238883	+	1.25227i
$751$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$751$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$752$	−1.11716	+	0.614163i	−1.11716	+	0.614163i
$753$		0			0
$754$		0			0
$755$		0			0
$756$	0.373231	−	0.350487i	0.373231	−	0.350487i
$757$		0			0		0.535827	−	0.844328i	$-0.320000\pi$
$757$		0			0		−0.535827	+	0.844328i	$0.680000\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	0.371808	−	1.94908i	0.371808	−	1.94908i	0.0627905	−	0.998027i	$-0.480000\pi$
$761$	0.371808	−	1.94908i	0.371808	−	1.94908i	0.309017	−	0.951057i	$-0.400000\pi$
$762$	1.80760	−	0.993736i	1.80760	−	0.993736i
$763$	−1.19721	+	0.658170i	−1.19721	+	0.658170i
$764$		0			0
$765$		0			0
$766$	1.26480	+	1.52888i	1.26480	+	1.52888i
$767$		0			0
$768$	0.542804	−	1.15352i	0.542804	−	1.15352i
$769$	−1.56720	−	1.13864i	−1.56720	−	1.13864i	−0.929776	−	0.368125i	$-0.880000\pi$
$769$	−1.56720	−	1.13864i	−1.56720	−	1.13864i	−0.637424	−	0.770513i	$-0.720000\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0		0.187381	−	0.982287i	$-0.440000\pi$
$773$		0			0		−0.187381	+	0.982287i	$0.560000\pi$
$774$	1.17314	−	0.301210i	1.17314	−	0.301210i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	1.93717	+	0.497380i	1.93717	+	0.497380i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−0.217999	−	0.463271i	−0.217999	−	0.463271i
$784$	−0.147271	−	0.0186046i	−0.147271	−	0.0186046i
$785$		0			0
$786$		0			0
$787$	−1.73879	+	0.219661i	−1.73879	+	0.219661i	−0.929776	−	0.368125i	$-0.880000\pi$
$787$	−1.73879	+	0.219661i	−1.73879	+	0.219661i	−0.809017	+	0.587785i	$0.800000\pi$
$788$		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		−0.876307	−	0.481754i	$-0.840000\pi$
$797$		0			0		0.876307	+	0.481754i	$0.160000\pi$
$798$		0			0
$799$		0			0
$800$	−0.992115	+	0.125333i	−0.992115	+	0.125333i
$801$	0.940613	−	0.372415i	0.940613	−	0.372415i
$802$	0.190983	+	0.587785i	0.190983	+	0.587785i
$803$		0			0
$804$	0.0681659	−	0.144860i	0.0681659	−	0.144860i
$805$	1.51332	+	0.388554i	1.51332	+	0.388554i
$806$		0			0
$807$	1.08561			1.08561
$808$	0.968583	−	0.248690i	0.968583	−	0.248690i
$809$	1.07165			1.07165			0.535827	−	0.844328i	$-0.320000\pi$
$809$	1.07165			1.07165			0.535827	+	0.844328i	$0.320000\pi$
$810$	−0.661379	−	1.04217i	−0.661379	−	1.04217i
$811$		0			0		−0.968583	−	0.248690i	$-0.920000\pi$
$811$		0			0		0.968583	+	0.248690i	$0.0800000\pi$
$812$	−0.488983	+	1.03914i	−0.488983	+	1.03914i
$813$		0			0
$814$		0			0
$815$	−0.116762	+	0.0462295i	−0.116762	+	0.0462295i
$816$		0			0
$817$		0			0
$818$	1.45794			1.45794
$819$		0			0
$820$	1.18532	−	1.43281i	1.18532	−	1.43281i
$821$	−1.35556	−	0.536702i	−1.35556	−	0.536702i	−0.425779	−	0.904827i	$-0.640000\pi$
$821$	−1.35556	−	0.536702i	−1.35556	−	0.536702i	−0.929776	+	0.368125i	$0.880000\pi$
$822$		0			0
$823$	1.06279	−	0.998027i	1.06279	−	0.998027i	0.0627905	−	0.998027i	$-0.480000\pi$
$823$	1.06279	−	0.998027i	1.06279	−	0.998027i	1.00000			$0$
$824$	1.03137	+	1.24672i	1.03137	+	1.24672i
$825$		0			0
$826$		0			0
$827$	−0.929324	+	1.12336i	−0.929324	+	1.12336i	0.0627905	+	0.998027i	$0.480000\pi$
$827$	−0.929324	+	1.12336i	−0.929324	+	1.12336i	−0.992115	+	0.125333i	$0.960000\pi$
$828$	0.488437	+	0.769653i	0.488437	+	0.769653i
$829$	0.844844	−	0.106729i	0.844844	−	0.106729i	0.309017	−	0.951057i	$-0.400000\pi$
$829$	0.844844	−	0.106729i	0.844844	−	0.106729i	0.535827	+	0.844328i	$0.320000\pi$
$830$	0.121636	+	1.93334i	0.121636	+	1.93334i
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	1.06279	+	0.998027i	1.06279	+	0.998027i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		0.929776	−	0.368125i	$-0.120000\pi$
$839$		0			0		−0.929776	+	0.368125i	$0.880000\pi$
$840$	−0.422178	+	1.29933i	−0.422178	+	1.29933i
$841$	0.108209	+	0.101615i	0.108209	+	0.101615i
$842$	−1.56720	+	0.402389i	−1.56720	+	0.402389i
$843$	0.348276	−	1.82573i	0.348276	−	1.82573i
$844$		0			0
$845$	0.968583	−	0.248690i	0.968583	−	0.248690i
$846$	0.790797	+	0.0999009i	0.790797	+	0.0999009i
$847$	−0.866986	−	0.629902i	−0.866986	−	0.629902i
$848$		0			0
$849$	0.732570	+	2.25462i	0.732570	+	2.25462i
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		0.876307	−	0.481754i	$-0.160000\pi$
$853$		0			0		−0.876307	+	0.481754i	$0.840000\pi$
$854$	1.64587	−	0.904827i	1.64587	−	0.904827i
$855$		0			0
$856$	0.362576	+	0.770513i	0.362576	+	0.770513i
$857$		0			0		0.728969	−	0.684547i	$-0.240000\pi$
$857$		0			0		−0.728969	+	0.684547i	$0.760000\pi$
$858$		0			0
$859$		0			0		0.535827	−	0.844328i	$-0.320000\pi$
$859$		0			0		−0.535827	+	0.844328i	$0.680000\pi$
$860$	1.41213	−	1.32608i	1.41213	−	1.32608i
$861$	−1.08170	−	2.29872i	−1.08170	−	2.29872i
$862$		0			0
$863$	−1.62954	+	0.895846i	−1.62954	+	0.895846i	−0.637424	+	0.770513i	$0.720000\pi$
$863$	−1.62954	+	0.895846i	−1.62954	+	0.895846i	−0.992115	+	0.125333i	$0.960000\pi$
$864$	0.418669	−	0.230165i	0.418669	−	0.230165i
$865$		0			0
$866$		0			0
$867$	0.812619	+	0.982287i	0.812619	+	0.982287i
$868$		0			0
$869$		0			0
$870$	1.10528	+	0.803030i	1.10528	+	0.803030i
$871$		0			0
$872$	−1.23480	+	0.317042i	−1.23480	+	0.317042i
$873$		0			0
$874$		0			0
$875$	1.03799	−	0.266509i	1.03799	−	0.266509i
$876$		0			0
$877$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$877$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−0.116762	+	1.85588i	−0.116762	+	1.85588i	0.309017	+	0.951057i	$0.400000\pi$
$881$	−0.116762	+	1.85588i	−0.116762	+	1.85588i	−0.425779	+	0.904827i	$0.640000\pi$
$882$	0.0676564	+	0.0635336i	0.0676564	+	0.0635336i
$883$	0.348445	+	1.82662i	0.348445	+	1.82662i	0.535827	+	0.844328i	$0.320000\pi$
$883$	0.348445	+	1.82662i	0.348445	+	1.82662i	−0.187381	+	0.982287i	$0.560000\pi$
$884$		0			0
$885$		0			0
$886$	0.0388067	−	0.616814i	0.0388067	−	0.616814i
$887$	0.0672897	+	1.06954i	0.0672897	+	1.06954i	0.876307	+	0.481754i	$0.160000\pi$
$887$	0.0672897	+	1.06954i	0.0672897	+	1.06954i	−0.809017	+	0.587785i	$0.800000\pi$
$888$		0			0
$889$	−0.929109	−	1.46404i	−0.929109	−	1.46404i
$890$	1.03137	−	1.24672i	1.03137	−	1.24672i
$891$		0			0
$892$	−0.115808	+	0.356420i	−0.115808	+	0.356420i
$893$		0			0
$894$	−0.116705	+	0.109594i	−0.116705	+	0.109594i
$895$		0			0
$896$	−0.996398	−	0.394502i	−0.996398	−	0.394502i
$897$		0			0
$898$	1.53583	+	0.844328i	1.53583	+	0.844328i
$899$		0			0
$900$	0.547900	+	0.301210i	0.547900	+	0.301210i
$901$		0			0
$902$		0			0
$903$	−0.817828	−	2.51702i	−0.817828	−	2.51702i
$904$		0			0
$905$	−0.824805	+	1.75280i	−0.824805	+	1.75280i
$906$		0			0
$907$	−0.200808	−	0.316423i	−0.200808	−	0.316423i	0.728969	−	0.684547i	$-0.240000\pi$
$907$	−0.200808	−	0.316423i	−0.200808	−	0.316423i	−0.929776	+	0.368125i	$0.880000\pi$
$908$	0.125581			0.125581
$909$	−0.581331	−	0.230165i	−0.581331	−	0.230165i
$910$		0			0
$911$		0			0		−0.535827	−	0.844328i	$-0.680000\pi$
$911$		0			0		0.535827	+	0.844328i	$0.320000\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	−0.690441	−	2.12496i	−0.690441	−	2.12496i
$916$	−0.574633	+	0.227513i	−0.574633	+	0.227513i
$917$		0			0
$918$		0			0
$919$		0			0		1.00000			$0$
$919$		0			0		−1.00000			$\pi$
$920$	1.27760	+	0.702367i	1.27760	+	0.702367i
$921$	0.870846	−	1.05267i	0.870846	−	1.05267i
$922$	0.791759	+	0.313480i	0.791759	+	0.313480i
$923$		0			0
$924$		0			0
$925$		0			0
$926$	0.190983	−	0.587785i	0.190983	−	0.587785i
$927$	−0.0635224	−	1.00966i	−0.0635224	−	1.00966i
$928$	−0.683098	+	0.825723i	−0.683098	+	0.825723i
$929$	−0.996398	−	1.57007i	−0.996398	−	1.57007i	−0.809017	−	0.587785i	$-0.800000\pi$
$929$	−0.996398	−	1.57007i	−0.996398	−	1.57007i	−0.187381	−	0.982287i	$-0.560000\pi$
$930$		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		0.0627905	−	0.998027i	$-0.480000\pi$
$937$		0			0		−0.0627905	+	0.998027i	$0.520000\pi$
$938$	−0.125129	−	0.0495420i	−0.125129	−	0.0495420i
$939$		0			0
$940$	1.18532	−	0.469303i	1.18532	−	0.469303i
$941$	0.0388067	−	0.119435i	0.0388067	−	0.119435i	−0.929776	−	0.368125i	$-0.880000\pi$
$941$	0.0388067	−	0.119435i	0.0388067	−	0.119435i	0.968583	+	0.248690i	$0.0800000\pi$
$942$		0			0
$943$	−2.62594	+	0.674226i	−2.62594	+	0.674226i
$944$		0			0
$945$	−0.414216	+	0.300945i	−0.414216	+	0.300945i
$946$		0			0
$947$	0.371808	+	0.0469702i	0.371808	+	0.0469702i	0.309017	−	0.951057i	$-0.400000\pi$
$947$	0.371808	+	0.0469702i	0.371808	+	0.0469702i	0.0627905	+	0.998027i	$0.480000\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$953$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	−0.683098	+	1.07639i	−0.683098	+	1.07639i
$961$	0.728969	−	0.684547i	0.728969	−	0.684547i
$962$		0			0
$963$	0.0997667	−	0.522996i	0.0997667	−	0.522996i
$964$	1.53583	−	0.844328i	1.53583	−	0.844328i
$965$		0			0
$966$	1.61142	−	1.17077i	1.61142	−	1.17077i
$967$	0.371808	+	1.94908i	0.371808	+	1.94908i	0.309017	+	0.951057i	$0.400000\pi$
$967$	0.371808	+	1.94908i	0.371808	+	1.94908i	0.0627905	+	0.998027i	$0.480000\pi$
$968$	−0.637424	−	0.770513i	−0.637424	−	0.770513i
$969$		0			0
$970$		0			0
$971$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$971$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$972$	−1.08716	−	0.137340i	−1.08716	−	0.137340i
$973$		0			0
$974$	1.50441	−	1.09302i	1.50441	−	1.09302i
$975$		0			0
$976$	1.69755	−	0.435857i	1.69755	−	0.435857i
$977$		0			0		−0.728969	−	0.684547i	$-0.760000\pi$
$977$		0			0		0.728969	+	0.684547i	$0.240000\pi$
$978$	−0.0494726	+	0.152261i	−0.0494726	+	0.152261i
$979$		0			0
$980$	0.143778	+	0.0369159i	0.143778	+	0.0369159i
$981$	0.741109	+	0.293426i	0.741109	+	0.293426i
$982$		0			0
$983$	−1.35556	−	1.27295i	−1.35556	−	1.27295i	−0.929776	−	0.368125i	$-0.880000\pi$
$983$	−1.35556	−	1.27295i	−1.35556	−	1.27295i	−0.425779	−	0.904827i	$-0.640000\pi$
$984$	−0.444215	−	2.32866i	−0.444215	−	2.32866i
$985$		0			0
$986$		0			0
$987$	0.109362	−	1.73825i	0.109362	−	1.73825i
$988$		0			0
$989$	−2.80200	+	0.353975i	−2.80200	+	0.353975i
$990$		0			0
$991$		0			0		0.637424	−	0.770513i	$-0.280000\pi$
$991$		0			0		−0.637424	+	0.770513i	$0.720000\pi$
$992$		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	$-0.880000\pi$
$997$		0			0		0.929776	+	0.368125i	$0.120000\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2020.1.bu.a.1179.1	yes	20
4.3	odd	2		2020.1.bu.b.1179.1	yes	20
5.4	even	2		2020.1.bu.b.1179.1	yes	20
20.19	odd	2	CM	2020.1.bu.a.1179.1	yes	20
101.52	even	25	inner	2020.1.bu.a.759.1	✓	20
404.355	odd	50		2020.1.bu.b.759.1	yes	20
505.254	even	50		2020.1.bu.b.759.1	yes	20
2020.759	odd	50	inner	2020.1.bu.a.759.1	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2020.1.bu.a.759.1	✓	20	101.52	even	25	inner
2020.1.bu.a.759.1	✓	20	2020.759	odd	50	inner
2020.1.bu.a.1179.1	yes	20	1.1	even	1	trivial
2020.1.bu.a.1179.1	yes	20	20.19	odd	2	CM
2020.1.bu.b.759.1	yes	20	404.355	odd	50
2020.1.bu.b.759.1	yes	20	505.254	even	50
2020.1.bu.b.1179.1	yes	20	4.3	odd	2
2020.1.bu.b.1179.1	yes	20	5.4	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:	\( N \)	\(=\)	\( 2020 = 2^{2} \cdot 5 \cdot 101 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2020.bu (of order \(50\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.535827 + 0.844328i) q^{2} +(-1.23480 - 0.317042i) q^{3} +(-0.425779 + 0.904827i) q^{4} +(0.535827 - 0.844328i) q^{5} +(-0.393950 - 1.21245i) q^{6} +(-0.996398 + 0.394502i) q^{7} +(-0.992115 + 0.125333i) q^{8} +(0.547900 + 0.301210i) q^{9} +O(q^{10})\)	\(q+(0.535827 + 0.844328i) q^{2} +(-1.23480 - 0.317042i) q^{3} +(-0.425779 + 0.904827i) q^{4} +(0.535827 - 0.844328i) q^{5} +(-0.393950 - 1.21245i) q^{6} +(-0.996398 + 0.394502i) q^{7} +(-0.992115 + 0.125333i) q^{8} +(0.547900 + 0.301210i) q^{9} +1.00000 q^{10} +(0.812619 - 0.982287i) q^{12} +(-0.866986 - 0.629902i) q^{14} +(-0.929324 + 0.872693i) q^{15} +(-0.637424 - 0.770513i) q^{16} +(0.0392590 + 0.624004i) q^{18} +(0.535827 + 0.844328i) q^{20} +(1.35542 - 0.171230i) q^{21} +(0.0915446 - 1.45506i) q^{23} +(1.26480 + 0.159781i) q^{24} +(-0.425779 - 0.904827i) q^{25} +(0.348276 + 0.327053i) q^{27} +(0.0672897 - 1.06954i) q^{28} +(-0.996398 - 0.394502i) q^{29} +(-1.23480 - 0.317042i) q^{30} +(0.309017 - 0.951057i) q^{32} +(-0.200808 + 1.05267i) q^{35} +(-0.505828 + 0.367505i) q^{36} +(-0.425779 + 0.904827i) q^{40} +(-0.574633 - 1.76854i) q^{41} +(0.870846 + 1.05267i) q^{42} +(-0.362989 - 1.90285i) q^{43} +(0.547900 - 0.301210i) q^{45} +(1.27760 - 0.702367i) q^{46} +(0.238883 - 1.25227i) q^{47} +(0.542804 + 1.15352i) q^{48} +(0.108209 - 0.101615i) q^{49} +(0.535827 - 0.844328i) q^{50} +(-0.0895243 + 0.469303i) q^{54} +(0.939097 - 0.516273i) q^{56} +(-0.200808 - 1.05267i) q^{58} +(-0.393950 - 1.21245i) q^{60} +(-0.746226 + 1.58581i) q^{61} +(-0.664754 - 0.0839780i) q^{63} +(0.968583 - 0.248690i) q^{64} +(0.121636 - 0.0312307i) q^{67} +(-0.574354 + 1.76768i) q^{69} +(-0.996398 + 0.394502i) q^{70} +(-0.581331 - 0.230165i) q^{72} +(0.238883 + 1.25227i) q^{75} +(-0.992115 + 0.125333i) q^{80} +(-0.661379 - 1.04217i) q^{81} +(1.18532 - 1.43281i) q^{82} +(0.121636 + 1.93334i) q^{83} +(-0.422178 + 1.29933i) q^{84} +(1.41213 - 1.32608i) q^{86} +(1.10528 + 0.803030i) q^{87} +(1.03137 - 1.24672i) q^{89} +(0.547900 + 0.301210i) q^{90} +(1.27760 + 0.702367i) q^{92} +(1.18532 - 0.469303i) q^{94} +(-0.683098 + 1.07639i) q^{96} +(0.143778 + 0.0369159i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 5 q^{3} - 5 q^{7} - 5 q^{9}+O(q^{10}) \) 20 * q - 5 * q^3 - 5 * q^7 - 5 * q^9	\( 20 q - 5 q^{3} - 5 q^{7} - 5 q^{9} + 20 q^{10} + 20 q^{12} + 20 q^{21} - 5 q^{27} - 5 q^{28} - 5 q^{29} - 5 q^{30} - 5 q^{32} - 5 q^{36} - 5 q^{45} - 5 q^{46} - 5 q^{49} - 5 q^{54} - 5 q^{61} - 5 q^{63} - 5 q^{67} - 5 q^{70} - 5 q^{81} - 5 q^{82} - 5 q^{83} + 15 q^{84} - 10 q^{87} - 5 q^{90} - 5 q^{92} - 5 q^{94} - 5 q^{96}+O(q^{100}) \) 20 * q - 5 * q^3 - 5 * q^7 - 5 * q^9 + 20 * q^10 + 20 * q^12 + 20 * q^21 - 5 * q^27 - 5 * q^28 - 5 * q^29 - 5 * q^30 - 5 * q^32 - 5 * q^36 - 5 * q^45 - 5 * q^46 - 5 * q^49 - 5 * q^54 - 5 * q^61 - 5 * q^63 - 5 * q^67 - 5 * q^70 - 5 * q^81 - 5 * q^82 - 5 * q^83 + 15 * q^84 - 10 * q^87 - 5 * q^90 - 5 * q^92 - 5 * q^94 - 5 * q^96

Introduction

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