LMFDB - Embedded newform 2020.1.bu.a.1439.1

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			1439.1
Root			$0.637424 - 0.770513i$ of defining polynomial
Character	$\chi$	$=$	2020.1439
Dual form			2020.1.bu.a.299.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0627905 + 0.998027i) q^{2} +(-1.80113 - 0.713118i) q^{3} +(-0.992115 + 0.125333i) q^{4} +(0.0627905 - 0.998027i) q^{5} +(0.598617 - 1.84235i) q^{6} +(0.0672897 + 0.106032i) q^{7} +(-0.187381 - 0.982287i) q^{8} +(2.00657 + 1.88429i) q^{9} +O(q^{10})$	\(q+(0.0627905 + 0.998027i) q^{2} +(-1.80113 - 0.713118i) q^{3} +(-0.992115 + 0.125333i) q^{4} +(0.0627905 - 0.998027i) q^{5} +(0.598617 - 1.84235i) q^{6} +(0.0672897 + 0.106032i) q^{7} +(-0.187381 - 0.982287i) q^{8} +(2.00657 + 1.88429i) q^{9} +1.00000 q^{10} +(1.87631 + 0.481754i) q^{12} +(-0.101597 + 0.0738147i) q^{14} +(-0.824805 + 1.75280i) q^{15} +(0.968583 - 0.248690i) q^{16} +(-1.75458 + 2.12093i) q^{18} +(0.0627905 + 0.998027i) q^{20} +(-0.0455845 - 0.238962i) q^{21} +(0.542804 + 0.656137i) q^{23} +(-0.362989 + 1.90285i) q^{24} +(-0.992115 - 0.125333i) q^{25} +(-1.44556 - 3.07198i) q^{27} +(-0.0800484 - 0.0967619i) q^{28} +(0.0672897 - 0.106032i) q^{29} +(-1.80113 - 0.713118i) q^{30} +(0.309017 + 0.951057i) q^{32} +(0.110048 - 0.0604991i) q^{35} +(-2.22691 - 1.61795i) q^{36} +(-0.992115 + 0.125333i) q^{40} +(0.331159 - 1.01920i) q^{41} +(0.235629 - 0.0604991i) q^{42} +(-1.62954 - 0.895846i) q^{43} +(2.00657 - 1.88429i) q^{45} +(-0.620759 + 0.582932i) q^{46} +(1.69755 - 0.933237i) q^{47} +(-1.92189 - 0.242791i) q^{48} +(0.419064 - 0.890557i) q^{49} +(0.0627905 - 0.998027i) q^{50} +(2.97515 - 1.63560i) q^{54} +(0.0915446 - 0.0859661i) q^{56} +(0.110048 + 0.0604991i) q^{58} +(0.598617 - 1.84235i) q^{60} +(-1.44644 + 0.182728i) q^{61} +(-0.0647732 + 0.339553i) q^{63} +(-0.929776 + 0.368125i) q^{64} +(1.18532 - 0.469303i) q^{67} +(-0.509758 - 1.56887i) q^{69} +(0.0672897 + 0.106032i) q^{70} +(1.47492 - 2.32411i) q^{72} +(1.69755 + 0.933237i) q^{75} +(-0.187381 - 0.982287i) q^{80} +(0.240128 + 3.81672i) q^{81} +(1.03799 + 0.266509i) q^{82} +(1.18532 - 1.43281i) q^{83} +(0.0751750 + 0.231365i) q^{84} +(0.791759 - 1.68257i) q^{86} +(-0.196811 + 0.142991i) q^{87} +(-1.56720 - 0.402389i) q^{89} +(2.00657 + 1.88429i) q^{90} +(-0.620759 - 0.582932i) q^{92} +(1.03799 + 1.63560i) q^{94} +(0.121636 - 1.93334i) q^{96} +(0.915113 + 0.362319i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2020\mathbb{Z}\right)^\times$.

$n$	$1011$	$1617$	$1921$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{12}{25}\right)$

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 $

$2$	0.0627905	+	0.998027i	0.0627905	+	0.998027i
$2$	0.0627905	+	0.998027i	0.0627905	+	0.998027i
$3$	−1.80113	−	0.713118i	−1.80113	−	0.713118i	−0.992115	−	0.125333i	$-0.960000\pi$
$3$	−1.80113	−	0.713118i	−1.80113	−	0.713118i	−0.809017	−	0.587785i	$-0.800000\pi$
$4$	−0.992115	+	0.125333i	−0.992115	+	0.125333i
$5$	0.0627905	−	0.998027i	0.0627905	−	0.998027i
$5$	0.0627905	−	0.998027i	0.0627905	−	0.998027i
$6$	0.598617	−	1.84235i	0.598617	−	1.84235i
$7$	0.0672897	+	0.106032i	0.0672897	+	0.106032i	0.876307	−	0.481754i	$-0.160000\pi$
$7$	0.0672897	+	0.106032i	0.0672897	+	0.106032i	−0.809017	+	0.587785i	$0.800000\pi$
$8$	−0.187381	−	0.982287i	−0.187381	−	0.982287i
$9$	2.00657	+	1.88429i	2.00657	+	1.88429i
$10$	1.00000			1.00000
$11$		0			0		−0.728969	−	0.684547i	$-0.760000\pi$
$11$		0			0		0.728969	+	0.684547i	$0.240000\pi$
$12$	1.87631	+	0.481754i	1.87631	+	0.481754i
$13$		0			0		0.535827	−	0.844328i	$-0.320000\pi$
$13$		0			0		−0.535827	+	0.844328i	$0.680000\pi$
$14$	−0.101597	+	0.0738147i	−0.101597	+	0.0738147i
$15$	−0.824805	+	1.75280i	−0.824805	+	1.75280i
$16$	0.968583	−	0.248690i	0.968583	−	0.248690i
$17$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$17$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$18$	−1.75458	+	2.12093i	−1.75458	+	2.12093i
$19$		0			0		−0.968583	−	0.248690i	$-0.920000\pi$
$19$		0			0		0.968583	+	0.248690i	$0.0800000\pi$
$20$	0.0627905	+	0.998027i	0.0627905	+	0.998027i
$21$	−0.0455845	−	0.238962i	−0.0455845	−	0.238962i
$22$		0			0
$23$	0.542804	+	0.656137i	0.542804	+	0.656137i	0.968583	−	0.248690i	$-0.0800000\pi$
$23$	0.542804	+	0.656137i	0.542804	+	0.656137i	−0.425779	+	0.904827i	$0.640000\pi$
$24$	−0.362989	+	1.90285i	−0.362989	+	1.90285i
$25$	−0.992115	−	0.125333i	−0.992115	−	0.125333i
$26$		0			0
$27$	−1.44556	−	3.07198i	−1.44556	−	3.07198i
$28$	−0.0800484	−	0.0967619i	−0.0800484	−	0.0967619i
$29$	0.0672897	−	0.106032i	0.0672897	−	0.106032i	−0.809017	−	0.587785i	$-0.800000\pi$
$29$	0.0672897	−	0.106032i	0.0672897	−	0.106032i	0.876307	+	0.481754i	$0.160000\pi$
$30$	−1.80113	−	0.713118i	−1.80113	−	0.713118i
$31$		0			0		−0.535827	−	0.844328i	$-0.680000\pi$
$31$		0			0		0.535827	+	0.844328i	$0.320000\pi$
$32$	0.309017	+	0.951057i	0.309017	+	0.951057i
$33$		0			0
$34$		0			0
$35$	0.110048	−	0.0604991i	0.110048	−	0.0604991i
$36$	−2.22691	−	1.61795i	−2.22691	−	1.61795i
$37$		0			0		0.929776	−	0.368125i	$-0.120000\pi$
$37$		0			0		−0.929776	+	0.368125i	$0.880000\pi$
$38$		0			0
$39$		0			0
$40$	−0.992115	+	0.125333i	−0.992115	+	0.125333i
$41$	0.331159	−	1.01920i	0.331159	−	1.01920i	−0.637424	−	0.770513i	$-0.720000\pi$
$41$	0.331159	−	1.01920i	0.331159	−	1.01920i	0.968583	−	0.248690i	$-0.0800000\pi$
$42$	0.235629	−	0.0604991i	0.235629	−	0.0604991i
$43$	−1.62954	−	0.895846i	−1.62954	−	0.895846i	−0.992115	−	0.125333i	$-0.960000\pi$
$43$	−1.62954	−	0.895846i	−1.62954	−	0.895846i	−0.637424	−	0.770513i	$-0.720000\pi$
$44$		0			0
$45$	2.00657	−	1.88429i	2.00657	−	1.88429i
$46$	−0.620759	+	0.582932i	−0.620759	+	0.582932i
$47$	1.69755	−	0.933237i	1.69755	−	0.933237i	0.728969	−	0.684547i	$-0.240000\pi$
$47$	1.69755	−	0.933237i	1.69755	−	0.933237i	0.968583	−	0.248690i	$-0.0800000\pi$
$48$	−1.92189	−	0.242791i	−1.92189	−	0.242791i
$49$	0.419064	−	0.890557i	0.419064	−	0.890557i
$50$	0.0627905	−	0.998027i	0.0627905	−	0.998027i
$51$		0			0
$52$		0			0
$53$		0			0		−0.992115	−	0.125333i	$-0.960000\pi$
$53$		0			0		0.992115	+	0.125333i	$0.0400000\pi$
$54$	2.97515	−	1.63560i	2.97515	−	1.63560i
$55$		0			0
$56$	0.0915446	−	0.0859661i	0.0915446	−	0.0859661i
$57$		0			0
$58$	0.110048	+	0.0604991i	0.110048	+	0.0604991i
$59$		0			0		0.968583	−	0.248690i	$-0.0800000\pi$
$59$		0			0		−0.968583	+	0.248690i	$0.920000\pi$
$60$	0.598617	−	1.84235i	0.598617	−	1.84235i
$61$	−1.44644	+	0.182728i	−1.44644	+	0.182728i	−0.809017	−	0.587785i	$-0.800000\pi$
$61$	−1.44644	+	0.182728i	−1.44644	+	0.182728i	−0.637424	+	0.770513i	$0.720000\pi$
$62$		0			0
$63$	−0.0647732	+	0.339553i	−0.0647732	+	0.339553i
$64$	−0.929776	+	0.368125i	−0.929776	+	0.368125i
$65$		0			0
$66$		0			0
$67$	1.18532	−	0.469303i	1.18532	−	0.469303i	0.309017	−	0.951057i	$-0.400000\pi$
$67$	1.18532	−	0.469303i	1.18532	−	0.469303i	0.876307	+	0.481754i	$0.160000\pi$
$68$		0			0
$69$	−0.509758	−	1.56887i	−0.509758	−	1.56887i
$70$	0.0672897	+	0.106032i	0.0672897	+	0.106032i
$71$		0			0		−0.929776	−	0.368125i	$-0.880000\pi$
$71$		0			0		0.929776	+	0.368125i	$0.120000\pi$
$72$	1.47492	−	2.32411i	1.47492	−	2.32411i
$73$		0			0		−0.637424	−	0.770513i	$-0.720000\pi$
$73$		0			0		0.637424	+	0.770513i	$0.280000\pi$
$74$		0			0
$75$	1.69755	+	0.933237i	1.69755	+	0.933237i
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		0.637424	−	0.770513i	$-0.280000\pi$
$79$		0			0		−0.637424	+	0.770513i	$0.720000\pi$
$80$	−0.187381	−	0.982287i	−0.187381	−	0.982287i
$81$	0.240128	+	3.81672i	0.240128	+	3.81672i
$82$	1.03799	+	0.266509i	1.03799	+	0.266509i
$83$	1.18532	−	1.43281i	1.18532	−	1.43281i	0.309017	−	0.951057i	$-0.400000\pi$
$83$	1.18532	−	1.43281i	1.18532	−	1.43281i	0.876307	−	0.481754i	$-0.160000\pi$
$84$	0.0751750	+	0.231365i	0.0751750	+	0.231365i
$85$		0			0
$86$	0.791759	−	1.68257i	0.791759	−	1.68257i
$87$	−0.196811	+	0.142991i	−0.196811	+	0.142991i
$88$		0			0
$89$	−1.56720	−	0.402389i	−1.56720	−	0.402389i	−0.637424	−	0.770513i	$-0.720000\pi$
$89$	−1.56720	−	0.402389i	−1.56720	−	0.402389i	−0.929776	+	0.368125i	$0.880000\pi$
$90$	2.00657	+	1.88429i	2.00657	+	1.88429i
$91$		0			0
$92$	−0.620759	−	0.582932i	−0.620759	−	0.582932i
$93$		0			0
$94$	1.03799	+	1.63560i	1.03799	+	1.63560i
$95$		0			0
$96$	0.121636	−	1.93334i	0.121636	−	1.93334i
$97$		0			0		0.992115	−	0.125333i	$-0.0400000\pi$
$97$		0			0		−0.992115	+	0.125333i	$0.960000\pi$
$98$	0.915113	+	0.362319i	0.915113	+	0.362319i
$99$		0			0
$100$	1.00000			1.00000
$101$	−0.187381	−	0.982287i	−0.187381	−	0.982287i
$101$	−0.187381	−	0.982287i	−0.187381	−	0.982287i
$102$		0			0
$103$	−0.101597	−	1.61484i	−0.101597	−	1.61484i	−0.637424	−	0.770513i	$-0.720000\pi$
$103$	−0.101597	−	1.61484i	−0.101597	−	1.61484i	0.535827	−	0.844328i	$-0.320000\pi$
$104$		0			0
$105$	−0.241353	+	0.0304900i	−0.241353	+	0.0304900i
$106$		0			0
$107$	−0.613161	+	1.88711i	−0.613161	+	1.88711i	−0.187381	+	0.982287i	$0.560000\pi$
$107$	−0.613161	+	1.88711i	−0.613161	+	1.88711i	−0.425779	+	0.904827i	$0.640000\pi$
$108$	1.81919	+	2.86658i	1.81919	+	2.86658i
$109$	−0.362989	−	1.90285i	−0.362989	−	1.90285i	−0.425779	−	0.904827i	$-0.640000\pi$
$109$	−0.362989	−	1.90285i	−0.362989	−	1.90285i	0.0627905	−	0.998027i	$-0.480000\pi$
$110$		0			0
$111$		0			0
$112$	0.0915446	+	0.0859661i	0.0915446	+	0.0859661i
$113$		0			0		−0.968583	−	0.248690i	$-0.920000\pi$
$113$		0			0		0.968583	+	0.248690i	$0.0800000\pi$
$114$		0			0
$115$	0.688925	−	0.500534i	0.688925	−	0.500534i
$116$	−0.0534698	+	0.113629i	−0.0534698	+	0.113629i
$117$		0			0
$118$		0			0
$119$		0			0
$120$	1.87631	+	0.481754i	1.87631	+	0.481754i
$121$	0.0627905	+	0.998027i	0.0627905	+	0.998027i
$122$	−0.273190	−	1.43211i	−0.273190	−	1.43211i
$123$	−1.32327	+	1.59956i	−1.32327	+	1.59956i
$124$		0			0
$125$	−0.187381	+	0.982287i	−0.187381	+	0.982287i
$126$	−0.342950	−	0.0433247i	−0.342950	−	0.0433247i
$127$	−1.41789	−	0.779494i	−1.41789	−	0.779494i	−0.425779	−	0.904827i	$-0.640000\pi$
$127$	−1.41789	−	0.779494i	−1.41789	−	0.779494i	−0.992115	+	0.125333i	$0.960000\pi$
$128$	−0.425779	−	0.904827i	−0.425779	−	0.904827i
$129$	2.29617	+	2.77559i	2.29617	+	2.77559i
$130$		0			0
$131$		0			0		−0.929776	−	0.368125i	$-0.880000\pi$
$131$		0			0		0.929776	+	0.368125i	$0.120000\pi$
$132$		0			0
$133$		0			0
$134$	0.542804	+	1.15352i	0.542804	+	1.15352i
$135$	−3.15669	+	1.24982i	−3.15669	+	1.24982i
$136$		0			0
$137$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$137$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$138$	1.53377	−	0.607262i	1.53377	−	0.607262i
$139$		0			0		0.187381	−	0.982287i	$-0.440000\pi$
$139$		0			0		−0.187381	+	0.982287i	$0.560000\pi$
$140$	−0.101597	+	0.0738147i	−0.101597	+	0.0738147i
$141$	−3.72302	+	0.470327i	−3.72302	+	0.470327i
$142$		0			0
$143$		0			0
$144$	2.41213	+	1.32608i	2.41213	+	1.32608i
$145$	−0.101597	−	0.0738147i	−0.101597	−	0.0738147i
$146$		0			0
$147$	−1.38986	+	1.30517i	−1.38986	+	1.30517i
$148$		0			0
$149$	1.26480	+	0.159781i	1.26480	+	0.159781i	0.728969	−	0.684547i	$-0.240000\pi$
$149$	1.26480	+	0.159781i	1.26480	+	0.159781i	0.535827	+	0.844328i	$0.320000\pi$
$150$	−0.824805	+	1.75280i	−0.824805	+	1.75280i
$151$		0			0		0.0627905	−	0.998027i	$-0.480000\pi$
$151$		0			0		−0.0627905	+	0.998027i	$0.520000\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.728969	−	0.684547i	$-0.240000\pi$
$157$		0			0		−0.728969	+	0.684547i	$0.760000\pi$
$158$		0			0
$159$		0			0
$160$	0.968583	−	0.248690i	0.968583	−	0.248690i
$161$	−0.0330462	+	0.101706i	−0.0330462	+	0.101706i
$162$	−3.79411	+	0.479308i	−3.79411	+	0.479308i
$163$	1.03137	−	0.749337i	1.03137	−	0.749337i	0.0627905	−	0.998027i	$-0.480000\pi$
$163$	1.03137	−	0.749337i	1.03137	−	0.749337i	0.968583	+	0.248690i	$0.0800000\pi$
$164$	−0.200808	+	1.05267i	−0.200808	+	1.05267i
$165$		0			0
$166$	1.50441	+	1.09302i	1.50441	+	1.09302i
$167$	−0.746226	+	0.410241i	−0.746226	+	0.410241i	−0.809017	−	0.587785i	$-0.800000\pi$
$167$	−0.746226	+	0.410241i	−0.746226	+	0.410241i	0.0627905	+	0.998027i	$0.480000\pi$
$168$	−0.226188	+	0.0895542i	−0.226188	+	0.0895542i
$169$	−0.425779	−	0.904827i	−0.425779	−	0.904827i
$170$		0			0
$171$		0			0
$172$	1.72897	+	0.684547i	1.72897	+	0.684547i
$173$		0			0		0.535827	−	0.844328i	$-0.320000\pi$
$173$		0			0		−0.535827	+	0.844328i	$0.680000\pi$
$174$	−0.155067	−	0.187444i	−0.155067	−	0.187444i
$175$	−0.0534698	−	0.113629i	−0.0534698	−	0.113629i
$176$		0			0
$177$		0			0
$178$	0.303189	−	1.58937i	0.303189	−	1.58937i
$179$		0			0		−0.637424	−	0.770513i	$-0.720000\pi$
$179$		0			0		0.637424	+	0.770513i	$0.280000\pi$
$180$	−1.75458	+	2.12093i	−1.75458	+	2.12093i
$181$	0.348445	+	1.82662i	0.348445	+	1.82662i	0.535827	+	0.844328i	$0.320000\pi$
$181$	0.348445	+	1.82662i	0.348445	+	1.82662i	−0.187381	+	0.982287i	$0.560000\pi$
$182$		0			0
$183$	2.73554	+	0.702367i	2.73554	+	0.702367i
$184$	0.542804	−	0.656137i	0.542804	−	0.656137i
$185$		0			0
$186$		0			0
$187$		0			0
$188$	−1.56720	+	1.13864i	−1.56720	+	1.13864i
$189$	0.228455	−	0.359988i	0.228455	−	0.359988i
$190$		0			0
$191$		0			0		−0.728969	−	0.684547i	$-0.760000\pi$
$191$		0			0		0.728969	+	0.684547i	$0.240000\pi$
$192$	1.93717			1.93717
$193$		0			0		−0.728969	−	0.684547i	$-0.760000\pi$
$193$		0			0		0.728969	+	0.684547i	$0.240000\pi$
$194$		0			0
$195$		0			0
$196$	−0.304144	+	0.936058i	−0.304144	+	0.936058i
$197$		0			0		0.0627905	−	0.998027i	$-0.480000\pi$
$197$		0			0		−0.0627905	+	0.998027i	$0.520000\pi$
$198$		0			0
$199$		0			0		−0.929776	−	0.368125i	$-0.880000\pi$
$199$		0			0		0.929776	+	0.368125i	$0.120000\pi$
$200$	0.0627905	+	0.998027i	0.0627905	+	0.998027i
$201$	−2.46959			−2.46959
$202$	0.968583	−	0.248690i	0.968583	−	0.248690i
$203$	0.0157706			0.0157706
$204$		0			0
$205$	−0.996398	−	0.394502i	−0.996398	−	0.394502i
$206$	1.60528	−	0.202793i	1.60528	−	0.202793i
$207$	−0.147182	+	2.33939i	−0.147182	+	2.33939i
$208$		0			0
$209$		0			0
$210$	−0.0455845	−	0.238962i	−0.0455845	−	0.238962i
$211$		0			0		−0.728969	−	0.684547i	$-0.760000\pi$
$211$		0			0		0.728969	+	0.684547i	$0.240000\pi$
$212$		0			0
$213$		0			0
$214$	−1.92189	−	0.493458i	−1.92189	−	0.493458i
$215$	−0.996398	+	1.57007i	−0.996398	+	1.57007i
$216$	−2.74670	+	1.99559i	−2.74670	+	1.99559i
$217$		0			0
$218$	1.87631	−	0.481754i	1.87631	−	0.481754i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−0.328407	−	1.72157i	−0.328407	−	1.72157i	−0.637424	−	0.770513i	$-0.720000\pi$
$223$	−0.328407	−	1.72157i	−0.328407	−	1.72157i	0.309017	−	0.951057i	$-0.400000\pi$
$224$	−0.0800484	+	0.0967619i	−0.0800484	+	0.0967619i
$225$	−1.75458	−	2.12093i	−1.75458	−	2.12093i
$226$		0			0
$227$	1.26480	+	0.159781i	1.26480	+	0.159781i	0.728969	−	0.684547i	$-0.240000\pi$
$227$	1.26480	+	0.159781i	1.26480	+	0.159781i	0.535827	+	0.844328i	$0.320000\pi$
$228$		0			0
$229$	−0.263146	−	0.559214i	−0.263146	−	0.559214i	0.728969	−	0.684547i	$-0.240000\pi$
$229$	−0.263146	−	0.559214i	−0.263146	−	0.559214i	−0.992115	+	0.125333i	$0.960000\pi$
$230$	0.542804	+	0.656137i	0.542804	+	0.656137i
$231$		0			0
$232$	−0.116762	−	0.0462295i	−0.116762	−	0.0462295i
$233$		0			0		−0.535827	−	0.844328i	$-0.680000\pi$
$233$		0			0		0.535827	+	0.844328i	$0.320000\pi$
$234$		0			0
$235$	−0.824805	−	1.75280i	−0.824805	−	1.75280i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		0.929776	−	0.368125i	$-0.120000\pi$
$239$		0			0		−0.929776	+	0.368125i	$0.880000\pi$
$240$	−0.362989	+	1.90285i	−0.362989	+	1.90285i
$241$	−1.17950	+	0.856954i	−1.17950	+	0.856954i	−0.992115	−	0.125333i	$-0.960000\pi$
$241$	−1.17950	+	0.856954i	−1.17950	+	0.856954i	−0.187381	+	0.982287i	$0.560000\pi$
$242$	−0.992115	+	0.125333i	−0.992115	+	0.125333i
$243$	1.24013	−	3.81672i	1.24013	−	3.81672i
$244$	1.41213	−	0.362574i	1.41213	−	0.362574i
$245$	−0.862487	−	0.474156i	−0.862487	−	0.474156i
$246$	−1.67950	−	1.22023i	−1.67950	−	1.22023i
$247$		0			0
$248$		0			0
$249$	−3.15669	+	1.73540i	−3.15669	+	1.73540i
$250$	−0.992115	−	0.125333i	−0.992115	−	0.125333i
$251$		0			0		0.425779	−	0.904827i	$-0.360000\pi$
$251$		0			0		−0.425779	+	0.904827i	$0.640000\pi$
$252$	0.0217052	−	0.344994i	0.0217052	−	0.344994i
$253$		0			0
$254$	0.688925	−	1.46404i	0.688925	−	1.46404i
$255$		0			0
$256$	0.876307	−	0.481754i	0.876307	−	0.481754i
$257$		0			0		0.728969	−	0.684547i	$-0.240000\pi$
$257$		0			0		−0.728969	+	0.684547i	$0.760000\pi$
$258$	−2.62594	+	2.46592i	−2.62594	+	2.46592i
$259$		0			0
$260$		0			0
$261$	0.334816	−	0.0859661i	0.334816	−	0.0859661i
$262$		0			0
$263$	0.371808	−	0.0469702i	0.371808	−	0.0469702i	0.0627905	−	0.998027i	$-0.480000\pi$
$263$	0.371808	−	0.0469702i	0.371808	−	0.0469702i	0.309017	+	0.951057i	$0.400000\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	2.53578	+	1.84235i	2.53578	+	1.84235i
$268$	−1.11716	+	0.614163i	−1.11716	+	0.614163i
$269$	1.84489	−	0.730444i	1.84489	−	0.730444i	0.876307	−	0.481754i	$-0.160000\pi$
$269$	1.84489	−	0.730444i	1.84489	−	0.730444i	0.968583	−	0.248690i	$-0.0800000\pi$
$270$	−1.44556	−	3.07198i	−1.44556	−	3.07198i
$271$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$271$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$	0.702370	+	1.49261i	0.702370	+	1.49261i
$277$		0			0		−0.876307	−	0.481754i	$-0.840000\pi$
$277$		0			0		0.876307	+	0.481754i	$0.160000\pi$
$278$		0			0
$279$		0			0
$280$	−0.0800484	−	0.0967619i	−0.0800484	−	0.0967619i
$281$	0.542804	−	0.656137i	0.542804	−	0.656137i	−0.425779	−	0.904827i	$-0.640000\pi$
$281$	0.542804	−	0.656137i	0.542804	−	0.656137i	0.968583	+	0.248690i	$0.0800000\pi$
$282$	−0.703170	−	3.68614i	−0.703170	−	3.68614i
$283$	0.0672897	+	1.06954i	0.0672897	+	1.06954i	0.876307	+	0.481754i	$0.160000\pi$
$283$	0.0672897	+	1.06954i	0.0672897	+	1.06954i	−0.809017	+	0.587785i	$0.800000\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	0.130351	−	0.0334685i	0.130351	−	0.0334685i
$288$	−1.17201	+	2.49064i	−1.17201	+	2.49064i
$289$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$290$	0.0672897	−	0.106032i	0.0672897	−	0.106032i
$291$		0			0
$292$		0			0
$293$		0			0		1.00000			$0$
$293$		0			0		−1.00000			$\pi$
$294$	−1.38986	−	1.30517i	−1.38986	−	1.30517i
$295$		0			0
$296$		0			0
$297$		0			0
$298$	−0.0800484	+	1.27233i	−0.0800484	+	1.27233i
$299$		0			0
$300$	−1.80113	−	0.713118i	−1.80113	−	0.713118i
$301$	−0.0146631	−	0.233064i	−0.0146631	−	0.233064i
$302$		0			0
$303$	−0.362989	+	1.90285i	−0.362989	+	1.90285i
$304$		0			0
$305$	0.0915446	+	1.45506i	0.0915446	+	1.45506i
$306$		0			0
$307$	−0.124591	+	0.0157395i	−0.124591	+	0.0157395i	−0.187381	−	0.982287i	$-0.560000\pi$
$307$	−0.124591	+	0.0157395i	−0.124591	+	0.0157395i	0.0627905	+	0.998027i	$0.480000\pi$
$308$		0			0
$309$	−0.968583	+	2.98099i	−0.968583	+	2.98099i
$310$		0			0
$311$		0			0		−0.187381	−	0.982287i	$-0.560000\pi$
$311$		0			0		0.187381	+	0.982287i	$0.440000\pi$
$312$		0			0
$313$		0			0		1.00000			$0$
$313$		0			0		−1.00000			$\pi$
$314$		0			0
$315$	0.334816	+	0.0859661i	0.334816	+	0.0859661i
$316$		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
$321$	2.45012	−	2.96169i	2.45012	−	2.96169i
$322$	−0.103580	−	0.0265948i	−0.103580	−	0.0265948i
$323$		0			0
$324$	−0.716596	−	3.75653i	−0.716596	−	3.75653i
$325$		0			0
$326$	0.812619	+	0.982287i	0.812619	+	0.982287i
$327$	−0.703170	+	3.68614i	−0.703170	+	3.68614i
$328$	−1.06320	−	0.134314i	−1.06320	−	0.134314i
$329$	0.213180	+	0.117197i	0.213180	+	0.117197i
$330$		0			0
$331$		0			0		−0.637424	−	0.770513i	$-0.720000\pi$
$331$		0			0		0.637424	+	0.770513i	$0.280000\pi$
$332$	−0.996398	+	1.57007i	−0.996398	+	1.57007i
$333$		0			0
$334$	−0.456288	−	0.718995i	−0.456288	−	0.718995i
$335$	−0.393950	−	1.21245i	−0.393950	−	1.21245i
$336$	−0.103580	−	0.220119i	−0.103580	−	0.220119i
$337$		0			0		0.929776	−	0.368125i	$-0.120000\pi$
$337$		0			0		−0.929776	+	0.368125i	$0.880000\pi$
$338$	0.876307	−	0.481754i	0.876307	−	0.481754i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	0.247217	−	0.0312307i	0.247217	−	0.0312307i
$344$	−0.574633	+	1.76854i	−0.574633	+	1.76854i
$345$	−1.59779	+	0.410241i	−1.59779	+	0.410241i
$346$		0			0
$347$	1.60528	+	1.16630i	1.60528	+	1.16630i	0.876307	+	0.481754i	$0.160000\pi$
$347$	1.60528	+	1.16630i	1.60528	+	1.16630i	0.728969	+	0.684547i	$0.240000\pi$
$348$	0.177337	−	0.166531i	0.177337	−	0.166531i
$349$	1.27760	−	1.19975i	1.27760	−	1.19975i	0.309017	−	0.951057i	$-0.400000\pi$
$349$	1.27760	−	1.19975i	1.27760	−	1.19975i	0.968583	−	0.248690i	$-0.0800000\pi$
$350$	0.110048	−	0.0604991i	0.110048	−	0.0604991i
$351$		0			0
$352$		0			0
$353$		0			0		0.0627905	−	0.998027i	$-0.480000\pi$
$353$		0			0		−0.0627905	+	0.998027i	$0.520000\pi$
$354$		0			0
$355$		0			0
$356$	1.60528	+	0.202793i	1.60528	+	0.202793i
$357$		0			0
$358$		0			0
$359$		0			0		0.728969	−	0.684547i	$-0.240000\pi$
$359$		0			0		−0.728969	+	0.684547i	$0.760000\pi$
$360$	−2.22691	−	1.61795i	−2.22691	−	1.61795i
$361$	0.876307	+	0.481754i	0.876307	+	0.481754i
$362$	−1.80113	+	0.462452i	−1.80113	+	0.462452i
$363$	0.598617	−	1.84235i	0.598617	−	1.84235i
$364$		0			0
$365$		0			0
$366$	−0.529215	+	2.77424i	−0.529215	+	2.77424i
$367$	1.50441	−	0.595638i	1.50441	−	0.595638i	0.535827	−	0.844328i	$-0.320000\pi$
$367$	1.50441	−	0.595638i	1.50441	−	0.595638i	0.968583	+	0.248690i	$0.0800000\pi$
$368$	0.688925	+	0.500534i	0.688925	+	0.500534i
$369$	2.58497	−	1.42110i	2.58497	−	1.42110i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.535827	−	0.844328i	$-0.680000\pi$
$373$		0			0		0.535827	+	0.844328i	$0.320000\pi$
$374$		0			0
$375$	1.03799	−	1.63560i	1.03799	−	1.63560i
$376$	−1.23480	−	1.49261i	−1.23480	−	1.49261i
$377$		0			0
$378$	0.373623	+	0.205401i	0.373623	+	0.205401i
$379$		0			0		−0.992115	−	0.125333i	$-0.960000\pi$
$379$		0			0		0.992115	+	0.125333i	$0.0400000\pi$
$380$		0			0
$381$	1.99794	+	2.41510i	1.99794	+	2.41510i
$382$		0			0
$383$	0.0702235	+	0.368125i	0.0702235	+	0.368125i	1.00000			$0$
$383$	0.0702235	+	0.368125i	0.0702235	+	0.368125i	−0.929776	+	0.368125i	$0.880000\pi$
$384$	0.121636	+	1.93334i	0.121636	+	1.93334i
$385$		0			0
$386$		0			0
$387$	−1.58174	−	4.86811i	−1.58174	−	4.86811i
$388$		0			0
$389$	−0.851559	+	1.80965i	−0.851559	+	1.80965i	−0.425779	+	0.904827i	$0.640000\pi$
$389$	−0.851559	+	1.80965i	−0.851559	+	1.80965i	−0.425779	+	0.904827i	$0.640000\pi$
$390$		0			0
$391$		0			0
$392$	−0.953308	−	0.244768i	−0.953308	−	0.244768i
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$		0			0		−0.535827	−	0.844328i	$-0.680000\pi$
$397$		0			0		0.535827	+	0.844328i	$0.320000\pi$
$398$		0			0
$399$		0			0
$400$	−0.992115	+	0.125333i	−0.992115	+	0.125333i
$401$	−0.574633	−	0.227513i	−0.574633	−	0.227513i	0.0627905	−	0.998027i	$-0.480000\pi$
$401$	−0.574633	−	0.227513i	−0.574633	−	0.227513i	−0.637424	+	0.770513i	$0.720000\pi$
$402$	−0.155067	−	2.46472i	−0.155067	−	2.46472i
$403$		0			0
$404$	0.309017	+	0.951057i	0.309017	+	0.951057i
$405$	3.82427			3.82427
$406$	0.000990244		0.0157395i	0.000990244		0.0157395i
$407$		0			0
$408$		0			0
$409$	−0.0534698	+	0.849878i	−0.0534698	+	0.849878i	0.876307	+	0.481754i	$0.160000\pi$
$409$	−0.0534698	+	0.849878i	−0.0534698	+	0.849878i	−0.929776	+	0.368125i	$0.880000\pi$
$410$	0.331159	−	1.01920i	0.331159	−	1.01920i
$411$		0			0
$412$	0.303189	+	1.58937i	0.303189	+	1.58937i
$413$		0			0
$414$	−2.34401			−2.34401
$415$	−1.35556	−	1.27295i	−1.35556	−	1.27295i
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		0.425779	−	0.904827i	$-0.360000\pi$
$419$		0			0		−0.425779	+	0.904827i	$0.640000\pi$
$420$	0.235629	−	0.0604991i	0.235629	−	0.0604991i
$421$	−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
$423$	5.16475	+	1.32608i	5.16475	+	1.32608i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−0.116705	−	0.141073i	−0.116705	−	0.141073i
$428$	0.371808	−	1.94908i	0.371808	−	1.94908i
$429$		0			0
$430$	−1.62954	−	0.895846i	−1.62954	−	0.895846i
$431$		0			0		−0.425779	−	0.904827i	$-0.640000\pi$
$431$		0			0		0.425779	+	0.904827i	$0.360000\pi$
$432$	−2.16412	−	2.61597i	−2.16412	−	2.61597i
$433$		0			0		0.535827	−	0.844328i	$-0.320000\pi$
$433$		0			0		−0.535827	+	0.844328i	$0.680000\pi$
$434$		0			0
$435$	0.130351	+	0.205401i	0.130351	+	0.205401i
$436$	0.598617	+	1.84235i	0.598617	+	1.84235i
$437$		0			0
$438$		0			0
$439$		0			0		0.876307	−	0.481754i	$-0.160000\pi$
$439$		0			0		−0.876307	+	0.481754i	$0.840000\pi$
$440$		0			0
$441$	2.51895	−	0.997324i	2.51895	−	0.997324i
$442$		0			0
$443$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	−0.809017	−	0.587785i	$-0.800000\pi$
$443$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	0.309017	+	0.951057i	$0.400000\pi$
$444$		0			0
$445$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$446$	1.69755	−	0.435857i	1.69755	−	0.435857i
$447$	−2.16412	−	1.18974i	−2.16412	−	1.18974i
$448$	−0.101597	−	0.0738147i	−0.101597	−	0.0738147i
$449$	1.06279	−	0.998027i	1.06279	−	0.998027i	0.0627905	−	0.998027i	$-0.480000\pi$
$449$	1.06279	−	0.998027i	1.06279	−	0.998027i	1.00000			$0$
$450$	2.00657	−	1.88429i	2.00657	−	1.88429i
$451$		0			0
$452$		0			0
$453$		0			0
$454$	−0.0800484	+	1.27233i	−0.0800484	+	1.27233i
$455$		0			0
$456$		0			0
$457$		0			0		−0.992115	−	0.125333i	$-0.960000\pi$
$457$		0			0		0.992115	+	0.125333i	$0.0400000\pi$
$458$	0.541587	−	0.297740i	0.541587	−	0.297740i
$459$		0			0
$460$	−0.620759	+	0.582932i	−0.620759	+	0.582932i
$461$	1.60528	+	1.16630i	1.60528	+	1.16630i	0.876307	+	0.481754i	$0.160000\pi$
$461$	1.60528	+	1.16630i	1.60528	+	1.16630i	0.728969	+	0.684547i	$0.240000\pi$
$462$		0			0
$463$	0.598617	−	0.153699i	0.598617	−	0.153699i	0.0627905	−	0.998027i	$-0.480000\pi$
$463$	0.598617	−	0.153699i	0.598617	−	0.153699i	0.535827	+	0.844328i	$0.320000\pi$
$464$	0.0388067	−	0.119435i	0.0388067	−	0.119435i
$465$		0			0
$466$		0			0
$467$	−0.200808	+	1.05267i	−0.200808	+	1.05267i	0.728969	+	0.684547i	$0.240000\pi$
$467$	−0.200808	+	1.05267i	−0.200808	+	1.05267i	−0.929776	+	0.368125i	$0.880000\pi$
$468$		0			0
$469$	0.129521	+	0.0941025i	0.129521	+	0.0941025i
$470$	1.69755	−	0.933237i	1.69755	−	0.933237i
$471$		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		−0.876307	−	0.481754i	$-0.840000\pi$
$479$		0			0		0.876307	+	0.481754i	$0.160000\pi$
$480$	−1.92189	−	0.242791i	−1.92189	−	0.242791i
$481$		0			0
$482$	−0.929324	−	1.12336i	−0.929324	−	1.12336i
$483$	0.132049	−	0.159619i	0.132049	−	0.159619i
$484$	−0.187381	−	0.982287i	−0.187381	−	0.982287i
$485$		0			0
$486$	3.88706	+	0.998027i	3.88706	+	0.998027i
$487$	−0.683098	+	0.825723i	−0.683098	+	0.825723i	−0.992115	−	0.125333i	$-0.960000\pi$
$487$	−0.683098	+	0.825723i	−0.683098	+	0.825723i	0.309017	+	0.951057i	$0.400000\pi$
$488$	0.450527	+	1.38658i	0.450527	+	1.38658i
$489$	−2.39201	+	0.614163i	−2.39201	+	0.614163i
$490$	0.419064	−	0.890557i	0.419064	−	0.890557i
$491$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$491$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$492$	1.11236	−	1.75280i	1.11236	−	1.75280i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−1.93019	−	3.04149i	−1.93019	−	3.04149i
$499$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$499$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$500$	0.0627905	−	0.998027i	0.0627905	−	0.998027i
$501$	1.63660	−	0.206751i	1.63660	−	0.206751i
$502$		0			0
$503$	0.0915446	+	1.45506i	0.0915446	+	1.45506i	0.728969	+	0.684547i	$0.240000\pi$
$503$	0.0915446	+	1.45506i	0.0915446	+	1.45506i	−0.637424	+	0.770513i	$0.720000\pi$
$504$	0.345676			0.345676
$505$	−0.992115	+	0.125333i	−0.992115	+	0.125333i
$506$		0			0
$507$	0.121636	+	1.93334i	0.121636	+	1.93334i
$508$	1.50441	+	0.595638i	1.50441	+	0.595638i
$509$	1.84489	−	0.233064i	1.84489	−	0.233064i	0.876307	−	0.481754i	$-0.160000\pi$
$509$	1.84489	−	0.233064i	1.84489	−	0.233064i	0.968583	+	0.248690i	$0.0800000\pi$
$510$		0			0
$511$		0			0
$512$	0.535827	+	0.844328i	0.535827	+	0.844328i
$513$		0			0
$514$		0			0
$515$	−1.61803			−1.61803
$516$	−2.62594	−	2.46592i	−2.62594	−	2.46592i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	1.03799	−	0.266509i	1.03799	−	0.266509i	0.309017	−	0.951057i	$-0.400000\pi$
$521$	1.03799	−	0.266509i	1.03799	−	0.266509i	0.728969	+	0.684547i	$0.240000\pi$
$522$	0.106820	+	0.328757i	0.106820	+	0.328757i
$523$	−0.929324	+	1.12336i	−0.929324	+	1.12336i	0.0627905	+	0.998027i	$0.480000\pi$
$523$	−0.929324	+	1.12336i	−0.929324	+	1.12336i	−0.992115	+	0.125333i	$0.960000\pi$
$524$		0			0
$525$	0.0152751	+	0.242791i	0.0152751	+	0.242791i
$526$	0.0702235	+	0.368125i	0.0702235	+	0.368125i
$527$		0			0
$528$		0			0
$529$	0.0515014	−	0.269980i	0.0515014	−	0.269980i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$	−1.67950	+	2.64646i	−1.67950	+	2.64646i
$535$	1.84489	+	0.730444i	1.84489	+	0.730444i
$536$	−0.683098	−	1.07639i	−0.683098	−	1.07639i
$537$		0			0
$538$	0.844844	+	1.79538i	0.844844	+	1.79538i
$539$		0			0
$540$	2.97515	−	1.63560i	2.97515	−	1.63560i
$541$	−0.866986	−	0.629902i	−0.866986	−	0.629902i	0.0627905	−	0.998027i	$-0.480000\pi$
$541$	−0.866986	−	0.629902i	−0.866986	−	0.629902i	−0.929776	+	0.368125i	$0.880000\pi$
$542$		0			0
$543$	0.674997	−	3.53846i	0.674997	−	3.53846i
$544$		0			0
$545$	−1.92189	+	0.242791i	−1.92189	+	0.242791i
$546$		0			0
$547$	−1.92189	+	0.493458i	−1.92189	+	0.493458i	−0.929776	+	0.368125i	$0.880000\pi$
$547$	−1.92189	+	0.493458i	−1.92189	+	0.493458i	−0.992115	+	0.125333i	$0.960000\pi$
$548$		0			0
$549$	−3.24670	−	2.35886i	−3.24670	−	2.35886i
$550$		0			0
$551$		0			0
$552$	−1.44556	+	0.794706i	−1.44556	+	0.794706i
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$		0			0		0.425779	−	0.904827i	$-0.360000\pi$
$557$		0			0		−0.425779	+	0.904827i	$0.640000\pi$
$558$		0			0
$559$		0			0
$560$	0.0915446	−	0.0859661i	0.0915446	−	0.0859661i
$561$		0			0
$562$	0.688925	+	0.500534i	0.688925	+	0.500534i
$563$	−1.41789	−	0.779494i	−1.41789	−	0.779494i	−0.425779	−	0.904827i	$-0.640000\pi$
$563$	−1.41789	−	0.779494i	−1.41789	−	0.779494i	−0.992115	+	0.125333i	$0.960000\pi$
$564$	3.63472	−	0.933237i	3.63472	−	0.933237i
$565$		0			0
$566$	−1.06320	+	0.134314i	−1.06320	+	0.134314i
$567$	−0.388535	+	0.282287i	−0.388535	+	0.282287i
$568$		0			0
$569$	1.72897	−	0.684547i	1.72897	−	0.684547i	0.728969	−	0.684547i	$-0.240000\pi$
$569$	1.72897	−	0.684547i	1.72897	−	0.684547i	1.00000			$0$
$570$		0			0
$571$		0			0		0.876307	−	0.481754i	$-0.160000\pi$
$571$		0			0		−0.876307	+	0.481754i	$0.840000\pi$
$572$		0			0
$573$		0			0
$574$	0.0415873	+	0.127993i	0.0415873	+	0.127993i
$575$	−0.456288	−	0.718995i	−0.456288	−	0.718995i
$576$	−2.55932	−	1.01330i	−2.55932	−	1.01330i
$577$		0			0		0.535827	−	0.844328i	$-0.320000\pi$
$577$		0			0		−0.535827	+	0.844328i	$0.680000\pi$
$578$	−0.637424	−	0.770513i	−0.637424	−	0.770513i
$579$		0			0
$580$	0.110048	+	0.0604991i	0.110048	+	0.0604991i
$581$	0.231683	+	0.0292684i	0.231683	+	0.0292684i
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−0.362989	−	0.0931997i	−0.362989	−	0.0931997i	0.0627905	−	0.998027i	$-0.480000\pi$
$587$	−0.362989	−	0.0931997i	−0.362989	−	0.0931997i	−0.425779	+	0.904827i	$0.640000\pi$
$588$	1.21532	−	1.46907i	1.21532	−	1.46907i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$		0			0		0.535827	−	0.844328i	$-0.320000\pi$
$593$		0			0		−0.535827	+	0.844328i	$0.680000\pi$
$594$		0			0
$595$		0			0
$596$	−1.27485			−1.27485
$597$		0			0
$598$		0			0
$599$		0			0		−0.535827	−	0.844328i	$-0.680000\pi$
$599$		0			0		0.535827	+	0.844328i	$0.320000\pi$
$600$	0.598617	−	1.84235i	0.598617	−	1.84235i
$601$	0.0388067	−	0.616814i	0.0388067	−	0.616814i	−0.929776	−	0.368125i	$-0.880000\pi$
$601$	0.0388067	−	0.616814i	0.0388067	−	0.616814i	0.968583	−	0.248690i	$-0.0800000\pi$
$602$	0.231683	−	0.0292684i	0.231683	−	0.0292684i
$603$	3.26274	+	1.29181i	3.26274	+	1.29181i
$604$		0			0
$605$	1.00000			1.00000
$606$	−1.92189	−	0.242791i	−1.92189	−	0.242791i
$607$	−0.374763			−0.374763			−0.187381	−	0.982287i	$-0.560000\pi$
$607$	−0.374763			−0.374763			−0.187381	+	0.982287i	$0.560000\pi$
$608$		0			0
$609$	−0.0284049	−	0.0112463i	−0.0284049	−	0.0112463i
$610$	−1.44644	+	0.182728i	−1.44644	+	0.182728i
$611$		0			0
$612$		0			0
$613$		0			0		−0.535827	−	0.844328i	$-0.680000\pi$
$613$		0			0		0.535827	+	0.844328i	$0.320000\pi$
$614$	−0.0235315	−	0.123357i	−0.0235315	−	0.123357i
$615$	1.51332	+	1.42110i	1.51332	+	1.42110i
$616$		0			0
$617$		0			0		−0.728969	−	0.684547i	$-0.760000\pi$
$617$		0			0		0.728969	+	0.684547i	$0.240000\pi$
$618$	−3.03593	−	0.779494i	−3.03593	−	0.779494i
$619$		0			0		0.535827	−	0.844328i	$-0.320000\pi$
$619$		0			0		−0.535827	+	0.844328i	$0.680000\pi$
$620$		0			0
$621$	1.23098	−	2.61597i	1.23098	−	2.61597i
$622$		0			0
$623$	−0.0627905	−	0.193249i	−0.0627905	−	0.193249i
$624$		0			0
$625$	0.968583	+	0.248690i	0.968583	+	0.248690i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$	−0.0647732	+	0.339553i	−0.0647732	+	0.339553i
$631$		0			0		−0.992115	−	0.125333i	$-0.960000\pi$
$631$		0			0		0.992115	+	0.125333i	$0.0400000\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−0.866986	+	1.36615i	−0.866986	+	1.36615i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$	−0.929776	+	0.368125i	−0.929776	+	0.368125i
$641$	−1.41789	+	0.779494i	−1.41789	+	0.779494i	−0.992115	−	0.125333i	$-0.960000\pi$
$641$	−1.41789	+	0.779494i	−1.41789	+	0.779494i	−0.425779	+	0.904827i	$0.640000\pi$
$642$	3.10969	+	2.25932i	3.10969	+	2.25932i
$643$	−1.85955	+	0.736249i	−1.85955	+	0.736249i	−0.929776	+	0.368125i	$0.880000\pi$
$643$	−1.85955	+	0.736249i	−1.85955	+	0.736249i	−0.929776	+	0.368125i	$0.880000\pi$
$644$	0.0200385	−	0.105045i	0.0200385	−	0.105045i
$645$	2.91429	−	2.11736i	2.91429	−	2.11736i
$646$		0			0
$647$	0.541587	−	1.66683i	0.541587	−	1.66683i	−0.187381	−	0.982287i	$-0.560000\pi$
$647$	0.541587	−	1.66683i	0.541587	−	1.66683i	0.728969	−	0.684547i	$-0.240000\pi$
$648$	3.70412	−	0.951057i	3.70412	−	0.951057i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	−0.929324	+	0.872693i	−0.929324	+	0.872693i
$653$		0			0		0.876307	−	0.481754i	$-0.160000\pi$
$653$		0			0		−0.876307	+	0.481754i	$0.840000\pi$
$654$	−3.72302	−	0.470327i	−3.72302	−	0.470327i
$655$		0			0
$656$	0.0672897	−	1.06954i	0.0672897	−	1.06954i
$657$		0			0
$658$	−0.103580	+	0.220119i	−0.103580	+	0.220119i
$659$		0			0		−0.992115	−	0.125333i	$-0.960000\pi$
$659$		0			0		0.992115	+	0.125333i	$0.0400000\pi$
$660$		0			0
$661$	−0.273190	+	0.256543i	−0.273190	+	0.256543i	−0.809017	−	0.587785i	$-0.800000\pi$
$661$	−0.273190	+	0.256543i	−0.273190	+	0.256543i	0.535827	+	0.844328i	$0.320000\pi$
$662$		0			0
$663$		0			0
$664$	−1.62954	−	0.895846i	−1.62954	−	0.895846i
$665$		0			0
$666$		0			0
$667$	0.106096	−	0.0134031i	0.106096	−	0.0134031i
$668$	0.688925	−	0.500534i	0.688925	−	0.500534i
$669$	−0.636179	+	3.33497i	−0.636179	+	3.33497i
$670$	1.18532	−	0.469303i	1.18532	−	0.469303i
$671$		0			0
$672$	0.213180	−	0.117197i	0.213180	−	0.117197i
$673$		0			0		0.929776	−	0.368125i	$-0.120000\pi$
$673$		0			0		−0.929776	+	0.368125i	$0.880000\pi$
$674$		0			0
$675$	1.04914	+	3.22894i	1.04914	+	3.22894i
$676$	0.535827	+	0.844328i	0.535827	+	0.844328i
$677$		0			0		−0.929776	−	0.368125i	$-0.880000\pi$
$677$		0			0		0.929776	+	0.368125i	$0.120000\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−2.16412	−	1.18974i	−2.16412	−	1.18974i
$682$		0			0
$683$	−0.328407	+	1.72157i	−0.328407	+	1.72157i	0.309017	+	0.951057i	$0.400000\pi$
$683$	−0.328407	+	1.72157i	−0.328407	+	1.72157i	−0.637424	+	0.770513i	$0.720000\pi$
$684$		0			0
$685$		0			0
$686$	0.0466920	+	0.244768i	0.0466920	+	0.244768i
$687$	0.0751750	+	1.19487i	0.0751750	+	1.19487i
$688$	−1.80113	−	0.462452i	−1.80113	−	0.462452i
$689$		0			0
$690$	−0.509758	−	1.56887i	−0.509758	−	1.56887i
$691$		0			0		0.968583	−	0.248690i	$-0.0800000\pi$
$691$		0			0		−0.968583	+	0.248690i	$0.920000\pi$
$692$		0			0
$693$		0			0
$694$	−1.06320	+	1.67534i	−1.06320	+	1.67534i
$695$		0			0
$696$	0.177337	+	0.166531i	0.177337	+	0.166531i
$697$		0			0
$698$	1.27760	+	1.19975i	1.27760	+	1.19975i
$699$		0			0
$700$	0.0672897	+	0.106032i	0.0672897	+	0.106032i
$701$	0.331159	−	1.01920i	0.331159	−	1.01920i	−0.637424	−	0.770513i	$-0.720000\pi$
$701$	0.331159	−	1.01920i	0.331159	−	1.01920i	0.968583	−	0.248690i	$-0.0800000\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	0.235629	+	3.74521i	0.235629	+	3.74521i
$706$		0			0
$707$	0.0915446	−	0.0859661i	0.0915446	−	0.0859661i
$708$		0			0
$709$	−0.0235315	−	0.374023i	−0.0235315	−	0.374023i	−0.992115	−	0.125333i	$-0.960000\pi$
$709$	−0.0235315	−	0.374023i	−0.0235315	−	0.374023i	0.968583	−	0.248690i	$-0.0800000\pi$
$710$		0			0
$711$		0			0
$712$	−0.101597	+	1.61484i	−0.101597	+	1.61484i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		−0.968583	−	0.248690i	$-0.920000\pi$
$719$		0			0		0.968583	+	0.248690i	$0.0800000\pi$
$720$	1.47492	−	2.32411i	1.47492	−	2.32411i
$721$	0.164388	−	0.119435i	0.164388	−	0.119435i
$722$	−0.425779	+	0.904827i	−0.425779	+	0.904827i
$723$	2.73554	−	0.702367i	2.73554	−	0.702367i
$724$	−0.574633	−	1.76854i	−0.574633	−	1.76854i
$725$	−0.0800484	+	0.0967619i	−0.0800484	+	0.0967619i
$726$	1.87631	+	0.481754i	1.87631	+	0.481754i
$727$	0.0388067	+	0.616814i	0.0388067	+	0.616814i	0.968583	+	0.248690i	$0.0800000\pi$
$727$	0.0388067	+	0.616814i	0.0388067	+	0.616814i	−0.929776	+	0.368125i	$0.880000\pi$
$728$		0			0
$729$	−2.51773	+	3.04341i	−2.51773	+	3.04341i
$730$		0			0
$731$		0			0
$732$	−2.80200	−	0.353975i	−2.80200	−	0.353975i
$733$		0			0		−0.876307	−	0.481754i	$-0.840000\pi$
$733$		0			0		0.876307	+	0.481754i	$0.160000\pi$
$734$	0.688925	+	1.46404i	0.688925	+	1.46404i
$735$	1.21532	+	1.46907i	1.21532	+	1.46907i
$736$	−0.456288	+	0.718995i	−0.456288	+	0.718995i
$737$		0			0
$738$	1.58061	+	2.49064i	1.58061	+	2.49064i
$739$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$739$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	1.03137	+	0.749337i	1.03137	+	0.749337i	0.968583	−	0.248690i	$-0.0800000\pi$
$743$	1.03137	+	0.749337i	1.03137	+	0.749337i	0.0627905	+	0.998027i	$0.480000\pi$
$744$		0			0
$745$	0.238883	−	1.25227i	0.238883	−	1.25227i
$746$		0			0
$747$	5.07827	−	0.641534i	5.07827	−	0.641534i
$748$		0			0
$749$	−0.241353	+	0.0619689i	−0.241353	+	0.0619689i
$750$	1.69755	+	0.933237i	1.69755	+	0.933237i
$751$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$751$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$752$	1.41213	−	1.32608i	1.41213	−	1.32608i
$753$		0			0
$754$		0			0
$755$		0			0
$756$	−0.181536	+	0.385783i	−0.181536	+	0.385783i
$757$		0			0		0.0627905	−	0.998027i	$-0.480000\pi$
$757$		0			0		−0.0627905	+	0.998027i	$0.520000\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−0.328407	+	0.180543i	−0.328407	+	0.180543i	−0.637424	−	0.770513i	$-0.720000\pi$
$761$	−0.328407	+	0.180543i	−0.328407	+	0.180543i	0.309017	+	0.951057i	$0.400000\pi$
$762$	−2.28488	+	2.14565i	−2.28488	+	2.14565i
$763$	0.177337	−	0.166531i	0.177337	−	0.166531i
$764$		0			0
$765$		0			0
$766$	−0.362989	+	0.0931997i	−0.362989	+	0.0931997i
$767$		0			0
$768$	−1.92189	+	0.242791i	−1.92189	+	0.242791i
$769$	1.50441	−	1.09302i	1.50441	−	1.09302i	0.535827	−	0.844328i	$-0.320000\pi$
$769$	1.50441	−	1.09302i	1.50441	−	1.09302i	0.968583	−	0.248690i	$-0.0800000\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0		0.876307	−	0.481754i	$-0.160000\pi$
$773$		0			0		−0.876307	+	0.481754i	$0.840000\pi$
$774$	4.75918	−	1.88429i	4.75918	−	1.88429i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	−1.85955	−	0.736249i	−1.85955	−	0.736249i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−0.422999	−	0.0534372i	−0.422999	−	0.0534372i
$784$	0.184426	−	0.966796i	0.184426	−	0.966796i
$785$		0			0
$786$		0			0
$787$	−0.273190	−	1.43211i	−0.273190	−	1.43211i	−0.809017	−	0.587785i	$-0.800000\pi$
$787$	−0.273190	−	1.43211i	−0.273190	−	1.43211i	0.535827	−	0.844328i	$-0.320000\pi$
$788$		0			0
$789$	−0.703170	−	0.180543i	−0.703170	−	0.180543i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.728969	−	0.684547i	$-0.760000\pi$
$797$		0			0		0.728969	+	0.684547i	$0.240000\pi$
$798$		0			0
$799$		0			0
$800$	−0.187381	−	0.982287i	−0.187381	−	0.982287i
$801$	−2.38648	−	3.76049i	−2.38648	−	3.76049i
$802$	0.190983	−	0.587785i	0.190983	−	0.587785i
$803$		0			0
$804$	2.45012	−	0.309522i	2.45012	−	0.309522i
$805$	0.0994299	+	0.0393671i	0.0994299	+	0.0393671i
$806$		0			0
$807$	−3.84378			−3.84378
$808$	−0.929776	+	0.368125i	−0.929776	+	0.368125i
$809$	0.125581			0.125581			0.0627905	−	0.998027i	$-0.480000\pi$
$809$	0.125581			0.125581			0.0627905	+	0.998027i	$0.480000\pi$
$810$	0.240128	+	3.81672i	0.240128	+	3.81672i
$811$		0			0		−0.929776	−	0.368125i	$-0.880000\pi$
$811$		0			0		0.929776	+	0.368125i	$0.120000\pi$
$812$	−0.0156462	+	0.00197658i	−0.0156462	+	0.00197658i
$813$		0			0
$814$		0			0
$815$	−0.683098	−	1.07639i	−0.683098	−	1.07639i
$816$		0			0
$817$		0			0
$818$	−0.851559			−0.851559
$819$		0			0
$820$	1.03799	+	0.266509i	1.03799	+	0.266509i
$821$	−0.456288	+	0.718995i	−0.456288	+	0.718995i	−0.992115	−	0.125333i	$-0.960000\pi$
$821$	−0.456288	+	0.718995i	−0.456288	+	0.718995i	0.535827	+	0.844328i	$0.320000\pi$
$822$		0			0
$823$	0.362576	−	0.770513i	0.362576	−	0.770513i	−0.637424	−	0.770513i	$-0.720000\pi$
$823$	0.362576	−	0.770513i	0.362576	−	0.770513i	1.00000			$0$
$824$	−1.56720	+	0.402389i	−1.56720	+	0.402389i
$825$		0			0
$826$		0			0
$827$	−0.824805	−	0.211774i	−0.824805	−	0.211774i	−0.187381	−	0.982287i	$-0.560000\pi$
$827$	−0.824805	−	0.211774i	−0.824805	−	0.211774i	−0.637424	+	0.770513i	$0.720000\pi$
$828$	−0.147182	−	2.33939i	−0.147182	−	2.33939i
$829$	0.371808	+	1.94908i	0.371808	+	1.94908i	0.309017	+	0.951057i	$0.400000\pi$
$829$	0.371808	+	1.94908i	0.371808	+	1.94908i	0.0627905	+	0.998027i	$0.480000\pi$
$830$	1.18532	−	1.43281i	1.18532	−	1.43281i
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	0.362576	+	0.770513i	0.362576	+	0.770513i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		−0.535827	−	0.844328i	$-0.680000\pi$
$839$		0			0		0.535827	+	0.844328i	$0.320000\pi$
$840$	0.0751750	+	0.231365i	0.0751750	+	0.231365i
$841$	0.419064	+	0.890557i	0.419064	+	0.890557i
$842$	1.50441	−	0.595638i	1.50441	−	0.595638i
$843$	−1.44556	+	0.794706i	−1.44556	+	0.794706i
$844$		0			0
$845$	−0.929776	+	0.368125i	−0.929776	+	0.368125i
$846$	−0.999168	+	5.23782i	−0.999168	+	5.23782i
$847$	−0.101597	+	0.0738147i	−0.101597	+	0.0738147i
$848$		0			0
$849$	0.641510	−	1.97437i	0.641510	−	1.97437i
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		0.728969	−	0.684547i	$-0.240000\pi$
$853$		0			0		−0.728969	+	0.684547i	$0.760000\pi$
$854$	0.133466	−	0.125333i	0.133466	−	0.125333i
$855$		0			0
$856$	1.96858	+	0.248690i	1.96858	+	0.248690i
$857$		0			0		0.425779	−	0.904827i	$-0.360000\pi$
$857$		0			0		−0.425779	+	0.904827i	$0.640000\pi$
$858$		0			0
$859$		0			0		0.0627905	−	0.998027i	$-0.480000\pi$
$859$		0			0		−0.0627905	+	0.998027i	$0.520000\pi$
$860$	0.791759	−	1.68257i	0.791759	−	1.68257i
$861$	−0.258647	−	0.0326747i	−0.258647	−	0.0326747i
$862$		0			0
$863$	0.781202	−	0.733597i	0.781202	−	0.733597i	−0.187381	−	0.982287i	$-0.560000\pi$
$863$	0.781202	−	0.733597i	0.781202	−	0.733597i	0.968583	+	0.248690i	$0.0800000\pi$
$864$	2.47492	−	2.32411i	2.47492	−	2.32411i
$865$		0			0
$866$		0			0
$867$	1.87631	−	0.481754i	1.87631	−	0.481754i
$868$		0			0
$869$		0			0
$870$	−0.196811	+	0.142991i	−0.196811	+	0.142991i
$871$		0			0
$872$	−1.80113	+	0.713118i	−1.80113	+	0.713118i
$873$		0			0
$874$		0			0
$875$	−0.116762	+	0.0462295i	−0.116762	+	0.0462295i
$876$		0			0
$877$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$877$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−0.683098	−	0.825723i	−0.683098	−	0.825723i	0.309017	−	0.951057i	$-0.400000\pi$
$881$	−0.683098	−	0.825723i	−0.683098	−	0.825723i	−0.992115	+	0.125333i	$0.960000\pi$
$882$	1.15352	+	2.45136i	1.15352	+	2.45136i
$883$	0.939097	+	0.516273i	0.939097	+	0.516273i	0.876307	−	0.481754i	$-0.160000\pi$
$883$	0.939097	+	0.516273i	0.939097	+	0.516273i	0.0627905	+	0.998027i	$0.480000\pi$
$884$		0			0
$885$		0			0
$886$	−0.393950	−	0.476203i	−0.393950	−	0.476203i
$887$	−0.0800484	+	0.0967619i	−0.0800484	+	0.0967619i	−0.809017	−	0.587785i	$-0.800000\pi$
$887$	−0.0800484	+	0.0967619i	−0.0800484	+	0.0967619i	0.728969	+	0.684547i	$0.240000\pi$
$888$		0			0
$889$	−0.0127587	−	0.202793i	−0.0127587	−	0.202793i
$890$	−1.56720	−	0.402389i	−1.56720	−	0.402389i
$891$		0			0
$892$	0.541587	+	1.66683i	0.541587	+	1.66683i
$893$		0			0
$894$	1.05150	−	2.23455i	1.05150	−	2.23455i
$895$		0			0
$896$	0.0672897	−	0.106032i	0.0672897	−	0.106032i
$897$		0			0
$898$	1.06279	+	0.998027i	1.06279	+	0.998027i
$899$		0			0
$900$	2.00657	+	1.88429i	2.00657	+	1.88429i
$901$		0			0
$902$		0			0
$903$	−0.139792	+	0.430235i	−0.139792	+	0.430235i
$904$		0			0
$905$	1.84489	−	0.233064i	1.84489	−	0.233064i
$906$		0			0
$907$	0.110048	+	1.74915i	0.110048	+	1.74915i	0.535827	+	0.844328i	$0.320000\pi$
$907$	0.110048	+	1.74915i	0.110048	+	1.74915i	−0.425779	+	0.904827i	$0.640000\pi$
$908$	−1.27485			−1.27485
$909$	1.47492	−	2.32411i	1.47492	−	2.32411i
$910$		0			0
$911$		0			0		−0.0627905	−	0.998027i	$-0.520000\pi$
$911$		0			0		0.0627905	+	0.998027i	$0.480000\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	0.872746	−	2.68604i	0.872746	−	2.68604i
$916$	0.331159	+	0.521823i	0.331159	+	0.521823i
$917$		0			0
$918$		0			0
$919$		0			0		1.00000			$0$
$919$		0			0		−1.00000			$\pi$
$920$	−0.620759	−	0.582932i	−0.620759	−	0.582932i
$921$	0.235629	+	0.0604991i	0.235629	+	0.0604991i
$922$	−1.06320	+	1.67534i	−1.06320	+	1.67534i
$923$		0			0
$924$		0			0
$925$		0			0
$926$	0.190983	+	0.587785i	0.190983	+	0.587785i
$927$	2.83897	−	3.43173i	2.83897	−	3.43173i
$928$	0.121636	+	0.0312307i	0.121636	+	0.0312307i
$929$	0.0672897	+	1.06954i	0.0672897	+	1.06954i	0.876307	+	0.481754i	$0.160000\pi$
$929$	0.0672897	+	1.06954i	0.0672897	+	1.06954i	−0.809017	+	0.587785i	$0.800000\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$	−1.06320	−	0.134314i	−1.06320	−	0.134314i
$935$		0			0
$936$		0			0
$937$		0			0		−0.637424	−	0.770513i	$-0.720000\pi$
$937$		0			0		0.637424	+	0.770513i	$0.280000\pi$
$938$	−0.0857841	+	0.135174i	−0.0857841	+	0.135174i
$939$		0			0
$940$	1.03799	+	1.63560i	1.03799	+	1.63560i
$941$	−0.393950	−	1.21245i	−0.393950	−	1.21245i	−0.929776	−	0.368125i	$-0.880000\pi$
$941$	−0.393950	−	1.21245i	−0.393950	−	1.21245i	0.535827	−	0.844328i	$-0.320000\pi$
$942$		0			0
$943$	0.848492	−	0.335942i	0.848492	−	0.335942i
$944$		0			0
$945$	−0.344933	−	0.250608i	−0.344933	−	0.250608i
$946$		0			0
$947$	−0.328407	+	1.72157i	−0.328407	+	1.72157i	0.309017	+	0.951057i	$0.400000\pi$
$947$	−0.328407	+	1.72157i	−0.328407	+	1.72157i	−0.637424	+	0.770513i	$0.720000\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$953$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	0.121636	−	1.93334i	0.121636	−	1.93334i
$961$	−0.425779	+	0.904827i	−0.425779	+	0.904827i
$962$		0			0
$963$	−4.78623	+	2.63125i	−4.78623	+	2.63125i
$964$	1.06279	−	0.998027i	1.06279	−	0.998027i
$965$		0			0
$966$	0.167596	+	0.121765i	0.167596	+	0.121765i
$967$	−0.328407	−	0.180543i	−0.328407	−	0.180543i	0.309017	−	0.951057i	$-0.400000\pi$
$967$	−0.328407	−	0.180543i	−0.328407	−	0.180543i	−0.637424	+	0.770513i	$0.720000\pi$
$968$	0.968583	−	0.248690i	0.968583	−	0.248690i
$969$		0			0
$970$		0			0
$971$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$971$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$972$	−0.751987	+	3.94205i	−0.751987	+	3.94205i
$973$		0			0
$974$	−0.866986	−	0.629902i	−0.866986	−	0.629902i
$975$		0			0
$976$	−1.35556	+	0.536702i	−1.35556	+	0.536702i
$977$		0			0		−0.425779	−	0.904827i	$-0.640000\pi$
$977$		0			0		0.425779	+	0.904827i	$0.360000\pi$
$978$	−0.763146	−	2.34872i	−0.763146	−	2.34872i
$979$		0			0
$980$	0.915113	+	0.362319i	0.915113	+	0.362319i
$981$	2.85717	−	4.50218i	2.85717	−	4.50218i
$982$		0			0
$983$	−0.456288	−	0.969661i	−0.456288	−	0.969661i	−0.992115	−	0.125333i	$-0.960000\pi$
$983$	−0.456288	−	0.969661i	−0.456288	−	0.969661i	0.535827	−	0.844328i	$-0.320000\pi$
$984$	1.81919	+	1.00011i	1.81919	+	1.00011i
$985$		0			0
$986$		0			0
$987$	−0.300391	−	0.363110i	−0.300391	−	0.363110i
$988$		0			0
$989$	−0.296722	−	1.55547i	−0.296722	−	1.55547i
$990$		0			0
$991$		0			0		−0.968583	−	0.248690i	$-0.920000\pi$
$991$		0			0		0.968583	+	0.248690i	$0.0800000\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$	2.91429	−	2.11736i	2.91429	−	2.11736i
$997$		0			0		0.535827	−	0.844328i	$-0.320000\pi$
$997$		0			0		−0.535827	+	0.844328i	$0.680000\pi$
$998$		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.1439.1	yes	20
4.3	odd	2		2020.1.bu.b.1439.1	yes	20
5.4	even	2		2020.1.bu.b.1439.1	yes	20
20.19	odd	2	CM	2020.1.bu.a.1439.1	yes	20
101.97	even	25	inner	2020.1.bu.a.299.1	✓	20
404.299	odd	50		2020.1.bu.b.299.1	yes	20
505.299	even	50		2020.1.bu.b.299.1	yes	20
2020.299	odd	50	inner	2020.1.bu.a.299.1	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2020.1.bu.a.299.1	✓	20	101.97	even	25	inner
2020.1.bu.a.299.1	✓	20	2020.299	odd	50	inner
2020.1.bu.a.1439.1	yes	20	1.1	even	1	trivial
2020.1.bu.a.1439.1	yes	20	20.19	odd	2	CM
2020.1.bu.b.299.1	yes	20	404.299	odd	50
2020.1.bu.b.299.1	yes	20	505.299	even	50
2020.1.bu.b.1439.1	yes	20	4.3	odd	2
2020.1.bu.b.1439.1	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)

\(f(q)\)	\(=\)	\(q+(0.0627905 + 0.998027i) q^{2} +(-1.80113 - 0.713118i) q^{3} +(-0.992115 + 0.125333i) q^{4} +(0.0627905 - 0.998027i) q^{5} +(0.598617 - 1.84235i) q^{6} +(0.0672897 + 0.106032i) q^{7} +(-0.187381 - 0.982287i) q^{8} +(2.00657 + 1.88429i) q^{9} +O(q^{10})\)	\(q+(0.0627905 + 0.998027i) q^{2} +(-1.80113 - 0.713118i) q^{3} +(-0.992115 + 0.125333i) q^{4} +(0.0627905 - 0.998027i) q^{5} +(0.598617 - 1.84235i) q^{6} +(0.0672897 + 0.106032i) q^{7} +(-0.187381 - 0.982287i) q^{8} +(2.00657 + 1.88429i) q^{9} +1.00000 q^{10} +(1.87631 + 0.481754i) q^{12} +(-0.101597 + 0.0738147i) q^{14} +(-0.824805 + 1.75280i) q^{15} +(0.968583 - 0.248690i) q^{16} +(-1.75458 + 2.12093i) q^{18} +(0.0627905 + 0.998027i) q^{20} +(-0.0455845 - 0.238962i) q^{21} +(0.542804 + 0.656137i) q^{23} +(-0.362989 + 1.90285i) q^{24} +(-0.992115 - 0.125333i) q^{25} +(-1.44556 - 3.07198i) q^{27} +(-0.0800484 - 0.0967619i) q^{28} +(0.0672897 - 0.106032i) q^{29} +(-1.80113 - 0.713118i) q^{30} +(0.309017 + 0.951057i) q^{32} +(0.110048 - 0.0604991i) q^{35} +(-2.22691 - 1.61795i) q^{36} +(-0.992115 + 0.125333i) q^{40} +(0.331159 - 1.01920i) q^{41} +(0.235629 - 0.0604991i) q^{42} +(-1.62954 - 0.895846i) q^{43} +(2.00657 - 1.88429i) q^{45} +(-0.620759 + 0.582932i) q^{46} +(1.69755 - 0.933237i) q^{47} +(-1.92189 - 0.242791i) q^{48} +(0.419064 - 0.890557i) q^{49} +(0.0627905 - 0.998027i) q^{50} +(2.97515 - 1.63560i) q^{54} +(0.0915446 - 0.0859661i) q^{56} +(0.110048 + 0.0604991i) q^{58} +(0.598617 - 1.84235i) q^{60} +(-1.44644 + 0.182728i) q^{61} +(-0.0647732 + 0.339553i) q^{63} +(-0.929776 + 0.368125i) q^{64} +(1.18532 - 0.469303i) q^{67} +(-0.509758 - 1.56887i) q^{69} +(0.0672897 + 0.106032i) q^{70} +(1.47492 - 2.32411i) q^{72} +(1.69755 + 0.933237i) q^{75} +(-0.187381 - 0.982287i) q^{80} +(0.240128 + 3.81672i) q^{81} +(1.03799 + 0.266509i) q^{82} +(1.18532 - 1.43281i) q^{83} +(0.0751750 + 0.231365i) q^{84} +(0.791759 - 1.68257i) q^{86} +(-0.196811 + 0.142991i) q^{87} +(-1.56720 - 0.402389i) q^{89} +(2.00657 + 1.88429i) q^{90} +(-0.620759 - 0.582932i) q^{92} +(1.03799 + 1.63560i) q^{94} +(0.121636 - 1.93334i) q^{96} +(0.915113 + 0.362319i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 5 q^{3} - 5 q^{7} - 5 q^{9}+O(q^{10}) \) 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

L-functions

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