LMFDB - Embedded newform 2020.1.bt.c.1259.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("2020.279");

S:= CuspForms(chi, 1);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			1259.2
Root			$-0.248690 + 0.968583i$ of defining polynomial
Character	$\chi$	$=$	2020.1259
Dual form			2020.1.bt.c.1659.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.248690 - 0.968583i) q^{2} +(1.06954 + 0.0672897i) q^{3} +(-0.876307 - 0.481754i) q^{4} +(-0.968583 + 0.248690i) q^{5} +(0.331159 - 1.01920i) q^{6} +(-1.49261 - 1.23480i) q^{7} +(-0.684547 + 0.728969i) q^{8} +(0.147271 + 0.0186046i) q^{9} +O(q^{10})$	\(q+(0.248690 - 0.968583i) q^{2} +(1.06954 + 0.0672897i) q^{3} +(-0.876307 - 0.481754i) q^{4} +(-0.968583 + 0.248690i) q^{5} +(0.331159 - 1.01920i) q^{6} +(-1.49261 - 1.23480i) q^{7} +(-0.684547 + 0.728969i) q^{8} +(0.147271 + 0.0186046i) q^{9} +1.00000i q^{10} +(-0.904827 - 0.574221i) q^{12} +(-1.56720 + 1.13864i) q^{14} +(-1.05267 + 0.200808i) q^{15} +(0.535827 + 0.844328i) q^{16} +(0.0546449 - 0.138017i) q^{18} +(0.968583 + 0.248690i) q^{20} +(-1.51332 - 1.42110i) q^{21} +(-1.82662 + 0.723208i) q^{23} +(-0.781202 + 0.733597i) q^{24} +(0.876307 - 0.481754i) q^{25} +(-0.896412 - 0.171000i) q^{27} +(0.713118 + 1.80113i) q^{28} +(-0.383238 + 0.317042i) q^{29} +(-0.0672897 + 1.06954i) q^{30} +(0.951057 - 0.309017i) q^{32} +(1.75280 + 0.824805i) q^{35} +(-0.120092 - 0.0872517i) q^{36} +(0.481754 - 0.876307i) q^{40} +(-1.46560 - 0.476203i) q^{41} +(-1.75280 + 1.11236i) q^{42} +(-0.849878 - 1.80608i) q^{43} +(-0.147271 + 0.0186046i) q^{45} +(0.246226 + 1.94908i) q^{46} +(0.718995 - 1.52794i) q^{47} +(0.516273 + 0.939097i) q^{48} +(0.515788 + 2.70386i) q^{49} +(-0.248690 - 0.968583i) q^{50} +(-0.388556 + 0.825723i) q^{54} +(1.92189 - 0.242791i) q^{56} +(0.211774 + 0.450043i) q^{58} +(1.01920 + 0.331159i) q^{60} +(-0.120759 + 0.219661i) q^{61} +(-0.196845 - 0.209619i) q^{63} +(-0.0627905 - 0.998027i) q^{64} +(1.85588 - 0.116762i) q^{67} +(-2.00230 + 0.650587i) q^{69} +(1.23480 - 1.49261i) q^{70} +(-0.114376 + 0.0946201i) q^{72} +(0.969661 - 0.456288i) q^{75} +(-0.728969 - 0.684547i) q^{80} +(-1.09102 - 0.280126i) q^{81} +(-0.825723 + 1.30113i) q^{82} +(-0.0462295 + 0.116762i) q^{83} +(0.641510 + 1.97437i) q^{84} +(-1.96070 + 0.374023i) q^{86} +(-0.431221 + 0.313301i) q^{87} +(0.992567 + 0.629902i) q^{89} +(-0.0186046 + 0.147271i) q^{90} +(1.94908 + 0.246226i) q^{92} +(-1.30113 - 1.07639i) q^{94} +(1.03799 - 0.266509i) q^{96} +(2.74718 + 0.172838i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 10 q^{9}+O(q^{10}) $ 40 * q + 10 * q^9	$ 40 q + 10 q^{9} - 40 q^{21} - 10 q^{29} + 10 q^{30} - 10 q^{36} - 10 q^{45} - 10 q^{46} + 10 q^{49} + 10 q^{54} + 10 q^{61} + 10 q^{70} - 10 q^{81} + 30 q^{84} + 10 q^{94} - 10 q^{96}+O(q^{100}) $ 40 * q + 10 * q^9 - 40 * q^21 - 10 * q^29 + 10 * q^30 - 10 * q^36 - 10 * q^45 - 10 * q^46 + 10 * q^49 + 10 * q^54 + 10 * q^61 + 10 * q^70 - 10 * q^81 + 30 * q^84 + 10 * q^94 - 10 * q^96

Display 100 coefficients 10 coefficients

Character values

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

$n$	$1011$	$1617$	$1921$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{29}{50}\right)$

Coefficient data

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

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

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

$2$	0.248690	−	0.968583i	0.248690	−	0.968583i
$2$	0.248690	−	0.968583i	0.248690	−	0.968583i
$3$	1.06954	+	0.0672897i	1.06954	+	0.0672897i	0.587785	−	0.809017i	$-0.300000\pi$
$3$	1.06954	+	0.0672897i	1.06954	+	0.0672897i	0.481754	+	0.876307i	$0.340000\pi$
$4$	−0.876307	−	0.481754i	−0.876307	−	0.481754i
$5$	−0.968583	+	0.248690i	−0.968583	+	0.248690i
$5$	−0.968583	+	0.248690i	−0.968583	+	0.248690i
$6$	0.331159	−	1.01920i	0.331159	−	1.01920i
$7$	−1.49261	−	1.23480i	−1.49261	−	1.23480i	−0.904827	−	0.425779i	$-0.860000\pi$
$7$	−1.49261	−	1.23480i	−1.49261	−	1.23480i	−0.587785	−	0.809017i	$-0.700000\pi$
$8$	−0.684547	+	0.728969i	−0.684547	+	0.728969i
$9$	0.147271	+	0.0186046i	0.147271	+	0.0186046i
$10$			1.00000i			1.00000i
$11$		0			0		0.125333	−	0.992115i	$-0.460000\pi$
$11$		0			0		−0.125333	+	0.992115i	$0.540000\pi$
$12$	−0.904827	−	0.574221i	−0.904827	−	0.574221i
$13$		0			0		−0.637424	−	0.770513i	$-0.720000\pi$
$13$		0			0		0.637424	+	0.770513i	$0.280000\pi$
$14$	−1.56720	+	1.13864i	−1.56720	+	1.13864i
$15$	−1.05267	+	0.200808i	−1.05267	+	0.200808i
$16$	0.535827	+	0.844328i	0.535827	+	0.844328i
$17$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$17$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$18$	0.0546449	−	0.138017i	0.0546449	−	0.138017i
$19$		0			0		0.535827	−	0.844328i	$-0.320000\pi$
$19$		0			0		−0.535827	+	0.844328i	$0.680000\pi$
$20$	0.968583	+	0.248690i	0.968583	+	0.248690i
$21$	−1.51332	−	1.42110i	−1.51332	−	1.42110i
$22$		0			0
$23$	−1.82662	+	0.723208i	−1.82662	+	0.723208i	−0.844328	+	0.535827i	$0.820000\pi$
$23$	−1.82662	+	0.723208i	−1.82662	+	0.723208i	−0.982287	+	0.187381i	$0.940000\pi$
$24$	−0.781202	+	0.733597i	−0.781202	+	0.733597i
$25$	0.876307	−	0.481754i	0.876307	−	0.481754i
$26$		0			0
$27$	−0.896412	−	0.171000i	−0.896412	−	0.171000i
$28$	0.713118	+	1.80113i	0.713118	+	1.80113i
$29$	−0.383238	+	0.317042i	−0.383238	+	0.317042i	−0.809017	−	0.587785i	$-0.800000\pi$
$29$	−0.383238	+	0.317042i	−0.383238	+	0.317042i	0.425779	+	0.904827i	$0.360000\pi$
$30$	−0.0672897	+	1.06954i	−0.0672897	+	1.06954i
$31$		0			0		0.637424	−	0.770513i	$-0.280000\pi$
$31$		0			0		−0.637424	+	0.770513i	$0.720000\pi$
$32$	0.951057	−	0.309017i	0.951057	−	0.309017i
$33$		0			0
$34$		0			0
$35$	1.75280	+	0.824805i	1.75280	+	0.824805i
$36$	−0.120092	−	0.0872517i	−0.120092	−	0.0872517i
$37$		0			0		−0.0627905	−	0.998027i	$-0.520000\pi$
$37$		0			0		0.0627905	+	0.998027i	$0.480000\pi$
$38$		0			0
$39$		0			0
$40$	0.481754	−	0.876307i	0.481754	−	0.876307i
$41$	−1.46560	−	0.476203i	−1.46560	−	0.476203i	−0.535827	−	0.844328i	$-0.680000\pi$
$41$	−1.46560	−	0.476203i	−1.46560	−	0.476203i	−0.929776	+	0.368125i	$0.880000\pi$
$42$	−1.75280	+	1.11236i	−1.75280	+	1.11236i
$43$	−0.849878	−	1.80608i	−0.849878	−	1.80608i	−0.481754	−	0.876307i	$-0.660000\pi$
$43$	−0.849878	−	1.80608i	−0.849878	−	1.80608i	−0.368125	−	0.929776i	$-0.620000\pi$
$44$		0			0
$45$	−0.147271	+	0.0186046i	−0.147271	+	0.0186046i
$46$	0.246226	+	1.94908i	0.246226	+	1.94908i
$47$	0.718995	−	1.52794i	0.718995	−	1.52794i	−0.125333	−	0.992115i	$-0.540000\pi$
$47$	0.718995	−	1.52794i	0.718995	−	1.52794i	0.844328	−	0.535827i	$-0.180000\pi$
$48$	0.516273	+	0.939097i	0.516273	+	0.939097i
$49$	0.515788	+	2.70386i	0.515788	+	2.70386i
$50$	−0.248690	−	0.968583i	−0.248690	−	0.968583i
$51$		0			0
$52$		0			0
$53$		0			0		−0.481754	−	0.876307i	$-0.660000\pi$
$53$		0			0		0.481754	+	0.876307i	$0.340000\pi$
$54$	−0.388556	+	0.825723i	−0.388556	+	0.825723i
$55$		0			0
$56$	1.92189	−	0.242791i	1.92189	−	0.242791i
$57$		0			0
$58$	0.211774	+	0.450043i	0.211774	+	0.450043i
$59$		0			0		0.844328	−	0.535827i	$-0.180000\pi$
$59$		0			0		−0.844328	+	0.535827i	$0.820000\pi$
$60$	1.01920	+	0.331159i	1.01920	+	0.331159i
$61$	−0.120759	+	0.219661i	−0.120759	+	0.219661i	−0.929776	−	0.368125i	$-0.880000\pi$
$61$	−0.120759	+	0.219661i	−0.120759	+	0.219661i	0.809017	+	0.587785i	$0.200000\pi$
$62$		0			0
$63$	−0.196845	−	0.209619i	−0.196845	−	0.209619i
$64$	−0.0627905	−	0.998027i	−0.0627905	−	0.998027i
$65$		0			0
$66$		0			0
$67$	1.85588	−	0.116762i	1.85588	−	0.116762i	0.904827	−	0.425779i	$-0.140000\pi$
$67$	1.85588	−	0.116762i	1.85588	−	0.116762i	0.951057	+	0.309017i	$0.100000\pi$
$68$		0			0
$69$	−2.00230	+	0.650587i	−2.00230	+	0.650587i
$70$	1.23480	−	1.49261i	1.23480	−	1.49261i
$71$		0			0		0.0627905	−	0.998027i	$-0.480000\pi$
$71$		0			0		−0.0627905	+	0.998027i	$0.520000\pi$
$72$	−0.114376	+	0.0946201i	−0.114376	+	0.0946201i
$73$		0			0		−0.368125	−	0.929776i	$-0.620000\pi$
$73$		0			0		0.368125	+	0.929776i	$0.380000\pi$
$74$		0			0
$75$	0.969661	−	0.456288i	0.969661	−	0.456288i
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		−0.929776	−	0.368125i	$-0.880000\pi$
$79$		0			0		0.929776	+	0.368125i	$0.120000\pi$
$80$	−0.728969	−	0.684547i	−0.728969	−	0.684547i
$81$	−1.09102	−	0.280126i	−1.09102	−	0.280126i
$82$	−0.825723	+	1.30113i	−0.825723	+	1.30113i
$83$	−0.0462295	+	0.116762i	−0.0462295	+	0.116762i	−0.951057	−	0.309017i	$-0.900000\pi$
$83$	−0.0462295	+	0.116762i	−0.0462295	+	0.116762i	0.904827	+	0.425779i	$0.140000\pi$
$84$	0.641510	+	1.97437i	0.641510	+	1.97437i
$85$		0			0
$86$	−1.96070	+	0.374023i	−1.96070	+	0.374023i
$87$	−0.431221	+	0.313301i	−0.431221	+	0.313301i
$88$		0			0
$89$	0.992567	+	0.629902i	0.992567	+	0.629902i	0.929776	−	0.368125i	$-0.120000\pi$
$89$	0.992567	+	0.629902i	0.992567	+	0.629902i	0.0627905	+	0.998027i	$0.480000\pi$
$90$	−0.0186046	+	0.147271i	−0.0186046	+	0.147271i
$91$		0			0
$92$	1.94908	+	0.246226i	1.94908	+	0.246226i
$93$		0			0
$94$	−1.30113	−	1.07639i	−1.30113	−	1.07639i
$95$		0			0
$96$	1.03799	−	0.266509i	1.03799	−	0.266509i
$97$		0			0		−0.876307	−	0.481754i	$-0.840000\pi$
$97$		0			0		0.876307	+	0.481754i	$0.160000\pi$
$98$	2.74718	+	0.172838i	2.74718	+	0.172838i
$99$		0			0
$100$	−1.00000			−1.00000
$101$	−0.728969	−	0.684547i	−0.728969	−	0.684547i
$101$	−0.728969	−	0.684547i	−0.728969	−	0.684547i
$102$		0			0
$103$	0.402389	−	1.56720i	0.402389	−	1.56720i	−0.368125	−	0.929776i	$-0.620000\pi$
$103$	0.402389	−	1.56720i	0.402389	−	1.56720i	0.770513	−	0.637424i	$-0.220000\pi$
$104$		0			0
$105$	1.81919	+	1.00011i	1.81919	+	1.00011i
$106$		0			0
$107$	0.297740	−	0.916350i	0.297740	−	0.916350i	−0.684547	−	0.728969i	$-0.740000\pi$
$107$	0.297740	−	0.916350i	0.297740	−	0.916350i	0.982287	−	0.187381i	$-0.0600000\pi$
$108$	0.703152	+	0.581698i	0.703152	+	0.581698i
$109$	1.15596	−	1.23098i	1.15596	−	1.23098i	0.187381	−	0.982287i	$-0.440000\pi$
$109$	1.15596	−	1.23098i	1.15596	−	1.23098i	0.968583	−	0.248690i	$-0.0800000\pi$
$110$		0			0
$111$		0			0
$112$	0.242791	−	1.92189i	0.242791	−	1.92189i
$113$		0			0		−0.844328	−	0.535827i	$-0.820000\pi$
$113$		0			0		0.844328	+	0.535827i	$0.180000\pi$
$114$		0			0
$115$	1.58937	−	1.15475i	1.58937	−	1.15475i
$116$	0.488570	−	0.0931997i	0.488570	−	0.0931997i
$117$		0			0
$118$		0			0
$119$		0			0
$120$	0.574221	−	0.904827i	0.574221	−	0.904827i
$121$	−0.968583	−	0.248690i	−0.968583	−	0.248690i
$122$	0.182728	+	0.171593i	0.182728	+	0.171593i
$123$	−1.53548	−	0.607938i	−1.53548	−	0.607938i
$124$		0			0
$125$	−0.728969	+	0.684547i	−0.728969	+	0.684547i
$126$	−0.251987	+	0.138531i	−0.251987	+	0.138531i
$127$	−1.46404	+	0.688925i	−1.46404	+	0.688925i	−0.982287	−	0.187381i	$-0.940000\pi$
$127$	−1.46404	+	0.688925i	−1.46404	+	0.688925i	−0.481754	+	0.876307i	$0.660000\pi$
$128$	−0.982287	−	0.187381i	−0.982287	−	0.187381i
$129$	−0.787447	−	1.98886i	−0.787447	−	1.98886i
$130$		0			0
$131$		0			0		0.0627905	−	0.998027i	$-0.480000\pi$
$131$		0			0		−0.0627905	+	0.998027i	$0.520000\pi$
$132$		0			0
$133$		0			0
$134$	0.348445	−	1.82662i	0.348445	−	1.82662i
$135$	0.910775	−	0.0573011i	0.910775	−	0.0573011i
$136$		0			0
$137$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$137$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$138$	0.132196	+	2.10119i	0.132196	+	2.10119i
$139$		0			0		−0.684547	−	0.728969i	$-0.740000\pi$
$139$		0			0		0.684547	+	0.728969i	$0.260000\pi$
$140$	−1.13864	−	1.56720i	−1.13864	−	1.56720i
$141$	0.871808	−	1.58581i	0.871808	−	1.58581i
$142$		0			0
$143$		0			0
$144$	0.0632033	+	0.134314i	0.0632033	+	0.134314i
$145$	0.292352	−	0.402389i	0.292352	−	0.402389i
$146$		0			0
$147$	0.369714	+	2.92659i	0.369714	+	2.92659i
$148$		0			0
$149$	0.354691	+	0.645180i	0.354691	+	0.645180i	0.992115	−	0.125333i	$-0.0400000\pi$
$149$	0.354691	+	0.645180i	0.354691	+	0.645180i	−0.637424	+	0.770513i	$0.720000\pi$
$150$	−0.200808	−	1.05267i	−0.200808	−	1.05267i
$151$		0			0		−0.248690	−	0.968583i	$-0.580000\pi$
$151$		0			0		0.248690	+	0.968583i	$0.420000\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.992115	−	0.125333i	$-0.0400000\pi$
$157$		0			0		−0.992115	+	0.125333i	$0.960000\pi$
$158$		0			0
$159$		0			0
$160$	−0.844328	+	0.535827i	−0.844328	+	0.535827i
$161$	3.61944	+	1.17603i	3.61944	+	1.17603i
$162$	−0.542651	+	0.987078i	−0.542651	+	0.987078i
$163$	−1.09302	−	1.50441i	−1.09302	−	1.50441i	−0.844328	−	0.535827i	$-0.820000\pi$
$163$	−1.09302	−	1.50441i	−1.09302	−	1.50441i	−0.248690	−	0.968583i	$-0.580000\pi$
$164$	1.05491	+	1.12336i	1.05491	+	1.12336i
$165$		0			0
$166$	0.101597	+	0.0738147i	0.101597	+	0.0738147i
$167$	0.339095	+	0.159566i	0.339095	+	0.159566i	0.587785	−	0.809017i	$-0.300000\pi$
$167$	0.339095	+	0.159566i	0.339095	+	0.159566i	−0.248690	+	0.968583i	$0.580000\pi$
$168$	2.07187	−	0.130351i	2.07187	−	0.130351i
$169$	−0.187381	+	0.982287i	−0.187381	+	0.982287i
$170$		0			0
$171$		0			0
$172$	−0.125333	+	1.99211i	−0.125333	+	1.99211i
$173$		0			0		0.770513	−	0.637424i	$-0.220000\pi$
$173$		0			0		−0.770513	+	0.637424i	$0.780000\pi$
$174$	0.196217	+	0.495588i	0.196217	+	0.495588i
$175$	−1.90285	−	0.362989i	−1.90285	−	0.362989i
$176$		0			0
$177$		0			0
$178$	0.856954	−	0.804733i	0.856954	−	0.804733i
$179$		0			0		0.929776	−	0.368125i	$-0.120000\pi$
$179$		0			0		−0.929776	+	0.368125i	$0.880000\pi$
$180$	0.138017	+	0.0546449i	0.138017	+	0.0546449i
$181$	−0.0915446	−	0.0859661i	−0.0915446	−	0.0859661i	0.637424	−	0.770513i	$-0.280000\pi$
$181$	−0.0915446	−	0.0859661i	−0.0915446	−	0.0859661i	−0.728969	+	0.684547i	$0.760000\pi$
$182$		0			0
$183$	−0.143938	+	0.226810i	−0.143938	+	0.226810i
$184$	0.723208	−	1.82662i	0.723208	−	1.82662i
$185$		0			0
$186$		0			0
$187$		0			0
$188$	−1.36615	+	0.992567i	−1.36615	+	0.992567i
$189$	1.12685	+	1.36212i	1.12685	+	1.36212i
$190$		0			0
$191$		0			0		0.125333	−	0.992115i	$-0.460000\pi$
$191$		0			0		−0.125333	+	0.992115i	$0.540000\pi$
$192$		−	1.07165i		−	1.07165i
$193$		0			0		−0.992115	−	0.125333i	$-0.960000\pi$
$193$		0			0		0.992115	+	0.125333i	$0.0400000\pi$
$194$		0			0
$195$		0			0
$196$	0.850604	−	2.61789i	0.850604	−	2.61789i
$197$		0			0		0.968583	−	0.248690i	$-0.0800000\pi$
$197$		0			0		−0.968583	+	0.248690i	$0.920000\pi$
$198$		0			0
$199$		0			0		−0.998027	−	0.0627905i	$-0.980000\pi$
$199$		0			0		0.998027	+	0.0627905i	$0.0200000\pi$
$200$	−0.248690	+	0.968583i	−0.248690	+	0.968583i
$201$	1.99280			1.99280
$202$	−0.844328	+	0.535827i	−0.844328	+	0.535827i
$203$	0.963507			0.963507
$204$		0			0
$205$	1.53799	+	0.0967619i	1.53799	+	0.0967619i
$206$	−1.41789	−	0.779494i	−1.41789	−	0.779494i
$207$	−0.282462	+	0.0725240i	−0.282462	+	0.0725240i
$208$		0			0
$209$		0			0
$210$	1.42110	−	1.51332i	1.42110	−	1.51332i
$211$		0			0		−0.992115	−	0.125333i	$-0.960000\pi$
$211$		0			0		0.992115	+	0.125333i	$0.0400000\pi$
$212$		0			0
$213$		0			0
$214$	−0.813516	−	0.516273i	−0.813516	−	0.516273i
$215$	1.27233	+	1.53799i	1.27233	+	1.53799i
$216$	0.738289	−	0.536399i	0.738289	−	0.536399i
$217$		0			0
$218$	−0.904827	−	1.42578i	−0.904827	−	1.42578i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	1.31918	+	1.23879i	1.31918	+	1.23879i	0.951057	+	0.309017i	$0.100000\pi$
$223$	1.31918	+	1.23879i	1.31918	+	1.23879i	0.368125	+	0.929776i	$0.380000\pi$
$224$	−1.80113	−	0.713118i	−1.80113	−	0.713118i
$225$	0.138017	−	0.0546449i	0.138017	−	0.0546449i
$226$		0			0
$227$	−0.645180	+	0.354691i	−0.645180	+	0.354691i	−0.770513	−	0.637424i	$-0.780000\pi$
$227$	−0.645180	+	0.354691i	−0.645180	+	0.354691i	0.125333	+	0.992115i	$0.460000\pi$
$228$		0			0
$229$	1.86842	+	0.356420i	1.86842	+	0.356420i	0.992115	−	0.125333i	$-0.0400000\pi$
$229$	1.86842	+	0.356420i	1.86842	+	0.356420i	0.876307	+	0.481754i	$0.160000\pi$
$230$	−0.723208	−	1.82662i	−0.723208	−	1.82662i
$231$		0			0
$232$	0.0312307	−	0.496398i	0.0312307	−	0.496398i
$233$		0			0		0.637424	−	0.770513i	$-0.280000\pi$
$233$		0			0		−0.637424	+	0.770513i	$0.720000\pi$
$234$		0			0
$235$	−0.316423	+	1.65875i	−0.316423	+	1.65875i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		−0.0627905	−	0.998027i	$-0.520000\pi$
$239$		0			0		0.0627905	+	0.998027i	$0.480000\pi$
$240$	−0.733597	−	0.781202i	−0.733597	−	0.781202i
$241$	−0.147338	−	0.202793i	−0.147338	−	0.202793i	0.728969	−	0.684547i	$-0.240000\pi$
$241$	−0.147338	−	0.202793i	−0.147338	−	0.202793i	−0.876307	+	0.481754i	$0.840000\pi$
$242$	−0.481754	+	0.876307i	−0.481754	+	0.876307i
$243$	−0.280126	−	0.0910184i	−0.280126	−	0.0910184i
$244$	0.211645	−	0.134314i	0.211645	−	0.134314i
$245$	−1.17201	−	2.49064i	−1.17201	−	2.49064i
$246$	−0.970696	+	1.33605i	−0.970696	+	1.33605i
$247$		0			0
$248$		0			0
$249$	−0.0573011	+	0.121771i	−0.0573011	+	0.121771i
$250$	0.481754	+	0.876307i	0.481754	+	0.876307i
$251$		0			0		−0.187381	−	0.982287i	$-0.560000\pi$
$251$		0			0		0.187381	+	0.982287i	$0.440000\pi$
$252$	0.0715122	+	0.278522i	0.0715122	+	0.278522i
$253$		0			0
$254$	0.303189	+	1.58937i	0.303189	+	1.58937i
$255$		0			0
$256$	−0.425779	+	0.904827i	−0.425779	+	0.904827i
$257$		0			0		−0.125333	−	0.992115i	$-0.540000\pi$
$257$		0			0		0.125333	+	0.992115i	$0.460000\pi$
$258$	−2.12221	+	0.268098i	−2.12221	+	0.268098i
$259$		0			0
$260$		0			0
$261$	−0.0623382	+	0.0395610i	−0.0623382	+	0.0395610i
$262$		0			0
$263$	−0.702367	+	1.27760i	−0.702367	+	1.27760i	0.248690	+	0.968583i	$0.420000\pi$
$263$	−0.702367	+	1.27760i	−0.702367	+	1.27760i	−0.951057	+	0.309017i	$0.900000\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	1.01920	+	0.740494i	1.01920	+	0.740494i
$268$	−1.68257	−	0.791759i	−1.68257	−	0.791759i
$269$	−0.961606	+	0.0604991i	−0.961606	+	0.0604991i	−0.535827	−	0.844328i	$-0.680000\pi$
$269$	−0.961606	+	0.0604991i	−0.961606	+	0.0604991i	−0.425779	+	0.904827i	$0.640000\pi$
$270$	0.171000	−	0.896412i	0.171000	−	0.896412i
$271$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$271$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$	2.06805	+	0.394502i	2.06805	+	0.394502i
$277$		0			0		0.904827	−	0.425779i	$-0.140000\pi$
$277$		0			0		−0.904827	+	0.425779i	$0.860000\pi$
$278$		0			0
$279$		0			0
$280$	−1.80113	+	0.713118i	−1.80113	+	0.713118i
$281$	0.348445	+	0.137959i	0.348445	+	0.137959i	0.535827	−	0.844328i	$-0.320000\pi$
$281$	0.348445	+	0.137959i	0.348445	+	0.137959i	−0.187381	+	0.982287i	$0.560000\pi$
$282$	−1.31918	−	1.23879i	−1.31918	−	1.23879i
$283$	−1.49261	−	0.383238i	−1.49261	−	0.383238i	−0.587785	−	0.809017i	$-0.700000\pi$
$283$	−1.49261	−	0.383238i	−1.49261	−	0.383238i	−0.904827	+	0.425779i	$0.860000\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	1.59956	+	2.52051i	1.59956	+	2.52051i
$288$	0.145812	−	0.0278151i	0.145812	−	0.0278151i
$289$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$290$	−0.317042	−	0.383238i	−0.317042	−	0.383238i
$291$		0			0
$292$		0			0
$293$		0			0			−	1.00000i	$-0.5\pi$
$293$		0			0				1.00000i	$0.5\pi$
$294$	2.92659	+	0.369714i	2.92659	+	0.369714i
$295$		0			0
$296$		0			0
$297$		0			0
$298$	0.713118	−	0.183098i	0.713118	−	0.183098i
$299$		0			0
$300$	−1.06954	−	0.0672897i	−1.06954	−	0.0672897i
$301$	−0.961606	+	3.74521i	−0.961606	+	3.74521i
$302$		0			0
$303$	−0.733597	−	0.781202i	−0.733597	−	0.781202i
$304$		0			0
$305$	0.0623382	−	0.242791i	0.0623382	−	0.242791i
$306$		0			0
$307$	−0.435857	−	0.239615i	−0.435857	−	0.239615i	0.248690	−	0.968583i	$-0.420000\pi$
$307$	−0.435857	−	0.239615i	−0.435857	−	0.239615i	−0.684547	+	0.728969i	$0.740000\pi$
$308$		0			0
$309$	0.535827	−	1.64911i	0.535827	−	1.64911i
$310$		0			0
$311$		0			0		0.684547	−	0.728969i	$-0.260000\pi$
$311$		0			0		−0.684547	+	0.728969i	$0.740000\pi$
$312$		0			0
$313$		0			0			−	1.00000i	$-0.5\pi$
$313$		0			0				1.00000i	$0.5\pi$
$314$		0			0
$315$	0.242791	+	0.154080i	0.242791	+	0.154080i
$316$		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
$321$	0.380106	−	0.960037i	0.380106	−	0.960037i
$322$	2.03920	−	3.21327i	2.03920	−	3.21327i
$323$		0			0
$324$	0.821115	+	0.771078i	0.821115	+	0.771078i
$325$		0			0
$326$	−1.72897	+	0.684547i	−1.72897	+	0.684547i
$327$	1.31918	−	1.23879i	1.31918	−	1.23879i
$328$	1.35041	−	0.742395i	1.35041	−	0.742395i
$329$	−2.95988	+	1.39281i	−2.95988	+	1.39281i
$330$		0			0
$331$		0			0		−0.368125	−	0.929776i	$-0.620000\pi$
$331$		0			0		0.368125	+	0.929776i	$0.380000\pi$
$332$	0.0967619	−	0.0800484i	0.0967619	−	0.0800484i
$333$		0			0
$334$	0.238883	−	0.288760i	0.238883	−	0.288760i
$335$	−1.76854	+	0.574633i	−1.76854	+	0.574633i
$336$	0.388998	−	2.03920i	0.388998	−	2.03920i
$337$		0			0		0.998027	−	0.0627905i	$-0.0200000\pi$
$337$		0			0		−0.998027	+	0.0627905i	$0.980000\pi$
$338$	0.904827	+	0.425779i	0.904827	+	0.425779i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	1.63560	−	2.97515i	1.63560	−	2.97515i
$344$	1.89836	+	0.616814i	1.89836	+	0.616814i
$345$	1.77760	−	1.12810i	1.77760	−	1.12810i
$346$		0			0
$347$	−1.03016	+	1.41789i	−1.03016	+	1.41789i	−0.125333	+	0.992115i	$0.540000\pi$
$347$	−1.03016	+	1.41789i	−1.03016	+	1.41789i	−0.904827	+	0.425779i	$0.860000\pi$
$348$	0.528816	−	0.0668050i	0.528816	−	0.0668050i
$349$	−0.226810	−	1.79538i	−0.226810	−	1.79538i	−0.535827	−	0.844328i	$-0.680000\pi$
$349$	−0.226810	−	1.79538i	−0.226810	−	1.79538i	0.309017	−	0.951057i	$-0.400000\pi$
$350$	−0.824805	+	1.75280i	−0.824805	+	1.75280i
$351$		0			0
$352$		0			0
$353$		0			0		−0.248690	−	0.968583i	$-0.580000\pi$
$353$		0			0		0.248690	+	0.968583i	$0.420000\pi$
$354$		0			0
$355$		0			0
$356$	−0.566335	−	1.03016i	−0.566335	−	1.03016i
$357$		0			0
$358$		0			0
$359$		0			0		0.992115	−	0.125333i	$-0.0400000\pi$
$359$		0			0		−0.992115	+	0.125333i	$0.960000\pi$
$360$	0.0872517	−	0.120092i	0.0872517	−	0.120092i
$361$	−0.425779	−	0.904827i	−0.425779	−	0.904827i
$362$	−0.106032	+	0.0672897i	−0.106032	+	0.0672897i
$363$	−1.01920	−	0.331159i	−1.01920	−	0.331159i
$364$		0			0
$365$		0			0
$366$	0.183888	+	0.195821i	0.183888	+	0.195821i
$367$	−0.0738147	−	1.17325i	−0.0738147	−	1.17325i	−0.844328	−	0.535827i	$-0.820000\pi$
$367$	−0.0738147	−	1.17325i	−0.0738147	−	1.17325i	0.770513	−	0.637424i	$-0.220000\pi$
$368$	−1.58937	−	1.15475i	−1.58937	−	1.15475i
$369$	−0.206981	−	0.0973979i	−0.206981	−	0.0973979i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.637424	−	0.770513i	$-0.280000\pi$
$373$		0			0		−0.637424	+	0.770513i	$0.720000\pi$
$374$		0			0
$375$	−0.825723	+	0.683098i	−0.825723	+	0.683098i
$376$	0.621636	+	1.57007i	0.621636	+	1.57007i
$377$		0			0
$378$	1.59956	−	0.752697i	1.59956	−	0.752697i
$379$		0			0		0.876307	−	0.481754i	$-0.160000\pi$
$379$		0			0		−0.876307	+	0.481754i	$0.840000\pi$
$380$		0			0
$381$	−1.61221	+	0.638318i	−1.61221	+	0.638318i
$382$		0			0
$383$	0.998027	+	0.937209i	0.998027	+	0.937209i	0.998027	−	0.0627905i	$-0.0200000\pi$
$383$	0.998027	+	0.937209i	0.998027	+	0.937209i			1.00000i	$0.5\pi$
$384$	−1.03799	−	0.266509i	−1.03799	−	0.266509i
$385$		0			0
$386$		0			0
$387$	−0.0915608	−	0.281795i	−0.0915608	−	0.281795i
$388$		0			0
$389$		0			0		−0.187381	−	0.982287i	$-0.560000\pi$
$389$		0			0		0.187381	+	0.982287i	$0.440000\pi$
$390$		0			0
$391$		0			0
$392$	−2.32411	−	1.47492i	−2.32411	−	1.47492i
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$		0			0		−0.770513	−	0.637424i	$-0.780000\pi$
$397$		0			0		0.770513	+	0.637424i	$0.220000\pi$
$398$		0			0
$399$		0			0
$400$	0.876307	+	0.481754i	0.876307	+	0.481754i
$401$	1.89836	+	0.119435i	1.89836	+	0.119435i	0.968583	−	0.248690i	$-0.0800000\pi$
$401$	1.89836	+	0.119435i	1.89836	+	0.119435i	0.929776	+	0.368125i	$0.120000\pi$
$402$	0.495588	−	1.93019i	0.495588	−	1.93019i
$403$		0			0
$404$	0.309017	+	0.951057i	0.309017	+	0.951057i
$405$	1.12641			1.12641
$406$	0.239615	−	0.933237i	0.239615	−	0.933237i
$407$		0			0
$408$		0			0
$409$	0.362989	−	0.0931997i	0.362989	−	0.0931997i	−0.0627905	−	0.998027i	$-0.520000\pi$
$409$	0.362989	−	0.0931997i	0.362989	−	0.0931997i	0.425779	+	0.904827i	$0.360000\pi$
$410$	0.476203	−	1.46560i	0.476203	−	1.46560i
$411$		0			0
$412$	−1.10762	+	1.17950i	−1.10762	+	1.17950i
$413$		0			0
$414$			0.291624i			0.291624i
$415$	0.0157395	−	0.124591i	0.0157395	−	0.124591i
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		0.982287	−	0.187381i	$-0.0600000\pi$
$419$		0			0		−0.982287	+	0.187381i	$0.940000\pi$
$420$	−1.11236	−	1.75280i	−1.11236	−	1.75280i
$421$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	−0.809017	−	0.587785i	$-0.800000\pi$
$421$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	0.309017	−	0.951057i	$-0.400000\pi$
$422$		0			0
$423$	0.134314	−	0.211645i	0.134314	−	0.211645i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	0.451483	−	0.178755i	0.451483	−	0.178755i
$428$	−0.702367	+	0.659566i	−0.702367	+	0.659566i
$429$		0			0
$430$	1.80608	−	0.849878i	1.80608	−	0.849878i
$431$		0			0		−0.982287	−	0.187381i	$-0.940000\pi$
$431$		0			0		0.982287	+	0.187381i	$0.0600000\pi$
$432$	−0.335942	−	0.848492i	−0.335942	−	0.848492i
$433$		0			0		0.770513	−	0.637424i	$-0.220000\pi$
$433$		0			0		−0.770513	+	0.637424i	$0.780000\pi$
$434$		0			0
$435$	0.339759	−	0.410698i	0.339759	−	0.410698i
$436$	−1.60601	+	0.521823i	−1.60601	+	0.521823i
$437$		0			0
$438$		0			0
$439$		0			0		−0.904827	−	0.425779i	$-0.860000\pi$
$439$		0			0		0.904827	+	0.425779i	$0.140000\pi$
$440$		0			0
$441$	0.0256563	+	0.407796i	0.0256563	+	0.407796i
$442$		0			0
$443$	0.363271	+	0.500000i	0.363271	+	0.500000i	0.951057	−	0.309017i	$-0.100000\pi$
$443$	0.363271	+	0.500000i	0.363271	+	0.500000i	−0.587785	+	0.809017i	$0.700000\pi$
$444$		0			0
$445$	−1.11803	−	0.363271i	−1.11803	−	0.363271i
$446$	1.52794	−	0.969661i	1.52794	−	0.969661i
$447$	0.335942	+	0.713912i	0.335942	+	0.713912i
$448$	−1.13864	+	1.56720i	−1.13864	+	1.56720i
$449$	−1.96858	+	0.248690i	−1.96858	+	0.248690i	−0.968583	+	0.248690i	$0.920000\pi$
$449$	−1.96858	+	0.248690i	−1.96858	+	0.248690i	−1.00000			$1.00000\pi$
$450$	−0.0186046	−	0.147271i	−0.0186046	−	0.147271i
$451$		0			0
$452$		0			0
$453$		0			0
$454$	0.183098	+	0.713118i	0.183098	+	0.713118i
$455$		0			0
$456$		0			0
$457$		0			0		−0.481754	−	0.876307i	$-0.660000\pi$
$457$		0			0		0.481754	+	0.876307i	$0.340000\pi$
$458$	0.809880	−	1.72108i	0.809880	−	1.72108i
$459$		0			0
$460$	−1.94908	+	0.246226i	−1.94908	+	0.246226i
$461$	−0.566335	+	0.779494i	−0.566335	+	0.779494i	−0.992115	−	0.125333i	$-0.960000\pi$
$461$	−0.566335	+	0.779494i	−0.566335	+	0.779494i	0.425779	+	0.904827i	$0.360000\pi$
$462$		0			0
$463$	−0.521823	+	0.331159i	−0.521823	+	0.331159i	−0.770513	−	0.637424i	$-0.780000\pi$
$463$	−0.521823	+	0.331159i	−0.521823	+	0.331159i	0.248690	+	0.968583i	$0.420000\pi$
$464$	−0.473036	−	0.153699i	−0.473036	−	0.153699i
$465$		0			0
$466$		0			0
$467$	−0.872693	−	0.929324i	−0.872693	−	0.929324i	0.125333	−	0.992115i	$-0.460000\pi$
$467$	−0.872693	−	0.929324i	−0.872693	−	0.929324i	−0.998027	+	0.0627905i	$0.980000\pi$
$468$		0			0
$469$	−2.91429	−	2.11736i	−2.91429	−	2.11736i
$470$	1.52794	+	0.718995i	1.52794	+	0.718995i
$471$		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		0.904827	−	0.425779i	$-0.140000\pi$
$479$		0			0		−0.904827	+	0.425779i	$0.860000\pi$
$480$	−0.939097	+	0.516273i	−0.939097	+	0.516273i
$481$		0			0
$482$	−0.233064	+	0.0922765i	−0.233064	+	0.0922765i
$483$	3.79200	+	1.50136i	3.79200	+	1.50136i
$484$	0.728969	+	0.684547i	0.728969	+	0.684547i
$485$		0			0
$486$	−0.157823	+	0.248690i	−0.157823	+	0.248690i
$487$	0.469303	−	1.18532i	0.469303	−	1.18532i	−0.481754	−	0.876307i	$-0.660000\pi$
$487$	0.469303	−	1.18532i	0.469303	−	1.18532i	0.951057	−	0.309017i	$-0.100000\pi$
$488$	−0.0774602	−	0.238398i	−0.0774602	−	0.238398i
$489$	−1.06779	−	1.68257i	−1.06779	−	1.68257i
$490$	−2.70386	+	0.515788i	−2.70386	+	0.515788i
$491$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$491$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$492$	1.05267	+	1.27246i	1.05267	+	1.27246i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	0.103695	+	0.0857841i	0.103695	+	0.0857841i
$499$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$499$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$500$	0.968583	−	0.248690i	0.968583	−	0.248690i
$501$	0.351939	+	0.193480i	0.351939	+	0.193480i
$502$		0			0
$503$	0.493458	−	1.92189i	0.493458	−	1.92189i	0.125333	−	0.992115i	$-0.460000\pi$
$503$	0.493458	−	1.92189i	0.493458	−	1.92189i	0.368125	−	0.929776i	$-0.380000\pi$
$504$	0.287556			0.287556
$505$	0.876307	+	0.481754i	0.876307	+	0.481754i
$506$		0			0
$507$	−0.266509	+	1.03799i	−0.266509	+	1.03799i
$508$	1.61484	+	0.101597i	1.61484	+	0.101597i
$509$	−0.110048	−	0.0604991i	−0.110048	−	0.0604991i	0.425779	−	0.904827i	$-0.360000\pi$
$509$	−0.110048	−	0.0604991i	−0.110048	−	0.0604991i	−0.535827	+	0.844328i	$0.680000\pi$
$510$		0			0
$511$		0			0
$512$	0.770513	+	0.637424i	0.770513	+	0.637424i
$513$		0			0
$514$		0			0
$515$			1.61803i			1.61803i
$516$	−0.268098	+	2.12221i	−0.268098	+	2.12221i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	0.683098	+	1.07639i	0.683098	+	1.07639i	0.992115	+	0.125333i	$0.0400000\pi$
$521$	0.683098	+	1.07639i	0.683098	+	1.07639i	−0.309017	+	0.951057i	$0.600000\pi$
$522$	0.0228153	+	0.0702182i	0.0228153	+	0.0702182i
$523$	−0.730444	+	1.84489i	−0.730444	+	1.84489i	−0.248690	+	0.968583i	$0.580000\pi$
$523$	−0.730444	+	1.84489i	−0.730444	+	1.84489i	−0.481754	+	0.876307i	$0.660000\pi$
$524$		0			0
$525$	−2.01075	−	0.516273i	−2.01075	−	0.516273i
$526$	1.06279	+	0.998027i	1.06279	+	0.998027i
$527$		0			0
$528$		0			0
$529$	2.08452	−	1.95750i	2.08452	−	1.95750i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$	0.970696	−	0.803030i	0.970696	−	0.803030i
$535$	−0.0604991	+	0.961606i	−0.0604991	+	0.961606i
$536$	−1.18532	+	1.43281i	−1.18532	+	1.43281i
$537$		0			0
$538$	−0.180543	+	0.946441i	−0.180543	+	0.946441i
$539$		0			0
$540$	−0.825723	−	0.388556i	−0.825723	−	0.388556i
$541$	−1.03137	−	0.749337i	−1.03137	−	0.749337i	−0.0627905	−	0.998027i	$-0.520000\pi$
$541$	−1.03137	−	0.749337i	−1.03137	−	0.749337i	−0.968583	+	0.248690i	$0.920000\pi$
$542$		0			0
$543$	−0.0921259	−	0.0981041i	−0.0921259	−	0.0981041i
$544$		0			0
$545$	−0.813516	+	1.47978i	−0.813516	+	1.47978i
$546$		0			0
$547$	−1.47978	+	0.939097i	−1.47978	+	0.939097i	−0.481754	+	0.876307i	$0.660000\pi$
$547$	−1.47978	+	0.939097i	−1.47978	+	0.939097i	−0.998027	+	0.0627905i	$0.980000\pi$
$548$		0			0
$549$	−0.0218711	+	0.0301029i	−0.0218711	+	0.0301029i
$550$		0			0
$551$		0			0
$552$	0.896412	−	1.90497i	0.896412	−	1.90497i
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$		0			0		−0.187381	−	0.982287i	$-0.560000\pi$
$557$		0			0		0.187381	+	0.982287i	$0.440000\pi$
$558$		0			0
$559$		0			0
$560$	0.242791	+	1.92189i	0.242791	+	1.92189i
$561$		0			0
$562$	0.220280	−	0.303189i	0.220280	−	0.303189i
$563$	−0.500534	−	1.06369i	−0.500534	−	1.06369i	−0.982287	−	0.187381i	$-0.940000\pi$
$563$	−0.500534	−	1.06369i	−0.500534	−	1.06369i	0.481754	−	0.876307i	$-0.340000\pi$
$564$	−1.52794	+	0.969661i	−1.52794	+	0.969661i
$565$		0			0
$566$	−0.742395	+	1.35041i	−0.742395	+	1.35041i
$567$	1.28257	+	1.76530i	1.28257	+	1.76530i
$568$		0			0
$569$	0.00788530	+	0.125333i	0.00788530	+	0.125333i	1.00000			$0$
$569$	0.00788530	+	0.125333i	0.00788530	+	0.125333i	−0.992115	+	0.125333i	$0.960000\pi$
$570$		0			0
$571$		0			0		−0.904827	−	0.425779i	$-0.860000\pi$
$571$		0			0		0.904827	+	0.425779i	$0.140000\pi$
$572$		0			0
$573$		0			0
$574$	2.83912	−	0.922485i	2.83912	−	0.922485i
$575$	−1.25227	+	1.51373i	−1.25227	+	1.51373i
$576$	0.00932071	−	0.148149i	0.00932071	−	0.148149i
$577$		0			0		0.770513	−	0.637424i	$-0.220000\pi$
$577$		0			0		−0.770513	+	0.637424i	$0.780000\pi$
$578$	0.368125	+	0.929776i	0.368125	+	0.929776i
$579$		0			0
$580$	−0.450043	+	0.211774i	−0.450043	+	0.211774i
$581$	0.213180	−	0.117197i	0.213180	−	0.117197i
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$	0.733597	−	1.15596i	0.733597	−	1.15596i	−0.248690	−	0.968583i	$-0.580000\pi$
$587$	0.733597	−	1.15596i	0.733597	−	1.15596i	0.982287	−	0.187381i	$-0.0600000\pi$
$588$	1.08591	−	2.74270i	1.08591	−	2.74270i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$		0			0		−0.637424	−	0.770513i	$-0.720000\pi$
$593$		0			0		0.637424	+	0.770513i	$0.280000\pi$
$594$		0			0
$595$		0			0
$596$		−	0.736249i		−	0.736249i
$597$		0			0
$598$		0			0
$599$		0			0		−0.770513	−	0.637424i	$-0.780000\pi$
$599$		0			0		0.770513	+	0.637424i	$0.220000\pi$
$600$	−0.331159	+	1.01920i	−0.331159	+	1.01920i
$601$	0.598617	−	0.153699i	0.598617	−	0.153699i	0.0627905	−	0.998027i	$-0.480000\pi$
$601$	0.598617	−	0.153699i	0.598617	−	0.153699i	0.535827	+	0.844328i	$0.320000\pi$
$602$	3.38840	+	1.86279i	3.38840	+	1.86279i
$603$	0.275490	+	0.0173324i	0.275490	+	0.0173324i
$604$		0			0
$605$	1.00000			1.00000
$606$	−0.939097	+	0.516273i	−0.939097	+	0.516273i
$607$	1.36909			1.36909			0.684547	−	0.728969i	$-0.260000\pi$
$607$	1.36909			1.36909			0.684547	+	0.728969i	$0.260000\pi$
$608$		0			0
$609$	1.03051	+	0.0648341i	1.03051	+	0.0648341i
$610$	−0.219661	−	0.120759i	−0.219661	−	0.120759i
$611$		0			0
$612$		0			0
$613$		0			0		−0.770513	−	0.637424i	$-0.780000\pi$
$613$		0			0		0.770513	+	0.637424i	$0.220000\pi$
$614$	−0.340480	+	0.362574i	−0.340480	+	0.362574i
$615$	1.63842	+	0.206981i	1.63842	+	0.206981i
$616$		0			0
$617$		0			0		0.125333	−	0.992115i	$-0.460000\pi$
$617$		0			0		−0.125333	+	0.992115i	$0.540000\pi$
$618$	−1.46404	−	0.929109i	−1.46404	−	0.929109i
$619$		0			0		−0.637424	−	0.770513i	$-0.720000\pi$
$619$		0			0		0.637424	+	0.770513i	$0.280000\pi$
$620$		0			0
$621$	1.76107	−	0.335942i	1.76107	−	0.335942i
$622$		0			0
$623$	−0.703717	−	2.16582i	−0.703717	−	2.16582i
$624$		0			0
$625$	0.535827	−	0.844328i	0.535827	−	0.844328i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$	0.209619	−	0.196845i	0.209619	−	0.196845i
$631$		0			0		0.876307	−	0.481754i	$-0.160000\pi$
$631$		0			0		−0.876307	+	0.481754i	$0.840000\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	1.24672	−	1.03137i	1.24672	−	1.03137i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$	0.998027	−	0.0627905i	0.998027	−	0.0627905i
$641$	1.06369	+	0.500534i	1.06369	+	0.500534i	0.876307	−	0.481754i	$-0.160000\pi$
$641$	1.06369	+	0.500534i	1.06369	+	0.500534i	0.187381	+	0.982287i	$0.440000\pi$
$642$	−0.835347	−	0.606915i	−0.835347	−	0.606915i
$643$		0			0		0.998027	−	0.0627905i	$-0.0200000\pi$
$643$		0			0		−0.998027	+	0.0627905i	$0.980000\pi$
$644$	−2.60519	−	2.77424i	−2.60519	−	2.77424i
$645$	1.25732	+	1.73055i	1.25732	+	1.73055i
$646$		0			0
$647$	−0.809880	−	0.263146i	−0.809880	−	0.263146i	−0.125333	−	0.992115i	$-0.540000\pi$
$647$	−0.809880	−	0.263146i	−0.809880	−	0.263146i	−0.684547	+	0.728969i	$0.740000\pi$
$648$	0.951057	−	0.603559i	0.951057	−	0.603559i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	0.233064	+	1.84489i	0.233064	+	1.84489i
$653$		0			0		0.425779	−	0.904827i	$-0.360000\pi$
$653$		0			0		−0.425779	+	0.904827i	$0.640000\pi$
$654$	−0.871808	−	1.58581i	−0.871808	−	1.58581i
$655$		0			0
$656$	−0.383238	−	1.49261i	−0.383238	−	1.49261i
$657$		0			0
$658$	0.612963	+	3.21327i	0.612963	+	3.21327i
$659$		0			0		−0.481754	−	0.876307i	$-0.660000\pi$
$659$		0			0		0.481754	+	0.876307i	$0.340000\pi$
$660$		0			0
$661$	−0.171593	−	1.35830i	−0.171593	−	1.35830i	−0.809017	−	0.587785i	$-0.800000\pi$
$661$	−0.171593	−	1.35830i	−0.171593	−	1.35830i	0.637424	−	0.770513i	$-0.280000\pi$
$662$		0			0
$663$		0			0
$664$	−0.0534698	−	0.113629i	−0.0534698	−	0.113629i
$665$		0			0
$666$		0			0
$667$	0.470741	−	0.856274i	0.470741	−	0.856274i
$668$	−0.220280	−	0.303189i	−0.220280	−	0.303189i
$669$	1.32756	+	1.41371i	1.32756	+	1.41371i
$670$	0.116762	+	1.85588i	0.116762	+	1.85588i
$671$		0			0
$672$	−1.87839	−	0.883906i	−1.87839	−	0.883906i
$673$		0			0		0.998027	−	0.0627905i	$-0.0200000\pi$
$673$		0			0		−0.998027	+	0.0627905i	$0.980000\pi$
$674$		0			0
$675$	−0.867911	+	0.282001i	−0.867911	+	0.282001i
$676$	0.637424	−	0.770513i	0.637424	−	0.770513i
$677$		0			0		0.0627905	−	0.998027i	$-0.480000\pi$
$677$		0			0		−0.0627905	+	0.998027i	$0.520000\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−0.713912	+	0.335942i	−0.713912	+	0.335942i
$682$		0			0
$683$	−1.31918	+	1.23879i	−1.31918	+	1.23879i	−0.368125	+	0.929776i	$0.620000\pi$
$683$	−1.31918	+	1.23879i	−1.31918	+	1.23879i	−0.951057	+	0.309017i	$0.900000\pi$
$684$		0			0
$685$		0			0
$686$	−2.47492	−	2.32411i	−2.47492	−	2.32411i
$687$	1.97437	+	0.506931i	1.97437	+	0.506931i
$688$	1.06954	−	1.68532i	1.06954	−	1.68532i
$689$		0			0
$690$	−0.650587	−	2.00230i	−0.650587	−	2.00230i
$691$		0			0		−0.535827	−	0.844328i	$-0.680000\pi$
$691$		0			0		0.535827	+	0.844328i	$0.320000\pi$
$692$		0			0
$693$		0			0
$694$	1.11716	+	1.35041i	1.11716	+	1.35041i
$695$		0			0
$696$	0.0668050	−	0.528816i	0.0668050	−	0.528816i
$697$		0			0
$698$	−1.79538	−	0.226810i	−1.79538	−	0.226810i
$699$		0			0
$700$	1.49261	+	1.23480i	1.49261	+	1.23480i
$701$	−0.393950	+	1.21245i	−0.393950	+	1.21245i	0.535827	+	0.844328i	$0.320000\pi$
$701$	−0.393950	+	1.21245i	−0.393950	+	1.21245i	−0.929776	+	0.368125i	$0.880000\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	−0.450043	+	1.75280i	−0.450043	+	1.75280i
$706$		0			0
$707$	0.242791	+	1.92189i	0.242791	+	1.92189i
$708$		0			0
$709$	−0.340480	+	1.32608i	−0.340480	+	1.32608i	0.535827	+	0.844328i	$0.320000\pi$
$709$	−0.340480	+	1.32608i	−0.340480	+	1.32608i	−0.876307	+	0.481754i	$0.840000\pi$
$710$		0			0
$711$		0			0
$712$	−1.13864	+	0.292352i	−1.13864	+	0.292352i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		−0.844328	−	0.535827i	$-0.820000\pi$
$719$		0			0		0.844328	+	0.535827i	$0.180000\pi$
$720$	−0.0946201	−	0.114376i	−0.0946201	−	0.114376i
$721$	−2.53578	+	1.84235i	−2.53578	+	1.84235i
$722$	−0.982287	+	0.187381i	−0.982287	+	0.187381i
$723$	−0.143938	−	0.226810i	−0.143938	−	0.226810i
$724$	0.0388067	+	0.119435i	0.0388067	+	0.119435i
$725$	−0.183098	+	0.462452i	−0.183098	+	0.462452i
$726$	−0.574221	+	0.904827i	−0.574221	+	0.904827i
$727$	1.84235	+	0.473036i	1.84235	+	0.473036i	0.998027	−	0.0627905i	$-0.0200000\pi$
$727$	1.84235	+	0.473036i	1.84235	+	0.473036i	0.844328	+	0.535827i	$0.180000\pi$
$728$		0			0
$729$	0.753825	+	0.298461i	0.753825	+	0.298461i
$730$		0			0
$731$		0			0
$732$	0.235400	−	0.129412i	0.235400	−	0.129412i
$733$		0			0		0.904827	−	0.425779i	$-0.140000\pi$
$733$		0			0		−0.904827	+	0.425779i	$0.860000\pi$
$734$	−1.15475	−	0.220280i	−1.15475	−	0.220280i
$735$	−1.08591	−	2.74270i	−1.08591	−	2.74270i
$736$	−1.51373	+	1.25227i	−1.51373	+	1.25227i
$737$		0			0
$738$	−0.145812	+	0.176257i	−0.145812	+	0.176257i
$739$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$739$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−0.595638	−	0.432756i	−0.595638	−	0.432756i	0.248690	−	0.968583i	$-0.420000\pi$
$743$	−0.595638	−	0.432756i	−0.595638	−	0.432756i	−0.844328	+	0.535827i	$0.820000\pi$
$744$		0			0
$745$	−0.503997	−	0.536702i	−0.503997	−	0.536702i
$746$		0			0
$747$	−0.00898058	+	0.0163356i	−0.00898058	+	0.0163356i
$748$		0			0
$749$	−1.57592	+	1.00011i	−1.57592	+	1.00011i
$750$	0.456288	+	0.969661i	0.456288	+	0.969661i
$751$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$751$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$752$	1.67534	−	0.211645i	1.67534	−	0.211645i
$753$		0			0
$754$		0			0
$755$		0			0
$756$	−0.331255	−	1.73650i	−0.331255	−	1.73650i
$757$		0			0		−0.248690	−	0.968583i	$-0.580000\pi$
$757$		0			0		0.248690	+	0.968583i	$0.420000\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	0.620759	−	1.31918i	0.620759	−	1.31918i	−0.309017	−	0.951057i	$-0.600000\pi$
$761$	0.620759	−	1.31918i	0.620759	−	1.31918i	0.929776	−	0.368125i	$-0.120000\pi$
$762$	0.217324	+	1.72030i	0.217324	+	1.72030i
$763$	−3.24541	+	0.409991i	−3.24541	+	0.409991i
$764$		0			0
$765$		0			0
$766$	1.15596	−	0.733597i	1.15596	−	0.733597i
$767$		0			0
$768$	−0.516273	+	0.939097i	−0.516273	+	0.939097i
$769$	−1.17325	−	1.61484i	−1.17325	−	1.61484i	−0.637424	−	0.770513i	$-0.720000\pi$
$769$	−1.17325	−	1.61484i	−1.17325	−	1.61484i	−0.535827	−	0.844328i	$-0.680000\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0		−0.904827	−	0.425779i	$-0.860000\pi$
$773$		0			0		0.904827	+	0.425779i	$0.140000\pi$
$774$	−0.295712	+	0.0186046i	−0.295712	+	0.0186046i
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	0.397753	−	0.218666i	0.397753	−	0.218666i
$784$	−2.00657	+	1.88429i	−2.00657	+	1.88429i
$785$		0			0
$786$		0			0
$787$	0.182728	+	0.171593i	0.182728	+	0.171593i	0.770513	−	0.637424i	$-0.220000\pi$
$787$	0.182728	+	0.171593i	0.182728	+	0.171593i	−0.587785	+	0.809017i	$0.700000\pi$
$788$		0			0
$789$	−0.837178	+	1.31918i	−0.837178	+	1.31918i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.125333	−	0.992115i	$-0.460000\pi$
$797$		0			0		−0.125333	+	0.992115i	$0.540000\pi$
$798$		0			0
$799$		0			0
$800$	0.684547	−	0.728969i	0.684547	−	0.728969i
$801$	0.134457	+	0.111233i	0.134457	+	0.111233i
$802$	0.587785	−	1.80902i	0.587785	−	1.80902i
$803$		0			0
$804$	−1.74630	−	0.960037i	−1.74630	−	0.960037i
$805$	−3.79820	−	0.238962i	−3.79820	−	0.238962i
$806$		0			0
$807$	−1.03255			−1.03255
$808$	0.998027	−	0.0627905i	0.998027	−	0.0627905i
$809$	1.93717			1.93717			0.968583	−	0.248690i	$-0.0800000\pi$
$809$	1.93717			1.93717			0.968583	+	0.248690i	$0.0800000\pi$
$810$	0.280126	−	1.09102i	0.280126	−	1.09102i
$811$		0			0		−0.998027	−	0.0627905i	$-0.980000\pi$
$811$		0			0		0.998027	+	0.0627905i	$0.0200000\pi$
$812$	−0.844328	−	0.464173i	−0.844328	−	0.464173i
$813$		0			0
$814$		0			0
$815$	1.43281	+	1.18532i	1.43281	+	1.18532i
$816$		0			0
$817$		0			0
$818$		−	0.374763i		−	0.374763i
$819$		0			0
$820$	−1.30113	−	0.825723i	−1.30113	−	0.825723i
$821$	0.238883	+	0.288760i	0.238883	+	0.288760i	0.876307	−	0.481754i	$-0.160000\pi$
$821$	0.238883	+	0.288760i	0.238883	+	0.288760i	−0.637424	+	0.770513i	$0.720000\pi$
$822$		0			0
$823$	0.368125	−	0.0702235i	0.368125	−	0.0702235i		−	1.00000i	$-0.5\pi$
$823$	0.368125	−	0.0702235i	0.368125	−	0.0702235i	0.368125	+	0.929776i	$0.380000\pi$
$824$	0.866986	+	1.36615i	0.866986	+	1.36615i
$825$		0			0
$826$		0			0
$827$	1.05267	−	1.65875i	1.05267	−	1.65875i	0.368125	−	0.929776i	$-0.380000\pi$
$827$	1.05267	−	1.65875i	1.05267	−	1.65875i	0.684547	−	0.728969i	$-0.260000\pi$
$828$	0.282462	+	0.0725240i	0.282462	+	0.0725240i
$829$	1.27760	+	1.19975i	1.27760	+	1.19975i	0.968583	+	0.248690i	$0.0800000\pi$
$829$	1.27760	+	1.19975i	1.27760	+	1.19975i	0.309017	+	0.951057i	$0.400000\pi$
$830$	−0.116762	−	0.0462295i	−0.116762	−	0.0462295i
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−0.368125	−	0.0702235i	−0.368125	−	0.0702235i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		0.637424	−	0.770513i	$-0.280000\pi$
$839$		0			0		−0.637424	+	0.770513i	$0.720000\pi$
$840$	−1.97437	+	0.641510i	−1.97437	+	0.641510i
$841$	−0.141026	+	0.739283i	−0.141026	+	0.739283i
$842$	−1.61484	+	0.101597i	−1.61484	+	0.101597i
$843$	0.363393	+	0.171000i	0.363393	+	0.171000i
$844$		0			0
$845$	−0.0627905	−	0.998027i	−0.0627905	−	0.998027i
$846$	−0.171593	−	0.182728i	−0.171593	−	0.182728i
$847$	1.13864	+	1.56720i	1.13864	+	1.56720i
$848$		0			0
$849$	−1.57062	−	0.510325i	−1.57062	−	0.510325i
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		0.992115	−	0.125333i	$-0.0400000\pi$
$853$		0			0		−0.992115	+	0.125333i	$0.960000\pi$
$854$	−0.0608596	−	0.481754i	−0.0608596	−	0.481754i
$855$		0			0
$856$	0.464173	+	0.844328i	0.464173	+	0.844328i
$857$		0			0		−0.187381	−	0.982287i	$-0.560000\pi$
$857$		0			0		0.187381	+	0.982287i	$0.440000\pi$
$858$		0			0
$859$		0			0		−0.248690	−	0.968583i	$-0.580000\pi$
$859$		0			0		0.248690	+	0.968583i	$0.420000\pi$
$860$	−0.374023	−	1.96070i	−0.374023	−	1.96070i
$861$	1.54119	+	2.80342i	1.54119	+	2.80342i
$862$		0			0
$863$	0.159781	+	1.26480i	0.159781	+	1.26480i	0.844328	+	0.535827i	$0.180000\pi$
$863$	0.159781	+	1.26480i	0.159781	+	1.26480i	−0.684547	+	0.728969i	$0.740000\pi$
$864$	−0.905380	+	0.114376i	−0.905380	+	0.114376i
$865$		0			0
$866$		0			0
$867$	−0.904827	+	0.574221i	−0.904827	+	0.574221i
$868$		0			0
$869$		0			0
$870$	−0.313301	−	0.431221i	−0.313301	−	0.431221i
$871$		0			0
$872$	0.106032	+	1.68532i	0.106032	+	1.68532i
$873$		0			0
$874$		0			0
$875$	1.93334	−	0.121636i	1.93334	−	0.121636i
$876$		0			0
$877$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$877$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−0.567290	−	1.43281i	−0.567290	−	1.43281i	−0.876307	−	0.481754i	$-0.840000\pi$
$881$	−0.567290	−	1.43281i	−0.567290	−	1.43281i	0.309017	−	0.951057i	$-0.400000\pi$
$882$	0.401364	+	0.0765643i	0.401364	+	0.0765643i
$883$	−1.15352	+	0.542804i	−1.15352	+	0.542804i	−0.904827	−	0.425779i	$-0.860000\pi$
$883$	−1.15352	+	0.542804i	−1.15352	+	0.542804i	−0.248690	+	0.968583i	$0.580000\pi$
$884$		0			0
$885$		0			0
$886$	0.574633	−	0.227513i	0.574633	−	0.227513i
$887$	0.462452	+	0.183098i	0.462452	+	0.183098i	0.587785	−	0.809017i	$-0.300000\pi$
$887$	0.462452	+	0.183098i	0.462452	+	0.183098i	−0.125333	+	0.992115i	$0.540000\pi$
$888$		0			0
$889$	3.03593	+	0.779494i	3.03593	+	0.779494i
$890$	−0.629902	+	0.992567i	−0.629902	+	0.992567i
$891$		0			0
$892$	−0.559214	−	1.72108i	−0.559214	−	1.72108i
$893$		0			0
$894$	0.775029	−	0.147845i	0.775029	−	0.147845i
$895$		0			0
$896$	1.23480	+	1.49261i	1.23480	+	1.49261i
$897$		0			0
$898$	−0.248690	+	1.96858i	−0.248690	+	1.96858i
$899$		0			0
$900$	−0.147271	−	0.0186046i	−0.147271	−	0.0186046i
$901$		0			0
$902$		0			0
$903$	−1.28049	+	3.94094i	−1.28049	+	3.94094i
$904$		0			0
$905$	0.110048	+	0.0604991i	0.110048	+	0.0604991i
$906$		0			0
$907$	−0.211774	+	0.824805i	−0.211774	+	0.824805i	0.770513	+	0.637424i	$0.220000\pi$
$907$	−0.211774	+	0.824805i	−0.211774	+	0.824805i	−0.982287	+	0.187381i	$0.940000\pi$
$908$	0.736249			0.736249
$909$	−0.0946201	−	0.114376i	−0.0946201	−	0.114376i
$910$		0			0
$911$		0			0		0.248690	−	0.968583i	$-0.420000\pi$
$911$		0			0		−0.248690	+	0.968583i	$0.580000\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	0.0830105	−	0.255480i	0.0830105	−	0.255480i
$916$	−1.46560	−	1.21245i	−1.46560	−	1.21245i
$917$		0			0
$918$		0			0
$919$		0			0			−	1.00000i	$-0.5\pi$
$919$		0			0				1.00000i	$0.5\pi$
$920$	−0.246226	+	1.94908i	−0.246226	+	1.94908i
$921$	−0.450043	−	0.285606i	−0.450043	−	0.285606i
$922$	0.614163	+	0.742395i	0.614163	+	0.742395i
$923$		0			0
$924$		0			0
$925$		0			0
$926$	0.190983	+	0.587785i	0.190983	+	0.587785i
$927$	0.0884174	−	0.223317i	0.0884174	−	0.223317i
$928$	−0.266509	+	0.419952i	−0.266509	+	0.419952i
$929$	−1.23480	−	0.317042i	−1.23480	−	0.317042i	−0.425779	−	0.904827i	$-0.640000\pi$
$929$	−1.23480	−	0.317042i	−1.23480	−	0.317042i	−0.809017	+	0.587785i	$0.800000\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$	−1.11716	+	0.614163i	−1.11716	+	0.614163i
$935$		0			0
$936$		0			0
$937$		0			0		−0.368125	−	0.929776i	$-0.620000\pi$
$937$		0			0		0.368125	+	0.929776i	$0.380000\pi$
$938$	−2.77559	+	2.29617i	−2.77559	+	2.29617i
$939$		0			0
$940$	1.07639	−	1.30113i	1.07639	−	1.30113i
$941$	0.700215	−	0.227513i	0.700215	−	0.227513i	0.0627905	−	0.998027i	$-0.480000\pi$
$941$	0.700215	−	0.227513i	0.700215	−	0.227513i	0.637424	+	0.770513i	$0.280000\pi$
$942$		0			0
$943$	3.02149	−	0.190096i	3.02149	−	0.190096i
$944$		0			0
$945$	−1.43019	−	1.03909i	−1.43019	−	1.03909i
$946$		0			0
$947$	−0.582932	−	0.620759i	−0.582932	−	0.620759i	0.368125	−	0.929776i	$-0.380000\pi$
$947$	−0.582932	−	0.620759i	−0.582932	−	0.620759i	−0.951057	+	0.309017i	$0.900000\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$953$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	0.266509	+	1.03799i	0.266509	+	1.03799i
$961$	−0.187381	−	0.982287i	−0.187381	−	0.982287i
$962$		0			0
$963$	0.0608968	−	0.129412i	0.0608968	−	0.129412i
$964$	0.0314168	+	0.248690i	0.0314168	+	0.248690i
$965$		0			0
$966$	2.39722	−	3.29950i	2.39722	−	3.29950i
$967$	0.582932	+	1.23879i	0.582932	+	1.23879i	0.951057	+	0.309017i	$0.100000\pi$
$967$	0.582932	+	1.23879i	0.582932	+	1.23879i	−0.368125	+	0.929776i	$0.620000\pi$
$968$	0.844328	−	0.535827i	0.844328	−	0.535827i
$969$		0			0
$970$		0			0
$971$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$971$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$972$	0.201628	+	0.214712i	0.201628	+	0.214712i
$973$		0			0
$974$	−1.03137	−	0.749337i	−1.03137	−	0.749337i
$975$		0			0
$976$	−0.250172	+	0.0157395i	−0.250172	+	0.0157395i
$977$		0			0		0.187381	−	0.982287i	$-0.440000\pi$
$977$		0			0		−0.187381	+	0.982287i	$0.560000\pi$
$978$	−1.89526	+	0.615808i	−1.89526	+	0.615808i
$979$		0			0
$980$	−0.172838	+	2.74718i	−0.172838	+	2.74718i
$981$	0.193142	−	0.159781i	0.193142	−	0.159781i
$982$		0			0
$983$	−1.25227	−	0.238883i	−1.25227	−	0.238883i	−0.481754	−	0.876307i	$-0.660000\pi$
$983$	−1.25227	−	0.238883i	−1.25227	−	0.238883i	−0.770513	+	0.637424i	$0.780000\pi$
$984$	1.49427	−	0.703152i	1.49427	−	0.703152i
$985$		0			0
$986$		0			0
$987$	−3.25943	+	1.29050i	−3.25943	+	1.29050i
$988$		0			0
$989$	2.85857	+	2.68438i	2.85857	+	2.68438i
$990$		0			0
$991$		0			0		0.535827	−	0.844328i	$-0.320000\pi$
$991$		0			0		−0.535827	+	0.844328i	$0.680000\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$	0.108877	−	0.0791038i	0.108877	−	0.0791038i
$997$		0			0		−0.637424	−	0.770513i	$-0.720000\pi$
$997$		0			0		0.637424	+	0.770513i	$0.280000\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2020.1.bt.c.1259.2	yes	40
4.3	odd	2	inner	2020.1.bt.c.1259.1	✓	40
5.4	even	2	inner	2020.1.bt.c.1259.1	✓	40
20.19	odd	2	CM	2020.1.bt.c.1259.2	yes	40
101.43	even	50	inner	2020.1.bt.c.1659.2	yes	40
404.43	odd	50	inner	2020.1.bt.c.1659.1	yes	40
505.144	even	50	inner	2020.1.bt.c.1659.1	yes	40
2020.1659	odd	50	inner	2020.1.bt.c.1659.2	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2020.1.bt.c.1259.1	✓	40	4.3	odd	2	inner
2020.1.bt.c.1259.1	✓	40	5.4	even	2	inner
2020.1.bt.c.1259.2	yes	40	1.1	even	1	trivial
2020.1.bt.c.1259.2	yes	40	20.19	odd	2	CM
2020.1.bt.c.1659.1	yes	40	404.43	odd	50	inner
2020.1.bt.c.1659.1	yes	40	505.144	even	50	inner
2020.1.bt.c.1659.2	yes	40	101.43	even	50	inner
2020.1.bt.c.1659.2	yes	40	2020.1659	odd	50	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.248690 - 0.968583i) q^{2} +(1.06954 + 0.0672897i) q^{3} +(-0.876307 - 0.481754i) q^{4} +(-0.968583 + 0.248690i) q^{5} +(0.331159 - 1.01920i) q^{6} +(-1.49261 - 1.23480i) q^{7} +(-0.684547 + 0.728969i) q^{8} +(0.147271 + 0.0186046i) q^{9} +O(q^{10})\)	\(q+(0.248690 - 0.968583i) q^{2} +(1.06954 + 0.0672897i) q^{3} +(-0.876307 - 0.481754i) q^{4} +(-0.968583 + 0.248690i) q^{5} +(0.331159 - 1.01920i) q^{6} +(-1.49261 - 1.23480i) q^{7} +(-0.684547 + 0.728969i) q^{8} +(0.147271 + 0.0186046i) q^{9} +1.00000i q^{10} +(-0.904827 - 0.574221i) q^{12} +(-1.56720 + 1.13864i) q^{14} +(-1.05267 + 0.200808i) q^{15} +(0.535827 + 0.844328i) q^{16} +(0.0546449 - 0.138017i) q^{18} +(0.968583 + 0.248690i) q^{20} +(-1.51332 - 1.42110i) q^{21} +(-1.82662 + 0.723208i) q^{23} +(-0.781202 + 0.733597i) q^{24} +(0.876307 - 0.481754i) q^{25} +(-0.896412 - 0.171000i) q^{27} +(0.713118 + 1.80113i) q^{28} +(-0.383238 + 0.317042i) q^{29} +(-0.0672897 + 1.06954i) q^{30} +(0.951057 - 0.309017i) q^{32} +(1.75280 + 0.824805i) q^{35} +(-0.120092 - 0.0872517i) q^{36} +(0.481754 - 0.876307i) q^{40} +(-1.46560 - 0.476203i) q^{41} +(-1.75280 + 1.11236i) q^{42} +(-0.849878 - 1.80608i) q^{43} +(-0.147271 + 0.0186046i) q^{45} +(0.246226 + 1.94908i) q^{46} +(0.718995 - 1.52794i) q^{47} +(0.516273 + 0.939097i) q^{48} +(0.515788 + 2.70386i) q^{49} +(-0.248690 - 0.968583i) q^{50} +(-0.388556 + 0.825723i) q^{54} +(1.92189 - 0.242791i) q^{56} +(0.211774 + 0.450043i) q^{58} +(1.01920 + 0.331159i) q^{60} +(-0.120759 + 0.219661i) q^{61} +(-0.196845 - 0.209619i) q^{63} +(-0.0627905 - 0.998027i) q^{64} +(1.85588 - 0.116762i) q^{67} +(-2.00230 + 0.650587i) q^{69} +(1.23480 - 1.49261i) q^{70} +(-0.114376 + 0.0946201i) q^{72} +(0.969661 - 0.456288i) q^{75} +(-0.728969 - 0.684547i) q^{80} +(-1.09102 - 0.280126i) q^{81} +(-0.825723 + 1.30113i) q^{82} +(-0.0462295 + 0.116762i) q^{83} +(0.641510 + 1.97437i) q^{84} +(-1.96070 + 0.374023i) q^{86} +(-0.431221 + 0.313301i) q^{87} +(0.992567 + 0.629902i) q^{89} +(-0.0186046 + 0.147271i) q^{90} +(1.94908 + 0.246226i) q^{92} +(-1.30113 - 1.07639i) q^{94} +(1.03799 - 0.266509i) q^{96} +(2.74718 + 0.172838i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 10 q^{9}+O(q^{10}) \) 40 * q + 10 * q^9	\( 40 q + 10 q^{9} - 40 q^{21} - 10 q^{29} + 10 q^{30} - 10 q^{36} - 10 q^{45} - 10 q^{46} + 10 q^{49} + 10 q^{54} + 10 q^{61} + 10 q^{70} - 10 q^{81} + 30 q^{84} + 10 q^{94} - 10 q^{96}+O(q^{100}) \) 40 * q + 10 * q^9 - 40 * q^21 - 10 * q^29 + 10 * q^30 - 10 * q^36 - 10 * q^45 - 10 * q^46 + 10 * q^49 + 10 * q^54 + 10 * q^61 + 10 * q^70 - 10 * q^81 + 30 * q^84 + 10 * q^94 - 10 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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