LMFDB - Embedded newform 2020.1.bu.a.1199.1

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			1199.1
Root			$-0.728969 - 0.684547i$ of defining polynomial
Character	$\chi$	$=$	2020.1199
Dual form			2020.1.bu.a.839.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.876307 + 0.481754i) q^{2} +(0.844844 + 0.106729i) q^{3} +(0.535827 + 0.844328i) q^{4} +(0.876307 - 0.481754i) q^{5} +(0.688925 + 0.500534i) q^{6} +(-0.328407 - 1.72157i) q^{7} +(0.0627905 + 0.998027i) q^{8} +(-0.266213 - 0.0683519i) q^{9} +O(q^{10})$	\(q+(0.876307 + 0.481754i) q^{2} +(0.844844 + 0.106729i) q^{3} +(0.535827 + 0.844328i) q^{4} +(0.876307 - 0.481754i) q^{5} +(0.688925 + 0.500534i) q^{6} +(-0.328407 - 1.72157i) q^{7} +(0.0627905 + 0.998027i) q^{8} +(-0.266213 - 0.0683519i) q^{9} +1.00000 q^{10} +(0.362576 + 0.770513i) q^{12} +(0.541587 - 1.66683i) q^{14} +(0.791759 - 0.313480i) q^{15} +(-0.425779 + 0.904827i) q^{16} +(-0.200356 - 0.188146i) q^{18} +(0.876307 + 0.481754i) q^{20} +(-0.0937119 - 1.48951i) q^{21} +(-1.35556 + 1.27295i) q^{23} +(-0.0534698 + 0.849878i) q^{24} +(0.535827 - 0.844328i) q^{25} +(-1.00937 - 0.399639i) q^{27} +(1.27760 - 1.19975i) q^{28} +(-0.328407 + 1.72157i) q^{29} +(0.844844 + 0.106729i) q^{30} +(-0.809017 + 0.587785i) q^{32} +(-1.11716 - 1.35041i) q^{35} +(-0.0849327 - 0.261396i) q^{36} +(0.535827 + 0.844328i) q^{40} +(0.303189 + 0.220280i) q^{41} +(0.635456 - 1.35041i) q^{42} +(1.26480 - 1.52888i) q^{43} +(-0.266213 + 0.0683519i) q^{45} +(-1.80113 + 0.462452i) q^{46} +(0.542804 + 0.656137i) q^{47} +(-0.456288 + 0.718995i) q^{48} +(-1.92617 + 0.762627i) q^{49} +(0.876307 - 0.481754i) q^{50} +(-0.691992 - 0.836475i) q^{54} +(1.69755 - 0.435857i) q^{56} +(-1.11716 + 1.35041i) q^{58} +(0.688925 + 0.500534i) q^{60} +(1.03799 + 1.63560i) q^{61} +(-0.0302463 + 0.480752i) q^{63} +(-0.992115 + 0.125333i) q^{64} +(-1.44644 + 0.182728i) q^{67} +(-1.28109 + 0.930769i) q^{69} +(-0.328407 - 1.72157i) q^{70} +(0.0515014 - 0.269980i) q^{72} +(0.542804 - 0.656137i) q^{75} +(0.0627905 + 0.998027i) q^{80} +(-0.569258 - 0.312952i) q^{81} +(0.159566 + 0.339095i) q^{82} +(-1.44644 - 1.35830i) q^{83} +(1.20742 - 0.877242i) q^{84} +(1.84489 - 0.730444i) q^{86} +(-0.461193 + 1.41941i) q^{87} +(-0.263146 - 0.559214i) q^{89} +(-0.266213 - 0.0683519i) q^{90} +(-1.80113 - 0.462452i) q^{92} +(0.159566 + 0.836475i) q^{94} +(-0.746226 + 0.410241i) q^{96} +(-2.05532 - 0.259647i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2020\mathbb{Z}\right)^\times$.

$n$	$1011$	$1617$	$1921$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{4}{25}\right)$

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 $

$2$	0.876307	+	0.481754i	0.876307	+	0.481754i
$2$	0.876307	+	0.481754i	0.876307	+	0.481754i
$3$	0.844844	+	0.106729i	0.844844	+	0.106729i	0.535827	−	0.844328i	$-0.320000\pi$
$3$	0.844844	+	0.106729i	0.844844	+	0.106729i	0.309017	+	0.951057i	$0.400000\pi$
$4$	0.535827	+	0.844328i	0.535827	+	0.844328i
$5$	0.876307	−	0.481754i	0.876307	−	0.481754i
$5$	0.876307	−	0.481754i	0.876307	−	0.481754i
$6$	0.688925	+	0.500534i	0.688925	+	0.500534i
$7$	−0.328407	−	1.72157i	−0.328407	−	1.72157i	−0.637424	−	0.770513i	$-0.720000\pi$
$7$	−0.328407	−	1.72157i	−0.328407	−	1.72157i	0.309017	−	0.951057i	$-0.400000\pi$
$8$	0.0627905	+	0.998027i	0.0627905	+	0.998027i
$9$	−0.266213	−	0.0683519i	−0.266213	−	0.0683519i
$10$	1.00000			1.00000
$11$		0			0		−0.968583	−	0.248690i	$-0.920000\pi$
$11$		0			0		0.968583	+	0.248690i	$0.0800000\pi$
$12$	0.362576	+	0.770513i	0.362576	+	0.770513i
$13$		0			0		0.187381	−	0.982287i	$-0.440000\pi$
$13$		0			0		−0.187381	+	0.982287i	$0.560000\pi$
$14$	0.541587	−	1.66683i	0.541587	−	1.66683i
$15$	0.791759	−	0.313480i	0.791759	−	0.313480i
$16$	−0.425779	+	0.904827i	−0.425779	+	0.904827i
$17$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$17$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$18$	−0.200356	−	0.188146i	−0.200356	−	0.188146i
$19$		0			0		−0.425779	−	0.904827i	$-0.640000\pi$
$19$		0			0		0.425779	+	0.904827i	$0.360000\pi$
$20$	0.876307	+	0.481754i	0.876307	+	0.481754i
$21$	−0.0937119	−	1.48951i	−0.0937119	−	1.48951i
$22$		0			0
$23$	−1.35556	+	1.27295i	−1.35556	+	1.27295i	−0.425779	+	0.904827i	$0.640000\pi$
$23$	−1.35556	+	1.27295i	−1.35556	+	1.27295i	−0.929776	+	0.368125i	$0.880000\pi$
$24$	−0.0534698	+	0.849878i	−0.0534698	+	0.849878i
$25$	0.535827	−	0.844328i	0.535827	−	0.844328i
$26$		0			0
$27$	−1.00937	−	0.399639i	−1.00937	−	0.399639i
$28$	1.27760	−	1.19975i	1.27760	−	1.19975i
$29$	−0.328407	+	1.72157i	−0.328407	+	1.72157i	0.309017	+	0.951057i	$0.400000\pi$
$29$	−0.328407	+	1.72157i	−0.328407	+	1.72157i	−0.637424	+	0.770513i	$0.720000\pi$
$30$	0.844844	+	0.106729i	0.844844	+	0.106729i
$31$		0			0		−0.187381	−	0.982287i	$-0.560000\pi$
$31$		0			0		0.187381	+	0.982287i	$0.440000\pi$
$32$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$33$		0			0
$34$		0			0
$35$	−1.11716	−	1.35041i	−1.11716	−	1.35041i
$36$	−0.0849327	−	0.261396i	−0.0849327	−	0.261396i
$37$		0			0		0.992115	−	0.125333i	$-0.0400000\pi$
$37$		0			0		−0.992115	+	0.125333i	$0.960000\pi$
$38$		0			0
$39$		0			0
$40$	0.535827	+	0.844328i	0.535827	+	0.844328i
$41$	0.303189	+	0.220280i	0.303189	+	0.220280i	0.728969	−	0.684547i	$-0.240000\pi$
$41$	0.303189	+	0.220280i	0.303189	+	0.220280i	−0.425779	+	0.904827i	$0.640000\pi$
$42$	0.635456	−	1.35041i	0.635456	−	1.35041i
$43$	1.26480	−	1.52888i	1.26480	−	1.52888i	0.535827	−	0.844328i	$-0.320000\pi$
$43$	1.26480	−	1.52888i	1.26480	−	1.52888i	0.728969	−	0.684547i	$-0.240000\pi$
$44$		0			0
$45$	−0.266213	+	0.0683519i	−0.266213	+	0.0683519i
$46$	−1.80113	+	0.462452i	−1.80113	+	0.462452i
$47$	0.542804	+	0.656137i	0.542804	+	0.656137i	0.968583	−	0.248690i	$-0.0800000\pi$
$47$	0.542804	+	0.656137i	0.542804	+	0.656137i	−0.425779	+	0.904827i	$0.640000\pi$
$48$	−0.456288	+	0.718995i	−0.456288	+	0.718995i
$49$	−1.92617	+	0.762627i	−1.92617	+	0.762627i
$50$	0.876307	−	0.481754i	0.876307	−	0.481754i
$51$		0			0
$52$		0			0
$53$		0			0		0.535827	−	0.844328i	$-0.320000\pi$
$53$		0			0		−0.535827	+	0.844328i	$0.680000\pi$
$54$	−0.691992	−	0.836475i	−0.691992	−	0.836475i
$55$		0			0
$56$	1.69755	−	0.435857i	1.69755	−	0.435857i
$57$		0			0
$58$	−1.11716	+	1.35041i	−1.11716	+	1.35041i
$59$		0			0		0.425779	−	0.904827i	$-0.360000\pi$
$59$		0			0		−0.425779	+	0.904827i	$0.640000\pi$
$60$	0.688925	+	0.500534i	0.688925	+	0.500534i
$61$	1.03799	+	1.63560i	1.03799	+	1.63560i	0.728969	+	0.684547i	$0.240000\pi$
$61$	1.03799	+	1.63560i	1.03799	+	1.63560i	0.309017	+	0.951057i	$0.400000\pi$
$62$		0			0
$63$	−0.0302463	+	0.480752i	−0.0302463	+	0.480752i
$64$	−0.992115	+	0.125333i	−0.992115	+	0.125333i
$65$		0			0
$66$		0			0
$67$	−1.44644	+	0.182728i	−1.44644	+	0.182728i	−0.809017	−	0.587785i	$-0.800000\pi$
$67$	−1.44644	+	0.182728i	−1.44644	+	0.182728i	−0.637424	+	0.770513i	$0.720000\pi$
$68$		0			0
$69$	−1.28109	+	0.930769i	−1.28109	+	0.930769i
$70$	−0.328407	−	1.72157i	−0.328407	−	1.72157i
$71$		0			0		−0.992115	−	0.125333i	$-0.960000\pi$
$71$		0			0		0.992115	+	0.125333i	$0.0400000\pi$
$72$	0.0515014	−	0.269980i	0.0515014	−	0.269980i
$73$		0			0		0.728969	−	0.684547i	$-0.240000\pi$
$73$		0			0		−0.728969	+	0.684547i	$0.760000\pi$
$74$		0			0
$75$	0.542804	−	0.656137i	0.542804	−	0.656137i
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		−0.728969	−	0.684547i	$-0.760000\pi$
$79$		0			0		0.728969	+	0.684547i	$0.240000\pi$
$80$	0.0627905	+	0.998027i	0.0627905	+	0.998027i
$81$	−0.569258	−	0.312952i	−0.569258	−	0.312952i
$82$	0.159566	+	0.339095i	0.159566	+	0.339095i
$83$	−1.44644	−	1.35830i	−1.44644	−	1.35830i	−0.809017	−	0.587785i	$-0.800000\pi$
$83$	−1.44644	−	1.35830i	−1.44644	−	1.35830i	−0.637424	−	0.770513i	$-0.720000\pi$
$84$	1.20742	−	0.877242i	1.20742	−	0.877242i
$85$		0			0
$86$	1.84489	−	0.730444i	1.84489	−	0.730444i
$87$	−0.461193	+	1.41941i	−0.461193	+	1.41941i
$88$		0			0
$89$	−0.263146	−	0.559214i	−0.263146	−	0.559214i	0.728969	−	0.684547i	$-0.240000\pi$
$89$	−0.263146	−	0.559214i	−0.263146	−	0.559214i	−0.992115	+	0.125333i	$0.960000\pi$
$90$	−0.266213	−	0.0683519i	−0.266213	−	0.0683519i
$91$		0			0
$92$	−1.80113	−	0.462452i	−1.80113	−	0.462452i
$93$		0			0
$94$	0.159566	+	0.836475i	0.159566	+	0.836475i
$95$		0			0
$96$	−0.746226	+	0.410241i	−0.746226	+	0.410241i
$97$		0			0		−0.535827	−	0.844328i	$-0.680000\pi$
$97$		0			0		0.535827	+	0.844328i	$0.320000\pi$
$98$	−2.05532	−	0.259647i	−2.05532	−	0.259647i
$99$		0			0
$100$	1.00000			1.00000
$101$	0.0627905	+	0.998027i	0.0627905	+	0.998027i
$101$	0.0627905	+	0.998027i	0.0627905	+	0.998027i
$102$		0			0
$103$	0.541587	+	0.297740i	0.541587	+	0.297740i	0.728969	−	0.684547i	$-0.240000\pi$
$103$	0.541587	+	0.297740i	0.541587	+	0.297740i	−0.187381	+	0.982287i	$0.560000\pi$
$104$		0			0
$105$	−0.799696	−	1.26012i	−0.799696	−	1.26012i
$106$		0			0
$107$	−0.866986	−	0.629902i	−0.866986	−	0.629902i	0.0627905	−	0.998027i	$-0.480000\pi$
$107$	−0.866986	−	0.629902i	−0.866986	−	0.629902i	−0.929776	+	0.368125i	$0.880000\pi$
$108$	−0.203423	−	1.06638i	−0.203423	−	1.06638i
$109$	−0.0534698	−	0.849878i	−0.0534698	−	0.849878i	−0.929776	−	0.368125i	$-0.880000\pi$
$109$	−0.0534698	−	0.849878i	−0.0534698	−	0.849878i	0.876307	−	0.481754i	$-0.160000\pi$
$110$		0			0
$111$		0			0
$112$	1.69755	+	0.435857i	1.69755	+	0.435857i
$113$		0			0		−0.425779	−	0.904827i	$-0.640000\pi$
$113$		0			0		0.425779	+	0.904827i	$0.360000\pi$
$114$		0			0
$115$	−0.574633	+	1.76854i	−0.574633	+	1.76854i
$116$	−1.62954	+	0.645180i	−1.62954	+	0.645180i
$117$		0			0
$118$		0			0
$119$		0			0
$120$	0.362576	+	0.770513i	0.362576	+	0.770513i
$121$	0.876307	+	0.481754i	0.876307	+	0.481754i
$122$	0.121636	+	1.93334i	0.121636	+	1.93334i
$123$	0.232637	+	0.218461i	0.232637	+	0.218461i
$124$		0			0
$125$	0.0627905	−	0.998027i	0.0627905	−	0.998027i
$126$	−0.258109	+	0.406715i	−0.258109	+	0.406715i
$127$	−0.393950	+	0.476203i	−0.393950	+	0.476203i	−0.929776	−	0.368125i	$-0.880000\pi$
$127$	−0.393950	+	0.476203i	−0.393950	+	0.476203i	0.535827	+	0.844328i	$0.320000\pi$
$128$	−0.929776	−	0.368125i	−0.929776	−	0.368125i
$129$	1.23173	−	1.15667i	1.23173	−	1.15667i
$130$		0			0
$131$		0			0		−0.992115	−	0.125333i	$-0.960000\pi$
$131$		0			0		0.992115	+	0.125333i	$0.0400000\pi$
$132$		0			0
$133$		0			0
$134$	−1.35556	−	0.536702i	−1.35556	−	0.536702i
$135$	−1.07705	+	0.136063i	−1.07705	+	0.136063i
$136$		0			0
$137$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$137$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$138$	−1.57103	+	0.198467i	−1.57103	+	0.198467i
$139$		0			0		0.0627905	−	0.998027i	$-0.480000\pi$
$139$		0			0		−0.0627905	+	0.998027i	$0.520000\pi$
$140$	0.541587	−	1.66683i	0.541587	−	1.66683i
$141$	0.388556	+	0.612266i	0.388556	+	0.612266i
$142$		0			0
$143$		0			0
$144$	0.175195	−	0.211774i	0.175195	−	0.211774i
$145$	0.541587	+	1.66683i	0.541587	+	1.66683i
$146$		0			0
$147$	−1.70871	+	0.438722i	−1.70871	+	0.438722i
$148$		0			0
$149$	0.781202	−	1.23098i	0.781202	−	1.23098i	−0.187381	−	0.982287i	$-0.560000\pi$
$149$	0.781202	−	1.23098i	0.781202	−	1.23098i	0.968583	−	0.248690i	$-0.0800000\pi$
$150$	0.791759	−	0.313480i	0.791759	−	0.313480i
$151$		0			0		0.876307	−	0.481754i	$-0.160000\pi$
$151$		0			0		−0.876307	+	0.481754i	$0.840000\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.968583	−	0.248690i	$-0.0800000\pi$
$157$		0			0		−0.968583	+	0.248690i	$0.920000\pi$
$158$		0			0
$159$		0			0
$160$	−0.425779	+	0.904827i	−0.425779	+	0.904827i
$161$	2.63665	+	1.91564i	2.63665	+	1.91564i
$162$	−0.348079	−	0.548484i	−0.348079	−	0.548484i
$163$	0.450527	−	1.38658i	0.450527	−	1.38658i	−0.425779	−	0.904827i	$-0.640000\pi$
$163$	0.450527	−	1.38658i	0.450527	−	1.38658i	0.876307	−	0.481754i	$-0.160000\pi$
$164$	−0.0235315	+	0.374023i	−0.0235315	+	0.374023i
$165$		0			0
$166$	−0.613161	−	1.88711i	−0.613161	−	1.88711i
$167$	1.18532	+	1.43281i	1.18532	+	1.43281i	0.876307	+	0.481754i	$0.160000\pi$
$167$	1.18532	+	1.43281i	1.18532	+	1.43281i	0.309017	+	0.951057i	$0.400000\pi$
$168$	1.48068	−	0.187054i	1.48068	−	0.187054i
$169$	−0.929776	−	0.368125i	−0.929776	−	0.368125i
$170$		0			0
$171$		0			0
$172$	1.96858	+	0.248690i	1.96858	+	0.248690i
$173$		0			0		0.187381	−	0.982287i	$-0.440000\pi$
$173$		0			0		−0.187381	+	0.982287i	$0.560000\pi$
$174$	−1.08795	+	1.02165i	−1.08795	+	1.02165i
$175$	−1.62954	−	0.645180i	−1.62954	−	0.645180i
$176$		0			0
$177$		0			0
$178$	0.0388067	−	0.616814i	0.0388067	−	0.616814i
$179$		0			0		0.728969	−	0.684547i	$-0.240000\pi$
$179$		0			0		−0.728969	+	0.684547i	$0.760000\pi$
$180$	−0.200356	−	0.188146i	−0.200356	−	0.188146i
$181$	−0.124591	−	1.98031i	−0.124591	−	1.98031i	−0.187381	−	0.982287i	$-0.560000\pi$
$181$	−0.124591	−	1.98031i	−0.124591	−	1.98031i	0.0627905	−	0.998027i	$-0.480000\pi$
$182$		0			0
$183$	0.702370	+	1.49261i	0.702370	+	1.49261i
$184$	−1.35556	−	1.27295i	−1.35556	−	1.27295i
$185$		0			0
$186$		0			0
$187$		0			0
$188$	−0.263146	+	0.809880i	−0.263146	+	0.809880i
$189$	−0.356521	+	1.86895i	−0.356521	+	1.86895i
$190$		0			0
$191$		0			0		−0.968583	−	0.248690i	$-0.920000\pi$
$191$		0			0		0.968583	+	0.248690i	$0.0800000\pi$
$192$	−0.851559			−0.851559
$193$		0			0		−0.968583	−	0.248690i	$-0.920000\pi$
$193$		0			0		0.968583	+	0.248690i	$0.0800000\pi$
$194$		0			0
$195$		0			0
$196$	−1.67600	−	1.21769i	−1.67600	−	1.21769i
$197$		0			0		0.876307	−	0.481754i	$-0.160000\pi$
$197$		0			0		−0.876307	+	0.481754i	$0.840000\pi$
$198$		0			0
$199$		0			0		−0.992115	−	0.125333i	$-0.960000\pi$
$199$		0			0		0.992115	+	0.125333i	$0.0400000\pi$
$200$	0.876307	+	0.481754i	0.876307	+	0.481754i
$201$	−1.24152			−1.24152
$202$	−0.425779	+	0.904827i	−0.425779	+	0.904827i
$203$	3.07165			3.07165
$204$		0			0
$205$	0.371808	+	0.0469702i	0.371808	+	0.0469702i
$206$	0.331159	+	0.521823i	0.331159	+	0.521823i
$207$	0.447875	−	0.246222i	0.447875	−	0.246222i
$208$		0			0
$209$		0			0
$210$	−0.0937119	−	1.48951i	−0.0937119	−	1.48951i
$211$		0			0		−0.968583	−	0.248690i	$-0.920000\pi$
$211$		0			0		0.968583	+	0.248690i	$0.0800000\pi$
$212$		0			0
$213$		0			0
$214$	−0.456288	−	0.969661i	−0.456288	−	0.969661i
$215$	0.371808	−	1.94908i	0.371808	−	1.94908i
$216$	0.335471	−	1.03247i	0.335471	−	1.03247i
$217$		0			0
$218$	0.362576	−	0.770513i	0.362576	−	0.770513i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−0.0800484	−	1.27233i	−0.0800484	−	1.27233i	−0.809017	−	0.587785i	$-0.800000\pi$
$223$	−0.0800484	−	1.27233i	−0.0800484	−	1.27233i	0.728969	−	0.684547i	$-0.240000\pi$
$224$	1.27760	+	1.19975i	1.27760	+	1.19975i
$225$	−0.200356	+	0.188146i	−0.200356	+	0.188146i
$226$		0			0
$227$	0.781202	−	1.23098i	0.781202	−	1.23098i	−0.187381	−	0.982287i	$-0.560000\pi$
$227$	0.781202	−	1.23098i	0.781202	−	1.23098i	0.968583	−	0.248690i	$-0.0800000\pi$
$228$		0			0
$229$	1.50441	+	0.595638i	1.50441	+	0.595638i	0.968583	−	0.248690i	$-0.0800000\pi$
$229$	1.50441	+	0.595638i	1.50441	+	0.595638i	0.535827	+	0.844328i	$0.320000\pi$
$230$	−1.35556	+	1.27295i	−1.35556	+	1.27295i
$231$		0			0
$232$	−1.73879	−	0.219661i	−1.73879	−	0.219661i
$233$		0			0		−0.187381	−	0.982287i	$-0.560000\pi$
$233$		0			0		0.187381	+	0.982287i	$0.440000\pi$
$234$		0			0
$235$	0.791759	+	0.313480i	0.791759	+	0.313480i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		0.992115	−	0.125333i	$-0.0400000\pi$
$239$		0			0		−0.992115	+	0.125333i	$0.960000\pi$
$240$	−0.0534698	+	0.849878i	−0.0534698	+	0.849878i
$241$	0.598617	−	1.84235i	0.598617	−	1.84235i	0.0627905	−	0.998027i	$-0.480000\pi$
$241$	0.598617	−	1.84235i	0.598617	−	1.84235i	0.535827	−	0.844328i	$-0.320000\pi$
$242$	0.535827	+	0.844328i	0.535827	+	0.844328i
$243$	0.430742	+	0.312952i	0.430742	+	0.312952i
$244$	−0.824805	+	1.75280i	−0.824805	+	1.75280i
$245$	−1.32052	+	1.59624i	−1.32052	+	1.59624i
$246$	0.0986173	+	0.303513i	0.0986173	+	0.303513i
$247$		0			0
$248$		0			0
$249$	−1.07705	−	1.30193i	−1.07705	−	1.30193i
$250$	0.535827	−	0.844328i	0.535827	−	0.844328i
$251$		0			0		0.929776	−	0.368125i	$-0.120000\pi$
$251$		0			0		−0.929776	+	0.368125i	$0.880000\pi$
$252$	−0.422119	+	0.232062i	−0.422119	+	0.232062i
$253$		0			0
$254$	−0.574633	+	0.227513i	−0.574633	+	0.227513i
$255$		0			0
$256$	−0.637424	−	0.770513i	−0.637424	−	0.770513i
$257$		0			0		0.968583	−	0.248690i	$-0.0800000\pi$
$257$		0			0		−0.968583	+	0.248690i	$0.920000\pi$
$258$	1.63660	−	0.420208i	1.63660	−	0.420208i
$259$		0			0
$260$		0			0
$261$	0.205099	−	0.435857i	0.205099	−	0.435857i
$262$		0			0
$263$	0.0672897	+	0.106032i	0.0672897	+	0.106032i	0.876307	−	0.481754i	$-0.160000\pi$
$263$	0.0672897	+	0.106032i	0.0672897	+	0.106032i	−0.809017	+	0.587785i	$0.800000\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−0.162633	−	0.500534i	−0.162633	−	0.500534i
$268$	−0.929324	−	1.12336i	−0.929324	−	1.12336i
$269$	−1.06320	+	0.134314i	−1.06320	+	0.134314i	−0.637424	−	0.770513i	$-0.720000\pi$
$269$	−1.06320	+	0.134314i	−1.06320	+	0.134314i	−0.425779	+	0.904827i	$0.640000\pi$
$270$	−1.00937	−	0.399639i	−1.00937	−	0.399639i
$271$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$271$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$	−1.47232	−	0.582932i	−1.47232	−	0.582932i
$277$		0			0		0.637424	−	0.770513i	$-0.280000\pi$
$277$		0			0		−0.637424	+	0.770513i	$0.720000\pi$
$278$		0			0
$279$		0			0
$280$	1.27760	−	1.19975i	1.27760	−	1.19975i
$281$	−1.35556	−	1.27295i	−1.35556	−	1.27295i	−0.929776	−	0.368125i	$-0.880000\pi$
$281$	−1.35556	−	1.27295i	−1.35556	−	1.27295i	−0.425779	−	0.904827i	$-0.640000\pi$
$282$	0.0455327	+	0.723721i	0.0455327	+	0.723721i
$283$	−0.328407	−	0.180543i	−0.328407	−	0.180543i	0.309017	−	0.951057i	$-0.400000\pi$
$283$	−0.328407	−	0.180543i	−0.328407	−	0.180543i	−0.637424	+	0.770513i	$0.720000\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	0.279658	−	0.594303i	0.279658	−	0.594303i
$288$	0.255547	−	0.101178i	0.255547	−	0.101178i
$289$	0.309017	−	0.951057i	0.309017	−	0.951057i
$290$	−0.328407	+	1.72157i	−0.328407	+	1.72157i
$291$		0			0
$292$		0			0
$293$		0			0		1.00000			$0$
$293$		0			0		−1.00000			$\pi$
$294$	−1.70871	−	0.438722i	−1.70871	−	0.438722i
$295$		0			0
$296$		0			0
$297$		0			0
$298$	1.27760	−	0.702367i	1.27760	−	0.702367i
$299$		0			0
$300$	0.844844	+	0.106729i	0.844844	+	0.106729i
$301$	−3.04743	−	1.67534i	−3.04743	−	1.67534i
$302$		0			0
$303$	−0.0534698	+	0.849878i	−0.0534698	+	0.849878i
$304$		0			0
$305$	1.69755	+	0.933237i	1.69755	+	0.933237i
$306$		0			0
$307$	0.939097	+	1.47978i	0.939097	+	1.47978i	0.876307	+	0.481754i	$0.160000\pi$
$307$	0.939097	+	1.47978i	0.939097	+	1.47978i	0.0627905	+	0.998027i	$0.480000\pi$
$308$		0			0
$309$	0.425779	+	0.309347i	0.425779	+	0.309347i
$310$		0			0
$311$		0			0		−0.0627905	−	0.998027i	$-0.520000\pi$
$311$		0			0		0.0627905	+	0.998027i	$0.480000\pi$
$312$		0			0
$313$		0			0		1.00000			$0$
$313$		0			0		−1.00000			$\pi$
$314$		0			0
$315$	0.205099	+	0.435857i	0.205099	+	0.435857i
$316$		0			0
$317$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$317$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$318$		0			0
$319$		0			0
$320$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$321$	−0.665239	−	0.624701i	−0.665239	−	0.624701i
$322$	1.38765	+	2.94890i	1.38765	+	2.94890i
$323$		0			0
$324$	−0.0407894	−	0.648329i	−0.0407894	−	0.648329i
$325$		0			0
$326$	1.06279	−	0.998027i	1.06279	−	0.998027i
$327$	0.0455327	−	0.723721i	0.0455327	−	0.723721i
$328$	−0.200808	+	0.316423i	−0.200808	+	0.316423i
$329$	0.951325	−	1.14995i	0.951325	−	1.14995i
$330$		0			0
$331$		0			0		0.728969	−	0.684547i	$-0.240000\pi$
$331$		0			0		−0.728969	+	0.684547i	$0.760000\pi$
$332$	0.371808	−	1.94908i	0.371808	−	1.94908i
$333$		0			0
$334$	0.348445	+	1.82662i	0.348445	+	1.82662i
$335$	−1.17950	+	0.856954i	−1.17950	+	0.856954i
$336$	1.38765	+	0.549409i	1.38765	+	0.549409i
$337$		0			0		0.992115	−	0.125333i	$-0.0400000\pi$
$337$		0			0		−0.992115	+	0.125333i	$0.960000\pi$
$338$	−0.637424	−	0.770513i	−0.637424	−	0.770513i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	1.00639	+	1.58581i	1.00639	+	1.58581i
$344$	1.60528	+	1.16630i	1.60528	+	1.16630i
$345$	−0.674229	+	1.43281i	−0.674229	+	1.43281i
$346$		0			0
$347$	0.331159	+	1.01920i	0.331159	+	1.01920i	0.968583	+	0.248690i	$0.0800000\pi$
$347$	0.331159	+	1.01920i	0.331159	+	1.01920i	−0.637424	+	0.770513i	$0.720000\pi$
$348$	−1.44556	+	0.371158i	−1.44556	+	0.371158i
$349$	−1.23480	+	0.317042i	−1.23480	+	0.317042i	−0.809017	−	0.587785i	$-0.800000\pi$
$349$	−1.23480	+	0.317042i	−1.23480	+	0.317042i	−0.425779	+	0.904827i	$0.640000\pi$
$350$	−1.11716	−	1.35041i	−1.11716	−	1.35041i
$351$		0			0
$352$		0			0
$353$		0			0		0.876307	−	0.481754i	$-0.160000\pi$
$353$		0			0		−0.876307	+	0.481754i	$0.840000\pi$
$354$		0			0
$355$		0			0
$356$	0.331159	−	0.521823i	0.331159	−	0.521823i
$357$		0			0
$358$		0			0
$359$		0			0		0.968583	−	0.248690i	$-0.0800000\pi$
$359$		0			0		−0.968583	+	0.248690i	$0.920000\pi$
$360$	−0.0849327	−	0.261396i	−0.0849327	−	0.261396i
$361$	−0.637424	+	0.770513i	−0.637424	+	0.770513i
$362$	0.844844	−	1.79538i	0.844844	−	1.79538i
$363$	0.688925	+	0.500534i	0.688925	+	0.500534i
$364$		0			0
$365$		0			0
$366$	−0.103580	+	1.64636i	−0.103580	+	1.64636i
$367$	−0.613161	+	0.0774602i	−0.613161	+	0.0774602i	−0.425779	−	0.904827i	$-0.640000\pi$
$367$	−0.613161	+	0.0774602i	−0.613161	+	0.0774602i	−0.187381	+	0.982287i	$0.560000\pi$
$368$	−0.574633	−	1.76854i	−0.574633	−	1.76854i
$369$	−0.0656564	−	0.0793650i	−0.0656564	−	0.0793650i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.187381	−	0.982287i	$-0.560000\pi$
$373$		0			0		0.187381	+	0.982287i	$0.440000\pi$
$374$		0			0
$375$	0.159566	−	0.836475i	0.159566	−	0.836475i
$376$	−0.620759	+	0.582932i	−0.620759	+	0.582932i
$377$		0			0
$378$	−1.21280	+	1.46602i	−1.21280	+	1.46602i
$379$		0			0		0.535827	−	0.844328i	$-0.320000\pi$
$379$		0			0		−0.535827	+	0.844328i	$0.680000\pi$
$380$		0			0
$381$	−0.383650	+	0.360272i	−0.383650	+	0.360272i
$382$		0			0
$383$	0.00788530	+	0.125333i	0.00788530	+	0.125333i	1.00000			$0$
$383$	0.00788530	+	0.125333i	0.00788530	+	0.125333i	−0.992115	+	0.125333i	$0.960000\pi$
$384$	−0.746226	−	0.410241i	−0.746226	−	0.410241i
$385$		0			0
$386$		0			0
$387$	−0.441207	+	0.320555i	−0.441207	+	0.320555i
$388$		0			0
$389$	−1.85955	+	0.736249i	−1.85955	+	0.736249i	−0.929776	+	0.368125i	$0.880000\pi$
$389$	−1.85955	+	0.736249i	−1.85955	+	0.736249i	−0.929776	+	0.368125i	$0.880000\pi$
$390$		0			0
$391$		0			0
$392$	−0.882067	−	1.87449i	−0.882067	−	1.87449i
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$		0			0		−0.187381	−	0.982287i	$-0.560000\pi$
$397$		0			0		0.187381	+	0.982287i	$0.440000\pi$
$398$		0			0
$399$		0			0
$400$	0.535827	+	0.844328i	0.535827	+	0.844328i
$401$	1.60528	+	0.202793i	1.60528	+	0.202793i	0.876307	−	0.481754i	$-0.160000\pi$
$401$	1.60528	+	0.202793i	1.60528	+	0.202793i	0.728969	+	0.684547i	$0.240000\pi$
$402$	−1.08795	−	0.598106i	−1.08795	−	0.598106i
$403$		0			0
$404$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$405$	−0.649611			−0.649611
$406$	2.69171	+	1.47978i	2.69171	+	1.47978i
$407$		0			0
$408$		0			0
$409$	−1.62954	+	0.895846i	−1.62954	+	0.895846i	−0.637424	+	0.770513i	$0.720000\pi$
$409$	−1.62954	+	0.895846i	−1.62954	+	0.895846i	−0.992115	+	0.125333i	$0.960000\pi$
$410$	0.303189	+	0.220280i	0.303189	+	0.220280i
$411$		0			0
$412$	0.0388067	+	0.616814i	0.0388067	+	0.616814i
$413$		0			0
$414$	0.511094			0.511094
$415$	−1.92189	−	0.493458i	−1.92189	−	0.493458i
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		0.929776	−	0.368125i	$-0.120000\pi$
$419$		0			0		−0.929776	+	0.368125i	$0.880000\pi$
$420$	0.635456	−	1.35041i	0.635456	−	1.35041i
$421$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	−0.809017	−	0.587785i	$-0.800000\pi$
$421$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	0.309017	+	0.951057i	$0.400000\pi$
$422$		0			0
$423$	−0.0996533	−	0.211774i	−0.0996533	−	0.211774i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	2.47492	−	2.32411i	2.47492	−	2.32411i
$428$	0.0672897	−	1.06954i	0.0672897	−	1.06954i
$429$		0			0
$430$	1.26480	−	1.52888i	1.26480	−	1.52888i
$431$		0			0		−0.929776	−	0.368125i	$-0.880000\pi$
$431$		0			0		0.929776	+	0.368125i	$0.120000\pi$
$432$	0.791374	−	0.743150i	0.791374	−	0.743150i
$433$		0			0		0.187381	−	0.982287i	$-0.440000\pi$
$433$		0			0		−0.187381	+	0.982287i	$0.560000\pi$
$434$		0			0
$435$	0.279658	+	1.46602i	0.279658	+	1.46602i
$436$	0.688925	−	0.500534i	0.688925	−	0.500534i
$437$		0			0
$438$		0			0
$439$		0			0		−0.637424	−	0.770513i	$-0.720000\pi$
$439$		0			0		0.637424	+	0.770513i	$0.280000\pi$
$440$		0			0
$441$	0.564900	−	0.0713635i	0.564900	−	0.0713635i
$442$		0			0
$443$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	0.309017	+	0.951057i	$0.400000\pi$
$443$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	−0.809017	+	0.587785i	$0.800000\pi$
$444$		0			0
$445$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$446$	0.542804	−	1.15352i	0.542804	−	1.15352i
$447$	0.791374	−	0.956607i	0.791374	−	0.956607i
$448$	0.541587	+	1.66683i	0.541587	+	1.66683i
$449$	1.87631	−	0.481754i	1.87631	−	0.481754i	0.876307	−	0.481754i	$-0.160000\pi$
$449$	1.87631	−	0.481754i	1.87631	−	0.481754i	1.00000			$0$
$450$	−0.266213	+	0.0683519i	−0.266213	+	0.0683519i
$451$		0			0
$452$		0			0
$453$		0			0
$454$	1.27760	−	0.702367i	1.27760	−	0.702367i
$455$		0			0
$456$		0			0
$457$		0			0		0.535827	−	0.844328i	$-0.320000\pi$
$457$		0			0		−0.535827	+	0.844328i	$0.680000\pi$
$458$	1.03137	+	1.24672i	1.03137	+	1.24672i
$459$		0			0
$460$	−1.80113	+	0.462452i	−1.80113	+	0.462452i
$461$	0.331159	+	1.01920i	0.331159	+	1.01920i	0.968583	+	0.248690i	$0.0800000\pi$
$461$	0.331159	+	1.01920i	0.331159	+	1.01920i	−0.637424	+	0.770513i	$0.720000\pi$
$462$		0			0
$463$	0.688925	−	1.46404i	0.688925	−	1.46404i	−0.187381	−	0.982287i	$-0.560000\pi$
$463$	0.688925	−	1.46404i	0.688925	−	1.46404i	0.876307	−	0.481754i	$-0.160000\pi$
$464$	−1.41789	−	1.03016i	−1.41789	−	1.03016i
$465$		0			0
$466$		0			0
$467$	−0.0235315	+	0.374023i	−0.0235315	+	0.374023i	0.968583	+	0.248690i	$0.0800000\pi$
$467$	−0.0235315	+	0.374023i	−0.0235315	+	0.374023i	−0.992115	+	0.125333i	$0.960000\pi$
$468$		0			0
$469$	0.789600	+	2.43014i	0.789600	+	2.43014i
$470$	0.542804	+	0.656137i	0.542804	+	0.656137i
$471$		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		0.637424	−	0.770513i	$-0.280000\pi$
$479$		0			0		−0.637424	+	0.770513i	$0.720000\pi$
$480$	−0.456288	+	0.718995i	−0.456288	+	0.718995i
$481$		0			0
$482$	1.41213	−	1.32608i	1.41213	−	1.32608i
$483$	2.02310	+	1.89982i	2.02310	+	1.89982i
$484$	0.0627905	+	0.998027i	0.0627905	+	0.998027i
$485$		0			0
$486$	0.226696	+	0.481754i	0.226696	+	0.481754i
$487$	−0.273190	−	0.256543i	−0.273190	−	0.256543i	0.535827	−	0.844328i	$-0.320000\pi$
$487$	−0.273190	−	0.256543i	−0.273190	−	0.256543i	−0.809017	+	0.587785i	$0.800000\pi$
$488$	−1.56720	+	1.13864i	−1.56720	+	1.13864i
$489$	0.528613	−	1.12336i	0.528613	−	1.12336i
$490$	−1.92617	+	0.762627i	−1.92617	+	0.762627i
$491$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$491$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$492$	−0.0597994	+	0.313480i	−0.0597994	+	0.313480i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−0.316616	−	1.65976i	−0.316616	−	1.65976i
$499$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$499$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$500$	0.876307	−	0.481754i	0.876307	−	0.481754i
$501$	0.848492	+	1.33701i	0.848492	+	1.33701i
$502$		0			0
$503$	1.69755	+	0.933237i	1.69755	+	0.933237i	0.968583	+	0.248690i	$0.0800000\pi$
$503$	1.69755	+	0.933237i	1.69755	+	0.933237i	0.728969	+	0.684547i	$0.240000\pi$
$504$	−0.481702			−0.481702
$505$	0.535827	+	0.844328i	0.535827	+	0.844328i
$506$		0			0
$507$	−0.746226	−	0.410241i	−0.746226	−	0.410241i
$508$	−0.613161	−	0.0774602i	−0.613161	−	0.0774602i
$509$	−1.06320	−	1.67534i	−1.06320	−	1.67534i	−0.637424	−	0.770513i	$-0.720000\pi$
$509$	−1.06320	−	1.67534i	−1.06320	−	1.67534i	−0.425779	−	0.904827i	$-0.640000\pi$
$510$		0			0
$511$		0			0
$512$	−0.187381	−	0.982287i	−0.187381	−	0.982287i
$513$		0			0
$514$		0			0
$515$	0.618034			0.618034
$516$	1.63660	+	0.420208i	1.63660	+	0.420208i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	0.159566	−	0.339095i	0.159566	−	0.339095i	−0.809017	−	0.587785i	$-0.800000\pi$
$521$	0.159566	−	0.339095i	0.159566	−	0.339095i	0.968583	+	0.248690i	$0.0800000\pi$
$522$	0.389705	−	0.283137i	0.389705	−	0.283137i
$523$	1.41213	+	1.32608i	1.41213	+	1.32608i	0.876307	+	0.481754i	$0.160000\pi$
$523$	1.41213	+	1.32608i	1.41213	+	1.32608i	0.535827	+	0.844328i	$0.320000\pi$
$524$		0			0
$525$	−1.30785	−	0.718995i	−1.30785	−	0.718995i
$526$	0.00788530	+	0.125333i	0.00788530	+	0.125333i
$527$		0			0
$528$		0			0
$529$	0.154335	−	2.45309i	0.154335	−	2.45309i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$	0.0986173	−	0.516970i	0.0986173	−	0.516970i
$535$	−1.06320	−	0.134314i	−1.06320	−	0.134314i
$536$	−0.273190	−	1.43211i	−0.273190	−	1.43211i
$537$		0			0
$538$	−0.996398	−	0.394502i	−0.996398	−	0.394502i
$539$		0			0
$540$	−0.691992	−	0.836475i	−0.691992	−	0.836475i
$541$	−0.115808	−	0.356420i	−0.115808	−	0.356420i	0.876307	−	0.481754i	$-0.160000\pi$
$541$	−0.115808	−	0.356420i	−0.115808	−	0.356420i	−0.992115	+	0.125333i	$0.960000\pi$
$542$		0			0
$543$	0.106096	−	1.68635i	0.106096	−	1.68635i
$544$		0			0
$545$	−0.456288	−	0.718995i	−0.456288	−	0.718995i
$546$		0			0
$547$	−0.456288	+	0.969661i	−0.456288	+	0.969661i	0.535827	+	0.844328i	$0.320000\pi$
$547$	−0.456288	+	0.969661i	−0.456288	+	0.969661i	−0.992115	+	0.125333i	$0.960000\pi$
$548$		0			0
$549$	−0.164529	−	0.506367i	−0.164529	−	0.506367i
$550$		0			0
$551$		0			0
$552$	−1.00937	−	1.22012i	−1.00937	−	1.22012i
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$		0			0		0.929776	−	0.368125i	$-0.120000\pi$
$557$		0			0		−0.929776	+	0.368125i	$0.880000\pi$
$558$		0			0
$559$		0			0
$560$	1.69755	−	0.435857i	1.69755	−	0.435857i
$561$		0			0
$562$	−0.574633	−	1.76854i	−0.574633	−	1.76854i
$563$	−0.393950	+	0.476203i	−0.393950	+	0.476203i	−0.929776	−	0.368125i	$-0.880000\pi$
$563$	−0.393950	+	0.476203i	−0.393950	+	0.476203i	0.535827	+	0.844328i	$0.320000\pi$
$564$	−0.308755	+	0.656137i	−0.308755	+	0.656137i
$565$		0			0
$566$	−0.200808	−	0.316423i	−0.200808	−	0.316423i
$567$	−0.351821	+	1.08279i	−0.351821	+	1.08279i
$568$		0			0
$569$	1.96858	−	0.248690i	1.96858	−	0.248690i	0.968583	−	0.248690i	$-0.0800000\pi$
$569$	1.96858	−	0.248690i	1.96858	−	0.248690i	1.00000			$0$
$570$		0			0
$571$		0			0		−0.637424	−	0.770513i	$-0.720000\pi$
$571$		0			0		0.637424	+	0.770513i	$0.280000\pi$
$572$		0			0
$573$		0			0
$574$	0.531374	−	0.386066i	0.531374	−	0.386066i
$575$	0.348445	+	1.82662i	0.348445	+	1.82662i
$576$	0.272681	+	0.0344476i	0.272681	+	0.0344476i
$577$		0			0		0.187381	−	0.982287i	$-0.440000\pi$
$577$		0			0		−0.187381	+	0.982287i	$0.560000\pi$
$578$	0.728969	−	0.684547i	0.728969	−	0.684547i
$579$		0			0
$580$	−1.11716	+	1.35041i	−1.11716	+	1.35041i
$581$	−1.86338	+	2.93622i	−1.86338	+	2.93622i
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−0.0534698	−	0.113629i	−0.0534698	−	0.113629i	0.876307	−	0.481754i	$-0.160000\pi$
$587$	−0.0534698	−	0.113629i	−0.0534698	−	0.113629i	−0.929776	+	0.368125i	$0.880000\pi$
$588$	−1.28600	−	1.20763i	−1.28600	−	1.20763i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$		0			0		0.187381	−	0.982287i	$-0.440000\pi$
$593$		0			0		−0.187381	+	0.982287i	$0.560000\pi$
$594$		0			0
$595$		0			0
$596$	1.45794			1.45794
$597$		0			0
$598$		0			0
$599$		0			0		−0.187381	−	0.982287i	$-0.560000\pi$
$599$		0			0		0.187381	+	0.982287i	$0.440000\pi$
$600$	0.688925	+	0.500534i	0.688925	+	0.500534i
$601$	−1.41789	+	0.779494i	−1.41789	+	0.779494i	−0.992115	−	0.125333i	$-0.960000\pi$
$601$	−1.41789	+	0.779494i	−1.41789	+	0.779494i	−0.425779	+	0.904827i	$0.640000\pi$
$602$	−1.86338	−	2.93622i	−1.86338	−	2.93622i
$603$	0.397551	+	0.0502224i	0.397551	+	0.0502224i
$604$		0			0
$605$	1.00000			1.00000
$606$	−0.456288	+	0.718995i	−0.456288	+	0.718995i
$607$	0.125581			0.125581			0.0627905	−	0.998027i	$-0.480000\pi$
$607$	0.125581			0.125581			0.0627905	+	0.998027i	$0.480000\pi$
$608$		0			0
$609$	2.59507	+	0.327833i	2.59507	+	0.327833i
$610$	1.03799	+	1.63560i	1.03799	+	1.63560i
$611$		0			0
$612$		0			0
$613$		0			0		−0.187381	−	0.982287i	$-0.560000\pi$
$613$		0			0		0.187381	+	0.982287i	$0.440000\pi$
$614$	0.110048	+	1.74915i	0.110048	+	1.74915i
$615$	0.309106	+	0.0793650i	0.309106	+	0.0793650i
$616$		0			0
$617$		0			0		−0.968583	−	0.248690i	$-0.920000\pi$
$617$		0			0		0.968583	+	0.248690i	$0.0800000\pi$
$618$	0.224084	+	0.476203i	0.224084	+	0.476203i
$619$		0			0		0.187381	−	0.982287i	$-0.440000\pi$
$619$		0			0		−0.187381	+	0.982287i	$0.560000\pi$
$620$		0			0
$621$	1.87698	−	0.743150i	1.87698	−	0.743150i
$622$		0			0
$623$	−0.876307	+	0.636674i	−0.876307	+	0.636674i
$624$		0			0
$625$	−0.425779	−	0.904827i	−0.425779	−	0.904827i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$	−0.0302463	+	0.480752i	−0.0302463	+	0.480752i
$631$		0			0		0.535827	−	0.844328i	$-0.320000\pi$
$631$		0			0		−0.535827	+	0.844328i	$0.680000\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−0.115808	+	0.607087i	−0.115808	+	0.607087i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$	−0.992115	+	0.125333i	−0.992115	+	0.125333i
$641$	−0.393950	−	0.476203i	−0.393950	−	0.476203i	0.535827	−	0.844328i	$-0.320000\pi$
$641$	−0.393950	−	0.476203i	−0.393950	−	0.476203i	−0.929776	+	0.368125i	$0.880000\pi$
$642$	−0.282001	−	0.867911i	−0.282001	−	0.867911i
$643$	−1.98423	+	0.250666i	−1.98423	+	0.250666i	−0.992115	+	0.125333i	$0.960000\pi$
$643$	−1.98423	+	0.250666i	−1.98423	+	0.250666i	−0.992115	+	0.125333i	$0.960000\pi$
$644$	−0.204639	+	3.25265i	−0.204639	+	3.25265i
$645$	0.522142	−	1.60699i	0.522142	−	1.60699i
$646$		0			0
$647$	1.03137	+	0.749337i	1.03137	+	0.749337i	0.968583	−	0.248690i	$-0.0800000\pi$
$647$	1.03137	+	0.749337i	1.03137	+	0.749337i	0.0627905	+	0.998027i	$0.480000\pi$
$648$	0.276591	−	0.587785i	0.276591	−	0.587785i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	1.41213	−	0.362574i	1.41213	−	0.362574i
$653$		0			0		−0.637424	−	0.770513i	$-0.720000\pi$
$653$		0			0		0.637424	+	0.770513i	$0.280000\pi$
$654$	0.388556	−	0.612266i	0.388556	−	0.612266i
$655$		0			0
$656$	−0.328407	+	0.180543i	−0.328407	+	0.180543i
$657$		0			0
$658$	1.38765	−	0.549409i	1.38765	−	0.549409i
$659$		0			0		0.535827	−	0.844328i	$-0.320000\pi$
$659$		0			0		−0.535827	+	0.844328i	$0.680000\pi$
$660$		0			0
$661$	0.121636	−	0.0312307i	0.121636	−	0.0312307i	−0.187381	−	0.982287i	$-0.560000\pi$
$661$	0.121636	−	0.0312307i	0.121636	−	0.0312307i	0.309017	+	0.951057i	$0.400000\pi$
$662$		0			0
$663$		0			0
$664$	1.26480	−	1.52888i	1.26480	−	1.52888i
$665$		0			0
$666$		0			0
$667$	−1.74630	−	2.75173i	−1.74630	−	2.75173i
$668$	−0.574633	+	1.76854i	−0.574633	+	1.76854i
$669$	0.0681659	−	1.08347i	0.0681659	−	1.08347i
$670$	−1.44644	+	0.182728i	−1.44644	+	0.182728i
$671$		0			0
$672$	0.951325	+	1.14995i	0.951325	+	1.14995i
$673$		0			0		0.992115	−	0.125333i	$-0.0400000\pi$
$673$		0			0		−0.992115	+	0.125333i	$0.960000\pi$
$674$		0			0
$675$	−0.878275	+	0.638104i	−0.878275	+	0.638104i
$676$	−0.187381	−	0.982287i	−0.187381	−	0.982287i
$677$		0			0		−0.992115	−	0.125333i	$-0.960000\pi$
$677$		0			0		0.992115	+	0.125333i	$0.0400000\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	0.791374	−	0.956607i	0.791374	−	0.956607i
$682$		0			0
$683$	−0.0800484	+	1.27233i	−0.0800484	+	1.27233i	0.728969	+	0.684547i	$0.240000\pi$
$683$	−0.0800484	+	1.27233i	−0.0800484	+	1.27233i	−0.809017	+	0.587785i	$0.800000\pi$
$684$		0			0
$685$		0			0
$686$	0.117933	+	1.87449i	0.117933	+	1.87449i
$687$	1.20742	+	0.663785i	1.20742	+	0.663785i
$688$	0.844844	+	1.79538i	0.844844	+	1.79538i
$689$		0			0
$690$	−1.28109	+	0.930769i	−1.28109	+	0.930769i
$691$		0			0		0.425779	−	0.904827i	$-0.360000\pi$
$691$		0			0		−0.425779	+	0.904827i	$0.640000\pi$
$692$		0			0
$693$		0			0
$694$	−0.200808	+	1.05267i	−0.200808	+	1.05267i
$695$		0			0
$696$	−1.44556	−	0.371158i	−1.44556	−	0.371158i
$697$		0			0
$698$	−1.23480	−	0.317042i	−1.23480	−	0.317042i
$699$		0			0
$700$	−0.328407	−	1.72157i	−0.328407	−	1.72157i
$701$	0.303189	+	0.220280i	0.303189	+	0.220280i	0.728969	−	0.684547i	$-0.240000\pi$
$701$	0.303189	+	0.220280i	0.303189	+	0.220280i	−0.425779	+	0.904827i	$0.640000\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	0.635456	+	0.349345i	0.635456	+	0.349345i
$706$		0			0
$707$	1.69755	−	0.435857i	1.69755	−	0.435857i
$708$		0			0
$709$	0.110048	+	0.0604991i	0.110048	+	0.0604991i	0.535827	−	0.844328i	$-0.320000\pi$
$709$	0.110048	+	0.0604991i	0.110048	+	0.0604991i	−0.425779	+	0.904827i	$0.640000\pi$
$710$		0			0
$711$		0			0
$712$	0.541587	−	0.297740i	0.541587	−	0.297740i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		−0.425779	−	0.904827i	$-0.640000\pi$
$719$		0			0		0.425779	+	0.904827i	$0.360000\pi$
$720$	0.0515014	−	0.269980i	0.0515014	−	0.269980i
$721$	0.334719	−	1.03016i	0.334719	−	1.03016i
$722$	−0.929776	+	0.368125i	−0.929776	+	0.368125i
$723$	0.702370	−	1.49261i	0.702370	−	1.49261i
$724$	1.60528	−	1.16630i	1.60528	−	1.16630i
$725$	1.27760	+	1.19975i	1.27760	+	1.19975i
$726$	0.362576	+	0.770513i	0.362576	+	0.770513i
$727$	−1.41789	−	0.779494i	−1.41789	−	0.779494i	−0.425779	−	0.904827i	$-0.640000\pi$
$727$	−1.41789	−	0.779494i	−1.41789	−	0.779494i	−0.992115	+	0.125333i	$0.960000\pi$
$728$		0			0
$729$	0.804054	+	0.755057i	0.804054	+	0.755057i
$730$		0			0
$731$		0			0
$732$	−0.883906	+	1.39281i	−0.883906	+	1.39281i
$733$		0			0		0.637424	−	0.770513i	$-0.280000\pi$
$733$		0			0		−0.637424	+	0.770513i	$0.720000\pi$
$734$	−0.574633	−	0.227513i	−0.574633	−	0.227513i
$735$	−1.28600	+	1.20763i	−1.28600	+	1.20763i
$736$	0.348445	−	1.82662i	0.348445	−	1.82662i
$737$		0			0
$738$	−0.0193008	−	0.101178i	−0.0193008	−	0.101178i
$739$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$739$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	0.450527	+	1.38658i	0.450527	+	1.38658i	0.876307	+	0.481754i	$0.160000\pi$
$743$	0.450527	+	1.38658i	0.450527	+	1.38658i	−0.425779	+	0.904827i	$0.640000\pi$
$744$		0			0
$745$	0.0915446	−	1.45506i	0.0915446	−	1.45506i
$746$		0			0
$747$	0.292219	+	0.460464i	0.292219	+	0.460464i
$748$		0			0
$749$	−0.799696	+	1.69944i	−0.799696	+	1.69944i
$750$	0.542804	−	0.656137i	0.542804	−	0.656137i
$751$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$751$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$752$	−0.824805	+	0.211774i	−0.824805	+	0.211774i
$753$		0			0
$754$		0			0
$755$		0			0
$756$	−1.76904	+	0.700412i	−1.76904	+	0.700412i
$757$		0			0		0.876307	−	0.481754i	$-0.160000\pi$
$757$		0			0		−0.876307	+	0.481754i	$0.840000\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−0.0800484	−	0.0967619i	−0.0800484	−	0.0967619i	0.728969	−	0.684547i	$-0.240000\pi$
$761$	−0.0800484	−	0.0967619i	−0.0800484	−	0.0967619i	−0.809017	+	0.587785i	$0.800000\pi$
$762$	−0.509758	+	0.130884i	−0.509758	+	0.130884i
$763$	−1.44556	+	0.371158i	−1.44556	+	0.371158i
$764$		0			0
$765$		0			0
$766$	−0.0534698	+	0.113629i	−0.0534698	+	0.113629i
$767$		0			0
$768$	−0.456288	−	0.718995i	−0.456288	−	0.718995i
$769$	−0.613161	+	1.88711i	−0.613161	+	1.88711i	−0.187381	+	0.982287i	$0.560000\pi$
$769$	−0.613161	+	1.88711i	−0.613161	+	1.88711i	−0.425779	+	0.904827i	$0.640000\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0		−0.637424	−	0.770513i	$-0.720000\pi$
$773$		0			0		0.637424	+	0.770513i	$0.280000\pi$
$774$	−0.541061	+	0.0683519i	−0.541061	+	0.0683519i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	−1.98423	−	0.250666i	−1.98423	−	0.250666i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	1.01949	−	1.60646i	1.01949	−	1.60646i
$784$	0.130080	−	2.06757i	0.130080	−	2.06757i
$785$		0			0
$786$		0			0
$787$	0.121636	+	1.93334i	0.121636	+	1.93334i	0.309017	+	0.951057i	$0.400000\pi$
$787$	0.121636	+	1.93334i	0.121636	+	1.93334i	−0.187381	+	0.982287i	$0.560000\pi$
$788$		0			0
$789$	0.0455327	+	0.0967619i	0.0455327	+	0.0967619i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.968583	−	0.248690i	$-0.920000\pi$
$797$		0			0		0.968583	+	0.248690i	$0.0800000\pi$
$798$		0			0
$799$		0			0
$800$	0.0627905	+	0.998027i	0.0627905	+	0.998027i
$801$	0.0318296	+	0.166857i	0.0318296	+	0.166857i
$802$	1.30902	+	0.951057i	1.30902	+	0.951057i
$803$		0			0
$804$	−0.665239	−	1.04825i	−0.665239	−	1.04825i
$805$	3.23338	+	0.408471i	3.23338	+	0.408471i
$806$		0			0
$807$	−0.912576			−0.912576
$808$	−0.992115	+	0.125333i	−0.992115	+	0.125333i
$809$	1.75261			1.75261			0.876307	−	0.481754i	$-0.160000\pi$
$809$	1.75261			1.75261			0.876307	+	0.481754i	$0.160000\pi$
$810$	−0.569258	−	0.312952i	−0.569258	−	0.312952i
$811$		0			0		−0.992115	−	0.125333i	$-0.960000\pi$
$811$		0			0		0.992115	+	0.125333i	$0.0400000\pi$
$812$	1.64587	+	2.59348i	1.64587	+	2.59348i
$813$		0			0
$814$		0			0
$815$	−0.273190	−	1.43211i	−0.273190	−	1.43211i
$816$		0			0
$817$		0			0
$818$	−1.85955			−1.85955
$819$		0			0
$820$	0.159566	+	0.339095i	0.159566	+	0.339095i
$821$	0.348445	−	1.82662i	0.348445	−	1.82662i	−0.187381	−	0.982287i	$-0.560000\pi$
$821$	0.348445	−	1.82662i	0.348445	−	1.82662i	0.535827	−	0.844328i	$-0.320000\pi$
$822$		0			0
$823$	1.72897	−	0.684547i	1.72897	−	0.684547i	0.728969	−	0.684547i	$-0.240000\pi$
$823$	1.72897	−	0.684547i	1.72897	−	0.684547i	1.00000			$0$
$824$	−0.263146	+	0.559214i	−0.263146	+	0.559214i
$825$		0			0
$826$		0			0
$827$	0.791759	+	1.68257i	0.791759	+	1.68257i	0.728969	+	0.684547i	$0.240000\pi$
$827$	0.791759	+	1.68257i	0.791759	+	1.68257i	0.0627905	+	0.998027i	$0.480000\pi$
$828$	0.447875	+	0.246222i	0.447875	+	0.246222i
$829$	0.0672897	+	1.06954i	0.0672897	+	1.06954i	0.876307	+	0.481754i	$0.160000\pi$
$829$	0.0672897	+	1.06954i	0.0672897	+	1.06954i	−0.809017	+	0.587785i	$0.800000\pi$
$830$	−1.44644	−	1.35830i	−1.44644	−	1.35830i
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	1.72897	+	0.684547i	1.72897	+	0.684547i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		−0.187381	−	0.982287i	$-0.560000\pi$
$839$		0			0		0.187381	+	0.982287i	$0.440000\pi$
$840$	1.20742	−	0.877242i	1.20742	−	0.877242i
$841$	−1.92617	−	0.762627i	−1.92617	−	0.762627i
$842$	−0.613161	+	0.0774602i	−0.613161	+	0.0774602i
$843$	−1.00937	−	1.22012i	−1.00937	−	1.22012i
$844$		0			0
$845$	−0.992115	+	0.125333i	−0.992115	+	0.125333i
$846$	0.0146961	−	0.233587i	0.0146961	−	0.233587i
$847$	0.541587	−	1.66683i	0.541587	−	1.66683i
$848$		0			0
$849$	−0.258183	−	0.187581i	−0.258183	−	0.187581i
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		0.968583	−	0.248690i	$-0.0800000\pi$
$853$		0			0		−0.968583	+	0.248690i	$0.920000\pi$
$854$	3.28844	−	0.844328i	3.28844	−	0.844328i
$855$		0			0
$856$	0.574221	−	0.904827i	0.574221	−	0.904827i
$857$		0			0		0.929776	−	0.368125i	$-0.120000\pi$
$857$		0			0		−0.929776	+	0.368125i	$0.880000\pi$
$858$		0			0
$859$		0			0		0.876307	−	0.481754i	$-0.160000\pi$
$859$		0			0		−0.876307	+	0.481754i	$0.840000\pi$
$860$	1.84489	−	0.730444i	1.84489	−	0.730444i
$861$	0.299696	−	0.472246i	0.299696	−	0.472246i
$862$		0			0
$863$	−0.362989	+	0.0931997i	−0.362989	+	0.0931997i	−0.425779	−	0.904827i	$-0.640000\pi$
$863$	−0.362989	+	0.0931997i	−0.362989	+	0.0931997i	0.0627905	+	0.998027i	$0.480000\pi$
$864$	1.05150	−	0.269980i	1.05150	−	0.269980i
$865$		0			0
$866$		0			0
$867$	0.362576	−	0.770513i	0.362576	−	0.770513i
$868$		0			0
$869$		0			0
$870$	−0.461193	+	1.41941i	−0.461193	+	1.41941i
$871$		0			0
$872$	0.844844	−	0.106729i	0.844844	−	0.106729i
$873$		0			0
$874$		0			0
$875$	−1.73879	+	0.219661i	−1.73879	+	0.219661i
$876$		0			0
$877$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$877$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−0.273190	+	0.256543i	−0.273190	+	0.256543i	−0.809017	−	0.587785i	$-0.800000\pi$
$881$	−0.273190	+	0.256543i	−0.273190	+	0.256543i	0.535827	+	0.844328i	$0.320000\pi$
$882$	0.529405	+	0.209606i	0.529405	+	0.209606i
$883$	0.238883	−	0.288760i	0.238883	−	0.288760i	−0.637424	−	0.770513i	$-0.720000\pi$
$883$	0.238883	−	0.288760i	0.238883	−	0.288760i	0.876307	+	0.481754i	$0.160000\pi$
$884$		0			0
$885$		0			0
$886$	−1.17950	+	1.10762i	−1.17950	+	1.10762i
$887$	1.27760	+	1.19975i	1.27760	+	1.19975i	0.968583	+	0.248690i	$0.0800000\pi$
$887$	1.27760	+	1.19975i	1.27760	+	1.19975i	0.309017	+	0.951057i	$0.400000\pi$
$888$		0			0
$889$	0.949193	+	0.521823i	0.949193	+	0.521823i
$890$	−0.263146	−	0.559214i	−0.263146	−	0.559214i
$891$		0			0
$892$	1.03137	−	0.749337i	1.03137	−	0.749337i
$893$		0			0
$894$	1.15434	−	0.457034i	1.15434	−	0.457034i
$895$		0			0
$896$	−0.328407	+	1.72157i	−0.328407	+	1.72157i
$897$		0			0
$898$	1.87631	+	0.481754i	1.87631	+	0.481754i
$899$		0			0
$900$	−0.266213	−	0.0683519i	−0.266213	−	0.0683519i
$901$		0			0
$902$		0			0
$903$	−2.39580	−	1.74065i	−2.39580	−	1.74065i
$904$		0			0
$905$	−1.06320	−	1.67534i	−1.06320	−	1.67534i
$906$		0			0
$907$	−1.11716	−	0.614163i	−1.11716	−	0.614163i	−0.187381	−	0.982287i	$-0.560000\pi$
$907$	−1.11716	−	0.614163i	−1.11716	−	0.614163i	−0.929776	+	0.368125i	$0.880000\pi$
$908$	1.45794			1.45794
$909$	0.0515014	−	0.269980i	0.0515014	−	0.269980i
$910$		0			0
$911$		0			0		−0.876307	−	0.481754i	$-0.840000\pi$
$911$		0			0		0.876307	+	0.481754i	$0.160000\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	1.33456	+	0.969617i	1.33456	+	0.969617i
$916$	0.303189	+	1.58937i	0.303189	+	1.58937i
$917$		0			0
$918$		0			0
$919$		0			0		1.00000			$0$
$919$		0			0		−1.00000			$\pi$
$920$	−1.80113	−	0.462452i	−1.80113	−	0.462452i
$921$	0.635456	+	1.35041i	0.635456	+	1.35041i
$922$	−0.200808	+	1.05267i	−0.200808	+	1.05267i
$923$		0			0
$924$		0			0
$925$		0			0
$926$	1.30902	−	0.951057i	1.30902	−	0.951057i
$927$	−0.123827	−	0.116281i	−0.123827	−	0.116281i
$928$	−0.746226	−	1.58581i	−0.746226	−	1.58581i
$929$	−0.328407	−	0.180543i	−0.328407	−	0.180543i	0.309017	−	0.951057i	$-0.400000\pi$
$929$	−0.328407	−	0.180543i	−0.328407	−	0.180543i	−0.637424	+	0.770513i	$0.720000\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$	−0.200808	+	0.316423i	−0.200808	+	0.316423i
$935$		0			0
$936$		0			0
$937$		0			0		0.728969	−	0.684547i	$-0.240000\pi$
$937$		0			0		−0.728969	+	0.684547i	$0.760000\pi$
$938$	−0.478797	+	2.50994i	−0.478797	+	2.50994i
$939$		0			0
$940$	0.159566	+	0.836475i	0.159566	+	0.836475i
$941$	−1.17950	+	0.856954i	−1.17950	+	0.856954i	−0.992115	−	0.125333i	$-0.960000\pi$
$941$	−1.17950	+	0.856954i	−1.17950	+	0.856954i	−0.187381	+	0.982287i	$0.560000\pi$
$942$		0			0
$943$	−0.691396	+	0.0873436i	−0.691396	+	0.0873436i
$944$		0			0
$945$	0.587951	+	1.80953i	0.587951	+	1.80953i
$946$		0			0
$947$	−0.0800484	+	1.27233i	−0.0800484	+	1.27233i	0.728969	+	0.684547i	$0.240000\pi$
$947$	−0.0800484	+	1.27233i	−0.0800484	+	1.27233i	−0.809017	+	0.587785i	$0.800000\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$953$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	−0.746226	+	0.410241i	−0.746226	+	0.410241i
$961$	−0.929776	+	0.368125i	−0.929776	+	0.368125i
$962$		0			0
$963$	0.187748	+	0.226948i	0.187748	+	0.226948i
$964$	1.87631	−	0.481754i	1.87631	−	0.481754i
$965$		0			0
$966$	0.857613	+	2.63946i	0.857613	+	2.63946i
$967$	−0.0800484	+	0.0967619i	−0.0800484	+	0.0967619i	−0.809017	−	0.587785i	$-0.800000\pi$
$967$	−0.0800484	+	0.0967619i	−0.0800484	+	0.0967619i	0.728969	+	0.684547i	$0.240000\pi$
$968$	−0.425779	+	0.904827i	−0.425779	+	0.904827i
$969$		0			0
$970$		0			0
$971$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$971$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$972$	−0.0334313	+	0.531376i	−0.0334313	+	0.531376i
$973$		0			0
$974$	−0.115808	−	0.356420i	−0.115808	−	0.356420i
$975$		0			0
$976$	−1.92189	+	0.242791i	−1.92189	+	0.242791i
$977$		0			0		−0.929776	−	0.368125i	$-0.880000\pi$
$977$		0			0		0.929776	+	0.368125i	$0.120000\pi$
$978$	1.00441	−	0.729747i	1.00441	−	0.729747i
$979$		0			0
$980$	−2.05532	−	0.259647i	−2.05532	−	0.259647i
$981$	−0.0438564	+	0.229904i	−0.0438564	+	0.229904i
$982$		0			0
$983$	0.348445	+	0.137959i	0.348445	+	0.137959i	0.535827	−	0.844328i	$-0.320000\pi$
$983$	0.348445	+	0.137959i	0.348445	+	0.137959i	−0.187381	+	0.982287i	$0.560000\pi$
$984$	−0.203423	+	0.245896i	−0.203423	+	0.245896i
$985$		0			0
$986$		0			0
$987$	0.926454	−	0.869999i	0.926454	−	0.869999i
$988$		0			0
$989$	0.231683	+	3.68250i	0.231683	+	3.68250i
$990$		0			0
$991$		0			0		−0.425779	−	0.904827i	$-0.640000\pi$
$991$		0			0		0.425779	+	0.904827i	$0.360000\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$	0.522142	−	1.60699i	0.522142	−	1.60699i
$997$		0			0		0.187381	−	0.982287i	$-0.440000\pi$
$997$		0			0		−0.187381	+	0.982287i	$0.560000\pi$
$998$		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.1199.1	yes	20
4.3	odd	2		2020.1.bu.b.1199.1	yes	20
5.4	even	2		2020.1.bu.b.1199.1	yes	20
20.19	odd	2	CM	2020.1.bu.a.1199.1	yes	20
101.31	even	25	inner	2020.1.bu.a.839.1	✓	20
404.31	odd	50		2020.1.bu.b.839.1	yes	20
505.334	even	50		2020.1.bu.b.839.1	yes	20
2020.839	odd	50	inner	2020.1.bu.a.839.1	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2020.1.bu.a.839.1	✓	20	101.31	even	25	inner
2020.1.bu.a.839.1	✓	20	2020.839	odd	50	inner
2020.1.bu.a.1199.1	yes	20	1.1	even	1	trivial
2020.1.bu.a.1199.1	yes	20	20.19	odd	2	CM
2020.1.bu.b.839.1	yes	20	404.31	odd	50
2020.1.bu.b.839.1	yes	20	505.334	even	50
2020.1.bu.b.1199.1	yes	20	4.3	odd	2
2020.1.bu.b.1199.1	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)

\(f(q)\)	\(=\)	\(q+(0.876307 + 0.481754i) q^{2} +(0.844844 + 0.106729i) q^{3} +(0.535827 + 0.844328i) q^{4} +(0.876307 - 0.481754i) q^{5} +(0.688925 + 0.500534i) q^{6} +(-0.328407 - 1.72157i) q^{7} +(0.0627905 + 0.998027i) q^{8} +(-0.266213 - 0.0683519i) q^{9} +O(q^{10})\)	\(q+(0.876307 + 0.481754i) q^{2} +(0.844844 + 0.106729i) q^{3} +(0.535827 + 0.844328i) q^{4} +(0.876307 - 0.481754i) q^{5} +(0.688925 + 0.500534i) q^{6} +(-0.328407 - 1.72157i) q^{7} +(0.0627905 + 0.998027i) q^{8} +(-0.266213 - 0.0683519i) q^{9} +1.00000 q^{10} +(0.362576 + 0.770513i) q^{12} +(0.541587 - 1.66683i) q^{14} +(0.791759 - 0.313480i) q^{15} +(-0.425779 + 0.904827i) q^{16} +(-0.200356 - 0.188146i) q^{18} +(0.876307 + 0.481754i) q^{20} +(-0.0937119 - 1.48951i) q^{21} +(-1.35556 + 1.27295i) q^{23} +(-0.0534698 + 0.849878i) q^{24} +(0.535827 - 0.844328i) q^{25} +(-1.00937 - 0.399639i) q^{27} +(1.27760 - 1.19975i) q^{28} +(-0.328407 + 1.72157i) q^{29} +(0.844844 + 0.106729i) q^{30} +(-0.809017 + 0.587785i) q^{32} +(-1.11716 - 1.35041i) q^{35} +(-0.0849327 - 0.261396i) q^{36} +(0.535827 + 0.844328i) q^{40} +(0.303189 + 0.220280i) q^{41} +(0.635456 - 1.35041i) q^{42} +(1.26480 - 1.52888i) q^{43} +(-0.266213 + 0.0683519i) q^{45} +(-1.80113 + 0.462452i) q^{46} +(0.542804 + 0.656137i) q^{47} +(-0.456288 + 0.718995i) q^{48} +(-1.92617 + 0.762627i) q^{49} +(0.876307 - 0.481754i) q^{50} +(-0.691992 - 0.836475i) q^{54} +(1.69755 - 0.435857i) q^{56} +(-1.11716 + 1.35041i) q^{58} +(0.688925 + 0.500534i) q^{60} +(1.03799 + 1.63560i) q^{61} +(-0.0302463 + 0.480752i) q^{63} +(-0.992115 + 0.125333i) q^{64} +(-1.44644 + 0.182728i) q^{67} +(-1.28109 + 0.930769i) q^{69} +(-0.328407 - 1.72157i) q^{70} +(0.0515014 - 0.269980i) q^{72} +(0.542804 - 0.656137i) q^{75} +(0.0627905 + 0.998027i) q^{80} +(-0.569258 - 0.312952i) q^{81} +(0.159566 + 0.339095i) q^{82} +(-1.44644 - 1.35830i) q^{83} +(1.20742 - 0.877242i) q^{84} +(1.84489 - 0.730444i) q^{86} +(-0.461193 + 1.41941i) q^{87} +(-0.263146 - 0.559214i) q^{89} +(-0.266213 - 0.0683519i) q^{90} +(-1.80113 - 0.462452i) q^{92} +(0.159566 + 0.836475i) q^{94} +(-0.746226 + 0.410241i) q^{96} +(-2.05532 - 0.259647i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 5 q^{3} - 5 q^{7} - 5 q^{9}+O(q^{10}) \) 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

Modular forms

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Database

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