LMFDB - Embedded newform 1340.1.bl.b.1059.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1340,1,Mod(19,1340)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1340, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([33, 33, 10]))

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

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

chi := DirichletCharacter("1340.19");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 1340 = 2^{2} \cdot 5 \cdot 67 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1340.bl (of order $66$, 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:	$0.668747116928$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\Q(\zeta_{33})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{19} + x^{17} - x^{16} + x^{14} - x^{13} + x^{11} - x^{10} + x^{9} - x^{7} + x^{6} - x^{4} + x^{3} - x + 1 $ x^20 - x^19 + x^17 - x^16 + x^14 - x^13 + x^11 - x^10 + x^9 - x^7 + x^6 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{33}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{33} - \cdots)$

Embedding invariants

Embedding label			1059.1
Root			$-0.327068 + 0.945001i$ of defining polynomial
Character	$\chi$	$=$	1340.1059
Dual form			1340.1.bl.b.639.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.786053 + 0.618159i) q^{2} +(-0.308779 + 0.356349i) q^{3} +(0.235759 - 0.971812i) q^{4} +(0.841254 - 0.540641i) q^{5} +(0.0224357 - 0.470984i) q^{6} +(1.82318 + 0.729892i) q^{7} +(0.415415 + 0.909632i) q^{8} +(0.110674 + 0.769755i) q^{9} +O(q^{10})$	\(q+(-0.786053 + 0.618159i) q^{2} +(-0.308779 + 0.356349i) q^{3} +(0.235759 - 0.971812i) q^{4} +(0.841254 - 0.540641i) q^{5} +(0.0224357 - 0.470984i) q^{6} +(1.82318 + 0.729892i) q^{7} +(0.415415 + 0.909632i) q^{8} +(0.110674 + 0.769755i) q^{9} +(-0.327068 + 0.945001i) q^{10} +(0.273507 + 0.384087i) q^{12} +(-1.88431 + 0.553283i) q^{14} +(-0.0671040 + 0.466718i) q^{15} +(-0.888835 - 0.458227i) q^{16} +(-0.562827 - 0.536654i) q^{18} +(-0.327068 - 0.945001i) q^{20} +(-0.823056 + 0.424315i) q^{21} +(-0.981929 - 0.189251i) q^{23} +(-0.452418 - 0.132842i) q^{24} +(0.415415 - 0.909632i) q^{25} +(-0.705142 - 0.453167i) q^{27} +(1.13915 - 1.59971i) q^{28} +(0.327068 - 0.566498i) q^{29} +(-0.235759 - 0.408346i) q^{30} +(0.981929 - 0.189251i) q^{32} +(1.92837 - 0.371662i) q^{35} +(0.774150 + 0.0739223i) q^{36} +(0.841254 + 0.540641i) q^{40} +(-1.44091 + 1.37391i) q^{41} +(0.384672 - 0.842314i) q^{42} +(-1.38884 - 0.407799i) q^{43} +(0.509266 + 0.587724i) q^{45} +(0.888835 - 0.458227i) q^{46} +(-0.379436 - 1.09631i) q^{47} +(0.437742 - 0.175245i) q^{48} +(2.06752 + 1.97137i) q^{49} +(0.235759 + 0.971812i) q^{50} +(0.834408 - 0.0796763i) q^{54} +(0.0934441 + 1.96163i) q^{56} +(0.0930932 + 0.647478i) q^{58} +(0.437742 + 0.175245i) q^{60} +(0.0800569 - 1.68060i) q^{61} +(-0.360059 + 1.48418i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(0.723734 + 0.690079i) q^{67} +(0.370638 - 0.291473i) q^{69} +(-1.28605 + 1.48418i) q^{70} +(-0.654218 + 0.420441i) q^{72} +(0.195876 + 0.428908i) q^{75} +(-0.995472 + 0.0950560i) q^{80} +(-0.366951 + 0.107747i) q^{81} +(0.283341 - 1.97068i) q^{82} +(-1.65033 - 0.850806i) q^{83} +(0.218311 + 0.899892i) q^{84} +(1.34378 - 0.537970i) q^{86} +(0.100880 + 0.291473i) q^{87} +(0.186393 + 0.215109i) q^{89} +(-0.763617 - 0.147175i) q^{90} +(-0.415415 + 0.909632i) q^{92} +(0.975950 + 0.627205i) q^{94} +(-0.235759 + 0.408346i) q^{96} +(-2.84380 - 0.271550i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + q^{2} + 2 q^{3} + q^{4} - 2 q^{5} - q^{6} - q^{7} - 2 q^{8}+O(q^{10}) $ 20 * q + q^2 + 2 * q^3 + q^4 - 2 * q^5 - q^6 - q^7 - 2 * q^8	$ 20 q + q^{2} + 2 q^{3} + q^{4} - 2 q^{5} - q^{6} - q^{7} - 2 q^{8} + q^{10} - q^{12} + 2 q^{14} + 2 q^{15} + q^{16} + q^{20} - 10 q^{21} - q^{23} - 9 q^{24} - 2 q^{25} - 2 q^{27} - q^{28} - q^{29} - q^{30} + q^{32} + 21 q^{35} - 2 q^{40} - q^{41} + 20 q^{42} - 9 q^{43} - q^{46} - q^{47} - q^{48} + q^{50} + q^{54} - q^{56} + 2 q^{58} - q^{60} - 9 q^{61} - 11 q^{63} - 2 q^{64} + q^{67} + q^{69} - 9 q^{70} - 11 q^{72} + 2 q^{75} + q^{80} + 2 q^{81} + 2 q^{82} - q^{83} + q^{84} - q^{86} + q^{87} - 4 q^{89} + 2 q^{92} + 2 q^{94} - q^{96}+O(q^{100}) $ 20 * q + q^2 + 2 * q^3 + q^4 - 2 * q^5 - q^6 - q^7 - 2 * q^8 + q^10 - q^12 + 2 * q^14 + 2 * q^15 + q^16 + q^20 - 10 * q^21 - q^23 - 9 * q^24 - 2 * q^25 - 2 * q^27 - q^28 - q^29 - q^30 + q^32 + 21 * q^35 - 2 * q^40 - q^41 + 20 * q^42 - 9 * q^43 - q^46 - q^47 - q^48 + q^50 + q^54 - q^56 + 2 * q^58 - q^60 - 9 * q^61 - 11 * q^63 - 2 * q^64 + q^67 + q^69 - 9 * q^70 - 11 * q^72 + 2 * q^75 + q^80 + 2 * q^81 + 2 * q^82 - q^83 + q^84 - q^86 + q^87 - 4 * q^89 + 2 * q^92 + 2 * q^94 - q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1340\mathbb{Z}\right)^\times$.

$n$	$537$	$671$	$1141$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{26}{33}\right)$

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 $

$2$	−0.786053	+	0.618159i	−0.786053	+	0.618159i
$2$	−0.786053	+	0.618159i	−0.786053	+	0.618159i
$3$	−0.308779	+	0.356349i	−0.308779	+	0.356349i	−0.888835	−	0.458227i	$-0.848485\pi$
$3$	−0.308779	+	0.356349i	−0.308779	+	0.356349i	0.580057	+	0.814576i	$0.303030\pi$
$4$	0.235759	−	0.971812i	0.235759	−	0.971812i
$5$	0.841254	−	0.540641i	0.841254	−	0.540641i
$5$	0.841254	−	0.540641i	0.841254	−	0.540641i
$6$	0.0224357	−	0.470984i	0.0224357	−	0.470984i
$7$	1.82318	+	0.729892i	1.82318	+	0.729892i	0.981929	+	0.189251i	$0.0606061\pi$
$7$	1.82318	+	0.729892i	1.82318	+	0.729892i	0.841254	+	0.540641i	$0.181818\pi$
$8$	0.415415	+	0.909632i	0.415415	+	0.909632i
$9$	0.110674	+	0.769755i	0.110674	+	0.769755i
$10$	−0.327068	+	0.945001i	−0.327068	+	0.945001i
$11$		0			0		−0.0475819	−	0.998867i	$-0.515152\pi$
$11$		0			0		0.0475819	+	0.998867i	$0.484848\pi$
$12$	0.273507	+	0.384087i	0.273507	+	0.384087i
$13$		0			0		0.995472	−	0.0950560i	$-0.0303030\pi$
$13$		0			0		−0.995472	+	0.0950560i	$0.969697\pi$
$14$	−1.88431	+	0.553283i	−1.88431	+	0.553283i
$15$	−0.0671040	+	0.466718i	−0.0671040	+	0.466718i
$16$	−0.888835	−	0.458227i	−0.888835	−	0.458227i
$17$		0			0		−0.235759	−	0.971812i	$-0.575758\pi$
$17$		0			0		0.235759	+	0.971812i	$0.424242\pi$
$18$	−0.562827	−	0.536654i	−0.562827	−	0.536654i
$19$		0			0		0.928368	−	0.371662i	$-0.121212\pi$
$19$		0			0		−0.928368	+	0.371662i	$0.878788\pi$
$20$	−0.327068	−	0.945001i	−0.327068	−	0.945001i
$21$	−0.823056	+	0.424315i	−0.823056	+	0.424315i
$22$		0			0
$23$	−0.981929	−	0.189251i	−0.981929	−	0.189251i	−0.327068	−	0.945001i	$-0.606061\pi$
$23$	−0.981929	−	0.189251i	−0.981929	−	0.189251i	−0.654861	+	0.755750i	$0.727273\pi$
$24$	−0.452418	−	0.132842i	−0.452418	−	0.132842i
$25$	0.415415	−	0.909632i	0.415415	−	0.909632i
$26$		0			0
$27$	−0.705142	−	0.453167i	−0.705142	−	0.453167i
$28$	1.13915	−	1.59971i	1.13915	−	1.59971i
$29$	0.327068	−	0.566498i	0.327068	−	0.566498i	−0.654861	−	0.755750i	$-0.727273\pi$
$29$	0.327068	−	0.566498i	0.327068	−	0.566498i	0.981929	+	0.189251i	$0.0606061\pi$
$30$	−0.235759	−	0.408346i	−0.235759	−	0.408346i
$31$		0			0		−0.995472	−	0.0950560i	$-0.969697\pi$
$31$		0			0		0.995472	+	0.0950560i	$0.0303030\pi$
$32$	0.981929	−	0.189251i	0.981929	−	0.189251i
$33$		0			0
$34$		0			0
$35$	1.92837	−	0.371662i	1.92837	−	0.371662i
$36$	0.774150	+	0.0739223i	0.774150	+	0.0739223i
$37$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$37$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$38$		0			0
$39$		0			0
$40$	0.841254	+	0.540641i	0.841254	+	0.540641i
$41$	−1.44091	+	1.37391i	−1.44091	+	1.37391i	−0.654861	+	0.755750i	$0.727273\pi$
$41$	−1.44091	+	1.37391i	−1.44091	+	1.37391i	−0.786053	+	0.618159i	$0.787879\pi$
$42$	0.384672	−	0.842314i	0.384672	−	0.842314i
$43$	−1.38884	−	0.407799i	−1.38884	−	0.407799i	−0.500000	−	0.866025i	$-0.666667\pi$
$43$	−1.38884	−	0.407799i	−1.38884	−	0.407799i	−0.888835	+	0.458227i	$0.848485\pi$
$44$		0			0
$45$	0.509266	+	0.587724i	0.509266	+	0.587724i
$46$	0.888835	−	0.458227i	0.888835	−	0.458227i
$47$	−0.379436	−	1.09631i	−0.379436	−	1.09631i	−0.959493	−	0.281733i	$-0.909091\pi$
$47$	−0.379436	−	1.09631i	−0.379436	−	1.09631i	0.580057	−	0.814576i	$-0.303030\pi$
$48$	0.437742	−	0.175245i	0.437742	−	0.175245i
$49$	2.06752	+	1.97137i	2.06752	+	1.97137i
$50$	0.235759	+	0.971812i	0.235759	+	0.971812i
$51$		0			0
$52$		0			0
$53$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$53$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$54$	0.834408	−	0.0796763i	0.834408	−	0.0796763i
$55$		0			0
$56$	0.0934441	+	1.96163i	0.0934441	+	1.96163i
$57$		0			0
$58$	0.0930932	+	0.647478i	0.0930932	+	0.647478i
$59$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$59$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$60$	0.437742	+	0.175245i	0.437742	+	0.175245i
$61$	0.0800569	−	1.68060i	0.0800569	−	1.68060i	−0.500000	−	0.866025i	$-0.666667\pi$
$61$	0.0800569	−	1.68060i	0.0800569	−	1.68060i	0.580057	−	0.814576i	$-0.303030\pi$
$62$		0			0
$63$	−0.360059	+	1.48418i	−0.360059	+	1.48418i
$64$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$65$		0			0
$66$		0			0
$67$	0.723734	+	0.690079i	0.723734	+	0.690079i
$67$	0.723734	+	0.690079i	0.723734	+	0.690079i
$68$		0			0
$69$	0.370638	−	0.291473i	0.370638	−	0.291473i
$70$	−1.28605	+	1.48418i	−1.28605	+	1.48418i
$71$		0			0		0.235759	−	0.971812i	$-0.424242\pi$
$71$		0			0		−0.235759	+	0.971812i	$0.575758\pi$
$72$	−0.654218	+	0.420441i	−0.654218	+	0.420441i
$73$		0			0		0.0475819	−	0.998867i	$-0.484848\pi$
$73$		0			0		−0.0475819	+	0.998867i	$0.515152\pi$
$74$		0			0
$75$	0.195876	+	0.428908i	0.195876	+	0.428908i
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		−0.580057	−	0.814576i	$-0.696970\pi$
$79$		0			0		0.580057	+	0.814576i	$0.303030\pi$
$80$	−0.995472	+	0.0950560i	−0.995472	+	0.0950560i
$81$	−0.366951	+	0.107747i	−0.366951	+	0.107747i
$82$	0.283341	−	1.97068i	0.283341	−	1.97068i
$83$	−1.65033	−	0.850806i	−1.65033	−	0.850806i	−0.995472	−	0.0950560i	$-0.969697\pi$
$83$	−1.65033	−	0.850806i	−1.65033	−	0.850806i	−0.654861	−	0.755750i	$-0.727273\pi$
$84$	0.218311	+	0.899892i	0.218311	+	0.899892i
$85$		0			0
$86$	1.34378	−	0.537970i	1.34378	−	0.537970i
$87$	0.100880	+	0.291473i	0.100880	+	0.291473i
$88$		0			0
$89$	0.186393	+	0.215109i	0.186393	+	0.215109i	0.841254	−	0.540641i	$-0.181818\pi$
$89$	0.186393	+	0.215109i	0.186393	+	0.215109i	−0.654861	+	0.755750i	$0.727273\pi$
$90$	−0.763617	−	0.147175i	−0.763617	−	0.147175i
$91$		0			0
$92$	−0.415415	+	0.909632i	−0.415415	+	0.909632i
$93$		0			0
$94$	0.975950	+	0.627205i	0.975950	+	0.627205i
$95$		0			0
$96$	−0.235759	+	0.408346i	−0.235759	+	0.408346i
$97$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$97$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$98$	−2.84380	−	0.271550i	−2.84380	−	0.271550i
$99$		0			0
$100$	−0.786053	−	0.618159i	−0.786053	−	0.618159i
$101$	0.223734	+	0.175946i	0.223734	+	0.175946i	0.723734	−	0.690079i	$-0.242424\pi$
$101$	0.223734	+	0.175946i	0.223734	+	0.175946i	−0.500000	+	0.866025i	$0.666667\pi$
$102$		0			0
$103$	1.56499	+	0.149438i	1.56499	+	0.149438i	0.841254	−	0.540641i	$-0.181818\pi$
$103$	1.56499	+	0.149438i	1.56499	+	0.149438i	0.723734	+	0.690079i	$0.242424\pi$
$104$		0			0
$105$	−0.462997	+	0.801934i	−0.462997	+	0.801934i
$106$		0			0
$107$	0.698939	+	0.449181i	0.698939	+	0.449181i	0.841254	−	0.540641i	$-0.181818\pi$
$107$	0.698939	+	0.449181i	0.698939	+	0.449181i	−0.142315	+	0.989821i	$0.545455\pi$
$108$	−0.606636	+	0.578427i	−0.606636	+	0.578427i
$109$	−0.653077	+	1.43004i	−0.653077	+	1.43004i	0.235759	+	0.971812i	$0.424242\pi$
$109$	−0.653077	+	1.43004i	−0.653077	+	1.43004i	−0.888835	+	0.458227i	$0.848485\pi$
$110$		0			0
$111$		0			0
$112$	−1.28605	−	1.48418i	−1.28605	−	1.48418i
$113$		0			0		0.888835	−	0.458227i	$-0.151515\pi$
$113$		0			0		−0.888835	+	0.458227i	$0.848485\pi$
$114$		0			0
$115$	−0.928368	+	0.371662i	−0.928368	+	0.371662i
$116$	−0.473420	−	0.451405i	−0.473420	−	0.451405i
$117$		0			0
$118$		0			0
$119$		0			0
$120$	−0.452418	+	0.132842i	−0.452418	+	0.132842i
$121$	−0.995472	+	0.0950560i	−0.995472	+	0.0950560i
$122$	0.975950	+	1.37053i	0.975950	+	1.37053i
$123$	−0.0446683	−	0.937702i	−0.0446683	−	0.937702i
$124$		0			0
$125$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$126$	−0.634436	−	1.38922i	−0.634436	−	1.38922i
$127$	0.0883470	+	0.0353688i	0.0883470	+	0.0353688i	0.415415	−	0.909632i	$-0.363636\pi$
$127$	0.0883470	+	0.0353688i	0.0883470	+	0.0353688i	−0.327068	+	0.945001i	$0.606061\pi$
$128$	0.0475819	−	0.998867i	0.0475819	−	0.998867i
$129$	0.574161	−	0.368991i	0.574161	−	0.368991i
$130$		0			0
$131$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$131$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$132$		0			0
$133$		0			0
$134$	−0.995472	−	0.0950560i	−0.995472	−	0.0950560i
$135$	−0.838204			−0.838204
$136$		0			0
$137$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$137$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$138$	−0.111165	+	0.458227i	−0.111165	+	0.458227i
$139$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$139$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$140$	0.0934441	−	1.96163i	0.0934441	−	1.96163i
$141$	0.507831	+	0.203305i	0.507831	+	0.203305i
$142$		0			0
$143$		0			0
$144$	0.254351	−	0.734900i	0.254351	−	0.734900i
$145$	−0.0311250	−	0.653395i	−0.0311250	−	0.653395i
$146$		0			0
$147$	−1.34090	+	0.128041i	−1.34090	+	0.128041i
$148$		0			0
$149$	0.283341	−	1.97068i	0.283341	−	1.97068i	0.0475819	−	0.998867i	$-0.484848\pi$
$149$	0.283341	−	1.97068i	0.283341	−	1.97068i	0.235759	−	0.971812i	$-0.424242\pi$
$150$	−0.419102	−	0.216062i	−0.419102	−	0.216062i
$151$		0			0		−0.235759	−	0.971812i	$-0.575758\pi$
$151$		0			0		0.235759	+	0.971812i	$0.424242\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		−0.981929	−	0.189251i	$-0.939394\pi$
$157$		0			0		0.981929	+	0.189251i	$0.0606061\pi$
$158$		0			0
$159$		0			0
$160$	0.723734	−	0.690079i	0.723734	−	0.690079i
$161$	−1.65210	−	1.06174i	−1.65210	−	1.06174i
$162$	0.221839	−	0.311529i	0.221839	−	0.311529i
$163$	0.959493	−	1.66189i	0.959493	−	1.66189i	0.235759	−	0.971812i	$-0.424242\pi$
$163$	0.959493	−	1.66189i	0.959493	−	1.66189i	0.723734	−	0.690079i	$-0.242424\pi$
$164$	0.995472	+	1.72421i	0.995472	+	1.72421i
$165$		0			0
$166$	1.82318	−	0.351390i	1.82318	−	0.351390i
$167$	1.02951	+	0.809616i	1.02951	+	0.809616i	0.981929	−	0.189251i	$-0.0606061\pi$
$167$	1.02951	+	0.809616i	1.02951	+	0.809616i	0.0475819	+	0.998867i	$0.484848\pi$
$168$	−0.727880	−	0.572411i	−0.727880	−	0.572411i
$169$	0.981929	−	0.189251i	0.981929	−	0.189251i
$170$		0			0
$171$		0			0
$172$	−0.723734	+	1.25354i	−0.723734	+	1.25354i
$173$		0			0		0.580057	−	0.814576i	$-0.303030\pi$
$173$		0			0		−0.580057	+	0.814576i	$0.696970\pi$
$174$	−0.259474	−	0.166754i	−0.259474	−	0.166754i
$175$	1.42131	−	1.35522i	1.42131	−	1.35522i
$176$		0			0
$177$		0			0
$178$	−0.279486	−	0.0538665i	−0.279486	−	0.0538665i
$179$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$179$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$180$	0.691221	−	0.356349i	0.691221	−	0.356349i
$181$	0.627639	+	1.81344i	0.627639	+	1.81344i	0.580057	+	0.814576i	$0.303030\pi$
$181$	0.627639	+	1.81344i	0.627639	+	1.81344i	0.0475819	+	0.998867i	$0.484848\pi$
$182$		0			0
$183$	0.574161	+	0.547462i	0.574161	+	0.547462i
$184$	−0.235759	−	0.971812i	−0.235759	−	0.971812i
$185$		0			0
$186$		0			0
$187$		0			0
$188$	−1.15486	+	0.110276i	−1.15486	+	0.110276i
$189$	−0.954839	−	1.34088i	−0.954839	−	1.34088i
$190$		0			0
$191$		0			0		0.327068	−	0.945001i	$-0.393939\pi$
$191$		0			0		−0.327068	+	0.945001i	$0.606061\pi$
$192$	−0.0671040	−	0.466718i	−0.0671040	−	0.466718i
$193$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$193$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$194$		0			0
$195$		0			0
$196$	2.40324	−	1.54447i	2.40324	−	1.54447i
$197$		0			0		0.235759	−	0.971812i	$-0.424242\pi$
$197$		0			0		−0.235759	+	0.971812i	$0.575758\pi$
$198$		0			0
$199$		0			0		0.786053	−	0.618159i	$-0.212121\pi$
$199$		0			0		−0.786053	+	0.618159i	$0.787879\pi$
$200$	1.00000			1.00000
$201$	−0.469383	+	0.0448206i	−0.469383	+	0.0448206i
$202$	−0.284630			−0.284630
$203$	1.00979	−	0.794105i	1.00979	−	0.794105i
$204$		0			0
$205$	−0.469383	+	1.93482i	−0.469383	+	1.93482i
$206$	−1.32254	+	0.849945i	−1.32254	+	0.849945i
$207$	0.0370031	−	0.776790i	0.0370031	−	0.776790i
$208$		0			0
$209$		0			0
$210$	−0.131783	−	0.916569i	−0.131783	−	0.916569i
$211$		0			0		0.327068	−	0.945001i	$-0.393939\pi$
$211$		0			0		−0.327068	+	0.945001i	$0.606061\pi$
$212$		0			0
$213$		0			0
$214$	−0.827068	+	0.0789754i	−0.827068	+	0.0789754i
$215$	−1.38884	+	0.407799i	−1.38884	+	0.407799i
$216$	0.119289	−	0.829672i	0.119289	−	0.829672i
$217$		0			0
$218$	−0.370638	−	1.52779i	−0.370638	−	1.52779i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−1.10181	−	1.27155i	−1.10181	−	1.27155i	−0.959493	−	0.281733i	$-0.909091\pi$
$223$	−1.10181	−	1.27155i	−1.10181	−	1.27155i	−0.142315	−	0.989821i	$-0.545455\pi$
$224$	1.92837	+	0.371662i	1.92837	+	0.371662i
$225$	0.746170	+	0.219095i	0.746170	+	0.219095i
$226$		0			0
$227$	−0.205996	+	0.196417i	−0.205996	+	0.196417i	−0.786053	−	0.618159i	$-0.787879\pi$
$227$	−0.205996	+	0.196417i	−0.205996	+	0.196417i	0.580057	+	0.814576i	$0.303030\pi$
$228$		0			0
$229$	0.0552004	−	0.0775182i	0.0552004	−	0.0775182i	−0.786053	−	0.618159i	$-0.787879\pi$
$229$	0.0552004	−	0.0775182i	0.0552004	−	0.0775182i	0.841254	+	0.540641i	$0.181818\pi$
$230$	0.500000	−	0.866025i	0.500000	−	0.866025i
$231$		0			0
$232$	0.651174	+	0.0621796i	0.651174	+	0.0621796i
$233$		0			0		0.981929	−	0.189251i	$-0.0606061\pi$
$233$		0			0		−0.981929	+	0.189251i	$0.939394\pi$
$234$		0			0
$235$	−0.911911	−	0.717135i	−0.911911	−	0.717135i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$239$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$240$	0.273507	−	0.384087i	0.273507	−	0.384087i
$241$	−1.32254	−	0.849945i	−1.32254	−	0.849945i	−0.327068	−	0.945001i	$-0.606061\pi$
$241$	−1.32254	−	0.849945i	−1.32254	−	0.849945i	−0.995472	+	0.0950560i	$0.969697\pi$
$242$	0.723734	−	0.690079i	0.723734	−	0.690079i
$243$	0.423114	−	0.926490i	0.423114	−	0.926490i
$244$	−1.61435	−	0.474017i	−1.61435	−	0.474017i
$245$	2.80511	+	0.540641i	2.80511	+	0.540641i
$246$	0.614761	+	0.709472i	0.614761	+	0.709472i
$247$		0			0
$248$		0			0
$249$	0.812771	−	0.325385i	0.812771	−	0.325385i
$250$	0.723734	+	0.690079i	0.723734	+	0.690079i
$251$		0			0		−0.235759	−	0.971812i	$-0.575758\pi$
$251$		0			0		0.235759	+	0.971812i	$0.424242\pi$
$252$	1.35746	+	0.699819i	1.35746	+	0.699819i
$253$		0			0
$254$	−0.0913090	+	0.0268107i	−0.0913090	+	0.0268107i
$255$		0			0
$256$	0.580057	+	0.814576i	0.580057	+	0.814576i
$257$		0			0		−0.0475819	−	0.998867i	$-0.515152\pi$
$257$		0			0		0.0475819	+	0.998867i	$0.484848\pi$
$258$	−0.223226	+	0.644970i	−0.223226	+	0.644970i
$259$		0			0
$260$		0			0
$261$	0.472263	+	0.189066i	0.472263	+	0.189066i
$262$		0			0
$263$	−1.49547	+	0.961081i	−1.49547	+	0.961081i	−0.500000	+	0.866025i	$0.666667\pi$
$263$	−1.49547	+	0.961081i	−1.49547	+	0.961081i	−0.995472	+	0.0950560i	$0.969697\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−0.134208			−0.134208
$268$	0.841254	−	0.540641i	0.841254	−	0.540641i
$269$	−1.91899			−1.91899			−0.959493	−	0.281733i	$-0.909091\pi$
$269$	−1.91899			−1.91899			−0.959493	+	0.281733i	$0.909091\pi$
$270$	0.658873	−	0.518143i	0.658873	−	0.518143i
$271$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$271$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$	−0.195876	−	0.428908i	−0.195876	−	0.428908i
$277$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$277$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$278$		0			0
$279$		0			0
$280$	1.13915	+	1.59971i	1.13915	+	1.59971i
$281$	−1.15486	+	0.110276i	−1.15486	+	0.110276i	−0.654861	−	0.755750i	$-0.727273\pi$
$281$	−1.15486	+	0.110276i	−1.15486	+	0.110276i	−0.500000	+	0.866025i	$0.666667\pi$
$282$	−0.524856	+	0.154112i	−0.524856	+	0.154112i
$283$	0.252989	−	1.75958i	0.252989	−	1.75958i	−0.327068	−	0.945001i	$-0.606061\pi$
$283$	0.252989	−	1.75958i	0.252989	−	1.75958i	0.580057	−	0.814576i	$-0.303030\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−3.62985	+	1.45317i	−3.62985	+	1.45317i
$288$	0.254351	+	0.734900i	0.254351	+	0.734900i
$289$	−0.888835	+	0.458227i	−0.888835	+	0.458227i
$290$	0.428368	+	0.494363i	0.428368	+	0.494363i
$291$		0			0
$292$		0			0
$293$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$293$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$294$	0.974871	−	0.929538i	0.974871	−	0.929538i
$295$		0			0
$296$		0			0
$297$		0			0
$298$	0.995472	+	1.72421i	0.995472	+	1.72421i
$299$		0			0
$300$	0.462997	−	0.0892353i	0.462997	−	0.0892353i
$301$	−2.23445	−	1.75719i	−2.23445	−	1.75719i
$302$		0			0
$303$	−0.131783	+	0.0253990i	−0.131783	+	0.0253990i
$304$		0			0
$305$	−0.841254	−	1.45709i	−0.841254	−	1.45709i
$306$		0			0
$307$	0.481929	−	0.676774i	0.481929	−	0.676774i	−0.500000	−	0.866025i	$-0.666667\pi$
$307$	0.481929	−	0.676774i	0.481929	−	0.676774i	0.981929	+	0.189251i	$0.0606061\pi$
$308$		0			0
$309$	−0.536487	+	0.511539i	−0.536487	+	0.511539i
$310$		0			0
$311$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$311$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$312$		0			0
$313$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$313$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$314$		0			0
$315$	0.499510	+	1.44324i	0.499510	+	1.44324i
$316$		0			0
$317$		0			0		−0.723734	−	0.690079i	$-0.757576\pi$
$317$		0			0		0.723734	+	0.690079i	$0.242424\pi$
$318$		0			0
$319$		0			0
$320$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$321$	−0.375883	+	0.110369i	−0.375883	+	0.110369i
$322$	1.95496	−	0.186677i	1.95496	−	0.186677i
$323$		0			0
$324$	0.0181974	+	0.382010i	0.0181974	+	0.382010i
$325$		0			0
$326$	0.273100	+	1.89945i	0.273100	+	1.89945i
$327$	−0.307937	−	0.674289i	−0.307937	−	0.674289i
$328$	−1.84833	−	0.739959i	−1.84833	−	0.739959i
$329$	0.108406	−	2.27572i	0.108406	−	2.27572i
$330$		0			0
$331$		0			0		0.235759	−	0.971812i	$-0.424242\pi$
$331$		0			0		−0.235759	+	0.971812i	$0.575758\pi$
$332$	−1.21590	+	1.40323i	−1.21590	+	1.40323i
$333$		0			0
$334$	−1.30972			−1.30972
$335$	0.981929	+	0.189251i	0.981929	+	0.189251i
$336$	0.925994			0.925994
$337$		0			0		0.786053	−	0.618159i	$-0.212121\pi$
$337$		0			0		−0.786053	+	0.618159i	$0.787879\pi$
$338$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	1.51475	+	3.31685i	1.51475	+	3.31685i
$344$	−0.205996	−	1.43273i	−0.205996	−	1.43273i
$345$	0.154218	−	0.445585i	0.154218	−	0.445585i
$346$		0			0
$347$	0.975950	+	1.37053i	0.975950	+	1.37053i	0.928368	+	0.371662i	$0.121212\pi$
$347$	0.975950	+	1.37053i	0.975950	+	1.37053i	0.0475819	+	0.998867i	$0.484848\pi$
$348$	0.307040	−	0.0293188i	0.307040	−	0.0293188i
$349$	−1.38884	+	0.407799i	−1.38884	+	0.407799i	−0.888835	−	0.458227i	$-0.848485\pi$
$349$	−1.38884	+	0.407799i	−1.38884	+	0.407799i	−0.500000	+	0.866025i	$0.666667\pi$
$350$	−0.279486	+	1.94387i	−0.279486	+	1.94387i
$351$		0			0
$352$		0			0
$353$		0			0		−0.723734	−	0.690079i	$-0.757576\pi$
$353$		0			0		0.723734	+	0.690079i	$0.242424\pi$
$354$		0			0
$355$		0			0
$356$	0.252989	−	0.130425i	0.252989	−	0.130425i
$357$		0			0
$358$		0			0
$359$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$359$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$360$	−0.323056	+	0.707394i	−0.323056	+	0.707394i
$361$	0.723734	−	0.690079i	0.723734	−	0.690079i
$362$	−1.61435	−	1.03748i	−1.61435	−	1.03748i
$363$	0.273507	−	0.384087i	0.273507	−	0.384087i
$364$		0			0
$365$		0			0
$366$	−0.789740	−	0.0754110i	−0.789740	−	0.0754110i
$367$	−1.54370	+	0.297523i	−1.54370	+	0.297523i	−0.888835	−	0.458227i	$-0.848485\pi$
$367$	−1.54370	+	0.297523i	−1.54370	+	0.297523i	−0.654861	+	0.755750i	$0.727273\pi$
$368$	0.786053	+	0.618159i	0.786053	+	0.618159i
$369$	−1.21705	−	0.957095i	−1.21705	−	0.957095i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$373$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$374$		0			0
$375$	0.396666	+	0.254922i	0.396666	+	0.254922i
$376$	0.839614	−	0.800570i	0.839614	−	0.800570i
$377$		0			0
$378$	1.57943	+	0.463763i	1.57943	+	0.463763i
$379$		0			0		−0.981929	−	0.189251i	$-0.939394\pi$
$379$		0			0		0.981929	+	0.189251i	$0.0606061\pi$
$380$		0			0
$381$	−0.0398833	+	0.0205613i	−0.0398833	+	0.0205613i
$382$		0			0
$383$	1.07701	−	0.431171i	1.07701	−	0.431171i	0.235759	−	0.971812i	$-0.424242\pi$
$383$	1.07701	−	0.431171i	1.07701	−	0.431171i	0.841254	+	0.540641i	$0.181818\pi$
$384$	0.341254	+	0.325385i	0.341254	+	0.325385i
$385$		0			0
$386$		0			0
$387$	0.160197	−	1.11420i	0.160197	−	1.11420i
$388$		0			0
$389$	1.56499	−	0.149438i	1.56499	−	0.149438i	0.723734	−	0.690079i	$-0.242424\pi$
$389$	1.56499	−	0.149438i	1.56499	−	0.149438i	0.841254	+	0.540641i	$0.181818\pi$
$390$		0			0
$391$		0			0
$392$	−0.934347	+	2.69962i	−0.934347	+	2.69962i
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$397$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$398$		0			0
$399$		0			0
$400$	−0.786053	+	0.618159i	−0.786053	+	0.618159i
$401$	1.96386			1.96386			0.981929	−	0.189251i	$-0.0606061\pi$
$401$	1.96386			1.96386			0.981929	+	0.189251i	$0.0606061\pi$
$402$	0.341254	−	0.325385i	0.341254	−	0.325385i
$403$		0			0
$404$	0.223734	−	0.175946i	0.223734	−	0.175946i
$405$	−0.250447	+	0.289031i	−0.250447	+	0.289031i
$406$	−0.302863	+	1.24842i	−0.302863	+	1.24842i
$407$		0			0
$408$		0			0
$409$	−1.78153	−	0.713215i	−1.78153	−	0.713215i	−0.995472	−	0.0950560i	$-0.969697\pi$
$409$	−1.78153	−	0.713215i	−1.78153	−	0.713215i	−0.786053	−	0.618159i	$-0.787879\pi$
$410$	−0.827068	−	1.81103i	−0.827068	−	1.81103i
$411$		0			0
$412$	0.514186	−	1.48564i	0.514186	−	1.48564i
$413$		0			0
$414$	0.451093	+	0.633472i	0.451093	+	0.633472i
$415$	−1.84833	+	0.176494i	−1.84833	+	0.176494i
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		−0.235759	−	0.971812i	$-0.575758\pi$
$419$		0			0		0.235759	+	0.971812i	$0.424242\pi$
$420$	0.670173	+	0.639009i	0.670173	+	0.639009i
$421$	−1.21590	+	0.486774i	−1.21590	+	0.486774i	−0.888835	−	0.458227i	$-0.848485\pi$
$421$	−1.21590	+	0.486774i	−1.21590	+	0.486774i	−0.327068	+	0.945001i	$0.606061\pi$
$422$		0			0
$423$	0.801896	−	0.413406i	0.801896	−	0.413406i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	1.37262	−	3.00561i	1.37262	−	3.00561i
$428$	0.601300	−	0.573338i	0.601300	−	0.573338i
$429$		0			0
$430$	0.839614	−	1.17907i	0.839614	−	1.17907i
$431$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$431$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$432$	0.419102	+	0.725906i	0.419102	+	0.725906i
$433$		0			0		−0.995472	−	0.0950560i	$-0.969697\pi$
$433$		0			0		0.995472	+	0.0950560i	$0.0303030\pi$
$434$		0			0
$435$	0.242448	+	0.190663i	0.242448	+	0.190663i
$436$	1.23576	+	0.971812i	1.23576	+	0.971812i
$437$		0			0
$438$		0			0
$439$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$439$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$440$		0			0
$441$	−1.28865	+	1.80966i	−1.28865	+	1.80966i
$442$		0			0
$443$	−0.473420	+	0.451405i	−0.473420	+	0.451405i	−0.888835	−	0.458227i	$-0.848485\pi$
$443$	−0.473420	+	0.451405i	−0.473420	+	0.451405i	0.415415	+	0.909632i	$0.363636\pi$
$444$		0			0
$445$	0.273100	+	0.0801894i	0.273100	+	0.0801894i
$446$	1.65210	+	0.318417i	1.65210	+	0.318417i
$447$	0.614761	+	0.709472i	0.614761	+	0.709472i
$448$	−1.74555	+	0.899892i	−1.74555	+	0.899892i
$449$	−0.379436	−	1.09631i	−0.379436	−	1.09631i	−0.959493	−	0.281733i	$-0.909091\pi$
$449$	−0.379436	−	1.09631i	−0.379436	−	1.09631i	0.580057	−	0.814576i	$-0.303030\pi$
$450$	−0.721965	+	0.289031i	−0.721965	+	0.289031i
$451$		0			0
$452$		0			0
$453$		0			0
$454$	0.0405070	−	0.281733i	0.0405070	−	0.281733i
$455$		0			0
$456$		0			0
$457$		0			0		−0.580057	−	0.814576i	$-0.696970\pi$
$457$		0			0		0.580057	+	0.814576i	$0.303030\pi$
$458$	0.00452808	+	0.0950560i	0.00452808	+	0.0950560i
$459$		0			0
$460$	0.142315	+	0.989821i	0.142315	+	0.989821i
$461$	0.771316	+	1.68895i	0.771316	+	1.68895i	0.723734	+	0.690079i	$0.242424\pi$
$461$	0.771316	+	1.68895i	0.771316	+	1.68895i	0.0475819	+	0.998867i	$0.484848\pi$
$462$		0			0
$463$	−0.0913090	+	1.91681i	−0.0913090	+	1.91681i	0.235759	+	0.971812i	$0.424242\pi$
$463$	−0.0913090	+	1.91681i	−0.0913090	+	1.91681i	−0.327068	+	0.945001i	$0.606061\pi$
$464$	−0.550294	+	0.353653i	−0.550294	+	0.353653i
$465$		0			0
$466$		0			0
$467$	−0.0748038	+	0.0588264i	−0.0748038	+	0.0588264i	−0.654861	−	0.755750i	$-0.727273\pi$
$467$	−0.0748038	+	0.0588264i	−0.0748038	+	0.0588264i	0.580057	+	0.814576i	$0.303030\pi$
$468$		0			0
$469$	0.815816	+	1.78639i	0.815816	+	1.78639i
$470$	1.16011			1.16011
$471$		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		0.327068	−	0.945001i	$-0.393939\pi$
$479$		0			0		−0.327068	+	0.945001i	$0.606061\pi$
$480$	0.0224357	+	0.470984i	0.0224357	+	0.470984i
$481$		0			0
$482$	1.56499	−	0.149438i	1.56499	−	0.149438i
$483$	0.888485	−	0.260883i	0.888485	−	0.260883i
$484$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$485$		0			0
$486$	0.240128	+	0.989821i	0.240128	+	0.989821i
$487$	1.34378	+	1.28129i	1.34378	+	1.28129i	0.928368	+	0.371662i	$0.121212\pi$
$487$	1.34378	+	1.28129i	1.34378	+	1.28129i	0.415415	+	0.909632i	$0.363636\pi$
$488$	1.56199	−	0.625325i	1.56199	−	0.625325i
$489$	0.295943	+	0.855071i	0.295943	+	0.855071i
$490$	−2.53917	+	1.30903i	−2.53917	+	1.30903i
$491$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$491$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$492$	−0.921801	−	0.177663i	−0.921801	−	0.177663i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−0.437742	+	0.758192i	−0.437742	+	0.758192i
$499$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$499$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$500$	−0.995472	−	0.0950560i	−0.995472	−	0.0950560i
$501$	−0.606397	+	0.116873i	−0.606397	+	0.116873i
$502$		0			0
$503$	1.56499	+	1.23072i	1.56499	+	1.23072i	0.841254	+	0.540641i	$0.181818\pi$
$503$	1.56499	+	1.23072i	1.56499	+	1.23072i	0.723734	+	0.690079i	$0.242424\pi$
$504$	−1.49964	+	0.289031i	−1.49964	+	0.289031i
$505$	0.283341	+	0.0270558i	0.283341	+	0.0270558i
$506$		0			0
$507$	−0.235759	+	0.408346i	−0.235759	+	0.408346i
$508$	0.0552004	−	0.0775182i	0.0552004	−	0.0775182i
$509$	−1.10181	−	0.708089i	−1.10181	−	0.708089i	−0.142315	−	0.989821i	$-0.545455\pi$
$509$	−1.10181	−	0.708089i	−1.10181	−	0.708089i	−0.959493	+	0.281733i	$0.909091\pi$
$510$		0			0
$511$		0			0
$512$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$513$		0			0
$514$		0			0
$515$	1.39734	−	0.720381i	1.39734	−	0.720381i
$516$	−0.223226	−	0.644970i	−0.223226	−	0.644970i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	0.142315	−	0.989821i	0.142315	−	0.989821i	−0.786053	−	0.618159i	$-0.787879\pi$
$521$	0.142315	−	0.989821i	0.142315	−	0.989821i	0.928368	−	0.371662i	$-0.121212\pi$
$522$	−0.488096	+	0.143318i	−0.488096	+	0.143318i
$523$	−1.44091	+	0.137591i	−1.44091	+	0.137591i	−0.786053	−	0.618159i	$-0.787879\pi$
$523$	−1.44091	+	0.137591i	−1.44091	+	0.137591i	−0.654861	+	0.755750i	$0.727273\pi$
$524$		0			0
$525$	0.0440606	+	0.924945i	0.0440606	+	0.924945i
$526$	0.581419	−	1.67990i	0.581419	−	1.67990i
$527$		0			0
$528$		0			0
$529$		0			0
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$	0.105495	−	0.0829619i	0.105495	−	0.0829619i
$535$	0.830830			0.830830
$536$	−0.327068	+	0.945001i	−0.327068	+	0.945001i
$537$		0			0
$538$	1.50842	−	1.18624i	1.50842	−	1.18624i
$539$		0			0
$540$	−0.197614	+	0.814576i	−0.197614	+	0.814576i
$541$	1.21769	−	0.782560i	1.21769	−	0.782560i	0.235759	−	0.971812i	$-0.424242\pi$
$541$	1.21769	−	0.782560i	1.21769	−	0.782560i	0.981929	+	0.189251i	$0.0606061\pi$
$542$		0			0
$543$	−0.840021	−	0.336294i	−0.840021	−	0.336294i
$544$		0			0
$545$	0.223734	+	1.55610i	0.223734	+	1.55610i
$546$		0			0
$547$	0.00452808	+	0.0950560i	0.00452808	+	0.0950560i	1.00000			$0$
$547$	0.00452808	+	0.0950560i	0.00452808	+	0.0950560i	−0.995472	+	0.0950560i	$0.969697\pi$
$548$		0			0
$549$	1.30251	−	0.124375i	1.30251	−	0.124375i
$550$		0			0
$551$		0			0
$552$	0.419102	+	0.216062i	0.419102	+	0.216062i
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$		0			0		0.888835	−	0.458227i	$-0.151515\pi$
$557$		0			0		−0.888835	+	0.458227i	$0.848485\pi$
$558$		0			0
$559$		0			0
$560$	−1.88431	−	0.553283i	−1.88431	−	0.553283i
$561$		0			0
$562$	0.839614	−	0.800570i	0.839614	−	0.800570i
$563$	1.21769	+	0.782560i	1.21769	+	0.782560i	0.981929	−	0.189251i	$-0.0606061\pi$
$563$	1.21769	+	0.782560i	1.21769	+	0.782560i	0.235759	+	0.971812i	$0.424242\pi$
$564$	0.317299	−	0.445585i	0.317299	−	0.445585i
$565$		0			0
$566$	0.888835	+	1.53951i	0.888835	+	1.53951i
$567$	−0.747662	−	0.0713931i	−0.747662	−	0.0713931i
$568$		0			0
$569$	1.02951	+	0.809616i	1.02951	+	0.809616i	0.981929	−	0.189251i	$-0.0606061\pi$
$569$	1.02951	+	0.809616i	1.02951	+	0.809616i	0.0475819	+	0.998867i	$0.484848\pi$
$570$		0			0
$571$		0			0		0.981929	−	0.189251i	$-0.0606061\pi$
$571$		0			0		−0.981929	+	0.189251i	$0.939394\pi$
$572$		0			0
$573$		0			0
$574$	1.95496	−	3.38610i	1.95496	−	3.38610i
$575$	−0.580057	+	0.814576i	−0.580057	+	0.814576i
$576$	−0.654218	−	0.420441i	−0.654218	−	0.420441i
$577$		0			0		0.723734	−	0.690079i	$-0.242424\pi$
$577$		0			0		−0.723734	+	0.690079i	$0.757576\pi$
$578$	0.415415	−	0.909632i	0.415415	−	0.909632i
$579$		0			0
$580$	−0.642315	−	0.123796i	−0.642315	−	0.123796i
$581$	−2.38786	−	2.75574i	−2.38786	−	2.75574i
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−0.738471	−	0.380708i	−0.738471	−	0.380708i	0.0475819	−	0.998867i	$-0.484848\pi$
$587$	−0.738471	−	0.380708i	−0.738471	−	0.380708i	−0.786053	+	0.618159i	$0.787879\pi$
$588$	−0.191698	+	1.33329i	−0.191698	+	1.33329i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$		0			0		0.327068	−	0.945001i	$-0.393939\pi$
$593$		0			0		−0.327068	+	0.945001i	$0.606061\pi$
$594$		0			0
$595$		0			0
$596$	−1.84833	−	0.739959i	−1.84833	−	0.739959i
$597$		0			0
$598$		0			0
$599$		0			0		0.235759	−	0.971812i	$-0.424242\pi$
$599$		0			0		−0.235759	+	0.971812i	$0.575758\pi$
$600$	−0.308779	+	0.356349i	−0.308779	+	0.356349i
$601$	−1.13779	+	0.894765i	−1.13779	+	0.894765i	−0.995472	−	0.0950560i	$-0.969697\pi$
$601$	−1.13779	+	0.894765i	−1.13779	+	0.894765i	−0.142315	+	0.989821i	$0.545455\pi$
$602$	2.84262			2.84262
$603$	−0.451093	+	0.633472i	−0.451093	+	0.633472i
$604$		0			0
$605$	−0.786053	+	0.618159i	−0.786053	+	0.618159i
$606$	0.0878875	−	0.101428i	0.0878875	−	0.101428i
$607$	0.273507	−	1.12741i	0.273507	−	1.12741i	−0.654861	−	0.755750i	$-0.727273\pi$
$607$	0.273507	−	1.12741i	0.273507	−	1.12741i	0.928368	−	0.371662i	$-0.121212\pi$
$608$		0			0
$609$	−0.0288216	+	0.605040i	−0.0288216	+	0.605040i
$610$	1.56199	+	0.625325i	1.56199	+	0.625325i
$611$		0			0
$612$		0			0
$613$		0			0		0.327068	−	0.945001i	$-0.393939\pi$
$613$		0			0		−0.327068	+	0.945001i	$0.606061\pi$
$614$	0.0395325	+	0.829889i	0.0395325	+	0.829889i
$615$	−0.544537	−	0.764696i	−0.544537	−	0.764696i
$616$		0			0
$617$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$617$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$618$	0.105495	−	0.733731i	0.105495	−	0.733731i
$619$		0			0		−0.888835	−	0.458227i	$-0.848485\pi$
$619$		0			0		0.888835	+	0.458227i	$0.151515\pi$
$620$		0			0
$621$	0.606636	+	0.578427i	0.606636	+	0.578427i
$622$		0			0
$623$	0.182822	+	0.528229i	0.182822	+	0.528229i
$624$		0			0
$625$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$	−1.28479	−	0.825685i	−1.28479	−	0.825685i
$631$		0			0		0.580057	−	0.814576i	$-0.303030\pi$
$631$		0			0		−0.580057	+	0.814576i	$0.696970\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	0.0934441	−	0.0180099i	0.0934441	−	0.0180099i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$641$	0.888835	−	1.53951i	0.888835	−	1.53951i	0.0475819	−	0.998867i	$-0.484848\pi$
$641$	0.888835	−	1.53951i	0.888835	−	1.53951i	0.841254	−	0.540641i	$-0.181818\pi$
$642$	0.227238	−	0.319111i	0.227238	−	0.319111i
$643$	−0.550294	−	0.353653i	−0.550294	−	0.353653i	0.235759	−	0.971812i	$-0.424242\pi$
$643$	−0.550294	−	0.353653i	−0.550294	−	0.353653i	−0.786053	+	0.618159i	$0.787879\pi$
$644$	−1.42131	+	1.35522i	−1.42131	+	1.35522i
$645$	0.283524	−	0.620830i	0.283524	−	0.620830i
$646$		0			0
$647$	1.13915	+	0.219553i	1.13915	+	0.219553i	0.723734	−	0.690079i	$-0.242424\pi$
$647$	1.13915	+	0.219553i	1.13915	+	0.219553i	0.415415	+	0.909632i	$0.363636\pi$
$648$	−0.250447	−	0.289031i	−0.250447	−	0.289031i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	−1.38884	−	1.32425i	−1.38884	−	1.32425i
$653$		0			0		−0.235759	−	0.971812i	$-0.575758\pi$
$653$		0			0		0.235759	+	0.971812i	$0.424242\pi$
$654$	0.658873	+	0.339672i	0.658873	+	0.339672i
$655$		0			0
$656$	1.91030	−	0.560914i	1.91030	−	0.560914i
$657$		0			0
$658$	1.32154	+	1.85585i	1.32154	+	1.85585i
$659$		0			0		−0.0475819	−	0.998867i	$-0.515152\pi$
$659$		0			0		0.0475819	+	0.998867i	$0.484848\pi$
$660$		0			0
$661$	0.186393	+	1.29639i	0.186393	+	1.29639i	0.841254	+	0.540641i	$0.181818\pi$
$661$	0.186393	+	1.29639i	0.186393	+	1.29639i	−0.654861	+	0.755750i	$0.727273\pi$
$662$		0			0
$663$		0			0
$664$	0.0883470	−	1.85463i	0.0883470	−	1.85463i
$665$		0			0
$666$		0			0
$667$	−0.428368	+	0.494363i	−0.428368	+	0.494363i
$668$	1.02951	−	0.809616i	1.02951	−	0.809616i
$669$	0.793332			0.793332
$670$	−0.888835	+	0.458227i	−0.888835	+	0.458227i
$671$		0			0
$672$	−0.727880	+	0.572411i	−0.727880	+	0.572411i
$673$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$673$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$674$		0			0
$675$	−0.705142	+	0.453167i	−0.705142	+	0.453167i
$676$	0.0475819	−	0.998867i	0.0475819	−	0.998867i
$677$		0			0		−0.928368	−	0.371662i	$-0.878788\pi$
$677$		0			0		0.928368	+	0.371662i	$0.121212\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−0.00638587	−	0.134056i	−0.00638587	−	0.134056i
$682$		0			0
$683$	−0.827068	+	0.0789754i	−0.827068	+	0.0789754i	−0.500000	−	0.866025i	$-0.666667\pi$
$683$	−0.827068	+	0.0789754i	−0.827068	+	0.0789754i	−0.327068	+	0.945001i	$0.606061\pi$
$684$		0			0
$685$		0			0
$686$	−3.24102	−	1.67086i	−3.24102	−	1.67086i
$687$	0.0105788	+	0.0436066i	0.0105788	+	0.0436066i
$688$	1.04758	+	0.998867i	1.04758	+	0.998867i
$689$		0			0
$690$	0.154218	+	0.445585i	0.154218	+	0.445585i
$691$		0			0		0.888835	−	0.458227i	$-0.151515\pi$
$691$		0			0		−0.888835	+	0.458227i	$0.848485\pi$
$692$		0			0
$693$		0			0
$694$	−1.61435	−	0.474017i	−1.61435	−	0.474017i
$695$		0			0
$696$	−0.223226	+	0.212846i	−0.223226	+	0.212846i
$697$		0			0
$698$	0.839614	−	1.17907i	0.839614	−	1.17907i
$699$		0			0
$700$	−0.981929	−	1.70075i	−0.981929	−	1.70075i
$701$	0.995472	+	0.0950560i	0.995472	+	0.0950560i	0.580057	−	0.814576i	$-0.303030\pi$
$701$	0.995472	+	0.0950560i	0.995472	+	0.0950560i	0.415415	+	0.909632i	$0.363636\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	0.537129	−	0.103523i	0.537129	−	0.103523i
$706$		0			0
$707$	0.279486	+	0.484084i	0.279486	+	0.484084i
$708$		0			0
$709$	−0.580057	+	0.814576i	−0.580057	+	0.814576i	−0.995472	−	0.0950560i	$-0.969697\pi$
$709$	−0.580057	+	0.814576i	−0.580057	+	0.814576i	0.415415	+	0.909632i	$0.363636\pi$
$710$		0			0
$711$		0			0
$712$	−0.118239	+	0.258908i	−0.118239	+	0.258908i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		−0.723734	−	0.690079i	$-0.757576\pi$
$719$		0			0		0.723734	+	0.690079i	$0.242424\pi$
$720$	−0.183343	−	0.755750i	−0.183343	−	0.755750i
$721$	2.74418	+	1.41473i	2.74418	+	1.41473i
$722$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$723$	0.711249	−	0.208842i	0.711249	−	0.208842i
$724$	1.91030	−	0.182411i	1.91030	−	0.182411i
$725$	−0.379436	−	0.532843i	−0.379436	−	0.532843i
$726$	0.0224357	+	0.470984i	0.0224357	+	0.470984i
$727$	0.651174	−	1.88144i	0.651174	−	1.88144i	0.235759	−	0.971812i	$-0.424242\pi$
$727$	0.651174	−	1.88144i	0.651174	−	1.88144i	0.415415	−	0.909632i	$-0.363636\pi$
$728$		0			0
$729$	0.0406331	+	0.0889741i	0.0406331	+	0.0889741i
$730$		0			0
$731$		0			0
$732$	0.667393	−	0.428908i	0.667393	−	0.428908i
$733$		0			0		0.235759	−	0.971812i	$-0.424242\pi$
$733$		0			0		−0.235759	+	0.971812i	$0.575758\pi$
$734$	1.02951	−	1.18812i	1.02951	−	1.18812i
$735$	−1.05882	+	0.832661i	−1.05882	+	0.832661i
$736$	−1.00000			−1.00000
$737$		0			0
$738$	1.54830			1.54830
$739$		0			0		0.786053	−	0.618159i	$-0.212121\pi$
$739$		0			0		−0.786053	+	0.618159i	$0.787879\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−0.0913090	+	1.91681i	−0.0913090	+	1.91681i	0.235759	+	0.971812i	$0.424242\pi$
$743$	−0.0913090	+	1.91681i	−0.0913090	+	1.91681i	−0.327068	+	0.945001i	$0.606061\pi$
$744$		0			0
$745$	−0.827068	−	1.81103i	−0.827068	−	1.81103i
$746$		0			0
$747$	0.472263	−	1.36451i	0.472263	−	1.36451i
$748$		0			0
$749$	0.946439	+	1.32909i	0.946439	+	1.32909i
$750$	−0.469383	+	0.0448206i	−0.469383	+	0.0448206i
$751$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$751$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$752$	−0.165101	+	1.14831i	−0.165101	+	1.14831i
$753$		0			0
$754$		0			0
$755$		0			0
$756$	−1.52820	+	0.611798i	−1.52820	+	0.611798i
$757$		0			0		−0.327068	−	0.945001i	$-0.606061\pi$
$757$		0			0		0.327068	+	0.945001i	$0.393939\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	1.84125	+	0.540641i	1.84125	+	0.540641i	1.00000			$0$
$761$	1.84125	+	0.540641i	1.84125	+	0.540641i	0.841254	+	0.540641i	$0.181818\pi$
$762$	0.0186403	−	0.0408165i	0.0186403	−	0.0408165i
$763$	−2.23445	+	2.13054i	−2.23445	+	2.13054i
$764$		0			0
$765$		0			0
$766$	−0.580057	+	1.00469i	−0.580057	+	1.00469i
$767$		0			0
$768$	−0.469383	−	0.0448206i	−0.469383	−	0.0448206i
$769$	0.462997	−	0.0892353i	0.462997	−	0.0892353i	0.0475819	−	0.998867i	$-0.484848\pi$
$769$	0.462997	−	0.0892353i	0.462997	−	0.0892353i	0.415415	+	0.909632i	$0.363636\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0		−0.995472	−	0.0950560i	$-0.969697\pi$
$773$		0			0		0.995472	+	0.0950560i	$0.0303030\pi$
$774$	0.562827	+	0.974845i	0.562827	+	0.974845i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	−1.13779	+	1.08488i	−1.13779	+	1.08488i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−0.487348	+	0.251245i	−0.487348	+	0.251245i
$784$	−0.934347	−	2.69962i	−0.934347	−	2.69962i
$785$		0			0
$786$		0			0
$787$	0.0224357	+	0.0924813i	0.0224357	+	0.0924813i	0.981929	−	0.189251i	$-0.0606061\pi$
$787$	0.0224357	+	0.0924813i	0.0224357	+	0.0924813i	−0.959493	+	0.281733i	$0.909091\pi$
$788$		0			0
$789$	0.119289	−	0.829672i	0.119289	−	0.829672i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.928368	−	0.371662i	$-0.878788\pi$
$797$		0			0		0.928368	+	0.371662i	$0.121212\pi$
$798$		0			0
$799$		0			0
$800$	0.235759	−	0.971812i	0.235759	−	0.971812i
$801$	−0.144952	+	0.167284i	−0.144952	+	0.167284i
$802$	−1.54370	+	1.21398i	−1.54370	+	1.21398i
$803$		0			0
$804$	−0.0671040	+	0.466718i	−0.0671040	+	0.466718i
$805$	−1.96386			−1.96386
$806$		0			0
$807$	0.592542	−	0.683830i	0.592542	−	0.683830i
$808$	−0.0671040	+	0.276606i	−0.0671040	+	0.276606i
$809$	0.0800569	−	0.0514495i	0.0800569	−	0.0514495i	−0.500000	−	0.866025i	$-0.666667\pi$
$809$	0.0800569	−	0.0514495i	0.0800569	−	0.0514495i	0.580057	+	0.814576i	$0.303030\pi$
$810$	0.0181974	−	0.382010i	0.0181974	−	0.382010i
$811$		0			0		−0.928368	−	0.371662i	$-0.878788\pi$
$811$		0			0		0.928368	+	0.371662i	$0.121212\pi$
$812$	−0.533654	−	1.16854i	−0.533654	−	1.16854i
$813$		0			0
$814$		0			0
$815$	−0.0913090	−	1.91681i	−0.0913090	−	1.91681i
$816$		0			0
$817$		0			0
$818$	1.84125	−	0.540641i	1.84125	−	0.540641i
$819$		0			0
$820$	1.76962	+	0.912303i	1.76962	+	0.912303i
$821$	0.396666	+	1.63508i	0.396666	+	1.63508i	0.723734	+	0.690079i	$0.242424\pi$
$821$	0.396666	+	1.63508i	0.396666	+	1.63508i	−0.327068	+	0.945001i	$0.606061\pi$
$822$		0			0
$823$	−0.607279	+	0.243118i	−0.607279	+	0.243118i	−0.654861	−	0.755750i	$-0.727273\pi$
$823$	−0.607279	+	0.243118i	−0.607279	+	0.243118i	0.0475819	+	0.998867i	$0.484848\pi$
$824$	0.514186	+	1.48564i	0.514186	+	1.48564i
$825$		0			0
$826$		0			0
$827$	−1.95496	−	0.376789i	−1.95496	−	0.376789i	−0.995472	−	0.0950560i	$-0.969697\pi$
$827$	−1.95496	−	0.376789i	−1.95496	−	0.376789i	−0.959493	−	0.281733i	$-0.909091\pi$
$828$	−0.746170	−	0.219095i	−0.746170	−	0.219095i
$829$	0.698939	−	1.53046i	0.698939	−	1.53046i	−0.142315	−	0.989821i	$-0.545455\pi$
$829$	0.698939	−	1.53046i	0.698939	−	1.53046i	0.841254	−	0.540641i	$-0.181818\pi$
$830$	1.34378	−	1.28129i	1.34378	−	1.28129i
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	1.30379	+	0.124497i	1.30379	+	0.124497i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		0.981929	−	0.189251i	$-0.0606061\pi$
$839$		0			0		−0.981929	+	0.189251i	$0.939394\pi$
$840$	−0.921801	−	0.0880213i	−0.921801	−	0.0880213i
$841$	0.286053	+	0.495458i	0.286053	+	0.495458i
$842$	0.654861	−	1.13425i	0.654861	−	1.13425i
$843$	0.317299	−	0.445585i	0.317299	−	0.445585i
$844$		0			0
$845$	0.723734	−	0.690079i	0.723734	−	0.690079i
$846$	−0.374782	+	0.820658i	−0.374782	+	0.820658i
$847$	−1.88431	−	0.553283i	−1.88431	−	0.553283i
$848$		0			0
$849$	0.548907	+	0.633472i	0.548907	+	0.633472i
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		−0.723734	−	0.690079i	$-0.757576\pi$
$853$		0			0		0.723734	+	0.690079i	$0.242424\pi$
$854$	0.778996	+	3.21106i	0.778996	+	3.21106i
$855$		0			0
$856$	−0.118239	+	0.822373i	−0.118239	+	0.822373i
$857$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$857$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$858$		0			0
$859$		0			0		−0.580057	−	0.814576i	$-0.696970\pi$
$859$		0			0		0.580057	+	0.814576i	$0.303030\pi$
$860$	0.0688733	+	1.44583i	0.0688733	+	1.44583i
$861$	0.602983	−	1.74221i	0.602983	−	1.74221i
$862$		0			0
$863$	−0.738471	−	1.61703i	−0.738471	−	1.61703i	−0.786053	−	0.618159i	$-0.787879\pi$
$863$	−0.738471	−	1.61703i	−0.738471	−	1.61703i	0.0475819	−	0.998867i	$-0.484848\pi$
$864$	−0.778161	−	0.311529i	−0.778161	−	0.311529i
$865$		0			0
$866$		0			0
$867$	0.111165	−	0.458227i	0.111165	−	0.458227i
$868$		0			0
$869$		0			0
$870$	−0.308437			−0.308437
$871$		0			0
$872$	−1.57211			−1.57211
$873$		0			0
$874$		0			0
$875$	0.462997	−	1.90850i	0.462997	−	1.90850i
$876$		0			0
$877$		0			0		0.0475819	−	0.998867i	$-0.484848\pi$
$877$		0			0		−0.0475819	+	0.998867i	$0.515152\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	0.327068	−	0.945001i	0.327068	−	0.945001i	−0.654861	−	0.755750i	$-0.727273\pi$
$881$	0.327068	−	0.945001i	0.327068	−	0.945001i	0.981929	−	0.189251i	$-0.0606061\pi$
$882$	−0.105708	−	2.21908i	−0.105708	−	2.21908i
$883$	0.481929	+	0.676774i	0.481929	+	0.676774i	0.981929	−	0.189251i	$-0.0606061\pi$
$883$	0.481929	+	0.676774i	0.481929	+	0.676774i	−0.500000	+	0.866025i	$0.666667\pi$
$884$		0			0
$885$		0			0
$886$	0.0930932	−	0.647478i	0.0930932	−	0.647478i
$887$	0.581419	+	0.299742i	0.581419	+	0.299742i	0.723734	−	0.690079i	$-0.242424\pi$
$887$	0.581419	+	0.299742i	0.581419	+	0.299742i	−0.142315	+	0.989821i	$0.545455\pi$
$888$		0			0
$889$	0.135257	+	0.128968i	0.135257	+	0.128968i
$890$	−0.264241	+	0.105786i	−0.264241	+	0.105786i
$891$		0			0
$892$	−1.49547	+	0.770969i	−1.49547	+	0.770969i
$893$		0			0
$894$	−0.921801	−	0.177663i	−0.921801	−	0.177663i
$895$		0			0
$896$	0.815816	−	1.78639i	0.815816	−	1.78639i
$897$		0			0
$898$	0.975950	+	0.627205i	0.975950	+	0.627205i
$899$		0			0
$900$	0.388835	−	0.673483i	0.388835	−	0.673483i
$901$		0			0
$902$		0			0
$903$	1.31612	−	0.253662i	1.31612	−	0.253662i
$904$		0			0
$905$	1.50842	+	1.18624i	1.50842	+	1.18624i
$906$		0			0
$907$	−1.67489	−	0.159932i	−1.67489	−	0.159932i	−0.786053	−	0.618159i	$-0.787879\pi$
$907$	−1.67489	−	0.159932i	−1.67489	−	0.159932i	−0.888835	+	0.458227i	$0.848485\pi$
$908$	0.142315	+	0.246497i	0.142315	+	0.246497i
$909$	−0.110674	+	0.191693i	−0.110674	+	0.191693i
$910$		0			0
$911$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$911$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	0.778996	+	0.150139i	0.778996	+	0.150139i
$916$	−0.0623191	−	0.0719200i	−0.0623191	−	0.0719200i
$917$		0			0
$918$		0			0
$919$		0			0		0.928368	−	0.371662i	$-0.121212\pi$
$919$		0			0		−0.928368	+	0.371662i	$0.878788\pi$
$920$	−0.723734	−	0.690079i	−0.723734	−	0.690079i
$921$	0.0923588	+	0.380708i	0.0923588	+	0.380708i
$922$	−1.65033	−	0.850806i	−1.65033	−	0.850806i
$923$		0			0
$924$		0			0
$925$		0			0
$926$	−1.11312	−	1.56316i	−1.11312	−	1.56316i
$927$	0.0581728	+	1.22120i	0.0581728	+	1.22120i
$928$	0.213947	−	0.618159i	0.213947	−	0.618159i
$929$	−0.264241	−	1.83784i	−0.264241	−	1.83784i	−0.500000	−	0.866025i	$-0.666667\pi$
$929$	−0.264241	−	1.83784i	−0.264241	−	1.83784i	0.235759	−	0.971812i	$-0.424242\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$	0.0224357	−	0.0924813i	0.0224357	−	0.0924813i
$935$		0			0
$936$		0			0
$937$		0			0		1.00000			$0$
$937$		0			0		−1.00000			$\pi$
$938$	−1.74555	−	0.899892i	−1.74555	−	0.899892i
$939$		0			0
$940$	−0.911911	+	0.717135i	−0.911911	+	0.717135i
$941$	−0.544078	+	0.627899i	−0.544078	+	0.627899i	−0.959493	−	0.281733i	$-0.909091\pi$
$941$	−0.544078	+	0.627899i	−0.544078	+	0.627899i	0.415415	+	0.909632i	$0.363636\pi$
$942$		0			0
$943$	1.67489	−	1.07639i	1.67489	−	1.07639i
$944$		0			0
$945$	−1.52820	−	0.611798i	−1.52820	−	0.611798i
$946$		0			0
$947$	−0.205996	−	1.43273i	−0.205996	−	1.43273i	−0.786053	−	0.618159i	$-0.787879\pi$
$947$	−0.205996	−	1.43273i	−0.205996	−	1.43273i	0.580057	−	0.814576i	$-0.303030\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$953$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	−0.308779	−	0.356349i	−0.308779	−	0.356349i
$961$	0.981929	+	0.189251i	0.981929	+	0.189251i
$962$		0			0
$963$	−0.268405	+	0.587724i	−0.268405	+	0.587724i
$964$	−1.13779	+	1.08488i	−1.13779	+	1.08488i
$965$		0			0
$966$	−0.537129	+	0.754292i	−0.537129	+	0.754292i
$967$	−0.415415	+	0.719520i	−0.415415	+	0.719520i	−0.995472	−	0.0950560i	$-0.969697\pi$
$967$	−0.415415	+	0.719520i	−0.415415	+	0.719520i	0.580057	+	0.814576i	$0.303030\pi$
$968$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$969$		0			0
$970$		0			0
$971$		0			0		−0.786053	−	0.618159i	$-0.787879\pi$
$971$		0			0		0.786053	+	0.618159i	$0.212121\pi$
$972$	−0.800620	−	0.629615i	−0.800620	−	0.629615i
$973$		0			0
$974$	−1.84833	−	0.176494i	−1.84833	−	0.176494i
$975$		0			0
$976$	−0.841254	+	1.45709i	−0.841254	+	1.45709i
$977$		0			0		0.580057	−	0.814576i	$-0.303030\pi$
$977$		0			0		−0.580057	+	0.814576i	$0.696970\pi$
$978$	−0.761197	−	0.489191i	−0.761197	−	0.489191i
$979$		0			0
$980$	1.18673	−	2.59858i	1.18673	−	2.59858i
$981$	−1.17306	−	0.344441i	−1.17306	−	0.344441i
$982$		0			0
$983$	0.857685	+	0.989821i	0.857685	+	0.989821i	1.00000			$0$
$983$	0.857685	+	0.989821i	0.857685	+	0.989821i	−0.142315	+	0.989821i	$0.545455\pi$
$984$	0.834408	−	0.430167i	0.834408	−	0.430167i
$985$		0			0
$986$		0			0
$987$	0.777477	+	0.741323i	0.777477	+	0.741323i
$988$		0			0
$989$	1.28656	+	0.663268i	1.28656	+	0.663268i
$990$		0			0
$991$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$991$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$	−0.124594	−	0.866573i	−0.124594	−	0.866573i
$997$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$997$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1340.1.bl.b.1059.1	yes	20
4.3	odd	2		1340.1.bl.a.1059.1	yes	20
5.4	even	2		1340.1.bl.a.1059.1	yes	20
20.19	odd	2	CM	1340.1.bl.b.1059.1	yes	20
67.36	even	33	inner	1340.1.bl.b.639.1	yes	20
268.103	odd	66		1340.1.bl.a.639.1	✓	20
335.304	even	66		1340.1.bl.a.639.1	✓	20
1340.639	odd	66	inner	1340.1.bl.b.639.1	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1340.1.bl.a.639.1	✓	20	268.103	odd	66
1340.1.bl.a.639.1	✓	20	335.304	even	66
1340.1.bl.a.1059.1	yes	20	4.3	odd	2
1340.1.bl.a.1059.1	yes	20	5.4	even	2
1340.1.bl.b.639.1	yes	20	67.36	even	33	inner
1340.1.bl.b.639.1	yes	20	1340.639	odd	66	inner
1340.1.bl.b.1059.1	yes	20	1.1	even	1	trivial
1340.1.bl.b.1059.1	yes	20	20.19	odd	2	CM

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:	\( N \)	\(=\)	\( 1340 = 2^{2} \cdot 5 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1340.bl (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.786053 + 0.618159i) q^{2} +(-0.308779 + 0.356349i) q^{3} +(0.235759 - 0.971812i) q^{4} +(0.841254 - 0.540641i) q^{5} +(0.0224357 - 0.470984i) q^{6} +(1.82318 + 0.729892i) q^{7} +(0.415415 + 0.909632i) q^{8} +(0.110674 + 0.769755i) q^{9} +O(q^{10})\)	\(q+(-0.786053 + 0.618159i) q^{2} +(-0.308779 + 0.356349i) q^{3} +(0.235759 - 0.971812i) q^{4} +(0.841254 - 0.540641i) q^{5} +(0.0224357 - 0.470984i) q^{6} +(1.82318 + 0.729892i) q^{7} +(0.415415 + 0.909632i) q^{8} +(0.110674 + 0.769755i) q^{9} +(-0.327068 + 0.945001i) q^{10} +(0.273507 + 0.384087i) q^{12} +(-1.88431 + 0.553283i) q^{14} +(-0.0671040 + 0.466718i) q^{15} +(-0.888835 - 0.458227i) q^{16} +(-0.562827 - 0.536654i) q^{18} +(-0.327068 - 0.945001i) q^{20} +(-0.823056 + 0.424315i) q^{21} +(-0.981929 - 0.189251i) q^{23} +(-0.452418 - 0.132842i) q^{24} +(0.415415 - 0.909632i) q^{25} +(-0.705142 - 0.453167i) q^{27} +(1.13915 - 1.59971i) q^{28} +(0.327068 - 0.566498i) q^{29} +(-0.235759 - 0.408346i) q^{30} +(0.981929 - 0.189251i) q^{32} +(1.92837 - 0.371662i) q^{35} +(0.774150 + 0.0739223i) q^{36} +(0.841254 + 0.540641i) q^{40} +(-1.44091 + 1.37391i) q^{41} +(0.384672 - 0.842314i) q^{42} +(-1.38884 - 0.407799i) q^{43} +(0.509266 + 0.587724i) q^{45} +(0.888835 - 0.458227i) q^{46} +(-0.379436 - 1.09631i) q^{47} +(0.437742 - 0.175245i) q^{48} +(2.06752 + 1.97137i) q^{49} +(0.235759 + 0.971812i) q^{50} +(0.834408 - 0.0796763i) q^{54} +(0.0934441 + 1.96163i) q^{56} +(0.0930932 + 0.647478i) q^{58} +(0.437742 + 0.175245i) q^{60} +(0.0800569 - 1.68060i) q^{61} +(-0.360059 + 1.48418i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(0.723734 + 0.690079i) q^{67} +(0.370638 - 0.291473i) q^{69} +(-1.28605 + 1.48418i) q^{70} +(-0.654218 + 0.420441i) q^{72} +(0.195876 + 0.428908i) q^{75} +(-0.995472 + 0.0950560i) q^{80} +(-0.366951 + 0.107747i) q^{81} +(0.283341 - 1.97068i) q^{82} +(-1.65033 - 0.850806i) q^{83} +(0.218311 + 0.899892i) q^{84} +(1.34378 - 0.537970i) q^{86} +(0.100880 + 0.291473i) q^{87} +(0.186393 + 0.215109i) q^{89} +(-0.763617 - 0.147175i) q^{90} +(-0.415415 + 0.909632i) q^{92} +(0.975950 + 0.627205i) q^{94} +(-0.235759 + 0.408346i) q^{96} +(-2.84380 - 0.271550i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + q^{2} + 2 q^{3} + q^{4} - 2 q^{5} - q^{6} - q^{7} - 2 q^{8}+O(q^{10}) \) 20 * q + q^2 + 2 * q^3 + q^4 - 2 * q^5 - q^6 - q^7 - 2 * q^8	\( 20 q + q^{2} + 2 q^{3} + q^{4} - 2 q^{5} - q^{6} - q^{7} - 2 q^{8} + q^{10} - q^{12} + 2 q^{14} + 2 q^{15} + q^{16} + q^{20} - 10 q^{21} - q^{23} - 9 q^{24} - 2 q^{25} - 2 q^{27} - q^{28} - q^{29} - q^{30} + q^{32} + 21 q^{35} - 2 q^{40} - q^{41} + 20 q^{42} - 9 q^{43} - q^{46} - q^{47} - q^{48} + q^{50} + q^{54} - q^{56} + 2 q^{58} - q^{60} - 9 q^{61} - 11 q^{63} - 2 q^{64} + q^{67} + q^{69} - 9 q^{70} - 11 q^{72} + 2 q^{75} + q^{80} + 2 q^{81} + 2 q^{82} - q^{83} + q^{84} - q^{86} + q^{87} - 4 q^{89} + 2 q^{92} + 2 q^{94} - q^{96}+O(q^{100}) \) 20 * q + q^2 + 2 * q^3 + q^4 - 2 * q^5 - q^6 - q^7 - 2 * q^8 + q^10 - q^12 + 2 * q^14 + 2 * q^15 + q^16 + q^20 - 10 * q^21 - q^23 - 9 * q^24 - 2 * q^25 - 2 * q^27 - q^28 - q^29 - q^30 + q^32 + 21 * q^35 - 2 * q^40 - q^41 + 20 * q^42 - 9 * q^43 - q^46 - q^47 - q^48 + q^50 + q^54 - q^56 + 2 * q^58 - q^60 - 9 * q^61 - 11 * q^63 - 2 * q^64 + q^67 + q^69 - 9 * q^70 - 11 * q^72 + 2 * q^75 + q^80 + 2 * q^81 + 2 * q^82 - q^83 + q^84 - q^86 + q^87 - 4 * q^89 + 2 * q^92 + 2 * q^94 - q^96

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