LMFDB - Embedded newform 1340.1.bl.a.839.1

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			839.1
Root			$-0.786053 - 0.618159i$ of defining polynomial
Character	$\chi$	$=$	1340.839
Dual form			1340.1.bl.a.559.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.235759 + 0.971812i) q^{2} +(-0.252989 - 1.75958i) q^{3} +(-0.888835 - 0.458227i) q^{4} +(0.415415 - 0.909632i) q^{5} +(1.76962 + 0.168978i) q^{6} +(-1.34378 - 1.28129i) q^{7} +(0.654861 - 0.755750i) q^{8} +(-2.07261 + 0.608574i) q^{9} +O(q^{10})$	\(q+(-0.235759 + 0.971812i) q^{2} +(-0.252989 - 1.75958i) q^{3} +(-0.888835 - 0.458227i) q^{4} +(0.415415 - 0.909632i) q^{5} +(1.76962 + 0.168978i) q^{6} +(-1.34378 - 1.28129i) q^{7} +(0.654861 - 0.755750i) q^{8} +(-2.07261 + 0.608574i) q^{9} +(0.786053 + 0.618159i) q^{10} +(-0.581419 + 1.67990i) q^{12} +(1.56199 - 1.00383i) q^{14} +(-1.70566 - 0.500828i) q^{15} +(0.580057 + 0.814576i) q^{16} +(-0.102782 - 2.15767i) q^{18} +(-0.786053 + 0.618159i) q^{20} +(-1.91457 + 2.68864i) q^{21} +(0.928368 + 0.371662i) q^{23} +(-1.49547 - 0.961081i) q^{24} +(-0.654861 - 0.755750i) q^{25} +(0.856711 + 1.87593i) q^{27} +(0.607279 + 1.75462i) q^{28} +(0.786053 + 1.36148i) q^{29} +(0.888835 - 1.53951i) q^{30} +(-0.928368 + 0.371662i) q^{32} +(-1.72373 + 0.690079i) q^{35} +(2.12108 + 0.408804i) q^{36} +(-0.415415 - 0.909632i) q^{40} +(0.0934441 - 1.96163i) q^{41} +(-2.16148 - 2.49448i) q^{42} +(-0.0800569 - 0.0514495i) q^{43} +(-0.307416 + 2.13813i) q^{45} +(-0.580057 + 0.814576i) q^{46} +(-0.514186 + 0.404360i) q^{47} +(1.28656 - 1.22673i) q^{48} +(0.116455 + 2.44470i) q^{49} +(0.888835 - 0.458227i) q^{50} +(-2.02503 + 0.390293i) q^{54} +(-1.84833 + 0.176494i) q^{56} +(-1.50842 + 0.442913i) q^{58} +(1.28656 + 1.22673i) q^{60} +(-0.827068 - 0.0789754i) q^{61} +(3.56491 + 1.83784i) q^{63} +(-0.142315 - 0.989821i) q^{64} +(-0.0475819 - 0.998867i) q^{67} +(0.419102 - 1.72756i) q^{69} +(-0.264241 - 1.83784i) q^{70} +(-0.897344 + 1.96491i) q^{72} +(-1.16413 + 1.34347i) q^{75} +(0.981929 - 0.189251i) q^{80} +(1.26691 - 0.814193i) q^{81} +(1.88431 + 0.553283i) q^{82} +(-0.839614 - 1.17907i) q^{83} +(2.93375 - 1.51245i) q^{84} +(0.0688733 - 0.0656706i) q^{86} +(2.19677 - 1.72756i) q^{87} +(0.273100 - 1.89945i) q^{89} +(-2.00538 - 0.802833i) q^{90} +(-0.654861 - 0.755750i) q^{92} +(-0.271738 - 0.595023i) q^{94} +(0.888835 + 1.53951i) q^{96} +(-2.40324 - 0.463186i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1340\mathbb{Z}\right)^\times$.

$n$	$537$	$671$	$1141$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{19}{33}\right)$

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 $

$2$	−0.235759	+	0.971812i	−0.235759	+	0.971812i
$2$	−0.235759	+	0.971812i	−0.235759	+	0.971812i
$3$	−0.252989	−	1.75958i	−0.252989	−	1.75958i	−0.580057	−	0.814576i	$-0.696970\pi$
$3$	−0.252989	−	1.75958i	−0.252989	−	1.75958i	0.327068	−	0.945001i	$-0.393939\pi$
$4$	−0.888835	−	0.458227i	−0.888835	−	0.458227i
$5$	0.415415	−	0.909632i	0.415415	−	0.909632i
$5$	0.415415	−	0.909632i	0.415415	−	0.909632i
$6$	1.76962	+	0.168978i	1.76962	+	0.168978i
$7$	−1.34378	−	1.28129i	−1.34378	−	1.28129i	−0.928368	−	0.371662i	$-0.878788\pi$
$7$	−1.34378	−	1.28129i	−1.34378	−	1.28129i	−0.415415	−	0.909632i	$-0.636364\pi$
$8$	0.654861	−	0.755750i	0.654861	−	0.755750i
$9$	−2.07261	+	0.608574i	−2.07261	+	0.608574i
$10$	0.786053	+	0.618159i	0.786053	+	0.618159i
$11$		0			0		0.995472	−	0.0950560i	$-0.0303030\pi$
$11$		0			0		−0.995472	+	0.0950560i	$0.969697\pi$
$12$	−0.581419	+	1.67990i	−0.581419	+	1.67990i
$13$		0			0		0.981929	−	0.189251i	$-0.0606061\pi$
$13$		0			0		−0.981929	+	0.189251i	$0.939394\pi$
$14$	1.56199	−	1.00383i	1.56199	−	1.00383i
$15$	−1.70566	−	0.500828i	−1.70566	−	0.500828i
$16$	0.580057	+	0.814576i	0.580057	+	0.814576i
$17$		0			0		0.888835	−	0.458227i	$-0.151515\pi$
$17$		0			0		−0.888835	+	0.458227i	$0.848485\pi$
$18$	−0.102782	−	2.15767i	−0.102782	−	2.15767i
$19$		0			0		0.723734	−	0.690079i	$-0.242424\pi$
$19$		0			0		−0.723734	+	0.690079i	$0.757576\pi$
$20$	−0.786053	+	0.618159i	−0.786053	+	0.618159i
$21$	−1.91457	+	2.68864i	−1.91457	+	2.68864i
$22$		0			0
$23$	0.928368	+	0.371662i	0.928368	+	0.371662i	0.786053	−	0.618159i	$-0.212121\pi$
$23$	0.928368	+	0.371662i	0.928368	+	0.371662i	0.142315	+	0.989821i	$0.454545\pi$
$24$	−1.49547	−	0.961081i	−1.49547	−	0.961081i
$25$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$26$		0			0
$27$	0.856711	+	1.87593i	0.856711	+	1.87593i
$28$	0.607279	+	1.75462i	0.607279	+	1.75462i
$29$	0.786053	+	1.36148i	0.786053	+	1.36148i	0.928368	+	0.371662i	$0.121212\pi$
$29$	0.786053	+	1.36148i	0.786053	+	1.36148i	−0.142315	+	0.989821i	$0.545455\pi$
$30$	0.888835	−	1.53951i	0.888835	−	1.53951i
$31$		0			0		−0.981929	−	0.189251i	$-0.939394\pi$
$31$		0			0		0.981929	+	0.189251i	$0.0606061\pi$
$32$	−0.928368	+	0.371662i	−0.928368	+	0.371662i
$33$		0			0
$34$		0			0
$35$	−1.72373	+	0.690079i	−1.72373	+	0.690079i
$36$	2.12108	+	0.408804i	2.12108	+	0.408804i
$37$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$37$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$38$		0			0
$39$		0			0
$40$	−0.415415	−	0.909632i	−0.415415	−	0.909632i
$41$	0.0934441	−	1.96163i	0.0934441	−	1.96163i	−0.142315	−	0.989821i	$-0.545455\pi$
$41$	0.0934441	−	1.96163i	0.0934441	−	1.96163i	0.235759	−	0.971812i	$-0.424242\pi$
$42$	−2.16148	−	2.49448i	−2.16148	−	2.49448i
$43$	−0.0800569	−	0.0514495i	−0.0800569	−	0.0514495i	0.500000	−	0.866025i	$-0.333333\pi$
$43$	−0.0800569	−	0.0514495i	−0.0800569	−	0.0514495i	−0.580057	+	0.814576i	$0.696970\pi$
$44$		0			0
$45$	−0.307416	+	2.13813i	−0.307416	+	2.13813i
$46$	−0.580057	+	0.814576i	−0.580057	+	0.814576i
$47$	−0.514186	+	0.404360i	−0.514186	+	0.404360i	−0.841254	−	0.540641i	$-0.818182\pi$
$47$	−0.514186	+	0.404360i	−0.514186	+	0.404360i	0.327068	+	0.945001i	$0.393939\pi$
$48$	1.28656	−	1.22673i	1.28656	−	1.22673i
$49$	0.116455	+	2.44470i	0.116455	+	2.44470i
$50$	0.888835	−	0.458227i	0.888835	−	0.458227i
$51$		0			0
$52$		0			0
$53$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$53$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$54$	−2.02503	+	0.390293i	−2.02503	+	0.390293i
$55$		0			0
$56$	−1.84833	+	0.176494i	−1.84833	+	0.176494i
$57$		0			0
$58$	−1.50842	+	0.442913i	−1.50842	+	0.442913i
$59$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$59$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$60$	1.28656	+	1.22673i	1.28656	+	1.22673i
$61$	−0.827068	−	0.0789754i	−0.827068	−	0.0789754i	−0.327068	−	0.945001i	$-0.606061\pi$
$61$	−0.827068	−	0.0789754i	−0.827068	−	0.0789754i	−0.500000	+	0.866025i	$0.666667\pi$
$62$		0			0
$63$	3.56491	+	1.83784i	3.56491	+	1.83784i
$64$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$65$		0			0
$66$		0			0
$67$	−0.0475819	−	0.998867i	−0.0475819	−	0.998867i
$67$	−0.0475819	−	0.998867i	−0.0475819	−	0.998867i
$68$		0			0
$69$	0.419102	−	1.72756i	0.419102	−	1.72756i
$70$	−0.264241	−	1.83784i	−0.264241	−	1.83784i
$71$		0			0		−0.888835	−	0.458227i	$-0.848485\pi$
$71$		0			0		0.888835	+	0.458227i	$0.151515\pi$
$72$	−0.897344	+	1.96491i	−0.897344	+	1.96491i
$73$		0			0		−0.995472	−	0.0950560i	$-0.969697\pi$
$73$		0			0		0.995472	+	0.0950560i	$0.0303030\pi$
$74$		0			0
$75$	−1.16413	+	1.34347i	−1.16413	+	1.34347i
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		0.327068	−	0.945001i	$-0.393939\pi$
$79$		0			0		−0.327068	+	0.945001i	$0.606061\pi$
$80$	0.981929	−	0.189251i	0.981929	−	0.189251i
$81$	1.26691	−	0.814193i	1.26691	−	0.814193i
$82$	1.88431	+	0.553283i	1.88431	+	0.553283i
$83$	−0.839614	−	1.17907i	−0.839614	−	1.17907i	−0.981929	−	0.189251i	$-0.939394\pi$
$83$	−0.839614	−	1.17907i	−0.839614	−	1.17907i	0.142315	−	0.989821i	$-0.454545\pi$
$84$	2.93375	−	1.51245i	2.93375	−	1.51245i
$85$		0			0
$86$	0.0688733	−	0.0656706i	0.0688733	−	0.0656706i
$87$	2.19677	−	1.72756i	2.19677	−	1.72756i
$88$		0			0
$89$	0.273100	−	1.89945i	0.273100	−	1.89945i	−0.142315	−	0.989821i	$-0.545455\pi$
$89$	0.273100	−	1.89945i	0.273100	−	1.89945i	0.415415	−	0.909632i	$-0.363636\pi$
$90$	−2.00538	−	0.802833i	−2.00538	−	0.802833i
$91$		0			0
$92$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$93$		0			0
$94$	−0.271738	−	0.595023i	−0.271738	−	0.595023i
$95$		0			0
$96$	0.888835	+	1.53951i	0.888835	+	1.53951i
$97$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$97$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$98$	−2.40324	−	0.463186i	−2.40324	−	0.463186i
$99$		0			0
$100$	0.235759	+	0.971812i	0.235759	+	0.971812i
$101$	−0.452418	−	1.86489i	−0.452418	−	1.86489i	−0.500000	−	0.866025i	$-0.666667\pi$
$101$	−0.452418	−	1.86489i	−0.452418	−	1.86489i	0.0475819	−	0.998867i	$-0.484848\pi$
$102$		0			0
$103$	−0.462997	−	0.0892353i	−0.462997	−	0.0892353i	−0.0475819	−	0.998867i	$-0.515152\pi$
$103$	−0.462997	−	0.0892353i	−0.462997	−	0.0892353i	−0.415415	+	0.909632i	$0.636364\pi$
$104$		0			0
$105$	1.65033	+	2.85846i	1.65033	+	2.85846i
$106$		0			0
$107$	0.544078	+	1.19136i	0.544078	+	1.19136i	0.959493	+	0.281733i	$0.0909091\pi$
$107$	0.544078	+	1.19136i	0.544078	+	1.19136i	−0.415415	+	0.909632i	$0.636364\pi$
$108$	0.0981282	−	2.05996i	0.0981282	−	2.05996i
$109$	−0.308779	−	0.356349i	−0.308779	−	0.356349i	0.580057	−	0.814576i	$-0.303030\pi$
$109$	−0.308779	−	0.356349i	−0.308779	−	0.356349i	−0.888835	+	0.458227i	$0.848485\pi$
$110$		0			0
$111$		0			0
$112$	0.264241	−	1.83784i	0.264241	−	1.83784i
$113$		0			0		0.580057	−	0.814576i	$-0.303030\pi$
$113$		0			0		−0.580057	+	0.814576i	$0.696970\pi$
$114$		0			0
$115$	0.723734	−	0.690079i	0.723734	−	0.690079i
$116$	−0.0748038	−	1.57033i	−0.0748038	−	1.57033i
$117$		0			0
$118$		0			0
$119$		0			0
$120$	−1.49547	+	0.961081i	−1.49547	+	0.961081i
$121$	0.981929	−	0.189251i	0.981929	−	0.189251i
$122$	0.271738	−	0.785135i	0.271738	−	0.785135i
$123$	−3.47528	+	0.331849i	−3.47528	+	0.331849i
$124$		0			0
$125$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$126$	−2.62649	+	3.03113i	−2.62649	+	3.03113i
$127$	1.44091	+	1.37391i	1.44091	+	1.37391i	0.786053	+	0.618159i	$0.212121\pi$
$127$	1.44091	+	1.37391i	1.44091	+	1.37391i	0.654861	+	0.755750i	$0.272727\pi$
$128$	0.995472	+	0.0950560i	0.995472	+	0.0950560i
$129$	−0.0702757	+	0.153882i	−0.0702757	+	0.153882i
$130$		0			0
$131$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$131$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$132$		0			0
$133$		0			0
$134$	0.981929	+	0.189251i	0.981929	+	0.189251i
$135$	2.06230			2.06230
$136$		0			0
$137$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$137$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$138$	1.58006	+	0.814576i	1.58006	+	0.814576i
$139$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$139$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$140$	1.84833	+	0.176494i	1.84833	+	0.176494i
$141$	0.841586	+	0.802450i	0.841586	+	0.802450i
$142$		0			0
$143$		0			0
$144$	−1.69796	−	1.33529i	−1.69796	−	1.33529i
$145$	1.56499	−	0.149438i	1.56499	−	0.149438i
$146$		0			0
$147$	4.27217	−	0.823393i	4.27217	−	0.823393i
$148$		0			0
$149$	−1.88431	−	0.553283i	−1.88431	−	0.553283i	−0.995472	−	0.0950560i	$-0.969697\pi$
$149$	−1.88431	−	0.553283i	−1.88431	−	0.553283i	−0.888835	−	0.458227i	$-0.848485\pi$
$150$	−1.03115	−	1.44805i	−1.03115	−	1.44805i
$151$		0			0		0.888835	−	0.458227i	$-0.151515\pi$
$151$		0			0		−0.888835	+	0.458227i	$0.848485\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		−0.928368	−	0.371662i	$-0.878788\pi$
$157$		0			0		0.928368	+	0.371662i	$0.121212\pi$
$158$		0			0
$159$		0			0
$160$	−0.0475819	+	0.998867i	−0.0475819	+	0.998867i
$161$	−0.771316	−	1.68895i	−0.771316	−	1.68895i
$162$	0.492557	+	1.42315i	0.492557	+	1.42315i
$163$	0.841254	+	1.45709i	0.841254	+	1.45709i	0.888835	+	0.458227i	$0.151515\pi$
$163$	0.841254	+	1.45709i	0.841254	+	1.45709i	−0.0475819	+	0.998867i	$0.515152\pi$
$164$	−0.981929	+	1.70075i	−0.981929	+	1.70075i
$165$		0			0
$166$	1.34378	−	0.537970i	1.34378	−	0.537970i
$167$	0.0671040	+	0.276606i	0.0671040	+	0.276606i	0.995472	−	0.0950560i	$-0.0303030\pi$
$167$	0.0671040	+	0.276606i	0.0671040	+	0.276606i	−0.928368	+	0.371662i	$0.878788\pi$
$168$	0.778161	+	3.20762i	0.778161	+	3.20762i
$169$	0.928368	−	0.371662i	0.928368	−	0.371662i
$170$		0			0
$171$		0			0
$172$	0.0475819	+	0.0824143i	0.0475819	+	0.0824143i
$173$		0			0		−0.327068	−	0.945001i	$-0.606061\pi$
$173$		0			0		0.327068	+	0.945001i	$0.393939\pi$
$174$	1.16096	+	2.54214i	1.16096	+	2.54214i
$175$	−0.0883470	+	1.85463i	−0.0883470	+	1.85463i
$176$		0			0
$177$		0			0
$178$	1.78153	+	0.713215i	1.78153	+	0.713215i
$179$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$179$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$180$	1.25299	−	1.75958i	1.25299	−	1.75958i
$181$	−1.32254	+	1.04006i	−1.32254	+	1.04006i	−0.327068	+	0.945001i	$0.606061\pi$
$181$	−1.32254	+	1.04006i	−1.32254	+	1.04006i	−0.995472	+	0.0950560i	$0.969697\pi$
$182$		0			0
$183$	0.0702757	+	1.47527i	0.0702757	+	1.47527i
$184$	0.888835	−	0.458227i	0.888835	−	0.458227i
$185$		0			0
$186$		0			0
$187$		0			0
$188$	0.642315	−	0.123796i	0.642315	−	0.123796i
$189$	1.25239	−	3.61855i	1.25239	−	3.61855i
$190$		0			0
$191$		0			0		−0.786053	−	0.618159i	$-0.787879\pi$
$191$		0			0		0.786053	+	0.618159i	$0.212121\pi$
$192$	−1.70566	+	0.500828i	−1.70566	+	0.500828i
$193$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$193$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$194$		0			0
$195$		0			0
$196$	1.01671	−	2.22630i	1.01671	−	2.22630i
$197$		0			0		−0.888835	−	0.458227i	$-0.848485\pi$
$197$		0			0		0.888835	+	0.458227i	$0.151515\pi$
$198$		0			0
$199$		0			0		0.235759	−	0.971812i	$-0.424242\pi$
$199$		0			0		−0.235759	+	0.971812i	$0.575758\pi$
$200$	−1.00000			−1.00000
$201$	−1.74555	+	0.336426i	−1.74555	+	0.336426i
$202$	1.91899			1.91899
$203$	0.688177	−	2.83670i	0.688177	−	2.83670i
$204$		0			0
$205$	−1.74555	−	0.899892i	−1.74555	−	0.899892i
$206$	0.195876	−	0.428908i	0.195876	−	0.428908i
$207$	−2.15033	−	0.205332i	−2.15033	−	0.205332i
$208$		0			0
$209$		0			0
$210$	−3.16697	+	0.929905i	−3.16697	+	0.929905i
$211$		0			0		−0.786053	−	0.618159i	$-0.787879\pi$
$211$		0			0		0.786053	+	0.618159i	$0.212121\pi$
$212$		0			0
$213$		0			0
$214$	−1.28605	+	0.247866i	−1.28605	+	0.247866i
$215$	−0.0800569	+	0.0514495i	−0.0800569	+	0.0514495i
$216$	1.97876	+	0.581017i	1.97876	+	0.581017i
$217$		0			0
$218$	0.419102	−	0.216062i	0.419102	−	0.216062i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	0.118239	−	0.822373i	0.118239	−	0.822373i	−0.841254	−	0.540641i	$-0.818182\pi$
$223$	0.118239	−	0.822373i	0.118239	−	0.822373i	0.959493	−	0.281733i	$-0.0909091\pi$
$224$	1.72373	+	0.690079i	1.72373	+	0.690079i
$225$	1.81720	+	1.16785i	1.81720	+	1.16785i
$226$		0			0
$227$	0.0913090	−	1.91681i	0.0913090	−	1.91681i	−0.235759	−	0.971812i	$-0.575758\pi$
$227$	0.0913090	−	1.91681i	0.0913090	−	1.91681i	0.327068	−	0.945001i	$-0.393939\pi$
$228$		0			0
$229$	0.651174	+	1.88144i	0.651174	+	1.88144i	0.415415	+	0.909632i	$0.363636\pi$
$229$	0.651174	+	1.88144i	0.651174	+	1.88144i	0.235759	+	0.971812i	$0.424242\pi$
$230$	0.500000	+	0.866025i	0.500000	+	0.866025i
$231$		0			0
$232$	1.54370	+	0.297523i	1.54370	+	0.297523i
$233$		0			0		0.928368	−	0.371662i	$-0.121212\pi$
$233$		0			0		−0.928368	+	0.371662i	$0.878788\pi$
$234$		0			0
$235$	0.154218	+	0.635697i	0.154218	+	0.635697i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$239$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$240$	−0.581419	−	1.67990i	−0.581419	−	1.67990i
$241$	0.195876	+	0.428908i	0.195876	+	0.428908i	0.981929	−	0.189251i	$-0.0606061\pi$
$241$	0.195876	+	0.428908i	0.195876	+	0.428908i	−0.786053	+	0.618159i	$0.787879\pi$
$242$	−0.0475819	+	0.998867i	−0.0475819	+	0.998867i
$243$	−0.402630	−	0.464659i	−0.402630	−	0.464659i
$244$	0.698939	+	0.449181i	0.698939	+	0.449181i
$245$	2.27215	+	0.909632i	2.27215	+	0.909632i
$246$	0.496834	−	3.45556i	0.496834	−	3.45556i
$247$		0			0
$248$		0			0
$249$	−1.86226	+	1.77566i	−1.86226	+	1.77566i
$250$	−0.0475819	−	0.998867i	−0.0475819	−	0.998867i
$251$		0			0		0.888835	−	0.458227i	$-0.151515\pi$
$251$		0			0		−0.888835	+	0.458227i	$0.848485\pi$
$252$	−2.32647	−	3.26707i	−2.32647	−	3.26707i
$253$		0			0
$254$	−1.67489	+	1.07639i	−1.67489	+	1.07639i
$255$		0			0
$256$	−0.327068	+	0.945001i	−0.327068	+	0.945001i
$257$		0			0		0.995472	−	0.0950560i	$-0.0303030\pi$
$257$		0			0		−0.995472	+	0.0950560i	$0.969697\pi$
$258$	−0.132977	−	0.104574i	−0.132977	−	0.104574i
$259$		0			0
$260$		0			0
$261$	−2.45775	−	2.34346i	−2.45775	−	2.34346i
$262$		0			0
$263$	−0.481929	+	1.05528i	−0.481929	+	1.05528i	0.500000	+	0.866025i	$0.333333\pi$
$263$	−0.481929	+	1.05528i	−0.481929	+	1.05528i	−0.981929	+	0.189251i	$0.939394\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−3.41133			−3.41133
$268$	−0.415415	+	0.909632i	−0.415415	+	0.909632i
$269$	1.68251			1.68251			0.841254	−	0.540641i	$-0.181818\pi$
$269$	1.68251			1.68251			0.841254	+	0.540641i	$0.181818\pi$
$270$	−0.486206	+	2.00417i	−0.486206	+	2.00417i
$271$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$271$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$	−1.16413	+	1.34347i	−1.16413	+	1.34347i
$277$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$277$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$278$		0			0
$279$		0			0
$280$	−0.607279	+	1.75462i	−0.607279	+	1.75462i
$281$	−0.642315	+	0.123796i	−0.642315	+	0.123796i	−0.500000	−	0.866025i	$-0.666667\pi$
$281$	−0.642315	+	0.123796i	−0.642315	+	0.123796i	−0.142315	+	0.989821i	$0.545455\pi$
$282$	−0.978242	+	0.628678i	−0.978242	+	0.628678i
$283$	1.11312	+	0.326842i	1.11312	+	0.326842i	0.786053	−	0.618159i	$-0.212121\pi$
$283$	1.11312	+	0.326842i	1.11312	+	0.326842i	0.327068	+	0.945001i	$0.393939\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−2.63900	+	2.51628i	−2.63900	+	2.51628i
$288$	1.69796	−	1.33529i	1.69796	−	1.33529i
$289$	0.580057	−	0.814576i	0.580057	−	0.814576i
$290$	−0.223734	+	1.55610i	−0.223734	+	1.55610i
$291$		0			0
$292$		0			0
$293$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$293$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$294$	−0.207019	+	4.34586i	−0.207019	+	4.34586i
$295$		0			0
$296$		0			0
$297$		0			0
$298$	0.981929	−	1.70075i	0.981929	−	1.70075i
$299$		0			0
$300$	1.65033	−	0.660694i	1.65033	−	0.660694i
$301$	0.0416572	+	0.171713i	0.0416572	+	0.171713i
$302$		0			0
$303$	−3.16697	+	1.26786i	−3.16697	+	1.26786i
$304$		0			0
$305$	−0.415415	+	0.719520i	−0.415415	+	0.719520i
$306$		0			0
$307$	−0.428368	−	1.23769i	−0.428368	−	1.23769i	−0.928368	−	0.371662i	$-0.878788\pi$
$307$	−0.428368	−	1.23769i	−0.428368	−	1.23769i	0.500000	−	0.866025i	$-0.333333\pi$
$308$		0			0
$309$	−0.0398833	+	0.837254i	−0.0398833	+	0.837254i
$310$		0			0
$311$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$311$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$312$		0			0
$313$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$313$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$314$		0			0
$315$	3.15267	−	2.47929i	3.15267	−	2.47929i
$316$		0			0
$317$		0			0		−0.0475819	−	0.998867i	$-0.515152\pi$
$317$		0			0		0.0475819	+	0.998867i	$0.484848\pi$
$318$		0			0
$319$		0			0
$320$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$321$	1.95865	−	1.25875i	1.95865	−	1.25875i
$322$	1.82318	−	0.351390i	1.82318	−	0.351390i
$323$		0			0
$324$	−1.49916	+	0.143152i	−1.49916	+	0.143152i
$325$		0			0
$326$	−1.61435	+	0.474017i	−1.61435	+	0.474017i
$327$	−0.548907	+	0.633472i	−0.548907	+	0.633472i
$328$	−1.42131	−	1.35522i	−1.42131	−	1.35522i
$329$	1.20906	+	0.115451i	1.20906	+	0.115451i
$330$		0			0
$331$		0			0		−0.888835	−	0.458227i	$-0.848485\pi$
$331$		0			0		0.888835	+	0.458227i	$0.151515\pi$
$332$	0.205996	+	1.43273i	0.205996	+	1.43273i
$333$		0			0
$334$	−0.284630			−0.284630
$335$	−0.928368	−	0.371662i	−0.928368	−	0.371662i
$336$	−3.30067			−3.30067
$337$		0			0		0.235759	−	0.971812i	$-0.424242\pi$
$337$		0			0		−0.235759	+	0.971812i	$0.575758\pi$
$338$	0.142315	+	0.989821i	0.142315	+	0.989821i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	1.75998	−	2.03113i	1.75998	−	2.03113i
$344$	−0.0913090	+	0.0268107i	−0.0913090	+	0.0268107i
$345$	−1.39734	−	1.09888i	−1.39734	−	1.09888i
$346$		0			0
$347$	0.271738	−	0.785135i	0.271738	−	0.785135i	−0.723734	−	0.690079i	$-0.757576\pi$
$347$	0.271738	−	0.785135i	0.271738	−	0.785135i	0.995472	−	0.0950560i	$-0.0303030\pi$
$348$	−2.74418	+	0.528898i	−2.74418	+	0.528898i
$349$	0.0800569	−	0.0514495i	0.0800569	−	0.0514495i	−0.500000	−	0.866025i	$-0.666667\pi$
$349$	0.0800569	−	0.0514495i	0.0800569	−	0.0514495i	0.580057	+	0.814576i	$0.303030\pi$
$350$	−1.78153	−	0.523103i	−1.78153	−	0.523103i
$351$		0			0
$352$		0			0
$353$		0			0		−0.0475819	−	0.998867i	$-0.515152\pi$
$353$		0			0		0.0475819	+	0.998867i	$0.484848\pi$
$354$		0			0
$355$		0			0
$356$	−1.11312	+	1.56316i	−1.11312	+	1.56316i
$357$		0			0
$358$		0			0
$359$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$359$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$360$	1.41457	+	1.63251i	1.41457	+	1.63251i
$361$	0.0475819	−	0.998867i	0.0475819	−	0.998867i
$362$	−0.698939	−	1.53046i	−0.698939	−	1.53046i
$363$	−0.581419	−	1.67990i	−0.581419	−	1.67990i
$364$		0			0
$365$		0			0
$366$	−1.45025	−	0.279513i	−1.45025	−	0.279513i
$367$	−0.437742	+	0.175245i	−0.437742	+	0.175245i	−0.580057	−	0.814576i	$-0.696970\pi$
$367$	−0.437742	+	0.175245i	−0.437742	+	0.175245i	0.142315	+	0.989821i	$0.454545\pi$
$368$	0.235759	+	0.971812i	0.235759	+	0.971812i
$369$	1.00013	+	4.12258i	1.00013	+	4.12258i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$373$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$374$		0			0
$375$	0.738471	+	1.61703i	0.738471	+	1.61703i
$376$	−0.0311250	+	0.653395i	−0.0311250	+	0.653395i
$377$		0			0
$378$	3.22128	+	2.07019i	3.22128	+	2.07019i
$379$		0			0		−0.928368	−	0.371662i	$-0.878788\pi$
$379$		0			0		0.928368	+	0.371662i	$0.121212\pi$
$380$		0			0
$381$	2.05296	−	2.88298i	2.05296	−	2.88298i
$382$		0			0
$383$	0.473420	−	0.451405i	0.473420	−	0.451405i	−0.415415	−	0.909632i	$-0.636364\pi$
$383$	0.473420	−	0.451405i	0.473420	−	0.451405i	0.888835	+	0.458227i	$0.151515\pi$
$384$	−0.0845850	−	1.77566i	−0.0845850	−	1.77566i
$385$		0			0
$386$		0			0
$387$	0.197238	+	0.0579143i	0.197238	+	0.0579143i
$388$		0			0
$389$	0.462997	−	0.0892353i	0.462997	−	0.0892353i	0.0475819	−	0.998867i	$-0.484848\pi$
$389$	0.462997	−	0.0892353i	0.462997	−	0.0892353i	0.415415	+	0.909632i	$0.363636\pi$
$390$		0			0
$391$		0			0
$392$	1.92384	+	1.51292i	1.92384	+	1.51292i
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$397$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$398$		0			0
$399$		0			0
$400$	0.235759	−	0.971812i	0.235759	−	0.971812i
$401$	1.85674			1.85674			0.928368	−	0.371662i	$-0.121212\pi$
$401$	1.85674			1.85674			0.928368	+	0.371662i	$0.121212\pi$
$402$	0.0845850	−	1.77566i	0.0845850	−	1.77566i
$403$		0			0
$404$	−0.452418	+	1.86489i	−0.452418	+	1.86489i
$405$	−0.214323	−	1.49065i	−0.214323	−	1.49065i
$406$	2.59450	+	1.33756i	2.59450	+	1.33756i
$407$		0			0
$408$		0			0
$409$	1.21769	+	1.16106i	1.21769	+	1.16106i	0.981929	+	0.189251i	$0.0606061\pi$
$409$	1.21769	+	1.16106i	1.21769	+	1.16106i	0.235759	+	0.971812i	$0.424242\pi$
$410$	1.28605	−	1.48418i	1.28605	−	1.48418i
$411$		0			0
$412$	0.370638	+	0.291473i	0.370638	+	0.291473i
$413$		0			0
$414$	0.706504	−	2.04131i	0.706504	−	2.04131i
$415$	−1.42131	+	0.273935i	−1.42131	+	0.273935i
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		0.888835	−	0.458227i	$-0.151515\pi$
$419$		0			0		−0.888835	+	0.458227i	$0.848485\pi$
$420$	−0.157052	−	3.29693i	−0.157052	−	3.29693i
$421$	−0.205996	+	0.196417i	−0.205996	+	0.196417i	−0.786053	−	0.618159i	$-0.787879\pi$
$421$	−0.205996	+	0.196417i	−0.205996	+	0.196417i	0.580057	+	0.814576i	$0.303030\pi$
$422$		0			0
$423$	0.819625	−	1.15100i	0.819625	−	1.15100i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	1.01021	+	1.16584i	1.01021	+	1.16584i
$428$	0.0623191	−	1.30824i	0.0623191	−	1.30824i
$429$		0			0
$430$	−0.0311250	−	0.0899299i	−0.0311250	−	0.0899299i
$431$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$431$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$432$	−1.03115	+	1.78600i	−1.03115	+	1.78600i
$433$		0			0		−0.981929	−	0.189251i	$-0.939394\pi$
$433$		0			0		0.981929	+	0.189251i	$0.0606061\pi$
$434$		0			0
$435$	−0.658873	−	2.71591i	−0.658873	−	2.71591i
$436$	0.111165	+	0.458227i	0.111165	+	0.458227i
$437$		0			0
$438$		0			0
$439$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$439$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$440$		0			0
$441$	−1.72915	−	4.99604i	−1.72915	−	4.99604i
$442$		0			0
$443$	0.0748038	−	1.57033i	0.0748038	−	1.57033i	−0.580057	−	0.814576i	$-0.696970\pi$
$443$	0.0748038	−	1.57033i	0.0748038	−	1.57033i	0.654861	−	0.755750i	$-0.272727\pi$
$444$		0			0
$445$	−1.61435	−	1.03748i	−1.61435	−	1.03748i
$446$	0.771316	+	0.308788i	0.771316	+	0.308788i
$447$	−0.496834	+	3.45556i	−0.496834	+	3.45556i
$448$	−1.07701	+	1.51245i	−1.07701	+	1.51245i
$449$	0.514186	−	0.404360i	0.514186	−	0.404360i	−0.327068	−	0.945001i	$-0.606061\pi$
$449$	0.514186	−	0.404360i	0.514186	−	0.404360i	0.841254	+	0.540641i	$0.181818\pi$
$450$	−1.56335	+	1.49065i	−1.56335	+	1.49065i
$451$		0			0
$452$		0			0
$453$		0			0
$454$	1.84125	+	0.540641i	1.84125	+	0.540641i
$455$		0			0
$456$		0			0
$457$		0			0		0.327068	−	0.945001i	$-0.393939\pi$
$457$		0			0		−0.327068	+	0.945001i	$0.606061\pi$
$458$	−1.98193	+	0.189251i	−1.98193	+	0.189251i
$459$		0			0
$460$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$461$	−0.947890	+	1.09392i	−0.947890	+	1.09392i	0.0475819	+	0.998867i	$0.484848\pi$
$461$	−0.947890	+	1.09392i	−0.947890	+	1.09392i	−0.995472	+	0.0950560i	$0.969697\pi$
$462$		0			0
$463$	1.67489	+	0.159932i	1.67489	+	0.159932i	0.888835	−	0.458227i	$-0.151515\pi$
$463$	1.67489	+	0.159932i	1.67489	+	0.159932i	0.786053	+	0.618159i	$0.212121\pi$
$464$	−0.653077	+	1.43004i	−0.653077	+	1.43004i
$465$		0			0
$466$		0			0
$467$	0.469383	−	1.93482i	0.469383	−	1.93482i	0.142315	−	0.989821i	$-0.454545\pi$
$467$	0.469383	−	1.93482i	0.469383	−	1.93482i	0.327068	−	0.945001i	$-0.393939\pi$
$468$		0			0
$469$	−1.21590	+	1.40323i	−1.21590	+	1.40323i
$470$	−0.654136			−0.654136
$471$		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		−0.786053	−	0.618159i	$-0.787879\pi$
$479$		0			0		0.786053	+	0.618159i	$0.212121\pi$
$480$	1.76962	−	0.168978i	1.76962	−	0.168978i
$481$		0			0
$482$	−0.462997	+	0.0892353i	−0.462997	+	0.0892353i
$483$	−2.77670	+	1.78447i	−2.77670	+	1.78447i
$484$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$485$		0			0
$486$	0.546485	−	0.281733i	0.546485	−	0.281733i
$487$	−0.0688733	−	1.44583i	−0.0688733	−	1.44583i	−0.723734	−	0.690079i	$-0.757576\pi$
$487$	−0.0688733	−	1.44583i	−0.0688733	−	1.44583i	0.654861	−	0.755750i	$-0.272727\pi$
$488$	−0.601300	+	0.573338i	−0.601300	+	0.573338i
$489$	2.35104	−	1.84888i	2.35104	−	1.84888i
$490$	−1.41967	+	1.99365i	−1.41967	+	1.99365i
$491$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$491$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$492$	3.24102	+	1.29751i	3.24102	+	1.29751i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−1.28656	−	2.22839i	−1.28656	−	2.22839i
$499$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$499$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$500$	0.981929	+	0.189251i	0.981929	+	0.189251i
$501$	0.469734	−	0.188053i	0.469734	−	0.188053i
$502$		0			0
$503$	−0.462997	−	1.90850i	−0.462997	−	1.90850i	−0.415415	−	0.909632i	$-0.636364\pi$
$503$	−0.462997	−	1.90850i	−0.462997	−	1.90850i	−0.0475819	−	0.998867i	$-0.515152\pi$
$504$	3.72346	−	1.49065i	3.72346	−	1.49065i
$505$	−1.88431	−	0.363170i	−1.88431	−	0.363170i
$506$		0			0
$507$	−0.888835	−	1.53951i	−0.888835	−	1.53951i
$508$	−0.651174	−	1.88144i	−0.651174	−	1.88144i
$509$	−0.118239	−	0.258908i	−0.118239	−	0.258908i	0.841254	−	0.540641i	$-0.181818\pi$
$509$	−0.118239	−	0.258908i	−0.118239	−	0.258908i	−0.959493	+	0.281733i	$0.909091\pi$
$510$		0			0
$511$		0			0
$512$	−0.841254	−	0.540641i	−0.841254	−	0.540641i
$513$		0			0
$514$		0			0
$515$	−0.273507	+	0.384087i	−0.273507	+	0.384087i
$516$	0.132977	−	0.104574i	0.132977	−	0.104574i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	0.959493	+	0.281733i	0.959493	+	0.281733i	0.723734	−	0.690079i	$-0.242424\pi$
$521$	0.959493	+	0.281733i	0.959493	+	0.281733i	0.235759	+	0.971812i	$0.424242\pi$
$522$	2.85684	−	1.83598i	2.85684	−	1.83598i
$523$	−0.0934441	+	0.0180099i	−0.0934441	+	0.0180099i	−0.235759	−	0.971812i	$-0.575758\pi$
$523$	−0.0934441	+	0.0180099i	−0.0934441	+	0.0180099i	0.142315	+	0.989821i	$0.454545\pi$
$524$		0			0
$525$	3.28572	−	0.313748i	3.28572	−	0.313748i
$526$	−0.911911	−	0.717135i	−0.911911	−	0.717135i
$527$		0			0
$528$		0			0
$529$		0			0
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$	0.804250	−	3.31517i	0.804250	−	3.31517i
$535$	1.30972			1.30972
$536$	−0.786053	−	0.618159i	−0.786053	−	0.618159i
$537$		0			0
$538$	−0.396666	+	1.63508i	−0.396666	+	1.63508i
$539$		0			0
$540$	−1.83305	−	0.945001i	−1.83305	−	0.945001i
$541$	0.0395325	−	0.0865641i	0.0395325	−	0.0865641i	−0.888835	−	0.458227i	$-0.848485\pi$
$541$	0.0395325	−	0.0865641i	0.0395325	−	0.0865641i	0.928368	+	0.371662i	$0.121212\pi$
$542$		0			0
$543$	2.16465	+	2.06399i	2.16465	+	2.06399i
$544$		0			0
$545$	−0.452418	+	0.132842i	−0.452418	+	0.132842i
$546$		0			0
$547$	−1.98193	+	0.189251i	−1.98193	+	0.189251i	−0.981929	+	0.189251i	$0.939394\pi$
$547$	−1.98193	+	0.189251i	−1.98193	+	0.189251i	−1.00000			$\pi$
$548$		0			0
$549$	1.76226	−	0.339647i	1.76226	−	0.339647i
$550$		0			0
$551$		0			0
$552$	−1.03115	−	1.44805i	−1.03115	−	1.44805i
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$		0			0		0.580057	−	0.814576i	$-0.303030\pi$
$557$		0			0		−0.580057	+	0.814576i	$0.696970\pi$
$558$		0			0
$559$		0			0
$560$	−1.56199	−	1.00383i	−1.56199	−	1.00383i
$561$		0			0
$562$	0.0311250	−	0.653395i	0.0311250	−	0.653395i
$563$	−0.0395325	−	0.0865641i	−0.0395325	−	0.0865641i	0.888835	−	0.458227i	$-0.151515\pi$
$563$	−0.0395325	−	0.0865641i	−0.0395325	−	0.0865641i	−0.928368	+	0.371662i	$0.878788\pi$
$564$	−0.380327	−	1.09888i	−0.380327	−	1.09888i
$565$		0			0
$566$	−0.580057	+	1.00469i	−0.580057	+	1.00469i
$567$	−2.74567	−	0.529185i	−2.74567	−	0.529185i
$568$		0			0
$569$	−0.0671040	−	0.276606i	−0.0671040	−	0.276606i	0.928368	−	0.371662i	$-0.121212\pi$
$569$	−0.0671040	−	0.276606i	−0.0671040	−	0.276606i	−0.995472	+	0.0950560i	$0.969697\pi$
$570$		0			0
$571$		0			0		0.928368	−	0.371662i	$-0.121212\pi$
$571$		0			0		−0.928368	+	0.371662i	$0.878788\pi$
$572$		0			0
$573$		0			0
$574$	−1.82318	−	3.15784i	−1.82318	−	3.15784i
$575$	−0.327068	−	0.945001i	−0.327068	−	0.945001i
$576$	0.897344	+	1.96491i	0.897344	+	1.96491i
$577$		0			0		0.0475819	−	0.998867i	$-0.484848\pi$
$577$		0			0		−0.0475819	+	0.998867i	$0.515152\pi$
$578$	0.654861	+	0.755750i	0.654861	+	0.755750i
$579$		0			0
$580$	−1.45949	−	0.584293i	−1.45949	−	0.584293i
$581$	−0.382481	+	2.66021i	−0.382481	+	2.66021i
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$	0.759713	+	1.06687i	0.759713	+	1.06687i	0.995472	+	0.0950560i	$0.0303030\pi$
$587$	0.759713	+	1.06687i	0.759713	+	1.06687i	−0.235759	+	0.971812i	$0.575758\pi$
$588$	−4.17456	−	1.22576i	−4.17456	−	1.22576i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$		0			0		−0.786053	−	0.618159i	$-0.787879\pi$
$593$		0			0		0.786053	+	0.618159i	$0.212121\pi$
$594$		0			0
$595$		0			0
$596$	1.42131	+	1.35522i	1.42131	+	1.35522i
$597$		0			0
$598$		0			0
$599$		0			0		−0.888835	−	0.458227i	$-0.848485\pi$
$599$		0			0		0.888835	+	0.458227i	$0.151515\pi$
$600$	0.252989	+	1.75958i	0.252989	+	1.75958i
$601$	0.0224357	−	0.0924813i	0.0224357	−	0.0924813i	−0.959493	−	0.281733i	$-0.909091\pi$
$601$	0.0224357	−	0.0924813i	0.0224357	−	0.0924813i	0.981929	+	0.189251i	$0.0606061\pi$
$602$	−0.176694			−0.176694
$603$	0.706504	+	2.04131i	0.706504	+	2.04131i
$604$		0			0
$605$	0.235759	−	0.971812i	0.235759	−	0.971812i
$606$	−0.485482	−	3.37660i	−0.485482	−	3.37660i
$607$	−0.581419	−	0.299742i	−0.581419	−	0.299742i	0.142315	−	0.989821i	$-0.454545\pi$
$607$	−0.581419	−	0.299742i	−0.581419	−	0.299742i	−0.723734	+	0.690079i	$0.757576\pi$
$608$		0			0
$609$	−5.16550	−	0.493245i	−5.16550	−	0.493245i
$610$	−0.601300	−	0.573338i	−0.601300	−	0.573338i
$611$		0			0
$612$		0			0
$613$		0			0		−0.786053	−	0.618159i	$-0.787879\pi$
$613$		0			0		0.786053	+	0.618159i	$0.212121\pi$
$614$	1.30379	−	0.124497i	1.30379	−	0.124497i
$615$	−1.14182	+	3.29908i	−1.14182	+	3.29908i
$616$		0			0
$617$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$617$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$618$	−0.804250	−	0.236149i	−0.804250	−	0.236149i
$619$		0			0		−0.580057	−	0.814576i	$-0.696970\pi$
$619$		0			0		0.580057	+	0.814576i	$0.303030\pi$
$620$		0			0
$621$	0.0981282	+	2.05996i	0.0981282	+	2.05996i
$622$		0			0
$623$	−2.80075	+	2.20253i	−2.80075	+	2.20253i
$624$		0			0
$625$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$	1.66613	+	3.64832i	1.66613	+	3.64832i
$631$		0			0		−0.327068	−	0.945001i	$-0.606061\pi$
$631$		0			0		0.327068	+	0.945001i	$0.393939\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	1.84833	−	0.739959i	1.84833	−	0.739959i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$	0.500000	−	0.866025i	0.500000	−	0.866025i
$641$	−0.580057	−	1.00469i	−0.580057	−	1.00469i	−0.995472	−	0.0950560i	$-0.969697\pi$
$641$	−0.580057	−	1.00469i	−0.580057	−	1.00469i	0.415415	−	0.909632i	$-0.363636\pi$
$642$	0.761497	+	2.20020i	0.761497	+	2.20020i
$643$	0.653077	+	1.43004i	0.653077	+	1.43004i	0.888835	+	0.458227i	$0.151515\pi$
$643$	0.653077	+	1.43004i	0.653077	+	1.43004i	−0.235759	+	0.971812i	$0.575758\pi$
$644$	−0.0883470	+	1.85463i	−0.0883470	+	1.85463i
$645$	0.110783	+	0.127850i	0.110783	+	0.127850i
$646$		0			0
$647$	0.607279	+	0.243118i	0.607279	+	0.243118i	0.654861	−	0.755750i	$-0.272727\pi$
$647$	0.607279	+	0.243118i	0.607279	+	0.243118i	−0.0475819	+	0.998867i	$0.515152\pi$
$648$	0.214323	−	1.49065i	0.214323	−	1.49065i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	−0.0800569	−	1.68060i	−0.0800569	−	1.68060i
$653$		0			0		0.888835	−	0.458227i	$-0.151515\pi$
$653$		0			0		−0.888835	+	0.458227i	$0.848485\pi$
$654$	−0.486206	−	0.682780i	−0.486206	−	0.682780i
$655$		0			0
$656$	1.65210	−	1.06174i	1.65210	−	1.06174i
$657$		0			0
$658$	−0.397243	+	1.14776i	−0.397243	+	1.14776i
$659$		0			0		0.995472	−	0.0950560i	$-0.0303030\pi$
$659$		0			0		−0.995472	+	0.0950560i	$0.969697\pi$
$660$		0			0
$661$	0.273100	−	0.0801894i	0.273100	−	0.0801894i	−0.142315	−	0.989821i	$-0.545455\pi$
$661$	0.273100	−	0.0801894i	0.273100	−	0.0801894i	0.415415	+	0.909632i	$0.363636\pi$
$662$		0			0
$663$		0			0
$664$	−1.44091	−	0.137591i	−1.44091	−	0.137591i
$665$		0			0
$666$		0			0
$667$	0.223734	+	1.55610i	0.223734	+	1.55610i
$668$	0.0671040	−	0.276606i	0.0671040	−	0.276606i
$669$	−1.47694			−1.47694
$670$	0.580057	−	0.814576i	0.580057	−	0.814576i
$671$		0			0
$672$	0.778161	−	3.20762i	0.778161	−	3.20762i
$673$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$673$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$674$		0			0
$675$	0.856711	−	1.87593i	0.856711	−	1.87593i
$676$	−0.995472	−	0.0950560i	−0.995472	−	0.0950560i
$677$		0			0		−0.723734	−	0.690079i	$-0.757576\pi$
$677$		0			0		0.723734	+	0.690079i	$0.242424\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−3.39588	+	0.324267i	−3.39588	+	0.324267i
$682$		0			0
$683$	1.28605	−	0.247866i	1.28605	−	0.247866i	0.500000	−	0.866025i	$-0.333333\pi$
$683$	1.28605	−	0.247866i	1.28605	−	0.247866i	0.786053	+	0.618159i	$0.212121\pi$
$684$		0			0
$685$		0			0
$686$	1.55894	+	2.18923i	1.55894	+	2.18923i
$687$	3.14580	−	1.62177i	3.14580	−	1.62177i
$688$	−0.00452808	−	0.0950560i	−0.00452808	−	0.0950560i
$689$		0			0
$690$	1.39734	−	1.09888i	1.39734	−	1.09888i
$691$		0			0		0.580057	−	0.814576i	$-0.303030\pi$
$691$		0			0		−0.580057	+	0.814576i	$0.696970\pi$
$692$		0			0
$693$		0			0
$694$	0.698939	+	0.449181i	0.698939	+	0.449181i
$695$		0			0
$696$	0.132977	−	2.79152i	0.132977	−	2.79152i
$697$		0			0
$698$	0.0311250	+	0.0899299i	0.0311250	+	0.0899299i
$699$		0			0
$700$	0.928368	−	1.60798i	0.928368	−	1.60798i
$701$	−0.981929	−	0.189251i	−0.981929	−	0.189251i	−0.327068	−	0.945001i	$-0.606061\pi$
$701$	−0.981929	−	0.189251i	−0.981929	−	0.189251i	−0.654861	+	0.755750i	$0.727273\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	1.07954	−	0.432183i	1.07954	−	0.432183i
$706$		0			0
$707$	−1.78153	+	3.08569i	−1.78153	+	3.08569i
$708$		0			0
$709$	0.327068	+	0.945001i	0.327068	+	0.945001i	0.981929	+	0.189251i	$0.0606061\pi$
$709$	0.327068	+	0.945001i	0.327068	+	0.945001i	−0.654861	+	0.755750i	$0.727273\pi$
$710$		0			0
$711$		0			0
$712$	−1.25667	−	1.45027i	−1.25667	−	1.45027i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		−0.0475819	−	0.998867i	$-0.515152\pi$
$719$		0			0		0.0475819	+	0.998867i	$0.484848\pi$
$720$	−1.91999	+	0.989821i	−1.91999	+	0.989821i
$721$	0.507831	+	0.713148i	0.507831	+	0.713148i
$722$	0.959493	+	0.281733i	0.959493	+	0.281733i
$723$	0.705142	−	0.453167i	0.705142	−	0.453167i
$724$	1.65210	−	0.318417i	1.65210	−	0.318417i
$725$	0.514186	−	1.48564i	0.514186	−	1.48564i
$726$	1.76962	−	0.168978i	1.76962	−	0.168978i
$727$	1.54370	+	1.21398i	1.54370	+	1.21398i	0.888835	+	0.458227i	$0.151515\pi$
$727$	1.54370	+	1.21398i	1.54370	+	1.21398i	0.654861	+	0.755750i	$0.272727\pi$
$728$		0			0
$729$	0.270463	−	0.312131i	0.270463	−	0.312131i
$730$		0			0
$731$		0			0
$732$	0.613544	−	1.34347i	0.613544	−	1.34347i
$733$		0			0		−0.888835	−	0.458227i	$-0.848485\pi$
$733$		0			0		0.888835	+	0.458227i	$0.151515\pi$
$734$	−0.0671040	−	0.466718i	−0.0671040	−	0.466718i
$735$	1.02574	−	4.22815i	1.02574	−	4.22815i
$736$	−1.00000			−1.00000
$737$		0			0
$738$	−4.24216			−4.24216
$739$		0			0		0.235759	−	0.971812i	$-0.424242\pi$
$739$		0			0		−0.235759	+	0.971812i	$0.575758\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	1.67489	+	0.159932i	1.67489	+	0.159932i	0.888835	−	0.458227i	$-0.151515\pi$
$743$	1.67489	+	0.159932i	1.67489	+	0.159932i	0.786053	+	0.618159i	$0.212121\pi$
$744$		0			0
$745$	−1.28605	+	1.48418i	−1.28605	+	1.48418i
$746$		0			0
$747$	2.45775	+	1.93280i	2.45775	+	1.93280i
$748$		0			0
$749$	0.795366	−	2.29806i	0.795366	−	2.29806i
$750$	−1.74555	+	0.336426i	−1.74555	+	0.336426i
$751$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$751$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$752$	−0.627639	−	0.184291i	−0.627639	−	0.184291i
$753$		0			0
$754$		0			0
$755$		0			0
$756$	−2.77128	+	2.64241i	−2.77128	+	2.64241i
$757$		0			0		0.786053	−	0.618159i	$-0.212121\pi$
$757$		0			0		−0.786053	+	0.618159i	$0.787879\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	1.41542	+	0.909632i	1.41542	+	0.909632i	1.00000			$0$
$761$	1.41542	+	0.909632i	1.41542	+	0.909632i	0.415415	+	0.909632i	$0.363636\pi$
$762$	2.31771	+	2.67478i	2.31771	+	2.67478i
$763$	−0.0416572	+	0.874493i	−0.0416572	+	0.874493i
$764$		0			0
$765$		0			0
$766$	0.327068	+	0.566498i	0.327068	+	0.566498i
$767$		0			0
$768$	1.74555	+	0.336426i	1.74555	+	0.336426i
$769$	−1.65033	+	0.660694i	−1.65033	+	0.660694i	−0.995472	−	0.0950560i	$-0.969697\pi$
$769$	−1.65033	+	0.660694i	−1.65033	+	0.660694i	−0.654861	+	0.755750i	$0.727273\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0		−0.981929	−	0.189251i	$-0.939394\pi$
$773$		0			0		0.981929	+	0.189251i	$0.0606061\pi$
$774$	−0.102782	+	0.178024i	−0.102782	+	0.178024i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	−0.0224357	+	0.470984i	−0.0224357	+	0.470984i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−1.88063	+	2.64098i	−1.88063	+	2.64098i
$784$	−1.92384	+	1.51292i	−1.92384	+	1.51292i
$785$		0			0
$786$		0			0
$787$	−1.76962	+	0.912303i	−1.76962	+	0.912303i	−0.841254	+	0.540641i	$0.818182\pi$
$787$	−1.76962	+	0.912303i	−1.76962	+	0.912303i	−0.928368	+	0.371662i	$0.878788\pi$
$788$		0			0
$789$	1.97876	+	0.581017i	1.97876	+	0.581017i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.723734	−	0.690079i	$-0.757576\pi$
$797$		0			0		0.723734	+	0.690079i	$0.242424\pi$
$798$		0			0
$799$		0			0
$800$	0.888835	+	0.458227i	0.888835	+	0.458227i
$801$	0.589927	+	4.10304i	0.589927	+	4.10304i
$802$	−0.437742	+	1.80440i	−0.437742	+	1.80440i
$803$		0			0
$804$	1.70566	+	0.500828i	1.70566	+	0.500828i
$805$	−1.85674			−1.85674
$806$		0			0
$807$	−0.425656	−	2.96050i	−0.425656	−	2.96050i
$808$	−1.70566	−	0.879330i	−1.70566	−	0.879330i
$809$	−0.827068	+	1.81103i	−0.827068	+	1.81103i	−0.327068	+	0.945001i	$0.606061\pi$
$809$	−0.827068	+	1.81103i	−0.827068	+	1.81103i	−0.500000	+	0.866025i	$0.666667\pi$
$810$	1.49916	+	0.143152i	1.49916	+	0.143152i
$811$		0			0		−0.723734	−	0.690079i	$-0.757576\pi$
$811$		0			0		0.723734	+	0.690079i	$0.242424\pi$
$812$	−1.91153	+	2.20602i	−1.91153	+	2.20602i
$813$		0			0
$814$		0			0
$815$	1.67489	−	0.159932i	1.67489	−	0.159932i
$816$		0			0
$817$		0			0
$818$	−1.41542	+	0.909632i	−1.41542	+	0.909632i
$819$		0			0
$820$	1.13915	+	1.59971i	1.13915	+	1.59971i
$821$	−0.738471	+	0.380708i	−0.738471	+	0.380708i	−0.786053	−	0.618159i	$-0.787879\pi$
$821$	−0.738471	+	0.380708i	−0.738471	+	0.380708i	0.0475819	+	0.998867i	$0.484848\pi$
$822$		0			0
$823$	1.13779	−	1.08488i	1.13779	−	1.08488i	0.142315	−	0.989821i	$-0.454545\pi$
$823$	1.13779	−	1.08488i	1.13779	−	1.08488i	0.995472	−	0.0950560i	$-0.0303030\pi$
$824$	−0.370638	+	0.291473i	−0.370638	+	0.291473i
$825$		0			0
$826$		0			0
$827$	−1.82318	−	0.729892i	−1.82318	−	0.729892i	−0.981929	−	0.189251i	$-0.939394\pi$
$827$	−1.82318	−	0.729892i	−1.82318	−	0.729892i	−0.841254	−	0.540641i	$-0.818182\pi$
$828$	1.81720	+	1.16785i	1.81720	+	1.16785i
$829$	−0.544078	−	0.627899i	−0.544078	−	0.627899i	0.415415	−	0.909632i	$-0.363636\pi$
$829$	−0.544078	−	0.627899i	−0.544078	−	0.627899i	−0.959493	+	0.281733i	$0.909091\pi$
$830$	0.0688733	−	1.44583i	0.0688733	−	1.44583i
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	0.279486	+	0.0538665i	0.279486	+	0.0538665i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		0.928368	−	0.371662i	$-0.121212\pi$
$839$		0			0		−0.928368	+	0.371662i	$0.878788\pi$
$840$	3.24102	+	0.624655i	3.24102	+	0.624655i
$841$	−0.735759	+	1.27437i	−0.735759	+	1.27437i
$842$	−0.142315	−	0.246497i	−0.142315	−	0.246497i
$843$	0.380327	+	1.09888i	0.380327	+	1.09888i
$844$		0			0
$845$	0.0475819	−	0.998867i	0.0475819	−	0.998867i
$846$	0.925323	+	1.06788i	0.925323	+	1.06788i
$847$	−1.56199	−	1.00383i	−1.56199	−	1.00383i
$848$		0			0
$849$	0.293496	−	2.04131i	0.293496	−	2.04131i
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		−0.0475819	−	0.998867i	$-0.515152\pi$
$853$		0			0		0.0475819	+	0.998867i	$0.484848\pi$
$854$	−1.37115	+	0.706875i	−1.37115	+	0.706875i
$855$		0			0
$856$	1.25667	+	0.368991i	1.25667	+	0.368991i
$857$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$857$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$858$		0			0
$859$		0			0		0.327068	−	0.945001i	$-0.393939\pi$
$859$		0			0		−0.327068	+	0.945001i	$0.606061\pi$
$860$	0.0947329	−	0.00904590i	0.0947329	−	0.00904590i
$861$	5.09522	+	4.00693i	5.09522	+	4.00693i
$862$		0			0
$863$	0.759713	−	0.876756i	0.759713	−	0.876756i	−0.235759	−	0.971812i	$-0.575758\pi$
$863$	0.759713	−	0.876756i	0.759713	−	0.876756i	0.995472	+	0.0950560i	$0.0303030\pi$
$864$	−1.49256	−	1.42315i	−1.49256	−	1.42315i
$865$		0			0
$866$		0			0
$867$	−1.58006	−	0.814576i	−1.58006	−	0.814576i
$868$		0			0
$869$		0			0
$870$	2.79469			2.79469
$871$		0			0
$872$	−0.471518			−0.471518
$873$		0			0
$874$		0			0
$875$	1.65033	+	0.850806i	1.65033	+	0.850806i
$876$		0			0
$877$		0			0		−0.995472	−	0.0950560i	$-0.969697\pi$
$877$		0			0		0.995472	+	0.0950560i	$0.0303030\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	0.786053	+	0.618159i	0.786053	+	0.618159i	0.928368	−	0.371662i	$-0.121212\pi$
$881$	0.786053	+	0.618159i	0.786053	+	0.618159i	−0.142315	+	0.989821i	$0.545455\pi$
$882$	5.26287	−	0.502543i	5.26287	−	0.502543i
$883$	−0.428368	+	1.23769i	−0.428368	+	1.23769i	0.500000	+	0.866025i	$0.333333\pi$
$883$	−0.428368	+	1.23769i	−0.428368	+	1.23769i	−0.928368	+	0.371662i	$0.878788\pi$
$884$		0			0
$885$		0			0
$886$	1.50842	+	0.442913i	1.50842	+	0.442913i
$887$	0.911911	+	1.28060i	0.911911	+	1.28060i	0.959493	+	0.281733i	$0.0909091\pi$
$887$	0.911911	+	1.28060i	0.911911	+	1.28060i	−0.0475819	+	0.998867i	$0.515152\pi$
$888$		0			0
$889$	−0.175894	−	3.69247i	−0.175894	−	3.69247i
$890$	1.38884	−	1.32425i	1.38884	−	1.32425i
$891$		0			0
$892$	−0.481929	+	0.676774i	−0.481929	+	0.676774i
$893$		0			0
$894$	−3.24102	−	1.29751i	−3.24102	−	1.29751i
$895$		0			0
$896$	−1.21590	−	1.40323i	−1.21590	−	1.40323i
$897$		0			0
$898$	0.271738	+	0.595023i	0.271738	+	0.595023i
$899$		0			0
$900$	−1.08006	−	1.87071i	−1.08006	−	1.87071i
$901$		0			0
$902$		0			0
$903$	0.291604	−	0.116741i	0.291604	−	0.116741i
$904$		0			0
$905$	0.396666	+	1.63508i	0.396666	+	1.63508i
$906$		0			0
$907$	−0.815816	−	0.157236i	−0.815816	−	0.157236i	−0.235759	−	0.971812i	$-0.575758\pi$
$907$	−0.815816	−	0.157236i	−0.815816	−	0.157236i	−0.580057	+	0.814576i	$0.696970\pi$
$908$	−0.959493	+	1.66189i	−0.959493	+	1.66189i
$909$	2.07261	+	3.58987i	2.07261	+	3.58987i
$910$		0			0
$911$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$911$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	1.37115	+	0.548924i	1.37115	+	0.548924i
$916$	0.283341	−	1.97068i	0.283341	−	1.97068i
$917$		0			0
$918$		0			0
$919$		0			0		0.723734	−	0.690079i	$-0.242424\pi$
$919$		0			0		−0.723734	+	0.690079i	$0.757576\pi$
$920$	−0.0475819	−	0.998867i	−0.0475819	−	0.998867i
$921$	−2.06943	+	1.06687i	−2.06943	+	1.06687i
$922$	−0.839614	−	1.17907i	−0.839614	−	1.17907i
$923$		0			0
$924$		0			0
$925$		0			0
$926$	−0.550294	+	1.58997i	−0.550294	+	1.58997i
$927$	1.01392	−	0.0968176i	1.01392	−	0.0968176i
$928$	−1.23576	−	0.971812i	−1.23576	−	0.971812i
$929$	−1.38884	+	0.407799i	−1.38884	+	0.407799i	−0.888835	−	0.458227i	$-0.848485\pi$
$929$	−1.38884	+	0.407799i	−1.38884	+	0.407799i	−0.500000	+	0.866025i	$0.666667\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$	1.76962	+	0.912303i	1.76962	+	0.912303i
$935$		0			0
$936$		0			0
$937$		0			0		1.00000			$0$
$937$		0			0		−1.00000			$\pi$
$938$	−1.07701	−	1.51245i	−1.07701	−	1.51245i
$939$		0			0
$940$	0.154218	−	0.635697i	0.154218	−	0.635697i
$941$	0.186393	+	1.29639i	0.186393	+	1.29639i	0.841254	+	0.540641i	$0.181818\pi$
$941$	0.186393	+	1.29639i	0.186393	+	1.29639i	−0.654861	+	0.755750i	$0.727273\pi$
$942$		0			0
$943$	0.815816	−	1.78639i	0.815816	−	1.78639i
$944$		0			0
$945$	−2.77128	−	2.64241i	−2.77128	−	2.64241i
$946$		0			0
$947$	0.0913090	−	0.0268107i	0.0913090	−	0.0268107i	−0.235759	−	0.971812i	$-0.575758\pi$
$947$	0.0913090	−	0.0268107i	0.0913090	−	0.0268107i	0.327068	+	0.945001i	$0.393939\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$953$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	−0.252989	+	1.75958i	−0.252989	+	1.75958i
$961$	0.928368	+	0.371662i	0.928368	+	0.371662i
$962$		0			0
$963$	−1.85270	−	2.13813i	−1.85270	−	2.13813i
$964$	0.0224357	−	0.470984i	0.0224357	−	0.470984i
$965$		0			0
$966$	−1.07954	−	3.11913i	−1.07954	−	3.11913i
$967$	−0.654861	−	1.13425i	−0.654861	−	1.13425i	−0.981929	−	0.189251i	$-0.939394\pi$
$967$	−0.654861	−	1.13425i	−0.654861	−	1.13425i	0.327068	−	0.945001i	$-0.393939\pi$
$968$	0.500000	−	0.866025i	0.500000	−	0.866025i
$969$		0			0
$970$		0			0
$971$		0			0		−0.235759	−	0.971812i	$-0.575758\pi$
$971$		0			0		0.235759	+	0.971812i	$0.424242\pi$
$972$	0.144952	+	0.597501i	0.144952	+	0.597501i
$973$		0			0
$974$	1.42131	+	0.273935i	1.42131	+	0.273935i
$975$		0			0
$976$	−0.415415	−	0.719520i	−0.415415	−	0.719520i
$977$		0			0		−0.327068	−	0.945001i	$-0.606061\pi$
$977$		0			0		0.327068	+	0.945001i	$0.393939\pi$
$978$	1.24248	+	2.72066i	1.24248	+	2.72066i
$979$		0			0
$980$	−1.60275	−	1.84967i	−1.60275	−	1.84967i
$981$	0.856844	+	0.550660i	0.856844	+	0.550660i
$982$		0			0
$983$	−0.0405070	+	0.281733i	−0.0405070	+	0.281733i	0.959493	+	0.281733i	$0.0909091\pi$
$983$	−0.0405070	+	0.281733i	−0.0405070	+	0.281733i	−1.00000			$1.00000\pi$
$984$	−2.02503	+	2.84376i	−2.02503	+	2.84376i
$985$		0			0
$986$		0			0
$987$	−0.102733	−	2.15664i	−0.102733	−	2.15664i
$988$		0			0
$989$	−0.0552004	−	0.0775182i	−0.0552004	−	0.0775182i
$990$		0			0
$991$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$991$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$	2.46889	−	0.724932i	2.46889	−	0.724932i
$997$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$997$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1340.1.bl.a.839.1	yes	20
4.3	odd	2		1340.1.bl.b.839.1	yes	20
5.4	even	2		1340.1.bl.b.839.1	yes	20
20.19	odd	2	CM	1340.1.bl.a.839.1	yes	20
67.23	even	33	inner	1340.1.bl.a.559.1	✓	20
268.23	odd	66		1340.1.bl.b.559.1	yes	20
335.224	even	66		1340.1.bl.b.559.1	yes	20
1340.559	odd	66	inner	1340.1.bl.a.559.1	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1340.1.bl.a.559.1	✓	20	67.23	even	33	inner
1340.1.bl.a.559.1	✓	20	1340.559	odd	66	inner
1340.1.bl.a.839.1	yes	20	1.1	even	1	trivial
1340.1.bl.a.839.1	yes	20	20.19	odd	2	CM
1340.1.bl.b.559.1	yes	20	268.23	odd	66
1340.1.bl.b.559.1	yes	20	335.224	even	66
1340.1.bl.b.839.1	yes	20	4.3	odd	2
1340.1.bl.b.839.1	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:	\( N \)	\(=\)	\( 1340 = 2^{2} \cdot 5 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1340.bl (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.235759 + 0.971812i) q^{2} +(-0.252989 - 1.75958i) q^{3} +(-0.888835 - 0.458227i) q^{4} +(0.415415 - 0.909632i) q^{5} +(1.76962 + 0.168978i) q^{6} +(-1.34378 - 1.28129i) q^{7} +(0.654861 - 0.755750i) q^{8} +(-2.07261 + 0.608574i) q^{9} +O(q^{10})\)	\(q+(-0.235759 + 0.971812i) q^{2} +(-0.252989 - 1.75958i) q^{3} +(-0.888835 - 0.458227i) q^{4} +(0.415415 - 0.909632i) q^{5} +(1.76962 + 0.168978i) q^{6} +(-1.34378 - 1.28129i) q^{7} +(0.654861 - 0.755750i) q^{8} +(-2.07261 + 0.608574i) q^{9} +(0.786053 + 0.618159i) q^{10} +(-0.581419 + 1.67990i) q^{12} +(1.56199 - 1.00383i) q^{14} +(-1.70566 - 0.500828i) q^{15} +(0.580057 + 0.814576i) q^{16} +(-0.102782 - 2.15767i) q^{18} +(-0.786053 + 0.618159i) q^{20} +(-1.91457 + 2.68864i) q^{21} +(0.928368 + 0.371662i) q^{23} +(-1.49547 - 0.961081i) q^{24} +(-0.654861 - 0.755750i) q^{25} +(0.856711 + 1.87593i) q^{27} +(0.607279 + 1.75462i) q^{28} +(0.786053 + 1.36148i) q^{29} +(0.888835 - 1.53951i) q^{30} +(-0.928368 + 0.371662i) q^{32} +(-1.72373 + 0.690079i) q^{35} +(2.12108 + 0.408804i) q^{36} +(-0.415415 - 0.909632i) q^{40} +(0.0934441 - 1.96163i) q^{41} +(-2.16148 - 2.49448i) q^{42} +(-0.0800569 - 0.0514495i) q^{43} +(-0.307416 + 2.13813i) q^{45} +(-0.580057 + 0.814576i) q^{46} +(-0.514186 + 0.404360i) q^{47} +(1.28656 - 1.22673i) q^{48} +(0.116455 + 2.44470i) q^{49} +(0.888835 - 0.458227i) q^{50} +(-2.02503 + 0.390293i) q^{54} +(-1.84833 + 0.176494i) q^{56} +(-1.50842 + 0.442913i) q^{58} +(1.28656 + 1.22673i) q^{60} +(-0.827068 - 0.0789754i) q^{61} +(3.56491 + 1.83784i) q^{63} +(-0.142315 - 0.989821i) q^{64} +(-0.0475819 - 0.998867i) q^{67} +(0.419102 - 1.72756i) q^{69} +(-0.264241 - 1.83784i) q^{70} +(-0.897344 + 1.96491i) q^{72} +(-1.16413 + 1.34347i) q^{75} +(0.981929 - 0.189251i) q^{80} +(1.26691 - 0.814193i) q^{81} +(1.88431 + 0.553283i) q^{82} +(-0.839614 - 1.17907i) q^{83} +(2.93375 - 1.51245i) q^{84} +(0.0688733 - 0.0656706i) q^{86} +(2.19677 - 1.72756i) q^{87} +(0.273100 - 1.89945i) q^{89} +(-2.00538 - 0.802833i) q^{90} +(-0.654861 - 0.755750i) q^{92} +(-0.271738 - 0.595023i) q^{94} +(0.888835 + 1.53951i) q^{96} +(-2.40324 - 0.463186i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - q^{2} - 2 q^{3} + q^{4} - 2 q^{5} - q^{6} + q^{7} + 2 q^{8}+O(q^{10}) \) 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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