LMFDB - Embedded newform 1340.1.bl.b.619.1

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			619.1
Root			$-0.995472 + 0.0950560i$ of defining polynomial
Character	$\chi$	$=$	1340.619
Dual form			1340.1.bl.b.959.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.981929 + 0.189251i) q^{2} +(0.771316 + 1.68895i) q^{3} +(0.928368 + 0.371662i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(0.437742 + 1.80440i) q^{6} +(-0.379436 - 1.09631i) q^{7} +(0.841254 + 0.540641i) q^{8} +(-1.60275 + 1.84967i) q^{9} +O(q^{10})$	\(q+(0.981929 + 0.189251i) q^{2} +(0.771316 + 1.68895i) q^{3} +(0.928368 + 0.371662i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(0.437742 + 1.80440i) q^{6} +(-0.379436 - 1.09631i) q^{7} +(0.841254 + 0.540641i) q^{8} +(-1.60275 + 1.84967i) q^{9} +(-0.995472 + 0.0950560i) q^{10} +(0.0883470 + 1.85463i) q^{12} +(-0.165101 - 1.14831i) q^{14} +(-1.21590 - 1.40323i) q^{15} +(0.723734 + 0.690079i) q^{16} +(-1.92384 + 1.51292i) q^{18} +(-0.995472 - 0.0950560i) q^{20} +(1.55894 - 1.48645i) q^{21} +(-0.580057 + 0.814576i) q^{23} +(-0.264241 + 1.83784i) q^{24} +(0.841254 - 0.540641i) q^{25} +(-2.57870 - 0.757175i) q^{27} +(0.0552004 - 1.15880i) q^{28} +(0.995472 - 1.72421i) q^{29} +(-0.928368 - 1.60798i) q^{30} +(0.580057 + 0.814576i) q^{32} +(0.672932 + 0.945001i) q^{35} +(-2.17540 + 1.12149i) q^{36} +(-0.959493 - 0.281733i) q^{40} +(1.39734 + 1.09888i) q^{41} +(1.81208 - 1.16455i) q^{42} +(0.223734 - 1.55610i) q^{43} +(1.01671 - 2.22630i) q^{45} +(-0.723734 + 0.690079i) q^{46} +(-0.0947329 - 0.00904590i) q^{47} +(-0.607279 + 1.75462i) q^{48} +(-0.271868 + 0.213799i) q^{49} +(0.928368 - 0.371662i) q^{50} +(-2.38880 - 1.23151i) q^{54} +(0.273507 - 1.12741i) q^{56} +(1.30379 - 1.50465i) q^{58} +(-0.607279 - 1.75462i) q^{60} +(-0.452418 - 1.86489i) q^{61} +(2.63595 + 1.05528i) q^{63} +(0.415415 + 0.909632i) q^{64} +(-0.786053 + 0.618159i) q^{67} +(-1.82318 - 0.351390i) q^{69} +(0.481929 + 1.05528i) q^{70} +(-2.34833 + 0.689531i) q^{72} +(1.56199 + 1.00383i) q^{75} +(-0.888835 - 0.458227i) q^{80} +(-0.361854 - 2.51675i) q^{81} +(1.16413 + 1.34347i) q^{82} +(-0.473420 - 0.451405i) q^{83} +(1.99973 - 0.800570i) q^{84} +(0.514186 - 1.48564i) q^{86} +(3.67992 + 0.351390i) q^{87} +(-0.544078 + 1.19136i) q^{89} +(1.41967 - 1.99365i) q^{90} +(-0.841254 + 0.540641i) q^{92} +(-0.0913090 - 0.0268107i) q^{94} +(-0.928368 + 1.60798i) q^{96} +(-0.307416 + 0.158484i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1340\mathbb{Z}\right)^\times$.

$n$	$537$	$671$	$1141$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{2}{33}\right)$

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 $

$2$	0.981929	+	0.189251i	0.981929	+	0.189251i
$2$	0.981929	+	0.189251i	0.981929	+	0.189251i
$3$	0.771316	+	1.68895i	0.771316	+	1.68895i	0.723734	+	0.690079i	$0.242424\pi$
$3$	0.771316	+	1.68895i	0.771316	+	1.68895i	0.0475819	+	0.998867i	$0.484848\pi$
$4$	0.928368	+	0.371662i	0.928368	+	0.371662i
$5$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$5$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$6$	0.437742	+	1.80440i	0.437742	+	1.80440i
$7$	−0.379436	−	1.09631i	−0.379436	−	1.09631i	−0.959493	−	0.281733i	$-0.909091\pi$
$7$	−0.379436	−	1.09631i	−0.379436	−	1.09631i	0.580057	−	0.814576i	$-0.303030\pi$
$8$	0.841254	+	0.540641i	0.841254	+	0.540641i
$9$	−1.60275	+	1.84967i	−1.60275	+	1.84967i
$10$	−0.995472	+	0.0950560i	−0.995472	+	0.0950560i
$11$		0			0		0.235759	−	0.971812i	$-0.424242\pi$
$11$		0			0		−0.235759	+	0.971812i	$0.575758\pi$
$12$	0.0883470	+	1.85463i	0.0883470	+	1.85463i
$13$		0			0		−0.888835	−	0.458227i	$-0.848485\pi$
$13$		0			0		0.888835	+	0.458227i	$0.151515\pi$
$14$	−0.165101	−	1.14831i	−0.165101	−	1.14831i
$15$	−1.21590	−	1.40323i	−1.21590	−	1.40323i
$16$	0.723734	+	0.690079i	0.723734	+	0.690079i
$17$		0			0		0.928368	−	0.371662i	$-0.121212\pi$
$17$		0			0		−0.928368	+	0.371662i	$0.878788\pi$
$18$	−1.92384	+	1.51292i	−1.92384	+	1.51292i
$19$		0			0		0.327068	−	0.945001i	$-0.393939\pi$
$19$		0			0		−0.327068	+	0.945001i	$0.606061\pi$
$20$	−0.995472	−	0.0950560i	−0.995472	−	0.0950560i
$21$	1.55894	−	1.48645i	1.55894	−	1.48645i
$22$		0			0
$23$	−0.580057	+	0.814576i	−0.580057	+	0.814576i	−0.995472	−	0.0950560i	$-0.969697\pi$
$23$	−0.580057	+	0.814576i	−0.580057	+	0.814576i	0.415415	+	0.909632i	$0.363636\pi$
$24$	−0.264241	+	1.83784i	−0.264241	+	1.83784i
$25$	0.841254	−	0.540641i	0.841254	−	0.540641i
$26$		0			0
$27$	−2.57870	−	0.757175i	−2.57870	−	0.757175i
$28$	0.0552004	−	1.15880i	0.0552004	−	1.15880i
$29$	0.995472	−	1.72421i	0.995472	−	1.72421i	0.415415	−	0.909632i	$-0.363636\pi$
$29$	0.995472	−	1.72421i	0.995472	−	1.72421i	0.580057	−	0.814576i	$-0.303030\pi$
$30$	−0.928368	−	1.60798i	−0.928368	−	1.60798i
$31$		0			0		0.888835	−	0.458227i	$-0.151515\pi$
$31$		0			0		−0.888835	+	0.458227i	$0.848485\pi$
$32$	0.580057	+	0.814576i	0.580057	+	0.814576i
$33$		0			0
$34$		0			0
$35$	0.672932	+	0.945001i	0.672932	+	0.945001i
$36$	−2.17540	+	1.12149i	−2.17540	+	1.12149i
$37$		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
$40$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$41$	1.39734	+	1.09888i	1.39734	+	1.09888i	0.981929	+	0.189251i	$0.0606061\pi$
$41$	1.39734	+	1.09888i	1.39734	+	1.09888i	0.415415	+	0.909632i	$0.363636\pi$
$42$	1.81208	−	1.16455i	1.81208	−	1.16455i
$43$	0.223734	−	1.55610i	0.223734	−	1.55610i	−0.500000	−	0.866025i	$-0.666667\pi$
$43$	0.223734	−	1.55610i	0.223734	−	1.55610i	0.723734	−	0.690079i	$-0.242424\pi$
$44$		0			0
$45$	1.01671	−	2.22630i	1.01671	−	2.22630i
$46$	−0.723734	+	0.690079i	−0.723734	+	0.690079i
$47$	−0.0947329	−	0.00904590i	−0.0947329	−	0.00904590i	0.0475819	−	0.998867i	$-0.484848\pi$
$47$	−0.0947329	−	0.00904590i	−0.0947329	−	0.00904590i	−0.142315	+	0.989821i	$0.545455\pi$
$48$	−0.607279	+	1.75462i	−0.607279	+	1.75462i
$49$	−0.271868	+	0.213799i	−0.271868	+	0.213799i
$50$	0.928368	−	0.371662i	0.928368	−	0.371662i
$51$		0			0
$52$		0			0
$53$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$53$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$54$	−2.38880	−	1.23151i	−2.38880	−	1.23151i
$55$		0			0
$56$	0.273507	−	1.12741i	0.273507	−	1.12741i
$57$		0			0
$58$	1.30379	−	1.50465i	1.30379	−	1.50465i
$59$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$59$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$60$	−0.607279	−	1.75462i	−0.607279	−	1.75462i
$61$	−0.452418	−	1.86489i	−0.452418	−	1.86489i	−0.500000	−	0.866025i	$-0.666667\pi$
$61$	−0.452418	−	1.86489i	−0.452418	−	1.86489i	0.0475819	−	0.998867i	$-0.484848\pi$
$62$		0			0
$63$	2.63595	+	1.05528i	2.63595	+	1.05528i
$64$	0.415415	+	0.909632i	0.415415	+	0.909632i
$65$		0			0
$66$		0			0
$67$	−0.786053	+	0.618159i	−0.786053	+	0.618159i
$67$	−0.786053	+	0.618159i	−0.786053	+	0.618159i
$68$		0			0
$69$	−1.82318	−	0.351390i	−1.82318	−	0.351390i
$70$	0.481929	+	1.05528i	0.481929	+	1.05528i
$71$		0			0		−0.928368	−	0.371662i	$-0.878788\pi$
$71$		0			0		0.928368	+	0.371662i	$0.121212\pi$
$72$	−2.34833	+	0.689531i	−2.34833	+	0.689531i
$73$		0			0		−0.235759	−	0.971812i	$-0.575758\pi$
$73$		0			0		0.235759	+	0.971812i	$0.424242\pi$
$74$		0			0
$75$	1.56199	+	1.00383i	1.56199	+	1.00383i
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		−0.0475819	−	0.998867i	$-0.515152\pi$
$79$		0			0		0.0475819	+	0.998867i	$0.484848\pi$
$80$	−0.888835	−	0.458227i	−0.888835	−	0.458227i
$81$	−0.361854	−	2.51675i	−0.361854	−	2.51675i
$82$	1.16413	+	1.34347i	1.16413	+	1.34347i
$83$	−0.473420	−	0.451405i	−0.473420	−	0.451405i	0.415415	−	0.909632i	$-0.363636\pi$
$83$	−0.473420	−	0.451405i	−0.473420	−	0.451405i	−0.888835	+	0.458227i	$0.848485\pi$
$84$	1.99973	−	0.800570i	1.99973	−	0.800570i
$85$		0			0
$86$	0.514186	−	1.48564i	0.514186	−	1.48564i
$87$	3.67992	+	0.351390i	3.67992	+	0.351390i
$88$		0			0
$89$	−0.544078	+	1.19136i	−0.544078	+	1.19136i	0.415415	+	0.909632i	$0.363636\pi$
$89$	−0.544078	+	1.19136i	−0.544078	+	1.19136i	−0.959493	+	0.281733i	$0.909091\pi$
$90$	1.41967	−	1.99365i	1.41967	−	1.99365i
$91$		0			0
$92$	−0.841254	+	0.540641i	−0.841254	+	0.540641i
$93$		0			0
$94$	−0.0913090	−	0.0268107i	−0.0913090	−	0.0268107i
$95$		0			0
$96$	−0.928368	+	1.60798i	−0.928368	+	1.60798i
$97$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$97$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$98$	−0.307416	+	0.158484i	−0.307416	+	0.158484i
$99$		0			0
$100$	0.981929	−	0.189251i	0.981929	−	0.189251i
$101$	−1.28605	+	0.247866i	−1.28605	+	0.247866i	−0.786053	−	0.618159i	$-0.787879\pi$
$101$	−1.28605	+	0.247866i	−1.28605	+	0.247866i	−0.500000	+	0.866025i	$0.666667\pi$
$102$		0			0
$103$	−1.74555	+	0.899892i	−1.74555	+	0.899892i	−0.786053	+	0.618159i	$0.787879\pi$
$103$	−1.74555	+	0.899892i	−1.74555	+	0.899892i	−0.959493	+	0.281733i	$0.909091\pi$
$104$		0			0
$105$	−1.07701	+	1.86544i	−1.07701	+	1.86544i
$106$		0			0
$107$	−1.61435	−	0.474017i	−1.61435	−	0.474017i	−0.654861	−	0.755750i	$-0.727273\pi$
$107$	−1.61435	−	0.474017i	−1.61435	−	0.474017i	−0.959493	+	0.281733i	$0.909091\pi$
$108$	−2.11257	−	1.66134i	−2.11257	−	1.66134i
$109$	1.65210	−	1.06174i	1.65210	−	1.06174i	0.723734	−	0.690079i	$-0.242424\pi$
$109$	1.65210	−	1.06174i	1.65210	−	1.06174i	0.928368	−	0.371662i	$-0.121212\pi$
$110$		0			0
$111$		0			0
$112$	0.481929	−	1.05528i	0.481929	−	1.05528i
$113$		0			0		0.723734	−	0.690079i	$-0.242424\pi$
$113$		0			0		−0.723734	+	0.690079i	$0.757576\pi$
$114$		0			0
$115$	0.327068	−	0.945001i	0.327068	−	0.945001i
$116$	1.56499	−	1.23072i	1.56499	−	1.23072i
$117$		0			0
$118$		0			0
$119$		0			0
$120$	−0.264241	−	1.83784i	−0.264241	−	1.83784i
$121$	−0.888835	−	0.458227i	−0.888835	−	0.458227i
$122$	−0.0913090	−	1.91681i	−0.0913090	−	1.91681i
$123$	−0.778161	+	3.20762i	−0.778161	+	3.20762i
$124$		0			0
$125$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$126$	2.38861	+	1.53506i	2.38861	+	1.53506i
$127$	−0.154218	−	0.445585i	−0.154218	−	0.445585i	0.841254	−	0.540641i	$-0.181818\pi$
$127$	−0.154218	−	0.445585i	−0.154218	−	0.445585i	−0.995472	+	0.0950560i	$0.969697\pi$
$128$	0.235759	+	0.971812i	0.235759	+	0.971812i
$129$	2.80075	−	0.822373i	2.80075	−	0.822373i
$130$		0			0
$131$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$131$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$132$		0			0
$133$		0			0
$134$	−0.888835	+	0.458227i	−0.888835	+	0.458227i
$135$	2.68757			2.68757
$136$		0			0
$137$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$137$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$138$	−1.72373	−	0.690079i	−1.72373	−	0.690079i
$139$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$139$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$140$	0.273507	+	1.12741i	0.273507	+	1.12741i
$141$	−0.0577910	−	0.166976i	−0.0577910	−	0.166976i
$142$		0			0
$143$		0			0
$144$	−2.43639	+	0.232647i	−2.43639	+	0.232647i
$145$	−0.469383	+	1.93482i	−0.469383	+	1.93482i
$146$		0			0
$147$	−0.570791	−	0.294263i	−0.570791	−	0.294263i
$148$		0			0
$149$	1.16413	+	1.34347i	1.16413	+	1.34347i	0.928368	+	0.371662i	$0.121212\pi$
$149$	1.16413	+	1.34347i	1.16413	+	1.34347i	0.235759	+	0.971812i	$0.424242\pi$
$150$	1.34378	+	1.28129i	1.34378	+	1.28129i
$151$		0			0		0.928368	−	0.371662i	$-0.121212\pi$
$151$		0			0		−0.928368	+	0.371662i	$0.878788\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.580057	−	0.814576i	$-0.303030\pi$
$157$		0			0		−0.580057	+	0.814576i	$0.696970\pi$
$158$		0			0
$159$		0			0
$160$	−0.786053	−	0.618159i	−0.786053	−	0.618159i
$161$	1.11312	+	0.326842i	1.11312	+	0.326842i
$162$	0.120983	−	2.53975i	0.120983	−	2.53975i
$163$	0.142315	−	0.246497i	0.142315	−	0.246497i	−0.786053	−	0.618159i	$-0.787879\pi$
$163$	0.142315	−	0.246497i	0.142315	−	0.246497i	0.928368	+	0.371662i	$0.121212\pi$
$164$	0.888835	+	1.53951i	0.888835	+	1.53951i
$165$		0			0
$166$	−0.379436	−	0.532843i	−0.379436	−	0.532843i
$167$	0.815816	−	0.157236i	0.815816	−	0.157236i	0.235759	−	0.971812i	$-0.424242\pi$
$167$	0.815816	−	0.157236i	0.815816	−	0.157236i	0.580057	+	0.814576i	$0.303030\pi$
$168$	2.11510	−	0.407652i	2.11510	−	0.407652i
$169$	0.580057	+	0.814576i	0.580057	+	0.814576i
$170$		0			0
$171$		0			0
$172$	0.786053	−	1.36148i	0.786053	−	1.36148i
$173$		0			0		0.0475819	−	0.998867i	$-0.484848\pi$
$173$		0			0		−0.0475819	+	0.998867i	$0.515152\pi$
$174$	3.54692	+	1.04147i	3.54692	+	1.04147i
$175$	−0.911911	−	0.717135i	−0.911911	−	0.717135i
$176$		0			0
$177$		0			0
$178$	−0.759713	+	1.06687i	−0.759713	+	1.06687i
$179$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$179$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$180$	1.77132	−	1.68895i	1.77132	−	1.68895i
$181$	0.283341	+	0.0270558i	0.283341	+	0.0270558i	0.235759	−	0.971812i	$-0.424242\pi$
$181$	0.283341	+	0.0270558i	0.283341	+	0.0270558i	0.0475819	+	0.998867i	$0.484848\pi$
$182$		0			0
$183$	2.80075	−	2.20253i	2.80075	−	2.20253i
$184$	−0.928368	+	0.371662i	−0.928368	+	0.371662i
$185$		0			0
$186$		0			0
$187$		0			0
$188$	−0.0845850	−	0.0436066i	−0.0845850	−	0.0436066i
$189$	0.148355	+	3.11435i	0.148355	+	3.11435i
$190$		0			0
$191$		0			0		0.995472	−	0.0950560i	$-0.0303030\pi$
$191$		0			0		−0.995472	+	0.0950560i	$0.969697\pi$
$192$	−1.21590	+	1.40323i	−1.21590	+	1.40323i
$193$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$193$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$194$		0			0
$195$		0			0
$196$	−0.331854	+	0.0974412i	−0.331854	+	0.0974412i
$197$		0			0		−0.928368	−	0.371662i	$-0.878788\pi$
$197$		0			0		0.928368	+	0.371662i	$0.121212\pi$
$198$		0			0
$199$		0			0		−0.981929	−	0.189251i	$-0.939394\pi$
$199$		0			0		0.981929	+	0.189251i	$0.0606061\pi$
$200$	1.00000			1.00000
$201$	−1.65033	−	0.850806i	−1.65033	−	0.850806i
$202$	−1.30972			−1.30972
$203$	−2.26798	−	0.437118i	−2.26798	−	0.437118i
$204$		0			0
$205$	−1.65033	−	0.660694i	−1.65033	−	0.660694i
$206$	−1.88431	+	0.553283i	−1.88431	+	0.553283i
$207$	−0.577012	−	2.37848i	−0.577012	−	2.37848i
$208$		0			0
$209$		0			0
$210$	−1.41059	+	1.62790i	−1.41059	+	1.62790i
$211$		0			0		0.995472	−	0.0950560i	$-0.0303030\pi$
$211$		0			0		−0.995472	+	0.0950560i	$0.969697\pi$
$212$		0			0
$213$		0			0
$214$	−1.49547	−	0.770969i	−1.49547	−	0.770969i
$215$	0.223734	+	1.55610i	0.223734	+	1.55610i
$216$	−1.75998	−	2.03113i	−1.75998	−	2.03113i
$217$		0			0
$218$	1.82318	−	0.729892i	1.82318	−	0.729892i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−0.797176	+	1.74557i	−0.797176	+	1.74557i	−0.142315	+	0.989821i	$0.545455\pi$
$223$	−0.797176	+	1.74557i	−0.797176	+	1.74557i	−0.654861	+	0.755750i	$0.727273\pi$
$224$	0.672932	−	0.945001i	0.672932	−	0.945001i
$225$	−0.348311	+	2.42256i	−0.348311	+	2.42256i
$226$		0			0
$227$	1.02951	+	0.809616i	1.02951	+	0.809616i	0.981929	−	0.189251i	$-0.0606061\pi$
$227$	1.02951	+	0.809616i	1.02951	+	0.809616i	0.0475819	+	0.998867i	$0.484848\pi$
$228$		0			0
$229$	0.0224357	−	0.470984i	0.0224357	−	0.470984i	−0.959493	−	0.281733i	$-0.909091\pi$
$229$	0.0224357	−	0.470984i	0.0224357	−	0.470984i	0.981929	−	0.189251i	$-0.0606061\pi$
$230$	0.500000	−	0.866025i	0.500000	−	0.866025i
$231$		0			0
$232$	1.76962	−	0.912303i	1.76962	−	0.912303i
$233$		0			0		−0.580057	−	0.814576i	$-0.696970\pi$
$233$		0			0		0.580057	+	0.814576i	$0.303030\pi$
$234$		0			0
$235$	0.0934441	−	0.0180099i	0.0934441	−	0.0180099i
$236$		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	$0.666667\pi$
$240$	0.0883470	−	1.85463i	0.0883470	−	1.85463i
$241$	−1.88431	−	0.553283i	−1.88431	−	0.553283i	−0.995472	−	0.0950560i	$-0.969697\pi$
$241$	−1.88431	−	0.553283i	−1.88431	−	0.553283i	−0.888835	−	0.458227i	$-0.848485\pi$
$242$	−0.786053	−	0.618159i	−0.786053	−	0.618159i
$243$	1.71063	−	1.09936i	1.71063	−	1.09936i
$244$	0.273100	−	1.89945i	0.273100	−	1.89945i
$245$	0.200621	−	0.281733i	0.200621	−	0.281733i
$246$	−1.37115	+	3.00239i	−1.37115	+	3.00239i
$247$		0			0
$248$		0			0
$249$	0.397243	−	1.14776i	0.397243	−	1.14776i
$250$	−0.786053	+	0.618159i	−0.786053	+	0.618159i
$251$		0			0		0.928368	−	0.371662i	$-0.121212\pi$
$251$		0			0		−0.928368	+	0.371662i	$0.878788\pi$
$252$	2.05493	+	1.95937i	2.05493	+	1.95937i
$253$		0			0
$254$	−0.0671040	−	0.466718i	−0.0671040	−	0.466718i
$255$		0			0
$256$	0.0475819	+	0.998867i	0.0475819	+	0.998867i
$257$		0			0		0.235759	−	0.971812i	$-0.424242\pi$
$257$		0			0		−0.235759	+	0.971812i	$0.575758\pi$
$258$	2.90577	−	0.277467i	2.90577	−	0.277467i
$259$		0			0
$260$		0			0
$261$	1.59373	+	4.60477i	1.59373	+	4.60477i
$262$		0			0
$263$	−1.38884	+	0.407799i	−1.38884	+	0.407799i	−0.888835	−	0.458227i	$-0.848485\pi$
$263$	−1.38884	+	0.407799i	−1.38884	+	0.407799i	−0.500000	+	0.866025i	$0.666667\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−2.43181			−2.43181
$268$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$269$	−0.284630			−0.284630			−0.142315	−	0.989821i	$-0.545455\pi$
$269$	−0.284630			−0.284630			−0.142315	+	0.989821i	$0.545455\pi$
$270$	2.63900	+	0.508625i	2.63900	+	0.508625i
$271$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$271$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$	−1.56199	−	1.00383i	−1.56199	−	1.00383i
$277$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$277$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$278$		0			0
$279$		0			0
$280$	0.0552004	+	1.15880i	0.0552004	+	1.15880i
$281$	−0.0845850	−	0.0436066i	−0.0845850	−	0.0436066i	0.415415	−	0.909632i	$-0.363636\pi$
$281$	−0.0845850	−	0.0436066i	−0.0845850	−	0.0436066i	−0.500000	+	0.866025i	$0.666667\pi$
$282$	−0.0251462	−	0.174896i	−0.0251462	−	0.174896i
$283$	−0.947890	−	1.09392i	−0.947890	−	1.09392i	−0.995472	−	0.0950560i	$-0.969697\pi$
$283$	−0.947890	−	1.09392i	−0.947890	−	1.09392i	0.0475819	−	0.998867i	$-0.484848\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	0.674512	−	1.94888i	0.674512	−	1.94888i
$288$	−2.43639	−	0.232647i	−2.43639	−	0.232647i
$289$	0.723734	−	0.690079i	0.723734	−	0.690079i
$290$	−0.827068	+	1.81103i	−0.827068	+	1.81103i
$291$		0			0
$292$		0			0
$293$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$293$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$294$	−0.504786	−	0.396968i	−0.504786	−	0.396968i
$295$		0			0
$296$		0			0
$297$		0			0
$298$	0.888835	+	1.53951i	0.888835	+	1.53951i
$299$		0			0
$300$	1.07701	+	1.51245i	1.07701	+	1.51245i
$301$	−1.79086	+	0.345161i	−1.79086	+	0.345161i
$302$		0			0
$303$	−1.41059	−	1.98089i	−1.41059	−	1.98089i
$304$		0			0
$305$	0.959493	+	1.66189i	0.959493	+	1.66189i
$306$		0			0
$307$	0.0800569	−	1.68060i	0.0800569	−	1.68060i	−0.500000	−	0.866025i	$-0.666667\pi$
$307$	0.0800569	−	1.68060i	0.0800569	−	1.68060i	0.580057	−	0.814576i	$-0.303030\pi$
$308$		0			0
$309$	−2.86624	−	2.25403i	−2.86624	−	2.25403i
$310$		0			0
$311$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$311$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$312$		0			0
$313$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$313$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$314$		0			0
$315$	−2.82648	−	0.269897i	−2.82648	−	0.269897i
$316$		0			0
$317$		0			0		0.786053	−	0.618159i	$-0.212121\pi$
$317$		0			0		−0.786053	+	0.618159i	$0.787879\pi$
$318$		0			0
$319$		0			0
$320$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$321$	−0.444587	−	3.09217i	−0.444587	−	3.09217i
$322$	1.03115	+	0.531595i	1.03115	+	0.531595i
$323$		0			0
$324$	0.599448	−	2.47096i	0.599448	−	2.47096i
$325$		0			0
$326$	0.186393	−	0.215109i	0.186393	−	0.215109i
$327$	3.06752	+	1.97137i	3.06752	+	1.97137i
$328$	0.581419	+	1.67990i	0.581419	+	1.67990i
$329$	0.0260280	+	0.107289i	0.0260280	+	0.107289i
$330$		0			0
$331$		0			0		−0.928368	−	0.371662i	$-0.878788\pi$
$331$		0			0		0.928368	+	0.371662i	$0.121212\pi$
$332$	−0.271738	−	0.595023i	−0.271738	−	0.595023i
$333$		0			0
$334$	0.830830			0.830830
$335$	0.580057	−	0.814576i	0.580057	−	0.814576i
$336$	2.15402			2.15402
$337$		0			0		−0.981929	−	0.189251i	$-0.939394\pi$
$337$		0			0		0.981929	+	0.189251i	$0.0606061\pi$
$338$	0.415415	+	0.909632i	0.415415	+	0.909632i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−0.638404	−	0.410277i	−0.638404	−	0.410277i
$344$	1.02951	−	1.18812i	1.02951	−	1.18812i
$345$	1.84833	−	0.176494i	1.84833	−	0.176494i
$346$		0			0
$347$	−0.0913090	−	1.91681i	−0.0913090	−	1.91681i	−0.327068	−	0.945001i	$-0.606061\pi$
$347$	−0.0913090	−	1.91681i	−0.0913090	−	1.91681i	0.235759	−	0.971812i	$-0.424242\pi$
$348$	3.28572	+	1.69391i	3.28572	+	1.69391i
$349$	0.223734	+	1.55610i	0.223734	+	1.55610i	0.723734	+	0.690079i	$0.242424\pi$
$349$	0.223734	+	1.55610i	0.223734	+	1.55610i	−0.500000	+	0.866025i	$0.666667\pi$
$350$	−0.759713	−	0.876756i	−0.759713	−	0.876756i
$351$		0			0
$352$		0			0
$353$		0			0		0.786053	−	0.618159i	$-0.212121\pi$
$353$		0			0		−0.786053	+	0.618159i	$0.787879\pi$
$354$		0			0
$355$		0			0
$356$	−0.947890	+	0.903811i	−0.947890	+	0.903811i
$357$		0			0
$358$		0			0
$359$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$359$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$360$	2.05894	−	1.32320i	2.05894	−	1.32320i
$361$	−0.786053	−	0.618159i	−0.786053	−	0.618159i
$362$	0.273100	+	0.0801894i	0.273100	+	0.0801894i
$363$	0.0883470	−	1.85463i	0.0883470	−	1.85463i
$364$		0			0
$365$		0			0
$366$	3.16697	−	1.63268i	3.16697	−	1.63268i
$367$	1.13915	+	1.59971i	1.13915	+	1.59971i	0.723734	+	0.690079i	$0.242424\pi$
$367$	1.13915	+	1.59971i	1.13915	+	1.59971i	0.415415	+	0.909632i	$0.363636\pi$
$368$	−0.981929	+	0.189251i	−0.981929	+	0.189251i
$369$	−4.27217	+	0.823393i	−4.27217	+	0.823393i
$370$		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
$375$	−1.78153	−	0.523103i	−1.78153	−	0.523103i
$376$	−0.0748038	−	0.0588264i	−0.0748038	−	0.0588264i
$377$		0			0
$378$	−0.443721	+	3.08615i	−0.443721	+	3.08615i
$379$		0			0		0.580057	−	0.814576i	$-0.303030\pi$
$379$		0			0		−0.580057	+	0.814576i	$0.696970\pi$
$380$		0			0
$381$	0.633618	−	0.604153i	0.633618	−	0.604153i
$382$		0			0
$383$	−0.0311250	+	0.0899299i	−0.0311250	+	0.0899299i	−0.959493	−	0.281733i	$-0.909091\pi$
$383$	−0.0311250	+	0.0899299i	−0.0311250	+	0.0899299i	0.928368	+	0.371662i	$0.121212\pi$
$384$	−1.45949	+	1.14776i	−1.45949	+	1.14776i
$385$		0			0
$386$		0			0
$387$	2.51969	+	2.90788i	2.51969	+	2.90788i
$388$		0			0
$389$	−1.74555	−	0.899892i	−1.74555	−	0.899892i	−0.959493	−	0.281733i	$-0.909091\pi$
$389$	−1.74555	−	0.899892i	−1.74555	−	0.899892i	−0.786053	−	0.618159i	$-0.787879\pi$
$390$		0			0
$391$		0			0
$392$	−0.344298	+	0.0328765i	−0.344298	+	0.0328765i
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$397$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$398$		0			0
$399$		0			0
$400$	0.981929	+	0.189251i	0.981929	+	0.189251i
$401$	1.16011			1.16011			0.580057	−	0.814576i	$-0.303030\pi$
$401$	1.16011			1.16011			0.580057	+	0.814576i	$0.303030\pi$
$402$	−1.45949	−	1.14776i	−1.45949	−	1.14776i
$403$		0			0
$404$	−1.28605	−	0.247866i	−1.28605	−	0.247866i
$405$	1.05625	+	2.31286i	1.05625	+	2.31286i
$406$	−2.14427	−	0.858437i	−2.14427	−	0.858437i
$407$		0			0
$408$		0			0
$409$	0.0930932	+	0.268975i	0.0930932	+	0.268975i	0.981929	−	0.189251i	$-0.0606061\pi$
$409$	0.0930932	+	0.268975i	0.0930932	+	0.268975i	−0.888835	+	0.458227i	$0.848485\pi$
$410$	−1.49547	−	0.961081i	−1.49547	−	0.961081i
$411$		0			0
$412$	−1.95496	+	0.186677i	−1.95496	+	0.186677i
$413$		0			0
$414$	−0.116455	−	2.44470i	−0.116455	−	2.44470i
$415$	0.581419	+	0.299742i	0.581419	+	0.299742i
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		0.928368	−	0.371662i	$-0.121212\pi$
$419$		0			0		−0.928368	+	0.371662i	$0.878788\pi$
$420$	−1.69318	+	1.33153i	−1.69318	+	1.33153i
$421$	−0.271738	+	0.785135i	−0.271738	+	0.785135i	0.723734	+	0.690079i	$0.242424\pi$
$421$	−0.271738	+	0.785135i	−0.271738	+	0.785135i	−0.995472	+	0.0950560i	$0.969697\pi$
$422$		0			0
$423$	0.168565	−	0.160727i	0.168565	−	0.160727i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−1.87283	+	1.20360i	−1.87283	+	1.20360i
$428$	−1.32254	−	1.04006i	−1.32254	−	1.04006i
$429$		0			0
$430$	−0.0748038	+	1.57033i	−0.0748038	+	1.57033i
$431$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$431$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$432$	−1.34378	−	2.32750i	−1.34378	−	2.32750i
$433$		0			0		0.888835	−	0.458227i	$-0.151515\pi$
$433$		0			0		−0.888835	+	0.458227i	$0.848485\pi$
$434$		0			0
$435$	−3.62985	+	0.699597i	−3.62985	+	0.699597i
$436$	1.92837	−	0.371662i	1.92837	−	0.371662i
$437$		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
$441$	0.0402777	−	0.845532i	0.0402777	−	0.845532i
$442$		0			0
$443$	1.56499	+	1.23072i	1.56499	+	1.23072i	0.841254	+	0.540641i	$0.181818\pi$
$443$	1.56499	+	1.23072i	1.56499	+	1.23072i	0.723734	+	0.690079i	$0.242424\pi$
$444$		0			0
$445$	0.186393	−	1.29639i	0.186393	−	1.29639i
$446$	−1.11312	+	1.56316i	−1.11312	+	1.56316i
$447$	−1.37115	+	3.00239i	−1.37115	+	3.00239i
$448$	0.839614	−	0.800570i	0.839614	−	0.800570i
$449$	−0.0947329	−	0.00904590i	−0.0947329	−	0.00904590i	0.0475819	−	0.998867i	$-0.484848\pi$
$449$	−0.0947329	−	0.00904590i	−0.0947329	−	0.00904590i	−0.142315	+	0.989821i	$0.545455\pi$
$450$	−0.800488	+	2.31286i	−0.800488	+	2.31286i
$451$		0			0
$452$		0			0
$453$		0			0
$454$	0.857685	+	0.989821i	0.857685	+	0.989821i
$455$		0			0
$456$		0			0
$457$		0			0		−0.0475819	−	0.998867i	$-0.515152\pi$
$457$		0			0		0.0475819	+	0.998867i	$0.484848\pi$
$458$	0.111165	−	0.458227i	0.111165	−	0.458227i
$459$		0			0
$460$	0.654861	−	0.755750i	0.654861	−	0.755750i
$461$	−0.550294	−	0.353653i	−0.550294	−	0.353653i	0.235759	−	0.971812i	$-0.424242\pi$
$461$	−0.550294	−	0.353653i	−0.550294	−	0.353653i	−0.786053	+	0.618159i	$0.787879\pi$
$462$		0			0
$463$	−0.0671040	−	0.276606i	−0.0671040	−	0.276606i	0.928368	−	0.371662i	$-0.121212\pi$
$463$	−0.0671040	−	0.276606i	−0.0671040	−	0.276606i	−0.995472	+	0.0950560i	$0.969697\pi$
$464$	1.91030	−	0.560914i	1.91030	−	0.560914i
$465$		0			0
$466$		0			0
$467$	0.462997	+	0.0892353i	0.462997	+	0.0892353i	0.415415	−	0.909632i	$-0.363636\pi$
$467$	0.462997	+	0.0892353i	0.462997	+	0.0892353i	0.0475819	+	0.998867i	$0.484848\pi$
$468$		0			0
$469$	0.975950	+	0.627205i	0.975950	+	0.627205i
$470$	0.0951638			0.0951638
$471$		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		0.995472	−	0.0950560i	$-0.0303030\pi$
$479$		0			0		−0.995472	+	0.0950560i	$0.969697\pi$
$480$	0.437742	−	1.80440i	0.437742	−	1.80440i
$481$		0			0
$482$	−1.74555	−	0.899892i	−1.74555	−	0.899892i
$483$	0.306550	+	2.13210i	0.306550	+	2.13210i
$484$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$485$		0			0
$486$	1.88777	−	0.755750i	1.88777	−	0.755750i
$487$	0.514186	−	0.404360i	0.514186	−	0.404360i	−0.327068	−	0.945001i	$-0.606061\pi$
$487$	0.514186	−	0.404360i	0.514186	−	0.404360i	0.841254	+	0.540641i	$0.181818\pi$
$488$	0.627639	−	1.81344i	0.627639	−	1.81344i
$489$	0.526089	+	0.0502354i	0.526089	+	0.0502354i
$490$	0.250314	−	0.238674i	0.250314	−	0.238674i
$491$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$491$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$492$	−1.91457	+	2.68864i	−1.91457	+	2.68864i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	0.607279	−	1.05184i	0.607279	−	1.05184i
$499$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$499$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$500$	−0.888835	+	0.458227i	−0.888835	+	0.458227i
$501$	0.894814	+	1.25659i	0.894814	+	1.25659i
$502$		0			0
$503$	−1.74555	+	0.336426i	−1.74555	+	0.336426i	−0.959493	−	0.281733i	$-0.909091\pi$
$503$	−1.74555	+	0.336426i	−1.74555	+	0.336426i	−0.786053	+	0.618159i	$0.787879\pi$
$504$	1.64698	+	2.31286i	1.64698	+	2.31286i
$505$	1.16413	−	0.600149i	1.16413	−	0.600149i
$506$		0			0
$507$	−0.928368	+	1.60798i	−0.928368	+	1.60798i
$508$	0.0224357	−	0.470984i	0.0224357	−	0.470984i
$509$	−0.797176	−	0.234072i	−0.797176	−	0.234072i	−0.142315	−	0.989821i	$-0.545455\pi$
$509$	−0.797176	−	0.234072i	−0.797176	−	0.234072i	−0.654861	+	0.755750i	$0.727273\pi$
$510$		0			0
$511$		0			0
$512$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$513$		0			0
$514$		0			0
$515$	1.42131	−	1.35522i	1.42131	−	1.35522i
$516$	2.90577	+	0.277467i	2.90577	+	0.277467i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	0.654861	+	0.755750i	0.654861	+	0.755750i	0.981929	−	0.189251i	$-0.0606061\pi$
$521$	0.654861	+	0.755750i	0.654861	+	0.755750i	−0.327068	+	0.945001i	$0.606061\pi$
$522$	0.693468	+	4.82317i	0.693468	+	4.82317i
$523$	1.39734	+	0.720381i	1.39734	+	0.720381i	0.981929	−	0.189251i	$-0.0606061\pi$
$523$	1.39734	+	0.720381i	1.39734	+	0.720381i	0.415415	+	0.909632i	$0.363636\pi$
$524$		0			0
$525$	0.507831	−	2.09331i	0.507831	−	2.09331i
$526$	−1.44091	+	0.137591i	−1.44091	+	0.137591i
$527$		0			0
$528$		0			0
$529$		0			0
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$	−2.38786	−	0.460222i	−2.38786	−	0.460222i
$535$	1.68251			1.68251
$536$	−0.995472	+	0.0950560i	−0.995472	+	0.0950560i
$537$		0			0
$538$	−0.279486	−	0.0538665i	−0.279486	−	0.0538665i
$539$		0			0
$540$	2.49505	+	0.998867i	2.49505	+	0.998867i
$541$	1.50842	−	0.442913i	1.50842	−	0.442913i	0.580057	−	0.814576i	$-0.303030\pi$
$541$	1.50842	−	0.442913i	1.50842	−	0.442913i	0.928368	+	0.371662i	$0.121212\pi$
$542$		0			0
$543$	0.172850	+	0.499416i	0.172850	+	0.499416i
$544$		0			0
$545$	−1.28605	+	1.48418i	−1.28605	+	1.48418i
$546$		0			0
$547$	0.111165	−	0.458227i	0.111165	−	0.458227i	−0.888835	−	0.458227i	$-0.848485\pi$
$547$	0.111165	−	0.458227i	0.111165	−	0.458227i	1.00000			$0$
$548$		0			0
$549$	4.17456	+	2.15213i	4.17456	+	2.15213i
$550$		0			0
$551$		0			0
$552$	−1.34378	−	1.28129i	−1.34378	−	1.28129i
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$		0			0		0.723734	−	0.690079i	$-0.242424\pi$
$557$		0			0		−0.723734	+	0.690079i	$0.757576\pi$
$558$		0			0
$559$		0			0
$560$	−0.165101	+	1.14831i	−0.165101	+	1.14831i
$561$		0			0
$562$	−0.0748038	−	0.0588264i	−0.0748038	−	0.0588264i
$563$	1.50842	+	0.442913i	1.50842	+	0.442913i	0.928368	−	0.371662i	$-0.121212\pi$
$563$	1.50842	+	0.442913i	1.50842	+	0.442913i	0.580057	+	0.814576i	$0.303030\pi$
$564$	0.00840744	−	0.176494i	0.00840744	−	0.176494i
$565$		0			0
$566$	−0.723734	−	1.25354i	−0.723734	−	1.25354i
$567$	−2.62184	+	1.35165i	−2.62184	+	1.35165i
$568$		0			0
$569$	0.815816	−	0.157236i	0.815816	−	0.157236i	0.235759	−	0.971812i	$-0.424242\pi$
$569$	0.815816	−	0.157236i	0.815816	−	0.157236i	0.580057	+	0.814576i	$0.303030\pi$
$570$		0			0
$571$		0			0		−0.580057	−	0.814576i	$-0.696970\pi$
$571$		0			0		0.580057	+	0.814576i	$0.303030\pi$
$572$		0			0
$573$		0			0
$574$	1.03115	−	1.78600i	1.03115	−	1.78600i
$575$	−0.0475819	+	0.998867i	−0.0475819	+	0.998867i
$576$	−2.34833	−	0.689531i	−2.34833	−	0.689531i
$577$		0			0		−0.786053	−	0.618159i	$-0.787879\pi$
$577$		0			0		0.786053	+	0.618159i	$0.212121\pi$
$578$	0.841254	−	0.540641i	0.841254	−	0.540641i
$579$		0			0
$580$	−1.15486	+	1.62177i	−1.15486	+	1.62177i
$581$	−0.315247	+	0.690294i	−0.315247	+	0.690294i
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$	1.21769	+	1.16106i	1.21769	+	1.16106i	0.981929	+	0.189251i	$0.0606061\pi$
$587$	1.21769	+	1.16106i	1.21769	+	1.16106i	0.235759	+	0.971812i	$0.424242\pi$
$588$	−0.420537	−	0.485326i	−0.420537	−	0.485326i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$		0			0		0.995472	−	0.0950560i	$-0.0303030\pi$
$593$		0			0		−0.995472	+	0.0950560i	$0.969697\pi$
$594$		0			0
$595$		0			0
$596$	0.581419	+	1.67990i	0.581419	+	1.67990i
$597$		0			0
$598$		0			0
$599$		0			0		−0.928368	−	0.371662i	$-0.878788\pi$
$599$		0			0		0.928368	+	0.371662i	$0.121212\pi$
$600$	0.771316	+	1.68895i	0.771316	+	1.68895i
$601$	−1.54370	−	0.297523i	−1.54370	−	0.297523i	−0.654861	−	0.755750i	$-0.727273\pi$
$601$	−1.54370	−	0.297523i	−1.54370	−	0.297523i	−0.888835	+	0.458227i	$0.848485\pi$
$602$	−1.82382			−1.82382
$603$	0.116455	−	2.44470i	0.116455	−	2.44470i
$604$		0			0
$605$	0.981929	+	0.189251i	0.981929	+	0.189251i
$606$	−1.01021	−	2.21205i	−1.01021	−	2.21205i
$607$	0.0883470	+	0.0353688i	0.0883470	+	0.0353688i	0.415415	−	0.909632i	$-0.363636\pi$
$607$	0.0883470	+	0.0353688i	0.0883470	+	0.0353688i	−0.327068	+	0.945001i	$0.606061\pi$
$608$		0			0
$609$	−1.01106	−	4.16766i	−1.01106	−	4.16766i
$610$	0.627639	+	1.81344i	0.627639	+	1.81344i
$611$		0			0
$612$		0			0
$613$		0			0		0.995472	−	0.0950560i	$-0.0303030\pi$
$613$		0			0		−0.995472	+	0.0950560i	$0.969697\pi$
$614$	0.396666	−	1.63508i	0.396666	−	1.63508i
$615$	−0.157052	−	3.29693i	−0.157052	−	3.29693i
$616$		0			0
$617$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$617$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$618$	−2.38786	−	2.75574i	−2.38786	−	2.75574i
$619$		0			0		−0.723734	−	0.690079i	$-0.757576\pi$
$619$		0			0		0.723734	+	0.690079i	$0.242424\pi$
$620$		0			0
$621$	2.11257	−	1.66134i	2.11257	−	1.66134i
$622$		0			0
$623$	1.51255	+	0.144431i	1.51255	+	0.144431i
$624$		0			0
$625$	0.415415	−	0.909632i	0.415415	−	0.909632i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$	−2.72433	−	0.799935i	−2.72433	−	0.799935i
$631$		0			0		0.0475819	−	0.998867i	$-0.484848\pi$
$631$		0			0		−0.0475819	+	0.998867i	$0.515152\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	0.273507	+	0.384087i	0.273507	+	0.384087i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$641$	−0.723734	+	1.25354i	−0.723734	+	1.25354i	0.235759	+	0.971812i	$0.424242\pi$
$641$	−0.723734	+	1.25354i	−0.723734	+	1.25354i	−0.959493	+	0.281733i	$0.909091\pi$
$642$	0.148645	−	3.12043i	0.148645	−	3.12043i
$643$	1.91030	+	0.560914i	1.91030	+	0.560914i	0.981929	+	0.189251i	$0.0606061\pi$
$643$	1.91030	+	0.560914i	1.91030	+	0.560914i	0.928368	+	0.371662i	$0.121212\pi$
$644$	0.911911	+	0.717135i	0.911911	+	0.717135i
$645$	−2.45561	+	1.57812i	−2.45561	+	1.57812i
$646$		0			0
$647$	0.0552004	−	0.0775182i	0.0552004	−	0.0775182i	−0.786053	−	0.618159i	$-0.787879\pi$
$647$	0.0552004	−	0.0775182i	0.0552004	−	0.0775182i	0.841254	+	0.540641i	$0.181818\pi$
$648$	1.05625	−	2.31286i	1.05625	−	2.31286i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	0.223734	−	0.175946i	0.223734	−	0.175946i
$653$		0			0		0.928368	−	0.371662i	$-0.121212\pi$
$653$		0			0		−0.928368	+	0.371662i	$0.878788\pi$
$654$	2.63900	+	2.51628i	2.63900	+	2.51628i
$655$		0			0
$656$	0.252989	+	1.75958i	0.252989	+	1.75958i
$657$		0			0
$658$	0.00525309	+	0.110276i	0.00525309	+	0.110276i
$659$		0			0		0.235759	−	0.971812i	$-0.424242\pi$
$659$		0			0		−0.235759	+	0.971812i	$0.575758\pi$
$660$		0			0
$661$	−0.544078	+	0.627899i	−0.544078	+	0.627899i	−0.959493	−	0.281733i	$-0.909091\pi$
$661$	−0.544078	+	0.627899i	−0.544078	+	0.627899i	0.415415	+	0.909632i	$0.363636\pi$
$662$		0			0
$663$		0			0
$664$	−0.154218	−	0.635697i	−0.154218	−	0.635697i
$665$		0			0
$666$		0			0
$667$	0.827068	+	1.81103i	0.827068	+	1.81103i
$668$	0.815816	+	0.157236i	0.815816	+	0.157236i
$669$	−3.56305			−3.56305
$670$	0.723734	−	0.690079i	0.723734	−	0.690079i
$671$		0			0
$672$	2.11510	+	0.407652i	2.11510	+	0.407652i
$673$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$673$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$674$		0			0
$675$	−2.57870	+	0.757175i	−2.57870	+	0.757175i
$676$	0.235759	+	0.971812i	0.235759	+	0.971812i
$677$		0			0		−0.327068	−	0.945001i	$-0.606061\pi$
$677$		0			0		0.327068	+	0.945001i	$0.393939\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−0.573320	+	2.36326i	−0.573320	+	2.36326i
$682$		0			0
$683$	−1.49547	−	0.770969i	−1.49547	−	0.770969i	−0.500000	−	0.866025i	$-0.666667\pi$
$683$	−1.49547	−	0.770969i	−1.49547	−	0.770969i	−0.995472	+	0.0950560i	$0.969697\pi$
$684$		0			0
$685$		0			0
$686$	−0.549222	−	0.523682i	−0.549222	−	0.523682i
$687$	0.812771	−	0.325385i	0.812771	−	0.325385i
$688$	1.23576	−	0.971812i	1.23576	−	0.971812i
$689$		0			0
$690$	1.84833	+	0.176494i	1.84833	+	0.176494i
$691$		0			0		0.723734	−	0.690079i	$-0.242424\pi$
$691$		0			0		−0.723734	+	0.690079i	$0.757576\pi$
$692$		0			0
$693$		0			0
$694$	0.273100	−	1.89945i	0.273100	−	1.89945i
$695$		0			0
$696$	2.90577	+	2.28512i	2.90577	+	2.28512i
$697$		0			0
$698$	−0.0748038	+	1.57033i	−0.0748038	+	1.57033i
$699$		0			0
$700$	−0.580057	−	1.00469i	−0.580057	−	1.00469i
$701$	0.888835	−	0.458227i	0.888835	−	0.458227i	0.0475819	−	0.998867i	$-0.484848\pi$
$701$	0.888835	−	0.458227i	0.888835	−	0.458227i	0.841254	+	0.540641i	$0.181818\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	0.102493	+	0.143931i	0.102493	+	0.143931i
$706$		0			0
$707$	0.759713	+	1.31586i	0.759713	+	1.31586i
$708$		0			0
$709$	−0.0475819	+	0.998867i	−0.0475819	+	0.998867i	0.841254	+	0.540641i	$0.181818\pi$
$709$	−0.0475819	+	0.998867i	−0.0475819	+	0.998867i	−0.888835	+	0.458227i	$0.848485\pi$
$710$		0			0
$711$		0			0
$712$	−1.10181	+	0.708089i	−1.10181	+	0.708089i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		0.786053	−	0.618159i	$-0.212121\pi$
$719$		0			0		−0.786053	+	0.618159i	$0.787879\pi$
$720$	2.27215	−	0.909632i	2.27215	−	0.909632i
$721$	1.64888	+	1.57221i	1.64888	+	1.57221i
$722$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$723$	−0.518932	−	3.60925i	−0.518932	−	3.60925i
$724$	0.252989	+	0.130425i	0.252989	+	0.130425i
$725$	−0.0947329	−	1.98869i	−0.0947329	−	1.98869i
$726$	0.437742	−	1.80440i	0.437742	−	1.80440i
$727$	1.76962	−	0.168978i	1.76962	−	0.168978i	0.841254	−	0.540641i	$-0.181818\pi$
$727$	1.76962	−	0.168978i	1.76962	−	0.168978i	0.928368	+	0.371662i	$0.121212\pi$
$728$		0			0
$729$	1.03719	+	0.666562i	1.03719	+	0.666562i
$730$		0			0
$731$		0			0
$732$	3.41872	−	1.00383i	3.41872	−	1.00383i
$733$		0			0		−0.928368	−	0.371662i	$-0.878788\pi$
$733$		0			0		0.928368	+	0.371662i	$0.121212\pi$
$734$	0.815816	+	1.78639i	0.815816	+	1.78639i
$735$	0.630573	+	0.121533i	0.630573	+	0.121533i
$736$	−1.00000			−1.00000
$737$		0			0
$738$	−4.35079			−4.35079
$739$		0			0		−0.981929	−	0.189251i	$-0.939394\pi$
$739$		0			0		0.981929	+	0.189251i	$0.0606061\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−0.0671040	−	0.276606i	−0.0671040	−	0.276606i	0.928368	−	0.371662i	$-0.121212\pi$
$743$	−0.0671040	−	0.276606i	−0.0671040	−	0.276606i	−0.995472	+	0.0950560i	$0.969697\pi$
$744$		0			0
$745$	−1.49547	−	0.961081i	−1.49547	−	0.961081i
$746$		0			0
$747$	1.59373	−	0.152183i	1.59373	−	0.152183i
$748$		0			0
$749$	0.0928751	+	1.94969i	0.0928751	+	1.94969i
$750$	−1.65033	−	0.850806i	−1.65033	−	0.850806i
$751$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$751$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$752$	−0.0623191	−	0.0719200i	−0.0623191	−	0.0719200i
$753$		0			0
$754$		0			0
$755$		0			0
$756$	−1.01976	+	2.94640i	−1.01976	+	2.94640i
$757$		0			0		−0.995472	−	0.0950560i	$-0.969697\pi$
$757$		0			0		0.995472	+	0.0950560i	$0.0303030\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	0.0405070	−	0.281733i	0.0405070	−	0.281733i	−0.959493	−	0.281733i	$-0.909091\pi$
$761$	0.0405070	−	0.281733i	0.0405070	−	0.281733i	1.00000			$0$
$762$	0.736504	−	0.473322i	0.736504	−	0.473322i
$763$	−1.79086	−	1.40835i	−1.79086	−	1.40835i
$764$		0			0
$765$		0			0
$766$	−0.0475819	+	0.0824143i	−0.0475819	+	0.0824143i
$767$		0			0
$768$	−1.65033	+	0.850806i	−1.65033	+	0.850806i
$769$	1.07701	+	1.51245i	1.07701	+	1.51245i	0.841254	+	0.540641i	$0.181818\pi$
$769$	1.07701	+	1.51245i	1.07701	+	1.51245i	0.235759	+	0.971812i	$0.424242\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0		0.888835	−	0.458227i	$-0.151515\pi$
$773$		0			0		−0.888835	+	0.458227i	$0.848485\pi$
$774$	1.92384	+	3.33219i	1.92384	+	3.33219i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	−1.54370	−	1.21398i	−1.54370	−	1.21398i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−3.87255	+	3.69247i	−3.87255	+	3.69247i
$784$	−0.344298	−	0.0328765i	−0.344298	−	0.0328765i
$785$		0			0
$786$		0			0
$787$	0.437742	−	0.175245i	0.437742	−	0.175245i	−0.142315	−	0.989821i	$-0.545455\pi$
$787$	0.437742	−	0.175245i	0.437742	−	0.175245i	0.580057	+	0.814576i	$0.303030\pi$
$788$		0			0
$789$	−1.75998	−	2.03113i	−1.75998	−	2.03113i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.327068	−	0.945001i	$-0.606061\pi$
$797$		0			0		0.327068	+	0.945001i	$0.393939\pi$
$798$		0			0
$799$		0			0
$800$	0.928368	+	0.371662i	0.928368	+	0.371662i
$801$	−1.33161	−	2.91583i	−1.33161	−	2.91583i
$802$	1.13915	+	0.219553i	1.13915	+	0.219553i
$803$		0			0
$804$	−1.21590	−	1.40323i	−1.21590	−	1.40323i
$805$	−1.16011			−1.16011
$806$		0			0
$807$	−0.219539	−	0.480724i	−0.219539	−	0.480724i
$808$	−1.21590	−	0.486774i	−1.21590	−	0.486774i
$809$	−0.452418	+	0.132842i	−0.452418	+	0.132842i	−0.500000	−	0.866025i	$-0.666667\pi$
$809$	−0.452418	+	0.132842i	−0.452418	+	0.132842i	0.0475819	+	0.998867i	$0.484848\pi$
$810$	0.599448	+	2.47096i	0.599448	+	2.47096i
$811$		0			0		−0.327068	−	0.945001i	$-0.606061\pi$
$811$		0			0		0.327068	+	0.945001i	$0.393939\pi$
$812$	−1.94306	−	1.24873i	−1.94306	−	1.24873i
$813$		0			0
$814$		0			0
$815$	−0.0671040	+	0.276606i	−0.0671040	+	0.276606i
$816$		0			0
$817$		0			0
$818$	0.0405070	+	0.281733i	0.0405070	+	0.281733i
$819$		0			0
$820$	−1.28656	−	1.22673i	−1.28656	−	1.22673i
$821$	−1.78153	+	0.713215i	−1.78153	+	0.713215i	−0.786053	+	0.618159i	$0.787879\pi$
$821$	−1.78153	+	0.713215i	−1.78153	+	0.713215i	−0.995472	+	0.0950560i	$0.969697\pi$
$822$		0			0
$823$	0.651174	−	1.88144i	0.651174	−	1.88144i	0.235759	−	0.971812i	$-0.424242\pi$
$823$	0.651174	−	1.88144i	0.651174	−	1.88144i	0.415415	−	0.909632i	$-0.363636\pi$
$824$	−1.95496	−	0.186677i	−1.95496	−	0.186677i
$825$		0			0
$826$		0			0
$827$	−1.03115	+	1.44805i	−1.03115	+	1.44805i	−0.142315	+	0.989821i	$0.545455\pi$
$827$	−1.03115	+	1.44805i	−1.03115	+	1.44805i	−0.888835	+	0.458227i	$0.848485\pi$
$828$	0.348311	−	2.42256i	0.348311	−	2.42256i
$829$	−1.61435	+	1.03748i	−1.61435	+	1.03748i	−0.654861	+	0.755750i	$0.727273\pi$
$829$	−1.61435	+	1.03748i	−1.61435	+	1.03748i	−0.959493	+	0.281733i	$0.909091\pi$
$830$	0.514186	+	0.404360i	0.514186	+	0.404360i
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−0.738471	+	0.380708i	−0.738471	+	0.380708i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		−0.580057	−	0.814576i	$-0.696970\pi$
$839$		0			0		0.580057	+	0.814576i	$0.303030\pi$
$840$	−1.91457	+	0.987031i	−1.91457	+	0.987031i
$841$	−1.48193	−	2.56678i	−1.48193	−	2.56678i
$842$	−0.415415	+	0.719520i	−0.415415	+	0.719520i
$843$	0.00840744	−	0.176494i	0.00840744	−	0.176494i
$844$		0			0
$845$	−0.786053	−	0.618159i	−0.786053	−	0.618159i
$846$	0.195937	−	0.125921i	0.195937	−	0.125921i
$847$	−0.165101	+	1.14831i	−0.165101	+	1.14831i
$848$		0			0
$849$	1.11646	−	2.44470i	1.11646	−	2.44470i
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		0.786053	−	0.618159i	$-0.212121\pi$
$853$		0			0		−0.786053	+	0.618159i	$0.787879\pi$
$854$	−2.06677	+	0.827411i	−2.06677	+	0.827411i
$855$		0			0
$856$	−1.10181	−	1.27155i	−1.10181	−	1.27155i
$857$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$857$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$858$		0			0
$859$		0			0		−0.0475819	−	0.998867i	$-0.515152\pi$
$859$		0			0		0.0475819	+	0.998867i	$0.484848\pi$
$860$	−0.370638	+	1.52779i	−0.370638	+	1.52779i
$861$	3.81181	−	0.363984i	3.81181	−	0.363984i
$862$		0			0
$863$	1.21769	+	0.782560i	1.21769	+	0.782560i	0.981929	−	0.189251i	$-0.0606061\pi$
$863$	1.21769	+	0.782560i	1.21769	+	0.782560i	0.235759	+	0.971812i	$0.424242\pi$
$864$	−0.879017	−	2.53975i	−0.879017	−	2.53975i
$865$		0			0
$866$		0			0
$867$	1.72373	+	0.690079i	1.72373	+	0.690079i
$868$		0			0
$869$		0			0
$870$	−3.69666			−3.69666
$871$		0			0
$872$	1.96386			1.96386
$873$		0			0
$874$		0			0
$875$	1.07701	+	0.431171i	1.07701	+	0.431171i
$876$		0			0
$877$		0			0		−0.235759	−	0.971812i	$-0.575758\pi$
$877$		0			0		0.235759	+	0.971812i	$0.424242\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	0.995472	−	0.0950560i	0.995472	−	0.0950560i	0.415415	−	0.909632i	$-0.363636\pi$
$881$	0.995472	−	0.0950560i	0.995472	−	0.0950560i	0.580057	+	0.814576i	$0.303030\pi$
$882$	0.199568	−	0.822630i	0.199568	−	0.822630i
$883$	0.0800569	+	1.68060i	0.0800569	+	1.68060i	0.580057	+	0.814576i	$0.303030\pi$
$883$	0.0800569	+	1.68060i	0.0800569	+	1.68060i	−0.500000	+	0.866025i	$0.666667\pi$
$884$		0			0
$885$		0			0
$886$	1.30379	+	1.50465i	1.30379	+	1.50465i
$887$	−1.44091	−	1.37391i	−1.44091	−	1.37391i	−0.786053	−	0.618159i	$-0.787879\pi$
$887$	−1.44091	−	1.37391i	−1.44091	−	1.37391i	−0.654861	−	0.755750i	$-0.727273\pi$
$888$		0			0
$889$	−0.429982	+	0.338142i	−0.429982	+	0.338142i
$890$	0.428368	−	1.23769i	0.428368	−	1.23769i
$891$		0			0
$892$	−1.38884	+	1.32425i	−1.38884	+	1.32425i
$893$		0			0
$894$	−1.91457	+	2.68864i	−1.91457	+	2.68864i
$895$		0			0
$896$	0.975950	−	0.627205i	0.975950	−	0.627205i
$897$		0			0
$898$	−0.0913090	−	0.0268107i	−0.0913090	−	0.0268107i
$899$		0			0
$900$	−1.22373	+	2.11957i	−1.22373	+	2.11957i
$901$		0			0
$902$		0			0
$903$	−1.96428	−	2.75844i	−1.96428	−	2.75844i
$904$		0			0
$905$	−0.279486	+	0.0538665i	−0.279486	+	0.0538665i
$906$		0			0
$907$	1.70566	−	0.879330i	1.70566	−	0.879330i	0.723734	−	0.690079i	$-0.242424\pi$
$907$	1.70566	−	0.879330i	1.70566	−	0.879330i	0.981929	−	0.189251i	$-0.0606061\pi$
$908$	0.654861	+	1.13425i	0.654861	+	1.13425i
$909$	1.60275	−	2.77605i	1.60275	−	2.77605i
$910$		0			0
$911$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$911$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	−2.06677	+	2.90237i	−2.06677	+	2.90237i
$916$	0.195876	−	0.428908i	0.195876	−	0.428908i
$917$		0			0
$918$		0			0
$919$		0			0		0.327068	−	0.945001i	$-0.393939\pi$
$919$		0			0		−0.327068	+	0.945001i	$0.606061\pi$
$920$	0.786053	−	0.618159i	0.786053	−	0.618159i
$921$	2.90019	−	1.16106i	2.90019	−	1.16106i
$922$	−0.473420	−	0.451405i	−0.473420	−	0.451405i
$923$		0			0
$924$		0			0
$925$		0			0
$926$	−0.0135432	−	0.284307i	−0.0135432	−	0.284307i
$927$	1.13317	−	4.67099i	1.13317	−	4.67099i
$928$	1.98193	−	0.189251i	1.98193	−	0.189251i
$929$	0.428368	−	0.494363i	0.428368	−	0.494363i	−0.500000	−	0.866025i	$-0.666667\pi$
$929$	0.428368	−	0.494363i	0.428368	−	0.494363i	0.928368	+	0.371662i	$0.121212\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$	0.437742	+	0.175245i	0.437742	+	0.175245i
$935$		0			0
$936$		0			0
$937$		0			0		1.00000			$0$
$937$		0			0		−1.00000			$\pi$
$938$	0.839614	+	0.800570i	0.839614	+	0.800570i
$939$		0			0
$940$	0.0934441	+	0.0180099i	0.0934441	+	0.0180099i
$941$	0.698939	+	1.53046i	0.698939	+	1.53046i	0.841254	+	0.540641i	$0.181818\pi$
$941$	0.698939	+	1.53046i	0.698939	+	1.53046i	−0.142315	+	0.989821i	$0.545455\pi$
$942$		0			0
$943$	−1.70566	+	0.500828i	−1.70566	+	0.500828i
$944$		0			0
$945$	−1.01976	−	2.94640i	−1.01976	−	2.94640i
$946$		0			0
$947$	1.02951	−	1.18812i	1.02951	−	1.18812i	0.0475819	−	0.998867i	$-0.484848\pi$
$947$	1.02951	−	1.18812i	1.02951	−	1.18812i	0.981929	−	0.189251i	$-0.0606061\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$953$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	0.771316	−	1.68895i	0.771316	−	1.68895i
$961$	0.580057	−	0.814576i	0.580057	−	0.814576i
$962$		0			0
$963$	3.46418	−	2.22630i	3.46418	−	2.22630i
$964$	−1.54370	−	1.21398i	−1.54370	−	1.21398i
$965$		0			0
$966$	−0.102493	+	2.15159i	−0.102493	+	2.15159i
$967$	−0.841254	+	1.45709i	−0.841254	+	1.45709i	0.0475819	+	0.998867i	$0.484848\pi$
$967$	−0.841254	+	1.45709i	−0.841254	+	1.45709i	−0.888835	+	0.458227i	$0.848485\pi$
$968$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$969$		0			0
$970$		0			0
$971$		0			0		0.981929	−	0.189251i	$-0.0606061\pi$
$971$		0			0		−0.981929	+	0.189251i	$0.939394\pi$
$972$	1.99668	−	0.384829i	1.99668	−	0.384829i
$973$		0			0
$974$	0.581419	−	0.299742i	0.581419	−	0.299742i
$975$		0			0
$976$	0.959493	−	1.66189i	0.959493	−	1.66189i
$977$		0			0		0.0475819	−	0.998867i	$-0.484848\pi$
$977$		0			0		−0.0475819	+	0.998867i	$0.515152\pi$
$978$	0.507075	+	0.148891i	0.507075	+	0.148891i
$979$		0			0
$980$	0.290959	−	0.186988i	0.290959	−	0.186988i
$981$	−0.684033	+	4.75756i	−0.684033	+	4.75756i
$982$		0			0
$983$	0.345139	−	0.755750i	0.345139	−	0.755750i	−0.654861	−	0.755750i	$-0.727273\pi$
$983$	0.345139	−	0.755750i	0.345139	−	0.755750i	1.00000			$0$
$984$	−2.38880	+	2.27772i	−2.38880	+	2.27772i
$985$		0			0
$986$		0			0
$987$	−0.161129	+	0.126713i	−0.161129	+	0.126713i
$988$		0			0
$989$	1.13779	+	1.08488i	1.13779	+	1.08488i
$990$		0			0
$991$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$991$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$	0.795366	−	0.917901i	0.795366	−	0.917901i
$997$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$997$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$998$		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.619.1	yes	20
4.3	odd	2		1340.1.bl.a.619.1	✓	20
5.4	even	2		1340.1.bl.a.619.1	✓	20
20.19	odd	2	CM	1340.1.bl.b.619.1	yes	20
67.21	even	33	inner	1340.1.bl.b.959.1	yes	20
268.155	odd	66		1340.1.bl.a.959.1	yes	20
335.289	even	66		1340.1.bl.a.959.1	yes	20
1340.959	odd	66	inner	1340.1.bl.b.959.1	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1340.1.bl.a.619.1	✓	20	4.3	odd	2
1340.1.bl.a.619.1	✓	20	5.4	even	2
1340.1.bl.a.959.1	yes	20	268.155	odd	66
1340.1.bl.a.959.1	yes	20	335.289	even	66
1340.1.bl.b.619.1	yes	20	1.1	even	1	trivial
1340.1.bl.b.619.1	yes	20	20.19	odd	2	CM
1340.1.bl.b.959.1	yes	20	67.21	even	33	inner
1340.1.bl.b.959.1	yes	20	1340.959	odd	66	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.981929 + 0.189251i) q^{2} +(0.771316 + 1.68895i) q^{3} +(0.928368 + 0.371662i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(0.437742 + 1.80440i) q^{6} +(-0.379436 - 1.09631i) q^{7} +(0.841254 + 0.540641i) q^{8} +(-1.60275 + 1.84967i) q^{9} +O(q^{10})\)	\(q+(0.981929 + 0.189251i) q^{2} +(0.771316 + 1.68895i) q^{3} +(0.928368 + 0.371662i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(0.437742 + 1.80440i) q^{6} +(-0.379436 - 1.09631i) q^{7} +(0.841254 + 0.540641i) q^{8} +(-1.60275 + 1.84967i) q^{9} +(-0.995472 + 0.0950560i) q^{10} +(0.0883470 + 1.85463i) q^{12} +(-0.165101 - 1.14831i) q^{14} +(-1.21590 - 1.40323i) q^{15} +(0.723734 + 0.690079i) q^{16} +(-1.92384 + 1.51292i) q^{18} +(-0.995472 - 0.0950560i) q^{20} +(1.55894 - 1.48645i) q^{21} +(-0.580057 + 0.814576i) q^{23} +(-0.264241 + 1.83784i) q^{24} +(0.841254 - 0.540641i) q^{25} +(-2.57870 - 0.757175i) q^{27} +(0.0552004 - 1.15880i) q^{28} +(0.995472 - 1.72421i) q^{29} +(-0.928368 - 1.60798i) q^{30} +(0.580057 + 0.814576i) q^{32} +(0.672932 + 0.945001i) q^{35} +(-2.17540 + 1.12149i) q^{36} +(-0.959493 - 0.281733i) q^{40} +(1.39734 + 1.09888i) q^{41} +(1.81208 - 1.16455i) q^{42} +(0.223734 - 1.55610i) q^{43} +(1.01671 - 2.22630i) q^{45} +(-0.723734 + 0.690079i) q^{46} +(-0.0947329 - 0.00904590i) q^{47} +(-0.607279 + 1.75462i) q^{48} +(-0.271868 + 0.213799i) q^{49} +(0.928368 - 0.371662i) q^{50} +(-2.38880 - 1.23151i) q^{54} +(0.273507 - 1.12741i) q^{56} +(1.30379 - 1.50465i) q^{58} +(-0.607279 - 1.75462i) q^{60} +(-0.452418 - 1.86489i) q^{61} +(2.63595 + 1.05528i) q^{63} +(0.415415 + 0.909632i) q^{64} +(-0.786053 + 0.618159i) q^{67} +(-1.82318 - 0.351390i) q^{69} +(0.481929 + 1.05528i) q^{70} +(-2.34833 + 0.689531i) q^{72} +(1.56199 + 1.00383i) q^{75} +(-0.888835 - 0.458227i) q^{80} +(-0.361854 - 2.51675i) q^{81} +(1.16413 + 1.34347i) q^{82} +(-0.473420 - 0.451405i) q^{83} +(1.99973 - 0.800570i) q^{84} +(0.514186 - 1.48564i) q^{86} +(3.67992 + 0.351390i) q^{87} +(-0.544078 + 1.19136i) q^{89} +(1.41967 - 1.99365i) q^{90} +(-0.841254 + 0.540641i) q^{92} +(-0.0913090 - 0.0268107i) q^{94} +(-0.928368 + 1.60798i) q^{96} +(-0.307416 + 0.158484i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + q^{2} + 2 q^{3} + q^{4} - 2 q^{5} - q^{6} - q^{7} - 2 q^{8}+O(q^{10}) \) 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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