LMFDB - Embedded newform 1340.1.bl.b.419.1

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			419.1
Root			$0.0475819 - 0.998867i$ of defining polynomial
Character	$\chi$	$=$	1340.419
Dual form			1340.1.bl.b.339.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.995472 + 0.0950560i) q^{2} +(1.65210 - 1.06174i) q^{3} +(0.981929 - 0.189251i) q^{4} +(-0.142315 + 0.989821i) q^{5} +(-1.54370 + 1.21398i) q^{6} +(-1.03115 - 1.44805i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(1.18673 - 2.59858i) q^{9} +O(q^{10})$	\(q+(-0.995472 + 0.0950560i) q^{2} +(1.65210 - 1.06174i) q^{3} +(0.981929 - 0.189251i) q^{4} +(-0.142315 + 0.989821i) q^{5} +(-1.54370 + 1.21398i) q^{6} +(-1.03115 - 1.44805i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(1.18673 - 2.59858i) q^{9} +(0.0475819 - 0.998867i) q^{10} +(1.42131 - 1.35522i) q^{12} +(1.16413 + 1.34347i) q^{14} +(0.815816 + 1.78639i) q^{15} +(0.928368 - 0.371662i) q^{16} +(-0.934347 + 2.69962i) q^{18} +(0.0475819 + 0.998867i) q^{20} +(-3.24102 - 1.29751i) q^{21} +(0.888835 + 0.458227i) q^{23} +(-1.28605 + 1.48418i) q^{24} +(-0.959493 - 0.281733i) q^{25} +(-0.518932 - 3.60925i) q^{27} +(-1.28656 - 1.22673i) q^{28} +(-0.0475819 + 0.0824143i) q^{29} +(-0.981929 - 1.70075i) q^{30} +(-0.888835 + 0.458227i) q^{32} +(1.58006 - 0.814576i) q^{35} +(0.673501 - 2.77621i) q^{36} +(-0.142315 - 0.989821i) q^{40} +(-0.154218 - 0.445585i) q^{41} +(3.34968 + 0.983554i) q^{42} +(0.428368 - 0.494363i) q^{43} +(2.40324 + 1.54447i) q^{45} +(-0.928368 - 0.371662i) q^{46} +(0.0688733 + 1.44583i) q^{47} +(1.13915 - 1.59971i) q^{48} +(-0.706504 + 2.04131i) q^{49} +(0.981929 + 0.189251i) q^{50} +(0.859663 + 3.54358i) q^{54} +(1.39734 + 1.09888i) q^{56} +(0.0395325 - 0.0865641i) q^{58} +(1.13915 + 1.59971i) q^{60} +(0.223734 - 0.175946i) q^{61} +(-4.98656 + 0.961081i) q^{63} +(0.841254 - 0.540641i) q^{64} +(-0.327068 + 0.945001i) q^{67} +(1.95496 - 0.186677i) q^{69} +(-1.49547 + 0.961081i) q^{70} +(-0.406556 + 2.82766i) q^{72} +(-1.88431 + 0.553283i) q^{75} +(0.235759 + 0.971812i) q^{80} +(-2.81865 - 3.25290i) q^{81} +(0.195876 + 0.428908i) q^{82} +(1.07701 - 0.431171i) q^{83} +(-3.42800 - 0.660694i) q^{84} +(-0.379436 + 0.532843i) q^{86} +(0.00889250 + 0.186677i) q^{87} +(0.698939 + 0.449181i) q^{89} +(-2.53917 - 1.30903i) q^{90} +(0.959493 + 0.281733i) q^{92} +(-0.205996 - 1.43273i) q^{94} +(-0.981929 + 1.70075i) q^{96} +(0.509266 - 2.09922i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1340\mathbb{Z}\right)^\times$.

$n$	$537$	$671$	$1141$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{32}{33}\right)$

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 $

$2$	−0.995472	+	0.0950560i	−0.995472	+	0.0950560i
$2$	−0.995472	+	0.0950560i	−0.995472	+	0.0950560i
$3$	1.65210	−	1.06174i	1.65210	−	1.06174i	0.723734	−	0.690079i	$-0.242424\pi$
$3$	1.65210	−	1.06174i	1.65210	−	1.06174i	0.928368	−	0.371662i	$-0.121212\pi$
$4$	0.981929	−	0.189251i	0.981929	−	0.189251i
$5$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$5$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$6$	−1.54370	+	1.21398i	−1.54370	+	1.21398i
$7$	−1.03115	−	1.44805i	−1.03115	−	1.44805i	−0.888835	−	0.458227i	$-0.848485\pi$
$7$	−1.03115	−	1.44805i	−1.03115	−	1.44805i	−0.142315	−	0.989821i	$-0.545455\pi$
$8$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$9$	1.18673	−	2.59858i	1.18673	−	2.59858i
$10$	0.0475819	−	0.998867i	0.0475819	−	0.998867i
$11$		0			0		−0.786053	−	0.618159i	$-0.787879\pi$
$11$		0			0		0.786053	+	0.618159i	$0.212121\pi$
$12$	1.42131	−	1.35522i	1.42131	−	1.35522i
$13$		0			0		−0.235759	−	0.971812i	$-0.575758\pi$
$13$		0			0		0.235759	+	0.971812i	$0.424242\pi$
$14$	1.16413	+	1.34347i	1.16413	+	1.34347i
$15$	0.815816	+	1.78639i	0.815816	+	1.78639i
$16$	0.928368	−	0.371662i	0.928368	−	0.371662i
$17$		0			0		−0.981929	−	0.189251i	$-0.939394\pi$
$17$		0			0		0.981929	+	0.189251i	$0.0606061\pi$
$18$	−0.934347	+	2.69962i	−0.934347	+	2.69962i
$19$		0			0		0.580057	−	0.814576i	$-0.303030\pi$
$19$		0			0		−0.580057	+	0.814576i	$0.696970\pi$
$20$	0.0475819	+	0.998867i	0.0475819	+	0.998867i
$21$	−3.24102	−	1.29751i	−3.24102	−	1.29751i
$22$		0			0
$23$	0.888835	+	0.458227i	0.888835	+	0.458227i	0.841254	−	0.540641i	$-0.181818\pi$
$23$	0.888835	+	0.458227i	0.888835	+	0.458227i	0.0475819	+	0.998867i	$0.484848\pi$
$24$	−1.28605	+	1.48418i	−1.28605	+	1.48418i
$25$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$26$		0			0
$27$	−0.518932	−	3.60925i	−0.518932	−	3.60925i
$28$	−1.28656	−	1.22673i	−1.28656	−	1.22673i
$29$	−0.0475819	+	0.0824143i	−0.0475819	+	0.0824143i	−0.888835	−	0.458227i	$-0.848485\pi$
$29$	−0.0475819	+	0.0824143i	−0.0475819	+	0.0824143i	0.841254	+	0.540641i	$0.181818\pi$
$30$	−0.981929	−	1.70075i	−0.981929	−	1.70075i
$31$		0			0		0.235759	−	0.971812i	$-0.424242\pi$
$31$		0			0		−0.235759	+	0.971812i	$0.575758\pi$
$32$	−0.888835	+	0.458227i	−0.888835	+	0.458227i
$33$		0			0
$34$		0			0
$35$	1.58006	−	0.814576i	1.58006	−	0.814576i
$36$	0.673501	−	2.77621i	0.673501	−	2.77621i
$37$		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
$40$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$41$	−0.154218	−	0.445585i	−0.154218	−	0.445585i	0.841254	−	0.540641i	$-0.181818\pi$
$41$	−0.154218	−	0.445585i	−0.154218	−	0.445585i	−0.995472	+	0.0950560i	$0.969697\pi$
$42$	3.34968	+	0.983554i	3.34968	+	0.983554i
$43$	0.428368	−	0.494363i	0.428368	−	0.494363i	−0.500000	−	0.866025i	$-0.666667\pi$
$43$	0.428368	−	0.494363i	0.428368	−	0.494363i	0.928368	+	0.371662i	$0.121212\pi$
$44$		0			0
$45$	2.40324	+	1.54447i	2.40324	+	1.54447i
$46$	−0.928368	−	0.371662i	−0.928368	−	0.371662i
$47$	0.0688733	+	1.44583i	0.0688733	+	1.44583i	0.723734	+	0.690079i	$0.242424\pi$
$47$	0.0688733	+	1.44583i	0.0688733	+	1.44583i	−0.654861	+	0.755750i	$0.727273\pi$
$48$	1.13915	−	1.59971i	1.13915	−	1.59971i
$49$	−0.706504	+	2.04131i	−0.706504	+	2.04131i
$50$	0.981929	+	0.189251i	0.981929	+	0.189251i
$51$		0			0
$52$		0			0
$53$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$53$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$54$	0.859663	+	3.54358i	0.859663	+	3.54358i
$55$		0			0
$56$	1.39734	+	1.09888i	1.39734	+	1.09888i
$57$		0			0
$58$	0.0395325	−	0.0865641i	0.0395325	−	0.0865641i
$59$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$59$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$60$	1.13915	+	1.59971i	1.13915	+	1.59971i
$61$	0.223734	−	0.175946i	0.223734	−	0.175946i	−0.500000	−	0.866025i	$-0.666667\pi$
$61$	0.223734	−	0.175946i	0.223734	−	0.175946i	0.723734	+	0.690079i	$0.242424\pi$
$62$		0			0
$63$	−4.98656	+	0.961081i	−4.98656	+	0.961081i
$64$	0.841254	−	0.540641i	0.841254	−	0.540641i
$65$		0			0
$66$		0			0
$67$	−0.327068	+	0.945001i	−0.327068	+	0.945001i
$67$	−0.327068	+	0.945001i	−0.327068	+	0.945001i
$68$		0			0
$69$	1.95496	−	0.186677i	1.95496	−	0.186677i
$70$	−1.49547	+	0.961081i	−1.49547	+	0.961081i
$71$		0			0		0.981929	−	0.189251i	$-0.0606061\pi$
$71$		0			0		−0.981929	+	0.189251i	$0.939394\pi$
$72$	−0.406556	+	2.82766i	−0.406556	+	2.82766i
$73$		0			0		0.786053	−	0.618159i	$-0.212121\pi$
$73$		0			0		−0.786053	+	0.618159i	$0.787879\pi$
$74$		0			0
$75$	−1.88431	+	0.553283i	−1.88431	+	0.553283i
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		0.723734	−	0.690079i	$-0.242424\pi$
$79$		0			0		−0.723734	+	0.690079i	$0.757576\pi$
$80$	0.235759	+	0.971812i	0.235759	+	0.971812i
$81$	−2.81865	−	3.25290i	−2.81865	−	3.25290i
$82$	0.195876	+	0.428908i	0.195876	+	0.428908i
$83$	1.07701	−	0.431171i	1.07701	−	0.431171i	0.235759	−	0.971812i	$-0.424242\pi$
$83$	1.07701	−	0.431171i	1.07701	−	0.431171i	0.841254	+	0.540641i	$0.181818\pi$
$84$	−3.42800	−	0.660694i	−3.42800	−	0.660694i
$85$		0			0
$86$	−0.379436	+	0.532843i	−0.379436	+	0.532843i
$87$	0.00889250	+	0.186677i	0.00889250	+	0.186677i
$88$		0			0
$89$	0.698939	+	0.449181i	0.698939	+	0.449181i	0.841254	−	0.540641i	$-0.181818\pi$
$89$	0.698939	+	0.449181i	0.698939	+	0.449181i	−0.142315	+	0.989821i	$0.545455\pi$
$90$	−2.53917	−	1.30903i	−2.53917	−	1.30903i
$91$		0			0
$92$	0.959493	+	0.281733i	0.959493	+	0.281733i
$93$		0			0
$94$	−0.205996	−	1.43273i	−0.205996	−	1.43273i
$95$		0			0
$96$	−0.981929	+	1.70075i	−0.981929	+	1.70075i
$97$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$97$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$98$	0.509266	−	2.09922i	0.509266	−	2.09922i
$99$		0			0
$100$	−0.995472	−	0.0950560i	−0.995472	−	0.0950560i
$101$	−0.827068	−	0.0789754i	−0.827068	−	0.0789754i	−0.327068	−	0.945001i	$-0.606061\pi$
$101$	−0.827068	−	0.0789754i	−0.827068	−	0.0789754i	−0.500000	+	0.866025i	$0.666667\pi$
$102$		0			0
$103$	−0.469383	+	1.93482i	−0.469383	+	1.93482i	−0.142315	+	0.989821i	$0.545455\pi$
$103$	−0.469383	+	1.93482i	−0.469383	+	1.93482i	−0.327068	+	0.945001i	$0.606061\pi$
$104$		0			0
$105$	1.74555	−	3.02337i	1.74555	−	3.02337i
$106$		0			0
$107$	0.273100	+	1.89945i	0.273100	+	1.89945i	0.415415	+	0.909632i	$0.363636\pi$
$107$	0.273100	+	1.89945i	0.273100	+	1.89945i	−0.142315	+	0.989821i	$0.545455\pi$
$108$	−1.19261	−	3.44582i	−1.19261	−	3.44582i
$109$	1.91030	+	0.560914i	1.91030	+	0.560914i	0.981929	+	0.189251i	$0.0606061\pi$
$109$	1.91030	+	0.560914i	1.91030	+	0.560914i	0.928368	+	0.371662i	$0.121212\pi$
$110$		0			0
$111$		0			0
$112$	−1.49547	−	0.961081i	−1.49547	−	0.961081i
$113$		0			0		−0.928368	−	0.371662i	$-0.878788\pi$
$113$		0			0		0.928368	+	0.371662i	$0.121212\pi$
$114$		0			0
$115$	−0.580057	+	0.814576i	−0.580057	+	0.814576i
$116$	−0.0311250	+	0.0899299i	−0.0311250	+	0.0899299i
$117$		0			0
$118$		0			0
$119$		0			0
$120$	−1.28605	−	1.48418i	−1.28605	−	1.48418i
$121$	0.235759	+	0.971812i	0.235759	+	0.971812i
$122$	−0.205996	+	0.196417i	−0.205996	+	0.196417i
$123$	−0.727880	−	0.572411i	−0.727880	−	0.572411i
$124$		0			0
$125$	0.415415	−	0.909632i	0.415415	−	0.909632i
$126$	4.87263	−	1.43073i	4.87263	−	1.43073i
$127$	−0.911911	−	1.28060i	−0.911911	−	1.28060i	−0.959493	−	0.281733i	$-0.909091\pi$
$127$	−0.911911	−	1.28060i	−0.911911	−	1.28060i	0.0475819	−	0.998867i	$-0.484848\pi$
$128$	−0.786053	+	0.618159i	−0.786053	+	0.618159i
$129$	0.182822	−	1.27155i	0.182822	−	1.27155i
$130$		0			0
$131$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$131$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$132$		0			0
$133$		0			0
$134$	0.235759	−	0.971812i	0.235759	−	0.971812i
$135$	3.64636			3.64636
$136$		0			0
$137$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$137$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$138$	−1.92837	+	0.371662i	−1.92837	+	0.371662i
$139$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$139$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$140$	1.39734	−	1.09888i	1.39734	−	1.09888i
$141$	1.64888	+	2.31553i	1.64888	+	2.31553i
$142$		0			0
$143$		0			0
$144$	0.135929	−	2.85350i	0.135929	−	2.85350i
$145$	−0.0748038	−	0.0588264i	−0.0748038	−	0.0588264i
$146$		0			0
$147$	1.00013	+	4.12258i	1.00013	+	4.12258i
$148$		0			0
$149$	0.195876	+	0.428908i	0.195876	+	0.428908i	0.981929	−	0.189251i	$-0.0606061\pi$
$149$	0.195876	+	0.428908i	0.195876	+	0.428908i	−0.786053	+	0.618159i	$0.787879\pi$
$150$	1.82318	−	0.729892i	1.82318	−	0.729892i
$151$		0			0		−0.981929	−	0.189251i	$-0.939394\pi$
$151$		0			0		0.981929	+	0.189251i	$0.0606061\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		−0.888835	−	0.458227i	$-0.848485\pi$
$157$		0			0		0.888835	+	0.458227i	$0.151515\pi$
$158$		0			0
$159$		0			0
$160$	−0.327068	−	0.945001i	−0.327068	−	0.945001i
$161$	−0.252989	−	1.75958i	−0.252989	−	1.75958i
$162$	3.11510	+	2.97024i	3.11510	+	2.97024i
$163$	0.654861	−	1.13425i	0.654861	−	1.13425i	−0.327068	−	0.945001i	$-0.606061\pi$
$163$	0.654861	−	1.13425i	0.654861	−	1.13425i	0.981929	−	0.189251i	$-0.0606061\pi$
$164$	−0.235759	−	0.408346i	−0.235759	−	0.408346i
$165$		0			0
$166$	−1.03115	+	0.531595i	−1.03115	+	0.531595i
$167$	−1.67489	−	0.159932i	−1.67489	−	0.159932i	−0.786053	−	0.618159i	$-0.787879\pi$
$167$	−1.67489	−	0.159932i	−1.67489	−	0.159932i	−0.888835	+	0.458227i	$0.848485\pi$
$168$	3.47528	+	0.331849i	3.47528	+	0.331849i
$169$	−0.888835	+	0.458227i	−0.888835	+	0.458227i
$170$		0			0
$171$		0			0
$172$	0.327068	−	0.566498i	0.327068	−	0.566498i
$173$		0			0		−0.723734	−	0.690079i	$-0.757576\pi$
$173$		0			0		0.723734	+	0.690079i	$0.242424\pi$
$174$	−0.0265970	−	0.184986i	−0.0265970	−	0.184986i
$175$	0.581419	+	1.67990i	0.581419	+	1.67990i
$176$		0			0
$177$		0			0
$178$	−0.738471	−	0.380708i	−0.738471	−	0.380708i
$179$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$179$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$180$	2.65210	+	1.06174i	2.65210	+	1.06174i
$181$	−0.0623191	−	1.30824i	−0.0623191	−	1.30824i	−0.786053	−	0.618159i	$-0.787879\pi$
$181$	−0.0623191	−	1.30824i	−0.0623191	−	1.30824i	0.723734	−	0.690079i	$-0.242424\pi$
$182$		0			0
$183$	0.182822	−	0.528229i	0.182822	−	0.528229i
$184$	−0.981929	−	0.189251i	−0.981929	−	0.189251i
$185$		0			0
$186$		0			0
$187$		0			0
$188$	0.341254	+	1.40667i	0.341254	+	1.40667i
$189$	−4.69127	+	4.47312i	−4.69127	+	4.47312i
$190$		0			0
$191$		0			0		0.0475819	−	0.998867i	$-0.484848\pi$
$191$		0			0		−0.0475819	+	0.998867i	$0.515152\pi$
$192$	0.815816	−	1.78639i	0.815816	−	1.78639i
$193$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$193$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$194$		0			0
$195$		0			0
$196$	−0.307416	+	2.13813i	−0.307416	+	2.13813i
$197$		0			0		0.981929	−	0.189251i	$-0.0606061\pi$
$197$		0			0		−0.981929	+	0.189251i	$0.939394\pi$
$198$		0			0
$199$		0			0		0.995472	−	0.0950560i	$-0.0303030\pi$
$199$		0			0		−0.995472	+	0.0950560i	$0.969697\pi$
$200$	1.00000			1.00000
$201$	0.462997	+	1.90850i	0.462997	+	1.90850i
$202$	0.830830			0.830830
$203$	0.168404	−	0.0160806i	0.168404	−	0.0160806i
$204$		0			0
$205$	0.462997	−	0.0892353i	0.462997	−	0.0892353i
$206$	0.283341	−	1.97068i	0.283341	−	1.97068i
$207$	2.24555	−	1.76592i	2.24555	−	1.76592i
$208$		0			0
$209$		0			0
$210$	−1.45025	+	3.17561i	−1.45025	+	3.17561i
$211$		0			0		0.0475819	−	0.998867i	$-0.484848\pi$
$211$		0			0		−0.0475819	+	0.998867i	$0.515152\pi$
$212$		0			0
$213$		0			0
$214$	−0.452418	−	1.86489i	−0.452418	−	1.86489i
$215$	0.428368	+	0.494363i	0.428368	+	0.494363i
$216$	1.51475	+	3.31685i	1.51475	+	3.31685i
$217$		0			0
$218$	−1.95496	−	0.376789i	−1.95496	−	0.376789i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−0.239446	−	0.153882i	−0.239446	−	0.153882i	0.415415	−	0.909632i	$-0.363636\pi$
$223$	−0.239446	−	0.153882i	−0.239446	−	0.153882i	−0.654861	+	0.755750i	$0.727273\pi$
$224$	1.58006	+	0.814576i	1.58006	+	0.814576i
$225$	−1.87076	+	2.15898i	−1.87076	+	2.15898i
$226$		0			0
$227$	−0.271738	−	0.785135i	−0.271738	−	0.785135i	−0.995472	−	0.0950560i	$-0.969697\pi$
$227$	−0.271738	−	0.785135i	−0.271738	−	0.785135i	0.723734	−	0.690079i	$-0.242424\pi$
$228$		0			0
$229$	−1.13779	−	1.08488i	−1.13779	−	1.08488i	−0.995472	−	0.0950560i	$-0.969697\pi$
$229$	−1.13779	−	1.08488i	−1.13779	−	1.08488i	−0.142315	−	0.989821i	$-0.545455\pi$
$230$	0.500000	−	0.866025i	0.500000	−	0.866025i
$231$		0			0
$232$	0.0224357	−	0.0924813i	0.0224357	−	0.0924813i
$233$		0			0		0.888835	−	0.458227i	$-0.151515\pi$
$233$		0			0		−0.888835	+	0.458227i	$0.848485\pi$
$234$		0			0
$235$	−1.44091	−	0.137591i	−1.44091	−	0.137591i
$236$		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	$0.666667\pi$
$240$	1.42131	+	1.35522i	1.42131	+	1.35522i
$241$	0.283341	+	1.97068i	0.283341	+	1.97068i	0.235759	+	0.971812i	$0.424242\pi$
$241$	0.283341	+	1.97068i	0.283341	+	1.97068i	0.0475819	+	0.998867i	$0.484848\pi$
$242$	−0.327068	−	0.945001i	−0.327068	−	0.945001i
$243$	−4.61178	−	1.35414i	−4.61178	−	1.35414i
$244$	0.186393	−	0.215109i	0.186393	−	0.215109i
$245$	−1.91999	−	0.989821i	−1.91999	−	0.989821i
$246$	0.778996	+	0.500630i	0.778996	+	0.500630i
$247$		0			0
$248$		0			0
$249$	1.32154	−	1.85585i	1.32154	−	1.85585i
$250$	−0.327068	+	0.945001i	−0.327068	+	0.945001i
$251$		0			0		−0.981929	−	0.189251i	$-0.939394\pi$
$251$		0			0		0.981929	+	0.189251i	$0.0606061\pi$
$252$	−4.71456	+	1.88743i	−4.71456	+	1.88743i
$253$		0			0
$254$	1.02951	+	1.18812i	1.02951	+	1.18812i
$255$		0			0
$256$	0.723734	−	0.690079i	0.723734	−	0.690079i
$257$		0			0		−0.786053	−	0.618159i	$-0.787879\pi$
$257$		0			0		0.786053	+	0.618159i	$0.212121\pi$
$258$	−0.0611251	+	1.28317i	−0.0611251	+	1.28317i
$259$		0			0
$260$		0			0
$261$	0.157693	+	0.221449i	0.157693	+	0.221449i
$262$		0			0
$263$	−0.264241	+	1.83784i	−0.264241	+	1.83784i	0.235759	+	0.971812i	$0.424242\pi$
$263$	−0.264241	+	1.83784i	−0.264241	+	1.83784i	−0.500000	+	0.866025i	$0.666667\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	1.63163			1.63163
$268$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$269$	−1.30972			−1.30972			−0.654861	−	0.755750i	$-0.727273\pi$
$269$	−1.30972			−1.30972			−0.654861	+	0.755750i	$0.727273\pi$
$270$	−3.62985	+	0.346609i	−3.62985	+	0.346609i
$271$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$271$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$	1.88431	−	0.553283i	1.88431	−	0.553283i
$277$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$277$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$278$		0			0
$279$		0			0
$280$	−1.28656	+	1.22673i	−1.28656	+	1.22673i
$281$	0.341254	+	1.40667i	0.341254	+	1.40667i	0.841254	+	0.540641i	$0.181818\pi$
$281$	0.341254	+	1.40667i	0.341254	+	1.40667i	−0.500000	+	0.866025i	$0.666667\pi$
$282$	−1.86152	−	2.14831i	−1.86152	−	2.14831i
$283$	0.771316	+	1.68895i	0.771316	+	1.68895i	0.723734	+	0.690079i	$0.242424\pi$
$283$	0.771316	+	1.68895i	0.771316	+	1.68895i	0.0475819	+	0.998867i	$0.484848\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−0.486206	+	0.682780i	−0.486206	+	0.682780i
$288$	0.135929	+	2.85350i	0.135929	+	2.85350i
$289$	0.928368	+	0.371662i	0.928368	+	0.371662i
$290$	0.0800569	+	0.0514495i	0.0800569	+	0.0514495i
$291$		0			0
$292$		0			0
$293$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$293$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$294$	−1.38747	−	4.00884i	−1.38747	−	4.00884i
$295$		0			0
$296$		0			0
$297$		0			0
$298$	−0.235759	−	0.408346i	−0.235759	−	0.408346i
$299$		0			0
$300$	−1.74555	+	0.899892i	−1.74555	+	0.899892i
$301$	−1.15757	−	0.110535i	−1.15757	−	0.110535i
$302$		0			0
$303$	−1.45025	+	0.747657i	−1.45025	+	0.747657i
$304$		0			0
$305$	0.142315	+	0.246497i	0.142315	+	0.246497i
$306$		0			0
$307$	−1.38884	−	1.32425i	−1.38884	−	1.32425i	−0.888835	−	0.458227i	$-0.848485\pi$
$307$	−1.38884	−	1.32425i	−1.38884	−	1.32425i	−0.500000	−	0.866025i	$-0.666667\pi$
$308$		0			0
$309$	1.27881	+	3.69489i	1.27881	+	3.69489i
$310$		0			0
$311$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$311$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$312$		0			0
$313$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$313$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$314$		0			0
$315$	−0.241637	−	5.07258i	−0.241637	−	5.07258i
$316$		0			0
$317$		0			0		0.327068	−	0.945001i	$-0.393939\pi$
$317$		0			0		−0.327068	+	0.945001i	$0.606061\pi$
$318$		0			0
$319$		0			0
$320$	0.415415	+	0.909632i	0.415415	+	0.909632i
$321$	2.46792	+	2.84813i	2.46792	+	2.84813i
$322$	0.419102	+	1.72756i	0.419102	+	1.72756i
$323$		0			0
$324$	−3.38333	−	2.66068i	−3.38333	−	2.66068i
$325$		0			0
$326$	−0.544078	+	1.19136i	−0.544078	+	1.19136i
$327$	3.75155	−	1.10155i	3.75155	−	1.10155i
$328$	0.273507	+	0.384087i	0.273507	+	0.384087i
$329$	2.02261	−	1.59060i	2.02261	−	1.59060i
$330$		0			0
$331$		0			0		0.981929	−	0.189251i	$-0.0606061\pi$
$331$		0			0		−0.981929	+	0.189251i	$0.939394\pi$
$332$	0.975950	−	0.627205i	0.975950	−	0.627205i
$333$		0			0
$334$	1.68251			1.68251
$335$	−0.888835	−	0.458227i	−0.888835	−	0.458227i
$336$	−3.49109			−3.49109
$337$		0			0		0.995472	−	0.0950560i	$-0.0303030\pi$
$337$		0			0		−0.995472	+	0.0950560i	$0.969697\pi$
$338$	0.841254	−	0.540641i	0.841254	−	0.540641i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	1.97876	−	0.581017i	1.97876	−	0.581017i
$344$	−0.271738	+	0.595023i	−0.271738	+	0.595023i
$345$	−0.0934441	+	1.96163i	−0.0934441	+	1.96163i
$346$		0			0
$347$	−0.205996	+	0.196417i	−0.205996	+	0.196417i	−0.786053	−	0.618159i	$-0.787879\pi$
$347$	−0.205996	+	0.196417i	−0.205996	+	0.196417i	0.580057	+	0.814576i	$0.303030\pi$
$348$	0.0440606	+	0.181620i	0.0440606	+	0.181620i
$349$	0.428368	+	0.494363i	0.428368	+	0.494363i	0.928368	−	0.371662i	$-0.121212\pi$
$349$	0.428368	+	0.494363i	0.428368	+	0.494363i	−0.500000	+	0.866025i	$0.666667\pi$
$350$	−0.738471	−	1.61703i	−0.738471	−	1.61703i
$351$		0			0
$352$		0			0
$353$		0			0		0.327068	−	0.945001i	$-0.393939\pi$
$353$		0			0		−0.327068	+	0.945001i	$0.606061\pi$
$354$		0			0
$355$		0			0
$356$	0.771316	+	0.308788i	0.771316	+	0.308788i
$357$		0			0
$358$		0			0
$359$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$359$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$360$	−2.74102	−	0.804835i	−2.74102	−	0.804835i
$361$	−0.327068	−	0.945001i	−0.327068	−	0.945001i
$362$	0.186393	+	1.29639i	0.186393	+	1.29639i
$363$	1.42131	+	1.35522i	1.42131	+	1.35522i
$364$		0			0
$365$		0			0
$366$	−0.131783	+	0.543216i	−0.131783	+	0.543216i
$367$	1.76962	−	0.912303i	1.76962	−	0.912303i	0.841254	−	0.540641i	$-0.181818\pi$
$367$	1.76962	−	0.912303i	1.76962	−	0.912303i	0.928368	−	0.371662i	$-0.121212\pi$
$368$	0.995472	+	0.0950560i	0.995472	+	0.0950560i
$369$	−1.34090	−	0.128041i	−1.34090	−	0.128041i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$373$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$374$		0			0
$375$	−0.279486	−	1.94387i	−0.279486	−	1.94387i
$376$	−0.473420	−	1.36786i	−0.473420	−	1.36786i
$377$		0			0
$378$	4.24483	−	4.89880i	4.24483	−	4.89880i
$379$		0			0		−0.888835	−	0.458227i	$-0.848485\pi$
$379$		0			0		0.888835	+	0.458227i	$0.151515\pi$
$380$		0			0
$381$	−2.86624	−	1.14747i	−2.86624	−	1.14747i
$382$		0			0
$383$	0.839614	−	1.17907i	0.839614	−	1.17907i	−0.142315	−	0.989821i	$-0.545455\pi$
$383$	0.839614	−	1.17907i	0.839614	−	1.17907i	0.981929	−	0.189251i	$-0.0606061\pi$
$384$	−0.642315	+	1.85585i	−0.642315	+	1.85585i
$385$		0			0
$386$		0			0
$387$	−0.776283	−	1.69982i	−0.776283	−	1.69982i
$388$		0			0
$389$	−0.469383	−	1.93482i	−0.469383	−	1.93482i	−0.327068	−	0.945001i	$-0.606061\pi$
$389$	−0.469383	−	1.93482i	−0.469383	−	1.93482i	−0.142315	−	0.989821i	$-0.545455\pi$
$390$		0			0
$391$		0			0
$392$	0.102782	−	2.15767i	0.102782	−	2.15767i
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$397$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$398$		0			0
$399$		0			0
$400$	−0.995472	+	0.0950560i	−0.995472	+	0.0950560i
$401$	−1.77767			−1.77767			−0.888835	−	0.458227i	$-0.848485\pi$
$401$	−1.77767			−1.77767			−0.888835	+	0.458227i	$0.848485\pi$
$402$	−0.642315	−	1.85585i	−0.642315	−	1.85585i
$403$		0			0
$404$	−0.827068	+	0.0789754i	−0.827068	+	0.0789754i
$405$	3.62093	−	2.32703i	3.62093	−	2.32703i
$406$	−0.166113	+	0.0320156i	−0.166113	+	0.0320156i
$407$		0			0
$408$		0			0
$409$	−0.759713	−	1.06687i	−0.759713	−	1.06687i	−0.995472	−	0.0950560i	$-0.969697\pi$
$409$	−0.759713	−	1.06687i	−0.759713	−	1.06687i	0.235759	−	0.971812i	$-0.424242\pi$
$410$	−0.452418	+	0.132842i	−0.452418	+	0.132842i
$411$		0			0
$412$	−0.0947329	+	1.98869i	−0.0947329	+	1.98869i
$413$		0			0
$414$	−2.06752	+	1.97137i	−2.06752	+	1.97137i
$415$	0.273507	+	1.12741i	0.273507	+	1.12741i
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		−0.981929	−	0.189251i	$-0.939394\pi$
$419$		0			0		0.981929	+	0.189251i	$0.0606061\pi$
$420$	1.14182	−	3.29908i	1.14182	−	3.29908i
$421$	0.975950	−	1.37053i	0.975950	−	1.37053i	0.0475819	−	0.998867i	$-0.484848\pi$
$421$	0.975950	−	1.37053i	0.975950	−	1.37053i	0.928368	−	0.371662i	$-0.121212\pi$
$422$		0			0
$423$	3.83883	+	1.53684i	3.83883	+	1.53684i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−0.485482	−	0.142550i	−0.485482	−	0.142550i
$428$	0.627639	+	1.81344i	0.627639	+	1.81344i
$429$		0			0
$430$	−0.473420	−	0.451405i	−0.473420	−	0.451405i
$431$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$431$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$432$	−1.82318	−	3.15784i	−1.82318	−	3.15784i
$433$		0			0		0.235759	−	0.971812i	$-0.424242\pi$
$433$		0			0		−0.235759	+	0.971812i	$0.575758\pi$
$434$		0			0
$435$	−0.186042	−	0.0177649i	−0.186042	−	0.0177649i
$436$	1.98193	+	0.189251i	1.98193	+	0.189251i
$437$		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
$441$	4.46607	+	4.25839i	4.46607	+	4.25839i
$442$		0			0
$443$	−0.0311250	−	0.0899299i	−0.0311250	−	0.0899299i	0.928368	−	0.371662i	$-0.121212\pi$
$443$	−0.0311250	−	0.0899299i	−0.0311250	−	0.0899299i	−0.959493	+	0.281733i	$0.909091\pi$
$444$		0			0
$445$	−0.544078	+	0.627899i	−0.544078	+	0.627899i
$446$	0.252989	+	0.130425i	0.252989	+	0.130425i
$447$	0.778996	+	0.500630i	0.778996	+	0.500630i
$448$	−1.65033	−	0.660694i	−1.65033	−	0.660694i
$449$	0.0688733	+	1.44583i	0.0688733	+	1.44583i	0.723734	+	0.690079i	$0.242424\pi$
$449$	0.0688733	+	1.44583i	0.0688733	+	1.44583i	−0.654861	+	0.755750i	$0.727273\pi$
$450$	1.65707	−	2.32703i	1.65707	−	2.32703i
$451$		0			0
$452$		0			0
$453$		0			0
$454$	0.345139	+	0.755750i	0.345139	+	0.755750i
$455$		0			0
$456$		0			0
$457$		0			0		0.723734	−	0.690079i	$-0.242424\pi$
$457$		0			0		−0.723734	+	0.690079i	$0.757576\pi$
$458$	1.23576	+	0.971812i	1.23576	+	0.971812i
$459$		0			0
$460$	−0.415415	+	0.909632i	−0.415415	+	0.909632i
$461$	−1.11312	+	0.326842i	−1.11312	+	0.326842i	−0.786053	−	0.618159i	$-0.787879\pi$
$461$	−1.11312	+	0.326842i	−1.11312	+	0.326842i	−0.327068	+	0.945001i	$0.606061\pi$
$462$		0			0
$463$	1.02951	−	0.809616i	1.02951	−	0.809616i	0.0475819	−	0.998867i	$-0.484848\pi$
$463$	1.02951	−	0.809616i	1.02951	−	0.809616i	0.981929	+	0.189251i	$0.0606061\pi$
$464$	−0.0135432	+	0.0941952i	−0.0135432	+	0.0941952i
$465$		0			0
$466$		0			0
$467$	1.56499	−	0.149438i	1.56499	−	0.149438i	0.723734	−	0.690079i	$-0.242424\pi$
$467$	1.56499	−	0.149438i	1.56499	−	0.149438i	0.841254	+	0.540641i	$0.181818\pi$
$468$		0			0
$469$	1.70566	−	0.500828i	1.70566	−	0.500828i
$470$	1.44747			1.44747
$471$		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		0.0475819	−	0.998867i	$-0.484848\pi$
$479$		0			0		−0.0475819	+	0.998867i	$0.515152\pi$
$480$	−1.54370	−	1.21398i	−1.54370	−	1.21398i
$481$		0			0
$482$	−0.469383	−	1.93482i	−0.469383	−	1.93482i
$483$	−2.28618	−	2.63839i	−2.28618	−	2.63839i
$484$	0.415415	+	0.909632i	0.415415	+	0.909632i
$485$		0			0
$486$	4.71962	+	0.909632i	4.71962	+	0.909632i
$487$	−0.379436	+	1.09631i	−0.379436	+	1.09631i	0.580057	+	0.814576i	$0.303030\pi$
$487$	−0.379436	+	1.09631i	−0.379436	+	1.09631i	−0.959493	+	0.281733i	$0.909091\pi$
$488$	−0.165101	+	0.231852i	−0.165101	+	0.231852i
$489$	−0.122386	−	2.56919i	−0.122386	−	2.56919i
$490$	2.00538	+	0.802833i	2.00538	+	0.802833i
$491$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$491$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$492$	−0.823056	−	0.424315i	−0.823056	−	0.424315i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−1.13915	+	1.97306i	−1.13915	+	1.97306i
$499$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$499$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$500$	0.235759	−	0.971812i	0.235759	−	0.971812i
$501$	−2.93689	+	1.51407i	−2.93689	+	1.51407i
$502$		0			0
$503$	−0.469383	−	0.0448206i	−0.469383	−	0.0448206i	−0.142315	−	0.989821i	$-0.545455\pi$
$503$	−0.469383	−	0.0448206i	−0.469383	−	0.0448206i	−0.327068	+	0.945001i	$0.606061\pi$
$504$	4.51381	−	2.32703i	4.51381	−	2.32703i
$505$	0.195876	−	0.807410i	0.195876	−	0.807410i
$506$		0			0
$507$	−0.981929	+	1.70075i	−0.981929	+	1.70075i
$508$	−1.13779	−	1.08488i	−1.13779	−	1.08488i
$509$	−0.239446	−	1.66538i	−0.239446	−	1.66538i	−0.654861	−	0.755750i	$-0.727273\pi$
$509$	−0.239446	−	1.66538i	−0.239446	−	1.66538i	0.415415	−	0.909632i	$-0.363636\pi$
$510$		0			0
$511$		0			0
$512$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$513$		0			0
$514$		0			0
$515$	−1.84833	−	0.739959i	−1.84833	−	0.739959i
$516$	−0.0611251	−	1.28317i	−0.0611251	−	1.28317i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−0.415415	−	0.909632i	−0.415415	−	0.909632i	−0.995472	−	0.0950560i	$-0.969697\pi$
$521$	−0.415415	−	0.909632i	−0.415415	−	0.909632i	0.580057	−	0.814576i	$-0.303030\pi$
$522$	−0.178029	−	0.205457i	−0.178029	−	0.205457i
$523$	−0.154218	−	0.635697i	−0.154218	−	0.635697i	−0.995472	−	0.0950560i	$-0.969697\pi$
$523$	−0.154218	−	0.635697i	−0.154218	−	0.635697i	0.841254	−	0.540641i	$-0.181818\pi$
$524$		0			0
$525$	2.74418	+	2.15805i	2.74418	+	2.15805i
$526$	0.0883470	−	1.85463i	0.0883470	−	1.85463i
$527$		0			0
$528$		0			0
$529$		0			0
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$	−1.62424	+	0.155096i	−1.62424	+	0.155096i
$535$	−1.91899			−1.91899
$536$	0.0475819	−	0.998867i	0.0475819	−	0.998867i
$537$		0			0
$538$	1.30379	−	0.124497i	1.30379	−	0.124497i
$539$		0			0
$540$	3.58047	−	0.690079i	3.58047	−	0.690079i
$541$	0.0930932	−	0.647478i	0.0930932	−	0.647478i	−0.888835	−	0.458227i	$-0.848485\pi$
$541$	0.0930932	−	0.647478i	0.0930932	−	0.647478i	0.981929	−	0.189251i	$-0.0606061\pi$
$542$		0			0
$543$	−1.49197	−	2.09518i	−1.49197	−	2.09518i
$544$		0			0
$545$	−0.827068	+	1.81103i	−0.827068	+	1.81103i
$546$		0			0
$547$	1.23576	+	0.971812i	1.23576	+	0.971812i	1.00000			$0$
$547$	1.23576	+	0.971812i	1.23576	+	0.971812i	0.235759	+	0.971812i	$0.424242\pi$
$548$		0			0
$549$	−0.191698	−	0.790191i	−0.191698	−	0.790191i
$550$		0			0
$551$		0			0
$552$	−1.82318	+	0.729892i	−1.82318	+	0.729892i
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$		0			0		−0.928368	−	0.371662i	$-0.878788\pi$
$557$		0			0		0.928368	+	0.371662i	$0.121212\pi$
$558$		0			0
$559$		0			0
$560$	1.16413	−	1.34347i	1.16413	−	1.34347i
$561$		0			0
$562$	−0.473420	−	1.36786i	−0.473420	−	1.36786i
$563$	0.0930932	+	0.647478i	0.0930932	+	0.647478i	0.981929	+	0.189251i	$0.0606061\pi$
$563$	0.0930932	+	0.647478i	0.0930932	+	0.647478i	−0.888835	+	0.458227i	$0.848485\pi$
$564$	2.05730	+	1.96163i	2.05730	+	1.96163i
$565$		0			0
$566$	−0.928368	−	1.60798i	−0.928368	−	1.60798i
$567$	−1.80390	+	7.43578i	−1.80390	+	7.43578i
$568$		0			0
$569$	−1.67489	−	0.159932i	−1.67489	−	0.159932i	−0.786053	−	0.618159i	$-0.787879\pi$
$569$	−1.67489	−	0.159932i	−1.67489	−	0.159932i	−0.888835	+	0.458227i	$0.848485\pi$
$570$		0			0
$571$		0			0		0.888835	−	0.458227i	$-0.151515\pi$
$571$		0			0		−0.888835	+	0.458227i	$0.848485\pi$
$572$		0			0
$573$		0			0
$574$	0.419102	−	0.725906i	0.419102	−	0.725906i
$575$	−0.723734	−	0.690079i	−0.723734	−	0.690079i
$576$	−0.406556	−	2.82766i	−0.406556	−	2.82766i
$577$		0			0		−0.327068	−	0.945001i	$-0.606061\pi$
$577$		0			0		0.327068	+	0.945001i	$0.393939\pi$
$578$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$579$		0			0
$580$	−0.0845850	−	0.0436066i	−0.0845850	−	0.0436066i
$581$	−1.73492	−	1.11496i	−1.73492	−	1.11496i
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−1.78153	+	0.713215i	−1.78153	+	0.713215i	−0.786053	+	0.618159i	$0.787879\pi$
$587$	−1.78153	+	0.713215i	−1.78153	+	0.713215i	−0.995472	+	0.0950560i	$0.969697\pi$
$588$	1.76226	+	3.85880i	1.76226	+	3.85880i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$		0			0		0.0475819	−	0.998867i	$-0.484848\pi$
$593$		0			0		−0.0475819	+	0.998867i	$0.515152\pi$
$594$		0			0
$595$		0			0
$596$	0.273507	+	0.384087i	0.273507	+	0.384087i
$597$		0			0
$598$		0			0
$599$		0			0		0.981929	−	0.189251i	$-0.0606061\pi$
$599$		0			0		−0.981929	+	0.189251i	$0.939394\pi$
$600$	1.65210	−	1.06174i	1.65210	−	1.06174i
$601$	0.651174	−	0.0621796i	0.651174	−	0.0621796i	0.235759	−	0.971812i	$-0.424242\pi$
$601$	0.651174	−	0.0621796i	0.651174	−	0.0621796i	0.415415	+	0.909632i	$0.363636\pi$
$602$	1.16284			1.16284
$603$	2.06752	+	1.97137i	2.06752	+	1.97137i
$604$		0			0
$605$	−0.995472	+	0.0950560i	−0.995472	+	0.0950560i
$606$	1.37262	−	0.882127i	1.37262	−	0.882127i
$607$	1.42131	−	0.273935i	1.42131	−	0.273935i	0.580057	−	0.814576i	$-0.303030\pi$
$607$	1.42131	−	0.273935i	1.42131	−	0.273935i	0.841254	+	0.540641i	$0.181818\pi$
$608$		0			0
$609$	0.261147	−	0.205368i	0.261147	−	0.205368i
$610$	−0.165101	−	0.231852i	−0.165101	−	0.231852i
$611$		0			0
$612$		0			0
$613$		0			0		0.0475819	−	0.998867i	$-0.484848\pi$
$613$		0			0		−0.0475819	+	0.998867i	$0.515152\pi$
$614$	1.50842	+	1.18624i	1.50842	+	1.18624i
$615$	0.670173	−	0.639009i	0.670173	−	0.639009i
$616$		0			0
$617$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$617$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$618$	−1.62424	−	3.55660i	−1.62424	−	3.55660i
$619$		0			0		0.928368	−	0.371662i	$-0.121212\pi$
$619$		0			0		−0.928368	+	0.371662i	$0.878788\pi$
$620$		0			0
$621$	1.19261	−	3.44582i	1.19261	−	3.44582i
$622$		0			0
$623$	−0.0702757	−	1.47527i	−0.0702757	−	1.47527i
$624$		0			0
$625$	0.841254	+	0.540641i	0.841254	+	0.540641i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$	0.722723	+	5.02665i	0.722723	+	5.02665i
$631$		0			0		−0.723734	−	0.690079i	$-0.757576\pi$
$631$		0			0		0.723734	+	0.690079i	$0.242424\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	1.39734	−	0.720381i	1.39734	−	0.720381i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$641$	−0.928368	+	1.60798i	−0.928368	+	1.60798i	−0.142315	+	0.989821i	$0.545455\pi$
$641$	−0.928368	+	1.60798i	−0.928368	+	1.60798i	−0.786053	+	0.618159i	$0.787879\pi$
$642$	−2.72747	−	2.60064i	−2.72747	−	2.60064i
$643$	−0.0135432	−	0.0941952i	−0.0135432	−	0.0941952i	0.981929	−	0.189251i	$-0.0606061\pi$
$643$	−0.0135432	−	0.0941952i	−0.0135432	−	0.0941952i	−0.995472	+	0.0950560i	$0.969697\pi$
$644$	−0.581419	−	1.67990i	−0.581419	−	1.67990i
$645$	1.23259	+	0.361922i	1.23259	+	0.361922i
$646$		0			0
$647$	−1.28656	−	0.663268i	−1.28656	−	0.663268i	−0.327068	−	0.945001i	$-0.606061\pi$
$647$	−1.28656	−	0.663268i	−1.28656	−	0.663268i	−0.959493	+	0.281733i	$0.909091\pi$
$648$	3.62093	+	2.32703i	3.62093	+	2.32703i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	0.428368	−	1.23769i	0.428368	−	1.23769i
$653$		0			0		−0.981929	−	0.189251i	$-0.939394\pi$
$653$		0			0		0.981929	+	0.189251i	$0.0606061\pi$
$654$	−3.62985	+	1.45317i	−3.62985	+	1.45317i
$655$		0			0
$656$	−0.308779	−	0.356349i	−0.308779	−	0.356349i
$657$		0			0
$658$	−1.86226	+	1.77566i	−1.86226	+	1.77566i
$659$		0			0		−0.786053	−	0.618159i	$-0.787879\pi$
$659$		0			0		0.786053	+	0.618159i	$0.212121\pi$
$660$		0			0
$661$	0.698939	−	1.53046i	0.698939	−	1.53046i	−0.142315	−	0.989821i	$-0.545455\pi$
$661$	0.698939	−	1.53046i	0.698939	−	1.53046i	0.841254	−	0.540641i	$-0.181818\pi$
$662$		0			0
$663$		0			0
$664$	−0.911911	+	0.717135i	−0.911911	+	0.717135i
$665$		0			0
$666$		0			0
$667$	−0.0800569	+	0.0514495i	−0.0800569	+	0.0514495i
$668$	−1.67489	+	0.159932i	−1.67489	+	0.159932i
$669$	−0.558972			−0.558972
$670$	0.928368	+	0.371662i	0.928368	+	0.371662i
$671$		0			0
$672$	3.47528	−	0.331849i	3.47528	−	0.331849i
$673$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$673$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$674$		0			0
$675$	−0.518932	+	3.60925i	−0.518932	+	3.60925i
$676$	−0.786053	+	0.618159i	−0.786053	+	0.618159i
$677$		0			0		−0.580057	−	0.814576i	$-0.696970\pi$
$677$		0			0		0.580057	+	0.814576i	$0.303030\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−1.28255	−	1.00861i	−1.28255	−	1.00861i
$682$		0			0
$683$	−0.452418	−	1.86489i	−0.452418	−	1.86489i	−0.500000	−	0.866025i	$-0.666667\pi$
$683$	−0.452418	−	1.86489i	−0.452418	−	1.86489i	0.0475819	−	0.998867i	$-0.484848\pi$
$684$		0			0
$685$		0			0
$686$	−1.91457	+	0.766480i	−1.91457	+	0.766480i
$687$	−3.03160	−	0.584293i	−3.03160	−	0.584293i
$688$	0.213947	−	0.618159i	0.213947	−	0.618159i
$689$		0			0
$690$	−0.0934441	−	1.96163i	−0.0934441	−	1.96163i
$691$		0			0		−0.928368	−	0.371662i	$-0.878788\pi$
$691$		0			0		0.928368	+	0.371662i	$0.121212\pi$
$692$		0			0
$693$		0			0
$694$	0.186393	−	0.215109i	0.186393	−	0.215109i
$695$		0			0
$696$	−0.0611251	−	0.176609i	−0.0611251	−	0.176609i
$697$		0			0
$698$	−0.473420	−	0.451405i	−0.473420	−	0.451405i
$699$		0			0
$700$	0.888835	+	1.53951i	0.888835	+	1.53951i
$701$	−0.235759	+	0.971812i	−0.235759	+	0.971812i	0.723734	+	0.690079i	$0.242424\pi$
$701$	−0.235759	+	0.971812i	−0.235759	+	0.971812i	−0.959493	+	0.281733i	$0.909091\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	−2.52662	+	1.30256i	−2.52662	+	1.30256i
$706$		0			0
$707$	0.738471	+	1.27907i	0.738471	+	1.27907i
$708$		0			0
$709$	−0.723734	−	0.690079i	−0.723734	−	0.690079i	0.235759	−	0.971812i	$-0.424242\pi$
$709$	−0.723734	−	0.690079i	−0.723734	−	0.690079i	−0.959493	+	0.281733i	$0.909091\pi$
$710$		0			0
$711$		0			0
$712$	−0.797176	−	0.234072i	−0.797176	−	0.234072i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		0.327068	−	0.945001i	$-0.393939\pi$
$719$		0			0		−0.327068	+	0.945001i	$0.606061\pi$
$720$	2.80511	+	0.540641i	2.80511	+	0.540641i
$721$	3.28572	−	1.31540i	3.28572	−	1.31540i
$722$	0.415415	+	0.909632i	0.415415	+	0.909632i
$723$	2.56046	+	2.95493i	2.56046	+	2.95493i
$724$	−0.308779	−	1.27280i	−0.308779	−	1.27280i
$725$	0.0688733	−	0.0656706i	0.0688733	−	0.0656706i
$726$	−1.54370	−	1.21398i	−1.54370	−	1.21398i
$727$	0.0224357	−	0.470984i	0.0224357	−	0.470984i	−0.959493	−	0.281733i	$-0.909091\pi$
$727$	0.0224357	−	0.470984i	0.0224357	−	0.470984i	0.981929	−	0.189251i	$-0.0606061\pi$
$728$		0			0
$729$	−4.92703	+	1.44671i	−4.92703	+	1.44671i
$730$		0			0
$731$		0			0
$732$	0.0795500	−	0.553283i	0.0795500	−	0.553283i
$733$		0			0		0.981929	−	0.189251i	$-0.0606061\pi$
$733$		0			0		−0.981929	+	0.189251i	$0.939394\pi$
$734$	−1.67489	+	1.07639i	−1.67489	+	1.07639i
$735$	−4.22295	+	0.403243i	−4.22295	+	0.403243i
$736$	−1.00000			−1.00000
$737$		0			0
$738$	1.34700			1.34700
$739$		0			0		0.995472	−	0.0950560i	$-0.0303030\pi$
$739$		0			0		−0.995472	+	0.0950560i	$0.969697\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	1.02951	−	0.809616i	1.02951	−	0.809616i	0.0475819	−	0.998867i	$-0.484848\pi$
$743$	1.02951	−	0.809616i	1.02951	−	0.809616i	0.981929	+	0.189251i	$0.0606061\pi$
$744$		0			0
$745$	−0.452418	+	0.132842i	−0.452418	+	0.132842i
$746$		0			0
$747$	0.157693	−	3.31038i	0.157693	−	3.31038i
$748$		0			0
$749$	2.46889	−	2.35408i	2.46889	−	2.35408i
$750$	0.462997	+	1.90850i	0.462997	+	1.90850i
$751$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$751$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$752$	0.601300	+	1.31666i	0.601300	+	1.31666i
$753$		0			0
$754$		0			0
$755$		0			0
$756$	−3.75995	+	5.28011i	−3.75995	+	5.28011i
$757$		0			0		−0.0475819	−	0.998867i	$-0.515152\pi$
$757$		0			0		0.0475819	+	0.998867i	$0.484848\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	0.857685	−	0.989821i	0.857685	−	0.989821i	−0.142315	−	0.989821i	$-0.545455\pi$
$761$	0.857685	−	0.989821i	0.857685	−	0.989821i	1.00000			$0$
$762$	2.96233	+	0.869819i	2.96233	+	0.869819i
$763$	−1.15757	−	3.34459i	−1.15757	−	3.34459i
$764$		0			0
$765$		0			0
$766$	−0.723734	+	1.25354i	−0.723734	+	1.25354i
$767$		0			0
$768$	0.462997	−	1.90850i	0.462997	−	1.90850i
$769$	−1.74555	+	0.899892i	−1.74555	+	0.899892i	−0.786053	+	0.618159i	$0.787879\pi$
$769$	−1.74555	+	0.899892i	−1.74555	+	0.899892i	−0.959493	+	0.281733i	$0.909091\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0		0.235759	−	0.971812i	$-0.424242\pi$
$773$		0			0		−0.235759	+	0.971812i	$0.575758\pi$
$774$	0.934347	+	1.61834i	0.934347	+	1.61834i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	0.651174	+	1.88144i	0.651174	+	1.88144i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	0.322146	+	0.128968i	0.322146	+	0.128968i
$784$	0.102782	+	2.15767i	0.102782	+	2.15767i
$785$		0			0
$786$		0			0
$787$	−1.54370	−	0.297523i	−1.54370	−	0.297523i	−0.654861	−	0.755750i	$-0.727273\pi$
$787$	−1.54370	−	0.297523i	−1.54370	−	0.297523i	−0.888835	+	0.458227i	$0.848485\pi$
$788$		0			0
$789$	1.51475	+	3.31685i	1.51475	+	3.31685i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.580057	−	0.814576i	$-0.696970\pi$
$797$		0			0		0.580057	+	0.814576i	$0.303030\pi$
$798$		0			0
$799$		0			0
$800$	0.981929	−	0.189251i	0.981929	−	0.189251i
$801$	1.99668	−	1.28319i	1.99668	−	1.28319i
$802$	1.76962	−	0.168978i	1.76962	−	0.168978i
$803$		0			0
$804$	0.815816	+	1.78639i	0.815816	+	1.78639i
$805$	1.77767			1.77767
$806$		0			0
$807$	−2.16379	+	1.39059i	−2.16379	+	1.39059i
$808$	0.815816	−	0.157236i	0.815816	−	0.157236i
$809$	0.223734	−	1.55610i	0.223734	−	1.55610i	−0.500000	−	0.866025i	$-0.666667\pi$
$809$	0.223734	−	1.55610i	0.223734	−	1.55610i	0.723734	−	0.690079i	$-0.242424\pi$
$810$	−3.38333	+	2.66068i	−3.38333	+	2.66068i
$811$		0			0		−0.580057	−	0.814576i	$-0.696970\pi$
$811$		0			0		0.580057	+	0.814576i	$0.303030\pi$
$812$	0.162317	−	0.0476607i	0.162317	−	0.0476607i
$813$		0			0
$814$		0			0
$815$	1.02951	+	0.809616i	1.02951	+	0.809616i
$816$		0			0
$817$		0			0
$818$	0.857685	+	0.989821i	0.857685	+	0.989821i
$819$		0			0
$820$	0.437742	−	0.175245i	0.437742	−	0.175245i
$821$	−0.279486	−	0.0538665i	−0.279486	−	0.0538665i	0.0475819	−	0.998867i	$-0.484848\pi$
$821$	−0.279486	−	0.0538665i	−0.279486	−	0.0538665i	−0.327068	+	0.945001i	$0.606061\pi$
$822$		0			0
$823$	0.0552004	−	0.0775182i	0.0552004	−	0.0775182i	−0.786053	−	0.618159i	$-0.787879\pi$
$823$	0.0552004	−	0.0775182i	0.0552004	−	0.0775182i	0.841254	+	0.540641i	$0.181818\pi$
$824$	−0.0947329	−	1.98869i	−0.0947329	−	1.98869i
$825$		0			0
$826$		0			0
$827$	−0.419102	−	0.216062i	−0.419102	−	0.216062i	0.235759	−	0.971812i	$-0.424242\pi$
$827$	−0.419102	−	0.216062i	−0.419102	−	0.216062i	−0.654861	+	0.755750i	$0.727273\pi$
$828$	1.87076	−	2.15898i	1.87076	−	2.15898i
$829$	0.273100	+	0.0801894i	0.273100	+	0.0801894i	0.415415	−	0.909632i	$-0.363636\pi$
$829$	0.273100	+	0.0801894i	0.273100	+	0.0801894i	−0.142315	+	0.989821i	$0.545455\pi$
$830$	−0.379436	−	1.09631i	−0.379436	−	1.09631i
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	0.396666	−	1.63508i	0.396666	−	1.63508i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		0.888835	−	0.458227i	$-0.151515\pi$
$839$		0			0		−0.888835	+	0.458227i	$0.848485\pi$
$840$	−0.823056	+	3.39268i	−0.823056	+	3.39268i
$841$	0.495472	+	0.858183i	0.495472	+	0.858183i
$842$	−0.841254	+	1.45709i	−0.841254	+	1.45709i
$843$	2.05730	+	1.96163i	2.05730	+	1.96163i
$844$		0			0
$845$	−0.327068	−	0.945001i	−0.327068	−	0.945001i
$846$	−3.96754	−	1.16497i	−3.96754	−	1.16497i
$847$	1.16413	−	1.34347i	1.16413	−	1.34347i
$848$		0			0
$849$	3.06752	+	1.97137i	3.06752	+	1.97137i
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		0.327068	−	0.945001i	$-0.393939\pi$
$853$		0			0		−0.327068	+	0.945001i	$0.606061\pi$
$854$	0.496834	+	0.0957569i	0.496834	+	0.0957569i
$855$		0			0
$856$	−0.797176	−	1.74557i	−0.797176	−	1.74557i
$857$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$857$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$858$		0			0
$859$		0			0		0.723734	−	0.690079i	$-0.242424\pi$
$859$		0			0		−0.723734	+	0.690079i	$0.757576\pi$
$860$	0.514186	+	0.404360i	0.514186	+	0.404360i
$861$	−0.0783252	+	1.64425i	−0.0783252	+	1.64425i
$862$		0			0
$863$	−1.78153	+	0.523103i	−1.78153	+	0.523103i	−0.995472	−	0.0950560i	$-0.969697\pi$
$863$	−1.78153	+	0.523103i	−1.78153	+	0.523103i	−0.786053	+	0.618159i	$0.787879\pi$
$864$	2.11510	+	2.97024i	2.11510	+	2.97024i
$865$		0			0
$866$		0			0
$867$	1.92837	−	0.371662i	1.92837	−	0.371662i
$868$		0			0
$869$		0			0
$870$	0.186888			0.186888
$871$		0			0
$872$	−1.99094			−1.99094
$873$		0			0
$874$		0			0
$875$	−1.74555	+	0.336426i	−1.74555	+	0.336426i
$876$		0			0
$877$		0			0		0.786053	−	0.618159i	$-0.212121\pi$
$877$		0			0		−0.786053	+	0.618159i	$0.787879\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−0.0475819	+	0.998867i	−0.0475819	+	0.998867i	0.841254	+	0.540641i	$0.181818\pi$
$881$	−0.0475819	+	0.998867i	−0.0475819	+	0.998867i	−0.888835	+	0.458227i	$0.848485\pi$
$882$	−4.85064	−	3.81458i	−4.85064	−	3.81458i
$883$	−1.38884	+	1.32425i	−1.38884	+	1.32425i	−0.500000	+	0.866025i	$0.666667\pi$
$883$	−1.38884	+	1.32425i	−1.38884	+	1.32425i	−0.888835	+	0.458227i	$0.848485\pi$
$884$		0			0
$885$		0			0
$886$	0.0395325	+	0.0865641i	0.0395325	+	0.0865641i
$887$	0.0883470	−	0.0353688i	0.0883470	−	0.0353688i	−0.327068	−	0.945001i	$-0.606061\pi$
$887$	0.0883470	−	0.0353688i	0.0883470	−	0.0353688i	0.415415	+	0.909632i	$0.363636\pi$
$888$		0			0
$889$	−0.914053	+	2.64098i	−0.914053	+	2.64098i
$890$	0.481929	−	0.676774i	0.481929	−	0.676774i
$891$		0			0
$892$	−0.264241	−	0.105786i	−0.264241	−	0.105786i
$893$		0			0
$894$	−0.823056	−	0.424315i	−0.823056	−	0.424315i
$895$		0			0
$896$	1.70566	+	0.500828i	1.70566	+	0.500828i
$897$		0			0
$898$	−0.205996	−	1.43273i	−0.205996	−	1.43273i
$899$		0			0
$900$	−1.42837	+	2.47401i	−1.42837	+	2.47401i
$901$		0			0
$902$		0			0
$903$	−2.02979	+	1.04643i	−2.02979	+	1.04643i
$904$		0			0
$905$	1.30379	+	0.124497i	1.30379	+	0.124497i
$906$		0			0
$907$	−0.0671040	+	0.276606i	−0.0671040	+	0.276606i	−0.995472	−	0.0950560i	$-0.969697\pi$
$907$	−0.0671040	+	0.276606i	−0.0671040	+	0.276606i	0.928368	+	0.371662i	$0.121212\pi$
$908$	−0.415415	−	0.719520i	−0.415415	−	0.719520i
$909$	−1.18673	+	2.05548i	−1.18673	+	2.05548i
$910$		0			0
$911$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$911$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	0.496834	+	0.256136i	0.496834	+	0.256136i
$916$	−1.32254	−	0.849945i	−1.32254	−	0.849945i
$917$		0			0
$918$		0			0
$919$		0			0		0.580057	−	0.814576i	$-0.303030\pi$
$919$		0			0		−0.580057	+	0.814576i	$0.696970\pi$
$920$	0.327068	−	0.945001i	0.327068	−	0.945001i
$921$	−3.70051	−	0.713215i	−3.70051	−	0.713215i
$922$	1.07701	−	0.431171i	1.07701	−	0.431171i
$923$		0			0
$924$		0			0
$925$		0			0
$926$	−0.947890	+	0.903811i	−0.947890	+	0.903811i
$927$	4.47076	+	3.51584i	4.47076	+	3.51584i
$928$	0.00452808	−	0.0950560i	0.00452808	−	0.0950560i
$929$	0.481929	−	1.05528i	0.481929	−	1.05528i	−0.500000	−	0.866025i	$-0.666667\pi$
$929$	0.481929	−	1.05528i	0.481929	−	1.05528i	0.981929	−	0.189251i	$-0.0606061\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$	−1.54370	+	0.297523i	−1.54370	+	0.297523i
$935$		0			0
$936$		0			0
$937$		0			0		1.00000			$0$
$937$		0			0		−1.00000			$\pi$
$938$	−1.65033	+	0.660694i	−1.65033	+	0.660694i
$939$		0			0
$940$	−1.44091	+	0.137591i	−1.44091	+	0.137591i
$941$	−1.61435	+	1.03748i	−1.61435	+	1.03748i	−0.654861	+	0.755750i	$0.727273\pi$
$941$	−1.61435	+	1.03748i	−1.61435	+	1.03748i	−0.959493	+	0.281733i	$0.909091\pi$
$942$		0			0
$943$	0.0671040	−	0.466718i	0.0671040	−	0.466718i
$944$		0			0
$945$	−3.75995	−	5.28011i	−3.75995	−	5.28011i
$946$		0			0
$947$	−0.271738	+	0.595023i	−0.271738	+	0.595023i	−0.995472	−	0.0950560i	$-0.969697\pi$
$947$	−0.271738	+	0.595023i	−0.271738	+	0.595023i	0.723734	+	0.690079i	$0.242424\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$953$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	1.65210	+	1.06174i	1.65210	+	1.06174i
$961$	−0.888835	−	0.458227i	−0.888835	−	0.458227i
$962$		0			0
$963$	5.25998	+	1.54447i	5.25998	+	1.54447i
$964$	0.651174	+	1.88144i	0.651174	+	1.88144i
$965$		0			0
$966$	2.52662	+	2.40913i	2.52662	+	2.40913i
$967$	0.959493	−	1.66189i	0.959493	−	1.66189i	0.235759	−	0.971812i	$-0.424242\pi$
$967$	0.959493	−	1.66189i	0.959493	−	1.66189i	0.723734	−	0.690079i	$-0.242424\pi$
$968$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$969$		0			0
$970$		0			0
$971$		0			0		−0.995472	−	0.0950560i	$-0.969697\pi$
$971$		0			0		0.995472	+	0.0950560i	$0.0303030\pi$
$972$	−4.78471	−	0.456885i	−4.78471	−	0.456885i
$973$		0			0
$974$	0.273507	−	1.12741i	0.273507	−	1.12741i
$975$		0			0
$976$	0.142315	−	0.246497i	0.142315	−	0.246497i
$977$		0			0		−0.723734	−	0.690079i	$-0.757576\pi$
$977$		0			0		0.723734	+	0.690079i	$0.242424\pi$
$978$	0.366049	+	2.54593i	0.366049	+	2.54593i
$979$		0			0
$980$	−2.07261	−	0.608574i	−2.07261	−	0.608574i
$981$	3.72459	−	4.29840i	3.72459	−	4.29840i
$982$		0			0
$983$	1.41542	+	0.909632i	1.41542	+	0.909632i	1.00000			$0$
$983$	1.41542	+	0.909632i	1.41542	+	0.909632i	0.415415	+	0.909632i	$0.363636\pi$
$984$	0.859663	+	0.344157i	0.859663	+	0.344157i
$985$		0			0
$986$		0			0
$987$	1.65275	−	4.77532i	1.65275	−	4.77532i
$988$		0			0
$989$	0.607279	−	0.243118i	0.607279	−	0.243118i
$990$		0			0
$991$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$991$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$	0.946439	−	2.07241i	0.946439	−	2.07241i
$997$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$997$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$998$		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.419.1	yes	20
4.3	odd	2		1340.1.bl.a.419.1	yes	20
5.4	even	2		1340.1.bl.a.419.1	yes	20
20.19	odd	2	CM	1340.1.bl.b.419.1	yes	20
67.4	even	33	inner	1340.1.bl.b.339.1	yes	20
268.71	odd	66		1340.1.bl.a.339.1	✓	20
335.4	even	66		1340.1.bl.a.339.1	✓	20
1340.339	odd	66	inner	1340.1.bl.b.339.1	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1340.1.bl.a.339.1	✓	20	268.71	odd	66
1340.1.bl.a.339.1	✓	20	335.4	even	66
1340.1.bl.a.419.1	yes	20	4.3	odd	2
1340.1.bl.a.419.1	yes	20	5.4	even	2
1340.1.bl.b.339.1	yes	20	67.4	even	33	inner
1340.1.bl.b.339.1	yes	20	1340.339	odd	66	inner
1340.1.bl.b.419.1	yes	20	1.1	even	1	trivial
1340.1.bl.b.419.1	yes	20	20.19	odd	2	CM

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.995472 + 0.0950560i) q^{2} +(1.65210 - 1.06174i) q^{3} +(0.981929 - 0.189251i) q^{4} +(-0.142315 + 0.989821i) q^{5} +(-1.54370 + 1.21398i) q^{6} +(-1.03115 - 1.44805i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(1.18673 - 2.59858i) q^{9} +O(q^{10})\)	\(q+(-0.995472 + 0.0950560i) q^{2} +(1.65210 - 1.06174i) q^{3} +(0.981929 - 0.189251i) q^{4} +(-0.142315 + 0.989821i) q^{5} +(-1.54370 + 1.21398i) q^{6} +(-1.03115 - 1.44805i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(1.18673 - 2.59858i) q^{9} +(0.0475819 - 0.998867i) q^{10} +(1.42131 - 1.35522i) q^{12} +(1.16413 + 1.34347i) q^{14} +(0.815816 + 1.78639i) q^{15} +(0.928368 - 0.371662i) q^{16} +(-0.934347 + 2.69962i) q^{18} +(0.0475819 + 0.998867i) q^{20} +(-3.24102 - 1.29751i) q^{21} +(0.888835 + 0.458227i) q^{23} +(-1.28605 + 1.48418i) q^{24} +(-0.959493 - 0.281733i) q^{25} +(-0.518932 - 3.60925i) q^{27} +(-1.28656 - 1.22673i) q^{28} +(-0.0475819 + 0.0824143i) q^{29} +(-0.981929 - 1.70075i) q^{30} +(-0.888835 + 0.458227i) q^{32} +(1.58006 - 0.814576i) q^{35} +(0.673501 - 2.77621i) q^{36} +(-0.142315 - 0.989821i) q^{40} +(-0.154218 - 0.445585i) q^{41} +(3.34968 + 0.983554i) q^{42} +(0.428368 - 0.494363i) q^{43} +(2.40324 + 1.54447i) q^{45} +(-0.928368 - 0.371662i) q^{46} +(0.0688733 + 1.44583i) q^{47} +(1.13915 - 1.59971i) q^{48} +(-0.706504 + 2.04131i) q^{49} +(0.981929 + 0.189251i) q^{50} +(0.859663 + 3.54358i) q^{54} +(1.39734 + 1.09888i) q^{56} +(0.0395325 - 0.0865641i) q^{58} +(1.13915 + 1.59971i) q^{60} +(0.223734 - 0.175946i) q^{61} +(-4.98656 + 0.961081i) q^{63} +(0.841254 - 0.540641i) q^{64} +(-0.327068 + 0.945001i) q^{67} +(1.95496 - 0.186677i) q^{69} +(-1.49547 + 0.961081i) q^{70} +(-0.406556 + 2.82766i) q^{72} +(-1.88431 + 0.553283i) q^{75} +(0.235759 + 0.971812i) q^{80} +(-2.81865 - 3.25290i) q^{81} +(0.195876 + 0.428908i) q^{82} +(1.07701 - 0.431171i) q^{83} +(-3.42800 - 0.660694i) q^{84} +(-0.379436 + 0.532843i) q^{86} +(0.00889250 + 0.186677i) q^{87} +(0.698939 + 0.449181i) q^{89} +(-2.53917 - 1.30903i) q^{90} +(0.959493 + 0.281733i) q^{92} +(-0.205996 - 1.43273i) q^{94} +(-0.981929 + 1.70075i) q^{96} +(0.509266 - 2.09922i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + q^{2} + 2 q^{3} + q^{4} - 2 q^{5} - q^{6} - q^{7} - 2 q^{8}+O(q^{10}) \) 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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