LMFDB - Embedded newform 418.2.e.i.353.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(45,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("418.45");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.e (of order $3$, degree $2$, 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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.101617200.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 8x^{4} - 4x^{3} + 64x^{2} - 16x + 4 $ x^6 + 8x^4 - 4x^3 + 64x^2 - 16x + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			353.3
Root			$-1.47300 + 2.55131i$ of defining polynomial
Character	$\chi$	$=$	418.353
Dual form			418.2.e.i.45.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(1.47300 - 2.55131i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.00000 + 1.73205i) q^{5} +(-1.47300 - 2.55131i) q^{6} +4.94600 q^{7} -1.00000 q^{8} +(-2.83944 - 4.91806i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(1.47300 - 2.55131i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.00000 + 1.73205i) q^{5} +(-1.47300 - 2.55131i) q^{6} +4.94600 q^{7} -1.00000 q^{8} +(-2.83944 - 4.91806i) q^{9} +(1.00000 + 1.73205i) q^{10} +1.00000 q^{11} -2.94600 q^{12} +(-2.83944 - 4.91806i) q^{13} +(2.47300 - 4.28336i) q^{14} +(2.94600 + 5.10261i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.86645 + 3.23278i) q^{17} -5.67889 q^{18} +(-2.70589 + 3.41733i) q^{19} +2.00000 q^{20} +(7.28544 - 12.6188i) q^{21} +(0.500000 - 0.866025i) q^{22} +(0.945995 + 1.63851i) q^{23} +(-1.47300 + 2.55131i) q^{24} +(0.500000 + 0.866025i) q^{25} -5.67889 q^{26} -7.89199 q^{27} +(-2.47300 - 4.28336i) q^{28} +(0.500000 + 0.866025i) q^{29} +5.89199 q^{30} +3.21310 q^{31} +(0.500000 + 0.866025i) q^{32} +(1.47300 - 2.55131i) q^{33} +(1.86645 + 3.23278i) q^{34} +(-4.94600 + 8.56671i) q^{35} +(-2.83944 + 4.91806i) q^{36} -4.15910 q^{37} +(1.60655 + 4.05204i) q^{38} -16.7300 q^{39} +(1.00000 - 1.73205i) q^{40} +(-4.81244 + 8.33539i) q^{41} +(-7.28544 - 12.6188i) q^{42} +(2.31244 - 4.00527i) q^{43} +(-0.500000 - 0.866025i) q^{44} +11.3578 q^{45} +1.89199 q^{46} +(3.70589 + 6.41879i) q^{47} +(1.47300 + 2.55131i) q^{48} +17.4629 q^{49} +1.00000 q^{50} +(5.49854 + 9.52375i) q^{51} +(-2.83944 + 4.91806i) q^{52} +(-5.89199 - 10.2052i) q^{53} +(-3.94600 + 6.83466i) q^{54} +(-1.00000 + 1.73205i) q^{55} -4.94600 q^{56} +(4.73289 + 11.9373i) q^{57} +1.00000 q^{58} +(2.94600 - 5.10261i) q^{60} +(2.78544 + 4.82452i) q^{61} +(1.60655 - 2.78263i) q^{62} +(-14.0439 - 24.3247i) q^{63} +1.00000 q^{64} +11.3578 q^{65} +(-1.47300 - 2.55131i) q^{66} +(-4.41899 - 7.65392i) q^{67} +3.73289 q^{68} +5.57379 q^{69} +(4.94600 + 8.56671i) q^{70} +(-2.31244 + 4.00527i) q^{71} +(2.83944 + 4.91806i) q^{72} +(1.81244 - 3.13924i) q^{73} +(-2.07955 + 3.60188i) q^{74} +2.94600 q^{75} +(4.31244 + 0.634704i) q^{76} +4.94600 q^{77} +(-8.36499 + 14.4886i) q^{78} +(3.41899 - 5.92187i) q^{79} +(-1.00000 - 1.73205i) q^{80} +(-3.10655 + 5.38070i) q^{81} +(4.81244 + 8.33539i) q^{82} +14.5169 q^{83} -14.5709 q^{84} +(-3.73289 - 6.46556i) q^{85} +(-2.31244 - 4.00527i) q^{86} +2.94600 q^{87} -1.00000 q^{88} +(0.232893 + 0.403382i) q^{89} +(5.67889 - 9.83612i) q^{90} +(-14.0439 - 24.3247i) q^{91} +(0.945995 - 1.63851i) q^{92} +(4.73289 - 8.19761i) q^{93} +7.41178 q^{94} +(-3.21310 - 8.10407i) q^{95} +2.94600 q^{96} +(0.767107 - 1.32867i) q^{97} +(8.73143 - 15.1233i) q^{98} +(-2.83944 - 4.91806i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - 3 q^{4} - 6 q^{5} + 12 q^{7} - 6 q^{8} - 7 q^{9}+O(q^{10}) $ 6 * q + 3 * q^2 - 3 * q^4 - 6 * q^5 + 12 * q^7 - 6 * q^8 - 7 * q^9	$ 6 q + 3 q^{2} - 3 q^{4} - 6 q^{5} + 12 q^{7} - 6 q^{8} - 7 q^{9} + 6 q^{10} + 6 q^{11} - 7 q^{13} + 6 q^{14} - 3 q^{16} - 10 q^{17} - 14 q^{18} - 5 q^{19} + 12 q^{20} + 16 q^{21} + 3 q^{22} - 12 q^{23} + 3 q^{25} - 14 q^{26} - 12 q^{27} - 6 q^{28} + 3 q^{29} + 4 q^{31} + 3 q^{32} + 10 q^{34} - 12 q^{35} - 7 q^{36} + 8 q^{37} + 2 q^{38} - 12 q^{39} + 6 q^{40} - 10 q^{41} - 16 q^{42} - 5 q^{43} - 3 q^{44} + 28 q^{45} - 24 q^{46} + 11 q^{47} + 14 q^{49} + 6 q^{50} - 10 q^{51} - 7 q^{52} - 6 q^{54} - 6 q^{55} - 12 q^{56} + 26 q^{57} + 6 q^{58} - 11 q^{61} + 2 q^{62} - 20 q^{63} + 6 q^{64} + 28 q^{65} + 20 q^{68} + 64 q^{69} + 12 q^{70} + 5 q^{71} + 7 q^{72} - 8 q^{73} + 4 q^{74} + 7 q^{76} + 12 q^{77} - 6 q^{78} - 6 q^{79} - 6 q^{80} - 11 q^{81} + 10 q^{82} + 14 q^{83} - 32 q^{84} - 20 q^{85} + 5 q^{86} - 6 q^{88} - q^{89} + 14 q^{90} - 20 q^{91} - 12 q^{92} + 26 q^{93} + 22 q^{94} - 4 q^{95} + 7 q^{97} + 7 q^{98} - 7 q^{99}+O(q^{100}) $ 6 * q + 3 * q^2 - 3 * q^4 - 6 * q^5 + 12 * q^7 - 6 * q^8 - 7 * q^9 + 6 * q^10 + 6 * q^11 - 7 * q^13 + 6 * q^14 - 3 * q^16 - 10 * q^17 - 14 * q^18 - 5 * q^19 + 12 * q^20 + 16 * q^21 + 3 * q^22 - 12 * q^23 + 3 * q^25 - 14 * q^26 - 12 * q^27 - 6 * q^28 + 3 * q^29 + 4 * q^31 + 3 * q^32 + 10 * q^34 - 12 * q^35 - 7 * q^36 + 8 * q^37 + 2 * q^38 - 12 * q^39 + 6 * q^40 - 10 * q^41 - 16 * q^42 - 5 * q^43 - 3 * q^44 + 28 * q^45 - 24 * q^46 + 11 * q^47 + 14 * q^49 + 6 * q^50 - 10 * q^51 - 7 * q^52 - 6 * q^54 - 6 * q^55 - 12 * q^56 + 26 * q^57 + 6 * q^58 - 11 * q^61 + 2 * q^62 - 20 * q^63 + 6 * q^64 + 28 * q^65 + 20 * q^68 + 64 * q^69 + 12 * q^70 + 5 * q^71 + 7 * q^72 - 8 * q^73 + 4 * q^74 + 7 * q^76 + 12 * q^77 - 6 * q^78 - 6 * q^79 - 6 * q^80 - 11 * q^81 + 10 * q^82 + 14 * q^83 - 32 * q^84 - 20 * q^85 + 5 * q^86 - 6 * q^88 - q^89 + 14 * q^90 - 20 * q^91 - 12 * q^92 + 26 * q^93 + 22 * q^94 - 4 * q^95 + 7 * q^97 + 7 * q^98 - 7 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	1.47300	−	2.55131i	0.850436	−	1.47300i	−0.0303802	−	0.999538i	$-0.509672\pi$
$3$	1.47300	−	2.55131i	0.850436	−	1.47300i	0.880816	−	0.473459i	$-0.156995\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.00000	+	1.73205i	−0.447214	+	0.774597i	−0.998203	−	0.0599153i	$-0.980917\pi$
$5$	−1.00000	+	1.73205i	−0.447214	+	0.774597i	0.550990	+	0.834512i	$0.314250\pi$
$6$	−1.47300	−	2.55131i	−0.601349	−	1.04157i
$7$	4.94600			1.86941			0.934705	−	0.355424i	$-0.115663\pi$
$7$	4.94600			1.86941			0.934705	+	0.355424i	$0.115663\pi$
$8$	−1.00000			−0.353553
$9$	−2.83944	−	4.91806i	−0.946481	−	1.63935i
$10$	1.00000	+	1.73205i	0.316228	+	0.547723i
$11$	1.00000			0.301511
$11$	1.00000			0.301511
$12$	−2.94600			−0.850436
$13$	−2.83944	−	4.91806i	−0.787520	−	1.36402i	−0.927482	−	0.373868i	$-0.878031\pi$
$13$	−2.83944	−	4.91806i	−0.787520	−	1.36402i	0.139962	−	0.990157i	$-0.455302\pi$
$14$	2.47300	−	4.28336i	0.660936	−	1.14478i
$15$	2.94600	+	5.10261i	0.760653	+	1.31749i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.86645	+	3.23278i	−0.452680	+	0.784064i	−0.998551	−	0.0538045i	$-0.982865\pi$
$17$	−1.86645	+	3.23278i	−0.452680	+	0.784064i	0.545872	+	0.837869i	$0.316199\pi$
$18$	−5.67889			−1.33853
$19$	−2.70589	+	3.41733i	−0.620774	+	0.783990i
$19$	−2.70589	+	3.41733i	−0.620774	+	0.783990i
$20$	2.00000			0.447214
$21$	7.28544	−	12.6188i	1.58981	−	2.75364i
$22$	0.500000	−	0.866025i	0.106600	−	0.184637i
$23$	0.945995	+	1.63851i	0.197254	+	0.341653i	0.947637	−	0.319350i	$-0.103464\pi$
$23$	0.945995	+	1.63851i	0.197254	+	0.341653i	−0.750383	+	0.661003i	$0.770131\pi$
$24$	−1.47300	+	2.55131i	−0.300674	+	0.520783i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	−5.67889			−1.11372
$27$	−7.89199			−1.51881
$28$	−2.47300	−	4.28336i	−0.467353	−	0.809478i
$29$	0.500000	+	0.866025i	0.0928477	+	0.160817i	0.908708	−	0.417432i	$-0.137070\pi$
$29$	0.500000	+	0.866025i	0.0928477	+	0.160817i	−0.815861	+	0.578249i	$0.803736\pi$
$30$	5.89199			1.07573
$31$	3.21310			0.577090			0.288545	−	0.957466i	$-0.406828\pi$
$31$	3.21310			0.577090			0.288545	+	0.957466i	$0.406828\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	1.47300	−	2.55131i	0.256416	−	0.444125i
$34$	1.86645	+	3.23278i	0.320093	+	0.554417i
$35$	−4.94600	+	8.56671i	−0.836026	+	1.44804i
$36$	−2.83944	+	4.91806i	−0.473241	+	0.819677i
$37$	−4.15910			−0.683751			−0.341876	−	0.939745i	$-0.611062\pi$
$37$	−4.15910			−0.683751			−0.341876	+	0.939745i	$0.611062\pi$
$38$	1.60655	+	4.05204i	0.260617	+	0.657327i
$39$	−16.7300			−2.67894
$40$	1.00000	−	1.73205i	0.158114	−	0.273861i
$41$	−4.81244	+	8.33539i	−0.751577	+	1.30177i	0.195481	+	0.980707i	$0.437373\pi$
$41$	−4.81244	+	8.33539i	−0.751577	+	1.30177i	−0.947058	+	0.321062i	$0.895960\pi$
$42$	−7.28544	−	12.6188i	−1.12417	−	1.94712i
$43$	2.31244	−	4.00527i	0.352644	−	0.610797i	−0.634068	−	0.773277i	$-0.718616\pi$
$43$	2.31244	−	4.00527i	0.352644	−	0.610797i	0.986712	+	0.162480i	$0.0519493\pi$
$44$	−0.500000	−	0.866025i	−0.0753778	−	0.130558i
$45$	11.3578			1.69312
$46$	1.89199			0.278959
$47$	3.70589	+	6.41879i	0.540560	+	0.936277i	0.998872	+	0.0474855i	$0.0151208\pi$
$47$	3.70589	+	6.41879i	0.540560	+	0.936277i	−0.458312	+	0.888791i	$0.651546\pi$
$48$	1.47300	+	2.55131i	0.212609	+	0.368249i
$49$	17.4629			2.49470
$50$	1.00000			0.141421
$51$	5.49854	+	9.52375i	0.769950	+	1.33359i
$52$	−2.83944	+	4.91806i	−0.393760	+	0.682012i
$53$	−5.89199	−	10.2052i	−0.809327	−	1.40180i	−0.913331	−	0.407219i	$-0.866499\pi$
$53$	−5.89199	−	10.2052i	−0.809327	−	1.40180i	0.104004	−	0.994577i	$-0.466835\pi$
$54$	−3.94600	+	6.83466i	−0.536982	+	0.930080i
$55$	−1.00000	+	1.73205i	−0.134840	+	0.233550i
$56$	−4.94600			−0.660936
$57$	4.73289	+	11.9373i	0.626887	+	1.58113i
$58$	1.00000			0.131306
$59$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$59$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$60$	2.94600	−	5.10261i	0.380326	−	0.658745i
$61$	2.78544	+	4.82452i	0.356639	+	0.617717i	0.987397	−	0.158263i	$-0.0505893\pi$
$61$	2.78544	+	4.82452i	0.356639	+	0.617717i	−0.630758	+	0.775980i	$0.717256\pi$
$62$	1.60655	−	2.78263i	0.204032	−	0.353394i
$63$	−14.0439	−	24.3247i	−1.76936	−	3.06462i
$64$	1.00000			0.125000
$65$	11.3578			1.40876
$66$	−1.47300	−	2.55131i	−0.181313	−	0.314044i
$67$	−4.41899	−	7.65392i	−0.539866	−	0.935075i	−0.998911	−	0.0466621i	$-0.985142\pi$
$67$	−4.41899	−	7.65392i	−0.539866	−	0.935075i	0.459045	−	0.888413i	$-0.348192\pi$
$68$	3.73289			0.452680
$69$	5.57379			0.671006
$70$	4.94600	+	8.56671i	0.591159	+	1.02392i
$71$	−2.31244	+	4.00527i	−0.274436	+	0.475338i	−0.969993	−	0.243134i	$-0.921825\pi$
$71$	−2.31244	+	4.00527i	−0.274436	+	0.475338i	0.695556	+	0.718471i	$0.255158\pi$
$72$	2.83944	+	4.91806i	0.334632	+	0.579599i
$73$	1.81244	−	3.13924i	0.212130	−	0.367420i	−0.740251	−	0.672331i	$-0.765293\pi$
$73$	1.81244	−	3.13924i	0.212130	−	0.367420i	0.952381	+	0.304911i	$0.0986266\pi$
$74$	−2.07955	+	3.60188i	−0.241743	+	0.418711i
$75$	2.94600			0.340174
$76$	4.31244	+	0.634704i	0.494671	+	0.0728055i
$77$	4.94600			0.563648
$78$	−8.36499	+	14.4886i	−0.947148	+	1.64051i
$79$	3.41899	−	5.92187i	0.384667	−	0.666262i	−0.607056	−	0.794659i	$-0.707650\pi$
$79$	3.41899	−	5.92187i	0.384667	−	0.666262i	0.991723	+	0.128397i	$0.0409830\pi$
$80$	−1.00000	−	1.73205i	−0.111803	−	0.193649i
$81$	−3.10655	+	5.38070i	−0.345172	+	0.597856i
$82$	4.81244	+	8.33539i	0.531445	+	0.920490i
$83$	14.5169			1.59343			0.796717	−	0.604353i	$-0.206568\pi$
$83$	14.5169			1.59343			0.796717	+	0.604353i	$0.206568\pi$
$84$	−14.5709			−1.58981
$85$	−3.73289	−	6.46556i	−0.404889	−	0.701288i
$86$	−2.31244	−	4.00527i	−0.249357	−	0.431899i
$87$	2.94600			0.315844
$88$	−1.00000			−0.106600
$89$	0.232893	+	0.403382i	0.0246866	+	0.0427584i	0.878105	−	0.478468i	$-0.158808\pi$
$89$	0.232893	+	0.403382i	0.0246866	+	0.0427584i	−0.853418	+	0.521227i	$0.825475\pi$
$90$	5.67889	−	9.83612i	0.598607	−	1.03682i
$91$	−14.0439	−	24.3247i	−1.47220	−	2.54992i
$92$	0.945995	−	1.63851i	0.0986268	−	0.170827i
$93$	4.73289	−	8.19761i	0.490778	−	0.850053i
$94$	7.41178			0.764467
$95$	−3.21310	−	8.10407i	−0.329657	−	0.831460i
$96$	2.94600			0.300674
$97$	0.767107	−	1.32867i	0.0778880	−	0.134906i	−0.824451	−	0.565934i	$-0.808516\pi$
$97$	0.767107	−	1.32867i	0.0778880	−	0.134906i	0.902339	+	0.431028i	$0.141849\pi$
$98$	8.73143	−	15.1233i	0.882008	−	1.52768i
$99$	−2.83944	−	4.91806i	−0.285375	−	0.494284i
$100$	0.500000	−	0.866025i	0.0500000	−	0.0866025i
$101$	0.839444	+	1.45396i	0.0835278	+	0.144674i	0.904763	−	0.425916i	$-0.140048\pi$
$101$	0.839444	+	1.45396i	0.0835278	+	0.144674i	−0.821235	+	0.570590i	$0.806715\pi$
$102$	10.9971			1.08887
$103$	−7.41178			−0.730304			−0.365152	−	0.930948i	$-0.618983\pi$
$103$	−7.41178			−0.730304			−0.365152	+	0.930948i	$0.618983\pi$
$104$	2.83944	+	4.91806i	0.278430	+	0.482256i
$105$	14.5709	+	25.2375i	1.42197	+	2.46293i
$106$	−11.7840			−1.14456
$107$	16.3722			1.58276			0.791380	−	0.611324i	$-0.209363\pi$
$107$	16.3722			1.58276			0.791380	+	0.611324i	$0.209363\pi$
$108$	3.94600	+	6.83466i	0.379704	+	0.657666i
$109$	−8.73143	+	15.1233i	−0.836320	+	1.44855i	0.0566317	+	0.998395i	$0.481964\pi$
$109$	−8.73143	+	15.1233i	−0.836320	+	1.44855i	−0.892951	+	0.450153i	$0.851369\pi$
$110$	1.00000	+	1.73205i	0.0953463	+	0.165145i
$111$	−6.12634	+	10.6111i	−0.581487	+	1.00716i
$112$	−2.47300	+	4.28336i	−0.233676	+	0.404739i
$113$	−3.53421			−0.332471			−0.166235	−	0.986086i	$-0.553161\pi$
$113$	−3.53421			−0.332471			−0.166235	+	0.986086i	$0.553161\pi$
$114$	12.7044	+	1.86983i	1.18988	+	0.175126i
$115$	−3.78398			−0.352858
$116$	0.500000	−	0.866025i	0.0464238	−	0.0804084i
$117$	−16.1249	+	27.9291i	−1.49075	+	2.58205i
$118$		0			0
$119$	−9.23143	+	15.9893i	−0.846244	+	1.46574i
$120$	−2.94600	−	5.10261i	−0.268931	−	0.465803i
$121$	1.00000			0.0909091
$122$	5.57088			0.504364
$123$	14.1774	+	24.5560i	1.27834	+	2.21414i
$124$	−1.60655	−	2.78263i	−0.144273	−	0.249887i
$125$	−12.0000			−1.07331
$126$	−28.0878			−2.50226
$127$	2.67889	+	4.63997i	0.237713	+	0.411731i	0.960058	−	0.279802i	$-0.0902689\pi$
$127$	2.67889	+	4.63997i	0.237713	+	0.411731i	−0.722345	+	0.691533i	$0.756936\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−6.81244	−	11.7995i	−0.599802	−	1.03889i
$130$	5.67889	−	9.83612i	0.498071	−	0.862685i
$131$	−5.18610	+	8.98259i	−0.453112	+	0.784812i	−0.998577	−	0.0533206i	$-0.983019\pi$
$131$	−5.18610	+	8.98259i	−0.453112	+	0.784812i	0.545466	+	0.838133i	$0.316353\pi$
$132$	−2.94600			−0.256416
$133$	−13.3833	+	16.9021i	−1.16048	+	1.46560i
$134$	−8.83799			−0.763486
$135$	7.89199	−	13.6693i	0.679234	−	1.17647i
$136$	1.86645	−	3.23278i	0.160046	−	0.277209i
$137$	−7.05255	−	12.2154i	−0.602540	−	1.04363i	−0.992435	−	0.122770i	$-0.960822\pi$
$137$	−7.05255	−	12.2154i	−0.602540	−	1.04363i	0.389895	−	0.920859i	$-0.372511\pi$
$138$	2.78690	−	4.82705i	0.237236	−	0.410906i
$139$	6.83799	+	11.8437i	0.579990	+	1.00457i	0.995480	+	0.0949747i	$0.0302770\pi$
$139$	6.83799	+	11.8437i	0.579990	+	1.00457i	−0.415489	+	0.909598i	$0.636390\pi$
$140$	9.89199			0.836026
$141$	21.8351			1.83884
$142$	2.31244	+	4.00527i	0.194056	+	0.336114i
$143$	−2.83944	−	4.91806i	−0.237446	−	0.411269i
$144$	5.67889			0.473241
$145$	−2.00000			−0.166091
$146$	−1.81244	−	3.13924i	−0.149999	−	0.259805i
$147$	25.7228	−	44.5531i	2.12158	−	3.67468i
$148$	2.07955	+	3.60188i	0.170938	+	0.296073i
$149$	−9.49854	+	16.4520i	−0.778151	+	1.34780i	0.154856	+	0.987937i	$0.450509\pi$
$149$	−9.49854	+	16.4520i	−0.778151	+	1.34780i	−0.933006	+	0.359860i	$0.882825\pi$
$150$	1.47300	−	2.55131i	0.120270	−	0.208313i
$151$	−23.6615			−1.92555			−0.962775	−	0.270305i	$-0.912875\pi$
$151$	−23.6615			−1.92555			−0.962775	+	0.270305i	$0.912875\pi$
$152$	2.70589	−	3.41733i	0.219477	−	0.277182i
$153$	21.1987			1.71381
$154$	2.47300	−	4.28336i	0.199280	−	0.345163i
$155$	−3.21310	+	5.56526i	−0.258083	+	0.447012i
$156$	8.36499	+	14.4886i	0.669735	+	1.16002i
$157$	5.89199	−	10.2052i	0.470232	−	0.814466i	−0.529188	−	0.848504i	$-0.677504\pi$
$157$	5.89199	−	10.2052i	0.470232	−	0.814466i	0.999421	+	0.0340385i	$0.0108369\pi$
$158$	−3.41899	−	5.92187i	−0.272000	−	0.471119i
$159$	−34.7156			−2.75312
$160$	−2.00000			−0.158114
$161$	4.67889	+	8.10407i	0.368748	+	0.638690i
$162$	3.10655	+	5.38070i	0.244074	+	0.422748i
$163$	−10.8236			−0.847767			−0.423883	−	0.905717i	$-0.639333\pi$
$163$	−10.8236			−0.847767			−0.423883	+	0.905717i	$0.639333\pi$
$164$	9.62488			0.751577
$165$	2.94600	+	5.10261i	0.229345	+	0.397238i
$166$	7.25844	−	12.5720i	0.563364	−	0.975775i
$167$	−2.00721	−	3.47659i	−0.155323	−	0.269027i	0.777854	−	0.628445i	$-0.216308\pi$
$167$	−2.00721	−	3.47659i	−0.155323	−	0.269027i	−0.933177	+	0.359418i	$0.882975\pi$
$168$	−7.28544	+	12.6188i	−0.562084	+	0.973558i
$169$	−9.62488	+	16.6708i	−0.740376	+	1.28237i
$170$	−7.46579			−0.572600
$171$	24.4899	+	3.60441i	1.87279	+	0.275636i
$172$	−4.62488			−0.352644
$173$	3.60655	−	6.24673i	0.274201	−	0.474930i	−0.695732	−	0.718301i	$-0.744920\pi$
$173$	3.60655	−	6.24673i	0.274201	−	0.474930i	0.969933	+	0.243371i	$0.0782533\pi$
$174$	1.47300	−	2.55131i	0.111668	−	0.193414i
$175$	2.47300	+	4.28336i	0.186941	+	0.323791i
$176$	−0.500000	+	0.866025i	−0.0376889	+	0.0652791i
$177$		0			0
$178$	0.465785			0.0349121
$179$	4.10801			0.307047			0.153524	−	0.988145i	$-0.450938\pi$
$179$	4.10801			0.307047			0.153524	+	0.988145i	$0.450938\pi$
$180$	−5.67889	−	9.83612i	−0.423279	−	0.733141i
$181$	−7.70443	−	13.3445i	−0.572666	−	0.991886i	−0.996291	−	0.0860488i	$-0.972576\pi$
$181$	−7.70443	−	13.3445i	−0.572666	−	0.991886i	0.423625	−	0.905838i	$-0.360757\pi$
$182$	−28.0878			−2.08200
$183$	16.4118			1.21319
$184$	−0.945995	−	1.63851i	−0.0697397	−	0.120793i
$185$	4.15910	−	7.20377i	0.305783	−	0.529632i
$186$	−4.73289	−	8.19761i	−0.347033	−	0.601078i
$187$	−1.86645	+	3.23278i	−0.136488	+	0.236404i
$188$	3.70589	−	6.41879i	0.270280	−	0.468138i
$189$	−39.0337			−2.83929
$190$	−8.62488	−	1.26941i	−0.625715	−	0.0920925i
$191$	10.5882			0.766137			0.383068	−	0.923720i	$-0.374867\pi$
$191$	10.5882			0.766137			0.383068	+	0.923720i	$0.374867\pi$
$192$	1.47300	−	2.55131i	0.106304	−	0.184125i
$193$	2.75844	−	4.77775i	0.198557	−	0.343910i	−0.749504	−	0.662000i	$-0.769708\pi$
$193$	2.75844	−	4.77775i	0.198557	−	0.343910i	0.948061	+	0.318090i	$0.103041\pi$
$194$	−0.767107	−	1.32867i	−0.0550751	−	0.0953929i
$195$	16.7300	−	28.9772i	1.19806	−	2.07510i
$196$	−8.73143	−	15.1233i	−0.623674	−	1.08023i
$197$	−9.53421			−0.679285			−0.339642	−	0.940555i	$-0.610306\pi$
$197$	−9.53421			−0.679285			−0.339642	+	0.940555i	$0.610306\pi$
$198$	−5.67889			−0.403581
$199$	−10.3124	−	17.8617i	−0.731030	−	1.26618i	−0.956444	−	0.291917i	$-0.905707\pi$
$199$	−10.3124	−	17.8617i	−0.731030	−	1.26618i	0.225414	−	0.974263i	$-0.427627\pi$
$200$	−0.500000	−	0.866025i	−0.0353553	−	0.0612372i
$201$	−26.0367			−1.83648
$202$	1.67889			0.118126
$203$	2.47300	+	4.28336i	0.173570	+	0.300633i
$204$	5.49854	−	9.52375i	0.384975	−	0.666796i
$205$	−9.62488	−	16.6708i	−0.672231	−	1.16434i
$206$	−3.70589	+	6.41879i	−0.258202	+	0.447218i
$207$	5.37220	−	9.30492i	0.373394	−	0.646737i
$208$	5.67889			0.393760
$209$	−2.70589	+	3.41733i	−0.187170	+	0.236382i
$210$	29.1418			2.01097
$211$	12.8380	−	22.2360i	0.883803	−	1.53079i	0.0367243	−	0.999325i	$-0.488308\pi$
$211$	12.8380	−	22.2360i	0.883803	−	1.53079i	0.847079	−	0.531467i	$-0.178359\pi$
$212$	−5.89199	+	10.2052i	−0.404664	+	0.700898i
$213$	6.81244	+	11.7995i	0.466781	+	0.808488i
$214$	8.18610	−	14.1787i	0.559590	−	0.969239i
$215$	4.62488	+	8.01053i	0.315414	+	0.546314i
$216$	7.89199			0.536982
$217$	15.8920			1.07882
$218$	8.73143	+	15.1233i	0.591367	+	1.02428i
$219$	−5.33944	−	9.24819i	−0.360806	−	0.624935i
$220$	2.00000			0.134840
$221$	21.1987			1.42598
$222$	6.12634	+	10.6111i	0.411173	+	0.712173i
$223$	3.68756	−	6.38704i	0.246937	−	0.427708i	−0.715737	−	0.698370i	$-0.753909\pi$
$223$	3.68756	−	6.38704i	0.246937	−	0.427708i	0.962674	+	0.270662i	$0.0872425\pi$
$224$	2.47300	+	4.28336i	0.165234	+	0.286194i
$225$	2.83944	−	4.91806i	0.189296	−	0.327871i
$226$	−1.76711	+	3.06072i	−0.117546	+	0.203596i
$227$	−28.3549			−1.88198			−0.940989	−	0.338437i	$-0.890102\pi$
$227$	−28.3549			−1.88198			−0.940989	+	0.338437i	$0.890102\pi$
$228$	7.97154	−	10.0674i	0.527928	−	0.666733i
$229$	−4.98266			−0.329263			−0.164632	−	0.986355i	$-0.552644\pi$
$229$	−4.98266			−0.329263			−0.164632	+	0.986355i	$0.552644\pi$
$230$	−1.89199	+	3.27702i	−0.124754	+	0.216081i
$231$	7.28544	−	12.6188i	0.479347	−	0.830253i
$232$	−0.500000	−	0.866025i	−0.0328266	−	0.0568574i
$233$	−11.2242	+	19.4409i	−0.735323	+	1.27362i	0.219258	+	0.975667i	$0.429636\pi$
$233$	−11.2242	+	19.4409i	−0.735323	+	1.27362i	−0.954581	+	0.297950i	$0.903697\pi$
$234$	16.1249	+	27.9291i	1.05412	+	1.82578i
$235$	−14.8236			−0.966982
$236$		0			0
$237$	−10.0723	−	17.4458i	−0.654269	−	1.13323i
$238$	9.23143	+	15.9893i	0.598385	+	1.03643i
$239$	−23.7840			−1.53846			−0.769229	−	0.638973i	$-0.779359\pi$
$239$	−23.7840			−1.53846			−0.769229	+	0.638973i	$0.779359\pi$
$240$	−5.89199			−0.380326
$241$	10.5709	+	18.3093i	0.680930	+	1.17941i	0.974697	+	0.223529i	$0.0717576\pi$
$241$	10.5709	+	18.3093i	0.680930	+	1.17941i	−0.293767	+	0.955877i	$0.594909\pi$
$242$	0.500000	−	0.866025i	0.0321412	−	0.0556702i
$243$	−2.68610	−	4.65246i	−0.172313	−	0.298456i
$244$	2.78544	−	4.82452i	0.178319	−	0.308858i
$245$	−17.4629	+	30.2466i	−1.11566	+	1.93238i
$246$	28.3549			1.80784
$247$	24.4899	+	3.60441i	1.55825	+	0.229343i
$248$	−3.21310			−0.204032
$249$	21.3833	−	37.0370i	1.35511	−	2.34712i
$250$	−6.00000	+	10.3923i	−0.379473	+	0.657267i
$251$	−0.259895	−	0.450151i	−0.0164044	−	0.0284133i	0.857707	−	0.514139i	$-0.171889\pi$
$251$	−0.259895	−	0.450151i	−0.0164044	−	0.0284133i	−0.874111	+	0.485726i	$0.838555\pi$
$252$	−14.0439	+	24.3247i	−0.884681	+	1.53231i
$253$	0.945995	+	1.63851i	0.0594742	+	0.103012i
$254$	5.35778			0.336177
$255$	−21.9942			−1.37733
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	5.41178	+	9.37348i	0.337578	+	0.584702i	0.983977	−	0.178298i	$-0.0570591\pi$
$257$	5.41178	+	9.37348i	0.337578	+	0.584702i	−0.646399	+	0.763000i	$0.723726\pi$
$258$	−13.6249			−0.848248
$259$	−20.5709			−1.27821
$260$	−5.67889	−	9.83612i	−0.352190	−	0.610010i
$261$	2.83944	−	4.91806i	0.175757	−	0.304420i
$262$	5.18610	+	8.98259i	0.320398	+	0.554946i
$263$	6.51687	−	11.2876i	0.401848	−	0.696021i	−0.592101	−	0.805864i	$-0.701701\pi$
$263$	6.51687	−	11.2876i	0.401848	−	0.696021i	0.993949	+	0.109843i	$0.0350348\pi$
$264$	−1.47300	+	2.55131i	−0.0906567	+	0.157022i
$265$	23.5680			1.44777
$266$	7.94600	+	20.0413i	0.487200	+	1.22881i
$267$	1.37220			0.0839773
$268$	−4.41899	+	7.65392i	−0.269933	+	0.467538i
$269$	2.86645	−	4.96483i	0.174770	−	0.302711i	−0.765311	−	0.643660i	$-0.777415\pi$
$269$	2.86645	−	4.96483i	0.174770	−	0.302711i	0.940082	+	0.340949i	$0.110748\pi$
$270$	−7.89199	−	13.6693i	−0.480291	−	0.831889i
$271$	6.00000	−	10.3923i	0.364474	−	0.631288i	−0.624218	−	0.781251i	$-0.714582\pi$
$271$	6.00000	−	10.3923i	0.364474	−	0.631288i	0.988692	+	0.149963i	$0.0479155\pi$
$272$	−1.86645	−	3.23278i	−0.113170	−	0.196016i
$273$	−82.7464			−5.00804
$274$	−14.1051			−0.852120
$275$	0.500000	+	0.866025i	0.0301511	+	0.0522233i
$276$	−2.78690	−	4.82705i	−0.167752	−	0.290554i
$277$	13.5709			0.815395			0.407698	−	0.913117i	$-0.366332\pi$
$277$	13.5709			0.815395			0.407698	+	0.913117i	$0.366332\pi$
$278$	13.6760			0.820230
$279$	−9.12342	−	15.8022i	−0.546205	−	0.946055i
$280$	4.94600	−	8.56671i	0.295580	−	0.511959i
$281$	−0.599339	−	1.03809i	−0.0357536	−	0.0619270i	0.847595	−	0.530644i	$-0.178050\pi$
$281$	−0.599339	−	1.03809i	−0.0357536	−	0.0619270i	−0.883348	+	0.468717i	$0.844716\pi$
$282$	10.9175	−	18.9097i	0.650130	−	1.12606i
$283$	2.41178	−	4.17733i	0.143365	−	0.248316i	−0.785396	−	0.618993i	$-0.787541\pi$
$283$	2.41178	−	4.17733i	0.143365	−	0.248316i	0.928762	+	0.370677i	$0.120874\pi$
$284$	4.62488			0.274436
$285$	−25.4089	−	3.73967i	−1.50509	−	0.221519i
$286$	−5.67889			−0.335800
$287$	−23.8023	+	41.2268i	−1.40501	+	2.43354i
$288$	2.83944	−	4.91806i	0.167316	−	0.289800i
$289$	1.53276	+	2.65481i	0.0901622	+	0.156165i
$290$	−1.00000	+	1.73205i	−0.0587220	+	0.101710i
$291$	−2.25989	−	3.91425i	−0.132477	−	0.229458i
$292$	−3.62488			−0.212130
$293$	1.21602			0.0710406			0.0355203	−	0.999369i	$-0.488691\pi$
$293$	1.21602			0.0710406			0.0355203	+	0.999369i	$0.488691\pi$
$294$	−25.7228	−	44.5531i	−1.50018	−	2.59839i
$295$		0			0
$296$	4.15910			0.241743
$297$	−7.89199			−0.457940
$298$	9.49854	+	16.4520i	0.550236	+	0.953036i
$299$	5.37220	−	9.30492i	0.310682	−	0.538118i
$300$	−1.47300	−	2.55131i	−0.0850436	−	0.147300i
$301$	11.4373	−	19.8100i	0.659236	−	1.14183i
$302$	−11.8308	+	20.4915i	−0.680784	+	1.17915i
$303$	4.94600			0.284140
$304$	−1.60655	−	4.05204i	−0.0921420	−	0.232400i
$305$	−11.1418			−0.637975
$306$	10.5993	−	18.3586i	0.605924	−	1.04949i
$307$	−16.0241	+	27.7545i	−0.914543	+	1.58403i	−0.106974	+	0.994262i	$0.534116\pi$
$307$	−16.0241	+	27.7545i	−0.914543	+	1.58403i	−0.807569	+	0.589773i	$0.799217\pi$
$308$	−2.47300	−	4.28336i	−0.140912	−	0.244067i
$309$	−10.9175	+	18.9097i	−0.621077	+	1.07574i
$310$	3.21310	+	5.56526i	0.182492	+	0.316085i
$311$	−18.3722			−1.04179			−0.520896	−	0.853620i	$-0.674402\pi$
$311$	−18.3722			−1.04179			−0.520896	+	0.853620i	$0.674402\pi$
$312$	16.7300			0.947148
$313$	−0.572336	−	0.991316i	−0.0323504	−	0.0560325i	0.849397	−	0.527755i	$-0.176966\pi$
$313$	−0.572336	−	0.991316i	−0.0323504	−	0.0560325i	−0.881747	+	0.471722i	$0.843633\pi$
$314$	−5.89199	−	10.2052i	−0.332504	−	0.575914i
$315$	56.1755			3.16513
$316$	−6.83799			−0.384667
$317$	−12.2242	−	21.1730i	−0.686581	−	1.18919i	−0.972937	−	0.231070i	$-0.925778\pi$
$317$	−12.2242	−	21.1730i	−0.686581	−	1.18919i	0.286357	−	0.958123i	$-0.407556\pi$
$318$	−17.3578	+	30.0645i	−0.973376	+	1.68594i
$319$	0.500000	+	0.866025i	0.0279946	+	0.0484881i
$320$	−1.00000	+	1.73205i	−0.0559017	+	0.0968246i
$321$	24.1162	−	41.7705i	1.34604	−	2.33140i
$322$	9.35778			0.521488
$323$	−5.99708	−	15.1258i	−0.333687	−	0.841623i
$324$	6.21310			0.345172
$325$	2.83944	−	4.91806i	0.157504	−	0.272805i
$326$	−5.41178	+	9.37348i	−0.299731	+	0.519149i
$327$	25.7228	+	44.5531i	1.42247	+	2.46379i
$328$	4.81244	−	8.33539i	0.265723	−	0.460245i
$329$	18.3293	+	31.7473i	1.01053	+	1.75029i
$330$	5.89199			0.324343
$331$	−6.30377			−0.346487			−0.173243	−	0.984879i	$-0.555425\pi$
$331$	−6.30377			−0.346487			−0.173243	+	0.984879i	$0.555425\pi$
$332$	−7.25844	−	12.5720i	−0.398358	−	0.689977i
$333$	11.8095	+	20.4547i	0.647158	+	1.12091i
$334$	−4.01443			−0.219660
$335$	17.6760			0.965741
$336$	7.28544	+	12.6188i	0.397453	+	0.688409i
$337$	5.14467	−	8.91083i	0.280248	−	0.485404i	−0.691198	−	0.722666i	$-0.742917\pi$
$337$	5.14467	−	8.91083i	0.280248	−	0.485404i	0.971446	+	0.237262i	$0.0762499\pi$
$338$	9.62488	+	16.6708i	0.523525	+	0.906771i
$339$	−5.20589	+	9.01687i	−0.282745	+	0.489729i
$340$	−3.73289	+	6.46556i	−0.202445	+	0.350644i
$341$	3.21310			0.173999
$342$	15.3664	−	19.4066i	0.830922	−	1.04939i
$343$	51.7493			2.79420
$344$	−2.31244	+	4.00527i	−0.124678	+	0.215949i
$345$	−5.57379	+	9.65410i	−0.300083	+	0.519759i
$346$	−3.60655	−	6.24673i	−0.193889	−	0.335826i
$347$	9.59788	−	16.6240i	0.515241	−	0.892424i	−0.484602	−	0.874735i	$-0.661036\pi$
$347$	9.59788	−	16.6240i	0.515241	−	0.892424i	0.999844	−	0.0176894i	$-0.00563100\pi$
$348$	−1.47300	−	2.55131i	−0.0789610	−	0.136764i
$349$	32.9653			1.76459			0.882296	−	0.470694i	$-0.155996\pi$
$349$	32.9653			1.76459			0.882296	+	0.470694i	$0.155996\pi$
$350$	4.94600			0.264375
$351$	22.4089	+	38.8133i	1.19610	+	2.07170i
$352$	0.500000	+	0.866025i	0.0266501	+	0.0461593i
$353$	33.2835			1.77150			0.885751	−	0.464160i	$-0.153644\pi$
$353$	33.2835			1.77150			0.885751	+	0.464160i	$0.153644\pi$
$354$		0			0
$355$	−4.62488	−	8.01053i	−0.245463	−	0.425155i
$356$	0.232893	−	0.403382i	0.0123433	−	0.0213792i
$357$	27.1958	+	47.1044i	1.43935	+	2.49303i
$358$	2.05400	−	3.55764i	0.108558	−	0.188027i
$359$	−2.84090	+	4.92059i	−0.149937	+	0.259699i	−0.931204	−	0.364498i	$-0.881240\pi$
$359$	−2.84090	+	4.92059i	−0.149937	+	0.259699i	0.781267	+	0.624197i	$0.214574\pi$
$360$	−11.3578			−0.598607
$361$	−4.35632	−	18.4939i	−0.229280	−	0.973361i
$362$	−15.4089			−0.809872
$363$	1.47300	−	2.55131i	0.0773123	−	0.133909i
$364$	−14.0439	+	24.3247i	−0.736099	+	1.27496i
$365$	3.62488	+	6.27848i	0.189735	+	0.328631i
$366$	8.20589	−	14.2130i	0.428929	−	0.742926i
$367$	−8.84666	−	15.3229i	−0.461792	−	0.799847i	0.537259	−	0.843418i	$-0.319460\pi$
$367$	−8.84666	−	15.3229i	−0.461792	−	0.799847i	−0.999050	+	0.0435709i	$0.986127\pi$
$368$	−1.89199			−0.0986268
$369$	54.6586			2.84541
$370$	−4.15910	−	7.20377i	−0.216221	−	0.374506i
$371$	−29.1418	−	50.4750i	−1.51296	−	2.62053i
$372$	−9.46579			−0.490778
$373$	−37.1051			−1.92123			−0.960614	−	0.277885i	$-0.910367\pi$
$373$	−37.1051			−1.92123			−0.960614	+	0.277885i	$0.910367\pi$
$374$	1.86645	+	3.23278i	0.0965116	+	0.167163i
$375$	−17.6760	+	30.6157i	−0.912783	+	1.58099i
$376$	−3.70589	−	6.41879i	−0.191117	−	0.331024i
$377$	2.83944	−	4.91806i	0.146239	−	0.253293i
$378$	−19.5169	+	33.8042i	−1.00384	+	1.73870i
$379$	13.5535			0.696198			0.348099	−	0.937458i	$-0.386827\pi$
$379$	13.5535			0.696198			0.348099	+	0.937458i	$0.386827\pi$
$380$	−5.41178	+	6.83466i	−0.277618	+	0.350611i
$381$	15.7840			0.808638
$382$	5.29411	−	9.16967i	0.270870	−	0.469161i
$383$	−4.83799	+	8.37964i	−0.247210	+	0.428179i	−0.962751	−	0.270391i	$-0.912847\pi$
$383$	−4.83799	+	8.37964i	−0.247210	+	0.428179i	0.715541	+	0.698571i	$0.246180\pi$
$384$	−1.47300	−	2.55131i	−0.0751686	−	0.130196i
$385$	−4.94600	+	8.56671i	−0.252071	+	0.436600i
$386$	−2.75844	−	4.77775i	−0.140401	−	0.243181i
$387$	−26.2642			−1.33508
$388$	−1.53421			−0.0778880
$389$	−6.40066	−	11.0863i	−0.324526	−	0.562096i	0.656890	−	0.753986i	$-0.271872\pi$
$389$	−6.40066	−	11.0863i	−0.324526	−	0.562096i	−0.981416	+	0.191890i	$0.938538\pi$
$390$	−16.7300	−	28.9772i	−0.847155	−	1.46732i
$391$	−7.06260			−0.357171
$392$	−17.4629			−0.882008
$393$	15.2782	+	26.4627i	0.770685	+	1.33486i
$394$	−4.76711	+	8.25687i	−0.240163	+	0.415975i
$395$	6.83799	+	11.8437i	0.344056	+	0.595923i
$396$	−2.83944	+	4.91806i	−0.142687	+	0.247142i
$397$	9.07955	−	15.7262i	0.455689	−	0.789277i	−0.543038	−	0.839708i	$-0.682726\pi$
$397$	9.07955	−	15.7262i	0.455689	−	0.789277i	0.998728	+	0.0504307i	$0.0160594\pi$
$398$	−20.6249			−1.03383
$399$	23.4089	+	59.0417i	1.17191	+	2.95578i
$400$	−1.00000			−0.0500000
$401$	3.91032	−	6.77288i	0.195272	−	0.338221i	−0.751718	−	0.659485i	$-0.770774\pi$
$401$	3.91032	−	6.77288i	0.195272	−	0.338221i	0.946990	+	0.321264i	$0.104108\pi$
$402$	−13.0183	+	22.5484i	−0.649295	+	1.12461i
$403$	−9.12342	−	15.8022i	−0.454470	−	0.787165i
$404$	0.839444	−	1.45396i	0.0417639	−	0.0723372i
$405$	−6.21310	−	10.7614i	−0.308732	−	0.534739i
$406$	4.94600			0.245466
$407$	−4.15910			−0.206159
$408$	−5.49854	−	9.52375i	−0.272218	−	0.471496i
$409$	10.5058	+	18.1965i	0.519476	+	0.899759i	0.999744	+	0.0226370i	$0.00720621\pi$
$409$	10.5058	+	18.1965i	0.519476	+	0.899759i	−0.480268	+	0.877122i	$0.659460\pi$
$410$	−19.2498			−0.950678
$411$	−41.5535			−2.04968
$412$	3.70589	+	6.41879i	0.182576	+	0.316231i
$413$		0			0
$414$	−5.37220	−	9.30492i	−0.264029	−	0.457312i
$415$	−14.5169	+	25.1440i	−0.712605	+	1.23427i
$416$	2.83944	−	4.91806i	0.139215	−	0.241128i
$417$	40.2893			1.97298
$418$	1.60655	+	4.05204i	0.0785790	+	0.198192i
$419$	−11.0540			−0.540023			−0.270012	−	0.962857i	$-0.587028\pi$
$419$	−11.0540			−0.540023			−0.270012	+	0.962857i	$0.587028\pi$
$420$	14.5709	−	25.2375i	0.710986	−	1.23146i
$421$	−2.24156	+	3.88250i	−0.109247	+	0.189222i	−0.915465	−	0.402397i	$-0.868177\pi$
$421$	−2.24156	+	3.88250i	−0.109247	+	0.189222i	0.806218	+	0.591618i	$0.201511\pi$
$422$	−12.8380	−	22.2360i	−0.624943	−	1.08243i
$423$	21.0453	−	36.4516i	1.02326	−	1.77234i
$424$	5.89199	+	10.2052i	0.286140	+	0.495610i
$425$	−3.73289			−0.181072
$426$	13.6249			0.660128
$427$	13.7768	+	23.8621i	0.666705	+	1.15477i
$428$	−8.18610	−	14.1787i	−0.395690	−	0.685355i
$429$	−16.7300			−0.807731
$430$	9.24977			0.446063
$431$	−1.09788	−	1.90158i	−0.0528830	−	0.0915961i	0.838372	−	0.545098i	$-0.183508\pi$
$431$	−1.09788	−	1.90158i	−0.0528830	−	0.0915961i	−0.891255	+	0.453502i	$0.850174\pi$
$432$	3.94600	−	6.83466i	0.189852	−	0.328833i
$433$	15.9301	+	27.5918i	0.765552	+	1.32598i	0.939954	+	0.341301i	$0.110868\pi$
$433$	15.9301	+	27.5918i	0.765552	+	1.32598i	−0.174402	+	0.984675i	$0.555799\pi$
$434$	7.94600	−	13.7629i	0.381420	−	0.660639i
$435$	−2.94600	+	5.10261i	−0.141250	+	0.244652i
$436$	17.4629			0.836320
$437$	−8.15910	−	1.20085i	−0.390303	−	0.0574446i
$438$	−10.6789			−0.510257
$439$	5.32111	−	9.21644i	0.253963	−	0.439877i	−0.710650	−	0.703545i	$-0.751599\pi$
$439$	5.32111	−	9.21644i	0.253963	−	0.439877i	0.964613	+	0.263669i	$0.0849326\pi$
$440$	1.00000	−	1.73205i	0.0476731	−	0.0825723i
$441$	−49.5848	−	85.8835i	−2.36118	−	4.08969i
$442$	10.5993	−	18.3586i	0.504159	−	0.873229i
$443$	−15.7228	−	27.2326i	−0.747011	−	1.29386i	−0.949249	−	0.314525i	$-0.898155\pi$
$443$	−15.7228	−	27.2326i	−0.747011	−	1.29386i	0.202238	−	0.979336i	$-0.435178\pi$
$444$	12.2527			0.581487
$445$	−0.931570			−0.0441607
$446$	−3.68756	−	6.38704i	−0.174611	−	0.302435i
$447$	27.9827	+	48.4674i	1.32353	+	2.29243i
$448$	4.94600			0.233676
$449$	13.8553			0.653873			0.326937	−	0.945046i	$-0.393984\pi$
$449$	13.8553			0.653873			0.326937	+	0.945046i	$0.393984\pi$
$450$	−2.83944	−	4.91806i	−0.133853	−	0.231840i
$451$	−4.81244	+	8.33539i	−0.226609	+	0.392498i
$452$	1.76711	+	3.06072i	0.0831177	+	0.143964i
$453$	−34.8534	+	60.3679i	−1.63756	+	2.83633i
$454$	−14.1774	+	24.5560i	−0.665380	+	1.15247i
$455$	56.1755			2.63355
$456$	−4.73289	−	11.9373i	−0.221638	−	0.559014i
$457$	−15.7329			−0.735954			−0.367977	−	0.929835i	$-0.619949\pi$
$457$	−15.7329			−0.735954			−0.367977	+	0.929835i	$0.619949\pi$
$458$	−2.49133	+	4.31511i	−0.116412	+	0.201632i
$459$	14.7300	−	25.5131i	0.687536	−	1.19085i
$460$	1.89199	+	3.27702i	0.0882145	+	0.152792i
$461$	10.3563	−	17.9377i	0.482342	−	0.835440i	−0.517453	−	0.855712i	$-0.673120\pi$
$461$	10.3563	−	17.9377i	0.482342	−	0.835440i	0.999795	+	0.0202713i	$0.00645300\pi$
$462$	−7.28544	−	12.6188i	−0.338949	−	0.587077i
$463$	−14.3722			−0.667933			−0.333966	−	0.942585i	$-0.608387\pi$
$463$	−14.3722			−0.667933			−0.333966	+	0.942585i	$0.608387\pi$
$464$	−1.00000			−0.0464238
$465$	9.46579	+	16.3952i	0.438965	+	0.760310i
$466$	11.2242	+	19.4409i	0.519952	+	0.900583i
$467$	−10.3038			−0.476802			−0.238401	−	0.971167i	$-0.576623\pi$
$467$	−10.3038			−0.476802			−0.238401	+	0.971167i	$0.576623\pi$
$468$	32.2498			1.49075
$469$	−21.8563	−	37.8563i	−1.00923	−	1.74804i
$470$	−7.41178	+	12.8376i	−0.341880	+	0.592153i
$471$	−17.3578	−	30.0645i	−0.799804	−	1.38530i
$472$		0			0
$473$	2.31244	−	4.00527i	0.106326	−	0.184162i
$474$	−20.1447			−0.925275
$475$	−4.31244	−	0.634704i	−0.197868	−	0.0291222i
$476$	18.4629			0.846244
$477$	−33.4600	+	57.9543i	−1.53203	+	2.65355i
$478$	−11.8920	+	20.5975i	−0.543927	+	0.942109i
$479$	−3.79411	−	6.57159i	−0.173357	−	0.300264i	0.766234	−	0.642561i	$-0.222128\pi$
$479$	−3.79411	−	6.57159i	−0.173357	−	0.300264i	−0.939592	+	0.342298i	$0.888795\pi$
$480$	−2.94600	+	5.10261i	−0.134466	+	0.232901i
$481$	11.8095	+	20.4547i	0.538468	+	0.932654i
$482$	21.1418			0.962981
$483$	27.5680			1.25439
$484$	−0.500000	−	0.866025i	−0.0227273	−	0.0393648i
$485$	1.53421	+	2.65734i	0.0696651	+	0.120664i
$486$	−5.37220			−0.243688
$487$	−0.414697			−0.0187917			−0.00939585	−	0.999956i	$-0.502991\pi$
$487$	−0.414697			−0.0187917			−0.00939585	+	0.999956i	$0.502991\pi$
$488$	−2.78544	−	4.82452i	−0.126091	−	0.218396i
$489$	−15.9431	+	27.6142i	−0.720971	+	1.24876i
$490$	17.4629	+	30.2466i	0.788892	+	1.36640i
$491$	0.411780	−	0.713224i	0.0185834	−	0.0321874i	−0.856584	−	0.516007i	$-0.827418\pi$
$491$	0.411780	−	0.713224i	0.0185834	−	0.0321874i	0.875168	+	0.483820i	$0.160751\pi$
$492$	14.1774	−	24.5560i	0.639168	−	1.10707i
$493$	−3.73289			−0.168121
$494$	15.3664	−	19.4066i	0.691369	−	0.873146i
$495$	11.3578			0.510494
$496$	−1.60655	+	2.78263i	−0.0721363	+	0.124944i
$497$	−11.4373	+	19.8100i	−0.513034	+	0.888601i
$498$	−21.3833	−	37.0370i	−0.958209	−	1.65967i
$499$	−2.67889	+	4.63997i	−0.119923	+	0.207714i	−0.919737	−	0.392535i	$-0.871598\pi$
$499$	−2.67889	+	4.63997i	−0.119923	+	0.207714i	0.799814	+	0.600248i	$0.204932\pi$
$500$	6.00000	+	10.3923i	0.268328	+	0.464758i
$501$	−11.8265			−0.528368
$502$	−0.519790			−0.0231994
$503$	−2.78690	−	4.82705i	−0.124262	−	0.215227i	0.797182	−	0.603738i	$-0.206323\pi$
$503$	−2.78690	−	4.82705i	−0.124262	−	0.215227i	−0.921444	+	0.388511i	$0.872990\pi$
$504$	14.0439	+	24.3247i	0.625564	+	1.08351i
$505$	−3.35778			−0.149419
$506$	1.89199			0.0841092
$507$	28.3549	+	49.1121i	1.25928	+	2.18114i
$508$	2.67889	−	4.63997i	0.118856	−	0.205865i
$509$	9.21310	+	15.9576i	0.408364	+	0.707306i	0.994707	−	0.102756i	$-0.0327662\pi$
$509$	9.21310	+	15.9576i	0.408364	+	0.707306i	−0.586343	+	0.810063i	$0.699433\pi$
$510$	−10.9971	+	19.0475i	−0.486959	+	0.843438i
$511$	8.96433	−	15.5267i	0.396558	−	0.686859i
$512$	−1.00000			−0.0441942
$513$	21.3549	−	26.9696i	0.942840	−	1.19073i
$514$	10.8236			0.477407
$515$	7.41178	−	12.8376i	0.326602	−	0.565691i
$516$	−6.81244	+	11.7995i	−0.299901	+	0.519444i
$517$	3.70589	+	6.41879i	0.162985	+	0.282298i
$518$	−10.2854	+	17.8149i	−0.451916	+	0.782742i
$519$	−10.6249	−	18.4028i	−0.466381	−	0.807795i
$520$	−11.3578			−0.498071
$521$	−9.24685			−0.405112			−0.202556	−	0.979271i	$-0.564925\pi$
$521$	−9.24685			−0.405112			−0.202556	+	0.979271i	$0.564925\pi$
$522$	−2.83944	−	4.91806i	−0.124279	−	0.215258i
$523$	9.70589	+	16.8111i	0.424409	+	0.735098i	0.996365	−	0.0851864i	$-0.0271486\pi$
$523$	9.70589	+	16.8111i	0.424409	+	0.735098i	−0.571956	+	0.820284i	$0.693815\pi$
$524$	10.3722			0.453112
$525$	14.5709			0.635925
$526$	−6.51687	−	11.2876i	−0.284149	−	0.492161i
$527$	−5.99708	+	10.3873i	−0.261237	+	0.452476i
$528$	1.47300	+	2.55131i	0.0641040	+	0.111031i
$529$	9.71019	−	16.8185i	0.422182	−	0.731241i
$530$	11.7840	−	20.4105i	0.511863	−	0.886573i
$531$		0			0
$532$	21.3293	+	3.13924i	0.924743	+	0.136103i
$533$	54.6586			2.36753
$534$	0.686100	−	1.18836i	0.0296905	−	0.0514254i
$535$	−16.3722	+	28.3575i	−0.707832	+	1.22600i
$536$	4.41899	+	7.65392i	0.190871	+	0.330599i
$537$	6.05109	−	10.4808i	0.261124	−	0.452280i
$538$	−2.86645	−	4.96483i	−0.123581	−	0.214049i
$539$	17.4629			0.752179
$540$	−15.7840			−0.679234
$541$	−9.80231	−	16.9781i	−0.421434	−	0.729946i	0.574646	−	0.818402i	$-0.305140\pi$
$541$	−9.80231	−	16.9781i	−0.421434	−	0.729946i	−0.996080	+	0.0884566i	$0.971807\pi$
$542$	−6.00000	−	10.3923i	−0.257722	−	0.446388i
$543$	−45.3944			−1.94806
$544$	−3.73289			−0.160046
$545$	−17.4629	−	30.2466i	−0.748027	−	1.29562i
$546$	−41.3732	+	71.6605i	−1.77061	+	3.06678i
$547$	2.31244	+	4.00527i	0.0988729	+	0.171253i	0.911218	−	0.411924i	$-0.135143\pi$
$547$	2.31244	+	4.00527i	0.0988729	+	0.171253i	−0.812346	+	0.583176i	$0.801810\pi$
$548$	−7.05255	+	12.2154i	−0.301270	+	0.521815i
$549$	15.8182	−	27.3979i	0.675104	−	1.16931i
$550$	1.00000			0.0426401
$551$	−4.31244	−	0.634704i	−0.183716	−	0.0270393i
$552$	−5.57379			−0.237236
$553$	16.9103	−	29.2895i	0.719100	−	1.24552i
$554$	6.78544	−	11.7527i	0.288286	−	0.499325i
$555$	−12.2527	−	21.2223i	−0.520097	−	0.900835i
$556$	6.83799	−	11.8437i	0.289995	−	0.502286i
$557$	−11.1606	−	19.3307i	−0.472888	−	0.819066i	0.526631	−	0.850094i	$-0.323455\pi$
$557$	−11.1606	−	19.3307i	−0.472888	−	0.819066i	−0.999519	+	0.0310283i	$0.990122\pi$
$558$	−18.2468			−0.772451
$559$	−26.2642			−1.11086
$560$	−4.94600	−	8.56671i	−0.209006	−	0.362010i
$561$	5.49854	+	9.52375i	0.232149	+	0.402093i
$562$	−1.19868			−0.0505632
$563$	29.6760			1.25069			0.625347	−	0.780347i	$-0.284958\pi$
$563$	29.6760			1.25069			0.625347	+	0.780347i	$0.284958\pi$
$564$	−10.9175	−	18.9097i	−0.459711	−	0.796243i
$565$	3.53421	−	6.12144i	0.148686	−	0.257531i
$566$	−2.41178	−	4.17733i	−0.101375	−	0.175586i
$567$	−15.3650	+	26.6129i	−0.645269	+	1.11764i
$568$	2.31244	−	4.00527i	0.0970279	−	0.168057i
$569$	−34.0733			−1.42843			−0.714214	−	0.699927i	$-0.753216\pi$
$569$	−34.0733			−1.42843			−0.714214	+	0.699927i	$0.753216\pi$
$570$	−15.9431	+	20.1349i	−0.667782	+	0.843358i
$571$	16.3722			0.685155			0.342578	−	0.939490i	$-0.388700\pi$
$571$	16.3722			0.685155			0.342578	+	0.939490i	$0.388700\pi$
$572$	−2.83944	+	4.91806i	−0.118723	+	0.205634i
$573$	15.5964	−	27.0138i	0.651550	−	1.12852i
$574$	23.8023	+	41.2268i	0.993489	+	1.72077i
$575$	−0.945995	+	1.63851i	−0.0394507	+	0.0683307i
$576$	−2.83944	−	4.91806i	−0.118310	−	0.204919i
$577$	23.2864			0.969427			0.484713	−	0.874673i	$-0.338924\pi$
$577$	23.2864			0.969427			0.484713	+	0.874673i	$0.338924\pi$
$578$	3.06551			0.127509
$579$	−8.12634	−	14.0752i	−0.337719	−	0.584947i
$580$	1.00000	+	1.73205i	0.0415227	+	0.0719195i
$581$	71.8004			2.97878
$582$	−4.51979			−0.187351
$583$	−5.89199	−	10.2052i	−0.244021	−	0.422657i
$584$	−1.81244	+	3.13924i	−0.0749994	+	0.129903i
$585$	−32.2498	−	55.8582i	−1.33336	−	2.30945i
$586$	0.608010	−	1.05310i	0.0251166	−	0.0435033i
$587$	−9.52700	+	16.5013i	−0.393221	+	0.681080i	−0.992872	−	0.119182i	$-0.961973\pi$
$587$	−9.52700	+	16.5013i	−0.393221	+	0.681080i	0.599651	+	0.800262i	$0.295306\pi$
$588$	−51.4455			−2.12158
$589$	−8.69430	+	10.9802i	−0.358243	+	0.452433i
$590$		0			0
$591$	−14.0439	+	24.3247i	−0.577688	+	1.00058i
$592$	2.07955	−	3.60188i	0.0854689	−	0.148037i
$593$	−0.786897	−	1.36295i	−0.0323140	−	0.0559695i	0.849416	−	0.527724i	$-0.176954\pi$
$593$	−0.786897	−	1.36295i	−0.0323140	−	0.0559695i	−0.881730	+	0.471754i	$0.843621\pi$
$594$	−3.94600	+	6.83466i	−0.161906	+	0.280430i
$595$	−18.4629	−	31.9786i	−0.756904	−	1.31100i
$596$	18.9971			0.778151
$597$	−60.7608			−2.48677
$598$	−5.37220	−	9.30492i	−0.219686	−	0.380507i
$599$	11.3664	+	19.6873i	0.464420	+	0.804400i	0.999175	−	0.0406076i	$-0.0129293\pi$
$599$	11.3664	+	19.6873i	0.464420	+	0.804400i	−0.534755	+	0.845007i	$0.679596\pi$
$600$	−2.94600			−0.120270
$601$	10.8524			0.442679			0.221340	−	0.975197i	$-0.428957\pi$
$601$	10.8524			0.442679			0.221340	+	0.975197i	$0.428957\pi$
$602$	−11.4373	−	19.8100i	−0.466151	−	0.807396i
$603$	−25.0950	+	43.4658i	−1.02195	+	1.77006i
$604$	11.8308	+	20.4915i	0.481387	+	0.833787i
$605$	−1.00000	+	1.73205i	−0.0406558	+	0.0704179i
$606$	2.47300	−	4.28336i	0.100459	−	0.174000i
$607$	−12.3038			−0.499395			−0.249697	−	0.968324i	$-0.580331\pi$
$607$	−12.3038			−0.499395			−0.249697	+	0.968324i	$0.580331\pi$
$608$	−4.31244	−	0.634704i	−0.174893	−	0.0257406i
$609$	14.5709			0.590442
$610$	−5.57088	+	9.64904i	−0.225558	+	0.390678i
$611$	21.0453	−	36.4516i	0.851403	−	1.47467i
$612$	−10.5993	−	18.3586i	−0.428453	−	0.742102i
$613$	−22.5154	+	38.9978i	−0.909389	+	1.57511i	−0.0944742	+	0.995527i	$0.530117\pi$
$613$	−22.5154	+	38.9978i	−0.909389	+	1.57511i	−0.814915	+	0.579581i	$0.803216\pi$
$614$	16.0241	+	27.7545i	0.646679	+	1.12008i
$615$	−56.7097			−2.28676
$616$	−4.94600			−0.199280
$617$	−10.7314	−	18.5874i	−0.432031	−	0.748300i	0.565017	−	0.825079i	$-0.308870\pi$
$617$	−10.7314	−	18.5874i	−0.432031	−	0.748300i	−0.997048	+	0.0767793i	$0.975536\pi$
$618$	10.9175	+	18.9097i	0.439168	+	0.760661i
$619$	6.96625			0.279997			0.139999	−	0.990152i	$-0.455290\pi$
$619$	6.96625			0.279997			0.139999	+	0.990152i	$0.455290\pi$
$620$	6.42621			0.258083
$621$	−7.46579	−	12.9311i	−0.299592	−	0.518908i
$622$	−9.18610	+	15.9108i	−0.368329	+	0.637965i
$623$	1.15189	+	1.99512i	0.0461493	+	0.0799330i
$624$	8.36499	−	14.4886i	0.334868	−	0.580008i
$625$	9.50000	−	16.4545i	0.380000	−	0.658179i
$626$	−1.14467			−0.0457503
$627$	4.73289	+	11.9373i	0.189014	+	0.476729i
$628$	−11.7840			−0.470232
$629$	7.76273	−	13.4454i	0.309520	−	0.536105i
$630$	28.0878	−	48.6494i	1.11904	−	1.93824i
$631$	20.2044	+	34.9951i	0.804326	+	1.39313i	0.916745	+	0.399472i	$0.130807\pi$
$631$	20.2044	+	34.9951i	0.804326	+	1.39313i	−0.112420	+	0.993661i	$0.535860\pi$
$632$	−3.41899	+	5.92187i	−0.136000	+	0.235559i
$633$	−37.8206	−	65.5073i	−1.50324	−	2.60368i
$634$	−24.4484			−0.970972
$635$	−10.7156			−0.425234
$636$	17.3578	+	30.0645i	0.688281	+	1.19214i
$637$	−49.5848	−	85.8835i	−1.96462	−	3.40283i
$638$	1.00000			0.0395904
$639$	26.2642			1.03900
$640$	1.00000	+	1.73205i	0.0395285	+	0.0684653i
$641$	13.3920	−	23.1956i	0.528952	−	0.916171i	−0.470478	−	0.882412i	$-0.655919\pi$
$641$	13.3920	−	23.1956i	0.528952	−	0.916171i	0.999430	−	0.0337598i	$-0.0107481\pi$
$642$	−24.1162	−	41.7705i	−0.951791	−	1.64855i
$643$	1.63210	−	2.82687i	0.0643636	−	0.111481i	−0.832048	−	0.554704i	$-0.812832\pi$
$643$	1.63210	−	2.82687i	0.0643636	−	0.111481i	0.896411	+	0.443223i	$0.146165\pi$
$644$	4.67889	−	8.10407i	0.184374	−	0.319345i
$645$	27.2498			1.07296
$646$	−16.0979	−	2.36928i	−0.633363	−	0.0932181i
$647$	−10.3355			−0.406332			−0.203166	−	0.979144i	$-0.565123\pi$
$647$	−10.3355			−0.406332			−0.203166	+	0.979144i	$0.565123\pi$
$648$	3.10655	−	5.38070i	0.122037	−	0.211374i
$649$		0			0
$650$	−2.83944	−	4.91806i	−0.111372	−	0.192902i
$651$	23.4089	−	40.5453i	0.917466	−	1.58910i
$652$	5.41178	+	9.37348i	0.211942	+	0.367094i
$653$	16.5853			0.649033			0.324517	−	0.945880i	$-0.394798\pi$
$653$	16.5853			0.649033			0.324517	+	0.945880i	$0.394798\pi$
$654$	51.4455			2.01168
$655$	−10.3722	−	17.9652i	−0.405275	−	0.701958i
$656$	−4.81244	−	8.33539i	−0.187894	−	0.325442i
$657$	−20.5853			−0.803109
$658$	36.6586			1.42910
$659$	16.7059	+	28.9355i	0.650769	+	1.12717i	0.982937	+	0.183945i	$0.0588867\pi$
$659$	16.7059	+	28.9355i	0.650769	+	1.12717i	−0.332168	+	0.943220i	$0.607780\pi$
$660$	2.94600	−	5.10261i	0.114673	−	0.198619i
$661$	5.13355	+	8.89158i	0.199672	+	0.345842i	0.948422	−	0.317010i	$-0.102679\pi$
$661$	5.13355	+	8.89158i	0.199672	+	0.345842i	−0.748750	+	0.662852i	$0.769346\pi$
$662$	−3.15189	+	5.45923i	−0.122502	+	0.212179i
$663$	31.2256	−	54.0843i	1.21270	−	2.10046i
$664$	−14.5169			−0.563364
$665$	−15.8920	−	40.0827i	−0.616265	−	1.55434i
$666$	23.6190			0.915220
$667$	−0.945995	+	1.63851i	−0.0366291	+	0.0634434i
$668$	−2.00721	+	3.47659i	−0.0776614	+	0.134513i
$669$	−10.8635	−	18.8162i	−0.420008	−	0.727476i
$670$	8.83799	−	15.3078i	0.341441	−	0.591393i
$671$	2.78544	+	4.82452i	0.107531	+	0.186249i
$672$	14.5709			0.562084
$673$	47.6190			1.83558			0.917790	−	0.397067i	$-0.129972\pi$
$673$	47.6190			1.83558			0.917790	+	0.397067i	$0.129972\pi$
$674$	−5.14467	−	8.91083i	−0.198165	−	0.343233i
$675$	−3.94600	−	6.83466i	−0.151881	−	0.263066i
$676$	19.2498			0.740376
$677$	6.64514			0.255394			0.127697	−	0.991813i	$-0.459242\pi$
$677$	6.64514			0.255394			0.127697	+	0.991813i	$0.459242\pi$
$678$	5.20589	+	9.01687i	0.199931	+	0.346291i
$679$	3.79411	−	6.57159i	0.145605	−	0.252195i
$680$	3.73289	+	6.46556i	0.143150	+	0.247943i
$681$	−41.7666	+	72.3419i	−1.60050	+	2.77215i
$682$	1.60655	−	2.78263i	0.0615180	−	0.106552i
$683$	21.7984			0.834093			0.417046	−	0.908885i	$-0.363065\pi$
$683$	21.7984			0.834093			0.417046	+	0.908885i	$0.363065\pi$
$684$	−9.12342	−	23.0111i	−0.348843	−	0.879850i
$685$	28.2102			1.07786
$686$	25.8746	−	44.8162i	0.987899	−	1.71109i
$687$	−7.33944	+	12.7123i	−0.280017	+	0.485004i
$688$	2.31244	+	4.00527i	0.0881610	+	0.152699i
$689$	−33.4600	+	57.9543i	−1.27472	+	2.20788i
$690$	5.57379	+	9.65410i	0.212191	+	0.367525i
$691$	−13.2700			−0.504816			−0.252408	−	0.967621i	$-0.581222\pi$
$691$	−13.2700			−0.504816			−0.252408	+	0.967621i	$0.581222\pi$
$692$	−7.21310			−0.274201
$693$	−14.0439	−	24.3247i	−0.533483	−	0.924019i
$694$	−9.59788	−	16.6240i	−0.364331	−	0.631039i
$695$	−27.3519			−1.03752
$696$	−2.94600			−0.111668
$697$	−17.9643	−	31.1151i	−0.680447	−	1.17857i
$698$	16.4827	−	28.5488i	0.623878	−	1.08059i
$699$	33.0665	+	57.2729i	1.25069	+	2.16626i
$700$	2.47300	−	4.28336i	0.0934705	−	0.161896i
$701$	−6.34090	+	10.9828i	−0.239493	+	0.414813i	−0.960569	−	0.278042i	$-0.910314\pi$
$701$	−6.34090	+	10.9828i	−0.239493	+	0.414813i	0.721076	+	0.692856i	$0.243648\pi$
$702$	44.8177			1.69154
$703$	11.2541	−	14.2130i	0.424455	−	0.536054i
$704$	1.00000			0.0376889
$705$	−21.8351	+	37.8194i	−0.822356	+	1.42436i
$706$	16.6418	−	28.8244i	0.626321	−	1.08482i
$707$	4.15189	+	7.19128i	0.156148	+	0.270456i
$708$		0			0
$709$	−18.7840	−	32.5348i	−0.705447	−	1.22187i	−0.966530	−	0.256554i	$-0.917413\pi$
$709$	−18.7840	−	32.5348i	−0.705447	−	1.22187i	0.261083	−	0.965316i	$-0.415920\pi$
$710$	−9.24977			−0.347138
$711$	−38.8322			−1.45632
$712$	−0.232893	−	0.403382i	−0.00872802	−	0.0151174i
$713$	3.03958	+	5.26471i	0.113833	+	0.197165i
$714$	54.3915			2.03555
$715$	11.3578			0.424757
$716$	−2.05400	−	3.55764i	−0.0767618	−	0.132955i
$717$	−35.0337	+	60.6802i	−1.30836	+	2.26614i
$718$	2.84090	+	4.92059i	0.106022	+	0.183635i
$719$	1.47154	−	2.54878i	0.0548792	−	0.0950535i	−0.837281	−	0.546773i	$-0.815856\pi$
$719$	1.47154	−	2.54878i	0.0548792	−	0.0950535i	0.892160	+	0.451720i	$0.149189\pi$
$720$	−5.67889	+	9.83612i	−0.211640	+	0.366571i
$721$	−36.6586			−1.36524
$722$	−18.1943	−	5.47424i	−0.677122	−	0.203730i
$723$	62.2835			2.31635
$724$	−7.70443	+	13.3445i	−0.286333	+	0.495943i
$725$	−0.500000	+	0.866025i	−0.0185695	+	0.0321634i
$726$	−1.47300	−	2.55131i	−0.0546681	−	0.0946879i
$727$	−13.7753	+	23.8595i	−0.510898	+	0.884901i	0.489022	+	0.872271i	$0.337354\pi$
$727$	−13.7753	+	23.8595i	−0.510898	+	0.884901i	−0.999920	+	0.0126299i	$0.995980\pi$
$728$	14.0439	+	24.3247i	0.520501	+	0.901534i
$729$	−34.4658			−1.27651
$730$	7.24977			0.268326
$731$	8.63210	+	14.9512i	0.319270	+	0.552991i
$732$	−8.20589	−	14.2130i	−0.303298	−	0.525328i
$733$	37.6393			1.39024			0.695120	−	0.718894i	$-0.255351\pi$
$733$	37.6393			1.39024			0.695120	+	0.718894i	$0.255351\pi$
$734$	−17.6933			−0.653072
$735$	51.4455	+	89.1063i	1.89760	+	3.28673i
$736$	−0.945995	+	1.63851i	−0.0348698	+	0.0603963i
$737$	−4.41899	−	7.65392i	−0.162776	−	0.281936i
$738$	27.3293	−	47.3358i	1.00601	−	1.74245i
$739$	−2.59788	+	4.49966i	−0.0955646	+	0.165523i	−0.909844	−	0.414950i	$-0.863799\pi$
$739$	−2.59788	+	4.49966i	−0.0955646	+	0.165523i	0.814280	+	0.580473i	$0.197132\pi$
$740$	−8.31820			−0.305783
$741$	45.2695	−	57.1719i	1.66302	−	2.10026i
$742$	−58.2835			−2.13966
$743$	0.989871	−	1.71451i	0.0363148	−	0.0628992i	−0.847297	−	0.531120i	$-0.821771\pi$
$743$	0.989871	−	1.71451i	0.0363148	−	0.0628992i	0.883612	+	0.468221i	$0.155105\pi$
$744$	−4.73289	+	8.19761i	−0.173516	+	0.300539i
$745$	−18.9971	−	32.9039i	−0.695999	−	1.20551i
$746$	−18.5525	+	32.1340i	−0.679257	+	1.17651i
$747$	−41.2198	−	71.3949i	−1.50816	−	2.61220i
$748$	3.73289			0.136488
$749$	80.9768			2.95883
$750$	17.6760	+	30.6157i	0.645435	+	1.11793i
$751$	1.67022	+	2.89290i	0.0609471	+	0.105563i	0.894889	−	0.446289i	$-0.147255\pi$
$751$	1.67022	+	2.89290i	0.0609471	+	0.105563i	−0.833942	+	0.551852i	$0.813921\pi$
$752$	−7.41178			−0.270280
$753$	−1.53130			−0.0558036
$754$	−2.83944	−	4.91806i	−0.103406	−	0.179105i
$755$	23.6615	−	40.9830i	0.861132	−	1.49152i
$756$	19.5169	+	33.8042i	0.709822	+	1.22945i
$757$	21.3549	−	36.9877i	0.776156	−	1.34434i	−0.157987	−	0.987441i	$-0.550500\pi$
$757$	21.3549	−	36.9877i	0.776156	−	1.34434i	0.934143	−	0.356900i	$-0.116166\pi$
$758$	6.77677	−	11.7377i	0.246143	−	0.426333i
$759$	5.57379			0.202316
$760$	3.21310	+	8.10407i	0.116551	+	0.293966i
$761$	−10.5054			−0.380819			−0.190410	−	0.981705i	$-0.560982\pi$
$761$	−10.5054			−0.380819			−0.190410	+	0.981705i	$0.560982\pi$
$762$	7.89199	−	13.6693i	0.285897	−	0.495188i
$763$	−43.1856	+	74.7997i	−1.56342	+	2.70793i
$764$	−5.29411	−	9.16967i	−0.191534	−	0.331747i
$765$	−21.1987	+	36.7172i	−0.766440	+	1.32751i
$766$	4.83799	+	8.37964i	0.174804	+	0.302769i
$767$		0			0
$768$	−2.94600			−0.106304
$769$	1.53713	+	2.66239i	0.0554304	+	0.0960082i	0.892409	−	0.451227i	$-0.149014\pi$
$769$	1.53713	+	2.66239i	0.0554304	+	0.0960082i	−0.836979	+	0.547235i	$0.815680\pi$
$770$	4.94600	+	8.56671i	0.178241	+	0.308723i
$771$	31.8862			1.14835
$772$	−5.51687			−0.198557
$773$	−2.72177	−	4.71425i	−0.0978954	−	0.169560i	0.812918	−	0.582378i	$-0.197878\pi$
$773$	−2.72177	−	4.71425i	−0.0978954	−	0.169560i	−0.910813	+	0.412818i	$0.864544\pi$
$774$	−13.1321	+	22.7455i	−0.472023	+	0.817569i
$775$	1.60655	+	2.78263i	0.0577090	+	0.0999550i
$776$	−0.767107	+	1.32867i	−0.0275376	+	0.0476964i
$777$	−30.3009	+	52.4826i	−1.08704	+	1.88280i
$778$	−12.8013			−0.458950
$779$	−15.4629	−	39.0004i	−0.554015	−	1.39733i
$780$	−33.4600			−1.19806
$781$	−2.31244	+	4.00527i	−0.0827457	+	0.143320i
$782$	−3.53130	+	6.11639i	−0.126279	+	0.218722i
$783$	−3.94600	−	6.83466i	−0.141018	−	0.244251i
$784$	−8.73143	+	15.1233i	−0.311837	+	0.540117i
$785$	11.7840	+	20.4105i	0.420588	+	0.728480i
$786$	30.5565			1.08991
$787$	−4.22753			−0.150695			−0.0753475	−	0.997157i	$-0.524007\pi$
$787$	−4.22753			−0.150695			−0.0753475	+	0.997157i	$0.524007\pi$
$788$	4.76711	+	8.25687i	0.169821	+	0.294139i
$789$	−19.1987	−	33.2531i	−0.683491	−	1.18384i
$790$	13.6760			0.486569
$791$	−17.4802			−0.621525
$792$	2.83944	+	4.91806i	0.100895	+	0.174756i
$793$	15.8182	−	27.3979i	0.561721	−	0.972929i
$794$	−9.07955	−	15.7262i	−0.322221	−	0.558103i
$795$	34.7156	−	60.1291i	1.23123	−	2.13256i
$796$	−10.3124	+	17.8617i	−0.365515	+	0.633090i
$797$	−1.44355			−0.0511331			−0.0255665	−	0.999673i	$-0.508139\pi$
$797$	−1.44355			−0.0511331			−0.0255665	+	0.999673i	$0.508139\pi$
$798$	62.8361	+	9.24819i	2.22437	+	0.327382i
$799$	−27.6674			−0.978802
$800$	−0.500000	+	0.866025i	−0.0176777	+	0.0306186i
$801$	1.32257	−	2.29076i	0.0467307	−	0.0809400i
$802$	−3.91032	−	6.77288i	−0.138078	−	0.239159i
$803$	1.81244	−	3.13924i	0.0639597	−	0.110781i
$804$	13.0183	+	22.5484i	0.459121	+	0.795221i
$805$	−18.7156			−0.659636
$806$	−18.2468			−0.642718
$807$	−8.44454	−	14.6264i	−0.297262	−	0.514873i
$808$	−0.839444	−	1.45396i	−0.0295315	−	0.0511501i
$809$	−28.7378			−1.01037			−0.505183	−	0.863012i	$-0.668575\pi$
$809$	−28.7378			−1.01037			−0.505183	+	0.863012i	$0.668575\pi$
$810$	−12.4262			−0.436612
$811$	12.7242	+	22.0390i	0.446808	+	0.773894i	0.998176	−	0.0603680i	$-0.0192274\pi$
$811$	12.7242	+	22.0390i	0.446808	+	0.773894i	−0.551368	+	0.834262i	$0.685894\pi$
$812$	2.47300	−	4.28336i	0.0867852	−	0.150316i
$813$	−17.6760	−	30.6157i	−0.619923	−	1.07374i
$814$	−2.07955	+	3.60188i	−0.0728882	+	0.126246i
$815$	10.8236	−	18.7470i	0.379133	−	0.656677i
$816$	−10.9971			−0.384975
$817$	7.43011	+	18.7402i	0.259947	+	0.655636i
$818$	21.0115			0.734650
$819$	−79.7536	+	138.137i	−2.78682	+	4.82691i
$820$	−9.62488	+	16.6708i	−0.336115	+	0.582169i
$821$	13.7512	+	23.8178i	0.479921	+	0.831248i	0.999735	−	0.0230320i	$-0.00733197\pi$
$821$	13.7512	+	23.8178i	0.479921	+	0.831248i	−0.519814	+	0.854280i	$0.673999\pi$
$822$	−20.7768	+	35.9864i	−0.724673	+	1.25517i
$823$	−8.77432	−	15.1976i	−0.305854	−	0.529754i	0.671597	−	0.740916i	$-0.265608\pi$
$823$	−8.77432	−	15.1976i	−0.305854	−	0.529754i	−0.977451	+	0.211162i	$0.932275\pi$
$824$	7.41178			0.258202
$825$	2.94600			0.102566
$826$		0			0
$827$	16.6162	+	28.7801i	0.577802	+	1.00078i	0.995731	+	0.0923031i	$0.0294229\pi$
$827$	16.6162	+	28.7801i	0.577802	+	1.00078i	−0.417929	+	0.908480i	$0.637244\pi$
$828$	−10.7444			−0.373394
$829$	31.8062			1.10468			0.552338	−	0.833620i	$-0.313736\pi$
$829$	31.8062			1.10468			0.552338	+	0.833620i	$0.313736\pi$
$830$	14.5169	+	25.1440i	0.503888	+	0.872760i
$831$	19.9899	−	34.6235i	0.693441	−	1.20107i
$832$	−2.83944	−	4.91806i	−0.0984400	−	0.170503i
$833$	−32.5935	+	56.4536i	−1.12930	+	1.95600i
$834$	20.1447	−	34.8916i	0.697553	−	1.20820i
$835$	8.02885			0.277850
$836$	4.31244	+	0.634704i	0.149149	+	0.0219517i
$837$	−25.3578			−0.876493
$838$	−5.52700	+	9.57305i	−0.190927	+	0.330695i
$839$	1.16777	−	2.02263i	0.0403159	−	0.0698291i	−0.845163	−	0.534508i	$-0.820497\pi$
$839$	1.16777	−	2.02263i	0.0403159	−	0.0698291i	0.885479	+	0.464679i	$0.153830\pi$
$840$	−14.5709	−	25.2375i	−0.502743	−	0.870777i
$841$	14.0000	−	24.2487i	0.482759	−	0.836162i
$842$	2.24156	+	3.88250i	0.0772494	+	0.133800i
$843$	−3.53130			−0.121624
$844$	−25.6760			−0.883803
$845$	−19.2498	−	33.3416i	−0.662212	−	1.14698i
$846$	−21.0453	−	36.4516i	−0.723553	−	1.25323i
$847$	4.94600			0.169946
$848$	11.7840			0.404664
$849$	−7.10509	−	12.3064i	−0.243846	−	0.422354i
$850$	−1.86645	+	3.23278i	−0.0640186	+	0.110883i
$851$	−3.93449	−	6.81473i	−0.134872	−	0.233606i
$852$	6.81244	−	11.7995i	0.233390	−	0.404244i
$853$	2.51588	−	4.35764i	0.0861422	−	0.149203i	−0.819735	−	0.572743i	$-0.805879\pi$
$853$	2.51588	−	4.35764i	0.0861422	−	0.149203i	0.905877	+	0.423540i	$0.139213\pi$
$854$	27.5535			0.942863
$855$	−30.7329	+	38.8133i	−1.05104	+	1.32739i
$856$	−16.3722			−0.559590
$857$	−4.65043	+	8.05478i	−0.158856	+	0.275146i	−0.934456	−	0.356078i	$-0.884114\pi$
$857$	−4.65043	+	8.05478i	−0.158856	+	0.275146i	0.775601	+	0.631224i	$0.217447\pi$
$858$	−8.36499	+	14.4886i	−0.285576	+	0.494632i
$859$	16.7696	+	29.0457i	0.572170	+	0.991027i	0.996343	+	0.0854461i	$0.0272315\pi$
$859$	16.7696	+	29.0457i	0.572170	+	0.991027i	−0.424173	+	0.905581i	$0.639435\pi$
$860$	4.62488	−	8.01053i	0.157707	−	0.273157i
$861$	70.1215	+	121.454i	2.38973	+	4.13914i
$862$	−2.19576			−0.0747879
$863$	52.6557			1.79242			0.896211	−	0.443629i	$-0.146309\pi$
$863$	52.6557			1.79242			0.896211	+	0.443629i	$0.146309\pi$
$864$	−3.94600	−	6.83466i	−0.134245	−	0.232520i
$865$	7.21310	+	12.4935i	0.245253	+	0.424790i
$866$	31.8602			1.08265
$867$	9.03099			0.306708
$868$	−7.94600	−	13.7629i	−0.269705	−	0.467142i
$869$	3.41899	−	5.92187i	0.115981	−	0.200886i
$870$	2.94600	+	5.10261i	0.0998786	+	0.172995i
$871$	−25.0950	+	43.4658i	−0.850310	+	1.47278i
$872$	8.73143	−	15.1233i	0.295684	−	0.512139i
$873$	−8.71263			−0.294878
$874$	−5.11952	+	6.46556i	−0.173170	+	0.218701i
$875$	−59.3519			−2.00646
$876$	−5.33944	+	9.24819i	−0.180403	+	0.312467i
$877$	−5.64222	+	9.77262i	−0.190524	+	0.329998i	−0.945424	−	0.325842i	$-0.894352\pi$
$877$	−5.64222	+	9.77262i	−0.190524	+	0.329998i	0.754900	+	0.655840i	$0.227685\pi$
$878$	−5.32111	−	9.21644i	−0.179579	−	0.311040i
$879$	1.79119	−	3.10244i	0.0604155	−	0.104643i
$880$	−1.00000	−	1.73205i	−0.0337100	−	0.0583874i
$881$	−21.6105			−0.728075			−0.364037	−	0.931384i	$-0.618602\pi$
$881$	−21.6105			−0.728075			−0.364037	+	0.931384i	$0.618602\pi$
$882$	−99.1697			−3.33922
$883$	−8.47008	−	14.6706i	−0.285041	−	0.493705i	0.687578	−	0.726110i	$-0.258674\pi$
$883$	−8.47008	−	14.6706i	−0.285041	−	0.493705i	−0.972619	+	0.232405i	$0.925341\pi$
$884$	−10.5993	−	18.3586i	−0.356494	−	0.617466i
$885$		0			0
$886$	−31.4455			−1.05643
$887$	22.2936	+	38.6137i	0.748547	+	1.29652i	0.948519	+	0.316720i	$0.102582\pi$
$887$	22.2936	+	38.6137i	0.748547	+	1.29652i	−0.199972	+	0.979802i	$0.564085\pi$
$888$	6.12634	−	10.6111i	0.205587	−	0.356086i
$889$	13.2498	+	22.9493i	0.444383	+	0.769694i
$890$	−0.465785	+	0.806763i	−0.0156132	+	0.0270428i
$891$	−3.10655	+	5.38070i	−0.104073	+	0.180260i
$892$	−7.37512			−0.246937
$893$	−31.9629	−	4.70428i	−1.06960	−	0.157423i
$894$	55.9653			1.87176
$895$	−4.10801	+	7.11528i	−0.137316	+	0.237838i
$896$	2.47300	−	4.28336i	0.0826171	−	0.143097i
$897$	−15.8265	−	27.4123i	−0.528431	−	0.915269i
$898$	6.92766	−	11.9991i	0.231179	−	0.400414i
$899$	1.60655	+	2.78263i	0.0535815	+	0.0928059i
$900$	−5.67889			−0.189296
$901$	43.9883			1.46546
$902$	4.81244	+	8.33539i	0.160237	+	0.277538i
$903$	−33.6943	−	58.3602i	−1.12128	−	1.94211i
$904$	3.53421			0.117546
$905$	30.8177			1.02442
$906$	34.8534	+	60.3679i	1.15793	+	2.00559i
$907$	−17.4484	+	30.2216i	−0.579366	+	1.00349i	0.416186	+	0.909279i	$0.363366\pi$
$907$	−17.4484	+	30.2216i	−0.579366	+	1.00349i	−0.995552	+	0.0942120i	$0.969967\pi$
$908$	14.1774	+	24.5560i	0.470495	+	0.814920i
$909$	4.76711	−	8.25687i	0.158115	−	0.273863i
$910$	28.0878	−	48.6494i	0.931100	−	1.61271i
$911$	21.8631			0.724358			0.362179	−	0.932109i	$-0.382033\pi$
$911$	21.8631			0.724358			0.362179	+	0.932109i	$0.382033\pi$
$912$	−12.7044	−	1.86983i	−0.420686	−	0.0619164i
$913$	14.5169			0.480438
$914$	−7.86645	+	13.6251i	−0.260199	+	0.450678i
$915$	−16.4118	+	28.4260i	−0.542557	+	0.939736i
$916$	2.49133	+	4.31511i	0.0823158	+	0.142575i
$917$	−25.6504	+	44.4278i	−0.847052	+	1.46714i
$918$	−14.7300	−	25.5131i	−0.486162	−	0.842057i
$919$	31.9509			1.05396			0.526981	−	0.849877i	$-0.323324\pi$
$919$	31.9509			1.05396			0.526981	+	0.849877i	$0.323324\pi$
$920$	3.78398			0.124754
$921$	47.2069	+	81.7647i	1.55552	+	2.69424i
$922$	−10.3563	−	17.9377i	−0.341067	−	0.590746i
$923$	26.2642			0.864496
$924$	−14.5709			−0.479347
$925$	−2.07955	−	3.60188i	−0.0683751	−	0.118429i
$926$	−7.18610	+	12.4467i	−0.236150	+	0.409024i
$927$	21.0453	+	36.4516i	0.691219	+	1.19723i
$928$	−0.500000	+	0.866025i	−0.0164133	+	0.0284287i
$929$	−10.0342	+	17.3798i	−0.329212	+	0.570212i	−0.982356	−	0.187022i	$-0.940116\pi$
$929$	−10.0342	+	17.3798i	−0.329212	+	0.570212i	0.653144	+	0.757234i	$0.273450\pi$
$930$	18.9316			0.620791
$931$	−47.2526	+	59.6764i	−1.54864	+	1.95582i
$932$	22.4484			0.735323
$933$	−27.0622	+	46.8731i	−0.885977	+	1.53456i
$934$	−5.15189	+	8.92333i	−0.168575	+	0.291980i
$935$	−3.73289	−	6.46556i	−0.122079	−	0.211446i
$936$	16.1249	−	27.9291i	0.527058	−	0.912892i
$937$	22.5680	+	39.0889i	0.737263	+	1.27698i	0.953723	+	0.300686i	$0.0972155\pi$
$937$	22.5680	+	39.0889i	0.737263	+	1.27698i	−0.216460	+	0.976291i	$0.569451\pi$
$938$	−43.7126			−1.42727
$939$	−3.37220			−0.110048
$940$	7.41178	+	12.8376i	0.241746	+	0.418716i
$941$	−17.0010	−	29.4466i	−0.554216	−	0.959931i	−0.997964	−	0.0637792i	$-0.979685\pi$
$941$	−17.0010	−	29.4466i	−0.554216	−	0.959931i	0.443748	−	0.896152i	$-0.353649\pi$
$942$	−34.7156			−1.13109
$943$	−18.2102			−0.593005
$944$		0			0
$945$	39.0337	−	67.6084i	1.26977	−	2.19930i
$946$	−2.31244	−	4.00527i	−0.0751840	−	0.130222i
$947$	26.4089	−	45.7415i	0.858173	−	1.48640i	−0.0154973	−	0.999880i	$-0.504933\pi$
$947$	26.4089	−	45.7415i	0.858173	−	1.48640i	0.873670	−	0.486519i	$-0.161734\pi$
$948$	−10.0723	+	17.4458i	−0.327134	+	0.566613i
$949$	−20.5853			−0.668227
$950$	−2.70589	+	3.41733i	−0.0877907	+	0.110873i
$951$	−72.0250			−2.33557
$952$	9.23143	−	15.9893i	0.299193	−	0.518217i
$953$	6.35778	−	11.0120i	0.205949	−	0.356713i	−0.744486	−	0.667638i	$-0.767305\pi$
$953$	6.35778	−	11.0120i	0.205949	−	0.356713i	0.950435	+	0.310925i	$0.100639\pi$
$954$	33.4600	+	57.9543i	1.08331	+	1.87634i
$955$	−10.5882	+	18.3393i	−0.342627	+	0.593447i
$956$	11.8920	+	20.5975i	0.384614	+	0.666172i
$957$	2.94600			0.0952305
$958$	−7.58822			−0.245164
$959$	−34.8819	−	60.4172i	−1.12639	−	1.95097i
$960$	2.94600	+	5.10261i	0.0950816	+	0.164686i
$961$	−20.6760			−0.666967
$962$	23.6190			0.761509
$963$	−46.4879	−	80.5195i	−1.49805	−	2.59470i
$964$	10.5709	−	18.3093i	0.340465	−	0.589703i
$965$	5.51687	+	9.55550i	0.177594	+	0.307603i
$966$	13.7840	−	23.8746i	0.443492	−	0.768151i
$967$	4.73289	−	8.19761i	0.152200	−	0.263617i	−0.779836	−	0.625984i	$-0.784698\pi$
$967$	4.73289	−	8.19761i	0.152200	−	0.263617i	0.932036	+	0.362366i	$0.118031\pi$
$968$	−1.00000			−0.0321412
$969$	−47.4243	−	6.97989i	−1.52349	−	0.224226i
$970$	3.06843			0.0985213
$971$	14.5607	−	25.2200i	0.467277	−	0.809347i	−0.532024	−	0.846729i	$-0.678569\pi$
$971$	14.5607	−	25.2200i	0.467277	−	0.809347i	0.999301	+	0.0373821i	$0.0119019\pi$
$972$	−2.68610	+	4.65246i	−0.0861567	+	0.149228i
$973$	33.8206	+	58.5791i	1.08424	+	1.87796i
$974$	−0.207348	+	0.359138i	−0.00664387	+	0.0115075i
$975$	−8.36499	−	14.4886i	−0.267894	−	0.464006i
$976$	−5.57088			−0.178319
$977$	−1.75023			−0.0559950			−0.0279975	−	0.999608i	$-0.508913\pi$
$977$	−1.75023			−0.0559950			−0.0279975	+	0.999608i	$0.508913\pi$
$978$	15.9431	+	27.6142i	0.509803	+	0.883005i
$979$	0.232893	+	0.403382i	0.00744328	+	0.0128921i
$980$	34.9257			1.11566
$981$	99.1697			3.16624
$982$	−0.411780	−	0.713224i	−0.0131404	−	0.0227599i
$983$	12.0058	−	20.7946i	0.382924	−	0.663244i	−0.608555	−	0.793512i	$-0.708250\pi$
$983$	12.0058	−	20.7946i	0.382924	−	0.663244i	0.991479	+	0.130268i	$0.0415837\pi$
$984$	−14.1774	−	24.5560i	−0.451960	−	0.782818i
$985$	9.53421	−	16.5137i	0.303785	−	0.526172i
$986$	−1.86645	+	3.23278i	−0.0594398	+	0.102953i
$987$	107.996			3.43756
$988$	−9.12342	−	23.0111i	−0.290255	−	0.732079i
$989$	8.75023			0.278241
$990$	5.67889	−	9.83612i	0.180487	−	0.312612i
$991$	−22.9017	+	39.6668i	−0.727495	+	1.26006i	0.230444	+	0.973086i	$0.425982\pi$
$991$	−22.9017	+	39.6668i	−0.727495	+	1.26006i	−0.957939	+	0.286973i	$0.907351\pi$
$992$	1.60655	+	2.78263i	0.0510081	+	0.0883485i
$993$	−9.28544	+	16.0829i	−0.294665	+	0.510374i
$994$	11.4373	+	19.8100i	0.362770	+	0.628336i
$995$	41.2498			1.30771
$996$	−42.7666			−1.35511
$997$	−2.57379	−	4.45794i	−0.0815129	−	0.141184i	0.822387	−	0.568928i	$-0.192642\pi$
$997$	−2.57379	−	4.45794i	−0.0815129	−	0.141184i	−0.903900	+	0.427744i	$0.859309\pi$
$998$	2.67889	+	4.63997i	0.0847987	+	0.146876i
$999$	32.8236			1.03849

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.e.i.353.3	yes	6
19.7	even	3	inner	418.2.e.i.45.3	✓	6
19.8	odd	6		7942.2.a.bj.1.3		3
19.11	even	3		7942.2.a.bd.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.e.i.45.3	✓	6	19.7	even	3	inner
418.2.e.i.353.3	yes	6	1.1	even	1	trivial
7942.2.a.bd.1.1		3	19.11	even	3
7942.2.a.bj.1.3		3	19.8	odd	6

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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(1.47300 - 2.55131i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.00000 + 1.73205i) q^{5} +(-1.47300 - 2.55131i) q^{6} +4.94600 q^{7} -1.00000 q^{8} +(-2.83944 - 4.91806i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(1.47300 - 2.55131i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.00000 + 1.73205i) q^{5} +(-1.47300 - 2.55131i) q^{6} +4.94600 q^{7} -1.00000 q^{8} +(-2.83944 - 4.91806i) q^{9} +(1.00000 + 1.73205i) q^{10} +1.00000 q^{11} -2.94600 q^{12} +(-2.83944 - 4.91806i) q^{13} +(2.47300 - 4.28336i) q^{14} +(2.94600 + 5.10261i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.86645 + 3.23278i) q^{17} -5.67889 q^{18} +(-2.70589 + 3.41733i) q^{19} +2.00000 q^{20} +(7.28544 - 12.6188i) q^{21} +(0.500000 - 0.866025i) q^{22} +(0.945995 + 1.63851i) q^{23} +(-1.47300 + 2.55131i) q^{24} +(0.500000 + 0.866025i) q^{25} -5.67889 q^{26} -7.89199 q^{27} +(-2.47300 - 4.28336i) q^{28} +(0.500000 + 0.866025i) q^{29} +5.89199 q^{30} +3.21310 q^{31} +(0.500000 + 0.866025i) q^{32} +(1.47300 - 2.55131i) q^{33} +(1.86645 + 3.23278i) q^{34} +(-4.94600 + 8.56671i) q^{35} +(-2.83944 + 4.91806i) q^{36} -4.15910 q^{37} +(1.60655 + 4.05204i) q^{38} -16.7300 q^{39} +(1.00000 - 1.73205i) q^{40} +(-4.81244 + 8.33539i) q^{41} +(-7.28544 - 12.6188i) q^{42} +(2.31244 - 4.00527i) q^{43} +(-0.500000 - 0.866025i) q^{44} +11.3578 q^{45} +1.89199 q^{46} +(3.70589 + 6.41879i) q^{47} +(1.47300 + 2.55131i) q^{48} +17.4629 q^{49} +1.00000 q^{50} +(5.49854 + 9.52375i) q^{51} +(-2.83944 + 4.91806i) q^{52} +(-5.89199 - 10.2052i) q^{53} +(-3.94600 + 6.83466i) q^{54} +(-1.00000 + 1.73205i) q^{55} -4.94600 q^{56} +(4.73289 + 11.9373i) q^{57} +1.00000 q^{58} +(2.94600 - 5.10261i) q^{60} +(2.78544 + 4.82452i) q^{61} +(1.60655 - 2.78263i) q^{62} +(-14.0439 - 24.3247i) q^{63} +1.00000 q^{64} +11.3578 q^{65} +(-1.47300 - 2.55131i) q^{66} +(-4.41899 - 7.65392i) q^{67} +3.73289 q^{68} +5.57379 q^{69} +(4.94600 + 8.56671i) q^{70} +(-2.31244 + 4.00527i) q^{71} +(2.83944 + 4.91806i) q^{72} +(1.81244 - 3.13924i) q^{73} +(-2.07955 + 3.60188i) q^{74} +2.94600 q^{75} +(4.31244 + 0.634704i) q^{76} +4.94600 q^{77} +(-8.36499 + 14.4886i) q^{78} +(3.41899 - 5.92187i) q^{79} +(-1.00000 - 1.73205i) q^{80} +(-3.10655 + 5.38070i) q^{81} +(4.81244 + 8.33539i) q^{82} +14.5169 q^{83} -14.5709 q^{84} +(-3.73289 - 6.46556i) q^{85} +(-2.31244 - 4.00527i) q^{86} +2.94600 q^{87} -1.00000 q^{88} +(0.232893 + 0.403382i) q^{89} +(5.67889 - 9.83612i) q^{90} +(-14.0439 - 24.3247i) q^{91} +(0.945995 - 1.63851i) q^{92} +(4.73289 - 8.19761i) q^{93} +7.41178 q^{94} +(-3.21310 - 8.10407i) q^{95} +2.94600 q^{96} +(0.767107 - 1.32867i) q^{97} +(8.73143 - 15.1233i) q^{98} +(-2.83944 - 4.91806i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 3 q^{4} - 6 q^{5} + 12 q^{7} - 6 q^{8} - 7 q^{9}+O(q^{10}) \) 6 * q + 3 * q^2 - 3 * q^4 - 6 * q^5 + 12 * q^7 - 6 * q^8 - 7 * q^9	\( 6 q + 3 q^{2} - 3 q^{4} - 6 q^{5} + 12 q^{7} - 6 q^{8} - 7 q^{9} + 6 q^{10} + 6 q^{11} - 7 q^{13} + 6 q^{14} - 3 q^{16} - 10 q^{17} - 14 q^{18} - 5 q^{19} + 12 q^{20} + 16 q^{21} + 3 q^{22} - 12 q^{23} + 3 q^{25} - 14 q^{26} - 12 q^{27} - 6 q^{28} + 3 q^{29} + 4 q^{31} + 3 q^{32} + 10 q^{34} - 12 q^{35} - 7 q^{36} + 8 q^{37} + 2 q^{38} - 12 q^{39} + 6 q^{40} - 10 q^{41} - 16 q^{42} - 5 q^{43} - 3 q^{44} + 28 q^{45} - 24 q^{46} + 11 q^{47} + 14 q^{49} + 6 q^{50} - 10 q^{51} - 7 q^{52} - 6 q^{54} - 6 q^{55} - 12 q^{56} + 26 q^{57} + 6 q^{58} - 11 q^{61} + 2 q^{62} - 20 q^{63} + 6 q^{64} + 28 q^{65} + 20 q^{68} + 64 q^{69} + 12 q^{70} + 5 q^{71} + 7 q^{72} - 8 q^{73} + 4 q^{74} + 7 q^{76} + 12 q^{77} - 6 q^{78} - 6 q^{79} - 6 q^{80} - 11 q^{81} + 10 q^{82} + 14 q^{83} - 32 q^{84} - 20 q^{85} + 5 q^{86} - 6 q^{88} - q^{89} + 14 q^{90} - 20 q^{91} - 12 q^{92} + 26 q^{93} + 22 q^{94} - 4 q^{95} + 7 q^{97} + 7 q^{98} - 7 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 - 3 * q^4 - 6 * q^5 + 12 * q^7 - 6 * q^8 - 7 * q^9 + 6 * q^10 + 6 * q^11 - 7 * q^13 + 6 * q^14 - 3 * q^16 - 10 * q^17 - 14 * q^18 - 5 * q^19 + 12 * q^20 + 16 * q^21 + 3 * q^22 - 12 * q^23 + 3 * q^25 - 14 * q^26 - 12 * q^27 - 6 * q^28 + 3 * q^29 + 4 * q^31 + 3 * q^32 + 10 * q^34 - 12 * q^35 - 7 * q^36 + 8 * q^37 + 2 * q^38 - 12 * q^39 + 6 * q^40 - 10 * q^41 - 16 * q^42 - 5 * q^43 - 3 * q^44 + 28 * q^45 - 24 * q^46 + 11 * q^47 + 14 * q^49 + 6 * q^50 - 10 * q^51 - 7 * q^52 - 6 * q^54 - 6 * q^55 - 12 * q^56 + 26 * q^57 + 6 * q^58 - 11 * q^61 + 2 * q^62 - 20 * q^63 + 6 * q^64 + 28 * q^65 + 20 * q^68 + 64 * q^69 + 12 * q^70 + 5 * q^71 + 7 * q^72 - 8 * q^73 + 4 * q^74 + 7 * q^76 + 12 * q^77 - 6 * q^78 - 6 * q^79 - 6 * q^80 - 11 * q^81 + 10 * q^82 + 14 * q^83 - 32 * q^84 - 20 * q^85 + 5 * q^86 - 6 * q^88 - q^89 + 14 * q^90 - 20 * q^91 - 12 * q^92 + 26 * q^93 + 22 * q^94 - 4 * q^95 + 7 * q^97 + 7 * q^98 - 7 * q^99

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