LMFDB - Embedded newform 1110.2.i.p.121.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(121,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("1110.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.i (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:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 15x^{8} - 6x^{7} + 123x^{6} - 62x^{5} + 458x^{4} + 100x^{3} + 844x^{2} - 312x + 144 $ x^10 - 2x^9 + 15x^8 - 6x^7 + 123x^6 - 62x^5 + 458x^4 + 100x^3 + 844x^2 - 312*x + 144
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.1
Root			$1.10642 - 1.91637i$ of defining polynomial
Character	$\chi$	$=$	1110.121
Dual form			1110.2.i.p.211.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +1.00000 q^{6} +(-2.44097 - 4.22788i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +1.00000 q^{6} +(-2.44097 - 4.22788i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +1.00000 q^{10} +2.56573 q^{11} +(-0.500000 + 0.866025i) q^{12} +(-1.71283 - 2.96671i) q^{13} +4.88194 q^{14} +(-0.500000 + 0.866025i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.90879 - 3.30612i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(1.76452 + 3.05624i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(-2.44097 + 4.22788i) q^{21} +(-1.28286 + 2.22198i) q^{22} -5.27386 q^{23} +(-0.500000 - 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} +3.42566 q^{26} +1.00000 q^{27} +(-2.44097 + 4.22788i) q^{28} +6.98532 q^{29} +(-0.500000 - 0.866025i) q^{30} -7.03041 q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.28286 - 2.22198i) q^{33} +(1.90879 + 3.30612i) q^{34} +(-2.44097 + 4.22788i) q^{35} +1.00000 q^{36} +(-3.11859 + 5.22249i) q^{37} -3.52904 q^{38} +(-1.71283 + 2.96671i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(-3.87094 - 6.70466i) q^{41} +(-2.44097 - 4.22788i) q^{42} +4.73346 q^{43} +(-1.28286 - 2.22198i) q^{44} +1.00000 q^{45} +(2.63693 - 4.56730i) q^{46} -7.62381 q^{47} +1.00000 q^{48} +(-8.41666 + 14.5781i) q^{49} +(-0.500000 - 0.866025i) q^{50} -3.81758 q^{51} +(-1.71283 + 2.96671i) q^{52} +(0.554725 - 0.960812i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-1.28286 - 2.22198i) q^{55} +(-2.44097 - 4.22788i) q^{56} +(1.76452 - 3.05624i) q^{57} +(-3.49266 + 6.04946i) q^{58} +(-6.20383 + 10.7453i) q^{59} +1.00000 q^{60} +(-4.12045 - 7.13683i) q^{61} +(3.51521 - 6.08852i) q^{62} +4.88194 q^{63} +1.00000 q^{64} +(-1.71283 + 2.96671i) q^{65} +2.56573 q^{66} +(5.59173 + 9.68517i) q^{67} -3.81758 q^{68} +(2.63693 + 4.56730i) q^{69} +(-2.44097 - 4.22788i) q^{70} +(-0.0742379 - 0.128584i) q^{71} +(-0.500000 + 0.866025i) q^{72} -1.89896 q^{73} +(-2.96352 - 5.31202i) q^{74} +1.00000 q^{75} +(1.76452 - 3.05624i) q^{76} +(-6.26286 - 10.8476i) q^{77} +(-1.71283 - 2.96671i) q^{78} +(1.61859 + 2.80348i) q^{79} +1.00000 q^{80} +(-0.500000 - 0.866025i) q^{81} +7.74187 q^{82} +(2.63996 - 4.57255i) q^{83} +4.88194 q^{84} -3.81758 q^{85} +(-2.36673 + 4.09930i) q^{86} +(-3.49266 - 6.04946i) q^{87} +2.56573 q^{88} +(-1.96782 + 3.40837i) q^{89} +(-0.500000 + 0.866025i) q^{90} +(-8.36193 + 14.4833i) q^{91} +(2.63693 + 4.56730i) q^{92} +(3.51521 + 6.08852i) q^{93} +(3.81191 - 6.60241i) q^{94} +(1.76452 - 3.05624i) q^{95} +(-0.500000 + 0.866025i) q^{96} +12.3686 q^{97} +(-8.41666 - 14.5781i) q^{98} +(-1.28286 + 2.22198i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 5 q^{2} - 5 q^{3} - 5 q^{4} - 5 q^{5} + 10 q^{6} + 10 q^{8} - 5 q^{9}+O(q^{10}) $ 10 * q - 5 * q^2 - 5 * q^3 - 5 * q^4 - 5 * q^5 + 10 * q^6 + 10 * q^8 - 5 * q^9	$ 10 q - 5 q^{2} - 5 q^{3} - 5 q^{4} - 5 q^{5} + 10 q^{6} + 10 q^{8} - 5 q^{9} + 10 q^{10} - 2 q^{11} - 5 q^{12} + q^{13} - 5 q^{15} - 5 q^{16} - 5 q^{18} - 2 q^{19} - 5 q^{20} + q^{22} - 2 q^{23} - 5 q^{24} - 5 q^{25} - 2 q^{26} + 10 q^{27} + 18 q^{29} - 5 q^{30} - 14 q^{31} - 5 q^{32} + q^{33} + 10 q^{36} + 4 q^{38} + q^{39} - 5 q^{40} - 10 q^{41} + 6 q^{43} + q^{44} + 10 q^{45} + q^{46} + 30 q^{47} + 10 q^{48} - 11 q^{49} - 5 q^{50} + q^{52} - 2 q^{53} - 5 q^{54} + q^{55} - 2 q^{57} - 9 q^{58} - 7 q^{59} + 10 q^{60} - 6 q^{61} + 7 q^{62} + 10 q^{64} + q^{65} - 2 q^{66} - 5 q^{67} + q^{69} + 3 q^{71} - 5 q^{72} - 18 q^{73} - 3 q^{74} + 10 q^{75} - 2 q^{76} - 32 q^{77} + q^{78} - 15 q^{79} + 10 q^{80} - 5 q^{81} + 20 q^{82} - 5 q^{83} - 3 q^{86} - 9 q^{87} - 2 q^{88} - 25 q^{89} - 5 q^{90} - 18 q^{91} + q^{92} + 7 q^{93} - 15 q^{94} - 2 q^{95} - 5 q^{96} + 6 q^{97} - 11 q^{98} + q^{99}+O(q^{100}) $ 10 * q - 5 * q^2 - 5 * q^3 - 5 * q^4 - 5 * q^5 + 10 * q^6 + 10 * q^8 - 5 * q^9 + 10 * q^10 - 2 * q^11 - 5 * q^12 + q^13 - 5 * q^15 - 5 * q^16 - 5 * q^18 - 2 * q^19 - 5 * q^20 + q^22 - 2 * q^23 - 5 * q^24 - 5 * q^25 - 2 * q^26 + 10 * q^27 + 18 * q^29 - 5 * q^30 - 14 * q^31 - 5 * q^32 + q^33 + 10 * q^36 + 4 * q^38 + q^39 - 5 * q^40 - 10 * q^41 + 6 * q^43 + q^44 + 10 * q^45 + q^46 + 30 * q^47 + 10 * q^48 - 11 * q^49 - 5 * q^50 + q^52 - 2 * q^53 - 5 * q^54 + q^55 - 2 * q^57 - 9 * q^58 - 7 * q^59 + 10 * q^60 - 6 * q^61 + 7 * q^62 + 10 * q^64 + q^65 - 2 * q^66 - 5 * q^67 + q^69 + 3 * q^71 - 5 * q^72 - 18 * q^73 - 3 * q^74 + 10 * q^75 - 2 * q^76 - 32 * q^77 + q^78 - 15 * q^79 + 10 * q^80 - 5 * q^81 + 20 * q^82 - 5 * q^83 - 3 * q^86 - 9 * q^87 - 2 * q^88 - 25 * q^89 - 5 * q^90 - 18 * q^91 + q^92 + 7 * q^93 - 15 * q^94 - 2 * q^95 - 5 * q^96 + 6 * q^97 - 11 * q^98 + q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	1.00000			0.408248
$7$	−2.44097	−	4.22788i	−0.922599	−	1.59799i	−0.795377	−	0.606115i	$-0.792727\pi$
$7$	−2.44097	−	4.22788i	−0.922599	−	1.59799i	−0.127222	−	0.991874i	$-0.540606\pi$
$8$	1.00000			0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	1.00000			0.316228
$11$	2.56573			0.773596			0.386798	−	0.922165i	$-0.373581\pi$
$11$	2.56573			0.773596			0.386798	+	0.922165i	$0.373581\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	−1.71283	−	2.96671i	−0.475054	−	0.822817i	0.524538	−	0.851387i	$-0.324238\pi$
$13$	−1.71283	−	2.96671i	−0.475054	−	0.822817i	−0.999592	+	0.0285698i	$0.990905\pi$
$14$	4.88194			1.30475
$15$	−0.500000	+	0.866025i	−0.129099	+	0.223607i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.90879	−	3.30612i	0.462950	−	0.801853i	−0.536157	−	0.844119i	$-0.680124\pi$
$17$	1.90879	−	3.30612i	0.462950	−	0.801853i	0.999106	+	0.0422659i	$0.0134576\pi$
$18$	−0.500000	−	0.866025i	−0.117851	−	0.204124i
$19$	1.76452	+	3.05624i	0.404809	+	0.701150i	0.994299	−	0.106626i	$-0.0340047\pi$
$19$	1.76452	+	3.05624i	0.404809	+	0.701150i	−0.589490	+	0.807775i	$0.700671\pi$
$20$	−0.500000	+	0.866025i	−0.111803	+	0.193649i
$21$	−2.44097	+	4.22788i	−0.532663	+	0.922599i
$22$	−1.28286	+	2.22198i	−0.273507	+	0.473729i
$23$	−5.27386			−1.09968			−0.549838	−	0.835271i	$-0.685310\pi$
$23$	−5.27386			−1.09968			−0.549838	+	0.835271i	$0.685310\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	3.42566			0.671827
$27$	1.00000			0.192450
$28$	−2.44097	+	4.22788i	−0.461300	+	0.798995i
$29$	6.98532			1.29714			0.648571	−	0.761155i	$-0.275367\pi$
$29$	6.98532			1.29714			0.648571	+	0.761155i	$0.275367\pi$
$30$	−0.500000	−	0.866025i	−0.0912871	−	0.158114i
$31$	−7.03041			−1.26270			−0.631350	−	0.775498i	$-0.717499\pi$
$31$	−7.03041			−1.26270			−0.631350	+	0.775498i	$0.717499\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−1.28286	−	2.22198i	−0.223318	−	0.386798i
$34$	1.90879	+	3.30612i	0.327355	+	0.566996i
$35$	−2.44097	+	4.22788i	−0.412599	+	0.714642i
$36$	1.00000			0.166667
$37$	−3.11859	+	5.22249i	−0.512693	+	0.858572i
$37$	−3.11859	+	5.22249i	−0.512693	+	0.858572i
$38$	−3.52904			−0.572486
$39$	−1.71283	+	2.96671i	−0.274272	+	0.475054i
$40$	−0.500000	−	0.866025i	−0.0790569	−	0.136931i
$41$	−3.87094	−	6.70466i	−0.604539	−	1.04709i	−0.992124	−	0.125258i	$-0.960024\pi$
$41$	−3.87094	−	6.70466i	−0.604539	−	1.04709i	0.387586	−	0.921834i	$-0.373309\pi$
$42$	−2.44097	−	4.22788i	−0.376650	−	0.652376i
$43$	4.73346			0.721846			0.360923	−	0.932596i	$-0.382462\pi$
$43$	4.73346			0.721846			0.360923	+	0.932596i	$0.382462\pi$
$44$	−1.28286	−	2.22198i	−0.193399	−	0.334977i
$45$	1.00000			0.149071
$46$	2.63693	−	4.56730i	0.388794	−	0.673411i
$47$	−7.62381			−1.11205			−0.556023	−	0.831167i	$-0.687674\pi$
$47$	−7.62381			−1.11205			−0.556023	+	0.831167i	$0.687674\pi$
$48$	1.00000			0.144338
$49$	−8.41666	+	14.5781i	−1.20238	+	2.08258i
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$	−3.81758			−0.534568
$52$	−1.71283	+	2.96671i	−0.237527	+	0.411409i
$53$	0.554725	−	0.960812i	0.0761973	−	0.131978i	−0.825409	−	0.564535i	$-0.809055\pi$
$53$	0.554725	−	0.960812i	0.0761973	−	0.131978i	0.901606	+	0.432558i	$0.142389\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	−1.28286	−	2.22198i	−0.172981	−	0.299612i
$56$	−2.44097	−	4.22788i	−0.326188	−	0.564974i
$57$	1.76452	−	3.05624i	0.233717	−	0.404809i
$58$	−3.49266	+	6.04946i	−0.458609	+	0.794333i
$59$	−6.20383	+	10.7453i	−0.807669	+	1.39892i	0.106805	+	0.994280i	$0.465938\pi$
$59$	−6.20383	+	10.7453i	−0.807669	+	1.39892i	−0.914474	+	0.404644i	$0.867395\pi$
$60$	1.00000			0.129099
$61$	−4.12045	−	7.13683i	−0.527570	−	0.913778i	−0.999484	−	0.0321329i	$-0.989770\pi$
$61$	−4.12045	−	7.13683i	−0.527570	−	0.913778i	0.471914	−	0.881645i	$-0.343563\pi$
$62$	3.51521	−	6.08852i	0.446432	−	0.773242i
$63$	4.88194			0.615066
$64$	1.00000			0.125000
$65$	−1.71283	+	2.96671i	−0.212450	+	0.367975i
$66$	2.56573			0.315819
$67$	5.59173	+	9.68517i	0.683139	+	1.18323i	0.974018	+	0.226472i	$0.0727190\pi$
$67$	5.59173	+	9.68517i	0.683139	+	1.18323i	−0.290879	+	0.956760i	$0.593948\pi$
$68$	−3.81758			−0.462950
$69$	2.63693	+	4.56730i	0.317449	+	0.549838i
$70$	−2.44097	−	4.22788i	−0.291752	−	0.505329i
$71$	−0.0742379	−	0.128584i	−0.00881041	−	0.0152601i	0.861587	−	0.507611i	$-0.169471\pi$
$71$	−0.0742379	−	0.128584i	−0.00881041	−	0.0152601i	−0.870397	+	0.492351i	$0.836138\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	−1.89896			−0.222257			−0.111128	−	0.993806i	$-0.535446\pi$
$73$	−1.89896			−0.222257			−0.111128	+	0.993806i	$0.535446\pi$
$74$	−2.96352	−	5.31202i	−0.344502	−	0.617510i
$75$	1.00000			0.115470
$76$	1.76452	−	3.05624i	0.202404	−	0.350575i
$77$	−6.26286	−	10.8476i	−0.713719	−	1.23620i
$78$	−1.71283	−	2.96671i	−0.193940	−	0.335914i
$79$	1.61859	+	2.80348i	0.182105	+	0.315416i	0.942597	−	0.333932i	$-0.108375\pi$
$79$	1.61859	+	2.80348i	0.182105	+	0.315416i	−0.760492	+	0.649347i	$0.775042\pi$
$80$	1.00000			0.111803
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	7.74187			0.854947
$83$	2.63996	−	4.57255i	0.289774	−	0.501903i	−0.683982	−	0.729499i	$-0.739753\pi$
$83$	2.63996	−	4.57255i	0.289774	−	0.501903i	0.973756	+	0.227596i	$0.0730866\pi$
$84$	4.88194			0.532663
$85$	−3.81758			−0.414075
$86$	−2.36673	+	4.09930i	−0.255211	+	0.442039i
$87$	−3.49266	−	6.04946i	−0.374452	−	0.648571i
$88$	2.56573			0.273507
$89$	−1.96782	+	3.40837i	−0.208589	+	0.361286i	−0.951270	−	0.308359i	$-0.900220\pi$
$89$	−1.96782	+	3.40837i	−0.208589	+	0.361286i	0.742681	+	0.669645i	$0.233554\pi$
$90$	−0.500000	+	0.866025i	−0.0527046	+	0.0912871i
$91$	−8.36193	+	14.4833i	−0.876569	+	1.51826i
$92$	2.63693	+	4.56730i	0.274919	+	0.476174i
$93$	3.51521	+	6.08852i	0.364510	+	0.631350i
$94$	3.81191	−	6.60241i	0.393168	−	0.680987i
$95$	1.76452	−	3.05624i	0.181036	−	0.313564i
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$	12.3686			1.25584			0.627922	−	0.778276i	$-0.283906\pi$
$97$	12.3686			1.25584			0.627922	+	0.778276i	$0.283906\pi$
$98$	−8.41666	−	14.5781i	−0.850211	−	1.47261i
$99$	−1.28286	+	2.22198i	−0.128933	+	0.223318i
$100$	1.00000			0.100000
$101$	−6.73014			−0.669673			−0.334837	−	0.942276i	$-0.608681\pi$
$101$	−6.73014			−0.669673			−0.334837	+	0.942276i	$0.608681\pi$
$102$	1.90879	−	3.30612i	0.188999	−	0.327355i
$103$	−15.1862			−1.49634			−0.748171	−	0.663506i	$-0.769068\pi$
$103$	−15.1862			−1.49634			−0.748171	+	0.663506i	$0.769068\pi$
$104$	−1.71283	−	2.96671i	−0.167957	−	0.290910i
$105$	4.88194			0.476428
$106$	0.554725	+	0.960812i	0.0538797	+	0.0933223i
$107$	−8.35763	−	14.4758i	−0.807962	−	1.39943i	−0.914273	−	0.405099i	$-0.867237\pi$
$107$	−8.35763	−	14.4758i	−0.807962	−	1.39943i	0.106311	−	0.994333i	$-0.466096\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$	7.41676	−	12.8462i	0.710397	−	1.23044i	−0.254312	−	0.967122i	$-0.581849\pi$
$109$	7.41676	−	12.8462i	0.710397	−	1.23044i	0.964708	−	0.263321i	$-0.0848177\pi$
$110$	2.56573			0.244632
$111$	6.08210	+	0.0895303i	0.577288	+	0.00849784i
$112$	4.88194			0.461300
$113$	1.78120	−	3.08513i	0.167561	−	0.290224i	−0.770001	−	0.638043i	$-0.779744\pi$
$113$	1.78120	−	3.08513i	0.167561	−	0.290224i	0.937562	+	0.347819i	$0.113077\pi$
$114$	1.76452	+	3.05624i	0.165263	+	0.286243i
$115$	2.63693	+	4.56730i	0.245895	+	0.425903i
$116$	−3.49266	−	6.04946i	−0.324285	−	0.561679i
$117$	3.42566			0.316702
$118$	−6.20383	−	10.7453i	−0.571109	−	0.989189i
$119$	−18.6372			−1.70847
$120$	−0.500000	+	0.866025i	−0.0456435	+	0.0790569i
$121$	−4.41705			−0.401550
$122$	8.24090			0.746096
$123$	−3.87094	+	6.70466i	−0.349031	+	0.604539i
$124$	3.51521	+	6.08852i	0.315675	+	0.546765i
$125$	1.00000			0.0894427
$126$	−2.44097	+	4.22788i	−0.217459	+	0.376650i
$127$	−4.76169	+	8.24748i	−0.422531	+	0.731846i	−0.996186	−	0.0872512i	$-0.972192\pi$
$127$	−4.76169	+	8.24748i	−0.422531	+	0.731846i	0.573655	+	0.819097i	$0.305525\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−2.36673	−	4.09930i	−0.208379	−	0.360923i
$130$	−1.71283	−	2.96671i	−0.150225	−	0.260198i
$131$	6.48552	−	11.2332i	0.566642	−	0.981453i	−0.430252	−	0.902709i	$-0.641575\pi$
$131$	6.48552	−	11.2332i	0.566642	−	0.981453i	0.996895	−	0.0787448i	$-0.0250912\pi$
$132$	−1.28286	+	2.22198i	−0.111659	+	0.193399i
$133$	8.61428	−	14.9204i	0.746953	−	1.29376i
$134$	−11.1835			−0.966104
$135$	−0.500000	−	0.866025i	−0.0430331	−	0.0745356i
$136$	1.90879	−	3.30612i	0.163678	−	0.283498i
$137$	9.50117			0.811740			0.405870	−	0.913931i	$-0.366969\pi$
$137$	9.50117			0.811740			0.405870	+	0.913931i	$0.366969\pi$
$138$	−5.27386			−0.448941
$139$	−8.64215	+	14.9686i	−0.733018	+	1.26962i	0.222570	+	0.974917i	$0.428555\pi$
$139$	−8.64215	+	14.9686i	−0.733018	+	1.26962i	−0.955588	+	0.294707i	$0.904778\pi$
$140$	4.88194			0.412599
$141$	3.81191	+	6.60241i	0.321020	+	0.556023i
$142$	0.148476			0.0124598
$143$	−4.39465	−	7.61176i	−0.367499	−	0.636528i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−3.49266	−	6.04946i	−0.290050	−	0.502381i
$146$	0.949480	−	1.64455i	0.0785796	−	0.136104i
$147$	16.8333			1.38839
$148$	6.08210	+	0.0895303i	0.499946	+	0.00735934i
$149$	18.7492			1.53599			0.767997	−	0.640454i	$-0.221254\pi$
$149$	18.7492			1.53599			0.767997	+	0.640454i	$0.221254\pi$
$150$	−0.500000	+	0.866025i	−0.0408248	+	0.0707107i
$151$	−3.91045	−	6.77311i	−0.318228	−	0.551188i	0.661890	−	0.749601i	$-0.269755\pi$
$151$	−3.91045	−	6.77311i	−0.318228	−	0.551188i	−0.980118	+	0.198413i	$0.936421\pi$
$152$	1.76452	+	3.05624i	0.143122	+	0.247894i
$153$	1.90879	+	3.30612i	0.154317	+	0.267284i
$154$	12.5257			1.00935
$155$	3.51521	+	6.08852i	0.282348	+	0.489041i
$156$	3.42566			0.274272
$157$	−9.48532	+	16.4291i	−0.757011	+	1.31118i	0.187358	+	0.982292i	$0.440008\pi$
$157$	−9.48532	+	16.4291i	−0.757011	+	1.31118i	−0.944368	+	0.328889i	$0.893326\pi$
$158$	−3.23717			−0.257536
$159$	−1.10945			−0.0879851
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	12.8733	+	22.2973i	1.01456	+	1.75727i
$162$	1.00000			0.0785674
$163$	−4.62025	+	8.00251i	−0.361886	+	0.626805i	−0.988271	−	0.152709i	$-0.951200\pi$
$163$	−4.62025	+	8.00251i	−0.361886	+	0.626805i	0.626385	+	0.779514i	$0.284534\pi$
$164$	−3.87094	+	6.70466i	−0.302269	+	0.523546i
$165$	−1.28286	+	2.22198i	−0.0998708	+	0.172981i
$166$	2.63996	+	4.57255i	0.204901	+	0.354899i
$167$	−0.566897	−	0.981894i	−0.0438678	−	0.0759813i	0.843258	−	0.537509i	$-0.180635\pi$
$167$	−0.566897	−	0.981894i	−0.0438678	−	0.0759813i	−0.887126	+	0.461528i	$0.847301\pi$
$168$	−2.44097	+	4.22788i	−0.188325	+	0.326188i
$169$	0.632423	−	1.09539i	0.0486479	−	0.0842606i
$170$	1.90879	−	3.30612i	0.146398	−	0.253568i
$171$	−3.52904			−0.269873
$172$	−2.36673	−	4.09930i	−0.180462	−	0.312569i
$173$	−1.33172	+	2.30661i	−0.101249	+	0.175368i	−0.912199	−	0.409747i	$-0.865617\pi$
$173$	−1.33172	+	2.30661i	−0.101249	+	0.175368i	0.810951	+	0.585115i	$0.198950\pi$
$174$	6.98532			0.529556
$175$	4.88194			0.369040
$176$	−1.28286	+	2.22198i	−0.0966994	+	0.167488i
$177$	12.4077			0.932616
$178$	−1.96782	−	3.40837i	−0.147495	−	0.255468i
$179$	−3.93565			−0.294164			−0.147082	−	0.989124i	$-0.546988\pi$
$179$	−3.93565			−0.294164			−0.147082	+	0.989124i	$0.546988\pi$
$180$	−0.500000	−	0.866025i	−0.0372678	−	0.0645497i
$181$	−12.3825	−	21.4471i	−0.920381	−	1.59415i	−0.798826	−	0.601562i	$-0.794545\pi$
$181$	−12.3825	−	21.4471i	−0.920381	−	1.59415i	−0.121555	−	0.992585i	$-0.538788\pi$
$182$	−8.36193	−	14.4833i	−0.619828	−	1.07357i
$183$	−4.12045	+	7.13683i	−0.304593	+	0.527570i
$184$	−5.27386			−0.388794
$185$	6.08210	+	0.0895303i	0.447165	+	0.00658240i
$186$	−7.03041			−0.515495
$187$	4.89744	−	8.48261i	0.358136	−	0.620310i
$188$	3.81191	+	6.60241i	0.278012	+	0.481530i
$189$	−2.44097	−	4.22788i	−0.177554	−	0.307533i
$190$	1.76452	+	3.05624i	0.128012	+	0.221723i
$191$	17.3602			1.25614			0.628071	−	0.778156i	$-0.283845\pi$
$191$	17.3602			1.25614			0.628071	+	0.778156i	$0.283845\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	−4.75546			−0.342306			−0.171153	−	0.985244i	$-0.554749\pi$
$193$	−4.75546			−0.342306			−0.171153	+	0.985244i	$0.554749\pi$
$194$	−6.18431	+	10.7115i	−0.444008	+	0.769044i
$195$	3.42566			0.245317
$196$	16.8333			1.20238
$197$	8.91235	−	15.4366i	0.634979	−	1.09982i	−0.351541	−	0.936173i	$-0.614342\pi$
$197$	8.91235	−	15.4366i	0.634979	−	1.09982i	0.986520	−	0.163643i	$-0.0523245\pi$
$198$	−1.28286	−	2.22198i	−0.0911691	−	0.157910i
$199$	−11.2568			−0.797976			−0.398988	−	0.916956i	$-0.630638\pi$
$199$	−11.2568			−0.797976			−0.398988	+	0.916956i	$0.630638\pi$
$200$	−0.500000	+	0.866025i	−0.0353553	+	0.0612372i
$201$	5.59173	−	9.68517i	0.394410	−	0.683139i
$202$	3.36507	−	5.82847i	0.236765	−	0.410090i
$203$	−17.0509	−	29.5331i	−1.19674	−	2.07282i
$204$	1.90879	+	3.30612i	0.133642	+	0.231475i
$205$	−3.87094	+	6.70466i	−0.270358	+	0.468274i
$206$	7.59310	−	13.1516i	0.529037	−	0.916318i
$207$	2.63693	−	4.56730i	0.183279	−	0.317449i
$208$	3.42566			0.237527
$209$	4.52728	+	7.84148i	0.313158	+	0.542406i
$210$	−2.44097	+	4.22788i	−0.168443	+	0.291752i
$211$	4.96829			0.342032			0.171016	−	0.985268i	$-0.445295\pi$
$211$	4.96829			0.342032			0.171016	+	0.985268i	$0.445295\pi$
$212$	−1.10945			−0.0761973
$213$	−0.0742379	+	0.128584i	−0.00508670	+	0.00881041i
$214$	16.7153			1.14263
$215$	−2.36673	−	4.09930i	−0.161410	−	0.279570i
$216$	1.00000			0.0680414
$217$	17.1610	+	29.7238i	1.16497	+	2.01778i
$218$	7.41676	+	12.8462i	0.502326	+	0.870055i
$219$	0.949480	+	1.64455i	0.0641599	+	0.111128i
$220$	−1.28286	+	2.22198i	−0.0864906	+	0.149806i
$221$	−13.0777			−0.879704
$222$	−3.11859	+	5.22249i	−0.209306	+	0.350511i
$223$	8.33364			0.558062			0.279031	−	0.960282i	$-0.409987\pi$
$223$	8.33364			0.558062			0.279031	+	0.960282i	$0.409987\pi$
$224$	−2.44097	+	4.22788i	−0.163094	+	0.282487i
$225$	−0.500000	−	0.866025i	−0.0333333	−	0.0577350i
$226$	1.78120	+	3.08513i	0.118484	+	0.205220i
$227$	−7.93417	−	13.7424i	−0.526610	−	0.912114i	−0.999519	−	0.0310036i	$-0.990130\pi$
$227$	−7.93417	−	13.7424i	−0.526610	−	0.912114i	0.472910	−	0.881111i	$-0.343204\pi$
$228$	−3.52904			−0.233717
$229$	7.06386	+	12.2350i	0.466793	+	0.808509i	0.999280	−	0.0379285i	$-0.0120759\pi$
$229$	7.06386	+	12.2350i	0.466793	+	0.808509i	−0.532487	+	0.846438i	$0.678743\pi$
$230$	−5.27386			−0.347748
$231$	−6.26286	+	10.8476i	−0.412066	+	0.713719i
$232$	6.98532			0.458609
$233$	19.6542			1.28759			0.643795	−	0.765198i	$-0.277359\pi$
$233$	19.6542			1.28759			0.643795	+	0.765198i	$0.277359\pi$
$234$	−1.71283	+	2.96671i	−0.111971	+	0.193940i
$235$	3.81191	+	6.60241i	0.248661	+	0.430694i
$236$	12.4077			0.807669
$237$	1.61859	−	2.80348i	0.105139	−	0.182105i
$238$	9.31860	−	16.1403i	0.604035	−	1.04622i
$239$	1.14959	−	1.99116i	0.0743611	−	0.128797i	−0.826447	−	0.563014i	$-0.809642\pi$
$239$	1.14959	−	1.99116i	0.0743611	−	0.128797i	0.900808	+	0.434217i	$0.142975\pi$
$240$	−0.500000	−	0.866025i	−0.0322749	−	0.0559017i
$241$	8.84042	+	15.3121i	0.569462	+	0.986337i	0.996619	+	0.0821593i	$0.0261816\pi$
$241$	8.84042	+	15.3121i	0.569462	+	0.986337i	−0.427158	+	0.904177i	$0.640485\pi$
$242$	2.20852	−	3.82528i	0.141969	−	0.245898i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−4.12045	+	7.13683i	−0.263785	+	0.456889i
$245$	16.8333			1.07544
$246$	−3.87094	−	6.70466i	−0.246802	−	0.427473i
$247$	6.04465	−	10.4696i	0.384612	−	0.666167i
$248$	−7.03041			−0.446432
$249$	−5.27993			−0.334602
$250$	−0.500000	+	0.866025i	−0.0316228	+	0.0547723i
$251$	7.50175			0.473506			0.236753	−	0.971570i	$-0.423917\pi$
$251$	7.50175			0.473506			0.236753	+	0.971570i	$0.423917\pi$
$252$	−2.44097	−	4.22788i	−0.153767	−	0.266332i
$253$	−13.5313			−0.850704
$254$	−4.76169	−	8.24748i	−0.298775	−	0.517493i
$255$	1.90879	+	3.30612i	0.119533	+	0.207037i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	8.27122	−	14.3262i	0.515944	−	0.893642i	−0.483884	−	0.875132i	$-0.660774\pi$
$257$	8.27122	−	14.3262i	0.515944	−	0.893642i	0.999829	−	0.0185098i	$-0.00589218\pi$
$258$	4.73346			0.294692
$259$	29.6924	+	0.437081i	1.84500	+	0.0271589i
$260$	3.42566			0.212450
$261$	−3.49266	+	6.04946i	−0.216190	+	0.374452i
$262$	6.48552	+	11.2332i	0.400677	+	0.693992i
$263$	−2.05418	−	3.55794i	−0.126666	−	0.219392i	0.795717	−	0.605669i	$-0.207094\pi$
$263$	−2.05418	−	3.55794i	−0.126666	−	0.219392i	−0.922383	+	0.386277i	$0.873761\pi$
$264$	−1.28286	−	2.22198i	−0.0789548	−	0.136754i
$265$	−1.10945			−0.0681530
$266$	8.61428	+	14.9204i	0.528175	+	0.914827i
$267$	3.93565			0.240858
$268$	5.59173	−	9.68517i	0.341569	−	0.591616i
$269$	−14.8704			−0.906663			−0.453332	−	0.891342i	$-0.649765\pi$
$269$	−14.8704			−0.906663			−0.453332	+	0.891342i	$0.649765\pi$
$270$	1.00000			0.0608581
$271$	−10.3059	+	17.8504i	−0.626041	+	1.08433i	0.362298	+	0.932062i	$0.381992\pi$
$271$	−10.3059	+	17.8504i	−0.626041	+	1.08433i	−0.988339	+	0.152272i	$0.951341\pi$
$272$	1.90879	+	3.30612i	0.115737	+	0.200463i
$273$	16.7239			1.01217
$274$	−4.75058	+	8.22825i	−0.286993	+	0.497087i
$275$	−1.28286	+	2.22198i	−0.0773596	+	0.133991i
$276$	2.63693	−	4.56730i	0.158725	−	0.274919i
$277$	−4.43931	−	7.68910i	−0.266732	−	0.461993i	0.701284	−	0.712882i	$-0.252611\pi$
$277$	−4.43931	−	7.68910i	−0.266732	−	0.461993i	−0.968016	+	0.250889i	$0.919277\pi$
$278$	−8.64215	−	14.9686i	−0.518322	−	0.897760i
$279$	3.51521	−	6.08852i	0.210450	−	0.364510i
$280$	−2.44097	+	4.22788i	−0.145876	+	0.252664i
$281$	8.83508	−	15.3028i	0.527057	−	0.912889i	−0.472446	−	0.881359i	$-0.656629\pi$
$281$	8.83508	−	15.3028i	0.527057	−	0.912889i	0.999503	−	0.0315293i	$-0.0100377\pi$
$282$	−7.62381			−0.453991
$283$	−12.5188	−	21.6831i	−0.744163	−	1.28893i	−0.950585	−	0.310466i	$-0.899515\pi$
$283$	−12.5188	−	21.6831i	−0.744163	−	1.28893i	0.206421	−	0.978463i	$-0.433818\pi$
$284$	−0.0742379	+	0.128584i	−0.00440521	+	0.00763004i
$285$	−3.52904			−0.209042
$286$	8.78931			0.519723
$287$	−18.8977	+	32.7317i	−1.11549	+	1.93209i
$288$	1.00000			0.0589256
$289$	1.21303	+	2.10103i	0.0713548	+	0.123590i
$290$	6.98532			0.410192
$291$	−6.18431	−	10.7115i	−0.362531	−	0.627922i
$292$	0.949480	+	1.64455i	0.0555641	+	0.0962399i
$293$	12.1940	+	21.1207i	0.712384	+	1.23388i	0.963960	+	0.266047i	$0.0857177\pi$
$293$	12.1940	+	21.1207i	0.712384	+	1.23388i	−0.251576	+	0.967837i	$0.580949\pi$
$294$	−8.41666	+	14.5781i	−0.490869	+	0.850211i
$295$	12.4077			0.722401
$296$	−3.11859	+	5.22249i	−0.181264	+	0.303551i
$297$	2.56573			0.148879
$298$	−9.37460	+	16.2373i	−0.543056	+	0.940600i
$299$	9.03323	+	15.6460i	0.522405	+	0.904832i
$300$	−0.500000	−	0.866025i	−0.0288675	−	0.0500000i
$301$	−11.5542	−	20.0125i	−0.665975	−	1.15350i
$302$	7.82091			0.450043
$303$	3.36507	+	5.82847i	0.193318	+	0.334837i
$304$	−3.52904			−0.202404
$305$	−4.12045	+	7.13683i	−0.235936	+	0.408654i
$306$	−3.81758			−0.218237
$307$	−3.01319			−0.171972			−0.0859859	−	0.996296i	$-0.527404\pi$
$307$	−3.01319			−0.171972			−0.0859859	+	0.996296i	$0.527404\pi$
$308$	−6.26286	+	10.8476i	−0.356859	+	0.618099i
$309$	7.59310	+	13.1516i	0.431957	+	0.748171i
$310$	−7.03041			−0.399301
$311$	−5.53163	+	9.58107i	−0.313670	+	0.543293i	−0.979154	−	0.203120i	$-0.934892\pi$
$311$	−5.53163	+	9.58107i	−0.313670	+	0.543293i	0.665484	+	0.746412i	$0.268225\pi$
$312$	−1.71283	+	2.96671i	−0.0969699	+	0.167957i
$313$	2.36907	−	4.10335i	0.133908	−	0.231935i	−0.791272	−	0.611465i	$-0.790581\pi$
$313$	2.36907	−	4.10335i	0.133908	−	0.231935i	0.925180	+	0.379529i	$0.123914\pi$
$314$	−9.48532	−	16.4291i	−0.535287	−	0.927145i
$315$	−2.44097	−	4.22788i	−0.137533	−	0.238214i
$316$	1.61859	−	2.80348i	0.0910526	−	0.157708i
$317$	−9.25268	+	16.0261i	−0.519682	+	0.900116i	0.480056	+	0.877238i	$0.340616\pi$
$317$	−9.25268	+	16.0261i	−0.519682	+	0.900116i	−0.999738	+	0.0228784i	$0.992717\pi$
$318$	0.554725	−	0.960812i	0.0311074	−	0.0538797i
$319$	17.9224			1.00346
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$	−8.35763	+	14.4758i	−0.466477	+	0.807962i
$322$	−25.7467			−1.43480
$323$	13.4724			0.749625
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	3.42566			0.190021
$326$	−4.62025	−	8.00251i	−0.255892	−	0.443218i
$327$	−14.8335			−0.820295
$328$	−3.87094	−	6.70466i	−0.213737	−	0.370203i
$329$	18.6095	+	32.2326i	1.02597	+	1.77704i
$330$	−1.28286	−	2.22198i	−0.0706193	−	0.122316i
$331$	9.36977	−	16.2289i	0.515009	−	0.892022i	−0.484839	−	0.874603i	$-0.661122\pi$
$331$	9.36977	−	16.2289i	0.515009	−	0.892022i	0.999848	−	0.0174184i	$-0.00554472\pi$
$332$	−5.27993			−0.289774
$333$	−2.96352	−	5.31202i	−0.162400	−	0.291097i
$334$	1.13379			0.0620384
$335$	5.59173	−	9.68517i	0.305509	−	0.529157i
$336$	−2.44097	−	4.22788i	−0.133166	−	0.230650i
$337$	−2.78434	−	4.82261i	−0.151672	−	0.262704i	0.780170	−	0.625568i	$-0.215133\pi$
$337$	−2.78434	−	4.82261i	−0.151672	−	0.262704i	−0.931842	+	0.362863i	$0.881799\pi$
$338$	0.632423	+	1.09539i	0.0343993	+	0.0595813i
$339$	−3.56240			−0.193483
$340$	1.90879	+	3.30612i	0.103519	+	0.179300i
$341$	−18.0381			−0.976819
$342$	1.76452	−	3.05624i	0.0954144	−	0.165263i
$343$	48.0056			2.59206
$344$	4.73346			0.255211
$345$	2.63693	−	4.56730i	0.141968	−	0.245895i
$346$	−1.33172	−	2.30661i	−0.0715937	−	0.124004i
$347$	−6.31601			−0.339061			−0.169531	−	0.985525i	$-0.554225\pi$
$347$	−6.31601			−0.339061			−0.169531	+	0.985525i	$0.554225\pi$
$348$	−3.49266	+	6.04946i	−0.187226	+	0.324285i
$349$	−12.7335	+	22.0550i	−0.681607	+	1.18058i	0.292884	+	0.956148i	$0.405385\pi$
$349$	−12.7335	+	22.0550i	−0.681607	+	1.18058i	−0.974490	+	0.224429i	$0.927948\pi$
$350$	−2.44097	+	4.22788i	−0.130475	+	0.225990i
$351$	−1.71283	−	2.96671i	−0.0914241	−	0.158351i
$352$	−1.28286	−	2.22198i	−0.0683768	−	0.118432i
$353$	−12.7151	+	22.0232i	−0.676757	+	1.17218i	0.299194	+	0.954192i	$0.403282\pi$
$353$	−12.7151	+	22.0232i	−0.676757	+	1.17218i	−0.975952	+	0.217986i	$0.930051\pi$
$354$	−6.20383	+	10.7453i	−0.329730	+	0.571109i
$355$	−0.0742379	+	0.128584i	−0.00394014	+	0.00682452i
$356$	3.93565			0.208589
$357$	9.31860	+	16.1403i	0.493193	+	0.854235i
$358$	1.96782	−	3.40837i	0.104003	−	0.180138i
$359$	10.0363			0.529695			0.264847	−	0.964290i	$-0.414678\pi$
$359$	10.0363			0.529695			0.264847	+	0.964290i	$0.414678\pi$
$360$	1.00000			0.0527046
$361$	3.27293	−	5.66888i	0.172260	−	0.298362i
$362$	24.7649			1.30162
$363$	2.20852	+	3.82528i	0.115917	+	0.200775i
$364$	16.7239			0.876569
$365$	0.949480	+	1.64455i	0.0496981	+	0.0860796i
$366$	−4.12045	−	7.13683i	−0.215379	−	0.373048i
$367$	−17.0803	−	29.5839i	−0.891584	−	1.54427i	−0.837977	−	0.545706i	$-0.816261\pi$
$367$	−17.0803	−	29.5839i	−0.891584	−	1.54427i	−0.0536072	−	0.998562i	$-0.517072\pi$
$368$	2.63693	−	4.56730i	0.137459	−	0.238087i
$369$	7.74187			0.403026
$370$	−3.11859	+	5.22249i	−0.162128	+	0.271504i
$371$	−5.41627			−0.281198
$372$	3.51521	−	6.08852i	0.182255	−	0.315675i
$373$	−11.2737	−	19.5265i	−0.583728	−	1.01105i	−0.995033	−	0.0995485i	$-0.968260\pi$
$373$	−11.2737	−	19.5265i	−0.583728	−	1.01105i	0.411305	−	0.911498i	$-0.365073\pi$
$374$	4.89744	+	8.48261i	0.253240	+	0.438625i
$375$	−0.500000	−	0.866025i	−0.0258199	−	0.0447214i
$376$	−7.62381			−0.393168
$377$	−11.9647	−	20.7234i	−0.616212	−	1.06731i
$378$	4.88194			0.251100
$379$	8.03626	−	13.9192i	0.412795	−	0.714982i	−0.582399	−	0.812903i	$-0.697886\pi$
$379$	8.03626	−	13.9192i	0.412795	−	0.714982i	0.995194	+	0.0979210i	$0.0312192\pi$
$380$	−3.52904			−0.181036
$381$	9.52337			0.487897
$382$	−8.68011	+	15.0344i	−0.444113	+	0.769226i
$383$	−9.58714	−	16.6054i	−0.489880	−	0.848497i	0.510052	−	0.860143i	$-0.329626\pi$
$383$	−9.58714	−	16.6054i	−0.489880	−	0.848497i	−0.999932	+	0.0116467i	$0.996293\pi$
$384$	1.00000			0.0510310
$385$	−6.26286	+	10.8476i	−0.319185	+	0.552844i
$386$	2.37773	−	4.11835i	0.121023	−	0.209619i
$387$	−2.36673	+	4.09930i	−0.120308	+	0.208379i
$388$	−6.18431	−	10.7115i	−0.313961	−	0.543796i
$389$	17.6057	+	30.4939i	0.892643	+	1.54610i	0.836695	+	0.547669i	$0.184485\pi$
$389$	17.6057	+	30.4939i	0.892643	+	1.54610i	0.0559478	+	0.998434i	$0.482182\pi$
$390$	−1.71283	+	2.96671i	−0.0867325	+	0.150225i
$391$	−10.0667	+	17.4360i	−0.509095	+	0.881778i
$392$	−8.41666	+	14.5781i	−0.425105	+	0.736304i
$393$	−12.9710			−0.654302
$394$	8.91235	+	15.4366i	0.448998	+	0.777687i
$395$	1.61859	−	2.80348i	0.0814400	−	0.141058i
$396$	2.56573			0.128933
$397$	−26.0599			−1.30791			−0.653955	−	0.756534i	$-0.726891\pi$
$397$	−26.0599			−1.30791			−0.653955	+	0.756534i	$0.726891\pi$
$398$	5.62842	−	9.74871i	0.282127	−	0.488658i
$399$	−17.2286			−0.862507
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	−14.8156			−0.739857			−0.369928	−	0.929060i	$-0.620618\pi$
$401$	−14.8156			−0.739857			−0.369928	+	0.929060i	$0.620618\pi$
$402$	5.59173	+	9.68517i	0.278890	+	0.483052i
$403$	12.0419	+	20.8572i	0.599850	+	1.03897i
$404$	3.36507	+	5.82847i	0.167418	+	0.289977i
$405$	−0.500000	+	0.866025i	−0.0248452	+	0.0430331i
$406$	34.1019			1.69245
$407$	−8.00144	+	13.3995i	−0.396617	+	0.664188i
$408$	−3.81758			−0.188999
$409$	15.4592	−	26.7761i	0.764409	−	1.32399i	−0.176150	−	0.984363i	$-0.556364\pi$
$409$	15.4592	−	26.7761i	0.764409	−	1.32399i	0.940559	−	0.339631i	$-0.110302\pi$
$410$	−3.87094	−	6.70466i	−0.191172	−	0.331119i
$411$	−4.75058	−	8.22825i	−0.234329	−	0.405870i
$412$	7.59310	+	13.1516i	0.374085	+	0.647935i
$413$	60.5734			2.98062
$414$	2.63693	+	4.56730i	0.129598	+	0.224470i
$415$	−5.27993			−0.259181
$416$	−1.71283	+	2.96671i	−0.0839784	+	0.145455i
$417$	17.2843			0.846416
$418$	−9.05456			−0.442873
$419$	13.2607	−	22.9683i	0.647830	−	1.12207i	−0.335811	−	0.941929i	$-0.609010\pi$
$419$	13.2607	−	22.9683i	0.647830	−	1.12207i	0.983640	−	0.180144i	$-0.0576564\pi$
$420$	−2.44097	−	4.22788i	−0.119107	−	0.206300i
$421$	4.62256			0.225290			0.112645	−	0.993635i	$-0.464068\pi$
$421$	4.62256			0.225290			0.112645	+	0.993635i	$0.464068\pi$
$422$	−2.48415	+	4.30267i	−0.120926	+	0.209451i
$423$	3.81191	−	6.60241i	0.185341	−	0.321020i
$424$	0.554725	−	0.960812i	0.0269398	−	0.0466611i
$425$	1.90879	+	3.30612i	0.0925900	+	0.160371i
$426$	−0.0742379	−	0.128584i	−0.00359684	−	0.00622990i
$427$	−20.1158	+	34.8416i	−0.973471	+	1.68610i
$428$	−8.35763	+	14.4758i	−0.403981	+	0.699716i
$429$	−4.39465	+	7.61176i	−0.212176	+	0.367499i
$430$	4.73346			0.228268
$431$	−18.2724	−	31.6487i	−0.880150	−	1.52446i	−0.851174	−	0.524884i	$-0.824109\pi$
$431$	−18.2724	−	31.6487i	−0.880150	−	1.52446i	−0.0289763	−	0.999580i	$-0.509225\pi$
$432$	−0.500000	+	0.866025i	−0.0240563	+	0.0416667i
$433$	13.1189			0.630455			0.315227	−	0.949016i	$-0.397919\pi$
$433$	13.1189			0.630455			0.315227	+	0.949016i	$0.397919\pi$
$434$	−34.3220			−1.64751
$435$	−3.49266	+	6.04946i	−0.167460	+	0.290050i
$436$	−14.8335			−0.710397
$437$	−9.30583	−	16.1182i	−0.445158	−	0.771037i
$438$	−1.89896			−0.0907359
$439$	−11.3980	−	19.7418i	−0.543995	−	0.942227i	−0.998669	−	0.0515693i	$-0.983578\pi$
$439$	−11.3980	−	19.7418i	−0.543995	−	0.942227i	0.454674	−	0.890658i	$-0.349756\pi$
$440$	−1.28286	−	2.22198i	−0.0611581	−	0.105929i
$441$	−8.41666	−	14.5781i	−0.400793	−	0.694194i
$442$	6.53887	−	11.3257i	0.311022	−	0.538707i
$443$	−27.5307			−1.30802			−0.654011	−	0.756485i	$-0.726915\pi$
$443$	−27.5307			−1.30802			−0.654011	+	0.756485i	$0.726915\pi$
$444$	−2.96352	−	5.31202i	−0.140642	−	0.252097i
$445$	3.93565			0.186567
$446$	−4.16682	+	7.21714i	−0.197305	+	0.341742i
$447$	−9.37460	−	16.2373i	−0.443403	−	0.767997i
$448$	−2.44097	−	4.22788i	−0.115325	−	0.199749i
$449$	−14.0644	−	24.3602i	−0.663738	−	1.14963i	−0.979626	−	0.200831i	$-0.935636\pi$
$449$	−14.0644	−	24.3602i	−0.663738	−	1.14963i	0.315888	−	0.948797i	$-0.397698\pi$
$450$	1.00000			0.0471405
$451$	−9.93176	−	17.2023i	−0.467668	−	0.810026i
$452$	−3.56240			−0.167561
$453$	−3.91045	+	6.77311i	−0.183729	+	0.318228i
$454$	15.8683			0.744738
$455$	16.7239			0.784027
$456$	1.76452	−	3.05624i	0.0826313	−	0.143122i
$457$	−15.7333	−	27.2508i	−0.735971	−	1.27474i	−0.954296	−	0.298863i	$-0.903393\pi$
$457$	−15.7333	−	27.2508i	−0.735971	−	1.27474i	0.218325	−	0.975876i	$-0.429941\pi$
$458$	−14.1277			−0.660145
$459$	1.90879	−	3.30612i	0.0890947	−	0.154317i
$460$	2.63693	−	4.56730i	0.122947	−	0.212951i
$461$	12.7579	−	22.0973i	0.594195	−	1.02918i	−0.399465	−	0.916748i	$-0.630804\pi$
$461$	12.7579	−	22.0973i	0.594195	−	1.02918i	0.993660	−	0.112427i	$-0.0358626\pi$
$462$	−6.26286	−	10.8476i	−0.291375	−	0.504675i
$463$	3.64907	+	6.32037i	0.169587	+	0.293733i	0.938275	−	0.345891i	$-0.112423\pi$
$463$	3.64907	+	6.32037i	0.169587	+	0.293733i	−0.768688	+	0.639624i	$0.779090\pi$
$464$	−3.49266	+	6.04946i	−0.162143	+	0.280839i
$465$	3.51521	−	6.08852i	0.163014	−	0.282348i
$466$	−9.82711	+	17.0211i	−0.455232	+	0.788485i
$467$	−3.19045			−0.147636			−0.0738181	−	0.997272i	$-0.523518\pi$
$467$	−3.19045			−0.147636			−0.0738181	+	0.997272i	$0.523518\pi$
$468$	−1.71283	−	2.96671i	−0.0791756	−	0.137136i
$469$	27.2985	−	47.2824i	1.26053	−	2.18330i
$470$	−7.62381			−0.351660
$471$	18.9706			0.874121
$472$	−6.20383	+	10.7453i	−0.285554	+	0.494594i
$473$	12.1448			0.558417
$474$	1.61859	+	2.80348i	0.0743442	+	0.128768i
$475$	−3.52904			−0.161924
$476$	9.31860	+	16.1403i	0.427117	+	0.739789i
$477$	0.554725	+	0.960812i	0.0253991	+	0.0439926i
$478$	1.14959	+	1.99116i	0.0525812	+	0.0910733i
$479$	9.05574	−	15.6850i	0.413767	−	0.716666i	−0.581531	−	0.813524i	$-0.697546\pi$
$479$	9.05574	−	15.6850i	0.413767	−	0.716666i	0.995298	+	0.0968582i	$0.0308793\pi$
$480$	1.00000			0.0456435
$481$	20.8352	+	0.306700i	0.950005	+	0.0139843i
$482$	−17.6808			−0.805340
$483$	12.8733	−	22.2973i	0.585757	−	1.01456i
$484$	2.20852	+	3.82528i	0.100387	+	0.173876i
$485$	−6.18431	−	10.7115i	−0.280815	−	0.486386i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	2.30387			0.104398			0.0521992	−	0.998637i	$-0.483377\pi$
$487$	2.30387			0.104398			0.0521992	+	0.998637i	$0.483377\pi$
$488$	−4.12045	−	7.13683i	−0.186524	−	0.323069i
$489$	9.24050			0.417870
$490$	−8.41666	+	14.5781i	−0.380226	+	0.658570i
$491$	−16.2912			−0.735214			−0.367607	−	0.929981i	$-0.619823\pi$
$491$	−16.2912			−0.735214			−0.367607	+	0.929981i	$0.619823\pi$
$492$	7.74187			0.349031
$493$	13.3335	−	23.0943i	0.600511	−	1.04012i
$494$	6.04465	+	10.4696i	0.271962	+	0.471051i
$495$	2.56573			0.115321
$496$	3.51521	−	6.08852i	0.157837	−	0.273382i
$497$	−0.362425	+	0.627738i	−0.0162570	+	0.0281579i
$498$	2.63996	−	4.57255i	0.118300	−	0.204901i
$499$	−20.9633	−	36.3095i	−0.938446	−	1.62544i	−0.768371	−	0.640005i	$-0.778932\pi$
$499$	−20.9633	−	36.3095i	−0.938446	−	1.62544i	−0.170075	−	0.985431i	$-0.554401\pi$
$500$	−0.500000	−	0.866025i	−0.0223607	−	0.0387298i
$501$	−0.566897	+	0.981894i	−0.0253271	+	0.0438678i
$502$	−3.75088	+	6.49671i	−0.167410	+	0.289962i
$503$	9.31778	−	16.1389i	0.415459	−	0.719597i	−0.580017	−	0.814604i	$-0.696954\pi$
$503$	9.31778	−	16.1389i	0.415459	−	0.719597i	0.995477	+	0.0950074i	$0.0302875\pi$
$504$	4.88194			0.217459
$505$	3.36507	+	5.82847i	0.149744	+	0.259363i
$506$	6.76564	−	11.7184i	0.300769	−	0.520948i
$507$	−1.26485			−0.0561737
$508$	9.52337			0.422531
$509$	11.2467	−	19.4799i	0.498501	−	0.863430i	−0.501497	−	0.865159i	$-0.667217\pi$
$509$	11.2467	−	19.4799i	0.498501	−	0.863430i	0.999999	+	0.00172960i	$0.000550550\pi$
$510$	−3.81758			−0.169045
$511$	4.63530	+	8.02858i	0.205054	+	0.355164i
$512$	1.00000			0.0441942
$513$	1.76452	+	3.05624i	0.0779055	+	0.134936i
$514$	8.27122	+	14.3262i	0.364828	+	0.631900i
$515$	7.59310	+	13.1516i	0.334592	+	0.579531i
$516$	−2.36673	+	4.09930i	−0.104190	+	0.180462i
$517$	−19.5606			−0.860275
$518$	−15.2247	+	25.4959i	−0.668937	+	1.12022i
$519$	2.66344			0.116912
$520$	−1.71283	+	2.96671i	−0.0751126	+	0.130099i
$521$	−0.220664	−	0.382201i	−0.00966747	−	0.0167445i	0.861151	−	0.508349i	$-0.169744\pi$
$521$	−0.220664	−	0.382201i	−0.00966747	−	0.0167445i	−0.870819	+	0.491604i	$0.836411\pi$
$522$	−3.49266	−	6.04946i	−0.152870	−	0.264778i
$523$	0.564880	+	0.978400i	0.0247005	+	0.0427825i	0.878111	−	0.478456i	$-0.158803\pi$
$523$	0.564880	+	0.978400i	0.0247005	+	0.0427825i	−0.853411	+	0.521239i	$0.825470\pi$
$524$	−12.9710			−0.566642
$525$	−2.44097	−	4.22788i	−0.106533	−	0.184520i
$526$	4.10836			0.179133
$527$	−13.4196	+	23.2434i	−0.584567	+	1.01250i
$528$	2.56573			0.111659
$529$	4.81359			0.209286
$530$	0.554725	−	0.960812i	0.0240957	−	0.0417350i
$531$	−6.20383	−	10.7453i	−0.269223	−	0.466308i
$532$	−17.2286			−0.746953
$533$	−13.2605	+	22.9679i	−0.574377	+	0.994850i
$534$	−1.96782	+	3.40837i	−0.0851560	+	0.147495i
$535$	−8.35763	+	14.4758i	−0.361332	+	0.625845i
$536$	5.59173	+	9.68517i	0.241526	+	0.418335i
$537$	1.96782	+	3.40837i	0.0849178	+	0.147082i
$538$	7.43519	−	12.8781i	0.320554	−	0.555215i
$539$	−21.5948	+	37.4034i	−0.930156	+	1.61108i
$540$	−0.500000	+	0.866025i	−0.0215166	+	0.0372678i
$541$	−37.3075			−1.60397			−0.801987	−	0.597342i	$-0.796223\pi$
$541$	−37.3075			−1.60397			−0.801987	+	0.597342i	$0.796223\pi$
$542$	−10.3059	−	17.8504i	−0.442678	−	0.766741i
$543$	−12.3825	+	21.4471i	−0.531382	+	0.920381i
$544$	−3.81758			−0.163678
$545$	−14.8335			−0.635398
$546$	−8.36193	+	14.4833i	−0.357858	+	0.619828i
$547$	−43.2027			−1.84722			−0.923608	−	0.383339i	$-0.874774\pi$
$547$	−43.2027			−1.84722			−0.923608	+	0.383339i	$0.874774\pi$
$548$	−4.75058	−	8.22825i	−0.202935	−	0.351494i
$549$	8.24090			0.351713
$550$	−1.28286	−	2.22198i	−0.0547015	−	0.0947457i
$551$	12.3257	+	21.3488i	0.525094	+	0.909490i
$552$	2.63693	+	4.56730i	0.112235	+	0.194397i
$553$	7.90184	−	13.6864i	0.336021	−	0.582005i
$554$	8.87861			0.377216
$555$	−2.96352	−	5.31202i	−0.125794	−	0.225483i
$556$	17.2843			0.733018
$557$	15.9445	−	27.6167i	0.675591	−	1.17016i	−0.300704	−	0.953717i	$-0.597222\pi$
$557$	15.9445	−	27.6167i	0.675591	−	1.17016i	0.976296	−	0.216441i	$-0.0694449\pi$
$558$	3.51521	+	6.08852i	0.148811	+	0.257747i
$559$	−8.10762	−	14.0428i	−0.342916	−	0.593947i
$560$	−2.44097	−	4.22788i	−0.103150	−	0.178661i
$561$	−9.79487			−0.413540
$562$	8.83508	+	15.3028i	0.372685	+	0.645510i
$563$	−29.4401			−1.24075			−0.620376	−	0.784304i	$-0.713020\pi$
$563$	−29.4401			−1.24075			−0.620376	+	0.784304i	$0.713020\pi$
$564$	3.81191	−	6.60241i	0.160510	−	0.278012i
$565$	−3.56240			−0.149871
$566$	25.0375			1.05241
$567$	−2.44097	+	4.22788i	−0.102511	+	0.177554i
$568$	−0.0742379	−	0.128584i	−0.00311495	−	0.00539525i
$569$	−18.0478			−0.756605			−0.378302	−	0.925682i	$-0.623492\pi$
$569$	−18.0478			−0.756605			−0.378302	+	0.925682i	$0.623492\pi$
$570$	1.76452	−	3.05624i	0.0739076	−	0.128012i
$571$	−13.2260	+	22.9081i	−0.553492	+	0.958676i	0.444527	+	0.895765i	$0.353372\pi$
$571$	−13.2260	+	22.9081i	−0.553492	+	0.958676i	−0.998019	+	0.0629105i	$0.979962\pi$
$572$	−4.39465	+	7.61176i	−0.183750	+	0.318264i
$573$	−8.68011	−	15.0344i	−0.362617	−	0.628071i
$574$	−18.8977	−	32.7317i	−0.788773	−	1.36620i
$575$	2.63693	−	4.56730i	0.109968	−	0.190469i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	11.8200	−	20.4728i	0.492072	−	0.852293i	−0.507886	−	0.861424i	$-0.669573\pi$
$577$	11.8200	−	20.4728i	0.492072	−	0.852293i	0.999958	+	0.00913057i	$0.00290639\pi$
$578$	−2.42606			−0.100911
$579$	2.37773	+	4.11835i	0.0988152	+	0.171153i
$580$	−3.49266	+	6.04946i	−0.145025	+	0.251190i
$581$	−25.7763			−1.06938
$582$	12.3686			0.512696
$583$	1.42327	−	2.46518i	0.0589459	−	0.102097i
$584$	−1.89896			−0.0785796
$585$	−1.71283	−	2.96671i	−0.0708168	−	0.122658i
$586$	−24.3881			−1.00746
$587$	−0.130182	−	0.225482i	−0.00537319	−	0.00930663i	0.863326	−	0.504646i	$-0.168377\pi$
$587$	−0.130182	−	0.225482i	−0.00537319	−	0.00930663i	−0.868699	+	0.495339i	$0.835044\pi$
$588$	−8.41666	−	14.5781i	−0.347097	−	0.601190i
$589$	−12.4053	−	21.4866i	−0.511152	−	0.885341i
$590$	−6.20383	+	10.7453i	−0.255407	+	0.442379i
$591$	−17.8247			−0.733210
$592$	−2.96352	−	5.31202i	−0.121800	−	0.218323i
$593$	−14.2025			−0.583229			−0.291614	−	0.956536i	$-0.594192\pi$
$593$	−14.2025			−0.583229			−0.291614	+	0.956536i	$0.594192\pi$
$594$	−1.28286	+	2.22198i	−0.0526365	+	0.0911691i
$595$	9.31860	+	16.1403i	0.382025	+	0.661687i
$596$	−9.37460	−	16.2373i	−0.383998	−	0.665105i
$597$	5.62842	+	9.74871i	0.230356	+	0.398988i
$598$	−18.0665			−0.738792
$599$	11.5280	+	19.9670i	0.471020	+	0.815831i	0.999451	−	0.0331458i	$-0.0105526\pi$
$599$	11.5280	+	19.9670i	0.471020	+	0.815831i	−0.528430	+	0.848977i	$0.677219\pi$
$600$	1.00000			0.0408248
$601$	−1.98910	+	3.44522i	−0.0811371	+	0.140534i	−0.903739	−	0.428085i	$-0.859188\pi$
$601$	−1.98910	+	3.44522i	−0.0811371	+	0.140534i	0.822602	+	0.568618i	$0.192522\pi$
$602$	23.1085			0.941831
$603$	−11.1835			−0.455426
$604$	−3.91045	+	6.77311i	−0.159114	+	0.275594i
$605$	2.20852	+	3.82528i	0.0897893	+	0.155520i
$606$	−6.73014			−0.273393
$607$	−14.6386	+	25.3548i	−0.594163	+	1.02912i	0.399501	+	0.916733i	$0.369183\pi$
$607$	−14.6386	+	25.3548i	−0.594163	+	1.02912i	−0.993664	+	0.112388i	$0.964150\pi$
$608$	1.76452	−	3.05624i	0.0715608	−	0.123947i
$609$	−17.0509	+	29.5331i	−0.690939	+	1.19674i
$610$	−4.12045	−	7.13683i	−0.166832	−	0.288962i
$611$	13.0583	+	22.6176i	0.528282	+	0.915011i
$612$	1.90879	−	3.30612i	0.0771583	−	0.133642i
$613$	15.1477	−	26.2366i	0.611810	−	1.05969i	−0.379125	−	0.925345i	$-0.623775\pi$
$613$	15.1477	−	26.2366i	0.611810	−	1.05969i	0.990935	−	0.134341i	$-0.0428917\pi$
$614$	1.50659	−	2.60950i	0.0608012	−	0.105311i
$615$	7.74187			0.312182
$616$	−6.26286	−	10.8476i	−0.252338	−	0.437062i
$617$	−0.839284	+	1.45368i	−0.0337883	+	0.0585230i	−0.882425	−	0.470453i	$-0.844091\pi$
$617$	−0.839284	+	1.45368i	−0.0337883	+	0.0585230i	0.848637	+	0.528976i	$0.177424\pi$
$618$	−15.1862			−0.610879
$619$	−6.18307			−0.248518			−0.124259	−	0.992250i	$-0.539655\pi$
$619$	−6.18307			−0.248518			−0.124259	+	0.992250i	$0.539655\pi$
$620$	3.51521	−	6.08852i	0.141174	−	0.244521i
$621$	−5.27386			−0.211633
$622$	−5.53163	−	9.58107i	−0.221798	−	0.384166i
$623$	19.2136			0.769776
$624$	−1.71283	−	2.96671i	−0.0685681	−	0.118763i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	2.36907	+	4.10335i	0.0946872	+	0.164003i
$627$	4.52728	−	7.84148i	0.180802	−	0.313158i
$628$	18.9706			0.757011
$629$	11.3135	+	20.2791i	0.451098	+	0.808580i
$630$	4.88194			0.194501
$631$	5.43027	−	9.40550i	0.216176	−	0.374427i	−0.737460	−	0.675391i	$-0.763975\pi$
$631$	5.43027	−	9.40550i	0.216176	−	0.374427i	0.953636	+	0.300964i	$0.0973083\pi$
$632$	1.61859	+	2.80348i	0.0643839	+	0.111516i
$633$	−2.48415	−	4.30267i	−0.0987360	−	0.171016i
$634$	−9.25268	−	16.0261i	−0.367471	−	0.636478i
$635$	9.52337			0.377924
$636$	0.554725	+	0.960812i	0.0219963	+	0.0380987i
$637$	57.6652			2.28478
$638$	−8.96121	+	15.5213i	−0.354778	+	0.614493i
$639$	0.148476			0.00587361
$640$	1.00000			0.0395285
$641$	−9.19772	+	15.9309i	−0.363288	+	0.629234i	−0.988500	−	0.151222i	$-0.951679\pi$
$641$	−9.19772	+	15.9309i	−0.363288	+	0.629234i	0.625212	+	0.780455i	$0.285013\pi$
$642$	−8.35763	−	14.4758i	−0.329849	−	0.571316i
$643$	18.7633			0.739952			0.369976	−	0.929041i	$-0.379366\pi$
$643$	18.7633			0.739952			0.369976	+	0.929041i	$0.379366\pi$
$644$	12.8733	−	22.2973i	0.507280	−	0.878635i
$645$	−2.36673	+	4.09930i	−0.0931899	+	0.161410i
$646$	−6.73620	+	11.6674i	−0.265032	+	0.459050i
$647$	2.50301	+	4.33535i	0.0984037	+	0.170440i	0.911024	−	0.412353i	$-0.135293\pi$
$647$	2.50301	+	4.33535i	0.0984037	+	0.170440i	−0.812620	+	0.582793i	$0.801960\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	−15.9173	+	27.5696i	−0.624809	+	1.08220i
$650$	−1.71283	+	2.96671i	−0.0671827	+	0.116364i
$651$	17.1610	−	29.7238i	0.672593	−	1.16497i
$652$	9.24050			0.361886
$653$	−8.80467	−	15.2501i	−0.344553	−	0.596784i	0.640719	−	0.767775i	$-0.278636\pi$
$653$	−8.80467	−	15.2501i	−0.344553	−	0.596784i	−0.985272	+	0.170992i	$0.945303\pi$
$654$	7.41676	−	12.8462i	0.290018	−	0.502326i
$655$	−12.9710			−0.506820
$656$	7.74187			0.302269
$657$	0.949480	−	1.64455i	0.0370428	−	0.0641599i
$658$	−37.2190			−1.45095
$659$	10.1395	+	17.5621i	0.394978	+	0.684122i	0.993098	−	0.117285i	$-0.0374190\pi$
$659$	10.1395	+	17.5621i	0.394978	+	0.684122i	−0.598121	+	0.801406i	$0.704086\pi$
$660$	2.56573			0.0998708
$661$	−4.00190	−	6.93149i	−0.155656	−	0.269604i	0.777642	−	0.628707i	$-0.216416\pi$
$661$	−4.00190	−	6.93149i	−0.155656	−	0.269604i	−0.933298	+	0.359104i	$0.883082\pi$
$662$	9.36977	+	16.2289i	0.364166	+	0.630754i
$663$	6.53887	+	11.3257i	0.253949	+	0.439852i
$664$	2.63996	−	4.57255i	0.102450	−	0.177449i
$665$	−17.2286			−0.668095
$666$	6.08210	+	0.0895303i	0.235677	+	0.00346923i
$667$	−36.8396			−1.42643
$668$	−0.566897	+	0.981894i	−0.0219339	+	0.0379906i
$669$	−4.16682	−	7.21714i	−0.161098	−	0.279031i
$670$	5.59173	+	9.68517i	0.216028	+	0.374171i
$671$	−10.5719	−	18.3112i	−0.408126	−	0.706894i
$672$	4.88194			0.188325
$673$	15.8927	+	27.5270i	0.612620	+	1.06109i	0.990797	+	0.135356i	$0.0432177\pi$
$673$	15.8927	+	27.5270i	0.612620	+	1.06109i	−0.378177	+	0.925733i	$0.623449\pi$
$674$	5.56867			0.214497
$675$	−0.500000	+	0.866025i	−0.0192450	+	0.0333333i
$676$	−1.26485			−0.0486479
$677$	42.7796			1.64415			0.822077	−	0.569376i	$-0.192815\pi$
$677$	42.7796			1.64415			0.822077	+	0.569376i	$0.192815\pi$
$678$	1.78120	−	3.08513i	0.0684066	−	0.118484i
$679$	−30.1914	−	52.2931i	−1.15864	−	2.00682i
$680$	−3.81758			−0.146398
$681$	−7.93417	+	13.7424i	−0.304038	+	0.526610i
$682$	9.01906	−	15.6215i	0.345358	−	0.598177i
$683$	10.3076	−	17.8533i	0.394409	−	0.683137i	−0.598616	−	0.801036i	$-0.704283\pi$
$683$	10.3076	−	17.8533i	0.394409	−	0.683137i	0.993026	+	0.117899i	$0.0376159\pi$
$684$	1.76452	+	3.05624i	0.0674681	+	0.116858i
$685$	−4.75058	−	8.22825i	−0.181511	−	0.314385i
$686$	−24.0028	+	41.5741i	−0.916432	+	1.58731i
$687$	7.06386	−	12.2350i	0.269503	−	0.466793i
$688$	−2.36673	+	4.09930i	−0.0902308	+	0.156284i
$689$	−3.80060			−0.144791
$690$	2.63693	+	4.56730i	0.100386	+	0.173874i
$691$	−4.09280	+	7.08894i	−0.155698	+	0.269676i	−0.933313	−	0.359064i	$-0.883096\pi$
$691$	−4.09280	+	7.08894i	−0.155698	+	0.269676i	0.777615	+	0.628740i	$0.216429\pi$
$692$	2.66344			0.101249
$693$	12.5257			0.475813
$694$	3.15800	−	5.46982i	0.119876	−	0.207632i
$695$	17.2843			0.655631
$696$	−3.49266	−	6.04946i	−0.132389	−	0.229304i
$697$	−29.5552			−1.11948
$698$	−12.7335	−	22.0550i	−0.481969	−	0.834794i
$699$	−9.82711	−	17.0211i	−0.371695	−	0.643795i
$700$	−2.44097	−	4.22788i	−0.0922599	−	0.159799i
$701$	11.2870	−	19.5497i	0.426305	−	0.738381i	−0.570237	−	0.821481i	$-0.693148\pi$
$701$	11.2870	−	19.5497i	0.426305	−	0.738381i	0.996541	+	0.0830991i	$0.0264818\pi$
$702$	3.42566			0.129293
$703$	−21.4640	−	0.315956i	−0.809530	−	0.0119165i
$704$	2.56573			0.0966994
$705$	3.81191	−	6.60241i	0.143565	−	0.248661i
$706$	−12.7151	−	22.0232i	−0.478540	−	0.828855i
$707$	16.4281	+	28.4542i	0.617840	+	1.07013i
$708$	−6.20383	−	10.7453i	−0.233154	−	0.403835i
$709$	−9.10816			−0.342064			−0.171032	−	0.985265i	$-0.554710\pi$
$709$	−9.10816			−0.342064			−0.171032	+	0.985265i	$0.554710\pi$
$710$	−0.0742379	−	0.128584i	−0.00278610	−	0.00482566i
$711$	−3.23717			−0.121404
$712$	−1.96782	+	3.40837i	−0.0737473	+	0.127734i
$713$	37.0774			1.38856
$714$	−18.6372			−0.697480
$715$	−4.39465	+	7.61176i	−0.164351	+	0.284664i
$716$	1.96782	+	3.40837i	0.0735410	+	0.127377i
$717$	−2.29919			−0.0858648
$718$	−5.01814	+	8.69168i	−0.187275	+	0.324370i
$719$	−18.0058	+	31.1870i	−0.671505	+	1.16308i	0.305973	+	0.952040i	$0.401018\pi$
$719$	−18.0058	+	31.1870i	−0.671505	+	1.16308i	−0.977477	+	0.211040i	$0.932315\pi$
$720$	−0.500000	+	0.866025i	−0.0186339	+	0.0322749i
$721$	37.0691	+	64.2055i	1.38052	+	2.39114i
$722$	3.27293	+	5.66888i	0.121806	+	0.210974i
$723$	8.84042	−	15.3121i	0.328779	−	0.569462i
$724$	−12.3825	+	21.4471i	−0.460191	+	0.797073i
$725$	−3.49266	+	6.04946i	−0.129714	+	0.224671i
$726$	−4.41705			−0.163932
$727$	23.4049	+	40.5385i	0.868040	+	1.50349i	0.863997	+	0.503498i	$0.167954\pi$
$727$	23.4049	+	40.5385i	0.868040	+	1.50349i	0.00404341	+	0.999992i	$0.498713\pi$
$728$	−8.36193	+	14.4833i	−0.309914	+	0.536786i
$729$	1.00000			0.0370370
$730$	−1.89896			−0.0702837
$731$	9.03519	−	15.6494i	0.334179	−	0.578814i
$732$	8.24090			0.304593
$733$	−0.0679345	−	0.117666i	−0.00250922	−	0.00434609i	0.864768	−	0.502171i	$-0.167465\pi$
$733$	−0.0679345	−	0.117666i	−0.00250922	−	0.00434609i	−0.867277	+	0.497825i	$0.834132\pi$
$734$	34.1606			1.26089
$735$	−8.41666	−	14.5781i	−0.310453	−	0.537720i
$736$	2.63693	+	4.56730i	0.0971985	+	0.168353i
$737$	14.3469	+	24.8495i	0.528473	+	0.915343i
$738$	−3.87094	+	6.70466i	−0.142491	+	0.246802i
$739$	43.6507			1.60572			0.802858	−	0.596170i	$-0.203311\pi$
$739$	43.6507			1.60572			0.802858	+	0.596170i	$0.203311\pi$
$740$	−2.96352	−	5.31202i	−0.108941	−	0.195274i
$741$	−12.0893			−0.444112
$742$	2.70813	−	4.69062i	0.0994187	−	0.172198i
$743$	−10.7362	−	18.5956i	−0.393873	−	0.682208i	0.599084	−	0.800686i	$-0.295532\pi$
$743$	−10.7362	−	18.5956i	−0.393873	−	0.682208i	−0.992957	+	0.118479i	$0.962198\pi$
$744$	3.51521	+	6.08852i	0.128874	+	0.223216i
$745$	−9.37460	−	16.2373i	−0.343459	−	0.594888i
$746$	22.5473			0.825516
$747$	2.63996	+	4.57255i	0.0965912	+	0.167301i
$748$	−9.79487			−0.358136
$749$	−40.8014	+	70.6701i	−1.49085	+	2.58223i
$750$	1.00000			0.0365148
$751$	−4.67310			−0.170524			−0.0852619	−	0.996359i	$-0.527173\pi$
$751$	−4.67310			−0.170524			−0.0852619	+	0.996359i	$0.527173\pi$
$752$	3.81191	−	6.60241i	0.139006	−	0.240765i
$753$	−3.75088	−	6.49671i	−0.136690	−	0.236753i
$754$	23.9293			0.871455
$755$	−3.91045	+	6.77311i	−0.142316	+	0.246499i
$756$	−2.44097	+	4.22788i	−0.0887772	+	0.153767i
$757$	−2.01848	+	3.49610i	−0.0733627	+	0.127068i	−0.900373	−	0.435119i	$-0.856706\pi$
$757$	−2.01848	+	3.49610i	−0.0733627	+	0.127068i	0.827010	+	0.562187i	$0.190040\pi$
$758$	8.03626	+	13.9192i	0.291890	+	0.505569i
$759$	6.76564	+	11.7184i	0.245577	+	0.425352i
$760$	1.76452	−	3.05624i	0.0640059	−	0.110861i
$761$	25.5733	−	44.2942i	0.927030	−	1.60566i	0.138767	−	0.990325i	$-0.455686\pi$
$761$	25.5733	−	44.2942i	0.927030	−	1.60566i	0.788263	−	0.615339i	$-0.210981\pi$
$762$	−4.76169	+	8.24748i	−0.172498	+	0.298775i
$763$	−72.4163			−2.62165
$764$	−8.68011	−	15.0344i	−0.314035	−	0.543925i
$765$	1.90879	−	3.30612i	0.0690125	−	0.119533i
$766$	19.1743			0.692795
$767$	42.5044			1.53475
$768$	−0.500000	+	0.866025i	−0.0180422	+	0.0312500i
$769$	0.0817392			0.00294759			0.00147380	−	0.999999i	$-0.499531\pi$
$769$	0.0817392			0.00294759			0.00147380	+	0.999999i	$0.499531\pi$
$770$	−6.26286	−	10.8476i	−0.225698	−	0.390920i
$771$	−16.5424			−0.595761
$772$	2.37773	+	4.11835i	0.0855765	+	0.148223i
$773$	10.5055	+	18.1961i	0.377857	+	0.654468i	0.990750	−	0.135698i	$-0.0433276\pi$
$773$	10.5055	+	18.1961i	0.377857	+	0.654468i	−0.612893	+	0.790166i	$0.709994\pi$
$774$	−2.36673	−	4.09930i	−0.0850704	−	0.147346i
$775$	3.51521	−	6.08852i	0.126270	−	0.218706i
$776$	12.3686			0.444008
$777$	−14.4677	−	25.9330i	−0.519026	−	0.930340i
$778$	−35.2113			−1.26239
$779$	13.6607	−	23.6610i	0.489445	−	0.847744i
$780$	−1.71283	−	2.96671i	−0.0613292	−	0.106225i
$781$	−0.190474	−	0.329911i	−0.00681570	−	0.0118051i
$782$	−10.0667	−	17.4360i	−0.359984	−	0.623511i
$783$	6.98532			0.249635
$784$	−8.41666	−	14.5781i	−0.300595	−	0.520646i
$785$	18.9706			0.677091
$786$	6.48552	−	11.2332i	0.231331	−	0.400677i
$787$	25.5483			0.910699			0.455349	−	0.890313i	$-0.349514\pi$
$787$	25.5483			0.910699			0.455349	+	0.890313i	$0.349514\pi$
$788$	−17.8247			−0.634979
$789$	−2.05418	+	3.55794i	−0.0731307	+	0.126666i
$790$	1.61859	+	2.80348i	0.0575868	+	0.0997432i
$791$	−17.3914			−0.618367
$792$	−1.28286	+	2.22198i	−0.0455846	+	0.0789548i
$793$	−14.1153	+	24.4484i	−0.501248	+	0.868187i
$794$	13.0300	−	22.5685i	0.462416	−	0.800928i
$795$	0.554725	+	0.960812i	0.0196741	+	0.0340765i
$796$	5.62842	+	9.74871i	0.199494	+	0.345534i
$797$	22.6074	−	39.1571i	0.800794	−	1.38702i	−0.118300	−	0.992978i	$-0.537745\pi$
$797$	22.6074	−	39.1571i	0.800794	−	1.38702i	0.919094	−	0.394038i	$-0.128922\pi$
$798$	8.61428	−	14.9204i	0.304942	−	0.528175i
$799$	−14.5523	+	25.2053i	−0.514822	+	0.891698i
$800$	1.00000			0.0353553
$801$	−1.96782	−	3.40837i	−0.0695296	−	0.120429i
$802$	7.40781	−	12.8307i	0.261579	−	0.453068i
$803$	−4.87221			−0.171937
$804$	−11.1835			−0.394410
$805$	12.8733	−	22.2973i	0.453725	−	0.785875i
$806$	−24.0838			−0.848316
$807$	7.43519	+	12.8781i	0.261731	+	0.453332i
$808$	−6.73014			−0.236765
$809$	−20.8705	−	36.1487i	−0.733767	−	1.27092i	−0.955262	−	0.295760i	$-0.904427\pi$
$809$	−20.8705	−	36.1487i	−0.733767	−	1.27092i	0.221496	−	0.975161i	$-0.428906\pi$
$810$	−0.500000	−	0.866025i	−0.0175682	−	0.0304290i
$811$	−25.8492	−	44.7721i	−0.907688	−	1.57216i	−0.817267	−	0.576259i	$-0.804512\pi$
$811$	−25.8492	−	44.7721i	−0.907688	−	1.57216i	−0.0904210	−	0.995904i	$-0.528821\pi$
$812$	−17.0509	+	29.5331i	−0.598371	+	1.03641i
$813$	20.6119			0.722890
$814$	−7.60357	−	13.6292i	−0.266505	−	0.477703i
$815$	9.24050			0.323681
$816$	1.90879	−	3.30612i	0.0668211	−	0.115737i
$817$	8.35229	+	14.4666i	0.292210	+	0.506122i
$818$	15.4592	+	26.7761i	0.540519	+	0.936206i
$819$	−8.36193	−	14.4833i	−0.292190	−	0.506087i
$820$	7.74187			0.270358
$821$	26.7602	+	46.3501i	0.933939	+	1.61763i	0.776515	+	0.630099i	$0.216986\pi$
$821$	26.7602	+	46.3501i	0.933939	+	1.61763i	0.157424	+	0.987531i	$0.449681\pi$
$822$	9.50117			0.331391
$823$	13.4697	−	23.3302i	0.469524	−	0.813239i	−0.529869	−	0.848079i	$-0.677759\pi$
$823$	13.4697	−	23.3302i	0.469524	−	0.813239i	0.999393	+	0.0348403i	$0.0110923\pi$
$824$	−15.1862			−0.529037
$825$	2.56573			0.0893271
$826$	−30.2867	+	52.4581i	−1.05381	+	1.82525i
$827$	22.3658	+	38.7387i	0.777736	+	1.34708i	0.933244	+	0.359243i	$0.116965\pi$
$827$	22.3658	+	38.7387i	0.777736	+	1.34708i	−0.155508	+	0.987835i	$0.549702\pi$
$828$	−5.27386			−0.183279
$829$	14.9286	−	25.8571i	0.518491	−	0.898052i	−0.481278	−	0.876568i	$-0.659827\pi$
$829$	14.9286	−	25.8571i	0.518491	−	0.898052i	0.999769	−	0.0214846i	$-0.00683930\pi$
$830$	2.63996	−	4.57255i	0.0916345	−	0.158716i
$831$	−4.43931	+	7.68910i	−0.153998	+	0.266732i
$832$	−1.71283	−	2.96671i	−0.0593817	−	0.102852i
$833$	32.1313	+	55.6530i	1.11328	+	1.92826i
$834$	−8.64215	+	14.9686i	−0.299253	+	0.518322i
$835$	−0.566897	+	0.981894i	−0.0196183	+	0.0339799i
$836$	4.52728	−	7.84148i	0.156579	−	0.271203i
$837$	−7.03041			−0.243007
$838$	13.2607	+	22.9683i	0.458085	+	0.793426i
$839$	17.1836	−	29.7629i	0.593244	−	1.02753i	−0.400548	−	0.916276i	$-0.631180\pi$
$839$	17.1836	−	29.7629i	0.593244	−	1.02753i	0.993792	−	0.111254i	$-0.0354866\pi$
$840$	4.88194			0.168443
$841$	19.7947			0.682575
$842$	−2.31128	+	4.00325i	−0.0796519	+	0.137961i
$843$	−17.6702			−0.608593
$844$	−2.48415	−	4.30267i	−0.0855079	−	0.148104i
$845$	−1.26485			−0.0435120
$846$	3.81191	+	6.60241i	0.131056	+	0.226996i
$847$	10.7819	+	18.6748i	0.370470	+	0.641672i
$848$	0.554725	+	0.960812i	0.0190493	+	0.0329944i
$849$	−12.5188	+	21.6831i	−0.429643	+	0.744163i
$850$	−3.81758			−0.130942
$851$	16.4470	−	27.5427i	0.563796	−	0.944151i
$852$	0.148476			0.00508670
$853$	−12.4418	+	21.5498i	−0.425999	+	0.737851i	−0.996513	−	0.0834363i	$-0.973410\pi$
$853$	−12.4418	+	21.5498i	−0.425999	+	0.737851i	0.570515	+	0.821288i	$0.306744\pi$
$854$	−20.1158	−	34.8416i	−0.688348	−	1.19225i
$855$	1.76452	+	3.05624i	0.0603453	+	0.104521i
$856$	−8.35763	−	14.4758i	−0.285658	−	0.494774i
$857$	−28.8779			−0.986450			−0.493225	−	0.869902i	$-0.664182\pi$
$857$	−28.8779			−0.986450			−0.493225	+	0.869902i	$0.664182\pi$
$858$	−4.39465	−	7.61176i	−0.150031	−	0.259861i
$859$	−49.0319			−1.67295			−0.836474	−	0.548007i	$-0.815387\pi$
$859$	−49.0319			−1.67295			−0.836474	+	0.548007i	$0.815387\pi$
$860$	−2.36673	+	4.09930i	−0.0807049	+	0.139785i
$861$	37.7953			1.28806
$862$	36.5448			1.24472
$863$	−23.3596	+	40.4601i	−0.795171	+	1.37728i	0.127560	+	0.991831i	$0.459286\pi$
$863$	−23.3596	+	40.4601i	−0.795171	+	1.37728i	−0.922731	+	0.385445i	$0.874048\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$	2.66344			0.0905596
$866$	−6.55946	+	11.3613i	−0.222899	+	0.386073i
$867$	1.21303	−	2.10103i	0.0411967	−	0.0713548i
$868$	17.1610	−	29.7238i	0.582483	−	1.00889i
$869$	4.15285	+	7.19295i	0.140876	+	0.244004i
$870$	−3.49266	−	6.04946i	−0.118412	−	0.205096i
$871$	19.1554	−	33.1781i	0.649055	−	1.12420i
$872$	7.41676	−	12.8462i	0.251163	−	0.435027i
$873$	−6.18431	+	10.7115i	−0.209307	+	0.362531i
$874$	18.6117			0.629549
$875$	−2.44097	−	4.22788i	−0.0825198	−	0.142928i
$876$	0.949480	−	1.64455i	0.0320800	−	0.0555641i
$877$	−53.9436			−1.82155			−0.910773	−	0.412907i	$-0.864513\pi$
$877$	−53.9436			−1.82155			−0.910773	+	0.412907i	$0.864513\pi$
$878$	22.7959			0.769325
$879$	12.1940	−	21.1207i	0.411295	−	0.712384i
$880$	2.56573			0.0864906
$881$	19.2851	+	33.4027i	0.649731	+	1.12537i	0.983187	+	0.182601i	$0.0584518\pi$
$881$	19.2851	+	33.4027i	0.649731	+	1.12537i	−0.333456	+	0.942766i	$0.608215\pi$
$882$	16.8333			0.566807
$883$	15.5179	+	26.8778i	0.522220	+	0.904511i	0.999666	+	0.0258499i	$0.00822919\pi$
$883$	15.5179	+	26.8778i	0.522220	+	0.904511i	−0.477446	+	0.878661i	$0.658437\pi$
$884$	6.53887	+	11.3257i	0.219926	+	0.380923i
$885$	−6.20383	−	10.7453i	−0.208539	−	0.361201i
$886$	13.7653	−	23.8423i	0.462456	−	0.800997i
$887$	−21.8318			−0.733039			−0.366519	−	0.930410i	$-0.619451\pi$
$887$	−21.8318			−0.733039			−0.366519	+	0.930410i	$0.619451\pi$
$888$	6.08210	+	0.0895303i	0.204102	+	0.00300444i
$889$	46.4925			1.55931
$890$	−1.96782	+	3.40837i	−0.0659616	+	0.114249i
$891$	−1.28286	−	2.22198i	−0.0429775	−	0.0744393i
$892$	−4.16682	−	7.21714i	−0.139515	−	0.241648i
$893$	−13.4524	−	23.3002i	−0.450166	−	0.779711i
$894$	18.7492			0.627067
$895$	1.96782	+	3.40837i	0.0657771	+	0.113929i
$896$	4.88194			0.163094
$897$	9.03323	−	15.6460i	0.301611	−	0.522405i
$898$	28.1287			0.938667
$899$	−49.1097			−1.63790
$900$	−0.500000	+	0.866025i	−0.0166667	+	0.0288675i
$901$	−2.11771	−	3.66798i	−0.0705511	−	0.122198i
$902$	19.8635			0.661383
$903$	−11.5542	+	20.0125i	−0.384501	+	0.665975i
$904$	1.78120	−	3.08513i	0.0592418	−	0.102610i
$905$	−12.3825	+	21.4471i	−0.411607	+	0.712924i
$906$	−3.91045	−	6.77311i	−0.129916	−	0.225021i
$907$	18.8109	+	32.5814i	0.624605	+	1.08185i	0.988617	+	0.150453i	$0.0480732\pi$
$907$	18.8109	+	32.5814i	0.624605	+	1.08185i	−0.364013	+	0.931394i	$0.618594\pi$
$908$	−7.93417	+	13.7424i	−0.263305	+	0.456057i
$909$	3.36507	−	5.82847i	0.111612	−	0.193318i
$910$	−8.36193	+	14.4833i	−0.277195	+	0.480116i
$911$	5.15051			0.170644			0.0853220	−	0.996353i	$-0.472808\pi$
$911$	5.15051			0.170644			0.0853220	+	0.996353i	$0.472808\pi$
$912$	1.76452	+	3.05624i	0.0584291	+	0.101202i
$913$	6.77343	−	11.7319i	0.224168	−	0.388270i
$914$	31.4665			1.04082
$915$	8.24090			0.272436
$916$	7.06386	−	12.2350i	0.233397	−	0.404255i
$917$	−63.3238			−2.09114
$918$	1.90879	+	3.30612i	0.0629995	+	0.109118i
$919$	46.2365			1.52520			0.762600	−	0.646870i	$-0.223922\pi$
$919$	46.2365			1.52520			0.762600	+	0.646870i	$0.223922\pi$
$920$	2.63693	+	4.56730i	0.0869370	+	0.150579i
$921$	1.50659	+	2.60950i	0.0496440	+	0.0859859i
$922$	12.7579	+	22.0973i	0.420159	+	0.727737i
$923$	−0.254314	+	0.440484i	−0.00837084	+	0.0144987i
$924$	12.5257			0.412066
$925$	−2.96352	−	5.31202i	−0.0974398	−	0.174658i
$926$	−7.29814			−0.239832
$927$	7.59310	−	13.1516i	0.249390	−	0.431957i
$928$	−3.49266	−	6.04946i	−0.114652	−	0.198583i
$929$	9.51554	+	16.4814i	0.312195	+	0.540737i	0.978837	−	0.204640i	$-0.0656025\pi$
$929$	9.51554	+	16.4814i	0.312195	+	0.540737i	−0.666642	+	0.745378i	$0.732269\pi$
$930$	3.51521	+	6.08852i	0.115268	+	0.199650i
$931$	−59.4055			−1.94694
$932$	−9.82711	−	17.0211i	−0.321898	−	0.557543i
$933$	11.0633			0.362195
$934$	1.59522	−	2.76301i	0.0521973	−	0.0904084i
$935$	−9.79487			−0.320327
$936$	3.42566			0.111971
$937$	−14.4109	+	24.9604i	−0.470783	+	0.815420i	−0.999442	−	0.0334143i	$-0.989362\pi$
$937$	−14.4109	+	24.9604i	−0.470783	+	0.815420i	0.528658	+	0.848835i	$0.322695\pi$
$938$	27.2985	+	47.2824i	0.891327	+	1.54382i
$939$	−4.73814			−0.154624
$940$	3.81191	−	6.60241i	0.124331	−	0.215347i
$941$	6.91476	−	11.9767i	0.225415	−	0.390430i	−0.731029	−	0.682346i	$-0.760960\pi$
$941$	6.91476	−	11.9767i	0.225415	−	0.390430i	0.956444	+	0.291917i	$0.0942930\pi$
$942$	−9.48532	+	16.4291i	−0.309048	+	0.535287i
$943$	20.4148	+	35.3594i	0.664796	+	1.15146i
$944$	−6.20383	−	10.7453i	−0.201917	−	0.349731i
$945$	−2.44097	+	4.22788i	−0.0794047	+	0.137533i
$946$	−6.07238	+	10.5177i	−0.197430	+	0.341959i
$947$	−6.87515	+	11.9081i	−0.223412	+	0.386962i	−0.955842	−	0.293881i	$-0.905053\pi$
$947$	−6.87515	+	11.9081i	−0.223412	+	0.386962i	0.732430	+	0.680843i	$0.238386\pi$
$948$	−3.23717			−0.105139
$949$	3.25260	+	5.63367i	0.105584	+	0.182877i
$950$	1.76452	−	3.05624i	0.0572486	−	0.0991575i
$951$	18.5054			0.600078
$952$	−18.6372			−0.604035
$953$	18.0267	−	31.2231i	0.583941	−	1.01142i	−0.411065	−	0.911606i	$-0.634843\pi$
$953$	18.0267	−	31.2231i	0.583941	−	1.01142i	0.995006	−	0.0998102i	$-0.0318236\pi$
$954$	−1.10945			−0.0359198
$955$	−8.68011	−	15.0344i	−0.280882	−	0.486501i
$956$	−2.29919			−0.0743611
$957$	−8.96121	−	15.5213i	−0.289675	−	0.501731i
$958$	9.05574	+	15.6850i	0.292578	+	0.506760i
$959$	−23.1921	−	40.1698i	−0.748911	−	1.29715i
$960$	−0.500000	+	0.866025i	−0.0161374	+	0.0279508i
$961$	18.4267			0.594410
$962$	−10.6832	+	17.8905i	−0.344441	+	0.576812i
$963$	16.7153			0.538641
$964$	8.84042	−	15.3121i	0.284731	−	0.493168i
$965$	2.37773	+	4.11835i	0.0765419	+	0.132574i
$966$	12.8733	+	22.2973i	0.414192	+	0.717402i
$967$	9.30646	+	16.1193i	0.299276	+	0.518361i	0.975970	−	0.217903i	$-0.0699217\pi$
$967$	9.30646	+	16.1193i	0.299276	+	0.518361i	−0.676695	+	0.736264i	$0.736588\pi$
$968$	−4.41705			−0.141969
$969$	−6.73620	−	11.6674i	−0.216398	−	0.374812i
$970$	12.3686			0.397133
$971$	−4.25675	+	7.37290i	−0.136605	+	0.236608i	−0.926210	−	0.377009i	$-0.876953\pi$
$971$	−4.25675	+	7.37290i	−0.136605	+	0.236608i	0.789604	+	0.613617i	$0.210286\pi$
$972$	1.00000			0.0320750
$973$	84.3809			2.70513
$974$	−1.15194	+	1.99521i	−0.0369104	+	0.0639307i
$975$	−1.71283	−	2.96671i	−0.0548545	−	0.0950107i
$976$	8.24090			0.263785
$977$	−6.03404	+	10.4513i	−0.193046	+	0.334366i	−0.946258	−	0.323412i	$-0.895170\pi$
$977$	−6.03404	+	10.4513i	−0.193046	+	0.334366i	0.753212	+	0.657778i	$0.228503\pi$
$978$	−4.62025	+	8.00251i	−0.147739	+	0.255892i
$979$	−5.04889	+	8.74494i	−0.161363	+	0.279490i
$980$	−8.41666	−	14.5781i	−0.268860	−	0.465680i
$981$	7.41676	+	12.8462i	0.236799	+	0.410148i
$982$	8.14562	−	14.1086i	0.259937	−	0.450224i
$983$	23.4261	−	40.5753i	0.747178	−	1.29415i	−0.201993	−	0.979387i	$-0.564742\pi$
$983$	23.4261	−	40.5753i	0.747178	−	1.29415i	0.949170	−	0.314763i	$-0.101925\pi$
$984$	−3.87094	+	6.70466i	−0.123401	+	0.213737i
$985$	−17.8247			−0.567942
$986$	13.3335	+	23.0943i	0.424626	+	0.735473i
$987$	18.6095	−	32.2326i	0.592346	−	1.02597i
$988$	−12.0893			−0.384612
$989$	−24.9636			−0.793797
$990$	−1.28286	+	2.22198i	−0.0407721	+	0.0706193i
$991$	1.97369			0.0626962			0.0313481	−	0.999509i	$-0.490020\pi$
$991$	1.97369			0.0626962			0.0313481	+	0.999509i	$0.490020\pi$
$992$	3.51521	+	6.08852i	0.111608	+	0.193311i
$993$	−18.7395			−0.594681
$994$	−0.362425	−	0.627738i	−0.0114954	−	0.0199106i
$995$	5.62842	+	9.74871i	0.178433	+	0.309055i
$996$	2.63996	+	4.57255i	0.0836505	+	0.144887i
$997$	−19.4368	+	33.6656i	−0.615571	+	1.06620i	0.374713	+	0.927141i	$0.377741\pi$
$997$	−19.4368	+	33.6656i	−0.615571	+	1.06620i	−0.990284	+	0.139059i	$0.955592\pi$
$998$	41.9266			1.32716
$999$	−3.11859	+	5.22249i	−0.0986677	+	0.165232i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.i.p.121.1	✓	10
37.26	even	3	inner	1110.2.i.p.211.1	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.i.p.121.1	✓	10	1.1	even	1	trivial
1110.2.i.p.211.1	yes	10	37.26	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +1.00000 q^{6} +(-2.44097 - 4.22788i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +1.00000 q^{6} +(-2.44097 - 4.22788i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +1.00000 q^{10} +2.56573 q^{11} +(-0.500000 + 0.866025i) q^{12} +(-1.71283 - 2.96671i) q^{13} +4.88194 q^{14} +(-0.500000 + 0.866025i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.90879 - 3.30612i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(1.76452 + 3.05624i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(-2.44097 + 4.22788i) q^{21} +(-1.28286 + 2.22198i) q^{22} -5.27386 q^{23} +(-0.500000 - 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} +3.42566 q^{26} +1.00000 q^{27} +(-2.44097 + 4.22788i) q^{28} +6.98532 q^{29} +(-0.500000 - 0.866025i) q^{30} -7.03041 q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.28286 - 2.22198i) q^{33} +(1.90879 + 3.30612i) q^{34} +(-2.44097 + 4.22788i) q^{35} +1.00000 q^{36} +(-3.11859 + 5.22249i) q^{37} -3.52904 q^{38} +(-1.71283 + 2.96671i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(-3.87094 - 6.70466i) q^{41} +(-2.44097 - 4.22788i) q^{42} +4.73346 q^{43} +(-1.28286 - 2.22198i) q^{44} +1.00000 q^{45} +(2.63693 - 4.56730i) q^{46} -7.62381 q^{47} +1.00000 q^{48} +(-8.41666 + 14.5781i) q^{49} +(-0.500000 - 0.866025i) q^{50} -3.81758 q^{51} +(-1.71283 + 2.96671i) q^{52} +(0.554725 - 0.960812i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-1.28286 - 2.22198i) q^{55} +(-2.44097 - 4.22788i) q^{56} +(1.76452 - 3.05624i) q^{57} +(-3.49266 + 6.04946i) q^{58} +(-6.20383 + 10.7453i) q^{59} +1.00000 q^{60} +(-4.12045 - 7.13683i) q^{61} +(3.51521 - 6.08852i) q^{62} +4.88194 q^{63} +1.00000 q^{64} +(-1.71283 + 2.96671i) q^{65} +2.56573 q^{66} +(5.59173 + 9.68517i) q^{67} -3.81758 q^{68} +(2.63693 + 4.56730i) q^{69} +(-2.44097 - 4.22788i) q^{70} +(-0.0742379 - 0.128584i) q^{71} +(-0.500000 + 0.866025i) q^{72} -1.89896 q^{73} +(-2.96352 - 5.31202i) q^{74} +1.00000 q^{75} +(1.76452 - 3.05624i) q^{76} +(-6.26286 - 10.8476i) q^{77} +(-1.71283 - 2.96671i) q^{78} +(1.61859 + 2.80348i) q^{79} +1.00000 q^{80} +(-0.500000 - 0.866025i) q^{81} +7.74187 q^{82} +(2.63996 - 4.57255i) q^{83} +4.88194 q^{84} -3.81758 q^{85} +(-2.36673 + 4.09930i) q^{86} +(-3.49266 - 6.04946i) q^{87} +2.56573 q^{88} +(-1.96782 + 3.40837i) q^{89} +(-0.500000 + 0.866025i) q^{90} +(-8.36193 + 14.4833i) q^{91} +(2.63693 + 4.56730i) q^{92} +(3.51521 + 6.08852i) q^{93} +(3.81191 - 6.60241i) q^{94} +(1.76452 - 3.05624i) q^{95} +(-0.500000 + 0.866025i) q^{96} +12.3686 q^{97} +(-8.41666 - 14.5781i) q^{98} +(-1.28286 + 2.22198i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 5 q^{2} - 5 q^{3} - 5 q^{4} - 5 q^{5} + 10 q^{6} + 10 q^{8} - 5 q^{9}+O(q^{10}) \) 10 * q - 5 * q^2 - 5 * q^3 - 5 * q^4 - 5 * q^5 + 10 * q^6 + 10 * q^8 - 5 * q^9	\( 10 q - 5 q^{2} - 5 q^{3} - 5 q^{4} - 5 q^{5} + 10 q^{6} + 10 q^{8} - 5 q^{9} + 10 q^{10} - 2 q^{11} - 5 q^{12} + q^{13} - 5 q^{15} - 5 q^{16} - 5 q^{18} - 2 q^{19} - 5 q^{20} + q^{22} - 2 q^{23} - 5 q^{24} - 5 q^{25} - 2 q^{26} + 10 q^{27} + 18 q^{29} - 5 q^{30} - 14 q^{31} - 5 q^{32} + q^{33} + 10 q^{36} + 4 q^{38} + q^{39} - 5 q^{40} - 10 q^{41} + 6 q^{43} + q^{44} + 10 q^{45} + q^{46} + 30 q^{47} + 10 q^{48} - 11 q^{49} - 5 q^{50} + q^{52} - 2 q^{53} - 5 q^{54} + q^{55} - 2 q^{57} - 9 q^{58} - 7 q^{59} + 10 q^{60} - 6 q^{61} + 7 q^{62} + 10 q^{64} + q^{65} - 2 q^{66} - 5 q^{67} + q^{69} + 3 q^{71} - 5 q^{72} - 18 q^{73} - 3 q^{74} + 10 q^{75} - 2 q^{76} - 32 q^{77} + q^{78} - 15 q^{79} + 10 q^{80} - 5 q^{81} + 20 q^{82} - 5 q^{83} - 3 q^{86} - 9 q^{87} - 2 q^{88} - 25 q^{89} - 5 q^{90} - 18 q^{91} + q^{92} + 7 q^{93} - 15 q^{94} - 2 q^{95} - 5 q^{96} + 6 q^{97} - 11 q^{98} + q^{99}+O(q^{100}) \) 10 * q - 5 * q^2 - 5 * q^3 - 5 * q^4 - 5 * q^5 + 10 * q^6 + 10 * q^8 - 5 * q^9 + 10 * q^10 - 2 * q^11 - 5 * q^12 + q^13 - 5 * q^15 - 5 * q^16 - 5 * q^18 - 2 * q^19 - 5 * q^20 + q^22 - 2 * q^23 - 5 * q^24 - 5 * q^25 - 2 * q^26 + 10 * q^27 + 18 * q^29 - 5 * q^30 - 14 * q^31 - 5 * q^32 + q^33 + 10 * q^36 + 4 * q^38 + q^39 - 5 * q^40 - 10 * q^41 + 6 * q^43 + q^44 + 10 * q^45 + q^46 + 30 * q^47 + 10 * q^48 - 11 * q^49 - 5 * q^50 + q^52 - 2 * q^53 - 5 * q^54 + q^55 - 2 * q^57 - 9 * q^58 - 7 * q^59 + 10 * q^60 - 6 * q^61 + 7 * q^62 + 10 * q^64 + q^65 - 2 * q^66 - 5 * q^67 + q^69 + 3 * q^71 - 5 * q^72 - 18 * q^73 - 3 * q^74 + 10 * q^75 - 2 * q^76 - 32 * q^77 + q^78 - 15 * q^79 + 10 * q^80 - 5 * q^81 + 20 * q^82 - 5 * q^83 - 3 * q^86 - 9 * q^87 - 2 * q^88 - 25 * q^89 - 5 * q^90 - 18 * q^91 + q^92 + 7 * q^93 - 15 * q^94 - 2 * q^95 - 5 * q^96 + 6 * q^97 - 11 * q^98 + q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more