LMFDB - Embedded newform 1110.2.x.d.841.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(751,1110)]

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, 5]))

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

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

chi := DirichletCharacter("1110.751");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.x (of order $6$, 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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 60x^{14} + 1362x^{12} + 15028x^{10} + 86441x^{8} + 260376x^{6} + 382684x^{4} + 224224x^{2} + 38416 $ x^16 + 60x^14 + 1362x^12 + 15028x^10 + 86441x^8 + 260376x^6 + 382684x^4 + 224224*x^2 + 38416
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			841.4
Root			$-1.68974i$ of defining polynomial
Character	$\chi$	$=$	1110.841
Dual form			1110.2.x.d.751.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} +1.00000i q^{6} +(0.844871 + 1.46336i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} +1.00000i q^{6} +(0.844871 + 1.46336i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +1.00000 q^{10} -3.20374 q^{11} +(0.500000 - 0.866025i) q^{12} +(3.91698 - 2.26147i) q^{13} -1.68974i q^{14} +(0.866025 + 0.500000i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.32938 - 1.34487i) q^{17} +(0.866025 - 0.500000i) q^{18} +(-2.29583 + 1.32550i) q^{19} +(-0.866025 - 0.500000i) q^{20} +(0.844871 - 1.46336i) q^{21} +(2.77452 + 1.60187i) q^{22} +6.25499i q^{23} +(-0.866025 + 0.500000i) q^{24} +(0.500000 - 0.866025i) q^{25} -4.52294 q^{26} +1.00000 q^{27} +(-0.844871 + 1.46336i) q^{28} -6.29373i q^{29} +(-0.500000 - 0.866025i) q^{30} -2.13231i q^{31} +(0.866025 - 0.500000i) q^{32} +(1.60187 + 2.77452i) q^{33} +(1.34487 + 2.32938i) q^{34} +(-1.46336 - 0.844871i) q^{35} -1.00000 q^{36} +(-6.07812 - 0.237625i) q^{37} +2.65100 q^{38} +(-3.91698 - 2.26147i) q^{39} +(0.500000 + 0.866025i) q^{40} +(-5.65066 - 9.78723i) q^{41} +(-1.46336 + 0.844871i) q^{42} -4.12268i q^{43} +(-1.60187 - 2.77452i) q^{44} -1.00000i q^{45} +(3.12749 - 5.41698i) q^{46} -8.83821 q^{47} +1.00000 q^{48} +(2.07239 - 3.58948i) q^{49} +(-0.866025 + 0.500000i) q^{50} +2.68974i q^{51} +(3.91698 + 2.26147i) q^{52} +(-6.84663 + 11.8587i) q^{53} +(-0.866025 - 0.500000i) q^{54} +(2.77452 - 1.60187i) q^{55} +(1.46336 - 0.844871i) q^{56} +(2.29583 + 1.32550i) q^{57} +(-3.14687 + 5.45053i) q^{58} +(0.611376 + 0.352978i) q^{59} +1.00000i q^{60} +(-8.81565 + 5.08972i) q^{61} +(-1.06615 + 1.84663i) q^{62} -1.68974 q^{63} -1.00000 q^{64} +(-2.26147 + 3.91698i) q^{65} -3.20374i q^{66} +(-0.212277 - 0.367674i) q^{67} -2.68974i q^{68} +(5.41698 - 3.12749i) q^{69} +(0.844871 + 1.46336i) q^{70} +(3.72548 + 6.45271i) q^{71} +(0.866025 + 0.500000i) q^{72} -11.3277 q^{73} +(5.14499 + 3.24485i) q^{74} -1.00000 q^{75} +(-2.29583 - 1.32550i) q^{76} +(-2.70674 - 4.68822i) q^{77} +(2.26147 + 3.91698i) q^{78} +(3.03296 - 1.75108i) q^{79} -1.00000i q^{80} +(-0.500000 - 0.866025i) q^{81} +11.3013i q^{82} +(3.09959 - 5.36864i) q^{83} +1.68974 q^{84} +2.68974 q^{85} +(-2.06134 + 3.57035i) q^{86} +(-5.45053 + 3.14687i) q^{87} +3.20374i q^{88} +(1.23065 + 0.710515i) q^{89} +(-0.500000 + 0.866025i) q^{90} +(6.61868 + 3.82130i) q^{91} +(-5.41698 + 3.12749i) q^{92} +(-1.84663 + 1.06615i) q^{93} +(7.65411 + 4.41910i) q^{94} +(1.32550 - 2.29583i) q^{95} +(-0.866025 - 0.500000i) q^{96} +12.9663i q^{97} +(-3.58948 + 2.07239i) q^{98} +(1.60187 - 2.77452i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{3} + 8 q^{4} - 2 q^{7} - 8 q^{9}+O(q^{10}) $ 16 * q - 8 * q^3 + 8 * q^4 - 2 * q^7 - 8 * q^9	$ 16 q - 8 q^{3} + 8 q^{4} - 2 q^{7} - 8 q^{9} + 16 q^{10} - 8 q^{11} + 8 q^{12} - 6 q^{13} - 8 q^{16} + 6 q^{17} - 12 q^{19} - 2 q^{21} + 8 q^{25} + 4 q^{26} + 16 q^{27} + 2 q^{28} - 8 q^{30} + 4 q^{33} + 6 q^{34} + 6 q^{35} - 16 q^{36} + 12 q^{37} - 4 q^{38} + 6 q^{39} + 8 q^{40} + 4 q^{41} + 6 q^{42} - 4 q^{44} - 2 q^{46} + 68 q^{47} + 16 q^{48} - 4 q^{49} - 6 q^{52} - 12 q^{53} - 6 q^{56} + 12 q^{57} - 6 q^{58} + 6 q^{59} + 12 q^{61} + 4 q^{62} + 4 q^{63} - 16 q^{64} + 2 q^{65} - 36 q^{67} + 18 q^{69} - 2 q^{70} + 6 q^{71} - 16 q^{73} + 14 q^{74} - 16 q^{75} - 12 q^{76} + 26 q^{77} - 2 q^{78} - 24 q^{79} - 8 q^{81} + 12 q^{83} - 4 q^{84} + 12 q^{85} - 2 q^{86} + 24 q^{89} - 8 q^{90} + 60 q^{91} - 18 q^{92} - 30 q^{93} + 6 q^{94} - 2 q^{95} - 12 q^{98} + 4 q^{99}+O(q^{100}) $ 16 * q - 8 * q^3 + 8 * q^4 - 2 * q^7 - 8 * q^9 + 16 * q^10 - 8 * q^11 + 8 * q^12 - 6 * q^13 - 8 * q^16 + 6 * q^17 - 12 * q^19 - 2 * q^21 + 8 * q^25 + 4 * q^26 + 16 * q^27 + 2 * q^28 - 8 * q^30 + 4 * q^33 + 6 * q^34 + 6 * q^35 - 16 * q^36 + 12 * q^37 - 4 * q^38 + 6 * q^39 + 8 * q^40 + 4 * q^41 + 6 * q^42 - 4 * q^44 - 2 * q^46 + 68 * q^47 + 16 * q^48 - 4 * q^49 - 6 * q^52 - 12 * q^53 - 6 * q^56 + 12 * q^57 - 6 * q^58 + 6 * q^59 + 12 * q^61 + 4 * q^62 + 4 * q^63 - 16 * q^64 + 2 * q^65 - 36 * q^67 + 18 * q^69 - 2 * q^70 + 6 * q^71 - 16 * q^73 + 14 * q^74 - 16 * q^75 - 12 * q^76 + 26 * q^77 - 2 * q^78 - 24 * q^79 - 8 * q^81 + 12 * q^83 - 4 * q^84 + 12 * q^85 - 2 * q^86 + 24 * q^89 - 8 * q^90 + 60 * q^91 - 18 * q^92 - 30 * q^93 + 6 * q^94 - 2 * q^95 - 12 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	−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
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$6$			1.00000i			0.408248i
$7$	0.844871	+	1.46336i	0.319331	+	0.553098i	0.980349	−	0.197273i	$-0.0632085\pi$
$7$	0.844871	+	1.46336i	0.319331	+	0.553098i	−0.661018	+	0.750370i	$0.729875\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	1.00000			0.316228
$11$	−3.20374			−0.965963			−0.482981	−	0.875631i	$-0.660446\pi$
$11$	−3.20374			−0.965963			−0.482981	+	0.875631i	$0.660446\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	3.91698	−	2.26147i	1.08637	−	0.627219i	0.153766	−	0.988107i	$-0.450860\pi$
$13$	3.91698	−	2.26147i	1.08637	−	0.627219i	0.932609	+	0.360889i	$0.117527\pi$
$14$		−	1.68974i		−	0.451602i
$15$	0.866025	+	0.500000i	0.223607	+	0.129099i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.32938	−	1.34487i	−0.564959	−	0.326179i	0.190175	−	0.981750i	$-0.439095\pi$
$17$	−2.32938	−	1.34487i	−0.564959	−	0.326179i	−0.755133	+	0.655571i	$0.772428\pi$
$18$	0.866025	−	0.500000i	0.204124	−	0.117851i
$19$	−2.29583	+	1.32550i	−0.526700	+	0.304090i	−0.739671	−	0.672968i	$-0.765019\pi$
$19$	−2.29583	+	1.32550i	−0.526700	+	0.304090i	0.212972	+	0.977058i	$0.431686\pi$
$20$	−0.866025	−	0.500000i	−0.193649	−	0.111803i
$21$	0.844871	−	1.46336i	0.184366	−	0.319331i
$22$	2.77452	+	1.60187i	0.591529	+	0.341519i
$23$			6.25499i			1.30426i	0.758109	+	0.652128i	$0.226123\pi$
$23$			6.25499i			1.30426i	−0.758109	+	0.652128i	$0.773877\pi$
$24$	−0.866025	+	0.500000i	−0.176777	+	0.102062i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	−4.52294			−0.887021
$27$	1.00000			0.192450
$28$	−0.844871	+	1.46336i	−0.159666	+	0.276549i
$29$		−	6.29373i		−	1.16872i	−0.811496	−	0.584359i	$-0.801346\pi$
$29$		−	6.29373i		−	1.16872i	0.811496	−	0.584359i	$-0.198654\pi$
$30$	−0.500000	−	0.866025i	−0.0912871	−	0.158114i
$31$		−	2.13231i		−	0.382974i	−0.981495	−	0.191487i	$-0.938669\pi$
$31$		−	2.13231i		−	0.382974i	0.981495	−	0.191487i	$-0.0613309\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	1.60187	+	2.77452i	0.278849	+	0.482981i
$34$	1.34487	+	2.32938i	0.230643	+	0.399486i
$35$	−1.46336	−	0.844871i	−0.247353	−	0.142809i
$36$	−1.00000			−0.166667
$37$	−6.07812	−	0.237625i	−0.999237	−	0.0390653i
$37$	−6.07812	−	0.237625i	−0.999237	−	0.0390653i
$38$	2.65100			0.430048
$39$	−3.91698	−	2.26147i	−0.627219	−	0.362125i
$40$	0.500000	+	0.866025i	0.0790569	+	0.136931i
$41$	−5.65066	−	9.78723i	−0.882485	−	1.52851i	−0.848569	−	0.529084i	$-0.822536\pi$
$41$	−5.65066	−	9.78723i	−0.882485	−	1.52851i	−0.0339158	−	0.999425i	$-0.510798\pi$
$42$	−1.46336	+	0.844871i	−0.225801	+	0.130366i
$43$		−	4.12268i		−	0.628703i	−0.949307	−	0.314352i	$-0.898213\pi$
$43$		−	4.12268i		−	0.628703i	0.949307	−	0.314352i	$-0.101787\pi$
$44$	−1.60187	−	2.77452i	−0.241491	−	0.418274i
$45$		−	1.00000i		−	0.149071i
$46$	3.12749	−	5.41698i	0.461124	−	0.798690i
$47$	−8.83821			−1.28919			−0.644593	−	0.764526i	$-0.722973\pi$
$47$	−8.83821			−1.28919			−0.644593	+	0.764526i	$0.722973\pi$
$48$	1.00000			0.144338
$49$	2.07239	−	3.58948i	0.296055	−	0.512783i
$50$	−0.866025	+	0.500000i	−0.122474	+	0.0707107i
$51$			2.68974i			0.376639i
$52$	3.91698	+	2.26147i	0.543187	+	0.313609i
$53$	−6.84663	+	11.8587i	−0.940456	+	1.62892i	−0.175854	+	0.984416i	$0.556269\pi$
$53$	−6.84663	+	11.8587i	−0.940456	+	1.62892i	−0.764603	+	0.644502i	$0.777065\pi$
$54$	−0.866025	−	0.500000i	−0.117851	−	0.0680414i
$55$	2.77452	−	1.60187i	0.374116	−	0.215996i
$56$	1.46336	−	0.844871i	0.195550	−	0.112901i
$57$	2.29583	+	1.32550i	0.304090	+	0.175567i
$58$	−3.14687	+	5.45053i	−0.413204	+	0.715690i
$59$	0.611376	+	0.352978i	0.0795943	+	0.0459538i	0.539269	−	0.842134i	$-0.318701\pi$
$59$	0.611376	+	0.352978i	0.0795943	+	0.0459538i	−0.459675	+	0.888087i	$0.652034\pi$
$60$			1.00000i			0.129099i
$61$	−8.81565	+	5.08972i	−1.12873	+	0.651672i	−0.943615	−	0.331045i	$-0.892599\pi$
$61$	−8.81565	+	5.08972i	−1.12873	+	0.651672i	−0.185114	+	0.982717i	$0.559265\pi$
$62$	−1.06615	+	1.84663i	−0.135402	+	0.234523i
$63$	−1.68974			−0.212887
$64$	−1.00000			−0.125000
$65$	−2.26147	+	3.91698i	−0.280501	+	0.485842i
$66$		−	3.20374i		−	0.394353i
$67$	−0.212277	−	0.367674i	−0.0259337	−	0.0449185i	0.852767	−	0.522291i	$-0.174923\pi$
$67$	−0.212277	−	0.367674i	−0.0259337	−	0.0449185i	−0.878701	+	0.477373i	$0.841589\pi$
$68$		−	2.68974i		−	0.326179i
$69$	5.41698	−	3.12749i	0.652128	−	0.376506i
$70$	0.844871	+	1.46336i	0.100981	+	0.174905i
$71$	3.72548	+	6.45271i	0.442133	+	0.765796i	0.997848	−	0.0655766i	$-0.0208887\pi$
$71$	3.72548	+	6.45271i	0.442133	+	0.765796i	−0.555715	+	0.831373i	$0.687555\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$	−11.3277			−1.32581			−0.662906	−	0.748703i	$-0.730677\pi$
$73$	−11.3277			−1.32581			−0.662906	+	0.748703i	$0.730677\pi$
$74$	5.14499	+	3.24485i	0.598093	+	0.377206i
$75$	−1.00000			−0.115470
$76$	−2.29583	−	1.32550i	−0.263350	−	0.152045i
$77$	−2.70674	−	4.68822i	−0.308462	−	0.534272i
$78$	2.26147	+	3.91698i	0.256061	+	0.443511i
$79$	3.03296	−	1.75108i	0.341235	−	0.197012i	−0.319583	−	0.947558i	$-0.603543\pi$
$79$	3.03296	−	1.75108i	0.341235	−	0.197012i	0.660818	+	0.750546i	$0.270209\pi$
$80$		−	1.00000i		−	0.111803i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$			11.3013i			1.24802i
$83$	3.09959	−	5.36864i	0.340224	−	0.589285i	−0.644250	−	0.764815i	$-0.722830\pi$
$83$	3.09959	−	5.36864i	0.340224	−	0.589285i	0.984474	+	0.175530i	$0.0561638\pi$
$84$	1.68974			0.184366
$85$	2.68974			0.291743
$86$	−2.06134	+	3.57035i	−0.222280	+	0.385000i
$87$	−5.45053	+	3.14687i	−0.584359	+	0.337380i
$88$			3.20374i			0.341519i
$89$	1.23065	+	0.710515i	0.130448	+	0.0753144i	0.563804	−	0.825909i	$-0.309337\pi$
$89$	1.23065	+	0.710515i	0.130448	+	0.0753144i	−0.433356	+	0.901223i	$0.642671\pi$
$90$	−0.500000	+	0.866025i	−0.0527046	+	0.0912871i
$91$	6.61868	+	3.82130i	0.693826	+	0.400581i
$92$	−5.41698	+	3.12749i	−0.564759	+	0.326064i
$93$	−1.84663	+	1.06615i	−0.191487	+	0.110555i
$94$	7.65411	+	4.41910i	0.789461	+	0.455796i
$95$	1.32550	−	2.29583i	0.135993	−	0.235547i
$96$	−0.866025	−	0.500000i	−0.0883883	−	0.0510310i
$97$			12.9663i			1.31652i	0.752789	+	0.658262i	$0.228708\pi$
$97$			12.9663i			1.31652i	−0.752789	+	0.658262i	$0.771292\pi$
$98$	−3.58948	+	2.07239i	−0.362592	+	0.209343i
$99$	1.60187	−	2.77452i	0.160994	−	0.278849i
$100$	1.00000			0.100000
$101$	−16.4457			−1.63641			−0.818205	−	0.574926i	$-0.805031\pi$
$101$	−16.4457			−1.63641			−0.818205	+	0.574926i	$0.805031\pi$
$102$	1.34487	−	2.32938i	0.133162	−	0.230643i
$103$			17.8336i			1.75720i	0.477557	+	0.878601i	$0.341522\pi$
$103$			17.8336i			1.75720i	−0.477557	+	0.878601i	$0.658478\pi$
$104$	−2.26147	−	3.91698i	−0.221755	−	0.384091i
$105$			1.68974i			0.164902i
$106$	11.8587	−	6.84663i	1.15182	−	0.665003i
$107$	−1.97061	−	3.41320i	−0.190506	−	0.329966i	0.754912	−	0.655826i	$-0.227680\pi$
$107$	−1.97061	−	3.41320i	−0.190506	−	0.329966i	−0.945418	+	0.325860i	$0.894346\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	−10.1898	−	5.88311i	−0.976010	−	0.563500i	−0.0749471	−	0.997188i	$-0.523879\pi$
$109$	−10.1898	−	5.88311i	−0.976010	−	0.563500i	−0.901063	+	0.433688i	$0.857212\pi$
$110$	−3.20374			−0.305464
$111$	2.83327	+	5.38262i	0.268922	+	0.510896i
$112$	−1.68974			−0.159666
$113$	−11.1458	−	6.43505i	−1.04851	−	0.605358i	−0.126279	−	0.991995i	$-0.540303\pi$
$113$	−11.1458	−	6.43505i	−1.04851	−	0.605358i	−0.922232	+	0.386636i	$0.873637\pi$
$114$	−1.32550	−	2.29583i	−0.124144	−	0.215024i
$115$	−3.12749	−	5.41698i	−0.291640	−	0.505136i
$116$	5.45053	−	3.14687i	0.506069	−	0.292179i
$117$			4.52294i			0.418146i
$118$	−0.352978	−	0.611376i	−0.0324942	−	0.0562817i
$119$		−	4.54497i		−	0.416636i
$120$	0.500000	−	0.866025i	0.0456435	−	0.0790569i
$121$	−0.736075			−0.0669159
$122$	10.1794			0.921603
$123$	−5.65066	+	9.78723i	−0.509503	+	0.882485i
$124$	1.84663	−	1.06615i	0.165832	−	0.0957434i
$125$			1.00000i			0.0894427i
$126$	1.46336	+	0.844871i	0.130366	+	0.0752671i
$127$	1.49587	−	2.59092i	0.132737	−	0.229907i	−0.791994	−	0.610529i	$-0.790957\pi$
$127$	1.49587	−	2.59092i	0.132737	−	0.229907i	0.924731	+	0.380622i	$0.124290\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−3.57035	+	2.06134i	−0.314352	+	0.181491i
$130$	3.91698	−	2.26147i	0.343542	−	0.198344i
$131$	−11.4234	−	6.59528i	−0.998063	−	0.576232i	−0.0903884	−	0.995907i	$-0.528811\pi$
$131$	−11.4234	−	6.59528i	−0.998063	−	0.576232i	−0.907675	+	0.419675i	$0.862144\pi$
$132$	−1.60187	+	2.77452i	−0.139425	+	0.241491i
$133$	−3.87936	−	2.23975i	−0.336383	−	0.194211i
$134$			0.424553i			0.0366758i
$135$	−0.866025	+	0.500000i	−0.0745356	+	0.0430331i
$136$	−1.34487	+	2.32938i	−0.115322	+	0.199743i
$137$	21.7604			1.85912			0.929559	−	0.368674i	$-0.120188\pi$
$137$	21.7604			1.85912			0.929559	+	0.368674i	$0.120188\pi$
$138$	−6.25499			−0.532460
$139$	8.83491	−	15.3025i	0.749367	−	1.29794i	−0.198759	−	0.980048i	$-0.563691\pi$
$139$	8.83491	−	15.3025i	0.749367	−	1.29794i	0.948126	−	0.317894i	$-0.102976\pi$
$140$		−	1.68974i		−	0.142809i
$141$	4.41910	+	7.65411i	0.372156	+	0.644593i
$142$		−	7.45095i		−	0.625270i
$143$	−12.5490	+	7.24515i	−1.04940	+	0.605870i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	3.14687	+	5.45053i	0.261333	+	0.452642i
$146$	9.81011	+	5.66387i	0.811890	+	0.468745i
$147$	−4.14477			−0.341855
$148$	−2.83327	−	5.38262i	−0.232893	−	0.442448i
$149$	2.80828			0.230064			0.115032	−	0.993362i	$-0.463303\pi$
$149$	2.80828			0.230064			0.115032	+	0.993362i	$0.463303\pi$
$150$	0.866025	+	0.500000i	0.0707107	+	0.0408248i
$151$	6.91805	+	11.9824i	0.562983	+	0.975114i	0.997234	+	0.0743228i	$0.0236795\pi$
$151$	6.91805	+	11.9824i	0.562983	+	0.975114i	−0.434252	+	0.900792i	$0.642987\pi$
$152$	1.32550	+	2.29583i	0.107512	+	0.186216i
$153$	2.32938	−	1.34487i	0.188320	−	0.108726i
$154$			5.41349i			0.436231i
$155$	1.06615	+	1.84663i	0.0856355	+	0.148325i
$156$		−	4.52294i		−	0.362125i
$157$	−4.72532	+	8.18450i	−0.377122	+	0.653194i	−0.990642	−	0.136485i	$-0.956419\pi$
$157$	−4.72532	+	8.18450i	−0.377122	+	0.653194i	0.613520	+	0.789679i	$0.289753\pi$
$158$	−3.50216			−0.278617
$159$	13.6933			1.08595
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	−9.15329	+	5.28466i	−0.721381	+	0.416489i
$162$			1.00000i			0.0785674i
$163$	13.7430	+	7.93450i	1.07643	+	0.621478i	0.929932	−	0.367733i	$-0.119866\pi$
$163$	13.7430	+	7.93450i	1.07643	+	0.621478i	0.146500	+	0.989211i	$0.453199\pi$
$164$	5.65066	−	9.78723i	0.441243	−	0.764254i
$165$	−2.77452	−	1.60187i	−0.215996	−	0.124705i
$166$	−5.36864	+	3.09959i	−0.416688	+	0.240575i
$167$	−20.2100	+	11.6682i	−1.56390	+	0.902915i	−0.567039	+	0.823691i	$0.691911\pi$
$167$	−20.2100	+	11.6682i	−1.56390	+	0.902915i	−0.996857	+	0.0792243i	$0.974756\pi$
$168$	−1.46336	−	0.844871i	−0.112901	−	0.0651832i
$169$	3.72849	−	6.45793i	0.286807	−	0.496764i
$170$	−2.32938	−	1.34487i	−0.178656	−	0.103147i
$171$		−	2.65100i		−	0.202727i
$172$	3.57035	−	2.06134i	0.272236	−	0.157176i
$173$	10.2250	−	17.7102i	0.777391	−	1.34648i	−0.156049	−	0.987749i	$-0.549876\pi$
$173$	10.2250	−	17.7102i	0.777391	−	1.34648i	0.933441	−	0.358732i	$-0.116791\pi$
$174$	6.29373			0.477127
$175$	1.68974			0.127732
$176$	1.60187	−	2.77452i	0.120745	−	0.209137i
$177$		−	0.705956i		−	0.0530629i
$178$	−0.710515	−	1.23065i	−0.0532554	−	0.0922410i
$179$		−	22.0238i		−	1.64614i	−0.567943	−	0.823068i	$-0.692261\pi$
$179$		−	22.0238i		−	1.64614i	0.567943	−	0.823068i	$-0.307739\pi$
$180$	0.866025	−	0.500000i	0.0645497	−	0.0372678i
$181$	−7.63876	−	13.2307i	−0.567785	−	0.983432i	−0.996785	−	0.0801272i	$-0.974467\pi$
$181$	−7.63876	−	13.2307i	−0.567785	−	0.983432i	0.429000	−	0.903304i	$-0.358866\pi$
$182$	−3.82130	−	6.61868i	−0.283253	−	0.490609i
$183$	8.81565	+	5.08972i	0.651672	+	0.376243i
$184$	6.25499			0.461124
$185$	5.38262	−	2.83327i	0.395738	−	0.208306i
$186$	2.13231			0.156348
$187$	7.46273	+	4.30861i	0.545729	+	0.315077i
$188$	−4.41910	−	7.65411i	−0.322296	−	0.558234i
$189$	0.844871	+	1.46336i	0.0614553	+	0.106444i
$190$	−2.29583	+	1.32550i	−0.166557	+	0.0961618i
$191$			3.18103i			0.230171i	0.993356	+	0.115086i	$0.0367142\pi$
$191$			3.18103i			0.230171i	−0.993356	+	0.115086i	$0.963286\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$		−	7.53505i		−	0.542385i	−0.962525	−	0.271192i	$-0.912582\pi$
$193$		−	7.53505i		−	0.542385i	0.962525	−	0.271192i	$-0.0874180\pi$
$194$	6.48313	−	11.2291i	0.465462	−	0.806204i
$195$	4.52294			0.323894
$196$	4.14477			0.296055
$197$	−2.33537	+	4.04497i	−0.166388	+	0.288192i	−0.937147	−	0.348934i	$-0.886544\pi$
$197$	−2.33537	+	4.04497i	−0.166388	+	0.288192i	0.770759	+	0.637126i	$0.219877\pi$
$198$	−2.77452	+	1.60187i	−0.197176	+	0.113840i
$199$		−	10.3566i		−	0.734159i	−0.930190	−	0.367079i	$-0.880358\pi$
$199$		−	10.3566i		−	0.734159i	0.930190	−	0.367079i	$-0.119642\pi$
$200$	−0.866025	−	0.500000i	−0.0612372	−	0.0353553i
$201$	−0.212277	+	0.367674i	−0.0149728	+	0.0259337i
$202$	14.2424	+	8.22286i	1.00209	+	0.578559i
$203$	9.20999	−	5.31739i	0.646415	−	0.373208i
$204$	−2.32938	+	1.34487i	−0.163090	+	0.0941598i
$205$	9.78723	+	5.65066i	0.683570	+	0.394659i
$206$	8.91682	−	15.4444i	0.621265	−	1.07606i
$207$	−5.41698	−	3.12749i	−0.376506	−	0.217376i
$208$			4.52294i			0.313609i
$209$	7.35524	−	4.24655i	0.508772	−	0.293740i
$210$	0.844871	−	1.46336i	0.0583016	−	0.100981i
$211$	−24.5039			−1.68692			−0.843458	−	0.537195i	$-0.819484\pi$
$211$	−24.5039			−1.68692			−0.843458	+	0.537195i	$0.819484\pi$
$212$	−13.6933			−0.940456
$213$	3.72548	−	6.45271i	0.255265	−	0.442133i
$214$			3.94122i			0.269416i
$215$	2.06134	+	3.57035i	0.140582	+	0.243496i
$216$		−	1.00000i		−	0.0680414i
$217$	3.12033	−	1.80152i	0.211822	−	0.122295i
$218$	5.88311	+	10.1898i	0.398455	+	0.690144i
$219$	5.66387	+	9.81011i	0.382729	+	0.662906i
$220$	2.77452	+	1.60187i	0.187058	+	0.107998i
$221$	−12.1655			−0.818342
$222$	0.237625	−	6.07812i	0.0159483	−	0.407937i
$223$	11.9045			0.797182			0.398591	−	0.917129i	$-0.369499\pi$
$223$	11.9045			0.797182			0.398591	+	0.917129i	$0.369499\pi$
$224$	1.46336	+	0.844871i	0.0977748	+	0.0564503i
$225$	0.500000	+	0.866025i	0.0333333	+	0.0577350i
$226$	6.43505	+	11.1458i	0.428053	+	0.741409i
$227$	4.70710	−	2.71765i	0.312421	−	0.180377i	−0.335588	−	0.942009i	$-0.608935\pi$
$227$	4.70710	−	2.71765i	0.312421	−	0.180377i	0.648010	+	0.761632i	$0.275602\pi$
$228$			2.65100i			0.175567i
$229$	−8.22859	−	14.2523i	−0.543761	−	0.941821i	−0.998684	−	0.0512904i	$-0.983667\pi$
$229$	−8.22859	−	14.2523i	−0.543761	−	0.941821i	0.454923	−	0.890531i	$-0.349667\pi$
$230$			6.25499i			0.412442i
$231$	−2.70674	+	4.68822i	−0.178091	+	0.308462i
$232$	−6.29373			−0.413204
$233$	1.39922			0.0916660			0.0458330	−	0.998949i	$-0.485406\pi$
$233$	1.39922			0.0916660			0.0458330	+	0.998949i	$0.485406\pi$
$234$	2.26147	−	3.91698i	0.147837	−	0.256061i
$235$	7.65411	−	4.41910i	0.499299	−	0.288271i
$236$			0.705956i			0.0459538i
$237$	−3.03296	−	1.75108i	−0.197012	−	0.113745i
$238$	−2.27248	+	3.93606i	−0.147303	+	0.255137i
$239$	9.20151	+	5.31250i	0.595196	+	0.343637i	0.767150	−	0.641468i	$-0.221674\pi$
$239$	9.20151	+	5.31250i	0.595196	+	0.343637i	−0.171953	+	0.985105i	$0.555008\pi$
$240$	−0.866025	+	0.500000i	−0.0559017	+	0.0322749i
$241$	−2.56645	+	1.48174i	−0.165319	+	0.0954473i	−0.580377	−	0.814348i	$-0.697095\pi$
$241$	−2.56645	+	1.48174i	−0.165319	+	0.0954473i	0.415058	+	0.909795i	$0.363761\pi$
$242$	0.637460	+	0.368038i	0.0409775	+	0.0236584i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−8.81565	−	5.08972i	−0.564364	−	0.325836i
$245$			4.14477i			0.264800i
$246$	9.78723	−	5.65066i	0.624011	−	0.360273i
$247$	−5.99515	+	10.3839i	−0.381462	+	0.660712i
$248$	−2.13231			−0.135402
$249$	−6.19918			−0.392857
$250$	0.500000	−	0.866025i	0.0316228	−	0.0547723i
$251$			5.17276i			0.326502i	0.986585	+	0.163251i	$0.0521980\pi$
$251$			5.17276i			0.326502i	−0.986585	+	0.163251i	$0.947802\pi$
$252$	−0.844871	−	1.46336i	−0.0532219	−	0.0921829i
$253$		−	20.0393i		−	1.25986i
$254$	−2.59092	+	1.49587i	−0.162569	+	0.0938591i
$255$	−1.34487	−	2.32938i	−0.0842191	−	0.145872i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	4.55097	+	2.62750i	0.283881	+	0.163899i	0.635179	−	0.772365i	$-0.280926\pi$
$257$	4.55097	+	2.62750i	0.283881	+	0.163899i	−0.351298	+	0.936264i	$0.614260\pi$
$258$	4.12268			0.256667
$259$	−4.78749	−	9.09523i	−0.297480	−	0.565150i
$260$	−4.52294			−0.280501
$261$	5.45053	+	3.14687i	0.337380	+	0.194786i
$262$	6.59528	+	11.4234i	0.407458	+	0.705737i
$263$	−6.35462	−	11.0065i	−0.391843	−	0.678691i	0.600850	−	0.799362i	$-0.294829\pi$
$263$	−6.35462	−	11.0065i	−0.391843	−	0.678691i	−0.992693	+	0.120670i	$0.961496\pi$
$264$	2.77452	−	1.60187i	0.170760	−	0.0985882i
$265$		−	13.6933i		−	0.841170i
$266$	2.23975	+	3.87936i	0.137328	+	0.237859i
$267$		−	1.42103i		−	0.0869656i
$268$	0.212277	−	0.367674i	0.0129669	−	0.0224593i
$269$	16.9804			1.03531			0.517656	−	0.855589i	$-0.326805\pi$
$269$	16.9804			1.03531			0.517656	+	0.855589i	$0.326805\pi$
$270$	1.00000			0.0608581
$271$	2.29413	−	3.97356i	0.139359	−	0.241376i	−0.787895	−	0.615809i	$-0.788829\pi$
$271$	2.29413	−	3.97356i	0.139359	−	0.241376i	0.927254	+	0.374433i	$0.122163\pi$
$272$	2.32938	−	1.34487i	0.141240	−	0.0815448i
$273$		−	7.64260i		−	0.462551i
$274$	−18.8451	−	10.8802i	−1.13847	−	0.657297i
$275$	−1.60187	+	2.77452i	−0.0965963	+	0.167310i
$276$	5.41698	+	3.12749i	0.326064	+	0.188253i
$277$	19.0145	−	10.9780i	1.14247	−	0.659604i	0.195428	−	0.980718i	$-0.437390\pi$
$277$	19.0145	−	10.9780i	1.14247	−	0.659604i	0.947041	+	0.321114i	$0.104057\pi$
$278$	−15.3025	+	8.83491i	−0.917784	+	0.529883i
$279$	1.84663	+	1.06615i	0.110555	+	0.0638289i
$280$	−0.844871	+	1.46336i	−0.0504907	+	0.0874524i
$281$	−2.88933	−	1.66816i	−0.172363	−	0.0995138i	0.411337	−	0.911484i	$-0.365062\pi$
$281$	−2.88933	−	1.66816i	−0.172363	−	0.0995138i	−0.583700	+	0.811970i	$0.698395\pi$
$282$		−	8.83821i		−	0.526308i
$283$	3.97186	−	2.29315i	0.236102	−	0.136314i	−0.377282	−	0.926099i	$-0.623141\pi$
$283$	3.97186	−	2.29315i	0.236102	−	0.136314i	0.613384	+	0.789785i	$0.289808\pi$
$284$	−3.72548	+	6.45271i	−0.221066	+	0.382898i
$285$	−2.65100			−0.157031
$286$	14.4903			0.856829
$287$	9.54816	−	16.5379i	0.563610	−	0.976201i
$288$			1.00000i			0.0589256i
$289$	−4.88265	−	8.45699i	−0.287214	−	0.497470i
$290$		−	6.29373i		−	0.369581i
$291$	11.2291	−	6.48313i	0.658262	−	0.380048i
$292$	−5.66387	−	9.81011i	−0.331453	−	0.574093i
$293$	9.06792	+	15.7061i	0.529754	+	0.917560i	0.999398	+	0.0347042i	$0.0110489\pi$
$293$	9.06792	+	15.7061i	0.529754	+	0.917560i	−0.469644	+	0.882856i	$0.655618\pi$
$294$	3.58948	+	2.07239i	0.209343	+	0.120864i
$295$	−0.705956			−0.0411023
$296$	−0.237625	+	6.07812i	−0.0138117	+	0.353284i
$297$	−3.20374			−0.185900
$298$	−2.43205	−	1.40414i	−0.140885	−	0.0813398i
$299$	14.1455	+	24.5007i	0.818053	+	1.41691i
$300$	−0.500000	−	0.866025i	−0.0288675	−	0.0500000i
$301$	6.03296	−	3.48313i	0.347734	−	0.200764i
$302$		−	13.8361i		−	0.796178i
$303$	8.22286	+	14.2424i	0.472391	+	0.818205i
$304$		−	2.65100i		−	0.152045i
$305$	5.08972	−	8.81565i	0.291436	−	0.504783i
$306$	−2.68974			−0.153762
$307$	9.93260			0.566883			0.283442	−	0.958990i	$-0.408524\pi$
$307$	9.93260			0.566883			0.283442	+	0.958990i	$0.408524\pi$
$308$	2.70674	−	4.68822i	0.154231	−	0.267136i
$309$	15.4444	−	8.91682i	0.878601	−	0.507260i
$310$		−	2.13231i		−	0.121107i
$311$	29.2291	+	16.8754i	1.65743	+	0.956918i	0.973895	+	0.227000i	$0.0728918\pi$
$311$	29.2291	+	16.8754i	1.65743	+	0.956918i	0.683535	+	0.729917i	$0.260442\pi$
$312$	−2.26147	+	3.91698i	−0.128030	+	0.221755i
$313$	−4.94889	−	2.85724i	−0.279728	−	0.161501i	0.353572	−	0.935407i	$-0.384967\pi$
$313$	−4.94889	−	2.85724i	−0.279728	−	0.161501i	−0.633300	+	0.773906i	$0.718300\pi$
$314$	8.18450	−	4.72532i	0.461878	−	0.266665i
$315$	1.46336	−	0.844871i	0.0824509	−	0.0476031i
$316$	3.03296	+	1.75108i	0.170618	+	0.0985061i
$317$	8.93237	−	15.4713i	0.501692	−	0.868956i	−0.498306	−	0.867001i	$-0.666044\pi$
$317$	8.93237	−	15.4713i	0.501692	−	0.868956i	0.999998	−	0.00195502i	$-0.000622302\pi$
$318$	−11.8587	−	6.84663i	−0.665003	−	0.383940i
$319$			20.1635i			1.12894i
$320$	0.866025	−	0.500000i	0.0484123	−	0.0279508i
$321$	−1.97061	+	3.41320i	−0.109989	+	0.190506i
$322$	10.5693			0.589005
$323$	7.13050			0.396751
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$		−	4.52294i		−	0.250887i
$326$	−7.93450	−	13.7430i	−0.439451	−	0.761152i
$327$			11.7662i			0.650674i
$328$	−9.78723	+	5.65066i	−0.540410	+	0.312006i
$329$	−7.46714	−	12.9335i	−0.411677	−	0.713045i
$330$	1.60187	+	2.77452i	0.0881799	+	0.152732i
$331$	19.5912	+	11.3110i	1.07683	+	0.621709i	0.930040	−	0.367459i	$-0.119772\pi$
$331$	19.5912	+	11.3110i	1.07683	+	0.621709i	0.146791	+	0.989168i	$0.453105\pi$
$332$	6.19918			0.340224
$333$	3.24485	−	5.14499i	0.177817	−	0.281944i
$334$	23.3365			1.27692
$335$	0.367674	+	0.212277i	0.0200882	+	0.0115979i
$336$	0.844871	+	1.46336i	0.0460915	+	0.0798328i
$337$	1.22150	+	2.11570i	0.0665395	+	0.115250i	0.897376	−	0.441267i	$-0.145471\pi$
$337$	1.22150	+	2.11570i	0.0665395	+	0.115250i	−0.830836	+	0.556517i	$0.812138\pi$
$338$	−6.45793	+	3.72849i	−0.351265	+	0.202803i
$339$			12.8701i			0.699008i
$340$	1.34487	+	2.32938i	0.0729359	+	0.126329i
$341$			6.83135i			0.369938i
$342$	−1.32550	+	2.29583i	−0.0716747	+	0.124144i
$343$	18.8318			1.01682
$344$	−4.12268			−0.222280
$345$	−3.12749	+	5.41698i	−0.168379	+	0.291640i
$346$	−17.7102	+	10.2250i	−0.952106	+	0.549699i
$347$			9.90993i			0.531993i	0.963974	+	0.265997i	$0.0857010\pi$
$347$			9.90993i			0.531993i	−0.963974	+	0.265997i	$0.914299\pi$
$348$	−5.45053	−	3.14687i	−0.292179	−	0.168690i
$349$	0.418227	−	0.724391i	0.0223872	−	0.0387758i	−0.854615	−	0.519263i	$-0.826207\pi$
$349$	0.418227	−	0.724391i	0.0223872	−	0.0387758i	0.877002	+	0.480487i	$0.159540\pi$
$350$	−1.46336	−	0.844871i	−0.0782198	−	0.0451602i
$351$	3.91698	−	2.26147i	0.209073	−	0.120708i
$352$	−2.77452	+	1.60187i	−0.147882	+	0.0853799i
$353$	−5.21645	−	3.01172i	−0.277643	−	0.160298i	0.354713	−	0.934975i	$-0.384579\pi$
$353$	−5.21645	−	3.01172i	−0.277643	−	0.160298i	−0.632356	+	0.774678i	$0.717912\pi$
$354$	−0.352978	+	0.611376i	−0.0187606	+	0.0324942i
$355$	−6.45271	−	3.72548i	−0.342475	−	0.197728i
$356$			1.42103i			0.0753144i
$357$	−3.93606	+	2.27248i	−0.208318	+	0.120273i
$358$	−11.0119	+	19.0732i	−0.581997	+	1.00805i
$359$	9.58722			0.505994			0.252997	−	0.967467i	$-0.418584\pi$
$359$	9.58722			0.505994			0.252997	+	0.967467i	$0.418584\pi$
$360$	−1.00000			−0.0527046
$361$	−5.98611	+	10.3682i	−0.315058	+	0.545697i
$362$			15.2775i			0.802969i
$363$	0.368038	+	0.637460i	0.0193170	+	0.0334580i
$364$			7.64260i			0.400581i
$365$	9.81011	−	5.66387i	0.513484	−	0.296460i
$366$	−5.08972	−	8.81565i	−0.266044	−	0.460802i
$367$	−14.0314	−	24.3030i	−0.732431	−	1.26861i	−0.955841	−	0.293883i	$-0.905052\pi$
$367$	−14.0314	−	24.3030i	−0.732431	−	1.26861i	0.223410	−	0.974724i	$-0.428281\pi$
$368$	−5.41698	−	3.12749i	−0.282380	−	0.163032i
$369$	11.3013			0.588323
$370$	−6.07812	−	0.237625i	−0.315986	−	0.0123535i
$371$	−23.1381			−1.20127
$372$	−1.84663	−	1.06615i	−0.0957434	−	0.0552775i
$373$	2.84842	+	4.93361i	0.147486	+	0.255452i	0.930297	−	0.366806i	$-0.119549\pi$
$373$	2.84842	+	4.93361i	0.147486	+	0.255452i	−0.782812	+	0.622258i	$0.786215\pi$
$374$	−4.30861	−	7.46273i	−0.222793	−	0.385889i
$375$	0.866025	−	0.500000i	0.0447214	−	0.0258199i
$376$			8.83821i			0.455796i
$377$	−14.2331	−	24.6524i	−0.733041	−	1.26966i
$378$		−	1.68974i		−	0.0869109i
$379$	−7.05060	+	12.2120i	−0.362165	+	0.627288i	−0.988317	−	0.152413i	$-0.951296\pi$
$379$	−7.05060	+	12.2120i	−0.362165	+	0.627288i	0.626152	+	0.779701i	$0.284629\pi$
$380$	2.65100			0.135993
$381$	−2.99173			−0.153271
$382$	1.59051	−	2.75485i	0.0813778	−	0.140950i
$383$	−23.7339	+	13.7028i	−1.21275	+	0.700180i	−0.963357	−	0.268223i	$-0.913564\pi$
$383$	−23.7339	+	13.7028i	−1.21275	+	0.700180i	−0.249391	+	0.968403i	$0.580230\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	4.68822	+	2.70674i	0.238934	+	0.137948i
$386$	−3.76753	+	6.52555i	−0.191762	+	0.332141i
$387$	3.57035	+	2.06134i	0.181491	+	0.104784i
$388$	−11.2291	+	6.48313i	−0.570072	+	0.329131i
$389$	27.5718	−	15.9186i	1.39794	−	0.807103i	0.403767	−	0.914862i	$-0.367701\pi$
$389$	27.5718	−	15.9186i	1.39794	−	0.807103i	0.994177	+	0.107759i	$0.0343674\pi$
$390$	−3.91698	−	2.26147i	−0.198344	−	0.114514i
$391$	8.41215	−	14.5703i	0.425421	−	0.736850i
$392$	−3.58948	−	2.07239i	−0.181296	−	0.104671i
$393$			13.1906i			0.665375i
$394$	4.04497	−	2.33537i	0.203783	−	0.117654i
$395$	−1.75108	+	3.03296i	−0.0881065	+	0.152605i
$396$	3.20374			0.160994
$397$	13.9486			0.700058			0.350029	−	0.936739i	$-0.386172\pi$
$397$	13.9486			0.700058			0.350029	+	0.936739i	$0.386172\pi$
$398$	−5.17829	+	8.96907i	−0.259564	+	0.449579i
$399$			4.47950i			0.224255i
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$			13.2809i			0.663219i	0.943417	+	0.331609i	$0.107592\pi$
$401$			13.2809i			0.663219i	−0.943417	+	0.331609i	$0.892408\pi$
$402$	0.367674	−	0.212277i	0.0183379	−	0.0105874i
$403$	−4.82215	−	8.35220i	−0.240208	−	0.416053i
$404$	−8.22286	−	14.2424i	−0.409103	−	0.708587i
$405$	0.866025	+	0.500000i	0.0430331	+	0.0248452i
$406$	−10.6348			−0.527795
$407$	19.4727	+	0.761288i	0.965225	+	0.0377356i
$408$	2.68974			0.133162
$409$	−26.2478	−	15.1542i	−1.29787	−	0.749325i	−0.317833	−	0.948147i	$-0.602955\pi$
$409$	−26.2478	−	15.1542i	−1.29787	−	0.749325i	−0.980036	+	0.198822i	$0.936289\pi$
$410$	−5.65066	−	9.78723i	−0.279066	−	0.483357i
$411$	−10.8802	−	18.8451i	−0.536681	−	0.929559i
$412$	−15.4444	+	8.91682i	−0.760891	+	0.439300i
$413$			1.19288i			0.0586979i
$414$	3.12749	+	5.41698i	0.153708	+	0.266230i
$415$			6.19918i			0.304306i
$416$	2.26147	−	3.91698i	0.110878	−	0.192046i
$417$	−17.6698			−0.865295
$418$	−8.49309			−0.415411
$419$	−5.06884	+	8.77949i	−0.247629	+	0.428906i	−0.962867	−	0.269974i	$-0.912985\pi$
$419$	−5.06884	+	8.77949i	−0.247629	+	0.428906i	0.715238	+	0.698881i	$0.246318\pi$
$420$	−1.46336	+	0.844871i	−0.0714046	+	0.0412255i
$421$			9.14846i			0.445869i	0.974833	+	0.222934i	$0.0715636\pi$
$421$			9.14846i			0.445869i	−0.974833	+	0.222934i	$0.928436\pi$
$422$	21.2210	+	12.2519i	1.03302	+	0.596415i
$423$	4.41910	−	7.65411i	0.214864	−	0.372156i
$424$	11.8587	+	6.84663i	0.575910	+	0.332502i
$425$	−2.32938	+	1.34487i	−0.112992	+	0.0652358i
$426$	−6.45271	+	3.72548i	−0.312635	+	0.180500i
$427$	−14.8962	−	8.60031i	−0.720876	−	0.416198i
$428$	1.97061	−	3.41320i	0.0952530	−	0.164983i
$429$	12.5490	+	7.24515i	0.605870	+	0.349799i
$430$		−	4.12268i		−	0.198813i
$431$	−22.1050	+	12.7623i	−1.06476	+	0.614739i	−0.926745	−	0.375692i	$-0.877405\pi$
$431$	−22.1050	+	12.7623i	−1.06476	+	0.614739i	−0.138014	+	0.990430i	$0.544072\pi$
$432$	−0.500000	+	0.866025i	−0.0240563	+	0.0416667i
$433$	−28.5890			−1.37390			−0.686949	−	0.726705i	$-0.741051\pi$
$433$	−28.5890			−1.37390			−0.686949	+	0.726705i	$0.741051\pi$
$434$	−3.60305			−0.172952
$435$	3.14687	−	5.45053i	0.150881	−	0.261333i
$436$		−	11.7662i		−	0.563500i
$437$	−8.29098	−	14.3604i	−0.396611	−	0.686951i
$438$		−	11.3277i		−	0.541260i
$439$	−3.72066	+	2.14812i	−0.177577	+	0.102524i	−0.586154	−	0.810200i	$-0.699359\pi$
$439$	−3.72066	+	2.14812i	−0.177577	+	0.102524i	0.408577	+	0.912724i	$0.366025\pi$
$440$	−1.60187	−	2.77452i	−0.0763661	−	0.132270i
$441$	2.07239	+	3.58948i	0.0986851	+	0.170928i
$442$	10.5357	+	6.08277i	0.501130	+	0.289328i
$443$	34.1211			1.62114			0.810570	−	0.585642i	$-0.199157\pi$
$443$	34.1211			1.62114			0.810570	+	0.585642i	$0.199157\pi$
$444$	−3.24485	+	5.14499i	−0.153994	+	0.244171i
$445$	−1.42103			−0.0673633
$446$	−10.3096	−	5.95223i	−0.488172	−	0.281846i
$447$	−1.40414	−	2.43205i	−0.0664137	−	0.115032i
$448$	−0.844871	−	1.46336i	−0.0399164	−	0.0691372i
$449$	−17.4477	+	10.0734i	−0.823406	+	0.475394i	−0.851590	−	0.524209i	$-0.824361\pi$
$449$	−17.4477	+	10.0734i	−0.823406	+	0.475394i	0.0281834	+	0.999603i	$0.491028\pi$
$450$		−	1.00000i		−	0.0471405i
$451$	18.1032	+	31.3557i	0.852448	+	1.47648i
$452$		−	12.8701i		−	0.605358i
$453$	6.91805	−	11.9824i	0.325038	−	0.562983i
$454$	−5.43530			−0.255091
$455$	−7.64260			−0.358290
$456$	1.32550	−	2.29583i	0.0620721	−	0.107512i
$457$	−20.6810	+	11.9402i	−0.967416	+	0.558538i	−0.898447	−	0.439081i	$-0.855304\pi$
$457$	−20.6810	+	11.9402i	−0.967416	+	0.558538i	−0.0689682	+	0.997619i	$0.521971\pi$
$458$			16.4572i			0.768994i
$459$	−2.32938	−	1.34487i	−0.108726	−	0.0627732i
$460$	3.12749	−	5.41698i	0.145820	−	0.252568i
$461$	−20.1330	−	11.6238i	−0.937688	−	0.541375i	−0.0484534	−	0.998825i	$-0.515429\pi$
$461$	−20.1330	−	11.6238i	−0.937688	−	0.541375i	−0.889235	+	0.457451i	$0.848763\pi$
$462$	4.68822	−	2.70674i	0.218116	−	0.125929i
$463$	−16.5274	+	9.54213i	−0.768096	+	0.443460i	−0.832195	−	0.554483i	$-0.812916\pi$
$463$	−16.5274	+	9.54213i	−0.768096	+	0.443460i	0.0640992	+	0.997944i	$0.479583\pi$
$464$	5.45053	+	3.14687i	0.253035	+	0.146090i
$465$	1.06615	−	1.84663i	0.0494417	−	0.0856355i
$466$	−1.21176	−	0.699610i	−0.0561337	−	0.0324088i
$467$			22.4662i			1.03961i	0.854284	+	0.519806i	$0.173996\pi$
$467$			22.4662i			1.03961i	−0.854284	+	0.519806i	$0.826004\pi$
$468$	−3.91698	+	2.26147i	−0.181062	+	0.104536i
$469$	0.358693	−	0.621274i	0.0165629	−	0.0286878i
$470$	−8.83821			−0.407676
$471$	9.45064			0.435463
$472$	0.352978	−	0.611376i	0.0162471	−	0.0281408i
$473$			13.2080i			0.607304i
$474$	1.75108	+	3.03296i	0.0804299	+	0.139309i
$475$			2.65100i			0.121636i
$476$	3.93606	−	2.27248i	0.180409	−	0.104159i
$477$	−6.84663	−	11.8587i	−0.313485	−	0.542973i
$478$	−5.31250	−	9.20151i	−0.242988	−	0.420867i
$479$	19.9551	+	11.5211i	0.911772	+	0.526412i	0.881001	−	0.473115i	$-0.156870\pi$
$479$	19.9551	+	11.5211i	0.911772	+	0.526412i	0.0307711	+	0.999526i	$0.490204\pi$
$480$	1.00000			0.0456435
$481$	−24.3453	+	12.8147i	−1.11005	+	0.584300i
$482$	2.96348			0.134983
$483$	9.15329	+	5.28466i	0.416489	+	0.240460i
$484$	−0.368038	−	0.637460i	−0.0167290	−	0.0289755i
$485$	−6.48313	−	11.2291i	−0.294384	−	0.509888i
$486$	0.866025	−	0.500000i	0.0392837	−	0.0226805i
$487$			13.1644i			0.596537i	0.954482	+	0.298268i	$0.0964090\pi$
$487$			13.1644i			0.596537i	−0.954482	+	0.298268i	$0.903591\pi$
$488$	5.08972	+	8.81565i	0.230401	+	0.399066i
$489$		−	15.8690i		−	0.717621i
$490$	2.07239	−	3.58948i	0.0936209	−	0.162156i
$491$	3.21588			0.145131			0.0725653	−	0.997364i	$-0.476881\pi$
$491$	3.21588			0.145131			0.0725653	+	0.997364i	$0.476881\pi$
$492$	−11.3013			−0.509503
$493$	−8.46426	+	14.6605i	−0.381211	+	0.660277i
$494$	10.3839	−	5.99515i	0.467194	−	0.269734i
$495$			3.20374i			0.143997i
$496$	1.84663	+	1.06615i	0.0829162	+	0.0478717i
$497$	−6.29509	+	10.9034i	−0.282373	+	0.489085i
$498$	5.36864	+	3.09959i	0.240575	+	0.138896i
$499$	−16.1143	+	9.30362i	−0.721377	+	0.416487i	−0.815259	−	0.579096i	$-0.803406\pi$
$499$	−16.1143	+	9.30362i	−0.721377	+	0.416487i	0.0938822	+	0.995583i	$0.470072\pi$
$500$	−0.866025	+	0.500000i	−0.0387298	+	0.0223607i
$501$	20.2100	+	11.6682i	0.902915	+	0.521298i
$502$	2.58638	−	4.47974i	0.115436	−	0.199941i
$503$	19.1727	+	11.0694i	0.854869	+	0.493559i	0.862291	−	0.506414i	$-0.169029\pi$
$503$	19.1727	+	11.0694i	0.854869	+	0.493559i	−0.00742159	+	0.999972i	$0.502362\pi$
$504$			1.68974i			0.0752671i
$505$	14.2424	−	8.22286i	0.633779	−	0.365913i
$506$	−10.0197	+	17.3546i	−0.445429	+	0.771505i
$507$	−7.45697			−0.331176
$508$	2.99173			0.132737
$509$	17.3019	−	29.9677i	0.766892	−	1.32830i	−0.172349	−	0.985036i	$-0.555136\pi$
$509$	17.3019	−	29.9677i	0.766892	−	1.32830i	0.939241	−	0.343259i	$-0.111531\pi$
$510$			2.68974i			0.119104i
$511$	−9.57047	−	16.5765i	−0.423373	−	0.733303i
$512$			1.00000i			0.0441942i
$513$	−2.29583	+	1.32550i	−0.101363	+	0.0585222i
$514$	−2.62750	−	4.55097i	−0.115894	−	0.200734i
$515$	−8.91682	−	15.4444i	−0.392922	−	0.680561i
$516$	−3.57035	−	2.06134i	−0.157176	−	0.0907455i
$517$	28.3153			1.24530
$518$	−0.401525	+	10.2704i	−0.0176420	+	0.451258i
$519$	−20.4500			−0.897654
$520$	3.91698	+	2.26147i	0.171771	+	0.0991720i
$521$	18.5319	+	32.0981i	0.811896	+	1.40625i	0.911535	+	0.411222i	$0.134898\pi$
$521$	18.5319	+	32.0981i	0.811896	+	1.40625i	−0.0996392	+	0.995024i	$0.531769\pi$
$522$	−3.14687	−	5.45053i	−0.137735	−	0.238563i
$523$	−30.5973	+	17.6653i	−1.33792	+	0.772451i	−0.986499	−	0.163765i	$-0.947636\pi$
$523$	−30.5973	+	17.6653i	−1.33792	+	0.772451i	−0.351425	+	0.936216i	$0.614303\pi$
$524$		−	13.1906i		−	0.576232i
$525$	−0.844871	−	1.46336i	−0.0368732	−	0.0638662i
$526$			12.7092i			0.554149i
$527$	−2.86768	+	4.96696i	−0.124918	+	0.216364i
$528$	−3.20374			−0.139425
$529$	−16.1249			−0.701082
$530$	−6.84663	+	11.8587i	−0.297398	+	0.515109i
$531$	−0.611376	+	0.352978i	−0.0265314	+	0.0153179i
$532$		−	4.47950i		−	0.194211i
$533$	−44.2671	−	25.5576i	−1.91742	−	1.10702i
$534$	−0.710515	+	1.23065i	−0.0307470	+	0.0532554i
$535$	3.41320	+	1.97061i	0.147565	+	0.0851969i
$536$	−0.367674	+	0.212277i	−0.0158811	+	0.00916895i
$537$	−19.0732	+	11.0119i	−0.823068	+	0.475198i
$538$	−14.7054	−	8.49019i	−0.633996	−	0.366038i
$539$	−6.63938	+	11.4997i	−0.285978	+	0.495329i
$540$	−0.866025	−	0.500000i	−0.0372678	−	0.0215166i
$541$		−	27.4851i		−	1.18168i	−0.806790	−	0.590838i	$-0.798797\pi$
$541$		−	27.4851i		−	1.18168i	0.806790	−	0.590838i	$-0.201203\pi$
$542$	−3.97356	+	2.29413i	−0.170679	+	0.0985415i
$543$	−7.63876	+	13.2307i	−0.327811	+	0.567785i
$544$	−2.68974			−0.115322
$545$	11.7662			0.504010
$546$	−3.82130	+	6.61868i	−0.163536	+	0.283253i
$547$		−	30.7640i		−	1.31537i	−0.753292	−	0.657686i	$-0.771535\pi$
$547$		−	30.7640i		−	1.31537i	0.753292	−	0.657686i	$-0.228465\pi$
$548$	10.8802	+	18.8451i	0.464779	+	0.805021i
$549$		−	10.1794i		−	0.434448i
$550$	2.77452	−	1.60187i	0.118306	−	0.0683039i
$551$	8.34233	+	14.4493i	0.355395	+	0.615563i
$552$	−3.12749	−	5.41698i	−0.133115	−	0.230562i
$553$	5.12492	+	2.95888i	0.217934	+	0.125824i
$554$	−21.9560			−0.932822
$555$	−5.14499	−	3.24485i	−0.218393	−	0.137736i
$556$	17.6698			0.749367
$557$	14.7174	+	8.49710i	0.623597	+	0.360034i	0.778268	−	0.627932i	$-0.216099\pi$
$557$	14.7174	+	8.49710i	0.623597	+	0.360034i	−0.154671	+	0.987966i	$0.549432\pi$
$558$	−1.06615	−	1.84663i	−0.0451339	−	0.0781742i
$559$	−9.32332	−	16.1485i	−0.394334	−	0.683007i
$560$	1.46336	−	0.844871i	0.0618382	−	0.0357023i
$561$		−	8.61722i		−	0.363819i
$562$	1.66816	+	2.88933i	0.0703669	+	0.121879i
$563$			3.67732i			0.154980i	0.996993	+	0.0774902i	$0.0246907\pi$
$563$			3.67732i			0.154980i	−0.996993	+	0.0774902i	$0.975309\pi$
$564$	−4.41910	+	7.65411i	−0.186078	+	0.322296i
$565$	12.8701			0.541449
$566$	−4.58630			−0.192777
$567$	0.844871	−	1.46336i	0.0354812	−	0.0614553i
$568$	6.45271	−	3.72548i	0.270750	−	0.156318i
$569$			8.07668i			0.338592i	0.985565	+	0.169296i	$0.0541494\pi$
$569$			8.07668i			0.338592i	−0.985565	+	0.169296i	$0.945851\pi$
$570$	2.29583	+	1.32550i	0.0961618	+	0.0555190i
$571$	−5.54346	+	9.60155i	−0.231986	+	0.401812i	−0.958393	−	0.285453i	$-0.907856\pi$
$571$	−5.54346	+	9.60155i	−0.231986	+	0.401812i	0.726406	+	0.687266i	$0.241189\pi$
$572$	−12.5490	−	7.24515i	−0.524699	−	0.302935i
$573$	2.75485	−	1.59051i	0.115086	−	0.0664447i
$574$	−16.5379	+	9.54816i	−0.690278	+	0.398532i
$575$	5.41698	+	3.12749i	0.225904	+	0.130426i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	21.0142	+	12.1325i	0.874831	+	0.505084i	0.868951	−	0.494899i	$-0.164795\pi$
$577$	21.0142	+	12.1325i	0.874831	+	0.505084i	0.00588031	+	0.999983i	$0.498128\pi$
$578$			9.76529i			0.406183i
$579$	−6.52555	+	3.76753i	−0.271192	+	0.156573i
$580$	−3.14687	+	5.45053i	−0.130667	+	0.226321i
$581$	10.4750			0.434576
$582$	−12.9663			−0.537469
$583$	21.9348	−	37.9922i	0.908446	−	1.57347i
$584$			11.3277i			0.468745i
$585$	−2.26147	−	3.91698i	−0.0935002	−	0.161947i
$586$		−	18.1358i		−	0.749185i
$587$	−27.2504	+	15.7330i	−1.12474	+	0.649370i	−0.942607	−	0.333903i	$-0.891634\pi$
$587$	−27.2504	+	15.7330i	−1.12474	+	0.649370i	−0.182135	+	0.983274i	$0.558301\pi$
$588$	−2.07239	−	3.58948i	−0.0854638	−	0.148028i
$589$	2.82637	+	4.89542i	0.116459	+	0.201712i
$590$	0.611376	+	0.352978i	0.0251699	+	0.0145319i
$591$	4.67073			0.192128
$592$	3.24485	−	5.14499i	0.133362	−	0.211458i
$593$	27.4169			1.12588			0.562938	−	0.826499i	$-0.309671\pi$
$593$	27.4169			1.12588			0.562938	+	0.826499i	$0.309671\pi$
$594$	2.77452	+	1.60187i	0.113840	+	0.0657254i
$595$	2.27248	+	3.93606i	0.0931627	+	0.161363i
$596$	1.40414	+	2.43205i	0.0575159	+	0.0996205i
$597$	−8.96907	+	5.17829i	−0.367079	+	0.211933i
$598$		−	28.2909i		−	1.15690i
$599$	16.5443	+	28.6556i	0.675982	+	1.17084i	0.976181	+	0.216959i	$0.0696138\pi$
$599$	16.5443	+	28.6556i	0.675982	+	1.17084i	−0.300198	+	0.953877i	$0.597053\pi$
$600$			1.00000i			0.0408248i
$601$	16.2965	−	28.2263i	0.664748	−	1.15138i	−0.314606	−	0.949222i	$-0.601872\pi$
$601$	16.2965	−	28.2263i	0.664748	−	1.15138i	0.979354	−	0.202154i	$-0.0647942\pi$
$602$	−6.96627			−0.283924
$603$	0.424553			0.0172891
$604$	−6.91805	+	11.9824i	−0.281491	+	0.487557i
$605$	0.637460	−	0.368038i	0.0259164	−	0.0149629i
$606$		−	16.4457i		−	0.668062i
$607$	−14.5982	−	8.42827i	−0.592522	−	0.342093i	0.173572	−	0.984821i	$-0.444469\pi$
$607$	−14.5982	−	8.42827i	−0.592522	−	0.342093i	−0.766094	+	0.642728i	$0.777802\pi$
$608$	−1.32550	+	2.29583i	−0.0537561	+	0.0931082i
$609$	−9.20999	−	5.31739i	−0.373208	−	0.215472i
$610$	−8.81565	+	5.08972i	−0.356935	+	0.206077i
$611$	−34.6191	+	19.9873i	−1.40054	+	0.808601i
$612$	2.32938	+	1.34487i	0.0941598	+	0.0543632i
$613$	−8.50922	+	14.7384i	−0.343684	+	0.595279i	−0.985114	−	0.171903i	$-0.945008\pi$
$613$	−8.50922	+	14.7384i	−0.343684	+	0.595279i	0.641430	+	0.767182i	$0.278342\pi$
$614$	−8.60188	−	4.96630i	−0.347144	−	0.200423i
$615$		−	11.3013i		−	0.455713i
$616$	−4.68822	+	2.70674i	−0.188894	+	0.109058i
$617$	−9.62460	+	16.6703i	−0.387472	+	0.671121i	−0.992109	−	0.125380i	$-0.959985\pi$
$617$	−9.62460	+	16.6703i	−0.387472	+	0.671121i	0.604637	+	0.796501i	$0.293318\pi$
$618$	−17.8336			−0.717375
$619$	−2.21721			−0.0891171			−0.0445585	−	0.999007i	$-0.514188\pi$
$619$	−2.21721			−0.0891171			−0.0445585	+	0.999007i	$0.514188\pi$
$620$	−1.06615	+	1.84663i	−0.0428178	+	0.0741625i
$621$			6.25499i			0.251004i
$622$	−16.8754	−	29.2291i	−0.676643	−	1.17198i
$623$			2.40117i			0.0962010i
$624$	3.91698	−	2.26147i	0.156805	−	0.0905312i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	2.85724	+	4.94889i	0.114198	+	0.197798i
$627$	−7.35524	−	4.24655i	−0.293740	−	0.169591i
$628$	−9.45064			−0.377122
$629$	13.8387	+	8.72780i	0.551785	+	0.348000i
$630$	−1.68974			−0.0673209
$631$	−33.8176	−	19.5246i	−1.34626	−	0.777262i	−0.358540	−	0.933514i	$-0.616725\pi$
$631$	−33.8176	−	19.5246i	−1.34626	−	0.777262i	−0.987717	+	0.156252i	$0.950059\pi$
$632$	−1.75108	−	3.03296i	−0.0696543	−	0.120645i
$633$	12.2519	+	21.2210i	0.486971	+	0.843458i
$634$	−15.4713	+	8.93237i	−0.614445	+	0.354750i
$635$			2.99173i			0.118723i
$636$	6.84663	+	11.8587i	0.271486	+	0.470228i
$637$		−	18.7466i		−	0.742766i
$638$	10.0817	−	17.4621i	0.399140	−	0.691330i
$639$	−7.45095			−0.294755
$640$	−1.00000			−0.0395285
$641$	12.0650	−	20.8972i	0.476539	−	0.825389i	−0.523100	−	0.852271i	$-0.675225\pi$
$641$	12.0650	−	20.8972i	0.476539	−	0.825389i	0.999639	+	0.0268821i	$0.00855785\pi$
$642$	3.41320	−	1.97061i	0.134708	−	0.0777738i
$643$		−	23.7974i		−	0.938478i	−0.883071	−	0.469239i	$-0.844528\pi$
$643$		−	23.7974i		−	0.938478i	0.883071	−	0.469239i	$-0.155472\pi$
$644$	−9.15329	−	5.28466i	−0.360690	−	0.208245i
$645$	2.06134	−	3.57035i	0.0811652	−	0.140582i
$646$	−6.17519	−	3.56525i	−0.242960	−	0.140273i
$647$	2.35379	−	1.35896i	0.0925371	−	0.0534263i	−0.453017	−	0.891502i	$-0.649652\pi$
$647$	2.35379	−	1.35896i	0.0925371	−	0.0534263i	0.545554	+	0.838075i	$0.316319\pi$
$648$	−0.866025	+	0.500000i	−0.0340207	+	0.0196419i
$649$	−1.95869	−	1.13085i	−0.0768851	−	0.0443897i
$650$	−2.26147	+	3.91698i	−0.0887021	+	0.153637i
$651$	−3.12033	−	1.80152i	−0.122295	−	0.0706073i
$652$			15.8690i			0.621478i
$653$	31.8316	−	18.3780i	1.24567	−	0.719186i	0.275424	−	0.961323i	$-0.411182\pi$
$653$	31.8316	−	18.3780i	1.24567	−	0.719186i	0.970242	+	0.242137i	$0.0778483\pi$
$654$	5.88311	−	10.1898i	0.230048	−	0.398455i
$655$	13.1906			0.515398
$656$	11.3013			0.441243
$657$	5.66387	−	9.81011i	0.220969	−	0.382729i
$658$			14.9343i			0.582199i
$659$	−2.01447	−	3.48917i	−0.0784727	−	0.135919i	0.824118	−	0.566418i	$-0.191671\pi$
$659$	−2.01447	−	3.48917i	−0.0784727	−	0.135919i	−0.902591	+	0.430499i	$0.858338\pi$
$660$		−	3.20374i		−	0.124705i
$661$	−34.3561	+	19.8355i	−1.33630	+	0.771512i	−0.986256	−	0.165222i	$-0.947166\pi$
$661$	−34.3561	+	19.8355i	−1.33630	+	0.771512i	−0.350042	+	0.936734i	$0.613833\pi$
$662$	−11.3110	−	19.5912i	−0.439614	−	0.761434i
$663$	6.08277	+	10.5357i	0.236235	+	0.409171i
$664$	−5.36864	−	3.09959i	−0.208344	−	0.120287i
$665$	4.47950			0.173708
$666$	−5.38262	+	2.83327i	−0.208572	+	0.109787i
$667$	39.3672			1.52431
$668$	−20.2100	−	11.6682i	−0.781948	−	0.451458i
$669$	−5.95223	−	10.3096i	−0.230127	−	0.398591i
$670$	−0.212277	−	0.367674i	−0.00820096	−	0.0142045i
$671$	28.2430	−	16.3061i	1.09031	−	0.629491i
$672$		−	1.68974i		−	0.0651832i
$673$	9.22709	+	15.9818i	0.355678	+	0.616053i	0.987234	−	0.159278i	$-0.0509166\pi$
$673$	9.22709	+	15.9818i	0.355678	+	0.616053i	−0.631556	+	0.775331i	$0.717583\pi$
$674$		−	2.44300i		−	0.0941010i
$675$	0.500000	−	0.866025i	0.0192450	−	0.0333333i
$676$	7.45697			0.286807
$677$	3.66094			0.140701			0.0703506	−	0.997522i	$-0.477588\pi$
$677$	3.66094			0.140701			0.0703506	+	0.997522i	$0.477588\pi$
$678$	6.43505	−	11.1458i	0.247136	−	0.428053i
$679$	−18.9743	+	10.9548i	−0.728167	+	0.420407i
$680$		−	2.68974i		−	0.103147i
$681$	−4.70710	−	2.71765i	−0.180377	−	0.104140i
$682$	3.41567	−	5.91612i	0.130793	−	0.226540i
$683$	−11.6297	−	6.71440i	−0.444997	−	0.256919i	0.260718	−	0.965415i	$-0.416041\pi$
$683$	−11.6297	−	6.71440i	−0.444997	−	0.256919i	−0.705715	+	0.708496i	$0.749374\pi$
$684$	2.29583	−	1.32550i	0.0877833	−	0.0506817i
$685$	−18.8451	+	10.8802i	−0.720033	+	0.415711i
$686$	−16.3088	−	9.41589i	−0.622673	−	0.359500i
$687$	−8.22859	+	14.2523i	−0.313940	+	0.543761i
$688$	3.57035	+	2.06134i	0.136118	+	0.0785879i
$689$			61.9337i			2.35949i
$690$	5.41698	−	3.12749i	0.206221	−	0.119062i
$691$	−0.0307256	+	0.0532183i	−0.00116886	+	0.00202452i	−0.866609	−	0.498987i	$-0.833705\pi$
$691$	−0.0307256	+	0.0532183i	−0.00116886	+	0.00202452i	0.865440	+	0.501012i	$0.167039\pi$
$692$	20.4500			0.777391
$693$	5.41349			0.205641
$694$	4.95497	−	8.58225i	0.188088	−	0.325778i
$695$			17.6698i			0.670255i
$696$	3.14687	+	5.45053i	0.119282	+	0.206602i
$697$			30.3976i			1.15139i
$698$	−0.724391	+	0.418227i	−0.0274186	+	0.0158301i
$699$	−0.699610	−	1.21176i	−0.0264617	−	0.0458330i
$700$	0.844871	+	1.46336i	0.0319331	+	0.0553098i
$701$	−7.26675	−	4.19546i	−0.274461	−	0.158460i	0.356452	−	0.934314i	$-0.383986\pi$
$701$	−7.26675	−	4.19546i	−0.274461	−	0.158460i	−0.630913	+	0.775853i	$0.717320\pi$
$702$	−4.52294			−0.170707
$703$	14.2693	−	7.51099i	0.538177	−	0.283282i
$704$	3.20374			0.120745
$705$	−7.65411	−	4.41910i	−0.288271	−	0.166433i
$706$	3.01172	+	5.21645i	0.113347	+	0.196324i
$707$	−13.8945	−	24.0660i	−0.522557	−	0.905095i
$708$	0.611376	−	0.352978i	0.0229769	−	0.0132657i
$709$			17.1872i			0.645478i	0.946488	+	0.322739i	$0.104604\pi$
$709$			17.1872i			0.645478i	−0.946488	+	0.322739i	$0.895396\pi$
$710$	3.72548	+	6.45271i	0.139815	+	0.242166i
$711$			3.50216i			0.131341i
$712$	0.710515	−	1.23065i	0.0266277	−	0.0461205i
$713$	13.3376			0.499496
$714$	4.54497			0.170091
$715$	7.24515	−	12.5490i	0.270953	−	0.469305i
$716$	19.0732	−	11.0119i	0.712798	−	0.411534i
$717$		−	10.6250i		−	0.396798i
$718$	−8.30278	−	4.79361i	−0.309857	−	0.178896i
$719$	−14.8025	+	25.6386i	−0.552039	+	0.956160i	0.446088	+	0.894989i	$0.352817\pi$
$719$	−14.8025	+	25.6386i	−0.552039	+	0.956160i	−0.998127	+	0.0611710i	$0.980516\pi$
$720$	0.866025	+	0.500000i	0.0322749	+	0.0186339i
$721$	−26.0970	+	15.0671i	−0.971904	+	0.561129i
$722$	10.3682	−	5.98611i	0.385866	−	0.222780i
$723$	2.56645	+	1.48174i	0.0954473	+	0.0551065i
$724$	7.63876	−	13.2307i	0.283892	−	0.491716i
$725$	−5.45053	−	3.14687i	−0.202428	−	0.116872i
$726$		−	0.736075i		−	0.0273183i
$727$	26.0563	−	15.0436i	0.966373	−	0.557936i	0.0682444	−	0.997669i	$-0.478260\pi$
$727$	26.0563	−	15.0436i	0.966373	−	0.557936i	0.898129	+	0.439733i	$0.144927\pi$
$728$	3.82130	−	6.61868i	0.141627	−	0.245305i
$729$	1.00000			0.0370370
$730$	−11.3277			−0.419258
$731$	−5.54447	+	9.60331i	−0.205070	+	0.355191i
$732$			10.1794i			0.376243i
$733$	−22.3192	−	38.6579i	−0.824377	−	1.42786i	−0.902395	−	0.430910i	$-0.858192\pi$
$733$	−22.3192	−	38.6579i	−0.824377	−	1.42786i	0.0780180	−	0.996952i	$-0.475141\pi$
$734$			28.0627i			1.03581i
$735$	3.58948	−	2.07239i	0.132400	−	0.0764411i
$736$	3.12749	+	5.41698i	0.115281	+	0.199673i
$737$	0.680078	+	1.17793i	0.0250510	+	0.0433896i
$738$	−9.78723	−	5.65066i	−0.360273	−	0.208004i
$739$	−5.42290			−0.199484			−0.0997422	−	0.995013i	$-0.531802\pi$
$739$	−5.42290			−0.199484			−0.0997422	+	0.995013i	$0.531802\pi$
$740$	5.14499	+	3.24485i	0.189134	+	0.119283i
$741$	11.9903			0.440474
$742$	20.0381	+	11.5690i	0.735623	+	0.424712i
$743$	−10.3549	−	17.9352i	−0.379884	−	0.657978i	0.611161	−	0.791506i	$-0.290703\pi$
$743$	−10.3549	−	17.9352i	−0.379884	−	0.657978i	−0.991045	+	0.133528i	$0.957369\pi$
$744$	1.06615	+	1.84663i	0.0390871	+	0.0677008i
$745$	−2.43205	+	1.40414i	−0.0891033	+	0.0514438i
$746$		−	5.69684i		−	0.208576i
$747$	3.09959	+	5.36864i	0.113408	+	0.196428i
$748$			8.61722i			0.315077i
$749$	3.32982	−	5.76742i	0.121669	−	0.210737i
$750$	−1.00000			−0.0365148
$751$	2.54287			0.0927906			0.0463953	−	0.998923i	$-0.485227\pi$
$751$	2.54287			0.0927906			0.0463953	+	0.998923i	$0.485227\pi$
$752$	4.41910	−	7.65411i	0.161148	−	0.279117i
$753$	4.47974	−	2.58638i	0.163251	−	0.0942530i
$754$			28.4662i			1.03668i
$755$	−11.9824	−	6.91805i	−0.436084	−	0.251773i
$756$	−0.844871	+	1.46336i	−0.0307276	+	0.0532219i
$757$	16.2988	+	9.41009i	0.592389	+	0.342016i	0.766041	−	0.642791i	$-0.222224\pi$
$757$	16.2988	+	9.41009i	0.592389	+	0.342016i	−0.173653	+	0.984807i	$0.555557\pi$
$758$	12.2120	−	7.05060i	0.443560	−	0.256089i
$759$	−17.3546	+	10.0197i	−0.629931	+	0.363691i
$760$	−2.29583	−	1.32550i	−0.0832785	−	0.0480809i
$761$	9.17785	−	15.8965i	0.332697	−	0.576248i	−0.650343	−	0.759641i	$-0.725375\pi$
$761$	9.17785	−	15.8965i	0.332697	−	0.576248i	0.983040	+	0.183393i	$0.0587081\pi$
$762$	2.59092	+	1.49587i	0.0938591	+	0.0541896i
$763$		−	19.8819i		−	0.719772i
$764$	−2.75485	+	1.59051i	−0.0996670	+	0.0575428i
$765$	−1.34487	+	2.32938i	−0.0486239	+	0.0842191i
$766$	27.4056			0.990204
$767$	3.19299			0.115292
$768$	−0.500000	+	0.866025i	−0.0180422	+	0.0312500i
$769$		−	12.0032i		−	0.432846i	−0.976300	−	0.216423i	$-0.930561\pi$
$769$		−	12.0032i		−	0.432846i	0.976300	−	0.216423i	$-0.0694390\pi$
$770$	−2.70674	−	4.68822i	−0.0975442	−	0.168952i
$771$		−	5.25500i		−	0.189254i
$772$	6.52555	−	3.76753i	0.234860	−	0.135596i
$773$	8.17897	+	14.1664i	0.294177	+	0.509530i	0.974793	−	0.223111i	$-0.0716211\pi$
$773$	8.17897	+	14.1664i	0.294177	+	0.509530i	−0.680616	+	0.732640i	$0.738288\pi$
$774$	−2.06134	−	3.57035i	−0.0740934	−	0.128333i
$775$	−1.84663	−	1.06615i	−0.0663330	−	0.0382974i
$776$	12.9663			0.465462
$777$	−5.48296	+	8.69371i	−0.196700	+	0.311885i
$778$	−31.8371			−1.14142
$779$	25.9459	+	14.9799i	0.929609	+	0.536710i
$780$	2.26147	+	3.91698i	0.0809736	+	0.140250i
$781$	−11.9354	−	20.6728i	−0.427084	−	0.739731i
$782$	−14.5703	+	8.41215i	−0.521032	+	0.300818i
$783$		−	6.29373i		−	0.224920i
$784$	2.07239	+	3.58948i	0.0740138	+	0.128196i
$785$		−	9.45064i		−	0.337308i
$786$	6.59528	−	11.4234i	0.235246	−	0.407458i
$787$	37.2559			1.32803			0.664015	−	0.747719i	$-0.268851\pi$
$787$	37.2559			1.32803			0.664015	+	0.747719i	$0.268851\pi$
$788$	−4.67073			−0.166388
$789$	−6.35462	+	11.0065i	−0.226230	+	0.391843i
$790$	3.03296	−	1.75108i	0.107908	−	0.0623007i
$791$		−	21.7471i		−	0.773239i
$792$	−2.77452	−	1.60187i	−0.0985882	−	0.0569199i
$793$	−23.0205	+	39.8727i	−0.817482	+	1.41592i
$794$	−12.0798	−	6.97428i	−0.428696	−	0.247508i
$795$	−11.8587	+	6.84663i	−0.420585	+	0.242825i
$796$	8.96907	−	5.17829i	0.317900	−	0.183540i
$797$	25.0185	+	14.4444i	0.886200	+	0.511648i	0.872697	−	0.488261i	$-0.162369\pi$
$797$	25.0185	+	14.4444i	0.886200	+	0.511648i	0.0135021	+	0.999909i	$0.495702\pi$
$798$	2.23975	−	3.87936i	0.0792863	−	0.137328i
$799$	20.5876	+	11.8862i	0.728336	+	0.420505i
$800$		−	1.00000i		−	0.0353553i
$801$	−1.23065	+	0.710515i	−0.0434828	+	0.0251048i
$802$	6.64047	−	11.5016i	0.234483	−	0.406137i
$803$	36.2911			1.28068
$804$	−0.424553			−0.0149728
$805$	5.28466	−	9.15329i	0.186260	−	0.322611i
$806$			9.64429i			0.339706i
$807$	−8.49019	−	14.7054i	−0.298869	−	0.517656i
$808$			16.4457i			0.578559i
$809$	−13.9657	+	8.06309i	−0.491007	+	0.283483i	−0.724992	−	0.688757i	$-0.758157\pi$
$809$	−13.9657	+	8.06309i	−0.491007	+	0.283483i	0.233985	+	0.972240i	$0.424823\pi$
$810$	−0.500000	−	0.866025i	−0.0175682	−	0.0304290i
$811$	−5.09248	−	8.82043i	−0.178821	−	0.309727i	0.762656	−	0.646804i	$-0.223895\pi$
$811$	−5.09248	−	8.82043i	−0.178821	−	0.309727i	−0.941477	+	0.337077i	$0.890562\pi$
$812$	9.20999	+	5.31739i	0.323207	+	0.186604i
$813$	−4.58827			−0.160918
$814$	−16.4832	−	10.3956i	−0.577736	−	0.364367i
$815$	−15.8690			−0.555867
$816$	−2.32938	−	1.34487i	−0.0815448	−	0.0470799i
$817$	5.46461	+	9.46498i	0.191182	+	0.331138i
$818$	15.1542	+	26.2478i	0.529853	+	0.917732i
$819$	−6.61868	+	3.82130i	−0.231275	+	0.133527i
$820$			11.3013i			0.394659i
$821$	9.75708	+	16.8998i	0.340525	+	0.589806i	0.984530	−	0.175215i	$-0.0560620\pi$
$821$	9.75708	+	16.8998i	0.340525	+	0.589806i	−0.644006	+	0.765021i	$0.722729\pi$
$822$			21.7604i			0.758981i
$823$	−3.28738	+	5.69391i	−0.114591	+	0.198477i	−0.917616	−	0.397468i	$-0.869889\pi$
$823$	−3.28738	+	5.69391i	−0.114591	+	0.198477i	0.803025	+	0.595945i	$0.203222\pi$
$824$	17.8336			0.621265
$825$	3.20374			0.111540
$826$	0.596441	−	1.03307i	0.0207528	−	0.0359450i
$827$	−37.2984	+	21.5342i	−1.29699	+	0.748819i	−0.979883	−	0.199570i	$-0.936045\pi$
$827$	−37.2984	+	21.5342i	−1.29699	+	0.748819i	−0.317109	+	0.948389i	$0.602712\pi$
$828$		−	6.25499i		−	0.217376i
$829$	10.2374	+	5.91056i	0.355559	+	0.205282i	0.667131	−	0.744940i	$-0.267522\pi$
$829$	10.2374	+	5.91056i	0.355559	+	0.205282i	−0.311572	+	0.950223i	$0.600855\pi$
$830$	3.09959	−	5.36864i	0.107588	−	0.186348i
$831$	−19.0145	−	10.9780i	−0.659604	−	0.380823i
$832$	−3.91698	+	2.26147i	−0.135797	+	0.0784023i
$833$	−9.65477	+	5.57419i	−0.334518	+	0.193134i
$834$	15.3025	+	8.83491i	0.529883	+	0.305928i
$835$	11.6682	−	20.2100i	0.403796	−	0.699395i
$836$	7.35524	+	4.24655i	0.254386	+	0.146870i
$837$		−	2.13231i		−	0.0737033i
$838$	8.77949	−	5.06884i	0.303282	−	0.175100i
$839$	14.6792	−	25.4251i	0.506781	−	0.877771i	−0.493188	−	0.869923i	$-0.664169\pi$
$839$	14.6792	−	25.4251i	0.506781	−	0.877771i	0.999969	−	0.00784800i	$-0.00249812\pi$
$840$	1.68974			0.0583016
$841$	−10.6111			−0.365900
$842$	4.57423	−	7.92280i	0.157638	−	0.273038i
$843$			3.33631i			0.114909i
$844$	−12.2519	−	21.2210i	−0.421729	−	0.730456i
$845$			7.45697i			0.256528i
$846$	−7.65411	+	4.41910i	−0.263154	+	0.151932i
$847$	−0.621888	−	1.07714i	−0.0213683	−	0.0370111i
$848$	−6.84663	−	11.8587i	−0.235114	−	0.407230i
$849$	−3.97186	−	2.29315i	−0.136314	−	0.0787008i
$850$	2.68974			0.0922574
$851$	1.48634	−	38.0186i	0.0509511	−	1.30326i
$852$	7.45095			0.255265
$853$	35.7411	+	20.6351i	1.22375	+	0.706533i	0.965716	−	0.259602i	$-0.0835913\pi$
$853$	35.7411	+	20.6351i	1.22375	+	0.706533i	0.258036	+	0.966135i	$0.416925\pi$
$854$	8.60031	+	14.8962i	0.294297	+	0.509737i
$855$	1.32550	+	2.29583i	0.0453311	+	0.0785157i
$856$	−3.41320	+	1.97061i	−0.116661	+	0.0673541i
$857$			7.12163i			0.243270i	0.992575	+	0.121635i	$0.0388138\pi$
$857$			7.12163i			0.243270i	−0.992575	+	0.121635i	$0.961186\pi$
$858$	−7.24515	−	12.5490i	−0.247345	−	0.428415i
$859$		−	33.8063i		−	1.15346i	−0.816936	−	0.576729i	$-0.804329\pi$
$859$		−	33.8063i		−	1.15346i	0.816936	−	0.576729i	$-0.195671\pi$
$860$	−2.06134	+	3.57035i	−0.0702911	+	0.121748i
$861$	−19.0963			−0.650801
$862$	25.5246			0.869372
$863$	−24.8049	+	42.9633i	−0.844368	+	1.46249i	0.0418016	+	0.999126i	$0.486690\pi$
$863$	−24.8049	+	42.9633i	−0.844368	+	1.46249i	−0.886169	+	0.463362i	$0.846643\pi$
$864$	0.866025	−	0.500000i	0.0294628	−	0.0170103i
$865$			20.4500i			0.695320i
$866$	24.7588	+	14.2945i	0.841338	+	0.485746i
$867$	−4.88265	+	8.45699i	−0.165823	+	0.287214i
$868$	3.12033	+	1.80152i	0.105911	+	0.0611477i
$869$	−9.71681	+	5.61001i	−0.329620	+	0.190306i
$870$	−5.45053	+	3.14687i	−0.184790	+	0.106689i
$871$	−1.66297	−	0.960114i	−0.0563475	−	0.0325322i
$872$	−5.88311	+	10.1898i	−0.199227	+	0.345072i
$873$	−11.2291	−	6.48313i	−0.380048	−	0.219421i
$874$			16.5820i			0.560893i
$875$	−1.46336	+	0.844871i	−0.0494706	+	0.0285618i
$876$	−5.66387	+	9.81011i	−0.191364	+	0.331453i
$877$	−29.8043			−1.00642			−0.503210	−	0.864164i	$-0.667848\pi$
$877$	−29.8043			−1.00642			−0.503210	+	0.864164i	$0.667848\pi$
$878$	4.29625			0.144991
$879$	9.06792	−	15.7061i	0.305853	−	0.529754i
$880$			3.20374i			0.107998i
$881$	−28.0176	−	48.5280i	−0.943939	−	1.63495i	−0.757863	−	0.652414i	$-0.773756\pi$
$881$	−28.0176	−	48.5280i	−0.943939	−	1.63495i	−0.186076	−	0.982535i	$-0.559577\pi$
$882$		−	4.14477i		−	0.139562i
$883$	−7.02209	+	4.05421i	−0.236312	+	0.136435i	−0.613481	−	0.789710i	$-0.710231\pi$
$883$	−7.02209	+	4.05421i	−0.236312	+	0.136435i	0.377168	+	0.926145i	$0.376898\pi$
$884$	−6.08277	−	10.5357i	−0.204586	−	0.354353i
$885$	0.352978	+	0.611376i	0.0118652	+	0.0205512i
$886$	−29.5497	−	17.0605i	−0.992742	−	0.573160i
$887$	−36.6169			−1.22948			−0.614738	−	0.788731i	$-0.710738\pi$
$887$	−36.6169			−1.22948			−0.614738	+	0.788731i	$0.710738\pi$
$888$	5.38262	−	2.83327i	0.180629	−	0.0950783i
$889$	5.05526			0.169548
$890$	1.23065	+	0.710515i	0.0412514	+	0.0238165i
$891$	1.60187	+	2.77452i	0.0536646	+	0.0929498i
$892$	5.95223	+	10.3096i	0.199295	+	0.345190i
$893$	20.2910	−	11.7150i	0.679013	−	0.392029i
$894$			2.80828i			0.0939231i
$895$	11.0119	+	19.0732i	0.368087	+	0.637545i
$896$			1.68974i			0.0564503i
$897$	14.1455	−	24.5007i	0.472303	−	0.818053i
$898$	20.1468			0.672308
$899$	−13.4202			−0.447588
$900$	−0.500000	+	0.866025i	−0.0166667	+	0.0288675i
$901$	31.8968	−	18.4157i	1.06264	−	0.613514i
$902$		−	36.2065i		−	1.20554i
$903$	−6.03296	−	3.48313i	−0.200764	−	0.115911i
$904$	−6.43505	+	11.1458i	−0.214026	+	0.370705i
$905$	13.2307	+	7.63876i	0.439804	+	0.253921i
$906$	−11.9824	+	6.91805i	−0.398089	+	0.229837i
$907$	−10.9606	+	6.32808i	−0.363939	+	0.210121i	−0.670807	−	0.741632i	$-0.734052\pi$
$907$	−10.9606	+	6.32808i	−0.363939	+	0.210121i	0.306868	+	0.951752i	$0.400719\pi$
$908$	4.70710	+	2.71765i	0.156211	+	0.0901883i
$909$	8.22286	−	14.2424i	0.272735	−	0.472391i
$910$	6.61868	+	3.82130i	0.219407	+	0.126675i
$911$			44.6493i			1.47930i	0.672994	+	0.739648i	$0.265008\pi$
$911$			44.6493i			1.47930i	−0.672994	+	0.739648i	$0.734992\pi$
$912$	−2.29583	+	1.32550i	−0.0760225	+	0.0438916i
$913$	−9.93026	+	17.1997i	−0.328644	+	0.569228i
$914$	23.8803			0.789892
$915$	−10.1794			−0.336522
$916$	8.22859	−	14.2523i	0.271880	−	0.470911i
$917$		−	22.2886i		−	0.736035i
$918$	1.34487	+	2.32938i	0.0443873	+	0.0768811i
$919$			33.3213i			1.09917i	0.835438	+	0.549585i	$0.185214\pi$
$919$			33.3213i			1.09917i	−0.835438	+	0.549585i	$0.814786\pi$
$920$	−5.41698	+	3.12749i	−0.178593	+	0.103110i
$921$	−4.96630	−	8.60188i	−0.163645	−	0.283442i
$922$	11.6238	+	20.1330i	0.382810	+	0.663046i
$923$	29.1852	+	16.8501i	0.960644	+	0.554628i
$924$	−5.41349			−0.178091
$925$	−3.24485	+	5.14499i	−0.106690	+	0.169166i
$926$	19.0843			0.627147
$927$	−15.4444	−	8.91682i	−0.507260	−	0.292867i
$928$	−3.14687	−	5.45053i	−0.103301	−	0.178923i
$929$	−3.22840	−	5.59175i	−0.105920	−	0.183460i	0.808193	−	0.588917i	$-0.200446\pi$
$929$	−3.22840	−	5.59175i	−0.105920	−	0.183460i	−0.914114	+	0.405458i	$0.867112\pi$
$930$	−1.84663	+	1.06615i	−0.0605535	+	0.0349606i
$931$			10.9878i			0.360110i
$932$	0.699610	+	1.21176i	0.0229165	+	0.0396925i
$933$		−	33.7509i		−	1.10495i
$934$	11.2331	−	19.4563i	0.367558	−	0.636630i
$935$	−8.61722			−0.281813
$936$	4.52294			0.147837
$937$	11.9854	−	20.7594i	0.391547	−	0.678179i	−0.601107	−	0.799169i	$-0.705273\pi$
$937$	11.9854	−	20.7594i	0.391547	−	0.678179i	0.992654	+	0.120989i	$0.0386067\pi$
$938$	−0.621274	+	0.358693i	−0.0202853	+	0.0117117i
$939$			5.71449i			0.186485i
$940$	7.65411	+	4.41910i	0.249650	+	0.144135i
$941$	−9.39565	+	16.2737i	−0.306289	+	0.530509i	−0.977548	−	0.210715i	$-0.932421\pi$
$941$	−9.39565	+	16.2737i	−0.306289	+	0.530509i	0.671258	+	0.741224i	$0.265754\pi$
$942$	−8.18450	−	4.72532i	−0.266665	−	0.153959i
$943$	61.2190	−	35.3448i	1.99357	−	1.15099i
$944$	−0.611376	+	0.352978i	−0.0198986	+	0.0114884i
$945$	−1.46336	−	0.844871i	−0.0476031	−	0.0274836i
$946$	6.60399	−	11.4385i	0.214714	−	0.371896i
$947$	1.19306	+	0.688814i	0.0387693	+	0.0223834i	0.519259	−	0.854617i	$-0.326208\pi$
$947$	1.19306	+	0.688814i	0.0387693	+	0.0223834i	−0.480490	+	0.877000i	$0.659541\pi$
$948$		−	3.50216i		−	0.113745i
$949$	−44.3705	+	25.6173i	−1.44033	+	0.831574i
$950$	1.32550	−	2.29583i	0.0430048	−	0.0744866i
$951$	−17.8647			−0.579304
$952$	−4.54497			−0.147303
$953$	−3.19306	+	5.53054i	−0.103433	+	0.179152i	−0.913097	−	0.407742i	$-0.866316\pi$
$953$	−3.19306	+	5.53054i	−0.103433	+	0.179152i	0.809664	+	0.586894i	$0.199650\pi$
$954$			13.6933i			0.443335i
$955$	−1.59051	−	2.75485i	−0.0514678	−	0.0891449i
$956$			10.6250i			0.343637i
$957$	17.4621	−	10.0817i	0.564469	−	0.325896i
$958$	−11.5211	−	19.9551i	−0.372229	−	0.644720i
$959$	18.3847	+	31.8433i	0.593674	+	1.02827i
$960$	−0.866025	−	0.500000i	−0.0279508	−	0.0161374i
$961$	26.4533			0.853331
$962$	27.4910	+	1.07476i	0.886344	+	0.0346518i
$963$	3.94122			0.127004
$964$	−2.56645	−	1.48174i	−0.0826597	−	0.0477236i
$965$	3.76753	+	6.52555i	0.121281	+	0.210065i
$966$	−5.28466	−	9.15329i	−0.170031	−	0.294502i
$967$	−3.73599	+	2.15698i	−0.120141	+	0.0693637i	−0.558866	−	0.829258i	$-0.688764\pi$
$967$	−3.73599	+	2.15698i	−0.120141	+	0.0693637i	0.438725	+	0.898621i	$0.355430\pi$
$968$			0.736075i			0.0236584i
$969$	−3.56525	−	6.17519i	−0.114532	−	0.198376i
$970$			12.9663i			0.416322i
$971$	21.5272	−	37.2862i	0.690841	−	1.19657i	−0.280722	−	0.959789i	$-0.590574\pi$
$971$	21.5272	−	37.2862i	0.690841	−	1.19657i	0.971563	−	0.236783i	$-0.0760929\pi$
$972$	−1.00000			−0.0320750
$973$	29.8574			0.957185
$974$	6.58221	−	11.4007i	0.210908	−	0.365303i
$975$	−3.91698	+	2.26147i	−0.125444	+	0.0724250i
$976$		−	10.1794i		−	0.325836i
$977$	3.06411	+	1.76906i	0.0980294	+	0.0565973i	0.548213	−	0.836339i	$-0.315308\pi$
$977$	3.06411	+	1.76906i	0.0980294	+	0.0565973i	−0.450184	+	0.892936i	$0.648642\pi$
$978$	−7.93450	+	13.7430i	−0.253717	+	0.439451i
$979$	−3.94267	−	2.27630i	−0.126008	−	0.0727509i
$980$	−3.58948	+	2.07239i	−0.114662	+	0.0662000i
$981$	10.1898	−	5.88311i	0.325337	−	0.187833i
$982$	−2.78503	−	1.60794i	−0.0888740	−	0.0513114i
$983$	30.5226	−	52.8668i	0.973521	−	1.68619i	0.288789	−	0.957393i	$-0.406747\pi$
$983$	30.5226	−	52.8668i	0.973521	−	1.68619i	0.684732	−	0.728795i	$-0.259919\pi$
$984$	9.78723	+	5.65066i	0.312006	+	0.180137i
$985$		−	4.67073i		−	0.148822i
$986$	14.6605	−	8.46426i	0.466886	−	0.269557i
$987$	−7.46714	+	12.9335i	−0.237682	+	0.411677i
$988$	−11.9903			−0.381462
$989$	25.7873			0.819989
$990$	1.60187	−	2.77452i	0.0509107	−	0.0881799i
$991$		−	41.5859i		−	1.32102i	−0.750818	−	0.660509i	$-0.770340\pi$
$991$		−	41.5859i		−	1.32102i	0.750818	−	0.660509i	$-0.229660\pi$
$992$	−1.06615	−	1.84663i	−0.0338504	−	0.0586306i
$993$		−	22.6220i		−	0.717887i
$994$	10.9034	−	6.29509i	0.345835	−	0.199668i
$995$	5.17829	+	8.96907i	0.164163	+	0.284339i
$996$	−3.09959	−	5.36864i	−0.0982142	−	0.170112i
$997$	37.0458	+	21.3884i	1.17325	+	0.677378i	0.954444	−	0.298390i	$-0.0964497\pi$
$997$	37.0458	+	21.3884i	1.17325	+	0.677378i	0.218808	+	0.975768i	$0.429783\pi$
$998$	18.6072			0.589002
$999$	−6.07812	−	0.237625i	−0.192303	−	0.00751812i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.x.d.841.4	yes	16
37.11	even	6	inner	1110.2.x.d.751.4	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.x.d.751.4	✓	16	37.11	even	6	inner
1110.2.x.d.841.4	yes	16	1.1	even	1	trivial

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.x (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} +1.00000i q^{6} +(0.844871 + 1.46336i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} +1.00000i q^{6} +(0.844871 + 1.46336i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +1.00000 q^{10} -3.20374 q^{11} +(0.500000 - 0.866025i) q^{12} +(3.91698 - 2.26147i) q^{13} -1.68974i q^{14} +(0.866025 + 0.500000i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.32938 - 1.34487i) q^{17} +(0.866025 - 0.500000i) q^{18} +(-2.29583 + 1.32550i) q^{19} +(-0.866025 - 0.500000i) q^{20} +(0.844871 - 1.46336i) q^{21} +(2.77452 + 1.60187i) q^{22} +6.25499i q^{23} +(-0.866025 + 0.500000i) q^{24} +(0.500000 - 0.866025i) q^{25} -4.52294 q^{26} +1.00000 q^{27} +(-0.844871 + 1.46336i) q^{28} -6.29373i q^{29} +(-0.500000 - 0.866025i) q^{30} -2.13231i q^{31} +(0.866025 - 0.500000i) q^{32} +(1.60187 + 2.77452i) q^{33} +(1.34487 + 2.32938i) q^{34} +(-1.46336 - 0.844871i) q^{35} -1.00000 q^{36} +(-6.07812 - 0.237625i) q^{37} +2.65100 q^{38} +(-3.91698 - 2.26147i) q^{39} +(0.500000 + 0.866025i) q^{40} +(-5.65066 - 9.78723i) q^{41} +(-1.46336 + 0.844871i) q^{42} -4.12268i q^{43} +(-1.60187 - 2.77452i) q^{44} -1.00000i q^{45} +(3.12749 - 5.41698i) q^{46} -8.83821 q^{47} +1.00000 q^{48} +(2.07239 - 3.58948i) q^{49} +(-0.866025 + 0.500000i) q^{50} +2.68974i q^{51} +(3.91698 + 2.26147i) q^{52} +(-6.84663 + 11.8587i) q^{53} +(-0.866025 - 0.500000i) q^{54} +(2.77452 - 1.60187i) q^{55} +(1.46336 - 0.844871i) q^{56} +(2.29583 + 1.32550i) q^{57} +(-3.14687 + 5.45053i) q^{58} +(0.611376 + 0.352978i) q^{59} +1.00000i q^{60} +(-8.81565 + 5.08972i) q^{61} +(-1.06615 + 1.84663i) q^{62} -1.68974 q^{63} -1.00000 q^{64} +(-2.26147 + 3.91698i) q^{65} -3.20374i q^{66} +(-0.212277 - 0.367674i) q^{67} -2.68974i q^{68} +(5.41698 - 3.12749i) q^{69} +(0.844871 + 1.46336i) q^{70} +(3.72548 + 6.45271i) q^{71} +(0.866025 + 0.500000i) q^{72} -11.3277 q^{73} +(5.14499 + 3.24485i) q^{74} -1.00000 q^{75} +(-2.29583 - 1.32550i) q^{76} +(-2.70674 - 4.68822i) q^{77} +(2.26147 + 3.91698i) q^{78} +(3.03296 - 1.75108i) q^{79} -1.00000i q^{80} +(-0.500000 - 0.866025i) q^{81} +11.3013i q^{82} +(3.09959 - 5.36864i) q^{83} +1.68974 q^{84} +2.68974 q^{85} +(-2.06134 + 3.57035i) q^{86} +(-5.45053 + 3.14687i) q^{87} +3.20374i q^{88} +(1.23065 + 0.710515i) q^{89} +(-0.500000 + 0.866025i) q^{90} +(6.61868 + 3.82130i) q^{91} +(-5.41698 + 3.12749i) q^{92} +(-1.84663 + 1.06615i) q^{93} +(7.65411 + 4.41910i) q^{94} +(1.32550 - 2.29583i) q^{95} +(-0.866025 - 0.500000i) q^{96} +12.9663i q^{97} +(-3.58948 + 2.07239i) q^{98} +(1.60187 - 2.77452i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{3} + 8 q^{4} - 2 q^{7} - 8 q^{9}+O(q^{10}) \) 16 * q - 8 * q^3 + 8 * q^4 - 2 * q^7 - 8 * q^9	\( 16 q - 8 q^{3} + 8 q^{4} - 2 q^{7} - 8 q^{9} + 16 q^{10} - 8 q^{11} + 8 q^{12} - 6 q^{13} - 8 q^{16} + 6 q^{17} - 12 q^{19} - 2 q^{21} + 8 q^{25} + 4 q^{26} + 16 q^{27} + 2 q^{28} - 8 q^{30} + 4 q^{33} + 6 q^{34} + 6 q^{35} - 16 q^{36} + 12 q^{37} - 4 q^{38} + 6 q^{39} + 8 q^{40} + 4 q^{41} + 6 q^{42} - 4 q^{44} - 2 q^{46} + 68 q^{47} + 16 q^{48} - 4 q^{49} - 6 q^{52} - 12 q^{53} - 6 q^{56} + 12 q^{57} - 6 q^{58} + 6 q^{59} + 12 q^{61} + 4 q^{62} + 4 q^{63} - 16 q^{64} + 2 q^{65} - 36 q^{67} + 18 q^{69} - 2 q^{70} + 6 q^{71} - 16 q^{73} + 14 q^{74} - 16 q^{75} - 12 q^{76} + 26 q^{77} - 2 q^{78} - 24 q^{79} - 8 q^{81} + 12 q^{83} - 4 q^{84} + 12 q^{85} - 2 q^{86} + 24 q^{89} - 8 q^{90} + 60 q^{91} - 18 q^{92} - 30 q^{93} + 6 q^{94} - 2 q^{95} - 12 q^{98} + 4 q^{99}+O(q^{100}) \) 16 * q - 8 * q^3 + 8 * q^4 - 2 * q^7 - 8 * q^9 + 16 * q^10 - 8 * q^11 + 8 * q^12 - 6 * q^13 - 8 * q^16 + 6 * q^17 - 12 * q^19 - 2 * q^21 + 8 * q^25 + 4 * q^26 + 16 * q^27 + 2 * q^28 - 8 * q^30 + 4 * q^33 + 6 * q^34 + 6 * q^35 - 16 * q^36 + 12 * q^37 - 4 * q^38 + 6 * q^39 + 8 * q^40 + 4 * q^41 + 6 * q^42 - 4 * q^44 - 2 * q^46 + 68 * q^47 + 16 * q^48 - 4 * q^49 - 6 * q^52 - 12 * q^53 - 6 * q^56 + 12 * q^57 - 6 * q^58 + 6 * q^59 + 12 * q^61 + 4 * q^62 + 4 * q^63 - 16 * q^64 + 2 * q^65 - 36 * q^67 + 18 * q^69 - 2 * q^70 + 6 * q^71 - 16 * q^73 + 14 * q^74 - 16 * q^75 - 12 * q^76 + 26 * q^77 - 2 * q^78 - 24 * q^79 - 8 * q^81 + 12 * q^83 - 4 * q^84 + 12 * q^85 - 2 * q^86 + 24 * q^89 - 8 * q^90 + 60 * q^91 - 18 * q^92 - 30 * q^93 + 6 * q^94 - 2 * q^95 - 12 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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