LMFDB - Embedded newform 1110.2.x.d.751.6

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			751.6
Root			$1.95985i$ of defining polynomial
Character	$\chi$	$=$	1110.751
Dual form			1110.2.x.d.841.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{5} +1.00000i q^{6} +(-0.979923 + 1.69728i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(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} +(-0.979923 + 1.69728i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +1.00000 q^{10} +2.45634 q^{11} +(0.500000 + 0.866025i) q^{12} +(1.23082 + 0.710611i) q^{13} +1.95985i q^{14} +(-0.866025 + 0.500000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.831252 + 0.479923i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(3.95806 + 2.28518i) q^{19} +(0.866025 - 0.500000i) q^{20} +(-0.979923 - 1.69728i) q^{21} +(2.12726 - 1.22817i) q^{22} -3.15327i q^{23} +(0.866025 + 0.500000i) q^{24} +(0.500000 + 0.866025i) q^{25} +1.42122 q^{26} +1.00000 q^{27} +(0.979923 + 1.69728i) q^{28} +8.68349i q^{29} +(-0.500000 + 0.866025i) q^{30} +6.99935i q^{31} +(-0.866025 - 0.500000i) q^{32} +(-1.22817 + 2.12726i) q^{33} +(-0.479923 + 0.831252i) q^{34} +(-1.69728 + 0.979923i) q^{35} -1.00000 q^{36} +(5.73867 - 2.01686i) q^{37} +4.57037 q^{38} +(-1.23082 + 0.710611i) q^{39} +(0.500000 - 0.866025i) q^{40} +(-4.88647 + 8.46362i) q^{41} +(-1.69728 - 0.979923i) q^{42} -3.84608i q^{43} +(1.22817 - 2.12726i) q^{44} -1.00000i q^{45} +(-1.57664 - 2.73082i) q^{46} +13.5293 q^{47} +1.00000 q^{48} +(1.57950 + 2.73577i) q^{49} +(0.866025 + 0.500000i) q^{50} -0.959847i q^{51} +(1.23082 - 0.710611i) q^{52} +(-5.33799 - 9.24568i) q^{53} +(0.866025 - 0.500000i) q^{54} +(2.12726 + 1.22817i) q^{55} +(1.69728 + 0.979923i) q^{56} +(-3.95806 + 2.28518i) q^{57} +(4.34174 + 7.52012i) q^{58} +(6.41533 - 3.70389i) q^{59} +1.00000i q^{60} +(-7.96035 - 4.59591i) q^{61} +(3.49967 + 6.06161i) q^{62} +1.95985 q^{63} -1.00000 q^{64} +(0.710611 + 1.23082i) q^{65} +2.45634i q^{66} +(-4.23409 + 7.33365i) q^{67} +0.959847i q^{68} +(2.73082 + 1.57664i) q^{69} +(-0.979923 + 1.69728i) q^{70} +(-1.35088 + 2.33979i) q^{71} +(-0.866025 + 0.500000i) q^{72} -3.05026 q^{73} +(3.96140 - 4.61598i) q^{74} -1.00000 q^{75} +(3.95806 - 2.28518i) q^{76} +(-2.40703 + 4.16910i) q^{77} +(-0.710611 + 1.23082i) q^{78} +(3.52786 + 2.03681i) q^{79} -1.00000i q^{80} +(-0.500000 + 0.866025i) q^{81} +9.77295i q^{82} +(-2.77834 - 4.81222i) q^{83} -1.95985 q^{84} -0.959847 q^{85} +(-1.92304 - 3.33080i) q^{86} +(-7.52012 - 4.34174i) q^{87} -2.45634i q^{88} +(2.26457 - 1.30745i) q^{89} +(-0.500000 - 0.866025i) q^{90} +(-2.41221 + 1.39269i) q^{91} +(-2.73082 - 1.57664i) q^{92} +(-6.06161 - 3.49967i) q^{93} +(11.7167 - 6.76466i) q^{94} +(2.28518 + 3.95806i) q^{95} +(0.866025 - 0.500000i) q^{96} -1.53772i q^{97} +(2.73577 + 1.57950i) q^{98} +(-1.22817 - 2.12726i) 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 $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$

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
$7$	−0.979923	+	1.69728i	−0.370376	+	0.641510i	−0.989623	−	0.143686i	$-0.954105\pi$
$7$	−0.979923	+	1.69728i	−0.370376	+	0.641510i	0.619247	+	0.785196i	$0.287438\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	1.00000			0.316228
$11$	2.45634			0.740616			0.370308	−	0.928909i	$-0.379252\pi$
$11$	2.45634			0.740616			0.370308	+	0.928909i	$0.379252\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	1.23082	+	0.710611i	0.341367	+	0.197088i	0.660876	−	0.750495i	$-0.270185\pi$
$13$	1.23082	+	0.710611i	0.341367	+	0.197088i	−0.319510	+	0.947583i	$0.603518\pi$
$14$			1.95985i			0.523791i
$15$	−0.866025	+	0.500000i	−0.223607	+	0.129099i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.831252	+	0.479923i	−0.201608	+	0.116399i	−0.597405	−	0.801939i	$-0.703802\pi$
$17$	−0.831252	+	0.479923i	−0.201608	+	0.116399i	0.395797	+	0.918338i	$0.370468\pi$
$18$	−0.866025	−	0.500000i	−0.204124	−	0.117851i
$19$	3.95806	+	2.28518i	0.908040	+	0.524257i	0.879800	−	0.475344i	$-0.157676\pi$
$19$	3.95806	+	2.28518i	0.908040	+	0.524257i	0.0282402	+	0.999601i	$0.491010\pi$
$20$	0.866025	−	0.500000i	0.193649	−	0.111803i
$21$	−0.979923	−	1.69728i	−0.213837	−	0.370376i
$22$	2.12726	−	1.22817i	0.453533	−	0.261847i
$23$		−	3.15327i		−	0.657503i	−0.944416	−	0.328752i	$-0.893372\pi$
$23$		−	3.15327i		−	0.657503i	0.944416	−	0.328752i	$-0.106628\pi$
$24$	0.866025	+	0.500000i	0.176777	+	0.102062i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	1.42122			0.278725
$27$	1.00000			0.192450
$28$	0.979923	+	1.69728i	0.185188	+	0.320755i
$29$			8.68349i			1.61248i	0.591586	+	0.806242i	$0.298502\pi$
$29$			8.68349i			1.61248i	−0.591586	+	0.806242i	$0.701498\pi$
$30$	−0.500000	+	0.866025i	−0.0912871	+	0.158114i
$31$			6.99935i			1.25712i	0.777761	+	0.628560i	$0.216355\pi$
$31$			6.99935i			1.25712i	−0.777761	+	0.628560i	$0.783645\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	−1.22817	+	2.12726i	−0.213797	+	0.370308i
$34$	−0.479923	+	0.831252i	−0.0823062	+	0.142558i
$35$	−1.69728	+	0.979923i	−0.286892	+	0.165637i
$36$	−1.00000			−0.166667
$37$	5.73867	−	2.01686i	0.943431	−	0.331570i
$37$	5.73867	−	2.01686i	0.943431	−	0.331570i
$38$	4.57037			0.741412
$39$	−1.23082	+	0.710611i	−0.197088	+	0.113789i
$40$	0.500000	−	0.866025i	0.0790569	−	0.136931i
$41$	−4.88647	+	8.46362i	−0.763139	+	1.32180i	0.178086	+	0.984015i	$0.443009\pi$
$41$	−4.88647	+	8.46362i	−0.763139	+	1.32180i	−0.941225	+	0.337780i	$0.890324\pi$
$42$	−1.69728	−	0.979923i	−0.261896	−	0.151205i
$43$		−	3.84608i		−	0.586521i	−0.956033	−	0.293261i	$-0.905260\pi$
$43$		−	3.84608i		−	0.586521i	0.956033	−	0.293261i	$-0.0947403\pi$
$44$	1.22817	−	2.12726i	0.185154	−	0.320696i
$45$		−	1.00000i		−	0.149071i
$46$	−1.57664	−	2.73082i	−0.232462	−	0.402637i
$47$	13.5293			1.97345			0.986726	−	0.162391i	$-0.0519207\pi$
$47$	13.5293			1.97345			0.986726	+	0.162391i	$0.0519207\pi$
$48$	1.00000			0.144338
$49$	1.57950	+	2.73577i	0.225643	+	0.390825i
$50$	0.866025	+	0.500000i	0.122474	+	0.0707107i
$51$		−	0.959847i		−	0.134405i
$52$	1.23082	−	0.710611i	0.170683	−	0.0985441i
$53$	−5.33799	−	9.24568i	−0.733230	−	1.26999i	−0.955496	−	0.295005i	$-0.904679\pi$
$53$	−5.33799	−	9.24568i	−0.733230	−	1.26999i	0.222266	−	0.974986i	$-0.428655\pi$
$54$	0.866025	−	0.500000i	0.117851	−	0.0680414i
$55$	2.12726	+	1.22817i	0.286839	+	0.165607i
$56$	1.69728	+	0.979923i	0.226808	+	0.130948i
$57$	−3.95806	+	2.28518i	−0.524257	+	0.302680i
$58$	4.34174	+	7.52012i	0.570099	+	0.987440i
$59$	6.41533	−	3.70389i	0.835205	−	0.482206i	−0.0204265	−	0.999791i	$-0.506502\pi$
$59$	6.41533	−	3.70389i	0.835205	−	0.482206i	0.855631	+	0.517586i	$0.173169\pi$
$60$			1.00000i			0.129099i
$61$	−7.96035	−	4.59591i	−1.01922	−	0.588446i	−0.105340	−	0.994436i	$-0.533593\pi$
$61$	−7.96035	−	4.59591i	−1.01922	−	0.588446i	−0.913877	+	0.405991i	$0.866927\pi$
$62$	3.49967	+	6.06161i	0.444459	+	0.769826i
$63$	1.95985			0.246917
$64$	−1.00000			−0.125000
$65$	0.710611	+	1.23082i	0.0881405	+	0.152664i
$66$			2.45634i			0.302355i
$67$	−4.23409	+	7.33365i	−0.517276	+	0.895948i	0.482523	+	0.875883i	$0.339721\pi$
$67$	−4.23409	+	7.33365i	−0.517276	+	0.895948i	−0.999799	+	0.0200647i	$0.993613\pi$
$68$			0.959847i			0.116399i
$69$	2.73082	+	1.57664i	0.328752	+	0.189805i
$70$	−0.979923	+	1.69728i	−0.117123	+	0.202863i
$71$	−1.35088	+	2.33979i	−0.160319	+	0.277681i	−0.934983	−	0.354692i	$-0.884586\pi$
$71$	−1.35088	+	2.33979i	−0.160319	+	0.277681i	0.774664	+	0.632373i	$0.217919\pi$
$72$	−0.866025	+	0.500000i	−0.102062	+	0.0589256i
$73$	−3.05026			−0.357006			−0.178503	−	0.983939i	$-0.557125\pi$
$73$	−3.05026			−0.357006			−0.178503	+	0.983939i	$0.557125\pi$
$74$	3.96140	−	4.61598i	0.460503	−	0.536597i
$75$	−1.00000			−0.115470
$76$	3.95806	−	2.28518i	0.454020	−	0.262129i
$77$	−2.40703	+	4.16910i	−0.274306	+	0.475113i
$78$	−0.710611	+	1.23082i	−0.0804609	+	0.139362i
$79$	3.52786	+	2.03681i	0.396915	+	0.229159i	0.685152	−	0.728400i	$-0.259736\pi$
$79$	3.52786	+	2.03681i	0.396915	+	0.229159i	−0.288237	+	0.957559i	$0.593069\pi$
$80$		−	1.00000i		−	0.111803i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$			9.77295i			1.07924i
$83$	−2.77834	−	4.81222i	−0.304962	−	0.528210i	0.672291	−	0.740287i	$-0.265311\pi$
$83$	−2.77834	−	4.81222i	−0.304962	−	0.528210i	−0.977253	+	0.212077i	$0.931977\pi$
$84$	−1.95985			−0.213837
$85$	−0.959847			−0.104110
$86$	−1.92304	−	3.33080i	−0.207367	−	0.359169i
$87$	−7.52012	−	4.34174i	−0.806242	−	0.465484i
$88$		−	2.45634i		−	0.261847i
$89$	2.26457	−	1.30745i	0.240044	−	0.138590i	−0.375153	−	0.926963i	$-0.622410\pi$
$89$	2.26457	−	1.30745i	0.240044	−	0.138590i	0.615197	+	0.788373i	$0.289076\pi$
$90$	−0.500000	−	0.866025i	−0.0527046	−	0.0912871i
$91$	−2.41221	+	1.39269i	−0.252868	+	0.145994i
$92$	−2.73082	−	1.57664i	−0.284707	−	0.164376i
$93$	−6.06161	−	3.49967i	−0.628560	−	0.362899i
$94$	11.7167	−	6.76466i	1.20849	−	0.697721i
$95$	2.28518	+	3.95806i	0.234455	+	0.406088i
$96$	0.866025	−	0.500000i	0.0883883	−	0.0510310i
$97$		−	1.53772i		−	0.156132i	−0.996948	−	0.0780659i	$-0.975126\pi$
$97$		−	1.53772i		−	0.156132i	0.996948	−	0.0780659i	$-0.0248744\pi$
$98$	2.73577	+	1.57950i	0.276355	+	0.159554i
$99$	−1.22817	−	2.12726i	−0.123436	−	0.213797i
$100$	1.00000			0.100000
$101$	5.16988			0.514422			0.257211	−	0.966355i	$-0.417196\pi$
$101$	5.16988			0.514422			0.257211	+	0.966355i	$0.417196\pi$
$102$	−0.479923	−	0.831252i	−0.0475195	−	0.0823062i
$103$		−	10.6296i		−	1.04737i	−0.851912	−	0.523685i	$-0.824557\pi$
$103$		−	10.6296i		−	1.04737i	0.851912	−	0.523685i	$-0.175443\pi$
$104$	0.710611	−	1.23082i	0.0696812	−	0.120691i
$105$		−	1.95985i		−	0.191261i
$106$	−9.24568	−	5.33799i	−0.898020	−	0.518472i
$107$	4.87448	−	8.44284i	0.471234	−	0.816201i	−0.528225	−	0.849105i	$-0.677142\pi$
$107$	4.87448	−	8.44284i	0.471234	−	0.816201i	0.999459	+	0.0329039i	$0.0104755\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	−12.8257	+	7.40492i	−1.22848	+	0.709263i	−0.966712	−	0.255868i	$-0.917639\pi$
$109$	−12.8257	+	7.40492i	−1.22848	+	0.709263i	−0.261767	+	0.965131i	$0.584305\pi$
$110$	2.45634			0.234203
$111$	−1.12268	+	5.97826i	−0.106560	+	0.567431i
$112$	1.95985			0.185188
$113$	15.2963	−	8.83130i	1.43895	−	0.830779i	0.441174	−	0.897422i	$-0.354562\pi$
$113$	15.2963	−	8.83130i	1.43895	−	0.830779i	0.997777	+	0.0666430i	$0.0212289\pi$
$114$	−2.28518	+	3.95806i	−0.214027	+	0.370706i
$115$	1.57664	−	2.73082i	0.147022	−	0.254650i
$116$	7.52012	+	4.34174i	0.698226	+	0.403121i
$117$		−	1.42122i		−	0.131392i
$118$	3.70389	−	6.41533i	0.340971	−	0.590579i
$119$		−	1.88115i		−	0.172445i
$120$	0.500000	+	0.866025i	0.0456435	+	0.0790569i
$121$	−4.96637			−0.451489
$122$	−9.19181			−0.832188
$123$	−4.88647	−	8.46362i	−0.440598	−	0.763139i
$124$	6.06161	+	3.49967i	0.544349	+	0.314280i
$125$			1.00000i			0.0894427i
$126$	1.69728	−	0.979923i	0.151205	−	0.0872985i
$127$	1.59045	+	2.75473i	0.141129	+	0.244443i	0.927922	−	0.372774i	$-0.121593\pi$
$127$	1.59045	+	2.75473i	0.141129	+	0.244443i	−0.786793	+	0.617217i	$0.788260\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	3.33080	+	1.92304i	0.293261	+	0.169314i
$130$	1.23082	+	0.710611i	0.107950	+	0.0623247i
$131$	16.7556	−	9.67385i	1.46394	−	0.845208i	0.464753	−	0.885440i	$-0.346143\pi$
$131$	16.7556	−	9.67385i	1.46394	−	0.845208i	0.999190	+	0.0402323i	$0.0128098\pi$
$132$	1.22817	+	2.12726i	0.106899	+	0.185154i
$133$	−7.75718	+	4.47861i	−0.672633	+	0.388345i
$134$			8.46817i			0.731539i
$135$	0.866025	+	0.500000i	0.0745356	+	0.0430331i
$136$	0.479923	+	0.831252i	0.0411531	+	0.0712792i
$137$	−12.5602			−1.07309			−0.536543	−	0.843873i	$-0.680270\pi$
$137$	−12.5602			−1.07309			−0.536543	+	0.843873i	$0.680270\pi$
$138$	3.15327			0.268424
$139$	−6.81393	−	11.8021i	−0.577950	−	1.00104i	−0.995714	−	0.0924830i	$-0.970520\pi$
$139$	−6.81393	−	11.8021i	−0.577950	−	1.00104i	0.417764	−	0.908555i	$-0.362814\pi$
$140$			1.95985i			0.165637i
$141$	−6.76466	+	11.7167i	−0.569687	+	0.986726i
$142$			2.70175i			0.226726i
$143$	3.02331	+	1.74551i	0.252822	+	0.145967i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−4.34174	+	7.52012i	−0.360562	+	0.624512i
$146$	−2.64160	+	1.52513i	−0.218621	+	0.126221i
$147$	−3.15900			−0.260550
$148$	1.12268	−	5.97826i	0.0922838	−	0.491410i
$149$	−13.4425			−1.10125			−0.550625	−	0.834753i	$-0.685610\pi$
$149$	−13.4425			−1.10125			−0.550625	+	0.834753i	$0.685610\pi$
$150$	−0.866025	+	0.500000i	−0.0707107	+	0.0408248i
$151$	5.96442	−	10.3307i	0.485378	−	0.840699i	−0.514481	−	0.857502i	$-0.672015\pi$
$151$	5.96442	−	10.3307i	0.485378	−	0.840699i	0.999859	+	0.0168028i	$0.00534874\pi$
$152$	2.28518	−	3.95806i	0.185353	−	0.321041i
$153$	0.831252	+	0.479923i	0.0672027	+	0.0387995i
$154$			4.81406i			0.387928i
$155$	−3.49967	+	6.06161i	−0.281101	+	0.486881i
$156$			1.42122i			0.113789i
$157$	11.8965	+	20.6054i	0.949445	+	1.64449i	0.746596	+	0.665277i	$0.231687\pi$
$157$	11.8965	+	20.6054i	0.949445	+	1.64449i	0.202849	+	0.979210i	$0.434980\pi$
$158$	4.07362			0.324080
$159$	10.6760			0.846661
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	5.35198	+	3.08997i	0.421795	+	0.243523i
$162$			1.00000i			0.0785674i
$163$	−9.71043	+	5.60632i	−0.760580	+	0.439121i	−0.829504	−	0.558501i	$-0.811377\pi$
$163$	−9.71043	+	5.60632i	−0.760580	+	0.439121i	0.0689241	+	0.997622i	$0.478043\pi$
$164$	4.88647	+	8.46362i	0.381569	+	0.660898i
$165$	−2.12726	+	1.22817i	−0.165607	+	0.0956131i
$166$	−4.81222	−	2.77834i	−0.373501	−	0.215641i
$167$	−9.73668	−	5.62147i	−0.753447	−	0.435003i	0.0734911	−	0.997296i	$-0.476586\pi$
$167$	−9.73668	−	5.62147i	−0.753447	−	0.435003i	−0.826938	+	0.562293i	$0.809919\pi$
$168$	−1.69728	+	0.979923i	−0.130948	+	0.0756027i
$169$	−5.49006	−	9.50907i	−0.422313	−	0.731467i
$170$	−0.831252	+	0.479923i	−0.0637541	+	0.0368084i
$171$		−	4.57037i		−	0.349505i
$172$	−3.33080	−	1.92304i	−0.253971	−	0.146630i
$173$	−9.08041	−	15.7277i	−0.690371	−	1.19576i	−0.971716	−	0.236151i	$-0.924114\pi$
$173$	−9.08041	−	15.7277i	−0.690371	−	1.19576i	0.281346	−	0.959607i	$-0.409219\pi$
$174$	−8.68349			−0.658294
$175$	−1.95985			−0.148150
$176$	−1.22817	−	2.12726i	−0.0925770	−	0.160348i
$177$			7.40779i			0.556803i
$178$	1.30745	−	2.26457i	0.0979977	−	0.169737i
$179$		−	19.5613i		−	1.46208i	−0.682336	−	0.731039i	$-0.739036\pi$
$179$		−	19.5613i		−	1.46208i	0.682336	−	0.731039i	$-0.260964\pi$
$180$	−0.866025	−	0.500000i	−0.0645497	−	0.0372678i
$181$	−2.38223	+	4.12613i	−0.177069	+	0.306693i	−0.940875	−	0.338753i	$-0.889995\pi$
$181$	−2.38223	+	4.12613i	−0.177069	+	0.306693i	0.763806	+	0.645446i	$0.223328\pi$
$182$	−1.39269	+	2.41221i	−0.103233	+	0.178805i
$183$	7.96035	−	4.59591i	0.588446	−	0.339739i
$184$	−3.15327			−0.232462
$185$	5.97826	+	1.12268i	0.439530	+	0.0825412i
$186$	−6.99935			−0.513217
$187$	−2.04184	+	1.17886i	−0.149314	+	0.0862066i
$188$	6.76466	−	11.7167i	0.493363	−	0.854530i
$189$	−0.979923	+	1.69728i	−0.0712789	+	0.123459i
$190$	3.95806	+	2.28518i	0.287148	+	0.165785i
$191$		−	2.01489i		−	0.145792i	−0.997340	−	0.0728960i	$-0.976776\pi$
$191$		−	2.01489i		−	0.145792i	0.997340	−	0.0728960i	$-0.0232241\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$		−	10.7992i		−	0.777341i	−0.921377	−	0.388671i	$-0.872934\pi$
$193$		−	10.7992i		−	0.777341i	0.921377	−	0.388671i	$-0.127066\pi$
$194$	−0.768860	−	1.33170i	−0.0552009	−	0.0956108i
$195$	−1.42122			−0.101776
$196$	3.15900			0.225643
$197$	−7.10275	−	12.3023i	−0.506050	−	0.876505i	−0.999975	−	0.00700028i	$-0.997772\pi$
$197$	−7.10275	−	12.3023i	−0.506050	−	0.876505i	0.493925	−	0.869504i	$-0.335562\pi$
$198$	−2.12726	−	1.22817i	−0.151178	−	0.0872824i
$199$			24.0509i			1.70492i	0.522792	+	0.852460i	$0.324891\pi$
$199$			24.0509i			1.70492i	−0.522792	+	0.852460i	$0.675109\pi$
$200$	0.866025	−	0.500000i	0.0612372	−	0.0353553i
$201$	−4.23409	−	7.33365i	−0.298649	−	0.517276i
$202$	4.47725	−	2.58494i	0.315018	−	0.181876i
$203$	−14.7383	−	8.50915i	−1.03443	−	0.597226i
$204$	−0.831252	−	0.479923i	−0.0581993	−	0.0336014i
$205$	−8.46362	+	4.88647i	−0.591125	+	0.341286i
$206$	−5.31482	−	9.20554i	−0.370301	−	0.641381i
$207$	−2.73082	+	1.57664i	−0.189805	+	0.109584i
$208$		−	1.42122i		−	0.0985441i
$209$	9.72235	+	5.61320i	0.672509	+	0.388273i
$210$	−0.979923	−	1.69728i	−0.0676211	−	0.117123i
$211$	−8.79370			−0.605383			−0.302692	−	0.953089i	$-0.597885\pi$
$211$	−8.79370			−0.605383			−0.302692	+	0.953089i	$0.597885\pi$
$212$	−10.6760			−0.733230
$213$	−1.35088	−	2.33979i	−0.0925605	−	0.160319i
$214$		−	9.74896i		−	0.666425i
$215$	1.92304	−	3.33080i	0.131150	−	0.227159i
$216$		−	1.00000i		−	0.0680414i
$217$	−11.8798	−	6.85883i	−0.806456	−	0.465607i
$218$	−7.40492	+	12.8257i	−0.501524	+	0.868666i
$219$	1.52513	−	2.64160i	0.103059	−	0.178503i
$220$	2.12726	−	1.22817i	0.143420	−	0.0828033i
$221$	−1.36416			−0.0917631
$222$	2.01686	+	5.73867i	0.135363	+	0.385154i
$223$	−13.3323			−0.892794			−0.446397	−	0.894835i	$-0.647293\pi$
$223$	−13.3323			−0.892794			−0.446397	+	0.894835i	$0.647293\pi$
$224$	1.69728	−	0.979923i	0.113404	−	0.0654739i
$225$	0.500000	−	0.866025i	0.0333333	−	0.0577350i
$226$	8.83130	−	15.2963i	0.587449	−	1.01749i
$227$	−0.418906	−	0.241856i	−0.0278038	−	0.0160525i	0.486034	−	0.873940i	$-0.338443\pi$
$227$	−0.418906	−	0.241856i	−0.0278038	−	0.0160525i	−0.513837	+	0.857888i	$0.671777\pi$
$228$			4.57037i			0.302680i
$229$	−5.29548	+	9.17204i	−0.349935	+	0.606106i	−0.986238	−	0.165334i	$-0.947130\pi$
$229$	−5.29548	+	9.17204i	−0.349935	+	0.606106i	0.636302	+	0.771440i	$0.280463\pi$
$230$		−	3.15327i		−	0.207921i
$231$	−2.40703	−	4.16910i	−0.158371	−	0.274306i
$232$	8.68349			0.570099
$233$	1.71544			0.112382			0.0561912	−	0.998420i	$-0.482104\pi$
$233$	1.71544			0.112382			0.0561912	+	0.998420i	$0.482104\pi$
$234$	−0.710611	−	1.23082i	−0.0464541	−	0.0804609i
$235$	11.7167	+	6.76466i	0.764315	+	0.441277i
$236$		−	7.40779i		−	0.482206i
$237$	−3.52786	+	2.03681i	−0.229159	+	0.132305i
$238$	−0.940576	−	1.62913i	−0.0609685	−	0.105601i
$239$	0.476446	−	0.275076i	0.0308187	−	0.0177932i	−0.484511	−	0.874785i	$-0.661003\pi$
$239$	0.476446	−	0.275076i	0.0308187	−	0.0177932i	0.515330	+	0.856992i	$0.327669\pi$
$240$	0.866025	+	0.500000i	0.0559017	+	0.0322749i
$241$	−20.2817	−	11.7097i	−1.30646	−	0.754286i	−0.324957	−	0.945729i	$-0.605350\pi$
$241$	−20.2817	−	11.7097i	−1.30646	−	0.754286i	−0.981504	+	0.191443i	$0.938683\pi$
$242$	−4.30101	+	2.48319i	−0.276479	+	0.159625i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−7.96035	+	4.59591i	−0.509609	+	0.294223i
$245$			3.15900i			0.201821i
$246$	−8.46362	−	4.88647i	−0.539621	−	0.311550i
$247$	3.24776	+	5.62528i	0.206650	+	0.357928i
$248$	6.99935			0.444459
$249$	5.55668			0.352140
$250$	0.500000	+	0.866025i	0.0316228	+	0.0547723i
$251$			0.166006i			0.0104782i	0.999986	+	0.00523910i	$0.00166767\pi$
$251$			0.166006i			0.0104782i	−0.999986	+	0.00523910i	$0.998332\pi$
$252$	0.979923	−	1.69728i	0.0617294	−	0.106918i
$253$		−	7.74553i		−	0.486957i
$254$	2.75473	+	1.59045i	0.172847	+	0.0997934i
$255$	0.479923	−	0.831252i	0.0300540	−	0.0520550i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−6.31676	+	3.64698i	−0.394029	+	0.227493i	−0.683904	−	0.729572i	$-0.739719\pi$
$257$	−6.31676	+	3.64698i	−0.394029	+	0.227493i	0.289876	+	0.957064i	$0.406386\pi$
$258$	3.84608			0.239446
$259$	−2.20028	+	11.7165i	−0.136719	+	0.728026i
$260$	1.42122			0.0881405
$261$	7.52012	−	4.34174i	0.465484	−	0.268747i
$262$	9.67385	−	16.7556i	0.597652	−	1.03516i
$263$	9.39514	−	16.2729i	0.579329	−	1.00343i	−0.416227	−	0.909261i	$-0.636648\pi$
$263$	9.39514	−	16.2729i	0.579329	−	1.00343i	0.995556	−	0.0941669i	$-0.0300187\pi$
$264$	2.12726	+	1.22817i	0.130924	+	0.0755888i
$265$		−	10.6760i		−	0.655821i
$266$	−4.47861	+	7.75718i	−0.274601	+	0.475623i
$267$			2.61490i			0.160030i
$268$	4.23409	+	7.33365i	0.258638	+	0.447974i
$269$	28.7529			1.75310			0.876548	−	0.481314i	$-0.159840\pi$
$269$	28.7529			1.75310			0.876548	+	0.481314i	$0.159840\pi$
$270$	1.00000			0.0608581
$271$	−8.47039	−	14.6711i	−0.514540	−	0.891209i	−0.999858	−	0.0168711i	$-0.994630\pi$
$271$	−8.47039	−	14.6711i	−0.514540	−	0.891209i	0.485318	−	0.874338i	$-0.338704\pi$
$272$	0.831252	+	0.479923i	0.0504020	+	0.0290996i
$273$		−	2.78538i		−	0.168579i
$274$	−10.8774	+	6.28008i	−0.657129	+	0.379393i
$275$	1.22817	+	2.12726i	0.0740616	+	0.128278i
$276$	2.73082	−	1.57664i	0.164376	−	0.0949024i
$277$	−3.99658	−	2.30743i	−0.240131	−	0.138640i	0.375106	−	0.926982i	$-0.377606\pi$
$277$	−3.99658	−	2.30743i	−0.240131	−	0.138640i	−0.615237	+	0.788342i	$0.710940\pi$
$278$	−11.8021	−	6.81393i	−0.707841	−	0.408672i
$279$	6.06161	−	3.49967i	0.362899	−	0.209520i
$280$	0.979923	+	1.69728i	0.0585616	+	0.101432i
$281$	15.5544	−	8.98032i	0.927896	−	0.535721i	0.0417507	−	0.999128i	$-0.486706\pi$
$281$	15.5544	−	8.98032i	0.927896	−	0.535721i	0.886146	+	0.463407i	$0.153373\pi$
$282$			13.5293i			0.805659i
$283$	−3.55264	−	2.05112i	−0.211183	−	0.121926i	0.390678	−	0.920527i	$-0.372241\pi$
$283$	−3.55264	−	2.05112i	−0.211183	−	0.121926i	−0.601861	+	0.798601i	$0.705574\pi$
$284$	1.35088	+	2.33979i	0.0801597	+	0.138841i
$285$	−4.57037			−0.270725
$286$	3.49101			0.206428
$287$	−9.57674	−	16.5874i	−0.565297	−	0.979123i
$288$			1.00000i			0.0589256i
$289$	−8.03935	+	13.9246i	−0.472903	+	0.819092i
$290$			8.68349i			0.509912i
$291$	1.33170	+	0.768860i	0.0780659	+	0.0450713i
$292$	−1.52513	+	2.64160i	−0.0892515	+	0.154588i
$293$	5.98605	−	10.3681i	0.349709	−	0.605713i	−0.636489	−	0.771286i	$-0.719614\pi$
$293$	5.98605	−	10.3681i	0.349709	−	0.605713i	0.986198	+	0.165573i	$0.0529472\pi$
$294$	−2.73577	+	1.57950i	−0.159554	+	0.0921183i
$295$	7.40779			0.431298
$296$	−2.01686	−	5.73867i	−0.117228	−	0.333553i
$297$	2.45634			0.142532
$298$	−11.6415	+	6.72123i	−0.674375	+	0.389350i
$299$	2.24075	−	3.88110i	0.129586	−	0.224450i
$300$	−0.500000	+	0.866025i	−0.0288675	+	0.0500000i
$301$	6.52786	+	3.76886i	0.376259	+	0.217233i
$302$		−	11.9288i		−	0.686428i
$303$	−2.58494	+	4.47725i	−0.148501	+	0.257211i
$304$		−	4.57037i		−	0.262129i
$305$	−4.59591	−	7.96035i	−0.263161	−	0.455808i
$306$	0.959847			0.0548708
$307$	14.1554			0.807892			0.403946	−	0.914783i	$-0.367638\pi$
$307$	14.1554			0.807892			0.403946	+	0.914783i	$0.367638\pi$
$308$	2.40703	+	4.16910i	0.137153	+	0.237556i
$309$	9.20554	+	5.31482i	0.523685	+	0.302350i
$310$			6.99935i			0.397536i
$311$	2.16085	−	1.24756i	0.122530	−	0.0707429i	−0.437482	−	0.899227i	$-0.644130\pi$
$311$	2.16085	−	1.24756i	0.122530	−	0.0707429i	0.560012	+	0.828484i	$0.310796\pi$
$312$	0.710611	+	1.23082i	0.0402305	+	0.0696812i
$313$	−9.00030	+	5.19632i	−0.508727	+	0.293714i	−0.732310	−	0.680971i	$-0.761558\pi$
$313$	−9.00030	+	5.19632i	−0.508727	+	0.293714i	0.223583	+	0.974685i	$0.428225\pi$
$314$	20.6054	+	11.8965i	1.16283	+	0.671359i
$315$	1.69728	+	0.979923i	0.0956307	+	0.0552124i
$316$	3.52786	−	2.03681i	0.198457	−	0.114579i
$317$	15.1018	+	26.1571i	0.848201	+	1.46913i	0.882812	+	0.469727i	$0.155647\pi$
$317$	15.1018	+	26.1571i	0.848201	+	1.46913i	−0.0346109	+	0.999401i	$0.511019\pi$
$318$	9.24568	−	5.33799i	0.518472	−	0.299340i
$319$			21.3296i			1.19423i
$320$	−0.866025	−	0.500000i	−0.0484123	−	0.0279508i
$321$	4.87448	+	8.44284i	0.272067	+	0.471234i
$322$	6.17993			0.344394
$323$	−4.38685			−0.244091
$324$	0.500000	+	0.866025i	0.0277778	+	0.0481125i
$325$			1.42122i			0.0788353i
$326$	−5.60632	+	9.71043i	−0.310505	+	0.537811i
$327$		−	14.8098i		−	0.818986i
$328$	8.46362	+	4.88647i	0.467325	+	0.269810i
$329$	−13.2577	+	22.9630i	−0.730920	+	1.26599i
$330$	−1.22817	+	2.12726i	−0.0676086	+	0.117102i
$331$	11.8460	−	6.83928i	0.651114	−	0.375921i	−0.137769	−	0.990464i	$-0.543993\pi$
$331$	11.8460	−	6.83928i	0.651114	−	0.375921i	0.788883	+	0.614544i	$0.210660\pi$
$332$	−5.55668			−0.304962
$333$	−4.61598	−	3.96140i	−0.252954	−	0.217083i
$334$	−11.2429			−0.615187
$335$	−7.33365	+	4.23409i	−0.400680	+	0.231333i
$336$	−0.979923	+	1.69728i	−0.0534592	+	0.0925941i
$337$	−1.71735	+	2.97454i	−0.0935501	+	0.162034i	−0.909003	−	0.416791i	$-0.863155\pi$
$337$	−1.71735	+	2.97454i	−0.0935501	+	0.162034i	0.815452	+	0.578824i	$0.196488\pi$
$338$	−9.50907	−	5.49006i	−0.517225	−	0.298620i
$339$			17.6626i			0.959301i
$340$	−0.479923	+	0.831252i	−0.0260275	+	0.0450810i
$341$			17.1928i			0.931043i
$342$	−2.28518	−	3.95806i	−0.123569	−	0.214027i
$343$	−19.9101			−1.07504
$344$	−3.84608			−0.207367
$345$	1.57664	+	2.73082i	0.0848833	+	0.147022i
$346$	−15.7277	−	9.08041i	−0.845528	−	0.488166i
$347$			12.1793i			0.653819i	0.945056	+	0.326909i	$0.106007\pi$
$347$			12.1793i			0.653819i	−0.945056	+	0.326909i	$0.893993\pi$
$348$	−7.52012	+	4.34174i	−0.403121	+	0.232742i
$349$	−12.4499	−	21.5639i	−0.666428	−	1.15429i	−0.978896	−	0.204359i	$-0.934489\pi$
$349$	−12.4499	−	21.5639i	−0.666428	−	1.15429i	0.312468	−	0.949928i	$-0.398844\pi$
$350$	−1.69728	+	0.979923i	−0.0907233	+	0.0523791i
$351$	1.23082	+	0.710611i	0.0656961	+	0.0379296i
$352$	−2.12726	−	1.22817i	−0.113383	−	0.0654618i
$353$	−20.3650	+	11.7577i	−1.08392	+	0.625801i	−0.931951	−	0.362584i	$-0.881895\pi$
$353$	−20.3650	+	11.7577i	−1.08392	+	0.625801i	−0.151969	+	0.988385i	$0.548561\pi$
$354$	3.70389	+	6.41533i	0.196860	+	0.340971i
$355$	−2.33979	+	1.35088i	−0.124183	+	0.0716971i
$356$		−	2.61490i		−	0.138590i
$357$	1.62913	+	0.940576i	0.0862225	+	0.0497806i
$358$	−9.78063	−	16.9405i	−0.516922	−	0.895336i
$359$	1.98677			0.104858			0.0524289	−	0.998625i	$-0.483304\pi$
$359$	1.98677			0.104858			0.0524289	+	0.998625i	$0.483304\pi$
$360$	−1.00000			−0.0527046
$361$	0.944137	+	1.63529i	0.0496914	+	0.0860681i
$362$			4.76445i			0.250414i
$363$	2.48319	−	4.30101i	0.130334	−	0.225744i
$364$			2.78538i			0.145994i
$365$	−2.64160	−	1.52513i	−0.138268	−	0.0798290i
$366$	4.59591	−	7.96035i	0.240232	−	0.416094i
$367$	8.86266	−	15.3506i	0.462627	−	0.801293i	−0.536464	−	0.843923i	$-0.680240\pi$
$367$	8.86266	−	15.3506i	0.462627	−	0.801293i	0.999091	+	0.0426298i	$0.0135736\pi$
$368$	−2.73082	+	1.57664i	−0.142354	+	0.0821879i
$369$	9.77295			0.508759
$370$	5.73867	−	2.01686i	0.298339	−	0.104852i
$371$	20.9233			1.08628
$372$	−6.06161	+	3.49967i	−0.314280	+	0.181450i
$373$	−7.30423	+	12.6513i	−0.378199	+	0.655059i	−0.990800	−	0.135333i	$-0.956790\pi$
$373$	−7.30423	+	12.6513i	−0.378199	+	0.655059i	0.612602	+	0.790392i	$0.290123\pi$
$374$	−1.17886	+	2.04184i	−0.0609572	+	0.105581i
$375$	−0.866025	−	0.500000i	−0.0447214	−	0.0258199i
$376$		−	13.5293i		−	0.697721i
$377$	−6.17059	+	10.6878i	−0.317801	+	0.550448i
$378$			1.95985i			0.100804i
$379$	−0.713939	−	1.23658i	−0.0366726	−	0.0635188i	0.847107	−	0.531423i	$-0.178343\pi$
$379$	−0.713939	−	1.23658i	−0.0366726	−	0.0635188i	−0.883779	+	0.467904i	$0.845009\pi$
$380$	4.57037			0.234455
$381$	−3.18089			−0.162962
$382$	−1.00744	−	1.74494i	−0.0515453	−	0.0892790i
$383$	6.66805	+	3.84980i	0.340721	+	0.196716i	0.660591	−	0.750746i	$-0.270306\pi$
$383$	6.66805	+	3.84980i	0.340721	+	0.196716i	−0.319870	+	0.947462i	$0.603639\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	−4.16910	+	2.40703i	−0.212477	+	0.122674i
$386$	−5.39958	−	9.35235i	−0.274832	−	0.476022i
$387$	−3.33080	+	1.92304i	−0.169314	+	0.0977535i
$388$	−1.33170	−	0.768860i	−0.0676070	−	0.0390329i
$389$	−7.69776	−	4.44430i	−0.390292	−	0.225335i	0.291995	−	0.956420i	$-0.405681\pi$
$389$	−7.69776	−	4.44430i	−0.390292	−	0.225335i	−0.682287	+	0.731085i	$0.739014\pi$
$390$	−1.23082	+	0.710611i	−0.0623247	+	0.0359832i
$391$	1.51333	+	2.62116i	0.0765324	+	0.132558i
$392$	2.73577	−	1.57950i	0.138177	−	0.0797768i
$393$			19.3477i			0.975962i
$394$	−12.3023	−	7.10275i	−0.619782	−	0.357832i
$395$	2.03681	+	3.52786i	0.102483	+	0.177506i
$396$	−2.45634			−0.123436
$397$	24.6140			1.23534			0.617670	−	0.786437i	$-0.288077\pi$
$397$	24.6140			1.23534			0.617670	+	0.786437i	$0.288077\pi$
$398$	12.0254	+	20.8287i	0.602781	+	1.04405i
$399$		−	8.95722i		−	0.448422i
$400$	0.500000	−	0.866025i	0.0250000	−	0.0433013i
$401$			4.32734i			0.216097i	0.994146	+	0.108049i	$0.0344602\pi$
$401$			4.32734i			0.216097i	−0.994146	+	0.108049i	$0.965540\pi$
$402$	−7.33365	−	4.23409i	−0.365769	−	0.211177i
$403$	−4.97382	+	8.61491i	−0.247764	+	0.429139i
$404$	2.58494	−	4.47725i	0.128606	−	0.222751i
$405$	−0.866025	+	0.500000i	−0.0430331	+	0.0248452i
$406$	−17.0183			−0.844604
$407$	14.0961	−	4.95410i	0.698720	−	0.245566i
$408$	−0.959847			−0.0475195
$409$	25.9709	−	14.9943i	1.28418	−	0.741422i	0.306571	−	0.951848i	$-0.400818\pi$
$409$	25.9709	−	14.9943i	1.28418	−	0.741422i	0.977610	+	0.210426i	$0.0674850\pi$
$410$	−4.88647	+	8.46362i	−0.241326	+	0.417988i
$411$	6.28008	−	10.8774i	0.309773	−	0.536543i
$412$	−9.20554	−	5.31482i	−0.453525	−	0.261843i
$413$			14.5181i			0.714390i
$414$	−1.57664	+	2.73082i	−0.0774875	+	0.134212i
$415$		−	5.55668i		−	0.272767i
$416$	−0.710611	−	1.23082i	−0.0348406	−	0.0603457i
$417$	13.6279			0.667359
$418$	11.2264			0.549101
$419$	18.9838	+	32.8809i	0.927420	+	1.60634i	0.787622	+	0.616159i	$0.211312\pi$
$419$	18.9838	+	32.8809i	0.927420	+	1.60634i	0.139798	+	0.990180i	$0.455355\pi$
$420$	−1.69728	−	0.979923i	−0.0828186	−	0.0478154i
$421$			28.8277i			1.40498i	0.711695	+	0.702488i	$0.247928\pi$
$421$			28.8277i			1.40498i	−0.711695	+	0.702488i	$0.752072\pi$
$422$	−7.61557	+	4.39685i	−0.370720	+	0.214035i
$423$	−6.76466	−	11.7167i	−0.328909	−	0.569687i
$424$	−9.24568	+	5.33799i	−0.449010	+	0.259236i
$425$	−0.831252	−	0.479923i	−0.0403216	−	0.0232797i
$426$	−2.33979	−	1.35088i	−0.113363	−	0.0654502i
$427$	15.6011	−	9.00727i	0.754988	−	0.435893i
$428$	−4.87448	−	8.44284i	−0.235617	−	0.408100i
$429$	−3.02331	+	1.74551i	−0.145967	+	0.0842738i
$430$		−	3.84608i		−	0.185474i
$431$	12.0063	+	6.93184i	0.578323	+	0.333895i	0.760467	−	0.649377i	$-0.224970\pi$
$431$	12.0063	+	6.93184i	0.578323	+	0.333895i	−0.182144	+	0.983272i	$0.558304\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	1.13995			0.0547826			0.0273913	−	0.999625i	$-0.491280\pi$
$433$	1.13995			0.0547826			0.0273913	+	0.999625i	$0.491280\pi$
$434$	−13.7177			−0.658468
$435$	−4.34174	−	7.52012i	−0.208171	−	0.360562i
$436$			14.8098i			0.709263i
$437$	7.20581	−	12.4808i	0.344701	−	0.597039i
$438$		−	3.05026i		−	0.145747i
$439$	23.2357	+	13.4152i	1.10898	+	0.640271i	0.938565	−	0.345101i	$-0.112155\pi$
$439$	23.2357	+	13.4152i	1.10898	+	0.640271i	0.170416	+	0.985372i	$0.445489\pi$
$440$	1.22817	−	2.12726i	0.0585508	−	0.101413i
$441$	1.57950	−	2.73577i	0.0752143	−	0.130275i
$442$	−1.18139	+	0.682078i	−0.0561932	+	0.0324431i
$443$	20.6441			0.980830			0.490415	−	0.871489i	$-0.336845\pi$
$443$	20.6441			0.980830			0.490415	+	0.871489i	$0.336845\pi$
$444$	4.61598	+	3.96140i	0.219065	+	0.188000i
$445$	2.61490			0.123958
$446$	−11.5461	+	6.66613i	−0.546722	+	0.315650i
$447$	6.72123	−	11.6415i	0.317903	−	0.550625i
$448$	0.979923	−	1.69728i	0.0462970	−	0.0801888i
$449$	−8.94501	−	5.16440i	−0.422141	−	0.243723i	0.273852	−	0.961772i	$-0.411702\pi$
$449$	−8.94501	−	5.16440i	−0.422141	−	0.243723i	−0.695993	+	0.718049i	$0.745036\pi$
$450$		−	1.00000i		−	0.0471405i
$451$	−12.0029	+	20.7896i	−0.565193	+	0.978942i
$452$		−	17.6626i		−	0.830779i
$453$	5.96442	+	10.3307i	0.280233	+	0.485378i
$454$	−0.483711			−0.0227017
$455$	−2.78538			−0.130581
$456$	2.28518	+	3.95806i	0.107014	+	0.185353i
$457$	−12.4941	−	7.21346i	−0.584448	−	0.337431i	0.178451	−	0.983949i	$-0.442891\pi$
$457$	−12.4941	−	7.21346i	−0.584448	−	0.337431i	−0.762899	+	0.646518i	$0.776225\pi$
$458$			10.5910i			0.494883i
$459$	−0.831252	+	0.479923i	−0.0387995	+	0.0224009i
$460$	−1.57664	−	2.73082i	−0.0735111	−	0.127325i
$461$	22.3966	−	12.9307i	1.04311	−	0.602241i	0.122399	−	0.992481i	$-0.460941\pi$
$461$	22.3966	−	12.9307i	1.04311	−	0.602241i	0.920713	+	0.390240i	$0.127608\pi$
$462$	−4.16910	−	2.40703i	−0.193964	−	0.111985i
$463$	−14.2261	−	8.21342i	−0.661141	−	0.381710i	0.131571	−	0.991307i	$-0.457998\pi$
$463$	−14.2261	−	8.21342i	−0.661141	−	0.381710i	−0.792712	+	0.609597i	$0.791331\pi$
$464$	7.52012	−	4.34174i	0.349113	−	0.201560i
$465$	−3.49967	−	6.06161i	−0.162294	−	0.281101i
$466$	1.48562	−	0.857721i	0.0688199	−	0.0397332i
$467$		−	36.9384i		−	1.70931i	−0.519200	−	0.854653i	$-0.673770\pi$
$467$		−	36.9384i		−	1.70931i	0.519200	−	0.854653i	$-0.326230\pi$
$468$	−1.23082	−	0.710611i	−0.0568945	−	0.0328480i
$469$	−8.29816	−	14.3728i	−0.383173	−	0.663676i
$470$	13.5293			0.624061
$471$	−23.7930			−1.09632
$472$	−3.70389	−	6.41533i	−0.170486	−	0.295290i
$473$		−	9.44729i		−	0.434387i
$474$	−2.03681	+	3.52786i	−0.0935537	+	0.162040i
$475$			4.57037i			0.209703i
$476$	−1.62913	−	0.940576i	−0.0746709	−	0.0431112i
$477$	−5.33799	+	9.24568i	−0.244410	+	0.423331i
$478$	0.275076	−	0.476446i	0.0125817	−	0.0217921i
$479$	−16.4828	+	9.51634i	−0.753117	+	0.434813i	−0.826819	−	0.562468i	$-0.809852\pi$
$479$	−16.4828	+	9.51634i	−0.753117	+	0.434813i	0.0737018	+	0.997280i	$0.476519\pi$
$480$	1.00000			0.0456435
$481$	8.49644	+	1.59558i	0.387404	+	0.0727522i
$482$	−23.4193			−1.06672
$483$	−5.35198	+	3.08997i	−0.243523	+	0.140598i
$484$	−2.48319	+	4.30101i	−0.112872	+	0.195500i
$485$	0.768860	−	1.33170i	0.0349121	−	0.0604696i
$486$	−0.866025	−	0.500000i	−0.0392837	−	0.0226805i
$487$			9.27395i			0.420243i	0.977675	+	0.210121i	$0.0673859\pi$
$487$			9.27395i			0.420243i	−0.977675	+	0.210121i	$0.932614\pi$
$488$	−4.59591	+	7.96035i	−0.208047	+	0.360348i
$489$		−	11.2126i		−	0.507053i
$490$	1.57950	+	2.73577i	0.0713546	+	0.123590i
$491$	30.1195			1.35928			0.679638	−	0.733548i	$-0.262137\pi$
$491$	30.1195			1.35928			0.679638	+	0.733548i	$0.262137\pi$
$492$	−9.77295			−0.440598
$493$	−4.16741	−	7.21817i	−0.187691	−	0.325090i
$494$	5.62528	+	3.24776i	0.253093	+	0.146123i
$495$		−	2.45634i		−	0.110404i
$496$	6.06161	−	3.49967i	0.272175	−	0.157140i
$497$	−2.64751	−	4.58562i	−0.118757	−	0.205693i
$498$	4.81222	−	2.77834i	0.215641	−	0.124500i
$499$	−9.72002	−	5.61186i	−0.435128	−	0.251221i	0.266401	−	0.963862i	$-0.414166\pi$
$499$	−9.72002	−	5.61186i	−0.435128	−	0.251221i	−0.701529	+	0.712641i	$0.747499\pi$
$500$	0.866025	+	0.500000i	0.0387298	+	0.0223607i
$501$	9.73668	−	5.62147i	0.435003	−	0.251149i
$502$	0.0830030	+	0.143765i	0.00370460	+	0.00641656i
$503$	−10.2927	+	5.94248i	−0.458928	+	0.264962i	−0.711593	−	0.702592i	$-0.752026\pi$
$503$	−10.2927	+	5.94248i	−0.458928	+	0.264962i	0.252666	+	0.967554i	$0.418693\pi$
$504$		−	1.95985i		−	0.0872985i
$505$	4.47725	+	2.58494i	0.199235	+	0.115028i
$506$	−3.87276	−	6.70782i	−0.172165	−	0.298199i
$507$	10.9801			0.487644
$508$	3.18089			0.141129
$509$	11.5878	+	20.0707i	0.513621	+	0.889618i	0.999875	+	0.0158008i	$0.00502976\pi$
$509$	11.5878	+	20.0707i	0.513621	+	0.889618i	−0.486254	+	0.873818i	$0.661637\pi$
$510$		−	0.959847i		−	0.0425027i
$511$	2.98902	−	5.17714i	0.132227	−	0.229023i
$512$			1.00000i			0.0441942i
$513$	3.95806	+	2.28518i	0.174752	+	0.100893i
$514$	−3.64698	+	6.31676i	−0.160862	+	0.278620i
$515$	5.31482	−	9.20554i	0.234199	−	0.405645i
$516$	3.33080	−	1.92304i	0.146630	−	0.0846570i
$517$	33.2326			1.46157
$518$	3.95274	+	11.2469i	0.173673	+	0.494161i
$519$	18.1608			0.797172
$520$	1.23082	−	0.710611i	0.0539748	−	0.0311624i
$521$	11.8446	−	20.5154i	0.518920	−	0.898795i	−0.480839	−	0.876809i	$-0.659668\pi$
$521$	11.8446	−	20.5154i	0.518920	−	0.898795i	0.999758	−	0.0219860i	$-0.00699891\pi$
$522$	4.34174	−	7.52012i	0.190033	−	0.329147i
$523$	10.7377	+	6.19940i	0.469525	+	0.271081i	0.716041	−	0.698058i	$-0.245952\pi$
$523$	10.7377	+	6.19940i	0.469525	+	0.271081i	−0.246516	+	0.969139i	$0.579286\pi$
$524$		−	19.3477i		−	0.845208i
$525$	0.979923	−	1.69728i	0.0427674	−	0.0740752i
$526$		−	18.7903i		−	0.819295i
$527$	−3.35915	−	5.81822i	−0.146327	−	0.253446i
$528$	2.45634			0.106899
$529$	13.0569			0.567690
$530$	−5.33799	−	9.24568i	−0.231868	−	0.401607i
$531$	−6.41533	−	3.70389i	−0.278402	−	0.160735i
$532$			8.95722i			0.388345i
$533$	−12.0287	+	6.94477i	−0.521020	+	0.300811i
$534$	1.30745	+	2.26457i	0.0565790	+	0.0979977i
$535$	8.44284	−	4.87448i	0.365016	−	0.210742i
$536$	7.33365	+	4.23409i	0.316766	+	0.182885i
$537$	16.9405	+	9.78063i	0.731039	+	0.422065i
$538$	24.9008	−	14.3765i	1.07355	−	0.619813i
$539$	3.87980	+	6.72000i	0.167115	+	0.289451i
$540$	0.866025	−	0.500000i	0.0372678	−	0.0215166i
$541$		−	13.1696i		−	0.566207i	−0.959089	−	0.283103i	$-0.908636\pi$
$541$		−	13.1696i		−	0.566207i	0.959089	−	0.283103i	$-0.0913639\pi$
$542$	−14.6711	−	8.47039i	−0.630180	−	0.363834i
$543$	−2.38223	−	4.12613i	−0.102231	−	0.177069i
$544$	0.959847			0.0411531
$545$	−14.8098			−0.634384
$546$	−1.39269	−	2.41221i	−0.0596016	−	0.103233i
$547$			15.3546i			0.656514i	0.944589	+	0.328257i	$0.106461\pi$
$547$			15.3546i			0.656514i	−0.944589	+	0.328257i	$0.893539\pi$
$548$	−6.28008	+	10.8774i	−0.268272	+	0.464660i
$549$			9.19181i			0.392297i
$550$	2.12726	+	1.22817i	0.0907065	+	0.0523694i
$551$	−19.8434	+	34.3697i	−0.845356	+	1.46420i
$552$	1.57664	−	2.73082i	0.0671061	−	0.116231i
$553$	−6.91406	+	3.99183i	−0.294016	+	0.169750i
$554$	−4.61485			−0.196066
$555$	−3.96140	+	4.61598i	−0.168152	+	0.195938i
$556$	−13.6279			−0.577950
$557$	−27.4914	+	15.8721i	−1.16485	+	0.672524i	−0.952461	−	0.304662i	$-0.901457\pi$
$557$	−27.4914	+	15.8721i	−1.16485	+	0.672524i	−0.212386	+	0.977186i	$0.568123\pi$
$558$	3.49967	−	6.06161i	0.148153	−	0.256609i
$559$	2.73307	−	4.73381i	0.115596	−	0.200219i
$560$	1.69728	+	0.979923i	0.0717230	+	0.0414093i
$561$		−	2.35771i		−	0.0995428i
$562$	8.98032	−	15.5544i	0.378812	−	0.656122i
$563$		−	30.6776i		−	1.29291i	−0.762953	−	0.646454i	$-0.776251\pi$
$563$		−	30.6776i		−	1.29291i	0.762953	−	0.646454i	$-0.223749\pi$
$564$	6.76466	+	11.7167i	0.284843	+	0.493363i
$565$	17.6626			0.743071
$566$	−4.10224			−0.172430
$567$	−0.979923	−	1.69728i	−0.0411529	−	0.0712789i
$568$	2.33979	+	1.35088i	0.0981752	+	0.0566815i
$569$			7.51849i			0.315192i	0.987504	+	0.157596i	$0.0503743\pi$
$569$			7.51849i			0.315192i	−0.987504	+	0.157596i	$0.949626\pi$
$570$	−3.95806	+	2.28518i	−0.165785	+	0.0957158i
$571$	4.76931	+	8.26068i	0.199589	+	0.345699i	0.948395	−	0.317090i	$-0.102706\pi$
$571$	4.76931	+	8.26068i	0.199589	+	0.345699i	−0.748806	+	0.662789i	$0.769373\pi$
$572$	3.02331	−	1.74551i	0.126411	−	0.0729833i
$573$	1.74494	+	1.00744i	0.0728960	+	0.0420865i
$574$	−16.5874	−	9.57674i	−0.692345	−	0.399725i
$575$	2.73082	−	1.57664i	0.113883	−	0.0657503i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	3.03587	−	1.75276i	0.126385	−	0.0729685i	−0.435475	−	0.900201i	$-0.643419\pi$
$577$	3.03587	−	1.75276i	0.126385	−	0.0729685i	0.561860	+	0.827233i	$0.310086\pi$
$578$			16.0787i			0.668786i
$579$	9.35235	+	5.39958i	0.388671	+	0.224399i
$580$	4.34174	+	7.52012i	0.180281	+	0.312256i
$581$	10.8902			0.451803
$582$	1.53772			0.0637405
$583$	−13.1120	−	22.7106i	−0.543042	−	0.940576i
$584$			3.05026i			0.126221i
$585$	0.710611	−	1.23082i	0.0293802	−	0.0508879i
$586$		−	11.9721i		−	0.494563i
$587$	−10.9435	−	6.31826i	−0.451688	−	0.260782i	0.256855	−	0.966450i	$-0.417314\pi$
$587$	−10.9435	−	6.31826i	−0.451688	−	0.260782i	−0.708543	+	0.705668i	$0.750647\pi$
$588$	−1.57950	+	2.73577i	−0.0651375	+	0.112821i
$589$	−15.9948	+	27.7038i	−0.659054	+	1.14152i
$590$	6.41533	−	3.70389i	0.264115	−	0.152487i
$591$	14.2055			0.584336
$592$	−4.61598	−	3.96140i	−0.189716	−	0.162813i
$593$	4.99944			0.205302			0.102651	−	0.994717i	$-0.467267\pi$
$593$	4.99944			0.205302			0.102651	+	0.994717i	$0.467267\pi$
$594$	2.12726	−	1.22817i	0.0872824	−	0.0503925i
$595$	0.940576	−	1.62913i	0.0385599	−	0.0667876i
$596$	−6.72123	+	11.6415i	−0.275312	+	0.476855i
$597$	−20.8287	−	12.0254i	−0.852460	−	0.492168i
$598$		−	4.48150i		−	0.183262i
$599$	20.0086	−	34.6560i	0.817531	−	1.41601i	−0.0899648	−	0.995945i	$-0.528675\pi$
$599$	20.0086	−	34.6560i	0.817531	−	1.41601i	0.907496	−	0.420061i	$-0.137991\pi$
$600$			1.00000i			0.0408248i
$601$	11.3414	+	19.6439i	0.462625	+	0.801290i	0.999091	−	0.0426319i	$-0.0135743\pi$
$601$	11.3414	+	19.6439i	0.462625	+	0.801290i	−0.536466	+	0.843922i	$0.680241\pi$
$602$	7.53772			0.307215
$603$	8.46817			0.344851
$604$	−5.96442	−	10.3307i	−0.242689	−	0.420349i
$605$	−4.30101	−	2.48319i	−0.174861	−	0.100956i
$606$			5.16988i			0.210012i
$607$	28.8731	−	16.6699i	1.17192	−	0.676611i	0.217792	−	0.975995i	$-0.430114\pi$
$607$	28.8731	−	16.6699i	1.17192	−	0.676611i	0.954133	+	0.299384i	$0.0967812\pi$
$608$	−2.28518	−	3.95806i	−0.0926765	−	0.160520i
$609$	14.7383	−	8.50915i	0.597226	−	0.344808i
$610$	−7.96035	−	4.59591i	−0.322305	−	0.186083i
$611$	16.6521	+	9.61408i	0.673671	+	0.388944i
$612$	0.831252	−	0.479923i	0.0336014	−	0.0193998i
$613$	−11.0511	−	19.1411i	−0.446351	−	0.773102i	0.551795	−	0.833980i	$-0.313943\pi$
$613$	−11.0511	−	19.1411i	−0.446351	−	0.773102i	−0.998145	+	0.0608781i	$0.980610\pi$
$614$	12.2590	−	7.07771i	0.494731	−	0.285633i
$615$		−	9.77295i		−	0.394083i
$616$	4.16910	+	2.40703i	0.167978	+	0.0969820i
$617$	1.17946	+	2.04289i	0.0474833	+	0.0822436i	0.888790	−	0.458314i	$-0.151547\pi$
$617$	1.17946	+	2.04289i	0.0474833	+	0.0822436i	−0.841307	+	0.540558i	$0.818213\pi$
$618$	10.6296			0.427587
$619$	−43.1657			−1.73497			−0.867487	−	0.497459i	$-0.834266\pi$
$619$	−43.1657			−1.73497			−0.867487	+	0.497459i	$0.834266\pi$
$620$	3.49967	+	6.06161i	0.140550	+	0.243440i
$621$		−	3.15327i		−	0.126537i
$622$	1.24756	−	2.16085i	0.0500228	−	0.0866420i
$623$			5.12481i			0.205321i
$624$	1.23082	+	0.710611i	0.0492720	+	0.0284472i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−5.19632	+	9.00030i	−0.207687	+	0.359724i
$627$	−9.72235	+	5.61320i	−0.388273	+	0.224170i
$628$	23.7930			0.949445
$629$	−3.80234	+	4.43064i	−0.151609	+	0.176661i
$630$	1.95985			0.0780822
$631$	−6.45035	+	3.72411i	−0.256784	+	0.148255i	−0.622867	−	0.782328i	$-0.714032\pi$
$631$	−6.45035	+	3.72411i	−0.256784	+	0.148255i	0.366082	+	0.930582i	$0.380699\pi$
$632$	2.03681	−	3.52786i	0.0810199	−	0.140331i
$633$	4.39685	−	7.61557i	0.174759	−	0.302692i
$634$	26.1571	+	15.1018i	1.03883	+	0.599769i
$635$			3.18089i			0.126230i
$636$	5.33799	−	9.24568i	0.211665	−	0.366615i
$637$			4.48964i			0.177886i
$638$	10.6648	+	18.4720i	0.422224	+	0.731314i
$639$	2.70175			0.106880
$640$	−1.00000			−0.0395285
$641$	−24.0317	−	41.6241i	−0.949195	−	1.64405i	−0.747125	−	0.664684i	$-0.768566\pi$
$641$	−24.0317	−	41.6241i	−0.949195	−	1.64405i	−0.202071	−	0.979371i	$-0.564767\pi$
$642$	8.44284	+	4.87448i	0.333212	+	0.192380i
$643$			12.3081i			0.485382i	0.970104	+	0.242691i	$0.0780301\pi$
$643$			12.3081i			0.485382i	−0.970104	+	0.242691i	$0.921970\pi$
$644$	5.35198	−	3.08997i	0.210898	−	0.121762i
$645$	1.92304	+	3.33080i	0.0757195	+	0.131150i
$646$	−3.79913	+	2.19343i	−0.149475	+	0.0862992i
$647$	10.6408	+	6.14347i	0.418333	+	0.241525i	0.694364	−	0.719624i	$-0.255686\pi$
$647$	10.6408	+	6.14347i	0.418333	+	0.241525i	−0.276031	+	0.961149i	$0.589019\pi$
$648$	0.866025	+	0.500000i	0.0340207	+	0.0196419i
$649$	15.7583	−	9.09804i	0.618566	−	0.357129i
$650$	0.710611	+	1.23082i	0.0278725	+	0.0482765i
$651$	11.8798	−	6.85883i	0.465607	−	0.268819i
$652$			11.2126i			0.439121i
$653$	36.8075	+	21.2508i	1.44039	+	0.831610i	0.997875	−	0.0651515i	$-0.0207531\pi$
$653$	36.8075	+	21.2508i	1.44039	+	0.831610i	0.442515	+	0.896761i	$0.354086\pi$
$654$	−7.40492	−	12.8257i	−0.289555	−	0.501524i
$655$	19.3477			0.755977
$656$	9.77295			0.381569
$657$	1.52513	+	2.64160i	0.0595010	+	0.103059i
$658$			26.5154i			1.03368i
$659$	−19.1518	+	33.1719i	−0.746049	+	1.29219i	0.203655	+	0.979043i	$0.434718\pi$
$659$	−19.1518	+	33.1719i	−0.746049	+	1.29219i	−0.949703	+	0.313151i	$0.898615\pi$
$660$			2.45634i			0.0956131i
$661$	29.3666	+	16.9548i	1.14223	+	0.659467i	0.946982	−	0.321287i	$-0.104116\pi$
$661$	29.3666	+	16.9548i	1.14223	+	0.659467i	0.195248	+	0.980754i	$0.437449\pi$
$662$	6.83928	−	11.8460i	0.265816	−	0.460407i
$663$	0.682078	−	1.18139i	0.0264897	−	0.0458815i
$664$	−4.81222	+	2.77834i	−0.186751	+	0.107820i
$665$	−8.95722			−0.347346
$666$	−5.97826	−	1.12268i	−0.231653	−	0.0435030i
$667$	27.3814			1.06021
$668$	−9.73668	+	5.62147i	−0.376723	+	0.217501i
$669$	6.66613	−	11.5461i	0.257727	−	0.446397i
$670$	−4.23409	+	7.33365i	−0.163577	+	0.283324i
$671$	−19.5533	−	11.2891i	−0.754849	−	0.435812i
$672$			1.95985i			0.0756027i
$673$	−9.51980	+	16.4888i	−0.366961	+	0.635596i	−0.989089	−	0.147320i	$-0.952935\pi$
$673$	−9.51980	+	16.4888i	−0.366961	+	0.635596i	0.622127	+	0.782916i	$0.286269\pi$
$674$			3.43470i			0.132300i
$675$	0.500000	+	0.866025i	0.0192450	+	0.0333333i
$676$	−10.9801			−0.422313
$677$	−15.8403			−0.608792			−0.304396	−	0.952546i	$-0.598455\pi$
$677$	−15.8403			−0.608792			−0.304396	+	0.952546i	$0.598455\pi$
$678$	8.83130	+	15.2963i	0.339164	+	0.587449i
$679$	2.60994	+	1.50685i	0.100160	+	0.0578275i
$680$			0.959847i			0.0368084i
$681$	0.418906	−	0.241856i	0.0160525	−	0.00926793i
$682$	8.59641	+	14.8894i	0.329173	+	0.570145i
$683$	−39.2891	+	22.6836i	−1.50336	+	0.867964i	−0.503364	+	0.864074i	$0.667905\pi$
$683$	−39.2891	+	22.6836i	−1.50336	+	0.867964i	−0.999992	+	0.00388931i	$0.998762\pi$
$684$	−3.95806	−	2.28518i	−0.151340	−	0.0873762i
$685$	−10.8774	−	6.28008i	−0.415605	−	0.239949i
$686$	−17.2426	+	9.95504i	−0.658327	+	0.380085i
$687$	−5.29548	−	9.17204i	−0.202035	−	0.349935i
$688$	−3.33080	+	1.92304i	−0.126986	+	0.0733151i
$689$		−	15.1730i		−	0.578044i
$690$	2.73082	+	1.57664i	0.103960	+	0.0600215i
$691$	−9.76278	−	16.9096i	−0.371394	−	0.643273i	0.618387	−	0.785874i	$-0.287787\pi$
$691$	−9.76278	−	16.9096i	−0.371394	−	0.643273i	−0.989780	+	0.142601i	$0.954453\pi$
$692$	−18.1608			−0.690371
$693$	4.81406			0.182871
$694$	6.08965	+	10.5476i	0.231160	+	0.400380i
$695$		−	13.6279i		−	0.516934i
$696$	−4.34174	+	7.52012i	−0.164573	+	0.285050i
$697$		−	9.38053i		−	0.355313i
$698$	−21.5639	−	12.4499i	−0.816205	−	0.471236i
$699$	−0.857721	+	1.48562i	−0.0324420	+	0.0561912i
$700$	−0.979923	+	1.69728i	−0.0370376	+	0.0641510i
$701$	−43.6793	+	25.2183i	−1.64974	+	0.952481i	−0.672573	+	0.740031i	$0.734811\pi$
$701$	−43.6793	+	25.2183i	−1.64974	+	0.952481i	−0.977172	+	0.212449i	$0.931856\pi$
$702$	1.42122			0.0536406
$703$	27.3229	+	5.13107i	1.03050	+	0.193522i
$704$	−2.45634			−0.0925770
$705$	−11.7167	+	6.76466i	−0.441277	+	0.254772i
$706$	−11.7577	+	20.3650i	−0.442508	+	0.766447i
$707$	−5.06608	+	8.77472i	−0.190530	+	0.330007i
$708$	6.41533	+	3.70389i	0.241103	+	0.139201i
$709$		−	0.774617i		−	0.0290913i	−0.999894	−	0.0145457i	$-0.995370\pi$
$709$		−	0.774617i		−	0.0290913i	0.999894	−	0.0145457i	$-0.00463019\pi$
$710$	−1.35088	+	2.33979i	−0.0506975	+	0.0878106i
$711$		−	4.07362i		−	0.152773i
$712$	−1.30745	−	2.26457i	−0.0489988	−	0.0848685i
$713$	22.0709			0.826560
$714$	1.88115			0.0704004
$715$	1.74551	+	3.02331i	0.0652782	+	0.113065i
$716$	−16.9405	−	9.78063i	−0.633098	−	0.365519i
$717$			0.550152i			0.0205458i
$718$	1.72060	−	0.993387i	0.0642121	−	0.0370729i
$719$	−2.57835	−	4.46583i	−0.0961561	−	0.166547i	0.813934	−	0.580957i	$-0.197321\pi$
$719$	−2.57835	−	4.46583i	−0.0961561	−	0.166547i	−0.910091	+	0.414410i	$0.863988\pi$
$720$	−0.866025	+	0.500000i	−0.0322749	+	0.0186339i
$721$	18.0415	+	10.4162i	0.671899	+	0.387921i
$722$	1.63529	+	0.944137i	0.0608593	+	0.0351371i
$723$	20.2817	−	11.7097i	0.754286	−	0.435487i
$724$	2.38223	+	4.12613i	0.0885347	+	0.153347i
$725$	−7.52012	+	4.34174i	−0.279290	+	0.161248i
$726$		−	4.96637i		−	0.184319i
$727$	34.4957	+	19.9161i	1.27938	+	0.738648i	0.976734	−	0.214456i	$-0.0687979\pi$
$727$	34.4957	+	19.9161i	1.27938	+	0.738648i	0.302642	+	0.953104i	$0.402131\pi$
$728$	1.39269	+	2.41221i	0.0516165	+	0.0894024i
$729$	1.00000			0.0370370
$730$	−3.05026			−0.112895
$731$	1.84582	+	3.19706i	0.0682702	+	0.118247i
$732$		−	9.19181i		−	0.339739i
$733$	−2.65608	+	4.60046i	−0.0981045	+	0.169922i	−0.910900	−	0.412627i	$-0.864611\pi$
$733$	−2.65608	+	4.60046i	−0.0981045	+	0.169922i	0.812796	+	0.582549i	$0.197945\pi$
$734$		−	17.7253i		−	0.654253i
$735$	−2.73577	−	1.57950i	−0.100911	−	0.0582607i
$736$	−1.57664	+	2.73082i	−0.0581156	+	0.100659i
$737$	−10.4004	+	18.0140i	−0.383103	+	0.663553i
$738$	8.46362	−	4.88647i	0.311550	−	0.179874i
$739$	1.35357			0.0497918			0.0248959	−	0.999690i	$-0.492075\pi$
$739$	1.35357			0.0497918			0.0248959	+	0.999690i	$0.492075\pi$
$740$	3.96140	−	4.61598i	0.145624	−	0.169687i
$741$	−6.49551			−0.238619
$742$	18.1201	−	10.4617i	0.665210	−	0.384059i
$743$	6.76254	−	11.7131i	0.248094	−	0.429711i	−0.714903	−	0.699223i	$-0.753529\pi$
$743$	6.76254	−	11.7131i	0.248094	−	0.429711i	0.962997	+	0.269513i	$0.0868626\pi$
$744$	−3.49967	+	6.06161i	−0.128304	+	0.222230i
$745$	−11.6415	−	6.72123i	−0.426512	−	0.246247i
$746$			14.6085i			0.534854i
$747$	−2.77834	+	4.81222i	−0.101654	+	0.176070i
$748$			2.35771i			0.0862066i
$749$	9.55323	+	16.5467i	0.349067	+	0.604603i
$750$	−1.00000			−0.0365148
$751$	46.7414			1.70562			0.852809	−	0.522223i	$-0.174897\pi$
$751$	46.7414			1.70562			0.852809	+	0.522223i	$0.174897\pi$
$752$	−6.76466	−	11.7167i	−0.246682	−	0.427265i
$753$	−0.143765	−	0.0830030i	−0.00523910	−	0.00302480i
$754$			12.3412i			0.449439i
$755$	10.3307	−	5.96442i	0.375972	−	0.217068i
$756$	0.979923	+	1.69728i	0.0356395	+	0.0617294i
$757$	−26.4808	+	15.2887i	−0.962460	+	0.555677i	−0.896929	−	0.442174i	$-0.854207\pi$
$757$	−26.4808	+	15.2887i	−0.962460	+	0.555677i	−0.0655310	+	0.997851i	$0.520874\pi$
$758$	−1.23658	−	0.713939i	−0.0449146	−	0.0259314i
$759$	6.70782	+	3.87276i	0.243479	+	0.140572i
$760$	3.95806	−	2.28518i	0.143574	−	0.0828924i
$761$	3.30256	+	5.72021i	0.119718	+	0.207357i	0.919656	−	0.392725i	$-0.128468\pi$
$761$	3.30256	+	5.72021i	0.119718	+	0.207357i	−0.799938	+	0.600083i	$0.795134\pi$
$762$	−2.75473	+	1.59045i	−0.0997934	+	0.0576158i
$763$		−	29.0250i		−	1.05078i
$764$	−1.74494	−	1.00744i	−0.0631298	−	0.0364480i
$765$	0.479923	+	0.831252i	0.0173517	+	0.0300540i
$766$	7.69960			0.278198
$767$	10.5281			0.380148
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$		−	11.8201i		−	0.426243i	−0.977026	−	0.213122i	$-0.931637\pi$
$769$		−	11.8201i		−	0.426243i	0.977026	−	0.213122i	$-0.0683630\pi$
$770$	−2.40703	+	4.16910i	−0.0867433	+	0.150244i
$771$		−	7.29397i		−	0.262686i
$772$	−9.35235	−	5.39958i	−0.336599	−	0.194335i
$773$	12.8013	−	22.1725i	0.460430	−	0.797488i	−0.538552	−	0.842592i	$-0.681029\pi$
$773$	12.8013	−	22.1725i	0.460430	−	0.797488i	0.998982	+	0.0451041i	$0.0143620\pi$
$774$	−1.92304	+	3.33080i	−0.0691222	+	0.119723i
$775$	−6.06161	+	3.49967i	−0.217740	+	0.125712i
$776$	−1.53772			−0.0552009
$777$	−9.04662	−	7.76374i	−0.324546	−	0.278523i
$778$	−8.88861			−0.318672
$779$	−38.6819	+	22.3330i	−1.38592	+	0.800162i
$780$	−0.710611	+	1.23082i	−0.0254440	+	0.0440703i
$781$	−3.31822	+	5.74732i	−0.118735	+	0.205655i
$782$	2.62116	+	1.51333i	0.0937326	+	0.0541166i
$783$			8.68349i			0.310323i
$784$	1.57950	−	2.73577i	0.0564107	−	0.0977062i
$785$			23.7930i			0.849210i
$786$	9.67385	+	16.7556i	0.345055	+	0.597652i
$787$	43.6659			1.55652			0.778260	−	0.627942i	$-0.216102\pi$
$787$	43.6659			1.55652			0.778260	+	0.627942i	$0.216102\pi$
$788$	−14.2055			−0.506050
$789$	9.39514	+	16.2729i	0.334476	+	0.579329i
$790$	3.52786	+	2.03681i	0.125515	+	0.0724664i
$791$			34.6160i			1.23080i
$792$	−2.12726	+	1.22817i	−0.0755888	+	0.0436412i
$793$	−6.53181	−	11.3134i	−0.231951	−	0.401752i
$794$	21.3163	−	12.3070i	0.756489	−	0.436759i
$795$	9.24568	+	5.33799i	0.327910	+	0.189319i
$796$	20.8287	+	12.0254i	0.738252	+	0.426230i
$797$	−1.20501	+	0.695712i	−0.0426836	+	0.0246434i	−0.521190	−	0.853441i	$-0.674512\pi$
$797$	−1.20501	+	0.695712i	−0.0426836	+	0.0246434i	0.478506	+	0.878084i	$0.341178\pi$
$798$	−4.47861	−	7.75718i	−0.158541	−	0.274601i
$799$	−11.2463	+	6.49303i	−0.397864	+	0.229707i
$800$		−	1.00000i		−	0.0353553i
$801$	−2.26457	−	1.30745i	−0.0800148	−	0.0461965i
$802$	2.16367	+	3.74759i	0.0764018	+	0.132332i
$803$	−7.49249			−0.264404
$804$	−8.46817			−0.298649
$805$	3.08997	+	5.35198i	0.108907	+	0.188632i
$806$			9.94764i			0.350391i
$807$	−14.3765	+	24.9008i	−0.506075	+	0.876548i
$808$		−	5.16988i		−	0.181876i
$809$	−13.7664	−	7.94806i	−0.484003	−	0.279439i	0.238080	−	0.971245i	$-0.423482\pi$
$809$	−13.7664	−	7.94806i	−0.484003	−	0.279439i	−0.722083	+	0.691806i	$0.756815\pi$
$810$	−0.500000	+	0.866025i	−0.0175682	+	0.0304290i
$811$	4.07358	−	7.05566i	0.143043	−	0.247758i	−0.785598	−	0.618737i	$-0.787645\pi$
$811$	4.07358	−	7.05566i	0.143043	−	0.247758i	0.928641	+	0.370979i	$0.120978\pi$
$812$	−14.7383	+	8.50915i	−0.517213	+	0.298613i
$813$	16.9408			0.594139
$814$	9.73056	−	11.3384i	0.341056	−	0.397412i
$815$	−11.2126			−0.392762
$816$	−0.831252	+	0.479923i	−0.0290996	+	0.0168007i
$817$	8.78899	−	15.2230i	0.307488	−	0.532585i
$818$	14.9943	−	25.9709i	0.524265	−	0.908053i
$819$	2.41221	+	1.39269i	0.0842894	+	0.0486645i
$820$			9.77295i			0.341286i
$821$	−25.3526	+	43.9120i	−0.884812	+	1.53254i	−0.0388831	+	0.999244i	$0.512380\pi$
$821$	−25.3526	+	43.9120i	−0.884812	+	1.53254i	−0.845929	+	0.533296i	$0.820953\pi$
$822$		−	12.5602i		−	0.438086i
$823$	9.14160	+	15.8337i	0.318656	+	0.551929i	0.980208	−	0.197971i	$-0.0634351\pi$
$823$	9.14160	+	15.8337i	0.318656	+	0.551929i	−0.661552	+	0.749900i	$0.730102\pi$
$824$	−10.6296			−0.370301
$825$	−2.45634			−0.0855189
$826$	7.25906	+	12.5731i	0.252575	+	0.437473i
$827$	−0.0841560	−	0.0485875i	−0.00292639	−	0.00168955i	0.498536	−	0.866869i	$-0.333871\pi$
$827$	−0.0841560	−	0.0485875i	−0.00292639	−	0.00168955i	−0.501462	+	0.865179i	$0.667204\pi$
$828$			3.15327i			0.109584i
$829$	34.8321	−	20.1103i	1.20977	−	0.698461i	0.247061	−	0.969000i	$-0.420535\pi$
$829$	34.8321	−	20.1103i	1.20977	−	0.698461i	0.962709	+	0.270539i	$0.0872018\pi$
$830$	−2.77834	−	4.81222i	−0.0964376	−	0.167035i
$831$	3.99658	−	2.30743i	0.138640	−	0.0800437i
$832$	−1.23082	−	0.710611i	−0.0426708	−	0.0246360i
$833$	−2.62592	−	1.51608i	−0.0909829	−	0.0525290i
$834$	11.8021	−	6.81393i	0.408672	−	0.235947i
$835$	−5.62147	−	9.73668i	−0.194539	−	0.336952i
$836$	9.72235	−	5.61320i	0.336254	−	0.194137i
$837$			6.99935i			0.241933i
$838$	32.8809	+	18.9838i	1.13585	+	0.655785i
$839$	−18.7441	−	32.4657i	−0.647117	−	1.12084i	−0.983808	−	0.179224i	$-0.942641\pi$
$839$	−18.7441	−	32.4657i	−0.647117	−	1.12084i	0.336692	−	0.941615i	$-0.390692\pi$
$840$	−1.95985			−0.0676211
$841$	−46.4030			−1.60010
$842$	14.4139	+	24.9655i	0.496734	+	0.860369i
$843$			17.9606i			0.618598i
$844$	−4.39685	+	7.61557i	−0.151346	+	0.262139i
$845$		−	10.9801i		−	0.377728i
$846$	−11.7167	−	6.76466i	−0.402829	−	0.232574i
$847$	4.86667	−	8.42931i	0.167221	−	0.289635i
$848$	−5.33799	+	9.24568i	−0.183307	+	0.317498i
$849$	3.55264	−	2.05112i	0.121926	−	0.0703942i
$850$	−0.959847			−0.0329225
$851$	−6.35971	−	18.0956i	−0.218008	−	0.620309i
$852$	−2.70175			−0.0925605
$853$	−46.9579	+	27.1111i	−1.60781	+	0.928268i	−0.617948	+	0.786219i	$0.712036\pi$
$853$	−46.9579	+	27.1111i	−1.60781	+	0.928268i	−0.989860	+	0.142049i	$0.954631\pi$
$854$	9.00727	−	15.6011i	0.308223	−	0.533857i
$855$	2.28518	−	3.95806i	0.0781517	−	0.135363i
$856$	−8.44284	−	4.87448i	−0.288570	−	0.166606i
$857$		−	27.9341i		−	0.954209i	−0.878846	−	0.477105i	$-0.841686\pi$
$857$		−	27.9341i		−	0.954209i	0.878846	−	0.477105i	$-0.158314\pi$
$858$	−1.74551	+	3.02331i	−0.0595906	+	0.103214i
$859$			13.3856i			0.456711i	0.973578	+	0.228355i	$0.0733348\pi$
$859$			13.3856i			0.456711i	−0.973578	+	0.228355i	$0.926665\pi$
$860$	−1.92304	−	3.33080i	−0.0655750	−	0.113579i
$861$	19.1535			0.652749
$862$	13.8637			0.472199
$863$	−27.6377	−	47.8699i	−0.940797	−	1.62951i	−0.763955	−	0.645270i	$-0.776745\pi$
$863$	−27.6377	−	47.8699i	−0.940797	−	1.62951i	−0.176843	−	0.984239i	$-0.556588\pi$
$864$	−0.866025	−	0.500000i	−0.0294628	−	0.0170103i
$865$		−	18.1608i		−	0.617486i
$866$	0.987227	−	0.569976i	0.0335473	−	0.0193686i
$867$	−8.03935	−	13.9246i	−0.273031	−	0.472903i
$868$	−11.8798	+	6.85883i	−0.403228	+	0.232804i
$869$	8.66563	+	5.00310i	0.293961	+	0.169719i
$870$	−7.52012	−	4.34174i	−0.254956	−	0.147199i
$871$	−10.4228	+	6.01758i	−0.353162	+	0.203898i
$872$	7.40492	+	12.8257i	0.250762	+	0.434333i
$873$	−1.33170	+	0.768860i	−0.0450713	+	0.0260220i
$874$		−	14.4116i		−	0.487480i
$875$	−1.69728	−	0.979923i	−0.0573784	−	0.0331275i
$876$	−1.52513	−	2.64160i	−0.0515294	−	0.0892515i
$877$	−12.1802			−0.411296			−0.205648	−	0.978626i	$-0.565930\pi$
$877$	−12.1802			−0.411296			−0.205648	+	0.978626i	$0.565930\pi$
$878$	26.8303			0.905480
$879$	5.98605	+	10.3681i	0.201904	+	0.349709i
$880$		−	2.45634i		−	0.0828033i
$881$	13.7211	−	23.7657i	0.462276	−	0.800686i	−0.536798	−	0.843711i	$-0.680366\pi$
$881$	13.7211	−	23.7657i	0.462276	−	0.800686i	0.999074	+	0.0430247i	$0.0136994\pi$
$882$		−	3.15900i		−	0.106369i
$883$	−1.35365	−	0.781530i	−0.0455540	−	0.0263006i	0.477050	−	0.878876i	$-0.341706\pi$
$883$	−1.35365	−	0.781530i	−0.0455540	−	0.0263006i	−0.522604	+	0.852576i	$0.675039\pi$
$884$	−0.682078	+	1.18139i	−0.0229408	+	0.0397346i
$885$	−3.70389	+	6.41533i	−0.124505	+	0.215649i
$886$	17.8783	−	10.3220i	0.600633	−	0.346776i
$887$	−38.2018			−1.28269			−0.641346	−	0.767252i	$-0.721624\pi$
$887$	−38.2018			−1.28269			−0.641346	+	0.767252i	$0.721624\pi$
$888$	5.97826	+	1.12268i	0.200617	+	0.0376747i
$889$	−6.23406			−0.209084
$890$	2.26457	−	1.30745i	0.0759087	−	0.0438259i
$891$	−1.22817	+	2.12726i	−0.0411453	+	0.0712658i
$892$	−6.66613	+	11.5461i	−0.223198	+	0.386591i
$893$	53.5498	+	30.9170i	1.79197	+	1.03460i
$894$		−	13.4425i		−	0.449583i
$895$	9.78063	−	16.9405i	0.326930	−	0.566260i
$896$		−	1.95985i		−	0.0654739i
$897$	2.24075	+	3.88110i	0.0748165	+	0.129586i
$898$	−10.3288			−0.344677
$899$	−60.7788			−2.02709
$900$	−0.500000	−	0.866025i	−0.0166667	−	0.0288675i
$901$	8.87443	+	5.12366i	0.295650	+	0.170694i
$902$			24.0057i			0.799303i
$903$	−6.52786	+	3.76886i	−0.217233	+	0.125420i
$904$	−8.83130	−	15.2963i	−0.293725	−	0.508746i
$905$	−4.12613	+	2.38223i	−0.137157	+	0.0791878i
$906$	10.3307	+	5.96442i	0.343214	+	0.198155i
$907$	−15.8993	−	9.17944i	−0.527926	−	0.304798i	0.212245	−	0.977216i	$-0.431922\pi$
$907$	−15.8993	−	9.17944i	−0.527926	−	0.304798i	−0.740172	+	0.672418i	$0.765256\pi$
$908$	−0.418906	+	0.241856i	−0.0139019	+	0.00802626i
$909$	−2.58494	−	4.47725i	−0.0857370	−	0.148501i
$910$	−2.41221	+	1.39269i	−0.0799640	+	0.0461672i
$911$			16.3460i			0.541568i	0.962640	+	0.270784i	$0.0872829\pi$
$911$			16.3460i			0.541568i	−0.962640	+	0.270784i	$0.912717\pi$
$912$	3.95806	+	2.28518i	0.131064	+	0.0756700i
$913$	−6.82456	−	11.8205i	−0.225860	−	0.391201i
$914$	−14.4269			−0.477200
$915$	9.19181			0.303872
$916$	5.29548	+	9.17204i	0.174968	+	0.303053i
$917$			37.9185i			1.25218i
$918$	−0.479923	+	0.831252i	−0.0158398	+	0.0274354i
$919$		−	6.82315i		−	0.225075i	−0.993647	−	0.112538i	$-0.964102\pi$
$919$		−	6.82315i		−	0.225075i	0.993647	−	0.112538i	$-0.0358978\pi$
$920$	−2.73082	−	1.57664i	−0.0900323	−	0.0519802i
$921$	−7.07771	+	12.2590i	−0.233218	+	0.403946i
$922$	12.9307	−	22.3966i	0.425849	−	0.737591i
$923$	−3.32536	+	1.91990i	−0.109455	+	0.0631941i
$924$	−4.81406			−0.158371
$925$	4.61598	+	3.96140i	0.151773	+	0.130250i
$926$	−16.4268			−0.539819
$927$	−9.20554	+	5.31482i	−0.302350	+	0.174562i
$928$	4.34174	−	7.52012i	0.142525	−	0.246860i
$929$	−21.6643	+	37.5237i	−0.710783	+	1.23111i	0.253780	+	0.967262i	$0.418326\pi$
$929$	−21.6643	+	37.5237i	−0.710783	+	1.23111i	−0.964563	+	0.263851i	$0.915007\pi$
$930$	−6.06161	−	3.49967i	−0.198768	−	0.114759i
$931$			14.4378i			0.473180i
$932$	0.857721	−	1.48562i	0.0280956	−	0.0486630i
$933$			2.49513i			0.0816869i
$934$	−18.4692	−	31.9896i	−0.604331	−	1.04673i
$935$	−2.35771			−0.0771055
$936$	−1.42122			−0.0464541
$937$	−13.1944	−	22.8534i	−0.431043	−	0.746589i	0.565920	−	0.824460i	$-0.308521\pi$
$937$	−13.1944	−	22.8534i	−0.431043	−	0.746589i	−0.996963	+	0.0778712i	$0.975188\pi$
$938$	−14.3728	−	8.29816i	−0.469290	−	0.270945i
$939$		−	10.3926i		−	0.339151i
$940$	11.7167	−	6.76466i	0.382158	−	0.220639i
$941$	12.8476	+	22.2527i	0.418820	+	0.725417i	0.995821	−	0.0913263i	$-0.0291106\pi$
$941$	12.8476	+	22.2527i	0.418820	+	0.725417i	−0.577001	+	0.816743i	$0.695777\pi$
$942$	−20.6054	+	11.8965i	−0.671359	+	0.387609i
$943$	26.6881	+	15.4084i	0.869084	+	0.501766i
$944$	−6.41533	−	3.70389i	−0.208801	−	0.120551i
$945$	−1.69728	+	0.979923i	−0.0552124	+	0.0318769i
$946$	−4.72364	−	8.18159i	−0.153579	−	0.266006i
$947$	−12.3428	+	7.12611i	−0.401087	+	0.231568i	−0.686953	−	0.726702i	$-0.741052\pi$
$947$	−12.3428	+	7.12611i	−0.401087	+	0.231568i	0.285866	+	0.958270i	$0.407719\pi$
$948$			4.07362i			0.132305i
$949$	−3.75431	−	2.16755i	−0.121870	−	0.0703617i
$950$	2.28518	+	3.95806i	0.0741412	+	0.128416i
$951$	−30.2036			−0.979418
$952$	−1.88115			−0.0609685
$953$	−14.0161	−	24.2766i	−0.454026	−	0.786395i	0.544606	−	0.838692i	$-0.316679\pi$
$953$	−14.0161	−	24.2766i	−0.454026	−	0.786395i	−0.998632	+	0.0522967i	$0.983346\pi$
$954$			10.6760i			0.345648i
$955$	1.00744	−	1.74494i	0.0326001	−	0.0564650i
$956$		−	0.550152i		−	0.0177932i
$957$	−18.4720	−	10.6648i	−0.597115	−	0.344745i
$958$	−9.51634	+	16.4828i	−0.307459	+	0.532534i
$959$	12.3080	−	21.3181i	0.397446	−	0.688396i
$960$	0.866025	−	0.500000i	0.0279508	−	0.0161374i
$961$	−17.9909			−0.580351
$962$	8.15592	−	2.86641i	0.262958	−	0.0924167i
$963$	−9.74896			−0.314156
$964$	−20.2817	+	11.7097i	−0.653230	+	0.377143i
$965$	5.39958	−	9.35235i	0.173819	−	0.301063i
$966$	−3.08997	+	5.35198i	−0.0994180	+	0.172197i
$967$	47.7816	+	27.5867i	1.53655	+	0.887129i	0.999037	+	0.0438752i	$0.0139704\pi$
$967$	47.7816	+	27.5867i	1.53655	+	0.887129i	0.537516	+	0.843254i	$0.319363\pi$
$968$			4.96637i			0.159625i
$969$	2.19343	−	3.79913i	0.0704630	−	0.122046i
$970$		−	1.53772i		−	0.0493732i
$971$	−1.88359	−	3.26248i	−0.0604474	−	0.104698i	0.834218	−	0.551435i	$-0.185919\pi$
$971$	−1.88359	−	3.26248i	−0.0604474	−	0.104698i	−0.894665	+	0.446737i	$0.852586\pi$
$972$	−1.00000			−0.0320750
$973$	26.7085			0.856235
$974$	4.63698	+	8.03148i	0.148578	+	0.257345i
$975$	−1.23082	−	0.710611i	−0.0394176	−	0.0227578i
$976$			9.19181i			0.294223i
$977$	−22.1948	+	12.8142i	−0.710075	+	0.409962i	−0.811089	−	0.584923i	$-0.801125\pi$
$977$	−22.1948	+	12.8142i	−0.710075	+	0.409962i	0.101014	+	0.994885i	$0.467791\pi$
$978$	−5.60632	−	9.71043i	−0.179270	−	0.310505i
$979$	5.56257	−	3.21155i	0.177781	−	0.102642i
$980$	2.73577	+	1.57950i	0.0873911	+	0.0504553i
$981$	12.8257	+	7.40492i	0.409493	+	0.236421i
$982$	26.0843	−	15.0598i	0.832383	−	0.480576i
$983$	0.299103	+	0.518062i	0.00953991	+	0.0165236i	0.870756	−	0.491715i	$-0.163630\pi$
$983$	0.299103	+	0.518062i	0.00953991	+	0.0165236i	−0.861216	+	0.508239i	$0.830297\pi$
$984$	−8.46362	+	4.88647i	−0.269810	+	0.155775i
$985$		−	14.2055i		−	0.452625i
$986$	−7.21817	−	4.16741i	−0.229873	−	0.132717i
$987$	−13.2577	−	22.9630i	−0.421997	−	0.730920i
$988$	6.49551			0.206650
$989$	−12.1277			−0.385639
$990$	−1.22817	−	2.12726i	−0.0390339	−	0.0676086i
$991$		−	16.8782i		−	0.536155i	−0.963397	−	0.268077i	$-0.913612\pi$
$991$		−	16.8782i		−	0.536155i	0.963397	−	0.268077i	$-0.0863883\pi$
$992$	3.49967	−	6.06161i	0.111115	−	0.192456i
$993$			13.6786i			0.434076i
$994$	−4.58562	−	2.64751i	−0.145447	−	0.0839739i
$995$	−12.0254	+	20.8287i	−0.381232	+	0.660313i
$996$	2.77834	−	4.81222i	0.0880351	−	0.152481i
$997$	−4.24395	+	2.45025i	−0.134407	+	0.0776001i	−0.565696	−	0.824614i	$-0.691392\pi$
$997$	−4.24395	+	2.45025i	−0.134407	+	0.0776001i	0.431289	+	0.902214i	$0.358059\pi$
$998$	−11.2237			−0.355281
$999$	5.73867	−	2.01686i	0.181563	−	0.0638106i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.x.d.751.6	✓	16
37.27	even	6	inner	1110.2.x.d.841.6	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.x.d.751.6	✓	16	1.1	even	1	trivial
1110.2.x.d.841.6	yes	16	37.27	even	6	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.x (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{5} +1.00000i q^{6} +(-0.979923 + 1.69728i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(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} +(-0.979923 + 1.69728i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +1.00000 q^{10} +2.45634 q^{11} +(0.500000 + 0.866025i) q^{12} +(1.23082 + 0.710611i) q^{13} +1.95985i q^{14} +(-0.866025 + 0.500000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.831252 + 0.479923i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(3.95806 + 2.28518i) q^{19} +(0.866025 - 0.500000i) q^{20} +(-0.979923 - 1.69728i) q^{21} +(2.12726 - 1.22817i) q^{22} -3.15327i q^{23} +(0.866025 + 0.500000i) q^{24} +(0.500000 + 0.866025i) q^{25} +1.42122 q^{26} +1.00000 q^{27} +(0.979923 + 1.69728i) q^{28} +8.68349i q^{29} +(-0.500000 + 0.866025i) q^{30} +6.99935i q^{31} +(-0.866025 - 0.500000i) q^{32} +(-1.22817 + 2.12726i) q^{33} +(-0.479923 + 0.831252i) q^{34} +(-1.69728 + 0.979923i) q^{35} -1.00000 q^{36} +(5.73867 - 2.01686i) q^{37} +4.57037 q^{38} +(-1.23082 + 0.710611i) q^{39} +(0.500000 - 0.866025i) q^{40} +(-4.88647 + 8.46362i) q^{41} +(-1.69728 - 0.979923i) q^{42} -3.84608i q^{43} +(1.22817 - 2.12726i) q^{44} -1.00000i q^{45} +(-1.57664 - 2.73082i) q^{46} +13.5293 q^{47} +1.00000 q^{48} +(1.57950 + 2.73577i) q^{49} +(0.866025 + 0.500000i) q^{50} -0.959847i q^{51} +(1.23082 - 0.710611i) q^{52} +(-5.33799 - 9.24568i) q^{53} +(0.866025 - 0.500000i) q^{54} +(2.12726 + 1.22817i) q^{55} +(1.69728 + 0.979923i) q^{56} +(-3.95806 + 2.28518i) q^{57} +(4.34174 + 7.52012i) q^{58} +(6.41533 - 3.70389i) q^{59} +1.00000i q^{60} +(-7.96035 - 4.59591i) q^{61} +(3.49967 + 6.06161i) q^{62} +1.95985 q^{63} -1.00000 q^{64} +(0.710611 + 1.23082i) q^{65} +2.45634i q^{66} +(-4.23409 + 7.33365i) q^{67} +0.959847i q^{68} +(2.73082 + 1.57664i) q^{69} +(-0.979923 + 1.69728i) q^{70} +(-1.35088 + 2.33979i) q^{71} +(-0.866025 + 0.500000i) q^{72} -3.05026 q^{73} +(3.96140 - 4.61598i) q^{74} -1.00000 q^{75} +(3.95806 - 2.28518i) q^{76} +(-2.40703 + 4.16910i) q^{77} +(-0.710611 + 1.23082i) q^{78} +(3.52786 + 2.03681i) q^{79} -1.00000i q^{80} +(-0.500000 + 0.866025i) q^{81} +9.77295i q^{82} +(-2.77834 - 4.81222i) q^{83} -1.95985 q^{84} -0.959847 q^{85} +(-1.92304 - 3.33080i) q^{86} +(-7.52012 - 4.34174i) q^{87} -2.45634i q^{88} +(2.26457 - 1.30745i) q^{89} +(-0.500000 - 0.866025i) q^{90} +(-2.41221 + 1.39269i) q^{91} +(-2.73082 - 1.57664i) q^{92} +(-6.06161 - 3.49967i) q^{93} +(11.7167 - 6.76466i) q^{94} +(2.28518 + 3.95806i) q^{95} +(0.866025 - 0.500000i) q^{96} -1.53772i q^{97} +(2.73577 + 1.57950i) q^{98} +(-1.22817 - 2.12726i) 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

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