LMFDB - Embedded newform 1110.2.x.d.751.2

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			751.2
Root			$-0.535537i$ of defining polynomial
Character	$\chi$	$=$	1110.751
Dual form			1110.2.x.d.841.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} -1.00000i q^{6} +(-0.267768 + 0.463788i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(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} +(-0.267768 + 0.463788i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +1.00000 q^{10} +5.44426 q^{11} +(0.500000 + 0.866025i) q^{12} +(0.556002 + 0.321008i) q^{13} -0.535537i q^{14} +(0.866025 - 0.500000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.402237 + 0.232232i) q^{17} +(0.866025 + 0.500000i) q^{18} +(-7.12118 - 4.11142i) q^{19} +(-0.866025 + 0.500000i) q^{20} +(-0.267768 - 0.463788i) q^{21} +(-4.71487 + 2.72213i) q^{22} -2.37407i q^{23} +(-0.866025 - 0.500000i) q^{24} +(0.500000 + 0.866025i) q^{25} -0.642016 q^{26} +1.00000 q^{27} +(0.267768 + 0.463788i) q^{28} -5.38430i q^{29} +(-0.500000 + 0.866025i) q^{30} +1.32755i q^{31} +(0.866025 + 0.500000i) q^{32} +(-2.72213 + 4.71487i) q^{33} +(0.232232 - 0.402237i) q^{34} +(0.463788 - 0.267768i) q^{35} -1.00000 q^{36} +(6.01205 + 0.924822i) q^{37} +8.22283 q^{38} +(-0.556002 + 0.321008i) q^{39} +(0.500000 - 0.866025i) q^{40} +(4.86520 - 8.42677i) q^{41} +(0.463788 + 0.267768i) q^{42} +1.04652i q^{43} +(2.72213 - 4.71487i) q^{44} +1.00000i q^{45} +(1.18703 + 2.05600i) q^{46} +8.14127 q^{47} +1.00000 q^{48} +(3.35660 + 5.81380i) q^{49} +(-0.866025 - 0.500000i) q^{50} -0.464463i q^{51} +(0.556002 - 0.321008i) q^{52} +(2.89110 + 5.00753i) q^{53} +(-0.866025 + 0.500000i) q^{54} +(-4.71487 - 2.72213i) q^{55} +(-0.463788 - 0.267768i) q^{56} +(7.12118 - 4.11142i) q^{57} +(2.69215 + 4.66294i) q^{58} +(10.2224 - 5.90190i) q^{59} -1.00000i q^{60} +(2.55109 + 1.47287i) q^{61} +(-0.663773 - 1.14969i) q^{62} +0.535537 q^{63} -1.00000 q^{64} +(-0.321008 - 0.556002i) q^{65} -5.44426i q^{66} +(-2.04849 + 3.54808i) q^{67} +0.464463i q^{68} +(2.05600 + 1.18703i) q^{69} +(-0.267768 + 0.463788i) q^{70} +(2.17408 - 3.76562i) q^{71} +(0.866025 - 0.500000i) q^{72} -1.60237 q^{73} +(-5.66900 + 2.20510i) q^{74} -1.00000 q^{75} +(-7.12118 + 4.11142i) q^{76} +(-1.45780 + 2.52499i) q^{77} +(0.321008 - 0.556002i) q^{78} +(-3.48536 - 2.01228i) q^{79} +1.00000i q^{80} +(-0.500000 + 0.866025i) q^{81} +9.73039i q^{82} +(3.61426 + 6.26008i) q^{83} -0.535537 q^{84} +0.464463 q^{85} +(-0.523261 - 0.906314i) q^{86} +(4.66294 + 2.69215i) q^{87} +5.44426i q^{88} +(3.69105 - 2.13103i) q^{89} +(-0.500000 - 0.866025i) q^{90} +(-0.297759 + 0.171911i) q^{91} +(-2.05600 - 1.18703i) q^{92} +(-1.14969 - 0.663773i) q^{93} +(-7.05055 + 4.07063i) q^{94} +(4.11142 + 7.12118i) q^{95} +(-0.866025 + 0.500000i) q^{96} -5.43955i q^{97} +(-5.81380 - 3.35660i) q^{98} +(-2.72213 - 4.71487i) 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
$7$	−0.267768	+	0.463788i	−0.101207	+	0.175295i	−0.912182	−	0.409785i	$-0.865604\pi$
$7$	−0.267768	+	0.463788i	−0.101207	+	0.175295i	0.810975	+	0.585080i	$0.198937\pi$
$8$			1.00000i			0.353553i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	1.00000			0.316228
$11$	5.44426			1.64151			0.820754	−	0.571282i	$-0.193554\pi$
$11$	5.44426			1.64151			0.820754	+	0.571282i	$0.193554\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	0.556002	+	0.321008i	0.154207	+	0.0890316i	0.575118	−	0.818070i	$-0.304956\pi$
$13$	0.556002	+	0.321008i	0.154207	+	0.0890316i	−0.420911	+	0.907102i	$0.638289\pi$
$14$		−	0.535537i		−	0.143128i
$15$	0.866025	−	0.500000i	0.223607	−	0.129099i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.402237	+	0.232232i	−0.0975568	+	0.0563245i	−0.547985	−	0.836488i	$-0.684605\pi$
$17$	−0.402237	+	0.232232i	−0.0975568	+	0.0563245i	0.450428	+	0.892813i	$0.351271\pi$
$18$	0.866025	+	0.500000i	0.204124	+	0.117851i
$19$	−7.12118	−	4.11142i	−1.63371	−	0.943224i	−0.982935	−	0.183955i	$-0.941110\pi$
$19$	−7.12118	−	4.11142i	−1.63371	−	0.943224i	−0.650777	−	0.759269i	$-0.725557\pi$
$20$	−0.866025	+	0.500000i	−0.193649	+	0.111803i
$21$	−0.267768	−	0.463788i	−0.0584318	−	0.101207i
$22$	−4.71487	+	2.72213i	−1.00521	+	0.580360i
$23$		−	2.37407i		−	0.495027i	−0.968884	−	0.247514i	$-0.920387\pi$
$23$		−	2.37407i		−	0.495027i	0.968884	−	0.247514i	$-0.0796135\pi$
$24$	−0.866025	−	0.500000i	−0.176777	−	0.102062i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	−0.642016			−0.125910
$27$	1.00000			0.192450
$28$	0.267768	+	0.463788i	0.0506034	+	0.0876477i
$29$		−	5.38430i		−	0.999840i	−0.866072	−	0.499920i	$-0.833363\pi$
$29$		−	5.38430i		−	0.999840i	0.866072	−	0.499920i	$-0.166637\pi$
$30$	−0.500000	+	0.866025i	−0.0912871	+	0.158114i
$31$			1.32755i			0.238434i	0.992868	+	0.119217i	$0.0380385\pi$
$31$			1.32755i			0.238434i	−0.992868	+	0.119217i	$0.961962\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−2.72213	+	4.71487i	−0.473862	+	0.820754i
$34$	0.232232	−	0.402237i	0.0398274	−	0.0689831i
$35$	0.463788	−	0.267768i	0.0783945	−	0.0452611i
$36$	−1.00000			−0.166667
$37$	6.01205	+	0.924822i	0.988374	+	0.152040i
$37$	6.01205	+	0.924822i	0.988374	+	0.152040i
$38$	8.22283			1.33392
$39$	−0.556002	+	0.321008i	−0.0890316	+	0.0514024i
$40$	0.500000	−	0.866025i	0.0790569	−	0.136931i
$41$	4.86520	−	8.42677i	0.759816	−	1.31604i	−0.183128	−	0.983089i	$-0.558622\pi$
$41$	4.86520	−	8.42677i	0.759816	−	1.31604i	0.942944	−	0.332951i	$-0.108044\pi$
$42$	0.463788	+	0.267768i	0.0715641	+	0.0413175i
$43$			1.04652i			0.159593i	0.996811	+	0.0797965i	$0.0254270\pi$
$43$			1.04652i			0.159593i	−0.996811	+	0.0797965i	$0.974573\pi$
$44$	2.72213	−	4.71487i	0.410377	−	0.710793i
$45$			1.00000i			0.149071i
$46$	1.18703	+	2.05600i	0.175019	+	0.303141i
$47$	8.14127			1.18753			0.593763	−	0.804640i	$-0.297642\pi$
$47$	8.14127			1.18753			0.593763	+	0.804640i	$0.297642\pi$
$48$	1.00000			0.144338
$49$	3.35660	+	5.81380i	0.479514	+	0.830543i
$50$	−0.866025	−	0.500000i	−0.122474	−	0.0707107i
$51$		−	0.464463i		−	0.0650379i
$52$	0.556002	−	0.321008i	0.0771036	−	0.0445158i
$53$	2.89110	+	5.00753i	0.397123	+	0.687837i	0.993370	−	0.114964i	$-0.0366753\pi$
$53$	2.89110	+	5.00753i	0.397123	+	0.687837i	−0.596247	+	0.802801i	$0.703342\pi$
$54$	−0.866025	+	0.500000i	−0.117851	+	0.0680414i
$55$	−4.71487	−	2.72213i	−0.635753	−	0.367052i
$56$	−0.463788	−	0.267768i	−0.0619763	−	0.0357820i
$57$	7.12118	−	4.11142i	0.943224	−	0.544571i
$58$	2.69215	+	4.66294i	0.353497	+	0.612275i
$59$	10.2224	−	5.90190i	1.33084	−	0.768362i	0.345414	−	0.938450i	$-0.387739\pi$
$59$	10.2224	−	5.90190i	1.33084	−	0.768362i	0.985429	+	0.170088i	$0.0544052\pi$
$60$		−	1.00000i		−	0.129099i
$61$	2.55109	+	1.47287i	0.326633	+	0.188582i	0.654345	−	0.756196i	$-0.272944\pi$
$61$	2.55109	+	1.47287i	0.326633	+	0.188582i	−0.327712	+	0.944778i	$0.606278\pi$
$62$	−0.663773	−	1.14969i	−0.0842992	−	0.146011i
$63$	0.535537			0.0674713
$64$	−1.00000			−0.125000
$65$	−0.321008	−	0.556002i	−0.0398161	−	0.0689636i
$66$		−	5.44426i		−	0.670142i
$67$	−2.04849	+	3.54808i	−0.250263	+	0.433468i	−0.963598	−	0.267355i	$-0.913850\pi$
$67$	−2.04849	+	3.54808i	−0.250263	+	0.433468i	0.713335	+	0.700823i	$0.247184\pi$
$68$			0.464463i			0.0563245i
$69$	2.05600	+	1.18703i	0.247514	+	0.142902i
$70$	−0.267768	+	0.463788i	−0.0320044	+	0.0554333i
$71$	2.17408	−	3.76562i	0.258016	−	0.446897i	−0.707694	−	0.706519i	$-0.750265\pi$
$71$	2.17408	−	3.76562i	0.258016	−	0.446897i	0.965710	+	0.259622i	$0.0835979\pi$
$72$	0.866025	−	0.500000i	0.102062	−	0.0589256i
$73$	−1.60237			−0.187543			−0.0937716	−	0.995594i	$-0.529892\pi$
$73$	−1.60237			−0.187543			−0.0937716	+	0.995594i	$0.529892\pi$
$74$	−5.66900	+	2.20510i	−0.659007	+	0.256338i
$75$	−1.00000			−0.115470
$76$	−7.12118	+	4.11142i	−0.816856	+	0.471612i
$77$	−1.45780	+	2.52499i	−0.166132	+	0.287749i
$78$	0.321008	−	0.556002i	0.0363470	−	0.0629548i
$79$	−3.48536	−	2.01228i	−0.392134	−	0.226399i	0.290950	−	0.956738i	$-0.406029\pi$
$79$	−3.48536	−	2.01228i	−0.392134	−	0.226399i	−0.683084	+	0.730339i	$0.739362\pi$
$80$			1.00000i			0.111803i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$			9.73039i			1.07454i
$83$	3.61426	+	6.26008i	0.396716	+	0.687133i	0.993319	−	0.115404i	$-0.0368164\pi$
$83$	3.61426	+	6.26008i	0.396716	+	0.687133i	−0.596602	+	0.802537i	$0.703483\pi$
$84$	−0.535537			−0.0584318
$85$	0.464463			0.0503781
$86$	−0.523261	−	0.906314i	−0.0564246	−	0.0977303i
$87$	4.66294	+	2.69215i	0.499920	+	0.288629i
$88$			5.44426i			0.580360i
$89$	3.69105	−	2.13103i	0.391251	−	0.225889i	−0.291451	−	0.956586i	$-0.594138\pi$
$89$	3.69105	−	2.13103i	0.391251	−	0.225889i	0.682702	+	0.730697i	$0.260805\pi$
$90$	−0.500000	−	0.866025i	−0.0527046	−	0.0912871i
$91$	−0.297759	+	0.171911i	−0.0312137	+	0.0180212i
$92$	−2.05600	−	1.18703i	−0.214353	−	0.123757i
$93$	−1.14969	−	0.663773i	−0.119217	−	0.0688300i
$94$	−7.05055	+	4.07063i	−0.727208	+	0.419854i
$95$	4.11142	+	7.12118i	0.421823	+	0.730618i
$96$	−0.866025	+	0.500000i	−0.0883883	+	0.0510310i
$97$		−	5.43955i		−	0.552303i	−0.961114	−	0.276151i	$-0.910941\pi$
$97$		−	5.43955i		−	0.552303i	0.961114	−	0.276151i	$-0.0890591\pi$
$98$	−5.81380	−	3.35660i	−0.587283	−	0.339068i
$99$	−2.72213	−	4.71487i	−0.273585	−	0.473862i
$100$	1.00000			0.100000
$101$	9.15512			0.910969			0.455484	−	0.890244i	$-0.349466\pi$
$101$	9.15512			0.910969			0.455484	+	0.890244i	$0.349466\pi$
$102$	0.232232	+	0.402237i	0.0229944	+	0.0398274i
$103$		−	10.5315i		−	1.03770i	−0.854865	−	0.518850i	$-0.826360\pi$
$103$		−	10.5315i		−	1.03770i	0.854865	−	0.518850i	$-0.173640\pi$
$104$	−0.321008	+	0.556002i	−0.0314774	+	0.0545205i
$105$			0.535537i			0.0522630i
$106$	−5.00753	−	2.89110i	−0.486374	−	0.280808i
$107$	−7.54260	+	13.0642i	−0.729170	+	1.26296i	0.228064	+	0.973646i	$0.426760\pi$
$107$	−7.54260	+	13.0642i	−0.729170	+	1.26296i	−0.957234	+	0.289314i	$0.906573\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	3.84093	−	2.21756i	0.367894	−	0.212404i	−0.304644	−	0.952466i	$-0.598537\pi$
$109$	3.84093	−	2.21756i	0.367894	−	0.212404i	0.672538	+	0.740063i	$0.265204\pi$
$110$	5.44426			0.519090
$111$	−3.80694	+	4.74417i	−0.361339	+	0.450297i
$112$	0.535537			0.0506034
$113$	7.78200	−	4.49294i	0.732069	−	0.422660i	−0.0871097	−	0.996199i	$-0.527763\pi$
$113$	7.78200	−	4.49294i	0.732069	−	0.422660i	0.819179	+	0.573539i	$0.194430\pi$
$114$	−4.11142	+	7.12118i	−0.385070	+	0.666960i
$115$	−1.18703	+	2.05600i	−0.110691	+	0.191723i
$116$	−4.66294	−	2.69215i	−0.432944	−	0.249960i
$117$		−	0.642016i		−	0.0593544i
$118$	−5.90190	+	10.2224i	−0.543314	+	0.941048i
$119$		−	0.248737i		−	0.0228017i
$120$	0.500000	+	0.866025i	0.0456435	+	0.0790569i
$121$	18.6400			1.69455
$122$	−2.94574			−0.266695
$123$	4.86520	+	8.42677i	0.438680	+	0.759816i
$124$	1.14969	+	0.663773i	0.103245	+	0.0596086i
$125$		−	1.00000i		−	0.0894427i
$126$	−0.463788	+	0.267768i	−0.0413175	+	0.0238547i
$127$	5.95507	+	10.3145i	0.528427	+	0.915262i	0.999451	+	0.0331415i	$0.0105512\pi$
$127$	5.95507	+	10.3145i	0.528427	+	0.915262i	−0.471024	+	0.882120i	$0.656115\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−0.906314	−	0.523261i	−0.0797965	−	0.0460705i
$130$	0.556002	+	0.321008i	0.0487646	+	0.0281543i
$131$	7.32391	−	4.22846i	0.639893	−	0.369442i	−0.144680	−	0.989478i	$-0.546215\pi$
$131$	7.32391	−	4.22846i	0.639893	−	0.369442i	0.784573	+	0.620036i	$0.212882\pi$
$132$	2.72213	+	4.71487i	0.236931	+	0.410377i
$133$	3.81365	−	2.20181i	0.330686	−	0.190922i
$134$		−	4.09698i		−	0.353925i
$135$	−0.866025	−	0.500000i	−0.0745356	−	0.0430331i
$136$	−0.232232	−	0.402237i	−0.0199137	−	0.0344916i
$137$	19.7950			1.69120			0.845599	−	0.533818i	$-0.179243\pi$
$137$	19.7950			1.69120			0.845599	+	0.533818i	$0.179243\pi$
$138$	−2.37407			−0.202094
$139$	−3.66567	−	6.34913i	−0.310918	−	0.538526i	0.667643	−	0.744481i	$-0.267303\pi$
$139$	−3.66567	−	6.34913i	−0.310918	−	0.538526i	−0.978561	+	0.205955i	$0.933970\pi$
$140$		−	0.535537i		−	0.0452611i
$141$	−4.07063	+	7.05055i	−0.342809	+	0.593763i
$142$			4.34816i			0.364890i
$143$	3.02702	+	1.74765i	0.253132	+	0.146146i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−2.69215	+	4.66294i	−0.223571	+	0.387236i
$146$	1.38769	−	0.801185i	0.114846	−	0.0663065i
$147$	−6.71320			−0.553695
$148$	3.80694	−	4.74417i	0.312929	−	0.389969i
$149$	−8.22737			−0.674012			−0.337006	−	0.941502i	$-0.609414\pi$
$149$	−8.22737			−0.674012			−0.337006	+	0.941502i	$0.609414\pi$
$150$	0.866025	−	0.500000i	0.0707107	−	0.0408248i
$151$	−4.98628	+	8.63648i	−0.405777	+	0.702827i	−0.994412	−	0.105572i	$-0.966333\pi$
$151$	−4.98628	+	8.63648i	−0.405777	+	0.702827i	0.588634	+	0.808400i	$0.299666\pi$
$152$	4.11142	−	7.12118i	0.333480	−	0.577604i
$153$	0.402237	+	0.232232i	0.0325189	+	0.0187748i
$154$		−	2.91560i		−	0.234946i
$155$	0.663773	−	1.14969i	0.0533155	−	0.0923452i
$156$			0.642016i			0.0514024i
$157$	−2.88383	−	4.99495i	−0.230155	−	0.398640i	0.727699	−	0.685897i	$-0.240590\pi$
$157$	−2.88383	−	4.99495i	−0.230155	−	0.398640i	−0.957854	+	0.287257i	$0.907257\pi$
$158$	4.02455			0.320176
$159$	−5.78220			−0.458558
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	1.10106	+	0.635700i	0.0867760	+	0.0501002i
$162$		−	1.00000i		−	0.0785674i
$163$	0.511813	−	0.295495i	0.0400883	−	0.0231450i	−0.479822	−	0.877366i	$-0.659299\pi$
$163$	0.511813	−	0.295495i	0.0400883	−	0.0231450i	0.519910	+	0.854221i	$0.325965\pi$
$164$	−4.86520	−	8.42677i	−0.379908	−	0.658020i
$165$	4.71487	−	2.72213i	0.367052	−	0.211918i
$166$	−6.26008	−	3.61426i	−0.485876	−	0.280521i
$167$	−8.80330	−	5.08259i	−0.681220	−	0.393302i	0.119095	−	0.992883i	$-0.462001\pi$
$167$	−8.80330	−	5.08259i	−0.681220	−	0.393302i	−0.800314	+	0.599580i	$0.795334\pi$
$168$	0.463788	−	0.267768i	0.0357820	−	0.0206588i
$169$	−6.29391	−	10.9014i	−0.484147	−	0.838567i
$170$	−0.402237	+	0.232232i	−0.0308502	+	0.0178114i
$171$			8.22283i			0.628816i
$172$	0.906314	+	0.523261i	0.0691058	+	0.0398982i
$173$	−7.70420	−	13.3441i	−0.585739	−	1.01453i	−0.994783	−	0.102015i	$-0.967471\pi$
$173$	−7.70420	−	13.3441i	−0.585739	−	1.01453i	0.409043	−	0.912515i	$-0.365862\pi$
$174$	−5.38430			−0.408183
$175$	−0.535537			−0.0404828
$176$	−2.72213	−	4.71487i	−0.205188	−	0.355397i
$177$			11.8038i			0.887228i
$178$	−2.13103	+	3.69105i	−0.159728	+	0.276656i
$179$			7.91168i			0.591347i	0.955289	+	0.295673i	$0.0955440\pi$
$179$			7.91168i			0.591347i	−0.955289	+	0.295673i	$0.904456\pi$
$180$	0.866025	+	0.500000i	0.0645497	+	0.0372678i
$181$	4.86182	−	8.42093i	0.361377	−	0.625922i	−0.626811	−	0.779171i	$-0.715640\pi$
$181$	4.86182	−	8.42093i	0.361377	−	0.625922i	0.988188	+	0.153249i	$0.0489736\pi$
$182$	0.171911	−	0.297759i	0.0127429	−	0.0220714i
$183$	−2.55109	+	1.47287i	−0.188582	+	0.108878i
$184$	2.37407			0.175019
$185$	−4.74417	−	3.80694i	−0.348799	−	0.279892i
$186$	1.32755			0.0973404
$187$	−2.18988	+	1.26433i	−0.160140	+	0.0924570i
$188$	4.07063	−	7.05055i	0.296882	−	0.514214i
$189$	−0.267768	+	0.463788i	−0.0194773	+	0.0337356i
$190$	−7.12118	−	4.11142i	−0.516625	−	0.298274i
$191$			16.0144i			1.15876i	0.815057	+	0.579380i	$0.196705\pi$
$191$			16.0144i			1.15876i	−0.815057	+	0.579380i	$0.803295\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$			17.2656i			1.24281i	0.783490	+	0.621404i	$0.213437\pi$
$193$			17.2656i			1.24281i	−0.783490	+	0.621404i	$0.786563\pi$
$194$	2.71977	+	4.71079i	0.195268	+	0.338215i
$195$	0.642016			0.0459757
$196$	6.71320			0.479514
$197$	−12.1985	−	21.1285i	−0.869110	−	1.50534i	−0.862907	−	0.505363i	$-0.831359\pi$
$197$	−12.1985	−	21.1285i	−0.869110	−	1.50534i	−0.00620326	−	0.999981i	$-0.501975\pi$
$198$	4.71487	+	2.72213i	0.335071	+	0.193453i
$199$		−	0.826478i		−	0.0585875i	−0.999571	−	0.0292937i	$-0.990674\pi$
$199$		−	0.826478i		−	0.0585875i	0.999571	−	0.0292937i	$-0.00932582\pi$
$200$	−0.866025	+	0.500000i	−0.0612372	+	0.0353553i
$201$	−2.04849	−	3.54808i	−0.144489	−	0.250263i
$202$	−7.92857	+	4.57756i	−0.557852	+	0.322076i
$203$	2.49718	+	1.44175i	0.175267	+	0.101191i
$204$	−0.402237	−	0.232232i	−0.0281622	−	0.0162595i
$205$	−8.42677	+	4.86520i	−0.588551	+	0.339800i
$206$	5.26575	+	9.12055i	0.366882	+	0.635459i
$207$	−2.05600	+	1.18703i	−0.142902	+	0.0825045i
$208$		−	0.642016i		−	0.0445158i
$209$	−38.7696	−	22.3836i	−2.68175	−	1.54831i
$210$	−0.267768	−	0.463788i	−0.0184778	−	0.0320044i
$211$	4.70749			0.324077			0.162039	−	0.986784i	$-0.448193\pi$
$211$	4.70749			0.324077			0.162039	+	0.986784i	$0.448193\pi$
$212$	5.78220			0.397123
$213$	2.17408	+	3.76562i	0.148966	+	0.258016i
$214$		−	15.0852i		−	1.03120i
$215$	0.523261	−	0.906314i	0.0356861	−	0.0618101i
$216$			1.00000i			0.0680414i
$217$	−0.615700	−	0.355475i	−0.0417964	−	0.0241312i
$218$	−2.21756	+	3.84093i	−0.150192	+	0.260140i
$219$	0.801185	−	1.38769i	0.0541391	−	0.0937716i
$220$	−4.71487	+	2.72213i	−0.317876	+	0.183526i
$221$	−0.298193			−0.0200586
$222$	0.924822	−	6.01205i	0.0620700	−	0.403502i
$223$	−8.14374			−0.545345			−0.272673	−	0.962107i	$-0.587908\pi$
$223$	−8.14374			−0.545345			−0.272673	+	0.962107i	$0.587908\pi$
$224$	−0.463788	+	0.267768i	−0.0309882	+	0.0178910i
$225$	0.500000	−	0.866025i	0.0333333	−	0.0577350i
$226$	−4.49294	+	7.78200i	−0.298866	+	0.517651i
$227$	−3.39960	−	1.96276i	−0.225639	−	0.130273i	0.382919	−	0.923782i	$-0.374919\pi$
$227$	−3.39960	−	1.96276i	−0.225639	−	0.130273i	−0.608559	+	0.793509i	$0.708252\pi$
$228$		−	8.22283i		−	0.544571i
$229$	13.5993	−	23.5547i	0.898667	−	1.55654i	0.0694673	−	0.997584i	$-0.477870\pi$
$229$	13.5993	−	23.5547i	0.898667	−	1.55654i	0.829200	−	0.558953i	$-0.188797\pi$
$230$		−	2.37407i		−	0.156541i
$231$	−1.45780	−	2.52499i	−0.0959162	−	0.166132i
$232$	5.38430			0.353497
$233$	11.1032			0.727394			0.363697	−	0.931517i	$-0.381514\pi$
$233$	11.1032			0.727394			0.363697	+	0.931517i	$0.381514\pi$
$234$	0.321008	+	0.556002i	0.0209849	+	0.0363470i
$235$	−7.05055	−	4.07063i	−0.459927	−	0.265539i
$236$		−	11.8038i		−	0.768362i
$237$	3.48536	−	2.01228i	0.226399	−	0.130711i
$238$	0.124369	+	0.215413i	0.00806162	+	0.0139631i
$239$	−8.61437	+	4.97351i	−0.557217	+	0.321710i	−0.752028	−	0.659131i	$-0.770924\pi$
$239$	−8.61437	+	4.97351i	−0.557217	+	0.321710i	0.194810	+	0.980841i	$0.437591\pi$
$240$	−0.866025	−	0.500000i	−0.0559017	−	0.0322749i
$241$	−18.7127	−	10.8038i	−1.20539	−	0.695932i	−0.243641	−	0.969865i	$-0.578342\pi$
$241$	−18.7127	−	10.8038i	−1.20539	−	0.695932i	−0.961749	+	0.273933i	$0.911675\pi$
$242$	−16.1427	+	9.32000i	−1.03769	+	0.599112i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	2.55109	−	1.47287i	0.163317	−	0.0942910i
$245$		−	6.71320i		−	0.428891i
$246$	−8.42677	−	4.86520i	−0.537271	−	0.310194i
$247$	−2.63960	−	4.57191i	−0.167953	−	0.290904i
$248$	−1.32755			−0.0842992
$249$	−7.22851			−0.458088
$250$	0.500000	+	0.866025i	0.0316228	+	0.0547723i
$251$			5.10425i			0.322178i	0.986940	+	0.161089i	$0.0515005\pi$
$251$			5.10425i			0.322178i	−0.986940	+	0.161089i	$0.948499\pi$
$252$	0.267768	−	0.463788i	0.0168678	−	0.0292159i
$253$		−	12.9250i		−	0.812590i
$254$	−10.3145	−	5.95507i	−0.647188	−	0.373654i
$255$	−0.232232	+	0.402237i	−0.0145429	+	0.0251891i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	16.8491	−	9.72782i	1.05102	−	0.606805i	0.128083	−	0.991763i	$-0.459118\pi$
$257$	16.8491	−	9.72782i	1.05102	−	0.606805i	0.922934	+	0.384959i	$0.125784\pi$
$258$	1.04652			0.0651536
$259$	−2.03876	+	2.54068i	−0.126682	+	0.157870i
$260$	−0.642016			−0.0398161
$261$	−4.66294	+	2.69215i	−0.288629	+	0.166640i
$262$	−4.22846	+	7.32391i	−0.261235	+	0.452473i
$263$	−6.04317	+	10.4671i	−0.372638	+	0.645428i	−0.989970	−	0.141274i	$-0.954880\pi$
$263$	−6.04317	+	10.4671i	−0.372638	+	0.645428i	0.617332	+	0.786702i	$0.288213\pi$
$264$	−4.71487	−	2.72213i	−0.290180	−	0.167536i
$265$		−	5.78220i		−	0.355198i
$266$	−2.20181	+	3.81365i	−0.135002	+	0.233830i
$267$			4.26206i			0.260834i
$268$	2.04849	+	3.54808i	0.125131	+	0.216734i
$269$	−27.8139			−1.69584			−0.847921	−	0.530123i	$-0.822146\pi$
$269$	−27.8139			−1.69584			−0.847921	+	0.530123i	$0.822146\pi$
$270$	1.00000			0.0608581
$271$	2.68320	+	4.64744i	0.162993	+	0.282312i	0.935941	−	0.352158i	$-0.114552\pi$
$271$	2.68320	+	4.64744i	0.162993	+	0.282312i	−0.772948	+	0.634470i	$0.781219\pi$
$272$	0.402237	+	0.232232i	0.0243892	+	0.0140811i
$273$		−	0.343823i		−	0.0208091i
$274$	−17.1430	+	9.89749i	−1.03564	+	0.597929i
$275$	2.72213	+	4.71487i	0.164151	+	0.284317i
$276$	2.05600	−	1.18703i	0.123757	−	0.0714510i
$277$	−9.37602	−	5.41325i	−0.563350	−	0.325250i	0.191139	−	0.981563i	$-0.438782\pi$
$277$	−9.37602	−	5.41325i	−0.563350	−	0.325250i	−0.754489	+	0.656313i	$0.772115\pi$
$278$	6.34913	+	3.66567i	0.380795	+	0.219852i
$279$	1.14969	−	0.663773i	0.0688300	−	0.0397390i
$280$	0.267768	+	0.463788i	0.0160022	+	0.0277166i
$281$	12.7542	−	7.36363i	0.760851	−	0.439277i	−0.0687503	−	0.997634i	$-0.521901\pi$
$281$	12.7542	−	7.36363i	0.760851	−	0.439277i	0.829601	+	0.558356i	$0.188568\pi$
$282$		−	8.14127i		−	0.484806i
$283$	16.5272	+	9.54199i	0.982440	+	0.567212i	0.903006	−	0.429628i	$-0.141355\pi$
$283$	16.5272	+	9.54199i	0.982440	+	0.567212i	0.0794343	+	0.996840i	$0.474689\pi$
$284$	−2.17408	−	3.76562i	−0.129008	−	0.223448i
$285$	−8.22283			−0.487079
$286$	−3.49530			−0.206682
$287$	2.60549	+	4.51284i	0.153797	+	0.266385i
$288$		−	1.00000i		−	0.0589256i
$289$	−8.39214	+	14.5356i	−0.493655	+	0.855036i
$290$		−	5.38430i		−	0.316177i
$291$	4.71079	+	2.71977i	0.276151	+	0.159436i
$292$	−0.801185	+	1.38769i	−0.0468858	+	0.0812086i
$293$	−1.27637	+	2.21073i	−0.0745660	+	0.129152i	−0.900897	−	0.434032i	$-0.857090\pi$
$293$	−1.27637	+	2.21073i	−0.0745660	+	0.129152i	0.826331	+	0.563184i	$0.190424\pi$
$294$	5.81380	−	3.35660i	0.339068	−	0.195761i
$295$	−11.8038			−0.687244
$296$	−0.924822	+	6.01205i	−0.0537542	+	0.349443i
$297$	5.44426			0.315908
$298$	7.12511	−	4.11369i	0.412747	−	0.238299i
$299$	0.762094	−	1.31999i	0.0440731	−	0.0763368i
$300$	−0.500000	+	0.866025i	−0.0288675	+	0.0500000i
$301$	−0.485364	−	0.280225i	−0.0279759	−	0.0161519i
$302$		−	9.97255i		−	0.573856i
$303$	−4.57756	+	7.92857i	−0.262974	+	0.455484i
$304$			8.22283i			0.471612i
$305$	−1.47287	−	2.55109i	−0.0843364	−	0.146075i
$306$	−0.464463			−0.0265516
$307$	−1.60024			−0.0913305			−0.0456653	−	0.998957i	$-0.514541\pi$
$307$	−1.60024			−0.0913305			−0.0456653	+	0.998957i	$0.514541\pi$
$308$	1.45780	+	2.52499i	0.0830659	+	0.143874i
$309$	9.12055	+	5.26575i	0.518850	+	0.299558i
$310$			1.32755i			0.0753995i
$311$	−4.41158	+	2.54702i	−0.250157	+	0.144428i	−0.619836	−	0.784731i	$-0.712801\pi$
$311$	−4.41158	+	2.54702i	−0.250157	+	0.144428i	0.369679	+	0.929160i	$0.379468\pi$
$312$	−0.321008	−	0.556002i	−0.0181735	−	0.0314774i
$313$	−2.00909	+	1.15995i	−0.113561	+	0.0655642i	−0.555704	−	0.831380i	$-0.687551\pi$
$313$	−2.00909	+	1.15995i	−0.113561	+	0.0655642i	0.442144	+	0.896944i	$0.354218\pi$
$314$	4.99495	+	2.88383i	0.281881	+	0.162744i
$315$	−0.463788	−	0.267768i	−0.0261315	−	0.0150870i
$316$	−3.48536	+	2.01228i	−0.196067	+	0.113199i
$317$	6.42213	+	11.1235i	0.360703	+	0.624756i	0.988077	−	0.153963i	$-0.0492035\pi$
$317$	6.42213	+	11.1235i	0.360703	+	0.624756i	−0.627374	+	0.778718i	$0.715870\pi$
$318$	5.00753	−	2.89110i	0.280808	−	0.162125i
$319$		−	29.3136i		−	1.64124i
$320$	0.866025	+	0.500000i	0.0484123	+	0.0279508i
$321$	−7.54260	−	13.0642i	−0.420987	−	0.729170i
$322$	−1.27140			−0.0708523
$323$	3.81921			0.212506
$324$	0.500000	+	0.866025i	0.0277778	+	0.0481125i
$325$			0.642016i			0.0356126i
$326$	−0.295495	+	0.511813i	−0.0163660	+	0.0283467i
$327$			4.43512i			0.245263i
$328$	8.42677	+	4.86520i	0.465290	+	0.268636i
$329$	−2.17997	+	3.77582i	−0.120186	+	0.208168i
$330$	−2.72213	+	4.71487i	−0.149848	+	0.259545i
$331$	−6.20441	+	3.58212i	−0.341025	+	0.196891i	−0.660725	−	0.750628i	$-0.729751\pi$
$331$	−6.20441	+	3.58212i	−0.341025	+	0.196891i	0.319700	+	0.947519i	$0.396418\pi$
$332$	7.22851			0.396716
$333$	−2.20510	−	5.66900i	−0.120839	−	0.310659i
$334$	10.1652			0.556214
$335$	3.54808	−	2.04849i	0.193853	−	0.111921i
$336$	−0.267768	+	0.463788i	−0.0146080	+	0.0253017i
$337$	−11.4507	+	19.8331i	−0.623757	+	1.08038i	0.365023	+	0.930999i	$0.381061\pi$
$337$	−11.4507	+	19.8331i	−0.623757	+	1.08038i	−0.988780	+	0.149380i	$0.952272\pi$
$338$	10.9014	+	6.29391i	0.592956	+	0.342343i
$339$			8.98588i			0.488046i
$340$	0.232232	−	0.402237i	0.0125945	−	0.0218144i
$341$			7.22751i			0.391391i
$342$	−4.11142	−	7.12118i	−0.222320	−	0.385070i
$343$	−7.34392			−0.396534
$344$	−1.04652			−0.0564246
$345$	−1.18703	−	2.05600i	−0.0639077	−	0.110691i
$346$	13.3441	+	7.70420i	0.717381	+	0.414180i
$347$		−	27.5385i		−	1.47835i	−0.673516	−	0.739173i	$-0.735217\pi$
$347$		−	27.5385i		−	1.47835i	0.673516	−	0.739173i	$-0.264783\pi$
$348$	4.66294	−	2.69215i	0.249960	−	0.144315i
$349$	−11.8294	−	20.4892i	−0.633216	−	1.09676i	−0.986890	−	0.161393i	$-0.948401\pi$
$349$	−11.8294	−	20.4892i	−0.633216	−	1.09676i	0.353675	−	0.935369i	$-0.384932\pi$
$350$	0.463788	−	0.267768i	0.0247905	−	0.0143128i
$351$	0.556002	+	0.321008i	0.0296772	+	0.0171341i
$352$	4.71487	+	2.72213i	0.251303	+	0.145090i
$353$	−4.74750	+	2.74097i	−0.252684	+	0.145887i	−0.620992	−	0.783817i	$-0.713270\pi$
$353$	−4.74750	+	2.74097i	−0.252684	+	0.145887i	0.368309	+	0.929704i	$0.379937\pi$
$354$	−5.90190	−	10.2224i	−0.313683	−	0.543314i
$355$	−3.76562	+	2.17408i	−0.199858	+	0.115388i
$356$		−	4.26206i		−	0.225889i
$357$	0.215413	+	0.124369i	0.0114008	+	0.00658228i
$358$	−3.95584	−	6.85171i	−0.209073	−	0.362124i
$359$	−20.2538			−1.06895			−0.534477	−	0.845183i	$-0.679491\pi$
$359$	−20.2538			−1.06895			−0.534477	+	0.845183i	$0.679491\pi$
$360$	−1.00000			−0.0527046
$361$	24.3075	+	42.1018i	1.27934	+	2.21589i
$362$			9.72365i			0.511064i
$363$	−9.32000	+	16.1427i	−0.489173	+	0.847273i
$364$			0.343823i			0.0180212i
$365$	1.38769	+	0.801185i	0.0726352	+	0.0419359i
$366$	1.47287	−	2.55109i	0.0769882	−	0.133348i
$367$	−14.5637	+	25.2250i	−0.760217	+	1.31673i	0.182522	+	0.983202i	$0.441574\pi$
$367$	−14.5637	+	25.2250i	−0.760217	+	1.31673i	−0.942739	+	0.333532i	$0.891759\pi$
$368$	−2.05600	+	1.18703i	−0.107177	+	0.0618784i
$369$	−9.73039			−0.506544
$370$	6.01205	+	0.924822i	0.312551	+	0.0480792i
$371$	−3.09658			−0.160766
$372$	−1.14969	+	0.663773i	−0.0596086	+	0.0344150i
$373$	18.0747	−	31.3063i	0.935871	−	1.62098i	0.162799	−	0.986659i	$-0.447948\pi$
$373$	18.0747	−	31.3063i	0.935871	−	1.62098i	0.773073	−	0.634317i	$-0.218719\pi$
$374$	1.26433	−	2.18988i	0.0653770	−	0.113236i
$375$	0.866025	+	0.500000i	0.0447214	+	0.0258199i
$376$			8.14127i			0.419854i
$377$	1.72840	−	2.99368i	0.0890174	−	0.154183i
$378$		−	0.535537i		−	0.0275450i
$379$	10.8574	+	18.8055i	0.557706	+	0.965976i	0.997687	+	0.0679687i	$0.0216518\pi$
$379$	10.8574	+	18.8055i	0.557706	+	0.965976i	−0.439981	+	0.898007i	$0.645015\pi$
$380$	8.22283			0.421823
$381$	−11.9101			−0.610175
$382$	−8.00719	−	13.8689i	−0.409684	−	0.709593i
$383$	−27.9465	−	16.1349i	−1.42800	−	0.824456i	−0.431037	−	0.902334i	$-0.641852\pi$
$383$	−27.9465	−	16.1349i	−1.42800	−	0.824456i	−0.996963	+	0.0778783i	$0.975185\pi$
$384$			1.00000i			0.0510310i
$385$	2.52499	−	1.45780i	0.128685	−	0.0742964i
$386$	−8.63282	−	14.9525i	−0.439399	−	0.761061i
$387$	0.906314	−	0.523261i	0.0460705	−	0.0265988i
$388$	−4.71079	−	2.71977i	−0.239154	−	0.138076i
$389$	−28.9212	−	16.6976i	−1.46636	−	0.846604i	−0.467069	−	0.884221i	$-0.654690\pi$
$389$	−28.9212	−	16.6976i	−1.46636	−	0.846604i	−0.999292	+	0.0376165i	$0.988023\pi$
$390$	−0.556002	+	0.321008i	−0.0281543	+	0.0162549i
$391$	0.551334	+	0.954938i	0.0278821	+	0.0482933i
$392$	−5.81380	+	3.35660i	−0.293641	+	0.169534i
$393$			8.45692i			0.426595i
$394$	21.1285	+	12.1985i	1.06444	+	0.614554i
$395$	2.01228	+	3.48536i	0.101249	+	0.175368i
$396$	−5.44426			−0.273585
$397$	−8.82763			−0.443046			−0.221523	−	0.975155i	$-0.571103\pi$
$397$	−8.82763			−0.443046			−0.221523	+	0.975155i	$0.571103\pi$
$398$	0.413239	+	0.715751i	0.0207138	+	0.0358774i
$399$			4.40363i			0.220457i
$400$	0.500000	−	0.866025i	0.0250000	−	0.0433013i
$401$			35.0800i			1.75181i	0.482482	+	0.875906i	$0.339736\pi$
$401$			35.0800i			1.75181i	−0.482482	+	0.875906i	$0.660264\pi$
$402$	3.54808	+	2.04849i	0.176962	+	0.102169i
$403$	−0.426153	+	0.738118i	−0.0212282	+	0.0367683i
$404$	4.57756	−	7.92857i	0.227742	−	0.394461i
$405$	0.866025	−	0.500000i	0.0430331	−	0.0248452i
$406$	−2.88349			−0.143105
$407$	32.7312	+	5.03498i	1.62242	+	0.249575i
$408$	0.464463			0.0229944
$409$	31.4737	−	18.1714i	1.55627	−	0.898516i	0.558666	−	0.829392i	$-0.311313\pi$
$409$	31.4737	−	18.1714i	1.55627	−	0.898516i	0.997608	−	0.0691231i	$-0.0220201\pi$
$410$	4.86520	−	8.42677i	0.240275	−	0.416168i
$411$	−9.89749	+	17.1430i	−0.488207	+	0.845599i
$412$	−9.12055	−	5.26575i	−0.449337	−	0.259425i
$413$			6.32137i			0.311054i
$414$	1.18703	−	2.05600i	0.0583395	−	0.101047i
$415$		−	7.22851i		−	0.354834i
$416$	0.321008	+	0.556002i	0.0157387	+	0.0272602i
$417$	7.33134			0.359017
$418$	44.7673			2.18964
$419$	−6.93685	−	12.0150i	−0.338887	−	0.586970i	0.645336	−	0.763898i	$-0.276717\pi$
$419$	−6.93685	−	12.0150i	−0.338887	−	0.586970i	−0.984224	+	0.176929i	$0.943384\pi$
$420$	0.463788	+	0.267768i	0.0226305	+	0.0130658i
$421$		−	3.08809i		−	0.150504i	−0.997165	−	0.0752521i	$-0.976024\pi$
$421$		−	3.08809i		−	0.150504i	0.997165	−	0.0752521i	$-0.0239762\pi$
$422$	−4.07681	+	2.35375i	−0.198456	+	0.114579i
$423$	−4.07063	−	7.05055i	−0.197921	−	0.342809i
$424$	−5.00753	+	2.89110i	−0.243187	+	0.140404i
$425$	−0.402237	−	0.232232i	−0.0195114	−	0.0112649i
$426$	−3.76562	−	2.17408i	−0.182445	−	0.105335i
$427$	−1.36620	+	0.788777i	−0.0661151	+	0.0381716i
$428$	7.54260	+	13.0642i	0.364585	+	0.631480i
$429$	−3.02702	+	1.74765i	−0.146146	+	0.0843774i
$430$			1.04652i			0.0504677i
$431$	34.4243	+	19.8749i	1.65816	+	0.957341i	0.973562	+	0.228422i	$0.0733565\pi$
$431$	34.4243	+	19.8749i	1.65816	+	0.957341i	0.684600	+	0.728919i	$0.259977\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	2.97177			0.142814			0.0714070	−	0.997447i	$-0.477251\pi$
$433$	2.97177			0.142814			0.0714070	+	0.997447i	$0.477251\pi$
$434$	0.710949			0.0341267
$435$	−2.69215	−	4.66294i	−0.129079	−	0.223571i
$436$		−	4.43512i		−	0.212404i
$437$	−9.76078	+	16.9062i	−0.466921	+	0.808732i
$438$			1.60237i			0.0765642i
$439$	6.90136	+	3.98450i	0.329384	+	0.190170i	0.655568	−	0.755137i	$-0.272429\pi$
$439$	6.90136	+	3.98450i	0.329384	+	0.190170i	−0.326184	+	0.945306i	$0.605763\pi$
$440$	2.72213	−	4.71487i	0.129773	−	0.224773i
$441$	3.35660	−	5.81380i	0.159838	−	0.276848i
$442$	0.258243	−	0.149096i	0.0122834	−	0.00709180i
$443$	−34.0828			−1.61932			−0.809662	−	0.586897i	$-0.800349\pi$
$443$	−34.0828			−1.61932			−0.809662	+	0.586897i	$0.800349\pi$
$444$	2.20510	+	5.66900i	0.104650	+	0.269039i
$445$	−4.26206			−0.202041
$446$	7.05269	−	4.07187i	0.333955	−	0.192809i
$447$	4.11369	−	7.12511i	0.194571	−	0.337006i
$448$	0.267768	−	0.463788i	0.0126509	−	0.0219119i
$449$	24.4617	+	14.1230i	1.15442	+	0.666505i	0.949961	−	0.312370i	$-0.101123\pi$
$449$	24.4617	+	14.1230i	1.15442	+	0.666505i	0.204460	+	0.978875i	$0.434456\pi$
$450$			1.00000i			0.0471405i
$451$	26.4874	−	45.8775i	1.24724	−	2.16029i
$452$		−	8.98588i		−	0.422660i
$453$	−4.98628	−	8.63648i	−0.234276	−	0.405777i
$454$	3.92552			0.184234
$455$	0.343823			0.0161187
$456$	4.11142	+	7.12118i	0.192535	+	0.333480i
$457$	−26.8664	−	15.5113i	−1.25676	−	0.725588i	−0.284313	−	0.958731i	$-0.591766\pi$
$457$	−26.8664	−	15.5113i	−1.25676	−	0.725588i	−0.972442	+	0.233143i	$0.925099\pi$
$458$			27.1986i			1.27091i
$459$	−0.402237	+	0.232232i	−0.0187748	+	0.0108396i
$460$	1.18703	+	2.05600i	0.0553457	+	0.0958616i
$461$	−3.95564	+	2.28379i	−0.184233	+	0.106367i	−0.589280	−	0.807929i	$-0.700588\pi$
$461$	−3.95564	+	2.28379i	−0.184233	+	0.106367i	0.405047	+	0.914296i	$0.367255\pi$
$462$	2.52499	+	1.45780i	0.117473	+	0.0678230i
$463$	−5.59102	−	3.22798i	−0.259837	−	0.150017i	0.364423	−	0.931233i	$-0.381266\pi$
$463$	−5.59102	−	3.22798i	−0.259837	−	0.150017i	−0.624260	+	0.781217i	$0.714599\pi$
$464$	−4.66294	+	2.69215i	−0.216472	+	0.124980i
$465$	0.663773	+	1.14969i	0.0307817	+	0.0533155i
$466$	−9.61564	+	5.55159i	−0.445436	+	0.257173i
$467$		−	22.5295i		−	1.04254i	−0.853391	−	0.521271i	$-0.825458\pi$
$467$		−	22.5295i		−	1.04254i	0.853391	−	0.521271i	$-0.174542\pi$
$468$	−0.556002	−	0.321008i	−0.0257012	−	0.0148386i
$469$	−1.09704	−	1.90013i	−0.0506566	−	0.0877398i
$470$	8.14127			0.375529
$471$	5.76767			0.265760
$472$	5.90190	+	10.2224i	0.271657	+	0.470524i
$473$			5.69754i			0.261973i
$474$	−2.01228	+	3.48536i	−0.0924269	+	0.160088i
$475$		−	8.22283i		−	0.377290i
$476$	−0.215413	−	0.124369i	−0.00987342	−	0.00570042i
$477$	2.89110	−	5.00753i	0.132374	−	0.229279i
$478$	4.97351	−	8.61437i	0.227483	−	0.394012i
$479$	−7.02757	+	4.05737i	−0.321098	+	0.185386i	−0.651882	−	0.758321i	$-0.726020\pi$
$479$	−7.02757	+	4.05737i	−0.321098	+	0.185386i	0.330784	+	0.943706i	$0.392687\pi$
$480$	1.00000			0.0456435
$481$	3.04583	+	2.44412i	0.138878	+	0.111442i
$482$	21.6075			0.984196
$483$	−1.10106	+	0.635700i	−0.0501002	+	0.0289253i
$484$	9.32000	−	16.1427i	0.423636	−	0.733760i
$485$	−2.71977	+	4.71079i	−0.123499	+	0.213906i
$486$	0.866025	+	0.500000i	0.0392837	+	0.0226805i
$487$		−	5.69618i		−	0.258118i	−0.991637	−	0.129059i	$-0.958804\pi$
$487$		−	5.69618i		−	0.258118i	0.991637	−	0.129059i	$-0.0411957\pi$
$488$	−1.47287	+	2.55109i	−0.0666738	+	0.115482i
$489$			0.590991i			0.0267255i
$490$	3.35660	+	5.81380i	0.151636	+	0.262641i
$491$	26.7699			1.20811			0.604054	−	0.796943i	$-0.293551\pi$
$491$	26.7699			1.20811			0.604054	+	0.796943i	$0.293551\pi$
$492$	9.73039			0.438680
$493$	1.25041	+	2.16577i	0.0563155	+	0.0975413i
$494$	4.57191	+	2.63960i	0.205700	+	0.118761i
$495$			5.44426i			0.244701i
$496$	1.14969	−	0.663773i	0.0516225	−	0.0298043i
$497$	1.16430	+	2.01663i	0.0522260	+	0.0904581i
$498$	6.26008	−	3.61426i	0.280521	−	0.161959i
$499$	37.4524	+	21.6232i	1.67660	+	0.967986i	0.963802	+	0.266619i	$0.0859064\pi$
$499$	37.4524	+	21.6232i	1.67660	+	0.967986i	0.712800	+	0.701368i	$0.247427\pi$
$500$	−0.866025	−	0.500000i	−0.0387298	−	0.0223607i
$501$	8.80330	−	5.08259i	0.393302	−	0.227073i
$502$	−2.55213	−	4.42041i	−0.113907	−	0.197293i
$503$	−7.54680	+	4.35715i	−0.336495	+	0.194276i	−0.658721	−	0.752387i	$-0.728902\pi$
$503$	−7.54680	+	4.35715i	−0.336495	+	0.194276i	0.322226	+	0.946663i	$0.395569\pi$
$504$			0.535537i			0.0238547i
$505$	−7.92857	−	4.57756i	−0.352817	−	0.203699i
$506$	6.46252	+	11.1934i	0.287294	+	0.497608i
$507$	12.5878			0.559045
$508$	11.9101			0.528427
$509$	21.0800	+	36.5117i	0.934356	+	1.61835i	0.775778	+	0.631007i	$0.217358\pi$
$509$	21.0800	+	36.5117i	0.934356	+	1.61835i	0.158579	+	0.987346i	$0.449309\pi$
$510$		−	0.464463i		−	0.0205668i
$511$	0.429064	−	0.743160i	0.0189807	−	0.0328755i
$512$		−	1.00000i		−	0.0441942i
$513$	−7.12118	−	4.11142i	−0.314408	−	0.181524i
$514$	−9.72782	+	16.8491i	−0.429076	+	0.743181i
$515$	−5.26575	+	9.12055i	−0.232037	+	0.401900i
$516$	−0.906314	+	0.523261i	−0.0398982	+	0.0230353i
$517$	44.3232			1.94933
$518$	0.495276	−	3.21967i	0.0217612	−	0.141464i
$519$	15.4084			0.676354
$520$	0.556002	−	0.321008i	0.0243823	−	0.0140771i
$521$	18.1567	−	31.4484i	0.795461	−	1.37778i	−0.127086	−	0.991892i	$-0.540562\pi$
$521$	18.1567	−	31.4484i	0.795461	−	1.37778i	0.922546	−	0.385887i	$-0.126104\pi$
$522$	2.69215	−	4.66294i	0.117832	−	0.204092i
$523$	−11.5606	−	6.67449i	−0.505508	−	0.291855i	0.225477	−	0.974248i	$-0.427606\pi$
$523$	−11.5606	−	6.67449i	−0.505508	−	0.291855i	−0.730985	+	0.682393i	$0.760939\pi$
$524$		−	8.45692i		−	0.369442i
$525$	0.267768	−	0.463788i	0.0116864	−	0.0202414i
$526$		−	12.0863i		−	0.526990i
$527$	−0.308298	−	0.533988i	−0.0134297	−	0.0232609i
$528$	5.44426			0.236931
$529$	17.3638			0.754948
$530$	2.89110	+	5.00753i	0.125581	+	0.217513i
$531$	−10.2224	−	5.90190i	−0.443614	−	0.256121i
$532$		−	4.40363i		−	0.190922i
$533$	5.41012	−	3.12353i	0.234338	−	0.135295i
$534$	−2.13103	−	3.69105i	−0.0922187	−	0.159728i
$535$	13.0642	−	7.54260i	0.564813	−	0.326095i
$536$	−3.54808	−	2.04849i	−0.153254	−	0.0884812i
$537$	−6.85171	−	3.95584i	−0.295673	−	0.170707i
$538$	24.0875	−	13.9069i	1.03849	−	0.599570i
$539$	18.2742	+	31.6519i	0.787126	+	1.36334i
$540$	−0.866025	+	0.500000i	−0.0372678	+	0.0215166i
$541$			28.8021i			1.23830i	0.785273	+	0.619150i	$0.212523\pi$
$541$			28.8021i			1.23830i	−0.785273	+	0.619150i	$0.787477\pi$
$542$	−4.64744	−	2.68320i	−0.199625	−	0.115253i
$543$	4.86182	+	8.42093i	0.208641	+	0.361377i
$544$	−0.464463			−0.0199137
$545$	−4.43512			−0.189980
$546$	0.171911	+	0.297759i	0.00735713	+	0.0127429i
$547$		−	11.5425i		−	0.493524i	−0.969076	−	0.246762i	$-0.920633\pi$
$547$		−	11.5425i		−	0.493524i	0.969076	−	0.246762i	$-0.0793665\pi$
$548$	9.89749	−	17.1430i	0.422800	−	0.732311i
$549$		−	2.94574i		−	0.125721i
$550$	−4.71487	−	2.72213i	−0.201043	−	0.116072i
$551$	−22.1371	+	38.3426i	−0.943073	+	1.63345i
$552$	−1.18703	+	2.05600i	−0.0505235	+	0.0875093i
$553$	1.86654	−	1.07765i	0.0793733	−	0.0458262i
$554$	10.8265			0.459974
$555$	5.66900	−	2.20510i	0.240635	−	0.0936014i
$556$	−7.33134			−0.310918
$557$	−19.0151	+	10.9784i	−0.805694	+	0.465168i	−0.845458	−	0.534041i	$-0.820673\pi$
$557$	−19.0151	+	10.9784i	−0.805694	+	0.465168i	0.0397643	+	0.999209i	$0.487339\pi$
$558$	−0.663773	+	1.14969i	−0.0280997	+	0.0486702i
$559$	−0.335942	+	0.581868i	−0.0142088	+	0.0246104i
$560$	−0.463788	−	0.267768i	−0.0195986	−	0.0113153i
$561$		−	2.52866i		−	0.106760i
$562$	−7.36363	+	12.7542i	−0.310616	+	0.538003i
$563$			35.3758i			1.49091i	0.666555	+	0.745456i	$0.267768\pi$
$563$			35.3758i			1.49091i	−0.666555	+	0.745456i	$0.732232\pi$
$564$	4.07063	+	7.05055i	0.171405	+	0.296882i
$565$	−8.98588			−0.378039
$566$	−19.0840			−0.802159
$567$	−0.267768	−	0.463788i	−0.0112452	−	0.0194773i
$568$	3.76562	+	2.17408i	0.158002	+	0.0912225i
$569$		−	0.0883529i		−	0.00370395i	−0.999998	−	0.00185197i	$-0.999410\pi$
$569$		−	0.0883529i		−	0.00370395i	0.999998	−	0.00185197i	$-0.000589502\pi$
$570$	7.12118	−	4.11142i	0.298274	−	0.172208i
$571$	−21.1519	−	36.6361i	−0.885177	−	1.53317i	−0.845510	−	0.533959i	$-0.820704\pi$
$571$	−21.1519	−	36.6361i	−0.885177	−	1.53317i	−0.0396672	−	0.999213i	$-0.512630\pi$
$572$	3.02702	−	1.74765i	0.126566	−	0.0730730i
$573$	−13.8689	−	8.00719i	−0.579380	−	0.334505i
$574$	−4.51284	−	2.60549i	−0.188362	−	0.108751i
$575$	2.05600	−	1.18703i	0.0857412	−	0.0495027i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	−21.4986	+	12.4122i	−0.895000	+	0.516729i	−0.875575	−	0.483083i	$-0.839517\pi$
$577$	−21.4986	+	12.4122i	−0.895000	+	0.516729i	−0.0194254	+	0.999811i	$0.506184\pi$
$578$		−	16.7843i		−	0.698134i
$579$	−14.9525	−	8.63282i	−0.621404	−	0.358768i
$580$	2.69215	+	4.66294i	0.111786	+	0.193618i
$581$	−3.87113			−0.160602
$582$	−5.43955			−0.225477
$583$	15.7399	+	27.2623i	0.651880	+	1.12909i
$584$		−	1.60237i		−	0.0663065i
$585$	−0.321008	+	0.556002i	−0.0132720	+	0.0229879i
$586$		−	2.55273i		−	0.105452i
$587$	−27.7557	−	16.0248i	−1.14560	−	0.661412i	−0.197789	−	0.980245i	$-0.563376\pi$
$587$	−27.7557	−	16.0248i	−1.14560	−	0.661412i	−0.947811	+	0.318832i	$0.896709\pi$
$588$	−3.35660	+	5.81380i	−0.138424	+	0.239757i
$589$	5.45809	−	9.45370i	0.224897	−	0.389533i
$590$	10.2224	−	5.90190i	0.420849	−	0.242978i
$591$	24.3971			1.00356
$592$	−2.20510	−	5.66900i	−0.0906292	−	0.232994i
$593$	38.7563			1.59153			0.795765	−	0.605606i	$-0.207069\pi$
$593$	38.7563			1.59153			0.795765	+	0.605606i	$0.207069\pi$
$594$	−4.71487	+	2.72213i	−0.193453	+	0.111690i
$595$	−0.124369	+	0.215413i	−0.00509861	+	0.00883106i
$596$	−4.11369	+	7.12511i	−0.168503	+	0.291856i
$597$	0.715751	+	0.413239i	0.0292937	+	0.0169127i
$598$			1.52419i			0.0623287i
$599$	−11.6301	+	20.1440i	−0.475194	+	0.823060i	−0.999596	−	0.0284104i	$-0.990955\pi$
$599$	−11.6301	+	20.1440i	−0.475194	+	0.823060i	0.524402	+	0.851471i	$0.324289\pi$
$600$		−	1.00000i		−	0.0408248i
$601$	7.34067	+	12.7144i	0.299432	+	0.518631i	0.976006	−	0.217743i	$-0.0698695\pi$
$601$	7.34067	+	12.7144i	0.299432	+	0.518631i	−0.676574	+	0.736375i	$0.736536\pi$
$602$	0.560450			0.0228422
$603$	4.09698			0.166842
$604$	4.98628	+	8.63648i	0.202889	+	0.351414i
$605$	−16.1427	−	9.32000i	−0.656295	−	0.378912i
$606$		−	9.15512i		−	0.371902i
$607$	11.9650	−	6.90802i	0.485646	−	0.280388i	−0.237121	−	0.971480i	$-0.576204\pi$
$607$	11.9650	−	6.90802i	0.485646	−	0.280388i	0.722766	+	0.691093i	$0.242870\pi$
$608$	−4.11142	−	7.12118i	−0.166740	−	0.288802i
$609$	−2.49718	+	1.44175i	−0.101191	+	0.0584225i
$610$	2.55109	+	1.47287i	0.103291	+	0.0596348i
$611$	4.52656	+	2.61341i	0.183125	+	0.105727i
$612$	0.402237	−	0.232232i	0.0162595	−	0.00938741i
$613$	−9.87091	−	17.0969i	−0.398682	−	0.690538i	0.594881	−	0.803814i	$-0.297199\pi$
$613$	−9.87091	−	17.0969i	−0.398682	−	0.690538i	−0.993564	+	0.113276i	$0.963866\pi$
$614$	1.38585	−	0.800120i	0.0559283	−	0.0322902i
$615$		−	9.73039i		−	0.392367i
$616$	−2.52499	−	1.45780i	−0.101735	−	0.0587365i
$617$	7.09744	+	12.2931i	0.285732	+	0.494903i	0.972786	−	0.231703i	$-0.0744299\pi$
$617$	7.09744	+	12.2931i	0.285732	+	0.494903i	−0.687054	+	0.726606i	$0.741097\pi$
$618$	−10.5315			−0.423639
$619$	−16.2904			−0.654768			−0.327384	−	0.944891i	$-0.606167\pi$
$619$	−16.2904			−0.654768			−0.327384	+	0.944891i	$0.606167\pi$
$620$	−0.663773	−	1.14969i	−0.0266578	−	0.0461726i
$621$		−	2.37407i		−	0.0952680i
$622$	2.54702	−	4.41158i	0.102126	−	0.176888i
$623$			2.28249i			0.0914460i
$624$	0.556002	+	0.321008i	0.0222579	+	0.0128506i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	1.15995	−	2.00909i	0.0463609	−	0.0802994i
$627$	38.7696	−	22.3836i	1.54831	−	0.893916i
$628$	−5.76767			−0.230155
$629$	−2.63304	+	1.02419i	−0.104986	+	0.0408371i
$630$	0.535537			0.0213363
$631$	−24.7908	+	14.3130i	−0.986907	+	0.569791i	−0.904348	−	0.426795i	$-0.859643\pi$
$631$	−24.7908	+	14.3130i	−0.986907	+	0.569791i	−0.0825589	+	0.996586i	$0.526309\pi$
$632$	2.01228	−	3.48536i	0.0800440	−	0.138640i
$633$	−2.35375	+	4.07681i	−0.0935530	+	0.162039i
$634$	−11.1235	−	6.42213i	−0.441769	−	0.255055i
$635$		−	11.9101i		−	0.472639i
$636$	−2.89110	+	5.00753i	−0.114640	+	0.198562i
$637$			4.30998i			0.170768i
$638$	14.6568	+	25.3863i	0.580268	+	1.00505i
$639$	−4.34816			−0.172011
$640$	−1.00000			−0.0395285
$641$	−19.3732	−	33.5553i	−0.765194	−	1.32535i	−0.940144	−	0.340777i	$-0.889310\pi$
$641$	−19.3732	−	33.5553i	−0.765194	−	1.32535i	0.174950	−	0.984577i	$-0.444024\pi$
$642$	13.0642	+	7.54260i	0.515601	+	0.297683i
$643$			48.8691i			1.92721i	0.267331	+	0.963605i	$0.413858\pi$
$643$			48.8691i			1.92721i	−0.267331	+	0.963605i	$0.586142\pi$
$644$	1.10106	−	0.635700i	0.0433880	−	0.0250501i
$645$	0.523261	+	0.906314i	0.0206034	+	0.0356861i
$646$	−3.30753	+	1.90960i	−0.130133	+	0.0751323i
$647$	34.6610	+	20.0115i	1.36266	+	0.786734i	0.989978	−	0.141224i	$-0.0451037\pi$
$647$	34.6610	+	20.0115i	1.36266	+	0.786734i	0.372685	+	0.927958i	$0.378437\pi$
$648$	−0.866025	−	0.500000i	−0.0340207	−	0.0196419i
$649$	55.6534	−	32.1315i	2.18459	−	1.26127i
$650$	−0.321008	−	0.556002i	−0.0125910	−	0.0218082i
$651$	0.615700	−	0.355475i	0.0241312	−	0.0139321i
$652$		−	0.590991i		−	0.0231450i
$653$	−27.2595	−	15.7383i	−1.06675	−	0.615886i	−0.139456	−	0.990228i	$-0.544535\pi$
$653$	−27.2595	−	15.7383i	−1.06675	−	0.615886i	−0.927291	+	0.374342i	$0.877869\pi$
$654$	−2.21756	−	3.84093i	−0.0867135	−	0.150192i
$655$	−8.45692			−0.330439
$656$	−9.73039			−0.379908
$657$	0.801185	+	1.38769i	0.0312572	+	0.0541391i
$658$		−	4.35995i		−	0.169968i
$659$	−11.9225	+	20.6504i	−0.464436	+	0.804426i	−0.999176	−	0.0405905i	$-0.987076\pi$
$659$	−11.9225	+	20.6504i	−0.464436	+	0.804426i	0.534740	+	0.845016i	$0.320409\pi$
$660$		−	5.44426i		−	0.211918i
$661$	−1.01438	−	0.585655i	−0.0394550	−	0.0227793i	0.480143	−	0.877190i	$-0.340585\pi$
$661$	−1.01438	−	0.585655i	−0.0394550	−	0.0227793i	−0.519598	+	0.854411i	$0.673918\pi$
$662$	3.58212	−	6.20441i	0.139223	−	0.241141i
$663$	0.149096	−	0.258243i	0.00579043	−	0.0100293i
$664$	−6.26008	+	3.61426i	−0.242938	+	0.140260i
$665$	−4.40363			−0.170765
$666$	4.74417	+	3.80694i	0.183833	+	0.147516i
$667$	−12.7827			−0.494948
$668$	−8.80330	+	5.08259i	−0.340610	+	0.196651i
$669$	4.07187	−	7.05269i	0.157428	−	0.272673i
$670$	−2.04849	+	3.54808i	−0.0791400	+	0.137074i
$671$	13.8888	+	8.01870i	0.536171	+	0.309559i
$672$		−	0.535537i		−	0.0206588i
$673$	19.1006	−	33.0832i	0.736273	−	1.27526i	−0.217890	−	0.975973i	$-0.569917\pi$
$673$	19.1006	−	33.0832i	0.736273	−	1.27526i	0.954163	−	0.299289i	$-0.0967493\pi$
$674$		−	22.9013i		−	0.882126i
$675$	0.500000	+	0.866025i	0.0192450	+	0.0333333i
$676$	−12.5878			−0.484147
$677$	−27.9347			−1.07362			−0.536808	−	0.843704i	$-0.680370\pi$
$677$	−27.9347			−1.07362			−0.536808	+	0.843704i	$0.680370\pi$
$678$	−4.49294	−	7.78200i	−0.172550	−	0.298866i
$679$	2.52280	+	1.45654i	0.0968161	+	0.0558968i
$680$			0.464463i			0.0178114i
$681$	3.39960	−	1.96276i	0.130273	−	0.0752131i
$682$	−3.61375	−	6.25920i	−0.138378	−	0.239677i
$683$	17.2614	−	9.96585i	0.660487	−	0.381333i	−0.131975	−	0.991253i	$-0.542132\pi$
$683$	17.2614	−	9.96585i	0.660487	−	0.381333i	0.792463	+	0.609920i	$0.208799\pi$
$684$	7.12118	+	4.11142i	0.272285	+	0.157204i
$685$	−17.1430	−	9.89749i	−0.654999	−	0.378164i
$686$	6.36002	−	3.67196i	0.242827	−	0.140196i
$687$	13.5993	+	23.5547i	0.518846	+	0.898667i
$688$	0.906314	−	0.523261i	0.0345529	−	0.0199491i
$689$			3.71226i			0.141426i
$690$	2.05600	+	1.18703i	0.0782707	+	0.0451896i
$691$	−6.02368	−	10.4333i	−0.229152	−	0.396902i	0.728405	−	0.685147i	$-0.240262\pi$
$691$	−6.02368	−	10.4333i	−0.229152	−	0.396902i	−0.957557	+	0.288244i	$0.906929\pi$
$692$	−15.4084			−0.585739
$693$	2.91560			0.110755
$694$	13.7693	+	23.8491i	0.522674	+	0.905298i
$695$			7.33134i			0.278094i
$696$	−2.69215	+	4.66294i	−0.102046	+	0.176748i
$697$			4.51941i			0.171185i
$698$	20.4892	+	11.8294i	0.775528	+	0.447751i
$699$	−5.55159	+	9.61564i	−0.209980	+	0.363697i
$700$	−0.267768	+	0.463788i	−0.0101207	+	0.0175295i
$701$	34.1895	−	19.7393i	1.29132	−	0.745543i	0.312430	−	0.949941i	$-0.398857\pi$
$701$	34.1895	−	19.7393i	1.29132	−	0.745543i	0.978888	+	0.204398i	$0.0655236\pi$
$702$	−0.642016			−0.0242313
$703$	−39.0106	−	31.3039i	−1.47131	−	1.18065i
$704$	−5.44426			−0.205188
$705$	7.05055	−	4.07063i	0.265539	−	0.153309i
$706$	2.74097	−	4.74750i	0.103158	−	0.178674i
$707$	−2.45145	+	4.24604i	−0.0921963	+	0.159689i
$708$	10.2224	+	5.90190i	0.384181	+	0.221807i
$709$			14.5551i			0.546630i	0.961925	+	0.273315i	$0.0881202\pi$
$709$			14.5551i			0.546630i	−0.961925	+	0.273315i	$0.911880\pi$
$710$	2.17408	−	3.76562i	0.0815918	−	0.141321i
$711$			4.02455i			0.150932i
$712$	2.13103	+	3.69105i	0.0798638	+	0.138328i
$713$	3.15168			0.118031
$714$	−0.248737			−0.00930875
$715$	−1.74765	−	3.02702i	−0.0653585	−	0.113204i
$716$	6.85171	+	3.95584i	0.256061	+	0.147837i
$717$		−	9.94702i		−	0.371478i
$718$	17.5403	−	10.1269i	0.654597	−	0.377932i
$719$	3.55656	+	6.16015i	0.132637	+	0.229735i	0.924692	−	0.380715i	$-0.124322\pi$
$719$	3.55656	+	6.16015i	0.132637	+	0.229735i	−0.792055	+	0.610450i	$0.790989\pi$
$720$	0.866025	−	0.500000i	0.0322749	−	0.0186339i
$721$	4.88439	+	2.82000i	0.181904	+	0.105022i
$722$	−42.1018	−	24.3075i	−1.56687	−	0.904632i
$723$	18.7127	−	10.8038i	0.695932	−	0.401797i
$724$	−4.86182	−	8.42093i	−0.180688	−	0.312961i
$725$	4.66294	−	2.69215i	0.173177	−	0.0999840i
$726$		−	18.6400i		−	0.691795i
$727$	23.4383	+	13.5321i	0.869277	+	0.501877i	0.867108	−	0.498121i	$-0.165976\pi$
$727$	23.4383	+	13.5321i	0.869277	+	0.501877i	0.00216883	+	0.999998i	$0.499310\pi$
$728$	−0.171911	−	0.297759i	−0.00637146	−	0.0110357i
$729$	1.00000			0.0370370
$730$	−1.60237			−0.0593064
$731$	−0.243035	−	0.420950i	−0.00898899	−	0.0155694i
$732$			2.94574i			0.108878i
$733$	−26.0354	+	45.0947i	−0.961641	+	1.66561i	−0.243259	+	0.969961i	$0.578217\pi$
$733$	−26.0354	+	45.0947i	−0.961641	+	1.66561i	−0.718382	+	0.695649i	$0.755117\pi$
$734$		−	29.1273i		−	1.07511i
$735$	5.81380	+	3.35660i	0.214445	+	0.123810i
$736$	1.18703	−	2.05600i	0.0437546	−	0.0757852i
$737$	−11.1525	+	19.3167i	−0.410808	+	0.711540i
$738$	8.42677	−	4.86520i	0.310194	−	0.179090i
$739$	24.0955			0.886369			0.443184	−	0.896430i	$-0.353849\pi$
$739$	24.0955			0.886369			0.443184	+	0.896430i	$0.353849\pi$
$740$	−5.66900	+	2.20510i	−0.208396	+	0.0810612i
$741$	5.27919			0.193936
$742$	2.68172	−	1.54829i	0.0984489	−	0.0568395i
$743$	5.81888	−	10.0786i	0.213474	−	0.369748i	−0.739325	−	0.673348i	$-0.764856\pi$
$743$	5.81888	−	10.0786i	0.213474	−	0.369748i	0.952799	+	0.303601i	$0.0981888\pi$
$744$	0.663773	−	1.14969i	0.0243351	−	0.0421496i
$745$	7.12511	+	4.11369i	0.261044	+	0.150714i
$746$			36.1494i			1.32352i
$747$	3.61426	−	6.26008i	0.132239	−	0.229044i
$748$			2.52866i			0.0924570i
$749$	−4.03934	−	6.99633i	−0.147594	−	0.255641i
$750$	−1.00000			−0.0365148
$751$	−31.7490			−1.15854			−0.579268	−	0.815137i	$-0.696662\pi$
$751$	−31.7490			−1.15854			−0.579268	+	0.815137i	$0.696662\pi$
$752$	−4.07063	−	7.05055i	−0.148441	−	0.257107i
$753$	−4.42041	−	2.55213i	−0.161089	−	0.0930046i
$754$			3.45681i			0.125890i
$755$	8.63648	−	4.98628i	0.314314	−	0.181469i
$756$	0.267768	+	0.463788i	0.00973864	+	0.0168678i
$757$	11.4286	−	6.59830i	0.415379	−	0.239819i	−0.277719	−	0.960662i	$-0.589578\pi$
$757$	11.4286	−	6.59830i	0.415379	−	0.239819i	0.693098	+	0.720843i	$0.256245\pi$
$758$	−18.8055	−	10.8574i	−0.683048	−	0.394358i
$759$	11.1934	+	6.46252i	0.406295	+	0.234575i
$760$	−7.12118	+	4.11142i	−0.258312	+	0.149137i
$761$	4.53306	+	7.85149i	0.164323	+	0.284616i	0.936415	−	0.350895i	$-0.114123\pi$
$761$	4.53306	+	7.85149i	0.164323	+	0.284616i	−0.772091	+	0.635511i	$0.780789\pi$
$762$	10.3145	−	5.95507i	0.373654	−	0.215729i
$763$			2.37517i			0.0859869i
$764$	13.8689	+	8.00719i	0.501758	+	0.289690i
$765$	−0.232232	−	0.402237i	−0.00839636	−	0.0145429i
$766$	32.2698			1.16596
$767$	7.57823			0.273634
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$		−	18.2259i		−	0.657241i	−0.944462	−	0.328621i	$-0.893416\pi$
$769$		−	18.2259i		−	0.657241i	0.944462	−	0.328621i	$-0.106584\pi$
$770$	−1.45780	+	2.52499i	−0.0525355	+	0.0909941i
$771$			19.4556i			0.700678i
$772$	14.9525	+	8.63282i	0.538152	+	0.310702i
$773$	7.27509	−	12.6008i	0.261667	−	0.453220i	−0.705018	−	0.709189i	$-0.749061\pi$
$773$	7.27509	−	12.6008i	0.261667	−	0.453220i	0.966685	+	0.255969i	$0.0823946\pi$
$774$	−0.523261	+	0.906314i	−0.0188082	+	0.0325768i
$775$	−1.14969	+	0.663773i	−0.0412980	+	0.0238434i
$776$	5.43955			0.195268
$777$	−1.18091	−	3.03595i	−0.0423650	−	0.108914i
$778$	33.3953			1.19728
$779$	−69.2919	+	40.0057i	−2.48264	+	1.43335i
$780$	0.321008	−	0.556002i	0.0114939	−	0.0199081i
$781$	11.8363	−	20.5010i	0.423535	−	0.733584i
$782$	−0.954938	−	0.551334i	−0.0341485	−	0.0197157i
$783$		−	5.38430i		−	0.192419i
$784$	3.35660	−	5.81380i	0.119879	−	0.207636i
$785$			5.76767i			0.205857i
$786$	−4.22846	−	7.32391i	−0.150824	−	0.261235i
$787$	−4.49331			−0.160169			−0.0800846	−	0.996788i	$-0.525519\pi$
$787$	−4.49331			−0.160169			−0.0800846	+	0.996788i	$0.525519\pi$
$788$	−24.3971			−0.869110
$789$	−6.04317	−	10.4671i	−0.215143	−	0.372638i
$790$	−3.48536	−	2.01228i	−0.124004	−	0.0715936i
$791$			4.81227i			0.171104i
$792$	4.71487	−	2.72213i	0.167536	−	0.0967267i
$793$	0.945607	+	1.63784i	0.0335795	+	0.0581614i
$794$	7.64496	−	4.41382i	0.271309	−	0.156641i
$795$	5.00753	+	2.89110i	0.177599	+	0.102537i
$796$	−0.715751	−	0.413239i	−0.0253691	−	0.0146469i
$797$	−25.6774	+	14.8249i	−0.909542	+	0.525124i	−0.880284	−	0.474448i	$-0.842648\pi$
$797$	−25.6774	+	14.8249i	−0.909542	+	0.525124i	−0.0292581	+	0.999572i	$0.509314\pi$
$798$	−2.20181	−	3.81365i	−0.0779434	−	0.135002i
$799$	−3.27472	+	1.89066i	−0.115851	+	0.0668868i
$800$			1.00000i			0.0353553i
$801$	−3.69105	−	2.13103i	−0.130417	−	0.0752963i
$802$	−17.5400	−	30.3802i	−0.619359	−	1.07276i
$803$	−8.72372			−0.307854
$804$	−4.09698			−0.144489
$805$	−0.635700	−	1.10106i	−0.0224055	−	0.0388074i
$806$		−	0.852305i		−	0.0300212i
$807$	13.9069	−	24.0875i	0.489547	−	0.847921i
$808$			9.15512i			0.322076i
$809$	10.5228	+	6.07536i	0.369963	+	0.213598i	0.673442	−	0.739240i	$-0.264815\pi$
$809$	10.5228	+	6.07536i	0.369963	+	0.213598i	−0.303479	+	0.952838i	$0.598148\pi$
$810$	−0.500000	+	0.866025i	−0.0175682	+	0.0304290i
$811$	14.6180	−	25.3190i	0.513306	−	0.889072i	−0.486575	−	0.873639i	$-0.661754\pi$
$811$	14.6180	−	25.3190i	0.513306	−	0.889072i	0.999881	−	0.0154330i	$-0.00491268\pi$
$812$	2.49718	−	1.44175i	0.0876337	−	0.0505954i
$813$	−5.36640			−0.188208
$814$	−30.8635	+	12.0052i	−1.08177	+	0.420781i
$815$	−0.590991			−0.0207015
$816$	−0.402237	+	0.232232i	−0.0140811	+	0.00812974i
$817$	4.30269	−	7.45247i	0.150532	−	0.260729i
$818$	−18.1714	+	31.4737i	−0.635346	+	1.10045i
$819$	0.297759	+	0.171911i	0.0104046	+	0.00600707i
$820$			9.73039i			0.339800i
$821$	−6.87820	+	11.9134i	−0.240051	+	0.415780i	−0.960728	−	0.277490i	$-0.910497\pi$
$821$	−6.87820	+	11.9134i	−0.240051	+	0.415780i	0.720678	+	0.693270i	$0.243831\pi$
$822$		−	19.7950i		−	0.690429i
$823$	23.6773	+	41.0103i	0.825339	+	1.42953i	0.901660	+	0.432446i	$0.142349\pi$
$823$	23.6773	+	41.0103i	0.825339	+	1.42953i	−0.0763208	+	0.997083i	$0.524317\pi$
$824$	10.5315			0.366882
$825$	−5.44426			−0.189545
$826$	−3.16068	−	5.47447i	−0.109974	−	0.190481i
$827$	−2.27297	−	1.31230i	−0.0790391	−	0.0456332i	0.459960	−	0.887940i	$-0.347864\pi$
$827$	−2.27297	−	1.31230i	−0.0790391	−	0.0456332i	−0.538999	+	0.842307i	$0.681197\pi$
$828$			2.37407i			0.0825045i
$829$	−2.41185	+	1.39248i	−0.0837671	+	0.0483630i	−0.541298	−	0.840831i	$-0.682067\pi$
$829$	−2.41185	+	1.39248i	−0.0837671	+	0.0483630i	0.457531	+	0.889193i	$0.348734\pi$
$830$	3.61426	+	6.26008i	0.125453	+	0.217290i
$831$	9.37602	−	5.41325i	0.325250	−	0.187783i
$832$	−0.556002	−	0.321008i	−0.0192759	−	0.0111289i
$833$	−2.70030	−	1.55902i	−0.0935598	−	0.0540168i
$834$	−6.34913	+	3.66567i	−0.219852	+	0.126932i
$835$	5.08259	+	8.80330i	0.175890	+	0.304651i
$836$	−38.7696	+	22.3836i	−1.34087	+	0.774154i
$837$			1.32755i			0.0458867i
$838$	12.0150	+	6.93685i	0.415050	+	0.239629i
$839$	19.8987	+	34.4655i	0.686978	+	1.18988i	0.972811	+	0.231602i	$0.0743965\pi$
$839$	19.8987	+	34.4655i	0.686978	+	1.18988i	−0.285833	+	0.958280i	$0.592270\pi$
$840$	−0.535537			−0.0184778
$841$	0.00926425			0.000319457
$842$	1.54404	+	2.67436i	0.0532113	+	0.0921646i
$843$			14.7273i			0.507234i
$844$	2.35375	−	4.07681i	0.0810193	−	0.140330i
$845$			12.5878i			0.433034i
$846$	7.05055	+	4.07063i	0.242403	+	0.139951i
$847$	−4.99120	+	8.64501i	−0.171500	+	0.297046i
$848$	2.89110	−	5.00753i	0.0992808	−	0.171959i
$849$	−16.5272	+	9.54199i	−0.567212	+	0.327480i
$850$	0.464463			0.0159310
$851$	2.19559	−	14.2730i	0.0752639	−	0.489272i
$852$	4.34816			0.148966
$853$	10.3560	−	5.97906i	0.354584	−	0.204719i	−0.312118	−	0.950043i	$-0.601039\pi$
$853$	10.3560	−	5.97906i	0.354584	−	0.204719i	0.666702	+	0.745324i	$0.267705\pi$
$854$	0.788777	−	1.36620i	0.0269914	−	0.0467504i
$855$	4.11142	−	7.12118i	0.140608	−	0.243539i
$856$	−13.0642	−	7.54260i	−0.446524	−	0.257801i
$857$			11.9257i			0.407373i	0.979036	+	0.203687i	$0.0652924\pi$
$857$			11.9257i			0.407373i	−0.979036	+	0.203687i	$0.934708\pi$
$858$	1.74765	−	3.02702i	0.0596638	−	0.103341i
$859$			19.0697i			0.650651i	0.945602	+	0.325325i	$0.105474\pi$
$859$			19.0697i			0.650651i	−0.945602	+	0.325325i	$0.894526\pi$
$860$	−0.523261	−	0.906314i	−0.0178430	−	0.0309050i
$861$	−5.21098			−0.177590
$862$	−39.7498			−1.35388
$863$	1.15755	+	2.00494i	0.0394036	+	0.0682490i	0.885055	−	0.465487i	$-0.154121\pi$
$863$	1.15755	+	2.00494i	0.0394036	+	0.0682490i	−0.845651	+	0.533736i	$0.820788\pi$
$864$	0.866025	+	0.500000i	0.0294628	+	0.0170103i
$865$			15.4084i			0.523901i
$866$	−2.57363	+	1.48588i	−0.0874554	+	0.0504924i
$867$	−8.39214	−	14.5356i	−0.285012	−	0.493655i
$868$	−0.615700	+	0.355475i	−0.0208982	+	0.0120656i
$869$	−18.9752	−	10.9554i	−0.643691	−	0.371635i
$870$	4.66294	+	2.69215i	0.158089	+	0.0912725i
$871$	−2.27793	+	1.31516i	−0.0771846	+	0.0445626i
$872$	2.21756	+	3.84093i	0.0750961	+	0.130070i
$873$	−4.71079	+	2.71977i	−0.159436	+	0.0920504i
$874$		−	19.5216i		−	0.660327i
$875$	0.463788	+	0.267768i	0.0156789	+	0.00905222i
$876$	−0.801185	−	1.38769i	−0.0270695	−	0.0468858i
$877$	−21.3603			−0.721286			−0.360643	−	0.932704i	$-0.617443\pi$
$877$	−21.3603			−0.721286			−0.360643	+	0.932704i	$0.617443\pi$
$878$	−7.96901			−0.268941
$879$	−1.27637	−	2.21073i	−0.0430507	−	0.0745660i
$880$			5.44426i			0.183526i
$881$	2.08701	−	3.61481i	0.0703132	−	0.121786i	−0.828725	−	0.559656i	$-0.810933\pi$
$881$	2.08701	−	3.61481i	0.0703132	−	0.121786i	0.899039	+	0.437869i	$0.144267\pi$
$882$			6.71320i			0.226045i
$883$	−35.1398	−	20.2880i	−1.18255	−	0.682744i	−0.225945	−	0.974140i	$-0.572547\pi$
$883$	−35.1398	−	20.2880i	−1.18255	−	0.682744i	−0.956602	+	0.291396i	$0.905880\pi$
$884$	−0.149096	+	0.258243i	−0.00501466	+	0.00868564i
$885$	5.90190	−	10.2224i	0.198390	−	0.343622i
$886$	29.5166	−	17.0414i	0.991629	−	0.572517i
$887$	−1.35233			−0.0454068			−0.0227034	−	0.999742i	$-0.507227\pi$
$887$	−1.35233			−0.0454068			−0.0227034	+	0.999742i	$0.507227\pi$
$888$	−4.74417	−	3.80694i	−0.159204	−	0.127753i
$889$	−6.37831			−0.213922
$890$	3.69105	−	2.13103i	0.123724	−	0.0714323i
$891$	−2.72213	+	4.71487i	−0.0911948	+	0.157954i
$892$	−4.07187	+	7.05269i	−0.136336	+	0.236142i
$893$	−57.9755	−	33.4722i	−1.94008	−	1.12010i
$894$			8.22737i			0.275164i
$895$	3.95584	−	6.85171i	0.132229	−	0.229028i
$896$			0.535537i			0.0178910i
$897$	0.762094	+	1.31999i	0.0254456	+	0.0440731i
$898$	−28.2460			−0.942581
$899$	7.14791			0.238396
$900$	−0.500000	−	0.866025i	−0.0166667	−	0.0288675i
$901$	−2.32582	−	1.34281i	−0.0774841	−	0.0447355i
$902$			52.9748i			1.76387i
$903$	0.485364	−	0.280225i	0.0161519	−	0.00932531i
$904$	4.49294	+	7.78200i	0.149433	+	0.258825i
$905$	−8.42093	+	4.86182i	−0.279921	+	0.161612i
$906$	8.63648	+	4.98628i	0.286928	+	0.165658i
$907$	−49.1028	−	28.3495i	−1.63043	−	0.941330i	−0.983960	−	0.178392i	$-0.942911\pi$
$907$	−49.1028	−	28.3495i	−1.63043	−	0.941330i	−0.646472	−	0.762938i	$-0.723756\pi$
$908$	−3.39960	+	1.96276i	−0.112820	+	0.0651365i
$909$	−4.57756	−	7.92857i	−0.151828	−	0.262974i
$910$	−0.297759	+	0.171911i	−0.00987063	+	0.00569881i
$911$		−	33.5192i		−	1.11054i	−0.831670	−	0.555270i	$-0.812615\pi$
$911$		−	33.5192i		−	1.11054i	0.831670	−	0.555270i	$-0.187385\pi$
$912$	−7.12118	−	4.11142i	−0.235806	−	0.136143i
$913$	19.6770	+	34.0815i	0.651212	+	1.12793i
$914$	31.0226			1.02614
$915$	2.94574			0.0973833
$916$	−13.5993	−	23.5547i	−0.449333	−	0.778268i
$917$			4.52899i			0.149560i
$918$	0.232232	−	0.402237i	0.00766479	−	0.0132758i
$919$			8.24341i			0.271925i	0.990714	+	0.135962i	$0.0434127\pi$
$919$			8.24341i			0.271925i	−0.990714	+	0.135962i	$0.956587\pi$
$920$	−2.05600	−	1.18703i	−0.0677844	−	0.0391353i
$921$	0.800120	−	1.38585i	0.0263649	−	0.0456653i
$922$	2.28379	−	3.95564i	0.0752126	−	0.130272i
$923$	2.41759	−	1.39580i	0.0795759	−	0.0459432i
$924$	−2.91560			−0.0959162
$925$	2.20510	+	5.66900i	0.0725034	+	0.186395i
$926$	6.45595			0.212156
$927$	−9.12055	+	5.26575i	−0.299558	+	0.172950i
$928$	2.69215	−	4.66294i	0.0883742	−	0.153069i
$929$	−6.90082	+	11.9526i	−0.226409	+	0.392151i	−0.956741	−	0.290941i	$-0.906032\pi$
$929$	−6.90082	+	11.9526i	−0.226409	+	0.392151i	0.730332	+	0.683092i	$0.239365\pi$
$930$	−1.14969	−	0.663773i	−0.0376998	−	0.0217660i
$931$		−	55.2015i		−	1.80916i
$932$	5.55159	−	9.61564i	0.181848	−	0.314971i
$933$		−	5.09405i		−	0.166772i
$934$	11.2648	+	19.5111i	0.368594	+	0.638423i
$935$	2.52866			0.0826961
$936$	0.642016			0.0209849
$937$	−1.82077	−	3.15366i	−0.0594819	−	0.103026i	0.834751	−	0.550628i	$-0.185612\pi$
$937$	−1.82077	−	3.15366i	−0.0594819	−	0.103026i	−0.894233	+	0.447602i	$0.852278\pi$
$938$	1.90013	+	1.09704i	0.0620414	+	0.0358196i
$939$		−	2.31990i		−	0.0757070i
$940$	−7.05055	+	4.07063i	−0.229963	+	0.132769i
$941$	−17.0123	−	29.4662i	−0.554587	−	0.960572i	−0.997936	−	0.0642231i	$-0.979543\pi$
$941$	−17.0123	−	29.4662i	−0.554587	−	0.960572i	0.443349	−	0.896349i	$-0.353790\pi$
$942$	−4.99495	+	2.88383i	−0.162744	+	0.0939604i
$943$	−20.0057	−	11.5503i	−0.651476	−	0.376130i
$944$	−10.2224	−	5.90190i	−0.332711	−	0.192091i
$945$	0.463788	−	0.267768i	0.0150870	−	0.00871050i
$946$	−2.84877	−	4.93421i	−0.0926214	−	0.160425i
$947$	24.1406	−	13.9376i	0.784465	−	0.452911i	−0.0535456	−	0.998565i	$-0.517052\pi$
$947$	24.1406	−	13.9376i	0.784465	−	0.452911i	0.838010	+	0.545655i	$0.183719\pi$
$948$		−	4.02455i		−	0.130711i
$949$	−0.890921	−	0.514374i	−0.0289205	−	0.0166973i
$950$	4.11142	+	7.12118i	0.133392	+	0.231042i
$951$	−12.8443			−0.416504
$952$	0.248737			0.00806162
$953$	6.23960	+	10.8073i	0.202121	+	0.350083i	0.949211	−	0.314639i	$-0.101883\pi$
$953$	6.23960	+	10.8073i	0.202121	+	0.350083i	−0.747091	+	0.664722i	$0.768550\pi$
$954$			5.78220i			0.187206i
$955$	8.00719	−	13.8689i	0.259107	−	0.448786i
$956$			9.94702i			0.321710i
$957$	25.3863	+	14.6568i	0.820622	+	0.473787i
$958$	4.05737	−	7.02757i	0.131088	−	0.227050i
$959$	−5.30047	+	9.18068i	−0.171161	+	0.296460i
$960$	−0.866025	+	0.500000i	−0.0279508	+	0.0161374i
$961$	29.2376			0.943149
$962$	−3.85983	−	0.593751i	−0.124446	−	0.0191433i
$963$	15.0852			0.486114
$964$	−18.7127	+	10.8038i	−0.602695	+	0.347966i
$965$	8.63282	−	14.9525i	0.277900	−	0.481337i
$966$	0.635700	−	1.10106i	0.0204533	−	0.0354262i
$967$	−14.9080	−	8.60713i	−0.479409	−	0.276787i	0.240761	−	0.970584i	$-0.422603\pi$
$967$	−14.9080	−	8.60713i	−0.479409	−	0.276787i	−0.720170	+	0.693798i	$0.755936\pi$
$968$			18.6400i			0.599112i
$969$	−1.90960	+	3.30753i	−0.0613453	+	0.106253i
$970$		−	5.43955i		−	0.174653i
$971$	−9.96229	−	17.2552i	−0.319705	−	0.553745i	0.660721	−	0.750631i	$-0.270251\pi$
$971$	−9.96229	−	17.2552i	−0.319705	−	0.553745i	−0.980426	+	0.196886i	$0.936917\pi$
$972$	−1.00000			−0.0320750
$973$	3.92620			0.125868
$974$	2.84809	+	4.93303i	0.0912586	+	0.158065i
$975$	−0.556002	−	0.321008i	−0.0178063	−	0.0102805i
$976$		−	2.94574i		−	0.0942910i
$977$	19.3758	−	11.1866i	0.619886	−	0.357891i	−0.156939	−	0.987608i	$-0.550163\pi$
$977$	19.3758	−	11.1866i	0.619886	−	0.357891i	0.776825	+	0.629717i	$0.216829\pi$
$978$	−0.295495	−	0.511813i	−0.00944890	−	0.0163660i
$979$	20.0951	−	11.6019i	0.642241	−	0.370798i
$980$	−5.81380	−	3.35660i	−0.185715	−	0.107223i
$981$	−3.84093	−	2.21756i	−0.122631	−	0.0708013i
$982$	−23.1834	+	13.3850i	−0.739813	+	0.427131i
$983$	−20.8434	−	36.1018i	−0.664801	−	1.15147i	−0.979339	−	0.202224i	$-0.935183\pi$
$983$	−20.8434	−	36.1018i	−0.664801	−	1.15147i	0.314538	−	0.949245i	$-0.398150\pi$
$984$	−8.42677	+	4.86520i	−0.268636	+	0.155097i
$985$			24.3971i			0.777356i
$986$	−2.16577	−	1.25041i	−0.0689721	−	0.0398211i
$987$	−2.17997	−	3.77582i	−0.0693893	−	0.120186i
$988$	−5.27919			−0.167953
$989$	2.48451			0.0790029
$990$	−2.72213	−	4.71487i	−0.0865150	−	0.149848i
$991$			21.6734i			0.688479i	0.938882	+	0.344239i	$0.111863\pi$
$991$			21.6734i			0.688479i	−0.938882	+	0.344239i	$0.888137\pi$
$992$	−0.663773	+	1.14969i	−0.0210748	+	0.0365026i
$993$		−	7.16424i		−	0.227350i
$994$	−2.01663	−	1.16430i	−0.0639635	−	0.0369294i
$995$	−0.413239	+	0.715751i	−0.0131006	+	0.0226908i
$996$	−3.61426	+	6.26008i	−0.114522	+	0.198358i
$997$	−17.9779	+	10.3795i	−0.569365	+	0.328723i	−0.756896	−	0.653536i	$-0.773285\pi$
$997$	−17.9779	+	10.3795i	−0.569365	+	0.328723i	0.187531	+	0.982259i	$0.439952\pi$
$998$	−43.2464			−1.36894
$999$	6.01205	+	0.924822i	0.190213	+	0.0292601i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.x.d.751.2	✓	16
37.27	even	6	inner	1110.2.x.d.841.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.x.d.751.2	✓	16	1.1	even	1	trivial
1110.2.x.d.841.2	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)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} -1.00000i q^{6} +(-0.267768 + 0.463788i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(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} +(-0.267768 + 0.463788i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +1.00000 q^{10} +5.44426 q^{11} +(0.500000 + 0.866025i) q^{12} +(0.556002 + 0.321008i) q^{13} -0.535537i q^{14} +(0.866025 - 0.500000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.402237 + 0.232232i) q^{17} +(0.866025 + 0.500000i) q^{18} +(-7.12118 - 4.11142i) q^{19} +(-0.866025 + 0.500000i) q^{20} +(-0.267768 - 0.463788i) q^{21} +(-4.71487 + 2.72213i) q^{22} -2.37407i q^{23} +(-0.866025 - 0.500000i) q^{24} +(0.500000 + 0.866025i) q^{25} -0.642016 q^{26} +1.00000 q^{27} +(0.267768 + 0.463788i) q^{28} -5.38430i q^{29} +(-0.500000 + 0.866025i) q^{30} +1.32755i q^{31} +(0.866025 + 0.500000i) q^{32} +(-2.72213 + 4.71487i) q^{33} +(0.232232 - 0.402237i) q^{34} +(0.463788 - 0.267768i) q^{35} -1.00000 q^{36} +(6.01205 + 0.924822i) q^{37} +8.22283 q^{38} +(-0.556002 + 0.321008i) q^{39} +(0.500000 - 0.866025i) q^{40} +(4.86520 - 8.42677i) q^{41} +(0.463788 + 0.267768i) q^{42} +1.04652i q^{43} +(2.72213 - 4.71487i) q^{44} +1.00000i q^{45} +(1.18703 + 2.05600i) q^{46} +8.14127 q^{47} +1.00000 q^{48} +(3.35660 + 5.81380i) q^{49} +(-0.866025 - 0.500000i) q^{50} -0.464463i q^{51} +(0.556002 - 0.321008i) q^{52} +(2.89110 + 5.00753i) q^{53} +(-0.866025 + 0.500000i) q^{54} +(-4.71487 - 2.72213i) q^{55} +(-0.463788 - 0.267768i) q^{56} +(7.12118 - 4.11142i) q^{57} +(2.69215 + 4.66294i) q^{58} +(10.2224 - 5.90190i) q^{59} -1.00000i q^{60} +(2.55109 + 1.47287i) q^{61} +(-0.663773 - 1.14969i) q^{62} +0.535537 q^{63} -1.00000 q^{64} +(-0.321008 - 0.556002i) q^{65} -5.44426i q^{66} +(-2.04849 + 3.54808i) q^{67} +0.464463i q^{68} +(2.05600 + 1.18703i) q^{69} +(-0.267768 + 0.463788i) q^{70} +(2.17408 - 3.76562i) q^{71} +(0.866025 - 0.500000i) q^{72} -1.60237 q^{73} +(-5.66900 + 2.20510i) q^{74} -1.00000 q^{75} +(-7.12118 + 4.11142i) q^{76} +(-1.45780 + 2.52499i) q^{77} +(0.321008 - 0.556002i) q^{78} +(-3.48536 - 2.01228i) q^{79} +1.00000i q^{80} +(-0.500000 + 0.866025i) q^{81} +9.73039i q^{82} +(3.61426 + 6.26008i) q^{83} -0.535537 q^{84} +0.464463 q^{85} +(-0.523261 - 0.906314i) q^{86} +(4.66294 + 2.69215i) q^{87} +5.44426i q^{88} +(3.69105 - 2.13103i) q^{89} +(-0.500000 - 0.866025i) q^{90} +(-0.297759 + 0.171911i) q^{91} +(-2.05600 - 1.18703i) q^{92} +(-1.14969 - 0.663773i) q^{93} +(-7.05055 + 4.07063i) q^{94} +(4.11142 + 7.12118i) q^{95} +(-0.866025 + 0.500000i) q^{96} -5.43955i q^{97} +(-5.81380 - 3.35660i) q^{98} +(-2.72213 - 4.71487i) 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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