LMFDB - Embedded newform 1110.2.ba.a.619.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(529,1110)]

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, 3, 5]))

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

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

chi := DirichletCharacter("1110.529");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.ba (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:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			619.4
Character	$\chi$	$=$	1110.619
Dual form			1110.2.ba.a.529.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.18544 - 0.473136i) q^{5} -1.00000i q^{6} +(0.827955 - 0.478020i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.18544 - 0.473136i) q^{5} -1.00000i q^{6} +(0.827955 - 0.478020i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(-0.682971 + 2.12921i) q^{10} +0.252998 q^{11} +(0.866025 + 0.500000i) q^{12} +(-0.858827 - 1.48753i) q^{13} +0.956040i q^{14} +(-1.65608 + 1.50247i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.88164 + 4.99114i) q^{17} +(0.500000 + 0.866025i) q^{18} +(3.89488 - 2.24871i) q^{19} +(-1.50247 - 1.65608i) q^{20} +(-0.478020 + 0.827955i) q^{21} +(-0.126499 + 0.219103i) q^{22} +4.71996 q^{23} +(-0.866025 + 0.500000i) q^{24} +(4.55228 - 2.06802i) q^{25} +1.71765 q^{26} +1.00000i q^{27} +(-0.827955 - 0.478020i) q^{28} -6.74876i q^{29} +(-0.473136 - 2.18544i) q^{30} +0.279008i q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.219103 + 0.126499i) q^{33} +(-2.88164 - 4.99114i) q^{34} +(1.58328 - 1.43642i) q^{35} -1.00000 q^{36} +(3.20888 - 5.16750i) q^{37} +4.49741i q^{38} +(1.48753 + 0.858827i) q^{39} +(2.18544 - 0.473136i) q^{40} +(-2.96243 - 5.13107i) q^{41} +(-0.478020 - 0.827955i) q^{42} -1.27403 q^{43} +(-0.126499 - 0.219103i) q^{44} +(0.682971 - 2.12921i) q^{45} +(-2.35998 + 4.08761i) q^{46} -6.17905i q^{47} -1.00000i q^{48} +(-3.04299 + 5.27062i) q^{49} +(-0.485183 + 4.97640i) q^{50} -5.76327i q^{51} +(-0.858827 + 1.48753i) q^{52} +(7.10229 + 4.10051i) q^{53} +(-0.866025 - 0.500000i) q^{54} +(0.552912 - 0.119703i) q^{55} +(0.827955 - 0.478020i) q^{56} +(-2.24871 + 3.89488i) q^{57} +(5.84460 + 3.37438i) q^{58} +(13.0282 + 7.52184i) q^{59} +(2.12921 + 0.682971i) q^{60} +(3.43889 - 1.98545i) q^{61} +(-0.241628 - 0.139504i) q^{62} -0.956040i q^{63} +1.00000 q^{64} +(-2.58072 - 2.84457i) q^{65} -0.252998i q^{66} +(0.518394 - 0.299295i) q^{67} +5.76327 q^{68} +(-4.08761 + 2.35998i) q^{69} +(0.452337 + 2.08937i) q^{70} +(6.17507 + 10.6955i) q^{71} +(0.500000 - 0.866025i) q^{72} -10.7356i q^{73} +(2.87075 + 5.36272i) q^{74} +(-2.90838 + 4.06710i) q^{75} +(-3.89488 - 2.24871i) q^{76} +(0.209471 - 0.120938i) q^{77} +(-1.48753 + 0.858827i) q^{78} +(-2.20916 + 1.27546i) q^{79} +(-0.682971 + 2.12921i) q^{80} +(-0.500000 - 0.866025i) q^{81} +5.92485 q^{82} +(12.5267 + 7.23229i) q^{83} +0.956040 q^{84} +(-3.93615 + 12.2712i) q^{85} +(0.637017 - 1.10335i) q^{86} +(3.37438 + 5.84460i) q^{87} +0.252998 q^{88} +(6.84497 + 3.95194i) q^{89} +(1.50247 + 1.65608i) q^{90} +(-1.42214 - 0.821073i) q^{91} +(-2.35998 - 4.08761i) q^{92} +(-0.139504 - 0.241628i) q^{93} +(5.35121 + 3.08952i) q^{94} +(7.44807 - 6.75722i) q^{95} +(0.866025 + 0.500000i) q^{96} -17.8296 q^{97} +(-3.04299 - 5.27062i) q^{98} +(0.126499 - 0.219103i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 18 q^{2} - 18 q^{4} + 2 q^{5} + 36 q^{8} + 18 q^{9}+O(q^{10}) $ 36 * q - 18 * q^2 - 18 * q^4 + 2 * q^5 + 36 * q^8 + 18 * q^9	$ 36 q - 18 q^{2} - 18 q^{4} + 2 q^{5} + 36 q^{8} + 18 q^{9} + 2 q^{10} + 4 q^{11} - 14 q^{13} - 2 q^{15} - 18 q^{16} + 18 q^{18} + 6 q^{19} - 4 q^{20} - 2 q^{22} - 20 q^{23} + 4 q^{25} + 28 q^{26} - 2 q^{30} - 18 q^{32} - 6 q^{33} - 40 q^{35} - 36 q^{36} + 20 q^{37} + 6 q^{39} + 2 q^{40} + 10 q^{41} - 2 q^{44} - 2 q^{45} + 10 q^{46} + 10 q^{49} - 2 q^{50} - 14 q^{52} - 12 q^{53} + 56 q^{55} + 8 q^{57} + 30 q^{58} + 18 q^{59} + 4 q^{60} - 6 q^{61} - 12 q^{62} + 36 q^{64} + 40 q^{65} + 36 q^{67} + 12 q^{69} + 20 q^{70} - 24 q^{71} + 18 q^{72} - 34 q^{74} + 8 q^{75} - 6 q^{76} - 24 q^{77} - 6 q^{78} + 2 q^{80} - 18 q^{81} - 20 q^{82} + 36 q^{83} + 26 q^{85} - 10 q^{87} + 4 q^{88} + 4 q^{90} - 36 q^{91} + 10 q^{92} + 12 q^{93} + 12 q^{94} - 30 q^{95} + 52 q^{97} + 10 q^{98} + 2 q^{99}+O(q^{100}) $ 36 * q - 18 * q^2 - 18 * q^4 + 2 * q^5 + 36 * q^8 + 18 * q^9 + 2 * q^10 + 4 * q^11 - 14 * q^13 - 2 * q^15 - 18 * q^16 + 18 * q^18 + 6 * q^19 - 4 * q^20 - 2 * q^22 - 20 * q^23 + 4 * q^25 + 28 * q^26 - 2 * q^30 - 18 * q^32 - 6 * q^33 - 40 * q^35 - 36 * q^36 + 20 * q^37 + 6 * q^39 + 2 * q^40 + 10 * q^41 - 2 * q^44 - 2 * q^45 + 10 * q^46 + 10 * q^49 - 2 * q^50 - 14 * q^52 - 12 * q^53 + 56 * q^55 + 8 * q^57 + 30 * q^58 + 18 * q^59 + 4 * q^60 - 6 * q^61 - 12 * q^62 + 36 * q^64 + 40 * q^65 + 36 * q^67 + 12 * q^69 + 20 * q^70 - 24 * q^71 + 18 * q^72 - 34 * q^74 + 8 * q^75 - 6 * q^76 - 24 * q^77 - 6 * q^78 + 2 * q^80 - 18 * q^81 - 20 * q^82 + 36 * q^83 + 26 * q^85 - 10 * q^87 + 4 * q^88 + 4 * q^90 - 36 * q^91 + 10 * q^92 + 12 * q^93 + 12 * q^94 - 30 * q^95 + 52 * q^97 + 10 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	2.18544	−	0.473136i	0.977358	−	0.211593i
$5$	2.18544	−	0.473136i	0.977358	−	0.211593i
$6$		−	1.00000i		−	0.408248i
$7$	0.827955	−	0.478020i	0.312937	−	0.180675i	−0.335303	−	0.942110i	$-0.608839\pi$
$7$	0.827955	−	0.478020i	0.312937	−	0.180675i	0.648240	+	0.761436i	$0.275505\pi$
$8$	1.00000			0.353553
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−0.682971	+	2.12921i	−0.215974	+	0.673316i
$11$	0.252998			0.0762818			0.0381409	−	0.999272i	$-0.487856\pi$
$11$	0.252998			0.0762818			0.0381409	+	0.999272i	$0.487856\pi$
$12$	0.866025	+	0.500000i	0.250000	+	0.144338i
$13$	−0.858827	−	1.48753i	−0.238196	−	0.412567i	0.722001	−	0.691892i	$-0.243223\pi$
$13$	−0.858827	−	1.48753i	−0.238196	−	0.412567i	−0.960197	+	0.279325i	$0.909889\pi$
$14$			0.956040i			0.255512i
$15$	−1.65608	+	1.50247i	−0.427597	+	0.387935i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.88164	+	4.99114i	−0.698900	+	1.21053i	0.269949	+	0.962875i	$0.412993\pi$
$17$	−2.88164	+	4.99114i	−0.698900	+	1.21053i	−0.968848	+	0.247655i	$0.920340\pi$
$18$	0.500000	+	0.866025i	0.117851	+	0.204124i
$19$	3.89488	−	2.24871i	0.893546	−	0.515889i	0.0184451	−	0.999830i	$-0.494128\pi$
$19$	3.89488	−	2.24871i	0.893546	−	0.515889i	0.875101	+	0.483941i	$0.160795\pi$
$20$	−1.50247	−	1.65608i	−0.335962	−	0.370310i
$21$	−0.478020	+	0.827955i	−0.104312	+	0.180675i
$22$	−0.126499	+	0.219103i	−0.0269697	+	0.0467129i
$23$	4.71996			0.984180			0.492090	−	0.870544i	$-0.336233\pi$
$23$	4.71996			0.984180			0.492090	+	0.870544i	$0.336233\pi$
$24$	−0.866025	+	0.500000i	−0.176777	+	0.102062i
$25$	4.55228	−	2.06802i	0.910457	−	0.413604i
$26$	1.71765			0.336860
$27$			1.00000i			0.192450i
$28$	−0.827955	−	0.478020i	−0.156469	−	0.0903373i
$29$		−	6.74876i		−	1.25321i	−0.779336	−	0.626606i	$-0.784443\pi$
$29$		−	6.74876i		−	1.25321i	0.779336	−	0.626606i	$-0.215557\pi$
$30$	−0.473136	−	2.18544i	−0.0863825	−	0.399005i
$31$			0.279008i			0.0501114i	0.999686	+	0.0250557i	$0.00797630\pi$
$31$			0.279008i			0.0501114i	−0.999686	+	0.0250557i	$0.992024\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−0.219103	+	0.126499i	−0.0381409	+	0.0220207i
$34$	−2.88164	−	4.99114i	−0.494197	−	0.855974i
$35$	1.58328	−	1.43642i	0.267622	−	0.242799i
$36$	−1.00000			−0.166667
$37$	3.20888	−	5.16750i	0.527536	−	0.849532i
$37$	3.20888	−	5.16750i	0.527536	−	0.849532i
$38$			4.49741i			0.729577i
$39$	1.48753	+	0.858827i	0.238196	+	0.137522i
$40$	2.18544	−	0.473136i	0.345548	−	0.0748094i
$41$	−2.96243	−	5.13107i	−0.462653	−	0.801339i	0.536439	−	0.843939i	$-0.319769\pi$
$41$	−2.96243	−	5.13107i	−0.462653	−	0.801339i	−0.999092	+	0.0426000i	$0.986436\pi$
$42$	−0.478020	−	0.827955i	−0.0737601	−	0.127756i
$43$	−1.27403			−0.194288			−0.0971442	−	0.995270i	$-0.530971\pi$
$43$	−1.27403			−0.194288			−0.0971442	+	0.995270i	$0.530971\pi$
$44$	−0.126499	−	0.219103i	−0.0190705	−	0.0330310i
$45$	0.682971	−	2.12921i	0.101811	−	0.317404i
$46$	−2.35998	+	4.08761i	−0.347960	+	0.602685i
$47$		−	6.17905i		−	0.901307i	−0.892699	−	0.450654i	$-0.851191\pi$
$47$		−	6.17905i		−	0.901307i	0.892699	−	0.450654i	$-0.148809\pi$
$48$		−	1.00000i		−	0.144338i
$49$	−3.04299	+	5.27062i	−0.434713	+	0.752946i
$50$	−0.485183	+	4.97640i	−0.0686152	+	0.703770i
$51$		−	5.76327i		−	0.807020i
$52$	−0.858827	+	1.48753i	−0.119098	+	0.206284i
$53$	7.10229	+	4.10051i	0.975575	+	0.563248i	0.900931	−	0.433962i	$-0.142885\pi$
$53$	7.10229	+	4.10051i	0.975575	+	0.563248i	0.0746437	+	0.997210i	$0.476218\pi$
$54$	−0.866025	−	0.500000i	−0.117851	−	0.0680414i
$55$	0.552912	−	0.119703i	0.0745547	−	0.0161407i
$56$	0.827955	−	0.478020i	0.110640	−	0.0638781i
$57$	−2.24871	+	3.89488i	−0.297849	+	0.515889i
$58$	5.84460	+	3.37438i	0.767433	+	0.443078i
$59$	13.0282	+	7.52184i	1.69613	+	0.979260i	0.949368	+	0.314165i	$0.101725\pi$
$59$	13.0282	+	7.52184i	1.69613	+	0.979260i	0.746759	+	0.665094i	$0.231609\pi$
$60$	2.12921	+	0.682971i	0.274880	+	0.0881712i
$61$	3.43889	−	1.98545i	0.440305	−	0.254210i	−0.263422	−	0.964681i	$-0.584851\pi$
$61$	3.43889	−	1.98545i	0.440305	−	0.254210i	0.703727	+	0.710470i	$0.251518\pi$
$62$	−0.241628	−	0.139504i	−0.0306868	−	0.0177170i
$63$		−	0.956040i		−	0.120450i
$64$	1.00000			0.125000
$65$	−2.58072	−	2.84457i	−0.320099	−	0.352825i
$66$		−	0.252998i		−	0.0311419i
$67$	0.518394	−	0.299295i	0.0633319	−	0.0365647i	−0.468000	−	0.883729i	$-0.655025\pi$
$67$	0.518394	−	0.299295i	0.0633319	−	0.0365647i	0.531332	+	0.847164i	$0.321692\pi$
$68$	5.76327			0.698900
$69$	−4.08761	+	2.35998i	−0.492090	+	0.284108i
$70$	0.452337	+	2.08937i	0.0540646	+	0.249727i
$71$	6.17507	+	10.6955i	0.732846	+	1.26933i	0.955662	+	0.294466i	$0.0951417\pi$
$71$	6.17507	+	10.6955i	0.732846	+	1.26933i	−0.222816	+	0.974861i	$0.571525\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$		−	10.7356i		−	1.25650i	−0.778011	−	0.628251i	$-0.783771\pi$
$73$		−	10.7356i		−	1.25650i	0.778011	−	0.628251i	$-0.216229\pi$
$74$	2.87075	+	5.36272i	0.333718	+	0.623404i
$75$	−2.90838	+	4.06710i	−0.335831	+	0.469628i
$76$	−3.89488	−	2.24871i	−0.446773	−	0.257944i
$77$	0.209471	−	0.120938i	0.0238714	−	0.0137822i
$78$	−1.48753	+	0.858827i	−0.168430	+	0.0972430i
$79$	−2.20916	+	1.27546i	−0.248550	+	0.143500i	−0.619100	−	0.785312i	$-0.712503\pi$
$79$	−2.20916	+	1.27546i	−0.248550	+	0.143500i	0.370550	+	0.928813i	$0.379169\pi$
$80$	−0.682971	+	2.12921i	−0.0763585	+	0.238053i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	5.92485			0.654291
$83$	12.5267	+	7.23229i	1.37498	+	0.793847i	0.991550	−	0.129722i	$-0.0414084\pi$
$83$	12.5267	+	7.23229i	1.37498	+	0.793847i	0.383433	+	0.923569i	$0.374742\pi$
$84$	0.956040			0.104312
$85$	−3.93615	+	12.2712i	−0.426935	+	1.33100i
$86$	0.637017	−	1.10335i	0.0686913	−	0.118977i
$87$	3.37438	+	5.84460i	0.361771	+	0.626606i
$88$	0.252998			0.0269697
$89$	6.84497	+	3.95194i	0.725565	+	0.418905i	0.816798	−	0.576924i	$-0.195747\pi$
$89$	6.84497	+	3.95194i	0.725565	+	0.418905i	−0.0912324	+	0.995830i	$0.529081\pi$
$90$	1.50247	+	1.65608i	0.158374	+	0.174566i
$91$	−1.42214	−	0.821073i	−0.149081	−	0.0860718i
$92$	−2.35998	−	4.08761i	−0.246045	−	0.426163i
$93$	−0.139504	−	0.241628i	−0.0144659	−	0.0250557i
$94$	5.35121	+	3.08952i	0.551936	+	0.318660i
$95$	7.44807	−	6.75722i	0.764155	−	0.693276i
$96$	0.866025	+	0.500000i	0.0883883	+	0.0510310i
$97$	−17.8296			−1.81032			−0.905158	−	0.425075i	$-0.860248\pi$
$97$	−17.8296			−1.81032			−0.905158	+	0.425075i	$0.860248\pi$
$98$	−3.04299	−	5.27062i	−0.307389	−	0.532413i
$99$	0.126499	−	0.219103i	0.0127136	−	0.0220207i
$100$	−4.06710	−	2.90838i	−0.406710	−	0.290838i
$101$	13.2413			1.31756			0.658781	−	0.752335i	$-0.271072\pi$
$101$	13.2413			1.31756			0.658781	+	0.752335i	$0.271072\pi$
$102$	4.99114	+	2.88164i	0.494197	+	0.285325i
$103$	10.6557			1.04993			0.524966	−	0.851123i	$-0.324078\pi$
$103$	10.6557			1.04993			0.524966	+	0.851123i	$0.324078\pi$
$104$	−0.858827	−	1.48753i	−0.0842149	−	0.145865i
$105$	−0.652947	+	2.03561i	−0.0637211	+	0.198655i
$106$	−7.10229	+	4.10051i	−0.689836	+	0.398277i
$107$	−13.0826	+	7.55326i	−1.26475	+	0.730201i	−0.973989	−	0.226596i	$-0.927240\pi$
$107$	−13.0826	+	7.55326i	−1.26475	+	0.730201i	−0.290757	+	0.956797i	$0.593907\pi$
$108$	0.866025	−	0.500000i	0.0833333	−	0.0481125i
$109$	−10.6230	−	6.13320i	−1.01750	−	0.587454i	−0.104121	−	0.994565i	$-0.533203\pi$
$109$	−10.6230	−	6.13320i	−1.01750	−	0.587454i	−0.913379	+	0.407111i	$0.866536\pi$
$110$	−0.172790	+	0.538687i	−0.0164749	+	0.0513618i
$111$	−0.195218	+	6.07963i	−0.0185293	+	0.577053i
$112$			0.956040i			0.0903373i
$113$	1.13408	−	1.96429i	0.106685	−	0.184785i	−0.807740	−	0.589539i	$-0.799310\pi$
$113$	1.13408	−	1.96429i	0.106685	−	0.184785i	0.914426	+	0.404754i	$0.132643\pi$
$114$	−2.24871	−	3.89488i	−0.210611	−	0.364789i
$115$	10.3152	−	2.23319i	0.961896	−	0.208246i
$116$	−5.84460	+	3.37438i	−0.542657	+	0.313303i
$117$	−1.71765			−0.158797
$118$	−13.0282	+	7.52184i	−1.19934	+	0.692441i
$119$			5.50992i			0.505093i
$120$	−1.65608	+	1.50247i	−0.151178	+	0.137156i
$121$	−10.9360			−0.994181
$122$			3.97089i			0.359508i
$123$	5.13107	+	2.96243i	0.462653	+	0.267113i
$124$	0.241628	−	0.139504i	0.0216989	−	0.0125278i
$125$	8.97028	−	6.67339i	0.802326	−	0.596886i
$126$	0.827955	+	0.478020i	0.0737601	+	0.0425854i
$127$	−2.12642	−	1.22769i	−0.188690	−	0.108940i	0.402679	−	0.915341i	$-0.368079\pi$
$127$	−2.12642	−	1.22769i	−0.188690	−	0.108940i	−0.591369	+	0.806401i	$0.701412\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	1.10335	−	0.637017i	0.0971442	−	0.0560862i
$130$	3.75383	−	0.812685i	0.329232	−	0.0712772i
$131$	15.2442	+	8.80126i	1.33189	+	0.768969i	0.985590	−	0.169153i	$-0.0541032\pi$
$131$	15.2442	+	8.80126i	1.33189	+	0.768969i	0.346304	+	0.938122i	$0.387436\pi$
$132$	0.219103	+	0.126499i	0.0190705	+	0.0110103i
$133$	2.14985	−	3.72366i	0.186416	−	0.322882i
$134$			0.598590i			0.0517103i
$135$	0.473136	+	2.18544i	0.0407211	+	0.188093i
$136$	−2.88164	+	4.99114i	−0.247098	+	0.427987i
$137$			1.17190i			0.100123i	0.998746	+	0.0500613i	$0.0159417\pi$
$137$			1.17190i			0.100123i	−0.998746	+	0.0500613i	$0.984058\pi$
$138$		−	4.71996i		−	0.401790i
$139$	1.65873	−	2.87300i	0.140691	−	0.243684i	−0.787066	−	0.616869i	$-0.788401\pi$
$139$	1.65873	−	2.87300i	0.140691	−	0.243684i	0.927757	+	0.373185i	$0.121734\pi$
$140$	−2.03561	−	0.652947i	−0.172041	−	0.0551841i
$141$	3.08952	+	5.35121i	0.260185	+	0.450654i
$142$	−12.3501			−1.03640
$143$	−0.217282	−	0.376343i	−0.0181700	−	0.0314714i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	−3.19308	−	14.7490i	−0.265171	−	1.22484i
$146$	9.29726	+	5.36778i	0.769447	+	0.444240i
$147$		−	6.08599i		−	0.501964i
$148$	−6.07963	−	0.195218i	−0.499742	−	0.0160468i
$149$	−5.82788			−0.477439			−0.238719	−	0.971089i	$-0.576728\pi$
$149$	−5.82788			−0.477439			−0.238719	+	0.971089i	$0.576728\pi$
$150$	−2.06802	−	4.55228i	−0.168853	−	0.371692i
$151$	9.73722	+	16.8654i	0.792404	+	1.37248i	0.924475	+	0.381244i	$0.124504\pi$
$151$	9.73722	+	16.8654i	0.792404	+	1.37248i	−0.132071	+	0.991240i	$0.542163\pi$
$152$	3.89488	−	2.24871i	0.315916	−	0.182394i
$153$	2.88164	+	4.99114i	0.232967	+	0.403510i
$154$			0.241876i			0.0194910i
$155$	0.132009	+	0.609755i	0.0106032	+	0.0489767i
$156$		−	1.71765i		−	0.137522i
$157$	−1.24648	−	0.719657i	−0.0994801	−	0.0574348i	0.449435	−	0.893313i	$-0.351625\pi$
$157$	−1.24648	−	0.719657i	−0.0994801	−	0.0574348i	−0.548915	+	0.835878i	$0.684959\pi$
$158$		−	2.55092i		−	0.202940i
$159$	−8.20102			−0.650383
$160$	−1.50247	−	1.65608i	−0.118780	−	0.130924i
$161$	3.90791	−	2.25624i	0.307987	−	0.177816i
$162$	1.00000			0.0785674
$163$	−4.06999	+	7.04943i	−0.318786	+	0.552154i	−0.980235	−	0.197836i	$-0.936609\pi$
$163$	−4.06999	+	7.04943i	−0.318786	+	0.552154i	0.661449	+	0.749990i	$0.269942\pi$
$164$	−2.96243	+	5.13107i	−0.231327	+	0.400670i
$165$	−0.418985	+	0.380122i	−0.0326179	+	0.0295924i
$166$	−12.5267	+	7.23229i	−0.972260	+	0.561335i
$167$	−8.98184	−	15.5570i	−0.695036	−	1.20384i	−0.970169	−	0.242431i	$-0.922055\pi$
$167$	−8.98184	−	15.5570i	−0.695036	−	1.20384i	0.275133	−	0.961406i	$-0.411278\pi$
$168$	−0.478020	+	0.827955i	−0.0368800	+	0.0638781i
$169$	5.02483	−	8.70326i	0.386526	−	0.669482i
$170$	−8.65913	−	9.54442i	−0.664125	−	0.732024i
$171$		−	4.49741i		−	0.343926i
$172$	0.637017	+	1.10335i	0.0485721	+	0.0841294i
$173$	−11.7107	−	6.76116i	−0.890346	−	0.514042i	−0.0162904	−	0.999867i	$-0.505186\pi$
$173$	−11.7107	−	6.76116i	−0.890346	−	0.514042i	−0.874056	+	0.485826i	$0.838519\pi$
$174$	−6.74876			−0.511622
$175$	2.78053	−	3.88831i	0.210188	−	0.293929i
$176$	−0.126499	+	0.219103i	−0.00953523	+	0.0165155i
$177$	−15.0437			−1.13075
$178$	−6.84497	+	3.95194i	−0.513052	+	0.296211i
$179$			4.23810i			0.316771i	0.987377	+	0.158385i	$0.0506288\pi$
$179$			4.23810i			0.316771i	−0.987377	+	0.158385i	$0.949371\pi$
$180$	−2.18544	+	0.473136i	−0.162893	+	0.0352655i
$181$	−4.72246	−	8.17955i	−0.351018	−	0.607981i	0.635410	−	0.772175i	$-0.280831\pi$
$181$	−4.72246	−	8.17955i	−0.351018	−	0.607981i	−0.986428	+	0.164194i	$0.947498\pi$
$182$	1.42214	−	0.821073i	0.105416	−	0.0608620i
$183$	−1.98545	+	3.43889i	−0.146768	+	0.254210i
$184$	4.71996			0.347960
$185$	4.56787	−	12.8115i	0.335837	−	0.941920i
$186$	0.279008			0.0204579
$187$	−0.729049	+	1.26275i	−0.0533133	+	0.0923414i
$188$	−5.35121	+	3.08952i	−0.390277	+	0.225327i
$189$	0.478020	+	0.827955i	0.0347708	+	0.0602248i
$190$	2.12789	+	9.82882i	0.154373	+	0.713058i
$191$		−	14.5601i		−	1.05353i	−0.850010	−	0.526766i	$-0.823404\pi$
$191$		−	14.5601i		−	1.05353i	0.850010	−	0.526766i	$-0.176596\pi$
$192$	−0.866025	+	0.500000i	−0.0625000	+	0.0360844i
$193$	9.43753			0.679329			0.339664	−	0.940547i	$-0.389687\pi$
$193$	9.43753			0.679329			0.339664	+	0.940547i	$0.389687\pi$
$194$	8.91478	−	15.4408i	0.640044	−	1.10859i
$195$	3.65725	+	1.17311i	0.261901	+	0.0840080i
$196$	6.08599			0.434713
$197$	−13.6839	−	7.90037i	−0.974934	−	0.562878i	−0.0741971	−	0.997244i	$-0.523639\pi$
$197$	−13.6839	−	7.90037i	−0.974934	−	0.562878i	−0.900737	+	0.434365i	$0.856973\pi$
$198$	0.126499	+	0.219103i	0.00898990	+	0.0155710i
$199$		−	3.54416i		−	0.251239i	−0.992079	−	0.125619i	$-0.959908\pi$
$199$		−	3.54416i		−	0.251239i	0.992079	−	0.125619i	$-0.0400918\pi$
$200$	4.55228	−	2.06802i	0.321895	−	0.146231i
$201$	−0.299295	+	0.518394i	−0.0211106	+	0.0365647i
$202$	−6.62067	+	11.4673i	−0.465829	+	0.806839i
$203$	−3.22604	−	5.58767i	−0.226424	−	0.392177i
$204$	−4.99114	+	2.88164i	−0.349450	+	0.201755i
$205$	−8.90190	−	9.81202i	−0.621736	−	0.685301i
$206$	−5.32783	+	9.22806i	−0.371207	+	0.642950i
$207$	2.35998	−	4.08761i	0.164030	−	0.284108i
$208$	1.71765			0.119098
$209$	0.985397	−	0.568919i	0.0681613	−	0.0393530i
$210$	−1.43642	−	1.58328i	−0.0991223	−	0.109256i
$211$	−19.4199			−1.33692			−0.668461	−	0.743747i	$-0.733047\pi$
$211$	−19.4199			−1.33692			−0.668461	+	0.743747i	$0.733047\pi$
$212$		−	8.20102i		−	0.563248i
$213$	−10.6955	−	6.17507i	−0.732846	−	0.423109i
$214$		−	15.1065i		−	1.03266i
$215$	−2.78432	+	0.602792i	−0.189889	+	0.0411101i
$216$			1.00000i			0.0680414i
$217$	0.133371	+	0.231006i	0.00905384	+	0.0156817i
$218$	10.6230	−	6.13320i	0.719481	−	0.415392i
$219$	5.36778	+	9.29726i	0.362721	+	0.628251i
$220$	−0.380122	−	0.418985i	−0.0256278	−	0.0282479i
$221$	9.89931			0.665900
$222$	−5.16750	−	3.20888i	−0.346820	−	0.215366i
$223$		−	11.3168i		−	0.757826i	−0.925432	−	0.378913i	$-0.876298\pi$
$223$		−	11.3168i		−	0.757826i	0.925432	−	0.378913i	$-0.123702\pi$
$224$	−0.827955	−	0.478020i	−0.0553200	−	0.0319390i
$225$	0.485183	−	4.97640i	0.0323455	−	0.331760i
$226$	1.13408	+	1.96429i	0.0754380	+	0.130662i
$227$	−3.47406	−	6.01725i	−0.230581	−	0.399379i	0.727398	−	0.686216i	$-0.240729\pi$
$227$	−3.47406	−	6.01725i	−0.230581	−	0.399379i	−0.957979	+	0.286837i	$0.907396\pi$
$228$	4.49741			0.297849
$229$	10.4066	+	18.0248i	0.687690	+	1.19111i	0.972583	+	0.232555i	$0.0747084\pi$
$229$	10.4066	+	18.0248i	0.687690	+	1.19111i	−0.284894	+	0.958559i	$0.591958\pi$
$230$	−3.22360	+	10.0498i	−0.212558	+	0.662665i
$231$	−0.120938	+	0.209471i	−0.00795715	+	0.0137822i
$232$		−	6.74876i		−	0.443078i
$233$		−	1.61054i		−	0.105510i	−0.998607	−	0.0527550i	$-0.983200\pi$
$233$		−	1.61054i		−	0.105510i	0.998607	−	0.0527550i	$-0.0168003\pi$
$234$	0.858827	−	1.48753i	0.0561433	−	0.0972430i
$235$	−2.92353	−	13.5039i	−0.190710	−	0.880899i
$236$		−	15.0437i		−	0.979260i
$237$	1.27546	−	2.20916i	0.0828501	−	0.143500i
$238$	−4.77173	−	2.75496i	−0.309305	−	0.178577i
$239$	7.21821	+	4.16744i	0.466907	+	0.269569i	0.714944	−	0.699181i	$-0.246452\pi$
$239$	7.21821	+	4.16744i	0.466907	+	0.269569i	−0.248037	+	0.968751i	$0.579785\pi$
$240$	−0.473136	−	2.18544i	−0.0305408	−	0.141069i
$241$	−20.3057	+	11.7235i	−1.30800	+	0.755176i	−0.981763	−	0.190110i	$-0.939115\pi$
$241$	−20.3057	+	11.7235i	−1.30800	+	0.755176i	−0.326241	+	0.945287i	$0.605782\pi$
$242$	5.46800	−	9.47085i	0.351496	−	0.608809i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	−3.43889	−	1.98545i	−0.220153	−	0.127105i
$245$	−4.15655	+	12.9584i	−0.265552	+	0.827880i
$246$	−5.13107	+	2.96243i	−0.327145	+	0.188877i
$247$	−6.69005	−	3.86250i	−0.425678	−	0.245765i
$248$			0.279008i			0.0177170i
$249$	−14.4646			−0.916656
$250$	1.29418	+	11.1052i	0.0818512	+	0.702353i
$251$			6.35514i			0.401133i	0.979680	+	0.200566i	$0.0642783\pi$
$251$			6.35514i			0.401133i	−0.979680	+	0.200566i	$0.935722\pi$
$252$	−0.827955	+	0.478020i	−0.0521562	+	0.0301124i
$253$	1.19414			0.0750751
$254$	2.12642	−	1.22769i	0.133424	−	0.0770322i
$255$	−2.72681	−	12.5953i	−0.170760	−	0.788747i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−11.3520	+	19.6623i	−0.708119	+	1.22650i	0.257435	+	0.966296i	$0.417123\pi$
$257$	−11.3520	+	19.6623i	−0.708119	+	1.22650i	−0.965554	+	0.260203i	$0.916211\pi$
$258$			1.27403i			0.0793179i
$259$	0.186636	−	5.81237i	0.0115970	−	0.361163i
$260$	−1.17311	+	3.65725i	−0.0727531	+	0.226813i
$261$	−5.84460	−	3.37438i	−0.361771	−	0.208869i
$262$	−15.2442	+	8.80126i	−0.941791	+	0.543743i
$263$	15.7566	−	9.09708i	0.971594	−	0.560950i	0.0718724	−	0.997414i	$-0.477103\pi$
$263$	15.7566	−	9.09708i	0.971594	−	0.560950i	0.899722	+	0.436464i	$0.143769\pi$
$264$	−0.219103	+	0.126499i	−0.0134849	+	0.00778548i
$265$	17.4617	+	5.60106i	1.07267	+	0.344070i
$266$	2.14985	+	3.72366i	0.131816	+	0.228312i
$267$	−7.90389			−0.483710
$268$	−0.518394	−	0.299295i	−0.0316659	−	0.0182823i
$269$	−14.0186			−0.854729			−0.427365	−	0.904079i	$-0.640558\pi$
$269$	−14.0186			−0.854729			−0.427365	+	0.904079i	$0.640558\pi$
$270$	−2.12921	−	0.682971i	−0.129580	−	0.0415643i
$271$	3.39607	−	5.88217i	0.206297	−	0.357316i	−0.744248	−	0.667903i	$-0.767192\pi$
$271$	3.39607	−	5.88217i	0.206297	−	0.357316i	0.950545	+	0.310587i	$0.100525\pi$
$272$	−2.88164	−	4.99114i	−0.174725	−	0.302632i
$273$	1.64215			0.0993872
$274$	−1.01490	−	0.585952i	−0.0613123	−	0.0353987i
$275$	1.15172	−	0.523206i	0.0694513	−	0.0315505i
$276$	4.08761	+	2.35998i	0.246045	+	0.142054i
$277$	−5.09774	−	8.82954i	−0.306293	−	0.530516i	0.671255	−	0.741226i	$-0.265756\pi$
$277$	−5.09774	−	8.82954i	−0.306293	−	0.530516i	−0.977548	+	0.210711i	$0.932422\pi$
$278$	1.65873	+	2.87300i	0.0994838	+	0.172311i
$279$	0.241628	+	0.139504i	0.0144659	+	0.00835189i
$280$	1.58328	−	1.43642i	0.0946188	−	0.0858424i
$281$	15.7170	+	9.07419i	0.937595	+	0.541321i	0.889206	−	0.457508i	$-0.151258\pi$
$281$	15.7170	+	9.07419i	0.937595	+	0.541321i	0.0483896	+	0.998829i	$0.484591\pi$
$282$	−6.17905			−0.367957
$283$	−1.22946	−	2.12948i	−0.0730835	−	0.126584i	0.827168	−	0.561955i	$-0.189951\pi$
$283$	−1.22946	−	2.12948i	−0.0730835	−	0.126584i	−0.900251	+	0.435371i	$0.856617\pi$
$284$	6.17507	−	10.6955i	0.366423	−	0.634663i
$285$	−3.07160	+	9.57596i	−0.181946	+	0.567231i
$286$	0.434563			0.0256963
$287$	−4.90551	−	2.83220i	−0.289563	−	0.167179i
$288$	−1.00000			−0.0589256
$289$	−8.10766	−	14.0429i	−0.476921	−	0.826052i
$290$	14.3695	+	4.60921i	0.843809	+	0.270662i
$291$	15.4408	−	8.91478i	0.905158	−	0.522593i
$292$	−9.29726	+	5.36778i	−0.544081	+	0.314125i
$293$	−14.7982	+	8.54373i	−0.864518	+	0.499130i	−0.865523	−	0.500870i	$-0.833014\pi$
$293$	−14.7982	+	8.54373i	−0.864518	+	0.499130i	0.00100443	+	0.999999i	$0.499680\pi$
$294$	5.27062	+	3.04299i	0.307389	+	0.177471i
$295$	32.0312	+	10.2744i	1.86493	+	0.598198i
$296$	3.20888	−	5.16750i	0.186512	−	0.300355i
$297$			0.252998i			0.0146804i
$298$	2.91394	−	5.04710i	0.168800	−	0.292370i
$299$	−4.05363	−	7.02110i	−0.234428	−	0.406040i
$300$	4.97640	+	0.485183i	0.287313	+	0.0280120i
$301$	−1.05484	+	0.609014i	−0.0608001	+	0.0351030i
$302$	−19.4744			−1.12063
$303$	−11.4673	+	6.62067i	−0.658781	+	0.380348i
$304$			4.49741i			0.257944i
$305$	6.57610	−	5.96614i	0.376547	−	0.341620i
$306$	−5.76327			−0.329464
$307$		−	18.3619i		−	1.04797i	−0.851729	−	0.523983i	$-0.824445\pi$
$307$		−	18.3619i		−	1.04797i	0.851729	−	0.523983i	$-0.175555\pi$
$308$	−0.209471	−	0.120938i	−0.0119357	−	0.00689109i
$309$	−9.22806	+	5.32783i	−0.524966	+	0.303089i
$310$	−0.594068	−	0.190555i	−0.0337408	−	0.0108228i
$311$	−8.27066	−	4.77507i	−0.468986	−	0.270769i	0.246829	−	0.969059i	$-0.420611\pi$
$311$	−8.27066	−	4.77507i	−0.468986	−	0.270769i	−0.715815	+	0.698290i	$0.753945\pi$
$312$	1.48753	+	0.858827i	0.0842149	+	0.0486215i
$313$	−2.40463	+	4.16495i	−0.135918	+	0.235417i	−0.925948	−	0.377652i	$-0.876732\pi$
$313$	−2.40463	+	4.16495i	−0.135918	+	0.235417i	0.790030	+	0.613068i	$0.210065\pi$
$314$	1.24648	−	0.719657i	0.0703430	−	0.0406126i
$315$	−0.452337	−	2.08937i	−0.0254863	−	0.117722i
$316$	2.20916	+	1.27546i	0.124275	+	0.0717502i
$317$	12.6914	+	7.32737i	0.712818	+	0.411546i	0.812104	−	0.583513i	$-0.198322\pi$
$317$	12.6914	+	7.32737i	0.712818	+	0.411546i	−0.0992854	+	0.995059i	$0.531656\pi$
$318$	4.10051	−	7.10229i	0.229945	−	0.398277i
$319$		−	1.70742i		−	0.0955974i
$320$	2.18544	−	0.473136i	0.122170	−	0.0264491i
$321$	7.55326	−	13.0826i	0.421582	−	0.730201i
$322$			4.51247i			0.251470i
$323$			25.9198i			1.44222i
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	−6.98587	−	4.99560i	−0.387507	−	0.277106i
$326$	−4.06999	−	7.04943i	−0.225416	−	0.390432i
$327$	12.2664			0.678333
$328$	−2.96243	−	5.13107i	−0.163573	−	0.283316i
$329$	−2.95371	−	5.11597i	−0.162843	−	0.282053i
$330$	−0.119703	−	0.552912i	−0.00658942	−	0.0304368i
$331$	−8.57428	−	4.95036i	−0.471285	−	0.272097i	0.245492	−	0.969399i	$-0.421050\pi$
$331$	−8.57428	−	4.95036i	−0.471285	−	0.272097i	−0.716778	+	0.697302i	$0.754384\pi$
$332$		−	14.4646i		−	0.793847i
$333$	−2.87075	−	5.36272i	−0.157316	−	0.293875i
$334$	17.9637			0.982929
$335$	0.991311	−	0.899362i	0.0541611	−	0.0491374i
$336$	−0.478020	−	0.827955i	−0.0260781	−	0.0451686i
$337$	20.2823	−	11.7100i	1.10485	−	0.637883i	0.167356	−	0.985897i	$-0.446477\pi$
$337$	20.2823	−	11.7100i	1.10485	−	0.637883i	0.937489	+	0.348014i	$0.113144\pi$
$338$	5.02483	+	8.70326i	0.273315	+	0.473395i
$339$			2.26816i			0.123190i
$340$	12.5953	−	2.72681i	0.683075	−	0.147882i
$341$			0.0705886i			0.00382259i
$342$	3.89488	+	2.24871i	0.210611	+	0.121596i
$343$			12.5107i			0.675516i
$344$	−1.27403			−0.0686913
$345$	−7.81662	+	7.09159i	−0.420833	+	0.381798i
$346$	11.7107	−	6.76116i	0.629570	−	0.363482i
$347$	−36.3696			−1.95242			−0.976211	−	0.216821i	$-0.930431\pi$
$347$	−36.3696			−1.95242			−0.976211	+	0.216821i	$0.930431\pi$
$348$	3.37438	−	5.84460i	0.180886	−	0.313303i
$349$	−1.19043	+	2.06189i	−0.0637225	+	0.110371i	−0.896127	−	0.443799i	$-0.853631\pi$
$349$	−1.19043	+	2.06189i	−0.0637225	+	0.110371i	0.832404	+	0.554169i	$0.186964\pi$
$350$	1.97711	+	4.35216i	0.105681	+	0.232633i
$351$	1.48753	−	0.858827i	0.0793986	−	0.0458408i
$352$	−0.126499	−	0.219103i	−0.00674243	−	0.0116782i
$353$	5.59944	−	9.69852i	0.298028	−	0.516200i	−0.677657	−	0.735378i	$-0.737004\pi$
$353$	5.59944	−	9.69852i	0.298028	−	0.516200i	0.975685	+	0.219179i	$0.0703377\pi$
$354$	7.52184	−	13.0282i	0.399781	−	0.692441i
$355$	18.5557	+	20.4528i	0.984833	+	1.08552i
$356$		−	7.90389i		−	0.418905i
$357$	−2.75496	−	4.77173i	−0.145808	−	0.252547i
$358$	−3.67031	−	2.11905i	−0.193982	−	0.111995i
$359$	−11.1332			−0.587590			−0.293795	−	0.955868i	$-0.594918\pi$
$359$	−11.1332			−0.587590			−0.293795	+	0.955868i	$0.594918\pi$
$360$	0.682971	−	2.12921i	0.0359957	−	0.112219i
$361$	0.613370	−	1.06239i	0.0322826	−	0.0559151i
$362$	9.44493			0.496414
$363$	9.47085	−	5.46800i	0.497091	−	0.286995i
$364$			1.64215i			0.0860718i
$365$	−5.07938	−	23.4619i	−0.265867	−	1.22805i
$366$	−1.98545	−	3.43889i	−0.103781	−	0.179754i
$367$	−18.2562	+	10.5402i	−0.952967	+	0.550196i	−0.894001	−	0.448064i	$-0.852114\pi$
$367$	−18.2562	+	10.5402i	−0.952967	+	0.550196i	−0.0589660	+	0.998260i	$0.518780\pi$
$368$	−2.35998	+	4.08761i	−0.123023	+	0.213081i
$369$	−5.92485			−0.308436
$370$	8.81115	+	10.3616i	0.458070	+	0.538676i
$371$	7.84050			0.407059
$372$	−0.139504	+	0.241628i	−0.00723295	+	0.0125278i
$373$	5.11640	−	2.95396i	0.264917	−	0.152950i	−0.361658	−	0.932311i	$-0.617789\pi$
$373$	5.11640	−	2.95396i	0.264917	−	0.152950i	0.626576	+	0.779361i	$0.284456\pi$
$374$	−0.729049	−	1.26275i	−0.0376982	−	0.0652952i
$375$	−4.43180	+	10.2645i	−0.228857	+	0.530055i
$376$		−	6.17905i		−	0.318660i
$377$	−10.0390	+	5.79602i	−0.517035	+	0.298510i
$378$	−0.956040			−0.0491734
$379$	−11.0088	+	19.0677i	−0.565482	+	0.979444i	0.431522	+	0.902102i	$0.357977\pi$
$379$	−11.0088	+	19.0677i	−0.565482	+	0.979444i	−0.997005	+	0.0773420i	$0.975357\pi$
$380$	−9.57596	−	3.07160i	−0.491236	−	0.157570i
$381$	2.45538			0.125793
$382$	12.6094	+	7.28005i	0.645154	+	0.372480i
$383$	−2.98389	−	5.16824i	−0.152470	−	0.264085i	0.779665	−	0.626197i	$-0.215389\pi$
$383$	−2.98389	−	5.16824i	−0.152470	−	0.264085i	−0.932135	+	0.362112i	$0.882056\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	0.400566	−	0.363411i	0.0204147	−	0.0185212i
$386$	−4.71877	+	8.17314i	−0.240179	+	0.416002i
$387$	−0.637017	+	1.10335i	−0.0323814	+	0.0560862i
$388$	8.91478	+	15.4408i	0.452579	+	0.783890i
$389$	−5.95890	+	3.44038i	−0.302128	+	0.174434i	−0.643399	−	0.765531i	$-0.722476\pi$
$389$	−5.95890	+	3.44038i	−0.302128	+	0.174434i	0.341270	+	0.939965i	$0.389143\pi$
$390$	−2.84457	+	2.58072i	−0.144040	+	0.130680i
$391$	−13.6012	+	23.5580i	−0.687843	+	1.19138i
$392$	−3.04299	+	5.27062i	−0.153694	+	0.266207i
$393$	−17.6025			−0.887929
$394$	13.6839	−	7.90037i	0.689382	−	0.398015i
$395$	−4.22452	+	3.83268i	−0.212559	+	0.192843i
$396$	−0.252998			−0.0127136
$397$			8.30320i			0.416726i	0.978052	+	0.208363i	$0.0668135\pi$
$397$			8.30320i			0.416726i	−0.978052	+	0.208363i	$0.933186\pi$
$398$	3.06933	+	1.77208i	0.153852	+	0.0888263i
$399$			4.29971i			0.215255i
$400$	−0.485183	+	4.97640i	−0.0242591	+	0.248820i
$401$			13.4756i			0.672937i	0.941695	+	0.336469i	$0.109233\pi$
$401$			13.4756i			0.672937i	−0.941695	+	0.336469i	$0.890767\pi$
$402$	−0.299295	−	0.518394i	−0.0149275	−	0.0258551i
$403$	0.415034	−	0.239620i	0.0206743	−	0.0119363i
$404$	−6.62067	−	11.4673i	−0.329391	−	0.570521i
$405$	−1.50247	−	1.65608i	−0.0746582	−	0.0822911i
$406$	6.45208			0.320211
$407$	0.811841	−	1.30737i	0.0402414	−	0.0648039i
$408$		−	5.76327i		−	0.285325i
$409$	−13.6292	−	7.86885i	−0.673923	−	0.389090i	0.123638	−	0.992327i	$-0.460544\pi$
$409$	−13.6292	−	7.86885i	−0.673923	−	0.389090i	−0.797561	+	0.603238i	$0.793877\pi$
$410$	12.9484	−	2.80326i	0.639476	−	0.138443i
$411$	−0.585952	−	1.01490i	−0.0289029	−	0.0500613i
$412$	−5.32783	−	9.22806i	−0.262483	−	0.454634i
$413$	14.3823			0.707709
$414$	2.35998	+	4.08761i	0.115987	+	0.200895i
$415$	30.7982	+	9.87889i	1.51182	+	0.484936i
$416$	−0.858827	+	1.48753i	−0.0421075	+	0.0729323i
$417$			3.31745i			0.162456i
$418$			1.13784i			0.0556535i
$419$	−17.2973	+	29.9597i	−0.845027	+	1.46363i	0.0405714	+	0.999177i	$0.487082\pi$
$419$	−17.2973	+	29.9597i	−0.845027	+	1.46363i	−0.885598	+	0.464452i	$0.846251\pi$
$420$	2.08937	−	0.452337i	0.101951	−	0.0220718i
$421$		−	24.6521i		−	1.20147i	−0.799449	−	0.600734i	$-0.794875\pi$
$421$		−	24.6521i		−	1.20147i	0.799449	−	0.600734i	$-0.205125\pi$
$422$	9.70996	−	16.8181i	0.472673	−	0.818694i
$423$	−5.35121	−	3.08952i	−0.260185	−	0.150218i
$424$	7.10229	+	4.10051i	0.344918	+	0.199138i
$425$	−2.79624	+	28.6804i	−0.135638	+	1.39120i
$426$	10.6955	−	6.17507i	0.518200	−	0.299183i
$427$	1.89817	−	3.28772i	0.0918586	−	0.159104i
$428$	13.0826	+	7.55326i	0.632373	+	0.365101i
$429$	0.376343	+	0.217282i	0.0181700	+	0.0104905i
$430$	0.870129	−	2.71269i	0.0419613	−	0.130818i
$431$	1.32424	−	0.764551i	0.0637864	−	0.0368271i	−0.467768	−	0.883851i	$-0.654942\pi$
$431$	1.32424	−	0.764551i	0.0637864	−	0.0368271i	0.531554	+	0.847024i	$0.321608\pi$
$432$	−0.866025	−	0.500000i	−0.0416667	−	0.0240563i
$433$		−	0.749467i		−	0.0360171i	−0.999838	−	0.0180085i	$-0.994267\pi$
$433$		−	0.749467i		−	0.0360171i	0.999838	−	0.0180085i	$-0.00573261\pi$
$434$	−0.266743			−0.0128041
$435$	10.1398	+	11.1765i	0.486166	+	0.535870i
$436$			12.2664i			0.587454i
$437$	18.3837	−	10.6138i	0.879410	−	0.507728i
$438$	−10.7356			−0.512965
$439$	5.66201	−	3.26896i	0.270233	−	0.156019i	−0.358760	−	0.933430i	$-0.616801\pi$
$439$	5.66201	−	3.26896i	0.270233	−	0.156019i	0.628994	+	0.777410i	$0.283467\pi$
$440$	0.552912	−	0.119703i	0.0263591	−	0.00570660i
$441$	3.04299	+	5.27062i	0.144904	+	0.250982i
$442$	−4.94966	+	8.57305i	−0.235431	+	0.407779i
$443$			31.0306i			1.47431i	0.675724	+	0.737155i	$0.263831\pi$
$443$			31.0306i			1.47431i	−0.675724	+	0.737155i	$0.736169\pi$
$444$	5.36272	−	2.87075i	0.254504	−	0.136240i
$445$	16.8291	+	5.39813i	0.797774	+	0.255896i
$446$	9.80060	+	5.65838i	0.464072	+	0.267932i
$447$	5.04710	−	2.91394i	0.238719	−	0.137825i
$448$	0.827955	−	0.478020i	0.0391172	−	0.0225843i
$449$	−30.7650	+	17.7622i	−1.45189	+	0.838249i	−0.998589	−	0.0531078i	$-0.983087\pi$
$449$	−30.7650	+	17.7622i	−1.45189	+	0.838249i	−0.453302	+	0.891357i	$0.649754\pi$
$450$	4.06710	+	2.90838i	0.191725	+	0.137102i
$451$	−0.749489	−	1.29815i	−0.0352921	−	0.0611276i
$452$	−2.26816			−0.106685
$453$	−16.8654	−	9.73722i	−0.792404	−	0.457495i
$454$	6.94812			0.326091
$455$	−3.49648	−	1.12154i	−0.163917	−	0.0525785i
$456$	−2.24871	+	3.89488i	−0.105305	+	0.182394i
$457$	12.4644	+	21.5890i	0.583061	+	1.00989i	0.995114	+	0.0987315i	$0.0314785\pi$
$457$	12.4644	+	21.5890i	0.583061	+	1.00989i	−0.412053	+	0.911160i	$0.635188\pi$
$458$	−20.8133			−0.972540
$459$	−4.99114	−	2.88164i	−0.232967	−	0.134503i
$460$	−7.09159	−	7.81662i	−0.330647	−	0.364452i
$461$	−25.5860	−	14.7721i	−1.19166	−	0.688004i	−0.232975	−	0.972483i	$-0.574846\pi$
$461$	−25.5860	−	14.7721i	−1.19166	−	0.688004i	−0.958682	+	0.284479i	$0.908180\pi$
$462$	−0.120938	−	0.209471i	−0.00562655	−	0.00974548i
$463$	−10.2303	−	17.7195i	−0.475444	−	0.823493i	0.524160	−	0.851620i	$-0.324379\pi$
$463$	−10.2303	−	17.7195i	−0.475444	−	0.823493i	−0.999604	+	0.0281264i	$0.991046\pi$
$464$	5.84460	+	3.37438i	0.271329	+	0.156652i
$465$	−0.419201	−	0.462059i	−0.0194400	−	0.0214275i
$466$	1.39477	+	0.805271i	0.0646115	+	0.0373035i
$467$	−14.8626			−0.687760			−0.343880	−	0.939014i	$-0.611741\pi$
$467$	−14.8626			−0.687760			−0.343880	+	0.939014i	$0.611741\pi$
$468$	0.858827	+	1.48753i	0.0396993	+	0.0687612i
$469$	0.286138	−	0.495605i	0.0132126	−	0.0228849i
$470$	13.1565	+	4.22011i	0.606865	+	0.194659i
$471$	1.43931			0.0663200
$472$	13.0282	+	7.52184i	0.599672	+	0.346221i
$473$	−0.322329			−0.0148207
$474$	1.27546	+	2.20916i	0.0585838	+	0.101470i
$475$	13.0802	−	18.2914i	0.600161	−	0.839269i
$476$	4.77173	−	2.75496i	0.218712	−	0.126273i
$477$	7.10229	−	4.10051i	0.325192	−	0.187749i
$478$	−7.21821	+	4.16744i	−0.330153	+	0.190614i
$479$	12.3586	+	7.13524i	0.564679	+	0.326017i	0.755021	−	0.655700i	$-0.227627\pi$
$479$	12.3586	+	7.13524i	0.564679	+	0.326017i	−0.190343	+	0.981718i	$0.560960\pi$
$480$	2.12921	+	0.682971i	0.0971849	+	0.0311732i
$481$	−10.4427	−	0.335317i	−0.476146	−	0.0152891i
$482$		−	23.4470i		−	1.06798i
$483$	−2.25624	+	3.90791i	−0.102662	+	0.177816i
$484$	5.46800	+	9.47085i	0.248545	+	0.430493i
$485$	−38.9654	+	8.43581i	−1.76933	+	0.383050i
$486$	−0.866025	+	0.500000i	−0.0392837	+	0.0226805i
$487$	9.99983			0.453136			0.226568	−	0.973995i	$-0.427250\pi$
$487$	9.99983			0.453136			0.226568	+	0.973995i	$0.427250\pi$
$488$	3.43889	−	1.98545i	0.155671	−	0.0898769i
$489$		−	8.13998i		−	0.368103i
$490$	−9.14400	−	10.0789i	−0.413084	−	0.455317i
$491$	2.92058			0.131804			0.0659020	−	0.997826i	$-0.479008\pi$
$491$	2.92058			0.131804			0.0659020	+	0.997826i	$0.479008\pi$
$492$		−	5.92485i		−	0.267113i
$493$	33.6840	+	19.4475i	1.51705	+	0.875870i
$494$	6.69005	−	3.86250i	0.301000	−	0.173782i
$495$	0.172790	−	0.538687i	0.00776635	−	0.0242122i
$496$	−0.241628	−	0.139504i	−0.0108494	−	0.00626392i
$497$	10.2254	+	5.90361i	0.458670	+	0.264813i
$498$	7.23229	−	12.5267i	0.324087	−	0.561335i
$499$	−15.7111	+	9.07079i	−0.703324	+	0.406064i	−0.808584	−	0.588380i	$-0.799766\pi$
$499$	−15.7111	+	9.07079i	−0.703324	+	0.406064i	0.105260	+	0.994445i	$0.466432\pi$
$500$	−10.2645	−	4.43180i	−0.459041	−	0.198196i
$501$	15.5570	+	8.98184i	0.695036	+	0.401279i
$502$	−5.50371	−	3.17757i	−0.245643	−	0.141822i
$503$	19.8786	−	34.4308i	0.886344	−	1.53519i	0.0421784	−	0.999110i	$-0.486570\pi$
$503$	19.8786	−	34.4308i	0.886344	−	1.53519i	0.844166	−	0.536083i	$-0.180096\pi$
$504$		−	0.956040i		−	0.0425854i
$505$	28.9381	−	6.26496i	1.28773	−	0.278787i
$506$	−0.597071	+	1.03416i	−0.0265430	+	0.0459739i
$507$			10.0497i			0.446321i
$508$			2.45538i			0.108940i
$509$	−13.2095	+	22.8795i	−0.585501	+	1.01412i	0.409312	+	0.912394i	$0.365769\pi$
$509$	−13.2095	+	22.8795i	−0.585501	+	1.01412i	−0.994813	+	0.101723i	$0.967565\pi$
$510$	12.2712	+	3.93615i	0.543380	+	0.174296i
$511$	−5.13181	−	8.88855i	−0.227018	−	0.393206i
$512$	1.00000			0.0441942
$513$	2.24871	+	3.89488i	0.0992829	+	0.171963i
$514$	−11.3520	−	19.6623i	−0.500716	−	0.867265i
$515$	23.2873	−	5.04158i	1.02616	−	0.222158i
$516$	−1.10335	−	0.637017i	−0.0485721	−	0.0280431i
$517$		−	1.56329i		−	0.0687534i
$518$	4.94034	+	3.06781i	0.217066	+	0.134792i
$519$	13.5223			0.593564
$520$	−2.58072	−	2.84457i	−0.113172	−	0.124743i
$521$	−15.6202	−	27.0551i	−0.684335	−	1.18530i	−0.973645	−	0.228068i	$-0.926759\pi$
$521$	−15.6202	−	27.0551i	−0.684335	−	1.18530i	0.289310	−	0.957235i	$-0.406574\pi$
$522$	5.84460	−	3.37438i	0.255811	−	0.147693i
$523$	−2.75025	−	4.76357i	−0.120260	−	0.208296i	0.799610	−	0.600519i	$-0.205039\pi$
$523$	−2.75025	−	4.76357i	−0.120260	−	0.208296i	−0.919870	+	0.392223i	$0.871706\pi$
$524$		−	17.6025i		−	0.768969i
$525$	−0.463854	+	4.75764i	−0.0202442	+	0.207640i
$526$			18.1942i			0.793303i
$527$	−1.39257	−	0.804000i	−0.0606613	−	0.0350228i
$528$		−	0.252998i		−	0.0110103i
$529$	−0.721957			−0.0313894
$530$	−13.5815	+	12.3218i	−0.589944	+	0.535223i
$531$	13.0282	−	7.52184i	0.565376	−	0.326420i
$532$	−4.29971			−0.186416
$533$	−5.08843	+	8.81341i	−0.220404	+	0.381751i
$534$	3.95194	−	6.84497i	0.171017	−	0.296211i
$535$	−25.0176	+	22.6971i	−1.08160	+	0.981279i
$536$	0.518394	−	0.299295i	0.0223912	−	0.0129276i
$537$	−2.11905	−	3.67031i	−0.0914438	−	0.158385i
$538$	7.00930	−	12.1405i	0.302192	−	0.523413i
$539$	−0.769872	+	1.33346i	−0.0331607	+	0.0574361i
$540$	1.65608	−	1.50247i	0.0712662	−	0.0646559i
$541$			20.1172i			0.864904i	0.901657	+	0.432452i	$0.142351\pi$
$541$			20.1172i			0.864904i	−0.901657	+	0.432452i	$0.857649\pi$
$542$	3.39607	+	5.88217i	0.145874	+	0.252661i
$543$	8.17955	+	4.72246i	0.351018	+	0.202660i
$544$	5.76327			0.247098
$545$	−26.1178	−	8.37759i	−1.11876	−	0.358857i
$546$	−0.821073	+	1.42214i	−0.0351387	+	0.0608620i
$547$	−17.4376			−0.745580			−0.372790	−	0.927916i	$-0.621599\pi$
$547$	−17.4376			−0.745580			−0.372790	+	0.927916i	$0.621599\pi$
$548$	1.01490	−	0.585952i	0.0433544	−	0.0250306i
$549$		−	3.97089i		−	0.169474i
$550$	−0.122750	+	1.25902i	−0.00523409	+	0.0536849i
$551$	−15.1760	−	26.2856i	−0.646519	−	1.11980i
$552$	−4.08761	+	2.35998i	−0.173980	+	0.100447i
$553$	−1.21939	+	2.11205i	−0.0518538	+	0.0898134i
$554$	10.1955			0.433164
$555$	2.44986	+	13.3790i	0.103991	+	0.567908i
$556$	−3.31745			−0.140691
$557$	−5.96951	+	10.3395i	−0.252936	+	0.438098i	−0.964333	−	0.264692i	$-0.914730\pi$
$557$	−5.96951	+	10.3395i	−0.252936	+	0.438098i	0.711397	+	0.702791i	$0.248063\pi$
$558$	−0.241628	+	0.139504i	−0.0102289	+	0.00590568i
$559$	1.09418	+	1.89517i	0.0462787	+	0.0801570i
$560$	0.452337	+	2.08937i	0.0191147	+	0.0882918i
$561$		−	1.45810i		−	0.0615609i
$562$	−15.7170	+	9.07419i	−0.662980	+	0.382772i
$563$	26.5836			1.12036			0.560182	−	0.828370i	$-0.310731\pi$
$563$	26.5836			1.12036			0.560182	+	0.828370i	$0.310731\pi$
$564$	3.08952	−	5.35121i	0.130092	−	0.225327i
$565$	1.54909	−	4.82940i	0.0651707	−	0.203175i
$566$	2.45891			0.103356
$567$	−0.827955	−	0.478020i	−0.0347708	−	0.0200749i
$568$	6.17507	+	10.6955i	0.259100	+	0.448775i
$569$		−	31.4826i		−	1.31982i	−0.751344	−	0.659911i	$-0.770594\pi$
$569$		−	31.4826i		−	1.31982i	0.751344	−	0.659911i	$-0.229406\pi$
$570$	−6.75722	−	7.44807i	−0.283029	−	0.311965i
$571$	−21.1332	+	36.6037i	−0.884395	+	1.53182i	−0.0379900	+	0.999278i	$0.512096\pi$
$571$	−21.1332	+	36.6037i	−0.884395	+	1.53182i	−0.846405	+	0.532539i	$0.821238\pi$
$572$	−0.217282	+	0.376343i	−0.00908501	+	0.0157357i
$573$	7.28005	+	12.6094i	0.304128	+	0.526766i
$574$	4.90551	−	2.83220i	0.204752	−	0.118214i
$575$	21.4866	−	9.76098i	0.896053	−	0.407061i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	2.58269	−	4.47335i	0.107519	−	0.186228i	−0.807246	−	0.590216i	$-0.799043\pi$
$577$	2.58269	−	4.47335i	0.107519	−	0.186228i	0.914765	+	0.403987i	$0.132376\pi$
$578$	16.2153			0.674468
$579$	−8.17314	+	4.71877i	−0.339664	+	0.196105i
$580$	−11.1765	+	10.1398i	−0.464077	+	0.421032i
$581$	13.8287			0.573712
$582$			17.8296i			0.739059i
$583$	1.79687	+	1.03742i	0.0744187	+	0.0429656i
$584$		−	10.7356i		−	0.444240i
$585$	−3.75383	+	0.812685i	−0.155202	+	0.0336004i
$586$		−	17.0875i		−	0.705876i
$587$	19.1660	+	33.1964i	0.791064	+	1.37016i	0.925309	+	0.379215i	$0.123806\pi$
$587$	19.1660	+	33.1964i	0.791064	+	1.37016i	−0.134244	+	0.990948i	$0.542861\pi$
$588$	−5.27062	+	3.04299i	−0.217357	+	0.125491i
$589$	0.627408	+	1.08670i	0.0258519	+	0.0447768i
$590$	−24.9135	+	22.6026i	−1.02567	+	0.930536i
$591$	15.8007			0.649956
$592$	2.87075	+	5.36272i	0.117987	+	0.220407i
$593$			44.1228i			1.81191i	0.423379	+	0.905953i	$0.360844\pi$
$593$			44.1228i			1.81191i	−0.423379	+	0.905953i	$0.639156\pi$
$594$	−0.219103	−	0.126499i	−0.00898990	−	0.00519032i
$595$	2.60694	+	12.0416i	0.106874	+	0.493657i
$596$	2.91394	+	5.04710i	0.119360	+	0.206737i
$597$	1.77208	+	3.06933i	0.0725264	+	0.125619i
$598$	8.10726			0.331531
$599$	−9.68215	−	16.7700i	−0.395602	−	0.685202i	0.597576	−	0.801812i	$-0.296131\pi$
$599$	−9.68215	−	16.7700i	−0.395602	−	0.685202i	−0.993178	+	0.116610i	$0.962797\pi$
$600$	−2.90838	+	4.06710i	−0.118734	+	0.166039i
$601$	16.6840	−	28.8976i	0.680555	−	1.17876i	−0.294257	−	0.955726i	$-0.595072\pi$
$601$	16.6840	−	28.8976i	0.680555	−	1.17876i	0.974812	−	0.223030i	$-0.0715947\pi$
$602$		−	1.21803i		−	0.0496431i
$603$		−	0.598590i		−	0.0243765i
$604$	9.73722	−	16.8654i	0.396202	−	0.686242i
$605$	−23.8999	+	5.17422i	−0.971671	+	0.210362i
$606$		−	13.2413i		−	0.537893i
$607$	8.61613	−	14.9236i	0.349718	−	0.605730i	−0.636481	−	0.771292i	$-0.719611\pi$
$607$	8.61613	−	14.9236i	0.349718	−	0.605730i	0.986199	+	0.165563i	$0.0529440\pi$
$608$	−3.89488	−	2.24871i	−0.157958	−	0.0911971i
$609$	5.58767	+	3.22604i	0.226424	+	0.130726i
$610$	1.87877	+	8.67814i	0.0760693	+	0.351368i
$611$	−9.19154	+	5.30674i	−0.371850	+	0.214688i
$612$	2.88164	−	4.99114i	0.116483	−	0.201755i
$613$	12.5282	+	7.23314i	0.506008	+	0.292144i	0.731191	−	0.682173i	$-0.238965\pi$
$613$	12.5282	+	7.23314i	0.506008	+	0.292144i	−0.225183	+	0.974316i	$0.572298\pi$
$614$	15.9018	+	9.18093i	0.641746	+	0.370512i
$615$	12.6153	+	4.04650i	0.508697	+	0.163171i
$616$	0.209471	−	0.120938i	0.00843983	−	0.00487274i
$617$	12.2964	+	7.09933i	0.495035	+	0.285808i	0.726661	−	0.686996i	$-0.241071\pi$
$617$	12.2964	+	7.09933i	0.495035	+	0.285808i	−0.231626	+	0.972805i	$0.574405\pi$
$618$		−	10.6557i		−	0.428633i
$619$	35.2133			1.41534			0.707670	−	0.706543i	$-0.249746\pi$
$619$	35.2133			1.41534			0.707670	+	0.706543i	$0.249746\pi$
$620$	0.462059	−	0.419201i	0.0185567	−	0.0168355i
$621$			4.71996i			0.189406i
$622$	8.27066	−	4.77507i	0.331623	−	0.191463i
$623$	7.55643			0.302742
$624$	−1.48753	+	0.858827i	−0.0595489	+	0.0343806i
$625$	16.4466	−	18.8284i	0.657863	−	0.753138i
$626$	−2.40463	−	4.16495i	−0.0961085	−	0.166465i
$627$	−0.568919	+	0.985397i	−0.0227204	+	0.0393530i
$628$			1.43931i			0.0574348i
$629$	16.5449	+	30.9068i	0.659689	+	1.23234i
$630$	2.03561	+	0.652947i	0.0811007	+	0.0260140i
$631$	−30.6967	−	17.7227i	−1.22202	−	0.705531i	−0.256668	−	0.966500i	$-0.582625\pi$
$631$	−30.6967	−	17.7227i	−1.22202	−	0.705531i	−0.965347	+	0.260968i	$0.915958\pi$
$632$	−2.20916	+	1.27546i	−0.0878757	+	0.0507351i
$633$	16.8181	−	9.70996i	0.668461	−	0.385936i
$634$	−12.6914	+	7.32737i	−0.504039	+	0.291007i
$635$	−5.22803	−	1.67695i	−0.207468	−	0.0665479i
$636$	4.10051	+	7.10229i	0.162596	+	0.281624i
$637$	10.4536			0.414188
$638$	1.47867	+	0.853712i	0.0585412	+	0.0337988i
$639$	12.3501			0.488564
$640$	−0.682971	+	2.12921i	−0.0269968	+	0.0841646i
$641$	10.9838	−	19.0244i	0.433833	−	0.751420i	−0.563367	−	0.826207i	$-0.690494\pi$
$641$	10.9838	−	19.0244i	0.433833	−	0.751420i	0.997200	+	0.0747865i	$0.0238275\pi$
$642$	7.55326	+	13.0826i	0.298103	+	0.516330i
$643$	−17.8210			−0.702792			−0.351396	−	0.936227i	$-0.614293\pi$
$643$	−17.8210			−0.702792			−0.351396	+	0.936227i	$0.614293\pi$
$644$	−3.90791	−	2.25624i	−0.153993	−	0.0889081i
$645$	2.10990	−	1.91420i	0.0830772	−	0.0753714i
$646$	−22.4472	−	12.9599i	−0.883174	−	0.509901i
$647$	14.0846	+	24.3952i	0.553722	+	0.959075i	0.998002	+	0.0631867i	$0.0201264\pi$
$647$	14.0846	+	24.3952i	0.553722	+	0.959075i	−0.444280	+	0.895888i	$0.646540\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	3.29611	+	1.90301i	0.129384	+	0.0746997i
$650$	7.81925	−	3.55215i	0.306696	−	0.139327i
$651$	−0.231006	−	0.133371i	−0.00905384	−	0.00522724i
$652$	8.13998			0.318786
$653$	21.2537	+	36.8125i	0.831722	+	1.44058i	0.896672	+	0.442696i	$0.145978\pi$
$653$	21.2537	+	36.8125i	0.831722	+	1.44058i	−0.0649503	+	0.997888i	$0.520689\pi$
$654$	−6.13320	+	10.6230i	−0.239827	+	0.415392i
$655$	37.4795	+	12.0220i	1.46445	+	0.469739i
$656$	5.92485			0.231327
$657$	−9.29726	−	5.36778i	−0.362721	−	0.209417i
$658$	5.90742			0.230295
$659$	−8.89609	−	15.4085i	−0.346543	−	0.600229i	0.639090	−	0.769132i	$-0.279311\pi$
$659$	−8.89609	−	15.4085i	−0.346543	−	0.600229i	−0.985633	+	0.168902i	$0.945978\pi$
$660$	0.538687	+	0.172790i	0.0209684	+	0.00672586i
$661$	−3.69052	+	2.13072i	−0.143545	+	0.0828755i	−0.570052	−	0.821608i	$-0.693077\pi$
$661$	−3.69052	+	2.13072i	−0.143545	+	0.0828755i	0.426508	+	0.904484i	$0.359744\pi$
$662$	8.57428	−	4.95036i	0.333249	−	0.192401i
$663$	−8.57305	+	4.94966i	−0.332950	+	0.192229i
$664$	12.5267	+	7.23229i	0.486130	+	0.280667i
$665$	2.93658	−	9.15499i	0.113876	−	0.355015i
$666$	6.07963	+	0.195218i	0.235581	+	0.00756454i
$667$		−	31.8539i		−	1.23339i
$668$	−8.98184	+	15.5570i	−0.347518	+	0.601919i
$669$	5.65838	+	9.80060i	0.218765	+	0.378913i
$670$	0.283215	+	1.30818i	0.0109415	+	0.0505394i
$671$	0.870034	−	0.502314i	0.0335873	−	0.0193916i
$672$	0.956040			0.0368800
$673$	−27.5111	+	15.8835i	−1.06047	+	0.612265i	−0.925563	−	0.378593i	$-0.876408\pi$
$673$	−27.5111	+	15.8835i	−1.06047	+	0.612265i	−0.134910	+	0.990858i	$0.543075\pi$
$674$			23.4199i			0.902102i
$675$	2.06802	+	4.55228i	0.0795982	+	0.175217i
$676$	−10.0497			−0.386526
$677$		−	1.40856i		−	0.0541352i	−0.999634	−	0.0270676i	$-0.991383\pi$
$677$		−	1.40856i		−	0.0541352i	0.999634	−	0.0270676i	$-0.00861694\pi$
$678$	−1.96429	−	1.13408i	−0.0754380	−	0.0435541i
$679$	−14.7621	+	8.52288i	−0.566516	+	0.327078i
$680$	−3.93615	+	12.2712i	−0.150944	+	0.470581i
$681$	6.01725	+	3.47406i	0.230581	+	0.133126i
$682$	−0.0611315	−	0.0352943i	−0.00234085	−	0.00135149i
$683$	3.02507	−	5.23957i	0.115751	−	0.200487i	−0.802329	−	0.596882i	$-0.796406\pi$
$683$	3.02507	−	5.23957i	0.115751	−	0.200487i	0.918080	+	0.396396i	$0.129739\pi$
$684$	−3.89488	+	2.24871i	−0.148924	+	0.0859815i
$685$	0.554471	+	2.56113i	0.0211852	+	0.0978556i
$686$	−10.8346	−	6.25536i	−0.413667	−	0.238831i
$687$	−18.0248	−	10.4066i	−0.687690	−	0.397038i
$688$	0.637017	−	1.10335i	0.0242861	−	0.0420647i
$689$		−	14.0865i		−	0.536654i
$690$	−2.23319	−	10.3152i	−0.0850160	−	0.392692i
$691$	11.8687	−	20.5572i	0.451507	−	0.782034i	−0.546973	−	0.837151i	$-0.684220\pi$
$691$	11.8687	−	20.5572i	0.451507	−	0.782034i	0.998480	+	0.0551168i	$0.0175531\pi$
$692$			13.5223i			0.514042i
$693$		−	0.241876i		−	0.00918812i
$694$	18.1848	−	31.4970i	0.690286	−	1.19561i
$695$	2.26572	−	7.06356i	0.0859438	−	0.267936i
$696$	3.37438	+	5.84460i	0.127906	+	0.221539i
$697$	34.1466			1.29339
$698$	−1.19043	−	2.06189i	−0.0450586	−	0.0780438i
$699$	0.805271	+	1.39477i	0.0304581	+	0.0527550i
$700$	−4.75764	−	0.463854i	−0.179822	−	0.0175320i
$701$	−8.52293	−	4.92071i	−0.321906	−	0.185853i	0.330336	−	0.943864i	$-0.392838\pi$
$701$	−8.52293	−	4.92071i	−0.321906	−	0.185853i	−0.652242	+	0.758011i	$0.726171\pi$
$702$			1.71765i			0.0648287i
$703$	0.877976	−	27.3426i	0.0331135	−	1.03125i
$704$	0.252998			0.00953523
$705$	9.28382	+	10.2330i	0.349649	+	0.385396i
$706$	5.59944	+	9.69852i	0.210738	+	0.365008i
$707$	10.9632	−	6.32962i	0.412315	−	0.238050i
$708$	7.52184	+	13.0282i	0.282688	+	0.489630i
$709$		−	2.32525i		−	0.0873267i	−0.999046	−	0.0436634i	$-0.986097\pi$
$709$		−	2.32525i		−	0.0873267i	0.999046	−	0.0436634i	$-0.0139029\pi$
$710$	−26.9905	+	5.84330i	−1.01293	+	0.219295i
$711$			2.55092i			0.0956670i
$712$	6.84497	+	3.95194i	0.256526	+	0.148105i
$713$			1.31691i			0.0493186i
$714$	5.50992			0.206203
$715$	−0.652918	−	0.719671i	−0.0244177	−	0.0269142i
$716$	3.67031	−	2.11905i	0.137166	−	0.0791927i
$717$	−8.33488			−0.311272
$718$	5.56662	−	9.64167i	0.207744	−	0.359824i
$719$	−16.1985	+	28.0566i	−0.604102	+	1.04634i	0.388090	+	0.921621i	$0.373135\pi$
$719$	−16.1985	+	28.0566i	−0.604102	+	1.04634i	−0.992193	+	0.124714i	$0.960199\pi$
$720$	1.50247	+	1.65608i	0.0559937	+	0.0617183i
$721$	8.82240	−	5.09361i	0.328563	−	0.189696i
$722$	0.613370	+	1.06239i	0.0228273	+	0.0395380i
$723$	11.7235	−	20.3057i	0.436001	−	0.755176i
$724$	−4.72246	+	8.17955i	−0.175509	+	0.303990i
$725$	−13.9566	−	30.7223i	−0.518334	−	1.14100i
$726$			10.9360i			0.405873i
$727$	1.19340	+	2.06703i	0.0442608	+	0.0766620i	0.887307	−	0.461179i	$-0.152573\pi$
$727$	1.19340	+	2.06703i	0.0442608	+	0.0766620i	−0.843046	+	0.537841i	$0.819240\pi$
$728$	−1.42214	−	0.821073i	−0.0527080	−	0.0304310i
$729$	−1.00000			−0.0370370
$730$	22.8583	+	7.33207i	0.846023	+	0.271372i
$731$	3.67130	−	6.35889i	0.135788	−	0.235192i
$732$	3.97089			0.146768
$733$	−3.61173	+	2.08523i	−0.133402	+	0.0770199i	−0.565216	−	0.824943i	$-0.691207\pi$
$733$	−3.61173	+	2.08523i	−0.133402	+	0.0770199i	0.431814	+	0.901963i	$0.357874\pi$
$734$		−	21.0805i		−	0.778095i
$735$	−2.87950	−	13.3006i	−0.106212	−	0.490598i
$736$	−2.35998	−	4.08761i	−0.0869901	−	0.150671i
$737$	0.131153	−	0.0757211i	0.00483107	−	0.00278922i
$738$	2.96243	−	5.13107i	0.109048	−	0.188877i
$739$	16.3015			0.599659			0.299829	−	0.953993i	$-0.403070\pi$
$739$	16.3015			0.599659			0.299829	+	0.953993i	$0.403070\pi$
$740$	−13.3790	+	2.44986i	−0.491823	+	0.0900586i
$741$	7.72500			0.283785
$742$	−3.92025	+	6.79007i	−0.143917	+	0.249271i
$743$	6.04362	−	3.48928i	0.221719	−	0.128009i	−0.385027	−	0.922905i	$-0.625808\pi$
$743$	6.04362	−	3.48928i	0.221719	−	0.128009i	0.606746	+	0.794896i	$0.292475\pi$
$744$	−0.139504	−	0.241628i	−0.00511447	−	0.00885852i
$745$	−12.7365	+	2.75738i	−0.466629	+	0.101023i
$746$			5.90791i			0.216304i
$747$	12.5267	−	7.23229i	0.458328	−	0.264616i
$748$	1.45810			0.0533133
$749$	−7.22121	+	12.5075i	−0.263857	+	0.457015i
$750$	−6.67339	−	8.97028i	−0.243678	−	0.327548i
$751$	−33.5526			−1.22435			−0.612176	−	0.790721i	$-0.709706\pi$
$751$	−33.5526			−1.22435			−0.612176	+	0.790721i	$0.709706\pi$
$752$	5.35121	+	3.08952i	0.195139	+	0.112663i
$753$	−3.17757	−	5.50371i	−0.115797	−	0.200566i
$754$		−	11.5920i		−	0.422157i
$755$	29.2597	+	32.2512i	1.06487	+	1.17374i
$756$	0.478020	−	0.827955i	0.0173854	−	0.0301124i
$757$	−18.3507	+	31.7843i	−0.666967	+	1.15522i	0.311781	+	0.950154i	$0.399074\pi$
$757$	−18.3507	+	31.7843i	−0.666967	+	1.15522i	−0.978748	+	0.205067i	$0.934259\pi$
$758$	−11.0088	−	19.0677i	−0.399856	−	0.692572i
$759$	−1.03416	+	0.597071i	−0.0375375	+	0.0216723i
$760$	7.44807	−	6.75722i	0.270170	−	0.245110i
$761$	13.3114	−	23.0559i	0.482536	−	0.835777i	−0.517263	−	0.855827i	$-0.673049\pi$
$761$	13.3114	−	23.0559i	0.482536	−	0.835777i	0.999799	+	0.0200493i	$0.00638233\pi$
$762$	−1.22769	+	2.12642i	−0.0444746	+	0.0770322i
$763$	−11.7272			−0.424552
$764$	−12.6094	+	7.28005i	−0.456193	+	0.263383i
$765$	8.65913	+	9.54442i	0.313072	+	0.345079i
$766$	5.96777			0.215624
$767$		−	25.8398i		−	0.933022i
$768$	0.866025	+	0.500000i	0.0312500	+	0.0180422i
$769$			20.2744i			0.731112i	0.930789	+	0.365556i	$0.119121\pi$
$769$			20.2744i			0.731112i	−0.930789	+	0.365556i	$0.880879\pi$
$770$	0.114441	+	0.528606i	0.00412415	+	0.0190496i
$771$		−	22.7040i		−	0.817666i
$772$	−4.71877	−	8.17314i	−0.169832	−	0.294158i
$773$	−18.6843	+	10.7874i	−0.672027	+	0.387995i	−0.796844	−	0.604185i	$-0.793499\pi$
$773$	−18.6843	+	10.7874i	−0.672027	+	0.387995i	0.124817	+	0.992180i	$0.460166\pi$
$774$	−0.637017	−	1.10335i	−0.0228971	−	0.0396590i
$775$	0.576995	+	1.27012i	0.0207263	+	0.0456242i
$776$	−17.8296			−0.640044
$777$	2.74455	+	5.12698i	0.0984602	+	0.183929i
$778$		−	6.88075i		−	0.246687i
$779$	−23.0766	−	13.3233i	−0.826804	−	0.477355i
$780$	−0.812685	−	3.75383i	−0.0290988	−	0.134409i
$781$	1.56228	+	2.70595i	0.0559028	+	0.0968266i
$782$	−13.6012	−	23.5580i	−0.486378	−	0.842432i
$783$	6.74876			0.241181
$784$	−3.04299	−	5.27062i	−0.108678	−	0.188236i
$785$	−3.06460	−	0.983009i	−0.109380	−	0.0350851i
$786$	8.80126	−	15.2442i	0.313930	−	0.543743i
$787$		−	7.75971i		−	0.276604i	−0.990390	−	0.138302i	$-0.955836\pi$
$787$		−	7.75971i		−	0.276604i	0.990390	−	0.138302i	$-0.0441644\pi$
$788$			15.8007i			0.562878i
$789$	−9.09708	+	15.7566i	−0.323865	+	0.560950i
$790$	−1.20693	−	5.57488i	−0.0429408	−	0.198345i
$791$		−	2.16845i		−	0.0771013i
$792$	0.126499	−	0.219103i	0.00449495	−	0.00778548i
$793$	−5.90683	−	3.41031i	−0.209758	−	0.121104i
$794$	−7.19079	−	4.15160i	−0.255191	−	0.147335i
$795$	−17.9228	+	3.88020i	−0.635657	+	0.137617i
$796$	−3.06933	+	1.77208i	−0.108790	+	0.0628097i
$797$	−2.81503	+	4.87578i	−0.0997136	+	0.172709i	−0.911566	−	0.411154i	$-0.865126\pi$
$797$	−2.81503	+	4.87578i	−0.0997136	+	0.172709i	0.811852	+	0.583863i	$0.198459\pi$
$798$	−3.72366	−	2.14985i	−0.131816	−	0.0761040i
$799$	30.8405	+	17.8058i	1.09106	+	0.629923i
$800$	−4.06710	−	2.90838i	−0.143794	−	0.102827i
$801$	6.84497	−	3.95194i	0.241855	−	0.139635i
$802$	−11.6702	−	6.73778i	−0.412088	−	0.237919i
$803$		−	2.71608i		−	0.0958482i
$804$	0.598590			0.0211106
$805$	7.47300	−	6.77984i	0.263389	−	0.238958i
$806$			0.479240i			0.0168805i
$807$	12.1405	−	7.00930i	0.427365	−	0.246739i
$808$	13.2413			0.465829
$809$	15.7762	−	9.10838i	0.554661	−	0.320233i	−0.196339	−	0.980536i	$-0.562905\pi$
$809$	15.7762	−	9.10838i	0.554661	−	0.320233i	0.751000	+	0.660303i	$0.229572\pi$
$810$	2.18544	−	0.473136i	0.0767885	−	0.0166243i
$811$	4.50143	+	7.79671i	0.158067	+	0.273779i	0.934171	−	0.356825i	$-0.116141\pi$
$811$	4.50143	+	7.79671i	0.158067	+	0.273779i	−0.776105	+	0.630604i	$0.782807\pi$
$812$	−3.22604	+	5.58767i	−0.113212	+	0.196089i
$813$			6.79214i			0.238211i
$814$	0.726295	+	1.35676i	0.0254566	+	0.0475544i
$815$	−5.55937	+	17.3318i	−0.194736	+	0.607105i
$816$	4.99114	+	2.88164i	0.174725	+	0.100877i
$817$	−4.96221	+	2.86493i	−0.173606	+	0.100231i
$818$	13.6292	−	7.86885i	0.476536	−	0.275128i
$819$	−1.42214	+	0.821073i	−0.0496936	+	0.0286906i
$820$	−4.04650	+	12.6153i	−0.141310	+	0.440545i
$821$	18.1541	+	31.4439i	0.633584	+	1.09740i	0.986813	+	0.161863i	$0.0517503\pi$
$821$	18.1541	+	31.4439i	0.633584	+	1.09740i	−0.353229	+	0.935537i	$0.614916\pi$
$822$	1.17190			0.0408749
$823$	26.3572	+	15.2173i	0.918754	+	0.530443i	0.883237	−	0.468926i	$-0.155359\pi$
$823$	26.3572	+	15.2173i	0.918754	+	0.530443i	0.0355169	+	0.999369i	$0.488692\pi$
$824$	10.6557			0.371207
$825$	−0.735816	+	1.02897i	−0.0256178	+	0.0358241i
$826$	−7.19117	+	12.4555i	−0.250213	+	0.433382i
$827$	25.9253	+	44.9040i	0.901511	+	1.56146i	0.825533	+	0.564354i	$0.190875\pi$
$827$	25.9253	+	44.9040i	0.901511	+	1.56146i	0.0759784	+	0.997109i	$0.475792\pi$
$828$	−4.71996			−0.164030
$829$	7.90980	+	4.56672i	0.274719	+	0.158609i	0.631030	−	0.775758i	$-0.282632\pi$
$829$	7.90980	+	4.56672i	0.274719	+	0.158609i	−0.356311	+	0.934367i	$0.615966\pi$
$830$	−23.9545	+	21.7326i	−0.831472	+	0.754348i
$831$	8.82954	+	5.09774i	0.306293	+	0.176839i
$832$	−0.858827	−	1.48753i	−0.0297745	−	0.0515709i
$833$	−17.5376	−	30.3760i	−0.607642	−	1.05247i
$834$	−2.87300	−	1.65873i	−0.0994838	−	0.0574370i
$835$	−26.9899	−	29.7493i	−0.934022	−	1.02952i
$836$	−0.985397	−	0.568919i	−0.0340807	−	0.0196765i
$837$	−0.279008			−0.00964393
$838$	−17.2973	−	29.9597i	−0.597524	−	1.03494i
$839$	6.58584	−	11.4070i	0.227369	−	0.393814i	−0.729659	−	0.683811i	$-0.760321\pi$
$839$	6.58584	−	11.4070i	0.227369	−	0.393814i	0.957027	+	0.289997i	$0.0936544\pi$
$840$	−0.652947	+	2.03561i	−0.0225288	+	0.0702353i
$841$	−16.5457			−0.570543
$842$	21.3493	+	12.3260i	0.735746	+	0.424783i
$843$	−18.1484			−0.625063
$844$	9.70996	+	16.8181i	0.334230	+	0.578904i
$845$	6.86363	−	21.3979i	0.236116	−	0.736109i
$846$	5.35121	−	3.08952i	0.183979	−	0.106220i
$847$	−9.05450	+	5.22762i	−0.311116	+	0.179623i
$848$	−7.10229	+	4.10051i	−0.243894	+	0.140812i
$849$	2.12948	+	1.22946i	0.0730835	+	0.0421948i
$850$	−23.4398	−	16.7618i	−0.803979	−	0.574925i
$851$	15.1458	−	24.3904i	0.519191	−	0.836093i
$852$			12.3501i			0.423109i
$853$	15.3279	−	26.5488i	0.524819	−	0.909013i	−0.474763	−	0.880114i	$-0.657466\pi$
$853$	15.3279	−	26.5488i	0.524819	−	0.909013i	0.999582	−	0.0288996i	$-0.00920033\pi$
$854$	1.89817	+	3.28772i	0.0649539	+	0.112503i
$855$	−2.12789	−	9.82882i	−0.0727723	−	0.336139i
$856$	−13.0826	+	7.55326i	−0.447155	+	0.258165i
$857$	−32.2960			−1.10321			−0.551605	−	0.834106i	$-0.685984\pi$
$857$	−32.2960			−1.10321			−0.551605	+	0.834106i	$0.685984\pi$
$858$	−0.376343	+	0.217282i	−0.0128481	+	0.00741788i
$859$			2.86266i			0.0976725i	0.998807	+	0.0488363i	$0.0155513\pi$
$859$			2.86266i			0.0976725i	−0.998807	+	0.0488363i	$0.984449\pi$
$860$	1.91420	+	2.10990i	0.0652735	+	0.0719470i
$861$	5.66440			0.193042
$862$			1.52910i			0.0520814i
$863$	−47.6216	−	27.4943i	−1.62106	−	0.935918i	−0.986638	−	0.162929i	$-0.947906\pi$
$863$	−47.6216	−	27.4943i	−1.62106	−	0.935918i	−0.634419	−	0.772989i	$-0.718761\pi$
$864$	0.866025	−	0.500000i	0.0294628	−	0.0170103i
$865$	−28.7919	−	9.23535i	−0.978954	−	0.314011i
$866$	0.649057	+	0.374733i	0.0220559	+	0.0127340i
$867$	14.0429	+	8.10766i	0.476921	+	0.275351i
$868$	0.133371	−	0.231006i	0.00452692	−	0.00784086i
$869$	−0.558914	+	0.322689i	−0.0189599	+	0.0109465i
$870$	−14.7490	+	3.19308i	−0.500038	+	0.108256i
$871$	−0.890422	−	0.514085i	−0.0301708	−	0.0174191i
$872$	−10.6230	−	6.13320i	−0.359740	−	0.207696i
$873$	−8.91478	+	15.4408i	−0.301719	+	0.522593i
$874$			21.2276i			0.718035i
$875$	4.23697	−	9.81323i	0.143236	−	0.331748i
$876$	5.36778	−	9.29726i	0.181360	−	0.314125i
$877$		−	2.38369i		−	0.0804914i	−0.999190	−	0.0402457i	$-0.987186\pi$
$877$		−	2.38369i		−	0.0804914i	0.999190	−	0.0402457i	$-0.0128141\pi$
$878$			6.53793i			0.220644i
$879$	8.54373	−	14.7982i	0.288173	−	0.499130i
$880$	−0.172790	+	0.538687i	−0.00582477	+	0.0181591i
$881$	−21.4024	−	37.0701i	−0.721066	−	1.24892i	−0.960573	−	0.278028i	$-0.910319\pi$
$881$	−21.4024	−	37.0701i	−0.721066	−	1.24892i	0.239507	−	0.970895i	$-0.423014\pi$
$882$	−6.08599			−0.204926
$883$	−15.5187	−	26.8792i	−0.522246	−	0.904557i	−0.999665	−	0.0258813i	$-0.991761\pi$
$883$	−15.5187	−	26.8792i	−0.522246	−	0.904557i	0.477419	−	0.878676i	$-0.341573\pi$
$884$	−4.94966	−	8.57305i	−0.166475	−	0.288343i
$885$	−32.8770	+	7.11771i	−1.10515	+	0.239259i
$886$	−26.8733	−	15.5153i	−0.902827	−	0.521247i
$887$			12.9751i			0.435661i	0.975987	+	0.217830i	$0.0698979\pi$
$887$			12.9751i			0.435661i	−0.975987	+	0.217830i	$0.930102\pi$
$888$	−0.195218	+	6.07963i	−0.00655108	+	0.204019i
$889$	−2.34744			−0.0787307
$890$	−13.0894	+	11.8753i	−0.438759	+	0.398062i
$891$	−0.126499	−	0.219103i	−0.00423788	−	0.00734022i
$892$	−9.80060	+	5.65838i	−0.328148	+	0.189456i
$893$	−13.8949	−	24.0666i	−0.464974	−	0.805359i
$894$			5.82788i			0.194914i
$895$	2.00520	+	9.26212i	0.0670265	+	0.309598i
$896$			0.956040i			0.0319390i
$897$	7.02110	+	4.05363i	0.234428	+	0.135347i
$898$		−	35.5244i		−	1.18546i
$899$	1.88296			0.0628002
$900$	−4.55228	+	2.06802i	−0.151743	+	0.0689340i
$901$	−40.9325	+	23.6324i	−1.36366	+	0.787308i
$902$	1.49898			0.0499105
$903$	0.609014	−	1.05484i	0.0202667	−	0.0351030i
$904$	1.13408	−	1.96429i	0.0377190	−	0.0653312i
$905$	−14.1907	−	15.6415i	−0.471715	−	0.519942i
$906$	16.8654	−	9.73722i	0.560314	−	0.323498i
$907$	−1.68909	−	2.92558i	−0.0560852	−	0.0971424i	0.836620	−	0.547784i	$-0.184529\pi$
$907$	−1.68909	−	2.92558i	−0.0560852	−	0.0971424i	−0.892705	+	0.450642i	$0.851195\pi$
$908$	−3.47406	+	6.01725i	−0.115291	+	0.199689i
$909$	6.62067	−	11.4673i	0.219594	−	0.380348i
$910$	2.71952	−	2.46727i	0.0901512	−	0.0817892i
$911$			52.6354i			1.74389i	0.489606	+	0.871944i	$0.337140\pi$
$911$			52.6354i			1.74389i	−0.489606	+	0.871944i	$0.662860\pi$
$912$	−2.24871	−	3.89488i	−0.0744621	−	0.128972i
$913$	3.16923	+	1.82976i	0.104886	+	0.0605561i
$914$	−24.9288			−0.824573
$915$	−2.71200	+	8.45488i	−0.0896561	+	0.279510i
$916$	10.4066	−	18.0248i	0.343845	−	0.595557i
$917$	16.8287			0.555733
$918$	4.99114	−	2.88164i	0.164732	−	0.0951082i
$919$			41.4110i			1.36602i	0.730408	+	0.683012i	$0.239330\pi$
$919$			41.4110i			1.36602i	−0.730408	+	0.683012i	$0.760670\pi$
$920$	10.3152	−	2.23319i	0.340082	−	0.0736260i
$921$	9.18093	+	15.9018i	0.302522	+	0.523983i
$922$	25.5860	−	14.7721i	0.842629	−	0.486492i
$923$	10.6066	−	18.3712i	0.349122	−	0.604696i
$924$	0.241876			0.00795715
$925$	3.92121	−	30.1600i	0.128929	−	0.991654i
$926$	20.4607			0.672379
$927$	5.32783	−	9.22806i	0.174989	−	0.303089i
$928$	−5.84460	+	3.37438i	−0.191858	+	0.110769i
$929$	−27.8990	−	48.3224i	−0.915335	−	1.58541i	−0.806410	−	0.591357i	$-0.798592\pi$
$929$	−27.8990	−	48.3224i	−0.915335	−	1.58541i	−0.108926	−	0.994050i	$-0.534741\pi$
$930$	0.609755	−	0.132009i	0.0199947	−	0.00432874i
$931$			27.3712i			0.897055i
$932$	−1.39477	+	0.805271i	−0.0456872	+	0.0263775i
$933$	9.55013			0.312657
$934$	7.43131	−	12.8714i	0.243160	−	0.421165i
$935$	−0.995839	+	3.10460i	−0.0325674	+	0.101531i
$936$	−1.71765			−0.0561433
$937$	5.82792	+	3.36475i	0.190390	+	0.109922i	0.592165	−	0.805817i	$-0.298273\pi$
$937$	5.82792	+	3.36475i	0.190390	+	0.109922i	−0.401775	+	0.915738i	$0.631607\pi$
$938$	0.286138	+	0.495605i	0.00934273	+	0.0161821i
$939$		−	4.80927i		−	0.156944i
$940$	−10.2330	+	9.28382i	−0.333763	+	0.302805i
$941$	−3.47951	+	6.02669i	−0.113429	+	0.196465i	−0.917151	−	0.398541i	$-0.869517\pi$
$941$	−3.47951	+	6.02669i	−0.113429	+	0.196465i	0.803722	+	0.595005i	$0.202850\pi$
$942$	−0.719657	+	1.24648i	−0.0234477	+	0.0406126i
$943$	−13.9825	−	24.2185i	−0.455334	−	0.788662i
$944$	−13.0282	+	7.52184i	−0.424032	+	0.244815i
$945$	1.43642	+	1.58328i	0.0467267	+	0.0515040i
$946$	0.161164	−	0.279145i	0.00523990	−	0.00907578i
$947$	−1.67107	+	2.89439i	−0.0543026	+	0.0940549i	−0.891899	−	0.452235i	$-0.850627\pi$
$947$	−1.67107	+	2.89439i	−0.0543026	+	0.0940549i	0.837596	+	0.546290i	$0.183960\pi$
$948$	−2.55092			−0.0828501
$949$	−15.9695	+	9.21998i	−0.518391	+	0.299293i
$950$	9.30075	+	20.4735i	0.301756	+	0.664248i
$951$	−14.6547			−0.475212
$952$			5.50992i			0.178577i
$953$	−45.9834	−	26.5485i	−1.48955	−	0.859991i	−0.489619	−	0.871936i	$-0.662864\pi$
$953$	−45.9834	−	26.5485i	−1.48955	−	0.859991i	−0.999929	+	0.0119456i	$0.996197\pi$
$954$			8.20102i			0.265518i
$955$	−6.88891	−	31.8202i	−0.222920	−	1.02968i
$956$		−	8.33488i		−	0.269569i
$957$	0.853712	+	1.47867i	0.0275966	+	0.0477987i
$958$	−12.3586	+	7.13524i	−0.399288	+	0.230529i
$959$	0.560194	+	0.970284i	0.0180896	+	0.0313321i
$960$	−1.65608	+	1.50247i	−0.0534497	+	0.0484919i
$961$	30.9222			0.997489
$962$	5.51174	−	8.87599i	0.177706	−	0.286173i
$963$			15.1065i			0.486801i
$964$	20.3057	+	11.7235i	0.654002	+	0.377588i
$965$	20.6252	−	4.46524i	0.663947	−	0.143741i
$966$	−2.25624	−	3.90791i	−0.0725932	−	0.125735i
$967$	−18.9926	−	32.8961i	−0.610760	−	1.05787i	−0.991113	−	0.133026i	$-0.957531\pi$
$967$	−18.9926	−	32.8961i	−0.610760	−	1.05787i	0.380352	−	0.924842i	$-0.375803\pi$
$968$	−10.9360			−0.351496
$969$	−12.9599	−	22.4472i	−0.416332	−	0.721109i
$970$	12.1771	−	37.9629i	0.390982	−	1.21892i
$971$	12.6992	−	21.9956i	0.407535	−	0.705872i	−0.587078	−	0.809531i	$-0.699722\pi$
$971$	12.6992	−	21.9956i	0.407535	−	0.705872i	0.994613	+	0.103659i	$0.0330551\pi$
$972$		−	1.00000i		−	0.0320750i
$973$		−	3.17162i		−	0.101677i
$974$	−4.99992	+	8.66011i	−0.160208	+	0.277488i
$975$	8.54774	+	0.833376i	0.273747	+	0.0266894i
$976$			3.97089i			0.127105i
$977$	−17.3271	+	30.0113i	−0.554342	+	0.960148i	0.443613	+	0.896219i	$0.353697\pi$
$977$	−17.3271	+	30.0113i	−0.554342	+	0.960148i	−0.997954	+	0.0639293i	$0.979637\pi$
$978$	7.04943	+	4.06999i	0.225416	+	0.130144i
$979$	1.73176	+	0.999835i	0.0553474	+	0.0319549i
$980$	13.3006	−	2.87950i	0.424871	−	0.0919824i
$981$	−10.6230	+	6.13320i	−0.339167	+	0.195818i
$982$	−1.46029	+	2.52930i	−0.0465997	+	0.0807131i
$983$	16.3507	+	9.44010i	0.521508	+	0.301092i	0.737551	−	0.675291i	$-0.235982\pi$
$983$	16.3507	+	9.44010i	0.521508	+	0.301092i	−0.216044	+	0.976384i	$0.569315\pi$
$984$	5.13107	+	2.96243i	0.163573	+	0.0944387i
$985$	−33.6432	−	10.7915i	−1.07196	−	0.343844i
$986$	−33.6840	+	19.4475i	−1.07272	+	0.619334i
$987$	5.11597	+	2.95371i	0.162843	+	0.0940176i
$988$			7.72500i			0.245765i
$989$	−6.01340			−0.191215
$990$	0.380122	+	0.418985i	0.0120811	+	0.0133162i
$991$		−	35.4075i		−	1.12475i	−0.826881	−	0.562377i	$-0.809887\pi$
$991$		−	35.4075i		−	1.12475i	0.826881	−	0.562377i	$-0.190113\pi$
$992$	0.241628	−	0.139504i	0.00767170	−	0.00442926i
$993$	9.90073			0.314190
$994$	−10.2254	+	5.90361i	−0.324329	+	0.187251i
$995$	−1.67687	−	7.74554i	−0.0531604	−	0.245550i
$996$	7.23229	+	12.5267i	0.229164	+	0.396924i
$997$	24.8163	−	42.9831i	0.785940	−	1.36129i	−0.142496	−	0.989795i	$-0.545513\pi$
$997$	24.8163	−	42.9831i	0.785940	−	1.36129i	0.928436	−	0.371492i	$-0.121154\pi$
$998$		−	18.1416i		−	0.574262i
$999$	5.16750	+	3.20888i	0.163493	+	0.101524i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.ba.a.619.4	yes	36
5.4	even	2		1110.2.ba.b.619.15	yes	36
37.11	even	6		1110.2.ba.b.529.15	yes	36
185.159	even	6	inner	1110.2.ba.a.529.4	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.ba.a.529.4	✓	36	185.159	even	6	inner
1110.2.ba.a.619.4	yes	36	1.1	even	1	trivial
1110.2.ba.b.529.15	yes	36	37.11	even	6
1110.2.ba.b.619.15	yes	36	5.4	even	2

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

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.18544 - 0.473136i) q^{5} -1.00000i q^{6} +(0.827955 - 0.478020i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.18544 - 0.473136i) q^{5} -1.00000i q^{6} +(0.827955 - 0.478020i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(-0.682971 + 2.12921i) q^{10} +0.252998 q^{11} +(0.866025 + 0.500000i) q^{12} +(-0.858827 - 1.48753i) q^{13} +0.956040i q^{14} +(-1.65608 + 1.50247i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.88164 + 4.99114i) q^{17} +(0.500000 + 0.866025i) q^{18} +(3.89488 - 2.24871i) q^{19} +(-1.50247 - 1.65608i) q^{20} +(-0.478020 + 0.827955i) q^{21} +(-0.126499 + 0.219103i) q^{22} +4.71996 q^{23} +(-0.866025 + 0.500000i) q^{24} +(4.55228 - 2.06802i) q^{25} +1.71765 q^{26} +1.00000i q^{27} +(-0.827955 - 0.478020i) q^{28} -6.74876i q^{29} +(-0.473136 - 2.18544i) q^{30} +0.279008i q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.219103 + 0.126499i) q^{33} +(-2.88164 - 4.99114i) q^{34} +(1.58328 - 1.43642i) q^{35} -1.00000 q^{36} +(3.20888 - 5.16750i) q^{37} +4.49741i q^{38} +(1.48753 + 0.858827i) q^{39} +(2.18544 - 0.473136i) q^{40} +(-2.96243 - 5.13107i) q^{41} +(-0.478020 - 0.827955i) q^{42} -1.27403 q^{43} +(-0.126499 - 0.219103i) q^{44} +(0.682971 - 2.12921i) q^{45} +(-2.35998 + 4.08761i) q^{46} -6.17905i q^{47} -1.00000i q^{48} +(-3.04299 + 5.27062i) q^{49} +(-0.485183 + 4.97640i) q^{50} -5.76327i q^{51} +(-0.858827 + 1.48753i) q^{52} +(7.10229 + 4.10051i) q^{53} +(-0.866025 - 0.500000i) q^{54} +(0.552912 - 0.119703i) q^{55} +(0.827955 - 0.478020i) q^{56} +(-2.24871 + 3.89488i) q^{57} +(5.84460 + 3.37438i) q^{58} +(13.0282 + 7.52184i) q^{59} +(2.12921 + 0.682971i) q^{60} +(3.43889 - 1.98545i) q^{61} +(-0.241628 - 0.139504i) q^{62} -0.956040i q^{63} +1.00000 q^{64} +(-2.58072 - 2.84457i) q^{65} -0.252998i q^{66} +(0.518394 - 0.299295i) q^{67} +5.76327 q^{68} +(-4.08761 + 2.35998i) q^{69} +(0.452337 + 2.08937i) q^{70} +(6.17507 + 10.6955i) q^{71} +(0.500000 - 0.866025i) q^{72} -10.7356i q^{73} +(2.87075 + 5.36272i) q^{74} +(-2.90838 + 4.06710i) q^{75} +(-3.89488 - 2.24871i) q^{76} +(0.209471 - 0.120938i) q^{77} +(-1.48753 + 0.858827i) q^{78} +(-2.20916 + 1.27546i) q^{79} +(-0.682971 + 2.12921i) q^{80} +(-0.500000 - 0.866025i) q^{81} +5.92485 q^{82} +(12.5267 + 7.23229i) q^{83} +0.956040 q^{84} +(-3.93615 + 12.2712i) q^{85} +(0.637017 - 1.10335i) q^{86} +(3.37438 + 5.84460i) q^{87} +0.252998 q^{88} +(6.84497 + 3.95194i) q^{89} +(1.50247 + 1.65608i) q^{90} +(-1.42214 - 0.821073i) q^{91} +(-2.35998 - 4.08761i) q^{92} +(-0.139504 - 0.241628i) q^{93} +(5.35121 + 3.08952i) q^{94} +(7.44807 - 6.75722i) q^{95} +(0.866025 + 0.500000i) q^{96} -17.8296 q^{97} +(-3.04299 - 5.27062i) q^{98} +(0.126499 - 0.219103i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 18 q^{2} - 18 q^{4} + 2 q^{5} + 36 q^{8} + 18 q^{9}+O(q^{10}) \) 36 * q - 18 * q^2 - 18 * q^4 + 2 * q^5 + 36 * q^8 + 18 * q^9	\( 36 q - 18 q^{2} - 18 q^{4} + 2 q^{5} + 36 q^{8} + 18 q^{9} + 2 q^{10} + 4 q^{11} - 14 q^{13} - 2 q^{15} - 18 q^{16} + 18 q^{18} + 6 q^{19} - 4 q^{20} - 2 q^{22} - 20 q^{23} + 4 q^{25} + 28 q^{26} - 2 q^{30} - 18 q^{32} - 6 q^{33} - 40 q^{35} - 36 q^{36} + 20 q^{37} + 6 q^{39} + 2 q^{40} + 10 q^{41} - 2 q^{44} - 2 q^{45} + 10 q^{46} + 10 q^{49} - 2 q^{50} - 14 q^{52} - 12 q^{53} + 56 q^{55} + 8 q^{57} + 30 q^{58} + 18 q^{59} + 4 q^{60} - 6 q^{61} - 12 q^{62} + 36 q^{64} + 40 q^{65} + 36 q^{67} + 12 q^{69} + 20 q^{70} - 24 q^{71} + 18 q^{72} - 34 q^{74} + 8 q^{75} - 6 q^{76} - 24 q^{77} - 6 q^{78} + 2 q^{80} - 18 q^{81} - 20 q^{82} + 36 q^{83} + 26 q^{85} - 10 q^{87} + 4 q^{88} + 4 q^{90} - 36 q^{91} + 10 q^{92} + 12 q^{93} + 12 q^{94} - 30 q^{95} + 52 q^{97} + 10 q^{98} + 2 q^{99}+O(q^{100}) \) 36 * q - 18 * q^2 - 18 * q^4 + 2 * q^5 + 36 * q^8 + 18 * q^9 + 2 * q^10 + 4 * q^11 - 14 * q^13 - 2 * q^15 - 18 * q^16 + 18 * q^18 + 6 * q^19 - 4 * q^20 - 2 * q^22 - 20 * q^23 + 4 * q^25 + 28 * q^26 - 2 * q^30 - 18 * q^32 - 6 * q^33 - 40 * q^35 - 36 * q^36 + 20 * q^37 + 6 * q^39 + 2 * q^40 + 10 * q^41 - 2 * q^44 - 2 * q^45 + 10 * q^46 + 10 * q^49 - 2 * q^50 - 14 * q^52 - 12 * q^53 + 56 * q^55 + 8 * q^57 + 30 * q^58 + 18 * q^59 + 4 * q^60 - 6 * q^61 - 12 * q^62 + 36 * q^64 + 40 * q^65 + 36 * q^67 + 12 * q^69 + 20 * q^70 - 24 * q^71 + 18 * q^72 - 34 * q^74 + 8 * q^75 - 6 * q^76 - 24 * q^77 - 6 * q^78 + 2 * q^80 - 18 * q^81 - 20 * q^82 + 36 * q^83 + 26 * q^85 - 10 * q^87 + 4 * q^88 + 4 * q^90 - 36 * q^91 + 10 * q^92 + 12 * q^93 + 12 * q^94 - 30 * q^95 + 52 * q^97 + 10 * q^98 + 2 * q^99

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