LMFDB - Embedded newform 931.2.x.a.765.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [931,2,Mod(226,931)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(931, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([6, 10]))

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

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

chi := DirichletCharacter("931.226");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 931 = 7^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	931.x (of order $9$, degree $6$, not 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:	$7.43407242818$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 19)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			765.1
Root			$-0.173648 + 0.984808i$ of defining polynomial
Character	$\chi$	$=$	931.765
Dual form			931.2.x.a.802.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.152704 - 0.866025i) q^{2} +(-0.500000 + 0.181985i) q^{3} +(1.15270 + 0.419550i) q^{4} +(2.37939 - 0.866025i) q^{5} +(0.0812519 + 0.460802i) q^{6} +(1.41875 - 2.45734i) q^{8} +(-2.08125 + 1.74638i) q^{9} +O(q^{10})$	\(q+(0.152704 - 0.866025i) q^{2} +(-0.500000 + 0.181985i) q^{3} +(1.15270 + 0.419550i) q^{4} +(2.37939 - 0.866025i) q^{5} +(0.0812519 + 0.460802i) q^{6} +(1.41875 - 2.45734i) q^{8} +(-2.08125 + 1.74638i) q^{9} +(-0.386659 - 2.19285i) q^{10} +3.41147 q^{11} -0.652704 q^{12} +(-0.918748 - 5.21048i) q^{13} +(-1.03209 + 0.866025i) q^{15} +(-0.0320889 - 0.0269258i) q^{16} +(1.26604 + 1.06234i) q^{17} +(1.19459 + 2.06910i) q^{18} +(-1.81908 - 3.96118i) q^{19} +3.10607 q^{20} +(0.520945 - 2.95442i) q^{22} +(0.305407 + 1.73205i) q^{23} +(-0.262174 + 1.48686i) q^{24} +(1.08125 - 0.907278i) q^{25} -4.65270 q^{26} +(1.52094 - 2.63435i) q^{27} +(3.25877 + 1.18610i) q^{29} +(0.592396 + 1.02606i) q^{30} +(-0.971782 + 1.68317i) q^{31} +(4.31908 - 3.62414i) q^{32} +(-1.70574 + 0.620838i) q^{33} +(1.11334 - 0.934204i) q^{34} +(-3.13176 + 1.13987i) q^{36} +(0.418748 - 0.725293i) q^{37} +(-3.70826 + 0.970481i) q^{38} +(1.40760 + 2.43804i) q^{39} +(1.24763 - 7.07564i) q^{40} +(-0.779715 + 4.42198i) q^{41} +(3.67752 + 3.08580i) q^{43} +(3.93242 + 1.43128i) q^{44} +(-3.43969 + 5.95772i) q^{45} +1.54664 q^{46} +(0.549163 - 0.460802i) q^{47} +(0.0209445 + 0.00762319i) q^{48} +(-0.620615 - 1.07494i) q^{50} +(-0.826352 - 0.300767i) q^{51} +(1.12701 - 6.39160i) q^{52} +(5.73783 + 2.08840i) q^{53} +(-2.04916 - 1.71945i) q^{54} +(8.11721 - 2.95442i) q^{55} +(1.63041 + 1.64955i) q^{57} +(1.52481 - 2.64106i) q^{58} +(-8.24170 - 6.91560i) q^{59} +(-1.55303 + 0.565258i) q^{60} +(0.762174 + 4.32250i) q^{61} +(1.30928 + 1.09861i) q^{62} +(-2.52094 - 4.36640i) q^{64} +(-6.69846 - 11.6021i) q^{65} +(0.277189 + 1.57202i) q^{66} +(2.46791 + 13.9962i) q^{67} +(1.01367 + 1.75573i) q^{68} +(-0.467911 - 0.810446i) q^{69} +(-10.5398 - 8.84397i) q^{71} +(1.33868 + 7.59202i) q^{72} +(7.06418 - 2.57115i) q^{73} +(-0.564178 - 0.473401i) q^{74} +(-0.375515 + 0.650411i) q^{75} +(-0.434945 - 5.32926i) q^{76} +(2.32635 - 0.846723i) q^{78} +(-5.33409 - 4.47584i) q^{79} +(-0.0996702 - 0.0362770i) q^{80} +(1.13429 - 6.43285i) q^{81} +(3.71048 + 1.35051i) q^{82} +(-1.25624 - 2.17588i) q^{83} +(3.93242 + 1.43128i) q^{85} +(3.23396 - 2.71361i) q^{86} -1.84524 q^{87} +(4.84002 - 8.38316i) q^{88} +(2.14543 + 0.780873i) q^{89} +(4.63429 + 3.88863i) q^{90} +(-0.374638 + 2.12467i) q^{92} +(0.179578 - 1.01844i) q^{93} +(-0.315207 - 0.545955i) q^{94} +(-7.75877 - 7.84981i) q^{95} +(-1.50000 + 2.59808i) q^{96} +(1.71301 - 0.623485i) q^{97} +(-7.10014 + 5.95772i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - 3 q^{3} + 9 q^{4} + 3 q^{5} + 3 q^{6} + 6 q^{8} - 15 q^{9}+O(q^{10}) $ 6 * q + 3 * q^2 - 3 * q^3 + 9 * q^4 + 3 * q^5 + 3 * q^6 + 6 * q^8 - 15 * q^9	$ 6 q + 3 q^{2} - 3 q^{3} + 9 q^{4} + 3 q^{5} + 3 q^{6} + 6 q^{8} - 15 q^{9} - 9 q^{10} - 6 q^{12} - 3 q^{13} + 3 q^{15} + 9 q^{16} + 3 q^{17} + 3 q^{18} + 6 q^{19} - 6 q^{20} + 6 q^{23} - 21 q^{24} + 9 q^{25} - 30 q^{26} + 6 q^{27} - 3 q^{29} + 9 q^{31} + 9 q^{32} - 24 q^{36} + 3 q^{38} + 12 q^{39} - 9 q^{40} + 21 q^{41} - 3 q^{43} - 15 q^{45} + 36 q^{46} + 15 q^{47} - 3 q^{48} - 15 q^{50} - 6 q^{51} - 21 q^{52} + 15 q^{53} - 24 q^{54} + 18 q^{55} + 24 q^{57} - 18 q^{58} - 6 q^{59} + 3 q^{60} + 24 q^{61} - 12 q^{62} - 12 q^{64} - 12 q^{65} - 9 q^{66} + 24 q^{67} - 15 q^{68} - 12 q^{69} - 6 q^{71} - 3 q^{72} + 24 q^{73} + 15 q^{74} - 15 q^{75} + 36 q^{76} + 15 q^{78} + 15 q^{79} - 15 q^{80} - 3 q^{81} + 45 q^{82} + 24 q^{86} + 42 q^{87} + 9 q^{88} - 3 q^{89} + 18 q^{90} + 42 q^{92} + 27 q^{93} - 9 q^{94} - 24 q^{95} - 9 q^{96} + 18 q^{97} + 9 q^{99}+O(q^{100}) $ 6 * q + 3 * q^2 - 3 * q^3 + 9 * q^4 + 3 * q^5 + 3 * q^6 + 6 * q^8 - 15 * q^9 - 9 * q^10 - 6 * q^12 - 3 * q^13 + 3 * q^15 + 9 * q^16 + 3 * q^17 + 3 * q^18 + 6 * q^19 - 6 * q^20 + 6 * q^23 - 21 * q^24 + 9 * q^25 - 30 * q^26 + 6 * q^27 - 3 * q^29 + 9 * q^31 + 9 * q^32 - 24 * q^36 + 3 * q^38 + 12 * q^39 - 9 * q^40 + 21 * q^41 - 3 * q^43 - 15 * q^45 + 36 * q^46 + 15 * q^47 - 3 * q^48 - 15 * q^50 - 6 * q^51 - 21 * q^52 + 15 * q^53 - 24 * q^54 + 18 * q^55 + 24 * q^57 - 18 * q^58 - 6 * q^59 + 3 * q^60 + 24 * q^61 - 12 * q^62 - 12 * q^64 - 12 * q^65 - 9 * q^66 + 24 * q^67 - 15 * q^68 - 12 * q^69 - 6 * q^71 - 3 * q^72 + 24 * q^73 + 15 * q^74 - 15 * q^75 + 36 * q^76 + 15 * q^78 + 15 * q^79 - 15 * q^80 - 3 * q^81 + 45 * q^82 + 24 * q^86 + 42 * q^87 + 9 * q^88 - 3 * q^89 + 18 * q^90 + 42 * q^92 + 27 * q^93 - 9 * q^94 - 24 * q^95 - 9 * q^96 + 18 * q^97 + 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/931\mathbb{Z}\right)^\times$.

$n$	$248$	$344$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{8}{9}\right)$

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 $

$2$	0.152704	−	0.866025i	0.107978	−	0.612372i	−0.882011	−	0.471228i	$-0.843811\pi$
$2$	0.152704	−	0.866025i	0.107978	−	0.612372i	0.989989	−	0.141144i	$-0.0450781\pi$
$3$	−0.500000	+	0.181985i	−0.288675	+	0.105069i	−0.482299	−	0.876007i	$-0.660198\pi$
$3$	−0.500000	+	0.181985i	−0.288675	+	0.105069i	0.193624	+	0.981076i	$0.437976\pi$
$4$	1.15270	+	0.419550i	0.576352	+	0.209775i
$5$	2.37939	−	0.866025i	1.06409	−	0.387298i	0.250129	−	0.968213i	$-0.419527\pi$
$5$	2.37939	−	0.866025i	1.06409	−	0.387298i	0.813965	+	0.580914i	$0.197305\pi$
$6$	0.0812519	+	0.460802i	0.0331710	+	0.188122i
$7$		0			0
$7$		0			0
$8$	1.41875	−	2.45734i	0.501603	−	0.868802i
$9$	−2.08125	+	1.74638i	−0.693751	+	0.582126i
$10$	−0.386659	−	2.19285i	−0.122272	−	0.693441i
$11$	3.41147			1.02860			0.514299	−	0.857611i	$-0.328052\pi$
$11$	3.41147			1.02860			0.514299	+	0.857611i	$0.328052\pi$
$12$	−0.652704			−0.188419
$13$	−0.918748	−	5.21048i	−0.254815	−	1.44513i	−0.796547	−	0.604576i	$-0.793343\pi$
$13$	−0.918748	−	5.21048i	−0.254815	−	1.44513i	0.541733	−	0.840551i	$-0.317769\pi$
$14$		0			0
$15$	−1.03209	+	0.866025i	−0.266484	+	0.223607i
$16$	−0.0320889	−	0.0269258i	−0.00802222	−	0.00673144i
$17$	1.26604	+	1.06234i	0.307061	+	0.257655i	0.783276	−	0.621674i	$-0.213547\pi$
$17$	1.26604	+	1.06234i	0.307061	+	0.257655i	−0.476215	+	0.879329i	$0.657992\pi$
$18$	1.19459	+	2.06910i	0.281568	+	0.487690i
$19$	−1.81908	−	3.96118i	−0.417325	−	0.908757i
$19$	−1.81908	−	3.96118i	−0.417325	−	0.908757i
$20$	3.10607			0.694538
$21$		0			0
$22$	0.520945	−	2.95442i	0.111066	−	0.629885i
$23$	0.305407	+	1.73205i	0.0636818	+	0.361158i	0.999951	+	0.00987481i	$0.00314330\pi$
$23$	0.305407	+	1.73205i	0.0636818	+	0.361158i	−0.936269	+	0.351283i	$0.885746\pi$
$24$	−0.262174	+	1.48686i	−0.0535161	+	0.303505i
$25$	1.08125	−	0.907278i	0.216250	−	0.181456i
$26$	−4.65270			−0.912470
$27$	1.52094	−	2.63435i	0.292706	−	0.506982i
$28$		0			0
$29$	3.25877	+	1.18610i	0.605138	+	0.220252i	0.626375	−	0.779522i	$-0.284538\pi$
$29$	3.25877	+	1.18610i	0.605138	+	0.220252i	−0.0212363	+	0.999774i	$0.506760\pi$
$30$	0.592396	+	1.02606i	0.108156	+	0.187332i
$31$	−0.971782	+	1.68317i	−0.174537	+	0.302307i	−0.940001	−	0.341172i	$-0.889176\pi$
$31$	−0.971782	+	1.68317i	−0.174537	+	0.302307i	0.765464	+	0.643479i	$0.222510\pi$
$32$	4.31908	−	3.62414i	0.763512	−	0.640663i
$33$	−1.70574	+	0.620838i	−0.296931	+	0.108074i
$34$	1.11334	−	0.934204i	0.190936	−	0.160215i
$35$		0			0
$36$	−3.13176	+	1.13987i	−0.521960	+	0.189978i
$37$	0.418748	−	0.725293i	0.0688418	−	0.119237i	−0.829550	−	0.558433i	$-0.811403\pi$
$37$	0.418748	−	0.725293i	0.0688418	−	0.119237i	0.898392	+	0.439195i	$0.144736\pi$
$38$	−3.70826	+	0.970481i	−0.601560	+	0.157433i
$39$	1.40760	+	2.43804i	0.225397	+	0.390399i
$40$	1.24763	−	7.07564i	0.197267	−	1.11876i
$41$	−0.779715	+	4.42198i	−0.121771	+	0.690598i	0.861402	+	0.507923i	$0.169587\pi$
$41$	−0.779715	+	4.42198i	−0.121771	+	0.690598i	−0.983173	+	0.182675i	$0.941524\pi$
$42$		0			0
$43$	3.67752	+	3.08580i	0.560816	+	0.470581i	0.878584	−	0.477588i	$-0.158489\pi$
$43$	3.67752	+	3.08580i	0.560816	+	0.470581i	−0.317768	+	0.948169i	$0.602933\pi$
$44$	3.93242	+	1.43128i	0.592834	+	0.215774i
$45$	−3.43969	+	5.95772i	−0.512759	+	0.888125i
$46$	1.54664			0.228039
$47$	0.549163	−	0.460802i	0.0801037	−	0.0672150i	−0.601857	−	0.798604i	$-0.705572\pi$
$47$	0.549163	−	0.460802i	0.0801037	−	0.0672150i	0.681960	+	0.731389i	$0.261128\pi$
$48$	0.0209445	+	0.00762319i	0.00302308	+	0.00110031i
$49$		0			0
$50$	−0.620615	−	1.07494i	−0.0877682	−	0.152019i
$51$	−0.826352	−	0.300767i	−0.115712	−	0.0421159i
$52$	1.12701	−	6.39160i	0.156288	−	0.886355i
$53$	5.73783	+	2.08840i	0.788151	+	0.286864i	0.704567	−	0.709637i	$-0.251141\pi$
$53$	5.73783	+	2.08840i	0.788151	+	0.286864i	0.0835838	+	0.996501i	$0.473363\pi$
$54$	−2.04916	−	1.71945i	−0.278856	−	0.233988i
$55$	8.11721	−	2.95442i	1.09452	−	0.398374i
$56$		0			0
$57$	1.63041	+	1.64955i	0.215954	+	0.218488i
$58$	1.52481	−	2.64106i	0.200218	−	0.346788i
$59$	−8.24170	−	6.91560i	−1.07298	−	0.900335i	−0.0776586	−	0.996980i	$-0.524744\pi$
$59$	−8.24170	−	6.91560i	−1.07298	−	0.900335i	−0.995319	+	0.0966450i	$0.969189\pi$
$60$	−1.55303	+	0.565258i	−0.200496	+	0.0729745i
$61$	0.762174	+	4.32250i	0.0975864	+	0.553440i	0.993924	+	0.110068i	$0.0351068\pi$
$61$	0.762174	+	4.32250i	0.0975864	+	0.553440i	−0.896338	+	0.443372i	$0.853782\pi$
$62$	1.30928	+	1.09861i	0.166278	+	0.139524i
$63$		0			0
$64$	−2.52094	−	4.36640i	−0.315118	−	0.545801i
$65$	−6.69846	−	11.6021i	−0.830842	−	1.43906i
$66$	0.277189	+	1.57202i	0.0341196	+	0.193502i
$67$	2.46791	+	13.9962i	0.301503	+	1.70991i	0.639524	+	0.768772i	$0.279132\pi$
$67$	2.46791	+	13.9962i	0.301503	+	1.70991i	−0.338020	+	0.941139i	$0.609757\pi$
$68$	1.01367	+	1.75573i	0.122926	+	0.212913i
$69$	−0.467911	−	0.810446i	−0.0563299	−	0.0975662i
$70$		0			0
$71$	−10.5398	−	8.84397i	−1.25085	−	1.04959i	−0.996595	−	0.0824479i	$-0.973726\pi$
$71$	−10.5398	−	8.84397i	−1.25085	−	1.04959i	−0.254252	−	0.967138i	$-0.581829\pi$
$72$	1.33868	+	7.59202i	0.157765	+	0.894728i
$73$	7.06418	−	2.57115i	0.826799	−	0.300930i	0.106255	−	0.994339i	$-0.466114\pi$
$73$	7.06418	−	2.57115i	0.826799	−	0.300930i	0.720545	+	0.693409i	$0.243892\pi$
$74$	−0.564178	−	0.473401i	−0.0655843	−	0.0550318i
$75$	−0.375515	+	0.650411i	−0.0433607	+	0.0751030i
$76$	−0.434945	−	5.32926i	−0.0498916	−	0.611308i
$77$		0			0
$78$	2.32635	−	0.846723i	0.263407	−	0.0958725i
$79$	−5.33409	−	4.47584i	−0.600132	−	0.503571i	0.291356	−	0.956615i	$-0.405894\pi$
$79$	−5.33409	−	4.47584i	−0.600132	−	0.503571i	−0.891488	+	0.453044i	$0.850338\pi$
$80$	−0.0996702	−	0.0362770i	−0.0111435	−	0.00405589i
$81$	1.13429	−	6.43285i	0.126032	−	0.714761i
$82$	3.71048	+	1.35051i	0.409754	+	0.149138i
$83$	−1.25624	−	2.17588i	−0.137891	−	0.238834i	0.788807	−	0.614641i	$-0.210699\pi$
$83$	−1.25624	−	2.17588i	−0.137891	−	0.238834i	−0.926698	+	0.375807i	$0.877366\pi$
$84$		0			0
$85$	3.93242	+	1.43128i	0.426531	+	0.155244i
$86$	3.23396	−	2.71361i	0.348726	−	0.292616i
$87$	−1.84524			−0.197830
$88$	4.84002	−	8.38316i	0.515948	−	0.893648i
$89$	2.14543	+	0.780873i	0.227415	+	0.0827723i	0.453214	−	0.891401i	$-0.350277\pi$
$89$	2.14543	+	0.780873i	0.227415	+	0.0827723i	−0.225799	+	0.974174i	$0.572499\pi$
$90$	4.63429	+	3.88863i	0.488497	+	0.409897i
$91$		0			0
$92$	−0.374638	+	2.12467i	−0.0390587	+	0.221513i
$93$	0.179578	−	1.01844i	0.0186214	−	0.105607i
$94$	−0.315207	−	0.545955i	−0.0325112	−	0.0563110i
$95$	−7.75877	−	7.84981i	−0.796033	−	0.805373i
$96$	−1.50000	+	2.59808i	−0.153093	+	0.265165i
$97$	1.71301	−	0.623485i	0.173930	−	0.0633053i	−0.253587	−	0.967312i	$-0.581611\pi$
$97$	1.71301	−	0.623485i	0.173930	−	0.0633053i	0.427517	+	0.904007i	$0.359388\pi$
$98$		0			0
$99$	−7.10014	+	5.95772i	−0.713591	+	0.598774i
$100$	1.62701	−	0.592184i	0.162701	−	0.0592184i
$101$	−6.06805	+	5.09170i	−0.603793	+	0.506643i	−0.892662	−	0.450726i	$-0.851165\pi$
$101$	−6.06805	+	5.09170i	−0.603793	+	0.506643i	0.288869	+	0.957369i	$0.406721\pi$
$102$	−0.386659	+	0.669713i	−0.0382850	+	0.0663115i
$103$	0.00727396	+	0.0125989i	0.000716725	+	0.00124140i	0.866384	−	0.499379i	$-0.166439\pi$
$103$	0.00727396	+	0.0125989i	0.000716725	+	0.00124140i	−0.865667	+	0.500621i	$0.833105\pi$
$104$	−14.1074	−	5.13468i	−1.38335	−	0.503497i
$105$		0			0
$106$	2.68479	−	4.65020i	0.260770	−	0.451667i
$107$	−3.55438			−0.343615			−0.171807	−	0.985131i	$-0.554961\pi$
$107$	−3.55438			−0.343615			−0.171807	+	0.985131i	$0.554961\pi$
$108$	2.85844	−	2.39852i	0.275054	−	0.230797i
$109$	1.27972	−	7.25762i	0.122574	−	0.695154i	−0.860144	−	0.510050i	$-0.829627\pi$
$109$	1.27972	−	7.25762i	0.122574	−	0.695154i	0.982719	−	0.185104i	$-0.0592622\pi$
$110$	−1.31908	−	7.48086i	−0.125769	−	0.713272i
$111$	−0.0773815	+	0.438852i	−0.00734473	+	0.0416540i
$112$		0			0
$113$	7.37733			0.694000			0.347000	−	0.937865i	$-0.387200\pi$
$113$	7.37733			0.694000			0.347000	+	0.937865i	$0.387200\pi$
$114$	1.67752	−	1.16009i	0.157114	−	0.108652i
$115$	2.22668	+	3.85673i	0.207639	+	0.359642i
$116$	3.25877	+	2.73443i	0.302569	+	0.253886i
$117$	11.0116	+	9.23984i	1.01802	+	0.854223i
$118$	−7.24763	+	6.08148i	−0.667198	+	0.559846i
$119$		0			0
$120$	0.663848	+	3.76487i	0.0606008	+	0.343684i
$121$	0.638156			0.0580142
$122$	3.85978			0.349449
$123$	−0.414878	−	2.35289i	−0.0374083	−	0.212153i
$124$	−1.82635	+	1.53249i	−0.164011	+	0.137622i
$125$	−4.54323	+	7.86911i	−0.406359	+	0.703835i
$126$		0			0
$127$	−0.0175410	−	0.0994798i	−0.00155651	−	0.00882740i	0.984020	−	0.178060i	$-0.0569822\pi$
$127$	−0.0175410	−	0.0994798i	−0.00155651	−	0.00882740i	−0.985576	+	0.169233i	$0.945871\pi$
$128$	6.42989	−	2.34029i	0.568328	−	0.206854i
$129$	−2.40033	−	0.873649i	−0.211337	−	0.0769205i
$130$	−11.0706	+	4.02936i	−0.970954	+	0.353398i
$131$	−0.527341	+	2.99070i	−0.0460740	+	0.261299i	−0.999140	−	0.0414639i	$-0.986798\pi$
$131$	−0.527341	+	2.99070i	−0.0460740	+	0.261299i	0.953066	+	0.302763i	$0.0979089\pi$
$132$	−2.22668			−0.193808
$133$		0			0
$134$	12.4979			1.07966
$135$	1.33750	−	7.58532i	0.115113	−	0.652840i
$136$	4.40673	−	1.60392i	0.377874	−	0.137535i
$137$	−18.3614	−	6.68302i	−1.56872	−	0.570969i	−0.596009	−	0.802977i	$-0.703248\pi$
$137$	−18.3614	−	6.68302i	−1.56872	−	0.570969i	−0.972714	+	0.232009i	$0.925470\pi$
$138$	−0.773318	+	0.281465i	−0.0658292	+	0.0239599i
$139$	2.67365	+	15.1630i	0.226776	+	1.28611i	0.859261	+	0.511537i	$0.170924\pi$
$139$	2.67365	+	15.1630i	0.226776	+	1.28611i	−0.632485	+	0.774573i	$0.717965\pi$
$140$		0			0
$141$	−0.190722	+	0.330341i	−0.0160617	+	0.0278197i
$142$	−9.26857	+	7.77725i	−0.777801	+	0.652653i
$143$	−3.13429	−	17.7754i	−0.262102	−	1.48645i
$144$	0.113808			0.00948397
$145$	8.78106			0.729227
$146$	−1.14796	−	6.51038i	−0.0950055	−	0.538803i
$147$		0			0
$148$	0.786989	−	0.660362i	0.0646901	−	0.0542814i
$149$	−2.88532	−	2.42107i	−0.236374	−	0.198342i	0.516904	−	0.856043i	$-0.327084\pi$
$149$	−2.88532	−	2.42107i	−0.236374	−	0.198342i	−0.753278	+	0.657702i	$0.771529\pi$
$150$	0.505930	+	0.424525i	0.0413090	+	0.0346624i
$151$	7.29813	+	12.6407i	0.593914	+	1.02869i	0.993699	+	0.112080i	$0.0357513\pi$
$151$	7.29813	+	12.6407i	0.593914	+	1.02869i	−0.399786	+	0.916609i	$0.630915\pi$
$152$	−12.3148	−	1.14982i	−0.998862	−	0.0932626i
$153$	−4.49020			−0.363011
$154$		0			0
$155$	−0.854570	+	4.84651i	−0.0686407	+	0.389281i
$156$	0.599670	+	3.40090i	0.0480120	+	0.272290i
$157$	−1.80154	+	10.2170i	−0.143778	+	0.815407i	0.824562	+	0.565772i	$0.191422\pi$
$157$	−1.80154	+	10.2170i	−0.143778	+	0.815407i	−0.968340	+	0.249635i	$0.919689\pi$
$158$	−4.69072	+	3.93598i	−0.373174	+	0.313130i
$159$	−3.24897			−0.257660
$160$	7.13816	−	12.3636i	0.564321	−	0.977432i
$161$		0			0
$162$	−5.39780	−	1.96464i	−0.424091	−	0.154357i
$163$	1.01114	+	1.75135i	0.0791989	+	0.137177i	0.902905	−	0.429841i	$-0.141430\pi$
$163$	1.01114	+	1.75135i	0.0791989	+	0.137177i	−0.823706	+	0.567018i	$0.808097\pi$
$164$	−2.75402	+	4.77011i	−0.215053	+	0.372483i
$165$	−3.52094	+	2.95442i	−0.274105	+	0.230002i
$166$	−2.07620	+	0.755675i	−0.161144	+	0.0586517i
$167$	−17.8157	+	14.9491i	−1.37862	+	1.15680i	−0.408898	+	0.912580i	$0.634087\pi$
$167$	−17.8157	+	14.9491i	−1.37862	+	1.15680i	−0.969720	+	0.244218i	$0.921469\pi$
$168$		0			0
$169$	−14.0890	+	5.12797i	−1.08377	+	0.394460i
$170$	1.84002	−	3.18701i	0.141123	−	0.244433i
$171$	10.7037	+	5.06742i	0.818531	+	0.387515i
$172$	2.94444	+	5.09992i	0.224511	+	0.388865i
$173$	0.155697	−	0.883000i	0.0118374	−	0.0671332i	−0.978317	−	0.207114i	$-0.933593\pi$
$173$	0.155697	−	0.883000i	0.0118374	−	0.0671332i	0.990154	+	0.139981i	$0.0447040\pi$
$174$	−0.281774	+	1.59802i	−0.0213613	+	0.121146i
$175$		0			0
$176$	−0.109470	−	0.0918566i	−0.00825164	−	0.00692395i
$177$	5.37939	+	1.95794i	0.404339	+	0.147167i
$178$	1.00387	−	1.73875i	0.0752433	−	0.130325i
$179$	−21.3182			−1.59340			−0.796699	−	0.604377i	$-0.793422\pi$
$179$	−21.3182			−1.59340			−0.796699	+	0.604377i	$0.793422\pi$
$180$	−6.46451	+	5.42437i	−0.481836	+	0.404308i
$181$	15.1284	+	5.50627i	1.12448	+	0.409278i	0.836286	−	0.548294i	$-0.184722\pi$
$181$	15.1284	+	5.50627i	1.12448	+	0.409278i	0.288196	+	0.957571i	$0.406945\pi$
$182$		0			0
$183$	−1.16772	−	2.02255i	−0.0863202	−	0.149511i
$184$	4.68954	+	1.70685i	0.345717	+	0.125831i
$185$	0.368241	−	2.08840i	0.0270736	−	0.153542i
$186$	−0.854570	−	0.311038i	−0.0626601	−	0.0228064i
$187$	4.31908	+	3.62414i	0.315842	+	0.265023i
$188$	0.826352	−	0.300767i	0.0602679	−	0.0219357i
$189$		0			0
$190$	−7.98293	+	5.52060i	−0.579142	+	0.400506i
$191$	−9.47431	+	16.4100i	−0.685537	+	1.18738i	0.287731	+	0.957711i	$0.407099\pi$
$191$	−9.47431	+	16.4100i	−0.685537	+	1.18738i	−0.973268	+	0.229673i	$0.926234\pi$
$192$	2.05509	+	1.72443i	0.148314	+	0.124450i
$193$	−12.1236	+	4.41263i	−0.872676	+	0.317628i	−0.739250	−	0.673431i	$-0.764820\pi$
$193$	−12.1236	+	4.41263i	−0.872676	+	0.317628i	−0.133426	+	0.991059i	$0.542598\pi$
$194$	−0.278371	−	1.57872i	−0.0199859	−	0.113345i
$195$	5.46064	+	4.58202i	0.391044	+	0.328125i
$196$		0			0
$197$	11.6001	+	20.0920i	0.826476	+	1.43150i	0.900786	+	0.434263i	$0.142991\pi$
$197$	11.6001	+	20.0920i	0.826476	+	1.43150i	−0.0743108	+	0.997235i	$0.523676\pi$
$198$	4.07532	+	7.05866i	0.289621	+	0.501637i
$199$	1.60132	+	9.08153i	0.113515	+	0.643773i	0.987475	+	0.157776i	$0.0504323\pi$
$199$	1.60132	+	9.08153i	0.113515	+	0.643773i	−0.873960	+	0.485997i	$0.838457\pi$
$200$	−0.695470	−	3.94421i	−0.0491772	−	0.278898i
$201$	−3.78106	−	6.54899i	−0.266695	−	0.461930i
$202$	3.48293	+	6.03260i	0.245058	+	0.424453i
$203$		0			0
$204$	−0.826352	−	0.693392i	−0.0578562	−	0.0485471i
$205$	1.97431	+	11.1969i	0.137892	+	0.782022i
$206$	0.0120217	−	0.00437554i	0.000837592	−	0.000304858i
$207$	−3.66044	−	3.07148i	−0.254418	−	0.213482i
$208$	−0.110815	+	0.191936i	−0.00768361	+	0.0133084i
$209$	−6.20574	−	13.5135i	−0.429260	−	0.934746i
$210$		0			0
$211$	−13.7417	+	5.00157i	−0.946017	+	0.344322i	−0.768539	−	0.639803i	$-0.779016\pi$
$211$	−13.7417	+	5.00157i	−0.946017	+	0.344322i	−0.177478	+	0.984125i	$0.556794\pi$
$212$	5.73783	+	4.81461i	0.394076	+	0.330669i
$213$	6.87939	+	2.50389i	0.471368	+	0.171564i
$214$	−0.542766	+	3.07818i	−0.0371027	+	0.210420i
$215$	11.4226	+	4.15749i	0.779016	+	0.283539i
$216$	−4.31567	−	7.47497i	−0.293644	−	0.508607i
$217$		0			0
$218$	−6.08987	−	2.21653i	−0.412458	−	0.150122i
$219$	−3.06418	+	2.57115i	−0.207058	+	0.173742i
$220$	10.5963			0.714400
$221$	4.37211	−	7.57272i	0.294100	−	0.509396i
$222$	0.368241	+	0.134029i	0.0247147	+	0.00899542i
$223$	−2.30928	−	1.93771i	−0.154641	−	0.129759i	0.562185	−	0.827012i	$-0.309961\pi$
$223$	−2.30928	−	1.93771i	−0.154641	−	0.129759i	−0.716825	+	0.697253i	$0.754405\pi$
$224$		0			0
$225$	−0.665907	+	3.77655i	−0.0443938	+	0.251770i
$226$	1.12654	−	6.38895i	0.0749366	−	0.424987i
$227$	6.86097	+	11.8835i	0.455378	+	0.788738i	0.998710	−	0.0507798i	$-0.0161707\pi$
$227$	6.86097	+	11.8835i	0.455378	+	0.788738i	−0.543332	+	0.839518i	$0.682837\pi$
$228$	1.18732	+	2.58548i	0.0786321	+	0.171227i
$229$	−4.70708	+	8.15290i	−0.311053	+	0.538759i	−0.978591	−	0.205817i	$-0.934015\pi$
$229$	−4.70708	+	8.15290i	−0.311053	+	0.538759i	0.667538	+	0.744576i	$0.267348\pi$
$230$	3.68004	−	1.33943i	0.242655	−	0.0883192i
$231$		0			0
$232$	7.53802	−	6.32515i	0.494895	−	0.415266i
$233$	22.7271	−	8.27201i	1.48890	−	0.541917i	0.535744	−	0.844380i	$-0.320031\pi$
$233$	22.7271	−	8.27201i	1.48890	−	0.541917i	0.953161	+	0.302463i	$0.0978090\pi$
$234$	9.68345	−	8.12538i	0.633027	−	0.531173i
$235$	0.907604	−	1.57202i	0.0592055	−	0.102547i
$236$	−6.59879	−	11.4294i	−0.429545	−	0.743993i
$237$	3.48158	+	1.26719i	0.226153	+	0.0823130i
$238$		0			0
$239$	11.6630	−	20.2009i	0.754415	−	1.30668i	−0.191250	−	0.981541i	$-0.561254\pi$
$239$	11.6630	−	20.2009i	0.754415	−	1.30668i	0.945665	−	0.325143i	$-0.105413\pi$
$240$	0.0564370			0.00364299
$241$	0.228026	−	0.191336i	0.0146884	−	0.0123251i	−0.635414	−	0.772172i	$-0.719170\pi$
$241$	0.228026	−	0.191336i	0.0146884	−	0.0123251i	0.650102	+	0.759847i	$0.274726\pi$
$242$	0.0974487	−	0.552659i	0.00626424	−	0.0355263i
$243$	2.18820	+	12.4099i	0.140373	+	0.796094i
$244$	−0.934945	+	5.30234i	−0.0598537	+	0.339447i
$245$		0			0
$246$	−2.10101			−0.133956
$247$	−18.9684	+	13.1176i	−1.20693	+	0.834653i
$248$	2.75743	+	4.77600i	0.175097	+	0.303276i
$249$	1.02410	+	0.859322i	0.0648997	+	0.0544573i
$250$	6.12108	+	5.13620i	0.387131	+	0.324842i
$251$	−12.4081	+	10.4116i	−0.783190	+	0.657175i	−0.944050	−	0.329802i	$-0.893018\pi$
$251$	−12.4081	+	10.4116i	−0.783190	+	0.657175i	0.160859	+	0.986977i	$0.448573\pi$
$252$		0			0
$253$	1.04189	+	5.90885i	0.0655030	+	0.371486i
$254$	−0.0888306			−0.00557373
$255$	−2.22668			−0.139440
$256$	−2.79591	−	15.8564i	−0.174744	−	0.991025i
$257$	11.7626	−	9.87003i	0.733733	−	0.615675i	−0.197413	−	0.980320i	$-0.563254\pi$
$257$	11.7626	−	9.87003i	0.733733	−	0.615675i	0.931147	+	0.364645i	$0.118810\pi$
$258$	−1.12314	+	1.94534i	−0.0699237	+	0.121111i
$259$		0			0
$260$	−2.85369	−	16.1841i	−0.176979	−	1.00370i
$261$	−8.85369	+	3.22248i	−0.548030	+	0.199467i
$262$	2.50950	+	0.913382i	0.155037	+	0.0564289i
$263$	−9.06165	+	3.29817i	−0.558765	+	0.203374i	−0.605937	−	0.795513i	$-0.707202\pi$
$263$	−9.06165	+	3.29817i	−0.558765	+	0.203374i	0.0471713	+	0.998887i	$0.484979\pi$
$264$	−0.894400	+	5.07239i	−0.0550465	+	0.312184i
$265$	15.4611			0.949768
$266$		0			0
$267$	−1.21482			−0.0743459
$268$	−3.02734	+	17.1689i	−0.184924	+	1.04876i
$269$	17.1766	−	6.25179i	1.04728	−	0.381178i	0.239643	−	0.970861i	$-0.422969\pi$
$269$	17.1766	−	6.25179i	1.04728	−	0.381178i	0.807635	+	0.589683i	$0.200747\pi$
$270$	−6.36484	−	2.31661i	−0.387352	−	0.140984i
$271$	−17.8204	+	6.48610i	−1.08251	+	0.394003i	−0.820843	−	0.571154i	$-0.806496\pi$
$271$	−17.8204	+	6.48610i	−1.08251	+	0.394003i	−0.261671	+	0.965157i	$0.584274\pi$
$272$	−0.0120217	−	0.0681784i	−0.000728923	−	0.00413393i
$273$		0			0
$274$	−8.59152	+	14.8809i	−0.519033	+	0.898991i
$275$	3.68866	−	3.09516i	0.222435	−	0.186645i
$276$	−0.199340	−	1.13052i	−0.0119989	−	0.0680491i
$277$	13.7638			0.826988			0.413494	−	0.910507i	$-0.364308\pi$
$277$	13.7638			0.826988			0.413494	+	0.910507i	$0.364308\pi$
$278$	13.5398			0.812065
$279$	−0.916937	−	5.20021i	−0.0548956	−	0.311328i
$280$		0			0
$281$	10.0437	−	8.42767i	0.599157	−	0.502752i	−0.292018	−	0.956413i	$-0.594327\pi$
$281$	10.0437	−	8.42767i	0.599157	−	0.502752i	0.891175	+	0.453661i	$0.149882\pi$
$282$	0.256959	+	0.215615i	0.0153017	+	0.0128397i
$283$	−13.3118	−	11.1699i	−0.791305	−	0.663983i	0.154763	−	0.987952i	$-0.450538\pi$
$283$	−13.3118	−	11.1699i	−0.791305	−	0.663983i	−0.946068	+	0.323968i	$0.894983\pi$
$284$	−8.43882	−	14.6165i	−0.500752	−	0.867327i
$285$	5.30793	+	2.51292i	0.314415	+	0.148853i
$286$	−15.8726			−0.938565
$287$		0			0
$288$	−2.65998	+	15.0855i	−0.156741	+	0.888921i
$289$	−2.47771	−	14.0518i	−0.145748	−	0.826576i
$290$	1.34090	−	7.60462i	0.0787403	−	0.446559i
$291$	−0.743041	+	0.623485i	−0.0435578	+	0.0365493i
$292$	9.22163			0.539655
$293$	−7.80200	+	13.5135i	−0.455798	+	0.789465i	−0.998734	−	0.0503091i	$-0.983979\pi$
$293$	−7.80200	+	13.5135i	−0.455798	+	0.789465i	0.542936	+	0.839774i	$0.317313\pi$
$294$		0			0
$295$	−25.5993	−	9.31737i	−1.49045	−	0.542478i
$296$	−1.18820	−	2.05802i	−0.0690625	−	0.119620i
$297$	5.18866	−	8.98703i	0.301077	−	0.521480i
$298$	−2.53730	+	2.12905i	−0.146982	+	0.123333i
$299$	8.74422	−	3.18264i	0.505691	−	0.184057i
$300$	−0.705737	+	0.592184i	−0.0407457	+	0.0341897i
$301$		0			0
$302$	12.0617	−	4.39008i	0.694070	−	0.252621i
$303$	2.10741	−	3.65014i	0.121068	−	0.209695i
$304$	−0.0482857	+	0.176090i	−0.00276937	+	0.0100995i
$305$	5.55690	+	9.62484i	0.318187	+	0.551117i
$306$	−0.685670	+	3.88863i	−0.0391971	+	0.222298i
$307$	3.73695	−	21.1933i	0.213279	−	1.20956i	−0.670589	−	0.741829i	$-0.733959\pi$
$307$	3.73695	−	21.1933i	0.213279	−	1.20956i	0.883868	−	0.467736i	$-0.154930\pi$
$308$		0			0
$309$	−0.00592979	−	0.00497568i	−0.000337334	−	0.000283057i
$310$	4.06670	+	1.48016i	0.230973	+	0.0840674i
$311$	−7.24763	+	12.5533i	−0.410975	+	0.711830i	−0.994997	−	0.0999083i	$-0.968145\pi$
$311$	−7.24763	+	12.5533i	−0.410975	+	0.711830i	0.584021	+	0.811738i	$0.301478\pi$
$312$	7.98814			0.452239
$313$	14.9520	−	12.5462i	0.845138	−	0.709155i	−0.113575	−	0.993529i	$-0.536230\pi$
$313$	14.9520	−	12.5462i	0.845138	−	0.709155i	0.958713	+	0.284374i	$0.0917859\pi$
$314$	8.57310	+	3.12035i	0.483808	+	0.176092i
$315$		0			0
$316$	−4.27079	−	7.39723i	−0.240251	−	0.416127i
$317$	−26.6377	−	9.69535i	−1.49612	−	0.544545i	−0.541071	−	0.840977i	$-0.681981\pi$
$317$	−26.6377	−	9.69535i	−1.49612	−	0.544545i	−0.955054	+	0.296432i	$0.904203\pi$
$318$	−0.496130	+	2.81369i	−0.0278216	+	0.157784i
$319$	11.1172	+	4.04633i	0.622444	+	0.226551i
$320$	−9.77972	−	8.20616i	−0.546703	−	0.458738i
$321$	1.77719	−	0.646844i	0.0991930	−	0.0361033i
$322$		0			0
$323$	1.90508	−	6.94751i	0.106001	−	0.386570i
$324$	4.00640	−	6.93928i	0.222578	−	0.385516i
$325$	−5.72075	−	4.80028i	−0.317330	−	0.266272i
$326$	1.67112	−	0.608239i	0.0925549	−	0.0336872i
$327$	0.680922	+	3.86170i	0.0376551	+	0.213553i
$328$	9.76011	+	8.18971i	0.538912	+	0.452201i
$329$		0			0
$330$	2.02094	+	3.50038i	0.111249	+	0.192690i
$331$	0.855037	+	1.48097i	0.0469971	+	0.0814014i	0.888567	−	0.458747i	$-0.151702\pi$
$331$	0.855037	+	1.48097i	0.0469971	+	0.0814014i	−0.841570	+	0.540148i	$0.818368\pi$
$332$	−0.535188	−	3.03520i	−0.0293722	−	0.166578i
$333$	0.395115	+	2.24081i	0.0216522	+	0.122796i
$334$	10.2258	+	17.7116i	0.559531	+	0.969136i
$335$	17.9932	+	31.1651i	0.983073	+	1.70273i
$336$		0			0
$337$	19.4873	+	16.3518i	1.06154	+	0.890737i	0.994259	−	0.106997i	$-0.0341236\pi$
$337$	19.4873	+	16.3518i	1.06154	+	0.890737i	0.0672796	+	0.997734i	$0.478568\pi$
$338$	2.28952	+	12.9845i	0.124533	+	0.706263i
$339$	−3.68866	+	1.34256i	−0.200341	+	0.0729180i
$340$	3.93242	+	3.29969i	0.213265	+	0.178951i
$341$	−3.31521	+	5.74211i	−0.179529	+	0.310953i
$342$	6.02300	−	8.49584i	0.325687	−	0.459403i
$343$		0			0
$344$	12.8004	−	4.65895i	0.690149	−	0.251194i
$345$	−1.81521	−	1.52314i	−0.0977275	−	0.0820031i
$346$	−0.740925	−	0.269675i	−0.0398324	−	0.0144978i
$347$	1.33750	−	7.58532i	0.0718006	−	0.407201i	−0.927631	−	0.373497i	$-0.878159\pi$
$347$	1.33750	−	7.58532i	0.0718006	−	0.407201i	0.999432	−	0.0337040i	$-0.0107303\pi$
$348$	−2.12701	−	0.774169i	−0.114020	−	0.0414998i
$349$	−11.3785	−	19.7082i	−0.609078	−	1.05495i	−0.991393	−	0.130921i	$-0.958206\pi$
$349$	−11.3785	−	19.7082i	−0.609078	−	1.05495i	0.382315	−	0.924032i	$-0.375127\pi$
$350$		0			0
$351$	−15.1236	−	5.50454i	−0.807238	−	0.293811i
$352$	14.7344	−	12.3636i	0.785347	−	0.658985i
$353$	−11.4456			−0.609189			−0.304595	−	0.952482i	$-0.598521\pi$
$353$	−11.4456			−0.609189			−0.304595	+	0.952482i	$0.598521\pi$
$354$	2.51707	−	4.35970i	0.133781	−	0.231715i
$355$	−32.7374	−	11.9154i	−1.73752	−	0.632406i
$356$	2.14543	+	1.80023i	0.113708	+	0.0954120i
$357$		0			0
$358$	−3.25537	+	18.4621i	−0.172051	+	0.975752i
$359$	1.80319	−	10.2264i	0.0951685	−	0.539727i	−0.899527	−	0.436865i	$-0.856089\pi$
$359$	1.80319	−	10.2264i	0.0951685	−	0.539727i	0.994696	−	0.102862i	$-0.0328001\pi$
$360$	9.76011	+	16.9050i	0.514403	+	0.890972i
$361$	−12.3819	+	14.4114i	−0.651680	+	0.758494i
$362$	7.07873	−	12.2607i	0.372050	−	0.644409i
$363$	−0.319078	+	0.116135i	−0.0167472	+	0.00609550i
$364$		0			0
$365$	14.5817	−	12.2355i	0.763242	−	0.640436i
$366$	−1.92989	+	0.702423i	−0.100877	+	0.0367163i
$367$	−24.9217	+	20.9118i	−1.30090	+	1.09159i	−0.310916	+	0.950437i	$0.600636\pi$
$367$	−24.9217	+	20.9118i	−1.30090	+	1.09159i	−0.989988	+	0.141151i	$0.954920\pi$
$368$	0.0368366	−	0.0638029i	0.00192024	−	0.00332596i
$369$	−6.09967	−	10.5649i	−0.317536	−	0.549989i
$370$	−1.75237	−	0.637812i	−0.0911016	−	0.0331583i
$371$		0			0
$372$	0.634285	−	1.09861i	0.0328862	−	0.0569605i
$373$	30.4858			1.57849			0.789246	−	0.614077i	$-0.210471\pi$
$373$	30.4858			1.57849			0.789246	+	0.614077i	$0.210471\pi$
$374$	3.79813	−	3.18701i	0.196397	−	0.164796i
$375$	0.839556	−	4.76136i	0.0433545	−	0.245875i
$376$	−0.353226	−	2.00324i	−0.0182162	−	0.103309i
$377$	3.18614	−	18.0695i	0.164094	−	0.930626i
$378$		0			0
$379$	17.8598			0.917396			0.458698	−	0.888592i	$-0.348316\pi$
$379$	17.8598			0.917396			0.458698	+	0.888592i	$0.348316\pi$
$380$	−5.65018	−	12.3037i	−0.289848	−	0.631166i
$381$	0.0268743	+	0.0465477i	0.00137681	+	0.00238471i
$382$	12.7647	+	10.7109i	0.653099	+	0.548015i
$383$	−17.9684	−	15.0773i	−0.918141	−	0.770412i	0.0555091	−	0.998458i	$-0.482322\pi$
$383$	−17.9684	−	15.0773i	−0.918141	−	0.770412i	−0.973650	+	0.228046i	$0.926766\pi$
$384$	−2.78905	+	2.34029i	−0.142328	+	0.119427i
$385$		0			0
$386$	1.97013	+	11.1732i	0.100277	+	0.568700i
$387$	−13.0428			−0.663004
$388$	2.23618			0.113525
$389$	0.678863	+	3.85002i	0.0344197	+	0.195204i	0.997169	−	0.0751913i	$-0.0239568\pi$
$389$	0.678863	+	3.85002i	0.0344197	+	0.195204i	−0.962749	+	0.270395i	$0.912846\pi$
$390$	4.80200	−	4.02936i	0.243159	−	0.204035i
$391$	−1.45336	+	2.51730i	−0.0734997	+	0.127305i
$392$		0			0
$393$	−0.280592	−	1.59132i	−0.0141540	−	0.0802714i
$394$	19.1716	−	6.97789i	0.965851	−	0.351541i
$395$	−16.5680	−	6.03028i	−0.833629	−	0.303416i
$396$	−10.6839	+	3.88863i	−0.536887	+	0.195411i
$397$	1.55572	−	8.82294i	0.0780794	−	0.442810i	−0.920557	−	0.390608i	$-0.872265\pi$
$397$	1.55572	−	8.82294i	0.0780794	−	0.442810i	0.998637	−	0.0522024i	$-0.0166241\pi$
$398$	8.10936			0.406486
$399$		0			0
$400$	−0.0591253			−0.00295627
$401$	−0.352044	+	1.99654i	−0.0175802	+	0.0997025i	−0.992335	−	0.123574i	$-0.960564\pi$
$401$	−0.352044	+	1.99654i	−0.0175802	+	0.0997025i	0.974755	+	0.223277i	$0.0716754\pi$
$402$	−6.24897	+	2.27444i	−0.311670	+	0.113439i
$403$	9.66297	+	3.51703i	0.481347	+	0.175196i
$404$	−9.13088	+	3.32337i	−0.454278	+	0.165344i
$405$	−2.87211	−	16.2886i	−0.142716	−	0.809385i
$406$		0			0
$407$	1.42855	−	2.47432i	0.0708105	−	0.122647i
$408$	−1.91147	+	1.60392i	−0.0946321	+	0.0794057i
$409$	−5.59286	−	31.7187i	−0.276549	−	1.56839i	−0.733997	−	0.679152i	$-0.762347\pi$
$409$	−5.59286	−	31.7187i	−0.276549	−	1.56839i	0.457448	−	0.889236i	$-0.348764\pi$
$410$	9.99825			0.493778
$411$	10.3969			0.512843
$412$	0.00309887	+	0.0175745i	0.000152670	+	0.000865836i
$413$		0			0
$414$	−3.21894	+	2.70101i	−0.158202	+	0.132747i
$415$	−4.87346	−	4.08931i	−0.239229	−	0.200737i
$416$	−22.8516	−	19.1748i	−1.12039	−	0.940122i
$417$	−4.09627	−	7.09494i	−0.200595	−	0.347441i
$418$	−12.6506	+	3.31077i	−0.618763	+	0.161935i
$419$	−23.2499			−1.13583			−0.567916	−	0.823086i	$-0.692250\pi$
$419$	−23.2499			−1.13583			−0.567916	+	0.823086i	$0.692250\pi$
$420$		0			0
$421$	1.12061	−	6.35532i	0.0546154	−	0.309739i	−0.945246	−	0.326357i	$-0.894179\pi$
$421$	1.12061	−	6.35532i	0.0546154	−	0.309739i	0.999862	+	0.0166178i	$0.00528986\pi$
$422$	2.23308	+	12.6644i	0.108705	+	0.616494i
$423$	−0.338211	+	1.91809i	−0.0164444	+	0.0932608i
$424$	13.2724	−	11.1369i	0.644567	−	0.540856i
$425$	2.33275			0.113155
$426$	3.21894	−	5.57537i	0.155958	−	0.270128i
$427$		0			0
$428$	−4.09714	−	1.49124i	−0.198043	−	0.0720817i
$429$	4.80200	+	8.31731i	0.231843	+	0.401564i
$430$	5.34477	−	9.25741i	0.257748	−	0.446432i
$431$	−10.7226	+	8.99730i	−0.516488	+	0.433385i	−0.863405	−	0.504511i	$-0.831673\pi$
$431$	−10.7226	+	8.99730i	−0.516488	+	0.433385i	0.346918	+	0.937896i	$0.387228\pi$
$432$	−0.119737	+	0.0435809i	−0.00576087	+	0.00209678i
$433$	−21.9800	+	18.4434i	−1.05629	+	0.886333i	−0.993741	−	0.111709i	$-0.964368\pi$
$433$	−21.9800	+	18.4434i	−1.05629	+	0.886333i	−0.0625499	+	0.998042i	$0.519923\pi$
$434$		0			0
$435$	−4.39053	+	1.59802i	−0.210510	+	0.0766193i
$436$	4.52007	−	7.82899i	0.216472	−	0.374940i
$437$	6.30541	−	4.36051i	0.301629	−	0.208591i
$438$	1.75877	+	3.04628i	0.0840373	+	0.145557i
$439$	−2.31686	+	13.1395i	−0.110578	+	0.627116i	0.878268	+	0.478169i	$0.158699\pi$
$439$	−2.31686	+	13.1395i	−0.110578	+	0.627116i	−0.988845	+	0.148947i	$0.952412\pi$
$440$	4.25624	−	24.1384i	0.202908	−	1.15075i
$441$		0			0
$442$	−5.89053	−	4.94274i	−0.280184	−	0.235102i
$443$	−31.8396	−	11.5887i	−1.51275	−	0.550594i	−0.553421	−	0.832901i	$-0.686678\pi$
$443$	−31.8396	−	11.5887i	−1.51275	−	0.550594i	−0.959324	+	0.282307i	$0.908900\pi$
$444$	−0.273318	+	0.473401i	−0.0129711	+	0.0224666i
$445$	5.78106			0.274048
$446$	−2.03074	+	1.70400i	−0.0961585	+	0.0806866i
$447$	1.88326	+	0.685449i	0.0890749	+	0.0324206i
$448$		0			0
$449$	−9.42009	−	16.3161i	−0.444562	−	0.770003i	0.553460	−	0.832876i	$-0.313307\pi$
$449$	−9.42009	−	16.3161i	−0.444562	−	0.770003i	−0.998022	+	0.0628725i	$0.979974\pi$
$450$	3.16890	+	1.15339i	0.149383	+	0.0543711i
$451$	−2.65998	+	15.0855i	−0.125253	+	0.710348i
$452$	8.50387	+	3.09516i	0.399988	+	0.145584i
$453$	−5.94949	−	4.99222i	−0.279532	−	0.234555i
$454$	11.3391	−	4.12711i	0.532172	−	0.193695i
$455$		0			0
$456$	6.36665	−	1.66620i	0.298146	−	0.0780270i
$457$	−7.13950	+	12.3660i	−0.333972	+	0.578456i	−0.983287	−	0.182064i	$-0.941722\pi$
$457$	−7.13950	+	12.3660i	−0.333972	+	0.578456i	0.649315	+	0.760520i	$0.275056\pi$
$458$	6.34183	+	5.32143i	0.296334	+	0.248654i
$459$	4.72416	−	1.71945i	0.220505	−	0.0802571i
$460$	0.948615	+	5.37987i	0.0442294	+	0.250838i
$461$	−10.6695	−	8.95280i	−0.496930	−	0.416973i	0.359572	−	0.933117i	$-0.382923\pi$
$461$	−10.6695	−	8.95280i	−0.496930	−	0.416973i	−0.856502	+	0.516144i	$0.827367\pi$
$462$		0			0
$463$	0.881445	+	1.52671i	0.0409642	+	0.0709521i	0.885781	−	0.464104i	$-0.153624\pi$
$463$	0.881445	+	1.52671i	0.0409642	+	0.0709521i	−0.844816	+	0.535056i	$0.820290\pi$
$464$	−0.0726338	−	0.125805i	−0.00337194	−	0.00584037i
$465$	−0.454707	−	2.57877i	−0.0210865	−	0.119588i
$466$	−3.69325	−	20.9455i	−0.171086	−	0.970279i
$467$	−11.0209	−	19.0888i	−0.509988	−	0.883326i	−0.999933	−	0.0115724i	$-0.996316\pi$
$467$	−11.0209	−	19.0888i	−0.509988	−	0.883326i	0.489945	−	0.871754i	$-0.337017\pi$
$468$	8.81655	+	15.2707i	0.407545	+	0.705889i
$469$		0			0
$470$	−1.22281	−	1.02606i	−0.0564041	−	0.0473286i
$471$	−0.958578	−	5.43636i	−0.0441689	−	0.250494i
$472$	−28.6869	+	10.4412i	−1.32042	+	0.480594i
$473$	12.5458	+	10.5271i	0.576855	+	0.484039i
$474$	1.62907	−	2.82163i	0.0748257	−	0.129602i
$475$	−5.56077	−	2.63263i	−0.255146	−	0.120793i
$476$		0			0
$477$	−15.5890	+	5.67393i	−0.713771	+	0.259791i
$478$	−15.7135	−	13.1852i	−0.718718	−	0.603076i
$479$	23.9217	+	8.70680i	1.09301	+	0.397824i	0.824736	−	0.565518i	$-0.191324\pi$
$479$	23.9217	+	8.70680i	1.09301	+	0.397824i	0.268276	+	0.963342i	$0.413546\pi$
$480$	−1.31908	+	7.48086i	−0.0602074	+	0.341453i
$481$	−4.16385	−	1.51552i	−0.189855	−	0.0691016i
$482$	−0.130882	−	0.226694i	−0.00596150	−	0.0103256i
$483$		0			0
$484$	0.735604	+	0.267738i	0.0334366	+	0.0121699i
$485$	3.53596	−	2.96702i	0.160560	−	0.134726i
$486$	11.0814			0.502663
$487$	11.2554	−	19.4949i	0.510029	−	0.883397i	−0.489903	−	0.871777i	$-0.662968\pi$
$487$	11.2554	−	19.4949i	0.510029	−	0.883397i	0.999932	−	0.0116199i	$-0.00369881\pi$
$488$	11.7032	+	4.25962i	0.529779	+	0.192824i
$489$	−0.824292	−	0.691663i	−0.0372758	−	0.0312781i
$490$		0			0
$491$	2.71482	−	15.3965i	0.122518	−	0.694835i	−0.860233	−	0.509902i	$-0.829682\pi$
$491$	2.71482	−	15.3965i	0.122518	−	0.694835i	0.982751	−	0.184934i	$-0.0592071\pi$
$492$	0.508923	−	2.88624i	0.0229440	−	0.130122i
$493$	2.86571	+	4.96356i	0.129065	+	0.223548i
$494$	8.46363	+	18.4302i	0.380797	+	0.829214i
$495$	−11.7344	+	20.3246i	−0.527423	+	0.913524i
$496$	0.0765042	−	0.0278452i	0.00343514	−	0.00125029i
$497$		0			0
$498$	0.900578	−	0.755675i	0.0403559	−	0.0338626i
$499$	26.8910	−	9.78752i	1.20381	−	0.438150i	0.339255	−	0.940694i	$-0.389825\pi$
$499$	26.8910	−	9.78752i	1.20381	−	0.438150i	0.864551	+	0.502545i	$0.167603\pi$
$500$	−8.53849	+	7.16464i	−0.381853	+	0.320412i
$501$	6.18732	−	10.7168i	0.276429	−	0.478789i
$502$	7.12196	+	12.3356i	0.317869	+	0.550565i
$503$	23.5351	+	8.56607i	1.04938	+	0.381942i	0.808428	−	0.588595i	$-0.200319\pi$
$503$	23.5351	+	8.56607i	1.04938	+	0.381942i	0.240950	+	0.970538i	$0.422541\pi$
$504$		0			0
$505$	−10.0287	+	17.3702i	−0.446271	+	0.772963i
$506$	5.27631			0.234561
$507$	6.11128	−	5.12797i	0.271412	−	0.227741i
$508$	0.0215172	−	0.122030i	0.000954671	−	0.00541421i
$509$	5.82089	+	33.0119i	0.258006	+	1.46323i	0.788236	+	0.615373i	$0.210995\pi$
$509$	5.82089	+	33.0119i	0.258006	+	1.46323i	−0.530230	+	0.847854i	$0.677894\pi$
$510$	−0.340022	+	1.92836i	−0.0150564	+	0.0853893i
$511$		0			0
$512$	−0.473897			−0.0209435
$513$	−13.2019	−	1.23264i	−0.582877	−	0.0544225i
$514$	−6.75150	−	11.6939i	−0.297796	−	0.515797i
$515$	0.0282185	+	0.0236781i	0.00124346	+	0.00104338i
$516$	−2.40033	−	2.01412i	−0.105669	−	0.0886665i
$517$	1.87346	−	1.57202i	0.0823945	−	0.0691372i
$518$		0			0
$519$	0.0828445	+	0.469834i	0.00363647	+	0.0206234i
$520$	−38.0137			−1.66701
$521$	−27.4783			−1.20385			−0.601924	−	0.798553i	$-0.705599\pi$
$521$	−27.4783			−1.20385			−0.601924	+	0.798553i	$0.705599\pi$
$522$	1.43876	+	8.15961i	0.0629728	+	0.357136i
$523$	−7.93423	+	6.65761i	−0.346940	+	0.291117i	−0.799560	−	0.600587i	$-0.794934\pi$
$523$	−7.93423	+	6.65761i	−0.346940	+	0.291117i	0.452620	+	0.891703i	$0.350489\pi$
$524$	−1.86262	+	3.22615i	−0.0813687	+	0.140935i
$525$		0			0
$526$	1.47255	+	8.35126i	0.0642064	+	0.364132i
$527$	−3.01842	+	1.09861i	−0.131484	+	0.0478564i
$528$	0.0714517	+	0.0260063i	0.00310954	+	0.00113178i
$529$	18.7062	−	6.80850i	0.813313	−	0.296022i
$530$	2.36097	−	13.3897i	0.102554	−	0.581612i
$531$	29.2303			1.26849
$532$		0			0
$533$	23.7570			1.02903
$534$	−0.185508	+	1.05207i	−0.00802771	+	0.0455274i
$535$	−8.45723	+	3.07818i	−0.365638	+	0.133081i
$536$	37.8949	+	13.7926i	1.63681	+	0.595750i
$537$	10.6591	−	3.87960i	0.459974	−	0.167417i
$538$	−2.79127	−	15.8301i	−0.120340	−	0.682483i
$539$		0			0
$540$	4.72416	−	8.18248i	0.203295	−	0.352118i
$541$	1.93376	−	1.62262i	0.0831390	−	0.0697619i	−0.600271	−	0.799797i	$-0.704941\pi$
$541$	1.93376	−	1.62262i	0.0831390	−	0.0697619i	0.683410	+	0.730035i	$0.260496\pi$
$542$	2.89589	+	16.4234i	0.124389	+	0.705445i
$543$	−8.56624			−0.367612
$544$	9.31820			0.399515
$545$	−3.24035	−	18.3770i	−0.138801	−	0.787182i
$546$		0			0
$547$	5.87939	−	4.93339i	0.251384	−	0.210937i	−0.508384	−	0.861131i	$-0.669757\pi$
$547$	5.87939	−	4.93339i	0.251384	−	0.210937i	0.759768	+	0.650194i	$0.225312\pi$
$548$	−18.3614	−	15.4071i	−0.784362	−	0.658158i
$549$	−9.13500	−	7.66518i	−0.389872	−	0.327142i
$550$	−2.11721	−	3.66712i	−0.0902782	−	0.156366i
$551$	−1.22962	−	15.0662i	−0.0523835	−	0.641841i
$552$	−2.65539			−0.113021
$553$		0			0
$554$	2.10179	−	11.9198i	0.0892963	−	0.506425i
$555$	0.195937	+	1.11121i	0.00831706	+	0.0471684i
$556$	−3.27972	+	18.6002i	−0.139091	+	0.788824i
$557$	2.49407	−	2.09277i	0.105677	−	0.0886737i	−0.588418	−	0.808557i	$-0.700249\pi$
$557$	2.49407	−	2.09277i	0.105677	−	0.0886737i	0.694095	+	0.719883i	$0.255805\pi$
$558$	−4.64353			−0.196576
$559$	12.6998	−	21.9967i	0.537145	−	0.930362i
$560$		0			0
$561$	−2.81908	−	1.02606i	−0.119022	−	0.0433203i
$562$	−5.76486	−	9.98503i	−0.243176	−	0.421193i
$563$	−2.62954	+	4.55449i	−0.110822	+	0.191949i	−0.916102	−	0.400946i	$-0.868682\pi$
$563$	−2.62954	+	4.55449i	−0.110822	+	0.191949i	0.805280	+	0.592895i	$0.202015\pi$
$564$	−0.358441	+	0.300767i	−0.0150931	+	0.0126646i
$565$	17.5535	−	6.38895i	0.738481	−	0.268785i
$566$	−11.7062	+	9.82267i	−0.492048	+	0.412878i
$567$		0			0
$568$	−36.6860	+	13.3526i	−1.53931	+	0.560264i
$569$	14.9782	−	25.9430i	0.627918	−	1.08759i	−0.360051	−	0.932933i	$-0.617241\pi$
$569$	14.9782	−	25.9430i	0.627918	−	1.08759i	0.987969	−	0.154653i	$-0.0494260\pi$
$570$	2.98680	−	4.21307i	0.125103	−	0.176466i
$571$	8.35504	+	14.4713i	0.349647	+	0.605607i	0.986187	−	0.165637i	$-0.0529680\pi$
$571$	8.35504	+	14.4713i	0.349647	+	0.605607i	−0.636539	+	0.771244i	$0.719635\pi$
$572$	3.84477	−	21.8048i	0.160758	−	0.911703i
$573$	1.75078	−	9.92917i	0.0731399	−	0.414797i
$574$		0			0
$575$	1.90167	+	1.59569i	0.0793053	+	0.0665450i
$576$	12.8721	+	4.68507i	0.536338	+	0.195211i
$577$	6.84002	−	11.8473i	0.284754	−	0.493208i	−0.687796	−	0.725904i	$-0.741421\pi$
$577$	6.84002	−	11.8473i	0.284754	−	0.493208i	0.972549	+	0.232696i	$0.0747548\pi$
$578$	−12.5476			−0.521910
$579$	5.25877	−	4.41263i	0.218547	−	0.183383i
$580$	10.1220	+	3.68409i	0.420291	+	0.152974i
$581$		0			0
$582$	0.426489	+	0.738700i	0.0176785	+	0.0306201i
$583$	19.5744	+	7.12452i	0.810691	+	0.295067i
$584$	3.70409	−	21.0069i	0.153276	−	0.869273i
$585$	34.2028	+	12.4488i	1.41411	+	0.514695i
$586$	10.5116	+	8.82029i	0.434231	+	0.364363i
$587$	22.5872	−	8.22108i	0.932275	−	0.339320i	0.169164	−	0.985588i	$-0.445893\pi$
$587$	22.5872	−	8.22108i	0.932275	−	0.339320i	0.763111	+	0.646268i	$0.223671\pi$
$588$		0			0
$589$	8.43511	+	0.787576i	0.347563	+	0.0324515i
$590$	−11.9782	+	20.7468i	−0.493134	+	0.854133i
$591$	−9.45652	−	7.93496i	−0.388989	−	0.326401i
$592$	−0.0329662	+	0.0119987i	−0.00135490	+	0.000493145i
$593$	−0.736482	−	4.17680i	−0.0302437	−	0.171520i	0.965945	−	0.258749i	$-0.0833102\pi$
$593$	−0.736482	−	4.17680i	−0.0302437	−	0.171520i	−0.996188	+	0.0872283i	$0.972199\pi$
$594$	−6.99067	−	5.86587i	−0.286831	−	0.240679i
$595$		0			0
$596$	−2.31016	−	4.00131i	−0.0946276	−	0.163900i
$597$	−2.45336	−	4.24935i	−0.100409	−	0.173914i
$598$	−1.42097	−	8.05872i	−0.0581078	−	0.329546i
$599$	−4.56242	−	25.8748i	−0.186416	−	1.05722i	−0.924123	−	0.382095i	$-0.875203\pi$
$599$	−4.56242	−	25.8748i	−0.186416	−	1.05722i	0.737708	−	0.675120i	$-0.235908\pi$
$600$	1.06552	+	1.84554i	0.0434998	+	0.0753438i
$601$	21.1197	+	36.5805i	0.861492	+	1.49215i	0.870489	+	0.492188i	$0.163803\pi$
$601$	21.1197	+	36.5805i	0.861492	+	1.49215i	−0.00899659	+	0.999960i	$0.502864\pi$
$602$		0			0
$603$	−29.5790	−	24.8198i	−1.20455	−	1.01074i
$604$	3.10917	+	17.6330i	0.126510	+	0.717475i
$605$	1.51842	−	0.552659i	0.0617325	−	0.0224688i
$606$	−2.83931	−	2.38246i	−0.115339	−	0.0967809i
$607$	11.0484	−	19.1365i	0.448443	−	0.776725i	−0.549842	−	0.835269i	$-0.685312\pi$
$607$	11.0484	−	19.1365i	0.448443	−	0.776725i	0.998285	+	0.0585431i	$0.0186455\pi$
$608$	−22.2126	−	10.5161i	−0.900840	−	0.426483i
$609$		0			0
$610$	9.18392	−	3.34267i	0.371846	−	0.135341i
$611$	−2.90554	−	2.43804i	−0.117546	−	0.0986326i
$612$	−5.17587	−	1.88386i	−0.209222	−	0.0761506i
$613$	1.24628	−	7.06802i	0.0503369	−	0.285474i	−0.949240	−	0.314552i	$-0.898146\pi$
$613$	1.24628	−	7.06802i	0.0503369	−	0.285474i	0.999577	+	0.0290773i	$0.00925690\pi$
$614$	−17.7833	−	6.47258i	−0.717675	−	0.261212i
$615$	−3.02481	−	5.23913i	−0.121972	−	0.211262i
$616$		0			0
$617$	46.3953	+	16.8865i	1.86781	+	0.679826i	0.971811	+	0.235761i	$0.0757583\pi$
$617$	46.3953	+	16.8865i	1.86781	+	0.679826i	0.895995	+	0.444065i	$0.146464\pi$
$618$	−0.00521457	+	0.00437554i	−0.000209761	+	0.000176010i
$619$	26.4979			1.06504			0.532521	−	0.846417i	$-0.321245\pi$
$619$	26.4979			1.06504			0.532521	+	0.846417i	$0.321245\pi$
$620$	−3.01842	+	5.22805i	−0.121223	+	0.209964i
$621$	5.02734	+	1.82980i	0.201740	+	0.0734274i
$622$	9.76470	+	8.19356i	0.391529	+	0.328532i
$623$		0			0
$624$	0.0204777	−	0.116135i	0.000819764	−	0.00464911i
$625$	−5.22075	+	29.6084i	−0.208830	+	1.18433i
$626$	−8.58213	−	14.8647i	−0.343011	−	0.594112i
$627$	5.56212	+	5.62738i	0.222130	+	0.224736i
$628$	−6.36319	+	11.0214i	−0.253919	+	0.439800i
$629$	1.30066	−	0.473401i	0.0518607	−	0.0188757i
$630$		0			0
$631$	25.5253	−	21.4183i	1.01615	−	0.852647i	0.0270071	−	0.999635i	$-0.491402\pi$
$631$	25.5253	−	21.4183i	1.01615	−	0.852647i	0.989138	+	0.146988i	$0.0469579\pi$
$632$	−18.5664	+	6.75762i	−0.738532	+	0.268804i
$633$	5.96064	−	5.00157i	0.236914	−	0.198794i
$634$	−12.4641	+	21.5884i	−0.495013	+	0.857387i
$635$	−0.127889	−	0.221510i	−0.00507511	−	0.00879035i
$636$	−3.74510	−	1.36310i	−0.148503	−	0.0540506i
$637$		0			0
$638$	5.20187	−	9.00990i	0.205944	−	0.356705i
$639$	37.3809			1.47877
$640$	13.2724	−	11.1369i	0.524639	−	0.440225i
$641$	−0.0236329	+	0.134029i	−0.000933443	+	0.00529382i	−0.985271	−	0.171001i	$-0.945300\pi$
$641$	−0.0236329	+	0.134029i	−0.000933443	+	0.00529382i	0.984337	+	0.176294i	$0.0564111\pi$
$642$	−0.288800	−	1.63787i	−0.0113980	−	0.0646414i
$643$	8.36602	−	47.4461i	0.329924	−	1.87109i	−0.142613	−	0.989779i	$-0.545550\pi$
$643$	8.36602	−	47.4461i	0.329924	−	1.87109i	0.472536	−	0.881311i	$-0.343339\pi$
$644$		0			0
$645$	−6.46791			−0.254674
$646$	−5.72580	−	2.71075i	−0.225279	−	0.106653i
$647$	18.4859	+	32.0186i	0.726756	+	1.25878i	0.958247	+	0.285942i	$0.0923065\pi$
$647$	18.4859	+	32.0186i	0.726756	+	1.25878i	−0.231490	+	0.972837i	$0.574360\pi$
$648$	−14.1985	−	11.9139i	−0.557768	−	0.468023i
$649$	−28.1163	−	23.5924i	−1.10366	−	0.926083i
$650$	−5.03074	+	4.22130i	−0.197322	+	0.165573i
$651$		0			0
$652$	0.430770	+	2.44302i	0.0168702	+	0.0956759i
$653$	27.0000			1.05659			0.528296	−	0.849060i	$-0.322831\pi$
$653$	27.0000			1.05659			0.528296	+	0.849060i	$0.322831\pi$
$654$	3.44831			0.134840
$655$	1.33527	+	7.57272i	0.0521735	+	0.295891i
$656$	0.144086	−	0.120902i	0.00562559	−	0.00472043i
$657$	−10.2121	+	17.6879i	−0.398413	+	0.690072i
$658$		0			0
$659$	3.27760	+	18.5882i	0.127677	+	0.724093i	0.979682	+	0.200559i	$0.0642757\pi$
$659$	3.27760	+	18.5882i	0.127677	+	0.724093i	−0.852005	+	0.523534i	$0.824613\pi$
$660$	−5.29813	+	1.92836i	−0.206230	+	0.0750614i
$661$	28.7656	+	10.4698i	1.11885	+	0.407229i	0.834234	−	0.551411i	$-0.185910\pi$
$661$	28.7656	+	10.4698i	1.11885	+	0.407229i	0.284620	+	0.958640i	$0.408133\pi$
$662$	1.41312	−	0.514335i	0.0549226	−	0.0199902i
$663$	−0.807934	+	4.58202i	−0.0313775	+	0.177951i
$664$	−7.12918			−0.276666
$665$		0			0
$666$	2.00093			0.0775346
$667$	−1.05913	+	6.00660i	−0.0410095	+	0.232576i
$668$	−26.8081	+	9.75735i	−1.03724	+	0.377523i
$669$	1.50727	+	0.548603i	0.0582746	+	0.0212102i
$670$	29.7374	−	10.8235i	1.14886	−	0.418150i
$671$	2.60014	+	14.7461i	0.100377	+	0.569267i
$672$		0			0
$673$	−5.95471	+	10.3139i	−0.229537	+	0.397570i	−0.957671	−	0.287865i	$-0.907055\pi$
$673$	−5.95471	+	10.3139i	−0.229537	+	0.397570i	0.728134	+	0.685435i	$0.240388\pi$
$674$	17.1368	−	14.3795i	0.660085	−	0.553877i
$675$	−0.745567	−	4.22832i	−0.0286969	−	0.162748i
$676$	−18.3919			−0.707380
$677$	5.78106			0.222184			0.111092	−	0.993810i	$-0.464565\pi$
$677$	5.78106			0.222184			0.111092	+	0.993810i	$0.464565\pi$
$678$	0.599422	+	3.39949i	0.0230207	+	0.130557i
$679$		0			0
$680$	9.09627	−	7.63267i	0.348826	−	0.292700i
$681$	−5.59311	−	4.69318i	−0.214328	−	0.179843i
$682$	4.46657	+	3.74789i	0.171034	+	0.143514i
$683$	−10.5248	−	18.2295i	−0.402721	−	0.697533i	0.591332	−	0.806428i	$-0.298602\pi$
$683$	−10.5248	−	18.2295i	−0.402721	−	0.697533i	−0.994053	+	0.108895i	$0.965269\pi$
$684$	10.2121	+	10.3320i	0.390471	+	0.395052i
$685$	−49.4766			−1.89040
$686$		0			0
$687$	0.869833	−	4.93307i	0.0331862	−	0.188208i
$688$	−0.0349198	−	0.198040i	−0.00133131	−	0.00755021i
$689$	5.60994	−	31.8155i	0.213722	−	1.21208i
$690$	−1.59627	+	1.33943i	−0.0607688	+	0.0509911i
$691$	−32.9377			−1.25301			−0.626504	−	0.779418i	$-0.715515\pi$
$691$	−32.9377			−1.25301			−0.626504	+	0.779418i	$0.715515\pi$
$692$	0.549935	−	0.952515i	0.0209054	−	0.0362092i
$693$		0			0
$694$	−6.36484	−	2.31661i	−0.241606	−	0.0879374i
$695$	19.4932	+	33.7632i	0.739419	+	1.28071i
$696$	−2.61793	+	4.53438i	−0.0992322	+	0.171875i
$697$	−5.68479	+	4.77011i	−0.215327	+	0.180681i
$698$	−18.8053	+	6.84457i	−0.711791	+	0.259071i
$699$	−9.85819	+	8.27201i	−0.372871	+	0.312876i
$700$		0			0
$701$	−20.0694	+	7.30466i	−0.758010	+	0.275893i	−0.691973	−	0.721924i	$-0.743258\pi$
$701$	−20.0694	+	7.30466i	−0.758010	+	0.275893i	−0.0660380	+	0.997817i	$0.521036\pi$
$702$	−7.07650	+	12.2569i	−0.267085	+	0.462606i
$703$	−3.63475	−	0.339373i	−0.137087	−	0.0127997i
$704$	−8.60014	−	14.8959i	−0.324130	−	0.561409i
$705$	−0.167718	+	0.951178i	−0.00631664	+	0.0358234i
$706$	−1.74779	+	9.91220i	−0.0657789	+	0.373051i
$707$		0			0
$708$	5.37939	+	4.51384i	0.202170	+	0.169641i
$709$	14.8195	+	5.39387i	0.556560	+	0.202571i	0.604959	−	0.796257i	$-0.293190\pi$
$709$	14.8195	+	5.39387i	0.556560	+	0.202571i	−0.0483989	+	0.998828i	$0.515412\pi$
$710$	−15.3182	+	26.5319i	−0.574882	+	0.995725i
$711$	18.9181			0.709484
$712$	4.96270	−	4.16420i	0.185985	−	0.156060i
$713$	−3.21213	−	1.16912i	−0.120295	−	0.0437839i
$714$		0			0
$715$	−22.8516	−	39.5802i	−0.854603	−	1.48022i
$716$	−24.5736	−	8.94405i	−0.918357	−	0.334255i
$717$	−2.15523	+	12.2229i	−0.0804885	+	0.456473i
$718$	−8.58095	−	3.12321i	−0.320238	−	0.116557i
$719$	−27.0631	−	22.7086i	−1.00928	−	0.846888i	−0.0210385	−	0.999779i	$-0.506697\pi$
$719$	−27.0631	−	22.7086i	−1.00928	−	0.846888i	−0.988243	+	0.152891i	$0.951142\pi$
$720$	0.270792	−	0.0985603i	0.0100918	−	0.00367313i
$721$		0			0
$722$	10.5899	+	12.9237i	0.394114	+	0.480971i
$723$	−0.0791925	+	0.137165i	−0.00294520	+	0.00510124i
$724$	15.1284	+	12.6942i	0.562241	+	0.471776i
$725$	4.59967	−	1.67414i	0.170827	−	0.0621761i
$726$	0.0518514	+	0.294064i	0.00192438	+	0.0109137i
$727$	30.9647	+	25.9825i	1.14842	+	0.963637i	0.999681	−	0.0252396i	$-0.00803487\pi$
$727$	30.9647	+	25.9825i	1.14842	+	0.963637i	0.148737	+	0.988877i	$0.452479\pi$
$728$		0			0
$729$	6.44562	+	11.1641i	0.238727	+	0.413487i
$730$	−8.36959	−	14.4965i	−0.309772	−	0.536541i
$731$	1.37774	+	7.81353i	0.0509574	+	0.288994i
$732$	−0.497474	−	2.82131i	−0.0183872	−	0.104279i
$733$	18.1382	+	31.4162i	0.669948	+	1.16038i	0.977918	+	0.208988i	$0.0670170\pi$
$733$	18.1382	+	31.4162i	0.669948	+	1.16038i	−0.307970	+	0.951396i	$0.599650\pi$
$734$	14.3045	+	24.7762i	0.527990	+	0.914505i
$735$		0			0
$736$	7.59627	+	6.37402i	0.280002	+	0.234950i
$737$	8.41921	+	47.7477i	0.310126	+	1.75881i
$738$	−10.0809	+	3.66916i	−0.371085	+	0.135064i
$739$	−15.8387	−	13.2902i	−0.582635	−	0.488889i	0.303176	−	0.952935i	$-0.401953\pi$
$739$	−15.8387	−	13.2902i	−0.582635	−	0.488889i	−0.885811	+	0.464046i	$0.846397\pi$
$740$	1.30066	−	2.25281i	0.0478132	−	0.0828149i
$741$	7.09698	−	10.0108i	0.260714	−	0.367754i
$742$		0			0
$743$	−6.29978	+	2.29293i	−0.231117	+	0.0841196i	−0.454982	−	0.890500i	$-0.650354\pi$
$743$	−6.29978	+	2.29293i	−0.231117	+	0.0841196i	0.223866	+	0.974620i	$0.428132\pi$
$744$	−2.24787	−	1.88619i	−0.0824111	−	0.0691511i
$745$	−8.96198	−	3.26189i	−0.328342	−	0.119507i
$746$	4.65529	−	26.4014i	0.170442	−	0.966625i
$747$	6.41447	+	2.33468i	0.234693	+	0.0854213i
$748$	3.45811	+	5.98962i	0.126441	+	0.219002i
$749$		0			0
$750$	−3.99525	−	1.45415i	−0.145886	−	0.0530982i
$751$	8.20233	−	6.88258i	0.299307	−	0.251149i	−0.480749	−	0.876859i	$-0.659635\pi$
$751$	8.20233	−	6.88258i	0.299307	−	0.251149i	0.780056	+	0.625710i	$0.215191\pi$
$752$	−0.0300295			−0.00109506
$753$	4.30928	−	7.46389i	0.157039	−	0.271999i
$754$	−15.1621	−	5.51855i	−0.552171	−	0.200974i
$755$	28.3123	+	23.7568i	1.03039	+	0.864599i
$756$		0			0
$757$	−0.705432	+	4.00071i	−0.0256394	+	0.145408i	−0.994940	−	0.100470i	$-0.967965\pi$
$757$	−0.705432	+	4.00071i	−0.0256394	+	0.145408i	0.969301	+	0.245878i	$0.0790764\pi$
$758$	2.72725	−	15.4670i	0.0990583	−	0.561788i
$759$	−1.59627	−	2.76481i	−0.0579408	−	0.100356i
$760$	−30.2974	+	7.92907i	−1.09900	+	0.287617i
$761$	5.50387	−	9.53298i	0.199515	−	0.345570i	−0.748856	−	0.662733i	$-0.769397\pi$
$761$	5.50387	−	9.53298i	0.199515	−	0.345570i	0.948371	+	0.317162i	$0.102730\pi$
$762$	0.0444153	−	0.0161658i	0.00160900	−	0.000585627i
$763$		0			0
$764$	−17.8059	+	14.9409i	−0.644194	+	0.540543i
$765$	−10.6839	+	3.88863i	−0.386278	+	0.140594i
$766$	−15.8011	+	13.2587i	−0.570918	+	0.479057i
$767$	−28.4616	+	49.2969i	−1.02769	+	1.78001i
$768$	4.28359	+	7.41939i	0.154571	+	0.267724i
$769$	−20.0599	−	7.30121i	−0.723378	−	0.263288i	−0.0460191	−	0.998941i	$-0.514654\pi$
$769$	−20.0599	−	7.30121i	−0.723378	−	0.263288i	−0.677359	+	0.735652i	$0.736876\pi$
$770$		0			0
$771$	−4.08512	+	7.07564i	−0.147122	+	0.254823i
$772$	−15.8262			−0.569599
$773$	13.7253	−	11.5169i	0.493666	−	0.414235i	−0.361672	−	0.932305i	$-0.617794\pi$
$773$	13.7253	−	11.5169i	0.493666	−	0.414235i	0.855338	+	0.518070i	$0.173349\pi$
$774$	−1.99169	+	11.2954i	−0.0715897	+	0.406005i
$775$	0.476367	+	2.70161i	0.0171116	+	0.0970448i
$776$	0.898214	−	5.09403i	0.0322440	−	0.182865i
$777$		0			0
$778$	3.43788			0.123254
$779$	18.9346	−	4.95534i	0.678404	−	0.177543i
$780$	4.37211	+	7.57272i	0.156547	+	0.271147i
$781$	−35.9564	−	30.1710i	−1.28662	−	1.07960i
$782$	1.95811	+	1.64305i	0.0700219	+	0.0587554i
$783$	8.08100	−	6.78077i	0.288792	−	0.242325i
$784$		0			0
$785$	4.56165	+	25.8704i	0.162812	+	0.923355i
$786$	−1.42097			−0.0506843
$787$	48.8316			1.74066			0.870330	−	0.492470i	$-0.163906\pi$
$787$	48.8316			1.74066			0.870330	+	0.492470i	$0.163906\pi$
$788$	4.94191	+	28.0270i	0.176048	+	0.998420i
$789$	3.93061	−	3.29817i	0.139933	−	0.117418i
$790$	−7.75237	+	13.4275i	−0.275817	+	0.477729i
$791$		0			0
$792$	4.56687	+	25.9000i	0.162277	+	0.920316i
$793$	21.8221	−	7.94258i	0.774924	−	0.282049i
$794$	−7.40332	−	2.69459i	−0.262734	−	0.0956274i
$795$	−7.73055	+	2.81369i	−0.274174	+	0.0997913i
$796$	−1.96431	+	11.1401i	−0.0696231	+	0.394852i
$797$	−28.5262			−1.01045			−0.505225	−	0.862988i	$-0.668591\pi$
$797$	−28.5262			−1.01045			−0.505225	+	0.862988i	$0.668591\pi$
$798$		0			0
$799$	1.18479			0.0419149
$800$	1.38191	−	7.83721i	0.0488579	−	0.277087i
$801$	−5.82888	+	2.12154i	−0.205953	+	0.0749609i
$802$	1.67530	+	0.609758i	0.0591568	+	0.0215313i
$803$	24.0993	−	8.77141i	0.850444	−	0.309536i
$804$	−1.61081	−	9.13538i	−0.0568091	−	0.322180i
$805$		0			0
$806$	4.52141	−	7.83131i	0.159260	−	0.275846i
$807$	−7.45059	+	6.25179i	−0.262273	+	0.220073i
$808$	3.90302	+	22.1351i	0.137308	+	0.778711i
$809$	−14.8367			−0.521630			−0.260815	−	0.965389i	$-0.583991\pi$
$809$	−14.8367			−0.521630			−0.260815	+	0.965389i	$0.583991\pi$
$810$	−14.5449			−0.511055
$811$	−1.45471	−	8.25006i	−0.0510817	−	0.289699i	0.948556	−	0.316609i	$-0.102544\pi$
$811$	−1.45471	−	8.25006i	−0.0510817	−	0.289699i	−0.999638	+	0.0269103i	$0.991433\pi$
$812$		0			0
$813$	7.72984	−	6.48610i	0.271097	−	0.227478i
$814$	−1.92468	−	1.61500i	−0.0674599	−	0.0566056i
$815$	3.92262	+	3.29147i	0.137403	+	0.115295i
$816$	0.0184183	+	0.0319015i	0.000644770	+	0.00111677i
$817$	5.53374	−	20.1806i	0.193601	−	0.706031i
$818$	−28.3233			−0.990299
$819$		0			0
$820$	−2.42185	+	13.7350i	−0.0845746	+	0.479646i
$821$	1.09034	+	6.18361i	0.0380530	+	0.215809i	0.997905	−	0.0646980i	$-0.0206084\pi$
$821$	1.09034	+	6.18361i	0.0380530	+	0.215809i	−0.959852	+	0.280507i	$0.909497\pi$
$822$	1.58765	−	9.00400i	0.0553756	−	0.314051i
$823$	8.44672	−	7.08764i	0.294434	−	0.247060i	−0.483589	−	0.875295i	$-0.660667\pi$
$823$	8.44672	−	7.08764i	0.294434	−	0.247060i	0.778023	+	0.628236i	$0.216223\pi$
$824$	0.0412797			0.00143805
$825$	−1.28106	+	2.21886i	−0.0446008	+	0.0772508i
$826$		0			0
$827$	−31.8892	−	11.6067i	−1.10890	−	0.403606i	−0.278309	−	0.960492i	$-0.589774\pi$
$827$	−31.8892	−	11.6067i	−1.10890	−	0.403606i	−0.830589	+	0.556886i	$0.811996\pi$
$828$	−2.93077	−	5.07624i	−0.101851	−	0.176412i
$829$	10.1834	−	17.6382i	0.353686	−	0.612602i	−0.633206	−	0.773983i	$-0.718262\pi$
$829$	10.1834	−	17.6382i	0.353686	−	0.612602i	0.986892	+	0.161381i	$0.0515949\pi$
$830$	−4.28564	+	3.59608i	−0.148757	+	0.124822i
$831$	−6.88191	+	2.50481i	−0.238731	+	0.0868909i
$832$	−20.4349	+	17.1470i	−0.708454	+	0.594464i
$833$		0			0
$834$	−6.76991	+	2.46405i	−0.234423	+	0.0853230i
$835$	−29.4440	+	50.9986i	−1.01895	+	1.76488i
$836$	−1.48380	−	18.1806i	−0.0513184	−	0.628791i
$837$	2.95605	+	5.12003i	0.102176	+	0.176974i
$838$	−3.55035	+	20.1350i	−0.122645	+	0.695552i
$839$	2.74526	−	15.5692i	0.0947770	−	0.537507i	−0.900038	−	0.435810i	$-0.856462\pi$
$839$	2.74526	−	15.5692i	0.0947770	−	0.537507i	0.994815	−	0.101697i	$-0.0324271\pi$
$840$		0			0
$841$	−13.0025	−	10.9104i	−0.448363	−	0.376221i
$842$	−5.33275	−	1.94096i	−0.183779	−	0.0668900i
$843$	−3.48814	+	6.04164i	−0.120138	+	0.208085i
$844$	−17.9385			−0.617469
$845$	−29.0822	+	24.4029i	−1.00046	+	0.839484i
$846$	1.60947	+	0.585799i	0.0553347	+	0.0201402i
$847$		0			0
$848$	−0.127889	−	0.221510i	−0.00439172	−	0.00760668i
$849$	8.68866	+	3.16241i	0.298194	+	0.108534i
$850$	0.356219	−	2.02022i	0.0122182	−	0.0692930i
$851$	1.38413	+	0.503783i	0.0474475	+	0.0172695i
$852$	6.87939	+	5.77249i	0.235684	+	0.197762i
$853$	49.4741	−	18.0071i	1.69396	−	0.616551i	0.698845	−	0.715274i	$-0.253698\pi$
$853$	49.4741	−	18.0071i	1.69396	−	0.616551i	0.995115	+	0.0987227i	$0.0314757\pi$
$854$		0			0
$855$	29.8567	+	2.78768i	1.02108	+	0.0953368i
$856$	−5.04277	+	8.73433i	−0.172358	+	0.298533i
$857$	−17.6400	−	14.8017i	−0.602570	−	0.505616i	0.289701	−	0.957117i	$-0.406444\pi$
$857$	−17.6400	−	14.8017i	−0.602570	−	0.505616i	−0.892271	+	0.451501i	$0.850889\pi$
$858$	7.93629	−	2.88857i	0.270940	−	0.0986143i
$859$	1.54710	+	8.77406i	0.0527865	+	0.299367i	0.999759	−	0.0219471i	$-0.00698655\pi$
$859$	1.54710	+	8.77406i	0.0527865	+	0.299367i	−0.946973	+	0.321314i	$0.895875\pi$
$860$	11.4226	+	9.58471i	0.389508	+	0.326836i
$861$		0			0
$862$	6.15451	+	10.6599i	0.209624	+	0.363079i
$863$	−14.8849	−	25.7814i	−0.506688	−	0.877609i	−0.999970	−	0.00773998i	$-0.997536\pi$
$863$	−14.8849	−	25.7814i	−0.506688	−	0.877609i	0.493282	−	0.869869i	$-0.335797\pi$
$864$	−2.97818	−	16.8901i	−0.101320	−	0.574612i
$865$	−0.394238	−	2.23583i	−0.0134045	−	0.0760206i
$866$	12.6160	+	21.8516i	0.428710	+	0.742548i
$867$	3.79607	+	6.57499i	0.128921	+	0.223298i
$868$		0			0
$869$	−18.1971	−	15.2692i	−0.617295	−	0.517972i
$870$	0.713478	+	4.04633i	0.0241892	+	0.137184i
$871$	70.6596	−	25.7180i	2.39421	−	0.871421i
$872$	−16.0189	−	13.4414i	−0.542468	−	0.455185i
$873$	−2.47637	+	4.28919i	−0.0838123	+	0.145167i
$874$	−2.81345	−	6.12651i	−0.0951665	−	0.207232i
$875$		0			0
$876$	−4.61081	+	1.67820i	−0.155785	+	0.0567011i
$877$	−19.1741	−	16.0890i	−0.647464	−	0.543287i	0.258836	−	0.965921i	$-0.416661\pi$
$877$	−19.1741	−	16.0890i	−0.647464	−	0.543287i	−0.906300	+	0.422635i	$0.861105\pi$
$878$	11.0254	+	4.01291i	0.372089	+	0.135429i
$879$	1.44175	−	8.17658i	0.0486291	−	0.275789i
$880$	−0.340022	−	0.123758i	−0.0114622	−	0.00417188i
$881$	−10.1980	−	17.6634i	−0.343579	−	0.595097i	0.641515	−	0.767110i	$-0.278306\pi$
$881$	−10.1980	−	17.6634i	−0.343579	−	0.595097i	−0.985095	+	0.172014i	$0.944973\pi$
$882$		0			0
$883$	9.98710	+	3.63501i	0.336093	+	0.122328i	0.504553	−	0.863381i	$-0.331657\pi$
$883$	9.98710	+	3.63501i	0.336093	+	0.122328i	−0.168460	+	0.985708i	$0.553880\pi$
$884$	8.21688	−	6.89478i	0.276364	−	0.231897i
$885$	14.4953			0.487253
$886$	−14.8981	+	25.8043i	−0.500512	+	0.866912i
$887$	52.9411	+	19.2690i	1.77759	+	0.646989i	0.999830	+	0.0184249i	$0.00586515\pi$
$887$	52.9411	+	19.2690i	1.77759	+	0.646989i	0.777758	+	0.628564i	$0.216357\pi$
$888$	0.968626	+	0.812774i	0.0325050	+	0.0272749i
$889$		0			0
$890$	0.882789	−	5.00654i	0.0295911	−	0.167820i
$891$	3.86959	−	21.9455i	0.129636	−	0.735202i
$892$	−1.84895	−	3.20247i	−0.0619073	−	0.107227i
$893$	−2.82429	−	1.33710i	−0.0945113	−	0.0447443i
$894$	0.881196	−	1.52628i	0.0294716	−	0.0510463i
$895$	−50.7242	+	18.4621i	−1.69552	+	0.617120i
$896$		0			0
$897$	−3.79292	+	3.18264i	−0.126642	+	0.106265i
$898$	−15.5686	+	5.66651i	−0.519532	+	0.189094i
$899$	−5.16322	+	4.33246i	−0.172203	+	0.144495i
$900$	−2.35204	+	4.07386i	−0.0784015	+	0.135795i
$901$	5.04576	+	8.73951i	0.168099	+	0.291155i
$902$	12.6582	+	4.60722i	0.421473	+	0.153404i
$903$		0			0
$904$	10.4666	−	18.1286i	0.348113	−	0.602949i
$905$	40.7648			1.35507
$906$	−5.23190	+	4.39008i	−0.173818	+	0.145851i
$907$	−1.02863	+	5.83365i	−0.0341551	+	0.193703i	−0.997111	−	0.0759549i	$-0.975800\pi$
$907$	−1.02863	+	5.83365i	−0.0341551	+	0.193703i	0.962956	+	0.269658i	$0.0869106\pi$
$908$	2.92292	+	16.5767i	0.0970006	+	0.550118i
$909$	3.73711	−	21.1942i	0.123952	−	0.702968i
$910$		0			0
$911$	−34.0591			−1.12843			−0.564215	−	0.825628i	$-0.690821\pi$
$911$	−34.0591			−1.12843			−0.564215	+	0.825628i	$0.690821\pi$
$912$	−0.00790291	−	0.0968323i	−0.000261692	−	0.00320644i
$913$	−4.28564	−	7.42295i	−0.141834	−	0.245664i
$914$	9.61902	+	8.07132i	0.318169	+	0.266975i
$915$	−4.53003	−	3.80115i	−0.149758	−	0.125662i
$916$	−8.84642	+	7.42303i	−0.292294	+	0.245264i
$917$		0			0
$918$	−0.767693	−	4.35381i	−0.0253377	−	0.143697i
$919$	−6.27395			−0.206958			−0.103479	−	0.994632i	$-0.532998\pi$
$919$	−6.27395			−0.206958			−0.103479	+	0.994632i	$0.532998\pi$
$920$	12.6364			0.416610
$921$	1.98839	+	11.2767i	0.0655196	+	0.371580i
$922$	−9.38263	+	7.87296i	−0.309000	+	0.259282i
$923$	−36.3979	+	63.0429i	−1.19805	+	2.07508i
$924$		0			0
$925$	−0.205270	−	1.16415i	−0.00674924	−	0.0382769i
$926$	1.45677	−	0.530220i	0.0478723	−	0.0174241i
$927$	−0.0371413	−	0.0135183i	−0.00121988	−	0.000444000i
$928$	18.3735	−	6.68739i	0.603138	−	0.219524i
$929$	4.91828	−	27.8930i	0.161364	−	0.915138i	−0.791371	−	0.611336i	$-0.790633\pi$
$929$	4.91828	−	27.8930i	0.161364	−	0.915138i	0.952735	−	0.303803i	$-0.0982563\pi$
$930$	−2.30272			−0.0755091
$931$		0			0
$932$	29.6682			0.971814
$933$	1.33931	−	7.59559i	0.0438469	−	0.248668i
$934$	−18.2144	+	6.62948i	−0.595992	+	0.216923i
$935$	13.4153	+	4.88279i	0.438729	+	0.159684i
$936$	38.3282	−	13.9503i	1.25280	−	0.455980i
$937$	−3.48545	−	19.7670i	−0.113865	−	0.645759i	−0.987306	−	0.158830i	$-0.949228\pi$
$937$	−3.48545	−	19.7670i	−0.113865	−	0.645759i	0.873441	−	0.486930i	$-0.161883\pi$
$938$		0			0
$939$	−5.19278	+	8.99416i	−0.169460	+	0.293513i
$940$	1.70574	−	1.43128i	0.0556350	−	0.0466833i
$941$	0.936862	+	5.31321i	0.0305408	+	0.173206i	0.996263	−	0.0863726i	$-0.0275276\pi$
$941$	0.936862	+	5.31321i	0.0305408	+	0.173206i	−0.965722	+	0.259578i	$0.916416\pi$
$942$	−4.85441			−0.158165
$943$	−7.89723			−0.257169
$944$	0.0782589	+	0.443828i	0.00254711	+	0.0144454i
$945$		0			0
$946$	11.0326	−	9.25741i	0.358699	−	0.300984i
$947$	5.08899	+	4.27017i	0.165370	+	0.138762i	0.721717	−	0.692188i	$-0.243353\pi$
$947$	5.08899	+	4.27017i	0.165370	+	0.138762i	−0.556347	+	0.830950i	$0.687798\pi$
$948$	3.48158	+	2.92139i	0.113077	+	0.0948825i
$949$	−19.8871	−	34.4455i	−0.645563	−	1.11815i
$950$	−3.12907	+	4.41376i	−0.101520	+	0.143201i
$951$	15.0833			0.489109
$952$		0			0
$953$	−2.57414	+	14.5987i	−0.0833846	+	0.472897i	0.914309	+	0.405018i	$0.132735\pi$
$953$	−2.57414	+	14.5987i	−0.0833846	+	0.472897i	−0.997693	+	0.0678799i	$0.978377\pi$
$954$	2.53327	+	14.3669i	0.0820177	+	0.465145i
$955$	−8.33157	+	47.2507i	−0.269603	+	1.52900i
$956$	21.9192	−	18.3924i	0.708918	−	0.594853i
$957$	−6.29498			−0.203488
$958$	11.1932	−	19.3873i	0.361637	−	0.626374i
$959$		0			0
$960$	6.38326	+	2.32332i	0.206019	+	0.0749847i
$961$	13.6113	+	23.5754i	0.439074	+	0.760498i
$962$	−1.94831	+	3.37457i	−0.0628161	+	0.108801i
$963$	7.39756	−	6.20729i	0.238383	−	0.200027i
$964$	0.343121	−	0.124886i	0.0110512	−	0.00402230i
$965$	−25.0253	+	20.9987i	−0.805592	+	0.675972i
$966$		0			0
$967$	−19.9418	+	7.25822i	−0.641285	+	0.233409i	−0.642136	−	0.766591i	$-0.721951\pi$
$967$	−19.9418	+	7.25822i	−0.641285	+	0.233409i	0.000850519		1.00000i	$0.499729\pi$
$968$	0.905382	−	1.56817i	0.0291001	−	0.0504028i
$969$	0.311804	+	3.82045i	0.0100166	+	0.122730i
$970$	−2.02956	−	3.51531i	−0.0651653	−	0.112870i
$971$	−6.53033	+	37.0354i	−0.209568	+	1.18852i	0.680519	+	0.732731i	$0.261755\pi$
$971$	−6.53033	+	37.0354i	−0.209568	+	1.18852i	−0.890087	+	0.455791i	$0.849357\pi$
$972$	−2.68422	+	15.2230i	−0.0860964	+	0.488277i
$973$		0			0
$974$	−15.1643	−	12.7244i	−0.485896	−	0.407715i
$975$	3.73396	+	1.35905i	0.119582	+	0.0435244i
$976$	0.0919294	−	0.159226i	0.00294259	−	0.00509671i
$977$	−46.0215			−1.47236			−0.736179	−	0.676787i	$-0.763372\pi$
$977$	−46.0215			−1.47236			−0.736179	+	0.676787i	$0.763372\pi$
$978$	−0.724871	+	0.608239i	−0.0231788	+	0.0194493i
$979$	7.31908	+	2.66393i	0.233919	+	0.0851395i
$980$		0			0
$981$	10.0111	+	17.3398i	0.319631	+	0.553618i
$982$	−12.9192	−	4.70221i	−0.412269	−	0.150054i
$983$	10.5225	−	59.6758i	0.335614	−	1.90336i	−0.0854708	−	0.996341i	$-0.527239\pi$
$983$	10.5225	−	59.6758i	0.335614	−	1.90336i	0.421085	−	0.907021i	$-0.361649\pi$
$984$	−6.37046	−	2.31866i	−0.203083	−	0.0739161i
$985$	45.0014	+	37.7607i	1.43386	+	1.20315i
$986$	4.73618	−	1.72383i	0.150831	−	0.0548979i
$987$		0			0
$988$	−27.3684	+	7.16252i	−0.870705	+	0.227870i
$989$	−4.22163	+	7.31208i	−0.134240	+	0.232510i
$990$	15.8097	+	13.2660i	0.502467	+	0.421620i
$991$	−39.3714	+	14.3300i	−1.25067	+	0.455208i	−0.880629	−	0.473806i	$-0.842880\pi$
$991$	−39.3714	+	14.3300i	−1.25067	+	0.455208i	−0.370044	+	0.929014i	$0.620658\pi$
$992$	1.90286	+	10.7916i	0.0604157	+	0.342635i
$993$	−0.697033	−	0.584880i	−0.0221197	−	0.0185606i
$994$		0			0
$995$	11.6750	+	20.2217i	0.370122	+	0.641070i
$996$	0.819955	+	1.42020i	0.0259813	+	0.0450009i
$997$	5.85457	+	33.2029i	0.185416	+	1.05155i	0.925420	+	0.378944i	$0.123713\pi$
$997$	5.85457	+	33.2029i	0.185416	+	1.05155i	−0.740004	+	0.672603i	$0.765176\pi$
$998$	−4.36989	−	24.7829i	−0.138326	−	0.784488i
$999$	−1.27379	−	2.20626i	−0.0403008	−	0.0698030i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	931.2.x.a.765.1		6
7.2	even	3		19.2.e.a.5.1	yes	6
7.3	odd	6		931.2.v.a.214.1		6
7.4	even	3		931.2.v.b.214.1		6
7.5	odd	6		931.2.w.a.442.1		6
7.6	odd	2		931.2.x.b.765.1		6
19.4	even	9		931.2.v.b.422.1		6
21.2	odd	6		171.2.u.c.100.1		6
28.23	odd	6		304.2.u.b.81.1		6
35.2	odd	12		475.2.u.a.24.1		12
35.9	even	6		475.2.l.a.176.1		6
35.23	odd	12		475.2.u.a.24.2		12
133.2	odd	18		361.2.a.h.1.1		3
133.4	even	9	inner	931.2.x.a.802.1		6
133.9	even	9		361.2.e.f.234.1		6
133.16	even	9		361.2.c.i.292.1		6
133.23	even	9		19.2.e.a.4.1	✓	6
133.30	even	3		361.2.e.f.54.1		6
133.37	odd	6		361.2.e.h.62.1		6
133.44	even	9		361.2.e.g.28.1		6
133.51	odd	18		361.2.e.a.28.1		6
133.61	odd	18		931.2.w.a.99.1		6
133.65	odd	6		361.2.e.b.54.1		6
133.72	odd	18		361.2.e.h.99.1		6
133.79	odd	18		361.2.c.h.292.3		6
133.80	odd	18		931.2.x.b.802.1		6
133.86	odd	18		361.2.e.b.234.1		6
133.93	even	9		361.2.a.g.1.3		3
133.100	even	9		361.2.c.i.68.1		6
133.107	odd	6		361.2.e.a.245.1		6
133.118	odd	18		931.2.v.a.422.1		6
133.121	even	3		361.2.e.g.245.1		6
133.128	odd	18		361.2.c.h.68.3		6
399.2	even	18		3249.2.a.s.1.3		3
399.23	odd	18		171.2.u.c.118.1		6
399.359	odd	18		3249.2.a.z.1.1		3
532.23	odd	18		304.2.u.b.289.1		6
532.135	even	18		5776.2.a.bi.1.3		3
532.359	odd	18		5776.2.a.br.1.1		3
665.23	odd	36		475.2.u.a.99.1		12
665.289	even	18		475.2.l.a.251.1		6
665.359	even	18		9025.2.a.bd.1.1		3
665.422	odd	36		475.2.u.a.99.2		12
665.534	odd	18		9025.2.a.x.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.2.e.a.4.1	✓	6	133.23	even	9
19.2.e.a.5.1	yes	6	7.2	even	3
171.2.u.c.100.1		6	21.2	odd	6
171.2.u.c.118.1		6	399.23	odd	18
304.2.u.b.81.1		6	28.23	odd	6
304.2.u.b.289.1		6	532.23	odd	18
361.2.a.g.1.3		3	133.93	even	9
361.2.a.h.1.1		3	133.2	odd	18
361.2.c.h.68.3		6	133.128	odd	18
361.2.c.h.292.3		6	133.79	odd	18
361.2.c.i.68.1		6	133.100	even	9
361.2.c.i.292.1		6	133.16	even	9
361.2.e.a.28.1		6	133.51	odd	18
361.2.e.a.245.1		6	133.107	odd	6
361.2.e.b.54.1		6	133.65	odd	6
361.2.e.b.234.1		6	133.86	odd	18
361.2.e.f.54.1		6	133.30	even	3
361.2.e.f.234.1		6	133.9	even	9
361.2.e.g.28.1		6	133.44	even	9
361.2.e.g.245.1		6	133.121	even	3
361.2.e.h.62.1		6	133.37	odd	6
361.2.e.h.99.1		6	133.72	odd	18
475.2.l.a.176.1		6	35.9	even	6
475.2.l.a.251.1		6	665.289	even	18
475.2.u.a.24.1		12	35.2	odd	12
475.2.u.a.24.2		12	35.23	odd	12
475.2.u.a.99.1		12	665.23	odd	36
475.2.u.a.99.2		12	665.422	odd	36
931.2.v.a.214.1		6	7.3	odd	6
931.2.v.a.422.1		6	133.118	odd	18
931.2.v.b.214.1		6	7.4	even	3
931.2.v.b.422.1		6	19.4	even	9
931.2.w.a.99.1		6	133.61	odd	18
931.2.w.a.442.1		6	7.5	odd	6
931.2.x.a.765.1		6	1.1	even	1	trivial
931.2.x.a.802.1		6	133.4	even	9	inner
931.2.x.b.765.1		6	7.6	odd	2
931.2.x.b.802.1		6	133.80	odd	18
3249.2.a.s.1.3		3	399.2	even	18
3249.2.a.z.1.1		3	399.359	odd	18
5776.2.a.bi.1.3		3	532.135	even	18
5776.2.a.br.1.1		3	532.359	odd	18
9025.2.a.x.1.3		3	665.534	odd	18
9025.2.a.bd.1.1		3	665.359	even	18

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:	\( N \)	\(=\)	\( 931 = 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	931.x (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.152704 - 0.866025i) q^{2} +(-0.500000 + 0.181985i) q^{3} +(1.15270 + 0.419550i) q^{4} +(2.37939 - 0.866025i) q^{5} +(0.0812519 + 0.460802i) q^{6} +(1.41875 - 2.45734i) q^{8} +(-2.08125 + 1.74638i) q^{9} +O(q^{10})\)	\(q+(0.152704 - 0.866025i) q^{2} +(-0.500000 + 0.181985i) q^{3} +(1.15270 + 0.419550i) q^{4} +(2.37939 - 0.866025i) q^{5} +(0.0812519 + 0.460802i) q^{6} +(1.41875 - 2.45734i) q^{8} +(-2.08125 + 1.74638i) q^{9} +(-0.386659 - 2.19285i) q^{10} +3.41147 q^{11} -0.652704 q^{12} +(-0.918748 - 5.21048i) q^{13} +(-1.03209 + 0.866025i) q^{15} +(-0.0320889 - 0.0269258i) q^{16} +(1.26604 + 1.06234i) q^{17} +(1.19459 + 2.06910i) q^{18} +(-1.81908 - 3.96118i) q^{19} +3.10607 q^{20} +(0.520945 - 2.95442i) q^{22} +(0.305407 + 1.73205i) q^{23} +(-0.262174 + 1.48686i) q^{24} +(1.08125 - 0.907278i) q^{25} -4.65270 q^{26} +(1.52094 - 2.63435i) q^{27} +(3.25877 + 1.18610i) q^{29} +(0.592396 + 1.02606i) q^{30} +(-0.971782 + 1.68317i) q^{31} +(4.31908 - 3.62414i) q^{32} +(-1.70574 + 0.620838i) q^{33} +(1.11334 - 0.934204i) q^{34} +(-3.13176 + 1.13987i) q^{36} +(0.418748 - 0.725293i) q^{37} +(-3.70826 + 0.970481i) q^{38} +(1.40760 + 2.43804i) q^{39} +(1.24763 - 7.07564i) q^{40} +(-0.779715 + 4.42198i) q^{41} +(3.67752 + 3.08580i) q^{43} +(3.93242 + 1.43128i) q^{44} +(-3.43969 + 5.95772i) q^{45} +1.54664 q^{46} +(0.549163 - 0.460802i) q^{47} +(0.0209445 + 0.00762319i) q^{48} +(-0.620615 - 1.07494i) q^{50} +(-0.826352 - 0.300767i) q^{51} +(1.12701 - 6.39160i) q^{52} +(5.73783 + 2.08840i) q^{53} +(-2.04916 - 1.71945i) q^{54} +(8.11721 - 2.95442i) q^{55} +(1.63041 + 1.64955i) q^{57} +(1.52481 - 2.64106i) q^{58} +(-8.24170 - 6.91560i) q^{59} +(-1.55303 + 0.565258i) q^{60} +(0.762174 + 4.32250i) q^{61} +(1.30928 + 1.09861i) q^{62} +(-2.52094 - 4.36640i) q^{64} +(-6.69846 - 11.6021i) q^{65} +(0.277189 + 1.57202i) q^{66} +(2.46791 + 13.9962i) q^{67} +(1.01367 + 1.75573i) q^{68} +(-0.467911 - 0.810446i) q^{69} +(-10.5398 - 8.84397i) q^{71} +(1.33868 + 7.59202i) q^{72} +(7.06418 - 2.57115i) q^{73} +(-0.564178 - 0.473401i) q^{74} +(-0.375515 + 0.650411i) q^{75} +(-0.434945 - 5.32926i) q^{76} +(2.32635 - 0.846723i) q^{78} +(-5.33409 - 4.47584i) q^{79} +(-0.0996702 - 0.0362770i) q^{80} +(1.13429 - 6.43285i) q^{81} +(3.71048 + 1.35051i) q^{82} +(-1.25624 - 2.17588i) q^{83} +(3.93242 + 1.43128i) q^{85} +(3.23396 - 2.71361i) q^{86} -1.84524 q^{87} +(4.84002 - 8.38316i) q^{88} +(2.14543 + 0.780873i) q^{89} +(4.63429 + 3.88863i) q^{90} +(-0.374638 + 2.12467i) q^{92} +(0.179578 - 1.01844i) q^{93} +(-0.315207 - 0.545955i) q^{94} +(-7.75877 - 7.84981i) q^{95} +(-1.50000 + 2.59808i) q^{96} +(1.71301 - 0.623485i) q^{97} +(-7.10014 + 5.95772i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 3 q^{3} + 9 q^{4} + 3 q^{5} + 3 q^{6} + 6 q^{8} - 15 q^{9}+O(q^{10}) \) 6 * q + 3 * q^2 - 3 * q^3 + 9 * q^4 + 3 * q^5 + 3 * q^6 + 6 * q^8 - 15 * q^9	\( 6 q + 3 q^{2} - 3 q^{3} + 9 q^{4} + 3 q^{5} + 3 q^{6} + 6 q^{8} - 15 q^{9} - 9 q^{10} - 6 q^{12} - 3 q^{13} + 3 q^{15} + 9 q^{16} + 3 q^{17} + 3 q^{18} + 6 q^{19} - 6 q^{20} + 6 q^{23} - 21 q^{24} + 9 q^{25} - 30 q^{26} + 6 q^{27} - 3 q^{29} + 9 q^{31} + 9 q^{32} - 24 q^{36} + 3 q^{38} + 12 q^{39} - 9 q^{40} + 21 q^{41} - 3 q^{43} - 15 q^{45} + 36 q^{46} + 15 q^{47} - 3 q^{48} - 15 q^{50} - 6 q^{51} - 21 q^{52} + 15 q^{53} - 24 q^{54} + 18 q^{55} + 24 q^{57} - 18 q^{58} - 6 q^{59} + 3 q^{60} + 24 q^{61} - 12 q^{62} - 12 q^{64} - 12 q^{65} - 9 q^{66} + 24 q^{67} - 15 q^{68} - 12 q^{69} - 6 q^{71} - 3 q^{72} + 24 q^{73} + 15 q^{74} - 15 q^{75} + 36 q^{76} + 15 q^{78} + 15 q^{79} - 15 q^{80} - 3 q^{81} + 45 q^{82} + 24 q^{86} + 42 q^{87} + 9 q^{88} - 3 q^{89} + 18 q^{90} + 42 q^{92} + 27 q^{93} - 9 q^{94} - 24 q^{95} - 9 q^{96} + 18 q^{97} + 9 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 - 3 * q^3 + 9 * q^4 + 3 * q^5 + 3 * q^6 + 6 * q^8 - 15 * q^9 - 9 * q^10 - 6 * q^12 - 3 * q^13 + 3 * q^15 + 9 * q^16 + 3 * q^17 + 3 * q^18 + 6 * q^19 - 6 * q^20 + 6 * q^23 - 21 * q^24 + 9 * q^25 - 30 * q^26 + 6 * q^27 - 3 * q^29 + 9 * q^31 + 9 * q^32 - 24 * q^36 + 3 * q^38 + 12 * q^39 - 9 * q^40 + 21 * q^41 - 3 * q^43 - 15 * q^45 + 36 * q^46 + 15 * q^47 - 3 * q^48 - 15 * q^50 - 6 * q^51 - 21 * q^52 + 15 * q^53 - 24 * q^54 + 18 * q^55 + 24 * q^57 - 18 * q^58 - 6 * q^59 + 3 * q^60 + 24 * q^61 - 12 * q^62 - 12 * q^64 - 12 * q^65 - 9 * q^66 + 24 * q^67 - 15 * q^68 - 12 * q^69 - 6 * q^71 - 3 * q^72 + 24 * q^73 + 15 * q^74 - 15 * q^75 + 36 * q^76 + 15 * q^78 + 15 * q^79 - 15 * q^80 - 3 * q^81 + 45 * q^82 + 24 * q^86 + 42 * q^87 + 9 * q^88 - 3 * q^89 + 18 * q^90 + 42 * q^92 + 27 * q^93 - 9 * q^94 - 24 * q^95 - 9 * q^96 + 18 * q^97 + 9 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more