LMFDB - Embedded newform 1089.2.e.m.727.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1089,2,Mod(364,1089)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1089, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("1089.364");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1089 = 3^{2} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1089.e (of order $3$, 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:	$8.69570878012$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 15 x^{18} - 2 x^{17} + 150 x^{16} - 30 x^{15} + 830 x^{14} - 321 x^{13} + 3324 x^{12} + \cdots + 9 $ x^20 + 15x^18 - 2x^17 + 150x^16 - 30x^15 + 830x^14 - 321x^13 + 3324x^12 - 1529x^11 + 8388x^10 - 4959x^9 + 15449x^8 - 9234x^7 + 16749x^6 - 11141x^5 + 12630x^4 - 5604x^3 + 2737x^2 - 165x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			727.5
Root			$0.342978 + 0.594056i$ of defining polynomial
Character	$\chi$	$=$	1089.727
Dual form			1089.2.e.m.364.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.342978 + 0.594056i) q^{2} +(-0.510856 - 1.65500i) q^{3} +(0.764732 + 1.32455i) q^{4} +(1.07171 + 1.85626i) q^{5} +(1.15838 + 0.264152i) q^{6} +(0.684647 - 1.18584i) q^{7} -2.42106 q^{8} +(-2.47805 + 1.69093i) q^{9} +O(q^{10})$	\(q+(-0.342978 + 0.594056i) q^{2} +(-0.510856 - 1.65500i) q^{3} +(0.764732 + 1.32455i) q^{4} +(1.07171 + 1.85626i) q^{5} +(1.15838 + 0.264152i) q^{6} +(0.684647 - 1.18584i) q^{7} -2.42106 q^{8} +(-2.47805 + 1.69093i) q^{9} -1.47030 q^{10} +(1.80147 - 1.94229i) q^{12} +(-1.84469 - 3.19509i) q^{13} +(0.469638 + 0.813437i) q^{14} +(2.52463 - 2.72197i) q^{15} +(-0.699093 + 1.21086i) q^{16} +5.72966 q^{17} +(-0.154590 - 2.05205i) q^{18} +6.04848 q^{19} +(-1.63915 + 2.83909i) q^{20} +(-2.31233 - 0.527296i) q^{21} +(3.00398 + 5.20304i) q^{23} +(1.23681 + 4.00685i) q^{24} +(0.202854 - 0.351353i) q^{25} +2.53075 q^{26} +(4.06442 + 3.23736i) q^{27} +2.09428 q^{28} +(-1.38325 + 2.39586i) q^{29} +(0.751111 + 2.43335i) q^{30} +(2.93221 + 5.07873i) q^{31} +(-2.90061 - 5.02400i) q^{32} +(-1.96515 + 3.40374i) q^{34} +2.93498 q^{35} +(-4.13478 - 1.98921i) q^{36} -10.4062 q^{37} +(-2.07450 + 3.59313i) q^{38} +(-4.34551 + 4.68519i) q^{39} +(-2.59468 - 4.49413i) q^{40} +(2.95744 + 5.12243i) q^{41} +(1.10632 - 1.19280i) q^{42} +(1.94730 - 3.37282i) q^{43} +(-5.79459 - 2.78772i) q^{45} -4.12120 q^{46} +(-0.570634 + 0.988368i) q^{47} +(2.36112 + 0.538422i) q^{48} +(2.56252 + 4.43841i) q^{49} +(0.139149 + 0.241013i) q^{50} +(-2.92703 - 9.48259i) q^{51} +(2.82138 - 4.88678i) q^{52} +6.47721 q^{53} +(-3.31718 + 1.30415i) q^{54} +(-1.65757 + 2.87100i) q^{56} +(-3.08990 - 10.0102i) q^{57} +(-0.948850 - 1.64346i) q^{58} +(4.43365 + 7.67931i) q^{59} +(5.53606 + 1.26243i) q^{60} +(-4.42873 + 7.67078i) q^{61} -4.02273 q^{62} +(0.308590 + 4.09627i) q^{63} +1.18301 q^{64} +(3.95396 - 6.84846i) q^{65} +(-1.00040 - 1.73274i) q^{67} +(4.38165 + 7.58925i) q^{68} +(7.07644 - 7.62959i) q^{69} +(-1.00664 + 1.74354i) q^{70} +2.39698 q^{71} +(5.99951 - 4.09385i) q^{72} -10.7276 q^{73} +(3.56909 - 6.18185i) q^{74} +(-0.685119 - 0.156233i) q^{75} +(4.62546 + 8.01154i) q^{76} +(-1.29285 - 4.18840i) q^{78} +(2.23734 - 3.87519i) q^{79} -2.99691 q^{80} +(3.28149 - 8.38044i) q^{81} -4.05735 q^{82} +(-4.96371 + 8.59739i) q^{83} +(-1.06988 - 3.46604i) q^{84} +(6.14056 + 10.6358i) q^{85} +(1.33576 + 2.31361i) q^{86} +(4.67179 + 1.06534i) q^{87} +11.0155 q^{89} +(3.64348 - 2.48618i) q^{90} -5.05184 q^{91} +(-4.59448 + 7.95787i) q^{92} +(6.90736 - 7.44730i) q^{93} +(-0.391430 - 0.677977i) q^{94} +(6.48224 + 11.2276i) q^{95} +(-6.83293 + 7.36704i) q^{96} +(8.50035 - 14.7230i) q^{97} -3.51555 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - q^{3} - 10 q^{4} - 3 q^{5} + 10 q^{6} - q^{7} - 6 q^{8} + q^{9}+O(q^{10}) $ 20 * q - q^3 - 10 * q^4 - 3 * q^5 + 10 * q^6 - q^7 - 6 * q^8 + q^9	$ 20 q - q^{3} - 10 q^{4} - 3 q^{5} + 10 q^{6} - q^{7} - 6 q^{8} + q^{9} - 5 q^{12} - q^{13} - 15 q^{14} - 7 q^{15} - 10 q^{16} - 6 q^{17} + 17 q^{18} - 4 q^{19} - 15 q^{20} + 4 q^{21} - 18 q^{23} - 27 q^{24} - 7 q^{25} + 12 q^{26} + 23 q^{27} + 8 q^{28} - 12 q^{29} - 26 q^{30} + 7 q^{31} - 24 q^{32} + 6 q^{34} - 36 q^{35} + 20 q^{36} - 2 q^{37} + 12 q^{38} + 4 q^{39} + 12 q^{40} + 6 q^{41} + 2 q^{42} + 8 q^{43} - 35 q^{45} + 36 q^{46} - 27 q^{47} + 19 q^{48} - 15 q^{49} - 15 q^{50} - 2 q^{51} + 5 q^{52} + 12 q^{53} - 44 q^{54} - 60 q^{56} + 27 q^{57} - 9 q^{58} - 21 q^{59} - 5 q^{60} + 20 q^{61} + 6 q^{62} + 74 q^{63} + 62 q^{64} - 12 q^{65} + 10 q^{67} + 69 q^{68} + 16 q^{69} - 6 q^{70} + 36 q^{71} - 102 q^{72} + 14 q^{73} + 6 q^{74} - 26 q^{75} + 2 q^{76} + 92 q^{78} - q^{79} + 102 q^{80} - 35 q^{81} - 60 q^{82} - 30 q^{83} - 70 q^{84} + 24 q^{85} - 36 q^{86} + 60 q^{87} + 108 q^{89} + 11 q^{90} + 20 q^{91} - 6 q^{92} - 19 q^{93} + 15 q^{94} - 12 q^{95} - 106 q^{96} + 16 q^{97} + 120 q^{98}+O(q^{100}) $ 20 * q - q^3 - 10 * q^4 - 3 * q^5 + 10 * q^6 - q^7 - 6 * q^8 + q^9 - 5 * q^12 - q^13 - 15 * q^14 - 7 * q^15 - 10 * q^16 - 6 * q^17 + 17 * q^18 - 4 * q^19 - 15 * q^20 + 4 * q^21 - 18 * q^23 - 27 * q^24 - 7 * q^25 + 12 * q^26 + 23 * q^27 + 8 * q^28 - 12 * q^29 - 26 * q^30 + 7 * q^31 - 24 * q^32 + 6 * q^34 - 36 * q^35 + 20 * q^36 - 2 * q^37 + 12 * q^38 + 4 * q^39 + 12 * q^40 + 6 * q^41 + 2 * q^42 + 8 * q^43 - 35 * q^45 + 36 * q^46 - 27 * q^47 + 19 * q^48 - 15 * q^49 - 15 * q^50 - 2 * q^51 + 5 * q^52 + 12 * q^53 - 44 * q^54 - 60 * q^56 + 27 * q^57 - 9 * q^58 - 21 * q^59 - 5 * q^60 + 20 * q^61 + 6 * q^62 + 74 * q^63 + 62 * q^64 - 12 * q^65 + 10 * q^67 + 69 * q^68 + 16 * q^69 - 6 * q^70 + 36 * q^71 - 102 * q^72 + 14 * q^73 + 6 * q^74 - 26 * q^75 + 2 * q^76 + 92 * q^78 - q^79 + 102 * q^80 - 35 * q^81 - 60 * q^82 - 30 * q^83 - 70 * q^84 + 24 * q^85 - 36 * q^86 + 60 * q^87 + 108 * q^89 + 11 * q^90 + 20 * q^91 - 6 * q^92 - 19 * q^93 + 15 * q^94 - 12 * q^95 - 106 * q^96 + 16 * q^97 + 120 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1089\mathbb{Z}\right)^\times$.

$n$	$244$	$848$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.342978	+	0.594056i	−0.242522	+	0.420061i	−0.961432	−	0.275042i	$-0.911308\pi$
$2$	−0.342978	+	0.594056i	−0.242522	+	0.420061i	0.718910	+	0.695103i	$0.244641\pi$
$3$	−0.510856	−	1.65500i	−0.294943	−	0.955515i
$3$	−0.510856	−	1.65500i	−0.294943	−	0.955515i
$4$	0.764732	+	1.32455i	0.382366	+	0.662277i
$5$	1.07171	+	1.85626i	0.479286	+	0.830147i	0.999718	−	0.0237561i	$-0.00756251\pi$
$5$	1.07171	+	1.85626i	0.479286	+	0.830147i	−0.520432	+	0.853903i	$0.674229\pi$
$6$	1.15838	+	0.264152i	0.472905	+	0.107840i
$7$	0.684647	−	1.18584i	0.258772	−	0.448206i	−0.707141	−	0.707072i	$-0.750015\pi$
$7$	0.684647	−	1.18584i	0.258772	−	0.448206i	0.965913	+	0.258866i	$0.0833488\pi$
$8$	−2.42106			−0.855974
$9$	−2.47805	+	1.69093i	−0.826018	+	0.563644i
$10$	−1.47030			−0.464950
$11$		0			0
$11$		0			0
$12$	1.80147	−	1.94229i	0.520040	−	0.560690i
$13$	−1.84469	−	3.19509i	−0.511625	−	0.886160i	−0.999909	−	0.0134753i	$-0.995711\pi$
$13$	−1.84469	−	3.19509i	−0.511625	−	0.886160i	0.488285	−	0.872684i	$-0.337623\pi$
$14$	0.469638	+	0.813437i	0.125516	+	0.217400i
$15$	2.52463	−	2.72197i	0.651856	−	0.702810i
$16$	−0.699093	+	1.21086i	−0.174773	+	0.302716i
$17$	5.72966			1.38965			0.694823	−	0.719181i	$-0.255483\pi$
$17$	5.72966			1.38965			0.694823	+	0.719181i	$0.255483\pi$
$18$	−0.154590	−	2.05205i	−0.0364373	−	0.483674i
$19$	6.04848			1.38762			0.693808	−	0.720160i	$-0.255932\pi$
$19$	6.04848			1.38762			0.693808	+	0.720160i	$0.255932\pi$
$20$	−1.63915	+	2.83909i	−0.366525	+	0.634840i
$21$	−2.31233	−	0.527296i	−0.504591	−	0.115065i
$22$		0			0
$23$	3.00398	+	5.20304i	0.626373	+	1.08491i	0.988274	+	0.152693i	$0.0487946\pi$
$23$	3.00398	+	5.20304i	0.626373	+	1.08491i	−0.361901	+	0.932217i	$0.617872\pi$
$24$	1.23681	+	4.00685i	0.252463	+	0.817895i
$25$	0.202854	−	0.351353i	0.0405708	−	0.0702707i
$26$	2.53075			0.496321
$27$	4.06442	+	3.23736i	0.782199	+	0.623029i
$28$	2.09428			0.395783
$29$	−1.38325	+	2.39586i	−0.256863	+	0.444900i	−0.965400	−	0.260774i	$-0.916022\pi$
$29$	−1.38325	+	2.39586i	−0.256863	+	0.444900i	0.708537	+	0.705674i	$0.249356\pi$
$30$	0.751111	+	2.43335i	0.137134	+	0.444266i
$31$	2.93221	+	5.07873i	0.526640	+	0.912167i	0.999518	+	0.0310391i	$0.00988163\pi$
$31$	2.93221	+	5.07873i	0.526640	+	0.912167i	−0.472878	+	0.881128i	$0.656785\pi$
$32$	−2.90061	−	5.02400i	−0.512760	−	0.888126i
$33$		0			0
$34$	−1.96515	+	3.40374i	−0.337020	+	0.583736i
$35$	2.93498			0.496103
$36$	−4.13478	−	1.98921i	−0.689130	−	0.331534i
$37$	−10.4062			−1.71076			−0.855382	−	0.517997i	$-0.826678\pi$
$37$	−10.4062			−1.71076			−0.855382	+	0.517997i	$0.826678\pi$
$38$	−2.07450	+	3.59313i	−0.336528	+	0.582883i
$39$	−4.34551	+	4.68519i	−0.695839	+	0.750231i
$40$	−2.59468	−	4.49413i	−0.410256	−	0.710584i
$41$	2.95744	+	5.12243i	0.461874	+	0.799990i	0.999054	−	0.0434778i	$-0.0138438\pi$
$41$	2.95744	+	5.12243i	0.461874	+	0.799990i	−0.537180	+	0.843468i	$0.680510\pi$
$42$	1.10632	−	1.19280i	0.170709	−	0.184053i
$43$	1.94730	−	3.37282i	0.296960	−	0.514350i	−0.678479	−	0.734620i	$-0.737360\pi$
$43$	1.94730	−	3.37282i	0.296960	−	0.514350i	0.975439	+	0.220270i	$0.0706937\pi$
$44$		0			0
$45$	−5.79459	−	2.78772i	−0.863806	−	0.415569i
$46$	−4.12120			−0.607637
$47$	−0.570634	+	0.988368i	−0.0832356	+	0.144168i	−0.904638	−	0.426181i	$-0.859859\pi$
$47$	−0.570634	+	0.988368i	−0.0832356	+	0.144168i	0.821402	+	0.570349i	$0.193192\pi$
$48$	2.36112	+	0.538422i	0.340798	+	0.0777145i
$49$	2.56252	+	4.43841i	0.366074	+	0.634059i
$50$	0.139149	+	0.241013i	0.0196786	+	0.0340844i
$51$	−2.92703	−	9.48259i	−0.409866	−	1.32783i
$52$	2.82138	−	4.88678i	0.391256	−	0.677675i
$53$	6.47721			0.889713			0.444856	−	0.895602i	$-0.353255\pi$
$53$	6.47721			0.889713			0.444856	+	0.895602i	$0.353255\pi$
$54$	−3.31718	+	1.30415i	−0.451411	+	0.177473i
$55$		0			0
$56$	−1.65757	+	2.87100i	−0.221502	+	0.383653i
$57$	−3.08990	−	10.0102i	−0.409267	−	1.32589i
$58$	−0.948850	−	1.64346i	−0.124590	−	0.215796i
$59$	4.43365	+	7.67931i	0.577212	+	0.999761i	0.995797	+	0.0915835i	$0.0291928\pi$
$59$	4.43365	+	7.67931i	0.577212	+	0.999761i	−0.418585	+	0.908178i	$0.637474\pi$
$60$	5.53606	+	1.26243i	0.714703	+	0.162979i
$61$	−4.42873	+	7.67078i	−0.567040	+	0.982143i	0.429816	+	0.902916i	$0.358578\pi$
$61$	−4.42873	+	7.67078i	−0.567040	+	0.982143i	−0.996857	+	0.0792263i	$0.974755\pi$
$62$	−4.02273			−0.510887
$63$	0.308590	+	4.09627i	0.0388787	+	0.516082i
$64$	1.18301			0.147876
$65$	3.95396	−	6.84846i	0.490428	−	0.849447i
$66$		0			0
$67$	−1.00040	−	1.73274i	−0.122218	−	0.211688i	0.798424	−	0.602096i	$-0.205667\pi$
$67$	−1.00040	−	1.73274i	−0.122218	−	0.211688i	−0.920642	+	0.390407i	$0.872334\pi$
$68$	4.38165	+	7.58925i	0.531353	+	0.920331i
$69$	7.07644	−	7.62959i	0.851903	−	0.918495i
$70$	−1.00664	+	1.74354i	−0.120316	+	0.208393i
$71$	2.39698			0.284469			0.142235	−	0.989833i	$-0.454571\pi$
$71$	2.39698			0.284469			0.142235	+	0.989833i	$0.454571\pi$
$72$	5.99951	−	4.09385i	0.707049	−	0.482465i
$73$	−10.7276			−1.25556			−0.627782	−	0.778389i	$-0.716037\pi$
$73$	−10.7276			−1.25556			−0.627782	+	0.778389i	$0.716037\pi$
$74$	3.56909	−	6.18185i	0.414898	−	0.718625i
$75$	−0.685119	−	0.156233i	−0.0791108	−	0.0180402i
$76$	4.62546	+	8.01154i	0.530577	+	0.918986i
$77$		0			0
$78$	−1.29285	−	4.18840i	−0.146386	−	0.474242i
$79$	2.23734	−	3.87519i	0.251720	−	0.435993i	−0.712279	−	0.701896i	$-0.752337\pi$
$79$	2.23734	−	3.87519i	0.251720	−	0.435993i	0.964000	+	0.265904i	$0.0856703\pi$
$80$	−2.99691			−0.335065
$81$	3.28149	−	8.38044i	0.364610	−	0.931160i
$82$	−4.05735			−0.448059
$83$	−4.96371	+	8.59739i	−0.544838	+	0.943686i	0.453780	+	0.891114i	$0.350075\pi$
$83$	−4.96371	+	8.59739i	−0.544838	+	0.943686i	−0.998617	+	0.0525724i	$0.983258\pi$
$84$	−1.06988	−	3.46604i	−0.116733	−	0.378176i
$85$	6.14056	+	10.6358i	0.666037	+	1.15361i
$86$	1.33576	+	2.31361i	0.144039	+	0.249483i
$87$	4.67179	+	1.06534i	0.500869	+	0.114217i
$88$		0			0
$89$	11.0155			1.16764			0.583822	−	0.811882i	$-0.301557\pi$
$89$	11.0155			1.16764			0.583822	+	0.811882i	$0.301557\pi$
$90$	3.64348	−	2.48618i	0.384057	−	0.262066i
$91$	−5.05184			−0.529577
$92$	−4.59448	+	7.95787i	−0.479007	+	0.829665i
$93$	6.90736	−	7.44730i	0.716260	−	0.772249i
$94$	−0.391430	−	0.677977i	−0.0403730	−	0.0699280i
$95$	6.48224	+	11.2276i	0.665064	+	1.15192i
$96$	−6.83293	+	7.36704i	−0.697383	+	0.751896i
$97$	8.50035	−	14.7230i	0.863080	−	1.49490i	−0.00586071	−	0.999983i	$-0.501866\pi$
$97$	8.50035	−	14.7230i	0.863080	−	1.49490i	0.868941	−	0.494916i	$-0.164801\pi$
$98$	−3.51555			−0.355124
$99$		0			0
$100$	0.620516			0.0620516
$101$	−5.54282	+	9.60045i	−0.551532	+	0.955281i	0.446633	+	0.894717i	$0.352623\pi$
$101$	−5.54282	+	9.60045i	−0.551532	+	0.955281i	−0.998164	+	0.0605633i	$0.980710\pi$
$102$	6.63709	+	1.51350i	0.657170	+	0.149859i
$103$	−1.59363	−	2.76024i	−0.157025	−	0.271975i	0.776770	−	0.629785i	$-0.216857\pi$
$103$	−1.59363	−	2.76024i	−0.157025	−	0.271975i	−0.933794	+	0.357810i	$0.883524\pi$
$104$	4.46610	+	7.73551i	0.437937	+	0.758529i
$105$	−1.49935	−	4.85740i	−0.146322	−	0.474034i
$106$	−2.22154	+	3.84782i	−0.215775	+	0.373733i
$107$	−11.6071			−1.12210			−0.561048	−	0.827783i	$-0.689602\pi$
$107$	−11.6071			−1.12210			−0.561048	+	0.827783i	$0.689602\pi$
$108$	−1.17986	+	7.85926i	−0.113532	+	0.756257i
$109$	14.2844			1.36819			0.684097	−	0.729391i	$-0.260197\pi$
$109$	14.2844			1.36819			0.684097	+	0.729391i	$0.260197\pi$
$110$		0			0
$111$	5.31605	+	17.2222i	0.504578	+	1.63466i
$112$	0.957264	+	1.65803i	0.0904529	+	0.156669i
$113$	3.67658	+	6.36803i	0.345864	+	0.599054i	0.985510	−	0.169615i	$-0.0542525\pi$
$113$	3.67658	+	6.36803i	0.345864	+	0.599054i	−0.639646	+	0.768669i	$0.720919\pi$
$114$	7.00640	+	1.59772i	0.656210	+	0.149640i
$115$	−6.43882	+	11.1524i	−0.600423	+	1.03996i
$116$	−4.23126			−0.392863
$117$	9.97393	+	4.79837i	0.922090	+	0.443609i
$118$	−6.08259			−0.559947
$119$	3.92279	−	6.79448i	0.359602	−	0.622849i
$120$	−6.11227	+	6.59005i	−0.557971	+	0.601587i
$121$		0			0
$122$	−3.03791	−	5.26182i	−0.275040	−	0.476383i
$123$	6.96681	−	7.51139i	0.628176	−	0.677279i
$124$	−4.48470	+	7.76773i	−0.402738	+	0.697563i
$125$	11.5868			1.03635
$126$	−2.53925	−	1.22161i	−0.226215	−	0.108830i
$127$	14.0945			1.25069			0.625343	−	0.780350i	$-0.284959\pi$
$127$	14.0945			1.25069			0.625343	+	0.780350i	$0.284959\pi$
$128$	5.39547	−	9.34522i	0.476896	−	0.826009i
$129$	−6.57681	−	1.49976i	−0.579056	−	0.132046i
$130$	2.71225	+	4.69775i	0.237880	+	0.412020i
$131$	−9.21039	−	15.9529i	−0.804716	−	1.39381i	−0.916483	−	0.400074i	$-0.868984\pi$
$131$	−9.21039	−	15.9529i	−0.804716	−	1.39381i	0.111767	−	0.993734i	$-0.464349\pi$
$132$		0			0
$133$	4.14107	−	7.17254i	0.359076	−	0.621938i
$134$	1.37246			0.118563
$135$	−1.65349	+	11.0142i	−0.142309	+	0.947949i
$136$	−13.8718			−1.18950
$137$	7.57484	−	13.1200i	0.647162	−	1.12092i	−0.336635	−	0.941635i	$-0.609289\pi$
$137$	7.57484	−	13.1200i	0.647162	−	1.12092i	0.983798	−	0.179283i	$-0.0573778\pi$
$138$	2.10534	+	6.82058i	0.179218	+	0.580607i
$139$	−4.70308	−	8.14597i	−0.398910	−	0.690932i	0.594682	−	0.803961i	$-0.297278\pi$
$139$	−4.70308	−	8.14597i	−0.398910	−	0.690932i	−0.993592	+	0.113029i	$0.963945\pi$
$140$	2.24448	+	3.88755i	0.189693	+	0.328558i
$141$	1.92726	+	0.439487i	0.162305	+	0.0370115i
$142$	−0.822112	+	1.42394i	−0.0689901	+	0.119494i
$143$		0			0
$144$	−0.315102	−	4.18271i	−0.0262585	−	0.348559i
$145$	−5.92980			−0.492443
$146$	3.67932	−	6.37276i	0.304502	−	0.527414i
$147$	6.03650	−	6.50836i	0.497882	−	0.536800i
$148$	−7.95793	−	13.7835i	−0.654138	−	1.13300i
$149$	−5.04442	−	8.73719i	−0.413255	−	0.715779i	0.581989	−	0.813197i	$-0.302275\pi$
$149$	−5.04442	−	8.73719i	−0.413255	−	0.715779i	−0.995244	+	0.0974183i	$0.968942\pi$
$150$	0.327792	−	0.353415i	0.0267641	−	0.0288562i
$151$	−0.751653	+	1.30190i	−0.0611687	+	0.105947i	−0.894988	−	0.446090i	$-0.852816\pi$
$151$	−0.751653	+	1.30190i	−0.0611687	+	0.105947i	0.833819	+	0.552037i	$0.186149\pi$
$152$	−14.6437			−1.18776
$153$	−14.1984	+	9.68847i	−1.14787	+	0.783266i
$154$		0			0
$155$	−6.28498	+	10.8859i	−0.504822	+	0.874377i
$156$	−9.52894	−	2.17295i	−0.762926	−	0.173975i
$157$	−5.60545	−	9.70893i	−0.447364	−	0.774857i	0.550850	−	0.834604i	$-0.314304\pi$
$157$	−5.60545	−	9.70893i	−0.447364	−	0.774857i	−0.998214	+	0.0597475i	$0.980970\pi$
$158$	1.53472	+	2.65821i	0.122096	+	0.211476i
$159$	−3.30892	−	10.7198i	−0.262414	−	0.850134i
$160$	6.21725	−	10.7686i	0.491516	−	0.851331i
$161$	8.22666			0.648351
$162$	3.85297	+	4.82370i	0.302718	+	0.378986i
$163$	−6.39578			−0.500956			−0.250478	−	0.968122i	$-0.580588\pi$
$163$	−6.39578			−0.500956			−0.250478	+	0.968122i	$0.580588\pi$
$164$	−4.52330	+	7.83458i	−0.353210	+	0.611778i
$165$		0			0
$166$	−3.40489	−	5.89744i	−0.264270	−	0.457730i
$167$	7.69946	+	13.3359i	0.595802	+	1.03196i	0.993433	+	0.114414i	$0.0364991\pi$
$167$	7.69946	+	13.3359i	0.595802	+	1.03196i	−0.397631	+	0.917545i	$0.630168\pi$
$168$	5.59828	+	1.27661i	0.431916	+	0.0984929i
$169$	−0.305752	+	0.529578i	−0.0235194	+	0.0407368i
$170$	−8.42432			−0.646116
$171$	−14.9884	+	10.2276i	−1.14619	+	0.782122i
$172$	5.95665			0.454190
$173$	11.9208	−	20.6474i	0.906322	−	1.56980i	0.0871895	−	0.996192i	$-0.472211\pi$
$173$	11.9208	−	20.6474i	0.906322	−	1.56980i	0.819133	−	0.573604i	$-0.194455\pi$
$174$	−2.23519	+	2.40992i	−0.169450	+	0.182695i
$175$	−0.277767	−	0.481106i	−0.0209972	−	0.0363682i
$176$		0			0
$177$	10.4443	−	11.2607i	0.785042	−	0.846407i
$178$	−3.77809	+	6.54384i	−0.283180	+	0.490481i
$179$	2.83082			0.211586			0.105793	−	0.994388i	$-0.466262\pi$
$179$	2.83082			0.211586			0.105793	+	0.994388i	$0.466262\pi$
$180$	−0.738813	−	9.80710i	−0.0550679	−	0.730978i
$181$	−8.88926			−0.660734			−0.330367	−	0.943853i	$-0.607172\pi$
$181$	−8.88926			−0.660734			−0.330367	+	0.943853i	$0.607172\pi$
$182$	1.73267	−	3.00107i	0.128434	−	0.222454i
$183$	14.9576	+	3.41088i	1.10570	+	0.252140i
$184$	−7.27281	−	12.5969i	−0.536159	−	0.928654i
$185$	−11.1525	−	19.3166i	−0.819945	−	1.42019i
$186$	2.05504	+	6.65762i	0.150683	+	0.488161i
$187$		0			0
$188$	−1.74553			−0.127306
$189$	6.62169	−	2.60332i	0.481657	−	0.189364i
$190$	−8.89307			−0.645171
$191$	−11.4503	+	19.8324i	−0.828512	+	1.43503i	0.0706928	+	0.997498i	$0.477479\pi$
$191$	−11.4503	+	19.8324i	−0.828512	+	1.43503i	−0.899205	+	0.437527i	$0.855854\pi$
$192$	−0.604346	−	1.95788i	−0.0436149	−	0.141298i
$193$	−7.04977	−	12.2106i	−0.507454	−	0.878935i	−0.999963	−	0.00862808i	$-0.997254\pi$
$193$	−7.04977	−	12.2106i	−0.507454	−	0.878935i	0.492509	−	0.870307i	$-0.336080\pi$
$194$	5.83087	+	10.0994i	0.418632	+	0.725092i
$195$	−13.3541	−	3.04523i	−0.956308	−	0.218073i
$196$	−3.91928	+	6.78839i	−0.279948	+	0.484885i
$197$	1.01874			0.0725819			0.0362910	−	0.999341i	$-0.488446\pi$
$197$	1.01874			0.0725819			0.0362910	+	0.999341i	$0.488446\pi$
$198$		0			0
$199$	−18.9740			−1.34503			−0.672515	−	0.740083i	$-0.734786\pi$
$199$	−18.9740			−1.34503			−0.672515	+	0.740083i	$0.734786\pi$
$200$	−0.491122	+	0.850647i	−0.0347275	+	0.0601499i
$201$	−2.35663	+	2.54085i	−0.166224	+	0.179217i
$202$	−3.80214	−	6.58549i	−0.267517	−	0.463354i
$203$	1.89408	+	3.28064i	0.132938	+	0.230255i
$204$	10.3218	−	11.1286i	0.722671	−	0.779161i
$205$	−6.33906	+	10.9796i	−0.442739	+	0.766847i
$206$	2.18632			0.152328
$207$	−16.2420	−	7.81389i	−1.12890	−	0.543103i
$208$	5.15844			0.357673
$209$		0			0
$210$	3.39981	+	0.775283i	0.234609	+	0.0534996i
$211$	−4.76046	−	8.24537i	−0.327724	−	0.567634i	0.654336	−	0.756204i	$-0.272948\pi$
$211$	−4.76046	−	8.24537i	−0.327724	−	0.567634i	−0.982060	+	0.188570i	$0.939615\pi$
$212$	4.95332	+	8.57941i	0.340196	+	0.589236i
$213$	−1.22451	−	3.96700i	−0.0839021	−	0.271815i
$214$	3.98097	−	6.89524i	0.272133	−	0.471349i
$215$	8.34780			0.569315
$216$	−9.84021	−	7.83783i	−0.669541	−	0.533297i
$217$	8.03010			0.545119
$218$	−4.89922	+	8.48571i	−0.331817	+	0.574724i
$219$	5.48023	+	17.7541i	0.370320	+	1.19971i
$220$		0			0
$221$	−10.5694	−	18.3068i	−0.710977	−	1.23145i
$222$	−12.0543	−	2.74881i	−0.809028	−	0.184488i
$223$	2.88139	−	4.99071i	0.192952	−	0.334202i	−0.753275	−	0.657705i	$-0.771527\pi$
$223$	2.88139	−	4.99071i	0.192952	−	0.334202i	0.946227	+	0.323503i	$0.104861\pi$
$224$	−7.94356			−0.530752
$225$	0.0914323	+	1.21369i	0.00609549	+	0.0809123i
$226$	−5.04395			−0.335519
$227$	−12.4119	+	21.4980i	−0.823805	+	1.42687i	0.0790241	+	0.996873i	$0.474820\pi$
$227$	−12.4119	+	21.4980i	−0.823805	+	1.42687i	−0.902829	+	0.429999i	$0.858514\pi$
$228$	10.8962	−	11.7479i	0.721615	−	0.778022i
$229$	−5.06989	−	8.78131i	−0.335028	−	0.580285i	0.648462	−	0.761247i	$-0.275412\pi$
$229$	−5.06989	−	8.78131i	−0.335028	−	0.580285i	−0.983490	+	0.180961i	$0.942079\pi$
$230$	−4.41675	−	7.65003i	−0.291232	−	0.504428i
$231$		0			0
$232$	3.34893	−	5.80052i	0.219868	−	0.380823i
$233$	2.67675			0.175360			0.0876799	−	0.996149i	$-0.472055\pi$
$233$	2.67675			0.175360			0.0876799	+	0.996149i	$0.472055\pi$
$234$	−6.27134	+	4.27933i	−0.409970	+	0.279749i
$235$	−2.44623			−0.159574
$236$	−6.78111	+	11.7452i	−0.441413	+	0.764549i
$237$	−7.55639	−	1.72314i	−0.490841	−	0.111930i
$238$	2.69087	+	4.66071i	0.174423	+	0.302109i
$239$	−7.93925	−	13.7512i	−0.513547	−	0.889490i	−0.999877	−	0.0157145i	$-0.994998\pi$
$239$	−7.93925	−	13.7512i	−0.513547	−	0.889490i	0.486329	−	0.873776i	$-0.338336\pi$
$240$	1.53099	+	4.95989i	0.0988250	+	0.320160i
$241$	9.08331	−	15.7328i	0.585107	−	1.01344i	−0.409755	−	0.912196i	$-0.634386\pi$
$241$	9.08331	−	15.7328i	0.585107	−	1.01344i	0.994862	−	0.101240i	$-0.0322809\pi$
$242$		0			0
$243$	−15.5460	−	1.14967i	−0.997277	−	0.0737513i
$244$	−13.5472			−0.867268
$245$	−5.49258	+	9.51342i	−0.350908	+	0.607790i
$246$	2.07272	+	6.71491i	0.132152	+	0.428127i
$247$	−11.1576	−	19.3255i	−0.709938	−	1.22965i
$248$	−7.09904	−	12.2959i	−0.450790	−	0.780791i
$249$	16.7644	+	3.82291i	1.06240	+	0.242267i
$250$	−3.97401	+	6.88318i	−0.251338	+	0.435331i
$251$	11.8793			0.749817			0.374909	−	0.927062i	$-0.377674\pi$
$251$	11.8793			0.749817			0.374909	+	0.927062i	$0.377674\pi$
$252$	−5.18975	+	3.54129i	−0.326923	+	0.223081i
$253$		0			0
$254$	−4.83411	+	8.37293i	−0.303319	+	0.525364i
$255$	14.4653	−	15.5960i	0.905849	−	0.976658i
$256$	4.88406	+	8.45944i	0.305254	+	0.528715i
$257$	−9.25543	−	16.0309i	−0.577338	−	0.999979i	−0.995783	−	0.0917368i	$-0.970758\pi$
$257$	−9.25543	−	16.0309i	−0.577338	−	0.999979i	0.418445	−	0.908242i	$-0.362575\pi$
$258$	3.14664	−	3.39261i	0.195901	−	0.211215i
$259$	−7.12455	+	12.3401i	−0.442698	+	0.766776i
$260$	12.0949			0.750093
$261$	−0.623472	−	8.27605i	−0.0385919	−	0.512275i
$262$	12.6359			0.780646
$263$	−6.67860	+	11.5677i	−0.411820	+	0.713293i	−0.995089	−	0.0989860i	$-0.968440\pi$
$263$	−6.67860	+	11.5677i	−0.411820	+	0.713293i	0.583269	+	0.812279i	$0.301773\pi$
$264$		0			0
$265$	6.94172	+	12.0234i	0.426426	+	0.738592i
$266$	2.84059	+	4.92005i	0.174168	+	0.301668i
$267$	−5.62735	−	18.2307i	−0.344388	−	1.11570i
$268$	1.53008	−	2.65017i	0.0934643	−	0.161885i
$269$	−0.0436030			−0.00265852			−0.00132926	−	0.999999i	$-0.500423\pi$
$269$	−0.0436030			−0.00265852			−0.00132926	+	0.999999i	$0.500423\pi$
$270$	−5.97592	−	4.75988i	−0.363683	−	0.289677i
$271$	−6.88320			−0.418124			−0.209062	−	0.977902i	$-0.567041\pi$
$271$	−6.88320			−0.418124			−0.209062	+	0.977902i	$0.567041\pi$
$272$	−4.00557	+	6.93784i	−0.242873	+	0.420668i
$273$	2.58076	+	8.36080i	0.156195	+	0.506018i
$274$	5.19601	+	8.99976i	0.313903	+	0.543695i
$275$		0			0
$276$	15.5174	+	3.53854i	0.934037	+	0.212995i
$277$	−10.0420	+	17.3932i	−0.603363	+	1.04506i	0.388945	+	0.921261i	$0.372840\pi$
$277$	−10.0420	+	17.3932i	−0.603363	+	1.04506i	−0.992308	+	0.123794i	$0.960494\pi$
$278$	6.45221			0.386978
$279$	−15.8540	−	7.62719i	−0.949151	−	0.456628i
$280$	−7.10577			−0.424651
$281$	−2.34325	+	4.05862i	−0.139786	+	0.242117i	−0.927416	−	0.374032i	$-0.877975\pi$
$281$	−2.34325	+	4.05862i	−0.139786	+	0.242117i	0.787629	+	0.616149i	$0.211308\pi$
$282$	−0.922088	+	0.994166i	−0.0549095	+	0.0592017i
$283$	3.95488	+	6.85005i	0.235093	+	0.407193i	0.959300	−	0.282390i	$-0.0911271\pi$
$283$	3.95488	+	6.85005i	0.235093	+	0.407193i	−0.724207	+	0.689583i	$0.757794\pi$
$284$	1.83305	+	3.17493i	0.108771	+	0.188397i
$285$	15.2701	−	16.4638i	0.904525	−	0.975230i
$286$		0			0
$287$	8.09920			0.478081
$288$	15.6831	+	7.54500i	0.924135	+	0.444593i
$289$	15.8290			0.931117
$290$	2.03379	−	3.52263i	0.119428	−	0.206856i
$291$	−28.7091	−	6.54674i	−1.68296	−	0.383776i
$292$	−8.20370	−	14.2092i	−0.480085	−	0.831532i
$293$	3.71639	+	6.43697i	0.217114	+	0.376052i	0.953924	−	0.300047i	$-0.0970024\pi$
$293$	3.71639	+	6.43697i	0.217114	+	0.376052i	−0.736811	+	0.676099i	$0.763669\pi$
$294$	1.79594	+	5.81824i	0.104741	+	0.339327i
$295$	−9.50322	+	16.4601i	−0.553299	+	0.958342i
$296$	25.1940			1.46437
$297$		0			0
$298$	6.92051			0.400894
$299$	11.0828	−	19.1960i	0.640935	−	1.11013i
$300$	−0.316994	−	1.02695i	−0.0183017	−	0.0592912i
$301$	−2.66642	−	4.61838i	−0.153690	−	0.266199i
$302$	−0.515601	−	0.893048i	−0.0296695	−	0.0513891i
$303$	18.7203	+	4.26893i	1.07546	+	0.245244i
$304$	−4.22845	+	7.32389i	−0.242518	+	0.420054i
$305$	−18.9853			−1.08710
$306$	−0.885750	−	11.7576i	−0.0506350	−	0.672136i
$307$	14.6293			0.834941			0.417470	−	0.908690i	$-0.362917\pi$
$307$	14.6293			0.834941			0.417470	+	0.908690i	$0.362917\pi$
$308$		0			0
$309$	−3.75409	+	4.04754i	−0.213563	+	0.230257i
$310$	−4.31122	−	7.46725i	−0.244861	−	0.424112i
$311$	−8.05760	−	13.9562i	−0.456905	−	0.791382i	0.541891	−	0.840449i	$-0.317709\pi$
$311$	−8.05760	−	13.9562i	−0.456905	−	0.791382i	−0.998795	+	0.0490668i	$0.984375\pi$
$312$	10.5207	−	11.3431i	0.595620	−	0.642178i
$313$	3.02746	−	5.24372i	0.171122	−	0.296392i	−0.767690	−	0.640821i	$-0.778594\pi$
$313$	3.02746	−	5.24372i	0.171122	−	0.296392i	0.938812	+	0.344429i	$0.111927\pi$
$314$	7.69019			0.433983
$315$	−7.27305	+	4.96286i	−0.409790	+	0.279626i
$316$	6.84386			0.384997
$317$	5.92368	−	10.2601i	0.332707	−	0.576265i	−0.650335	−	0.759648i	$-0.725371\pi$
$317$	5.92368	−	10.2601i	0.332707	−	0.576265i	0.983042	+	0.183382i	$0.0587047\pi$
$318$	7.50303	+	1.71097i	0.420749	+	0.0959464i
$319$		0			0
$320$	1.26785	+	2.19597i	0.0708748	+	0.122759i
$321$	5.92953	+	19.2097i	0.330954	+	1.07218i
$322$	−2.82156	+	4.88709i	−0.157240	+	0.272347i
$323$	34.6557			1.92830
$324$	13.6098	−	2.06228i	0.756101	−	0.114571i
$325$	−1.49681			−0.0830281
$326$	2.19361	−	3.79945i	0.121493	−	0.210432i
$327$	−7.29725	−	23.6406i	−0.403539	−	1.30733i
$328$	−7.16013	−	12.4017i	−0.395352	−	0.684770i
$329$	0.781366	+	1.35337i	0.0430781	+	0.0746134i
$330$		0			0
$331$	−4.44985	+	7.70736i	−0.244586	+	0.423635i	−0.962015	−	0.272996i	$-0.911985\pi$
$331$	−4.44985	+	7.70736i	−0.244586	+	0.423635i	0.717429	+	0.696631i	$0.245319\pi$
$332$	−15.1836			−0.833309
$333$	25.7870	−	17.5961i	1.41312	−	0.964263i
$334$	−10.5630			−0.577981
$335$	2.14429	−	3.71402i	0.117155	−	0.202918i
$336$	2.25502	−	2.43129i	0.123021	−	0.132637i
$337$	0.429141	+	0.743294i	0.0233768	+	0.0404898i	0.877477	−	0.479618i	$-0.159225\pi$
$337$	0.429141	+	0.743294i	0.0233768	+	0.0404898i	−0.854100	+	0.520108i	$0.825892\pi$
$338$	−0.209733	−	0.363268i	−0.0114080	−	0.0197592i
$339$	8.66089	−	9.33789i	0.470395	−	0.507165i
$340$	−9.39177	+	16.2670i	−0.509340	+	0.882203i
$341$		0			0
$342$	−0.935036	−	12.4118i	−0.0505610	−	0.671154i
$343$	16.6027			0.896463
$344$	−4.71453	+	8.16580i	−0.254190	+	0.440270i
$345$	21.7465	+	4.95900i	1.17079	+	0.266984i
$346$	8.17716	+	14.1632i	0.439607	+	0.761421i
$347$	−10.9803	−	19.0185i	−0.589456	−	1.02097i	−0.994304	−	0.106583i	$-0.966009\pi$
$347$	−10.9803	−	19.0185i	−0.589456	−	1.02097i	0.404848	−	0.914384i	$-0.367324\pi$
$348$	2.16157	+	7.00274i	0.115872	+	0.375386i
$349$	9.47927	−	16.4186i	0.507414	−	0.878867i	−0.492549	−	0.870285i	$-0.663935\pi$
$349$	9.47927	−	16.4186i	0.507414	−	0.878867i	0.999963	−	0.00858207i	$-0.00273179\pi$
$350$	0.381072			0.0203691
$351$	2.84606	−	18.9581i	0.151911	−	1.01191i
$352$		0			0
$353$	−0.645277	+	1.11765i	−0.0343446	+	0.0594866i	−0.882687	−	0.469962i	$-0.844268\pi$
$353$	−0.645277	+	1.11765i	−0.0343446	+	0.0594866i	0.848342	+	0.529448i	$0.177601\pi$
$354$	3.10732	+	10.0667i	0.165152	+	0.535038i
$355$	2.56888	+	4.44943i	0.136342	+	0.236151i
$356$	8.42393	+	14.5907i	0.446467	+	0.773304i
$357$	−13.2488	−	3.02123i	−0.701203	−	0.159900i
$358$	−0.970910	+	1.68167i	−0.0513142	+	0.0888788i
$359$	−27.3780			−1.44495			−0.722477	−	0.691395i	$-0.756997\pi$
$359$	−27.3780			−1.44495			−0.722477	+	0.691395i	$0.756997\pi$
$360$	14.0290	+	6.74924i	0.739395	+	0.355716i
$361$	17.5841			0.925477
$362$	3.04882	−	5.28072i	0.160243	−	0.277548i
$363$		0			0
$364$	−3.86330	−	6.69144i	−0.202492	−	0.350727i
$365$	−11.4969	−	19.9132i	−0.601774	−	1.04230i
$366$	−7.15638	+	7.71578i	−0.374070	+	0.403310i
$367$	2.84147	−	4.92157i	0.148323	−	0.256904i	−0.782284	−	0.622921i	$-0.785946\pi$
$367$	2.84147	−	4.92157i	0.148323	−	0.256904i	0.930608	+	0.366018i	$0.119279\pi$
$368$	−8.40024			−0.437893
$369$	−15.9904	−	7.69283i	−0.832426	−	0.400473i
$370$	15.3002			0.795419
$371$	4.43460	−	7.68095i	0.230233	−	0.398775i
$372$	15.1466	+	3.45399i	0.785316	+	0.179081i
$373$	−8.80577	−	15.2520i	−0.455946	−	0.789721i	0.542796	−	0.839864i	$-0.317366\pi$
$373$	−8.80577	−	15.2520i	−0.455946	−	0.789721i	−0.998742	+	0.0501432i	$0.984032\pi$
$374$		0			0
$375$	−5.91916	−	19.1761i	−0.305664	−	0.990249i
$376$	1.38154	−	2.39290i	0.0712474	−	0.123404i
$377$	10.2067			0.525670
$378$	−0.724577	+	4.82653i	−0.0372682	+	0.248250i
$379$	28.1765			1.44733			0.723665	−	0.690152i	$-0.242456\pi$
$379$	28.1765			1.44733			0.723665	+	0.690152i	$0.242456\pi$
$380$	−9.91435	+	17.1722i	−0.508596	+	0.880913i
$381$	−7.20026	−	23.3264i	−0.368881	−	1.19505i
$382$	−7.85439	−	13.6042i	−0.401865	−	0.696051i
$383$	−6.60926	−	11.4476i	−0.337717	−	0.584944i	0.646286	−	0.763096i	$-0.276321\pi$
$383$	−6.60926	−	11.4476i	−0.337717	−	0.584944i	−0.984003	+	0.178152i	$0.942988\pi$
$384$	−18.2227	−	4.15544i	−0.929921	−	0.212056i
$385$		0			0
$386$	9.67167			0.492275
$387$	0.877705	+	11.6508i	0.0446163	+	0.592243i
$388$	26.0020			1.32005
$389$	−1.38419	+	2.39749i	−0.0701812	+	0.121557i	−0.898981	−	0.437988i	$-0.855691\pi$
$389$	−1.38419	+	2.39749i	−0.0701812	+	0.121557i	0.828799	+	0.559546i	$0.189024\pi$
$390$	6.38921	−	6.88864i	0.323530	−	0.348820i
$391$	17.2118	+	29.8117i	0.870437	+	1.50764i
$392$	−6.20401	−	10.7457i	−0.313350	−	0.542737i
$393$	−21.6968	+	23.3928i	−1.09446	+	1.18001i
$394$	−0.349404	+	0.605186i	−0.0176027	+	0.0304888i
$395$	9.59116			0.482584
$396$		0			0
$397$	−6.31419			−0.316900			−0.158450	−	0.987367i	$-0.550650\pi$
$397$	−6.31419			−0.316900			−0.158450	+	0.987367i	$0.550650\pi$
$398$	6.50767	−	11.2716i	0.326200	−	0.564995i
$399$	−13.9860	−	3.18934i	−0.700178	−	0.159667i
$400$	0.283628	+	0.491258i	0.0141814	+	0.0245629i
$401$	1.53483	+	2.65840i	0.0766457	+	0.132754i	0.901801	−	0.432152i	$-0.142246\pi$
$401$	1.53483	+	2.65840i	0.0766457	+	0.132754i	−0.825155	+	0.564906i	$0.808912\pi$
$402$	−0.701130	−	2.27143i	−0.0349692	−	0.113288i
$403$	10.8180	−	18.7373i	0.538884	−	0.933374i
$404$	−16.9551			−0.843547
$405$	19.0731	−	2.89013i	0.947752	−	0.143612i
$406$	−2.59851			−0.128962
$407$		0			0
$408$	7.08651	+	22.9579i	0.350835	+	1.13659i
$409$	−0.119985	−	0.207820i	−0.00593288	−	0.0102760i	0.863044	−	0.505129i	$-0.168555\pi$
$409$	−0.119985	−	0.207820i	−0.00593288	−	0.0102760i	−0.868977	+	0.494853i	$0.835222\pi$
$410$	−4.34832	−	7.53151i	−0.214748	−	0.371955i
$411$	−25.5833	−	5.83393i	−1.26193	−	0.287767i
$412$	2.43740	−	4.22169i	0.120082	−	0.207988i
$413$	12.1419			0.597466
$414$	10.2125	−	6.96867i	0.501919	−	0.342491i
$415$	−21.2787			−1.04453
$416$	−10.7014	+	18.5354i	−0.524681	+	0.908774i
$417$	−11.0790	+	11.9450i	−0.542540	+	0.584950i
$418$		0			0
$419$	−10.8535	−	18.7989i	−0.530229	−	0.918384i	−0.999378	−	0.0352650i	$-0.988772\pi$
$419$	−10.8535	−	18.7989i	−0.530229	−	0.918384i	0.469149	−	0.883119i	$-0.344561\pi$
$420$	5.28729	−	5.70058i	0.257993	−	0.278160i
$421$	2.07096	−	3.58701i	0.100933	−	0.174820i	−0.811137	−	0.584857i	$-0.801151\pi$
$421$	2.07096	−	3.58701i	0.100933	−	0.174820i	0.912069	+	0.410036i	$0.134484\pi$
$422$	6.53094			0.317921
$423$	−0.257202	−	3.41413i	−0.0125056	−	0.166001i
$424$	−15.6817			−0.761570
$425$	1.16228	−	2.01314i	0.0563791	−	0.0976514i
$426$	2.77660	+	0.633168i	0.134527	+	0.0306771i
$427$	6.06423	+	10.5035i	0.293468	+	0.508302i
$428$	−8.87629	−	15.3742i	−0.429051	−	0.743139i
$429$		0			0
$430$	−2.86311	+	4.95906i	−0.138072	+	0.239147i
$431$	−8.85447			−0.426505			−0.213252	−	0.976997i	$-0.568406\pi$
$431$	−8.85447			−0.426505			−0.213252	+	0.976997i	$0.568406\pi$
$432$	−6.76141	+	2.65825i	−0.325308	+	0.127895i
$433$	27.8710			1.33939			0.669697	−	0.742634i	$-0.266424\pi$
$433$	27.8710			1.33939			0.669697	+	0.742634i	$0.266424\pi$
$434$	−2.75415	+	4.77033i	−0.132203	+	0.228983i
$435$	3.02927	+	9.81382i	0.145243	+	0.470537i
$436$	10.9237	+	18.9204i	0.523150	+	0.906123i
$437$	18.1695	+	31.4705i	0.869165	+	1.50544i
$438$	−12.4265	−	2.83371i	−0.593762	−	0.135400i
$439$	−15.2585	+	26.4286i	−0.728250	+	1.26137i	0.229372	+	0.973339i	$0.426333\pi$
$439$	−15.2585	+	26.4286i	−0.728250	+	1.26137i	−0.957622	+	0.288028i	$0.907000\pi$
$440$		0			0
$441$	−13.8551	−	6.66557i	−0.659767	−	0.317408i
$442$	14.5003			0.689711
$443$	−15.9606	+	27.6446i	−0.758311	+	1.31343i	0.185400	+	0.982663i	$0.440642\pi$
$443$	−15.9606	+	27.6446i	−0.758311	+	1.31343i	−0.943711	+	0.330770i	$0.892691\pi$
$444$	−18.7464	+	20.2118i	−0.889665	+	0.959209i
$445$	11.8055	+	20.4477i	0.559635	+	0.969316i
$446$	1.97651	+	3.42341i	0.0935902	+	0.162103i
$447$	−11.8831	+	12.8120i	−0.562051	+	0.605985i
$448$	0.809942	−	1.40286i	0.0382662	−	0.0662789i
$449$	−0.285090			−0.0134542			−0.00672711	−	0.999977i	$-0.502141\pi$
$449$	−0.285090			−0.0134542			−0.00672711	+	0.999977i	$0.502141\pi$
$450$	−0.752356	−	0.361952i	−0.0354664	−	0.0170626i
$451$		0			0
$452$	−5.62320	+	9.73967i	−0.264493	+	0.458116i
$453$	2.53863	+	0.578902i	0.119275	+	0.0271992i
$454$	−8.51401	−	14.7467i	−0.399582	−	0.692097i
$455$	−5.41413	−	9.37755i	−0.253818	−	0.439626i
$456$	7.48083	+	24.2354i	0.350322	+	1.13492i
$457$	−5.23552	+	9.06818i	−0.244907	+	0.424192i	−0.962105	−	0.272678i	$-0.912091\pi$
$457$	−5.23552	+	9.06818i	−0.244907	+	0.424192i	0.717198	+	0.696869i	$0.245424\pi$
$458$	6.95545			0.325007
$459$	23.2878	+	18.5489i	1.08698	+	0.865790i
$460$	−19.6959			−0.918325
$461$	−13.1220	+	22.7279i	−0.611150	+	1.05854i	0.379897	+	0.925029i	$0.375960\pi$
$461$	−13.1220	+	22.7279i	−0.611150	+	1.05854i	−0.991047	+	0.133514i	$0.957374\pi$
$462$		0			0
$463$	13.4913	+	23.3676i	0.626994	+	1.08599i	0.988152	+	0.153480i	$0.0490482\pi$
$463$	13.4913	+	23.3676i	0.626994	+	1.08599i	−0.361158	+	0.932505i	$0.617618\pi$
$464$	−1.93404	−	3.34986i	−0.0897856	−	0.155513i
$465$	21.2269	+	4.84051i	0.984373	+	0.224474i
$466$	−0.918067	+	1.59014i	−0.0425287	+	0.0736618i
$467$	8.87197			0.410546			0.205273	−	0.978705i	$-0.434192\pi$
$467$	8.87197			0.410546			0.205273	+	0.978705i	$0.434192\pi$
$468$	1.27168	+	16.8805i	0.0587835	+	0.780300i
$469$	−2.73968			−0.126507
$470$	0.839003	−	1.45320i	0.0387003	−	0.0670310i
$471$	−13.2047	+	14.2369i	−0.608441	+	0.656001i
$472$	−10.7341	−	18.5921i	−0.494078	−	0.855769i
$473$		0			0
$474$	3.61532	−	3.89792i	0.166057	−	0.179037i
$475$	1.22696	−	2.12515i	0.0562967	−	0.0975087i
$476$	11.9995			0.549998
$477$	−16.0509	+	10.9525i	−0.734918	+	0.501481i
$478$	10.8920			0.498187
$479$	1.94438	−	3.36776i	0.0888408	−	0.153877i	−0.818181	−	0.574961i	$-0.805017\pi$
$479$	1.94438	−	3.36776i	0.0888408	−	0.153877i	0.907021	+	0.421085i	$0.138350\pi$
$480$	−20.9981	−	4.78835i	−0.958429	−	0.218557i
$481$	19.1961	+	33.2487i	0.875269	+	1.51601i
$482$	6.23075	+	10.7920i	0.283803	+	0.491561i
$483$	−4.20264	−	13.6151i	−0.191227	−	0.619509i
$484$		0			0
$485$	36.4398			1.65465
$486$	6.01491	−	8.84088i	0.272842	−	0.401031i
$487$	−26.9313			−1.22037			−0.610186	−	0.792258i	$-0.708905\pi$
$487$	−26.9313			−1.22037			−0.610186	+	0.792258i	$0.708905\pi$
$488$	10.7222	−	18.5714i	0.485371	−	0.840688i
$489$	3.26732	+	10.5850i	0.147753	+	0.478671i
$490$	−3.76767	−	6.52580i	−0.170206	−	0.294805i
$491$	−17.3361	−	30.0271i	−0.782369	−	1.35510i	−0.930558	−	0.366144i	$-0.880678\pi$
$491$	−17.3361	−	30.0271i	−0.782369	−	1.35510i	0.148189	−	0.988959i	$-0.452656\pi$
$492$	15.2770	+	3.48372i	0.688739	+	0.157058i
$493$	−7.92555	+	13.7275i	−0.356949	+	0.618254i
$494$	15.3072			0.688703
$495$		0			0
$496$	−8.19954			−0.368170
$497$	1.64108	−	2.84244i	0.0736127	−	0.127501i
$498$	−8.02085	+	8.64783i	−0.359423	+	0.387519i
$499$	9.88648	+	17.1239i	0.442580	+	0.766571i	0.997880	−	0.0650793i	$-0.0207300\pi$
$499$	9.88648	+	17.1239i	0.442580	+	0.766571i	−0.555300	+	0.831650i	$0.687397\pi$
$500$	8.86076	+	15.3473i	0.396265	+	0.686352i
$501$	18.1375	−	19.5553i	0.810325	−	0.873667i
$502$	−4.07436	+	7.05699i	−0.181847	+	0.314969i
$503$	7.94193			0.354113			0.177057	−	0.984201i	$-0.443342\pi$
$503$	7.94193			0.354113			0.177057	+	0.984201i	$0.443342\pi$
$504$	−0.747116	−	9.91732i	−0.0332792	−	0.441752i
$505$	−23.7613			−1.05736
$506$		0			0
$507$	1.03265	+	0.235482i	0.0458615	+	0.0104581i
$508$	10.7785	+	18.6689i	0.478220	+	0.828301i
$509$	−10.3893	−	17.9947i	−0.460496	−	0.797603i	0.538489	−	0.842632i	$-0.318995\pi$
$509$	−10.3893	−	17.9947i	−0.460496	−	0.797603i	−0.998986	+	0.0450293i	$0.985662\pi$
$510$	4.30361	+	13.9422i	0.190567	+	0.617373i
$511$	−7.34458	+	12.7212i	−0.324905	+	0.562752i
$512$	14.8814			0.657669
$513$	24.5836	+	19.5811i	1.08539	+	0.864525i
$514$	12.6977			0.560069
$515$	3.41583	−	5.91639i	0.150519	−	0.260707i
$516$	−3.04299	−	9.85825i	−0.133960	−	0.433985i
$517$		0			0
$518$	−4.88713	−	8.46476i	−0.214728	−	0.371920i
$519$	−40.2613	−	9.18107i	−1.76728	−	0.403004i
$520$	−9.57277	+	16.5805i	−0.419794	+	0.727104i
$521$	−41.3132			−1.80997			−0.904983	−	0.425448i	$-0.860117\pi$
$521$	−41.3132			−1.80997			−0.904983	+	0.425448i	$0.860117\pi$
$522$	5.13027	+	2.46813i	0.224546	+	0.108027i
$523$	0.0689754			0.00301608			0.00150804	−	0.999999i	$-0.499520\pi$
$523$	0.0689754			0.00301608			0.00150804	+	0.999999i	$0.499520\pi$
$524$	14.0870	−	24.3993i	0.615392	−	1.06589i
$525$	−0.654332	+	0.705480i	−0.0285574	+	0.0307897i
$526$	−4.58123	−	7.93492i	−0.199751	−	0.345979i
$527$	16.8005	+	29.0994i	0.731843	+	1.26759i
$528$		0			0
$529$	−6.54778	+	11.3411i	−0.284686	+	0.493091i
$530$	−9.52343			−0.413672
$531$	−23.9720	−	11.5327i	−1.04030	−	0.500478i
$532$	12.6672			0.549194
$533$	10.9111	−	18.8986i	0.472613	−	0.818589i
$534$	12.7601	+	2.90978i	0.552184	+	0.125918i
$535$	−12.4395	−	21.5458i	−0.537805	−	0.931505i
$536$	2.42203	+	4.19508i	0.104616	+	0.181200i
$537$	−1.44614	−	4.68501i	−0.0624056	−	0.202173i
$538$	0.0149549	−	0.0259026i	0.000644751	−	0.00111674i
$539$		0			0
$540$	−15.8533	+	6.23275i	−0.682219	+	0.268215i
$541$	−11.1278			−0.478421			−0.239211	−	0.970968i	$-0.576889\pi$
$541$	−11.1278			−0.478421			−0.239211	+	0.970968i	$0.576889\pi$
$542$	2.36079	−	4.08900i	0.101404	−	0.175638i
$543$	4.54113	+	14.7117i	0.194879	+	0.631341i
$544$	−16.6195	−	28.7858i	−0.712555	−	1.23418i
$545$	15.3088	+	26.5155i	0.655755	+	1.13580i
$546$	−5.85192	−	1.33446i	−0.250439	−	0.0571094i
$547$	−10.8499	+	18.7925i	−0.463907	+	0.803511i	−0.999151	−	0.0411862i	$-0.986886\pi$
$547$	−10.8499	+	18.7925i	−0.463907	+	0.803511i	0.535244	+	0.844697i	$0.320220\pi$
$548$	23.1709			0.989811
$549$	−1.99616	−	26.4973i	−0.0851939	−	1.13088i
$550$		0			0
$551$	−8.36656	+	14.4913i	−0.356427	+	0.617350i
$552$	−17.1325	+	18.4717i	−0.729207	+	0.786207i
$553$	−3.06358	−	5.30627i	−0.130276	−	0.225645i
$554$	−6.88835	−	11.9310i	−0.292658	−	0.506898i
$555$	−26.2717	+	28.3253i	−1.11517	+	1.20234i
$556$	7.19318	−	12.4590i	0.305059	−	0.528378i
$557$	3.05296			0.129358			0.0646790	−	0.997906i	$-0.479398\pi$
$557$	3.05296			0.129358			0.0646790	+	0.997906i	$0.479398\pi$
$558$	9.96854	−	6.80217i	0.422002	−	0.287959i
$559$	−14.3686			−0.607729
$560$	−2.05183	+	3.55387i	−0.0867055	+	0.150178i
$561$		0			0
$562$	−1.60737	−	2.78404i	−0.0678026	−	0.117438i
$563$	14.3904	+	24.9250i	0.606484	+	1.05046i	0.991815	+	0.127683i	$0.0407540\pi$
$563$	14.3904	+	24.9250i	0.606484	+	1.05046i	−0.385331	+	0.922778i	$0.625913\pi$
$564$	0.891714	+	2.88885i	0.0375479	+	0.121643i
$565$	−7.88050	+	13.6494i	−0.331535	+	0.574236i
$566$	−5.42575			−0.228061
$567$	−7.69123	−	9.62897i	−0.323001	−	0.404379i
$568$	−5.80323			−0.243498
$569$	1.72557	−	2.98877i	0.0723396	−	0.125296i	−0.827587	−	0.561338i	$-0.810287\pi$
$569$	1.72557	−	2.98877i	0.0723396	−	0.125296i	0.899926	+	0.436042i	$0.143620\pi$
$570$	4.54308	+	14.7180i	0.190289	+	0.616471i
$571$	−1.92564	−	3.33530i	−0.0805854	−	0.139578i	0.822916	−	0.568163i	$-0.192346\pi$
$571$	−1.92564	−	3.33530i	−0.0805854	−	0.139578i	−0.903502	+	0.428585i	$0.859012\pi$
$572$		0			0
$573$	38.6721	+	8.81868i	1.61555	+	0.368406i
$574$	−2.77785	+	4.81138i	−0.115945	+	0.200823i
$575$	2.43748			0.101650
$576$	−2.93155	+	2.00039i	−0.122148	+	0.0833494i
$577$	15.5116			0.645755			0.322878	−	0.946441i	$-0.395350\pi$
$577$	15.5116			0.645755			0.322878	+	0.946441i	$0.395350\pi$
$578$	−5.42900	+	9.40331i	−0.225817	+	0.391126i
$579$	−16.6071	+	17.9052i	−0.690166	+	0.744115i
$580$	−4.53471	−	7.85434i	−0.188293	−	0.326134i
$581$	6.79677	+	11.7724i	0.281978	+	0.488399i
$582$	13.7357	−	14.8094i	0.569364	−	0.613870i
$583$		0			0
$584$	25.9720			1.07473
$585$	1.78217	+	23.6567i	0.0736835	+	0.978085i
$586$	−5.09856			−0.210620
$587$	−5.29597	+	9.17289i	−0.218588	+	0.378606i	−0.954377	−	0.298606i	$-0.903478\pi$
$587$	−5.29597	+	9.17289i	−0.218588	+	0.378606i	0.735788	+	0.677212i	$0.236812\pi$
$588$	13.2370	+	3.01852i	0.545883	+	0.124482i
$589$	17.7354	+	30.7186i	0.730773	+	1.26574i
$590$	−6.51880	−	11.2909i	−0.268375	−	0.464839i
$591$	−0.520427	−	1.68601i	−0.0214075	−	0.0693531i
$592$	7.27488	−	12.6005i	0.298996	−	0.517876i
$593$	−38.8714			−1.59626			−0.798128	−	0.602488i	$-0.794176\pi$
$593$	−38.8714			−1.59626			−0.798128	+	0.602488i	$0.794176\pi$
$594$		0			0
$595$	16.8165			0.689408
$596$	7.71526	−	13.3632i	0.316029	−	0.547379i
$597$	9.69297	+	31.4020i	0.396707	+	1.28520i
$598$	7.60233	+	13.1676i	0.310882	+	0.538464i
$599$	−10.7975	−	18.7018i	−0.441174	−	0.764136i	0.556603	−	0.830779i	$-0.312104\pi$
$599$	−10.7975	−	18.7018i	−0.441174	−	0.764136i	−0.997777	+	0.0666430i	$0.978771\pi$
$600$	1.65871	+	0.378248i	0.0677167	+	0.0154419i
$601$	21.1928	−	36.7071i	0.864474	−	1.49731i	−0.00309446	−	0.999995i	$-0.500985\pi$
$601$	21.1928	−	36.7071i	0.864474	−	1.49731i	0.867568	−	0.497318i	$-0.165682\pi$
$602$	3.65810			0.149093
$603$	5.40900	+	2.60222i	0.220272	+	0.105971i
$604$	−2.29925			−0.0935552
$605$		0			0
$606$	−8.95665	+	9.65677i	−0.363839	+	0.392280i
$607$	0.790523	+	1.36923i	0.0320863	+	0.0555752i	0.881623	−	0.471955i	$-0.156452\pi$
$607$	0.790523	+	1.36923i	0.0320863	+	0.0555752i	−0.849536	+	0.527530i	$0.823118\pi$
$608$	−17.5442	−	30.3875i	−0.711513	−	1.23238i
$609$	4.46185	−	4.81063i	0.180803	−	0.194936i
$610$	6.51156	−	11.2783i	0.263645	−	0.456647i
$611$	4.21057			0.170341
$612$	−23.6909	−	11.3975i	−0.957647	−	0.460715i
$613$	−18.4824			−0.746498			−0.373249	−	0.927731i	$-0.621756\pi$
$613$	−18.4824			−0.746498			−0.373249	+	0.927731i	$0.621756\pi$
$614$	−5.01755	+	8.69065i	−0.202492	+	0.350726i
$615$	21.4096	+	4.88217i	0.863317	+	0.196868i
$616$		0			0
$617$	−13.4291	−	23.2599i	−0.540634	−	0.936406i	−0.998868	−	0.0475744i	$-0.984851\pi$
$617$	−13.4291	−	23.2599i	−0.540634	−	0.936406i	0.458233	−	0.888832i	$-0.348482\pi$
$618$	−1.11689	−	3.61836i	−0.0449281	−	0.145552i
$619$	−0.162939	+	0.282218i	−0.00654906	+	0.0113433i	−0.869281	−	0.494318i	$-0.835418\pi$
$619$	−0.162939	+	0.282218i	−0.00654906	+	0.0113433i	0.862732	+	0.505661i	$0.168751\pi$
$620$	−19.2253			−0.772106
$621$	−4.63466	+	30.8723i	−0.185983	+	1.23886i
$622$	11.0543			0.443238
$623$	7.54175	−	13.0627i	0.302154	−	0.523345i
$624$	−2.63522	−	8.53721i	−0.105493	−	0.341762i
$625$	11.4034	+	19.7513i	0.456137	+	0.790053i
$626$	2.07671	+	3.59696i	0.0830019	+	0.143764i
$627$		0			0
$628$	8.57334	−	14.8495i	0.342113	−	0.592558i
$629$	−59.6238			−2.37736
$630$	−0.453720	−	6.02275i	−0.0180767	−	0.239952i
$631$	25.7694			1.02586			0.512931	−	0.858430i	$-0.328560\pi$
$631$	25.7694			1.02586			0.512931	+	0.858430i	$0.328560\pi$
$632$	−5.41673	+	9.38206i	−0.215466	+	0.373198i
$633$	−11.2142	+	12.0908i	−0.445723	+	0.480565i
$634$	4.06339	+	7.03799i	0.161378	+	0.279514i
$635$	15.1053	+	26.1631i	0.599436	+	1.03825i
$636$	11.6685	−	12.5806i	0.462686	−	0.498853i
$637$	9.45410	−	16.3750i	0.374585	−	0.648800i
$638$		0			0
$639$	−5.93984	+	4.05313i	−0.234977	+	0.160339i
$640$	23.1296			0.914278
$641$	16.3536	−	28.3253i	0.645929	−	1.11878i	−0.338157	−	0.941090i	$-0.609804\pi$
$641$	16.3536	−	28.3253i	0.645929	−	1.11878i	0.984086	−	0.177692i	$-0.0568630\pi$
$642$	−13.4453	−	3.06603i	−0.530645	−	0.121007i
$643$	19.4986	+	33.7725i	0.768948	+	1.33186i	0.938134	+	0.346273i	$0.112553\pi$
$643$	19.4986	+	33.7725i	0.768948	+	1.33186i	−0.169186	+	0.985584i	$0.554114\pi$
$644$	6.29119	+	10.8967i	0.247907	+	0.429388i
$645$	−4.26452	−	13.8156i	−0.167915	−	0.543989i
$646$	−11.8862	+	20.5874i	−0.467655	+	0.810001i
$647$	12.1525			0.477765			0.238882	−	0.971048i	$-0.423219\pi$
$647$	12.1525			0.477765			0.238882	+	0.971048i	$0.423219\pi$
$648$	−7.94468	+	20.2895i	−0.312097	+	0.797049i
$649$		0			0
$650$	0.513373	−	0.889189i	0.0201362	−	0.0348769i
$651$	−4.10222	−	13.2898i	−0.160779	−	0.520869i
$652$	−4.89105	−	8.47156i	−0.191548	−	0.331772i
$653$	−22.2161	−	38.4794i	−0.869382	−	1.50581i	−0.862629	−	0.505837i	$-0.831184\pi$
$653$	−22.2161	−	38.4794i	−0.869382	−	1.50581i	−0.00675301	−	0.999977i	$-0.502150\pi$
$654$	16.5466	+	3.77325i	0.647025	+	0.147546i
$655$	19.7418	−	34.1939i	0.771377	−	1.33606i
$656$	−8.27010			−0.322893
$657$	26.5834	−	18.1396i	1.03712	−	0.707692i
$658$	−1.07197			−0.0417896
$659$	2.81177	−	4.87012i	0.109531	−	0.189713i	−0.806049	−	0.591848i	$-0.798398\pi$
$659$	2.81177	−	4.87012i	0.109531	−	0.189713i	0.915580	+	0.402135i	$0.131732\pi$
$660$		0			0
$661$	2.88357	+	4.99450i	0.112158	+	0.194263i	0.916640	−	0.399713i	$-0.130890\pi$
$661$	2.88357	+	4.99450i	0.112158	+	0.194263i	−0.804482	+	0.593977i	$0.797557\pi$
$662$	−3.05240	−	5.28691i	−0.118635	−	0.205482i
$663$	−24.8983	+	26.8446i	−0.966970	+	1.04256i
$664$	12.0174	−	20.8148i	0.466367	−	0.807771i
$665$	17.7522			0.688400
$666$	1.60869	+	21.3540i	0.0623357	+	0.827452i
$667$	−16.6210			−0.643568
$668$	−11.7760	+	20.3967i	−0.455629	+	0.789172i
$669$	−9.73159	−	2.21916i	−0.376245	−	0.0857978i
$670$	1.47089	+	2.54765i	0.0568254	+	0.0984245i
$671$		0			0
$672$	4.05801	+	13.1466i	0.156541	+	0.507141i
$673$	15.9825	−	27.6826i	0.616082	−	1.06709i	−0.374112	−	0.927384i	$-0.622052\pi$
$673$	15.9825	−	27.6826i	0.616082	−	1.06709i	0.990194	−	0.139701i	$-0.0446143\pi$
$674$	−0.588744			−0.0226776
$675$	1.96194	−	0.771339i	0.0755151	−	0.0296888i
$676$	−0.935274			−0.0359721
$677$	5.08124	−	8.80097i	0.195288	−	0.338249i	−0.751707	−	0.659497i	$-0.770769\pi$
$677$	5.08124	−	8.80097i	0.195288	−	0.338249i	0.946995	+	0.321249i	$0.104103\pi$
$678$	2.57673	+	8.34775i	0.0989589	+	0.320593i
$679$	−11.6395	−	20.1602i	−0.446682	−	0.773676i
$680$	−14.8667	−	25.7498i	−0.570110	−	0.987460i
$681$	41.9199	+	9.55928i	1.60637	+	0.366312i
$682$		0			0
$683$	−29.7864			−1.13974			−0.569872	−	0.821733i	$-0.693007\pi$
$683$	−29.7864			−1.13974			−0.569872	+	0.821733i	$0.693007\pi$
$684$	−25.0091	−	12.0317i	−0.956247	−	0.460042i
$685$	32.4723			1.24070
$686$	−5.69438	+	9.86295i	−0.217412	+	0.376569i
$687$	−11.9431	+	12.8767i	−0.455657	+	0.491275i
$688$	2.72269	+	4.71583i	0.103801	+	0.179789i
$689$	−11.9484	−	20.6953i	−0.455199	−	0.788427i
$690$	−10.4045	+	11.2178i	−0.396092	+	0.427054i
$691$	3.95182	−	6.84476i	0.150334	−	0.260387i	−0.781016	−	0.624511i	$-0.785298\pi$
$691$	3.95182	−	6.84476i	0.150334	−	0.260387i	0.931350	+	0.364124i	$0.118632\pi$
$692$	36.4649			1.38619
$693$		0			0
$694$	15.0641			0.571825
$695$	10.0807	−	17.4603i	0.382383	−	0.662307i
$696$	−11.3107	−	2.57925i	−0.428730	−	0.0977663i
$697$	16.9451	+	29.3498i	0.641842	+	1.11170i
$698$	6.50237	+	11.2624i	0.246118	+	0.426289i
$699$	−1.36743	−	4.43002i	−0.0517211	−	0.167559i
$700$	0.424834	−	0.735834i	0.0160572	−	0.0278119i
$701$	25.1868			0.951293			0.475646	−	0.879637i	$-0.342214\pi$
$701$	25.1868			0.951293			0.475646	+	0.879637i	$0.342214\pi$
$702$	10.2860	+	8.19294i	0.388222	+	0.309223i
$703$	−62.9415			−2.37388
$704$		0			0
$705$	1.24967	+	4.04851i	0.0470653	+	0.152476i
$706$	−0.442632	−	0.766661i	−0.0166587	−	0.0288537i
$707$	7.58975	+	13.1458i	0.285442	+	0.494400i
$708$	22.9025	+	5.22262i	0.860730	+	0.196278i
$709$	−17.1455	+	29.6969i	−0.643913	+	1.11529i	0.340639	+	0.940194i	$0.389357\pi$
$709$	−17.1455	+	29.6969i	−0.643913	+	1.11529i	−0.984551	+	0.175095i	$0.943977\pi$
$710$	−3.52428			−0.132264
$711$	1.00844	+	13.3861i	0.0378193	+	0.502018i
$712$	−26.6692			−0.999472
$713$	−17.6166	+	30.5128i	−0.659746	+	1.14271i
$714$	6.33884	−	6.83434i	0.237225	−	0.255769i
$715$		0			0
$716$	2.16482	+	3.74958i	0.0809031	+	0.140128i
$717$	−18.7024	+	20.1643i	−0.698454	+	0.753051i
$718$	9.39005	−	16.2640i	0.350434	−	0.606969i
$719$	45.9743			1.71455			0.857276	−	0.514856i	$-0.172155\pi$
$719$	45.9743			1.71455			0.857276	+	0.514856i	$0.172155\pi$
$720$	7.42651	−	5.06758i	0.276770	−	0.188858i
$721$	−4.36429			−0.162535
$722$	−6.03095	+	10.4459i	−0.224449	+	0.388757i
$723$	−30.6780	−	6.99571i	−1.14093	−	0.260173i
$724$	−6.79790	−	11.7743i	−0.252642	−	0.437589i
$725$	0.561196	+	0.972020i	0.0208423	+	0.0360999i
$726$		0			0
$727$	11.2760	−	19.5306i	0.418203	−	0.724348i	−0.577556	−	0.816351i	$-0.695993\pi$
$727$	11.2760	−	19.5306i	0.418203	−	0.724348i	0.995759	+	0.0920026i	$0.0293268\pi$
$728$	12.2308			0.453304
$729$	6.03906	+	26.3160i	0.223669	+	0.974665i
$730$	15.7727			0.583774
$731$	11.1574	−	19.3251i	0.412670	−	0.714765i
$732$	6.92064	+	22.4205i	0.255794	+	0.828687i
$733$	10.8990	+	18.8777i	0.402565	+	0.697263i	0.994035	−	0.109064i	$-0.0347854\pi$
$733$	10.8990	+	18.8777i	0.402565	+	0.697263i	−0.591470	+	0.806327i	$0.701452\pi$
$734$	1.94912	+	3.37598i	0.0719435	+	0.124610i
$735$	18.5506	+	4.23023i	0.684250	+	0.156034i
$736$	17.4267	−	30.1840i	0.642357	−	1.11260i
$737$		0			0
$738$	10.0543	−	6.86071i	0.370105	−	0.252546i
$739$	45.2082			1.66301			0.831505	−	0.555517i	$-0.187479\pi$
$739$	45.2082			1.66301			0.831505	+	0.555517i	$0.187479\pi$
$740$	17.0573	−	29.5441i	0.627038	−	1.08606i
$741$	−26.2837	+	28.3383i	−0.965557	+	1.04103i
$742$	3.04194	+	5.26880i	0.111673	+	0.193424i
$743$	−15.9975	−	27.7085i	−0.586892	−	1.01653i	−0.994637	−	0.103431i	$-0.967018\pi$
$743$	−15.9975	−	27.7085i	−0.586892	−	1.01653i	0.407744	−	0.913096i	$-0.366315\pi$
$744$	−16.7231	+	18.0304i	−0.613100	+	0.661025i
$745$	10.8124	−	18.7276i	0.396134	−	0.686125i
$746$	12.0808			0.442308
$747$	−2.23729	−	29.6981i	−0.0818581	−	1.08660i
$748$		0			0
$749$	−7.94673	+	13.7641i	−0.290367	+	0.502931i
$750$	13.4218	+	3.06067i	0.490095	+	0.111760i
$751$	15.7708	+	27.3158i	0.575485	+	0.996769i	0.995989	+	0.0894781i	$0.0285199\pi$
$751$	15.7708	+	27.3158i	0.575485	+	0.996769i	−0.420504	+	0.907291i	$0.638147\pi$
$752$	−0.797853	−	1.38192i	−0.0290947	−	0.0503935i
$753$	−6.06863	−	19.6603i	−0.221153	−	0.716462i
$754$	−3.50066	+	6.06333i	−0.127487	+	0.220813i
$755$	−3.22223			−0.117269
$756$	8.51206	+	6.77994i	0.309581	+	0.246584i
$757$	3.36048			0.122139			0.0610694	−	0.998134i	$-0.480549\pi$
$757$	3.36048			0.122139			0.0610694	+	0.998134i	$0.480549\pi$
$758$	−9.66392	+	16.7384i	−0.351010	+	0.607966i
$759$		0			0
$760$	−15.6939	−	27.1826i	−0.569277	−	0.986017i
$761$	−3.45878	−	5.99078i	−0.125381	−	0.217165i	0.796501	−	0.604637i	$-0.206682\pi$
$761$	−3.45878	−	5.99078i	−0.125381	−	0.217165i	−0.921882	+	0.387472i	$0.873349\pi$
$762$	16.3267	+	3.72310i	0.591455	+	0.134874i
$763$	9.77974	−	16.9390i	0.354050	−	0.613233i
$764$	−35.0255			−1.26718
$765$	−33.2010	−	15.9727i	−1.20038	−	0.577494i
$766$	9.06733			0.327616
$767$	16.3574	−	28.3319i	0.590632	−	1.02300i
$768$	11.5053	−	12.4047i	0.415163	−	0.447615i
$769$	−12.3504	−	21.3916i	−0.445368	−	0.771400i	0.552710	−	0.833374i	$-0.313594\pi$
$769$	−12.3504	−	21.3916i	−0.445368	−	0.771400i	−0.998078	+	0.0619737i	$0.980260\pi$
$770$		0			0
$771$	−21.8029	+	23.5072i	−0.785213	+	0.846592i
$772$	10.7824	−	18.6756i	0.388066	−	0.672150i
$773$	−0.164443			−0.00591459			−0.00295730	−	0.999996i	$-0.500941\pi$
$773$	−0.164443			−0.00591459			−0.00295730	+	0.999996i	$0.500941\pi$
$774$	−7.22225	−	3.47456i	−0.259598	−	0.124890i
$775$	2.37924			0.0854648
$776$	−20.5799	+	35.6454i	−0.738774	+	1.27959i
$777$	24.0625	+	5.48713i	0.863236	+	0.196850i
$778$	−0.949494	−	1.64457i	−0.0340410	−	0.0589607i
$779$	17.8880	+	30.9829i	0.640904	+	1.11008i
$780$	−6.17874	−	20.0170i	−0.221234	−	0.716725i
$781$		0			0
$782$	−23.6131			−0.844401
$783$	−13.3784	+	5.25971i	−0.478104	+	0.187967i
$784$	−7.16575			−0.255920
$785$	12.0149	−	20.8104i	0.428830	−	0.742755i
$786$	−6.45510	−	20.9124i	−0.230246	−	0.745919i
$787$	−16.7268	−	28.9716i	−0.596245	−	1.03273i	−0.993370	−	0.114962i	$-0.963325\pi$
$787$	−16.7268	−	28.9716i	−0.596245	−	1.03273i	0.397125	−	0.917764i	$-0.370008\pi$
$788$	0.779060	+	1.34937i	0.0277529	+	0.0480694i
$789$	22.5563	+	5.14367i	0.803026	+	0.183120i
$790$	−3.28956	+	5.69769i	−0.117037	+	0.202715i
$791$	10.0686			0.358000
$792$		0			0
$793$	32.6785			1.16045
$794$	2.16563	−	3.75098i	0.0768553	−	0.133117i
$795$	16.3525	−	17.6308i	0.579964	−	0.625299i
$796$	−14.5100	−	25.1321i	−0.514294	−	0.890783i
$797$	−14.4645	−	25.0533i	−0.512359	−	0.887432i	−0.999897	−	0.0143304i	$-0.995438\pi$
$797$	−14.4645	−	25.0533i	−0.512359	−	0.887432i	0.487538	−	0.873102i	$-0.337895\pi$
$798$	6.69155	−	7.21462i	0.236878	−	0.255395i
$799$	−3.26954	+	5.66301i	−0.115668	+	0.200343i
$800$	−2.35360			−0.0832123
$801$	−27.2971	+	18.6265i	−0.964494	+	0.658136i
$802$	−2.10565			−0.0743531
$803$		0			0
$804$	−5.16768	−	1.17842i	−0.182250	−	0.0415597i
$805$	8.81663	+	15.2709i	0.310745	+	0.538227i
$806$	7.42069	+	12.8530i	0.261383	+	0.452728i
$807$	0.0222749	+	0.0721630i	0.000784112	+	0.00254026i
$808$	13.4195	−	23.2433i	0.472096	−	0.817695i
$809$	−14.2312			−0.500342			−0.250171	−	0.968202i	$-0.580487\pi$
$809$	−14.2312			−0.500342			−0.250171	+	0.968202i	$0.580487\pi$
$810$	−4.82477	+	12.3218i	−0.169525	+	0.432943i
$811$	9.10230			0.319625			0.159812	−	0.987147i	$-0.448911\pi$
$811$	9.10230			0.319625			0.159812	+	0.987147i	$0.448911\pi$
$812$	−2.89692	+	5.01761i	−0.101662	+	0.176084i
$813$	3.51632	+	11.3917i	0.123323	+	0.399524i
$814$		0			0
$815$	−6.85445	−	11.8723i	−0.240101	−	0.415867i
$816$	13.5284	+	3.08497i	0.473589	+	0.107996i
$817$	11.7782	−	20.4004i	0.412067	−	0.713721i
$818$	0.164609			0.00575542
$819$	12.5187	−	8.54232i	0.437440	−	0.298493i
$820$	−19.3907			−0.677154
$821$	−13.4254	+	23.2535i	−0.468550	+	0.811552i	−0.999354	−	0.0359423i	$-0.988557\pi$
$821$	−13.4254	+	23.2535i	−0.468550	+	0.811552i	0.530804	+	0.847495i	$0.321890\pi$
$822$	12.2402	−	13.1970i	0.426926	−	0.460298i
$823$	−2.33369	−	4.04206i	−0.0813472	−	0.140897i	0.822482	−	0.568792i	$-0.192589\pi$
$823$	−2.33369	−	4.04206i	−0.0813472	−	0.140897i	−0.903829	+	0.427894i	$0.859256\pi$
$824$	3.85827	+	6.68271i	0.134409	+	0.232803i
$825$		0			0
$826$	−4.16442	+	7.21299i	−0.144899	+	0.250972i
$827$	51.9048			1.80491			0.902454	−	0.430786i	$-0.141764\pi$
$827$	51.9048			1.80491			0.902454	+	0.430786i	$0.141764\pi$
$828$	−2.07087	−	27.4890i	−0.0719676	−	0.955308i
$829$	9.85306			0.342211			0.171105	−	0.985253i	$-0.445266\pi$
$829$	9.85306			0.342211			0.171105	+	0.985253i	$0.445266\pi$
$830$	7.29814	−	12.6407i	0.253322	−	0.438767i
$831$	33.9157	+	7.73404i	1.17652	+	0.268291i
$832$	−2.18228	−	3.77982i	−0.0756569	−	0.131042i
$833$	14.6824	+	25.4306i	0.508713	+	0.881118i
$834$	−3.29615	−	10.6784i	−0.114136	−	0.369763i
$835$	−16.5033	+	28.5845i	−0.571119	+	0.989207i
$836$		0			0
$837$	−4.52393	+	30.1347i	−0.156370	+	1.04161i
$838$	14.8901			0.514370
$839$	−11.9855	+	20.7595i	−0.413785	+	0.716697i	−0.995300	−	0.0968386i	$-0.969127\pi$
$839$	−11.9855	+	20.7595i	−0.413785	+	0.716697i	0.581515	+	0.813536i	$0.302460\pi$
$840$	3.63002	+	11.7601i	0.125248	+	0.405760i
$841$	10.6732	+	18.4866i	0.368043	+	0.637469i
$842$	1.42059	+	2.46054i	0.0489568	+	0.0847957i
$843$	7.91409	+	1.80470i	0.272576	+	0.0621573i
$844$	7.28096	−	12.6110i	0.250621	−	0.434088i
$845$	−1.31072			−0.0450900
$846$	2.11640	+	1.01818i	0.0727633	+	0.0350058i
$847$		0			0
$848$	−4.52817	+	7.84302i	−0.155498	+	0.269330i
$849$	9.31646	−	10.0447i	0.319740	−	0.344734i
$850$	0.797277	+	1.38092i	0.0273464	+	0.0473653i
$851$	−31.2599	−	54.1438i	−1.07158	−	1.85602i
$852$	4.31809	−	4.65563i	0.147935	−	0.159499i
$853$	−16.1487	+	27.9704i	−0.552921	+	0.957687i	0.445141	+	0.895460i	$0.353154\pi$
$853$	−16.1487	+	27.9704i	−0.552921	+	0.957687i	−0.998062	+	0.0622268i	$0.980180\pi$
$854$	−8.31959			−0.284691
$855$	−35.0484	−	16.8615i	−1.19863	−	0.576650i
$856$	28.1014			0.960485
$857$	−23.0918	+	39.9962i	−0.788801	+	1.36624i	0.137901	+	0.990446i	$0.455965\pi$
$857$	−23.0918	+	39.9962i	−0.788801	+	1.36624i	−0.926702	+	0.375798i	$0.877369\pi$
$858$		0			0
$859$	−11.6493	−	20.1771i	−0.397468	−	0.688435i	0.595945	−	0.803026i	$-0.296778\pi$
$859$	−11.6493	−	20.1771i	−0.397468	−	0.688435i	−0.993413	+	0.114590i	$0.963444\pi$
$860$	6.38383	+	11.0571i	0.217687	+	0.377044i
$861$	−4.13752	−	13.4042i	−0.141006	−	0.456813i
$862$	3.03689	−	5.26005i	0.103437	−	0.179158i
$863$	17.2073			0.585744			0.292872	−	0.956152i	$-0.405389\pi$
$863$	17.2073			0.585744			0.292872	+	0.956152i	$0.405389\pi$
$864$	4.47517	−	29.8099i	0.152249	−	1.01415i
$865$	51.1028			1.73755
$866$	−9.55915	+	16.5569i	−0.324833	+	0.562627i
$867$	−8.08634	−	26.1970i	−0.274626	−	0.889697i
$868$	6.14087	+	10.6363i	0.208435	+	0.361020i
$869$		0			0
$870$	−6.86893	−	1.56637i	−0.232879	−	0.0531049i
$871$	−3.69085	+	6.39275i	−0.125060	+	0.216610i
$872$	−34.5833			−1.17114
$873$	3.83136	+	50.8580i	0.129672	+	1.72128i
$874$	−24.9270			−0.843167
$875$	7.93283	−	13.7401i	0.268179	−	0.464499i
$876$	−19.3254	+	20.8360i	−0.652944	+	0.703983i
$877$	−7.06330	−	12.2340i	−0.238511	−	0.413113i	0.721776	−	0.692126i	$-0.243326\pi$
$877$	−7.06330	−	12.2340i	−0.238511	−	0.413113i	−0.960287	+	0.279014i	$0.909993\pi$
$878$	−10.4667	−	18.1288i	−0.353234	−	0.611819i
$879$	8.75466	−	9.43899i	0.295287	−	0.318369i
$880$		0			0
$881$	27.1843			0.915862			0.457931	−	0.888988i	$-0.348591\pi$
$881$	27.1843			0.915862			0.457931	+	0.888988i	$0.348591\pi$
$882$	8.71172	−	5.94456i	0.293339	−	0.200164i
$883$	−11.2659			−0.379128			−0.189564	−	0.981868i	$-0.560707\pi$
$883$	−11.2659			−0.379128			−0.189564	+	0.981868i	$0.560707\pi$
$884$	16.1656	−	27.9996i	0.543707	−	0.941728i
$885$	32.0962	+	7.31912i	1.07890	+	0.246029i
$886$	−10.9483	−	18.9630i	−0.367815	−	0.637074i
$887$	10.6846	+	18.5063i	0.358755	+	0.621381i	0.987753	−	0.156025i	$-0.0498681\pi$
$887$	10.6846	+	18.5063i	0.358755	+	0.621381i	−0.628998	+	0.777407i	$0.716535\pi$
$888$	−12.8705	−	41.6960i	−0.431905	−	1.39923i
$889$	9.64976	−	16.7139i	0.323643	−	0.560565i
$890$	−16.1961			−0.542896
$891$		0			0
$892$	8.81395			0.295113
$893$	−3.45147	+	5.97812i	−0.115499	+	0.200050i
$894$	−3.53538	−	11.4534i	−0.118241	−	0.383060i
$895$	3.03383	+	5.25475i	0.101410	+	0.175647i
$896$	−7.38798	−	12.7964i	−0.246815	−	0.427496i
$897$	−37.4311	−	8.53567i	−1.24979	−	0.284998i
$898$	0.0977797	−	0.169359i	0.00326295	−	0.00565160i
$899$	−16.2239			−0.541097
$900$	−1.53767	+	1.04925i	−0.0512557	+	0.0349750i
$901$	37.1122			1.23639
$902$		0			0
$903$	−6.28127	+	6.77226i	−0.209027	+	0.225367i
$904$	−8.90123	−	15.4174i	−0.296050	−	0.512774i
$905$	−9.52676	−	16.5008i	−0.316680	−	0.548506i
$906$	−1.21460	+	1.30954i	−0.0403523	+	0.0435065i
$907$	8.62478	−	14.9386i	0.286381	−	0.496027i	−0.686562	−	0.727071i	$-0.740881\pi$
$907$	8.62478	−	14.9386i	0.286381	−	0.496027i	0.972943	+	0.231045i	$0.0742143\pi$
$908$	−37.9670			−1.25998
$909$	−2.49831	−	33.1630i	−0.0828638	−	1.09995i
$910$	7.42772			0.246226
$911$	−0.303170	+	0.525106i	−0.0100445	+	0.0173975i	−0.871004	−	0.491276i	$-0.836531\pi$
$911$	−0.303170	+	0.525106i	−0.0100445	+	0.0173975i	0.860959	+	0.508674i	$0.169864\pi$
$912$	14.2812	+	3.25663i	0.472897	+	0.107838i
$913$		0			0
$914$	−3.59134	−	6.22038i	−0.118791	−	0.205752i
$915$	9.69877	+	31.4207i	0.320631	+	1.03874i
$916$	7.75422	−	13.4307i	0.256207	−	0.443763i
$917$	−25.2235			−0.832952
$918$	−19.0063	+	7.47234i	−0.627301	+	0.246624i
$919$	24.0754			0.794175			0.397088	−	0.917781i	$-0.370021\pi$
$919$	24.0754			0.794175			0.397088	+	0.917781i	$0.370021\pi$
$920$	15.5888	−	27.0005i	0.513946	−	0.890181i
$921$	−7.47349	−	24.2116i	−0.246260	−	0.797799i
$922$	−9.00109	−	15.5903i	−0.296435	−	0.513441i
$923$	−4.42168	−	7.65858i	−0.145541	−	0.252085i
$924$		0			0
$925$	−2.11093	+	3.65625i	−0.0694071	+	0.120217i
$926$	−18.5089			−0.608240
$927$	8.61648	+	4.14531i	0.283002	+	0.136150i
$928$	16.0491			0.526836
$929$	−6.96640	+	12.0662i	−0.228560	+	0.395878i	−0.957382	−	0.288826i	$-0.906735\pi$
$929$	−6.96640	+	12.0662i	−0.228560	+	0.395878i	0.728821	+	0.684704i	$0.240068\pi$
$930$	−10.1559	+	10.9498i	−0.333025	+	0.359057i
$931$	15.4993	+	26.8456i	0.507970	+	0.879830i
$932$	2.04700	+	3.54550i	0.0670516	+	0.116137i
$933$	−18.9812	+	20.4649i	−0.621417	+	0.669992i
$934$	−3.04289	+	5.27045i	−0.0995666	+	0.172454i
$935$		0			0
$936$	−24.1475	−	11.6171i	−0.789284	−	0.379718i
$937$	−38.4520			−1.25617			−0.628086	−	0.778144i	$-0.716162\pi$
$937$	−38.4520			−1.25617			−0.628086	+	0.778144i	$0.716162\pi$
$938$	0.939652	−	1.62752i	0.0306807	−	0.0531406i
$939$	−10.2249	−	2.33167i	−0.333679	−	0.0760911i
$940$	−1.87071	−	3.24016i	−0.0610158	−	0.105682i
$941$	−12.0367	−	20.8482i	−0.392385	−	0.679631i	0.600378	−	0.799716i	$-0.295017\pi$
$941$	−12.0367	−	20.8482i	−0.392385	−	0.679631i	−0.992764	+	0.120085i	$0.961683\pi$
$942$	−3.92858	−	12.7273i	−0.128000	−	0.414677i
$943$	−17.7682	+	30.7754i	−0.578611	+	1.00218i
$944$	−12.3981			−0.403525
$945$	11.9290	+	9.50159i	0.388051	+	0.309087i
$946$		0			0
$947$	3.61890	−	6.26811i	0.117598	−	0.203686i	−0.801217	−	0.598374i	$-0.795814\pi$
$947$	3.61890	−	6.26811i	0.117598	−	0.203686i	0.918815	+	0.394688i	$0.129147\pi$
$948$	−3.49623	−	11.3266i	−0.113552	−	0.367871i
$949$	19.7890	+	34.2755i	0.642378	+	1.11263i
$950$	0.841640	+	1.45776i	0.0273064	+	0.0472961i
$951$	−20.0066	−	4.56225i	−0.648760	−	0.147941i
$952$	−9.49731	+	16.4498i	−0.307810	+	0.533142i
$953$	35.5820			1.15262			0.576308	−	0.817233i	$-0.304493\pi$
$953$	35.5820			1.15262			0.576308	+	0.817233i	$0.304493\pi$
$954$	−1.00131	−	13.2916i	−0.0324187	−	0.430331i
$955$	−49.0857			−1.58838
$956$	12.1428	−	21.0319i	0.392726	−	0.680221i
$957$		0			0
$958$	1.33376	+	2.31014i	0.0430917	+	0.0746371i
$959$	−10.3722	−	17.9651i	−0.334935	−	0.580125i
$960$	2.98665	−	3.22011i	0.0963938	−	0.103929i
$961$	−1.69566	+	2.93697i	−0.0546987	+	0.0947410i
$962$	−26.3354			−0.849089
$963$	28.7629	−	19.6268i	0.926872	−	0.632463i
$964$	27.7852			0.894900
$965$	15.1107	−	26.1725i	0.486430	−	0.842522i
$966$	9.52955	+	2.17309i	0.306608	+	0.0699180i
$967$	13.8183	+	23.9341i	0.444368	+	0.769667i	0.998008	−	0.0630886i	$-0.0200951\pi$
$967$	13.8183	+	23.9341i	0.444368	+	0.769667i	−0.553640	+	0.832756i	$0.686762\pi$
$968$		0			0
$969$	−17.7041	−	57.3552i	−0.568737	−	1.84251i
$970$	−12.4981	+	21.6473i	−0.401289	+	0.695053i
$971$	−20.4599			−0.656589			−0.328294	−	0.944575i	$-0.606474\pi$
$971$	−20.4599			−0.656589			−0.328294	+	0.944575i	$0.606474\pi$
$972$	−10.3657	−	21.4707i	−0.332481	−	0.688674i
$973$	−12.8798			−0.412907
$974$	9.23684	−	15.9987i	0.295968	−	0.512631i
$975$	0.764654	+	2.47722i	0.0244885	+	0.0793346i
$976$	−6.19218	−	10.7252i	−0.198207	−	0.343305i
$977$	7.60195	+	13.1670i	0.243208	+	0.421249i	0.961626	−	0.274363i	$-0.0884669\pi$
$977$	7.60195	+	13.1670i	0.243208	+	0.421249i	−0.718418	+	0.695611i	$0.755134\pi$
$978$	−7.40871	−	1.68946i	−0.236904	−	0.0540230i
$979$		0			0
$980$	−16.8014			−0.536701
$981$	−35.3974	+	24.1539i	−1.13015	+	0.771174i
$982$	23.7837			0.758968
$983$	−2.28983	+	3.96609i	−0.0730341	+	0.126499i	−0.900230	−	0.435415i	$-0.856602\pi$
$983$	−2.28983	+	3.96609i	−0.0730341	+	0.126499i	0.827196	+	0.561914i	$0.189935\pi$
$984$	−16.8670	+	18.1855i	−0.537702	+	0.579733i
$985$	1.09179	+	1.89104i	0.0347875	+	0.0602537i
$986$	−5.43659	−	9.41644i	−0.173136	−	0.299881i
$987$	1.84065	−	1.98454i	0.0585887	−	0.0631684i
$988$	17.0651	−	29.5576i	0.542912	−	0.940352i
$989$	23.3986			0.744032
$990$		0			0
$991$	12.0458			0.382647			0.191323	−	0.981527i	$-0.438722\pi$
$991$	12.0458			0.382647			0.191323	+	0.981527i	$0.438722\pi$
$992$	17.0103	−	29.4628i	0.540079	−	0.935444i
$993$	15.0289	+	3.42715i	0.476928	+	0.108757i
$994$	1.12571	+	1.94979i	0.0357054	+	0.0618436i
$995$	−20.3347	−	35.2208i	−0.644654	−	1.11657i
$996$	7.75664	+	25.1289i	0.245779	+	0.796239i
$997$	−6.25594	+	10.8356i	−0.198128	+	0.343167i	−0.947921	−	0.318505i	$-0.896819\pi$
$997$	−6.25594	+	10.8356i	−0.198128	+	0.343167i	0.749794	+	0.661672i	$0.230153\pi$
$998$	−13.5634			−0.429342
$999$	−42.2951	−	33.6885i	−1.33816	−	1.06586i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1089.2.e.m.727.5	yes	20
9.2	odd	6		9801.2.a.cc.1.5		10
9.4	even	3	inner	1089.2.e.m.364.5	yes	20
9.7	even	3		9801.2.a.ce.1.6		10
11.10	odd	2		1089.2.e.l.727.6	yes	20
99.43	odd	6		9801.2.a.cd.1.5		10
99.65	even	6		9801.2.a.cb.1.6		10
99.76	odd	6		1089.2.e.l.364.6	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1089.2.e.l.364.6	✓	20	99.76	odd	6
1089.2.e.l.727.6	yes	20	11.10	odd	2
1089.2.e.m.364.5	yes	20	9.4	even	3	inner
1089.2.e.m.727.5	yes	20	1.1	even	1	trivial
9801.2.a.cb.1.6		10	99.65	even	6
9801.2.a.cc.1.5		10	9.2	odd	6
9801.2.a.cd.1.5		10	99.43	odd	6
9801.2.a.ce.1.6		10	9.7	even	3

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:	\( N \)	\(=\)	\( 1089 = 3^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1089.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.342978 + 0.594056i) q^{2} +(-0.510856 - 1.65500i) q^{3} +(0.764732 + 1.32455i) q^{4} +(1.07171 + 1.85626i) q^{5} +(1.15838 + 0.264152i) q^{6} +(0.684647 - 1.18584i) q^{7} -2.42106 q^{8} +(-2.47805 + 1.69093i) q^{9} +O(q^{10})\)	\(q+(-0.342978 + 0.594056i) q^{2} +(-0.510856 - 1.65500i) q^{3} +(0.764732 + 1.32455i) q^{4} +(1.07171 + 1.85626i) q^{5} +(1.15838 + 0.264152i) q^{6} +(0.684647 - 1.18584i) q^{7} -2.42106 q^{8} +(-2.47805 + 1.69093i) q^{9} -1.47030 q^{10} +(1.80147 - 1.94229i) q^{12} +(-1.84469 - 3.19509i) q^{13} +(0.469638 + 0.813437i) q^{14} +(2.52463 - 2.72197i) q^{15} +(-0.699093 + 1.21086i) q^{16} +5.72966 q^{17} +(-0.154590 - 2.05205i) q^{18} +6.04848 q^{19} +(-1.63915 + 2.83909i) q^{20} +(-2.31233 - 0.527296i) q^{21} +(3.00398 + 5.20304i) q^{23} +(1.23681 + 4.00685i) q^{24} +(0.202854 - 0.351353i) q^{25} +2.53075 q^{26} +(4.06442 + 3.23736i) q^{27} +2.09428 q^{28} +(-1.38325 + 2.39586i) q^{29} +(0.751111 + 2.43335i) q^{30} +(2.93221 + 5.07873i) q^{31} +(-2.90061 - 5.02400i) q^{32} +(-1.96515 + 3.40374i) q^{34} +2.93498 q^{35} +(-4.13478 - 1.98921i) q^{36} -10.4062 q^{37} +(-2.07450 + 3.59313i) q^{38} +(-4.34551 + 4.68519i) q^{39} +(-2.59468 - 4.49413i) q^{40} +(2.95744 + 5.12243i) q^{41} +(1.10632 - 1.19280i) q^{42} +(1.94730 - 3.37282i) q^{43} +(-5.79459 - 2.78772i) q^{45} -4.12120 q^{46} +(-0.570634 + 0.988368i) q^{47} +(2.36112 + 0.538422i) q^{48} +(2.56252 + 4.43841i) q^{49} +(0.139149 + 0.241013i) q^{50} +(-2.92703 - 9.48259i) q^{51} +(2.82138 - 4.88678i) q^{52} +6.47721 q^{53} +(-3.31718 + 1.30415i) q^{54} +(-1.65757 + 2.87100i) q^{56} +(-3.08990 - 10.0102i) q^{57} +(-0.948850 - 1.64346i) q^{58} +(4.43365 + 7.67931i) q^{59} +(5.53606 + 1.26243i) q^{60} +(-4.42873 + 7.67078i) q^{61} -4.02273 q^{62} +(0.308590 + 4.09627i) q^{63} +1.18301 q^{64} +(3.95396 - 6.84846i) q^{65} +(-1.00040 - 1.73274i) q^{67} +(4.38165 + 7.58925i) q^{68} +(7.07644 - 7.62959i) q^{69} +(-1.00664 + 1.74354i) q^{70} +2.39698 q^{71} +(5.99951 - 4.09385i) q^{72} -10.7276 q^{73} +(3.56909 - 6.18185i) q^{74} +(-0.685119 - 0.156233i) q^{75} +(4.62546 + 8.01154i) q^{76} +(-1.29285 - 4.18840i) q^{78} +(2.23734 - 3.87519i) q^{79} -2.99691 q^{80} +(3.28149 - 8.38044i) q^{81} -4.05735 q^{82} +(-4.96371 + 8.59739i) q^{83} +(-1.06988 - 3.46604i) q^{84} +(6.14056 + 10.6358i) q^{85} +(1.33576 + 2.31361i) q^{86} +(4.67179 + 1.06534i) q^{87} +11.0155 q^{89} +(3.64348 - 2.48618i) q^{90} -5.05184 q^{91} +(-4.59448 + 7.95787i) q^{92} +(6.90736 - 7.44730i) q^{93} +(-0.391430 - 0.677977i) q^{94} +(6.48224 + 11.2276i) q^{95} +(-6.83293 + 7.36704i) q^{96} +(8.50035 - 14.7230i) q^{97} -3.51555 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - q^{3} - 10 q^{4} - 3 q^{5} + 10 q^{6} - q^{7} - 6 q^{8} + q^{9}+O(q^{10}) \) 20 * q - q^3 - 10 * q^4 - 3 * q^5 + 10 * q^6 - q^7 - 6 * q^8 + q^9	\( 20 q - q^{3} - 10 q^{4} - 3 q^{5} + 10 q^{6} - q^{7} - 6 q^{8} + q^{9} - 5 q^{12} - q^{13} - 15 q^{14} - 7 q^{15} - 10 q^{16} - 6 q^{17} + 17 q^{18} - 4 q^{19} - 15 q^{20} + 4 q^{21} - 18 q^{23} - 27 q^{24} - 7 q^{25} + 12 q^{26} + 23 q^{27} + 8 q^{28} - 12 q^{29} - 26 q^{30} + 7 q^{31} - 24 q^{32} + 6 q^{34} - 36 q^{35} + 20 q^{36} - 2 q^{37} + 12 q^{38} + 4 q^{39} + 12 q^{40} + 6 q^{41} + 2 q^{42} + 8 q^{43} - 35 q^{45} + 36 q^{46} - 27 q^{47} + 19 q^{48} - 15 q^{49} - 15 q^{50} - 2 q^{51} + 5 q^{52} + 12 q^{53} - 44 q^{54} - 60 q^{56} + 27 q^{57} - 9 q^{58} - 21 q^{59} - 5 q^{60} + 20 q^{61} + 6 q^{62} + 74 q^{63} + 62 q^{64} - 12 q^{65} + 10 q^{67} + 69 q^{68} + 16 q^{69} - 6 q^{70} + 36 q^{71} - 102 q^{72} + 14 q^{73} + 6 q^{74} - 26 q^{75} + 2 q^{76} + 92 q^{78} - q^{79} + 102 q^{80} - 35 q^{81} - 60 q^{82} - 30 q^{83} - 70 q^{84} + 24 q^{85} - 36 q^{86} + 60 q^{87} + 108 q^{89} + 11 q^{90} + 20 q^{91} - 6 q^{92} - 19 q^{93} + 15 q^{94} - 12 q^{95} - 106 q^{96} + 16 q^{97} + 120 q^{98}+O(q^{100}) \) 20 * q - q^3 - 10 * q^4 - 3 * q^5 + 10 * q^6 - q^7 - 6 * q^8 + q^9 - 5 * q^12 - q^13 - 15 * q^14 - 7 * q^15 - 10 * q^16 - 6 * q^17 + 17 * q^18 - 4 * q^19 - 15 * q^20 + 4 * q^21 - 18 * q^23 - 27 * q^24 - 7 * q^25 + 12 * q^26 + 23 * q^27 + 8 * q^28 - 12 * q^29 - 26 * q^30 + 7 * q^31 - 24 * q^32 + 6 * q^34 - 36 * q^35 + 20 * q^36 - 2 * q^37 + 12 * q^38 + 4 * q^39 + 12 * q^40 + 6 * q^41 + 2 * q^42 + 8 * q^43 - 35 * q^45 + 36 * q^46 - 27 * q^47 + 19 * q^48 - 15 * q^49 - 15 * q^50 - 2 * q^51 + 5 * q^52 + 12 * q^53 - 44 * q^54 - 60 * q^56 + 27 * q^57 - 9 * q^58 - 21 * q^59 - 5 * q^60 + 20 * q^61 + 6 * q^62 + 74 * q^63 + 62 * q^64 - 12 * q^65 + 10 * q^67 + 69 * q^68 + 16 * q^69 - 6 * q^70 + 36 * q^71 - 102 * q^72 + 14 * q^73 + 6 * q^74 - 26 * q^75 + 2 * q^76 + 92 * q^78 - q^79 + 102 * q^80 - 35 * q^81 - 60 * q^82 - 30 * q^83 - 70 * q^84 + 24 * q^85 - 36 * q^86 + 60 * q^87 + 108 * q^89 + 11 * q^90 + 20 * q^91 - 6 * q^92 - 19 * q^93 + 15 * q^94 - 12 * q^95 - 106 * q^96 + 16 * q^97 + 120 * q^98

Introduction

L-functions

Modular forms

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