LMFDB - Embedded newform 539.2.q.g.520.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [539,2,Mod(214,539)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(539, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 12]))

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

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

chi := DirichletCharacter("539.214");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 539 = 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	539.q (of order $15$, degree $8$, 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:	$4.30393666895$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			520.3
Character	$\chi$	$=$	539.520
Dual form			539.2.q.g.312.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0236455 - 0.224972i) q^{2} +(-0.146626 + 0.162845i) q^{3} +(1.90624 - 0.405184i) q^{4} +(-2.27977 + 1.01502i) q^{5} +(0.0401026 + 0.0291363i) q^{6} +(-0.276036 - 0.849550i) q^{8} +(0.308566 + 2.93581i) q^{9} +O(q^{10})$	\(q+(-0.0236455 - 0.224972i) q^{2} +(-0.146626 + 0.162845i) q^{3} +(1.90624 - 0.405184i) q^{4} +(-2.27977 + 1.01502i) q^{5} +(0.0401026 + 0.0291363i) q^{6} +(-0.276036 - 0.849550i) q^{8} +(0.308566 + 2.93581i) q^{9} +(0.282258 + 0.488885i) q^{10} +(-0.375645 + 3.29528i) q^{11} +(-0.213523 + 0.369833i) q^{12} +(-4.15429 + 3.01827i) q^{13} +(0.168984 - 0.520079i) q^{15} +(3.37609 - 1.50313i) q^{16} +(0.150262 - 1.42965i) q^{17} +(0.653179 - 0.138838i) q^{18} +(5.93587 + 1.26171i) q^{19} +(-3.93453 + 2.85860i) q^{20} +(0.750229 + 0.00659095i) q^{22} +(-3.54146 + 6.13399i) q^{23} +(0.178819 + 0.0796154i) q^{24} +(0.821451 - 0.912313i) q^{25} +(0.777257 + 0.863231i) q^{26} +(-1.05516 - 0.766622i) q^{27} +(2.01408 - 6.19869i) q^{29} +(-0.120999 - 0.0257191i) q^{30} +(7.02421 + 3.12738i) q^{31} +(-1.31126 - 2.27117i) q^{32} +(-0.481541 - 0.544347i) q^{33} -0.325184 q^{34} +(1.77775 + 5.47134i) q^{36} +(-2.66603 - 2.96093i) q^{37} +(0.143492 - 1.36524i) q^{38} +(0.117618 - 1.11906i) q^{39} +(1.49161 + 1.65660i) q^{40} +(2.08556 + 6.41868i) q^{41} -0.802299 q^{43} +(0.619127 + 6.43381i) q^{44} +(-3.68337 - 6.37979i) q^{45} +(1.46372 + 0.651689i) q^{46} +(-6.60467 - 1.40387i) q^{47} +(-0.250246 + 0.770178i) q^{48} +(-0.224669 - 0.163231i) q^{50} +(0.210779 + 0.234094i) q^{51} +(-6.69613 + 7.43680i) q^{52} +(6.01266 + 2.67701i) q^{53} +(-0.147519 + 0.255510i) q^{54} +(-2.48840 - 7.89379i) q^{55} +(-1.07582 + 0.781627i) q^{57} +(-1.44216 - 0.306540i) q^{58} +(-2.81340 + 0.598006i) q^{59} +(0.111396 - 1.05986i) q^{60} +(-0.781393 + 0.347899i) q^{61} +(0.537482 - 1.65420i) q^{62} +(5.49964 - 3.99573i) q^{64} +(6.40724 - 11.0977i) q^{65} +(-0.111077 + 0.121205i) q^{66} +(0.823340 + 1.42607i) q^{67} +(-0.292835 - 2.78614i) q^{68} +(-0.479618 - 1.47611i) q^{69} +(-3.65738 - 2.65724i) q^{71} +(2.40894 - 1.07253i) q^{72} +(14.5235 - 3.08706i) q^{73} +(-0.603087 + 0.669796i) q^{74} +(0.0281194 + 0.267538i) q^{75} +11.8264 q^{76} -0.254539 q^{78} +(-0.256398 - 2.43947i) q^{79} +(-6.17101 + 6.85360i) q^{80} +(-8.38287 + 1.78183i) q^{81} +(1.39471 - 0.620965i) q^{82} +(-1.81851 - 1.32122i) q^{83} +(1.10856 + 3.41180i) q^{85} +(0.0189708 + 0.180495i) q^{86} +(0.714109 + 1.23687i) q^{87} +(2.90320 - 0.590486i) q^{88} +(-0.867830 + 1.50313i) q^{89} +(-1.34818 + 0.979509i) q^{90} +(-4.26549 + 13.1278i) q^{92} +(-1.53921 + 0.685301i) q^{93} +(-0.159660 + 1.51906i) q^{94} +(-14.8131 + 3.14862i) q^{95} +(0.562114 + 0.119481i) q^{96} +(9.77095 - 7.09901i) q^{97} +(-9.79024 - 0.0860098i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 3 q^{2} + 2 q^{3} + 11 q^{4} + 5 q^{5} + 6 q^{6} - 10 q^{8} + 12 q^{9}+O(q^{10}) $ 32 * q + 3 * q^2 + 2 * q^3 + 11 * q^4 + 5 * q^5 + 6 * q^6 - 10 * q^8 + 12 * q^9	$ 32 q + 3 q^{2} + 2 q^{3} + 11 q^{4} + 5 q^{5} + 6 q^{6} - 10 q^{8} + 12 q^{9} - 12 q^{10} + 3 q^{11} - 18 q^{12} - 14 q^{13} - 36 q^{15} - 17 q^{16} + 5 q^{17} - 11 q^{18} - 19 q^{19} + 2 q^{20} - 66 q^{22} - 32 q^{23} + 35 q^{24} - 7 q^{25} + 27 q^{26} + 20 q^{27} + 6 q^{29} + 2 q^{30} + 7 q^{31} - 32 q^{32} + 26 q^{33} - 48 q^{34} + 104 q^{36} - 4 q^{37} + 5 q^{38} - 11 q^{39} + 10 q^{40} - 20 q^{41} - 16 q^{43} + 38 q^{44} - 70 q^{45} + 42 q^{46} + 23 q^{47} - 72 q^{48} + 104 q^{50} + 29 q^{51} - 33 q^{52} - 4 q^{53} - 60 q^{54} - 24 q^{55} - 22 q^{57} - 20 q^{58} - 17 q^{59} + 30 q^{60} + 7 q^{61} + 158 q^{62} + 14 q^{64} + 8 q^{65} - 8 q^{66} + 38 q^{67} + 2 q^{68} + 20 q^{69} - 28 q^{71} + 35 q^{73} + 29 q^{74} - 9 q^{75} + 104 q^{76} - 116 q^{78} - 15 q^{79} + 87 q^{80} + 14 q^{81} - 19 q^{82} + 10 q^{83} + 12 q^{85} + 52 q^{86} + 72 q^{87} - 55 q^{88} - 74 q^{89} - 28 q^{90} - 110 q^{92} - 32 q^{93} + 24 q^{94} - 32 q^{95} + 42 q^{96} + 40 q^{97} + 32 q^{99}+O(q^{100}) $ 32 * q + 3 * q^2 + 2 * q^3 + 11 * q^4 + 5 * q^5 + 6 * q^6 - 10 * q^8 + 12 * q^9 - 12 * q^10 + 3 * q^11 - 18 * q^12 - 14 * q^13 - 36 * q^15 - 17 * q^16 + 5 * q^17 - 11 * q^18 - 19 * q^19 + 2 * q^20 - 66 * q^22 - 32 * q^23 + 35 * q^24 - 7 * q^25 + 27 * q^26 + 20 * q^27 + 6 * q^29 + 2 * q^30 + 7 * q^31 - 32 * q^32 + 26 * q^33 - 48 * q^34 + 104 * q^36 - 4 * q^37 + 5 * q^38 - 11 * q^39 + 10 * q^40 - 20 * q^41 - 16 * q^43 + 38 * q^44 - 70 * q^45 + 42 * q^46 + 23 * q^47 - 72 * q^48 + 104 * q^50 + 29 * q^51 - 33 * q^52 - 4 * q^53 - 60 * q^54 - 24 * q^55 - 22 * q^57 - 20 * q^58 - 17 * q^59 + 30 * q^60 + 7 * q^61 + 158 * q^62 + 14 * q^64 + 8 * q^65 - 8 * q^66 + 38 * q^67 + 2 * q^68 + 20 * q^69 - 28 * q^71 + 35 * q^73 + 29 * q^74 - 9 * q^75 + 104 * q^76 - 116 * q^78 - 15 * q^79 + 87 * q^80 + 14 * q^81 - 19 * q^82 + 10 * q^83 + 12 * q^85 + 52 * q^86 + 72 * q^87 - 55 * q^88 - 74 * q^89 - 28 * q^90 - 110 * q^92 - 32 * q^93 + 24 * q^94 - 32 * q^95 + 42 * q^96 + 40 * q^97 + 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/539\mathbb{Z}\right)^\times$.

$n$	$199$	$442$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−0.0236455	−	0.224972i	−0.0167199	−	0.159079i	0.982976	−	0.183733i	$-0.0588183\pi$
$2$	−0.0236455	−	0.224972i	−0.0167199	−	0.159079i	−0.999696	+	0.0246540i	$0.992152\pi$
$3$	−0.146626	+	0.162845i	−0.0846547	+	0.0940186i	−0.783984	−	0.620781i	$-0.786816\pi$
$3$	−0.146626	+	0.162845i	−0.0846547	+	0.0940186i	0.699329	+	0.714800i	$0.253482\pi$
$4$	1.90624	−	0.405184i	0.953121	−	0.202592i
$5$	−2.27977	+	1.01502i	−1.01955	+	0.453931i	−0.847295	−	0.531122i	$-0.821771\pi$
$5$	−2.27977	+	1.01502i	−1.01955	+	0.453931i	−0.172251	+	0.985053i	$0.555104\pi$
$6$	0.0401026	+	0.0291363i	0.0163718	+	0.0118948i
$7$		0			0
$7$		0			0
$8$	−0.276036	−	0.849550i	−0.0975933	−	0.300361i
$9$	0.308566	+	2.93581i	0.102855	+	0.978604i
$10$	0.282258	+	0.488885i	0.0892578	+	0.154599i
$11$	−0.375645	+	3.29528i	−0.113261	+	0.993565i
$11$	−0.375645	+	3.29528i	−0.113261	+	0.993565i
$12$	−0.213523	+	0.369833i	−0.0616388	+	0.106761i
$13$	−4.15429	+	3.01827i	−1.15219	+	0.837117i	−0.988771	−	0.149439i	$-0.952253\pi$
$13$	−4.15429	+	3.01827i	−1.15219	+	0.837117i	−0.163422	+	0.986556i	$0.552253\pi$
$14$		0			0
$15$	0.168984	−	0.520079i	0.0436314	−	0.134284i
$16$	3.37609	−	1.50313i	0.844022	−	0.375783i
$17$	0.150262	−	1.42965i	0.0364439	−	0.346741i	−0.961072	−	0.276298i	$-0.910892\pi$
$17$	0.150262	−	1.42965i	0.0364439	−	0.346741i	0.997516	−	0.0704426i	$-0.0224412\pi$
$18$	0.653179	−	0.138838i	0.153956	−	0.0327243i
$19$	5.93587	+	1.26171i	1.36178	+	0.289456i	0.830159	−	0.557526i	$-0.188249\pi$
$19$	5.93587	+	1.26171i	1.36178	+	0.289456i	0.531622	+	0.846982i	$0.321583\pi$
$20$	−3.93453	+	2.85860i	−0.879788	+	0.639203i
$21$		0			0
$22$	0.750229	+	0.00659095i	0.159949	+	0.00140520i
$23$	−3.54146	+	6.13399i	−0.738446	+	1.27903i	0.214749	+	0.976669i	$0.431107\pi$
$23$	−3.54146	+	6.13399i	−0.738446	+	1.27903i	−0.953195	+	0.302356i	$0.902227\pi$
$24$	0.178819	+	0.0796154i	0.0365013	+	0.0162514i
$25$	0.821451	−	0.912313i	0.164290	−	0.182463i
$26$	0.777257	+	0.863231i	0.152433	+	0.169294i
$27$	−1.05516	−	0.766622i	−0.203067	−	0.147536i
$28$		0			0
$29$	2.01408	−	6.19869i	0.374004	−	1.15107i	−0.570143	−	0.821545i	$-0.693112\pi$
$29$	2.01408	−	6.19869i	0.374004	−	1.15107i	0.944148	−	0.329522i	$-0.106888\pi$
$30$	−0.120999	−	0.0257191i	−0.0220913	−	0.00469565i
$31$	7.02421	+	3.12738i	1.26158	+	0.561694i	0.925003	−	0.379960i	$-0.124062\pi$
$31$	7.02421	+	3.12738i	1.26158	+	0.561694i	0.336582	+	0.941654i	$0.390729\pi$
$32$	−1.31126	−	2.27117i	−0.231801	−	0.401490i
$33$	−0.481541	−	0.544347i	−0.0838255	−	0.0947586i
$34$	−0.325184			−0.0557687
$35$		0			0
$36$	1.77775	+	5.47134i	0.296291	+	0.911890i
$37$	−2.66603	−	2.96093i	−0.438293	−	0.486774i	0.483012	−	0.875614i	$-0.339543\pi$
$37$	−2.66603	−	2.96093i	−0.438293	−	0.486774i	−0.921305	+	0.388840i	$0.872876\pi$
$38$	0.143492	−	1.36524i	0.0232775	−	0.221471i
$39$	0.117618	−	1.11906i	0.0188340	−	0.179193i
$40$	1.49161	+	1.65660i	0.235844	+	0.261932i
$41$	2.08556	+	6.41868i	0.325709	+	1.00243i	0.971120	+	0.238594i	$0.0766864\pi$
$41$	2.08556	+	6.41868i	0.325709	+	1.00243i	−0.645410	+	0.763836i	$0.723314\pi$
$42$		0			0
$43$	−0.802299			−0.122349			−0.0611747	−	0.998127i	$-0.519485\pi$
$43$	−0.802299			−0.122349			−0.0611747	+	0.998127i	$0.519485\pi$
$44$	0.619127	+	6.43381i	0.0933368	+	0.969934i
$45$	−3.68337	−	6.37979i	−0.549085	−	0.951042i
$46$	1.46372	+	0.651689i	0.215813	+	0.0960862i
$47$	−6.60467	−	1.40387i	−0.963390	−	0.204775i	−0.300742	−	0.953706i	$-0.597234\pi$
$47$	−6.60467	−	1.40387i	−0.963390	−	0.204775i	−0.662648	+	0.748931i	$0.730567\pi$
$48$	−0.250246	+	0.770178i	−0.0361199	+	0.111166i
$49$		0			0
$50$	−0.224669	−	0.163231i	−0.0317729	−	0.0230844i
$51$	0.210779	+	0.234094i	0.0295149	+	0.0327797i
$52$	−6.69613	+	7.43680i	−0.928586	+	1.03130i
$53$	6.01266	+	2.67701i	0.825902	+	0.367715i	0.775761	−	0.631027i	$-0.217366\pi$
$53$	6.01266	+	2.67701i	0.825902	+	0.367715i	0.0501411	+	0.998742i	$0.484033\pi$
$54$	−0.147519	+	0.255510i	−0.0200747	+	0.0347705i
$55$	−2.48840	−	7.89379i	−0.335535	−	1.06440i
$56$		0			0
$57$	−1.07582	+	0.781627i	−0.142495	+	0.103529i
$58$	−1.44216	−	0.306540i	−0.189364	−	0.0402506i
$59$	−2.81340	+	0.598006i	−0.366273	+	0.0778538i	−0.387372	−	0.921924i	$-0.626617\pi$
$59$	−2.81340	+	0.598006i	−0.366273	+	0.0778538i	0.0210985	+	0.999777i	$0.493284\pi$
$60$	0.111396	−	1.05986i	0.0143812	−	0.136828i
$61$	−0.781393	+	0.347899i	−0.100047	+	0.0445439i	−0.456150	−	0.889903i	$-0.650772\pi$
$61$	−0.781393	+	0.347899i	−0.100047	+	0.0445439i	0.356103	+	0.934447i	$0.384105\pi$
$62$	0.537482	−	1.65420i	0.0682603	−	0.210084i
$63$		0			0
$64$	5.49964	−	3.99573i	0.687455	−	0.499466i
$65$	6.40724	−	11.0977i	0.794720	−	1.37650i
$66$	−0.111077	+	0.121205i	−0.0136726	+	0.0149193i
$67$	0.823340	+	1.42607i	0.100587	+	0.174222i	0.911927	−	0.410353i	$-0.134595\pi$
$67$	0.823340	+	1.42607i	0.100587	+	0.174222i	−0.811340	+	0.584575i	$0.801261\pi$
$68$	−0.292835	−	2.78614i	−0.0355115	−	0.337869i
$69$	−0.479618	−	1.47611i	−0.0577393	−	0.177703i
$70$		0			0
$71$	−3.65738	−	2.65724i	−0.434051	−	0.315357i	0.349216	−	0.937042i	$-0.386448\pi$
$71$	−3.65738	−	2.65724i	−0.434051	−	0.315357i	−0.783267	+	0.621686i	$0.786448\pi$
$72$	2.40894	−	1.07253i	0.283897	−	0.126399i
$73$	14.5235	−	3.08706i	1.69985	−	0.361313i	0.747013	−	0.664810i	$-0.231487\pi$
$73$	14.5235	−	3.08706i	1.69985	−	0.361313i	0.952832	+	0.303497i	$0.0981541\pi$
$74$	−0.603087	+	0.669796i	−0.0701074	+	0.0778622i
$75$	0.0281194	+	0.267538i	0.00324695	+	0.0308926i
$76$	11.8264			1.35658
$77$		0			0
$78$	−0.254539			−0.0288209
$79$	−0.256398	−	2.43947i	−0.0288471	−	0.274462i	−0.999432	−	0.0337023i	$-0.989270\pi$
$79$	−0.256398	−	2.43947i	−0.0288471	−	0.274462i	0.970585	−	0.240759i	$-0.0773965\pi$
$80$	−6.17101	+	6.85360i	−0.689940	+	0.766256i
$81$	−8.38287	+	1.78183i	−0.931430	+	0.197982i
$82$	1.39471	−	0.620965i	0.154020	−	0.0685741i
$83$	−1.81851	−	1.32122i	−0.199607	−	0.145023i	0.483492	−	0.875349i	$-0.339368\pi$
$83$	−1.81851	−	1.32122i	−0.199607	−	0.145023i	−0.683099	+	0.730326i	$0.739368\pi$
$84$		0			0
$85$	1.10856	+	3.41180i	0.120240	+	0.370061i
$86$	0.0189708	+	0.180495i	0.00204567	+	0.0194633i
$87$	0.714109	+	1.23687i	0.0765605	+	0.132607i
$88$	2.90320	−	0.590486i	0.309482	−	0.0629460i
$89$	−0.867830	+	1.50313i	−0.0919898	+	0.159331i	−0.908348	−	0.418214i	$-0.862656\pi$
$89$	−0.867830	+	1.50313i	−0.0919898	+	0.159331i	0.816358	+	0.577546i	$0.195989\pi$
$90$	−1.34818	+	0.979509i	−0.142111	+	0.103249i
$91$		0			0
$92$	−4.26549	+	13.1278i	−0.444708	+	1.36867i
$93$	−1.53921	+	0.685301i	−0.159609	+	0.0710624i
$94$	−0.159660	+	1.51906i	−0.0164676	+	0.156679i
$95$	−14.8131	+	3.14862i	−1.51979	+	0.323042i
$96$	0.562114	+	0.119481i	0.0573706	+	0.0121945i
$97$	9.77095	−	7.09901i	0.992089	−	0.720795i	0.0317117	−	0.999497i	$-0.489904\pi$
$97$	9.77095	−	7.09901i	0.992089	−	0.720795i	0.960378	+	0.278702i	$0.0899042\pi$
$98$		0			0
$99$	−9.79024	−	0.0860098i	−0.983956	−	0.00864431i
$100$	1.19623	−	2.07193i	0.119623	−	0.207193i
$101$	−3.37407	−	1.50223i	−0.335733	−	0.149478i	0.231945	−	0.972729i	$-0.425491\pi$
$101$	−3.37407	−	1.50223i	−0.335733	−	0.149478i	−0.567677	+	0.823251i	$0.692158\pi$
$102$	0.0476806	−	0.0529546i	0.00472108	−	0.00524329i
$103$	−0.770546	−	0.855778i	−0.0759242	−	0.0843223i	0.703986	−	0.710214i	$-0.251402\pi$
$103$	−0.770546	−	0.855778i	−0.0759242	−	0.0843223i	−0.779910	+	0.625892i	$0.784735\pi$
$104$	3.71090	+	2.69613i	0.363884	+	0.264377i
$105$		0			0
$106$	0.460080	−	1.41598i	0.0446869	−	0.137532i
$107$	−1.14163	−	0.242661i	−0.110366	−	0.0234590i	0.152398	−	0.988319i	$-0.451301\pi$
$107$	−1.14163	−	0.242661i	−0.110366	−	0.0234590i	−0.262763	+	0.964860i	$0.584634\pi$
$108$	−2.32202	−	1.03383i	−0.223437	−	0.0994804i
$109$	−4.65117	−	8.05606i	−0.445501	−	0.771631i	0.552586	−	0.833456i	$-0.313641\pi$
$109$	−4.65117	−	8.05606i	−0.445501	−	0.771631i	−0.998087	+	0.0618251i	$0.980308\pi$
$110$	−1.71704	+	0.746472i	−0.163714	+	0.0711734i
$111$	0.873083			0.0828694
$112$		0			0
$113$	1.01893	+	3.13595i	0.0958529	+	0.295005i	0.987475	−	0.157775i	$-0.0504322\pi$
$113$	1.01893	+	3.13595i	0.0958529	+	0.295005i	−0.891622	+	0.452780i	$0.850432\pi$
$114$	0.201282	+	0.223547i	0.0188518	+	0.0209371i
$115$	1.84760	−	17.5788i	0.172290	−	1.63923i
$116$	1.32771	−	12.6323i	0.123274	−	1.17288i
$117$	−10.1429	−	11.2649i	−0.937715	−	1.04144i
$118$	0.201059	+	0.618796i	0.0185090	+	0.0569648i
$119$		0			0
$120$	−0.488478			−0.0445918
$121$	−10.7178	−	2.47571i	−0.974344	−	0.225065i
$122$	0.0967440	+	0.167565i	0.00875879	+	0.0151707i
$123$	−1.35105	−	0.601525i	−0.121820	−	0.0542377i
$124$	14.6570	+	3.11544i	1.31624	+	0.279775i
$125$	2.90909	−	8.95326i	0.260197	−	0.800804i
$126$		0			0
$127$	0.233972	+	0.169990i	0.0207616	+	0.0150842i	0.598118	−	0.801408i	$-0.295916\pi$
$127$	0.233972	+	0.169990i	0.0207616	+	0.0150842i	−0.577356	+	0.816492i	$0.695916\pi$
$128$	−4.53859	−	5.04062i	−0.401159	−	0.445532i
$129$	0.117638	−	0.130650i	0.0103575	−	0.0115031i
$130$	−2.64817	−	1.17904i	−0.232260	−	0.103409i
$131$	8.25293	−	14.2945i	0.721062	−	1.24892i	−0.239513	−	0.970893i	$-0.576988\pi$
$131$	8.25293	−	14.2945i	0.721062	−	1.24892i	0.960575	−	0.278023i	$-0.0896790\pi$
$132$	−1.13849	−	0.842544i	−0.0990932	−	0.0733341i
$133$		0			0
$134$	0.301357	−	0.218949i	0.0260333	−	0.0189143i
$135$	3.18367	+	0.676711i	0.274007	+	0.0582420i
$136$	−1.25604	+	0.266979i	−0.107704	+	0.0228932i
$137$	−0.974820	+	9.27479i	−0.0832845	+	0.792399i	0.870553	+	0.492075i	$0.163761\pi$
$137$	−0.974820	+	9.27479i	−0.0832845	+	0.792399i	−0.953837	+	0.300324i	$0.902905\pi$
$138$	−0.320744	+	0.142804i	−0.0273035	+	0.0121563i
$139$	1.49147	−	4.59026i	0.126505	−	0.389341i	−0.867668	−	0.497145i	$-0.834382\pi$
$139$	1.49147	−	4.59026i	0.126505	−	0.389341i	0.994172	+	0.107804i	$0.0343818\pi$
$140$		0			0
$141$	1.19703	−	0.869693i	0.100808	−	0.0732414i
$142$	−0.511325	+	0.885641i	−0.0429094	+	0.0743213i
$143$	−8.38551	−	14.8234i	−0.701232	−	1.23959i
$144$	5.45466	+	9.44774i	0.454555	+	0.787312i
$145$	1.70016	+	16.1759i	0.141191	+	1.34334i
$146$	−1.03792	−	3.19438i	−0.0858987	−	0.264369i
$147$		0			0
$148$	−6.28183	−	4.56401i	−0.516363	−	0.375160i
$149$	0.842211	−	0.374976i	0.0689966	−	0.0307193i	−0.371948	−	0.928253i	$-0.621310\pi$
$149$	0.842211	−	0.374976i	0.0689966	−	0.0307193i	0.440945	+	0.897534i	$0.354643\pi$
$150$	0.0595237	−	0.0126522i	0.00486009	−	0.00103304i
$151$	12.1089	−	13.4483i	0.985405	−	1.09440i	−0.0101237	−	0.999949i	$-0.503223\pi$
$151$	12.1089	−	13.4483i	0.985405	−	1.09440i	0.995529	−	0.0944548i	$-0.0301108\pi$
$152$	−0.566627	−	5.39109i	−0.0459595	−	0.437275i
$153$	4.24355			0.343070
$154$		0			0
$155$	−19.1880			−1.54121
$156$	−0.229218	−	2.18086i	−0.0183521	−	0.174609i
$157$	−8.21246	+	9.12086i	−0.655425	+	0.727924i	−0.975629	−	0.219425i	$-0.929582\pi$
$157$	−8.21246	+	9.12086i	−0.655425	+	0.727924i	0.320204	+	0.947349i	$0.396249\pi$
$158$	−0.542750	+	0.115365i	−0.0431789	+	0.00917795i
$159$	−1.31755	+	0.586611i	−0.104489	+	0.0465213i
$160$	5.29467	+	3.84680i	0.418580	+	0.304116i
$161$		0			0
$162$	0.599080	+	1.84378i	0.0470682	+	0.144861i
$163$	−0.846590	−	8.05476i	−0.0663100	−	0.630898i	−0.976323	−	0.216318i	$-0.930595\pi$
$163$	−0.846590	−	8.05476i	−0.0663100	−	0.630898i	0.910013	−	0.414580i	$-0.136071\pi$
$164$	6.57632	+	11.3905i	0.513524	+	0.889450i
$165$	1.65033	+	0.752214i	0.128478	+	0.0585598i
$166$	−0.254239	+	0.440355i	−0.0197328	+	0.0341781i
$167$	10.5590	−	7.67154i	0.817077	−	0.593641i	−0.0987965	−	0.995108i	$-0.531499\pi$
$167$	10.5590	−	7.67154i	0.817077	−	0.593641i	0.915874	+	0.401466i	$0.131499\pi$
$168$		0			0
$169$	4.13096	−	12.7138i	0.317766	−	0.977985i
$170$	0.741347	−	0.330069i	0.0568587	−	0.0253151i
$171$	−1.87253	+	17.8159i	−0.143196	+	1.36242i
$172$	−1.52938	+	0.325079i	−0.116614	+	0.0247870i
$173$	−5.78299	−	1.22921i	−0.439673	−	0.0934554i	−0.0172438	−	0.999851i	$-0.505489\pi$
$173$	−5.78299	−	1.22921i	−0.439673	−	0.0934554i	−0.422429	+	0.906396i	$0.638822\pi$
$174$	0.261376	−	0.189901i	0.0198149	−	0.0143964i
$175$		0			0
$176$	3.68503	+	11.6898i	0.277770	+	0.881153i
$177$	0.315136	−	0.545831i	0.0236870	−	0.0410272i
$178$	0.358682	+	0.159695i	0.0268843	+	0.0119697i
$179$	2.90073	−	3.22159i	0.216811	−	0.240793i	−0.624922	−	0.780687i	$-0.714869\pi$
$179$	2.90073	−	3.22159i	0.216811	−	0.240793i	0.841733	+	0.539894i	$0.181536\pi$
$180$	−9.60638	−	10.6690i	−0.716018	−	0.795218i
$181$	−8.76223	−	6.36613i	−0.651291	−	0.473191i	0.212420	−	0.977179i	$-0.431866\pi$
$181$	−8.76223	−	6.36613i	−0.651291	−	0.473191i	−0.863711	+	0.503988i	$0.831866\pi$
$182$		0			0
$183$	0.0579192	−	0.178257i	0.00428151	−	0.0131771i
$184$	6.18870	+	1.31545i	0.456237	+	0.0969762i
$185$	9.08336	+	4.04417i	0.667822	+	0.297333i
$186$	0.190569	+	0.330075i	0.0139732	+	0.0242023i
$187$	4.65466	+	1.03220i	0.340382	+	0.0754817i
$188$	−13.1589			−0.959713
$189$		0			0
$190$	1.05862	+	3.25808i	0.0768000	+	0.236366i
$191$	7.79913	+	8.66181i	0.564325	+	0.626746i	0.956003	−	0.293356i	$-0.0947721\pi$
$191$	7.79913	+	8.66181i	0.564325	+	0.626746i	−0.391678	+	0.920102i	$0.628105\pi$
$192$	−0.155709	+	1.48147i	−0.0112373	+	0.106916i
$193$	−2.34619	+	22.3225i	−0.168882	+	1.60681i	0.501748	+	0.865014i	$0.332691\pi$
$193$	−2.34619	+	22.3225i	−0.168882	+	1.60681i	−0.670630	+	0.741792i	$0.733976\pi$
$194$	−1.82812	−	2.03033i	−0.131251	−	0.145769i
$195$	0.867729	+	2.67060i	0.0621394	+	0.191245i
$196$		0			0
$197$	24.1022			1.71721			0.858604	−	0.512639i	$-0.171332\pi$
$197$	24.1022			1.71721			0.858604	+	0.512639i	$0.171332\pi$
$198$	0.212146	+	2.20456i	0.0150765	+	0.156672i
$199$	−9.36026	−	16.2125i	−0.663531	−	1.14927i	−0.979681	−	0.200561i	$-0.935724\pi$
$199$	−9.36026	−	16.2125i	−0.663531	−	1.14927i	0.316150	−	0.948709i	$-0.397610\pi$
$200$	−1.00181	−	0.446032i	−0.0708383	−	0.0315393i
$201$	−0.352951	−	0.0750221i	−0.0248953	−	0.00529165i
$202$	−0.258179	+	0.794593i	−0.0181654	+	0.0559074i
$203$		0			0
$204$	0.496647	+	0.360835i	0.0347722	+	0.0252635i
$205$	−11.2697	−	12.5163i	−0.787109	−	0.874174i
$206$	−0.174306	+	0.193587i	−0.0121445	+	0.0134878i
$207$	−19.1010	−	8.50432i	−1.32761	−	0.591091i
$208$	−9.48840	+	16.4344i	−0.657902	+	1.13952i
$209$	−6.38746	+	19.0864i	−0.441830	+	1.32023i
$210$		0			0
$211$	6.12131	−	4.44739i	0.421408	−	0.306171i	−0.356796	−	0.934182i	$-0.616131\pi$
$211$	6.12131	−	4.44739i	0.421408	−	0.306171i	0.778204	+	0.628011i	$0.216131\pi$
$212$	12.5463	+	2.66679i	0.861681	+	0.183156i
$213$	0.968987	−	0.205964i	0.0663939	−	0.0141125i
$214$	−0.0275975	+	0.262573i	−0.00188653	+	0.0179491i
$215$	1.82906	−	0.814350i	0.124741	−	0.0555382i
$216$	−0.360021	+	1.10803i	−0.0244963	+	0.0753919i
$217$		0			0
$218$	−1.70241	+	1.23687i	−0.115302	+	0.0837717i
$219$	−1.62681	+	2.81772i	−0.109930	+	0.190404i
$220$	−7.94192	−	14.0392i	−0.535444	−	0.946524i
$221$	3.69083	+	6.39271i	0.248272	+	0.430020i
$222$	−0.0206445	−	0.196419i	−0.00138557	−	0.0131828i
$223$	5.41533	+	16.6667i	0.362637	+	1.11608i	0.951447	+	0.307811i	$0.0995966\pi$
$223$	5.41533	+	16.6667i	0.362637	+	1.11608i	−0.588810	+	0.808271i	$0.700403\pi$
$224$		0			0
$225$	2.93185	+	2.13011i	0.195457	+	0.142008i
$226$	0.681407	−	0.303382i	0.0453265	−	0.0201807i
$227$	25.1162	−	5.33860i	1.66702	−	0.354335i	0.724702	−	0.689062i	$-0.241977\pi$
$227$	25.1162	−	5.33860i	1.66702	−	0.354335i	0.942315	+	0.334727i	$0.108644\pi$
$228$	−1.73406	+	1.92587i	−0.114841	+	0.127544i
$229$	2.07352	+	19.7282i	0.137022	+	1.30368i	0.819630	+	0.572893i	$0.194179\pi$
$229$	2.07352	+	19.7282i	0.137022	+	1.30368i	−0.682608	+	0.730784i	$0.739154\pi$
$230$	−3.99842			−0.263648
$231$		0			0
$232$	−5.82205			−0.382236
$233$	2.11300	+	20.1038i	0.138427	+	1.31705i	0.814479	+	0.580193i	$0.197023\pi$
$233$	2.11300	+	20.1038i	0.138427	+	1.31705i	−0.676052	+	0.736854i	$0.736311\pi$
$234$	−2.29445	+	2.54824i	−0.149993	+	0.166584i
$235$	16.4821	−	3.50338i	1.07517	−	0.228535i
$236$	−5.12071	+	2.27989i	−0.333330	+	0.148408i
$237$	0.434850	+	0.315937i	0.0282465	+	0.0205223i
$238$		0			0
$239$	5.28431	+	16.2634i	0.341814	+	1.05199i	0.963267	+	0.268544i	$0.0865424\pi$
$239$	5.28431	+	16.2634i	0.341814	+	1.05199i	−0.621454	+	0.783451i	$0.713458\pi$
$240$	−0.211242	−	2.00984i	−0.0136356	−	0.129734i
$241$	12.0764	+	20.9170i	0.777912	+	1.34738i	0.933143	+	0.359505i	$0.117055\pi$
$241$	12.0764	+	20.9170i	0.777912	+	1.34738i	−0.155231	+	0.987878i	$0.549612\pi$
$242$	−0.303539	+	2.46974i	−0.0195122	+	0.158761i
$243$	2.89537	−	5.01493i	0.185738	−	0.321708i
$244$	−1.34856	+	0.979787i	−0.0863328	+	0.0627245i
$245$		0			0
$246$	−0.103380	+	0.318171i	−0.00659128	+	0.0202859i
$247$	−28.4675	+	12.6745i	−1.81134	+	0.806462i
$248$	0.717934	−	6.83068i	0.0455888	−	0.433749i
$249$	0.481796	−	0.102409i	0.0305325	−	0.00648989i
$250$	−2.08302	−	0.442760i	−0.131742	−	0.0280026i
$251$	−9.62305	+	6.99156i	−0.607402	+	0.441303i	−0.848498	−	0.529198i	$-0.822493\pi$
$251$	−9.62305	+	6.99156i	−0.607402	+	0.441303i	0.241097	+	0.970501i	$0.422493\pi$
$252$		0			0
$253$	−18.8829	−	13.9743i	−1.18716	−	0.878558i
$254$	0.0327107	−	0.0566567i	0.00205245	−	0.00355495i
$255$	−0.718138	−	0.319736i	−0.0449716	−	0.0200226i
$256$	8.07073	−	8.96345i	0.504421	−	0.560216i
$257$	15.3638	+	17.0633i	0.958370	+	1.06438i	0.997875	+	0.0651583i	$0.0207552\pi$
$257$	15.3638	+	17.0633i	0.958370	+	1.06438i	−0.0395050	+	0.999219i	$0.512578\pi$
$258$	−0.0321743	−	0.0233760i	−0.00200308	−	0.00145533i
$259$		0			0
$260$	7.71715	−	23.7509i	0.478597	−	1.47297i
$261$	18.8197	+	4.00024i	1.16491	+	0.247609i
$262$	−3.41101	−	1.51868i	−0.210733	−	0.0938243i
$263$	−0.968871	−	1.67813i	−0.0597432	−	0.103478i	0.834607	−	0.550846i	$-0.185695\pi$
$263$	−0.968871	−	1.67813i	−0.0597432	−	0.103478i	−0.894350	+	0.447368i	$0.852362\pi$
$264$	−0.329528	+	0.559352i	−0.0202810	+	0.0344257i
$265$	−16.4247			−1.00896
$266$		0			0
$267$	−0.117530	−	0.361720i	−0.00719271	−	0.0221369i
$268$	2.14731	+	2.38482i	0.131168	+	0.145676i
$269$	−0.751221	+	7.14739i	−0.0458027	+	0.435784i	0.947458	+	0.319881i	$0.103643\pi$
$269$	−0.751221	+	7.14739i	−0.0458027	+	0.435784i	−0.993261	+	0.115903i	$0.963024\pi$
$270$	0.0769614	−	0.732239i	0.00468372	−	0.0445627i
$271$	0.797003	+	0.885161i	0.0484145	+	0.0537697i	0.766866	−	0.641808i	$-0.221815\pi$
$271$	0.797003	+	0.885161i	0.0484145	+	0.0537697i	−0.718451	+	0.695577i	$0.755149\pi$
$272$	−1.64165	−	5.05249i	−0.0995398	−	0.306352i
$273$		0			0
$274$	2.10962			0.127447
$275$	2.69776	+	3.04962i	0.162681	+	0.183899i
$276$	−1.51237	−	2.61950i	−0.0910337	−	0.157675i
$277$	9.44628	+	4.20576i	0.567572	+	0.252699i	0.670400	−	0.742000i	$-0.266122\pi$
$277$	9.44628	+	4.20576i	0.567572	+	0.252699i	−0.102828	+	0.994699i	$0.532789\pi$
$278$	−1.06795	−	0.226999i	−0.0640512	−	0.0136145i
$279$	−7.01396	+	21.5867i	−0.419915	+	1.29236i
$280$		0			0
$281$	10.6396	+	7.73015i	0.634707	+	0.461142i	0.858028	−	0.513603i	$-0.171690\pi$
$281$	10.6396	+	7.73015i	0.634707	+	0.461142i	−0.223321	+	0.974745i	$0.571690\pi$
$282$	−0.223961	−	0.248734i	−0.0133367	−	0.0148119i
$283$	0.200760	−	0.222966i	0.0119339	−	0.0132540i	−0.737148	−	0.675731i	$-0.763828\pi$
$283$	0.200760	−	0.222966i	0.0119339	−	0.0132540i	0.749082	+	0.662477i	$0.230495\pi$
$284$	−8.04852	−	3.58343i	−0.477592	−	0.212638i
$285$	1.65925	−	2.87391i	0.0982856	−	0.170236i
$286$	−3.13656	+	2.23701i	−0.185469	+	0.132277i
$287$		0			0
$288$	6.26312	−	4.55042i	0.369058	−	0.268136i
$289$	14.6072	+	3.10485i	0.859246	+	0.182638i
$290$	3.59893	−	0.764977i	0.211337	−	0.0449210i
$291$	−0.276640	+	2.63205i	−0.0162169	+	0.154294i
$292$	26.4344	−	11.7694i	1.54696	−	0.688750i
$293$	4.98880	−	15.3539i	0.291449	−	0.896987i	−0.692942	−	0.720993i	$-0.743686\pi$
$293$	4.98880	−	15.3539i	0.291449	−	0.896987i	0.984391	−	0.175994i	$-0.0563140\pi$
$294$		0			0
$295$	5.80692	−	4.21898i	0.338092	−	0.245638i
$296$	−1.77954	+	3.08225i	−0.103434	+	0.179152i
$297$	2.92260	−	3.18909i	0.169587	−	0.185050i
$298$	−0.104274	−	0.180607i	−0.00604042	−	0.0104623i
$299$	−3.80177	−	36.1715i	−0.219862	−	2.09185i
$300$	0.162005	+	0.498599i	0.00935334	+	0.0287866i
$301$		0			0
$302$	−3.31180	−	2.40617i	−0.190573	−	0.138459i
$303$	0.739359	−	0.329184i	0.0424750	−	0.0189111i
$304$	21.9365	−	4.66275i	1.25815	−	0.267427i
$305$	1.42828	−	1.58626i	0.0817829	−	0.0908291i
$306$	−0.100341	−	0.954680i	−0.00573611	−	0.0545754i
$307$	−28.6376			−1.63443			−0.817217	−	0.576330i	$-0.804484\pi$
$307$	−28.6376			−1.63443			−0.817217	+	0.576330i	$0.804484\pi$
$308$		0			0
$309$	0.252341			0.0143552
$310$	0.453709	+	4.31676i	0.0257690	+	0.245175i
$311$	−21.2936	+	23.6489i	−1.20745	+	1.34101i	−0.283272	+	0.959039i	$0.591420\pi$
$311$	−21.2936	+	23.6489i	−1.20745	+	1.34101i	−0.924176	+	0.381968i	$0.875247\pi$
$312$	−0.983167	+	0.208979i	−0.0556609	+	0.0118311i
$313$	0.0312645	−	0.0139198i	0.00176717	−	0.000786796i	−0.405853	−	0.913938i	$-0.633025\pi$
$313$	0.0312645	−	0.0139198i	0.00176717	−	0.000786796i	0.407620	+	0.913152i	$0.366359\pi$
$314$	2.24613	+	1.63191i	0.126756	+	0.0920938i
$315$		0			0
$316$	−1.47719	−	4.54633i	−0.0830985	−	0.255751i
$317$	−2.34033	−	22.2668i	−0.131446	−	1.25063i	−0.839065	−	0.544032i	$-0.816897\pi$
$317$	−2.34033	−	22.2668i	−0.131446	−	1.25063i	0.707618	−	0.706595i	$-0.249770\pi$
$318$	0.163125	+	0.282541i	0.00914762	+	0.0158441i
$319$	19.6699	+	8.96546i	1.10130	+	0.501969i
$320$	−8.48220	+	14.6916i	−0.474170	+	0.821286i
$321$	0.206909	−	0.150328i	0.0115486	−	0.00839052i
$322$		0			0
$323$	2.69574	−	8.29662i	0.149995	−	0.461636i
$324$	−15.2578	+	6.79321i	−0.847656	+	0.377401i
$325$	−0.658938	+	6.26937i	−0.0365513	+	0.347762i
$326$	−1.79208	+	0.380918i	−0.0992541	+	0.0210971i
$327$	1.99387	+	0.423811i	0.110261	+	0.0234368i
$328$	4.87730	−	3.54357i	0.269304	−	0.195661i
$329$		0			0
$330$	0.130204	−	0.389064i	0.00716751	−	0.0214173i
$331$	−5.37885	+	9.31644i	−0.295648	+	0.512078i	−0.975136	−	0.221609i	$-0.928869\pi$
$331$	−5.37885	+	9.31644i	−0.295648	+	0.512078i	0.679487	+	0.733687i	$0.262202\pi$
$332$	−4.00185	−	1.78174i	−0.219630	−	0.0977857i
$333$	7.87008	−	8.74061i	0.431278	−	0.478983i
$334$	−1.97555	−	2.19408i	−0.108098	−	0.120054i
$335$	−3.32452	−	2.41540i	−0.181638	−	0.131968i
$336$		0			0
$337$	2.31915	−	7.13761i	0.126332	−	0.388810i	−0.867809	−	0.496897i	$-0.834473\pi$
$337$	2.31915	−	7.13761i	0.126332	−	0.388810i	0.994141	+	0.108087i	$0.0344726\pi$
$338$	−2.95793	−	0.628727i	−0.160890	−	0.0341983i
$339$	−0.660075	−	0.293884i	−0.0358504	−	0.0159616i
$340$	3.49559	+	6.05454i	0.189575	+	0.328354i
$341$	−12.9442	+	21.9720i	−0.700968	+	1.18985i
$342$	4.05236			0.219126
$343$		0			0
$344$	0.221463	+	0.681593i	0.0119405	+	0.0367490i
$345$	2.59171	+	2.87838i	0.139533	+	0.154967i
$346$	−0.139797	+	1.33008i	−0.00751552	+	0.0715054i
$347$	2.89354	−	27.5302i	0.155333	−	1.47790i	−0.587938	−	0.808906i	$-0.700060\pi$
$347$	2.89354	−	27.5302i	0.155333	−	1.47790i	0.743271	−	0.668990i	$-0.233273\pi$
$348$	1.86243	+	2.06843i	0.0998365	+	0.110880i
$349$	−3.41788	−	10.5192i	−0.182955	−	0.563078i	0.816952	−	0.576706i	$-0.195662\pi$
$349$	−3.41788	−	10.5192i	−0.182955	−	0.563078i	−0.999907	+	0.0136278i	$0.995662\pi$
$350$		0			0
$351$	6.69733			0.357477
$352$	7.97672	−	3.46782i	0.425161	−	0.184836i
$353$	−15.9601	−	27.6437i	−0.849469	−	1.47132i	−0.881683	−	0.471843i	$-0.843589\pi$
$353$	−15.9601	−	27.6437i	−0.849469	−	1.47132i	0.0322133	−	0.999481i	$-0.489744\pi$
$354$	−0.130248	−	0.0579903i	−0.00692262	−	0.00308215i
$355$	11.0352	+	2.34560i	0.585685	+	0.124491i
$356$	−1.04525	+	3.21695i	−0.0553982	+	0.170498i
$357$		0			0
$358$	−0.793358	−	0.576408i	−0.0419303	−	0.0304641i
$359$	2.39433	+	2.65917i	0.126368	+	0.140346i	0.803008	−	0.595968i	$-0.203232\pi$
$359$	2.39433	+	2.65917i	0.126368	+	0.140346i	−0.676640	+	0.736314i	$0.736565\pi$
$360$	−4.40321	+	4.89026i	−0.232069	+	0.257739i
$361$	16.2852	+	7.25066i	0.857118	+	0.381614i
$362$	−1.22501	+	2.12179i	−0.0643853	+	0.111519i
$363$	1.97467	−	1.38233i	0.103643	−	0.0725536i
$364$		0			0
$365$	−29.9768	+	21.7794i	−1.56906	+	1.13999i
$366$	−0.0414724	−	0.00881523i	−0.00216780	−	0.000460780i
$367$	−2.24384	+	0.476942i	−0.117127	+	0.0248962i	−0.266102	−	0.963945i	$-0.585736\pi$
$367$	−2.24384	+	0.476942i	−0.117127	+	0.0248962i	0.148975	+	0.988841i	$0.452403\pi$
$368$	−2.73609	+	26.0322i	−0.142629	+	1.35702i
$369$	−18.2005	+	8.10339i	−0.947480	+	0.421845i
$370$	0.695045	−	2.13913i	0.0361337	−	0.111208i
$371$		0			0
$372$	−2.65644	+	1.93001i	−0.137730	+	0.100067i
$373$	−3.98428	+	6.90097i	−0.206298	+	0.357319i	−0.950546	−	0.310585i	$-0.899475\pi$
$373$	−3.98428	+	6.90097i	−0.206298	+	0.357319i	0.744247	+	0.667904i	$0.232808\pi$
$374$	0.122154	−	1.07157i	0.00631643	−	0.0554098i
$375$	1.03144	+	1.78651i	0.0532636	+	0.0922552i
$376$	0.630469	+	5.99851i	0.0325140	+	0.309350i
$377$	10.3423	+	31.8302i	0.532653	+	1.63934i
$378$		0			0
$379$	9.40174	+	6.83077i	0.482935	+	0.350873i	0.802461	−	0.596705i	$-0.203524\pi$
$379$	9.40174	+	6.83077i	0.482935	+	0.350873i	−0.319526	+	0.947578i	$0.603524\pi$
$380$	−26.9616	+	12.0041i	−1.38310	+	0.615796i
$381$	−0.0619885	+	0.0131761i	−0.00317577	+	0.000675030i
$382$	1.76425	−	1.95940i	0.0902669	−	0.100252i
$383$	−1.31481	−	12.5095i	−0.0671835	−	0.639208i	−0.975360	−	0.220620i	$-0.929192\pi$
$383$	−1.31481	−	12.5095i	−0.0671835	−	0.639208i	0.908176	−	0.418588i	$-0.137475\pi$
$384$	1.48632			0.0758482
$385$		0			0
$386$	5.07741			0.258433
$387$	−0.247562	−	2.35540i	−0.0125843	−	0.119732i
$388$	15.7494	−	17.4915i	0.799554	−	0.887994i
$389$	0.428716	−	0.0911264i	0.0217368	−	0.00462029i	−0.197030	−	0.980397i	$-0.563130\pi$
$389$	0.428716	−	0.0911264i	0.0217368	−	0.00462029i	0.218767	+	0.975777i	$0.429796\pi$
$390$	0.580292	−	0.258363i	0.0293842	−	0.0130827i
$391$	8.23731	+	5.98476i	0.416579	+	0.302662i
$392$		0			0
$393$	1.11769	+	3.43990i	0.0563800	+	0.173520i
$394$	−0.569908	−	5.42232i	−0.0287116	−	0.273172i
$395$	3.06064	+	5.30119i	0.153998	+	0.266732i
$396$	−18.6974	+	3.80290i	−0.939580	+	0.191103i
$397$	−8.40734	+	14.5619i	−0.421952	+	0.730843i	−0.996130	−	0.0878876i	$-0.971988\pi$
$397$	−8.40734	+	14.5619i	−0.421952	+	0.730843i	0.574178	+	0.818730i	$0.305322\pi$
$398$	−3.42602	+	2.48915i	−0.171731	+	0.124770i
$399$		0			0
$400$	1.40196	−	4.31480i	0.0700981	−	0.215740i
$401$	33.6741	−	14.9927i	1.68160	−	0.748698i	0.681750	−	0.731585i	$-0.261219\pi$
$401$	33.6741	−	14.9927i	1.68160	−	0.748698i	0.999854	−	0.0171134i	$-0.00544763\pi$
$402$	−0.00853216	+	0.0811781i	−0.000425546	+	0.00404880i
$403$	−38.6199	+	8.20891i	−1.92379	+	0.408915i
$404$	−7.04048	−	1.49650i	−0.350277	−	0.0744536i
$405$	17.3024	−	12.5710i	0.859766	−	0.624656i
$406$		0			0
$407$	10.7586	−	7.67308i	0.533283	−	0.380340i
$408$	0.140692	−	0.243685i	0.00696528	−	0.0120642i
$409$	14.8669	+	6.61919i	0.735123	+	0.327298i	0.739924	−	0.672691i	$-0.234861\pi$
$409$	14.8669	+	6.61919i	0.735123	+	0.327298i	−0.00480078	+	0.999988i	$0.501528\pi$
$410$	−2.54933	+	2.83132i	−0.125903	+	0.139829i
$411$	−1.36742	−	1.51867i	−0.0674498	−	0.0749106i
$412$	−1.81559	−	1.31911i	−0.0894479	−	0.0649877i
$413$		0			0
$414$	−1.46158	+	4.49828i	−0.0718328	+	0.221079i
$415$	5.48686	+	1.16627i	0.269339	+	0.0572498i
$416$	12.3024	+	5.47737i	0.603173	+	0.268550i
$417$	0.528813	+	0.915931i	0.0258961	+	0.0448533i
$418$	4.44494	+	0.985693i	0.217409	+	0.0482118i
$419$	5.56352			0.271796			0.135898	−	0.990723i	$-0.456608\pi$
$419$	5.56352			0.271796			0.135898	+	0.990723i	$0.456608\pi$
$420$		0			0
$421$	6.64120	+	20.4395i	0.323672	+	0.996161i	0.972036	+	0.234831i	$0.0754536\pi$
$421$	6.64120	+	20.4395i	0.323672	+	0.996161i	−0.648364	+	0.761331i	$0.724546\pi$
$422$	−1.14528	−	1.27196i	−0.0557514	−	0.0619182i
$423$	2.08351	−	19.8232i	0.101304	−	0.963839i
$424$	0.614545	−	5.84700i	0.0298449	−	0.283956i
$425$	−1.18086	−	1.31147i	−0.0572799	−	0.0636158i
$426$	−0.0692485	−	0.213125i	−0.00335510	−	0.0103259i
$427$		0			0
$428$	−2.27455			−0.109944
$429$	3.64345	+	0.807956i	0.175907	+	0.0390085i
$430$	−0.226455	−	0.392232i	−0.0109206	−	0.0189151i
$431$	−25.3223	−	11.2742i	−1.21973	−	0.543061i	−0.307037	−	0.951697i	$-0.599338\pi$
$431$	−25.3223	−	11.2742i	−1.21973	−	0.543061i	−0.912697	+	0.408637i	$0.866004\pi$
$432$	−4.71466	−	1.00213i	−0.226834	−	0.0482151i
$433$	2.87019	−	8.83352i	0.137932	−	0.424512i	−0.858102	−	0.513479i	$-0.828356\pi$
$433$	2.87019	−	8.83352i	0.137932	−	0.424512i	0.996035	+	0.0889667i	$0.0283565\pi$
$434$		0			0
$435$	−2.88346	−	2.09496i	−0.138251	−	0.100445i
$436$	−12.1304	−	13.4722i	−0.580943	−	0.645203i
$437$	−28.7609	+	31.9423i	−1.37582	+	1.52801i
$438$	0.672375	+	0.299361i	0.0321273	+	0.0143040i
$439$	7.35590	−	12.7408i	0.351078	−	0.608085i	−0.635361	−	0.772216i	$-0.719148\pi$
$439$	7.35590	−	12.7408i	0.351078	−	0.608085i	0.986439	+	0.164131i	$0.0524818\pi$
$440$	−6.01928	+	4.29298i	−0.286958	+	0.204660i
$441$		0			0
$442$	1.35091	−	0.981494i	0.0642563	−	0.0466849i
$443$	−2.39005	−	0.508022i	−0.113555	−	0.0241368i	0.150784	−	0.988567i	$-0.451820\pi$
$443$	−2.39005	−	0.508022i	−0.113555	−	0.0241368i	−0.264339	+	0.964430i	$0.585154\pi$
$444$	1.66431	−	0.353759i	0.0789845	−	0.0167887i
$445$	0.452753	−	4.30766i	0.0214625	−	0.204202i
$446$	3.62149	−	1.61239i	0.171482	−	0.0763489i
$447$	−0.0624272	+	0.192131i	−0.00295271	+	0.00908750i
$448$		0			0
$449$	−3.85849	+	2.80335i	−0.182093	+	0.132298i	−0.675098	−	0.737728i	$-0.735899\pi$
$449$	−3.85849	+	2.80335i	−0.182093	+	0.132298i	0.493005	+	0.870027i	$0.335899\pi$
$450$	0.409891	−	0.709952i	0.0193225	−	0.0334675i
$451$	−21.9348	+	4.46135i	−1.03287	+	0.210077i
$452$	3.21296	+	5.56502i	0.151125	+	0.261756i
$453$	0.414503	+	3.94374i	0.0194751	+	0.185293i
$454$	−1.79492	−	5.52420i	−0.0842398	−	0.259264i
$455$		0			0
$456$	0.960995	+	0.698203i	0.0450027	+	0.0326964i
$457$	28.3998	−	12.6444i	1.32849	−	0.591481i	0.385009	−	0.922913i	$-0.374198\pi$
$457$	28.3998	−	12.6444i	1.32849	−	0.591481i	0.943479	+	0.331431i	$0.107532\pi$
$458$	4.38927	−	0.932968i	0.205097	−	0.0435947i
$459$	−1.25455	+	1.39332i	−0.0585575	+	0.0650347i
$460$	−3.60066	−	34.2580i	−0.167882	−	1.59729i
$461$	29.7215			1.38427			0.692134	−	0.721769i	$-0.256671\pi$
$461$	29.7215			1.38427			0.692134	+	0.721769i	$0.256671\pi$
$462$		0			0
$463$	−25.4553			−1.18301			−0.591505	−	0.806302i	$-0.701466\pi$
$463$	−25.4553			−1.18301			−0.591505	+	0.806302i	$0.701466\pi$
$464$	−2.51774	−	23.9547i	−0.116883	−	1.11207i
$465$	2.81346	−	3.12466i	0.130471	−	0.144903i
$466$	4.47284	−	0.950732i	0.207200	−	0.0440418i
$467$	−2.90956	+	1.29542i	−0.134638	+	0.0599449i	−0.472950	−	0.881089i	$-0.656811\pi$
$467$	−2.90956	+	1.29542i	−0.134638	+	0.0599449i	0.338312	+	0.941034i	$0.390144\pi$
$468$	−23.8992	−	17.3638i	−1.10474	−	0.802643i
$469$		0			0
$470$	−1.17789	−	3.62517i	−0.0543320	−	0.167217i
$471$	−0.281124	−	2.67471i	−0.0129535	−	0.123244i
$472$	1.28463	+	2.22505i	0.0591301	+	0.102416i
$473$	0.301379	−	2.64380i	0.0138574	−	0.121562i
$474$	0.0607948	−	0.105300i	0.00279240	−	0.00483657i
$475$	6.02709	−	4.37894i	0.276542	−	0.200920i
$476$		0			0
$477$	−6.00389	+	18.4781i	−0.274899	+	0.846052i
$478$	3.53387	−	1.57338i	0.161635	−	0.0719648i
$479$	−0.337997	+	3.21582i	−0.0154435	+	0.146935i	−0.999526	−	0.0307755i	$-0.990202\pi$
$479$	−0.337997	+	3.21582i	−0.0154435	+	0.146935i	0.984083	+	0.177710i	$0.0568690\pi$
$480$	−1.40277	+	0.298168i	−0.0640274	+	0.0136094i
$481$	20.0124	+	4.25376i	0.912485	+	0.193955i
$482$	4.42019	−	3.21146i	0.201334	−	0.146278i
$483$		0			0
$484$	−21.4338	−	0.376632i	−0.974264	−	0.0171196i
$485$	−15.0699	+	26.1019i	−0.684289	+	1.18522i
$486$	−1.19668	−	0.532797i	−0.0542826	−	0.0241681i
$487$	6.60496	−	7.33555i	0.299299	−	0.332406i	−0.574671	−	0.818384i	$-0.694870\pi$
$487$	6.60496	−	7.33555i	0.299299	−	0.332406i	0.873971	+	0.485979i	$0.161537\pi$
$488$	0.511250	+	0.567800i	0.0231432	+	0.0257031i
$489$	1.43581	+	1.04318i	0.0649296	+	0.0471741i
$490$		0			0
$491$	1.30591	−	4.01917i	0.0589348	−	0.181383i	−0.917255	−	0.398300i	$-0.869600\pi$
$491$	1.30591	−	4.01917i	0.0589348	−	0.181383i	0.976190	+	0.216918i	$0.0696003\pi$
$492$	−2.81915	−	0.599229i	−0.127097	−	0.0270153i
$493$	−8.55931	−	3.81085i	−0.385492	−	0.171632i
$494$	3.52455	+	6.10470i	0.158577	+	0.274663i
$495$	22.4068	−	9.74122i	1.00711	−	0.437835i
$496$	28.4152			1.27588
$497$		0			0
$498$	−0.0344314	−	0.105969i	−0.00154291	−	0.00474859i
$499$	−13.6471	−	15.1566i	−0.610928	−	0.678505i	0.355726	−	0.934590i	$-0.384234\pi$
$499$	−13.6471	−	15.1566i	−0.610928	−	0.678505i	−0.966654	+	0.256086i	$0.917567\pi$
$500$	1.91771	−	18.2458i	0.0857626	−	0.815977i
$501$	−0.298950	+	2.84432i	−0.0133561	+	0.127075i
$502$	1.80045	+	1.99960i	0.0803579	+	0.0892465i
$503$	−7.40382	−	22.7866i	−0.330120	−	1.01600i	−0.969076	−	0.246762i	$-0.920634\pi$
$503$	−7.40382	−	22.7866i	−0.330120	−	1.01600i	0.638956	−	0.769243i	$-0.279366\pi$
$504$		0			0
$505$	9.21692			0.410147
$506$	−2.69734	+	4.57856i	−0.119911	+	0.203542i
$507$	1.46467	+	2.53688i	0.0650483	+	0.112667i
$508$	0.514884	+	0.229241i	0.0228443	+	0.0101709i
$509$	−3.61270	−	0.767903i	−0.160130	−	0.0340367i	0.127149	−	0.991884i	$-0.459417\pi$
$509$	−3.61270	−	0.767903i	−0.160130	−	0.0340367i	−0.287279	+	0.957847i	$0.592751\pi$
$510$	−0.0549509	+	0.169121i	−0.00243327	+	0.00748882i
$511$		0			0
$512$	−13.1822	−	9.57742i	−0.582576	−	0.423266i
$513$	−5.29606	−	5.88187i	−0.233827	−	0.259691i
$514$	3.47547	−	3.85991i	0.153297	−	0.170253i
$515$	2.62530	+	1.16886i	0.115685	+	0.0515061i
$516$	0.171309	−	0.296716i	0.00754147	−	0.0130622i
$517$	7.10714	−	21.2369i	0.312572	−	0.933997i
$518$		0			0
$519$	1.04811	−	0.761497i	0.0460069	−	0.0334260i
$520$	−11.1966	−	2.37992i	−0.491005	−	0.104366i
$521$	0.233063	−	0.0495390i	0.0102107	−	0.00217034i	−0.202804	−	0.979219i	$-0.565005\pi$
$521$	0.233063	−	0.0495390i	0.0102107	−	0.00217034i	0.213014	+	0.977049i	$0.431672\pi$
$522$	0.454942	−	4.32849i	0.0199123	−	0.189453i
$523$	−20.0902	+	8.94472i	−0.878482	+	0.391125i	−0.795878	−	0.605457i	$-0.792990\pi$
$523$	−20.0902	+	8.94472i	−0.878482	+	0.391125i	−0.0826041	+	0.996582i	$0.526324\pi$
$524$	9.94018	−	30.5927i	0.434239	−	1.33645i
$525$		0			0
$526$	−0.354624	+	0.257649i	−0.0154623	+	0.0112340i
$527$	5.52653	−	9.57223i	0.240739	−	0.416973i
$528$	−2.44395	−	1.11394i	−0.106359	−	0.0484782i
$529$	−13.5839	−	23.5280i	−0.590604	−	1.02296i
$530$	0.388371	+	3.69510i	0.0168698	+	0.160505i
$531$	−2.62375	−	8.07508i	−0.113861	−	0.350429i
$532$		0			0
$533$	−28.0373	−	20.3703i	−1.21443	−	0.882336i
$534$	−0.0785978	+	0.0349940i	−0.00340126	+	0.00151434i
$535$	2.84897	−	0.605567i	0.123172	−	0.0261809i
$536$	0.984244	−	1.09311i	0.0425129	−	0.0472153i
$537$	0.0992962	+	0.944740i	0.00428495	+	0.0407685i
$538$	1.62573			0.0700900
$539$		0			0
$540$	6.34305			0.272961
$541$	−2.99275	−	28.4741i	−0.128668	−	1.22420i	−0.848177	−	0.529713i	$-0.822300\pi$
$541$	−2.99275	−	28.4741i	−0.128668	−	1.22420i	0.719509	−	0.694483i	$-0.244367\pi$
$542$	0.180291	−	0.200234i	0.00774417	−	0.00860077i
$543$	2.32146	−	0.493443i	0.0996236	−	0.0211756i
$544$	−3.44401	+	1.53337i	−0.147661	+	0.0657429i
$545$	18.7807	+	13.6450i	0.804477	+	0.584486i
$546$		0			0
$547$	1.98033	+	6.09482i	0.0846727	+	0.260596i	0.984425	−	0.175805i	$-0.0562529\pi$
$547$	1.98033	+	6.09482i	0.0846727	+	0.260596i	−0.899752	+	0.436401i	$0.856253\pi$
$548$	1.89976	+	18.0750i	0.0811536	+	0.772125i
$549$	−1.26248	−	2.18667i	−0.0538812	−	0.0933250i
$550$	0.622289	−	0.679030i	0.0265345	−	0.0289539i
$551$	19.7762	−	34.2534i	0.842495	−	1.45924i
$552$	−1.12164	+	0.814919i	−0.0477402	+	0.0346853i
$553$		0			0
$554$	0.722815	−	2.22460i	0.0307095	−	0.0945141i
$555$	−1.99043	+	0.886198i	−0.0844891	+	0.0376170i
$556$	0.983194	−	9.35447i	0.0416967	−	0.396718i
$557$	22.0272	−	4.68202i	0.933321	−	0.198383i	0.283936	−	0.958843i	$-0.408360\pi$
$557$	22.0272	−	4.68202i	0.933321	−	0.198383i	0.649385	+	0.760460i	$0.275026\pi$
$558$	5.02227	+	1.06752i	0.212609	+	0.0451915i
$559$	3.33298	−	2.42155i	0.140970	−	0.102421i
$560$		0			0
$561$	−0.850583	+	0.606640i	−0.0359116	+	0.0256124i
$562$	1.48749	−	2.57640i	0.0627459	−	0.108679i
$563$	−27.2481	−	12.1316i	−1.14837	−	0.511287i	−0.257828	−	0.966191i	$-0.583007\pi$
$563$	−27.2481	−	12.1316i	−1.14837	−	0.511287i	−0.890540	+	0.454904i	$0.849673\pi$
$564$	1.92944	−	2.14286i	0.0812442	−	0.0902308i
$565$	−5.50598	−	6.11501i	−0.231638	−	0.257261i
$566$	−0.0549082	−	0.0398932i	−0.00230797	−	0.00167684i
$567$		0			0
$568$	−1.24789	+	3.84062i	−0.0523604	+	0.161149i
$569$	−28.6366	−	6.08690i	−1.20051	−	0.255176i	−0.436095	−	0.899901i	$-0.643639\pi$
$569$	−28.6366	−	6.08690i	−1.20051	−	0.255176i	−0.764415	+	0.644725i	$0.776972\pi$
$570$	−0.685783	−	0.305330i	−0.0287243	−	0.0127889i
$571$	−18.9626	−	32.8442i	−0.793559	−	1.37449i	−0.923750	−	0.382996i	$-0.874892\pi$
$571$	−18.9626	−	32.8442i	−0.793559	−	1.37449i	0.130190	−	0.991489i	$-0.458441\pi$
$572$	−21.9910	−	24.8592i	−0.919490	−	1.03942i
$573$	−2.55409			−0.106699
$574$		0			0
$575$	2.68699	+	8.26969i	0.112055	+	0.344870i
$576$	13.4277	+	14.9130i	0.559487	+	0.621374i
$577$	−0.916990	+	8.72458i	−0.0381748	+	0.363209i	0.958713	+	0.284375i	$0.0917862\pi$
$577$	−0.916990	+	8.72458i	−0.0381748	+	0.363209i	−0.996888	+	0.0788334i	$0.974880\pi$
$578$	0.353111	−	3.35963i	0.0146875	−	0.139742i
$579$	−3.29109	−	3.65512i	−0.136773	−	0.151902i
$580$	9.79515	+	30.1464i	0.406721	+	1.25176i
$581$		0			0
$582$	0.598679			0.0248161
$583$	−11.0801	+	18.8078i	−0.458892	+	0.778940i
$584$	−6.63161	−	11.4863i	−0.274418	−	0.475306i
$585$	34.5577	+	15.3861i	1.42879	+	0.636136i
$586$	−3.57217	−	0.759289i	−0.147565	−	0.0313659i
$587$	2.83372	−	8.72130i	0.116960	−	0.359966i	−0.875391	−	0.483416i	$-0.839396\pi$
$587$	2.83372	−	8.72130i	0.116960	−	0.359966i	0.992351	+	0.123450i	$0.0393958\pi$
$588$		0			0
$589$	37.7489	+	27.4262i	1.55542	+	1.13008i
$590$	−1.08646	−	1.20664i	−0.0447288	−	0.0496764i
$591$	−3.53401	+	3.92492i	−0.145370	+	0.161450i
$592$	−13.4514	−	5.98896i	−0.552850	−	0.246145i
$593$	−3.62798	+	6.28385i	−0.148983	+	0.258047i	−0.930852	−	0.365396i	$-0.880933\pi$
$593$	−3.62798	+	6.28385i	−0.148983	+	0.258047i	0.781869	+	0.623443i	$0.214267\pi$
$594$	−0.786562	−	0.582097i	−0.0322730	−	0.0238837i
$595$		0			0
$596$	1.45352	−	1.05605i	0.0595386	−	0.0432573i
$597$	4.01258	+	0.852899i	0.164224	+	0.0349069i
$598$	−8.04768	+	1.71059i	−0.329094	+	0.0699511i
$599$	2.09246	−	19.9084i	0.0854955	−	0.813435i	−0.864807	−	0.502105i	$-0.832559\pi$
$599$	2.09246	−	19.9084i	0.0854955	−	0.813435i	0.950302	−	0.311330i	$-0.100774\pi$
$600$	0.219525	−	0.0977389i	0.00896208	−	0.00399017i
$601$	−3.48280	+	10.7189i	−0.142066	+	0.437235i	−0.996622	−	0.0821246i	$-0.973829\pi$
$601$	−3.48280	+	10.7189i	−0.142066	+	0.437235i	0.854556	+	0.519360i	$0.173829\pi$
$602$		0			0
$603$	−3.93261	+	2.85721i	−0.160148	+	0.116354i
$604$	17.6334	−	30.5419i	0.717493	−	1.24273i
$605$	26.9470	−	5.23471i	1.09555	−	0.212821i
$606$	−0.0915397	−	0.158551i	−0.00371854	−	0.00644071i
$607$	1.41386	+	13.4519i	0.0573866	+	0.545997i	0.985012	+	0.172485i	$0.0551798\pi$
$607$	1.41386	+	13.4519i	0.0573866	+	0.545997i	−0.927625	+	0.373512i	$0.878154\pi$
$608$	−4.91792	−	15.1358i	−0.199448	−	0.613838i
$609$		0			0
$610$	−0.390637	−	0.283814i	−0.0158164	−	0.0114913i
$611$	31.6750	−	14.1026i	1.28143	−	0.570530i
$612$	8.08923	−	1.71942i	0.326988	−	0.0695034i
$613$	−20.6071	+	22.8865i	−0.832312	+	0.924376i	−0.998089	−	0.0617871i	$-0.980320\pi$
$613$	−20.6071	+	22.8865i	−0.832312	+	0.924376i	0.165777	+	0.986163i	$0.446987\pi$
$614$	0.677151	+	6.44266i	0.0273276	+	0.260005i
$615$	3.69064			0.148821
$616$		0			0
$617$	23.6896			0.953707			0.476853	−	0.878983i	$-0.341777\pi$
$617$	23.6896			0.953707			0.476853	+	0.878983i	$0.341777\pi$
$618$	−0.00596675	−	0.0567698i	−0.000240018	−	0.00228362i
$619$	−21.7386	+	24.1431i	−0.873747	+	0.970395i	−0.999766	−	0.0216333i	$-0.993113\pi$
$619$	−21.7386	+	24.1431i	−0.873747	+	0.970395i	0.126019	+	0.992028i	$0.459780\pi$
$620$	−36.5769	+	7.77466i	−1.46896	+	0.312238i
$621$	8.43928	−	3.75741i	0.338656	−	0.150780i
$622$	5.82385	+	4.23127i	0.233515	+	0.169659i
$623$		0			0
$624$	−1.28501	−	3.95485i	−0.0514415	−	0.158321i
$625$	3.09729	+	29.4688i	0.123892	+	1.17875i
$626$	−0.00387084	−	0.00670450i	−0.000154710	−	0.000267966i
$627$	−2.17156	−	3.83873i	−0.0867236	−	0.153304i
$628$	−11.9593	+	20.7141i	−0.477228	+	0.826583i
$629$	−4.63370	+	3.36658i	−0.184758	+	0.134234i
$630$		0			0
$631$	−4.67646	+	14.3927i	−0.186167	+	0.572962i	−0.999967	−	0.00818299i	$-0.997395\pi$
$631$	−4.67646	+	14.3927i	−0.186167	+	0.572962i	0.813800	+	0.581145i	$0.197395\pi$
$632$	−2.00168	+	0.891203i	−0.0796224	+	0.0354502i
$633$	−0.173309	+	1.64893i	−0.00688843	+	0.0655391i
$634$	−4.95407	+	1.05302i	−0.196751	+	0.0418207i
$635$	−0.705947	−	0.150054i	−0.0280146	−	0.00595470i
$636$	−2.27388	+	1.65207i	−0.0901654	+	0.0655090i
$637$		0			0
$638$	1.55187	−	4.63716i	0.0614393	−	0.183587i
$639$	6.67262	−	11.5573i	0.263965	−	0.457200i
$640$	15.4633	+	6.88470i	0.611240	+	0.272142i
$641$	−11.0743	+	12.2992i	−0.437407	+	0.485790i	−0.921033	−	0.389485i	$-0.872653\pi$
$641$	−11.0743	+	12.2992i	−0.437407	+	0.485790i	0.483625	+	0.875275i	$0.339320\pi$
$642$	−0.0387122	−	0.0429942i	−0.00152785	−	0.00169685i
$643$	−1.61403	−	1.17266i	−0.0636513	−	0.0462454i	0.555505	−	0.831513i	$-0.312525\pi$
$643$	−1.61403	−	1.17266i	−0.0636513	−	0.0462454i	−0.619156	+	0.785268i	$0.712525\pi$
$644$		0			0
$645$	−0.135575	+	0.417258i	−0.00533828	+	0.0164295i
$646$	−1.93025	−	0.410288i	−0.0759447	−	0.0161425i
$647$	36.9545	+	16.4532i	1.45283	+	0.646842i	0.973060	−	0.230553i	$-0.0740534\pi$
$647$	36.9545	+	16.4532i	1.45283	+	0.646842i	0.479770	+	0.877394i	$0.340720\pi$
$648$	3.82773	+	6.62982i	0.150367	+	0.260444i
$649$	−0.913761	−	9.49558i	−0.0358682	−	0.372734i
$650$	1.42602			0.0559329
$651$		0			0
$652$	−4.87747	−	15.0113i	−0.191016	−	0.587888i
$653$	−27.7593	−	30.8298i	−1.08631	−	1.20646i	−0.977175	−	0.212437i	$-0.931860\pi$
$653$	−27.7593	−	30.8298i	−1.08631	−	1.20646i	−0.109131	−	0.994027i	$-0.534807\pi$
$654$	0.0481995	−	0.458587i	0.00188475	−	0.0179322i
$655$	−4.30561	+	40.9651i	−0.168234	+	1.60064i
$656$	16.6891	+	18.5352i	0.651602	+	0.723677i
$657$	13.5445	+	41.6856i	0.528421	+	1.62631i
$658$		0			0
$659$	−51.1359			−1.99197			−0.995985	−	0.0895158i	$-0.971468\pi$
$659$	−51.1359			−1.99197			−0.995985	+	0.0895158i	$0.971468\pi$
$660$	3.45071	+	0.765215i	0.134319	+	0.0297860i
$661$	21.4420	+	37.1387i	0.833998	+	1.44453i	0.894844	+	0.446380i	$0.147287\pi$
$661$	21.4420	+	37.1387i	0.833998	+	1.44453i	−0.0608459	+	0.998147i	$0.519380\pi$
$662$	2.22313	+	0.989799i	0.0864042	+	0.0384696i
$663$	−1.58219	−	0.336306i	−0.0614473	−	0.0130610i
$664$	−0.620472	+	1.90962i	−0.0240790	+	0.0741075i
$665$		0			0
$666$	−2.15249	−	1.56387i	−0.0834072	−	0.0605988i
$667$	30.8899	+	34.3067i	1.19606	+	1.32836i
$668$	17.0196	−	18.9021i	0.658506	−	0.731345i
$669$	−3.50811	−	1.56191i	−0.135632	−	0.0603870i
$670$	−0.464789	+	0.805037i	−0.0179563	+	0.0311013i
$671$	−0.852898	−	2.70560i	−0.0329258	−	0.104448i
$672$		0			0
$673$	20.2313	−	14.6989i	0.779858	−	0.566600i	−0.125078	−	0.992147i	$-0.539918\pi$
$673$	20.2313	−	14.6989i	0.779858	−	0.566600i	0.904936	+	0.425547i	$0.139918\pi$
$674$	−1.66060	−	0.352971i	−0.0639639	−	0.0135959i
$675$	−1.56616	+	0.332899i	−0.0602817	+	0.0128133i
$676$	2.72319	−	25.9094i	0.104738	−	0.996515i
$677$	−9.06137	+	4.03438i	−0.348257	+	0.155054i	−0.573408	−	0.819270i	$-0.694379\pi$
$677$	−9.06137	+	4.03438i	−0.348257	+	0.155054i	0.225151	+	0.974324i	$0.427712\pi$
$678$	−0.0505080	+	0.155448i	−0.00193975	+	0.00596993i
$679$		0			0
$680$	2.59249	−	1.88356i	0.0994175	−	0.0722310i
$681$	−2.81332	+	4.87282i	−0.107807	+	0.186727i
$682$	5.24915	+	2.39255i	0.201000	+	0.0916154i
$683$	19.9490	+	34.5527i	0.763328	+	1.32212i	0.941126	+	0.338056i	$0.109769\pi$
$683$	19.9490	+	34.5527i	0.763328	+	1.32212i	−0.177798	+	0.984067i	$0.556897\pi$
$684$	3.64923	+	34.7201i	0.139532	+	1.32756i
$685$	−7.19174	−	22.1339i	−0.274782	−	0.845692i
$686$		0			0
$687$	−3.51667	−	2.55501i	−0.134169	−	0.0974798i
$688$	−2.70863	+	1.20596i	−0.103266	+	0.0459768i
$689$	−33.0583	+	7.02675i	−1.25942	+	0.267698i
$690$	0.586274	−	0.651123i	0.0223191	−	0.0247878i
$691$	0.691352	+	6.57777i	0.0263003	+	0.250230i	0.999771	+	0.0214172i	$0.00681782\pi$
$691$	0.691352	+	6.57777i	0.0263003	+	0.250230i	−0.973470	+	0.228813i	$0.926516\pi$
$692$	−11.5218			−0.437995
$693$		0			0
$694$	−6.26194			−0.237700
$695$	1.25900	+	11.9786i	0.0477568	+	0.454375i
$696$	0.853666	−	0.948092i	0.0323581	−	0.0359373i
$697$	9.48985	−	2.01713i	0.359454	−	0.0764042i
$698$	−2.28570	+	1.01766i	−0.0865150	+	0.0385190i
$699$	−3.58363	−	2.60366i	−0.135545	−	0.0984795i
$700$		0			0
$701$	4.51215	+	13.8870i	0.170421	+	0.524503i	0.999395	−	0.0347848i	$-0.0110746\pi$
$701$	4.51215	+	13.8870i	0.170421	+	0.524503i	−0.828973	+	0.559288i	$0.811075\pi$
$702$	−0.158362	−	1.50671i	−0.00597699	−	0.0568672i
$703$	−12.0894	−	20.9394i	−0.455960	−	0.789746i
$704$	11.1011	+	19.6239i	0.418390	+	0.739602i
$705$	−1.84620	+	3.19771i	−0.0695320	+	0.120433i
$706$	−5.84167	+	4.24422i	−0.219854	+	0.159733i
$707$		0			0
$708$	0.379563	−	1.16817i	0.0142648	−	0.0439027i
$709$	−3.78579	+	1.68554i	−0.142178	+	0.0633018i	−0.476592	−	0.879124i	$-0.658128\pi$
$709$	−3.78579	+	1.68554i	−0.142178	+	0.0633018i	0.334414	+	0.942426i	$0.391462\pi$
$710$	0.266761	−	2.53807i	0.0100114	−	0.0952519i
$711$	7.08270	−	1.50547i	0.265622	−	0.0564597i
$712$	1.51653	+	0.322349i	0.0568345	+	0.0120805i
$713$	−44.0593	+	32.0109i	−1.65003	+	1.19882i
$714$		0			0
$715$	34.1631	+	25.2824i	1.27763	+	0.945510i
$716$	4.22416	−	7.31646i	0.157864	−	0.273429i
$717$	−3.42324	−	1.52412i	−0.127843	−	0.0569195i
$718$	0.541624	−	0.601534i	0.0202132	−	0.0224491i
$719$	11.3901	+	12.6500i	0.424780	+	0.471766i	0.917105	−	0.398646i	$-0.130520\pi$
$719$	11.3901	+	12.6500i	0.424780	+	0.471766i	−0.492325	+	0.870411i	$0.663853\pi$
$720$	−22.0250	−	16.0021i	−0.820825	−	0.596364i
$721$		0			0
$722$	1.24612	−	3.83517i	0.0463759	−	0.142730i
$723$	−5.17696	−	1.10040i	−0.192533	−	0.0409242i
$724$	−19.2824	−	8.58507i	−0.716624	−	0.319062i
$725$	−4.00068	−	6.92938i	−0.148582	−	0.257351i
$726$	−0.357678	−	0.411559i	−0.0132747	−	0.0152744i
$727$	−21.6199			−0.801837			−0.400918	−	0.916114i	$-0.631309\pi$
$727$	−21.6199			−0.801837			−0.400918	+	0.916114i	$0.631309\pi$
$728$		0			0
$729$	−7.55284	−	23.2453i	−0.279735	−	0.860936i
$730$	5.60859	+	6.22897i	0.207583	+	0.230544i
$731$	−0.120555	+	1.14701i	−0.00445890	+	0.0424236i
$732$	0.0381811	−	0.363269i	0.00141121	−	0.0134268i
$733$	−32.2739	−	35.8438i	−1.19206	−	1.32392i	−0.933779	−	0.357851i	$-0.883510\pi$
$733$	−32.2739	−	35.8438i	−1.19206	−	1.32392i	−0.258284	−	0.966069i	$-0.583157\pi$
$734$	0.160355	+	0.493523i	0.00591883	+	0.0182163i
$735$		0			0
$736$	18.5751			0.684688
$737$	−5.00858	+	2.17744i	−0.184493	+	0.0802072i
$738$	2.25340	+	3.90300i	0.0829487	+	0.143671i
$739$	−7.45770	−	3.32038i	−0.274336	−	0.122142i	0.264958	−	0.964260i	$-0.414642\pi$
$739$	−7.45770	−	3.32038i	−0.274336	−	0.122142i	−0.539294	+	0.842118i	$0.681309\pi$
$740$	18.9537	+	4.02874i	0.696752	+	0.148099i
$741$	2.11010	−	6.49421i	0.0775163	−	0.238571i
$742$		0			0
$743$	−15.8254	−	11.4978i	−0.580577	−	0.421814i	0.258355	−	0.966050i	$-0.416820\pi$
$743$	−15.8254	−	11.4978i	−0.580577	−	0.421814i	−0.838932	+	0.544236i	$0.816820\pi$
$744$	1.00707	+	1.11847i	0.0369211	+	0.0410051i
$745$	−1.53944	+	1.70972i	−0.0564008	+	0.0626394i
$746$	1.64674	+	0.733174i	0.0602913	+	0.0268434i
$747$	3.31773	−	5.74648i	0.121389	−	0.210253i
$748$	9.29113	+	0.0816249i	0.339717	+	0.00298450i
$749$		0			0
$750$	0.377527	−	0.274289i	0.0137853	−	0.0100156i
$751$	−1.09190	−	0.232091i	−0.0398441	−	0.00846913i	0.187946	−	0.982179i	$-0.439817\pi$
$751$	−1.09190	−	0.232091i	−0.0398441	−	0.00846913i	−0.227791	+	0.973710i	$0.573150\pi$
$752$	−24.4081	+	5.18811i	−0.890073	+	0.189191i
$753$	0.272452	−	2.59221i	0.00992872	−	0.0944654i
$754$	6.91635	−	3.07936i	0.251879	−	0.112144i
$755$	−13.9552	+	42.9497i	−0.507882	+	1.56310i
$756$		0			0
$757$	21.5015	−	15.6218i	0.781485	−	0.567782i	−0.123939	−	0.992290i	$-0.539553\pi$
$757$	21.5015	−	15.6218i	0.781485	−	0.567782i	0.905424	+	0.424508i	$0.139553\pi$
$758$	1.31442	−	2.27665i	0.0477420	−	0.0826916i
$759$	5.04438	−	1.02598i	0.183099	−	0.0372408i
$760$	6.76385	+	11.7153i	0.245351	+	0.424960i
$761$	−0.658532	−	6.26551i	−0.0238718	−	0.227125i	−0.999953	−	0.00971759i	$-0.996907\pi$
$761$	−0.658532	−	6.26551i	−0.0238718	−	0.227125i	0.976081	−	0.217407i	$-0.0697599\pi$
$762$	0.00443000	+	0.0136341i	0.000160482	+	0.000493913i
$763$		0			0
$764$	18.3766	+	13.3514i	0.664844	+	0.483037i
$765$	−9.67433	+	4.30729i	−0.349776	+	0.155730i
$766$	−2.78321	+	0.591590i	−0.100561	+	0.0213750i
$767$	9.88273	−	10.9759i	0.356845	−	0.396316i
$768$	0.276272	+	2.62856i	0.00996912	+	0.0948498i
$769$	13.1916			0.475700			0.237850	−	0.971302i	$-0.423557\pi$
$769$	13.1916			0.475700			0.237850	+	0.971302i	$0.423557\pi$
$770$		0			0
$771$	−5.03141			−0.181202
$772$	4.57231	+	43.5027i	0.164561	+	1.56569i
$773$	30.6581	−	34.0492i	1.10269	−	1.22467i	0.130263	−	0.991480i	$-0.458418\pi$
$773$	30.6581	−	34.0492i	1.10269	−	1.22467i	0.972432	−	0.233187i	$-0.0749154\pi$
$774$	−0.524045	+	0.111389i	−0.0188364	+	0.00400380i
$775$	8.62319	−	3.83929i	0.309754	−	0.137911i
$776$	−8.72809	−	6.34133i	−0.313320	−	0.227640i
$777$		0			0
$778$	−0.0306381	−	0.0942944i	−0.00109843	−	0.00338062i
$779$	4.28108	+	40.7318i	0.153386	+	1.45937i
$780$	2.73619	+	4.73921i	0.0979711	+	0.169691i
$781$	10.1302	−	11.0539i	0.362489	−	0.395541i
$782$	1.15163	−	1.99468i	0.0411821	−	0.0713295i
$783$	−6.87723	+	4.99660i	−0.245772	+	0.178564i
$784$		0			0
$785$	9.46469	−	29.1293i	0.337809	−	1.03967i
$786$	0.747453	−	0.332787i	0.0266607	−	0.0118701i
$787$	1.97015	−	18.7447i	0.0702281	−	0.668176i	−0.901614	−	0.432542i	$-0.857617\pi$
$787$	1.97015	−	18.7447i	0.0702281	−	0.668176i	0.971842	−	0.235634i	$-0.0757166\pi$
$788$	45.9446	−	9.76582i	1.63671	−	0.347893i
$789$	0.415338	+	0.0882828i	0.0147864	+	0.00314295i
$790$	1.12025	−	0.813909i	0.0398567	−	0.0289576i
$791$		0			0
$792$	2.62938	+	8.34104i	0.0934311	+	0.296386i
$793$	2.19608	−	3.80373i	0.0779852	−	0.135074i
$794$	3.47483	+	1.54709i	0.123317	+	0.0549043i
$795$	2.40830	−	2.67468i	0.0854134	−	0.0948612i
$796$	−24.4120	−	27.1122i	−0.865259	−	0.960967i
$797$	22.7830	+	16.5528i	0.807016	+	0.586331i	0.912964	−	0.408040i	$-0.133788\pi$
$797$	22.7830	+	16.5528i	0.807016	+	0.586331i	−0.105948	+	0.994372i	$0.533788\pi$
$798$		0			0
$799$	−2.99947	+	9.23141i	−0.106114	+	0.326584i
$800$	−3.14916	−	0.669374i	−0.111340	−	0.0236659i
$801$	−4.68068	−	2.08397i	−0.165384	−	0.0736335i
$802$	−4.16917	−	7.22122i	−0.147219	−	0.254990i
$803$	4.71707	+	49.0186i	0.166462	+	1.72983i
$804$	−0.703208			−0.0248002
$805$		0			0
$806$	2.75996	+	8.49429i	0.0972155	+	0.299199i
$807$	−1.05377	−	1.17033i	−0.0370944	−	0.0411975i
$808$	−0.344859	+	3.28111i	−0.0121321	+	0.115429i
$809$	0.684193	−	6.50966i	0.0240549	−	0.228868i	−0.975889	−	0.218268i	$-0.929959\pi$
$809$	0.684193	−	6.50966i	0.0240549	−	0.228868i	0.999944	−	0.0105996i	$-0.00337401\pi$
$810$	−3.23724	−	3.59532i	−0.113745	−	0.126327i
$811$	5.81096	+	17.8843i	0.204050	+	0.628002i	0.999751	+	0.0223122i	$0.00710279\pi$
$811$	5.81096	+	17.8843i	0.204050	+	0.628002i	−0.795701	+	0.605690i	$0.792897\pi$
$812$		0			0
$813$	−0.261006			−0.00915387
$814$	−1.98062	−	2.23895i	−0.0694207	−	0.0784751i
$815$	10.1058	+	17.5037i	0.353990	+	0.613129i
$816$	1.06348	+	0.473493i	0.0372293	+	0.0165756i
$817$	−4.76234	−	1.01227i	−0.166613	−	0.0354147i
$818$	1.13760	−	3.50116i	0.0397751	−	0.122415i
$819$		0			0
$820$	−26.5542	−	19.2927i	−0.927311	−	0.673731i
$821$	−7.75388	−	8.61156i	−0.270612	−	0.300545i	0.592487	−	0.805580i	$-0.298146\pi$
$821$	−7.75388	−	8.61156i	−0.270612	−	0.300545i	−0.863099	+	0.505035i	$0.831480\pi$
$822$	−0.309326	+	0.343541i	−0.0107890	+	0.0119824i
$823$	11.2790	+	5.02173i	0.393161	+	0.175046i	0.593789	−	0.804621i	$-0.297632\pi$
$823$	11.2790	+	5.02173i	0.393161	+	0.175046i	−0.200628	+	0.979668i	$0.564298\pi$
$824$	−0.514328	+	0.890843i	−0.0179175	+	0.0310340i
$825$	−0.892177	−	0.00783800i	−0.0310616	−	0.000272884i
$826$		0			0
$827$	3.63717	−	2.64256i	0.126477	−	0.0918907i	−0.522748	−	0.852487i	$-0.675093\pi$
$827$	3.63717	−	2.64256i	0.126477	−	0.0918907i	0.649225	+	0.760596i	$0.275093\pi$
$828$	−39.8570	−	8.47186i	−1.38513	−	0.294417i
$829$	19.4288	−	4.12972i	0.674790	−	0.143431i	0.142244	−	0.989832i	$-0.454568\pi$
$829$	19.4288	−	4.12972i	0.674790	−	0.143431i	0.532547	+	0.846401i	$0.321235\pi$
$830$	0.132638	−	1.26197i	0.00460393	−	0.0438035i
$831$	−2.06996	+	0.921605i	−0.0718061	+	0.0319701i
$832$	−10.7869	+	33.1988i	−0.373970	+	1.15096i
$833$		0			0
$834$	0.193555	−	0.140626i	0.00670226	−	0.00486947i
$835$	−16.2853	+	28.2069i	−0.563576	+	0.976142i
$836$	−4.44254	+	38.9714i	−0.153648	+	1.34785i
$837$	−5.01418	−	8.68481i	−0.173315	−	0.300191i
$838$	−0.131552	−	1.25164i	−0.00454440	−	0.0432371i
$839$	−13.5513	−	41.7065i	−0.467842	−	1.43987i	−0.855373	−	0.518012i	$-0.826672\pi$
$839$	−13.5513	−	41.7065i	−0.467842	−	1.43987i	0.387532	−	0.921856i	$-0.373328\pi$
$840$		0			0
$841$	−10.9057	−	7.92348i	−0.376060	−	0.273224i
$842$	4.44129	−	1.97739i	0.153057	−	0.0681453i
$843$	−2.81886	+	0.599168i	−0.0970869	+	0.0206365i
$844$	9.86669	−	10.9581i	0.339625	−	0.377192i
$845$	3.48711	+	33.1776i	0.119960	+	1.14134i
$846$	−4.50894			−0.155021
$847$		0			0
$848$	24.3232			0.835261
$849$	0.00687228	+	0.0653854i	0.000235856	+	0.00224402i
$850$	−0.267123	+	0.296670i	−0.00916224	+	0.0101757i
$851$	27.6040	−	5.86740i	0.946252	−	0.201132i
$852$	1.76367	−	0.785236i	0.0604223	−	0.0269017i
$853$	−31.6655	−	23.0063i	−1.08421	−	0.787721i	−0.105794	−	0.994388i	$-0.533738\pi$
$853$	−31.6655	−	23.0063i	−1.08421	−	0.787721i	−0.978411	+	0.206667i	$0.933738\pi$
$854$		0			0
$855$	−13.8146	−	42.5169i	−0.472449	−	1.45405i
$856$	0.108978	+	1.03686i	0.00372479	+	0.0354390i
$857$	−17.5262	−	30.3563i	−0.598684	−	1.03695i	−0.993016	−	0.117982i	$-0.962357\pi$
$857$	−17.5262	−	30.3563i	−0.598684	−	1.03695i	0.394332	−	0.918968i	$-0.370976\pi$
$858$	0.0956163	−	0.838778i	0.00326429	−	0.0286354i
$859$	16.2603	−	28.1636i	0.554794	−	0.960931i	−0.443126	−	0.896459i	$-0.646130\pi$
$859$	16.2603	−	28.1636i	0.554794	−	0.960931i	0.997920	−	0.0644717i	$-0.0205362\pi$
$860$	3.15667	−	2.29345i	0.107642	−	0.0782061i
$861$		0			0
$862$	−1.93763	+	5.96341i	−0.0659959	+	0.203114i
$863$	11.5965	−	5.16310i	0.394750	−	0.175754i	−0.199755	−	0.979846i	$-0.564015\pi$
$863$	11.5965	−	5.16310i	0.394750	−	0.175754i	0.594505	+	0.804092i	$0.297348\pi$
$864$	−0.357533	+	3.40170i	−0.0121635	+	0.115728i
$865$	14.4316	−	3.06753i	0.490689	−	0.104299i
$866$	−2.05516	−	0.436839i	−0.0698373	−	0.0148444i
$867$	−2.64741	+	1.92345i	−0.0899107	+	0.0653239i
$868$		0			0
$869$	8.13505	+	0.0714685i	0.275963	+	0.00242440i
$870$	−0.403126	+	0.698234i	−0.0136672	+	0.0236724i
$871$	−7.72465	−	3.43924i	−0.261740	−	0.116534i
$872$	−5.56014	+	6.17516i	−0.188290	+	0.209117i
$873$	23.8563	+	26.4951i	0.807414	+	0.896725i
$874$	7.86619	+	5.71512i	0.266078	+	0.193317i
$875$		0			0
$876$	−1.95940	+	6.03041i	−0.0662020	+	0.203749i
$877$	27.5192	+	5.84938i	0.929257	+	0.197520i	0.647587	−	0.761992i	$-0.275778\pi$
$877$	27.5192	+	5.84938i	0.929257	+	0.197520i	0.281670	+	0.959511i	$0.409112\pi$
$878$	−3.04026	−	1.35361i	−0.102604	−	0.0456821i
$879$	1.76882	+	3.06369i	0.0596610	+	0.103336i
$880$	−20.2664	−	22.9097i	−0.683182	−	0.772287i
$881$	−36.7964			−1.23970			−0.619850	−	0.784720i	$-0.712807\pi$
$881$	−36.7964			−1.23970			−0.619850	+	0.784720i	$0.712807\pi$
$882$		0			0
$883$	−0.705855	−	2.17240i	−0.0237539	−	0.0731070i	0.938477	−	0.345342i	$-0.112237\pi$
$883$	−0.705855	−	2.17240i	−0.0237539	−	0.0731070i	−0.962231	+	0.272235i	$0.912237\pi$
$884$	9.62585	+	10.6906i	0.323752	+	0.359563i
$885$	−0.164408	+	1.56424i	−0.00552653	+	0.0525814i
$886$	−0.0577766	+	0.549708i	−0.00194104	+	0.0184678i
$887$	28.2826	+	31.4110i	0.949636	+	1.05468i	0.998438	+	0.0558690i	$0.0177929\pi$
$887$	28.2826	+	31.4110i	0.949636	+	1.05468i	−0.0488023	+	0.998808i	$0.515540\pi$
$888$	−0.241002	−	0.741728i	−0.00808750	−	0.0248908i
$889$		0			0
$890$	−0.979808			−0.0328432
$891$	−2.72266	−	28.2933i	−0.0912127	−	0.947860i
$892$	17.0760	+	29.5765i	0.571747	+	0.990295i
$893$	−37.4332	−	16.6663i	−1.25265	−	0.557717i
$894$	0.0447003	+	0.00950134i	0.00149500	+	0.000317772i
$895$	−3.34304	+	10.2888i	−0.111745	+	0.343917i
$896$		0			0
$897$	6.44778	+	4.68459i	0.215285	+	0.156414i
$898$	0.721913	+	0.801765i	0.0240905	+	0.0267552i
$899$	33.5329	−	37.2421i	1.11839	−	1.24209i
$900$	6.45191	+	2.87257i	0.215064	+	0.0957525i
$901$	4.73066	−	8.19374i	0.157601	−	0.272973i
$902$	1.52234	+	4.82923i	0.0506884	+	0.160796i
$903$		0			0
$904$	2.38288	−	1.73127i	0.0792535	−	0.0575810i
$905$	26.4377	+	5.61950i	0.878817	+	0.186798i
$906$	0.877429	−	0.186503i	0.0291506	−	0.00619616i
$907$	−4.13186	+	39.3120i	−0.137196	+	1.30533i	0.681801	+	0.731537i	$0.261197\pi$
$907$	−4.13186	+	39.3120i	−0.137196	+	1.30533i	−0.818998	+	0.573797i	$0.805470\pi$
$908$	45.7143	−	20.3533i	1.51708	−	0.675449i
$909$	3.36915	−	10.3692i	0.111748	−	0.343924i
$910$		0			0
$911$	28.5013	−	20.7074i	0.944291	−	0.686067i	−0.00515893	−	0.999987i	$-0.501642\pi$
$911$	28.5013	−	20.7074i	0.944291	−	0.686067i	0.949450	+	0.313919i	$0.101642\pi$
$912$	−2.45717	+	4.25593i	−0.0813649	+	0.140928i
$913$	5.03692	−	5.49619i	0.166698	−	0.181897i
$914$	−3.51617	−	6.09019i	−0.116305	−	0.201446i
$915$	0.0488919	+	0.465175i	0.00161632	+	0.0153782i
$916$	11.9462	+	36.7666i	0.394713	+	1.21480i
$917$		0			0
$918$	0.343123	+	0.249293i	0.0113247	+	0.00822791i
$919$	−36.1860	+	16.1110i	−1.19366	+	0.531454i	−0.904767	−	0.425906i	$-0.859955\pi$
$919$	−36.1860	+	16.1110i	−1.19366	+	0.531454i	−0.288897	+	0.957360i	$0.593289\pi$
$920$	−15.4440	+	3.28273i	−0.509175	+	0.108229i
$921$	4.19903	−	4.66349i	0.138363	−	0.153667i
$922$	−0.702780	−	6.68651i	−0.0231448	−	0.220208i
$923$	23.2141			0.764101
$924$		0			0
$925$	−4.89131			−0.160825
$926$	0.601905	+	5.72674i	0.0197798	+	0.188192i
$927$	2.27464	−	2.52624i	0.0747089	−	0.0829727i
$928$	−16.7193	+	3.55379i	−0.548837	+	0.116659i
$929$	2.39036	−	1.06425i	0.0784250	−	0.0349171i	−0.367149	−	0.930162i	$-0.619666\pi$
$929$	2.39036	−	1.06425i	0.0784250	−	0.0349171i	0.445574	+	0.895245i	$0.353000\pi$
$930$	−0.769488	−	0.559066i	−0.0252325	−	0.0183325i
$931$		0			0
$932$	12.1736	+	37.4666i	0.398761	+	1.22726i
$933$	−0.728909	−	6.93511i	−0.0238634	−	0.227045i
$934$	0.360232	+	0.623939i	0.0117871	+	0.0204159i
$935$	−11.6593	+	2.37140i	−0.381299	+	0.0775529i
$936$	−6.77026	+	11.7264i	−0.221293	+	0.383291i
$937$	−43.5575	+	31.6464i	−1.42296	+	1.03384i	−0.431689	+	0.902022i	$0.642082\pi$
$937$	−43.5575	+	31.6464i	−1.42296	+	1.03384i	−0.991274	+	0.131820i	$0.957918\pi$
$938$		0			0
$939$	−0.00231742	+	0.00713228i	−7.56261e−5	+	0.000232753i
$940$	29.9994	−	13.3566i	0.978471	−	0.435643i
$941$	−3.09902	+	29.4852i	−0.101025	+	0.961190i	0.820178	+	0.572108i	$0.193874\pi$
$941$	−3.09902	+	29.4852i	−0.101025	+	0.961190i	−0.921203	+	0.389082i	$0.872792\pi$
$942$	−0.595089	+	0.126490i	−0.0193890	+	0.00412127i
$943$	−46.7580	−	9.93873i	−1.52265	−	0.323650i
$944$	−8.59940	+	6.24783i	−0.279887	+	0.203349i
$945$		0			0
$946$	−0.601908	−	0.00528791i	−0.0195697	−	0.000171925i
$947$	7.89306	−	13.6712i	0.256490	−	0.444254i	−0.708809	−	0.705400i	$-0.750767\pi$
$947$	7.89306	−	13.6712i	0.256490	−	0.444254i	0.965299	+	0.261146i	$0.0841006\pi$
$948$	0.956942	+	0.426058i	0.0310800	+	0.0138377i
$949$	−51.0172	+	56.6603i	−1.65609	+	1.83927i
$950$	−1.12765	−	1.25239i	−0.0365859	−	0.0406328i
$951$	3.96919	+	2.88378i	0.128710	+	0.0935131i
$952$		0			0
$953$	−10.8502	+	33.3934i	−0.351472	+	1.08172i	0.606555	+	0.795041i	$0.292551\pi$
$953$	−10.8502	+	33.3934i	−0.351472	+	1.08172i	−0.958027	+	0.286678i	$0.907449\pi$
$954$	4.29901	+	0.913784i	0.139186	+	0.0295848i
$955$	−26.5722	−	11.8307i	−0.859855	−	0.382832i
$956$	16.6629	+	28.8609i	0.538916	+	0.933429i
$957$	−4.34410	+	1.88857i	−0.140425	+	0.0610487i
$958$	0.731463			0.0236325
$959$		0			0
$960$	−1.14874	−	3.53546i	−0.0370754	−	0.114106i
$961$	18.8159	+	20.8972i	0.606966	+	0.674104i
$962$	0.483774	−	4.60281i	0.0155975	−	0.148400i
$963$	0.360139	−	3.42649i	0.0116053	−	0.110417i
$964$	31.4959	+	34.9797i	1.01441	+	1.12662i
$965$	−17.3090	−	53.2716i	−0.557196	−	1.71487i
$966$		0			0
$967$	−49.2820			−1.58480			−0.792401	−	0.610001i	$-0.791169\pi$
$967$	−49.2820			−1.58480			−0.792401	+	0.610001i	$0.791169\pi$
$968$	0.855247	+	9.78868i	0.0274887	+	0.314620i
$969$	0.955798	+	1.65549i	0.0307046	+	0.0531820i
$970$	6.22853	+	2.77312i	0.199986	+	0.0890395i
$971$	−36.5264	−	7.76393i	−1.17219	−	0.249156i	−0.419638	−	0.907691i	$-0.637843\pi$
$971$	−36.5264	−	7.76393i	−1.17219	−	0.249156i	−0.752550	+	0.658535i	$0.771176\pi$
$972$	3.48730	−	10.7328i	0.111855	−	0.344255i
$973$		0			0
$974$	−1.80647	−	1.31248i	−0.0578831	−	0.0420545i
$975$	−0.924318	−	1.02656i	−0.0296019	−	0.0328762i
$976$	−2.11512	+	2.34907i	−0.0677032	+	0.0751920i
$977$	36.5861	+	16.2892i	1.17049	+	0.521137i	0.897558	−	0.440896i	$-0.145339\pi$
$977$	36.5861	+	16.2892i	1.17049	+	0.521137i	0.272935	+	0.962033i	$0.412006\pi$
$978$	0.200735	−	0.347684i	0.00641881	−	0.0111177i
$979$	−4.62723	−	3.42439i	−0.147887	−	0.109444i
$980$		0			0
$981$	22.2159	−	16.1408i	0.709299	−	0.515336i
$982$	−0.935080	−	0.198757i	−0.0298396	−	0.00634260i
$983$	50.9042	−	10.8200i	1.62359	−	0.345105i	0.695810	−	0.718226i	$-0.255046\pi$
$983$	50.9042	−	10.8200i	1.62359	−	0.345105i	0.927783	+	0.373121i	$0.121712\pi$
$984$	−0.138089	+	1.31382i	−0.00440210	+	0.0418832i
$985$	−54.9475	+	24.4642i	−1.75077	+	0.779494i
$986$	−0.654946	+	2.01572i	−0.0208577	+	0.0641935i
$987$		0			0
$988$	−49.1304	+	35.6953i	−1.56305	+	1.13562i
$989$	2.84131	−	4.92129i	0.0903484	−	0.156488i
$990$	−2.72132	−	4.81058i	−0.0864893	−	0.152890i
$991$	−22.7414	−	39.3892i	−0.722404	−	1.25124i	−0.960034	−	0.279885i	$-0.909704\pi$
$991$	−22.7414	−	39.3892i	−0.722404	−	1.25124i	0.237630	−	0.971356i	$-0.423630\pi$
$992$	−2.10776	−	20.0540i	−0.0669214	−	0.636715i
$993$	−0.728455	−	2.24195i	−0.0231168	−	0.0711463i
$994$		0			0
$995$	37.7953	+	27.4599i	1.19819	+	0.870536i
$996$	0.876924	−	0.390432i	0.0277864	−	0.0123713i
$997$	−27.3484	+	5.81308i	−0.866132	+	0.184102i	−0.619490	−	0.785005i	$-0.712661\pi$
$997$	−27.3484	+	5.81308i	−0.866132	+	0.184102i	−0.246642	+	0.969107i	$0.579327\pi$
$998$	−3.08713	+	3.42860i	−0.0977214	+	0.108531i
$999$	0.543190	+	5.16811i	0.0171858	+	0.163512i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	539.2.q.g.520.3		32
7.2	even	3		77.2.f.b.36.3	yes	16
7.3	odd	6		539.2.q.f.410.2		32
7.4	even	3	inner	539.2.q.g.410.2		32
7.5	odd	6		539.2.f.e.344.3		16
7.6	odd	2		539.2.q.f.520.3		32
11.4	even	5	inner	539.2.q.g.422.2		32
21.2	odd	6		693.2.m.i.190.2		16
77.2	odd	30		847.2.a.o.1.5		8
77.4	even	15	inner	539.2.q.g.312.3		32
77.9	even	15		847.2.a.p.1.4		8
77.16	even	15		847.2.f.w.372.2		16
77.26	odd	30		539.2.f.e.246.3		16
77.30	odd	30		847.2.f.v.148.3		16
77.37	even	15		77.2.f.b.15.3	✓	16
77.48	odd	10		539.2.q.f.422.2		32
77.51	odd	30		847.2.f.x.323.2		16
77.58	even	15		847.2.f.w.148.2		16
77.59	odd	30		539.2.q.f.312.3		32
77.65	odd	6		847.2.f.x.729.2		16
77.68	even	30		5929.2.a.bs.1.5		8
77.72	odd	30		847.2.f.v.372.3		16
77.75	odd	30		5929.2.a.bt.1.4		8
231.2	even	30		7623.2.a.cw.1.4		8
231.86	odd	30		7623.2.a.ct.1.5		8
231.191	odd	30		693.2.m.i.631.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.b.15.3	✓	16	77.37	even	15
77.2.f.b.36.3	yes	16	7.2	even	3
539.2.f.e.246.3		16	77.26	odd	30
539.2.f.e.344.3		16	7.5	odd	6
539.2.q.f.312.3		32	77.59	odd	30
539.2.q.f.410.2		32	7.3	odd	6
539.2.q.f.422.2		32	77.48	odd	10
539.2.q.f.520.3		32	7.6	odd	2
539.2.q.g.312.3		32	77.4	even	15	inner
539.2.q.g.410.2		32	7.4	even	3	inner
539.2.q.g.422.2		32	11.4	even	5	inner
539.2.q.g.520.3		32	1.1	even	1	trivial
693.2.m.i.190.2		16	21.2	odd	6
693.2.m.i.631.2		16	231.191	odd	30
847.2.a.o.1.5		8	77.2	odd	30
847.2.a.p.1.4		8	77.9	even	15
847.2.f.v.148.3		16	77.30	odd	30
847.2.f.v.372.3		16	77.72	odd	30
847.2.f.w.148.2		16	77.58	even	15
847.2.f.w.372.2		16	77.16	even	15
847.2.f.x.323.2		16	77.51	odd	30
847.2.f.x.729.2		16	77.65	odd	6
5929.2.a.bs.1.5		8	77.68	even	30
5929.2.a.bt.1.4		8	77.75	odd	30
7623.2.a.ct.1.5		8	231.86	odd	30
7623.2.a.cw.1.4		8	231.2	even	30

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:	\( N \)	\(=\)	\( 539 = 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	539.q (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.0236455 - 0.224972i) q^{2} +(-0.146626 + 0.162845i) q^{3} +(1.90624 - 0.405184i) q^{4} +(-2.27977 + 1.01502i) q^{5} +(0.0401026 + 0.0291363i) q^{6} +(-0.276036 - 0.849550i) q^{8} +(0.308566 + 2.93581i) q^{9} +O(q^{10})\)	\(q+(-0.0236455 - 0.224972i) q^{2} +(-0.146626 + 0.162845i) q^{3} +(1.90624 - 0.405184i) q^{4} +(-2.27977 + 1.01502i) q^{5} +(0.0401026 + 0.0291363i) q^{6} +(-0.276036 - 0.849550i) q^{8} +(0.308566 + 2.93581i) q^{9} +(0.282258 + 0.488885i) q^{10} +(-0.375645 + 3.29528i) q^{11} +(-0.213523 + 0.369833i) q^{12} +(-4.15429 + 3.01827i) q^{13} +(0.168984 - 0.520079i) q^{15} +(3.37609 - 1.50313i) q^{16} +(0.150262 - 1.42965i) q^{17} +(0.653179 - 0.138838i) q^{18} +(5.93587 + 1.26171i) q^{19} +(-3.93453 + 2.85860i) q^{20} +(0.750229 + 0.00659095i) q^{22} +(-3.54146 + 6.13399i) q^{23} +(0.178819 + 0.0796154i) q^{24} +(0.821451 - 0.912313i) q^{25} +(0.777257 + 0.863231i) q^{26} +(-1.05516 - 0.766622i) q^{27} +(2.01408 - 6.19869i) q^{29} +(-0.120999 - 0.0257191i) q^{30} +(7.02421 + 3.12738i) q^{31} +(-1.31126 - 2.27117i) q^{32} +(-0.481541 - 0.544347i) q^{33} -0.325184 q^{34} +(1.77775 + 5.47134i) q^{36} +(-2.66603 - 2.96093i) q^{37} +(0.143492 - 1.36524i) q^{38} +(0.117618 - 1.11906i) q^{39} +(1.49161 + 1.65660i) q^{40} +(2.08556 + 6.41868i) q^{41} -0.802299 q^{43} +(0.619127 + 6.43381i) q^{44} +(-3.68337 - 6.37979i) q^{45} +(1.46372 + 0.651689i) q^{46} +(-6.60467 - 1.40387i) q^{47} +(-0.250246 + 0.770178i) q^{48} +(-0.224669 - 0.163231i) q^{50} +(0.210779 + 0.234094i) q^{51} +(-6.69613 + 7.43680i) q^{52} +(6.01266 + 2.67701i) q^{53} +(-0.147519 + 0.255510i) q^{54} +(-2.48840 - 7.89379i) q^{55} +(-1.07582 + 0.781627i) q^{57} +(-1.44216 - 0.306540i) q^{58} +(-2.81340 + 0.598006i) q^{59} +(0.111396 - 1.05986i) q^{60} +(-0.781393 + 0.347899i) q^{61} +(0.537482 - 1.65420i) q^{62} +(5.49964 - 3.99573i) q^{64} +(6.40724 - 11.0977i) q^{65} +(-0.111077 + 0.121205i) q^{66} +(0.823340 + 1.42607i) q^{67} +(-0.292835 - 2.78614i) q^{68} +(-0.479618 - 1.47611i) q^{69} +(-3.65738 - 2.65724i) q^{71} +(2.40894 - 1.07253i) q^{72} +(14.5235 - 3.08706i) q^{73} +(-0.603087 + 0.669796i) q^{74} +(0.0281194 + 0.267538i) q^{75} +11.8264 q^{76} -0.254539 q^{78} +(-0.256398 - 2.43947i) q^{79} +(-6.17101 + 6.85360i) q^{80} +(-8.38287 + 1.78183i) q^{81} +(1.39471 - 0.620965i) q^{82} +(-1.81851 - 1.32122i) q^{83} +(1.10856 + 3.41180i) q^{85} +(0.0189708 + 0.180495i) q^{86} +(0.714109 + 1.23687i) q^{87} +(2.90320 - 0.590486i) q^{88} +(-0.867830 + 1.50313i) q^{89} +(-1.34818 + 0.979509i) q^{90} +(-4.26549 + 13.1278i) q^{92} +(-1.53921 + 0.685301i) q^{93} +(-0.159660 + 1.51906i) q^{94} +(-14.8131 + 3.14862i) q^{95} +(0.562114 + 0.119481i) q^{96} +(9.77095 - 7.09901i) q^{97} +(-9.79024 - 0.0860098i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 3 q^{2} + 2 q^{3} + 11 q^{4} + 5 q^{5} + 6 q^{6} - 10 q^{8} + 12 q^{9}+O(q^{10}) \) 32 * q + 3 * q^2 + 2 * q^3 + 11 * q^4 + 5 * q^5 + 6 * q^6 - 10 * q^8 + 12 * q^9	\( 32 q + 3 q^{2} + 2 q^{3} + 11 q^{4} + 5 q^{5} + 6 q^{6} - 10 q^{8} + 12 q^{9} - 12 q^{10} + 3 q^{11} - 18 q^{12} - 14 q^{13} - 36 q^{15} - 17 q^{16} + 5 q^{17} - 11 q^{18} - 19 q^{19} + 2 q^{20} - 66 q^{22} - 32 q^{23} + 35 q^{24} - 7 q^{25} + 27 q^{26} + 20 q^{27} + 6 q^{29} + 2 q^{30} + 7 q^{31} - 32 q^{32} + 26 q^{33} - 48 q^{34} + 104 q^{36} - 4 q^{37} + 5 q^{38} - 11 q^{39} + 10 q^{40} - 20 q^{41} - 16 q^{43} + 38 q^{44} - 70 q^{45} + 42 q^{46} + 23 q^{47} - 72 q^{48} + 104 q^{50} + 29 q^{51} - 33 q^{52} - 4 q^{53} - 60 q^{54} - 24 q^{55} - 22 q^{57} - 20 q^{58} - 17 q^{59} + 30 q^{60} + 7 q^{61} + 158 q^{62} + 14 q^{64} + 8 q^{65} - 8 q^{66} + 38 q^{67} + 2 q^{68} + 20 q^{69} - 28 q^{71} + 35 q^{73} + 29 q^{74} - 9 q^{75} + 104 q^{76} - 116 q^{78} - 15 q^{79} + 87 q^{80} + 14 q^{81} - 19 q^{82} + 10 q^{83} + 12 q^{85} + 52 q^{86} + 72 q^{87} - 55 q^{88} - 74 q^{89} - 28 q^{90} - 110 q^{92} - 32 q^{93} + 24 q^{94} - 32 q^{95} + 42 q^{96} + 40 q^{97} + 32 q^{99}+O(q^{100}) \) 32 * q + 3 * q^2 + 2 * q^3 + 11 * q^4 + 5 * q^5 + 6 * q^6 - 10 * q^8 + 12 * q^9 - 12 * q^10 + 3 * q^11 - 18 * q^12 - 14 * q^13 - 36 * q^15 - 17 * q^16 + 5 * q^17 - 11 * q^18 - 19 * q^19 + 2 * q^20 - 66 * q^22 - 32 * q^23 + 35 * q^24 - 7 * q^25 + 27 * q^26 + 20 * q^27 + 6 * q^29 + 2 * q^30 + 7 * q^31 - 32 * q^32 + 26 * q^33 - 48 * q^34 + 104 * q^36 - 4 * q^37 + 5 * q^38 - 11 * q^39 + 10 * q^40 - 20 * q^41 - 16 * q^43 + 38 * q^44 - 70 * q^45 + 42 * q^46 + 23 * q^47 - 72 * q^48 + 104 * q^50 + 29 * q^51 - 33 * q^52 - 4 * q^53 - 60 * q^54 - 24 * q^55 - 22 * q^57 - 20 * q^58 - 17 * q^59 + 30 * q^60 + 7 * q^61 + 158 * q^62 + 14 * q^64 + 8 * q^65 - 8 * q^66 + 38 * q^67 + 2 * q^68 + 20 * q^69 - 28 * q^71 + 35 * q^73 + 29 * q^74 - 9 * q^75 + 104 * q^76 - 116 * q^78 - 15 * q^79 + 87 * q^80 + 14 * q^81 - 19 * q^82 + 10 * q^83 + 12 * q^85 + 52 * q^86 + 72 * q^87 - 55 * q^88 - 74 * q^89 - 28 * q^90 - 110 * q^92 - 32 * q^93 + 24 * q^94 - 32 * q^95 + 42 * q^96 + 40 * q^97 + 32 * q^99

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