LMFDB - Embedded newform 539.2.q.f.214.4

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			214.4
Character	$\chi$	$=$	539.214
Dual form			539.2.q.f.471.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.70758 - 1.89646i) q^{2} +(0.375100 - 0.167005i) q^{3} +(-0.471675 - 4.48769i) q^{4} +(3.35405 - 0.712924i) q^{5} +(0.323795 - 0.996539i) q^{6} +(-5.18703 - 3.76860i) q^{8} +(-1.89458 + 2.10415i) q^{9} +O(q^{10})$	\(q+(1.70758 - 1.89646i) q^{2} +(0.375100 - 0.167005i) q^{3} +(-0.471675 - 4.48769i) q^{4} +(3.35405 - 0.712924i) q^{5} +(0.323795 - 0.996539i) q^{6} +(-5.18703 - 3.76860i) q^{8} +(-1.89458 + 2.10415i) q^{9} +(4.37528 - 7.57820i) q^{10} +(-2.85728 - 1.68403i) q^{11} +(-0.926394 - 1.60456i) q^{12} +(0.672122 + 2.06858i) q^{13} +(1.13904 - 0.827562i) q^{15} +(-7.17669 + 1.52545i) q^{16} +(3.02256 + 3.35690i) q^{17} +(0.755280 + 7.18601i) q^{18} +(-0.253357 + 2.41053i) q^{19} +(-4.78140 - 14.7156i) q^{20} +(-8.07274 + 2.54311i) q^{22} +(-0.324201 - 0.561533i) q^{23} +(-2.57503 - 0.547340i) q^{24} +(6.17363 - 2.74868i) q^{25} +(5.07069 + 2.25761i) q^{26} +(-0.739900 + 2.27718i) q^{27} +(1.01366 - 0.736466i) q^{29} +(0.375567 - 3.57328i) q^{30} +(-7.86378 - 1.67150i) q^{31} +(-2.95031 + 5.11008i) q^{32} +(-1.35301 - 0.154498i) q^{33} +11.5275 q^{34} +(10.3364 + 7.50983i) q^{36} +(4.57987 + 2.03909i) q^{37} +(4.13886 + 4.59667i) q^{38} +(0.597577 + 0.663676i) q^{39} +(-20.0843 - 8.94209i) q^{40} +(-2.12100 - 1.54100i) q^{41} -1.46138 q^{43} +(-6.20969 + 13.6169i) q^{44} +(-4.85442 + 8.40810i) q^{45} +(-1.61853 - 0.344029i) q^{46} +(-0.526864 + 5.01278i) q^{47} +(-2.43722 + 1.77074i) q^{48} +(5.32922 - 16.4017i) q^{50} +(1.69438 + 0.754388i) q^{51} +(8.96612 - 3.99197i) q^{52} +(-13.1053 - 2.78561i) q^{53} +(3.05514 + 5.29166i) q^{54} +(-10.7840 - 3.61128i) q^{55} +(0.307538 + 0.946503i) q^{57} +(0.334226 - 3.17994i) q^{58} +(0.801710 + 7.62777i) q^{59} +(-4.25110 - 4.72132i) q^{60} +(14.0216 - 2.98038i) q^{61} +(-16.5980 + 12.0591i) q^{62} +(0.118654 + 0.365178i) q^{64} +(3.72907 + 6.45893i) q^{65} +(-2.60337 + 2.30211i) q^{66} +(-3.11348 + 5.39271i) q^{67} +(13.6390 - 15.1477i) q^{68} +(-0.215387 - 0.156488i) q^{69} +(1.30713 - 4.02294i) q^{71} +(17.7570 - 3.77436i) q^{72} +(-0.619349 - 5.89271i) q^{73} +(11.6876 - 5.20364i) q^{74} +(1.85669 - 2.06206i) q^{75} +10.9372 q^{76} +2.27905 q^{78} +(6.53284 - 7.25546i) q^{79} +(-22.9834 + 10.2329i) q^{80} +(-0.785124 - 7.46996i) q^{81} +(-6.54424 + 1.39102i) q^{82} +(2.58881 - 7.96754i) q^{83} +(12.5310 + 9.10432i) q^{85} +(-2.49543 + 2.77145i) q^{86} +(0.257230 - 0.445535i) q^{87} +(8.47438 + 19.5031i) q^{88} +(2.38125 + 4.12444i) q^{89} +(7.65633 + 23.5637i) q^{90} +(-2.36707 + 1.71978i) q^{92} +(-3.22886 + 0.686314i) q^{93} +(8.60688 + 9.55891i) q^{94} +(0.868756 + 8.26566i) q^{95} +(-0.253250 + 2.40951i) q^{96} +(2.69021 + 8.27962i) q^{97} +(8.95679 - 2.82161i) 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 $\left(\mathbb{Z}/539\mathbb{Z}\right)^\times$.

$n$	$199$	$442$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	1.70758	−	1.89646i	1.20744	−	1.34100i	0.283264	−	0.959042i	$-0.408583\pi$
$2$	1.70758	−	1.89646i	1.20744	−	1.34100i	0.924179	−	0.381960i	$-0.124751\pi$
$3$	0.375100	−	0.167005i	0.216564	−	0.0964206i	−0.295587	−	0.955316i	$-0.595515\pi$
$3$	0.375100	−	0.167005i	0.216564	−	0.0964206i	0.512151	+	0.858895i	$0.328849\pi$
$4$	−0.471675	−	4.48769i	−0.235838	−	2.24385i
$5$	3.35405	−	0.712924i	1.49997	−	0.318829i	0.616517	−	0.787341i	$-0.288543\pi$
$5$	3.35405	−	0.712924i	1.49997	−	0.318829i	0.883457	+	0.468512i	$0.155210\pi$
$6$	0.323795	−	0.996539i	0.132189	−	0.406835i
$7$		0			0
$7$		0			0
$8$	−5.18703	−	3.76860i	−1.83389	−	1.33240i
$9$	−1.89458	+	2.10415i	−0.631527	+	0.701382i
$10$	4.37528	−	7.57820i	1.38358	−	2.39644i
$11$	−2.85728	−	1.68403i	−0.861502	−	0.507753i
$11$	−2.85728	−	1.68403i	−0.861502	−	0.507753i
$12$	−0.926394	−	1.60456i	−0.267427	−	0.463197i
$13$	0.672122	+	2.06858i	0.186413	+	0.573720i	0.999970	−	0.00776501i	$-0.00247170\pi$
$13$	0.672122	+	2.06858i	0.186413	+	0.573720i	−0.813557	+	0.581486i	$0.802472\pi$
$14$		0			0
$15$	1.13904	−	0.827562i	0.294099	−	0.213675i
$16$	−7.17669	+	1.52545i	−1.79417	+	0.381363i
$17$	3.02256	+	3.35690i	0.733079	+	0.814167i	0.988269	−	0.152724i	$-0.0488046\pi$
$17$	3.02256	+	3.35690i	0.733079	+	0.814167i	−0.255190	+	0.966891i	$0.582138\pi$
$18$	0.755280	+	7.18601i	0.178021	+	1.69376i
$19$	−0.253357	+	2.41053i	−0.0581241	+	0.553014i	0.926248	+	0.376914i	$0.123015\pi$
$19$	−0.253357	+	2.41053i	−0.0581241	+	0.553014i	−0.984372	+	0.176100i	$0.943652\pi$
$20$	−4.78140	−	14.7156i	−1.06915	−	3.29052i
$21$		0			0
$22$	−8.07274	+	2.54311i	−1.72111	+	0.542193i
$23$	−0.324201	−	0.561533i	−0.0676006	−	0.117088i	0.830244	−	0.557400i	$-0.188201\pi$
$23$	−0.324201	−	0.561533i	−0.0676006	−	0.117088i	−0.897845	+	0.440312i	$0.854868\pi$
$24$	−2.57503	−	0.547340i	−0.525626	−	0.111725i
$25$	6.17363	−	2.74868i	1.23473	−	0.549736i
$26$	5.07069	+	2.25761i	0.994443	+	0.442755i
$27$	−0.739900	+	2.27718i	−0.142394	+	0.438243i
$28$		0			0
$29$	1.01366	−	0.736466i	0.188232	−	0.136758i	−0.489678	−	0.871903i	$-0.662886\pi$
$29$	1.01366	−	0.736466i	0.188232	−	0.136758i	0.677910	+	0.735145i	$0.262886\pi$
$30$	0.375567	−	3.57328i	0.0685688	−	0.652388i
$31$	−7.86378	−	1.67150i	−1.41238	−	0.300210i	−0.562328	−	0.826914i	$-0.690094\pi$
$31$	−7.86378	−	1.67150i	−1.41238	−	0.300210i	−0.850049	+	0.526704i	$0.823428\pi$
$32$	−2.95031	+	5.11008i	−0.521545	+	0.903343i
$33$	−1.35301	−	0.154498i	−0.235528	−	0.0268946i
$34$	11.5275			1.97695
$35$		0			0
$36$	10.3364	+	7.50983i	1.72273	+	1.25164i
$37$	4.57987	+	2.03909i	0.752926	+	0.335224i	0.747058	−	0.664758i	$-0.231466\pi$
$37$	4.57987	+	2.03909i	0.752926	+	0.335224i	0.00586779	+	0.999983i	$0.498132\pi$
$38$	4.13886	+	4.59667i	0.671411	+	0.745678i
$39$	0.597577	+	0.663676i	0.0956889	+	0.106273i
$40$	−20.0843	−	8.94209i	−3.17560	−	1.41387i
$41$	−2.12100	−	1.54100i	−0.331245	−	0.240664i	0.409714	−	0.912214i	$-0.365629\pi$
$41$	−2.12100	−	1.54100i	−0.331245	−	0.240664i	−0.740959	+	0.671551i	$0.765629\pi$
$42$		0			0
$43$	−1.46138			−0.222858			−0.111429	−	0.993772i	$-0.535543\pi$
$43$	−1.46138			−0.222858			−0.111429	+	0.993772i	$0.535543\pi$
$44$	−6.20969	+	13.6169i	−0.936145	+	2.05283i
$45$	−4.85442	+	8.40810i	−0.723654	+	1.25341i
$46$	−1.61853	−	0.344029i	−0.238639	−	0.0507242i
$47$	−0.526864	+	5.01278i	−0.0768510	+	0.731189i	0.886461	+	0.462804i	$0.153157\pi$
$47$	−0.526864	+	5.01278i	−0.0768510	+	0.731189i	−0.963312	+	0.268385i	$0.913510\pi$
$48$	−2.43722	+	1.77074i	−0.351782	+	0.255585i
$49$		0			0
$50$	5.32922	−	16.4017i	0.753666	−	2.31954i
$51$	1.69438	+	0.754388i	0.237261	+	0.105635i
$52$	8.96612	−	3.99197i	1.24338	−	0.553587i
$53$	−13.1053	−	2.78561i	−1.80014	−	0.382633i	−0.818676	−	0.574256i	$-0.805292\pi$
$53$	−13.1053	−	2.78561i	−1.80014	−	0.382633i	−0.981469	+	0.191623i	$0.938625\pi$
$54$	3.05514	+	5.29166i	0.415752	+	0.720104i
$55$	−10.7840	−	3.61128i	−1.45412	−	0.486945i
$56$		0			0
$57$	0.307538	+	0.946503i	0.0407343	+	0.125367i
$58$	0.334226	−	3.17994i	0.0438860	−	0.417547i
$59$	0.801710	+	7.62777i	0.104374	+	0.993050i	0.913892	+	0.405956i	$0.133061\pi$
$59$	0.801710	+	7.62777i	0.104374	+	0.993050i	−0.809519	+	0.587094i	$0.800272\pi$
$60$	−4.25110	−	4.72132i	−0.548814	−	0.609520i
$61$	14.0216	−	2.98038i	1.79528	−	0.381598i	0.815038	−	0.579407i	$-0.196716\pi$
$61$	14.0216	−	2.98038i	1.79528	−	0.381598i	0.980241	+	0.197809i	$0.0633826\pi$
$62$	−16.5980	+	12.0591i	−2.10795	+	1.53151i
$63$		0			0
$64$	0.118654	+	0.365178i	0.0148317	+	0.0456473i
$65$	3.72907	+	6.45893i	0.462534	+	0.801132i
$66$	−2.60337	+	2.30211i	−0.320453	+	0.283370i
$67$	−3.11348	+	5.39271i	−0.380372	+	0.658824i	−0.991115	−	0.133005i	$-0.957537\pi$
$67$	−3.11348	+	5.39271i	−0.380372	+	0.658824i	0.610743	+	0.791829i	$0.290871\pi$
$68$	13.6390	−	15.1477i	1.65398	−	1.83693i
$69$	−0.215387	−	0.156488i	−0.0259295	−	0.0188389i
$70$		0			0
$71$	1.30713	−	4.02294i	0.155128	−	0.477435i	−0.843046	−	0.537842i	$-0.819240\pi$
$71$	1.30713	−	4.02294i	0.155128	−	0.477435i	0.998174	+	0.0604069i	$0.0192398\pi$
$72$	17.7570	−	3.77436i	2.09268	−	0.444812i
$73$	−0.619349	−	5.89271i	−0.0724893	−	0.689690i	−0.969066	−	0.246801i	$-0.920620\pi$
$73$	−0.619349	−	5.89271i	−0.0724893	−	0.689690i	0.896577	−	0.442888i	$-0.146046\pi$
$74$	11.6876	−	5.20364i	1.35865	−	0.604911i
$75$	1.85669	−	2.06206i	0.214392	−	0.238106i
$76$	10.9372			1.25459
$77$		0			0
$78$	2.27905			0.258051
$79$	6.53284	−	7.25546i	0.735002	−	0.816303i	−0.253527	−	0.967328i	$-0.581591\pi$
$79$	6.53284	−	7.25546i	0.735002	−	0.816303i	0.988530	+	0.151025i	$0.0482575\pi$
$80$	−22.9834	+	10.2329i	−2.56962	+	1.14407i
$81$	−0.785124	−	7.46996i	−0.0872360	−	0.829995i
$82$	−6.54424	+	1.39102i	−0.722690	+	0.153613i
$83$	2.58881	−	7.96754i	0.284159	−	0.874551i	−0.702491	−	0.711693i	$-0.747929\pi$
$83$	2.58881	−	7.96754i	0.284159	−	0.874551i	0.986650	−	0.162858i	$-0.0520712\pi$
$84$		0			0
$85$	12.5310	+	9.10432i	1.35918	+	0.987503i
$86$	−2.49543	+	2.77145i	−0.269089	+	0.298853i
$87$	0.257230	−	0.445535i	0.0275779	−	0.0477664i
$88$	8.47438	+	19.5031i	0.903372	+	2.07903i
$89$	2.38125	+	4.12444i	0.252412	+	0.437190i	0.964189	−	0.265215i	$-0.0854430\pi$
$89$	2.38125	+	4.12444i	0.252412	+	0.437190i	−0.711778	+	0.702405i	$0.752110\pi$
$90$	7.65633	+	23.5637i	0.807048	+	2.48384i
$91$		0			0
$92$	−2.36707	+	1.71978i	−0.246784	+	0.179299i
$93$	−3.22886	+	0.686314i	−0.334817	+	0.0711675i
$94$	8.60688	+	9.55891i	0.887732	+	0.985926i
$95$	0.868756	+	8.26566i	0.0891325	+	0.848039i
$96$	−0.253250	+	2.40951i	−0.0258472	+	0.245919i
$97$	2.69021	+	8.27962i	0.273150	+	0.840668i	0.989703	+	0.143136i	$0.0457185\pi$
$97$	2.69021	+	8.27962i	0.273150	+	0.840668i	−0.716554	+	0.697532i	$0.754281\pi$
$98$		0			0
$99$	8.95679	−	2.82161i	0.900192	−	0.283582i
$100$	−15.2472	−	26.4089i	−1.52472	−	2.64089i
$101$	−5.64843	−	1.20061i	−0.562040	−	0.119465i	−0.0818736	−	0.996643i	$-0.526090\pi$
$101$	−5.64843	−	1.20061i	−0.562040	−	0.119465i	−0.480166	+	0.877177i	$0.659424\pi$
$102$	4.32397	−	1.92516i	0.428137	−	0.190619i
$103$	4.23975	+	1.88766i	0.417755	+	0.185996i	0.604839	−	0.796347i	$-0.293237\pi$
$103$	4.23975	+	1.88766i	0.417755	+	0.185996i	−0.187085	+	0.982344i	$0.559904\pi$
$104$	4.30933	−	13.2627i	0.422564	−	1.30052i
$105$		0			0
$106$	−27.6611	+	20.0970i	−2.68668	+	1.95199i
$107$	0.420416	−	3.99999i	0.0406431	−	0.386694i	−0.955225	−	0.295881i	$-0.904387\pi$
$107$	0.420416	−	3.99999i	0.0406431	−	0.386694i	0.995868	−	0.0908127i	$-0.0289465\pi$
$108$	10.5683	+	2.24635i	1.01693	+	0.216155i
$109$	3.07381	−	5.32400i	0.294418	−	0.509946i	−0.680432	−	0.732812i	$-0.738208\pi$
$109$	3.07381	−	5.32400i	0.294418	−	0.509946i	0.974849	+	0.222865i	$0.0715410\pi$
$110$	−25.2633	+	14.2850i	−2.40876	+	1.36202i
$111$	2.05845			0.195379
$112$		0			0
$113$	2.00504	+	1.45675i	0.188618	+	0.137039i	0.678087	−	0.734982i	$-0.262809\pi$
$113$	2.00504	+	1.45675i	0.188618	+	0.137039i	−0.489469	+	0.872021i	$0.662809\pi$
$114$	2.32015	+	1.03300i	0.217302	+	0.0967492i
$115$	−1.48772	−	1.65228i	−0.138730	−	0.154076i
$116$	−3.78315	−	4.20161i	−0.351257	−	0.390110i
$117$	−5.62598	−	2.50485i	−0.520122	−	0.231573i
$118$	15.8348	+	11.5046i	1.45771	+	1.05909i
$119$		0			0
$120$	−9.02699			−0.824048
$121$	5.32810	+	9.62348i	0.484373	+	0.874862i
$122$	18.2908	−	31.6806i	1.65597	−	2.86823i
$123$	−1.05294	−	0.223810i	−0.0949408	−	0.0201803i
$124$	−3.79202	+	36.0786i	−0.340533	+	3.23996i
$125$	4.87654	−	3.54301i	0.436171	−	0.316897i
$126$		0			0
$127$	−2.14890	+	6.61362i	−0.190684	+	0.586864i	−1.00000		0.000509338i	$-0.999838\pi$
$127$	−2.14890	+	6.61362i	−0.190684	+	0.586864i	0.809316	+	0.587373i	$0.199838\pi$
$128$	−9.88579	−	4.40144i	−0.873789	−	0.389036i
$129$	−0.548164	+	0.244058i	−0.0482631	+	0.0214881i
$130$	18.6168	+	3.95713i	1.63280	+	0.347063i
$131$	−10.4694	−	18.1335i	−0.914715	−	1.58433i	−0.807319	−	0.590116i	$-0.799082\pi$
$131$	−10.4694	−	18.1335i	−0.914715	−	1.58433i	−0.107396	−	0.994216i	$-0.534251\pi$
$132$	−0.0551580	+	6.14475i	−0.00480089	+	0.534832i
$133$		0			0
$134$	4.91054	+	15.1131i	0.424206	+	1.30557i
$135$	−0.858202	+	8.16525i	−0.0738623	+	0.702753i
$136$	−3.02733	−	28.8032i	−0.259592	−	2.46985i
$137$	6.11347	+	6.78970i	0.522309	+	0.580083i	0.945362	−	0.326022i	$-0.105708\pi$
$137$	6.11347	+	6.78970i	0.522309	+	0.580083i	−0.423053	+	0.906105i	$0.639042\pi$
$138$	−0.664564	+	0.141258i	−0.0565715	+	0.0120246i
$139$	8.69844	−	6.31979i	0.737792	−	0.536037i	−0.154227	−	0.988035i	$-0.549289\pi$
$139$	8.69844	−	6.31979i	0.737792	−	0.536037i	0.892019	+	0.451998i	$0.149289\pi$
$140$		0			0
$141$	0.639534	+	1.96828i	0.0538585	+	0.165759i
$142$	−5.39731	−	9.34842i	−0.452933	−	0.784502i
$143$	1.56310	−	7.04238i	0.130713	−	0.588914i
$144$	10.3871	−	17.9909i	0.865588	−	1.49924i
$145$	2.87481	−	3.19280i	0.238740	−	0.265148i
$146$	−12.2329	−	8.88772i	−1.01240	−	0.735553i
$147$		0			0
$148$	6.99059	−	21.5148i	0.574623	−	1.76851i
$149$	−10.5204	+	2.23618i	−0.861864	+	0.183195i	−0.617579	−	0.786509i	$-0.711886\pi$
$149$	−10.5204	+	2.23618i	−0.861864	+	0.183195i	−0.244285	+	0.969704i	$0.578553\pi$
$150$	−0.740173	−	7.04227i	−0.0604348	−	0.574999i
$151$	−7.00162	+	3.11732i	−0.569783	+	0.253684i	−0.671345	−	0.741145i	$-0.734283\pi$
$151$	−7.00162	+	3.11732i	−0.569783	+	0.253684i	0.101561	+	0.994829i	$0.467616\pi$
$152$	10.3985	−	11.5487i	0.843430	−	0.936724i
$153$	−12.7899			−1.03400
$154$		0			0
$155$	−27.5671			−2.21425
$156$	2.69651	−	2.99478i	0.215894	−	0.239774i
$157$	−16.7627	+	7.46322i	−1.33781	+	0.595630i	−0.945925	−	0.324386i	$-0.894842\pi$
$157$	−16.7627	+	7.46322i	−1.33781	+	0.595630i	−0.391882	+	0.920016i	$0.628176\pi$
$158$	−2.60434	−	24.7786i	−0.207190	−	1.97128i
$159$	−5.38099	+	1.14377i	−0.426740	+	0.0907065i
$160$	−6.25236	+	19.2428i	−0.494292	+	1.52128i
$161$		0			0
$162$	−15.5072	−	11.2666i	−1.21836	−	0.885189i
$163$	0.252654	−	0.280600i	0.0197894	−	0.0219783i	−0.733169	−	0.680047i	$-0.761960\pi$
$163$	0.252654	−	0.280600i	0.0197894	−	0.0219783i	0.752958	+	0.658068i	$0.228626\pi$
$164$	−5.91510	+	10.2453i	−0.461892	+	0.800020i
$165$	−4.64820	+	0.446400i	−0.361862	+	0.0347522i
$166$	−10.6895	−	18.5148i	−0.829668	−	1.43703i
$167$	0.0352708	+	0.108552i	0.00272934	+	0.00840003i	0.952412	−	0.304814i	$-0.0985943\pi$
$167$	0.0352708	+	0.108552i	0.00272934	+	0.00840003i	−0.949683	+	0.313214i	$0.898594\pi$
$168$		0			0
$169$	6.68995	−	4.86053i	0.514612	−	0.373887i
$170$	38.6638	−	8.21824i	2.96538	−	0.630310i
$171$	−4.59211	−	5.10005i	−0.351167	−	0.390011i
$172$	0.689297	+	6.55822i	0.0525584	+	0.500060i
$173$	−1.39034	+	13.2282i	−0.105705	+	1.00572i	0.805172	+	0.593041i	$0.202073\pi$
$173$	−1.39034	+	13.2282i	−0.105705	+	1.00572i	−0.910877	+	0.412677i	$0.864594\pi$
$174$	−0.405700	−	1.24861i	−0.0307560	−	0.0946572i
$175$		0			0
$176$	23.0747	+	7.72710i	1.73932	+	0.582452i
$177$	1.57460	+	2.72729i	0.118354	+	0.204995i
$178$	11.8880	+	2.52688i	0.891045	+	0.189397i
$179$	10.3605	−	4.61279i	0.774380	−	0.344776i	0.0187922	−	0.999823i	$-0.494018\pi$
$179$	10.3605	−	4.61279i	0.774380	−	0.344776i	0.755588	+	0.655047i	$0.227351\pi$
$180$	40.0227	+	17.8192i	2.98311	+	1.32817i
$181$	−3.63307	+	11.1814i	−0.270044	+	0.831109i	0.720445	+	0.693512i	$0.243938\pi$
$181$	−3.63307	+	11.1814i	−0.270044	+	0.831109i	−0.990488	+	0.137597i	$0.956062\pi$
$182$		0			0
$183$	4.76176	−	3.45962i	0.351999	−	0.255742i
$184$	−0.434551	+	4.13448i	−0.0320355	+	0.304798i
$185$	16.8148	+	3.57410i	1.23625	+	0.262773i
$186$	−4.21197	+	7.29534i	−0.308836	+	0.534920i
$187$	−2.98320	−	14.6817i	−0.218154	−	1.07363i
$188$	22.7443			1.65880
$189$		0			0
$190$	17.1590	+	12.4667i	1.24484	+	0.904432i
$191$	−20.5862	−	9.16556i	−1.48956	−	0.663197i	−0.509246	−	0.860621i	$-0.670076\pi$
$191$	−20.5862	−	9.16556i	−1.48956	−	0.663197i	−0.980318	+	0.197424i	$0.936742\pi$
$192$	0.105494	+	0.117163i	0.00761335	+	0.00845549i
$193$	2.30397	+	2.55882i	0.165843	+	0.184188i	0.820338	−	0.571879i	$-0.193785\pi$
$193$	2.30397	+	2.55882i	0.165843	+	0.184188i	−0.654495	+	0.756067i	$0.727119\pi$
$194$	20.2957	+	9.03625i	1.45715	+	0.648765i
$195$	2.47745	+	1.79997i	0.177414	+	0.128899i
$196$		0			0
$197$	−2.18213			−0.155470			−0.0777352	−	0.996974i	$-0.524769\pi$
$197$	−2.18213			−0.155470			−0.0777352	+	0.996974i	$0.524769\pi$
$198$	9.94339	−	21.8044i	0.706646	−	1.54957i
$199$	1.16717	−	2.02160i	0.0827386	−	0.143307i	−0.821687	−	0.569939i	$-0.806967\pi$
$199$	1.16717	−	2.02160i	0.0827386	−	0.143307i	0.904425	+	0.426632i	$0.140300\pi$
$200$	−42.3815	−	9.00847i	−2.99682	−	0.636995i
$201$	−0.267256	+	2.54277i	−0.0188508	+	0.179353i
$202$	−11.9221	+	8.66190i	−0.838835	+	0.609449i
$203$		0			0
$204$	2.58626	−	7.95969i	0.181075	−	0.557290i
$205$	−8.21256	−	3.65647i	−0.573590	−	0.255379i
$206$	10.8196	−	4.81719i	0.753836	−	0.335630i
$207$	1.79577	+	0.381704i	0.124815	+	0.0265302i
$208$	−7.97913	−	13.8203i	−0.553253	−	0.958263i
$209$	4.78332	−	6.46091i	0.330869	−	0.446910i
$210$		0			0
$211$	−4.22360	−	12.9989i	−0.290765	−	0.894882i	−0.984611	−	0.174759i	$-0.944085\pi$
$211$	−4.22360	−	12.9989i	−0.290765	−	0.894882i	0.693846	−	0.720123i	$-0.255915\pi$
$212$	−6.31952	+	60.1262i	−0.434026	+	4.12949i
$213$	−0.181547	−	1.72730i	−0.0124394	−	0.118353i
$214$	−6.86794	−	7.62762i	−0.469482	−	0.521413i
$215$	−4.90154	+	1.04185i	−0.334282	+	0.0710538i
$216$	12.4197	−	9.02341i	0.845051	−	0.613965i
$217$		0			0
$218$	−4.84798	−	14.9205i	−0.328346	−	1.01055i
$219$	−1.21643	−	2.10692i	−0.0821989	−	0.142373i
$220$	−11.1197	+	50.0988i	−0.749693	+	3.37766i
$221$	−4.91247	+	8.50865i	−0.330449	+	0.572354i
$222$	3.51497	−	3.90377i	0.235909	−	0.262004i
$223$	−4.34333	−	3.15561i	−0.290851	−	0.211315i	0.432786	−	0.901497i	$-0.357531\pi$
$223$	−4.34333	−	3.15561i	−0.290851	−	0.211315i	−0.723636	+	0.690181i	$0.757531\pi$
$224$		0			0
$225$	−5.91283	+	18.1978i	−0.394189	+	1.21319i
$226$	6.18644	−	1.31497i	0.411516	−	0.0874704i
$227$	1.10936	+	10.5548i	0.0736307	+	0.700549i	0.967612	+	0.252444i	$0.0812343\pi$
$227$	1.10936	+	10.5548i	0.0736307	+	0.700549i	−0.893981	+	0.448105i	$0.852099\pi$
$228$	4.10256	−	1.82658i	0.271698	−	0.120968i
$229$	−15.1498	+	16.8255i	−1.00112	+	1.11186i	−0.00740393	+	0.999973i	$0.502357\pi$
$229$	−15.1498	+	16.8255i	−1.00112	+	1.11186i	−0.993721	+	0.111889i	$0.964310\pi$
$230$	−5.67388			−0.374125
$231$		0			0
$232$	−8.03333			−0.527414
$233$	9.91894	−	11.0161i	0.649812	−	0.721689i	−0.324752	−	0.945799i	$-0.605281\pi$
$233$	9.91894	−	11.0161i	0.649812	−	0.721689i	0.974564	+	0.224110i	$0.0719476\pi$
$234$	−14.3572	+	6.39223i	−0.938559	+	0.417873i
$235$	1.80660	+	17.1887i	0.117850	+	1.12127i
$236$	33.8529	−	7.19566i	2.20364	−	0.468397i
$237$	1.23877	−	3.81254i	0.0804668	−	0.247651i
$238$		0			0
$239$	−1.58511	−	1.15165i	−0.102532	−	0.0744938i	0.535338	−	0.844638i	$-0.320184\pi$
$239$	−1.58511	−	1.15165i	−0.102532	−	0.0744938i	−0.637870	+	0.770144i	$0.720184\pi$
$240$	−6.91214	+	7.67671i	−0.446177	+	0.495529i
$241$	0.395126	−	0.684379i	0.0254523	−	0.0440847i	−0.853019	−	0.521880i	$-0.825231\pi$
$241$	0.395126	−	0.684379i	0.0254523	−	0.0440847i	0.878471	+	0.477796i	$0.158564\pi$
$242$	27.3487	+	6.32833i	1.75804	+	0.406801i
$243$	−5.13357	−	8.89161i	−0.329319	−	0.570397i
$244$	−19.9886	−	61.5187i	−1.27964	−	3.93833i
$245$		0			0
$246$	−2.22244	+	1.61469i	−0.141697	+	0.102949i
$247$	−5.15666	+	1.09608i	−0.328111	+	0.0697421i
$248$	34.4905	+	38.3056i	2.19015	+	2.43241i
$249$	−0.359558	−	3.42097i	−0.0227861	−	0.216795i
$250$	1.60790	−	15.2982i	0.101693	−	0.967541i
$251$	6.37051	+	19.6064i	0.402103	+	1.23755i	0.923290	+	0.384103i	$0.125489\pi$
$251$	6.37051	+	19.6064i	0.402103	+	1.23755i	−0.521187	+	0.853442i	$0.674511\pi$
$252$		0			0
$253$	−0.0193031	+	2.15042i	−0.00121358	+	0.135196i
$254$	8.87307	+	15.3686i	0.556746	+	0.964312i
$255$	6.22086	+	1.32228i	0.389565	+	0.0828047i
$256$	−25.9295	+	11.5446i	−1.62060	+	0.721536i
$257$	−4.73181	−	2.10674i	−0.295162	−	0.131415i	0.253813	−	0.967253i	$-0.418315\pi$
$257$	−4.73181	−	2.10674i	−0.295162	−	0.131415i	−0.548975	+	0.835839i	$0.684982\pi$
$258$	−0.473188	+	1.45632i	−0.0294594	+	0.0906667i
$259$		0			0
$260$	27.2268	−	19.7814i	1.68853	−	1.22679i
$261$	−0.370827	+	3.52818i	−0.0229536	+	0.218389i
$262$	−52.2669	−	11.1097i	−3.22906	−	0.686357i
$263$	−11.5960	+	20.0849i	−0.715041	+	1.23849i	0.247903	+	0.968785i	$0.420258\pi$
$263$	−11.5960	+	20.0849i	−0.715041	+	1.23849i	−0.962944	+	0.269702i	$0.913075\pi$
$264$	6.43586	+	5.90033i	0.396100	+	0.363140i
$265$	−45.9415			−2.82217
$266$		0			0
$267$	1.58201	+	1.14940i	0.0968174	+	0.0703420i
$268$	25.6693	+	11.4287i	1.56800	+	0.698121i
$269$	−12.4860	−	13.8671i	−0.761283	−	0.845490i	0.230547	−	0.973061i	$-0.425949\pi$
$269$	−12.4860	−	13.8671i	−0.761283	−	0.845490i	−0.991829	+	0.127571i	$0.959282\pi$
$270$	14.0196	+	15.5704i	0.853208	+	0.947584i
$271$	−27.6153	−	12.2951i	−1.67751	−	0.746877i	−0.999935	−	0.0114257i	$-0.996363\pi$
$271$	−27.6153	−	12.2951i	−1.67751	−	0.746877i	−0.677578	−	0.735451i	$-0.736970\pi$
$272$	−26.8128	−	19.4806i	−1.62576	−	1.18119i
$273$		0			0
$274$	23.3157			1.40855
$275$	−22.2686	−	2.54282i	−1.34285	−	0.153338i
$276$	−0.600676	+	1.04040i	−0.0361565	+	0.0626248i
$277$	−13.1972	−	2.80516i	−0.792945	−	0.168546i	−0.206406	−	0.978466i	$-0.566177\pi$
$277$	−13.1972	−	2.80516i	−0.792945	−	0.168546i	−0.586539	+	0.809921i	$0.699510\pi$
$278$	2.86807	−	27.2878i	0.172015	−	1.63661i
$279$	18.4157	−	13.3798i	1.10252	−	0.801025i
$280$		0			0
$281$	2.50388	−	7.70614i	0.149369	−	0.459710i	−0.848178	−	0.529711i	$-0.822300\pi$
$281$	2.50388	−	7.70614i	0.149369	−	0.459710i	0.997547	+	0.0700014i	$0.0223004\pi$
$282$	4.82483	+	2.14815i	0.287315	+	0.127921i
$283$	−9.12739	+	4.06378i	−0.542567	+	0.241566i	−0.659673	−	0.751553i	$-0.729305\pi$
$283$	−9.12739	+	4.06378i	−0.542567	+	0.241566i	0.117106	+	0.993119i	$0.462638\pi$
$284$	−18.6702	−	3.96848i	−1.10787	−	0.235486i
$285$	1.70628	+	2.95536i	0.101071	+	0.175061i
$286$	−10.6865	−	14.9898i	−0.631905	−	0.886366i
$287$		0			0
$288$	−5.16276	−	15.8893i	−0.304219	−	0.936288i
$289$	−0.355882	+	3.38599i	−0.0209342	+	0.199176i
$290$	−1.14605	−	10.9040i	−0.0672985	−	0.640302i
$291$	2.39184	+	2.65641i	0.140212	+	0.155721i
$292$	−26.1525	+	5.55889i	−1.53046	+	0.325310i
$293$	24.8608	−	18.0624i	1.45238	−	1.05522i	0.467116	−	0.884196i	$-0.345293\pi$
$293$	24.8608	−	18.0624i	1.45238	−	1.05522i	0.985267	−	0.171022i	$-0.0547069\pi$
$294$		0			0
$295$	8.12699	+	25.0123i	0.473172	+	1.45627i
$296$	−16.0714	−	27.8365i	−0.934133	−	1.61797i
$297$	5.94893	−	5.26052i	0.345192	−	0.305247i
$298$	−13.7236	+	23.7700i	−0.794987	+	1.37696i
$299$	0.943673	−	1.04805i	0.0545740	−	0.0606106i
$300$	−10.1296	−	7.35961i	−0.584835	−	0.424907i
$301$		0			0
$302$	−6.04396	+	18.6014i	−0.347791	+	1.07039i
$303$	−2.31924	+	0.492969i	−0.133237	+	0.0283203i
$304$	−1.85889	−	17.6861i	−0.106615	−	1.01437i
$305$	44.9042	−	19.9926i	2.57121	−	1.14478i
$306$	−21.8398	+	24.2556i	−1.24850	+	1.38660i
$307$	20.0677			1.14532			0.572661	−	0.819792i	$-0.305911\pi$
$307$	20.0677			1.14532			0.572661	+	0.819792i	$0.305911\pi$
$308$		0			0
$309$	1.90558			0.108405
$310$	−47.0732	+	52.2800i	−2.67358	+	2.96931i
$311$	21.4375	−	9.54457i	1.21561	−	0.541223i	0.304152	−	0.952624i	$-0.401627\pi$
$311$	21.4375	−	9.54457i	1.21561	−	0.541223i	0.911455	+	0.411401i	$0.134960\pi$
$312$	−0.598520	−	5.69454i	−0.0338845	−	0.322390i
$313$	−14.3523	+	3.05069i	−0.811243	+	0.172435i	−0.594814	−	0.803863i	$-0.702774\pi$
$313$	−14.3523	+	3.05069i	−0.811243	+	0.172435i	−0.216429	+	0.976298i	$0.569441\pi$
$314$	−14.4699	+	44.5338i	−0.816585	+	2.51319i
$315$		0			0
$316$	−35.6416	−	25.8952i	−2.00500	−	1.45672i
$317$	12.0784	−	13.4145i	0.678392	−	0.753431i	−0.301389	−	0.953501i	$-0.597450\pi$
$317$	12.0784	−	13.4145i	0.678392	−	0.753431i	0.979782	+	0.200070i	$0.0641171\pi$
$318$	−7.01938	+	12.1579i	−0.393627	+	0.681783i
$319$	−4.13654	+	0.397261i	−0.231602	+	0.0222424i
$320$	0.658314	+	1.14023i	0.0368009	+	0.0637410i
$321$	−0.510322	−	1.57061i	−0.0284834	−	0.0876628i
$322$		0			0
$323$	−8.85770	+	6.43549i	−0.492855	+	0.358080i
$324$	−33.1525	+	7.04679i	−1.84181	+	0.391488i
$325$	9.83529	+	10.9232i	0.545564	+	0.605910i
$326$	−0.100721	−	0.958296i	−0.00557842	−	0.0530751i
$327$	0.263851	−	2.51038i	0.0145910	−	0.138824i
$328$	5.19431	+	15.9864i	0.286808	+	0.882703i
$329$		0			0
$330$	−7.09060	+	9.57739i	−0.390325	+	0.527218i
$331$	9.91502	+	17.1733i	0.544979	+	0.943931i	0.998608	+	0.0527404i	$0.0167956\pi$
$331$	9.91502	+	17.1733i	0.544979	+	0.943931i	−0.453630	+	0.891190i	$0.649871\pi$
$332$	−36.9769	−	7.85969i	−2.02937	−	0.431356i
$333$	−12.9675	+	5.77350i	−0.710614	+	0.316386i
$334$	0.266093	+	0.118472i	0.0145600	+	0.00648252i
$335$	−6.59816	+	20.3071i	−0.360496	+	1.10949i
$336$		0			0
$337$	15.7826	−	11.4667i	0.859734	−	0.624633i	−0.0680789	−	0.997680i	$-0.521687\pi$
$337$	15.7826	−	11.4667i	0.859734	−	0.624633i	0.927812	+	0.373047i	$0.121687\pi$
$338$	2.20582	−	20.9870i	0.119981	−	1.14154i
$339$	0.995376	+	0.211574i	0.0540614	+	0.0114911i
$340$	34.9468	−	60.5297i	1.89526	−	3.28268i
$341$	19.6542	+	18.0188i	1.06433	+	0.975771i
$342$	−17.5135			−0.947020
$343$		0			0
$344$	7.58023	+	5.50736i	0.408698	+	0.296937i
$345$	−0.833982	−	0.371313i	−0.0449001	−	0.0199908i
$346$	22.7126	+	25.2249i	1.22104	+	1.35610i
$347$	−19.0335	−	21.1388i	−1.02177	−	1.13479i	−0.990808	−	0.135272i	$-0.956809\pi$
$347$	−19.0335	−	21.1388i	−1.02177	−	1.13479i	−0.0309635	−	0.999521i	$-0.509858\pi$
$348$	−2.12075	−	0.944220i	−0.113684	−	0.0506155i
$349$	16.2506	+	11.8067i	0.869873	+	0.632000i	0.930553	−	0.366158i	$-0.119327\pi$
$349$	16.2506	+	11.8067i	0.869873	+	0.632000i	−0.0606798	+	0.998157i	$0.519327\pi$
$350$		0			0
$351$	−5.20782			−0.277973
$352$	17.0354	−	9.63253i	0.907988	−	0.513416i
$353$	4.49850	−	7.79163i	0.239431	−	0.414707i	−0.721120	−	0.692810i	$-0.756372\pi$
$353$	4.49850	−	7.79163i	0.239431	−	0.414707i	0.960551	+	0.278103i	$0.0897058\pi$
$354$	7.86096	+	1.67090i	0.417805	+	0.0888072i
$355$	1.51613	−	14.4250i	0.0804677	−	0.765599i
$356$	17.3860	−	12.6317i	0.921458	−	0.669479i
$357$		0			0
$358$	8.94342	−	27.5250i	0.472675	−	1.45474i
$359$	8.64763	+	3.85017i	0.456404	+	0.203204i	0.622044	−	0.782982i	$-0.286302\pi$
$359$	8.64763	+	3.85017i	0.456404	+	0.203204i	−0.165640	+	0.986186i	$0.552969\pi$
$360$	56.8668	−	25.3187i	2.99714	−	1.33441i
$361$	12.8383	+	2.72887i	0.675701	+	0.143625i
$362$	15.0014	+	25.9832i	0.788456	+	1.36565i
$363$	3.60574	+	2.71995i	0.189253	+	0.142760i
$364$		0			0
$365$	−6.27838	−	19.3229i	−0.328625	−	1.01141i
$366$	1.57006	−	14.9381i	0.0820681	−	0.780826i
$367$	0.143740	+	1.36760i	0.00750319	+	0.0713881i	0.997633	−	0.0687671i	$-0.0219065\pi$
$367$	0.143740	+	1.36760i	0.00750319	+	0.0713881i	−0.990130	+	0.140155i	$0.955240\pi$
$368$	3.18329	+	3.53540i	0.165940	+	0.184295i
$369$	7.26091	−	1.54335i	0.377988	−	0.0803438i
$370$	35.4908	−	25.7856i	1.84508	−	1.34053i
$371$		0			0
$372$	4.60294	+	14.1664i	0.238651	+	0.734493i
$373$	−2.53590	−	4.39230i	−0.131304	−	0.227425i	0.792876	−	0.609384i	$-0.208583\pi$
$373$	−2.53590	−	4.39230i	−0.131304	−	0.227425i	−0.924179	+	0.381959i	$0.875250\pi$
$374$	−32.9373	−	19.4126i	−1.70315	−	1.00380i
$375$	1.23749	−	2.14339i	0.0639036	−	0.110684i
$376$	21.6240	−	24.0159i	1.11517	−	1.23853i
$377$	2.20474	+	1.60184i	0.113550	+	0.0824989i
$378$		0			0
$379$	−8.64698	+	26.6127i	−0.444166	+	1.36700i	0.439231	+	0.898374i	$0.355251\pi$
$379$	−8.64698	+	26.6127i	−0.444166	+	1.36700i	−0.883396	+	0.468627i	$0.844749\pi$
$380$	36.6840	−	7.79742i	1.88185	−	0.399999i
$381$	0.298459	+	2.83965i	0.0152905	+	0.145479i
$382$	−52.5348	+	23.3900i	−2.68791	+	1.19674i
$383$	20.9308	−	23.2460i	1.06951	−	1.18781i	0.0880584	−	0.996115i	$-0.471934\pi$
$383$	20.9308	−	23.2460i	1.06951	−	1.18781i	0.981454	−	0.191698i	$-0.0613995\pi$
$384$	−4.44323			−0.226742
$385$		0			0
$386$	8.78692			0.447243
$387$	2.76871	−	3.07496i	0.140741	−	0.156309i
$388$	35.8875	−	15.9781i	1.82191	−	0.811166i
$389$	−1.11360	−	10.5952i	−0.0564619	−	0.537199i	−0.985795	−	0.167955i	$-0.946284\pi$
$389$	−1.11360	−	10.5952i	−0.0564619	−	0.537199i	0.929333	−	0.369243i	$-0.120383\pi$
$390$	7.64403	−	1.62479i	0.387071	−	0.0822744i
$391$	0.905090	−	2.78558i	0.0457723	−	0.140873i
$392$		0			0
$393$	−6.95546	−	5.05344i	−0.350857	−	0.254912i
$394$	−3.72617	+	4.13833i	−0.187722	+	0.208486i
$395$	16.7389	−	28.9926i	0.842224	−	1.45877i
$396$	−16.8872	−	38.8644i	−0.848614	−	1.95301i
$397$	10.5878	+	18.3385i	0.531385	+	0.920385i	0.999329	+	0.0366273i	$0.0116614\pi$
$397$	10.5878	+	18.3385i	0.531385	+	0.920385i	−0.467944	+	0.883758i	$0.655005\pi$
$398$	−1.84085	−	5.66554i	−0.0922733	−	0.283988i
$399$		0			0
$400$	−40.1133	+	29.1440i	−2.00566	+	1.45720i
$401$	32.9743	−	7.00890i	1.64666	−	0.350008i	0.711075	−	0.703116i	$-0.248209\pi$
$401$	32.9743	−	7.00890i	1.64666	−	0.350008i	0.935582	+	0.353109i	$0.114875\pi$
$402$	4.36591	+	4.84884i	0.217752	+	0.241838i
$403$	−1.82779	−	17.3903i	−0.0910489	−	0.866273i
$404$	−2.72375	+	25.9147i	−0.135511	+	1.28931i
$405$	−7.95886	−	24.4948i	−0.395479	−	1.21716i
$406$		0			0
$407$	−9.65209	−	13.5389i	−0.478436	−	0.671097i
$408$	−5.94584	−	10.2985i	−0.294363	−	0.509851i
$409$	−2.58626	−	0.549726i	−0.127882	−	0.0271822i	0.143526	−	0.989647i	$-0.454156\pi$
$409$	−2.58626	−	0.549726i	−0.127882	−	0.0271822i	−0.271408	+	0.962464i	$0.587489\pi$
$410$	−20.9580	+	9.33109i	−1.03504	+	0.460830i
$411$	3.42708	+	1.52583i	0.169045	+	0.0752639i
$412$	6.47144	−	19.9170i	0.318825	−	0.981242i
$413$		0			0
$414$	3.79032	−	2.75383i	0.186284	−	0.135343i
$415$	3.00273	−	28.5691i	0.147398	−	1.40240i
$416$	−12.5536	−	2.66834i	−0.615489	−	0.130826i
$417$	2.20735	−	3.82324i	0.108094	−	0.187225i
$418$	−4.08496	−	20.1039i	−0.199802	−	0.983315i
$419$	−33.0757			−1.61585			−0.807926	−	0.589284i	$-0.799410\pi$
$419$	−33.0757			−1.61585			−0.807926	+	0.589284i	$0.799410\pi$
$420$		0			0
$421$	−27.2492	−	19.7977i	−1.32804	−	0.964881i	−0.999794	−	0.0202902i	$-0.993541\pi$
$421$	−27.2492	−	19.7977i	−1.32804	−	0.964881i	−0.328251	−	0.944591i	$-0.606459\pi$
$422$	−31.8641	−	14.1868i	−1.55112	−	0.690604i
$423$	−9.54943	−	10.6057i	−0.464309	−	0.515668i
$424$	57.4795	+	63.8375i	2.79145	+	3.10022i
$425$	27.8872	+	12.4162i	1.35273	+	0.602274i
$426$	−3.58577	−	2.60521i	−0.173731	−	0.126223i
$427$		0			0
$428$	−18.1490			−0.877266
$429$	−0.589795	−	2.90264i	−0.0284756	−	0.140141i
$430$	−6.39394	+	11.0746i	−0.308343	+	0.534066i
$431$	29.1024	+	6.18591i	1.40181	+	0.297965i	0.845930	−	0.533295i	$-0.179046\pi$
$431$	29.1024	+	6.18591i	1.40181	+	0.297965i	0.555885	+	0.831260i	$0.312380\pi$
$432$	1.83631	−	17.4713i	0.0883493	−	0.840588i
$433$	−18.7295	+	13.6078i	−0.900083	+	0.653949i	−0.938487	−	0.345314i	$-0.887773\pi$
$433$	−18.7295	+	13.6078i	−0.900083	+	0.653949i	0.0384041	+	0.999262i	$0.487773\pi$
$434$		0			0
$435$	0.545128	−	1.67773i	0.0261369	−	0.0804410i
$436$	−25.3423	−	11.2831i	−1.21368	−	0.540363i
$437$	1.43573	−	0.639229i	0.0686804	−	0.0305785i
$438$	−6.07286	−	1.29083i	−0.290172	−	0.0616780i
$439$	7.90829	+	13.6976i	0.377442	+	0.653749i	0.990689	−	0.136142i	$-0.0434704\pi$
$439$	7.90829	+	13.6976i	0.377442	+	0.653749i	−0.613247	+	0.789891i	$0.710137\pi$
$440$	42.3277	+	59.3725i	2.01789	+	2.83047i
$441$		0			0
$442$	7.74789	+	23.8456i	0.368530	+	1.13422i
$443$	1.04807	−	9.97173i	0.0497954	−	0.473771i	−0.941000	−	0.338406i	$-0.890112\pi$
$443$	1.04807	−	9.97173i	0.0497954	−	0.473771i	0.990796	−	0.135366i	$-0.0432209\pi$
$444$	−0.970920	−	9.23768i	−0.0460778	−	0.438401i
$445$	10.9272	+	12.1359i	0.518000	+	0.575297i
$446$	−13.4011	+	2.84849i	−0.634560	+	0.134880i
$447$	−3.57275	+	2.59575i	−0.168985	+	0.122775i
$448$		0			0
$449$	0.496363	+	1.52765i	0.0234248	+	0.0720942i	0.962086	−	0.272748i	$-0.0879325\pi$
$449$	0.496363	+	1.52765i	0.0234248	+	0.0720942i	−0.938661	+	0.344842i	$0.887932\pi$
$450$	24.4148	+	42.2878i	1.15093	+	1.99346i
$451$	3.46522	+	7.97490i	0.163171	+	0.375523i
$452$	5.59171	−	9.68512i	0.263012	−	0.455550i
$453$	−2.10570	+	2.33861i	−0.0989343	+	0.109878i
$454$	21.9112	+	15.9194i	1.02834	+	0.747134i
$455$		0			0
$456$	1.97178	−	6.06853i	0.0923373	−	0.284185i
$457$	−3.67486	+	0.781115i	−0.171902	+	0.0365390i	−0.293059	−	0.956094i	$-0.594673\pi$
$457$	−3.67486	+	0.781115i	−0.171902	+	0.0365390i	0.121156	+	0.992633i	$0.461340\pi$
$458$	6.03949	+	57.4619i	0.282207	+	2.68502i
$459$	−9.88064	+	4.39915i	−0.461189	+	0.205335i
$460$	−6.71319	+	7.45575i	−0.313004	+	0.347626i
$461$	14.1849			0.660657			0.330329	−	0.943866i	$-0.392840\pi$
$461$	14.1849			0.660657			0.330329	+	0.943866i	$0.392840\pi$
$462$		0			0
$463$	−5.34265			−0.248294			−0.124147	−	0.992264i	$-0.539619\pi$
$463$	−5.34265			−0.248294			−0.124147	+	0.992264i	$0.539619\pi$
$464$	−6.15127	+	6.83168i	−0.285566	+	0.317153i
$465$	−10.3404	+	4.60386i	−0.479526	+	0.213499i
$466$	−3.95421	−	37.6218i	−0.183175	−	1.74280i
$467$	−23.3479	+	4.96276i	−1.08041	+	0.229649i	−0.713535	−	0.700619i	$-0.752907\pi$
$467$	−23.3479	+	4.96276i	−1.08041	+	0.229649i	−0.366879	+	0.930269i	$0.619574\pi$
$468$	−8.58735	+	26.4292i	−0.396950	+	1.22169i
$469$		0			0
$470$	35.6826	+	25.9250i	1.64592	+	1.19583i
$471$	−5.04128	+	5.59891i	−0.232290	+	0.257984i
$472$	24.5875	−	42.5868i	1.13173	−	1.96022i
$473$	4.17557	+	2.46100i	0.191993	+	0.113157i
$474$	−5.11504	−	8.85952i	−0.234942	−	0.406931i
$475$	5.06164	+	15.5781i	0.232244	+	0.714774i
$476$		0			0
$477$	30.6903	−	22.2978i	1.40521	−	1.02095i
$478$	−4.89075	+	1.03956i	−0.223698	+	0.0475484i
$479$	0.292086	+	0.324395i	0.0133458	+	0.0148220i	0.749781	−	0.661686i	$-0.230159\pi$
$479$	0.292086	+	0.324395i	0.0133458	+	0.0148220i	−0.736435	+	0.676508i	$0.763492\pi$
$480$	0.868387	+	8.26215i	0.0396362	+	0.377114i
$481$	−1.13979	+	10.8443i	−0.0519698	+	0.494459i
$482$	−0.623188	−	1.91798i	−0.0283854	−	0.0873614i
$483$		0			0
$484$	40.6741	−	28.4500i	1.84882	−	1.29318i
$485$	14.9258	+	25.8523i	0.677747	+	1.17389i
$486$	−25.6286	−	5.44753i	−1.16254	−	0.247105i
$487$	0.670250	−	0.298414i	0.0303719	−	0.0135225i	−0.391494	−	0.920180i	$-0.628042\pi$
$487$	0.670250	−	0.298414i	0.0303719	−	0.0135225i	0.421866	+	0.906658i	$0.361375\pi$
$488$	−83.9622	−	37.3824i	−3.80079	−	1.69222i
$489$	0.0479087	−	0.147448i	0.00216650	−	0.00666782i
$490$		0			0
$491$	−2.10952	+	1.53266i	−0.0952013	+	0.0691678i	−0.634368	−	0.773032i	$-0.718739\pi$
$491$	−2.10952	+	1.53266i	−0.0952013	+	0.0691678i	0.539166	+	0.842199i	$0.318739\pi$
$492$	−0.507743	+	4.83085i	−0.0228908	+	0.217792i
$493$	5.53609	+	1.17673i	0.249333	+	0.0529973i
$494$	−6.72675	+	11.6511i	−0.302651	+	0.524207i
$495$	28.0299	−	15.8493i	1.25985	−	0.712374i
$496$	58.9857			2.64854
$497$		0			0
$498$	−7.10172	−	5.15970i	−0.318236	−	0.231212i
$499$	−7.54406	−	3.35883i	−0.337719	−	0.150362i	0.230869	−	0.972985i	$-0.425843\pi$
$499$	−7.54406	−	3.35883i	−0.337719	−	0.150362i	−0.568587	+	0.822623i	$0.692510\pi$
$500$	−18.2001	−	20.2132i	−0.813933	−	0.903964i
$501$	0.0313589	+	0.0348276i	0.00140101	+	0.00155598i
$502$	48.0610	+	21.3981i	2.14507	+	0.955045i
$503$	27.4351	+	19.9328i	1.22327	+	0.888759i	0.996367	−	0.0851577i	$-0.0271394\pi$
$503$	27.4351	+	19.9328i	1.22327	+	0.888759i	0.226905	+	0.973917i	$0.427139\pi$
$504$		0			0
$505$	−19.8010			−0.881135
$506$	4.04523	+	3.70863i	0.179833	+	0.164869i
$507$	1.69767	−	2.94044i	0.0753960	−	0.130590i
$508$	30.6935	+	6.52410i	1.36180	+	0.289460i
$509$	−3.05680	+	29.0835i	−0.135490	+	1.28910i	0.689637	+	0.724155i	$0.257770\pi$
$509$	−3.05680	+	29.0835i	−0.135490	+	1.28910i	−0.825127	+	0.564947i	$0.808896\pi$
$510$	13.1303	−	9.53972i	0.581419	−	0.422426i
$511$		0			0
$512$	−15.6950	+	48.3043i	−0.693628	+	2.13477i
$513$	−5.30175	−	2.36049i	−0.234078	−	0.104218i
$514$	−12.0753	+	5.37627i	−0.532619	+	0.237137i
$515$	15.5661	+	3.30867i	0.685923	+	0.145797i
$516$	1.35381	+	2.34487i	0.0595983	+	0.103227i
$517$	9.94705	−	13.4357i	0.437471	−	0.590899i
$518$		0			0
$519$	1.68766	+	5.19408i	0.0740800	+	0.227995i
$520$	4.99834	−	47.5561i	0.219192	−	2.08547i
$521$	−1.01555	−	9.66228i	−0.0444919	−	0.423312i	−0.993984	−	0.109522i	$-0.965068\pi$
$521$	−1.01555	−	9.66228i	−0.0444919	−	0.423312i	0.949492	−	0.313790i	$-0.101599\pi$
$522$	6.05785	+	6.72793i	0.265145	+	0.294473i
$523$	−12.5455	+	2.66662i	−0.548575	+	0.116603i	−0.473858	−	0.880601i	$-0.657139\pi$
$523$	−12.5455	+	2.66662i	−0.548575	+	0.116603i	−0.0747177	+	0.997205i	$0.523806\pi$
$524$	−76.4394	+	55.5365i	−3.33927	+	2.42612i
$525$		0			0
$526$	18.2891	+	56.2880i	0.797442	+	2.45427i
$527$	−18.1577	−	31.4501i	−0.790963	−	1.36999i
$528$	9.94580	−	0.955167i	0.432835	−	0.0415683i
$529$	11.2898	−	19.5545i	0.490860	−	0.850195i
$530$	−78.4490	+	87.1264i	−3.40761	+	3.78453i
$531$	−17.5688	−	12.7645i	−0.762423	−	0.553933i
$532$		0			0
$533$	1.76211	−	5.42320i	0.0763253	−	0.234905i
$534$	4.88120	−	1.03753i	0.211230	−	0.0448984i
$535$	−1.44160	−	13.7159i	−0.0623256	−	0.592989i
$536$	36.4727	−	16.2387i	1.57538	−	0.701404i
$537$	3.11586	−	3.46052i	0.134459	−	0.149332i
$538$	−47.6192			−2.05301
$539$		0			0
$540$	37.0479			1.59429
$541$	−4.61784	+	5.12863i	−0.198536	+	0.220497i	−0.834190	−	0.551478i	$-0.814064\pi$
$541$	−4.61784	+	5.12863i	−0.198536	+	0.220497i	0.635653	+	0.771975i	$0.280731\pi$
$542$	−70.4728	+	31.3765i	−3.02706	+	1.34774i
$543$	0.504595	+	4.80090i	0.0216542	+	0.206026i
$544$	−26.0715	+	5.54167i	−1.11781	+	0.237597i
$545$	6.51410	−	20.0483i	0.279033	−	0.858776i
$546$		0			0
$547$	14.3372	+	10.4166i	0.613016	+	0.445382i	0.850475	−	0.526015i	$-0.176315\pi$
$547$	14.3372	+	10.4166i	0.613016	+	0.445382i	−0.237459	+	0.971398i	$0.576315\pi$
$548$	27.5865	−	30.6379i	1.17844	−	1.30879i
$549$	−20.2939	+	35.1500i	−0.866122	+	1.50017i
$550$	−42.8479	+	37.8896i	−1.82704	+	1.61562i
$551$	1.51846	+	2.63005i	0.0646885	+	0.112044i
$552$	0.527479	+	1.62341i	0.0224510	+	0.0690971i
$553$		0			0
$554$	−27.8552	+	20.2380i	−1.18346	+	0.859831i
$555$	6.90413	−	1.46752i	0.293064	−	0.0622927i
$556$	−32.4641	−	36.0550i	−1.37678	−	1.52907i
$557$	−4.53939	−	43.1894i	−0.192340	−	1.82999i	−0.485856	−	0.874039i	$-0.661492\pi$
$557$	−4.53939	−	43.1894i	−0.192340	−	1.82999i	0.293516	−	0.955954i	$-0.405175\pi$
$558$	6.07205	−	57.7717i	0.257050	−	2.44567i
$559$	−0.982226	−	3.02298i	−0.0415437	−	0.127858i
$560$		0			0
$561$	−3.57092	−	5.00889i	−0.150764	−	0.211475i
$562$	−10.3388	−	17.9074i	−0.436117	−	0.755377i
$563$	21.8261	+	4.63929i	0.919862	+	0.195523i	0.643425	−	0.765509i	$-0.277513\pi$
$563$	21.8261	+	4.63929i	0.919862	+	0.195523i	0.276437	+	0.961032i	$0.410846\pi$
$564$	8.53139	−	3.79842i	0.359236	−	0.159942i
$565$	7.76355	+	3.45656i	0.326615	+	0.145418i
$566$	−7.87898	+	24.2490i	−0.331178	+	1.01926i
$567$		0			0
$568$	−21.9410	+	15.9411i	−0.920623	+	0.668872i
$569$	−2.36956	+	22.5449i	−0.0993373	+	0.945131i	0.825406	+	0.564540i	$0.190946\pi$
$569$	−2.36956	+	22.5449i	−0.0993373	+	0.945131i	−0.924743	+	0.380592i	$0.875720\pi$
$570$	8.51835	+	1.81063i	0.356795	+	0.0758390i
$571$	−17.5497	+	30.3970i	−0.734432	+	1.27207i	0.220540	+	0.975378i	$0.429218\pi$
$571$	−17.5497	+	30.3970i	−0.734432	+	1.27207i	−0.954972	+	0.296695i	$0.904115\pi$
$572$	−32.3413	−	3.69300i	−1.35226	−	0.154412i
$573$	−9.25258			−0.386532
$574$		0			0
$575$	−3.54497	−	2.57557i	−0.147836	−	0.107409i
$576$	−0.993188	−	0.442196i	−0.0413828	−	0.0184248i
$577$	21.8376	+	24.2531i	0.909111	+	1.00967i	0.999905	+	0.0138000i	$0.00439281\pi$
$577$	21.8376	+	24.2531i	0.909111	+	1.00967i	−0.0907941	+	0.995870i	$0.528941\pi$
$578$	5.81370	+	6.45677i	0.241818	+	0.268566i
$579$	1.29156	+	0.575038i	0.0536752	+	0.0238978i
$580$	−15.6843	−	11.3953i	−0.651255	−	0.473164i
$581$		0			0
$582$	9.12204			0.378121
$583$	32.7543	+	30.0289i	1.35655	+	1.24367i
$584$	−18.9947	+	32.8998i	−0.786006	+	1.36140i
$585$	−20.6556	−	4.39048i	−0.854003	−	0.181524i
$586$	8.19715	−	77.9907i	0.338621	−	3.22176i
$587$	29.9477	−	21.7583i	1.23607	−	0.898061i	0.238744	−	0.971082i	$-0.423264\pi$
$587$	29.9477	−	21.7583i	1.23607	−	0.898061i	0.997330	+	0.0730216i	$0.0232642\pi$
$588$		0			0
$589$	6.02155	−	18.5324i	0.248114	−	0.763615i
$590$	61.3124	+	27.2981i	2.52419	+	1.12384i
$591$	−0.818518	+	0.364428i	−0.0336693	+	0.0149906i
$592$	−35.9789	−	7.64754i	−1.47872	−	0.314312i
$593$	−8.10805	−	14.0436i	−0.332958	−	0.576700i	0.650133	−	0.759821i	$-0.274713\pi$
$593$	−8.10805	−	14.0436i	−0.332958	−	0.576700i	−0.983090	+	0.183121i	$0.941380\pi$
$594$	0.181905	−	20.2647i	0.00746364	−	0.831471i
$595$		0			0
$596$	14.9975	+	46.1575i	0.614321	+	1.89068i
$597$	0.100188	−	0.953226i	0.00410043	−	0.0390129i
$598$	−0.376197	−	3.57928i	−0.0153839	−	0.146368i
$599$	7.05767	+	7.83834i	0.288369	+	0.320266i	0.869871	−	0.493279i	$-0.164202\pi$
$599$	7.05767	+	7.83834i	0.288369	+	0.320266i	−0.581503	+	0.813545i	$0.697535\pi$
$600$	−17.4018	+	3.69886i	−0.710424	+	0.151005i
$601$	−29.5220	+	21.4490i	−1.20423	+	0.874921i	−0.994694	−	0.102880i	$-0.967194\pi$
$601$	−29.5220	+	21.4490i	−1.20423	+	0.874921i	−0.209532	+	0.977802i	$0.567194\pi$
$602$		0			0
$603$	−5.44830	−	16.7681i	−0.221872	−	0.682852i
$604$	17.2921	+	29.9507i	0.703604	+	1.21868i
$605$	24.7315	+	28.4790i	1.00548	+	1.15784i
$606$	−3.02539	+	5.24013i	−0.122898	+	0.212866i
$607$	22.5573	−	25.0525i	0.915574	−	1.01685i	−0.0842179	−	0.996447i	$-0.526839\pi$
$607$	22.5573	−	25.0525i	0.915574	−	1.01685i	0.999792	−	0.0204006i	$-0.00649416\pi$
$608$	−11.5705	−	8.40648i	−0.469247	−	0.340928i
$609$		0			0
$610$	38.7624	−	119.298i	1.56944	−	4.83025i
$611$	−10.7234	+	2.27934i	−0.433824	+	0.0922121i
$612$	6.03268	+	57.3971i	0.243857	+	2.32014i
$613$	22.1139	−	9.84573i	0.893171	−	0.397665i	0.0917612	−	0.995781i	$-0.470750\pi$
$613$	22.1139	−	9.84573i	0.893171	−	0.397665i	0.801410	+	0.598116i	$0.204084\pi$
$614$	34.2672	−	38.0576i	1.38291	−	1.53588i
$615$	−3.69118			−0.148843
$616$		0			0
$617$	17.6040			0.708710			0.354355	−	0.935111i	$-0.384700\pi$
$617$	17.6040			0.708710			0.354355	+	0.935111i	$0.384700\pi$
$618$	3.25393	−	3.61386i	0.130892	−	0.145371i
$619$	22.2152	−	9.89086i	0.892906	−	0.397547i	0.0915954	−	0.995796i	$-0.470803\pi$
$619$	22.2152	−	9.89086i	0.892906	−	0.397547i	0.801310	+	0.598249i	$0.204137\pi$
$620$	13.0027	+	123.713i	0.522202	+	4.96842i
$621$	1.51859	−	0.322786i	0.0609388	−	0.0129529i
$622$	18.5053	−	56.9535i	0.741995	−	2.28363i
$623$		0			0
$624$	−5.30103	−	3.85142i	−0.212211	−	0.154180i
$625$	−8.77929	+	9.75039i	−0.351172	+	0.390016i
$626$	−18.7223	+	32.4280i	−0.748294	+	1.29608i
$627$	0.715216	−	3.22233i	0.0285630	−	0.128687i
$628$	41.3992	+	71.7055i	1.65201	+	2.86136i
$629$	6.99793	+	21.5374i	0.279026	+	0.858754i
$630$		0			0
$631$	−3.26881	+	2.37493i	−0.130129	+	0.0945443i	−0.650946	−	0.759124i	$-0.725628\pi$
$631$	−3.26881	+	2.37493i	−0.130129	+	0.0945443i	0.520817	+	0.853669i	$0.325628\pi$
$632$	−61.2290	+	13.0146i	−2.43556	+	0.517694i
$633$	−3.75516	−	4.17053i	−0.149254	−	0.165764i
$634$	−4.81510	−	45.8126i	−0.191232	−	1.81945i
$635$	−2.49248	+	23.7144i	−0.0989111	+	0.941076i
$636$	7.67095	+	23.6087i	0.304173	+	0.936148i
$637$		0			0
$638$	−6.31009	+	8.52315i	−0.249819	+	0.337435i
$639$	5.98838	+	10.3722i	0.236897	+	0.410317i
$640$	−36.2953	−	7.71480i	−1.43470	−	0.304954i
$641$	−19.5208	+	8.69124i	−0.771027	+	0.343283i	−0.754260	−	0.656576i	$-0.772004\pi$
$641$	−19.5208	+	8.69124i	−0.771027	+	0.343283i	−0.0167671	+	0.999859i	$0.505337\pi$
$642$	−3.85002	−	1.71414i	−0.151948	−	0.0676516i
$643$	−6.97607	+	21.4701i	−0.275109	+	0.846700i	0.714081	+	0.700063i	$0.246845\pi$
$643$	−6.97607	+	21.4701i	−0.275109	+	0.846700i	−0.989190	+	0.146637i	$0.953155\pi$
$644$		0			0
$645$	−1.66457	+	1.20938i	−0.0655424	+	0.0476194i
$646$	−2.92058	+	27.7874i	−0.114909	+	1.09328i
$647$	16.7430	+	3.55884i	0.658237	+	0.139913i	0.524908	−	0.851159i	$-0.324100\pi$
$647$	16.7430	+	3.55884i	0.658237	+	0.139913i	0.133329	+	0.991072i	$0.457433\pi$
$648$	−24.0788	+	41.7057i	−0.945905	+	1.63836i
$649$	10.5547	−	23.1448i	0.414306	−	0.908512i
$650$	37.5100			1.47126
$651$		0			0
$652$	−1.37842	−	1.00148i	−0.0539830	−	0.0392209i
$653$	−12.0964	−	5.38564i	−0.473367	−	0.210757i	0.156165	−	0.987731i	$-0.450087\pi$
$653$	−12.0964	−	5.38564i	−0.473367	−	0.210757i	−0.629532	+	0.776974i	$0.716753\pi$
$654$	−4.31029	−	4.78706i	−0.168545	−	0.187189i
$655$	−48.0426	−	53.3567i	−1.87718	−	2.08482i
$656$	17.5725	+	7.82379i	0.686091	+	0.305468i
$657$	13.5725	+	9.86103i	0.529515	+	0.384715i
$658$		0			0
$659$	28.3747			1.10532			0.552660	−	0.833407i	$-0.313613\pi$
$659$	28.3747			1.10532			0.552660	+	0.833407i	$0.313613\pi$
$660$	4.19574	+	20.6491i	0.163319	+	0.803765i
$661$	9.48284	−	16.4248i	0.368840	−	0.638849i	−0.620545	−	0.784171i	$-0.713088\pi$
$661$	9.48284	−	16.4248i	0.368840	−	0.638849i	0.989384	+	0.145322i	$0.0464218\pi$
$662$	49.4993	+	10.5214i	1.92384	+	0.408926i
$663$	−0.421679	+	4.01201i	−0.0163766	+	0.155813i
$664$	−43.4547	+	31.5717i	−1.68637	+	1.22522i
$665$		0			0
$666$	−11.1938	+	34.4511i	−0.433752	+	1.33495i
$667$	−0.742180	−	0.330440i	−0.0287373	−	0.0127947i
$668$	0.470513	−	0.209486i	0.0182047	−	0.00810525i
$669$	−2.15619	−	0.458312i	−0.0833630	−	0.0177194i
$670$	27.2447	+	47.1891i	1.05255	+	1.82308i
$671$	−45.0826	−	15.0969i	−1.74039	−	0.582811i
$672$		0			0
$673$	14.3830	+	44.2662i	0.554423	+	1.70634i	0.697462	+	0.716621i	$0.254312\pi$
$673$	14.3830	+	44.2662i	0.554423	+	1.70634i	−0.143039	+	0.989717i	$0.545688\pi$
$674$	5.20387	−	49.5115i	0.200446	−	1.90711i
$675$	1.69136	+	16.0922i	0.0651004	+	0.619389i
$676$	−24.9681	−	27.7298i	−0.960310	−	1.06653i
$677$	27.9452	−	5.93993i	1.07402	−	0.228290i	0.363233	−	0.931698i	$-0.381673\pi$
$677$	27.9452	−	5.93993i	1.07402	−	0.228290i	0.710786	+	0.703408i	$0.248339\pi$
$678$	2.10093	−	1.52641i	0.0806857	−	0.0586216i
$679$		0			0
$680$	−30.6883	−	94.4489i	−1.17684	−	3.62195i
$681$	2.17883	+	3.77385i	0.0834931	+	0.144614i
$682$	67.7331	−	6.50489i	2.59363	−	0.249085i
$683$	10.9725	−	19.0050i	0.419852	−	0.727205i	−0.576072	−	0.817399i	$-0.695415\pi$
$683$	10.9725	−	19.0050i	0.419852	−	0.727205i	0.995924	+	0.0901940i	$0.0287487\pi$
$684$	−20.7215	+	23.0135i	−0.792306	+	0.879945i
$685$	25.3454	+	18.4145i	0.968398	+	0.703582i
$686$		0			0
$687$	−2.87273	+	8.84135i	−0.109601	+	0.337318i
$688$	10.4879	−	2.22927i	0.399846	−	0.0849900i
$689$	−3.04608	−	28.9815i	−0.116046	−	1.10411i
$690$	−2.12827	+	0.947568i	−0.0810220	+	0.0360733i
$691$	−7.44715	+	8.27090i	−0.283303	+	0.314640i	−0.867954	−	0.496645i	$-0.834565\pi$
$691$	−7.44715	+	8.27090i	−0.283303	+	0.314640i	0.584651	+	0.811285i	$0.301232\pi$
$692$	60.0197			2.28161
$693$		0			0
$694$	−72.5903			−2.75549
$695$	24.6694	−	27.3982i	0.935765	−	1.03927i
$696$	−3.01330	+	1.34161i	−0.114219	+	0.0508536i
$697$	−1.23789	−	11.7778i	−0.0468885	−	0.446114i
$698$	50.1402	−	10.6576i	1.89784	−	0.403397i
$699$	1.88085	−	5.78866i	0.0711402	−	0.218947i
$700$		0			0
$701$	31.0633	+	22.5688i	1.17324	+	0.852411i	0.991394	−	0.130915i	$-0.0417917\pi$
$701$	31.0633	+	22.5688i	1.17324	+	0.852411i	0.181849	+	0.983326i	$0.441792\pi$
$702$	−8.89279	+	9.87644i	−0.335637	+	0.372762i
$703$	−6.07564	+	10.5233i	−0.229147	+	0.396894i
$704$	0.275944	−	1.24323i	0.0104000	−	0.0468561i
$705$	3.54826	+	6.14577i	0.133635	+	0.231463i
$706$	−7.09498	−	21.8361i	−0.267023	−	0.821812i
$707$		0			0
$708$	11.4965	−	8.35271i	0.432066	−	0.313914i
$709$	0.470002	−	0.0999020i	0.0176513	−	0.00375190i	−0.199078	−	0.979984i	$-0.563795\pi$
$709$	0.470002	−	0.0999020i	0.0176513	−	0.00375190i	0.216729	+	0.976232i	$0.430461\pi$
$710$	−24.7676	−	27.5072i	−0.929510	−	1.03233i
$711$	2.88954	+	27.4921i	0.108366	+	1.03104i
$712$	3.19176	−	30.3676i	0.119616	−	1.13807i
$713$	1.61085	+	4.95768i	0.0603267	+	0.185666i
$714$		0			0
$715$	0.222031	−	24.7348i	0.00830348	−	0.925031i
$716$	−25.5876	−	44.3190i	−0.956253	−	1.65628i
$717$	−0.786904	−	0.167262i	−0.0293875	−	0.00624650i
$718$	22.0683	−	9.82542i	0.823580	−	0.366681i
$719$	−33.3168	−	14.8336i	−1.24251	−	0.553199i	−0.323046	−	0.946383i	$-0.604707\pi$
$719$	−33.3168	−	14.8336i	−1.24251	−	0.553199i	−0.919460	+	0.393184i	$0.871374\pi$
$720$	22.0125	−	67.7475i	0.820358	−	2.52480i
$721$		0			0
$722$	27.0977	−	19.6876i	1.00847	−	0.732698i
$723$	0.0339170	−	0.322699i	0.00126139	−	0.0120013i
$724$	51.8924	+	11.0301i	1.92857	+	0.409930i
$725$	4.23365	−	7.33289i	0.157234	−	0.272337i
$726$	11.3154	−	2.19363i	0.419953	−	0.0814132i
$727$	33.6867			1.24937			0.624686	−	0.780876i	$-0.285227\pi$
$727$	33.6867			1.24937			0.624686	+	0.780876i	$0.285227\pi$
$728$		0			0
$729$	14.8193	+	10.7668i	0.548862	+	0.398772i
$730$	−47.3660	−	21.0887i	−1.75309	−	0.780527i
$731$	−4.41711	−	4.90570i	−0.163373	−	0.181444i
$732$	−17.7717	−	19.7375i	−0.656861	−	0.729518i
$733$	24.7239	+	11.0078i	0.913198	+	0.406582i	0.808888	−	0.587963i	$-0.200070\pi$
$733$	24.7239	+	11.0078i	0.913198	+	0.406582i	0.104310	+	0.994545i	$0.466737\pi$
$734$	2.83905	+	2.06269i	0.104791	+	0.0761353i
$735$		0			0
$736$	3.82597			0.141027
$737$	17.9776	−	10.1653i	0.662212	−	0.374443i
$738$	9.47169	−	16.4054i	0.348658	−	0.603893i
$739$	10.1851	+	2.16491i	0.374664	+	0.0796374i	0.391395	−	0.920223i	$-0.371993\pi$
$739$	10.1851	+	2.16491i	0.374664	+	0.0796374i	−0.0167308	+	0.999860i	$0.505326\pi$
$740$	8.10832	−	77.1455i	0.298068	−	2.83592i
$741$	−1.75121	+	1.27233i	−0.0643324	+	0.0467403i
$742$		0			0
$743$	14.6944	−	45.2248i	0.539086	−	1.65914i	−0.195565	−	0.980691i	$-0.562654\pi$
$743$	14.6944	−	45.2248i	0.539086	−	1.65914i	0.734651	−	0.678446i	$-0.237346\pi$
$744$	19.3346	+	8.60833i	0.708842	+	0.315597i
$745$	−33.6916	+	15.0005i	−1.23437	+	0.549575i
$746$	−12.6601	−	2.69099i	−0.463519	−	0.0985240i
$747$	11.8602	+	20.5424i	0.433940	+	0.751607i
$748$	−64.4797	+	20.3127i	−2.35761	+	0.742705i
$749$		0			0
$750$	−1.95175	−	6.00687i	−0.0712679	−	0.219340i
$751$	3.10186	−	29.5122i	0.113189	−	1.07692i	−0.779549	−	0.626341i	$-0.784552\pi$
$751$	3.10186	−	29.5122i	0.113189	−	1.07692i	0.892738	−	0.450576i	$-0.148781\pi$
$752$	−3.86561	−	36.7789i	−0.140964	−	1.34119i
$753$	5.66395	+	6.29046i	0.206406	+	0.229237i
$754$	6.80260	−	1.44594i	0.247736	−	0.0526580i
$755$	−21.2613	+	15.4473i	−0.773779	+	0.562183i
$756$		0			0
$757$	−9.57305	−	29.4628i	−0.347938	−	1.07084i	−0.959992	−	0.280028i	$-0.909656\pi$
$757$	−9.57305	−	29.4628i	−0.347938	−	1.07084i	0.612053	−	0.790816i	$-0.290344\pi$
$758$	35.7045	+	61.8420i	1.29685	+	2.24620i
$759$	0.351891	+	0.809847i	0.0127728	+	0.0293956i
$760$	26.6437	−	46.1483i	0.966469	−	1.67397i
$761$	−7.87385	+	8.74479i	−0.285427	+	0.316999i	−0.868759	−	0.495235i	$-0.835082\pi$
$761$	−7.87385	+	8.74479i	−0.285427	+	0.316999i	0.583332	+	0.812234i	$0.301749\pi$
$762$	5.89493	+	4.28292i	0.213551	+	0.155154i
$763$		0			0
$764$	−31.4222	+	96.7076i	−1.13682	+	3.49876i
$765$	−42.8979	+	9.11823i	−1.55098	+	0.329670i
$766$	−8.34410	−	79.3888i	−0.301485	−	2.86844i
$767$	−15.2398	+	6.78519i	−0.550277	+	0.244999i
$768$	−7.79816	+	8.66074i	−0.281392	+	0.312518i
$769$	−4.17897			−0.150697			−0.0753487	−	0.997157i	$-0.524007\pi$
$769$	−4.17897			−0.150697			−0.0753487	+	0.997157i	$0.524007\pi$
$770$		0			0
$771$	−2.12674			−0.0765926
$772$	10.3965	−	11.5464i	0.374177	−	0.415565i
$773$	−0.0765496	+	0.0340821i	−0.00275330	+	0.00122585i	−0.408113	−	0.912931i	$-0.633813\pi$
$773$	−0.0765496	+	0.0340821i	−0.00275330	+	0.00122585i	0.405360	+	0.914157i	$0.367146\pi$
$774$	−1.10375	−	10.5015i	−0.0396735	−	0.377468i
$775$	−53.1425	+	11.2958i	−1.90894	+	0.405757i
$776$	17.2484	−	53.0850i	0.619180	−	1.90564i
$777$		0			0
$778$	−21.9950	−	15.9803i	−0.788559	−	0.572922i
$779$	4.25200	−	4.72233i	0.152344	−	0.169195i
$780$	6.90917	−	11.9670i	0.247388	−	0.428489i
$781$	−10.5096	+	9.29341i	−0.376062	+	0.332544i
$782$	−3.73723	−	6.47308i	−0.133643	−	0.231477i
$783$	0.927059	+	2.85319i	0.0331304	+	0.101965i
$784$		0			0
$785$	−50.9020	+	36.9825i	−1.81677	+	1.31996i
$786$	−21.4607	+	4.56161i	−0.765477	+	0.162707i
$787$	−8.99276	−	9.98747i	−0.320557	−	0.356015i	0.561232	−	0.827659i	$-0.310328\pi$
$787$	−8.99276	−	9.98747i	−0.320557	−	0.356015i	−0.881789	+	0.471644i	$0.843661\pi$
$788$	1.02926	+	9.79273i	0.0366658	+	0.348852i
$789$	−0.995383	+	9.47044i	−0.0354366	+	0.337156i
$790$	−26.4003	−	81.2518i	−0.939281	−	2.89081i
$791$		0			0
$792$	−57.0927	−	19.1188i	−2.02870	−	0.679357i
$793$	15.5894	+	27.0016i	0.553594	+	0.958853i
$794$	52.8579	+	11.2353i	1.87586	+	0.398725i
$795$	−17.2327	+	7.67248i	−0.611180	+	0.272115i
$796$	−9.62284	−	4.28436i	−0.341072	−	0.151855i
$797$	4.20197	−	12.9323i	0.148842	−	0.458087i	−0.848643	−	0.528965i	$-0.822580\pi$
$797$	4.20197	−	12.9323i	0.148842	−	0.458087i	0.997485	+	0.0708782i	$0.0225802\pi$
$798$		0			0
$799$	−18.4199	+	13.3828i	−0.651648	+	0.473450i
$800$	−4.16814	+	39.6572i	−0.147366	+	1.40209i
$801$	−13.1899	−	2.80360i	−0.466042	−	0.0990603i
$802$	43.0142	−	74.5028i	1.51888	−	2.63078i
$803$	−8.15383	+	17.8801i	−0.287743	+	0.630976i
$804$	11.5372			0.406887
$805$		0			0
$806$	−36.1012	−	26.2290i	−1.27161	−	0.923879i
$807$	−6.99936	−	3.11632i	−0.246389	−	0.109700i
$808$	24.7740	+	27.5143i	0.871546	+	0.967949i
$809$	29.7763	+	33.0700i	1.04688	+	1.16268i	0.986375	+	0.164510i	$0.0526043\pi$
$809$	29.7763	+	33.0700i	1.04688	+	1.16268i	0.0605046	+	0.998168i	$0.480729\pi$
$810$	−60.0440	−	26.7333i	−2.10973	−	0.939312i
$811$	−19.5819	−	14.2271i	−0.687612	−	0.499579i	0.188262	−	0.982119i	$-0.439715\pi$
$811$	−19.5819	−	14.2271i	−0.687612	−	0.499579i	−0.875874	+	0.482539i	$0.839715\pi$
$812$		0			0
$813$	−12.4119			−0.435303
$814$	−42.1577	−	4.81392i	−1.47763	−	0.168728i
$815$	0.647365	−	1.12127i	0.0226762	−	0.0392763i
$816$	−13.3109	−	2.82931i	−0.465973	−	0.0990456i
$817$	0.370251	−	3.52270i	0.0129535	−	0.123244i
$818$	−5.45879	+	3.96604i	−0.190862	+	0.138669i
$819$		0			0
$820$	−12.5354	+	38.5801i	−0.437756	+	1.34728i
$821$	−8.47804	−	3.77466i	−0.295885	−	0.131737i	0.253425	−	0.967355i	$-0.418443\pi$
$821$	−8.47804	−	3.77466i	−0.295885	−	0.131737i	−0.549310	+	0.835618i	$0.685110\pi$
$822$	8.74571	−	3.89384i	0.305042	−	0.135813i
$823$	22.9701	+	4.88245i	0.800688	+	0.170192i	0.590044	−	0.807371i	$-0.299110\pi$
$823$	22.9701	+	4.88245i	0.800688	+	0.170192i	0.210644	+	0.977563i	$0.432444\pi$
$824$	−14.8779	−	25.7692i	−0.518296	−	0.897714i
$825$	−8.77764	+	2.76517i	−0.305598	+	0.0962709i
$826$		0			0
$827$	−6.09962	−	18.7727i	−0.212105	−	0.652791i	−0.999346	−	0.0361466i	$-0.988492\pi$
$827$	−6.09962	−	18.7727i	−0.212105	−	0.652791i	0.787242	−	0.616644i	$-0.211508\pi$
$828$	0.865945	−	8.23892i	0.0300937	−	0.286322i
$829$	−4.18049	−	39.7747i	−0.145194	−	1.38143i	−0.788128	−	0.615511i	$-0.788950\pi$
$829$	−4.18049	−	39.7747i	−0.145194	−	1.38143i	0.642934	−	0.765922i	$-0.277717\pi$
$830$	−49.0528	−	54.4787i	−1.70265	−	1.89098i
$831$	−5.41876	+	1.15179i	−0.187975	+	0.0399553i
$832$	−0.675650	+	0.490889i	−0.0234240	+	0.0170185i
$833$		0			0
$834$	−3.48140	−	10.7146i	−0.120551	−	0.371018i
$835$	0.195689	+	0.338944i	0.00677211	+	0.0117296i
$836$	−31.2507	−	18.4186i	−1.08083	−	0.637020i
$837$	9.62471	−	16.6705i	0.332679	−	0.576216i
$838$	−56.4794	+	62.7268i	−1.95105	+	2.16686i
$839$	−6.34929	−	4.61303i	−0.219202	−	0.159259i	0.472766	−	0.881188i	$-0.343256\pi$
$839$	−6.34929	−	4.61303i	−0.219202	−	0.159259i	−0.691967	+	0.721929i	$0.743256\pi$
$840$		0			0
$841$	−8.47637	+	26.0876i	−0.292289	+	0.899572i
$842$	−84.0759	+	17.8709i	−2.89745	+	0.615871i
$843$	−0.347762	−	3.30873i	−0.0119776	−	0.113959i
$844$	−56.3430	+	25.0855i	−1.93940	+	0.863479i
$845$	18.9732	−	21.0719i	0.652698	−	0.724895i
$846$	−36.4198			−1.25214
$847$		0			0
$848$	98.3017			3.37569
$849$	−2.74501	+	3.04865i	−0.0942086	+	0.104629i
$850$	71.1666	−	31.6854i	2.44099	−	1.08680i
$851$	−0.339784	−	3.23282i	−0.0116476	−	0.110820i
$852$	−7.66597	+	1.62945i	−0.262632	+	0.0558241i
$853$	12.6694	−	38.9924i	0.433792	−	1.33507i	−0.460528	−	0.887645i	$-0.652340\pi$
$853$	12.6694	−	38.9924i	0.433792	−	1.33507i	0.894320	−	0.447428i	$-0.147660\pi$
$854$		0			0
$855$	−19.0381	−	13.8320i	−0.651089	−	0.473044i
$856$	−17.2551	+	19.1637i	−0.589766	+	0.655002i
$857$	15.5946	−	27.0107i	0.532702	−	0.922666i	−0.466569	−	0.884485i	$-0.654510\pi$
$857$	15.5946	−	27.0107i	0.532702	−	0.922666i	0.999271	−	0.0381817i	$-0.0121566\pi$
$858$	−6.51188	−	3.83798i	−0.222312	−	0.131027i
$859$	3.97913	+	6.89205i	0.135766	+	0.235154i	0.925890	−	0.377794i	$-0.123317\pi$
$859$	3.97913	+	6.89205i	0.135766	+	0.235154i	−0.790124	+	0.612947i	$0.789984\pi$
$860$	6.98745	+	21.5052i	0.238270	+	0.733320i
$861$		0			0
$862$	61.4261	−	44.6287i	2.09218	−	1.52006i
$863$	−30.4245	+	6.46693i	−1.03566	+	0.220137i	−0.694218	−	0.719765i	$-0.744250\pi$
$863$	−30.4245	+	6.46693i	−1.03566	+	0.220137i	−0.341445	+	0.939902i	$0.610916\pi$
$864$	−9.45363	−	10.4993i	−0.321619	−	0.357194i
$865$	4.76743	+	45.3590i	0.162097	+	1.54225i
$866$	−6.17553	+	58.7563i	−0.209853	+	1.99662i
$867$	0.431987	+	1.32952i	0.0146710	+	0.0451528i
$868$		0			0
$869$	−30.8846	+	9.72939i	−1.04769	+	0.330047i
$870$	−2.25090	−	3.89868i	−0.0763127	−	0.132178i
$871$	−13.2479	−	2.81592i	−0.448887	−	0.0954139i
$872$	−36.0080	+	16.0318i	−1.21938	+	0.542905i
$873$	−22.5184	−	10.0258i	−0.762131	−	0.339323i
$874$	1.23936	−	3.81435i	0.0419219	−	0.129022i
$875$		0			0
$876$	−8.88145	+	6.45275i	−0.300077	+	0.218018i
$877$	5.42473	−	51.6128i	0.183180	−	1.74284i	−0.387680	−	0.921794i	$-0.626723\pi$
$877$	5.42473	−	51.6128i	0.183180	−	1.74284i	0.570860	−	0.821048i	$-0.306610\pi$
$878$	39.4810	+	8.39194i	1.33242	+	0.283214i
$879$	6.30877	−	10.9271i	0.212789	−	0.368562i
$880$	82.9025	+	9.46651i	2.79464	+	0.319116i
$881$	−42.1448			−1.41989			−0.709947	−	0.704256i	$-0.751281\pi$
$881$	−42.1448			−1.41989			−0.709947	+	0.704256i	$0.751281\pi$
$882$		0			0
$883$	14.2855	+	10.3790i	0.480744	+	0.349281i	0.801614	−	0.597842i	$-0.203975\pi$
$883$	14.2855	+	10.3790i	0.480744	+	0.349281i	−0.320870	+	0.947123i	$0.603975\pi$
$884$	40.5013	+	18.0323i	1.36221	+	0.606493i
$885$	7.22563	+	8.02487i	0.242887	+	0.269753i
$886$	−17.1214	−	19.0152i	−0.575203	−	0.638828i
$887$	9.73197	+	4.33295i	0.326768	+	0.145486i	0.563563	−	0.826073i	$-0.309430\pi$
$887$	9.73197	+	4.33295i	0.326768	+	0.145486i	−0.236795	+	0.971560i	$0.576097\pi$
$888$	−10.6772	−	7.75747i	−0.358305	−	0.260324i
$889$		0			0
$890$	41.6744			1.39693
$891$	−10.3363	+	22.6659i	−0.346279	+	0.759337i
$892$	−12.1128	+	20.9799i	−0.405566	+	0.702460i
$893$	−11.9500	−	2.54005i	−0.399891	−	0.0849994i
$894$	−1.17801	+	11.2080i	−0.0393986	+	0.374853i
$895$	31.4610	−	22.8578i	1.05163	−	0.764051i
$896$		0			0
$897$	0.178941	−	0.550724i	0.00597467	−	0.0183881i
$898$	3.74471	+	1.66725i	0.124963	+	0.0556370i
$899$	−9.20220	+	4.09708i	−0.306910	+	0.136645i
$900$	84.4551	+	17.9515i	2.81517	+	0.598383i
$901$	−30.2605	−	52.4126i	−1.00812	−	1.74612i
$902$	21.0412	+	7.04614i	0.700597	+	0.234611i
$903$		0			0
$904$	−4.91032	−	15.1124i	−0.163315	−	0.502631i
$905$	−4.21396	+	40.0931i	−0.140077	+	1.33274i
$906$	0.839442	+	7.98676i	0.0278886	+	0.265342i
$907$	33.6576	+	37.3805i	1.11758	+	1.24120i	0.967594	+	0.252512i	$0.0812569\pi$
$907$	33.6576	+	37.3805i	1.11758	+	1.24120i	0.149988	+	0.988688i	$0.452076\pi$
$908$	46.8436	−	9.95691i	1.55456	−	0.330432i
$909$	13.2277	−	9.61047i	0.438735	−	0.318759i
$910$		0			0
$911$	−7.11891	−	21.9097i	−0.235860	−	0.725902i	−0.997006	−	0.0773220i	$-0.975363\pi$
$911$	−7.11891	−	21.9097i	−0.235860	−	0.725902i	0.761146	−	0.648580i	$-0.224637\pi$
$912$	−3.65095	−	6.32363i	−0.120895	−	0.209396i
$913$	−20.8145	+	18.4059i	−0.688860	+	0.609145i
$914$	−4.79377	+	8.30304i	−0.158564	+	0.274640i
$915$	13.5047	−	14.9985i	0.446452	−	0.495835i
$916$	82.6535	+	60.0513i	2.73095	+	1.98415i
$917$		0			0
$918$	−8.52920	+	26.2502i	−0.281506	+	0.866385i
$919$	37.2337	−	7.91426i	1.22823	−	0.261067i	0.452285	−	0.891874i	$-0.350609\pi$
$919$	37.2337	−	7.91426i	1.22823	−	0.261067i	0.775940	+	0.630806i	$0.217276\pi$
$920$	1.49007	+	14.1770i	0.0491260	+	0.467403i
$921$	7.52739	−	3.35141i	0.248036	−	0.110433i
$922$	24.2219	−	26.9012i	0.797706	−	0.885943i
$923$	9.20031			0.302832
$924$		0			0
$925$	33.8792			1.11394
$926$	−9.12302	+	10.1321i	−0.299801	+	0.332963i
$927$	−12.0045	+	5.34473i	−0.394278	+	0.175544i
$928$	0.772798	+	7.35268i	0.0253683	+	0.241363i
$929$	−17.1549	+	3.64639i	−0.562835	+	0.119634i	−0.480539	−	0.876974i	$-0.659559\pi$
$929$	−17.1549	+	3.64639i	−0.562835	+	0.119634i	−0.0822965	+	0.996608i	$0.526225\pi$
$930$	−8.92610	+	27.4717i	−0.292699	+	0.900833i
$931$		0			0
$932$	−54.1154	−	39.3171i	−1.77261	−	1.28788i
$933$	6.44720	−	7.16034i	0.211072	−	0.234419i
$934$	−30.4569	+	52.7528i	−0.996579	+	1.72613i
$935$	−20.4727	−	47.1162i	−0.669530	−	1.54086i
$936$	19.7424	+	34.1948i	0.645300	+	1.11769i
$937$	17.5395	+	53.9810i	0.572990	+	1.76348i	0.642924	+	0.765930i	$0.277721\pi$
$937$	17.5395	+	53.9810i	0.572990	+	1.76348i	−0.0699341	+	0.997552i	$0.522279\pi$
$938$		0			0
$939$	−4.87409	+	3.54123i	−0.159060	+	0.115564i
$940$	76.2854	−	16.2150i	2.48816	−	0.528874i
$941$	14.9206	+	16.5711i	0.486399	+	0.540201i	0.935522	−	0.353269i	$-0.114930\pi$
$941$	14.9206	+	16.5711i	0.486399	+	0.540201i	−0.449123	+	0.893470i	$0.648263\pi$
$942$	2.00972	+	19.1212i	0.0654802	+	0.623003i
$943$	−0.177690	+	1.69061i	−0.00578638	+	0.0550538i
$944$	−17.3894	−	53.5192i	−0.565978	−	1.74190i
$945$		0			0
$946$	11.7973	−	3.71645i	0.383565	−	0.120832i
$947$	−22.3891	−	38.7791i	−0.727548	−	1.26015i	−0.957917	−	0.287047i	$-0.907326\pi$
$947$	−22.3891	−	38.7791i	−0.727548	−	1.26015i	0.230368	−	0.973103i	$-0.426007\pi$
$948$	−17.6938	−	3.76094i	−0.574668	−	0.122150i
$949$	11.7733	−	5.24179i	0.382176	−	0.170156i
$950$	38.1865	+	17.0017i	1.23893	+	0.551609i
$951$	2.29034	−	7.04893i	0.0742692	−	0.228577i
$952$		0			0
$953$	−1.49815	+	1.08847i	−0.0485298	+	0.0352590i	−0.611786	−	0.791024i	$-0.709549\pi$
$953$	−1.49815	+	1.08847i	−0.0485298	+	0.0352590i	0.563256	+	0.826283i	$0.309549\pi$
$954$	10.1193	−	96.2784i	0.327623	−	3.11713i
$955$	−75.5814	−	16.0653i	−2.44576	−	0.519861i
$956$	−4.42058	+	7.65666i	−0.142972	+	0.247634i
$957$	−1.48527	+	0.839837i	−0.0480120	+	0.0271481i
$958$	1.11396			0.0359906
$959$		0			0
$960$	0.437359	+	0.317760i	0.0141157	+	0.0102557i
$961$	30.7253	+	13.6798i	0.991138	+	0.441283i
$962$	18.6196	+	20.6792i	0.600320	+	0.666723i
$963$	7.62005	+	8.46293i	0.245553	+	0.272714i
$964$	−3.25765	−	1.45040i	−0.104922	−	0.0467142i
$965$	9.55186	+	6.93984i	0.307485	+	0.223401i
$966$		0			0
$967$	−33.5800			−1.07986			−0.539930	−	0.841710i	$-0.681549\pi$
$967$	−33.5800			−1.07986			−0.539930	+	0.841710i	$0.681549\pi$
$968$	8.62999	−	69.9968i	0.277378	−	2.24978i
$969$	−2.24776	+	3.89324i	−0.0722085	+	0.125069i
$970$	74.5150	+	15.8387i	2.39253	+	0.508549i
$971$	4.43977	−	42.2416i	0.142479	−	1.35560i	−0.656539	−	0.754292i	$-0.727980\pi$
$971$	4.43977	−	42.2416i	0.142479	−	1.35560i	0.799019	−	0.601306i	$-0.205353\pi$
$972$	−37.4814	+	27.2318i	−1.20222	+	0.873462i
$973$		0			0
$974$	0.578575	−	1.78067i	0.0185387	−	0.0570564i
$975$	5.51345	+	2.45475i	0.176572	+	0.0786148i
$976$	−96.0821	+	42.7785i	−3.07551	+	1.36931i
$977$	−45.3202	−	9.63310i	−1.44992	−	0.308190i	−0.585383	−	0.810757i	$-0.699056\pi$
$977$	−45.3202	−	9.63310i	−1.44992	−	0.308190i	−0.864538	+	0.502567i	$0.832389\pi$
$978$	−0.197821	−	0.342636i	−0.00632562	−	0.0109563i
$979$	0.141781	−	15.7948i	0.00453133	−	0.504803i
$980$		0			0
$981$	5.37888	+	16.5545i	0.171735	+	0.528545i
$982$	−0.695555	+	6.61777i	−0.0221961	+	0.211181i
$983$	2.62269	+	24.9532i	0.0836507	+	0.795884i	0.953262	+	0.302146i	$0.0977030\pi$
$983$	2.62269	+	24.9532i	0.0836507	+	0.795884i	−0.869611	+	0.493738i	$0.835630\pi$
$984$	4.61820	+	5.12904i	0.147223	+	0.163508i
$985$	−7.31897	+	1.55570i	−0.233202	+	0.0495686i
$986$	11.6850	−	8.48962i	0.372125	−	0.270365i
$987$		0			0
$988$	7.35115	+	22.6245i	0.233871	+	0.719782i
$989$	0.473781	+	0.820613i	0.0150654	+	0.0260940i
$990$	17.8057	−	80.2217i	0.565903	−	2.54961i
$991$	−18.7823	+	32.5318i	−0.596638	+	1.03341i	0.396675	+	0.917959i	$0.370164\pi$
$991$	−18.7823	+	32.5318i	−0.596638	+	1.03341i	−0.993313	+	0.115449i	$0.963169\pi$
$992$	31.7421	−	35.2531i	1.00781	−	1.11929i
$993$	6.58716	+	4.78585i	0.209037	+	0.151874i
$994$		0			0
$995$	2.47350	−	7.61264i	0.0784151	−	0.241337i
$996$	−15.1827	+	3.22717i	−0.481081	+	0.102257i
$997$	3.74620	+	35.6427i	0.118643	+	1.12882i	0.878173	+	0.478343i	$0.158762\pi$
$997$	3.74620	+	35.6427i	0.118643	+	1.12882i	−0.759530	+	0.650472i	$0.774571\pi$
$998$	−19.2520	+	8.57155i	−0.609412	+	0.271328i
$999$	−8.03202	+	8.92046i	−0.254122	+	0.282231i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	539.2.q.f.214.4		32
7.2	even	3	inner	539.2.q.f.324.1		32
7.3	odd	6		77.2.f.b.71.4	yes	16
7.4	even	3		539.2.f.e.148.4		16
7.5	odd	6		539.2.q.g.324.1		32
7.6	odd	2		539.2.q.g.214.4		32
11.9	even	5	inner	539.2.q.f.361.1		32
21.17	even	6		693.2.m.i.379.1		16
77.3	odd	30		847.2.a.p.1.8		8
77.9	even	15	inner	539.2.q.f.471.4		32
77.10	even	6		847.2.f.x.148.1		16
77.17	even	30		847.2.f.v.323.4		16
77.20	odd	10		539.2.q.g.361.1		32
77.24	even	30		847.2.f.x.372.1		16
77.25	even	15		5929.2.a.bt.1.8		8
77.31	odd	30		77.2.f.b.64.4	✓	16
77.38	odd	30		847.2.f.w.323.1		16
77.52	even	30		847.2.a.o.1.1		8
77.53	even	15		539.2.f.e.295.4		16
77.59	odd	30		847.2.f.w.729.1		16
77.73	even	30		847.2.f.v.729.4		16
77.74	odd	30		5929.2.a.bs.1.1		8
77.75	odd	30		539.2.q.g.471.4		32
231.80	even	30		7623.2.a.ct.1.1		8
231.185	even	30		693.2.m.i.64.1		16
231.206	odd	30		7623.2.a.cw.1.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.b.64.4	✓	16	77.31	odd	30
77.2.f.b.71.4	yes	16	7.3	odd	6
539.2.f.e.148.4		16	7.4	even	3
539.2.f.e.295.4		16	77.53	even	15
539.2.q.f.214.4		32	1.1	even	1	trivial
539.2.q.f.324.1		32	7.2	even	3	inner
539.2.q.f.361.1		32	11.9	even	5	inner
539.2.q.f.471.4		32	77.9	even	15	inner
539.2.q.g.214.4		32	7.6	odd	2
539.2.q.g.324.1		32	7.5	odd	6
539.2.q.g.361.1		32	77.20	odd	10
539.2.q.g.471.4		32	77.75	odd	30
693.2.m.i.64.1		16	231.185	even	30
693.2.m.i.379.1		16	21.17	even	6
847.2.a.o.1.1		8	77.52	even	30
847.2.a.p.1.8		8	77.3	odd	30
847.2.f.v.323.4		16	77.17	even	30
847.2.f.v.729.4		16	77.73	even	30
847.2.f.w.323.1		16	77.38	odd	30
847.2.f.w.729.1		16	77.59	odd	30
847.2.f.x.148.1		16	77.10	even	6
847.2.f.x.372.1		16	77.24	even	30
5929.2.a.bs.1.1		8	77.74	odd	30
5929.2.a.bt.1.8		8	77.25	even	15
7623.2.a.ct.1.1		8	231.80	even	30
7623.2.a.cw.1.8		8	231.206	odd	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)

\(f(q)\)	\(=\)	\(q+(1.70758 - 1.89646i) q^{2} +(0.375100 - 0.167005i) q^{3} +(-0.471675 - 4.48769i) q^{4} +(3.35405 - 0.712924i) q^{5} +(0.323795 - 0.996539i) q^{6} +(-5.18703 - 3.76860i) q^{8} +(-1.89458 + 2.10415i) q^{9} +O(q^{10})\)	\(q+(1.70758 - 1.89646i) q^{2} +(0.375100 - 0.167005i) q^{3} +(-0.471675 - 4.48769i) q^{4} +(3.35405 - 0.712924i) q^{5} +(0.323795 - 0.996539i) q^{6} +(-5.18703 - 3.76860i) q^{8} +(-1.89458 + 2.10415i) q^{9} +(4.37528 - 7.57820i) q^{10} +(-2.85728 - 1.68403i) q^{11} +(-0.926394 - 1.60456i) q^{12} +(0.672122 + 2.06858i) q^{13} +(1.13904 - 0.827562i) q^{15} +(-7.17669 + 1.52545i) q^{16} +(3.02256 + 3.35690i) q^{17} +(0.755280 + 7.18601i) q^{18} +(-0.253357 + 2.41053i) q^{19} +(-4.78140 - 14.7156i) q^{20} +(-8.07274 + 2.54311i) q^{22} +(-0.324201 - 0.561533i) q^{23} +(-2.57503 - 0.547340i) q^{24} +(6.17363 - 2.74868i) q^{25} +(5.07069 + 2.25761i) q^{26} +(-0.739900 + 2.27718i) q^{27} +(1.01366 - 0.736466i) q^{29} +(0.375567 - 3.57328i) q^{30} +(-7.86378 - 1.67150i) q^{31} +(-2.95031 + 5.11008i) q^{32} +(-1.35301 - 0.154498i) q^{33} +11.5275 q^{34} +(10.3364 + 7.50983i) q^{36} +(4.57987 + 2.03909i) q^{37} +(4.13886 + 4.59667i) q^{38} +(0.597577 + 0.663676i) q^{39} +(-20.0843 - 8.94209i) q^{40} +(-2.12100 - 1.54100i) q^{41} -1.46138 q^{43} +(-6.20969 + 13.6169i) q^{44} +(-4.85442 + 8.40810i) q^{45} +(-1.61853 - 0.344029i) q^{46} +(-0.526864 + 5.01278i) q^{47} +(-2.43722 + 1.77074i) q^{48} +(5.32922 - 16.4017i) q^{50} +(1.69438 + 0.754388i) q^{51} +(8.96612 - 3.99197i) q^{52} +(-13.1053 - 2.78561i) q^{53} +(3.05514 + 5.29166i) q^{54} +(-10.7840 - 3.61128i) q^{55} +(0.307538 + 0.946503i) q^{57} +(0.334226 - 3.17994i) q^{58} +(0.801710 + 7.62777i) q^{59} +(-4.25110 - 4.72132i) q^{60} +(14.0216 - 2.98038i) q^{61} +(-16.5980 + 12.0591i) q^{62} +(0.118654 + 0.365178i) q^{64} +(3.72907 + 6.45893i) q^{65} +(-2.60337 + 2.30211i) q^{66} +(-3.11348 + 5.39271i) q^{67} +(13.6390 - 15.1477i) q^{68} +(-0.215387 - 0.156488i) q^{69} +(1.30713 - 4.02294i) q^{71} +(17.7570 - 3.77436i) q^{72} +(-0.619349 - 5.89271i) q^{73} +(11.6876 - 5.20364i) q^{74} +(1.85669 - 2.06206i) q^{75} +10.9372 q^{76} +2.27905 q^{78} +(6.53284 - 7.25546i) q^{79} +(-22.9834 + 10.2329i) q^{80} +(-0.785124 - 7.46996i) q^{81} +(-6.54424 + 1.39102i) q^{82} +(2.58881 - 7.96754i) q^{83} +(12.5310 + 9.10432i) q^{85} +(-2.49543 + 2.77145i) q^{86} +(0.257230 - 0.445535i) q^{87} +(8.47438 + 19.5031i) q^{88} +(2.38125 + 4.12444i) q^{89} +(7.65633 + 23.5637i) q^{90} +(-2.36707 + 1.71978i) q^{92} +(-3.22886 + 0.686314i) q^{93} +(8.60688 + 9.55891i) q^{94} +(0.868756 + 8.26566i) q^{95} +(-0.253250 + 2.40951i) q^{96} +(2.69021 + 8.27962i) q^{97} +(8.95679 - 2.82161i) 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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