LMFDB - Embedded newform 61.2.g.a.3.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [61,2,Mod(3,61)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(61, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("61.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	61.g (of order $10$, degree $4$, 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:	$0.487087452330$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 17x^{14} + 111x^{12} + 361x^{10} + 624x^{8} + 558x^{6} + 229x^{4} + 34x^{2} + 1 $ x^16 + 17x^14 + 111x^12 + 361x^10 + 624x^8 + 558x^6 + 229x^4 + 34*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			3.4
Root			$1.60228i$ of defining polynomial
Character	$\chi$	$=$	61.3
Dual form			61.2.g.a.41.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.52385 + 0.495130i) q^{2} +(-0.221623 + 0.682087i) q^{3} +(0.458946 + 0.333444i) q^{4} +(-1.72728 - 1.25494i) q^{5} +(-0.675444 + 0.929669i) q^{6} +(-1.05248 + 0.341973i) q^{7} +(-1.34932 - 1.85718i) q^{8} +(2.01093 + 1.46102i) q^{9} +O(q^{10})$	\(q+(1.52385 + 0.495130i) q^{2} +(-0.221623 + 0.682087i) q^{3} +(0.458946 + 0.333444i) q^{4} +(-1.72728 - 1.25494i) q^{5} +(-0.675444 + 0.929669i) q^{6} +(-1.05248 + 0.341973i) q^{7} +(-1.34932 - 1.85718i) q^{8} +(2.01093 + 1.46102i) q^{9} +(-2.01077 - 2.76758i) q^{10} +0.435796i q^{11} +(-0.329151 + 0.239142i) q^{12} +1.11430 q^{13} -1.77315 q^{14} +(1.23879 - 0.900031i) q^{15} +(-1.48722 - 4.57721i) q^{16} +(0.493346 - 0.679032i) q^{17} +(2.34096 + 3.22206i) q^{18} +(-2.55549 + 7.86500i) q^{19} +(-0.374276 - 1.15190i) q^{20} -0.793674i q^{21} +(-0.215776 + 0.664091i) q^{22} +(3.00873 - 4.14117i) q^{23} +(1.56580 - 0.508759i) q^{24} +(-0.136467 - 0.420002i) q^{25} +(1.69804 + 0.551726i) q^{26} +(-3.18287 + 2.31249i) q^{27} +(-0.597061 - 0.193997i) q^{28} +1.64759i q^{29} +(2.33336 - 0.758156i) q^{30} +(-1.59254 + 0.517447i) q^{31} -3.12017i q^{32} +(-0.297251 - 0.0965827i) q^{33} +(1.08800 - 0.790476i) q^{34} +(2.24709 + 0.730124i) q^{35} +(0.435737 + 1.34106i) q^{36} +(8.59295 - 2.79202i) q^{37} +(-7.78840 + 10.7198i) q^{38} +(-0.246956 + 0.760053i) q^{39} +4.90119i q^{40} +(-3.14061 - 9.66579i) q^{41} +(0.392972 - 1.20944i) q^{42} +(5.29215 + 7.28402i) q^{43} +(-0.145314 + 0.200007i) q^{44} +(-1.63993 - 5.04719i) q^{45} +(6.63529 - 4.82082i) q^{46} +5.01610 q^{47} +3.45166 q^{48} +(-4.67234 + 3.39466i) q^{49} -0.707592i q^{50} +(0.353822 + 0.486994i) q^{51} +(0.511406 + 0.371558i) q^{52} +(-4.38942 - 6.04152i) q^{53} +(-5.99521 + 1.94796i) q^{54} +(0.546900 - 0.752743i) q^{55} +(2.05524 + 1.49322i) q^{56} +(-4.79825 - 3.48614i) q^{57} +(-0.815773 + 2.51069i) q^{58} +(-13.0831 - 4.25094i) q^{59} +0.868645 q^{60} +(-6.95587 - 3.55189i) q^{61} -2.68300 q^{62} +(-2.61610 - 0.850021i) q^{63} +(-1.42956 + 4.39973i) q^{64} +(-1.92472 - 1.39839i) q^{65} +(-0.405146 - 0.294356i) q^{66} +(-1.72423 + 2.37320i) q^{67} +(0.452838 - 0.147136i) q^{68} +(2.15783 + 2.97000i) q^{69} +(3.06273 + 2.22521i) q^{70} +(-4.64567 - 6.39422i) q^{71} -5.70604i q^{72} +(7.02889 - 5.10679i) q^{73} +14.4768 q^{74} +0.316722 q^{75} +(-3.79537 + 2.75749i) q^{76} +(-0.149030 - 0.458669i) q^{77} +(-0.752651 + 1.03593i) q^{78} +(6.96524 + 9.58683i) q^{79} +(-3.17528 + 9.77251i) q^{80} +(1.43240 + 4.40846i) q^{81} -16.2843i q^{82} +(-1.79702 + 5.53065i) q^{83} +(0.264646 - 0.364253i) q^{84} +(-1.70429 + 0.553758i) q^{85} +(4.45793 + 13.7201i) q^{86} +(-1.12380 - 0.365145i) q^{87} +(0.809352 - 0.588029i) q^{88} +(14.5648 + 4.73239i) q^{89} -8.50317i q^{90} +(-1.17279 + 0.381062i) q^{91} +(2.76169 - 0.897328i) q^{92} -1.20093i q^{93} +(7.64381 + 2.48362i) q^{94} +(14.2842 - 10.3781i) q^{95} +(2.12823 + 0.691503i) q^{96} +(0.316525 + 0.974163i) q^{97} +(-8.80077 + 2.85954i) q^{98} +(-0.636709 + 0.876354i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 5 q^{2} - q^{3} + 3 q^{4} - 15 q^{6} + 10 q^{7} - 5 q^{8} + q^{9}+O(q^{10}) $ 16 * q - 5 * q^2 - q^3 + 3 * q^4 - 15 * q^6 + 10 * q^7 - 5 * q^8 + q^9	$ 16 q - 5 q^{2} - q^{3} + 3 q^{4} - 15 q^{6} + 10 q^{7} - 5 q^{8} + q^{9} - 5 q^{10} - 12 q^{13} - 18 q^{14} - 13 q^{15} + 19 q^{16} - 10 q^{18} + 3 q^{19} - 13 q^{20} + 19 q^{22} - 15 q^{23} + 10 q^{24} - 2 q^{25} + 10 q^{26} - 4 q^{27} + 35 q^{28} + 45 q^{30} - 15 q^{31} + 25 q^{33} - 14 q^{34} + 10 q^{35} + 37 q^{36} - 5 q^{37} - 15 q^{38} - 3 q^{39} + 12 q^{41} - 15 q^{42} - 25 q^{43} - 50 q^{44} + 36 q^{45} + 27 q^{46} + 6 q^{47} - 20 q^{48} - 30 q^{49} + 50 q^{51} - 46 q^{52} - 20 q^{53} - 20 q^{54} + 20 q^{55} - 28 q^{56} - 11 q^{57} - 41 q^{58} + 5 q^{59} + 14 q^{60} - 53 q^{61} + 16 q^{62} - 5 q^{63} + 17 q^{64} + 20 q^{65} + 13 q^{66} - 55 q^{67} + 80 q^{68} - 15 q^{69} - 17 q^{70} - 50 q^{71} - 11 q^{73} + 24 q^{74} - 88 q^{75} - 19 q^{76} + 63 q^{77} + 50 q^{78} + 40 q^{79} - 49 q^{80} - 19 q^{81} + 31 q^{83} - 25 q^{84} + 55 q^{85} + 35 q^{86} + 25 q^{87} + 27 q^{88} + 60 q^{89} - 15 q^{91} - 5 q^{92} + 65 q^{94} + 48 q^{95} - 25 q^{96} + 45 q^{97} + 10 q^{98} - 5 q^{99}+O(q^{100}) $ 16 * q - 5 * q^2 - q^3 + 3 * q^4 - 15 * q^6 + 10 * q^7 - 5 * q^8 + q^9 - 5 * q^10 - 12 * q^13 - 18 * q^14 - 13 * q^15 + 19 * q^16 - 10 * q^18 + 3 * q^19 - 13 * q^20 + 19 * q^22 - 15 * q^23 + 10 * q^24 - 2 * q^25 + 10 * q^26 - 4 * q^27 + 35 * q^28 + 45 * q^30 - 15 * q^31 + 25 * q^33 - 14 * q^34 + 10 * q^35 + 37 * q^36 - 5 * q^37 - 15 * q^38 - 3 * q^39 + 12 * q^41 - 15 * q^42 - 25 * q^43 - 50 * q^44 + 36 * q^45 + 27 * q^46 + 6 * q^47 - 20 * q^48 - 30 * q^49 + 50 * q^51 - 46 * q^52 - 20 * q^53 - 20 * q^54 + 20 * q^55 - 28 * q^56 - 11 * q^57 - 41 * q^58 + 5 * q^59 + 14 * q^60 - 53 * q^61 + 16 * q^62 - 5 * q^63 + 17 * q^64 + 20 * q^65 + 13 * q^66 - 55 * q^67 + 80 * q^68 - 15 * q^69 - 17 * q^70 - 50 * q^71 - 11 * q^73 + 24 * q^74 - 88 * q^75 - 19 * q^76 + 63 * q^77 + 50 * q^78 + 40 * q^79 - 49 * q^80 - 19 * q^81 + 31 * q^83 - 25 * q^84 + 55 * q^85 + 35 * q^86 + 25 * q^87 + 27 * q^88 + 60 * q^89 - 15 * q^91 - 5 * q^92 + 65 * q^94 + 48 * q^95 - 25 * q^96 + 45 * q^97 + 10 * q^98 - 5 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/61\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{10}\right)$

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 $

$2$	1.52385	+	0.495130i	1.07753	+	0.350110i	0.793415	−	0.608681i	$-0.208301\pi$
$2$	1.52385	+	0.495130i	1.07753	+	0.350110i	0.284113	+	0.958791i	$0.408301\pi$
$3$	−0.221623	+	0.682087i	−0.127954	+	0.393803i	−0.994428	−	0.105420i	$-0.966381\pi$
$3$	−0.221623	+	0.682087i	−0.127954	+	0.393803i	0.866473	+	0.499223i	$0.166381\pi$
$4$	0.458946	+	0.333444i	0.229473	+	0.166722i
$5$	−1.72728	−	1.25494i	−0.772464	−	0.561228i	0.130244	−	0.991482i	$-0.458424\pi$
$5$	−1.72728	−	1.25494i	−0.772464	−	0.561228i	−0.902708	+	0.430254i	$0.858424\pi$
$6$	−0.675444	+	0.929669i	−0.275749	+	0.379536i
$7$	−1.05248	+	0.341973i	−0.397801	+	0.129253i	−0.501084	−	0.865399i	$-0.667065\pi$
$7$	−1.05248	+	0.341973i	−0.397801	+	0.129253i	0.103283	+	0.994652i	$0.467065\pi$
$8$	−1.34932	−	1.85718i	−0.477057	−	0.656612i
$9$	2.01093	+	1.46102i	0.670308	+	0.487008i
$10$	−2.01077	−	2.76758i	−0.635860	−	0.875186i
$11$			0.435796i			0.131398i	0.997840	+	0.0656988i	$0.0209276\pi$
$11$			0.435796i			0.131398i	−0.997840	+	0.0656988i	$0.979072\pi$
$12$	−0.329151	+	0.239142i	−0.0950176	+	0.0690343i
$13$	1.11430			0.309053			0.154526	−	0.987989i	$-0.450615\pi$
$13$	1.11430			0.309053			0.154526	+	0.987989i	$0.450615\pi$
$14$	−1.77315			−0.473895
$15$	1.23879	−	0.900031i	0.319853	−	0.232387i
$16$	−1.48722	−	4.57721i	−0.371806	−	1.14430i
$17$	0.493346	−	0.679032i	0.119654	−	0.164689i	−0.744988	−	0.667077i	$-0.767545\pi$
$17$	0.493346	−	0.679032i	0.119654	−	0.164689i	0.864642	+	0.502388i	$0.167545\pi$
$18$	2.34096	+	3.22206i	0.551770	+	0.759446i
$19$	−2.55549	+	7.86500i	−0.586270	+	1.80435i	0.00783887	+	0.999969i	$0.497505\pi$
$19$	−2.55549	+	7.86500i	−0.586270	+	1.80435i	−0.594109	+	0.804385i	$0.702495\pi$
$20$	−0.374276	−	1.15190i	−0.0836906	−	0.257573i
$21$		−	0.793674i		−	0.173194i
$22$	−0.215776	+	0.664091i	−0.0460036	+	0.141585i
$23$	3.00873	−	4.14117i	0.627364	−	0.863493i	−0.370499	−	0.928833i	$-0.620813\pi$
$23$	3.00873	−	4.14117i	0.627364	−	0.863493i	0.997863	+	0.0653402i	$0.0208133\pi$
$24$	1.56580	−	0.508759i	0.319617	−	0.103850i
$25$	−0.136467	−	0.420002i	−0.0272934	−	0.0840005i
$26$	1.69804	+	0.551726i	0.333013	+	0.108202i
$27$	−3.18287	+	2.31249i	−0.612543	+	0.445038i
$28$	−0.597061	−	0.193997i	−0.112834	−	0.0366620i
$29$			1.64759i			0.305950i	0.988230	+	0.152975i	$0.0488854\pi$
$29$			1.64759i			0.305950i	−0.988230	+	0.152975i	$0.951115\pi$
$30$	2.33336	−	0.758156i	0.426012	−	0.138420i
$31$	−1.59254	+	0.517447i	−0.286028	+	0.0929362i	−0.448517	−	0.893774i	$-0.648048\pi$
$31$	−1.59254	+	0.517447i	−0.286028	+	0.0929362i	0.162489	+	0.986710i	$0.448048\pi$
$32$		−	3.12017i		−	0.551574i
$33$	−0.297251	−	0.0965827i	−0.0517448	−	0.0168129i
$34$	1.08800	−	0.790476i	0.186590	−	0.135565i
$35$	2.24709	+	0.730124i	0.379828	+	0.123414i
$36$	0.435737	+	1.34106i	0.0726228	+	0.223510i
$37$	8.59295	−	2.79202i	1.41267	−	0.459005i	0.499406	−	0.866368i	$-0.333552\pi$
$37$	8.59295	−	2.79202i	1.41267	−	0.459005i	0.913266	+	0.407363i	$0.133552\pi$
$38$	−7.78840	+	10.7198i	−1.26345	+	1.73898i
$39$	−0.246956	+	0.760053i	−0.0395446	+	0.121706i
$40$			4.90119i			0.774946i
$41$	−3.14061	−	9.66579i	−0.490480	−	1.50954i	−0.823884	−	0.566759i	$-0.808197\pi$
$41$	−3.14061	−	9.66579i	−0.490480	−	1.50954i	0.333404	−	0.942784i	$-0.391803\pi$
$42$	0.392972	−	1.20944i	0.0606370	−	0.186621i
$43$	5.29215	+	7.28402i	0.807045	+	1.11080i	0.991773	+	0.128013i	$0.0408599\pi$
$43$	5.29215	+	7.28402i	0.807045	+	1.11080i	−0.184727	+	0.982790i	$0.559140\pi$
$44$	−0.145314	+	0.200007i	−0.0219068	+	0.0301522i
$45$	−1.63993	−	5.04719i	−0.244467	−	0.752391i
$46$	6.63529	−	4.82082i	0.978320	−	0.710791i
$47$	5.01610			0.731674			0.365837	−	0.930679i	$-0.380783\pi$
$47$	5.01610			0.731674			0.365837	+	0.930679i	$0.380783\pi$
$48$	3.45166			0.498204
$49$	−4.67234	+	3.39466i	−0.667478	+	0.484951i
$50$		−	0.707592i		−	0.100069i
$51$	0.353822	+	0.486994i	0.0495450	+	0.0681928i
$52$	0.511406	+	0.371558i	0.0709192	+	0.0515258i
$53$	−4.38942	−	6.04152i	−0.602933	−	0.829866i	0.393040	−	0.919521i	$-0.371423\pi$
$53$	−4.38942	−	6.04152i	−0.602933	−	0.829866i	−0.995973	+	0.0896553i	$0.971423\pi$
$54$	−5.99521	+	1.94796i	−0.815845	+	0.265084i
$55$	0.546900	−	0.752743i	0.0737440	−	0.101500i
$56$	2.05524	+	1.49322i	0.274643	+	0.199540i
$57$	−4.79825	−	3.48614i	−0.635544	−	0.461750i
$58$	−0.815773	+	2.51069i	−0.107116	+	0.329670i
$59$	−13.0831	−	4.25094i	−1.70327	−	0.553425i	−0.714078	−	0.700066i	$-0.753154\pi$
$59$	−13.0831	−	4.25094i	−1.70327	−	0.553425i	−0.989190	+	0.146640i	$0.953154\pi$
$60$	0.868645			0.112142
$61$	−6.95587	−	3.55189i	−0.890608	−	0.454773i
$61$	−6.95587	−	3.55189i	−0.890608	−	0.454773i
$62$	−2.68300			−0.340741
$63$	−2.61610	−	0.850021i	−0.329597	−	0.107093i
$64$	−1.42956	+	4.39973i	−0.178695	+	0.549966i
$65$	−1.92472	−	1.39839i	−0.238732	−	0.173449i
$66$	−0.405146	−	0.294356i	−0.0498701	−	0.0362327i
$67$	−1.72423	+	2.37320i	−0.210648	+	0.289932i	−0.901247	−	0.433306i	$-0.857347\pi$
$67$	−1.72423	+	2.37320i	−0.210648	+	0.289932i	0.690599	+	0.723238i	$0.257347\pi$
$68$	0.452838	−	0.147136i	0.0549146	−	0.0178429i
$69$	2.15783	+	2.97000i	0.259772	+	0.357546i
$70$	3.06273	+	2.22521i	0.366067	+	0.265963i
$71$	−4.64567	−	6.39422i	−0.551340	−	0.758854i	0.438853	−	0.898559i	$-0.355385\pi$
$71$	−4.64567	−	6.39422i	−0.551340	−	0.758854i	−0.990193	+	0.139704i	$0.955385\pi$
$72$		−	5.70604i		−	0.672463i
$73$	7.02889	−	5.10679i	0.822669	−	0.597704i	−0.0948067	−	0.995496i	$-0.530223\pi$
$73$	7.02889	−	5.10679i	0.822669	−	0.597704i	0.917476	+	0.397792i	$0.130223\pi$
$74$	14.4768			1.68290
$75$	0.316722			0.0365720
$76$	−3.79537	+	2.75749i	−0.435358	+	0.316306i
$77$	−0.149030	−	0.458669i	−0.0169836	−	0.0522701i
$78$	−0.752651	+	1.03593i	−0.0852209	+	0.117297i
$79$	6.96524	+	9.58683i	0.783651	+	1.07860i	0.994870	+	0.101164i	$0.0322567\pi$
$79$	6.96524	+	9.58683i	0.783651	+	1.07860i	−0.211219	+	0.977439i	$0.567743\pi$
$80$	−3.17528	+	9.77251i	−0.355007	+	1.09260i
$81$	1.43240	+	4.40846i	0.159155	+	0.489829i
$82$		−	16.2843i		−	1.79830i
$83$	−1.79702	+	5.53065i	−0.197248	+	0.607067i	0.802695	+	0.596390i	$0.203399\pi$
$83$	−1.79702	+	5.53065i	−0.197248	+	0.607067i	−0.999943	+	0.0106774i	$0.996601\pi$
$84$	0.264646	−	0.364253i	0.0288752	−	0.0397433i
$85$	−1.70429	+	0.553758i	−0.184857	+	0.0600635i
$86$	4.45793	+	13.7201i	0.480711	+	1.47948i
$87$	−1.12380	−	0.365145i	−0.120484	−	0.0391477i
$88$	0.809352	−	0.588029i	0.0862772	−	0.0626841i
$89$	14.5648	+	4.73239i	1.54386	+	0.501632i	0.952439	−	0.304728i	$-0.0985655\pi$
$89$	14.5648	+	4.73239i	1.54386	+	0.501632i	0.591425	+	0.806360i	$0.298566\pi$
$90$		−	8.50317i		−	0.896313i
$91$	−1.17279	+	0.381062i	−0.122942	+	0.0399461i
$92$	2.76169	−	0.897328i	0.287926	−	0.0935529i
$93$		−	1.20093i		−	0.124530i
$94$	7.64381	+	2.48362i	0.788399	+	0.256166i
$95$	14.2842	−	10.3781i	1.46553	−	1.06477i
$96$	2.12823	+	0.691503i	0.217211	+	0.0705762i
$97$	0.316525	+	0.974163i	0.0321382	+	0.0989112i	0.965839	−	0.259143i	$-0.0834402\pi$
$97$	0.316525	+	0.974163i	0.0321382	+	0.0989112i	−0.933701	+	0.358055i	$0.883440\pi$
$98$	−8.80077	+	2.85954i	−0.889012	+	0.288858i
$99$	−0.636709	+	0.876354i	−0.0639916	+	0.0880769i
$100$	0.0774161	−	0.238262i	0.00774161	−	0.0238262i
$101$			12.3838i			1.23223i	0.787654	+	0.616117i	$0.211295\pi$
$101$			12.3838i			1.23223i	−0.787654	+	0.616117i	$0.788705\pi$
$102$	0.298048	+	0.917296i	0.0295111	+	0.0908259i
$103$	1.13583	−	3.49572i	0.111917	−	0.344444i	−0.879375	−	0.476130i	$-0.842039\pi$
$103$	1.13583	−	3.49572i	0.111917	−	0.344444i	0.991291	+	0.131686i	$0.0420392\pi$
$104$	−1.50355	−	2.06946i	−0.147436	−	0.202928i
$105$	−0.996016	+	1.37090i	−0.0972012	+	0.133786i
$106$	−3.69750	−	11.3797i	−0.359133	−	1.10530i
$107$	6.29282	−	4.57200i	0.608350	−	0.441992i	−0.240483	−	0.970653i	$-0.577306\pi$
$107$	6.29282	−	4.57200i	0.608350	−	0.441992i	0.848833	+	0.528661i	$0.177306\pi$
$108$	−2.23185			−0.214760
$109$	−10.7859			−1.03310			−0.516549	−	0.856257i	$-0.672784\pi$
$109$	−10.7859			−1.03310			−0.516549	+	0.856257i	$0.672784\pi$
$110$	1.20610	−	0.876284i	0.114997	−	0.0835504i
$111$			6.47992i			0.615046i
$112$	3.13056	+	4.30884i	0.295810	+	0.407148i
$113$	7.86692	+	5.71565i	0.740057	+	0.537683i	0.892729	−	0.450594i	$-0.148788\pi$
$113$	7.86692	+	5.71565i	0.740057	+	0.537683i	−0.152672	+	0.988277i	$0.548788\pi$
$114$	−5.58575	−	7.68813i	−0.523154	−	0.720059i
$115$	−10.3939	+	3.37717i	−0.969232	+	0.314923i
$116$	−0.549379	+	0.756155i	−0.0510086	+	0.0702073i
$117$	2.24078	+	1.62802i	0.207161	+	0.150511i
$118$	−17.8319	−	12.9556i	−1.64156	−	1.19266i
$119$	−0.287028	+	0.883381i	−0.0263118	+	0.0809794i
$120$	−3.34304	−	1.08622i	−0.305176	−	0.0991578i
$121$	10.8101			0.982735
$122$	−8.84109	−	8.85662i	−0.800434	−	0.801841i
$123$	7.28894			0.657222
$124$	−0.903428	−	0.293542i	−0.0811302	−	0.0263608i
$125$	−3.59018	+	11.0494i	−0.321115	+	0.988291i
$126$	−3.56568	−	2.59062i	−0.317656	−	0.230791i
$127$	−8.99964	−	6.53862i	−0.798589	−	0.580209i	0.111911	−	0.993718i	$-0.464303\pi$
$127$	−8.99964	−	6.53862i	−0.798589	−	0.580209i	−0.910500	+	0.413510i	$0.864303\pi$
$128$	−8.02486	+	11.0453i	−0.709304	+	0.976273i
$129$	−6.14120	+	1.99540i	−0.540702	+	0.175685i
$130$	−2.24061	−	3.08393i	−0.196514	−	0.270478i
$131$	−1.92061	−	1.39541i	−0.167805	−	0.121917i	0.500713	−	0.865613i	$-0.333071\pi$
$131$	−1.92061	−	1.39541i	−0.167805	−	0.121917i	−0.668518	+	0.743696i	$0.733071\pi$
$132$	−0.104217	−	0.143443i	−0.00907095	−	0.0124851i
$133$		−	9.15169i		−	0.793552i
$134$	−3.80252	+	2.76269i	−0.328488	+	0.238660i
$135$	8.39975			0.722935
$136$	−1.92676			−0.165219
$137$	−10.5095	+	7.63559i	−0.897886	+	0.652352i	−0.937922	−	0.346846i	$-0.887253\pi$
$137$	−10.5095	+	7.63559i	−0.897886	+	0.652352i	0.0400360	+	0.999198i	$0.487253\pi$
$138$	1.81768	+	5.59425i	0.154731	+	0.476214i
$139$	−2.05824	+	2.83293i	−0.174578	+	0.240286i	−0.887335	−	0.461125i	$-0.847446\pi$
$139$	−2.05824	+	2.83293i	−0.174578	+	0.240286i	0.712758	+	0.701411i	$0.247446\pi$
$140$	0.787838	+	1.08437i	0.0665844	+	0.0916456i
$141$	−1.11169	+	3.42142i	−0.0936208	+	0.288135i
$142$	−3.91336	−	12.0441i	−0.328402	−	1.01072i
$143$			0.485610i			0.0406088i
$144$	3.69671	−	11.3773i	0.308059	−	0.948108i
$145$	2.06763	−	2.84585i	0.171708	−	0.236335i
$146$	13.2395	−	4.30178i	1.09571	−	0.356018i
$147$	−1.27995	−	3.93928i	−0.105568	−	0.324906i
$148$	4.87468	+	1.58388i	0.400696	+	0.130194i
$149$	12.2525	−	8.90194i	1.00376	−	0.729276i	0.0408703	−	0.999164i	$-0.486987\pi$
$149$	12.2525	−	8.90194i	1.00376	−	0.729276i	0.962891	+	0.269889i	$0.0869870\pi$
$150$	0.482639	+	0.156819i	0.0394073	+	0.0128042i
$151$			9.08595i			0.739404i	0.929150	+	0.369702i	$0.120540\pi$
$151$			9.08595i			0.739404i	−0.929150	+	0.369702i	$0.879460\pi$
$152$	18.0549	−	5.86639i	1.46444	−	0.475827i
$153$	1.98416	−	0.644693i	0.160410	−	0.0521204i
$154$		−	0.772734i		−	0.0622687i
$155$	3.40013	+	1.10477i	0.273105	+	0.0887371i
$156$	−0.366774	+	0.266477i	−0.0293654	+	0.0213352i
$157$	4.81158	+	1.56338i	0.384006	+	0.124771i	0.494657	−	0.869088i	$-0.335294\pi$
$157$	4.81158	+	1.56338i	0.384006	+	0.124771i	−0.110651	+	0.993859i	$0.535294\pi$
$158$	5.86728	+	18.0576i	0.466776	+	1.43659i
$159$	5.09364	−	1.65502i	0.403952	−	0.131252i
$160$	−3.91564	+	5.38941i	−0.309558	+	0.426071i
$161$	−1.75048	+	5.38741i	−0.137957	+	0.424588i
$162$			7.42708i			0.583526i
$163$	−6.93430	−	21.3416i	−0.543136	−	1.67160i	−0.725381	−	0.688348i	$-0.758336\pi$
$163$	−6.93430	−	21.3416i	−0.543136	−	1.67160i	0.182244	−	0.983253i	$-0.441664\pi$
$164$	1.78163	−	5.48329i	0.139122	−	0.428173i
$165$	0.392230	+	0.539859i	0.0305351	+	0.0420279i
$166$	−5.47678	+	7.53815i	−0.425081	+	0.585074i
$167$	−0.909108	−	2.79795i	−0.0703489	−	0.216512i	0.909701	−	0.415264i	$-0.136311\pi$
$167$	−0.909108	−	2.79795i	−0.0703489	−	0.216512i	−0.980050	+	0.198753i	$0.936311\pi$
$168$	−1.47400	+	1.07092i	−0.113721	+	0.0826233i
$169$	−11.7583			−0.904487
$170$	−2.87128			−0.220217
$171$	−16.6298	+	12.0823i	−1.27172	+	0.923956i
$172$			5.10760i			0.389451i
$173$	2.41530	+	3.32437i	0.183632	+	0.252747i	0.890902	−	0.454196i	$-0.150073\pi$
$173$	2.41530	+	3.32437i	0.183632	+	0.252747i	−0.707270	+	0.706944i	$0.750073\pi$
$174$	−1.53172	−	1.11286i	−0.116119	−	0.0843654i
$175$	0.287259	+	0.395378i	0.0217147	+	0.0298877i
$176$	1.99473	−	0.648127i	0.150358	−	0.0488544i
$177$	5.79902	−	7.98167i	0.435881	−	0.599939i
$178$	19.8515	+	14.4229i	1.48793	+	1.08105i
$179$	7.11717	+	5.17093i	0.531962	+	0.386493i	0.821091	−	0.570797i	$-0.193366\pi$
$179$	7.11717	+	5.17093i	0.531962	+	0.386493i	−0.289129	+	0.957290i	$0.593366\pi$
$180$	0.930315	−	2.86321i	0.0693416	−	0.213411i
$181$	13.1673	+	4.27832i	0.978718	+	0.318005i	0.754330	−	0.656495i	$-0.227962\pi$
$181$	13.1673	+	4.27832i	0.978718	+	0.318005i	0.224388	+	0.974500i	$0.427962\pi$
$182$	−1.97583			−0.146458
$183$	3.96428	−	3.95732i	0.293048	−	0.292534i
$184$	−11.7506			−0.866268
$185$	−18.3463	−	5.96106i	−1.34884	−	0.438266i
$186$	0.594616	−	1.83004i	0.0435994	−	0.134185i
$187$	0.295920	+	0.214998i	0.0216398	+	0.0157222i
$188$	2.30212	+	1.67259i	0.167899	+	0.121986i
$189$	2.55911	−	3.52231i	0.186148	−	0.256210i
$190$	26.9055	−	8.74213i	1.95193	−	0.634221i
$191$	1.00316	+	1.38073i	0.0725862	+	0.0999064i	0.843766	−	0.536711i	$-0.180333\pi$
$191$	1.00316	+	1.38073i	0.0725862	+	0.0999064i	−0.771180	+	0.636617i	$0.780333\pi$
$192$	−2.68417	−	1.95017i	−0.193713	−	0.140741i
$193$	−0.258171	−	0.355342i	−0.0185835	−	0.0255780i	0.799624	−	0.600501i	$-0.205032\pi$
$193$	−0.258171	−	0.355342i	−0.0185835	−	0.0255780i	−0.818208	+	0.574923i	$0.805032\pi$
$194$			1.64120i			0.117832i
$195$	1.38039	−	1.00291i	0.0988515	−	0.0718198i
$196$	−3.27628			−0.234020
$197$	−20.9868			−1.49525			−0.747624	−	0.664123i	$-0.768805\pi$
$197$	−20.9868			−1.49525			−0.747624	+	0.664123i	$0.768805\pi$
$198$	−1.40416	+	1.02018i	−0.0997894	+	0.0725012i
$199$	−0.848783	−	2.61229i	−0.0601687	−	0.185180i	0.916454	−	0.400139i	$-0.131038\pi$
$199$	−0.848783	−	2.61229i	−0.0601687	−	0.185180i	−0.976623	+	0.214959i	$0.931038\pi$
$200$	−0.595882	+	0.820161i	−0.0421352	+	0.0579941i
$201$	−1.23660	−	1.70203i	−0.0872229	−	0.120052i
$202$	−6.13160	+	18.8711i	−0.431418	+	1.32777i
$203$	−0.563431	−	1.73406i	−0.0395451	−	0.121707i
$204$			0.341483i			0.0239086i
$205$	−6.70531	+	20.6368i	−0.468319	+	1.44134i
$206$	3.46168	−	4.76459i	0.241186	−	0.331965i
$207$	12.1007	−	3.93175i	0.841055	−	0.273275i
$208$	−1.65722	−	5.10040i	−0.114908	−	0.353649i
$209$	−3.42754	−	1.11367i	−0.237088	−	0.0770345i
$210$	−2.19656	+	1.59589i	−0.151577	+	0.110127i
$211$	3.41637	+	1.11004i	0.235192	+	0.0764186i	0.424242	−	0.905549i	$-0.360541\pi$
$211$	3.41637	+	1.11004i	0.235192	+	0.0764186i	−0.189049	+	0.981968i	$0.560541\pi$
$212$		−	4.23635i		−	0.290954i
$213$	5.39100	−	1.75164i	0.369385	−	0.120021i
$214$	11.8531	−	3.85130i	0.810260	−	0.263270i
$215$		−	19.2229i		−	1.31099i
$216$	8.58941	+	2.79087i	0.584435	+	0.189894i
$217$	1.49917	−	1.08921i	0.101770	−	0.0739403i
$218$	−16.4361	−	5.34041i	−1.11319	−	0.361698i
$219$	1.92551	+	5.92610i	0.130114	+	0.400448i
$220$	0.501995	−	0.163108i	0.0338445	−	0.0109967i
$221$	0.549737	−	0.756649i	0.0369793	−	0.0508977i
$222$	−3.20840	+	9.87445i	−0.215334	+	0.662730i
$223$		−	23.1292i		−	1.54885i	−0.632668	−	0.774423i	$-0.718040\pi$
$223$		−	23.1292i		−	1.54885i	0.632668	−	0.774423i	$-0.281960\pi$
$224$	1.06701	+	3.28393i	0.0712928	+	0.219417i
$225$	0.339208	−	1.04397i	0.0226139	−	0.0695983i
$226$	9.15805	+	12.6050i	0.609184	+	0.838470i
$227$	−0.565833	+	0.778802i	−0.0375556	+	0.0516909i	−0.827382	−	0.561640i	$-0.810171\pi$
$227$	−0.565833	+	0.778802i	−0.0375556	+	0.0516909i	0.789826	+	0.613331i	$0.210171\pi$
$228$	−1.03971	−	3.19989i	−0.0688564	−	0.211918i
$229$	6.72236	−	4.88408i	0.444226	−	0.322749i	−0.343086	−	0.939304i	$-0.611472\pi$
$229$	6.72236	−	4.88408i	0.444226	−	0.322749i	0.787312	+	0.616555i	$0.211472\pi$
$230$	−17.5109			−1.15463
$231$	0.345880			0.0227573
$232$	3.05987	−	2.22313i	0.200891	−	0.145956i
$233$			11.8626i			0.777146i	0.921418	+	0.388573i	$0.127032\pi$
$233$			11.8626i			0.777146i	−0.921418	+	0.388573i	$0.872968\pi$
$234$	2.60854	+	3.59035i	0.170526	+	0.234709i
$235$	−8.66422	−	6.29492i	−0.565191	−	0.410635i
$236$	−4.58696	−	6.31341i	−0.298586	−	0.410968i
$237$	−8.08271	+	2.62623i	−0.525029	+	0.170592i
$238$	−0.874777	+	1.20403i	−0.0567034	+	0.0780455i
$239$	−11.7212	−	8.51594i	−0.758181	−	0.550851i	0.140171	−	0.990127i	$-0.455235\pi$
$239$	−11.7212	−	8.51594i	−0.758181	−	0.550851i	−0.898352	+	0.439277i	$0.855235\pi$
$240$	−5.96198	−	4.33163i	−0.384844	−	0.279606i
$241$	1.80897	−	5.56743i	0.116526	−	0.358629i	−0.875736	−	0.482789i	$-0.839624\pi$
$241$	1.80897	−	5.56743i	0.116526	−	0.358629i	0.992262	+	0.124160i	$0.0396236\pi$
$242$	16.4730	+	5.35240i	1.05892	+	0.344065i
$243$	−15.1271			−0.970405
$244$	−2.00801	−	3.94951i	−0.128550	−	0.252842i
$245$	12.3306			0.787770
$246$	11.1073	+	3.60898i	0.708175	+	0.230100i
$247$	−2.84760	+	8.76400i	−0.181188	+	0.557640i
$248$	3.10983	+	2.25943i	0.197475	+	0.143474i
$249$	−3.37412	−	2.45144i	−0.213826	−	0.155354i
$250$	−10.9418	+	15.0601i	−0.692021	+	0.952485i
$251$	1.49203	−	0.484789i	0.0941760	−	0.0305996i	−0.261550	−	0.965190i	$-0.584234\pi$
$251$	1.49203	−	0.484789i	0.0941760	−	0.0305996i	0.355726	+	0.934590i	$0.384234\pi$
$252$	−0.917212	−	1.26243i	−0.0577789	−	0.0795259i
$253$	1.80471	+	1.31120i	0.113461	+	0.0824341i
$254$	−10.4767	−	14.4199i	−0.657365	−	0.904785i
$255$		−	1.28520i		−	0.0804825i
$256$	−10.2123	+	7.41968i	−0.638269	+	0.463730i
$257$	12.3055			0.767594			0.383797	−	0.923417i	$-0.374616\pi$
$257$	12.3055			0.767594			0.383797	+	0.923417i	$0.374616\pi$
$258$	−10.3463			−0.644131
$259$	−8.08914	+	5.87711i	−0.502635	+	0.365186i
$260$	−0.417057	−	1.28357i	−0.0258648	−	0.0796036i
$261$	−2.40717	+	3.31318i	−0.149000	+	0.205081i
$262$	−2.23583	−	3.07736i	−0.138130	−	0.190120i
$263$	5.79551	−	17.8367i	0.357366	−	1.09986i	−0.597259	−	0.802049i	$-0.703743\pi$
$263$	5.79551	−	17.8367i	0.357366	−	1.09986i	0.954625	−	0.297811i	$-0.0962566\pi$
$264$	0.221715	+	0.682369i	0.0136456	+	0.0419969i
$265$			15.9439i			0.979424i
$266$	4.53128	−	13.9458i	0.277831	−	0.855074i
$267$	−6.45580	+	8.88564i	−0.395088	+	0.543793i
$268$	−1.58266	+	0.514236i	−0.0966761	+	0.0314120i
$269$	−5.28029	−	16.2511i	−0.321945	−	0.990845i	−0.972801	−	0.231644i	$-0.925590\pi$
$269$	−5.28029	−	16.2511i	−0.321945	−	0.990845i	0.650856	−	0.759202i	$-0.274410\pi$
$270$	12.8000	+	4.15897i	0.778983	+	0.253107i
$271$	8.46337	−	6.14900i	0.514113	−	0.373525i	−0.300268	−	0.953855i	$-0.597076\pi$
$271$	8.46337	−	6.14900i	0.514113	−	0.373525i	0.814382	+	0.580330i	$0.197076\pi$
$272$	−3.84179	−	1.24827i	−0.232942	−	0.0756876i
$273$		−	0.884395i		−	0.0535260i
$274$	−19.7955	+	6.43196i	−1.19589	+	0.388569i
$275$	0.183036	−	0.0594718i	0.0110375	−	0.00358629i
$276$			2.08258i			0.125357i
$277$	7.83596	+	2.54606i	0.470817	+	0.152978i	0.534810	−	0.844973i	$-0.320383\pi$
$277$	7.83596	+	2.54606i	0.470817	+	0.152978i	−0.0639923	+	0.997950i	$0.520383\pi$
$278$	−4.53913	+	3.29787i	−0.272239	+	0.197793i
$279$	−3.95848	−	1.28619i	−0.236988	−	0.0770020i
$280$	−1.67607	−	5.15842i	−0.100165	−	0.308275i
$281$	−11.6371	+	3.78113i	−0.694213	+	0.225564i	−0.634807	−	0.772670i	$-0.718921\pi$
$281$	−11.6371	+	3.78113i	−0.694213	+	0.225564i	−0.0594058	+	0.998234i	$0.518921\pi$
$282$	−3.38810	+	4.66331i	−0.201758	+	0.277696i
$283$	6.58796	−	20.2757i	0.391614	−	1.20526i	−0.539954	−	0.841695i	$-0.681558\pi$
$283$	6.58796	−	20.2757i	0.391614	−	1.20526i	0.931568	−	0.363568i	$-0.118442\pi$
$284$		−	4.48367i		−	0.266057i
$285$	3.91303	+	12.0431i	0.231788	+	0.713370i
$286$	−0.240440	+	0.739999i	−0.0142175	+	0.0437571i
$287$	6.61087	+	9.09908i	0.390227	+	0.537102i
$288$	4.55864	−	6.27443i	0.268621	−	0.369724i
$289$	5.03559	+	15.4980i	0.296211	+	0.911645i
$290$	4.55984	−	3.31292i	0.267763	−	0.194541i
$291$	−0.734613			−0.0430638
$292$	4.92870			0.288431
$293$	0.629090	−	0.457061i	0.0367519	−	0.0267018i	−0.569258	−	0.822159i	$-0.692769\pi$
$293$	0.629090	−	0.457061i	0.0367519	−	0.0267018i	0.606010	+	0.795457i	$0.292769\pi$
$294$		−	6.63663i		−	0.387056i
$295$	17.2634	+	23.7611i	1.00512	+	1.38342i
$296$	−16.7799	−	12.1913i	−0.975313	−	0.708606i
$297$	−1.00777	−	1.38708i	−0.0584770	−	0.0804866i
$298$	23.0786	−	7.49870i	1.33691	−	0.434388i
$299$	3.35265	−	4.61452i	0.193889	−	0.266865i
$300$	0.145358	+	0.105609i	0.00839227	+	0.00609734i
$301$	−8.06084	−	5.85654i	−0.464619	−	0.337565i
$302$	−4.49873	+	13.8457i	−0.258873	+	0.796729i
$303$	−8.44683	−	2.74454i	−0.485258	−	0.157670i
$304$	39.8003			2.28270
$305$	7.55732	+	14.8643i	0.432731	+	0.851129i
$306$	3.34278			0.191094
$307$	26.3751	+	8.56979i	1.50531	+	0.489104i	0.941560	−	0.336844i	$-0.109359\pi$
$307$	26.3751	+	8.56979i	1.50531	+	0.489104i	0.563747	+	0.825948i	$0.309359\pi$
$308$	0.0845432	−	0.260197i	0.00481730	−	0.0148261i
$309$	2.13266	+	1.54947i	0.121323	+	0.0881461i
$310$	4.63430	+	3.36701i	0.263210	+	0.191234i
$311$	10.0444	−	13.8250i	0.569567	−	0.783942i	−0.422936	−	0.906160i	$-0.639000\pi$
$311$	10.0444	−	13.8250i	0.569567	−	0.783942i	0.992503	+	0.122217i	$0.0390005\pi$
$312$	1.74478	−	0.566912i	0.0987785	−	0.0320951i
$313$	2.28118	+	3.13977i	0.128940	+	0.177470i	0.868606	−	0.495504i	$-0.165017\pi$
$313$	2.28118	+	3.13977i	0.128940	+	0.177470i	−0.739666	+	0.672974i	$0.765017\pi$
$314$	6.55807	+	4.76472i	0.370094	+	0.268889i
$315$	3.45200	+	4.75128i	0.194498	+	0.267704i
$316$			6.72235i			0.378162i
$317$	−23.7090	+	17.2256i	−1.33163	+	0.967486i	−0.331923	+	0.943306i	$0.607697\pi$
$317$	−23.7090	+	17.2256i	−1.33163	+	0.967486i	−0.999708	+	0.0241800i	$0.992303\pi$
$318$	8.58142			0.481222
$319$	−0.718015			−0.0402011
$320$	7.99066	−	5.80555i	0.446691	−	0.324540i
$321$	1.72387	+	5.30551i	0.0962168	+	0.296125i
$322$	−5.33494	+	7.34292i	−0.297305	+	0.409205i
$323$	4.07984	+	5.61542i	0.227009	+	0.312450i
$324$	−0.812581	+	2.50087i	−0.0451434	+	0.138937i
$325$	−0.152066	−	0.468011i	−0.00843510	−	0.0259606i
$326$		−	35.9549i		−	1.99136i
$327$	2.39040	−	7.35690i	0.132189	−	0.406837i
$328$	−13.7134	+	18.8749i	−0.757197	+	1.04219i
$329$	−5.27936	+	1.71537i	−0.291061	+	0.0945714i
$330$	0.330402	+	1.01687i	0.0181880	+	0.0559769i
$331$	−14.6193	−	4.75011i	−0.803551	−	0.261089i	−0.121687	−	0.992569i	$-0.538830\pi$
$331$	−14.6193	−	4.75011i	−0.803551	−	0.261089i	−0.681864	+	0.731479i	$0.738830\pi$
$332$	−2.66889	+	1.93906i	−0.146474	+	0.106420i
$333$	21.3590	+	6.93995i	1.17047	+	0.380307i
$334$		−	4.71379i		−	0.257927i
$335$	5.95646	−	1.93537i	0.325436	−	0.105741i
$336$	−3.63281	+	1.18037i	−0.198186	+	0.0643946i
$337$		−	9.19500i		−	0.500883i	−0.968132	−	0.250442i	$-0.919424\pi$
$337$		−	9.19500i		−	0.500883i	0.968132	−	0.250442i	$-0.0805758\pi$
$338$	−17.9180	−	5.82191i	−0.974610	−	0.316670i
$339$	−5.64206	+	4.09920i	−0.306435	+	0.222638i
$340$	−0.966825	−	0.314141i	−0.0524335	−	0.0170367i
$341$	−0.225502	−	0.694022i	−0.0122116	−	0.0375834i
$342$	−31.3238	+	10.1777i	−1.69380	+	0.550348i
$343$	8.30998	−	11.4377i	0.448697	−	0.617578i
$344$	6.38693	−	19.6569i	0.344360	−	1.05983i
$345$		−	7.83797i		−	0.421982i
$346$	2.03457	+	6.26175i	0.109379	+	0.336634i
$347$	−0.869255	+	2.67529i	−0.0466641	+	0.143617i	−0.971674	−	0.236326i	$-0.924057\pi$
$347$	−0.869255	+	2.67529i	−0.0466641	+	0.143617i	0.925010	+	0.379944i	$0.124057\pi$
$348$	−0.394008	−	0.542306i	−0.0211211	−	0.0290707i
$349$	6.99525	−	9.62814i	0.374447	−	0.515382i	−0.579656	−	0.814862i	$-0.696813\pi$
$349$	6.99525	−	9.62814i	0.374447	−	0.515382i	0.954103	+	0.299479i	$0.0968129\pi$
$350$	0.241977	+	0.744728i	0.0129342	+	0.0398074i
$351$	−3.54668	+	2.57682i	−0.189308	+	0.137540i
$352$	1.35976			0.0724754
$353$	−14.0536			−0.747999			−0.373999	−	0.927429i	$-0.622014\pi$
$353$	−14.0536			−0.747999			−0.373999	+	0.927429i	$0.622014\pi$
$354$	12.7888	−	9.29163i	0.679719	−	0.493845i
$355$			16.8747i			0.895615i
$356$	5.10646	+	7.02845i	0.270642	+	0.372507i
$357$	−0.538930	−	0.391556i	−0.0285232	−	0.0207233i
$358$	8.28525	+	11.4037i	0.437889	+	0.602703i
$359$	−5.93160	+	1.92729i	−0.313058	+	0.101719i	−0.461332	−	0.887228i	$-0.652628\pi$
$359$	−5.93160	+	1.92729i	−0.313058	+	0.101719i	0.148274	+	0.988946i	$0.452628\pi$
$360$	−7.16075	+	9.85593i	−0.377405	+	0.519453i
$361$	−39.9563	−	29.0300i	−2.10296	−	1.52789i
$362$	17.9467	+	13.0391i	0.943260	+	0.685318i
$363$	−2.39577	+	7.37342i	−0.125745	+	0.387004i
$364$	−0.665308	−	0.216172i	−0.0348716	−	0.0113305i
$365$	−18.5496			−0.970930
$366$	8.00038	−	4.06755i	0.418187	−	0.212614i
$367$	−16.6378			−0.868485			−0.434242	−	0.900796i	$-0.642984\pi$
$367$	−16.6378			−0.868485			−0.434242	+	0.900796i	$0.642984\pi$
$368$	−23.4296	−	7.61275i	−1.22135	−	0.396842i
$369$	7.80642	−	24.0257i	0.406386	−	1.25073i
$370$	−25.0055	−	18.1676i	−1.29998	−	0.944488i
$371$	6.68582	+	4.85754i	0.347111	+	0.252191i
$372$	0.400442	−	0.551161i	0.0207619	−	0.0285764i
$373$	23.5665	−	7.65722i	1.22023	−	0.396476i	0.373063	−	0.927806i	$-0.378308\pi$
$373$	23.5665	−	7.65722i	1.22023	−	0.396476i	0.847165	+	0.531330i	$0.178308\pi$
$374$	0.344487	+	0.474145i	0.0178130	+	0.0245175i
$375$	−6.74100	−	4.89762i	−0.348104	−	0.252912i
$376$	−6.76832	−	9.31580i	−0.349050	−	0.480426i
$377$			1.83592i			0.0945547i
$378$	5.64371	−	4.10039i	0.290281	−	0.210902i
$379$	−23.4657			−1.20535			−0.602676	−	0.797986i	$-0.705899\pi$
$379$	−23.4657			−1.20535			−0.602676	+	0.797986i	$0.705899\pi$
$380$	10.0162			0.513818
$381$	6.45444	−	4.68942i	0.330671	−	0.240246i
$382$	0.845030	+	2.60073i	0.0432355	+	0.133065i
$383$	−21.6099	+	29.7435i	−1.10421	+	1.51982i	−0.274538	+	0.961576i	$0.588525\pi$
$383$	−21.6099	+	29.7435i	−1.10421	+	1.51982i	−0.829677	+	0.558244i	$0.811475\pi$
$384$	−5.75534	−	7.92154i	−0.293701	−	0.404244i
$385$	−0.318186	+	0.979274i	−0.0162162	+	0.0499084i
$386$	−0.217474	−	0.669317i	−0.0110692	−	0.0340674i
$387$			22.3796i			1.13762i
$388$	−0.179561	+	0.552631i	−0.00911581	+	0.0280556i
$389$	3.76778	−	5.18591i	0.191034	−	0.262936i	−0.702746	−	0.711440i	$-0.748043\pi$
$389$	3.76778	−	5.18591i	0.191034	−	0.262936i	0.893781	+	0.448504i	$0.148043\pi$
$390$	2.60008	−	0.844817i	0.131660	−	0.0427790i
$391$	−1.32764	−	4.08605i	−0.0671416	−	0.206641i
$392$	12.6090	+	4.09690i	0.636849	+	0.206925i
$393$	1.37744	−	1.00077i	0.0694828	−	0.0504822i
$394$	−31.9808	−	10.3912i	−1.61117	−	0.523501i
$395$		−	25.3001i		−	1.27299i
$396$	−0.584429	+	0.189893i	−0.0293687	+	0.00954246i
$397$	−25.4675	+	8.27490i	−1.27818	+	0.415305i	−0.867938	−	0.496672i	$-0.834555\pi$
$397$	−25.4675	+	8.27490i	−1.27818	+	0.415305i	−0.410240	+	0.911977i	$0.634555\pi$
$398$		−	4.40100i		−	0.220602i
$399$	6.24225	+	2.02823i	0.312503	+	0.101538i
$400$	−1.71948	+	1.24928i	−0.0859740	+	0.0624638i
$401$	24.8946	+	8.08874i	1.24318	+	0.403933i	0.855471	−	0.517851i	$-0.173268\pi$
$401$	24.8946	+	8.08874i	1.24318	+	0.403933i	0.387706	+	0.921783i	$0.373268\pi$
$402$	−1.04167	−	3.20593i	−0.0519537	−	0.159897i
$403$	−1.77457	+	0.576594i	−0.0883978	+	0.0287222i
$404$	−4.12930	+	5.68349i	−0.205440	+	0.282764i
$405$	3.05822	−	9.41223i	0.151964	−	0.467697i
$406$		−	2.92143i		−	0.144988i
$407$	1.21675	+	3.74478i	0.0603121	+	0.185622i
$408$	0.427016	−	1.31422i	0.0211405	−	0.0650636i
$409$	19.2601	+	26.5092i	0.952349	+	1.31080i	0.950476	+	0.310797i	$0.100596\pi$
$409$	19.2601	+	26.5092i	0.952349	+	1.31080i	0.00187261	+	0.999998i	$0.499404\pi$
$410$	−20.4358	+	28.1275i	−1.00925	+	1.38912i
$411$	−2.87899	−	8.86061i	−0.142010	−	0.437062i
$412$	1.68691	−	1.22561i	0.0831081	−	0.0603816i
$413$	15.2234			0.749095
$414$	20.3864			1.00194
$415$	10.0446	−	7.29783i	0.493070	−	0.358236i
$416$		−	3.47682i		−	0.170465i
$417$	−1.47615	−	2.03174i	−0.0722872	−	0.0994948i
$418$	−4.67166	−	3.39416i	−0.228498	−	0.166014i
$419$	9.55743	+	13.1547i	0.466911	+	0.642648i	0.975924	−	0.218111i	$-0.0699894\pi$
$419$	9.55743	+	13.1547i	0.466911	+	0.642648i	−0.509013	+	0.860759i	$0.669989\pi$
$420$	−0.914235	+	0.297053i	−0.0446101	+	0.0144947i
$421$	10.8415	−	14.9220i	0.528381	−	0.727254i	−0.458502	−	0.888694i	$-0.651614\pi$
$421$	10.8415	−	14.9220i	0.528381	−	0.727254i	0.986883	+	0.161440i	$0.0516137\pi$
$422$	4.65643	+	3.38309i	0.226671	+	0.164686i
$423$	10.0870	+	7.32864i	0.490447	+	0.356331i
$424$	−5.29745	+	16.3039i	−0.257267	+	0.791786i
$425$	−0.352520	−	0.114541i	−0.0170998	−	0.00555605i
$426$	9.08240			0.440044
$427$	8.53558	+	1.35959i	0.413066	+	0.0657950i
$428$	4.41257			0.213290
$429$	−0.331228	−	0.107623i	−0.0159919	−	0.00519607i
$430$	9.51784	−	29.2929i	0.458991	−	1.41263i
$431$	22.3468	+	16.2359i	1.07641	+	0.782057i	0.977053	−	0.212995i	$-0.0683220\pi$
$431$	22.3468	+	16.2359i	1.07641	+	0.782057i	0.0993553	+	0.995052i	$0.468322\pi$
$432$	15.3184	+	11.1294i	0.737006	+	0.535466i
$433$	13.6061	−	18.7272i	0.653869	−	0.899974i	−0.345390	−	0.938459i	$-0.612253\pi$
$433$	13.6061	−	18.7272i	0.653869	−	0.899974i	0.999259	+	0.0384855i	$0.0122533\pi$
$434$	2.82381	−	0.917513i	0.135547	−	0.0440420i
$435$	1.48288	+	2.04101i	0.0710988	+	0.0978592i
$436$	−4.95013	−	3.59648i	−0.237068	−	0.172240i
$437$	24.8815	+	34.2464i	1.19024	+	1.63823i
$438$			9.98389i			0.477049i
$439$	−1.12619	+	0.818228i	−0.0537503	+	0.0390519i	−0.614336	−	0.789045i	$-0.710576\pi$
$439$	−1.12619	+	0.818228i	−0.0537503	+	0.0390519i	0.560586	+	0.828096i	$0.310576\pi$
$440$	−2.13592			−0.101826
$441$	−14.3554			−0.683591
$442$	1.21236	−	0.880831i	0.0576661	−	0.0418969i
$443$	7.36127	+	22.6557i	0.349744	+	1.07640i	0.958995	+	0.283424i	$0.0914705\pi$
$443$	7.36127	+	22.6557i	0.349744	+	1.07640i	−0.609250	+	0.792978i	$0.708529\pi$
$444$	−2.16069	+	2.97393i	−0.102542	+	0.141136i
$445$	−19.2186	−	26.4521i	−0.911050	−	1.25395i
$446$	11.4520	−	35.2455i	0.542267	−	1.66893i
$447$	3.35646	+	10.3301i	0.158755	+	0.488598i
$448$		−	5.11951i		−	0.241874i
$449$	8.34920	−	25.6962i	0.394023	−	1.21268i	−0.535697	−	0.844410i	$-0.679951\pi$
$449$	8.34920	−	25.6962i	0.394023	−	1.21268i	0.929720	−	0.368268i	$-0.120049\pi$
$450$	1.03381	−	1.42291i	0.0487342	−	0.0670768i
$451$	4.21232	−	1.36866i	0.198350	−	0.0644479i
$452$	1.70464	+	5.24635i	0.0801796	+	0.246767i
$453$	−6.19741	−	2.01366i	−0.291180	−	0.0946100i
$454$	−1.24786	+	0.906620i	−0.0585648	+	0.0425498i
$455$	2.50394	+	0.813581i	0.117387	+	0.0381413i
$456$			13.6151i			0.637587i
$457$	−26.0487	+	8.46372i	−1.21851	+	0.395916i	−0.846537	−	0.532329i	$-0.821317\pi$
$457$	−26.0487	+	8.46372i	−1.21851	+	0.395916i	−0.371968	+	0.928246i	$0.621317\pi$
$458$	12.6622	−	4.11419i	0.591664	−	0.192243i
$459$			3.30212i			0.154130i
$460$	−5.89631	−	1.91583i	−0.274917	−	0.0893259i
$461$	−19.7125	+	14.3220i	−0.918103	+	0.667041i	−0.943051	−	0.332648i	$-0.892058\pi$
$461$	−19.7125	+	14.3220i	−0.918103	+	0.667041i	0.0249480	+	0.999689i	$0.492058\pi$
$462$	0.527072	+	0.171256i	0.0245216	+	0.00796755i
$463$	1.28274	+	3.94787i	0.0596140	+	0.183473i	0.976429	−	0.215840i	$-0.0692488\pi$
$463$	1.28274	+	3.94787i	0.0596140	+	0.183473i	−0.916815	+	0.399313i	$0.869249\pi$
$464$	7.54137	−	2.45034i	0.350099	−	0.113754i
$465$	−1.50710	+	2.07434i	−0.0698899	+	0.0961952i
$466$	−5.87354	+	18.0769i	−0.272087	+	0.837397i
$467$		−	10.6645i		−	0.493493i	−0.969080	−	0.246746i	$-0.920639\pi$
$467$		−	10.6645i		−	0.493493i	0.969080	−	0.246746i	$-0.0793615\pi$
$468$	0.485544	+	1.49435i	0.0224443	+	0.0690764i
$469$	1.00315	−	3.08739i	0.0463214	−	0.142562i
$470$	−10.0862	−	13.8825i	−0.465242	−	0.640351i
$471$	−2.13272	+	2.93543i	−0.0982705	+	0.135258i
$472$	9.75846	+	30.0334i	0.449169	+	1.38240i
$473$	−3.17435	+	2.30630i	−0.145957	+	0.106044i
$474$	−13.6172			−0.625459
$475$	3.65206			0.167568
$476$	−0.426288	+	0.309716i	−0.0195389	+	0.0141958i
$477$		−	18.5621i		−	0.849899i
$478$	−13.6449	−	18.7806i	−0.624103	−	0.859004i
$479$	−3.22472	−	2.34289i	−0.147341	−	0.107050i	0.511673	−	0.859181i	$-0.329026\pi$
$479$	−3.22472	−	2.34289i	−0.147341	−	0.107050i	−0.659014	+	0.752131i	$0.729026\pi$
$480$	−2.80825	−	3.86523i	−0.128179	−	0.176423i
$481$	9.57517	−	3.11116i	0.436590	−	0.141857i
$482$	5.51320	−	7.58828i	0.251120	−	0.345636i
$483$	−3.28674	−	2.38795i	−0.149552	−	0.108656i
$484$	4.96124	+	3.60455i	0.225511	+	0.163843i
$485$	0.675792	−	2.07987i	0.0306861	−	0.0944422i
$486$	−23.0515	−	7.48990i	−1.04564	−	0.339749i
$487$	−31.4670			−1.42591			−0.712954	−	0.701211i	$-0.752643\pi$
$487$	−31.4670			−1.42591			−0.712954	+	0.701211i	$0.752643\pi$
$488$	2.78920	+	17.7109i	0.126261	+	0.801736i
$489$	16.0936			0.727778
$490$	18.7900	+	6.10523i	0.848844	+	0.275806i
$491$	−4.43301	+	13.6434i	−0.200059	+	0.615718i	0.799821	+	0.600238i	$0.204928\pi$
$491$	−4.43301	+	13.6434i	−0.200059	+	0.615718i	−0.999880	+	0.0154797i	$0.995072\pi$
$492$	3.34523	+	2.43045i	0.150815	+	0.109573i
$493$	1.11877	+	0.812832i	0.0503868	+	0.0366081i
$494$	−8.67865	+	11.9451i	−0.390471	+	0.537437i
$495$	2.19955	−	0.714677i	0.0988624	−	0.0321223i
$496$	4.73692	+	6.51982i	0.212694	+	0.292748i
$497$	7.07614	+	5.14112i	0.317408	+	0.230611i
$498$	−3.92789	−	5.40627i	−0.176013	−	0.242261i
$499$		−	7.98018i		−	0.357242i	−0.983918	−	0.178621i	$-0.942836\pi$
$499$		−	7.98018i		−	0.357242i	0.983918	−	0.178621i	$-0.0571636\pi$
$500$	−5.33206	+	3.87397i	−0.238457	+	0.173249i
$501$	2.10992			0.0942644
$502$	2.51367			0.112191
$503$	−14.2623	+	10.3622i	−0.635925	+	0.462026i	−0.858448	−	0.512901i	$-0.828571\pi$
$503$	−14.2623	+	10.3622i	−0.635925	+	0.462026i	0.222523	+	0.974927i	$0.428571\pi$
$504$	1.95131	+	6.00551i	0.0869182	+	0.267507i
$505$	15.5410	−	21.3903i	0.691564	−	0.951856i
$506$	2.10090	+	2.89164i	0.0933962	+	0.128549i
$507$	2.60592	−	8.02020i	0.115733	−	0.356190i
$508$	−1.95008	−	6.00174i	−0.0865210	−	0.266284i
$509$			1.34069i			0.0594249i	0.999558	+	0.0297125i	$0.00945916\pi$
$509$			1.34069i			0.0594249i	−0.999558	+	0.0297125i	$0.990541\pi$
$510$	0.636343	−	1.95846i	0.0281777	−	0.0867221i
$511$	−5.65141	+	7.77849i	−0.250004	+	0.344100i
$512$	6.73320	−	2.18775i	0.297568	−	0.0966858i
$513$	−10.0539	−	30.9428i	−0.443891	−	1.36616i
$514$	18.7517	+	6.09281i	0.827104	+	0.268742i
$515$	−6.34883	+	4.61269i	−0.279763	+	0.203260i
$516$	−3.48383	−	1.13197i	−0.153367	−	0.0498320i
$517$			2.18600i			0.0961401i
$518$	−15.2366	+	4.95068i	−0.669459	+	0.217520i
$519$	−2.80280	+	0.910684i	−0.123029	+	0.0399746i
$520$			5.46142i			0.239499i
$521$	−12.7086	−	4.12928i	−0.556775	−	0.180907i	0.0170948	−	0.999854i	$-0.494558\pi$
$521$	−12.7086	−	4.12928i	−0.556775	−	0.180907i	−0.573869	+	0.818947i	$0.694558\pi$
$522$	−5.30864	+	3.85695i	−0.232353	+	0.168814i
$523$	1.20306	+	0.390897i	0.0526060	+	0.0170927i	0.335202	−	0.942146i	$-0.391196\pi$
$523$	1.20306	+	0.390897i	0.0526060	+	0.0170927i	−0.282596	+	0.959239i	$0.591196\pi$
$524$	−0.416168	−	1.28083i	−0.0181804	−	0.0559535i
$525$	−0.333345	+	0.108310i	−0.0145484	+	0.00472705i
$526$	17.6630	−	24.3111i	0.770144	−	1.06001i
$527$	−0.434309	+	1.33666i	−0.0189188	+	0.0582260i
$528$			1.50422i			0.0654628i
$529$	−0.989388	−	3.04502i	−0.0430169	−	0.132392i
$530$	−7.89430	+	24.2961i	−0.342906	+	1.05536i
$531$	−20.0983	−	27.6630i	−0.872193	−	1.20047i
$532$	3.05157	−	4.20013i	0.132302	−	0.182099i
$533$	−3.49959	−	10.7706i	−0.151584	−	0.466528i
$534$	−14.2373	+	10.3440i	−0.616106	+	0.447627i
$535$	−16.6071			−0.717987
$536$	6.73399			0.290864
$537$	−5.10435	+	3.70853i	−0.220269	+	0.160035i
$538$		−	27.3787i		−	1.18038i
$539$	−1.47938	−	2.03619i	−0.0637214	−	0.0877049i
$540$	3.85503	+	2.80084i	0.165894	+	0.120529i
$541$	22.6776	+	31.2131i	0.974987	+	1.34195i	0.939487	+	0.342584i	$0.111302\pi$
$541$	22.6776	+	31.2131i	0.974987	+	1.34195i	0.0354996	+	0.999370i	$0.488698\pi$
$542$	15.9415	−	5.17971i	0.684747	−	0.222488i
$543$	−5.83637	+	8.03307i	−0.250463	+	0.344732i
$544$	−2.11870	−	1.53932i	−0.0908383	−	0.0659979i
$545$	18.6302	+	13.5356i	0.798031	+	0.579803i
$546$	0.437891	−	1.34769i	0.0187400	−	0.0576758i
$547$	28.4266	+	9.23635i	1.21543	+	0.394918i	0.845416	−	0.534108i	$-0.179352\pi$
$547$	28.4266	+	9.23635i	1.21543	+	0.394918i	0.370016	+	0.929025i	$0.379352\pi$
$548$	−7.36932			−0.314802
$549$	−8.79834	−	17.3053i	−0.375504	−	0.738571i
$550$	0.308366			0.0131488
$551$	−12.9583	−	4.21041i	−0.552042	−	0.179369i
$552$	2.60422	−	8.01495i	0.110843	−	0.341139i
$553$	−10.6092	−	7.70806i	−0.451150	−	0.327780i
$554$	10.6802	+	7.75965i	0.453760	+	0.329676i
$555$	8.13193	−	11.1926i	0.345181	−	0.475101i
$556$	−1.88924	+	0.613852i	−0.0801217	+	0.0260331i
$557$	−23.8373	−	32.8092i	−1.01002	−	1.39017i	−0.918972	−	0.394322i	$-0.870979\pi$
$557$	−23.8373	−	32.8092i	−1.01002	−	1.39017i	−0.0910448	−	0.995847i	$-0.529021\pi$
$558$	−5.39531	−	3.91993i	−0.228402	−	0.165944i
$559$	5.89707	+	8.11662i	0.249419	+	0.343296i
$560$		−	11.3713i		−	0.480523i
$561$	−0.212230	+	0.154194i	−0.00896037	+	0.00651009i
$562$	−19.6055			−0.827006
$563$	2.20109			0.0927650			0.0463825	−	0.998924i	$-0.485231\pi$
$563$	2.20109			0.0927650			0.0463825	+	0.998924i	$0.485231\pi$
$564$	−1.65105	+	1.19956i	−0.0695219	+	0.0505106i
$565$	−6.41556	−	19.7451i	−0.269905	−	0.830681i
$566$	20.0782	−	27.6353i	0.843949	−	1.16160i
$567$	−3.01515	−	4.14999i	−0.126624	−	0.174283i
$568$	−5.60671	+	17.2557i	−0.235253	+	0.724033i
$569$	7.25649	+	22.3332i	0.304208	+	0.936256i	0.979972	+	0.199138i	$0.0638141\pi$
$569$	7.25649	+	22.3332i	0.304208	+	0.936256i	−0.675763	+	0.737119i	$0.736186\pi$
$570$			20.2894i			0.849828i
$571$	−13.3458	+	41.0740i	−0.558503	+	1.71890i	0.128006	+	0.991773i	$0.459142\pi$
$571$	−13.3458	+	41.0740i	−0.558503	+	1.71890i	−0.686509	+	0.727122i	$0.740858\pi$
$572$	−0.161924	+	0.222869i	−0.00677037	+	0.00931861i
$573$	−1.16410	+	0.378241i	−0.0486312	+	0.0158012i
$574$	5.56877	+	17.1389i	0.232436	+	0.715365i
$575$	−2.14989	−	0.698542i	−0.0896567	−	0.0291312i
$576$	−9.30283	+	6.75890i	−0.387618	+	0.281621i
$577$	7.96921	+	2.58935i	0.331763	+	0.107796i	0.470162	−	0.882580i	$-0.344196\pi$
$577$	7.96921	+	2.58935i	0.331763	+	0.107796i	−0.138399	+	0.990377i	$0.544196\pi$
$578$			26.1099i			1.08603i
$579$	0.299591	−	0.0973429i	0.0124506	−	0.00404543i
$580$	1.89786	−	0.616654i	0.0788045	−	0.0256051i
$581$		−	6.43544i		−	0.266987i
$582$	−1.11944	−	0.363729i	−0.0464024	−	0.0150771i
$583$	2.63287	−	1.91289i	0.109042	−	0.0792239i
$584$	−18.9684	−	6.16322i	−0.784919	−	0.255036i
$585$	−1.82739	−	5.62411i	−0.0755531	−	0.232528i
$586$	1.18495	−	0.385013i	0.0489497	−	0.0159047i
$587$	24.6724	−	33.9586i	1.01834	−	1.40162i	0.104977	−	0.994475i	$-0.466523\pi$
$587$	24.6724	−	33.9586i	1.01834	−	1.40162i	0.913362	−	0.407148i	$-0.133477\pi$
$588$	0.726100	−	2.23471i	0.0299439	−	0.0921577i
$589$		−	13.8476i		−	0.570582i
$590$	14.5421	+	44.7561i	0.598690	+	1.84258i
$591$	4.65117	−	14.3148i	0.191323	−	0.588833i
$592$	−25.5593	−	35.1794i	−1.05048	−	1.44586i
$593$	5.37537	−	7.39857i	0.220740	−	0.303823i	−0.684257	−	0.729241i	$-0.739873\pi$
$593$	5.37537	−	7.39857i	0.220740	−	0.303823i	0.904997	+	0.425419i	$0.139873\pi$
$594$	−0.848915	−	2.61269i	−0.0348314	−	0.107200i
$595$	1.60437	−	1.16564i	0.0657728	−	0.0477867i
$596$	8.59152			0.351922
$597$	1.96992			0.0806233
$598$	7.39374	−	5.37186i	0.302352	−	0.219672i
$599$			11.9577i			0.488577i	0.969703	+	0.244288i	$0.0785544\pi$
$599$			11.9577i			0.488577i	−0.969703	+	0.244288i	$0.921446\pi$
$600$	−0.427360	−	0.588210i	−0.0174469	−	0.0240136i
$601$	20.0300	+	14.5526i	0.817040	+	0.593614i	0.915863	−	0.401491i	$-0.131508\pi$
$601$	20.0300	+	14.5526i	0.817040	+	0.593614i	−0.0988232	+	0.995105i	$0.531508\pi$
$602$	−9.38379	−	12.9157i	−0.382455	−	0.526404i
$603$	−6.93459	+	2.25319i	−0.282399	+	0.0917568i
$604$	−3.02965	+	4.16996i	−0.123275	+	0.169673i
$605$	−18.6721	−	13.5660i	−0.759127	−	0.551538i
$606$	−11.5128	−	8.36457i	−0.467677	−	0.339787i
$607$	6.23199	−	19.1801i	0.252949	−	0.778496i	−0.741278	−	0.671198i	$-0.765780\pi$
$607$	6.23199	−	19.1801i	0.252949	−	0.778496i	0.994227	−	0.107298i	$-0.0342199\pi$
$608$	24.5401	+	7.97357i	0.995234	+	0.323371i
$609$	1.30765			0.0529887
$610$	4.15648	+	26.3929i	0.168291	+	1.06862i
$611$	5.58947			0.226126
$612$	1.12559	+	0.365727i	0.0454994	+	0.0147836i
$613$	−8.93492	+	27.4989i	−0.360878	+	1.11067i	0.591644	+	0.806199i	$0.298479\pi$
$613$	−8.93492	+	27.4989i	−0.360878	+	1.11067i	−0.952522	+	0.304469i	$0.901521\pi$
$614$	35.9487	+	26.1182i	1.45077	+	1.05405i
$615$	−12.5900	−	9.14721i	−0.507680	−	0.368851i
$616$	−0.650740	+	0.895667i	−0.0262191	+	0.0360874i
$617$	−42.6232	+	13.8491i	−1.71595	+	0.557545i	−0.991305	−	0.131581i	$-0.957995\pi$
$617$	−42.6232	+	13.8491i	−1.71595	+	0.557545i	−0.724641	+	0.689126i	$0.757995\pi$
$618$	2.48267	+	3.41711i	0.0998678	+	0.137456i
$619$	−20.9878	−	15.2485i	−0.843570	−	0.612890i	0.0797954	−	0.996811i	$-0.474573\pi$
$619$	−20.9878	−	15.2485i	−0.843570	−	0.612890i	−0.923366	+	0.383922i	$0.874573\pi$
$620$	1.19210	+	1.64078i	0.0478757	+	0.0658953i
$621$			20.1384i			0.808127i
$622$	22.1514	−	16.0939i	0.888191	−	0.645309i
$623$	−16.9475			−0.678989
$624$	3.84620			0.153971
$625$	18.2813	−	13.2821i	0.731251	−	0.531285i
$626$	1.92159	+	5.91404i	0.0768021	+	0.236372i
$627$	1.51925	−	2.09106i	0.0606728	−	0.0835090i
$628$	1.68696	+	2.32190i	0.0673169	+	0.0926537i
$629$	2.34342	−	7.21232i	0.0934384	−	0.287574i
$630$	2.90785	+	8.94945i	0.115852	+	0.356555i
$631$			35.5787i			1.41637i	0.706029	+	0.708183i	$0.250485\pi$
$631$			35.5787i			1.41637i	−0.706029	+	0.708183i	$0.749515\pi$
$632$	8.40613	−	25.8714i	0.334378	−	1.02911i
$633$	−1.51429	+	2.08425i	−0.0601878	+	0.0828414i
$634$	−44.6580	+	14.5103i	−1.77360	+	0.576276i
$635$	7.33931	+	22.5881i	0.291252	+	0.896380i
$636$	2.88956	+	0.938875i	0.114579	+	0.0372288i
$637$	−5.20641	+	3.78268i	−0.206286	+	0.149875i
$638$	−1.09415	−	0.355511i	−0.0433178	−	0.0140748i
$639$		−	19.6457i		−	0.777173i
$640$	27.7224	−	9.00755i	1.09582	−	0.356055i
$641$	−3.21488	+	1.04458i	−0.126980	+	0.0412583i	−0.371818	−	0.928306i	$-0.621265\pi$
$641$	−3.21488	+	1.04458i	−0.126980	+	0.0412583i	0.244838	+	0.969564i	$0.421265\pi$
$642$			8.93837i			0.352769i
$643$	2.99226	+	0.972246i	0.118003	+	0.0383416i	0.367423	−	0.930054i	$-0.380240\pi$
$643$	2.99226	+	0.972246i	0.118003	+	0.0383416i	−0.249420	+	0.968395i	$0.580240\pi$
$644$	−2.59977	+	1.88884i	−0.102445	+	0.0744309i
$645$	13.1117	+	4.26025i	0.516272	+	0.167747i
$646$	3.43672	+	10.5771i	0.135216	+	0.416152i
$647$	21.2394	−	6.90110i	0.835007	−	0.271310i	0.139854	−	0.990172i	$-0.455337\pi$
$647$	21.2394	−	6.90110i	0.835007	−	0.271310i	0.695153	+	0.718862i	$0.255337\pi$
$648$	6.25454	−	8.60864i	0.245702	−	0.338179i
$649$	1.85254	−	5.70155i	0.0727187	−	0.223805i
$650$		−	0.788473i		−	0.0309264i
$651$	0.410684	+	1.26396i	0.0160960	+	0.0495384i
$652$	3.93375	−	12.1068i	0.154057	−	0.474140i
$653$	−11.8244	−	16.2749i	−0.462724	−	0.636884i	0.512347	−	0.858778i	$-0.328776\pi$
$653$	−11.8244	−	16.2749i	−0.462724	−	0.636884i	−0.975071	+	0.221894i	$0.928776\pi$
$654$	7.28525	−	10.0273i	0.284876	−	0.392098i
$655$	1.56628	+	4.82053i	0.0611998	+	0.188354i
$656$	−39.5715	+	28.7504i	−1.54501	+	1.12251i
$657$	21.5957			0.842528
$658$	−8.89432			−0.346737
$659$	10.3585	−	7.52591i	0.403511	−	0.293168i	−0.367459	−	0.930040i	$-0.619772\pi$
$659$	10.3585	−	7.52591i	0.403511	−	0.293168i	0.770970	+	0.636872i	$0.219772\pi$
$660$			0.378553i			0.0147351i
$661$	2.82958	+	3.89459i	0.110058	+	0.151482i	0.860493	−	0.509463i	$-0.170156\pi$
$661$	2.82958	+	3.89459i	0.110058	+	0.151482i	−0.750435	+	0.660945i	$0.770156\pi$
$662$	−19.9258	−	14.4769i	−0.774438	−	0.562662i
$663$	0.394265	+	0.542660i	0.0153120	+	0.0210752i
$664$	12.6961	−	4.12523i	0.492706	−	0.160090i
$665$	−11.4848	+	15.8075i	−0.445363	+	0.612990i
$666$	29.1118	+	21.1510i	1.12806	+	0.819583i
$667$	6.82295	+	4.95716i	0.264186	+	0.191942i
$668$	0.515726	−	1.58724i	0.0199540	−	0.0614122i
$669$	15.7761	+	5.12597i	0.609940	+	0.198182i
$670$	10.0350			0.387687
$671$	1.54790	−	3.03134i	0.0597560	−	0.117024i
$672$	−2.47640			−0.0955292
$673$	32.4177	+	10.5332i	1.24961	+	0.406024i	0.857782	−	0.514014i	$-0.171842\pi$
$673$	32.4177	+	10.5332i	1.24961	+	0.406024i	0.391830	+	0.920038i	$0.371842\pi$
$674$	4.55272	−	14.0118i	0.175364	−	0.539716i
$675$	1.40561	+	1.02123i	0.0541018	+	0.0393073i
$676$	−5.39643	−	3.92074i	−0.207555	−	0.150798i
$677$	−2.86632	+	3.94515i	−0.110162	+	0.151625i	−0.860538	−	0.509386i	$-0.829872\pi$
$677$	−2.86632	+	3.94515i	−0.110162	+	0.151625i	0.750376	+	0.661011i	$0.229872\pi$
$678$	−10.6273	+	3.45303i	−0.408140	+	0.132613i
$679$	−0.666274	−	0.917047i	−0.0255692	−	0.0351930i
$680$	3.32806	+	2.41798i	0.127625	+	0.0927253i
$681$	−0.405809	−	0.558548i	−0.0155506	−	0.0214036i
$682$		−	1.16924i		−	0.0447726i
$683$	18.4332	−	13.3925i	0.705325	−	0.512449i	−0.176337	−	0.984330i	$-0.556425\pi$
$683$	18.4332	−	13.3925i	0.705325	−	0.512449i	0.881662	+	0.471881i	$0.156425\pi$
$684$	−11.6610			−0.445868
$685$	27.7351			1.05970
$686$	18.3264	−	13.3149i	0.699704	−	0.508364i
$687$	1.84153	+	5.66766i	0.0702589	+	0.216235i
$688$	25.4699	−	35.0562i	0.971029	−	1.33651i
$689$	−4.89115	−	6.73209i	−0.186338	−	0.256472i
$690$	3.88082	−	11.9439i	0.147740	−	0.454698i
$691$	−12.3350	−	37.9632i	−0.469245	−	1.44419i	−0.853564	−	0.520988i	$-0.825564\pi$
$691$	−12.3350	−	37.9632i	−0.469245	−	1.44419i	0.384319	−	0.923200i	$-0.374436\pi$
$692$			2.33107i			0.0886141i
$693$	0.370436	−	1.14009i	0.0140717	−	0.0433082i
$694$	−2.64924	+	3.64636i	−0.100564	+	0.138414i
$695$	7.11032	−	2.31028i	0.269710	−	0.0876341i
$696$	0.838227	+	2.57980i	0.0317729	+	0.0977870i
$697$	−8.11278	−	2.63600i	−0.307294	−	0.0998457i
$698$	15.4269	−	11.2083i	0.583918	−	0.424241i
$699$	−8.09134	−	2.62903i	−0.306042	−	0.0994392i
$700$			0.277241i			0.0104787i
$701$	−2.20656	+	0.716954i	−0.0833406	+	0.0270790i	−0.350391	−	0.936604i	$-0.613951\pi$
$701$	−2.20656	+	0.716954i	−0.0833406	+	0.0270790i	0.267050	+	0.963683i	$0.413951\pi$
$702$	−6.68049	+	2.17062i	−0.252139	+	0.0819249i
$703$			74.7185i			2.81806i
$704$	−1.91739	−	0.622996i	−0.0722642	−	0.0234801i
$705$	6.21388	−	4.51465i	0.234028	−	0.170031i
$706$	−21.4157	−	6.95838i	−0.805990	−	0.261882i
$707$	−4.23492	−	13.0337i	−0.159271	−	0.490185i
$708$	5.32287	−	1.72951i	0.200046	−	0.0649988i
$709$	−21.4683	+	29.5486i	−0.806258	+	1.10972i	0.185632	+	0.982619i	$0.440567\pi$
$709$	−21.4683	+	29.5486i	−0.806258	+	1.10972i	−0.991890	+	0.127100i	$0.959433\pi$
$710$	−8.35517	+	25.7146i	−0.313564	+	0.965050i
$711$			29.4548i			1.10464i
$712$	−10.8637	−	33.4349i	−0.407133	−	1.25303i
$713$	−2.64869	+	8.15182i	−0.0991942	+	0.305288i
$714$	−0.627380	−	0.863515i	−0.0234791	−	0.0323162i
$715$	0.609413	−	0.838785i	0.0227908	−	0.0313688i
$716$	1.54218	+	4.74635i	0.0576341	+	0.177379i
$717$	8.40630	−	6.10754i	0.313939	−	0.228090i
$718$	−9.99316			−0.372941
$719$	−36.6090			−1.36529			−0.682643	−	0.730752i	$-0.739170\pi$
$719$	−36.6090			−1.36529			−0.682643	+	0.730752i	$0.739170\pi$
$720$	−20.6631	+	15.0126i	−0.770069	+	0.559488i
$721$			4.06761i			0.151486i
$722$	−46.5140	−	64.0210i	−1.73107	−	2.38262i
$723$	3.39656	+	2.46774i	0.126319	+	0.0917764i
$724$	4.61650	+	6.35407i	0.171571	+	0.236147i
$725$	0.691992	−	0.224842i	0.0257000	−	0.00835042i
$726$	−7.30161	+	10.0498i	−0.270988	+	0.372983i
$727$	30.5547	+	22.1993i	1.13321	+	0.823325i	0.986159	−	0.165804i	$-0.0530219\pi$
$727$	30.5547	+	22.1993i	1.13321	+	0.823325i	0.147051	+	0.989129i	$0.453022\pi$
$728$	2.29016	+	1.66390i	0.0848792	+	0.0616683i
$729$	−0.944662	+	2.90737i	−0.0349875	+	0.107680i
$730$	−28.2669	−	9.18447i	−1.04620	−	0.339932i
$731$	7.55694			0.279504
$732$	3.13893	−	0.494334i	0.116018	−	0.0182711i
$733$	−26.6989			−0.986146			−0.493073	−	0.869988i	$-0.664126\pi$
$733$	−26.6989			−0.986146			−0.493073	+	0.869988i	$0.664126\pi$
$734$	−25.3536	−	8.23787i	−0.935817	−	0.304065i
$735$	−2.73274	+	8.41051i	−0.100799	+	0.310226i
$736$	−12.9211	−	9.38776i	−0.476280	−	0.346037i
$737$	−1.03423	−	0.751413i	−0.0380964	−	0.0276787i
$738$	23.7917	−	32.7465i	0.875784	−	1.20541i
$739$	−27.7358	+	9.01191i	−1.02028	+	0.331509i	−0.770940	−	0.636908i	$-0.780213\pi$
$739$	−27.7358	+	9.01191i	−1.02028	+	0.331509i	−0.249338	+	0.968416i	$0.580213\pi$
$740$	−6.43226	−	8.85325i	−0.236455	−	0.325452i
$741$	−5.34672	−	3.88462i	−0.196417	−	0.142705i
$742$	7.78311	+	10.7125i	0.285727	+	0.393270i
$743$			14.3532i			0.526569i	0.964718	+	0.263285i	$0.0848059\pi$
$743$			14.3532i			0.526569i	−0.964718	+	0.263285i	$0.915194\pi$
$744$	−2.23034	+	1.62044i	−0.0817682	+	0.0594080i
$745$	−32.3349			−1.18466
$746$	39.7033			1.45364
$747$	−11.6941	+	8.49624i	−0.427863	+	0.310861i
$748$	0.0641213	+	0.197345i	0.00234451	+	0.00721565i
$749$	−5.05959	+	6.96393i	−0.184873	+	0.254456i
$750$	−7.84735	−	10.8009i	−0.286545	−	0.394395i
$751$	9.48591	−	29.1946i	0.346146	−	1.06533i	−0.614822	−	0.788666i	$-0.710772\pi$
$751$	9.48591	−	29.1946i	0.346146	−	1.06533i	0.960968	−	0.276661i	$-0.0892278\pi$
$752$	−7.46007	−	22.9597i	−0.272041	−	0.837255i
$753$			1.12513i			0.0410021i
$754$	−0.909020	+	2.79768i	−0.0331046	+	0.101885i
$755$	11.4024	−	15.6940i	0.414974	−	0.571163i
$756$	2.34898	−	0.763231i	0.0854317	−	0.0277584i
$757$	−3.03081	−	9.32787i	−0.110157	−	0.339027i	0.880750	−	0.473582i	$-0.157039\pi$
$757$	−3.03081	−	9.32787i	−0.110157	−	0.339027i	−0.990906	+	0.134555i	$0.957039\pi$
$758$	−35.7583	−	11.6186i	−1.29880	−	0.422006i
$759$	−1.29431	+	0.940374i	−0.0469806	+	0.0341334i
$760$	−38.5478	−	12.5250i	−1.39828	−	0.454328i
$761$			15.3059i			0.554838i	0.960749	+	0.277419i	$0.0894790\pi$
$761$			15.3059i			0.554838i	−0.960749	+	0.277419i	$0.910521\pi$
$762$	12.1575	−	3.95021i	0.440420	−	0.143101i
$763$	11.3519	−	3.68847i	0.410968	−	0.133532i
$764$			0.968180i			0.0350275i
$765$	−4.23626	−	1.37644i	−0.153162	−	0.0497655i
$766$	−47.6573	+	34.6250i	−1.72193	+	1.25105i
$767$	−14.5785	−	4.73684i	−0.526399	−	0.171038i
$768$	−2.79758	−	8.61006i	−0.100949	−	0.310689i
$769$	24.1571	−	7.84913i	0.871129	−	0.283047i	0.160860	−	0.986977i	$-0.448573\pi$
$769$	24.1571	−	7.84913i	0.871129	−	0.283047i	0.710269	+	0.703930i	$0.248573\pi$
$770$	−0.969737	+	1.33473i	−0.0349469	+	0.0481003i
$771$	−2.72718	+	8.39340i	−0.0982170	+	0.302281i
$772$		−	0.249168i		−	0.00896775i
$773$	10.1401	+	31.2082i	0.364716	+	1.12248i	0.950159	+	0.311766i	$0.100921\pi$
$773$	10.1401	+	31.2082i	0.364716	+	1.12248i	−0.585443	+	0.810713i	$0.699079\pi$
$774$	−11.0808	+	34.1032i	−0.398291	+	1.22582i
$775$	0.434658	+	0.598255i	0.0156134	+	0.0214900i
$776$	1.38210	−	1.90230i	0.0496146	−	0.0682886i
$777$	−2.21595	−	6.82000i	−0.0794969	−	0.244666i
$778$	8.30926	−	6.03703i	0.297901	−	0.216438i
$779$	84.0472			3.01130
$780$	0.967936			0.0346577
$781$	2.78658	−	2.02457i	0.0997116	−	0.0724447i
$782$		−	6.88390i		−	0.246168i
$783$	−3.81004	−	5.24406i	−0.136160	−	0.187408i
$784$	22.4869	+	16.3377i	0.803102	+	0.583488i
$785$	−6.34900	−	8.73865i	−0.226606	−	0.311896i
$786$	2.59454	−	0.843016i	0.0925440	−	0.0300694i
$787$	29.5872	−	40.7233i	1.05467	−	1.45163i	0.169982	−	0.985447i	$-0.445629\pi$
$787$	29.5872	−	40.7233i	1.05467	−	1.45163i	0.884689	−	0.466182i	$-0.154371\pi$
$788$	−9.63180	−	6.99791i	−0.343119	−	0.249290i
$789$	10.8818	+	7.90608i	0.387402	+	0.281464i
$790$	12.5269	−	38.5537i	0.445686	−	1.37168i
$791$	−10.2344	−	3.32536i	−0.363893	−	0.118236i
$792$	2.48667			0.0883600
$793$	−7.75096	−	3.95788i	−0.275245	−	0.140549i
$794$	−42.9060			−1.52268
$795$	−10.8751	−	3.53354i	−0.385700	−	0.125322i
$796$	0.481505	−	1.48192i	0.0170665	−	0.0525252i
$797$	−12.5296	−	9.10330i	−0.443822	−	0.322455i	0.343330	−	0.939215i	$-0.388445\pi$
$797$	−12.5296	−	9.10330i	−0.443822	−	0.322455i	−0.787152	+	0.616759i	$0.788445\pi$
$798$	8.50804	+	6.18145i	0.301181	+	0.218821i
$799$	2.47467	−	3.40609i	0.0875476	−	0.120499i
$800$	−1.31048	+	0.425800i	−0.0463324	+	0.0150543i
$801$	22.3746	+	30.7960i	0.790567	+	1.08812i
$802$	33.9308	+	24.6521i	1.19814	+	0.870498i
$803$	2.22552	+	3.06316i	0.0785369	+	0.108097i
$804$		−	1.19348i		−	0.0420906i
$805$	9.78446	−	7.10883i	0.344857	−	0.250553i
$806$	−2.98968			−0.105307
$807$	12.2549			0.431392
$808$	22.9989	−	16.7097i	0.809100	−	0.587846i
$809$	−7.00801	−	21.5684i	−0.246388	−	0.758306i	−0.995405	−	0.0957544i	$-0.969474\pi$
$809$	−7.00801	−	21.5684i	−0.246388	−	0.758306i	0.749017	−	0.662551i	$-0.230526\pi$
$810$	9.32056	−	12.8287i	0.327491	−	0.450753i
$811$	11.3622	+	15.6387i	0.398980	+	0.549148i	0.960488	−	0.278323i	$-0.0897786\pi$
$811$	11.3622	+	15.6387i	0.398980	+	0.549148i	−0.561508	+	0.827471i	$0.689779\pi$
$812$	0.319628	−	0.983714i	0.0112167	−	0.0345216i
$813$	2.31847	+	7.13552i	0.0813123	+	0.250254i
$814$			6.30895i			0.221129i
$815$	−14.8050	+	45.5651i	−0.518596	+	1.59607i
$816$	1.70286	−	2.34379i	0.0596120	−	0.0820489i
$817$	−70.8128	+	23.0085i	−2.47743	+	0.804965i
$818$	16.2240	+	49.9324i	0.567260	+	1.74585i
$819$	−2.91513	−	0.947182i	−0.101863	−	0.0330972i
$820$	−9.95859	+	7.23534i	−0.347769	+	0.252669i
$821$	37.0878	+	12.0505i	1.29437	+	0.420567i	0.873620	−	0.486609i	$-0.161766\pi$
$821$	37.0878	+	12.0505i	1.29437	+	0.420567i	0.420752	+	0.907176i	$0.361766\pi$
$822$		−	14.9278i		−	0.520665i
$823$	−5.97760	+	1.94224i	−0.208366	+	0.0677023i	−0.411340	−	0.911482i	$-0.634939\pi$
$823$	−5.97760	+	1.94224i	−0.208366	+	0.0677023i	0.202974	+	0.979184i	$0.434939\pi$
$824$	−8.02478	+	2.60741i	−0.279556	+	0.0908334i
$825$			0.138026i			0.00480547i
$826$	23.1983	+	7.53757i	0.807170	+	0.262266i
$827$	32.8465	−	23.8644i	1.14218	−	0.829846i	0.154763	−	0.987952i	$-0.450539\pi$
$827$	32.8465	−	23.8644i	1.14218	−	0.829846i	0.987422	+	0.158106i	$0.0505387\pi$
$828$	6.86457	+	2.23043i	0.238560	+	0.0775129i
$829$	−10.9029	−	33.5557i	−0.378674	−	1.16544i	−0.940966	−	0.338500i	$-0.890081\pi$
$829$	−10.9029	−	33.5557i	−0.378674	−	1.16544i	0.562293	−	0.826938i	$-0.309919\pi$
$830$	18.9199	−	6.14745i	0.656719	−	0.213381i
$831$	−3.47327	+	4.78054i	−0.120486	+	0.165835i
$832$	−1.59296	+	4.90264i	−0.0552261	+	0.169968i
$833$			4.84741i			0.167953i
$834$	−1.24346	−	3.82697i	−0.0430574	−	0.132517i
$835$	−1.94098	+	5.97372i	−0.0671703	+	0.206729i
$836$	−1.20171	−	1.65401i	−0.0415619	−	0.0572050i
$837$	3.87225	−	5.32969i	0.133844	−	0.184221i
$838$	8.05086	+	24.7780i	0.278112	+	0.855942i
$839$	−15.5313	+	11.2842i	−0.536200	+	0.389572i	−0.822672	−	0.568516i	$-0.807518\pi$
$839$	−15.5313	+	11.2842i	−0.536200	+	0.389572i	0.286472	+	0.958089i	$0.407518\pi$
$840$	3.88995			0.134216
$841$	26.2854			0.906394
$842$	23.9092	−	17.3710i	0.823964	−	0.598645i
$843$		−	8.77553i		−	0.302245i
$844$	1.19779	+	1.64862i	0.0412296	+	0.0567477i
$845$	20.3099	+	14.7560i	0.698683	+	0.507623i
$846$	11.7425	+	16.1622i	0.403716	+	0.555667i
$847$	−11.3774	+	3.69675i	−0.390933	+	0.127022i
$848$	−21.1252	+	29.0764i	−0.725443	+	0.998487i
$849$	12.3697	+	8.98712i	0.424528	+	0.308437i
$850$	−0.480477	−	0.349087i	−0.0164802	−	0.0119736i
$851$	14.2917	−	43.9853i	0.489912	−	1.50780i
$852$	3.05825	+	0.993687i	0.104774	+	0.0340431i
$853$	3.33306			0.114122			0.0570609	−	0.998371i	$-0.481827\pi$
$853$	3.33306			0.114122			0.0570609	+	0.998371i	$0.481827\pi$
$854$	12.3338	+	6.29804i	0.422055	+	0.215514i
$855$	43.8870			1.50090
$856$	−16.9821	−	5.51780i	−0.580435	−	0.188595i
$857$	4.11872	−	12.6761i	0.140693	−	0.433008i	−0.855739	−	0.517408i	$-0.826897\pi$
$857$	4.11872	−	12.6761i	0.140693	−	0.433008i	0.996432	+	0.0843993i	$0.0268971\pi$
$858$	−0.451457	−	0.328002i	−0.0154125	−	0.0111978i
$859$	−6.23836	−	4.53243i	−0.212850	−	0.154645i	0.476252	−	0.879309i	$-0.341995\pi$
$859$	−6.23836	−	4.53243i	−0.212850	−	0.154645i	−0.689102	+	0.724664i	$0.741995\pi$
$860$	6.40975	−	8.82227i	0.218571	−	0.300837i
$861$	−7.67149	+	2.49262i	−0.261444	+	0.0849482i
$862$	26.0144	+	35.8058i	0.886055	+	1.21955i
$863$	−37.6703	−	27.3691i	−1.28231	−	0.931654i	−0.282692	−	0.959211i	$-0.591227\pi$
$863$	−37.6703	−	27.3691i	−1.28231	−	0.931654i	−0.999620	+	0.0275567i	$0.991227\pi$
$864$	7.21536	+	9.93109i	0.245471	+	0.337862i
$865$		−	8.77319i		−	0.298297i
$866$	30.0062	−	21.8008i	1.01965	−	0.740821i
$867$	−11.6870			−0.396910
$868$	1.05123			0.0356809
$869$	−4.17791	+	3.03543i	−0.141726	+	0.102970i
$870$	1.24913	+	3.84443i	0.0423495	+	0.130338i
$871$	−1.92132	+	2.64447i	−0.0651014	+	0.0896043i
$872$	14.5536	+	20.0313i	0.492846	+	0.678345i
$873$	−0.786766	+	2.42142i	−0.0266280	+	0.0819526i
$874$	20.9593	+	64.5061i	0.708959	+	2.18195i
$875$		−	12.8571i		−	0.434649i
$876$	−1.09232	+	3.36180i	−0.0369060	+	0.113585i
$877$	11.5634	−	15.9157i	0.390469	−	0.537435i	−0.567851	−	0.823132i	$-0.692225\pi$
$877$	11.5634	−	15.9157i	0.390469	−	0.537435i	0.958320	+	0.285697i	$0.0922249\pi$
$878$	−2.12129	+	0.689248i	−0.0715899	+	0.0232610i
$879$	0.172334	+	0.530390i	0.00581268	+	0.0178896i
$880$	−4.25882	−	1.38378i	−0.143565	−	0.0466471i
$881$	−11.7017	+	8.50177i	−0.394240	+	0.286432i	−0.767191	−	0.641419i	$-0.778346\pi$
$881$	−11.7017	+	8.50177i	−0.394240	+	0.286432i	0.372951	+	0.927851i	$0.378346\pi$
$882$	−21.8756	−	7.10780i	−0.736588	−	0.239332i
$883$		−	0.385556i		−	0.0129750i	−0.999979	−	0.00648749i	$-0.997935\pi$
$883$		−	0.385556i		−	0.0129750i	0.999979	−	0.00648749i	$-0.00206505\pi$
$884$	0.504599	−	0.163954i	0.0169715	−	0.00551438i
$885$	−20.0331	+	6.50914i	−0.673405	+	0.218802i
$886$			38.1687i			1.28230i
$887$	−29.0518	−	9.43950i	−0.975464	−	0.316948i	−0.222444	−	0.974945i	$-0.571404\pi$
$887$	−29.0518	−	9.43950i	−0.975464	−	0.316948i	−0.753020	+	0.657998i	$0.771404\pi$
$888$	12.0344	−	8.74348i	0.403847	−	0.293412i
$889$	11.7080	+	3.80416i	0.392674	+	0.127587i
$890$	−16.1891	−	49.8250i	−0.542660	−	1.67014i
$891$	−1.92119	+	0.624233i	−0.0643623	+	0.0209126i
$892$	7.71229	−	10.6150i	0.258226	−	0.355418i
$893$	−12.8186	+	39.4516i	−0.428958	+	1.32020i
$894$			17.4035i			0.582060i
$895$	−5.80414	−	17.8633i	−0.194011	−	0.597104i
$896$	4.66885	−	14.3692i	0.155975	−	0.480043i
$897$	2.40448	+	3.30948i	0.0802832	+	0.110500i
$898$	25.4459	−	35.0233i	0.849142	−	1.16874i
$899$	−0.852542	−	2.62385i	−0.0284339	−	0.0875104i
$900$	0.503785	−	0.366021i	0.0167928	−	0.0122007i
$901$	−6.26788			−0.208813
$902$	7.09663			0.236292
$903$	5.78114	−	4.20024i	0.192384	−	0.139775i
$904$		−	22.3225i		−	0.742436i
$905$	−17.3746	−	23.9141i	−0.577551	−	0.794931i
$906$	−8.44693	−	6.13705i	−0.280630	−	0.203890i
$907$	−21.5696	−	29.6880i	−0.716207	−	0.985775i	−0.999641	−	0.0267830i	$-0.991474\pi$
$907$	−21.5696	−	29.6880i	−0.716207	−	0.985775i	0.283434	−	0.958992i	$-0.408526\pi$
$908$	−0.519373	+	0.168755i	−0.0172360	+	0.00560032i
$909$	−18.0930	+	24.9029i	−0.600108	+	0.825977i
$910$	3.41282	+	2.47956i	0.113134	+	0.0821966i
$911$	−14.6044	−	10.6107i	−0.483865	−	0.351549i	0.318955	−	0.947770i	$-0.396668\pi$
$911$	−14.6044	−	10.6107i	−0.483865	−	0.351549i	−0.802820	+	0.596221i	$0.796668\pi$
$912$	−8.82068	+	27.1473i	−0.292082	+	0.898936i
$913$	−2.41024	−	0.783133i	−0.0797672	−	0.0259179i
$914$	−43.8850			−1.45159
$915$	−11.8136	+	1.86047i	−0.390547	+	0.0615052i
$916$	4.71377			0.155747
$917$	2.49861	+	0.811847i	0.0825113	+	0.0268095i
$918$	−1.63498	+	5.03196i	−0.0539624	+	0.166079i
$919$	−9.25171	−	6.72176i	−0.305186	−	0.221730i	0.424642	−	0.905361i	$-0.360400\pi$
$919$	−9.25171	−	6.72176i	−0.305186	−	0.221730i	−0.729828	+	0.683631i	$0.760400\pi$
$920$	20.2966	+	14.7464i	0.669160	+	0.486174i
$921$	−11.6907	+	16.0908i	−0.385221	+	0.530212i
$922$	−37.1303	+	12.0644i	−1.22282	+	0.397318i
$923$	−5.17670	−	7.12511i	−0.170393	−	0.234526i
$924$	0.158740	+	0.115332i	0.00522217	+	0.00379413i
$925$	−2.34531	−	3.22804i	−0.0771133	−	0.106137i
$926$			6.65110i			0.218569i
$927$	7.39140	−	5.37016i	0.242765	−	0.176379i
$928$	5.14077			0.168754
$929$	35.0763			1.15081			0.575407	−	0.817867i	$-0.304843\pi$
$929$	35.0763			1.15081			0.575407	+	0.817867i	$0.304843\pi$
$930$	−3.32367	+	2.41478i	−0.108987	+	0.0791839i
$931$	−14.7588	−	45.4230i	−0.483701	−	1.48868i
$932$	−3.95551	+	5.44430i	−0.129567	+	0.178334i
$933$	7.20375	+	9.91511i	0.235840	+	0.324606i
$934$	5.28031	−	16.2511i	0.172777	−	0.531753i
$935$	−0.241326	−	0.742725i	−0.00789220	−	0.0242897i
$936$		−	6.35826i		−	0.207826i
$937$	−3.88641	+	11.9612i	−0.126964	+	0.390754i	−0.994254	−	0.107049i	$-0.965860\pi$
$937$	−3.88641	+	11.9612i	−0.126964	+	0.390754i	0.867290	+	0.497803i	$0.165860\pi$
$938$	3.05732	−	4.20804i	0.0998251	−	0.137398i
$939$	−2.64716	+	0.860114i	−0.0863868	+	0.0280688i
$940$	−1.87740	−	5.77806i	−0.0612342	−	0.188459i
$941$	−19.4288	−	6.31279i	−0.633360	−	0.205791i	−0.0252970	−	0.999680i	$-0.508053\pi$
$941$	−19.4288	−	6.31279i	−0.633360	−	0.205791i	−0.608063	+	0.793889i	$0.708053\pi$
$942$	−4.70338	+	3.41720i	−0.153244	+	0.111338i
$943$	−49.4769	−	16.0760i	−1.61119	−	0.523507i
$944$			66.2059i			2.15482i
$945$	−8.84059	+	2.87248i	−0.287585	+	0.0934419i
$946$	−5.97917	+	1.94275i	−0.194400	+	0.0631642i
$947$		−	38.3667i		−	1.24675i	−0.781923	−	0.623375i	$-0.785761\pi$
$947$		−	38.3667i		−	1.24675i	0.781923	−	0.623375i	$-0.214239\pi$
$948$	−4.58523	−	1.48983i	−0.148921	−	0.0483875i
$949$	7.83232	−	5.69052i	0.254248	−	0.184722i
$950$	5.56521	+	1.80824i	0.180559	+	0.0586672i
$951$	−6.49489	−	19.9892i	−0.210611	−	0.648194i
$952$	2.02789	−	0.658901i	0.0657242	−	0.0213551i
$953$	−5.62694	+	7.74482i	−0.182275	+	0.250879i	−0.890370	−	0.455237i	$-0.849554\pi$
$953$	−5.62694	+	7.74482i	−0.182275	+	0.250879i	0.708096	+	0.706116i	$0.249554\pi$
$954$	9.19065	−	28.2859i	0.297558	−	0.915791i
$955$		−	3.64383i		−	0.117911i
$956$	−2.53980	−	7.81671i	−0.0821431	−	0.252811i
$957$	0.159129	−	0.489748i	0.00514391	−	0.0158313i
$958$	−3.75396	−	5.16689i	−0.121285	−	0.166935i
$959$	8.44990	−	11.6303i	0.272861	−	0.375562i
$960$	2.18897	+	6.73697i	0.0706488	+	0.217435i
$961$	−22.8111	+	16.5732i	−0.735842	+	0.534620i
$962$	16.1316			0.520103
$963$	19.3342			0.623036
$964$	2.68664	−	1.95196i	0.0865309	−	0.0628683i
$965$			0.937765i			0.0301877i
$966$	−3.82616	−	5.26626i	−0.123105	−	0.169439i
$967$	34.8063	+	25.2882i	1.11929	+	0.813214i	0.984102	−	0.177605i	$-0.0568350\pi$
$967$	34.8063	+	25.2882i	1.11929	+	0.813214i	0.135192	+	0.990819i	$0.456835\pi$
$968$	−14.5863	−	20.0763i	−0.468820	−	0.645275i
$969$	−4.73439	+	1.53830i	−0.152091	+	0.0494173i
$970$	2.05962	−	2.83482i	0.0661303	−	0.0910206i
$971$	−10.6113	−	7.70957i	−0.340533	−	0.247412i	0.404354	−	0.914603i	$-0.367497\pi$
$971$	−10.6113	−	7.70957i	−0.340533	−	0.247412i	−0.744887	+	0.667191i	$0.767497\pi$
$972$	−6.94253	−	5.04404i	−0.222682	−	0.161788i
$973$	1.19748	−	3.68547i	0.0383895	−	0.118151i
$974$	−47.9512	−	15.5803i	−1.53646	−	0.499224i
$975$	0.352925			0.0113027
$976$	−5.91278	+	37.1209i	−0.189264	+	1.18821i
$977$	7.54442			0.241367			0.120684	−	0.992691i	$-0.461491\pi$
$977$	7.54442			0.241367			0.120684	+	0.992691i	$0.461491\pi$
$978$	24.5243	+	7.96844i	0.784202	+	0.254803i
$979$	−2.06236	+	6.34728i	−0.0659132	+	0.202860i
$980$	5.65905	+	4.11154i	0.180772	+	0.131338i
$981$	−21.6896	−	15.7584i	−0.692495	−	0.503127i
$982$	−13.5105	+	18.5956i	−0.431138	+	0.593411i
$983$	−40.7265	+	13.2329i	−1.29897	+	0.422062i	−0.875225	−	0.483717i	$-0.839286\pi$
$983$	−40.7265	+	13.2329i	−1.29897	+	0.422062i	−0.423750	+	0.905779i	$0.639286\pi$
$984$	−9.83511	−	13.5369i	−0.313532	−	0.431540i
$985$	36.2501	+	26.3372i	1.15502	+	0.839174i
$986$	1.30238	+	1.79257i	0.0414763	+	0.0570872i
$987$		−	3.98115i		−	0.126721i
$988$	−4.22919	+	3.07269i	−0.134549	+	0.0977553i
$989$	46.0870			1.46548
$990$	3.70565			0.117773
$991$	20.5719	−	14.9464i	0.653489	−	0.474787i	−0.210969	−	0.977493i	$-0.567662\pi$
$991$	20.5719	−	14.9464i	0.653489	−	0.474787i	0.864458	+	0.502705i	$0.167662\pi$
$992$	1.61452	+	4.96899i	0.0512612	+	0.157766i
$993$	6.47997	−	8.91891i	0.205636	−	0.283033i
$994$	8.23749	+	11.3379i	0.261277	+	0.359617i
$995$	−1.81218	+	5.57733i	−0.0574501	+	0.176813i
$996$	−0.731121	−	2.25016i	−0.0231664	−	0.0712990i
$997$		−	16.9511i		−	0.536845i	−0.963301	−	0.268423i	$-0.913498\pi$
$997$		−	16.9511i		−	0.536845i	0.963301	−	0.268423i	$-0.0865024\pi$
$998$	3.95123	−	12.1606i	0.125074	−	0.384938i
$999$	−20.8937	+	28.7577i	−0.661047	+	0.909854i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	61.2.g.a.3.4	✓	16
3.2	odd	2		549.2.y.b.64.1		16
4.3	odd	2		976.2.bd.b.369.2		16
61.23	odd	20		3721.2.a.k.1.14		16
61.38	odd	20		3721.2.a.k.1.3		16
61.41	even	10	inner	61.2.g.a.41.4	yes	16
183.41	odd	10		549.2.y.b.163.1		16
244.163	odd	10		976.2.bd.b.529.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
61.2.g.a.3.4	✓	16	1.1	even	1	trivial
61.2.g.a.41.4	yes	16	61.41	even	10	inner
549.2.y.b.64.1		16	3.2	odd	2
549.2.y.b.163.1		16	183.41	odd	10
976.2.bd.b.369.2		16	4.3	odd	2
976.2.bd.b.529.2		16	244.163	odd	10
3721.2.a.k.1.3		16	61.38	odd	20
3721.2.a.k.1.14		16	61.23	odd	20

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:	\( N \)	\(=\)	\( 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	61.g (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.52385 + 0.495130i) q^{2} +(-0.221623 + 0.682087i) q^{3} +(0.458946 + 0.333444i) q^{4} +(-1.72728 - 1.25494i) q^{5} +(-0.675444 + 0.929669i) q^{6} +(-1.05248 + 0.341973i) q^{7} +(-1.34932 - 1.85718i) q^{8} +(2.01093 + 1.46102i) q^{9} +O(q^{10})\)	\(q+(1.52385 + 0.495130i) q^{2} +(-0.221623 + 0.682087i) q^{3} +(0.458946 + 0.333444i) q^{4} +(-1.72728 - 1.25494i) q^{5} +(-0.675444 + 0.929669i) q^{6} +(-1.05248 + 0.341973i) q^{7} +(-1.34932 - 1.85718i) q^{8} +(2.01093 + 1.46102i) q^{9} +(-2.01077 - 2.76758i) q^{10} +0.435796i q^{11} +(-0.329151 + 0.239142i) q^{12} +1.11430 q^{13} -1.77315 q^{14} +(1.23879 - 0.900031i) q^{15} +(-1.48722 - 4.57721i) q^{16} +(0.493346 - 0.679032i) q^{17} +(2.34096 + 3.22206i) q^{18} +(-2.55549 + 7.86500i) q^{19} +(-0.374276 - 1.15190i) q^{20} -0.793674i q^{21} +(-0.215776 + 0.664091i) q^{22} +(3.00873 - 4.14117i) q^{23} +(1.56580 - 0.508759i) q^{24} +(-0.136467 - 0.420002i) q^{25} +(1.69804 + 0.551726i) q^{26} +(-3.18287 + 2.31249i) q^{27} +(-0.597061 - 0.193997i) q^{28} +1.64759i q^{29} +(2.33336 - 0.758156i) q^{30} +(-1.59254 + 0.517447i) q^{31} -3.12017i q^{32} +(-0.297251 - 0.0965827i) q^{33} +(1.08800 - 0.790476i) q^{34} +(2.24709 + 0.730124i) q^{35} +(0.435737 + 1.34106i) q^{36} +(8.59295 - 2.79202i) q^{37} +(-7.78840 + 10.7198i) q^{38} +(-0.246956 + 0.760053i) q^{39} +4.90119i q^{40} +(-3.14061 - 9.66579i) q^{41} +(0.392972 - 1.20944i) q^{42} +(5.29215 + 7.28402i) q^{43} +(-0.145314 + 0.200007i) q^{44} +(-1.63993 - 5.04719i) q^{45} +(6.63529 - 4.82082i) q^{46} +5.01610 q^{47} +3.45166 q^{48} +(-4.67234 + 3.39466i) q^{49} -0.707592i q^{50} +(0.353822 + 0.486994i) q^{51} +(0.511406 + 0.371558i) q^{52} +(-4.38942 - 6.04152i) q^{53} +(-5.99521 + 1.94796i) q^{54} +(0.546900 - 0.752743i) q^{55} +(2.05524 + 1.49322i) q^{56} +(-4.79825 - 3.48614i) q^{57} +(-0.815773 + 2.51069i) q^{58} +(-13.0831 - 4.25094i) q^{59} +0.868645 q^{60} +(-6.95587 - 3.55189i) q^{61} -2.68300 q^{62} +(-2.61610 - 0.850021i) q^{63} +(-1.42956 + 4.39973i) q^{64} +(-1.92472 - 1.39839i) q^{65} +(-0.405146 - 0.294356i) q^{66} +(-1.72423 + 2.37320i) q^{67} +(0.452838 - 0.147136i) q^{68} +(2.15783 + 2.97000i) q^{69} +(3.06273 + 2.22521i) q^{70} +(-4.64567 - 6.39422i) q^{71} -5.70604i q^{72} +(7.02889 - 5.10679i) q^{73} +14.4768 q^{74} +0.316722 q^{75} +(-3.79537 + 2.75749i) q^{76} +(-0.149030 - 0.458669i) q^{77} +(-0.752651 + 1.03593i) q^{78} +(6.96524 + 9.58683i) q^{79} +(-3.17528 + 9.77251i) q^{80} +(1.43240 + 4.40846i) q^{81} -16.2843i q^{82} +(-1.79702 + 5.53065i) q^{83} +(0.264646 - 0.364253i) q^{84} +(-1.70429 + 0.553758i) q^{85} +(4.45793 + 13.7201i) q^{86} +(-1.12380 - 0.365145i) q^{87} +(0.809352 - 0.588029i) q^{88} +(14.5648 + 4.73239i) q^{89} -8.50317i q^{90} +(-1.17279 + 0.381062i) q^{91} +(2.76169 - 0.897328i) q^{92} -1.20093i q^{93} +(7.64381 + 2.48362i) q^{94} +(14.2842 - 10.3781i) q^{95} +(2.12823 + 0.691503i) q^{96} +(0.316525 + 0.974163i) q^{97} +(-8.80077 + 2.85954i) q^{98} +(-0.636709 + 0.876354i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 5 q^{2} - q^{3} + 3 q^{4} - 15 q^{6} + 10 q^{7} - 5 q^{8} + q^{9}+O(q^{10}) \) 16 * q - 5 * q^2 - q^3 + 3 * q^4 - 15 * q^6 + 10 * q^7 - 5 * q^8 + q^9	\( 16 q - 5 q^{2} - q^{3} + 3 q^{4} - 15 q^{6} + 10 q^{7} - 5 q^{8} + q^{9} - 5 q^{10} - 12 q^{13} - 18 q^{14} - 13 q^{15} + 19 q^{16} - 10 q^{18} + 3 q^{19} - 13 q^{20} + 19 q^{22} - 15 q^{23} + 10 q^{24} - 2 q^{25} + 10 q^{26} - 4 q^{27} + 35 q^{28} + 45 q^{30} - 15 q^{31} + 25 q^{33} - 14 q^{34} + 10 q^{35} + 37 q^{36} - 5 q^{37} - 15 q^{38} - 3 q^{39} + 12 q^{41} - 15 q^{42} - 25 q^{43} - 50 q^{44} + 36 q^{45} + 27 q^{46} + 6 q^{47} - 20 q^{48} - 30 q^{49} + 50 q^{51} - 46 q^{52} - 20 q^{53} - 20 q^{54} + 20 q^{55} - 28 q^{56} - 11 q^{57} - 41 q^{58} + 5 q^{59} + 14 q^{60} - 53 q^{61} + 16 q^{62} - 5 q^{63} + 17 q^{64} + 20 q^{65} + 13 q^{66} - 55 q^{67} + 80 q^{68} - 15 q^{69} - 17 q^{70} - 50 q^{71} - 11 q^{73} + 24 q^{74} - 88 q^{75} - 19 q^{76} + 63 q^{77} + 50 q^{78} + 40 q^{79} - 49 q^{80} - 19 q^{81} + 31 q^{83} - 25 q^{84} + 55 q^{85} + 35 q^{86} + 25 q^{87} + 27 q^{88} + 60 q^{89} - 15 q^{91} - 5 q^{92} + 65 q^{94} + 48 q^{95} - 25 q^{96} + 45 q^{97} + 10 q^{98} - 5 q^{99}+O(q^{100}) \) 16 * q - 5 * q^2 - q^3 + 3 * q^4 - 15 * q^6 + 10 * q^7 - 5 * q^8 + q^9 - 5 * q^10 - 12 * q^13 - 18 * q^14 - 13 * q^15 + 19 * q^16 - 10 * q^18 + 3 * q^19 - 13 * q^20 + 19 * q^22 - 15 * q^23 + 10 * q^24 - 2 * q^25 + 10 * q^26 - 4 * q^27 + 35 * q^28 + 45 * q^30 - 15 * q^31 + 25 * q^33 - 14 * q^34 + 10 * q^35 + 37 * q^36 - 5 * q^37 - 15 * q^38 - 3 * q^39 + 12 * q^41 - 15 * q^42 - 25 * q^43 - 50 * q^44 + 36 * q^45 + 27 * q^46 + 6 * q^47 - 20 * q^48 - 30 * q^49 + 50 * q^51 - 46 * q^52 - 20 * q^53 - 20 * q^54 + 20 * q^55 - 28 * q^56 - 11 * q^57 - 41 * q^58 + 5 * q^59 + 14 * q^60 - 53 * q^61 + 16 * q^62 - 5 * q^63 + 17 * q^64 + 20 * q^65 + 13 * q^66 - 55 * q^67 + 80 * q^68 - 15 * q^69 - 17 * q^70 - 50 * q^71 - 11 * q^73 + 24 * q^74 - 88 * q^75 - 19 * q^76 + 63 * q^77 + 50 * q^78 + 40 * q^79 - 49 * q^80 - 19 * q^81 + 31 * q^83 - 25 * q^84 + 55 * q^85 + 35 * q^86 + 25 * q^87 + 27 * q^88 + 60 * q^89 - 15 * q^91 - 5 * q^92 + 65 * q^94 + 48 * q^95 - 25 * q^96 + 45 * q^97 + 10 * q^98 - 5 * q^99

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