LMFDB - Embedded newform 61.2.g.a.41.4

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			41.4
Root			$-1.60228i$ of defining polynomial
Character	$\chi$	$=$	61.41
Dual form			61.2.g.a.3.4

$q$-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 $\left(\mathbb{Z}/61\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{9}{10}\right)$

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	0.284113	−	0.958791i	$-0.408301\pi$
$2$	1.52385	−	0.495130i	1.07753	−	0.350110i	0.793415	+	0.608681i	$0.208301\pi$
$3$	−0.221623	−	0.682087i	−0.127954	−	0.393803i	0.866473	−	0.499223i	$-0.166381\pi$
$3$	−0.221623	−	0.682087i	−0.127954	−	0.393803i	−0.994428	+	0.105420i	$0.966381\pi$
$4$	0.458946	−	0.333444i	0.229473	−	0.166722i
$5$	−1.72728	+	1.25494i	−0.772464	+	0.561228i	−0.902708	−	0.430254i	$-0.858424\pi$
$5$	−1.72728	+	1.25494i	−0.772464	+	0.561228i	0.130244	+	0.991482i	$0.458424\pi$
$6$	−0.675444	−	0.929669i	−0.275749	−	0.379536i
$7$	−1.05248	−	0.341973i	−0.397801	−	0.129253i	0.103283	−	0.994652i	$-0.467065\pi$
$7$	−1.05248	−	0.341973i	−0.397801	−	0.129253i	−0.501084	+	0.865399i	$0.667065\pi$
$8$	−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	$-0.979072\pi$
$11$		−	0.435796i		−	0.131398i	0.997840	−	0.0656988i	$-0.0209276\pi$
$12$	−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	0.864642	−	0.502388i	$-0.167545\pi$
$17$	0.493346	+	0.679032i	0.119654	+	0.164689i	−0.744988	+	0.667077i	$0.767545\pi$
$18$	2.34096	−	3.22206i	0.551770	−	0.759446i
$19$	−2.55549	−	7.86500i	−0.586270	−	1.80435i	−0.594109	−	0.804385i	$-0.702495\pi$
$19$	−2.55549	−	7.86500i	−0.586270	−	1.80435i	0.00783887	−	0.999969i	$-0.497505\pi$
$20$	−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	0.997863	−	0.0653402i	$-0.0208133\pi$
$23$	3.00873	+	4.14117i	0.627364	+	0.863493i	−0.370499	+	0.928833i	$0.620813\pi$
$24$	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	$-0.951115\pi$
$29$		−	1.64759i		−	0.305950i	0.988230	−	0.152975i	$-0.0488854\pi$
$30$	2.33336	+	0.758156i	0.426012	+	0.138420i
$31$	−1.59254	−	0.517447i	−0.286028	−	0.0929362i	0.162489	−	0.986710i	$-0.448048\pi$
$31$	−1.59254	−	0.517447i	−0.286028	−	0.0929362i	−0.448517	+	0.893774i	$0.648048\pi$
$32$			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	0.913266	−	0.407363i	$-0.133552\pi$
$37$	8.59295	+	2.79202i	1.41267	+	0.459005i	0.499406	+	0.866368i	$0.333552\pi$
$38$	−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	0.333404	+	0.942784i	$0.391803\pi$
$41$	−3.14061	+	9.66579i	−0.490480	+	1.50954i	−0.823884	+	0.566759i	$0.808197\pi$
$42$	0.392972	+	1.20944i	0.0606370	+	0.186621i
$43$	5.29215	−	7.28402i	0.807045	−	1.11080i	−0.184727	−	0.982790i	$-0.559140\pi$
$43$	5.29215	−	7.28402i	0.807045	−	1.11080i	0.991773	−	0.128013i	$-0.0408599\pi$
$44$	−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	−0.995973	−	0.0896553i	$-0.971423\pi$
$53$	−4.38942	+	6.04152i	−0.602933	+	0.829866i	0.393040	+	0.919521i	$0.371423\pi$
$54$	−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	−0.989190	−	0.146640i	$-0.953154\pi$
$59$	−13.0831	+	4.25094i	−1.70327	+	0.553425i	−0.714078	+	0.700066i	$0.753154\pi$
$60$	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	0.690599	−	0.723238i	$-0.257347\pi$
$67$	−1.72423	−	2.37320i	−0.210648	−	0.289932i	−0.901247	+	0.433306i	$0.857347\pi$
$68$	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	−0.990193	−	0.139704i	$-0.955385\pi$
$71$	−4.64567	+	6.39422i	−0.551340	+	0.758854i	0.438853	+	0.898559i	$0.355385\pi$
$72$			5.70604i			0.672463i
$73$	7.02889	+	5.10679i	0.822669	+	0.597704i	0.917476	−	0.397792i	$-0.130223\pi$
$73$	7.02889	+	5.10679i	0.822669	+	0.597704i	−0.0948067	+	0.995496i	$0.530223\pi$
$74$	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	−0.211219	−	0.977439i	$-0.567743\pi$
$79$	6.96524	−	9.58683i	0.783651	−	1.07860i	0.994870	−	0.101164i	$-0.0322567\pi$
$80$	−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	−0.999943	−	0.0106774i	$-0.996601\pi$
$83$	−1.79702	−	5.53065i	−0.197248	−	0.607067i	0.802695	−	0.596390i	$-0.203399\pi$
$84$	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	0.591425	−	0.806360i	$-0.298566\pi$
$89$	14.5648	−	4.73239i	1.54386	−	0.501632i	0.952439	+	0.304728i	$0.0985655\pi$
$90$			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	−0.933701	−	0.358055i	$-0.883440\pi$
$97$	0.316525	−	0.974163i	0.0321382	−	0.0989112i	0.965839	+	0.259143i	$0.0834402\pi$
$98$	−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	$-0.788705\pi$
$101$		−	12.3838i		−	1.23223i	0.787654	−	0.616117i	$-0.211295\pi$
$102$	0.298048	−	0.917296i	0.0295111	−	0.0908259i
$103$	1.13583	+	3.49572i	0.111917	+	0.344444i	0.991291	−	0.131686i	$-0.0420392\pi$
$103$	1.13583	+	3.49572i	0.111917	+	0.344444i	−0.879375	+	0.476130i	$0.842039\pi$
$104$	−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	0.848833	−	0.528661i	$-0.177306\pi$
$107$	6.29282	+	4.57200i	0.608350	+	0.441992i	−0.240483	+	0.970653i	$0.577306\pi$
$108$	−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	−0.152672	−	0.988277i	$-0.548788\pi$
$113$	7.86692	−	5.71565i	0.740057	−	0.537683i	0.892729	+	0.450594i	$0.148788\pi$
$114$	−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	−0.910500	−	0.413510i	$-0.864303\pi$
$127$	−8.99964	+	6.53862i	−0.798589	+	0.580209i	0.111911	+	0.993718i	$0.464303\pi$
$128$	−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	−0.668518	−	0.743696i	$-0.733071\pi$
$131$	−1.92061	+	1.39541i	−0.167805	+	0.121917i	0.500713	+	0.865613i	$0.333071\pi$
$132$	−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	0.0400360	−	0.999198i	$-0.487253\pi$
$137$	−10.5095	−	7.63559i	−0.897886	−	0.652352i	−0.937922	+	0.346846i	$0.887253\pi$
$138$	1.81768	−	5.59425i	0.154731	−	0.476214i
$139$	−2.05824	−	2.83293i	−0.174578	−	0.240286i	0.712758	−	0.701411i	$-0.247446\pi$
$139$	−2.05824	−	2.83293i	−0.174578	−	0.240286i	−0.887335	+	0.461125i	$0.847446\pi$
$140$	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	0.962891	−	0.269889i	$-0.0869870\pi$
$149$	12.2525	+	8.90194i	1.00376	+	0.729276i	0.0408703	+	0.999164i	$0.486987\pi$
$150$	0.482639	−	0.156819i	0.0394073	−	0.0128042i
$151$		−	9.08595i		−	0.739404i	−0.929150	−	0.369702i	$-0.879460\pi$
$151$		−	9.08595i		−	0.739404i	0.929150	−	0.369702i	$-0.120540\pi$
$152$	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	−0.110651	−	0.993859i	$-0.535294\pi$
$157$	4.81158	−	1.56338i	0.384006	−	0.124771i	0.494657	+	0.869088i	$0.335294\pi$
$158$	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	0.182244	+	0.983253i	$0.441664\pi$
$163$	−6.93430	+	21.3416i	−0.543136	+	1.67160i	−0.725381	+	0.688348i	$0.758336\pi$
$164$	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	−0.980050	−	0.198753i	$-0.936311\pi$
$167$	−0.909108	+	2.79795i	−0.0703489	+	0.216512i	0.909701	+	0.415264i	$0.136311\pi$
$168$	−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	−0.707270	−	0.706944i	$-0.750073\pi$
$173$	2.41530	−	3.32437i	0.183632	−	0.252747i	0.890902	+	0.454196i	$0.150073\pi$
$174$	−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	−0.289129	−	0.957290i	$-0.593366\pi$
$179$	7.11717	−	5.17093i	0.531962	−	0.386493i	0.821091	+	0.570797i	$0.193366\pi$
$180$	0.930315	+	2.86321i	0.0693416	+	0.213411i
$181$	13.1673	−	4.27832i	0.978718	−	0.318005i	0.224388	−	0.974500i	$-0.427962\pi$
$181$	13.1673	−	4.27832i	0.978718	−	0.318005i	0.754330	+	0.656495i	$0.227962\pi$
$182$	−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	−0.771180	−	0.636617i	$-0.780333\pi$
$191$	1.00316	−	1.38073i	0.0725862	−	0.0999064i	0.843766	+	0.536711i	$0.180333\pi$
$192$	−2.68417	+	1.95017i	−0.193713	+	0.140741i
$193$	−0.258171	+	0.355342i	−0.0185835	+	0.0255780i	−0.818208	−	0.574923i	$-0.805032\pi$
$193$	−0.258171	+	0.355342i	−0.0185835	+	0.0255780i	0.799624	+	0.600501i	$0.205032\pi$
$194$		−	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	−0.976623	−	0.214959i	$-0.931038\pi$
$199$	−0.848783	+	2.61229i	−0.0601687	+	0.185180i	0.916454	+	0.400139i	$0.131038\pi$
$200$	−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	−0.189049	−	0.981968i	$-0.560541\pi$
$211$	3.41637	−	1.11004i	0.235192	−	0.0764186i	0.424242	+	0.905549i	$0.360541\pi$
$212$			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	$0.281960\pi$
$223$			23.1292i			1.54885i	−0.632668	+	0.774423i	$0.718040\pi$
$224$	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	0.789826	−	0.613331i	$-0.210171\pi$
$227$	−0.565833	−	0.778802i	−0.0375556	−	0.0516909i	−0.827382	+	0.561640i	$0.810171\pi$
$228$	−1.03971	+	3.19989i	−0.0688564	+	0.211918i
$229$	6.72236	+	4.88408i	0.444226	+	0.322749i	0.787312	−	0.616555i	$-0.211472\pi$
$229$	6.72236	+	4.88408i	0.444226	+	0.322749i	−0.343086	+	0.939304i	$0.611472\pi$
$230$	−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	$-0.872968\pi$
$233$		−	11.8626i		−	0.777146i	0.921418	−	0.388573i	$-0.127032\pi$
$234$	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	−0.898352	−	0.439277i	$-0.855235\pi$
$239$	−11.7212	+	8.51594i	−0.758181	+	0.550851i	0.140171	+	0.990127i	$0.455235\pi$
$240$	−5.96198	+	4.33163i	−0.384844	+	0.279606i
$241$	1.80897	+	5.56743i	0.116526	+	0.358629i	0.992262	−	0.124160i	$-0.0396236\pi$
$241$	1.80897	+	5.56743i	0.116526	+	0.358629i	−0.875736	+	0.482789i	$0.839624\pi$
$242$	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	0.355726	−	0.934590i	$-0.384234\pi$
$251$	1.49203	+	0.484789i	0.0941760	+	0.0305996i	−0.261550	+	0.965190i	$0.584234\pi$
$252$	−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	0.954625	+	0.297811i	$0.0962566\pi$
$263$	5.79551	+	17.8367i	0.357366	+	1.09986i	−0.597259	+	0.802049i	$0.703743\pi$
$264$	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	0.650856	+	0.759202i	$0.274410\pi$
$269$	−5.28029	+	16.2511i	−0.321945	+	0.990845i	−0.972801	+	0.231644i	$0.925590\pi$
$270$	12.8000	−	4.15897i	0.778983	−	0.253107i
$271$	8.46337	+	6.14900i	0.514113	+	0.373525i	0.814382	−	0.580330i	$-0.197076\pi$
$271$	8.46337	+	6.14900i	0.514113	+	0.373525i	−0.300268	+	0.953855i	$0.597076\pi$
$272$	−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	−0.0639923	−	0.997950i	$-0.520383\pi$
$277$	7.83596	−	2.54606i	0.470817	−	0.152978i	0.534810	+	0.844973i	$0.320383\pi$
$278$	−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	−0.0594058	−	0.998234i	$-0.518921\pi$
$281$	−11.6371	−	3.78113i	−0.694213	−	0.225564i	−0.634807	+	0.772670i	$0.718921\pi$
$282$	−3.38810	−	4.66331i	−0.201758	−	0.277696i
$283$	6.58796	+	20.2757i	0.391614	+	1.20526i	0.931568	+	0.363568i	$0.118442\pi$
$283$	6.58796	+	20.2757i	0.391614	+	1.20526i	−0.539954	+	0.841695i	$0.681558\pi$
$284$			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	0.606010	−	0.795457i	$-0.292769\pi$
$293$	0.629090	+	0.457061i	0.0367519	+	0.0267018i	−0.569258	+	0.822159i	$0.692769\pi$
$294$			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	0.563747	−	0.825948i	$-0.309359\pi$
$307$	26.3751	−	8.56979i	1.50531	−	0.489104i	0.941560	+	0.336844i	$0.109359\pi$
$308$	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	0.992503	−	0.122217i	$-0.0390005\pi$
$311$	10.0444	+	13.8250i	0.569567	+	0.783942i	−0.422936	+	0.906160i	$0.639000\pi$
$312$	1.74478	+	0.566912i	0.0987785	+	0.0320951i
$313$	2.28118	−	3.13977i	0.128940	−	0.177470i	−0.739666	−	0.672974i	$-0.765017\pi$
$313$	2.28118	−	3.13977i	0.128940	−	0.177470i	0.868606	+	0.495504i	$0.165017\pi$
$314$	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	−0.999708	−	0.0241800i	$-0.992303\pi$
$317$	−23.7090	−	17.2256i	−1.33163	−	0.967486i	−0.331923	−	0.943306i	$-0.607697\pi$
$318$	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	−0.681864	−	0.731479i	$-0.738830\pi$
$331$	−14.6193	+	4.75011i	−0.803551	+	0.261089i	−0.121687	+	0.992569i	$0.538830\pi$
$332$	−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	$0.0805758\pi$
$337$			9.19500i			0.500883i	−0.968132	+	0.250442i	$0.919424\pi$
$338$	−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	0.925010	−	0.379944i	$-0.124057\pi$
$347$	−0.869255	−	2.67529i	−0.0466641	−	0.143617i	−0.971674	+	0.236326i	$0.924057\pi$
$348$	−0.394008	+	0.542306i	−0.0211211	+	0.0290707i
$349$	6.99525	+	9.62814i	0.374447	+	0.515382i	0.954103	−	0.299479i	$-0.0968129\pi$
$349$	6.99525	+	9.62814i	0.374447	+	0.515382i	−0.579656	+	0.814862i	$0.696813\pi$
$350$	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	0.148274	−	0.988946i	$-0.452628\pi$
$359$	−5.93160	−	1.92729i	−0.313058	−	0.101719i	−0.461332	+	0.887228i	$0.652628\pi$
$360$	−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	0.847165	−	0.531330i	$-0.178308\pi$
$373$	23.5665	+	7.65722i	1.22023	+	0.396476i	0.373063	+	0.927806i	$0.378308\pi$
$374$	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	−0.829677	−	0.558244i	$-0.811475\pi$
$383$	−21.6099	−	29.7435i	−1.10421	−	1.51982i	−0.274538	−	0.961576i	$-0.588525\pi$
$384$	−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	0.893781	−	0.448504i	$-0.148043\pi$
$389$	3.76778	+	5.18591i	0.191034	+	0.262936i	−0.702746	+	0.711440i	$0.748043\pi$
$390$	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	−0.410240	−	0.911977i	$-0.634555\pi$
$397$	−25.4675	−	8.27490i	−1.27818	−	0.415305i	−0.867938	+	0.496672i	$0.834555\pi$
$398$			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	0.387706	−	0.921783i	$-0.373268\pi$
$401$	24.8946	−	8.08874i	1.24318	−	0.403933i	0.855471	+	0.517851i	$0.173268\pi$
$402$	−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	0.00187261	−	0.999998i	$-0.499404\pi$
$409$	19.2601	−	26.5092i	0.952349	−	1.31080i	0.950476	−	0.310797i	$-0.100596\pi$
$410$	−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	−0.509013	−	0.860759i	$-0.669989\pi$
$419$	9.55743	−	13.1547i	0.466911	−	0.642648i	0.975924	+	0.218111i	$0.0699894\pi$
$420$	−0.914235	−	0.297053i	−0.0446101	−	0.0144947i
$421$	10.8415	+	14.9220i	0.528381	+	0.727254i	0.986883	−	0.161440i	$-0.0516137\pi$
$421$	10.8415	+	14.9220i	0.528381	+	0.727254i	−0.458502	+	0.888694i	$0.651614\pi$
$422$	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	0.0993553	−	0.995052i	$-0.468322\pi$
$431$	22.3468	−	16.2359i	1.07641	−	0.782057i	0.977053	+	0.212995i	$0.0683220\pi$
$432$	15.3184	−	11.1294i	0.737006	−	0.535466i
$433$	13.6061	+	18.7272i	0.653869	+	0.899974i	0.999259	−	0.0384855i	$-0.0122533\pi$
$433$	13.6061	+	18.7272i	0.653869	+	0.899974i	−0.345390	+	0.938459i	$0.612253\pi$
$434$	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	0.560586	−	0.828096i	$-0.310576\pi$
$439$	−1.12619	−	0.818228i	−0.0537503	−	0.0390519i	−0.614336	+	0.789045i	$0.710576\pi$
$440$	−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	−0.609250	−	0.792978i	$-0.708529\pi$
$443$	7.36127	−	22.6557i	0.349744	−	1.07640i	0.958995	−	0.283424i	$-0.0914705\pi$
$444$	−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	0.929720	+	0.368268i	$0.120049\pi$
$449$	8.34920	+	25.6962i	0.394023	+	1.21268i	−0.535697	+	0.844410i	$0.679951\pi$
$450$	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	−0.371968	−	0.928246i	$-0.621317\pi$
$457$	−26.0487	−	8.46372i	−1.21851	−	0.395916i	−0.846537	+	0.532329i	$0.821317\pi$
$458$	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	0.0249480	−	0.999689i	$-0.492058\pi$
$461$	−19.7125	−	14.3220i	−0.918103	−	0.667041i	−0.943051	+	0.332648i	$0.892058\pi$
$462$	0.527072	−	0.171256i	0.0245216	−	0.00796755i
$463$	1.28274	−	3.94787i	0.0596140	−	0.183473i	−0.916815	−	0.399313i	$-0.869249\pi$
$463$	1.28274	−	3.94787i	0.0596140	−	0.183473i	0.976429	+	0.215840i	$0.0692488\pi$
$464$	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	$0.0793615\pi$
$467$			10.6645i			0.493493i	−0.969080	+	0.246746i	$0.920639\pi$
$468$	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	−0.659014	−	0.752131i	$-0.729026\pi$
$479$	−3.22472	+	2.34289i	−0.147341	+	0.107050i	0.511673	+	0.859181i	$0.329026\pi$
$480$	−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	−0.999880	−	0.0154797i	$-0.995072\pi$
$491$	−4.43301	−	13.6434i	−0.200059	−	0.615718i	0.799821	−	0.600238i	$-0.204928\pi$
$492$	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	$0.0571636\pi$
$499$			7.98018i			0.357242i	−0.983918	+	0.178621i	$0.942836\pi$
$500$	−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	0.222523	−	0.974927i	$-0.428571\pi$
$503$	−14.2623	−	10.3622i	−0.635925	−	0.462026i	−0.858448	+	0.512901i	$0.828571\pi$
$504$	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	$-0.990541\pi$
$509$		−	1.34069i		−	0.0594249i	0.999558	−	0.0297125i	$-0.00945916\pi$
$510$	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	−0.573869	−	0.818947i	$-0.694558\pi$
$521$	−12.7086	+	4.12928i	−0.556775	+	0.180907i	0.0170948	+	0.999854i	$0.494558\pi$
$522$	−5.30864	−	3.85695i	−0.232353	−	0.168814i
$523$	1.20306	−	0.390897i	0.0526060	−	0.0170927i	−0.282596	−	0.959239i	$-0.591196\pi$
$523$	1.20306	−	0.390897i	0.0526060	−	0.0170927i	0.335202	+	0.942146i	$0.391196\pi$
$524$	−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	0.0354996	−	0.999370i	$-0.488698\pi$
$541$	22.6776	−	31.2131i	0.974987	−	1.34195i	0.939487	−	0.342584i	$-0.111302\pi$
$542$	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	0.370016	−	0.929025i	$-0.379352\pi$
$547$	28.4266	−	9.23635i	1.21543	−	0.394918i	0.845416	+	0.534108i	$0.179352\pi$
$548$	−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	−0.0910448	+	0.995847i	$0.529021\pi$
$557$	−23.8373	+	32.8092i	−1.01002	+	1.39017i	−0.918972	+	0.394322i	$0.870979\pi$
$558$	−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	−0.675763	−	0.737119i	$-0.736186\pi$
$569$	7.25649	−	22.3332i	0.304208	−	0.936256i	0.979972	−	0.199138i	$-0.0638141\pi$
$570$		−	20.2894i		−	0.849828i
$571$	−13.3458	−	41.0740i	−0.558503	−	1.71890i	−0.686509	−	0.727122i	$-0.740858\pi$
$571$	−13.3458	−	41.0740i	−0.558503	−	1.71890i	0.128006	−	0.991773i	$-0.459142\pi$
$572$	−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	−0.138399	−	0.990377i	$-0.544196\pi$
$577$	7.96921	−	2.58935i	0.331763	−	0.107796i	0.470162	+	0.882580i	$0.344196\pi$
$578$		−	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	0.913362	+	0.407148i	$0.133477\pi$
$587$	24.6724	+	33.9586i	1.01834	+	1.40162i	0.104977	+	0.994475i	$0.466523\pi$
$588$	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	0.904997	−	0.425419i	$-0.139873\pi$
$593$	5.37537	+	7.39857i	0.220740	+	0.303823i	−0.684257	+	0.729241i	$0.739873\pi$
$594$	−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	$-0.921446\pi$
$599$		−	11.9577i		−	0.488577i	0.969703	−	0.244288i	$-0.0785544\pi$
$600$	−0.427360	+	0.588210i	−0.0174469	+	0.0240136i
$601$	20.0300	−	14.5526i	0.817040	−	0.593614i	−0.0988232	−	0.995105i	$-0.531508\pi$
$601$	20.0300	−	14.5526i	0.817040	−	0.593614i	0.915863	+	0.401491i	$0.131508\pi$
$602$	−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	0.994227	+	0.107298i	$0.0342199\pi$
$607$	6.23199	+	19.1801i	0.252949	+	0.778496i	−0.741278	+	0.671198i	$0.765780\pi$
$608$	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	−0.952522	−	0.304469i	$-0.901521\pi$
$613$	−8.93492	−	27.4989i	−0.360878	−	1.11067i	0.591644	−	0.806199i	$-0.298479\pi$
$614$	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	−0.724641	−	0.689126i	$-0.757995\pi$
$617$	−42.6232	−	13.8491i	−1.71595	−	0.557545i	−0.991305	+	0.131581i	$0.957995\pi$
$618$	2.48267	−	3.41711i	0.0998678	−	0.137456i
$619$	−20.9878	+	15.2485i	−0.843570	+	0.612890i	−0.923366	−	0.383922i	$-0.874573\pi$
$619$	−20.9878	+	15.2485i	−0.843570	+	0.612890i	0.0797954	+	0.996811i	$0.474573\pi$
$620$	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	$-0.749515\pi$
$631$		−	35.5787i		−	1.41637i	0.706029	−	0.708183i	$-0.250485\pi$
$632$	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	0.244838	−	0.969564i	$-0.421265\pi$
$641$	−3.21488	−	1.04458i	−0.126980	−	0.0412583i	−0.371818	+	0.928306i	$0.621265\pi$
$642$		−	8.93837i		−	0.352769i
$643$	2.99226	−	0.972246i	0.118003	−	0.0383416i	−0.249420	−	0.968395i	$-0.580240\pi$
$643$	2.99226	−	0.972246i	0.118003	−	0.0383416i	0.367423	+	0.930054i	$0.380240\pi$
$644$	−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	0.695153	−	0.718862i	$-0.255337\pi$
$647$	21.2394	+	6.90110i	0.835007	+	0.271310i	0.139854	+	0.990172i	$0.455337\pi$
$648$	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	−0.975071	−	0.221894i	$-0.928776\pi$
$653$	−11.8244	+	16.2749i	−0.462724	+	0.636884i	0.512347	+	0.858778i	$0.328776\pi$
$654$	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	0.770970	−	0.636872i	$-0.219772\pi$
$659$	10.3585	+	7.52591i	0.403511	+	0.293168i	−0.367459	+	0.930040i	$0.619772\pi$
$660$		−	0.378553i		−	0.0147351i
$661$	2.82958	−	3.89459i	0.110058	−	0.151482i	−0.750435	−	0.660945i	$-0.770156\pi$
$661$	2.82958	−	3.89459i	0.110058	−	0.151482i	0.860493	+	0.509463i	$0.170156\pi$
$662$	−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	0.391830	−	0.920038i	$-0.371842\pi$
$673$	32.4177	−	10.5332i	1.24961	−	0.406024i	0.857782	+	0.514014i	$0.171842\pi$
$674$	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	0.750376	−	0.661011i	$-0.229872\pi$
$677$	−2.86632	−	3.94515i	−0.110162	−	0.151625i	−0.860538	+	0.509386i	$0.829872\pi$
$678$	−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	0.881662	−	0.471881i	$-0.156425\pi$
$683$	18.4332	+	13.3925i	0.705325	+	0.512449i	−0.176337	+	0.984330i	$0.556425\pi$
$684$	−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	0.384319	+	0.923200i	$0.374436\pi$
$691$	−12.3350	+	37.9632i	−0.469245	+	1.44419i	−0.853564	+	0.520988i	$0.825564\pi$
$692$		−	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	0.267050	−	0.963683i	$-0.413951\pi$
$701$	−2.20656	−	0.716954i	−0.0833406	−	0.0270790i	−0.350391	+	0.936604i	$0.613951\pi$
$702$	−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	−0.991890	−	0.127100i	$-0.959433\pi$
$709$	−21.4683	−	29.5486i	−0.806258	−	1.10972i	0.185632	−	0.982619i	$-0.440567\pi$
$710$	−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	0.147051	−	0.989129i	$-0.453022\pi$
$727$	30.5547	−	22.1993i	1.13321	−	0.823325i	0.986159	+	0.165804i	$0.0530219\pi$
$728$	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	−0.249338	−	0.968416i	$-0.580213\pi$
$739$	−27.7358	−	9.01191i	−1.02028	−	0.331509i	−0.770940	+	0.636908i	$0.780213\pi$
$740$	−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	$-0.915194\pi$
$743$		−	14.3532i		−	0.526569i	0.964718	−	0.263285i	$-0.0848059\pi$
$744$	−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	0.960968	+	0.276661i	$0.0892278\pi$
$751$	9.48591	+	29.1946i	0.346146	+	1.06533i	−0.614822	+	0.788666i	$0.710772\pi$
$752$	−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	−0.990906	−	0.134555i	$-0.957039\pi$
$757$	−3.03081	+	9.32787i	−0.110157	+	0.339027i	0.880750	+	0.473582i	$0.157039\pi$
$758$	−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	$-0.910521\pi$
$761$		−	15.3059i		−	0.554838i	0.960749	−	0.277419i	$-0.0894790\pi$
$762$	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	0.710269	−	0.703930i	$-0.248573\pi$
$769$	24.1571	+	7.84913i	0.871129	+	0.283047i	0.160860	+	0.986977i	$0.448573\pi$
$770$	−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	−0.585443	−	0.810713i	$-0.699079\pi$
$773$	10.1401	−	31.2082i	0.364716	−	1.12248i	0.950159	−	0.311766i	$-0.100921\pi$
$774$	−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	0.884689	+	0.466182i	$0.154371\pi$
$787$	29.5872	+	40.7233i	1.05467	+	1.45163i	0.169982	+	0.985447i	$0.445629\pi$
$788$	−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	−0.787152	−	0.616759i	$-0.788445\pi$
$797$	−12.5296	+	9.10330i	−0.443822	+	0.322455i	0.343330	+	0.939215i	$0.388445\pi$
$798$	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	0.749017	+	0.662551i	$0.230526\pi$
$809$	−7.00801	+	21.5684i	−0.246388	+	0.758306i	−0.995405	+	0.0957544i	$0.969474\pi$
$810$	9.32056	+	12.8287i	0.327491	+	0.450753i
$811$	11.3622	−	15.6387i	0.398980	−	0.549148i	−0.561508	−	0.827471i	$-0.689779\pi$
$811$	11.3622	−	15.6387i	0.398980	−	0.549148i	0.960488	+	0.278323i	$0.0897786\pi$
$812$	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	0.420752	−	0.907176i	$-0.361766\pi$
$821$	37.0878	−	12.0505i	1.29437	−	0.420567i	0.873620	+	0.486609i	$0.161766\pi$
$822$			14.9278i			0.520665i
$823$	−5.97760	−	1.94224i	−0.208366	−	0.0677023i	0.202974	−	0.979184i	$-0.434939\pi$
$823$	−5.97760	−	1.94224i	−0.208366	−	0.0677023i	−0.411340	+	0.911482i	$0.634939\pi$
$824$	−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	0.987422	−	0.158106i	$-0.0505387\pi$
$827$	32.8465	+	23.8644i	1.14218	+	0.829846i	0.154763	+	0.987952i	$0.450539\pi$
$828$	6.86457	−	2.23043i	0.238560	−	0.0775129i
$829$	−10.9029	+	33.5557i	−0.378674	+	1.16544i	0.562293	+	0.826938i	$0.309919\pi$
$829$	−10.9029	+	33.5557i	−0.378674	+	1.16544i	−0.940966	+	0.338500i	$0.890081\pi$
$830$	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	0.286472	−	0.958089i	$-0.407518\pi$
$839$	−15.5313	−	11.2842i	−0.536200	−	0.389572i	−0.822672	+	0.568516i	$0.807518\pi$
$840$	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	0.996432	−	0.0843993i	$-0.0268971\pi$
$857$	4.11872	+	12.6761i	0.140693	+	0.433008i	−0.855739	+	0.517408i	$0.826897\pi$
$858$	−0.451457	+	0.328002i	−0.0154125	+	0.0111978i
$859$	−6.23836	+	4.53243i	−0.212850	+	0.154645i	−0.689102	−	0.724664i	$-0.741995\pi$
$859$	−6.23836	+	4.53243i	−0.212850	+	0.154645i	0.476252	+	0.879309i	$0.341995\pi$
$860$	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	−0.999620	−	0.0275567i	$-0.991227\pi$
$863$	−37.6703	+	27.3691i	−1.28231	+	0.931654i	−0.282692	+	0.959211i	$0.591227\pi$
$864$	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	0.958320	−	0.285697i	$-0.0922249\pi$
$877$	11.5634	+	15.9157i	0.390469	+	0.537435i	−0.567851	+	0.823132i	$0.692225\pi$
$878$	−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	0.372951	−	0.927851i	$-0.378346\pi$
$881$	−11.7017	−	8.50177i	−0.394240	−	0.286432i	−0.767191	+	0.641419i	$0.778346\pi$
$882$	−21.8756	+	7.10780i	−0.736588	+	0.239332i
$883$			0.385556i			0.0129750i	0.999979	+	0.00648749i	$0.00206505\pi$
$883$			0.385556i			0.0129750i	−0.999979	+	0.00648749i	$0.997935\pi$
$884$	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	−0.753020	−	0.657998i	$-0.771404\pi$
$887$	−29.0518	+	9.43950i	−0.975464	+	0.316948i	−0.222444	+	0.974945i	$0.571404\pi$
$888$	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	0.283434	+	0.958992i	$0.408526\pi$
$907$	−21.5696	+	29.6880i	−0.716207	+	0.985775i	−0.999641	+	0.0267830i	$0.991474\pi$
$908$	−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	−0.802820	−	0.596221i	$-0.796668\pi$
$911$	−14.6044	+	10.6107i	−0.483865	+	0.351549i	0.318955	+	0.947770i	$0.396668\pi$
$912$	−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	−0.729828	−	0.683631i	$-0.760400\pi$
$919$	−9.25171	+	6.72176i	−0.305186	+	0.221730i	0.424642	+	0.905361i	$0.360400\pi$
$920$	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	0.867290	−	0.497803i	$-0.165860\pi$
$937$	−3.88641	−	11.9612i	−0.126964	−	0.390754i	−0.994254	+	0.107049i	$0.965860\pi$
$938$	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	−0.608063	−	0.793889i	$-0.708053\pi$
$941$	−19.4288	+	6.31279i	−0.633360	+	0.205791i	−0.0252970	+	0.999680i	$0.508053\pi$
$942$	−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	$0.214239\pi$
$947$			38.3667i			1.24675i	−0.781923	+	0.623375i	$0.785761\pi$
$948$	−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	0.708096	−	0.706116i	$-0.249554\pi$
$953$	−5.62694	−	7.74482i	−0.182275	−	0.250879i	−0.890370	+	0.455237i	$0.849554\pi$
$954$	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	0.135192	−	0.990819i	$-0.456835\pi$
$967$	34.8063	−	25.2882i	1.11929	−	0.813214i	0.984102	+	0.177605i	$0.0568350\pi$
$968$	−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	−0.744887	−	0.667191i	$-0.767497\pi$
$971$	−10.6113	+	7.70957i	−0.340533	+	0.247412i	0.404354	+	0.914603i	$0.367497\pi$
$972$	−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	−0.423750	−	0.905779i	$-0.639286\pi$
$983$	−40.7265	−	13.2329i	−1.29897	−	0.422062i	−0.875225	+	0.483717i	$0.839286\pi$
$984$	−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	0.864458	−	0.502705i	$-0.167662\pi$
$991$	20.5719	+	14.9464i	0.653489	+	0.474787i	−0.210969	+	0.977493i	$0.567662\pi$
$992$	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	$0.0865024\pi$
$997$			16.9511i			0.536845i	−0.963301	+	0.268423i	$0.913498\pi$
$998$	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.41.4	yes	16
3.2	odd	2		549.2.y.b.163.1		16
4.3	odd	2		976.2.bd.b.529.2		16
61.3	even	10	inner	61.2.g.a.3.4	✓	16
61.8	odd	20		3721.2.a.k.1.14		16
61.53	odd	20		3721.2.a.k.1.3		16
183.125	odd	10		549.2.y.b.64.1		16
244.3	odd	10		976.2.bd.b.369.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
61.2.g.a.3.4	✓	16	61.3	even	10	inner
61.2.g.a.41.4	yes	16	1.1	even	1	trivial
549.2.y.b.64.1		16	183.125	odd	10
549.2.y.b.163.1		16	3.2	odd	2
976.2.bd.b.369.2		16	244.3	odd	10
976.2.bd.b.529.2		16	4.3	odd	2
3721.2.a.k.1.3		16	61.53	odd	20
3721.2.a.k.1.14		16	61.8	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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