LMFDB - Embedded newform 561.2.m.d.103.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [561,2,Mod(103,561)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(561, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("561.103");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 561 = 3 \cdot 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	561.m (of order $5$, 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:	$4.47960755339$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			103.4
Character	$\chi$	$=$	561.103
Dual form			561.2.m.d.256.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.357186 + 0.259511i) q^{2} +(0.309017 - 0.951057i) q^{3} +(-0.557798 - 1.71673i) q^{4} +(3.46967 - 2.52087i) q^{5} +(0.357186 - 0.259511i) q^{6} +(0.982692 + 3.02442i) q^{7} +(0.519138 - 1.59774i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(0.357186 + 0.259511i) q^{2} +(0.309017 - 0.951057i) q^{3} +(-0.557798 - 1.71673i) q^{4} +(3.46967 - 2.52087i) q^{5} +(0.357186 - 0.259511i) q^{6} +(0.982692 + 3.02442i) q^{7} +(0.519138 - 1.59774i) q^{8} +(-0.809017 - 0.587785i) q^{9} +1.89351 q^{10} +(3.28652 - 0.445822i) q^{11} -1.80507 q^{12} +(1.67324 + 1.21568i) q^{13} +(-0.433865 + 1.33530i) q^{14} +(-1.32530 - 4.07885i) q^{15} +(-2.32061 + 1.68602i) q^{16} +(-0.809017 + 0.587785i) q^{17} +(-0.136433 - 0.419898i) q^{18} +(-2.03036 + 6.24882i) q^{19} +(-6.26301 - 4.55035i) q^{20} +3.18006 q^{21} +(1.28960 + 0.693648i) q^{22} -4.53626 q^{23} +(-1.35912 - 0.987458i) q^{24} +(4.13879 - 12.7379i) q^{25} +(0.282176 + 0.868450i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(4.64395 - 3.37403i) q^{28} +(0.837857 + 2.57866i) q^{29} +(0.585128 - 1.80084i) q^{30} +(-6.01941 - 4.37335i) q^{31} -4.62636 q^{32} +(0.591590 - 3.26344i) q^{33} -0.441507 q^{34} +(11.0338 + 8.01650i) q^{35} +(-0.557798 + 1.71673i) q^{36} +(0.750404 + 2.30951i) q^{37} +(-2.34686 + 1.70509i) q^{38} +(1.67324 - 1.21568i) q^{39} +(-2.22645 - 6.85232i) q^{40} +(1.58166 - 4.86784i) q^{41} +(1.13587 + 0.825261i) q^{42} -8.01474 q^{43} +(-2.59857 - 5.39338i) q^{44} -4.28875 q^{45} +(-1.62029 - 1.17721i) q^{46} +(-2.61064 + 8.03474i) q^{47} +(0.886393 + 2.72804i) q^{48} +(-2.51829 + 1.82964i) q^{49} +(4.78394 - 3.47574i) q^{50} +(0.309017 + 0.951057i) q^{51} +(1.15366 - 3.55060i) q^{52} +(-1.62369 - 1.17968i) q^{53} -0.441507 q^{54} +(10.2793 - 9.83175i) q^{55} +5.34239 q^{56} +(5.31556 + 3.86198i) q^{57} +(-0.369919 + 1.13849i) q^{58} +(3.21633 + 9.89884i) q^{59} +(-6.26301 + 4.55035i) q^{60} +(-6.80158 + 4.94164i) q^{61} +(-1.01512 - 3.12421i) q^{62} +(0.982692 - 3.02442i) q^{63} +(2.98874 + 2.17145i) q^{64} +8.87018 q^{65} +(1.05821 - 1.01213i) q^{66} +10.6245 q^{67} +(1.46033 + 1.06099i) q^{68} +(-1.40178 + 4.31424i) q^{69} +(1.86074 + 5.72677i) q^{70} +(9.60251 - 6.97663i) q^{71} +(-1.35912 + 0.987458i) q^{72} +(-1.62234 - 4.99305i) q^{73} +(-0.331309 + 1.01966i) q^{74} +(-10.8355 - 7.87245i) q^{75} +11.8600 q^{76} +(4.57799 + 9.50171i) q^{77} +0.913142 q^{78} +(-5.92238 - 4.30286i) q^{79} +(-3.80152 + 11.6999i) q^{80} +(0.309017 + 0.951057i) q^{81} +(1.82821 - 1.32827i) q^{82} +(-6.16278 + 4.47752i) q^{83} +(-1.77383 - 5.45929i) q^{84} +(-1.32530 + 4.07885i) q^{85} +(-2.86275 - 2.07991i) q^{86} +2.71136 q^{87} +(0.993851 - 5.48246i) q^{88} -8.06013 q^{89} +(-1.53188 - 1.11298i) q^{90} +(-2.03244 + 6.25522i) q^{91} +(2.53031 + 7.78751i) q^{92} +(-6.01941 + 4.37335i) q^{93} +(-3.01759 + 2.19241i) q^{94} +(8.70773 + 26.7996i) q^{95} +(-1.42962 + 4.39993i) q^{96} +(0.748010 + 0.543461i) q^{97} -1.37431 q^{98} +(-2.92090 - 1.57109i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{2} - 6 q^{3} - 7 q^{4} + 7 q^{5} + 3 q^{6} + 5 q^{7} - 10 q^{8} - 6 q^{9}+O(q^{10}) $ 24 * q + 3 * q^2 - 6 * q^3 - 7 * q^4 + 7 * q^5 + 3 * q^6 + 5 * q^7 - 10 * q^8 - 6 * q^9	\( 24 q + 3 q^{2} - 6 q^{3} - 7 q^{4} + 7 q^{5} + 3 q^{6} + 5 q^{7} - 10 q^{8} - 6 q^{9} + 16 q^{10} - 7 q^{11} + 18 q^{12} + 6 q^{13} - 6 q^{14} + 7 q^{15} - 23 q^{16} - 6 q^{17} - 2 q^{18} + 6 q^{19} + 3 q^{20} - 10 q^{21} + 23 q^{22} - 78 q^{23} + 10 q^{24} + q^{25} + 10 q^{26} - 6 q^{27} - 13 q^{28} + 20 q^{29} + 11 q^{30} + 5 q^{31} - 22 q^{32} - 2 q^{33} - 2 q^{34} + 29 q^{35} - 7 q^{36} - 10 q^{37} + 2 q^{38} + 6 q^{39} + 44 q^{40} - 16 q^{41} + 19 q^{42} - 36 q^{43} + 3 q^{44} - 28 q^{45} + 23 q^{46} + 19 q^{47} + 12 q^{48} - 15 q^{49} + 34 q^{50} - 6 q^{51} - 6 q^{52} - 5 q^{53} - 2 q^{54} + 24 q^{55} - 50 q^{56} - 9 q^{57} - 79 q^{58} + 34 q^{59} + 3 q^{60} - 14 q^{61} + 36 q^{62} + 5 q^{63} - 20 q^{64} + 6 q^{65} + 3 q^{66} - 18 q^{67} - 2 q^{68} + 7 q^{69} + 46 q^{70} - 8 q^{71} + 10 q^{72} + 7 q^{73} + 47 q^{74} - 9 q^{75} + 58 q^{76} + 43 q^{77} - 50 q^{78} + 14 q^{79} - 51 q^{80} - 6 q^{81} - 88 q^{82} - 47 q^{83} + 22 q^{84} + 7 q^{85} - 13 q^{86} + 20 q^{87} + 115 q^{88} - 124 q^{89} - 19 q^{90} + 10 q^{91} - 19 q^{92} + 5 q^{93} + 28 q^{94} - 13 q^{95} - 27 q^{96} - 30 q^{97} - 14 q^{98} - 7 q^{99}+O(q^{100}) \) 24 * q + 3 * q^2 - 6 * q^3 - 7 * q^4 + 7 * q^5 + 3 * q^6 + 5 * q^7 - 10 * q^8 - 6 * q^9 + 16 * q^10 - 7 * q^11 + 18 * q^12 + 6 * q^13 - 6 * q^14 + 7 * q^15 - 23 * q^16 - 6 * q^17 - 2 * q^18 + 6 * q^19 + 3 * q^20 - 10 * q^21 + 23 * q^22 - 78 * q^23 + 10 * q^24 + q^25 + 10 * q^26 - 6 * q^27 - 13 * q^28 + 20 * q^29 + 11 * q^30 + 5 * q^31 - 22 * q^32 - 2 * q^33 - 2 * q^34 + 29 * q^35 - 7 * q^36 - 10 * q^37 + 2 * q^38 + 6 * q^39 + 44 * q^40 - 16 * q^41 + 19 * q^42 - 36 * q^43 + 3 * q^44 - 28 * q^45 + 23 * q^46 + 19 * q^47 + 12 * q^48 - 15 * q^49 + 34 * q^50 - 6 * q^51 - 6 * q^52 - 5 * q^53 - 2 * q^54 + 24 * q^55 - 50 * q^56 - 9 * q^57 - 79 * q^58 + 34 * q^59 + 3 * q^60 - 14 * q^61 + 36 * q^62 + 5 * q^63 - 20 * q^64 + 6 * q^65 + 3 * q^66 - 18 * q^67 - 2 * q^68 + 7 * q^69 + 46 * q^70 - 8 * q^71 + 10 * q^72 + 7 * q^73 + 47 * q^74 - 9 * q^75 + 58 * q^76 + 43 * q^77 - 50 * q^78 + 14 * q^79 - 51 * q^80 - 6 * q^81 - 88 * q^82 - 47 * q^83 + 22 * q^84 + 7 * q^85 - 13 * q^86 + 20 * q^87 + 115 * q^88 - 124 * q^89 - 19 * q^90 + 10 * q^91 - 19 * q^92 + 5 * q^93 + 28 * q^94 - 13 * q^95 - 27 * q^96 - 30 * q^97 - 14 * q^98 - 7 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/561\mathbb{Z}\right)^\times$.

$n$	$188$	$409$	$496$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.357186	+	0.259511i	0.252569	+	0.183502i	0.706865	−	0.707349i	$-0.250109\pi$
$2$	0.357186	+	0.259511i	0.252569	+	0.183502i	−0.454296	+	0.890851i	$0.650109\pi$
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i
$4$	−0.557798	−	1.71673i	−0.278899	−	0.858363i
$5$	3.46967	−	2.52087i	1.55169	−	1.12737i	0.609250	−	0.792978i	$-0.291471\pi$
$5$	3.46967	−	2.52087i	1.55169	−	1.12737i	0.942436	−	0.334388i	$-0.108529\pi$
$6$	0.357186	−	0.259511i	0.145821	−	0.105945i
$7$	0.982692	+	3.02442i	0.371423	+	1.14312i	0.945860	+	0.324574i	$0.105221\pi$
$7$	0.982692	+	3.02442i	0.371423	+	1.14312i	−0.574438	+	0.818548i	$0.694779\pi$
$8$	0.519138	−	1.59774i	0.183543	−	0.564887i
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$	1.89351			0.598781
$11$	3.28652	−	0.445822i	0.990924	−	0.134420i
$11$	3.28652	−	0.445822i	0.990924	−	0.134420i
$12$	−1.80507			−0.521079
$13$	1.67324	+	1.21568i	0.464074	+	0.337169i	0.795127	−	0.606443i	$-0.207404\pi$
$13$	1.67324	+	1.21568i	0.464074	+	0.337169i	−0.331053	+	0.943612i	$0.607404\pi$
$14$	−0.433865	+	1.33530i	−0.115955	+	0.356874i
$15$	−1.32530	−	4.07885i	−0.342190	−	1.05315i
$16$	−2.32061	+	1.68602i	−0.580152	+	0.421505i
$17$	−0.809017	+	0.587785i	−0.196215	+	0.142559i
$17$	−0.809017	+	0.587785i	−0.196215	+	0.142559i
$18$	−0.136433	−	0.419898i	−0.0321576	−	0.0989708i
$19$	−2.03036	+	6.24882i	−0.465797	+	1.43358i	0.392179	+	0.919889i	$0.371721\pi$
$19$	−2.03036	+	6.24882i	−0.465797	+	1.43358i	−0.857977	+	0.513688i	$0.828279\pi$
$20$	−6.26301	−	4.55035i	−1.40045	−	1.01749i
$21$	3.18006			0.693946
$22$	1.28960	+	0.693648i	0.274943	+	0.147886i
$23$	−4.53626			−0.945875			−0.472937	−	0.881096i	$-0.656806\pi$
$23$	−4.53626			−0.945875			−0.472937	+	0.881096i	$0.656806\pi$
$24$	−1.35912	−	0.987458i	−0.277429	−	0.201564i
$25$	4.13879	−	12.7379i	0.827758	−	2.54758i
$26$	0.282176	+	0.868450i	0.0553393	+	0.170317i
$27$	−0.809017	+	0.587785i	−0.155695	+	0.113119i
$28$	4.64395	−	3.37403i	0.877624	−	0.637631i
$29$	0.837857	+	2.57866i	0.155586	+	0.478845i	0.998220	−	0.0596423i	$-0.0189960\pi$
$29$	0.837857	+	2.57866i	0.155586	+	0.478845i	−0.842634	+	0.538487i	$0.818996\pi$
$30$	0.585128	−	1.80084i	0.106829	−	0.328787i
$31$	−6.01941	−	4.37335i	−1.08112	−	0.785478i	−0.103240	−	0.994656i	$-0.532921\pi$
$31$	−6.01941	−	4.37335i	−1.08112	−	0.785478i	−0.977877	+	0.209179i	$0.932921\pi$
$32$	−4.62636			−0.817832
$33$	0.591590	−	3.26344i	0.102983	−	0.568091i
$34$	−0.441507			−0.0757178
$35$	11.0338	+	8.01650i	1.86505	+	1.35504i
$36$	−0.557798	+	1.71673i	−0.0929663	+	0.286121i
$37$	0.750404	+	2.30951i	0.123366	+	0.379681i	0.993600	−	0.112958i	$-0.0360325\pi$
$37$	0.750404	+	2.30951i	0.123366	+	0.379681i	−0.870234	+	0.492639i	$0.836032\pi$
$38$	−2.34686	+	1.70509i	−0.380710	+	0.276602i
$39$	1.67324	−	1.21568i	0.267933	−	0.194665i
$40$	−2.22645	−	6.85232i	−0.352033	−	1.08345i
$41$	1.58166	−	4.86784i	0.247013	−	0.760229i	−0.748285	−	0.663377i	$-0.769123\pi$
$41$	1.58166	−	4.86784i	0.247013	−	0.760229i	0.995299	−	0.0968522i	$-0.0308774\pi$
$42$	1.13587	+	0.825261i	0.175269	+	0.127340i
$43$	−8.01474			−1.22224			−0.611118	−	0.791540i	$-0.709280\pi$
$43$	−8.01474			−1.22224			−0.611118	+	0.791540i	$0.709280\pi$
$44$	−2.59857	−	5.39338i	−0.391749	−	0.813083i
$45$	−4.28875			−0.639330
$46$	−1.62029	−	1.17721i	−0.238899	−	0.173570i
$47$	−2.61064	+	8.03474i	−0.380802	+	1.17199i	0.558679	+	0.829384i	$0.311308\pi$
$47$	−2.61064	+	8.03474i	−0.380802	+	1.17199i	−0.939480	+	0.342603i	$0.888692\pi$
$48$	0.886393	+	2.72804i	0.127940	+	0.393758i
$49$	−2.51829	+	1.82964i	−0.359756	+	0.261378i
$50$	4.78394	−	3.47574i	0.676552	−	0.491544i
$51$	0.309017	+	0.951057i	0.0432710	+	0.133175i
$52$	1.15366	−	3.55060i	0.159984	−	0.492380i
$53$	−1.62369	−	1.17968i	−0.223031	−	0.162042i	0.470659	−	0.882315i	$-0.344016\pi$
$53$	−1.62369	−	1.17968i	−0.223031	−	0.162042i	−0.693690	+	0.720274i	$0.744016\pi$
$54$	−0.441507			−0.0600814
$55$	10.2793	−	9.83175i	1.38606	−	1.32571i
$56$	5.34239			0.713906
$57$	5.31556	+	3.86198i	0.704063	+	0.511532i
$58$	−0.369919	+	1.13849i	−0.0485728	+	0.149492i
$59$	3.21633	+	9.89884i	0.418730	+	1.28872i	0.908871	+	0.417076i	$0.136945\pi$
$59$	3.21633	+	9.89884i	0.418730	+	1.28872i	−0.490141	+	0.871643i	$0.663055\pi$
$60$	−6.26301	+	4.55035i	−0.808551	+	0.587447i
$61$	−6.80158	+	4.94164i	−0.870853	+	0.632712i	−0.930816	−	0.365489i	$-0.880902\pi$
$61$	−6.80158	+	4.94164i	−0.870853	+	0.632712i	0.0599624	+	0.998201i	$0.480902\pi$
$62$	−1.01512	−	3.12421i	−0.128920	−	0.396774i
$63$	0.982692	−	3.02442i	0.123808	−	0.381041i
$64$	2.98874	+	2.17145i	0.373593	+	0.271431i
$65$	8.87018			1.10021
$66$	1.05821	−	1.01213i	0.130256	−	0.124585i
$67$	10.6245			1.29799			0.648995	−	0.760792i	$-0.275189\pi$
$67$	10.6245			1.29799			0.648995	+	0.760792i	$0.275189\pi$
$68$	1.46033	+	1.06099i	0.177091	+	0.128665i
$69$	−1.40178	+	4.31424i	−0.168755	+	0.519373i
$70$	1.86074	+	5.72677i	0.222401	+	0.684480i
$71$	9.60251	−	6.97663i	1.13961	−	0.827974i	0.152543	−	0.988297i	$-0.451254\pi$
$71$	9.60251	−	6.97663i	1.13961	−	0.827974i	0.987065	+	0.160323i	$0.0512536\pi$
$72$	−1.35912	+	0.987458i	−0.160174	+	0.116373i
$73$	−1.62234	−	4.99305i	−0.189881	−	0.584392i	0.810118	−	0.586267i	$-0.199403\pi$
$73$	−1.62234	−	4.99305i	−0.189881	−	0.584392i	−0.999998	+	0.00187507i	$0.999403\pi$
$74$	−0.331309	+	1.01966i	−0.0385138	+	0.118533i
$75$	−10.8355	−	7.87245i	−1.25118	−	0.909032i
$76$	11.8600			1.36044
$77$	4.57799	+	9.50171i	0.521711	+	1.08282i
$78$	0.913142			0.103393
$79$	−5.92238	−	4.30286i	−0.666320	−	0.484110i	0.202471	−	0.979288i	$-0.435103\pi$
$79$	−5.92238	−	4.30286i	−0.666320	−	0.484110i	−0.868791	+	0.495178i	$0.835103\pi$
$80$	−3.80152	+	11.6999i	−0.425023	+	1.30809i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	1.82821	−	1.32827i	0.201892	−	0.146683i
$83$	−6.16278	+	4.47752i	−0.676453	+	0.491472i	−0.872179	−	0.489187i	$-0.837294\pi$
$83$	−6.16278	+	4.47752i	−0.676453	+	0.491472i	0.195726	+	0.980659i	$0.437294\pi$
$84$	−1.77383	−	5.45929i	−0.193541	−	0.595657i
$85$	−1.32530	+	4.07885i	−0.143749	+	0.442413i
$86$	−2.86275	−	2.07991i	−0.308699	−	0.224283i
$87$	2.71136			0.290689
$88$	0.993851	−	5.48246i	0.105945	−	0.584432i
$89$	−8.06013			−0.854373			−0.427186	−	0.904164i	$-0.640495\pi$
$89$	−8.06013			−0.854373			−0.427186	+	0.904164i	$0.640495\pi$
$90$	−1.53188	−	1.11298i	−0.161475	−	0.117318i
$91$	−2.03244	+	6.25522i	−0.213058	+	0.655725i
$92$	2.53031	+	7.78751i	0.263804	+	0.811904i
$93$	−6.01941	+	4.37335i	−0.624183	+	0.453496i
$94$	−3.01759	+	2.19241i	−0.311241	+	0.226129i
$95$	8.70773	+	26.7996i	0.893394	+	2.74959i
$96$	−1.42962	+	4.39993i	−0.145910	+	0.449066i
$97$	0.748010	+	0.543461i	0.0759489	+	0.0551801i	0.625112	−	0.780535i	$-0.285053\pi$
$97$	0.748010	+	0.543461i	0.0759489	+	0.0551801i	−0.549163	+	0.835715i	$0.685053\pi$
$98$	−1.37431			−0.138826
$99$	−2.92090	−	1.57109i	−0.293562	−	0.157901i
$100$	−24.1761			−2.41761
$101$	8.67601	+	6.30349i	0.863295	+	0.627221i	0.928779	−	0.370633i	$-0.120859\pi$
$101$	8.67601	+	6.30349i	0.863295	+	0.627221i	−0.0654844	+	0.997854i	$0.520859\pi$
$102$	−0.136433	+	0.419898i	−0.0135089	+	0.0415761i
$103$	−1.50042	−	4.61783i	−0.147841	−	0.455008i	0.849524	−	0.527549i	$-0.176889\pi$
$103$	−1.50042	−	4.61783i	−0.147841	−	0.455008i	−0.997365	+	0.0725414i	$0.976889\pi$
$104$	2.81099	−	2.04230i	0.275640	−	0.200264i
$105$	11.0338	−	8.01650i	1.07679	−	0.782331i
$106$	−0.273820	−	0.842732i	−0.0265958	−	0.0818534i
$107$	1.42380	−	4.38200i	0.137644	−	0.423624i	−0.858348	−	0.513068i	$-0.828509\pi$
$107$	1.42380	−	4.38200i	0.137644	−	0.423624i	0.995992	+	0.0894438i	$0.0285090\pi$
$108$	1.46033	+	1.06099i	0.140521	+	0.102094i
$109$	−1.29614			−0.124148			−0.0620740	−	0.998072i	$-0.519771\pi$
$109$	−1.29614			−0.124148			−0.0620740	+	0.998072i	$0.519771\pi$
$110$	6.22308	−	0.844169i	0.593347	−	0.0804884i
$111$	2.42836			0.230490
$112$	−7.37967	−	5.36164i	−0.697313	−	0.506628i
$113$	−0.776316	+	2.38926i	−0.0730297	+	0.224762i	−0.980908	−	0.194471i	$-0.937701\pi$
$113$	−0.776316	+	2.38926i	−0.0730297	+	0.224762i	0.907879	+	0.419233i	$0.137701\pi$
$114$	0.896419	+	2.75889i	0.0839573	+	0.258394i
$115$	−15.7393	+	11.4353i	−1.46770	+	1.06635i
$116$	3.95949	−	2.87674i	0.367630	−	0.267099i
$117$	−0.639122	−	1.96701i	−0.0590868	−	0.181850i
$118$	−1.42003	+	4.37040i	−0.130724	+	0.402328i
$119$	−2.57272	−	1.86919i	−0.235841	−	0.171349i
$120$	−7.20495			−0.657719
$121$	10.6025	−	2.93041i	0.963862	−	0.266401i
$122$	−3.71184			−0.336054
$123$	−4.14083	−	3.00849i	−0.373366	−	0.271267i
$124$	−4.15024	+	12.7731i	−0.372702	+	1.14706i
$125$	−11.1238	−	34.2354i	−0.994940	−	3.06211i
$126$	1.13587	−	0.825261i	0.101192	−	0.0735201i
$127$	−16.2750	+	11.8245i	−1.44418	+	1.04926i	−0.457027	+	0.889453i	$0.651086\pi$
$127$	−16.2750	+	11.8245i	−1.44418	+	1.04926i	−0.987149	+	0.159802i	$0.948914\pi$
$128$	3.36327	+	10.3511i	0.297274	+	0.914915i
$129$	−2.47669	+	7.62247i	−0.218060	+	0.671121i
$130$	3.16831	+	2.30191i	0.277879	+	0.201891i
$131$	−0.456557			−0.0398896			−0.0199448	−	0.999801i	$-0.506349\pi$
$131$	−0.456557			−0.0398896			−0.0199448	+	0.999801i	$0.506349\pi$
$132$	−5.93241	+	0.804740i	−0.516350	+	0.0700437i
$133$	−20.8942			−1.81176
$134$	3.79493	+	2.75718i	0.327832	+	0.238184i
$135$	−1.32530	+	4.07885i	−0.114063	+	0.351051i
$136$	0.519138	+	1.59774i	0.0445157	+	0.137005i
$137$	−6.77399	+	4.92159i	−0.578741	+	0.420480i	−0.838270	−	0.545255i	$-0.816433\pi$
$137$	−6.77399	+	4.92159i	−0.578741	+	0.420480i	0.259529	+	0.965735i	$0.416433\pi$
$138$	−1.62029	+	1.17721i	−0.137928	+	0.100211i
$139$	−3.48548	−	10.7272i	−0.295635	−	0.909871i	−0.983007	−	0.183566i	$-0.941236\pi$
$139$	−3.48548	−	10.7272i	−0.295635	−	0.909871i	0.687372	−	0.726305i	$-0.258764\pi$
$140$	7.60752	−	23.4135i	0.642953	−	1.97881i
$141$	6.83475	+	4.96574i	0.575590	+	0.418191i
$142$	5.24040			0.439764
$143$	6.04113	+	3.24940i	0.505184	+	0.271728i
$144$	2.86843			0.239036
$145$	9.40755	+	6.83498i	0.781254	+	0.567614i
$146$	0.716274	−	2.20446i	0.0592792	−	0.182443i
$147$	0.961901	+	2.96043i	0.0793363	+	0.244172i
$148$	3.54622	−	2.57648i	0.291497	−	0.211785i
$149$	18.2779	−	13.2797i	1.49738	−	1.08791i	0.525975	−	0.850500i	$-0.323700\pi$
$149$	18.2779	−	13.2797i	1.49738	−	1.08791i	0.971409	−	0.237413i	$-0.0762996\pi$
$150$	−1.82730	−	5.62386i	−0.149199	−	0.459186i
$151$	4.16581	−	12.8210i	0.339009	−	1.04336i	−0.625705	−	0.780060i	$-0.715189\pi$
$151$	4.16581	−	12.8210i	0.339009	−	1.04336i	0.964714	−	0.263302i	$-0.0848115\pi$
$152$	8.92995	+	6.48799i	0.724315	+	0.526246i
$153$	1.00000			0.0808452
$154$	−0.830603	+	4.58192i	−0.0669319	+	0.369222i
$155$	−31.9100			−2.56307
$156$	−3.02032	−	2.19439i	−0.241819	−	0.175692i
$157$	5.53752	−	17.0427i	0.441942	−	1.36016i	−0.443861	−	0.896096i	$-0.646391\pi$
$157$	5.53752	−	17.0427i	0.441942	−	1.36016i	0.885803	−	0.464062i	$-0.153609\pi$
$158$	−0.998753	−	3.07385i	−0.0794566	−	0.244542i
$159$	−1.62369	+	1.17968i	−0.128767	+	0.0935548i
$160$	−16.0520	+	11.6624i	−1.26902	+	0.921996i
$161$	−4.45775	−	13.7195i	−0.351320	−	1.08125i
$162$	−0.136433	+	0.419898i	−0.0107192	+	0.0329903i
$163$	17.7597	+	12.9031i	1.39104	+	1.01065i	0.995750	+	0.0920976i	$0.0293572\pi$
$163$	17.7597	+	12.9031i	1.39104	+	1.01065i	0.395294	+	0.918555i	$0.370643\pi$
$164$	−9.23899			−0.721444
$165$	−6.17406	−	12.8144i	−0.480650	−	0.997599i
$166$	−3.36323			−0.261037
$167$	11.1854	+	8.12669i	0.865555	+	0.628862i	0.929390	−	0.369098i	$-0.120333\pi$
$167$	11.1854	+	8.12669i	0.865555	+	0.628862i	−0.0638358	+	0.997960i	$0.520333\pi$
$168$	1.65089	−	5.08091i	0.127369	−	0.392001i
$169$	−2.69536	−	8.29548i	−0.207336	−	0.638114i
$170$	−1.53188	+	1.11298i	−0.117490	+	0.0853616i
$171$	5.31556	−	3.86198i	0.406491	−	0.295333i
$172$	4.47060	+	13.7591i	0.340880	+	1.04912i
$173$	−3.50485	+	10.7868i	−0.266469	+	0.820106i	0.724883	+	0.688872i	$0.241894\pi$
$173$	−3.50485	+	10.7868i	−0.266469	+	0.820106i	−0.991351	+	0.131234i	$0.958106\pi$
$174$	0.968462	+	0.703629i	0.0734189	+	0.0533419i
$175$	42.5918			3.21964
$176$	−6.87507	+	6.57572i	−0.518228	+	0.495664i
$177$	10.4083			0.782333
$178$	−2.87897	−	2.09169i	−0.215788	−	0.156779i
$179$	−0.501496	+	1.54344i	−0.0374835	+	0.115362i	−0.968048	−	0.250767i	$-0.919317\pi$
$179$	−0.501496	+	1.54344i	−0.0374835	+	0.115362i	0.930564	+	0.366129i	$0.119317\pi$
$180$	2.39226	+	7.36261i	0.178308	+	0.548777i
$181$	10.0847	−	7.32698i	0.749592	−	0.544610i	−0.146109	−	0.989269i	$-0.546675\pi$
$181$	10.0847	−	7.32698i	0.749592	−	0.544610i	0.895700	+	0.444658i	$0.146675\pi$
$182$	−2.34926	+	1.70684i	−0.174139	+	0.126519i
$183$	2.59797	+	7.99574i	0.192048	+	0.591062i
$184$	−2.35494	+	7.24776i	−0.173609	+	0.534312i
$185$	8.42562	+	6.12157i	0.619464	+	0.450067i
$186$	−3.28498			−0.240867
$187$	−2.39681	+	2.29245i	−0.175272	+	0.167640i
$188$	15.2496			1.11219
$189$	−2.57272	−	1.86919i	−0.187138	−	0.135964i
$190$	−3.84452	+	11.8322i	−0.278911	+	0.858399i
$191$	2.04842	+	6.30438i	0.148218	+	0.456169i	0.997411	−	0.0719143i	$-0.0229108\pi$
$191$	2.04842	+	6.30438i	0.148218	+	0.456169i	−0.849192	+	0.528083i	$0.822911\pi$
$192$	2.98874	−	2.17145i	0.215694	−	0.156711i
$193$	−13.6843	+	9.94224i	−0.985019	+	0.715658i	−0.958825	−	0.283998i	$-0.908339\pi$
$193$	−13.6843	+	9.94224i	−0.985019	+	0.715658i	−0.0261946	+	0.999657i	$0.508339\pi$
$194$	0.126145	+	0.388234i	0.00905666	+	0.0278735i
$195$	2.74103	−	8.43604i	0.196290	−	0.604117i
$196$	4.54569	+	3.30264i	0.324692	+	0.235903i
$197$	−2.01403			−0.143493			−0.0717467	−	0.997423i	$-0.522857\pi$
$197$	−2.01403			−0.143493			−0.0717467	+	0.997423i	$0.522857\pi$
$198$	−0.635590	−	1.31918i	−0.0451694	−	0.0937500i
$199$	5.50328			0.390117			0.195059	−	0.980792i	$-0.437510\pi$
$199$	5.50328			0.390117			0.195059	+	0.980792i	$0.437510\pi$
$200$	−18.2032	−	13.2254i	−1.28716	−	0.935179i
$201$	3.28316	−	10.1045i	0.231576	−	0.712717i
$202$	1.46313	+	4.50304i	0.102945	+	0.316833i
$203$	−6.97558	+	5.06806i	−0.489590	+	0.355708i
$204$	1.46033	−	1.06099i	0.102244	−	0.0742845i
$205$	−6.78334	−	20.8770i	−0.473769	−	1.45811i
$206$	0.662447	−	2.03880i	0.0461548	−	0.142050i
$207$	3.66991	+	2.66634i	0.255076	+	0.185324i
$208$	−5.93260			−0.411352
$209$	−3.88698	+	21.4421i	−0.268868	+	1.48318i
$210$	6.02148			0.415522
$211$	15.3598	+	11.1595i	1.05741	+	0.768255i	0.973608	−	0.228228i	$-0.0732931\pi$
$211$	15.3598	+	11.1595i	1.05741	+	0.768255i	0.0838039	+	0.996482i	$0.473293\pi$
$212$	−1.11950	+	3.44546i	−0.0768874	+	0.236635i
$213$	−3.66783	−	11.2884i	−0.251316	−	0.773470i
$214$	1.64574	−	1.19570i	0.112500	−	0.0817363i
$215$	−27.8085	+	20.2041i	−1.89653	+	1.37791i
$216$	0.519138	+	1.59774i	0.0353228	+	0.108713i
$217$	7.31162	−	22.5029i	0.496345	−	1.52759i
$218$	−0.462965	−	0.336364i	−0.0313559	−	0.0227814i
$219$	−5.25000			−0.354762
$220$	−22.6122	−	12.1626i	−1.52451	−	0.820005i
$221$	−2.06824			−0.139125
$222$	0.867377	+	0.630186i	0.0582145	+	0.0422953i
$223$	3.50491	−	10.7870i	0.234706	−	0.722351i	−0.762454	−	0.647042i	$-0.776006\pi$
$223$	3.50491	−	10.7870i	0.234706	−	0.722351i	0.997160	−	0.0753089i	$-0.0239943\pi$
$224$	−4.54629	−	13.9920i	−0.303762	−	0.934882i
$225$	−10.8355	+	7.87245i	−0.722366	+	0.524830i
$226$	−0.897328	+	0.651947i	−0.0596894	+	0.0433669i
$227$	−6.17006	−	18.9895i	−0.409521	−	1.26038i	−0.917061	−	0.398748i	$-0.869445\pi$
$227$	−6.17006	−	18.9895i	−0.409521	−	1.26038i	0.507540	−	0.861628i	$-0.330555\pi$
$228$	3.66495	−	11.2796i	0.242717	−	0.747007i
$229$	0.899451	+	0.653490i	0.0594374	+	0.0431838i	0.617107	−	0.786879i	$-0.288304\pi$
$229$	0.899451	+	0.653490i	0.0594374	+	0.0431838i	−0.557670	+	0.830063i	$0.688304\pi$
$230$	−8.58946			−0.566372
$231$	10.4513	−	1.41774i	0.687648	−	0.0932804i
$232$	4.55499			0.299050
$233$	10.6592	+	7.74436i	0.698307	+	0.507350i	0.879381	−	0.476120i	$-0.157957\pi$
$233$	10.6592	+	7.74436i	0.698307	+	0.507350i	−0.181073	+	0.983470i	$0.557957\pi$
$234$	0.282176	−	0.868450i	0.0184464	−	0.0567723i
$235$	11.1964	+	34.4590i	0.730373	+	2.24786i
$236$	15.1995	−	11.0431i	0.989405	−	0.718845i
$237$	−5.92238	+	4.30286i	−0.384700	+	0.279501i
$238$	−0.433865	−	1.33530i	−0.0281233	−	0.0865546i
$239$	3.59552	−	11.0659i	0.232575	−	0.715791i	−0.764859	−	0.644197i	$-0.777192\pi$
$239$	3.59552	−	11.0659i	0.232575	−	0.715791i	0.997434	−	0.0715937i	$-0.0228085\pi$
$240$	9.95251	+	7.23092i	0.642432	+	0.466754i
$241$	−0.254029			−0.0163635			−0.00818174	−	0.999967i	$-0.502604\pi$
$241$	−0.254029			−0.0163635			−0.00818174	+	0.999967i	$0.502604\pi$
$242$	4.54754	+	1.70476i	0.292327	+	0.109586i
$243$	1.00000			0.0641500
$244$	12.2773	+	8.92001i	0.785976	+	0.571045i
$245$	−4.12536	+	12.6965i	−0.263559	+	0.811153i
$246$	−0.698312	−	2.14918i	−0.0445228	−	0.137027i
$247$	−10.9939	+	7.98751i	−0.699523	+	0.508233i
$248$	−10.1124	+	7.34708i	−0.642137	+	0.466540i
$249$	2.35397	+	7.24478i	0.149177	+	0.459119i
$250$	4.91122	−	15.1152i	0.310613	−	0.955967i
$251$	12.2809	+	8.92257i	0.775161	+	0.563188i	0.903523	−	0.428540i	$-0.140972\pi$
$251$	12.2809	+	8.92257i	0.775161	+	0.563188i	−0.128362	+	0.991727i	$0.540972\pi$
$252$	−5.74024			−0.361601
$253$	−14.9085	+	2.02236i	−0.937291	+	0.127145i
$254$	−8.88181			−0.557294
$255$	3.46967	+	2.52087i	0.217279	+	0.157863i
$256$	0.798290	−	2.45689i	0.0498932	−	0.153555i
$257$	−4.14977	−	12.7717i	−0.258856	−	0.796675i	−0.993045	−	0.117731i	$-0.962438\pi$
$257$	−4.14977	−	12.7717i	−0.258856	−	0.796675i	0.734190	−	0.678944i	$-0.237562\pi$
$258$	−2.86275	+	2.07991i	−0.178227	+	0.129490i
$259$	−6.24750	+	4.53907i	−0.388200	+	0.282044i
$260$	−4.94777	−	15.2277i	−0.306847	−	0.944379i
$261$	0.837857	−	2.57866i	0.0518621	−	0.159615i
$262$	−0.163076	−	0.118482i	−0.0100749	−	0.00731982i
$263$	−0.182236			−0.0112371			−0.00561857	−	0.999984i	$-0.501788\pi$
$263$	−0.182236			−0.0112371			−0.00561857	+	0.999984i	$0.501788\pi$
$264$	−4.90701	−	2.63938i	−0.302006	−	0.162443i
$265$	−8.60751			−0.528755
$266$	−7.46314	−	5.42229i	−0.457594	−	0.332462i
$267$	−2.49072	+	7.66564i	−0.152430	+	0.469130i
$268$	−5.92633	−	18.2394i	−0.362008	−	1.11415i
$269$	16.0300	−	11.6465i	0.977368	−	0.710099i	0.0202488	−	0.999795i	$-0.493554\pi$
$269$	16.0300	−	11.6465i	0.977368	−	0.710099i	0.957119	+	0.289696i	$0.0935542\pi$
$270$	−1.53188	+	1.11298i	−0.0932275	+	0.0677337i
$271$	−3.97955	−	12.2478i	−0.241740	−	0.744000i	−0.996155	−	0.0876027i	$-0.972079\pi$
$271$	−3.97955	−	12.2478i	−0.241740	−	0.744000i	0.754415	−	0.656398i	$-0.227921\pi$
$272$	0.886393	−	2.72804i	0.0537455	−	0.165412i
$273$	5.32101	+	3.86594i	0.322042	+	0.233977i
$274$	−3.69679			−0.223331
$275$	7.92341	−	43.7086i	0.477800	−	2.63572i
$276$	8.18827			0.492876
$277$	0.564572	+	0.410185i	0.0339218	+	0.0246457i	0.604617	−	0.796516i	$-0.293326\pi$
$277$	0.564572	+	0.410185i	0.0339218	+	0.0246457i	−0.570695	+	0.821162i	$0.693326\pi$
$278$	1.53886	−	4.73614i	0.0922950	−	0.284055i
$279$	2.29921	+	7.07624i	0.137650	+	0.423643i
$280$	18.5363	−	13.4674i	1.10776	−	0.804834i
$281$	−11.1029	+	8.06676i	−0.662346	+	0.481223i	−0.867454	−	0.497517i	$-0.834245\pi$
$281$	−11.1029	+	8.06676i	−0.662346	+	0.481223i	0.205108	+	0.978739i	$0.434245\pi$
$282$	1.15262	+	3.54739i	0.0686373	+	0.211244i
$283$	0.814868	−	2.50790i	0.0484389	−	0.149079i	−0.923912	−	0.382606i	$-0.875027\pi$
$283$	0.814868	−	2.50790i	0.0484389	−	0.149079i	0.972350	+	0.233527i	$0.0750266\pi$
$284$	−17.3332	−	12.5933i	−1.02854	−	0.747276i
$285$	28.1788			1.66917
$286$	1.31455	+	2.72838i	0.0777312	+	0.161333i
$287$	16.2767			0.960781
$288$	3.74280	+	2.71931i	0.220547	+	0.160237i
$289$	0.309017	−	0.951057i	0.0181775	−	0.0559445i
$290$	1.58649	+	4.88272i	0.0931621	+	0.286723i
$291$	0.748010	−	0.543461i	0.0438491	−	0.0318582i
$292$	−7.66676	+	5.57022i	−0.448663	+	0.325973i
$293$	0.162890	+	0.501325i	0.00951616	+	0.0292877i	0.955702	−	0.294336i	$-0.0950986\pi$
$293$	0.162890	+	0.501325i	0.00951616	+	0.0292877i	−0.946186	+	0.323624i	$0.895099\pi$
$294$	−0.424686	+	1.30705i	−0.0247682	+	0.0762286i
$295$	36.1133	+	26.2378i	2.10260	+	1.52763i
$296$	4.07956			0.237119
$297$	−2.39681	+	2.29245i	−0.139077	+	0.133021i
$298$	9.97484			0.577827
$299$	−7.59026	−	5.51464i	−0.438956	−	0.318920i
$300$	−7.47082	+	22.9928i	−0.431328	+	1.32749i
$301$	−7.87602	−	24.2399i	−0.453966	−	1.39716i
$302$	4.81517	−	3.49843i	0.277082	−	0.201312i
$303$	8.67601	−	6.30349i	0.498424	−	0.362126i
$304$	−5.82395	−	17.9243i	−0.334027	−	1.02803i
$305$	−11.1421	+	34.2918i	−0.637993	+	1.96354i
$306$	0.357186	+	0.259511i	0.0204190	+	0.0148353i
$307$	14.5402			0.829853			0.414926	−	0.909855i	$-0.363807\pi$
$307$	14.5402			0.829853			0.414926	+	0.909855i	$0.363807\pi$
$308$	13.7582	−	13.1592i	0.783948	−	0.749815i
$309$	−4.85547			−0.276218
$310$	−11.3978	−	8.28100i	−0.647353	−	0.470329i
$311$	−10.5522	+	32.4764i	−0.598362	+	1.84157i	−0.0611369	+	0.998129i	$0.519473\pi$
$311$	−10.5522	+	32.4764i	−0.598362	+	1.84157i	−0.537225	+	0.843439i	$0.680527\pi$
$312$	−1.07370	−	3.30451i	−0.0607864	−	0.187081i
$313$	19.3542	−	14.0616i	1.09396	−	0.794809i	0.113897	−	0.993493i	$-0.463666\pi$
$313$	19.3542	−	14.0616i	1.09396	−	0.794809i	0.980064	+	0.198683i	$0.0636665\pi$
$314$	6.40070	−	4.65038i	0.361213	−	0.262436i
$315$	−4.21453	−	12.9710i	−0.237462	−	0.730832i
$316$	−4.08334	+	12.5672i	−0.229706	+	0.706962i
$317$	−3.07535	−	2.23437i	−0.172729	−	0.125495i	0.498062	−	0.867141i	$-0.334045\pi$
$317$	−3.07535	−	2.23437i	−0.172729	−	0.125495i	−0.670791	+	0.741647i	$0.734045\pi$
$318$	−0.886101			−0.0496901
$319$	3.90326	+	8.10129i	0.218541	+	0.453585i
$320$	15.8439			0.885701
$321$	−3.72755	−	2.70822i	−0.208052	−	0.151158i
$322$	1.96812	−	6.05726i	0.109679	−	0.337558i
$323$	−2.03036	−	6.24882i	−0.112972	−	0.347694i
$324$	1.46033	−	1.06099i	0.0811297	−	0.0589441i
$325$	22.4104	−	16.2821i	1.24311	−	0.903169i
$326$	2.99500	+	9.21765i	0.165878	+	0.510519i
$327$	−0.400531	+	1.23271i	−0.0221494	+	0.0681688i
$328$	−6.95645	−	5.05416i	−0.384106	−	0.279069i
$329$	−26.8658			−1.48116
$330$	1.12018	−	6.17936i	0.0616641	−	0.340163i
$331$	−19.1942			−1.05501			−0.527504	−	0.849552i	$-0.676872\pi$
$331$	−19.1942			−1.05501			−0.527504	+	0.849552i	$0.676872\pi$
$332$	11.1243	+	8.08225i	0.610523	+	0.443571i
$333$	0.750404	−	2.30951i	0.0411219	−	0.126560i
$334$	1.88632	+	5.80549i	0.103215	+	0.317662i
$335$	36.8636	−	26.7830i	2.01407	−	1.46331i
$336$	−7.37967	+	5.36164i	−0.402594	+	0.292502i
$337$	0.954844	+	2.93871i	0.0520137	+	0.160082i	0.973689	−	0.227880i	$-0.0731794\pi$
$337$	0.954844	+	2.93871i	0.0520137	+	0.160082i	−0.921676	+	0.387961i	$0.873179\pi$
$338$	1.19002	−	3.66251i	0.0647286	−	0.199214i
$339$	2.03242	+	1.47664i	0.110386	+	0.0802001i
$340$	7.74151			0.419842
$341$	−21.7327	−	11.6896i	−1.17689	−	0.633025i
$342$	2.90087			0.156861
$343$	10.0007	+	7.26596i	0.539989	+	0.392325i
$344$	−4.16075	+	12.8055i	−0.224333	+	0.690425i
$345$	6.01189	+	18.5027i	0.323669	+	0.996152i
$346$	−4.05118	+	2.94335i	−0.217793	+	0.158236i
$347$	19.1325	−	13.9006i	1.02708	−	0.746221i	0.0593618	−	0.998237i	$-0.481093\pi$
$347$	19.1325	−	13.9006i	1.02708	−	0.746221i	0.967723	+	0.252016i	$0.0810934\pi$
$348$	−1.51239	−	4.65466i	−0.0810727	−	0.249516i
$349$	−0.0927683	+	0.285511i	−0.00496577	+	0.0152831i	−0.953509	−	0.301365i	$-0.902558\pi$
$349$	−0.0927683	+	0.285511i	−0.00496577	+	0.0152831i	0.948543	+	0.316649i	$0.102558\pi$
$350$	15.2132	+	11.0531i	0.813181	+	0.590811i
$351$	−2.06824			−0.110395
$352$	−15.2046	+	2.06253i	−0.810410	+	0.109933i
$353$	−24.7245			−1.31595			−0.657975	−	0.753040i	$-0.728587\pi$
$353$	−24.7245			−1.31595			−0.657975	+	0.753040i	$0.728587\pi$
$354$	3.71769	+	2.70106i	0.197593	+	0.143560i
$355$	15.7304	−	48.4133i	0.834884	−	2.56951i
$356$	4.49593	+	13.8370i	0.238284	+	0.733362i
$357$	−2.57272	+	1.86919i	−0.136163	+	0.0989281i
$358$	−0.579668	+	0.421154i	−0.0306364	+	0.0222587i
$359$	−10.0376	−	30.8926i	−0.529765	−	1.63045i	−0.754697	−	0.656074i	$-0.772216\pi$
$359$	−10.0376	−	30.8926i	−0.529765	−	1.63045i	0.224932	−	0.974375i	$-0.427784\pi$
$360$	−2.22645	+	6.85232i	−0.117344	+	0.361149i
$361$	−19.5540	−	14.2068i	−1.02916	−	0.747728i
$362$	5.50356			0.289261
$363$	0.489365	−	10.9891i	0.0256850	−	0.576779i
$364$	11.8722			0.622272
$365$	−18.2158	−	13.2346i	−0.953459	−	0.692728i
$366$	−1.14702	+	3.53017i	−0.0599558	+	0.184525i
$367$	−3.03841	−	9.35126i	−0.158604	−	0.488132i	0.839905	−	0.542734i	$-0.182611\pi$
$367$	−3.03841	−	9.35126i	−0.158604	−	0.488132i	−0.998508	+	0.0546023i	$0.982611\pi$
$368$	10.5269	−	7.64822i	0.548751	−	0.398691i
$369$	−4.14083	+	3.00849i	−0.215563	+	0.156616i
$370$	1.42090	+	4.37308i	0.0738691	+	0.227346i
$371$	1.97226	−	6.06999i	0.102395	−	0.315138i
$372$	10.8655	+	7.89422i	0.563348	+	0.409296i
$373$	−25.3181			−1.31092			−0.655460	−	0.755230i	$-0.727525\pi$
$373$	−25.3181			−1.31092			−0.655460	+	0.755230i	$0.727525\pi$
$374$	−1.45102	+	0.196833i	−0.0750306	+	0.0101780i
$375$	−35.9973			−1.85889
$376$	11.4821	+	8.34227i	0.592146	+	0.430219i
$377$	−1.73289	+	5.33329i	−0.0892484	+	0.274678i
$378$	−0.433865	−	1.33530i	−0.0223156	−	0.0686804i
$379$	−8.79305	+	6.38852i	−0.451669	+	0.328156i	−0.790254	−	0.612779i	$-0.790052\pi$
$379$	−8.79305	+	6.38852i	−0.451669	+	0.328156i	0.338586	+	0.940936i	$0.390052\pi$
$380$	41.1505	−	29.8976i	2.11097	−	1.53371i
$381$	6.21651	+	19.1325i	0.318481	+	0.980185i
$382$	−0.904390	+	2.78343i	−0.0462726	+	0.142412i
$383$	23.5669	+	17.1224i	1.20421	+	0.874913i	0.994693	−	0.102891i	$-0.0328093\pi$
$383$	23.5669	+	17.1224i	1.20421	+	0.874913i	0.209522	+	0.977804i	$0.432809\pi$
$384$	10.8838			0.555410
$385$	39.8367	+	21.4273i	2.03027	+	1.09204i
$386$	−7.46798			−0.380110
$387$	6.48406	+	4.71094i	0.329603	+	0.239471i
$388$	0.515735	−	1.58727i	0.0261825	−	0.0805814i
$389$	−8.98695	−	27.6590i	−0.455656	−	1.40237i	−0.870363	−	0.492411i	$-0.836116\pi$
$389$	−8.98695	−	27.6590i	−0.455656	−	1.40237i	0.414707	−	0.909955i	$-0.363884\pi$
$390$	3.16831	−	2.30191i	0.160433	−	0.116562i
$391$	3.66991	−	2.66634i	0.185595	−	0.134843i
$392$	1.61596	+	4.97341i	0.0816183	+	0.251195i
$393$	−0.141084	+	0.434212i	−0.00711674	+	0.0219031i
$394$	−0.719383	−	0.522662i	−0.0362420	−	0.0263313i
$395$	−31.3957			−1.57969
$396$	−1.06786	+	5.89074i	−0.0536621	+	0.296021i
$397$	−10.1358			−0.508699			−0.254350	−	0.967112i	$-0.581861\pi$
$397$	−10.1358			−0.508699			−0.254350	+	0.967112i	$0.581861\pi$
$398$	1.96570	+	1.42816i	0.0985315	+	0.0715873i
$399$	−6.45668	+	19.8716i	−0.323238	+	0.994825i
$400$	11.8718	+	36.5377i	0.593591	+	1.82689i
$401$	−9.56730	+	6.95105i	−0.477768	+	0.347119i	−0.800461	−	0.599385i	$-0.795412\pi$
$401$	−9.56730	+	6.95105i	−0.477768	+	0.347119i	0.322693	+	0.946504i	$0.395412\pi$
$402$	3.79493	−	2.75718i	0.189274	−	0.137516i
$403$	−4.75532	−	14.6354i	−0.236879	−	0.729039i
$404$	5.98190	−	18.4104i	0.297611	−	0.915951i
$405$	3.46967	+	2.52087i	0.172410	+	0.125263i
$406$	−3.80680			−0.188928
$407$	3.49585	+	7.25571i	0.173283	+	0.359652i
$408$	1.67996			0.0831706
$409$	−16.4445	−	11.9477i	−0.813130	−	0.590773i	0.101606	−	0.994825i	$-0.467602\pi$
$409$	−16.4445	−	11.9477i	−0.813130	−	0.590773i	−0.914736	+	0.404051i	$0.867602\pi$
$410$	2.99489	−	9.21732i	0.147907	−	0.455211i
$411$	2.58744	+	7.96331i	0.127629	+	0.392801i
$412$	−7.09061	+	5.15163i	−0.349329	+	0.253803i
$413$	−26.7776	+	19.4550i	−1.31764	+	0.957320i
$414$	0.618895	+	1.90476i	0.0304170	+	0.0936140i
$415$	−10.0956	+	31.0711i	−0.495574	+	1.52522i
$416$	−7.74102	−	5.62418i	−0.379535	−	0.275748i
$417$	−11.2793			−0.552348
$418$	−6.95283	+	6.65010i	−0.340074	+	0.325267i
$419$	−8.25294			−0.403183			−0.201591	−	0.979470i	$-0.564611\pi$
$419$	−8.25294			−0.403183			−0.201591	+	0.979470i	$0.564611\pi$
$420$	−19.9168	−	14.4704i	−0.971838	−	0.706082i
$421$	−10.0678	+	30.9856i	−0.490675	+	1.51014i	0.332914	+	0.942957i	$0.391968\pi$
$421$	−10.0678	+	30.9856i	−0.490675	+	1.51014i	−0.823589	+	0.567187i	$0.808032\pi$
$422$	2.59028	+	7.97207i	0.126093	+	0.388074i
$423$	6.83475	−	4.96574i	0.332317	−	0.241443i
$424$	−2.72775	+	1.98182i	−0.132471	+	0.0962458i
$425$	4.13879	+	12.7379i	0.200761	+	0.617878i
$426$	1.61937	−	4.98391i	0.0784588	−	0.241471i
$427$	−21.6294	−	15.7147i	−1.04672	−	0.760488i
$428$	−8.31688			−0.402012
$429$	4.95717	−	4.74133i	0.239335	−	0.228914i
$430$	−15.1760			−0.731852
$431$	−13.0928	−	9.51245i	−0.630656	−	0.458199i	0.225971	−	0.974134i	$-0.427444\pi$
$431$	−13.0928	−	9.51245i	−0.630656	−	0.458199i	−0.856628	+	0.515935i	$0.827444\pi$
$432$	0.886393	−	2.72804i	0.0426466	−	0.131253i
$433$	−1.65572	−	5.09578i	−0.0795687	−	0.244887i	0.903357	−	0.428889i	$-0.141095\pi$
$433$	−1.65572	−	5.09578i	−0.0795687	−	0.244887i	−0.982926	+	0.184002i	$0.941095\pi$
$434$	8.45135	−	6.14027i	0.405678	−	0.294742i
$435$	9.40755	−	6.83498i	0.451057	−	0.327712i
$436$	0.722987	+	2.22512i	0.0346248	+	0.106564i
$437$	9.21025	−	28.3462i	0.440586	−	1.35598i
$438$	−1.87523	−	1.36243i	−0.0896019	−	0.0650996i
$439$	−14.8465			−0.708583			−0.354291	−	0.935135i	$-0.615278\pi$
$439$	−14.8465			−0.708583			−0.354291	+	0.935135i	$0.615278\pi$
$440$	−10.3722	−	21.5277i	−0.494475	−	1.02629i
$441$	3.11278			0.148228
$442$	−0.738747	−	0.536731i	−0.0351386	−	0.0255297i
$443$	2.85099	−	8.77446i	0.135455	−	0.416887i	−0.860206	−	0.509947i	$-0.829665\pi$
$443$	2.85099	−	8.77446i	0.135455	−	0.416887i	0.995660	+	0.0930602i	$0.0296649\pi$
$444$	−1.35453	−	4.16883i	−0.0642833	−	0.197844i
$445$	−27.9660	+	20.3185i	−1.32572	+	0.963190i
$446$	4.05125	−	2.94341i	0.191832	−	0.139374i
$447$	−6.98154	−	21.4870i	−0.330215	−	1.01630i
$448$	−3.63035	+	11.1731i	−0.171518	+	0.527878i
$449$	0.765345	+	0.556056i	0.0361189	+	0.0262419i	0.605698	−	0.795694i	$-0.292894\pi$
$449$	0.765345	+	0.556056i	0.0361189	+	0.0262419i	−0.569579	+	0.821936i	$0.692894\pi$
$450$	−5.91328			−0.278755
$451$	3.02797	−	16.7034i	0.142581	−	0.786533i
$452$	4.53472			0.213295
$453$	−10.9062	−	7.92384i	−0.512419	−	0.372294i
$454$	2.72412	−	8.38398i	0.127849	−	0.393480i
$455$	8.71665	+	26.8271i	0.408643	+	1.25767i
$456$	8.92995	−	6.48799i	0.418183	−	0.303828i
$457$	11.0718	−	8.04410i	0.517915	−	0.376287i	−0.297903	−	0.954596i	$-0.596287\pi$
$457$	11.0718	−	8.04410i	0.517915	−	0.376287i	0.815818	+	0.578309i	$0.196287\pi$
$458$	0.151684	+	0.466835i	0.00708772	+	0.0218138i
$459$	0.309017	−	0.951057i	0.0144237	−	0.0443915i
$460$	28.4106	+	20.6415i	1.32465	+	0.962417i
$461$	−21.6426			−1.00800			−0.503999	−	0.863704i	$-0.668138\pi$
$461$	−21.6426			−1.00800			−0.503999	+	0.863704i	$0.668138\pi$
$462$	4.10100	+	2.20584i	0.190796	+	0.102625i
$463$	−7.87106			−0.365799			−0.182900	−	0.983132i	$-0.558548\pi$
$463$	−7.87106			−0.365799			−0.182900	+	0.983132i	$0.558548\pi$
$464$	−6.29201	−	4.57141i	−0.292099	−	0.212222i
$465$	−9.86074	+	30.3482i	−0.457281	+	1.40737i
$466$	1.79757	+	5.53236i	0.0832710	+	0.256282i
$467$	−6.41762	+	4.66268i	−0.296972	+	0.215763i	−0.726286	−	0.687392i	$-0.758755\pi$
$467$	−6.41762	+	4.66268i	−0.296972	+	0.215763i	0.429314	+	0.903155i	$0.358755\pi$
$468$	−3.02032	+	2.19439i	−0.139614	+	0.101436i
$469$	10.4406	+	32.1329i	0.482103	+	1.48376i
$470$	−4.94329	+	15.2139i	−0.228017	+	0.701764i
$471$	−14.4974	−	10.5330i	−0.668005	−	0.485334i
$472$	17.4855			0.804836
$473$	−26.3406	+	3.57314i	−1.21114	+	0.164293i
$474$	−3.23203			−0.148452
$475$	71.1935	+	51.7251i	3.26658	+	2.37331i
$476$	−1.77383	+	5.45929i	−0.0813034	+	0.250226i
$477$	0.620195	+	1.90877i	0.0283968	+	0.0873964i
$478$	4.15598	−	3.01950i	0.190090	−	0.138109i
$479$	−21.9903	+	15.9769i	−1.00476	+	0.730004i	−0.963105	−	0.269128i	$-0.913265\pi$
$479$	−21.9903	+	15.9769i	−1.00476	+	0.730004i	−0.0416601	+	0.999132i	$0.513265\pi$
$480$	6.13130	+	18.8702i	0.279854	+	0.861303i
$481$	−1.55202	+	4.77662i	−0.0707659	+	0.217795i
$482$	−0.0907359	−	0.0659235i	−0.00413290	−	0.00300273i
$483$	−14.4256			−0.656386
$484$	−10.9448	−	16.5670i	−0.497489	−	0.753045i
$485$	3.96534			0.180057
$486$	0.357186	+	0.259511i	0.0162023	+	0.0117717i
$487$	−10.0456	+	30.9172i	−0.455209	+	1.40099i	0.415680	+	0.909511i	$0.363544\pi$
$487$	−10.0456	+	30.9172i	−0.455209	+	1.40099i	−0.870889	+	0.491479i	$0.836456\pi$
$488$	4.36450	+	13.4326i	0.197572	+	0.608063i
$489$	17.7597	−	12.9031i	0.803119	−	0.583500i
$490$	−4.76842	+	3.46446i	−0.215415	+	0.156508i
$491$	3.88876	+	11.9684i	0.175497	+	0.540125i	0.999656	−	0.0262340i	$-0.00835149\pi$
$491$	3.88876	+	11.9684i	0.175497	+	0.540125i	−0.824159	+	0.566359i	$0.808351\pi$
$492$	−2.85501	+	8.78681i	−0.128714	+	0.396140i
$493$	−2.19354	−	1.59370i	−0.0987920	−	0.0717766i
$494$	−5.99970			−0.269939
$495$	−14.0951	+	1.91202i	−0.633527	+	0.0859389i
$496$	21.3422			0.958295
$497$	30.5365	+	22.1861i	1.36975	+	0.995183i
$498$	−1.03929	+	3.19862i	−0.0465719	+	0.143334i
$499$	−10.3581	−	31.8788i	−0.463690	−	1.42709i	−0.860622	−	0.509244i	$-0.829925\pi$
$499$	−10.3581	−	31.8788i	−0.463690	−	1.42709i	0.396932	−	0.917848i	$-0.370075\pi$
$500$	−52.5680	+	38.1929i	−2.35091	+	1.70804i
$501$	11.1854	−	8.12669i	0.499728	−	0.363074i
$502$	2.07105	+	6.37404i	0.0924355	+	0.284487i
$503$	4.96156	−	15.2701i	0.221225	−	0.680861i	−0.777428	−	0.628972i	$-0.783476\pi$
$503$	4.96156	−	15.2701i	0.221225	−	0.680861i	0.998653	−	0.0518887i	$-0.0165241\pi$
$504$	−4.32208	−	3.14018i	−0.192521	−	0.139875i
$505$	45.9932			2.04667
$506$	−5.84994	−	3.14657i	−0.260062	−	0.139882i
$507$	−8.72238			−0.387375
$508$	29.3776	+	21.3441i	1.30342	+	0.946991i
$509$	5.26089	−	16.1914i	0.233185	−	0.717670i	−0.764172	−	0.645013i	$-0.776852\pi$
$509$	5.26089	−	16.1914i	0.233185	−	0.717670i	0.997357	−	0.0726571i	$-0.0231479\pi$
$510$	0.585128	+	1.80084i	0.0259099	+	0.0797424i
$511$	13.5068	−	9.81326i	0.597506	−	0.434113i
$512$	18.5330	−	13.4650i	0.819052	−	0.595076i
$513$	−2.03036	−	6.24882i	−0.0896428	−	0.275892i
$514$	1.83215	−	5.63878i	0.0808127	−	0.248716i
$515$	−16.8469	−	12.2400i	−0.742363	−	0.539359i
$516$	14.4672			0.636882
$517$	−4.99788	+	27.5702i	−0.219807	+	1.21254i
$518$	−3.40946			−0.149803
$519$	9.17581	+	6.66661i	0.402773	+	0.292632i
$520$	4.60484	−	14.1722i	0.201936	−	0.621494i
$521$	5.31526	+	16.3587i	0.232866	+	0.716687i	0.997397	+	0.0721005i	$0.0229702\pi$
$521$	5.31526	+	16.3587i	0.232866	+	0.716687i	−0.764532	+	0.644586i	$0.777030\pi$
$522$	0.968462	−	0.703629i	0.0423884	−	0.0307970i
$523$	−25.7585	+	18.7146i	−1.12634	+	0.818333i	−0.985158	−	0.171651i	$-0.945090\pi$
$523$	−25.7585	+	18.7146i	−1.12634	+	0.818333i	−0.141181	+	0.989984i	$0.545090\pi$
$524$	0.254667	+	0.783783i	0.0111252	+	0.0342397i
$525$	13.1616	−	40.5072i	0.574419	−	1.76788i
$526$	−0.0650922	−	0.0472922i	−0.00283815	−	0.00206204i
$527$	7.44040			0.324109
$528$	4.12937	+	8.57059i	0.179708	+	0.372987i
$529$	−2.42237			−0.105321
$530$	−3.07448	−	2.23374i	−0.133547	−	0.0970276i
$531$	3.21633	−	9.89884i	0.139577	−	0.429573i
$532$	11.6548	+	35.8697i	0.505298	+	1.55515i
$533$	8.56424	−	6.22229i	0.370958	−	0.269517i
$534$	−2.87897	+	2.09169i	−0.124585	+	0.0905165i
$535$	−6.10632	−	18.7933i	−0.263999	−	0.812506i
$536$	5.51558	−	16.9752i	0.238237	−	0.733218i
$537$	1.31293	+	0.953901i	0.0566572	+	0.0411639i
$538$	8.74810			0.377157
$539$	−7.46073	+	7.13588i	−0.321356	+	0.307364i
$540$	7.74151			0.333142
$541$	−28.8389	−	20.9527i	−1.23988	−	0.900827i	−0.242292	−	0.970203i	$-0.577899\pi$
$541$	−28.8389	−	20.9527i	−1.23988	−	0.900827i	−0.997591	+	0.0693759i	$0.977899\pi$
$542$	1.75700	−	5.40748i	0.0754695	−	0.232271i
$543$	−3.85202	−	11.8553i	−0.165306	−	0.508760i
$544$	3.74280	−	2.71931i	0.160471	−	0.116589i
$545$	−4.49720	+	3.26741i	−0.192639	+	0.139960i
$546$	0.897338	+	2.76172i	0.0384025	+	0.118191i
$547$	−0.841658	+	2.59036i	−0.0359867	+	0.110756i	−0.967436	−	0.253115i	$-0.918545\pi$
$547$	−0.841658	+	2.59036i	−0.0359867	+	0.110756i	0.931450	+	0.363870i	$0.118545\pi$
$548$	12.2275	+	8.88383i	0.522335	+	0.379499i
$549$	8.40722			0.358811
$550$	14.1730	−	13.5559i	0.604338	−	0.578025i
$551$	−17.8147			−0.758933
$552$	6.16532	+	4.47936i	0.262413	+	0.190654i
$553$	7.19377	−	22.1401i	0.305910	−	0.941494i
$554$	0.0952097	+	0.293025i	0.00404507	+	0.0124495i
$555$	8.42562	−	6.12157i	0.357648	−	0.259846i
$556$	−16.4715	+	11.9672i	−0.698547	+	0.507524i
$557$	−4.53567	−	13.9594i	−0.192183	−	0.591478i	−0.999998	−	0.00204172i	$-0.999350\pi$
$557$	−4.53567	−	13.9594i	−0.192183	−	0.591478i	0.807815	−	0.589436i	$-0.200650\pi$
$558$	−1.01512	+	3.12421i	−0.0429733	+	0.132258i
$559$	−13.4106	−	9.74337i	−0.567208	−	0.412100i
$560$	−39.1210			−1.65317
$561$	1.43959	+	2.98790i	0.0607797	+	0.126149i
$562$	−6.05923			−0.255593
$563$	13.9872	+	10.1623i	0.589489	+	0.428289i	0.842133	−	0.539270i	$-0.181300\pi$
$563$	13.9872	+	10.1623i	0.589489	+	0.428289i	−0.252643	+	0.967559i	$0.581300\pi$
$564$	4.71240	−	14.5033i	0.198428	−	0.610698i
$565$	3.32943	+	10.2469i	0.140070	+	0.431092i
$566$	0.941889	−	0.684322i	0.0395905	−	0.0287642i
$567$	−2.57272	+	1.86919i	−0.108044	+	0.0784987i
$568$	−6.16183	−	18.9642i	−0.258544	−	0.795718i
$569$	10.8888	−	33.5121i	0.456480	−	1.40490i	−0.412908	−	0.910773i	$-0.635487\pi$
$569$	10.8888	−	33.5121i	0.456480	−	1.40490i	0.869388	−	0.494129i	$-0.164513\pi$
$570$	10.0651	+	7.31271i	0.421580	+	0.306296i
$571$	−15.1074			−0.632226			−0.316113	−	0.948722i	$-0.602378\pi$
$571$	−15.1074			−0.632226			−0.316113	+	0.948722i	$0.602378\pi$
$572$	2.20860	−	12.1835i	0.0923461	−	0.509416i
$573$	6.62882			0.276923
$574$	5.81380	+	4.22397i	0.242663	+	0.176305i
$575$	−18.7746	+	57.7823i	−0.782956	+	2.40969i
$576$	−1.14160	−	3.51348i	−0.0475666	−	0.146395i
$577$	−6.90594	+	5.01746i	−0.287498	+	0.208880i	−0.722181	−	0.691704i	$-0.756860\pi$
$577$	−6.90594	+	5.01746i	−0.287498	+	0.208880i	0.434683	+	0.900583i	$0.356860\pi$
$578$	0.357186	−	0.259511i	0.0148570	−	0.0107942i
$579$	5.22695	+	16.0869i	0.217225	+	0.668548i
$580$	6.48628	−	19.9627i	0.269328	−	0.828906i
$581$	−19.5980	−	14.2388i	−0.813062	−	0.590724i
$582$	0.408213			0.0169210
$583$	−5.86223	−	3.15318i	−0.242789	−	0.130591i
$584$	−8.81982			−0.364967
$585$	−7.17612	−	5.21376i	−0.296696	−	0.215562i
$586$	−0.0719172	+	0.221338i	−0.00297087	+	0.00914340i
$587$	13.2935	+	40.9131i	0.548680	+	1.68866i	0.712075	+	0.702104i	$0.247756\pi$
$587$	13.2935	+	40.9131i	0.548680	+	1.68866i	−0.163395	+	0.986561i	$0.552244\pi$
$588$	4.54569	−	3.30264i	0.187461	−	0.136199i
$589$	39.5499	−	28.7347i	1.62962	−	1.18399i
$590$	6.09016	+	18.7436i	0.250728	+	0.771661i
$591$	−0.622368	+	1.91545i	−0.0256008	+	0.0787912i
$592$	−5.63527	−	4.09426i	−0.231608	−	0.168273i
$593$	21.3278			0.875830			0.437915	−	0.899016i	$-0.355717\pi$
$593$	21.3278			0.875830			0.437915	+	0.899016i	$0.355717\pi$
$594$	−1.45102	+	0.196833i	−0.0595362	+	0.00807617i
$595$	−13.6385			−0.559124
$596$	−32.9929	−	23.9708i	−1.35144	−	0.981881i
$597$	1.70061	−	5.23393i	0.0696012	−	0.214211i
$598$	−1.28002	−	3.93951i	−0.0523441	−	0.161099i
$599$	29.8852	−	21.7129i	1.22108	−	0.887165i	0.224888	−	0.974385i	$-0.427798\pi$
$599$	29.8852	−	21.7129i	1.22108	−	0.887165i	0.996189	+	0.0872198i	$0.0277983\pi$
$600$	−18.2032	+	13.2254i	−0.743144	+	0.539926i
$601$	10.7085	+	32.9572i	0.436807	+	1.34435i	0.891223	+	0.453565i	$0.149848\pi$
$601$	10.7085	+	32.9572i	0.436807	+	1.34435i	−0.454416	+	0.890789i	$0.650152\pi$
$602$	3.47731	−	10.7021i	0.141725	−	0.436184i
$603$	−8.59541	−	6.24493i	−0.350032	−	0.254313i
$604$	−24.3339			−0.990132
$605$	29.4000	−	36.8950i	1.19528	−	1.50000i
$606$	4.73478			0.192337
$607$	15.6038	+	11.3368i	0.633340	+	0.460148i	0.857556	−	0.514391i	$-0.171982\pi$
$607$	15.6038	+	11.3368i	0.633340	+	0.460148i	−0.224216	+	0.974540i	$0.571982\pi$
$608$	9.39319	−	28.9093i	0.380944	−	1.17243i
$609$	2.66444	+	8.20029i	0.107968	+	0.332292i
$610$	−12.8789	+	9.35706i	−0.521451	+	0.378856i
$611$	−14.1359	+	10.2703i	−0.571878	+	0.415494i
$612$	−0.557798	−	1.71673i	−0.0225476	−	0.0693945i
$613$	0.551225	−	1.69650i	0.0222638	−	0.0685208i	−0.939307	−	0.343077i	$-0.888531\pi$
$613$	0.551225	−	1.69650i	0.0222638	−	0.0685208i	0.961571	+	0.274556i	$0.0885309\pi$
$614$	5.19356	+	3.77334i	0.209595	+	0.152280i
$615$	−21.9514			−0.885164
$616$	17.5579	−	2.38175i	0.707427	−	0.0959635i
$617$	25.0626			1.00898			0.504492	−	0.863417i	$-0.331680\pi$
$617$	25.0626			1.00898			0.504492	+	0.863417i	$0.331680\pi$
$618$	−1.73431	−	1.26005i	−0.0697641	−	0.0506866i
$619$	−10.2664	+	31.5968i	−0.412642	+	1.26998i	0.501701	+	0.865041i	$0.332708\pi$
$619$	−10.2664	+	31.5968i	−0.412642	+	1.26998i	−0.914343	+	0.404941i	$0.867292\pi$
$620$	17.7993	+	54.7808i	0.714839	+	2.20005i
$621$	3.66991	−	2.66634i	0.147268	−	0.106997i
$622$	−12.1971	+	8.86171i	−0.489059	+	0.355322i
$623$	−7.92063	−	24.3772i	−0.317333	−	0.976652i
$624$	−1.83327	+	5.64224i	−0.0733897	+	0.225870i
$625$	−70.7213	−	51.3821i	−2.82885	−	2.05528i
$626$	10.5622			0.422150
$627$	19.1915	+	10.3227i	0.766434	+	0.412249i
$628$	−32.3465			−1.29077
$629$	−1.96458	−	1.42735i	−0.0783331	−	0.0569123i
$630$	1.86074	−	5.72677i	0.0741337	−	0.228160i
$631$	−2.44085	−	7.51217i	−0.0971688	−	0.299055i	0.890644	−	0.454701i	$-0.150254\pi$
$631$	−2.44085	−	7.51217i	−0.0971688	−	0.299055i	−0.987813	+	0.155646i	$0.950254\pi$
$632$	−9.94939	+	7.22865i	−0.395765	+	0.287540i
$633$	15.3598	−	11.1595i	0.610497	−	0.443552i
$634$	−0.518629	−	1.59617i	−0.0205974	−	0.0633922i
$635$	−26.6611	+	82.0544i	−1.05801	+	3.25623i
$636$	2.93088	+	2.12941i	0.116217	+	0.0844366i
$637$	−6.43797			−0.255082
$638$	−0.708183	+	3.90661i	−0.0280373	+	0.154664i
$639$	−11.8694			−0.469544
$640$	37.7631	+	27.4365i	1.49272	+	1.08452i
$641$	9.92905	−	30.5585i	0.392174	−	1.20699i	−0.538967	−	0.842327i	$-0.681185\pi$
$641$	9.92905	−	30.5585i	0.392174	−	1.20699i	0.931141	−	0.364660i	$-0.118815\pi$
$642$	−0.628616	−	1.93468i	−0.0248095	−	0.0763558i
$643$	−21.8208	+	15.8537i	−0.860528	+	0.625210i	−0.928029	−	0.372509i	$-0.878498\pi$
$643$	−21.8208	+	15.8537i	−0.860528	+	0.625210i	0.0675003	+	0.997719i	$0.478498\pi$
$644$	−21.0661	+	15.3054i	−0.830122	+	0.603119i
$645$	10.6219	+	32.6909i	0.418237	+	1.28720i
$646$	0.896419	−	2.75889i	0.0352691	−	0.108547i
$647$	−6.38659	−	4.64013i	−0.251083	−	0.182422i	0.455124	−	0.890428i	$-0.349595\pi$
$647$	−6.38659	−	4.64013i	−0.251083	−	0.182422i	−0.706207	+	0.708006i	$0.749595\pi$
$648$	1.67996			0.0659952
$649$	14.9837	+	31.0989i	0.588160	+	1.22074i
$650$	12.2301			0.479703
$651$	−19.1421	−	13.9075i	−0.750237	−	0.545079i
$652$	12.2449	−	37.6858i	0.479546	−	1.47589i
$653$	6.14662	+	18.9173i	0.240536	+	0.740293i	0.996339	+	0.0854938i	$0.0272468\pi$
$653$	6.14662	+	18.9173i	0.240536	+	0.740293i	−0.755803	+	0.654799i	$0.772753\pi$
$654$	−0.462965	+	0.336364i	−0.0181034	+	0.0131529i
$655$	−1.58410	+	1.15092i	−0.0618961	+	0.0449701i
$656$	4.53687	+	13.9631i	0.177135	+	0.545166i
$657$	−1.62234	+	4.99305i	−0.0632935	+	0.194797i
$658$	−9.59611	−	6.97198i	−0.374095	−	0.271796i
$659$	49.0773			1.91178			0.955889	−	0.293727i	$-0.0948956\pi$
$659$	49.0773			1.91178			0.955889	+	0.293727i	$0.0948956\pi$
$660$	−18.5549	+	17.7470i	−0.722249	+	0.690801i
$661$	−3.13401			−0.121899			−0.0609495	−	0.998141i	$-0.519413\pi$
$661$	−3.13401			−0.121899			−0.0609495	+	0.998141i	$0.519413\pi$
$662$	−6.85591	−	4.98111i	−0.266462	−	0.193596i
$663$	−0.639122	+	1.96701i	−0.0248214	+	0.0763925i
$664$	3.95459	+	12.1710i	0.153468	+	0.472325i
$665$	−72.4962	+	52.6716i	−2.81128	+	2.04252i
$666$	0.867377	−	0.630186i	0.0336102	−	0.0244192i
$667$	−3.80073	−	11.6975i	−0.147165	−	0.452927i
$668$	7.71209	−	23.7354i	0.298390	−	0.918349i
$669$	−9.17597	−	6.66673i	−0.354764	−	0.257751i
$670$	20.1177			0.777213
$671$	−20.1505	+	19.2731i	−0.777901	+	0.744030i
$672$	−14.7121			−0.567531
$673$	24.2610	+	17.6266i	0.935191	+	0.679456i	0.947258	−	0.320471i	$-0.103841\pi$
$673$	24.2610	+	17.6266i	0.935191	+	0.679456i	−0.0120670	+	0.999927i	$0.503841\pi$
$674$	−0.421570	+	1.29746i	−0.0162383	+	0.0499762i
$675$	4.13879	+	12.7379i	0.159302	+	0.490282i
$676$	−12.7376	+	9.25440i	−0.489907	+	0.355938i
$677$	20.6970	−	15.0372i	0.795450	−	0.577928i	−0.114126	−	0.993466i	$-0.536407\pi$
$677$	20.6970	−	15.0372i	0.795450	−	0.577928i	0.909576	+	0.415538i	$0.136407\pi$
$678$	0.342749	+	1.05487i	0.0131632	+	0.0405121i
$679$	−0.908588	+	2.79635i	−0.0348684	+	0.107314i
$680$	5.82893	+	4.23497i	0.223529	+	0.162404i
$681$	−19.9667			−0.765126
$682$	−4.72904	−	9.81522i	−0.181084	−	0.375844i
$683$	15.9574			0.610591			0.305296	−	0.952258i	$-0.401245\pi$
$683$	15.9574			0.610591			0.305296	+	0.952258i	$0.401245\pi$
$684$	−9.59497	−	6.97115i	−0.366873	−	0.266549i
$685$	−11.0969	+	34.1527i	−0.423990	+	1.30491i
$686$	1.68653	+	5.19061i	0.0643920	+	0.198178i
$687$	0.899451	−	0.653490i	0.0343162	−	0.0249322i
$688$	18.5991	−	13.5130i	0.709082	−	0.515179i
$689$	−1.28271	−	3.94779i	−0.0488675	−	0.150399i
$690$	−2.65429	+	8.16906i	−0.101047	+	0.310991i
$691$	−6.18079	−	4.49061i	−0.235128	−	0.170831i	0.463982	−	0.885845i	$-0.346420\pi$
$691$	−6.18079	−	4.49061i	−0.235128	−	0.170831i	−0.699110	+	0.715014i	$0.746420\pi$
$692$	20.4730			0.778266
$693$	1.88129	−	10.3779i	0.0714644	−	0.394225i
$694$	10.4412			0.396343
$695$	−39.1354	−	28.4335i	−1.48449	−	1.07854i
$696$	1.40757	−	4.33205i	0.0533538	−	0.164206i
$697$	1.58166	+	4.86784i	0.0599096	+	0.184383i
$698$	−0.107229	+	0.0779064i	−0.00405867	+	0.00294880i
$699$	10.6592	−	7.74436i	0.403168	−	0.292919i
$700$	−23.7576	−	73.1185i	−0.897954	−	2.76362i
$701$	−12.9051	+	39.7177i	−0.487417	+	1.50012i	0.341032	+	0.940052i	$0.389223\pi$
$701$	−12.9051	+	39.7177i	−0.487417	+	1.50012i	−0.828449	+	0.560064i	$0.810777\pi$
$702$	−0.738747	−	0.536731i	−0.0278822	−	0.0202576i
$703$	−15.9553			−0.601765
$704$	10.7907	+	5.80407i	0.406688	+	0.218749i
$705$	36.2323			1.36459
$706$	−8.83124	−	6.41627i	−0.332368	−	0.241480i
$707$	−10.5385	+	32.4342i	−0.396342	+	1.21982i
$708$	−5.80570	−	17.8681i	−0.218192	−	0.671525i
$709$	−21.7361	+	15.7922i	−0.816315	+	0.593087i	−0.915654	−	0.401966i	$-0.868327\pi$
$709$	−21.7361	+	15.7922i	−0.816315	+	0.593087i	0.0993398	+	0.995054i	$0.468327\pi$
$710$	18.1825	−	13.2103i	0.682376	−	0.495775i
$711$	2.26215	+	6.96218i	0.0848372	+	0.261102i
$712$	−4.18432	+	12.8780i	−0.156814	+	0.482624i
$713$	27.3056	+	19.8387i	1.02260	+	0.742964i
$714$	−1.40402			−0.0525440
$715$	29.1520	−	3.95452i	1.09022	−	0.147891i
$716$	2.92940			0.109477
$717$	−9.41318	−	6.83908i	−0.351542	−	0.255410i
$718$	4.43167	−	13.6393i	0.165389	−	0.509013i
$719$	−0.0678450	−	0.208805i	−0.00253019	−	0.00778712i	0.949783	−	0.312908i	$-0.101303\pi$
$719$	−0.0678450	−	0.208805i	−0.00253019	−	0.00778712i	−0.952314	+	0.305121i	$0.901303\pi$
$720$	9.95251	−	7.23092i	0.370908	−	0.269481i
$721$	12.4918	−	9.07581i	0.465218	−	0.338001i
$722$	−3.29760	−	10.1490i	−0.122724	−	0.377706i
$723$	−0.0784994	+	0.241596i	−0.00291942	+	0.00898507i
$724$	−18.2037	−	13.2257i	−0.676533	−	0.491530i
$725$	36.3144			1.34868
$726$	3.02659	−	3.79816i	0.112327	−	0.140963i
$727$	−24.0985			−0.893763			−0.446881	−	0.894593i	$-0.647465\pi$
$727$	−24.0985			−0.893763			−0.446881	+	0.894593i	$0.647465\pi$
$728$	8.93910	+	6.49464i	0.331305	+	0.240707i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	−3.07192	−	9.45440i	−0.113697	−	0.349923i
$731$	6.48406	−	4.71094i	0.239822	−	0.174241i
$732$	12.2773	−	8.92001i	0.453784	−	0.329693i
$733$	10.9067	+	33.5675i	0.402850	+	1.23984i	0.922677	+	0.385573i	$0.125996\pi$
$733$	10.9067	+	33.5675i	0.402850	+	1.23984i	−0.519827	+	0.854271i	$0.674004\pi$
$734$	1.34148	−	4.12864i	0.0495148	−	0.152391i
$735$	10.8003	+	7.84690i	0.398376	+	0.289437i
$736$	20.9864			0.773567
$737$	34.9177	−	4.73664i	1.28621	−	0.174476i
$738$	−2.25979			−0.0831839
$739$	−29.4310	−	21.3829i	−1.08264	−	0.786581i	−0.104495	−	0.994525i	$-0.533323\pi$
$739$	−29.4310	−	21.3829i	−1.08264	−	0.786581i	−0.978141	+	0.207944i	$0.933323\pi$
$740$	5.80926	−	17.8791i	0.213553	−	0.657248i
$741$	4.19928	+	12.9241i	0.154264	+	0.474777i
$742$	2.27969	−	1.65629i	0.0836901	−	0.0608044i
$743$	−7.64496	+	5.55439i	−0.280466	+	0.203771i	−0.719121	−	0.694885i	$-0.755455\pi$
$743$	−7.64496	+	5.55439i	−0.280466	+	0.203771i	0.438654	+	0.898656i	$0.355455\pi$
$744$	3.86259	+	11.8878i	0.141609	+	0.435829i
$745$	29.9421	−	92.1523i	1.09699	−	3.37620i
$746$	−9.04326	−	6.57032i	−0.331097	−	0.240556i
$747$	7.61761			0.278714
$748$	5.27244	+	2.83594i	0.192779	+	0.103692i
$749$	14.6521			0.535378
$750$	−12.8577	−	9.34169i	−0.469498	−	0.341110i
$751$	11.9227	−	36.6943i	0.435066	−	1.33899i	−0.457953	−	0.888976i	$-0.651417\pi$
$751$	11.9227	−	36.6943i	0.435066	−	1.33899i	0.893019	−	0.450019i	$-0.148583\pi$
$752$	−7.48844	−	23.0471i	−0.273075	−	0.840440i
$753$	12.2809	−	8.92257i	0.447539	−	0.325156i
$754$	−2.00301	+	1.45527i	−0.0729454	+	0.0529979i
$755$	−17.8661	−	54.9863i	−0.650215	−	2.00116i
$756$	−1.77383	+	5.45929i	−0.0645136	+	0.198552i
$757$	33.4612	+	24.3110i	1.21617	+	0.883598i	0.995776	−	0.0918136i	$-0.0292664\pi$
$757$	33.4612	+	24.3110i	1.21617	+	0.883598i	0.220392	+	0.975411i	$0.429266\pi$
$758$	−4.79865			−0.174295
$759$	−2.68361	+	14.8038i	−0.0974087	+	0.537343i
$760$	47.3394			1.71718
$761$	−11.1758	−	8.11972i	−0.405124	−	0.294340i	0.366501	−	0.930418i	$-0.380556\pi$
$761$	−11.1758	−	8.11972i	−0.405124	−	0.294340i	−0.771625	+	0.636078i	$0.780556\pi$
$762$	−2.74463	+	8.44710i	−0.0994275	+	0.306006i
$763$	−1.27371	−	3.92008i	−0.0461114	−	0.141916i
$764$	9.68029	−	7.03314i	0.350221	−	0.254450i
$765$	3.46967	−	2.52087i	0.125446	−	0.0911421i
$766$	3.97434	+	12.2318i	0.143599	+	0.441952i
$767$	−6.65214	+	20.4732i	−0.240195	+	0.739244i
$768$	−2.08995	−	1.51844i	−0.0754146	−	0.0547919i
$769$	−43.8890			−1.58268			−0.791338	−	0.611379i	$-0.790615\pi$
$769$	−43.8890			−1.58268			−0.791338	+	0.611379i	$0.790615\pi$
$770$	8.66849	+	17.9916i	0.312391	+	0.648373i
$771$	−13.4289			−0.483631
$772$	24.7012	+	17.9465i	0.889015	+	0.645907i
$773$	−8.06867	+	24.8328i	−0.290210	+	0.893174i	0.694578	+	0.719417i	$0.255591\pi$
$773$	−8.06867	+	24.8328i	−0.290210	+	0.893174i	−0.984788	+	0.173758i	$0.944409\pi$
$774$	1.09347	+	3.36537i	0.0393041	+	0.120966i
$775$	−80.6204	+	58.5741i	−2.89597	+	2.10405i
$776$	1.25663	−	0.912995i	0.0451104	−	0.0327746i
$777$	2.38633	+	7.34437i	0.0856091	+	0.263478i
$778$	3.96780	−	12.2116i	0.142252	−	0.437808i
$779$	27.2069	+	19.7670i	0.974789	+	0.708226i
$780$	−16.0113			−0.573297
$781$	28.4485	−	27.2099i	1.01797	−	0.973646i
$782$	2.00279			0.0716195
$783$	−2.19354	−	1.59370i	−0.0783907	−	0.0569542i
$784$	2.75914	−	8.49178i	0.0985409	−	0.303278i
$785$	−23.7491	−	73.0921i	−0.847640	−	2.60877i
$786$	−0.163076	+	0.118482i	−0.00581673	+	0.00422610i
$787$	−4.55737	+	3.31112i	−0.162453	+	0.118029i	−0.666042	−	0.745915i	$-0.732013\pi$
$787$	−4.55737	+	3.31112i	−0.162453	+	0.118029i	0.503589	+	0.863943i	$0.332013\pi$
$788$	1.12342	+	3.45753i	0.0400202	+	0.123169i
$789$	−0.0563140	+	0.173317i	−0.00200483	+	0.00617023i
$790$	−11.2141	−	8.14753i	−0.398980	−	0.289876i
$791$	−7.98898			−0.284056
$792$	−4.02655	+	3.85123i	−0.143077	+	0.136848i
$793$	−17.3882			−0.617471
$794$	−3.62036	−	2.63034i	−0.128482	−	0.0933474i
$795$	−2.65987	+	8.18622i	−0.0943357	+	0.290335i
$796$	−3.06972	−	9.44762i	−0.108803	−	0.334862i
$797$	−11.8900	+	8.63858i	−0.421165	+	0.305994i	−0.778106	−	0.628133i	$-0.783820\pi$
$797$	−11.8900	+	8.63858i	−0.421165	+	0.305994i	0.356942	+	0.934127i	$0.383820\pi$
$798$	−7.46314	+	5.42229i	−0.264192	+	0.191947i
$799$	−2.61064	−	8.03474i	−0.0923579	−	0.284248i
$800$	−19.1475	+	58.9300i	−0.676968	+	2.08349i
$801$	6.52079	+	4.73763i	0.230401	+	0.167396i
$802$	−5.22119			−0.184366
$803$	−7.55787	−	15.6865i	−0.266711	−	0.553565i
$804$	−19.1780			−0.676356
$805$	−50.0520	−	36.3649i	−1.76410	−	1.28170i
$806$	2.09950	−	6.46161i	0.0739519	−	0.227600i
$807$	−6.12292	−	18.8444i	−0.215537	−	0.663355i
$808$	14.5754	−	10.5896i	0.512760	−	0.372542i
$809$	16.5239	−	12.0053i	0.580950	−	0.422085i	−0.258117	−	0.966114i	$-0.583102\pi$
$809$	16.5239	−	12.0053i	0.580950	−	0.422085i	0.839066	+	0.544029i	$0.183102\pi$
$810$	0.585128	+	1.80084i	0.0205593	+	0.0632750i
$811$	12.1713	−	37.4596i	0.427394	−	1.31538i	−0.473290	−	0.880907i	$-0.656934\pi$
$811$	12.1713	−	37.4596i	0.427394	−	1.31538i	0.900683	−	0.434476i	$-0.143066\pi$
$812$	12.5914	+	9.14821i	0.441872	+	0.321039i
$813$	−12.8781			−0.451654
$814$	−0.634266	+	3.49885i	−0.0222310	+	0.122635i
$815$	94.1473			3.29784
$816$	−2.32061	−	1.68602i	−0.0812375	−	0.0590225i
$817$	16.2728	−	50.0826i	0.569314	−	1.75217i
$818$	−2.77321	−	8.53508i	−0.0969632	−	0.298422i
$819$	5.32101	−	3.86594i	0.185931	−	0.135087i
$820$	−32.0563	+	23.2903i	−1.11945	+	0.813331i
$821$	7.42083	+	22.8390i	0.258989	+	0.797085i	0.993018	+	0.117967i	$0.0376377\pi$
$821$	7.42083	+	22.8390i	0.258989	+	0.797085i	−0.734029	+	0.679118i	$0.762362\pi$
$822$	−1.14237	+	3.51585i	−0.0398447	+	0.122629i
$823$	−39.4087	−	28.6321i	−1.37370	−	0.998051i	−0.997438	−	0.0715377i	$-0.977209\pi$
$823$	−39.4087	−	28.6321i	−1.37370	−	0.998051i	−0.376262	−	0.926513i	$-0.622791\pi$
$824$	−8.15702			−0.284163
$825$	−39.1208	−	21.0423i	−1.36201	−	0.732599i
$826$	−14.6134			−0.508464
$827$	5.52723	+	4.01577i	0.192201	+	0.139642i	0.679724	−	0.733468i	$-0.262100\pi$
$827$	5.52723	+	4.01577i	0.192201	+	0.139642i	−0.487523	+	0.873110i	$0.662100\pi$
$828$	2.53031	−	7.78751i	0.0879345	−	0.270635i
$829$	−13.3104	−	40.9651i	−0.462289	−	1.42278i	−0.862361	−	0.506294i	$-0.831015\pi$
$829$	−13.3104	−	40.9651i	−0.462289	−	1.42278i	0.400072	−	0.916484i	$-0.368985\pi$
$830$	−11.6693	+	8.47824i	−0.405047	+	0.294284i
$831$	0.564572	−	0.410185i	0.0195848	−	0.0142292i
$832$	2.36110	+	7.26672i	0.0818564	+	0.251928i
$833$	0.961901	−	2.96043i	0.0333279	−	0.102573i
$834$	−4.02880	−	2.92709i	−0.139506	−	0.101357i
$835$	59.2961			2.05203
$836$	38.9783	−	5.28746i	1.34809	−	0.182871i
$837$	7.44040			0.257178
$838$	−2.94784	−	2.14173i	−0.101831	−	0.0739848i
$839$	3.16552	−	9.74246i	0.109286	−	0.336347i	−0.881427	−	0.472321i	$-0.843416\pi$
$839$	3.16552	−	9.74246i	0.109286	−	0.336347i	0.990712	+	0.135974i	$0.0434163\pi$
$840$	−7.08025	−	21.7908i	−0.244292	−	0.751853i
$841$	17.5140	−	12.7247i	0.603932	−	0.438782i
$842$	−11.6372	+	8.45491i	−0.401044	+	0.291375i
$843$	4.24095	+	13.0523i	0.146066	+	0.449545i
$844$	10.5902	−	32.5933i	0.364530	−	1.12191i
$845$	−30.2638	−	21.9880i	−1.04111	−	0.756409i
$846$	3.72995			0.128238
$847$	19.2818	+	29.1866i	0.662529	+	1.00286i
$848$	5.75692			0.197693
$849$	−2.13335	−	1.54997i	−0.0732164	−	0.0531948i
$850$	−1.82730	+	5.62386i	−0.0626760	+	0.192897i
$851$	−3.40403	−	10.4765i	−0.116689	−	0.359130i
$852$	−17.3332	+	12.5933i	−0.593826	+	0.431440i
$853$	34.8342	−	25.3085i	1.19270	−	0.866548i	0.199154	−	0.979968i	$-0.436181\pi$
$853$	34.8342	−	25.3085i	1.19270	−	0.866548i	0.993547	+	0.113421i	$0.0361807\pi$
$854$	−3.64760	−	11.2262i	−0.124818	−	0.384151i
$855$	8.70773	−	26.7996i	0.297798	−	0.916528i
$856$	−6.26215	−	4.54972i	−0.214036	−	0.155506i
$857$	22.1856			0.757845			0.378923	−	0.925428i	$-0.376295\pi$
$857$	22.1856			0.757845			0.378923	+	0.925428i	$0.376295\pi$
$858$	3.00106	−	0.407098i	0.102455	−	0.0138981i
$859$	25.7259			0.877755			0.438878	−	0.898547i	$-0.355376\pi$
$859$	25.7259			0.877755			0.438878	+	0.898547i	$0.355376\pi$
$860$	50.1964	+	36.4698i	1.71168	+	1.24361i
$861$	5.02977	−	15.4800i	0.171414	−	0.527558i
$862$	−2.20797	−	6.79544i	−0.0752038	−	0.231453i
$863$	24.8273	−	18.0381i	0.845132	−	0.614025i	−0.0786673	−	0.996901i	$-0.525066\pi$
$863$	24.8273	−	18.0381i	0.845132	−	0.614025i	0.923800	+	0.382876i	$0.125066\pi$
$864$	3.74280	−	2.71931i	0.127333	−	0.0925127i
$865$	15.0314	+	46.2620i	0.511084	+	1.57295i
$866$	0.731011	−	2.24982i	0.0248407	−	0.0764520i
$867$	−0.809017	−	0.587785i	−0.0274757	−	0.0199622i
$868$	−42.7096			−1.44966
$869$	−21.3824	−	11.5011i	−0.725347	−	0.390149i
$870$	5.13400			0.174059
$871$	17.7774	+	12.9160i	0.602364	+	0.437643i
$872$	−0.672877	+	2.07090i	−0.0227865	+	0.0701296i
$873$	−0.285714	−	0.879338i	−0.00966996	−	0.0297611i
$874$	10.6459	−	7.73473i	0.360104	−	0.261631i
$875$	92.6110	−	67.2858i	3.13082	−	2.27468i
$876$	2.92844	+	9.01281i	0.0989428	+	0.304515i
$877$	−6.90913	+	21.2641i	−0.233305	+	0.718038i	0.764037	+	0.645172i	$0.223214\pi$
$877$	−6.90913	+	21.2641i	−0.233305	+	0.718038i	−0.997342	+	0.0728657i	$0.976786\pi$
$878$	−5.30295	−	3.85282i	−0.178966	−	0.130026i
$879$	0.527124			0.0177795
$880$	−7.27773	+	40.1468i	−0.245332	+	1.35335i
$881$	−4.38917			−0.147875			−0.0739374	−	0.997263i	$-0.523557\pi$
$881$	−4.38917			−0.147875			−0.0739374	+	0.997263i	$0.523557\pi$
$882$	1.11184	+	0.807800i	0.0374377	+	0.0272000i
$883$	8.46668	−	26.0578i	0.284926	−	0.876914i	−0.701494	−	0.712675i	$-0.747483\pi$
$883$	8.46668	−	26.0578i	0.284926	−	0.876914i	0.986421	−	0.164238i	$-0.0525166\pi$
$884$	1.15366	+	3.55060i	0.0388018	+	0.119420i
$885$	36.1133	−	26.2378i	1.21393	−	0.881975i
$886$	3.29540	−	2.39425i	0.110711	−	0.0804364i
$887$	13.3794	+	41.1775i	0.449236	+	1.38261i	0.877771	+	0.479080i	$0.159030\pi$
$887$	13.3794	+	41.1775i	0.449236	+	1.38261i	−0.428535	+	0.903525i	$0.640970\pi$
$888$	1.26065	−	3.87989i	0.0423047	−	0.130201i
$889$	−51.7556	−	37.6026i	−1.73583	−	1.26115i
$890$	−15.2620			−0.511582
$891$	1.43959	+	2.98790i	0.0482282	+	0.100099i
$892$	−20.4734			−0.685499
$893$	−44.9070	−	32.6269i	−1.50276	−	1.09182i
$894$	3.08239	−	9.48664i	0.103091	−	0.317281i
$895$	2.15079	+	6.61946i	0.0718930	+	0.221264i
$896$	−28.0009	+	20.3439i	−0.935445	+	0.679641i
$897$	−7.59026	+	5.51464i	−0.253431	+	0.184129i
$898$	0.129068	+	0.397231i	0.00430706	+	0.0132558i
$899$	6.23399	−	19.1862i	0.207915	−	0.639897i
$900$	19.5589	+	14.2103i	0.651962	+	0.473678i
$901$	2.00699			0.0668627
$902$	5.41627	−	5.18044i	0.180342	−	0.172490i
$903$	−25.4873			−0.848165
$904$	3.41440	+	2.48070i	0.113561	+	0.0825070i
$905$	16.5204	−	50.8445i	0.549156	−	1.69013i
$906$	−1.83923	−	5.66057i	−0.0611044	−	0.188060i
$907$	0.409591	−	0.297585i	0.0136002	−	0.00988116i	−0.580964	−	0.813929i	$-0.697324\pi$
$907$	0.409591	−	0.297585i	0.0136002	−	0.00988116i	0.594565	+	0.804048i	$0.297324\pi$
$908$	−29.1581	+	21.1846i	−0.967645	+	0.703035i
$909$	−3.31394	−	10.1993i	−0.109916	−	0.338288i
$910$	−3.84846	+	11.8443i	−0.127575	+	0.392636i
$911$	42.0227	+	30.5313i	1.39227	+	1.01155i	0.995612	+	0.0935812i	$0.0298315\pi$
$911$	42.0227	+	30.5313i	1.39227	+	1.01155i	0.396662	+	0.917965i	$0.370169\pi$
$912$	−18.8467			−0.624077
$913$	−18.2579	+	17.4630i	−0.604250	+	0.577940i
$914$	6.04221			0.199859
$915$	29.1703	+	21.1935i	0.964341	+	0.700635i
$916$	0.620150	−	1.90863i	0.0204903	−	0.0630628i
$917$	−0.448655	−	1.38082i	−0.0148159	−	0.0455986i
$918$	0.357186	−	0.259511i	0.0117889	−	0.00856514i
$919$	−48.0239	+	34.8914i	−1.58416	+	1.15096i	−0.672443	+	0.740149i	$0.734755\pi$
$919$	−48.0239	+	34.8914i	−1.58416	+	1.15096i	−0.911720	+	0.410813i	$0.865245\pi$
$920$	10.0998	+	31.0839i	0.332979	+	1.02481i
$921$	4.49317	−	13.8286i	0.148055	−	0.455666i
$922$	−7.73045	−	5.61650i	−0.254589	−	0.184970i
$923$	24.5487			0.808030
$924$	−8.26361	−	17.1513i	−0.271853	−	0.564235i
$925$	32.5240			1.06938
$926$	−2.81143	−	2.04263i	−0.0923895	−	0.0671249i
$927$	−1.50042	+	4.61783i	−0.0492804	+	0.151669i
$928$	−3.87623	−	11.9298i	−0.127243	−	0.391615i
$929$	−7.80111	+	5.66784i	−0.255946	+	0.185956i	−0.708358	−	0.705853i	$-0.750564\pi$
$929$	−7.80111	+	5.66784i	−0.255946	+	0.185956i	0.452412	+	0.891809i	$0.350564\pi$
$930$	−11.3978	+	8.28100i	−0.373749	+	0.271545i
$931$	−6.32007	−	19.4512i	−0.207132	−	0.637487i
$932$	7.34926	−	22.6187i	0.240733	−	0.740901i
$933$	27.6261	+	20.0715i	0.904437	+	0.657112i
$934$	−3.50230			−0.114599
$935$	−2.53719	+	13.9961i	−0.0829748	+	0.457721i
$936$	−3.47457			−0.113570
$937$	17.1025	+	12.4257i	0.558715	+	0.405930i	0.830988	−	0.556290i	$-0.187776\pi$
$937$	17.1025	+	12.4257i	0.558715	+	0.405930i	−0.272274	+	0.962220i	$0.587776\pi$
$938$	−4.60961	+	14.1869i	−0.150509	+	0.463219i
$939$	−7.39263	−	22.7522i	−0.241249	−	0.742489i
$940$	52.9113	−	38.4423i	1.72578	−	1.25385i
$941$	16.0729	−	11.6776i	0.523961	−	0.380680i	−0.294133	−	0.955765i	$-0.595031\pi$
$941$	16.0729	−	11.6776i	0.523961	−	0.380680i	0.818094	+	0.575085i	$0.195031\pi$
$942$	−2.44485	−	7.52448i	−0.0796575	−	0.245161i
$943$	−7.17481	+	22.0818i	−0.233644	+	0.719082i
$944$	−24.1535	−	17.5485i	−0.786129	−	0.571156i
$945$	−13.6385			−0.443660
$946$	−10.3358	−	5.55941i	−0.336045	−	0.180752i
$947$	−41.3595			−1.34400			−0.672001	−	0.740550i	$-0.734565\pi$
$947$	−41.3595			−1.34400			−0.672001	+	0.740550i	$0.734565\pi$
$948$	10.6903	+	7.76698i	0.347206	+	0.252260i
$949$	3.35539	−	10.3268i	0.108921	−	0.335223i
$950$	12.0061	+	36.9510i	0.389530	+	1.19885i
$951$	−3.07535	+	2.23437i	−0.0997251	+	0.0724545i
$952$	−4.32208	+	3.14018i	−0.140079	+	0.101774i
$953$	4.37100	+	13.4526i	0.141591	+	0.435771i	0.996557	−	0.0829126i	$-0.0264222\pi$
$953$	4.37100	+	13.4526i	0.141591	+	0.435771i	−0.854966	+	0.518684i	$0.826422\pi$
$954$	−0.273820	+	0.842732i	−0.00886526	+	0.0272845i
$955$	22.9999	+	16.7104i	0.744258	+	0.540735i
$956$	−21.0026			−0.679273
$957$	8.91096	−	1.20878i	0.288050	−	0.0390744i
$958$	−12.0008			−0.387730
$959$	−21.5417	−	15.6510i	−0.695618	−	0.505396i
$960$	4.89603	−	15.0684i	0.158019	−	0.486332i
$961$	7.52750	+	23.1672i	0.242822	+	0.747331i
$962$	−1.79394	+	1.30338i	−0.0578391	+	0.0420226i
$963$	−3.72755	+	2.70822i	−0.120119	+	0.0872713i
$964$	0.141697	+	0.436099i	0.00456376	+	0.0140458i
$965$	−22.4171	+	68.9927i	−0.721632	+	2.22095i
$966$	−5.15262	−	3.74359i	−0.165783	−	0.120448i
$967$	−34.2641			−1.10186			−0.550929	−	0.834552i	$-0.685726\pi$
$967$	−34.2641			−1.10186			−0.550929	+	0.834552i	$0.685726\pi$
$968$	0.822115	−	18.4613i	0.0264238	−	0.593369i
$969$	−6.57040			−0.211072
$970$	1.41637	+	1.02905i	0.0454768	+	0.0330408i
$971$	−6.49895	+	20.0017i	−0.208561	+	0.641886i	0.790987	+	0.611833i	$0.209568\pi$
$971$	−6.49895	+	20.0017i	−0.208561	+	0.641886i	−0.999548	+	0.0300529i	$0.990432\pi$
$972$	−0.557798	−	1.71673i	−0.0178914	−	0.0550640i
$973$	29.0184	−	21.0831i	0.930288	−	0.675894i
$974$	−11.6115	+	8.43624i	−0.372056	+	0.270315i
$975$	−8.56002	−	26.3450i	−0.274140	−	0.843716i
$976$	7.45210	−	22.9352i	0.238536	−	0.734138i
$977$	5.07954	+	3.69050i	0.162509	+	0.118070i	0.666068	−	0.745891i	$-0.267976\pi$
$977$	5.07954	+	3.69050i	0.162509	+	0.118070i	−0.503559	+	0.863961i	$0.667976\pi$
$978$	9.69202			0.309916
$979$	−26.4898	+	3.59338i	−0.846619	+	0.114845i
$980$	24.0976			0.769770
$981$	1.04860	+	0.761854i	0.0334793	+	0.0243241i
$982$	−1.71691	+	5.28412i	−0.0547889	+	0.168623i
$983$	−5.88533	−	18.1132i	−0.187713	−	0.577721i	0.812272	−	0.583279i	$-0.198231\pi$
$983$	−5.88533	−	18.1132i	−0.187713	−	0.577721i	−0.999985	+	0.00555852i	$0.998231\pi$
$984$	−6.95645	+	5.05416i	−0.221764	+	0.161121i
$985$	−6.98802	+	5.07709i	−0.222657	+	0.161770i
$986$	−0.369919	−	1.13849i	−0.0117806	−	0.0362571i
$987$	−8.30200	+	25.5509i	−0.264256	+	0.813295i
$988$	19.8447	+	14.4180i	0.631344	+	0.458699i
$989$	36.3569			1.15608
$990$	−5.53077	−	2.97489i	−0.175779	−	0.0945481i
$991$	−12.5386			−0.398301			−0.199151	−	0.979969i	$-0.563818\pi$
$991$	−12.5386			−0.398301			−0.199151	+	0.979969i	$0.563818\pi$
$992$	27.8479	+	20.2327i	0.884173	+	0.642389i
$993$	−5.93133	+	18.2548i	−0.188225	+	0.579298i
$994$	5.14970	+	15.8491i	0.163339	+	0.502704i
$995$	19.0946	−	13.8730i	0.605339	−	0.439805i
$996$	11.1243	−	8.08225i	0.352486	−	0.256096i
$997$	7.33756	+	22.5827i	0.232383	+	0.715201i	0.997458	+	0.0712596i	$0.0227019\pi$
$997$	7.33756	+	22.5827i	0.232383	+	0.715201i	−0.765075	+	0.643941i	$0.777298\pi$
$998$	4.57315	−	14.0747i	0.144760	−	0.445527i
$999$	−1.96458	−	1.42735i	−0.0621567	−	0.0451595i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	561.2.m.d.103.4	✓	24
11.3	even	5	inner	561.2.m.d.256.4	yes	24
11.5	even	5		6171.2.a.bk.1.5		12
11.6	odd	10		6171.2.a.bl.1.8		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
561.2.m.d.103.4	✓	24	1.1	even	1	trivial
561.2.m.d.256.4	yes	24	11.3	even	5	inner
6171.2.a.bk.1.5		12	11.5	even	5
6171.2.a.bl.1.8		12	11.6	odd	10

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:	\( N \)	\(=\)	\( 561 = 3 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	561.m (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.357186 + 0.259511i) q^{2} +(0.309017 - 0.951057i) q^{3} +(-0.557798 - 1.71673i) q^{4} +(3.46967 - 2.52087i) q^{5} +(0.357186 - 0.259511i) q^{6} +(0.982692 + 3.02442i) q^{7} +(0.519138 - 1.59774i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.357186 + 0.259511i) q^{2} +(0.309017 - 0.951057i) q^{3} +(-0.557798 - 1.71673i) q^{4} +(3.46967 - 2.52087i) q^{5} +(0.357186 - 0.259511i) q^{6} +(0.982692 + 3.02442i) q^{7} +(0.519138 - 1.59774i) q^{8} +(-0.809017 - 0.587785i) q^{9} +1.89351 q^{10} +(3.28652 - 0.445822i) q^{11} -1.80507 q^{12} +(1.67324 + 1.21568i) q^{13} +(-0.433865 + 1.33530i) q^{14} +(-1.32530 - 4.07885i) q^{15} +(-2.32061 + 1.68602i) q^{16} +(-0.809017 + 0.587785i) q^{17} +(-0.136433 - 0.419898i) q^{18} +(-2.03036 + 6.24882i) q^{19} +(-6.26301 - 4.55035i) q^{20} +3.18006 q^{21} +(1.28960 + 0.693648i) q^{22} -4.53626 q^{23} +(-1.35912 - 0.987458i) q^{24} +(4.13879 - 12.7379i) q^{25} +(0.282176 + 0.868450i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(4.64395 - 3.37403i) q^{28} +(0.837857 + 2.57866i) q^{29} +(0.585128 - 1.80084i) q^{30} +(-6.01941 - 4.37335i) q^{31} -4.62636 q^{32} +(0.591590 - 3.26344i) q^{33} -0.441507 q^{34} +(11.0338 + 8.01650i) q^{35} +(-0.557798 + 1.71673i) q^{36} +(0.750404 + 2.30951i) q^{37} +(-2.34686 + 1.70509i) q^{38} +(1.67324 - 1.21568i) q^{39} +(-2.22645 - 6.85232i) q^{40} +(1.58166 - 4.86784i) q^{41} +(1.13587 + 0.825261i) q^{42} -8.01474 q^{43} +(-2.59857 - 5.39338i) q^{44} -4.28875 q^{45} +(-1.62029 - 1.17721i) q^{46} +(-2.61064 + 8.03474i) q^{47} +(0.886393 + 2.72804i) q^{48} +(-2.51829 + 1.82964i) q^{49} +(4.78394 - 3.47574i) q^{50} +(0.309017 + 0.951057i) q^{51} +(1.15366 - 3.55060i) q^{52} +(-1.62369 - 1.17968i) q^{53} -0.441507 q^{54} +(10.2793 - 9.83175i) q^{55} +5.34239 q^{56} +(5.31556 + 3.86198i) q^{57} +(-0.369919 + 1.13849i) q^{58} +(3.21633 + 9.89884i) q^{59} +(-6.26301 + 4.55035i) q^{60} +(-6.80158 + 4.94164i) q^{61} +(-1.01512 - 3.12421i) q^{62} +(0.982692 - 3.02442i) q^{63} +(2.98874 + 2.17145i) q^{64} +8.87018 q^{65} +(1.05821 - 1.01213i) q^{66} +10.6245 q^{67} +(1.46033 + 1.06099i) q^{68} +(-1.40178 + 4.31424i) q^{69} +(1.86074 + 5.72677i) q^{70} +(9.60251 - 6.97663i) q^{71} +(-1.35912 + 0.987458i) q^{72} +(-1.62234 - 4.99305i) q^{73} +(-0.331309 + 1.01966i) q^{74} +(-10.8355 - 7.87245i) q^{75} +11.8600 q^{76} +(4.57799 + 9.50171i) q^{77} +0.913142 q^{78} +(-5.92238 - 4.30286i) q^{79} +(-3.80152 + 11.6999i) q^{80} +(0.309017 + 0.951057i) q^{81} +(1.82821 - 1.32827i) q^{82} +(-6.16278 + 4.47752i) q^{83} +(-1.77383 - 5.45929i) q^{84} +(-1.32530 + 4.07885i) q^{85} +(-2.86275 - 2.07991i) q^{86} +2.71136 q^{87} +(0.993851 - 5.48246i) q^{88} -8.06013 q^{89} +(-1.53188 - 1.11298i) q^{90} +(-2.03244 + 6.25522i) q^{91} +(2.53031 + 7.78751i) q^{92} +(-6.01941 + 4.37335i) q^{93} +(-3.01759 + 2.19241i) q^{94} +(8.70773 + 26.7996i) q^{95} +(-1.42962 + 4.39993i) q^{96} +(0.748010 + 0.543461i) q^{97} -1.37431 q^{98} +(-2.92090 - 1.57109i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{2} - 6 q^{3} - 7 q^{4} + 7 q^{5} + 3 q^{6} + 5 q^{7} - 10 q^{8} - 6 q^{9}+O(q^{10}) \) 24 * q + 3 * q^2 - 6 * q^3 - 7 * q^4 + 7 * q^5 + 3 * q^6 + 5 * q^7 - 10 * q^8 - 6 * q^9	\( 24 q + 3 q^{2} - 6 q^{3} - 7 q^{4} + 7 q^{5} + 3 q^{6} + 5 q^{7} - 10 q^{8} - 6 q^{9} + 16 q^{10} - 7 q^{11} + 18 q^{12} + 6 q^{13} - 6 q^{14} + 7 q^{15} - 23 q^{16} - 6 q^{17} - 2 q^{18} + 6 q^{19} + 3 q^{20} - 10 q^{21} + 23 q^{22} - 78 q^{23} + 10 q^{24} + q^{25} + 10 q^{26} - 6 q^{27} - 13 q^{28} + 20 q^{29} + 11 q^{30} + 5 q^{31} - 22 q^{32} - 2 q^{33} - 2 q^{34} + 29 q^{35} - 7 q^{36} - 10 q^{37} + 2 q^{38} + 6 q^{39} + 44 q^{40} - 16 q^{41} + 19 q^{42} - 36 q^{43} + 3 q^{44} - 28 q^{45} + 23 q^{46} + 19 q^{47} + 12 q^{48} - 15 q^{49} + 34 q^{50} - 6 q^{51} - 6 q^{52} - 5 q^{53} - 2 q^{54} + 24 q^{55} - 50 q^{56} - 9 q^{57} - 79 q^{58} + 34 q^{59} + 3 q^{60} - 14 q^{61} + 36 q^{62} + 5 q^{63} - 20 q^{64} + 6 q^{65} + 3 q^{66} - 18 q^{67} - 2 q^{68} + 7 q^{69} + 46 q^{70} - 8 q^{71} + 10 q^{72} + 7 q^{73} + 47 q^{74} - 9 q^{75} + 58 q^{76} + 43 q^{77} - 50 q^{78} + 14 q^{79} - 51 q^{80} - 6 q^{81} - 88 q^{82} - 47 q^{83} + 22 q^{84} + 7 q^{85} - 13 q^{86} + 20 q^{87} + 115 q^{88} - 124 q^{89} - 19 q^{90} + 10 q^{91} - 19 q^{92} + 5 q^{93} + 28 q^{94} - 13 q^{95} - 27 q^{96} - 30 q^{97} - 14 q^{98} - 7 q^{99}+O(q^{100}) \) 24 * q + 3 * q^2 - 6 * q^3 - 7 * q^4 + 7 * q^5 + 3 * q^6 + 5 * q^7 - 10 * q^8 - 6 * q^9 + 16 * q^10 - 7 * q^11 + 18 * q^12 + 6 * q^13 - 6 * q^14 + 7 * q^15 - 23 * q^16 - 6 * q^17 - 2 * q^18 + 6 * q^19 + 3 * q^20 - 10 * q^21 + 23 * q^22 - 78 * q^23 + 10 * q^24 + q^25 + 10 * q^26 - 6 * q^27 - 13 * q^28 + 20 * q^29 + 11 * q^30 + 5 * q^31 - 22 * q^32 - 2 * q^33 - 2 * q^34 + 29 * q^35 - 7 * q^36 - 10 * q^37 + 2 * q^38 + 6 * q^39 + 44 * q^40 - 16 * q^41 + 19 * q^42 - 36 * q^43 + 3 * q^44 - 28 * q^45 + 23 * q^46 + 19 * q^47 + 12 * q^48 - 15 * q^49 + 34 * q^50 - 6 * q^51 - 6 * q^52 - 5 * q^53 - 2 * q^54 + 24 * q^55 - 50 * q^56 - 9 * q^57 - 79 * q^58 + 34 * q^59 + 3 * q^60 - 14 * q^61 + 36 * q^62 + 5 * q^63 - 20 * q^64 + 6 * q^65 + 3 * q^66 - 18 * q^67 - 2 * q^68 + 7 * q^69 + 46 * q^70 - 8 * q^71 + 10 * q^72 + 7 * q^73 + 47 * q^74 - 9 * q^75 + 58 * q^76 + 43 * q^77 - 50 * q^78 + 14 * q^79 - 51 * q^80 - 6 * q^81 - 88 * q^82 - 47 * q^83 + 22 * q^84 + 7 * q^85 - 13 * q^86 + 20 * q^87 + 115 * q^88 - 124 * q^89 - 19 * q^90 + 10 * q^91 - 19 * q^92 + 5 * q^93 + 28 * q^94 - 13 * q^95 - 27 * q^96 - 30 * q^97 - 14 * q^98 - 7 * q^99

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