LMFDB - Embedded newform 650.2.l.c.131.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [650,2,Mod(131,650)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(650, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("650.131");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	650.l (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:	$5.19027613138$
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			131.6
Character	$\chi$	$=$	650.131
Dual form			650.2.l.c.521.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 + 0.951057i) q^{2} +(2.44993 - 1.77998i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.597375 - 2.15480i) q^{5} +(2.44993 + 1.77998i) q^{6} -0.954033 q^{7} +(-0.809017 - 0.587785i) q^{8} +(1.90678 - 5.86846i) q^{9} +O(q^{10})$	\(q+(0.309017 + 0.951057i) q^{2} +(2.44993 - 1.77998i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.597375 - 2.15480i) q^{5} +(2.44993 + 1.77998i) q^{6} -0.954033 q^{7} +(-0.809017 - 0.587785i) q^{8} +(1.90678 - 5.86846i) q^{9} +(2.23393 - 0.0977310i) q^{10} +(-0.0305024 - 0.0938766i) q^{11} +(-0.935789 + 2.88006i) q^{12} +(0.309017 - 0.951057i) q^{13} +(-0.294812 - 0.907339i) q^{14} +(-2.37196 - 6.34241i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-2.18604 - 1.58825i) q^{17} +6.17046 q^{18} +(-0.0598531 - 0.0434859i) q^{19} +(0.783270 + 2.09439i) q^{20} +(-2.33731 + 1.69816i) q^{21} +(0.0798562 - 0.0580189i) q^{22} +(2.52405 + 7.76822i) q^{23} -3.02828 q^{24} +(-4.28629 - 2.57444i) q^{25} +1.00000 q^{26} +(-2.96688 - 9.13113i) q^{27} +(0.771829 - 0.560766i) q^{28} +(3.21875 - 2.33856i) q^{29} +(5.29901 - 4.21578i) q^{30} +(3.92264 + 2.84996i) q^{31} +1.00000 q^{32} +(-0.241827 - 0.175697i) q^{33} +(0.834992 - 2.56984i) q^{34} +(-0.569915 + 2.05575i) q^{35} +(1.90678 + 5.86846i) q^{36} +(-1.66226 + 5.11591i) q^{37} +(0.0228619 - 0.0703616i) q^{38} +(-0.935789 - 2.88006i) q^{39} +(-1.74984 + 1.39214i) q^{40} +(-1.18165 + 3.63676i) q^{41} +(-2.33731 - 1.69816i) q^{42} +7.38043 q^{43} +(0.0798562 + 0.0580189i) q^{44} +(-11.5063 - 7.61439i) q^{45} +(-6.60804 + 4.80102i) q^{46} +(2.90253 - 2.10881i) q^{47} +(-0.935789 - 2.88006i) q^{48} -6.08982 q^{49} +(1.12390 - 4.87205i) q^{50} -8.18268 q^{51} +(0.309017 + 0.951057i) q^{52} +(9.24360 - 6.71587i) q^{53} +(7.76740 - 5.64335i) q^{54} +(-0.220506 + 0.00964680i) q^{55} +(0.771829 + 0.560766i) q^{56} -0.224040 q^{57} +(3.21875 + 2.33856i) q^{58} +(-3.08891 + 9.50669i) q^{59} +(5.64693 + 3.73691i) q^{60} +(-1.18211 - 3.63815i) q^{61} +(-1.49831 + 4.61134i) q^{62} +(-1.81913 + 5.59870i) q^{63} +(0.309017 + 0.951057i) q^{64} +(-1.86473 - 1.23401i) q^{65} +(0.0923696 - 0.284284i) q^{66} +(-1.34228 - 0.975225i) q^{67} +2.70209 q^{68} +(20.0110 + 14.5388i) q^{69} +(-2.13124 + 0.0932386i) q^{70} +(3.18666 - 2.31525i) q^{71} +(-4.99201 + 3.62691i) q^{72} +(1.62189 + 4.99168i) q^{73} -5.37918 q^{74} +(-15.0835 + 1.32229i) q^{75} +0.0739826 q^{76} +(0.0291003 + 0.0895614i) q^{77} +(2.44993 - 1.77998i) q^{78} +(-1.82129 + 1.32325i) q^{79} +(-1.86473 - 1.23401i) q^{80} +(-8.54582 - 6.20890i) q^{81} -3.82392 q^{82} +(-6.64240 - 4.82599i) q^{83} +(0.892773 - 2.74767i) q^{84} +(-4.72824 + 3.76168i) q^{85} +(2.28068 + 7.01921i) q^{86} +(3.72313 - 11.4586i) q^{87} +(-0.0305024 + 0.0938766i) q^{88} +(4.38200 + 13.4864i) q^{89} +(3.68608 - 13.2961i) q^{90} +(-0.294812 + 0.907339i) q^{91} +(-6.60804 - 4.80102i) q^{92} +14.6830 q^{93} +(2.90253 + 2.10881i) q^{94} +(-0.129458 + 0.102994i) q^{95} +(2.44993 - 1.77998i) q^{96} +(-12.1173 + 8.80373i) q^{97} +(-1.88186 - 5.79176i) q^{98} -0.609072 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 6 q^{2} + 3 q^{3} - 6 q^{4} - q^{5} + 3 q^{6} - 6 q^{8} + 7 q^{9}+O(q^{10}) $ 24 * q - 6 * q^2 + 3 * q^3 - 6 * q^4 - q^5 + 3 * q^6 - 6 * q^8 + 7 * q^9	\( 24 q - 6 q^{2} + 3 q^{3} - 6 q^{4} - q^{5} + 3 q^{6} - 6 q^{8} + 7 q^{9} - q^{10} + 2 q^{11} - 2 q^{12} - 6 q^{13} + 20 q^{15} - 6 q^{16} + 9 q^{17} + 22 q^{18} + 12 q^{19} + 4 q^{20} + 25 q^{21} + 2 q^{22} - 6 q^{23} - 2 q^{24} - 41 q^{25} + 24 q^{26} - 6 q^{27} - 2 q^{29} + 10 q^{30} + 13 q^{31} + 24 q^{32} - 34 q^{33} + 14 q^{34} + 7 q^{36} + 5 q^{37} + 22 q^{38} - 2 q^{39} - q^{40} - 10 q^{41} + 25 q^{42} - 18 q^{43} + 2 q^{44} + 3 q^{45} + 9 q^{46} - 5 q^{47} - 2 q^{48} + 32 q^{49} - 11 q^{50} - 56 q^{51} - 6 q^{52} + 34 q^{53} + 19 q^{54} + 20 q^{55} - 12 q^{57} - 2 q^{58} - 15 q^{60} - 2 q^{61} - 12 q^{62} + 10 q^{63} - 6 q^{64} - q^{65} + 26 q^{66} + 2 q^{67} - 46 q^{68} + 33 q^{69} - 20 q^{70} + 29 q^{71} - 18 q^{72} - 11 q^{73} - 30 q^{74} - 25 q^{75} - 68 q^{76} + 15 q^{77} + 3 q^{78} + 20 q^{79} - q^{80} - 9 q^{81} - 20 q^{82} - 69 q^{83} - 20 q^{84} - 27 q^{85} + 22 q^{86} - 18 q^{87} + 2 q^{88} + 19 q^{89} + 8 q^{90} + 9 q^{92} + 40 q^{93} - 5 q^{94} + 78 q^{95} + 3 q^{96} - 49 q^{97} + 2 q^{98} - 28 q^{99}+O(q^{100}) \) 24 * q - 6 * q^2 + 3 * q^3 - 6 * q^4 - q^5 + 3 * q^6 - 6 * q^8 + 7 * q^9 - q^10 + 2 * q^11 - 2 * q^12 - 6 * q^13 + 20 * q^15 - 6 * q^16 + 9 * q^17 + 22 * q^18 + 12 * q^19 + 4 * q^20 + 25 * q^21 + 2 * q^22 - 6 * q^23 - 2 * q^24 - 41 * q^25 + 24 * q^26 - 6 * q^27 - 2 * q^29 + 10 * q^30 + 13 * q^31 + 24 * q^32 - 34 * q^33 + 14 * q^34 + 7 * q^36 + 5 * q^37 + 22 * q^38 - 2 * q^39 - q^40 - 10 * q^41 + 25 * q^42 - 18 * q^43 + 2 * q^44 + 3 * q^45 + 9 * q^46 - 5 * q^47 - 2 * q^48 + 32 * q^49 - 11 * q^50 - 56 * q^51 - 6 * q^52 + 34 * q^53 + 19 * q^54 + 20 * q^55 - 12 * q^57 - 2 * q^58 - 15 * q^60 - 2 * q^61 - 12 * q^62 + 10 * q^63 - 6 * q^64 - q^65 + 26 * q^66 + 2 * q^67 - 46 * q^68 + 33 * q^69 - 20 * q^70 + 29 * q^71 - 18 * q^72 - 11 * q^73 - 30 * q^74 - 25 * q^75 - 68 * q^76 + 15 * q^77 + 3 * q^78 + 20 * q^79 - q^80 - 9 * q^81 - 20 * q^82 - 69 * q^83 - 20 * q^84 - 27 * q^85 + 22 * q^86 - 18 * q^87 + 2 * q^88 + 19 * q^89 + 8 * q^90 + 9 * q^92 + 40 * q^93 - 5 * q^94 + 78 * q^95 + 3 * q^96 - 49 * q^97 + 2 * q^98 - 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/650\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$

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 $

$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$3$	2.44993	−	1.77998i	1.41447	−	1.02767i	0.421812	−	0.906683i	$-0.361394\pi$
$3$	2.44993	−	1.77998i	1.41447	−	1.02767i	0.992654	−	0.120987i	$-0.0386058\pi$
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	0.597375	−	2.15480i	0.267154	−	0.963654i
$5$	0.597375	−	2.15480i	0.267154	−	0.963654i
$6$	2.44993	+	1.77998i	1.00018	+	0.726672i
$7$	−0.954033			−0.360590			−0.180295	−	0.983613i	$-0.557705\pi$
$7$	−0.954033			−0.360590			−0.180295	+	0.983613i	$0.557705\pi$
$8$	−0.809017	−	0.587785i	−0.286031	−	0.207813i
$9$	1.90678	−	5.86846i	0.635592	−	1.95615i
$10$	2.23393	−	0.0977310i	0.706431	−	0.0309053i
$11$	−0.0305024	−	0.0938766i	−0.00919681	−	0.0283049i	0.946353	−	0.323135i	$-0.104737\pi$
$11$	−0.0305024	−	0.0938766i	−0.00919681	−	0.0283049i	−0.955550	+	0.294830i	$0.904737\pi$
$12$	−0.935789	+	2.88006i	−0.270139	+	0.831402i
$13$	0.309017	−	0.951057i	0.0857059	−	0.263776i
$13$	0.309017	−	0.951057i	0.0857059	−	0.263776i
$14$	−0.294812	−	0.907339i	−0.0787919	−	0.242497i
$15$	−2.37196	−	6.34241i	−0.612437	−	1.63760i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−2.18604	−	1.58825i	−0.530192	−	0.385207i	0.290238	−	0.956955i	$-0.406266\pi$
$17$	−2.18604	−	1.58825i	−0.530192	−	0.385207i	−0.820430	+	0.571748i	$0.806266\pi$
$18$	6.17046			1.45439
$19$	−0.0598531	−	0.0434859i	−0.0137313	−	0.00997634i	0.580898	−	0.813976i	$-0.302701\pi$
$19$	−0.0598531	−	0.0434859i	−0.0137313	−	0.00997634i	−0.594630	+	0.804000i	$0.702701\pi$
$20$	0.783270	+	2.09439i	0.175145	+	0.468321i
$21$	−2.33731	+	1.69816i	−0.510043	+	0.370568i
$22$	0.0798562	−	0.0580189i	0.0170254	−	0.0123697i
$23$	2.52405	+	7.76822i	0.526300	+	1.61979i	0.761731	+	0.647894i	$0.224350\pi$
$23$	2.52405	+	7.76822i	0.526300	+	1.61979i	−0.235430	+	0.971891i	$0.575650\pi$
$24$	−3.02828			−0.618144
$25$	−4.28629	−	2.57444i	−0.857257	−	0.514888i
$26$	1.00000			0.196116
$27$	−2.96688	−	9.13113i	−0.570977	−	1.75729i
$28$	0.771829	−	0.560766i	0.145862	−	0.105975i
$29$	3.21875	−	2.33856i	0.597708	−	0.434260i	−0.247357	−	0.968924i	$-0.579562\pi$
$29$	3.21875	−	2.33856i	0.597708	−	0.434260i	0.845064	+	0.534664i	$0.179562\pi$
$30$	5.29901	−	4.21578i	0.967463	−	0.769692i
$31$	3.92264	+	2.84996i	0.704526	+	0.511868i	0.881403	−	0.472365i	$-0.156599\pi$
$31$	3.92264	+	2.84996i	0.704526	+	0.511868i	−0.176877	+	0.984233i	$0.556599\pi$
$32$	1.00000			0.176777
$33$	−0.241827	−	0.175697i	−0.0420966	−	0.0305850i
$34$	0.834992	−	2.56984i	0.143200	−	0.440724i
$35$	−0.569915	+	2.05575i	−0.0963333	+	0.347484i
$36$	1.90678	+	5.86846i	0.317796	+	0.978076i
$37$	−1.66226	+	5.11591i	−0.273274	+	0.841050i	0.716397	+	0.697692i	$0.245790\pi$
$37$	−1.66226	+	5.11591i	−0.273274	+	0.841050i	−0.989671	+	0.143357i	$0.954210\pi$
$38$	0.0228619	−	0.0703616i	0.00370868	−	0.0114142i
$39$	−0.935789	−	2.88006i	−0.149846	−	0.461179i
$40$	−1.74984	+	1.39214i	−0.276675	+	0.220116i
$41$	−1.18165	+	3.63676i	−0.184543	+	0.567966i	−0.999940	−	0.0109362i	$-0.996519\pi$
$41$	−1.18165	+	3.63676i	−0.184543	+	0.567966i	0.815397	+	0.578903i	$0.196519\pi$
$42$	−2.33731	−	1.69816i	−0.360655	−	0.262031i
$43$	7.38043			1.12551			0.562753	−	0.826625i	$-0.309742\pi$
$43$	7.38043			1.12551			0.562753	+	0.826625i	$0.309742\pi$
$44$	0.0798562	+	0.0580189i	0.0120388	+	0.00874668i
$45$	−11.5063	−	7.61439i	−1.71525	−	1.13509i
$46$	−6.60804	+	4.80102i	−0.974302	+	0.707872i
$47$	2.90253	−	2.10881i	0.423378	−	0.307602i	−0.355617	−	0.934632i	$-0.615729\pi$
$47$	2.90253	−	2.10881i	0.423378	−	0.307602i	0.778996	+	0.627029i	$0.215729\pi$
$48$	−0.935789	−	2.88006i	−0.135070	−	0.415701i
$49$	−6.08982			−0.869975
$50$	1.12390	−	4.87205i	0.158944	−	0.689011i
$51$	−8.18268			−1.14580
$52$	0.309017	+	0.951057i	0.0428529	+	0.131888i
$53$	9.24360	−	6.71587i	1.26971	−	0.922496i	0.270516	−	0.962716i	$-0.412806\pi$
$53$	9.24360	−	6.71587i	1.26971	−	0.922496i	0.999191	+	0.0402199i	$0.0128059\pi$
$54$	7.76740	−	5.64335i	1.05701	−	0.767962i
$55$	−0.220506	+	0.00964680i	−0.0297331	+	0.00130077i
$56$	0.771829	+	0.560766i	0.103140	+	0.0749356i
$57$	−0.224040			−0.0296748
$58$	3.21875	+	2.33856i	0.422643	+	0.307068i
$59$	−3.08891	+	9.50669i	−0.402142	+	1.23767i	0.521116	+	0.853486i	$0.325516\pi$
$59$	−3.08891	+	9.50669i	−0.402142	+	1.23767i	−0.923258	+	0.384180i	$0.874484\pi$
$60$	5.64693	+	3.73691i	0.729015	+	0.482433i
$61$	−1.18211	−	3.63815i	−0.151353	−	0.465818i	0.846420	−	0.532516i	$-0.178753\pi$
$61$	−1.18211	−	3.63815i	−0.151353	−	0.465818i	−0.997773	+	0.0666984i	$0.978753\pi$
$62$	−1.49831	+	4.61134i	−0.190286	+	0.585640i
$63$	−1.81913	+	5.59870i	−0.229189	+	0.705370i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	−1.86473	−	1.23401i	−0.231292	−	0.153060i
$66$	0.0923696	−	0.284284i	0.0113699	−	0.0349930i
$67$	−1.34228	−	0.975225i	−0.163986	−	0.119143i	0.502766	−	0.864423i	$-0.332316\pi$
$67$	−1.34228	−	0.975225i	−0.163986	−	0.119143i	−0.666752	+	0.745280i	$0.732316\pi$
$68$	2.70209			0.327677
$69$	20.0110	+	14.5388i	2.40904	+	1.75027i
$70$	−2.13124	+	0.0932386i	−0.254732	+	0.0111441i
$71$	3.18666	−	2.31525i	0.378187	−	0.274769i	−0.382410	−	0.923993i	$-0.624906\pi$
$71$	3.18666	−	2.31525i	0.378187	−	0.274769i	0.760598	+	0.649223i	$0.224906\pi$
$72$	−4.99201	+	3.62691i	−0.588314	+	0.427435i
$73$	1.62189	+	4.99168i	0.189828	+	0.584232i	0.999998	−	0.00196365i	$-0.000625051\pi$
$73$	1.62189	+	4.99168i	0.189828	+	0.584232i	−0.810170	+	0.586195i	$0.800625\pi$
$74$	−5.37918			−0.625317
$75$	−15.0835	+	1.32229i	−1.74170	+	0.152685i
$76$	0.0739826			0.00848638
$77$	0.0291003	+	0.0895614i	0.00331628	+	0.0102065i
$78$	2.44993	−	1.77998i	0.277400	−	0.201543i
$79$	−1.82129	+	1.32325i	−0.204911	+	0.148877i	−0.685508	−	0.728065i	$-0.740420\pi$
$79$	−1.82129	+	1.32325i	−0.204911	+	0.148877i	0.480597	+	0.876942i	$0.340420\pi$
$80$	−1.86473	−	1.23401i	−0.208484	−	0.137966i
$81$	−8.54582	−	6.20890i	−0.949535	−	0.689878i
$82$	−3.82392			−0.422281
$83$	−6.64240	−	4.82599i	−0.729098	−	0.529721i	0.160180	−	0.987088i	$-0.448793\pi$
$83$	−6.64240	−	4.82599i	−0.729098	−	0.529721i	−0.889278	+	0.457367i	$0.848793\pi$
$84$	0.892773	−	2.74767i	0.0974096	−	0.299796i
$85$	−4.72824	+	3.76168i	−0.512849	+	0.408012i
$86$	2.28068	+	7.01921i	0.245932	+	0.756901i
$87$	3.72313	−	11.4586i	0.399161	−	1.22849i
$88$	−0.0305024	+	0.0938766i	−0.00325156	+	0.0100073i
$89$	4.38200	+	13.4864i	0.464491	+	1.42956i	0.859622	+	0.510931i	$0.170699\pi$
$89$	4.38200	+	13.4864i	0.464491	+	1.42956i	−0.395131	+	0.918625i	$0.629301\pi$
$90$	3.68608	−	13.2961i	0.388547	−	1.40153i
$91$	−0.294812	+	0.907339i	−0.0309047	+	0.0951150i
$92$	−6.60804	−	4.80102i	−0.688936	−	0.500541i
$93$	14.6830			1.52256
$94$	2.90253	+	2.10881i	0.299374	+	0.217508i
$95$	−0.129458	+	0.102994i	−0.0132821	+	0.0105670i
$96$	2.44993	−	1.77998i	0.250045	−	0.181668i
$97$	−12.1173	+	8.80373i	−1.23032	+	0.893883i	−0.996914	−	0.0784955i	$-0.974988\pi$
$97$	−12.1173	+	8.80373i	−1.23032	+	0.893883i	−0.233410	+	0.972378i	$0.574988\pi$
$98$	−1.88186	−	5.79176i	−0.190096	−	0.585057i
$99$	−0.609072			−0.0612141
$100$	4.98090	−	0.436649i	0.498090	−	0.0436649i
$101$	4.82112			0.479719			0.239860	−	0.970808i	$-0.422899\pi$
$101$	4.82112			0.479719			0.239860	+	0.970808i	$0.422899\pi$
$102$	−2.52859	−	7.78219i	−0.250367	−	0.770552i
$103$	8.00765	−	5.81790i	0.789017	−	0.573254i	−0.118655	−	0.992936i	$-0.537858\pi$
$103$	8.00765	−	5.81790i	0.789017	−	0.573254i	0.907672	+	0.419681i	$0.137858\pi$
$104$	−0.809017	+	0.587785i	−0.0793306	+	0.0576371i
$105$	2.26293	+	6.05086i	0.220839	+	0.590504i
$106$	9.24360	+	6.71587i	0.897818	+	0.652303i
$107$	9.05514			0.875394			0.437697	−	0.899123i	$-0.355794\pi$
$107$	9.05514			0.875394			0.437697	+	0.899123i	$0.355794\pi$
$108$	7.76740	+	5.64335i	0.747418	+	0.543031i
$109$	0.536063	−	1.64983i	0.0513455	−	0.158025i	−0.922096	−	0.386961i	$-0.873525\pi$
$109$	0.536063	−	1.64983i	0.0513455	−	0.158025i	0.973441	+	0.228936i	$0.0735247\pi$
$110$	−0.0773148	−	0.206733i	−0.00737168	−	0.0197112i
$111$	5.03378	+	15.4924i	0.477785	+	1.47047i
$112$	−0.294812	+	0.907339i	−0.0278571	+	0.0857355i
$113$	−6.13231	+	18.8733i	−0.576879	+	1.77545i	0.0528119	+	0.998604i	$0.483182\pi$
$113$	−6.13231	+	18.8733i	−0.576879	+	1.77545i	−0.629691	+	0.776846i	$0.716818\pi$
$114$	−0.0692321	−	0.213074i	−0.00648418	−	0.0199562i
$115$	18.2467	−	0.798265i	1.70152	−	0.0744386i
$116$	−1.22945	+	3.78387i	−0.114152	+	0.351324i
$117$	−4.99201	−	3.62691i	−0.461511	−	0.335308i
$118$	−9.99593			−0.920200
$119$	2.08555	+	1.51524i	0.191182	+	0.138902i
$120$	−1.80902	+	6.52532i	−0.165140	+	0.595677i
$121$	8.89130	−	6.45991i	0.808300	−	0.587265i
$122$	3.09480	−	2.24850i	0.280190	−	0.203570i
$123$	3.57838	+	11.0131i	0.322651	+	0.993019i
$124$	−4.84865			−0.435421
$125$	−8.10792	+	7.69816i	−0.725194	+	0.688545i
$126$	−5.88682			−0.524440
$127$	3.36843	+	10.3669i	0.298899	+	0.919918i	0.981884	+	0.189485i	$0.0606817\pi$
$127$	3.36843	+	10.3669i	0.298899	+	0.919918i	−0.682984	+	0.730433i	$0.739318\pi$
$128$	−0.809017	+	0.587785i	−0.0715077	+	0.0519534i
$129$	18.0815	−	13.1370i	1.59199	−	1.15665i
$130$	0.597375	−	2.15480i	0.0523933	−	0.188988i
$131$	−12.7717	−	9.27919i	−1.11587	−	0.810726i	−0.132291	−	0.991211i	$-0.542233\pi$
$131$	−12.7717	−	9.27919i	−1.11587	−	0.810726i	−0.983578	+	0.180485i	$0.942233\pi$
$132$	0.298914			0.0260172
$133$	0.0571019	+	0.0414869i	0.00495136	+	0.00359737i
$134$	0.512706	−	1.57795i	0.0442910	−	0.136314i
$135$	−21.4481	+	0.938319i	−1.84595	+	0.0807576i
$136$	0.834992	+	2.56984i	0.0716000	+	0.220362i
$137$	−3.53002	+	10.8643i	−0.301590	+	0.928199i	0.679337	+	0.733826i	$0.262267\pi$
$137$	−3.53002	+	10.8643i	−0.301590	+	0.928199i	−0.980928	+	0.194373i	$0.937733\pi$
$138$	−7.64351	+	23.5243i	−0.650659	+	2.00252i
$139$	−5.55675	−	17.1019i	−0.471317	−	1.45056i	−0.850861	−	0.525391i	$-0.823919\pi$
$139$	−5.55675	−	17.1019i	−0.471317	−	1.45056i	0.379544	−	0.925174i	$-0.376081\pi$
$140$	−0.747266	−	1.99812i	−0.0631555	−	0.168872i
$141$	3.35736	−	10.3329i	0.282741	−	0.870186i
$142$	3.18666	+	2.31525i	0.267419	+	0.194291i
$143$	−0.0987077			−0.00825435
$144$	−4.99201	−	3.62691i	−0.416001	−	0.302242i
$145$	−3.11632	−	8.33275i	−0.258796	−	0.691998i
$146$	−4.24618	+	3.08503i	−0.351416	+	0.255319i
$147$	−14.9196	+	10.8397i	−1.23055	+	0.894047i
$148$	−1.66226	−	5.11591i	−0.136637	−	0.420525i
$149$	−17.6732			−1.44785			−0.723923	−	0.689881i	$-0.757663\pi$
$149$	−17.6732			−1.44785			−0.723923	+	0.689881i	$0.757663\pi$
$150$	−5.91864	−	13.9367i	−0.483255	−	1.13793i
$151$	−18.1612			−1.47794			−0.738971	−	0.673738i	$-0.764688\pi$
$151$	−18.1612			−1.47794			−0.738971	+	0.673738i	$0.764688\pi$
$152$	0.0228619	+	0.0703616i	0.00185434	+	0.00570708i
$153$	−13.4889	+	9.80023i	−1.09051	+	0.792302i
$154$	−0.0761854	+	0.0553520i	−0.00613920	+	0.00446039i
$155$	8.48437	−	6.74998i	0.681481	−	0.542172i
$156$	2.44993	+	1.77998i	0.196151	+	0.142512i
$157$	19.0991			1.52427			0.762136	−	0.647417i	$-0.224151\pi$
$157$	19.0991			1.52427			0.762136	+	0.647417i	$0.224151\pi$
$158$	−1.82129	−	1.32325i	−0.144894	−	0.105272i
$159$	10.6921	−	32.9068i	0.847936	−	2.60968i
$160$	0.597375	−	2.15480i	0.0472266	−	0.170352i
$161$	−2.40802	−	7.41113i	−0.189779	−	0.584079i
$162$	3.26421	−	10.0462i	0.256461	−	0.789305i
$163$	3.28832	−	10.1204i	0.257561	−	0.792691i	−0.735754	−	0.677249i	$-0.763172\pi$
$163$	3.28832	−	10.1204i	0.257561	−	0.792691i	0.993314	−	0.115441i	$-0.0368282\pi$
$164$	−1.18165	−	3.63676i	−0.0922717	−	0.283983i
$165$	−0.523053	+	0.416130i	−0.0407196	+	0.0323957i
$166$	2.53717	−	7.80861i	0.196923	−	0.606066i
$167$	−6.43585	−	4.67592i	−0.498021	−	0.361833i	0.310240	−	0.950658i	$-0.399591\pi$
$167$	−6.43585	−	4.67592i	−0.498021	−	0.361833i	−0.808260	+	0.588825i	$0.799591\pi$
$168$	2.88908			0.222897
$169$	−0.809017	−	0.587785i	−0.0622321	−	0.0452143i
$170$	−5.03868	−	3.33440i	−0.386449	−	0.255737i
$171$	−0.369322	+	0.268328i	−0.0282427	+	0.0205195i
$172$	−5.97090	+	4.33811i	−0.455277	+	0.330778i
$173$	1.33118	+	4.09695i	0.101208	+	0.311486i	0.988822	−	0.149103i	$-0.0476385\pi$
$173$	1.33118	+	4.09695i	0.101208	+	0.311486i	−0.887614	+	0.460588i	$0.847638\pi$
$174$	12.0483			0.913379
$175$	4.08926	+	2.45610i	0.309119	+	0.185664i
$176$	−0.0987077			−0.00744037
$177$	9.35408	+	28.7889i	0.703096	+	2.16391i
$178$	−11.4722	+	8.33505i	−0.859879	+	0.624739i
$179$	−9.31059	+	6.76454i	−0.695906	+	0.505605i	−0.878596	−	0.477565i	$-0.841519\pi$
$179$	−9.31059	+	6.76454i	−0.695906	+	0.505605i	0.182690	+	0.983171i	$0.441519\pi$
$180$	13.7844	−	0.603045i	1.02743	−	0.0449483i
$181$	−20.3064	−	14.7534i	−1.50936	−	1.09661i	−0.966460	−	0.256816i	$-0.917326\pi$
$181$	−20.3064	−	14.7534i	−1.50936	−	1.09661i	−0.542900	−	0.839798i	$-0.682674\pi$
$182$	−0.954033			−0.0707176
$183$	−9.37191	−	6.80909i	−0.692791	−	0.503342i
$184$	2.52405	−	7.76822i	0.186075	−	0.572681i
$185$	10.0307	+	6.63794i	0.737474	+	0.488031i
$186$	4.53731	+	13.9644i	0.332692	+	1.02392i
$187$	−0.0824202	+	0.253663i	−0.00602716	+	0.0185497i
$188$	−1.10867	+	3.41213i	−0.0808580	+	0.248855i
$189$	2.83050	+	8.71139i	0.205889	+	0.633661i
$190$	−0.137958	−	0.0912949i	−0.0100085	−	0.00662323i
$191$	−0.0521113	+	0.160382i	−0.00377064	+	0.0116048i	−0.952924	−	0.303209i	$-0.901942\pi$
$191$	−0.0521113	+	0.160382i	−0.00377064	+	0.0116048i	0.949153	+	0.314814i	$0.101942\pi$
$192$	2.44993	+	1.77998i	0.176808	+	0.128459i
$193$	−27.3559			−1.96912			−0.984561	−	0.175039i	$-0.943995\pi$
$193$	−27.3559			−1.96912			−0.984561	+	0.175039i	$0.943995\pi$
$194$	−12.1173	−	8.80373i	−0.869971	−	0.632071i
$195$	−6.76496	+	0.295956i	−0.484449	+	0.0211939i
$196$	4.92677	−	3.57951i	0.351912	−	0.255679i
$197$	−8.99935	+	6.53841i	−0.641177	+	0.465842i	−0.860254	−	0.509865i	$-0.829695\pi$
$197$	−8.99935	+	6.53841i	−0.641177	+	0.465842i	0.219077	+	0.975707i	$0.429695\pi$
$198$	−0.188214	−	0.579262i	−0.0133758	−	0.0411664i
$199$	−8.32643			−0.590245			−0.295123	−	0.955459i	$-0.595361\pi$
$199$	−8.32643			−0.590245			−0.295123	+	0.955459i	$0.595361\pi$
$200$	1.95446	+	4.60218i	0.138201	+	0.325423i
$201$	−5.02437			−0.354392
$202$	1.48981	+	4.58516i	0.104823	+	0.322611i
$203$	−3.07080	+	2.23106i	−0.215528	+	0.156590i
$204$	6.61993	−	4.80966i	0.463488	−	0.336744i
$205$	7.13058	+	4.71873i	0.498021	+	0.329571i
$206$	8.00765	+	5.81790i	0.557919	+	0.405352i
$207$	50.4002			3.50306
$208$	−0.809017	−	0.587785i	−0.0560952	−	0.0407556i
$209$	−0.00225664	+	0.00694523i	−0.000156095	+	0.000480412i
$210$	−5.05543	+	4.02199i	−0.348858	+	0.277544i
$211$	−1.27619	−	3.92770i	−0.0878563	−	0.270394i	0.897470	−	0.441076i	$-0.145403\pi$
$211$	−1.27619	−	3.92770i	−0.0878563	−	0.270394i	−0.985326	+	0.170682i	$0.945403\pi$
$212$	−3.53074	+	10.8665i	−0.242492	+	0.746315i
$213$	3.68601	−	11.3444i	0.252561	−	0.777304i
$214$	2.79819	+	8.61195i	0.191281	+	0.588701i
$215$	4.40889	−	15.9033i	0.300684	−	1.08460i
$216$	−2.96688	+	9.13113i	−0.201871	+	0.621294i
$217$	−3.74232	−	2.71896i	−0.254045	−	0.184575i
$218$	1.73474			0.117491
$219$	12.8586	+	9.34232i	0.868903	+	0.631295i
$220$	0.172723	−	0.137415i	0.0116450	−	0.00926450i
$221$	−2.18604	+	1.58825i	−0.147049	+	0.106837i
$222$	−13.1786	+	9.57482i	−0.884490	+	0.642620i
$223$	−3.52225	−	10.8404i	−0.235868	−	0.725926i	−0.997005	−	0.0773354i	$-0.975359\pi$
$223$	−3.52225	−	10.8404i	−0.235868	−	0.725926i	0.761138	−	0.648591i	$-0.224641\pi$
$224$	−0.954033			−0.0637440
$225$	−23.2810	+	20.2450i	−1.55207	+	1.34967i
$226$	−19.8446			−1.32004
$227$	8.51439	+	26.2046i	0.565120	+	1.73926i	0.667595	+	0.744525i	$0.267324\pi$
$227$	8.51439	+	26.2046i	0.565120	+	1.73926i	−0.102475	+	0.994736i	$0.532676\pi$
$228$	0.181252	−	0.131687i	0.0120037	−	0.00872120i
$229$	21.8898	−	15.9039i	1.44652	−	1.05096i	0.459893	−	0.887974i	$-0.347888\pi$
$229$	21.8898	−	15.9039i	1.44652	−	1.05096i	0.986628	−	0.162985i	$-0.0521123\pi$
$230$	6.39774	+	17.1070i	0.421855	+	1.12800i
$231$	0.230711	+	0.167621i	0.0151796	+	0.0110287i
$232$	−3.97860			−0.261208
$233$	9.23422	+	6.70905i	0.604954	+	0.439525i	0.847634	−	0.530582i	$-0.178027\pi$
$233$	9.23422	+	6.70905i	0.604954	+	0.439525i	−0.242680	+	0.970106i	$0.578027\pi$
$234$	1.90678	−	5.86846i	0.124650	−	0.383633i
$235$	−2.81016	−	7.51412i	−0.183315	−	0.490167i
$236$	−3.08891	−	9.50669i	−0.201071	−	0.618833i
$237$	−2.10669	+	6.48372i	−0.136844	+	0.421163i
$238$	−0.796610	+	2.45171i	−0.0516365	+	0.158921i
$239$	−4.42514	−	13.6192i	−0.286239	−	0.880952i	−0.986025	−	0.166599i	$-0.946721\pi$
$239$	−4.42514	−	13.6192i	−0.286239	−	0.880952i	0.699786	−	0.714352i	$-0.253279\pi$
$240$	−6.76496	+	0.295956i	−0.436676	+	0.0191039i
$241$	2.79335	−	8.59706i	0.179936	−	0.553785i	−0.819889	−	0.572523i	$-0.805965\pi$
$241$	2.79335	−	8.59706i	0.179936	−	0.553785i	0.999824	+	0.0187376i	$0.00596472\pi$
$242$	8.89130	+	6.45991i	0.571555	+	0.415259i
$243$	−3.18522			−0.204332
$244$	3.09480	+	2.24850i	0.198124	+	0.143946i
$245$	−3.63791	+	13.1223i	−0.232417	+	0.838354i
$246$	−9.36831	+	6.80648i	−0.597302	+	0.433965i
$247$	−0.0598531	+	0.0434859i	−0.00380836	+	0.00276694i
$248$	−1.49831	−	4.61134i	−0.0951430	−	0.292820i
$249$	−24.8635			−1.57566
$250$	−9.82687	−	5.33222i	−0.621506	−	0.337239i
$251$	17.8588			1.12724			0.563620	−	0.826034i	$-0.309408\pi$
$251$	17.8588			1.12724			0.563620	+	0.826034i	$0.309408\pi$
$252$	−1.81913	−	5.59870i	−0.114594	−	0.352685i
$253$	0.652265	−	0.473898i	0.0410075	−	0.0297937i
$254$	−8.81865	+	6.40713i	−0.553331	+	0.402019i
$255$	−4.88813	+	17.6320i	−0.306107	+	1.10416i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−28.9971			−1.80879			−0.904395	−	0.426697i	$-0.859677\pi$
$257$	−28.9971			−1.80879			−0.904395	+	0.426697i	$0.859677\pi$
$258$	18.0815	+	13.1370i	1.12571	+	0.817874i
$259$	1.58585	−	4.88074i	0.0985398	−	0.303274i
$260$	2.23393	−	0.0977310i	0.138543	−	0.00606102i
$261$	−7.58630	−	23.3482i	−0.469580	−	1.44522i
$262$	4.87836	−	15.0140i	0.301386	−	0.927570i
$263$	−1.95132	+	6.00555i	−0.120324	+	0.370318i	−0.993020	−	0.117945i	$-0.962369\pi$
$263$	−1.95132	+	6.00555i	−0.120324	+	0.370318i	0.872696	+	0.488263i	$0.162369\pi$
$264$	0.0923696	+	0.284284i	0.00568496	+	0.0174965i
$265$	−8.94943	−	23.9300i	−0.549759	−	1.47001i
$266$	−0.0218110	+	0.0671273i	−0.00133732	+	0.00411584i
$267$	34.7410	+	25.2408i	2.12612	+	1.54471i
$268$	1.65915			0.101349
$269$	16.7247	+	12.1512i	1.01972	+	0.740870i	0.966225	−	0.257698i	$-0.0829640\pi$
$269$	16.7247	+	12.1512i	1.01972	+	0.740870i	0.0534947	+	0.998568i	$0.482964\pi$
$270$	−7.52021	−	20.1084i	−0.457665	−	1.22376i
$271$	9.16881	−	6.66153i	0.556966	−	0.404659i	−0.273381	−	0.961906i	$-0.588142\pi$
$271$	9.16881	−	6.66153i	0.556966	−	0.404659i	0.830347	+	0.557246i	$0.188142\pi$
$272$	−2.18604	+	1.58825i	−0.132548	+	0.0963018i
$273$	0.892773	+	2.74767i	0.0540331	+	0.166297i
$274$	−11.4234			−0.690112
$275$	−0.110938	+	0.480909i	−0.00668982	+	0.0289999i
$276$	−24.7349			−1.48887
$277$	−1.01752	−	3.13161i	−0.0611369	−	0.188160i	0.915823	−	0.401581i	$-0.131539\pi$
$277$	−1.01752	−	3.13161i	−0.0611369	−	0.188160i	−0.976960	+	0.213421i	$0.931539\pi$
$278$	14.5478	−	10.5696i	0.872516	−	0.633920i
$279$	24.2045	−	17.5856i	1.44908	−	1.05282i
$280$	1.66941	−	1.32814i	0.0997662	−	0.0793718i
$281$	−17.5091	−	12.7211i	−1.04451	−	0.758879i	−0.0733472	−	0.997306i	$-0.523368\pi$
$281$	−17.5091	−	12.7211i	−1.04451	−	0.758879i	−0.971160	+	0.238427i	$0.923368\pi$
$282$	10.8646			0.646980
$283$	−14.5298	−	10.5565i	−0.863707	−	0.627520i	0.0651838	−	0.997873i	$-0.479237\pi$
$283$	−14.5298	−	10.5565i	−0.863707	−	0.627520i	−0.928891	+	0.370353i	$0.879237\pi$
$284$	−1.21720	+	3.74615i	−0.0722274	+	0.222293i
$285$	−0.133836	+	0.482760i	−0.00792774	+	0.0285962i
$286$	−0.0305024	−	0.0938766i	−0.00180364	−	0.00555104i
$287$	1.12734	−	3.46959i	0.0665446	−	0.204803i
$288$	1.90678	−	5.86846i	0.112358	−	0.345802i
$289$	−2.99706	−	9.22401i	−0.176298	−	0.542589i
$290$	6.96192	−	5.53876i	0.408818	−	0.325247i
$291$	−14.0161	+	43.1370i	−0.821636	+	2.52873i
$292$	−4.24618	−	3.08503i	−0.248489	−	0.180538i
$293$	0.233438			0.0136376			0.00681879	−	0.999977i	$-0.497829\pi$
$293$	0.233438			0.0136376			0.00681879	+	0.999977i	$0.497829\pi$
$294$	−14.9196	−	10.8397i	−0.870130	−	0.632186i
$295$	18.6397	+	12.3350i	1.08525	+	0.718173i
$296$	4.35185	−	3.16180i	0.252946	−	0.183776i
$297$	−0.766702	+	0.557042i	−0.0444886	+	0.0323229i
$298$	−5.46132	−	16.8082i	−0.316366	−	0.973674i
$299$	8.16799			0.472367
$300$	11.4256	−	9.93564i	0.659658	−	0.573634i
$301$	−7.04118			−0.405847
$302$	−5.61213	−	17.2724i	−0.322942	−	0.993913i
$303$	11.8114	−	8.58148i	0.678547	−	0.492993i
$304$	−0.0598531	+	0.0434859i	−0.00343281	+	0.00249408i
$305$	−8.54564	+	0.373858i	−0.489322	+	0.0214071i
$306$	−13.4889	−	9.80023i	−0.771107	−	0.560242i
$307$	33.3422			1.90294			0.951469	−	0.307746i	$-0.0995746\pi$
$307$	33.3422			1.90294			0.951469	+	0.307746i	$0.0995746\pi$
$308$	−0.0761854	−	0.0553520i	−0.00434107	−	0.00315397i
$309$	9.26244	−	28.5069i	0.526922	−	1.62170i
$310$	9.04143	+	5.98326i	0.513519	+	0.339826i
$311$	−1.21907	−	3.75190i	−0.0691269	−	0.212751i	0.910525	−	0.413453i	$-0.135677\pi$
$311$	−1.21907	−	3.75190i	−0.0691269	−	0.212751i	−0.979652	+	0.200703i	$0.935677\pi$
$312$	−0.935789	+	2.88006i	−0.0529786	+	0.163051i
$313$	0.0147186	−	0.0452992i	0.000831945	−	0.00256046i	−0.950640	−	0.310297i	$-0.899572\pi$
$313$	0.0147186	−	0.0452992i	0.000831945	−	0.00256046i	0.951472	+	0.307736i	$0.0995715\pi$
$314$	5.90194	+	18.1643i	0.333066	+	1.02507i
$315$	10.9774	+	7.26437i	0.618504	+	0.409301i
$316$	0.695672	−	2.14106i	0.0391346	−	0.120444i
$317$	3.37108	+	2.44923i	0.189339	+	0.137562i	0.678416	−	0.734678i	$-0.262667\pi$
$317$	3.37108	+	2.44923i	0.189339	+	0.137562i	−0.489078	+	0.872240i	$0.662667\pi$
$318$	34.6002			1.94029
$319$	−0.317716	−	0.230834i	−0.0177887	−	0.0129242i
$320$	2.23393	−	0.0977310i	0.124881	−	0.00546333i
$321$	22.1844	−	16.1179i	1.23821	−	0.899616i
$322$	6.30429	−	4.58033i	0.351324	−	0.255252i
$323$	0.0617749	+	0.190123i	0.00343724	+	0.0105788i
$324$	10.5632			0.586845
$325$	−3.77297	+	3.28095i	−0.209287	+	0.181995i
$326$	10.6412			0.589362
$327$	−1.62335	−	4.99615i	−0.0897713	−	0.276288i
$328$	3.09361	−	2.24764i	0.170816	−	0.124105i
$329$	−2.76911	+	2.01188i	−0.152666	+	0.110918i
$330$	−0.557395	−	0.368862i	−0.0306836	−	0.0203052i
$331$	9.09826	+	6.61027i	0.500086	+	0.363333i	0.809050	−	0.587740i	$-0.199982\pi$
$331$	9.09826	+	6.61027i	0.500086	+	0.363333i	−0.308964	+	0.951074i	$0.599982\pi$
$332$	8.21046			0.450607
$333$	26.8529	+	19.5098i	1.47153	+	1.06913i
$334$	2.45827	−	7.56579i	0.134511	−	0.413982i
$335$	−2.90325	+	2.30977i	−0.158622	+	0.126196i
$336$	0.892773	+	2.74767i	0.0487048	+	0.149898i
$337$	−4.26108	+	13.1143i	−0.232116	+	0.714379i	0.765375	+	0.643584i	$0.222553\pi$
$337$	−4.26108	+	13.1143i	−0.232116	+	0.714379i	−0.997491	+	0.0707945i	$0.977447\pi$
$338$	0.309017	−	0.951057i	0.0168083	−	0.0517307i
$339$	18.5703	+	57.1536i	1.00860	+	3.10416i
$340$	1.61416	−	5.82245i	0.0875402	−	0.315767i
$341$	0.147895	−	0.455174i	0.00800897	−	0.0246491i
$342$	−0.369322	−	0.268328i	−0.0199706	−	0.0145095i
$343$	12.4881			0.674295
$344$	−5.97090	−	4.33811i	−0.321929	−	0.233895i
$345$	43.2822	−	34.4344i	2.33024	−	1.85389i
$346$	−3.48508	+	2.53206i	−0.187359	+	0.136124i
$347$	10.2736	−	7.46424i	0.551518	−	0.400701i	−0.276827	−	0.960920i	$-0.589283\pi$
$347$	10.2736	−	7.46424i	0.551518	−	0.400701i	0.828345	+	0.560219i	$0.189283\pi$
$348$	3.72313	+	11.4586i	0.199581	+	0.614246i
$349$	17.2281			0.922202			0.461101	−	0.887348i	$-0.347455\pi$
$349$	17.2281			0.922202			0.461101	+	0.887348i	$0.347455\pi$
$350$	−1.07224	+	4.64809i	−0.0573137	+	0.248451i
$351$	−9.60103			−0.512465
$352$	−0.0305024	−	0.0938766i	−0.00162578	−	0.00500364i
$353$	10.2120	−	7.41942i	0.543528	−	0.394896i	−0.281866	−	0.959454i	$-0.590953\pi$
$353$	10.2120	−	7.41942i	0.543528	−	0.394896i	0.825393	+	0.564558i	$0.190953\pi$
$354$	−24.4893	+	17.7925i	−1.30159	+	0.945661i
$355$	−3.08525	−	8.24968i	−0.163748	−	0.437847i
$356$	−11.4722	−	8.33505i	−0.608026	−	0.441757i
$357$	7.80655			0.413166
$358$	−9.31059	−	6.76454i	−0.492080	−	0.357517i
$359$	3.80017	−	11.6957i	0.200566	−	0.617277i	−0.799301	−	0.600931i	$-0.794797\pi$
$359$	3.80017	−	11.6957i	0.200566	−	0.617277i	0.999866	−	0.0163461i	$-0.00520337\pi$
$360$	4.83314	+	12.9234i	0.254729	+	0.681122i
$361$	−5.86963	−	18.0649i	−0.308928	−	0.950783i
$362$	7.75634	−	23.8716i	0.407664	−	1.25466i
$363$	10.2846	−	31.6526i	0.539800	−	1.66133i
$364$	−0.294812	−	0.907339i	−0.0154524	−	0.0475575i
$365$	11.7249	−	0.512947i	0.613711	−	0.0268489i
$366$	3.57975	−	11.0173i	0.187117	−	0.575885i
$367$	26.5591	+	19.2963i	1.38637	+	1.00726i	0.996252	+	0.0864936i	$0.0275662\pi$
$367$	26.5591	+	19.2963i	1.38637	+	1.00726i	0.390119	+	0.920764i	$0.372434\pi$
$368$	8.16799			0.425786
$369$	19.0890	+	13.8690i	0.993734	+	0.721990i
$370$	−3.21339	+	11.5910i	−0.167056	+	0.602589i
$371$	−8.81870	+	6.40716i	−0.457844	+	0.332643i
$372$	−11.8788	+	8.63048i	−0.615889	+	0.447469i
$373$	−5.59816	−	17.2294i	−0.289862	−	0.892103i	−0.984899	−	0.173129i	$-0.944612\pi$
$373$	−5.59816	−	17.2294i	−0.289862	−	0.892103i	0.695037	−	0.718974i	$-0.255388\pi$
$374$	−0.266717			−0.0137916
$375$	−6.16126	+	33.2918i	−0.318166	+	1.71918i
$376$	−3.58773			−0.185023
$377$	−1.22945	−	3.78387i	−0.0633201	−	0.194879i
$378$	−7.41035	+	5.38394i	−0.381147	+	0.276920i
$379$	13.1792	−	9.57524i	0.676970	−	0.491847i	−0.195381	−	0.980727i	$-0.562594\pi$
$379$	13.1792	−	9.57524i	0.676970	−	0.491847i	0.872351	+	0.488880i	$0.162594\pi$
$380$	0.0441953	−	0.159417i	0.00226717	−	0.00817793i
$381$	26.7053	+	19.4026i	1.36816	+	0.994023i
$382$	−0.168636			−0.00862815
$383$	24.0325	+	17.4606i	1.22800	+	0.892197i	0.996739	−	0.0806934i	$-0.0257135\pi$
$383$	24.0325	+	17.4606i	1.22800	+	0.892197i	0.231265	+	0.972891i	$0.425713\pi$
$384$	−0.935789	+	2.88006i	−0.0477543	+	0.146973i
$385$	0.210370	−	0.00920337i	0.0107215	−	0.000469047i
$386$	−8.45345	−	26.0170i	−0.430269	−	1.32423i
$387$	14.0728	−	43.3118i	0.715363	−	2.20166i
$388$	4.62839	−	14.2447i	0.234971	−	0.723167i
$389$	2.96324	+	9.11991i	0.150242	+	0.462398i	0.997648	−	0.0685481i	$-0.0218367\pi$
$389$	2.96324	+	9.11991i	0.150242	+	0.462398i	−0.847406	+	0.530946i	$0.821837\pi$
$390$	−2.37196	−	6.34241i	−0.120109	−	0.321160i
$391$	6.82020	−	20.9904i	0.344913	−	1.06153i
$392$	4.92677	+	3.57951i	0.248839	+	0.180792i
$393$	−47.8065			−2.41152
$394$	−8.99935	−	6.53841i	−0.453380	−	0.329400i
$395$	1.76333	+	4.71499i	0.0887228	+	0.237237i
$396$	0.492750	−	0.358004i	0.0247616	−	0.0179904i
$397$	−22.0017	+	15.9852i	−1.10423	+	0.802273i	−0.981746	−	0.190197i	$-0.939087\pi$
$397$	−22.0017	+	15.9852i	−1.10423	+	0.802273i	−0.122488	+	0.992470i	$0.539087\pi$
$398$	−2.57301	−	7.91891i	−0.128973	−	0.396939i
$399$	0.213741			0.0107004
$400$	−3.77297	+	3.28095i	−0.188649	+	0.164048i
$401$	−29.1365			−1.45501			−0.727504	−	0.686104i	$-0.759320\pi$
$401$	−29.1365			−1.45501			−0.727504	+	0.686104i	$0.759320\pi$
$402$	−1.55262	−	4.77846i	−0.0774374	−	0.238328i
$403$	3.92264	−	2.84996i	0.195400	−	0.141967i
$404$	−3.90037	+	2.83378i	−0.194051	+	0.140986i
$405$	−18.4840	+	14.7054i	−0.918475	+	0.730719i
$406$	−3.07080	−	2.23106i	−0.152401	−	0.110726i
$407$	0.530967			0.0263190
$408$	6.61993	+	4.80966i	0.327735	+	0.238114i
$409$	8.03570	−	24.7313i	0.397340	−	1.22289i	−0.529785	−	0.848132i	$-0.677727\pi$
$409$	8.03570	−	24.7313i	0.397340	−	1.22289i	0.927124	−	0.374754i	$-0.122273\pi$
$410$	−2.28431	+	8.23975i	−0.112814	+	0.406932i
$411$	10.6899	+	32.9001i	0.527293	+	1.62284i
$412$	−3.05865	+	9.41356i	−0.150689	+	0.463773i
$413$	2.94692	−	9.06969i	0.145009	−	0.446290i
$414$	15.5745	+	47.9335i	0.765446	+	2.35580i
$415$	−14.3670	+	11.4301i	−0.705249	+	0.561081i
$416$	0.309017	−	0.951057i	0.0151508	−	0.0466294i
$417$	−44.0546	−	32.0076i	−2.15736	−	1.56742i
$418$	−0.00730265			−0.000357184
$419$	−4.14787	−	3.01360i	−0.202636	−	0.147224i	0.481839	−	0.876260i	$-0.339969\pi$
$419$	−4.14787	−	3.01360i	−0.202636	−	0.147224i	−0.684476	+	0.729036i	$0.739969\pi$
$420$	−5.38735	−	3.56514i	−0.262876	−	0.173961i
$421$	0.968115	−	0.703377i	0.0471831	−	0.0342805i	−0.563944	−	0.825813i	$-0.690717\pi$
$421$	0.968115	−	0.703377i	0.0471831	−	0.0342805i	0.611127	+	0.791533i	$0.290717\pi$
$422$	3.34110	−	2.42745i	0.162642	−	0.118166i
$423$	−6.84100	−	21.0544i	−0.332621	−	1.02370i
$424$	−11.4257			−0.554882
$425$	5.28113	+	12.4355i	0.256172	+	0.603211i
$426$	11.9282			0.577922
$427$	1.12777	+	3.47092i	0.0545766	+	0.167969i
$428$	−7.32576	+	5.32248i	−0.354104	+	0.257272i
$429$	−0.241827	+	0.175697i	−0.0116755	+	0.00848275i
$430$	16.4874	−	0.721297i	0.795092	−	0.0347840i
$431$	20.5522	+	14.9320i	0.989962	+	0.719250i	0.959913	−	0.280299i	$-0.0904335\pi$
$431$	20.5522	+	14.9320i	0.989962	+	0.719250i	0.0300494	+	0.999548i	$0.490434\pi$
$432$	−9.60103			−0.461930
$433$	−4.14805	−	3.01373i	−0.199342	−	0.144831i	0.483636	−	0.875269i	$-0.339316\pi$
$433$	−4.14805	−	3.01373i	−0.199342	−	0.144831i	−0.682979	+	0.730438i	$0.739316\pi$
$434$	1.42944	−	4.39936i	0.0686153	−	0.211176i
$435$	−22.4669	−	14.8677i	−1.07720	−	0.712850i
$436$	0.536063	+	1.64983i	0.0256728	+	0.0790127i
$437$	0.186735	−	0.574712i	0.00893277	−	0.0274922i
$438$	−4.91155	+	15.1162i	−0.234683	+	0.722279i
$439$	−2.28162	−	7.02211i	−0.108896	−	0.335147i	0.881729	−	0.471756i	$-0.156380\pi$
$439$	−2.28162	−	7.02211i	−0.108896	−	0.335147i	−0.990625	+	0.136609i	$0.956380\pi$
$440$	0.184064	+	0.121806i	0.00877489	+	0.00580687i
$441$	−11.6119	+	35.7379i	−0.552949	+	1.70180i
$442$	−2.18604	−	1.58825i	−0.103979	−	0.0755453i
$443$	−29.8381			−1.41765			−0.708826	−	0.705383i	$-0.750775\pi$
$443$	−29.8381			−1.41765			−0.708826	+	0.705383i	$0.750775\pi$
$444$	−13.1786	−	9.57482i	−0.625429	−	0.454401i
$445$	31.6781	−	1.38587i	1.50169	−	0.0656965i
$446$	9.22138	−	6.69973i	0.436645	−	0.317241i
$447$	−43.2981	+	31.4579i	−2.04793	+	1.48791i
$448$	−0.294812	−	0.907339i	−0.0139286	−	0.0428677i
$449$	−12.4505			−0.587576			−0.293788	−	0.955871i	$-0.594916\pi$
$449$	−12.4505			−0.587576			−0.293788	+	0.955871i	$0.594916\pi$
$450$	−26.4484	−	15.8855i	−1.24679	−	0.748849i
$451$	0.377450			0.0177734
$452$	−6.13231	−	18.8733i	−0.288439	−	0.887725i
$453$	−44.4937	+	32.3266i	−2.09050	+	1.51884i
$454$	−22.2910	+	16.1953i	−1.04617	+	0.760085i
$455$	1.77902	+	1.17728i	0.0834016	+	0.0551918i
$456$	0.181252	+	0.131687i	0.00848790	+	0.00616682i
$457$	−21.9639			−1.02743			−0.513713	−	0.857962i	$-0.671731\pi$
$457$	−21.9639			−1.02743			−0.513713	+	0.857962i	$0.671731\pi$
$458$	21.8898	+	15.9039i	1.02285	+	0.743141i
$459$	−8.01679	+	24.6731i	−0.374192	+	1.15164i
$460$	−14.2927	+	11.3710i	−0.666400	+	0.530174i
$461$	5.91347	+	18.1998i	0.275418	+	0.847648i	0.989109	+	0.147187i	$0.0470221\pi$
$461$	5.91347	+	18.1998i	0.275418	+	0.847648i	−0.713691	+	0.700461i	$0.752978\pi$
$462$	−0.0881236	+	0.271217i	−0.00409988	+	0.0126181i
$463$	1.89284	−	5.82557i	0.0879678	−	0.270737i	−0.897389	−	0.441239i	$-0.854539\pi$
$463$	1.89284	−	5.82557i	0.0879678	−	0.270737i	0.985357	+	0.170502i	$0.0545390\pi$
$464$	−1.22945	−	3.78387i	−0.0570760	−	0.175662i
$465$	8.77128	−	31.6389i	0.406758	−	1.46722i
$466$	−3.52716	+	10.8555i	−0.163392	+	0.502870i
$467$	6.82644	+	4.95970i	0.315890	+	0.229508i	0.734420	−	0.678696i	$-0.237454\pi$
$467$	6.82644	+	4.95970i	0.315890	+	0.229508i	−0.418530	+	0.908203i	$0.637454\pi$
$468$	6.17046			0.285230
$469$	1.28058	+	0.930396i	0.0591317	+	0.0429617i
$470$	6.27797	−	4.99461i	0.289581	−	0.230384i
$471$	46.7913	−	33.9959i	2.15603	−	1.56645i
$472$	8.08687	−	5.87546i	0.372229	−	0.270440i
$473$	−0.225121	−	0.692850i	−0.0103511	−	0.0318573i
$474$	−6.81738			−0.313133
$475$	0.144596	+	0.340481i	0.00663451	+	0.0156224i
$476$	−2.57788			−0.118157
$477$	−21.7863	−	67.0514i	−0.997526	−	3.07007i
$478$	11.5852	−	8.41712i	0.529893	−	0.384990i
$479$	−27.5113	+	19.9881i	−1.25702	+	0.913281i	−0.998608	−	0.0527521i	$-0.983201\pi$
$479$	−27.5113	+	19.9881i	−1.25702	+	0.913281i	−0.258416	+	0.966034i	$0.583201\pi$
$480$	−2.37196	−	6.34241i	−0.108265	−	0.289490i
$481$	4.35185	+	3.16180i	0.198427	+	0.144166i
$482$	9.03948			0.411737
$483$	−19.0911	−	13.8705i	−0.868676	−	0.631130i
$484$	−3.39618	+	10.4524i	−0.154372	+	0.475107i
$485$	11.7317	+	31.3694i	0.532707	+	1.42441i
$486$	−0.984286	−	3.02932i	−0.0446481	−	0.137413i
$487$	5.74559	−	17.6831i	0.260358	−	0.801299i	−0.732369	−	0.680908i	$-0.761585\pi$
$487$	5.74559	−	17.6831i	0.260358	−	0.801299i	0.992727	−	0.120391i	$-0.0384147\pi$
$488$	−1.18211	+	3.63815i	−0.0535115	+	0.164691i
$489$	−9.95793	−	30.6474i	−0.450313	−	1.38592i
$490$	−13.6042	+	0.595164i	−0.614577	+	0.0268868i
$491$	8.36444	−	25.7431i	0.377482	−	1.16177i	−0.564307	−	0.825565i	$-0.690856\pi$
$491$	8.36444	−	25.7431i	0.377482	−	1.16177i	0.941789	−	0.336205i	$-0.109144\pi$
$492$	−9.36831	−	6.80648i	−0.422356	−	0.306860i
$493$	−10.7505			−0.484180
$494$	−0.0598531	−	0.0434859i	−0.00269292	−	0.00195652i
$495$	−0.363845	+	1.31243i	−0.0163536	+	0.0589892i
$496$	3.92264	−	2.84996i	0.176132	−	0.127967i
$497$	−3.04018	+	2.20882i	−0.136371	+	0.0990792i
$498$	−7.68326	−	23.6466i	−0.344295	−	1.05963i
$499$	−13.4830			−0.603583			−0.301791	−	0.953374i	$-0.597585\pi$
$499$	−13.4830			−0.603583			−0.301791	+	0.953374i	$0.597585\pi$
$500$	2.03458	−	10.9937i	0.0909890	−	0.491651i
$501$	−24.0904			−1.07628
$502$	5.51868	+	16.9848i	0.246311	+	0.758067i
$503$	19.5802	−	14.2258i	0.873038	−	0.634299i	−0.0583625	−	0.998295i	$-0.518588\pi$
$503$	19.5802	−	14.2258i	0.873038	−	0.634299i	0.931400	+	0.363996i	$0.118588\pi$
$504$	4.76254	−	3.46019i	0.212140	−	0.154129i
$505$	2.88002	−	10.3885i	0.128159	−	0.462283i
$506$	0.652265	+	0.473898i	0.0289967	+	0.0210673i
$507$	−3.02828			−0.134491
$508$	−8.81865	−	6.40713i	−0.391264	−	0.284270i
$509$	−9.46857	+	29.1413i	−0.419687	+	1.29166i	0.488304	+	0.872674i	$0.337616\pi$
$509$	−9.46857	+	29.1413i	−0.419687	+	1.29166i	−0.907991	+	0.418990i	$0.862384\pi$
$510$	−18.2795	+	0.799702i	−0.809432	+	0.0354114i
$511$	−1.54734	−	4.76222i	−0.0684503	−	0.210668i
$512$	0.309017	−	0.951057i	0.0136568	−	0.0420312i
$513$	−0.219498	+	0.675544i	−0.00969105	+	0.0298260i
$514$	−8.96059	−	27.5779i	−0.395235	−	1.21641i
$515$	−7.75281	−	20.7303i	−0.341630	−	0.913487i
$516$	−6.90653	+	21.2561i	−0.304043	+	0.935748i
$517$	−0.286503	−	0.208156i	−0.0126004	−	0.00915470i
$518$	5.13191			0.225483
$519$	10.5538	+	7.66777i	0.463259	+	0.336578i
$520$	0.783270	+	2.09439i	0.0343487	+	0.0918453i
$521$	−0.325788	+	0.236699i	−0.0142731	+	0.0103700i	−0.594899	−	0.803801i	$-0.702808\pi$
$521$	−0.325788	+	0.236699i	−0.0142731	+	0.0103700i	0.580626	+	0.814171i	$0.302808\pi$
$522$	19.8612	−	14.4300i	0.869301	−	0.631584i
$523$	−1.55288	−	4.77927i	−0.0679026	−	0.208983i	0.911348	−	0.411638i	$-0.135043\pi$
$523$	−1.55288	−	4.77927i	−0.0679026	−	0.208983i	−0.979250	+	0.202655i	$0.935043\pi$
$524$	15.7867			0.689645
$525$	14.3902	−	1.26151i	0.628039	−	0.0550568i
$526$	−6.31461			−0.275330
$527$	−4.04858	−	12.4603i	−0.176359	−	0.542777i
$528$	−0.241827	+	0.175697i	−0.0105242	+	0.00764625i
$529$	−35.3670	+	25.6956i	−1.53770	+	1.11720i
$530$	19.9932	−	15.9062i	0.868450	−	0.690920i
$531$	49.8997	+	36.2543i	2.16546	+	1.57330i
$532$	−0.0705818			−0.00306011
$533$	3.09361	+	2.24764i	0.133999	+	0.0973561i
$534$	−13.2699	+	40.8405i	−0.574245	+	1.76734i
$535$	5.40932	−	19.5120i	0.233865	−	0.843576i
$536$	0.512706	+	1.57795i	0.0221455	+	0.0681569i
$537$	−10.7695	+	33.1453i	−0.464740	+	1.43032i
$538$	−6.38825	+	19.6610i	−0.275417	+	0.847646i
$539$	0.185754	+	0.571692i	0.00800099	+	0.0246245i
$540$	16.8003	−	13.3660i	0.722970	−	0.575180i
$541$	2.27169	−	6.99154i	0.0976676	−	0.300590i	−0.890272	−	0.455429i	$-0.849486\pi$
$541$	2.27169	−	6.99154i	0.0976676	−	0.300590i	0.987940	+	0.154839i	$0.0494859\pi$
$542$	9.16881	+	6.66153i	0.393834	+	0.286137i
$543$	−76.0099			−3.26190
$544$	−2.18604	−	1.58825i	−0.0937256	−	0.0680956i
$545$	−3.23482	−	2.14068i	−0.138565	−	0.0916964i
$546$	−2.33731	+	1.69816i	−0.100028	+	0.0726744i
$547$	−28.6860	+	20.8416i	−1.22652	+	0.891121i	−0.996625	−	0.0820933i	$-0.973839\pi$
$547$	−28.6860	+	20.8416i	−1.22652	+	0.891121i	−0.229899	+	0.973215i	$0.573839\pi$
$548$	−3.53002	−	10.8643i	−0.150795	−	0.464100i
$549$	−23.6044			−1.00741
$550$	−0.491653	+	0.0431006i	−0.0209642	+	0.00183782i
$551$	−0.294347			−0.0125396
$552$	−7.64351	−	23.5243i	−0.325329	−	1.00126i
$553$	1.73757	−	1.26242i	0.0738891	−	0.0536836i
$554$	2.66390	−	1.93544i	0.113178	−	0.0822290i
$555$	36.3900	−	1.59200i	1.54467	−	0.0675768i
$556$	14.5478	+	10.5696i	0.616962	+	0.448249i
$557$	−4.66782			−0.197782			−0.0988910	−	0.995098i	$-0.531530\pi$
$557$	−4.66782			−0.197782			−0.0988910	+	0.995098i	$0.531530\pi$
$558$	24.2045	+	17.5856i	1.02466	+	0.744457i
$559$	2.28068	−	7.01921i	0.0964625	−	0.296881i
$560$	1.77902	+	1.17728i	0.0751772	+	0.0497492i
$561$	0.249591	+	0.768162i	0.0105377	+	0.0324318i
$562$	6.68790	−	20.5832i	0.282112	−	0.868251i
$563$	4.41888	−	13.5999i	0.186234	−	0.573168i	−0.813734	−	0.581238i	$-0.802569\pi$
$563$	4.41888	−	13.5999i	0.186234	−	0.573168i	0.999967	+	0.00806974i	$0.00256871\pi$
$564$	3.35736	+	10.3329i	0.141370	+	0.435093i
$565$	37.0048	+	24.4883i	1.55680	+	1.03023i
$566$	5.54989	−	17.0808i	0.233279	−	0.717960i
$567$	8.15299	+	5.92349i	0.342393	+	0.248763i
$568$	−3.93893			−0.165274
$569$	−3.30453	−	2.40088i	−0.138533	−	0.100650i	0.516360	−	0.856371i	$-0.327287\pi$
$569$	−3.30453	−	2.40088i	−0.138533	−	0.100650i	−0.654894	+	0.755721i	$0.727287\pi$
$570$	−0.500489	+	0.0218956i	−0.0209632	+	0.000917106i
$571$	−15.7063	+	11.4113i	−0.657289	+	0.477549i	−0.865746	−	0.500483i	$-0.833156\pi$
$571$	−15.7063	+	11.4113i	−0.657289	+	0.477549i	0.208457	+	0.978031i	$0.433156\pi$
$572$	0.0798562	−	0.0580189i	0.00333896	−	0.00242589i
$573$	0.157807	+	0.485681i	0.00659250	+	0.0202896i
$574$	3.64814			0.152270
$575$	9.18004	−	39.7948i	0.382834	−	1.65956i
$576$	6.17046			0.257103
$577$	6.07423	+	18.6946i	0.252873	+	0.778264i	0.994241	+	0.107165i	$0.0341775\pi$
$577$	6.07423	+	18.6946i	0.252873	+	0.778264i	−0.741368	+	0.671099i	$0.765823\pi$
$578$	7.84641	−	5.70075i	0.326368	−	0.237120i
$579$	−67.0200	+	48.6929i	−2.78526	+	2.02361i
$580$	7.41902	+	4.90961i	0.308058	+	0.203861i
$581$	6.33707	+	4.60415i	0.262906	+	0.191012i
$582$	−45.3569			−1.88010
$583$	−0.912415	−	0.662908i	−0.0377884	−	0.0274549i
$584$	1.62189	−	4.99168i	0.0671145	−	0.206557i
$585$	−10.7973	+	8.59013i	−0.446415	+	0.355158i
$586$	0.0721362	+	0.222012i	0.00297992	+	0.00917125i
$587$	6.49921	−	20.0025i	0.268251	−	0.825592i	−0.722676	−	0.691187i	$-0.757088\pi$
$587$	6.49921	−	20.0025i	0.268251	−	0.825592i	0.990927	−	0.134404i	$-0.0429121\pi$
$588$	5.69879	−	17.5391i	0.235014	−	0.723299i
$589$	−0.110849	−	0.341158i	−0.00456746	−	0.0140572i
$590$	−5.97132	+	21.5392i	−0.245835	+	0.886754i
$591$	−10.4095	+	32.0372i	−0.428191	+	1.31784i
$592$	4.35185	+	3.16180i	0.178860	+	0.129949i
$593$	36.4702			1.49765			0.748825	−	0.662767i	$-0.230618\pi$
$593$	36.4702			1.49765			0.748825	+	0.662767i	$0.230618\pi$
$594$	−0.766702	−	0.557042i	−0.0314582	−	0.0228557i
$595$	4.51089	−	3.58877i	0.184929	−	0.147125i
$596$	14.2979	−	10.3881i	0.585666	−	0.425511i
$597$	−20.3992	+	14.8209i	−0.834882	+	0.606577i
$598$	2.52405	+	7.76822i	0.103216	+	0.317666i
$599$	3.54549			0.144865			0.0724324	−	0.997373i	$-0.476924\pi$
$599$	3.54549			0.144865			0.0724324	+	0.997373i	$0.476924\pi$
$600$	12.9801	+	7.79612i	0.529909	+	0.318275i
$601$	−14.4436			−0.589167			−0.294584	−	0.955626i	$-0.595181\pi$
$601$	−14.4436			−0.589167			−0.294584	+	0.955626i	$0.595181\pi$
$602$	−2.17584	−	6.69656i	−0.0886807	−	0.272931i
$603$	−8.28250	+	6.01759i	−0.337289	+	0.245055i
$604$	14.6928	−	10.6749i	0.597840	−	0.434356i
$605$	−8.60834	−	23.0179i	−0.349979	−	0.935812i
$606$	11.8114	+	8.58148i	0.479805	+	0.348599i
$607$	−45.6733			−1.85382			−0.926912	−	0.375279i	$-0.877547\pi$
$607$	−45.6733			−1.85382			−0.926912	+	0.375279i	$0.877547\pi$
$608$	−0.0598531	−	0.0434859i	−0.00242737	−	0.00176358i
$609$	−3.55199	+	10.9319i	−0.143934	+	0.442983i
$610$	−2.99631	−	8.01186i	−0.121317	−	0.324391i
$611$	−1.10867	−	3.41213i	−0.0448520	−	0.138040i
$612$	5.15229	−	15.8571i	0.208269	−	0.640986i
$613$	−10.8510	+	33.3960i	−0.438268	+	1.34885i	0.451432	+	0.892306i	$0.350913\pi$
$613$	−10.8510	+	33.3960i	−0.438268	+	1.34885i	−0.889700	+	0.456545i	$0.849087\pi$
$614$	10.3033	+	31.7103i	0.415807	+	1.27972i
$615$	25.8686	−	1.13171i	1.04312	−	0.0456351i
$616$	0.0291003	−	0.0895614i	0.00117248	−	0.00360853i
$617$	26.5632	+	19.2993i	1.06939	+	0.776960i	0.975803	−	0.218651i	$-0.0701656\pi$
$617$	26.5632	+	19.2993i	1.06939	+	0.776960i	0.0935902	+	0.995611i	$0.470166\pi$
$618$	29.9739			1.20573
$619$	−1.95775	−	1.42239i	−0.0786886	−	0.0571706i	0.547745	−	0.836645i	$-0.315486\pi$
$619$	−1.95775	−	1.42239i	−0.0786886	−	0.0571706i	−0.626434	+	0.779474i	$0.715486\pi$
$620$	−2.89646	+	10.4478i	−0.116325	+	0.419595i
$621$	63.4440	−	46.0948i	2.54592	−	1.84972i
$622$	3.19156	−	2.31880i	0.127970	−	0.0929754i
$623$	−4.18057	−	12.8665i	−0.167491	−	0.515484i
$624$	−3.02828			−0.121228
$625$	11.7445	+	22.0696i	0.469780	+	0.882784i
$626$	0.0476304			0.00190369
$627$	0.00683374	+	0.0210321i	0.000272913	+	0.000839941i
$628$	−15.4515	+	11.2262i	−0.616581	+	0.447972i
$629$	11.7591	−	8.54348i	0.468866	−	0.340651i
$630$	−3.51664	+	12.6849i	−0.140106	+	0.505378i
$631$	−0.187375	−	0.136136i	−0.00745926	−	0.00541947i	0.584049	−	0.811718i	$-0.301467\pi$
$631$	−0.187375	−	0.136136i	−0.00745926	−	0.00541947i	−0.591509	+	0.806299i	$0.701467\pi$
$632$	2.25124			0.0895496
$633$	−10.1178	−	7.35099i	−0.402145	−	0.292176i
$634$	−1.28764	+	3.96294i	−0.0511386	+	0.157388i
$635$	24.3509	−	1.06531i	0.966335	−	0.0422756i
$636$	10.6921	+	32.9068i	0.423968	+	1.30484i
$637$	−1.88186	+	5.79176i	−0.0745619	+	0.229478i
$638$	0.121357	−	0.373497i	0.00480456	−	0.0147869i
$639$	−7.51067	−	23.1155i	−0.297117	−	0.914433i
$640$	0.783270	+	2.09439i	0.0309615	+	0.0827882i
$641$	2.73742	−	8.42492i	0.108122	−	0.332764i	−0.882329	−	0.470634i	$-0.844025\pi$
$641$	2.73742	−	8.42492i	0.108122	−	0.332764i	0.990450	+	0.137869i	$0.0440254\pi$
$642$	22.1844	+	16.1179i	0.875550	+	0.636124i
$643$	8.49698			0.335088			0.167544	−	0.985865i	$-0.446416\pi$
$643$	8.49698			0.335088			0.167544	+	0.985865i	$0.446416\pi$
$644$	6.30429	+	4.58033i	0.248424	+	0.180490i
$645$	−17.5061	−	46.8097i	−0.689302	−	1.84313i
$646$	−0.161729	+	0.117503i	−0.00636313	+	0.00462308i
$647$	−10.4529	+	7.59446i	−0.410945	+	0.298569i	−0.773984	−	0.633205i	$-0.781739\pi$
$647$	−10.4529	+	7.59446i	−0.410945	+	0.298569i	0.363039	+	0.931774i	$0.381739\pi$
$648$	3.26421	+	10.0462i	0.128230	+	0.394652i
$649$	0.986675			0.0387304
$650$	−4.28629	−	2.57444i	−0.168122	−	0.100978i
$651$	−14.0081			−0.549021
$652$	3.28832	+	10.1204i	0.128780	+	0.396345i
$653$	37.8597	−	27.5067i	1.48156	−	1.07642i	0.504514	−	0.863403i	$-0.331672\pi$
$653$	37.8597	−	27.5067i	1.48156	−	1.07642i	0.977049	−	0.213015i	$-0.0683284\pi$
$654$	4.24998	−	3.08779i	0.166187	−	0.120742i
$655$	−27.6242	+	21.9773i	−1.07937	+	0.858722i
$656$	3.09361	+	2.24764i	0.120785	+	0.0877556i
$657$	32.3860			1.26350
$658$	−2.76911	−	2.01188i	−0.107951	−	0.0784312i
$659$	−15.1392	+	46.5936i	−0.589738	+	1.81503i	−0.0103933	+	0.999946i	$0.503308\pi$
$659$	−15.1392	+	46.5936i	−0.589738	+	1.81503i	−0.579345	+	0.815082i	$0.696692\pi$
$660$	0.178564	−	0.644099i	0.00695059	−	0.0250715i
$661$	−6.40197	−	19.7032i	−0.249008	−	0.766367i	−0.994951	−	0.100358i	$-0.968001\pi$
$661$	−6.40197	−	19.7032i	−0.249008	−	0.766367i	0.745943	−	0.666009i	$-0.231999\pi$
$662$	−3.47523	+	10.6956i	−0.135069	+	0.415698i
$663$	−2.52859	+	7.78219i	−0.0982022	+	0.302235i
$664$	2.53717	+	7.80861i	0.0984613	+	0.303033i
$665$	0.123507	−	0.0982596i	0.00478940	−	0.00381034i
$666$	−10.2569	+	31.5675i	−0.397447	+	1.22322i
$667$	26.2907	+	19.1013i	1.01798	+	0.739607i
$668$	7.95514			0.307794
$669$	−27.9249	−	20.2886i	−1.07964	−	0.784404i
$670$	−3.09387	−	2.04740i	−0.119527	−	0.0790980i
$671$	−0.305481	+	0.221945i	−0.0117929	+	0.00856808i
$672$	−2.33731	+	1.69816i	−0.0901637	+	0.0655078i
$673$	5.71154	+	17.5783i	0.220164	+	0.677594i	0.998747	+	0.0500523i	$0.0159388\pi$
$673$	5.71154	+	17.5783i	0.220164	+	0.677594i	−0.778583	+	0.627542i	$0.784061\pi$
$674$	−13.7891			−0.531138
$675$	−10.7906	+	46.7767i	−0.415332	+	1.80044i
$676$	1.00000			0.0384615
$677$	−9.18556	−	28.2702i	−0.353030	−	1.08651i	−0.957143	−	0.289615i	$-0.906473\pi$
$677$	−9.18556	−	28.2702i	−0.353030	−	1.08651i	0.604113	−	0.796898i	$-0.293527\pi$
$678$	−48.6177	+	35.3228i	−1.86715	+	1.35657i
$679$	11.5603	−	8.39904i	0.443643	−	0.322326i
$680$	6.03629	−	0.264078i	0.231481	−	0.0101269i
$681$	67.5032	+	49.0439i	2.58673	+	1.87937i
$682$	0.478599			0.0183265
$683$	−21.2641	−	15.4493i	−0.813648	−	0.591150i	0.101238	−	0.994862i	$-0.467720\pi$
$683$	−21.2641	−	15.4493i	−0.813648	−	0.591150i	−0.914886	+	0.403713i	$0.867720\pi$
$684$	0.141068	−	0.434163i	0.00539388	−	0.0166007i
$685$	21.3016	+	14.0965i	0.813892	+	0.538601i
$686$	3.85904	+	11.8769i	0.147339	+	0.453462i
$687$	25.3200	−	77.9268i	0.966017	−	2.97309i
$688$	2.28068	−	7.01921i	0.0869501	−	0.267605i
$689$	−3.53074	−	10.8665i	−0.134511	−	0.413981i
$690$	46.1240	+	30.5230i	1.75591	+	1.16199i
$691$	9.97825	−	30.7099i	0.379590	−	1.16826i	−0.560739	−	0.827993i	$-0.689483\pi$
$691$	9.97825	−	30.7099i	0.379590	−	1.16826i	0.940329	−	0.340266i	$-0.110517\pi$
$692$	−3.48508	−	2.53206i	−0.132483	−	0.0962544i
$693$	0.581075			0.0220732
$694$	10.2736	+	7.46424i	0.389982	+	0.283339i
$695$	−40.1706	+	1.75740i	−1.52376	+	0.0666620i
$696$	−9.74728	+	7.08181i	−0.369470	+	0.268435i
$697$	8.35922	−	6.07333i	0.316628	−	0.230044i
$698$	5.32379	+	16.3849i	0.201508	+	0.620179i
$699$	34.5651			1.30737
$700$	−4.75194	+	0.416577i	−0.179606	+	0.0157451i
$701$	−50.5368			−1.90875			−0.954374	−	0.298612i	$-0.903476\pi$
$701$	−50.5368			−1.90875			−0.954374	+	0.298612i	$0.903476\pi$
$702$	−2.96688	−	9.13113i	−0.111978	−	0.344632i
$703$	0.321961	−	0.233918i	0.0121430	−	0.00882240i
$704$	0.0798562	−	0.0580189i	0.00300969	−	0.00218667i
$705$	−20.2597	−	13.4070i	−0.763023	−	0.504938i
$706$	10.2120	+	7.41942i	0.384332	+	0.279234i
$707$	−4.59951			−0.172982
$708$	−24.4893	−	17.7925i	−0.920364	−	0.668684i
$709$	7.81495	−	24.0519i	0.293497	−	0.903290i	−0.690226	−	0.723594i	$-0.742489\pi$
$709$	7.81495	−	24.0519i	0.293497	−	0.903290i	0.983722	−	0.179696i	$-0.0575113\pi$
$710$	6.89252	−	5.48354i	0.258672	−	0.205794i
$711$	4.29262	+	13.2113i	0.160986	+	0.495463i
$712$	4.38200	−	13.4864i	0.164222	−	0.505424i
$713$	−12.2382	+	37.6653i	−0.458324	+	1.41058i
$714$	2.41236	+	7.42447i	0.0902801	+	0.277854i
$715$	−0.0589655	+	0.212695i	−0.00220519	+	0.00795434i
$716$	3.55633	−	10.9453i	0.132906	−	0.409043i
$717$	−35.0831	−	25.4894i	−1.31020	−	0.951918i
$718$	12.2976			0.458943
$719$	26.2693	+	19.0857i	0.979679	+	0.711778i	0.957637	−	0.287979i	$-0.0929833\pi$
$719$	26.2693	+	19.0857i	0.979679	+	0.711778i	0.0220419	+	0.999757i	$0.492983\pi$
$720$	−10.7973	+	8.59013i	−0.402393	+	0.320135i
$721$	−7.63956	+	5.55046i	−0.284512	+	0.206710i
$722$	15.3669	−	11.1647i	0.571897	−	0.415507i
$723$	−8.45905	−	26.0343i	−0.314595	−	0.968225i
$724$	25.1000			0.932836
$725$	−19.8170	+	1.73725i	−0.735985	+	0.0645198i
$726$	33.2815			1.23519
$727$	−1.06000	−	3.26234i	−0.0393132	−	0.120994i	0.929474	−	0.368888i	$-0.120261\pi$
$727$	−1.06000	−	3.26234i	−0.0393132	−	0.120994i	−0.968787	+	0.247894i	$0.920261\pi$
$728$	0.771829	−	0.560766i	0.0286059	−	0.0207834i
$729$	17.8339	−	12.9571i	0.660515	−	0.479892i
$730$	4.11104	+	10.9926i	0.152157	+	0.406853i
$731$	−16.1339	−	11.7220i	−0.596734	−	0.433553i
$732$	11.5843			0.428169
$733$	21.4267	+	15.5674i	0.791412	+	0.574994i	0.908382	−	0.418141i	$-0.137318\pi$
$733$	21.4267	+	15.5674i	0.791412	+	0.574994i	−0.116970	+	0.993135i	$0.537318\pi$
$734$	−10.1447	+	31.2220i	−0.374446	+	1.15243i
$735$	14.4448	+	38.6241i	0.532805	+	1.42467i
$736$	2.52405	+	7.76822i	0.0930376	+	0.286340i
$737$	−0.0506080	+	0.155755i	−0.00186417	+	0.00573733i
$738$	−7.29135	+	22.4405i	−0.268398	+	0.826046i
$739$	−11.9376	−	36.7400i	−0.439130	−	1.35150i	−0.888794	−	0.458306i	$-0.848456\pi$
$739$	−11.9376	−	36.7400i	−0.439130	−	1.35150i	0.449664	−	0.893198i	$-0.351544\pi$
$740$	−12.0167	+	0.525713i	−0.441743	+	0.0193256i
$741$	−0.0692321	+	0.213074i	−0.00254330	+	0.00782748i
$742$	−8.81870	−	6.40716i	−0.323745	−	0.235214i
$743$	−1.94976			−0.0715297			−0.0357649	−	0.999360i	$-0.511387\pi$
$743$	−1.94976			−0.0715297			−0.0357649	+	0.999360i	$0.511387\pi$
$744$	−11.8788	−	8.63048i	−0.435499	−	0.316409i
$745$	−10.5575	+	38.0822i	−0.386798	+	1.39522i
$746$	14.6562	−	10.6483i	0.536601	−	0.389863i
$747$	−40.9867	+	29.7786i	−1.49962	+	1.08954i
$748$	−0.0824202	−	0.253663i	−0.00301358	−	0.00927485i
$749$	−8.63890			−0.315659
$750$	−33.5664	+	4.42804i	−1.22567	+	0.161689i
$751$	34.7285			1.26726			0.633631	−	0.773635i	$-0.281564\pi$
$751$	34.7285			1.26726			0.633631	+	0.773635i	$0.281564\pi$
$752$	−1.10867	−	3.41213i	−0.0404290	−	0.124428i
$753$	43.7529	−	31.7883i	1.59444	−	1.15843i
$754$	3.21875	−	2.33856i	0.117220	−	0.0851654i
$755$	−10.8491	+	39.1338i	−0.394838	+	1.42422i
$756$	−7.41035	−	5.38394i	−0.269512	−	0.195812i
$757$	−31.9997			−1.16305			−0.581525	−	0.813528i	$-0.697544\pi$
$757$	−31.9997			−1.16305			−0.581525	+	0.813528i	$0.697544\pi$
$758$	13.1792	+	9.57524i	0.478690	+	0.347789i
$759$	0.754474	−	2.32203i	0.0273857	−	0.0842844i
$760$	0.165272	−	0.00723039i	0.00599504	−	0.000262274i
$761$	−13.0255	−	40.0883i	−0.472173	−	1.45320i	−0.849733	−	0.527213i	$-0.823237\pi$
$761$	−13.0255	−	40.0883i	−0.472173	−	1.45320i	0.377560	−	0.925985i	$-0.376763\pi$
$762$	−10.2005	+	31.3940i	−0.369526	+	1.13728i
$763$	−0.511422	+	1.57399i	−0.0185147	+	0.0569824i
$764$	−0.0521113	−	0.160382i	−0.00188532	−	0.00580242i
$765$	13.0596	+	34.9202i	0.472170	+	1.26254i
$766$	−9.17960	+	28.2519i	−0.331673	+	1.02078i
$767$	8.08687	+	5.87546i	0.292000	+	0.212150i
$768$	−3.02828			−0.109274
$769$	−32.4054	−	23.5439i	−1.16857	−	0.849016i	−0.177733	−	0.984079i	$-0.556876\pi$
$769$	−32.4054	−	23.5439i	−1.16857	−	0.849016i	−0.990837	+	0.135063i	$0.956876\pi$
$770$	0.0737609	+	0.197230i	0.00265816	+	0.00710767i
$771$	−71.0408	+	51.6141i	−2.55847	+	1.85884i
$772$	22.1314	−	16.0794i	0.796527	−	0.578711i
$773$	2.65008	+	8.15610i	0.0953167	+	0.293355i	0.987336	−	0.158642i	$-0.0507117\pi$
$773$	2.65008	+	8.15610i	0.0953167	+	0.293355i	−0.892019	+	0.451997i	$0.850712\pi$
$774$	45.5407			1.63693
$775$	−9.47648	−	22.3144i	−0.340405	−	0.801555i
$776$	14.9778			0.537671
$777$	−4.80239	−	14.7802i	−0.172285	−	0.530238i
$778$	−7.75786	+	5.63642i	−0.278133	+	0.202075i
$779$	0.228873	−	0.166286i	0.00820024	−	0.00595782i
$780$	5.29901	−	4.21578i	0.189735	−	0.150949i
$781$	−0.314548	−	0.228533i	−0.0112554	−	0.00817754i
$782$	22.0706			0.789245
$783$	−30.9034	−	22.4526i	−1.10440	−	0.802391i
$784$	−1.88186	+	5.79176i	−0.0672092	+	0.206849i
$785$	11.4093	−	41.1546i	0.407216	−	1.46887i
$786$	−14.7730	−	45.4667i	−0.526936	−	1.62174i
$787$	0.129979	−	0.400035i	0.00463326	−	0.0142597i	−0.948713	−	0.316138i	$-0.897614\pi$
$787$	0.129979	−	0.400035i	0.00463326	−	0.0142597i	0.953346	+	0.301878i	$0.0976137\pi$
$788$	3.43744	−	10.5794i	0.122454	−	0.376874i
$789$	5.90915	+	18.1865i	0.210371	+	0.647456i
$790$	−3.93932	+	3.13404i	−0.140155	+	0.111504i
$791$	5.85042	−	18.0057i	0.208017	−	0.640210i
$792$	0.492750	+	0.358004i	0.0175091	+	0.0127211i
$793$	−3.82538			−0.135843
$794$	−22.0017	−	15.9852i	−0.780812	−	0.567293i
$795$	−64.5202	−	42.6969i	−2.28830	−	1.51430i
$796$	6.73623	−	4.89416i	0.238759	−	0.173469i
$797$	20.7508	−	15.0764i	0.735033	−	0.534033i	−0.156119	−	0.987738i	$-0.549898\pi$
$797$	20.7508	−	15.0764i	0.735033	−	0.534033i	0.891152	+	0.453706i	$0.149898\pi$
$798$	0.0660496	+	0.203280i	0.00233813	+	0.00719603i
$799$	−9.69437			−0.342962
$800$	−4.28629	−	2.57444i	−0.151543	−	0.0910203i
$801$	87.4998			3.09166
$802$	−9.00367	−	27.7105i	−0.317931	−	0.978490i
$803$	0.419130	−	0.304516i	0.0147908	−	0.0107461i
$804$	4.06480	−	2.95325i	0.143354	−	0.104153i
$805$	−17.4080	+	0.761571i	−0.613550	+	0.0268419i
$806$	3.92264	+	2.84996i	0.138169	+	0.100386i
$807$	62.6030			2.20373
$808$	−3.90037	−	2.83378i	−0.137214	−	0.0996922i
$809$	−12.6497	+	38.9317i	−0.444739	+	1.36877i	0.438030	+	0.898960i	$0.355676\pi$
$809$	−12.6497	+	38.9317i	−0.444739	+	1.36877i	−0.882769	+	0.469807i	$0.844324\pi$
$810$	−19.6976	−	13.0351i	−0.692102	−	0.458005i
$811$	−2.80928	−	8.64608i	−0.0986472	−	0.303605i	0.889540	−	0.456858i	$-0.151025\pi$
$811$	−2.80928	−	8.64608i	−0.0986472	−	0.303605i	−0.988187	+	0.153253i	$0.951025\pi$
$812$	1.17294	−	3.60994i	0.0411621	−	0.126684i
$813$	10.6056	−	32.6405i	0.371953	−	1.14475i
$814$	0.164078	+	0.504979i	0.00575092	+	0.0176995i
$815$	−19.8430	−	13.1313i	−0.695071	−	0.459970i
$816$	−2.52859	+	7.78219i	−0.0885183	+	0.272431i
$817$	−0.441742	−	0.320944i	−0.0154546	−	0.0112284i
$818$	26.0041			0.909211
$819$	4.76254	+	3.46019i	0.166417	+	0.120909i
$820$	−8.54236	+	0.373715i	−0.298312	+	0.0130507i
$821$	−7.36249	+	5.34916i	−0.256953	+	0.186687i	−0.708803	−	0.705407i	$-0.750764\pi$
$821$	−7.36249	+	5.34916i	−0.256953	+	0.186687i	0.451850	+	0.892094i	$0.350764\pi$
$822$	−27.9865	+	20.3334i	−0.976141	+	0.709208i
$823$	15.3798	+	47.3340i	0.536105	+	1.64996i	0.741250	+	0.671229i	$0.234233\pi$
$823$	15.3798	+	47.3340i	0.536105	+	1.64996i	−0.205146	+	0.978731i	$0.565767\pi$
$824$	−9.89800			−0.344813
$825$	0.584216	+	1.37566i	0.0203398	+	0.0478943i
$826$	9.53644			0.331815
$827$	−3.10743	−	9.56370i	−0.108056	−	0.332562i	0.882380	−	0.470538i	$-0.155940\pi$
$827$	−3.10743	−	9.56370i	−0.108056	−	0.332562i	−0.990436	+	0.137976i	$0.955940\pi$
$828$	−40.7747	+	29.6245i	−1.41702	+	1.02952i
$829$	−23.5484	+	17.1089i	−0.817870	+	0.594217i	−0.916102	−	0.400946i	$-0.868681\pi$
$829$	−23.5484	+	17.1089i	−0.817870	+	0.594217i	0.0982316	+	0.995164i	$0.468681\pi$
$830$	−15.3103	−	10.1318i	−0.531429	−	0.351678i
$831$	−8.06704	−	5.86105i	−0.279843	−	0.203318i
$832$	1.00000			0.0346688
$833$	13.3126	+	9.67216i	0.461254	+	0.335120i
$834$	16.8274	−	51.7893i	0.582684	−	1.79332i
$835$	−13.9203	+	11.0747i	−0.481730	+	0.383254i
$836$	−0.00225664	−	0.00694523i	−7.80476e−5	−	0.000240206i
$837$	14.3854	−	44.2736i	0.497231	−	1.53032i
$838$	1.58434	−	4.87611i	0.0547302	−	0.168442i
$839$	−8.13850	−	25.0477i	−0.280972	−	0.864743i	−0.987577	−	0.157135i	$-0.949774\pi$
$839$	−8.13850	−	25.0477i	−0.280972	−	0.864743i	0.706605	−	0.707608i	$-0.250226\pi$
$840$	1.72586	−	6.22537i	0.0595479	−	0.214796i
$841$	−4.06999	+	12.5261i	−0.140344	+	0.431936i
$842$	0.968115	+	0.703377i	0.0333635	+	0.0242400i
$843$	−65.5394			−2.25730
$844$	3.34110	+	2.42745i	0.115005	+	0.0835563i
$845$	−1.74984	+	1.39214i	−0.0601964	+	0.0478910i
$846$	17.9100	−	13.0124i	0.615758	−	0.447374i
$847$	−8.48259	+	6.16297i	−0.291465	+	0.211762i
$848$	−3.53074	−	10.8665i	−0.121246	−	0.373157i
$849$	−54.3873			−1.86657
$850$	−10.1949	+	8.86544i	−0.349683	+	0.304082i
$851$	−43.9371			−1.50614
$852$	3.68601	+	11.3444i	0.126281	+	0.388652i
$853$	38.8715	−	28.2418i	1.33093	−	0.966980i	0.331209	−	0.943558i	$-0.392544\pi$
$853$	38.8715	−	28.2418i	1.33093	−	0.966980i	0.999726	−	0.0234229i	$-0.00745642\pi$
$854$	−2.95254	+	2.14515i	−0.101034	+	0.0734054i
$855$	0.357568	+	0.956105i	0.0122286	+	0.0326981i
$856$	−7.32576	−	5.32248i	−0.250389	−	0.181919i
$857$	−8.12953			−0.277699			−0.138850	−	0.990313i	$-0.544341\pi$
$857$	−8.12953			−0.277699			−0.138850	+	0.990313i	$0.544341\pi$
$858$	−0.241827	−	0.175697i	−0.00825583	−	0.00599821i
$859$	−13.3400	+	41.0564i	−0.455156	+	1.40083i	0.415795	+	0.909458i	$0.363503\pi$
$859$	−13.3400	+	41.0564i	−0.455156	+	1.40083i	−0.870951	+	0.491369i	$0.836497\pi$
$860$	5.78088	+	15.4575i	0.197126	+	0.527098i
$861$	−3.41389	−	10.5069i	−0.116345	−	0.358073i
$862$	−7.85022	+	24.1605i	−0.267380	+	0.822910i
$863$	8.92129	−	27.4569i	0.303684	−	0.934644i	−0.676481	−	0.736460i	$-0.736496\pi$
$863$	8.92129	−	27.4569i	0.303684	−	0.934644i	0.980165	−	0.198184i	$-0.0635043\pi$
$864$	−2.96688	−	9.13113i	−0.100935	−	0.310647i
$865$	9.62331	−	0.421005i	0.327202	−	0.0143146i
$866$	1.58441	−	4.87632i	0.0538405	−	0.165704i
$867$	−23.7611	−	17.2635i	−0.806970	−	0.586298i
$868$	4.62577			0.157009
$869$	0.179776	+	0.130615i	0.00609847	+	0.00443080i
$870$	7.19735	−	25.9616i	0.244013	−	0.880181i
$871$	−1.34228	+	0.975225i	−0.0454815	+	0.0330442i
$872$	−1.40343	+	1.01965i	−0.0475262	+	0.0345298i
$873$	28.5593	+	87.8965i	0.966587	+	2.97485i
$874$	0.604288			0.0204404
$875$	7.73522	−	7.34430i	0.261498	−	0.248283i
$876$	−15.8941			−0.537012
$877$	0.935110	+	2.87797i	0.0315764	+	0.0971823i	0.965603	−	0.260022i	$-0.0837299\pi$
$877$	0.935110	+	2.87797i	0.0315764	+	0.0971823i	−0.934026	+	0.357205i	$0.883730\pi$
$878$	5.97337	−	4.33991i	0.201591	−	0.146465i
$879$	0.571906	−	0.415514i	0.0192899	−	0.0140149i
$880$	−0.0589655	+	0.212695i	−0.00198773	+	0.00716995i
$881$	17.4567	+	12.6831i	0.588133	+	0.427303i	0.841647	−	0.540028i	$-0.181586\pi$
$881$	17.4567	+	12.6831i	0.588133	+	0.427303i	−0.253514	+	0.967332i	$0.581586\pi$
$882$	−37.5770			−1.26528
$883$	−19.4140	−	14.1051i	−0.653334	−	0.474675i	0.211071	−	0.977471i	$-0.432305\pi$
$883$	−19.4140	−	14.1051i	−0.653334	−	0.474675i	−0.864405	+	0.502796i	$0.832305\pi$
$884$	0.834992	−	2.56984i	0.0280838	−	0.0864331i
$885$	67.6221	−	2.95836i	2.27309	−	0.0994442i
$886$	−9.22049	−	28.3778i	−0.309769	−	0.953370i
$887$	0.958056	−	2.94859i	0.0321684	−	0.0990040i	−0.933683	−	0.358100i	$-0.883425\pi$
$887$	0.958056	−	2.94859i	0.0321684	−	0.0990040i	0.965852	+	0.259096i	$0.0834246\pi$
$888$	5.03378	−	15.4924i	0.168923	−	0.519890i
$889$	−3.21359	−	9.89041i	−0.107780	−	0.331714i
$890$	11.1071	+	29.6994i	0.372311	+	0.995527i
$891$	−0.322203	+	0.991638i	−0.0107942	+	0.0332211i
$892$	9.22138	+	6.69973i	0.308755	+	0.224323i
$893$	−0.265429			−0.00888226
$894$	−43.2981	−	31.4579i	−1.44811	−	1.05211i
$895$	9.01428	+	24.1034i	0.301314	+	0.805687i
$896$	0.771829	−	0.560766i	0.0257850	−	0.0187339i
$897$	20.0110	−	14.5388i	0.668147	−	0.485437i
$898$	−3.84742	−	11.8411i	−0.128390	−	0.395144i
$899$	19.2908			0.643385
$900$	6.93501	−	30.0628i	0.231167	−	1.00209i
$901$	−30.8733			−1.02854
$902$	0.116638	+	0.358976i	0.00388364	+	0.0119526i
$903$	−17.2504	+	12.5331i	−0.574056	+	0.417076i
$904$	16.0546	−	11.6643i	0.533968	−	0.387950i
$905$	−43.9211	+	34.9427i	−1.45999	+	1.16154i
$906$	−44.4937	−	32.3266i	−1.47821	−	1.07398i
$907$	27.8191			0.923718			0.461859	−	0.886953i	$-0.347183\pi$
$907$	27.8191			0.923718			0.461859	+	0.886953i	$0.347183\pi$
$908$	−22.2910	−	16.1953i	−0.739752	−	0.537461i
$909$	9.19280	−	28.2925i	0.304906	−	0.938404i
$910$	−0.569915	+	2.05575i	−0.0188925	+	0.0681473i
$911$	5.57745	+	17.1656i	0.184789	+	0.568723i	0.999945	−	0.0105195i	$-0.00334854\pi$
$911$	5.57745	+	17.1656i	0.184789	+	0.568723i	−0.815155	+	0.579242i	$0.803349\pi$
$912$	−0.0692321	+	0.213074i	−0.00229250	+	0.00705560i
$913$	−0.250438	+	0.770770i	−0.00828830	+	0.0255088i
$914$	−6.78721	−	20.8889i	−0.224501	−	0.690943i
$915$	−20.2707	+	16.1270i	−0.670130	+	0.533141i
$916$	−8.36118	+	25.7331i	−0.276261	+	0.850244i
$917$	12.1846	+	8.85265i	0.402372	+	0.292340i
$918$	−25.9429			−0.856242
$919$	46.3414	+	33.6690i	1.52866	+	1.11064i	0.956976	+	0.290167i	$0.0937110\pi$
$919$	46.3414	+	33.6690i	1.52866	+	1.11064i	0.571687	+	0.820471i	$0.306289\pi$
$920$	−15.2311	−	10.0793i	−0.502155	−	0.332306i
$921$	81.6859	−	59.3483i	2.69164	−	1.95559i
$922$	−15.4817	+	11.2481i	−0.509861	+	0.370436i
$923$	−1.21720	−	3.74615i	−0.0400645	−	0.123306i
$924$	−0.285174			−0.00938154
$925$	20.2955	−	17.6488i	0.667312	−	0.580291i
$926$	6.12537			0.201292
$927$	−18.8733	−	58.0860i	−0.619880	−	1.90779i
$928$	3.21875	−	2.33856i	0.105661	−	0.0767670i
$929$	32.5506	−	23.6494i	1.06795	−	0.775911i	0.0924074	−	0.995721i	$-0.470544\pi$
$929$	32.5506	−	23.6494i	1.06795	−	0.775911i	0.975543	+	0.219810i	$0.0705438\pi$
$930$	32.8009	−	1.43499i	1.07558	−	0.0470551i
$931$	0.364495	+	0.264821i	0.0119458	+	0.00867916i
$932$	−11.4141			−0.373882
$933$	−9.66491	−	7.02197i	−0.316415	−	0.229889i
$934$	−2.60747	+	8.02497i	−0.0853190	+	0.262585i
$935$	0.497357	+	0.329131i	0.0162653	+	0.0107637i
$936$	1.90678	+	5.86846i	0.0623250	+	0.191817i
$937$	0.0256454	−	0.0789285i	0.000837800	−	0.00257848i	−0.950637	−	0.310306i	$-0.899569\pi$
$937$	0.0256454	−	0.0789285i	0.000837800	−	0.00257848i	0.951475	+	0.307727i	$0.0995685\pi$
$938$	−0.489138	+	1.50541i	−0.0159709	+	0.0491535i
$939$	−0.0445720	−	0.137179i	−0.00145455	−	0.00447666i
$940$	6.69016	+	4.42728i	0.218209	+	0.144402i
$941$	−6.61691	+	20.3647i	−0.215705	+	0.663872i	0.783398	+	0.621521i	$0.213485\pi$
$941$	−6.61691	+	20.3647i	−0.215705	+	0.663872i	−0.999103	+	0.0423511i	$0.986515\pi$
$942$	46.7913	+	33.9959i	1.52454	+	1.10765i
$943$	−31.2337			−1.01711
$944$	8.08687	+	5.87546i	0.263205	+	0.191230i
$945$	20.4621	−	0.895187i	0.665634	−	0.0291204i
$946$	0.589374	−	0.428205i	0.0191622	−	0.0139221i
$947$	7.72866	−	5.61520i	0.251148	−	0.182470i	−0.455088	−	0.890447i	$-0.650392\pi$
$947$	7.72866	−	5.61520i	0.251148	−	0.182470i	0.706235	+	0.707977i	$0.250392\pi$
$948$	−2.10669	−	6.48372i	−0.0684220	−	0.210581i
$949$	5.24856			0.170376
$950$	−0.279134	+	0.242733i	−0.00905631	+	0.00787531i
$951$	12.6185			0.409182
$952$	−0.796610	−	2.45171i	−0.0258183	−	0.0794605i
$953$	−31.3756	+	22.7957i	−1.01636	+	0.738426i	−0.965533	−	0.260282i	$-0.916185\pi$
$953$	−31.3756	+	22.7957i	−1.01636	+	0.738426i	−0.0508233	+	0.998708i	$0.516185\pi$
$954$	57.0373	−	41.4400i	1.84665	−	1.34167i
$955$	0.314461	+	0.208097i	0.0101757	+	0.00673387i
$956$	11.5852	+	8.41712i	0.374691	+	0.272229i
$957$	−1.18926			−0.0384433
$958$	−27.5113	−	19.9881i	−0.888850	−	0.645788i
$959$	3.36776	−	10.3649i	0.108751	−	0.334700i
$960$	5.29901	−	4.21578i	0.171025	−	0.136064i
$961$	−2.31473	−	7.12402i	−0.0746689	−	0.229807i
$962$	−1.66226	+	5.11591i	−0.0535934	+	0.164943i
$963$	17.2661	−	53.1397i	0.556394	−	1.71240i
$964$	2.79335	+	8.59706i	0.0899679	+	0.276893i
$965$	−16.3417	+	58.9464i	−0.526059	+	1.89755i
$966$	7.29216	−	22.4430i	0.234621	−	0.722090i
$967$	1.32583	+	0.963268i	0.0426357	+	0.0309766i	0.608899	−	0.793248i	$-0.291611\pi$
$967$	1.32583	+	0.963268i	0.0426357	+	0.0309766i	−0.566263	+	0.824224i	$0.691611\pi$
$968$	−10.9903			−0.353240
$969$	0.489759	+	0.355831i	0.0157333	+	0.0114309i
$970$	−26.2088	+	20.8512i	−0.841514	+	0.669490i
$971$	16.0970	−	11.6952i	0.516578	−	0.375316i	−0.298735	−	0.954336i	$-0.596565\pi$
$971$	16.0970	−	11.6952i	0.516578	−	0.375316i	0.815313	+	0.579020i	$0.196565\pi$
$972$	2.57689	−	1.87222i	0.0826539	−	0.0600516i
$973$	5.30132	+	16.3158i	0.169952	+	0.523060i
$974$	18.5931			0.595762
$975$	−3.40349	+	14.7539i	−0.108999	+	0.472503i
$976$	−3.82538			−0.122447
$977$	6.51330	+	20.0459i	0.208379	+	0.641324i	0.999558	+	0.0297392i	$0.00946769\pi$
$977$	6.51330	+	20.0459i	0.208379	+	0.641324i	−0.791179	+	0.611585i	$0.790532\pi$
$978$	26.0702	−	18.9411i	0.833633	−	0.605670i
$979$	1.13240	−	0.822734i	0.0361915	−	0.0262947i
$980$	−4.76998	−	12.7545i	−0.152371	−	0.407427i
$981$	−8.65982	−	6.29173i	−0.276487	−	0.200879i
$982$	27.0679			0.863772
$983$	26.8054	+	19.4752i	0.854959	+	0.621164i	0.926509	−	0.376273i	$-0.122795\pi$
$983$	26.8054	+	19.4752i	0.854959	+	0.621164i	−0.0715499	+	0.997437i	$0.522795\pi$
$984$	3.57838	−	11.0131i	0.114075	−	0.351085i
$985$	8.71295	+	23.2976i	0.277618	+	0.742324i
$986$	−3.32210	−	10.2244i	−0.105797	−	0.325610i
$987$	−3.20303	+	9.85791i	−0.101954	+	0.313781i
$988$	0.0228619	−	0.0703616i	0.000727333	−	0.00223850i
$989$	18.6286	+	57.3328i	0.592354	+	1.82308i
$990$	−1.36063	+	0.0595252i	−0.0432435	+	0.00189184i
$991$	1.61000	−	4.95506i	0.0511432	−	0.157403i	−0.922223	−	0.386658i	$-0.873629\pi$
$991$	1.61000	−	4.95506i	0.0511432	−	0.157403i	0.973366	+	0.229256i	$0.0736292\pi$
$992$	3.92264	+	2.84996i	0.124544	+	0.0904864i
$993$	34.0562			1.08074
$994$	−3.04018	−	2.20882i	−0.0964287	−	0.0700595i
$995$	−4.97400	+	17.9418i	−0.157687	+	0.568792i
$996$	20.1150	−	14.6144i	0.637369	−	0.463076i
$997$	11.8602	−	8.61696i	0.375617	−	0.272902i	−0.383919	−	0.923367i	$-0.625426\pi$
$997$	11.8602	−	8.61696i	0.375617	−	0.272902i	0.759536	+	0.650465i	$0.225426\pi$
$998$	−4.16648	−	12.8231i	−0.131888	−	0.405908i
$999$	51.6457			1.63400

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	650.2.l.c.131.6	✓	24
25.21	even	5	inner	650.2.l.c.521.6	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
650.2.l.c.131.6	✓	24	1.1	even	1	trivial
650.2.l.c.521.6	yes	24	25.21	even	5	inner

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:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	650.l (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 + 0.951057i) q^{2} +(2.44993 - 1.77998i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.597375 - 2.15480i) q^{5} +(2.44993 + 1.77998i) q^{6} -0.954033 q^{7} +(-0.809017 - 0.587785i) q^{8} +(1.90678 - 5.86846i) q^{9} +O(q^{10})\)	\(q+(0.309017 + 0.951057i) q^{2} +(2.44993 - 1.77998i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.597375 - 2.15480i) q^{5} +(2.44993 + 1.77998i) q^{6} -0.954033 q^{7} +(-0.809017 - 0.587785i) q^{8} +(1.90678 - 5.86846i) q^{9} +(2.23393 - 0.0977310i) q^{10} +(-0.0305024 - 0.0938766i) q^{11} +(-0.935789 + 2.88006i) q^{12} +(0.309017 - 0.951057i) q^{13} +(-0.294812 - 0.907339i) q^{14} +(-2.37196 - 6.34241i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-2.18604 - 1.58825i) q^{17} +6.17046 q^{18} +(-0.0598531 - 0.0434859i) q^{19} +(0.783270 + 2.09439i) q^{20} +(-2.33731 + 1.69816i) q^{21} +(0.0798562 - 0.0580189i) q^{22} +(2.52405 + 7.76822i) q^{23} -3.02828 q^{24} +(-4.28629 - 2.57444i) q^{25} +1.00000 q^{26} +(-2.96688 - 9.13113i) q^{27} +(0.771829 - 0.560766i) q^{28} +(3.21875 - 2.33856i) q^{29} +(5.29901 - 4.21578i) q^{30} +(3.92264 + 2.84996i) q^{31} +1.00000 q^{32} +(-0.241827 - 0.175697i) q^{33} +(0.834992 - 2.56984i) q^{34} +(-0.569915 + 2.05575i) q^{35} +(1.90678 + 5.86846i) q^{36} +(-1.66226 + 5.11591i) q^{37} +(0.0228619 - 0.0703616i) q^{38} +(-0.935789 - 2.88006i) q^{39} +(-1.74984 + 1.39214i) q^{40} +(-1.18165 + 3.63676i) q^{41} +(-2.33731 - 1.69816i) q^{42} +7.38043 q^{43} +(0.0798562 + 0.0580189i) q^{44} +(-11.5063 - 7.61439i) q^{45} +(-6.60804 + 4.80102i) q^{46} +(2.90253 - 2.10881i) q^{47} +(-0.935789 - 2.88006i) q^{48} -6.08982 q^{49} +(1.12390 - 4.87205i) q^{50} -8.18268 q^{51} +(0.309017 + 0.951057i) q^{52} +(9.24360 - 6.71587i) q^{53} +(7.76740 - 5.64335i) q^{54} +(-0.220506 + 0.00964680i) q^{55} +(0.771829 + 0.560766i) q^{56} -0.224040 q^{57} +(3.21875 + 2.33856i) q^{58} +(-3.08891 + 9.50669i) q^{59} +(5.64693 + 3.73691i) q^{60} +(-1.18211 - 3.63815i) q^{61} +(-1.49831 + 4.61134i) q^{62} +(-1.81913 + 5.59870i) q^{63} +(0.309017 + 0.951057i) q^{64} +(-1.86473 - 1.23401i) q^{65} +(0.0923696 - 0.284284i) q^{66} +(-1.34228 - 0.975225i) q^{67} +2.70209 q^{68} +(20.0110 + 14.5388i) q^{69} +(-2.13124 + 0.0932386i) q^{70} +(3.18666 - 2.31525i) q^{71} +(-4.99201 + 3.62691i) q^{72} +(1.62189 + 4.99168i) q^{73} -5.37918 q^{74} +(-15.0835 + 1.32229i) q^{75} +0.0739826 q^{76} +(0.0291003 + 0.0895614i) q^{77} +(2.44993 - 1.77998i) q^{78} +(-1.82129 + 1.32325i) q^{79} +(-1.86473 - 1.23401i) q^{80} +(-8.54582 - 6.20890i) q^{81} -3.82392 q^{82} +(-6.64240 - 4.82599i) q^{83} +(0.892773 - 2.74767i) q^{84} +(-4.72824 + 3.76168i) q^{85} +(2.28068 + 7.01921i) q^{86} +(3.72313 - 11.4586i) q^{87} +(-0.0305024 + 0.0938766i) q^{88} +(4.38200 + 13.4864i) q^{89} +(3.68608 - 13.2961i) q^{90} +(-0.294812 + 0.907339i) q^{91} +(-6.60804 - 4.80102i) q^{92} +14.6830 q^{93} +(2.90253 + 2.10881i) q^{94} +(-0.129458 + 0.102994i) q^{95} +(2.44993 - 1.77998i) q^{96} +(-12.1173 + 8.80373i) q^{97} +(-1.88186 - 5.79176i) q^{98} -0.609072 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 6 q^{2} + 3 q^{3} - 6 q^{4} - q^{5} + 3 q^{6} - 6 q^{8} + 7 q^{9}+O(q^{10}) \) 24 * q - 6 * q^2 + 3 * q^3 - 6 * q^4 - q^5 + 3 * q^6 - 6 * q^8 + 7 * q^9	\( 24 q - 6 q^{2} + 3 q^{3} - 6 q^{4} - q^{5} + 3 q^{6} - 6 q^{8} + 7 q^{9} - q^{10} + 2 q^{11} - 2 q^{12} - 6 q^{13} + 20 q^{15} - 6 q^{16} + 9 q^{17} + 22 q^{18} + 12 q^{19} + 4 q^{20} + 25 q^{21} + 2 q^{22} - 6 q^{23} - 2 q^{24} - 41 q^{25} + 24 q^{26} - 6 q^{27} - 2 q^{29} + 10 q^{30} + 13 q^{31} + 24 q^{32} - 34 q^{33} + 14 q^{34} + 7 q^{36} + 5 q^{37} + 22 q^{38} - 2 q^{39} - q^{40} - 10 q^{41} + 25 q^{42} - 18 q^{43} + 2 q^{44} + 3 q^{45} + 9 q^{46} - 5 q^{47} - 2 q^{48} + 32 q^{49} - 11 q^{50} - 56 q^{51} - 6 q^{52} + 34 q^{53} + 19 q^{54} + 20 q^{55} - 12 q^{57} - 2 q^{58} - 15 q^{60} - 2 q^{61} - 12 q^{62} + 10 q^{63} - 6 q^{64} - q^{65} + 26 q^{66} + 2 q^{67} - 46 q^{68} + 33 q^{69} - 20 q^{70} + 29 q^{71} - 18 q^{72} - 11 q^{73} - 30 q^{74} - 25 q^{75} - 68 q^{76} + 15 q^{77} + 3 q^{78} + 20 q^{79} - q^{80} - 9 q^{81} - 20 q^{82} - 69 q^{83} - 20 q^{84} - 27 q^{85} + 22 q^{86} - 18 q^{87} + 2 q^{88} + 19 q^{89} + 8 q^{90} + 9 q^{92} + 40 q^{93} - 5 q^{94} + 78 q^{95} + 3 q^{96} - 49 q^{97} + 2 q^{98} - 28 q^{99}+O(q^{100}) \) 24 * q - 6 * q^2 + 3 * q^3 - 6 * q^4 - q^5 + 3 * q^6 - 6 * q^8 + 7 * q^9 - q^10 + 2 * q^11 - 2 * q^12 - 6 * q^13 + 20 * q^15 - 6 * q^16 + 9 * q^17 + 22 * q^18 + 12 * q^19 + 4 * q^20 + 25 * q^21 + 2 * q^22 - 6 * q^23 - 2 * q^24 - 41 * q^25 + 24 * q^26 - 6 * q^27 - 2 * q^29 + 10 * q^30 + 13 * q^31 + 24 * q^32 - 34 * q^33 + 14 * q^34 + 7 * q^36 + 5 * q^37 + 22 * q^38 - 2 * q^39 - q^40 - 10 * q^41 + 25 * q^42 - 18 * q^43 + 2 * q^44 + 3 * q^45 + 9 * q^46 - 5 * q^47 - 2 * q^48 + 32 * q^49 - 11 * q^50 - 56 * q^51 - 6 * q^52 + 34 * q^53 + 19 * q^54 + 20 * q^55 - 12 * q^57 - 2 * q^58 - 15 * q^60 - 2 * q^61 - 12 * q^62 + 10 * q^63 - 6 * q^64 - q^65 + 26 * q^66 + 2 * q^67 - 46 * q^68 + 33 * q^69 - 20 * q^70 + 29 * q^71 - 18 * q^72 - 11 * q^73 - 30 * q^74 - 25 * q^75 - 68 * q^76 + 15 * q^77 + 3 * q^78 + 20 * q^79 - q^80 - 9 * q^81 - 20 * q^82 - 69 * q^83 - 20 * q^84 - 27 * q^85 + 22 * q^86 - 18 * q^87 + 2 * q^88 + 19 * q^89 + 8 * q^90 + 9 * q^92 + 40 * q^93 - 5 * q^94 + 78 * q^95 + 3 * q^96 - 49 * q^97 + 2 * q^98 - 28 * q^99

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