LMFDB - Embedded newform 143.2.h.c.14.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [143,2,Mod(14,143)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(143, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8, 0]))

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

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

chi := DirichletCharacter("143.14");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 143 = 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	143.h (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:	$1.14186074890$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			14.5
Character	$\chi$	$=$	143.14
Dual form			143.2.h.c.92.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.203919 - 0.148156i) q^{2} +(0.947227 + 2.91527i) q^{3} +(-0.598401 + 1.84169i) q^{4} +(-1.49221 - 1.08415i) q^{5} +(0.625071 + 0.454140i) q^{6} +(0.992247 - 3.05382i) q^{7} +(0.306612 + 0.943653i) q^{8} +(-5.17449 + 3.75949i) q^{9} +O(q^{10})$	\(q+(0.203919 - 0.148156i) q^{2} +(0.947227 + 2.91527i) q^{3} +(-0.598401 + 1.84169i) q^{4} +(-1.49221 - 1.08415i) q^{5} +(0.625071 + 0.454140i) q^{6} +(0.992247 - 3.05382i) q^{7} +(0.306612 + 0.943653i) q^{8} +(-5.17449 + 3.75949i) q^{9} -0.464913 q^{10} +(3.18285 + 0.932455i) q^{11} -5.93584 q^{12} +(-0.809017 + 0.587785i) q^{13} +(-0.250103 - 0.769738i) q^{14} +(1.74714 - 5.37713i) q^{15} +(-2.93094 - 2.12945i) q^{16} +(4.91855 + 3.57354i) q^{17} +(-0.498186 + 1.53326i) q^{18} +(-1.04960 - 3.23035i) q^{19} +(2.88962 - 2.09943i) q^{20} +9.84259 q^{21} +(0.787191 - 0.281412i) q^{22} +7.01119 q^{23} +(-2.46057 + 1.78771i) q^{24} +(-0.493784 - 1.51971i) q^{25} +(-0.0778900 + 0.239721i) q^{26} +(-8.42170 - 6.11872i) q^{27} +(5.03043 + 3.65482i) q^{28} +(1.18771 - 3.65539i) q^{29} +(-0.440378 - 1.35535i) q^{30} +(-3.96029 + 2.87732i) q^{31} -2.89759 q^{32} +(0.296527 + 10.1621i) q^{33} +1.53242 q^{34} +(-4.79145 + 3.48119i) q^{35} +(-3.82739 - 11.7795i) q^{36} +(0.477278 - 1.46891i) q^{37} +(-0.692628 - 0.503224i) q^{38} +(-2.47987 - 1.80173i) q^{39} +(0.565537 - 1.74054i) q^{40} +(-1.69912 - 5.22934i) q^{41} +(2.00709 - 1.45823i) q^{42} -6.07661 q^{43} +(-3.62191 + 5.30384i) q^{44} +11.7973 q^{45} +(1.42971 - 1.03875i) q^{46} +(-1.32057 - 4.06429i) q^{47} +(3.43165 - 10.5615i) q^{48} +(-2.67815 - 1.94579i) q^{49} +(-0.325846 - 0.236741i) q^{50} +(-5.75882 + 17.7238i) q^{51} +(-0.598401 - 1.84169i) q^{52} +(-1.82705 + 1.32743i) q^{53} -2.62386 q^{54} +(-3.73855 - 4.84212i) q^{55} +3.18598 q^{56} +(8.42311 - 6.11975i) q^{57} +(-0.299370 - 0.921368i) q^{58} +(-0.741585 + 2.28236i) q^{59} +(8.85752 + 6.43536i) q^{60} +(1.14241 + 0.830012i) q^{61} +(-0.381287 + 1.17348i) q^{62} +(6.34643 + 19.5323i) q^{63} +(5.27100 - 3.82961i) q^{64} +1.84447 q^{65} +(1.56604 + 2.02831i) q^{66} -15.7025 q^{67} +(-9.52461 + 6.92003i) q^{68} +(6.64120 + 20.4395i) q^{69} +(-0.461308 + 1.41976i) q^{70} +(3.62190 + 2.63146i) q^{71} +(-5.13421 - 3.73022i) q^{72} +(0.860955 - 2.64975i) q^{73} +(-0.120301 - 0.370250i) q^{74} +(3.96264 - 2.87903i) q^{75} +6.57738 q^{76} +(6.00572 - 8.79463i) q^{77} -0.772630 q^{78} +(7.17961 - 5.21629i) q^{79} +(2.06492 + 6.35518i) q^{80} +(3.93100 - 12.0984i) q^{81} +(-1.12124 - 0.814627i) q^{82} +(-7.23835 - 5.25897i) q^{83} +(-5.88982 + 18.1270i) q^{84} +(-3.46525 - 10.6649i) q^{85} +(-1.23913 + 0.900284i) q^{86} +11.7815 q^{87} +(0.0959839 + 3.28941i) q^{88} +0.928281 q^{89} +(2.40569 - 1.74783i) q^{90} +(0.992247 + 3.05382i) q^{91} +(-4.19551 + 12.9124i) q^{92} +(-12.1395 - 8.81983i) q^{93} +(-0.871436 - 0.633135i) q^{94} +(-1.93597 + 5.95829i) q^{95} +(-2.74468 - 8.44726i) q^{96} +(-8.68068 + 6.30689i) q^{97} -0.834405 q^{98} +(-19.9752 + 7.14090i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 3 q^{2} - 7 q^{3} - 5 q^{4} - 7 q^{5} - 4 q^{6} - 7 q^{7} + q^{8} - 6 q^{9}+O(q^{10}) $ 28 * q - 3 * q^2 - 7 * q^3 - 5 * q^4 - 7 * q^5 - 4 * q^6 - 7 * q^7 + q^8 - 6 * q^9	\( 28 q - 3 q^{2} - 7 q^{3} - 5 q^{4} - 7 q^{5} - 4 q^{6} - 7 q^{7} + q^{8} - 6 q^{9} - 24 q^{10} - 5 q^{11} + 38 q^{12} - 7 q^{13} - 7 q^{14} + 8 q^{15} - 19 q^{16} + 7 q^{17} + 5 q^{18} + 5 q^{19} + 9 q^{20} - 33 q^{22} + 50 q^{23} - 7 q^{24} - 34 q^{25} + 2 q^{26} - 19 q^{27} + 30 q^{28} + 8 q^{29} - 6 q^{30} + 17 q^{31} + 24 q^{32} - 26 q^{33} + 26 q^{34} - 4 q^{35} - 27 q^{36} + 17 q^{37} - 51 q^{38} - 2 q^{39} + 39 q^{40} - 23 q^{41} + 80 q^{42} - 32 q^{43} + q^{44} + 78 q^{45} - 31 q^{46} - 29 q^{47} + 52 q^{48} - 52 q^{49} + 6 q^{50} + 7 q^{51} - 5 q^{52} - 16 q^{53} - 42 q^{54} - 5 q^{55} + 34 q^{56} - 7 q^{57} - 13 q^{58} - 11 q^{59} - 74 q^{60} + 37 q^{61} + 23 q^{62} - 38 q^{63} + 67 q^{64} + 18 q^{65} - 65 q^{66} + 58 q^{67} - 68 q^{68} - 28 q^{69} + 44 q^{70} - 47 q^{71} + 10 q^{72} + 44 q^{73} - 46 q^{74} + 17 q^{75} + 6 q^{76} + 21 q^{77} + 26 q^{78} + 51 q^{79} + 23 q^{80} - 14 q^{81} - 47 q^{82} - 13 q^{83} - 107 q^{84} - q^{85} + 38 q^{86} - 12 q^{87} + 9 q^{88} + 38 q^{89} - 74 q^{90} - 7 q^{91} - 41 q^{92} - 51 q^{93} - 5 q^{94} + 47 q^{95} - 71 q^{96} - 20 q^{97} + 162 q^{98} + 60 q^{99}+O(q^{100}) \) 28 * q - 3 * q^2 - 7 * q^3 - 5 * q^4 - 7 * q^5 - 4 * q^6 - 7 * q^7 + q^8 - 6 * q^9 - 24 * q^10 - 5 * q^11 + 38 * q^12 - 7 * q^13 - 7 * q^14 + 8 * q^15 - 19 * q^16 + 7 * q^17 + 5 * q^18 + 5 * q^19 + 9 * q^20 - 33 * q^22 + 50 * q^23 - 7 * q^24 - 34 * q^25 + 2 * q^26 - 19 * q^27 + 30 * q^28 + 8 * q^29 - 6 * q^30 + 17 * q^31 + 24 * q^32 - 26 * q^33 + 26 * q^34 - 4 * q^35 - 27 * q^36 + 17 * q^37 - 51 * q^38 - 2 * q^39 + 39 * q^40 - 23 * q^41 + 80 * q^42 - 32 * q^43 + q^44 + 78 * q^45 - 31 * q^46 - 29 * q^47 + 52 * q^48 - 52 * q^49 + 6 * q^50 + 7 * q^51 - 5 * q^52 - 16 * q^53 - 42 * q^54 - 5 * q^55 + 34 * q^56 - 7 * q^57 - 13 * q^58 - 11 * q^59 - 74 * q^60 + 37 * q^61 + 23 * q^62 - 38 * q^63 + 67 * q^64 + 18 * q^65 - 65 * q^66 + 58 * q^67 - 68 * q^68 - 28 * q^69 + 44 * q^70 - 47 * q^71 + 10 * q^72 + 44 * q^73 - 46 * q^74 + 17 * q^75 + 6 * q^76 + 21 * q^77 + 26 * q^78 + 51 * q^79 + 23 * q^80 - 14 * q^81 - 47 * q^82 - 13 * q^83 - 107 * q^84 - q^85 + 38 * q^86 - 12 * q^87 + 9 * q^88 + 38 * q^89 - 74 * q^90 - 7 * q^91 - 41 * q^92 - 51 * q^93 - 5 * q^94 + 47 * q^95 - 71 * q^96 - 20 * q^97 + 162 * q^98 + 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/143\mathbb{Z}\right)^\times$.

$n$	$67$	$79$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	0.203919	−	0.148156i	0.144192	−	0.104762i	−0.513350	−	0.858179i	$-0.671596\pi$
$2$	0.203919	−	0.148156i	0.144192	−	0.104762i	0.657543	+	0.753417i	$0.271596\pi$
$3$	0.947227	+	2.91527i	0.546882	+	1.68313i	0.716473	+	0.697615i	$0.245755\pi$
$3$	0.947227	+	2.91527i	0.546882	+	1.68313i	−0.169591	+	0.985515i	$0.554245\pi$
$4$	−0.598401	+	1.84169i	−0.299201	+	0.920845i
$5$	−1.49221	−	1.08415i	−0.667337	−	0.484848i	0.201796	−	0.979428i	$-0.435322\pi$
$5$	−1.49221	−	1.08415i	−0.667337	−	0.484848i	−0.869133	+	0.494579i	$0.835322\pi$
$6$	0.625071	+	0.454140i	0.255184	+	0.185402i
$7$	0.992247	−	3.05382i	0.375034	−	1.15424i	−0.568422	−	0.822737i	$-0.692446\pi$
$7$	0.992247	−	3.05382i	0.375034	−	1.15424i	0.943456	−	0.331499i	$-0.107554\pi$
$8$	0.306612	+	0.943653i	0.108404	+	0.333632i
$9$	−5.17449	+	3.75949i	−1.72483	+	1.25316i
$10$	−0.464913			−0.147018
$11$	3.18285	+	0.932455i	0.959665	+	0.281146i
$11$	3.18285	+	0.932455i	0.959665	+	0.281146i
$12$	−5.93584			−1.71353
$13$	−0.809017	+	0.587785i	−0.224381	+	0.163022i
$13$	−0.809017	+	0.587785i	−0.224381	+	0.163022i
$14$	−0.250103	−	0.769738i	−0.0668429	−	0.205721i
$15$	1.74714	−	5.37713i	0.451108	−	1.38837i
$16$	−2.93094	−	2.12945i	−0.732735	−	0.532363i
$17$	4.91855	+	3.57354i	1.19292	+	0.866710i	0.993570	−	0.113218i	$-0.0361158\pi$
$17$	4.91855	+	3.57354i	1.19292	+	0.866710i	0.199353	+	0.979928i	$0.436116\pi$
$18$	−0.498186	+	1.53326i	−0.117424	+	0.361393i
$19$	−1.04960	−	3.23035i	−0.240796	−	0.741093i	−0.996300	−	0.0859486i	$-0.972608\pi$
$19$	−1.04960	−	3.23035i	−0.240796	−	0.741093i	0.755504	−	0.655144i	$-0.227392\pi$
$20$	2.88962	−	2.09943i	0.646138	−	0.469446i
$21$	9.84259			2.14783
$22$	0.787191	−	0.281412i	0.167830	−	0.0599972i
$23$	7.01119			1.46193			0.730967	−	0.682412i	$-0.239069\pi$
$23$	7.01119			1.46193			0.730967	+	0.682412i	$0.239069\pi$
$24$	−2.46057	+	1.78771i	−0.502262	+	0.364914i
$25$	−0.493784	−	1.51971i	−0.0987569	−	0.303942i
$26$	−0.0778900	+	0.239721i	−0.0152755	+	0.0470131i
$27$	−8.42170	−	6.11872i	−1.62076	−	1.17755i
$28$	5.03043	+	3.65482i	0.950662	+	0.690696i
$29$	1.18771	−	3.65539i	0.220552	−	0.678789i	−0.778161	−	0.628065i	$-0.783847\pi$
$29$	1.18771	−	3.65539i	0.220552	−	0.678789i	0.998713	−	0.0507236i	$-0.0161528\pi$
$30$	−0.440378	−	1.35535i	−0.0804017	−	0.247451i
$31$	−3.96029	+	2.87732i	−0.711290	+	0.516782i	−0.883589	−	0.468262i	$-0.844880\pi$
$31$	−3.96029	+	2.87732i	−0.711290	+	0.516782i	0.172300	+	0.985045i	$0.444880\pi$
$32$	−2.89759			−0.512227
$33$	0.296527	+	10.1621i	0.0516187	+	1.76899i
$34$	1.53242			0.262809
$35$	−4.79145	+	3.48119i	−0.809903	+	0.588429i
$36$	−3.82739	−	11.7795i	−0.637898	−	1.96325i
$37$	0.477278	−	1.46891i	0.0784640	−	0.241487i	−0.904129	−	0.427260i	$-0.859479\pi$
$37$	0.477278	−	1.46891i	0.0784640	−	0.241487i	0.982593	+	0.185773i	$0.0594789\pi$
$38$	−0.692628	−	0.503224i	−0.112359	−	0.0816337i
$39$	−2.47987	−	1.80173i	−0.397098	−	0.288508i
$40$	0.565537	−	1.74054i	0.0894192	−	0.275204i
$41$	−1.69912	−	5.22934i	−0.265357	−	0.816686i	−0.991611	−	0.129259i	$-0.958740\pi$
$41$	−1.69912	−	5.22934i	−0.265357	−	0.816686i	0.726253	−	0.687427i	$-0.241260\pi$
$42$	2.00709	−	1.45823i	0.309700	−	0.225010i
$43$	−6.07661			−0.926674			−0.463337	−	0.886182i	$-0.653348\pi$
$43$	−6.07661			−0.926674			−0.463337	+	0.886182i	$0.653348\pi$
$44$	−3.62191	+	5.30384i	−0.546024	+	0.799584i
$45$	11.7973			1.75864
$46$	1.42971	−	1.03875i	0.210800	−	0.153155i
$47$	−1.32057	−	4.06429i	−0.192625	−	0.592838i	−0.999996	−	0.00279416i	$-0.999111\pi$
$47$	−1.32057	−	4.06429i	−0.192625	−	0.592838i	0.807371	−	0.590043i	$-0.200889\pi$
$48$	3.43165	−	10.5615i	0.495316	−	1.52443i
$49$	−2.67815	−	1.94579i	−0.382593	−	0.277970i
$50$	−0.325846	−	0.236741i	−0.0460815	−	0.0334802i
$51$	−5.75882	+	17.7238i	−0.806397	+	2.48183i
$52$	−0.598401	−	1.84169i	−0.0829833	−	0.255396i
$53$	−1.82705	+	1.32743i	−0.250965	+	0.182337i	−0.706154	−	0.708058i	$-0.749572\pi$
$53$	−1.82705	+	1.32743i	−0.250965	+	0.182337i	0.455189	+	0.890395i	$0.349572\pi$
$54$	−2.62386			−0.357063
$55$	−3.73855	−	4.84212i	−0.504107	−	0.652911i
$56$	3.18598			0.425745
$57$	8.42311	−	6.11975i	1.11567	−	0.810581i
$58$	−0.299370	−	0.921368i	−0.0393093	−	0.120981i
$59$	−0.741585	+	2.28236i	−0.0965461	+	0.297138i	−0.987654	−	0.156654i	$-0.949929\pi$
$59$	−0.741585	+	2.28236i	−0.0965461	+	0.297138i	0.891107	+	0.453792i	$0.149929\pi$
$60$	8.85752	+	6.43536i	1.14350	+	0.830802i
$61$	1.14241	+	0.830012i	0.146271	+	0.106272i	0.658514	−	0.752568i	$-0.271185\pi$
$61$	1.14241	+	0.830012i	0.146271	+	0.106272i	−0.512243	+	0.858841i	$0.671185\pi$
$62$	−0.381287	+	1.17348i	−0.0484234	+	0.149032i
$63$	6.34643	+	19.5323i	0.799575	+	2.46084i
$64$	5.27100	−	3.82961i	0.658875	−	0.478701i
$65$	1.84447			0.228779
$66$	1.56604	+	2.02831i	0.192766	+	0.249668i
$67$	−15.7025			−1.91836			−0.959181	−	0.282794i	$-0.908739\pi$
$67$	−15.7025			−1.91836			−0.959181	+	0.282794i	$0.908739\pi$
$68$	−9.52461	+	6.92003i	−1.15503	+	0.839177i
$69$	6.64120	+	20.4395i	0.799506	+	2.46063i
$70$	−0.461308	+	1.41976i	−0.0551369	+	0.169694i
$71$	3.62190	+	2.63146i	0.429840	+	0.312297i	0.781585	−	0.623799i	$-0.214412\pi$
$71$	3.62190	+	2.63146i	0.429840	+	0.312297i	−0.351745	+	0.936096i	$0.614412\pi$
$72$	−5.13421	−	3.73022i	−0.605072	−	0.439611i
$73$	0.860955	−	2.64975i	0.100767	−	0.310129i	−0.887947	−	0.459947i	$-0.847869\pi$
$73$	0.860955	−	2.64975i	0.100767	−	0.310129i	0.988714	+	0.149817i	$0.0478685\pi$
$74$	−0.120301	−	0.370250i	−0.0139848	−	0.0430406i
$75$	3.96264	−	2.87903i	0.457566	−	0.332441i
$76$	6.57738			0.754478
$77$	6.00572	−	8.79463i	0.684416	−	1.00224i
$78$	−0.772630			−0.0874831
$79$	7.17961	−	5.21629i	0.807769	−	0.586878i	−0.105414	−	0.994428i	$-0.533617\pi$
$79$	7.17961	−	5.21629i	0.807769	−	0.586878i	0.913183	+	0.407550i	$0.133617\pi$
$80$	2.06492	+	6.35518i	0.230865	+	0.710530i
$81$	3.93100	−	12.0984i	0.436778	−	1.34426i
$82$	−1.12124	−	0.814627i	−0.123820	−	0.0899605i
$83$	−7.23835	−	5.25897i	−0.794512	−	0.577247i	0.114787	−	0.993390i	$-0.463381\pi$
$83$	−7.23835	−	5.25897i	−0.794512	−	0.577247i	−0.909299	+	0.416144i	$0.863381\pi$
$84$	−5.88982	+	18.1270i	−0.642632	+	1.97782i
$85$	−3.46525	−	10.6649i	−0.375859	−	1.15677i
$86$	−1.23913	+	0.900284i	−0.133619	+	0.0970801i
$87$	11.7815			1.26311
$88$	0.0959839	+	3.28941i	0.0102319	+	0.350652i
$89$	0.928281			0.0983976			0.0491988	−	0.998789i	$-0.484333\pi$
$89$	0.928281			0.0983976			0.0491988	+	0.998789i	$0.484333\pi$
$90$	2.40569	−	1.74783i	0.253582	−	0.184238i
$91$	0.992247	+	3.05382i	0.104016	+	0.320127i
$92$	−4.19551	+	12.9124i	−0.437412	+	1.34622i
$93$	−12.1395	−	8.81983i	−1.25880	−	0.914574i
$94$	−0.871436	−	0.633135i	−0.0898818	−	0.0653029i
$95$	−1.93597	+	5.95829i	−0.198626	+	0.611308i
$96$	−2.74468	−	8.44726i	−0.280128	−	0.862145i
$97$	−8.68068	+	6.30689i	−0.881390	+	0.640367i	−0.933619	−	0.358268i	$-0.883367\pi$
$97$	−8.68068	+	6.30689i	−0.881390	+	0.640367i	0.0522290	+	0.998635i	$0.483367\pi$
$98$	−0.834405			−0.0842877
$99$	−19.9752	+	7.14090i	−2.00758	+	0.717687i
$100$	3.09432			0.309432
$101$	−9.18181	+	6.67097i	−0.913624	+	0.663787i	−0.941929	−	0.335813i	$-0.890989\pi$
$101$	−9.18181	+	6.67097i	−0.913624	+	0.663787i	0.0283049	+	0.999599i	$0.490989\pi$
$102$	1.45155	+	4.46742i	0.143725	+	0.442341i
$103$	3.65584	−	11.2515i	0.360221	−	1.10865i	−0.592699	−	0.805424i	$-0.701938\pi$
$103$	3.65584	−	11.2515i	0.360221	−	1.10865i	0.952920	−	0.303222i	$-0.0980623\pi$
$104$	−0.802719	−	0.583210i	−0.0787131	−	0.0571884i
$105$	−14.6872	−	10.6709i	−1.43332	−	1.04137i
$106$	−0.175904	+	0.541377i	−0.0170853	+	0.0525832i
$107$	3.17202	+	9.76246i	0.306650	+	0.943773i	0.979056	+	0.203590i	$0.0652610\pi$
$107$	3.17202	+	9.76246i	0.306650	+	0.943773i	−0.672406	+	0.740183i	$0.734739\pi$
$108$	16.3083	−	11.8487i	1.56927	−	1.14014i
$109$	17.0997			1.63786			0.818929	−	0.573895i	$-0.194568\pi$
$109$	17.0997			1.63786			0.818929	+	0.573895i	$0.194568\pi$
$110$	−1.47975	−	0.433511i	−0.141088	−	0.0413336i
$111$	4.73435			0.449365
$112$	−9.41118	+	6.83762i	−0.889273	+	0.646094i
$113$	−2.37168	−	7.29927i	−0.223109	−	0.686658i	−0.998478	−	0.0551499i	$-0.982436\pi$
$113$	−2.37168	−	7.29927i	−0.223109	−	0.686658i	0.775369	−	0.631508i	$-0.217564\pi$
$114$	0.810955	−	2.49586i	0.0759529	−	0.233759i
$115$	−10.4622	−	7.60121i	−0.975603	−	0.708817i
$116$	6.02136	+	4.37478i	0.559070	+	0.406188i
$117$	1.97648	−	6.08297i	0.182725	−	0.562371i
$118$	0.186922	+	0.575287i	0.0172076	+	0.0529594i
$119$	15.7934	−	11.4745i	1.44777	−	1.05187i
$120$	5.60984			0.512106
$121$	9.26106	+	5.93573i	0.841914	+	0.539612i
$122$	0.355930			0.0322244
$123$	13.6355	−	9.90675i	1.22947	−	0.893262i
$124$	−2.92929	−	9.01542i	−0.263058	−	0.809609i
$125$	−3.76064	+	11.5741i	−0.336362	+	1.03522i
$126$	4.18798	+	3.04274i	0.373094	+	0.271069i
$127$	−8.75209	−	6.35877i	−0.776622	−	0.564249i	0.127341	−	0.991859i	$-0.459356\pi$
$127$	−8.75209	−	6.35877i	−0.776622	−	0.564249i	−0.903963	+	0.427610i	$0.859356\pi$
$128$	2.29829	−	7.07341i	0.203142	−	0.625207i
$129$	−5.75593	−	17.7149i	−0.506782	−	1.55971i
$130$	0.376123	−	0.273269i	0.0329881	−	0.0239673i
$131$	0.802380			0.0701043			0.0350521	−	0.999385i	$-0.488840\pi$
$131$	0.802380			0.0701043			0.0350521	+	0.999385i	$0.488840\pi$
$132$	−18.8929	−	5.53490i	−1.64441	−	0.481751i
$133$	−10.9064			−0.945702
$134$	−3.20203	+	2.32641i	−0.276613	+	0.200971i
$135$	5.93330	+	18.2608i	0.510657	+	1.57164i
$136$	−1.86409	+	5.73709i	−0.159845	+	0.491952i
$137$	8.20593	+	5.96196i	0.701080	+	0.509365i	0.880284	−	0.474447i	$-0.157352\pi$
$137$	8.20593	+	5.96196i	0.701080	+	0.509365i	−0.179204	+	0.983812i	$0.557352\pi$
$138$	4.38249	+	3.18407i	0.373062	+	0.271046i
$139$	−6.13238	+	18.8735i	−0.520142	+	1.60083i	0.253586	+	0.967313i	$0.418390\pi$
$139$	−6.13238	+	18.8735i	−0.520142	+	1.60083i	−0.773727	+	0.633519i	$0.781610\pi$
$140$	−3.54407	−	10.9075i	−0.299528	−	0.921854i
$141$	10.5976	−	7.69961i	0.892480	−	0.648425i
$142$	1.12844			0.0946964
$143$	−3.12306	+	1.11646i	−0.261164	+	0.0933630i
$144$	23.1717			1.93098
$145$	−5.73531	+	4.16695i	−0.476292	+	0.346046i
$146$	−0.217010	−	0.667888i	−0.0179599	−	0.0552748i
$147$	3.13568	−	9.65064i	0.258627	−	0.795971i
$148$	2.41967	+	1.75799i	0.198896	+	0.144506i
$149$	0.522667	+	0.379740i	0.0428185	+	0.0311095i	0.608989	−	0.793179i	$-0.291575\pi$
$149$	0.522667	+	0.379740i	0.0428185	+	0.0311095i	−0.566170	+	0.824288i	$0.691575\pi$
$150$	0.381512	−	1.17417i	0.0311504	−	0.0958709i
$151$	1.43776	+	4.42497i	0.117003	+	0.360099i	0.992360	−	0.123379i	$-0.0393732\pi$
$151$	1.43776	+	4.42497i	0.117003	+	0.360099i	−0.875356	+	0.483478i	$0.839373\pi$
$152$	2.72651	−	1.98092i	0.221149	−	0.160674i
$153$	−38.8856			−3.14372
$154$	−0.0782941	−	2.68317i	−0.00630912	−	0.216216i
$155$	9.02905			0.725231
$156$	4.80219	−	3.48900i	0.384483	−	0.279343i
$157$	−2.15944	−	6.64609i	−0.172342	−	0.530416i	0.827160	−	0.561967i	$-0.189955\pi$
$157$	−2.15944	−	6.64609i	−0.172342	−	0.530416i	−0.999502	+	0.0315514i	$0.989955\pi$
$158$	0.691234	−	2.12740i	0.0549916	−	0.169247i
$159$	−5.60046	−	4.06897i	−0.444145	−	0.322690i
$160$	4.32382	+	3.14144i	0.341828	+	0.248353i
$161$	6.95683	−	21.4109i	0.548275	−	1.68742i
$162$	−0.990838	−	3.04949i	−0.0778476	−	0.239590i
$163$	−7.36401	+	5.35026i	−0.576794	+	0.419065i	−0.837567	−	0.546335i	$-0.816023\pi$
$163$	−7.36401	+	5.35026i	−0.576794	+	0.419065i	0.260773	+	0.965400i	$0.416023\pi$
$164$	10.6476			0.831436
$165$	10.5748	−	15.4855i	0.823247	−	1.20554i
$166$	−2.25518			−0.175036
$167$	−7.74160	+	5.62460i	−0.599063	+	0.435245i	−0.845546	−	0.533902i	$-0.820725\pi$
$167$	−7.74160	+	5.62460i	−0.599063	+	0.435245i	0.246483	+	0.969147i	$0.420725\pi$
$168$	3.01785	+	9.28799i	0.232832	+	0.716584i
$169$	0.309017	−	0.951057i	0.0237705	−	0.0731582i
$170$	−2.28670	−	1.66138i	−0.175382	−	0.127422i
$171$	17.5756	+	12.7694i	1.34404	+	0.976502i
$172$	3.63625	−	11.1912i	0.277262	−	0.853323i
$173$	−1.45508	−	4.47829i	−0.110628	−	0.340478i	0.880382	−	0.474265i	$-0.157286\pi$
$173$	−1.45508	−	4.47829i	−0.110628	−	0.340478i	−0.991010	+	0.133787i	$0.957286\pi$
$174$	2.40246	−	1.74549i	0.182130	−	0.132325i
$175$	−5.13088			−0.387858
$176$	−7.34312	−	9.51069i	−0.553508	−	0.716895i
$177$	−7.35615			−0.552922
$178$	0.189294	−	0.137530i	0.0141882	−	0.0103083i
$179$	−0.734289	−	2.25991i	−0.0548833	−	0.168914i	0.919857	−	0.392253i	$-0.128304\pi$
$179$	−0.734289	−	2.25991i	−0.0548833	−	0.168914i	−0.974741	+	0.223339i	$0.928304\pi$
$180$	−7.05951	+	21.7269i	−0.526185	+	1.61943i
$181$	8.88408	+	6.45466i	0.660349	+	0.479771i	0.866781	−	0.498690i	$-0.166185\pi$
$181$	8.88408	+	6.45466i	0.660349	+	0.479771i	−0.206432	+	0.978461i	$0.566185\pi$
$182$	0.654779	+	0.475724i	0.0485354	+	0.0352630i
$183$	−1.33758	+	4.11665i	−0.0988768	+	0.304311i
$184$	2.14971	+	6.61614i	0.158479	+	0.487748i
$185$	−2.30472	+	1.67448i	−0.169447	+	0.123110i
$186$	−3.78217			−0.277322
$187$	12.3228	+	15.9604i	0.901135	+	1.16714i
$188$	8.27539			0.603545
$189$	−27.0419	+	19.6471i	−1.96701	+	1.42911i
$190$	0.487974	+	1.50183i	0.0354014	+	0.108954i
$191$	−0.826491	+	2.54368i	−0.0598028	+	0.184054i	−0.976495	−	0.215540i	$-0.930849\pi$
$191$	−0.826491	+	2.54368i	−0.0598028	+	0.184054i	0.916692	+	0.399594i	$0.130849\pi$
$192$	16.1572	+	11.7389i	1.16604	+	0.847180i
$193$	9.66618	+	7.02289i	0.695787	+	0.505519i	0.878557	−	0.477637i	$-0.158507\pi$
$193$	9.66618	+	7.02289i	0.695787	+	0.505519i	−0.182770	+	0.983156i	$0.558507\pi$
$194$	−0.835753	+	2.57218i	−0.0600036	+	0.184672i
$195$	1.74714	+	5.37713i	0.125115	+	0.385064i
$196$	5.18615	−	3.76796i	0.370440	−	0.269140i
$197$	4.24305			0.302305			0.151152	−	0.988510i	$-0.451702\pi$
$197$	4.24305			0.302305			0.151152	+	0.988510i	$0.451702\pi$
$198$	−3.01535	+	4.41560i	−0.214291	+	0.313803i
$199$	−17.9236			−1.27057			−0.635287	−	0.772276i	$-0.719118\pi$
$199$	−17.9236			−1.27057			−0.635287	+	0.772276i	$0.719118\pi$
$200$	1.28268	−	0.931922i	0.0906992	−	0.0658969i
$201$	−14.8738	−	45.7769i	−1.04912	−	3.22885i
$202$	−0.884000	+	2.72067i	−0.0621980	+	0.191426i
$203$	−9.98440	−	7.25409i	−0.700768	−	0.509138i
$204$	−29.1957	−	21.2119i	−2.04411	−	1.48513i
$205$	−3.13397	+	9.64538i	−0.218886	+	0.673663i
$206$	−0.921482	−	2.83603i	−0.0642027	−	0.197596i
$207$	−36.2793	+	26.3585i	−2.52159	+	1.83204i
$208$	3.62284			0.251199
$209$	−0.328576	−	11.2604i	−0.0227281	−	0.778899i
$210$	−4.57595			−0.315770
$211$	18.0048	−	13.0812i	1.23950	−	0.900550i	0.241936	−	0.970292i	$-0.422218\pi$
$211$	18.0048	−	13.0812i	1.23950	−	0.900550i	0.997565	+	0.0697421i	$0.0222176\pi$
$212$	−1.35141	−	4.15921i	−0.0928151	−	0.285655i
$213$	−4.24065	+	13.0514i	−0.290565	+	0.894266i
$214$	2.09320	+	1.52080i	0.143088	+	0.103960i
$215$	9.06758	+	6.58798i	0.618404	+	0.449297i
$216$	3.19176	−	9.82323i	0.217172	−	0.668386i
$217$	4.85724	+	14.9490i	0.329731	+	1.01481i
$218$	3.48696	−	2.53342i	0.236166	−	0.171585i
$219$	8.54024			0.577096
$220$	11.1548	−	3.98773i	0.752059	−	0.268853i
$221$	−6.07966			−0.408962
$222$	0.965423	−	0.701421i	0.0647950	−	0.0470763i
$223$	0.531120	+	1.63462i	0.0355664	+	0.109462i	0.967264	−	0.253774i	$-0.0816719\pi$
$223$	0.531120	+	1.63462i	0.0355664	+	0.109462i	−0.931697	+	0.363236i	$0.881672\pi$
$224$	−2.87513	+	8.84874i	−0.192103	+	0.591231i
$225$	8.26841	+	6.00735i	0.551228	+	0.400490i
$226$	−1.56506	−	1.13708i	−0.104106	−	0.0756375i
$227$	−7.45546	+	22.9455i	−0.494836	+	1.52295i	0.322375	+	0.946612i	$0.395519\pi$
$227$	−7.45546	+	22.9455i	−0.494836	+	1.52295i	−0.817212	+	0.576338i	$0.804481\pi$
$228$	6.23028	+	19.1748i	0.412610	+	1.26988i
$229$	−3.08058	+	2.23817i	−0.203570	+	0.147903i	−0.684900	−	0.728637i	$-0.740154\pi$
$229$	−3.08058	+	2.23817i	−0.203570	+	0.147903i	0.481329	+	0.876540i	$0.340154\pi$
$230$	−3.25960			−0.214931
$231$	31.3275	+	9.17777i	2.06120	+	0.603853i
$232$	3.81358			0.250374
$233$	7.34568	−	5.33695i	0.481231	−	0.349635i	−0.320571	−	0.947225i	$-0.603875\pi$
$233$	7.34568	−	5.33695i	0.481231	−	0.349635i	0.801802	+	0.597589i	$0.203875\pi$
$234$	−0.498186	−	1.53326i	−0.0325674	−	0.100232i
$235$	−2.43575	+	7.49647i	−0.158891	+	0.489016i
$236$	−3.75964	−	2.73154i	−0.244732	−	0.177808i
$237$	22.0076	+	15.9895i	1.42955	+	1.03863i
$238$	1.52054	−	4.67975i	0.0985621	−	0.303343i
$239$	−3.15771	−	9.71843i	−0.204255	−	0.628633i	−0.999743	−	0.0226637i	$-0.992785\pi$
$239$	−3.15771	−	9.71843i	−0.204255	−	0.628633i	0.795488	−	0.605970i	$-0.207215\pi$
$240$	−16.5711	+	12.0396i	−1.06966	+	0.777153i
$241$	18.0160			1.16051			0.580257	−	0.814434i	$-0.302952\pi$
$241$	18.0160			1.16051			0.580257	+	0.814434i	$0.302952\pi$
$242$	2.76791	−	0.161671i	0.177928	−	0.0103926i
$243$	7.76420			0.498074
$244$	−2.21225	+	1.60729i	−0.141624	+	0.102896i
$245$	1.88683	+	5.80706i	0.120545	+	0.370999i
$246$	1.31279	−	4.04035i	0.0837003	−	0.257603i
$247$	2.74790	+	1.99646i	0.174845	+	0.127032i
$248$	−3.92946	−	2.85492i	−0.249521	−	0.181288i
$249$	8.47493	−	26.0831i	0.537077	−	1.65295i
$250$	0.947897	+	2.91733i	0.0599503	+	0.184508i
$251$	−7.91714	+	5.75214i	−0.499725	+	0.363072i	−0.808912	−	0.587930i	$-0.799943\pi$
$251$	−7.91714	+	5.75214i	−0.499725	+	0.363072i	0.309187	+	0.951001i	$0.399943\pi$
$252$	−39.7701			−2.50528
$253$	22.3156	+	6.53762i	1.40297	+	0.411017i
$254$	−2.72680			−0.171095
$255$	27.8087	−	20.2042i	1.74145	−	1.26524i
$256$	3.44739	+	10.6100i	0.215462	+	0.663123i
$257$	−1.33960	+	4.12285i	−0.0835617	+	0.257177i	−0.984104	−	0.177591i	$-0.943170\pi$
$257$	−1.33960	+	4.12285i	−0.0835617	+	0.257177i	0.900543	+	0.434768i	$0.143170\pi$
$258$	−3.79831	−	2.75963i	−0.236472	−	0.171807i
$259$	−4.01221	−	2.91504i	−0.249307	−	0.181132i
$260$	−1.10373	+	3.39695i	−0.0684507	+	0.210670i
$261$	7.59660	+	23.3799i	0.470218	+	1.44718i
$262$	0.163620	−	0.118877i	0.0101085	−	0.00734425i
$263$	10.7766			0.664514			0.332257	−	0.943189i	$-0.392190\pi$
$263$	10.7766			0.664514			0.332257	+	0.943189i	$0.392190\pi$
$264$	−9.49858	+	3.39564i	−0.584597	+	0.208987i
$265$	4.16549			0.255884
$266$	−2.22401	+	1.61584i	−0.136363	+	0.0990735i
$267$	0.879293	+	2.70619i	0.0538119	+	0.165616i
$268$	9.39637	−	28.9191i	0.573975	−	1.76651i
$269$	−7.83476	−	5.69228i	−0.477694	−	0.347065i	0.322739	−	0.946488i	$-0.395397\pi$
$269$	−7.83476	−	5.69228i	−0.477694	−	0.347065i	−0.800432	+	0.599423i	$0.795397\pi$
$270$	3.91536	+	2.84467i	0.238281	+	0.173121i
$271$	5.45763	−	16.7969i	0.331527	−	1.02034i	−0.636880	−	0.770963i	$-0.719775\pi$
$271$	5.45763	−	16.7969i	0.331527	−	1.02034i	0.968407	−	0.249373i	$-0.0802246\pi$
$272$	−6.80630	−	20.9476i	−0.412692	−	1.27014i
$273$	−7.96282	+	5.78533i	−0.481932	+	0.350144i
$274$	2.55664			0.154452
$275$	−0.154578	−	5.29744i	−0.00932140	−	0.319448i
$276$	−41.6173			−2.50507
$277$	4.40091	−	3.19745i	0.264425	−	0.192116i	−0.447671	−	0.894199i	$-0.647746\pi$
$277$	4.40091	−	3.19745i	0.264425	−	0.192116i	0.712096	+	0.702083i	$0.247746\pi$
$278$	1.54571	+	4.75721i	0.0927056	+	0.285319i
$279$	9.67524	−	29.7773i	0.579241	−	1.78272i
$280$	−4.75415	−	3.45410i	−0.284115	−	0.206422i
$281$	22.8192	+	16.5791i	1.36128	+	0.989026i	0.998363	+	0.0572036i	$0.0182184\pi$
$281$	22.8192	+	16.5791i	1.36128	+	0.989026i	0.362915	+	0.931822i	$0.381782\pi$
$282$	1.02031	−	3.14019i	0.0607586	−	0.186996i
$283$	−6.01313	−	18.5065i	−0.357443	−	1.10010i	−0.954579	−	0.297957i	$-0.903695\pi$
$283$	−6.01313	−	18.5065i	−0.357443	−	1.10010i	0.597136	−	0.802140i	$-0.296305\pi$
$284$	−7.01368	+	5.09574i	−0.416186	+	0.302376i
$285$	−19.2038			−1.13754
$286$	−0.471441	+	0.690366i	−0.0278769	+	0.0408222i
$287$	−17.6554			−1.04217
$288$	14.9936	−	10.8935i	0.883504	−	0.641904i
$289$	6.16869	+	18.9853i	0.362864	+	1.11678i
$290$	−0.552181	+	1.69944i	−0.0324252	+	0.0997944i
$291$	−26.6088	−	19.3324i	−1.55984	−	1.13329i
$292$	4.36482	+	3.17122i	0.255431	+	0.185582i
$293$	6.13456	−	18.8802i	0.358385	−	1.10299i	−0.595636	−	0.803254i	$-0.703100\pi$
$293$	6.13456	−	18.8802i	0.358385	−	1.10299i	0.954021	−	0.299740i	$-0.0968999\pi$
$294$	−0.790372	−	2.43251i	−0.0460954	−	0.141867i
$295$	3.58103	−	2.60177i	0.208496	−	0.151481i
$296$	1.53248			0.0890736
$297$	−21.0996	−	27.3278i	−1.22432	−	1.58572i
$298$	0.162842			0.00943319
$299$	−5.67217	+	4.12108i	−0.328030	+	0.238328i
$300$	2.93102	+	9.02076i	0.169223	+	0.520814i
$301$	−6.02950	+	18.5569i	−0.347534	+	1.06960i
$302$	0.948770	+	0.689322i	0.0545956	+	0.0396660i
$303$	−28.1449	−	20.4485i	−1.61688	−	1.17473i
$304$	−3.80255	+	11.7030i	−0.218091	+	0.671215i
$305$	−0.804860	−	2.47710i	−0.0460861	−	0.141839i
$306$	−7.92951	+	5.76113i	−0.453300	+	0.329342i
$307$	−28.6421			−1.63469			−0.817345	−	0.576149i	$-0.804555\pi$
$307$	−28.6421			−1.63469			−0.817345	+	0.576149i	$0.804555\pi$
$308$	12.6031	+	16.3234i	0.718131	+	0.930112i
$309$	36.2641			2.06299
$310$	1.84119	−	1.33770i	0.104573	−	0.0759765i
$311$	−8.70834	−	26.8015i	−0.493805	−	1.51978i	−0.818811	−	0.574063i	$-0.805366\pi$
$311$	−8.70834	−	26.8015i	−0.493805	−	1.51978i	0.325006	−	0.945712i	$-0.394634\pi$
$312$	0.939854	−	2.89257i	0.0532088	−	0.163760i
$313$	−1.40337	−	1.01961i	−0.0793234	−	0.0576318i	0.547417	−	0.836860i	$-0.315611\pi$
$313$	−1.40337	−	1.01961i	−0.0793234	−	0.0576318i	−0.626740	+	0.779228i	$0.715611\pi$
$314$	−1.42501	−	1.03533i	−0.0804178	−	0.0584269i
$315$	11.7058	−	36.0268i	0.659548	−	2.02988i
$316$	5.31050	+	16.3440i	0.298739	+	0.919424i
$317$	−3.91151	+	2.84188i	−0.219692	+	0.159616i	−0.692188	−	0.721717i	$-0.743353\pi$
$317$	−3.91151	+	2.84188i	−0.219692	+	0.159616i	0.472496	+	0.881333i	$0.343353\pi$
$318$	−1.74488			−0.0978480
$319$	7.18878	−	10.5271i	0.402494	−	0.589402i
$320$	−12.0173			−0.671789
$321$	−25.4556	+	18.4945i	−1.42079	+	1.03226i
$322$	−1.75352	−	5.39678i	−0.0977199	−	0.300751i
$323$	6.38124	−	19.6394i	0.355062	−	1.09277i
$324$	19.9292	+	14.4794i	1.10718	+	0.804410i
$325$	1.29274	+	0.939234i	0.0717085	+	0.0520993i
$326$	−0.708987	+	2.18204i	−0.0392672	+	0.120852i
$327$	16.1973	+	49.8503i	0.895715	+	2.75673i
$328$	4.41372	−	3.20675i	0.243707	−	0.177063i
$329$	−13.7219			−0.756515
$330$	−0.137859	−	4.72449i	−0.00758891	−	0.260075i
$331$	−0.708422			−0.0389384			−0.0194692	−	0.999810i	$-0.506198\pi$
$331$	−0.708422			−0.0389384			−0.0194692	+	0.999810i	$0.506198\pi$
$332$	14.0168	−	10.1838i	0.769273	−	0.558909i
$333$	3.05268	+	9.39517i	0.167286	+	0.514852i
$334$	−0.745341	+	2.29392i	−0.0407833	+	0.125518i
$335$	23.4314	+	17.0239i	1.28019	+	0.930114i
$336$	−28.8480	−	20.9593i	−1.57379	−	1.14342i
$337$	1.27882	−	3.93580i	0.0696618	−	0.214397i	−0.910165	−	0.414246i	$-0.864045\pi$
$337$	1.27882	−	3.93580i	0.0696618	−	0.214397i	0.979827	+	0.199849i	$0.0640453\pi$
$338$	−0.0778900	−	0.239721i	−0.00423666	−	0.0130391i
$339$	19.0328	−	13.8281i	1.03372	−	0.751042i
$340$	21.7151			1.17767
$341$	−15.2880	+	5.46528i	−0.827891	+	0.295962i
$342$	5.47586			0.296100
$343$	9.58466	−	6.96366i	0.517523	−	0.376002i
$344$	−1.86316	−	5.73421i	−0.100455	−	0.309168i
$345$	12.2495	−	37.7001i	0.659491	−	2.02971i
$346$	−0.960203	−	0.697628i	−0.0516208	−	0.0375047i
$347$	2.78201	+	2.02125i	0.149346	+	0.108506i	0.659949	−	0.751310i	$-0.270578\pi$
$347$	2.78201	+	2.02125i	0.149346	+	0.108506i	−0.510603	+	0.859817i	$0.670578\pi$
$348$	−7.05004	+	21.6978i	−0.377922	+	1.16312i
$349$	2.90042	+	8.92659i	0.155256	+	0.477829i	0.998187	−	0.0601930i	$-0.0191716\pi$
$349$	2.90042	+	8.92659i	0.155256	+	0.477829i	−0.842931	+	0.538022i	$0.819172\pi$
$350$	−1.04628	+	0.760169i	−0.0559262	+	0.0406328i
$351$	10.4098			0.555633
$352$	−9.22261	−	2.70188i	−0.491567	−	0.144011i
$353$	6.22558			0.331354			0.165677	−	0.986180i	$-0.447019\pi$
$353$	6.22558			0.331354			0.165677	+	0.986180i	$0.447019\pi$
$354$	−1.50006	+	1.08985i	−0.0797271	+	0.0579251i
$355$	−2.55172	−	7.85339i	−0.135431	−	0.416814i
$356$	−0.555485	+	1.70961i	−0.0294406	+	0.0906089i
$357$	48.4113	+	35.1728i	2.56220	+	1.86154i
$358$	−0.484553	−	0.352049i	−0.0256094	−	0.0186064i
$359$	9.44738	−	29.0760i	0.498614	−	1.53457i	−0.312635	−	0.949873i	$-0.601212\pi$
$359$	9.44738	−	29.0760i	0.498614	−	1.53457i	0.811249	−	0.584701i	$-0.198788\pi$
$360$	3.61718	+	11.1325i	0.190642	+	0.586737i
$361$	6.03784	−	4.38675i	0.317781	−	0.230882i
$362$	2.76793			0.145479
$363$	−8.53190	+	32.6209i	−0.447809	+	1.71215i
$364$	−6.21795			−0.325909
$365$	−4.15746	+	3.02057i	−0.217611	+	0.158104i
$366$	0.337147	+	1.03763i	0.0176230	+	0.0542379i
$367$	−10.1805	+	31.3324i	−0.531419	+	1.63554i	0.219844	+	0.975535i	$0.429445\pi$
$367$	−10.1805	+	31.3324i	−0.531419	+	1.63554i	−0.751263	+	0.660004i	$0.770555\pi$
$368$	−20.5494	−	14.9300i	−1.07121	−	0.778280i
$369$	28.4517	+	20.6714i	1.48114	+	1.07611i
$370$	−0.221893	+	0.682915i	−0.0115357	+	0.0355031i
$371$	2.24085	+	6.89664i	0.116339	+	0.358056i
$372$	23.5077	−	17.0793i	1.21882	−	0.885521i
$373$	−21.6720			−1.12213			−0.561066	−	0.827771i	$-0.689608\pi$
$373$	−21.6720			−1.12213			−0.561066	+	0.827771i	$0.689608\pi$
$374$	4.87747	+	1.42892i	0.252208	+	0.0738875i
$375$	−37.3036			−1.92635
$376$	3.43038	−	2.49232i	0.176908	−	0.128531i
$377$	1.18771	+	3.65539i	0.0611701	+	0.188262i
$378$	−2.60352	+	8.01281i	−0.133911	+	0.412135i
$379$	−5.14859	−	3.74067i	−0.264465	−	0.192145i	0.447648	−	0.894210i	$-0.352262\pi$
$379$	−5.14859	−	3.74067i	−0.264465	−	0.192145i	−0.712113	+	0.702065i	$0.752262\pi$
$380$	−9.81484	−	7.13090i	−0.503490	−	0.365807i
$381$	10.2473	−	31.5379i	0.524984	−	1.61573i
$382$	0.208323	+	0.641153i	0.0106587	+	0.0328042i
$383$	−28.5504	+	20.7431i	−1.45886	+	1.05992i	−0.475202	+	0.879877i	$0.657625\pi$
$383$	−28.5504	+	20.7431i	−1.45886	+	1.05992i	−0.983658	+	0.180047i	$0.942375\pi$
$384$	22.7979			1.16340
$385$	−18.4965	+	6.61230i	−0.942670	+	0.336994i
$386$	3.01160			0.153286
$387$	31.4433	−	22.8449i	1.59836	−	1.16127i
$388$	−6.42079	−	19.7612i	−0.325966	−	1.00322i
$389$	−10.2383	+	31.5102i	−0.519101	+	1.59763i	0.256592	+	0.966520i	$0.417400\pi$
$389$	−10.2383	+	31.5102i	−0.519101	+	1.59763i	−0.775693	+	0.631110i	$0.782600\pi$
$390$	1.15293	+	0.837650i	0.0583807	+	0.0424160i
$391$	34.4849	+	25.0548i	1.74398	+	1.26707i
$392$	1.01500	−	3.12385i	0.0512653	−	0.157778i
$393$	0.760036	+	2.33915i	0.0383388	+	0.117995i
$394$	0.865238	−	0.628632i	0.0435901	−	0.0316700i
$395$	−16.3687			−0.823601
$396$	−1.19815	−	41.0612i	−0.0602094	−	2.06340i
$397$	−10.2548			−0.514674			−0.257337	−	0.966322i	$-0.582845\pi$
$397$	−10.2548			−0.514674			−0.257337	+	0.966322i	$0.582845\pi$
$398$	−3.65497	+	2.65549i	−0.183207	+	0.133108i
$399$	−10.3308	−	31.7950i	−0.517188	−	1.59174i
$400$	−1.78890	+	5.50567i	−0.0894450	+	0.275284i
$401$	18.0550	+	13.1177i	0.901624	+	0.655068i	0.938883	−	0.344237i	$-0.111862\pi$
$401$	18.0550	+	13.1177i	0.901624	+	0.655068i	−0.0372585	+	0.999306i	$0.511862\pi$
$402$	−9.81515	−	7.13112i	−0.489535	−	0.355668i
$403$	1.51270	−	4.65560i	0.0753528	−	0.231912i
$404$	−6.79146	−	20.9020i	−0.337888	−	1.03991i
$405$	−18.9824	+	13.7915i	−0.943243	+	0.685306i
$406$	−3.11074			−0.154384
$407$	2.88880	−	4.23028i	0.143192	−	0.209687i
$408$	−18.4909			−0.915435
$409$	−22.4546	+	16.3142i	−1.11031	+	0.806687i	−0.982712	−	0.185139i	$-0.940727\pi$
$409$	−22.4546	+	16.3142i	−1.11031	+	0.806687i	−0.127597	+	0.991826i	$0.540727\pi$
$410$	0.789941	+	2.43119i	0.0390124	+	0.120068i
$411$	−9.60782	+	29.5698i	−0.473919	+	1.45857i
$412$	18.5342	+	13.4659i	0.913112	+	0.663415i
$413$	6.23410	+	4.52934i	0.306760	+	0.222874i
$414$	−3.49288	+	10.7500i	−0.171666	+	0.528332i
$415$	5.09960	+	15.6950i	0.250330	+	0.770435i
$416$	2.34420	−	1.70316i	0.114934	−	0.0835045i
$417$	−60.8301			−2.97886
$418$	−1.73530	−	2.24753i	−0.0848762	−	0.109930i
$419$	35.9414			1.75585			0.877926	−	0.478797i	$-0.158927\pi$
$419$	35.9414			1.75585			0.877926	+	0.478797i	$0.158927\pi$
$420$	28.4413	−	20.6638i	1.38779	−	1.00829i
$421$	0.0569580	+	0.175299i	0.00277596	+	0.00854354i	0.952435	−	0.304742i	$-0.0985703\pi$
$421$	0.0569580	+	0.175299i	0.00277596	+	0.00854354i	−0.949659	+	0.313286i	$0.898570\pi$
$422$	1.73345	−	5.33502i	0.0843832	−	0.259705i
$423$	22.1129	+	16.0660i	1.07517	+	0.781154i
$424$	−1.81283	−	1.31710i	−0.0880389	−	0.0639640i
$425$	3.00204	−	9.23933i	0.145620	−	0.448174i
$426$	1.06889	+	3.28970i	0.0517878	+	0.159386i
$427$	3.66826	−	2.66515i	0.177520	−	0.128976i
$428$	−19.8776			−0.960818
$429$	−6.21303	−	8.04702i	−0.299968	−	0.388514i
$430$	2.82510			0.136238
$431$	−18.9486	+	13.7670i	−0.912723	+	0.663132i	−0.941702	−	0.336448i	$-0.890774\pi$
$431$	−18.9486	+	13.7670i	−0.912723	+	0.663132i	0.0289792	+	0.999580i	$0.490774\pi$
$432$	11.6540	+	35.8672i	0.560701	+	1.72566i
$433$	−10.5213	+	32.3811i	−0.505620	+	1.55614i	0.294107	+	0.955773i	$0.404978\pi$
$433$	−10.5213	+	32.3811i	−0.505620	+	1.55614i	−0.799726	+	0.600365i	$0.795022\pi$
$434$	3.20527	+	2.32876i	0.153858	+	0.111784i
$435$	−17.5804	−	12.7729i	−0.842916	−	0.612414i
$436$	−10.2325	+	31.4924i	−0.490048	+	1.50821i
$437$	−7.35898	−	22.6486i	−0.352028	−	1.08343i
$438$	1.74151	−	1.26528i	0.0832128	−	0.0604576i
$439$	−20.9143			−0.998184			−0.499092	−	0.866549i	$-0.666333\pi$
$439$	−20.9143			−0.998184			−0.499092	+	0.866549i	$0.666333\pi$
$440$	3.42300	−	5.01255i	0.163185	−	0.238964i
$441$	21.1732			1.00825
$442$	−1.23976	+	0.900736i	−0.0589692	+	0.0428437i
$443$	5.72541	+	17.6210i	0.272022	+	0.837199i	0.989992	+	0.141124i	$0.0450717\pi$
$443$	5.72541	+	17.6210i	0.272022	+	0.837199i	−0.717970	+	0.696074i	$0.754928\pi$
$444$	−2.83304	+	8.71921i	−0.134450	+	0.413795i
$445$	−1.38519	−	1.00640i	−0.0656643	−	0.0477079i
$446$	0.350484	+	0.254641i	0.0165959	+	0.0120576i
$447$	−0.611958	+	1.88341i	−0.0289446	+	0.0890823i
$448$	−6.46480	−	19.8966i	−0.305433	−	0.940027i
$449$	5.10124	−	3.70627i	0.240742	−	0.174910i	−0.460872	−	0.887467i	$-0.652463\pi$
$449$	5.10124	−	3.70627i	0.240742	−	0.174910i	0.701614	+	0.712557i	$0.252463\pi$
$450$	2.57611			0.121439
$451$	−0.531904	−	18.2286i	−0.0250464	−	0.858349i
$452$	14.8622			0.699059
$453$	−11.5381	+	8.38290i	−0.542106	+	0.393863i
$454$	1.87920	+	5.78360i	0.0881954	+	0.271438i
$455$	1.83017	−	5.63269i	0.0857998	−	0.264065i
$456$	8.35754	+	6.07211i	0.391378	+	0.284353i
$457$	−31.1919	−	22.6622i	−1.45909	−	1.06009i	−0.983598	−	0.180376i	$-0.942269\pi$
$457$	−31.1919	−	22.6622i	−1.45909	−	1.06009i	−0.475496	−	0.879718i	$-0.657731\pi$
$458$	−0.296590	+	0.912810i	−0.0138587	+	0.0426528i
$459$	−19.5571	−	60.1905i	−0.912846	−	2.80945i
$460$	20.2597	−	14.7195i	0.944611	−	0.686300i
$461$	19.3870			0.902941			0.451471	−	0.892286i	$-0.350900\pi$
$461$	19.3870			0.902941			0.451471	+	0.892286i	$0.350900\pi$
$462$	7.74799	−	2.76982i	0.360469	−	0.128864i
$463$	−36.0570			−1.67571			−0.837855	−	0.545892i	$-0.816191\pi$
$463$	−36.0570			−1.67571			−0.837855	+	0.545892i	$0.816191\pi$
$464$	−11.2651	+	8.18455i	−0.522968	+	0.379958i
$465$	8.55256	+	26.3221i	0.396616	+	1.22066i
$466$	0.707223	−	2.17661i	0.0327615	−	0.100829i
$467$	16.3206	+	11.8576i	0.755226	+	0.548704i	0.897442	−	0.441132i	$-0.145423\pi$
$467$	16.3206	+	11.8576i	0.755226	+	0.548704i	−0.142216	+	0.989836i	$0.545423\pi$
$468$	10.0202	+	7.28012i	0.463185	+	0.336524i
$469$	−15.5807	+	47.9525i	−0.719451	+	2.21424i
$470$	0.613949	+	1.88954i	0.0283194	+	0.0871581i
$471$	17.3296	−	12.5907i	0.798507	−	0.580149i
$472$	−2.38114			−0.109601
$473$	−19.3409	−	5.66617i	−0.889297	−	0.260531i
$474$	6.85669			0.314938
$475$	−4.39092	+	3.19019i	−0.201469	+	0.146376i
$476$	11.6818	+	35.9528i	0.535434	+	1.64790i
$477$	4.46361	−	13.7376i	0.204375	−	0.629000i
$478$	−2.08376	−	1.51394i	−0.0953088	−	0.0692459i
$479$	4.53567	+	3.29536i	0.207240	+	0.150569i	0.686564	−	0.727069i	$-0.259118\pi$
$479$	4.53567	+	3.29536i	0.207240	+	0.150569i	−0.479324	+	0.877638i	$0.659118\pi$
$480$	−5.06249	+	15.5807i	−0.231070	+	0.711160i
$481$	0.477278	+	1.46891i	0.0217620	+	0.0669765i
$482$	3.67380	−	2.66917i	0.167337	−	0.121578i
$483$	69.0083			3.13999
$484$	−16.4736	+	13.5040i	−0.748800	+	0.613820i
$485$	19.7910			0.898665
$486$	1.58327	−	1.15031i	0.0718184	−	0.0521791i
$487$	−7.55044	−	23.2379i	−0.342143	−	1.05301i	−0.963096	−	0.269160i	$-0.913254\pi$
$487$	−7.55044	−	23.2379i	−0.342143	−	1.05301i	0.620953	−	0.783848i	$-0.286746\pi$
$488$	−0.432966	+	1.33253i	−0.0195995	+	0.0603209i
$489$	−22.5728	−	16.4001i	−1.02078	−	0.741639i
$490$	1.24511	+	0.904624i	0.0562483	+	0.0408667i
$491$	−3.40525	+	10.4803i	−0.153677	+	0.472968i	−0.998024	−	0.0628273i	$-0.979988\pi$
$491$	−3.40525	+	10.4803i	−0.153677	+	0.472968i	0.844348	+	0.535796i	$0.179988\pi$
$492$	10.0857	+	31.0405i	0.454698	+	1.39942i
$493$	18.9045	−	13.7349i	0.851414	−	0.618589i
$494$	0.856135			0.0385194
$495$	37.5490	+	11.0004i	1.68770	+	0.494433i
$496$	17.7345			0.796302
$497$	11.6298	−	8.44957i	0.521669	−	0.379015i
$498$	−2.13617	−	6.57445i	−0.0957240	−	0.294608i
$499$	7.14198	−	21.9808i	0.319719	−	0.983994i	−0.654049	−	0.756452i	$-0.726931\pi$
$499$	7.14198	−	21.9808i	0.319719	−	0.983994i	0.973768	−	0.227542i	$-0.0730690\pi$
$500$	−19.0655	−	13.8519i	−0.852633	−	0.619474i
$501$	−23.7303	−	17.2411i	−1.06019	−	0.770274i
$502$	−0.762241	+	2.34594i	−0.0340205	+	0.104704i
$503$	−6.18482	−	19.0349i	−0.275767	−	0.848725i	−0.989015	−	0.147813i	$-0.952777\pi$
$503$	−6.18482	−	19.0349i	−0.275767	−	0.848725i	0.713248	−	0.700912i	$-0.247223\pi$
$504$	−16.4858	+	11.9777i	−0.734337	+	0.533527i
$505$	20.9335			0.931531
$506$	5.51915	−	1.97303i	0.245356	−	0.0877120i
$507$	3.06529			0.136134
$508$	16.9481	−	12.3135i	0.751952	−	0.546325i
$509$	7.67235	+	23.6131i	0.340071	+	1.04663i	0.964170	+	0.265286i	$0.0854662\pi$
$509$	7.67235	+	23.6131i	0.340071	+	1.04663i	−0.624099	+	0.781345i	$0.714534\pi$
$510$	2.67735	−	8.24004i	0.118555	−	0.364875i
$511$	−7.23757	−	5.25841i	−0.320171	−	0.232618i
$512$	14.3089	+	10.3960i	0.632371	+	0.459444i
$513$	−10.9262	+	33.6272i	−0.482401	+	1.48468i
$514$	0.337655	+	1.03920i	0.0148933	+	0.0458370i
$515$	−17.6537	+	12.8261i	−0.777914	+	0.565187i
$516$	36.0698			1.58788
$517$	−0.413400	−	14.1674i	−0.0181813	−	0.623081i
$518$	−1.25004			−0.0549238
$519$	11.6771	−	8.48392i	0.512568	−	0.372403i
$520$	0.565537	+	1.74054i	0.0248004	+	0.0763278i
$521$	6.23865	−	19.2006i	0.273320	−	0.841193i	−0.716339	−	0.697753i	$-0.754183\pi$
$521$	6.23865	−	19.2006i	0.273320	−	0.841193i	0.989659	−	0.143440i	$-0.0458165\pi$
$522$	5.01296	+	3.64213i	0.219411	+	0.159412i
$523$	−7.54216	−	5.47970i	−0.329796	−	0.239611i	0.410548	−	0.911839i	$-0.365337\pi$
$523$	−7.54216	−	5.47970i	−0.329796	−	0.239611i	−0.740344	+	0.672228i	$0.765337\pi$
$524$	−0.480145	+	1.47773i	−0.0209752	+	0.0645551i
$525$	−4.86011	−	14.9579i	−0.212113	−	0.652816i
$526$	2.19755	−	1.59661i	0.0958178	−	0.0696157i
$527$	−29.7611			−1.29641
$528$	20.7706	−	30.4159i	0.903924	−	1.32368i
$529$	26.1568			1.13725
$530$	0.849422	−	0.617141i	0.0368965	−	0.0268069i
$531$	−4.74319	−	14.5980i	−0.205837	−	0.633501i
$532$	6.52639	−	20.0862i	0.282955	−	0.870845i
$533$	4.44834	+	3.23191i	0.192679	+	0.139990i
$534$	0.580241	+	0.421570i	0.0251095	+	0.0182431i
$535$	5.85070	−	18.0066i	0.252948	−	0.778493i
$536$	−4.81456	−	14.8177i	−0.207957	−	0.640026i
$537$	5.89270	−	4.28130i	0.254289	−	0.184752i
$538$	−2.44100			−0.105239
$539$	−6.70979	−	8.69042i	−0.289011	−	0.374323i
$540$	−37.1813			−1.60003
$541$	6.35208	−	4.61506i	0.273097	−	0.198417i	−0.442804	−	0.896619i	$-0.646016\pi$
$541$	6.35208	−	4.61506i	0.273097	−	0.198417i	0.715901	+	0.698202i	$0.246016\pi$
$542$	−1.37564	−	4.23377i	−0.0590886	−	0.181856i
$543$	−10.4018	+	32.0135i	−0.446385	+	1.37383i
$544$	−14.2520	−	10.3547i	−0.611048	−	0.443952i
$545$	−25.5164	−	18.5387i	−1.09300	−	0.794113i
$546$	−0.766639	+	2.35947i	−0.0328091	+	0.100976i
$547$	0.721488	+	2.22051i	0.0308486	+	0.0949422i	0.965295	−	0.261161i	$-0.0841053\pi$
$547$	0.721488	+	2.22051i	0.0308486	+	0.0949422i	−0.934447	+	0.356103i	$0.884105\pi$
$548$	−15.8905	+	11.5451i	−0.678809	+	0.493184i
$549$	−9.03182			−0.385469
$550$	−0.816368	−	1.05735i	−0.0348100	−	0.0450854i
$551$	−13.0548			−0.556153
$552$	−17.2515	+	12.5340i	−0.734274	+	0.533481i
$553$	−8.80567	−	27.1011i	−0.374455	−	1.15246i
$554$	0.423708	−	1.30404i	0.0180016	−	0.0554033i
$555$	−7.06465	−	5.13277i	−0.299878	−	0.217874i
$556$	−31.0896	−	22.5879i	−1.31849	−	0.957940i
$557$	11.8471	−	36.4616i	0.501978	−	1.54493i	−0.303815	−	0.952731i	$-0.598260\pi$
$557$	11.8471	−	36.4616i	0.501978	−	1.54493i	0.805793	−	0.592198i	$-0.201740\pi$
$558$	−2.43872	−	7.50559i	−0.103239	−	0.317737i
$559$	4.91608	−	3.57174i	0.207928	−	0.151069i
$560$	21.4565			0.906702
$561$	−34.8561	+	51.0424i	−1.47163	+	2.15501i
$562$	7.10954			0.299898
$563$	−26.3975	+	19.1789i	−1.11252	+	0.808294i	−0.983059	−	0.183290i	$-0.941325\pi$
$563$	−26.3975	+	19.1789i	−1.11252	+	0.808294i	−0.129463	+	0.991584i	$0.541325\pi$
$564$	7.83868	+	24.1250i	0.330068	+	1.01584i
$565$	−4.37449	+	13.4633i	−0.184036	+	0.566406i
$566$	−3.96803	−	2.88294i	−0.166789	−	0.121179i
$567$	−33.0458	−	24.0092i	−1.38779	−	1.00829i
$568$	−1.37267	+	4.22465i	−0.0575960	+	0.177262i
$569$	−2.26827	−	6.98103i	−0.0950909	−	0.292660i	0.892186	−	0.451667i	$-0.149171\pi$
$569$	−2.26827	−	6.98103i	−0.0950909	−	0.292660i	−0.987277	+	0.159007i	$0.949171\pi$
$570$	−3.91601	+	2.84515i	−0.164024	+	0.119170i
$571$	36.5717			1.53048			0.765239	−	0.643747i	$-0.222621\pi$
$571$	36.5717			1.53048			0.765239	+	0.643747i	$0.222621\pi$
$572$	−0.187328	−	6.41980i	−0.00783257	−	0.268425i
$573$	−8.19837			−0.342492
$574$	−3.60027	+	2.61575i	−0.150272	+	0.109179i
$575$	−3.46202	−	10.6550i	−0.144376	−	0.444344i
$576$	−12.8774	+	39.6325i	−0.536558	+	1.65135i
$577$	33.9736	+	24.6833i	1.41434	+	1.02758i	0.992673	+	0.120829i	$0.0385551\pi$
$577$	33.9736	+	24.6833i	1.41434	+	1.02758i	0.421668	+	0.906750i	$0.361445\pi$
$578$	4.07069	+	2.95753i	0.169318	+	0.123017i
$579$	−11.3175	+	34.8318i	−0.470340	+	1.44756i
$580$	−4.24221	−	13.0562i	−0.176148	−	0.542128i
$581$	−23.2422	+	16.8864i	−0.964248	+	0.700567i
$582$	−8.29025			−0.343642
$583$	−7.05301	+	2.52137i	−0.292106	+	0.104425i
$584$	2.76442			0.114393
$585$	−9.54420	+	6.93427i	−0.394604	+	0.286697i
$586$	−1.54626	−	4.75890i	−0.0638754	−	0.196588i
$587$	−0.424035	+	1.30505i	−0.0175018	+	0.0538650i	−0.959426	−	0.281961i	$-0.909015\pi$
$587$	−0.424035	+	1.30505i	−0.0175018	+	0.0538650i	0.941924	+	0.335826i	$0.109015\pi$
$588$	15.8971	+	11.5499i	0.655585	+	0.476310i
$589$	13.4515	+	9.77308i	0.554259	+	0.402693i
$590$	0.344773	−	1.06110i	0.0141941	−	0.0436848i
$591$	4.01914	+	12.3696i	0.165325	+	0.508819i
$592$	−4.52684	+	3.28894i	−0.186052	+	0.135175i
$593$	37.5996			1.54403			0.772015	−	0.635605i	$-0.219249\pi$
$593$	37.5996			1.54403			0.772015	+	0.635605i	$0.219249\pi$
$594$	−8.35136	−	2.44664i	−0.342661	−	0.100387i
$595$	−36.0072			−1.47615
$596$	−1.01213	+	0.735353i	−0.0414583	+	0.0301212i
$597$	−16.9778	−	52.2522i	−0.694854	−	2.13854i
$598$	−0.546102	+	1.68073i	−0.0223318	+	0.0687301i
$599$	−9.36717	−	6.80565i	−0.382732	−	0.278071i	0.379739	−	0.925094i	$-0.376014\pi$
$599$	−9.36717	−	6.80565i	−0.382732	−	0.278071i	−0.762471	+	0.647023i	$0.776014\pi$
$600$	3.93179	+	2.85661i	0.160515	+	0.116621i
$601$	−0.608357	+	1.87233i	−0.0248154	+	0.0763740i	−0.962697	−	0.270581i	$-0.912784\pi$
$601$	−0.608357	+	1.87233i	−0.0248154	+	0.0763740i	0.937882	+	0.346955i	$0.112784\pi$
$602$	1.51978	+	4.67740i	0.0619416	+	0.190637i
$603$	81.2522	−	59.0332i	3.30885	−	2.40402i
$604$	−9.00977			−0.366602
$605$	−7.38420	−	18.8978i	−0.300210	−	0.768303i
$606$	−8.76883			−0.356210
$607$	25.5722	−	18.5793i	1.03794	−	0.754109i	0.0680596	−	0.997681i	$-0.478319\pi$
$607$	25.5722	−	18.5793i	1.03794	−	0.754109i	0.969883	+	0.243572i	$0.0783192\pi$
$608$	3.04133	+	9.36024i	0.123342	+	0.379608i
$609$	11.6901	−	35.9785i	0.473707	−	1.45792i
$610$	−0.531123	−	0.385883i	−0.0215045	−	0.0156240i
$611$	3.45729	+	2.51187i	0.139867	+	0.101619i
$612$	23.2692	−	71.6153i	0.940602	−	2.89488i
$613$	−4.71264	−	14.5040i	−0.190342	−	0.585812i	0.809657	−	0.586903i	$-0.199653\pi$
$613$	−4.71264	−	14.5040i	−0.190342	−	0.585812i	−0.999999	+	0.00109050i	$0.999653\pi$
$614$	−5.84066	+	4.24348i	−0.235710	+	0.171253i
$615$	−31.0874			−1.25357
$616$	10.1405	+	2.97079i	0.408572	+	0.119696i
$617$	28.2471			1.13719			0.568593	−	0.822619i	$-0.307488\pi$
$617$	28.2471			1.13719			0.568593	+	0.822619i	$0.307488\pi$
$618$	7.39493	−	5.37273i	0.297468	−	0.216123i
$619$	0.516947	+	1.59100i	0.0207779	+	0.0639477i	0.960908	−	0.276868i	$-0.0892966\pi$
$619$	0.516947	+	1.59100i	0.0207779	+	0.0639477i	−0.940130	+	0.340816i	$0.889297\pi$
$620$	−5.40299	+	16.6287i	−0.216989	+	0.667825i
$621$	−59.0461	−	42.8995i	−2.36944	−	1.72150i
$622$	−5.74659	−	4.17514i	−0.230417	−	0.167408i
$623$	0.921084	−	2.83480i	0.0369024	−	0.113574i
$624$	3.43165	+	10.5615i	0.137376	+	0.422800i
$625$	11.6960	−	8.49764i	0.467840	−	0.339906i
$626$	−0.437236			−0.0174754
$627$	32.5159	−	11.6241i	1.29856	−	0.464220i
$628$	13.5322			0.539995
$629$	7.59672	−	5.51934i	0.302901	−	0.220070i
$630$	−2.95054	−	9.08082i	−0.117552	−	0.361789i
$631$	−1.79204	+	5.51533i	−0.0713399	+	0.219562i	−0.980369	−	0.197171i	$-0.936825\pi$
$631$	−1.79204	+	5.51533i	−0.0713399	+	0.219562i	0.909029	+	0.416732i	$0.136825\pi$
$632$	7.12372	+	5.17568i	0.283366	+	0.205878i
$633$	55.1900	+	40.0978i	2.19360	+	1.59375i
$634$	−0.376590	+	1.15902i	−0.0149563	+	0.0460307i
$635$	6.16607	+	18.9772i	0.244693	+	0.753088i
$636$	10.8451	−	7.87943i	0.430036	−	0.312440i
$637$	3.31038			0.131162
$638$	−0.0937171	−	3.21172i	−0.00371030	−	0.127153i
$639$	−28.6344			−1.13276
$640$	−11.0982	+	8.06331i	−0.438695	+	0.318730i
$641$	7.94639	+	24.4565i	0.313863	+	0.965972i	0.976220	+	0.216783i	$0.0695565\pi$
$641$	7.94639	+	24.4565i	0.313863	+	0.965972i	−0.662356	+	0.749189i	$0.730444\pi$
$642$	−2.45079	+	7.54277i	−0.0967251	+	0.297689i
$643$	5.00001	+	3.63272i	0.197181	+	0.143261i	0.681995	−	0.731357i	$-0.261113\pi$
$643$	5.00001	+	3.63272i	0.197181	+	0.143261i	−0.484814	+	0.874617i	$0.661113\pi$
$644$	35.2693	+	25.6247i	1.38981	+	1.00975i
$645$	−10.6167	+	32.6747i	−0.418031	+	1.28657i
$646$	−1.60844	−	4.95026i	−0.0632831	−	0.194765i
$647$	−8.92601	+	6.48513i	−0.350918	+	0.254957i	−0.749254	−	0.662283i	$-0.769588\pi$
$647$	−8.92601	+	6.48513i	−0.350918	+	0.254957i	0.398336	+	0.917239i	$0.369588\pi$
$648$	12.6220			0.495838
$649$	−4.48855	+	6.57292i	−0.176191	+	0.258010i
$650$	0.402767			0.0157978
$651$	−38.9795	+	28.3203i	−1.52773	+	1.10996i
$652$	−5.44690	−	16.7638i	−0.213317	−	0.656522i
$653$	−5.45584	+	16.7914i	−0.213504	+	0.657096i	0.785753	+	0.618541i	$0.212276\pi$
$653$	−5.45584	+	16.7914i	−0.213504	+	0.657096i	−0.999256	+	0.0385558i	$0.987724\pi$
$654$	10.6885	+	7.76568i	0.417955	+	0.303662i
$655$	−1.19732	−	0.869903i	−0.0467831	−	0.0339899i
$656$	−6.15562	+	18.9451i	−0.240337	+	0.739681i
$657$	5.50668	+	16.9478i	0.214836	+	0.661198i
$658$	−2.79816	+	2.03298i	−0.109084	+	0.0792539i
$659$	29.1242			1.13452			0.567260	−	0.823539i	$-0.308004\pi$
$659$	29.1242			1.13452			0.567260	+	0.823539i	$0.308004\pi$
$660$	22.1915	+	28.7420i	0.863801	+	1.11878i
$661$	−22.3098			−0.867752			−0.433876	−	0.900973i	$-0.642854\pi$
$661$	−22.3098			−0.867752			−0.433876	+	0.900973i	$0.642854\pi$
$662$	−0.144460	+	0.104957i	−0.00561462	+	0.00407926i
$663$	−5.75882	−	17.7238i	−0.223654	−	0.688337i
$664$	2.74328	−	8.44295i	0.106460	−	0.327650i
$665$	16.2746	+	11.8242i	0.631102	+	0.458522i
$666$	2.01445	+	1.46358i	0.0780582	+	0.0567126i
$667$	8.32725	−	25.6286i	0.322432	−	0.992345i
$668$	−5.72619	−	17.6234i	−0.221553	−	0.681870i
$669$	−4.26226	+	3.09671i	−0.164789	+	0.119726i
$670$	7.30028			0.282034
$671$	2.86218	+	3.70705i	0.110493	+	0.143109i
$672$	−28.5198			−1.10018
$673$	−10.8549	+	7.88655i	−0.418426	+	0.304004i	−0.777004	−	0.629496i	$-0.783262\pi$
$673$	−10.8549	+	7.88655i	−0.418426	+	0.304004i	0.358578	+	0.933500i	$0.383262\pi$
$674$	−0.322336	−	0.992048i	−0.0124159	−	0.0382123i
$675$	−5.14019	+	15.8199i	−0.197846	+	0.608907i
$676$	1.56663	+	1.13823i	0.0602552	+	0.0437780i
$677$	30.1453	+	21.9018i	1.15858	+	0.841756i	0.989598	−	0.143863i	$-0.0459524\pi$
$677$	30.1453	+	21.9018i	1.15858	+	0.841756i	0.168981	+	0.985619i	$0.445952\pi$
$678$	1.83243	−	5.63963i	0.0703740	−	0.216589i
$679$	10.6467	+	32.7672i	0.408584	+	1.25749i
$680$	9.00151	−	6.53998i	0.345192	−	0.250797i
$681$	−73.9544			−2.83394
$682$	−2.30779	+	3.37947i	−0.0883700	+	0.129407i
$683$	28.2710			1.08176			0.540881	−	0.841099i	$-0.318091\pi$
$683$	28.2710			1.08176			0.540881	+	0.841099i	$0.318091\pi$
$684$	−34.0346	+	24.7276i	−1.30134	+	0.945482i
$685$	−5.78129	−	17.7930i	−0.220892	−	0.679835i
$686$	0.922786	−	2.84004i	0.0352321	−	0.108433i
$687$	−9.44287	−	6.86065i	−0.360268	−	0.261750i
$688$	17.8102	+	12.9398i	0.679006	+	0.493327i
$689$	0.697873	−	2.14783i	0.0265868	−	0.0818259i
$690$	−3.08758	−	9.50259i	−0.117542	−	0.361757i
$691$	15.0930	−	10.9657i	0.574164	−	0.417155i	−0.262451	−	0.964945i	$-0.584531\pi$
$691$	15.0930	−	10.9657i	0.574164	−	0.417155i	0.836616	+	0.547790i	$0.184531\pi$
$692$	9.11834			0.346627
$693$	1.98673	+	68.0861i	0.0754697	+	2.58638i
$694$	0.866763			0.0329019
$695$	29.6126	−	21.5148i	1.12327	−	0.816104i
$696$	3.61233	+	11.1176i	0.136925	+	0.421412i
$697$	10.3301	−	31.7926i	0.391279	−	1.20423i
$698$	1.91398	+	1.39058i	0.0724450	+	0.0526344i
$699$	22.5167	+	16.3593i	0.851658	+	0.618766i
$700$	3.07033	−	9.44950i	0.116047	−	0.357157i
$701$	9.81840	+	30.2179i	0.370836	+	1.14131i	0.946245	+	0.323450i	$0.104843\pi$
$701$	9.81840	+	30.2179i	0.370836	+	1.14131i	−0.575410	+	0.817865i	$0.695157\pi$
$702$	2.12275	−	1.54227i	0.0801181	−	0.0582092i
$703$	−5.24604			−0.197858
$704$	20.3477	−	7.27409i	0.766884	−	0.274153i
$705$	−24.1614			−0.909972
$706$	1.26951	−	0.922355i	0.0477787	−	0.0347133i
$707$	11.2613	+	34.6588i	0.423526	+	1.30348i
$708$	4.40193	−	13.5477i	0.165435	−	0.509155i
$709$	−32.2946	−	23.4634i	−1.21285	−	0.881187i	−0.217364	−	0.976091i	$-0.569746\pi$
$709$	−32.2946	−	23.4634i	−1.21285	−	0.881187i	−0.995486	+	0.0949035i	$0.969746\pi$
$710$	−1.68387	−	1.22340i	−0.0631944	−	0.0459134i
$711$	−17.5402	+	53.9832i	−0.657810	+	2.02453i
$712$	0.284622	+	0.875975i	0.0106666	+	0.0328286i
$713$	−27.7664	+	20.1735i	−1.03986	+	0.755502i
$714$	15.0830			0.564468
$715$	5.87068	+	1.71989i	0.219551	+	0.0643202i
$716$	4.60145			0.171964
$717$	25.3408	−	18.4111i	0.946368	−	0.687576i
$718$	−2.38128	−	7.32883i	−0.0888686	−	0.273510i
$719$	14.6619	−	45.1247i	0.546796	−	1.68287i	−0.169884	−	0.985464i	$-0.554339\pi$
$719$	14.6619	−	45.1247i	0.546796	−	1.68287i	0.716681	−	0.697402i	$-0.245661\pi$
$720$	−34.5771	−	25.1217i	−1.28861	−	0.936232i
$721$	−30.7327	−	22.3286i	−1.14454	−	0.831560i
$722$	0.581307	−	1.78908i	0.0216340	−	0.0665827i
$723$	17.0653	+	52.5215i	0.634664	+	1.95330i
$724$	−17.2037	+	12.4992i	−0.639372	+	0.464531i
$725$	−6.14161			−0.228094
$726$	3.09316	+	7.91607i	0.114798	+	0.293793i
$727$	32.5058			1.20557			0.602786	−	0.797903i	$-0.294057\pi$
$727$	32.5058			1.20557			0.602786	+	0.797903i	$0.294057\pi$
$728$	−2.57751	+	1.87267i	−0.0955290	+	0.0694059i
$729$	−4.43855	−	13.6604i	−0.164391	−	0.505942i
$730$	−0.400269	+	1.23190i	−0.0148146	+	0.0455947i
$731$	−29.8881	−	21.7150i	−1.10545	−	0.803158i
$732$	−6.78118	−	4.92681i	−0.250640	−	0.182100i
$733$	3.73487	−	11.4947i	0.137950	−	0.424568i	−0.858087	−	0.513505i	$-0.828347\pi$
$733$	3.73487	−	11.4947i	0.137950	−	0.424568i	0.996037	+	0.0889369i	$0.0283469\pi$
$734$	2.56607	+	7.89757i	0.0947156	+	0.291504i
$735$	−15.1419	+	11.0012i	−0.558516	+	0.405786i
$736$	−20.3156			−0.748843
$737$	−49.9786	−	14.6418i	−1.84098	−	0.539339i
$738$	8.86441			0.326304
$739$	−7.25046	+	5.26777i	−0.266712	+	0.193778i	−0.713101	−	0.701061i	$-0.752710\pi$
$739$	−7.25046	+	5.26777i	−0.266712	+	0.193778i	0.446389	+	0.894839i	$0.352710\pi$
$740$	−1.70472	−	5.24660i	−0.0626668	−	0.192869i
$741$	−3.21734	+	9.90196i	−0.118192	+	0.363758i
$742$	1.47873	+	1.07436i	0.0542858	+	0.0394410i
$743$	−27.2485	−	19.7972i	−0.999651	−	0.726289i	−0.0376379	−	0.999291i	$-0.511983\pi$
$743$	−27.2485	−	19.7972i	−0.999651	−	0.726289i	−0.962013	+	0.273002i	$0.911983\pi$
$744$	4.60076	−	14.1597i	0.168672	−	0.519120i
$745$	−0.368232	−	1.13330i	−0.0134910	−	0.0415210i
$746$	−4.41932	+	3.21082i	−0.161803	+	0.117557i
$747$	57.2257			2.09378
$748$	−36.7680	+	13.1442i	−1.34437	+	0.480598i
$749$	32.9602			1.20434
$750$	−7.60691	+	5.52674i	−0.277765	+	0.201808i
$751$	8.65591	+	26.6402i	0.315859	+	0.972113i	0.975400	+	0.220444i	$0.0707508\pi$
$751$	8.65591	+	26.6402i	0.315859	+	0.972113i	−0.659541	+	0.751669i	$0.729249\pi$
$752$	−4.78420	+	14.7243i	−0.174462	+	0.536939i
$753$	−24.2683	−	17.6320i	−0.884388	−	0.642545i
$754$	0.783762	+	0.569437i	0.0285429	+	0.0207377i
$755$	2.65191	−	8.16173i	0.0965128	−	0.297036i
$756$	−20.0019	−	61.5596i	−0.727463	−	2.23890i
$757$	9.60309	−	6.97705i	0.349030	−	0.253585i	−0.399432	−	0.916763i	$-0.630793\pi$
$757$	9.60309	−	6.97705i	0.349030	−	0.253585i	0.748462	+	0.663178i	$0.230793\pi$
$758$	−1.60409			−0.0582633
$759$	2.07901	+	71.2484i	0.0754632	+	2.58615i
$760$	−6.21615			−0.225483
$761$	11.0413	−	8.02200i	0.400248	−	0.290797i	−0.369394	−	0.929273i	$-0.620435\pi$
$761$	11.0413	−	8.02200i	0.400248	−	0.290797i	0.769642	+	0.638476i	$0.220435\pi$
$762$	−2.58290	−	7.94935i	−0.0935687	−	0.287975i
$763$	16.9672	−	52.2195i	0.614252	−	1.89047i
$764$	−4.19009	−	3.04428i	−0.151592	−	0.110138i
$765$	58.0255	+	42.1580i	2.09792	+	1.52423i
$766$	−2.74876	+	8.45982i	−0.0993168	+	0.305666i
$767$	−0.741585	−	2.28236i	−0.0267771	−	0.0824114i
$768$	−27.6654	+	20.1001i	−0.998290	+	0.725300i
$769$	−34.5268			−1.24507			−0.622535	−	0.782592i	$-0.713897\pi$
$769$	−34.5268			−1.24507			−0.622535	+	0.782592i	$0.713897\pi$
$770$	−2.79214	+	4.08874i	−0.100622	+	0.147348i
$771$	−13.2881			−0.478560
$772$	−18.7182	+	13.5996i	−0.673684	+	0.489460i
$773$	6.67846	+	20.5542i	0.240208	+	0.739283i	0.996388	+	0.0849197i	$0.0270634\pi$
$773$	6.67846	+	20.5542i	0.240208	+	0.739283i	−0.756180	+	0.654364i	$0.772937\pi$
$774$	3.02728	−	9.31702i	0.108813	−	0.334893i
$775$	6.32823	+	4.59773i	0.227317	+	0.165155i
$776$	−8.61311	−	6.25779i	−0.309193	−	0.224642i
$777$	4.69765	−	14.4579i	0.168527	−	0.518673i
$778$	2.58063	+	7.94237i	0.0925202	+	0.284748i
$779$	−15.1092	+	10.9775i	−0.541343	+	0.393309i
$780$	−10.9485			−0.392019
$781$	9.07423	+	11.7528i	0.324701	+	0.420548i
$782$	10.7441			0.384209
$783$	−32.3688	+	23.5173i	−1.15677	+	0.840440i
$784$	3.70603	+	11.4060i	0.132358	+	0.407357i
$785$	−3.98304	+	12.2585i	−0.142161	+	0.437526i
$786$	0.501544	+	0.364393i	0.0178895	+	0.0129975i
$787$	−11.9429	−	8.67705i	−0.425720	−	0.309303i	0.354215	−	0.935164i	$-0.384748\pi$
$787$	−11.9429	−	8.67705i	−0.425720	−	0.309303i	−0.779935	+	0.625860i	$0.784748\pi$
$788$	−2.53905	+	7.81439i	−0.0904498	+	0.278376i
$789$	10.2079	+	31.4167i	0.363411	+	1.11846i
$790$	−3.33789	+	2.42512i	−0.118757	+	0.0862819i
$791$	−24.6440			−0.876238
$792$	−12.8631	−	16.6601i	−0.457072	−	0.591992i
$793$	−1.41210			−0.0501451
$794$	−2.09115	+	1.51931i	−0.0742121	+	0.0539182i
$795$	3.94567	+	12.1435i	0.139938	+	0.430686i
$796$	10.7255	−	33.0098i	0.380156	−	1.17000i
$797$	−32.3585	−	23.5098i	−1.14620	−	0.832761i	−0.158227	−	0.987403i	$-0.550578\pi$
$797$	−32.3585	−	23.5098i	−1.14620	−	0.832761i	−0.987971	+	0.154642i	$0.950578\pi$
$798$	−6.81725	−	4.95302i	−0.241328	−	0.175335i
$799$	8.02861	−	24.7095i	0.284032	−	0.874160i
$800$	1.43079	+	4.40351i	0.0505859	+	0.155688i
$801$	−4.80338	+	3.48986i	−0.169719	+	0.123308i
$802$	5.62522			0.198633
$803$	5.21106	−	7.63094i	0.183894	−	0.269290i
$804$	93.2073			3.28717
$805$	−33.5938	+	24.4073i	−1.18403	+	0.860245i
$806$	−0.381287	−	1.17348i	−0.0134302	−	0.0413340i
$807$	9.17323	−	28.2323i	0.322913	−	0.993824i
$808$	−9.11033	−	6.61904i	−0.320500	−	0.232857i
$809$	−24.6279	−	17.8932i	−0.865872	−	0.629093i	0.0636041	−	0.997975i	$-0.479740\pi$
$809$	−24.6279	−	17.8932i	−0.865872	−	0.629093i	−0.929476	+	0.368882i	$0.879740\pi$
$810$	−1.82757	+	5.62470i	−0.0642144	+	0.197632i
$811$	−12.9581	−	39.8811i	−0.455022	−	1.40041i	−0.871109	−	0.491089i	$-0.836599\pi$
$811$	−12.9581	−	39.8811i	−0.455022	−	1.40041i	0.416087	−	0.909325i	$-0.363401\pi$
$812$	19.3345	−	14.0473i	0.678507	−	0.492964i
$813$	54.1369			1.89866
$814$	−0.0376600	−	1.29062i	−0.00131998	−	0.0452364i
$815$	16.7892			0.588098
$816$	54.6208	−	39.6843i	1.91211	−	1.38923i
$817$	6.37803	+	19.6296i	0.223139	+	0.686752i
$818$	−2.16187	+	6.65356i	−0.0755881	+	0.232636i
$819$	−16.6152	−	12.0716i	−0.580581	−	0.421817i
$820$	−15.8884	−	11.5436i	−0.554848	−	0.403121i
$821$	−0.266405	+	0.819912i	−0.00929762	+	0.0286151i	−0.955598	−	0.294674i	$-0.904789\pi$
$821$	−0.266405	+	0.819912i	−0.00929762	+	0.0286151i	0.946300	+	0.323290i	$0.104789\pi$
$822$	2.42172	+	7.45329i	0.0844672	+	0.259963i
$823$	26.4028	−	19.1828i	0.920344	−	0.668669i	−0.0232659	−	0.999729i	$-0.507406\pi$
$823$	26.4028	−	19.1828i	0.920344	−	0.668669i	0.943610	+	0.331061i	$0.107406\pi$
$824$	11.7385			0.408929
$825$	15.2970	−	5.46852i	0.532575	−	0.190389i
$826$	1.94230			0.0675811
$827$	1.11516	−	0.810215i	0.0387781	−	0.0281739i	−0.568227	−	0.822872i	$-0.692371\pi$
$827$	1.11516	−	0.810215i	0.0387781	−	0.0281739i	0.607005	+	0.794698i	$0.292371\pi$
$828$	−26.8345	−	82.5882i	−0.932565	−	2.87014i
$829$	5.58973	−	17.2034i	0.194139	−	0.597499i	−0.805846	−	0.592125i	$-0.798289\pi$
$829$	5.58973	−	17.2034i	0.194139	−	0.597499i	0.999986	−	0.00537442i	$-0.00171074\pi$
$830$	3.36520	+	2.44496i	0.116808	+	0.0848659i
$831$	13.4901	+	9.80112i	0.467966	+	0.339997i
$832$	−2.01334	+	6.19644i	−0.0698001	+	0.214823i
$833$	−6.21927	−	19.1410i	−0.215485	−	0.663195i
$834$	−12.4044	+	9.01232i	−0.429529	+	0.312071i
$835$	17.6500			0.610805
$836$	20.9348	+	6.13311i	0.724046	+	0.212118i
$837$	50.9579			1.76136
$838$	7.32912	−	5.32492i	0.253180	−	0.183946i
$839$	10.7474	+	33.0772i	0.371042	+	1.14195i	0.946110	+	0.323845i	$0.104976\pi$
$839$	10.7474	+	33.0772i	0.371042	+	1.14195i	−0.575068	+	0.818106i	$0.695024\pi$
$840$	5.56634	−	17.1314i	0.192057	−	0.591091i
$841$	11.5103	+	8.36271i	0.396906	+	0.288369i
$842$	0.0375863	+	0.0273081i	0.00129531	+	0.000941098i
$843$	−26.7175	+	82.2281i	−0.920201	+	2.83209i
$844$	13.3175	+	40.9871i	0.458407	+	1.41083i
$845$	−1.49221	+	1.08415i	−0.0513336	+	0.0372960i
$846$	6.88950			0.236866
$847$	27.3159	−	22.3919i	0.938586	−	0.769395i
$848$	8.18169			0.280960
$849$	48.2556	−	35.0597i	1.65613	−	1.20325i
$850$	−0.756687	−	2.32884i	−0.0259541	−	0.0798786i
$851$	3.34629	−	10.2988i	0.114709	−	0.353039i
$852$	−21.4990	−	15.6199i	−0.736543	−	0.535130i
$853$	4.59667	+	3.33968i	0.157387	+	0.114348i	0.663691	−	0.748006i	$-0.268989\pi$
$853$	4.59667	+	3.33968i	0.157387	+	0.114348i	−0.506304	+	0.862355i	$0.668989\pi$
$854$	0.353171	−	1.08695i	0.0120853	−	0.0371946i
$855$	−12.3825	−	38.1093i	−0.423472	−	1.30331i
$856$	−8.23980	+	5.98657i	−0.281631	+	0.204617i
$857$	−56.3706			−1.92558			−0.962792	−	0.270244i	$-0.912896\pi$
$857$	−56.3706			−1.92558			−0.962792	+	0.270244i	$0.912896\pi$
$858$	−2.45916	−	0.720442i	−0.0839545	−	0.0245955i
$859$	−21.8633			−0.745966			−0.372983	−	0.927838i	$-0.621665\pi$
$859$	−21.8633			−0.745966			−0.372983	+	0.927838i	$0.621665\pi$
$860$	−17.5591	+	12.7574i	−0.598759	+	0.435024i
$861$	−16.7237	−	51.4703i	−0.569942	−	1.75410i
$862$	−1.82432	+	5.61469i	−0.0621367	+	0.191237i
$863$	−0.781041	−	0.567459i	−0.0265869	−	0.0193165i	0.574412	−	0.818566i	$-0.305231\pi$
$863$	−0.781041	−	0.567459i	−0.0265869	−	0.0193165i	−0.600999	+	0.799249i	$0.705231\pi$
$864$	24.4027	+	17.7296i	0.830195	+	0.603172i
$865$	−2.68386	+	8.26008i	−0.0912541	+	0.280851i
$866$	2.65196	+	8.16190i	0.0901173	+	0.277353i
$867$	−49.5040	+	35.9667i	−1.68124	+	1.22149i
$868$	−30.4381			−1.03314
$869$	27.7156	−	9.90800i	0.940186	−	0.336106i
$870$	−5.47735			−0.185700
$871$	12.7036	−	9.22968i	0.430444	−	0.312736i
$872$	5.24298	+	16.1362i	0.177550	+	0.546441i
$873$	21.2074	−	65.2698i	0.717763	−	2.20905i
$874$	−4.85615	−	3.52820i	−0.164262	−	0.119343i
$875$	31.6136	+	22.9686i	1.06874	+	0.776482i
$876$	−5.11049	+	15.7285i	−0.172667	+	0.531416i
$877$	12.6517	+	38.9381i	0.427219	+	1.31484i	0.900853	+	0.434123i	$0.142942\pi$
$877$	12.6517	+	38.9381i	0.427219	+	1.31484i	−0.473634	+	0.880722i	$0.657058\pi$
$878$	−4.26481	+	3.09857i	−0.143931	+	0.104572i
$879$	60.8517			2.05248
$880$	0.646418	+	22.1530i	0.0217908	+	0.746778i
$881$	22.1828			0.747359			0.373680	−	0.927558i	$-0.378096\pi$
$881$	22.1828			0.747359			0.373680	+	0.927558i	$0.378096\pi$
$882$	4.31762	−	3.13694i	0.145382	−	0.105626i
$883$	11.2957	+	34.7646i	0.380131	+	1.16992i	0.939951	+	0.341309i	$0.110870\pi$
$883$	11.2957	+	34.7646i	0.380131	+	1.16992i	−0.559820	+	0.828614i	$0.689130\pi$
$884$	3.63808	−	11.1969i	0.122362	−	0.376591i
$885$	10.9769	+	7.97520i	0.368985	+	0.268083i
$886$	3.77817	+	2.74500i	0.126930	+	0.0922200i
$887$	−9.33350	+	28.7255i	−0.313388	+	0.964510i	0.663025	+	0.748598i	$0.269272\pi$
$887$	−9.33350	+	28.7255i	−0.313388	+	0.964510i	−0.976413	+	0.215912i	$0.930728\pi$
$888$	1.45161	+	4.46759i	0.0487128	+	0.149922i
$889$	−28.1028	+	20.4179i	−0.942537	+	0.684793i
$890$	−0.431570			−0.0144663
$891$	23.7930	−	34.8418i	0.797095	−	1.16725i
$892$	−3.32829			−0.111439
$893$	−11.7430	+	8.53179i	−0.392964	+	0.285505i
$894$	0.154248	+	0.474728i	0.00515884	+	0.0158773i
$895$	−1.35438	+	4.16834i	−0.0452718	+	0.139332i
$896$	−19.3205	−	14.0371i	−0.645451	−	0.468948i
$897$	−17.3869	−	12.6323i	−0.580531	−	0.421780i
$898$	0.491134	−	1.51155i	0.0163893	−	0.0504412i
$899$	5.81406	+	17.8938i	0.193910	+	0.596792i
$900$	−16.0115	+	11.6330i	−0.533717	+	0.387768i
$901$	−13.7301			−0.457416
$902$	−2.80913	−	3.63834i	−0.0935337	−	0.121143i
$903$	−59.8096			−1.99034
$904$	6.16080	−	4.47608i	0.204905	−	0.148872i
$905$	−6.25907	−	19.2634i	−0.208058	−	0.640338i
$906$	−1.11086	+	3.41886i	−0.0369057	+	0.113584i
$907$	−5.87254	−	4.26665i	−0.194994	−	0.141672i	0.486004	−	0.873957i	$-0.338454\pi$
$907$	−5.87254	−	4.26665i	−0.194994	−	0.141672i	−0.680999	+	0.732285i	$0.738454\pi$
$908$	−37.7972	−	27.4613i	−1.25434	−	0.911335i
$909$	22.4317	−	69.0377i	0.744013	−	2.28984i
$910$	−0.461308	−	1.41976i	−0.0152922	−	0.0470646i
$911$	−5.89659	+	4.28413i	−0.195363	+	0.141939i	−0.681166	−	0.732129i	$-0.738527\pi$
$911$	−5.89659	+	4.28413i	−0.195363	+	0.141939i	0.485804	+	0.874068i	$0.338527\pi$
$912$	−37.7193			−1.24901
$913$	−18.1348	−	23.4879i	−0.600175	−	0.777337i
$914$	−9.71814			−0.321447
$915$	6.45903	−	4.69276i	0.213529	−	0.155138i
$916$	−2.27859	−	7.01279i	−0.0752869	−	0.231709i
$917$	0.796159	−	2.45033i	0.0262915	−	0.0809169i
$918$	−12.9056	−	9.37647i	−0.425949	−	0.309470i
$919$	−9.28436	−	6.74548i	−0.306263	−	0.222513i	0.424028	−	0.905649i	$-0.360616\pi$
$919$	−9.28436	−	6.74548i	−0.306263	−	0.222513i	−0.730291	+	0.683136i	$0.760616\pi$
$920$	3.96509	−	12.2033i	0.130725	−	0.402330i
$921$	−27.1306	−	83.4993i	−0.893982	−	2.75139i
$922$	3.95337	−	2.87229i	0.130197	−	0.0945938i
$923$	−4.47691			−0.147359
$924$	−35.6490	+	52.2035i	−1.17277	+	1.71737i
$925$	−2.46799			−0.0811471
$926$	−7.35270	+	5.34205i	−0.241625	+	0.175551i
$927$	23.3828	+	71.9650i	0.767993	+	2.36364i
$928$	−3.44150	+	10.5918i	−0.112973	+	0.347694i
$929$	−31.3665	−	22.7891i	−1.02910	−	0.747686i	−0.0609724	−	0.998139i	$-0.519420\pi$
$929$	−31.3665	−	22.7891i	−1.02910	−	0.747686i	−0.968129	+	0.250454i	$0.919420\pi$
$930$	5.64379	+	4.10045i	0.185067	+	0.134459i
$931$	−3.47459	+	10.6937i	−0.113875	+	0.350471i
$932$	5.43334	+	16.7221i	0.177975	+	0.547751i
$933$	69.8848	−	50.7743i	2.28793	−	1.66228i
$934$	5.08484			0.166381
$935$	−1.08479	−	37.1761i	−0.0354763	−	1.21579i
$936$	6.34623			0.207433
$937$	18.5124	−	13.4501i	0.604774	−	0.439394i	−0.242796	−	0.970077i	$-0.578065\pi$
$937$	18.5124	−	13.4501i	0.604774	−	0.439394i	0.847570	+	0.530683i	$0.178065\pi$
$938$	3.92724	+	12.0868i	0.128229	+	0.394648i
$939$	1.64312	−	5.05701i	0.0536213	−	0.165029i
$940$	−12.3486	−	8.97180i	−0.402768	−	0.292628i
$941$	−21.8709	−	15.8901i	−0.712970	−	0.518003i	0.171161	−	0.985243i	$-0.445248\pi$
$941$	−21.8709	−	15.8901i	−0.712970	−	0.518003i	−0.884130	+	0.467240i	$0.845248\pi$
$942$	1.66845	−	5.13496i	0.0543611	−	0.167306i
$943$	−11.9128	−	36.6639i	−0.387935	−	1.19394i
$944$	7.03372	−	5.11030i	0.228928	−	0.166326i
$945$	61.6526			2.00556
$946$	−4.78345	+	1.71003i	−0.155523	+	0.0555979i
$947$	−23.2276			−0.754797			−0.377399	−	0.926051i	$-0.623181\pi$
$947$	−23.2276			−0.754797			−0.377399	+	0.926051i	$0.623181\pi$
$948$	−42.6170	+	30.9630i	−1.38414	+	1.00563i
$949$	0.860955	+	2.64975i	0.0279478	+	0.0860144i
$950$	−0.422746	+	1.30108i	−0.0137157	+	0.0422126i
$951$	−11.9899	−	8.71118i	−0.388800	−	0.282479i
$952$	15.6704	+	11.3852i	0.507881	+	0.368997i
$953$	−14.3890	+	44.2849i	−0.466107	+	1.43453i	0.391479	+	0.920187i	$0.371964\pi$
$953$	−14.3890	+	44.2849i	−0.466107	+	1.43453i	−0.857585	+	0.514342i	$0.828036\pi$
$954$	−1.12509	−	3.46266i	−0.0364260	−	0.112108i
$955$	3.99104	−	2.89966i	0.129147	−	0.0938307i
$956$	19.7879			0.639987
$957$	37.4986	+	10.9857i	1.21216	+	0.355117i
$958$	1.41313			0.0456563
$959$	26.3491	−	19.1437i	0.850856	−	0.618183i
$960$	−11.3831	−	35.0337i	−0.367389	−	1.13071i
$961$	−2.17459	+	6.69269i	−0.0701479	+	0.215893i
$962$	0.314953	+	0.228827i	0.0101545	+	0.00737767i
$963$	−53.1154	−	38.5906i	−1.71162	−	1.24356i
$964$	−10.7808	+	33.1799i	−0.347226	+	1.06865i
$965$	−6.81008	−	20.9593i	−0.219224	−	0.674702i
$966$	14.0721	−	10.2240i	0.452762	−	0.328951i
$967$	−14.0562			−0.452015			−0.226008	−	0.974126i	$-0.572567\pi$
$967$	−14.0562			−0.452015			−0.226008	+	0.974126i	$0.572567\pi$
$968$	−2.76172	+	10.5592i	−0.0887651	+	0.339385i
$969$	63.2986			2.03345
$970$	4.03576	−	2.93215i	0.129581	−	0.0941458i
$971$	3.08022	+	9.47993i	0.0988488	+	0.304225i	0.988238	−	0.152926i	$-0.0488697\pi$
$971$	3.08022	+	9.47993i	0.0988488	+	0.304225i	−0.889389	+	0.457152i	$0.848870\pi$
$972$	−4.64611	+	14.2992i	−0.149024	+	0.458649i
$973$	51.5516	+	37.4544i	1.65267	+	1.20073i
$974$	−4.98249	−	3.61999i	−0.159649	−	0.115992i
$975$	−1.51359	+	4.65836i	−0.0484738	+	0.149187i
$976$	−1.58087	−	4.86543i	−0.0506025	−	0.155738i
$977$	21.2982	−	15.4740i	0.681389	−	0.495058i	−0.192429	−	0.981311i	$-0.561637\pi$
$977$	21.2982	−	15.4740i	0.681389	−	0.495058i	0.873818	+	0.486253i	$0.161637\pi$
$978$	−7.03279			−0.224884
$979$	2.95458	+	0.865580i	0.0944287	+	0.0276641i
$980$	−11.8239			−0.377700
$981$	−88.4824	+	64.2862i	−2.82502	+	2.05250i
$982$	0.858318	+	2.64163i	0.0273900	+	0.0842979i
$983$	−1.82042	+	5.60269i	−0.0580625	+	0.178698i	−0.975881	−	0.218301i	$-0.929948\pi$
$983$	−1.82042	+	5.60269i	−0.0580625	+	0.178698i	0.917819	+	0.396999i	$0.129948\pi$
$984$	13.5293	+	9.82964i	0.431299	+	0.313357i
$985$	−6.33153	−	4.60012i	−0.201739	−	0.146572i
$986$	1.82007	−	5.60160i	0.0579629	−	0.178391i
$987$	−12.9978	−	40.0031i	−0.413725	−	1.27331i
$988$	−5.32121	+	3.86609i	−0.169290	+	0.122997i
$989$	−42.6043			−1.35474
$990$	9.28671	−	3.31990i	0.295151	−	0.105513i
$991$	6.05897			0.192470			0.0962348	−	0.995359i	$-0.469320\pi$
$991$	6.05897			0.192470			0.0962348	+	0.995359i	$0.469320\pi$
$992$	11.4753	−	8.33731i	0.364342	−	0.264710i
$993$	−0.671037	−	2.06524i	−0.0212947	−	0.0655384i
$994$	1.11969	−	3.44605i	0.0355144	−	0.109302i
$995$	26.7458	+	19.4320i	0.847900	+	0.616036i
$996$	42.9656	+	31.2164i	1.36142	+	0.989129i
$997$	−1.63747	+	5.03960i	−0.0518591	+	0.159606i	−0.973632	−	0.228124i	$-0.926741\pi$
$997$	−1.63747	+	5.03960i	−0.0518591	+	0.159606i	0.921773	+	0.387730i	$0.126741\pi$
$998$	−1.80019	−	5.54042i	−0.0569840	−	0.175379i
$999$	−13.0073	+	9.45038i	−0.411534	+	0.298997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.2.h.c.14.5	✓	28
11.2	odd	10		1573.2.a.r.1.8		14
11.4	even	5	inner	143.2.h.c.92.5	yes	28
11.9	even	5		1573.2.a.s.1.7		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.2.h.c.14.5	✓	28	1.1	even	1	trivial
143.2.h.c.92.5	yes	28	11.4	even	5	inner
1573.2.a.r.1.8		14	11.2	odd	10
1573.2.a.s.1.7		14	11.9	even	5

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:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	143.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.203919 - 0.148156i) q^{2} +(0.947227 + 2.91527i) q^{3} +(-0.598401 + 1.84169i) q^{4} +(-1.49221 - 1.08415i) q^{5} +(0.625071 + 0.454140i) q^{6} +(0.992247 - 3.05382i) q^{7} +(0.306612 + 0.943653i) q^{8} +(-5.17449 + 3.75949i) q^{9} +O(q^{10})\)	\(q+(0.203919 - 0.148156i) q^{2} +(0.947227 + 2.91527i) q^{3} +(-0.598401 + 1.84169i) q^{4} +(-1.49221 - 1.08415i) q^{5} +(0.625071 + 0.454140i) q^{6} +(0.992247 - 3.05382i) q^{7} +(0.306612 + 0.943653i) q^{8} +(-5.17449 + 3.75949i) q^{9} -0.464913 q^{10} +(3.18285 + 0.932455i) q^{11} -5.93584 q^{12} +(-0.809017 + 0.587785i) q^{13} +(-0.250103 - 0.769738i) q^{14} +(1.74714 - 5.37713i) q^{15} +(-2.93094 - 2.12945i) q^{16} +(4.91855 + 3.57354i) q^{17} +(-0.498186 + 1.53326i) q^{18} +(-1.04960 - 3.23035i) q^{19} +(2.88962 - 2.09943i) q^{20} +9.84259 q^{21} +(0.787191 - 0.281412i) q^{22} +7.01119 q^{23} +(-2.46057 + 1.78771i) q^{24} +(-0.493784 - 1.51971i) q^{25} +(-0.0778900 + 0.239721i) q^{26} +(-8.42170 - 6.11872i) q^{27} +(5.03043 + 3.65482i) q^{28} +(1.18771 - 3.65539i) q^{29} +(-0.440378 - 1.35535i) q^{30} +(-3.96029 + 2.87732i) q^{31} -2.89759 q^{32} +(0.296527 + 10.1621i) q^{33} +1.53242 q^{34} +(-4.79145 + 3.48119i) q^{35} +(-3.82739 - 11.7795i) q^{36} +(0.477278 - 1.46891i) q^{37} +(-0.692628 - 0.503224i) q^{38} +(-2.47987 - 1.80173i) q^{39} +(0.565537 - 1.74054i) q^{40} +(-1.69912 - 5.22934i) q^{41} +(2.00709 - 1.45823i) q^{42} -6.07661 q^{43} +(-3.62191 + 5.30384i) q^{44} +11.7973 q^{45} +(1.42971 - 1.03875i) q^{46} +(-1.32057 - 4.06429i) q^{47} +(3.43165 - 10.5615i) q^{48} +(-2.67815 - 1.94579i) q^{49} +(-0.325846 - 0.236741i) q^{50} +(-5.75882 + 17.7238i) q^{51} +(-0.598401 - 1.84169i) q^{52} +(-1.82705 + 1.32743i) q^{53} -2.62386 q^{54} +(-3.73855 - 4.84212i) q^{55} +3.18598 q^{56} +(8.42311 - 6.11975i) q^{57} +(-0.299370 - 0.921368i) q^{58} +(-0.741585 + 2.28236i) q^{59} +(8.85752 + 6.43536i) q^{60} +(1.14241 + 0.830012i) q^{61} +(-0.381287 + 1.17348i) q^{62} +(6.34643 + 19.5323i) q^{63} +(5.27100 - 3.82961i) q^{64} +1.84447 q^{65} +(1.56604 + 2.02831i) q^{66} -15.7025 q^{67} +(-9.52461 + 6.92003i) q^{68} +(6.64120 + 20.4395i) q^{69} +(-0.461308 + 1.41976i) q^{70} +(3.62190 + 2.63146i) q^{71} +(-5.13421 - 3.73022i) q^{72} +(0.860955 - 2.64975i) q^{73} +(-0.120301 - 0.370250i) q^{74} +(3.96264 - 2.87903i) q^{75} +6.57738 q^{76} +(6.00572 - 8.79463i) q^{77} -0.772630 q^{78} +(7.17961 - 5.21629i) q^{79} +(2.06492 + 6.35518i) q^{80} +(3.93100 - 12.0984i) q^{81} +(-1.12124 - 0.814627i) q^{82} +(-7.23835 - 5.25897i) q^{83} +(-5.88982 + 18.1270i) q^{84} +(-3.46525 - 10.6649i) q^{85} +(-1.23913 + 0.900284i) q^{86} +11.7815 q^{87} +(0.0959839 + 3.28941i) q^{88} +0.928281 q^{89} +(2.40569 - 1.74783i) q^{90} +(0.992247 + 3.05382i) q^{91} +(-4.19551 + 12.9124i) q^{92} +(-12.1395 - 8.81983i) q^{93} +(-0.871436 - 0.633135i) q^{94} +(-1.93597 + 5.95829i) q^{95} +(-2.74468 - 8.44726i) q^{96} +(-8.68068 + 6.30689i) q^{97} -0.834405 q^{98} +(-19.9752 + 7.14090i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 3 q^{2} - 7 q^{3} - 5 q^{4} - 7 q^{5} - 4 q^{6} - 7 q^{7} + q^{8} - 6 q^{9}+O(q^{10}) \) 28 * q - 3 * q^2 - 7 * q^3 - 5 * q^4 - 7 * q^5 - 4 * q^6 - 7 * q^7 + q^8 - 6 * q^9	\( 28 q - 3 q^{2} - 7 q^{3} - 5 q^{4} - 7 q^{5} - 4 q^{6} - 7 q^{7} + q^{8} - 6 q^{9} - 24 q^{10} - 5 q^{11} + 38 q^{12} - 7 q^{13} - 7 q^{14} + 8 q^{15} - 19 q^{16} + 7 q^{17} + 5 q^{18} + 5 q^{19} + 9 q^{20} - 33 q^{22} + 50 q^{23} - 7 q^{24} - 34 q^{25} + 2 q^{26} - 19 q^{27} + 30 q^{28} + 8 q^{29} - 6 q^{30} + 17 q^{31} + 24 q^{32} - 26 q^{33} + 26 q^{34} - 4 q^{35} - 27 q^{36} + 17 q^{37} - 51 q^{38} - 2 q^{39} + 39 q^{40} - 23 q^{41} + 80 q^{42} - 32 q^{43} + q^{44} + 78 q^{45} - 31 q^{46} - 29 q^{47} + 52 q^{48} - 52 q^{49} + 6 q^{50} + 7 q^{51} - 5 q^{52} - 16 q^{53} - 42 q^{54} - 5 q^{55} + 34 q^{56} - 7 q^{57} - 13 q^{58} - 11 q^{59} - 74 q^{60} + 37 q^{61} + 23 q^{62} - 38 q^{63} + 67 q^{64} + 18 q^{65} - 65 q^{66} + 58 q^{67} - 68 q^{68} - 28 q^{69} + 44 q^{70} - 47 q^{71} + 10 q^{72} + 44 q^{73} - 46 q^{74} + 17 q^{75} + 6 q^{76} + 21 q^{77} + 26 q^{78} + 51 q^{79} + 23 q^{80} - 14 q^{81} - 47 q^{82} - 13 q^{83} - 107 q^{84} - q^{85} + 38 q^{86} - 12 q^{87} + 9 q^{88} + 38 q^{89} - 74 q^{90} - 7 q^{91} - 41 q^{92} - 51 q^{93} - 5 q^{94} + 47 q^{95} - 71 q^{96} - 20 q^{97} + 162 q^{98} + 60 q^{99}+O(q^{100}) \) 28 * q - 3 * q^2 - 7 * q^3 - 5 * q^4 - 7 * q^5 - 4 * q^6 - 7 * q^7 + q^8 - 6 * q^9 - 24 * q^10 - 5 * q^11 + 38 * q^12 - 7 * q^13 - 7 * q^14 + 8 * q^15 - 19 * q^16 + 7 * q^17 + 5 * q^18 + 5 * q^19 + 9 * q^20 - 33 * q^22 + 50 * q^23 - 7 * q^24 - 34 * q^25 + 2 * q^26 - 19 * q^27 + 30 * q^28 + 8 * q^29 - 6 * q^30 + 17 * q^31 + 24 * q^32 - 26 * q^33 + 26 * q^34 - 4 * q^35 - 27 * q^36 + 17 * q^37 - 51 * q^38 - 2 * q^39 + 39 * q^40 - 23 * q^41 + 80 * q^42 - 32 * q^43 + q^44 + 78 * q^45 - 31 * q^46 - 29 * q^47 + 52 * q^48 - 52 * q^49 + 6 * q^50 + 7 * q^51 - 5 * q^52 - 16 * q^53 - 42 * q^54 - 5 * q^55 + 34 * q^56 - 7 * q^57 - 13 * q^58 - 11 * q^59 - 74 * q^60 + 37 * q^61 + 23 * q^62 - 38 * q^63 + 67 * q^64 + 18 * q^65 - 65 * q^66 + 58 * q^67 - 68 * q^68 - 28 * q^69 + 44 * q^70 - 47 * q^71 + 10 * q^72 + 44 * q^73 - 46 * q^74 + 17 * q^75 + 6 * q^76 + 21 * q^77 + 26 * q^78 + 51 * q^79 + 23 * q^80 - 14 * q^81 - 47 * q^82 - 13 * q^83 - 107 * q^84 - q^85 + 38 * q^86 - 12 * q^87 + 9 * q^88 + 38 * q^89 - 74 * q^90 - 7 * q^91 - 41 * q^92 - 51 * q^93 - 5 * q^94 + 47 * q^95 - 71 * q^96 - 20 * q^97 + 162 * q^98 + 60 * q^99

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