Properties

Label 462.2.j.e.169.2
Level $462$
Weight $2$
Character 462.169
Analytic conductor $3.689$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [462,2,Mod(169,462)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(462, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("462.169");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 462.j (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: \(3.68908857338\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{5})\)
Coefficient field: 8.0.484000000.9
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} + x^{6} + 16x^{4} + 66x^{2} + 121 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 169.2
Root \(0.476925 - 1.46782i\) of defining polynomial
Character \(\chi\) \(=\) 462.169
Dual form 462.2.j.e.421.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.809017 - 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{3} +(0.309017 + 0.951057i) q^{4} +(2.52029 - 1.83110i) q^{5} +(-0.809017 + 0.587785i) q^{6} +(0.309017 + 0.951057i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\) \(q+(-0.809017 - 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{3} +(0.309017 + 0.951057i) q^{4} +(2.52029 - 1.83110i) q^{5} +(-0.809017 + 0.587785i) q^{6} +(0.309017 + 0.951057i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.809017 - 0.587785i) q^{9} -3.11525 q^{10} +(2.97414 - 1.46782i) q^{11} +1.00000 q^{12} +(1.74861 + 1.27044i) q^{13} +(0.309017 - 0.951057i) q^{14} +(-0.962664 - 2.96278i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-0.574672 + 0.417524i) q^{17} +(0.309017 + 0.951057i) q^{18} +(0.0949591 - 0.292254i) q^{19} +(2.52029 + 1.83110i) q^{20} +1.00000 q^{21} +(-3.26889 - 0.560659i) q^{22} +0.879178 q^{23} +(-0.809017 - 0.587785i) q^{24} +(1.45385 - 4.47449i) q^{25} +(-0.667908 - 2.05561i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(-0.809017 + 0.587785i) q^{28} +(2.03082 + 6.25023i) q^{29} +(-0.962664 + 2.96278i) q^{30} +(-6.21902 - 4.51838i) q^{31} +1.00000 q^{32} +(-0.476925 - 3.28216i) q^{33} +0.710334 q^{34} +(2.52029 + 1.83110i) q^{35} +(0.309017 - 0.951057i) q^{36} +(-1.19873 - 3.68932i) q^{37} +(-0.248606 + 0.180623i) q^{38} +(1.74861 - 1.27044i) q^{39} +(-0.962664 - 2.96278i) q^{40} +(1.32558 - 4.07972i) q^{41} +(-0.809017 - 0.587785i) q^{42} -8.24254 q^{43} +(2.31504 + 2.37499i) q^{44} -3.11525 q^{45} +(-0.711270 - 0.516768i) q^{46} +(3.10205 - 9.54713i) q^{47} +(0.309017 + 0.951057i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(-3.80623 + 2.76539i) q^{50} +(0.219505 + 0.675568i) q^{51} +(-0.667908 + 2.05561i) q^{52} +(5.32652 + 3.86994i) q^{53} +1.00000 q^{54} +(4.80795 - 9.14527i) q^{55} +1.00000 q^{56} +(-0.248606 - 0.180623i) q^{57} +(2.03082 - 6.25023i) q^{58} +(-1.77713 - 5.46944i) q^{59} +(2.52029 - 1.83110i) q^{60} +(-2.52759 + 1.83640i) q^{61} +(2.37545 + 7.31090i) q^{62} +(0.309017 - 0.951057i) q^{63} +(-0.809017 - 0.587785i) q^{64} +6.73328 q^{65} +(-1.54336 + 2.93565i) q^{66} -6.67624 q^{67} +(-0.574672 - 0.417524i) q^{68} +(0.271681 - 0.836148i) q^{69} +(-0.962664 - 2.96278i) q^{70} +(-8.77385 + 6.37458i) q^{71} +(-0.809017 + 0.587785i) q^{72} +(3.32049 + 10.2194i) q^{73} +(-1.19873 + 3.68932i) q^{74} +(-3.80623 - 2.76539i) q^{75} +0.307294 q^{76} +(2.31504 + 2.37499i) q^{77} -2.16140 q^{78} +(7.86013 + 5.71072i) q^{79} +(-0.962664 + 2.96278i) q^{80} +(0.309017 + 0.951057i) q^{81} +(-3.47041 + 2.52140i) q^{82} +(-12.7701 + 9.27804i) q^{83} +(0.309017 + 0.951057i) q^{84} +(-0.683813 + 2.10456i) q^{85} +(6.66836 + 4.84485i) q^{86} +6.57188 q^{87} +(-0.476925 - 3.28216i) q^{88} +14.8726 q^{89} +(2.52029 + 1.83110i) q^{90} +(-0.667908 + 2.05561i) q^{91} +(0.271681 + 0.836148i) q^{92} +(-6.21902 + 4.51838i) q^{93} +(-8.12127 + 5.90045i) q^{94} +(-0.295821 - 0.910443i) q^{95} +(0.309017 - 0.951057i) q^{96} +(0.211270 + 0.153497i) q^{97} +1.00000 q^{98} +(-3.26889 - 0.560659i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} - 2 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} - 2 q^{7} - 2 q^{8} - 2 q^{9} + 4 q^{10} + 8 q^{12} + 4 q^{13} - 2 q^{14} - 6 q^{15} - 2 q^{16} - 8 q^{17} - 2 q^{18} - 12 q^{19} + 4 q^{20} + 8 q^{21} - 4 q^{23} - 2 q^{24} + 4 q^{25} - 6 q^{26} - 2 q^{27} - 2 q^{28} - 4 q^{29} - 6 q^{30} - 14 q^{31} + 8 q^{32} + 12 q^{34} + 4 q^{35} - 2 q^{36} + 10 q^{37} + 8 q^{38} + 4 q^{39} - 6 q^{40} - 12 q^{41} - 2 q^{42} + 20 q^{43} + 4 q^{45} + 6 q^{46} + 28 q^{47} - 2 q^{48} - 2 q^{49} - 6 q^{50} + 2 q^{51} - 6 q^{52} + 2 q^{53} + 8 q^{54} + 4 q^{55} + 8 q^{56} + 8 q^{57} - 4 q^{58} + 4 q^{60} - 34 q^{61} + 6 q^{62} - 2 q^{63} - 2 q^{64} + 16 q^{65} - 24 q^{67} - 8 q^{68} - 4 q^{69} - 6 q^{70} - 2 q^{72} + 10 q^{74} - 6 q^{75} + 8 q^{76} + 4 q^{78} + 22 q^{79} - 6 q^{80} - 2 q^{81} - 2 q^{82} - 30 q^{83} - 2 q^{84} - 28 q^{85} + 36 q^{87} - 4 q^{89} + 4 q^{90} - 6 q^{91} - 4 q^{92} - 14 q^{93} - 22 q^{94} - 30 q^{95} - 2 q^{96} - 10 q^{97} + 8 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(211\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{5}\right)\)

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 \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.809017 0.587785i −0.572061 0.415627i
\(3\) 0.309017 0.951057i 0.178411 0.549093i
\(4\) 0.309017 + 0.951057i 0.154508 + 0.475528i
\(5\) 2.52029 1.83110i 1.12711 0.818891i 0.141835 0.989890i \(-0.454700\pi\)
0.985271 + 0.170999i \(0.0546996\pi\)
\(6\) −0.809017 + 0.587785i −0.330280 + 0.239962i
\(7\) 0.309017 + 0.951057i 0.116797 + 0.359466i
\(8\) 0.309017 0.951057i 0.109254 0.336249i
\(9\) −0.809017 0.587785i −0.269672 0.195928i
\(10\) −3.11525 −0.985127
\(11\) 2.97414 1.46782i 0.896736 0.442566i
\(12\) 1.00000 0.288675
\(13\) 1.74861 + 1.27044i 0.484976 + 0.352356i 0.803249 0.595643i \(-0.203103\pi\)
−0.318273 + 0.947999i \(0.603103\pi\)
\(14\) 0.309017 0.951057i 0.0825883 0.254181i
\(15\) −0.962664 2.96278i −0.248559 0.764985i
\(16\) −0.809017 + 0.587785i −0.202254 + 0.146946i
\(17\) −0.574672 + 0.417524i −0.139378 + 0.101264i −0.655290 0.755378i \(-0.727453\pi\)
0.515911 + 0.856642i \(0.327453\pi\)
\(18\) 0.309017 + 0.951057i 0.0728360 + 0.224166i
\(19\) 0.0949591 0.292254i 0.0217851 0.0670476i −0.939573 0.342349i \(-0.888778\pi\)
0.961358 + 0.275301i \(0.0887776\pi\)
\(20\) 2.52029 + 1.83110i 0.563553 + 0.409445i
\(21\) 1.00000 0.218218
\(22\) −3.26889 0.560659i −0.696930 0.119533i
\(23\) 0.879178 0.183321 0.0916606 0.995790i \(-0.470782\pi\)
0.0916606 + 0.995790i \(0.470782\pi\)
\(24\) −0.809017 0.587785i −0.165140 0.119981i
\(25\) 1.45385 4.47449i 0.290770 0.894898i
\(26\) −0.667908 2.05561i −0.130988 0.403138i
\(27\) −0.809017 + 0.587785i −0.155695 + 0.113119i
\(28\) −0.809017 + 0.587785i −0.152890 + 0.111081i
\(29\) 2.03082 + 6.25023i 0.377115 + 1.16064i 0.942041 + 0.335498i \(0.108905\pi\)
−0.564926 + 0.825141i \(0.691095\pi\)
\(30\) −0.962664 + 2.96278i −0.175758 + 0.540926i
\(31\) −6.21902 4.51838i −1.11697 0.811525i −0.133222 0.991086i \(-0.542532\pi\)
−0.983747 + 0.179561i \(0.942532\pi\)
\(32\) 1.00000 0.176777
\(33\) −0.476925 3.28216i −0.0830220 0.571350i
\(34\) 0.710334 0.121821
\(35\) 2.52029 + 1.83110i 0.426006 + 0.309512i
\(36\) 0.309017 0.951057i 0.0515028 0.158509i
\(37\) −1.19873 3.68932i −0.197070 0.606520i −0.999946 0.0103738i \(-0.996698\pi\)
0.802876 0.596146i \(-0.203302\pi\)
\(38\) −0.248606 + 0.180623i −0.0403292 + 0.0293009i
\(39\) 1.74861 1.27044i 0.280001 0.203433i
\(40\) −0.962664 2.96278i −0.152211 0.468456i
\(41\) 1.32558 4.07972i 0.207021 0.637144i −0.792604 0.609737i \(-0.791275\pi\)
0.999624 0.0274071i \(-0.00872506\pi\)
\(42\) −0.809017 0.587785i −0.124834 0.0906972i
\(43\) −8.24254 −1.25698 −0.628488 0.777819i \(-0.716326\pi\)
−0.628488 + 0.777819i \(0.716326\pi\)
\(44\) 2.31504 + 2.37499i 0.349006 + 0.358043i
\(45\) −3.11525 −0.464393
\(46\) −0.711270 0.516768i −0.104871 0.0761933i
\(47\) 3.10205 9.54713i 0.452480 1.39259i −0.421587 0.906788i \(-0.638527\pi\)
0.874068 0.485804i \(-0.161473\pi\)
\(48\) 0.309017 + 0.951057i 0.0446028 + 0.137273i
\(49\) −0.809017 + 0.587785i −0.115574 + 0.0839693i
\(50\) −3.80623 + 2.76539i −0.538282 + 0.391085i
\(51\) 0.219505 + 0.675568i 0.0307369 + 0.0945984i
\(52\) −0.667908 + 2.05561i −0.0926222 + 0.285062i
\(53\) 5.32652 + 3.86994i 0.731653 + 0.531577i 0.890086 0.455793i \(-0.150644\pi\)
−0.158433 + 0.987370i \(0.550644\pi\)
\(54\) 1.00000 0.136083
\(55\) 4.80795 9.14527i 0.648304 1.23315i
\(56\) 1.00000 0.133631
\(57\) −0.248606 0.180623i −0.0329287 0.0239241i
\(58\) 2.03082 6.25023i 0.266660 0.820696i
\(59\) −1.77713 5.46944i −0.231362 0.712060i −0.997583 0.0694828i \(-0.977865\pi\)
0.766221 0.642577i \(-0.222135\pi\)
\(60\) 2.52029 1.83110i 0.325368 0.236393i
\(61\) −2.52759 + 1.83640i −0.323624 + 0.235127i −0.737720 0.675106i \(-0.764098\pi\)
0.414096 + 0.910233i \(0.364098\pi\)
\(62\) 2.37545 + 7.31090i 0.301683 + 0.928485i
\(63\) 0.309017 0.951057i 0.0389325 0.119822i
\(64\) −0.809017 0.587785i −0.101127 0.0734732i
\(65\) 6.73328 0.835161
\(66\) −1.54336 + 2.93565i −0.189975 + 0.361353i
\(67\) −6.67624 −0.815632 −0.407816 0.913064i \(-0.633710\pi\)
−0.407816 + 0.913064i \(0.633710\pi\)
\(68\) −0.574672 0.417524i −0.0696892 0.0506322i
\(69\) 0.271681 0.836148i 0.0327065 0.100660i
\(70\) −0.962664 2.96278i −0.115060 0.354119i
\(71\) −8.77385 + 6.37458i −1.04126 + 0.756523i −0.970532 0.240972i \(-0.922534\pi\)
−0.0707328 + 0.997495i \(0.522534\pi\)
\(72\) −0.809017 + 0.587785i −0.0953436 + 0.0692712i
\(73\) 3.32049 + 10.2194i 0.388634 + 1.19609i 0.933810 + 0.357770i \(0.116463\pi\)
−0.545176 + 0.838322i \(0.683537\pi\)
\(74\) −1.19873 + 3.68932i −0.139350 + 0.428874i
\(75\) −3.80623 2.76539i −0.439505 0.319319i
\(76\) 0.307294 0.0352490
\(77\) 2.31504 + 2.37499i 0.263824 + 0.270655i
\(78\) −2.16140 −0.244730
\(79\) 7.86013 + 5.71072i 0.884333 + 0.642506i 0.934394 0.356240i \(-0.115942\pi\)
−0.0500609 + 0.998746i \(0.515942\pi\)
\(80\) −0.962664 + 2.96278i −0.107629 + 0.331248i
\(81\) 0.309017 + 0.951057i 0.0343352 + 0.105673i
\(82\) −3.47041 + 2.52140i −0.383243 + 0.278442i
\(83\) −12.7701 + 9.27804i −1.40170 + 1.01840i −0.407240 + 0.913321i \(0.633509\pi\)
−0.994464 + 0.105076i \(0.966491\pi\)
\(84\) 0.309017 + 0.951057i 0.0337165 + 0.103769i
\(85\) −0.683813 + 2.10456i −0.0741699 + 0.228271i
\(86\) 6.66836 + 4.84485i 0.719068 + 0.522433i
\(87\) 6.57188 0.704580
\(88\) −0.476925 3.28216i −0.0508404 0.349879i
\(89\) 14.8726 1.57650 0.788248 0.615358i \(-0.210989\pi\)
0.788248 + 0.615358i \(0.210989\pi\)
\(90\) 2.52029 + 1.83110i 0.265662 + 0.193014i
\(91\) −0.667908 + 2.05561i −0.0700158 + 0.215486i
\(92\) 0.271681 + 0.836148i 0.0283247 + 0.0871745i
\(93\) −6.21902 + 4.51838i −0.644882 + 0.468534i
\(94\) −8.12127 + 5.90045i −0.837645 + 0.608585i
\(95\) −0.295821 0.910443i −0.0303506 0.0934095i
\(96\) 0.309017 0.951057i 0.0315389 0.0970668i
\(97\) 0.211270 + 0.153497i 0.0214512 + 0.0155852i 0.598459 0.801153i \(-0.295780\pi\)
−0.577008 + 0.816739i \(0.695780\pi\)
\(98\) 1.00000 0.101015
\(99\) −3.26889 0.560659i −0.328536 0.0563484i
\(100\) 4.70476 0.470476
\(101\) −2.06365 1.49933i −0.205341 0.149189i 0.480362 0.877070i \(-0.340505\pi\)
−0.685703 + 0.727881i \(0.740505\pi\)
\(102\) 0.219505 0.675568i 0.0217343 0.0668912i
\(103\) 5.82249 + 17.9198i 0.573707 + 1.76569i 0.640540 + 0.767925i \(0.278711\pi\)
−0.0668329 + 0.997764i \(0.521289\pi\)
\(104\) 1.74861 1.27044i 0.171465 0.124577i
\(105\) 2.52029 1.83110i 0.245955 0.178697i
\(106\) −2.03455 6.26170i −0.197613 0.608190i
\(107\) −1.05094 + 3.23446i −0.101598 + 0.312687i −0.988917 0.148470i \(-0.952565\pi\)
0.887319 + 0.461156i \(0.152565\pi\)
\(108\) −0.809017 0.587785i −0.0778477 0.0565597i
\(109\) 6.96590 0.667212 0.333606 0.942713i \(-0.391734\pi\)
0.333606 + 0.942713i \(0.391734\pi\)
\(110\) −9.26517 + 4.57263i −0.883399 + 0.435984i
\(111\) −3.87918 −0.368195
\(112\) −0.809017 0.587785i −0.0764449 0.0555405i
\(113\) −0.432012 + 1.32960i −0.0406403 + 0.125078i −0.969318 0.245809i \(-0.920946\pi\)
0.928678 + 0.370887i \(0.120946\pi\)
\(114\) 0.0949591 + 0.292254i 0.00889373 + 0.0273721i
\(115\) 2.21578 1.60986i 0.206623 0.150120i
\(116\) −5.31677 + 3.86286i −0.493649 + 0.358657i
\(117\) −0.667908 2.05561i −0.0617481 0.190041i
\(118\) −1.77713 + 5.46944i −0.163598 + 0.503503i
\(119\) −0.574672 0.417524i −0.0526801 0.0382743i
\(120\) −3.11525 −0.284382
\(121\) 6.69098 8.73102i 0.608271 0.793729i
\(122\) 3.12427 0.282858
\(123\) −3.47041 2.52140i −0.312917 0.227347i
\(124\) 2.37545 7.31090i 0.213322 0.656538i
\(125\) 0.284219 + 0.874736i 0.0254213 + 0.0782388i
\(126\) −0.809017 + 0.587785i −0.0720730 + 0.0523641i
\(127\) −12.9791 + 9.42987i −1.15171 + 0.836765i −0.988707 0.149860i \(-0.952118\pi\)
−0.163002 + 0.986626i \(0.552118\pi\)
\(128\) 0.309017 + 0.951057i 0.0273135 + 0.0840623i
\(129\) −2.54709 + 7.83913i −0.224258 + 0.690196i
\(130\) −5.44734 3.95772i −0.477763 0.347115i
\(131\) 19.8696 1.73601 0.868007 0.496551i \(-0.165400\pi\)
0.868007 + 0.496551i \(0.165400\pi\)
\(132\) 2.97414 1.46782i 0.258865 0.127758i
\(133\) 0.307294 0.0266458
\(134\) 5.40119 + 3.92419i 0.466592 + 0.338999i
\(135\) −0.962664 + 2.96278i −0.0828529 + 0.254995i
\(136\) 0.219505 + 0.675568i 0.0188224 + 0.0579294i
\(137\) −1.87963 + 1.36563i −0.160587 + 0.116674i −0.665177 0.746686i \(-0.731644\pi\)
0.504589 + 0.863359i \(0.331644\pi\)
\(138\) −0.711270 + 0.516768i −0.0605473 + 0.0439902i
\(139\) 2.31208 + 7.11586i 0.196108 + 0.603559i 0.999962 + 0.00873210i \(0.00277955\pi\)
−0.803854 + 0.594827i \(0.797220\pi\)
\(140\) −0.962664 + 2.96278i −0.0813600 + 0.250400i
\(141\) −8.12127 5.90045i −0.683934 0.496907i
\(142\) 10.8451 0.910099
\(143\) 7.06537 + 1.21181i 0.590836 + 0.101336i
\(144\) 1.00000 0.0833333
\(145\) 16.5630 + 12.0337i 1.37549 + 0.999348i
\(146\) 3.32049 10.2194i 0.274806 0.845765i
\(147\) 0.309017 + 0.951057i 0.0254873 + 0.0784418i
\(148\) 3.13832 2.28012i 0.257968 0.187425i
\(149\) −1.15492 + 0.839099i −0.0946147 + 0.0687416i −0.634087 0.773262i \(-0.718624\pi\)
0.539472 + 0.842003i \(0.318624\pi\)
\(150\) 1.45385 + 4.47449i 0.118706 + 0.365341i
\(151\) −3.07840 + 9.47433i −0.250516 + 0.771010i 0.744164 + 0.667997i \(0.232848\pi\)
−0.994680 + 0.103013i \(0.967152\pi\)
\(152\) −0.248606 0.180623i −0.0201646 0.0146504i
\(153\) 0.710334 0.0574271
\(154\) −0.476925 3.28216i −0.0384317 0.264484i
\(155\) −23.9473 −1.92349
\(156\) 1.74861 + 1.27044i 0.140001 + 0.101716i
\(157\) −7.61459 + 23.4353i −0.607710 + 1.87034i −0.130749 + 0.991415i \(0.541738\pi\)
−0.476961 + 0.878924i \(0.658262\pi\)
\(158\) −3.00230 9.24013i −0.238850 0.735106i
\(159\) 5.32652 3.86994i 0.422420 0.306906i
\(160\) 2.52029 1.83110i 0.199246 0.144761i
\(161\) 0.271681 + 0.836148i 0.0214115 + 0.0658977i
\(162\) 0.309017 0.951057i 0.0242787 0.0747221i
\(163\) −11.6069 8.43289i −0.909121 0.660515i 0.0316713 0.999498i \(-0.489917\pi\)
−0.940792 + 0.338983i \(0.889917\pi\)
\(164\) 4.28967 0.334967
\(165\) −7.21193 7.39868i −0.561448 0.575986i
\(166\) 15.7847 1.22513
\(167\) −11.3518 8.24754i −0.878426 0.638214i 0.0544087 0.998519i \(-0.482673\pi\)
−0.932835 + 0.360305i \(0.882673\pi\)
\(168\) 0.309017 0.951057i 0.0238412 0.0733756i
\(169\) −2.57361 7.92075i −0.197970 0.609288i
\(170\) 1.79024 1.30069i 0.137306 0.0997583i
\(171\) −0.248606 + 0.180623i −0.0190114 + 0.0138126i
\(172\) −2.54709 7.83913i −0.194213 0.597728i
\(173\) 4.38107 13.4836i 0.333087 1.02514i −0.634570 0.772865i \(-0.718823\pi\)
0.967657 0.252270i \(-0.0811772\pi\)
\(174\) −5.31677 3.86286i −0.403063 0.292842i
\(175\) 4.70476 0.355646
\(176\) −1.54336 + 2.93565i −0.116335 + 0.221283i
\(177\) −5.75091 −0.432265
\(178\) −12.0322 8.74191i −0.901852 0.655234i
\(179\) −4.91066 + 15.1135i −0.367040 + 1.12963i 0.581654 + 0.813436i \(0.302406\pi\)
−0.948694 + 0.316196i \(0.897594\pi\)
\(180\) −0.962664 2.96278i −0.0717527 0.220832i
\(181\) 14.3675 10.4386i 1.06793 0.775897i 0.0923916 0.995723i \(-0.470549\pi\)
0.975539 + 0.219826i \(0.0705488\pi\)
\(182\) 1.74861 1.27044i 0.129615 0.0941710i
\(183\) 0.965452 + 2.97136i 0.0713683 + 0.219649i
\(184\) 0.271681 0.836148i 0.0200286 0.0616416i
\(185\) −9.77664 7.10315i −0.718793 0.522234i
\(186\) 7.68713 0.563648
\(187\) −1.09630 + 2.08529i −0.0801695 + 0.152492i
\(188\) 10.0384 0.732129
\(189\) −0.809017 0.587785i −0.0588473 0.0427551i
\(190\) −0.295821 + 0.910443i −0.0214611 + 0.0660505i
\(191\) −8.12423 25.0038i −0.587849 1.80921i −0.587516 0.809213i \(-0.699894\pi\)
−0.000332794 1.00000i \(-0.500106\pi\)
\(192\) −0.809017 + 0.587785i −0.0583858 + 0.0424197i
\(193\) −4.50451 + 3.27272i −0.324242 + 0.235575i −0.737983 0.674819i \(-0.764222\pi\)
0.413742 + 0.910394i \(0.364222\pi\)
\(194\) −0.0806980 0.248363i −0.00579378 0.0178314i
\(195\) 2.08070 6.40373i 0.149002 0.458581i
\(196\) −0.809017 0.587785i −0.0577869 0.0419847i
\(197\) −11.8089 −0.841346 −0.420673 0.907212i \(-0.638206\pi\)
−0.420673 + 0.907212i \(0.638206\pi\)
\(198\) 2.31504 + 2.37499i 0.164523 + 0.168783i
\(199\) 9.53591 0.675983 0.337991 0.941149i \(-0.390252\pi\)
0.337991 + 0.941149i \(0.390252\pi\)
\(200\) −3.80623 2.76539i −0.269141 0.195542i
\(201\) −2.06307 + 6.34948i −0.145518 + 0.447858i
\(202\) 0.788244 + 2.42596i 0.0554606 + 0.170690i
\(203\) −5.31677 + 3.86286i −0.373164 + 0.271119i
\(204\) −0.574672 + 0.417524i −0.0402351 + 0.0292325i
\(205\) −4.12951 12.7093i −0.288417 0.887657i
\(206\) 5.82249 17.9198i 0.405672 1.24853i
\(207\) −0.711270 0.516768i −0.0494367 0.0359179i
\(208\) −2.16140 −0.149866
\(209\) −0.146556 1.00859i −0.0101375 0.0697654i
\(210\) −3.11525 −0.214972
\(211\) 9.67135 + 7.02665i 0.665803 + 0.483735i 0.868618 0.495483i \(-0.165009\pi\)
−0.202814 + 0.979217i \(0.565009\pi\)
\(212\) −2.03455 + 6.26170i −0.139733 + 0.430055i
\(213\) 3.35131 + 10.3143i 0.229628 + 0.706723i
\(214\) 2.75139 1.99900i 0.188081 0.136649i
\(215\) −20.7736 + 15.0929i −1.41675 + 1.02933i
\(216\) 0.309017 + 0.951057i 0.0210259 + 0.0647112i
\(217\) 2.37545 7.31090i 0.161256 0.496296i
\(218\) −5.63553 4.09445i −0.381686 0.277311i
\(219\) 10.7453 0.726102
\(220\) 10.1834 + 1.74659i 0.686565 + 0.117755i
\(221\) −1.53531 −0.103276
\(222\) 3.13832 + 2.28012i 0.210630 + 0.153032i
\(223\) −2.71282 + 8.34921i −0.181664 + 0.559104i −0.999875 0.0158139i \(-0.994966\pi\)
0.818211 + 0.574918i \(0.194966\pi\)
\(224\) 0.309017 + 0.951057i 0.0206471 + 0.0635451i
\(225\) −3.80623 + 2.76539i −0.253749 + 0.184359i
\(226\) 1.13102 0.821736i 0.0752345 0.0546610i
\(227\) −6.02667 18.5482i −0.400004 1.23109i −0.924995 0.379979i \(-0.875931\pi\)
0.524991 0.851108i \(-0.324069\pi\)
\(228\) 0.0949591 0.292254i 0.00628882 0.0193550i
\(229\) 5.88938 + 4.27888i 0.389181 + 0.282757i 0.765120 0.643888i \(-0.222680\pi\)
−0.375939 + 0.926645i \(0.622680\pi\)
\(230\) −2.73886 −0.180595
\(231\) 2.97414 1.46782i 0.195684 0.0965758i
\(232\) 6.57188 0.431465
\(233\) 2.21054 + 1.60605i 0.144817 + 0.105216i 0.657835 0.753162i \(-0.271472\pi\)
−0.513018 + 0.858378i \(0.671472\pi\)
\(234\) −0.667908 + 2.05561i −0.0436625 + 0.134379i
\(235\) −9.66365 29.7417i −0.630387 1.94013i
\(236\) 4.65258 3.38030i 0.302857 0.220039i
\(237\) 7.86013 5.71072i 0.510570 0.370951i
\(238\) 0.219505 + 0.675568i 0.0142284 + 0.0437905i
\(239\) 8.00283 24.6302i 0.517660 1.59319i −0.260729 0.965412i \(-0.583963\pi\)
0.778389 0.627782i \(-0.216037\pi\)
\(240\) 2.52029 + 1.83110i 0.162684 + 0.118197i
\(241\) −6.36034 −0.409705 −0.204853 0.978793i \(-0.565672\pi\)
−0.204853 + 0.978793i \(0.565672\pi\)
\(242\) −10.5451 + 3.13068i −0.677864 + 0.201248i
\(243\) 1.00000 0.0641500
\(244\) −2.52759 1.83640i −0.161812 0.117563i
\(245\) −0.962664 + 2.96278i −0.0615023 + 0.189285i
\(246\) 1.32558 + 4.07972i 0.0845159 + 0.260113i
\(247\) 0.537336 0.390397i 0.0341899 0.0248404i
\(248\) −6.21902 + 4.51838i −0.394908 + 0.286918i
\(249\) 4.87776 + 15.0122i 0.309115 + 0.951359i
\(250\) 0.284219 0.874736i 0.0179756 0.0553232i
\(251\) 10.4223 + 7.57222i 0.657847 + 0.477954i 0.865935 0.500156i \(-0.166724\pi\)
−0.208088 + 0.978110i \(0.566724\pi\)
\(252\) 1.00000 0.0629941
\(253\) 2.61480 1.29048i 0.164391 0.0811317i
\(254\) 16.0430 1.00663
\(255\) 1.79024 + 1.30069i 0.112109 + 0.0814523i
\(256\) 0.309017 0.951057i 0.0193136 0.0594410i
\(257\) 1.61565 + 4.97247i 0.100782 + 0.310174i 0.988717 0.149794i \(-0.0478610\pi\)
−0.887936 + 0.459968i \(0.847861\pi\)
\(258\) 6.66836 4.84485i 0.415154 0.301627i
\(259\) 3.13832 2.28012i 0.195006 0.141680i
\(260\) 2.08070 + 6.40373i 0.129039 + 0.397142i
\(261\) 2.03082 6.25023i 0.125705 0.386880i
\(262\) −16.0748 11.6791i −0.993107 0.721535i
\(263\) 26.8248 1.65409 0.827043 0.562139i \(-0.190021\pi\)
0.827043 + 0.562139i \(0.190021\pi\)
\(264\) −3.26889 0.560659i −0.201186 0.0345062i
\(265\) 20.5106 1.25995
\(266\) −0.248606 0.180623i −0.0152430 0.0110747i
\(267\) 4.59590 14.1447i 0.281264 0.865642i
\(268\) −2.06307 6.34948i −0.126022 0.387856i
\(269\) 8.93180 6.48934i 0.544582 0.395662i −0.281202 0.959649i \(-0.590733\pi\)
0.825784 + 0.563987i \(0.190733\pi\)
\(270\) 2.52029 1.83110i 0.153380 0.111437i
\(271\) −5.59734 17.2268i −0.340014 1.04646i −0.964199 0.265179i \(-0.914569\pi\)
0.624185 0.781277i \(-0.285431\pi\)
\(272\) 0.219505 0.675568i 0.0133095 0.0409623i
\(273\) 1.74861 + 1.27044i 0.105830 + 0.0768903i
\(274\) 2.32335 0.140359
\(275\) −2.24382 15.4417i −0.135307 0.931172i
\(276\) 0.879178 0.0529203
\(277\) −9.15906 6.65445i −0.550314 0.399827i 0.277587 0.960701i \(-0.410465\pi\)
−0.827901 + 0.560874i \(0.810465\pi\)
\(278\) 2.31208 7.11586i 0.138670 0.426781i
\(279\) 2.37545 + 7.31090i 0.142215 + 0.437692i
\(280\) 2.52029 1.83110i 0.150616 0.109429i
\(281\) −20.3541 + 14.7881i −1.21422 + 0.882184i −0.995607 0.0936276i \(-0.970154\pi\)
−0.218614 + 0.975811i \(0.570154\pi\)
\(282\) 3.10205 + 9.54713i 0.184724 + 0.568523i
\(283\) 1.73590 5.34254i 0.103188 0.317581i −0.886113 0.463470i \(-0.846604\pi\)
0.989301 + 0.145889i \(0.0466042\pi\)
\(284\) −8.77385 6.37458i −0.520632 0.378262i
\(285\) −0.957296 −0.0567053
\(286\) −5.00372 5.13329i −0.295876 0.303538i
\(287\) 4.28967 0.253211
\(288\) −0.809017 0.587785i −0.0476718 0.0346356i
\(289\) −5.09737 + 15.6881i −0.299845 + 0.922828i
\(290\) −6.32652 19.4710i −0.371506 1.14338i
\(291\) 0.211270 0.153497i 0.0123849 0.00899813i
\(292\) −8.69316 + 6.31595i −0.508728 + 0.369613i
\(293\) 2.56520 + 7.89487i 0.149861 + 0.461223i 0.997604 0.0691831i \(-0.0220393\pi\)
−0.847743 + 0.530407i \(0.822039\pi\)
\(294\) 0.309017 0.951057i 0.0180222 0.0554667i
\(295\) −14.4939 10.5305i −0.843870 0.613107i
\(296\) −3.87918 −0.225473
\(297\) −1.54336 + 2.93565i −0.0895549 + 0.170344i
\(298\) 1.42756 0.0826963
\(299\) 1.53734 + 1.11694i 0.0889064 + 0.0645943i
\(300\) 1.45385 4.47449i 0.0839381 0.258335i
\(301\) −2.54709 7.83913i −0.146812 0.451840i
\(302\) 8.05935 5.85546i 0.463763 0.336944i
\(303\) −2.06365 + 1.49933i −0.118554 + 0.0861342i
\(304\) 0.0949591 + 0.292254i 0.00544628 + 0.0167619i
\(305\) −3.00762 + 9.25650i −0.172216 + 0.530026i
\(306\) −0.574672 0.417524i −0.0328518 0.0238682i
\(307\) 1.44088 0.0822355 0.0411178 0.999154i \(-0.486908\pi\)
0.0411178 + 0.999154i \(0.486908\pi\)
\(308\) −1.54336 + 2.93565i −0.0879412 + 0.167274i
\(309\) 18.8420 1.07188
\(310\) 19.3738 + 14.0759i 1.10036 + 0.799456i
\(311\) 3.05749 9.41000i 0.173375 0.533592i −0.826181 0.563405i \(-0.809491\pi\)
0.999556 + 0.0298128i \(0.00949111\pi\)
\(312\) −0.667908 2.05561i −0.0378128 0.116376i
\(313\) 4.49721 3.26742i 0.254197 0.184685i −0.453388 0.891313i \(-0.649785\pi\)
0.707585 + 0.706628i \(0.249785\pi\)
\(314\) 19.9352 14.4838i 1.12501 0.817369i
\(315\) −0.962664 2.96278i −0.0542400 0.166933i
\(316\) −3.00230 + 9.24013i −0.168893 + 0.519798i
\(317\) 0.561684 + 0.408087i 0.0315473 + 0.0229205i 0.603447 0.797403i \(-0.293793\pi\)
−0.571900 + 0.820323i \(0.693793\pi\)
\(318\) −6.58394 −0.369209
\(319\) 15.2142 + 15.6082i 0.851831 + 0.873889i
\(320\) −3.11525 −0.174148
\(321\) 2.75139 + 1.99900i 0.153568 + 0.111574i
\(322\) 0.271681 0.836148i 0.0151402 0.0465967i
\(323\) 0.0674526 + 0.207598i 0.00375316 + 0.0115511i
\(324\) −0.809017 + 0.587785i −0.0449454 + 0.0326547i
\(325\) 8.22677 5.97710i 0.456339 0.331550i
\(326\) 4.43343 + 13.6447i 0.245545 + 0.755710i
\(327\) 2.15258 6.62497i 0.119038 0.366361i
\(328\) −3.47041 2.52140i −0.191621 0.139221i
\(329\) 10.0384 0.553437
\(330\) 1.48574 + 10.2247i 0.0817872 + 0.562852i
\(331\) −31.0269 −1.70539 −0.852696 0.522408i \(-0.825034\pi\)
−0.852696 + 0.522408i \(0.825034\pi\)
\(332\) −12.7701 9.27804i −0.700852 0.509199i
\(333\) −1.19873 + 3.68932i −0.0656901 + 0.202173i
\(334\) 4.33599 + 13.3448i 0.237255 + 0.730195i
\(335\) −16.8260 + 12.2248i −0.919304 + 0.667914i
\(336\) −0.809017 + 0.587785i −0.0441355 + 0.0320663i
\(337\) 5.07933 + 15.6326i 0.276689 + 0.851561i 0.988768 + 0.149461i \(0.0477539\pi\)
−0.712079 + 0.702100i \(0.752246\pi\)
\(338\) −2.57361 + 7.92075i −0.139986 + 0.430832i
\(339\) 1.13102 + 0.821736i 0.0614287 + 0.0446306i
\(340\) −2.21286 −0.120009
\(341\) −25.1284 4.30986i −1.36078 0.233392i
\(342\) 0.307294 0.0166166
\(343\) −0.809017 0.587785i −0.0436828 0.0317374i
\(344\) −2.54709 + 7.83913i −0.137330 + 0.422657i
\(345\) −0.846353 2.60481i −0.0455661 0.140238i
\(346\) −11.4698 + 8.33330i −0.616620 + 0.448001i
\(347\) −28.3634 + 20.6072i −1.52263 + 1.10625i −0.562462 + 0.826823i \(0.690146\pi\)
−0.960166 + 0.279430i \(0.909854\pi\)
\(348\) 2.03082 + 6.25023i 0.108864 + 0.335048i
\(349\) 2.66588 8.20475i 0.142702 0.439190i −0.854007 0.520262i \(-0.825834\pi\)
0.996708 + 0.0810718i \(0.0258343\pi\)
\(350\) −3.80623 2.76539i −0.203451 0.147816i
\(351\) −2.16140 −0.115367
\(352\) 2.97414 1.46782i 0.158522 0.0782353i
\(353\) −28.0551 −1.49322 −0.746611 0.665261i \(-0.768320\pi\)
−0.746611 + 0.665261i \(0.768320\pi\)
\(354\) 4.65258 + 3.38030i 0.247282 + 0.179661i
\(355\) −10.4402 + 32.1315i −0.554107 + 1.70536i
\(356\) 4.59590 + 14.1447i 0.243582 + 0.749668i
\(357\) −0.574672 + 0.417524i −0.0304149 + 0.0220977i
\(358\) 12.8563 9.34063i 0.679475 0.493668i
\(359\) −5.76547 17.7443i −0.304290 0.936508i −0.979941 0.199287i \(-0.936138\pi\)
0.675651 0.737221i \(-0.263862\pi\)
\(360\) −0.962664 + 2.96278i −0.0507368 + 0.156152i
\(361\) 15.2949 + 11.1124i 0.804996 + 0.584864i
\(362\) −17.7593 −0.933406
\(363\) −6.23607 9.06154i −0.327309 0.475607i
\(364\) −2.16140 −0.113288
\(365\) 27.0813 + 19.6757i 1.41750 + 1.02987i
\(366\) 0.965452 2.97136i 0.0504650 0.155315i
\(367\) −0.465624 1.43304i −0.0243054 0.0748042i 0.938168 0.346180i \(-0.112521\pi\)
−0.962473 + 0.271376i \(0.912521\pi\)
\(368\) −0.711270 + 0.516768i −0.0370775 + 0.0269384i
\(369\) −3.47041 + 2.52140i −0.180662 + 0.131259i
\(370\) 3.73434 + 11.4931i 0.194139 + 0.597499i
\(371\) −2.03455 + 6.26170i −0.105628 + 0.325091i
\(372\) −6.21902 4.51838i −0.322441 0.234267i
\(373\) −34.9467 −1.80947 −0.904737 0.425971i \(-0.859933\pi\)
−0.904737 + 0.425971i \(0.859933\pi\)
\(374\) 2.11263 1.04265i 0.109241 0.0539139i
\(375\) 0.919752 0.0474958
\(376\) −8.12127 5.90045i −0.418823 0.304292i
\(377\) −4.38941 + 13.5092i −0.226066 + 0.695761i
\(378\) 0.309017 + 0.951057i 0.0158941 + 0.0489171i
\(379\) −9.65258 + 7.01301i −0.495820 + 0.360234i −0.807418 0.589980i \(-0.799136\pi\)
0.311598 + 0.950214i \(0.399136\pi\)
\(380\) 0.774469 0.562685i 0.0397294 0.0288651i
\(381\) 4.95757 + 15.2578i 0.253984 + 0.781683i
\(382\) −8.12423 + 25.0038i −0.415672 + 1.27931i
\(383\) −14.6245 10.6253i −0.747278 0.542929i 0.147704 0.989032i \(-0.452812\pi\)
−0.894982 + 0.446103i \(0.852812\pi\)
\(384\) 1.00000 0.0510310
\(385\) 10.1834 + 1.74659i 0.518994 + 0.0890145i
\(386\) 5.56788 0.283398
\(387\) 6.66836 + 4.84485i 0.338972 + 0.246277i
\(388\) −0.0806980 + 0.248363i −0.00409682 + 0.0126087i
\(389\) −0.468412 1.44162i −0.0237494 0.0730932i 0.938479 0.345335i \(-0.112235\pi\)
−0.962229 + 0.272242i \(0.912235\pi\)
\(390\) −5.44734 + 3.95772i −0.275837 + 0.200407i
\(391\) −0.505239 + 0.367078i −0.0255510 + 0.0185639i
\(392\) 0.309017 + 0.951057i 0.0156077 + 0.0480356i
\(393\) 6.14004 18.8971i 0.309724 0.953233i
\(394\) 9.55356 + 6.94107i 0.481301 + 0.349686i
\(395\) 30.2666 1.52288
\(396\) −0.476925 3.28216i −0.0239664 0.164935i
\(397\) 32.2351 1.61783 0.808917 0.587924i \(-0.200054\pi\)
0.808917 + 0.587924i \(0.200054\pi\)
\(398\) −7.71472 5.60507i −0.386704 0.280957i
\(399\) 0.0949591 0.292254i 0.00475390 0.0146310i
\(400\) 1.45385 + 4.47449i 0.0726925 + 0.223725i
\(401\) −7.22677 + 5.25055i −0.360888 + 0.262200i −0.753422 0.657537i \(-0.771598\pi\)
0.392535 + 0.919737i \(0.371598\pi\)
\(402\) 5.40119 3.92419i 0.269387 0.195721i
\(403\) −5.13430 15.8017i −0.255758 0.787141i
\(404\) 0.788244 2.42596i 0.0392166 0.120696i
\(405\) 2.52029 + 1.83110i 0.125234 + 0.0909879i
\(406\) 6.57188 0.326157
\(407\) −8.98046 9.21301i −0.445145 0.456672i
\(408\) 0.710334 0.0351668
\(409\) 17.3829 + 12.6294i 0.859527 + 0.624483i 0.927756 0.373186i \(-0.121735\pi\)
−0.0682290 + 0.997670i \(0.521735\pi\)
\(410\) −4.12951 + 12.7093i −0.203942 + 0.627668i
\(411\) 0.717954 + 2.20964i 0.0354141 + 0.108993i
\(412\) −15.2435 + 11.0750i −0.750992 + 0.545628i
\(413\) 4.65258 3.38030i 0.228939 0.166334i
\(414\) 0.271681 + 0.836148i 0.0133524 + 0.0410944i
\(415\) −15.1954 + 46.7667i −0.745913 + 2.29568i
\(416\) 1.74861 + 1.27044i 0.0857325 + 0.0622883i
\(417\) 7.48206 0.366398
\(418\) −0.474266 + 0.902107i −0.0231971 + 0.0441235i
\(419\) 22.3380 1.09128 0.545642 0.838018i \(-0.316286\pi\)
0.545642 + 0.838018i \(0.316286\pi\)
\(420\) 2.52029 + 1.83110i 0.122977 + 0.0893483i
\(421\) 3.05944 9.41598i 0.149108 0.458907i −0.848408 0.529342i \(-0.822439\pi\)
0.997516 + 0.0704352i \(0.0224388\pi\)
\(422\) −3.69413 11.3694i −0.179827 0.553452i
\(423\) −8.12127 + 5.90045i −0.394870 + 0.286890i
\(424\) 5.32652 3.86994i 0.258678 0.187941i
\(425\) 1.03272 + 3.17838i 0.0500942 + 0.154174i
\(426\) 3.35131 10.3143i 0.162372 0.499729i
\(427\) −2.52759 1.83640i −0.122318 0.0888696i
\(428\) −3.40091 −0.164389
\(429\) 3.33582 6.34510i 0.161055 0.306344i
\(430\) 25.6776 1.23828
\(431\) −1.31574 0.955939i −0.0633768 0.0460460i 0.555646 0.831419i \(-0.312471\pi\)
−0.619023 + 0.785373i \(0.712471\pi\)
\(432\) 0.309017 0.951057i 0.0148676 0.0457577i
\(433\) −5.08416 15.6474i −0.244329 0.751967i −0.995746 0.0921398i \(-0.970629\pi\)
0.751417 0.659828i \(-0.229371\pi\)
\(434\) −6.21902 + 4.51838i −0.298522 + 0.216889i
\(435\) 16.5630 12.0337i 0.794137 0.576974i
\(436\) 2.15258 + 6.62497i 0.103090 + 0.317278i
\(437\) 0.0834859 0.256943i 0.00399367 0.0122913i
\(438\) −8.69316 6.31595i −0.415375 0.301788i
\(439\) −6.45481 −0.308071 −0.154036 0.988065i \(-0.549227\pi\)
−0.154036 + 0.988065i \(0.549227\pi\)
\(440\) −7.21193 7.39868i −0.343815 0.352718i
\(441\) 1.00000 0.0476190
\(442\) 1.24209 + 0.902434i 0.0590804 + 0.0429244i
\(443\) 10.7204 32.9941i 0.509344 1.56760i −0.284000 0.958824i \(-0.591662\pi\)
0.793344 0.608774i \(-0.208338\pi\)
\(444\) −1.19873 3.68932i −0.0568893 0.175087i
\(445\) 37.4833 27.2332i 1.77688 1.29098i
\(446\) 7.10226 5.16009i 0.336302 0.244337i
\(447\) 0.441140 + 1.35769i 0.0208652 + 0.0642165i
\(448\) 0.309017 0.951057i 0.0145997 0.0449332i
\(449\) 29.3647 + 21.3347i 1.38581 + 1.00685i 0.996311 + 0.0858192i \(0.0273508\pi\)
0.389496 + 0.921028i \(0.372649\pi\)
\(450\) 4.70476 0.221784
\(451\) −2.04585 14.0794i −0.0963353 0.662971i
\(452\) −1.39802 −0.0657573
\(453\) 8.05935 + 5.85546i 0.378661 + 0.275113i
\(454\) −6.02667 + 18.5482i −0.282846 + 0.870509i
\(455\) 2.08070 + 6.40373i 0.0975446 + 0.300211i
\(456\) −0.248606 + 0.180623i −0.0116420 + 0.00845844i
\(457\) −17.2230 + 12.5133i −0.805660 + 0.585346i −0.912569 0.408923i \(-0.865905\pi\)
0.106909 + 0.994269i \(0.465905\pi\)
\(458\) −2.24954 6.92338i −0.105114 0.323508i
\(459\) 0.219505 0.675568i 0.0102456 0.0315328i
\(460\) 2.21578 + 1.60986i 0.103311 + 0.0750601i
\(461\) −34.3997 −1.60215 −0.801076 0.598562i \(-0.795739\pi\)
−0.801076 + 0.598562i \(0.795739\pi\)
\(462\) −3.26889 0.560659i −0.152083 0.0260842i
\(463\) 33.4916 1.55648 0.778242 0.627964i \(-0.216111\pi\)
0.778242 + 0.627964i \(0.216111\pi\)
\(464\) −5.31677 3.86286i −0.246825 0.179329i
\(465\) −7.40012 + 22.7752i −0.343172 + 1.05618i
\(466\) −0.844352 2.59865i −0.0391138 0.120380i
\(467\) 20.1500 14.6398i 0.932429 0.677449i −0.0141572 0.999900i \(-0.504507\pi\)
0.946586 + 0.322450i \(0.104507\pi\)
\(468\) 1.74861 1.27044i 0.0808293 0.0587260i
\(469\) −2.06307 6.34948i −0.0952637 0.293192i
\(470\) −9.66365 + 29.7417i −0.445751 + 1.37188i
\(471\) 19.9352 + 14.4838i 0.918568 + 0.667379i
\(472\) −5.75091 −0.264707
\(473\) −24.5145 + 12.0986i −1.12718 + 0.556295i
\(474\) −9.71565 −0.446255
\(475\) −1.16963 0.849787i −0.0536664 0.0389909i
\(476\) 0.219505 0.675568i 0.0100610 0.0309646i
\(477\) −2.03455 6.26170i −0.0931556 0.286703i
\(478\) −20.9517 + 15.2223i −0.958308 + 0.696251i
\(479\) 21.0876 15.3211i 0.963518 0.700037i 0.00955297 0.999954i \(-0.496959\pi\)
0.953965 + 0.299917i \(0.0969591\pi\)
\(480\) −0.962664 2.96278i −0.0439394 0.135232i
\(481\) 2.59093 7.97408i 0.118136 0.363587i
\(482\) 5.14562 + 3.73851i 0.234377 + 0.170285i
\(483\) 0.879178 0.0400040
\(484\) 10.3713 + 3.66547i 0.471424 + 0.166612i
\(485\) 0.813528 0.0369404
\(486\) −0.809017 0.587785i −0.0366978 0.0266625i
\(487\) −3.41038 + 10.4961i −0.154539 + 0.475623i −0.998114 0.0613891i \(-0.980447\pi\)
0.843575 + 0.537012i \(0.180447\pi\)
\(488\) 0.965452 + 2.97136i 0.0437040 + 0.134507i
\(489\) −11.6069 + 8.43289i −0.524881 + 0.381349i
\(490\) 2.52029 1.83110i 0.113855 0.0827205i
\(491\) 0.0565149 + 0.173935i 0.00255048 + 0.00784958i 0.952324 0.305090i \(-0.0986864\pi\)
−0.949773 + 0.312939i \(0.898686\pi\)
\(492\) 1.32558 4.07972i 0.0597618 0.183928i
\(493\) −3.77668 2.74392i −0.170093 0.123580i
\(494\) −0.664184 −0.0298830
\(495\) −9.26517 + 4.57263i −0.416438 + 0.205525i
\(496\) 7.68713 0.345162
\(497\) −8.77385 6.37458i −0.393561 0.285939i
\(498\) 4.87776 15.0122i 0.218577 0.672712i
\(499\) 5.21872 + 16.0616i 0.233622 + 0.719014i 0.997301 + 0.0734185i \(0.0233909\pi\)
−0.763679 + 0.645596i \(0.776609\pi\)
\(500\) −0.744095 + 0.540617i −0.0332769 + 0.0241771i
\(501\) −11.3518 + 8.24754i −0.507159 + 0.368473i
\(502\) −3.98095 12.2521i −0.177678 0.546838i
\(503\) 1.26201 3.88407i 0.0562703 0.173182i −0.918971 0.394325i \(-0.870979\pi\)
0.975242 + 0.221142i \(0.0709786\pi\)
\(504\) −0.809017 0.587785i −0.0360365 0.0261820i
\(505\) −7.94640 −0.353610
\(506\) −2.87394 0.492919i −0.127762 0.0219129i
\(507\) −8.32837 −0.369876
\(508\) −12.9791 9.42987i −0.575854 0.418383i
\(509\) 11.5255 35.4719i 0.510860 1.57227i −0.279831 0.960049i \(-0.590278\pi\)
0.790691 0.612216i \(-0.209722\pi\)
\(510\) −0.683813 2.10456i −0.0302797 0.0931914i
\(511\) −8.69316 + 6.31595i −0.384563 + 0.279401i
\(512\) −0.809017 + 0.587785i −0.0357538 + 0.0259767i
\(513\) 0.0949591 + 0.292254i 0.00419254 + 0.0129033i
\(514\) 1.61565 4.97247i 0.0712634 0.219326i
\(515\) 47.4872 + 34.5015i 2.09254 + 1.52032i
\(516\) −8.24254 −0.362858
\(517\) −4.78759 32.9477i −0.210558 1.44904i
\(518\) −3.87918 −0.170441
\(519\) −11.4698 8.33330i −0.503468 0.365791i
\(520\) 2.08070 6.40373i 0.0912446 0.280822i
\(521\) −0.291138 0.896030i −0.0127550 0.0392558i 0.944476 0.328579i \(-0.106570\pi\)
−0.957231 + 0.289323i \(0.906570\pi\)
\(522\) −5.31677 + 3.86286i −0.232709 + 0.169073i
\(523\) −18.6008 + 13.5143i −0.813357 + 0.590938i −0.914802 0.403903i \(-0.867653\pi\)
0.101445 + 0.994841i \(0.467653\pi\)
\(524\) 6.14004 + 18.8971i 0.268229 + 0.825524i
\(525\) 1.45385 4.47449i 0.0634512 0.195283i
\(526\) −21.7017 15.7672i −0.946239 0.687483i
\(527\) 5.46043 0.237860
\(528\) 2.31504 + 2.37499i 0.100749 + 0.103358i
\(529\) −22.2270 −0.966393
\(530\) −16.5934 12.0558i −0.720772 0.523671i
\(531\) −1.77713 + 5.46944i −0.0771208 + 0.237353i
\(532\) 0.0949591 + 0.292254i 0.00411700 + 0.0126708i
\(533\) 7.50094 5.44975i 0.324902 0.236055i
\(534\) −12.0322 + 8.74191i −0.520685 + 0.378300i
\(535\) 3.27393 + 10.0761i 0.141544 + 0.435629i
\(536\) −2.06307 + 6.34948i −0.0891111 + 0.274256i
\(537\) 12.8563 + 9.34063i 0.554789 + 0.403078i
\(538\) −11.0403 −0.475982
\(539\) −1.54336 + 2.93565i −0.0664773 + 0.126447i
\(540\) −3.11525 −0.134059
\(541\) −15.1643 11.0175i −0.651964 0.473680i 0.211976 0.977275i \(-0.432010\pi\)
−0.863940 + 0.503595i \(0.832010\pi\)
\(542\) −5.59734 + 17.2268i −0.240426 + 0.739956i
\(543\) −5.48791 16.8901i −0.235509 0.724822i
\(544\) −0.574672 + 0.417524i −0.0246389 + 0.0179012i
\(545\) 17.5561 12.7552i 0.752019 0.546374i
\(546\) −0.667908 2.05561i −0.0285838 0.0879720i
\(547\) 8.12818 25.0160i 0.347536 1.06961i −0.612676 0.790334i \(-0.709907\pi\)
0.960212 0.279271i \(-0.0900929\pi\)
\(548\) −1.87963 1.36563i −0.0802937 0.0583368i
\(549\) 3.12427 0.133341
\(550\) −7.26114 + 13.8115i −0.309616 + 0.588925i
\(551\) 2.01950 0.0860336
\(552\) −0.711270 0.516768i −0.0302737 0.0219951i
\(553\) −3.00230 + 9.24013i −0.127671 + 0.392930i
\(554\) 3.49845 + 10.7671i 0.148635 + 0.457451i
\(555\) −9.77664 + 7.10315i −0.414995 + 0.301512i
\(556\) −6.05311 + 4.39784i −0.256709 + 0.186510i
\(557\) −2.36860 7.28979i −0.100361 0.308879i 0.888253 0.459355i \(-0.151919\pi\)
−0.988614 + 0.150476i \(0.951919\pi\)
\(558\) 2.37545 7.31090i 0.100561 0.309495i
\(559\) −14.4130 10.4716i −0.609603 0.442903i
\(560\) −3.11525 −0.131643
\(561\) 1.64445 + 1.68704i 0.0694289 + 0.0712267i
\(562\) 25.1590 1.06127
\(563\) 32.5519 + 23.6503i 1.37190 + 0.996742i 0.997586 + 0.0694397i \(0.0221211\pi\)
0.374312 + 0.927303i \(0.377879\pi\)
\(564\) 3.10205 9.54713i 0.130620 0.402007i
\(565\) 1.34582 + 4.14202i 0.0566192 + 0.174256i
\(566\) −4.54464 + 3.30187i −0.191025 + 0.138788i
\(567\) −0.809017 + 0.587785i −0.0339755 + 0.0246847i
\(568\) 3.35131 + 10.3143i 0.140618 + 0.432778i
\(569\) −9.29055 + 28.5934i −0.389480 + 1.19870i 0.543698 + 0.839281i \(0.317024\pi\)
−0.933178 + 0.359415i \(0.882976\pi\)
\(570\) 0.774469 + 0.562685i 0.0324389 + 0.0235683i
\(571\) −21.9318 −0.917817 −0.458909 0.888483i \(-0.651760\pi\)
−0.458909 + 0.888483i \(0.651760\pi\)
\(572\) 1.03082 + 7.09404i 0.0431009 + 0.296617i
\(573\) −26.2906 −1.09830
\(574\) −3.47041 2.52140i −0.144852 0.105241i
\(575\) 1.27819 3.93387i 0.0533043 0.164054i
\(576\) 0.309017 + 0.951057i 0.0128757 + 0.0396274i
\(577\) 29.3684 21.3374i 1.22262 0.888287i 0.226308 0.974056i \(-0.427335\pi\)
0.996315 + 0.0857685i \(0.0273345\pi\)
\(578\) 13.3451 9.69577i 0.555082 0.403291i
\(579\) 1.72057 + 5.29537i 0.0715045 + 0.220068i
\(580\) −6.32652 + 19.4710i −0.262694 + 0.808490i
\(581\) −12.7701 9.27804i −0.529794 0.384918i
\(582\) −0.261144 −0.0108248
\(583\) 21.5222 + 3.69134i 0.891358 + 0.152880i
\(584\) 10.7453 0.444645
\(585\) −5.44734 3.95772i −0.225220 0.163632i
\(586\) 2.56520 7.89487i 0.105967 0.326134i
\(587\) −1.81885 5.59783i −0.0750718 0.231047i 0.906478 0.422252i \(-0.138760\pi\)
−0.981550 + 0.191205i \(0.938760\pi\)
\(588\) −0.809017 + 0.587785i −0.0333633 + 0.0242399i
\(589\) −1.91107 + 1.38847i −0.0787441 + 0.0572110i
\(590\) 5.53619 + 17.0386i 0.227921 + 0.701470i
\(591\) −3.64914 + 11.2309i −0.150105 + 0.461977i
\(592\) 3.13832 + 2.28012i 0.128984 + 0.0937125i
\(593\) −10.5795 −0.434449 −0.217224 0.976122i \(-0.569700\pi\)
−0.217224 + 0.976122i \(0.569700\pi\)
\(594\) 2.97414 1.46782i 0.122030 0.0602256i
\(595\) −2.21286 −0.0907186
\(596\) −1.15492 0.839099i −0.0473074 0.0343708i
\(597\) 2.94676 9.06919i 0.120603 0.371177i
\(598\) −0.587210 1.80725i −0.0240128 0.0739038i
\(599\) 9.76734 7.09639i 0.399083 0.289951i −0.370085 0.928998i \(-0.620671\pi\)
0.769167 + 0.639047i \(0.220671\pi\)
\(600\) −3.80623 + 2.76539i −0.155389 + 0.112896i
\(601\) −13.3021 40.9395i −0.542602 1.66996i −0.726623 0.687036i \(-0.758911\pi\)
0.184021 0.982922i \(-0.441089\pi\)
\(602\) −2.54709 + 7.83913i −0.103811 + 0.319499i
\(603\) 5.40119 + 3.92419i 0.219953 + 0.159805i
\(604\) −9.96190 −0.405344
\(605\) 0.875861 34.2565i 0.0356088 1.39273i
\(606\) 2.55081 0.103620
\(607\) −9.57439 6.95620i −0.388613 0.282344i 0.376274 0.926508i \(-0.377205\pi\)
−0.764887 + 0.644165i \(0.777205\pi\)
\(608\) 0.0949591 0.292254i 0.00385110 0.0118525i
\(609\) 2.03082 + 6.25023i 0.0822931 + 0.253272i
\(610\) 7.87405 5.72083i 0.318811 0.231630i
\(611\) 17.5533 12.7532i 0.710130 0.515940i
\(612\) 0.219505 + 0.675568i 0.00887297 + 0.0273082i
\(613\) 11.6416 35.8292i 0.470200 1.44713i −0.382122 0.924112i \(-0.624807\pi\)
0.852323 0.523016i \(-0.175193\pi\)
\(614\) −1.16570 0.846930i −0.0470438 0.0341793i
\(615\) −13.3634 −0.538863
\(616\) 2.97414 1.46782i 0.119831 0.0591403i
\(617\) −40.5797 −1.63368 −0.816838 0.576867i \(-0.804275\pi\)
−0.816838 + 0.576867i \(0.804275\pi\)
\(618\) −15.2435 11.0750i −0.613183 0.445503i
\(619\) −7.14425 + 21.9878i −0.287152 + 0.883762i 0.698594 + 0.715519i \(0.253810\pi\)
−0.985745 + 0.168244i \(0.946190\pi\)
\(620\) −7.40012 22.7752i −0.297196 0.914676i
\(621\) −0.711270 + 0.516768i −0.0285423 + 0.0207372i
\(622\) −8.00462 + 5.81570i −0.320956 + 0.233188i
\(623\) 4.59590 + 14.1447i 0.184131 + 0.566696i
\(624\) −0.667908 + 2.05561i −0.0267377 + 0.0822902i
\(625\) 21.3492 + 15.5111i 0.853967 + 0.620444i
\(626\) −5.55886 −0.222177
\(627\) −1.00451 0.172287i −0.0401163 0.00688048i
\(628\) −24.6413 −0.983296
\(629\) 2.22926 + 1.61965i 0.0888862 + 0.0645796i
\(630\) −0.962664 + 2.96278i −0.0383535 + 0.118040i
\(631\) −5.69945 17.5411i −0.226891 0.698300i −0.998094 0.0617103i \(-0.980345\pi\)
0.771203 0.636590i \(-0.219655\pi\)
\(632\) 7.86013 5.71072i 0.312659 0.227160i
\(633\) 9.67135 7.02665i 0.384402 0.279284i
\(634\) −0.214544 0.660299i −0.00852064 0.0262238i
\(635\) −15.4441 + 47.5319i −0.612879 + 1.88625i
\(636\) 5.32652 + 3.86994i 0.211210 + 0.153453i
\(637\) −2.16140 −0.0856376
\(638\) −3.13430 21.5699i −0.124088 0.853962i
\(639\) 10.8451 0.429025
\(640\) 2.52029 + 1.83110i 0.0996231 + 0.0723804i
\(641\) −2.37656 + 7.31431i −0.0938686 + 0.288898i −0.986957 0.160983i \(-0.948534\pi\)
0.893089 + 0.449881i \(0.148534\pi\)
\(642\) −1.05094 3.23446i −0.0414773 0.127654i
\(643\) −13.1343 + 9.54260i −0.517965 + 0.376323i −0.815837 0.578282i \(-0.803723\pi\)
0.297872 + 0.954606i \(0.403723\pi\)
\(644\) −0.711270 + 0.516768i −0.0280280 + 0.0203635i
\(645\) 7.93480 + 24.4208i 0.312432 + 0.961568i
\(646\) 0.0674526 0.207598i 0.00265389 0.00816783i
\(647\) 11.8174 + 8.58586i 0.464591 + 0.337545i 0.795329 0.606177i \(-0.207298\pi\)
−0.330739 + 0.943722i \(0.607298\pi\)
\(648\) 1.00000 0.0392837
\(649\) −13.3136 13.6583i −0.522604 0.536137i
\(650\) −10.1688 −0.398855
\(651\) −6.21902 4.51838i −0.243743 0.177089i
\(652\) 4.43343 13.6447i 0.173627 0.534368i
\(653\) −4.36249 13.4264i −0.170717 0.525414i 0.828695 0.559701i \(-0.189084\pi\)
−0.999412 + 0.0342870i \(0.989084\pi\)
\(654\) −5.63553 + 4.09445i −0.220367 + 0.160106i
\(655\) 50.0771 36.3831i 1.95667 1.42161i
\(656\) 1.32558 + 4.07972i 0.0517552 + 0.159286i
\(657\) 3.32049 10.2194i 0.129545 0.398697i
\(658\) −8.12127 5.90045i −0.316600 0.230023i
\(659\) 33.9283 1.32166 0.660829 0.750536i \(-0.270205\pi\)
0.660829 + 0.750536i \(0.270205\pi\)
\(660\) 4.80795 9.14527i 0.187149 0.355979i
\(661\) 18.7723 0.730157 0.365079 0.930977i \(-0.381042\pi\)
0.365079 + 0.930977i \(0.381042\pi\)
\(662\) 25.1013 + 18.2371i 0.975589 + 0.708807i
\(663\) −0.474438 + 1.46017i −0.0184256 + 0.0567083i
\(664\) 4.87776 + 15.0122i 0.189294 + 0.582586i
\(665\) 0.774469 0.562685i 0.0300326 0.0218200i
\(666\) 3.13832 2.28012i 0.121607 0.0883530i
\(667\) 1.78546 + 5.49507i 0.0691331 + 0.212770i
\(668\) 4.33599 13.3448i 0.167764 0.516326i
\(669\) 7.10226 + 5.16009i 0.274589 + 0.199501i
\(670\) 20.7981 0.803501
\(671\) −4.82188 + 9.17175i −0.186146 + 0.354072i
\(672\) 1.00000 0.0385758
\(673\) −21.4093 15.5547i −0.825266 0.599591i 0.0929499 0.995671i \(-0.470370\pi\)
−0.918216 + 0.396080i \(0.870370\pi\)
\(674\) 5.07933 15.6326i 0.195649 0.602144i
\(675\) 1.45385 + 4.47449i 0.0559587 + 0.172223i
\(676\) 6.73779 4.89529i 0.259146 0.188280i
\(677\) −9.60943 + 6.98166i −0.369320 + 0.268327i −0.756929 0.653497i \(-0.773301\pi\)
0.387609 + 0.921824i \(0.373301\pi\)
\(678\) −0.432012 1.32960i −0.0165913 0.0510628i
\(679\) −0.0806980 + 0.248363i −0.00309690 + 0.00953129i
\(680\) 1.79024 + 1.30069i 0.0686528 + 0.0498791i
\(681\) −19.5027 −0.747346
\(682\) 17.7960 + 18.2569i 0.681445 + 0.699091i
\(683\) −35.6132 −1.36270 −0.681351 0.731957i \(-0.738607\pi\)
−0.681351 + 0.731957i \(0.738607\pi\)
\(684\) −0.248606 0.180623i −0.00950569 0.00690629i
\(685\) −2.23660 + 6.88356i −0.0854562 + 0.263007i
\(686\) 0.309017 + 0.951057i 0.0117983 + 0.0363115i
\(687\) 5.88938 4.27888i 0.224694 0.163250i
\(688\) 6.66836 4.84485i 0.254229 0.184708i
\(689\) 4.39746 + 13.5340i 0.167530 + 0.515604i
\(690\) −0.846353 + 2.60481i −0.0322201 + 0.0991633i
\(691\) −3.14171 2.28258i −0.119516 0.0868336i 0.526421 0.850224i \(-0.323533\pi\)
−0.645938 + 0.763390i \(0.723533\pi\)
\(692\) 14.1774 0.538946
\(693\) −0.476925 3.28216i −0.0181169 0.124679i
\(694\) 35.0591 1.33083
\(695\) 18.8569 + 13.7004i 0.715284 + 0.519684i
\(696\) 2.03082 6.25023i 0.0769782 0.236914i
\(697\) 0.941604 + 2.89796i 0.0356658 + 0.109768i
\(698\) −6.97938 + 5.07081i −0.264173 + 0.191933i
\(699\) 2.21054 1.60605i 0.0836104 0.0607465i
\(700\) 1.45385 + 4.47449i 0.0549504 + 0.169120i
\(701\) 10.5574 32.4925i 0.398749 1.22722i −0.527254 0.849707i \(-0.676779\pi\)
0.926003 0.377515i \(-0.123221\pi\)
\(702\) 1.74861 + 1.27044i 0.0659969 + 0.0479495i
\(703\) −1.19205 −0.0449589
\(704\) −3.26889 0.560659i −0.123201 0.0211306i
\(705\) −31.2722 −1.17778
\(706\) 22.6971 + 16.4904i 0.854215 + 0.620623i
\(707\) 0.788244 2.42596i 0.0296450 0.0912378i
\(708\) −1.77713 5.46944i −0.0667886 0.205554i
\(709\) 38.6479 28.0794i 1.45145 1.05454i 0.465964 0.884803i \(-0.345707\pi\)
0.985489 0.169739i \(-0.0542925\pi\)
\(710\) 27.3327 19.8584i 1.02578 0.745272i
\(711\) −3.00230 9.24013i −0.112595 0.346532i
\(712\) 4.59590 14.1447i 0.172238 0.530095i
\(713\) −5.46762 3.97246i −0.204764 0.148770i
\(714\) 0.710334 0.0265836
\(715\) 20.0257 9.88327i 0.748919 0.369613i
\(716\) −15.8912 −0.593883
\(717\) −20.9517 15.2223i −0.782455 0.568487i
\(718\) −5.76547 + 17.7443i −0.215165 + 0.662211i
\(719\) 1.01560 + 3.12571i 0.0378756 + 0.116569i 0.968207 0.250152i \(-0.0804804\pi\)
−0.930331 + 0.366721i \(0.880480\pi\)
\(720\) 2.52029 1.83110i 0.0939256 0.0682409i
\(721\) −15.2435 + 11.0750i −0.567697 + 0.412456i
\(722\) −5.84214 17.9803i −0.217422 0.669156i
\(723\) −1.96545 + 6.04904i −0.0730959 + 0.224966i
\(724\) 14.3675 + 10.4386i 0.533965 + 0.387949i
\(725\) 30.9191 1.14831
\(726\) −0.281153 + 10.9964i −0.0104346 + 0.408115i
\(727\) −6.49508 −0.240889 −0.120445 0.992720i \(-0.538432\pi\)
−0.120445 + 0.992720i \(0.538432\pi\)
\(728\) 1.74861 + 1.27044i 0.0648077 + 0.0470855i
\(729\) 0.309017 0.951057i 0.0114451 0.0352243i
\(730\) −10.3441 31.8360i −0.382854 1.17830i
\(731\) 4.73676 3.44146i 0.175195 0.127287i
\(732\) −2.52759 + 1.83640i −0.0934223 + 0.0678752i
\(733\) −15.4915 47.6778i −0.572190 1.76102i −0.645553 0.763715i \(-0.723373\pi\)
0.0733629 0.997305i \(-0.476627\pi\)
\(734\) −0.465624 + 1.43304i −0.0171865 + 0.0528946i
\(735\) 2.52029 + 1.83110i 0.0929622 + 0.0675410i
\(736\) 0.879178 0.0324069
\(737\) −19.8560 + 9.79954i −0.731407 + 0.360971i
\(738\) 4.28967 0.157905
\(739\) −12.3163 8.94833i −0.453063 0.329170i 0.337741 0.941239i \(-0.390337\pi\)
−0.790804 + 0.612070i \(0.790337\pi\)
\(740\) 3.73434 11.4931i 0.137277 0.422496i
\(741\) −0.205244 0.631676i −0.00753983 0.0232052i
\(742\) 5.32652 3.86994i 0.195543 0.142070i
\(743\) 19.0139 13.8144i 0.697554 0.506803i −0.181581 0.983376i \(-0.558121\pi\)
0.879135 + 0.476573i \(0.158121\pi\)
\(744\) 2.37545 + 7.31090i 0.0870884 + 0.268030i
\(745\) −1.37426 + 4.22954i −0.0503490 + 0.154958i
\(746\) 28.2725 + 20.5412i 1.03513 + 0.752066i
\(747\) 15.7847 0.577534
\(748\) −2.32201 0.398255i −0.0849009 0.0145616i
\(749\) −3.40091 −0.124267
\(750\) −0.744095 0.540617i −0.0271705 0.0197405i
\(751\) 5.12915 15.7859i 0.187165 0.576036i −0.812814 0.582524i \(-0.802065\pi\)
0.999979 + 0.00648819i \(0.00206527\pi\)
\(752\) 3.10205 + 9.54713i 0.113120 + 0.348148i
\(753\) 10.4223 7.57222i 0.379808 0.275947i
\(754\) 11.4916 8.34916i 0.418501 0.304059i
\(755\) 9.58996 + 29.5149i 0.349014 + 1.07416i
\(756\) 0.309017 0.951057i 0.0112388 0.0345896i
\(757\) 1.29103 + 0.937989i 0.0469233 + 0.0340918i 0.611000 0.791631i \(-0.290768\pi\)
−0.564076 + 0.825723i \(0.690768\pi\)
\(758\) 11.9312 0.433362
\(759\) −0.419302 2.88560i −0.0152197 0.104741i
\(760\) −0.957296 −0.0347248
\(761\) −2.91975 2.12132i −0.105841 0.0768979i 0.533606 0.845733i \(-0.320837\pi\)
−0.639447 + 0.768835i \(0.720837\pi\)
\(762\) 4.95757 15.2578i 0.179594 0.552733i
\(763\) 2.15258 + 6.62497i 0.0779287 + 0.239840i
\(764\) 21.2695 15.4532i 0.769504 0.559077i
\(765\) 1.79024 1.30069i 0.0647264 0.0470265i
\(766\) 5.58607 + 17.1921i 0.201833 + 0.621177i
\(767\) 3.84108 11.8216i 0.138693 0.426854i
\(768\) −0.809017 0.587785i −0.0291929 0.0212099i
\(769\) −38.6906 −1.39522 −0.697609 0.716479i \(-0.745753\pi\)
−0.697609 + 0.716479i \(0.745753\pi\)
\(770\) −7.21193 7.39868i −0.259900 0.266630i
\(771\) 5.22836 0.188295
\(772\) −4.50451 3.27272i −0.162121 0.117788i
\(773\) 0.534756 1.64581i 0.0192338 0.0591957i −0.940979 0.338465i \(-0.890092\pi\)
0.960213 + 0.279269i \(0.0900923\pi\)
\(774\) −2.54709 7.83913i −0.0915531 0.281772i
\(775\) −29.2590 + 21.2579i −1.05101 + 0.763606i
\(776\) 0.211270 0.153497i 0.00758415 0.00551021i
\(777\) −1.19873 3.68932i −0.0430043 0.132354i
\(778\) −0.468412 + 1.44162i −0.0167934 + 0.0516847i
\(779\) −1.06644 0.774812i −0.0382091 0.0277605i
\(780\) 6.73328 0.241090
\(781\) −16.7379 + 31.8373i −0.598929 + 1.13923i
\(782\) 0.624510 0.0223324
\(783\) −5.31677 3.86286i −0.190006 0.138047i
\(784\) 0.309017 0.951057i 0.0110363 0.0339663i
\(785\) 23.7213 + 73.0067i 0.846650 + 2.60572i
\(786\) −16.0748 + 11.6791i −0.573371 + 0.416578i
\(787\) −2.10005 + 1.52577i −0.0748587 + 0.0543880i −0.624585 0.780957i \(-0.714732\pi\)
0.549727 + 0.835345i \(0.314732\pi\)
\(788\) −3.64914 11.2309i −0.129995 0.400084i
\(789\) 8.28931 25.5119i 0.295107 0.908247i
\(790\) −24.4862 17.7903i −0.871181 0.632950i
\(791\) −1.39802 −0.0497079
\(792\) −1.54336 + 2.93565i −0.0548410 + 0.104314i
\(793\) −6.75278 −0.239798
\(794\) −26.0787 18.9473i −0.925500 0.672415i
\(795\) 6.33812 19.5067i 0.224790 0.691832i
\(796\) 2.94676 + 9.06919i 0.104445 + 0.321449i
\(797\) −24.3171 + 17.6674i −0.861355 + 0.625811i −0.928253 0.371948i \(-0.878690\pi\)
0.0668980 + 0.997760i \(0.478690\pi\)
\(798\) −0.248606 + 0.180623i −0.00880056 + 0.00639398i
\(799\) 2.20349 + 6.78165i 0.0779539 + 0.239917i
\(800\) 1.45385 4.47449i 0.0514014 0.158197i
\(801\) −12.0322 8.74191i −0.425137 0.308880i
\(802\) 8.93278 0.315427
\(803\) 24.8759 + 25.5201i 0.877852 + 0.900583i
\(804\) −6.67624 −0.235453
\(805\) 2.21578 + 1.60986i 0.0780960 + 0.0567401i
\(806\) −5.13430 + 15.8017i −0.180848 + 0.556593i
\(807\) −3.41165 10.5000i −0.120096 0.369616i
\(808\) −2.06365 + 1.49933i −0.0725989 + 0.0527462i
\(809\) −25.0367 + 18.1903i −0.880245 + 0.639535i −0.933316 0.359055i \(-0.883099\pi\)
0.0530713 + 0.998591i \(0.483099\pi\)
\(810\) −0.962664 2.96278i −0.0338246 0.104101i
\(811\) 3.91631 12.0532i 0.137520 0.423243i −0.858453 0.512892i \(-0.828574\pi\)
0.995973 + 0.0896482i \(0.0285743\pi\)
\(812\) −5.31677 3.86286i −0.186582 0.135560i
\(813\) −18.1134 −0.635264
\(814\) 1.85008 + 12.7321i 0.0648452 + 0.446259i
\(815\) −44.6941 −1.56557
\(816\) −0.574672 0.417524i −0.0201175 0.0146163i
\(817\) −0.782704 + 2.40892i −0.0273834 + 0.0842773i
\(818\) −6.63966 20.4348i −0.232150 0.714485i
\(819\) 1.74861 1.27044i 0.0611012 0.0443926i
\(820\) 10.8112 7.85479i 0.377543 0.274301i
\(821\) −1.18204 3.63795i −0.0412535 0.126965i 0.928309 0.371810i \(-0.121263\pi\)
−0.969562 + 0.244845i \(0.921263\pi\)
\(822\) 0.717954 2.20964i 0.0250415 0.0770699i
\(823\) 38.8927 + 28.2572i 1.35571 + 0.984985i 0.998705 + 0.0508841i \(0.0162039\pi\)
0.357010 + 0.934100i \(0.383796\pi\)
\(824\) 18.8420 0.656391
\(825\) −15.3793 2.63776i −0.535440 0.0918352i
\(826\) −5.75091 −0.200100
\(827\) 35.4298 + 25.7413i 1.23202 + 0.895112i 0.997040 0.0768886i \(-0.0244986\pi\)
0.234977 + 0.972001i \(0.424499\pi\)
\(828\) 0.271681 0.836148i 0.00944157 0.0290582i
\(829\) 15.3747 + 47.3184i 0.533985 + 1.64344i 0.745832 + 0.666134i \(0.232052\pi\)
−0.211847 + 0.977303i \(0.567948\pi\)
\(830\) 39.7821 28.9034i 1.38086 1.00325i
\(831\) −9.15906 + 6.65445i −0.317724 + 0.230840i
\(832\) −0.667908 2.05561i −0.0231555 0.0712654i
\(833\) 0.219505 0.675568i 0.00760540 0.0234070i
\(834\) −6.05311 4.39784i −0.209602 0.152285i
\(835\) −43.7117 −1.51271
\(836\) 0.913934 0.451054i 0.0316091 0.0156000i
\(837\) 7.68713 0.265706
\(838\) −18.0718 13.1300i −0.624282 0.453567i
\(839\) −5.92774 + 18.2437i −0.204648 + 0.629842i 0.795079 + 0.606505i \(0.207429\pi\)
−0.999728 + 0.0233371i \(0.992571\pi\)
\(840\) −0.962664 2.96278i −0.0332151 0.102225i
\(841\) −11.4797 + 8.34047i −0.395851 + 0.287603i
\(842\) −8.00971 + 5.81940i −0.276033 + 0.200550i
\(843\) 7.77456 + 23.9276i 0.267770 + 0.824112i
\(844\) −3.69413 + 11.3694i −0.127157 + 0.391349i
\(845\) −20.9899 15.2500i −0.722074 0.524617i
\(846\) 10.0384 0.345129
\(847\) 10.3713 + 3.66547i 0.356363 + 0.125947i
\(848\) −6.58394 −0.226093
\(849\) −4.54464 3.30187i −0.155971 0.113320i
\(850\) 1.03272 3.17838i 0.0354220 0.109018i
\(851\) −1.05390 3.24357i −0.0361272 0.111188i
\(852\) −8.77385 + 6.37458i −0.300587 + 0.218389i
\(853\) 27.9632 20.3165i 0.957442 0.695623i 0.00488696 0.999988i \(-0.498444\pi\)
0.952555 + 0.304366i \(0.0984444\pi\)
\(854\) 0.965452 + 2.97136i 0.0330371 + 0.101678i
\(855\) −0.295821 + 0.910443i −0.0101169 + 0.0311365i
\(856\) 2.75139 + 1.99900i 0.0940407 + 0.0683246i
\(857\) −1.15867 −0.0395792 −0.0197896 0.999804i \(-0.506300\pi\)
−0.0197896 + 0.999804i \(0.506300\pi\)
\(858\) −6.42829 + 3.17255i −0.219458 + 0.108309i
\(859\) −13.5036 −0.460737 −0.230369 0.973103i \(-0.573993\pi\)
−0.230369 + 0.973103i \(0.573993\pi\)
\(860\) −20.7736 15.0929i −0.708373 0.514663i
\(861\) 1.32558 4.07972i 0.0451756 0.139036i
\(862\) 0.502567 + 1.54674i 0.0171175 + 0.0526822i
\(863\) −25.2030 + 18.3110i −0.857919 + 0.623315i −0.927318 0.374274i \(-0.877892\pi\)
0.0693991 + 0.997589i \(0.477892\pi\)
\(864\) −0.809017 + 0.587785i −0.0275233 + 0.0199969i
\(865\) −13.6481 42.0046i −0.464050 1.42820i
\(866\) −5.08416 + 15.6474i −0.172767 + 0.531721i
\(867\) 13.3451 + 9.69577i 0.453223 + 0.329286i
\(868\) 7.68713 0.260918
\(869\) 31.7594 + 5.44717i 1.07736 + 0.184783i
\(870\) −20.4730 −0.694101
\(871\) −11.6741 8.48173i −0.395562 0.287393i
\(872\) 2.15258 6.62497i 0.0728956 0.224350i
\(873\) −0.0806980 0.248363i −0.00273121 0.00840581i
\(874\) −0.218569 + 0.158800i −0.00739321 + 0.00537148i
\(875\) −0.744095 + 0.540617i −0.0251550 + 0.0182762i
\(876\) 3.32049 + 10.2194i 0.112189 + 0.345282i
\(877\) 9.55294 29.4009i 0.322580 0.992799i −0.649941 0.759984i \(-0.725207\pi\)
0.972521 0.232814i \(-0.0747935\pi\)
\(878\) 5.22205 + 3.79404i 0.176236 + 0.128043i
\(879\) 8.30116 0.279991
\(880\) 1.48574 + 10.2247i 0.0500842 + 0.344675i
\(881\) 23.1676 0.780535 0.390268 0.920701i \(-0.372382\pi\)
0.390268 + 0.920701i \(0.372382\pi\)
\(882\) −0.809017 0.587785i −0.0272410 0.0197918i
\(883\) −4.67092 + 14.3756i −0.157189 + 0.483778i −0.998376 0.0569659i \(-0.981857\pi\)
0.841187 + 0.540744i \(0.181857\pi\)
\(884\) −0.474438 1.46017i −0.0159571 0.0491108i
\(885\) −14.4939 + 10.5305i −0.487208 + 0.353978i
\(886\) −28.0665 + 20.3915i −0.942912 + 0.685066i
\(887\) −2.97262 9.14879i −0.0998109 0.307186i 0.888667 0.458554i \(-0.151632\pi\)
−0.988478 + 0.151367i \(0.951632\pi\)
\(888\) −1.19873 + 3.68932i −0.0402268 + 0.123805i
\(889\) −12.9791 9.42987i −0.435305 0.316268i
\(890\) −46.3319 −1.55305
\(891\) 2.31504 + 2.37499i 0.0775569 + 0.0795652i
\(892\) −8.77887 −0.293938
\(893\) −2.49562 1.81317i −0.0835127 0.0606755i
\(894\) 0.441140 1.35769i 0.0147539 0.0454079i
\(895\) 15.2979 + 47.0821i 0.511353 + 1.57378i
\(896\) −0.809017 + 0.587785i −0.0270274 + 0.0196365i
\(897\) 1.53734 1.11694i 0.0513302 0.0372935i
\(898\) −11.2163 34.5203i −0.374294 1.15196i
\(899\) 15.6112 48.0464i 0.520663 1.60244i
\(900\) −3.80623 2.76539i −0.126874 0.0921796i
\(901\) −4.67679 −0.155807
\(902\) −6.62051 + 12.5930i −0.220439 + 0.419299i
\(903\) −8.24254 −0.274295
\(904\) 1.13102 + 0.821736i 0.0376172 + 0.0273305i
\(905\) 17.0962 52.6167i 0.568297 1.74904i
\(906\) −3.07840 9.47433i −0.102273 0.314764i
\(907\) 18.5057 13.4452i 0.614471 0.446439i −0.236515 0.971628i \(-0.576005\pi\)
0.850986 + 0.525189i \(0.176005\pi\)
\(908\) 15.7780 11.4634i 0.523612 0.380427i
\(909\) 0.788244 + 2.42596i 0.0261444 + 0.0804642i
\(910\) 2.08070 6.40373i 0.0689745 0.212282i
\(911\) −19.0630 13.8501i −0.631584 0.458873i 0.225364 0.974275i \(-0.427643\pi\)
−0.856949 + 0.515402i \(0.827643\pi\)
\(912\) 0.307294 0.0101755
\(913\) −24.3616 + 46.3385i −0.806251 + 1.53358i
\(914\) 21.2889 0.704173
\(915\) 7.87405 + 5.72083i 0.260308 + 0.189125i
\(916\) −2.24954 + 6.92338i −0.0743270 + 0.228755i
\(917\) 6.14004 + 18.8971i 0.202762 + 0.624038i
\(918\) −0.574672 + 0.417524i −0.0189670 + 0.0137803i
\(919\) −24.9845 + 18.1523i −0.824161 + 0.598788i −0.917901 0.396809i \(-0.870118\pi\)
0.0937404 + 0.995597i \(0.470118\pi\)
\(920\) −0.846353 2.60481i −0.0279034 0.0858779i
\(921\) 0.445257 1.37036i 0.0146717 0.0451549i
\(922\) 27.8299 + 20.2196i 0.916530 + 0.665898i
\(923\) −23.4405 −0.771554
\(924\) 2.31504 + 2.37499i 0.0761593 + 0.0781314i
\(925\) −18.2506 −0.600076
\(926\) −27.0952 19.6858i −0.890405 0.646917i
\(927\) 5.82249 17.9198i 0.191236 0.588563i
\(928\) 2.03082 + 6.25023i 0.0666651 + 0.205174i
\(929\) 33.1831 24.1090i 1.08870 0.790989i 0.109523 0.993984i \(-0.465068\pi\)
0.979180 + 0.202995i \(0.0650676\pi\)
\(930\) 19.3738 14.0759i 0.635291 0.461566i
\(931\) 0.0949591 + 0.292254i 0.00311216 + 0.00957823i
\(932\) −0.844352 + 2.59865i −0.0276577 + 0.0851215i
\(933\) −8.00462 5.81570i −0.262060 0.190397i
\(934\) −24.9067 −0.814973
\(935\) 1.05537 + 7.26296i 0.0345143 + 0.237524i
\(936\) −2.16140 −0.0706474
\(937\) 2.92275 + 2.12350i 0.0954820 + 0.0693717i 0.634502 0.772921i \(-0.281205\pi\)
−0.539020 + 0.842293i \(0.681205\pi\)
\(938\) −2.06307 + 6.34948i −0.0673616 + 0.207318i
\(939\) −1.71778 5.28679i −0.0560577 0.172528i
\(940\) 25.2998 18.3814i 0.825187 0.599534i
\(941\) 32.4823 23.5997i 1.05889 0.769330i 0.0850086 0.996380i \(-0.472908\pi\)
0.973883 + 0.227050i \(0.0729082\pi\)
\(942\) −7.61459 23.4353i −0.248097 0.763563i
\(943\) 1.16542 3.58680i 0.0379513 0.116802i
\(944\) 4.65258 + 3.38030i 0.151429 + 0.110019i
\(945\) −3.11525 −0.101339
\(946\) 26.9440 + 4.62126i 0.876025 + 0.150250i
\(947\) −33.8239 −1.09913 −0.549564 0.835452i \(-0.685206\pi\)
−0.549564 + 0.835452i \(0.685206\pi\)
\(948\) 7.86013 + 5.71072i 0.255285 + 0.185475i
\(949\) −7.17689 + 22.0882i −0.232972 + 0.717014i
\(950\) 0.446759 + 1.37498i 0.0144948 + 0.0446104i
\(951\) 0.561684 0.408087i 0.0182139 0.0132331i
\(952\) −0.574672 + 0.417524i −0.0186252 + 0.0135320i
\(953\) 10.3116 + 31.7359i 0.334026 + 1.02803i 0.967200 + 0.254017i \(0.0817520\pi\)
−0.633173 + 0.774010i \(0.718248\pi\)
\(954\) −2.03455 + 6.26170i −0.0658709 + 0.202730i
\(955\) −66.2598 48.1405i −2.14412 1.55779i
\(956\) 25.8977 0.837592
\(957\) 19.5457 9.64637i 0.631822 0.311823i
\(958\) −26.0657 −0.842146
\(959\) −1.87963 1.36563i −0.0606964 0.0440985i
\(960\) −0.962664 + 2.96278i −0.0310698 + 0.0956232i
\(961\) 8.68090 + 26.7171i 0.280029 + 0.861840i
\(962\) −6.78315 + 4.92825i −0.218698 + 0.158893i
\(963\) 2.75139 1.99900i 0.0886624 0.0644170i
\(964\) −1.96545 6.04904i −0.0633029 0.194826i
\(965\) −5.36000 + 16.4964i −0.172544 + 0.531037i
\(966\) −0.711270 0.516768i −0.0228847 0.0166267i
\(967\) 48.0391 1.54483 0.772417 0.635116i \(-0.219048\pi\)
0.772417 + 0.635116i \(0.219048\pi\)
\(968\) −6.23607 9.06154i −0.200435 0.291249i
\(969\) 0.218281 0.00701220
\(970\) −0.658158 0.478180i −0.0211322 0.0153534i
\(971\) −12.5807 + 38.7193i −0.403733 + 1.24256i 0.518216 + 0.855250i \(0.326596\pi\)
−0.921949 + 0.387312i \(0.873404\pi\)
\(972\) 0.309017 + 0.951057i 0.00991172 + 0.0305052i
\(973\) −6.05311 + 4.39784i −0.194054 + 0.140988i
\(974\) 8.92850 6.48693i 0.286087 0.207855i
\(975\) −3.14235 9.67115i −0.100636 0.309725i
\(976\) 0.965452 2.97136i 0.0309034 0.0951108i
\(977\) −2.26347 1.64450i −0.0724147 0.0526124i 0.550989 0.834513i \(-0.314251\pi\)
−0.623404 + 0.781900i \(0.714251\pi\)
\(978\) 14.3469 0.458763
\(979\) 44.2332 21.8304i 1.41370 0.697703i
\(980\) −3.11525 −0.0995129
\(981\) −5.63553 4.09445i −0.179929 0.130726i
\(982\) 0.0565149 0.173935i 0.00180346 0.00555049i
\(983\) 9.02142 + 27.7651i 0.287739 + 0.885568i 0.985564 + 0.169301i \(0.0541509\pi\)
−0.697826 + 0.716267i \(0.745849\pi\)
\(984\) −3.47041 + 2.52140i −0.110633 + 0.0803794i
\(985\) −29.7617 + 21.6231i −0.948286 + 0.688970i
\(986\) 1.44256 + 4.43975i 0.0459406 + 0.141390i
\(987\) 3.10205 9.54713i 0.0987393 0.303888i
\(988\) 0.537336 + 0.390397i 0.0170949 + 0.0124202i
\(989\) −7.24666 −0.230430
\(990\) 10.1834 + 1.74659i 0.323650 + 0.0555103i
\(991\) 49.6877 1.57838 0.789191 0.614148i \(-0.210500\pi\)
0.789191 + 0.614148i \(0.210500\pi\)
\(992\) −6.21902 4.51838i −0.197454 0.143459i
\(993\) −9.58783 + 29.5083i −0.304261 + 0.936418i
\(994\) 3.35131 + 10.3143i 0.106297 + 0.327149i
\(995\) 24.0332 17.4612i 0.761905 0.553556i
\(996\) −12.7701 + 9.27804i −0.404637 + 0.293986i
\(997\) −10.1095 31.1138i −0.320171 0.985385i −0.973573 0.228374i \(-0.926659\pi\)
0.653402 0.757011i \(-0.273341\pi\)
\(998\) 5.21872 16.0616i 0.165196 0.508420i
\(999\) 3.13832 + 2.28012i 0.0992921 + 0.0721399i
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 462.2.j.e.169.2 8
11.3 even 5 inner 462.2.j.e.421.2 yes 8
11.5 even 5 5082.2.a.cf.1.1 4
11.6 odd 10 5082.2.a.ca.1.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
462.2.j.e.169.2 8 1.1 even 1 trivial
462.2.j.e.421.2 yes 8 11.3 even 5 inner
5082.2.a.ca.1.1 4 11.6 odd 10
5082.2.a.cf.1.1 4 11.5 even 5