Properties

Label 260.2.o.a.27.13
Level $260$
Weight $2$
Character 260.27
Analytic conductor $2.076$
Analytic rank $0$
Dimension $72$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [260,2,Mod(27,260)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(260, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("260.27");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 260.o (of order \(4\), degree \(2\), 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: \(2.07611045255\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(36\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 27.13
Character \(\chi\) \(=\) 260.27
Dual form 260.2.o.a.183.13

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.516756 + 1.31642i) q^{2} +(-2.23963 - 2.23963i) q^{3} +(-1.46593 - 1.36054i) q^{4} +(-2.20168 - 0.390628i) q^{5} +(4.10564 - 1.79095i) q^{6} +(0.918543 - 0.918543i) q^{7} +(2.54856 - 1.22671i) q^{8} +7.03189i q^{9} +O(q^{10})\) \(q+(-0.516756 + 1.31642i) q^{2} +(-2.23963 - 2.23963i) q^{3} +(-1.46593 - 1.36054i) q^{4} +(-2.20168 - 0.390628i) q^{5} +(4.10564 - 1.79095i) q^{6} +(0.918543 - 0.918543i) q^{7} +(2.54856 - 1.22671i) q^{8} +7.03189i q^{9} +(1.65196 - 2.69648i) q^{10} +3.84514i q^{11} +(0.236035 + 6.33023i) q^{12} +(-0.707107 + 0.707107i) q^{13} +(0.734526 + 1.68385i) q^{14} +(4.05610 + 5.80582i) q^{15} +(0.297882 + 3.98889i) q^{16} +(-1.82590 - 1.82590i) q^{17} +(-9.25693 - 3.63377i) q^{18} -2.11964 q^{19} +(2.69604 + 3.56810i) q^{20} -4.11439 q^{21} +(-5.06183 - 1.98700i) q^{22} +(4.88785 + 4.88785i) q^{23} +(-8.45522 - 2.96046i) q^{24} +(4.69482 + 1.72008i) q^{25} +(-0.565448 - 1.29625i) q^{26} +(9.02994 - 9.02994i) q^{27} +(-2.59623 + 0.0968054i) q^{28} +8.40499i q^{29} +(-9.73891 + 2.33934i) q^{30} -2.11067i q^{31} +(-5.40499 - 1.66915i) q^{32} +(8.61170 - 8.61170i) q^{33} +(3.34719 - 1.46011i) q^{34} +(-2.38115 + 1.66353i) q^{35} +(9.56714 - 10.3082i) q^{36} +(-4.85589 - 4.85589i) q^{37} +(1.09534 - 2.79033i) q^{38} +3.16732 q^{39} +(-6.09032 + 1.70529i) q^{40} +1.76398 q^{41} +(2.12614 - 5.41627i) q^{42} +(-0.980214 - 0.980214i) q^{43} +(5.23146 - 5.63670i) q^{44} +(2.74685 - 15.4820i) q^{45} +(-8.96029 + 3.90864i) q^{46} +(-6.80504 + 6.80504i) q^{47} +(8.26650 - 9.60079i) q^{48} +5.31256i q^{49} +(-4.69042 + 5.29150i) q^{50} +8.17867i q^{51} +(1.99861 - 0.0745222i) q^{52} +(-2.86242 + 2.86242i) q^{53} +(7.22093 + 16.5535i) q^{54} +(1.50202 - 8.46579i) q^{55} +(1.21418 - 3.46775i) q^{56} +(4.74721 + 4.74721i) q^{57} +(-11.0645 - 4.34333i) q^{58} -8.24159 q^{59} +(1.95309 - 14.0294i) q^{60} +2.94727 q^{61} +(2.77852 + 1.09070i) q^{62} +(6.45909 + 6.45909i) q^{63} +(4.99036 - 6.25270i) q^{64} +(1.83304 - 1.28061i) q^{65} +(6.88647 + 15.7868i) q^{66} +(1.81327 - 1.81327i) q^{67} +(0.192432 + 5.16083i) q^{68} -21.8940i q^{69} +(-0.959435 - 3.99423i) q^{70} -3.60503i q^{71} +(8.62610 + 17.9212i) q^{72} +(-11.5580 + 11.5580i) q^{73} +(8.90171 - 3.88309i) q^{74} +(-6.66232 - 14.3670i) q^{75} +(3.10723 + 2.88384i) q^{76} +(3.53193 + 3.53193i) q^{77} +(-1.63673 + 4.16952i) q^{78} +4.41904 q^{79} +(0.902332 - 8.89864i) q^{80} -19.3518 q^{81} +(-0.911545 + 2.32213i) q^{82} +(4.20776 + 4.20776i) q^{83} +(6.03140 + 5.59778i) q^{84} +(3.30680 + 4.73329i) q^{85} +(1.79691 - 0.783843i) q^{86} +(18.8241 - 18.8241i) q^{87} +(4.71688 + 9.79960i) q^{88} +9.46948i q^{89} +(18.9614 + 11.6164i) q^{90} +1.29902i q^{91} +(-0.515132 - 13.8153i) q^{92} +(-4.72711 + 4.72711i) q^{93} +(-5.44175 - 12.4748i) q^{94} +(4.66677 + 0.827990i) q^{95} +(8.36692 + 15.8435i) q^{96} +(2.33396 + 2.33396i) q^{97} +(-6.99356 - 2.74530i) q^{98} -27.0386 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72 q - 8 q^{6} - 12 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 72 q - 8 q^{6} - 12 q^{8} - 8 q^{10} - 8 q^{12} - 8 q^{16} + 28 q^{18} - 16 q^{21} - 8 q^{22} - 20 q^{28} - 32 q^{30} - 40 q^{32} + 16 q^{33} + 32 q^{36} - 12 q^{38} - 8 q^{40} - 40 q^{42} - 8 q^{46} + 60 q^{48} + 40 q^{50} + 8 q^{52} - 48 q^{53} + 8 q^{56} - 60 q^{58} + 20 q^{60} - 64 q^{61} + 60 q^{62} + 8 q^{66} - 16 q^{68} - 60 q^{70} + 40 q^{72} - 16 q^{73} - 72 q^{76} + 48 q^{77} - 20 q^{80} + 8 q^{81} - 12 q^{82} + 48 q^{85} + 48 q^{86} + 12 q^{88} + 44 q^{90} - 36 q^{92} + 16 q^{93} + 32 q^{96} - 80 q^{97} - 32 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/260\mathbb{Z}\right)^\times\).

\(n\) \(41\) \(131\) \(157\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.516756 + 1.31642i −0.365402 + 0.930850i
\(3\) −2.23963 2.23963i −1.29305 1.29305i −0.932890 0.360161i \(-0.882722\pi\)
−0.360161 0.932890i \(-0.617278\pi\)
\(4\) −1.46593 1.36054i −0.732963 0.680268i
\(5\) −2.20168 0.390628i −0.984623 0.174694i
\(6\) 4.10564 1.79095i 1.67612 0.731154i
\(7\) 0.918543 0.918543i 0.347177 0.347177i −0.511880 0.859057i \(-0.671051\pi\)
0.859057 + 0.511880i \(0.171051\pi\)
\(8\) 2.54856 1.22671i 0.901054 0.433708i
\(9\) 7.03189i 2.34396i
\(10\) 1.65196 2.69648i 0.522397 0.852703i
\(11\) 3.84514i 1.15935i 0.814846 + 0.579677i \(0.196821\pi\)
−0.814846 + 0.579677i \(0.803179\pi\)
\(12\) 0.236035 + 6.33023i 0.0681375 + 1.82738i
\(13\) −0.707107 + 0.707107i −0.196116 + 0.196116i
\(14\) 0.734526 + 1.68385i 0.196310 + 0.450028i
\(15\) 4.05610 + 5.80582i 1.04728 + 1.49906i
\(16\) 0.297882 + 3.98889i 0.0744704 + 0.997223i
\(17\) −1.82590 1.82590i −0.442845 0.442845i 0.450122 0.892967i \(-0.351380\pi\)
−0.892967 + 0.450122i \(0.851380\pi\)
\(18\) −9.25693 3.63377i −2.18188 0.856488i
\(19\) −2.11964 −0.486278 −0.243139 0.969991i \(-0.578177\pi\)
−0.243139 + 0.969991i \(0.578177\pi\)
\(20\) 2.69604 + 3.56810i 0.602853 + 0.797852i
\(21\) −4.11439 −0.897834
\(22\) −5.06183 1.98700i −1.07919 0.423630i
\(23\) 4.88785 + 4.88785i 1.01919 + 1.01919i 0.999812 + 0.0193750i \(0.00616763\pi\)
0.0193750 + 0.999812i \(0.493832\pi\)
\(24\) −8.45522 2.96046i −1.72591 0.604302i
\(25\) 4.69482 + 1.72008i 0.938964 + 0.344016i
\(26\) −0.565448 1.29625i −0.110894 0.254216i
\(27\) 9.02994 9.02994i 1.73781 1.73781i
\(28\) −2.59623 + 0.0968054i −0.490641 + 0.0182945i
\(29\) 8.40499i 1.56077i 0.625301 + 0.780383i \(0.284976\pi\)
−0.625301 + 0.780383i \(0.715024\pi\)
\(30\) −9.73891 + 2.33934i −1.77807 + 0.427102i
\(31\) 2.11067i 0.379087i −0.981872 0.189543i \(-0.939299\pi\)
0.981872 0.189543i \(-0.0607008\pi\)
\(32\) −5.40499 1.66915i −0.955477 0.295066i
\(33\) 8.61170 8.61170i 1.49910 1.49910i
\(34\) 3.34719 1.46011i 0.574038 0.250406i
\(35\) −2.38115 + 1.66353i −0.402488 + 0.281188i
\(36\) 9.56714 10.3082i 1.59452 1.71804i
\(37\) −4.85589 4.85589i −0.798304 0.798304i 0.184524 0.982828i \(-0.440926\pi\)
−0.982828 + 0.184524i \(0.940926\pi\)
\(38\) 1.09534 2.79033i 0.177687 0.452652i
\(39\) 3.16732 0.507176
\(40\) −6.09032 + 1.70529i −0.962964 + 0.269630i
\(41\) 1.76398 0.275487 0.137743 0.990468i \(-0.456015\pi\)
0.137743 + 0.990468i \(0.456015\pi\)
\(42\) 2.12614 5.41627i 0.328070 0.835749i
\(43\) −0.980214 0.980214i −0.149481 0.149481i 0.628405 0.777886i \(-0.283708\pi\)
−0.777886 + 0.628405i \(0.783708\pi\)
\(44\) 5.23146 5.63670i 0.788672 0.849764i
\(45\) 2.74685 15.4820i 0.409477 2.30792i
\(46\) −8.96029 + 3.90864i −1.32112 + 0.576298i
\(47\) −6.80504 + 6.80504i −0.992617 + 0.992617i −0.999973 0.00735546i \(-0.997659\pi\)
0.00735546 + 0.999973i \(0.497659\pi\)
\(48\) 8.26650 9.60079i 1.19317 1.38575i
\(49\) 5.31256i 0.758937i
\(50\) −4.69042 + 5.29150i −0.663326 + 0.748331i
\(51\) 8.17867i 1.14524i
\(52\) 1.99861 0.0745222i 0.277157 0.0103344i
\(53\) −2.86242 + 2.86242i −0.393183 + 0.393183i −0.875820 0.482637i \(-0.839679\pi\)
0.482637 + 0.875820i \(0.339679\pi\)
\(54\) 7.22093 + 16.5535i 0.982644 + 2.25264i
\(55\) 1.50202 8.46579i 0.202532 1.14153i
\(56\) 1.21418 3.46775i 0.162252 0.463398i
\(57\) 4.74721 + 4.74721i 0.628783 + 0.628783i
\(58\) −11.0645 4.34333i −1.45284 0.570307i
\(59\) −8.24159 −1.07296 −0.536482 0.843912i \(-0.680247\pi\)
−0.536482 + 0.843912i \(0.680247\pi\)
\(60\) 1.95309 14.0294i 0.252143 1.81118i
\(61\) 2.94727 0.377359 0.188679 0.982039i \(-0.439579\pi\)
0.188679 + 0.982039i \(0.439579\pi\)
\(62\) 2.77852 + 1.09070i 0.352873 + 0.138519i
\(63\) 6.45909 + 6.45909i 0.813769 + 0.813769i
\(64\) 4.99036 6.25270i 0.623795 0.781588i
\(65\) 1.83304 1.28061i 0.227361 0.158840i
\(66\) 6.88647 + 15.7868i 0.847666 + 1.94322i
\(67\) 1.81327 1.81327i 0.221526 0.221526i −0.587615 0.809141i \(-0.699933\pi\)
0.809141 + 0.587615i \(0.199933\pi\)
\(68\) 0.192432 + 5.16083i 0.0233358 + 0.625842i
\(69\) 21.8940i 2.63572i
\(70\) −0.959435 3.99423i −0.114674 0.477402i
\(71\) 3.60503i 0.427839i −0.976851 0.213919i \(-0.931377\pi\)
0.976851 0.213919i \(-0.0686230\pi\)
\(72\) 8.62610 + 17.9212i 1.01660 + 2.11204i
\(73\) −11.5580 + 11.5580i −1.35276 + 1.35276i −0.470201 + 0.882559i \(0.655819\pi\)
−0.882559 + 0.470201i \(0.844181\pi\)
\(74\) 8.90171 3.88309i 1.03480 0.451400i
\(75\) −6.66232 14.3670i −0.769299 1.65896i
\(76\) 3.10723 + 2.88384i 0.356424 + 0.330800i
\(77\) 3.53193 + 3.53193i 0.402501 + 0.402501i
\(78\) −1.63673 + 4.16952i −0.185323 + 0.472105i
\(79\) 4.41904 0.497181 0.248590 0.968609i \(-0.420033\pi\)
0.248590 + 0.968609i \(0.420033\pi\)
\(80\) 0.902332 8.89864i 0.100884 0.994898i
\(81\) −19.3518 −2.15020
\(82\) −0.911545 + 2.32213i −0.100663 + 0.256437i
\(83\) 4.20776 + 4.20776i 0.461861 + 0.461861i 0.899265 0.437404i \(-0.144102\pi\)
−0.437404 + 0.899265i \(0.644102\pi\)
\(84\) 6.03140 + 5.59778i 0.658079 + 0.610768i
\(85\) 3.30680 + 4.73329i 0.358673 + 0.513398i
\(86\) 1.79691 0.783843i 0.193765 0.0845239i
\(87\) 18.8241 18.8241i 2.01815 2.01815i
\(88\) 4.71688 + 9.79960i 0.502821 + 1.04464i
\(89\) 9.46948i 1.00376i 0.864936 + 0.501882i \(0.167359\pi\)
−0.864936 + 0.501882i \(0.832641\pi\)
\(90\) 18.9614 + 11.6164i 1.99870 + 1.22448i
\(91\) 1.29902i 0.136174i
\(92\) −0.515132 13.8153i −0.0537062 1.44035i
\(93\) −4.72711 + 4.72711i −0.490179 + 0.490179i
\(94\) −5.44175 12.4748i −0.561274 1.28668i
\(95\) 4.66677 + 0.827990i 0.478801 + 0.0849500i
\(96\) 8.36692 + 15.8435i 0.853945 + 1.61702i
\(97\) 2.33396 + 2.33396i 0.236977 + 0.236977i 0.815597 0.578620i \(-0.196409\pi\)
−0.578620 + 0.815597i \(0.696409\pi\)
\(98\) −6.99356 2.74530i −0.706456 0.277317i
\(99\) −27.0386 −2.71748
\(100\) −4.54203 8.90898i −0.454203 0.890898i
\(101\) 3.70148 0.368311 0.184155 0.982897i \(-0.441045\pi\)
0.184155 + 0.982897i \(0.441045\pi\)
\(102\) −10.7666 4.22637i −1.06605 0.418473i
\(103\) −11.8324 11.8324i −1.16588 1.16588i −0.983167 0.182711i \(-0.941513\pi\)
−0.182711 0.983167i \(-0.558487\pi\)
\(104\) −0.934692 + 2.66952i −0.0916541 + 0.261768i
\(105\) 9.05859 + 1.60720i 0.884028 + 0.156846i
\(106\) −2.28897 5.24732i −0.222325 0.509664i
\(107\) −5.22115 + 5.22115i −0.504748 + 0.504748i −0.912910 0.408162i \(-0.866170\pi\)
0.408162 + 0.912910i \(0.366170\pi\)
\(108\) −25.5228 + 0.951668i −2.45593 + 0.0915743i
\(109\) 8.97655i 0.859797i −0.902877 0.429899i \(-0.858549\pi\)
0.902877 0.429899i \(-0.141451\pi\)
\(110\) 10.3684 + 6.35204i 0.988584 + 0.605643i
\(111\) 21.7508i 2.06450i
\(112\) 3.93759 + 3.39035i 0.372067 + 0.320358i
\(113\) −3.62969 + 3.62969i −0.341452 + 0.341452i −0.856913 0.515461i \(-0.827621\pi\)
0.515461 + 0.856913i \(0.327621\pi\)
\(114\) −8.70247 + 3.79617i −0.815061 + 0.355544i
\(115\) −8.85217 12.6708i −0.825469 1.18156i
\(116\) 11.4353 12.3211i 1.06174 1.14398i
\(117\) −4.97230 4.97230i −0.459689 0.459689i
\(118\) 4.25889 10.8494i 0.392063 0.998768i
\(119\) −3.35433 −0.307491
\(120\) 17.4593 + 9.82085i 1.59381 + 0.896517i
\(121\) −3.78513 −0.344103
\(122\) −1.52302 + 3.87984i −0.137888 + 0.351264i
\(123\) −3.95065 3.95065i −0.356219 0.356219i
\(124\) −2.87164 + 3.09408i −0.257881 + 0.277857i
\(125\) −9.66460 5.62100i −0.864428 0.502757i
\(126\) −11.8407 + 5.16511i −1.05485 + 0.460144i
\(127\) −4.53841 + 4.53841i −0.402719 + 0.402719i −0.879190 0.476471i \(-0.841916\pi\)
0.476471 + 0.879190i \(0.341916\pi\)
\(128\) 5.65239 + 9.80054i 0.499605 + 0.866253i
\(129\) 4.39063i 0.386574i
\(130\) 0.738586 + 3.07482i 0.0647783 + 0.269679i
\(131\) 17.3332i 1.51441i 0.653180 + 0.757203i \(0.273435\pi\)
−0.653180 + 0.757203i \(0.726565\pi\)
\(132\) −24.3407 + 0.907589i −2.11858 + 0.0789955i
\(133\) −1.94698 + 1.94698i −0.168824 + 0.168824i
\(134\) 1.45001 + 3.32404i 0.125261 + 0.287153i
\(135\) −23.4084 + 16.3537i −2.01468 + 1.40750i
\(136\) −6.89326 2.41357i −0.591092 0.206962i
\(137\) −5.36795 5.36795i −0.458615 0.458615i 0.439586 0.898201i \(-0.355125\pi\)
−0.898201 + 0.439586i \(0.855125\pi\)
\(138\) 28.8217 + 11.3138i 2.45346 + 0.963097i
\(139\) −16.6018 −1.40815 −0.704073 0.710128i \(-0.748637\pi\)
−0.704073 + 0.710128i \(0.748637\pi\)
\(140\) 5.75389 + 0.801024i 0.486292 + 0.0676989i
\(141\) 30.4816 2.56701
\(142\) 4.74574 + 1.86292i 0.398254 + 0.156333i
\(143\) −2.71893 2.71893i −0.227368 0.227368i
\(144\) −28.0495 + 2.09467i −2.33745 + 0.174556i
\(145\) 3.28322 18.5051i 0.272657 1.53677i
\(146\) −9.24252 21.1878i −0.764916 1.75352i
\(147\) 11.8982 11.8982i 0.981344 0.981344i
\(148\) 0.511764 + 13.7250i 0.0420667 + 1.12819i
\(149\) 14.1914i 1.16260i −0.813688 0.581302i \(-0.802543\pi\)
0.813688 0.581302i \(-0.197457\pi\)
\(150\) 22.3558 1.34618i 1.82534 0.109916i
\(151\) 4.46986i 0.363752i −0.983321 0.181876i \(-0.941783\pi\)
0.983321 0.181876i \(-0.0582169\pi\)
\(152\) −5.40203 + 2.60018i −0.438163 + 0.210903i
\(153\) 12.8395 12.8395i 1.03801 1.03801i
\(154\) −6.47465 + 2.82436i −0.521742 + 0.227593i
\(155\) −0.824485 + 4.64702i −0.0662242 + 0.373257i
\(156\) −4.64305 4.30925i −0.371742 0.345016i
\(157\) 13.1851 + 13.1851i 1.05229 + 1.05229i 0.998555 + 0.0537332i \(0.0171121\pi\)
0.0537332 + 0.998555i \(0.482888\pi\)
\(158\) −2.28357 + 5.81732i −0.181671 + 0.462801i
\(159\) 12.8215 1.01681
\(160\) 11.2481 + 5.78627i 0.889238 + 0.457445i
\(161\) 8.97940 0.707676
\(162\) 10.0002 25.4751i 0.785687 2.00151i
\(163\) 12.3293 + 12.3293i 0.965704 + 0.965704i 0.999431 0.0337267i \(-0.0107376\pi\)
−0.0337267 + 0.999431i \(0.510738\pi\)
\(164\) −2.58586 2.39995i −0.201922 0.187405i
\(165\) −22.3242 + 15.5963i −1.73794 + 1.21417i
\(166\) −7.71356 + 3.36479i −0.598688 + 0.261159i
\(167\) 4.32625 4.32625i 0.334776 0.334776i −0.519621 0.854397i \(-0.673927\pi\)
0.854397 + 0.519621i \(0.173927\pi\)
\(168\) −10.4858 + 5.04717i −0.808997 + 0.389398i
\(169\) 1.00000i 0.0769231i
\(170\) −7.93981 + 1.90718i −0.608956 + 0.146274i
\(171\) 14.9051i 1.13982i
\(172\) 0.103305 + 2.77054i 0.00787693 + 0.211252i
\(173\) 7.96635 7.96635i 0.605670 0.605670i −0.336141 0.941812i \(-0.609122\pi\)
0.941812 + 0.336141i \(0.109122\pi\)
\(174\) 15.0529 + 34.5078i 1.14116 + 2.61603i
\(175\) 5.89236 2.73243i 0.445420 0.206552i
\(176\) −15.3379 + 1.14540i −1.15614 + 0.0863376i
\(177\) 18.4581 + 18.4581i 1.38740 + 1.38740i
\(178\) −12.4658 4.89341i −0.934353 0.366777i
\(179\) 11.8615 0.886572 0.443286 0.896380i \(-0.353813\pi\)
0.443286 + 0.896380i \(0.353813\pi\)
\(180\) −25.0905 + 18.9583i −1.87014 + 1.41307i
\(181\) 2.12699 0.158098 0.0790488 0.996871i \(-0.474812\pi\)
0.0790488 + 0.996871i \(0.474812\pi\)
\(182\) −1.71005 0.671274i −0.126757 0.0497581i
\(183\) −6.60079 6.60079i −0.487944 0.487944i
\(184\) 18.4530 + 6.46102i 1.36037 + 0.476313i
\(185\) 8.79429 + 12.5880i 0.646569 + 0.925487i
\(186\) −3.78010 8.66563i −0.277171 0.635395i
\(187\) 7.02083 7.02083i 0.513414 0.513414i
\(188\) 19.2342 0.717185i 1.40280 0.0523061i
\(189\) 16.5888i 1.20666i
\(190\) −3.50156 + 5.71557i −0.254030 + 0.414651i
\(191\) 18.0502i 1.30607i −0.757330 0.653033i \(-0.773496\pi\)
0.757330 0.653033i \(-0.226504\pi\)
\(192\) −25.1803 + 2.82718i −1.81723 + 0.204034i
\(193\) −15.6724 + 15.6724i −1.12812 + 1.12812i −0.137642 + 0.990482i \(0.543952\pi\)
−0.990482 + 0.137642i \(0.956048\pi\)
\(194\) −4.27855 + 1.86638i −0.307182 + 0.133998i
\(195\) −6.97343 1.23724i −0.499377 0.0886008i
\(196\) 7.22793 7.78782i 0.516281 0.556273i
\(197\) 3.07519 + 3.07519i 0.219098 + 0.219098i 0.808118 0.589020i \(-0.200486\pi\)
−0.589020 + 0.808118i \(0.700486\pi\)
\(198\) 13.9724 35.5942i 0.992973 2.52957i
\(199\) 8.16946 0.579117 0.289559 0.957160i \(-0.406491\pi\)
0.289559 + 0.957160i \(0.406491\pi\)
\(200\) 14.0751 1.37546i 0.995259 0.0972594i
\(201\) −8.12210 −0.572889
\(202\) −1.91276 + 4.87270i −0.134581 + 0.342842i
\(203\) 7.72034 + 7.72034i 0.541862 + 0.541862i
\(204\) 11.1274 11.9893i 0.779072 0.839421i
\(205\) −3.88372 0.689058i −0.271251 0.0481259i
\(206\) 21.6908 9.46193i 1.51127 0.659244i
\(207\) −34.3708 + 34.3708i −2.38894 + 2.38894i
\(208\) −3.03121 2.60994i −0.210176 0.180967i
\(209\) 8.15031i 0.563769i
\(210\) −6.79683 + 11.0944i −0.469026 + 0.765585i
\(211\) 18.9671i 1.30575i 0.757467 + 0.652873i \(0.226437\pi\)
−0.757467 + 0.652873i \(0.773563\pi\)
\(212\) 8.09052 0.301671i 0.555659 0.0207188i
\(213\) −8.07394 + 8.07394i −0.553217 + 0.553217i
\(214\) −4.17517 9.57130i −0.285409 0.654280i
\(215\) 1.77522 + 2.54102i 0.121069 + 0.173296i
\(216\) 11.9363 34.0905i 0.812160 2.31957i
\(217\) −1.93874 1.93874i −0.131610 0.131610i
\(218\) 11.8169 + 4.63868i 0.800342 + 0.314171i
\(219\) 51.7713 3.49838
\(220\) −13.7199 + 10.3667i −0.924993 + 0.698921i
\(221\) 2.58221 0.173698
\(222\) −28.6332 11.2399i −1.92174 0.754370i
\(223\) 0.848283 + 0.848283i 0.0568052 + 0.0568052i 0.734939 0.678134i \(-0.237211\pi\)
−0.678134 + 0.734939i \(0.737211\pi\)
\(224\) −6.49790 + 3.43153i −0.434159 + 0.229279i
\(225\) −12.0954 + 33.0135i −0.806360 + 2.20090i
\(226\) −2.90253 6.65385i −0.193073 0.442608i
\(227\) −9.33049 + 9.33049i −0.619286 + 0.619286i −0.945348 0.326062i \(-0.894278\pi\)
0.326062 + 0.945348i \(0.394278\pi\)
\(228\) −0.500309 13.4178i −0.0331338 0.888616i
\(229\) 0.978640i 0.0646704i −0.999477 0.0323352i \(-0.989706\pi\)
0.999477 0.0323352i \(-0.0102944\pi\)
\(230\) 21.2546 5.10545i 1.40148 0.336643i
\(231\) 15.8204i 1.04091i
\(232\) 10.3105 + 21.4206i 0.676917 + 1.40633i
\(233\) 9.95655 9.95655i 0.652275 0.652275i −0.301265 0.953540i \(-0.597409\pi\)
0.953540 + 0.301265i \(0.0974090\pi\)
\(234\) 9.11510 3.97617i 0.595873 0.259930i
\(235\) 17.6408 12.3243i 1.15076 0.803949i
\(236\) 12.0816 + 11.2130i 0.786443 + 0.729903i
\(237\) −9.89702 9.89702i −0.642881 0.642881i
\(238\) 1.73337 4.41571i 0.112358 0.286228i
\(239\) −7.98982 −0.516819 −0.258409 0.966036i \(-0.583198\pi\)
−0.258409 + 0.966036i \(0.583198\pi\)
\(240\) −21.9506 + 17.9088i −1.41690 + 1.15601i
\(241\) 17.0010 1.09513 0.547565 0.836763i \(-0.315555\pi\)
0.547565 + 0.836763i \(0.315555\pi\)
\(242\) 1.95599 4.98282i 0.125736 0.320308i
\(243\) 16.2511 + 16.2511i 1.04251 + 1.04251i
\(244\) −4.32048 4.00986i −0.276590 0.256705i
\(245\) 2.07523 11.6966i 0.132582 0.747267i
\(246\) 7.24225 3.15920i 0.461749 0.201423i
\(247\) 1.49881 1.49881i 0.0953670 0.0953670i
\(248\) −2.58918 5.37917i −0.164413 0.341578i
\(249\) 18.8476i 1.19442i
\(250\) 12.3938 9.81799i 0.783855 0.620944i
\(251\) 1.82190i 0.114997i 0.998346 + 0.0574985i \(0.0183125\pi\)
−0.998346 + 0.0574985i \(0.981688\pi\)
\(252\) −0.680725 18.2564i −0.0428817 1.15004i
\(253\) −18.7945 + 18.7945i −1.18160 + 1.18160i
\(254\) −3.62921 8.31970i −0.227717 0.522025i
\(255\) 3.19482 18.0068i 0.200067 1.12763i
\(256\) −15.8225 + 2.37644i −0.988908 + 0.148527i
\(257\) −17.1141 17.1141i −1.06755 1.06755i −0.997547 0.0700002i \(-0.977700\pi\)
−0.0700002 0.997547i \(-0.522300\pi\)
\(258\) −5.77992 2.26889i −0.359842 0.141255i
\(259\) −8.92069 −0.554305
\(260\) −4.42942 0.616639i −0.274701 0.0382423i
\(261\) −59.1029 −3.65838
\(262\) −22.8177 8.95702i −1.40968 0.553366i
\(263\) −5.80407 5.80407i −0.357895 0.357895i 0.505142 0.863036i \(-0.331440\pi\)
−0.863036 + 0.505142i \(0.831440\pi\)
\(264\) 11.3834 32.5115i 0.700600 2.00095i
\(265\) 7.42028 5.18400i 0.455824 0.318450i
\(266\) −1.55693 3.56915i −0.0954615 0.218839i
\(267\) 21.2081 21.2081i 1.29792 1.29792i
\(268\) −5.12513 + 0.191101i −0.313067 + 0.0116733i
\(269\) 2.30491i 0.140533i 0.997528 + 0.0702664i \(0.0223849\pi\)
−0.997528 + 0.0702664i \(0.977615\pi\)
\(270\) −9.43194 39.2662i −0.574010 2.38967i
\(271\) 17.1855i 1.04394i −0.852963 0.521971i \(-0.825197\pi\)
0.852963 0.521971i \(-0.174803\pi\)
\(272\) 6.73940 7.82721i 0.408636 0.474594i
\(273\) 2.90932 2.90932i 0.176080 0.176080i
\(274\) 9.84041 4.29256i 0.594481 0.259323i
\(275\) −6.61395 + 18.0523i −0.398836 + 1.08859i
\(276\) −29.7875 + 32.0949i −1.79300 + 1.93189i
\(277\) 1.69205 + 1.69205i 0.101666 + 0.101666i 0.756110 0.654444i \(-0.227097\pi\)
−0.654444 + 0.756110i \(0.727097\pi\)
\(278\) 8.57907 21.8549i 0.514538 1.31077i
\(279\) 14.8420 0.888566
\(280\) −4.02784 + 7.16060i −0.240709 + 0.427928i
\(281\) −12.7153 −0.758532 −0.379266 0.925288i \(-0.623823\pi\)
−0.379266 + 0.925288i \(0.623823\pi\)
\(282\) −15.7515 + 40.1266i −0.937990 + 2.38950i
\(283\) 12.4780 + 12.4780i 0.741737 + 0.741737i 0.972912 0.231175i \(-0.0742569\pi\)
−0.231175 + 0.972912i \(0.574257\pi\)
\(284\) −4.90478 + 5.28471i −0.291045 + 0.313590i
\(285\) −8.59745 12.3062i −0.509269 0.728958i
\(286\) 4.98427 2.17423i 0.294726 0.128565i
\(287\) 1.62029 1.62029i 0.0956425 0.0956425i
\(288\) 11.7373 38.0073i 0.691624 2.23960i
\(289\) 10.3322i 0.607777i
\(290\) 22.6639 + 13.8847i 1.33087 + 0.815339i
\(291\) 10.4544i 0.612848i
\(292\) 32.6682 1.21810i 1.91176 0.0712839i
\(293\) −1.44715 + 1.44715i −0.0845432 + 0.0845432i −0.748114 0.663571i \(-0.769040\pi\)
0.663571 + 0.748114i \(0.269040\pi\)
\(294\) 9.51454 + 21.8114i 0.554900 + 1.27207i
\(295\) 18.1454 + 3.21940i 1.05646 + 0.187440i
\(296\) −18.3323 6.41878i −1.06555 0.373084i
\(297\) 34.7214 + 34.7214i 2.01474 + 2.01474i
\(298\) 18.6818 + 7.33349i 1.08221 + 0.424817i
\(299\) −6.91246 −0.399758
\(300\) −9.78035 + 30.1253i −0.564669 + 1.73929i
\(301\) −1.80074 −0.103793
\(302\) 5.88421 + 2.30982i 0.338598 + 0.132915i
\(303\) −8.28995 8.28995i −0.476245 0.476245i
\(304\) −0.631401 8.45501i −0.0362133 0.484928i
\(305\) −6.48895 1.15128i −0.371556 0.0659224i
\(306\) 10.2673 + 23.5371i 0.586942 + 1.34553i
\(307\) 2.02392 2.02392i 0.115511 0.115511i −0.646988 0.762500i \(-0.723972\pi\)
0.762500 + 0.646988i \(0.223972\pi\)
\(308\) −0.372231 9.98287i −0.0212098 0.568827i
\(309\) 53.0003i 3.01508i
\(310\) −5.69137 3.48674i −0.323248 0.198034i
\(311\) 21.9636i 1.24544i 0.782444 + 0.622722i \(0.213973\pi\)
−0.782444 + 0.622722i \(0.786027\pi\)
\(312\) 8.07211 3.88538i 0.456993 0.219966i
\(313\) 9.29451 9.29451i 0.525357 0.525357i −0.393827 0.919184i \(-0.628849\pi\)
0.919184 + 0.393827i \(0.128849\pi\)
\(314\) −24.1707 + 10.5437i −1.36403 + 0.595015i
\(315\) −11.6978 16.7440i −0.659095 0.943416i
\(316\) −6.47799 6.01227i −0.364415 0.338216i
\(317\) −24.5364 24.5364i −1.37810 1.37810i −0.847823 0.530279i \(-0.822087\pi\)
−0.530279 0.847823i \(-0.677913\pi\)
\(318\) −6.62559 + 16.8785i −0.371545 + 0.946500i
\(319\) −32.3184 −1.80948
\(320\) −13.4297 + 11.8171i −0.750742 + 0.660596i
\(321\) 23.3869 1.30533
\(322\) −4.64016 + 11.8207i −0.258586 + 0.658740i
\(323\) 3.87024 + 3.87024i 0.215346 + 0.215346i
\(324\) 28.3683 + 26.3288i 1.57602 + 1.46271i
\(325\) −4.53602 + 2.10346i −0.251613 + 0.116679i
\(326\) −22.6018 + 9.85930i −1.25180 + 0.546056i
\(327\) −20.1042 + 20.1042i −1.11176 + 1.11176i
\(328\) 4.49561 2.16389i 0.248228 0.119481i
\(329\) 12.5014i 0.689227i
\(330\) −8.99508 37.4475i −0.495163 2.06142i
\(331\) 8.67620i 0.476887i −0.971156 0.238444i \(-0.923363\pi\)
0.971156 0.238444i \(-0.0766372\pi\)
\(332\) −0.443456 11.8931i −0.0243378 0.652717i
\(333\) 34.1461 34.1461i 1.87120 1.87120i
\(334\) 3.45955 + 7.93079i 0.189298 + 0.433953i
\(335\) −4.70056 + 3.28393i −0.256819 + 0.179420i
\(336\) −1.22560 16.4119i −0.0668621 0.895341i
\(337\) −5.34559 5.34559i −0.291193 0.291193i 0.546358 0.837551i \(-0.316014\pi\)
−0.837551 + 0.546358i \(0.816014\pi\)
\(338\) 1.31642 + 0.516756i 0.0716038 + 0.0281078i
\(339\) 16.2583 0.883030
\(340\) 1.59229 11.4377i 0.0863541 0.620295i
\(341\) 8.11581 0.439496
\(342\) 19.6213 + 7.70228i 1.06100 + 0.416491i
\(343\) 11.3096 + 11.3096i 0.610662 + 0.610662i
\(344\) −3.70058 1.29570i −0.199522 0.0698594i
\(345\) −8.55239 + 48.2036i −0.460445 + 2.59519i
\(346\) 6.37041 + 14.6037i 0.342475 + 0.785101i
\(347\) −4.16909 + 4.16909i −0.223809 + 0.223809i −0.810100 0.586292i \(-0.800587\pi\)
0.586292 + 0.810100i \(0.300587\pi\)
\(348\) −53.2055 + 1.98387i −2.85211 + 0.106347i
\(349\) 2.32016i 0.124195i −0.998070 0.0620976i \(-0.980221\pi\)
0.998070 0.0620976i \(-0.0197790\pi\)
\(350\) 0.552113 + 9.16882i 0.0295117 + 0.490094i
\(351\) 12.7703i 0.681627i
\(352\) 6.41811 20.7830i 0.342086 1.10774i
\(353\) −20.9071 + 20.9071i −1.11277 + 1.11277i −0.119997 + 0.992774i \(0.538288\pi\)
−0.992774 + 0.119997i \(0.961712\pi\)
\(354\) −33.8370 + 14.7603i −1.79842 + 0.784501i
\(355\) −1.40823 + 7.93714i −0.0747409 + 0.421260i
\(356\) 12.8836 13.8816i 0.682828 0.735722i
\(357\) 7.51246 + 7.51246i 0.397601 + 0.397601i
\(358\) −6.12951 + 15.6147i −0.323955 + 0.825265i
\(359\) −1.85375 −0.0978370 −0.0489185 0.998803i \(-0.515577\pi\)
−0.0489185 + 0.998803i \(0.515577\pi\)
\(360\) −11.9914 42.8265i −0.632002 2.25715i
\(361\) −14.5071 −0.763533
\(362\) −1.09913 + 2.80001i −0.0577692 + 0.147165i
\(363\) 8.47729 + 8.47729i 0.444942 + 0.444942i
\(364\) 1.76736 1.90426i 0.0926347 0.0998104i
\(365\) 29.9619 20.9322i 1.56828 1.09564i
\(366\) 12.1004 5.27842i 0.632499 0.275907i
\(367\) −2.30679 + 2.30679i −0.120414 + 0.120414i −0.764746 0.644332i \(-0.777135\pi\)
0.644332 + 0.764746i \(0.277135\pi\)
\(368\) −18.0411 + 20.9531i −0.940458 + 1.09226i
\(369\) 12.4041i 0.645731i
\(370\) −21.1156 + 5.07207i −1.09775 + 0.263684i
\(371\) 5.25851i 0.273008i
\(372\) 13.3610 0.498191i 0.692736 0.0258300i
\(373\) 23.9386 23.9386i 1.23949 1.23949i 0.279284 0.960209i \(-0.409903\pi\)
0.960209 0.279284i \(-0.0900970\pi\)
\(374\) 5.61431 + 12.8704i 0.290309 + 0.665514i
\(375\) 9.05617 + 34.2341i 0.467659 + 1.76784i
\(376\) −8.99527 + 25.6909i −0.463896 + 1.32491i
\(377\) −5.94322 5.94322i −0.306092 0.306092i
\(378\) 21.8378 + 8.57235i 1.12322 + 0.440914i
\(379\) 20.2186 1.03856 0.519279 0.854605i \(-0.326201\pi\)
0.519279 + 0.854605i \(0.326201\pi\)
\(380\) −5.71463 7.56308i −0.293155 0.387978i
\(381\) 20.3287 1.04147
\(382\) 23.7616 + 9.32754i 1.21575 + 0.477239i
\(383\) −3.38104 3.38104i −0.172763 0.172763i 0.615429 0.788192i \(-0.288983\pi\)
−0.788192 + 0.615429i \(0.788983\pi\)
\(384\) 9.29032 34.6088i 0.474095 1.76613i
\(385\) −6.39652 9.15586i −0.325997 0.466626i
\(386\) −12.5327 28.7303i −0.637896 1.46233i
\(387\) 6.89276 6.89276i 0.350379 0.350379i
\(388\) −0.245976 6.59684i −0.0124875 0.334904i
\(389\) 3.25593i 0.165082i 0.996588 + 0.0825410i \(0.0263035\pi\)
−0.996588 + 0.0825410i \(0.973696\pi\)
\(390\) 5.23229 8.54061i 0.264947 0.432471i
\(391\) 17.8494i 0.902684i
\(392\) 6.51697 + 13.5394i 0.329157 + 0.683843i
\(393\) 38.8199 38.8199i 1.95820 1.95820i
\(394\) −5.63737 + 2.45912i −0.284007 + 0.123889i
\(395\) −9.72933 1.72620i −0.489536 0.0868546i
\(396\) 39.6366 + 36.7870i 1.99182 + 1.84862i
\(397\) 4.48113 + 4.48113i 0.224901 + 0.224901i 0.810559 0.585657i \(-0.199164\pi\)
−0.585657 + 0.810559i \(0.699164\pi\)
\(398\) −4.22161 + 10.7544i −0.211610 + 0.539071i
\(399\) 8.72102 0.436597
\(400\) −5.46271 + 19.2395i −0.273135 + 0.961976i
\(401\) −15.9771 −0.797860 −0.398930 0.916981i \(-0.630618\pi\)
−0.398930 + 0.916981i \(0.630618\pi\)
\(402\) 4.19714 10.6921i 0.209335 0.533274i
\(403\) 1.49247 + 1.49247i 0.0743450 + 0.0743450i
\(404\) −5.42610 5.03600i −0.269958 0.250550i
\(405\) 42.6066 + 7.55936i 2.11714 + 0.375627i
\(406\) −14.1527 + 6.17368i −0.702389 + 0.306395i
\(407\) 18.6716 18.6716i 0.925517 0.925517i
\(408\) 10.0329 + 20.8439i 0.496701 + 1.03192i
\(409\) 8.03499i 0.397305i −0.980070 0.198652i \(-0.936344\pi\)
0.980070 0.198652i \(-0.0636565\pi\)
\(410\) 2.91402 4.75653i 0.143913 0.234908i
\(411\) 24.0445i 1.18603i
\(412\) 1.24702 + 33.4437i 0.0614361 + 1.64765i
\(413\) −7.57025 + 7.57025i −0.372508 + 0.372508i
\(414\) −27.4851 63.0078i −1.35082 3.09666i
\(415\) −7.62048 10.9078i −0.374075 0.535443i
\(416\) 5.00217 2.64164i 0.245252 0.129517i
\(417\) 37.1819 + 37.1819i 1.82080 + 1.82080i
\(418\) 10.7292 + 4.21172i 0.524784 + 0.206002i
\(419\) −10.1291 −0.494838 −0.247419 0.968909i \(-0.579582\pi\)
−0.247419 + 0.968909i \(0.579582\pi\)
\(420\) −11.0926 14.6806i −0.541262 0.716339i
\(421\) 6.38901 0.311381 0.155691 0.987806i \(-0.450240\pi\)
0.155691 + 0.987806i \(0.450240\pi\)
\(422\) −24.9686 9.80134i −1.21545 0.477122i
\(423\) −47.8523 47.8523i −2.32666 2.32666i
\(424\) −3.78370 + 10.8064i −0.183753 + 0.524806i
\(425\) −5.43157 11.7129i −0.263470 0.568161i
\(426\) −6.45645 14.8010i −0.312816 0.717109i
\(427\) 2.70719 2.70719i 0.131010 0.131010i
\(428\) 14.7574 0.550259i 0.713326 0.0265978i
\(429\) 12.1788i 0.587997i
\(430\) −4.26241 + 1.02385i −0.205552 + 0.0493745i
\(431\) 20.5386i 0.989310i −0.869089 0.494655i \(-0.835294\pi\)
0.869089 0.494655i \(-0.164706\pi\)
\(432\) 38.7093 + 33.3296i 1.86240 + 1.60357i
\(433\) −16.7017 + 16.7017i −0.802631 + 0.802631i −0.983506 0.180875i \(-0.942107\pi\)
0.180875 + 0.983506i \(0.442107\pi\)
\(434\) 3.55405 1.55034i 0.170600 0.0744187i
\(435\) −48.7978 + 34.0914i −2.33968 + 1.63456i
\(436\) −12.2129 + 13.1590i −0.584893 + 0.630200i
\(437\) −10.3605 10.3605i −0.495609 0.495609i
\(438\) −26.7531 + 68.1527i −1.27831 + 3.25646i
\(439\) 26.9755 1.28747 0.643735 0.765249i \(-0.277384\pi\)
0.643735 + 0.765249i \(0.277384\pi\)
\(440\) −6.55708 23.4182i −0.312596 1.11642i
\(441\) −37.3573 −1.77892
\(442\) −1.33437 + 3.39927i −0.0634696 + 0.161687i
\(443\) −20.1664 20.1664i −0.958132 0.958132i 0.0410258 0.999158i \(-0.486937\pi\)
−0.999158 + 0.0410258i \(0.986937\pi\)
\(444\) 29.5928 31.8851i 1.40441 1.51320i
\(445\) 3.69904 20.8488i 0.175352 0.988328i
\(446\) −1.55505 + 0.678342i −0.0736338 + 0.0321204i
\(447\) −31.7835 + 31.7835i −1.50331 + 1.50331i
\(448\) −1.15951 10.3272i −0.0547819 0.487916i
\(449\) 18.7329i 0.884062i 0.897000 + 0.442031i \(0.145742\pi\)
−0.897000 + 0.442031i \(0.854258\pi\)
\(450\) −37.2092 32.9825i −1.75406 1.55481i
\(451\) 6.78274i 0.319387i
\(452\) 10.2592 0.382533i 0.482551 0.0179929i
\(453\) −10.0108 + 10.0108i −0.470350 + 0.470350i
\(454\) −7.46126 17.1044i −0.350174 0.802751i
\(455\) 0.507432 2.86002i 0.0237888 0.134080i
\(456\) 17.9220 + 6.27511i 0.839275 + 0.293859i
\(457\) −0.912019 0.912019i −0.0426624 0.0426624i 0.685454 0.728116i \(-0.259604\pi\)
−0.728116 + 0.685454i \(0.759604\pi\)
\(458\) 1.28830 + 0.505718i 0.0601984 + 0.0236307i
\(459\) −32.9755 −1.53916
\(460\) −4.26250 + 30.6182i −0.198740 + 1.42758i
\(461\) −13.6853 −0.637387 −0.318693 0.947858i \(-0.603244\pi\)
−0.318693 + 0.947858i \(0.603244\pi\)
\(462\) 20.8263 + 8.17530i 0.968929 + 0.380349i
\(463\) −2.10470 2.10470i −0.0978137 0.0978137i 0.656507 0.754320i \(-0.272033\pi\)
−0.754320 + 0.656507i \(0.772033\pi\)
\(464\) −33.5266 + 2.50369i −1.55643 + 0.116231i
\(465\) 12.2541 8.56106i 0.568272 0.397010i
\(466\) 7.96190 + 18.2521i 0.368828 + 0.845513i
\(467\) 28.5364 28.5364i 1.32051 1.32051i 0.407143 0.913365i \(-0.366525\pi\)
0.913365 0.407143i \(-0.133475\pi\)
\(468\) 0.524032 + 14.0540i 0.0242234 + 0.649647i
\(469\) 3.33113i 0.153817i
\(470\) 7.10799 + 29.5914i 0.327867 + 1.36495i
\(471\) 59.0597i 2.72133i
\(472\) −21.0042 + 10.1100i −0.966798 + 0.465353i
\(473\) 3.76906 3.76906i 0.173302 0.173302i
\(474\) 18.1430 7.91430i 0.833335 0.363516i
\(475\) −9.95132 3.64594i −0.456598 0.167287i
\(476\) 4.91720 + 4.56369i 0.225379 + 0.209176i
\(477\) −20.1282 20.1282i −0.921607 0.921607i
\(478\) 4.12879 10.5180i 0.188846 0.481081i
\(479\) −19.8088 −0.905086 −0.452543 0.891743i \(-0.649483\pi\)
−0.452543 + 0.891743i \(0.649483\pi\)
\(480\) −12.2324 38.1506i −0.558330 1.74133i
\(481\) 6.86727 0.313121
\(482\) −8.78536 + 22.3804i −0.400162 + 1.01940i
\(483\) −20.1105 20.1105i −0.915061 0.915061i
\(484\) 5.54872 + 5.14981i 0.252215 + 0.234082i
\(485\) −4.22692 6.05034i −0.191935 0.274732i
\(486\) −29.7911 + 12.9954i −1.35135 + 0.589484i
\(487\) −9.20752 + 9.20752i −0.417232 + 0.417232i −0.884249 0.467016i \(-0.845329\pi\)
0.467016 + 0.884249i \(0.345329\pi\)
\(488\) 7.51130 3.61544i 0.340020 0.163663i
\(489\) 55.2261i 2.49741i
\(490\) 14.3252 + 8.77615i 0.647147 + 0.396466i
\(491\) 23.5043i 1.06073i 0.847768 + 0.530367i \(0.177946\pi\)
−0.847768 + 0.530367i \(0.822054\pi\)
\(492\) 0.416360 + 11.1664i 0.0187710 + 0.503419i
\(493\) 15.3466 15.3466i 0.691178 0.691178i
\(494\) 1.19855 + 2.74758i 0.0539251 + 0.123620i
\(495\) 59.5305 + 10.5620i 2.67570 + 0.474729i
\(496\) 8.41922 0.628729i 0.378034 0.0282307i
\(497\) −3.31138 3.31138i −0.148536 0.148536i
\(498\) 24.8114 + 9.73963i 1.11183 + 0.436443i
\(499\) −22.4244 −1.00386 −0.501928 0.864910i \(-0.667376\pi\)
−0.501928 + 0.864910i \(0.667376\pi\)
\(500\) 6.52002 + 21.3890i 0.291584 + 0.956545i
\(501\) −19.3784 −0.865764
\(502\) −2.39838 0.941476i −0.107045 0.0420201i
\(503\) 24.2077 + 24.2077i 1.07937 + 1.07937i 0.996566 + 0.0828029i \(0.0263872\pi\)
0.0828029 + 0.996566i \(0.473613\pi\)
\(504\) 24.3848 + 8.53797i 1.08619 + 0.380312i
\(505\) −8.14949 1.44590i −0.362647 0.0643418i
\(506\) −15.0293 34.4536i −0.668133 1.53165i
\(507\) −2.23963 + 2.23963i −0.0994655 + 0.0994655i
\(508\) 12.8276 0.478304i 0.569135 0.0212213i
\(509\) 42.3216i 1.87587i 0.346808 + 0.937936i \(0.387266\pi\)
−0.346808 + 0.937936i \(0.612734\pi\)
\(510\) 22.0536 + 13.5109i 0.976551 + 0.598271i
\(511\) 21.2330i 0.939293i
\(512\) 5.04800 22.0571i 0.223092 0.974797i
\(513\) −19.1402 + 19.1402i −0.845061 + 0.845061i
\(514\) 31.3731 13.6855i 1.38381 0.603643i
\(515\) 21.4291 + 30.6732i 0.944278 + 1.35162i
\(516\) 5.97362 6.43635i 0.262974 0.283344i
\(517\) −26.1664 26.1664i −1.15080 1.15080i
\(518\) 4.60982 11.7434i 0.202544 0.515975i
\(519\) −35.6834 −1.56633
\(520\) 3.10069 5.51233i 0.135974 0.241732i
\(521\) −13.0136 −0.570136 −0.285068 0.958507i \(-0.592016\pi\)
−0.285068 + 0.958507i \(0.592016\pi\)
\(522\) 30.5418 77.8043i 1.33678 3.40540i
\(523\) 24.0226 + 24.0226i 1.05043 + 1.05043i 0.998659 + 0.0517748i \(0.0164878\pi\)
0.0517748 + 0.998659i \(0.483512\pi\)
\(524\) 23.5824 25.4092i 1.03020 1.11000i
\(525\) −19.3163 7.07708i −0.843034 0.308869i
\(526\) 10.6399 4.64131i 0.463921 0.202371i
\(527\) −3.85386 + 3.85386i −0.167877 + 0.167877i
\(528\) 36.9164 + 31.7859i 1.60658 + 1.38330i
\(529\) 24.7822i 1.07749i
\(530\) 2.98985 + 12.4471i 0.129871 + 0.540666i
\(531\) 57.9539i 2.51499i
\(532\) 5.50306 0.205192i 0.238588 0.00889622i
\(533\) −1.24732 + 1.24732i −0.0540274 + 0.0540274i
\(534\) 16.9594 + 38.8783i 0.733905 + 1.68243i
\(535\) 13.5349 9.45580i 0.585163 0.408810i
\(536\) 2.39687 6.84559i 0.103529 0.295684i
\(537\) −26.5654 26.5654i −1.14638 1.14638i
\(538\) −3.03423 1.19108i −0.130815 0.0513509i
\(539\) −20.4275 −0.879877
\(540\) 56.5649 + 7.87465i 2.43416 + 0.338871i
\(541\) 27.8612 1.19785 0.598923 0.800807i \(-0.295596\pi\)
0.598923 + 0.800807i \(0.295596\pi\)
\(542\) 22.6233 + 8.88069i 0.971754 + 0.381458i
\(543\) −4.76366 4.76366i −0.204428 0.204428i
\(544\) 6.82127 + 12.9166i 0.292459 + 0.553797i
\(545\) −3.50649 + 19.7635i −0.150202 + 0.846576i
\(546\) 2.32648 + 5.33329i 0.0995640 + 0.228244i
\(547\) −15.6942 + 15.6942i −0.671038 + 0.671038i −0.957955 0.286918i \(-0.907369\pi\)
0.286918 + 0.957955i \(0.407369\pi\)
\(548\) 0.565730 + 15.1723i 0.0241668 + 0.648129i
\(549\) 20.7249i 0.884515i
\(550\) −20.3466 18.0353i −0.867580 0.769030i
\(551\) 17.8155i 0.758967i
\(552\) −26.8576 55.7982i −1.14313 2.37493i
\(553\) 4.05908 4.05908i 0.172610 0.172610i
\(554\) −3.10183 + 1.35308i −0.131784 + 0.0574867i
\(555\) 8.49648 47.8884i 0.360655 2.03275i
\(556\) 24.3370 + 22.5873i 1.03212 + 0.957916i
\(557\) −26.1672 26.1672i −1.10874 1.10874i −0.993317 0.115422i \(-0.963178\pi\)
−0.115422 0.993317i \(-0.536822\pi\)
\(558\) −7.66968 + 19.5383i −0.324683 + 0.827121i
\(559\) 1.38623 0.0586314
\(560\) −7.34495 9.00261i −0.310381 0.380430i
\(561\) −31.4482 −1.32774
\(562\) 6.57072 16.7387i 0.277169 0.706080i
\(563\) −27.4350 27.4350i −1.15625 1.15625i −0.985276 0.170971i \(-0.945310\pi\)
−0.170971 0.985276i \(-0.554690\pi\)
\(564\) −44.6837 41.4713i −1.88152 1.74626i
\(565\) 9.40927 6.57356i 0.395851 0.276552i
\(566\) −22.8743 + 9.97818i −0.961478 + 0.419414i
\(567\) −17.7755 + 17.7755i −0.746499 + 0.746499i
\(568\) −4.42233 9.18766i −0.185557 0.385506i
\(569\) 9.90886i 0.415401i −0.978192 0.207701i \(-0.933402\pi\)
0.978192 0.207701i \(-0.0665980\pi\)
\(570\) 20.6430 4.95854i 0.864639 0.207691i
\(571\) 23.0063i 0.962784i −0.876505 0.481392i \(-0.840131\pi\)
0.876505 0.481392i \(-0.159869\pi\)
\(572\) 0.286548 + 7.68495i 0.0119812 + 0.321324i
\(573\) −40.4257 + 40.4257i −1.68881 + 1.68881i
\(574\) 1.29569 + 2.97027i 0.0540809 + 0.123977i
\(575\) 14.5401 + 31.3551i 0.606364 + 1.30760i
\(576\) 43.9683 + 35.0917i 1.83201 + 1.46215i
\(577\) 14.0786 + 14.0786i 0.586101 + 0.586101i 0.936573 0.350472i \(-0.113979\pi\)
−0.350472 + 0.936573i \(0.613979\pi\)
\(578\) 13.6015 + 5.33923i 0.565749 + 0.222083i
\(579\) 70.2008 2.91745
\(580\) −29.9898 + 22.6602i −1.24526 + 0.940914i
\(581\) 7.73001 0.320695
\(582\) 13.7624 + 5.40237i 0.570469 + 0.223935i
\(583\) −11.0064 11.0064i −0.455839 0.455839i
\(584\) −15.2780 + 43.6346i −0.632207 + 1.80561i
\(585\) 9.00511 + 12.8897i 0.372315 + 0.532925i
\(586\) −1.15723 2.65287i −0.0478048 0.109589i
\(587\) 8.08122 8.08122i 0.333547 0.333547i −0.520385 0.853932i \(-0.674211\pi\)
0.853932 + 0.520385i \(0.174211\pi\)
\(588\) −33.6297 + 1.25395i −1.38687 + 0.0517121i
\(589\) 4.47385i 0.184342i
\(590\) −13.6148 + 22.2233i −0.560513 + 0.914919i
\(591\) 13.7746i 0.566611i
\(592\) 17.9232 20.8161i 0.736637 0.855537i
\(593\) 9.04916 9.04916i 0.371605 0.371605i −0.496457 0.868061i \(-0.665366\pi\)
0.868061 + 0.496457i \(0.165366\pi\)
\(594\) −63.6505 + 27.7655i −2.61161 + 1.13923i
\(595\) 7.38517 + 1.31029i 0.302762 + 0.0537168i
\(596\) −19.3079 + 20.8035i −0.790883 + 0.852146i
\(597\) −18.2966 18.2966i −0.748828 0.748828i
\(598\) 3.57206 9.09971i 0.146072 0.372115i
\(599\) −9.45761 −0.386428 −0.193214 0.981157i \(-0.561891\pi\)
−0.193214 + 0.981157i \(0.561891\pi\)
\(600\) −34.6035 28.4425i −1.41268 1.16116i
\(601\) 36.3082 1.48104 0.740522 0.672032i \(-0.234578\pi\)
0.740522 + 0.672032i \(0.234578\pi\)
\(602\) 0.930542 2.37053i 0.0379260 0.0966155i
\(603\) 12.7507 + 12.7507i 0.519249 + 0.519249i
\(604\) −6.08140 + 6.55248i −0.247449 + 0.266617i
\(605\) 8.33366 + 1.47858i 0.338811 + 0.0601127i
\(606\) 15.1969 6.62918i 0.617333 0.269292i
\(607\) −8.30758 + 8.30758i −0.337194 + 0.337194i −0.855310 0.518116i \(-0.826634\pi\)
0.518116 + 0.855310i \(0.326634\pi\)
\(608\) 11.4566 + 3.53799i 0.464628 + 0.143484i
\(609\) 34.5814i 1.40131i
\(610\) 4.86878 7.94725i 0.197131 0.321775i
\(611\) 9.62378i 0.389337i
\(612\) −36.2904 + 1.35316i −1.46695 + 0.0546982i
\(613\) −0.566575 + 0.566575i −0.0228838 + 0.0228838i −0.718456 0.695572i \(-0.755151\pi\)
0.695572 + 0.718456i \(0.255151\pi\)
\(614\) 1.61846 + 3.71021i 0.0653157 + 0.149732i
\(615\) 7.15485 + 10.2413i 0.288512 + 0.412970i
\(616\) 13.3340 + 4.66869i 0.537242 + 0.188107i
\(617\) 32.2437 + 32.2437i 1.29808 + 1.29808i 0.929657 + 0.368426i \(0.120103\pi\)
0.368426 + 0.929657i \(0.379897\pi\)
\(618\) −69.7706 27.3882i −2.80659 1.10171i
\(619\) −26.0469 −1.04691 −0.523457 0.852052i \(-0.675358\pi\)
−0.523457 + 0.852052i \(0.675358\pi\)
\(620\) 7.53107 5.69045i 0.302455 0.228534i
\(621\) 88.2740 3.54231
\(622\) −28.9134 11.3498i −1.15932 0.455087i
\(623\) 8.69813 + 8.69813i 0.348483 + 0.348483i
\(624\) 0.943485 + 12.6341i 0.0377696 + 0.505768i
\(625\) 19.0827 + 16.1509i 0.763306 + 0.646037i
\(626\) 7.43250 + 17.0385i 0.297062 + 0.680995i
\(627\) −18.2537 + 18.2537i −0.728982 + 0.728982i
\(628\) −1.38958 37.2673i −0.0554505 1.48713i
\(629\) 17.7327i 0.707050i
\(630\) 28.0870 6.74664i 1.11901 0.268793i
\(631\) 36.4532i 1.45118i 0.688128 + 0.725589i \(0.258433\pi\)
−0.688128 + 0.725589i \(0.741567\pi\)
\(632\) 11.2622 5.42089i 0.447987 0.215631i
\(633\) 42.4792 42.4792i 1.68840 1.68840i
\(634\) 44.9796 19.6209i 1.78637 0.779246i
\(635\) 11.7650 8.21931i 0.466879 0.326173i
\(636\) −18.7954 17.4441i −0.745286 0.691705i
\(637\) −3.75655 3.75655i −0.148840 0.148840i
\(638\) 16.7007 42.5446i 0.661188 1.68436i
\(639\) 25.3502 1.00284
\(640\) −8.61641 23.7857i −0.340593 0.940211i
\(641\) 40.5177 1.60035 0.800177 0.599764i \(-0.204739\pi\)
0.800177 + 0.599764i \(0.204739\pi\)
\(642\) −12.0853 + 30.7870i −0.476970 + 1.21507i
\(643\) −0.831375 0.831375i −0.0327862 0.0327862i 0.690524 0.723310i \(-0.257380\pi\)
−0.723310 + 0.690524i \(0.757380\pi\)
\(644\) −13.1631 12.2168i −0.518700 0.481409i
\(645\) 1.71510 9.66679i 0.0675322 0.380629i
\(646\) −7.09483 + 3.09489i −0.279142 + 0.121767i
\(647\) 18.6491 18.6491i 0.733170 0.733170i −0.238076 0.971246i \(-0.576517\pi\)
0.971246 + 0.238076i \(0.0765168\pi\)
\(648\) −49.3193 + 23.7391i −1.93745 + 0.932559i
\(649\) 31.6901i 1.24394i
\(650\) −0.425024 7.05828i −0.0166708 0.276849i
\(651\) 8.68411i 0.340357i
\(652\) −1.29939 34.8483i −0.0508879 1.36476i
\(653\) −13.4285 + 13.4285i −0.525499 + 0.525499i −0.919227 0.393728i \(-0.871185\pi\)
0.393728 + 0.919227i \(0.371185\pi\)
\(654\) −16.0766 36.8545i −0.628644 1.44112i
\(655\) 6.77082 38.1622i 0.264558 1.49112i
\(656\) 0.525456 + 7.03631i 0.0205156 + 0.274722i
\(657\) −81.2745 81.2745i −3.17082 3.17082i
\(658\) −16.4572 6.46020i −0.641567 0.251845i
\(659\) 14.8202 0.577314 0.288657 0.957433i \(-0.406791\pi\)
0.288657 + 0.957433i \(0.406791\pi\)
\(660\) 53.9449 + 7.50992i 2.09980 + 0.292323i
\(661\) 13.3113 0.517749 0.258874 0.965911i \(-0.416648\pi\)
0.258874 + 0.965911i \(0.416648\pi\)
\(662\) 11.4215 + 4.48348i 0.443910 + 0.174255i
\(663\) −5.78319 5.78319i −0.224601 0.224601i
\(664\) 15.8854 + 5.56204i 0.616474 + 0.215849i
\(665\) 5.04717 3.52608i 0.195721 0.136736i
\(666\) 27.3054 + 62.5959i 1.05806 + 2.42554i
\(667\) −41.0823 + 41.0823i −1.59071 + 1.59071i
\(668\) −12.2280 + 0.455945i −0.473115 + 0.0176410i
\(669\) 3.79968i 0.146904i
\(670\) −1.89399 7.88490i −0.0731713 0.304620i
\(671\) 11.3327i 0.437493i
\(672\) 22.2383 + 6.86752i 0.857860 + 0.264921i
\(673\) −12.2894 + 12.2894i −0.473722 + 0.473722i −0.903117 0.429395i \(-0.858727\pi\)
0.429395 + 0.903117i \(0.358727\pi\)
\(674\) 9.79941 4.27468i 0.377459 0.164655i
\(675\) 57.9262 26.8617i 2.22958 1.03391i
\(676\) −1.36054 + 1.46593i −0.0523283 + 0.0563818i
\(677\) 13.2252 + 13.2252i 0.508286 + 0.508286i 0.914000 0.405714i \(-0.132977\pi\)
−0.405714 + 0.914000i \(0.632977\pi\)
\(678\) −8.40158 + 21.4028i −0.322661 + 0.821968i
\(679\) 4.28768 0.164546
\(680\) 14.2340 + 8.00661i 0.545848 + 0.307040i
\(681\) 41.7937 1.60154
\(682\) −4.19389 + 10.6838i −0.160593 + 0.409105i
\(683\) 2.26846 + 2.26846i 0.0868002 + 0.0868002i 0.749174 0.662374i \(-0.230451\pi\)
−0.662374 + 0.749174i \(0.730451\pi\)
\(684\) −20.2789 + 21.8497i −0.775382 + 0.835445i
\(685\) 9.72166 + 13.9154i 0.371446 + 0.531680i
\(686\) −20.7325 + 9.04390i −0.791571 + 0.345298i
\(687\) −2.19179 + 2.19179i −0.0836221 + 0.0836221i
\(688\) 3.61798 4.20196i 0.137934 0.160198i
\(689\) 4.04807i 0.154219i
\(690\) −59.0367 36.1680i −2.24749 1.37689i
\(691\) 27.3699i 1.04120i 0.853800 + 0.520601i \(0.174292\pi\)
−0.853800 + 0.520601i \(0.825708\pi\)
\(692\) −22.5166 + 0.839576i −0.855953 + 0.0319159i
\(693\) −24.8361 + 24.8361i −0.943447 + 0.943447i
\(694\) −3.33388 7.64268i −0.126552 0.290112i
\(695\) 36.5519 + 6.48512i 1.38649 + 0.245995i
\(696\) 24.8827 71.0660i 0.943175 2.69375i
\(697\) −3.22084 3.22084i −0.121998 0.121998i
\(698\) 3.05430 + 1.19896i 0.115607 + 0.0453811i
\(699\) −44.5980 −1.68685
\(700\) −12.3553 4.01123i −0.466988 0.151610i
\(701\) 19.5520 0.738467 0.369234 0.929337i \(-0.379620\pi\)
0.369234 + 0.929337i \(0.379620\pi\)
\(702\) −16.8110 6.59911i −0.634492 0.249067i
\(703\) 10.2927 + 10.2927i 0.388198 + 0.388198i
\(704\) 24.0425 + 19.1887i 0.906137 + 0.723200i
\(705\) −67.1108 11.9070i −2.52754 0.448442i
\(706\) −16.7186 38.3263i −0.629214 1.44243i
\(707\) 3.39997 3.39997i 0.127869 0.127869i
\(708\) −1.94531 52.1712i −0.0731090 1.96071i
\(709\) 23.8454i 0.895532i 0.894151 + 0.447766i \(0.147780\pi\)
−0.894151 + 0.447766i \(0.852220\pi\)
\(710\) −9.72091 5.95538i −0.364819 0.223502i
\(711\) 31.0742i 1.16537i
\(712\) 11.6163 + 24.1336i 0.435340 + 0.904444i
\(713\) 10.3166 10.3166i 0.386360 0.386360i
\(714\) −13.7717 + 6.00745i −0.515391 + 0.224823i
\(715\) 4.92413 + 7.04831i 0.184152 + 0.263592i
\(716\) −17.3881 16.1380i −0.649824 0.603106i
\(717\) 17.8942 + 17.8942i 0.668273 + 0.668273i
\(718\) 0.957934 2.44031i 0.0357498 0.0910715i
\(719\) 15.9103 0.593354 0.296677 0.954978i \(-0.404122\pi\)
0.296677 + 0.954978i \(0.404122\pi\)
\(720\) 62.5743 + 6.34510i 2.33200 + 0.236468i
\(721\) −21.7371 −0.809531
\(722\) 7.49665 19.0975i 0.278996 0.710735i
\(723\) −38.0759 38.0759i −1.41606 1.41606i
\(724\) −3.11801 2.89384i −0.115880 0.107549i
\(725\) −14.4572 + 39.4599i −0.536928 + 1.46550i
\(726\) −15.5404 + 6.77899i −0.576757 + 0.251592i
\(727\) 8.05611 8.05611i 0.298785 0.298785i −0.541753 0.840538i \(-0.682239\pi\)
0.840538 + 0.541753i \(0.182239\pi\)
\(728\) 1.59352 + 3.31063i 0.0590597 + 0.122700i
\(729\) 14.7373i 0.545828i
\(730\) 12.0725 + 50.2593i 0.446825 + 1.86018i
\(731\) 3.57954i 0.132394i
\(732\) 0.695659 + 18.6569i 0.0257123 + 0.689578i
\(733\) −1.51240 + 1.51240i −0.0558618 + 0.0558618i −0.734486 0.678624i \(-0.762577\pi\)
0.678624 + 0.734486i \(0.262577\pi\)
\(734\) −1.84466 4.22876i −0.0680877 0.156086i
\(735\) −30.8438 + 21.5482i −1.13769 + 0.794819i
\(736\) −18.2603 34.5773i −0.673082 1.27454i
\(737\) 6.97228 + 6.97228i 0.256827 + 0.256827i
\(738\) −16.3290 6.40988i −0.601079 0.235951i
\(739\) 3.38051 0.124354 0.0621771 0.998065i \(-0.480196\pi\)
0.0621771 + 0.998065i \(0.480196\pi\)
\(740\) 4.23463 30.4180i 0.155668 1.11819i
\(741\) −6.71356 −0.246629
\(742\) −6.92240 2.71736i −0.254129 0.0997576i
\(743\) −31.2491 31.2491i −1.14642 1.14642i −0.987252 0.159167i \(-0.949119\pi\)
−0.159167 0.987252i \(-0.550881\pi\)
\(744\) −6.24855 + 17.8461i −0.229083 + 0.654272i
\(745\) −5.54355 + 31.2450i −0.203100 + 1.14473i
\(746\) 19.1428 + 43.8836i 0.700869 + 1.60669i
\(747\) −29.5885 + 29.5885i −1.08259 + 1.08259i
\(748\) −19.8441 + 0.739927i −0.725573 + 0.0270544i
\(749\) 9.59171i 0.350473i
\(750\) −49.7463 5.76893i −1.81648 0.210652i
\(751\) 3.27690i 0.119576i 0.998211 + 0.0597879i \(0.0190424\pi\)
−0.998211 + 0.0597879i \(0.980958\pi\)
\(752\) −29.1717 25.1175i −1.06378 0.915941i
\(753\) 4.08038 4.08038i 0.148697 0.148697i
\(754\) 10.8950 4.75258i 0.396772 0.173079i
\(755\) −1.74605 + 9.84121i −0.0635453 + 0.358158i
\(756\) −22.5696 + 24.3179i −0.820850 + 0.884435i
\(757\) 31.9796 + 31.9796i 1.16232 + 1.16232i 0.983967 + 0.178353i \(0.0570768\pi\)
0.178353 + 0.983967i \(0.442923\pi\)
\(758\) −10.4481 + 26.6161i −0.379491 + 0.966741i
\(759\) 84.1854 3.05574
\(760\) 12.9093 3.61459i 0.468268 0.131115i
\(761\) 28.7698 1.04290 0.521451 0.853281i \(-0.325391\pi\)
0.521451 + 0.853281i \(0.325391\pi\)
\(762\) −10.5050 + 26.7611i −0.380555 + 0.969454i
\(763\) −8.24534 8.24534i −0.298501 0.298501i
\(764\) −24.5579 + 26.4602i −0.888475 + 0.957298i
\(765\) −33.2840 + 23.2531i −1.20339 + 0.840716i
\(766\) 6.19804 2.70370i 0.223944 0.0976885i
\(767\) 5.82768 5.82768i 0.210425 0.210425i
\(768\) 40.7590 + 30.1143i 1.47076 + 1.08666i
\(769\) 17.7747i 0.640972i −0.947253 0.320486i \(-0.896154\pi\)
0.947253 0.320486i \(-0.103846\pi\)
\(770\) 15.3584 3.68916i 0.553478 0.132948i
\(771\) 76.6584i 2.76079i
\(772\) 44.2975 1.65172i 1.59430 0.0594467i
\(773\) 4.56344 4.56344i 0.164136 0.164136i −0.620260 0.784396i \(-0.712973\pi\)
0.784396 + 0.620260i \(0.212973\pi\)
\(774\) 5.51190 + 12.6356i 0.198121 + 0.454179i
\(775\) 3.63051 9.90920i 0.130412 0.355949i
\(776\) 8.81132 + 3.08515i 0.316308 + 0.110750i
\(777\) 19.9791 + 19.9791i 0.716745 + 0.716745i
\(778\) −4.28617 1.68252i −0.153667 0.0603212i
\(779\) −3.73899 −0.133963
\(780\) 8.53922 + 11.3013i 0.305753 + 0.404652i
\(781\) 13.8619 0.496017
\(782\) 23.4973 + 9.22379i 0.840263 + 0.329842i
\(783\) 75.8965 + 75.8965i 2.71232 + 2.71232i
\(784\) −21.1912 + 1.58251i −0.756830 + 0.0565183i
\(785\) −23.8790 34.1800i −0.852279 1.21994i
\(786\) 31.0429 + 71.1637i 1.10726 + 2.53833i
\(787\) 11.7845 11.7845i 0.420073 0.420073i −0.465156 0.885229i \(-0.654002\pi\)
0.885229 + 0.465156i \(0.154002\pi\)
\(788\) −0.324095 8.69192i −0.0115454 0.309637i
\(789\) 25.9980i 0.925552i
\(790\) 7.30010 11.9159i 0.259726 0.423947i
\(791\) 6.66804i 0.237088i
\(792\) −68.9097 + 33.1686i −2.44860 + 1.17859i
\(793\) −2.08403 + 2.08403i −0.0740061 + 0.0740061i
\(794\) −8.21470 + 3.58340i −0.291529 + 0.127170i
\(795\) −28.2289 5.00844i −1.00118 0.177631i
\(796\) −11.9758 11.1148i −0.424472 0.393955i
\(797\) 31.4689 + 31.4689i 1.11469 + 1.11469i 0.992508 + 0.122179i \(0.0389881\pi\)
0.122179 + 0.992508i \(0.461012\pi\)
\(798\) −4.50664 + 11.4805i −0.159533 + 0.406407i
\(799\) 24.8506 0.879151
\(800\) −22.5044 17.1334i −0.795651 0.605755i
\(801\) −66.5884 −2.35278
\(802\) 8.25628 21.0326i 0.291539 0.742688i
\(803\) −44.4421 44.4421i −1.56833 1.56833i
\(804\) 11.9064 + 11.0504i 0.419906 + 0.389718i
\(805\) −19.7698 3.50760i −0.696794 0.123627i
\(806\) −2.73595 + 1.19347i −0.0963699 + 0.0420383i
\(807\) 5.16215 5.16215i 0.181716 0.181716i
\(808\) 9.43346 4.54065i 0.331868 0.159739i
\(809\) 40.1623i 1.41203i 0.708196 + 0.706016i \(0.249509\pi\)
−0.708196 + 0.706016i \(0.750491\pi\)
\(810\) −31.9685 + 52.1818i −1.12326 + 1.83348i
\(811\) 26.5593i 0.932622i −0.884621 0.466311i \(-0.845583\pi\)
0.884621 0.466311i \(-0.154417\pi\)
\(812\) −0.813648 21.8213i −0.0285535 0.765776i
\(813\) −38.4891 + 38.4891i −1.34987 + 1.34987i
\(814\) 14.9310 + 34.2284i 0.523332 + 1.19970i
\(815\) −22.3290 31.9614i −0.782152 1.11956i
\(816\) −32.6238 + 2.43627i −1.14206 + 0.0852867i
\(817\) 2.07770 + 2.07770i 0.0726895 + 0.0726895i
\(818\) 10.5774 + 4.15213i 0.369831 + 0.145176i
\(819\) −9.13454 −0.319186
\(820\) 4.75575 + 6.29405i 0.166078 + 0.219798i
\(821\) −12.2484 −0.427472 −0.213736 0.976891i \(-0.568563\pi\)
−0.213736 + 0.976891i \(0.568563\pi\)
\(822\) −31.6526 12.4251i −1.10401 0.433376i
\(823\) −1.10742 1.10742i −0.0386021 0.0386021i 0.687542 0.726144i \(-0.258690\pi\)
−0.726144 + 0.687542i \(0.758690\pi\)
\(824\) −44.6704 15.6407i −1.55617 0.544868i
\(825\) 55.2432 25.6176i 1.92332 0.891890i
\(826\) −6.05366 13.8776i −0.210634 0.482864i
\(827\) −1.25920 + 1.25920i −0.0437865 + 0.0437865i −0.728661 0.684875i \(-0.759857\pi\)
0.684875 + 0.728661i \(0.259857\pi\)
\(828\) 97.1479 3.62235i 3.37612 0.125885i
\(829\) 36.0843i 1.25326i −0.779317 0.626630i \(-0.784434\pi\)
0.779317 0.626630i \(-0.215566\pi\)
\(830\) 18.2972 4.39508i 0.635105 0.152555i
\(831\) 7.57915i 0.262918i
\(832\) 0.892610 + 7.95005i 0.0309457 + 0.275618i
\(833\) 9.70018 9.70018i 0.336091 0.336091i
\(834\) −68.1609 + 29.7330i −2.36022 + 1.02957i
\(835\) −11.2150 + 7.83508i −0.388111 + 0.271144i
\(836\) −11.0888 + 11.9478i −0.383514 + 0.413222i
\(837\) −19.0592 19.0592i −0.658782 0.658782i
\(838\) 5.23427 13.3341i 0.180815 0.460620i
\(839\) 10.5460 0.364087 0.182044 0.983290i \(-0.441729\pi\)
0.182044 + 0.983290i \(0.441729\pi\)
\(840\) 25.0580 7.01623i 0.864582 0.242083i
\(841\) −41.6438 −1.43599
\(842\) −3.30156 + 8.41062i −0.113779 + 0.289849i
\(843\) 28.4776 + 28.4776i 0.980821 + 0.980821i
\(844\) 25.8054 27.8043i 0.888258 0.957064i
\(845\) −0.390628 + 2.20168i −0.0134380 + 0.0757402i
\(846\) 87.7217 38.2658i 3.01594 1.31561i
\(847\) −3.47680 + 3.47680i −0.119464 + 0.119464i
\(848\) −12.2705 10.5652i −0.421372 0.362811i
\(849\) 55.8920i 1.91821i
\(850\) 18.2260 1.09750i 0.625145 0.0376439i
\(851\) 47.4698i 1.62724i
\(852\) 22.8207 0.850915i 0.781824 0.0291519i
\(853\) −24.0809 + 24.0809i −0.824516 + 0.824516i −0.986752 0.162236i \(-0.948129\pi\)
0.162236 + 0.986752i \(0.448129\pi\)
\(854\) 2.16484 + 4.96276i 0.0740795 + 0.169822i
\(855\) −5.82233 + 32.8162i −0.199120 + 1.12229i
\(856\) −6.90160 + 19.7113i −0.235892 + 0.673718i
\(857\) 14.8214 + 14.8214i 0.506290 + 0.506290i 0.913386 0.407096i \(-0.133458\pi\)
−0.407096 + 0.913386i \(0.633458\pi\)
\(858\) −16.0324 6.29346i −0.547337 0.214855i
\(859\) 17.3686 0.592610 0.296305 0.955093i \(-0.404245\pi\)
0.296305 + 0.955093i \(0.404245\pi\)
\(860\) 0.854805 6.14020i 0.0291486 0.209379i
\(861\) −7.25769 −0.247341
\(862\) 27.0375 + 10.6135i 0.920900 + 0.361496i
\(863\) −22.2917 22.2917i −0.758819 0.758819i 0.217288 0.976107i \(-0.430279\pi\)
−0.976107 + 0.217288i \(0.930279\pi\)
\(864\) −63.8791 + 33.7345i −2.17321 + 1.14767i
\(865\) −20.6513 + 14.4275i −0.702164 + 0.490550i
\(866\) −13.3557 30.6171i −0.453847 1.04041i
\(867\) −23.1403 + 23.1403i −0.785886 + 0.785886i
\(868\) 0.204324 + 5.47977i 0.00693521 + 0.185995i
\(869\) 16.9918i 0.576409i
\(870\) −19.6621 81.8554i −0.666607 2.77516i
\(871\) 2.56435i 0.0868896i
\(872\) −11.0116 22.8773i −0.372901 0.774723i
\(873\) −16.4121 + 16.4121i −0.555466 + 0.555466i
\(874\) 18.9926 8.28490i 0.642433 0.280241i
\(875\) −14.0405 + 3.71422i −0.474654 + 0.125564i
\(876\) −75.8929 70.4367i −2.56418 2.37983i
\(877\) 19.8938 + 19.8938i 0.671766 + 0.671766i 0.958123 0.286357i \(-0.0924443\pi\)
−0.286357 + 0.958123i \(0.592444\pi\)
\(878\) −13.9397 + 35.5111i −0.470444 + 1.19844i
\(879\) 6.48215 0.218637
\(880\) 34.2165 + 3.46960i 1.15344 + 0.116960i
\(881\) −54.9836 −1.85244 −0.926222 0.376977i \(-0.876963\pi\)
−0.926222 + 0.376977i \(0.876963\pi\)
\(882\) 19.3046 49.1780i 0.650020 1.65591i
\(883\) 3.75066 + 3.75066i 0.126220 + 0.126220i 0.767395 0.641175i \(-0.221553\pi\)
−0.641175 + 0.767395i \(0.721553\pi\)
\(884\) −3.78533 3.51319i −0.127314 0.118161i
\(885\) −33.4287 47.8492i −1.12369 1.60843i
\(886\) 36.9685 16.1263i 1.24198 0.541774i
\(887\) 1.40851 1.40851i 0.0472932 0.0472932i −0.683065 0.730358i \(-0.739353\pi\)
0.730358 + 0.683065i \(0.239353\pi\)
\(888\) 26.6820 + 55.4334i 0.895388 + 1.86022i
\(889\) 8.33745i 0.279629i
\(890\) 25.5343 + 15.6432i 0.855911 + 0.524363i
\(891\) 74.4105i 2.49284i
\(892\) −0.0894007 2.39764i −0.00299336 0.0802789i
\(893\) 14.4242 14.4242i 0.482688 0.482688i
\(894\) −25.4161 58.2647i −0.850042 1.94866i
\(895\) −26.1153 4.63344i −0.872939 0.154879i
\(896\) 14.1942 + 3.81025i 0.474194 + 0.127292i
\(897\) 15.4814 + 15.4814i 0.516908 + 0.516908i
\(898\) −24.6604 9.68036i −0.822929 0.323038i
\(899\) 17.7401 0.591666
\(900\) 62.6470 31.9391i 2.08823 1.06464i
\(901\) 10.4530 0.348238
\(902\) −8.92894 3.50502i −0.297301 0.116704i
\(903\) 4.03299 + 4.03299i 0.134209 + 0.134209i
\(904\) −4.79791 + 13.7031i −0.159576 + 0.455757i
\(905\) −4.68295 0.830861i −0.155667 0.0276187i
\(906\) −8.00530 18.3516i −0.265958 0.609692i
\(907\) −2.56253 + 2.56253i −0.0850874 + 0.0850874i −0.748369 0.663282i \(-0.769163\pi\)
0.663282 + 0.748369i \(0.269163\pi\)
\(908\) 26.3723 0.983343i 0.875195 0.0326334i
\(909\) 26.0284i 0.863307i
\(910\) 3.50277 + 2.14593i 0.116116 + 0.0711368i
\(911\) 9.22555i 0.305656i −0.988253 0.152828i \(-0.951162\pi\)
0.988253 0.152828i \(-0.0488381\pi\)
\(912\) −17.5220 + 20.3502i −0.580211 + 0.673862i
\(913\) −16.1794 + 16.1794i −0.535461 + 0.535461i
\(914\) 1.67189 0.729309i 0.0553012 0.0241234i
\(915\) 11.9544 + 17.1113i 0.395200 + 0.565682i
\(916\) −1.33148 + 1.43461i −0.0439932 + 0.0474010i
\(917\) 15.9213 + 15.9213i 0.525766 + 0.525766i
\(918\) 17.0403 43.4096i 0.562413 1.43273i
\(919\) 22.0203 0.726383 0.363191 0.931715i \(-0.381687\pi\)
0.363191 + 0.931715i \(0.381687\pi\)
\(920\) −38.1038 21.4334i −1.25624 0.706638i
\(921\) −9.06568 −0.298724
\(922\) 7.07195 18.0156i 0.232902 0.593312i
\(923\) 2.54914 + 2.54914i 0.0839061 + 0.0839061i
\(924\) −21.5243 + 23.1916i −0.708097 + 0.762947i
\(925\) −14.4450 31.1501i −0.474950 1.02421i
\(926\) 3.85829 1.68305i 0.126791 0.0553086i
\(927\) 83.2039 83.2039i 2.73277 2.73277i
\(928\) 14.0292 45.4289i 0.460530 1.49128i
\(929\) 43.7617i 1.43578i −0.696159 0.717888i \(-0.745109\pi\)
0.696159 0.717888i \(-0.254891\pi\)
\(930\) 4.93756 + 20.5556i 0.161909 + 0.674044i
\(931\) 11.2607i 0.369055i
\(932\) −28.1418 + 1.04932i −0.921816 + 0.0343717i
\(933\) 49.1904 49.1904i 1.61042 1.61042i
\(934\) 22.8196 + 52.3123i 0.746679 + 1.71171i
\(935\) −18.2002 + 12.7151i −0.595210 + 0.415829i
\(936\) −18.7718 6.57265i −0.613575 0.214834i
\(937\) −32.3888 32.3888i −1.05810 1.05810i −0.998205 0.0598906i \(-0.980925\pi\)
−0.0598906 0.998205i \(-0.519075\pi\)
\(938\) 4.38517 + 1.72138i 0.143181 + 0.0562051i
\(939\) −41.6326 −1.35863
\(940\) −42.6278 5.93440i −1.39036 0.193559i
\(941\) −22.7847 −0.742760 −0.371380 0.928481i \(-0.621115\pi\)
−0.371380 + 0.928481i \(0.621115\pi\)
\(942\) 77.7474 + 30.5194i 2.53315 + 0.994377i
\(943\) 8.62205 + 8.62205i 0.280773 + 0.280773i
\(944\) −2.45502 32.8748i −0.0799040 1.06998i
\(945\) −6.48004 + 36.5232i −0.210796 + 1.18810i
\(946\) 3.01399 + 6.90936i 0.0979932 + 0.224643i
\(947\) 42.9277 42.9277i 1.39496 1.39496i 0.581213 0.813752i \(-0.302578\pi\)
0.813752 0.581213i \(-0.197422\pi\)
\(948\) 1.04305 + 27.9736i 0.0338767 + 0.908539i
\(949\) 16.3455i 0.530596i
\(950\) 9.94200 11.2161i 0.322561 0.363897i
\(951\) 109.905i 3.56391i
\(952\) −8.54872 + 4.11479i −0.277066 + 0.133361i
\(953\) 36.5000 36.5000i 1.18235 1.18235i 0.203218 0.979134i \(-0.434860\pi\)
0.979134 0.203218i \(-0.0651399\pi\)
\(954\) 36.8985 16.0958i 1.19463 0.521121i
\(955\) −7.05091 + 39.7408i −0.228162 + 1.28598i
\(956\) 11.7125 + 10.8704i 0.378809 + 0.351575i
\(957\) 72.3812 + 72.3812i 2.33975 + 2.33975i
\(958\) 10.2363 26.0767i 0.330720 0.842499i
\(959\) −9.86139 −0.318441
\(960\) 56.5434 + 3.61158i 1.82493 + 0.116563i
\(961\) 26.5451 0.856293
\(962\) −3.54870 + 9.04022i −0.114415 + 0.291468i
\(963\) −36.7146 36.7146i −1.18311 1.18311i
\(964\) −24.9222 23.1305i −0.802690 0.744982i
\(965\) 40.6278 28.3836i 1.30785 0.913700i
\(966\) 36.8662 16.0817i 1.18615 0.517420i
\(967\) −20.2300 + 20.2300i −0.650551 + 0.650551i −0.953126 0.302574i \(-0.902154\pi\)
0.302574 + 0.953126i \(0.402154\pi\)
\(968\) −9.64665 + 4.64326i −0.310055 + 0.149240i
\(969\) 17.3358i 0.556907i
\(970\) 10.1491 2.43786i 0.325867 0.0782750i
\(971\) 40.0097i 1.28397i 0.766717 + 0.641986i \(0.221889\pi\)
−0.766717 + 0.641986i \(0.778111\pi\)
\(972\) −1.71270 45.9330i −0.0549350 1.47330i
\(973\) −15.2494 + 15.2494i −0.488875 + 0.488875i
\(974\) −7.36293 16.8790i −0.235923 0.540838i
\(975\) 14.8700 + 5.44803i 0.476220 + 0.174477i
\(976\) 0.877936 + 11.7563i 0.0281021 + 0.376311i
\(977\) −7.48988 7.48988i −0.239623 0.239623i 0.577071 0.816694i \(-0.304195\pi\)
−0.816694 + 0.577071i \(0.804195\pi\)
\(978\) 72.7008 + 28.5384i 2.32471 + 0.912558i
\(979\) −36.4115 −1.16372
\(980\) −18.9558 + 14.3229i −0.605519 + 0.457528i
\(981\) 63.1221 2.01533
\(982\) −30.9416 12.1460i −0.987385 0.387594i
\(983\) 36.2016 + 36.2016i 1.15465 + 1.15465i 0.985609 + 0.169042i \(0.0540672\pi\)
0.169042 + 0.985609i \(0.445933\pi\)
\(984\) −14.9148 5.22219i −0.475467 0.166477i
\(985\) −5.56934 7.97185i −0.177454 0.254004i
\(986\) 12.2722 + 28.1331i 0.390825 + 0.895940i
\(987\) 27.9986 27.9986i 0.891206 0.891206i
\(988\) −4.23633 + 0.157960i −0.134776 + 0.00502538i
\(989\) 9.58228i 0.304699i
\(990\) −44.6668 + 72.9092i −1.41961 + 2.31721i
\(991\) 45.2754i 1.43822i −0.694897 0.719110i \(-0.744550\pi\)
0.694897 0.719110i \(-0.255450\pi\)
\(992\) −3.52301 + 11.4081i −0.111856 + 0.362209i
\(993\) −19.4315 + 19.4315i −0.616639 + 0.616639i
\(994\) 6.07034 2.64799i 0.192539 0.0839892i
\(995\) −17.9866 3.19122i −0.570212 0.101168i
\(996\) −25.6429 + 27.6292i −0.812526 + 0.875466i
\(997\) −13.5950 13.5950i −0.430558 0.430558i 0.458260 0.888818i \(-0.348473\pi\)
−0.888818 + 0.458260i \(0.848473\pi\)
\(998\) 11.5880 29.5200i 0.366810 0.934439i
\(999\) −87.6969 −2.77461
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 260.2.o.a.27.13 72
4.3 odd 2 inner 260.2.o.a.27.32 yes 72
5.3 odd 4 inner 260.2.o.a.183.32 yes 72
20.3 even 4 inner 260.2.o.a.183.13 yes 72
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
260.2.o.a.27.13 72 1.1 even 1 trivial
260.2.o.a.27.32 yes 72 4.3 odd 2 inner
260.2.o.a.183.13 yes 72 20.3 even 4 inner
260.2.o.a.183.32 yes 72 5.3 odd 4 inner