Properties

Label 539.2.q.f.520.3
Level $539$
Weight $2$
Character 539.520
Analytic conductor $4.304$
Analytic rank $0$
Dimension $32$
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] = [539,2,Mod(214,539)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(539, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([20, 12]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("539.214");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 539 = 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 539.q (of order \(15\), degree \(8\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.30393666895\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(4\) over \(\Q(\zeta_{15})\)
Twist minimal: no (minimal twist has level 77)
Sato-Tate group: $\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label 520.3
Character \(\chi\) \(=\) 539.520
Dual form 539.2.q.f.312.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.0236455 - 0.224972i) q^{2} +(0.146626 - 0.162845i) q^{3} +(1.90624 - 0.405184i) q^{4} +(2.27977 - 1.01502i) q^{5} +(-0.0401026 - 0.0291363i) q^{6} +(-0.276036 - 0.849550i) q^{8} +(0.308566 + 2.93581i) q^{9} +O(q^{10})\) \(q+(-0.0236455 - 0.224972i) q^{2} +(0.146626 - 0.162845i) q^{3} +(1.90624 - 0.405184i) q^{4} +(2.27977 - 1.01502i) q^{5} +(-0.0401026 - 0.0291363i) q^{6} +(-0.276036 - 0.849550i) q^{8} +(0.308566 + 2.93581i) q^{9} +(-0.282258 - 0.488885i) q^{10} +(-0.375645 + 3.29528i) q^{11} +(0.213523 - 0.369833i) q^{12} +(4.15429 - 3.01827i) q^{13} +(0.168984 - 0.520079i) q^{15} +(3.37609 - 1.50313i) q^{16} +(-0.150262 + 1.42965i) q^{17} +(0.653179 - 0.138838i) q^{18} +(-5.93587 - 1.26171i) q^{19} +(3.93453 - 2.85860i) q^{20} +(0.750229 + 0.00659095i) q^{22} +(-3.54146 + 6.13399i) q^{23} +(-0.178819 - 0.0796154i) q^{24} +(0.821451 - 0.912313i) q^{25} +(-0.777257 - 0.863231i) q^{26} +(1.05516 + 0.766622i) q^{27} +(2.01408 - 6.19869i) q^{29} +(-0.120999 - 0.0257191i) q^{30} +(-7.02421 - 3.12738i) q^{31} +(-1.31126 - 2.27117i) q^{32} +(0.481541 + 0.544347i) q^{33} +0.325184 q^{34} +(1.77775 + 5.47134i) q^{36} +(-2.66603 - 2.96093i) q^{37} +(-0.143492 + 1.36524i) q^{38} +(0.117618 - 1.11906i) q^{39} +(-1.49161 - 1.65660i) q^{40} +(-2.08556 - 6.41868i) q^{41} -0.802299 q^{43} +(0.619127 + 6.43381i) q^{44} +(3.68337 + 6.37979i) q^{45} +(1.46372 + 0.651689i) q^{46} +(6.60467 + 1.40387i) q^{47} +(0.250246 - 0.770178i) q^{48} +(-0.224669 - 0.163231i) q^{50} +(0.210779 + 0.234094i) q^{51} +(6.69613 - 7.43680i) q^{52} +(6.01266 + 2.67701i) q^{53} +(0.147519 - 0.255510i) q^{54} +(2.48840 + 7.89379i) q^{55} +(-1.07582 + 0.781627i) q^{57} +(-1.44216 - 0.306540i) q^{58} +(2.81340 - 0.598006i) q^{59} +(0.111396 - 1.05986i) q^{60} +(0.781393 - 0.347899i) q^{61} +(-0.537482 + 1.65420i) q^{62} +(5.49964 - 3.99573i) q^{64} +(6.40724 - 11.0977i) q^{65} +(0.111077 - 0.121205i) q^{66} +(0.823340 + 1.42607i) q^{67} +(0.292835 + 2.78614i) q^{68} +(0.479618 + 1.47611i) q^{69} +(-3.65738 - 2.65724i) q^{71} +(2.40894 - 1.07253i) q^{72} +(-14.5235 + 3.08706i) q^{73} +(-0.603087 + 0.669796i) q^{74} +(-0.0281194 - 0.267538i) q^{75} -11.8264 q^{76} -0.254539 q^{78} +(-0.256398 - 2.43947i) q^{79} +(6.17101 - 6.85360i) q^{80} +(-8.38287 + 1.78183i) q^{81} +(-1.39471 + 0.620965i) q^{82} +(1.81851 + 1.32122i) q^{83} +(1.10856 + 3.41180i) q^{85} +(0.0189708 + 0.180495i) q^{86} +(-0.714109 - 1.23687i) q^{87} +(2.90320 - 0.590486i) q^{88} +(0.867830 - 1.50313i) q^{89} +(1.34818 - 0.979509i) q^{90} +(-4.26549 + 13.1278i) q^{92} +(-1.53921 + 0.685301i) q^{93} +(0.159660 - 1.51906i) q^{94} +(-14.8131 + 3.14862i) q^{95} +(-0.562114 - 0.119481i) q^{96} +(-9.77095 + 7.09901i) q^{97} +(-9.79024 - 0.0860098i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 3 q^{2} - 2 q^{3} + 11 q^{4} - 5 q^{5} - 6 q^{6} - 10 q^{8} + 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 3 q^{2} - 2 q^{3} + 11 q^{4} - 5 q^{5} - 6 q^{6} - 10 q^{8} + 12 q^{9} + 12 q^{10} + 3 q^{11} + 18 q^{12} + 14 q^{13} - 36 q^{15} - 17 q^{16} - 5 q^{17} - 11 q^{18} + 19 q^{19} - 2 q^{20} - 66 q^{22} - 32 q^{23} - 35 q^{24} - 7 q^{25} - 27 q^{26} - 20 q^{27} + 6 q^{29} + 2 q^{30} - 7 q^{31} - 32 q^{32} - 26 q^{33} + 48 q^{34} + 104 q^{36} - 4 q^{37} - 5 q^{38} - 11 q^{39} - 10 q^{40} + 20 q^{41} - 16 q^{43} + 38 q^{44} + 70 q^{45} + 42 q^{46} - 23 q^{47} + 72 q^{48} + 104 q^{50} + 29 q^{51} + 33 q^{52} - 4 q^{53} + 60 q^{54} + 24 q^{55} - 22 q^{57} - 20 q^{58} + 17 q^{59} + 30 q^{60} - 7 q^{61} - 158 q^{62} + 14 q^{64} + 8 q^{65} + 8 q^{66} + 38 q^{67} - 2 q^{68} - 20 q^{69} - 28 q^{71} - 35 q^{73} + 29 q^{74} + 9 q^{75} - 104 q^{76} - 116 q^{78} - 15 q^{79} - 87 q^{80} + 14 q^{81} + 19 q^{82} - 10 q^{83} + 12 q^{85} + 52 q^{86} - 72 q^{87} - 55 q^{88} + 74 q^{89} + 28 q^{90} - 110 q^{92} - 32 q^{93} - 24 q^{94} - 32 q^{95} - 42 q^{96} - 40 q^{97} + 32 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/539\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(442\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{4}{5}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.0236455 0.224972i −0.0167199 0.159079i 0.982976 0.183733i \(-0.0588183\pi\)
−0.999696 + 0.0246540i \(0.992152\pi\)
\(3\) 0.146626 0.162845i 0.0846547 0.0940186i −0.699329 0.714800i \(-0.746518\pi\)
0.783984 + 0.620781i \(0.213184\pi\)
\(4\) 1.90624 0.405184i 0.953121 0.202592i
\(5\) 2.27977 1.01502i 1.01955 0.453931i 0.172251 0.985053i \(-0.444896\pi\)
0.847295 + 0.531122i \(0.178229\pi\)
\(6\) −0.0401026 0.0291363i −0.0163718 0.0118948i
\(7\) 0 0
\(8\) −0.276036 0.849550i −0.0975933 0.300361i
\(9\) 0.308566 + 2.93581i 0.102855 + 0.978604i
\(10\) −0.282258 0.488885i −0.0892578 0.154599i
\(11\) −0.375645 + 3.29528i −0.113261 + 0.993565i
\(12\) 0.213523 0.369833i 0.0616388 0.106761i
\(13\) 4.15429 3.01827i 1.15219 0.837117i 0.163422 0.986556i \(-0.447747\pi\)
0.988771 + 0.149439i \(0.0477468\pi\)
\(14\) 0 0
\(15\) 0.168984 0.520079i 0.0436314 0.134284i
\(16\) 3.37609 1.50313i 0.844022 0.375783i
\(17\) −0.150262 + 1.42965i −0.0364439 + 0.346741i 0.961072 + 0.276298i \(0.0891078\pi\)
−0.997516 + 0.0704426i \(0.977559\pi\)
\(18\) 0.653179 0.138838i 0.153956 0.0327243i
\(19\) −5.93587 1.26171i −1.36178 0.289456i −0.531622 0.846982i \(-0.678417\pi\)
−0.830159 + 0.557526i \(0.811751\pi\)
\(20\) 3.93453 2.85860i 0.879788 0.639203i
\(21\) 0 0
\(22\) 0.750229 + 0.00659095i 0.159949 + 0.00140520i
\(23\) −3.54146 + 6.13399i −0.738446 + 1.27903i 0.214749 + 0.976669i \(0.431107\pi\)
−0.953195 + 0.302356i \(0.902227\pi\)
\(24\) −0.178819 0.0796154i −0.0365013 0.0162514i
\(25\) 0.821451 0.912313i 0.164290 0.182463i
\(26\) −0.777257 0.863231i −0.152433 0.169294i
\(27\) 1.05516 + 0.766622i 0.203067 + 0.147536i
\(28\) 0 0
\(29\) 2.01408 6.19869i 0.374004 1.15107i −0.570143 0.821545i \(-0.693112\pi\)
0.944148 0.329522i \(-0.106888\pi\)
\(30\) −0.120999 0.0257191i −0.0220913 0.00469565i
\(31\) −7.02421 3.12738i −1.26158 0.561694i −0.336582 0.941654i \(-0.609271\pi\)
−0.925003 + 0.379960i \(0.875938\pi\)
\(32\) −1.31126 2.27117i −0.231801 0.401490i
\(33\) 0.481541 + 0.544347i 0.0838255 + 0.0947586i
\(34\) 0.325184 0.0557687
\(35\) 0 0
\(36\) 1.77775 + 5.47134i 0.296291 + 0.911890i
\(37\) −2.66603 2.96093i −0.438293 0.486774i 0.483012 0.875614i \(-0.339543\pi\)
−0.921305 + 0.388840i \(0.872876\pi\)
\(38\) −0.143492 + 1.36524i −0.0232775 + 0.221471i
\(39\) 0.117618 1.11906i 0.0188340 0.179193i
\(40\) −1.49161 1.65660i −0.235844 0.261932i
\(41\) −2.08556 6.41868i −0.325709 1.00243i −0.971120 0.238594i \(-0.923314\pi\)
0.645410 0.763836i \(-0.276686\pi\)
\(42\) 0 0
\(43\) −0.802299 −0.122349 −0.0611747 0.998127i \(-0.519485\pi\)
−0.0611747 + 0.998127i \(0.519485\pi\)
\(44\) 0.619127 + 6.43381i 0.0933368 + 0.969934i
\(45\) 3.68337 + 6.37979i 0.549085 + 0.951042i
\(46\) 1.46372 + 0.651689i 0.215813 + 0.0960862i
\(47\) 6.60467 + 1.40387i 0.963390 + 0.204775i 0.662648 0.748931i \(-0.269433\pi\)
0.300742 + 0.953706i \(0.402766\pi\)
\(48\) 0.250246 0.770178i 0.0361199 0.111166i
\(49\) 0 0
\(50\) −0.224669 0.163231i −0.0317729 0.0230844i
\(51\) 0.210779 + 0.234094i 0.0295149 + 0.0327797i
\(52\) 6.69613 7.43680i 0.928586 1.03130i
\(53\) 6.01266 + 2.67701i 0.825902 + 0.367715i 0.775761 0.631027i \(-0.217366\pi\)
0.0501411 + 0.998742i \(0.484033\pi\)
\(54\) 0.147519 0.255510i 0.0200747 0.0347705i
\(55\) 2.48840 + 7.89379i 0.335535 + 1.06440i
\(56\) 0 0
\(57\) −1.07582 + 0.781627i −0.142495 + 0.103529i
\(58\) −1.44216 0.306540i −0.189364 0.0402506i
\(59\) 2.81340 0.598006i 0.366273 0.0778538i −0.0210985 0.999777i \(-0.506716\pi\)
0.387372 + 0.921924i \(0.373383\pi\)
\(60\) 0.111396 1.05986i 0.0143812 0.136828i
\(61\) 0.781393 0.347899i 0.100047 0.0445439i −0.356103 0.934447i \(-0.615895\pi\)
0.456150 + 0.889903i \(0.349228\pi\)
\(62\) −0.537482 + 1.65420i −0.0682603 + 0.210084i
\(63\) 0 0
\(64\) 5.49964 3.99573i 0.687455 0.499466i
\(65\) 6.40724 11.0977i 0.794720 1.37650i
\(66\) 0.111077 0.121205i 0.0136726 0.0149193i
\(67\) 0.823340 + 1.42607i 0.100587 + 0.174222i 0.911927 0.410353i \(-0.134595\pi\)
−0.811340 + 0.584575i \(0.801261\pi\)
\(68\) 0.292835 + 2.78614i 0.0355115 + 0.337869i
\(69\) 0.479618 + 1.47611i 0.0577393 + 0.177703i
\(70\) 0 0
\(71\) −3.65738 2.65724i −0.434051 0.315357i 0.349216 0.937042i \(-0.386448\pi\)
−0.783267 + 0.621686i \(0.786448\pi\)
\(72\) 2.40894 1.07253i 0.283897 0.126399i
\(73\) −14.5235 + 3.08706i −1.69985 + 0.361313i −0.952832 0.303497i \(-0.901846\pi\)
−0.747013 + 0.664810i \(0.768513\pi\)
\(74\) −0.603087 + 0.669796i −0.0701074 + 0.0778622i
\(75\) −0.0281194 0.267538i −0.00324695 0.0308926i
\(76\) −11.8264 −1.35658
\(77\) 0 0
\(78\) −0.254539 −0.0288209
\(79\) −0.256398 2.43947i −0.0288471 0.274462i −0.999432 0.0337023i \(-0.989270\pi\)
0.970585 0.240759i \(-0.0773965\pi\)
\(80\) 6.17101 6.85360i 0.689940 0.766256i
\(81\) −8.38287 + 1.78183i −0.931430 + 0.197982i
\(82\) −1.39471 + 0.620965i −0.154020 + 0.0685741i
\(83\) 1.81851 + 1.32122i 0.199607 + 0.145023i 0.683099 0.730326i \(-0.260632\pi\)
−0.483492 + 0.875349i \(0.660632\pi\)
\(84\) 0 0
\(85\) 1.10856 + 3.41180i 0.120240 + 0.370061i
\(86\) 0.0189708 + 0.180495i 0.00204567 + 0.0194633i
\(87\) −0.714109 1.23687i −0.0765605 0.132607i
\(88\) 2.90320 0.590486i 0.309482 0.0629460i
\(89\) 0.867830 1.50313i 0.0919898 0.159331i −0.816358 0.577546i \(-0.804011\pi\)
0.908348 + 0.418214i \(0.137344\pi\)
\(90\) 1.34818 0.979509i 0.142111 0.103249i
\(91\) 0 0
\(92\) −4.26549 + 13.1278i −0.444708 + 1.36867i
\(93\) −1.53921 + 0.685301i −0.159609 + 0.0710624i
\(94\) 0.159660 1.51906i 0.0164676 0.156679i
\(95\) −14.8131 + 3.14862i −1.51979 + 0.323042i
\(96\) −0.562114 0.119481i −0.0573706 0.0121945i
\(97\) −9.77095 + 7.09901i −0.992089 + 0.720795i −0.960378 0.278702i \(-0.910096\pi\)
−0.0317117 + 0.999497i \(0.510096\pi\)
\(98\) 0 0
\(99\) −9.79024 0.0860098i −0.983956 0.00864431i
\(100\) 1.19623 2.07193i 0.119623 0.207193i
\(101\) 3.37407 + 1.50223i 0.335733 + 0.149478i 0.567677 0.823251i \(-0.307842\pi\)
−0.231945 + 0.972729i \(0.574509\pi\)
\(102\) 0.0476806 0.0529546i 0.00472108 0.00524329i
\(103\) 0.770546 + 0.855778i 0.0759242 + 0.0843223i 0.779910 0.625892i \(-0.215265\pi\)
−0.703986 + 0.710214i \(0.748598\pi\)
\(104\) −3.71090 2.69613i −0.363884 0.264377i
\(105\) 0 0
\(106\) 0.460080 1.41598i 0.0446869 0.137532i
\(107\) −1.14163 0.242661i −0.110366 0.0234590i 0.152398 0.988319i \(-0.451301\pi\)
−0.262763 + 0.964860i \(0.584634\pi\)
\(108\) 2.32202 + 1.03383i 0.223437 + 0.0994804i
\(109\) −4.65117 8.05606i −0.445501 0.771631i 0.552586 0.833456i \(-0.313641\pi\)
−0.998087 + 0.0618251i \(0.980308\pi\)
\(110\) 1.71704 0.746472i 0.163714 0.0711734i
\(111\) −0.873083 −0.0828694
\(112\) 0 0
\(113\) 1.01893 + 3.13595i 0.0958529 + 0.295005i 0.987475 0.157775i \(-0.0504322\pi\)
−0.891622 + 0.452780i \(0.850432\pi\)
\(114\) 0.201282 + 0.223547i 0.0188518 + 0.0209371i
\(115\) −1.84760 + 17.5788i −0.172290 + 1.63923i
\(116\) 1.32771 12.6323i 0.123274 1.17288i
\(117\) 10.1429 + 11.2649i 0.937715 + 1.04144i
\(118\) −0.201059 0.618796i −0.0185090 0.0569648i
\(119\) 0 0
\(120\) −0.488478 −0.0445918
\(121\) −10.7178 2.47571i −0.974344 0.225065i
\(122\) −0.0967440 0.167565i −0.00875879 0.0151707i
\(123\) −1.35105 0.601525i −0.121820 0.0542377i
\(124\) −14.6570 3.11544i −1.31624 0.279775i
\(125\) −2.90909 + 8.95326i −0.260197 + 0.800804i
\(126\) 0 0
\(127\) 0.233972 + 0.169990i 0.0207616 + 0.0150842i 0.598118 0.801408i \(-0.295916\pi\)
−0.577356 + 0.816492i \(0.695916\pi\)
\(128\) −4.53859 5.04062i −0.401159 0.445532i
\(129\) −0.117638 + 0.130650i −0.0103575 + 0.0115031i
\(130\) −2.64817 1.17904i −0.232260 0.103409i
\(131\) −8.25293 + 14.2945i −0.721062 + 1.24892i 0.239513 + 0.970893i \(0.423012\pi\)
−0.960575 + 0.278023i \(0.910321\pi\)
\(132\) 1.13849 + 0.842544i 0.0990932 + 0.0733341i
\(133\) 0 0
\(134\) 0.301357 0.218949i 0.0260333 0.0189143i
\(135\) 3.18367 + 0.676711i 0.274007 + 0.0582420i
\(136\) 1.25604 0.266979i 0.107704 0.0228932i
\(137\) −0.974820 + 9.27479i −0.0832845 + 0.792399i 0.870553 + 0.492075i \(0.163761\pi\)
−0.953837 + 0.300324i \(0.902905\pi\)
\(138\) 0.320744 0.142804i 0.0273035 0.0121563i
\(139\) −1.49147 + 4.59026i −0.126505 + 0.389341i −0.994172 0.107804i \(-0.965618\pi\)
0.867668 + 0.497145i \(0.165618\pi\)
\(140\) 0 0
\(141\) 1.19703 0.869693i 0.100808 0.0732414i
\(142\) −0.511325 + 0.885641i −0.0429094 + 0.0743213i
\(143\) 8.38551 + 14.8234i 0.701232 + 1.23959i
\(144\) 5.45466 + 9.44774i 0.454555 + 0.787312i
\(145\) −1.70016 16.1759i −0.141191 1.34334i
\(146\) 1.03792 + 3.19438i 0.0858987 + 0.264369i
\(147\) 0 0
\(148\) −6.28183 4.56401i −0.516363 0.375160i
\(149\) 0.842211 0.374976i 0.0689966 0.0307193i −0.371948 0.928253i \(-0.621310\pi\)
0.440945 + 0.897534i \(0.354643\pi\)
\(150\) −0.0595237 + 0.0126522i −0.00486009 + 0.00103304i
\(151\) 12.1089 13.4483i 0.985405 1.09440i −0.0101237 0.999949i \(-0.503223\pi\)
0.995529 0.0944548i \(-0.0301108\pi\)
\(152\) 0.566627 + 5.39109i 0.0459595 + 0.437275i
\(153\) −4.24355 −0.343070
\(154\) 0 0
\(155\) −19.1880 −1.54121
\(156\) −0.229218 2.18086i −0.0183521 0.174609i
\(157\) 8.21246 9.12086i 0.655425 0.727924i −0.320204 0.947349i \(-0.603751\pi\)
0.975629 + 0.219425i \(0.0704181\pi\)
\(158\) −0.542750 + 0.115365i −0.0431789 + 0.00917795i
\(159\) 1.31755 0.586611i 0.104489 0.0465213i
\(160\) −5.29467 3.84680i −0.418580 0.304116i
\(161\) 0 0
\(162\) 0.599080 + 1.84378i 0.0470682 + 0.144861i
\(163\) −0.846590 8.05476i −0.0663100 0.630898i −0.976323 0.216318i \(-0.930595\pi\)
0.910013 0.414580i \(-0.136071\pi\)
\(164\) −6.57632 11.3905i −0.513524 0.889450i
\(165\) 1.65033 + 0.752214i 0.128478 + 0.0585598i
\(166\) 0.254239 0.440355i 0.0197328 0.0341781i
\(167\) −10.5590 + 7.67154i −0.817077 + 0.593641i −0.915874 0.401466i \(-0.868501\pi\)
0.0987965 + 0.995108i \(0.468501\pi\)
\(168\) 0 0
\(169\) 4.13096 12.7138i 0.317766 0.977985i
\(170\) 0.741347 0.330069i 0.0568587 0.0253151i
\(171\) 1.87253 17.8159i 0.143196 1.36242i
\(172\) −1.52938 + 0.325079i −0.116614 + 0.0247870i
\(173\) 5.78299 + 1.22921i 0.439673 + 0.0934554i 0.422429 0.906396i \(-0.361178\pi\)
0.0172438 + 0.999851i \(0.494511\pi\)
\(174\) −0.261376 + 0.189901i −0.0198149 + 0.0143964i
\(175\) 0 0
\(176\) 3.68503 + 11.6898i 0.277770 + 0.881153i
\(177\) 0.315136 0.545831i 0.0236870 0.0410272i
\(178\) −0.358682 0.159695i −0.0268843 0.0119697i
\(179\) 2.90073 3.22159i 0.216811 0.240793i −0.624922 0.780687i \(-0.714869\pi\)
0.841733 + 0.539894i \(0.181536\pi\)
\(180\) 9.60638 + 10.6690i 0.716018 + 0.795218i
\(181\) 8.76223 + 6.36613i 0.651291 + 0.473191i 0.863711 0.503988i \(-0.168134\pi\)
−0.212420 + 0.977179i \(0.568134\pi\)
\(182\) 0 0
\(183\) 0.0579192 0.178257i 0.00428151 0.0131771i
\(184\) 6.18870 + 1.31545i 0.456237 + 0.0969762i
\(185\) −9.08336 4.04417i −0.667822 0.297333i
\(186\) 0.190569 + 0.330075i 0.0139732 + 0.0242023i
\(187\) −4.65466 1.03220i −0.340382 0.0754817i
\(188\) 13.1589 0.959713
\(189\) 0 0
\(190\) 1.05862 + 3.25808i 0.0768000 + 0.236366i
\(191\) 7.79913 + 8.66181i 0.564325 + 0.626746i 0.956003 0.293356i \(-0.0947721\pi\)
−0.391678 + 0.920102i \(0.628105\pi\)
\(192\) 0.155709 1.48147i 0.0112373 0.106916i
\(193\) −2.34619 + 22.3225i −0.168882 + 1.60681i 0.501748 + 0.865014i \(0.332691\pi\)
−0.670630 + 0.741792i \(0.733976\pi\)
\(194\) 1.82812 + 2.03033i 0.131251 + 0.145769i
\(195\) −0.867729 2.67060i −0.0621394 0.191245i
\(196\) 0 0
\(197\) 24.1022 1.71721 0.858604 0.512639i \(-0.171332\pi\)
0.858604 + 0.512639i \(0.171332\pi\)
\(198\) 0.212146 + 2.20456i 0.0150765 + 0.156672i
\(199\) 9.36026 + 16.2125i 0.663531 + 1.14927i 0.979681 + 0.200561i \(0.0642764\pi\)
−0.316150 + 0.948709i \(0.602390\pi\)
\(200\) −1.00181 0.446032i −0.0708383 0.0315393i
\(201\) 0.352951 + 0.0750221i 0.0248953 + 0.00529165i
\(202\) 0.258179 0.794593i 0.0181654 0.0559074i
\(203\) 0 0
\(204\) 0.496647 + 0.360835i 0.0347722 + 0.0252635i
\(205\) −11.2697 12.5163i −0.787109 0.874174i
\(206\) 0.174306 0.193587i 0.0121445 0.0134878i
\(207\) −19.1010 8.50432i −1.32761 0.591091i
\(208\) 9.48840 16.4344i 0.657902 1.13952i
\(209\) 6.38746 19.0864i 0.441830 1.32023i
\(210\) 0 0
\(211\) 6.12131 4.44739i 0.421408 0.306171i −0.356796 0.934182i \(-0.616131\pi\)
0.778204 + 0.628011i \(0.216131\pi\)
\(212\) 12.5463 + 2.66679i 0.861681 + 0.183156i
\(213\) −0.968987 + 0.205964i −0.0663939 + 0.0141125i
\(214\) −0.0275975 + 0.262573i −0.00188653 + 0.0179491i
\(215\) −1.82906 + 0.814350i −0.124741 + 0.0555382i
\(216\) 0.360021 1.10803i 0.0244963 0.0753919i
\(217\) 0 0
\(218\) −1.70241 + 1.23687i −0.115302 + 0.0837717i
\(219\) −1.62681 + 2.81772i −0.109930 + 0.190404i
\(220\) 7.94192 + 14.0392i 0.535444 + 0.946524i
\(221\) 3.69083 + 6.39271i 0.248272 + 0.430020i
\(222\) 0.0206445 + 0.196419i 0.00138557 + 0.0131828i
\(223\) −5.41533 16.6667i −0.362637 1.11608i −0.951447 0.307811i \(-0.900403\pi\)
0.588810 0.808271i \(-0.299597\pi\)
\(224\) 0 0
\(225\) 2.93185 + 2.13011i 0.195457 + 0.142008i
\(226\) 0.681407 0.303382i 0.0453265 0.0201807i
\(227\) −25.1162 + 5.33860i −1.66702 + 0.354335i −0.942315 0.334727i \(-0.891356\pi\)
−0.724702 + 0.689062i \(0.758023\pi\)
\(228\) −1.73406 + 1.92587i −0.114841 + 0.127544i
\(229\) −2.07352 19.7282i −0.137022 1.30368i −0.819630 0.572893i \(-0.805821\pi\)
0.682608 0.730784i \(-0.260846\pi\)
\(230\) 3.99842 0.263648
\(231\) 0 0
\(232\) −5.82205 −0.382236
\(233\) 2.11300 + 20.1038i 0.138427 + 1.31705i 0.814479 + 0.580193i \(0.197023\pi\)
−0.676052 + 0.736854i \(0.736311\pi\)
\(234\) 2.29445 2.54824i 0.149993 0.166584i
\(235\) 16.4821 3.50338i 1.07517 0.228535i
\(236\) 5.12071 2.27989i 0.333330 0.148408i
\(237\) −0.434850 0.315937i −0.0282465 0.0205223i
\(238\) 0 0
\(239\) 5.28431 + 16.2634i 0.341814 + 1.05199i 0.963267 + 0.268544i \(0.0865424\pi\)
−0.621454 + 0.783451i \(0.713458\pi\)
\(240\) −0.211242 2.00984i −0.0136356 0.129734i
\(241\) −12.0764 20.9170i −0.777912 1.34738i −0.933143 0.359505i \(-0.882945\pi\)
0.155231 0.987878i \(-0.450388\pi\)
\(242\) −0.303539 + 2.46974i −0.0195122 + 0.158761i
\(243\) −2.89537 + 5.01493i −0.185738 + 0.321708i
\(244\) 1.34856 0.979787i 0.0863328 0.0627245i
\(245\) 0 0
\(246\) −0.103380 + 0.318171i −0.00659128 + 0.0202859i
\(247\) −28.4675 + 12.6745i −1.81134 + 0.806462i
\(248\) −0.717934 + 6.83068i −0.0455888 + 0.433749i
\(249\) 0.481796 0.102409i 0.0305325 0.00648989i
\(250\) 2.08302 + 0.442760i 0.131742 + 0.0280026i
\(251\) 9.62305 6.99156i 0.607402 0.441303i −0.241097 0.970501i \(-0.577507\pi\)
0.848498 + 0.529198i \(0.177507\pi\)
\(252\) 0 0
\(253\) −18.8829 13.9743i −1.18716 0.878558i
\(254\) 0.0327107 0.0566567i 0.00205245 0.00355495i
\(255\) 0.718138 + 0.319736i 0.0449716 + 0.0200226i
\(256\) 8.07073 8.96345i 0.504421 0.560216i
\(257\) −15.3638 17.0633i −0.958370 1.06438i −0.997875 0.0651583i \(-0.979245\pi\)
0.0395050 0.999219i \(-0.487422\pi\)
\(258\) 0.0321743 + 0.0233760i 0.00200308 + 0.00145533i
\(259\) 0 0
\(260\) 7.71715 23.7509i 0.478597 1.47297i
\(261\) 18.8197 + 4.00024i 1.16491 + 0.247609i
\(262\) 3.41101 + 1.51868i 0.210733 + 0.0938243i
\(263\) −0.968871 1.67813i −0.0597432 0.103478i 0.834607 0.550846i \(-0.185695\pi\)
−0.894350 + 0.447368i \(0.852362\pi\)
\(264\) 0.329528 0.559352i 0.0202810 0.0344257i
\(265\) 16.4247 1.00896
\(266\) 0 0
\(267\) −0.117530 0.361720i −0.00719271 0.0221369i
\(268\) 2.14731 + 2.38482i 0.131168 + 0.145676i
\(269\) 0.751221 7.14739i 0.0458027 0.435784i −0.947458 0.319881i \(-0.896357\pi\)
0.993261 0.115903i \(-0.0369762\pi\)
\(270\) 0.0769614 0.732239i 0.00468372 0.0445627i
\(271\) −0.797003 0.885161i −0.0484145 0.0537697i 0.718451 0.695577i \(-0.244851\pi\)
−0.766866 + 0.641808i \(0.778185\pi\)
\(272\) 1.64165 + 5.05249i 0.0995398 + 0.306352i
\(273\) 0 0
\(274\) 2.10962 0.127447
\(275\) 2.69776 + 3.04962i 0.162681 + 0.183899i
\(276\) 1.51237 + 2.61950i 0.0910337 + 0.157675i
\(277\) 9.44628 + 4.20576i 0.567572 + 0.252699i 0.670400 0.742000i \(-0.266122\pi\)
−0.102828 + 0.994699i \(0.532789\pi\)
\(278\) 1.06795 + 0.226999i 0.0640512 + 0.0136145i
\(279\) 7.01396 21.5867i 0.419915 1.29236i
\(280\) 0 0
\(281\) 10.6396 + 7.73015i 0.634707 + 0.461142i 0.858028 0.513603i \(-0.171690\pi\)
−0.223321 + 0.974745i \(0.571690\pi\)
\(282\) −0.223961 0.248734i −0.0133367 0.0148119i
\(283\) −0.200760 + 0.222966i −0.0119339 + 0.0132540i −0.749082 0.662477i \(-0.769505\pi\)
0.737148 + 0.675731i \(0.236172\pi\)
\(284\) −8.04852 3.58343i −0.477592 0.212638i
\(285\) −1.65925 + 2.87391i −0.0982856 + 0.170236i
\(286\) 3.13656 2.23701i 0.185469 0.132277i
\(287\) 0 0
\(288\) 6.26312 4.55042i 0.369058 0.268136i
\(289\) 14.6072 + 3.10485i 0.859246 + 0.182638i
\(290\) −3.59893 + 0.764977i −0.211337 + 0.0449210i
\(291\) −0.276640 + 2.63205i −0.0162169 + 0.154294i
\(292\) −26.4344 + 11.7694i −1.54696 + 0.688750i
\(293\) −4.98880 + 15.3539i −0.291449 + 0.896987i 0.692942 + 0.720993i \(0.256314\pi\)
−0.984391 + 0.175994i \(0.943686\pi\)
\(294\) 0 0
\(295\) 5.80692 4.21898i 0.338092 0.245638i
\(296\) −1.77954 + 3.08225i −0.103434 + 0.179152i
\(297\) −2.92260 + 3.18909i −0.169587 + 0.185050i
\(298\) −0.104274 0.180607i −0.00604042 0.0104623i
\(299\) 3.80177 + 36.1715i 0.219862 + 2.09185i
\(300\) −0.162005 0.498599i −0.00935334 0.0287866i
\(301\) 0 0
\(302\) −3.31180 2.40617i −0.190573 0.138459i
\(303\) 0.739359 0.329184i 0.0424750 0.0189111i
\(304\) −21.9365 + 4.66275i −1.25815 + 0.267427i
\(305\) 1.42828 1.58626i 0.0817829 0.0908291i
\(306\) 0.100341 + 0.954680i 0.00573611 + 0.0545754i
\(307\) 28.6376 1.63443 0.817217 0.576330i \(-0.195516\pi\)
0.817217 + 0.576330i \(0.195516\pi\)
\(308\) 0 0
\(309\) 0.252341 0.0143552
\(310\) 0.453709 + 4.31676i 0.0257690 + 0.245175i
\(311\) 21.2936 23.6489i 1.20745 1.34101i 0.283272 0.959039i \(-0.408580\pi\)
0.924176 0.381968i \(-0.124753\pi\)
\(312\) −0.983167 + 0.208979i −0.0556609 + 0.0118311i
\(313\) −0.0312645 + 0.0139198i −0.00176717 + 0.000786796i −0.407620 0.913152i \(-0.633641\pi\)
0.405853 + 0.913938i \(0.366975\pi\)
\(314\) −2.24613 1.63191i −0.126756 0.0920938i
\(315\) 0 0
\(316\) −1.47719 4.54633i −0.0830985 0.255751i
\(317\) −2.34033 22.2668i −0.131446 1.25063i −0.839065 0.544032i \(-0.816897\pi\)
0.707618 0.706595i \(-0.249770\pi\)
\(318\) −0.163125 0.282541i −0.00914762 0.0158441i
\(319\) 19.6699 + 8.96546i 1.10130 + 0.501969i
\(320\) 8.48220 14.6916i 0.474170 0.821286i
\(321\) −0.206909 + 0.150328i −0.0115486 + 0.00839052i
\(322\) 0 0
\(323\) 2.69574 8.29662i 0.149995 0.461636i
\(324\) −15.2578 + 6.79321i −0.847656 + 0.377401i
\(325\) 0.658938 6.26937i 0.0365513 0.347762i
\(326\) −1.79208 + 0.380918i −0.0992541 + 0.0210971i
\(327\) −1.99387 0.423811i −0.110261 0.0234368i
\(328\) −4.87730 + 3.54357i −0.269304 + 0.195661i
\(329\) 0 0
\(330\) 0.130204 0.389064i 0.00716751 0.0214173i
\(331\) −5.37885 + 9.31644i −0.295648 + 0.512078i −0.975136 0.221609i \(-0.928869\pi\)
0.679487 + 0.733687i \(0.262202\pi\)
\(332\) 4.00185 + 1.78174i 0.219630 + 0.0977857i
\(333\) 7.87008 8.74061i 0.431278 0.478983i
\(334\) 1.97555 + 2.19408i 0.108098 + 0.120054i
\(335\) 3.32452 + 2.41540i 0.181638 + 0.131968i
\(336\) 0 0
\(337\) 2.31915 7.13761i 0.126332 0.388810i −0.867809 0.496897i \(-0.834473\pi\)
0.994141 + 0.108087i \(0.0344726\pi\)
\(338\) −2.95793 0.628727i −0.160890 0.0341983i
\(339\) 0.660075 + 0.293884i 0.0358504 + 0.0159616i
\(340\) 3.49559 + 6.05454i 0.189575 + 0.328354i
\(341\) 12.9442 21.9720i 0.700968 1.18985i
\(342\) −4.05236 −0.219126
\(343\) 0 0
\(344\) 0.221463 + 0.681593i 0.0119405 + 0.0367490i
\(345\) 2.59171 + 2.87838i 0.139533 + 0.154967i
\(346\) 0.139797 1.33008i 0.00751552 0.0715054i
\(347\) 2.89354 27.5302i 0.155333 1.47790i −0.587938 0.808906i \(-0.700060\pi\)
0.743271 0.668990i \(-0.233273\pi\)
\(348\) −1.86243 2.06843i −0.0998365 0.110880i
\(349\) 3.41788 + 10.5192i 0.182955 + 0.563078i 0.999907 0.0136278i \(-0.00433799\pi\)
−0.816952 + 0.576706i \(0.804338\pi\)
\(350\) 0 0
\(351\) 6.69733 0.357477
\(352\) 7.97672 3.46782i 0.425161 0.184836i
\(353\) 15.9601 + 27.6437i 0.849469 + 1.47132i 0.881683 + 0.471843i \(0.156411\pi\)
−0.0322133 + 0.999481i \(0.510256\pi\)
\(354\) −0.130248 0.0579903i −0.00692262 0.00308215i
\(355\) −11.0352 2.34560i −0.585685 0.124491i
\(356\) 1.04525 3.21695i 0.0553982 0.170498i
\(357\) 0 0
\(358\) −0.793358 0.576408i −0.0419303 0.0304641i
\(359\) 2.39433 + 2.65917i 0.126368 + 0.140346i 0.803008 0.595968i \(-0.203232\pi\)
−0.676640 + 0.736314i \(0.736565\pi\)
\(360\) 4.40321 4.89026i 0.232069 0.257739i
\(361\) 16.2852 + 7.25066i 0.857118 + 0.381614i
\(362\) 1.22501 2.12179i 0.0643853 0.111519i
\(363\) −1.97467 + 1.38233i −0.103643 + 0.0725536i
\(364\) 0 0
\(365\) −29.9768 + 21.7794i −1.56906 + 1.13999i
\(366\) −0.0414724 0.00881523i −0.00216780 0.000460780i
\(367\) 2.24384 0.476942i 0.117127 0.0248962i −0.148975 0.988841i \(-0.547597\pi\)
0.266102 + 0.963945i \(0.414264\pi\)
\(368\) −2.73609 + 26.0322i −0.142629 + 1.35702i
\(369\) 18.2005 8.10339i 0.947480 0.421845i
\(370\) −0.695045 + 2.13913i −0.0361337 + 0.111208i
\(371\) 0 0
\(372\) −2.65644 + 1.93001i −0.137730 + 0.100067i
\(373\) −3.98428 + 6.90097i −0.206298 + 0.357319i −0.950546 0.310585i \(-0.899475\pi\)
0.744247 + 0.667904i \(0.232808\pi\)
\(374\) −0.122154 + 1.07157i −0.00631643 + 0.0554098i
\(375\) 1.03144 + 1.78651i 0.0532636 + 0.0922552i
\(376\) −0.630469 5.99851i −0.0325140 0.309350i
\(377\) −10.3423 31.8302i −0.532653 1.63934i
\(378\) 0 0
\(379\) 9.40174 + 6.83077i 0.482935 + 0.350873i 0.802461 0.596705i \(-0.203524\pi\)
−0.319526 + 0.947578i \(0.603524\pi\)
\(380\) −26.9616 + 12.0041i −1.38310 + 0.615796i
\(381\) 0.0619885 0.0131761i 0.00317577 0.000675030i
\(382\) 1.76425 1.95940i 0.0902669 0.100252i
\(383\) 1.31481 + 12.5095i 0.0671835 + 0.639208i 0.975360 + 0.220620i \(0.0708081\pi\)
−0.908176 + 0.418588i \(0.862525\pi\)
\(384\) −1.48632 −0.0758482
\(385\) 0 0
\(386\) 5.07741 0.258433
\(387\) −0.247562 2.35540i −0.0125843 0.119732i
\(388\) −15.7494 + 17.4915i −0.799554 + 0.887994i
\(389\) 0.428716 0.0911264i 0.0217368 0.00462029i −0.197030 0.980397i \(-0.563130\pi\)
0.218767 + 0.975777i \(0.429796\pi\)
\(390\) −0.580292 + 0.258363i −0.0293842 + 0.0130827i
\(391\) −8.23731 5.98476i −0.416579 0.302662i
\(392\) 0 0
\(393\) 1.11769 + 3.43990i 0.0563800 + 0.173520i
\(394\) −0.569908 5.42232i −0.0287116 0.273172i
\(395\) −3.06064 5.30119i −0.153998 0.266732i
\(396\) −18.6974 + 3.80290i −0.939580 + 0.191103i
\(397\) 8.40734 14.5619i 0.421952 0.730843i −0.574178 0.818730i \(-0.694678\pi\)
0.996130 + 0.0878876i \(0.0280116\pi\)
\(398\) 3.42602 2.48915i 0.171731 0.124770i
\(399\) 0 0
\(400\) 1.40196 4.31480i 0.0700981 0.215740i
\(401\) 33.6741 14.9927i 1.68160 0.748698i 0.681750 0.731585i \(-0.261219\pi\)
0.999854 0.0171134i \(-0.00544763\pi\)
\(402\) 0.00853216 0.0811781i 0.000425546 0.00404880i
\(403\) −38.6199 + 8.20891i −1.92379 + 0.408915i
\(404\) 7.04048 + 1.49650i 0.350277 + 0.0744536i
\(405\) −17.3024 + 12.5710i −0.859766 + 0.624656i
\(406\) 0 0
\(407\) 10.7586 7.67308i 0.533283 0.380340i
\(408\) 0.140692 0.243685i 0.00696528 0.0120642i
\(409\) −14.8669 6.61919i −0.735123 0.327298i 0.00480078 0.999988i \(-0.498472\pi\)
−0.739924 + 0.672691i \(0.765139\pi\)
\(410\) −2.54933 + 2.83132i −0.125903 + 0.139829i
\(411\) 1.36742 + 1.51867i 0.0674498 + 0.0749106i
\(412\) 1.81559 + 1.31911i 0.0894479 + 0.0649877i
\(413\) 0 0
\(414\) −1.46158 + 4.49828i −0.0718328 + 0.221079i
\(415\) 5.48686 + 1.16627i 0.269339 + 0.0572498i
\(416\) −12.3024 5.47737i −0.603173 0.268550i
\(417\) 0.528813 + 0.915931i 0.0258961 + 0.0448533i
\(418\) −4.44494 0.985693i −0.217409 0.0482118i
\(419\) −5.56352 −0.271796 −0.135898 0.990723i \(-0.543392\pi\)
−0.135898 + 0.990723i \(0.543392\pi\)
\(420\) 0 0
\(421\) 6.64120 + 20.4395i 0.323672 + 0.996161i 0.972036 + 0.234831i \(0.0754536\pi\)
−0.648364 + 0.761331i \(0.724546\pi\)
\(422\) −1.14528 1.27196i −0.0557514 0.0619182i
\(423\) −2.08351 + 19.8232i −0.101304 + 0.963839i
\(424\) 0.614545 5.84700i 0.0298449 0.283956i
\(425\) 1.18086 + 1.31147i 0.0572799 + 0.0636158i
\(426\) 0.0692485 + 0.213125i 0.00335510 + 0.0103259i
\(427\) 0 0
\(428\) −2.27455 −0.109944
\(429\) 3.64345 + 0.807956i 0.175907 + 0.0390085i
\(430\) 0.226455 + 0.392232i 0.0109206 + 0.0189151i
\(431\) −25.3223 11.2742i −1.21973 0.543061i −0.307037 0.951697i \(-0.599338\pi\)
−0.912697 + 0.408637i \(0.866004\pi\)
\(432\) 4.71466 + 1.00213i 0.226834 + 0.0482151i
\(433\) −2.87019 + 8.83352i −0.137932 + 0.424512i −0.996035 0.0889667i \(-0.971644\pi\)
0.858102 + 0.513479i \(0.171644\pi\)
\(434\) 0 0
\(435\) −2.88346 2.09496i −0.138251 0.100445i
\(436\) −12.1304 13.4722i −0.580943 0.645203i
\(437\) 28.7609 31.9423i 1.37582 1.52801i
\(438\) 0.672375 + 0.299361i 0.0321273 + 0.0143040i
\(439\) −7.35590 + 12.7408i −0.351078 + 0.608085i −0.986439 0.164131i \(-0.947518\pi\)
0.635361 + 0.772216i \(0.280852\pi\)
\(440\) 6.01928 4.29298i 0.286958 0.204660i
\(441\) 0 0
\(442\) 1.35091 0.981494i 0.0642563 0.0466849i
\(443\) −2.39005 0.508022i −0.113555 0.0241368i 0.150784 0.988567i \(-0.451820\pi\)
−0.264339 + 0.964430i \(0.585154\pi\)
\(444\) −1.66431 + 0.353759i −0.0789845 + 0.0167887i
\(445\) 0.452753 4.30766i 0.0214625 0.204202i
\(446\) −3.62149 + 1.61239i −0.171482 + 0.0763489i
\(447\) 0.0624272 0.192131i 0.00295271 0.00908750i
\(448\) 0 0
\(449\) −3.85849 + 2.80335i −0.182093 + 0.132298i −0.675098 0.737728i \(-0.735899\pi\)
0.493005 + 0.870027i \(0.335899\pi\)
\(450\) 0.409891 0.709952i 0.0193225 0.0334675i
\(451\) 21.9348 4.46135i 1.03287 0.210077i
\(452\) 3.21296 + 5.56502i 0.151125 + 0.261756i
\(453\) −0.414503 3.94374i −0.0194751 0.185293i
\(454\) 1.79492 + 5.52420i 0.0842398 + 0.259264i
\(455\) 0 0
\(456\) 0.960995 + 0.698203i 0.0450027 + 0.0326964i
\(457\) 28.3998 12.6444i 1.32849 0.591481i 0.385009 0.922913i \(-0.374198\pi\)
0.943479 + 0.331431i \(0.107532\pi\)
\(458\) −4.38927 + 0.932968i −0.205097 + 0.0435947i
\(459\) −1.25455 + 1.39332i −0.0585575 + 0.0650347i
\(460\) 3.60066 + 34.2580i 0.167882 + 1.59729i
\(461\) −29.7215 −1.38427 −0.692134 0.721769i \(-0.743329\pi\)
−0.692134 + 0.721769i \(0.743329\pi\)
\(462\) 0 0
\(463\) −25.4553 −1.18301 −0.591505 0.806302i \(-0.701466\pi\)
−0.591505 + 0.806302i \(0.701466\pi\)
\(464\) −2.51774 23.9547i −0.116883 1.11207i
\(465\) −2.81346 + 3.12466i −0.130471 + 0.144903i
\(466\) 4.47284 0.950732i 0.207200 0.0440418i
\(467\) 2.90956 1.29542i 0.134638 0.0599449i −0.338312 0.941034i \(-0.609856\pi\)
0.472950 + 0.881089i \(0.343189\pi\)
\(468\) 23.8992 + 17.3638i 1.10474 + 0.802643i
\(469\) 0 0
\(470\) −1.17789 3.62517i −0.0543320 0.167217i
\(471\) −0.281124 2.67471i −0.0129535 0.123244i
\(472\) −1.28463 2.22505i −0.0591301 0.102416i
\(473\) 0.301379 2.64380i 0.0138574 0.121562i
\(474\) −0.0607948 + 0.105300i −0.00279240 + 0.00483657i
\(475\) −6.02709 + 4.37894i −0.276542 + 0.200920i
\(476\) 0 0
\(477\) −6.00389 + 18.4781i −0.274899 + 0.846052i
\(478\) 3.53387 1.57338i 0.161635 0.0719648i
\(479\) 0.337997 3.21582i 0.0154435 0.146935i −0.984083 0.177710i \(-0.943131\pi\)
0.999526 + 0.0307755i \(0.00979770\pi\)
\(480\) −1.40277 + 0.298168i −0.0640274 + 0.0136094i
\(481\) −20.0124 4.25376i −0.912485 0.193955i
\(482\) −4.42019 + 3.21146i −0.201334 + 0.146278i
\(483\) 0 0
\(484\) −21.4338 0.376632i −0.974264 0.0171196i
\(485\) −15.0699 + 26.1019i −0.684289 + 1.18522i
\(486\) 1.19668 + 0.532797i 0.0542826 + 0.0241681i
\(487\) 6.60496 7.33555i 0.299299 0.332406i −0.574671 0.818384i \(-0.694870\pi\)
0.873971 + 0.485979i \(0.161537\pi\)
\(488\) −0.511250 0.567800i −0.0231432 0.0257031i
\(489\) −1.43581 1.04318i −0.0649296 0.0471741i
\(490\) 0 0
\(491\) 1.30591 4.01917i 0.0589348 0.181383i −0.917255 0.398300i \(-0.869600\pi\)
0.976190 + 0.216918i \(0.0696003\pi\)
\(492\) −2.81915 0.599229i −0.127097 0.0270153i
\(493\) 8.55931 + 3.81085i 0.385492 + 0.171632i
\(494\) 3.52455 + 6.10470i 0.158577 + 0.274663i
\(495\) −22.4068 + 9.74122i −1.00711 + 0.437835i
\(496\) −28.4152 −1.27588
\(497\) 0 0
\(498\) −0.0344314 0.105969i −0.00154291 0.00474859i
\(499\) −13.6471 15.1566i −0.610928 0.678505i 0.355726 0.934590i \(-0.384234\pi\)
−0.966654 + 0.256086i \(0.917567\pi\)
\(500\) −1.91771 + 18.2458i −0.0857626 + 0.815977i
\(501\) −0.298950 + 2.84432i −0.0133561 + 0.127075i
\(502\) −1.80045 1.99960i −0.0803579 0.0892465i
\(503\) 7.40382 + 22.7866i 0.330120 + 1.01600i 0.969076 + 0.246762i \(0.0793665\pi\)
−0.638956 + 0.769243i \(0.720634\pi\)
\(504\) 0 0
\(505\) 9.21692 0.410147
\(506\) −2.69734 + 4.57856i −0.119911 + 0.203542i
\(507\) −1.46467 2.53688i −0.0650483 0.112667i
\(508\) 0.514884 + 0.229241i 0.0228443 + 0.0101709i
\(509\) 3.61270 + 0.767903i 0.160130 + 0.0340367i 0.287279 0.957847i \(-0.407249\pi\)
−0.127149 + 0.991884i \(0.540583\pi\)
\(510\) 0.0549509 0.169121i 0.00243327 0.00748882i
\(511\) 0 0
\(512\) −13.1822 9.57742i −0.582576 0.423266i
\(513\) −5.29606 5.88187i −0.233827 0.259691i
\(514\) −3.47547 + 3.85991i −0.153297 + 0.170253i
\(515\) 2.62530 + 1.16886i 0.115685 + 0.0515061i
\(516\) −0.171309 + 0.296716i −0.00754147 + 0.0130622i
\(517\) −7.10714 + 21.2369i −0.312572 + 0.933997i
\(518\) 0 0
\(519\) 1.04811 0.761497i 0.0460069 0.0334260i
\(520\) −11.1966 2.37992i −0.491005 0.104366i
\(521\) −0.233063 + 0.0495390i −0.0102107 + 0.00217034i −0.213014 0.977049i \(-0.568328\pi\)
0.202804 + 0.979219i \(0.434995\pi\)
\(522\) 0.454942 4.32849i 0.0199123 0.189453i
\(523\) 20.0902 8.94472i 0.878482 0.391125i 0.0826041 0.996582i \(-0.473676\pi\)
0.795878 + 0.605457i \(0.207010\pi\)
\(524\) −9.94018 + 30.5927i −0.434239 + 1.33645i
\(525\) 0 0
\(526\) −0.354624 + 0.257649i −0.0154623 + 0.0112340i
\(527\) 5.52653 9.57223i 0.240739 0.416973i
\(528\) 2.44395 + 1.11394i 0.106359 + 0.0484782i
\(529\) −13.5839 23.5280i −0.590604 1.02296i
\(530\) −0.388371 3.69510i −0.0168698 0.160505i
\(531\) 2.62375 + 8.07508i 0.113861 + 0.350429i
\(532\) 0 0
\(533\) −28.0373 20.3703i −1.21443 0.882336i
\(534\) −0.0785978 + 0.0349940i −0.00340126 + 0.00151434i
\(535\) −2.84897 + 0.605567i −0.123172 + 0.0261809i
\(536\) 0.984244 1.09311i 0.0425129 0.0472153i
\(537\) −0.0992962 0.944740i −0.00428495 0.0407685i
\(538\) −1.62573 −0.0700900
\(539\) 0 0
\(540\) 6.34305 0.272961
\(541\) −2.99275 28.4741i −0.128668 1.22420i −0.848177 0.529713i \(-0.822300\pi\)
0.719509 0.694483i \(-0.244367\pi\)
\(542\) −0.180291 + 0.200234i −0.00774417 + 0.00860077i
\(543\) 2.32146 0.493443i 0.0996236 0.0211756i
\(544\) 3.44401 1.53337i 0.147661 0.0657429i
\(545\) −18.7807 13.6450i −0.804477 0.584486i
\(546\) 0 0
\(547\) 1.98033 + 6.09482i 0.0846727 + 0.260596i 0.984425 0.175805i \(-0.0562529\pi\)
−0.899752 + 0.436401i \(0.856253\pi\)
\(548\) 1.89976 + 18.0750i 0.0811536 + 0.772125i
\(549\) 1.26248 + 2.18667i 0.0538812 + 0.0933250i
\(550\) 0.622289 0.679030i 0.0265345 0.0289539i
\(551\) −19.7762 + 34.2534i −0.842495 + 1.45924i
\(552\) 1.12164 0.814919i 0.0477402 0.0346853i
\(553\) 0 0
\(554\) 0.722815 2.22460i 0.0307095 0.0945141i
\(555\) −1.99043 + 0.886198i −0.0844891 + 0.0376170i
\(556\) −0.983194 + 9.35447i −0.0416967 + 0.396718i
\(557\) 22.0272 4.68202i 0.933321 0.198383i 0.283936 0.958843i \(-0.408360\pi\)
0.649385 + 0.760460i \(0.275026\pi\)
\(558\) −5.02227 1.06752i −0.212609 0.0451915i
\(559\) −3.33298 + 2.42155i −0.140970 + 0.102421i
\(560\) 0 0
\(561\) −0.850583 + 0.606640i −0.0359116 + 0.0256124i
\(562\) 1.48749 2.57640i 0.0627459 0.108679i
\(563\) 27.2481 + 12.1316i 1.14837 + 0.511287i 0.890540 0.454904i \(-0.150327\pi\)
0.257828 + 0.966191i \(0.416993\pi\)
\(564\) 1.92944 2.14286i 0.0812442 0.0902308i
\(565\) 5.50598 + 6.11501i 0.231638 + 0.257261i
\(566\) 0.0549082 + 0.0398932i 0.00230797 + 0.00167684i
\(567\) 0 0
\(568\) −1.24789 + 3.84062i −0.0523604 + 0.161149i
\(569\) −28.6366 6.08690i −1.20051 0.255176i −0.436095 0.899901i \(-0.643639\pi\)
−0.764415 + 0.644725i \(0.776972\pi\)
\(570\) 0.685783 + 0.305330i 0.0287243 + 0.0127889i
\(571\) −18.9626 32.8442i −0.793559 1.37449i −0.923750 0.382996i \(-0.874892\pi\)
0.130190 0.991489i \(-0.458441\pi\)
\(572\) 21.9910 + 24.8592i 0.919490 + 1.03942i
\(573\) 2.55409 0.106699
\(574\) 0 0
\(575\) 2.68699 + 8.26969i 0.112055 + 0.344870i
\(576\) 13.4277 + 14.9130i 0.559487 + 0.621374i
\(577\) 0.916990 8.72458i 0.0381748 0.363209i −0.958713 0.284375i \(-0.908214\pi\)
0.996888 0.0788334i \(-0.0251195\pi\)
\(578\) 0.353111 3.35963i 0.0146875 0.139742i
\(579\) 3.29109 + 3.65512i 0.136773 + 0.151902i
\(580\) −9.79515 30.1464i −0.406721 1.25176i
\(581\) 0 0
\(582\) 0.598679 0.0248161
\(583\) −11.0801 + 18.8078i −0.458892 + 0.778940i
\(584\) 6.63161 + 11.4863i 0.274418 + 0.475306i
\(585\) 34.5577 + 15.3861i 1.42879 + 0.636136i
\(586\) 3.57217 + 0.759289i 0.147565 + 0.0313659i
\(587\) −2.83372 + 8.72130i −0.116960 + 0.359966i −0.992351 0.123450i \(-0.960604\pi\)
0.875391 + 0.483416i \(0.160604\pi\)
\(588\) 0 0
\(589\) 37.7489 + 27.4262i 1.55542 + 1.13008i
\(590\) −1.08646 1.20664i −0.0447288 0.0496764i
\(591\) 3.53401 3.92492i 0.145370 0.161450i
\(592\) −13.4514 5.98896i −0.552850 0.246145i
\(593\) 3.62798 6.28385i 0.148983 0.258047i −0.781869 0.623443i \(-0.785733\pi\)
0.930852 + 0.365396i \(0.119067\pi\)
\(594\) 0.786562 + 0.582097i 0.0322730 + 0.0238837i
\(595\) 0 0
\(596\) 1.45352 1.05605i 0.0595386 0.0432573i
\(597\) 4.01258 + 0.852899i 0.164224 + 0.0349069i
\(598\) 8.04768 1.71059i 0.329094 0.0699511i
\(599\) 2.09246 19.9084i 0.0854955 0.813435i −0.864807 0.502105i \(-0.832559\pi\)
0.950302 0.311330i \(-0.100774\pi\)
\(600\) −0.219525 + 0.0977389i −0.00896208 + 0.00399017i
\(601\) 3.48280 10.7189i 0.142066 0.437235i −0.854556 0.519360i \(-0.826171\pi\)
0.996622 + 0.0821246i \(0.0261705\pi\)
\(602\) 0 0
\(603\) −3.93261 + 2.85721i −0.160148 + 0.116354i
\(604\) 17.6334 30.5419i 0.717493 1.24273i
\(605\) −26.9470 + 5.23471i −1.09555 + 0.212821i
\(606\) −0.0915397 0.158551i −0.00371854 0.00644071i
\(607\) −1.41386 13.4519i −0.0573866 0.545997i −0.985012 0.172485i \(-0.944820\pi\)
0.927625 0.373512i \(-0.121846\pi\)
\(608\) 4.91792 + 15.1358i 0.199448 + 0.613838i
\(609\) 0 0
\(610\) −0.390637 0.283814i −0.0158164 0.0114913i
\(611\) 31.6750 14.1026i 1.28143 0.570530i
\(612\) −8.08923 + 1.71942i −0.326988 + 0.0695034i
\(613\) −20.6071 + 22.8865i −0.832312 + 0.924376i −0.998089 0.0617871i \(-0.980320\pi\)
0.165777 + 0.986163i \(0.446987\pi\)
\(614\) −0.677151 6.44266i −0.0273276 0.260005i
\(615\) −3.69064 −0.148821
\(616\) 0 0
\(617\) 23.6896 0.953707 0.476853 0.878983i \(-0.341777\pi\)
0.476853 + 0.878983i \(0.341777\pi\)
\(618\) −0.00596675 0.0567698i −0.000240018 0.00228362i
\(619\) 21.7386 24.1431i 0.873747 0.970395i −0.126019 0.992028i \(-0.540220\pi\)
0.999766 + 0.0216333i \(0.00688664\pi\)
\(620\) −36.5769 + 7.77466i −1.46896 + 0.312238i
\(621\) −8.43928 + 3.75741i −0.338656 + 0.150780i
\(622\) −5.82385 4.23127i −0.233515 0.169659i
\(623\) 0 0
\(624\) −1.28501 3.95485i −0.0514415 0.158321i
\(625\) 3.09729 + 29.4688i 0.123892 + 1.17875i
\(626\) 0.00387084 + 0.00670450i 0.000154710 + 0.000267966i
\(627\) −2.17156 3.83873i −0.0867236 0.153304i
\(628\) 11.9593 20.7141i 0.477228 0.826583i
\(629\) 4.63370 3.36658i 0.184758 0.134234i
\(630\) 0 0
\(631\) −4.67646 + 14.3927i −0.186167 + 0.572962i −0.999967 0.00818299i \(-0.997395\pi\)
0.813800 + 0.581145i \(0.197395\pi\)
\(632\) −2.00168 + 0.891203i −0.0796224 + 0.0354502i
\(633\) 0.173309 1.64893i 0.00688843 0.0655391i
\(634\) −4.95407 + 1.05302i −0.196751 + 0.0418207i
\(635\) 0.705947 + 0.150054i 0.0280146 + 0.00595470i
\(636\) 2.27388 1.65207i 0.0901654 0.0655090i
\(637\) 0 0
\(638\) 1.55187 4.63716i 0.0614393 0.183587i
\(639\) 6.67262 11.5573i 0.263965 0.457200i
\(640\) −15.4633 6.88470i −0.611240 0.272142i
\(641\) −11.0743 + 12.2992i −0.437407 + 0.485790i −0.921033 0.389485i \(-0.872653\pi\)
0.483625 + 0.875275i \(0.339320\pi\)
\(642\) 0.0387122 + 0.0429942i 0.00152785 + 0.00169685i
\(643\) 1.61403 + 1.17266i 0.0636513 + 0.0462454i 0.619156 0.785268i \(-0.287475\pi\)
−0.555505 + 0.831513i \(0.687475\pi\)
\(644\) 0 0
\(645\) −0.135575 + 0.417258i −0.00533828 + 0.0164295i
\(646\) −1.93025 0.410288i −0.0759447 0.0161425i
\(647\) −36.9545 16.4532i −1.45283 0.646842i −0.479770 0.877394i \(-0.659280\pi\)
−0.973060 + 0.230553i \(0.925947\pi\)
\(648\) 3.82773 + 6.62982i 0.150367 + 0.260444i
\(649\) 0.913761 + 9.49558i 0.0358682 + 0.372734i
\(650\) −1.42602 −0.0559329
\(651\) 0 0
\(652\) −4.87747 15.0113i −0.191016 0.587888i
\(653\) −27.7593 30.8298i −1.08631 1.20646i −0.977175 0.212437i \(-0.931860\pi\)
−0.109131 0.994027i \(-0.534807\pi\)
\(654\) −0.0481995 + 0.458587i −0.00188475 + 0.0179322i
\(655\) −4.30561 + 40.9651i −0.168234 + 1.60064i
\(656\) −16.6891 18.5352i −0.651602 0.723677i
\(657\) −13.5445 41.6856i −0.528421 1.62631i
\(658\) 0 0
\(659\) −51.1359 −1.99197 −0.995985 0.0895158i \(-0.971468\pi\)
−0.995985 + 0.0895158i \(0.971468\pi\)
\(660\) 3.45071 + 0.765215i 0.134319 + 0.0297860i
\(661\) −21.4420 37.1387i −0.833998 1.44453i −0.894844 0.446380i \(-0.852713\pi\)
0.0608459 0.998147i \(-0.480620\pi\)
\(662\) 2.22313 + 0.989799i 0.0864042 + 0.0384696i
\(663\) 1.58219 + 0.336306i 0.0614473 + 0.0130610i
\(664\) 0.620472 1.90962i 0.0240790 0.0741075i
\(665\) 0 0
\(666\) −2.15249 1.56387i −0.0834072 0.0605988i
\(667\) 30.8899 + 34.3067i 1.19606 + 1.32836i
\(668\) −17.0196 + 18.9021i −0.658506 + 0.731345i
\(669\) −3.50811 1.56191i −0.135632 0.0603870i
\(670\) 0.464789 0.805037i 0.0179563 0.0311013i
\(671\) 0.852898 + 2.70560i 0.0329258 + 0.104448i
\(672\) 0 0
\(673\) 20.2313 14.6989i 0.779858 0.566600i −0.125078 0.992147i \(-0.539918\pi\)
0.904936 + 0.425547i \(0.139918\pi\)
\(674\) −1.66060 0.352971i −0.0639639 0.0135959i
\(675\) 1.56616 0.332899i 0.0602817 0.0128133i
\(676\) 2.72319 25.9094i 0.104738 0.996515i
\(677\) 9.06137 4.03438i 0.348257 0.155054i −0.225151 0.974324i \(-0.572288\pi\)
0.573408 + 0.819270i \(0.305621\pi\)
\(678\) 0.0505080 0.155448i 0.00193975 0.00596993i
\(679\) 0 0
\(680\) 2.59249 1.88356i 0.0994175 0.0722310i
\(681\) −2.81332 + 4.87282i −0.107807 + 0.186727i
\(682\) −5.24915 2.39255i −0.201000 0.0916154i
\(683\) 19.9490 + 34.5527i 0.763328 + 1.32212i 0.941126 + 0.338056i \(0.109769\pi\)
−0.177798 + 0.984067i \(0.556897\pi\)
\(684\) −3.64923 34.7201i −0.139532 1.32756i
\(685\) 7.19174 + 22.1339i 0.274782 + 0.845692i
\(686\) 0 0
\(687\) −3.51667 2.55501i −0.134169 0.0974798i
\(688\) −2.70863 + 1.20596i −0.103266 + 0.0459768i
\(689\) 33.0583 7.02675i 1.25942 0.267698i
\(690\) 0.586274 0.651123i 0.0223191 0.0247878i
\(691\) −0.691352 6.57777i −0.0263003 0.250230i −0.999771 0.0214172i \(-0.993182\pi\)
0.973470 0.228813i \(-0.0734845\pi\)
\(692\) 11.5218 0.437995
\(693\) 0 0
\(694\) −6.26194 −0.237700
\(695\) 1.25900 + 11.9786i 0.0477568 + 0.454375i
\(696\) −0.853666 + 0.948092i −0.0323581 + 0.0359373i
\(697\) 9.48985 2.01713i 0.359454 0.0764042i
\(698\) 2.28570 1.01766i 0.0865150 0.0385190i
\(699\) 3.58363 + 2.60366i 0.135545 + 0.0984795i
\(700\) 0 0
\(701\) 4.51215 + 13.8870i 0.170421 + 0.524503i 0.999395 0.0347848i \(-0.0110746\pi\)
−0.828973 + 0.559288i \(0.811075\pi\)
\(702\) −0.158362 1.50671i −0.00597699 0.0568672i
\(703\) 12.0894 + 20.9394i 0.455960 + 0.789746i
\(704\) 11.1011 + 19.6239i 0.418390 + 0.739602i
\(705\) 1.84620 3.19771i 0.0695320 0.120433i
\(706\) 5.84167 4.24422i 0.219854 0.159733i
\(707\) 0 0
\(708\) 0.379563 1.16817i 0.0142648 0.0439027i
\(709\) −3.78579 + 1.68554i −0.142178 + 0.0633018i −0.476592 0.879124i \(-0.658128\pi\)
0.334414 + 0.942426i \(0.391462\pi\)
\(710\) −0.266761 + 2.53807i −0.0100114 + 0.0952519i
\(711\) 7.08270 1.50547i 0.265622 0.0564597i
\(712\) −1.51653 0.322349i −0.0568345 0.0120805i
\(713\) 44.0593 32.0109i 1.65003 1.19882i
\(714\) 0 0
\(715\) 34.1631 + 25.2824i 1.27763 + 0.945510i
\(716\) 4.22416 7.31646i 0.157864 0.273429i
\(717\) 3.42324 + 1.52412i 0.127843 + 0.0569195i
\(718\) 0.541624 0.601534i 0.0202132 0.0224491i
\(719\) −11.3901 12.6500i −0.424780 0.471766i 0.492325 0.870411i \(-0.336147\pi\)
−0.917105 + 0.398646i \(0.869480\pi\)
\(720\) 22.0250 + 16.0021i 0.820825 + 0.596364i
\(721\) 0 0
\(722\) 1.24612 3.83517i 0.0463759 0.142730i
\(723\) −5.17696 1.10040i −0.192533 0.0409242i
\(724\) 19.2824 + 8.58507i 0.716624 + 0.319062i
\(725\) −4.00068 6.92938i −0.148582 0.257351i
\(726\) 0.357678 + 0.411559i 0.0132747 + 0.0152744i
\(727\) 21.6199 0.801837 0.400918 0.916114i \(-0.368691\pi\)
0.400918 + 0.916114i \(0.368691\pi\)
\(728\) 0 0
\(729\) −7.55284 23.2453i −0.279735 0.860936i
\(730\) 5.60859 + 6.22897i 0.207583 + 0.230544i
\(731\) 0.120555 1.14701i 0.00445890 0.0424236i
\(732\) 0.0381811 0.363269i 0.00141121 0.0134268i
\(733\) 32.2739 + 35.8438i 1.19206 + 1.32392i 0.933779 + 0.357851i \(0.116490\pi\)
0.258284 + 0.966069i \(0.416843\pi\)
\(734\) −0.160355 0.493523i −0.00591883 0.0182163i
\(735\) 0 0
\(736\) 18.5751 0.684688
\(737\) −5.00858 + 2.17744i −0.184493 + 0.0802072i
\(738\) −2.25340 3.90300i −0.0829487 0.143671i
\(739\) −7.45770 3.32038i −0.274336 0.122142i 0.264958 0.964260i \(-0.414642\pi\)
−0.539294 + 0.842118i \(0.681309\pi\)
\(740\) −18.9537 4.02874i −0.696752 0.148099i
\(741\) −2.11010 + 6.49421i −0.0775163 + 0.238571i
\(742\) 0 0
\(743\) −15.8254 11.4978i −0.580577 0.421814i 0.258355 0.966050i \(-0.416820\pi\)
−0.838932 + 0.544236i \(0.816820\pi\)
\(744\) 1.00707 + 1.11847i 0.0369211 + 0.0410051i
\(745\) 1.53944 1.70972i 0.0564008 0.0626394i
\(746\) 1.64674 + 0.733174i 0.0602913 + 0.0268434i
\(747\) −3.31773 + 5.74648i −0.121389 + 0.210253i
\(748\) −9.29113 0.0816249i −0.339717 0.00298450i
\(749\) 0 0
\(750\) 0.377527 0.274289i 0.0137853 0.0100156i
\(751\) −1.09190 0.232091i −0.0398441 0.00846913i 0.187946 0.982179i \(-0.439817\pi\)
−0.227791 + 0.973710i \(0.573150\pi\)
\(752\) 24.4081 5.18811i 0.890073 0.189191i
\(753\) 0.272452 2.59221i 0.00992872 0.0944654i
\(754\) −6.91635 + 3.07936i −0.251879 + 0.112144i
\(755\) 13.9552 42.9497i 0.507882 1.56310i
\(756\) 0 0
\(757\) 21.5015 15.6218i 0.781485 0.567782i −0.123939 0.992290i \(-0.539553\pi\)
0.905424 + 0.424508i \(0.139553\pi\)
\(758\) 1.31442 2.27665i 0.0477420 0.0826916i
\(759\) −5.04438 + 1.02598i −0.183099 + 0.0372408i
\(760\) 6.76385 + 11.7153i 0.245351 + 0.424960i
\(761\) 0.658532 + 6.26551i 0.0238718 + 0.227125i 0.999953 + 0.00971759i \(0.00309325\pi\)
−0.976081 + 0.217407i \(0.930240\pi\)
\(762\) −0.00443000 0.0136341i −0.000160482 0.000493913i
\(763\) 0 0
\(764\) 18.3766 + 13.3514i 0.664844 + 0.483037i
\(765\) −9.67433 + 4.30729i −0.349776 + 0.155730i
\(766\) 2.78321 0.591590i 0.100561 0.0213750i
\(767\) 9.88273 10.9759i 0.356845 0.396316i
\(768\) −0.276272 2.62856i −0.00996912 0.0948498i
\(769\) −13.1916 −0.475700 −0.237850 0.971302i \(-0.576443\pi\)
−0.237850 + 0.971302i \(0.576443\pi\)
\(770\) 0 0
\(771\) −5.03141 −0.181202
\(772\) 4.57231 + 43.5027i 0.164561 + 1.56569i
\(773\) −30.6581 + 34.0492i −1.10269 + 1.22467i −0.130263 + 0.991480i \(0.541582\pi\)
−0.972432 + 0.233187i \(0.925085\pi\)
\(774\) −0.524045 + 0.111389i −0.0188364 + 0.00400380i
\(775\) −8.62319 + 3.83929i −0.309754 + 0.137911i
\(776\) 8.72809 + 6.34133i 0.313320 + 0.227640i
\(777\) 0 0
\(778\) −0.0306381 0.0942944i −0.00109843 0.00338062i
\(779\) 4.28108 + 40.7318i 0.153386 + 1.45937i
\(780\) −2.73619 4.73921i −0.0979711 0.169691i
\(781\) 10.1302 11.0539i 0.362489 0.395541i
\(782\) −1.15163 + 1.99468i −0.0411821 + 0.0713295i
\(783\) 6.87723 4.99660i 0.245772 0.178564i
\(784\) 0 0
\(785\) 9.46469 29.1293i 0.337809 1.03967i
\(786\) 0.747453 0.332787i 0.0266607 0.0118701i
\(787\) −1.97015 + 18.7447i −0.0702281 + 0.668176i 0.901614 + 0.432542i \(0.142383\pi\)
−0.971842 + 0.235634i \(0.924283\pi\)
\(788\) 45.9446 9.76582i 1.63671 0.347893i
\(789\) −0.415338 0.0882828i −0.0147864 0.00314295i
\(790\) −1.12025 + 0.813909i −0.0398567 + 0.0289576i
\(791\) 0 0
\(792\) 2.62938 + 8.34104i 0.0934311 + 0.296386i
\(793\) 2.19608 3.80373i 0.0779852 0.135074i
\(794\) −3.47483 1.54709i −0.123317 0.0549043i
\(795\) 2.40830 2.67468i 0.0854134 0.0948612i
\(796\) 24.4120 + 27.1122i 0.865259 + 0.960967i
\(797\) −22.7830 16.5528i −0.807016 0.586331i 0.105948 0.994372i \(-0.466212\pi\)
−0.912964 + 0.408040i \(0.866212\pi\)
\(798\) 0 0
\(799\) −2.99947 + 9.23141i −0.106114 + 0.326584i
\(800\) −3.14916 0.669374i −0.111340 0.0236659i
\(801\) 4.68068 + 2.08397i 0.165384 + 0.0736335i
\(802\) −4.16917 7.22122i −0.147219 0.254990i
\(803\) −4.71707 49.0186i −0.166462 1.72983i
\(804\) 0.703208 0.0248002
\(805\) 0 0
\(806\) 2.75996 + 8.49429i 0.0972155 + 0.299199i
\(807\) −1.05377 1.17033i −0.0370944 0.0411975i
\(808\) 0.344859 3.28111i 0.0121321 0.115429i
\(809\) 0.684193 6.50966i 0.0240549 0.228868i −0.975889 0.218268i \(-0.929959\pi\)
0.999944 0.0105996i \(-0.00337401\pi\)
\(810\) 3.23724 + 3.59532i 0.113745 + 0.126327i
\(811\) −5.81096 17.8843i −0.204050 0.628002i −0.999751 0.0223122i \(-0.992897\pi\)
0.795701 0.605690i \(-0.207103\pi\)
\(812\) 0 0
\(813\) −0.261006 −0.00915387
\(814\) −1.98062 2.23895i −0.0694207 0.0784751i
\(815\) −10.1058 17.5037i −0.353990 0.613129i
\(816\) 1.06348 + 0.473493i 0.0372293 + 0.0165756i
\(817\) 4.76234 + 1.01227i 0.166613 + 0.0354147i
\(818\) −1.13760 + 3.50116i −0.0397751 + 0.122415i
\(819\) 0 0
\(820\) −26.5542 19.2927i −0.927311 0.673731i
\(821\) −7.75388 8.61156i −0.270612 0.300545i 0.592487 0.805580i \(-0.298146\pi\)
−0.863099 + 0.505035i \(0.831480\pi\)
\(822\) 0.309326 0.343541i 0.0107890 0.0119824i
\(823\) 11.2790 + 5.02173i 0.393161 + 0.175046i 0.593789 0.804621i \(-0.297632\pi\)
−0.200628 + 0.979668i \(0.564298\pi\)
\(824\) 0.514328 0.890843i 0.0179175 0.0310340i
\(825\) 0.892177 + 0.00783800i 0.0310616 + 0.000272884i
\(826\) 0 0
\(827\) 3.63717 2.64256i 0.126477 0.0918907i −0.522748 0.852487i \(-0.675093\pi\)
0.649225 + 0.760596i \(0.275093\pi\)
\(828\) −39.8570 8.47186i −1.38513 0.294417i
\(829\) −19.4288 + 4.12972i −0.674790 + 0.143431i −0.532547 0.846401i \(-0.678765\pi\)
−0.142244 + 0.989832i \(0.545432\pi\)
\(830\) 0.132638 1.26197i 0.00460393 0.0438035i
\(831\) 2.06996 0.921605i 0.0718061 0.0319701i
\(832\) 10.7869 33.1988i 0.373970 1.15096i
\(833\) 0 0
\(834\) 0.193555 0.140626i 0.00670226 0.00486947i
\(835\) −16.2853 + 28.2069i −0.563576 + 0.976142i
\(836\) 4.44254 38.9714i 0.153648 1.34785i
\(837\) −5.01418 8.68481i −0.173315 0.300191i
\(838\) 0.131552 + 1.25164i 0.00454440 + 0.0432371i
\(839\) 13.5513 + 41.7065i 0.467842 + 1.43987i 0.855373 + 0.518012i \(0.173328\pi\)
−0.387532 + 0.921856i \(0.626672\pi\)
\(840\) 0 0
\(841\) −10.9057 7.92348i −0.376060 0.273224i
\(842\) 4.44129 1.97739i 0.153057 0.0681453i
\(843\) 2.81886 0.599168i 0.0970869 0.0206365i
\(844\) 9.86669 10.9581i 0.339625 0.377192i
\(845\) −3.48711 33.1776i −0.119960 1.14134i
\(846\) 4.50894 0.155021
\(847\) 0 0
\(848\) 24.3232 0.835261
\(849\) 0.00687228 + 0.0653854i 0.000235856 + 0.00224402i
\(850\) 0.267123 0.296670i 0.00916224 0.0101757i
\(851\) 27.6040 5.86740i 0.946252 0.201132i
\(852\) −1.76367 + 0.785236i −0.0604223 + 0.0269017i
\(853\) 31.6655 + 23.0063i 1.08421 + 0.787721i 0.978411 0.206667i \(-0.0662616\pi\)
0.105794 + 0.994388i \(0.466262\pi\)
\(854\) 0 0
\(855\) −13.8146 42.5169i −0.472449 1.45405i
\(856\) 0.108978 + 1.03686i 0.00372479 + 0.0354390i
\(857\) 17.5262 + 30.3563i 0.598684 + 1.03695i 0.993016 + 0.117982i \(0.0376427\pi\)
−0.394332 + 0.918968i \(0.629024\pi\)
\(858\) 0.0956163 0.838778i 0.00326429 0.0286354i
\(859\) −16.2603 + 28.1636i −0.554794 + 0.960931i 0.443126 + 0.896459i \(0.353870\pi\)
−0.997920 + 0.0644717i \(0.979464\pi\)
\(860\) −3.15667 + 2.29345i −0.107642 + 0.0782061i
\(861\) 0 0
\(862\) −1.93763 + 5.96341i −0.0659959 + 0.203114i
\(863\) 11.5965 5.16310i 0.394750 0.175754i −0.199755 0.979846i \(-0.564015\pi\)
0.594505 + 0.804092i \(0.297348\pi\)
\(864\) 0.357533 3.40170i 0.0121635 0.115728i
\(865\) 14.4316 3.06753i 0.490689 0.104299i
\(866\) 2.05516 + 0.436839i 0.0698373 + 0.0148444i
\(867\) 2.64741 1.92345i 0.0899107 0.0653239i
\(868\) 0 0
\(869\) 8.13505 + 0.0714685i 0.275963 + 0.00242440i
\(870\) −0.403126 + 0.698234i −0.0136672 + 0.0236724i
\(871\) 7.72465 + 3.43924i 0.261740 + 0.116534i
\(872\) −5.56014 + 6.17516i −0.188290 + 0.209117i
\(873\) −23.8563 26.4951i −0.807414 0.896725i
\(874\) −7.86619 5.71512i −0.266078 0.193317i
\(875\) 0 0
\(876\) −1.95940 + 6.03041i −0.0662020 + 0.203749i
\(877\) 27.5192 + 5.84938i 0.929257 + 0.197520i 0.647587 0.761992i \(-0.275778\pi\)
0.281670 + 0.959511i \(0.409112\pi\)
\(878\) 3.04026 + 1.35361i 0.102604 + 0.0456821i
\(879\) 1.76882 + 3.06369i 0.0596610 + 0.103336i
\(880\) 20.2664 + 22.9097i 0.683182 + 0.772287i
\(881\) 36.7964 1.23970 0.619850 0.784720i \(-0.287193\pi\)
0.619850 + 0.784720i \(0.287193\pi\)
\(882\) 0 0
\(883\) −0.705855 2.17240i −0.0237539 0.0731070i 0.938477 0.345342i \(-0.112237\pi\)
−0.962231 + 0.272235i \(0.912237\pi\)
\(884\) 9.62585 + 10.6906i 0.323752 + 0.359563i
\(885\) 0.164408 1.56424i 0.00552653 0.0525814i
\(886\) −0.0577766 + 0.549708i −0.00194104 + 0.0184678i
\(887\) −28.2826 31.4110i −0.949636 1.05468i −0.998438 0.0558690i \(-0.982207\pi\)
0.0488023 0.998808i \(-0.484460\pi\)
\(888\) 0.241002 + 0.741728i 0.00808750 + 0.0248908i
\(889\) 0 0
\(890\) −0.979808 −0.0328432
\(891\) −2.72266 28.2933i −0.0912127 0.947860i
\(892\) −17.0760 29.5765i −0.571747 0.990295i
\(893\) −37.4332 16.6663i −1.25265 0.557717i
\(894\) −0.0447003 0.00950134i −0.00149500 0.000317772i
\(895\) 3.34304 10.2888i 0.111745 0.343917i
\(896\) 0 0
\(897\) 6.44778 + 4.68459i 0.215285 + 0.156414i
\(898\) 0.721913 + 0.801765i 0.0240905 + 0.0267552i
\(899\) −33.5329 + 37.2421i −1.11839 + 1.24209i
\(900\) 6.45191 + 2.87257i 0.215064 + 0.0957525i
\(901\) −4.73066 + 8.19374i −0.157601 + 0.272973i
\(902\) −1.52234 4.82923i −0.0506884 0.160796i
\(903\) 0 0
\(904\) 2.38288 1.73127i 0.0792535 0.0575810i
\(905\) 26.4377 + 5.61950i 0.878817 + 0.186798i
\(906\) −0.877429 + 0.186503i −0.0291506 + 0.00619616i
\(907\) −4.13186 + 39.3120i −0.137196 + 1.30533i 0.681801 + 0.731537i \(0.261197\pi\)
−0.818998 + 0.573797i \(0.805470\pi\)
\(908\) −45.7143 + 20.3533i −1.51708 + 0.675449i
\(909\) −3.36915 + 10.3692i −0.111748 + 0.343924i
\(910\) 0 0
\(911\) 28.5013 20.7074i 0.944291 0.686067i −0.00515893 0.999987i \(-0.501642\pi\)
0.949450 + 0.313919i \(0.101642\pi\)
\(912\) −2.45717 + 4.25593i −0.0813649 + 0.140928i
\(913\) −5.03692 + 5.49619i −0.166698 + 0.181897i
\(914\) −3.51617 6.09019i −0.116305 0.201446i
\(915\) −0.0488919 0.465175i −0.00161632 0.0153782i
\(916\) −11.9462 36.7666i −0.394713 1.21480i
\(917\) 0 0
\(918\) 0.343123 + 0.249293i 0.0113247 + 0.00822791i
\(919\) −36.1860 + 16.1110i −1.19366 + 0.531454i −0.904767 0.425906i \(-0.859955\pi\)
−0.288897 + 0.957360i \(0.593289\pi\)
\(920\) 15.4440 3.28273i 0.509175 0.108229i
\(921\) 4.19903 4.66349i 0.138363 0.153667i
\(922\) 0.702780 + 6.68651i 0.0231448 + 0.220208i
\(923\) −23.2141 −0.764101
\(924\) 0 0
\(925\) −4.89131 −0.160825
\(926\) 0.601905 + 5.72674i 0.0197798 + 0.188192i
\(927\) −2.27464 + 2.52624i −0.0747089 + 0.0829727i
\(928\) −16.7193 + 3.55379i −0.548837 + 0.116659i
\(929\) −2.39036 + 1.06425i −0.0784250 + 0.0349171i −0.445574 0.895245i \(-0.647000\pi\)
0.367149 + 0.930162i \(0.380334\pi\)
\(930\) 0.769488 + 0.559066i 0.0252325 + 0.0183325i
\(931\) 0 0
\(932\) 12.1736 + 37.4666i 0.398761 + 1.22726i
\(933\) −0.728909 6.93511i −0.0238634 0.227045i
\(934\) −0.360232 0.623939i −0.0117871 0.0204159i
\(935\) −11.6593 + 2.37140i −0.381299 + 0.0775529i
\(936\) 6.77026 11.7264i 0.221293 0.383291i
\(937\) 43.5575 31.6464i 1.42296 1.03384i 0.431689 0.902022i \(-0.357918\pi\)
0.991274 0.131820i \(-0.0420822\pi\)
\(938\) 0 0
\(939\) −0.00231742 + 0.00713228i −7.56261e−5 + 0.000232753i
\(940\) 29.9994 13.3566i 0.978471 0.435643i
\(941\) 3.09902 29.4852i 0.101025 0.961190i −0.820178 0.572108i \(-0.806126\pi\)
0.921203 0.389082i \(-0.127208\pi\)
\(942\) −0.595089 + 0.126490i −0.0193890 + 0.00412127i
\(943\) 46.7580 + 9.93873i 1.52265 + 0.323650i
\(944\) 8.59940 6.24783i 0.279887 0.203349i
\(945\) 0 0
\(946\) −0.601908 0.00528791i −0.0195697 0.000171925i
\(947\) 7.89306 13.6712i 0.256490 0.444254i −0.708809 0.705400i \(-0.750767\pi\)
0.965299 + 0.261146i \(0.0841006\pi\)
\(948\) −0.956942 0.426058i −0.0310800 0.0138377i
\(949\) −51.0172 + 56.6603i −1.65609 + 1.83927i
\(950\) 1.12765 + 1.25239i 0.0365859 + 0.0406328i
\(951\) −3.96919 2.88378i −0.128710 0.0935131i
\(952\) 0 0
\(953\) −10.8502 + 33.3934i −0.351472 + 1.08172i 0.606555 + 0.795041i \(0.292551\pi\)
−0.958027 + 0.286678i \(0.907449\pi\)
\(954\) 4.29901 + 0.913784i 0.139186 + 0.0295848i
\(955\) 26.5722 + 11.8307i 0.859855 + 0.382832i
\(956\) 16.6629 + 28.8609i 0.538916 + 0.933429i
\(957\) 4.34410 1.88857i 0.140425 0.0610487i
\(958\) −0.731463 −0.0236325
\(959\) 0 0
\(960\) −1.14874 3.53546i −0.0370754 0.114106i
\(961\) 18.8159 + 20.8972i 0.606966 + 0.674104i
\(962\) −0.483774 + 4.60281i −0.0155975 + 0.148400i
\(963\) 0.360139 3.42649i 0.0116053 0.110417i
\(964\) −31.4959 34.9797i −1.01441 1.12662i
\(965\) 17.3090 + 53.2716i 0.557196 + 1.71487i
\(966\) 0 0
\(967\) −49.2820 −1.58480 −0.792401 0.610001i \(-0.791169\pi\)
−0.792401 + 0.610001i \(0.791169\pi\)
\(968\) 0.855247 + 9.78868i 0.0274887 + 0.314620i
\(969\) −0.955798 1.65549i −0.0307046 0.0531820i
\(970\) 6.22853 + 2.77312i 0.199986 + 0.0890395i
\(971\) 36.5264 + 7.76393i 1.17219 + 0.249156i 0.752550 0.658535i \(-0.228824\pi\)
0.419638 + 0.907691i \(0.362157\pi\)
\(972\) −3.48730 + 10.7328i −0.111855 + 0.344255i
\(973\) 0 0
\(974\) −1.80647 1.31248i −0.0578831 0.0420545i
\(975\) −0.924318 1.02656i −0.0296019 0.0328762i
\(976\) 2.11512 2.34907i 0.0677032 0.0751920i
\(977\) 36.5861 + 16.2892i 1.17049 + 0.521137i 0.897558 0.440896i \(-0.145339\pi\)
0.272935 + 0.962033i \(0.412006\pi\)
\(978\) −0.200735 + 0.347684i −0.00641881 + 0.0111177i
\(979\) 4.62723 + 3.42439i 0.147887 + 0.109444i
\(980\) 0 0
\(981\) 22.2159 16.1408i 0.709299 0.515336i
\(982\) −0.935080 0.198757i −0.0298396 0.00634260i
\(983\) −50.9042 + 10.8200i −1.62359 + 0.345105i −0.927783 0.373121i \(-0.878288\pi\)
−0.695810 + 0.718226i \(0.744954\pi\)
\(984\) −0.138089 + 1.31382i −0.00440210 + 0.0418832i
\(985\) 54.9475 24.4642i 1.75077 0.779494i
\(986\) 0.654946 2.01572i 0.0208577 0.0641935i
\(987\) 0 0
\(988\) −49.1304 + 35.6953i −1.56305 + 1.13562i
\(989\) 2.84131 4.92129i 0.0903484 0.156488i
\(990\) 2.72132 + 4.81058i 0.0864893 + 0.152890i
\(991\) −22.7414 39.3892i −0.722404 1.25124i −0.960034 0.279885i \(-0.909704\pi\)
0.237630 0.971356i \(-0.423630\pi\)
\(992\) 2.10776 + 20.0540i 0.0669214 + 0.636715i
\(993\) 0.728455 + 2.24195i 0.0231168 + 0.0711463i
\(994\) 0 0
\(995\) 37.7953 + 27.4599i 1.19819 + 0.870536i
\(996\) 0.876924 0.390432i 0.0277864 0.0123713i
\(997\) 27.3484 5.81308i 0.866132 0.184102i 0.246642 0.969107i \(-0.420673\pi\)
0.619490 + 0.785005i \(0.287339\pi\)
\(998\) −3.08713 + 3.42860i −0.0977214 + 0.108531i
\(999\) −0.543190 5.16811i −0.0171858 0.163512i
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 539.2.q.f.520.3 32
7.2 even 3 539.2.f.e.344.3 16
7.3 odd 6 539.2.q.g.410.2 32
7.4 even 3 inner 539.2.q.f.410.2 32
7.5 odd 6 77.2.f.b.36.3 yes 16
7.6 odd 2 539.2.q.g.520.3 32
11.4 even 5 inner 539.2.q.f.422.2 32
21.5 even 6 693.2.m.i.190.2 16
77.2 odd 30 5929.2.a.bs.1.5 8
77.4 even 15 inner 539.2.q.f.312.3 32
77.5 odd 30 847.2.f.w.372.2 16
77.9 even 15 5929.2.a.bt.1.4 8
77.19 even 30 847.2.f.v.148.3 16
77.26 odd 30 77.2.f.b.15.3 16
77.37 even 15 539.2.f.e.246.3 16
77.40 even 30 847.2.f.x.323.2 16
77.47 odd 30 847.2.f.w.148.2 16
77.48 odd 10 539.2.q.g.422.2 32
77.54 even 6 847.2.f.x.729.2 16
77.59 odd 30 539.2.q.g.312.3 32
77.61 even 30 847.2.f.v.372.3 16
77.68 even 30 847.2.a.o.1.5 8
77.75 odd 30 847.2.a.p.1.4 8
231.26 even 30 693.2.m.i.631.2 16
231.68 odd 30 7623.2.a.cw.1.4 8
231.152 even 30 7623.2.a.ct.1.5 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
77.2.f.b.15.3 16 77.26 odd 30
77.2.f.b.36.3 yes 16 7.5 odd 6
539.2.f.e.246.3 16 77.37 even 15
539.2.f.e.344.3 16 7.2 even 3
539.2.q.f.312.3 32 77.4 even 15 inner
539.2.q.f.410.2 32 7.4 even 3 inner
539.2.q.f.422.2 32 11.4 even 5 inner
539.2.q.f.520.3 32 1.1 even 1 trivial
539.2.q.g.312.3 32 77.59 odd 30
539.2.q.g.410.2 32 7.3 odd 6
539.2.q.g.422.2 32 77.48 odd 10
539.2.q.g.520.3 32 7.6 odd 2
693.2.m.i.190.2 16 21.5 even 6
693.2.m.i.631.2 16 231.26 even 30
847.2.a.o.1.5 8 77.68 even 30
847.2.a.p.1.4 8 77.75 odd 30
847.2.f.v.148.3 16 77.19 even 30
847.2.f.v.372.3 16 77.61 even 30
847.2.f.w.148.2 16 77.47 odd 30
847.2.f.w.372.2 16 77.5 odd 30
847.2.f.x.323.2 16 77.40 even 30
847.2.f.x.729.2 16 77.54 even 6
5929.2.a.bs.1.5 8 77.2 odd 30
5929.2.a.bt.1.4 8 77.9 even 15
7623.2.a.ct.1.5 8 231.152 even 30
7623.2.a.cw.1.4 8 231.68 odd 30