Properties

Label 750.2.l.c.107.3
Level $750$
Weight $2$
Character 750.107
Analytic conductor $5.989$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 750.l (of order \(20\), degree \(8\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.98878015160\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(10\) over \(\Q(\zeta_{20})\)
Twist minimal: no (minimal twist has level 150)
Sato-Tate group: $\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label 107.3
Character \(\chi\) \(=\) 750.107
Dual form 750.2.l.c.743.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.891007 - 0.453990i) q^{2} +(0.631448 - 1.61285i) q^{3} +(0.587785 + 0.809017i) q^{4} +(-1.29484 + 1.15039i) q^{6} +(-2.97677 - 2.97677i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(-2.20255 - 2.03686i) q^{9} +O(q^{10})\) \(q+(-0.891007 - 0.453990i) q^{2} +(0.631448 - 1.61285i) q^{3} +(0.587785 + 0.809017i) q^{4} +(-1.29484 + 1.15039i) q^{6} +(-2.97677 - 2.97677i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(-2.20255 - 2.03686i) q^{9} +(4.73921 - 1.53986i) q^{11} +(1.67598 - 0.437156i) q^{12} +(-0.801995 - 1.57400i) q^{13} +(1.30090 + 4.00375i) q^{14} +(-0.309017 + 0.951057i) q^{16} +(1.40961 - 0.223260i) q^{17} +(1.03777 + 2.81479i) q^{18} +(-1.09331 + 1.50481i) q^{19} +(-6.68076 + 2.92140i) q^{21} +(-4.92175 - 0.779529i) q^{22} +(-0.951606 + 1.86763i) q^{23} +(-1.69177 - 0.371369i) q^{24} +1.76655i q^{26} +(-4.67593 + 2.26620i) q^{27} +(0.658557 - 4.15797i) q^{28} +(-4.57938 + 3.32712i) q^{29} +(-5.23835 - 3.80588i) q^{31} +(0.707107 - 0.707107i) q^{32} +(0.509001 - 8.61596i) q^{33} +(-1.35733 - 0.441023i) q^{34} +(0.353226 - 2.97913i) q^{36} +(-2.29429 + 1.16900i) q^{37} +(1.65732 - 0.844446i) q^{38} +(-3.04504 + 0.299594i) q^{39} +(-3.58757 - 1.16567i) q^{41} +(7.27889 + 0.430011i) q^{42} +(6.26505 - 6.26505i) q^{43} +(4.03141 + 2.92899i) q^{44} +(1.69577 - 1.23205i) q^{46} +(-0.732319 + 4.62368i) q^{47} +(1.33878 + 1.09894i) q^{48} +10.7224i q^{49} +(0.530010 - 2.41446i) q^{51} +(0.801995 - 1.57400i) q^{52} +(-5.05783 - 0.801081i) q^{53} +(5.19512 + 0.103626i) q^{54} +(-2.47446 + 3.40580i) q^{56} +(1.73666 + 2.71355i) q^{57} +(5.59074 - 0.885486i) q^{58} +(3.44032 - 10.5882i) q^{59} +(-2.99979 - 9.23241i) q^{61} +(2.93957 + 5.76923i) q^{62} +(0.493226 + 12.6197i) q^{63} +(-0.951057 + 0.309017i) q^{64} +(-4.36509 + 7.44580i) q^{66} +(-1.01259 - 6.39326i) q^{67} +(1.00917 + 1.00917i) q^{68} +(2.41131 + 2.71411i) q^{69} +(8.85681 + 12.1904i) q^{71} +(-1.66722 + 2.49407i) q^{72} +(-8.23800 - 4.19747i) q^{73} +2.57494 q^{74} -1.86005 q^{76} +(-18.6914 - 9.52374i) q^{77} +(2.84917 + 1.11548i) q^{78} +(-2.20434 - 3.03401i) q^{79} +(0.702433 + 8.97255i) q^{81} +(2.66735 + 2.66735i) q^{82} +(2.63941 + 16.6646i) q^{83} +(-6.29032 - 3.68769i) q^{84} +(-8.42648 + 2.73793i) q^{86} +(2.47449 + 9.48674i) q^{87} +(-2.26228 - 4.43998i) q^{88} +(-0.351151 - 1.08073i) q^{89} +(-2.29810 + 7.07281i) q^{91} +(-2.07029 + 0.327901i) q^{92} +(-9.44605 + 6.04544i) q^{93} +(2.75161 - 3.78726i) q^{94} +(-0.693954 - 1.58696i) q^{96} +(3.47236 + 0.549968i) q^{97} +(4.86785 - 9.55370i) q^{98} +(-13.5748 - 6.26147i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q + 4q^{3} + 4q^{7} + O(q^{10}) \) \( 80q + 4q^{3} + 4q^{7} + 16q^{12} + 20q^{16} - 8q^{18} + 40q^{19} + 4q^{22} - 56q^{27} + 4q^{28} - 96q^{33} + 40q^{34} - 64q^{37} + 40q^{39} - 4q^{42} - 24q^{43} + 16q^{48} - 64q^{57} + 20q^{58} + 4q^{63} - 104q^{67} - 140q^{69} + 8q^{72} - 60q^{73} - 60q^{78} - 80q^{79} - 40q^{81} + 96q^{82} - 60q^{84} + 80q^{87} + 24q^{88} + 12q^{93} - 12q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/750\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(251\)
\(\chi(n)\) \(e\left(\frac{13}{20}\right)\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.891007 0.453990i −0.630037 0.321020i
\(3\) 0.631448 1.61285i 0.364566 0.931177i
\(4\) 0.587785 + 0.809017i 0.293893 + 0.404508i
\(5\) 0 0
\(6\) −1.29484 + 1.15039i −0.528617 + 0.469643i
\(7\) −2.97677 2.97677i −1.12511 1.12511i −0.990960 0.134155i \(-0.957168\pi\)
−0.134155 0.990960i \(-0.542832\pi\)
\(8\) −0.156434 0.987688i −0.0553079 0.349201i
\(9\) −2.20255 2.03686i −0.734183 0.678952i
\(10\) 0 0
\(11\) 4.73921 1.53986i 1.42893 0.464286i 0.510499 0.859878i \(-0.329461\pi\)
0.918426 + 0.395592i \(0.129461\pi\)
\(12\) 1.67598 0.437156i 0.483813 0.126196i
\(13\) −0.801995 1.57400i −0.222433 0.436550i 0.752640 0.658432i \(-0.228780\pi\)
−0.975074 + 0.221882i \(0.928780\pi\)
\(14\) 1.30090 + 4.00375i 0.347680 + 1.07005i
\(15\) 0 0
\(16\) −0.309017 + 0.951057i −0.0772542 + 0.237764i
\(17\) 1.40961 0.223260i 0.341881 0.0541486i 0.0168665 0.999858i \(-0.494631\pi\)
0.325014 + 0.945709i \(0.394631\pi\)
\(18\) 1.03777 + 2.81479i 0.244605 + 0.663452i
\(19\) −1.09331 + 1.50481i −0.250823 + 0.345228i −0.915799 0.401636i \(-0.868442\pi\)
0.664977 + 0.746864i \(0.268442\pi\)
\(20\) 0 0
\(21\) −6.68076 + 2.92140i −1.45786 + 0.637502i
\(22\) −4.92175 0.779529i −1.04932 0.166196i
\(23\) −0.951606 + 1.86763i −0.198424 + 0.389428i −0.968682 0.248303i \(-0.920127\pi\)
0.770259 + 0.637731i \(0.220127\pi\)
\(24\) −1.69177 0.371369i −0.345331 0.0758053i
\(25\) 0 0
\(26\) 1.76655i 0.346448i
\(27\) −4.67593 + 2.26620i −0.899883 + 0.436131i
\(28\) 0.658557 4.15797i 0.124456 0.785782i
\(29\) −4.57938 + 3.32712i −0.850370 + 0.617830i −0.925248 0.379363i \(-0.876143\pi\)
0.0748779 + 0.997193i \(0.476143\pi\)
\(30\) 0 0
\(31\) −5.23835 3.80588i −0.940835 0.683557i 0.00778619 0.999970i \(-0.497522\pi\)
−0.948622 + 0.316413i \(0.897522\pi\)
\(32\) 0.707107 0.707107i 0.125000 0.125000i
\(33\) 0.509001 8.61596i 0.0886057 1.49985i
\(34\) −1.35733 0.441023i −0.232780 0.0756348i
\(35\) 0 0
\(36\) 0.353226 2.97913i 0.0588710 0.496522i
\(37\) −2.29429 + 1.16900i −0.377178 + 0.192182i −0.632294 0.774729i \(-0.717886\pi\)
0.255116 + 0.966911i \(0.417886\pi\)
\(38\) 1.65732 0.844446i 0.268852 0.136987i
\(39\) −3.04504 + 0.299594i −0.487597 + 0.0479734i
\(40\) 0 0
\(41\) −3.58757 1.16567i −0.560285 0.182048i 0.0151644 0.999885i \(-0.495173\pi\)
−0.575449 + 0.817837i \(0.695173\pi\)
\(42\) 7.27889 + 0.430011i 1.12316 + 0.0663522i
\(43\) 6.26505 6.26505i 0.955411 0.955411i −0.0436361 0.999047i \(-0.513894\pi\)
0.999047 + 0.0436361i \(0.0138942\pi\)
\(44\) 4.03141 + 2.92899i 0.607758 + 0.441562i
\(45\) 0 0
\(46\) 1.69577 1.23205i 0.250028 0.181656i
\(47\) −0.732319 + 4.62368i −0.106820 + 0.674433i 0.874929 + 0.484251i \(0.160908\pi\)
−0.981749 + 0.190182i \(0.939092\pi\)
\(48\) 1.33878 + 1.09894i 0.193236 + 0.158618i
\(49\) 10.7224i 1.53177i
\(50\) 0 0
\(51\) 0.530010 2.41446i 0.0742163 0.338092i
\(52\) 0.801995 1.57400i 0.111217 0.218275i
\(53\) −5.05783 0.801081i −0.694746 0.110037i −0.200933 0.979605i \(-0.564397\pi\)
−0.493813 + 0.869568i \(0.664397\pi\)
\(54\) 5.19512 + 0.103626i 0.706966 + 0.0141017i
\(55\) 0 0
\(56\) −2.47446 + 3.40580i −0.330663 + 0.455119i
\(57\) 1.73666 + 2.71355i 0.230027 + 0.359419i
\(58\) 5.59074 0.885486i 0.734100 0.116270i
\(59\) 3.44032 10.5882i 0.447892 1.37847i −0.431389 0.902166i \(-0.641976\pi\)
0.879281 0.476303i \(-0.158024\pi\)
\(60\) 0 0
\(61\) −2.99979 9.23241i −0.384084 1.18209i −0.937142 0.348947i \(-0.886539\pi\)
0.553058 0.833143i \(-0.313461\pi\)
\(62\) 2.93957 + 5.76923i 0.373326 + 0.732693i
\(63\) 0.493226 + 12.6197i 0.0621407 + 1.58994i
\(64\) −0.951057 + 0.309017i −0.118882 + 0.0386271i
\(65\) 0 0
\(66\) −4.36509 + 7.44580i −0.537305 + 0.916514i
\(67\) −1.01259 6.39326i −0.123708 0.781061i −0.969055 0.246844i \(-0.920607\pi\)
0.845347 0.534217i \(-0.179393\pi\)
\(68\) 1.00917 + 1.00917i 0.122380 + 0.122380i
\(69\) 2.41131 + 2.71411i 0.290288 + 0.326740i
\(70\) 0 0
\(71\) 8.85681 + 12.1904i 1.05111 + 1.44673i 0.887842 + 0.460147i \(0.152203\pi\)
0.163268 + 0.986582i \(0.447797\pi\)
\(72\) −1.66722 + 2.49407i −0.196484 + 0.293928i
\(73\) −8.23800 4.19747i −0.964185 0.491277i −0.100295 0.994958i \(-0.531979\pi\)
−0.863890 + 0.503681i \(0.831979\pi\)
\(74\) 2.57494 0.299330
\(75\) 0 0
\(76\) −1.86005 −0.213363
\(77\) −18.6914 9.52374i −2.13008 1.08533i
\(78\) 2.84917 + 1.11548i 0.322605 + 0.126303i
\(79\) −2.20434 3.03401i −0.248007 0.341353i 0.666805 0.745232i \(-0.267661\pi\)
−0.914812 + 0.403880i \(0.867661\pi\)
\(80\) 0 0
\(81\) 0.702433 + 8.97255i 0.0780482 + 0.996950i
\(82\) 2.66735 + 2.66735i 0.294559 + 0.294559i
\(83\) 2.63941 + 16.6646i 0.289713 + 1.82918i 0.517761 + 0.855525i \(0.326766\pi\)
−0.228048 + 0.973650i \(0.573234\pi\)
\(84\) −6.29032 3.68769i −0.686330 0.402360i
\(85\) 0 0
\(86\) −8.42648 + 2.73793i −0.908650 + 0.295238i
\(87\) 2.47449 + 9.48674i 0.265293 + 1.01709i
\(88\) −2.26228 4.43998i −0.241160 0.473303i
\(89\) −0.351151 1.08073i −0.0372219 0.114557i 0.930719 0.365735i \(-0.119182\pi\)
−0.967941 + 0.251177i \(0.919182\pi\)
\(90\) 0 0
\(91\) −2.29810 + 7.07281i −0.240906 + 0.741432i
\(92\) −2.07029 + 0.327901i −0.215842 + 0.0341860i
\(93\) −9.44605 + 6.04544i −0.979510 + 0.626883i
\(94\) 2.75161 3.78726i 0.283807 0.390626i
\(95\) 0 0
\(96\) −0.693954 1.58696i −0.0708264 0.161968i
\(97\) 3.47236 + 0.549968i 0.352565 + 0.0558408i 0.330205 0.943909i \(-0.392882\pi\)
0.0223598 + 0.999750i \(0.492882\pi\)
\(98\) 4.86785 9.55370i 0.491728 0.965070i
\(99\) −13.5748 6.26147i −1.36432 0.629301i
\(100\) 0 0
\(101\) 16.6740i 1.65912i −0.558415 0.829562i \(-0.688590\pi\)
0.558415 0.829562i \(-0.311410\pi\)
\(102\) −1.56838 + 1.91068i −0.155293 + 0.189186i
\(103\) −0.415010 + 2.62027i −0.0408921 + 0.258183i −0.999662 0.0260012i \(-0.991723\pi\)
0.958770 + 0.284184i \(0.0917226\pi\)
\(104\) −1.42917 + 1.03835i −0.140141 + 0.101819i
\(105\) 0 0
\(106\) 4.14287 + 3.00997i 0.402391 + 0.292355i
\(107\) 8.35067 8.35067i 0.807290 0.807290i −0.176933 0.984223i \(-0.556618\pi\)
0.984223 + 0.176933i \(0.0566176\pi\)
\(108\) −4.58184 2.45087i −0.440888 0.235835i
\(109\) 12.6666 + 4.11563i 1.21324 + 0.394206i 0.844617 0.535372i \(-0.179828\pi\)
0.368625 + 0.929578i \(0.379828\pi\)
\(110\) 0 0
\(111\) 0.436691 + 4.43849i 0.0414489 + 0.421283i
\(112\) 3.75095 1.91121i 0.354432 0.180592i
\(113\) −1.33349 + 0.679445i −0.125444 + 0.0639168i −0.515586 0.856838i \(-0.672426\pi\)
0.390142 + 0.920755i \(0.372426\pi\)
\(114\) −0.315452 3.20622i −0.0295448 0.300290i
\(115\) 0 0
\(116\) −5.38339 1.74917i −0.499835 0.162406i
\(117\) −1.43959 + 5.10037i −0.133090 + 0.471529i
\(118\) −7.87230 + 7.87230i −0.724704 + 0.724704i
\(119\) −4.86069 3.53149i −0.445578 0.323732i
\(120\) 0 0
\(121\) 11.1898 8.12983i 1.01725 0.739076i
\(122\) −1.51859 + 9.58802i −0.137487 + 0.868058i
\(123\) −4.14542 + 5.05015i −0.373780 + 0.455356i
\(124\) 6.47496i 0.581468i
\(125\) 0 0
\(126\) 5.28978 11.4682i 0.471251 1.02167i
\(127\) −0.704349 + 1.38236i −0.0625009 + 0.122665i −0.920144 0.391581i \(-0.871928\pi\)
0.857643 + 0.514246i \(0.171928\pi\)
\(128\) 0.987688 + 0.156434i 0.0873001 + 0.0138270i
\(129\) −6.14851 14.0606i −0.541347 1.23797i
\(130\) 0 0
\(131\) 3.74251 5.15112i 0.326984 0.450055i −0.613599 0.789618i \(-0.710279\pi\)
0.940584 + 0.339562i \(0.110279\pi\)
\(132\) 7.26964 4.65255i 0.632741 0.404952i
\(133\) 7.73403 1.22495i 0.670625 0.106217i
\(134\) −2.00025 + 6.15614i −0.172795 + 0.531810i
\(135\) 0 0
\(136\) −0.441023 1.35733i −0.0378174 0.116390i
\(137\) −1.86549 3.66124i −0.159380 0.312800i 0.797483 0.603342i \(-0.206165\pi\)
−0.956862 + 0.290542i \(0.906165\pi\)
\(138\) −0.916318 3.51300i −0.0780022 0.299046i
\(139\) 10.1584 3.30065i 0.861621 0.279958i 0.155316 0.987865i \(-0.450361\pi\)
0.706305 + 0.707907i \(0.250361\pi\)
\(140\) 0 0
\(141\) 6.99487 + 4.10073i 0.589074 + 0.345344i
\(142\) −2.35717 14.8826i −0.197809 1.24892i
\(143\) −6.22457 6.22457i −0.520525 0.520525i
\(144\) 2.61779 1.46532i 0.218149 0.122110i
\(145\) 0 0
\(146\) 5.43450 + 7.47994i 0.449762 + 0.619045i
\(147\) 17.2935 + 6.77062i 1.42635 + 0.558431i
\(148\) −2.29429 1.16900i −0.188589 0.0960909i
\(149\) 5.13270 0.420487 0.210244 0.977649i \(-0.432574\pi\)
0.210244 + 0.977649i \(0.432574\pi\)
\(150\) 0 0
\(151\) 20.1314 1.63827 0.819136 0.573600i \(-0.194454\pi\)
0.819136 + 0.573600i \(0.194454\pi\)
\(152\) 1.65732 + 0.844446i 0.134426 + 0.0684936i
\(153\) −3.55948 2.37943i −0.287767 0.192366i
\(154\) 12.3305 + 16.9714i 0.993617 + 1.36760i
\(155\) 0 0
\(156\) −2.03221 2.28740i −0.162707 0.183138i
\(157\) −7.13510 7.13510i −0.569443 0.569443i 0.362529 0.931972i \(-0.381913\pi\)
−0.931972 + 0.362529i \(0.881913\pi\)
\(158\) 0.586667 + 3.70407i 0.0466727 + 0.294680i
\(159\) −4.48577 + 7.65166i −0.355745 + 0.606816i
\(160\) 0 0
\(161\) 8.39223 2.72680i 0.661401 0.214902i
\(162\) 3.44758 8.31350i 0.270867 0.653170i
\(163\) 2.55156 + 5.00771i 0.199853 + 0.392234i 0.969082 0.246739i \(-0.0793592\pi\)
−0.769228 + 0.638974i \(0.779359\pi\)
\(164\) −1.16567 3.58757i −0.0910238 0.280143i
\(165\) 0 0
\(166\) 5.21383 16.0465i 0.404672 1.24545i
\(167\) 16.5614 2.62306i 1.28156 0.202979i 0.521734 0.853109i \(-0.325286\pi\)
0.759823 + 0.650130i \(0.225286\pi\)
\(168\) 3.93054 + 6.14150i 0.303247 + 0.473827i
\(169\) 5.80692 7.99254i 0.446686 0.614810i
\(170\) 0 0
\(171\) 5.47316 1.08751i 0.418543 0.0831637i
\(172\) 8.75104 + 1.38603i 0.667260 + 0.105684i
\(173\) 2.03214 3.98829i 0.154500 0.303224i −0.800763 0.598982i \(-0.795572\pi\)
0.955263 + 0.295758i \(0.0955721\pi\)
\(174\) 2.10211 9.57614i 0.159360 0.725966i
\(175\) 0 0
\(176\) 4.98310i 0.375615i
\(177\) −14.9048 12.2346i −1.12031 0.919610i
\(178\) −0.177764 + 1.12236i −0.0133240 + 0.0841243i
\(179\) −0.141142 + 0.102546i −0.0105495 + 0.00766463i −0.593047 0.805167i \(-0.702075\pi\)
0.582498 + 0.812832i \(0.302075\pi\)
\(180\) 0 0
\(181\) 9.20445 + 6.68743i 0.684162 + 0.497072i 0.874736 0.484600i \(-0.161035\pi\)
−0.190574 + 0.981673i \(0.561035\pi\)
\(182\) 5.25861 5.25861i 0.389794 0.389794i
\(183\) −16.7847 0.991580i −1.24076 0.0732997i
\(184\) 1.99350 + 0.647728i 0.146963 + 0.0477511i
\(185\) 0 0
\(186\) 11.1611 1.09811i 0.818369 0.0805172i
\(187\) 6.33665 3.22868i 0.463382 0.236105i
\(188\) −4.17108 + 2.12527i −0.304207 + 0.155001i
\(189\) 20.6652 + 7.17321i 1.50317 + 0.521774i
\(190\) 0 0
\(191\) −17.5527 5.70322i −1.27007 0.412671i −0.404998 0.914318i \(-0.632728\pi\)
−0.865072 + 0.501647i \(0.832728\pi\)
\(192\) −0.102145 + 1.72904i −0.00737171 + 0.124782i
\(193\) −3.31568 + 3.31568i −0.238668 + 0.238668i −0.816298 0.577630i \(-0.803977\pi\)
0.577630 + 0.816298i \(0.303977\pi\)
\(194\) −2.84422 2.06644i −0.204203 0.148362i
\(195\) 0 0
\(196\) −8.67458 + 6.30245i −0.619613 + 0.450175i
\(197\) −1.98370 + 12.5246i −0.141333 + 0.892341i 0.810503 + 0.585734i \(0.199194\pi\)
−0.951836 + 0.306607i \(0.900806\pi\)
\(198\) 9.25260 + 11.7418i 0.657554 + 0.834457i
\(199\) 1.62602i 0.115266i 0.998338 + 0.0576328i \(0.0183553\pi\)
−0.998338 + 0.0576328i \(0.981645\pi\)
\(200\) 0 0
\(201\) −10.9507 2.40385i −0.772406 0.169555i
\(202\) −7.56983 + 14.8566i −0.532612 + 1.04531i
\(203\) 23.5359 + 3.72772i 1.65189 + 0.261634i
\(204\) 2.26487 0.990397i 0.158573 0.0693417i
\(205\) 0 0
\(206\) 1.55935 2.14627i 0.108645 0.149537i
\(207\) 5.90005 2.17526i 0.410082 0.151191i
\(208\) 1.74480 0.276349i 0.120980 0.0191613i
\(209\) −2.86422 + 8.81517i −0.198123 + 0.609758i
\(210\) 0 0
\(211\) −3.73259 11.4877i −0.256962 0.790848i −0.993437 0.114383i \(-0.963511\pi\)
0.736475 0.676465i \(-0.236489\pi\)
\(212\) −2.32483 4.56273i −0.159670 0.313370i
\(213\) 25.2538 6.58711i 1.73036 0.451341i
\(214\) −11.2316 + 3.64938i −0.767778 + 0.249466i
\(215\) 0 0
\(216\) 2.96978 + 4.26385i 0.202068 + 0.290118i
\(217\) 4.26413 + 26.9226i 0.289468 + 1.82763i
\(218\) −9.41758 9.41758i −0.637839 0.637839i
\(219\) −11.9717 + 10.6361i −0.808975 + 0.718724i
\(220\) 0 0
\(221\) −1.48191 2.03968i −0.0996842 0.137204i
\(222\) 1.62594 4.15298i 0.109126 0.278730i
\(223\) −5.54645 2.82606i −0.371418 0.189247i 0.258311 0.966062i \(-0.416834\pi\)
−0.629729 + 0.776815i \(0.716834\pi\)
\(224\) −4.20979 −0.281279
\(225\) 0 0
\(226\) 1.49661 0.0995528
\(227\) 8.15754 + 4.15647i 0.541435 + 0.275875i 0.703246 0.710947i \(-0.251733\pi\)
−0.161811 + 0.986822i \(0.551733\pi\)
\(228\) −1.17452 + 2.99998i −0.0777848 + 0.198678i
\(229\) −10.8714 14.9632i −0.718400 0.988793i −0.999575 0.0291365i \(-0.990724\pi\)
0.281175 0.959656i \(-0.409276\pi\)
\(230\) 0 0
\(231\) −27.1630 + 24.1326i −1.78719 + 1.58781i
\(232\) 4.00253 + 4.00253i 0.262779 + 0.262779i
\(233\) −2.15478 13.6047i −0.141164 0.891276i −0.952021 0.306032i \(-0.900999\pi\)
0.810857 0.585244i \(-0.199001\pi\)
\(234\) 3.59820 3.89090i 0.235222 0.254356i
\(235\) 0 0
\(236\) 10.5882 3.44032i 0.689234 0.223946i
\(237\) −6.28531 + 1.63944i −0.408275 + 0.106493i
\(238\) 2.72764 + 5.35329i 0.176806 + 0.347002i
\(239\) −6.40747 19.7202i −0.414465 1.27559i −0.912729 0.408566i \(-0.866029\pi\)
0.498264 0.867025i \(-0.333971\pi\)
\(240\) 0 0
\(241\) −1.92274 + 5.91757i −0.123854 + 0.381184i −0.993691 0.112156i \(-0.964224\pi\)
0.869836 + 0.493340i \(0.164224\pi\)
\(242\) −13.6610 + 2.16369i −0.878163 + 0.139087i
\(243\) 14.9149 + 4.53278i 0.956791 + 0.290778i
\(244\) 5.70595 7.85356i 0.365286 0.502773i
\(245\) 0 0
\(246\) 5.98631 2.61773i 0.381673 0.166900i
\(247\) 3.24541 + 0.514023i 0.206501 + 0.0327065i
\(248\) −2.93957 + 5.76923i −0.186663 + 0.366346i
\(249\) 28.5441 + 6.26585i 1.80891 + 0.397082i
\(250\) 0 0
\(251\) 3.76896i 0.237895i 0.992901 + 0.118947i \(0.0379520\pi\)
−0.992901 + 0.118947i \(0.962048\pi\)
\(252\) −9.91968 + 7.81673i −0.624881 + 0.492408i
\(253\) −1.63396 + 10.3164i −0.102726 + 0.648589i
\(254\) 1.25516 0.911927i 0.0787557 0.0572194i
\(255\) 0 0
\(256\) −0.809017 0.587785i −0.0505636 0.0367366i
\(257\) 21.7693 21.7693i 1.35793 1.35793i 0.481471 0.876462i \(-0.340103\pi\)
0.876462 0.481471i \(-0.159897\pi\)
\(258\) −0.905021 + 15.3195i −0.0563441 + 0.953749i
\(259\) 10.3094 + 3.34973i 0.640596 + 0.208142i
\(260\) 0 0
\(261\) 16.8632 + 1.99941i 1.04380 + 0.123760i
\(262\) −5.67316 + 2.89062i −0.350489 + 0.178583i
\(263\) 4.93937 2.51673i 0.304574 0.155188i −0.295023 0.955490i \(-0.595327\pi\)
0.599598 + 0.800302i \(0.295327\pi\)
\(264\) −8.58951 + 0.845099i −0.528648 + 0.0520123i
\(265\) 0 0
\(266\) −7.44718 2.41974i −0.456616 0.148364i
\(267\) −1.96479 0.116073i −0.120243 0.00710354i
\(268\) 4.57707 4.57707i 0.279589 0.279589i
\(269\) 2.80188 + 2.03568i 0.170834 + 0.124118i 0.669917 0.742436i \(-0.266330\pi\)
−0.499083 + 0.866554i \(0.666330\pi\)
\(270\) 0 0
\(271\) −3.81142 + 2.76916i −0.231528 + 0.168215i −0.697500 0.716584i \(-0.745704\pi\)
0.465973 + 0.884799i \(0.345704\pi\)
\(272\) −0.223260 + 1.40961i −0.0135371 + 0.0854701i
\(273\) 9.95623 + 8.17259i 0.602579 + 0.494627i
\(274\) 4.10910i 0.248240i
\(275\) 0 0
\(276\) −0.778423 + 3.54611i −0.0468556 + 0.213450i
\(277\) 11.2980 22.1735i 0.678829 1.33228i −0.252321 0.967644i \(-0.581194\pi\)
0.931151 0.364634i \(-0.118806\pi\)
\(278\) −10.5496 1.67090i −0.632725 0.100214i
\(279\) 3.78568 + 19.0524i 0.226643 + 1.14064i
\(280\) 0 0
\(281\) 5.67900 7.81648i 0.338781 0.466292i −0.605304 0.795994i \(-0.706948\pi\)
0.944085 + 0.329702i \(0.106948\pi\)
\(282\) −4.37078 6.82938i −0.260276 0.406684i
\(283\) −1.00775 + 0.159612i −0.0599044 + 0.00948793i −0.186315 0.982490i \(-0.559654\pi\)
0.126410 + 0.991978i \(0.459654\pi\)
\(284\) −4.65630 + 14.3306i −0.276301 + 0.850366i
\(285\) 0 0
\(286\) 2.72024 + 8.37203i 0.160851 + 0.495049i
\(287\) 7.20945 + 14.1493i 0.425561 + 0.835210i
\(288\) −2.99771 + 0.117162i −0.176642 + 0.00690381i
\(289\) −14.2308 + 4.62387i −0.837106 + 0.271992i
\(290\) 0 0
\(291\) 3.07963 5.25311i 0.180531 0.307943i
\(292\) −1.44635 9.13189i −0.0846412 0.534403i
\(293\) 1.45604 + 1.45604i 0.0850625 + 0.0850625i 0.748358 0.663295i \(-0.230843\pi\)
−0.663295 + 0.748358i \(0.730843\pi\)
\(294\) −12.3349 13.8838i −0.719384 0.809718i
\(295\) 0 0
\(296\) 1.51351 + 2.08317i 0.0879710 + 0.121082i
\(297\) −18.6706 + 17.9403i −1.08338 + 1.04100i
\(298\) −4.57327 2.33020i −0.264922 0.134985i
\(299\) 3.70284 0.214141
\(300\) 0 0
\(301\) −37.2993 −2.14990
\(302\) −17.9372 9.13947i −1.03217 0.525917i
\(303\) −26.8926 10.5288i −1.54494 0.604861i
\(304\) −1.09331 1.50481i −0.0627057 0.0863069i
\(305\) 0 0
\(306\) 2.09128 + 3.73606i 0.119551 + 0.213576i
\(307\) −11.9806 11.9806i −0.683767 0.683767i 0.277080 0.960847i \(-0.410633\pi\)
−0.960847 + 0.277080i \(0.910633\pi\)
\(308\) −3.28166 20.7196i −0.186990 1.18061i
\(309\) 3.96403 + 2.32391i 0.225506 + 0.132203i
\(310\) 0 0
\(311\) −3.64396 + 1.18399i −0.206630 + 0.0671381i −0.410503 0.911859i \(-0.634647\pi\)
0.203873 + 0.978997i \(0.434647\pi\)
\(312\) 0.772255 + 2.96069i 0.0437203 + 0.167616i
\(313\) −10.3817 20.3753i −0.586809 1.15168i −0.973333 0.229398i \(-0.926324\pi\)
0.386523 0.922280i \(-0.373676\pi\)
\(314\) 3.11815 + 9.59669i 0.175968 + 0.541573i
\(315\) 0 0
\(316\) 1.15889 3.56669i 0.0651926 0.200642i
\(317\) 8.64943 1.36994i 0.485800 0.0769432i 0.0912701 0.995826i \(-0.470907\pi\)
0.394530 + 0.918883i \(0.370907\pi\)
\(318\) 7.47063 4.78118i 0.418932 0.268115i
\(319\) −16.5794 + 22.8195i −0.928266 + 1.27765i
\(320\) 0 0
\(321\) −8.19534 18.7414i −0.457419 1.04604i
\(322\) −8.71548 1.38040i −0.485695 0.0769265i
\(323\) −1.20518 + 2.36529i −0.0670578 + 0.131608i
\(324\) −6.84606 + 5.84221i −0.380337 + 0.324567i
\(325\) 0 0
\(326\) 5.62029i 0.311279i
\(327\) 14.6362 17.8305i 0.809383 0.986029i
\(328\) −0.590102 + 3.72576i −0.0325829 + 0.205721i
\(329\) 15.9436 11.5837i 0.878999 0.638630i
\(330\) 0 0
\(331\) 4.85309 + 3.52598i 0.266750 + 0.193805i 0.713118 0.701044i \(-0.247283\pi\)
−0.446367 + 0.894850i \(0.647283\pi\)
\(332\) −11.9305 + 11.9305i −0.654773 + 0.654773i
\(333\) 7.43435 + 2.09836i 0.407400 + 0.114989i
\(334\) −15.9471 5.18154i −0.872588 0.283521i
\(335\) 0 0
\(336\) −0.713952 7.25654i −0.0389493 0.395877i
\(337\) −2.16556 + 1.10341i −0.117965 + 0.0601063i −0.511977 0.858999i \(-0.671087\pi\)
0.394012 + 0.919105i \(0.371087\pi\)
\(338\) −8.80254 + 4.48512i −0.478795 + 0.243958i
\(339\) 0.253814 + 2.57974i 0.0137853 + 0.140112i
\(340\) 0 0
\(341\) −30.6862 9.97055i −1.66175 0.539935i
\(342\) −5.37034 1.51579i −0.290394 0.0819643i
\(343\) 11.0807 11.0807i 0.598299 0.598299i
\(344\) −7.16799 5.20785i −0.386472 0.280788i
\(345\) 0 0
\(346\) −3.62129 + 2.63102i −0.194682 + 0.141445i
\(347\) −3.55504 + 22.4456i −0.190844 + 1.20494i 0.687237 + 0.726433i \(0.258823\pi\)
−0.878082 + 0.478511i \(0.841177\pi\)
\(348\) −6.22047 + 7.57807i −0.333452 + 0.406227i
\(349\) 12.5328i 0.670865i −0.942064 0.335432i \(-0.891118\pi\)
0.942064 0.335432i \(-0.108882\pi\)
\(350\) 0 0
\(351\) 7.31708 + 5.54245i 0.390557 + 0.295834i
\(352\) 2.26228 4.43998i 0.120580 0.236651i
\(353\) 7.05688 + 1.11770i 0.375600 + 0.0594892i 0.341381 0.939925i \(-0.389106\pi\)
0.0342193 + 0.999414i \(0.489106\pi\)
\(354\) 7.72587 + 17.6678i 0.410625 + 0.939031i
\(355\) 0 0
\(356\) 0.667929 0.919325i 0.0354002 0.0487241i
\(357\) −8.76503 + 5.60959i −0.463894 + 0.296891i
\(358\) 0.172313 0.0272918i 0.00910704 0.00144241i
\(359\) −3.28973 + 10.1247i −0.173625 + 0.534363i −0.999568 0.0293907i \(-0.990643\pi\)
0.825943 + 0.563754i \(0.190643\pi\)
\(360\) 0 0
\(361\) 4.80219 + 14.7796i 0.252747 + 0.777875i
\(362\) −5.16520 10.1373i −0.271477 0.532803i
\(363\) −6.04643 23.1809i −0.317355 1.21668i
\(364\) −7.07281 + 2.29810i −0.370716 + 0.120453i
\(365\) 0 0
\(366\) 14.5051 + 8.50359i 0.758193 + 0.444490i
\(367\) 0.656708 + 4.14629i 0.0342799 + 0.216435i 0.998882 0.0472753i \(-0.0150538\pi\)
−0.964602 + 0.263710i \(0.915054\pi\)
\(368\) −1.48216 1.48216i −0.0772630 0.0772630i
\(369\) 5.52749 + 9.87483i 0.287750 + 0.514063i
\(370\) 0 0
\(371\) 12.6714 + 17.4406i 0.657865 + 0.905473i
\(372\) −10.4431 4.08860i −0.541450 0.211984i
\(373\) 4.05536 + 2.06631i 0.209979 + 0.106990i 0.555817 0.831305i \(-0.312405\pi\)
−0.345838 + 0.938294i \(0.612405\pi\)
\(374\) −7.11179 −0.367742
\(375\) 0 0
\(376\) 4.68132 0.241420
\(377\) 8.90954 + 4.53964i 0.458864 + 0.233803i
\(378\) −15.1562 15.7732i −0.779552 0.811284i
\(379\) −19.3891 26.6869i −0.995954 1.37081i −0.927775 0.373139i \(-0.878281\pi\)
−0.0681783 0.997673i \(-0.521719\pi\)
\(380\) 0 0
\(381\) 1.78478 + 2.00890i 0.0914371 + 0.102919i
\(382\) 13.0504 + 13.0504i 0.667715 + 0.667715i
\(383\) 2.67339 + 16.8791i 0.136604 + 0.862482i 0.956873 + 0.290505i \(0.0938233\pi\)
−0.820270 + 0.571977i \(0.806177\pi\)
\(384\) 0.875978 1.49421i 0.0447021 0.0762511i
\(385\) 0 0
\(386\) 4.45958 1.44901i 0.226987 0.0737525i
\(387\) −26.5601 + 1.03807i −1.35012 + 0.0527679i
\(388\) 1.59607 + 3.13246i 0.0810281 + 0.159027i
\(389\) −4.34112 13.3606i −0.220104 0.677409i −0.998752 0.0499484i \(-0.984094\pi\)
0.778648 0.627461i \(-0.215906\pi\)
\(390\) 0 0
\(391\) −0.924425 + 2.84509i −0.0467502 + 0.143882i
\(392\) 10.5904 1.67735i 0.534894 0.0847189i
\(393\) −5.94477 9.28875i −0.299874 0.468556i
\(394\) 7.45354 10.2589i 0.375504 0.516837i
\(395\) 0 0
\(396\) −2.91344 14.6627i −0.146406 0.736826i
\(397\) −3.64376 0.577115i −0.182875 0.0289646i 0.0643251 0.997929i \(-0.479511\pi\)
−0.247200 + 0.968964i \(0.579511\pi\)
\(398\) 0.738199 1.44880i 0.0370026 0.0726216i
\(399\) 2.90798 13.2473i 0.145581 0.663194i
\(400\) 0 0
\(401\) 29.3144i 1.46389i 0.681364 + 0.731945i \(0.261387\pi\)
−0.681364 + 0.731945i \(0.738613\pi\)
\(402\) 8.66586 + 7.11338i 0.432214 + 0.354783i
\(403\) −1.78935 + 11.2975i −0.0891336 + 0.562768i
\(404\) 13.4895 9.80073i 0.671130 0.487604i
\(405\) 0 0
\(406\) −19.2783 14.0065i −0.956764 0.695130i
\(407\) −9.07301 + 9.07301i −0.449732 + 0.449732i
\(408\) −2.46765 0.145780i −0.122167 0.00721718i
\(409\) −7.27469 2.36369i −0.359710 0.116877i 0.123586 0.992334i \(-0.460561\pi\)
−0.483296 + 0.875457i \(0.660561\pi\)
\(410\) 0 0
\(411\) −7.08297 + 0.696875i −0.349377 + 0.0343743i
\(412\) −2.36378 + 1.20440i −0.116455 + 0.0593368i
\(413\) −41.7598 + 21.2777i −2.05487 + 1.04701i
\(414\) −6.24454 0.740395i −0.306902 0.0363884i
\(415\) 0 0
\(416\) −1.68008 0.545893i −0.0823729 0.0267646i
\(417\) 1.09103 18.4681i 0.0534279 0.904385i
\(418\) 6.55405 6.55405i 0.320569 0.320569i
\(419\) 8.86483 + 6.44067i 0.433075 + 0.314648i 0.782877 0.622176i \(-0.213751\pi\)
−0.349802 + 0.936824i \(0.613751\pi\)
\(420\) 0 0
\(421\) −11.3681 + 8.25943i −0.554048 + 0.402540i −0.829276 0.558839i \(-0.811247\pi\)
0.275227 + 0.961379i \(0.411247\pi\)
\(422\) −1.88956 + 11.9302i −0.0919823 + 0.580753i
\(423\) 11.0307 8.69225i 0.536333 0.422632i
\(424\) 5.12087i 0.248692i
\(425\) 0 0
\(426\) −25.4918 5.59582i −1.23508 0.271119i
\(427\) −18.5531 + 36.4125i −0.897848 + 1.76213i
\(428\) 11.6642 + 1.84743i 0.563812 + 0.0892991i
\(429\) −13.9698 + 6.10879i −0.674467 + 0.294935i
\(430\) 0 0
\(431\) 2.55158 3.51195i 0.122905 0.169164i −0.743131 0.669146i \(-0.766660\pi\)
0.866036 + 0.499982i \(0.166660\pi\)
\(432\) −0.710346 5.14737i −0.0341765 0.247653i
\(433\) 7.75206 1.22781i 0.372540 0.0590046i 0.0326428 0.999467i \(-0.489608\pi\)
0.339897 + 0.940463i \(0.389608\pi\)
\(434\) 8.42326 25.9241i 0.404329 1.24440i
\(435\) 0 0
\(436\) 4.11563 + 12.6666i 0.197103 + 0.606621i
\(437\) −1.77004 3.47389i −0.0846723 0.166179i
\(438\) 15.4956 4.04182i 0.740409 0.193126i
\(439\) 19.1294 6.21551i 0.912994 0.296650i 0.185405 0.982662i \(-0.440640\pi\)
0.727590 + 0.686012i \(0.240640\pi\)
\(440\) 0 0
\(441\) 21.8399 23.6165i 1.04000 1.12460i
\(442\) 0.394399 + 2.49014i 0.0187597 + 0.118444i
\(443\) 11.8995 + 11.8995i 0.565363 + 0.565363i 0.930826 0.365463i \(-0.119089\pi\)
−0.365463 + 0.930826i \(0.619089\pi\)
\(444\) −3.33413 + 2.96217i −0.158231 + 0.140578i
\(445\) 0 0
\(446\) 3.65892 + 5.03607i 0.173255 + 0.238465i
\(447\) 3.24103 8.27826i 0.153296 0.391548i
\(448\) 3.75095 + 1.91121i 0.177216 + 0.0902960i
\(449\) −3.55771 −0.167899 −0.0839495 0.996470i \(-0.526753\pi\)
−0.0839495 + 0.996470i \(0.526753\pi\)
\(450\) 0 0
\(451\) −18.7973 −0.885128
\(452\) −1.33349 0.679445i −0.0627219 0.0319584i
\(453\) 12.7119 32.4689i 0.597259 1.52552i
\(454\) −5.38142 7.40689i −0.252563 0.347623i
\(455\) 0 0
\(456\) 2.40847 2.13978i 0.112787 0.100204i
\(457\) −13.4412 13.4412i −0.628754 0.628754i 0.319001 0.947754i \(-0.396653\pi\)
−0.947754 + 0.319001i \(0.896653\pi\)
\(458\) 2.89333 + 18.2678i 0.135196 + 0.853597i
\(459\) −6.08528 + 4.23841i −0.284037 + 0.197832i
\(460\) 0 0
\(461\) −30.4642 + 9.89843i −1.41886 + 0.461016i −0.915240 0.402908i \(-0.867999\pi\)
−0.503621 + 0.863925i \(0.667999\pi\)
\(462\) 35.1583 9.17058i 1.63571 0.426654i
\(463\) −1.40792 2.76320i −0.0654317 0.128417i 0.855974 0.517019i \(-0.172958\pi\)
−0.921406 + 0.388602i \(0.872958\pi\)
\(464\) −1.74917 5.38339i −0.0812031 0.249918i
\(465\) 0 0
\(466\) −4.25650 + 13.1002i −0.197179 + 0.606853i
\(467\) −39.1577 + 6.20197i −1.81200 + 0.286993i −0.968295 0.249811i \(-0.919632\pi\)
−0.843707 + 0.536804i \(0.819632\pi\)
\(468\) −4.97245 + 1.83327i −0.229852 + 0.0847429i
\(469\) −16.0170 + 22.0455i −0.739598 + 1.01797i
\(470\) 0 0
\(471\) −16.0133 + 7.00238i −0.737852 + 0.322653i
\(472\) −10.9960 1.74160i −0.506134 0.0801638i
\(473\) 20.0441 39.3387i 0.921628 1.80880i
\(474\) 6.34454 + 1.39272i 0.291415 + 0.0639698i
\(475\) 0 0
\(476\) 6.00814i 0.275383i
\(477\) 9.50842 + 12.0665i 0.435361 + 0.552486i
\(478\) −3.24367 + 20.4797i −0.148362 + 0.936721i
\(479\) −10.9031 + 7.92157i −0.498176 + 0.361946i −0.808320 0.588744i \(-0.799623\pi\)
0.310144 + 0.950690i \(0.399623\pi\)
\(480\) 0 0
\(481\) 3.68001 + 2.67368i 0.167794 + 0.121910i
\(482\) 4.39969 4.39969i 0.200400 0.200400i
\(483\) 0.901343 15.2572i 0.0410125 0.694227i
\(484\) 13.1543 + 4.27411i 0.597925 + 0.194278i
\(485\) 0 0
\(486\) −11.2314 10.8100i −0.509468 0.490349i
\(487\) −1.85919 + 0.947305i −0.0842480 + 0.0429265i −0.495607 0.868547i \(-0.665054\pi\)
0.411359 + 0.911473i \(0.365054\pi\)
\(488\) −8.64948 + 4.40713i −0.391543 + 0.199501i
\(489\) 9.68785 0.953162i 0.438100 0.0431035i
\(490\) 0 0
\(491\) 15.8067 + 5.13592i 0.713348 + 0.231781i 0.643137 0.765751i \(-0.277633\pi\)
0.0702111 + 0.997532i \(0.477633\pi\)
\(492\) −6.52227 0.385313i −0.294047 0.0173712i
\(493\) −5.71233 + 5.71233i −0.257270 + 0.257270i
\(494\) −2.65832 1.93138i −0.119604 0.0868970i
\(495\) 0 0
\(496\) 5.23835 3.80588i 0.235209 0.170889i
\(497\) 9.92321 62.6527i 0.445117 2.81036i
\(498\) −22.5883 18.5416i −1.01221 0.830871i
\(499\) 36.0457i 1.61363i 0.590806 + 0.806813i \(0.298810\pi\)
−0.590806 + 0.806813i \(0.701190\pi\)
\(500\) 0 0
\(501\) 6.22704 28.3673i 0.278203 1.26736i
\(502\) 1.71107 3.35817i 0.0763689 0.149882i
\(503\) 31.1126 + 4.92776i 1.38724 + 0.219718i 0.804990 0.593289i \(-0.202171\pi\)
0.582255 + 0.813007i \(0.302171\pi\)
\(504\) 12.3872 2.46132i 0.551771 0.109636i
\(505\) 0 0
\(506\) 6.13944 8.45021i 0.272931 0.375658i
\(507\) −9.22397 14.4125i −0.409651 0.640083i
\(508\) −1.53236 + 0.242702i −0.0679876 + 0.0107682i
\(509\) 0.189892 0.584428i 0.00841683 0.0259043i −0.946760 0.321941i \(-0.895665\pi\)
0.955177 + 0.296036i \(0.0956649\pi\)
\(510\) 0 0
\(511\) 12.0277 + 37.0176i 0.532076 + 1.63756i
\(512\) 0.453990 + 0.891007i 0.0200637 + 0.0393773i
\(513\) 1.70203 9.51406i 0.0751465 0.420056i
\(514\) −29.2797 + 9.51354i −1.29147 + 0.419624i
\(515\) 0 0
\(516\) 7.76127 13.2389i 0.341671 0.582809i
\(517\) 3.64922 + 23.0403i 0.160493 + 1.01331i
\(518\) −7.66501 7.66501i −0.336781 0.336781i
\(519\) −5.14932 5.79592i −0.226030 0.254413i
\(520\) 0 0
\(521\) 19.3712 + 26.6622i 0.848668 + 1.16809i 0.984155 + 0.177312i \(0.0567401\pi\)
−0.135487 + 0.990779i \(0.543260\pi\)
\(522\) −14.1175 9.43721i −0.617905 0.413055i
\(523\) 35.5580 + 18.1177i 1.55484 + 0.792232i 0.999231 0.0392100i \(-0.0124841\pi\)
0.555612 + 0.831442i \(0.312484\pi\)
\(524\) 6.36713 0.278150
\(525\) 0 0
\(526\) −5.54358 −0.241712
\(527\) −8.23373 4.19530i −0.358667 0.182750i
\(528\) 8.03698 + 3.14657i 0.349765 + 0.136937i
\(529\) 10.9366 + 15.0529i 0.475503 + 0.654474i
\(530\) 0 0
\(531\) −29.1442 + 16.3136i −1.26475 + 0.707951i
\(532\) 5.53695 + 5.53695i 0.240057 + 0.240057i
\(533\) 1.04244 + 6.58172i 0.0451532 + 0.285086i
\(534\) 1.69794 + 0.995416i 0.0734771 + 0.0430759i
\(535\) 0 0
\(536\) −6.15614 + 2.00025i −0.265905 + 0.0863977i
\(537\) 0.0762667 + 0.292393i 0.00329115 + 0.0126177i
\(538\) −1.57231 3.08583i −0.0677872 0.133040i
\(539\) 16.5110 + 50.8156i 0.711178 + 2.18878i
\(540\) 0 0
\(541\) 7.82078 24.0699i 0.336242 1.03485i −0.629865 0.776704i \(-0.716890\pi\)
0.966107 0.258141i \(-0.0831100\pi\)
\(542\) 4.65318 0.736991i 0.199871 0.0316565i
\(543\) 16.5979 10.6226i 0.712285 0.455860i
\(544\) 0.838876 1.15461i 0.0359665 0.0495036i
\(545\) 0 0
\(546\) −5.16079 11.8019i −0.220861 0.505073i
\(547\) 40.6790 + 6.44292i 1.73931 + 0.275479i 0.943812 0.330482i \(-0.107211\pi\)
0.795495 + 0.605961i \(0.207211\pi\)
\(548\) 1.86549 3.66124i 0.0796899 0.156400i
\(549\) −12.1979 + 26.4450i −0.520594 + 1.12864i
\(550\) 0 0
\(551\) 10.5287i 0.448537i
\(552\) 2.30348 2.80621i 0.0980425 0.119440i
\(553\) −2.46975 + 15.5934i −0.105024 + 0.663098i
\(554\) −20.1331 + 14.6276i −0.855375 + 0.621466i
\(555\) 0 0
\(556\) 8.64122 + 6.27821i 0.366469 + 0.266256i
\(557\) −17.7694 + 17.7694i −0.752915 + 0.752915i −0.975022 0.222107i \(-0.928707\pi\)
0.222107 + 0.975022i \(0.428707\pi\)
\(558\) 5.27655 18.6945i 0.223374 0.791400i
\(559\) −14.8858 4.83667i −0.629600 0.204570i
\(560\) 0 0
\(561\) −1.20611 12.2588i −0.0509220 0.517566i
\(562\) −8.60864 + 4.38632i −0.363133 + 0.185026i
\(563\) −9.23868 + 4.70734i −0.389364 + 0.198391i −0.637703 0.770282i \(-0.720115\pi\)
0.248339 + 0.968673i \(0.420115\pi\)
\(564\) 0.793919 + 8.06931i 0.0334300 + 0.339779i
\(565\) 0 0
\(566\) 0.970373 + 0.315293i 0.0407878 + 0.0132528i
\(567\) 24.6183 28.8002i 1.03387 1.20950i
\(568\) 10.6548 10.6548i 0.447064 0.447064i
\(569\) 15.6879 + 11.3979i 0.657671 + 0.477826i 0.865876 0.500259i \(-0.166762\pi\)
−0.208205 + 0.978085i \(0.566762\pi\)
\(570\) 0 0
\(571\) 14.7088 10.6866i 0.615544 0.447219i −0.235818 0.971797i \(-0.575777\pi\)
0.851362 + 0.524579i \(0.175777\pi\)
\(572\) 1.37707 8.69450i 0.0575783 0.363535i
\(573\) −20.2820 + 24.7086i −0.847295 + 1.03221i
\(574\) 15.8802i 0.662826i
\(575\) 0 0
\(576\) 2.72417 + 1.25654i 0.113507 + 0.0523559i
\(577\) 2.69918 5.29743i 0.112368 0.220535i −0.827973 0.560768i \(-0.810506\pi\)
0.940341 + 0.340233i \(0.110506\pi\)
\(578\) 14.7789 + 2.34075i 0.614723 + 0.0973625i
\(579\) 3.25401 + 7.44137i 0.135232 + 0.309253i
\(580\) 0 0
\(581\) 41.7498 57.4636i 1.73207 2.38399i
\(582\) −5.12883 + 3.28243i −0.212597 + 0.136061i
\(583\) −25.2037 + 3.99187i −1.04383 + 0.165326i
\(584\) −2.85708 + 8.79320i −0.118227 + 0.363865i
\(585\) 0 0
\(586\) −0.636311 1.95836i −0.0262858 0.0808992i
\(587\) 11.8794 + 23.3146i 0.490314 + 0.962295i 0.995083 + 0.0990406i \(0.0315774\pi\)
−0.504770 + 0.863254i \(0.668423\pi\)
\(588\) 4.68734 + 17.9704i 0.193303 + 0.741088i
\(589\) 11.4543 3.72172i 0.471966 0.153351i
\(590\) 0 0
\(591\) 18.9476 + 11.1080i 0.779402 + 0.456923i
\(592\) −0.402809 2.54323i −0.0165553 0.104526i
\(593\) −23.6228 23.6228i −0.970072 0.970072i 0.0294930 0.999565i \(-0.490611\pi\)
−0.999565 + 0.0294930i \(0.990611\pi\)
\(594\) 24.7803 7.50867i 1.01675 0.308084i
\(595\) 0 0
\(596\) 3.01693 + 4.15244i 0.123578 + 0.170091i
\(597\) 2.62253 + 1.02675i 0.107333 + 0.0420220i
\(598\) −3.29926 1.68106i −0.134917 0.0687435i
\(599\) −7.73976 −0.316238 −0.158119 0.987420i \(-0.550543\pi\)
−0.158119 + 0.987420i \(0.550543\pi\)
\(600\) 0 0
\(601\) −16.7407 −0.682866 −0.341433 0.939906i \(-0.610912\pi\)
−0.341433 + 0.939906i \(0.610912\pi\)
\(602\) 33.2339 + 16.9335i 1.35451 + 0.690159i
\(603\) −10.7919 + 16.1440i −0.439479 + 0.657433i
\(604\) 11.8329 + 16.2867i 0.481476 + 0.662695i
\(605\) 0 0
\(606\) 19.1815 + 21.5902i 0.779196 + 0.877041i
\(607\) 22.6982 + 22.6982i 0.921293 + 0.921293i 0.997121 0.0758281i \(-0.0241600\pi\)
−0.0758281 + 0.997121i \(0.524160\pi\)
\(608\) 0.290976 + 1.83715i 0.0118006 + 0.0745063i
\(609\) 20.8739 35.6059i 0.845853 1.44282i
\(610\) 0 0
\(611\) 7.86501 2.55550i 0.318184 0.103384i
\(612\) −0.167211 4.27828i −0.00675909 0.172939i
\(613\) 19.6701 + 38.6048i 0.794470 + 1.55923i 0.828616 + 0.559818i \(0.189129\pi\)
−0.0341460 + 0.999417i \(0.510871\pi\)
\(614\) 5.23570 + 16.1138i 0.211296 + 0.650301i
\(615\) 0 0
\(616\) −6.48251 + 19.9511i −0.261188 + 0.803853i
\(617\) 24.0808 3.81403i 0.969458 0.153547i 0.348429 0.937335i \(-0.386715\pi\)
0.621028 + 0.783788i \(0.286715\pi\)
\(618\) −2.47695 3.87025i −0.0996374 0.155684i
\(619\) 23.7633 32.7074i 0.955130 1.31462i 0.00591868 0.999982i \(-0.498116\pi\)
0.949211 0.314641i \(-0.101884\pi\)
\(620\) 0 0
\(621\) 0.217209 10.8894i 0.00871630 0.436978i
\(622\) 3.78431 + 0.599376i 0.151737 + 0.0240328i
\(623\) −2.17180 + 4.26239i −0.0870112 + 0.170769i
\(624\) 0.656040 2.98859i 0.0262626 0.119639i
\(625\) 0 0
\(626\) 22.8677i 0.913977i
\(627\) 12.4089 + 10.1859i 0.495564 + 0.406785i
\(628\) 1.57851 9.96632i 0.0629894 0.397700i
\(629\) −2.97306 + 2.16005i −0.118544 + 0.0861269i
\(630\) 0 0
\(631\) −19.6592 14.2832i −0.782619 0.568606i 0.123145 0.992389i \(-0.460702\pi\)
−0.905764 + 0.423783i \(0.860702\pi\)
\(632\) −2.65182 + 2.65182i −0.105484 + 0.105484i
\(633\) −20.8849 1.23381i −0.830100 0.0490394i
\(634\) −8.32864 2.70614i −0.330772 0.107474i
\(635\) 0 0
\(636\) −8.82699 + 0.868465i −0.350013 + 0.0344369i
\(637\) 16.8771 8.59929i 0.668693 0.340716i
\(638\) 25.1322 12.8055i 0.994992 0.506974i
\(639\) 5.32245 44.8899i 0.210553 1.77582i
\(640\) 0 0
\(641\) 8.76326 + 2.84736i 0.346128 + 0.112464i 0.476922 0.878946i \(-0.341753\pi\)
−0.130794 + 0.991410i \(0.541753\pi\)
\(642\) −1.20630 + 20.4193i −0.0476089 + 0.805885i
\(643\) −32.6751 + 32.6751i −1.28858 + 1.28858i −0.352932 + 0.935649i \(0.614815\pi\)
−0.935649 + 0.352932i \(0.885185\pi\)
\(644\) 7.13886 + 5.18669i 0.281311 + 0.204384i
\(645\) 0 0
\(646\) 2.14764 1.56035i 0.0844978 0.0613912i
\(647\) 7.60579 48.0211i 0.299015 1.88790i −0.141152 0.989988i \(-0.545081\pi\)
0.440167 0.897916i \(-0.354919\pi\)
\(648\) 8.75219 2.09740i 0.343819 0.0823937i
\(649\) 55.4774i 2.17768i
\(650\) 0 0
\(651\) 46.1147 + 10.1229i 1.80738 + 0.396746i
\(652\) −2.55156 + 5.00771i −0.0999267 + 0.196117i
\(653\) −19.6349 3.10987i −0.768375 0.121699i −0.240073 0.970755i \(-0.577171\pi\)
−0.528302 + 0.849056i \(0.677171\pi\)
\(654\) −21.1358 + 9.24240i −0.826476 + 0.361407i
\(655\) 0 0
\(656\) 2.21724 3.05177i 0.0865688 0.119152i
\(657\) 9.59494 + 26.0247i 0.374334 + 1.01532i
\(658\) −19.4647 + 3.08291i −0.758815 + 0.120184i
\(659\) 9.29483 28.6066i 0.362075 1.11435i −0.589717 0.807610i \(-0.700761\pi\)
0.951792 0.306743i \(-0.0992393\pi\)
\(660\) 0 0
\(661\) −4.51392 13.8924i −0.175571 0.540352i 0.824088 0.566462i \(-0.191688\pi\)
−0.999659 + 0.0261096i \(0.991688\pi\)
\(662\) −2.72338 5.34493i −0.105847 0.207736i
\(663\) −4.22544 + 1.10215i −0.164102 + 0.0428039i
\(664\) 16.0465 5.21383i 0.622726 0.202336i
\(665\) 0 0
\(666\) −5.67142 5.24478i −0.219763 0.203231i
\(667\) −1.85606 11.7187i −0.0718670 0.453750i
\(668\) 11.8566 + 11.8566i 0.458747 + 0.458747i
\(669\) −8.06029 + 7.16107i −0.311629 + 0.276863i
\(670\) 0 0
\(671\) −28.4333 39.1351i −1.09766 1.51079i
\(672\) −2.65826 + 6.78975i −0.102545 + 0.261920i
\(673\) −30.1630 15.3688i −1.16270 0.592425i −0.237306 0.971435i \(-0.576264\pi\)
−0.925392 + 0.379010i \(0.876264\pi\)
\(674\) 2.43046 0.0936178
\(675\) 0 0
\(676\) 9.87932 0.379974
\(677\) −6.85459 3.49259i −0.263443 0.134231i 0.317280 0.948332i \(-0.397230\pi\)
−0.580724 + 0.814101i \(0.697230\pi\)
\(678\) 0.945029 2.41380i 0.0362936 0.0927013i
\(679\) −8.69931 11.9736i −0.333849 0.459503i
\(680\) 0 0
\(681\) 11.8548 10.5323i 0.454278 0.403597i
\(682\) 22.8151 + 22.8151i 0.873634 + 0.873634i
\(683\) −0.454547 2.86990i −0.0173928 0.109814i 0.977465 0.211099i \(-0.0677043\pi\)
−0.994857 + 0.101286i \(0.967704\pi\)
\(684\) 4.09685 + 3.78866i 0.156647 + 0.144863i
\(685\) 0 0
\(686\) −14.9035 + 4.84242i −0.569016 + 0.184885i
\(687\) −30.9980 + 8.08540i −1.18265 + 0.308477i
\(688\) 4.02241 + 7.89443i 0.153353 + 0.300972i
\(689\) 2.79545 + 8.60350i 0.106498 + 0.327767i
\(690\) 0 0
\(691\) −9.12811 + 28.0934i −0.347249 + 1.06872i 0.613119 + 0.789991i \(0.289915\pi\)
−0.960368 + 0.278733i \(0.910085\pi\)
\(692\) 4.42106 0.700227i 0.168063 0.0266186i
\(693\) 21.7702 + 59.0481i 0.826981 + 2.24305i
\(694\) 13.3577 18.3852i 0.507050 0.697894i
\(695\) 0 0
\(696\) 8.98285 3.92808i 0.340494 0.148893i
\(697\) −5.31733 0.842182i −0.201408 0.0318999i
\(698\) −5.68977 + 11.1668i −0.215361 + 0.422670i
\(699\) −23.3030 5.11535i −0.881400 0.193480i
\(700\) 0 0
\(701\) 41.1646i 1.55476i 0.629028 + 0.777382i \(0.283453\pi\)
−0.629028 + 0.777382i \(0.716547\pi\)
\(702\) −4.00335 8.26024i −0.151097 0.311763i
\(703\) 0.749245 4.73055i 0.0282583 0.178416i
\(704\) −4.03141 + 2.92899i −0.151940 + 0.110391i
\(705\) 0 0
\(706\) −5.78030 4.19963i −0.217544 0.158055i
\(707\) −49.6347 + 49.6347i −1.86671 + 1.86671i
\(708\) 1.13720 19.2496i 0.0427385 0.723443i
\(709\) −16.1533 5.24852i −0.606650 0.197112i −0.0104457 0.999945i \(-0.503325\pi\)
−0.596204 + 0.802833i \(0.703325\pi\)
\(710\) 0 0
\(711\) −1.32468 + 11.1725i −0.0496795 + 0.419000i
\(712\) −1.01249 + 0.515891i −0.0379448 + 0.0193338i
\(713\) 12.0928 6.16161i 0.452880 0.230754i
\(714\) 10.3564 1.01894i 0.387578 0.0381328i
\(715\) 0 0
\(716\) −0.165923 0.0539115i −0.00620082 0.00201477i
\(717\) −35.8516 2.11799i −1.33890 0.0790976i
\(718\) 7.52770 7.52770i 0.280931 0.280931i
\(719\) −17.4118 12.6504i −0.649349 0.471780i 0.213700 0.976899i \(-0.431448\pi\)
−0.863049 + 0.505120i \(0.831448\pi\)
\(720\) 0 0
\(721\) 9.03534 6.56456i 0.336493 0.244477i
\(722\) 2.43102 15.3489i 0.0904734 0.571226i
\(723\) 8.33003 + 6.83771i 0.309797 + 0.254297i
\(724\) 11.3773i 0.422835i
\(725\) 0 0
\(726\) −5.13651 + 23.3994i −0.190634 + 0.868432i
\(727\) 15.5168 30.4534i 0.575485 1.12945i −0.401443 0.915884i \(-0.631491\pi\)
0.976928 0.213569i \(-0.0685088\pi\)
\(728\) 7.34523 + 1.16337i 0.272233 + 0.0431174i
\(729\) 16.7286 21.1932i 0.619579 0.784934i
\(730\) 0 0
\(731\) 7.43254 10.2300i 0.274902 0.378371i
\(732\) −9.06358 14.1619i −0.335000 0.523440i
\(733\) 18.4191 2.91730i 0.680326 0.107753i 0.193299 0.981140i \(-0.438081\pi\)
0.487027 + 0.873387i \(0.338081\pi\)
\(734\) 1.29725 3.99251i 0.0478822 0.147366i
\(735\) 0 0
\(736\) 0.647728 + 1.99350i 0.0238756 + 0.0734815i
\(737\) −14.6436 28.7397i −0.539405 1.05864i
\(738\) −0.441957 11.3080i −0.0162687 0.416252i
\(739\) 1.28835 0.418609i 0.0473926 0.0153988i −0.285225 0.958461i \(-0.592068\pi\)
0.332617 + 0.943062i \(0.392068\pi\)
\(740\) 0 0
\(741\) 2.87835 4.90977i 0.105739 0.180365i
\(742\) −3.37239 21.2924i −0.123804 0.781669i
\(743\) −8.68111 8.68111i −0.318479 0.318479i 0.529704 0.848183i \(-0.322303\pi\)
−0.848183 + 0.529704i \(0.822303\pi\)
\(744\) 7.44870 + 8.38404i 0.273082 + 0.307374i
\(745\) 0 0
\(746\) −2.67527 3.68219i −0.0979486 0.134815i
\(747\) 28.1299 42.0806i 1.02922 1.53965i
\(748\) 6.33665 + 3.22868i 0.231691 + 0.118052i
\(749\) −49.7161 −1.81659
\(750\) 0 0
\(751\) 40.0140 1.46013 0.730066 0.683377i \(-0.239489\pi\)
0.730066 + 0.683377i \(0.239489\pi\)
\(752\) −4.17108 2.12527i −0.152104 0.0775007i
\(753\) 6.07875 + 2.37990i 0.221522 + 0.0867284i
\(754\) −5.87750 8.08969i −0.214046 0.294609i
\(755\) 0 0
\(756\) 6.34343 + 20.9348i 0.230708 + 0.761391i
\(757\) 23.3400 + 23.3400i 0.848305 + 0.848305i 0.989922 0.141616i \(-0.0452299\pi\)
−0.141616 + 0.989922i \(0.545230\pi\)
\(758\) 5.16027 + 32.5807i 0.187429 + 1.18338i
\(759\) 15.6071 + 9.14963i 0.566501 + 0.332110i
\(760\) 0 0
\(761\) −6.88486 + 2.23703i −0.249576 + 0.0810921i −0.431133 0.902288i \(-0.641886\pi\)
0.181558 + 0.983380i \(0.441886\pi\)
\(762\) −0.678231 2.60021i −0.0245697 0.0941958i
\(763\) −25.4544 49.9570i −0.921509 1.80856i
\(764\) −5.70322 17.5527i −0.206335 0.635035i
\(765\) 0 0
\(766\) 5.28095 16.2531i 0.190808 0.587248i
\(767\) −19.4250 + 3.07662i −0.701397 + 0.111090i
\(768\) −1.45886 + 0.933665i −0.0526420 + 0.0336907i
\(769\) 2.15066 2.96013i 0.0775549 0.106745i −0.768477 0.639877i \(-0.778985\pi\)
0.846032 + 0.533132i \(0.178985\pi\)
\(770\) 0 0
\(771\) −21.3644 48.8568i −0.769420 1.75953i
\(772\) −4.63135 0.733534i −0.166686 0.0264005i
\(773\) −15.0283 + 29.4947i −0.540531 + 1.06085i 0.445655 + 0.895205i \(0.352971\pi\)
−0.986185 + 0.165646i \(0.947029\pi\)
\(774\) 24.1365 + 11.1331i 0.867568 + 0.400171i
\(775\) 0 0
\(776\) 3.51564i 0.126204i
\(777\) 11.9125 14.5123i 0.427357 0.520626i
\(778\) −2.19762 + 13.8752i −0.0787884 + 0.497450i
\(779\) 5.67645 4.12419i 0.203380 0.147764i
\(780\) 0 0
\(781\) 60.7458 + 44.1344i 2.17366 + 1.57925i
\(782\) 2.11531 2.11531i 0.0756434 0.0756434i