Properties

Label 750.2.l.b.143.1
Level $750$
Weight $2$
Character 750.143
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 143.1
Character \(\chi\) \(=\) 750.143
Dual form 750.2.l.b.257.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.453990 + 0.891007i) q^{2} +(-1.72904 + 0.102145i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(0.693954 - 1.58696i) q^{6} +(2.97677 - 2.97677i) q^{7} +(0.987688 - 0.156434i) q^{8} +(2.97913 - 0.353226i) q^{9} +O(q^{10})\) \(q+(-0.453990 + 0.891007i) q^{2} +(-1.72904 + 0.102145i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(0.693954 - 1.58696i) q^{6} +(2.97677 - 2.97677i) q^{7} +(0.987688 - 0.156434i) q^{8} +(2.97913 - 0.353226i) q^{9} +(-4.73921 + 1.53986i) q^{11} +(1.09894 + 1.33878i) q^{12} +(-1.57400 + 0.801995i) q^{13} +(1.30090 + 4.00375i) q^{14} +(-0.309017 + 0.951057i) q^{16} +(-0.223260 - 1.40961i) q^{17} +(-1.03777 + 2.81479i) q^{18} +(1.09331 - 1.50481i) q^{19} +(-4.84289 + 5.45101i) q^{21} +(0.779529 - 4.92175i) q^{22} +(-1.86763 - 0.951606i) q^{23} +(-1.69177 + 0.371369i) q^{24} -1.76655i q^{26} +(-5.11495 + 0.915046i) q^{27} +(-4.15797 - 0.658557i) q^{28} +(-4.57938 + 3.32712i) q^{29} +(-5.23835 - 3.80588i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(8.03698 - 3.14657i) q^{33} +(1.35733 + 0.441023i) q^{34} +(-2.03686 - 2.20255i) q^{36} +(-1.16900 - 2.29429i) q^{37} +(0.844446 + 1.65732i) q^{38} +(2.63959 - 1.54746i) q^{39} +(3.58757 + 1.16567i) q^{41} +(-2.65826 - 6.78975i) q^{42} +(-6.26505 - 6.26505i) q^{43} +(4.03141 + 2.92899i) q^{44} +(1.69577 - 1.23205i) q^{46} +(4.62368 + 0.732319i) q^{47} +(0.437156 - 1.67598i) q^{48} -10.7224i q^{49} +(0.530010 + 2.41446i) q^{51} +(1.57400 + 0.801995i) q^{52} +(0.801081 - 5.05783i) q^{53} +(1.50683 - 4.97287i) q^{54} +(2.47446 - 3.40580i) q^{56} +(-1.73666 + 2.71355i) q^{57} +(-0.885486 - 5.59074i) q^{58} +(3.44032 - 10.5882i) q^{59} +(-2.99979 - 9.23241i) q^{61} +(5.76923 - 2.93957i) q^{62} +(7.81673 - 9.91968i) q^{63} +(0.951057 - 0.309017i) q^{64} +(-0.845099 + 8.58951i) q^{66} +(6.39326 - 1.01259i) q^{67} +(-1.00917 + 1.00917i) q^{68} +(3.32641 + 1.45459i) q^{69} +(-8.85681 - 12.1904i) q^{71} +(2.88720 - 0.814916i) q^{72} +(-4.19747 + 8.23800i) q^{73} +2.57494 q^{74} -1.86005 q^{76} +(-9.52374 + 18.6914i) q^{77} +(0.180445 + 3.05442i) q^{78} +(2.20434 + 3.03401i) q^{79} +(8.75046 - 2.10462i) q^{81} +(-2.66735 + 2.66735i) q^{82} +(-16.6646 + 2.63941i) q^{83} +(7.25654 + 0.713952i) q^{84} +(8.42648 - 2.73793i) q^{86} +(7.57807 - 6.22047i) q^{87} +(-4.43998 + 2.26228i) q^{88} +(-0.351151 - 1.08073i) q^{89} +(-2.29810 + 7.07281i) q^{91} +(0.327901 + 2.07029i) q^{92} +(9.44605 + 6.04544i) q^{93} +(-2.75161 + 3.78726i) q^{94} +(1.29484 + 1.15039i) q^{96} +(-0.549968 + 3.47236i) q^{97} +(9.55370 + 4.86785i) q^{98} +(-13.5748 + 6.26147i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q - 4q^{3} - 4q^{7} + O(q^{10}) \) \( 80q - 4q^{3} - 4q^{7} + 4q^{12} + 20q^{16} + 8q^{18} - 40q^{19} + 36q^{22} - 4q^{27} + 16q^{28} - 4q^{33} - 40q^{34} + 24q^{37} - 40q^{39} + 4q^{42} + 24q^{43} + 4q^{48} + 64q^{57} - 20q^{58} - 64q^{63} - 96q^{67} + 140q^{69} - 8q^{72} - 100q^{73} - 100q^{78} + 80q^{79} - 40q^{81} - 96q^{82} + 60q^{84} - 80q^{87} - 4q^{88} - 12q^{93} + 32q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(127\) \(251\)
\(\chi(n)\) \(e\left(\frac{3}{20}\right)\) \(-1\)

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:
<
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.453990 + 0.891007i −0.321020 + 0.630037i
\(3\) −1.72904 + 0.102145i −0.998260 + 0.0589737i
\(4\) −0.587785 0.809017i −0.293893 0.404508i
\(5\) 0 0
\(6\) 0.693954 1.58696i 0.283305 0.647872i
\(7\) 2.97677 2.97677i 1.12511 1.12511i 0.134155 0.990960i \(-0.457168\pi\)
0.990960 0.134155i \(-0.0428318\pi\)
\(8\) 0.987688 0.156434i 0.349201 0.0553079i
\(9\) 2.97913 0.353226i 0.993044 0.117742i
\(10\) 0 0
\(11\) −4.73921 + 1.53986i −1.42893 + 0.464286i −0.918426 0.395592i \(-0.870539\pi\)
−0.510499 + 0.859878i \(0.670539\pi\)
\(12\) 1.09894 + 1.33878i 0.317236 + 0.386473i
\(13\) −1.57400 + 0.801995i −0.436550 + 0.222433i −0.658432 0.752640i \(-0.728780\pi\)
0.221882 + 0.975074i \(0.428780\pi\)
\(14\) 1.30090 + 4.00375i 0.347680 + 1.07005i
\(15\) 0 0
\(16\) −0.309017 + 0.951057i −0.0772542 + 0.237764i
\(17\) −0.223260 1.40961i −0.0541486 0.341881i −0.999858 0.0168665i \(-0.994631\pi\)
0.945709 0.325014i \(-0.105369\pi\)
\(18\) −1.03777 + 2.81479i −0.244605 + 0.663452i
\(19\) 1.09331 1.50481i 0.250823 0.345228i −0.664977 0.746864i \(-0.731558\pi\)
0.915799 + 0.401636i \(0.131558\pi\)
\(20\) 0 0
\(21\) −4.84289 + 5.45101i −1.05680 + 1.18951i
\(22\) 0.779529 4.92175i 0.166196 1.04932i
\(23\) −1.86763 0.951606i −0.389428 0.198424i 0.248303 0.968682i \(-0.420127\pi\)
−0.637731 + 0.770259i \(0.720127\pi\)
\(24\) −1.69177 + 0.371369i −0.345331 + 0.0758053i
\(25\) 0 0
\(26\) 1.76655i 0.346448i
\(27\) −5.11495 + 0.915046i −0.984372 + 0.176101i
\(28\) −4.15797 0.658557i −0.785782 0.124456i
\(29\) −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
\(33\) 8.03698 3.14657i 1.39906 0.547747i
\(34\) 1.35733 + 0.441023i 0.232780 + 0.0756348i
\(35\) 0 0
\(36\) −2.03686 2.20255i −0.339476 0.367091i
\(37\) −1.16900 2.29429i −0.192182 0.377178i 0.774729 0.632294i \(-0.217886\pi\)
−0.966911 + 0.255116i \(0.917886\pi\)
\(38\) 0.844446 + 1.65732i 0.136987 + 0.268852i
\(39\) 2.63959 1.54746i 0.422673 0.247791i
\(40\) 0 0
\(41\) 3.58757 + 1.16567i 0.560285 + 0.182048i 0.575449 0.817837i \(-0.304827\pi\)
−0.0151644 + 0.999885i \(0.504827\pi\)
\(42\) −2.65826 6.78975i −0.410179 1.04768i
\(43\) −6.26505 6.26505i −0.955411 0.955411i 0.0436361 0.999047i \(-0.486106\pi\)
−0.999047 + 0.0436361i \(0.986106\pi\)
\(44\) 4.03141 + 2.92899i 0.607758 + 0.441562i
\(45\) 0 0
\(46\) 1.69577 1.23205i 0.250028 0.181656i
\(47\) 4.62368 + 0.732319i 0.674433 + 0.106820i 0.484251 0.874929i \(-0.339092\pi\)
0.190182 + 0.981749i \(0.439092\pi\)
\(48\) 0.437156 1.67598i 0.0630980 0.241906i
\(49\) 10.7224i 1.53177i
\(50\) 0 0
\(51\) 0.530010 + 2.41446i 0.0742163 + 0.338092i
\(52\) 1.57400 + 0.801995i 0.218275 + 0.111217i
\(53\) 0.801081 5.05783i 0.110037 0.694746i −0.869568 0.493813i \(-0.835603\pi\)
0.979605 0.200933i \(-0.0643973\pi\)
\(54\) 1.50683 4.97287i 0.205053 0.676722i
\(55\) 0 0
\(56\) 2.47446 3.40580i 0.330663 0.455119i
\(57\) −1.73666 + 2.71355i −0.230027 + 0.359419i
\(58\) −0.885486 5.59074i −0.116270 0.734100i
\(59\) 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 \(-0.313461\pi\)
\(62\) 5.76923 2.93957i 0.732693 0.373326i
\(63\) 7.81673 9.91968i 0.984816 1.24976i
\(64\) 0.951057 0.309017i 0.118882 0.0386271i
\(65\) 0 0
\(66\) −0.845099 + 8.58951i −0.104025 + 1.05730i
\(67\) 6.39326 1.01259i 0.781061 0.123708i 0.246844 0.969055i \(-0.420607\pi\)
0.534217 + 0.845347i \(0.320607\pi\)
\(68\) −1.00917 + 1.00917i −0.122380 + 0.122380i
\(69\) 3.32641 + 1.45459i 0.400452 + 0.175112i
\(70\) 0 0
\(71\) −8.85681 12.1904i −1.05111 1.44673i −0.887842 0.460147i \(-0.847797\pi\)
−0.163268 0.986582i \(-0.552203\pi\)
\(72\) 2.88720 0.814916i 0.340260 0.0960388i
\(73\) −4.19747 + 8.23800i −0.491277 + 0.964185i 0.503681 + 0.863890i \(0.331979\pi\)
−0.994958 + 0.100295i \(0.968021\pi\)
\(74\) 2.57494 0.299330
\(75\) 0 0
\(76\) −1.86005 −0.213363
\(77\) −9.52374 + 18.6914i −1.08533 + 2.13008i
\(78\) 0.180445 + 3.05442i 0.0204313 + 0.345845i
\(79\) 2.20434 + 3.03401i 0.248007 + 0.341353i 0.914812 0.403880i \(-0.132339\pi\)
−0.666805 + 0.745232i \(0.732339\pi\)
\(80\) 0 0
\(81\) 8.75046 2.10462i 0.972274 0.233846i
\(82\) −2.66735 + 2.66735i −0.294559 + 0.294559i
\(83\) −16.6646 + 2.63941i −1.82918 + 0.289713i −0.973650 0.228048i \(-0.926766\pi\)
−0.855525 + 0.517761i \(0.826766\pi\)
\(84\) 7.25654 + 0.713952i 0.791754 + 0.0778985i
\(85\) 0 0
\(86\) 8.42648 2.73793i 0.908650 0.295238i
\(87\) 7.57807 6.22047i 0.812454 0.666904i
\(88\) −4.43998 + 2.26228i −0.473303 + 0.241160i
\(89\) −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
\(92\) 0.327901 + 2.07029i 0.0341860 + 0.215842i
\(93\) 9.44605 + 6.04544i 0.979510 + 0.626883i
\(94\) −2.75161 + 3.78726i −0.283807 + 0.390626i
\(95\) 0 0
\(96\) 1.29484 + 1.15039i 0.132154 + 0.117411i
\(97\) −0.549968 + 3.47236i −0.0558408 + 0.352565i 0.943909 + 0.330205i \(0.107118\pi\)
−0.999750 + 0.0223598i \(0.992882\pi\)
\(98\) 9.55370 + 4.86785i 0.965070 + 0.491728i
\(99\) −13.5748 + 6.26147i −1.36432 + 0.629301i
\(100\) 0 0
\(101\) 16.6740i 1.65912i 0.558415 + 0.829562i \(0.311410\pi\)
−0.558415 + 0.829562i \(0.688590\pi\)
\(102\) −2.39192 0.623900i −0.236835 0.0617753i
\(103\) 2.62027 + 0.415010i 0.258183 + 0.0408921i 0.284184 0.958770i \(-0.408277\pi\)
−0.0260012 + 0.999662i \(0.508277\pi\)
\(104\) −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 \(-0.443382\pi\)
−0.984223 + 0.176933i \(0.943382\pi\)
\(108\) 3.74678 + 3.60023i 0.360534 + 0.346432i
\(109\) −12.6666 4.11563i −1.21324 0.394206i −0.368625 0.929578i \(-0.620172\pi\)
−0.844617 + 0.535372i \(0.820172\pi\)
\(110\) 0 0
\(111\) 2.25559 + 3.84749i 0.214091 + 0.365188i
\(112\) 1.91121 + 3.75095i 0.180592 + 0.354432i
\(113\) −0.679445 1.33349i −0.0639168 0.125444i 0.856838 0.515586i \(-0.172426\pi\)
−0.920755 + 0.390142i \(0.872426\pi\)
\(114\) −1.62936 2.77931i −0.152604 0.260306i
\(115\) 0 0
\(116\) 5.38339 + 1.74917i 0.499835 + 0.162406i
\(117\) −4.40588 + 2.94523i −0.407324 + 0.272286i
\(118\) 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
\(122\) 9.58802 + 1.51859i 0.868058 + 0.137487i
\(123\) −6.32211 1.64904i −0.570046 0.148689i
\(124\) 6.47496i 0.581468i
\(125\) 0 0
\(126\) 5.28978 + 11.4682i 0.471251 + 1.02167i
\(127\) −1.38236 0.704349i −0.122665 0.0625009i 0.391581 0.920144i \(-0.371928\pi\)
−0.514246 + 0.857643i \(0.671928\pi\)
\(128\) −0.156434 + 0.987688i −0.0138270 + 0.0873001i
\(129\) 11.4724 + 10.1926i 1.01009 + 0.897404i
\(130\) 0 0
\(131\) −3.74251 + 5.15112i −0.326984 + 0.450055i −0.940584 0.339562i \(-0.889721\pi\)
0.613599 + 0.789618i \(0.289721\pi\)
\(132\) −7.26964 4.65255i −0.632741 0.404952i
\(133\) −1.22495 7.73403i −0.106217 0.670625i
\(134\) −2.00025 + 6.15614i −0.172795 + 0.531810i
\(135\) 0 0
\(136\) −0.441023 1.35733i −0.0378174 0.116390i
\(137\) −3.66124 + 1.86549i −0.312800 + 0.159380i −0.603342 0.797483i \(-0.706165\pi\)
0.290542 + 0.956862i \(0.406165\pi\)
\(138\) −2.80621 + 2.30348i −0.238880 + 0.196085i
\(139\) −10.1584 + 3.30065i −0.861621 + 0.279958i −0.706305 0.707907i \(-0.749639\pi\)
−0.155316 + 0.987865i \(0.549639\pi\)
\(140\) 0 0
\(141\) −8.06931 0.793919i −0.679559 0.0668600i
\(142\) 14.8826 2.35717i 1.24892 0.197809i
\(143\) 6.22457 6.22457i 0.520525 0.520525i
\(144\) −0.584665 + 2.94248i −0.0487220 + 0.245206i
\(145\) 0 0
\(146\) −5.43450 7.47994i −0.449762 0.619045i
\(147\) 1.09524 + 18.5394i 0.0903339 + 1.52910i
\(148\) −1.16900 + 2.29429i −0.0960909 + 0.188589i
\(149\) 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 \(0.194454\pi\)
\(152\) 0.844446 1.65732i 0.0684936 0.134426i
\(153\) −1.16303 4.12055i −0.0940256 0.333127i
\(154\) −12.3305 16.9714i −0.993617 1.36760i
\(155\) 0 0
\(156\) −2.80343 1.22590i −0.224454 0.0981506i
\(157\) 7.13510 7.13510i 0.569443 0.569443i −0.362529 0.931972i \(-0.618087\pi\)
0.931972 + 0.362529i \(0.118087\pi\)
\(158\) −3.70407 + 0.586667i −0.294680 + 0.0466727i
\(159\) −0.868465 + 8.82699i −0.0688737 + 0.700026i
\(160\) 0 0
\(161\) −8.39223 + 2.72680i −0.661401 + 0.214902i
\(162\) −2.09740 + 8.75219i −0.164787 + 0.687637i
\(163\) 5.00771 2.55156i 0.392234 0.199853i −0.246739 0.969082i \(-0.579359\pi\)
0.638974 + 0.769228i \(0.279359\pi\)
\(164\) −1.16567 3.58757i −0.0910238 0.280143i
\(165\) 0 0
\(166\) 5.21383 16.0465i 0.404672 1.24545i
\(167\) −2.62306 16.5614i −0.202979 1.28156i −0.853109 0.521734i \(-0.825286\pi\)
0.650130 0.759823i \(-0.274714\pi\)
\(168\) −3.93054 + 6.14150i −0.303247 + 0.473827i
\(169\) −5.80692 + 7.99254i −0.446686 + 0.614810i
\(170\) 0 0
\(171\) 2.72558 4.86922i 0.208430 0.372359i
\(172\) −1.38603 + 8.75104i −0.105684 + 0.667260i
\(173\) 3.98829 + 2.03214i 0.303224 + 0.154500i 0.598982 0.800763i \(-0.295572\pi\)
−0.295758 + 0.955263i \(0.595572\pi\)
\(174\) 2.10211 + 9.57614i 0.159360 + 0.725966i
\(175\) 0 0
\(176\) 4.98310i 0.375615i
\(177\) −4.86690 + 18.6588i −0.365819 + 1.40248i
\(178\) 1.12236 + 0.177764i 0.0841243 + 0.0133240i
\(179\) −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
\(183\) 6.12980 + 15.6568i 0.453128 + 1.15738i
\(184\) −1.99350 0.647728i −0.146963 0.0477511i
\(185\) 0 0
\(186\) −9.67494 + 5.67192i −0.709401 + 0.415885i
\(187\) 3.22868 + 6.33665i 0.236105 + 0.463382i
\(188\) −2.12527 4.17108i −0.155001 0.304207i
\(189\) −12.5022 + 17.9499i −0.909398 + 1.30567i
\(190\) 0 0
\(191\) 17.5527 + 5.70322i 1.27007 + 0.412671i 0.865072 0.501647i \(-0.167272\pi\)
0.404998 + 0.914318i \(0.367272\pi\)
\(192\) −1.61285 + 0.631448i −0.116397 + 0.0455708i
\(193\) 3.31568 + 3.31568i 0.238668 + 0.238668i 0.816298 0.577630i \(-0.196023\pi\)
−0.577630 + 0.816298i \(0.696023\pi\)
\(194\) −2.84422 2.06644i −0.204203 0.148362i
\(195\) 0 0
\(196\) −8.67458 + 6.30245i −0.619613 + 0.450175i
\(197\) 12.5246 + 1.98370i 0.892341 + 0.141333i 0.585734 0.810503i \(-0.300806\pi\)
0.306607 + 0.951836i \(0.400806\pi\)
\(198\) 0.583828 14.9379i 0.0414909 1.06159i
\(199\) 1.62602i 0.115266i −0.998338 0.0576328i \(-0.981645\pi\)
0.998338 0.0576328i \(-0.0183553\pi\)
\(200\) 0 0
\(201\) −10.9507 + 2.40385i −0.772406 + 0.169555i
\(202\) −14.8566 7.56983i −1.04531 0.532612i
\(203\) −3.72772 + 23.5359i −0.261634 + 1.65189i
\(204\) 1.64181 1.84797i 0.114950 0.129384i
\(205\) 0 0
\(206\) −1.55935 + 2.14627i −0.108645 + 0.149537i
\(207\) −5.90005 2.17526i −0.410082 0.151191i
\(208\) −0.276349 1.74480i −0.0191613 0.120980i
\(209\) −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 \(-0.236489\pi\)
\(212\) −4.56273 + 2.32483i −0.313370 + 0.159670i
\(213\) 16.5589 + 20.1729i 1.13460 + 1.38222i
\(214\) 11.2316 3.64938i 0.767778 0.249466i
\(215\) 0 0
\(216\) −4.90883 + 1.70393i −0.334004 + 0.115938i
\(217\) −26.9226 + 4.26413i −1.82763 + 0.289468i
\(218\) 9.41758 9.41758i 0.637839 0.637839i
\(219\) 6.41610 14.6725i 0.433560 0.991479i
\(220\) 0 0
\(221\) 1.48191 + 2.03968i 0.0996842 + 0.137204i
\(222\) −4.45216 + 0.263018i −0.298809 + 0.0176526i
\(223\) −2.82606 + 5.54645i −0.189247 + 0.371418i −0.966062 0.258311i \(-0.916834\pi\)
0.776815 + 0.629729i \(0.216834\pi\)
\(224\) −4.20979 −0.281279
\(225\) 0 0
\(226\) 1.49661 0.0995528
\(227\) 4.15647 8.15754i 0.275875 0.541435i −0.710947 0.703246i \(-0.751733\pi\)
0.986822 + 0.161811i \(0.0517334\pi\)
\(228\) 3.21610 0.189996i 0.212991 0.0125828i
\(229\) 10.8714 + 14.9632i 0.718400 + 0.988793i 0.999575 + 0.0291365i \(0.00927575\pi\)
−0.281175 + 0.959656i \(0.590724\pi\)
\(230\) 0 0
\(231\) 14.5576 33.2909i 0.957823 2.19038i
\(232\) −4.00253 + 4.00253i −0.262779 + 0.262779i
\(233\) 13.6047 2.15478i 0.891276 0.141164i 0.306032 0.952021i \(-0.400999\pi\)
0.585244 + 0.810857i \(0.300999\pi\)
\(234\) −0.623990 5.26277i −0.0407915 0.344038i
\(235\) 0 0
\(236\) −10.5882 + 3.44032i −0.689234 + 0.223946i
\(237\) −4.12129 5.02075i −0.267706 0.326133i
\(238\) 5.35329 2.72764i 0.347002 0.176806i
\(239\) −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 \(0.164224\pi\)
\(242\) 2.16369 + 13.6610i 0.139087 + 0.878163i
\(243\) −14.9149 + 4.53278i −0.956791 + 0.290778i
\(244\) −5.70595 + 7.85356i −0.365286 + 0.502773i
\(245\) 0 0
\(246\) 4.33948 4.88440i 0.276675 0.311418i
\(247\) −0.514023 + 3.24541i −0.0327065 + 0.206501i
\(248\) −5.76923 2.93957i −0.366346 0.186663i
\(249\) 28.5441 6.26585i 1.80891 0.397082i
\(250\) 0 0
\(251\) 3.76896i 0.237895i −0.992901 0.118947i \(-0.962048\pi\)
0.992901 0.118947i \(-0.0379520\pi\)
\(252\) −12.6197 0.493226i −0.794969 0.0310703i
\(253\) 10.3164 + 1.63396i 0.648589 + 0.102726i
\(254\) 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 −0.876462 0.481471i \(-0.840103\pi\)
−0.481471 0.876462i \(-0.659897\pi\)
\(258\) −14.2900 + 5.59470i −0.889657 + 0.348311i
\(259\) −10.3094 3.34973i −0.640596 0.208142i
\(260\) 0 0
\(261\) −12.4674 + 11.5295i −0.771711 + 0.713657i
\(262\) −2.89062 5.67316i −0.178583 0.350489i
\(263\) 2.51673 + 4.93937i 0.155188 + 0.304574i 0.955490 0.295023i \(-0.0953273\pi\)
−0.800302 + 0.599598i \(0.795327\pi\)
\(264\) 7.44580 4.36509i 0.458257 0.268653i
\(265\) 0 0
\(266\) 7.44718 + 2.41974i 0.456616 + 0.148364i
\(267\) 0.717544 + 1.83276i 0.0439130 + 0.112163i
\(268\) −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 \(0.345704\pi\)
\(272\) 1.40961 + 0.223260i 0.0854701 + 0.0135371i
\(273\) 3.25104 12.4639i 0.196762 0.754349i
\(274\) 4.10910i 0.248240i
\(275\) 0 0
\(276\) −0.778423 3.54611i −0.0468556 0.213450i
\(277\) 22.1735 + 11.2980i 1.33228 + 0.678829i 0.967644 0.252321i \(-0.0811940\pi\)
0.364634 + 0.931151i \(0.381194\pi\)
\(278\) 1.67090 10.5496i 0.100214 0.632725i
\(279\) −16.9501 9.48791i −1.01477 0.568026i
\(280\) 0 0
\(281\) −5.67900 + 7.81648i −0.338781 + 0.466292i −0.944085 0.329702i \(-0.893052\pi\)
0.605304 + 0.795994i \(0.293052\pi\)
\(282\) 4.37078 6.82938i 0.260276 0.406684i
\(283\) 0.159612 + 1.00775i 0.00948793 + 0.0599044i 0.991978 0.126410i \(-0.0403456\pi\)
−0.982490 + 0.186315i \(0.940346\pi\)
\(284\) −4.65630 + 14.3306i −0.276301 + 0.850366i
\(285\) 0 0
\(286\) 2.72024 + 8.37203i 0.160851 + 0.495049i
\(287\) 14.1493 7.20945i 0.835210 0.425561i
\(288\) −2.35633 1.85680i −0.138848 0.109413i
\(289\) 14.2308 4.62387i 0.837106 0.271992i
\(290\) 0 0
\(291\) 0.596229 6.06002i 0.0349516 0.355244i
\(292\) 9.13189 1.44635i 0.534403 0.0846412i
\(293\) −1.45604 + 1.45604i −0.0850625 + 0.0850625i −0.748358 0.663295i \(-0.769157\pi\)
0.663295 + 0.748358i \(0.269157\pi\)
\(294\) −17.0159 7.44083i −0.992389 0.433958i
\(295\) 0 0
\(296\) −1.51351 2.08317i −0.0879710 0.121082i
\(297\) 22.8318 12.2129i 1.32483 0.708665i
\(298\) −2.33020 + 4.57327i −0.134985 + 0.264922i
\(299\) 3.70284 0.214141
\(300\) 0 0
\(301\) −37.2993 −2.14990
\(302\) −9.13947 + 17.9372i −0.525917 + 1.03217i
\(303\) −1.70317 28.8299i −0.0978446 1.65624i
\(304\) 1.09331 + 1.50481i 0.0627057 + 0.0863069i
\(305\) 0 0
\(306\) 4.19945 + 0.834422i 0.240066 + 0.0477007i
\(307\) 11.9806 11.9806i 0.683767 0.683767i −0.277080 0.960847i \(-0.589367\pi\)
0.960847 + 0.277080i \(0.0893667\pi\)
\(308\) 20.7196 3.28166i 1.18061 0.186990i
\(309\) −4.57293 0.449918i −0.260145 0.0255950i
\(310\) 0 0
\(311\) 3.64396 1.18399i 0.206630 0.0671381i −0.203873 0.978997i \(-0.565353\pi\)
0.410503 + 0.911859i \(0.365353\pi\)
\(312\) 2.36502 1.94133i 0.133893 0.109906i
\(313\) −20.3753 + 10.3817i −1.15168 + 0.586809i −0.922280 0.386523i \(-0.873676\pi\)
−0.229398 + 0.973333i \(0.573676\pi\)
\(314\) 3.11815 + 9.59669i 0.175968 + 0.541573i
\(315\) 0 0
\(316\) 1.15889 3.56669i 0.0651926 0.200642i
\(317\) −1.36994 8.64943i −0.0769432 0.485800i −0.995826 0.0912701i \(-0.970907\pi\)
0.918883 0.394530i \(-0.129093\pi\)
\(318\) −7.47063 4.78118i −0.418932 0.268115i
\(319\) 16.5794 22.8195i 0.928266 1.27765i
\(320\) 0 0
\(321\) 15.2916 + 13.5856i 0.853494 + 0.758276i
\(322\) 1.38040 8.71548i 0.0769265 0.485695i
\(323\) −2.36529 1.20518i −0.131608 0.0670578i
\(324\) −6.84606 5.84221i −0.380337 0.324567i
\(325\) 0 0
\(326\) 5.62029i 0.311279i
\(327\) 22.3214 + 5.82224i 1.23438 + 0.321971i
\(328\) 3.72576 + 0.590102i 0.205721 + 0.0325829i
\(329\) 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
\(333\) −4.29300 6.42206i −0.235255 0.351927i
\(334\) 15.9471 + 5.18154i 0.872588 + 0.283521i
\(335\) 0 0
\(336\) −3.68769 6.29032i −0.201180 0.343165i
\(337\) −1.10341 2.16556i −0.0601063 0.117965i 0.858999 0.511977i \(-0.171087\pi\)
−0.919105 + 0.394012i \(0.871087\pi\)
\(338\) −4.48512 8.80254i −0.243958 0.478795i
\(339\) 1.31099 + 2.23624i 0.0712035 + 0.121456i
\(340\) 0 0
\(341\) 30.6862 + 9.97055i 1.66175 + 0.539935i
\(342\) 3.10112 + 4.63909i 0.167690 + 0.250853i
\(343\) −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
\(347\) 22.4456 + 3.55504i 1.20494 + 0.190844i 0.726433 0.687237i \(-0.241177\pi\)
0.478511 + 0.878082i \(0.341177\pi\)
\(348\) −9.48674 2.47449i −0.508543 0.132646i
\(349\) 12.5328i 0.670865i 0.942064 + 0.335432i \(0.108882\pi\)
−0.942064 + 0.335432i \(0.891118\pi\)
\(350\) 0 0
\(351\) 7.31708 5.54245i 0.390557 0.295834i
\(352\) 4.43998 + 2.26228i 0.236651 + 0.120580i
\(353\) −1.11770 + 7.05688i −0.0594892 + 0.375600i 0.939925 + 0.341381i \(0.110894\pi\)
−0.999414 + 0.0342193i \(0.989106\pi\)
\(354\) −14.4156 12.8074i −0.766181 0.680704i
\(355\) 0 0
\(356\) −0.667929 + 0.919325i −0.0354002 + 0.0487241i
\(357\) 8.76503 + 5.60959i 0.463894 + 0.296891i
\(358\) −0.0272918 0.172313i −0.00144241 0.00910704i
\(359\) −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
\(362\) −10.1373 + 5.16520i −0.532803 + 0.271477i
\(363\) −18.5171 + 15.1998i −0.971894 + 0.797780i
\(364\) 7.07281 2.29810i 0.370716 0.120453i
\(365\) 0 0
\(366\) −16.7331 1.64633i −0.874656 0.0860551i
\(367\) −4.14629 + 0.656708i −0.216435 + 0.0342799i −0.263710 0.964602i \(-0.584946\pi\)
0.0472753 + 0.998882i \(0.484946\pi\)
\(368\) 1.48216 1.48216i 0.0772630 0.0772630i
\(369\) 11.0996 + 2.20547i 0.577822 + 0.114812i
\(370\) 0 0
\(371\) −12.6714 17.4406i −0.657865 0.905473i
\(372\) −0.661387 11.1954i −0.0342913 0.580456i
\(373\) 2.06631 4.05536i 0.106990 0.209979i −0.831305 0.555817i \(-0.812405\pi\)
0.938294 + 0.345838i \(0.112405\pi\)
\(374\) −7.11179 −0.367742
\(375\) 0 0
\(376\) 4.68132 0.241420
\(377\) 4.53964 8.90954i 0.233803 0.458864i
\(378\) −10.3176 19.2886i −0.530682 0.992099i
\(379\) 19.3891 + 26.6869i 0.995954 + 1.37081i 0.927775 + 0.373139i \(0.121719\pi\)
0.0681783 + 0.997673i \(0.478281\pi\)
\(380\) 0 0
\(381\) 2.46210 + 1.07664i 0.126137 + 0.0551581i
\(382\) −13.0504 + 13.0504i −0.667715 + 0.667715i
\(383\) −16.8791 + 2.67339i −0.862482 + 0.136604i −0.571977 0.820270i \(-0.693823\pi\)
−0.290505 + 0.956873i \(0.593823\pi\)
\(384\) 0.169593 1.72373i 0.00865451 0.0879636i
\(385\) 0 0
\(386\) −4.45958 + 1.44901i −0.226987 + 0.0737525i
\(387\) −20.8774 16.4514i −1.06126 0.836274i
\(388\) 3.13246 1.59607i 0.159027 0.0810281i
\(389\) −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
\(392\) −1.67735 10.5904i −0.0847189 0.534894i
\(393\) 5.94477 9.28875i 0.299874 0.468556i
\(394\) −7.45354 + 10.2589i −0.375504 + 0.516837i
\(395\) 0 0
\(396\) 13.0447 + 7.30186i 0.655521 + 0.366932i
\(397\) 0.577115 3.64376i 0.0289646 0.182875i −0.968964 0.247200i \(-0.920489\pi\)
0.997929 + 0.0643251i \(0.0204895\pi\)
\(398\) 1.44880 + 0.738199i 0.0726216 + 0.0370026i
\(399\) 2.90798 + 13.2473i 0.145581 + 0.663194i
\(400\) 0 0
\(401\) 29.3144i 1.46389i −0.681364 0.731945i \(-0.738613\pi\)
0.681364 0.731945i \(-0.261387\pi\)
\(402\) 2.82969 10.8485i 0.141132 0.541074i
\(403\) 11.2975 + 1.78935i 0.562768 + 0.0891336i
\(404\) 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
\(408\) 0.901190 + 2.30182i 0.0446155 + 0.113957i
\(409\) 7.27469 + 2.36369i 0.359710 + 0.116877i 0.483296 0.875457i \(-0.339439\pi\)
−0.123586 + 0.992334i \(0.539439\pi\)
\(410\) 0 0
\(411\) 6.13986 3.59948i 0.302857 0.177549i
\(412\) −1.20440 2.36378i −0.0593368 0.116455i
\(413\) −21.2777 41.7598i −1.04701 2.05487i
\(414\) 4.61674 4.26944i 0.226901 0.209831i
\(415\) 0 0
\(416\) 1.68008 + 0.545893i 0.0823729 + 0.0267646i
\(417\) 17.2270 6.74458i 0.843611 0.330283i
\(418\) −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 \(0.411247\pi\)
\(422\) 11.9302 + 1.88956i 0.580753 + 0.0919823i
\(423\) 14.0332 + 0.548470i 0.682319 + 0.0266675i
\(424\) 5.12087i 0.248692i
\(425\) 0 0
\(426\) −25.4918 + 5.59582i −1.23508 + 0.271119i
\(427\) −36.4125 18.5531i −1.76213 0.897848i
\(428\) −1.84743 + 11.6642i −0.0892991 + 0.563812i
\(429\) −10.1267 + 11.3983i −0.488922 + 0.550316i
\(430\) 0 0
\(431\) −2.55158 + 3.51195i −0.122905 + 0.169164i −0.866036 0.499982i \(-0.833340\pi\)
0.743131 + 0.669146i \(0.233340\pi\)
\(432\) 0.710346 5.14737i 0.0341765 0.247653i
\(433\) −1.22781 7.75206i −0.0590046 0.372540i −0.999467 0.0326428i \(-0.989608\pi\)
0.940463 0.339897i \(-0.110392\pi\)
\(434\) 8.42326 25.9241i 0.404329 1.24440i
\(435\) 0 0
\(436\) 4.11563 + 12.6666i 0.197103 + 0.606621i
\(437\) −3.47389 + 1.77004i −0.166179 + 0.0846723i
\(438\) 10.1605 + 12.3780i 0.485487 + 0.591443i
\(439\) −19.1294 + 6.21551i −0.912994 + 0.296650i −0.727590 0.686012i \(-0.759360\pi\)
−0.185405 + 0.982662i \(0.559360\pi\)
\(440\) 0 0
\(441\) −3.78742 31.9434i −0.180353 1.52111i
\(442\) −2.49014 + 0.394399i −0.118444 + 0.0187597i
\(443\) −11.8995 + 11.8995i −0.565363 + 0.565363i −0.930826 0.365463i \(-0.880911\pi\)
0.365463 + 0.930826i \(0.380911\pi\)
\(444\) 1.78689 4.08631i 0.0848019 0.193928i
\(445\) 0 0
\(446\) −3.65892 5.03607i −0.173255 0.238465i
\(447\) −8.87463 + 0.524282i −0.419755 + 0.0247977i
\(448\) 1.91121 3.75095i 0.0902960 0.177216i
\(449\) −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
\(452\) −0.679445 + 1.33349i −0.0319584 + 0.0627219i
\(453\) −34.8079 + 2.05633i −1.63542 + 0.0966149i
\(454\) 5.38142 + 7.40689i 0.252563 + 0.347623i
\(455\) 0 0
\(456\) −1.29079 + 2.95182i −0.0604468 + 0.138232i
\(457\) 13.4412 13.4412i 0.628754 0.628754i −0.319001 0.947754i \(-0.603347\pi\)
0.947754 + 0.319001i \(0.103347\pi\)
\(458\) −18.2678 + 2.89333i −0.853597 + 0.135196i
\(459\) 2.43182 + 7.00579i 0.113508 + 0.327002i
\(460\) 0 0
\(461\) 30.4642 9.89843i 1.41886 0.461016i 0.503621 0.863925i \(-0.332001\pi\)
0.915240 + 0.402908i \(0.132001\pi\)
\(462\) 23.0534 + 28.0847i 1.07254 + 1.30662i
\(463\) −2.76320 + 1.40792i −0.128417 + 0.0654317i −0.517019 0.855974i \(-0.672958\pi\)
0.388602 + 0.921406i \(0.372958\pi\)
\(464\) −1.74917 5.38339i −0.0812031 0.249918i
\(465\) 0 0
\(466\) −4.25650 + 13.1002i −0.197179 + 0.606853i
\(467\) 6.20197 + 39.1577i 0.286993 + 1.81200i 0.536804 + 0.843707i \(0.319632\pi\)
−0.249811 + 0.968295i \(0.580368\pi\)
\(468\) 4.97245 + 1.83327i 0.229852 + 0.0847429i
\(469\) 16.0170 22.0455i 0.739598 1.01797i
\(470\) 0 0
\(471\) −11.6080 + 13.0657i −0.534870 + 0.602034i
\(472\) 1.74160 10.9960i 0.0801638 0.506134i
\(473\) 39.3387 + 20.0441i 1.80880 + 0.921628i
\(474\) 6.34454 1.39272i 0.291415 0.0639698i
\(475\) 0 0
\(476\) 6.00814i 0.275383i
\(477\) 0.599970 15.3509i 0.0274707 0.702869i
\(478\) 20.4797 + 3.24367i 0.936721 + 0.148362i
\(479\) −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
\(483\) 14.2319 5.57197i 0.647576 0.253533i
\(484\) −13.1543 4.27411i −0.597925 0.194278i
\(485\) 0 0
\(486\) 2.73249 15.3471i 0.123948 0.696159i
\(487\) −0.947305 1.85919i −0.0429265 0.0842480i 0.868547 0.495607i \(-0.165054\pi\)
−0.911473 + 0.411359i \(0.865054\pi\)
\(488\) −4.40713 8.64948i −0.199501 0.391543i
\(489\) −8.39789 + 4.92325i −0.379766 + 0.222637i
\(490\) 0 0
\(491\) −15.8067 5.13592i −0.713348 0.231781i −0.0702111 0.997532i \(-0.522367\pi\)
−0.643137 + 0.765751i \(0.722367\pi\)
\(492\) 2.38195 + 6.08398i 0.107386 + 0.274287i
\(493\) 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
\(497\) −62.6527 9.92321i −2.81036 0.445117i
\(498\) −7.37582 + 28.2776i −0.330519 + 1.26715i
\(499\) 36.0457i 1.61363i −0.590806 0.806813i \(-0.701190\pi\)
0.590806 0.806813i \(-0.298810\pi\)
\(500\) 0 0
\(501\) 6.22704 + 28.3673i 0.278203 + 1.26736i
\(502\) 3.35817 + 1.71107i 0.149882 + 0.0763689i
\(503\) −4.92776 + 31.1126i −0.219718 + 1.38724i 0.593289 + 0.804990i \(0.297829\pi\)
−0.813007 + 0.582255i \(0.802171\pi\)
\(504\) 6.16871 11.0204i 0.274776 0.490886i
\(505\) 0 0
\(506\) −6.13944 + 8.45021i −0.272931 + 0.375658i
\(507\) 9.22397 14.4125i 0.409651 0.640083i
\(508\) 0.242702 + 1.53236i 0.0107682 + 0.0679876i
\(509\) 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
\(512\) 0.891007 0.453990i 0.0393773 0.0200637i
\(513\) −4.21525 + 8.69747i −0.186108 + 0.384003i
\(514\) 29.2797 9.51354i 1.29147 0.419624i
\(515\) 0 0
\(516\) 1.50261 15.2724i 0.0661489 0.672332i
\(517\) −23.0403 + 3.64922i −1.01331 + 0.160493i
\(518\) 7.66501 7.66501i 0.336781 0.336781i
\(519\) −7.10348 3.10625i −0.311808 0.136349i
\(520\) 0 0
\(521\) −19.3712 26.6622i −0.848668 1.16809i −0.984155 0.177312i \(-0.943260\pi\)
0.135487 0.990779i \(-0.456740\pi\)
\(522\) −4.61278 16.3428i −0.201896 0.715304i
\(523\) 18.1177 35.5580i 0.792232 1.55484i −0.0392100 0.999231i \(-0.512484\pi\)
0.831442 0.555612i \(-0.187516\pi\)
\(524\) 6.36713 0.278150
\(525\) 0 0
\(526\) −5.54358 −0.241712
\(527\) −4.19530 + 8.23373i −0.182750 + 0.358667i
\(528\) 0.509001 + 8.61596i 0.0221514 + 0.374962i
\(529\) −10.9366 15.0529i −0.475503 0.654474i
\(530\) 0 0
\(531\) 6.50914 32.7589i 0.282472 1.42162i
\(532\) −5.53695 + 5.53695i −0.240057 + 0.240057i
\(533\) −6.58172 + 1.04244i −0.285086 + 0.0451532i
\(534\) −1.95876 0.192717i −0.0847636 0.00833967i
\(535\) 0 0
\(536\) 6.15614 2.00025i 0.265905 0.0863977i
\(537\) 0.233565 0.191722i 0.0100791 0.00827343i
\(538\) −3.08583 + 1.57231i −0.133040 + 0.0677872i
\(539\) 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 \(-0.0831100\pi\)
\(542\) −0.736991 4.65318i −0.0316565 0.199871i
\(543\) −16.5979 10.6226i −0.712285 0.455860i
\(544\) −0.838876 + 1.15461i −0.0359665 + 0.0495036i
\(545\) 0 0
\(546\) 9.62947 + 8.55518i 0.412103 + 0.366128i
\(547\) −6.44292 + 40.6790i −0.275479 + 1.73931i 0.330482 + 0.943812i \(0.392789\pi\)
−0.605961 + 0.795495i \(0.707211\pi\)
\(548\) 3.66124 + 1.86549i 0.156400 + 0.0796899i
\(549\) −12.1979 26.4450i −0.520594 1.12864i
\(550\) 0 0
\(551\) 10.5287i 0.448537i
\(552\) 3.51300 + 0.916318i 0.149523 + 0.0390011i
\(553\) 15.5934 + 2.46975i 0.663098 + 0.105024i
\(554\) −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 \(-0.0712934\pi\)
−0.222107 + 0.975022i \(0.571293\pi\)
\(558\) 16.1490 10.7952i 0.683640 0.456998i
\(559\) 14.8858 + 4.83667i 0.629600 + 0.204570i
\(560\) 0 0
\(561\) −6.22977 10.6265i −0.263021 0.448651i
\(562\) −4.38632 8.60864i −0.185026 0.363133i
\(563\) −4.70734 9.23868i −0.198391 0.389364i 0.770282 0.637703i \(-0.220115\pi\)
−0.968673 + 0.248339i \(0.920115\pi\)
\(564\) 4.10073 + 6.99487i 0.172672 + 0.294537i
\(565\) 0 0
\(566\) −0.970373 0.315293i −0.0407878 0.0132528i
\(567\) 19.7832 32.3131i 0.830816 1.35702i
\(568\) −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 \(0.175777\pi\)
\(572\) −8.69450 1.37707i −0.363535 0.0575783i
\(573\) −30.9318 8.06815i −1.29220 0.337052i
\(574\) 15.8802i 0.662826i
\(575\) 0 0
\(576\) 2.72417 1.25654i 0.113507 0.0523559i
\(577\) 5.29743 + 2.69918i 0.220535 + 0.112368i 0.560768 0.827973i \(-0.310506\pi\)
−0.340233 + 0.940341i \(0.610506\pi\)
\(578\) −2.34075 + 14.7789i −0.0973625 + 0.614723i
\(579\) −6.07162 5.39425i −0.252328 0.224177i
\(580\) 0 0
\(581\) −41.7498 + 57.4636i −1.73207 + 2.38399i
\(582\) 5.12883 + 3.28243i 0.212597 + 0.136061i
\(583\) 3.99187 + 25.2037i 0.165326 + 1.04383i
\(584\) −2.85708 + 8.79320i −0.118227 + 0.363865i
\(585\) 0 0
\(586\) −0.636311 1.95836i −0.0262858 0.0808992i
\(587\) 23.3146 11.8794i 0.962295 0.490314i 0.0990406 0.995083i \(-0.468423\pi\)
0.863254 + 0.504770i \(0.168423\pi\)
\(588\) 14.3549 11.7832i 0.591986 0.485932i
\(589\) −11.4543 + 3.72172i −0.471966 + 0.153351i
\(590\) 0 0
\(591\) −21.8581 2.15056i −0.899122 0.0884623i
\(592\) 2.54323 0.402809i 0.104526 0.0165553i
\(593\) 23.6228 23.6228i 0.970072 0.970072i −0.0294930 0.999565i \(-0.509389\pi\)
0.999565 + 0.0294930i \(0.00938927\pi\)
\(594\) 0.516378 + 25.8878i 0.0211872 + 1.06219i
\(595\) 0 0
\(596\) −3.01693 4.15244i −0.123578 0.170091i
\(597\) 0.166091 + 2.81145i 0.00679764 + 0.115065i
\(598\) −1.68106 + 3.29926i −0.0687435 + 0.134917i
\(599\) −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 \(0.610912\pi\)
\(602\) 16.9335 33.2339i 0.690159 1.35451i
\(603\) 18.6887 5.27491i 0.761062 0.214811i
\(604\) −11.8329 16.2867i −0.481476 0.662695i
\(605\) 0 0
\(606\) 26.4609 + 11.5710i 1.07490 + 0.470039i
\(607\) −22.6982 + 22.6982i −0.921293 + 0.921293i −0.997121 0.0758281i \(-0.975840\pi\)
0.0758281 + 0.997121i \(0.475840\pi\)
\(608\) −1.83715 + 0.290976i −0.0745063 + 0.0118006i
\(609\) 4.04127 41.0751i 0.163761 1.66445i
\(610\) 0 0
\(611\) −7.86501 + 2.55550i −0.318184 + 0.103384i
\(612\) −2.64998 + 3.36291i −0.107119 + 0.135938i
\(613\) 38.6048 19.6701i 1.55923 0.794470i 0.559818 0.828616i \(-0.310871\pi\)
0.999417 + 0.0341460i \(0.0108711\pi\)
\(614\) 5.23570 + 16.1138i 0.211296 + 0.650301i
\(615\) 0 0
\(616\) −6.48251 + 19.9511i −0.261188 + 0.803853i
\(617\) −3.81403 24.0808i −0.153547 0.969458i −0.937335 0.348429i \(-0.886715\pi\)
0.783788 0.621028i \(-0.213285\pi\)
\(618\) 2.47695 3.87025i 0.0996374 0.155684i
\(619\) −23.7633 + 32.7074i −0.955130 + 1.31462i −0.00591868 + 0.999982i \(0.501884\pi\)
−0.949211 + 0.314641i \(0.898116\pi\)
\(620\) 0 0
\(621\) 10.4236 + 3.15845i 0.418285 + 0.126744i
\(622\) −0.599376 + 3.78431i −0.0240328 + 0.151737i
\(623\) −4.26239 2.17180i −0.170769 0.0870112i
\(624\) 0.656040 + 2.98859i 0.0262626 + 0.119639i
\(625\) 0 0
\(626\) 22.8677i 0.913977i
\(627\) 4.05192 15.5343i 0.161818 0.620381i
\(628\) −9.96632 1.57851i −0.397700 0.0629894i
\(629\) −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
\(633\) 7.62720 + 19.4814i 0.303154 + 0.774318i
\(634\) 8.32864 + 2.70614i 0.330772 + 0.107474i
\(635\) 0 0
\(636\) 7.65166 4.48577i 0.303408 0.177873i
\(637\) 8.59929 + 16.8771i 0.340716 + 0.668693i
\(638\) 12.8055 + 25.1322i 0.506974 + 0.994992i
\(639\) −30.6916 33.1882i −1.21414 1.31291i
\(640\) 0 0
\(641\) −8.76326 2.84736i −0.346128 0.112464i 0.130794 0.991410i \(-0.458247\pi\)
−0.476922 + 0.878946i \(0.658247\pi\)
\(642\) −19.0471 + 7.45716i −0.751730 + 0.294311i
\(643\) 32.6751 + 32.6751i 1.28858 + 1.28858i 0.935649 + 0.352932i \(0.114815\pi\)
0.352932 + 0.935649i \(0.385185\pi\)
\(644\) 7.13886 + 5.18669i 0.281311 + 0.204384i
\(645\) 0 0
\(646\) 2.14764 1.56035i 0.0844978 0.0613912i
\(647\) −48.0211 7.60579i −1.88790 0.299015i −0.897916 0.440167i \(-0.854919\pi\)
−0.989988 + 0.141152i \(0.954919\pi\)
\(648\) 8.31350 3.44758i 0.326585 0.135434i
\(649\) 55.4774i 2.17768i
\(650\) 0 0
\(651\) 46.1147 10.1229i 1.80738 0.396746i
\(652\) −5.00771 2.55156i −0.196117 0.0999267i
\(653\) 3.10987 19.6349i 0.121699 0.768375i −0.849056 0.528302i \(-0.822829\pi\)
0.970755 0.240073i \(-0.0771712\pi\)
\(654\) −15.3214 + 17.2453i −0.599113 + 0.674345i
\(655\) 0 0
\(656\) −2.21724 + 3.05177i −0.0865688 + 0.119152i
\(657\) −9.59494 + 26.0247i −0.374334 + 1.01532i
\(658\) 3.08291 + 19.4647i 0.120184 + 0.758815i
\(659\) 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 \(0.991688\pi\)
\(662\) −5.34493 + 2.72338i −0.207736 + 0.105847i
\(663\) −2.77062 3.37531i −0.107602 0.131086i
\(664\) −16.0465 + 5.21383i −0.622726 + 0.202336i
\(665\) 0 0
\(666\) 7.67108 0.909535i 0.297248 0.0352438i
\(667\) 11.7187 1.85606i 0.453750 0.0718670i
\(668\) −11.8566 + 11.8566i −0.458747 + 0.458747i
\(669\) 4.31981 9.87868i 0.167014 0.381932i
\(670\) 0 0
\(671\) 28.4333 + 39.1351i 1.09766 + 1.51079i
\(672\) 7.27889 0.430011i 0.280789 0.0165880i
\(673\) −15.3688 + 30.1630i −0.592425 + 1.16270i 0.379010 + 0.925392i \(0.376264\pi\)
−0.971435 + 0.237306i \(0.923736\pi\)
\(674\) 2.43046 0.0936178
\(675\) 0 0
\(676\) 9.87932 0.379974
\(677\) −3.49259 + 6.85459i −0.134231 + 0.263443i −0.948332 0.317280i \(-0.897230\pi\)
0.814101 + 0.580724i \(0.197230\pi\)
\(678\) −2.58769 + 0.152871i −0.0993795 + 0.00587099i
\(679\) 8.69931 + 11.9736i 0.333849 + 0.459503i
\(680\) 0 0
\(681\) −6.35344 + 14.5292i −0.243464 + 0.556762i
\(682\) −22.8151 + 22.8151i −0.873634 + 0.873634i
\(683\) 2.86990 0.454547i 0.109814 0.0173928i −0.101286 0.994857i \(-0.532296\pi\)
0.211099 + 0.977465i \(0.432296\pi\)
\(684\) −5.54134 + 0.657019i −0.211878 + 0.0251217i
\(685\) 0 0
\(686\) 14.9035 4.84242i 0.569016 0.184885i
\(687\) −20.3254 24.7614i −0.775463 0.944705i
\(688\) 7.89443 4.02241i 0.300972 0.153353i
\(689\) 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 \(0.910085\pi\)
\(692\) −0.700227 4.42106i −0.0266186 0.168063i
\(693\) −21.7702 + 59.0481i −0.826981 + 2.24305i
\(694\) −13.3577 + 18.3852i −0.507050 + 0.697894i
\(695\) 0 0
\(696\) 6.51168 7.32936i 0.246824 0.277819i
\(697\) 0.842182 5.31733i 0.0318999 0.201408i
\(698\) −11.1668 5.68977i −0.422670 0.215361i
\(699\) −23.3030 + 5.11535i −0.881400 + 0.193480i
\(700\) 0 0
\(701\) 41.1646i 1.55476i −0.629028 0.777382i \(-0.716547\pi\)
0.629028 0.777382i \(-0.283453\pi\)
\(702\) 1.61647 + 9.03579i 0.0610097 + 0.341034i
\(703\) −4.73055 0.749245i −0.178416 0.0282583i
\(704\) −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
\(708\) 17.9560 7.02998i 0.674828 0.264203i
\(709\) 16.1533 + 5.24852i 0.606650 + 0.197112i 0.596204 0.802833i \(-0.296675\pi\)
0.0104457 + 0.999945i \(0.496675\pi\)
\(710\) 0 0
\(711\) 7.63870 + 8.26008i 0.286474 + 0.309777i
\(712\) −0.515891 1.01249i −0.0193338 0.0379448i
\(713\) 6.16161 + 12.0928i 0.230754 + 0.452880i
\(714\) −8.97742 + 5.26300i −0.335971 + 0.196963i
\(715\) 0 0
\(716\) 0.165923 + 0.0539115i 0.00620082 + 0.00201477i
\(717\) 13.0931 + 33.4424i 0.488970 + 1.24893i
\(718\) −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
\(722\) −15.3489 2.43102i −0.571226 0.0904734i
\(723\) 2.72003 10.4281i 0.101159 0.387825i
\(724\) 11.3773i 0.422835i
\(725\) 0 0
\(726\) −5.13651 23.3994i −0.190634 0.868432i
\(727\) 30.4534 + 15.5168i 1.12945 + 0.575485i 0.915884 0.401443i \(-0.131491\pi\)
0.213569 + 0.976928i \(0.431491\pi\)
\(728\) −1.16337 + 7.34523i −0.0431174 + 0.272233i
\(729\) 25.3254 9.36082i 0.937977 0.346697i
\(730\) 0 0
\(731\) −7.43254 + 10.2300i −0.274902 + 0.378371i
\(732\) 9.06358 14.1619i 0.335000 0.523440i
\(733\) −2.91730 18.4191i −0.107753 0.680326i −0.981140 0.193299i \(-0.938081\pi\)
0.873387 0.487027i \(-0.161919\pi\)
\(734\) 1.29725 3.99251i 0.0478822 0.147366i
\(735\) 0 0
\(736\) 0.647728 + 1.99350i 0.0238756 + 0.0734815i
\(737\) −28.7397 + 14.6436i −1.05864 + 0.539405i
\(738\) −7.00421 + 8.88856i −0.257828 + 0.327192i
\(739\) −1.28835 + 0.418609i −0.0473926 + 0.0153988i −0.332617 0.943062i \(-0.607932\pi\)
0.285225 + 0.958461i \(0.407932\pi\)
\(740\) 0 0
\(741\) 0.557260 5.66394i 0.0204715 0.208070i
\(742\) 21.2924 3.37239i 0.781669 0.123804i
\(743\) 8.68111 8.68111i 0.318479 0.318479i −0.529704 0.848183i \(-0.677697\pi\)
0.848183 + 0.529704i \(0.177697\pi\)
\(744\) 10.2755 + 4.49332i 0.376717 + 0.164733i
\(745\) 0 0
\(746\) 2.67527 + 3.68219i 0.0979486 + 0.134815i
\(747\) −48.7137 + 13.7495i −1.78234 + 0.503069i
\(748\) 3.22868 6.33665i 0.118052 0.231691i
\(749\) −49.7161 −1.81659
\(750\) 0 0
\(751\) 40.0140 1.46013 0.730066 0.683377i \(-0.239489\pi\)
0.730066 + 0.683377i \(0.239489\pi\)
\(752\) −2.12527 + 4.17108i −0.0775007 + 0.152104i
\(753\) 0.384982 + 6.51667i 0.0140295 + 0.237481i
\(754\) 5.87750 + 8.08969i 0.214046 + 0.294609i
\(755\) 0 0
\(756\) 21.8704 0.436243i 0.795418 0.0158660i
\(757\) −23.3400 + 23.3400i −0.848305 + 0.848305i −0.989922 0.141616i \(-0.954770\pi\)
0.141616 + 0.989922i \(0.454770\pi\)
\(758\) −32.5807 + 5.16027i −1.18338 + 0.187429i
\(759\) −18.0044 1.77141i −0.653519 0.0642980i
\(760\) 0 0
\(761\) 6.88486 2.23703i 0.249576 0.0810921i −0.181558 0.983380i \(-0.558114\pi\)
0.431133 + 0.902288i \(0.358114\pi\)
\(762\) −2.07707 + 1.70496i −0.0752442 + 0.0617643i
\(763\) −49.9570 + 25.4544i −1.80856 + 0.921509i
\(764\) −5.70322 17.5527i −0.206335 0.635035i
\(765\) 0 0
\(766\) 5.28095 16.2531i 0.190808 0.587248i
\(767\) 3.07662 + 19.4250i 0.111090 + 0.701397i
\(768\) 1.45886 + 0.933665i 0.0526420 + 0.0336907i
\(769\) −2.15066 + 2.96013i −0.0775549 + 0.106745i −0.846032 0.533132i \(-0.821015\pi\)
0.768477 + 0.639877i \(0.221015\pi\)
\(770\) 0 0
\(771\) 39.8636 + 35.4163i 1.43565 + 1.27549i
\(772\) 0.733534 4.63135i 0.0264005 0.166686i
\(773\) −29.4947 15.0283i −1.06085 0.540531i −0.165646 0.986185i \(-0.552971\pi\)
−0.895205 + 0.445655i \(0.852971\pi\)
\(774\) 24.1365 11.1331i 0.867568 0.400171i
\(775\) 0 0
\(776\) 3.51564i 0.126204i
\(777\) 18.1675 + 4.73875i 0.651756 + 0.170002i
\(778\) 13.8752 + 2.19762i 0.497450 + 0.0787884i
\(779\) 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
\(783\) 20.3788