Properties

Label 819.2.bm.f.478.3
Level $819$
Weight $2$
Character 819.478
Analytic conductor $6.540$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 819.bm (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.53974792554\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: 12.0.2346760387617129.1
Defining polynomial: \(x^{12} - 3 x^{11} + x^{10} + 10 x^{9} - 15 x^{8} - 10 x^{7} + 45 x^{6} - 20 x^{5} - 60 x^{4} + 80 x^{3} + 16 x^{2} - 96 x + 64\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 478.3
Root \(0.655911 + 1.25291i\) of defining polynomial
Character \(\chi\) \(=\) 819.478
Dual form 819.2.bm.f.550.4

$q$-expansion

\(f(q)\) \(=\) \(q-0.180824i q^{2} +1.96730 q^{4} +(2.32670 + 1.34332i) q^{5} +(-2.46263 + 0.967177i) q^{7} -0.717383i q^{8} +O(q^{10})\) \(q-0.180824i q^{2} +1.96730 q^{4} +(2.32670 + 1.34332i) q^{5} +(-2.46263 + 0.967177i) q^{7} -0.717383i q^{8} +(0.242904 - 0.420723i) q^{10} +(-2.33328 - 1.34712i) q^{11} +(1.92153 + 3.05086i) q^{13} +(0.174889 + 0.445303i) q^{14} +3.80489 q^{16} +4.76493 q^{17} +(0.163180 - 0.0942122i) q^{19} +(4.57732 + 2.64272i) q^{20} +(-0.243592 + 0.421913i) q^{22} +4.39929 q^{23} +(1.10902 + 1.92088i) q^{25} +(0.551667 - 0.347458i) q^{26} +(-4.84475 + 1.90273i) q^{28} +(3.54280 + 6.13631i) q^{29} +(-3.20369 + 1.84965i) q^{31} -2.12278i q^{32} -0.861613i q^{34} +(-7.02904 - 1.05778i) q^{35} -7.95413i q^{37} +(-0.0170358 - 0.0295069i) q^{38} +(0.963675 - 1.66913i) q^{40} +(-4.70215 + 2.71479i) q^{41} +(-4.00533 + 6.93743i) q^{43} +(-4.59027 - 2.65020i) q^{44} -0.795496i q^{46} +(1.60118 + 0.924445i) q^{47} +(5.12914 - 4.76361i) q^{49} +(0.347341 - 0.200538i) q^{50} +(3.78023 + 6.00196i) q^{52} +(-3.53622 - 6.12491i) q^{53} +(-3.61923 - 6.26869i) q^{55} +(0.693836 + 1.76665i) q^{56} +(1.10959 - 0.640623i) q^{58} +7.58888i q^{59} +(0.205782 + 0.356425i) q^{61} +(0.334461 + 0.579304i) q^{62} +7.22592 q^{64} +(0.372548 + 9.67966i) q^{65} +(-9.87358 - 5.70051i) q^{67} +9.37407 q^{68} +(-0.191271 + 1.27102i) q^{70} +(-2.89675 - 1.67244i) q^{71} +(12.3112 - 7.10790i) q^{73} -1.43830 q^{74} +(0.321025 - 0.185344i) q^{76} +(7.04893 + 1.06077i) q^{77} +(-4.55529 + 7.89000i) q^{79} +(8.85283 + 5.11118i) q^{80} +(0.490899 + 0.850261i) q^{82} -16.5866i q^{83} +(11.0866 + 6.40083i) q^{85} +(1.25445 + 0.724258i) q^{86} +(-0.966401 + 1.67386i) q^{88} -5.89165i q^{89} +(-7.68275 - 5.65468i) q^{91} +8.65473 q^{92} +(0.167162 - 0.289532i) q^{94} +0.506229 q^{95} +(0.390659 + 0.225547i) q^{97} +(-0.861373 - 0.927470i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 8q^{4} + 3q^{5} - 3q^{7} + O(q^{10}) \) \( 12q - 8q^{4} + 3q^{5} - 3q^{7} + 12q^{10} - 12q^{11} - 2q^{13} - 4q^{14} + 16q^{16} + 34q^{17} + 9q^{19} + 3q^{20} - 15q^{22} + 6q^{23} - 5q^{25} + 6q^{26} - 9q^{28} + q^{29} + 18q^{31} + 6q^{35} - 19q^{38} - q^{40} + 6q^{41} + 11q^{43} + 33q^{44} + 15q^{47} - 3q^{49} - 18q^{50} - 7q^{52} + 8q^{53} - 15q^{55} - 27q^{56} - 24q^{58} + 5q^{61} - 41q^{62} + 2q^{64} - 21q^{65} + 15q^{67} - 22q^{68} + 3q^{70} - 30q^{71} + 42q^{73} - 66q^{74} - 45q^{76} + 19q^{77} - 35q^{79} + 63q^{80} + 5q^{82} - 21q^{85} + 57q^{86} - 14q^{88} - 7q^{91} + 66q^{92} + q^{94} + 4q^{95} - 3q^{97} + 18q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.180824i 0.127862i −0.997954 0.0639308i \(-0.979636\pi\)
0.997954 0.0639308i \(-0.0203637\pi\)
\(3\) 0 0
\(4\) 1.96730 0.983651
\(5\) 2.32670 + 1.34332i 1.04053 + 0.600751i 0.919984 0.391956i \(-0.128201\pi\)
0.120548 + 0.992708i \(0.461535\pi\)
\(6\) 0 0
\(7\) −2.46263 + 0.967177i −0.930788 + 0.365559i
\(8\) 0.717383i 0.253633i
\(9\) 0 0
\(10\) 0.242904 0.420723i 0.0768131 0.133044i
\(11\) −2.33328 1.34712i −0.703511 0.406172i 0.105143 0.994457i \(-0.466470\pi\)
−0.808654 + 0.588285i \(0.799803\pi\)
\(12\) 0 0
\(13\) 1.92153 + 3.05086i 0.532937 + 0.846155i
\(14\) 0.174889 + 0.445303i 0.0467409 + 0.119012i
\(15\) 0 0
\(16\) 3.80489 0.951221
\(17\) 4.76493 1.15567 0.577833 0.816155i \(-0.303898\pi\)
0.577833 + 0.816155i \(0.303898\pi\)
\(18\) 0 0
\(19\) 0.163180 0.0942122i 0.0374361 0.0216138i −0.481165 0.876630i \(-0.659786\pi\)
0.518601 + 0.855016i \(0.326453\pi\)
\(20\) 4.57732 + 2.64272i 1.02352 + 0.590930i
\(21\) 0 0
\(22\) −0.243592 + 0.421913i −0.0519339 + 0.0899521i
\(23\) 4.39929 0.917315 0.458657 0.888613i \(-0.348331\pi\)
0.458657 + 0.888613i \(0.348331\pi\)
\(24\) 0 0
\(25\) 1.10902 + 1.92088i 0.221804 + 0.384177i
\(26\) 0.551667 0.347458i 0.108191 0.0681422i
\(27\) 0 0
\(28\) −4.84475 + 1.90273i −0.915571 + 0.359582i
\(29\) 3.54280 + 6.13631i 0.657882 + 1.13948i 0.981163 + 0.193182i \(0.0618807\pi\)
−0.323281 + 0.946303i \(0.604786\pi\)
\(30\) 0 0
\(31\) −3.20369 + 1.84965i −0.575400 + 0.332207i −0.759303 0.650737i \(-0.774460\pi\)
0.183903 + 0.982944i \(0.441127\pi\)
\(32\) 2.12278i 0.375258i
\(33\) 0 0
\(34\) 0.861613i 0.147765i
\(35\) −7.02904 1.05778i −1.18812 0.178797i
\(36\) 0 0
\(37\) 7.95413i 1.30765i −0.756645 0.653826i \(-0.773163\pi\)
0.756645 0.653826i \(-0.226837\pi\)
\(38\) −0.0170358 0.0295069i −0.00276357 0.00478665i
\(39\) 0 0
\(40\) 0.963675 1.66913i 0.152370 0.263913i
\(41\) −4.70215 + 2.71479i −0.734353 + 0.423979i −0.820013 0.572345i \(-0.806034\pi\)
0.0856594 + 0.996324i \(0.472700\pi\)
\(42\) 0 0
\(43\) −4.00533 + 6.93743i −0.610807 + 1.05795i 0.380298 + 0.924864i \(0.375821\pi\)
−0.991105 + 0.133084i \(0.957512\pi\)
\(44\) −4.59027 2.65020i −0.692010 0.399532i
\(45\) 0 0
\(46\) 0.795496i 0.117289i
\(47\) 1.60118 + 0.924445i 0.233557 + 0.134844i 0.612212 0.790694i \(-0.290280\pi\)
−0.378655 + 0.925538i \(0.623613\pi\)
\(48\) 0 0
\(49\) 5.12914 4.76361i 0.732734 0.680515i
\(50\) 0.347341 0.200538i 0.0491215 0.0283603i
\(51\) 0 0
\(52\) 3.78023 + 6.00196i 0.524224 + 0.832322i
\(53\) −3.53622 6.12491i −0.485737 0.841321i 0.514128 0.857713i \(-0.328115\pi\)
−0.999866 + 0.0163917i \(0.994782\pi\)
\(54\) 0 0
\(55\) −3.61923 6.26869i −0.488017 0.845271i
\(56\) 0.693836 + 1.76665i 0.0927177 + 0.236079i
\(57\) 0 0
\(58\) 1.10959 0.640623i 0.145696 0.0841179i
\(59\) 7.58888i 0.987988i 0.869465 + 0.493994i \(0.164464\pi\)
−0.869465 + 0.493994i \(0.835536\pi\)
\(60\) 0 0
\(61\) 0.205782 + 0.356425i 0.0263477 + 0.0456355i 0.878899 0.477009i \(-0.158279\pi\)
−0.852551 + 0.522644i \(0.824946\pi\)
\(62\) 0.334461 + 0.579304i 0.0424766 + 0.0735716i
\(63\) 0 0
\(64\) 7.22592 0.903240
\(65\) 0.372548 + 9.67966i 0.0462089 + 1.20061i
\(66\) 0 0
\(67\) −9.87358 5.70051i −1.20625 0.696429i −0.244312 0.969697i \(-0.578562\pi\)
−0.961938 + 0.273268i \(0.911895\pi\)
\(68\) 9.37407 1.13677
\(69\) 0 0
\(70\) −0.191271 + 1.27102i −0.0228613 + 0.151916i
\(71\) −2.89675 1.67244i −0.343781 0.198482i 0.318162 0.948037i \(-0.396935\pi\)
−0.661943 + 0.749554i \(0.730268\pi\)
\(72\) 0 0
\(73\) 12.3112 7.10790i 1.44092 0.831917i 0.443011 0.896516i \(-0.353910\pi\)
0.997911 + 0.0645994i \(0.0205769\pi\)
\(74\) −1.43830 −0.167199
\(75\) 0 0
\(76\) 0.321025 0.185344i 0.0368241 0.0212604i
\(77\) 7.04893 + 1.06077i 0.803300 + 0.120886i
\(78\) 0 0
\(79\) −4.55529 + 7.89000i −0.512511 + 0.887695i 0.487384 + 0.873188i \(0.337951\pi\)
−0.999895 + 0.0145069i \(0.995382\pi\)
\(80\) 8.85283 + 5.11118i 0.989776 + 0.571448i
\(81\) 0 0
\(82\) 0.490899 + 0.850261i 0.0542107 + 0.0938956i
\(83\) 16.5866i 1.82061i −0.413934 0.910307i \(-0.635845\pi\)
0.413934 0.910307i \(-0.364155\pi\)
\(84\) 0 0
\(85\) 11.0866 + 6.40083i 1.20251 + 0.694268i
\(86\) 1.25445 + 0.724258i 0.135271 + 0.0780988i
\(87\) 0 0
\(88\) −0.966401 + 1.67386i −0.103019 + 0.178434i
\(89\) 5.89165i 0.624513i −0.949998 0.312257i \(-0.898915\pi\)
0.949998 0.312257i \(-0.101085\pi\)
\(90\) 0 0
\(91\) −7.68275 5.65468i −0.805371 0.592772i
\(92\) 8.65473 0.902318
\(93\) 0 0
\(94\) 0.167162 0.289532i 0.0172414 0.0298630i
\(95\) 0.506229 0.0519380
\(96\) 0 0
\(97\) 0.390659 + 0.225547i 0.0396654 + 0.0229008i 0.519702 0.854348i \(-0.326043\pi\)
−0.480036 + 0.877249i \(0.659376\pi\)
\(98\) −0.861373 0.927470i −0.0870118 0.0936886i
\(99\) 0 0
\(100\) 2.18178 + 3.77896i 0.218178 + 0.377896i
\(101\) 3.82840 6.63098i 0.380940 0.659807i −0.610257 0.792204i \(-0.708934\pi\)
0.991197 + 0.132396i \(0.0422671\pi\)
\(102\) 0 0
\(103\) 2.57870 4.46644i 0.254087 0.440091i −0.710560 0.703636i \(-0.751558\pi\)
0.964647 + 0.263545i \(0.0848918\pi\)
\(104\) 2.18863 1.37847i 0.214613 0.135170i
\(105\) 0 0
\(106\) −1.10753 + 0.639433i −0.107573 + 0.0621072i
\(107\) −8.03289 −0.776569 −0.388284 0.921540i \(-0.626932\pi\)
−0.388284 + 0.921540i \(0.626932\pi\)
\(108\) 0 0
\(109\) 1.15490 0.666781i 0.110619 0.0638660i −0.443670 0.896190i \(-0.646324\pi\)
0.554289 + 0.832324i \(0.312990\pi\)
\(110\) −1.13353 + 0.654443i −0.108078 + 0.0623987i
\(111\) 0 0
\(112\) −9.37004 + 3.68000i −0.885386 + 0.347727i
\(113\) −9.96917 + 17.2671i −0.937821 + 1.62435i −0.168296 + 0.985736i \(0.553827\pi\)
−0.769525 + 0.638617i \(0.779507\pi\)
\(114\) 0 0
\(115\) 10.2358 + 5.90965i 0.954495 + 0.551078i
\(116\) 6.96976 + 12.0720i 0.647126 + 1.12086i
\(117\) 0 0
\(118\) 1.37225 0.126326
\(119\) −11.7343 + 4.60853i −1.07568 + 0.422464i
\(120\) 0 0
\(121\) −1.87053 3.23985i −0.170048 0.294532i
\(122\) 0.0644501 0.0372103i 0.00583503 0.00336886i
\(123\) 0 0
\(124\) −6.30263 + 3.63883i −0.565993 + 0.326776i
\(125\) 7.47412i 0.668505i
\(126\) 0 0
\(127\) −3.98361 6.89981i −0.353488 0.612259i 0.633370 0.773849i \(-0.281671\pi\)
−0.986858 + 0.161590i \(0.948338\pi\)
\(128\) 5.55218i 0.490748i
\(129\) 0 0
\(130\) 1.75031 0.0673655i 0.153513 0.00590835i
\(131\) 5.00897 8.67579i 0.437636 0.758007i −0.559871 0.828580i \(-0.689149\pi\)
0.997507 + 0.0705727i \(0.0224827\pi\)
\(132\) 0 0
\(133\) −0.310734 + 0.389835i −0.0269440 + 0.0338029i
\(134\) −1.03079 + 1.78538i −0.0890465 + 0.154233i
\(135\) 0 0
\(136\) 3.41828i 0.293115i
\(137\) 5.06696i 0.432899i −0.976294 0.216450i \(-0.930552\pi\)
0.976294 0.216450i \(-0.0694477\pi\)
\(138\) 0 0
\(139\) −3.86289 + 6.69073i −0.327646 + 0.567500i −0.982044 0.188650i \(-0.939589\pi\)
0.654398 + 0.756150i \(0.272922\pi\)
\(140\) −13.8283 2.08097i −1.16870 0.175874i
\(141\) 0 0
\(142\) −0.302417 + 0.523802i −0.0253783 + 0.0439565i
\(143\) −0.373602 9.70704i −0.0312422 0.811744i
\(144\) 0 0
\(145\) 19.0365i 1.58089i
\(146\) −1.28528 2.22617i −0.106370 0.184239i
\(147\) 0 0
\(148\) 15.6482i 1.28627i
\(149\) −12.4002 + 7.15924i −1.01586 + 0.586507i −0.912902 0.408178i \(-0.866164\pi\)
−0.102958 + 0.994686i \(0.532831\pi\)
\(150\) 0 0
\(151\) 5.60534 3.23624i 0.456156 0.263362i −0.254271 0.967133i \(-0.581835\pi\)
0.710427 + 0.703771i \(0.248502\pi\)
\(152\) −0.0675862 0.117063i −0.00548197 0.00949504i
\(153\) 0 0
\(154\) 0.191812 1.27461i 0.0154567 0.102711i
\(155\) −9.93871 −0.798296
\(156\) 0 0
\(157\) −7.95937 13.7860i −0.635227 1.10025i −0.986467 0.163960i \(-0.947573\pi\)
0.351240 0.936285i \(-0.385760\pi\)
\(158\) 1.42670 + 0.823705i 0.113502 + 0.0655305i
\(159\) 0 0
\(160\) 2.85157 4.93907i 0.225437 0.390468i
\(161\) −10.8338 + 4.25489i −0.853826 + 0.335332i
\(162\) 0 0
\(163\) −4.14100 + 2.39081i −0.324348 + 0.187263i −0.653329 0.757074i \(-0.726628\pi\)
0.328981 + 0.944337i \(0.393295\pi\)
\(164\) −9.25056 + 5.34081i −0.722348 + 0.417048i
\(165\) 0 0
\(166\) −2.99925 −0.232787
\(167\) 2.34729 1.35521i 0.181639 0.104869i −0.406424 0.913685i \(-0.633224\pi\)
0.588062 + 0.808816i \(0.299891\pi\)
\(168\) 0 0
\(169\) −5.61544 + 11.7246i −0.431957 + 0.901894i
\(170\) 1.15742 2.00472i 0.0887703 0.153755i
\(171\) 0 0
\(172\) −7.87969 + 13.6480i −0.600821 + 1.04065i
\(173\) 0.449908 + 0.779264i 0.0342059 + 0.0592463i 0.882622 0.470084i \(-0.155776\pi\)
−0.848416 + 0.529331i \(0.822443\pi\)
\(174\) 0 0
\(175\) −4.58895 3.65781i −0.346892 0.276505i
\(176\) −8.87787 5.12564i −0.669195 0.386360i
\(177\) 0 0
\(178\) −1.06535 −0.0798513
\(179\) 5.52791 9.57462i 0.413175 0.715641i −0.582060 0.813146i \(-0.697753\pi\)
0.995235 + 0.0975054i \(0.0310863\pi\)
\(180\) 0 0
\(181\) −3.52898 −0.262307 −0.131153 0.991362i \(-0.541868\pi\)
−0.131153 + 0.991362i \(0.541868\pi\)
\(182\) −1.02250 + 1.38922i −0.0757928 + 0.102976i
\(183\) 0 0
\(184\) 3.15597i 0.232661i
\(185\) 10.6850 18.5069i 0.785573 1.36065i
\(186\) 0 0
\(187\) −11.1179 6.41894i −0.813024 0.469400i
\(188\) 3.15002 + 1.81866i 0.229738 + 0.132640i
\(189\) 0 0
\(190\) 0.0915382i 0.00664088i
\(191\) −10.2002 17.6672i −0.738059 1.27836i −0.953368 0.301810i \(-0.902409\pi\)
0.215309 0.976546i \(-0.430924\pi\)
\(192\) 0 0
\(193\) −14.9515 8.63228i −1.07624 0.621365i −0.146357 0.989232i \(-0.546755\pi\)
−0.929878 + 0.367867i \(0.880088\pi\)
\(194\) 0.0407842 0.0706403i 0.00292814 0.00507168i
\(195\) 0 0
\(196\) 10.0906 9.37146i 0.720755 0.669390i
\(197\) 4.29264 2.47836i 0.305838 0.176576i −0.339224 0.940705i \(-0.610165\pi\)
0.645063 + 0.764130i \(0.276831\pi\)
\(198\) 0 0
\(199\) −7.18195 −0.509115 −0.254557 0.967058i \(-0.581930\pi\)
−0.254557 + 0.967058i \(0.581930\pi\)
\(200\) 1.37801 0.795593i 0.0974399 0.0562569i
\(201\) 0 0
\(202\) −1.19904 0.692265i −0.0843641 0.0487076i
\(203\) −14.6595 11.6850i −1.02890 0.820125i
\(204\) 0 0
\(205\) −14.5873 −1.01882
\(206\) −0.807638 0.466290i −0.0562708 0.0324880i
\(207\) 0 0
\(208\) 7.31121 + 11.6082i 0.506941 + 0.804881i
\(209\) −0.507661 −0.0351157
\(210\) 0 0
\(211\) 8.79636 + 15.2357i 0.605566 + 1.04887i 0.991962 + 0.126539i \(0.0403868\pi\)
−0.386395 + 0.922333i \(0.626280\pi\)
\(212\) −6.95682 12.0496i −0.477796 0.827567i
\(213\) 0 0
\(214\) 1.45254i 0.0992934i
\(215\) −18.6384 + 10.7609i −1.27113 + 0.733886i
\(216\) 0 0
\(217\) 6.10058 7.65356i 0.414135 0.519557i
\(218\) −0.120570 0.208833i −0.00816602 0.0141440i
\(219\) 0 0
\(220\) −7.12013 12.3324i −0.480039 0.831452i
\(221\) 9.15597 + 14.5371i 0.615897 + 0.977873i
\(222\) 0 0
\(223\) 12.2157 7.05271i 0.818020 0.472284i −0.0317129 0.999497i \(-0.510096\pi\)
0.849733 + 0.527213i \(0.176763\pi\)
\(224\) 2.05310 + 5.22763i 0.137179 + 0.349286i
\(225\) 0 0
\(226\) 3.12230 + 1.80266i 0.207693 + 0.119911i
\(227\) 2.86877i 0.190407i −0.995458 0.0952035i \(-0.969650\pi\)
0.995458 0.0952035i \(-0.0303502\pi\)
\(228\) 0 0
\(229\) 7.59860 + 4.38706i 0.502130 + 0.289905i 0.729593 0.683882i \(-0.239710\pi\)
−0.227463 + 0.973787i \(0.573043\pi\)
\(230\) 1.06861 1.85088i 0.0704618 0.122043i
\(231\) 0 0
\(232\) 4.40208 2.54154i 0.289011 0.166861i
\(233\) −2.55371 + 4.42316i −0.167299 + 0.289771i −0.937469 0.348068i \(-0.886838\pi\)
0.770170 + 0.637839i \(0.220171\pi\)
\(234\) 0 0
\(235\) 2.48365 + 4.30181i 0.162016 + 0.280619i
\(236\) 14.9296i 0.971836i
\(237\) 0 0
\(238\) 0.833332 + 2.12184i 0.0540169 + 0.137538i
\(239\) 2.49797i 0.161580i −0.996731 0.0807901i \(-0.974256\pi\)
0.996731 0.0807901i \(-0.0257443\pi\)
\(240\) 0 0
\(241\) 7.98512i 0.514367i 0.966363 + 0.257183i \(0.0827944\pi\)
−0.966363 + 0.257183i \(0.917206\pi\)
\(242\) −0.585842 + 0.338236i −0.0376593 + 0.0217426i
\(243\) 0 0
\(244\) 0.404835 + 0.701195i 0.0259169 + 0.0448894i
\(245\) 18.3330 4.19341i 1.17125 0.267907i
\(246\) 0 0
\(247\) 0.600984 + 0.316808i 0.0382397 + 0.0201580i
\(248\) 1.32691 + 2.29827i 0.0842588 + 0.145941i
\(249\) 0 0
\(250\) −1.35150 −0.0854762
\(251\) −12.6285 + 21.8732i −0.797105 + 1.38063i 0.124389 + 0.992234i \(0.460303\pi\)
−0.921494 + 0.388393i \(0.873030\pi\)
\(252\) 0 0
\(253\) −10.2648 5.92637i −0.645341 0.372588i
\(254\) −1.24765 + 0.720331i −0.0782845 + 0.0451976i
\(255\) 0 0
\(256\) 13.4479 0.840493
\(257\) −3.37363 −0.210442 −0.105221 0.994449i \(-0.533555\pi\)
−0.105221 + 0.994449i \(0.533555\pi\)
\(258\) 0 0
\(259\) 7.69305 + 19.5881i 0.478023 + 1.21715i
\(260\) 0.732915 + 19.0428i 0.0454535 + 1.18099i
\(261\) 0 0
\(262\) −1.56879 0.905740i −0.0969201 0.0559568i
\(263\) −0.0794677 + 0.137642i −0.00490019 + 0.00848737i −0.868465 0.495750i \(-0.834893\pi\)
0.863565 + 0.504238i \(0.168226\pi\)
\(264\) 0 0
\(265\) 19.0011i 1.16723i
\(266\) 0.0704914 + 0.0561880i 0.00432210 + 0.00344511i
\(267\) 0 0
\(268\) −19.4243 11.2146i −1.18653 0.685043i
\(269\) 23.3266 1.42225 0.711124 0.703066i \(-0.248186\pi\)
0.711124 + 0.703066i \(0.248186\pi\)
\(270\) 0 0
\(271\) 11.8210i 0.718074i −0.933323 0.359037i \(-0.883105\pi\)
0.933323 0.359037i \(-0.116895\pi\)
\(272\) 18.1300 1.09929
\(273\) 0 0
\(274\) −0.916226 −0.0553513
\(275\) 5.97595i 0.360363i
\(276\) 0 0
\(277\) 27.3653 1.64422 0.822111 0.569327i \(-0.192796\pi\)
0.822111 + 0.569327i \(0.192796\pi\)
\(278\) 1.20984 + 0.698503i 0.0725615 + 0.0418934i
\(279\) 0 0
\(280\) −0.758831 + 5.04251i −0.0453488 + 0.301348i
\(281\) 28.5383i 1.70245i 0.524801 + 0.851225i \(0.324140\pi\)
−0.524801 + 0.851225i \(0.675860\pi\)
\(282\) 0 0
\(283\) 8.98604 15.5643i 0.534165 0.925201i −0.465038 0.885290i \(-0.653960\pi\)
0.999203 0.0399101i \(-0.0127072\pi\)
\(284\) −5.69879 3.29020i −0.338161 0.195237i
\(285\) 0 0
\(286\) −1.75526 + 0.0675561i −0.103791 + 0.00399468i
\(287\) 8.95400 11.2334i 0.528538 0.663084i
\(288\) 0 0
\(289\) 5.70459 0.335564
\(290\) 3.44225 0.202136
\(291\) 0 0
\(292\) 24.2199 13.9834i 1.41737 0.818316i
\(293\) −12.8943 7.44453i −0.753293 0.434914i 0.0735896 0.997289i \(-0.476554\pi\)
−0.826882 + 0.562375i \(0.809888\pi\)
\(294\) 0 0
\(295\) −10.1943 + 17.6570i −0.593535 + 1.02803i
\(296\) −5.70616 −0.331664
\(297\) 0 0
\(298\) 1.29456 + 2.24224i 0.0749918 + 0.129890i
\(299\) 8.45337 + 13.4216i 0.488871 + 0.776191i
\(300\) 0 0
\(301\) 3.15393 20.9582i 0.181790 1.20801i
\(302\) −0.585190 1.01358i −0.0336739 0.0583249i
\(303\) 0 0
\(304\) 0.620883 0.358467i 0.0356101 0.0205595i
\(305\) 1.10572i 0.0633136i
\(306\) 0 0
\(307\) 23.5161i 1.34214i 0.741396 + 0.671068i \(0.234164\pi\)
−0.741396 + 0.671068i \(0.765836\pi\)
\(308\) 13.8674 + 2.08686i 0.790167 + 0.118910i
\(309\) 0 0
\(310\) 1.79715i 0.102072i
\(311\) −0.815450 1.41240i −0.0462399 0.0800899i 0.841979 0.539510i \(-0.181391\pi\)
−0.888219 + 0.459420i \(0.848057\pi\)
\(312\) 0 0
\(313\) 0.348367 0.603389i 0.0196909 0.0341056i −0.856012 0.516956i \(-0.827065\pi\)
0.875703 + 0.482850i \(0.160398\pi\)
\(314\) −2.49284 + 1.43924i −0.140679 + 0.0812212i
\(315\) 0 0
\(316\) −8.96164 + 15.5220i −0.504132 + 0.873182i
\(317\) −18.5579 10.7144i −1.04231 0.601780i −0.121826 0.992551i \(-0.538875\pi\)
−0.920488 + 0.390771i \(0.872208\pi\)
\(318\) 0 0
\(319\) 19.0903i 1.06885i
\(320\) 16.8126 + 9.70673i 0.939850 + 0.542623i
\(321\) 0 0
\(322\) 0.769385 + 1.95901i 0.0428762 + 0.109172i
\(323\) 0.777544 0.448915i 0.0432637 0.0249783i
\(324\) 0 0
\(325\) −3.72932 + 7.07450i −0.206865 + 0.392423i
\(326\) 0.432315 + 0.748792i 0.0239437 + 0.0414717i
\(327\) 0 0
\(328\) 1.94754 + 3.37324i 0.107535 + 0.186256i
\(329\) −4.83723 0.727939i −0.266685 0.0401326i
\(330\) 0 0
\(331\) −1.31676 + 0.760232i −0.0723757 + 0.0417861i −0.535751 0.844376i \(-0.679971\pi\)
0.463375 + 0.886162i \(0.346638\pi\)
\(332\) 32.6308i 1.79085i
\(333\) 0 0
\(334\) −0.245054 0.424446i −0.0134088 0.0232247i
\(335\) −15.3152 26.5268i −0.836761 1.44931i
\(336\) 0 0
\(337\) −32.2304 −1.75570 −0.877850 0.478936i \(-0.841023\pi\)
−0.877850 + 0.478936i \(0.841023\pi\)
\(338\) 2.12009 + 1.01540i 0.115318 + 0.0552307i
\(339\) 0 0
\(340\) 21.8106 + 12.5924i 1.18285 + 0.682918i
\(341\) 9.96683 0.539734
\(342\) 0 0
\(343\) −8.02394 + 16.6918i −0.433252 + 0.901273i
\(344\) 4.97679 + 2.87335i 0.268331 + 0.154921i
\(345\) 0 0
\(346\) 0.140909 0.0813541i 0.00757534 0.00437362i
\(347\) −8.18431 −0.439357 −0.219678 0.975572i \(-0.570501\pi\)
−0.219678 + 0.975572i \(0.570501\pi\)
\(348\) 0 0
\(349\) −18.9220 + 10.9246i −1.01287 + 0.584782i −0.912031 0.410120i \(-0.865487\pi\)
−0.100841 + 0.994903i \(0.532153\pi\)
\(350\) −0.661419 + 0.829791i −0.0353543 + 0.0443542i
\(351\) 0 0
\(352\) −2.85964 + 4.95304i −0.152419 + 0.263998i
\(353\) 0.491192 + 0.283590i 0.0261435 + 0.0150940i 0.513015 0.858380i \(-0.328529\pi\)
−0.486871 + 0.873474i \(0.661862\pi\)
\(354\) 0 0
\(355\) −4.49325 7.78254i −0.238477 0.413054i
\(356\) 11.5907i 0.614303i
\(357\) 0 0
\(358\) −1.73132 0.999577i −0.0915030 0.0528293i
\(359\) 28.0630 + 16.2022i 1.48111 + 0.855118i 0.999771 0.0214184i \(-0.00681822\pi\)
0.481336 + 0.876536i \(0.340152\pi\)
\(360\) 0 0
\(361\) −9.48225 + 16.4237i −0.499066 + 0.864407i
\(362\) 0.638123i 0.0335390i
\(363\) 0 0
\(364\) −15.1143 11.1245i −0.792204 0.583081i
\(365\) 38.1928 1.99910
\(366\) 0 0
\(367\) 3.93444 6.81465i 0.205376 0.355722i −0.744876 0.667202i \(-0.767492\pi\)
0.950252 + 0.311481i \(0.100825\pi\)
\(368\) 16.7388 0.872569
\(369\) 0 0
\(370\) −3.34648 1.93209i −0.173975 0.100445i
\(371\) 14.6323 + 11.6633i 0.759671 + 0.605527i
\(372\) 0 0
\(373\) 1.04581 + 1.81140i 0.0541502 + 0.0937909i 0.891830 0.452371i \(-0.149422\pi\)
−0.837680 + 0.546162i \(0.816088\pi\)
\(374\) −1.16070 + 2.01039i −0.0600182 + 0.103955i
\(375\) 0 0
\(376\) 0.663180 1.14866i 0.0342009 0.0592377i
\(377\) −11.9134 + 22.5997i −0.613571 + 1.16394i
\(378\) 0 0
\(379\) 12.3983 7.15817i 0.636859 0.367691i −0.146545 0.989204i \(-0.546815\pi\)
0.783404 + 0.621513i \(0.213482\pi\)
\(380\) 0.995906 0.0510889
\(381\) 0 0
\(382\) −3.19466 + 1.84444i −0.163453 + 0.0943695i
\(383\) −21.8129 + 12.5937i −1.11459 + 0.643507i −0.940013 0.341138i \(-0.889188\pi\)
−0.174573 + 0.984644i \(0.555854\pi\)
\(384\) 0 0
\(385\) 14.9758 + 11.9371i 0.763237 + 0.608369i
\(386\) −1.56092 + 2.70359i −0.0794488 + 0.137609i
\(387\) 0 0
\(388\) 0.768544 + 0.443719i 0.0390169 + 0.0225264i
\(389\) −14.0512 24.3373i −0.712422 1.23395i −0.963946 0.266099i \(-0.914265\pi\)
0.251524 0.967851i \(-0.419068\pi\)
\(390\) 0 0
\(391\) 20.9623 1.06011
\(392\) −3.41733 3.67955i −0.172601 0.185845i
\(393\) 0 0
\(394\) −0.448146 0.776212i −0.0225773 0.0391050i
\(395\) −21.1976 + 12.2384i −1.06657 + 0.615783i
\(396\) 0 0
\(397\) −18.8590 + 10.8882i −0.946504 + 0.546465i −0.891993 0.452049i \(-0.850693\pi\)
−0.0545111 + 0.998513i \(0.517360\pi\)
\(398\) 1.29867i 0.0650963i
\(399\) 0 0
\(400\) 4.21970 + 7.30874i 0.210985 + 0.365437i
\(401\) 20.5290i 1.02517i −0.858637 0.512584i \(-0.828688\pi\)
0.858637 0.512584i \(-0.171312\pi\)
\(402\) 0 0
\(403\) −11.7990 6.21984i −0.587751 0.309832i
\(404\) 7.53162 13.0451i 0.374712 0.649020i
\(405\) 0 0
\(406\) −2.11292 + 2.65079i −0.104863 + 0.131557i
\(407\) −10.7152 + 18.5592i −0.531132 + 0.919947i
\(408\) 0 0
\(409\) 6.26862i 0.309963i 0.987917 + 0.154982i \(0.0495319\pi\)
−0.987917 + 0.154982i \(0.950468\pi\)
\(410\) 2.63774i 0.130269i
\(411\) 0 0
\(412\) 5.07308 8.78683i 0.249933 0.432896i
\(413\) −7.33979 18.6886i −0.361168 0.919608i
\(414\) 0 0
\(415\) 22.2811 38.5920i 1.09374 1.89441i
\(416\) 6.47629 4.07899i 0.317526 0.199989i
\(417\) 0 0
\(418\) 0.0917972i 0.00448995i
\(419\) 17.0817 + 29.5864i 0.834497 + 1.44539i 0.894439 + 0.447189i \(0.147575\pi\)
−0.0599424 + 0.998202i \(0.519092\pi\)
\(420\) 0 0
\(421\) 11.5233i 0.561613i 0.959764 + 0.280806i \(0.0906019\pi\)
−0.959764 + 0.280806i \(0.909398\pi\)
\(422\) 2.75498 1.59059i 0.134111 0.0774288i
\(423\) 0 0
\(424\) −4.39391 + 2.53682i −0.213387 + 0.123199i
\(425\) 5.28442 + 9.15288i 0.256332 + 0.443980i
\(426\) 0 0
\(427\) −0.851492 0.678716i −0.0412066 0.0328454i
\(428\) −15.8031 −0.763873
\(429\) 0 0
\(430\) 1.94582 + 3.37026i 0.0938359 + 0.162529i
\(431\) 7.59505 + 4.38500i 0.365841 + 0.211218i 0.671640 0.740878i \(-0.265590\pi\)
−0.305799 + 0.952096i \(0.598924\pi\)
\(432\) 0 0
\(433\) 11.0535 19.1452i 0.531196 0.920058i −0.468141 0.883654i \(-0.655076\pi\)
0.999337 0.0364046i \(-0.0115905\pi\)
\(434\) −1.38394 1.10313i −0.0664315 0.0529519i
\(435\) 0 0
\(436\) 2.27203 1.31176i 0.108811 0.0628219i
\(437\) 0.717877 0.414467i 0.0343407 0.0198266i
\(438\) 0 0
\(439\) 10.3709 0.494978 0.247489 0.968891i \(-0.420395\pi\)
0.247489 + 0.968891i \(0.420395\pi\)
\(440\) −4.49705 + 2.59637i −0.214389 + 0.123777i
\(441\) 0 0
\(442\) 2.62866 1.65562i 0.125032 0.0787496i
\(443\) 17.9068 31.0156i 0.850780 1.47359i −0.0297257 0.999558i \(-0.509463\pi\)
0.880506 0.474036i \(-0.157203\pi\)
\(444\) 0 0
\(445\) 7.91437 13.7081i 0.375177 0.649826i
\(446\) −1.27530 2.20888i −0.0603871 0.104593i
\(447\) 0 0
\(448\) −17.7948 + 6.98875i −0.840726 + 0.330187i
\(449\) 19.7023 + 11.3751i 0.929809 + 0.536825i 0.886751 0.462247i \(-0.152957\pi\)
0.0430575 + 0.999073i \(0.486290\pi\)
\(450\) 0 0
\(451\) 14.6286 0.688834
\(452\) −19.6124 + 33.9696i −0.922489 + 1.59780i
\(453\) 0 0
\(454\) −0.518742 −0.0243458
\(455\) −10.2794 23.4771i −0.481905 1.10063i
\(456\) 0 0
\(457\) 31.3172i 1.46496i 0.680791 + 0.732478i \(0.261636\pi\)
−0.680791 + 0.732478i \(0.738364\pi\)
\(458\) 0.793284 1.37401i 0.0370677 0.0642032i
\(459\) 0 0
\(460\) 20.1370 + 11.6261i 0.938891 + 0.542069i
\(461\) 7.28113 + 4.20376i 0.339116 + 0.195789i 0.659881 0.751370i \(-0.270607\pi\)
−0.320765 + 0.947159i \(0.603940\pi\)
\(462\) 0 0
\(463\) 10.0392i 0.466563i −0.972409 0.233281i \(-0.925054\pi\)
0.972409 0.233281i \(-0.0749463\pi\)
\(464\) 13.4800 + 23.3480i 0.625791 + 1.08390i
\(465\) 0 0
\(466\) 0.799813 + 0.461772i 0.0370506 + 0.0213912i
\(467\) 13.1756 22.8209i 0.609696 1.05602i −0.381594 0.924330i \(-0.624625\pi\)
0.991290 0.131695i \(-0.0420418\pi\)
\(468\) 0 0
\(469\) 29.8284 + 4.48878i 1.37735 + 0.207273i
\(470\) 0.777869 0.449103i 0.0358804 0.0207156i
\(471\) 0 0
\(472\) 5.44413 0.250586
\(473\) 18.6911 10.7913i 0.859418 0.496185i
\(474\) 0 0
\(475\) 0.361941 + 0.208967i 0.0166070 + 0.00958806i
\(476\) −23.0849 + 9.06638i −1.05809 + 0.415557i
\(477\) 0 0
\(478\) −0.451692 −0.0206599
\(479\) 7.43409 + 4.29207i 0.339672 + 0.196110i 0.660127 0.751154i \(-0.270502\pi\)
−0.320455 + 0.947264i \(0.603836\pi\)
\(480\) 0 0
\(481\) 24.2669 15.2841i 1.10648 0.696895i
\(482\) 1.44390 0.0657678
\(483\) 0 0
\(484\) −3.67990 6.37377i −0.167268 0.289717i
\(485\) 0.605963 + 1.04956i 0.0275154 + 0.0476580i
\(486\) 0 0
\(487\) 21.2562i 0.963212i 0.876388 + 0.481606i \(0.159946\pi\)
−0.876388 + 0.481606i \(0.840054\pi\)
\(488\) 0.255693 0.147624i 0.0115747 0.00668264i
\(489\) 0 0
\(490\) −0.758268 3.31504i −0.0342551 0.149758i
\(491\) 11.2268 + 19.4453i 0.506657 + 0.877556i 0.999970 + 0.00770409i \(0.00245231\pi\)
−0.493313 + 0.869852i \(0.664214\pi\)
\(492\) 0 0
\(493\) 16.8812 + 29.2391i 0.760292 + 1.31686i
\(494\) 0.0572864 0.108672i 0.00257744 0.00488939i
\(495\) 0 0
\(496\) −12.1897 + 7.03772i −0.547333 + 0.316003i
\(497\) 8.75119 + 1.31694i 0.392545 + 0.0590727i
\(498\) 0 0
\(499\) −33.6694 19.4390i −1.50725 0.870210i −0.999964 0.00843082i \(-0.997316\pi\)
−0.507284 0.861779i \(-0.669350\pi\)
\(500\) 14.7039i 0.657576i
\(501\) 0 0
\(502\) 3.95520 + 2.28354i 0.176529 + 0.101919i
\(503\) 2.72850 4.72591i 0.121658 0.210718i −0.798764 0.601645i \(-0.794512\pi\)
0.920422 + 0.390927i \(0.127846\pi\)
\(504\) 0 0
\(505\) 17.8151 10.2855i 0.792760 0.457700i
\(506\) −1.07163 + 1.85612i −0.0476397 + 0.0825144i
\(507\) 0 0
\(508\) −7.83697 13.5740i −0.347709 0.602250i
\(509\) 10.8925i 0.482800i 0.970426 + 0.241400i \(0.0776066\pi\)
−0.970426 + 0.241400i \(0.922393\pi\)
\(510\) 0 0
\(511\) −23.4435 + 29.4113i −1.03708 + 1.30108i
\(512\) 13.5360i 0.598214i
\(513\) 0 0
\(514\) 0.610033i 0.0269074i
\(515\) 11.9997 6.92804i 0.528771 0.305286i
\(516\) 0 0
\(517\) −2.49068 4.31398i −0.109540 0.189729i
\(518\) 3.54200 1.39109i 0.155626 0.0611209i
\(519\) 0 0
\(520\) 6.94402 0.267260i 0.304515 0.0117201i
\(521\) 13.9480 + 24.1587i 0.611074 + 1.05841i 0.991060 + 0.133419i \(0.0425957\pi\)
−0.379985 + 0.924993i \(0.624071\pi\)
\(522\) 0 0
\(523\) 16.7236 0.731272 0.365636 0.930758i \(-0.380852\pi\)
0.365636 + 0.930758i \(0.380852\pi\)
\(524\) 9.85416 17.0679i 0.430481 0.745615i
\(525\) 0 0
\(526\) 0.0248890 + 0.0143696i 0.00108521 + 0.000626546i
\(527\) −15.2654 + 8.81347i −0.664970 + 0.383921i
\(528\) 0 0
\(529\) −3.64627 −0.158534
\(530\) −3.43585 −0.149244
\(531\) 0 0
\(532\) −0.611307 + 0.766923i −0.0265035 + 0.0332503i
\(533\) −17.3178 9.12904i −0.750116 0.395423i
\(534\) 0 0
\(535\) −18.6901 10.7907i −0.808045 0.466525i
\(536\) −4.08945 + 7.08313i −0.176637 + 0.305945i
\(537\) 0 0
\(538\) 4.21800i 0.181851i
\(539\) −18.3849 + 4.20527i −0.791893 + 0.181134i
\(540\) 0 0
\(541\) 9.66528 + 5.58025i 0.415543 + 0.239914i 0.693169 0.720776i \(-0.256214\pi\)
−0.277626 + 0.960689i \(0.589547\pi\)
\(542\) −2.13751 −0.0918141
\(543\) 0 0
\(544\) 10.1149i 0.433673i
\(545\) 3.58280 0.153470
\(546\) 0 0
\(547\) 36.6556 1.56728 0.783640 0.621215i \(-0.213361\pi\)
0.783640 + 0.621215i \(0.213361\pi\)
\(548\) 9.96824i 0.425822i
\(549\) 0 0
\(550\) −1.08059 −0.0460767
\(551\) 1.15623 + 0.667551i 0.0492571 + 0.0284386i
\(552\) 0 0
\(553\) 3.58700 23.8360i 0.152535 1.01361i
\(554\) 4.94830i 0.210233i
\(555\) 0 0
\(556\) −7.59948 + 13.1627i −0.322290 + 0.558222i
\(557\) 28.6461 + 16.5388i 1.21377 + 0.700772i 0.963579 0.267424i \(-0.0861725\pi\)
0.250193 + 0.968196i \(0.419506\pi\)
\(558\) 0 0
\(559\) −28.8615 + 1.11081i −1.22071 + 0.0469823i
\(560\) −26.7447 4.02472i −1.13017 0.170076i
\(561\) 0 0
\(562\) 5.16039 0.217678
\(563\) 17.7967 0.750043 0.375021 0.927016i \(-0.377635\pi\)
0.375021 + 0.927016i \(0.377635\pi\)
\(564\) 0 0
\(565\) −46.3906 + 26.7836i −1.95167 + 1.12679i
\(566\) −2.81439 1.62489i −0.118298 0.0682992i
\(567\) 0 0
\(568\) −1.19978 + 2.07808i −0.0503417 + 0.0871943i
\(569\) −8.22094 −0.344640 −0.172320 0.985041i \(-0.555126\pi\)
−0.172320 + 0.985041i \(0.555126\pi\)
\(570\) 0 0
\(571\) −12.8776 22.3047i −0.538912 0.933424i −0.998963 0.0455309i \(-0.985502\pi\)
0.460051 0.887893i \(-0.347831\pi\)
\(572\) −0.734988 19.0967i −0.0307314 0.798473i
\(573\) 0 0
\(574\) −2.03126 1.61910i −0.0847830 0.0675798i
\(575\) 4.87891 + 8.45051i 0.203464 + 0.352411i
\(576\) 0 0
\(577\) −0.666314 + 0.384697i −0.0277390 + 0.0160151i −0.513805 0.857907i \(-0.671765\pi\)
0.486066 + 0.873922i \(0.338431\pi\)
\(578\) 1.03152i 0.0429058i
\(579\) 0 0
\(580\) 37.4505i 1.55505i
\(581\) 16.0422 + 40.8467i 0.665541 + 1.69461i
\(582\) 0 0
\(583\) 19.0549i 0.789172i
\(584\) −5.09908 8.83187i −0.211002 0.365465i
\(585\) 0 0
\(586\) −1.34615 + 2.33159i −0.0556088 + 0.0963173i
\(587\) 10.4727 6.04644i 0.432256 0.249563i −0.268051 0.963405i \(-0.586380\pi\)
0.700307 + 0.713841i \(0.253046\pi\)
\(588\) 0 0
\(589\) −0.348520 + 0.603654i −0.0143605 + 0.0248731i
\(590\) 3.19281 + 1.84337i 0.131446 + 0.0758904i
\(591\) 0 0
\(592\) 30.2646i 1.24387i
\(593\) 13.8115 + 7.97406i 0.567170 + 0.327456i 0.756018 0.654551i \(-0.227142\pi\)
−0.188848 + 0.982006i \(0.560475\pi\)
\(594\) 0 0
\(595\) −33.4929 5.04024i −1.37308 0.206630i
\(596\) −24.3949 + 14.0844i −0.999253 + 0.576919i
\(597\) 0 0
\(598\) 2.42694 1.52857i 0.0992450 0.0625078i
\(599\) −3.55511 6.15763i −0.145258 0.251594i 0.784211 0.620494i \(-0.213068\pi\)
−0.929469 + 0.368900i \(0.879734\pi\)
\(600\) 0 0
\(601\) −10.3953 18.0051i −0.424032 0.734445i 0.572297 0.820046i \(-0.306052\pi\)
−0.996329 + 0.0856011i \(0.972719\pi\)
\(602\) −3.78974 0.570306i −0.154458 0.0232439i
\(603\) 0 0
\(604\) 11.0274 6.36667i 0.448698 0.259056i
\(605\) 10.0509i 0.408626i
\(606\) 0 0
\(607\) 3.85702 + 6.68056i 0.156552 + 0.271156i 0.933623 0.358257i \(-0.116629\pi\)
−0.777071 + 0.629413i \(0.783296\pi\)
\(608\) −0.199992 0.346396i −0.00811074 0.0140482i
\(609\) 0 0
\(610\) 0.199941 0.00809539
\(611\) 0.256380 + 6.66133i 0.0103720 + 0.269489i
\(612\) 0 0
\(613\) −17.6997 10.2189i −0.714883 0.412738i 0.0979832 0.995188i \(-0.468761\pi\)
−0.812867 + 0.582450i \(0.802094\pi\)
\(614\) 4.25227 0.171608
\(615\) 0 0
\(616\) 0.760978 5.05678i 0.0306607 0.203743i
\(617\) 3.98209 + 2.29906i 0.160313 + 0.0925567i 0.578010 0.816030i \(-0.303829\pi\)
−0.417697 + 0.908586i \(0.637163\pi\)
\(618\) 0 0
\(619\) −8.70599 + 5.02641i −0.349923 + 0.202028i −0.664651 0.747154i \(-0.731420\pi\)
0.314728 + 0.949182i \(0.398087\pi\)
\(620\) −19.5525 −0.785245
\(621\) 0 0
\(622\) −0.255396 + 0.147453i −0.0102404 + 0.00591232i
\(623\) 5.69827 + 14.5090i 0.228296 + 0.581290i
\(624\) 0 0
\(625\) 15.5853 26.9944i 0.623410 1.07978i
\(626\) −0.109107 0.0629930i −0.00436080 0.00251771i
\(627\) 0 0
\(628\) −15.6585 27.1213i −0.624842 1.08226i
\(629\) 37.9009i 1.51121i
\(630\) 0 0
\(631\) −6.29923 3.63686i −0.250768 0.144781i 0.369348 0.929291i \(-0.379581\pi\)
−0.620116 + 0.784510i \(0.712914\pi\)
\(632\) 5.66015 + 3.26789i 0.225149 + 0.129990i
\(633\) 0 0
\(634\) −1.93742 + 3.35570i −0.0769447 + 0.133272i
\(635\) 21.4051i 0.849434i
\(636\) 0 0
\(637\) 24.3889 + 6.49484i 0.966322 + 0.257335i
\(638\) −3.45199 −0.136665
\(639\) 0 0
\(640\) 7.45835 12.9182i 0.294817 0.510639i
\(641\) 3.85033 0.152079 0.0760394 0.997105i \(-0.475773\pi\)
0.0760394 + 0.997105i \(0.475773\pi\)
\(642\) 0 0
\(643\) 2.49163 + 1.43855i 0.0982605 + 0.0567307i 0.548325 0.836265i \(-0.315266\pi\)
−0.450065 + 0.892996i \(0.648599\pi\)
\(644\) −21.3134 + 8.37066i −0.839867 + 0.329850i
\(645\) 0 0
\(646\) −0.0811745 0.140598i −0.00319377 0.00553177i
\(647\) −18.5501 + 32.1296i −0.729278 + 1.26315i 0.227911 + 0.973682i \(0.426810\pi\)
−0.957189 + 0.289464i \(0.906523\pi\)
\(648\) 0 0
\(649\) 10.2231 17.7070i 0.401293 0.695061i
\(650\) 1.27924 + 0.674349i 0.0501758 + 0.0264501i
\(651\) 0 0
\(652\) −8.14661 + 4.70345i −0.319046 + 0.184201i
\(653\) −20.0950 −0.786377 −0.393189 0.919458i \(-0.628628\pi\)
−0.393189 + 0.919458i \(0.628628\pi\)
\(654\) 0 0
\(655\) 23.3087 13.4573i 0.910748 0.525820i
\(656\) −17.8912 + 10.3295i −0.698532 + 0.403298i
\(657\) 0 0
\(658\) −0.131629 + 0.874687i −0.00513142 + 0.0340988i
\(659\) 4.95529 8.58281i 0.193031 0.334339i −0.753223 0.657766i \(-0.771502\pi\)
0.946253 + 0.323427i \(0.104835\pi\)
\(660\) 0 0
\(661\) 40.8994 + 23.6133i 1.59080 + 0.918450i 0.993170 + 0.116680i \(0.0372252\pi\)
0.597633 + 0.801770i \(0.296108\pi\)
\(662\) 0.137468 + 0.238102i 0.00534284 + 0.00925408i
\(663\) 0 0
\(664\) −11.8989 −0.461768
\(665\) −1.24666 + 0.489613i −0.0483433 + 0.0189864i
\(666\) 0 0
\(667\) 15.5858 + 26.9954i 0.603485 + 1.04527i
\(668\) 4.61783 2.66611i 0.178669 0.103155i
\(669\) 0 0
\(670\) −4.79667 + 2.76936i −0.185312 + 0.106990i
\(671\) 1.10885i 0.0428068i
\(672\) 0 0
\(673\) 3.45845 + 5.99020i 0.133313 + 0.230905i 0.924952 0.380084i \(-0.124105\pi\)
−0.791639 + 0.610990i \(0.790772\pi\)
\(674\) 5.82801i 0.224487i
\(675\) 0 0
\(676\) −11.0473 + 23.0659i −0.424895 + 0.887150i
\(677\) −6.16453 + 10.6773i −0.236922 + 0.410361i −0.959830 0.280584i \(-0.909472\pi\)
0.722908 + 0.690945i \(0.242805\pi\)
\(678\) 0 0
\(679\) −1.18019 0.177603i −0.0452916 0.00681579i
\(680\) 4.59185 7.95331i 0.176089 0.304996i
\(681\) 0 0
\(682\) 1.80224i 0.0690113i
\(683\) 24.5364i 0.938859i −0.882970 0.469430i \(-0.844460\pi\)
0.882970 0.469430i \(-0.155540\pi\)
\(684\) 0 0
\(685\) 6.80655 11.7893i 0.260065 0.450446i
\(686\) 3.01828 + 1.45092i 0.115238 + 0.0553963i
\(687\) 0 0
\(688\) −15.2398 + 26.3961i −0.581012 + 1.00634i
\(689\) 11.8913 22.5577i 0.453021 0.859380i
\(690\) 0 0
\(691\) 9.10716i 0.346453i 0.984882 + 0.173226i \(0.0554192\pi\)
−0.984882 + 0.173226i \(0.944581\pi\)
\(692\) 0.885106 + 1.53305i 0.0336467 + 0.0582777i
\(693\) 0 0
\(694\) 1.47992i 0.0561769i
\(695\) −17.9756 + 10.3782i −0.681853 + 0.393668i
\(696\) 0 0
\(697\) −22.4055 + 12.9358i −0.848667 + 0.489978i
\(698\) 1.97543 + 3.42155i 0.0747712 + 0.129508i
\(699\) 0 0
\(700\) −9.02785 7.19602i −0.341221 0.271984i
\(701\) −0.286950 −0.0108380 −0.00541898 0.999985i \(-0.501725\pi\)
−0.00541898 + 0.999985i \(0.501725\pi\)
\(702\) 0 0
\(703\) −0.749377 1.29796i −0.0282633 0.0489534i
\(704\) −16.8601 9.73419i −0.635440 0.366871i
\(705\) 0 0
\(706\) 0.0512797 0.0888191i 0.00192994 0.00334275i
\(707\) −3.01461 + 20.0324i −0.113376 + 0.753397i
\(708\) 0 0
\(709\) 16.0949 9.29241i 0.604457 0.348984i −0.166336 0.986069i \(-0.553194\pi\)
0.770793 + 0.637086i \(0.219860\pi\)
\(710\) −1.40727 + 0.812486i −0.0528138 + 0.0304921i
\(711\) 0 0
\(712\) −4.22656 −0.158397
\(713\) −14.0940 + 8.13715i −0.527823 + 0.304739i
\(714\) 0 0
\(715\) 12.1704 23.0872i 0.455148 0.863414i
\(716\) 10.8751 18.8362i 0.406421 0.703941i
\(717\) 0 0
\(718\) 2.92974 5.07445i 0.109337 0.189377i
\(719\) −20.8475 36.1088i −0.777479 1.34663i −0.933391 0.358862i \(-0.883165\pi\)
0.155912 0.987771i \(-0.450168\pi\)
\(720\) 0 0
\(721\) −2.03056 + 13.4933i −0.0756218 + 0.502515i
\(722\) 2.96980 + 1.71462i 0.110525 + 0.0638114i
\(723\) 0 0
\(724\) −6.94257 −0.258019
\(725\) −7.85809 + 13.6106i −0.291842 + 0.505486i
\(726\) 0 0
\(727\) 32.7039 1.21292 0.606461 0.795113i \(-0.292589\pi\)
0.606461 + 0.795113i \(0.292589\pi\)
\(728\) −4.05657 + 5.51147i −0.150346 + 0.204269i
\(729\) 0 0
\(730\) 6.90616i 0.255608i
\(731\) −19.0851 + 33.0564i −0.705888 + 1.22263i
\(732\) 0 0
\(733\) 8.60423 + 4.96765i 0.317804 + 0.183484i 0.650413 0.759580i \(-0.274596\pi\)
−0.332609 + 0.943065i \(0.607929\pi\)
\(734\) −1.23225 0.711440i −0.0454832 0.0262597i
\(735\) 0 0
\(736\) 9.33871i 0.344230i
\(737\) 15.3586 + 26.6018i 0.565740 + 0.979891i
\(738\) 0 0
\(739\) −9.00853 5.20108i −0.331384 0.191325i 0.325071 0.945690i \(-0.394612\pi\)
−0.656455 + 0.754365i \(0.727945\pi\)
\(740\) 21.0205 36.4086i 0.772730 1.33841i
\(741\) 0 0
\(742\) 2.10900 2.64587i 0.0774237 0.0971328i
\(743\) 1.47972 0.854317i 0.0542857 0.0313419i −0.472612 0.881271i \(-0.656689\pi\)
0.526897 + 0.849929i \(0.323355\pi\)
\(744\) 0 0
\(745\) −38.4686 −1.40938
\(746\) 0.327545 0.189108i 0.0119923 0.00692374i
\(747\) 0 0
\(748\) −21.8723 12.6280i −0.799732 0.461726i
\(749\) 19.7821 7.76923i 0.722821 0.283881i
\(750\) 0 0
\(751\) −29.9812 −1.09403 −0.547015 0.837123i \(-0.684236\pi\)
−0.547015 + 0.837123i \(0.684236\pi\)
\(752\) 6.09233 + 3.51741i 0.222164 + 0.128267i
\(753\) 0 0
\(754\) 4.08656 + 2.15423i 0.148824 + 0.0784523i
\(755\) 17.3893 0.632860
\(756\) 0 0
\(757\) −4.20229 7.27858i −0.152735 0.264545i 0.779497 0.626406i \(-0.215475\pi\)
−0.932232 + 0.361861i \(0.882141\pi\)
\(758\) −1.29437 2.24191i −0.0470136 0.0814299i
\(759\) 0 0
\(760\) 0.363160i 0.0131732i
\(761\) −44.2184 + 25.5295i −1.60292 + 0.925444i −0.612015 + 0.790846i \(0.709641\pi\)
−0.990900 + 0.134598i \(0.957026\pi\)
\(762\) 0 0
\(763\) −2.19920 + 2.75903i −0.0796163 + 0.0998835i
\(764\) −20.0668 34.7568i −0.725993 1.25746i
\(765\) 0 0
\(766\) 2.27723 + 3.94429i 0.0822798 + 0.142513i
\(767\) −23.1526 + 14.5823i −0.835991 + 0.526535i
\(768\) 0 0
\(769\) −0.610062 + 0.352220i −0.0219994 + 0.0127014i −0.510959 0.859605i \(-0.670710\pi\)
0.488960 + 0.872306i \(0.337376\pi\)
\(770\) 2.15850 2.70798i 0.0777871 0.0975887i
\(771\) 0 0
\(772\) −29.4142 16.9823i −1.05864 0.611206i
\(773\) 1.26521i 0.0455066i 0.999741 + 0.0227533i \(0.00724323\pi\)
−0.999741 + 0.0227533i \(0.992757\pi\)
\(774\) 0 0
\(775\) −7.10593 4.10261i −0.255253 0.147370i
\(776\) 0.161803 0.280252i 0.00580840 0.0100604i
\(777\) 0 0
\(778\) −4.40076 + 2.54078i −0.157775 + 0.0910914i
\(779\) −0.511533 + 0.886001i −0.0183276 + 0.0317443i
\(780\) 0 0
\(781\) 4.50596 + 7.80456i 0.161236 + 0.279269i
\(782\) 3.79048i 0.135547i
\(783\) 0 0
\(784\) 19.5158 18.1250i 0.696992 0.647321i
\(785\) 42.7679i 1.52645i
\(786\) 0 0
\(787\) 43.7969i 1.56119i 0.625037 + 0.780595i \(0.285084\pi\)
−0.625037 + 0.780595i \(0.714916\pi\)
\(788\) 8.44493 4.87568i