Properties

Label 819.2.bm.f.550.4
Level $819$
Weight $2$
Character 819.550
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 550.4
Root \(0.655911 - 1.25291i\) of defining polynomial
Character \(\chi\) \(=\) 819.550
Dual form 819.2.bm.f.478.3

$q$-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 \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\)

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 \(0.0203637\pi\)
−0.997954 + 0.0639308i \(0.979636\pi\)
\(3\) 0 0
\(4\) 1.96730 0.983651
\(5\) 2.32670 1.34332i 1.04053 0.600751i 0.120548 0.992708i \(-0.461535\pi\)
0.919984 + 0.391956i \(0.128201\pi\)
\(6\) 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 −0.808654 0.588285i \(-0.799803\pi\)
0.105143 + 0.994457i \(0.466470\pi\)
\(12\) 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 0.518601 0.855016i \(-0.326453\pi\)
−0.481165 + 0.876630i \(0.659786\pi\)
\(20\) 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 −0.323281 0.946303i \(-0.604786\pi\)
0.981163 0.193182i \(-0.0618807\pi\)
\(30\) 0 0
\(31\) −3.20369 1.84965i −0.575400 0.332207i 0.183903 0.982944i \(-0.441127\pi\)
−0.759303 + 0.650737i \(0.774460\pi\)
\(32\) 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 \(0.226837\pi\)
−0.756645 + 0.653826i \(0.773163\pi\)
\(38\) −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 0.0856594 0.996324i \(-0.472700\pi\)
−0.820013 + 0.572345i \(0.806034\pi\)
\(42\) 0 0
\(43\) −4.00533 6.93743i −0.610807 1.05795i −0.991105 0.133084i \(-0.957512\pi\)
0.380298 0.924864i \(-0.375821\pi\)
\(44\) −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 −0.378655 0.925538i \(-0.623613\pi\)
0.612212 + 0.790694i \(0.290280\pi\)
\(48\) 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 −0.999866 0.0163917i \(-0.994782\pi\)
0.514128 + 0.857713i \(0.328115\pi\)
\(54\) 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 \(-0.835536\pi\)
0.869465 0.493994i \(-0.164464\pi\)
\(60\) 0 0
\(61\) 0.205782 0.356425i 0.0263477 0.0456355i −0.852551 0.522644i \(-0.824946\pi\)
0.878899 + 0.477009i \(0.158279\pi\)
\(62\) 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 −0.961938 0.273268i \(-0.911895\pi\)
−0.244312 + 0.969697i \(0.578562\pi\)
\(68\) 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 −0.661943 0.749554i \(-0.730268\pi\)
0.318162 + 0.948037i \(0.396935\pi\)
\(72\) 0 0
\(73\) 12.3112 + 7.10790i 1.44092 + 0.831917i 0.997911 0.0645994i \(-0.0205769\pi\)
0.443011 + 0.896516i \(0.353910\pi\)
\(74\) −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 −0.999895 0.0145069i \(-0.995382\pi\)
0.487384 0.873188i \(-0.337951\pi\)
\(80\) 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 \(0.364155\pi\)
−0.413934 + 0.910307i \(0.635845\pi\)
\(84\) 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 \(0.101085\pi\)
−0.949998 + 0.312257i \(0.898915\pi\)
\(90\) 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 −0.480036 0.877249i \(-0.659376\pi\)
0.519702 + 0.854348i \(0.326043\pi\)
\(98\) −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 0.991197 0.132396i \(-0.0422671\pi\)
−0.610257 + 0.792204i \(0.708934\pi\)
\(102\) 0 0
\(103\) 2.57870 + 4.46644i 0.254087 + 0.440091i 0.964647 0.263545i \(-0.0848918\pi\)
−0.710560 + 0.703636i \(0.751558\pi\)
\(104\) 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 0.554289 0.832324i \(-0.312990\pi\)
−0.443670 + 0.896190i \(0.646324\pi\)
\(110\) −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 −0.769525 0.638617i \(-0.779507\pi\)
−0.168296 0.985736i \(-0.553827\pi\)
\(114\) 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 −0.986858 0.161590i \(-0.948338\pi\)
0.633370 + 0.773849i \(0.281671\pi\)
\(128\) 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 0.997507 0.0705727i \(-0.0224827\pi\)
−0.559871 + 0.828580i \(0.689149\pi\)
\(132\) 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 \(0.0694477\pi\)
−0.976294 + 0.216450i \(0.930552\pi\)
\(138\) 0 0
\(139\) −3.86289 6.69073i −0.327646 0.567500i 0.654398 0.756150i \(-0.272922\pi\)
−0.982044 + 0.188650i \(0.939589\pi\)
\(140\) −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 −0.102958 0.994686i \(-0.532831\pi\)
−0.912902 + 0.408178i \(0.866164\pi\)
\(150\) 0 0
\(151\) 5.60534 + 3.23624i 0.456156 + 0.263362i 0.710427 0.703771i \(-0.248502\pi\)
−0.254271 + 0.967133i \(0.581835\pi\)
\(152\) −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 0.351240 + 0.936285i \(0.385760\pi\)
−0.986467 + 0.163960i \(0.947573\pi\)
\(158\) 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 0.328981 0.944337i \(-0.393295\pi\)
−0.653329 + 0.757074i \(0.726628\pi\)
\(164\) −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 0.588062 0.808816i \(-0.299891\pi\)
−0.406424 + 0.913685i \(0.633224\pi\)
\(168\) 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 −0.848416 0.529331i \(-0.822443\pi\)
0.882622 + 0.470084i \(0.155776\pi\)
\(174\) 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 0.995235 0.0975054i \(-0.0310863\pi\)
−0.582060 + 0.813146i \(0.697753\pi\)
\(180\) 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 0.215309 + 0.976546i \(0.430924\pi\)
−0.953368 + 0.301810i \(0.902409\pi\)
\(192\) 0 0
\(193\) −14.9515 + 8.63228i −1.07624 + 0.621365i −0.929878 0.367867i \(-0.880088\pi\)
−0.146357 + 0.989232i \(0.546755\pi\)
\(194\) 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 0.645063 0.764130i \(-0.276831\pi\)
−0.339224 + 0.940705i \(0.610165\pi\)
\(198\) 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 −0.386395 0.922333i \(-0.626280\pi\)
0.991962 0.126539i \(-0.0403868\pi\)
\(212\) −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 0.849733 0.527213i \(-0.176763\pi\)
−0.0317129 + 0.999497i \(0.510096\pi\)
\(224\) 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 \(0.0303502\pi\)
−0.995458 + 0.0952035i \(0.969650\pi\)
\(228\) 0 0
\(229\) 7.59860 4.38706i 0.502130 0.289905i −0.227463 0.973787i \(-0.573043\pi\)
0.729593 + 0.683882i \(0.239710\pi\)
\(230\) 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 0.770170 0.637839i \(-0.220171\pi\)
−0.937469 + 0.348068i \(0.886838\pi\)
\(234\) 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 \(0.0257443\pi\)
−0.996731 + 0.0807901i \(0.974256\pi\)
\(240\) 0 0
\(241\) 7.98512i 0.514367i −0.966363 0.257183i \(-0.917206\pi\)
0.966363 0.257183i \(-0.0827944\pi\)
\(242\) −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 −0.921494 0.388393i \(-0.873030\pi\)
0.124389 0.992234i \(-0.460303\pi\)
\(252\) 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 0.863565 0.504238i \(-0.168226\pi\)
−0.868465 + 0.495750i \(0.834893\pi\)
\(264\) 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 \(0.116895\pi\)
−0.933323 + 0.359037i \(0.883105\pi\)
\(272\) 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 \(-0.675860\pi\)
0.524801 0.851225i \(-0.324140\pi\)
\(282\) 0 0
\(283\) 8.98604 + 15.5643i 0.534165 + 0.925201i 0.999203 + 0.0399101i \(0.0127072\pi\)
−0.465038 + 0.885290i \(0.653960\pi\)
\(284\) −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 −0.826882 0.562375i \(-0.809888\pi\)
0.0735896 + 0.997289i \(0.476554\pi\)
\(294\) 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 \(-0.765836\pi\)
0.741396 0.671068i \(-0.234164\pi\)
\(308\) 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 −0.888219 0.459420i \(-0.848057\pi\)
0.841979 + 0.539510i \(0.181391\pi\)
\(312\) 0 0
\(313\) 0.348367 + 0.603389i 0.0196909 + 0.0341056i 0.875703 0.482850i \(-0.160398\pi\)
−0.856012 + 0.516956i \(0.827065\pi\)
\(314\) −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 −0.920488 0.390771i \(-0.872208\pi\)
−0.121826 + 0.992551i \(0.538875\pi\)
\(318\) 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 0.463375 0.886162i \(-0.346638\pi\)
−0.535751 + 0.844376i \(0.679971\pi\)
\(332\) 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 −0.100841 0.994903i \(-0.532153\pi\)
−0.912031 + 0.410120i \(0.865487\pi\)
\(350\) −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 −0.486871 0.873474i \(-0.661862\pi\)
0.513015 + 0.858380i \(0.328529\pi\)
\(354\) 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 0.481336 0.876536i \(-0.340152\pi\)
0.999771 + 0.0214184i \(0.00681822\pi\)
\(360\) 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 0.950252 0.311481i \(-0.100825\pi\)
−0.744876 + 0.667202i \(0.767492\pi\)
\(368\) 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 −0.837680 0.546162i \(-0.816088\pi\)
0.891830 + 0.452371i \(0.149422\pi\)
\(374\) −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 0.783404 0.621513i \(-0.213482\pi\)
−0.146545 + 0.989204i \(0.546815\pi\)
\(380\) 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 −0.174573 0.984644i \(-0.555854\pi\)
−0.940013 + 0.341138i \(0.889188\pi\)
\(384\) 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 0.251524 + 0.967851i \(0.419068\pi\)
−0.963946 + 0.266099i \(0.914265\pi\)
\(390\) 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 −0.0545111 0.998513i \(-0.517360\pi\)
−0.891993 + 0.452049i \(0.850693\pi\)
\(398\) 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 \(0.171312\pi\)
−0.858637 + 0.512584i \(0.828688\pi\)
\(402\) 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 \(-0.950468\pi\)
0.987917 0.154982i \(-0.0495319\pi\)
\(410\) 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 −0.0599424 0.998202i \(-0.519092\pi\)
0.894439 0.447189i \(-0.147575\pi\)
\(420\) 0 0
\(421\) 11.5233i 0.561613i −0.959764 0.280806i \(-0.909398\pi\)
0.959764 0.280806i \(-0.0906019\pi\)
\(422\) 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 −0.305799 0.952096i \(-0.598924\pi\)
0.671640 + 0.740878i \(0.265590\pi\)
\(432\) 0 0
\(433\) 11.0535 + 19.1452i 0.531196 + 0.920058i 0.999337 + 0.0364046i \(0.0115905\pi\)
−0.468141 + 0.883654i \(0.655076\pi\)
\(434\) −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 0.880506 + 0.474036i \(0.157203\pi\)
−0.0297257 + 0.999558i \(0.509463\pi\)
\(444\) 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 0.0430575 0.999073i \(-0.486290\pi\)
0.886751 + 0.462247i \(0.152957\pi\)
\(450\) 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 \(-0.738364\pi\)
0.680791 0.732478i \(-0.261636\pi\)
\(458\) 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 −0.320765 0.947159i \(-0.603940\pi\)
0.659881 + 0.751370i \(0.270607\pi\)
\(462\) 0 0
\(463\) 10.0392i 0.466563i 0.972409 + 0.233281i \(0.0749463\pi\)
−0.972409 + 0.233281i \(0.925054\pi\)
\(464\) 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 0.991290 + 0.131695i \(0.0420418\pi\)
−0.381594 + 0.924330i \(0.624625\pi\)
\(468\) 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 −0.320455 0.947264i \(-0.603836\pi\)
0.660127 + 0.751154i \(0.270502\pi\)
\(480\) 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 \(-0.840054\pi\)
0.876388 0.481606i \(-0.159946\pi\)
\(488\) 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 −0.493313 0.869852i \(-0.664214\pi\)
0.999970 0.00770409i \(-0.00245231\pi\)
\(492\) 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 −0.507284 + 0.861779i \(0.669350\pi\)
−0.999964 + 0.00843082i \(0.997316\pi\)
\(500\) 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 0.920422 0.390927i \(-0.127846\pi\)
−0.798764 + 0.601645i \(0.794512\pi\)
\(504\) 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 \(-0.922393\pi\)
0.970426 0.241400i \(-0.0776066\pi\)
\(510\) 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 −0.379985 0.924993i \(-0.624071\pi\)
0.991060 0.133419i \(-0.0425957\pi\)
\(522\) 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 −0.277626 0.960689i \(-0.589547\pi\)
0.693169 + 0.720776i \(0.256214\pi\)
\(542\) −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 0.250193 0.968196i \(-0.419506\pi\)
0.963579 + 0.267424i \(0.0861725\pi\)
\(558\) 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 0.460051 + 0.887893i \(0.347831\pi\)
−0.998963 + 0.0455309i \(0.985502\pi\)
\(572\) −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 0.486066 0.873922i \(-0.338431\pi\)
−0.513805 + 0.857907i \(0.671765\pi\)
\(578\) 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 0.700307 0.713841i \(-0.253046\pi\)
−0.268051 + 0.963405i \(0.586380\pi\)
\(588\) 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 −0.188848 0.982006i \(-0.560475\pi\)
0.756018 + 0.654551i \(0.227142\pi\)
\(594\) 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 −0.929469 0.368900i \(-0.879734\pi\)
0.784211 + 0.620494i \(0.213068\pi\)
\(600\) 0 0
\(601\) −10.3953 + 18.0051i −0.424032 + 0.734445i −0.996329 0.0856011i \(-0.972719\pi\)
0.572297 + 0.820046i \(0.306052\pi\)
\(602\) −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 −0.777071 0.629413i \(-0.783296\pi\)
0.933623 + 0.358257i \(0.116629\pi\)
\(608\) −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 −0.812867 0.582450i \(-0.802094\pi\)
0.0979832 + 0.995188i \(0.468761\pi\)
\(614\) 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 −0.417697 0.908586i \(-0.637163\pi\)
0.578010 + 0.816030i \(0.303829\pi\)
\(618\) 0 0
\(619\) −8.70599 5.02641i −0.349923 0.202028i 0.314728 0.949182i \(-0.398087\pi\)
−0.664651 + 0.747154i \(0.731420\pi\)
\(620\) −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 −0.620116 0.784510i \(-0.712914\pi\)
0.369348 + 0.929291i \(0.379581\pi\)
\(632\) 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 −0.450065 0.892996i \(-0.648599\pi\)
0.548325 + 0.836265i \(0.315266\pi\)
\(644\) −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 −0.957189 0.289464i \(-0.906523\pi\)
0.227911 0.973682i \(-0.426810\pi\)
\(648\) 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 0.946253 0.323427i \(-0.104835\pi\)
−0.753223 + 0.657766i \(0.771502\pi\)
\(660\) 0 0
\(661\) 40.8994 23.6133i 1.59080 0.918450i 0.597633 0.801770i \(-0.296108\pi\)
0.993170 0.116680i \(-0.0372252\pi\)
\(662\) 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 −0.791639 0.610990i \(-0.790772\pi\)
0.924952 + 0.380084i \(0.124105\pi\)
\(674\) 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 0.722908 0.690945i \(-0.242805\pi\)
−0.959830 + 0.280584i \(0.909472\pi\)
\(678\) 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 \(0.155540\pi\)
−0.882970 + 0.469430i \(0.844460\pi\)
\(684\) 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 \(-0.944581\pi\)
0.984882 0.173226i \(-0.0554192\pi\)
\(692\) 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 0.770793 0.637086i \(-0.219860\pi\)
−0.166336 + 0.986069i \(0.553194\pi\)
\(710\) −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 0.155912 + 0.987771i \(0.450168\pi\)
−0.933391 + 0.358862i \(0.883165\pi\)
\(720\) 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 −0.332609 0.943065i \(-0.607929\pi\)
0.650413 + 0.759580i \(0.274596\pi\)
\(734\) −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 −0.656455 0.754365i \(-0.727945\pi\)
0.325071 + 0.945690i \(0.394612\pi\)
\(740\) 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 0.526897 0.849929i \(-0.323355\pi\)
−0.472612 + 0.881271i \(0.656689\pi\)
\(744\) 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 −0.932232 0.361861i \(-0.882141\pi\)
0.779497 + 0.626406i \(0.215475\pi\)
\(758\) −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 −0.990900 0.134598i \(-0.957026\pi\)
−0.612015 0.790846i \(-0.709641\pi\)
\(762\) 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 0.488960 0.872306i \(-0.337376\pi\)
−0.510959 + 0.859605i \(0.670710\pi\)
\(770\) 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 \(-0.992757\pi\)
0.999741 0.0227533i \(-0.00724323\pi\)
\(774\) 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 \(-0.714916\pi\)
0.625037 0.780595i \(-0.285084\pi\)
\(788\) 8.44493 + 4.87568i