Properties

Label 128.4.g.a.49.6
Level $128$
Weight $4$
Character 128.49
Analytic conductor $7.552$
Analytic rank $0$
Dimension $44$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 128 = 2^{7} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 128.g (of order \(8\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.55224448073\)
Analytic rank: \(0\)
Dimension: \(44\)
Relative dimension: \(11\) over \(\Q(\zeta_{8})\)
Twist minimal: no (minimal twist has level 32)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 49.6
Character \(\chi\) \(=\) 128.49
Dual form 128.4.g.a.81.6

$q$-expansion

\(f(q)\) \(=\) \(q+(1.36212 - 0.564209i) q^{3} +(6.58151 - 15.8892i) q^{5} +(-14.5517 - 14.5517i) q^{7} +(-17.5548 + 17.5548i) q^{9} +O(q^{10})\) \(q+(1.36212 - 0.564209i) q^{3} +(6.58151 - 15.8892i) q^{5} +(-14.5517 - 14.5517i) q^{7} +(-17.5548 + 17.5548i) q^{9} +(-34.4676 - 14.2769i) q^{11} +(15.3924 + 37.1606i) q^{13} -25.3563i q^{15} -103.310i q^{17} +(-12.4092 - 29.9584i) q^{19} +(-28.0313 - 11.6109i) q^{21} +(72.3950 - 72.3950i) q^{23} +(-120.761 - 120.761i) q^{25} +(-29.2409 + 70.5937i) q^{27} +(23.9061 - 9.90225i) q^{29} +124.769 q^{31} -55.0042 q^{33} +(-326.986 + 135.442i) q^{35} +(18.0425 - 43.5584i) q^{37} +(41.9327 + 41.9327i) q^{39} +(-45.1360 + 45.1360i) q^{41} +(457.470 + 189.490i) q^{43} +(163.395 + 394.469i) q^{45} -582.766i q^{47} +80.5012i q^{49} +(-58.2884 - 140.721i) q^{51} +(395.810 + 163.950i) q^{53} +(-453.698 + 453.698i) q^{55} +(-33.8056 - 33.8056i) q^{57} +(-142.805 + 344.762i) q^{59} +(-34.8958 + 14.4543i) q^{61} +510.904 q^{63} +691.757 q^{65} +(-196.686 + 81.4699i) q^{67} +(57.7649 - 139.457i) q^{69} +(520.831 + 520.831i) q^{71} +(-582.329 + 582.329i) q^{73} +(-232.626 - 96.3570i) q^{75} +(293.807 + 709.314i) q^{77} +157.779i q^{79} -557.655i q^{81} +(-54.5324 - 131.653i) q^{83} +(-1641.51 - 679.936i) q^{85} +(26.9761 - 26.9761i) q^{87} +(-272.884 - 272.884i) q^{89} +(316.763 - 764.733i) q^{91} +(169.951 - 70.3959i) q^{93} -557.686 q^{95} +788.873 q^{97} +(855.703 - 354.444i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + O(q^{10}) \) \( 44q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + 4q^{11} - 4q^{13} + 4q^{19} - 4q^{21} - 324q^{23} - 4q^{25} + 268q^{27} - 4q^{29} + 752q^{31} - 8q^{33} + 460q^{35} - 4q^{37} - 596q^{39} - 4q^{41} - 804q^{43} + 104q^{45} + 1384q^{51} + 748q^{53} + 292q^{55} - 4q^{57} - 1372q^{59} - 1828q^{61} - 2512q^{63} - 8q^{65} - 2036q^{67} - 1060q^{69} - 220q^{71} - 4q^{73} + 1712q^{75} + 1900q^{77} - 2436q^{83} + 496q^{85} + 1292q^{87} - 4q^{89} + 3604q^{91} - 112q^{93} + 6088q^{95} - 8q^{97} + 5424q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(127\)
\(\chi(n)\) \(e\left(\frac{5}{8}\right)\) \(1\)

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 0
\(3\) 1.36212 0.564209i 0.262140 0.108582i −0.247743 0.968826i \(-0.579689\pi\)
0.509883 + 0.860244i \(0.329689\pi\)
\(4\) 0 0
\(5\) 6.58151 15.8892i 0.588669 1.42117i −0.296107 0.955155i \(-0.595689\pi\)
0.884776 0.466017i \(-0.154311\pi\)
\(6\) 0 0
\(7\) −14.5517 14.5517i −0.785715 0.785715i 0.195073 0.980789i \(-0.437506\pi\)
−0.980789 + 0.195073i \(0.937506\pi\)
\(8\) 0 0
\(9\) −17.5548 + 17.5548i −0.650179 + 0.650179i
\(10\) 0 0
\(11\) −34.4676 14.2769i −0.944761 0.391333i −0.143502 0.989650i \(-0.545836\pi\)
−0.801259 + 0.598317i \(0.795836\pi\)
\(12\) 0 0
\(13\) 15.3924 + 37.1606i 0.328391 + 0.792807i 0.998712 + 0.0507354i \(0.0161565\pi\)
−0.670321 + 0.742071i \(0.733843\pi\)
\(14\) 0 0
\(15\) 25.3563i 0.436465i
\(16\) 0 0
\(17\) 103.310i 1.47390i −0.675946 0.736951i \(-0.736265\pi\)
0.675946 0.736951i \(-0.263735\pi\)
\(18\) 0 0
\(19\) −12.4092 29.9584i −0.149835 0.361733i 0.831085 0.556145i \(-0.187720\pi\)
−0.980920 + 0.194412i \(0.937720\pi\)
\(20\) 0 0
\(21\) −28.0313 11.6109i −0.291282 0.120653i
\(22\) 0 0
\(23\) 72.3950 72.3950i 0.656322 0.656322i −0.298186 0.954508i \(-0.596381\pi\)
0.954508 + 0.298186i \(0.0963815\pi\)
\(24\) 0 0
\(25\) −120.761 120.761i −0.966091 0.966091i
\(26\) 0 0
\(27\) −29.2409 + 70.5937i −0.208422 + 0.503176i
\(28\) 0 0
\(29\) 23.9061 9.90225i 0.153078 0.0634069i −0.304829 0.952407i \(-0.598599\pi\)
0.457907 + 0.889000i \(0.348599\pi\)
\(30\) 0 0
\(31\) 124.769 0.722877 0.361439 0.932396i \(-0.382286\pi\)
0.361439 + 0.932396i \(0.382286\pi\)
\(32\) 0 0
\(33\) −55.0042 −0.290152
\(34\) 0 0
\(35\) −326.986 + 135.442i −1.57916 + 0.654110i
\(36\) 0 0
\(37\) 18.0425 43.5584i 0.0801667 0.193540i −0.878714 0.477348i \(-0.841598\pi\)
0.958881 + 0.283809i \(0.0915980\pi\)
\(38\) 0 0
\(39\) 41.9327 + 41.9327i 0.172169 + 0.172169i
\(40\) 0 0
\(41\) −45.1360 + 45.1360i −0.171928 + 0.171928i −0.787826 0.615898i \(-0.788793\pi\)
0.615898 + 0.787826i \(0.288793\pi\)
\(42\) 0 0
\(43\) 457.470 + 189.490i 1.62241 + 0.672023i 0.994351 0.106144i \(-0.0338506\pi\)
0.628057 + 0.778168i \(0.283851\pi\)
\(44\) 0 0
\(45\) 163.395 + 394.469i 0.541276 + 1.30676i
\(46\) 0 0
\(47\) 582.766i 1.80862i −0.426877 0.904310i \(-0.640386\pi\)
0.426877 0.904310i \(-0.359614\pi\)
\(48\) 0 0
\(49\) 80.5012i 0.234697i
\(50\) 0 0
\(51\) −58.2884 140.721i −0.160039 0.386369i
\(52\) 0 0
\(53\) 395.810 + 163.950i 1.02582 + 0.424910i 0.831203 0.555969i \(-0.187653\pi\)
0.194620 + 0.980879i \(0.437653\pi\)
\(54\) 0 0
\(55\) −453.698 + 453.698i −1.11230 + 1.11230i
\(56\) 0 0
\(57\) −33.8056 33.8056i −0.0785555 0.0785555i
\(58\) 0 0
\(59\) −142.805 + 344.762i −0.315113 + 0.760750i 0.684387 + 0.729119i \(0.260070\pi\)
−0.999500 + 0.0316306i \(0.989930\pi\)
\(60\) 0 0
\(61\) −34.8958 + 14.4543i −0.0732450 + 0.0303391i −0.419005 0.907984i \(-0.637621\pi\)
0.345760 + 0.938323i \(0.387621\pi\)
\(62\) 0 0
\(63\) 510.904 1.02171
\(64\) 0 0
\(65\) 691.757 1.32003
\(66\) 0 0
\(67\) −196.686 + 81.4699i −0.358642 + 0.148554i −0.554727 0.832033i \(-0.687177\pi\)
0.196085 + 0.980587i \(0.437177\pi\)
\(68\) 0 0
\(69\) 57.7649 139.457i 0.100784 0.243313i
\(70\) 0 0
\(71\) 520.831 + 520.831i 0.870582 + 0.870582i 0.992536 0.121954i \(-0.0389161\pi\)
−0.121954 + 0.992536i \(0.538916\pi\)
\(72\) 0 0
\(73\) −582.329 + 582.329i −0.933649 + 0.933649i −0.997932 0.0642823i \(-0.979524\pi\)
0.0642823 + 0.997932i \(0.479524\pi\)
\(74\) 0 0
\(75\) −232.626 96.3570i −0.358152 0.148351i
\(76\) 0 0
\(77\) 293.807 + 709.314i 0.434837 + 1.04979i
\(78\) 0 0
\(79\) 157.779i 0.224702i 0.993669 + 0.112351i \(0.0358381\pi\)
−0.993669 + 0.112351i \(0.964162\pi\)
\(80\) 0 0
\(81\) 557.655i 0.764959i
\(82\) 0 0
\(83\) −54.5324 131.653i −0.0721170 0.174106i 0.883711 0.468034i \(-0.155037\pi\)
−0.955828 + 0.293928i \(0.905037\pi\)
\(84\) 0 0
\(85\) −1641.51 679.936i −2.09467 0.867640i
\(86\) 0 0
\(87\) 26.9761 26.9761i 0.0332430 0.0332430i
\(88\) 0 0
\(89\) −272.884 272.884i −0.325007 0.325007i 0.525677 0.850684i \(-0.323812\pi\)
−0.850684 + 0.525677i \(0.823812\pi\)
\(90\) 0 0
\(91\) 316.763 764.733i 0.364898 0.880943i
\(92\) 0 0
\(93\) 169.951 70.3959i 0.189495 0.0784915i
\(94\) 0 0
\(95\) −557.686 −0.602288
\(96\) 0 0
\(97\) 788.873 0.825752 0.412876 0.910787i \(-0.364524\pi\)
0.412876 + 0.910787i \(0.364524\pi\)
\(98\) 0 0
\(99\) 855.703 354.444i 0.868701 0.359828i
\(100\) 0 0
\(101\) 585.257 1412.93i 0.576586 1.39200i −0.319272 0.947663i \(-0.603438\pi\)
0.895858 0.444339i \(-0.146562\pi\)
\(102\) 0 0
\(103\) −1120.20 1120.20i −1.07161 1.07161i −0.997230 0.0743853i \(-0.976301\pi\)
−0.0743853 0.997230i \(-0.523699\pi\)
\(104\) 0 0
\(105\) −368.977 + 368.977i −0.342937 + 0.342937i
\(106\) 0 0
\(107\) 1665.63 + 689.926i 1.50488 + 0.623343i 0.974494 0.224413i \(-0.0720463\pi\)
0.530388 + 0.847755i \(0.322046\pi\)
\(108\) 0 0
\(109\) −342.786 827.559i −0.301220 0.727209i −0.999930 0.0118047i \(-0.996242\pi\)
0.698710 0.715405i \(-0.253758\pi\)
\(110\) 0 0
\(111\) 69.5116i 0.0594392i
\(112\) 0 0
\(113\) 924.353i 0.769521i 0.923016 + 0.384760i \(0.125716\pi\)
−0.923016 + 0.384760i \(0.874284\pi\)
\(114\) 0 0
\(115\) −673.829 1626.77i −0.546390 1.31910i
\(116\) 0 0
\(117\) −922.559 382.137i −0.728980 0.301953i
\(118\) 0 0
\(119\) −1503.33 + 1503.33i −1.15807 + 1.15807i
\(120\) 0 0
\(121\) 43.0249 + 43.0249i 0.0323253 + 0.0323253i
\(122\) 0 0
\(123\) −36.0145 + 86.9467i −0.0264010 + 0.0637376i
\(124\) 0 0
\(125\) −727.445 + 301.318i −0.520517 + 0.215605i
\(126\) 0 0
\(127\) −569.829 −0.398143 −0.199072 0.979985i \(-0.563793\pi\)
−0.199072 + 0.979985i \(0.563793\pi\)
\(128\) 0 0
\(129\) 730.042 0.498268
\(130\) 0 0
\(131\) −1171.87 + 485.406i −0.781581 + 0.323742i −0.737553 0.675289i \(-0.764019\pi\)
−0.0440278 + 0.999030i \(0.514019\pi\)
\(132\) 0 0
\(133\) −255.370 + 616.518i −0.166492 + 0.401947i
\(134\) 0 0
\(135\) 929.227 + 929.227i 0.592408 + 0.592408i
\(136\) 0 0
\(137\) 946.041 946.041i 0.589969 0.589969i −0.347654 0.937623i \(-0.613022\pi\)
0.937623 + 0.347654i \(0.113022\pi\)
\(138\) 0 0
\(139\) −1313.93 544.249i −0.801772 0.332105i −0.0561063 0.998425i \(-0.517869\pi\)
−0.745666 + 0.666320i \(0.767869\pi\)
\(140\) 0 0
\(141\) −328.802 793.797i −0.196384 0.474112i
\(142\) 0 0
\(143\) 1500.59i 0.877523i
\(144\) 0 0
\(145\) 445.021i 0.254876i
\(146\) 0 0
\(147\) 45.4195 + 109.652i 0.0254839 + 0.0615236i
\(148\) 0 0
\(149\) 2438.15 + 1009.92i 1.34054 + 0.555272i 0.933644 0.358201i \(-0.116610\pi\)
0.406900 + 0.913473i \(0.366610\pi\)
\(150\) 0 0
\(151\) 872.975 872.975i 0.470475 0.470475i −0.431594 0.902068i \(-0.642049\pi\)
0.902068 + 0.431594i \(0.142049\pi\)
\(152\) 0 0
\(153\) 1813.59 + 1813.59i 0.958301 + 0.958301i
\(154\) 0 0
\(155\) 821.170 1982.48i 0.425535 1.02733i
\(156\) 0 0
\(157\) −866.489 + 358.912i −0.440467 + 0.182447i −0.591885 0.806022i \(-0.701616\pi\)
0.151418 + 0.988470i \(0.451616\pi\)
\(158\) 0 0
\(159\) 631.643 0.315047
\(160\) 0 0
\(161\) −2106.94 −1.03136
\(162\) 0 0
\(163\) 745.455 308.777i 0.358212 0.148376i −0.196318 0.980540i \(-0.562898\pi\)
0.554529 + 0.832164i \(0.312898\pi\)
\(164\) 0 0
\(165\) −362.011 + 873.972i −0.170803 + 0.412355i
\(166\) 0 0
\(167\) 741.751 + 741.751i 0.343703 + 0.343703i 0.857758 0.514055i \(-0.171857\pi\)
−0.514055 + 0.857758i \(0.671857\pi\)
\(168\) 0 0
\(169\) 409.532 409.532i 0.186405 0.186405i
\(170\) 0 0
\(171\) 743.756 + 308.074i 0.332611 + 0.137772i
\(172\) 0 0
\(173\) −34.3941 83.0347i −0.0151152 0.0364914i 0.916142 0.400854i \(-0.131287\pi\)
−0.931257 + 0.364363i \(0.881287\pi\)
\(174\) 0 0
\(175\) 3514.56i 1.51815i
\(176\) 0 0
\(177\) 550.180i 0.233639i
\(178\) 0 0
\(179\) 1402.83 + 3386.73i 0.585768 + 1.41417i 0.887514 + 0.460781i \(0.152430\pi\)
−0.301746 + 0.953388i \(0.597570\pi\)
\(180\) 0 0
\(181\) 504.860 + 209.120i 0.207326 + 0.0858771i 0.483930 0.875107i \(-0.339209\pi\)
−0.276604 + 0.960984i \(0.589209\pi\)
\(182\) 0 0
\(183\) −39.3770 + 39.3770i −0.0159062 + 0.0159062i
\(184\) 0 0
\(185\) −573.361 573.361i −0.227861 0.227861i
\(186\) 0 0
\(187\) −1474.95 + 3560.85i −0.576786 + 1.39249i
\(188\) 0 0
\(189\) 1452.76 601.752i 0.559114 0.231593i
\(190\) 0 0
\(191\) 17.6918 0.00670226 0.00335113 0.999994i \(-0.498933\pi\)
0.00335113 + 0.999994i \(0.498933\pi\)
\(192\) 0 0
\(193\) −3321.63 −1.23884 −0.619420 0.785059i \(-0.712632\pi\)
−0.619420 + 0.785059i \(0.712632\pi\)
\(194\) 0 0
\(195\) 942.256 390.295i 0.346033 0.143331i
\(196\) 0 0
\(197\) −310.402 + 749.376i −0.112260 + 0.271020i −0.970018 0.243035i \(-0.921857\pi\)
0.857758 + 0.514054i \(0.171857\pi\)
\(198\) 0 0
\(199\) −1908.35 1908.35i −0.679795 0.679795i 0.280158 0.959954i \(-0.409613\pi\)
−0.959954 + 0.280158i \(0.909613\pi\)
\(200\) 0 0
\(201\) −221.944 + 221.944i −0.0778841 + 0.0778841i
\(202\) 0 0
\(203\) −491.968 203.780i −0.170095 0.0704559i
\(204\) 0 0
\(205\) 420.110 + 1014.24i 0.143131 + 0.345548i
\(206\) 0 0
\(207\) 2541.77i 0.853454i
\(208\) 0 0
\(209\) 1209.76i 0.400387i
\(210\) 0 0
\(211\) 969.860 + 2341.45i 0.316435 + 0.763943i 0.999438 + 0.0335266i \(0.0106739\pi\)
−0.683002 + 0.730416i \(0.739326\pi\)
\(212\) 0 0
\(213\) 1003.29 + 415.578i 0.322744 + 0.133685i
\(214\) 0 0
\(215\) 6021.69 6021.69i 1.91012 1.91012i
\(216\) 0 0
\(217\) −1815.60 1815.60i −0.567976 0.567976i
\(218\) 0 0
\(219\) −464.647 + 1121.76i −0.143370 + 0.346125i
\(220\) 0 0
\(221\) 3839.06 1590.19i 1.16852 0.484017i
\(222\) 0 0
\(223\) 267.474 0.0803200 0.0401600 0.999193i \(-0.487213\pi\)
0.0401600 + 0.999193i \(0.487213\pi\)
\(224\) 0 0
\(225\) 4239.89 1.25627
\(226\) 0 0
\(227\) 721.748 298.958i 0.211031 0.0874120i −0.274664 0.961540i \(-0.588567\pi\)
0.485695 + 0.874128i \(0.338567\pi\)
\(228\) 0 0
\(229\) −1403.35 + 3387.98i −0.404960 + 0.977660i 0.581484 + 0.813558i \(0.302472\pi\)
−0.986443 + 0.164101i \(0.947528\pi\)
\(230\) 0 0
\(231\) 800.402 + 800.402i 0.227977 + 0.227977i
\(232\) 0 0
\(233\) 95.4522 95.4522i 0.0268381 0.0268381i −0.693560 0.720399i \(-0.743959\pi\)
0.720399 + 0.693560i \(0.243959\pi\)
\(234\) 0 0
\(235\) −9259.67 3835.48i −2.57036 1.06468i
\(236\) 0 0
\(237\) 89.0201 + 214.913i 0.0243986 + 0.0589035i
\(238\) 0 0
\(239\) 2210.32i 0.598216i −0.954219 0.299108i \(-0.903311\pi\)
0.954219 0.299108i \(-0.0966890\pi\)
\(240\) 0 0
\(241\) 3029.15i 0.809645i −0.914395 0.404823i \(-0.867333\pi\)
0.914395 0.404823i \(-0.132667\pi\)
\(242\) 0 0
\(243\) −1104.14 2665.62i −0.291483 0.703703i
\(244\) 0 0
\(245\) 1279.10 + 529.820i 0.333545 + 0.138159i
\(246\) 0 0
\(247\) 922.264 922.264i 0.237580 0.237580i
\(248\) 0 0
\(249\) −148.560 148.560i −0.0378095 0.0378095i
\(250\) 0 0
\(251\) 134.300 324.230i 0.0337727 0.0815346i −0.906093 0.423078i \(-0.860950\pi\)
0.939866 + 0.341543i \(0.110950\pi\)
\(252\) 0 0
\(253\) −3528.86 + 1461.70i −0.876908 + 0.363227i
\(254\) 0 0
\(255\) −2619.56 −0.643307
\(256\) 0 0
\(257\) −7459.69 −1.81059 −0.905297 0.424779i \(-0.860352\pi\)
−0.905297 + 0.424779i \(0.860352\pi\)
\(258\) 0 0
\(259\) −896.396 + 371.299i −0.215055 + 0.0890788i
\(260\) 0 0
\(261\) −245.836 + 593.501i −0.0583022 + 0.140754i
\(262\) 0 0
\(263\) −4192.29 4192.29i −0.982919 0.982919i 0.0169374 0.999857i \(-0.494608\pi\)
−0.999857 + 0.0169374i \(0.994608\pi\)
\(264\) 0 0
\(265\) 5210.05 5210.05i 1.20774 1.20774i
\(266\) 0 0
\(267\) −525.664 217.737i −0.120487 0.0499075i
\(268\) 0 0
\(269\) −1275.44 3079.18i −0.289088 0.697921i 0.710897 0.703296i \(-0.248289\pi\)
−0.999986 + 0.00537488i \(0.998289\pi\)
\(270\) 0 0
\(271\) 1188.89i 0.266494i −0.991083 0.133247i \(-0.957460\pi\)
0.991083 0.133247i \(-0.0425404\pi\)
\(272\) 0 0
\(273\) 1220.38i 0.270552i
\(274\) 0 0
\(275\) 2438.25 + 5886.46i 0.534662 + 1.29079i
\(276\) 0 0
\(277\) 3832.51 + 1587.48i 0.831310 + 0.344340i 0.757421 0.652926i \(-0.226459\pi\)
0.0738890 + 0.997266i \(0.476459\pi\)
\(278\) 0 0
\(279\) −2190.30 + 2190.30i −0.470000 + 0.470000i
\(280\) 0 0
\(281\) 230.048 + 230.048i 0.0488382 + 0.0488382i 0.731104 0.682266i \(-0.239005\pi\)
−0.682266 + 0.731104i \(0.739005\pi\)
\(282\) 0 0
\(283\) 405.744 979.554i 0.0852261 0.205754i −0.875521 0.483181i \(-0.839481\pi\)
0.960747 + 0.277426i \(0.0894815\pi\)
\(284\) 0 0
\(285\) −759.635 + 314.651i −0.157884 + 0.0653977i
\(286\) 0 0
\(287\) 1313.61 0.270173
\(288\) 0 0
\(289\) −5759.94 −1.17239
\(290\) 0 0
\(291\) 1074.54 445.089i 0.216463 0.0896619i
\(292\) 0 0
\(293\) −614.388 + 1483.26i −0.122501 + 0.295744i −0.973220 0.229878i \(-0.926167\pi\)
0.850718 + 0.525622i \(0.176167\pi\)
\(294\) 0 0
\(295\) 4538.12 + 4538.12i 0.895659 + 0.895659i
\(296\) 0 0
\(297\) 2015.72 2015.72i 0.393819 0.393819i
\(298\) 0 0
\(299\) 3804.58 + 1575.91i 0.735867 + 0.304806i
\(300\) 0 0
\(301\) −3899.55 9414.34i −0.746732 1.80277i
\(302\) 0 0
\(303\) 2254.80i 0.427507i
\(304\) 0 0
\(305\) 649.596i 0.121953i
\(306\) 0 0
\(307\) −2158.05 5210.00i −0.401194 0.968569i −0.987377 0.158390i \(-0.949370\pi\)
0.586182 0.810179i \(-0.300630\pi\)
\(308\) 0 0
\(309\) −2157.87 893.819i −0.397272 0.164555i
\(310\) 0 0
\(311\) −182.317 + 182.317i −0.0332420 + 0.0332420i −0.723532 0.690290i \(-0.757483\pi\)
0.690290 + 0.723532i \(0.257483\pi\)
\(312\) 0 0
\(313\) 3731.88 + 3731.88i 0.673924 + 0.673924i 0.958618 0.284694i \(-0.0918921\pi\)
−0.284694 + 0.958618i \(0.591892\pi\)
\(314\) 0 0
\(315\) 3362.52 8117.84i 0.601450 1.45203i
\(316\) 0 0
\(317\) 2940.58 1218.03i 0.521007 0.215808i −0.106652 0.994296i \(-0.534013\pi\)
0.627659 + 0.778488i \(0.284013\pi\)
\(318\) 0 0
\(319\) −965.361 −0.169435
\(320\) 0 0
\(321\) 2658.05 0.462174
\(322\) 0 0
\(323\) −3095.00 + 1281.99i −0.533159 + 0.220842i
\(324\) 0 0
\(325\) 2628.75 6346.37i 0.448668 1.08318i
\(326\) 0 0
\(327\) −933.833 933.833i −0.157924 0.157924i
\(328\) 0 0
\(329\) −8480.20 + 8480.20i −1.42106 + 1.42106i
\(330\) 0 0
\(331\) 5918.75 + 2451.63i 0.982852 + 0.407111i 0.815481 0.578783i \(-0.196472\pi\)
0.167371 + 0.985894i \(0.446472\pi\)
\(332\) 0 0
\(333\) 447.928 + 1081.39i 0.0737127 + 0.177958i
\(334\) 0 0
\(335\) 3661.37i 0.597141i
\(336\) 0 0
\(337\) 11283.3i 1.82385i 0.410355 + 0.911926i \(0.365405\pi\)
−0.410355 + 0.911926i \(0.634595\pi\)
\(338\) 0 0
\(339\) 521.529 + 1259.08i 0.0835562 + 0.201722i
\(340\) 0 0
\(341\) −4300.49 1781.32i −0.682946 0.282886i
\(342\) 0 0
\(343\) −3819.79 + 3819.79i −0.601310 + 0.601310i
\(344\) 0 0
\(345\) −1835.67 1835.67i −0.286462 0.286462i
\(346\) 0 0
\(347\) −4803.69 + 11597.1i −0.743157 + 1.79414i −0.150630 + 0.988590i \(0.548130\pi\)
−0.592527 + 0.805550i \(0.701870\pi\)
\(348\) 0 0
\(349\) −5191.29 + 2150.30i −0.796228 + 0.329808i −0.743445 0.668798i \(-0.766809\pi\)
−0.0527834 + 0.998606i \(0.516809\pi\)
\(350\) 0 0
\(351\) −3073.39 −0.467366
\(352\) 0 0
\(353\) 9949.61 1.50018 0.750091 0.661335i \(-0.230010\pi\)
0.750091 + 0.661335i \(0.230010\pi\)
\(354\) 0 0
\(355\) 11703.4 4847.72i 1.74973 0.724762i
\(356\) 0 0
\(357\) −1199.53 + 2895.91i −0.177831 + 0.429322i
\(358\) 0 0
\(359\) 3301.10 + 3301.10i 0.485308 + 0.485308i 0.906822 0.421514i \(-0.138501\pi\)
−0.421514 + 0.906822i \(0.638501\pi\)
\(360\) 0 0
\(361\) 4106.53 4106.53i 0.598706 0.598706i
\(362\) 0 0
\(363\) 82.8802 + 34.3301i 0.0119837 + 0.00496381i
\(364\) 0 0
\(365\) 5420.12 + 13085.3i 0.777266 + 1.87649i
\(366\) 0 0
\(367\) 10621.1i 1.51067i 0.655340 + 0.755334i \(0.272526\pi\)
−0.655340 + 0.755334i \(0.727474\pi\)
\(368\) 0 0
\(369\) 1584.71i 0.223568i
\(370\) 0 0
\(371\) −3373.95 8145.43i −0.472147 1.13986i
\(372\) 0 0
\(373\) −527.627 218.550i −0.0732426 0.0303381i 0.345761 0.938322i \(-0.387621\pi\)
−0.419004 + 0.907984i \(0.637621\pi\)
\(374\) 0 0
\(375\) −820.862 + 820.862i −0.113038 + 0.113038i
\(376\) 0 0
\(377\) 735.947 + 735.947i 0.100539 + 0.100539i
\(378\) 0 0
\(379\) 3589.96 8666.94i 0.486554 1.17465i −0.469888 0.882726i \(-0.655706\pi\)
0.956443 0.291920i \(-0.0942941\pi\)
\(380\) 0 0
\(381\) −776.177 + 321.503i −0.104369 + 0.0432312i
\(382\) 0 0
\(383\) 4350.16 0.580372 0.290186 0.956970i \(-0.406283\pi\)
0.290186 + 0.956970i \(0.406283\pi\)
\(384\) 0 0
\(385\) 13204.1 1.74791
\(386\) 0 0
\(387\) −11357.3 + 4704.34i −1.49179 + 0.617920i
\(388\) 0 0
\(389\) 763.322 1842.82i 0.0994909 0.240192i −0.866295 0.499533i \(-0.833505\pi\)
0.965786 + 0.259340i \(0.0835051\pi\)
\(390\) 0 0
\(391\) −7479.13 7479.13i −0.967355 0.967355i
\(392\) 0 0
\(393\) −1322.36 + 1322.36i −0.169731 + 0.169731i
\(394\) 0 0
\(395\) 2506.97 + 1038.42i 0.319340 + 0.132275i
\(396\) 0 0
\(397\) 1876.19 + 4529.53i 0.237187 + 0.572621i 0.996990 0.0775330i \(-0.0247043\pi\)
−0.759802 + 0.650154i \(0.774704\pi\)
\(398\) 0 0
\(399\) 983.855i 0.123444i
\(400\) 0 0
\(401\) 14992.8i 1.86710i −0.358450 0.933549i \(-0.616695\pi\)
0.358450 0.933549i \(-0.383305\pi\)
\(402\) 0 0
\(403\) 1920.50 + 4636.49i 0.237387 + 0.573102i
\(404\) 0 0
\(405\) −8860.68 3670.21i −1.08714 0.450307i
\(406\) 0 0
\(407\) −1243.76 + 1243.76i −0.151477 + 0.151477i
\(408\) 0 0
\(409\) 8450.62 + 8450.62i 1.02165 + 1.02165i 0.999760 + 0.0218936i \(0.00696949\pi\)
0.0218936 + 0.999760i \(0.493031\pi\)
\(410\) 0 0
\(411\) 754.857 1822.39i 0.0905946 0.218715i
\(412\) 0 0
\(413\) 7094.91 2938.81i 0.845322 0.350144i
\(414\) 0 0
\(415\) −2450.76 −0.289887
\(416\) 0 0
\(417\) −2096.81 −0.246238
\(418\) 0 0
\(419\) 3136.96 1299.37i 0.365753 0.151500i −0.192235 0.981349i \(-0.561574\pi\)
0.557988 + 0.829849i \(0.311574\pi\)
\(420\) 0 0
\(421\) 3434.08 8290.60i 0.397546 0.959760i −0.590701 0.806891i \(-0.701149\pi\)
0.988246 0.152870i \(-0.0488514\pi\)
\(422\) 0 0
\(423\) 10230.4 + 10230.4i 1.17593 + 1.17593i
\(424\) 0 0
\(425\) −12475.9 + 12475.9i −1.42392 + 1.42392i
\(426\) 0 0
\(427\) 718.125 + 297.457i 0.0813876 + 0.0337118i
\(428\) 0 0
\(429\) −846.648 2043.99i −0.0952833 0.230034i
\(430\) 0 0
\(431\) 15375.3i 1.71833i −0.511699 0.859165i \(-0.670984\pi\)
0.511699 0.859165i \(-0.329016\pi\)
\(432\) 0 0
\(433\) 12522.9i 1.38987i 0.719073 + 0.694934i \(0.244567\pi\)
−0.719073 + 0.694934i \(0.755433\pi\)
\(434\) 0 0
\(435\) −251.085 606.172i −0.0276749 0.0668132i
\(436\) 0 0
\(437\) −3067.20 1270.48i −0.335753 0.139074i
\(438\) 0 0
\(439\) −6689.38 + 6689.38i −0.727259 + 0.727259i −0.970073 0.242814i \(-0.921929\pi\)
0.242814 + 0.970073i \(0.421929\pi\)
\(440\) 0 0
\(441\) −1413.19 1413.19i −0.152595 0.152595i
\(442\) 0 0
\(443\) −1232.30 + 2975.03i −0.132163 + 0.319070i −0.976083 0.217400i \(-0.930242\pi\)
0.843920 + 0.536470i \(0.180242\pi\)
\(444\) 0 0
\(445\) −6131.88 + 2539.91i −0.653212 + 0.270569i
\(446\) 0 0
\(447\) 3890.86 0.411703
\(448\) 0 0
\(449\) −2465.75 −0.259167 −0.129584 0.991569i \(-0.541364\pi\)
−0.129584 + 0.991569i \(0.541364\pi\)
\(450\) 0 0
\(451\) 2200.13 911.324i 0.229712 0.0951498i
\(452\) 0 0
\(453\) 696.557 1681.64i 0.0722453 0.174415i
\(454\) 0 0
\(455\) −10066.2 10066.2i −1.03717 1.03717i
\(456\) 0 0
\(457\) 720.641 720.641i 0.0737640 0.0737640i −0.669262 0.743026i \(-0.733390\pi\)
0.743026 + 0.669262i \(0.233390\pi\)
\(458\) 0 0
\(459\) 7293.03 + 3020.87i 0.741633 + 0.307194i
\(460\) 0 0
\(461\) 94.7149 + 228.662i 0.00956900 + 0.0231016i 0.928592 0.371103i \(-0.121020\pi\)
−0.919023 + 0.394204i \(0.871020\pi\)
\(462\) 0 0
\(463\) 6979.44i 0.700566i −0.936644 0.350283i \(-0.886085\pi\)
0.936644 0.350283i \(-0.113915\pi\)
\(464\) 0 0
\(465\) 3163.69i 0.315511i
\(466\) 0 0
\(467\) −795.725 1921.05i −0.0788475 0.190355i 0.879540 0.475825i \(-0.157850\pi\)
−0.958388 + 0.285470i \(0.907850\pi\)
\(468\) 0 0
\(469\) 4047.63 + 1676.58i 0.398512 + 0.165069i
\(470\) 0 0
\(471\) −977.762 + 977.762i −0.0956537 + 0.0956537i
\(472\) 0 0
\(473\) −13062.5 13062.5i −1.26980 1.26980i
\(474\) 0 0
\(475\) −2119.27 + 5116.37i −0.204713 + 0.494221i
\(476\) 0 0
\(477\) −9826.49 + 4070.26i −0.943237 + 0.390702i
\(478\) 0 0
\(479\) −973.751 −0.0928848 −0.0464424 0.998921i \(-0.514788\pi\)
−0.0464424 + 0.998921i \(0.514788\pi\)
\(480\) 0 0
\(481\) 1896.37 0.179766
\(482\) 0 0
\(483\) −2869.90 + 1188.75i −0.270362 + 0.111988i
\(484\) 0 0
\(485\) 5191.98 12534.6i 0.486094 1.17354i
\(486\) 0 0
\(487\) 11379.8 + 11379.8i 1.05887 + 1.05887i 0.998155 + 0.0607112i \(0.0193369\pi\)
0.0607112 + 0.998155i \(0.480663\pi\)
\(488\) 0 0
\(489\) 841.184 841.184i 0.0777907 0.0777907i
\(490\) 0 0
\(491\) 1394.56 + 577.645i 0.128178 + 0.0530932i 0.445851 0.895107i \(-0.352901\pi\)
−0.317672 + 0.948201i \(0.602901\pi\)
\(492\) 0 0
\(493\) −1023.00 2469.74i −0.0934557 0.225622i
\(494\) 0 0
\(495\) 15929.2i 1.44639i
\(496\) 0 0
\(497\) 15157.9i 1.36806i
\(498\) 0 0
\(499\) −5429.65 13108.3i −0.487103 1.17597i −0.956171 0.292809i \(-0.905410\pi\)
0.469068 0.883162i \(-0.344590\pi\)
\(500\) 0 0
\(501\) 1428.86 + 591.852i 0.127418 + 0.0527784i
\(502\) 0 0
\(503\) −11037.0 + 11037.0i −0.978362 + 0.978362i −0.999771 0.0214085i \(-0.993185\pi\)
0.0214085 + 0.999771i \(0.493185\pi\)
\(504\) 0 0
\(505\) −18598.5 18598.5i −1.63886 1.63886i
\(506\) 0 0
\(507\) 326.770 788.893i 0.0286240 0.0691045i
\(508\) 0 0
\(509\) 13984.8 5792.71i 1.21781 0.504435i 0.321099 0.947046i \(-0.395948\pi\)
0.896714 + 0.442611i \(0.145948\pi\)
\(510\) 0 0
\(511\) 16947.7 1.46717
\(512\) 0 0
\(513\) 2477.73 0.213244
\(514\) 0 0
\(515\) −25171.6 + 10426.4i −2.15377 + 0.892123i
\(516\) 0 0
\(517\) −8320.11 + 20086.5i −0.707772 + 1.70871i
\(518\) 0 0
\(519\) −93.6978 93.6978i −0.00792462 0.00792462i
\(520\) 0 0
\(521\) 8504.46 8504.46i 0.715139 0.715139i −0.252467 0.967606i \(-0.581242\pi\)
0.967606 + 0.252467i \(0.0812418\pi\)
\(522\) 0 0
\(523\) 2991.17 + 1238.98i 0.250086 + 0.103589i 0.504205 0.863584i \(-0.331786\pi\)
−0.254119 + 0.967173i \(0.581786\pi\)
\(524\) 0 0
\(525\) 1982.94 + 4787.25i 0.164843 + 0.397967i
\(526\) 0 0
\(527\) 12889.9i 1.06545i
\(528\) 0 0
\(529\) 1684.91i 0.138482i
\(530\) 0 0
\(531\) −3545.33 8559.17i −0.289744 0.699504i
\(532\) 0 0
\(533\) −2372.03 982.527i −0.192765 0.0798461i
\(534\) 0 0
\(535\) 21924.7 21924.7i 1.77175 1.77175i
\(536\) 0 0
\(537\) 3821.65 + 3821.65i 0.307107 + 0.307107i
\(538\) 0 0
\(539\) 1149.31 2774.68i 0.0918448 0.221733i
\(540\) 0 0
\(541\) 4615.58 1911.84i 0.366801 0.151934i −0.191667 0.981460i \(-0.561389\pi\)
0.558468 + 0.829526i \(0.311389\pi\)
\(542\) 0 0
\(543\) 805.668 0.0636732
\(544\) 0 0
\(545\) −15405.3 −1.21081
\(546\) 0 0
\(547\) −1759.02 + 728.609i −0.137496 + 0.0569526i −0.450370 0.892842i \(-0.648708\pi\)
0.312875 + 0.949794i \(0.398708\pi\)
\(548\) 0 0
\(549\) 358.847 866.332i 0.0278965 0.0673482i
\(550\) 0 0
\(551\) −593.311 593.311i −0.0458728 0.0458728i
\(552\) 0 0
\(553\) 2295.94 2295.94i 0.176552 0.176552i
\(554\) 0 0
\(555\) −1104.48 457.492i −0.0844733 0.0349900i
\(556\) 0 0
\(557\) 7305.07 + 17636.0i 0.555702 + 1.34158i 0.913140 + 0.407646i \(0.133650\pi\)
−0.357438 + 0.933937i \(0.616350\pi\)
\(558\) 0 0
\(559\) 19916.6i 1.50694i
\(560\) 0 0
\(561\) 5682.48i 0.427655i
\(562\) 0 0
\(563\) −498.470 1203.41i −0.0373144 0.0900849i 0.904124 0.427271i \(-0.140525\pi\)
−0.941438 + 0.337186i \(0.890525\pi\)
\(564\) 0 0
\(565\) 14687.2 + 6083.65i 1.09362 + 0.452993i
\(566\) 0 0
\(567\) −8114.80 + 8114.80i −0.601040 + 0.601040i
\(568\) 0 0
\(569\) 13188.4 + 13188.4i 0.971684 + 0.971684i 0.999610 0.0279264i \(-0.00889041\pi\)
−0.0279264 + 0.999610i \(0.508890\pi\)
\(570\) 0 0
\(571\) −5719.51 + 13808.1i −0.419184 + 1.01200i 0.563401 + 0.826184i \(0.309493\pi\)
−0.982585 + 0.185815i \(0.940507\pi\)
\(572\) 0 0
\(573\) 24.0983 9.98186i 0.00175693 0.000727746i
\(574\) 0 0
\(575\) −17485.1 −1.26813
\(576\) 0 0
\(577\) 7866.08 0.567538 0.283769 0.958893i \(-0.408415\pi\)
0.283769 + 0.958893i \(0.408415\pi\)
\(578\) 0 0
\(579\) −4524.46 + 1874.09i −0.324750 + 0.134516i
\(580\) 0 0
\(581\) −1122.23 + 2709.30i −0.0801342 + 0.193461i
\(582\) 0 0
\(583\) −11301.9 11301.9i −0.802877 0.802877i
\(584\) 0 0
\(585\) −12143.7 + 12143.7i −0.858255 + 0.858255i
\(586\) 0 0
\(587\) −13370.3 5538.16i −0.940122 0.389411i −0.140613 0.990065i \(-0.544907\pi\)
−0.799510 + 0.600653i \(0.794907\pi\)
\(588\) 0 0
\(589\) −1548.28 3737.88i −0.108312 0.261489i
\(590\) 0 0
\(591\) 1195.87i 0.0832346i
\(592\) 0 0
\(593\) 7176.23i 0.496952i 0.968638 + 0.248476i \(0.0799297\pi\)
−0.968638 + 0.248476i \(0.920070\pi\)
\(594\) 0 0
\(595\) 13992.5 + 33780.9i 0.964095 + 2.32753i
\(596\) 0 0
\(597\) −3676.11 1522.69i −0.252015 0.104388i
\(598\) 0 0
\(599\) 11813.4 11813.4i 0.805815 0.805815i −0.178183 0.983997i \(-0.557022\pi\)
0.983997 + 0.178183i \(0.0570218\pi\)
\(600\) 0 0
\(601\) −1438.92 1438.92i −0.0976618 0.0976618i 0.656588 0.754250i \(-0.271999\pi\)
−0.754250 + 0.656588i \(0.771999\pi\)
\(602\) 0 0
\(603\) 2022.60 4882.98i 0.136595 0.329768i
\(604\) 0 0
\(605\) 966.800 400.462i 0.0649686 0.0269109i
\(606\) 0 0
\(607\) 19331.1 1.29263 0.646314 0.763071i \(-0.276309\pi\)
0.646314 + 0.763071i \(0.276309\pi\)
\(608\) 0 0
\(609\) −785.094 −0.0522391
\(610\) 0 0
\(611\) 21655.9 8970.17i 1.43389 0.593935i
\(612\) 0 0
\(613\) 2013.56 4861.15i 0.132670 0.320294i −0.843559 0.537037i \(-0.819543\pi\)
0.976229 + 0.216743i \(0.0695435\pi\)
\(614\) 0 0
\(615\) 1144.48 + 1144.48i 0.0750406 + 0.0750406i
\(616\) 0 0
\(617\) −6574.52 + 6574.52i −0.428979 + 0.428979i −0.888281 0.459301i \(-0.848100\pi\)
0.459301 + 0.888281i \(0.348100\pi\)
\(618\) 0 0
\(619\) −2395.09 992.077i −0.155520 0.0644183i 0.303566 0.952810i \(-0.401823\pi\)
−0.459085 + 0.888392i \(0.651823\pi\)
\(620\) 0 0
\(621\) 2993.74 + 7227.53i 0.193454 + 0.467038i
\(622\) 0 0
\(623\) 7941.81i 0.510726i
\(624\) 0 0
\(625\) 7806.17i 0.499595i
\(626\) 0 0
\(627\) 682.557 + 1647.84i 0.0434748 + 0.104957i
\(628\) 0 0
\(629\) −4500.02 1863.97i −0.285258 0.118158i
\(630\) 0 0
\(631\) 2820.94 2820.94i 0.177971 0.177971i −0.612500 0.790471i \(-0.709836\pi\)
0.790471 + 0.612500i \(0.209836\pi\)
\(632\) 0 0
\(633\) 2642.13 + 2642.13i 0.165901 + 0.165901i
\(634\) 0 0
\(635\) −3750.34 + 9054.12i −0.234374 + 0.565830i
\(636\) 0 0
\(637\) −2991.47 + 1239.11i −0.186070 + 0.0770726i
\(638\) 0 0
\(639\) −18286.2 −1.13207
\(640\) 0 0
\(641\) 8220.77 0.506553 0.253277 0.967394i \(-0.418492\pi\)
0.253277 + 0.967394i \(0.418492\pi\)
\(642\) 0 0
\(643\) 21031.3 8711.45i 1.28988 0.534286i 0.370932 0.928660i \(-0.379038\pi\)
0.918950 + 0.394374i \(0.129038\pi\)
\(644\) 0 0
\(645\) 4804.78 11599.8i 0.293315 0.708124i
\(646\) 0 0
\(647\) 14749.1 + 14749.1i 0.896208 + 0.896208i 0.995098 0.0988901i \(-0.0315292\pi\)
−0.0988901 + 0.995098i \(0.531529\pi\)
\(648\) 0 0
\(649\) 9844.31 9844.31i 0.595413 0.595413i
\(650\) 0 0
\(651\) −3497.44 1448.69i −0.210561 0.0872174i
\(652\) 0 0
\(653\) −4279.06 10330.6i −0.256436 0.619091i 0.742262 0.670110i \(-0.233753\pi\)
−0.998698 + 0.0510191i \(0.983753\pi\)
\(654\) 0 0
\(655\) 21814.8i 1.30134i
\(656\) 0 0
\(657\) 20445.4i 1.21408i
\(658\) 0 0
\(659\) 11437.1 + 27611.6i 0.676063 + 1.63216i 0.771121 + 0.636689i \(0.219696\pi\)
−0.0950580 + 0.995472i \(0.530304\pi\)
\(660\) 0 0
\(661\) 19843.3 + 8219.36i 1.16765 + 0.483655i 0.880414 0.474205i \(-0.157265\pi\)
0.287233 + 0.957861i \(0.407265\pi\)
\(662\) 0 0
\(663\) 4332.06 4332.06i 0.253761 0.253761i
\(664\) 0 0
\(665\) 8115.25 + 8115.25i 0.473227 + 0.473227i
\(666\) 0 0
\(667\) 1013.81 2447.56i 0.0588530 0.142084i
\(668\) 0 0
\(669\) 364.332 150.911i 0.0210551 0.00872132i
\(670\) 0 0
\(671\) 1409.14 0.0810717
\(672\) 0 0
\(673\) −13639.3 −0.781216 −0.390608 0.920557i \(-0.627735\pi\)
−0.390608 + 0.920557i \(0.627735\pi\)
\(674\) 0 0
\(675\) 12056.2 4993.82i 0.687469 0.284759i
\(676\) 0 0
\(677\) −10163.0 + 24535.6i −0.576951 + 1.39288i 0.318586 + 0.947894i \(0.396792\pi\)
−0.895537 + 0.444988i \(0.853208\pi\)
\(678\) 0 0
\(679\) −11479.4 11479.4i −0.648806 0.648806i
\(680\) 0 0
\(681\) 814.433 814.433i 0.0458284 0.0458284i
\(682\) 0 0
\(683\) 12279.3 + 5086.25i 0.687928 + 0.284949i 0.699136 0.714988i \(-0.253568\pi\)
−0.0112089 + 0.999937i \(0.503568\pi\)
\(684\) 0 0
\(685\) −8805.43 21258.2i −0.491151 1.18574i
\(686\) 0 0
\(687\) 5406.62i 0.300255i
\(688\) 0 0
\(689\) 17232.1i 0.952817i
\(690\) 0 0
\(691\) −12427.1 30001.7i −0.684153 1.65169i −0.756241 0.654293i \(-0.772966\pi\)
0.0720884 0.997398i \(-0.477034\pi\)
\(692\) 0 0
\(693\) −17609.6 7294.15i −0.965273 0.399829i
\(694\) 0 0
\(695\) −17295.3 + 17295.3i −0.943956 + 0.943956i
\(696\) 0 0
\(697\) 4662.99 + 4662.99i 0.253405 + 0.253405i
\(698\) 0 0
\(699\) 76.1625 183.873i 0.00412122 0.00994950i
\(700\) 0 0
\(701\) −24563.9 + 10174.7i −1.32349 + 0.548207i −0.928791 0.370605i \(-0.879150\pi\)
−0.394697 + 0.918811i \(0.629150\pi\)
\(702\) 0 0
\(703\) −1528.83 −0.0820214
\(704\) 0 0
\(705\) −14776.8 −0.789399
\(706\) 0 0
\(707\) −29077.0 + 12044.1i −1.54675 + 0.640685i
\(708\) 0 0
\(709\) −4032.81 + 9736.05i −0.213618 + 0.515720i −0.993974 0.109616i \(-0.965038\pi\)
0.780356 + 0.625336i \(0.215038\pi\)
\(710\) 0 0
\(711\) −2769.78 2769.78i −0.146097 0.146097i
\(712\) 0 0
\(713\) 9032.67 9032.67i 0.474440 0.474440i
\(714\) 0 0
\(715\) −23843.2 9876.17i −1.24711 0.516570i
\(716\) 0 0
\(717\) −1247.08 3010.72i −0.0649555 0.156816i
\(718\) 0 0
\(719\) 2159.37i 0.112004i 0.998431 + 0.0560021i \(0.0178353\pi\)
−0.998431 + 0.0560021i \(0.982165\pi\)
\(720\) 0 0
\(721\) 32601.4i 1.68397i
\(722\) 0 0
\(723\) −1709.07 4126.06i −0.0879129 0.212241i
\(724\) 0 0
\(725\) −4082.75 1691.13i −0.209144 0.0866303i
\(726\) 0 0
\(727\) 15999.3 15999.3i 0.816204 0.816204i −0.169352 0.985556i \(-0.554167\pi\)
0.985556 + 0.169352i \(0.0541674\pi\)
\(728\) 0 0
\(729\) 7638.74 + 7638.74i 0.388088 + 0.388088i
\(730\) 0 0
\(731\) 19576.2 47261.2i 0.990497 2.39127i
\(732\) 0 0
\(733\) −2232.08 + 924.559i −0.112475 + 0.0465885i −0.438211 0.898872i \(-0.644388\pi\)
0.325737 + 0.945461i \(0.394388\pi\)
\(734\) 0 0
\(735\) 2041.22 0.102437
\(736\) 0 0
\(737\) 7942.43 0.396965
\(738\) 0 0
\(739\) 15900.0 6585.99i 0.791462 0.327834i 0.0499305 0.998753i \(-0.484100\pi\)
0.741531 + 0.670919i \(0.234100\pi\)
\(740\) 0 0
\(741\) 735.886 1776.59i 0.0364824 0.0880762i
\(742\) 0 0
\(743\) 6184.20 + 6184.20i 0.305352 + 0.305352i 0.843103 0.537751i \(-0.180726\pi\)
−0.537751 + 0.843103i \(0.680726\pi\)
\(744\) 0 0
\(745\) 32093.4 32093.4i 1.57827 1.57827i
\(746\) 0 0
\(747\) 3268.45 + 1353.84i 0.160089 + 0.0663110i
\(748\) 0 0
\(749\) −14198.1 34277.2i −0.692639 1.67218i
\(750\) 0 0
\(751\) 11095.5i 0.539122i 0.962983 + 0.269561i \(0.0868786\pi\)
−0.962983 + 0.269561i \(0.913121\pi\)
\(752\) 0 0
\(753\) 517.413i 0.0250406i
\(754\) 0 0
\(755\) −8125.36 19616.3i −0.391672 0.945579i
\(756\) 0 0
\(757\) 25020.9 + 10364.0i 1.20132 + 0.497604i 0.891426 0.453167i \(-0.149706\pi\)
0.309896 + 0.950771i \(0.399706\pi\)
\(758\) 0 0
\(759\) −3982.03 + 3982.03i −0.190433 + 0.190433i
\(760\) 0 0
\(761\) 2393.12 + 2393.12i 0.113995 + 0.113995i 0.761804 0.647808i \(-0.224314\pi\)
−0.647808 + 0.761804i \(0.724314\pi\)
\(762\) 0 0
\(763\) −7054.25 + 17030.5i −0.334706 + 0.808053i
\(764\) 0 0
\(765\) 40752.6 16880.3i 1.92603 0.797788i
\(766\) 0 0
\(767\) −15009.7 −0.706608
\(768\) 0 0
\(769\) −33544.1 −1.57299 −0.786496 0.617595i \(-0.788107\pi\)
−0.786496 + 0.617595i \(0.788107\pi\)
\(770\) 0 0
\(771\) −10161.0 + 4208.82i −0.474630 + 0.196598i
\(772\) 0 0
\(773\) 9560.71 23081.6i 0.444857 1.07398i −0.529366 0.848394i \(-0.677570\pi\)
0.974223 0.225587i \(-0.0724300\pi\)
\(774\) 0 0
\(775\) −15067.3 15067.3i −0.698365 0.698365i
\(776\) 0 0
\(777\) −1011.51 + 1011.51i −0.0467023 + 0.0467023i
\(778\) 0 0
\(779\) 1912.30 + 792.101i 0.0879529 + 0.0364313i
\(780\) 0 0
\(781\) −10515.9 25387.7i −0.481804 1.16318i
\(782\) 0 0
\(783\) 1977.17i 0.0902406i
\(784\) 0 0
\(785\) 16130.0i 0.733381i
\(786\) 0 0