Properties

Label 128.3.h.a.79.6
Level $128$
Weight $3$
Character 128.79
Analytic conductor $3.488$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 128 = 2^{7} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 128.h (of order \(8\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.48774738381\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(7\) over \(\Q(\zeta_{8})\)
Twist minimal: no (minimal twist has level 32)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 79.6
Character \(\chi\) \(=\) 128.79
Dual form 128.3.h.a.47.6

$q$-expansion

\(f(q)\) \(=\) \(q+(1.31872 + 3.18367i) q^{3} +(-0.659338 + 1.59178i) q^{5} +(-9.54718 + 9.54718i) q^{7} +(-2.03276 + 2.03276i) q^{9} +O(q^{10})\) \(q+(1.31872 + 3.18367i) q^{3} +(-0.659338 + 1.59178i) q^{5} +(-9.54718 + 9.54718i) q^{7} +(-2.03276 + 2.03276i) q^{9} +(3.96481 - 9.57189i) q^{11} +(1.91784 + 4.63007i) q^{13} -5.93719 q^{15} +15.3143i q^{17} +(-0.827335 + 0.342693i) q^{19} +(-42.9851 - 17.8050i) q^{21} +(12.9230 + 12.9230i) q^{23} +(15.5786 + 15.5786i) q^{25} +(19.5007 + 8.07746i) q^{27} +(23.7905 - 9.85436i) q^{29} -25.1562i q^{31} +35.7022 q^{33} +(-8.90221 - 21.4918i) q^{35} +(13.6161 - 32.8721i) q^{37} +(-12.2115 + 12.2115i) q^{39} +(-32.9116 + 32.9116i) q^{41} +(17.9473 - 43.3286i) q^{43} +(-1.89544 - 4.57600i) q^{45} -20.1127 q^{47} -133.297i q^{49} +(-48.7557 + 20.1953i) q^{51} +(35.0503 + 14.5183i) q^{53} +(12.6222 + 12.6222i) q^{55} +(-2.18204 - 2.18204i) q^{57} +(60.6706 + 25.1306i) q^{59} +(-27.9825 + 11.5907i) q^{61} -38.8143i q^{63} -8.63457 q^{65} +(-1.13412 - 2.73801i) q^{67} +(-24.1008 + 58.1845i) q^{69} +(45.6144 - 45.6144i) q^{71} +(-29.1727 + 29.1727i) q^{73} +(-29.0534 + 70.1410i) q^{75} +(53.5318 + 129.237i) q^{77} -3.27983 q^{79} +98.6086i q^{81} +(-56.7834 + 23.5205i) q^{83} +(-24.3770 - 10.0973i) q^{85} +(62.7460 + 62.7460i) q^{87} +(-44.5059 - 44.5059i) q^{89} +(-62.5140 - 25.8942i) q^{91} +(80.0891 - 33.1740i) q^{93} -1.54289i q^{95} -106.417 q^{97} +(11.3979 + 27.5169i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + O(q^{10}) \) \( 28q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + 4q^{11} - 4q^{13} + 8q^{15} + 4q^{19} - 4q^{21} + 68q^{23} - 4q^{25} + 100q^{27} - 4q^{29} - 8q^{33} - 92q^{35} - 4q^{37} - 188q^{39} - 4q^{41} - 92q^{43} - 40q^{45} + 8q^{47} - 224q^{51} - 164q^{53} - 252q^{55} - 4q^{57} - 124q^{59} - 68q^{61} - 8q^{65} + 164q^{67} + 188q^{69} + 260q^{71} - 4q^{73} + 488q^{75} + 220q^{77} + 520q^{79} + 484q^{83} + 96q^{85} + 452q^{87} - 4q^{89} + 196q^{91} + 32q^{93} - 8q^{97} - 216q^{99} + O(q^{100}) \)

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
\(3\) 1.31872 + 3.18367i 0.439573 + 1.06122i 0.976097 + 0.217337i \(0.0697372\pi\)
−0.536524 + 0.843885i \(0.680263\pi\)
\(4\) 0 0
\(5\) −0.659338 + 1.59178i −0.131868 + 0.318356i −0.975997 0.217782i \(-0.930118\pi\)
0.844130 + 0.536139i \(0.180118\pi\)
\(6\) 0 0
\(7\) −9.54718 + 9.54718i −1.36388 + 1.36388i −0.494975 + 0.868907i \(0.664823\pi\)
−0.868907 + 0.494975i \(0.835177\pi\)
\(8\) 0 0
\(9\) −2.03276 + 2.03276i −0.225863 + 0.225863i
\(10\) 0 0
\(11\) 3.96481 9.57189i 0.360437 0.870172i −0.634799 0.772677i \(-0.718917\pi\)
0.995236 0.0974947i \(-0.0310829\pi\)
\(12\) 0 0
\(13\) 1.91784 + 4.63007i 0.147526 + 0.356159i 0.980317 0.197428i \(-0.0632587\pi\)
−0.832792 + 0.553587i \(0.813259\pi\)
\(14\) 0 0
\(15\) −5.93719 −0.395813
\(16\) 0 0
\(17\) 15.3143i 0.900842i 0.892816 + 0.450421i \(0.148726\pi\)
−0.892816 + 0.450421i \(0.851274\pi\)
\(18\) 0 0
\(19\) −0.827335 + 0.342693i −0.0435439 + 0.0180365i −0.404349 0.914605i \(-0.632502\pi\)
0.360805 + 0.932641i \(0.382502\pi\)
\(20\) 0 0
\(21\) −42.9851 17.8050i −2.04691 0.847857i
\(22\) 0 0
\(23\) 12.9230 + 12.9230i 0.561871 + 0.561871i 0.929839 0.367968i \(-0.119946\pi\)
−0.367968 + 0.929839i \(0.619946\pi\)
\(24\) 0 0
\(25\) 15.5786 + 15.5786i 0.623145 + 0.623145i
\(26\) 0 0
\(27\) 19.5007 + 8.07746i 0.722249 + 0.299165i
\(28\) 0 0
\(29\) 23.7905 9.85436i 0.820363 0.339805i 0.0672825 0.997734i \(-0.478567\pi\)
0.753080 + 0.657929i \(0.228567\pi\)
\(30\) 0 0
\(31\) 25.1562i 0.811491i −0.913986 0.405746i \(-0.867012\pi\)
0.913986 0.405746i \(-0.132988\pi\)
\(32\) 0 0
\(33\) 35.7022 1.08188
\(34\) 0 0
\(35\) −8.90221 21.4918i −0.254349 0.614053i
\(36\) 0 0
\(37\) 13.6161 32.8721i 0.368001 0.888434i −0.626076 0.779762i \(-0.715340\pi\)
0.994078 0.108672i \(-0.0346599\pi\)
\(38\) 0 0
\(39\) −12.2115 + 12.2115i −0.313116 + 0.313116i
\(40\) 0 0
\(41\) −32.9116 + 32.9116i −0.802721 + 0.802721i −0.983520 0.180799i \(-0.942132\pi\)
0.180799 + 0.983520i \(0.442132\pi\)
\(42\) 0 0
\(43\) 17.9473 43.3286i 0.417379 1.00764i −0.565725 0.824594i \(-0.691404\pi\)
0.983104 0.183048i \(-0.0585964\pi\)
\(44\) 0 0
\(45\) −1.89544 4.57600i −0.0421209 0.101689i
\(46\) 0 0
\(47\) −20.1127 −0.427930 −0.213965 0.976841i \(-0.568638\pi\)
−0.213965 + 0.976841i \(0.568638\pi\)
\(48\) 0 0
\(49\) 133.297i 2.72035i
\(50\) 0 0
\(51\) −48.7557 + 20.1953i −0.955994 + 0.395986i
\(52\) 0 0
\(53\) 35.0503 + 14.5183i 0.661327 + 0.273931i 0.687997 0.725714i \(-0.258490\pi\)
−0.0266698 + 0.999644i \(0.508490\pi\)
\(54\) 0 0
\(55\) 12.6222 + 12.6222i 0.229495 + 0.229495i
\(56\) 0 0
\(57\) −2.18204 2.18204i −0.0382815 0.0382815i
\(58\) 0 0
\(59\) 60.6706 + 25.1306i 1.02832 + 0.425942i 0.832104 0.554619i \(-0.187136\pi\)
0.196212 + 0.980562i \(0.437136\pi\)
\(60\) 0 0
\(61\) −27.9825 + 11.5907i −0.458730 + 0.190012i −0.600067 0.799949i \(-0.704860\pi\)
0.141338 + 0.989961i \(0.454860\pi\)
\(62\) 0 0
\(63\) 38.8143i 0.616100i
\(64\) 0 0
\(65\) −8.63457 −0.132839
\(66\) 0 0
\(67\) −1.13412 2.73801i −0.0169272 0.0408659i 0.915190 0.403023i \(-0.132040\pi\)
−0.932117 + 0.362157i \(0.882040\pi\)
\(68\) 0 0
\(69\) −24.1008 + 58.1845i −0.349287 + 0.843253i
\(70\) 0 0
\(71\) 45.6144 45.6144i 0.642456 0.642456i −0.308702 0.951159i \(-0.599895\pi\)
0.951159 + 0.308702i \(0.0998947\pi\)
\(72\) 0 0
\(73\) −29.1727 + 29.1727i −0.399626 + 0.399626i −0.878101 0.478475i \(-0.841190\pi\)
0.478475 + 0.878101i \(0.341190\pi\)
\(74\) 0 0
\(75\) −29.0534 + 70.1410i −0.387378 + 0.935213i
\(76\) 0 0
\(77\) 53.5318 + 129.237i 0.695219 + 1.67841i
\(78\) 0 0
\(79\) −3.27983 −0.0415169 −0.0207584 0.999785i \(-0.506608\pi\)
−0.0207584 + 0.999785i \(0.506608\pi\)
\(80\) 0 0
\(81\) 98.6086i 1.21739i
\(82\) 0 0
\(83\) −56.7834 + 23.5205i −0.684138 + 0.283379i −0.697555 0.716531i \(-0.745729\pi\)
0.0134176 + 0.999910i \(0.495729\pi\)
\(84\) 0 0
\(85\) −24.3770 10.0973i −0.286789 0.118792i
\(86\) 0 0
\(87\) 62.7460 + 62.7460i 0.721218 + 0.721218i
\(88\) 0 0
\(89\) −44.5059 44.5059i −0.500066 0.500066i 0.411392 0.911458i \(-0.365043\pi\)
−0.911458 + 0.411392i \(0.865043\pi\)
\(90\) 0 0
\(91\) −62.5140 25.8942i −0.686967 0.284551i
\(92\) 0 0
\(93\) 80.0891 33.1740i 0.861173 0.356709i
\(94\) 0 0
\(95\) 1.54289i 0.0162409i
\(96\) 0 0
\(97\) −106.417 −1.09708 −0.548542 0.836123i \(-0.684817\pi\)
−0.548542 + 0.836123i \(0.684817\pi\)
\(98\) 0 0
\(99\) 11.3979 + 27.5169i 0.115130 + 0.277949i
\(100\) 0 0
\(101\) 3.62243 8.74531i 0.0358656 0.0865872i −0.904932 0.425557i \(-0.860078\pi\)
0.940797 + 0.338969i \(0.110078\pi\)
\(102\) 0 0
\(103\) −26.0911 + 26.0911i −0.253312 + 0.253312i −0.822327 0.569015i \(-0.807325\pi\)
0.569015 + 0.822327i \(0.307325\pi\)
\(104\) 0 0
\(105\) 56.6834 56.6834i 0.539842 0.539842i
\(106\) 0 0
\(107\) −32.1753 + 77.6781i −0.300704 + 0.725963i 0.699235 + 0.714892i \(0.253524\pi\)
−0.999939 + 0.0110713i \(0.996476\pi\)
\(108\) 0 0
\(109\) −36.0541 87.0422i −0.330771 0.798553i −0.998531 0.0541760i \(-0.982747\pi\)
0.667760 0.744377i \(-0.267253\pi\)
\(110\) 0 0
\(111\) 122.609 1.10459
\(112\) 0 0
\(113\) 6.32445i 0.0559686i 0.999608 + 0.0279843i \(0.00890884\pi\)
−0.999608 + 0.0279843i \(0.991091\pi\)
\(114\) 0 0
\(115\) −29.0913 + 12.0500i −0.252968 + 0.104783i
\(116\) 0 0
\(117\) −13.3104 5.51333i −0.113764 0.0471225i
\(118\) 0 0
\(119\) −146.208 146.208i −1.22864 1.22864i
\(120\) 0 0
\(121\) 9.65850 + 9.65850i 0.0798223 + 0.0798223i
\(122\) 0 0
\(123\) −148.181 61.3784i −1.20472 0.499011i
\(124\) 0 0
\(125\) −74.8639 + 31.0096i −0.598911 + 0.248077i
\(126\) 0 0
\(127\) 34.6015i 0.272453i 0.990678 + 0.136226i \(0.0434975\pi\)
−0.990678 + 0.136226i \(0.956503\pi\)
\(128\) 0 0
\(129\) 161.611 1.25280
\(130\) 0 0
\(131\) 68.0051 + 164.179i 0.519123 + 1.25327i 0.938443 + 0.345434i \(0.112268\pi\)
−0.419320 + 0.907838i \(0.637732\pi\)
\(132\) 0 0
\(133\) 4.62696 11.1705i 0.0347892 0.0839885i
\(134\) 0 0
\(135\) −25.7151 + 25.7151i −0.190482 + 0.190482i
\(136\) 0 0
\(137\) 71.5748 71.5748i 0.522444 0.522444i −0.395865 0.918309i \(-0.629555\pi\)
0.918309 + 0.395865i \(0.129555\pi\)
\(138\) 0 0
\(139\) 75.1916 181.529i 0.540947 1.30596i −0.383109 0.923703i \(-0.625147\pi\)
0.924056 0.382258i \(-0.124853\pi\)
\(140\) 0 0
\(141\) −26.5230 64.0322i −0.188107 0.454129i
\(142\) 0 0
\(143\) 51.9224 0.363094
\(144\) 0 0
\(145\) 44.3667i 0.305977i
\(146\) 0 0
\(147\) 424.374 175.781i 2.88690 1.19579i
\(148\) 0 0
\(149\) 211.685 + 87.6826i 1.42070 + 0.588474i 0.955037 0.296487i \(-0.0958152\pi\)
0.465665 + 0.884961i \(0.345815\pi\)
\(150\) 0 0
\(151\) −10.5820 10.5820i −0.0700794 0.0700794i 0.671198 0.741278i \(-0.265780\pi\)
−0.741278 + 0.671198i \(0.765780\pi\)
\(152\) 0 0
\(153\) −31.1304 31.1304i −0.203467 0.203467i
\(154\) 0 0
\(155\) 40.0432 + 16.5864i 0.258343 + 0.107009i
\(156\) 0 0
\(157\) 26.9641 11.1689i 0.171746 0.0711394i −0.295154 0.955450i \(-0.595371\pi\)
0.466900 + 0.884310i \(0.345371\pi\)
\(158\) 0 0
\(159\) 130.734i 0.822228i
\(160\) 0 0
\(161\) −246.757 −1.53265
\(162\) 0 0
\(163\) −111.743 269.771i −0.685540 1.65504i −0.753579 0.657357i \(-0.771674\pi\)
0.0680396 0.997683i \(-0.478326\pi\)
\(164\) 0 0
\(165\) −23.5398 + 56.8301i −0.142665 + 0.344425i
\(166\) 0 0
\(167\) 10.3664 10.3664i 0.0620741 0.0620741i −0.675388 0.737462i \(-0.736024\pi\)
0.737462 + 0.675388i \(0.236024\pi\)
\(168\) 0 0
\(169\) 101.742 101.742i 0.602021 0.602021i
\(170\) 0 0
\(171\) 0.985162 2.37839i 0.00576118 0.0139087i
\(172\) 0 0
\(173\) −88.6518 214.024i −0.512438 1.23714i −0.942461 0.334317i \(-0.891494\pi\)
0.430022 0.902818i \(-0.358506\pi\)
\(174\) 0 0
\(175\) −297.464 −1.69979
\(176\) 0 0
\(177\) 226.295i 1.27850i
\(178\) 0 0
\(179\) −2.58312 + 1.06996i −0.0144308 + 0.00597744i −0.389887 0.920863i \(-0.627486\pi\)
0.375456 + 0.926840i \(0.377486\pi\)
\(180\) 0 0
\(181\) −184.394 76.3786i −1.01875 0.421981i −0.190112 0.981762i \(-0.560885\pi\)
−0.828640 + 0.559781i \(0.810885\pi\)
\(182\) 0 0
\(183\) −73.8021 73.8021i −0.403290 0.403290i
\(184\) 0 0
\(185\) 43.3476 + 43.3476i 0.234311 + 0.234311i
\(186\) 0 0
\(187\) 146.587 + 60.7183i 0.783887 + 0.324697i
\(188\) 0 0
\(189\) −263.294 + 109.060i −1.39309 + 0.577036i
\(190\) 0 0
\(191\) 185.771i 0.972625i 0.873785 + 0.486313i \(0.161658\pi\)
−0.873785 + 0.486313i \(0.838342\pi\)
\(192\) 0 0
\(193\) 208.055 1.07800 0.539002 0.842305i \(-0.318802\pi\)
0.539002 + 0.842305i \(0.318802\pi\)
\(194\) 0 0
\(195\) −11.3866 27.4896i −0.0583926 0.140972i
\(196\) 0 0
\(197\) 123.852 299.006i 0.628691 1.51780i −0.212558 0.977148i \(-0.568180\pi\)
0.841250 0.540647i \(-0.181820\pi\)
\(198\) 0 0
\(199\) 253.762 253.762i 1.27519 1.27519i 0.331858 0.943329i \(-0.392324\pi\)
0.943329 0.331858i \(-0.107676\pi\)
\(200\) 0 0
\(201\) 7.22134 7.22134i 0.0359270 0.0359270i
\(202\) 0 0
\(203\) −133.051 + 321.214i −0.655424 + 1.58233i
\(204\) 0 0
\(205\) −30.6882 74.0879i −0.149699 0.361404i
\(206\) 0 0
\(207\) −52.5389 −0.253811
\(208\) 0 0
\(209\) 9.27787i 0.0443917i
\(210\) 0 0
\(211\) −102.533 + 42.4705i −0.485938 + 0.201282i −0.612182 0.790717i \(-0.709708\pi\)
0.126244 + 0.991999i \(0.459708\pi\)
\(212\) 0 0
\(213\) 205.374 + 85.0685i 0.964195 + 0.399383i
\(214\) 0 0
\(215\) 57.1364 + 57.1364i 0.265751 + 0.265751i
\(216\) 0 0
\(217\) 240.171 + 240.171i 1.10678 + 1.10678i
\(218\) 0 0
\(219\) −131.347 54.4056i −0.599757 0.248428i
\(220\) 0 0
\(221\) −70.9063 + 29.3704i −0.320843 + 0.132898i
\(222\) 0 0
\(223\) 187.153i 0.839252i 0.907697 + 0.419626i \(0.137839\pi\)
−0.907697 + 0.419626i \(0.862161\pi\)
\(224\) 0 0
\(225\) −63.3353 −0.281490
\(226\) 0 0
\(227\) 2.72348 + 6.57507i 0.0119977 + 0.0289650i 0.929765 0.368154i \(-0.120010\pi\)
−0.917767 + 0.397119i \(0.870010\pi\)
\(228\) 0 0
\(229\) −124.655 + 300.944i −0.544345 + 1.31416i 0.377286 + 0.926097i \(0.376857\pi\)
−0.921631 + 0.388068i \(0.873143\pi\)
\(230\) 0 0
\(231\) −340.855 + 340.855i −1.47556 + 1.47556i
\(232\) 0 0
\(233\) −208.047 + 208.047i −0.892904 + 0.892904i −0.994796 0.101891i \(-0.967511\pi\)
0.101891 + 0.994796i \(0.467511\pi\)
\(234\) 0 0
\(235\) 13.2611 32.0151i 0.0564301 0.136234i
\(236\) 0 0
\(237\) −4.32518 10.4419i −0.0182497 0.0440587i
\(238\) 0 0
\(239\) 277.832 1.16248 0.581239 0.813733i \(-0.302568\pi\)
0.581239 + 0.813733i \(0.302568\pi\)
\(240\) 0 0
\(241\) 63.2696i 0.262529i −0.991347 0.131265i \(-0.958096\pi\)
0.991347 0.131265i \(-0.0419038\pi\)
\(242\) 0 0
\(243\) −138.431 + 57.3398i −0.569673 + 0.235966i
\(244\) 0 0
\(245\) 212.180 + 87.8879i 0.866041 + 0.358726i
\(246\) 0 0
\(247\) −3.17339 3.17339i −0.0128477 0.0128477i
\(248\) 0 0
\(249\) −149.763 149.763i −0.601457 0.601457i
\(250\) 0 0
\(251\) −161.948 67.0812i −0.645212 0.267256i 0.0359886 0.999352i \(-0.488542\pi\)
−0.681201 + 0.732097i \(0.738542\pi\)
\(252\) 0 0
\(253\) 174.935 72.4605i 0.691443 0.286405i
\(254\) 0 0
\(255\) 90.9239i 0.356564i
\(256\) 0 0
\(257\) −82.9690 −0.322836 −0.161418 0.986886i \(-0.551607\pi\)
−0.161418 + 0.986886i \(0.551607\pi\)
\(258\) 0 0
\(259\) 183.840 + 443.830i 0.709809 + 1.71363i
\(260\) 0 0
\(261\) −28.3289 + 68.3921i −0.108540 + 0.262039i
\(262\) 0 0
\(263\) 148.394 148.394i 0.564235 0.564235i −0.366272 0.930508i \(-0.619366\pi\)
0.930508 + 0.366272i \(0.119366\pi\)
\(264\) 0 0
\(265\) −46.2200 + 46.2200i −0.174415 + 0.174415i
\(266\) 0 0
\(267\) 83.0012 200.383i 0.310866 0.750497i
\(268\) 0 0
\(269\) 78.7117 + 190.027i 0.292609 + 0.706420i 1.00000 0.000402393i \(-0.000128086\pi\)
−0.707391 + 0.706822i \(0.750128\pi\)
\(270\) 0 0
\(271\) 29.7996 0.109962 0.0549809 0.998487i \(-0.482490\pi\)
0.0549809 + 0.998487i \(0.482490\pi\)
\(272\) 0 0
\(273\) 233.171i 0.854106i
\(274\) 0 0
\(275\) 210.883 87.3507i 0.766848 0.317639i
\(276\) 0 0
\(277\) −368.831 152.775i −1.33152 0.551534i −0.400431 0.916327i \(-0.631140\pi\)
−0.931089 + 0.364793i \(0.881140\pi\)
\(278\) 0 0
\(279\) 51.1367 + 51.1367i 0.183286 + 0.183286i
\(280\) 0 0
\(281\) −280.258 280.258i −0.997358 0.997358i 0.00263807 0.999997i \(-0.499160\pi\)
−0.999997 + 0.00263807i \(0.999160\pi\)
\(282\) 0 0
\(283\) 176.650 + 73.1708i 0.624204 + 0.258554i 0.672288 0.740289i \(-0.265312\pi\)
−0.0480840 + 0.998843i \(0.515312\pi\)
\(284\) 0 0
\(285\) 4.91204 2.03463i 0.0172352 0.00713907i
\(286\) 0 0
\(287\) 628.425i 2.18963i
\(288\) 0 0
\(289\) 54.4719 0.188484
\(290\) 0 0
\(291\) −140.334 338.797i −0.482249 1.16425i
\(292\) 0 0
\(293\) 11.3590 27.4231i 0.0387679 0.0935940i −0.903310 0.428989i \(-0.858870\pi\)
0.942078 + 0.335395i \(0.108870\pi\)
\(294\) 0 0
\(295\) −80.0049 + 80.0049i −0.271203 + 0.271203i
\(296\) 0 0
\(297\) 154.633 154.633i 0.520651 0.520651i
\(298\) 0 0
\(299\) −35.0503 + 84.6188i −0.117225 + 0.283006i
\(300\) 0 0
\(301\) 242.320 + 585.012i 0.805049 + 1.94356i
\(302\) 0 0
\(303\) 32.6191 0.107654
\(304\) 0 0
\(305\) 52.1843i 0.171096i
\(306\) 0 0
\(307\) −463.833 + 192.126i −1.51086 + 0.625817i −0.975734 0.218957i \(-0.929734\pi\)
−0.535122 + 0.844775i \(0.679734\pi\)
\(308\) 0 0
\(309\) −117.472 48.6586i −0.380169 0.157471i
\(310\) 0 0
\(311\) −230.516 230.516i −0.741210 0.741210i 0.231601 0.972811i \(-0.425604\pi\)
−0.972811 + 0.231601i \(0.925604\pi\)
\(312\) 0 0
\(313\) 2.89884 + 2.89884i 0.00926146 + 0.00926146i 0.711722 0.702461i \(-0.247915\pi\)
−0.702461 + 0.711722i \(0.747915\pi\)
\(314\) 0 0
\(315\) 61.7839 + 25.5917i 0.196139 + 0.0812436i
\(316\) 0 0
\(317\) 510.087 211.285i 1.60911 0.666514i 0.616441 0.787401i \(-0.288574\pi\)
0.992666 + 0.120887i \(0.0385738\pi\)
\(318\) 0 0
\(319\) 266.791i 0.836335i
\(320\) 0 0
\(321\) −289.731 −0.902590
\(322\) 0 0
\(323\) −5.24811 12.6701i −0.0162480 0.0392262i
\(324\) 0 0
\(325\) −42.2528 + 102.007i −0.130009 + 0.313869i
\(326\) 0 0
\(327\) 229.568 229.568i 0.702044 0.702044i
\(328\) 0 0
\(329\) 192.020 192.020i 0.583647 0.583647i
\(330\) 0 0
\(331\) 95.3030 230.082i 0.287924 0.695111i −0.712051 0.702128i \(-0.752234\pi\)
0.999975 + 0.00701670i \(0.00223350\pi\)
\(332\) 0 0
\(333\) 39.1429 + 94.4994i 0.117546 + 0.283782i
\(334\) 0 0
\(335\) 5.10609 0.0152421
\(336\) 0 0
\(337\) 203.997i 0.605334i −0.953096 0.302667i \(-0.902123\pi\)
0.953096 0.302667i \(-0.0978769\pi\)
\(338\) 0 0
\(339\) −20.1349 + 8.34017i −0.0593951 + 0.0246023i
\(340\) 0 0
\(341\) −240.793 99.7396i −0.706137 0.292491i
\(342\) 0 0
\(343\) 804.800 + 804.800i 2.34636 + 2.34636i
\(344\) 0 0
\(345\) −76.7264 76.7264i −0.222395 0.222395i
\(346\) 0 0
\(347\) 120.709 + 49.9993i 0.347865 + 0.144090i 0.549773 0.835314i \(-0.314714\pi\)
−0.201908 + 0.979404i \(0.564714\pi\)
\(348\) 0 0
\(349\) 279.116 115.614i 0.799759 0.331271i 0.0548993 0.998492i \(-0.482516\pi\)
0.744860 + 0.667221i \(0.232516\pi\)
\(350\) 0 0
\(351\) 105.781i 0.301370i
\(352\) 0 0
\(353\) 608.156 1.72282 0.861410 0.507910i \(-0.169582\pi\)
0.861410 + 0.507910i \(0.169582\pi\)
\(354\) 0 0
\(355\) 42.5329 + 102.683i 0.119811 + 0.289249i
\(356\) 0 0
\(357\) 272.671 658.287i 0.763785 1.84394i
\(358\) 0 0
\(359\) −196.029 + 196.029i −0.546041 + 0.546041i −0.925293 0.379252i \(-0.876181\pi\)
0.379252 + 0.925293i \(0.376181\pi\)
\(360\) 0 0
\(361\) −254.699 + 254.699i −0.705536 + 0.705536i
\(362\) 0 0
\(363\) −18.0126 + 43.4863i −0.0496215 + 0.119797i
\(364\) 0 0
\(365\) −27.2019 65.6713i −0.0745259 0.179921i
\(366\) 0 0
\(367\) 33.0375 0.0900203 0.0450102 0.998987i \(-0.485668\pi\)
0.0450102 + 0.998987i \(0.485668\pi\)
\(368\) 0 0
\(369\) 133.803i 0.362609i
\(370\) 0 0
\(371\) −473.241 + 196.023i −1.27558 + 0.528363i
\(372\) 0 0
\(373\) 115.583 + 47.8760i 0.309874 + 0.128354i 0.532201 0.846618i \(-0.321365\pi\)
−0.222327 + 0.974972i \(0.571365\pi\)
\(374\) 0 0
\(375\) −197.449 197.449i −0.526530 0.526530i
\(376\) 0 0
\(377\) 91.2527 + 91.2527i 0.242050 + 0.242050i
\(378\) 0 0
\(379\) −164.874 68.2930i −0.435024 0.180193i 0.154415 0.988006i \(-0.450651\pi\)
−0.589438 + 0.807813i \(0.700651\pi\)
\(380\) 0 0
\(381\) −110.160 + 45.6297i −0.289133 + 0.119763i
\(382\) 0 0
\(383\) 307.309i 0.802373i −0.915996 0.401186i \(-0.868598\pi\)
0.915996 0.401186i \(-0.131402\pi\)
\(384\) 0 0
\(385\) −241.013 −0.626008
\(386\) 0 0
\(387\) 51.5942 + 124.559i 0.133318 + 0.321859i
\(388\) 0 0
\(389\) −204.874 + 494.611i −0.526669 + 1.27149i 0.407024 + 0.913418i \(0.366567\pi\)
−0.933693 + 0.358075i \(0.883433\pi\)
\(390\) 0 0
\(391\) −197.907 + 197.907i −0.506157 + 0.506157i
\(392\) 0 0
\(393\) −433.011 + 433.011i −1.10181 + 1.10181i
\(394\) 0 0
\(395\) 2.16252 5.22078i 0.00547473 0.0132172i
\(396\) 0 0
\(397\) −224.796 542.706i −0.566237 1.36702i −0.904705 0.426040i \(-0.859908\pi\)
0.338467 0.940978i \(-0.390092\pi\)
\(398\) 0 0
\(399\) 41.6647 0.104423
\(400\) 0 0
\(401\) 125.790i 0.313691i 0.987623 + 0.156846i \(0.0501325\pi\)
−0.987623 + 0.156846i \(0.949868\pi\)
\(402\) 0 0
\(403\) 116.475 48.2456i 0.289020 0.119716i
\(404\) 0 0
\(405\) −156.963 65.0164i −0.387564 0.160534i
\(406\) 0 0
\(407\) −260.663 260.663i −0.640449 0.640449i
\(408\) 0 0
\(409\) 492.952 + 492.952i 1.20526 + 1.20526i 0.972544 + 0.232717i \(0.0747617\pi\)
0.232717 + 0.972544i \(0.425238\pi\)
\(410\) 0 0
\(411\) 322.257 + 133.483i 0.784081 + 0.324777i
\(412\) 0 0
\(413\) −819.159 + 339.307i −1.98344 + 0.821567i
\(414\) 0 0
\(415\) 105.895i 0.255168i
\(416\) 0 0
\(417\) 677.084 1.62370
\(418\) 0 0
\(419\) −203.456 491.187i −0.485576 1.17228i −0.956925 0.290336i \(-0.906233\pi\)
0.471349 0.881947i \(-0.343767\pi\)
\(420\) 0 0
\(421\) −0.995616 + 2.40363i −0.00236488 + 0.00570934i −0.925058 0.379827i \(-0.875984\pi\)
0.922693 + 0.385536i \(0.125984\pi\)
\(422\) 0 0
\(423\) 40.8844 40.8844i 0.0966535 0.0966535i
\(424\) 0 0
\(425\) −238.576 + 238.576i −0.561355 + 0.561355i
\(426\) 0 0
\(427\) 156.495 377.813i 0.366499 0.884807i
\(428\) 0 0
\(429\) 68.4710 + 165.304i 0.159606 + 0.385323i
\(430\) 0 0
\(431\) −404.244 −0.937920 −0.468960 0.883219i \(-0.655371\pi\)
−0.468960 + 0.883219i \(0.655371\pi\)
\(432\) 0 0
\(433\) 446.431i 1.03102i −0.856884 0.515509i \(-0.827603\pi\)
0.856884 0.515509i \(-0.172397\pi\)
\(434\) 0 0
\(435\) −141.249 + 58.5072i −0.324710 + 0.134499i
\(436\) 0 0
\(437\) −15.1203 6.26304i −0.0346003 0.0143319i
\(438\) 0 0
\(439\) 203.077 + 203.077i 0.462590 + 0.462590i 0.899503 0.436914i \(-0.143928\pi\)
−0.436914 + 0.899503i \(0.643928\pi\)
\(440\) 0 0
\(441\) 270.962 + 270.962i 0.614426 + 0.614426i
\(442\) 0 0
\(443\) 440.203 + 182.338i 0.993685 + 0.411598i 0.819478 0.573111i \(-0.194264\pi\)
0.174207 + 0.984709i \(0.444264\pi\)
\(444\) 0 0
\(445\) 100.188 41.4993i 0.225142 0.0932568i
\(446\) 0 0
\(447\) 789.562i 1.76636i
\(448\) 0 0
\(449\) −636.256 −1.41705 −0.708526 0.705685i \(-0.750639\pi\)
−0.708526 + 0.705685i \(0.750639\pi\)
\(450\) 0 0
\(451\) 184.538 + 445.514i 0.409175 + 0.987836i
\(452\) 0 0
\(453\) 19.7349 47.6442i 0.0435648 0.105175i
\(454\) 0 0
\(455\) 82.4357 82.4357i 0.181177 0.181177i
\(456\) 0 0
\(457\) −359.285 + 359.285i −0.786181 + 0.786181i −0.980866 0.194685i \(-0.937632\pi\)
0.194685 + 0.980866i \(0.437632\pi\)
\(458\) 0 0
\(459\) −123.701 + 298.640i −0.269501 + 0.650632i
\(460\) 0 0
\(461\) 68.2156 + 164.687i 0.147973 + 0.357239i 0.980435 0.196844i \(-0.0630692\pi\)
−0.832462 + 0.554083i \(0.813069\pi\)
\(462\) 0 0
\(463\) −662.155 −1.43014 −0.715070 0.699053i \(-0.753605\pi\)
−0.715070 + 0.699053i \(0.753605\pi\)
\(464\) 0 0
\(465\) 149.357i 0.321198i
\(466\) 0 0
\(467\) 854.762 354.054i 1.83033 0.758146i 0.862718 0.505685i \(-0.168760\pi\)
0.967607 0.252461i \(-0.0812399\pi\)
\(468\) 0 0
\(469\) 36.9680 + 15.3126i 0.0788229 + 0.0326495i
\(470\) 0 0
\(471\) 71.1160 + 71.1160i 0.150989 + 0.150989i
\(472\) 0 0
\(473\) −343.579 343.579i −0.726383 0.726383i
\(474\) 0 0
\(475\) −18.2274 7.55005i −0.0383735 0.0158948i
\(476\) 0 0
\(477\) −100.761 + 41.7367i −0.211240 + 0.0874984i
\(478\) 0 0
\(479\) 926.802i 1.93487i 0.253122 + 0.967434i \(0.418542\pi\)
−0.253122 + 0.967434i \(0.581458\pi\)
\(480\) 0 0
\(481\) 178.313 0.370714
\(482\) 0 0
\(483\) −325.403 785.592i −0.673712 1.62648i
\(484\) 0 0
\(485\) 70.1649 169.393i 0.144670 0.349264i
\(486\) 0 0
\(487\) −586.001 + 586.001i −1.20329 + 1.20329i −0.230127 + 0.973161i \(0.573914\pi\)
−0.973161 + 0.230127i \(0.926086\pi\)
\(488\) 0 0
\(489\) 711.505 711.505i 1.45502 1.45502i
\(490\) 0 0
\(491\) 17.1543 41.4142i 0.0349375 0.0843466i −0.905448 0.424458i \(-0.860465\pi\)
0.940385 + 0.340111i \(0.110465\pi\)
\(492\) 0 0
\(493\) 150.913 + 364.335i 0.306111 + 0.739017i
\(494\) 0 0
\(495\) −51.3160 −0.103669
\(496\) 0 0
\(497\) 870.977i 1.75247i
\(498\) 0 0
\(499\) 143.291 59.3531i 0.287156 0.118944i −0.234456 0.972127i \(-0.575331\pi\)
0.521612 + 0.853183i \(0.325331\pi\)
\(500\) 0 0
\(501\) 46.6734 + 19.3328i 0.0931605 + 0.0385884i
\(502\) 0 0
\(503\) −74.0929 74.0929i −0.147302 0.147302i 0.629610 0.776912i \(-0.283215\pi\)
−0.776912 + 0.629610i \(0.783215\pi\)
\(504\) 0 0
\(505\) 11.5322 + 11.5322i 0.0228361 + 0.0228361i
\(506\) 0 0
\(507\) 458.080 + 189.743i 0.903511 + 0.374246i
\(508\) 0 0
\(509\) 467.540 193.661i 0.918546 0.380474i 0.127224 0.991874i \(-0.459393\pi\)
0.791322 + 0.611400i \(0.209393\pi\)
\(510\) 0 0
\(511\) 557.034i 1.09009i
\(512\) 0 0
\(513\) −18.9017 −0.0368455
\(514\) 0 0
\(515\) −24.3285 58.7343i −0.0472399 0.114047i
\(516\) 0 0
\(517\) −79.7431 + 192.517i −0.154242 + 0.372373i
\(518\) 0 0
\(519\) 564.476 564.476i 1.08762 1.08762i
\(520\) 0 0
\(521\) 694.307 694.307i 1.33264 1.33264i 0.429644 0.902998i \(-0.358639\pi\)
0.902998 0.429644i \(-0.141361\pi\)
\(522\) 0 0
\(523\) −67.4311 + 162.793i −0.128931 + 0.311268i −0.975142 0.221581i \(-0.928878\pi\)
0.846211 + 0.532848i \(0.178878\pi\)
\(524\) 0 0
\(525\) −392.271 947.026i −0.747183 1.80386i
\(526\) 0 0
\(527\) 385.250 0.731025
\(528\) 0 0
\(529\) 194.991i 0.368602i
\(530\) 0 0
\(531\) −174.414 + 72.2445i −0.328463 + 0.136054i
\(532\) 0 0
\(533\) −215.502 89.2638i −0.404319 0.167474i
\(534\) 0 0
\(535\) −102.432 102.432i −0.191462 0.191462i
\(536\) 0 0
\(537\) −6.81281 6.81281i −0.0126868 0.0126868i
\(538\) 0 0
\(539\) −1275.91 528.498i −2.36717 0.980515i
\(540\) 0 0
\(541\) 125.547 52.0035i 0.232066 0.0961247i −0.263620 0.964626i \(-0.584917\pi\)
0.495686 + 0.868502i \(0.334917\pi\)
\(542\) 0 0
\(543\) 687.772i 1.26661i
\(544\) 0 0
\(545\) 162.324 0.297842
\(546\) 0 0
\(547\) 278.945 + 673.432i 0.509954 + 1.23114i 0.943910 + 0.330204i \(0.107117\pi\)
−0.433956 + 0.900934i \(0.642883\pi\)
\(548\) 0 0
\(549\) 33.3206 80.4431i 0.0606933 0.146527i
\(550\) 0 0
\(551\) −16.3057 + 16.3057i −0.0295929 + 0.0295929i
\(552\) 0 0
\(553\) 31.3132 31.3132i 0.0566241 0.0566241i
\(554\) 0 0
\(555\) −80.8410 + 195.168i −0.145660 + 0.351653i
\(556\) 0 0
\(557\) −228.207 550.942i −0.409708 0.989123i −0.985214 0.171326i \(-0.945195\pi\)
0.575506 0.817797i \(-0.304805\pi\)
\(558\) 0 0
\(559\) 235.035 0.420455
\(560\) 0 0
\(561\) 546.754i 0.974607i
\(562\) 0 0
\(563\) 236.899 98.1268i 0.420780 0.174293i −0.162239 0.986752i \(-0.551871\pi\)
0.583019 + 0.812459i \(0.301871\pi\)
\(564\) 0 0
\(565\) −10.0671 4.16995i −0.0178180 0.00738044i
\(566\) 0 0
\(567\) −941.434 941.434i −1.66038 1.66038i
\(568\) 0 0
\(569\) −289.568 289.568i −0.508907 0.508907i 0.405284 0.914191i \(-0.367173\pi\)
−0.914191 + 0.405284i \(0.867173\pi\)
\(570\) 0 0
\(571\) −801.877 332.148i −1.40434 0.581695i −0.453464 0.891275i \(-0.649812\pi\)
−0.950874 + 0.309579i \(0.899812\pi\)
\(572\) 0 0
\(573\) −591.435 + 244.980i −1.03217 + 0.427540i
\(574\) 0 0
\(575\) 402.646i 0.700254i
\(576\) 0 0
\(577\) −107.872 −0.186953 −0.0934767 0.995621i \(-0.529798\pi\)
−0.0934767 + 0.995621i \(0.529798\pi\)
\(578\) 0 0
\(579\) 274.365 + 662.377i 0.473861 + 1.14400i
\(580\) 0 0
\(581\) 317.567 766.676i 0.546588 1.31958i
\(582\) 0 0
\(583\) 277.936 277.936i 0.476734 0.476734i
\(584\) 0 0
\(585\) 17.5520 17.5520i 0.0300035 0.0300035i
\(586\) 0 0
\(587\) 292.393 705.899i 0.498114 1.20255i −0.452384 0.891823i \(-0.649426\pi\)
0.950498 0.310730i \(-0.100574\pi\)
\(588\) 0 0
\(589\) 8.62087 + 20.8126i 0.0146365 + 0.0353355i
\(590\) 0 0
\(591\) 1115.26 1.88707
\(592\) 0 0
\(593\) 247.178i 0.416826i −0.978041 0.208413i \(-0.933170\pi\)
0.978041 0.208413i \(-0.0668298\pi\)
\(594\) 0 0
\(595\) 329.133 136.331i 0.553164 0.229128i
\(596\) 0 0
\(597\) 1142.54 + 473.254i 1.91380 + 0.792720i
\(598\) 0 0
\(599\) 633.115 + 633.115i 1.05695 + 1.05695i 0.998277 + 0.0586768i \(0.0186881\pi\)
0.0586768 + 0.998277i \(0.481312\pi\)
\(600\) 0 0
\(601\) −147.019 147.019i −0.244624 0.244624i 0.574136 0.818760i \(-0.305338\pi\)
−0.818760 + 0.574136i \(0.805338\pi\)
\(602\) 0 0
\(603\) 7.87114 + 3.26033i 0.0130533 + 0.00540685i
\(604\) 0 0
\(605\) −21.7424 + 9.00601i −0.0359379 + 0.0148860i
\(606\) 0 0
\(607\) 52.6594i 0.0867536i −0.999059 0.0433768i \(-0.986188\pi\)
0.999059 0.0433768i \(-0.0138116\pi\)
\(608\) 0 0
\(609\) −1198.09 −1.96731
\(610\) 0 0
\(611\) −38.5729 93.1233i −0.0631308 0.152411i
\(612\) 0 0
\(613\) −336.988 + 813.562i −0.549737 + 1.32718i 0.367939 + 0.929850i \(0.380064\pi\)
−0.917675 + 0.397331i \(0.869936\pi\)
\(614\) 0 0
\(615\) 195.402 195.402i 0.317727 0.317727i
\(616\) 0 0
\(617\) −150.269 + 150.269i −0.243547 + 0.243547i −0.818316 0.574769i \(-0.805092\pi\)
0.574769 + 0.818316i \(0.305092\pi\)
\(618\) 0 0
\(619\) −4.34083 + 10.4797i −0.00701265 + 0.0169300i −0.927347 0.374202i \(-0.877917\pi\)
0.920334 + 0.391132i \(0.127917\pi\)
\(620\) 0 0
\(621\) 147.623 + 356.394i 0.237718 + 0.573903i
\(622\) 0 0
\(623\) 849.811 1.36406
\(624\) 0 0
\(625\) 411.175i 0.657880i
\(626\) 0 0
\(627\) −29.5377 + 12.2349i −0.0471095 + 0.0195134i
\(628\) 0 0
\(629\) 503.413 + 208.520i 0.800338 + 0.331511i
\(630\) 0 0
\(631\) −356.485 356.485i −0.564952 0.564952i 0.365758 0.930710i \(-0.380810\pi\)
−0.930710 + 0.365758i \(0.880810\pi\)
\(632\) 0 0
\(633\) −270.424 270.424i −0.427210 0.427210i
\(634\) 0 0
\(635\) −55.0781 22.8141i −0.0867371 0.0359277i
\(636\) 0 0
\(637\) 617.175 255.642i 0.968878 0.401322i
\(638\) 0 0
\(639\) 185.447i 0.290214i
\(640\) 0 0
\(641\) 741.748 1.15717 0.578587 0.815621i \(-0.303604\pi\)
0.578587 + 0.815621i \(0.303604\pi\)
\(642\) 0 0
\(643\) −181.837 438.994i −0.282795 0.682729i 0.717103 0.696967i \(-0.245468\pi\)
−0.999899 + 0.0142385i \(0.995468\pi\)
\(644\) 0 0
\(645\) −106.556 + 257.250i −0.165204 + 0.398837i
\(646\) 0 0
\(647\) −520.304 + 520.304i −0.804180 + 0.804180i −0.983746 0.179566i \(-0.942531\pi\)
0.179566 + 0.983746i \(0.442531\pi\)
\(648\) 0 0
\(649\) 481.095 481.095i 0.741286 0.741286i
\(650\) 0 0
\(651\) −447.907 + 1081.34i −0.688029 + 1.66105i
\(652\) 0 0
\(653\) 161.753 + 390.507i 0.247708 + 0.598019i 0.998009 0.0630771i \(-0.0200914\pi\)
−0.750301 + 0.661096i \(0.770091\pi\)
\(654\) 0 0
\(655\) −306.175 −0.467443
\(656\) 0 0
\(657\) 118.603i 0.180521i
\(658\) 0 0
\(659\) −70.1853 + 29.0717i −0.106503 + 0.0441149i −0.435299 0.900286i \(-0.643357\pi\)
0.328796 + 0.944401i \(0.393357\pi\)
\(660\) 0 0
\(661\) −81.1193 33.6007i −0.122722 0.0508331i 0.320477 0.947256i \(-0.396157\pi\)
−0.443199 + 0.896423i \(0.646157\pi\)
\(662\) 0 0
\(663\) −187.011 187.011i −0.282068 0.282068i
\(664\) 0 0
\(665\) 14.7302 + 14.7302i 0.0221507 + 0.0221507i
\(666\) 0 0
\(667\) 434.794 + 180.097i 0.651865 + 0.270011i
\(668\) 0 0
\(669\) −595.833 + 246.802i −0.890633 + 0.368912i
\(670\) 0 0
\(671\) 313.801i 0.467661i
\(672\) 0 0
\(673\) −851.239 −1.26484 −0.632421 0.774625i \(-0.717939\pi\)
−0.632421 + 0.774625i \(0.717939\pi\)
\(674\) 0 0
\(675\) 177.959 + 429.630i 0.263642 + 0.636489i
\(676\) 0 0
\(677\) −380.410 + 918.390i −0.561905 + 1.35656i 0.346335 + 0.938111i \(0.387426\pi\)
−0.908241 + 0.418448i \(0.862574\pi\)
\(678\) 0 0
\(679\) 1015.98 1015.98i 1.49629 1.49629i
\(680\) 0 0
\(681\) −17.3413 + 17.3413i −0.0254645 + 0.0254645i
\(682\) 0 0
\(683\) −425.467 + 1027.17i −0.622939 + 1.50391i 0.225297 + 0.974290i \(0.427665\pi\)
−0.848236 + 0.529618i \(0.822335\pi\)
\(684\) 0 0
\(685\) 66.7395 + 161.123i 0.0974299 + 0.235217i
\(686\) 0 0
\(687\) −1122.49 −1.63390
\(688\) 0 0
\(689\) 190.129i 0.275950i
\(690\) 0 0
\(691\) −260.940 + 108.085i −0.377627 + 0.156418i −0.563420 0.826171i \(-0.690515\pi\)
0.185793 + 0.982589i \(0.440515\pi\)
\(692\) 0 0
\(693\) −371.526 153.891i −0.536113 0.222065i
\(694\) 0 0
\(695\) 239.377 + 239.377i 0.344428 + 0.344428i
\(696\) 0 0
\(697\) −504.018 504.018i −0.723124 0.723124i
\(698\) 0 0
\(699\) −936.707 387.997i −1.34007 0.555074i
\(700\) 0 0
\(701\) −727.192 + 301.213i −1.03736 + 0.429690i −0.835365 0.549695i \(-0.814744\pi\)
−0.201999 + 0.979386i \(0.564744\pi\)
\(702\) 0 0
\(703\) 31.8623i 0.0453234i
\(704\) 0 0
\(705\) 119.413 0.169380
\(706\) 0 0
\(707\) 48.9091 + 118.077i 0.0691783 + 0.167011i
\(708\) 0 0
\(709\) 259.577 626.675i 0.366118 0.883886i −0.628261 0.778003i \(-0.716233\pi\)
0.994379 0.105883i \(-0.0337670\pi\)
\(710\) 0 0
\(711\) 6.66713 6.66713i 0.00937711 0.00937711i
\(712\) 0 0
\(713\) 325.095 325.095i 0.455953 0.455953i
\(714\) 0 0
\(715\) −34.2344 + 82.6491i −0.0478803 + 0.115593i
\(716\) 0 0
\(717\) 366.383 + 884.526i 0.510994 + 1.23365i
\(718\) 0 0
\(719\) −1034.71 −1.43910 −0.719549 0.694442i \(-0.755651\pi\)
−0.719549 + 0.694442i \(0.755651\pi\)
\(720\) 0 0
\(721\) 498.193i 0.690975i
\(722\) 0 0
\(723\) 201.429 83.4348i 0.278602 0.115401i
\(724\) 0 0
\(725\) 524.141 + 217.106i 0.722953 + 0.299457i
\(726\) 0 0
\(727\) −227.066 227.066i −0.312332 0.312332i 0.533480 0.845813i \(-0.320884\pi\)
−0.845813 + 0.533480i \(0.820884\pi\)
\(728\) 0 0
\(729\) 262.439 + 262.439i 0.359999 + 0.359999i
\(730\) 0 0
\(731\) 663.548 + 274.850i 0.907726 + 0.375992i
\(732\) 0 0
\(733\) 973.386 403.190i 1.32795 0.550054i 0.397879 0.917438i \(-0.369746\pi\)
0.930070 + 0.367384i \(0.119746\pi\)
\(734\) 0 0
\(735\) 791.410i 1.07675i
\(736\) 0 0
\(737\) −30.7045 −0.0416615
\(738\) 0 0
\(739\) −387.131 934.616i −0.523857 1.26470i −0.935490 0.353354i \(-0.885041\pi\)
0.411632 0.911350i \(-0.364959\pi\)
\(740\) 0 0
\(741\) 5.91821 14.2878i 0.00798679 0.0192818i
\(742\) 0 0
\(743\) −528.819 + 528.819i −0.711735 + 0.711735i −0.966898 0.255163i \(-0.917871\pi\)
0.255163 + 0.966898i \(0.417871\pi\)
\(744\) 0 0
\(745\) −279.143 + 279.143i −0.374689 + 0.374689i
\(746\) 0 0
\(747\) 67.6158 163.239i 0.0905164 0.218526i
\(748\) 0 0
\(749\) −434.423 1048.79i −0.580004 1.40025i
\(750\) 0 0
\(751\) 176.760 0.235366 0.117683 0.993051i \(-0.462453\pi\)
0.117683 + 0.993051i \(0.462453\pi\)
\(752\) 0 0
\(753\) 604.051i 0.802192i
\(754\) 0 0
\(755\) 23.8213 9.86711i 0.0315514 0.0130690i
\(756\) 0 0
\(757\) −59.8575 24.7938i −0.0790720 0.0327527i 0.342797 0.939410i \(-0.388626\pi\)
−0.421869 + 0.906657i \(0.638626\pi\)
\(758\) 0 0
\(759\) 461.381 + 461.381i 0.607879 + 0.607879i
\(760\) 0 0
\(761\) 713.497 + 713.497i 0.937579 + 0.937579i 0.998163 0.0605844i \(-0.0192964\pi\)
−0.0605844 + 0.998163i \(0.519296\pi\)
\(762\) 0 0
\(763\) 1175.22 + 486.793i 1.54026 + 0.637999i
\(764\) 0 0
\(765\) 70.0782 29.0273i 0.0916055 0.0379442i
\(766\) 0 0
\(767\) 329.106i 0.429082i
\(768\) 0 0
\(769\) −147.511 −0.191821 −0.0959107 0.995390i \(-0.530576\pi\)
−0.0959107 + 0.995390i \(0.530576\pi\)
\(770\) 0 0
\(771\) −109.413 264.146i −0.141910 0.342601i
\(772\) 0 0
\(773\) 104.027 251.144i 0.134576 0.324896i −0.842198 0.539169i \(-0.818738\pi\)
0.976774 + 0.214273i \(0.0687384\pi\)
\(774\) 0 0
\(775\) 391.899 391.899i 0.505677 0.505677i
\(776\) 0 0
\(777\) −1170.57 + 1170.57i −1.50653 + 1.50653i
\(778\) 0 0
\(779\) 15.9503 38.5075i 0.0204754 0.0494319i
\(780\) 0 0
\(781\) −255.764 617.468i −0.327482 0.790612i
\(782\) 0 0
\(783\) 543.531 0.694164
\(784\) 0 0
\(785\) 50.2850i 0.0640573i
\(786\) 0 0
\(787\) −999.730 + 414.102i −1.27031 + 0.526178i −0.913057 0.407832i \(-0.866285\pi\)
−0.357248 + 0.934010i \(0.616285\pi\)
\(788\) 0 0