Properties

Label 128.3.h.a.47.2
Level $128$
Weight $3$
Character 128.47
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 47.2
Character \(\chi\) \(=\) 128.47
Dual form 128.3.h.a.79.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.936461 + 2.26082i) q^{3} +(-3.18221 - 7.68254i) q^{5} +(-3.67370 - 3.67370i) q^{7} +(2.12963 + 2.12963i) q^{9} +O(q^{10})\) \(q+(-0.936461 + 2.26082i) q^{3} +(-3.18221 - 7.68254i) q^{5} +(-3.67370 - 3.67370i) q^{7} +(2.12963 + 2.12963i) q^{9} +(-6.10089 - 14.7288i) q^{11} +(2.82075 - 6.80990i) q^{13} +20.3488 q^{15} -3.67152i q^{17} +(1.65751 + 0.686564i) q^{19} +(11.7458 - 4.86528i) q^{21} +(8.31529 - 8.31529i) q^{23} +(-31.2172 + 31.2172i) q^{25} +(-27.1564 + 11.2485i) q^{27} +(-38.8592 - 16.0960i) q^{29} -4.11293i q^{31} +39.0124 q^{33} +(-16.5328 + 39.9138i) q^{35} +(19.8759 + 47.9847i) q^{37} +(12.7544 + 12.7544i) q^{39} +(21.1187 + 21.1187i) q^{41} +(0.102495 + 0.247444i) q^{43} +(9.58403 - 23.1379i) q^{45} +39.3838 q^{47} -22.0079i q^{49} +(8.30063 + 3.43823i) q^{51} +(22.6154 - 9.36759i) q^{53} +(-93.7406 + 93.7406i) q^{55} +(-3.10439 + 3.10439i) q^{57} +(101.380 - 41.9931i) q^{59} +(-14.0475 - 5.81867i) q^{61} -15.6472i q^{63} -61.2936 q^{65} +(-3.67448 + 8.87098i) q^{67} +(11.0124 + 26.5863i) q^{69} +(-75.7712 - 75.7712i) q^{71} +(-29.0378 - 29.0378i) q^{73} +(-41.3427 - 99.8102i) q^{75} +(-31.6965 + 76.5221i) q^{77} -2.76556 q^{79} -44.8236i q^{81} +(79.1972 + 32.8045i) q^{83} +(-28.2066 + 11.6835i) q^{85} +(72.7802 - 72.7802i) q^{87} +(72.4200 - 72.4200i) q^{89} +(-35.3801 + 14.6549i) q^{91} +(9.29858 + 3.85160i) q^{93} -14.9187i q^{95} +66.0511 q^{97} +(18.3743 - 44.3596i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + O(q^{10}) \) \( 28q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + 4q^{11} - 4q^{13} + 8q^{15} + 4q^{19} - 4q^{21} + 68q^{23} - 4q^{25} + 100q^{27} - 4q^{29} - 8q^{33} - 92q^{35} - 4q^{37} - 188q^{39} - 4q^{41} - 92q^{43} - 40q^{45} + 8q^{47} - 224q^{51} - 164q^{53} - 252q^{55} - 4q^{57} - 124q^{59} - 68q^{61} - 8q^{65} + 164q^{67} + 188q^{69} + 260q^{71} - 4q^{73} + 488q^{75} + 220q^{77} + 520q^{79} + 484q^{83} + 96q^{85} + 452q^{87} - 4q^{89} + 196q^{91} + 32q^{93} - 8q^{97} - 216q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(5\) \(127\)
\(\chi(n)\) \(e\left(\frac{3}{8}\right)\) \(-1\)

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
\(3\) −0.936461 + 2.26082i −0.312154 + 0.753605i 0.687471 + 0.726212i \(0.258721\pi\)
−0.999625 + 0.0273938i \(0.991279\pi\)
\(4\) 0 0
\(5\) −3.18221 7.68254i −0.636442 1.53651i −0.831387 0.555693i \(-0.812453\pi\)
0.194945 0.980814i \(-0.437547\pi\)
\(6\) 0 0
\(7\) −3.67370 3.67370i −0.524814 0.524814i 0.394208 0.919021i \(-0.371019\pi\)
−0.919021 + 0.394208i \(0.871019\pi\)
\(8\) 0 0
\(9\) 2.12963 + 2.12963i 0.236625 + 0.236625i
\(10\) 0 0
\(11\) −6.10089 14.7288i −0.554626 1.33899i −0.913971 0.405781i \(-0.867000\pi\)
0.359345 0.933205i \(-0.383000\pi\)
\(12\) 0 0
\(13\) 2.82075 6.80990i 0.216981 0.523839i −0.777484 0.628902i \(-0.783505\pi\)
0.994466 + 0.105063i \(0.0335046\pi\)
\(14\) 0 0
\(15\) 20.3488 1.35659
\(16\) 0 0
\(17\) 3.67152i 0.215972i −0.994152 0.107986i \(-0.965560\pi\)
0.994152 0.107986i \(-0.0344401\pi\)
\(18\) 0 0
\(19\) 1.65751 + 0.686564i 0.0872375 + 0.0361349i 0.425875 0.904782i \(-0.359966\pi\)
−0.338638 + 0.940917i \(0.609966\pi\)
\(20\) 0 0
\(21\) 11.7458 4.86528i 0.559325 0.231680i
\(22\) 0 0
\(23\) 8.31529 8.31529i 0.361534 0.361534i −0.502843 0.864378i \(-0.667713\pi\)
0.864378 + 0.502843i \(0.167713\pi\)
\(24\) 0 0
\(25\) −31.2172 + 31.2172i −1.24869 + 1.24869i
\(26\) 0 0
\(27\) −27.1564 + 11.2485i −1.00579 + 0.416612i
\(28\) 0 0
\(29\) −38.8592 16.0960i −1.33997 0.555035i −0.406489 0.913656i \(-0.633247\pi\)
−0.933483 + 0.358621i \(0.883247\pi\)
\(30\) 0 0
\(31\) 4.11293i 0.132675i −0.997797 0.0663376i \(-0.978869\pi\)
0.997797 0.0663376i \(-0.0211314\pi\)
\(32\) 0 0
\(33\) 39.0124 1.18220
\(34\) 0 0
\(35\) −16.5328 + 39.9138i −0.472367 + 1.14039i
\(36\) 0 0
\(37\) 19.8759 + 47.9847i 0.537186 + 1.29688i 0.926679 + 0.375853i \(0.122650\pi\)
−0.389493 + 0.921030i \(0.627350\pi\)
\(38\) 0 0
\(39\) 12.7544 + 12.7544i 0.327036 + 0.327036i
\(40\) 0 0
\(41\) 21.1187 + 21.1187i 0.515091 + 0.515091i 0.916082 0.400991i \(-0.131334\pi\)
−0.400991 + 0.916082i \(0.631334\pi\)
\(42\) 0 0
\(43\) 0.102495 + 0.247444i 0.00238360 + 0.00575451i 0.925067 0.379804i \(-0.124009\pi\)
−0.922683 + 0.385559i \(0.874009\pi\)
\(44\) 0 0
\(45\) 9.58403 23.1379i 0.212978 0.514175i
\(46\) 0 0
\(47\) 39.3838 0.837952 0.418976 0.907997i \(-0.362389\pi\)
0.418976 + 0.907997i \(0.362389\pi\)
\(48\) 0 0
\(49\) 22.0079i 0.449141i
\(50\) 0 0
\(51\) 8.30063 + 3.43823i 0.162757 + 0.0674163i
\(52\) 0 0
\(53\) 22.6154 9.36759i 0.426705 0.176747i −0.158987 0.987281i \(-0.550823\pi\)
0.585692 + 0.810534i \(0.300823\pi\)
\(54\) 0 0
\(55\) −93.7406 + 93.7406i −1.70437 + 1.70437i
\(56\) 0 0
\(57\) −3.10439 + 3.10439i −0.0544630 + 0.0544630i
\(58\) 0 0
\(59\) 101.380 41.9931i 1.71831 0.711747i 0.718441 0.695588i \(-0.244856\pi\)
0.999869 0.0161592i \(-0.00514387\pi\)
\(60\) 0 0
\(61\) −14.0475 5.81867i −0.230287 0.0953880i 0.264556 0.964370i \(-0.414775\pi\)
−0.494843 + 0.868982i \(0.664775\pi\)
\(62\) 0 0
\(63\) 15.6472i 0.248369i
\(64\) 0 0
\(65\) −61.2936 −0.942978
\(66\) 0 0
\(67\) −3.67448 + 8.87098i −0.0548430 + 0.132403i −0.948926 0.315498i \(-0.897828\pi\)
0.894083 + 0.447901i \(0.147828\pi\)
\(68\) 0 0
\(69\) 11.0124 + 26.5863i 0.159600 + 0.385309i
\(70\) 0 0
\(71\) −75.7712 75.7712i −1.06720 1.06720i −0.997573 0.0696271i \(-0.977819\pi\)
−0.0696271 0.997573i \(-0.522181\pi\)
\(72\) 0 0
\(73\) −29.0378 29.0378i −0.397779 0.397779i 0.479670 0.877449i \(-0.340756\pi\)
−0.877449 + 0.479670i \(0.840756\pi\)
\(74\) 0 0
\(75\) −41.3427 99.8102i −0.551237 1.33080i
\(76\) 0 0
\(77\) −31.6965 + 76.5221i −0.411643 + 0.993793i
\(78\) 0 0
\(79\) −2.76556 −0.0350072 −0.0175036 0.999847i \(-0.505572\pi\)
−0.0175036 + 0.999847i \(0.505572\pi\)
\(80\) 0 0
\(81\) 44.8236i 0.553378i
\(82\) 0 0
\(83\) 79.1972 + 32.8045i 0.954183 + 0.395235i 0.804801 0.593544i \(-0.202272\pi\)
0.149381 + 0.988780i \(0.452272\pi\)
\(84\) 0 0
\(85\) −28.2066 + 11.6835i −0.331842 + 0.137453i
\(86\) 0 0
\(87\) 72.7802 72.7802i 0.836554 0.836554i
\(88\) 0 0
\(89\) 72.4200 72.4200i 0.813708 0.813708i −0.171480 0.985188i \(-0.554855\pi\)
0.985188 + 0.171480i \(0.0548548\pi\)
\(90\) 0 0
\(91\) −35.3801 + 14.6549i −0.388792 + 0.161043i
\(92\) 0 0
\(93\) 9.29858 + 3.85160i 0.0999847 + 0.0414150i
\(94\) 0 0
\(95\) 14.9187i 0.157039i
\(96\) 0 0
\(97\) 66.0511 0.680940 0.340470 0.940255i \(-0.389414\pi\)
0.340470 + 0.940255i \(0.389414\pi\)
\(98\) 0 0
\(99\) 18.3743 44.3596i 0.185599 0.448077i
\(100\) 0 0
\(101\) −7.51179 18.1351i −0.0743742 0.179555i 0.882320 0.470650i \(-0.155981\pi\)
−0.956694 + 0.291095i \(0.905981\pi\)
\(102\) 0 0
\(103\) −0.589180 0.589180i −0.00572020 0.00572020i 0.704241 0.709961i \(-0.251288\pi\)
−0.709961 + 0.704241i \(0.751288\pi\)
\(104\) 0 0
\(105\) −74.7554 74.7554i −0.711956 0.711956i
\(106\) 0 0
\(107\) 55.4567 + 133.884i 0.518287 + 1.25126i 0.938955 + 0.344041i \(0.111796\pi\)
−0.420668 + 0.907215i \(0.638204\pi\)
\(108\) 0 0
\(109\) 29.4015 70.9815i 0.269739 0.651207i −0.729732 0.683733i \(-0.760355\pi\)
0.999471 + 0.0325264i \(0.0103553\pi\)
\(110\) 0 0
\(111\) −127.098 −1.14502
\(112\) 0 0
\(113\) 134.274i 1.18826i −0.804368 0.594131i \(-0.797496\pi\)
0.804368 0.594131i \(-0.202504\pi\)
\(114\) 0 0
\(115\) −90.3436 37.4215i −0.785596 0.325405i
\(116\) 0 0
\(117\) 20.5097 8.49541i 0.175297 0.0726103i
\(118\) 0 0
\(119\) −13.4880 + 13.4880i −0.113345 + 0.113345i
\(120\) 0 0
\(121\) −94.1580 + 94.1580i −0.778166 + 0.778166i
\(122\) 0 0
\(123\) −67.5224 + 27.9687i −0.548963 + 0.227388i
\(124\) 0 0
\(125\) 147.104 + 60.9325i 1.17683 + 0.487460i
\(126\) 0 0
\(127\) 95.5030i 0.751992i 0.926621 + 0.375996i \(0.122699\pi\)
−0.926621 + 0.375996i \(0.877301\pi\)
\(128\) 0 0
\(129\) −0.655407 −0.00508068
\(130\) 0 0
\(131\) 67.1188 162.039i 0.512357 1.23694i −0.430151 0.902757i \(-0.641540\pi\)
0.942508 0.334183i \(-0.108460\pi\)
\(132\) 0 0
\(133\) −3.56697 8.61142i −0.0268193 0.0647475i
\(134\) 0 0
\(135\) 172.835 + 172.835i 1.28026 + 1.28026i
\(136\) 0 0
\(137\) 88.7244 + 88.7244i 0.647624 + 0.647624i 0.952418 0.304794i \(-0.0985878\pi\)
−0.304794 + 0.952418i \(0.598588\pi\)
\(138\) 0 0
\(139\) 27.6838 + 66.8346i 0.199164 + 0.480824i 0.991633 0.129087i \(-0.0412048\pi\)
−0.792469 + 0.609912i \(0.791205\pi\)
\(140\) 0 0
\(141\) −36.8813 + 89.0394i −0.261570 + 0.631485i
\(142\) 0 0
\(143\) −117.511 −0.821756
\(144\) 0 0
\(145\) 349.758i 2.41213i
\(146\) 0 0
\(147\) 49.7558 + 20.6095i 0.338475 + 0.140201i
\(148\) 0 0
\(149\) −100.536 + 41.6433i −0.674737 + 0.279485i −0.693625 0.720336i \(-0.743987\pi\)
0.0188878 + 0.999822i \(0.493987\pi\)
\(150\) 0 0
\(151\) 134.706 134.706i 0.892096 0.892096i −0.102624 0.994720i \(-0.532724\pi\)
0.994720 + 0.102624i \(0.0327239\pi\)
\(152\) 0 0
\(153\) 7.81897 7.81897i 0.0511044 0.0511044i
\(154\) 0 0
\(155\) −31.5977 + 13.0882i −0.203856 + 0.0844401i
\(156\) 0 0
\(157\) −56.0501 23.2167i −0.357007 0.147877i 0.196969 0.980410i \(-0.436890\pi\)
−0.553976 + 0.832533i \(0.686890\pi\)
\(158\) 0 0
\(159\) 59.9015i 0.376739i
\(160\) 0 0
\(161\) −61.0957 −0.379476
\(162\) 0 0
\(163\) −85.7621 + 207.048i −0.526148 + 1.27023i 0.407881 + 0.913035i \(0.366268\pi\)
−0.934029 + 0.357198i \(0.883732\pi\)
\(164\) 0 0
\(165\) −124.146 299.715i −0.752399 1.81645i
\(166\) 0 0
\(167\) −72.6395 72.6395i −0.434967 0.434967i 0.455347 0.890314i \(-0.349515\pi\)
−0.890314 + 0.455347i \(0.849515\pi\)
\(168\) 0 0
\(169\) 81.0829 + 81.0829i 0.479781 + 0.479781i
\(170\) 0 0
\(171\) 2.06776 + 4.99201i 0.0120922 + 0.0291930i
\(172\) 0 0
\(173\) −4.05480 + 9.78916i −0.0234382 + 0.0565847i −0.935165 0.354212i \(-0.884749\pi\)
0.911727 + 0.410796i \(0.134749\pi\)
\(174\) 0 0
\(175\) 229.365 1.31066
\(176\) 0 0
\(177\) 268.527i 1.51710i
\(178\) 0 0
\(179\) −214.146 88.7024i −1.19635 0.495544i −0.306531 0.951861i \(-0.599168\pi\)
−0.889817 + 0.456317i \(0.849168\pi\)
\(180\) 0 0
\(181\) −98.2125 + 40.6810i −0.542611 + 0.224757i −0.637116 0.770768i \(-0.719873\pi\)
0.0945057 + 0.995524i \(0.469873\pi\)
\(182\) 0 0
\(183\) 26.3099 26.3099i 0.143770 0.143770i
\(184\) 0 0
\(185\) 305.395 305.395i 1.65078 1.65078i
\(186\) 0 0
\(187\) −54.0772 + 22.3995i −0.289183 + 0.119783i
\(188\) 0 0
\(189\) 141.088 + 58.4405i 0.746497 + 0.309209i
\(190\) 0 0
\(191\) 181.842i 0.952052i −0.879431 0.476026i \(-0.842077\pi\)
0.879431 0.476026i \(-0.157923\pi\)
\(192\) 0 0
\(193\) −221.267 −1.14646 −0.573230 0.819394i \(-0.694310\pi\)
−0.573230 + 0.819394i \(0.694310\pi\)
\(194\) 0 0
\(195\) 57.3990 138.574i 0.294354 0.710633i
\(196\) 0 0
\(197\) −15.4361 37.2660i −0.0783556 0.189167i 0.879847 0.475256i \(-0.157645\pi\)
−0.958203 + 0.286089i \(0.907645\pi\)
\(198\) 0 0
\(199\) 135.618 + 135.618i 0.681498 + 0.681498i 0.960338 0.278840i \(-0.0899498\pi\)
−0.278840 + 0.960338i \(0.589950\pi\)
\(200\) 0 0
\(201\) −16.6146 16.6146i −0.0826599 0.0826599i
\(202\) 0 0
\(203\) 83.6250 + 201.889i 0.411946 + 0.994526i
\(204\) 0 0
\(205\) 95.0411 229.450i 0.463615 1.11927i
\(206\) 0 0
\(207\) 35.4170 0.171096
\(208\) 0 0
\(209\) 28.6019i 0.136851i
\(210\) 0 0
\(211\) −138.015 57.1678i −0.654100 0.270937i 0.0308532 0.999524i \(-0.490178\pi\)
−0.684954 + 0.728587i \(0.740178\pi\)
\(212\) 0 0
\(213\) 242.262 100.348i 1.13738 0.471118i
\(214\) 0 0
\(215\) 1.57484 1.57484i 0.00732483 0.00732483i
\(216\) 0 0
\(217\) −15.1097 + 15.1097i −0.0696298 + 0.0696298i
\(218\) 0 0
\(219\) 92.8420 38.4564i 0.423936 0.175600i
\(220\) 0 0
\(221\) −25.0027 10.3564i −0.113134 0.0468618i
\(222\) 0 0
\(223\) 30.6228i 0.137322i 0.997640 + 0.0686609i \(0.0218727\pi\)
−0.997640 + 0.0686609i \(0.978127\pi\)
\(224\) 0 0
\(225\) −132.962 −0.590944
\(226\) 0 0
\(227\) −8.41171 + 20.3077i −0.0370560 + 0.0894611i −0.941324 0.337504i \(-0.890417\pi\)
0.904268 + 0.426965i \(0.140417\pi\)
\(228\) 0 0
\(229\) 76.6532 + 185.057i 0.334730 + 0.808110i 0.998204 + 0.0599101i \(0.0190814\pi\)
−0.663474 + 0.748199i \(0.730919\pi\)
\(230\) 0 0
\(231\) −143.320 143.320i −0.620432 0.620432i
\(232\) 0 0
\(233\) −127.558 127.558i −0.547461 0.547461i 0.378245 0.925706i \(-0.376528\pi\)
−0.925706 + 0.378245i \(0.876528\pi\)
\(234\) 0 0
\(235\) −125.327 302.567i −0.533308 1.28752i
\(236\) 0 0
\(237\) 2.58984 6.25243i 0.0109276 0.0263816i
\(238\) 0 0
\(239\) −397.241 −1.66210 −0.831048 0.556200i \(-0.812259\pi\)
−0.831048 + 0.556200i \(0.812259\pi\)
\(240\) 0 0
\(241\) 401.128i 1.66443i −0.554451 0.832216i \(-0.687072\pi\)
0.554451 0.832216i \(-0.312928\pi\)
\(242\) 0 0
\(243\) −143.069 59.2612i −0.588763 0.243873i
\(244\) 0 0
\(245\) −169.077 + 70.0338i −0.690109 + 0.285852i
\(246\) 0 0
\(247\) 9.35087 9.35087i 0.0378578 0.0378578i
\(248\) 0 0
\(249\) −148.330 + 148.330i −0.595703 + 0.595703i
\(250\) 0 0
\(251\) −220.193 + 91.2070i −0.877264 + 0.363375i −0.775435 0.631427i \(-0.782469\pi\)
−0.101829 + 0.994802i \(0.532469\pi\)
\(252\) 0 0
\(253\) −173.205 71.7440i −0.684606 0.283573i
\(254\) 0 0
\(255\) 74.7111i 0.292985i
\(256\) 0 0
\(257\) 436.624 1.69893 0.849463 0.527648i \(-0.176926\pi\)
0.849463 + 0.527648i \(0.176926\pi\)
\(258\) 0 0
\(259\) 103.263 249.299i 0.398699 0.962545i
\(260\) 0 0
\(261\) −48.4771 117.034i −0.185736 0.448407i
\(262\) 0 0
\(263\) 324.662 + 324.662i 1.23445 + 1.23445i 0.962235 + 0.272219i \(0.0877576\pi\)
0.272219 + 0.962235i \(0.412242\pi\)
\(264\) 0 0
\(265\) −143.934 143.934i −0.543146 0.543146i
\(266\) 0 0
\(267\) 95.9098 + 231.547i 0.359213 + 0.867217i
\(268\) 0 0
\(269\) −98.7998 + 238.524i −0.367286 + 0.886706i 0.626907 + 0.779094i \(0.284320\pi\)
−0.994193 + 0.107612i \(0.965680\pi\)
\(270\) 0 0
\(271\) 91.7678 0.338627 0.169313 0.985562i \(-0.445845\pi\)
0.169313 + 0.985562i \(0.445845\pi\)
\(272\) 0 0
\(273\) 93.7117i 0.343266i
\(274\) 0 0
\(275\) 650.247 + 269.341i 2.36453 + 0.979422i
\(276\) 0 0
\(277\) 42.7749 17.7179i 0.154422 0.0639636i −0.304134 0.952629i \(-0.598367\pi\)
0.458556 + 0.888666i \(0.348367\pi\)
\(278\) 0 0
\(279\) 8.75902 8.75902i 0.0313943 0.0313943i
\(280\) 0 0
\(281\) −167.424 + 167.424i −0.595813 + 0.595813i −0.939196 0.343382i \(-0.888427\pi\)
0.343382 + 0.939196i \(0.388427\pi\)
\(282\) 0 0
\(283\) 494.380 204.779i 1.74693 0.723601i 0.748775 0.662824i \(-0.230642\pi\)
0.998151 0.0607762i \(-0.0193576\pi\)
\(284\) 0 0
\(285\) 33.7284 + 13.9708i 0.118345 + 0.0490202i
\(286\) 0 0
\(287\) 155.168i 0.540653i
\(288\) 0 0
\(289\) 275.520 0.953356
\(290\) 0 0
\(291\) −61.8543 + 149.329i −0.212558 + 0.513160i
\(292\) 0 0
\(293\) 146.767 + 354.328i 0.500913 + 1.20931i 0.948987 + 0.315314i \(0.102110\pi\)
−0.448075 + 0.893996i \(0.647890\pi\)
\(294\) 0 0
\(295\) −645.227 645.227i −2.18721 2.18721i
\(296\) 0 0
\(297\) 331.356 + 331.356i 1.11568 + 1.11568i
\(298\) 0 0
\(299\) −33.1709 80.0817i −0.110940 0.267832i
\(300\) 0 0
\(301\) 0.532500 1.28557i 0.00176910 0.00427099i
\(302\) 0 0
\(303\) 48.0346 0.158530
\(304\) 0 0
\(305\) 126.437i 0.414547i
\(306\) 0 0
\(307\) 53.4306 + 22.1317i 0.174041 + 0.0720902i 0.468003 0.883727i \(-0.344974\pi\)
−0.293962 + 0.955817i \(0.594974\pi\)
\(308\) 0 0
\(309\) 1.88377 0.780284i 0.00609635 0.00252519i
\(310\) 0 0
\(311\) −274.515 + 274.515i −0.882685 + 0.882685i −0.993807 0.111122i \(-0.964556\pi\)
0.111122 + 0.993807i \(0.464556\pi\)
\(312\) 0 0
\(313\) −78.4013 + 78.4013i −0.250483 + 0.250483i −0.821169 0.570685i \(-0.806678\pi\)
0.570685 + 0.821169i \(0.306678\pi\)
\(314\) 0 0
\(315\) −120.210 + 49.7928i −0.381620 + 0.158072i
\(316\) 0 0
\(317\) −136.520 56.5483i −0.430661 0.178386i 0.156814 0.987628i \(-0.449878\pi\)
−0.587475 + 0.809243i \(0.699878\pi\)
\(318\) 0 0
\(319\) 670.551i 2.10204i
\(320\) 0 0
\(321\) −354.621 −1.10474
\(322\) 0 0
\(323\) 2.52073 6.08558i 0.00780412 0.0188408i
\(324\) 0 0
\(325\) 124.530 + 300.643i 0.383170 + 0.925054i
\(326\) 0 0
\(327\) 132.943 + 132.943i 0.406553 + 0.406553i
\(328\) 0 0
\(329\) −144.684 144.684i −0.439769 0.439769i
\(330\) 0 0
\(331\) −143.690 346.898i −0.434109 1.04803i −0.977949 0.208843i \(-0.933030\pi\)
0.543841 0.839189i \(-0.316970\pi\)
\(332\) 0 0
\(333\) −59.8612 + 144.518i −0.179763 + 0.433987i
\(334\) 0 0
\(335\) 79.8446 0.238342
\(336\) 0 0
\(337\) 479.136i 1.42177i −0.703310 0.710884i \(-0.748295\pi\)
0.703310 0.710884i \(-0.251705\pi\)
\(338\) 0 0
\(339\) 303.568 + 125.742i 0.895481 + 0.370920i
\(340\) 0 0
\(341\) −60.5787 + 25.0925i −0.177650 + 0.0735851i
\(342\) 0 0
\(343\) −260.861 + 260.861i −0.760529 + 0.760529i
\(344\) 0 0
\(345\) 169.206 169.206i 0.490453 0.490453i
\(346\) 0 0
\(347\) −172.145 + 71.3048i −0.496095 + 0.205489i −0.616680 0.787214i \(-0.711523\pi\)
0.120585 + 0.992703i \(0.461523\pi\)
\(348\) 0 0
\(349\) 388.120 + 160.765i 1.11209 + 0.460644i 0.861658 0.507490i \(-0.169427\pi\)
0.250434 + 0.968134i \(0.419427\pi\)
\(350\) 0 0
\(351\) 216.662i 0.617269i
\(352\) 0 0
\(353\) −165.952 −0.470120 −0.235060 0.971981i \(-0.575529\pi\)
−0.235060 + 0.971981i \(0.575529\pi\)
\(354\) 0 0
\(355\) −340.995 + 823.235i −0.960550 + 2.31897i
\(356\) 0 0
\(357\) −17.8630 43.1250i −0.0500363 0.120798i
\(358\) 0 0
\(359\) −100.971 100.971i −0.281257 0.281257i 0.552353 0.833610i \(-0.313730\pi\)
−0.833610 + 0.552353i \(0.813730\pi\)
\(360\) 0 0
\(361\) −252.990 252.990i −0.700802 0.700802i
\(362\) 0 0
\(363\) −124.699 301.049i −0.343523 0.829337i
\(364\) 0 0
\(365\) −130.680 + 315.489i −0.358027 + 0.864353i
\(366\) 0 0
\(367\) 651.959 1.77645 0.888227 0.459405i \(-0.151937\pi\)
0.888227 + 0.459405i \(0.151937\pi\)
\(368\) 0 0
\(369\) 89.9501i 0.243767i
\(370\) 0 0
\(371\) −117.496 48.6683i −0.316700 0.131181i
\(372\) 0 0
\(373\) 605.919 250.980i 1.62445 0.672868i 0.629854 0.776713i \(-0.283115\pi\)
0.994593 + 0.103845i \(0.0331146\pi\)
\(374\) 0 0
\(375\) −275.515 + 275.515i −0.734705 + 0.734705i
\(376\) 0 0
\(377\) −219.224 + 219.224i −0.581497 + 0.581497i
\(378\) 0 0
\(379\) 431.591 178.771i 1.13876 0.471691i 0.268011 0.963416i \(-0.413634\pi\)
0.870750 + 0.491725i \(0.163634\pi\)
\(380\) 0 0
\(381\) −215.915 89.4348i −0.566705 0.234737i
\(382\) 0 0
\(383\) 583.987i 1.52477i −0.647124 0.762385i \(-0.724028\pi\)
0.647124 0.762385i \(-0.275972\pi\)
\(384\) 0 0
\(385\) 688.749 1.78896
\(386\) 0 0
\(387\) −0.308688 + 0.745239i −0.000797644 + 0.00192568i
\(388\) 0 0
\(389\) −57.9070 139.800i −0.148861 0.359383i 0.831806 0.555067i \(-0.187307\pi\)
−0.980667 + 0.195684i \(0.937307\pi\)
\(390\) 0 0
\(391\) −30.5297 30.5297i −0.0780812 0.0780812i
\(392\) 0 0
\(393\) 303.487 + 303.487i 0.772231 + 0.772231i
\(394\) 0 0
\(395\) 8.80061 + 21.2466i 0.0222800 + 0.0537888i
\(396\) 0 0
\(397\) 216.482 522.634i 0.545295 1.31646i −0.375649 0.926762i \(-0.622580\pi\)
0.920944 0.389696i \(-0.127420\pi\)
\(398\) 0 0
\(399\) 22.8092 0.0571658
\(400\) 0 0
\(401\) 271.900i 0.678055i −0.940776 0.339028i \(-0.889902\pi\)
0.940776 0.339028i \(-0.110098\pi\)
\(402\) 0 0
\(403\) −28.0087 11.6016i −0.0695004 0.0287880i
\(404\) 0 0
\(405\) −344.359 + 142.638i −0.850269 + 0.352193i
\(406\) 0 0
\(407\) 585.498 585.498i 1.43857 1.43857i
\(408\) 0 0
\(409\) −181.723 + 181.723i −0.444310 + 0.444310i −0.893458 0.449147i \(-0.851728\pi\)
0.449147 + 0.893458i \(0.351728\pi\)
\(410\) 0 0
\(411\) −283.677 + 117.503i −0.690211 + 0.285895i
\(412\) 0 0
\(413\) −526.710 218.171i −1.27533 0.528258i
\(414\) 0 0
\(415\) 712.826i 1.71765i
\(416\) 0 0
\(417\) −177.026 −0.424522
\(418\) 0 0
\(419\) 84.5458 204.112i 0.201780 0.487140i −0.790304 0.612715i \(-0.790077\pi\)
0.992084 + 0.125575i \(0.0400775\pi\)
\(420\) 0 0
\(421\) 13.1417 + 31.7269i 0.0312155 + 0.0753608i 0.938719 0.344685i \(-0.112014\pi\)
−0.907503 + 0.420045i \(0.862014\pi\)
\(422\) 0 0
\(423\) 83.8728 + 83.8728i 0.198281 + 0.198281i
\(424\) 0 0
\(425\) 114.615 + 114.615i 0.269682 + 0.269682i
\(426\) 0 0
\(427\) 30.2302 + 72.9823i 0.0707968 + 0.170919i
\(428\) 0 0
\(429\) 110.045 265.671i 0.256514 0.619280i
\(430\) 0 0
\(431\) −18.4839 −0.0428861 −0.0214431 0.999770i \(-0.506826\pi\)
−0.0214431 + 0.999770i \(0.506826\pi\)
\(432\) 0 0
\(433\) 370.297i 0.855190i 0.903970 + 0.427595i \(0.140639\pi\)
−0.903970 + 0.427595i \(0.859361\pi\)
\(434\) 0 0
\(435\) −790.739 327.535i −1.81779 0.752954i
\(436\) 0 0
\(437\) 19.4917 8.07372i 0.0446034 0.0184753i
\(438\) 0 0
\(439\) 1.47108 1.47108i 0.00335099 0.00335099i −0.705429 0.708780i \(-0.749246\pi\)
0.708780 + 0.705429i \(0.249246\pi\)
\(440\) 0 0
\(441\) 46.8687 46.8687i 0.106278 0.106278i
\(442\) 0 0
\(443\) −15.4970 + 6.41908i −0.0349820 + 0.0144900i −0.400106 0.916469i \(-0.631027\pi\)
0.365124 + 0.930959i \(0.381027\pi\)
\(444\) 0 0
\(445\) −786.825 325.914i −1.76815 0.732390i
\(446\) 0 0
\(447\) 266.290i 0.595728i
\(448\) 0 0
\(449\) −349.645 −0.778719 −0.389359 0.921086i \(-0.627304\pi\)
−0.389359 + 0.921086i \(0.627304\pi\)
\(450\) 0 0
\(451\) 182.211 439.897i 0.404016 0.975382i
\(452\) 0 0
\(453\) 178.399 + 430.694i 0.393817 + 0.950759i
\(454\) 0 0
\(455\) 225.174 + 225.174i 0.494888 + 0.494888i
\(456\) 0 0
\(457\) 167.442 + 167.442i 0.366393 + 0.366393i 0.866160 0.499767i \(-0.166581\pi\)
−0.499767 + 0.866160i \(0.666581\pi\)
\(458\) 0 0
\(459\) 41.2992 + 99.7051i 0.0899764 + 0.217222i
\(460\) 0 0
\(461\) 299.864 723.935i 0.650463 1.57036i −0.161644 0.986849i \(-0.551680\pi\)
0.812107 0.583508i \(-0.198320\pi\)
\(462\) 0 0
\(463\) 70.4485 0.152157 0.0760783 0.997102i \(-0.475760\pi\)
0.0760783 + 0.997102i \(0.475760\pi\)
\(464\) 0 0
\(465\) 83.6933i 0.179986i
\(466\) 0 0
\(467\) 89.8391 + 37.2126i 0.192375 + 0.0796843i 0.476791 0.879017i \(-0.341800\pi\)
−0.284416 + 0.958701i \(0.591800\pi\)
\(468\) 0 0
\(469\) 46.0882 19.0904i 0.0982691 0.0407044i
\(470\) 0 0
\(471\) 104.977 104.977i 0.222882 0.222882i
\(472\) 0 0
\(473\) 3.01925 3.01925i 0.00638320 0.00638320i
\(474\) 0 0
\(475\) −73.1756 + 30.3103i −0.154054 + 0.0638112i
\(476\) 0 0
\(477\) 68.1118 + 28.2128i 0.142792 + 0.0591464i
\(478\) 0 0
\(479\) 900.546i 1.88005i 0.341101 + 0.940027i \(0.389200\pi\)
−0.341101 + 0.940027i \(0.610800\pi\)
\(480\) 0 0
\(481\) 382.836 0.795917
\(482\) 0 0
\(483\) 57.2137 138.126i 0.118455 0.285976i
\(484\) 0 0
\(485\) −210.189 507.440i −0.433379 1.04627i
\(486\) 0 0
\(487\) 175.466 + 175.466i 0.360301 + 0.360301i 0.863924 0.503623i \(-0.168000\pi\)
−0.503623 + 0.863924i \(0.668000\pi\)
\(488\) 0 0
\(489\) −387.785 387.785i −0.793015 0.793015i
\(490\) 0 0
\(491\) 111.990 + 270.368i 0.228086 + 0.550648i 0.995944 0.0899713i \(-0.0286775\pi\)
−0.767858 + 0.640620i \(0.778678\pi\)
\(492\) 0 0
\(493\) −59.0968 + 142.672i −0.119872 + 0.289396i
\(494\) 0 0
\(495\) −399.265 −0.806596
\(496\) 0 0
\(497\) 556.721i 1.12016i
\(498\) 0 0
\(499\) −96.4128 39.9355i −0.193212 0.0800310i 0.283980 0.958830i \(-0.408345\pi\)
−0.477192 + 0.878799i \(0.658345\pi\)
\(500\) 0 0
\(501\) 232.249 96.2005i 0.463570 0.192017i
\(502\) 0 0
\(503\) −491.151 + 491.151i −0.976442 + 0.976442i −0.999729 0.0232864i \(-0.992587\pi\)
0.0232864 + 0.999729i \(0.492587\pi\)
\(504\) 0 0
\(505\) −115.419 + 115.419i −0.228553 + 0.228553i
\(506\) 0 0
\(507\) −259.245 + 107.383i −0.511331 + 0.211800i
\(508\) 0 0
\(509\) 891.336 + 369.204i 1.75115 + 0.725351i 0.997695 + 0.0678534i \(0.0216150\pi\)
0.753457 + 0.657498i \(0.228385\pi\)
\(510\) 0 0
\(511\) 213.352i 0.417519i
\(512\) 0 0
\(513\) −52.7348 −0.102797
\(514\) 0 0
\(515\) −2.65150 + 6.40130i −0.00514855 + 0.0124297i
\(516\) 0 0
\(517\) −240.276 580.077i −0.464750 1.12201i
\(518\) 0 0
\(519\) −18.3343 18.3343i −0.0353263 0.0353263i
\(520\) 0 0
\(521\) 285.723 + 285.723i 0.548413 + 0.548413i 0.925982 0.377569i \(-0.123240\pi\)
−0.377569 + 0.925982i \(0.623240\pi\)
\(522\) 0 0
\(523\) −260.696 629.375i −0.498462 1.20339i −0.950312 0.311300i \(-0.899236\pi\)
0.451849 0.892094i \(-0.350764\pi\)
\(524\) 0 0
\(525\) −214.792 + 518.553i −0.409127 + 0.987720i
\(526\) 0 0
\(527\) −15.1007 −0.0286541
\(528\) 0 0
\(529\) 390.712i 0.738586i
\(530\) 0 0
\(531\) 305.332 + 126.473i 0.575013 + 0.238178i
\(532\) 0 0
\(533\) 203.387 84.2457i 0.381589 0.158059i
\(534\) 0 0
\(535\) 852.096 852.096i 1.59270 1.59270i
\(536\) 0 0
\(537\) 401.079 401.079i 0.746889 0.746889i
\(538\) 0 0
\(539\) −324.151 + 134.268i −0.601393 + 0.249105i
\(540\) 0 0
\(541\) 355.077 + 147.078i 0.656335 + 0.271863i 0.685895 0.727700i \(-0.259411\pi\)
−0.0295603 + 0.999563i \(0.509411\pi\)
\(542\) 0 0
\(543\) 260.137i 0.479073i
\(544\) 0 0
\(545\) −638.880 −1.17226
\(546\) 0 0
\(547\) −404.897 + 977.508i −0.740214 + 1.78704i −0.135204 + 0.990818i \(0.543169\pi\)
−0.605010 + 0.796218i \(0.706831\pi\)
\(548\) 0 0
\(549\) −17.5244 42.3076i −0.0319205 0.0770630i
\(550\) 0 0
\(551\) −53.3586 53.3586i −0.0968396 0.0968396i
\(552\) 0 0
\(553\) 10.1598 + 10.1598i 0.0183722 + 0.0183722i
\(554\) 0 0
\(555\) 404.451 + 976.431i 0.728741 + 1.75934i
\(556\) 0 0
\(557\) −296.952 + 716.907i −0.533128 + 1.28709i 0.396313 + 0.918115i \(0.370289\pi\)
−0.929441 + 0.368970i \(0.879711\pi\)
\(558\) 0 0
\(559\) 1.97418 0.00353163
\(560\) 0 0
\(561\) 143.235i 0.255321i
\(562\) 0 0
\(563\) 44.6869 + 18.5099i 0.0793728 + 0.0328773i 0.422017 0.906588i \(-0.361322\pi\)
−0.342644 + 0.939465i \(0.611322\pi\)
\(564\) 0 0
\(565\) −1031.56 + 427.287i −1.82577 + 0.756260i
\(566\) 0 0
\(567\) −164.668 + 164.668i −0.290420 + 0.290420i
\(568\) 0 0
\(569\) 487.094 487.094i 0.856053 0.856053i −0.134818 0.990870i \(-0.543045\pi\)
0.990870 + 0.134818i \(0.0430449\pi\)
\(570\) 0 0
\(571\) 252.561 104.614i 0.442313 0.183212i −0.150401 0.988625i \(-0.548056\pi\)
0.592714 + 0.805413i \(0.298056\pi\)
\(572\) 0 0
\(573\) 411.111 + 170.288i 0.717472 + 0.297187i
\(574\) 0 0
\(575\) 519.161i 0.902889i
\(576\) 0 0
\(577\) 460.004 0.797234 0.398617 0.917118i \(-0.369490\pi\)
0.398617 + 0.917118i \(0.369490\pi\)
\(578\) 0 0
\(579\) 207.208 500.244i 0.357872 0.863979i
\(580\) 0 0
\(581\) −170.432 411.460i −0.293343 0.708193i
\(582\) 0 0
\(583\) −275.947 275.947i −0.473323 0.473323i
\(584\) 0 0
\(585\) −130.533 130.533i −0.223133 0.223133i
\(586\) 0 0
\(587\) −68.3015 164.895i −0.116357 0.280911i 0.854962 0.518690i \(-0.173580\pi\)
−0.971319 + 0.237780i \(0.923580\pi\)
\(588\) 0 0
\(589\) 2.82379 6.81723i 0.00479421 0.0115742i
\(590\) 0 0
\(591\) 98.7067 0.167016
\(592\) 0 0
\(593\) 167.545i 0.282538i 0.989971 + 0.141269i \(0.0451182\pi\)
−0.989971 + 0.141269i \(0.954882\pi\)
\(594\) 0 0
\(595\) 146.544 + 60.7006i 0.246293 + 0.102018i
\(596\) 0 0
\(597\) −433.609 + 179.607i −0.726313 + 0.300848i
\(598\) 0 0
\(599\) 316.998 316.998i 0.529213 0.529213i −0.391125 0.920338i \(-0.627914\pi\)
0.920338 + 0.391125i \(0.127914\pi\)
\(600\) 0 0
\(601\) −224.198 + 224.198i −0.373042 + 0.373042i −0.868584 0.495542i \(-0.834970\pi\)
0.495542 + 0.868584i \(0.334970\pi\)
\(602\) 0 0
\(603\) −26.7172 + 11.0666i −0.0443071 + 0.0183526i
\(604\) 0 0
\(605\) 1023.00 + 423.742i 1.69091 + 0.700400i
\(606\) 0 0
\(607\) 89.2468i 0.147029i 0.997294 + 0.0735146i \(0.0234216\pi\)
−0.997294 + 0.0735146i \(0.976578\pi\)
\(608\) 0 0
\(609\) −534.745 −0.878070
\(610\) 0 0
\(611\) 111.092 268.200i 0.181820 0.438952i
\(612\) 0 0
\(613\) 202.134 + 487.995i 0.329746 + 0.796076i 0.998611 + 0.0526926i \(0.0167803\pi\)
−0.668865 + 0.743384i \(0.733220\pi\)
\(614\) 0 0
\(615\) 429.741 + 429.741i 0.698766 + 0.698766i
\(616\) 0 0
\(617\) 380.984 + 380.984i 0.617479 + 0.617479i 0.944884 0.327405i \(-0.106174\pi\)
−0.327405 + 0.944884i \(0.606174\pi\)
\(618\) 0 0
\(619\) 371.320 + 896.447i 0.599871 + 1.44822i 0.873712 + 0.486443i \(0.161706\pi\)
−0.273841 + 0.961775i \(0.588294\pi\)
\(620\) 0 0
\(621\) −132.278 + 319.348i −0.213008 + 0.514248i
\(622\) 0 0
\(623\) −532.098 −0.854090
\(624\) 0 0
\(625\) 220.337i 0.352539i
\(626\) 0 0
\(627\) 64.6636 + 26.7845i 0.103132 + 0.0427186i
\(628\) 0 0
\(629\) 176.177 72.9747i 0.280090 0.116017i
\(630\) 0 0
\(631\) −384.726 + 384.726i −0.609708 + 0.609708i −0.942870 0.333162i \(-0.891885\pi\)
0.333162 + 0.942870i \(0.391885\pi\)
\(632\) 0 0
\(633\) 258.492 258.492i 0.408360 0.408360i
\(634\) 0 0
\(635\) 733.706 303.911i 1.15544 0.478600i
\(636\) 0 0
\(637\) −149.872 62.0789i −0.235277 0.0974551i
\(638\) 0 0
\(639\) 322.729i 0.505053i
\(640\) 0 0
\(641\) −407.931 −0.636398 −0.318199 0.948024i \(-0.603078\pi\)
−0.318199 + 0.948024i \(0.603078\pi\)
\(642\) 0 0
\(643\) 319.302 770.863i 0.496582 1.19885i −0.454732 0.890629i \(-0.650265\pi\)
0.951313 0.308226i \(-0.0997352\pi\)
\(644\) 0 0
\(645\) 2.08564 + 5.03519i 0.00323356 + 0.00780650i
\(646\) 0 0
\(647\) 48.6565 + 48.6565i 0.0752033 + 0.0752033i 0.743708 0.668505i \(-0.233065\pi\)
−0.668505 + 0.743708i \(0.733065\pi\)
\(648\) 0 0
\(649\) −1237.02 1237.02i −1.90604 1.90604i
\(650\) 0 0
\(651\) −20.0106 48.3098i −0.0307382 0.0742085i
\(652\) 0 0
\(653\) −290.106 + 700.378i −0.444267 + 1.07255i 0.530170 + 0.847892i \(0.322128\pi\)
−0.974436 + 0.224663i \(0.927872\pi\)
\(654\) 0 0
\(655\) −1458.46 −2.22665
\(656\) 0 0
\(657\) 123.680i 0.188249i
\(658\) 0 0
\(659\) −818.045 338.845i −1.24134 0.514181i −0.337209 0.941430i \(-0.609483\pi\)
−0.904134 + 0.427248i \(0.859483\pi\)
\(660\) 0 0
\(661\) −35.2123 + 14.5854i −0.0532712 + 0.0220657i −0.409160 0.912463i \(-0.634178\pi\)
0.355889 + 0.934528i \(0.384178\pi\)
\(662\) 0 0
\(663\) 46.8281 46.8281i 0.0706306 0.0706306i
\(664\) 0 0
\(665\) −54.8067 + 54.8067i −0.0824161 + 0.0824161i
\(666\) 0 0
\(667\) −456.969 + 189.283i −0.685110 + 0.283782i
\(668\) 0 0
\(669\) −69.2325 28.6770i −0.103487 0.0428655i
\(670\) 0 0
\(671\) 242.402i 0.361256i
\(672\) 0 0
\(673\) 114.199 0.169687 0.0848434 0.996394i \(-0.472961\pi\)
0.0848434 + 0.996394i \(0.472961\pi\)
\(674\) 0 0
\(675\) 496.599 1198.90i 0.735702 1.77614i
\(676\) 0 0
\(677\) −212.733 513.583i −0.314229 0.758617i −0.999539 0.0303647i \(-0.990333\pi\)
0.685310 0.728252i \(-0.259667\pi\)
\(678\) 0 0
\(679\) −242.652 242.652i −0.357366 0.357366i
\(680\) 0 0
\(681\) −38.0347 38.0347i −0.0558512 0.0558512i
\(682\) 0 0
\(683\) −363.453 877.454i −0.532142 1.28471i −0.930102 0.367302i \(-0.880281\pi\)
0.397959 0.917403i \(-0.369719\pi\)
\(684\) 0 0
\(685\) 399.289 963.969i 0.582904 1.40725i
\(686\) 0 0
\(687\) −490.163 −0.713483
\(688\) 0 0
\(689\) 180.432i 0.261875i
\(690\) 0 0
\(691\) 682.306 + 282.620i 0.987418 + 0.409002i 0.817168 0.576399i \(-0.195543\pi\)
0.170249 + 0.985401i \(0.445543\pi\)
\(692\) 0 0
\(693\) −230.465 + 95.4619i −0.332562 + 0.137752i
\(694\) 0 0
\(695\) 425.364 425.364i 0.612034 0.612034i
\(696\) 0 0
\(697\) 77.5377 77.5377i 0.111245 0.111245i
\(698\) 0 0
\(699\) 407.840 168.933i 0.583462 0.241678i
\(700\) 0 0
\(701\) −565.621 234.288i −0.806878 0.334220i −0.0591703 0.998248i \(-0.518846\pi\)
−0.747708 + 0.664028i \(0.768846\pi\)
\(702\) 0 0
\(703\) 93.1812i 0.132548i
\(704\) 0 0
\(705\) 801.413 1.13676
\(706\) 0 0
\(707\) −39.0267 + 94.2188i −0.0552004 + 0.133266i
\(708\) 0 0
\(709\) 447.695 + 1080.83i 0.631446 + 1.52444i 0.837806 + 0.545968i \(0.183838\pi\)
−0.206360 + 0.978476i \(0.566162\pi\)
\(710\) 0 0
\(711\) −5.88963 5.88963i −0.00828358 0.00828358i
\(712\) 0 0
\(713\) −34.2002 34.2002i −0.0479666 0.0479666i
\(714\) 0 0
\(715\) 373.945 + 902.783i 0.523000 + 1.26263i
\(716\) 0 0
\(717\) 372.001 898.089i 0.518829 1.25257i
\(718\) 0 0
\(719\) −122.001 −0.169681 −0.0848406 0.996395i \(-0.527038\pi\)
−0.0848406 + 0.996395i \(0.527038\pi\)
\(720\) 0 0
\(721\) 4.32894i 0.00600408i
\(722\) 0 0
\(723\) 906.877 + 375.641i 1.25433 + 0.519559i
\(724\) 0 0
\(725\) 1715.55 710.604i 2.36628 0.980144i
\(726\) 0 0
\(727\) −438.189 + 438.189i −0.602736 + 0.602736i −0.941038 0.338301i \(-0.890148\pi\)
0.338301 + 0.941038i \(0.390148\pi\)
\(728\) 0 0
\(729\) 553.213 553.213i 0.758866 0.758866i
\(730\) 0 0
\(731\) 0.908495 0.376311i 0.00124281 0.000514789i
\(732\) 0 0
\(733\) −629.241 260.640i −0.858446 0.355580i −0.0903463 0.995910i \(-0.528797\pi\)
−0.768099 + 0.640331i \(0.778797\pi\)
\(734\) 0 0
\(735\) 447.835i 0.609299i
\(736\) 0 0
\(737\) 153.077 0.207703
\(738\) 0 0
\(739\) −55.5902 + 134.207i −0.0752235 + 0.181606i −0.957018 0.290028i \(-0.906335\pi\)
0.881795 + 0.471633i \(0.156335\pi\)
\(740\) 0 0
\(741\) 12.3839 + 29.8973i 0.0167124 + 0.0403473i
\(742\) 0 0
\(743\) 180.295 + 180.295i 0.242658 + 0.242658i 0.817949 0.575291i \(-0.195111\pi\)
−0.575291 + 0.817949i \(0.695111\pi\)
\(744\) 0 0
\(745\) 639.853 + 639.853i 0.858863 + 0.858863i
\(746\) 0 0
\(747\) 98.7991 + 238.522i 0.132261 + 0.319307i
\(748\) 0 0
\(749\) 288.119 695.581i 0.384672 0.928680i
\(750\) 0 0
\(751\) 264.213 0.351815 0.175908 0.984407i \(-0.443714\pi\)
0.175908 + 0.984407i \(0.443714\pi\)
\(752\) 0 0
\(753\) 583.228i 0.774539i
\(754\) 0 0
\(755\) −1463.55 606.223i −1.93848 0.802945i
\(756\) 0 0
\(757\) −691.098 + 286.262i −0.912944 + 0.378154i −0.789183 0.614158i \(-0.789496\pi\)
−0.123761 + 0.992312i \(0.539496\pi\)
\(758\) 0 0
\(759\) 324.400 324.400i 0.427404 0.427404i
\(760\) 0 0
\(761\) 287.342 287.342i 0.377585 0.377585i −0.492645 0.870230i \(-0.663970\pi\)
0.870230 + 0.492645i \(0.163970\pi\)
\(762\) 0 0
\(763\) −368.777 + 152.752i −0.483325 + 0.200200i
\(764\) 0 0
\(765\) −84.9511 35.1879i −0.111047 0.0459973i
\(766\) 0 0
\(767\) 808.842i 1.05455i
\(768\) 0 0
\(769\) −1240.31 −1.61289 −0.806446 0.591308i \(-0.798612\pi\)
−0.806446 + 0.591308i \(0.798612\pi\)
\(770\) 0 0
\(771\) −408.881 + 987.127i −0.530326 + 1.28032i
\(772\) 0 0
\(773\) −318.633 769.248i −0.412203 0.995146i −0.984545 0.175131i \(-0.943965\pi\)
0.572342 0.820015i \(-0.306035\pi\)
\(774\) 0 0
\(775\) 128.394 + 128.394i 0.165670 + 0.165670i
\(776\) 0 0
\(777\) 466.918 + 466.918i 0.600924 + 0.600924i
\(778\) 0 0
\(779\) 20.5052 + 49.5039i 0.0263224 + 0.0635480i
\(780\) 0 0
\(781\) −653.751 + 1578.29i −0.837069 + 2.02086i
\(782\) 0 0
\(783\) 1236.33 1.57897
\(784\) 0 0
\(785\) 504.487i 0.642659i
\(786\) 0 0
\(787\) −584.664 242.176i −0.742902 0.307720i −0.0210600 0.999778i \(-0.506704\pi\)
−0.721842 + 0.692058i \(0.756704\pi\)
\(788\) 0 0
\(789\) −1038.03 + 429.967i −1.31563 + 0.544952i
\(790\) 0 0
\(791\) −493.280 + 493.280i −0.623616 + 0.623616i
\(792\) 0 0
\(793\) −79.2491 + 79.2491i −0.0999358 + 0.0999358i
\(794\) 0 0
\(795\) 460.196 190.619i 0.578863 0.239773i
\(796\) 0 0
\(797\) −651.965 270.053i −0.818024 0.338837i −0.0658733 0.997828i \(-0.520983\pi\)